LMFDB - Embedded newform 1740.1.cf.b.1319.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1740,1,Mod(119,1740)] 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("1740.119"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1740, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 14, 14, 5])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1740.cf (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$0.868373121981$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{28})$
Coefficient field:	$\Q(\zeta_{56})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{28}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{28} - \cdots)$

Embedding invariants

Embedding label			1319.1
Root			$0.846724 - 0.532032i$ of defining polynomial
Character	$\chi$	$=$	1740.1319
Dual form			1740.1.cf.b.839.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.993712 + 0.111964i) q^{2} +(0.943883 + 0.330279i) q^{3} +(0.974928 - 0.222521i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-0.974928 - 0.222521i) q^{6} +(-0.376828 + 1.65099i) q^{7} +(-0.943883 + 0.330279i) q^{8} +(0.781831 + 0.623490i) q^{9} +(0.532032 - 0.846724i) q^{10} +(0.993712 + 0.111964i) q^{12} +(0.189606 - 1.68280i) q^{14} +(-0.846724 + 0.532032i) q^{15} +(0.900969 - 0.433884i) q^{16} +(-0.846724 - 0.532032i) q^{18} +(-0.433884 + 0.900969i) q^{20} +(-0.900969 + 1.43388i) q^{21} +(0.175075 - 0.139617i) q^{23} -1.00000 q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.532032 + 0.846724i) q^{27} +1.69345i q^{28} +(0.222521 - 0.974928i) q^{29} +(0.781831 - 0.623490i) q^{30} +(-0.846724 + 0.532032i) q^{32} +(-1.05585 - 1.32399i) q^{35} +(0.900969 + 0.433884i) q^{36} +(0.330279 - 0.943883i) q^{40} +(-0.467085 + 0.467085i) q^{41} +(0.734760 - 1.52574i) q^{42} +(-1.79061 - 0.201753i) q^{43} +(-0.974928 + 0.222521i) q^{45} +(-0.158342 + 0.158342i) q^{46} +(-0.643997 + 1.84044i) q^{47} +(0.993712 - 0.111964i) q^{48} +(-1.68280 - 0.810394i) q^{49} +(0.330279 + 0.943883i) q^{50} +(-0.623490 - 0.781831i) q^{54} +(-0.189606 - 1.68280i) q^{56} +(-0.111964 + 0.993712i) q^{58} +(-0.707107 + 0.707107i) q^{60} +(0.752407 + 1.19745i) q^{61} +(-1.32399 + 1.05585i) q^{63} +(0.781831 - 0.623490i) q^{64} +(0.613604 - 1.27416i) q^{67} +(0.211363 - 0.0739590i) q^{69} +(1.19745 + 1.19745i) q^{70} +(-0.943883 - 0.330279i) q^{72} +(0.111964 - 0.993712i) q^{75} +(-0.222521 + 0.974928i) q^{80} +(0.222521 + 0.974928i) q^{81} +(0.411851 - 0.516445i) q^{82} +(1.84044 - 0.420068i) q^{83} +(-0.559311 + 1.59842i) q^{84} +1.80194 q^{86} +(0.532032 - 0.846724i) q^{87} +(1.05737 - 0.119137i) q^{89} +(0.943883 - 0.330279i) q^{90} +(0.139617 - 0.175075i) q^{92} +(0.433884 - 1.90097i) q^{94} +(-0.974928 + 0.222521i) q^{96} +(1.76295 + 0.616884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{5} - 4 q^{14} + 4 q^{16} - 4 q^{21} - 24 q^{24} - 4 q^{25} + 4 q^{29} + 4 q^{36} - 4 q^{41} - 4 q^{46} - 4 q^{49} + 4 q^{54} + 4 q^{56} - 4 q^{61} - 4 q^{69} + 4 q^{70} - 4 q^{80} + 4 q^{81}+ \cdots - 4 q^{89}+O(q^{100}) $ 24 * q + 4 * q^5 - 4 * q^14 + 4 * q^16 - 4 * q^21 - 24 * q^24 - 4 * q^25 + 4 * q^29 + 4 * q^36 - 4 * q^41 - 4 * q^46 - 4 * q^49 + 4 * q^54 + 4 * q^56 - 4 * q^61 - 4 * q^69 + 4 * q^70 - 4 * q^80 + 4 * q^81 + 4 * q^84 + 8 * q^86 - 4 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1740\mathbb{Z}\right)^\times$.

$n$	$581$	$697$	$871$	$901$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{13}{28}\right)$

Coefficient data

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

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

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

$2$	−0.993712	+	0.111964i	−0.993712	+	0.111964i
$2$	−0.993712	+	0.111964i	−0.993712	+	0.111964i
$3$	0.943883	+	0.330279i	0.943883	+	0.330279i
$3$	0.943883	+	0.330279i	0.943883	+	0.330279i
$4$	0.974928	−	0.222521i	0.974928	−	0.222521i
$5$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$5$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$6$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$7$	−0.376828	+	1.65099i	−0.376828	+	1.65099i	0.330279	+	0.943883i	$0.392857\pi$
$7$	−0.376828	+	1.65099i	−0.376828	+	1.65099i	−0.707107	+	0.707107i	$0.750000\pi$
$8$	−0.943883	+	0.330279i	−0.943883	+	0.330279i
$9$	0.781831	+	0.623490i	0.781831	+	0.623490i
$10$	0.532032	−	0.846724i	0.532032	−	0.846724i
$11$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$11$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$12$	0.993712	+	0.111964i	0.993712	+	0.111964i
$13$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$13$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$14$	0.189606	−	1.68280i	0.189606	−	1.68280i
$15$	−0.846724	+	0.532032i	−0.846724	+	0.532032i
$16$	0.900969	−	0.433884i	0.900969	−	0.433884i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	−0.846724	−	0.532032i	−0.846724	−	0.532032i
$19$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$19$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$20$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$21$	−0.900969	+	1.43388i	−0.900969	+	1.43388i
$22$		0			0
$23$	0.175075	−	0.139617i	0.175075	−	0.139617i	−0.532032	−	0.846724i	$-0.678571\pi$
$23$	0.175075	−	0.139617i	0.175075	−	0.139617i	0.707107	+	0.707107i	$0.250000\pi$
$24$	−1.00000			−1.00000
$25$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$26$		0			0
$27$	0.532032	+	0.846724i	0.532032	+	0.846724i
$28$			1.69345i			1.69345i
$29$	0.222521	−	0.974928i	0.222521	−	0.974928i
$29$	0.222521	−	0.974928i	0.222521	−	0.974928i
$30$	0.781831	−	0.623490i	0.781831	−	0.623490i
$31$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$31$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$32$	−0.846724	+	0.532032i	−0.846724	+	0.532032i
$33$		0			0
$34$		0			0
$35$	−1.05585	−	1.32399i	−1.05585	−	1.32399i
$36$	0.900969	+	0.433884i	0.900969	+	0.433884i
$37$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$37$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$38$		0			0
$39$		0			0
$40$	0.330279	−	0.943883i	0.330279	−	0.943883i
$41$	−0.467085	+	0.467085i	−0.467085	+	0.467085i	−0.900969	−	0.433884i	$-0.857143\pi$
$41$	−0.467085	+	0.467085i	−0.467085	+	0.467085i	0.433884	+	0.900969i	$0.357143\pi$
$42$	0.734760	−	1.52574i	0.734760	−	1.52574i
$43$	−1.79061	−	0.201753i	−1.79061	−	0.201753i	−0.846724	−	0.532032i	$-0.821429\pi$
$43$	−1.79061	−	0.201753i	−1.79061	−	0.201753i	−0.943883	+	0.330279i	$0.892857\pi$
$44$		0			0
$45$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$46$	−0.158342	+	0.158342i	−0.158342	+	0.158342i
$47$	−0.643997	+	1.84044i	−0.643997	+	1.84044i	−0.111964	+	0.993712i	$0.535714\pi$
$47$	−0.643997	+	1.84044i	−0.643997	+	1.84044i	−0.532032	+	0.846724i	$0.678571\pi$
$48$	0.993712	−	0.111964i	0.993712	−	0.111964i
$49$	−1.68280	−	0.810394i	−1.68280	−	0.810394i
$50$	0.330279	+	0.943883i	0.330279	+	0.943883i
$51$		0			0
$52$		0			0
$53$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$53$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$54$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$55$		0			0
$56$	−0.189606	−	1.68280i	−0.189606	−	1.68280i
$57$		0			0
$58$	−0.111964	+	0.993712i	−0.111964	+	0.993712i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$61$	0.752407	+	1.19745i	0.752407	+	1.19745i	0.974928	+	0.222521i	$0.0714286\pi$
$61$	0.752407	+	1.19745i	0.752407	+	1.19745i	−0.222521	+	0.974928i	$0.571429\pi$
$62$		0			0
$63$	−1.32399	+	1.05585i	−1.32399	+	1.05585i
$64$	0.781831	−	0.623490i	0.781831	−	0.623490i
$65$		0			0
$66$		0			0
$67$	0.613604	−	1.27416i	0.613604	−	1.27416i	−0.330279	−	0.943883i	$-0.607143\pi$
$67$	0.613604	−	1.27416i	0.613604	−	1.27416i	0.943883	−	0.330279i	$-0.107143\pi$
$68$		0			0
$69$	0.211363	−	0.0739590i	0.211363	−	0.0739590i
$70$	1.19745	+	1.19745i	1.19745	+	1.19745i
$71$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$71$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$72$	−0.943883	−	0.330279i	−0.943883	−	0.330279i
$73$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$73$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$74$		0			0
$75$	0.111964	−	0.993712i	0.111964	−	0.993712i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$79$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$80$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$81$	0.222521	+	0.974928i	0.222521	+	0.974928i
$82$	0.411851	−	0.516445i	0.411851	−	0.516445i
$83$	1.84044	−	0.420068i	1.84044	−	0.420068i	0.846724	−	0.532032i	$-0.178571\pi$
$83$	1.84044	−	0.420068i	1.84044	−	0.420068i	0.993712	+	0.111964i	$0.0357143\pi$
$84$	−0.559311	+	1.59842i	−0.559311	+	1.59842i
$85$		0			0
$86$	1.80194			1.80194
$87$	0.532032	−	0.846724i	0.532032	−	0.846724i
$88$		0			0
$89$	1.05737	−	0.119137i	1.05737	−	0.119137i	0.433884	−	0.900969i	$-0.357143\pi$
$89$	1.05737	−	0.119137i	1.05737	−	0.119137i	0.623490	+	0.781831i	$0.285714\pi$
$90$	0.943883	−	0.330279i	0.943883	−	0.330279i
$91$		0			0
$92$	0.139617	−	0.175075i	0.139617	−	0.175075i
$93$		0			0
$94$	0.433884	−	1.90097i	0.433884	−	1.90097i
$95$		0			0
$96$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$97$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$97$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$98$	1.76295	+	0.616884i	1.76295	+	0.616884i
$99$		0			0
$100$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$101$	−0.222521	+	1.97493i	−0.222521	+	1.97493i			1.00000i	$0.5\pi$
$101$	−0.222521	+	1.97493i	−0.222521	+	1.97493i	−0.222521	+	0.974928i	$0.571429\pi$
$102$		0			0
$103$	1.70082	−	0.819071i	1.70082	−	0.819071i	0.707107	−	0.707107i	$-0.250000\pi$
$103$	1.70082	−	0.819071i	1.70082	−	0.819071i	0.993712	−	0.111964i	$-0.0357143\pi$
$104$		0			0
$105$	−0.559311	−	1.59842i	−0.559311	−	1.59842i
$106$		0			0
$107$	0.862311	−	1.79061i	0.862311	−	1.79061i	0.330279	−	0.943883i	$-0.392857\pi$
$107$	0.862311	−	1.79061i	0.862311	−	1.79061i	0.532032	−	0.846724i	$-0.321429\pi$
$108$	0.707107	+	0.707107i	0.707107	+	0.707107i
$109$	−1.75676	−	0.400969i	−1.75676	−	0.400969i	−0.781831	−	0.623490i	$-0.785714\pi$
$109$	−1.75676	−	0.400969i	−1.75676	−	0.400969i	−0.974928	+	0.222521i	$0.928571\pi$
$110$		0			0
$111$		0			0
$112$	0.376828	+	1.65099i	0.376828	+	1.65099i
$113$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$113$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$114$		0			0
$115$			0.223929i			0.223929i
$116$		−	1.00000i		−	1.00000i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.623490	−	0.781831i	0.623490	−	0.781831i
$121$	0.781831	+	0.623490i	0.781831	+	0.623490i
$122$	−0.881748	−	1.10568i	−0.881748	−	1.10568i
$123$	−0.595142	+	0.286605i	−0.595142	+	0.286605i
$124$		0			0
$125$	0.900969	+	0.433884i	0.900969	+	0.433884i
$126$	1.19745	−	1.19745i	1.19745	−	1.19745i
$127$	−0.146988	+	0.420068i	−0.146988	+	0.420068i	−0.993712	−	0.111964i	$-0.964286\pi$
$127$	−0.146988	+	0.420068i	−0.146988	+	0.420068i	0.846724	+	0.532032i	$0.178571\pi$
$128$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$129$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$130$		0			0
$131$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$131$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$132$		0			0
$133$		0			0
$134$	−0.467085	+	1.33485i	−0.467085	+	1.33485i
$135$	−0.993712	−	0.111964i	−0.993712	−	0.111964i
$136$		0			0
$137$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$137$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$138$	−0.201753	+	0.0971591i	−0.201753	+	0.0971591i
$139$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$139$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$140$	−1.32399	−	1.05585i	−1.32399	−	1.05585i
$141$	−1.21572	+	1.52446i	−1.21572	+	1.52446i
$142$		0			0
$143$		0			0
$144$	0.974928	+	0.222521i	0.974928	+	0.222521i
$145$	0.623490	+	0.781831i	0.623490	+	0.781831i
$146$		0			0
$147$	−1.32071	−	1.32071i	−1.32071	−	1.32071i
$148$		0			0
$149$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$149$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$150$			1.00000i			1.00000i
$151$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$151$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$		0			0
$160$	0.111964	−	0.993712i	0.111964	−	0.993712i
$161$	0.164534	+	0.341658i	0.164534	+	0.341658i
$162$	−0.330279	−	0.943883i	−0.330279	−	0.943883i
$163$	0.819071	+	0.286605i	0.819071	+	0.286605i	0.707107	−	0.707107i	$-0.250000\pi$
$163$	0.819071	+	0.286605i	0.819071	+	0.286605i	0.111964	+	0.993712i	$0.464286\pi$
$164$	−0.351438	+	0.559311i	−0.351438	+	0.559311i
$165$		0			0
$166$	−1.78183	+	0.623490i	−1.78183	+	0.623490i
$167$	0.146988	−	0.643997i	0.146988	−	0.643997i	−0.846724	−	0.532032i	$-0.821429\pi$
$167$	0.146988	−	0.643997i	0.146988	−	0.643997i	0.993712	−	0.111964i	$-0.0357143\pi$
$168$	0.376828	−	1.65099i	0.376828	−	1.65099i
$169$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$170$		0			0
$171$		0			0
$172$	−1.79061	+	0.201753i	−1.79061	+	0.201753i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$175$	1.69345			1.69345
$176$		0			0
$177$		0			0
$178$	−1.03739	+	0.236777i	−1.03739	+	0.236777i
$179$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$179$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$180$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$181$	0.347948	−	1.52446i	0.347948	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$181$	0.347948	−	1.52446i	0.347948	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$182$		0			0
$183$	0.314692	+	1.37876i	0.314692	+	1.37876i
$184$	−0.119137	+	0.189606i	−0.119137	+	0.189606i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.218315	+	1.93760i	−0.218315	+	1.93760i
$189$	−1.59842	+	0.559311i	−1.59842	+	0.559311i
$190$		0			0
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	0.943883	−	0.330279i	0.943883	−	0.330279i
$193$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$193$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$194$		0			0
$195$		0			0
$196$	−1.82094	−	0.415617i	−1.82094	−	0.415617i
$197$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$197$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$198$		0			0
$199$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$199$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$200$	0.532032	+	0.846724i	0.532032	+	0.846724i
$201$	1.00000	−	1.00000i	1.00000	−	1.00000i
$202$		−	1.98742i		−	1.98742i
$203$	1.52574	+	0.734760i	1.52574	+	0.734760i
$204$		0			0
$205$	−0.0739590	−	0.656405i	−0.0739590	−	0.656405i
$206$	−1.59842	+	1.00435i	−1.59842	+	1.00435i
$207$	0.223929			0.223929
$208$		0			0
$209$		0			0
$210$	0.734760	+	1.52574i	0.734760	+	1.52574i
$211$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$211$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$212$		0			0
$213$		0			0
$214$	−0.656405	+	1.87590i	−0.656405	+	1.87590i
$215$	1.27416	−	1.27416i	1.27416	−	1.27416i
$216$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$217$		0			0
$218$	1.79061	+	0.201753i	1.79061	+	0.201753i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.958689	−	0.461680i	−0.958689	−	0.461680i	−0.111964	−	0.993712i	$-0.535714\pi$
$223$	−0.958689	−	0.461680i	−0.958689	−	0.461680i	−0.846724	+	0.532032i	$0.821429\pi$
$224$	−0.559311	−	1.59842i	−0.559311	−	1.59842i
$225$	0.433884	−	0.900969i	0.433884	−	0.900969i
$226$		0			0
$227$	0.516445	+	0.411851i	0.516445	+	0.411851i	0.846724	−	0.532032i	$-0.178571\pi$
$227$	0.516445	+	0.411851i	0.516445	+	0.411851i	−0.330279	+	0.943883i	$0.607143\pi$
$228$		0			0
$229$	1.59842	−	1.00435i	1.59842	−	1.00435i	0.623490	−	0.781831i	$-0.285714\pi$
$229$	1.59842	−	1.00435i	1.59842	−	1.00435i	0.974928	−	0.222521i	$-0.0714286\pi$
$230$	−0.0250721	−	0.222521i	−0.0250721	−	0.222521i
$231$		0			0
$232$	0.111964	+	0.993712i	0.111964	+	0.993712i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	−1.03739	−	1.65099i	−1.03739	−	1.65099i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$239$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$240$	−0.532032	+	0.846724i	−0.532032	+	0.846724i
$241$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$241$	−0.678448	+	1.40881i	−0.678448	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$242$	−0.846724	−	0.532032i	−0.846724	−	0.532032i
$243$	−0.111964	+	0.993712i	−0.111964	+	0.993712i
$244$	1.00000	+	1.00000i	1.00000	+	1.00000i
$245$	1.68280	−	0.810394i	1.68280	−	0.810394i
$246$	0.559311	−	0.351438i	0.559311	−	0.351438i
$247$		0			0
$248$		0			0
$249$	1.87590	+	0.211363i	1.87590	+	0.211363i
$250$	−0.943883	−	0.330279i	−0.943883	−	0.330279i
$251$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$251$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$252$	−1.05585	+	1.32399i	−1.05585	+	1.32399i
$253$		0			0
$254$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$255$		0			0
$256$	0.623490	−	0.781831i	0.623490	−	0.781831i
$257$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$257$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$258$	1.70082	+	0.595142i	1.70082	+	0.595142i
$259$		0			0
$260$		0			0
$261$	0.781831	−	0.623490i	0.781831	−	0.623490i
$262$		0			0
$263$	−0.442244	+	0.0498289i	−0.442244	+	0.0498289i	−0.330279	−	0.943883i	$-0.607143\pi$
$263$	−0.442244	+	0.0498289i	−0.442244	+	0.0498289i	−0.111964	+	0.993712i	$0.535714\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.03739	+	0.236777i	1.03739	+	0.236777i
$268$	0.314692	−	1.37876i	0.314692	−	1.37876i
$269$	−0.211363	+	0.0739590i	−0.211363	+	0.0739590i	−0.433884	−	0.900969i	$-0.642857\pi$
$269$	−0.211363	+	0.0739590i	−0.211363	+	0.0739590i	0.222521	+	0.974928i	$0.428571\pi$
$270$	1.00000			1.00000
$271$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$271$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.189606	−	0.119137i	0.189606	−	0.119137i
$277$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$277$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$278$		0			0
$279$		0			0
$280$	1.43388	+	0.900969i	1.43388	+	0.900969i
$281$	0.541044	−	1.12349i	0.541044	−	1.12349i	−0.433884	−	0.900969i	$-0.642857\pi$
$281$	0.541044	−	1.12349i	0.541044	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$282$	1.03739	−	1.65099i	1.03739	−	1.65099i
$283$	−1.93760	−	0.442244i	−1.93760	−	0.442244i	−0.993712	−	0.111964i	$-0.964286\pi$
$283$	−1.93760	−	0.442244i	−1.93760	−	0.442244i	−0.943883	−	0.330279i	$-0.892857\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.595142	−	0.947164i	−0.595142	−	0.947164i
$288$	−0.993712	−	0.111964i	−0.993712	−	0.111964i
$289$			1.00000i			1.00000i
$290$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$291$		0			0
$292$		0			0
$293$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$293$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$294$	1.46028	+	1.16453i	1.46028	+	1.16453i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−0.146988	−	0.420068i	−0.146988	−	0.420068i
$299$		0			0
$300$	−0.111964	−	0.993712i	−0.111964	−	0.993712i
$301$	1.00784	−	2.88025i	1.00784	−	2.88025i
$302$		0			0
$303$	−0.862311	+	1.79061i	−0.862311	+	1.79061i
$304$		0			0
$305$	−1.40532	−	0.158342i	−1.40532	−	0.158342i
$306$		0			0
$307$	0.881748	−	0.881748i	0.881748	−	0.881748i	−0.111964	−	0.993712i	$-0.535714\pi$
$307$	0.881748	−	0.881748i	0.881748	−	0.881748i	0.993712	+	0.111964i	$0.0357143\pi$
$308$		0			0
$309$	1.87590	−	0.211363i	1.87590	−	0.211363i
$310$		0			0
$311$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$311$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$312$		0			0
$313$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$313$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$314$		0			0
$315$		−	1.69345i		−	1.69345i
$316$		0			0
$317$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$317$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$318$		0			0
$319$		0			0
$320$			1.00000i			1.00000i
$321$	1.40532	−	1.40532i	1.40532	−	1.40532i
$322$	−0.201753	−	0.321088i	−0.201753	−	0.321088i
$323$		0			0
$324$	0.433884	+	0.900969i	0.433884	+	0.900969i
$325$		0			0
$326$	−0.846011	−	0.193096i	−0.846011	−	0.193096i
$327$	−1.52574	−	0.958689i	−1.52574	−	0.958689i
$328$	0.286605	−	0.595142i	0.286605	−	0.595142i
$329$	−2.79587	−	1.75676i	−2.79587	−	1.75676i
$330$		0			0
$331$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$331$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$332$	1.70082	−	0.819071i	1.70082	−	0.819071i
$333$		0			0
$334$	−0.0739590	+	0.656405i	−0.0739590	+	0.656405i
$335$	0.613604	+	1.27416i	0.613604	+	1.27416i
$336$	−0.189606	+	1.68280i	−0.189606	+	1.68280i
$337$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$337$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$338$	0.532032	−	0.846724i	0.532032	−	0.846724i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.916230	−	1.14892i	0.916230	−	1.14892i
$344$	1.75676	−	0.400969i	1.75676	−	0.400969i
$345$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i
$346$		0			0
$347$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$347$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$348$	0.330279	−	0.943883i	0.330279	−	0.943883i
$349$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$349$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$350$	−1.68280	+	0.189606i	−1.68280	+	0.189606i
$351$		0			0
$352$		0			0
$353$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$353$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$354$		0			0
$355$		0			0
$356$	1.00435	−	0.351438i	1.00435	−	0.351438i
$357$		0			0
$358$		0			0
$359$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$359$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$360$	0.846724	−	0.532032i	0.846724	−	0.532032i
$361$	0.433884	+	0.900969i	0.433884	+	0.900969i
$362$	−0.175075	+	1.55383i	−0.175075	+	1.55383i
$363$	0.532032	+	0.846724i	0.532032	+	0.846724i
$364$		0			0
$365$		0			0
$366$	−0.467085	−	1.33485i	−0.467085	−	1.33485i
$367$	1.65099	+	1.03739i	1.65099	+	1.03739i	0.943883	+	0.330279i	$0.107143\pi$
$367$	1.65099	+	1.03739i	1.65099	+	1.03739i	0.707107	+	0.707107i	$0.250000\pi$
$368$	0.0971591	−	0.201753i	0.0971591	−	0.201753i
$369$	−0.656405	+	0.0739590i	−0.656405	+	0.0739590i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$373$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$374$		0			0
$375$	0.707107	+	0.707107i	0.707107	+	0.707107i
$376$		−	1.94986i		−	1.94986i
$377$		0			0
$378$	1.52574	−	0.734760i	1.52574	−	0.734760i
$379$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$379$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$380$		0			0
$381$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$382$		0			0
$383$	−1.23914	−	1.55383i	−1.23914	−	1.55383i	−0.707107	−	0.707107i	$-0.750000\pi$
$383$	−1.23914	−	1.55383i	−1.23914	−	1.55383i	−0.532032	−	0.846724i	$-0.678571\pi$
$384$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$385$		0			0
$386$		0			0
$387$	−1.27416	−	1.27416i	−1.27416	−	1.27416i
$388$		0			0
$389$	1.40532	−	1.40532i	1.40532	−	1.40532i	0.623490	−	0.781831i	$-0.285714\pi$
$389$	1.40532	−	1.40532i	1.40532	−	1.40532i	0.781831	−	0.623490i	$-0.214286\pi$
$390$		0			0
$391$		0			0
$392$	1.85602	+	0.209124i	1.85602	+	0.209124i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$397$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$398$		0			0
$399$		0			0
$400$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$401$	0.347948	+	0.277479i	0.347948	+	0.277479i	0.781831	−	0.623490i	$-0.214286\pi$
$401$	0.347948	+	0.277479i	0.347948	+	0.277479i	−0.433884	+	0.900969i	$0.642857\pi$
$402$	−0.881748	+	1.10568i	−0.881748	+	1.10568i
$403$		0			0
$404$	0.222521	+	1.97493i	0.222521	+	1.97493i
$405$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$406$	−1.59842	−	0.559311i	−1.59842	−	0.559311i
$407$		0			0
$408$		0			0
$409$	−0.566116	−	0.900969i	−0.566116	−	0.900969i	0.433884	−	0.900969i	$-0.357143\pi$
$409$	−0.566116	−	0.900969i	−0.566116	−	0.900969i	−1.00000			$\pi$
$410$	0.146988	+	0.643997i	0.146988	+	0.643997i
$411$		0			0
$412$	1.47592	−	1.17700i	1.47592	−	1.17700i
$413$		0			0
$414$	−0.222521	+	0.0250721i	−0.222521	+	0.0250721i
$415$	−0.819071	+	1.70082i	−0.819071	+	1.70082i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$	−0.900969	−	1.43388i	−0.900969	−	1.43388i
$421$	−0.211363	+	1.87590i	−0.211363	+	1.87590i	0.222521	+	0.974928i	$0.428571\pi$
$421$	−0.211363	+	1.87590i	−0.211363	+	1.87590i	−0.433884	+	0.900969i	$0.642857\pi$
$422$		0			0
$423$	−1.65099	+	1.03739i	−1.65099	+	1.03739i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.26050	+	0.790985i	−2.26050	+	0.790985i
$428$	0.442244	−	1.93760i	0.442244	−	1.93760i
$429$		0			0
$430$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$431$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$431$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$432$	0.846724	+	0.532032i	0.846724	+	0.532032i
$433$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$433$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$434$		0			0
$435$	0.330279	+	0.943883i	0.330279	+	0.943883i
$436$	−1.80194			−1.80194
$437$		0			0
$438$		0			0
$439$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$439$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$440$		0			0
$441$	−0.810394	−	1.68280i	−0.810394	−	1.68280i
$442$		0			0
$443$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$443$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$444$		0			0
$445$	−0.566116	+	0.900969i	−0.566116	+	0.900969i
$446$	1.00435	+	0.351438i	1.00435	+	0.351438i
$447$	−0.0498289	+	0.442244i	−0.0498289	+	0.442244i
$448$	0.734760	+	1.52574i	0.734760	+	1.52574i
$449$	0.119137	−	1.05737i	0.119137	−	1.05737i	−0.781831	−	0.623490i	$-0.785714\pi$
$449$	0.119137	−	1.05737i	0.119137	−	1.05737i	0.900969	−	0.433884i	$-0.142857\pi$
$450$	−0.330279	+	0.943883i	−0.330279	+	0.943883i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.559311	−	0.351438i	−0.559311	−	0.351438i
$455$		0			0
$456$		0			0
$457$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$457$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$458$	−1.47592	+	1.17700i	−1.47592	+	1.17700i
$459$		0			0
$460$	0.0498289	+	0.218315i	0.0498289	+	0.218315i
$461$	−1.00435	−	1.59842i	−1.00435	−	1.59842i	−0.781831	−	0.623490i	$-0.785714\pi$
$461$	−1.00435	−	1.59842i	−1.00435	−	1.59842i	−0.222521	−	0.974928i	$-0.571429\pi$
$462$		0			0
$463$			0.660558i			0.660558i	0.943883	+	0.330279i	$0.107143\pi$
$463$			0.660558i			0.660558i	−0.943883	+	0.330279i	$0.892857\pi$
$464$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$465$		0			0
$466$		0			0
$467$	0.734760	−	0.461680i	0.734760	−	0.461680i	−0.111964	−	0.993712i	$-0.535714\pi$
$467$	0.734760	−	0.461680i	0.734760	−	0.461680i	0.846724	+	0.532032i	$0.178571\pi$
$468$		0			0
$469$	1.87241	+	1.49319i	1.87241	+	1.49319i
$470$	1.21572	+	1.52446i	1.21572	+	1.52446i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$479$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$480$	0.433884	−	0.900969i	0.433884	−	0.900969i
$481$		0			0
$482$	0.516445	−	1.47592i	0.516445	−	1.47592i
$483$	0.0424583	+	0.376828i	0.0424583	+	0.376828i
$484$	0.900969	+	0.433884i	0.900969	+	0.433884i
$485$		0			0
$486$		−	1.00000i		−	1.00000i
$487$	0.663433	+	0.831919i	0.663433	+	0.831919i	0.993712	−	0.111964i	$-0.0357143\pi$
$487$	0.663433	+	0.831919i	0.663433	+	0.831919i	−0.330279	+	0.943883i	$0.607143\pi$
$488$	−1.10568	−	0.881748i	−1.10568	−	0.881748i
$489$	0.678448	+	0.541044i	0.678448	+	0.541044i
$490$	−1.58148	+	0.993712i	−1.58148	+	0.993712i
$491$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$491$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$492$	−0.516445	+	0.411851i	−0.516445	+	0.411851i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.88777			−1.88777
$499$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$499$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$500$	0.974928	+	0.222521i	0.974928	+	0.222521i
$501$	0.351438	−	0.559311i	0.351438	−	0.559311i
$502$		0			0
$503$	−0.734760	−	0.461680i	−0.734760	−	0.461680i	0.111964	−	0.993712i	$-0.464286\pi$
$503$	−0.734760	−	0.461680i	−0.734760	−	0.461680i	−0.846724	+	0.532032i	$0.821429\pi$
$504$	0.900969	−	1.43388i	0.900969	−	1.43388i
$505$	−1.40532	−	1.40532i	−1.40532	−	1.40532i
$506$		0			0
$507$	−0.846724	+	0.532032i	−0.846724	+	0.532032i
$508$	−0.0498289	+	0.442244i	−0.0498289	+	0.442244i
$509$	−0.781831	−	1.62349i	−0.781831	−	1.62349i	−0.781831	−	0.623490i	$-0.785714\pi$
$509$	−0.781831	−	1.62349i	−0.781831	−	1.62349i		−	1.00000i	$-0.5\pi$
$510$		0			0
$511$		0			0
$512$	−0.532032	+	0.846724i	−0.532032	+	0.846724i
$513$		0			0
$514$		0			0
$515$	−0.420068	+	1.84044i	−0.420068	+	1.84044i
$516$	−1.75676	−	0.400969i	−1.75676	−	0.400969i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.94986			−1.94986			−0.974928	−	0.222521i	$-0.928571\pi$
$521$	−1.94986			−1.94986			−0.974928	+	0.222521i	$0.928571\pi$
$522$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$523$	0.660558			0.660558			0.330279	−	0.943883i	$-0.392857\pi$
$523$	0.660558			0.660558			0.330279	+	0.943883i	$0.392857\pi$
$524$		0			0
$525$	1.59842	+	0.559311i	1.59842	+	0.559311i
$526$	0.433884	−	0.0990311i	0.433884	−	0.0990311i
$527$		0			0
$528$		0			0
$529$	−0.211363	+	0.926041i	−0.211363	+	0.926041i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−1.05737	−	0.119137i	−1.05737	−	0.119137i
$535$	0.862311	+	1.79061i	0.862311	+	1.79061i
$536$	−0.158342	+	1.40532i	−0.158342	+	1.40532i
$537$		0			0
$538$	0.201753	−	0.0971591i	0.201753	−	0.0971591i
$539$		0			0
$540$	−0.993712	+	0.111964i	−0.993712	+	0.111964i
$541$	−1.43388	−	0.900969i	−1.43388	−	0.900969i	−0.433884	−	0.900969i	$-0.642857\pi$
$541$	−1.43388	−	0.900969i	−1.43388	−	0.900969i	−1.00000			$\pi$
$542$		0			0
$543$	0.831919	−	1.32399i	0.831919	−	1.32399i
$544$		0			0
$545$	1.40881	−	1.12349i	1.40881	−	1.12349i
$546$		0			0
$547$	0.420068	+	1.84044i	0.420068	+	1.84044i	0.532032	+	0.846724i	$0.321429\pi$
$547$	0.420068	+	1.84044i	0.420068	+	1.84044i	−0.111964	+	0.993712i	$0.535714\pi$
$548$		0			0
$549$	−0.158342	+	1.40532i	−0.158342	+	1.40532i
$550$		0			0
$551$		0			0
$552$	−0.175075	+	0.139617i	−0.175075	+	0.139617i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$557$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$558$		0			0
$559$		0			0
$560$	−1.52574	−	0.734760i	−1.52574	−	0.734760i
$561$		0			0
$562$	−0.411851	+	1.17700i	−0.411851	+	1.17700i
$563$	−0.314692	+	0.314692i	−0.314692	+	0.314692i	−0.846724	−	0.532032i	$-0.821429\pi$
$563$	−0.314692	+	0.314692i	−0.314692	+	0.314692i	0.532032	+	0.846724i	$0.321429\pi$
$564$	−0.846011	+	1.75676i	−0.846011	+	1.75676i
$565$		0			0
$566$	1.97493	+	0.222521i	1.97493	+	0.222521i
$567$	−1.69345			−1.69345
$568$		0			0
$569$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i	−0.974928	−	0.222521i	$-0.928571\pi$
$569$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i	0.900969	+	0.433884i	$0.142857\pi$
$570$		0			0
$571$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$571$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$572$		0			0
$573$		0			0
$574$	0.697449	+	0.874573i	0.697449	+	0.874573i
$575$	−0.175075	−	0.139617i	−0.175075	−	0.139617i
$576$	1.00000			1.00000
$577$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$577$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$578$	−0.111964	−	0.993712i	−0.111964	−	0.993712i
$579$		0			0
$580$	0.781831	+	0.623490i	0.781831	+	0.623490i
$581$			3.19684i			3.19684i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.93760	+	0.442244i	1.93760	+	0.442244i	0.993712	+	0.111964i	$0.0357143\pi$
$587$	1.93760	+	0.442244i	1.93760	+	0.442244i	0.943883	+	0.330279i	$0.107143\pi$
$588$	−1.58148	−	0.993712i	−1.58148	−	0.993712i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$593$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$594$		0			0
$595$		0			0
$596$	0.193096	+	0.400969i	0.193096	+	0.400969i
$597$		0			0
$598$		0			0
$599$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$599$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$600$	0.222521	+	0.974928i	0.222521	+	0.974928i
$601$	1.59842	−	0.559311i	1.59842	−	0.559311i	0.623490	−	0.781831i	$-0.285714\pi$
$601$	1.59842	−	0.559311i	1.59842	−	0.559311i	0.974928	+	0.222521i	$0.0714286\pi$
$602$	−0.679020	+	2.97498i	−0.679020	+	2.97498i
$603$	1.27416	−	0.613604i	1.27416	−	0.613604i
$604$		0			0
$605$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$606$	0.656405	−	1.87590i	0.656405	−	1.87590i
$607$	−1.23914	+	0.139617i	−1.23914	+	0.139617i	−0.707107	−	0.707107i	$-0.750000\pi$
$607$	−1.23914	+	0.139617i	−1.23914	+	0.139617i	−0.532032	+	0.846724i	$0.678571\pi$
$608$		0			0
$609$	1.19745	+	1.19745i	1.19745	+	1.19745i
$610$	1.41421			1.41421
$611$		0			0
$612$		0			0
$613$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$613$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$614$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$615$	0.146988	−	0.643997i	0.146988	−	0.643997i
$616$		0			0
$617$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$617$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$618$	−1.84044	+	0.420068i	−1.84044	+	0.420068i
$619$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$619$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$620$		0			0
$621$	0.211363	+	0.0739590i	0.211363	+	0.0739590i
$622$		0			0
$623$	−0.201753	+	1.79061i	−0.201753	+	1.79061i
$624$		0			0
$625$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.189606	+	1.68280i	0.189606	+	1.68280i
$631$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$631$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.236777	−	0.376828i	−0.236777	−	0.376828i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.111964	−	0.993712i	−0.111964	−	0.993712i
$641$	−1.68280	+	1.05737i	−1.68280	+	1.05737i	−0.781831	+	0.623490i	$0.785714\pi$
$641$	−1.68280	+	1.05737i	−1.68280	+	1.05737i	−0.900969	+	0.433884i	$0.857143\pi$
$642$	−1.23914	+	1.55383i	−1.23914	+	1.55383i
$643$	−0.175075	−	0.139617i	−0.175075	−	0.139617i	0.532032	−	0.846724i	$-0.321429\pi$
$643$	−0.175075	−	0.139617i	−0.175075	−	0.139617i	−0.707107	+	0.707107i	$0.750000\pi$
$644$	0.236435	+	0.296480i	0.236435	+	0.296480i
$645$	1.62349	−	0.781831i	1.62349	−	0.781831i
$646$		0			0
$647$	−0.958689	−	0.461680i	−0.958689	−	0.461680i	−0.111964	−	0.993712i	$-0.535714\pi$
$647$	−0.958689	−	0.461680i	−0.958689	−	0.461680i	−0.846724	+	0.532032i	$0.821429\pi$
$648$	−0.532032	−	0.846724i	−0.532032	−	0.846724i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.862311	+	0.0971591i	0.862311	+	0.0971591i
$653$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$653$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$654$	1.62349	+	0.781831i	1.62349	+	0.781831i
$655$		0			0
$656$	−0.218169	+	0.623490i	−0.218169	+	0.623490i
$657$		0			0
$658$	2.97498	+	1.43268i	2.97498	+	1.43268i
$659$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$659$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$660$		0			0
$661$	−0.974928	−	1.22252i	−0.974928	−	1.22252i	−0.974928	−	0.222521i	$-0.928571\pi$
$661$	−0.974928	−	1.22252i	−0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$662$		0			0
$663$		0			0
$664$	−1.59842	+	1.00435i	−1.59842	+	1.00435i
$665$		0			0
$666$		0			0
$667$	−0.0971591	−	0.201753i	−0.0971591	−	0.201753i
$668$		−	0.660558i		−	0.660558i
$669$	−0.752407	−	0.752407i	−0.752407	−	0.752407i
$670$	−0.752407	−	1.19745i	−0.752407	−	1.19745i
$671$		0			0
$672$		−	1.69345i		−	1.69345i
$673$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$673$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$674$		0			0
$675$	0.707107	−	0.707107i	0.707107	−	0.707107i
$676$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$677$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$677$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.351438	+	0.559311i	0.351438	+	0.559311i
$682$		0			0
$683$	−0.461680	−	0.958689i	−0.461680	−	0.958689i	−0.993712	−	0.111964i	$-0.964286\pi$
$683$	−0.461680	−	0.958689i	−0.461680	−	0.958689i	0.532032	−	0.846724i	$-0.321429\pi$
$684$		0			0
$685$		0			0
$686$	−0.781831	+	1.24428i	−0.781831	+	1.24428i
$687$	1.84044	−	0.420068i	1.84044	−	0.420068i
$688$	−1.70082	+	0.595142i	−1.70082	+	0.595142i
$689$		0			0
$690$	0.0498289	−	0.218315i	0.0498289	−	0.218315i
$691$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$691$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$692$		0			0
$693$		0			0
$694$	−1.40532	+	0.158342i	−1.40532	+	0.158342i
$695$		0			0
$696$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$697$		0			0
$698$	−1.79061	+	0.201753i	−1.79061	+	0.201753i
$699$		0			0
$700$	1.65099	−	0.376828i	1.65099	−	0.376828i
$701$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$701$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.433884	−	1.90097i	−0.433884	−	1.90097i
$706$		0			0
$707$	−3.17673	−	1.11159i	−3.17673	−	1.11159i
$708$		0			0
$709$	−0.541044	−	1.12349i	−0.541044	−	1.12349i	−0.974928	−	0.222521i	$-0.928571\pi$
$709$	−0.541044	−	1.12349i	−0.541044	−	1.12349i	0.433884	−	0.900969i	$-0.357143\pi$
$710$		0			0
$711$		0			0
$712$	−0.958689	+	0.461680i	−0.958689	+	0.461680i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$719$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$720$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$721$	0.711363	+	3.11668i	0.711363	+	3.11668i
$722$	−0.532032	−	0.846724i	−0.532032	−	0.846724i
$723$	−1.10568	+	1.10568i	−1.10568	+	1.10568i
$724$		−	1.56366i		−	1.56366i
$725$	−1.00000			−1.00000
$726$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$727$	−0.0971591	−	0.862311i	−0.0971591	−	0.862311i	−0.943883	−	0.330279i	$-0.892857\pi$
$727$	−0.0971591	−	0.862311i	−0.0971591	−	0.862311i	0.846724	−	0.532032i	$-0.178571\pi$
$728$		0			0
$729$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$730$		0			0
$731$		0			0
$732$	0.613604	+	1.27416i	0.613604	+	1.27416i
$733$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$733$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$734$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$735$	1.85602	−	0.209124i	1.85602	−	0.209124i
$736$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i
$737$		0			0
$738$	0.643997	−	0.146988i	0.643997	−	0.146988i
$739$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$739$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.286605	+	0.819071i	−0.286605	+	0.819071i	0.707107	+	0.707107i	$0.250000\pi$
$743$	−0.286605	+	0.819071i	−0.286605	+	0.819071i	−0.993712	+	0.111964i	$0.964286\pi$
$744$		0			0
$745$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$746$		0			0
$747$	1.70082	+	0.819071i	1.70082	+	0.819071i
$748$		0			0
$749$	2.63133	+	2.09842i	2.63133	+	2.09842i
$750$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$751$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$751$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$752$	0.218315	+	1.93760i	0.218315	+	1.93760i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.43388	+	0.900969i	−1.43388	+	0.900969i
$757$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$757$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.52446	+	0.347948i	1.52446	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$761$	1.52446	+	0.347948i	1.52446	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$762$	0.236777	−	0.376828i	0.236777	−	0.376828i
$763$	1.32399	−	2.74930i	1.32399	−	2.74930i
$764$		0			0
$765$		0			0
$766$	1.40532	+	1.40532i	1.40532	+	1.40532i
$767$		0			0
$768$	0.846724	−	0.532032i	0.846724	−	0.532032i
$769$	−0.119137	+	1.05737i	−0.119137	+	1.05737i	0.781831	+	0.623490i	$0.214286\pi$
$769$	−0.119137	+	1.05737i	−0.119137	+	1.05737i	−0.900969	+	0.433884i	$0.857143\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$773$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$774$	1.40881	+	1.12349i	1.40881	+	1.12349i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.23914	+	1.55383i	−1.23914	+	1.55383i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.943883	−	0.330279i	0.943883	−	0.330279i
$784$	−1.86777			−1.86777
$785$		0			0
$786$		0			0
$787$	−1.37876	+	0.314692i	−1.37876	+	0.314692i	−0.846724	−	0.532032i	$-0.821429\pi$
$787$	−1.37876	+	0.314692i	−1.37876	+	0.314692i	−0.532032	+	0.846724i	$0.678571\pi$
$788$		0			0
$789$	−0.433884	−	0.0990311i	−0.433884	−	0.0990311i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$797$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$798$		0			0
$799$		0			0
$800$	0.707107	+	0.707107i	0.707107	+	0.707107i
$801$	0.900969	+	0.566116i	0.900969	+	0.566116i
$802$	−0.376828	−	0.236777i	−0.376828	−	0.236777i
$803$		0			0
$804$	0.752407	−	1.19745i	0.752407	−	1.19745i
$805$	−0.369704	−	0.0843826i	−0.369704	−	0.0843826i
$806$		0			0
$807$	−0.223929			−0.223929
$808$	−0.442244	−	1.93760i	−0.442244	−	1.93760i
$809$	−0.119137	−	0.189606i	−0.119137	−	0.189606i	0.781831	−	0.623490i	$-0.214286\pi$
$809$	−0.119137	−	0.189606i	−0.119137	−	0.189606i	−0.900969	+	0.433884i	$0.857143\pi$
$810$	0.943883	+	0.330279i	0.943883	+	0.330279i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	1.65099	+	0.376828i	1.65099	+	0.376828i
$813$		0			0
$814$		0			0
$815$	−0.734760	+	0.461680i	−0.734760	+	0.461680i
$816$		0			0
$817$		0			0
$818$	0.663433	+	0.831919i	0.663433	+	0.831919i
$819$		0			0
$820$	−0.218169	−	0.623490i	−0.218169	−	0.623490i
$821$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$821$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$822$		0			0
$823$	0.643997	−	1.84044i	0.643997	−	1.84044i	0.111964	−	0.993712i	$-0.464286\pi$
$823$	0.643997	−	1.84044i	0.643997	−	1.84044i	0.532032	−	0.846724i	$-0.321429\pi$
$824$	−1.33485	+	1.33485i	−1.33485	+	1.33485i
$825$		0			0
$826$		0			0
$827$	−1.93760	−	0.218315i	−1.93760	−	0.218315i	−0.943883	−	0.330279i	$-0.892857\pi$
$827$	−1.93760	−	0.218315i	−1.93760	−	0.218315i	−0.993712	+	0.111964i	$0.964286\pi$
$828$	0.218315	−	0.0498289i	0.218315	−	0.0498289i
$829$	0.158342	−	0.158342i	0.158342	−	0.158342i	−0.623490	−	0.781831i	$-0.714286\pi$
$829$	0.158342	−	0.158342i	0.158342	−	0.158342i	0.781831	+	0.623490i	$0.214286\pi$
$830$	0.623490	−	1.78183i	0.623490	−	1.78183i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.411851	+	0.516445i	0.411851	+	0.516445i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$839$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$840$	1.05585	+	1.32399i	1.05585	+	1.32399i
$841$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$842$		−	1.88777i		−	1.88777i
$843$	0.881748	−	0.881748i	0.881748	−	0.881748i
$844$		0			0
$845$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$846$	1.52446	−	1.21572i	1.52446	−	1.21572i
$847$	−1.32399	+	1.05585i	−1.32399	+	1.05585i
$848$		0			0
$849$	−1.68280	−	1.05737i	−1.68280	−	1.05737i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$853$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$854$	2.15773	−	1.03911i	2.15773	−	1.03911i
$855$		0			0
$856$	−0.222521	+	1.97493i	−0.222521	+	1.97493i
$857$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$857$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$858$		0			0
$859$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$859$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$860$	0.958689	−	1.52574i	0.958689	−	1.52574i
$861$	−0.248917	−	1.09057i	−0.248917	−	1.09057i
$862$		0			0
$863$	−0.146988	+	0.643997i	−0.146988	+	0.643997i	0.846724	+	0.532032i	$0.178571\pi$
$863$	−0.146988	+	0.643997i	−0.146988	+	0.643997i	−0.993712	+	0.111964i	$0.964286\pi$
$864$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$865$		0			0
$866$		0			0
$867$	−0.330279	+	0.943883i	−0.330279	+	0.943883i
$868$		0			0
$869$		0			0
$870$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$871$		0			0
$872$	1.79061	−	0.201753i	1.79061	−	0.201753i
$873$		0			0
$874$		0			0
$875$	−1.05585	+	1.32399i	−1.05585	+	1.32399i
$876$		0			0
$877$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$877$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.78183	+	0.623490i	1.78183	+	0.623490i	1.00000			$0$
$881$	1.78183	+	0.623490i	1.78183	+	0.623490i	0.781831	+	0.623490i	$0.214286\pi$
$882$	0.993712	+	1.58148i	0.993712	+	1.58148i
$883$	−0.613604	−	1.27416i	−0.613604	−	1.27416i	−0.943883	−	0.330279i	$-0.892857\pi$
$883$	−0.613604	−	1.27416i	−0.613604	−	1.27416i	0.330279	−	0.943883i	$-0.392857\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.37876	+	1.37876i	1.37876	+	1.37876i	0.846724	+	0.532032i	$0.178571\pi$
$887$	1.37876	+	1.37876i	1.37876	+	1.37876i	0.532032	+	0.846724i	$0.321429\pi$
$888$		0			0
$889$	−0.638138	−	0.400969i	−0.638138	−	0.400969i
$890$	0.461680	−	0.958689i	0.461680	−	0.958689i
$891$		0			0
$892$	−1.03739	−	0.236777i	−1.03739	−	0.236777i
$893$		0			0
$894$		−	0.445042i		−	0.445042i
$895$		0			0
$896$	−0.900969	−	1.43388i	−0.900969	−	1.43388i
$897$		0			0
$898$			1.06406i			1.06406i
$899$		0			0
$900$	0.222521	−	0.974928i	0.222521	−	0.974928i
$901$		0			0
$902$		0			0
$903$	1.90257	−	2.38575i	1.90257	−	2.38575i
$904$		0			0
$905$	0.974928	+	1.22252i	0.974928	+	1.22252i
$906$		0			0
$907$	−0.595142	−	1.70082i	−0.595142	−	1.70082i	−0.707107	−	0.707107i	$-0.750000\pi$
$907$	−0.595142	−	1.70082i	−0.595142	−	1.70082i	0.111964	−	0.993712i	$-0.464286\pi$
$908$	0.595142	+	0.286605i	0.595142	+	0.286605i
$909$	−1.40532	+	1.40532i	−1.40532	+	1.40532i
$910$		0			0
$911$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$911$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−1.27416	−	0.613604i	−1.27416	−	0.613604i
$916$	1.33485	−	1.33485i	1.33485	−	1.33485i
$917$		0			0
$918$		0			0
$919$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$919$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$920$	−0.0739590	−	0.211363i	−0.0739590	−	0.211363i
$921$	1.12349	−	0.541044i	1.12349	−	0.541044i
$922$	1.17700	+	1.47592i	1.17700	+	1.47592i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.0739590	−	0.656405i	−0.0739590	−	0.656405i
$927$	1.84044	+	0.420068i	1.84044	+	0.420068i
$928$	0.330279	+	0.943883i	0.330279	+	0.943883i
$929$			1.56366i			1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$929$			1.56366i			1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.678448	+	0.541044i	−0.678448	+	0.541044i
$935$		0			0
$936$		0			0
$937$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$937$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$938$	−2.02782	−	1.27416i	−2.02782	−	1.27416i
$939$		0			0
$940$	−1.37876	−	1.37876i	−1.37876	−	1.37876i
$941$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$941$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$942$		0			0
$943$	−0.0165616	+	0.146988i	−0.0165616	+	0.146988i
$944$		0			0
$945$	0.559311	−	1.59842i	0.559311	−	1.59842i
$946$		0			0
$947$	−0.831919	+	1.32399i	−0.831919	+	1.32399i	0.111964	+	0.993712i	$0.464286\pi$
$947$	−0.831919	+	1.32399i	−0.831919	+	1.32399i	−0.943883	+	0.330279i	$0.892857\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$953$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.330279	+	0.943883i	−0.330279	+	0.943883i
$961$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$962$		0			0
$963$	1.79061	−	0.862311i	1.79061	−	0.862311i
$964$	−0.347948	+	1.52446i	−0.347948	+	1.52446i
$965$		0			0
$966$	−0.0843826	−	0.369704i	−0.0843826	−	0.369704i
$967$	0.461680	−	0.734760i	0.461680	−	0.734760i	−0.532032	−	0.846724i	$-0.678571\pi$
$967$	0.461680	−	0.734760i	0.461680	−	0.734760i	0.993712	+	0.111964i	$0.0357143\pi$
$968$	−0.943883	−	0.330279i	−0.943883	−	0.330279i
$969$		0			0
$970$		0			0
$971$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$971$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$972$	0.111964	+	0.993712i	0.111964	+	0.993712i
$973$		0			0
$974$	−0.752407	−	0.752407i	−0.752407	−	0.752407i
$975$		0			0
$976$	1.19745	+	0.752407i	1.19745	+	0.752407i
$977$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$977$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$978$	−0.734760	−	0.461680i	−0.734760	−	0.461680i
$979$		0			0
$980$	1.46028	−	1.16453i	1.46028	−	1.16453i
$981$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$982$		0			0
$983$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$983$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$984$	0.467085	−	0.467085i	0.467085	−	0.467085i
$985$		0			0
$986$		0			0
$987$	−2.05875	−	2.58159i	−2.05875	−	2.58159i
$988$		0			0
$989$	−0.341658	+	0.214678i	−0.341658	+	0.214678i
$990$		0			0
$991$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$991$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.87590	−	0.211363i	1.87590	−	0.211363i
$997$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$997$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1740.1.cf.b.1319.1	yes	24
3.2	odd	2		1740.1.cf.a.1319.2	yes	24
4.3	odd	2	inner	1740.1.cf.b.1319.2	yes	24
5.4	even	2	inner	1740.1.cf.b.1319.2	yes	24
12.11	even	2		1740.1.cf.a.1319.1	yes	24
15.14	odd	2		1740.1.cf.a.1319.1	yes	24
20.19	odd	2	CM	1740.1.cf.b.1319.1	yes	24
29.27	odd	28		1740.1.cf.a.839.2	yes	24
60.59	even	2		1740.1.cf.a.1319.2	yes	24
87.56	even	28	inner	1740.1.cf.b.839.1	yes	24
116.27	even	28		1740.1.cf.a.839.1	✓	24
145.114	odd	28		1740.1.cf.a.839.1	✓	24
348.143	odd	28	inner	1740.1.cf.b.839.2	yes	24
435.404	even	28	inner	1740.1.cf.b.839.2	yes	24
580.259	even	28		1740.1.cf.a.839.2	yes	24
1740.839	odd	28	inner	1740.1.cf.b.839.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1740.1.cf.a.839.1	✓	24	116.27	even	28
1740.1.cf.a.839.1	✓	24	145.114	odd	28
1740.1.cf.a.839.2	yes	24	29.27	odd	28
1740.1.cf.a.839.2	yes	24	580.259	even	28
1740.1.cf.a.1319.1	yes	24	12.11	even	2
1740.1.cf.a.1319.1	yes	24	15.14	odd	2
1740.1.cf.a.1319.2	yes	24	3.2	odd	2
1740.1.cf.a.1319.2	yes	24	60.59	even	2
1740.1.cf.b.839.1	yes	24	87.56	even	28	inner
1740.1.cf.b.839.1	yes	24	1740.839	odd	28	inner
1740.1.cf.b.839.2	yes	24	348.143	odd	28	inner
1740.1.cf.b.839.2	yes	24	435.404	even	28	inner
1740.1.cf.b.1319.1	yes	24	1.1	even	1	trivial
1740.1.cf.b.1319.1	yes	24	20.19	odd	2	CM
1740.1.cf.b.1319.2	yes	24	4.3	odd	2	inner
1740.1.cf.b.1319.2	yes	24	5.4	even	2	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:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1740.cf (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.993712 + 0.111964i) q^{2} +(0.943883 + 0.330279i) q^{3} +(0.974928 - 0.222521i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-0.974928 - 0.222521i) q^{6} +(-0.376828 + 1.65099i) q^{7} +(-0.943883 + 0.330279i) q^{8} +(0.781831 + 0.623490i) q^{9} +(0.532032 - 0.846724i) q^{10} +(0.993712 + 0.111964i) q^{12} +(0.189606 - 1.68280i) q^{14} +(-0.846724 + 0.532032i) q^{15} +(0.900969 - 0.433884i) q^{16} +(-0.846724 - 0.532032i) q^{18} +(-0.433884 + 0.900969i) q^{20} +(-0.900969 + 1.43388i) q^{21} +(0.175075 - 0.139617i) q^{23} -1.00000 q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.532032 + 0.846724i) q^{27} +1.69345i q^{28} +(0.222521 - 0.974928i) q^{29} +(0.781831 - 0.623490i) q^{30} +(-0.846724 + 0.532032i) q^{32} +(-1.05585 - 1.32399i) q^{35} +(0.900969 + 0.433884i) q^{36} +(0.330279 - 0.943883i) q^{40} +(-0.467085 + 0.467085i) q^{41} +(0.734760 - 1.52574i) q^{42} +(-1.79061 - 0.201753i) q^{43} +(-0.974928 + 0.222521i) q^{45} +(-0.158342 + 0.158342i) q^{46} +(-0.643997 + 1.84044i) q^{47} +(0.993712 - 0.111964i) q^{48} +(-1.68280 - 0.810394i) q^{49} +(0.330279 + 0.943883i) q^{50} +(-0.623490 - 0.781831i) q^{54} +(-0.189606 - 1.68280i) q^{56} +(-0.111964 + 0.993712i) q^{58} +(-0.707107 + 0.707107i) q^{60} +(0.752407 + 1.19745i) q^{61} +(-1.32399 + 1.05585i) q^{63} +(0.781831 - 0.623490i) q^{64} +(0.613604 - 1.27416i) q^{67} +(0.211363 - 0.0739590i) q^{69} +(1.19745 + 1.19745i) q^{70} +(-0.943883 - 0.330279i) q^{72} +(0.111964 - 0.993712i) q^{75} +(-0.222521 + 0.974928i) q^{80} +(0.222521 + 0.974928i) q^{81} +(0.411851 - 0.516445i) q^{82} +(1.84044 - 0.420068i) q^{83} +(-0.559311 + 1.59842i) q^{84} +1.80194 q^{86} +(0.532032 - 0.846724i) q^{87} +(1.05737 - 0.119137i) q^{89} +(0.943883 - 0.330279i) q^{90} +(0.139617 - 0.175075i) q^{92} +(0.433884 - 1.90097i) q^{94} +(-0.974928 + 0.222521i) q^{96} +(1.76295 + 0.616884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{5} - 4 q^{14} + 4 q^{16} - 4 q^{21} - 24 q^{24} - 4 q^{25} + 4 q^{29} + 4 q^{36} - 4 q^{41} - 4 q^{46} - 4 q^{49} + 4 q^{54} + 4 q^{56} - 4 q^{61} - 4 q^{69} + 4 q^{70} - 4 q^{80} + 4 q^{81}+ \cdots - 4 q^{89}+O(q^{100}) \) 24 * q + 4 * q^5 - 4 * q^14 + 4 * q^16 - 4 * q^21 - 24 * q^24 - 4 * q^25 + 4 * q^29 + 4 * q^36 - 4 * q^41 - 4 * q^46 - 4 * q^49 + 4 * q^54 + 4 * q^56 - 4 * q^61 - 4 * q^69 + 4 * q^70 - 4 * q^80 + 4 * q^81 + 4 * q^84 + 8 * q^86 - 4 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more