LMFDB - Embedded newform 2717.1.db.a.142.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2717,1,Mod(142,2717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2717, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 8]))

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

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

chi := DirichletCharacter("2717.142");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2717 = 11 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2717.db (of order $18$, degree $6$, 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:	$1.35595963932$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{9} - \cdots)$

Embedding invariants

Embedding label			142.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	2717.142
Dual form			2717.1.db.a.2430.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.326352 - 1.85083i) q^{2} +(-1.43969 + 1.20805i) q^{3} +(-2.37939 + 0.866025i) q^{4} +(2.70574 + 2.27038i) q^{6} +(0.939693 - 1.62760i) q^{7} +(1.43969 + 2.49362i) q^{8} +(0.439693 - 2.49362i) q^{9} +O(q^{10})$	\(q+(-0.326352 - 1.85083i) q^{2} +(-1.43969 + 1.20805i) q^{3} +(-2.37939 + 0.866025i) q^{4} +(2.70574 + 2.27038i) q^{6} +(0.939693 - 1.62760i) q^{7} +(1.43969 + 2.49362i) q^{8} +(0.439693 - 2.49362i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(2.37939 - 4.12122i) q^{12} +(0.766044 + 0.642788i) q^{13} +(-3.31908 - 1.20805i) q^{14} +(2.20574 - 1.85083i) q^{16} -4.75877 q^{18} +(0.766044 + 0.642788i) q^{19} +(0.613341 + 3.47843i) q^{21} +(-1.43969 + 1.20805i) q^{22} +(-0.326352 + 0.118782i) q^{23} +(-5.08512 - 1.85083i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.939693 - 1.62760i) q^{26} +(1.43969 + 2.49362i) q^{27} +(-0.826352 + 4.68647i) q^{28} +(-1.93969 - 1.62760i) q^{32} +(1.76604 + 0.642788i) q^{33} +(1.11334 + 6.31407i) q^{36} +(0.939693 - 1.62760i) q^{38} -1.87939 q^{39} +(0.266044 - 0.223238i) q^{41} +(6.23783 - 2.27038i) q^{42} +(1.93969 + 1.62760i) q^{44} +(0.326352 + 0.565258i) q^{46} +(-0.939693 + 5.32926i) q^{48} +(-1.26604 - 2.19285i) q^{49} +(0.939693 - 1.62760i) q^{50} +(-2.37939 - 0.866025i) q^{52} +(-0.326352 + 0.118782i) q^{53} +(4.14543 - 3.47843i) q^{54} +5.41147 q^{56} -1.87939 q^{57} +(-3.64543 - 3.05888i) q^{63} +(-0.939693 + 1.62760i) q^{64} +(0.613341 - 3.47843i) q^{66} +(0.326352 - 0.565258i) q^{69} +(6.85117 - 2.49362i) q^{72} +(1.53209 - 1.28558i) q^{73} -1.87939 q^{75} +(-2.37939 - 0.866025i) q^{76} -1.87939 q^{77} +(0.613341 + 3.47843i) q^{78} +(-2.70574 - 0.984808i) q^{81} +(-0.500000 - 0.419550i) q^{82} +(0.939693 - 1.62760i) q^{83} +(-4.47178 - 7.74535i) q^{84} +(1.43969 - 2.49362i) q^{88} +(1.76604 - 0.642788i) q^{91} +(0.673648 - 0.565258i) q^{92} +4.75877 q^{96} +(-3.64543 + 3.05888i) q^{98} +(-2.37939 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 3 q^{8} - 3 q^{9} - 3 q^{11} + 3 q^{12} - 3 q^{14} + 3 q^{16} - 6 q^{18} - 3 q^{21} - 3 q^{22} - 3 q^{23} - 9 q^{24} + 3 q^{27} - 6 q^{28} - 6 q^{32} + 6 q^{33} - 3 q^{41} + 18 q^{42} + 6 q^{44} + 3 q^{46} - 3 q^{49} - 3 q^{52} - 3 q^{53} + 9 q^{54} + 12 q^{56} - 6 q^{63} - 3 q^{66} + 3 q^{69} + 15 q^{72} - 3 q^{76} - 3 q^{78} - 6 q^{81} - 3 q^{82} - 12 q^{84} + 3 q^{88} + 6 q^{91} + 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 3 * q^8 - 3 * q^9 - 3 * q^11 + 3 * q^12 - 3 * q^14 + 3 * q^16 - 6 * q^18 - 3 * q^21 - 3 * q^22 - 3 * q^23 - 9 * q^24 + 3 * q^27 - 6 * q^28 - 6 * q^32 + 6 * q^33 - 3 * q^41 + 18 * q^42 + 6 * q^44 + 3 * q^46 - 3 * q^49 - 3 * q^52 - 3 * q^53 + 9 * q^54 + 12 * q^56 - 6 * q^63 - 3 * q^66 + 3 * q^69 + 15 * q^72 - 3 * q^76 - 3 * q^78 - 6 * q^81 - 3 * q^82 - 12 * q^84 + 3 * q^88 + 6 * q^91 + 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

$n$	$210$	$287$	$2224$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$	$-1$

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 $

$2$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$3$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$4$	−2.37939	+	0.866025i	−2.37939	+	0.866025i
$5$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$5$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$6$	2.70574	+	2.27038i	2.70574	+	2.27038i
$7$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$7$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$8$	1.43969	+	2.49362i	1.43969	+	2.49362i
$9$	0.439693	−	2.49362i	0.439693	−	2.49362i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$11$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$12$	2.37939	−	4.12122i	2.37939	−	4.12122i
$13$	0.766044	+	0.642788i	0.766044	+	0.642788i
$13$	0.766044	+	0.642788i	0.766044	+	0.642788i
$14$	−3.31908	−	1.20805i	−3.31908	−	1.20805i
$15$		0			0
$16$	2.20574	−	1.85083i	2.20574	−	1.85083i
$17$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$17$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$18$	−4.75877			−4.75877
$19$	0.766044	+	0.642788i	0.766044	+	0.642788i
$19$	0.766044	+	0.642788i	0.766044	+	0.642788i
$20$		0			0
$21$	0.613341	+	3.47843i	0.613341	+	3.47843i
$22$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$23$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$23$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$24$	−5.08512	−	1.85083i	−5.08512	−	1.85083i
$25$	0.766044	+	0.642788i	0.766044	+	0.642788i
$26$	0.939693	−	1.62760i	0.939693	−	1.62760i
$27$	1.43969	+	2.49362i	1.43969	+	2.49362i
$28$	−0.826352	+	4.68647i	−0.826352	+	4.68647i
$29$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$29$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	−1.93969	−	1.62760i	−1.93969	−	1.62760i
$33$	1.76604	+	0.642788i	1.76604	+	0.642788i
$34$		0			0
$35$		0			0
$36$	1.11334	+	6.31407i	1.11334	+	6.31407i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.939693	−	1.62760i	0.939693	−	1.62760i
$39$	−1.87939			−1.87939
$40$		0			0
$41$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$41$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$42$	6.23783	−	2.27038i	6.23783	−	2.27038i
$43$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$43$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$44$	1.93969	+	1.62760i	1.93969	+	1.62760i
$45$		0			0
$46$	0.326352	+	0.565258i	0.326352	+	0.565258i
$47$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$47$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$48$	−0.939693	+	5.32926i	−0.939693	+	5.32926i
$49$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$50$	0.939693	−	1.62760i	0.939693	−	1.62760i
$51$		0			0
$52$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$53$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$53$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$54$	4.14543	−	3.47843i	4.14543	−	3.47843i
$55$		0			0
$56$	5.41147			5.41147
$57$	−1.87939			−1.87939
$58$		0			0
$59$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$59$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$60$		0			0
$61$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$61$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$62$		0			0
$63$	−3.64543	−	3.05888i	−3.64543	−	3.05888i
$64$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$65$		0			0
$66$	0.613341	−	3.47843i	0.613341	−	3.47843i
$67$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$67$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$68$		0			0
$69$	0.326352	−	0.565258i	0.326352	−	0.565258i
$70$		0			0
$71$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$71$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$72$	6.85117	−	2.49362i	6.85117	−	2.49362i
$73$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$73$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$74$		0			0
$75$	−1.87939			−1.87939
$76$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$77$	−1.87939			−1.87939
$78$	0.613341	+	3.47843i	0.613341	+	3.47843i
$79$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$79$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$80$		0			0
$81$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$82$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$83$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$83$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$84$	−4.47178	−	7.74535i	−4.47178	−	7.74535i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	1.43969	−	2.49362i	1.43969	−	2.49362i
$89$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$89$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$90$		0			0
$91$	1.76604	−	0.642788i	1.76604	−	0.642788i
$92$	0.673648	−	0.565258i	0.673648	−	0.565258i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	4.75877			4.75877
$97$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$97$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$98$	−3.64543	+	3.05888i	−3.64543	+	3.05888i
$99$	−2.37939	+	0.866025i	−2.37939	+	0.866025i
$100$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$101$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$101$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$102$		0			0
$103$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$103$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$104$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$105$		0			0
$106$	0.326352	+	0.565258i	0.326352	+	0.565258i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−5.58512	−	4.68647i	−5.58512	−	4.68647i
$109$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$109$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$110$		0			0
$111$		0			0
$112$	−0.939693	−	5.32926i	−0.939693	−	5.32926i
$113$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$113$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$114$	0.613341	+	3.47843i	0.613341	+	3.47843i
$115$		0			0
$116$		0			0
$117$	1.93969	−	1.62760i	1.93969	−	1.62760i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$124$		0			0
$125$		0			0
$126$	−4.47178	+	7.74535i	−4.47178	+	7.74535i
$127$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$127$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$128$	0.939693	+	0.342020i	0.939693	+	0.342020i
$129$		0			0
$130$		0			0
$131$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$131$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$132$	−4.75877			−4.75877
$133$	1.76604	−	0.642788i	1.76604	−	0.642788i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$137$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$138$	−1.15270	−	0.419550i	−1.15270	−	0.419550i
$139$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$139$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.173648	−	0.984808i	0.173648	−	0.984808i
$144$	−3.64543	−	6.31407i	−3.64543	−	6.31407i
$145$		0			0
$146$	−2.87939	−	2.41609i	−2.87939	−	2.41609i
$147$	4.47178	+	1.62760i	4.47178	+	1.62760i
$148$		0			0
$149$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$149$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$150$	0.613341	+	3.47843i	0.613341	+	3.47843i
$151$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$151$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$152$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$153$		0			0
$154$	0.613341	+	3.47843i	0.613341	+	3.47843i
$155$		0			0
$156$	4.47178	−	1.62760i	4.47178	−	1.62760i
$157$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$157$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$158$		0			0
$159$	0.326352	−	0.565258i	0.326352	−	0.565258i
$160$		0			0
$161$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$162$	−0.939693	+	5.32926i	−0.939693	+	5.32926i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$165$		0			0
$166$	−3.31908	−	1.20805i	−3.31908	−	1.20805i
$167$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$167$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$168$	−7.79086	+	6.53731i	−7.79086	+	6.53731i
$169$	0.173648	+	0.984808i	0.173648	+	0.984808i
$170$		0			0
$171$	1.93969	−	1.62760i	1.93969	−	1.62760i
$172$		0			0
$173$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$173$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$174$		0			0
$175$	1.76604	−	0.642788i	1.76604	−	0.642788i
$176$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$177$		0			0
$178$		0			0
$179$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$179$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$180$		0			0
$181$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$181$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$182$	−1.76604	−	3.05888i	−1.76604	−	3.05888i
$183$		0			0
$184$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	5.41147			5.41147
$190$		0			0
$191$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$191$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$192$	−0.613341	−	3.47843i	−0.613341	−	3.47843i
$193$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$193$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$194$		0			0
$195$		0			0
$196$	4.91147	+	4.12122i	4.91147	+	4.12122i
$197$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$197$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$198$	2.37939	+	4.12122i	2.37939	+	4.12122i
$199$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$199$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$200$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$207$	0.152704	+	0.866025i	0.152704	+	0.866025i
$208$	2.87939			2.87939
$209$	0.173648	−	0.984808i	0.173648	−	0.984808i
$210$		0			0
$211$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$211$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$212$	0.673648	−	0.565258i	0.673648	−	0.565258i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−4.14543	+	7.18009i	−4.14543	+	7.18009i
$217$		0			0
$218$	0.326352	−	1.85083i	0.326352	−	1.85083i
$219$	−0.652704	+	3.70167i	−0.652704	+	3.70167i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$223$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$224$	−4.47178	+	1.62760i	−4.47178	+	1.62760i
$225$	1.93969	−	1.62760i	1.93969	−	1.62760i
$226$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$227$	2.00000			2.00000			1.00000			$0$
$227$	2.00000			2.00000			1.00000			$0$
$228$	4.47178	−	1.62760i	4.47178	−	1.62760i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	2.70574	−	2.27038i	2.70574	−	2.27038i
$232$		0			0
$233$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$233$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$234$	−3.64543	−	3.05888i	−3.64543	−	3.05888i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$239$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$240$		0			0
$241$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$241$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$242$	1.76604	+	0.642788i	1.76604	+	0.642788i
$243$	2.37939	−	0.866025i	2.37939	−	0.866025i
$244$		0			0
$245$		0			0
$246$	1.22668			1.22668
$247$	0.173648	+	0.984808i	0.173648	+	0.984808i
$248$		0			0
$249$	0.613341	+	3.47843i	0.613341	+	3.47843i
$250$		0			0
$251$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$251$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$252$	11.3229	+	4.12122i	11.3229	+	4.12122i
$253$	0.266044	+	0.223238i	0.266044	+	0.223238i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$257$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$263$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$264$	0.939693	+	5.32926i	0.939693	+	5.32926i
$265$		0			0
$266$	−1.76604	−	3.05888i	−1.76604	−	3.05888i
$267$		0			0
$268$		0			0
$269$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$269$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$270$		0			0
$271$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$271$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$272$		0			0
$273$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$274$		0			0
$275$	0.173648	−	0.984808i	0.173648	−	0.984808i
$276$	−0.286989	+	1.62760i	−0.286989	+	1.62760i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$282$		0			0
$283$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$283$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$284$		0			0
$285$		0			0
$286$	−1.87939			−1.87939
$287$	−0.113341	−	0.642788i	−0.113341	−	0.642788i
$288$	−4.91147	+	4.12122i	−4.91147	+	4.12122i
$289$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$290$		0			0
$291$		0			0
$292$	−2.53209	+	4.38571i	−2.53209	+	4.38571i
$293$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$293$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$294$	1.55303	−	8.80769i	1.55303	−	8.80769i
$295$		0			0
$296$		0			0
$297$	1.43969	−	2.49362i	1.43969	−	2.49362i
$298$	1.43969	+	1.20805i	1.43969	+	1.20805i
$299$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$300$	4.47178	−	1.62760i	4.47178	−	1.62760i
$301$		0			0
$302$	0.326352	+	1.85083i	0.326352	+	1.85083i
$303$		0			0
$304$	2.87939			2.87939
$305$		0			0
$306$		0			0
$307$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$307$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$308$	4.47178	−	1.62760i	4.47178	−	1.62760i
$309$	2.70574	+	0.984808i	2.70574	+	0.984808i
$310$		0			0
$311$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$311$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$312$	−2.70574	−	4.68647i	−2.70574	−	4.68647i
$313$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$313$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$314$	0.326352	−	1.85083i	0.326352	−	1.85083i
$315$		0			0
$316$		0			0
$317$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$317$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$318$	−1.15270	−	0.419550i	−1.15270	−	0.419550i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	1.22668			1.22668
$323$		0			0
$324$	7.29086			7.29086
$325$	0.173648	+	0.984808i	0.173648	+	0.984808i
$326$		0			0
$327$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$328$	0.939693	+	0.342020i	0.939693	+	0.342020i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	−0.826352	+	4.68647i	−0.826352	+	4.68647i
$333$		0			0
$334$	1.43969	+	2.49362i	1.43969	+	2.49362i
$335$		0			0
$336$	7.79086	+	6.53731i	7.79086	+	6.53731i
$337$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$337$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$338$	1.76604	−	0.642788i	1.76604	−	0.642788i
$339$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$340$		0			0
$341$		0			0
$342$	−3.64543	−	3.05888i	−3.64543	−	3.05888i
$343$	−2.87939			−2.87939
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$347$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$348$		0			0
$349$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$349$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$350$	−1.76604	−	3.05888i	−1.76604	−	3.05888i
$351$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$352$	−0.439693	+	2.49362i	−0.439693	+	2.49362i
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$359$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$359$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$360$		0			0
$361$	0.173648	+	0.984808i	0.173648	+	0.984808i
$362$	−0.652704			−0.652704
$363$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$364$	−3.64543	+	3.05888i	−3.64543	+	3.05888i
$365$		0			0
$366$		0			0
$367$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$367$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$368$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$369$	−0.439693	−	0.761570i	−0.439693	−	0.761570i
$370$		0			0
$371$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−1.76604	−	10.0157i	−1.76604	−	10.0157i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	0.326352	+	1.85083i	0.326352	+	1.85083i
$383$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$383$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$384$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$385$		0			0
$386$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$387$		0			0
$388$		0			0
$389$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$389$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$390$		0			0
$391$		0			0
$392$	3.64543	−	6.31407i	3.64543	−	6.31407i
$393$		0			0
$394$	0.613341	+	0.223238i	0.613341	+	0.223238i
$395$		0			0
$396$	4.91147	−	4.12122i	4.91147	−	4.12122i
$397$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$397$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$398$	−2.87939			−2.87939
$399$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$400$	2.87939			2.87939
$401$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$401$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$409$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$410$		0			0
$411$		0			0
$412$	2.97178	+	2.49362i	2.97178	+	2.49362i
$413$		0			0
$414$	1.55303	−	0.565258i	1.55303	−	0.565258i
$415$		0			0
$416$	−0.439693	−	2.49362i	−0.439693	−	2.49362i
$417$		0			0
$418$	−1.87939			−1.87939
$419$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$419$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$420$		0			0
$421$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$421$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$422$		0			0
$423$		0			0
$424$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.939693	+	1.62760i	0.939693	+	1.62760i
$430$		0			0
$431$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$431$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$432$	7.79086	+	2.83564i	7.79086	+	2.83564i
$433$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$433$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$434$		0			0
$435$		0			0
$436$	−2.53209			−2.53209
$437$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$438$	7.06418			7.06418
$439$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$439$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$440$		0			0
$441$	−6.02481	+	2.19285i	−6.02481	+	2.19285i
$442$		0			0
$443$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$443$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.326352	−	1.85083i	0.326352	−	1.85083i
$448$	1.76604	+	3.05888i	1.76604	+	3.05888i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	−3.64543	−	3.05888i	−3.64543	−	3.05888i
$451$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$452$	−3.64543	+	1.32683i	−3.64543	+	1.32683i
$453$	1.43969	−	1.20805i	1.43969	−	1.20805i
$454$	−0.652704	−	3.70167i	−0.652704	−	3.70167i
$455$		0			0
$456$	−2.70574	−	4.68647i	−2.70574	−	4.68647i
$457$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$457$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$461$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$462$	−5.08512	−	4.26692i	−5.08512	−	4.26692i
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$467$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$468$	−3.20574	+	5.55250i	−3.20574	+	5.55250i
$469$		0			0
$470$		0			0
$471$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.173648	+	0.984808i	0.173648	+	0.984808i
$476$		0			0
$477$	0.152704	+	0.866025i	0.152704	+	0.866025i
$478$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$479$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$479$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$480$		0			0
$481$		0			0
$482$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$483$	−0.613341	−	1.06234i	−0.613341	−	1.06234i
$484$	0.439693	−	2.49362i	0.439693	−	2.49362i
$485$		0			0
$486$	−2.37939	−	4.12122i	−2.37939	−	4.12122i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$491$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$492$	−0.286989	−	1.62760i	−0.286989	−	1.62760i
$493$		0			0
$494$	1.76604	−	0.642788i	1.76604	−	0.642788i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	6.23783	−	2.27038i	6.23783	−	2.27038i
$499$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$499$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$500$		0			0
$501$	1.43969	−	2.49362i	1.43969	−	2.49362i
$502$	1.87939	+	3.25519i	1.87939	+	3.25519i
$503$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$503$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$504$	2.37939	−	13.4942i	2.37939	−	13.4942i
$505$		0			0
$506$	0.326352	−	0.565258i	0.326352	−	0.565258i
$507$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$508$		0			0
$509$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$509$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$510$		0			0
$511$	−0.652704	−	3.70167i	−0.652704	−	3.70167i
$512$	1.00000			1.00000
$513$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$514$	−3.75877			−3.75877
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$523$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$524$		0			0
$525$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$526$		0			0
$527$		0			0
$528$	5.08512	−	1.85083i	5.08512	−	1.85083i
$529$	−0.673648	+	0.565258i	−0.673648	+	0.565258i
$530$		0			0
$531$		0			0
$532$	−3.64543	+	3.05888i	−3.64543	+	3.05888i
$533$	0.347296			0.347296
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.70574	+	0.984808i	2.70574	+	0.984808i
$538$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$539$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$540$		0			0
$541$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$541$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$542$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$543$	0.326352	+	0.565258i	0.326352	+	0.565258i
$544$		0			0
$545$		0			0
$546$	6.23783	+	2.27038i	6.23783	+	2.27038i
$547$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$547$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$548$		0			0
$549$		0			0
$550$	−1.87939			−1.87939
$551$		0			0
$552$	1.87939			1.87939
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$557$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.326352	+	0.565258i	0.326352	+	0.565258i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−4.14543	+	3.47843i	−4.14543	+	3.47843i
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$	0.439693	+	2.49362i	0.439693	+	2.49362i
$573$	1.43969	−	1.20805i	1.43969	−	1.20805i
$574$	−1.15270	+	0.419550i	−1.15270	+	0.419550i
$575$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$576$	3.64543	+	3.05888i	3.64543	+	3.05888i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.939693	+	1.62760i	0.939693	+	1.62760i
$579$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$580$		0			0
$581$	−1.76604	−	3.05888i	−1.76604	−	3.05888i
$582$		0			0
$583$	0.266044	+	0.223238i	0.266044	+	0.223238i
$584$	5.41147	+	1.96962i	5.41147	+	1.96962i
$585$		0			0
$586$	2.70574	−	2.27038i	2.70574	−	2.27038i
$587$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$587$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$588$	−12.0496			−12.0496
$589$		0			0
$590$		0			0
$591$	−0.113341	−	0.642788i	−0.113341	−	0.642788i
$592$		0			0
$593$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$593$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$594$	−5.08512	−	1.85083i	−5.08512	−	1.85083i
$595$		0			0
$596$	1.26604	−	2.19285i	1.26604	−	2.19285i
$597$	1.43969	+	2.49362i	1.43969	+	2.49362i
$598$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$599$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$599$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$600$	−2.70574	−	4.68647i	−2.70574	−	4.68647i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	2.37939	−	0.866025i	2.37939	−	0.866025i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.439693	−	2.49362i	−0.439693	−	2.49362i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$613$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$614$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$615$		0			0
$616$	−2.70574	−	4.68647i	−2.70574	−	4.68647i
$617$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$617$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$618$	0.939693	−	5.32926i	0.939693	−	5.32926i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$622$	−3.31908	−	1.20805i	−3.31908	−	1.20805i
$623$		0			0
$624$	−4.14543	+	3.47843i	−4.14543	+	3.47843i
$625$	0.173648	+	0.984808i	0.173648	+	0.984808i
$626$	1.87939			1.87939
$627$	0.939693	+	1.62760i	0.939693	+	1.62760i
$628$	−2.53209			−2.53209
$629$		0			0
$630$		0			0
$631$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$631$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.286989	+	1.62760i	−0.286989	+	1.62760i
$637$	0.439693	−	2.49362i	0.439693	−	2.49362i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$642$		0			0
$643$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$643$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$644$	−0.286989	−	1.62760i	−0.286989	−	1.62760i
$645$		0			0
$646$		0			0
$647$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$647$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$648$	−1.43969	−	8.16490i	−1.43969	−	8.16490i
$649$		0			0
$650$	1.76604	−	0.642788i	1.76604	−	0.642788i
$651$		0			0
$652$		0			0
$653$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$653$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$654$	1.76604	+	3.05888i	1.76604	+	3.05888i
$655$		0			0
$656$	0.173648	−	0.984808i	0.173648	−	0.984808i
$657$	−2.53209	−	4.38571i	−2.53209	−	4.38571i
$658$		0			0
$659$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$659$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$660$		0			0
$661$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$661$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$662$		0			0
$663$		0			0
$664$	5.41147			5.41147
$665$		0			0
$666$		0			0
$667$		0			0
$668$	2.97178	−	2.49362i	2.97178	−	2.49362i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	4.47178	−	7.74535i	4.47178	−	7.74535i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$676$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	4.14543	+	3.47843i	4.14543	+	3.47843i
$679$		0			0
$680$		0			0
$681$	−2.87939	+	2.41609i	−2.87939	+	2.41609i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−3.20574	+	5.55250i	−3.20574	+	5.55250i
$685$		0			0
$686$	0.939693	+	5.32926i	0.939693	+	5.32926i
$687$		0			0
$688$		0			0
$689$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	−0.826352	+	4.68647i	−0.826352	+	4.68647i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	2.70574	+	0.984808i	2.70574	+	0.984808i
$699$		0			0
$700$	−3.64543	+	3.05888i	−3.64543	+	3.05888i
$701$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$701$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$702$	5.41147			5.41147
$703$		0			0
$704$	1.87939			1.87939
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$709$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	2.97178	+	2.49362i	2.97178	+	2.49362i
$717$	2.70574	+	0.984808i	2.70574	+	0.984808i
$718$	0.613341	−	0.223238i	0.613341	−	0.223238i
$719$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$719$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$720$		0			0
$721$	−2.87939			−2.87939
$722$	1.76604	−	0.642788i	1.76604	−	0.642788i
$723$	3.53209			3.53209
$724$	0.152704	+	0.866025i	0.152704	+	0.866025i
$725$		0			0
$726$	−3.31908	+	1.20805i	−3.31908	+	1.20805i
$727$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$727$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$728$	4.14543	+	3.47843i	4.14543	+	3.47843i
$729$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$733$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$734$	1.87939	−	3.25519i	1.87939	−	3.25519i
$735$		0			0
$736$	0.826352	+	0.300767i	0.826352	+	0.300767i
$737$		0			0
$738$	−1.26604	+	1.06234i	−1.26604	+	1.06234i
$739$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$739$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$740$		0			0
$741$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$742$	1.22668			1.22668
$743$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$743$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.64543	−	3.05888i	−3.64543	−	3.05888i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$751$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$752$		0			0
$753$	1.87939	−	3.25519i	1.87939	−	3.25519i
$754$		0			0
$755$		0			0
$756$	−12.8760	+	4.68647i	−12.8760	+	4.68647i
$757$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$757$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$758$		0			0
$759$	−0.652704			−0.652704
$760$		0			0
$761$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$761$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$762$		0			0
$763$	1.43969	−	1.20805i	1.43969	−	1.20805i
$764$	2.37939	−	0.866025i	2.37939	−	0.866025i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$769$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$770$		0			0
$771$	1.87939	+	3.25519i	1.87939	+	3.25519i
$772$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$773$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$773$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.87939			1.87939
$779$	0.347296			0.347296
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−6.85117	−	2.49362i	−6.85117	−	2.49362i
$785$		0			0
$786$		0			0
$787$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$787$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$788$	0.152704	−	0.866025i	0.152704	−	0.866025i
$789$		0			0
$790$		0			0
$791$	1.43969	−	2.49362i	1.43969	−	2.49362i
$792$	−5.58512	−	4.68647i	−5.58512	−	4.68647i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.673648	+	3.82045i	0.673648	+	3.82045i
$797$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$797$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$798$	6.23783	+	2.27038i	6.23783	+	2.27038i
$799$		0			0
$800$	−0.439693	−	2.49362i	−0.439693	−	2.49362i
$801$		0			0
$802$		0			0
$803$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$		0			0
$811$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$811$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$812$		0			0
$813$	0.613341	−	0.223238i	0.613341	−	0.223238i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.652704			−0.652704
$819$	−0.826352	−	4.68647i	−0.826352	−	4.68647i
$820$		0			0
$821$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$821$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$822$		0			0
$823$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$823$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$824$	2.20574	−	3.82045i	2.20574	−	3.82045i
$825$	0.939693	+	1.62760i	0.939693	+	1.62760i
$826$		0			0
$827$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$827$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$828$	−1.11334	−	1.92836i	−1.11334	−	1.92836i
$829$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$829$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	0.439693	+	2.49362i	0.439693	+	2.49362i
$837$		0			0
$838$	0.326352	+	1.85083i	0.326352	+	1.85083i
$839$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$839$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$840$		0			0
$841$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$842$		0			0
$843$	0.326352	−	0.565258i	0.326352	−	0.565258i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.939693	+	1.62760i	0.939693	+	1.62760i
$848$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$853$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$857$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$858$	2.70574	−	2.27038i	2.70574	−	2.27038i
$859$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$860$		0			0
$861$	0.939693	+	0.788496i	0.939693	+	0.788496i
$862$	1.43969	−	2.49362i	1.43969	−	2.49362i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	1.26604	−	7.18009i	1.26604	−	7.18009i
$865$		0			0
$866$	1.43969	+	2.49362i	1.43969	+	2.49362i
$867$	0.939693	−	1.62760i	0.939693	−	1.62760i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.500000	+	2.83564i	0.500000	+	2.83564i
$873$		0			0
$874$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$875$		0			0
$876$	−1.65270	−	9.37295i	−1.65270	−	9.37295i
$877$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$877$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$878$		0			0
$879$	−3.31908	−	1.20805i	−3.31908	−	1.20805i
$880$		0			0
$881$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$881$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$882$	6.02481	+	10.4353i	6.02481	+	10.4353i
$883$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$883$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$884$		0			0
$885$		0			0
$886$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$887$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$887$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.500000	+	2.83564i	0.500000	+	2.83564i
$892$		0			0
$893$		0			0
$894$	−3.53209			−3.53209
$895$		0			0
$896$	1.43969	−	1.20805i	1.43969	−	1.20805i
$897$	0.613341	−	0.223238i	0.613341	−	0.223238i
$898$		0			0
$899$		0			0
$900$	−3.20574	+	5.55250i	−3.20574	+	5.55250i
$901$		0			0
$902$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$903$		0			0
$904$	2.20574	+	3.82045i	2.20574	+	3.82045i
$905$		0			0
$906$	−2.70574	−	2.27038i	−2.70574	−	2.27038i
$907$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$907$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$908$	−4.75877	+	1.73205i	−4.75877	+	1.73205i
$909$		0			0
$910$		0			0
$911$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$911$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$912$	−4.14543	+	3.47843i	−4.14543	+	3.47843i
$913$	−1.87939			−1.87939
$914$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$922$	0.326352	−	1.85083i	0.326352	−	1.85083i
$923$		0			0
$924$	−4.47178	+	7.74535i	−4.47178	+	7.74535i
$925$		0			0
$926$		0			0
$927$	−3.64543	+	1.32683i	−3.64543	+	1.32683i
$928$		0			0
$929$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$929$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$930$		0			0
$931$	0.439693	−	2.49362i	0.439693	−	2.49362i
$932$		0			0
$933$	0.613341	+	3.47843i	0.613341	+	3.47843i
$934$	−0.500000	+	0.419550i	−0.500000	+	0.419550i
$935$		0			0
$936$	6.85117	+	2.49362i	6.85117	+	2.49362i
$937$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$937$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$938$		0			0
$939$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$940$		0			0
$941$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$941$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$942$	1.76604	+	3.05888i	1.76604	+	3.05888i
$943$	−0.0603074	+	0.104455i	−0.0603074	+	0.104455i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$947$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$948$		0			0
$949$	2.00000			2.00000
$950$	1.76604	−	0.642788i	1.76604	−	0.642788i
$951$		0			0
$952$		0			0
$953$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$953$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$954$	1.55303	−	0.565258i	1.55303	−	0.565258i
$955$		0			0
$956$	2.97178	+	2.49362i	2.97178	+	2.49362i
$957$		0			0
$958$	−1.76604	−	3.05888i	−1.76604	−	3.05888i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	4.47178	+	1.62760i	4.47178	+	1.62760i
$965$		0			0
$966$	−1.76604	+	1.48189i	−1.76604	+	1.48189i
$967$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$967$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$968$	−2.87939			−2.87939
$969$		0			0
$970$		0			0
$971$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$971$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$972$	−4.91147	+	4.12122i	−4.91147	+	4.12122i
$973$		0			0
$974$		0			0
$975$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$976$		0			0
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.26604	−	2.19285i	1.26604	−	2.19285i
$982$		0			0
$983$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$983$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$984$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$989$		0			0
$990$		0			0
$991$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−4.47178	−	7.74535i	−4.47178	−	7.74535i
$997$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$997$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2717.1.db.a.142.1	✓	6
11.10	odd	2		2717.1.db.b.142.1	yes	6
13.12	even	2		2717.1.db.b.142.1	yes	6
19.17	even	9	inner	2717.1.db.a.2430.1	yes	6
143.142	odd	2	CM	2717.1.db.a.142.1	✓	6
209.131	odd	18		2717.1.db.b.2430.1	yes	6
247.207	even	18		2717.1.db.b.2430.1	yes	6
2717.2430	odd	18	inner	2717.1.db.a.2430.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.a.142.1	✓	6	1.1	even	1	trivial
2717.1.db.a.142.1	✓	6	143.142	odd	2	CM
2717.1.db.a.2430.1	yes	6	19.17	even	9	inner
2717.1.db.a.2430.1	yes	6	2717.2430	odd	18	inner
2717.1.db.b.142.1	yes	6	11.10	odd	2
2717.1.db.b.142.1	yes	6	13.12	even	2
2717.1.db.b.2430.1	yes	6	209.131	odd	18
2717.1.db.b.2430.1	yes	6	247.207	even	18

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:	\( N \)	\(=\)	\( 2717 = 11 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2717.db (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.326352 - 1.85083i) q^{2} +(-1.43969 + 1.20805i) q^{3} +(-2.37939 + 0.866025i) q^{4} +(2.70574 + 2.27038i) q^{6} +(0.939693 - 1.62760i) q^{7} +(1.43969 + 2.49362i) q^{8} +(0.439693 - 2.49362i) q^{9} +O(q^{10})\)	\(q+(-0.326352 - 1.85083i) q^{2} +(-1.43969 + 1.20805i) q^{3} +(-2.37939 + 0.866025i) q^{4} +(2.70574 + 2.27038i) q^{6} +(0.939693 - 1.62760i) q^{7} +(1.43969 + 2.49362i) q^{8} +(0.439693 - 2.49362i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(2.37939 - 4.12122i) q^{12} +(0.766044 + 0.642788i) q^{13} +(-3.31908 - 1.20805i) q^{14} +(2.20574 - 1.85083i) q^{16} -4.75877 q^{18} +(0.766044 + 0.642788i) q^{19} +(0.613341 + 3.47843i) q^{21} +(-1.43969 + 1.20805i) q^{22} +(-0.326352 + 0.118782i) q^{23} +(-5.08512 - 1.85083i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.939693 - 1.62760i) q^{26} +(1.43969 + 2.49362i) q^{27} +(-0.826352 + 4.68647i) q^{28} +(-1.93969 - 1.62760i) q^{32} +(1.76604 + 0.642788i) q^{33} +(1.11334 + 6.31407i) q^{36} +(0.939693 - 1.62760i) q^{38} -1.87939 q^{39} +(0.266044 - 0.223238i) q^{41} +(6.23783 - 2.27038i) q^{42} +(1.93969 + 1.62760i) q^{44} +(0.326352 + 0.565258i) q^{46} +(-0.939693 + 5.32926i) q^{48} +(-1.26604 - 2.19285i) q^{49} +(0.939693 - 1.62760i) q^{50} +(-2.37939 - 0.866025i) q^{52} +(-0.326352 + 0.118782i) q^{53} +(4.14543 - 3.47843i) q^{54} +5.41147 q^{56} -1.87939 q^{57} +(-3.64543 - 3.05888i) q^{63} +(-0.939693 + 1.62760i) q^{64} +(0.613341 - 3.47843i) q^{66} +(0.326352 - 0.565258i) q^{69} +(6.85117 - 2.49362i) q^{72} +(1.53209 - 1.28558i) q^{73} -1.87939 q^{75} +(-2.37939 - 0.866025i) q^{76} -1.87939 q^{77} +(0.613341 + 3.47843i) q^{78} +(-2.70574 - 0.984808i) q^{81} +(-0.500000 - 0.419550i) q^{82} +(0.939693 - 1.62760i) q^{83} +(-4.47178 - 7.74535i) q^{84} +(1.43969 - 2.49362i) q^{88} +(1.76604 - 0.642788i) q^{91} +(0.673648 - 0.565258i) q^{92} +4.75877 q^{96} +(-3.64543 + 3.05888i) q^{98} +(-2.37939 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 3 q^{8} - 3 q^{9} - 3 q^{11} + 3 q^{12} - 3 q^{14} + 3 q^{16} - 6 q^{18} - 3 q^{21} - 3 q^{22} - 3 q^{23} - 9 q^{24} + 3 q^{27} - 6 q^{28} - 6 q^{32} + 6 q^{33} - 3 q^{41} + 18 q^{42} + 6 q^{44} + 3 q^{46} - 3 q^{49} - 3 q^{52} - 3 q^{53} + 9 q^{54} + 12 q^{56} - 6 q^{63} - 3 q^{66} + 3 q^{69} + 15 q^{72} - 3 q^{76} - 3 q^{78} - 6 q^{81} - 3 q^{82} - 12 q^{84} + 3 q^{88} + 6 q^{91} + 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 3 * q^8 - 3 * q^9 - 3 * q^11 + 3 * q^12 - 3 * q^14 + 3 * q^16 - 6 * q^18 - 3 * q^21 - 3 * q^22 - 3 * q^23 - 9 * q^24 + 3 * q^27 - 6 * q^28 - 6 * q^32 + 6 * q^33 - 3 * q^41 + 18 * q^42 + 6 * q^44 + 3 * q^46 - 3 * q^49 - 3 * q^52 - 3 * q^53 + 9 * q^54 + 12 * q^56 - 6 * q^63 - 3 * q^66 + 3 * q^69 + 15 * q^72 - 3 * q^76 - 3 * q^78 - 6 * q^81 - 3 * q^82 - 12 * q^84 + 3 * q^88 + 6 * q^91 + 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more