LMFDB - Embedded newform 1620.1.bp.b.1399.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,1,Mod(79,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 28, 27]))

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

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

chi := DirichletCharacter("1620.79");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1620.bp (of order $54$, degree $18$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.808485320465$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\Q(\zeta_{54})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{9} + 1 $ x^18 - x^9 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{27}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{27} - \cdots)$

Embedding invariants

Embedding label			1399.1
Root			$-0.396080 - 0.918216i$ of defining polynomial
Character	$\chi$	$=$	1620.1399
Dual form			1620.1.bp.b.799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686242 - 0.727374i) q^{2} +(0.396080 - 0.918216i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-0.993238 + 0.116093i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(1.06728 + 0.536009i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-0.686242 - 0.727374i) q^{9} +O(q^{10})$	\(q+(-0.686242 - 0.727374i) q^{2} +(0.396080 - 0.918216i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-0.993238 + 0.116093i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(1.06728 + 0.536009i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-0.686242 - 0.727374i) q^{9} +(0.766044 + 0.642788i) q^{10} +(0.893633 + 0.448799i) q^{12} +(-0.342534 - 1.14414i) q^{14} +(-0.286803 + 0.957990i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.0581448 + 0.998308i) q^{18} +(-0.0581448 - 0.998308i) q^{20} +(0.914900 - 0.767692i) q^{21} +(1.59716 - 0.802123i) q^{23} +(-0.286803 - 0.957990i) q^{24} +(0.973045 - 0.230616i) q^{25} +(-0.939693 + 0.342020i) q^{27} +(-0.597159 + 1.03431i) q^{28} +(0.479241 - 1.60078i) q^{29} +(0.893633 - 0.448799i) q^{30} +(0.597159 + 0.802123i) q^{32} +(-1.12229 - 0.408481i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-0.686242 + 0.727374i) q^{40} +(-1.33549 + 1.41553i) q^{41} +(-1.18624 - 0.138652i) q^{42} +(0.914900 - 1.22892i) q^{43} +(0.766044 + 0.642788i) q^{45} +(-1.67948 - 0.611281i) q^{46} +(1.14669 - 0.754192i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.254625 + 0.342020i) q^{49} +(-0.835488 - 0.549509i) q^{50} +(0.893633 + 0.448799i) q^{54} +(1.16212 - 0.275428i) q^{56} +(-1.49324 + 0.749932i) q^{58} +(-0.939693 - 0.342020i) q^{60} +(-0.0460600 - 0.790819i) q^{61} +(-0.342534 - 1.14414i) q^{63} +(0.173648 - 0.984808i) q^{64} +(0.164512 + 0.549509i) q^{67} +(-0.103920 - 1.78424i) q^{69} +(0.473045 + 1.09664i) q^{70} +(-0.993238 - 0.116093i) q^{72} +(0.173648 - 0.984808i) q^{75} +1.00000 q^{80} +(-0.0581448 + 0.998308i) q^{81} +1.94609 q^{82} +(-1.33549 - 1.41553i) q^{83} +(0.713197 + 0.957990i) q^{84} +(-1.52173 + 0.177865i) q^{86} +(-1.28004 - 1.07408i) q^{87} +(-1.05138 + 0.882215i) q^{89} +(-0.0581448 - 0.998308i) q^{90} +(0.707900 + 1.64110i) q^{92} +(-1.33549 - 0.316516i) q^{94} +(0.973045 - 0.230616i) q^{96} +(0.0740425 - 0.419916i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * q	$ 18 q + 18 q^{23} - 9 q^{41} - 9 q^{42} - 9 q^{48} - 9 q^{58} + 18 q^{67} - 9 q^{69} - 9 q^{70} + 18 q^{80} - 9 q^{83} + 18 q^{84} - 9 q^{94}+O(q^{100}) $ 18 * q + 18 * q^23 - 9 * q^41 - 9 * q^42 - 9 * q^48 - 9 * q^58 + 18 * q^67 - 9 * q^69 - 9 * q^70 + 18 * q^80 - 9 * q^83 + 18 * q^84 - 9 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{27}\right)$

Coefficient data

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

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

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

$2$	−0.686242	−	0.727374i	−0.686242	−	0.727374i
$2$	−0.686242	−	0.727374i	−0.686242	−	0.727374i
$3$	0.396080	−	0.918216i	0.396080	−	0.918216i
$3$	0.396080	−	0.918216i	0.396080	−	0.918216i
$4$	−0.0581448	+	0.998308i	−0.0581448	+	0.998308i
$5$	−0.993238	+	0.116093i	−0.993238	+	0.116093i
$5$	−0.993238	+	0.116093i	−0.993238	+	0.116093i
$6$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$7$	1.06728	+	0.536009i	1.06728	+	0.536009i	0.893633	−	0.448799i	$-0.148148\pi$
$7$	1.06728	+	0.536009i	1.06728	+	0.536009i	0.173648	+	0.984808i	$0.444444\pi$
$8$	0.766044	−	0.642788i	0.766044	−	0.642788i
$9$	−0.686242	−	0.727374i	−0.686242	−	0.727374i
$10$	0.766044	+	0.642788i	0.766044	+	0.642788i
$11$		0			0		−0.396080	−	0.918216i	$-0.629630\pi$
$11$		0			0		0.396080	+	0.918216i	$0.370370\pi$
$12$	0.893633	+	0.448799i	0.893633	+	0.448799i
$13$		0			0		−0.973045	−	0.230616i	$-0.925926\pi$
$13$		0			0		0.973045	+	0.230616i	$0.0740741\pi$
$14$	−0.342534	−	1.14414i	−0.342534	−	1.14414i
$15$	−0.286803	+	0.957990i	−0.286803	+	0.957990i
$16$	−0.993238	−	0.116093i	−0.993238	−	0.116093i
$17$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$17$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$18$	−0.0581448	+	0.998308i	−0.0581448	+	0.998308i
$19$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$19$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$20$	−0.0581448	−	0.998308i	−0.0581448	−	0.998308i
$21$	0.914900	−	0.767692i	0.914900	−	0.767692i
$22$		0			0
$23$	1.59716	−	0.802123i	1.59716	−	0.802123i	0.597159	−	0.802123i	$-0.296296\pi$
$23$	1.59716	−	0.802123i	1.59716	−	0.802123i	1.00000			$0$
$24$	−0.286803	−	0.957990i	−0.286803	−	0.957990i
$25$	0.973045	−	0.230616i	0.973045	−	0.230616i
$26$		0			0
$27$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$28$	−0.597159	+	1.03431i	−0.597159	+	1.03431i
$29$	0.479241	−	1.60078i	0.479241	−	1.60078i	−0.286803	−	0.957990i	$-0.592593\pi$
$29$	0.479241	−	1.60078i	0.479241	−	1.60078i	0.766044	−	0.642788i	$-0.222222\pi$
$30$	0.893633	−	0.448799i	0.893633	−	0.448799i
$31$		0			0		−0.835488	−	0.549509i	$-0.814815\pi$
$31$		0			0		0.835488	+	0.549509i	$0.185185\pi$
$32$	0.597159	+	0.802123i	0.597159	+	0.802123i
$33$		0			0
$34$		0			0
$35$	−1.12229	−	0.408481i	−1.12229	−	0.408481i
$36$	0.766044	−	0.642788i	0.766044	−	0.642788i
$37$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$37$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$38$		0			0
$39$		0			0
$40$	−0.686242	+	0.727374i	−0.686242	+	0.727374i
$41$	−1.33549	+	1.41553i	−1.33549	+	1.41553i	−0.500000	+	0.866025i	$0.666667\pi$
$41$	−1.33549	+	1.41553i	−1.33549	+	1.41553i	−0.835488	+	0.549509i	$0.814815\pi$
$42$	−1.18624	−	0.138652i	−1.18624	−	0.138652i
$43$	0.914900	−	1.22892i	0.914900	−	1.22892i	−0.0581448	−	0.998308i	$-0.518519\pi$
$43$	0.914900	−	1.22892i	0.914900	−	1.22892i	0.973045	−	0.230616i	$-0.0740741\pi$
$44$		0			0
$45$	0.766044	+	0.642788i	0.766044	+	0.642788i
$46$	−1.67948	−	0.611281i	−1.67948	−	0.611281i
$47$	1.14669	−	0.754192i	1.14669	−	0.754192i	0.173648	−	0.984808i	$-0.444444\pi$
$47$	1.14669	−	0.754192i	1.14669	−	0.754192i	0.973045	+	0.230616i	$0.0740741\pi$
$48$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$49$	0.254625	+	0.342020i	0.254625	+	0.342020i
$50$	−0.835488	−	0.549509i	−0.835488	−	0.549509i
$51$		0			0
$52$		0			0
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$	0.893633	+	0.448799i	0.893633	+	0.448799i
$55$		0			0
$56$	1.16212	−	0.275428i	1.16212	−	0.275428i
$57$		0			0
$58$	−1.49324	+	0.749932i	−1.49324	+	0.749932i
$59$		0			0		0.396080	−	0.918216i	$-0.370370\pi$
$59$		0			0		−0.396080	+	0.918216i	$0.629630\pi$
$60$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$61$	−0.0460600	−	0.790819i	−0.0460600	−	0.790819i	−0.939693	−	0.342020i	$-0.888889\pi$
$61$	−0.0460600	−	0.790819i	−0.0460600	−	0.790819i	0.893633	−	0.448799i	$-0.148148\pi$
$62$		0			0
$63$	−0.342534	−	1.14414i	−0.342534	−	1.14414i
$64$	0.173648	−	0.984808i	0.173648	−	0.984808i
$65$		0			0
$66$		0			0
$67$	0.164512	+	0.549509i	0.164512	+	0.549509i	1.00000			$0$
$67$	0.164512	+	0.549509i	0.164512	+	0.549509i	−0.835488	+	0.549509i	$0.814815\pi$
$68$		0			0
$69$	−0.103920	−	1.78424i	−0.103920	−	1.78424i
$70$	0.473045	+	1.09664i	0.473045	+	1.09664i
$71$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$71$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$72$	−0.993238	−	0.116093i	−0.993238	−	0.116093i
$73$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$73$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$74$		0			0
$75$	0.173648	−	0.984808i	0.173648	−	0.984808i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.686242	−	0.727374i	$-0.740741\pi$
$79$		0			0		0.686242	+	0.727374i	$0.259259\pi$
$80$	1.00000			1.00000
$81$	−0.0581448	+	0.998308i	−0.0581448	+	0.998308i
$82$	1.94609			1.94609
$83$	−1.33549	−	1.41553i	−1.33549	−	1.41553i	−0.835488	−	0.549509i	$-0.814815\pi$
$83$	−1.33549	−	1.41553i	−1.33549	−	1.41553i	−0.500000	−	0.866025i	$-0.666667\pi$
$84$	0.713197	+	0.957990i	0.713197	+	0.957990i
$85$		0			0
$86$	−1.52173	+	0.177865i	−1.52173	+	0.177865i
$87$	−1.28004	−	1.07408i	−1.28004	−	1.07408i
$88$		0			0
$89$	−1.05138	+	0.882215i	−1.05138	+	0.882215i	−0.993238	−	0.116093i	$-0.962963\pi$
$89$	−1.05138	+	0.882215i	−1.05138	+	0.882215i	−0.0581448	+	0.998308i	$0.518519\pi$
$90$	−0.0581448	−	0.998308i	−0.0581448	−	0.998308i
$91$		0			0
$92$	0.707900	+	1.64110i	0.707900	+	1.64110i
$93$		0			0
$94$	−1.33549	−	0.316516i	−1.33549	−	0.316516i
$95$		0			0
$96$	0.973045	−	0.230616i	0.973045	−	0.230616i
$97$		0			0		−0.993238	−	0.116093i	$-0.962963\pi$
$97$		0			0		0.993238	+	0.116093i	$0.0370370\pi$
$98$	0.0740425	−	0.419916i	0.0740425	−	0.419916i
$99$		0			0
$100$	0.173648	+	0.984808i	0.173648	+	0.984808i
$101$	0.109277	+	1.87621i	0.109277	+	1.87621i	0.396080	+	0.918216i	$0.370370\pi$
$101$	0.109277	+	1.87621i	0.109277	+	1.87621i	−0.286803	+	0.957990i	$0.592593\pi$
$102$		0			0
$103$	0.137557	−	0.318893i	0.137557	−	0.318893i	−0.835488	−	0.549509i	$-0.814815\pi$
$103$	0.137557	−	0.318893i	0.137557	−	0.318893i	0.973045	+	0.230616i	$0.0740741\pi$
$104$		0			0
$105$	−0.819590	+	0.868715i	−0.819590	+	0.868715i
$106$		0			0
$107$	0.993238	+	1.72034i	0.993238	+	1.72034i	0.597159	+	0.802123i	$0.296296\pi$
$107$	0.993238	+	1.72034i	0.993238	+	1.72034i	0.396080	+	0.918216i	$0.370370\pi$
$108$	−0.286803	−	0.957990i	−0.286803	−	0.957990i
$109$	0.0581448	−	0.100710i	0.0581448	−	0.100710i	−0.835488	−	0.549509i	$-0.814815\pi$
$109$	0.0581448	−	0.100710i	0.0581448	−	0.100710i	0.893633	+	0.448799i	$0.148148\pi$
$110$		0			0
$111$		0			0
$112$	−0.997837	−	0.656288i	−0.997837	−	0.656288i
$113$		0			0		−0.597159	−	0.802123i	$-0.703704\pi$
$113$		0			0		0.597159	+	0.802123i	$0.296296\pi$
$114$		0			0
$115$	−1.49324	+	0.982118i	−1.49324	+	0.982118i
$116$	1.57020	+	0.571507i	1.57020	+	0.571507i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.396080	+	0.918216i	0.396080	+	0.918216i
$121$	−0.686242	+	0.727374i	−0.686242	+	0.727374i
$122$	−0.543613	+	0.576196i	−0.543613	+	0.576196i
$123$	0.770807	+	1.78693i	0.770807	+	1.78693i
$124$		0			0
$125$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$126$	−0.597159	+	1.03431i	−0.597159	+	1.03431i
$127$	0.109277	+	0.0397734i	0.109277	+	0.0397734i	0.396080	−	0.918216i	$-0.370370\pi$
$127$	0.109277	+	0.0397734i	0.109277	+	0.0397734i	−0.286803	+	0.957990i	$0.592593\pi$
$128$	−0.835488	+	0.549509i	−0.835488	+	0.549509i
$129$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$130$		0			0
$131$		0			0		−0.835488	−	0.549509i	$-0.814815\pi$
$131$		0			0		0.835488	+	0.549509i	$0.185185\pi$
$132$		0			0
$133$		0			0
$134$	0.286803	−	0.496758i	0.286803	−	0.496758i
$135$	0.893633	−	0.448799i	0.893633	−	0.448799i
$136$		0			0
$137$		0			0		0.973045	−	0.230616i	$-0.0740741\pi$
$137$		0			0		−0.973045	+	0.230616i	$0.925926\pi$
$138$	−1.22650	+	1.30001i	−1.22650	+	1.30001i
$139$		0			0		0.893633	−	0.448799i	$-0.148148\pi$
$139$		0			0		−0.893633	+	0.448799i	$0.851852\pi$
$140$	0.473045	−	1.09664i	0.473045	−	1.09664i
$141$	−0.238329	−	1.35163i	−0.238329	−	1.35163i
$142$		0			0
$143$		0			0
$144$	0.597159	+	0.802123i	0.597159	+	0.802123i
$145$	−0.290162	+	1.64559i	−0.290162	+	1.64559i
$146$		0			0
$147$	0.414900	−	0.0983331i	0.414900	−	0.0983331i
$148$		0			0
$149$	−0.113155	−	0.0268182i	−0.113155	−	0.0268182i	0.173648	−	0.984808i	$-0.444444\pi$
$149$	−0.113155	−	0.0268182i	−0.113155	−	0.0268182i	−0.286803	+	0.957990i	$0.592593\pi$
$150$	−0.835488	+	0.549509i	−0.835488	+	0.549509i
$151$		0			0		−0.396080	−	0.918216i	$-0.629630\pi$
$151$		0			0		0.396080	+	0.918216i	$0.370370\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.993238	−	0.116093i	$-0.0370370\pi$
$157$		0			0		−0.993238	+	0.116093i	$0.962963\pi$
$158$		0			0
$159$		0			0
$160$	−0.686242	−	0.727374i	−0.686242	−	0.727374i
$161$	2.13456			2.13456
$162$	0.766044	−	0.642788i	0.766044	−	0.642788i
$163$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$163$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$164$	−1.33549	−	1.41553i	−1.33549	−	1.41553i
$165$		0			0
$166$	−0.113155	+	1.94280i	−0.113155	+	1.94280i
$167$	1.65968	−	0.193988i	1.65968	−	0.193988i	0.766044	−	0.642788i	$-0.222222\pi$
$167$	1.65968	−	0.193988i	1.65968	−	0.193988i	0.893633	+	0.448799i	$0.148148\pi$
$168$	0.207391	−	1.17617i	0.207391	−	1.17617i
$169$	0.893633	+	0.448799i	0.893633	+	0.448799i
$170$		0			0
$171$		0			0
$172$	1.17365	+	0.984808i	1.17365	+	0.984808i
$173$		0			0		−0.396080	−	0.918216i	$-0.629630\pi$
$173$		0			0		0.396080	+	0.918216i	$0.370370\pi$
$174$	0.0971586	+	1.66815i	0.0971586	+	1.66815i
$175$	1.16212	+	0.275428i	1.16212	+	0.275428i
$176$		0			0
$177$		0			0
$178$	1.36320	+	0.159336i	1.36320	+	0.159336i
$179$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$179$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$180$	−0.686242	+	0.727374i	−0.686242	+	0.727374i
$181$	−0.344948	−	1.95630i	−0.344948	−	1.95630i	−0.286803	−	0.957990i	$-0.592593\pi$
$181$	−0.344948	−	1.95630i	−0.344948	−	1.95630i	−0.0581448	−	0.998308i	$-0.518519\pi$
$182$		0			0
$183$	−0.744386	−	0.270935i	−0.744386	−	0.270935i
$184$	0.707900	−	1.64110i	0.707900	−	1.64110i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.686242	+	1.18861i	0.686242	+	1.18861i
$189$	−1.18624	−	0.138652i	−1.18624	−	0.138652i
$190$		0			0
$191$		0			0		0.286803	−	0.957990i	$-0.407407\pi$
$191$		0			0		−0.286803	+	0.957990i	$0.592593\pi$
$192$	−0.835488	−	0.549509i	−0.835488	−	0.549509i
$193$		0			0		−0.835488	−	0.549509i	$-0.814815\pi$
$193$		0			0		0.835488	+	0.549509i	$0.185185\pi$
$194$		0			0
$195$		0			0
$196$	−0.356247	+	0.234307i	−0.356247	+	0.234307i
$197$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$197$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$198$		0			0
$199$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$199$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$200$	0.597159	−	0.802123i	0.597159	−	0.802123i
$201$	0.569728	+	0.0665916i	0.569728	+	0.0665916i
$202$	1.28971	−	1.36702i	1.28971	−	1.36702i
$203$	1.36952	−	1.45160i	1.36952	−	1.45160i
$204$		0			0
$205$	1.16212	−	1.56100i	1.16212	−	1.56100i
$206$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$207$	−1.67948	−	0.611281i	−1.67948	−	0.611281i
$208$		0			0
$209$		0			0
$210$	1.19432			1.19432
$211$		0			0		−0.597159	−	0.802123i	$-0.703704\pi$
$211$		0			0		0.597159	+	0.802123i	$0.296296\pi$
$212$		0			0
$213$		0			0
$214$	0.569728	−	1.90302i	0.569728	−	1.90302i
$215$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$216$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$217$		0			0
$218$	−0.113155	+	0.0268182i	−0.113155	+	0.0268182i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.0798028	+	1.37016i	0.0798028	+	1.37016i	0.766044	+	0.642788i	$0.222222\pi$
$223$	0.0798028	+	1.37016i	0.0798028	+	1.37016i	−0.686242	+	0.727374i	$0.740741\pi$
$224$	0.207391	+	1.17617i	0.207391	+	1.17617i
$225$	−0.835488	−	0.549509i	−0.835488	−	0.549509i
$226$		0			0
$227$	−0.344948	−	0.0403186i	−0.344948	−	0.0403186i	−0.0581448	−	0.998308i	$-0.518519\pi$
$227$	−0.344948	−	0.0403186i	−0.344948	−	0.0403186i	−0.286803	+	0.957990i	$0.592593\pi$
$228$		0			0
$229$	0.479241	+	1.60078i	0.479241	+	1.60078i	0.766044	+	0.642788i	$0.222222\pi$
$229$	0.479241	+	1.60078i	0.479241	+	1.60078i	−0.286803	+	0.957990i	$0.592593\pi$
$230$	1.73909	+	0.412172i	1.73909	+	0.412172i
$231$		0			0
$232$	−0.661840	−	1.53432i	−0.661840	−	1.53432i
$233$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$233$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$234$		0			0
$235$	−1.05138	+	0.882215i	−1.05138	+	0.882215i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.0581448	−	0.998308i	$-0.481481\pi$
$239$		0			0		−0.0581448	+	0.998308i	$0.518519\pi$
$240$	0.396080	−	0.918216i	0.396080	−	0.918216i
$241$	1.36320	+	1.44491i	1.36320	+	1.44491i	0.766044	+	0.642788i	$0.222222\pi$
$241$	1.36320	+	1.44491i	1.36320	+	1.44491i	0.597159	+	0.802123i	$0.296296\pi$
$242$	1.00000			1.00000
$243$	0.893633	+	0.448799i	0.893633	+	0.448799i
$244$	0.792160			0.792160
$245$	−0.292609	−	0.310147i	−0.292609	−	0.310147i
$246$	0.770807	−	1.78693i	0.770807	−	1.78693i
$247$		0			0
$248$		0			0
$249$	−1.82873	+	0.665602i	−1.82873	+	0.665602i
$250$	0.893633	+	0.448799i	0.893633	+	0.448799i
$251$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$251$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$252$	1.16212	−	0.275428i	1.16212	−	0.275428i
$253$		0			0
$254$	−0.0460600	−	0.106779i	−0.0460600	−	0.106779i
$255$		0			0
$256$	0.973045	+	0.230616i	0.973045	+	0.230616i
$257$		0			0		−0.286803	−	0.957990i	$-0.592593\pi$
$257$		0			0		0.286803	+	0.957990i	$0.407407\pi$
$258$	−0.439408	+	1.46773i	−0.439408	+	1.46773i
$259$		0			0
$260$		0			0
$261$	−1.49324	+	0.749932i	−1.49324	+	0.749932i
$262$		0			0
$263$	−0.0201935	−	0.346709i	−0.0201935	−	0.346709i	−0.993238	−	0.116093i	$-0.962963\pi$
$263$	−0.0201935	−	0.346709i	−0.0201935	−	0.346709i	0.973045	−	0.230616i	$-0.0740741\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.393633	+	1.31482i	0.393633	+	1.31482i
$268$	−0.558145	+	0.132283i	−0.558145	+	0.132283i
$269$	0.993238	+	1.72034i	0.993238	+	1.72034i	0.597159	+	0.802123i	$0.296296\pi$
$269$	0.993238	+	1.72034i	0.993238	+	1.72034i	0.396080	+	0.918216i	$0.370370\pi$
$270$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	1.78727			1.78727
$277$		0			0		0.835488	−	0.549509i	$-0.185185\pi$
$277$		0			0		−0.835488	+	0.549509i	$0.814815\pi$
$278$		0			0
$279$		0			0
$280$	−1.12229	+	0.408481i	−1.12229	+	0.408481i
$281$	0.473045	−	0.635410i	0.473045	−	0.635410i	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	0.473045	−	0.635410i	0.473045	−	0.635410i	0.973045	+	0.230616i	$0.0740741\pi$
$282$	−0.819590	+	1.10090i	−0.819590	+	1.10090i
$283$	0.0798028	−	0.0845860i	0.0798028	−	0.0845860i	−0.686242	−	0.727374i	$-0.740741\pi$
$283$	0.0798028	−	0.0845860i	0.0798028	−	0.0845860i	0.766044	+	0.642788i	$0.222222\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.18408	+	0.794940i	−2.18408	+	0.794940i
$288$	0.173648	−	0.984808i	0.173648	−	0.984808i
$289$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$290$	1.39608	−	0.918216i	1.39608	−	0.918216i
$291$		0			0
$292$		0			0
$293$		0			0		−0.835488	−	0.549509i	$-0.814815\pi$
$293$		0			0		0.835488	+	0.549509i	$0.185185\pi$
$294$	−0.356247	−	0.234307i	−0.356247	−	0.234307i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.0581448	+	0.100710i	0.0581448	+	0.100710i
$299$		0			0
$300$	0.973045	+	0.230616i	0.973045	+	0.230616i
$301$	1.63517	−	0.821213i	1.63517	−	0.821213i
$302$		0			0
$303$	1.76604	+	0.642788i	1.76604	+	0.642788i
$304$		0			0
$305$	0.137557	+	0.780125i	0.137557	+	0.780125i
$306$		0			0
$307$	0.310355	−	1.76011i	0.310355	−	1.76011i	−0.286803	−	0.957990i	$-0.592593\pi$
$307$	0.310355	−	1.76011i	0.310355	−	1.76011i	0.597159	−	0.802123i	$-0.296296\pi$
$308$		0			0
$309$	−0.238329	−	0.252614i	−0.238329	−	0.252614i
$310$		0			0
$311$		0			0		−0.973045	−	0.230616i	$-0.925926\pi$
$311$		0			0		0.973045	+	0.230616i	$0.0740741\pi$
$312$		0			0
$313$		0			0		−0.396080	−	0.918216i	$-0.629630\pi$
$313$		0			0		0.396080	+	0.918216i	$0.370370\pi$
$314$		0			0
$315$	0.473045	+	1.09664i	0.473045	+	1.09664i
$316$		0			0
$317$		0			0		−0.893633	−	0.448799i	$-0.851852\pi$
$317$		0			0		0.893633	+	0.448799i	$0.148148\pi$
$318$		0			0
$319$		0			0
$320$	−0.0581448	+	0.998308i	−0.0581448	+	0.998308i
$321$	1.97304	−	0.230616i	1.97304	−	0.230616i
$322$	−1.46483	−	1.55262i	−1.46483	−	1.55262i
$323$		0			0
$324$	−0.993238	−	0.116093i	−0.993238	−	0.116093i
$325$		0			0
$326$	1.28971	+	1.36702i	1.28971	+	1.36702i
$327$	−0.0694434	−	0.0932786i	−0.0694434	−	0.0932786i
$328$	−0.113155	+	1.94280i	−0.113155	+	1.94280i
$329$	1.62810	−	0.190297i	1.62810	−	0.190297i
$330$		0			0
$331$		0			0		−0.893633	−	0.448799i	$-0.851852\pi$
$331$		0			0		0.893633	+	0.448799i	$0.148148\pi$
$332$	1.49079	−	1.25092i	1.49079	−	1.25092i
$333$		0			0
$334$	−1.28004	−	1.07408i	−1.28004	−	1.07408i
$335$	−0.227194	−	0.526695i	−0.227194	−	0.526695i
$336$	−0.997837	+	0.656288i	−0.997837	+	0.656288i
$337$		0			0		−0.973045	−	0.230616i	$-0.925926\pi$
$337$		0			0		0.973045	+	0.230616i	$0.0740741\pi$
$338$	−0.286803	−	0.957990i	−0.286803	−	0.957990i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.118961	−	0.674660i	−0.118961	−	0.674660i
$344$	−0.0890830	−	1.52950i	−0.0890830	−	1.52950i
$345$	0.310355	+	1.76011i	0.310355	+	1.76011i
$346$		0			0
$347$	−1.67948	+	0.843467i	−1.67948	+	0.843467i	−0.686242	+	0.727374i	$0.740741\pi$
$347$	−1.67948	+	0.843467i	−1.67948	+	0.843467i	−0.993238	+	0.116093i	$0.962963\pi$
$348$	1.14669	−	1.21542i	1.14669	−	1.21542i
$349$	−1.33549	+	0.316516i	−1.33549	+	0.316516i	−0.835488	−	0.549509i	$-0.814815\pi$
$349$	−1.33549	+	0.316516i	−1.33549	+	0.316516i	−0.500000	+	0.866025i	$0.666667\pi$
$350$	−0.597159	−	1.03431i	−0.597159	−	1.03431i
$351$		0			0
$352$		0			0
$353$		0			0		0.286803	−	0.957990i	$-0.407407\pi$
$353$		0			0		−0.286803	+	0.957990i	$0.592593\pi$
$354$		0			0
$355$		0			0
$356$	−0.819590	−	1.10090i	−0.819590	−	1.10090i
$357$		0			0
$358$		0			0
$359$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$359$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$360$	1.00000			1.00000
$361$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$362$	−1.18624	+	1.59340i	−1.18624	+	1.59340i
$363$	0.396080	+	0.918216i	0.396080	+	0.918216i
$364$		0			0
$365$		0			0
$366$	0.313758	+	0.727374i	0.313758	+	0.727374i
$367$	−0.597159	+	0.802123i	−0.597159	+	0.802123i	−0.993238	−	0.116093i	$-0.962963\pi$
$367$	−0.597159	+	0.802123i	−0.597159	+	0.802123i	0.396080	+	0.918216i	$0.370370\pi$
$368$	−1.67948	+	0.611281i	−1.67948	+	0.611281i
$369$	1.94609			1.94609
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.597159	−	0.802123i	$-0.703704\pi$
$373$		0			0		0.597159	+	0.802123i	$0.296296\pi$
$374$		0			0
$375$	−0.0581448	+	0.998308i	−0.0581448	+	0.998308i
$376$	0.393633	−	1.31482i	0.393633	−	1.31482i
$377$		0			0
$378$	0.713197	+	0.957990i	0.713197	+	0.957990i
$379$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$379$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$380$		0			0
$381$	0.0798028	−	0.0845860i	0.0798028	−	0.0845860i
$382$		0			0
$383$	−0.744386	+	1.72568i	−0.744386	+	1.72568i	−0.0581448	+	0.998308i	$0.518519\pi$
$383$	−0.744386	+	1.72568i	−0.744386	+	1.72568i	−0.686242	+	0.727374i	$0.740741\pi$
$384$	0.173648	+	0.984808i	0.173648	+	0.984808i
$385$		0			0
$386$		0			0
$387$	−1.52173	+	0.177865i	−1.52173	+	0.177865i
$388$		0			0
$389$	0.569728	+	0.0665916i	0.569728	+	0.0665916i	0.396080	−	0.918216i	$-0.370370\pi$
$389$	0.569728	+	0.0665916i	0.569728	+	0.0665916i	0.173648	+	0.984808i	$0.444444\pi$
$390$		0			0
$391$		0			0
$392$	0.414900	+	0.0983331i	0.414900	+	0.0983331i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$397$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$398$		0			0
$399$		0			0
$400$	−0.993238	+	0.116093i	−0.993238	+	0.116093i
$401$	−0.0890830	+	1.52950i	−0.0890830	+	1.52950i	0.597159	+	0.802123i	$0.296296\pi$
$401$	−0.0890830	+	1.52950i	−0.0890830	+	1.52950i	−0.686242	+	0.727374i	$0.740741\pi$
$402$	−0.342534	−	0.460103i	−0.342534	−	0.460103i
$403$		0			0
$404$	−1.87939			−1.87939
$405$	−0.0581448	−	0.998308i	−0.0581448	−	0.998308i
$406$	−1.99567			−1.99567
$407$		0			0
$408$		0			0
$409$	−0.0201935	+	0.346709i	−0.0201935	+	0.346709i	0.973045	+	0.230616i	$0.0740741\pi$
$409$	−0.0201935	+	0.346709i	−0.0201935	+	0.346709i	−0.993238	+	0.116093i	$0.962963\pi$
$410$	−1.93293	+	0.225927i	−1.93293	+	0.225927i
$411$		0			0
$412$	0.310355	+	0.155866i	0.310355	+	0.155866i
$413$		0			0
$414$	0.707900	+	1.64110i	0.707900	+	1.64110i
$415$	1.49079	+	1.25092i	1.49079	+	1.25092i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.286803	−	0.957990i	$-0.592593\pi$
$419$		0			0		0.286803	+	0.957990i	$0.407407\pi$
$420$	−0.819590	−	0.868715i	−0.819590	−	0.868715i
$421$	−1.52173	−	0.177865i	−1.52173	−	0.177865i	−0.686242	−	0.727374i	$-0.740741\pi$
$421$	−1.52173	−	0.177865i	−1.52173	−	0.177865i	−0.835488	+	0.549509i	$0.814815\pi$
$422$		0			0
$423$	−1.33549	−	0.316516i	−1.33549	−	0.316516i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.374727	−	0.868715i	0.374727	−	0.868715i
$428$	−1.77518	+	0.891529i	−1.77518	+	0.891529i
$429$		0			0
$430$	1.49079	−	0.353324i	1.49079	−	0.353324i
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	0.973045	−	0.230616i	0.973045	−	0.230616i
$433$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$433$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$434$		0			0
$435$	1.39608	+	0.918216i	1.39608	+	0.918216i
$436$	0.0971586	+	0.0639022i	0.0971586	+	0.0639022i
$437$		0			0
$438$		0			0
$439$		0			0		0.835488	−	0.549509i	$-0.185185\pi$
$439$		0			0		−0.835488	+	0.549509i	$0.814815\pi$
$440$		0			0
$441$	0.0740425	−	0.419916i	0.0740425	−	0.419916i
$442$		0			0
$443$	−0.342534	+	0.460103i	−0.342534	+	0.460103i	−0.939693	−	0.342020i	$-0.888889\pi$
$443$	−0.342534	+	0.460103i	−0.342534	+	0.460103i	0.597159	+	0.802123i	$0.296296\pi$
$444$		0			0
$445$	0.941855	−	0.998308i	0.941855	−	0.998308i
$446$	0.941855	−	0.998308i	0.941855	−	0.998308i
$447$	−0.0694434	+	0.0932786i	−0.0694434	+	0.0932786i
$448$	0.713197	−	0.957990i	0.713197	−	0.957990i
$449$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$449$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$450$	0.173648	+	0.984808i	0.173648	+	0.984808i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.207391	+	0.278574i	0.207391	+	0.278574i
$455$		0			0
$456$		0			0
$457$		0			0		0.286803	−	0.957990i	$-0.407407\pi$
$457$		0			0		−0.286803	+	0.957990i	$0.592593\pi$
$458$	0.835488	−	1.44711i	0.835488	−	1.44711i
$459$		0			0
$460$	−0.893633	−	1.54782i	−0.893633	−	1.54782i
$461$	−1.93293	+	0.458113i	−1.93293	+	0.458113i	−0.939693	+	0.342020i	$0.888889\pi$
$461$	−1.93293	+	0.458113i	−1.93293	+	0.458113i	−0.993238	+	0.116093i	$0.962963\pi$
$462$		0			0
$463$	0.310355	−	0.155866i	0.310355	−	0.155866i	−0.286803	−	0.957990i	$-0.592593\pi$
$463$	0.310355	−	0.155866i	0.310355	−	0.155866i	0.597159	+	0.802123i	$0.296296\pi$
$464$	−0.661840	+	1.53432i	−0.661840	+	1.53432i
$465$		0			0
$466$		0			0
$467$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$467$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$	−0.118961	+	0.674660i	−0.118961	+	0.674660i
$470$	1.36320	+	0.159336i	1.36320	+	0.159336i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.893633	−	0.448799i	$-0.851852\pi$
$479$		0			0		0.893633	+	0.448799i	$0.148148\pi$
$480$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$481$		0			0
$482$	0.115503	−	1.98312i	0.115503	−	1.98312i
$483$	0.845457	−	1.95999i	0.845457	−	1.95999i
$484$	−0.686242	−	0.727374i	−0.686242	−	0.727374i
$485$		0			0
$486$	−0.286803	−	0.957990i	−0.286803	−	0.957990i
$487$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$487$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$488$	−0.543613	−	0.576196i	−0.543613	−	0.576196i
$489$	−0.744386	+	1.72568i	−0.744386	+	1.72568i
$490$	−0.0247926	+	0.425672i	−0.0247926	+	0.425672i
$491$		0			0		0.993238	−	0.116093i	$-0.0370370\pi$
$491$		0			0		−0.993238	+	0.116093i	$0.962963\pi$
$492$	−1.82873	+	0.665602i	−1.82873	+	0.665602i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.73909	+	0.873403i	1.73909	+	0.873403i
$499$		0			0		−0.973045	−	0.230616i	$-0.925926\pi$
$499$		0			0		0.973045	+	0.230616i	$0.0740741\pi$
$500$	−0.286803	−	0.957990i	−0.286803	−	0.957990i
$501$	0.479241	−	1.60078i	0.479241	−	1.60078i
$502$		0			0
$503$	0.137557	−	0.780125i	0.137557	−	0.780125i	−0.835488	−	0.549509i	$-0.814815\pi$
$503$	0.137557	−	0.780125i	0.137557	−	0.780125i	0.973045	−	0.230616i	$-0.0740741\pi$
$504$	−0.997837	−	0.656288i	−0.997837	−	0.656288i
$505$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$506$		0			0
$507$	0.766044	−	0.642788i	0.766044	−	0.642788i
$508$	−0.0460600	+	0.106779i	−0.0460600	+	0.106779i
$509$	0.707900	−	0.355521i	0.707900	−	0.355521i	−0.0581448	−	0.998308i	$-0.518519\pi$
$509$	0.707900	−	0.355521i	0.707900	−	0.355521i	0.766044	+	0.642788i	$0.222222\pi$
$510$		0			0
$511$		0			0
$512$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$513$		0			0
$514$		0			0
$515$	−0.0996057	+	0.332706i	−0.0996057	+	0.332706i
$516$	1.36912	−	0.687600i	1.36912	−	0.687600i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.67948	−	0.611281i	−1.67948	−	0.611281i	−0.686242	−	0.727374i	$-0.740741\pi$
$521$	−1.67948	−	0.611281i	−1.67948	−	0.611281i	−0.993238	+	0.116093i	$0.962963\pi$
$522$	1.57020	+	0.571507i	1.57020	+	0.571507i
$523$	−0.744386	+	0.270935i	−0.744386	+	0.270935i	−0.686242	−	0.727374i	$-0.740741\pi$
$523$	−0.744386	+	0.270935i	−0.744386	+	0.270935i	−0.0581448	+	0.998308i	$0.518519\pi$
$524$		0			0
$525$	0.713197	−	0.957990i	0.713197	−	0.957990i
$526$	−0.238329	+	0.252614i	−0.238329	+	0.252614i
$527$		0			0
$528$		0			0
$529$	1.31036	−	1.76011i	1.31036	−	1.76011i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.686242	−	1.18861i	0.686242	−	1.18861i
$535$	−1.18624	−	1.59340i	−1.18624	−	1.59340i
$536$	0.479241	+	0.315202i	0.479241	+	0.315202i
$537$		0			0
$538$	0.569728	−	1.90302i	0.569728	−	1.90302i
$539$		0			0
$540$	0.396080	+	0.918216i	0.396080	+	0.918216i
$541$	−0.396080	−	0.686030i	−0.396080	−	0.686030i	0.597159	−	0.802123i	$-0.296296\pi$
$541$	−0.396080	−	0.686030i	−0.396080	−	0.686030i	−0.993238	+	0.116093i	$0.962963\pi$
$542$		0			0
$543$	−1.93293	−	0.458113i	−1.93293	−	0.458113i
$544$		0			0
$545$	−0.0460600	+	0.106779i	−0.0460600	+	0.106779i
$546$		0			0
$547$	0.0333522	+	0.572636i	0.0333522	+	0.572636i	0.973045	+	0.230616i	$0.0740741\pi$
$547$	0.0333522	+	0.572636i	0.0333522	+	0.572636i	−0.939693	+	0.342020i	$0.888889\pi$
$548$		0			0
$549$	−0.543613	+	0.576196i	−0.543613	+	0.576196i
$550$		0			0
$551$		0			0
$552$	−1.22650	−	1.30001i	−1.22650	−	1.30001i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$557$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$558$		0			0
$559$		0			0
$560$	1.06728	+	0.536009i	1.06728	+	0.536009i
$561$		0			0
$562$	−0.786803	+	0.0919641i	−0.786803	+	0.0919641i
$563$	−0.113155	+	1.94280i	−0.113155	+	1.94280i	0.173648	+	0.984808i	$0.444444\pi$
$563$	−0.113155	+	1.94280i	−0.113155	+	1.94280i	−0.286803	+	0.957990i	$0.592593\pi$
$564$	1.36320	−	0.159336i	1.36320	−	0.159336i
$565$		0			0
$566$	−0.116290			−0.116290
$567$	−0.597159	+	1.03431i	−0.597159	+	1.03431i
$568$		0			0
$569$	−1.05138	−	1.11440i	−1.05138	−	1.11440i	−0.993238	−	0.116093i	$-0.962963\pi$
$569$	−1.05138	−	1.11440i	−1.05138	−	1.11440i	−0.0581448	−	0.998308i	$-0.518519\pi$
$570$		0			0
$571$		0			0		0.0581448	−	0.998308i	$-0.481481\pi$
$571$		0			0		−0.0581448	+	0.998308i	$0.518519\pi$
$572$		0			0
$573$		0			0
$574$	2.07702	+	1.04312i	2.07702	+	1.04312i
$575$	1.36912	−	1.14883i	1.36912	−	1.14883i
$576$	−0.835488	+	0.549509i	−0.835488	+	0.549509i
$577$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$577$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$578$	0.396080	+	0.918216i	0.396080	+	0.918216i
$579$		0			0
$580$	−1.62593	−	0.385353i	−1.62593	−	0.385353i
$581$	−0.666602	−	2.22661i	−0.666602	−	2.22661i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.0460600	−	0.790819i	−0.0460600	−	0.790819i	−0.939693	−	0.342020i	$-0.888889\pi$
$587$	−0.0460600	−	0.790819i	−0.0460600	−	0.790819i	0.893633	−	0.448799i	$-0.148148\pi$
$588$	0.0740425	+	0.419916i	0.0740425	+	0.419916i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$593$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$594$		0			0
$595$		0			0
$596$	0.0333522	−	0.111404i	0.0333522	−	0.111404i
$597$		0			0
$598$		0			0
$599$		0			0		−0.597159	−	0.802123i	$-0.703704\pi$
$599$		0			0		0.597159	+	0.802123i	$0.296296\pi$
$600$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$601$	−1.28004	+	0.841897i	−1.28004	+	0.841897i	−0.993238	−	0.116093i	$-0.962963\pi$
$601$	−1.28004	+	0.841897i	−1.28004	+	0.841897i	−0.286803	+	0.957990i	$0.592593\pi$
$602$	−1.71945	−	0.625828i	−1.71945	−	0.625828i
$603$	0.286803	−	0.496758i	0.286803	−	0.496758i
$604$		0			0
$605$	0.597159	−	0.802123i	0.597159	−	0.802123i
$606$	−0.744386	−	1.72568i	−0.744386	−	1.72568i
$607$	1.14669	−	1.21542i	1.14669	−	1.21542i	0.173648	−	0.984808i	$-0.444444\pi$
$607$	1.14669	−	1.21542i	1.14669	−	1.21542i	0.973045	−	0.230616i	$-0.0740741\pi$
$608$		0			0
$609$	−0.790446	−	1.83246i	−0.790446	−	1.83246i
$610$	0.473045	−	0.635410i	0.473045	−	0.635410i
$611$		0			0
$612$		0			0
$613$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$613$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$614$	−1.49324	+	0.982118i	−1.49324	+	0.982118i
$615$	−0.973045	−	1.68536i	−0.973045	−	1.68536i
$616$		0			0
$617$		0			0		−0.835488	−	0.549509i	$-0.814815\pi$
$617$		0			0		0.835488	+	0.549509i	$0.185185\pi$
$618$	−0.0201935	+	0.346709i	−0.0201935	+	0.346709i
$619$		0			0		0.286803	−	0.957990i	$-0.407407\pi$
$619$		0			0		−0.286803	+	0.957990i	$0.592593\pi$
$620$		0			0
$621$	−1.22650	+	1.30001i	−1.22650	+	1.30001i
$622$		0			0
$623$	−1.59500	+	0.378021i	−1.59500	+	0.378021i
$624$		0			0
$625$	0.893633	−	0.448799i	0.893633	−	0.448799i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.473045	−	1.09664i	0.473045	−	1.09664i
$631$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$631$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.113155	−	0.0268182i	−0.113155	−	0.0268182i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.766044	−	0.642788i	0.766044	−	0.642788i
$641$	−1.77518	−	0.891529i	−1.77518	−	0.891529i	−0.939693	−	0.342020i	$-0.888889\pi$
$641$	−1.77518	−	0.891529i	−1.77518	−	0.891529i	−0.835488	−	0.549509i	$-0.814815\pi$
$642$	−1.52173	−	1.27688i	−1.52173	−	1.27688i
$643$	1.65968	−	0.193988i	1.65968	−	0.193988i	0.766044	−	0.642788i	$-0.222222\pi$
$643$	1.65968	−	0.193988i	1.65968	−	0.193988i	0.893633	+	0.448799i	$0.148148\pi$
$644$	−0.124114	+	2.13095i	−0.124114	+	2.13095i
$645$	0.914900	+	1.22892i	0.914900	+	1.22892i
$646$		0			0
$647$	−0.116290			−0.116290			−0.0581448	−	0.998308i	$-0.518519\pi$
$647$	−0.116290			−0.116290			−0.0581448	+	0.998308i	$0.518519\pi$
$648$	0.597159	+	0.802123i	0.597159	+	0.802123i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.109277	−	1.87621i	0.109277	−	1.87621i
$653$		0			0		0.993238	−	0.116093i	$-0.0370370\pi$
$653$		0			0		−0.993238	+	0.116093i	$0.962963\pi$
$654$	−0.0201935	+	0.114523i	−0.0201935	+	0.114523i
$655$		0			0
$656$	1.49079	−	1.25092i	1.49079	−	1.25092i
$657$		0			0
$658$	−1.25569	−	1.05364i	−1.25569	−	1.05364i
$659$		0			0		−0.396080	−	0.918216i	$-0.629630\pi$
$659$		0			0		0.396080	+	0.918216i	$0.370370\pi$
$660$		0			0
$661$	0.337935	+	0.0800921i	0.337935	+	0.0800921i	0.396080	−	0.918216i	$-0.370370\pi$
$661$	0.337935	+	0.0800921i	0.337935	+	0.0800921i	−0.0581448	+	0.998308i	$0.518519\pi$
$662$		0			0
$663$		0			0
$664$	−1.93293	−	0.225927i	−1.93293	−	0.225927i
$665$		0			0
$666$		0			0
$667$	−0.518596	−	2.94111i	−0.518596	−	2.94111i
$668$	0.0971586	+	1.66815i	0.0971586	+	1.66815i
$669$	1.28971	+	0.469417i	1.28971	+	0.469417i
$670$	−0.227194	+	0.526695i	−0.227194	+	0.526695i
$671$		0			0
$672$	1.16212	+	0.275428i	1.16212	+	0.275428i
$673$		0			0		0.973045	−	0.230616i	$-0.0740741\pi$
$673$		0			0		−0.973045	+	0.230616i	$0.925926\pi$
$674$		0			0
$675$	−0.835488	+	0.549509i	−0.835488	+	0.549509i
$676$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$677$		0			0		0.286803	−	0.957990i	$-0.407407\pi$
$677$		0			0		−0.286803	+	0.957990i	$0.592593\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$682$		0			0
$683$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$683$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$684$		0			0
$685$		0			0
$686$	−0.409094	+	0.549509i	−0.409094	+	0.549509i
$687$	1.65968	+	0.193988i	1.65968	+	0.193988i
$688$	−1.05138	+	1.11440i	−1.05138	+	1.11440i
$689$		0			0
$690$	1.06728	−	1.43361i	1.06728	−	1.43361i
$691$		0			0		0.597159	−	0.802123i	$-0.296296\pi$
$691$		0			0		−0.597159	+	0.802123i	$0.703704\pi$
$692$		0			0
$693$		0			0
$694$	1.76604	+	0.642788i	1.76604	+	0.642788i
$695$		0			0
$696$	−1.67098			−1.67098
$697$		0			0
$698$	1.14669	+	0.754192i	1.14669	+	0.754192i
$699$		0			0
$700$	−0.342534	+	1.14414i	−0.342534	+	1.14414i
$701$	0.686242	−	1.18861i	0.686242	−	1.18861i	−0.286803	−	0.957990i	$-0.592593\pi$
$701$	0.686242	−	1.18861i	0.686242	−	1.18861i	0.973045	−	0.230616i	$-0.0740741\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.393633	+	1.31482i	0.393633	+	1.31482i
$706$		0			0
$707$	−0.889034	+	2.06101i	−0.889034	+	2.06101i
$708$		0			0
$709$	0.0333522	+	0.572636i	0.0333522	+	0.572636i	0.973045	+	0.230616i	$0.0740741\pi$
$709$	0.0333522	+	0.572636i	0.0333522	+	0.572636i	−0.939693	+	0.342020i	$0.888889\pi$
$710$		0			0
$711$		0			0
$712$	−0.238329	+	1.35163i	−0.238329	+	1.35163i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$719$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$720$	−0.686242	−	0.727374i	−0.686242	−	0.727374i
$721$	0.317741	−	0.266617i	0.317741	−	0.266617i
$722$	0.893633	+	0.448799i	0.893633	+	0.448799i
$723$	1.86668	−	0.679415i	1.86668	−	0.679415i
$724$	1.97304	−	0.230616i	1.97304	−	0.230616i
$725$	0.0971586	−	1.66815i	0.0971586	−	1.66815i
$726$	0.396080	−	0.918216i	0.396080	−	0.918216i
$727$	−0.543613	−	0.576196i	−0.543613	−	0.576196i	0.396080	−	0.918216i	$-0.370370\pi$
$727$	−0.543613	−	0.576196i	−0.543613	−	0.576196i	−0.939693	+	0.342020i	$0.888889\pi$
$728$		0			0
$729$	0.766044	−	0.642788i	0.766044	−	0.642788i
$730$		0			0
$731$		0			0
$732$	0.313758	−	0.727374i	0.313758	−	0.727374i
$733$		0			0		0.0581448	−	0.998308i	$-0.481481\pi$
$733$		0			0		−0.0581448	+	0.998308i	$0.518519\pi$
$734$	0.993238	−	0.116093i	0.993238	−	0.116093i
$735$	−0.400679	+	0.145835i	−0.400679	+	0.145835i
$736$	1.59716	+	0.802123i	1.59716	+	0.802123i
$737$		0			0
$738$	−1.33549	−	1.41553i	−1.33549	−	1.41553i
$739$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$739$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.393633	+	1.31482i	0.393633	+	1.31482i	0.893633	+	0.448799i	$0.148148\pi$
$743$	0.393633	+	1.31482i	0.393633	+	1.31482i	−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$	0.115503	+	0.0135004i	0.115503	+	0.0135004i
$746$		0			0
$747$	−0.113155	+	1.94280i	−0.113155	+	1.94280i
$748$		0			0
$749$	0.137948	+	2.36847i	0.137948	+	2.36847i
$750$	0.766044	−	0.642788i	0.766044	−	0.642788i
$751$		0			0		0.396080	−	0.918216i	$-0.370370\pi$
$751$		0			0		−0.396080	+	0.918216i	$0.629630\pi$
$752$	−1.22650	+	0.615969i	−1.22650	+	0.615969i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.207391	−	1.17617i	0.207391	−	1.17617i
$757$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$757$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.342534	−	0.460103i	−0.342534	−	0.460103i	0.597159	−	0.802123i	$-0.296296\pi$
$761$	−0.342534	−	0.460103i	−0.342534	−	0.460103i	−0.939693	+	0.342020i	$0.888889\pi$
$762$	−0.116290			−0.116290
$763$	0.116038	−	0.0763195i	0.116038	−	0.0763195i
$764$		0			0
$765$		0			0
$766$	1.76604	−	0.642788i	1.76604	−	0.642788i
$767$		0			0
$768$	0.597159	−	0.802123i	0.597159	−	0.802123i
$769$	−0.819590	+	0.868715i	−0.819590	+	0.868715i	−0.993238	−	0.116093i	$-0.962963\pi$
$769$	−0.819590	+	0.868715i	−0.819590	+	0.868715i	0.173648	+	0.984808i	$0.444444\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$773$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$774$	1.17365	+	0.984808i	1.17365	+	0.984808i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.342534	−	0.460103i	−0.342534	−	0.460103i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.0971586	+	1.66815i	0.0971586	+	1.66815i
$784$	−0.213197	−	0.369268i	−0.213197	−	0.369268i
$785$		0			0
$786$		0			0
$787$	−0.893633	+	0.448799i	−0.893633	+	0.448799i	−0.835488	−	0.549509i	$-0.814815\pi$
$787$	−0.893633	+	0.448799i	−0.893633	+	0.448799i	−0.0581448	+	0.998308i	$0.518519\pi$
$788$		0			0
$789$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.973045	−	0.230616i	$-0.925926\pi$
$797$		0			0		0.973045	+	0.230616i	$0.0740741\pi$
$798$		0			0
$799$		0			0
$800$	0.766044	+	0.642788i	0.766044	+	0.642788i
$801$	1.36320	+	0.159336i	1.36320	+	0.159336i
$802$	1.17365	−	0.984808i	1.17365	−	0.984808i
$803$		0			0
$804$	−0.0996057	+	0.564892i	−0.0996057	+	0.564892i
$805$	−2.12013	+	0.247807i	−2.12013	+	0.247807i
$806$		0			0
$807$	1.97304	−	0.230616i	1.97304	−	0.230616i
$808$	1.28971	+	1.36702i	1.28971	+	1.36702i
$809$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$809$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$810$	−0.686242	+	0.727374i	−0.686242	+	0.727374i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	1.36952	+	1.45160i	1.36952	+	1.45160i
$813$		0			0
$814$		0			0
$815$	1.86668	−	0.218183i	1.86668	−	0.218183i
$816$		0			0
$817$		0			0
$818$	0.266044	−	0.223238i	0.266044	−	0.223238i
$819$		0			0
$820$	1.49079	+	1.25092i	1.49079	+	1.25092i
$821$	0.707900	+	1.64110i	0.707900	+	1.64110i	0.766044	+	0.642788i	$0.222222\pi$
$821$	0.707900	+	1.64110i	0.707900	+	1.64110i	−0.0581448	+	0.998308i	$0.518519\pi$
$822$		0			0
$823$	0.770807	+	0.182685i	0.770807	+	0.182685i	0.597159	−	0.802123i	$-0.296296\pi$
$823$	0.770807	+	0.182685i	0.770807	+	0.182685i	0.173648	+	0.984808i	$0.444444\pi$
$824$	−0.0996057	−	0.332706i	−0.0996057	−	0.332706i
$825$		0			0
$826$		0			0
$827$	−0.290162	+	1.64559i	−0.290162	+	1.64559i	0.396080	+	0.918216i	$0.370370\pi$
$827$	−0.290162	+	1.64559i	−0.290162	+	1.64559i	−0.686242	+	0.727374i	$0.740741\pi$
$828$	0.707900	−	1.64110i	0.707900	−	1.64110i
$829$	0.310355	+	1.76011i	0.310355	+	1.76011i	0.597159	+	0.802123i	$0.296296\pi$
$829$	0.310355	+	1.76011i	0.310355	+	1.76011i	−0.286803	+	0.957990i	$0.592593\pi$
$830$	−0.113155	−	1.94280i	−0.113155	−	1.94280i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.62593	+	0.385353i	−1.62593	+	0.385353i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.286803	−	0.957990i	$-0.407407\pi$
$839$		0			0		−0.286803	+	0.957990i	$0.592593\pi$
$840$	−0.0694434	+	1.19230i	−0.0694434	+	1.19230i
$841$	−1.49733	−	0.984808i	−1.49733	−	0.984808i
$842$	0.914900	+	1.22892i	0.914900	+	1.22892i
$843$	−0.396080	−	0.686030i	−0.396080	−	0.686030i
$844$		0			0
$845$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$846$	0.686242	+	1.18861i	0.686242	+	1.18861i
$847$	−1.12229	+	0.408481i	−1.12229	+	0.408481i
$848$		0			0
$849$	−0.0460600	−	0.106779i	−0.0460600	−	0.106779i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.597159	−	0.802123i	$-0.296296\pi$
$853$		0			0		−0.597159	+	0.802123i	$0.703704\pi$
$854$	−0.889034	+	0.323582i	−0.889034	+	0.323582i
$855$		0			0
$856$	1.86668	+	0.679415i	1.86668	+	0.679415i
$857$		0			0		0.835488	−	0.549509i	$-0.185185\pi$
$857$		0			0		−0.835488	+	0.549509i	$0.814815\pi$
$858$		0			0
$859$		0			0		−0.597159	−	0.802123i	$-0.703704\pi$
$859$		0			0		0.597159	+	0.802123i	$0.296296\pi$
$860$	−1.28004	−	0.841897i	−1.28004	−	0.841897i
$861$	−0.135143	+	2.32032i	−0.135143	+	2.32032i
$862$		0			0
$863$	0.993238	−	1.72034i	0.993238	−	1.72034i	0.396080	−	0.918216i	$-0.370370\pi$
$863$	0.993238	−	1.72034i	0.993238	−	1.72034i	0.597159	−	0.802123i	$-0.296296\pi$
$864$	−0.835488	−	0.549509i	−0.835488	−	0.549509i
$865$		0			0
$866$		0			0
$867$	−0.686242	+	0.727374i	−0.686242	+	0.727374i
$868$		0			0
$869$		0			0
$870$	−0.290162	−	1.64559i	−0.290162	−	1.64559i
$871$		0			0
$872$	−0.0201935	−	0.114523i	−0.0201935	−	0.114523i
$873$		0			0
$874$		0			0
$875$	−1.18624	−	0.138652i	−1.18624	−	0.138652i
$876$		0			0
$877$		0			0		−0.286803	−	0.957990i	$-0.592593\pi$
$877$		0			0		0.286803	+	0.957990i	$0.407407\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.0890830	−	0.0747496i	−0.0890830	−	0.0747496i	0.597159	−	0.802123i	$-0.296296\pi$
$881$	−0.0890830	−	0.0747496i	−0.0890830	−	0.0747496i	−0.686242	+	0.727374i	$0.740741\pi$
$882$	−0.356247	+	0.234307i	−0.356247	+	0.234307i
$883$	1.49079	−	1.25092i	1.49079	−	1.25092i	0.597159	−	0.802123i	$-0.296296\pi$
$883$	1.49079	−	1.25092i	1.49079	−	1.25092i	0.893633	−	0.448799i	$-0.148148\pi$
$884$		0			0
$885$		0			0
$886$	0.569728	−	0.0665916i	0.569728	−	0.0665916i
$887$	0.109277	−	1.87621i	0.109277	−	1.87621i	−0.286803	−	0.957990i	$-0.592593\pi$
$887$	0.109277	−	1.87621i	0.109277	−	1.87621i	0.396080	−	0.918216i	$-0.370370\pi$
$888$		0			0
$889$	0.0953099	+	0.101023i	0.0953099	+	0.101023i
$890$	−1.37248			−1.37248
$891$		0			0
$892$	−1.37248			−1.37248
$893$		0			0
$894$	0.115503	−	0.0135004i	0.115503	−	0.0135004i
$895$		0			0
$896$	−1.18624	+	0.138652i	−1.18624	+	0.138652i
$897$		0			0
$898$	−1.67948	−	0.843467i	−1.67948	−	0.843467i
$899$		0			0
$900$	0.597159	−	0.802123i	0.597159	−	0.802123i
$901$		0			0
$902$		0			0
$903$	−0.106393	−	1.82670i	−0.106393	−	1.82670i
$904$		0			0
$905$	0.569728	+	1.90302i	0.569728	+	1.90302i
$906$		0			0
$907$	1.97304	+	0.230616i	1.97304	+	0.230616i	1.00000			$0$
$907$	1.97304	+	0.230616i	1.97304	+	0.230616i	0.973045	+	0.230616i	$0.0740741\pi$
$908$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$909$	1.28971	−	1.36702i	1.28971	−	1.36702i
$910$		0			0
$911$		0			0		−0.0581448	−	0.998308i	$-0.518519\pi$
$911$		0			0		0.0581448	+	0.998308i	$0.481481\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.770807	+	0.182685i	0.770807	+	0.182685i
$916$	−1.62593	+	0.385353i	−1.62593	+	0.385353i
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$	−0.512593	+	1.71218i	−0.512593	+	1.71218i
$921$	−1.49324	−	0.982118i	−1.49324	−	0.982118i
$922$	1.65968	+	1.09159i	1.65968	+	1.09159i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$927$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$928$	1.57020	−	0.571507i	1.57020	−	0.571507i
$929$	0.914900	−	1.22892i	0.914900	−	1.22892i	−0.0581448	−	0.998308i	$-0.518519\pi$
$929$	0.914900	−	1.22892i	0.914900	−	1.22892i	0.973045	−	0.230616i	$-0.0740741\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.914900	−	1.22892i	0.914900	−	1.22892i
$935$		0			0
$936$		0			0
$937$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$937$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$938$	0.572366	−	0.376451i	0.572366	−	0.376451i
$939$		0			0
$940$	−0.819590	−	1.10090i	−0.819590	−	1.10090i
$941$	−1.62593	−	1.06939i	−1.62593	−	1.06939i	−0.939693	−	0.342020i	$-0.888889\pi$
$941$	−1.62593	−	1.06939i	−1.62593	−	1.06939i	−0.686242	−	0.727374i	$-0.740741\pi$
$942$		0			0
$943$	−0.997553	+	3.33206i	−0.997553	+	3.33206i
$944$		0			0
$945$	1.19432			1.19432
$946$		0			0
$947$	1.89363	−	0.448799i	1.89363	−	0.448799i	0.893633	−	0.448799i	$-0.148148\pi$
$947$	1.89363	−	0.448799i	1.89363	−	0.448799i	1.00000			$0$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$953$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.893633	+	0.448799i	0.893633	+	0.448799i
$961$	0.396080	+	0.918216i	0.396080	+	0.918216i
$962$		0			0
$963$	0.569728	−	1.90302i	0.569728	−	1.90302i
$964$	−1.52173	+	1.27688i	−1.52173	+	1.27688i
$965$		0			0
$966$	−2.00583	+	0.730063i	−2.00583	+	0.730063i
$967$	−1.77518	+	0.207489i	−1.77518	+	0.207489i	−0.939693	−	0.342020i	$-0.888889\pi$
$967$	−1.77518	+	0.207489i	−1.77518	+	0.207489i	−0.835488	+	0.549509i	$0.814815\pi$
$968$	−0.0581448	+	0.998308i	−0.0581448	+	0.998308i
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$973$		0			0
$974$	0.686242	+	0.727374i	0.686242	+	0.727374i
$975$		0			0
$976$	−0.0460600	+	0.790819i	−0.0460600	+	0.790819i
$977$		0			0		0.993238	−	0.116093i	$-0.0370370\pi$
$977$		0			0		−0.993238	+	0.116093i	$0.962963\pi$
$978$	1.76604	−	0.642788i	1.76604	−	0.642788i
$979$		0			0
$980$	0.326636	−	0.274080i	0.326636	−	0.274080i
$981$	−0.113155	+	0.0268182i	−0.113155	+	0.0268182i
$982$		0			0
$983$	0.473045	+	1.09664i	0.473045	+	1.09664i	0.973045	+	0.230616i	$0.0740741\pi$
$983$	0.473045	+	1.09664i	0.473045	+	1.09664i	−0.500000	+	0.866025i	$0.666667\pi$
$984$	1.73909	+	0.873403i	1.73909	+	0.873403i
$985$		0			0
$986$		0			0
$987$	0.470122	−	1.57032i	0.470122	−	1.57032i
$988$		0			0
$989$	0.475492	−	2.69665i	0.475492	−	2.69665i
$990$		0			0
$991$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$991$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.558145	−	1.86433i	−0.558145	−	1.86433i
$997$		0			0		0.973045	−	0.230616i	$-0.0740741\pi$
$997$		0			0		−0.973045	+	0.230616i	$0.925926\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.1.bp.b.1399.1	yes	18
4.3	odd	2		1620.1.bp.a.1399.1	yes	18
5.4	even	2		1620.1.bp.a.1399.1	yes	18
20.19	odd	2	CM	1620.1.bp.b.1399.1	yes	18
81.70	even	27	inner	1620.1.bp.b.799.1	yes	18
324.151	odd	54		1620.1.bp.a.799.1	✓	18
405.394	even	54		1620.1.bp.a.799.1	✓	18
1620.799	odd	54	inner	1620.1.bp.b.799.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.1.bp.a.799.1	✓	18	324.151	odd	54
1620.1.bp.a.799.1	✓	18	405.394	even	54
1620.1.bp.a.1399.1	yes	18	4.3	odd	2
1620.1.bp.a.1399.1	yes	18	5.4	even	2
1620.1.bp.b.799.1	yes	18	81.70	even	27	inner
1620.1.bp.b.799.1	yes	18	1620.799	odd	54	inner
1620.1.bp.b.1399.1	yes	18	1.1	even	1	trivial
1620.1.bp.b.1399.1	yes	18	20.19	odd	2	CM

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1620.bp (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686242 - 0.727374i) q^{2} +(0.396080 - 0.918216i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-0.993238 + 0.116093i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(1.06728 + 0.536009i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-0.686242 - 0.727374i) q^{9} +O(q^{10})\)	\(q+(-0.686242 - 0.727374i) q^{2} +(0.396080 - 0.918216i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-0.993238 + 0.116093i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(1.06728 + 0.536009i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-0.686242 - 0.727374i) q^{9} +(0.766044 + 0.642788i) q^{10} +(0.893633 + 0.448799i) q^{12} +(-0.342534 - 1.14414i) q^{14} +(-0.286803 + 0.957990i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.0581448 + 0.998308i) q^{18} +(-0.0581448 - 0.998308i) q^{20} +(0.914900 - 0.767692i) q^{21} +(1.59716 - 0.802123i) q^{23} +(-0.286803 - 0.957990i) q^{24} +(0.973045 - 0.230616i) q^{25} +(-0.939693 + 0.342020i) q^{27} +(-0.597159 + 1.03431i) q^{28} +(0.479241 - 1.60078i) q^{29} +(0.893633 - 0.448799i) q^{30} +(0.597159 + 0.802123i) q^{32} +(-1.12229 - 0.408481i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-0.686242 + 0.727374i) q^{40} +(-1.33549 + 1.41553i) q^{41} +(-1.18624 - 0.138652i) q^{42} +(0.914900 - 1.22892i) q^{43} +(0.766044 + 0.642788i) q^{45} +(-1.67948 - 0.611281i) q^{46} +(1.14669 - 0.754192i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.254625 + 0.342020i) q^{49} +(-0.835488 - 0.549509i) q^{50} +(0.893633 + 0.448799i) q^{54} +(1.16212 - 0.275428i) q^{56} +(-1.49324 + 0.749932i) q^{58} +(-0.939693 - 0.342020i) q^{60} +(-0.0460600 - 0.790819i) q^{61} +(-0.342534 - 1.14414i) q^{63} +(0.173648 - 0.984808i) q^{64} +(0.164512 + 0.549509i) q^{67} +(-0.103920 - 1.78424i) q^{69} +(0.473045 + 1.09664i) q^{70} +(-0.993238 - 0.116093i) q^{72} +(0.173648 - 0.984808i) q^{75} +1.00000 q^{80} +(-0.0581448 + 0.998308i) q^{81} +1.94609 q^{82} +(-1.33549 - 1.41553i) q^{83} +(0.713197 + 0.957990i) q^{84} +(-1.52173 + 0.177865i) q^{86} +(-1.28004 - 1.07408i) q^{87} +(-1.05138 + 0.882215i) q^{89} +(-0.0581448 - 0.998308i) q^{90} +(0.707900 + 1.64110i) q^{92} +(-1.33549 - 0.316516i) q^{94} +(0.973045 - 0.230616i) q^{96} +(0.0740425 - 0.419916i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q + 18 q^{23} - 9 q^{41} - 9 q^{42} - 9 q^{48} - 9 q^{58} + 18 q^{67} - 9 q^{69} - 9 q^{70} + 18 q^{80} - 9 q^{83} + 18 q^{84} - 9 q^{94}+O(q^{100}) \) 18 * q + 18 * q^23 - 9 * q^41 - 9 * q^42 - 9 * q^48 - 9 * q^58 + 18 * q^67 - 9 * q^69 - 9 * q^70 + 18 * q^80 - 9 * q^83 + 18 * q^84 - 9 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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