LMFDB - Embedded newform 1573.1.s.b.928.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1573,1,Mod(148,1573)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1573.148"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1573, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([8, 15])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1573.s (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.785029264872$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.0.265837.1

Embedding invariants

Embedding label			928.1
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	1573.928
Dual form			1573.1.s.b.1334.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39680 - 0.221232i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.221232 - 1.39680i) q^{6} -1.00000i q^{12} +(0.587785 - 0.809017i) q^{13} +(-0.809017 + 0.587785i) q^{16} +(-0.587785 - 0.809017i) q^{17} +(-0.642040 - 1.26007i) q^{19} +1.00000i q^{23} +(0.951057 + 0.309017i) q^{25} +(0.642040 - 1.26007i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.309017 + 0.951057i) q^{29} +(-1.00000 + 1.00000i) q^{32} +(-1.00000 - 1.00000i) q^{34} +(-0.642040 + 1.26007i) q^{37} +(-1.17557 - 1.61803i) q^{38} +(-0.587785 - 0.809017i) q^{39} +1.00000i q^{43} +(0.221232 + 1.39680i) q^{46} +(-1.26007 + 0.642040i) q^{47} +(0.309017 + 0.951057i) q^{48} +(0.587785 + 0.809017i) q^{49} +(1.39680 + 0.221232i) q^{50} +(-0.951057 + 0.309017i) q^{51} +(0.309017 - 0.951057i) q^{52} +(-0.809017 - 0.587785i) q^{53} +(1.00000 - 1.00000i) q^{54} +(-1.39680 + 0.221232i) q^{57} +(0.642040 + 1.26007i) q^{58} +(-0.809017 + 0.587785i) q^{61} +(-0.587785 + 0.809017i) q^{64} +(-0.809017 - 0.587785i) q^{68} +(0.951057 + 0.309017i) q^{69} +(0.221232 - 1.39680i) q^{71} +(0.642040 - 1.26007i) q^{73} +(-0.618034 + 1.90211i) q^{74} +(0.587785 - 0.809017i) q^{75} +(-1.00000 - 1.00000i) q^{76} +(-1.00000 - 1.00000i) q^{78} +(-0.809017 - 0.587785i) q^{79} +(-0.309017 - 0.951057i) q^{81} +(-0.221232 + 1.39680i) q^{83} +(0.221232 + 1.39680i) q^{86} +1.00000 q^{87} +(0.309017 + 0.951057i) q^{92} +(-1.61803 + 1.17557i) q^{94} +(0.642040 + 1.26007i) q^{96} +(1.00000 + 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} + 2 q^{6} - 2 q^{16} - 2 q^{19} + 2 q^{26} + 2 q^{27} - 2 q^{29} - 8 q^{32} - 8 q^{34} - 2 q^{37} + 2 q^{46} + 2 q^{47} - 2 q^{48} + 2 q^{50} - 2 q^{52} - 2 q^{53} + 8 q^{54} - 2 q^{57}+ \cdots + 8 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 + 2 * q^6 - 2 * q^16 - 2 * q^19 + 2 * q^26 + 2 * q^27 - 2 * q^29 - 8 * q^32 - 8 * q^34 - 2 * q^37 + 2 * q^46 + 2 * q^47 - 2 * q^48 + 2 * q^50 - 2 * q^52 - 2 * q^53 + 8 * q^54 - 2 * q^57 + 2 * q^58 - 2 * q^61 - 2 * q^68 + 2 * q^71 + 2 * q^73 + 4 * q^74 - 8 * q^76 - 8 * q^78 - 2 * q^79 + 2 * q^81 - 2 * q^83 + 2 * q^86 + 8 * q^87 - 2 * q^92 - 4 * q^94 + 2 * q^96 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1573\mathbb{Z}\right)^\times$.

$n$	$365$	$1211$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.39680	−	0.221232i	1.39680	−	0.221232i	0.587785	−	0.809017i	$-0.300000\pi$
$2$	1.39680	−	0.221232i	1.39680	−	0.221232i	0.809017	+	0.587785i	$0.200000\pi$
$3$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$3$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$4$	0.951057	−	0.309017i	0.951057	−	0.309017i
$5$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$5$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$6$	0.221232	−	1.39680i	0.221232	−	1.39680i
$7$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$7$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		0			0
$11$		0			0
$12$		−	1.00000i		−	1.00000i
$13$	0.587785	−	0.809017i	0.587785	−	0.809017i
$13$	0.587785	−	0.809017i	0.587785	−	0.809017i
$14$		0			0
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$17$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$17$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$18$		0			0
$19$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	−0.951057	−	0.309017i	$-0.900000\pi$
$19$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	0.309017	−	0.951057i	$-0.400000\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$23$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	0.951057	+	0.309017i	0.951057	+	0.309017i
$26$	0.642040	−	1.26007i	0.642040	−	1.26007i
$27$	0.809017	−	0.587785i	0.809017	−	0.587785i
$28$		0			0
$29$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$29$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$30$		0			0
$31$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$31$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$32$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$33$		0			0
$34$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$35$		0			0
$36$		0			0
$37$	−0.642040	+	1.26007i	−0.642040	+	1.26007i	0.309017	+	0.951057i	$0.400000\pi$
$37$	−0.642040	+	1.26007i	−0.642040	+	1.26007i	−0.951057	+	0.309017i	$0.900000\pi$
$38$	−1.17557	−	1.61803i	−1.17557	−	1.61803i
$39$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$40$		0			0
$41$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$41$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$42$		0			0
$43$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$43$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$44$		0			0
$45$		0			0
$46$	0.221232	+	1.39680i	0.221232	+	1.39680i
$47$	−1.26007	+	0.642040i	−1.26007	+	0.642040i	−0.951057	−	0.309017i	$-0.900000\pi$
$47$	−1.26007	+	0.642040i	−1.26007	+	0.642040i	−0.309017	+	0.951057i	$0.600000\pi$
$48$	0.309017	+	0.951057i	0.309017	+	0.951057i
$49$	0.587785	+	0.809017i	0.587785	+	0.809017i
$50$	1.39680	+	0.221232i	1.39680	+	0.221232i
$51$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$52$	0.309017	−	0.951057i	0.309017	−	0.951057i
$53$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$53$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$54$	1.00000	−	1.00000i	1.00000	−	1.00000i
$55$		0			0
$56$		0			0
$57$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$58$	0.642040	+	1.26007i	0.642040	+	1.26007i
$59$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$59$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$60$		0			0
$61$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$61$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$62$		0			0
$63$		0			0
$64$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$65$		0			0
$66$		0			0
$67$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$67$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$68$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$69$	0.951057	+	0.309017i	0.951057	+	0.309017i
$70$		0			0
$71$	0.221232	−	1.39680i	0.221232	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$71$	0.221232	−	1.39680i	0.221232	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$72$		0			0
$73$	0.642040	−	1.26007i	0.642040	−	1.26007i	−0.309017	−	0.951057i	$-0.600000\pi$
$73$	0.642040	−	1.26007i	0.642040	−	1.26007i	0.951057	−	0.309017i	$-0.100000\pi$
$74$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$75$	0.587785	−	0.809017i	0.587785	−	0.809017i
$76$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$77$		0			0
$78$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$79$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$79$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$80$		0			0
$81$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$82$		0			0
$83$	−0.221232	+	1.39680i	−0.221232	+	1.39680i	0.587785	+	0.809017i	$0.300000\pi$
$83$	−0.221232	+	1.39680i	−0.221232	+	1.39680i	−0.809017	+	0.587785i	$0.800000\pi$
$84$		0			0
$85$		0			0
$86$	0.221232	+	1.39680i	0.221232	+	1.39680i
$87$	1.00000			1.00000
$88$		0			0
$89$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$89$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$90$		0			0
$91$		0			0
$92$	0.309017	+	0.951057i	0.309017	+	0.951057i
$93$		0			0
$94$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$95$		0			0
$96$	0.642040	+	1.26007i	0.642040	+	1.26007i
$97$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$97$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$98$	1.00000	+	1.00000i	1.00000	+	1.00000i
$99$		0			0
$100$	1.00000			1.00000
$101$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$101$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$102$	−1.26007	+	0.642040i	−1.26007	+	0.642040i
$103$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$103$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$104$		0			0
$105$		0			0
$106$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$107$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$107$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$108$	0.587785	−	0.809017i	0.587785	−	0.809017i
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$		0			0
$111$	1.00000	+	1.00000i	1.00000	+	1.00000i
$112$		0			0
$113$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$113$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$114$	−1.90211	+	0.618034i	−1.90211	+	0.618034i
$115$		0			0
$116$	0.587785	+	0.809017i	0.587785	+	0.809017i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$		0			0
$122$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$127$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$128$		0			0
$129$	0.951057	+	0.309017i	0.951057	+	0.309017i
$130$		0			0
$131$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$131$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.39680	+	0.221232i	1.39680	+	0.221232i	0.809017	−	0.587785i	$-0.200000\pi$
$137$	1.39680	+	0.221232i	1.39680	+	0.221232i	0.587785	+	0.809017i	$0.300000\pi$
$138$	1.39680	+	0.221232i	1.39680	+	0.221232i
$139$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$139$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$140$		0			0
$141$	0.221232	+	1.39680i	0.221232	+	1.39680i
$142$		−	2.00000i		−	2.00000i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	0.618034	−	1.90211i	0.618034	−	1.90211i
$147$	0.951057	−	0.309017i	0.951057	−	0.309017i
$148$	−0.221232	+	1.39680i	−0.221232	+	1.39680i
$149$	0.221232	−	1.39680i	0.221232	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$149$	0.221232	−	1.39680i	0.221232	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$150$	0.642040	−	1.26007i	0.642040	−	1.26007i
$151$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$151$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$157$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$157$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$158$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$159$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$160$		0			0
$161$		0			0
$162$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$163$	−0.221232	−	1.39680i	−0.221232	−	1.39680i	−0.809017	−	0.587785i	$-0.800000\pi$
$163$	−0.221232	−	1.39680i	−0.221232	−	1.39680i	0.587785	−	0.809017i	$-0.300000\pi$
$164$		0			0
$165$		0			0
$166$			2.00000i			2.00000i
$167$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$167$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$168$		0			0
$169$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$	0.309017	+	0.951057i	0.309017	+	0.951057i
$173$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$173$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$174$	1.39680	−	0.221232i	1.39680	−	0.221232i
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$179$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$180$		0			0
$181$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$181$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$182$		0			0
$183$	0.309017	+	0.951057i	0.309017	+	0.951057i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$189$		0			0
$190$		0			0
$191$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$191$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$192$	0.587785	+	0.809017i	0.587785	+	0.809017i
$193$	1.39680	+	0.221232i	1.39680	+	0.221232i	0.809017	−	0.587785i	$-0.200000\pi$
$193$	1.39680	+	0.221232i	1.39680	+	0.221232i	0.587785	+	0.809017i	$0.300000\pi$
$194$		0			0
$195$		0			0
$196$	0.809017	+	0.587785i	0.809017	+	0.587785i
$197$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$197$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$198$		0			0
$199$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$199$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$200$		0			0
$201$		0			0
$202$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$203$		0			0
$204$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$205$		0			0
$206$	1.26007	−	0.642040i	1.26007	−	0.642040i
$207$		0			0
$208$			1.00000i			1.00000i
$209$		0			0
$210$		0			0
$211$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$211$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$212$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$213$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$214$	−0.221232	+	1.39680i	−0.221232	+	1.39680i
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$220$		0			0
$221$	−1.00000			−1.00000
$222$	1.61803	+	1.17557i	1.61803	+	1.17557i
$223$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	−0.951057	−	0.309017i	$-0.900000\pi$
$223$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	0.309017	−	0.951057i	$-0.400000\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$227$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$228$	−1.26007	+	0.642040i	−1.26007	+	0.642040i
$229$	−0.221232	−	1.39680i	−0.221232	−	1.39680i	−0.809017	−	0.587785i	$-0.800000\pi$
$229$	−0.221232	−	1.39680i	−0.221232	−	1.39680i	0.587785	−	0.809017i	$-0.300000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.17557	−	1.61803i	1.17557	−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$233$	1.17557	−	1.61803i	1.17557	−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$238$		0			0
$239$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	−0.951057	−	0.309017i	$-0.900000\pi$
$239$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	0.309017	−	0.951057i	$-0.400000\pi$
$240$		0			0
$241$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$241$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$242$		0			0
$243$		0			0
$244$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$245$		0			0
$246$		0			0
$247$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$248$		0			0
$249$	1.26007	+	0.642040i	1.26007	+	0.642040i
$250$		0			0
$251$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$251$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$252$		0			0
$253$		0			0
$254$	1.00000	+	1.00000i	1.00000	+	1.00000i
$255$		0			0
$256$	0.309017	−	0.951057i	0.309017	−	0.951057i
$257$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$257$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$258$	1.39680	+	0.221232i	1.39680	+	0.221232i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$263$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$263$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$269$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$270$		0			0
$271$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$271$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$272$	0.951057	+	0.309017i	0.951057	+	0.309017i
$273$		0			0
$274$	2.00000			2.00000
$275$		0			0
$276$	1.00000			1.00000
$277$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$277$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$278$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$279$		0			0
$280$		0			0
$281$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$281$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$282$	0.618034	+	1.90211i	0.618034	+	1.90211i
$283$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$283$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$284$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$		0			0
$290$		0			0
$291$		0			0
$292$	0.221232	−	1.39680i	0.221232	−	1.39680i
$293$	−0.642040	+	1.26007i	−0.642040	+	1.26007i	0.309017	+	0.951057i	$0.400000\pi$
$293$	−0.642040	+	1.26007i	−0.642040	+	1.26007i	−0.951057	+	0.309017i	$0.900000\pi$
$294$	1.26007	−	0.642040i	1.26007	−	0.642040i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		−	2.00000i		−	2.00000i
$299$	0.809017	+	0.587785i	0.809017	+	0.587785i
$300$	0.309017	−	0.951057i	0.309017	−	0.951057i
$301$		0			0
$302$		0			0
$303$	0.587785	+	0.809017i	0.587785	+	0.809017i
$304$	1.26007	+	0.642040i	1.26007	+	0.642040i
$305$		0			0
$306$		0			0
$307$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$307$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$308$		0			0
$309$		−	1.00000i		−	1.00000i
$310$		0			0
$311$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$311$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$312$		0			0
$313$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$313$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$314$	−0.221232	+	1.39680i	−0.221232	+	1.39680i
$315$		0			0
$316$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$317$	−1.39680	+	0.221232i	−1.39680	+	0.221232i	−0.809017	−	0.587785i	$-0.800000\pi$
$317$	−1.39680	+	0.221232i	−1.39680	+	0.221232i	−0.587785	+	0.809017i	$0.700000\pi$
$318$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$319$		0			0
$320$		0			0
$321$	0.809017	+	0.587785i	0.809017	+	0.587785i
$322$		0			0
$323$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$324$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$325$	0.809017	−	0.587785i	0.809017	−	0.587785i
$326$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$331$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$332$	0.221232	+	1.39680i	0.221232	+	1.39680i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$337$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$338$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.39680	+	0.221232i	1.39680	+	0.221232i
$347$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$347$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$348$	0.951057	−	0.309017i	0.951057	−	0.309017i
$349$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$349$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$350$		0			0
$351$		−	1.00000i		−	1.00000i
$352$		0			0
$353$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$353$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$359$	−0.642040	+	1.26007i	−0.642040	+	1.26007i	0.309017	+	0.951057i	$0.400000\pi$
$359$	−0.642040	+	1.26007i	−0.642040	+	1.26007i	−0.951057	+	0.309017i	$0.900000\pi$
$360$		0			0
$361$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$362$	1.00000	+	1.00000i	1.00000	+	1.00000i
$363$		0			0
$364$		0			0
$365$		0			0
$366$	0.642040	+	1.26007i	0.642040	+	1.26007i
$367$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$367$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$368$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.951057	+	0.309017i	0.951057	+	0.309017i
$378$		0			0
$379$	0.221232	−	1.39680i	0.221232	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$379$	0.221232	−	1.39680i	0.221232	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$380$		0			0
$381$	0.951057	−	0.309017i	0.951057	−	0.309017i
$382$		0			0
$383$	1.39680	−	0.221232i	1.39680	−	0.221232i	0.587785	−	0.809017i	$-0.300000\pi$
$383$	1.39680	−	0.221232i	1.39680	−	0.221232i	0.809017	+	0.587785i	$0.200000\pi$
$384$		0			0
$385$		0			0
$386$	2.00000			2.00000
$387$		0			0
$388$		0			0
$389$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$389$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$390$		0			0
$391$	0.809017	−	0.587785i	0.809017	−	0.587785i
$392$		0			0
$393$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$397$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$398$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$399$		0			0
$400$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$401$	−1.39680	−	0.221232i	−1.39680	−	0.221232i	−0.587785	−	0.809017i	$-0.700000\pi$
$401$	−1.39680	−	0.221232i	−1.39680	−	0.221232i	−0.809017	+	0.587785i	$0.800000\pi$
$402$		0			0
$403$		0			0
$404$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$409$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$410$		0			0
$411$	0.642040	−	1.26007i	0.642040	−	1.26007i
$412$	0.809017	−	0.587785i	0.809017	−	0.587785i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.221232	+	1.39680i	0.221232	+	1.39680i
$417$	−1.00000			−1.00000
$418$		0			0
$419$	−2.00000			−2.00000			−1.00000			$\pi$
$419$	−2.00000			−2.00000			−1.00000			$\pi$
$420$		0			0
$421$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$421$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$426$	−1.90211	−	0.618034i	−1.90211	−	0.618034i
$427$		0			0
$428$			1.00000i			1.00000i
$429$		0			0
$430$		0			0
$431$	−1.39680	+	0.221232i	−1.39680	+	0.221232i	−0.809017	−	0.587785i	$-0.800000\pi$
$431$	−1.39680	+	0.221232i	−1.39680	+	0.221232i	−0.587785	+	0.809017i	$0.700000\pi$
$432$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$433$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$433$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.26007	−	0.642040i	1.26007	−	0.642040i
$438$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$439$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$439$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$		0			0
$442$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$443$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$443$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$444$	1.26007	+	0.642040i	1.26007	+	0.642040i
$445$		0			0
$446$	−1.17557	−	1.61803i	−1.17557	−	1.61803i
$447$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$448$		0			0
$449$	0.221232	+	1.39680i	0.221232	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$449$	0.221232	+	1.39680i	0.221232	+	1.39680i	−0.587785	+	0.809017i	$0.700000\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$457$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$458$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$459$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$460$		0			0
$461$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$461$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$462$		0			0
$463$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$463$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$464$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$465$		0			0
$466$	1.28408	−	2.52015i	1.28408	−	2.52015i
$467$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$467$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.809017	+	0.587785i	0.809017	+	0.587785i
$472$		0			0
$473$		0			0
$474$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$475$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$476$		0			0
$477$		0			0
$478$	−1.17557	−	1.61803i	−1.17557	−	1.61803i
$479$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$479$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$480$		0			0
$481$	0.642040	+	1.26007i	0.642040	+	1.26007i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.642040	+	1.26007i	0.642040	+	1.26007i	0.951057	+	0.309017i	$0.100000\pi$
$487$	0.642040	+	1.26007i	0.642040	+	1.26007i	−0.309017	+	0.951057i	$0.600000\pi$
$488$		0			0
$489$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$490$		0			0
$491$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$491$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$492$		0			0
$493$	0.587785	−	0.809017i	0.587785	−	0.809017i
$494$	−2.00000			−2.00000
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.90211	+	0.618034i	1.90211	+	0.618034i
$499$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$499$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$500$		0			0
$501$		0			0
$502$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$503$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$503$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.00000			−1.00000
$508$	0.809017	+	0.587785i	0.809017	+	0.587785i
$509$	0.642040	+	1.26007i	0.642040	+	1.26007i	0.951057	+	0.309017i	$0.100000\pi$
$509$	0.642040	+	1.26007i	0.642040	+	1.26007i	−0.309017	+	0.951057i	$0.600000\pi$
$510$		0			0
$511$		0			0
$512$	0.221232	−	1.39680i	0.221232	−	1.39680i
$513$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$514$		0			0
$515$		0			0
$516$	1.00000			1.00000
$517$		0			0
$518$		0			0
$519$	0.587785	−	0.809017i	0.587785	−	0.809017i
$520$		0			0
$521$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$521$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$522$		0			0
$523$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$523$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$524$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$525$		0			0
$526$	1.39680	−	0.221232i	1.39680	−	0.221232i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$538$		0			0
$539$		0			0
$540$		0			0
$541$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$541$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$542$		0			0
$543$	0.951057	−	0.309017i	0.951057	−	0.309017i
$544$	1.39680	+	0.221232i	1.39680	+	0.221232i
$545$		0			0
$546$		0			0
$547$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$547$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$548$	1.39680	−	0.221232i	1.39680	−	0.221232i
$549$		0			0
$550$		0			0
$551$	1.00000	−	1.00000i	1.00000	−	1.00000i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$557$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$557$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$558$		0			0
$559$	0.809017	+	0.587785i	0.809017	+	0.587785i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$563$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$564$	0.642040	+	1.26007i	0.642040	+	1.26007i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$569$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$570$		0			0
$571$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$571$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$576$		0			0
$577$	0.221232	−	1.39680i	0.221232	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$577$	0.221232	−	1.39680i	0.221232	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$578$		0			0
$579$	0.642040	−	1.26007i	0.642040	−	1.26007i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$587$	1.26007	+	0.642040i	1.26007	+	0.642040i	0.951057	−	0.309017i	$-0.100000\pi$
$587$	1.26007	+	0.642040i	1.26007	+	0.642040i	0.309017	+	0.951057i	$0.400000\pi$
$588$	0.809017	−	0.587785i	0.809017	−	0.587785i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$		0			0
$596$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$597$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$598$	1.26007	+	0.642040i	1.26007	+	0.642040i
$599$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$599$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$600$		0			0
$601$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$601$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	1.00000	+	1.00000i	1.00000	+	1.00000i
$607$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$607$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$608$	1.90211	+	0.618034i	1.90211	+	0.618034i
$609$		0			0
$610$		0			0
$611$	−0.221232	+	1.39680i	−0.221232	+	1.39680i
$612$		0			0
$613$	0.642040	+	1.26007i	0.642040	+	1.26007i	0.951057	+	0.309017i	$0.100000\pi$
$613$	0.642040	+	1.26007i	0.642040	+	1.26007i	−0.309017	+	0.951057i	$0.600000\pi$
$614$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$615$		0			0
$616$		0			0
$617$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$617$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$618$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$619$	1.26007	−	0.642040i	1.26007	−	0.642040i	0.309017	−	0.951057i	$-0.400000\pi$
$619$	1.26007	−	0.642040i	1.26007	−	0.642040i	0.951057	+	0.309017i	$0.100000\pi$
$620$		0			0
$621$	0.587785	+	0.809017i	0.587785	+	0.809017i
$622$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$623$		0			0
$624$	0.951057	+	0.309017i	0.951057	+	0.309017i
$625$	0.809017	+	0.587785i	0.809017	+	0.587785i
$626$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$627$		0			0
$628$			1.00000i			1.00000i
$629$	1.39680	−	0.221232i	1.39680	−	0.221232i
$630$		0			0
$631$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$631$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$632$		0			0
$633$		0			0
$634$	−1.90211	+	0.618034i	−1.90211	+	0.618034i
$635$		0			0
$636$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$637$	1.00000			1.00000
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$641$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$642$	1.26007	+	0.642040i	1.26007	+	0.642040i
$643$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$643$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$644$		0			0
$645$		0			0
$646$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$647$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$647$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$648$		0			0
$649$		0			0
$650$	1.00000	−	1.00000i	1.00000	−	1.00000i
$651$		0			0
$652$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$653$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$653$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$659$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$661$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$662$		0			0
$663$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$668$		0			0
$669$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$673$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$674$		0			0
$675$	0.951057	−	0.309017i	0.951057	−	0.309017i
$676$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$677$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$677$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$683$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$688$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$689$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$690$		0			0
$691$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$691$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$692$	1.00000			1.00000
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−1.17557	−	1.61803i	−1.17557	−	1.61803i
$700$		0			0
$701$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$701$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$702$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$703$	2.00000			2.00000
$704$		0			0
$705$		0			0
$706$	1.17557	−	1.61803i	1.17557	−	1.61803i
$707$		0			0
$708$		0			0
$709$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$709$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.00000			−1.00000
$717$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$718$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$719$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$719$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$720$		0			0
$721$		0			0
$722$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$723$		0			0
$724$	0.809017	+	0.587785i	0.809017	+	0.587785i
$725$			1.00000i			1.00000i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.309017	−	0.951057i
$730$		0			0
$731$	0.809017	−	0.587785i	0.809017	−	0.587785i
$732$	0.587785	+	0.809017i	0.587785	+	0.809017i
$733$	1.26007	+	0.642040i	1.26007	+	0.642040i	0.951057	−	0.309017i	$-0.100000\pi$
$733$	1.26007	+	0.642040i	1.26007	+	0.642040i	0.309017	+	0.951057i	$0.400000\pi$
$734$		0			0
$735$		0			0
$736$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$737$		0			0
$738$		0			0
$739$	0.221232	+	1.39680i	0.221232	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$739$	0.221232	+	1.39680i	0.221232	+	1.39680i	−0.587785	+	0.809017i	$0.700000\pi$
$740$		0			0
$741$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$742$		0			0
$743$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$743$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$751$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$752$	0.642040	−	1.26007i	0.642040	−	1.26007i
$753$	0.587785	+	0.809017i	0.587785	+	0.809017i
$754$	1.39680	+	0.221232i	1.39680	+	0.221232i
$755$		0			0
$756$		0			0
$757$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$757$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$758$		−	2.00000i		−	2.00000i
$759$		0			0
$760$		0			0
$761$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$761$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$762$	1.26007	−	0.642040i	1.26007	−	0.642040i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	1.90211	−	0.618034i	1.90211	−	0.618034i
$767$		0			0
$768$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$769$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$769$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$	1.39680	−	0.221232i	1.39680	−	0.221232i
$773$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$773$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.26007	−	0.642040i	1.26007	−	0.642040i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	1.00000	−	1.00000i	1.00000	−	1.00000i
$783$	0.809017	+	0.587785i	0.809017	+	0.587785i
$784$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$785$		0			0
$786$	−0.221232	+	1.39680i	−0.221232	+	1.39680i
$787$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$787$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$788$		0			0
$789$	0.309017	−	0.951057i	0.309017	−	0.951057i
$790$		0			0
$791$		0			0
$792$		0			0
$793$			1.00000i			1.00000i
$794$		0			0
$795$		0			0
$796$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$797$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$797$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$798$		0			0
$799$	1.26007	+	0.642040i	1.26007	+	0.642040i
$800$	−1.26007	+	0.642040i	−1.26007	+	0.642040i
$801$		0			0
$802$	−2.00000			−2.00000
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$809$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$810$		0			0
$811$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	−0.951057	−	0.309017i	$-0.900000\pi$
$811$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	0.309017	−	0.951057i	$-0.400000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.587785	−	0.809017i	0.587785	−	0.809017i
$817$	1.26007	−	0.642040i	1.26007	−	0.642040i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$821$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$822$	0.618034	−	1.90211i	0.618034	−	1.90211i
$823$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$823$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.221232	+	1.39680i	0.221232	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$827$	0.221232	+	1.39680i	0.221232	+	1.39680i	−0.587785	+	0.809017i	$0.700000\pi$
$828$		0			0
$829$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$829$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$830$		0			0
$831$		0			0
$832$	0.309017	+	0.951057i	0.309017	+	0.951057i
$833$	0.309017	−	0.951057i	0.309017	−	0.951057i
$834$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−2.79360	+	0.442463i	−2.79360	+	0.442463i
$839$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$839$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$840$		0			0
$841$		0			0
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$	1.00000			1.00000
$849$		0			0
$850$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$851$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$852$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$853$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$853$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$857$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$859$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$	−1.90211	+	0.618034i	−1.90211	+	0.618034i
$863$	−0.221232	+	1.39680i	−0.221232	+	1.39680i	0.587785	+	0.809017i	$0.300000\pi$
$863$	−0.221232	+	1.39680i	−0.221232	+	1.39680i	−0.809017	+	0.587785i	$0.800000\pi$
$864$	−0.221232	+	1.39680i	−0.221232	+	1.39680i
$865$		0			0
$866$	−1.26007	+	0.642040i	−1.26007	+	0.642040i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	1.61803	−	1.17557i	1.61803	−	1.17557i
$875$		0			0
$876$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$877$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$877$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$878$	0.221232	+	1.39680i	0.221232	+	1.39680i
$879$	1.00000	+	1.00000i	1.00000	+	1.00000i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$		0			0
$883$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$883$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$884$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$885$		0			0
$886$	0.221232	−	1.39680i	0.221232	−	1.39680i
$887$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$887$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$893$	1.61803	+	1.17557i	1.61803	+	1.17557i
$894$	−1.90211	−	0.618034i	−1.90211	−	0.618034i
$895$		0			0
$896$		0			0
$897$	0.809017	−	0.587785i	0.809017	−	0.587785i
$898$	0.618034	+	1.90211i	0.618034	+	1.90211i
$899$		0			0
$900$		0			0
$901$			1.00000i			1.00000i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$907$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$911$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$912$	1.00000	−	1.00000i	1.00000	−	1.00000i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$917$		0			0
$918$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$919$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$919$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$920$		0			0
$921$	−1.26007	+	0.642040i	−1.26007	+	0.642040i
$922$		0			0
$923$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$924$		0			0
$925$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$926$		0			0
$927$		0			0
$928$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$929$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$929$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$930$		0			0
$931$	0.642040	−	1.26007i	0.642040	−	1.26007i
$932$	0.618034	−	1.90211i	0.618034	−	1.90211i
$933$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$934$	1.00000	+	1.00000i	1.00000	+	1.00000i
$935$		0			0
$936$		0			0
$937$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$937$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$938$		0			0
$939$	0.309017	+	0.951057i	0.309017	+	0.951057i
$940$		0			0
$941$	0.221232	−	1.39680i	0.221232	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$941$	0.221232	−	1.39680i	0.221232	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$942$	1.26007	+	0.642040i	1.26007	+	0.642040i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$947$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$948$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$949$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$950$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$951$	−0.221232	+	1.39680i	−0.221232	+	1.39680i
$952$		0			0
$953$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$953$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$954$		0			0
$955$		0			0
$956$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$962$	1.17557	+	1.61803i	1.17557	+	1.61803i
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$967$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$968$		0			0
$969$	1.00000	+	1.00000i	1.00000	+	1.00000i
$970$		0			0
$971$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$971$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$972$		0			0
$973$		0			0
$974$	1.17557	+	1.61803i	1.17557	+	1.61803i
$975$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$976$	0.309017	−	0.951057i	0.309017	−	0.951057i
$977$	1.39680	−	0.221232i	1.39680	−	0.221232i	0.587785	−	0.809017i	$-0.300000\pi$
$977$	1.39680	−	0.221232i	1.39680	−	0.221232i	0.809017	+	0.587785i	$0.200000\pi$
$978$	−2.00000			−2.00000
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.26007	−	0.642040i	1.26007	−	0.642040i
$983$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$983$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$984$		0			0
$985$		0			0
$986$	0.642040	−	1.26007i	0.642040	−	1.26007i
$987$		0			0
$988$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$989$	−1.00000			−1.00000
$990$		0			0
$991$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$991$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.39680	+	0.221232i	1.39680	+	0.221232i
$997$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$997$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$998$		0			0
$999$	0.221232	+	1.39680i	0.221232	+	1.39680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.1.s.b.928.1		8
11.2	odd	10		1573.1.s.a.148.1		8
11.3	even	5	inner	1573.1.s.b.850.1		8
11.4	even	5	inner	1573.1.s.b.1461.1		8
11.5	even	5		1573.1.f.a.122.1	✓	2
11.6	odd	10		1573.1.f.b.122.1	yes	2
11.7	odd	10		1573.1.s.a.1461.1		8
11.8	odd	10		1573.1.s.a.850.1		8
11.9	even	5	inner	1573.1.s.b.148.1		8
11.10	odd	2		1573.1.s.a.928.1		8
13.8	odd	4	inner	1573.1.s.b.1412.1		8
143.8	even	20		1573.1.s.a.1334.1		8
143.21	even	4		1573.1.s.a.1412.1		8
143.47	odd	20	inner	1573.1.s.b.1334.1		8
143.60	odd	20		1573.1.f.a.606.1	yes	2
143.73	even	20		1573.1.s.a.372.1		8
143.86	odd	20	inner	1573.1.s.b.632.1		8
143.112	even	20		1573.1.s.a.632.1		8
143.125	odd	20	inner	1573.1.s.b.372.1		8
143.138	even	20		1573.1.f.b.606.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1573.1.f.a.122.1	✓	2	11.5	even	5
1573.1.f.a.606.1	yes	2	143.60	odd	20
1573.1.f.b.122.1	yes	2	11.6	odd	10
1573.1.f.b.606.1	yes	2	143.138	even	20
1573.1.s.a.148.1		8	11.2	odd	10
1573.1.s.a.372.1		8	143.73	even	20
1573.1.s.a.632.1		8	143.112	even	20
1573.1.s.a.850.1		8	11.8	odd	10
1573.1.s.a.928.1		8	11.10	odd	2
1573.1.s.a.1334.1		8	143.8	even	20
1573.1.s.a.1412.1		8	143.21	even	4
1573.1.s.a.1461.1		8	11.7	odd	10
1573.1.s.b.148.1		8	11.9	even	5	inner
1573.1.s.b.372.1		8	143.125	odd	20	inner
1573.1.s.b.632.1		8	143.86	odd	20	inner
1573.1.s.b.850.1		8	11.3	even	5	inner
1573.1.s.b.928.1		8	1.1	even	1	trivial
1573.1.s.b.1334.1		8	143.47	odd	20	inner
1573.1.s.b.1412.1		8	13.8	odd	4	inner
1573.1.s.b.1461.1		8	11.4	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1573.s (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39680 - 0.221232i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.951057 - 0.309017i) q^{4} +(0.221232 - 1.39680i) q^{6} -1.00000i q^{12} +(0.587785 - 0.809017i) q^{13} +(-0.809017 + 0.587785i) q^{16} +(-0.587785 - 0.809017i) q^{17} +(-0.642040 - 1.26007i) q^{19} +1.00000i q^{23} +(0.951057 + 0.309017i) q^{25} +(0.642040 - 1.26007i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.309017 + 0.951057i) q^{29} +(-1.00000 + 1.00000i) q^{32} +(-1.00000 - 1.00000i) q^{34} +(-0.642040 + 1.26007i) q^{37} +(-1.17557 - 1.61803i) q^{38} +(-0.587785 - 0.809017i) q^{39} +1.00000i q^{43} +(0.221232 + 1.39680i) q^{46} +(-1.26007 + 0.642040i) q^{47} +(0.309017 + 0.951057i) q^{48} +(0.587785 + 0.809017i) q^{49} +(1.39680 + 0.221232i) q^{50} +(-0.951057 + 0.309017i) q^{51} +(0.309017 - 0.951057i) q^{52} +(-0.809017 - 0.587785i) q^{53} +(1.00000 - 1.00000i) q^{54} +(-1.39680 + 0.221232i) q^{57} +(0.642040 + 1.26007i) q^{58} +(-0.809017 + 0.587785i) q^{61} +(-0.587785 + 0.809017i) q^{64} +(-0.809017 - 0.587785i) q^{68} +(0.951057 + 0.309017i) q^{69} +(0.221232 - 1.39680i) q^{71} +(0.642040 - 1.26007i) q^{73} +(-0.618034 + 1.90211i) q^{74} +(0.587785 - 0.809017i) q^{75} +(-1.00000 - 1.00000i) q^{76} +(-1.00000 - 1.00000i) q^{78} +(-0.809017 - 0.587785i) q^{79} +(-0.309017 - 0.951057i) q^{81} +(-0.221232 + 1.39680i) q^{83} +(0.221232 + 1.39680i) q^{86} +1.00000 q^{87} +(0.309017 + 0.951057i) q^{92} +(-1.61803 + 1.17557i) q^{94} +(0.642040 + 1.26007i) q^{96} +(1.00000 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} + 2 q^{6} - 2 q^{16} - 2 q^{19} + 2 q^{26} + 2 q^{27} - 2 q^{29} - 8 q^{32} - 8 q^{34} - 2 q^{37} + 2 q^{46} + 2 q^{47} - 2 q^{48} + 2 q^{50} - 2 q^{52} - 2 q^{53} + 8 q^{54} - 2 q^{57}+ \cdots + 8 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 + 2 * q^6 - 2 * q^16 - 2 * q^19 + 2 * q^26 + 2 * q^27 - 2 * q^29 - 8 * q^32 - 8 * q^34 - 2 * q^37 + 2 * q^46 + 2 * q^47 - 2 * q^48 + 2 * q^50 - 2 * q^52 - 2 * q^53 + 8 * q^54 - 2 * q^57 + 2 * q^58 - 2 * q^61 - 2 * q^68 + 2 * q^71 + 2 * q^73 + 4 * q^74 - 8 * q^76 - 8 * q^78 - 2 * q^79 + 2 * q^81 - 2 * q^83 + 2 * q^86 + 8 * q^87 - 2 * q^92 - 4 * q^94 + 2 * q^96 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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