LMFDB - Embedded newform 3640.1.hd.d.1299.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3640,1,Mod(779,3640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3640, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 2, 3]))

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

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

chi := DirichletCharacter("3640.779");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3640.hd (of order $6$, degree $2$, 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:	$1.81659664598$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{18}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{18} - \cdots)$

Embedding invariants

Embedding label			1299.1
Root			$-0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	3640.1299
Dual form			3640.1.hd.d.779.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.70574 - 0.984808i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.984808 + 0.173648i) q^{5} +1.96962 q^{6} +(0.984808 - 0.173648i) q^{7} +1.00000i q^{8} +(1.43969 + 2.49362i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.70574 - 0.984808i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.984808 + 0.173648i) q^{5} +1.96962 q^{6} +(0.984808 - 0.173648i) q^{7} +1.00000i q^{8} +(1.43969 + 2.49362i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(-1.70574 + 0.984808i) q^{12} -1.00000i q^{13} +(-0.766044 + 0.642788i) q^{14} +(-1.50881 - 1.26604i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.592396 + 0.342020i) q^{17} +(-2.49362 - 1.43969i) q^{18} +(0.642788 - 0.766044i) q^{20} +(-1.85083 - 0.673648i) q^{21} +(0.984808 - 1.70574i) q^{24} +(0.939693 + 0.342020i) q^{25} +(0.500000 + 0.866025i) q^{26} -3.70167i q^{27} +(0.342020 - 0.939693i) q^{28} +(1.93969 + 0.342020i) q^{30} +(0.866025 - 1.50000i) q^{31} +(0.866025 + 0.500000i) q^{32} -0.684040 q^{34} +1.00000 q^{35} +2.87939 q^{36} +(0.300767 - 0.173648i) q^{37} +(-0.984808 + 1.70574i) q^{39} +(-0.173648 + 0.984808i) q^{40} +(1.93969 - 0.342020i) q^{42} +1.28558i q^{43} +(0.984808 + 2.70574i) q^{45} +(-1.62760 + 0.939693i) q^{47} +1.96962i q^{48} +(0.939693 - 0.342020i) q^{49} +(-0.984808 + 0.173648i) q^{50} +(-0.673648 - 1.16679i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(1.85083 + 3.20574i) q^{54} +(0.173648 + 0.984808i) q^{56} +(-1.85083 + 0.673648i) q^{60} +1.73205i q^{62} +(1.85083 + 2.20574i) q^{63} -1.00000 q^{64} +(0.173648 - 0.984808i) q^{65} +(0.592396 - 0.342020i) q^{68} +(-0.866025 + 0.500000i) q^{70} +0.684040 q^{71} +(-2.49362 + 1.43969i) q^{72} +(-0.173648 + 0.300767i) q^{74} +(-1.26604 - 1.50881i) q^{75} -1.96962i q^{78} +(-0.342020 - 0.939693i) q^{80} +(-2.20574 + 3.82045i) q^{81} +(-1.50881 + 1.26604i) q^{84} +(0.524005 + 0.439693i) q^{85} +(-0.642788 - 1.11334i) q^{86} +(-2.20574 - 1.85083i) q^{90} +(-0.173648 - 0.984808i) q^{91} +(-2.95442 + 1.70574i) q^{93} +(0.939693 - 1.62760i) q^{94} +(-0.984808 - 1.70574i) q^{96} +(-0.642788 + 0.766044i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 6 * q^9	$ 12 q + 6 q^{4} + 6 q^{9} - 6 q^{16} + 6 q^{26} + 12 q^{30} + 12 q^{35} + 12 q^{36} + 12 q^{42} - 6 q^{51} - 12 q^{64} - 6 q^{75} - 6 q^{81} - 6 q^{90}+O(q^{100}) $ 12 * q + 6 * q^4 + 6 * q^9 - 6 * q^16 + 6 * q^26 + 12 * q^30 + 12 * q^35 + 12 * q^36 + 12 * q^42 - 6 * q^51 - 12 * q^64 - 6 * q^75 - 6 * q^81 - 6 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3640\mathbb{Z}\right)^\times$.

$n$	$521$	$561$	$911$	$1457$	$1821$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$2$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$3$	−1.70574	−	0.984808i	−1.70574	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$3$	−1.70574	−	0.984808i	−1.70574	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$4$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	0.984808	+	0.173648i	0.984808	+	0.173648i
$5$	0.984808	+	0.173648i	0.984808	+	0.173648i
$6$	1.96962			1.96962
$7$	0.984808	−	0.173648i	0.984808	−	0.173648i
$7$	0.984808	−	0.173648i	0.984808	−	0.173648i
$8$			1.00000i			1.00000i
$9$	1.43969	+	2.49362i	1.43969	+	2.49362i
$10$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−1.70574	+	0.984808i	−1.70574	+	0.984808i
$13$		−	1.00000i		−	1.00000i
$13$		−	1.00000i		−	1.00000i
$14$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$15$	−1.50881	−	1.26604i	−1.50881	−	1.26604i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$	0.592396	+	0.342020i	0.592396	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$17$	0.592396	+	0.342020i	0.592396	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$18$	−2.49362	−	1.43969i	−2.49362	−	1.43969i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	0.642788	−	0.766044i	0.642788	−	0.766044i
$21$	−1.85083	−	0.673648i	−1.85083	−	0.673648i
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	0.984808	−	1.70574i	0.984808	−	1.70574i
$25$	0.939693	+	0.342020i	0.939693	+	0.342020i
$26$	0.500000	+	0.866025i	0.500000	+	0.866025i
$27$		−	3.70167i		−	3.70167i
$28$	0.342020	−	0.939693i	0.342020	−	0.939693i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	1.93969	+	0.342020i	1.93969	+	0.342020i
$31$	0.866025	−	1.50000i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$31$	0.866025	−	1.50000i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$32$	0.866025	+	0.500000i	0.866025	+	0.500000i
$33$		0			0
$34$	−0.684040			−0.684040
$35$	1.00000			1.00000
$36$	2.87939			2.87939
$37$	0.300767	−	0.173648i	0.300767	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$37$	0.300767	−	0.173648i	0.300767	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$38$		0			0
$39$	−0.984808	+	1.70574i	−0.984808	+	1.70574i
$40$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	1.93969	−	0.342020i	1.93969	−	0.342020i
$43$			1.28558i			1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$43$			1.28558i			1.28558i	−0.766044	+	0.642788i	$0.777778\pi$
$44$		0			0
$45$	0.984808	+	2.70574i	0.984808	+	2.70574i
$46$		0			0
$47$	−1.62760	+	0.939693i	−1.62760	+	0.939693i	−0.642788	+	0.766044i	$0.722222\pi$
$47$	−1.62760	+	0.939693i	−1.62760	+	0.939693i	−0.984808	+	0.173648i	$0.944444\pi$
$48$			1.96962i			1.96962i
$49$	0.939693	−	0.342020i	0.939693	−	0.342020i
$50$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$51$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$52$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$	1.85083	+	3.20574i	1.85083	+	3.20574i
$55$		0			0
$56$	0.173648	+	0.984808i	0.173648	+	0.984808i
$57$		0			0
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$	−1.85083	+	0.673648i	−1.85083	+	0.673648i
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$			1.73205i			1.73205i
$63$	1.85083	+	2.20574i	1.85083	+	2.20574i
$64$	−1.00000			−1.00000
$65$	0.173648	−	0.984808i	0.173648	−	0.984808i
$66$		0			0
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$	0.592396	−	0.342020i	0.592396	−	0.342020i
$69$		0			0
$70$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$71$	0.684040			0.684040			0.342020	−	0.939693i	$-0.388889\pi$
$71$	0.684040			0.684040			0.342020	+	0.939693i	$0.388889\pi$
$72$	−2.49362	+	1.43969i	−2.49362	+	1.43969i
$73$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$73$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$74$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$75$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$76$		0			0
$77$		0			0
$78$		−	1.96962i		−	1.96962i
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$81$	−2.20574	+	3.82045i	−2.20574	+	3.82045i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−1.50881	+	1.26604i	−1.50881	+	1.26604i
$85$	0.524005	+	0.439693i	0.524005	+	0.439693i
$86$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$87$		0			0
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$91$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$92$		0			0
$93$	−2.95442	+	1.70574i	−2.95442	+	1.70574i
$94$	0.939693	−	1.62760i	0.939693	−	1.62760i
$95$		0			0
$96$	−0.984808	−	1.70574i	−0.984808	−	1.70574i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$99$		0			0
$100$	0.766044	−	0.642788i	0.766044	−	0.642788i
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$	1.16679	+	0.673648i	1.16679	+	0.673648i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	1.00000			1.00000
$105$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$106$		0			0
$107$	1.50000	−	0.866025i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$107$	1.50000	−	0.866025i	1.50000	−	0.866025i	1.00000			$0$
$108$	−3.20574	−	1.85083i	−3.20574	−	1.85083i
$109$	−0.642788	+	1.11334i	−0.642788	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$109$	−0.642788	+	1.11334i	−0.642788	+	1.11334i	−0.984808	+	0.173648i	$0.944444\pi$
$110$		0			0
$111$	−0.684040			−0.684040
$112$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$113$			1.73205i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$113$			1.73205i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.49362	−	1.43969i	2.49362	−	1.43969i
$118$		0			0
$119$	0.642788	+	0.233956i	0.642788	+	0.233956i
$120$	1.26604	−	1.50881i	1.26604	−	1.50881i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$125$	0.866025	+	0.500000i	0.866025	+	0.500000i
$126$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	0.866025	−	0.500000i	0.866025	−	0.500000i
$129$	1.26604	−	2.19285i	1.26604	−	2.19285i
$130$	0.342020	+	0.939693i	0.342020	+	0.939693i
$131$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$131$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.642788	−	3.64543i	0.642788	−	3.64543i
$136$	−0.342020	+	0.592396i	−0.342020	+	0.592396i
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$		0			0
$139$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$139$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$140$	0.500000	−	0.866025i	0.500000	−	0.866025i
$141$	3.70167			3.70167
$142$	−0.592396	+	0.342020i	−0.592396	+	0.342020i
$143$		0			0
$144$	1.43969	−	2.49362i	1.43969	−	2.49362i
$145$		0			0
$146$		0			0
$147$	−1.93969	−	0.342020i	−1.93969	−	0.342020i
$148$		−	0.347296i		−	0.347296i
$149$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$149$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$150$	1.85083	+	0.673648i	1.85083	+	0.673648i
$151$	0.342020	−	0.592396i	0.342020	−	0.592396i	−0.642788	−	0.766044i	$-0.722222\pi$
$151$	0.342020	−	0.592396i	0.342020	−	0.592396i	0.984808	+	0.173648i	$0.0555556\pi$
$152$		0			0
$153$			1.96962i			1.96962i
$154$		0			0
$155$	1.11334	−	1.32683i	1.11334	−	1.32683i
$156$	0.984808	+	1.70574i	0.984808	+	1.70574i
$157$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$157$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$158$		0			0
$159$		0			0
$160$	0.766044	+	0.642788i	0.766044	+	0.642788i
$161$		0			0
$162$		−	4.41147i		−	4.41147i
$163$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$163$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$168$	0.673648	−	1.85083i	0.673648	−	1.85083i
$169$	−1.00000			−1.00000
$170$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$171$		0			0
$172$	1.11334	+	0.642788i	1.11334	+	0.642788i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$	0.984808	+	0.173648i	0.984808	+	0.173648i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$179$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$180$	2.83564	+	0.500000i	2.83564	+	0.500000i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	0.642788	+	0.766044i	0.642788	+	0.766044i
$183$		0			0
$184$		0			0
$185$	0.326352	−	0.118782i	0.326352	−	0.118782i
$186$	1.70574	−	2.95442i	1.70574	−	2.95442i
$187$		0			0
$188$			1.87939i			1.87939i
$189$	−0.642788	−	3.64543i	−0.642788	−	3.64543i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	1.70574	+	0.984808i	1.70574	+	0.984808i
$193$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$193$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$194$		0			0
$195$	−1.26604	+	1.50881i	−1.26604	+	1.50881i
$196$	0.173648	−	0.984808i	0.173648	−	0.984808i
$197$		−	1.53209i		−	1.53209i	−0.642788	−	0.766044i	$-0.722222\pi$
$197$		−	1.53209i		−	1.53209i	0.642788	−	0.766044i	$-0.277778\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−1.34730			−1.34730
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$209$		0			0
$210$	1.96962			1.96962
$211$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$211$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$212$		0			0
$213$	−1.16679	−	0.673648i	−1.16679	−	0.673648i
$214$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$215$	−0.223238	+	1.26604i	−0.223238	+	1.26604i
$216$	3.70167			3.70167
$217$	0.592396	−	1.62760i	0.592396	−	1.62760i
$218$		−	1.28558i		−	1.28558i
$219$		0			0
$220$		0			0
$221$	0.342020	−	0.592396i	0.342020	−	0.592396i
$222$	0.592396	−	0.342020i	0.592396	−	0.342020i
$223$		−	0.347296i		−	0.347296i	−0.984808	−	0.173648i	$-0.944444\pi$
$223$		−	0.347296i		−	0.347296i	0.984808	−	0.173648i	$-0.0555556\pi$
$224$	0.939693	+	0.342020i	0.939693	+	0.342020i
$225$	0.500000	+	2.83564i	0.500000	+	2.83564i
$226$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$	−0.984808	−	1.70574i	−0.984808	−	1.70574i	−0.642788	−	0.766044i	$-0.722222\pi$
$229$	−0.984808	−	1.70574i	−0.984808	−	1.70574i	−0.342020	−	0.939693i	$-0.611111\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$233$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$234$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$235$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$236$		0			0
$237$		0			0
$238$	−0.673648	+	0.118782i	−0.673648	+	0.118782i
$239$	−1.96962			−1.96962			−0.984808	−	0.173648i	$-0.944444\pi$
$239$	−1.96962			−1.96962			−0.984808	+	0.173648i	$0.944444\pi$
$240$	−0.342020	+	1.93969i	−0.342020	+	1.93969i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	0.866025	+	0.500000i	0.866025	+	0.500000i
$243$	4.31908	−	2.49362i	4.31908	−	2.49362i
$244$		0			0
$245$	0.984808	−	0.173648i	0.984808	−	0.173648i
$246$		0			0
$247$		0			0
$248$	1.50000	+	0.866025i	1.50000	+	0.866025i
$249$		0			0
$250$	−1.00000			−1.00000
$251$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$251$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$252$	2.83564	−	0.500000i	2.83564	−	0.500000i
$253$		0			0
$254$		0			0
$255$	−0.460802	−	1.26604i	−0.460802	−	1.26604i
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	1.11334	−	0.642788i	1.11334	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$257$	1.11334	−	0.642788i	1.11334	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$258$			2.53209i			2.53209i
$259$	0.266044	−	0.223238i	0.266044	−	0.223238i
$260$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$261$		0			0
$262$	−1.32683	−	0.766044i	−1.32683	−	0.766044i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$	1.26604	+	3.47843i	1.26604	+	3.47843i
$271$	−0.642788	−	1.11334i	−0.642788	−	1.11334i	−0.984808	−	0.173648i	$-0.944444\pi$
$271$	−0.642788	−	1.11334i	−0.642788	−	1.11334i	0.342020	−	0.939693i	$-0.388889\pi$
$272$		−	0.684040i		−	0.684040i
$273$	−0.673648	+	1.85083i	−0.673648	+	1.85083i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$277$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$278$	−1.62760	+	0.939693i	−1.62760	+	0.939693i
$279$	4.98724			4.98724
$280$			1.00000i			1.00000i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−3.20574	+	1.85083i	−3.20574	+	1.85083i
$283$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$283$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$284$	0.342020	−	0.592396i	0.342020	−	0.592396i
$285$		0			0
$286$		0			0
$287$		0			0
$288$			2.87939i			2.87939i
$289$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	0.347296i		−	0.347296i	−0.984808	−	0.173648i	$-0.944444\pi$
$293$		−	0.347296i		−	0.347296i	0.984808	−	0.173648i	$-0.0555556\pi$
$294$	1.85083	−	0.673648i	1.85083	−	0.673648i
$295$		0			0
$296$	0.173648	+	0.300767i	0.173648	+	0.300767i
$297$		0			0
$298$	1.50000	+	0.866025i	1.50000	+	0.866025i
$299$		0			0
$300$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$301$	0.223238	+	1.26604i	0.223238	+	1.26604i
$302$			0.684040i			0.684040i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−0.984808	−	1.70574i	−0.984808	−	1.70574i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$	−0.300767	+	1.70574i	−0.300767	+	1.70574i
$311$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$311$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$312$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$313$	−0.592396	+	0.342020i	−0.592396	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$313$	−0.592396	+	0.342020i	−0.592396	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$314$		0			0
$315$	1.43969	+	2.49362i	1.43969	+	2.49362i
$316$		0			0
$317$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$317$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$318$		0			0
$319$		0			0
$320$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$321$	−3.41147			−3.41147
$322$		0			0
$323$		0			0
$324$	2.20574	+	3.82045i	2.20574	+	3.82045i
$325$	0.342020	−	0.939693i	0.342020	−	0.939693i
$326$		0			0
$327$	2.19285	−	1.26604i	2.19285	−	1.26604i
$328$		0			0
$329$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$		0			0
$333$	0.866025	+	0.500000i	0.866025	+	0.500000i
$334$	0.500000	+	0.866025i	0.500000	+	0.866025i
$335$		0			0
$336$	0.342020	+	1.93969i	0.342020	+	1.93969i
$337$			1.28558i			1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$337$			1.28558i			1.28558i	−0.766044	+	0.642788i	$0.777778\pi$
$338$	0.866025	−	0.500000i	0.866025	−	0.500000i
$339$	1.70574	−	2.95442i	1.70574	−	2.95442i
$340$	0.642788	−	0.233956i	0.642788	−	0.233956i
$341$		0			0
$342$		0			0
$343$	0.866025	−	0.500000i	0.866025	−	0.500000i
$344$	−1.28558			−1.28558
$345$		0			0
$346$		0			0
$347$	0.592396	+	0.342020i	0.592396	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$347$	0.592396	+	0.342020i	0.592396	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$348$		0			0
$349$	0.684040			0.684040			0.342020	−	0.939693i	$-0.388889\pi$
$349$	0.684040			0.684040			0.342020	+	0.939693i	$0.388889\pi$
$350$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$351$	−3.70167			−3.70167
$352$		0			0
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$		0			0
$355$	0.673648	+	0.118782i	0.673648	+	0.118782i
$356$		0			0
$357$	−0.866025	−	1.03209i	−0.866025	−	1.03209i
$358$		−	1.53209i		−	1.53209i
$359$	0.866025	+	1.50000i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$359$	0.866025	+	1.50000i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$360$	−2.70574	+	0.984808i	−2.70574	+	0.984808i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$			1.96962i			1.96962i
$364$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$365$		0			0
$366$		0			0
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$		0			0
$369$		0			0
$370$	−0.223238	+	0.266044i	−0.223238	+	0.266044i
$371$		0			0
$372$			3.41147i			3.41147i
$373$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$373$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$374$		0			0
$375$	−0.984808	−	1.70574i	−0.984808	−	1.70574i
$376$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$377$		0			0
$378$	2.37939	+	2.83564i	2.37939	+	2.83564i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.300767	−	0.173648i	0.300767	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$383$	0.300767	−	0.173648i	0.300767	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$384$	−1.96962			−1.96962
$385$		0			0
$386$		0			0
$387$	−3.20574	+	1.85083i	−3.20574	+	1.85083i
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$	0.342020	−	1.93969i	0.342020	−	1.93969i
$391$		0			0
$392$	0.342020	+	0.939693i	0.342020	+	0.939693i
$393$		−	3.01763i		−	3.01763i
$394$	0.766044	+	1.32683i	0.766044	+	1.32683i
$395$		0			0
$396$		0			0
$397$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$397$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$398$		0			0
$399$		0			0
$400$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$404$		0			0
$405$	−2.83564	+	3.37939i	−2.83564	+	3.37939i
$406$		0			0
$407$		0			0
$408$	1.16679	−	0.673648i	1.16679	−	0.673648i
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.500000	−	0.866025i	0.500000	−	0.866025i
$417$	−3.20574	−	1.85083i	−3.20574	−	1.85083i
$418$		0			0
$419$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$419$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$420$	−1.70574	+	0.984808i	−1.70574	+	0.984808i
$421$	1.28558			1.28558			0.642788	−	0.766044i	$-0.277778\pi$
$421$	1.28558			1.28558			0.642788	+	0.766044i	$0.277778\pi$
$422$	1.62760	−	0.939693i	1.62760	−	0.939693i
$423$	−4.68647	−	2.70574i	−4.68647	−	2.70574i
$424$		0			0
$425$	0.439693	+	0.524005i	0.439693	+	0.524005i
$426$	1.34730			1.34730
$427$		0			0
$428$		−	1.73205i		−	1.73205i
$429$		0			0
$430$	−0.439693	−	1.20805i	−0.439693	−	1.20805i
$431$	0.642788	−	1.11334i	0.642788	−	1.11334i	−0.342020	−	0.939693i	$-0.611111\pi$
$431$	0.642788	−	1.11334i	0.642788	−	1.11334i	0.984808	−	0.173648i	$-0.0555556\pi$
$432$	−3.20574	+	1.85083i	−3.20574	+	1.85083i
$433$		−	1.96962i		−	1.96962i	−0.173648	−	0.984808i	$-0.555556\pi$
$433$		−	1.96962i		−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$434$	0.300767	+	1.70574i	0.300767	+	1.70574i
$435$		0			0
$436$	0.642788	+	1.11334i	0.642788	+	1.11334i
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	2.20574	+	1.85083i	2.20574	+	1.85083i
$442$			0.684040i			0.684040i
$443$	−1.70574	+	0.984808i	−1.70574	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$443$	−1.70574	+	0.984808i	−1.70574	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$444$	−0.342020	+	0.592396i	−0.342020	+	0.592396i
$445$		0			0
$446$	0.173648	+	0.300767i	0.173648	+	0.300767i
$447$			3.41147i			3.41147i
$448$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−1.85083	−	2.20574i	−1.85083	−	2.20574i
$451$		0			0
$452$	1.50000	+	0.866025i	1.50000	+	0.866025i
$453$	−1.16679	+	0.673648i	−1.16679	+	0.673648i
$454$		0			0
$455$		−	1.00000i		−	1.00000i
$456$		0			0
$457$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$457$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$458$	1.70574	+	0.984808i	1.70574	+	0.984808i
$459$	1.26604	−	2.19285i	1.26604	−	2.19285i
$460$		0			0
$461$	−0.684040			−0.684040			−0.342020	−	0.939693i	$-0.611111\pi$
$461$	−0.684040			−0.684040			−0.342020	+	0.939693i	$0.611111\pi$
$462$		0			0
$463$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$463$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$464$		0			0
$465$	−3.20574	+	1.16679i	−3.20574	+	1.16679i
$466$	−0.984808	+	1.70574i	−0.984808	+	1.70574i
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$		−	2.87939i		−	2.87939i
$469$		0			0
$470$	1.20805	−	1.43969i	1.20805	−	1.43969i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	0.524005	−	0.439693i	0.524005	−	0.439693i
$477$		0			0
$478$	1.70574	−	0.984808i	1.70574	−	0.984808i
$479$	−0.984808	+	1.70574i	−0.984808	+	1.70574i	−0.342020	+	0.939693i	$0.611111\pi$
$479$	−0.984808	+	1.70574i	−0.984808	+	1.70574i	−0.642788	+	0.766044i	$0.722222\pi$
$480$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$481$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$482$		0			0
$483$		0			0
$484$	−1.00000			−1.00000
$485$		0			0
$486$	−2.49362	+	4.31908i	−2.49362	+	4.31908i
$487$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$487$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$488$		0			0
$489$		0			0
$490$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$491$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$491$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−1.73205			−1.73205
$497$	0.673648	−	0.118782i	0.673648	−	0.118782i
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	0.866025	−	0.500000i	0.866025	−	0.500000i
$501$	−0.984808	+	1.70574i	−0.984808	+	1.70574i
$502$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$505$		0			0
$506$		0			0
$507$	1.70574	+	0.984808i	1.70574	+	0.984808i
$508$		0			0
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$	1.03209	+	0.866025i	1.03209	+	0.866025i
$511$		0			0
$512$		−	1.00000i		−	1.00000i
$513$		0			0
$514$	−0.642788	+	1.11334i	−0.642788	+	1.11334i
$515$		0			0
$516$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$517$		0			0
$518$	−0.118782	+	0.326352i	−0.118782	+	0.326352i
$519$		0			0
$520$	0.984808	+	0.173648i	0.984808	+	0.173648i
$521$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$521$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$522$		0			0
$523$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$523$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−1.00000			$\pi$
$524$	1.53209			1.53209
$525$	−1.50881	−	1.26604i	−1.50881	−	1.26604i
$526$		0			0
$527$	1.02606	−	0.592396i	1.02606	−	0.592396i
$528$		0			0
$529$	0.500000	−	0.866025i	0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.62760	−	0.592396i	1.62760	−	0.592396i
$536$		0			0
$537$	2.61334	−	1.50881i	2.61334	−	1.50881i
$538$		0			0
$539$		0			0
$540$	−2.83564	−	2.37939i	−2.83564	−	2.37939i
$541$	−0.342020	−	0.592396i	−0.342020	−	0.592396i	0.642788	−	0.766044i	$-0.277778\pi$
$541$	−0.342020	−	0.592396i	−0.342020	−	0.592396i	−0.984808	+	0.173648i	$0.944444\pi$
$542$	1.11334	+	0.642788i	1.11334	+	0.642788i
$543$		0			0
$544$	0.342020	+	0.592396i	0.342020	+	0.592396i
$545$	−0.826352	+	0.984808i	−0.826352	+	0.984808i
$546$	−0.342020	−	1.93969i	−0.342020	−	1.93969i
$547$			1.96962i			1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$547$			1.96962i			1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$556$	0.939693	−	1.62760i	0.939693	−	1.62760i
$557$	0.300767	+	0.173648i	0.300767	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$557$	0.300767	+	0.173648i	0.300767	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$558$	−4.31908	+	2.49362i	−4.31908	+	2.49362i
$559$	1.28558			1.28558
$560$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$561$		0			0
$562$		0			0
$563$	−1.11334	−	0.642788i	−1.11334	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$563$	−1.11334	−	0.642788i	−1.11334	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$564$	1.85083	−	3.20574i	1.85083	−	3.20574i
$565$	−0.300767	+	1.70574i	−0.300767	+	1.70574i
$566$		0			0
$567$	−1.50881	+	4.14543i	−1.50881	+	4.14543i
$568$			0.684040i			0.684040i
$569$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$569$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$570$		0			0
$571$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$571$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$577$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$577$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$578$	0.460802	+	0.266044i	0.460802	+	0.266044i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	2.70574	−	0.984808i	2.70574	−	0.984808i
$586$	0.173648	+	0.300767i	0.173648	+	0.300767i
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$	−1.26604	+	1.50881i	−1.26604	+	1.50881i
$589$		0			0
$590$		0			0
$591$	−1.50881	+	2.61334i	−1.50881	+	2.61334i
$592$	−0.300767	−	0.173648i	−0.300767	−	0.173648i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$	0.592396	+	0.342020i	0.592396	+	0.342020i
$596$	−1.73205			−1.73205
$597$		0			0
$598$		0			0
$599$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$599$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$600$	1.50881	−	1.26604i	1.50881	−	1.26604i
$601$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$601$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$602$	−0.826352	−	0.984808i	−0.826352	−	0.984808i
$603$		0			0
$604$	−0.342020	−	0.592396i	−0.342020	−	0.592396i
$605$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$606$		0			0
$607$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$607$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.939693	+	1.62760i	0.939693	+	1.62760i
$612$	1.70574	+	0.984808i	1.70574	+	0.984808i
$613$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$613$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$	−0.592396	−	1.62760i	−0.592396	−	1.62760i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	1.96962			1.96962
$625$	0.766044	+	0.642788i	0.766044	+	0.642788i
$626$	0.342020	−	0.592396i	0.342020	−	0.592396i
$627$		0			0
$628$		0			0
$629$	0.237565			0.237565
$630$	−2.49362	−	1.43969i	−2.49362	−	1.43969i
$631$	1.96962			1.96962			0.984808	−	0.173648i	$-0.0555556\pi$
$631$	1.96962			1.96962			0.984808	+	0.173648i	$0.0555556\pi$
$632$		0			0
$633$	3.20574	+	1.85083i	3.20574	+	1.85083i
$634$	0.500000	−	0.866025i	0.500000	−	0.866025i
$635$		0			0
$636$		0			0
$637$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$638$		0			0
$639$	0.984808	+	1.70574i	0.984808	+	1.70574i
$640$	0.939693	−	0.342020i	0.939693	−	0.342020i
$641$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$641$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$642$	2.95442	−	1.70574i	2.95442	−	1.70574i
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$	1.62760	−	1.93969i	1.62760	−	1.93969i
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−3.82045	−	2.20574i	−3.82045	−	2.20574i
$649$		0			0
$650$	0.173648	+	0.984808i	0.173648	+	0.984808i
$651$	−2.61334	+	2.19285i	−2.61334	+	2.19285i
$652$		0			0
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$655$	0.524005	+	1.43969i	0.524005	+	1.43969i
$656$		0			0
$657$		0			0
$658$	0.642788	−	1.76604i	0.642788	−	1.76604i
$659$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$659$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	−0.866025	+	1.50000i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$661$	−0.866025	+	1.50000i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$662$		0			0
$663$	−1.16679	+	0.673648i	−1.16679	+	0.673648i
$664$		0			0
$665$		0			0
$666$	−1.00000			−1.00000
$667$		0			0
$668$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$669$	−0.342020	+	0.592396i	−0.342020	+	0.592396i
$670$		0			0
$671$		0			0
$672$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$673$		−	0.684040i		−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$673$		−	0.684040i		−	0.684040i	0.939693	−	0.342020i	$-0.111111\pi$
$674$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$675$	1.26604	−	3.47843i	1.26604	−	3.47843i
$676$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$			3.41147i			3.41147i
$679$		0			0
$680$	−0.439693	+	0.524005i	−0.439693	+	0.524005i
$681$		0			0
$682$		0			0
$683$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$683$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$684$		0			0
$685$		0			0
$686$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$687$			3.87939i			3.87939i
$688$	1.11334	−	0.642788i	1.11334	−	0.642788i
$689$		0			0
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$		0			0
$694$	−0.684040			−0.684040
$695$	1.85083	+	0.326352i	1.85083	+	0.326352i
$696$		0			0
$697$		0			0
$698$	−0.592396	+	0.342020i	−0.592396	+	0.342020i
$699$	−3.87939			−3.87939
$700$	0.642788	−	0.766044i	0.642788	−	0.766044i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	3.20574	−	1.85083i	3.20574	−	1.85083i
$703$		0			0
$704$		0			0
$705$	3.64543	+	0.642788i	3.64543	+	0.642788i
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$709$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$710$	−0.642788	+	0.233956i	−0.642788	+	0.233956i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	1.26604	+	0.460802i	1.26604	+	0.460802i
$715$		0			0
$716$	0.766044	+	1.32683i	0.766044	+	1.32683i
$717$	3.35965	+	1.93969i	3.35965	+	1.93969i
$718$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	1.85083	−	2.20574i	1.85083	−	2.20574i
$721$		0			0
$722$		−	1.00000i		−	1.00000i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.984808	−	1.70574i	−0.984808	−	1.70574i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	0.984808	−	0.173648i	0.984808	−	0.173648i
$729$	−5.41147			−5.41147
$730$		0			0
$731$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$732$		0			0
$733$	1.62760	−	0.939693i	1.62760	−	0.939693i	0.642788	−	0.766044i	$-0.277778\pi$
$733$	1.62760	−	0.939693i	1.62760	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$734$		0			0
$735$	−1.85083	−	0.673648i	−1.85083	−	0.673648i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$741$		0			0
$742$		0			0
$743$		−	1.87939i		−	1.87939i	−0.342020	−	0.939693i	$-0.611111\pi$
$743$		−	1.87939i		−	1.87939i	0.342020	−	0.939693i	$-0.388889\pi$
$744$	−1.70574	−	2.95442i	−1.70574	−	2.95442i
$745$	−0.592396	−	1.62760i	−0.592396	−	1.62760i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.32683	−	1.11334i	1.32683	−	1.11334i
$750$	1.70574	+	0.984808i	1.70574	+	0.984808i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	1.62760	+	0.939693i	1.62760	+	0.939693i
$753$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$754$		0			0
$755$	0.439693	−	0.524005i	0.439693	−	0.524005i
$756$	−3.47843	−	1.26604i	−3.47843	−	1.26604i
$757$		0			0			−	1.00000i	$-0.5\pi$
$757$		0			0				1.00000i	$0.5\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$		0			0
$763$	−0.439693	+	1.20805i	−0.439693	+	1.20805i
$764$		0			0
$765$	−0.342020	+	1.93969i	−0.342020	+	1.93969i
$766$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$767$		0			0
$768$	1.70574	−	0.984808i	1.70574	−	0.984808i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$	−2.53209			−2.53209
$772$		0			0
$773$	−0.300767	−	0.173648i	−0.300767	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$773$	−0.300767	−	0.173648i	−0.300767	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$774$	1.85083	−	3.20574i	1.85083	−	3.20574i
$775$	1.32683	−	1.11334i	1.32683	−	1.11334i
$776$		0			0
$777$	−0.673648	+	0.118782i	−0.673648	+	0.118782i
$778$		0			0
$779$		0			0
$780$	0.673648	+	1.85083i	0.673648	+	1.85083i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$785$		0			0
$786$	1.50881	+	2.61334i	1.50881	+	2.61334i
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	−1.32683	−	0.766044i	−1.32683	−	0.766044i
$789$		0			0
$790$		0			0
$791$	0.300767	+	1.70574i	0.300767	+	1.70574i
$792$		0			0
$793$		0			0
$794$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	−1.28558			−1.28558
$800$	0.642788	+	0.766044i	0.642788	+	0.766044i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	1.73205			1.73205
$807$		0			0
$808$		0			0
$809$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$809$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$810$	0.766044	−	4.34445i	0.766044	−	4.34445i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$			2.53209i			2.53209i
$814$		0			0
$815$		0			0
$816$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$817$		0			0
$818$		0			0
$819$	2.20574	−	1.85083i	2.20574	−	1.85083i
$820$		0			0
$821$	0.984808	+	1.70574i	0.984808	+	1.70574i	0.642788	+	0.766044i	$0.277778\pi$
$821$	0.984808	+	1.70574i	0.984808	+	1.70574i	0.342020	+	0.939693i	$0.388889\pi$
$822$		0			0
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$			1.00000i			1.00000i
$833$	0.673648	+	0.118782i	0.673648	+	0.118782i
$834$	3.70167			3.70167
$835$	0.173648	−	0.984808i	0.173648	−	0.984808i
$836$		0			0
$837$	−5.55250	−	3.20574i	−5.55250	−	3.20574i
$838$	1.32683	−	0.766044i	1.32683	−	0.766044i
$839$	−1.73205			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$839$	−1.73205			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$840$	0.984808	−	1.70574i	0.984808	−	1.70574i
$841$	1.00000			1.00000
$842$	−1.11334	+	0.642788i	−1.11334	+	0.642788i
$843$		0			0
$844$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$845$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$846$	5.41147			5.41147
$847$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$848$		0			0
$849$		0			0
$850$	−0.642788	−	0.233956i	−0.642788	−	0.233956i
$851$		0			0
$852$	−1.16679	+	0.673648i	−1.16679	+	0.673648i
$853$			0.347296i			0.347296i	0.984808	+	0.173648i	$0.0555556\pi$
$853$			0.347296i			0.347296i	−0.984808	+	0.173648i	$0.944444\pi$
$854$		0			0
$855$		0			0
$856$	0.866025	+	1.50000i	0.866025	+	1.50000i
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$860$	0.984808	+	0.826352i	0.984808	+	0.826352i
$861$		0			0
$862$			1.28558i			1.28558i
$863$	−0.300767	+	0.173648i	−0.300767	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$863$	−0.300767	+	0.173648i	−0.300767	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$864$	1.85083	−	3.20574i	1.85083	−	3.20574i
$865$		0			0
$866$	0.984808	+	1.70574i	0.984808	+	1.70574i
$867$			1.04801i			1.04801i
$868$	−1.11334	−	1.32683i	−1.11334	−	1.32683i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.11334	−	0.642788i	−1.11334	−	0.642788i
$873$		0			0
$874$		0			0
$875$	0.939693	+	0.342020i	0.939693	+	0.342020i
$876$		0			0
$877$	−1.32683	+	0.766044i	−1.32683	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$877$	−1.32683	+	0.766044i	−1.32683	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$878$		0			0
$879$	−0.342020	+	0.592396i	−0.342020	+	0.592396i
$880$		0			0
$881$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$881$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$882$	−2.83564	−	0.500000i	−2.83564	−	0.500000i
$883$			1.96962i			1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$883$			1.96962i			1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$884$	−0.342020	−	0.592396i	−0.342020	−	0.592396i
$885$		0			0
$886$	0.984808	−	1.70574i	0.984808	−	1.70574i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$		−	0.684040i		−	0.684040i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−0.300767	−	0.173648i	−0.300767	−	0.173648i
$893$		0			0
$894$	−1.70574	−	2.95442i	−1.70574	−	2.95442i
$895$	−0.984808	+	1.17365i	−0.984808	+	1.17365i
$896$	0.766044	−	0.642788i	0.766044	−	0.642788i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	2.70574	+	0.984808i	2.70574	+	0.984808i
$901$		0			0
$902$		0			0
$903$	0.866025	−	2.37939i	0.866025	−	2.37939i
$904$	−1.73205			−1.73205
$905$		0			0
$906$	0.673648	−	1.16679i	0.673648	−	1.16679i
$907$	−0.592396	−	0.342020i	−0.592396	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$907$	−0.592396	−	0.342020i	−0.592396	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$908$		0			0
$909$		0			0
$910$	0.500000	+	0.866025i	0.500000	+	0.866025i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.96962			−1.96962
$917$	0.984808	+	1.17365i	0.984808	+	1.17365i
$918$			2.53209i			2.53209i
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$		0			0
$922$	0.592396	−	0.342020i	0.592396	−	0.342020i
$923$		−	0.684040i		−	0.684040i
$924$		0			0
$925$	0.342020	−	0.0603074i	0.342020	−	0.0603074i
$926$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$927$		0			0
$928$		0			0
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$	2.19285	−	2.61334i	2.19285	−	2.61334i
$931$		0			0
$932$		−	1.96962i		−	1.96962i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	1.43969	+	2.49362i	1.43969	+	2.49362i
$937$			1.73205i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$937$			1.73205i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$	1.34730			1.34730
$940$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$941$	−0.342020	+	0.592396i	−0.342020	+	0.592396i	−0.984808	−	0.173648i	$-0.944444\pi$
$941$	−0.342020	+	0.592396i	−0.342020	+	0.592396i	0.642788	+	0.766044i	$0.277778\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		−	3.70167i		−	3.70167i
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	1.96962			1.96962
$952$	−0.233956	+	0.642788i	−0.233956	+	0.642788i
$953$		−	0.684040i		−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$953$		−	0.684040i		−	0.684040i	0.939693	−	0.342020i	$-0.111111\pi$
$954$		0			0
$955$		0			0
$956$	−0.984808	+	1.70574i	−0.984808	+	1.70574i
$957$		0			0
$958$		−	1.96962i		−	1.96962i
$959$		0			0
$960$	1.50881	+	1.26604i	1.50881	+	1.26604i
$961$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$962$	0.300767	+	0.173648i	0.300767	+	0.173648i
$963$	4.31908	+	2.49362i	4.31908	+	2.49362i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			1.53209i			1.53209i	0.642788	+	0.766044i	$0.277778\pi$
$967$			1.53209i			1.53209i	−0.642788	+	0.766044i	$0.722222\pi$
$968$	0.866025	−	0.500000i	0.866025	−	0.500000i
$969$		0			0
$970$		0			0
$971$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$971$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$972$		−	4.98724i		−	4.98724i
$973$	1.85083	−	0.326352i	1.85083	−	0.326352i
$974$	1.00000			1.00000
$975$	−1.50881	+	1.26604i	−1.50881	+	1.26604i
$976$		0			0
$977$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$977$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$978$		0			0
$979$		0			0
$980$	0.342020	−	0.939693i	0.342020	−	0.939693i
$981$	−3.70167			−3.70167
$982$	−1.32683	+	0.766044i	−1.32683	+	0.766044i
$983$	0.300767	+	0.173648i	0.300767	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$983$	0.300767	+	0.173648i	0.300767	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$984$		0			0
$985$	0.266044	−	1.50881i	0.266044	−	1.50881i
$986$		0			0
$987$	3.64543	−	0.642788i	3.64543	−	0.642788i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$	1.50000	−	0.866025i	1.50000	−	0.866025i
$993$		0			0
$994$	−0.524005	+	0.439693i	−0.524005	+	0.439693i
$995$		0			0
$996$		0			0
$997$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$997$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$998$		0			0
$999$	−0.642788	−	1.11334i	−0.642788	−	1.11334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3640.1.hd.d.1299.1	yes	12
5.4	even	2		3640.1.hd.c.1299.6	yes	12
7.2	even	3		3640.1.hd.c.779.6	yes	12
8.3	odd	2	inner	3640.1.hd.d.1299.4	yes	12
13.12	even	2	inner	3640.1.hd.d.1299.4	yes	12
35.9	even	6	inner	3640.1.hd.d.779.1	yes	12
40.19	odd	2		3640.1.hd.c.1299.3	yes	12
56.51	odd	6		3640.1.hd.c.779.3	✓	12
65.64	even	2		3640.1.hd.c.1299.3	yes	12
91.51	even	6		3640.1.hd.c.779.3	✓	12
104.51	odd	2	CM	3640.1.hd.d.1299.1	yes	12
280.219	odd	6	inner	3640.1.hd.d.779.4	yes	12
455.324	even	6	inner	3640.1.hd.d.779.4	yes	12
520.259	odd	2		3640.1.hd.c.1299.6	yes	12
728.51	odd	6		3640.1.hd.c.779.6	yes	12
3640.779	odd	6	inner	3640.1.hd.d.779.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3640.1.hd.c.779.3	✓	12	56.51	odd	6
3640.1.hd.c.779.3	✓	12	91.51	even	6
3640.1.hd.c.779.6	yes	12	7.2	even	3
3640.1.hd.c.779.6	yes	12	728.51	odd	6
3640.1.hd.c.1299.3	yes	12	40.19	odd	2
3640.1.hd.c.1299.3	yes	12	65.64	even	2
3640.1.hd.c.1299.6	yes	12	5.4	even	2
3640.1.hd.c.1299.6	yes	12	520.259	odd	2
3640.1.hd.d.779.1	yes	12	35.9	even	6	inner
3640.1.hd.d.779.1	yes	12	3640.779	odd	6	inner
3640.1.hd.d.779.4	yes	12	280.219	odd	6	inner
3640.1.hd.d.779.4	yes	12	455.324	even	6	inner
3640.1.hd.d.1299.1	yes	12	1.1	even	1	trivial
3640.1.hd.d.1299.1	yes	12	104.51	odd	2	CM
3640.1.hd.d.1299.4	yes	12	8.3	odd	2	inner
3640.1.hd.d.1299.4	yes	12	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3640.hd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.70574 - 0.984808i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.984808 + 0.173648i) q^{5} +1.96962 q^{6} +(0.984808 - 0.173648i) q^{7} +1.00000i q^{8} +(1.43969 + 2.49362i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.70574 - 0.984808i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.984808 + 0.173648i) q^{5} +1.96962 q^{6} +(0.984808 - 0.173648i) q^{7} +1.00000i q^{8} +(1.43969 + 2.49362i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(-1.70574 + 0.984808i) q^{12} -1.00000i q^{13} +(-0.766044 + 0.642788i) q^{14} +(-1.50881 - 1.26604i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.592396 + 0.342020i) q^{17} +(-2.49362 - 1.43969i) q^{18} +(0.642788 - 0.766044i) q^{20} +(-1.85083 - 0.673648i) q^{21} +(0.984808 - 1.70574i) q^{24} +(0.939693 + 0.342020i) q^{25} +(0.500000 + 0.866025i) q^{26} -3.70167i q^{27} +(0.342020 - 0.939693i) q^{28} +(1.93969 + 0.342020i) q^{30} +(0.866025 - 1.50000i) q^{31} +(0.866025 + 0.500000i) q^{32} -0.684040 q^{34} +1.00000 q^{35} +2.87939 q^{36} +(0.300767 - 0.173648i) q^{37} +(-0.984808 + 1.70574i) q^{39} +(-0.173648 + 0.984808i) q^{40} +(1.93969 - 0.342020i) q^{42} +1.28558i q^{43} +(0.984808 + 2.70574i) q^{45} +(-1.62760 + 0.939693i) q^{47} +1.96962i q^{48} +(0.939693 - 0.342020i) q^{49} +(-0.984808 + 0.173648i) q^{50} +(-0.673648 - 1.16679i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(1.85083 + 3.20574i) q^{54} +(0.173648 + 0.984808i) q^{56} +(-1.85083 + 0.673648i) q^{60} +1.73205i q^{62} +(1.85083 + 2.20574i) q^{63} -1.00000 q^{64} +(0.173648 - 0.984808i) q^{65} +(0.592396 - 0.342020i) q^{68} +(-0.866025 + 0.500000i) q^{70} +0.684040 q^{71} +(-2.49362 + 1.43969i) q^{72} +(-0.173648 + 0.300767i) q^{74} +(-1.26604 - 1.50881i) q^{75} -1.96962i q^{78} +(-0.342020 - 0.939693i) q^{80} +(-2.20574 + 3.82045i) q^{81} +(-1.50881 + 1.26604i) q^{84} +(0.524005 + 0.439693i) q^{85} +(-0.642788 - 1.11334i) q^{86} +(-2.20574 - 1.85083i) q^{90} +(-0.173648 - 0.984808i) q^{91} +(-2.95442 + 1.70574i) q^{93} +(0.939693 - 1.62760i) q^{94} +(-0.984808 - 1.70574i) q^{96} +(-0.642788 + 0.766044i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 6 * q^9	\( 12 q + 6 q^{4} + 6 q^{9} - 6 q^{16} + 6 q^{26} + 12 q^{30} + 12 q^{35} + 12 q^{36} + 12 q^{42} - 6 q^{51} - 12 q^{64} - 6 q^{75} - 6 q^{81} - 6 q^{90}+O(q^{100}) \) 12 * q + 6 * q^4 + 6 * q^9 - 6 * q^16 + 6 * q^26 + 12 * q^30 + 12 * q^35 + 12 * q^36 + 12 * q^42 - 6 * q^51 - 12 * q^64 - 6 * q^75 - 6 * q^81 - 6 * q^90

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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