LMFDB - Embedded newform 2760.1.cm.b.2309.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2760,1,Mod(29,2760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2760, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 11, 18]))

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

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

chi := DirichletCharacter("2760.29");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2760.cm (of order $22$, degree $10$, 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:	$1.37741943487$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{11}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{11} - \cdots)$

Embedding invariants

Embedding label			2309.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	2760.2309
Dual form			2760.1.cm.b.869.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(-0.273100 - 0.0801894i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-0.345139 - 0.755750i) q^{13} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-1.10181 - 0.708089i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(0.654861 + 0.755750i) q^{20} +0.284630 q^{22} +(-0.142315 + 0.989821i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(0.544078 + 0.627899i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(1.61435 + 1.03748i) q^{29} +(0.415415 - 0.909632i) q^{30} +(-1.10181 + 1.27155i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-0.118239 - 0.258908i) q^{33} +(1.25667 + 0.368991i) q^{34} +(0.415415 + 0.909632i) q^{36} +(-0.273100 + 1.89945i) q^{37} +(0.345139 - 0.755750i) q^{39} +(-0.841254 - 0.540641i) q^{40} +(0.544078 + 0.627899i) q^{43} +(-0.273100 + 0.0801894i) q^{44} -1.00000 q^{45} +(-0.142315 - 0.989821i) q^{46} -1.30972 q^{47} +(0.959493 - 0.281733i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(0.841254 - 0.540641i) q^{50} +(-0.186393 - 1.29639i) q^{51} +(-0.698939 - 0.449181i) q^{52} +(0.654861 - 0.755750i) q^{54} +(0.0405070 - 0.281733i) q^{55} +(-1.84125 - 0.540641i) q^{58} +(0.118239 + 0.258908i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(0.698939 - 1.53046i) q^{62} +(-0.142315 - 0.989821i) q^{64} +(0.698939 - 0.449181i) q^{65} +(0.186393 + 0.215109i) q^{66} +(1.61435 - 0.474017i) q^{67} -1.30972 q^{68} +(-0.841254 + 0.540641i) q^{69} +(-0.654861 - 0.755750i) q^{72} +(-0.273100 - 1.89945i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(-0.118239 + 0.822373i) q^{78} +(0.698939 + 1.53046i) q^{79} +(0.959493 + 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.544078 - 1.19136i) q^{85} +(-0.698939 - 0.449181i) q^{86} +(0.273100 + 1.89945i) q^{87} +(0.239446 - 0.153882i) q^{88} +(0.959493 - 0.281733i) q^{90} +(0.415415 + 0.909632i) q^{92} -1.68251 q^{93} +(1.25667 - 0.368991i) q^{94} +(-0.841254 + 0.540641i) q^{96} +(0.841254 + 0.540641i) q^{98} +(0.118239 - 0.258908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 + q^3 - q^4 + q^5 + q^6 - q^8 - q^9	$ 10 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{8} - q^{9} + q^{10} + 2 q^{11} + q^{12} - 9 q^{13} - q^{15} - q^{16} - 2 q^{17} - q^{18} + q^{20} + 2 q^{22} - q^{23} - 10 q^{24} - q^{25} + 2 q^{26} + q^{27} + 2 q^{29} - q^{30} - 2 q^{31} - q^{32} - 2 q^{33} - 2 q^{34} - q^{36} + 2 q^{37} + 9 q^{39} + q^{40} + 2 q^{43} + 2 q^{44} - 10 q^{45} - q^{46} - 2 q^{47} + q^{48} - q^{49} - q^{50} + 2 q^{51} + 2 q^{52} + q^{54} + 9 q^{55} - 9 q^{58} + 2 q^{59} - q^{60} - 2 q^{62} - q^{64} - 2 q^{65} - 2 q^{66} + 2 q^{67} - 2 q^{68} + q^{69} - q^{72} + 2 q^{74} + q^{75} - 2 q^{78} - 2 q^{79} + q^{80} - q^{81} + 2 q^{85} + 2 q^{86} - 2 q^{87} + 2 q^{88} + q^{90} - q^{92} + 2 q^{93} - 2 q^{94} + q^{96} - q^{98} + 2 q^{99}+O(q^{100}) $ 10 * q - q^2 + q^3 - q^4 + q^5 + q^6 - q^8 - q^9 + q^10 + 2 * q^11 + q^12 - 9 * q^13 - q^15 - q^16 - 2 * q^17 - q^18 + q^20 + 2 * q^22 - q^23 - 10 * q^24 - q^25 + 2 * q^26 + q^27 + 2 * q^29 - q^30 - 2 * q^31 - q^32 - 2 * q^33 - 2 * q^34 - q^36 + 2 * q^37 + 9 * q^39 + q^40 + 2 * q^43 + 2 * q^44 - 10 * q^45 - q^46 - 2 * q^47 + q^48 - q^49 - q^50 + 2 * q^51 + 2 * q^52 + q^54 + 9 * q^55 - 9 * q^58 + 2 * q^59 - q^60 - 2 * q^62 - q^64 - 2 * q^65 - 2 * q^66 + 2 * q^67 - 2 * q^68 + q^69 - q^72 + 2 * q^74 + q^75 - 2 * q^78 - 2 * q^79 + q^80 - q^81 + 2 * q^85 + 2 * q^86 - 2 * q^87 + 2 * q^88 + q^90 - q^92 + 2 * q^93 - 2 * q^94 + q^96 - q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2760\mathbb{Z}\right)^\times$.

$n$	$1201$	$1381$	$1657$	$1841$	$2071$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$2$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$3$	0.654861	+	0.755750i	0.654861	+	0.755750i
$3$	0.654861	+	0.755750i	0.654861	+	0.755750i
$4$	0.841254	−	0.540641i	0.841254	−	0.540641i
$5$	0.142315	+	0.989821i	0.142315	+	0.989821i
$5$	0.142315	+	0.989821i	0.142315	+	0.989821i
$6$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$7$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$7$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$8$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$9$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$10$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$11$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i	0.142315	−	0.989821i	$-0.454545\pi$
$11$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i	−0.415415	+	0.909632i	$0.636364\pi$
$12$	0.959493	+	0.281733i	0.959493	+	0.281733i
$13$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$13$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$14$		0			0
$15$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$16$	0.415415	−	0.909632i	0.415415	−	0.909632i
$17$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$17$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$18$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$19$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$19$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$20$	0.654861	+	0.755750i	0.654861	+	0.755750i
$21$		0			0
$22$	0.284630			0.284630
$23$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$23$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$24$	−1.00000			−1.00000
$25$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$26$	0.544078	+	0.627899i	0.544078	+	0.627899i
$27$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$28$		0			0
$29$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.959493	+	0.281733i	$0.0909091\pi$
$29$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.654861	+	0.755750i	$0.272727\pi$
$30$	0.415415	−	0.909632i	0.415415	−	0.909632i
$31$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$31$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$32$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$33$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$34$	1.25667	+	0.368991i	1.25667	+	0.368991i
$35$		0			0
$36$	0.415415	+	0.909632i	0.415415	+	0.909632i
$37$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$37$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$38$		0			0
$39$	0.345139	−	0.755750i	0.345139	−	0.755750i
$40$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$41$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$41$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$42$		0			0
$43$	0.544078	+	0.627899i	0.544078	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$43$	0.544078	+	0.627899i	0.544078	+	0.627899i	−0.415415	+	0.909632i	$0.636364\pi$
$44$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$45$	−1.00000			−1.00000
$46$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$47$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$47$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$48$	0.959493	−	0.281733i	0.959493	−	0.281733i
$49$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$50$	0.841254	−	0.540641i	0.841254	−	0.540641i
$51$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$52$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$53$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$53$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$54$	0.654861	−	0.755750i	0.654861	−	0.755750i
$55$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$56$		0			0
$57$		0			0
$58$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$59$	0.118239	+	0.258908i	0.118239	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$59$	0.118239	+	0.258908i	0.118239	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$60$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$61$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$61$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$62$	0.698939	−	1.53046i	0.698939	−	1.53046i
$63$		0			0
$64$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$65$	0.698939	−	0.449181i	0.698939	−	0.449181i
$66$	0.186393	+	0.215109i	0.186393	+	0.215109i
$67$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$67$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$68$	−1.30972			−1.30972
$69$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$70$		0			0
$71$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$71$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$72$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$73$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$73$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$74$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$75$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$76$		0			0
$77$		0			0
$78$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$79$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$79$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$80$	0.959493	+	0.281733i	0.959493	+	0.281733i
$81$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$82$		0			0
$83$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$83$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$84$		0			0
$85$	0.544078	−	1.19136i	0.544078	−	1.19136i
$86$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$87$	0.273100	+	1.89945i	0.273100	+	1.89945i
$88$	0.239446	−	0.153882i	0.239446	−	0.153882i
$89$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$89$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$90$	0.959493	−	0.281733i	0.959493	−	0.281733i
$91$		0			0
$92$	0.415415	+	0.909632i	0.415415	+	0.909632i
$93$	−1.68251			−1.68251
$94$	1.25667	−	0.368991i	1.25667	−	0.368991i
$95$		0			0
$96$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$97$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$97$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$98$	0.841254	+	0.540641i	0.841254	+	0.540641i
$99$	0.118239	−	0.258908i	0.118239	−	0.258908i
$100$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$101$	0.239446	−	1.66538i	0.239446	−	1.66538i	−0.415415	−	0.909632i	$-0.636364\pi$
$101$	0.239446	−	1.66538i	0.239446	−	1.66538i	0.654861	−	0.755750i	$-0.272727\pi$
$102$	0.544078	+	1.19136i	0.544078	+	1.19136i
$103$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$103$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$104$	0.797176	+	0.234072i	0.797176	+	0.234072i
$105$		0			0
$106$		0			0
$107$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$107$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$108$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$109$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$109$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$110$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$111$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$112$		0			0
$113$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$113$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$114$		0			0
$115$	−1.00000			−1.00000
$116$	1.91899			1.91899
$117$	0.797176	−	0.234072i	0.797176	−	0.234072i
$118$	−0.186393	−	0.215109i	−0.186393	−	0.215109i
$119$		0			0
$120$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$121$	−0.773100	−	0.496841i	−0.773100	−	0.496841i
$122$		0			0
$123$		0			0
$124$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$125$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$126$		0			0
$127$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$127$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$128$	0.415415	+	0.909632i	0.415415	+	0.909632i
$129$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$130$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$131$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$131$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$132$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$133$		0			0
$134$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$135$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$136$	1.25667	−	0.368991i	1.25667	−	0.368991i
$137$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$137$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$138$	0.654861	−	0.755750i	0.654861	−	0.755750i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		0			0
$141$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$142$		0			0
$143$	0.0336545	+	0.234072i	0.0336545	+	0.234072i
$144$	0.841254	+	0.540641i	0.841254	+	0.540641i
$145$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$146$		0			0
$147$	0.142315	−	0.989821i	0.142315	−	0.989821i
$148$	0.797176	+	1.74557i	0.797176	+	1.74557i
$149$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.959493	−	0.281733i	$-0.0909091\pi$
$149$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.654861	+	0.755750i	$0.272727\pi$
$150$	0.959493	+	0.281733i	0.959493	+	0.281733i
$151$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$151$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$152$		0			0
$153$	0.857685	−	0.989821i	0.857685	−	0.989821i
$154$		0			0
$155$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$156$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$157$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.142315	−	0.989821i	$-0.454545\pi$
$157$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.959493	+	0.281733i	$0.0909091\pi$
$158$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$159$		0			0
$160$	−1.00000			−1.00000
$161$		0			0
$162$	1.00000			1.00000
$163$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$163$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$164$		0			0
$165$	0.239446	−	0.153882i	0.239446	−	0.153882i
$166$		0			0
$167$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$167$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$168$		0			0
$169$	0.202824	−	0.234072i	0.202824	−	0.234072i
$170$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$171$		0			0
$172$	0.797176	+	0.234072i	0.797176	+	0.234072i
$173$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$173$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$174$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$175$		0			0
$176$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$177$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$178$		0			0
$179$	0.239446	+	1.66538i	0.239446	+	1.66538i	0.654861	+	0.755750i	$0.272727\pi$
$179$	0.239446	+	1.66538i	0.239446	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$180$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$181$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$181$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$182$		0			0
$183$		0			0
$184$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$185$	−1.91899			−1.91899
$186$	1.61435	−	0.474017i	1.61435	−	0.474017i
$187$	0.244123	+	0.281733i	0.244123	+	0.281733i
$188$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$189$		0			0
$190$		0			0
$191$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$191$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$192$	0.654861	−	0.755750i	0.654861	−	0.755750i
$193$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$193$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$194$		0			0
$195$	0.797176	+	0.234072i	0.797176	+	0.234072i
$196$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$197$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$197$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$198$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$199$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$199$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$200$	0.415415	−	0.909632i	0.415415	−	0.909632i
$201$	1.41542	+	0.909632i	1.41542	+	0.909632i
$202$	0.239446	+	1.66538i	0.239446	+	1.66538i
$203$		0			0
$204$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$205$		0			0
$206$		0			0
$207$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$208$	−0.830830			−0.830830
$209$		0			0
$210$		0			0
$211$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$211$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$216$	0.142315	−	0.989821i	0.142315	−	0.989821i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$221$	−0.154861	+	1.07708i	−0.154861	+	1.07708i
$222$	1.25667	−	1.45027i	1.25667	−	1.45027i
$223$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$223$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$224$		0			0
$225$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$226$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$227$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$227$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	0.959493	−	0.281733i	0.959493	−	0.281733i
$231$		0			0
$232$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$233$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$233$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$234$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$235$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$236$	0.239446	+	0.153882i	0.239446	+	0.153882i
$237$	−0.698939	+	1.53046i	−0.698939	+	1.53046i
$238$		0			0
$239$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$239$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$240$	0.415415	+	0.909632i	0.415415	+	0.909632i
$241$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$241$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$242$	0.881761	+	0.258908i	0.881761	+	0.258908i
$243$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$244$		0			0
$245$	0.654861	−	0.755750i	0.654861	−	0.755750i
$246$		0			0
$247$		0			0
$248$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$249$		0			0
$250$	0.654861	+	0.755750i	0.654861	+	0.755750i
$251$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−0.841254	+	0.540641i	$0.818182\pi$
$251$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−1.00000			$1.00000\pi$
$252$		0			0
$253$	0.118239	−	0.258908i	0.118239	−	0.258908i
$254$		0			0
$255$	1.25667	−	0.368991i	1.25667	−	0.368991i
$256$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$257$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$257$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$258$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$259$		0			0
$260$	0.345139	−	0.755750i	0.345139	−	0.755750i
$261$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$262$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$263$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$263$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$264$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$265$		0			0
$266$		0			0
$267$		0			0
$268$	1.10181	−	1.27155i	1.10181	−	1.27155i
$269$	0.118239	−	0.258908i	0.118239	−	0.258908i	−0.841254	−	0.540641i	$-0.818182\pi$
$269$	0.118239	−	0.258908i	0.118239	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$270$	0.841254	+	0.540641i	0.841254	+	0.540641i
$271$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$271$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$272$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$273$		0			0
$274$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$275$	0.284630			0.284630
$276$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$277$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$277$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$278$		0			0
$279$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$280$		0			0
$281$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$281$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$282$	1.10181	+	0.708089i	1.10181	+	0.708089i
$283$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$283$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$284$		0			0
$285$		0			0
$286$	−0.0982369	−	0.215109i	−0.0982369	−	0.215109i
$287$		0			0
$288$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$289$	0.297176	+	0.650724i	0.297176	+	0.650724i
$290$	0.273100	−	1.89945i	0.273100	−	1.89945i
$291$		0			0
$292$		0			0
$293$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$293$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$294$	0.142315	+	0.989821i	0.142315	+	0.989821i
$295$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$296$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$297$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$298$	−1.68251			−1.68251
$299$	0.797176	−	0.234072i	0.797176	−	0.234072i
$300$	−1.00000			−1.00000
$301$		0			0
$302$	1.25667	+	1.45027i	1.25667	+	1.45027i
$303$	1.41542	−	0.909632i	1.41542	−	0.909632i
$304$		0			0
$305$		0			0
$306$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$307$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$307$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$308$		0			0
$309$		0			0
$310$	1.61435	+	0.474017i	1.61435	+	0.474017i
$311$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$311$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$312$	0.345139	+	0.755750i	0.345139	+	0.755750i
$313$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$313$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$314$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$315$		0			0
$316$	1.41542	+	0.909632i	1.41542	+	0.909632i
$317$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$317$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$318$		0			0
$319$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$320$	0.959493	−	0.281733i	0.959493	−	0.281733i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$325$	0.544078	+	0.627899i	0.544078	+	0.627899i
$326$	0.239446	−	0.153882i	0.239446	−	0.153882i
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$331$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$331$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$332$		0			0
$333$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$334$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$335$	0.698939	+	1.53046i	0.698939	+	1.53046i
$336$		0			0
$337$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$337$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$338$	−0.128663	+	0.281733i	−0.128663	+	0.281733i
$339$	1.61435	+	1.03748i	1.61435	+	1.03748i
$340$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$341$	0.402869	−	0.258908i	0.402869	−	0.258908i
$342$		0			0
$343$		0			0
$344$	−0.830830			−0.830830
$345$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$346$		0			0
$347$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$347$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$348$	1.25667	+	1.45027i	1.25667	+	1.45027i
$349$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$349$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$350$		0			0
$351$	0.698939	+	0.449181i	0.698939	+	0.449181i
$352$	0.118239	−	0.258908i	0.118239	−	0.258908i
$353$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$353$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$354$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$359$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$359$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$360$	0.654861	−	0.755750i	0.654861	−	0.755750i
$361$	0.415415	−	0.909632i	0.415415	−	0.909632i
$362$		0			0
$363$	−0.130785	−	0.909632i	−0.130785	−	0.909632i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	0.841254	+	0.540641i	0.841254	+	0.540641i
$369$		0			0
$370$	1.84125	−	0.540641i	1.84125	−	0.540641i
$371$		0			0
$372$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$373$	0.118239	+	0.822373i	0.118239	+	0.822373i	0.959493	+	0.281733i	$0.0909091\pi$
$373$	0.118239	+	0.822373i	0.118239	+	0.822373i	−0.841254	+	0.540641i	$0.818182\pi$
$374$	−0.313607	−	0.201543i	−0.313607	−	0.201543i
$375$	0.415415	−	0.909632i	0.415415	−	0.909632i
$376$	0.857685	−	0.989821i	0.857685	−	0.989821i
$377$	0.226900	−	1.57812i	0.226900	−	1.57812i
$378$		0			0
$379$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$379$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$383$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$384$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$385$		0			0
$386$		0			0
$387$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$388$		0			0
$389$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$389$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$390$	−0.830830			−0.830830
$391$	0.857685	−	0.989821i	0.857685	−	0.989821i
$392$	1.00000			1.00000
$393$	1.25667	−	0.368991i	1.25667	−	0.368991i
$394$		0			0
$395$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$396$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$397$	0.239446	+	0.153882i	0.239446	+	0.153882i	0.654861	−	0.755750i	$-0.272727\pi$
$397$	0.239446	+	0.153882i	0.239446	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$398$	0.345139	−	0.755750i	0.345139	−	0.755750i
$399$		0			0
$400$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$401$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$401$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$402$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$403$	1.34125	+	0.393828i	1.34125	+	0.393828i
$404$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$405$	0.142315	−	0.989821i	0.142315	−	0.989821i
$406$		0			0
$407$	0.226900	−	0.496841i	0.226900	−	0.496841i
$408$	1.10181	+	0.708089i	1.10181	+	0.708089i
$409$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$409$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$410$		0			0
$411$	1.10181	+	1.27155i	1.10181	+	1.27155i
$412$		0			0
$413$		0			0
$414$	1.00000			1.00000
$415$		0			0
$416$	0.797176	−	0.234072i	0.797176	−	0.234072i
$417$		0			0
$418$		0			0
$419$	0.118239	+	0.822373i	0.118239	+	0.822373i	0.959493	+	0.281733i	$0.0909091\pi$
$419$	0.118239	+	0.822373i	0.118239	+	0.822373i	−0.841254	+	0.540641i	$0.818182\pi$
$420$		0			0
$421$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$421$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$422$		0			0
$423$	0.186393	−	1.29639i	0.186393	−	1.29639i
$424$		0			0
$425$	1.25667	+	0.368991i	1.25667	+	0.368991i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.154861	+	0.178719i	−0.154861	+	0.178719i
$430$	0.345139	−	0.755750i	0.345139	−	0.755750i
$431$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$431$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$432$	0.142315	+	0.989821i	0.142315	+	0.989821i
$433$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$433$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$434$		0			0
$435$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$439$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$440$	0.186393	+	0.215109i	0.186393	+	0.215109i
$441$	0.841254	−	0.540641i	0.841254	−	0.540641i
$442$	−0.154861	−	1.07708i	−0.154861	−	1.07708i
$443$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$443$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$444$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$445$		0			0
$446$		0			0
$447$	0.698939	+	1.53046i	0.698939	+	1.53046i
$448$		0			0
$449$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$449$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$450$	0.415415	+	0.909632i	0.415415	+	0.909632i
$451$		0			0
$452$	1.25667	−	1.45027i	1.25667	−	1.45027i
$453$	0.797176	−	1.74557i	0.797176	−	1.74557i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$457$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$458$		0			0
$459$	1.30972			1.30972
$460$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$461$	1.30972			1.30972			0.654861	−	0.755750i	$-0.272727\pi$
$461$	1.30972			1.30972			0.654861	+	0.755750i	$0.272727\pi$
$462$		0			0
$463$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$463$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$464$	1.61435	−	1.03748i	1.61435	−	1.03748i
$465$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$466$	0.698939	+	0.449181i	0.698939	+	0.449181i
$467$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$467$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$468$	0.544078	−	0.627899i	0.544078	−	0.627899i
$469$		0			0
$470$	0.544078	+	1.19136i	0.544078	+	1.19136i
$471$	1.25667	+	0.368991i	1.25667	+	0.368991i
$472$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$473$	−0.0982369	−	0.215109i	−0.0982369	−	0.215109i
$474$	0.239446	−	1.66538i	0.239446	−	1.66538i
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$479$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$480$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$481$	1.52977	−	0.449181i	1.52977	−	0.449181i
$482$	−0.284630			−0.284630
$483$		0			0
$484$	−0.918986			−0.918986
$485$		0			0
$486$	0.654861	+	0.755750i	0.654861	+	0.755750i
$487$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$487$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$488$		0			0
$489$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$490$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$491$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	0.142315	+	0.989821i	$0.454545\pi$
$491$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	−1.00000			$\pi$
$492$		0			0
$493$	−1.04408	−	2.28621i	−1.04408	−	2.28621i
$494$		0			0
$495$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$496$	0.698939	+	1.53046i	0.698939	+	1.53046i
$497$		0			0
$498$		0			0
$499$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$499$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$500$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$501$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$502$	1.61435	−	1.03748i	1.61435	−	1.03748i
$503$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$503$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$504$		0			0
$505$	1.68251			1.68251
$506$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$507$	0.309721			0.309721
$508$		0			0
$509$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$509$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$510$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$511$		0			0
$512$	0.841254	+	0.540641i	0.841254	+	0.540641i
$513$		0			0
$514$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$515$		0			0
$516$	0.345139	+	0.755750i	0.345139	+	0.755750i
$517$	0.357685	+	0.105026i	0.357685	+	0.105026i
$518$		0			0
$519$		0			0
$520$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$521$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$521$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$522$	0.797176	−	1.74557i	0.797176	−	1.74557i
$523$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.959493	+	0.281733i	$0.0909091\pi$
$523$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.654861	+	0.755750i	$0.272727\pi$
$524$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$525$		0			0
$526$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$527$	2.11435	−	0.620830i	2.11435	−	0.620830i
$528$	−0.284630			−0.284630
$529$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$530$		0			0
$531$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.698939	+	1.53046i	−0.698939	+	1.53046i
$537$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$538$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$539$	0.118239	+	0.258908i	0.118239	+	0.258908i
$540$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$541$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$541$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$542$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$543$		0			0
$544$	0.857685	−	0.989821i	0.857685	−	0.989821i
$545$		0			0
$546$		0			0
$547$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	−0.841254	−	0.540641i	$-0.818182\pi$
$547$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	0.654861	−	0.755750i	$-0.272727\pi$
$548$	1.41542	−	0.909632i	1.41542	−	0.909632i
$549$		0			0
$550$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$551$		0			0
$552$	0.142315	−	0.989821i	0.142315	−	0.989821i
$553$		0			0
$554$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$555$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$556$		0			0
$557$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$557$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$558$	1.41542	+	0.909632i	1.41542	+	0.909632i
$559$	0.286752	−	0.627899i	0.286752	−	0.627899i
$560$		0			0
$561$	−0.0530529	+	0.368991i	−0.0530529	+	0.368991i
$562$		0			0
$563$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$563$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$564$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$565$	0.797176	+	1.74557i	0.797176	+	1.74557i
$566$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$567$		0			0
$568$		0			0
$569$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$569$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$570$		0			0
$571$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$571$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$572$	0.154861	+	0.178719i	0.154861	+	0.178719i
$573$		0			0
$574$		0			0
$575$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$576$	1.00000			1.00000
$577$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$577$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$578$	−0.468468	−	0.540641i	−0.468468	−	0.540641i
$579$		0			0
$580$	0.273100	+	1.89945i	0.273100	+	1.89945i
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.345139	+	0.755750i	0.345139	+	0.755750i
$586$		0			0
$587$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$587$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$588$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$589$		0			0
$590$	0.186393	−	0.215109i	0.186393	−	0.215109i
$591$		0			0
$592$	1.61435	+	1.03748i	1.61435	+	1.03748i
$593$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$593$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$594$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$595$		0			0
$596$	1.61435	−	0.474017i	1.61435	−	0.474017i
$597$	−0.830830			−0.830830
$598$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	0.959493	−	0.281733i	0.959493	−	0.281733i
$601$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$601$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$602$		0			0
$603$	0.239446	+	1.66538i	0.239446	+	1.66538i
$604$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$605$	0.381761	−	0.835939i	0.381761	−	0.835939i
$606$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$607$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$607$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.452036	+	0.989821i	0.452036	+	0.989821i
$612$	0.186393	−	1.29639i	0.186393	−	1.29639i
$613$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	0.142315	+	0.989821i	$0.454545\pi$
$613$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	−1.00000			$\pi$
$614$	0.797176	−	1.74557i	0.797176	−	1.74557i
$615$		0			0
$616$		0			0
$617$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$617$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$618$		0			0
$619$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$619$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$620$	−1.68251			−1.68251
$621$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$622$		0			0
$623$		0			0
$624$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$625$	0.841254	−	0.540641i	0.841254	−	0.540641i
$626$		0			0
$627$		0			0
$628$	0.544078	−	1.19136i	0.544078	−	1.19136i
$629$	1.64589	−	1.89945i	1.64589	−	1.89945i
$630$		0			0
$631$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$631$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$632$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$638$	0.459493	+	0.295298i	0.459493	+	0.295298i
$639$		0			0
$640$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$641$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$641$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$642$		0			0
$643$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$643$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$644$		0			0
$645$	−0.830830			−0.830830
$646$		0			0
$647$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$647$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$648$	0.841254	−	0.540641i	0.841254	−	0.540641i
$649$	−0.0115295	−	0.0801894i	−0.0115295	−	0.0801894i
$650$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$651$		0			0
$652$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$653$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$653$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$654$		0			0
$655$	1.25667	+	0.368991i	1.25667	+	0.368991i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.544078	−	0.627899i	0.544078	−	0.627899i	−0.415415	−	0.909632i	$-0.636364\pi$
$659$	0.544078	−	0.627899i	0.544078	−	0.627899i	0.959493	+	0.281733i	$0.0909091\pi$
$660$	0.118239	−	0.258908i	0.118239	−	0.258908i
$661$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$661$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$662$		0			0
$663$	−0.915415	+	0.588302i	−0.915415	+	0.588302i
$664$		0			0
$665$		0			0
$666$	1.91899			1.91899
$667$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$668$	−0.284630			−0.284630
$669$		0			0
$670$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$671$		0			0
$672$		0			0
$673$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$673$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$674$		0			0
$675$	0.654861	−	0.755750i	0.654861	−	0.755750i
$676$	0.0440780	−	0.306569i	0.0440780	−	0.306569i
$677$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$677$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$678$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$679$		0			0
$680$	0.544078	+	1.19136i	0.544078	+	1.19136i
$681$		0			0
$682$	−0.313607	+	0.361922i	−0.313607	+	0.361922i
$683$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$683$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$684$		0			0
$685$	0.239446	+	1.66538i	0.239446	+	1.66538i
$686$		0			0
$687$		0			0
$688$	0.797176	−	0.234072i	0.797176	−	0.234072i
$689$		0			0
$690$	0.841254	+	0.540641i	0.841254	+	0.540641i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$697$		0			0
$698$		0			0
$699$	0.118239	−	0.822373i	0.118239	−	0.822373i
$700$		0			0
$701$	−1.25667	−	0.368991i	−1.25667	−	0.368991i	−0.415415	−	0.909632i	$-0.636364\pi$
$701$	−1.25667	−	0.368991i	−1.25667	−	0.368991i	−0.841254	+	0.540641i	$0.818182\pi$
$702$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$703$		0			0
$704$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$705$	0.857685	−	0.989821i	0.857685	−	0.989821i
$706$	0.345139	−	0.755750i	0.345139	−	0.755750i
$707$		0			0
$708$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$709$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$709$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$710$		0			0
$711$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$712$		0			0
$713$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$714$		0			0
$715$	−0.226900	+	0.0666238i	−0.226900	+	0.0666238i
$716$	1.10181	+	1.27155i	1.10181	+	1.27155i
$717$		0			0
$718$		0			0
$719$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$719$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$720$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$721$		0			0
$722$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$723$	0.118239	+	0.258908i	0.118239	+	0.258908i
$724$		0			0
$725$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$726$	0.381761	+	0.835939i	0.381761	+	0.835939i
$727$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$727$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.415415	−	0.909632i
$730$		0			0
$731$	−0.154861	−	1.07708i	−0.154861	−	1.07708i
$732$		0			0
$733$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$733$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$734$		0			0
$735$	1.00000			1.00000
$736$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$737$	−0.478891			−0.478891
$738$		0			0
$739$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$739$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$740$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$741$		0			0
$742$		0			0
$743$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$743$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$744$	1.10181	−	1.27155i	1.10181	−	1.27155i
$745$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$746$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$747$		0			0
$748$	0.357685	+	0.105026i	0.357685	+	0.105026i
$749$		0			0
$750$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$751$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$751$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$752$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$753$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$754$	0.226900	+	1.57812i	0.226900	+	1.57812i
$755$	1.61435	−	1.03748i	1.61435	−	1.03748i
$756$		0			0
$757$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$757$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$758$		0			0
$759$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$760$		0			0
$761$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$761$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.10181	+	0.708089i	1.10181	+	0.708089i
$766$	0.345139	−	0.755750i	0.345139	−	0.755750i
$767$	0.154861	−	0.178719i	0.154861	−	0.178719i
$768$	0.142315	−	0.989821i	0.142315	−	0.989821i
$769$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$769$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$770$		0			0
$771$	1.61435	+	0.474017i	1.61435	+	0.474017i
$772$		0			0
$773$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$773$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$774$	0.544078	−	0.627899i	0.544078	−	0.627899i
$775$	0.698939	−	1.53046i	0.698939	−	1.53046i
$776$		0			0
$777$		0			0
$778$	1.10181	−	0.708089i	1.10181	−	0.708089i
$779$		0			0
$780$	0.797176	−	0.234072i	0.797176	−	0.234072i
$781$		0			0
$782$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$783$	−1.91899			−1.91899
$784$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$785$	0.857685	+	0.989821i	0.857685	+	0.989821i
$786$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$787$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	0.959493	−	0.281733i	$-0.0909091\pi$
$787$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	−1.00000			$\pi$
$788$		0			0
$789$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$790$	1.10181	−	1.27155i	1.10181	−	1.27155i
$791$		0			0
$792$	0.118239	+	0.258908i	0.118239	+	0.258908i
$793$		0			0
$794$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$795$		0			0
$796$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$797$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$797$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$798$		0			0
$799$	1.44306	+	0.927399i	1.44306	+	0.927399i
$800$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	1.68251			1.68251
$805$		0			0
$806$	−1.39788			−1.39788
$807$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$808$	1.10181	+	1.27155i	1.10181	+	1.27155i
$809$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$809$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$810$	0.142315	+	0.989821i	0.142315	+	0.989821i
$811$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$811$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$812$		0			0
$813$	−0.857685	+	0.989821i	−0.857685	+	0.989821i
$814$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$815$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$816$	−1.25667	−	0.368991i	−1.25667	−	0.368991i
$817$		0			0
$818$	0.345139	+	0.755750i	0.345139	+	0.755750i
$819$		0			0
$820$		0			0
$821$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	0.654861	+	0.755750i	$0.272727\pi$
$821$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	−1.00000			$\pi$
$822$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$823$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$823$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$824$		0			0
$825$	0.186393	+	0.215109i	0.186393	+	0.215109i
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	1.25667	+	1.45027i	1.25667	+	1.45027i
$832$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$833$	0.186393	+	1.29639i	0.186393	+	1.29639i
$834$		0			0
$835$	0.118239	−	0.258908i	0.118239	−	0.258908i
$836$		0			0
$837$	0.239446	−	1.66538i	0.239446	−	1.66538i
$838$	−0.345139	−	0.755750i	−0.345139	−	0.755750i
$839$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$839$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$840$		0			0
$841$	1.11435	+	2.44009i	1.11435	+	2.44009i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.260554	+	0.167448i	0.260554	+	0.167448i
$846$	0.186393	+	1.29639i	0.186393	+	1.29639i
$847$		0			0
$848$		0			0
$849$	1.25667	−	0.368991i	1.25667	−	0.368991i
$850$	−1.30972			−1.30972
$851$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$852$		0			0
$853$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$853$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$857$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$858$	0.0982369	−	0.215109i	0.0982369	−	0.215109i
$859$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$859$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$860$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$861$		0			0
$862$		0			0
$863$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$863$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$864$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$865$		0			0
$866$		0			0
$867$	−0.297176	+	0.650724i	−0.297176	+	0.650724i
$868$		0			0
$869$	−0.0681534	−	0.474017i	−0.0681534	−	0.474017i
$870$	1.61435	−	1.03748i	1.61435	−	1.03748i
$871$	−0.915415	−	1.05645i	−0.915415	−	1.05645i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$877$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$878$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$879$		0			0
$880$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$881$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$881$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$882$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$883$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$883$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$884$	0.452036	+	0.989821i	0.452036	+	0.989821i
$885$	−0.273100	−	0.0801894i	−0.273100	−	0.0801894i
$886$		0			0
$887$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$887$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$888$	0.273100	−	1.89945i	0.273100	−	1.89945i
$889$		0			0
$890$		0			0
$891$	0.239446	+	0.153882i	0.239446	+	0.153882i
$892$		0			0
$893$		0			0
$894$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$895$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$896$		0			0
$897$	0.698939	+	0.449181i	0.698939	+	0.449181i
$898$		0			0
$899$	−3.09792	+	0.909632i	−3.09792	+	0.909632i
$900$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$905$		0			0
$906$	−0.273100	+	1.89945i	−0.273100	+	1.89945i
$907$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.654861	+	0.755750i	$0.272727\pi$
$907$	0.797176	+	1.74557i	0.797176	+	1.74557i	0.142315	+	0.989821i	$0.454545\pi$
$908$		0			0
$909$	1.61435	+	0.474017i	1.61435	+	0.474017i
$910$		0			0
$911$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$911$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$919$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$919$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$920$	0.654861	−	0.755750i	0.654861	−	0.755750i
$921$	−1.91899			−1.91899
$922$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$923$		0			0
$924$		0			0
$925$	−0.273100	−	1.89945i	−0.273100	−	1.89945i
$926$		0			0
$927$		0			0
$928$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$929$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$929$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$930$	0.698939	+	1.53046i	0.698939	+	1.53046i
$931$		0			0
$932$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$933$		0			0
$934$		0			0
$935$	−0.244123	+	0.281733i	−0.244123	+	0.281733i
$936$	−0.345139	+	0.755750i	−0.345139	+	0.755750i
$937$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$937$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$938$		0			0
$939$		0			0
$940$	−0.857685	−	0.989821i	−0.857685	−	0.989821i
$941$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$941$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$942$	−1.30972			−1.30972
$943$		0			0
$944$	0.284630			0.284630
$945$		0			0
$946$	0.154861	+	0.178719i	0.154861	+	0.178719i
$947$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$947$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$948$	0.239446	+	1.66538i	0.239446	+	1.66538i
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$953$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.0777324	−	0.540641i	0.0777324	−	0.540641i
$958$		0			0
$959$		0			0
$960$	0.841254	+	0.540641i	0.841254	+	0.540641i
$961$	−0.260554	−	1.81219i	−0.260554	−	1.81219i
$962$	−1.34125	+	0.861971i	−1.34125	+	0.861971i
$963$		0			0
$964$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.881761	−	0.258908i	0.881761	−	0.258908i
$969$		0			0
$970$		0			0
$971$	0.239446	+	1.66538i	0.239446	+	1.66538i	0.654861	+	0.755750i	$0.272727\pi$
$971$	0.239446	+	1.66538i	0.239446	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$972$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$973$		0			0
$974$		0			0
$975$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$976$		0			0
$977$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$977$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$978$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$979$		0			0
$980$	0.142315	−	0.989821i	0.142315	−	0.989821i
$981$		0			0
$982$	0.544078	−	1.19136i	0.544078	−	1.19136i
$983$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$983$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$984$		0			0
$985$		0			0
$986$	1.64589	+	1.89945i	1.64589	+	1.89945i
$987$		0			0
$988$		0			0
$989$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$990$	−0.284630			−0.284630
$991$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$991$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$992$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$993$		0			0
$994$		0			0
$995$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$996$		0			0
$997$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$997$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$998$		0			0
$999$	−0.797176	−	1.74557i	−0.797176	−	1.74557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2760.1.cm.b.2309.1	yes	10
3.2	odd	2		2760.1.cm.d.2309.1	yes	10
5.4	even	2		2760.1.cm.c.2309.1	yes	10
8.5	even	2		2760.1.cm.a.2309.1	yes	10
15.14	odd	2		2760.1.cm.a.2309.1	yes	10
23.18	even	11	inner	2760.1.cm.b.869.1	yes	10
24.5	odd	2		2760.1.cm.c.2309.1	yes	10
40.29	even	2		2760.1.cm.d.2309.1	yes	10
69.41	odd	22		2760.1.cm.d.869.1	yes	10
115.64	even	22		2760.1.cm.c.869.1	yes	10
120.29	odd	2	CM	2760.1.cm.b.2309.1	yes	10
184.133	even	22		2760.1.cm.a.869.1	✓	10
345.179	odd	22		2760.1.cm.a.869.1	✓	10
552.317	odd	22		2760.1.cm.c.869.1	yes	10
920.869	even	22		2760.1.cm.d.869.1	yes	10
2760.869	odd	22	inner	2760.1.cm.b.869.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2760.1.cm.a.869.1	✓	10	184.133	even	22
2760.1.cm.a.869.1	✓	10	345.179	odd	22
2760.1.cm.a.2309.1	yes	10	8.5	even	2
2760.1.cm.a.2309.1	yes	10	15.14	odd	2
2760.1.cm.b.869.1	yes	10	23.18	even	11	inner
2760.1.cm.b.869.1	yes	10	2760.869	odd	22	inner
2760.1.cm.b.2309.1	yes	10	1.1	even	1	trivial
2760.1.cm.b.2309.1	yes	10	120.29	odd	2	CM
2760.1.cm.c.869.1	yes	10	115.64	even	22
2760.1.cm.c.869.1	yes	10	552.317	odd	22
2760.1.cm.c.2309.1	yes	10	5.4	even	2
2760.1.cm.c.2309.1	yes	10	24.5	odd	2
2760.1.cm.d.869.1	yes	10	69.41	odd	22
2760.1.cm.d.869.1	yes	10	920.869	even	22
2760.1.cm.d.2309.1	yes	10	3.2	odd	2
2760.1.cm.d.2309.1	yes	10	40.29	even	2

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:	\( N \)	\(=\)	\( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2760.cm (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(0.654861 + 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.142315 + 0.989821i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.654861 + 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(-0.273100 - 0.0801894i) q^{11} +(0.959493 + 0.281733i) q^{12} +(-0.345139 - 0.755750i) q^{13} +(-0.654861 + 0.755750i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-1.10181 - 0.708089i) q^{17} +(-0.142315 - 0.989821i) q^{18} +(0.654861 + 0.755750i) q^{20} +0.284630 q^{22} +(-0.142315 + 0.989821i) q^{23} -1.00000 q^{24} +(-0.959493 + 0.281733i) q^{25} +(0.544078 + 0.627899i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(1.61435 + 1.03748i) q^{29} +(0.415415 - 0.909632i) q^{30} +(-1.10181 + 1.27155i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-0.118239 - 0.258908i) q^{33} +(1.25667 + 0.368991i) q^{34} +(0.415415 + 0.909632i) q^{36} +(-0.273100 + 1.89945i) q^{37} +(0.345139 - 0.755750i) q^{39} +(-0.841254 - 0.540641i) q^{40} +(0.544078 + 0.627899i) q^{43} +(-0.273100 + 0.0801894i) q^{44} -1.00000 q^{45} +(-0.142315 - 0.989821i) q^{46} -1.30972 q^{47} +(0.959493 - 0.281733i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(0.841254 - 0.540641i) q^{50} +(-0.186393 - 1.29639i) q^{51} +(-0.698939 - 0.449181i) q^{52} +(0.654861 - 0.755750i) q^{54} +(0.0405070 - 0.281733i) q^{55} +(-1.84125 - 0.540641i) q^{58} +(0.118239 + 0.258908i) q^{59} +(-0.142315 + 0.989821i) q^{60} +(0.698939 - 1.53046i) q^{62} +(-0.142315 - 0.989821i) q^{64} +(0.698939 - 0.449181i) q^{65} +(0.186393 + 0.215109i) q^{66} +(1.61435 - 0.474017i) q^{67} -1.30972 q^{68} +(-0.841254 + 0.540641i) q^{69} +(-0.654861 - 0.755750i) q^{72} +(-0.273100 - 1.89945i) q^{74} +(-0.841254 - 0.540641i) q^{75} +(-0.118239 + 0.822373i) q^{78} +(0.698939 + 1.53046i) q^{79} +(0.959493 + 0.281733i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.544078 - 1.19136i) q^{85} +(-0.698939 - 0.449181i) q^{86} +(0.273100 + 1.89945i) q^{87} +(0.239446 - 0.153882i) q^{88} +(0.959493 - 0.281733i) q^{90} +(0.415415 + 0.909632i) q^{92} -1.68251 q^{93} +(1.25667 - 0.368991i) q^{94} +(-0.841254 + 0.540641i) q^{96} +(0.841254 + 0.540641i) q^{98} +(0.118239 - 0.258908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 + q^3 - q^4 + q^5 + q^6 - q^8 - q^9	\( 10 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{8} - q^{9} + q^{10} + 2 q^{11} + q^{12} - 9 q^{13} - q^{15} - q^{16} - 2 q^{17} - q^{18} + q^{20} + 2 q^{22} - q^{23} - 10 q^{24} - q^{25} + 2 q^{26} + q^{27} + 2 q^{29} - q^{30} - 2 q^{31} - q^{32} - 2 q^{33} - 2 q^{34} - q^{36} + 2 q^{37} + 9 q^{39} + q^{40} + 2 q^{43} + 2 q^{44} - 10 q^{45} - q^{46} - 2 q^{47} + q^{48} - q^{49} - q^{50} + 2 q^{51} + 2 q^{52} + q^{54} + 9 q^{55} - 9 q^{58} + 2 q^{59} - q^{60} - 2 q^{62} - q^{64} - 2 q^{65} - 2 q^{66} + 2 q^{67} - 2 q^{68} + q^{69} - q^{72} + 2 q^{74} + q^{75} - 2 q^{78} - 2 q^{79} + q^{80} - q^{81} + 2 q^{85} + 2 q^{86} - 2 q^{87} + 2 q^{88} + q^{90} - q^{92} + 2 q^{93} - 2 q^{94} + q^{96} - q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - q^2 + q^3 - q^4 + q^5 + q^6 - q^8 - q^9 + q^10 + 2 * q^11 + q^12 - 9 * q^13 - q^15 - q^16 - 2 * q^17 - q^18 + q^20 + 2 * q^22 - q^23 - 10 * q^24 - q^25 + 2 * q^26 + q^27 + 2 * q^29 - q^30 - 2 * q^31 - q^32 - 2 * q^33 - 2 * q^34 - q^36 + 2 * q^37 + 9 * q^39 + q^40 + 2 * q^43 + 2 * q^44 - 10 * q^45 - q^46 - 2 * q^47 + q^48 - q^49 - q^50 + 2 * q^51 + 2 * q^52 + q^54 + 9 * q^55 - 9 * q^58 + 2 * q^59 - q^60 - 2 * q^62 - q^64 - 2 * q^65 - 2 * q^66 + 2 * q^67 - 2 * q^68 + q^69 - q^72 + 2 * q^74 + q^75 - 2 * q^78 - 2 * q^79 + q^80 - q^81 + 2 * q^85 + 2 * q^86 - 2 * q^87 + 2 * q^88 + q^90 - q^92 + 2 * q^93 - 2 * q^94 + q^96 - q^98 + 2 * q^99

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