LMFDB - Embedded newform 920.1.bh.a.179.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,1,Mod(59,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 11, 14]))

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

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

chi := DirichletCharacter("920.59");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	920.bh (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:	$0.459139811622$
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			179.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	920.179
Dual form			920.1.bh.a.699.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-0.797176 - 1.74557i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-0.797176 - 1.74557i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(-1.61435 + 0.474017i) q^{11} +(-0.118239 + 0.258908i) q^{13} +(0.273100 + 1.89945i) q^{14} +(0.415415 + 0.909632i) q^{16} +(-0.142315 + 0.989821i) q^{18} +(-1.10181 - 0.708089i) q^{19} +(-0.654861 + 0.755750i) q^{20} +1.68251 q^{22} +(-0.654861 + 0.755750i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(0.186393 - 0.215109i) q^{26} +(0.273100 - 1.89945i) q^{28} +(-0.142315 - 0.989821i) q^{32} +(1.84125 - 0.540641i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.118239 - 0.822373i) q^{37} +(0.857685 + 0.989821i) q^{38} +(0.841254 - 0.540641i) q^{40} +(0.186393 - 1.29639i) q^{41} +(-1.61435 - 0.474017i) q^{44} +1.00000 q^{45} +(0.841254 - 0.540641i) q^{46} +0.830830 q^{47} +(-1.75667 + 2.02730i) q^{49} +(0.841254 + 0.540641i) q^{50} +(-0.239446 + 0.153882i) q^{52} +(-0.118239 - 0.258908i) q^{53} +(-0.239446 - 1.66538i) q^{55} +(-0.797176 + 1.74557i) q^{56} +(0.345139 - 0.755750i) q^{59} +(-1.61435 + 1.03748i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.239446 - 0.153882i) q^{65} -1.91899 q^{70} +(-0.654861 + 0.755750i) q^{72} +(-0.118239 + 0.822373i) q^{74} +(-0.544078 - 1.19136i) q^{76} +(2.11435 + 2.44009i) q^{77} +(-0.959493 + 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-0.544078 + 1.19136i) q^{82} +(1.41542 + 0.909632i) q^{88} +(-0.544078 + 0.627899i) q^{89} +(-0.959493 - 0.281733i) q^{90} +0.546200 q^{91} +(-0.959493 + 0.281733i) q^{92} +(-0.797176 - 0.234072i) q^{94} +(0.857685 - 0.989821i) q^{95} +(2.25667 - 1.45027i) q^{98} +(0.698939 + 1.53046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - q^{5} - 2 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^4 - q^5 - 2 * q^7 - q^8 - q^9	$ 10 q - q^{2} - q^{4} - q^{5} - 2 q^{7} - q^{8} - q^{9} - q^{10} - 2 q^{11} - 2 q^{13} - 2 q^{14} - q^{16} - q^{18} - 2 q^{19} - q^{20} - 2 q^{22} - q^{23} - q^{25} - 2 q^{26} - 2 q^{28} - q^{32} + 9 q^{35} - q^{36} - 2 q^{37} + 9 q^{38} - q^{40} - 2 q^{41} - 2 q^{44} + 10 q^{45} - q^{46} - 2 q^{47} - 3 q^{49} - q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{55} - 2 q^{56} + 9 q^{59} - 2 q^{63} - q^{64} - 2 q^{65} - 2 q^{70} - q^{72} - 2 q^{74} - 2 q^{76} + 7 q^{77} - q^{80} - q^{81} - 2 q^{82} + 9 q^{88} - 2 q^{89} - q^{90} - 4 q^{91} - q^{92} - 2 q^{94} + 9 q^{95} + 8 q^{98} - 2 q^{99}+O(q^{100}) $ 10 * q - q^2 - q^4 - q^5 - 2 * q^7 - q^8 - q^9 - q^10 - 2 * q^11 - 2 * q^13 - 2 * q^14 - q^16 - q^18 - 2 * q^19 - q^20 - 2 * q^22 - q^23 - q^25 - 2 * q^26 - 2 * q^28 - q^32 + 9 * q^35 - q^36 - 2 * q^37 + 9 * q^38 - q^40 - 2 * q^41 - 2 * q^44 + 10 * q^45 - q^46 - 2 * q^47 - 3 * q^49 - q^50 - 2 * q^52 - 2 * q^53 - 2 * q^55 - 2 * q^56 + 9 * q^59 - 2 * q^63 - q^64 - 2 * q^65 - 2 * q^70 - q^72 - 2 * q^74 - 2 * q^76 + 7 * q^77 - q^80 - q^81 - 2 * q^82 + 9 * q^88 - 2 * q^89 - q^90 - 4 * q^91 - q^92 - 2 * q^94 + 9 * q^95 + 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{6}{11}\right)$	$-1$	$-1$

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			0		0.654861	−	0.755750i	$-0.272727\pi$
$3$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$4$	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			0
$7$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$7$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$8$	−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
$11$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$11$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$12$		0			0
$13$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$13$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$14$	0.273100	+	1.89945i	0.273100	+	1.89945i
$15$		0			0
$16$	0.415415	+	0.909632i	0.415415	+	0.909632i
$17$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$17$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$18$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$19$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$19$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$20$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$21$		0			0
$22$	1.68251			1.68251
$23$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$23$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$24$		0			0
$25$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$26$	0.186393	−	0.215109i	0.186393	−	0.215109i
$27$		0			0
$28$	0.273100	−	1.89945i	0.273100	−	1.89945i
$29$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$29$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$30$		0			0
$31$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$31$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$32$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$33$		0			0
$34$		0			0
$35$	1.84125	−	0.540641i	1.84125	−	0.540641i
$36$	0.415415	−	0.909632i	0.415415	−	0.909632i
$37$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$37$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$38$	0.857685	+	0.989821i	0.857685	+	0.989821i
$39$		0			0
$40$	0.841254	−	0.540641i	0.841254	−	0.540641i
$41$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$41$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$42$		0			0
$43$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$43$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$44$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$45$	1.00000			1.00000
$46$	0.841254	−	0.540641i	0.841254	−	0.540641i
$47$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$47$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$48$		0			0
$49$	−1.75667	+	2.02730i	−1.75667	+	2.02730i
$50$	0.841254	+	0.540641i	0.841254	+	0.540641i
$51$		0			0
$52$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$53$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$53$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$54$		0			0
$55$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$56$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$57$		0			0
$58$		0			0
$59$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$59$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$60$		0			0
$61$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$61$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$62$		0			0
$63$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$64$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$65$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$66$		0			0
$67$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$67$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$68$		0			0
$69$		0			0
$70$	−1.91899			−1.91899
$71$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$71$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$72$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$73$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$73$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$74$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$75$		0			0
$76$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$77$	2.11435	+	2.44009i	2.11435	+	2.44009i
$78$		0			0
$79$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$79$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$80$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$81$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$82$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$83$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$83$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	1.41542	+	0.909632i	1.41542	+	0.909632i
$89$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$89$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$90$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$91$	0.546200			0.546200
$92$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$93$		0			0
$94$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$95$	0.857685	−	0.989821i	0.857685	−	0.989821i
$96$		0			0
$97$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$97$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$98$	2.25667	−	1.45027i	2.25667	−	1.45027i
$99$	0.698939	+	1.53046i	0.698939	+	1.53046i
$100$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$101$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$101$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$102$		0			0
$103$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$103$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$104$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$105$		0			0
$106$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$107$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$107$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$108$		0			0
$109$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$109$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$110$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$111$		0			0
$112$	1.25667	−	1.45027i	1.25667	−	1.45027i
$113$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$113$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$114$		0			0
$115$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$116$		0			0
$117$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$118$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$119$		0			0
$120$		0			0
$121$	1.54019	−	0.989821i	1.54019	−	0.989821i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.415415	−	0.909632i	0.415415	−	0.909632i
$126$	1.84125	−	0.540641i	1.84125	−	0.540641i
$127$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$127$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$128$	0.415415	−	0.909632i	0.415415	−	0.909632i
$129$		0			0
$130$	0.186393	+	0.215109i	0.186393	+	0.215109i
$131$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$131$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$132$		0			0
$133$	−0.357685	+	2.48775i	−0.357685	+	2.48775i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$139$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$140$	1.84125	+	0.540641i	1.84125	+	0.540641i
$141$		0			0
$142$		0			0
$143$	0.0681534	−	0.474017i	0.0681534	−	0.474017i
$144$	0.841254	−	0.540641i	0.841254	−	0.540641i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.345139	−	0.755750i	0.345139	−	0.755750i
$149$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$149$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$150$		0			0
$151$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$151$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$152$	0.186393	+	1.29639i	0.186393	+	1.29639i
$153$		0			0
$154$	−1.34125	−	2.93694i	−1.34125	−	2.93694i
$155$		0			0
$156$		0			0
$157$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$157$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$158$		0			0
$159$		0			0
$160$	1.00000			1.00000
$161$	1.84125	+	0.540641i	1.84125	+	0.540641i
$162$	1.00000			1.00000
$163$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$163$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$164$	0.857685	−	0.989821i	0.857685	−	0.989821i
$165$		0			0
$166$		0			0
$167$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$167$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$168$		0			0
$169$	0.601808	+	0.694523i	0.601808	+	0.694523i
$170$		0			0
$171$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$172$		0			0
$173$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$173$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$174$		0			0
$175$	0.273100	+	1.89945i	0.273100	+	1.89945i
$176$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$177$		0			0
$178$	0.698939	−	0.449181i	0.698939	−	0.449181i
$179$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$179$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$180$	0.841254	+	0.540641i	0.841254	+	0.540641i
$181$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$181$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$182$	−0.524075	−	0.153882i	−0.524075	−	0.153882i
$183$		0			0
$184$	1.00000			1.00000
$185$	0.830830			0.830830
$186$		0			0
$187$		0			0
$188$	0.698939	+	0.449181i	0.698939	+	0.449181i
$189$		0			0
$190$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$191$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$191$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$192$		0			0
$193$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$193$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$194$		0			0
$195$		0			0
$196$	−2.57385	+	0.755750i	−2.57385	+	0.755750i
$197$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$197$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$198$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$199$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$199$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$200$	0.415415	+	0.909632i	0.415415	+	0.909632i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.25667	+	0.368991i	1.25667	+	0.368991i
$206$	−0.284630			−0.284630
$207$	0.841254	+	0.540641i	0.841254	+	0.540641i
$208$	−0.284630			−0.284630
$209$	2.11435	+	0.620830i	2.11435	+	0.620830i
$210$		0			0
$211$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$211$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$212$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.698939	−	1.53046i	0.698939	−	1.53046i
$221$		0			0
$222$		0			0
$223$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$223$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$224$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$225$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$226$		0			0
$227$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$227$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	0.415415	+	0.909632i	0.415415	+	0.909632i
$231$		0			0
$232$		0			0
$233$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$233$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$234$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$235$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$236$	0.698939	−	0.449181i	0.698939	−	0.449181i
$237$		0			0
$238$		0			0
$239$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$239$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$240$		0			0
$241$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$241$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$242$	−1.75667	+	0.515804i	−1.75667	+	0.515804i
$243$		0			0
$244$		0			0
$245$	−1.75667	−	2.02730i	−1.75667	−	2.02730i
$246$		0			0
$247$	0.313607	−	0.201543i	0.313607	−	0.201543i
$248$		0			0
$249$		0			0
$250$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$251$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$251$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$252$	−1.91899			−1.91899
$253$	0.698939	−	1.53046i	0.698939	−	1.53046i
$254$	−1.91899			−1.91899
$255$		0			0
$256$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$257$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$257$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$258$		0			0
$259$	−1.34125	+	0.861971i	−1.34125	+	0.861971i
$260$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$261$		0			0
$262$	0.186393	+	1.29639i	0.186393	+	1.29639i
$263$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$263$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$264$		0			0
$265$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$266$	1.04408	−	2.28621i	1.04408	−	2.28621i
$267$		0			0
$268$		0			0
$269$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$269$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$270$		0			0
$271$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$271$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.68251			1.68251
$276$		0			0
$277$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$277$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$278$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$279$		0			0
$280$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$281$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$281$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$282$		0			0
$283$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$283$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$284$		0			0
$285$		0			0
$286$	−0.198939	+	0.435615i	−0.198939	+	0.435615i
$287$	−2.41153	+	0.708089i	−2.41153	+	0.708089i
$288$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$289$	0.415415	−	0.909632i	0.415415	−	0.909632i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.41542	−	0.909632i	1.41542	−	0.909632i	0.415415	−	0.909632i	$-0.363636\pi$
$293$	1.41542	−	0.909632i	1.41542	−	0.909632i	1.00000			$0$
$294$		0			0
$295$	0.698939	+	0.449181i	0.698939	+	0.449181i
$296$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$297$		0			0
$298$		0			0
$299$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.186393	−	1.29639i	0.186393	−	1.29639i
$305$		0			0
$306$		0			0
$307$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$307$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$308$	0.459493	+	3.19584i	0.459493	+	3.19584i
$309$		0			0
$310$		0			0
$311$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$311$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$312$		0			0
$313$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$313$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$314$	0.857685	+	0.989821i	0.857685	+	0.989821i
$315$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$316$		0			0
$317$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$317$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$318$		0			0
$319$		0			0
$320$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$321$		0			0
$322$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$323$		0			0
$324$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$325$	0.186393	−	0.215109i	0.186393	−	0.215109i
$326$		0			0
$327$		0			0
$328$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$329$	−0.662317	−	1.45027i	−0.662317	−	1.45027i
$330$		0			0
$331$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$331$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$332$		0			0
$333$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$334$	1.84125	−	0.540641i	1.84125	−	0.540641i
$335$		0			0
$336$		0			0
$337$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$337$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$338$	−0.381761	−	0.835939i	−0.381761	−	0.835939i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	0.857685	−	0.989821i	0.857685	−	0.989821i
$343$	3.09792	+	0.909632i	3.09792	+	0.909632i
$344$		0			0
$345$		0			0
$346$	1.68251			1.68251
$347$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$347$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$348$		0			0
$349$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$349$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$350$	0.273100	−	1.89945i	0.273100	−	1.89945i
$351$		0			0
$352$	0.698939	+	1.53046i	0.698939	+	1.53046i
$353$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$353$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$354$		0			0
$355$		0			0
$356$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$357$		0			0
$358$	0.698939	−	1.53046i	0.698939	−	1.53046i
$359$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$359$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$360$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$361$	0.297176	+	0.650724i	0.297176	+	0.650724i
$362$		0			0
$363$		0			0
$364$	0.459493	+	0.295298i	0.459493	+	0.295298i
$365$		0			0
$366$		0			0
$367$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$367$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$368$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$369$	−1.30972			−1.30972
$370$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$371$	−0.357685	+	0.412791i	−0.357685	+	0.412791i
$372$		0			0
$373$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$373$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$374$		0			0
$375$		0			0
$376$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$377$		0			0
$378$		0			0
$379$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$379$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$380$	1.25667	−	0.368991i	1.25667	−	0.368991i
$381$		0			0
$382$		0			0
$383$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$383$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$384$		0			0
$385$	−2.71616	+	1.74557i	−2.71616	+	1.74557i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$389$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$390$		0			0
$391$		0			0
$392$	2.68251			2.68251
$393$		0			0
$394$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$395$		0			0
$396$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$397$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$397$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$398$		0			0
$399$		0			0
$400$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$401$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$401$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$406$		0			0
$407$	0.580699	+	1.27155i	0.580699	+	1.27155i
$408$		0			0
$409$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$409$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$410$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$411$		0			0
$412$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$413$	−1.59435			−1.59435
$414$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$415$		0			0
$416$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$417$		0			0
$418$	−1.85380	−	1.19136i	−1.85380	−	1.19136i
$419$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$419$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$420$		0			0
$421$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$421$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$422$	0.186393	+	0.215109i	0.186393	+	0.215109i
$423$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$424$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$431$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$432$		0			0
$433$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$433$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.25667	−	0.368991i	1.25667	−	0.368991i
$438$		0			0
$439$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$439$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$440$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$441$	2.25667	+	1.45027i	2.25667	+	1.45027i
$442$		0			0
$443$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$443$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$444$		0			0
$445$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$446$	0.186393	+	1.29639i	0.186393	+	1.29639i
$447$		0			0
$448$	1.84125	−	0.540641i	1.84125	−	0.540641i
$449$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$449$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$450$	0.415415	−	0.909632i	0.415415	−	0.909632i
$451$	0.313607	+	2.18119i	0.313607	+	2.18119i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0777324	+	0.540641i	−0.0777324	+	0.540641i
$456$		0			0
$457$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$457$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$458$		0			0
$459$		0			0
$460$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$463$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$467$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$468$	0.186393	+	0.215109i	0.186393	+	0.215109i
$469$		0			0
$470$	0.345139	−	0.755750i	0.345139	−	0.755750i
$471$		0			0
$472$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$473$		0			0
$474$		0			0
$475$	0.857685	+	0.989821i	0.857685	+	0.989821i
$476$		0			0
$477$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$478$		0			0
$479$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$479$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$480$		0			0
$481$	0.226900	+	0.0666238i	0.226900	+	0.0666238i
$482$	0.830830			0.830830
$483$		0			0
$484$	1.83083			1.83083
$485$		0			0
$486$		0			0
$487$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$487$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$488$		0			0
$489$		0			0
$490$	1.11435	+	2.44009i	1.11435	+	2.44009i
$491$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$491$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$492$		0			0
$493$		0			0
$494$	−0.357685	+	0.105026i	−0.357685	+	0.105026i
$495$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$499$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$500$	0.841254	−	0.540641i	0.841254	−	0.540641i
$501$		0			0
$502$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$503$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$503$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$504$	1.84125	+	0.540641i	1.84125	+	0.540641i
$505$		0			0
$506$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$507$		0			0
$508$	1.84125	+	0.540641i	1.84125	+	0.540641i
$509$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$509$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$510$		0			0
$511$		0			0
$512$	0.841254	−	0.540641i	0.841254	−	0.540641i
$513$		0			0
$514$		0			0
$515$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$516$		0			0
$517$	−1.34125	+	0.393828i	−1.34125	+	0.393828i
$518$	1.52977	−	0.449181i	1.52977	−	0.449181i
$519$		0			0
$520$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$521$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$521$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$522$		0			0
$523$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$523$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$524$	0.186393	−	1.29639i	0.186393	−	1.29639i
$525$		0			0
$526$	0.186393	−	0.215109i	0.186393	−	0.215109i
$527$		0			0
$528$		0			0
$529$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$530$	−0.284630			−0.284630
$531$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$532$	−1.64589	+	1.89945i	−1.64589	+	1.89945i
$533$	0.313607	+	0.201543i	0.313607	+	0.201543i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.87491	−	4.10548i	1.87491	−	4.10548i
$540$		0			0
$541$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$541$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$547$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$548$		0			0
$549$		0			0
$550$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	1.25667	+	0.368991i	1.25667	+	0.368991i
$555$		0			0
$556$	1.41542	+	0.909632i	1.41542	+	0.909632i
$557$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$557$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$558$		0			0
$559$		0			0
$560$	1.25667	+	1.45027i	1.25667	+	1.45027i
$561$		0			0
$562$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$563$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$563$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.25667	+	1.45027i	1.25667	+	1.45027i
$568$		0			0
$569$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$569$	1.68251	−	1.08128i	1.68251	−	1.08128i	0.841254	−	0.540641i	$-0.181818\pi$
$570$		0			0
$571$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$571$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$572$	0.313607	−	0.361922i	0.313607	−	0.361922i
$573$		0			0
$574$	2.51334			2.51334
$575$	0.841254	−	0.540641i	0.841254	−	0.540641i
$576$	1.00000			1.00000
$577$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$577$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$578$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.313607	+	0.361922i	0.313607	+	0.361922i
$584$		0			0
$585$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$586$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$587$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$587$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$588$		0			0
$589$		0			0
$590$	−0.544078	−	0.627899i	−0.544078	−	0.627899i
$591$		0			0
$592$	0.698939	−	0.449181i	0.698939	−	0.449181i
$593$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$593$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$601$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.760554	+	1.66538i	0.760554	+	1.66538i
$606$		0			0
$607$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	1.00000			$0$
$607$	0.0405070	+	0.281733i	0.0405070	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$608$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$609$		0			0
$610$		0			0
$611$	−0.0982369	+	0.215109i	−0.0982369	+	0.215109i
$612$		0			0
$613$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$613$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$614$		0			0
$615$		0			0
$616$	0.459493	−	3.19584i	0.459493	−	3.19584i
$617$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$617$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$618$		0			0
$619$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$619$	−1.91899	−	0.563465i	−1.91899	−	0.563465i	−0.959493	−	0.281733i	$-0.909091\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.52977	+	0.449181i	1.52977	+	0.449181i
$624$		0			0
$625$	0.841254	+	0.540641i	0.841254	+	0.540641i
$626$		0			0
$627$		0			0
$628$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$629$		0			0
$630$	0.273100	+	1.89945i	0.273100	+	1.89945i
$631$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$631$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$632$		0			0
$633$		0			0
$634$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$635$	0.273100	+	1.89945i	0.273100	+	1.89945i
$636$		0			0
$637$	−0.317178	−	0.694523i	−0.317178	−	0.694523i
$638$		0			0
$639$		0			0
$640$	0.841254	+	0.540641i	0.841254	+	0.540641i
$641$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$641$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$	1.25667	+	1.45027i	1.25667	+	1.45027i
$645$		0			0
$646$		0			0
$647$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.415415	−	0.909632i	$-0.363636\pi$
$647$	1.25667	−	1.45027i	1.25667	−	1.45027i	0.841254	−	0.540641i	$-0.181818\pi$
$648$	0.841254	+	0.540641i	0.841254	+	0.540641i
$649$	−0.198939	+	1.38365i	−0.198939	+	1.38365i
$650$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$651$		0			0
$652$		0			0
$653$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$653$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$654$		0			0
$655$	1.25667	−	0.368991i	1.25667	−	0.368991i
$656$	1.25667	−	0.368991i	1.25667	−	0.368991i
$657$		0			0
$658$	0.226900	+	1.57812i	0.226900	+	1.57812i
$659$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$659$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$660$		0			0
$661$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$661$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$662$	0.186393	−	1.29639i	0.186393	−	1.29639i
$663$		0			0
$664$		0			0
$665$	−2.41153	−	0.708089i	−2.41153	−	0.708089i
$666$	0.830830			0.830830
$667$		0			0
$668$	−1.91899			−1.91899
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$673$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$674$		0			0
$675$		0			0
$676$	0.130785	+	0.909632i	0.130785	+	0.909632i
$677$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$677$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$683$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$684$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$685$		0			0
$686$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$687$		0			0
$688$		0			0
$689$	0.0810141			0.0810141
$690$		0			0
$691$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$691$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$692$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$693$	2.11435	−	2.44009i	2.11435	−	2.44009i
$694$		0			0
$695$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$701$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$701$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$702$		0			0
$703$	−0.452036	+	0.989821i	−0.452036	+	0.989821i
$704$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$709$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$710$		0			0
$711$		0			0
$712$	0.830830			0.830830
$713$		0			0
$714$		0			0
$715$	0.459493	+	0.134919i	0.459493	+	0.134919i
$716$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$717$		0			0
$718$		0			0
$719$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$719$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$720$	0.415415	+	0.909632i	0.415415	+	0.909632i
$721$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$722$	−0.101808	−	0.708089i	−0.101808	−	0.708089i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$727$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$728$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$729$	0.415415	+	0.909632i	0.415415	+	0.909632i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$733$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$734$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$735$		0			0
$736$	0.841254	+	0.540641i	0.841254	+	0.540641i
$737$		0			0
$738$	1.25667	+	0.368991i	1.25667	+	0.368991i
$739$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$739$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$740$	0.698939	+	0.449181i	0.698939	+	0.449181i
$741$		0			0
$742$	0.459493	−	0.295298i	0.459493	−	0.295298i
$743$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$743$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$744$		0			0
$745$		0			0
$746$	0.698939	−	1.53046i	0.698939	−	1.53046i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$751$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$752$	0.345139	+	0.755750i	0.345139	+	0.755750i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$757$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$758$	−1.91899			−1.91899
$759$		0			0
$760$	−1.30972			−1.30972
$761$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$761$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.698939	+	1.53046i	0.698939	+	1.53046i
$767$	0.154861	+	0.178719i	0.154861	+	0.178719i
$768$		0			0
$769$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$769$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$770$	3.09792	−	0.909632i	3.09792	−	0.909632i
$771$		0			0
$772$		0			0
$773$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$773$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.12333	+	1.29639i	−1.12333	+	1.29639i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−2.57385	−	0.755750i	−2.57385	−	0.755750i
$785$	0.857685	−	0.989821i	0.857685	−	0.989821i
$786$		0			0
$787$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$787$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$788$	0.698939	−	0.449181i	0.698939	−	0.449181i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.698939	−	1.53046i	0.698939	−	1.53046i
$793$		0			0
$794$	1.84125	−	0.540641i	1.84125	−	0.540641i
$795$		0			0
$796$		0			0
$797$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$797$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$798$		0			0
$799$		0			0
$800$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$801$	0.698939	+	0.449181i	0.698939	+	0.449181i
$802$	1.25667	−	1.45027i	1.25667	−	1.45027i
$803$		0			0
$804$		0			0
$805$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$809$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$810$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$811$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$811$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$812$		0			0
$813$		0			0
$814$	−0.198939	−	1.38365i	−0.198939	−	1.38365i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$819$	−0.0777324	−	0.540641i	−0.0777324	−	0.540641i
$820$	0.857685	+	0.989821i	0.857685	+	0.989821i
$821$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$821$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$822$		0			0
$823$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$823$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$824$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$825$		0			0
$826$	1.52977	+	0.449181i	1.52977	+	0.449181i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	0.415415	+	0.909632i	0.415415	+	0.909632i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$833$		0			0
$834$		0			0
$835$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$836$	1.44306	+	1.66538i	1.44306	+	1.66538i
$837$		0			0
$838$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$839$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$839$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$840$		0			0
$841$	0.415415	−	0.909632i	0.415415	−	0.909632i
$842$		0			0
$843$		0			0
$844$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$845$	−0.773100	+	0.496841i	−0.773100	+	0.496841i
$846$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$847$	−2.95561	−	1.89945i	−2.95561	−	1.89945i
$848$	0.186393	−	0.215109i	0.186393	−	0.215109i
$849$		0			0
$850$		0			0
$851$	0.698939	+	0.449181i	0.698939	+	0.449181i
$852$		0			0
$853$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$853$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$854$		0			0
$855$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$856$		0			0
$857$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$857$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$858$		0			0
$859$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$859$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$863$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$864$		0			0
$865$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−1.30972			−1.30972
$875$	−1.91899			−1.91899
$876$		0			0
$877$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$877$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$878$		0			0
$879$		0			0
$880$	1.41542	−	0.909632i	1.41542	−	0.909632i
$881$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$881$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$882$	−1.75667	−	2.02730i	−1.75667	−	2.02730i
$883$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$883$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$887$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$888$		0			0
$889$	−2.41153	−	2.78305i	−2.41153	−	2.78305i
$890$	0.345139	+	0.755750i	0.345139	+	0.755750i
$891$	1.41542	−	0.909632i	1.41542	−	0.909632i
$892$	0.186393	−	1.29639i	0.186393	−	1.29639i
$893$	−0.915415	−	0.588302i	−0.915415	−	0.588302i
$894$		0			0
$895$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$896$	−1.91899			−1.91899
$897$		0			0
$898$	1.68251			1.68251
$899$		0			0
$900$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$901$		0			0
$902$	0.313607	−	2.18119i	0.313607	−	2.18119i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$907$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$908$		0			0
$909$		0			0
$910$	0.226900	−	0.496841i	0.226900	−	0.496841i
$911$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$911$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.64589	+	1.89945i	−1.64589	+	1.89945i
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$926$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$927$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$928$		0			0
$929$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$929$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$930$		0			0
$931$	3.37102	−	0.989821i	3.37102	−	0.989821i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$937$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$937$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$938$		0			0
$939$		0			0
$940$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$941$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$941$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$942$		0			0
$943$	0.857685	+	0.989821i	0.857685	+	0.989821i
$944$	0.830830			0.830830
$945$		0			0
$946$		0			0
$947$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$947$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$948$		0			0
$949$		0			0
$950$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$951$		0			0
$952$		0			0
$953$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$953$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$954$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$962$	−0.198939	−	0.127850i	−0.198939	−	0.127850i
$963$		0			0
$964$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$965$		0			0
$966$		0			0
$967$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$967$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$968$	−1.75667	−	0.515804i	−1.75667	−	0.515804i
$969$		0			0
$970$		0			0
$971$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$971$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$972$		0			0
$973$	−1.34125	−	2.93694i	−1.34125	−	2.93694i
$974$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$975$		0			0
$976$		0			0
$977$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$977$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$978$		0			0
$979$	0.580699	−	1.27155i	0.580699	−	1.27155i
$980$	−0.381761	−	2.65520i	−0.381761	−	2.65520i
$981$		0			0
$982$	0.698939	+	1.53046i	0.698939	+	1.53046i
$983$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$983$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$984$		0			0
$985$	0.698939	+	0.449181i	0.698939	+	0.449181i
$986$		0			0
$987$		0			0
$988$	0.372786			0.372786
$989$		0			0
$990$	1.68251			1.68251
$991$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$991$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$997$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$998$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.1.bh.a.179.1	✓	10
4.3	odd	2		3680.1.cn.a.2479.1		10
5.4	even	2		920.1.bh.b.179.1	yes	10
8.3	odd	2		920.1.bh.b.179.1	yes	10
8.5	even	2		3680.1.cn.b.2479.1		10
20.19	odd	2		3680.1.cn.b.2479.1		10
23.9	even	11	inner	920.1.bh.a.699.1	yes	10
40.19	odd	2	CM	920.1.bh.a.179.1	✓	10
40.29	even	2		3680.1.cn.a.2479.1		10
92.55	odd	22		3680.1.cn.a.239.1		10
115.9	even	22		920.1.bh.b.699.1	yes	10
184.101	even	22		3680.1.cn.b.239.1		10
184.147	odd	22		920.1.bh.b.699.1	yes	10
460.239	odd	22		3680.1.cn.b.239.1		10
920.469	even	22		3680.1.cn.a.239.1		10
920.699	odd	22	inner	920.1.bh.a.699.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.1.bh.a.179.1	✓	10	1.1	even	1	trivial
920.1.bh.a.179.1	✓	10	40.19	odd	2	CM
920.1.bh.a.699.1	yes	10	23.9	even	11	inner
920.1.bh.a.699.1	yes	10	920.699	odd	22	inner
920.1.bh.b.179.1	yes	10	5.4	even	2
920.1.bh.b.179.1	yes	10	8.3	odd	2
920.1.bh.b.699.1	yes	10	115.9	even	22
920.1.bh.b.699.1	yes	10	184.147	odd	22
3680.1.cn.a.239.1		10	92.55	odd	22
3680.1.cn.a.239.1		10	920.469	even	22
3680.1.cn.a.2479.1		10	4.3	odd	2
3680.1.cn.a.2479.1		10	40.29	even	2
3680.1.cn.b.239.1		10	184.101	even	22
3680.1.cn.b.239.1		10	460.239	odd	22
3680.1.cn.b.2479.1		10	8.5	even	2
3680.1.cn.b.2479.1		10	20.19	odd	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	920.bh (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-0.797176 - 1.74557i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-0.797176 - 1.74557i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(-1.61435 + 0.474017i) q^{11} +(-0.118239 + 0.258908i) q^{13} +(0.273100 + 1.89945i) q^{14} +(0.415415 + 0.909632i) q^{16} +(-0.142315 + 0.989821i) q^{18} +(-1.10181 - 0.708089i) q^{19} +(-0.654861 + 0.755750i) q^{20} +1.68251 q^{22} +(-0.654861 + 0.755750i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(0.186393 - 0.215109i) q^{26} +(0.273100 - 1.89945i) q^{28} +(-0.142315 - 0.989821i) q^{32} +(1.84125 - 0.540641i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.118239 - 0.822373i) q^{37} +(0.857685 + 0.989821i) q^{38} +(0.841254 - 0.540641i) q^{40} +(0.186393 - 1.29639i) q^{41} +(-1.61435 - 0.474017i) q^{44} +1.00000 q^{45} +(0.841254 - 0.540641i) q^{46} +0.830830 q^{47} +(-1.75667 + 2.02730i) q^{49} +(0.841254 + 0.540641i) q^{50} +(-0.239446 + 0.153882i) q^{52} +(-0.118239 - 0.258908i) q^{53} +(-0.239446 - 1.66538i) q^{55} +(-0.797176 + 1.74557i) q^{56} +(0.345139 - 0.755750i) q^{59} +(-1.61435 + 1.03748i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.239446 - 0.153882i) q^{65} -1.91899 q^{70} +(-0.654861 + 0.755750i) q^{72} +(-0.118239 + 0.822373i) q^{74} +(-0.544078 - 1.19136i) q^{76} +(2.11435 + 2.44009i) q^{77} +(-0.959493 + 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-0.544078 + 1.19136i) q^{82} +(1.41542 + 0.909632i) q^{88} +(-0.544078 + 0.627899i) q^{89} +(-0.959493 - 0.281733i) q^{90} +0.546200 q^{91} +(-0.959493 + 0.281733i) q^{92} +(-0.797176 - 0.234072i) q^{94} +(0.857685 - 0.989821i) q^{95} +(2.25667 - 1.45027i) q^{98} +(0.698939 + 1.53046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - q^{5} - 2 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^4 - q^5 - 2 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{4} - q^{5} - 2 q^{7} - q^{8} - q^{9} - q^{10} - 2 q^{11} - 2 q^{13} - 2 q^{14} - q^{16} - q^{18} - 2 q^{19} - q^{20} - 2 q^{22} - q^{23} - q^{25} - 2 q^{26} - 2 q^{28} - q^{32} + 9 q^{35} - q^{36} - 2 q^{37} + 9 q^{38} - q^{40} - 2 q^{41} - 2 q^{44} + 10 q^{45} - q^{46} - 2 q^{47} - 3 q^{49} - q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{55} - 2 q^{56} + 9 q^{59} - 2 q^{63} - q^{64} - 2 q^{65} - 2 q^{70} - q^{72} - 2 q^{74} - 2 q^{76} + 7 q^{77} - q^{80} - q^{81} - 2 q^{82} + 9 q^{88} - 2 q^{89} - q^{90} - 4 q^{91} - q^{92} - 2 q^{94} + 9 q^{95} + 8 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^4 - q^5 - 2 * q^7 - q^8 - q^9 - q^10 - 2 * q^11 - 2 * q^13 - 2 * q^14 - q^16 - q^18 - 2 * q^19 - q^20 - 2 * q^22 - q^23 - q^25 - 2 * q^26 - 2 * q^28 - q^32 + 9 * q^35 - q^36 - 2 * q^37 + 9 * q^38 - q^40 - 2 * q^41 - 2 * q^44 + 10 * q^45 - q^46 - 2 * q^47 - 3 * q^49 - q^50 - 2 * q^52 - 2 * q^53 - 2 * q^55 - 2 * q^56 + 9 * q^59 - 2 * q^63 - q^64 - 2 * q^65 - 2 * q^70 - q^72 - 2 * q^74 - 2 * q^76 + 7 * q^77 - q^80 - q^81 - 2 * q^82 + 9 * q^88 - 2 * q^89 - q^90 - 4 * q^91 - q^92 - 2 * q^94 + 9 * q^95 + 8 * q^98 - 2 * q^99

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