LMFDB - Embedded newform 2205.1.bu.a.1978.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2205,1,Mod(373,2205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2205, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 4]))

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

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

chi := DirichletCharacter("2205.373");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2205 = 3^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2205.bu (of order $12$, degree $4$, not 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:	$1.10043835286$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.3472875.1

Embedding invariants

Embedding label			1978.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2205.1978
Dual form			2205.1.bu.a.2137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(0.965926 - 0.258819i) q^{3} -1.00000i q^{4} +(-0.965926 + 0.258819i) q^{5} +(0.707107 - 1.22474i) q^{6} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(0.965926 - 0.258819i) q^{3} -1.00000i q^{4} +(-0.965926 + 0.258819i) q^{5} +(0.707107 - 1.22474i) q^{6} +(0.866025 - 0.500000i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(0.258819 - 0.965926i) q^{13} +(-0.866025 + 0.500000i) q^{15} +1.00000 q^{16} +(-0.258819 - 0.965926i) q^{17} +(0.366025 - 1.36603i) q^{18} +(0.258819 + 0.965926i) q^{20} +(1.36603 + 0.366025i) q^{22} +(-1.36603 + 0.366025i) q^{23} +(0.866025 - 0.500000i) q^{25} +(-0.707107 - 1.22474i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.366025 + 1.36603i) q^{30} +(1.00000 - 1.00000i) q^{32} +(0.707107 + 0.707107i) q^{33} +(-1.22474 - 0.707107i) q^{34} +(-0.500000 - 0.866025i) q^{36} +(-1.36603 - 0.366025i) q^{37} -1.00000i q^{39} +(0.707107 + 1.22474i) q^{41} +(0.866025 - 0.500000i) q^{44} +(-0.707107 + 0.707107i) q^{45} +(-1.00000 + 1.73205i) q^{46} +(-0.707107 + 0.707107i) q^{47} +(0.965926 - 0.258819i) q^{48} +(0.366025 - 1.36603i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(-0.965926 - 0.258819i) q^{52} +(1.36603 - 0.366025i) q^{53} -1.41421i q^{54} +(-0.707107 - 0.707107i) q^{55} +1.41421i q^{59} +(0.500000 + 0.866025i) q^{60} -1.00000i q^{64} +1.00000i q^{65} +1.41421 q^{66} +(-1.00000 + 1.00000i) q^{67} +(-0.965926 + 0.258819i) q^{68} +(-1.22474 + 0.707107i) q^{69} -1.00000 q^{71} +(-0.965926 + 0.258819i) q^{73} +(-1.73205 + 1.00000i) q^{74} +(0.707107 - 0.707107i) q^{75} +(-1.00000 - 1.00000i) q^{78} -1.00000i q^{79} +(-0.965926 + 0.258819i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.93185 + 0.517638i) q^{82} +(-0.965926 + 0.258819i) q^{83} +(0.500000 + 0.866025i) q^{85} +1.41421i q^{90} +(0.366025 + 1.36603i) q^{92} +1.41421i q^{94} +(0.707107 - 1.22474i) q^{96} +(0.258819 + 0.965926i) q^{97} +(0.866025 + 0.500000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2}+O(q^{10}) $ 8 * q + 8 * q^2	$ 8 q + 8 q^{2} + 4 q^{11} + 8 q^{16} - 4 q^{18} + 4 q^{22} - 4 q^{23} + 4 q^{30} + 8 q^{32} - 4 q^{36} - 4 q^{37} - 8 q^{46} - 4 q^{50} - 4 q^{51} + 4 q^{53} + 4 q^{60} - 8 q^{67} - 8 q^{71} - 8 q^{78} + 4 q^{81} + 4 q^{85} - 4 q^{92}+O(q^{100}) $ 8 * q + 8 * q^2 + 4 * q^11 + 8 * q^16 - 4 * q^18 + 4 * q^22 - 4 * q^23 + 4 * q^30 + 8 * q^32 - 4 * q^36 - 4 * q^37 - 8 * q^46 - 4 * q^50 - 4 * q^51 + 4 * q^53 + 4 * q^60 - 8 * q^67 - 8 * q^71 - 8 * q^78 + 4 * q^81 + 4 * q^85 - 4 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times$.

$n$	$442$	$1081$	$1226$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$2$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$3$	0.965926	−	0.258819i	0.965926	−	0.258819i
$3$	0.965926	−	0.258819i	0.965926	−	0.258819i
$4$		−	1.00000i		−	1.00000i
$5$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$5$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$6$	0.707107	−	1.22474i	0.707107	−	1.22474i
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.866025	−	0.500000i	0.866025	−	0.500000i
$10$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$12$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$13$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$13$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$14$		0			0
$15$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$16$	1.00000			1.00000
$17$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$17$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$18$	0.366025	−	1.36603i	0.366025	−	1.36603i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	0.258819	+	0.965926i	0.258819	+	0.965926i
$21$		0			0
$22$	1.36603	+	0.366025i	1.36603	+	0.366025i
$23$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$23$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$24$		0			0
$25$	0.866025	−	0.500000i	0.866025	−	0.500000i
$26$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$27$	0.707107	−	0.707107i	0.707107	−	0.707107i
$28$		0			0
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	1.00000	−	1.00000i	1.00000	−	1.00000i
$33$	0.707107	+	0.707107i	0.707107	+	0.707107i
$34$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$37$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$37$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$38$		0			0
$39$		−	1.00000i		−	1.00000i
$40$		0			0
$41$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$41$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$42$		0			0
$43$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$43$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$44$	0.866025	−	0.500000i	0.866025	−	0.500000i
$45$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$46$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$47$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$47$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$48$	0.965926	−	0.258819i	0.965926	−	0.258819i
$49$		0			0
$50$	0.366025	−	1.36603i	0.366025	−	1.36603i
$51$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$52$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$53$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$53$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$54$		−	1.41421i		−	1.41421i
$55$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$56$		0			0
$57$		0			0
$58$		0			0
$59$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$59$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$60$	0.500000	+	0.866025i	0.500000	+	0.866025i
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$		0			0
$63$		0			0
$64$		−	1.00000i		−	1.00000i
$65$			1.00000i			1.00000i
$66$	1.41421			1.41421
$67$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$67$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$68$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$69$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$70$		0			0
$71$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$71$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$72$		0			0
$73$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$73$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$74$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$75$	0.707107	−	0.707107i	0.707107	−	0.707107i
$76$		0			0
$77$		0			0
$78$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$79$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$79$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$80$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$	1.93185	+	0.517638i	1.93185	+	0.517638i
$83$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$83$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$84$		0			0
$85$	0.500000	+	0.866025i	0.500000	+	0.866025i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$			1.41421i			1.41421i
$91$		0			0
$92$	0.366025	+	1.36603i	0.366025	+	1.36603i
$93$		0			0
$94$			1.41421i			1.41421i
$95$		0			0
$96$	0.707107	−	1.22474i	0.707107	−	1.22474i
$97$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$97$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$98$		0			0
$99$	0.866025	+	0.500000i	0.866025	+	0.500000i
$100$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$103$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$103$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$104$		0			0
$105$		0			0
$106$	1.00000	−	1.73205i	1.00000	−	1.73205i
$107$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$108$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$109$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$109$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$110$	−1.41421			−1.41421
$111$	−1.41421			−1.41421
$112$		0			0
$113$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$113$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$114$		0			0
$115$	1.22474	−	0.707107i	1.22474	−	0.707107i
$116$		0			0
$117$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$118$	1.41421	+	1.41421i	1.41421	+	1.41421i
$119$		0			0
$120$		0			0
$121$		0			0
$122$		0			0
$123$	1.00000	+	1.00000i	1.00000	+	1.00000i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$126$		0			0
$127$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$127$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$128$		0			0
$129$		0			0
$130$	1.00000	+	1.00000i	1.00000	+	1.00000i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	0.707107	−	0.707107i	0.707107	−	0.707107i
$133$		0			0
$134$			2.00000i			2.00000i
$135$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$136$		0			0
$137$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$137$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$138$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$139$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$139$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$140$		0			0
$141$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$142$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$143$	0.965926	−	0.258819i	0.965926	−	0.258819i
$144$	0.866025	−	0.500000i	0.866025	−	0.500000i
$145$		0			0
$146$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$147$		0			0
$148$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$149$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$149$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$150$		−	1.41421i		−	1.41421i
$151$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$151$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$152$		0			0
$153$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$154$		0			0
$155$		0			0
$156$	−1.00000			−1.00000
$157$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$157$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$158$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$159$	1.22474	−	0.707107i	1.22474	−	0.707107i
$160$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$161$		0			0
$162$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$163$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$163$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$164$	1.22474	−	0.707107i	1.22474	−	0.707107i
$165$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$166$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$167$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$167$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$168$		0			0
$169$		0			0
$170$	1.36603	+	0.366025i	1.36603	+	0.366025i
$171$		0			0
$172$		0			0
$173$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$173$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$174$		0			0
$175$		0			0
$176$	0.500000	+	0.866025i	0.500000	+	0.866025i
$177$	0.366025	+	1.36603i	0.366025	+	1.36603i
$178$		0			0
$179$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$179$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$180$	0.707107	+	0.707107i	0.707107	+	0.707107i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.41421			1.41421
$186$		0			0
$187$	0.707107	−	0.707107i	0.707107	−	0.707107i
$188$	0.707107	+	0.707107i	0.707107	+	0.707107i
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$193$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$193$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$194$	1.22474	+	0.707107i	1.22474	+	0.707107i
$195$	0.258819	+	0.965926i	0.258819	+	0.965926i
$196$		0			0
$197$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$197$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$198$	1.36603	−	0.366025i	1.36603	−	0.366025i
$199$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$199$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$200$		0			0
$201$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$202$		0			0
$203$		0			0
$204$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$205$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$206$		0			0
$207$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$208$	0.258819	−	0.965926i	0.258819	−	0.965926i
$209$		0			0
$210$		0			0
$211$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$211$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$212$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$213$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$214$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$219$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$220$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$221$	−1.00000			−1.00000
$222$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$223$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$223$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$224$		0			0
$225$	0.500000	−	0.866025i	0.500000	−	0.866025i
$226$		0			0
$227$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$227$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$228$		0			0
$229$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$229$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$230$	0.517638	−	1.93185i	0.517638	−	1.93185i
$231$		0			0
$232$		0			0
$233$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$233$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$234$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$235$	0.500000	−	0.866025i	0.500000	−	0.866025i
$236$	1.41421			1.41421
$237$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$241$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$241$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$242$		0			0
$243$	0.258819	−	0.965926i	0.258819	−	0.965926i
$244$		0			0
$245$		0			0
$246$	2.00000			2.00000
$247$		0			0
$248$		0			0
$249$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$250$			1.41421i			1.41421i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$254$			2.00000i			2.00000i
$255$	0.707107	+	0.707107i	0.707107	+	0.707107i
$256$	1.00000			1.00000
$257$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$257$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$258$		0			0
$259$		0			0
$260$	1.00000			1.00000
$261$		0			0
$262$		0			0
$263$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$263$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$264$		0			0
$265$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$266$		0			0
$267$		0			0
$268$	1.00000	+	1.00000i	1.00000	+	1.00000i
$269$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$269$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$270$	0.366025	+	1.36603i	0.366025	+	1.36603i
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$273$		0			0
$274$		0			0
$275$	0.866025	+	0.500000i	0.866025	+	0.500000i
$276$	0.707107	+	1.22474i	0.707107	+	1.22474i
$277$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$277$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$278$	0.517638	−	1.93185i	0.517638	−	1.93185i
$279$		0			0
$280$		0			0
$281$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$281$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$282$	0.366025	+	1.36603i	0.366025	+	1.36603i
$283$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$283$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$284$			1.00000i			1.00000i
$285$		0			0
$286$	0.707107	−	1.22474i	0.707107	−	1.22474i
$287$		0			0
$288$	0.366025	−	1.36603i	0.366025	−	1.36603i
$289$		0			0
$290$		0			0
$291$	0.500000	+	0.866025i	0.500000	+	0.866025i
$292$	0.258819	+	0.965926i	0.258819	+	0.965926i
$293$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$293$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$294$		0			0
$295$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$296$		0			0
$297$	0.965926	+	0.258819i	0.965926	+	0.258819i
$298$	1.36603	−	0.366025i	1.36603	−	0.366025i
$299$			1.41421i			1.41421i
$300$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$301$		0			0
$302$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−1.41421			−1.41421
$307$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$307$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$311$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$312$		0			0
$313$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$313$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$314$		−	1.41421i		−	1.41421i
$315$		0			0
$316$	−1.00000			−1.00000
$317$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$317$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$318$	0.517638	−	1.93185i	0.517638	−	1.93185i
$319$		0			0
$320$	0.258819	+	0.965926i	0.258819	+	0.965926i
$321$	−1.41421			−1.41421
$322$		0			0
$323$		0			0
$324$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$325$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$326$		0			0
$327$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$328$		0			0
$329$		0			0
$330$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$331$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$331$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$332$	0.258819	+	0.965926i	0.258819	+	0.965926i
$333$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$334$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$335$	0.707107	−	1.22474i	0.707107	−	1.22474i
$336$		0			0
$337$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$337$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$338$		0			0
$339$		0			0
$340$	0.866025	−	0.500000i	0.866025	−	0.500000i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.00000	−	1.00000i	1.00000	−	1.00000i
$346$	2.82843			2.82843
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$		0			0
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$		0			0
$351$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$352$	1.36603	+	0.366025i	1.36603	+	0.366025i
$353$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$353$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$354$	1.73205	+	1.00000i	1.73205	+	1.00000i
$355$	0.965926	−	0.258819i	0.965926	−	0.258819i
$356$		0			0
$357$		0			0
$358$	1.36603	−	0.366025i	1.36603	−	0.366025i
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.866025	−	0.500000i	0.866025	−	0.500000i
$366$		0			0
$367$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$367$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$368$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$369$	1.22474	+	0.707107i	1.22474	+	0.707107i
$370$	1.41421	−	1.41421i	1.41421	−	1.41421i
$371$		0			0
$372$		0			0
$373$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$373$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$374$		−	1.41421i		−	1.41421i
$375$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$379$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$380$		0			0
$381$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$382$		0			0
$383$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$383$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.965926	−	0.258819i	0.965926	−	0.258819i
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$390$	1.22474	+	0.707107i	1.22474	+	0.707107i
$391$	0.707107	+	1.22474i	0.707107	+	1.22474i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.258819	+	0.965926i	0.258819	+	0.965926i
$396$	0.500000	−	0.866025i	0.500000	−	0.866025i
$397$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$397$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$398$	1.93185	−	0.517638i	1.93185	−	0.517638i
$399$		0			0
$400$	0.866025	−	0.500000i	0.866025	−	0.500000i
$401$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$401$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$402$	0.517638	+	1.93185i	0.517638	+	1.93185i
$403$		0			0
$404$		0			0
$405$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$406$		0			0
$407$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$408$		0			0
$409$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$409$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$410$	−2.00000			−2.00000
$411$		0			0
$412$		0			0
$413$		0			0
$414$			2.00000i			2.00000i
$415$	0.866025	−	0.500000i	0.866025	−	0.500000i
$416$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$417$	1.00000	−	1.00000i	1.00000	−	1.00000i
$418$		0			0
$419$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$419$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$420$		0			0
$421$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$421$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$422$	1.36603	+	0.366025i	1.36603	+	0.366025i
$423$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$424$		0			0
$425$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$426$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$427$		0			0
$428$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$429$	0.866025	−	0.500000i	0.866025	−	0.500000i
$430$		0			0
$431$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$431$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$432$	0.707107	−	0.707107i	0.707107	−	0.707107i
$433$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$433$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$434$		0			0
$435$		0			0
$436$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$437$		0			0
$438$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$		0			0
$442$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$			1.41421i			1.41421i
$445$		0			0
$446$	0.707107	−	1.22474i	0.707107	−	1.22474i
$447$	0.965926	+	0.258819i	0.965926	+	0.258819i
$448$		0			0
$449$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$449$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$450$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$451$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$452$		0			0
$453$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$454$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$455$		0			0
$456$		0			0
$457$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$457$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$458$		0			0
$459$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$460$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$461$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$461$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$462$		0			0
$463$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$463$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$467$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$468$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$469$		0			0
$470$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$471$	0.500000	−	0.866025i	0.500000	−	0.866025i
$472$		0			0
$473$		0			0
$474$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$475$		0			0
$476$		0			0
$477$	1.00000	−	1.00000i	1.00000	−	1.00000i
$478$		0			0
$479$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$479$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$480$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$481$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$482$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$483$		0			0
$484$		0			0
$485$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$486$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$487$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$487$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$491$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$492$	1.00000	−	1.00000i	1.00000	−	1.00000i
$493$		0			0
$494$		0			0
$495$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$496$		0			0
$497$		0			0
$498$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$499$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$499$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$500$	0.707107	+	0.707107i	0.707107	+	0.707107i
$501$	−1.00000			−1.00000
$502$		0			0
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$		0			0
$505$		0			0
$506$	−2.00000			−2.00000
$507$		0			0
$508$	1.00000	+	1.00000i	1.00000	+	1.00000i
$509$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$509$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$510$	1.41421			1.41421
$511$		0			0
$512$	1.00000	−	1.00000i	1.00000	−	1.00000i
$513$		0			0
$514$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$515$		0			0
$516$		0			0
$517$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$518$		0			0
$519$	1.73205	+	1.00000i	1.73205	+	1.00000i
$520$		0			0
$521$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$521$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$522$		0			0
$523$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$523$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$524$		0			0
$525$		0			0
$526$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$527$		0			0
$528$	0.707107	+	0.707107i	0.707107	+	0.707107i
$529$	0.866025	−	0.500000i	0.866025	−	0.500000i
$530$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$531$	0.707107	+	1.22474i	0.707107	+	1.22474i
$532$		0			0
$533$	1.36603	−	0.366025i	1.36603	−	0.366025i
$534$		0			0
$535$	1.41421			1.41421
$536$		0			0
$537$	0.965926	+	0.258819i	0.965926	+	0.258819i
$538$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$539$		0			0
$540$	0.866025	+	0.500000i	0.866025	+	0.500000i
$541$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$541$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$		0			0
$544$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$545$	0.965926	+	0.258819i	0.965926	+	0.258819i
$546$		0			0
$547$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$547$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$		0			0
$550$	1.36603	−	0.366025i	1.36603	−	0.366025i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.36603	−	0.366025i	1.36603	−	0.366025i
$556$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$557$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$557$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.500000	−	0.866025i	0.500000	−	0.866025i
$562$	0.366025	+	1.36603i	0.366025	+	1.36603i
$563$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$563$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$564$	0.866025	+	0.500000i	0.866025	+	0.500000i
$565$		0			0
$566$	−1.41421			−1.41421
$567$		0			0
$568$		0			0
$569$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$569$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$570$		0			0
$571$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$571$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$572$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$573$		0			0
$574$		0			0
$575$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$576$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$577$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$577$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$	1.36603	+	0.366025i	1.36603	+	0.366025i
$583$	1.00000	+	1.00000i	1.00000	+	1.00000i
$584$		0			0
$585$	0.500000	+	0.866025i	0.500000	+	0.866025i
$586$		0			0
$587$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$587$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$588$		0			0
$589$		0			0
$590$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$591$		0			0
$592$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$593$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$593$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$594$	1.22474	−	0.707107i	1.22474	−	0.707107i
$595$		0			0
$596$	0.500000	−	0.866025i	0.500000	−	0.866025i
$597$	1.36603	+	0.366025i	1.36603	+	0.366025i
$598$	1.41421	+	1.41421i	1.41421	+	1.41421i
$599$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$599$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$601$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$602$		0			0
$603$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$604$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$605$		0			0
$606$		0			0
$607$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$607$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.500000	+	0.866025i	0.500000	+	0.866025i
$612$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$613$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$613$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$614$		−	1.41421i		−	1.41421i
$615$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$616$		0			0
$617$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$617$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$618$		0			0
$619$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$619$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$620$		0			0
$621$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$622$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$623$		0			0
$624$		−	1.00000i		−	1.00000i
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$629$			1.41421i			1.41421i
$630$		0			0
$631$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$631$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$632$		0			0
$633$	0.707107	+	0.707107i	0.707107	+	0.707107i
$634$		−	2.00000i		−	2.00000i
$635$	0.707107	−	1.22474i	0.707107	−	1.22474i
$636$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$637$		0			0
$638$		0			0
$639$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$640$		0			0
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$643$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$643$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$647$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$648$		0			0
$649$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$650$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$651$		0			0
$652$		0			0
$653$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$653$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$654$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$655$		0			0
$656$	0.707107	+	1.22474i	0.707107	+	1.22474i
$657$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$658$		0			0
$659$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$659$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$660$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	1.00000	−	1.00000i	1.00000	−	1.00000i
$663$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$664$		0			0
$665$		0			0
$666$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$667$		0			0
$668$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$669$	0.866025	−	0.500000i	0.866025	−	0.500000i
$670$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$671$		0			0
$672$		0			0
$673$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$673$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$674$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$675$	0.258819	−	0.965926i	0.258819	−	0.965926i
$676$		0			0
$677$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$677$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.00000			−1.00000
$682$		0			0
$683$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$683$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		−	1.41421i		−	1.41421i
$690$		−	2.00000i		−	2.00000i
$691$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$691$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$692$	1.41421	−	1.41421i	1.41421	−	1.41421i
$693$		0			0
$694$		0			0
$695$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$696$		0			0
$697$	1.00000	−	1.00000i	1.00000	−	1.00000i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$701$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$702$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$703$		0			0
$704$	0.866025	−	0.500000i	0.866025	−	0.500000i
$705$	0.258819	−	0.965926i	0.258819	−	0.965926i
$706$		0			0
$707$		0			0
$708$	1.36603	−	0.366025i	1.36603	−	0.366025i
$709$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$709$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$710$	0.707107	−	1.22474i	0.707107	−	1.22474i
$711$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$716$	0.500000	−	0.866025i	0.500000	−	0.866025i
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$721$		0			0
$722$	0.366025	+	1.36603i	0.366025	+	1.36603i
$723$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$727$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$728$		0			0
$729$		−	1.00000i		−	1.00000i
$730$	0.366025	−	1.36603i	0.366025	−	1.36603i
$731$		0			0
$732$		0			0
$733$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$733$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$734$	1.22474	−	0.707107i	1.22474	−	0.707107i
$735$		0			0
$736$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$737$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$738$	1.93185	−	0.517638i	1.93185	−	0.517638i
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$		−	1.41421i		−	1.41421i
$741$		0			0
$742$		0			0
$743$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$743$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$744$		0			0
$745$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$746$		0			0
$747$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$748$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$749$		0			0
$750$	0.366025	+	1.36603i	0.366025	+	1.36603i
$751$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$751$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$752$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$753$		0			0
$754$		0			0
$755$	0.707107	+	0.707107i	0.707107	+	0.707107i
$756$		0			0
$757$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$757$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$758$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$759$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$	0.517638	+	1.93185i	0.517638	+	1.93185i
$763$		0			0
$764$		0			0
$765$	0.866025	+	0.500000i	0.866025	+	0.500000i
$766$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$767$	1.36603	+	0.366025i	1.36603	+	0.366025i
$768$	0.965926	−	0.258819i	0.965926	−	0.258819i
$769$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$769$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$770$		0			0
$771$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$772$		0			0
$773$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$773$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$779$		0			0
$780$	0.965926	−	0.258819i	0.965926	−	0.258819i
$781$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$782$	1.93185	+	0.517638i	1.93185	+	0.517638i
$783$		0			0
$784$		0			0
$785$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$786$		0			0
$787$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$787$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$788$		0			0
$789$		−	1.41421i		−	1.41421i
$790$	1.22474	+	0.707107i	1.22474	+	0.707107i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$796$	0.707107	−	1.22474i	0.707107	−	1.22474i
$797$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$797$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$798$		0			0
$799$	0.866025	+	0.500000i	0.866025	+	0.500000i
$800$	0.366025	−	1.36603i	0.366025	−	1.36603i
$801$		0			0
$802$		0			0
$803$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$804$	1.22474	+	0.707107i	1.22474	+	0.707107i
$805$		0			0
$806$		0			0
$807$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$808$		0			0
$809$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$809$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$810$	0.707107	+	1.22474i	0.707107	+	1.22474i
$811$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$811$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$812$		0			0
$813$		0			0
$814$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$815$		0			0
$816$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$817$		0			0
$818$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$819$		0			0
$820$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$821$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$821$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$822$		0			0
$823$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$823$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$824$		0			0
$825$	0.965926	+	0.258819i	0.965926	+	0.258819i
$826$		0			0
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	1.00000	+	1.00000i	1.00000	+	1.00000i
$829$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$829$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$830$	0.366025	−	1.36603i	0.366025	−	1.36603i
$831$		0			0
$832$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$833$		0			0
$834$		−	2.00000i		−	2.00000i
$835$	1.00000			1.00000
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$839$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$842$	0.366025	+	1.36603i	0.366025	+	1.36603i
$843$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$844$	0.866025	−	0.500000i	0.866025	−	0.500000i
$845$		0			0
$846$	0.707107	+	1.22474i	0.707107	+	1.22474i
$847$		0			0
$848$	1.36603	−	0.366025i	1.36603	−	0.366025i
$849$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$850$	−1.41421			−1.41421
$851$	2.00000			2.00000
$852$	0.258819	+	0.965926i	0.258819	+	0.965926i
$853$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$853$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$857$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$858$	0.366025	−	1.36603i	0.366025	−	1.36603i
$859$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$859$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$863$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$863$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$864$		−	1.41421i		−	1.41421i
$865$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$866$	2.82843			2.82843
$867$		0			0
$868$		0			0
$869$	0.866025	−	0.500000i	0.866025	−	0.500000i
$870$		0			0
$871$	0.707107	+	1.22474i	0.707107	+	1.22474i
$872$		0			0
$873$	0.707107	+	0.707107i	0.707107	+	0.707107i
$874$		0			0
$875$		0			0
$876$	0.500000	+	0.866025i	0.500000	+	0.866025i
$877$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$877$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$878$		0			0
$879$		0			0
$880$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$			1.00000i			1.00000i
$885$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$886$		0			0
$887$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$887$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.00000			1.00000
$892$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$893$		0			0
$894$	1.22474	−	0.707107i	1.22474	−	0.707107i
$895$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$896$		0			0
$897$	0.366025	+	1.36603i	0.366025	+	1.36603i
$898$	−2.00000	−	2.00000i	−2.00000	−	2.00000i
$899$		0			0
$900$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$901$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$902$	0.517638	+	1.93185i	0.517638	+	1.93185i
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−1.41421			−1.41421
$907$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$907$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$908$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$909$		0			0
$910$		0			0
$911$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$911$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$912$		0			0
$913$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$	0.500000	−	0.866025i	0.500000	−	0.866025i
$922$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$923$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$924$		0			0
$925$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$929$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$934$	1.22474	−	0.707107i	1.22474	−	0.707107i
$935$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$936$		0			0
$937$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$937$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$938$		0			0
$939$		0			0
$940$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$941$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$941$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$942$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$943$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$944$			1.41421i			1.41421i
$945$		0			0
$946$		0			0
$947$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$947$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$948$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$949$			1.00000i			1.00000i
$950$		0			0
$951$	0.707107	−	1.22474i	0.707107	−	1.22474i
$952$		0			0
$953$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$953$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$954$		−	2.00000i		−	2.00000i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.500000	+	0.866025i	0.500000	+	0.866025i
$961$	−1.00000			−1.00000
$962$	0.517638	+	1.93185i	0.517638	+	1.93185i
$963$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$964$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$965$		0			0
$966$		0			0
$967$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$967$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$968$		0			0
$969$		0			0
$970$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$973$		0			0
$974$		0			0
$975$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$976$		0			0
$977$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$977$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.00000			−1.00000
$982$	1.36603	+	0.366025i	1.36603	+	0.366025i
$983$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$983$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$991$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$991$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$992$		0			0
$993$	0.965926	−	0.258819i	0.965926	−	0.258819i
$994$		0			0
$995$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$996$	0.500000	+	0.866025i	0.500000	+	0.866025i
$997$	−1.93185	−	0.517638i	−1.93185	−	0.517638i	−0.965926	−	0.258819i	$-0.916667\pi$
$997$	−1.93185	−	0.517638i	−1.93185	−	0.517638i	−0.965926	−	0.258819i	$-0.916667\pi$
$998$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$999$	−1.22474	+	0.707107i	−1.22474	+	0.707107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2205.1.bu.a.1978.2		8
5.2	odd	4	inner	2205.1.bu.a.1537.1		8
7.2	even	3		2205.1.ci.a.1843.1		8
7.3	odd	6		2205.1.bz.a.1618.2	yes	8
7.4	even	3		2205.1.bz.a.1618.1	yes	8
7.5	odd	6		2205.1.ci.a.1843.2		8
7.6	odd	2	inner	2205.1.bu.a.1978.1		8
9.4	even	3		2205.1.ci.a.508.2		8
35.2	odd	12		2205.1.ci.a.1402.2		8
35.12	even	12		2205.1.ci.a.1402.1		8
35.17	even	12		2205.1.bz.a.1177.2	yes	8
35.27	even	4	inner	2205.1.bu.a.1537.2		8
35.32	odd	12		2205.1.bz.a.1177.1	yes	8
45.22	odd	12		2205.1.ci.a.67.1		8
63.4	even	3		2205.1.bz.a.148.1	✓	8
63.13	odd	6		2205.1.ci.a.508.1		8
63.31	odd	6		2205.1.bz.a.148.2	yes	8
63.40	odd	6	inner	2205.1.bu.a.373.2		8
63.58	even	3	inner	2205.1.bu.a.373.1		8
315.67	odd	12		2205.1.bz.a.1912.1	yes	8
315.157	even	12		2205.1.bz.a.1912.2	yes	8
315.202	even	12		2205.1.ci.a.67.2		8
315.247	odd	12	inner	2205.1.bu.a.2137.2		8
315.292	even	12	inner	2205.1.bu.a.2137.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2205.1.bu.a.373.1		8	63.58	even	3	inner
2205.1.bu.a.373.2		8	63.40	odd	6	inner
2205.1.bu.a.1537.1		8	5.2	odd	4	inner
2205.1.bu.a.1537.2		8	35.27	even	4	inner
2205.1.bu.a.1978.1		8	7.6	odd	2	inner
2205.1.bu.a.1978.2		8	1.1	even	1	trivial
2205.1.bu.a.2137.1		8	315.292	even	12	inner
2205.1.bu.a.2137.2		8	315.247	odd	12	inner
2205.1.bz.a.148.1	✓	8	63.4	even	3
2205.1.bz.a.148.2	yes	8	63.31	odd	6
2205.1.bz.a.1177.1	yes	8	35.32	odd	12
2205.1.bz.a.1177.2	yes	8	35.17	even	12
2205.1.bz.a.1618.1	yes	8	7.4	even	3
2205.1.bz.a.1618.2	yes	8	7.3	odd	6
2205.1.bz.a.1912.1	yes	8	315.67	odd	12
2205.1.bz.a.1912.2	yes	8	315.157	even	12
2205.1.ci.a.67.1		8	45.22	odd	12
2205.1.ci.a.67.2		8	315.202	even	12
2205.1.ci.a.508.1		8	63.13	odd	6
2205.1.ci.a.508.2		8	9.4	even	3
2205.1.ci.a.1402.1		8	35.12	even	12
2205.1.ci.a.1402.2		8	35.2	odd	12
2205.1.ci.a.1843.1		8	7.2	even	3
2205.1.ci.a.1843.2		8	7.5	odd	6

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:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2205.bu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(0.965926 - 0.258819i) q^{3} -1.00000i q^{4} +(-0.965926 + 0.258819i) q^{5} +(0.707107 - 1.22474i) q^{6} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(0.965926 - 0.258819i) q^{3} -1.00000i q^{4} +(-0.965926 + 0.258819i) q^{5} +(0.707107 - 1.22474i) q^{6} +(0.866025 - 0.500000i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(0.258819 - 0.965926i) q^{13} +(-0.866025 + 0.500000i) q^{15} +1.00000 q^{16} +(-0.258819 - 0.965926i) q^{17} +(0.366025 - 1.36603i) q^{18} +(0.258819 + 0.965926i) q^{20} +(1.36603 + 0.366025i) q^{22} +(-1.36603 + 0.366025i) q^{23} +(0.866025 - 0.500000i) q^{25} +(-0.707107 - 1.22474i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.366025 + 1.36603i) q^{30} +(1.00000 - 1.00000i) q^{32} +(0.707107 + 0.707107i) q^{33} +(-1.22474 - 0.707107i) q^{34} +(-0.500000 - 0.866025i) q^{36} +(-1.36603 - 0.366025i) q^{37} -1.00000i q^{39} +(0.707107 + 1.22474i) q^{41} +(0.866025 - 0.500000i) q^{44} +(-0.707107 + 0.707107i) q^{45} +(-1.00000 + 1.73205i) q^{46} +(-0.707107 + 0.707107i) q^{47} +(0.965926 - 0.258819i) q^{48} +(0.366025 - 1.36603i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(-0.965926 - 0.258819i) q^{52} +(1.36603 - 0.366025i) q^{53} -1.41421i q^{54} +(-0.707107 - 0.707107i) q^{55} +1.41421i q^{59} +(0.500000 + 0.866025i) q^{60} -1.00000i q^{64} +1.00000i q^{65} +1.41421 q^{66} +(-1.00000 + 1.00000i) q^{67} +(-0.965926 + 0.258819i) q^{68} +(-1.22474 + 0.707107i) q^{69} -1.00000 q^{71} +(-0.965926 + 0.258819i) q^{73} +(-1.73205 + 1.00000i) q^{74} +(0.707107 - 0.707107i) q^{75} +(-1.00000 - 1.00000i) q^{78} -1.00000i q^{79} +(-0.965926 + 0.258819i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.93185 + 0.517638i) q^{82} +(-0.965926 + 0.258819i) q^{83} +(0.500000 + 0.866025i) q^{85} +1.41421i q^{90} +(0.366025 + 1.36603i) q^{92} +1.41421i q^{94} +(0.707107 - 1.22474i) q^{96} +(0.258819 + 0.965926i) q^{97} +(0.866025 + 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2}+O(q^{10}) \) 8 * q + 8 * q^2	\( 8 q + 8 q^{2} + 4 q^{11} + 8 q^{16} - 4 q^{18} + 4 q^{22} - 4 q^{23} + 4 q^{30} + 8 q^{32} - 4 q^{36} - 4 q^{37} - 8 q^{46} - 4 q^{50} - 4 q^{51} + 4 q^{53} + 4 q^{60} - 8 q^{67} - 8 q^{71} - 8 q^{78} + 4 q^{81} + 4 q^{85} - 4 q^{92}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^11 + 8 * q^16 - 4 * q^18 + 4 * q^22 - 4 * q^23 + 4 * q^30 + 8 * q^32 - 4 * q^36 - 4 * q^37 - 8 * q^46 - 4 * q^50 - 4 * q^51 + 4 * q^53 + 4 * q^60 - 8 * q^67 - 8 * q^71 - 8 * q^78 + 4 * q^81 + 4 * q^85 - 4 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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