LMFDB - Embedded newform 2883.1.o.e.2738.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2883,1,Mod(338,2883)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2883, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 16]))

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

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

chi := DirichletCharacter("2883.338");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2883 = 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2883.o (of order $30$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.43880443142$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Coefficient field:	$\Q(\zeta_{120})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{32} + x^{28} - x^{20} - x^{16} - x^{12} + x^{4} + 1 $ x^32 + x^28 - x^20 - x^16 - x^12 + x^4 + 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 4.2.268119.1

Embedding invariants

Embedding label			2738.2
Root			$-0.0523360 + 0.998630i$ of defining polynomial
Character	$\chi$	$=$	2883.2738
Dual form			2883.1.o.e.338.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 + 0.809017i) q^{2} +(0.777146 + 0.629320i) q^{3} +(0.866025 - 0.500000i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.978148 + 0.207912i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.207912 + 0.978148i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-0.743145 + 0.669131i) q^{14} +(0.987688 + 0.156434i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.05097 + 0.946294i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(0.913545 - 0.406737i) q^{19} +(0.629320 + 0.777146i) q^{21} +(-0.544639 - 0.838671i) q^{24} +(-0.453990 + 0.891007i) q^{27} +(0.831254 - 1.14412i) q^{29} +(-0.707107 + 0.707107i) q^{30} +(-0.147826 - 1.40647i) q^{34} +(0.951057 - 0.309017i) q^{35} +(-0.207912 + 0.978148i) q^{38} +(-0.978148 + 0.207912i) q^{40} +(-0.994522 - 0.104528i) q^{41} +(-0.998630 + 0.0523360i) q^{42} +(-1.29195 + 0.575212i) q^{43} +(0.669131 + 0.743145i) q^{45} +(0.998630 + 0.0523360i) q^{48} +(-1.41228 + 0.0740142i) q^{51} +(-0.453990 - 0.891007i) q^{54} +(-0.866025 - 0.500000i) q^{56} +(0.965926 + 0.258819i) q^{57} +(0.437016 + 1.34500i) q^{58} +(0.994522 - 0.104528i) q^{59} +1.41421 q^{61} +1.00000i q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.309017 + 0.951057i) q^{70} +(-0.207912 - 0.978148i) q^{71} +(0.104528 - 0.994522i) q^{72} +(0.406737 - 0.913545i) q^{80} +(-0.913545 + 0.406737i) q^{81} +(0.669131 - 0.743145i) q^{82} +(-1.40647 - 0.147826i) q^{83} +(-0.437016 + 1.34500i) q^{85} +(0.294032 - 1.38331i) q^{86} +(1.36603 - 0.366025i) q^{87} +(-0.994522 + 0.104528i) q^{90} +(0.587785 - 0.809017i) q^{95} +(-0.309017 - 0.951057i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7} + 4 q^{10} + 8 q^{16} - 4 q^{18} + 4 q^{19} + 4 q^{40} + 4 q^{45} - 4 q^{51} + 8 q^{64} + 8 q^{70} - 4 q^{72} - 4 q^{81} + 4 q^{82} + 16 q^{87} + 8 q^{97}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 + 8 * q^16 - 4 * q^18 + 4 * q^19 + 4 * q^40 + 4 * q^45 - 4 * q^51 + 8 * q^64 + 8 * q^70 - 4 * q^72 - 4 * q^81 + 4 * q^82 + 16 * q^87 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2883\mathbb{Z}\right)^\times$.

$n$	$962$	$964$
$\chi(n)$	$-1$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$2$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$3$	0.777146	+	0.629320i	0.777146	+	0.629320i
$3$	0.777146	+	0.629320i	0.777146	+	0.629320i
$4$		0			0
$5$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$5$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$6$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$7$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$7$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$8$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$9$	0.207912	+	0.978148i	0.207912	+	0.978148i
$10$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$11$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$11$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$12$		0			0
$13$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$13$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$14$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$15$	0.987688	+	0.156434i	0.987688	+	0.156434i
$16$	0.809017	−	0.587785i	0.809017	−	0.587785i
$17$	−1.05097	+	0.946294i	−1.05097	+	0.946294i	−0.998630	−	0.0523360i	$-0.983333\pi$
$17$	−1.05097	+	0.946294i	−1.05097	+	0.946294i	−0.0523360	+	0.998630i	$0.516667\pi$
$18$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$19$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$19$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$20$		0			0
$21$	0.629320	+	0.777146i	0.629320	+	0.777146i
$22$		0			0
$23$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$23$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$24$	−0.544639	−	0.838671i	−0.544639	−	0.838671i
$25$		0			0
$26$		0			0
$27$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$28$		0			0
$29$	0.831254	−	1.14412i	0.831254	−	1.14412i	−0.156434	−	0.987688i	$-0.550000\pi$
$29$	0.831254	−	1.14412i	0.831254	−	1.14412i	0.987688	−	0.156434i	$-0.0500000\pi$
$30$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$31$		0			0
$31$		0			0
$32$		0			0
$33$		0			0
$34$	−0.147826	−	1.40647i	−0.147826	−	1.40647i
$35$	0.951057	−	0.309017i	0.951057	−	0.309017i
$36$		0			0
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$39$		0			0
$40$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$41$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$41$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$42$	−0.998630	+	0.0523360i	−0.998630	+	0.0523360i
$43$	−1.29195	+	0.575212i	−1.29195	+	0.575212i	−0.933580	−	0.358368i	$-0.883333\pi$
$43$	−1.29195	+	0.575212i	−1.29195	+	0.575212i	−0.358368	+	0.933580i	$0.616667\pi$
$44$		0			0
$45$	0.669131	+	0.743145i	0.669131	+	0.743145i
$46$		0			0
$47$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$47$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$48$	0.998630	+	0.0523360i	0.998630	+	0.0523360i
$49$		0			0
$50$		0			0
$51$	−1.41228	+	0.0740142i	−1.41228	+	0.0740142i
$52$		0			0
$53$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$53$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$54$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$55$		0			0
$56$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$57$	0.965926	+	0.258819i	0.965926	+	0.258819i
$58$	0.437016	+	1.34500i	0.437016	+	1.34500i
$59$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$59$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$60$		0			0
$61$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$61$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$62$		0			0
$63$			1.00000i			1.00000i
$64$	0.809017	+	0.587785i	0.809017	+	0.587785i
$65$		0			0
$66$		0			0
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$		0			0
$69$		0			0
$70$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$71$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$71$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$72$	0.104528	−	0.994522i	0.104528	−	0.994522i
$73$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$73$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$79$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$80$	0.406737	−	0.913545i	0.406737	−	0.913545i
$81$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$82$	0.669131	−	0.743145i	0.669131	−	0.743145i
$83$	−1.40647	−	0.147826i	−1.40647	−	0.147826i	−0.629320	−	0.777146i	$-0.716667\pi$
$83$	−1.40647	−	0.147826i	−1.40647	−	0.147826i	−0.777146	+	0.629320i	$0.783333\pi$
$84$		0			0
$85$	−0.437016	+	1.34500i	−0.437016	+	1.34500i
$86$	0.294032	−	1.38331i	0.294032	−	1.38331i
$87$	1.36603	−	0.366025i	1.36603	−	0.366025i
$88$		0			0
$89$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$89$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$90$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.587785	−	0.809017i	0.587785	−	0.809017i
$96$		0			0
$97$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$97$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$101$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$102$	0.770236	−	1.18606i	0.770236	−	1.18606i
$103$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$103$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$104$		0			0
$105$	0.933580	+	0.358368i	0.933580	+	0.358368i
$106$		0			0
$107$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$107$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$108$		0			0
$109$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$109$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$110$		0			0
$111$		0			0
$112$	0.913545	−	0.406737i	0.913545	−	0.406737i
$113$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$113$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$114$	−0.777146	+	0.629320i	−0.777146	+	0.629320i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$119$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$120$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$121$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$122$	−0.831254	+	1.14412i	−0.831254	+	1.14412i
$123$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$124$		0			0
$125$			1.00000i			1.00000i
$126$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$127$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$127$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$128$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$129$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$130$		0			0
$131$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$131$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$132$		0			0
$133$	0.978148	−	0.207912i	0.978148	−	0.207912i
$134$		0			0
$135$	0.0523360	+	0.998630i	0.0523360	+	0.998630i
$136$	1.29195	−	0.575212i	1.29195	−	0.575212i
$137$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$137$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$138$		0			0
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$		0			0
$141$		0			0
$142$	0.913545	+	0.406737i	0.913545	+	0.406737i
$143$		0			0
$144$	0.743145	+	0.669131i	0.743145	+	0.669131i
$145$	0.147826	−	1.40647i	0.147826	−	1.40647i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$149$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$150$		0			0
$151$	−0.437016	−	1.34500i	−0.437016	−	1.34500i	−0.891007	−	0.453990i	$-0.850000\pi$
$151$	−0.437016	−	1.34500i	−0.437016	−	1.34500i	0.453990	−	0.891007i	$-0.350000\pi$
$152$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$153$	−1.14412	−	0.831254i	−1.14412	−	0.831254i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$157$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.207912	−	0.978148i	0.207912	−	0.978148i
$163$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$163$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$164$		0			0
$165$		0			0
$166$	0.946294	−	1.05097i	0.946294	−	1.05097i
$167$	−0.575212	−	1.29195i	−0.575212	−	1.29195i	−0.933580	−	0.358368i	$-0.883333\pi$
$167$	−0.575212	−	1.29195i	−0.575212	−	1.29195i	0.358368	−	0.933580i	$-0.383333\pi$
$168$	−0.358368	−	0.933580i	−0.358368	−	0.933580i
$169$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$170$	−0.831254	−	1.14412i	−0.831254	−	1.14412i
$171$	0.587785	+	0.809017i	0.587785	+	0.809017i
$172$		0			0
$173$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$173$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$174$	−0.506809	+	1.32028i	−0.506809	+	1.32028i
$175$		0			0
$176$		0			0
$177$	0.838671	+	0.544639i	0.838671	+	0.544639i
$178$		0			0
$179$	−0.294032	+	1.38331i	−0.294032	+	1.38331i	0.544639	+	0.838671i	$0.316667\pi$
$179$	−0.294032	+	1.38331i	−0.294032	+	1.38331i	−0.838671	+	0.544639i	$0.816667\pi$
$180$		0			0
$181$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$181$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$182$		0			0
$183$	1.09905	+	0.889993i	1.09905	+	0.889993i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.629320	+	0.777146i	−0.629320	+	0.777146i
$190$	0.309017	+	0.951057i	0.309017	+	0.951057i
$191$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$191$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$192$	0.258819	+	0.965926i	0.258819	+	0.965926i
$193$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.309017	−	0.951057i	$-0.600000\pi$
$193$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.669131	+	0.743145i	$0.733333\pi$
$194$	0.951057	+	0.309017i	0.951057	+	0.309017i
$195$		0			0
$196$		0			0
$197$	−1.05097	−	0.946294i	−1.05097	−	0.946294i	−0.0523360	−	0.998630i	$-0.516667\pi$
$197$	−1.05097	−	0.946294i	−1.05097	−	0.946294i	−0.998630	+	0.0523360i	$0.983333\pi$
$198$		0			0
$199$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$199$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$200$		0			0
$201$		0			0
$202$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$203$	1.05097	−	0.946294i	1.05097	−	0.946294i
$204$		0			0
$205$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$206$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−0.838671	+	0.544639i	−0.838671	+	0.544639i
$211$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$211$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$212$		0			0
$213$	0.453990	−	0.891007i	0.453990	−	0.891007i
$214$	0.104528	+	0.994522i	0.104528	+	0.994522i
$215$	−0.831254	+	1.14412i	−0.831254	+	1.14412i
$216$	0.707107	−	0.707107i	0.707107	−	0.707107i
$217$		0			0
$218$		−	1.00000i		−	1.00000i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$223$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$224$		0			0
$225$		0			0
$226$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$227$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$227$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$228$		0			0
$229$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$229$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$230$		0			0
$231$		0			0
$232$	−1.14412	+	0.831254i	−1.14412	+	0.831254i
$233$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$233$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	0.147826	−	1.40647i	0.147826	−	1.40647i
$239$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$239$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$240$	0.891007	−	0.453990i	0.891007	−	0.453990i
$241$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$241$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$242$	0.866025	+	0.500000i	0.866025	+	0.500000i
$243$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$244$		0			0
$245$		0			0
$246$	0.987688	−	0.156434i	0.987688	−	0.156434i
$247$		0			0
$248$		0			0
$249$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$250$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$251$	−1.40647	+	0.147826i	−1.40647	+	0.147826i	−0.777146	−	0.629320i	$-0.783333\pi$
$251$	−1.40647	+	0.147826i	−1.40647	+	0.147826i	−0.629320	+	0.777146i	$0.716667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−1.18606	+	0.770236i	−1.18606	+	0.770236i
$256$		0			0
$257$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$257$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$258$	1.09905	−	0.889993i	1.09905	−	0.889993i
$259$		0			0
$260$		0			0
$261$	1.29195	+	0.575212i	1.29195	+	0.575212i
$262$		0			0
$263$	0.831254	+	1.14412i	0.831254	+	1.14412i	0.987688	+	0.156434i	$0.0500000\pi$
$263$	0.831254	+	1.14412i	0.831254	+	1.14412i	−0.156434	+	0.987688i	$0.550000\pi$
$264$		0			0
$265$		0			0
$266$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$267$		0			0
$268$		0			0
$269$	1.40647	+	0.147826i	1.40647	+	0.147826i	0.777146	−	0.629320i	$-0.216667\pi$
$269$	1.40647	+	0.147826i	1.40647	+	0.147826i	0.629320	+	0.777146i	$0.283333\pi$
$270$	−0.838671	−	0.544639i	−0.838671	−	0.544639i
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$	−0.294032	+	1.38331i	−0.294032	+	1.38331i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$277$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$278$		0			0
$279$		0			0
$280$	−1.00000			−1.00000
$281$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$281$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$282$		0			0
$283$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$283$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$284$		0			0
$285$	0.965926	−	0.258819i	0.965926	−	0.258819i
$286$		0			0
$287$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$288$		0			0
$289$	0.104528	−	0.994522i	0.104528	−	0.994522i
$290$	1.05097	+	0.946294i	1.05097	+	0.946294i
$291$	0.358368	−	0.933580i	0.358368	−	0.933580i
$292$		0			0
$293$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$293$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$294$		0			0
$295$	0.809017	−	0.587785i	0.809017	−	0.587785i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−1.38331	+	0.294032i	−1.38331	+	0.294032i
$302$	1.34500	+	0.437016i	1.34500	+	0.437016i
$303$	0.544639	+	0.838671i	0.544639	+	0.838671i
$304$	0.500000	−	0.866025i	0.500000	−	0.866025i
$305$	1.22474	−	0.707107i	1.22474	−	0.707107i
$306$	1.34500	−	0.437016i	1.34500	−	0.437016i
$307$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$307$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$308$		0			0
$309$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$310$		0			0
$311$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$311$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$312$		0			0
$313$	−0.147826	−	1.40647i	−0.147826	−	1.40647i	−0.777146	−	0.629320i	$-0.783333\pi$
$313$	−0.147826	−	1.40647i	−0.147826	−	1.40647i	0.629320	−	0.777146i	$-0.283333\pi$
$314$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$315$	0.500000	+	0.866025i	0.500000	+	0.866025i
$316$		0			0
$317$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$317$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$318$		0			0
$319$		0			0
$320$	0.994522	+	0.104528i	0.994522	+	0.104528i
$321$	0.998630	−	0.0523360i	0.998630	−	0.0523360i
$322$		0			0
$323$	−0.575212	+	1.29195i	−0.575212	+	1.29195i
$324$		0			0
$325$		0			0
$326$	0.587785	+	0.809017i	0.587785	+	0.809017i
$327$	−0.998630	−	0.0523360i	−0.998630	−	0.0523360i
$328$	0.913545	+	0.406737i	0.913545	+	0.406737i
$329$		0			0
$330$		0			0
$331$	−0.147826	+	1.40647i	−0.147826	+	1.40647i	0.629320	+	0.777146i	$0.283333\pi$
$331$	−0.147826	+	1.40647i	−0.147826	+	1.40647i	−0.777146	+	0.629320i	$0.783333\pi$
$332$		0			0
$333$		0			0
$334$	1.38331	+	0.294032i	1.38331	+	0.294032i
$335$		0			0
$336$	0.965926	+	0.258819i	0.965926	+	0.258819i
$337$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$337$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$338$	0.994522	−	0.104528i	0.994522	−	0.104528i
$339$	0.156434	+	0.987688i	0.156434	+	0.987688i
$340$		0			0
$341$		0			0
$342$	−1.00000			−1.00000
$343$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$344$	1.40647	−	0.147826i	1.40647	−	0.147826i
$345$		0			0
$346$		0			0
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$349$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.575212	+	1.29195i	0.575212	+	1.29195i	0.933580	+	0.358368i	$0.116667\pi$
$353$	0.575212	+	1.29195i	0.575212	+	1.29195i	−0.358368	+	0.933580i	$0.616667\pi$
$354$	−0.933580	+	0.358368i	−0.933580	+	0.358368i
$355$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$356$		0			0
$357$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$358$	−0.946294	−	1.05097i	−0.946294	−	1.05097i
$359$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	0.587785	+	0.809017i	$0.300000\pi$
$359$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	−0.994522	+	0.104528i	$0.966667\pi$
$360$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$361$		0			0
$362$	1.40647	+	0.147826i	1.40647	+	0.147826i
$363$	0.544639	−	0.838671i	0.544639	−	0.838671i
$364$		0			0
$365$		0			0
$366$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$367$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$367$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$368$		0			0
$369$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$373$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−0.629320	+	0.777146i	−0.629320	+	0.777146i
$376$		0			0
$377$		0			0
$378$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$379$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$379$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$380$		0			0
$381$		0			0
$382$	0.104528	−	0.994522i	0.104528	−	0.994522i
$383$	1.05097	+	0.946294i	1.05097	+	0.946294i	0.998630	−	0.0523360i	$-0.0166667\pi$
$383$	1.05097	+	0.946294i	1.05097	+	0.946294i	0.0523360	+	0.998630i	$0.483333\pi$
$384$	−0.933580	−	0.358368i	−0.933580	−	0.358368i
$385$		0			0
$386$	0.743145	−	0.669131i	0.743145	−	0.669131i
$387$	−0.831254	−	1.14412i	−0.831254	−	1.14412i
$388$		0			0
$389$	1.05097	−	0.946294i	1.05097	−	0.946294i	0.0523360	−	0.998630i	$-0.483333\pi$
$389$	1.05097	−	0.946294i	1.05097	−	0.946294i	0.998630	+	0.0523360i	$0.0166667\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	1.38331	−	0.294032i	1.38331	−	0.294032i
$395$		0			0
$396$		0			0
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$398$		0			0
$399$	0.891007	+	0.453990i	0.891007	+	0.453990i
$400$		0			0
$401$	0.831254	−	1.14412i	0.831254	−	1.14412i	−0.156434	−	0.987688i	$-0.550000\pi$
$401$	0.831254	−	1.14412i	0.831254	−	1.14412i	0.987688	−	0.156434i	$-0.0500000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$406$	0.147826	+	1.40647i	0.147826	+	1.40647i
$407$		0			0
$408$	1.36603	+	0.366025i	1.36603	+	0.366025i
$409$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$409$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$410$	0.207912	−	0.978148i	0.207912	−	0.978148i
$411$		0			0
$412$		0			0
$413$	0.994522	+	0.104528i	0.994522	+	0.104528i
$414$		0			0
$415$	−1.29195	+	0.575212i	−1.29195	+	0.575212i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$419$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$420$		0			0
$421$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$421$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$422$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	0.453990	+	0.891007i	0.453990	+	0.891007i
$427$	1.38331	+	0.294032i	1.38331	+	0.294032i
$428$		0			0
$429$		0			0
$430$	−0.437016	−	1.34500i	−0.437016	−	1.34500i
$431$	−1.98904	+	0.209057i	−1.98904	+	0.209057i	−0.994522	+	0.104528i	$0.966667\pi$
$431$	−1.98904	+	0.209057i	−1.98904	+	0.209057i	−0.994522	+	0.104528i	$0.966667\pi$
$432$	0.156434	+	0.987688i	0.156434	+	0.987688i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$	1.00000	−	1.00000i	1.00000	−	1.00000i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$439$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$443$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$444$		0			0
$445$		0			0
$446$	0.575212	+	1.29195i	0.575212	+	1.29195i
$447$		0			0
$448$	0.669131	+	0.743145i	0.669131	+	0.743145i
$449$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$449$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	0.506809	−	1.32028i	0.506809	−	1.32028i
$454$		0			0
$455$		0			0
$456$	−0.838671	−	0.544639i	−0.838671	−	0.544639i
$457$	0.437016	−	1.34500i	0.437016	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$457$	0.437016	−	1.34500i	0.437016	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$458$		0			0
$459$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$460$		0			0
$461$	1.34500	−	0.437016i	1.34500	−	0.437016i	0.453990	−	0.891007i	$-0.350000\pi$
$461$	1.34500	−	0.437016i	1.34500	−	0.437016i	0.891007	+	0.453990i	$0.150000\pi$
$462$		0			0
$463$	1.14412	+	0.831254i	1.14412	+	0.831254i	0.987688	−	0.156434i	$-0.0500000\pi$
$463$	1.14412	+	0.831254i	1.14412	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$464$		−	1.41421i		−	1.41421i
$465$		0			0
$466$	1.00000			1.00000
$467$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$467$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.258819	+	0.965926i	0.258819	+	0.965926i
$472$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$479$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$486$	0.777146	−	0.629320i	0.777146	−	0.629320i
$487$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$487$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$488$	−1.34500	−	0.437016i	−1.34500	−	0.437016i
$489$	0.838671	−	0.544639i	0.838671	−	0.544639i
$490$		0			0
$491$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$491$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$492$		0			0
$493$	0.209057	+	1.98904i	0.209057	+	1.98904i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	1.00000i		−	1.00000i
$498$	1.39680	−	0.221232i	1.39680	−	0.221232i
$499$	0.147826	+	1.40647i	0.147826	+	1.40647i	0.777146	+	0.629320i	$0.216667\pi$
$499$	0.147826	+	1.40647i	0.147826	+	1.40647i	−0.629320	+	0.777146i	$0.716667\pi$
$500$		0			0
$501$	0.366025	−	1.36603i	0.366025	−	1.36603i
$502$	0.707107	−	1.22474i	0.707107	−	1.22474i
$503$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$503$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$504$	0.309017	−	0.951057i	0.309017	−	0.951057i
$505$	0.978148	−	0.207912i	0.978148	−	0.207912i
$506$		0			0
$507$	−0.0523360	−	0.998630i	−0.0523360	−	0.998630i
$508$		0			0
$509$	0.575212	−	1.29195i	0.575212	−	1.29195i	−0.358368	−	0.933580i	$-0.616667\pi$
$509$	0.575212	−	1.29195i	0.575212	−	1.29195i	0.933580	−	0.358368i	$-0.116667\pi$
$510$	0.0740142	−	1.41228i	0.0740142	−	1.41228i
$511$		0			0
$512$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$513$	−0.0523360	+	0.998630i	−0.0523360	+	0.998630i
$514$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$515$	0.406737	+	0.913545i	0.406737	+	0.913545i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$		0			0
$525$		0			0
$526$	−1.41421			−1.41421
$527$		0			0
$528$		0			0
$529$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$530$		0			0
$531$	0.309017	+	0.951057i	0.309017	+	0.951057i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.309017	−	0.951057i	0.309017	−	0.951057i
$536$		0			0
$537$	−1.09905	+	0.889993i	−1.09905	+	0.889993i
$538$	−0.946294	+	1.05097i	−0.946294	+	1.05097i
$539$		0			0
$540$		0			0
$541$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$541$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$542$		0			0
$543$	0.221232	−	1.39680i	0.221232	−	1.39680i
$544$		0			0
$545$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$546$		0			0
$547$	0.669131	−	0.743145i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$547$	0.669131	−	0.743145i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$548$		0			0
$549$	0.294032	+	1.38331i	0.294032	+	1.38331i
$550$		0			0
$551$	0.294032	−	1.38331i	0.294032	−	1.38331i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$557$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$558$		0			0
$559$		0			0
$560$	0.587785	−	0.809017i	0.587785	−	0.809017i
$561$		0			0
$562$	0.309017	+	0.951057i	0.309017	+	0.951057i
$563$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$563$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$564$		0			0
$565$	0.978148	+	0.207912i	0.978148	+	0.207912i
$566$		0			0
$567$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$568$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$569$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$569$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$570$	−0.358368	+	0.933580i	−0.358368	+	0.933580i
$571$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$571$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$572$		0			0
$573$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$574$	0.809017	−	0.587785i	0.809017	−	0.587785i
$575$		0			0
$576$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$577$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$577$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$578$	0.743145	+	0.669131i	0.743145	+	0.669131i
$579$	−0.629320	−	0.777146i	−0.629320	−	0.777146i
$580$		0			0
$581$	−1.34500	−	0.437016i	−1.34500	−	0.437016i
$582$	0.544639	+	0.838671i	0.544639	+	0.838671i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$587$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$588$		0			0
$589$		0			0
$590$			1.00000i			1.00000i
$591$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$592$		0			0
$593$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$593$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$594$		0			0
$595$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$599$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$600$		0			0
$601$	1.29195	−	0.575212i	1.29195	−	0.575212i	0.358368	−	0.933580i	$-0.383333\pi$
$601$	1.29195	−	0.575212i	1.29195	−	0.575212i	0.933580	+	0.358368i	$0.116667\pi$
$602$	0.575212	−	1.29195i	0.575212	−	1.29195i
$603$		0			0
$604$		0			0
$605$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$606$	−0.998630	−	0.0523360i	−0.998630	−	0.0523360i
$607$	−1.82709	−	0.813473i	−1.82709	−	0.813473i	−0.913545	−	0.406737i	$-0.866667\pi$
$607$	−1.82709	−	0.813473i	−1.82709	−	0.813473i	−0.913545	−	0.406737i	$-0.866667\pi$
$608$		0			0
$609$	1.41228	−	0.0740142i	1.41228	−	0.0740142i
$610$	−0.147826	+	1.40647i	−0.147826	+	1.40647i
$611$		0			0
$612$		0			0
$613$	−1.38331	−	0.294032i	−1.38331	−	0.294032i	−0.544639	−	0.838671i	$-0.683333\pi$
$613$	−1.38331	−	0.294032i	−1.38331	−	0.294032i	−0.838671	+	0.544639i	$0.816667\pi$
$614$	0.866025	+	0.500000i	0.866025	+	0.500000i
$615$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$616$		0			0
$617$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$617$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$618$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$		0			0
$622$	0.809017	+	0.587785i	0.809017	+	0.587785i
$623$		0			0
$624$		0			0
$625$	0.500000	+	0.866025i	0.500000	+	0.866025i
$626$	1.22474	+	0.707107i	1.22474	+	0.707107i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$631$	0.946294	−	1.05097i	0.946294	−	1.05097i	−0.0523360	−	0.998630i	$-0.516667\pi$
$631$	0.946294	−	1.05097i	0.946294	−	1.05097i	0.998630	−	0.0523360i	$-0.0166667\pi$
$632$		0			0
$633$	−0.933580	+	0.358368i	−0.933580	+	0.358368i
$634$	0.669131	+	0.743145i	0.669131	+	0.743145i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.913545	−	0.406737i	0.913545	−	0.406737i
$640$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$641$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$641$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$642$	−0.544639	+	0.838671i	−0.544639	+	0.838671i
$643$	0.437016	−	1.34500i	0.437016	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$643$	0.437016	−	1.34500i	0.437016	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$644$		0			0
$645$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$646$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$647$	−1.34500	+	0.437016i	−1.34500	+	0.437016i	−0.891007	−	0.453990i	$-0.850000\pi$
$647$	−1.34500	+	0.437016i	−1.34500	+	0.437016i	−0.453990	+	0.891007i	$0.650000\pi$
$648$	0.994522	−	0.104528i	0.994522	−	0.104528i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.17557	+	1.61803i	−1.17557	+	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$653$	−1.17557	+	1.61803i	−1.17557	+	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$654$	0.629320	−	0.777146i	0.629320	−	0.777146i
$655$		0			0
$656$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$657$		0			0
$658$		0			0
$659$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$659$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$660$		0			0
$661$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$661$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$662$	−1.05097	−	0.946294i	−1.05097	−	0.946294i
$663$		0			0
$664$	1.29195	+	0.575212i	1.29195	+	0.575212i
$665$	0.743145	−	0.669131i	0.743145	−	0.669131i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	1.32028	−	0.506809i	1.32028	−	0.506809i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.38331	−	0.294032i	1.38331	−	0.294032i	0.544639	−	0.838671i	$-0.316667\pi$
$673$	1.38331	−	0.294032i	1.38331	−	0.294032i	0.838671	+	0.544639i	$0.183333\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$677$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$678$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$679$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$680$	0.831254	−	1.14412i	0.831254	−	1.14412i
$681$		0			0
$682$		0			0
$683$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$683$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$684$		0			0
$685$		0			0
$686$	0.951057	−	0.309017i	0.951057	−	0.309017i
$687$		0			0
$688$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$689$		0			0
$690$		0			0
$691$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.669131	−	0.743145i	$-0.733333\pi$
$691$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.309017	+	0.951057i	$0.600000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−1.41228	−	0.0740142i	−1.41228	−	0.0740142i
$697$	1.14412	−	0.831254i	1.14412	−	0.831254i
$698$		0			0
$699$	0.0523360	−	0.998630i	0.0523360	−	0.998630i
$700$		0			0
$701$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	−0.994522	−	0.104528i	$-0.966667\pi$
$701$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	0.587785	−	0.809017i	$-0.300000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−1.38331	−	0.294032i	−1.38331	−	0.294032i
$707$	0.866025	+	0.500000i	0.866025	+	0.500000i
$708$		0			0
$709$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$709$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$710$	0.994522	−	0.104528i	0.994522	−	0.104528i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	1.00000	−	1.00000i	1.00000	−	1.00000i
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	0.978148	+	0.207912i	0.978148	+	0.207912i
$721$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.358368	+	0.933580i	0.358368	+	0.933580i
$727$	0.669131	+	0.743145i	0.669131	+	0.743145i	0.978148	−	0.207912i	$-0.0666667\pi$
$727$	0.669131	+	0.743145i	0.669131	+	0.743145i	−0.309017	+	0.951057i	$0.600000\pi$
$728$		0			0
$729$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$730$		0			0
$731$	0.813473	−	1.82709i	0.813473	−	1.82709i
$732$		0			0
$733$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$733$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$734$	−1.40647	−	0.147826i	−1.40647	−	0.147826i
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.866025	+	0.500000i	0.866025	+	0.500000i
$739$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$739$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$743$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$744$		0			0
$745$		0			0
$746$	0.587785	−	0.809017i	0.587785	−	0.809017i
$747$	−0.147826	−	1.40647i	−0.147826	−	1.40647i
$748$		0			0
$749$	0.866025	−	0.500000i	0.866025	−	0.500000i
$750$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$751$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$751$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$752$		0			0
$753$	−1.18606	−	0.770236i	−1.18606	−	0.770236i
$754$		0			0
$755$	−1.05097	−	0.946294i	−1.05097	−	0.946294i
$756$		0			0
$757$	−1.29195	−	0.575212i	−1.29195	−	0.575212i	−0.358368	−	0.933580i	$-0.616667\pi$
$757$	−1.29195	−	0.575212i	−1.29195	−	0.575212i	−0.933580	+	0.358368i	$0.883333\pi$
$758$		0			0
$759$		0			0
$760$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$761$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$761$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$762$		0			0
$763$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$764$		0			0
$765$	−1.40647	−	0.147826i	−1.40647	−	0.147826i
$766$	−1.38331	+	0.294032i	−1.38331	+	0.294032i
$767$		0			0
$768$		0			0
$769$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$769$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$770$		0			0
$771$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$772$		0			0
$773$	−0.831254	+	1.14412i	−0.831254	+	1.14412i	0.156434	+	0.987688i	$0.450000\pi$
$773$	−0.831254	+	1.14412i	−0.831254	+	1.14412i	−0.987688	+	0.156434i	$0.950000\pi$
$774$	1.41421			1.41421
$775$		0			0
$776$			1.00000i			1.00000i
$777$		0			0
$778$	0.147826	+	1.40647i	0.147826	+	1.40647i
$779$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.642040	+	1.26007i	0.642040	+	1.26007i
$784$		0			0
$785$	0.994522	+	0.104528i	0.994522	+	0.104528i
$786$		0			0
$787$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$787$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$788$		0			0
$789$	−0.0740142	+	1.41228i	−0.0740142	+	1.41228i
$790$		0			0
$791$	0.587785	+	0.809017i	0.587785	+	0.809017i
$792$		0			0
$793$		0			0
$794$	0.406737	+	0.913545i	0.406737	+	0.913545i
$795$		0			0
$796$		0			0
$797$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$797$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$798$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	0.437016	+	1.34500i	0.437016	+	1.34500i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.00000	+	1.00000i	1.00000	+	1.00000i
$808$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$809$	1.40647	−	0.147826i	1.40647	−	0.147826i	0.629320	−	0.777146i	$-0.283333\pi$
$809$	1.40647	−	0.147826i	1.40647	−	0.147826i	0.777146	+	0.629320i	$0.216667\pi$
$810$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$811$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$811$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$816$	−1.09905	+	0.889993i	−1.09905	+	0.889993i
$817$	−0.946294	+	1.05097i	−0.946294	+	1.05097i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$821$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$822$		0			0
$823$	0.946294	+	1.05097i	0.946294	+	1.05097i	0.998630	+	0.0523360i	$0.0166667\pi$
$823$	0.946294	+	1.05097i	0.946294	+	1.05097i	−0.0523360	+	0.998630i	$0.516667\pi$
$824$	0.406737	−	0.913545i	0.406737	−	0.913545i
$825$		0			0
$826$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$827$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$827$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$828$		0			0
$829$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	0.453990	+	0.891007i	$0.350000\pi$
$829$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	−0.891007	+	0.453990i	$0.850000\pi$
$830$	0.294032	−	1.38331i	0.294032	−	1.38331i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.14412	−	0.831254i	−1.14412	−	0.831254i
$836$		0			0
$837$		0			0
$838$	−1.00000			−1.00000
$839$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$839$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$840$	−0.777146	−	0.629320i	−0.777146	−	0.629320i
$841$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$842$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$843$	0.965926	−	0.258819i	0.965926	−	0.258819i
$844$		0			0
$845$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$846$		0			0
$847$	0.104528	−	0.994522i	0.104528	−	0.994522i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$853$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$854$	−1.05097	+	0.946294i	−1.05097	+	0.946294i
$855$	0.913545	+	0.406737i	0.913545	+	0.406737i
$856$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$857$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$857$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$858$		0			0
$859$	−1.38331	+	0.294032i	−1.38331	+	0.294032i	−0.838671	−	0.544639i	$-0.816667\pi$
$859$	−1.38331	+	0.294032i	−1.38331	+	0.294032i	−0.544639	+	0.838671i	$0.683333\pi$
$860$		0			0
$861$	−0.544639	−	0.838671i	−0.544639	−	0.838671i
$862$	1.00000	−	1.73205i	1.00000	−	1.73205i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.707107	−	0.707107i	0.707107	−	0.707107i
$868$		0			0
$869$		0			0
$870$	0.221232	+	1.39680i	0.221232	+	1.39680i
$871$		0			0
$872$	0.951057	−	0.309017i	0.951057	−	0.309017i
$873$	0.866025	−	0.500000i	0.866025	−	0.500000i
$874$		0			0
$875$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$876$		0			0
$877$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$877$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$878$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$879$		0			0
$880$		0			0
$881$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$881$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$882$		0			0
$883$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$883$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$884$		0			0
$885$	0.998630	+	0.0523360i	0.998630	+	0.0523360i
$886$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$887$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$887$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	0.437016	+	1.34500i	0.437016	+	1.34500i
$896$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−1.26007	−	0.642040i	−1.26007	−	0.642040i
$904$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$905$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$906$	0.770236	+	1.18606i	0.770236	+	1.18606i
$907$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$907$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$908$		0			0
$909$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$910$		0			0
$911$	−0.575212	−	1.29195i	−0.575212	−	1.29195i	−0.933580	−	0.358368i	$-0.883333\pi$
$911$	−0.575212	−	1.29195i	−0.575212	−	1.29195i	0.358368	−	0.933580i	$-0.383333\pi$
$912$	0.933580	−	0.358368i	0.933580	−	0.358368i
$913$		0			0
$914$	0.831254	+	1.14412i	0.831254	+	1.14412i
$915$	1.39680	+	0.221232i	1.39680	+	0.221232i
$916$		0			0
$917$		0			0
$918$	1.32028	+	0.506809i	1.32028	+	0.506809i
$919$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$919$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$920$		0			0
$921$	0.544639	−	0.838671i	0.544639	−	0.838671i
$922$	−0.437016	+	1.34500i	−0.437016	+	1.34500i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−1.34500	+	0.437016i	−1.34500	+	0.437016i
$927$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$928$		0			0
$929$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$929$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	0.629320	−	0.777146i	0.629320	−	0.777146i
$934$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$935$		0			0
$936$		0			0
$937$	−1.95630	−	0.415823i	−1.95630	−	0.415823i	−0.978148	−	0.207912i	$-0.933333\pi$
$937$	−1.95630	−	0.415823i	−1.95630	−	0.415823i	−0.978148	−	0.207912i	$-0.933333\pi$
$938$		0			0
$939$	0.770236	−	1.18606i	0.770236	−	1.18606i
$940$		0			0
$941$	1.05097	+	0.946294i	1.05097	+	0.946294i	0.998630	−	0.0523360i	$-0.0166667\pi$
$941$	1.05097	+	0.946294i	1.05097	+	0.946294i	0.0523360	+	0.998630i	$0.483333\pi$
$942$	−0.933580	−	0.358368i	−0.933580	−	0.358368i
$943$		0			0
$944$	0.743145	−	0.669131i	0.743145	−	0.669131i
$945$	−0.156434	+	0.987688i	−0.156434	+	0.987688i
$946$		0			0
$947$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$947$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	0.777146	−	0.629320i	0.777146	−	0.629320i
$952$	1.38331	−	0.294032i	1.38331	−	0.294032i
$953$	1.34500	+	0.437016i	1.34500	+	0.437016i	0.891007	−	0.453990i	$-0.150000\pi$
$953$	1.34500	+	0.437016i	1.34500	+	0.437016i	0.453990	+	0.891007i	$0.350000\pi$
$954$		0			0
$955$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$956$		0			0
$957$		0			0
$958$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$959$		0			0
$960$	0.707107	+	0.707107i	0.707107	+	0.707107i
$961$		0			0
$962$		0			0
$963$	0.809017	+	0.587785i	0.809017	+	0.587785i
$964$		0			0
$965$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$966$		0			0
$967$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$967$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$968$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$969$	−1.26007	+	0.642040i	−1.26007	+	0.642040i
$970$	0.978148	−	0.207912i	0.978148	−	0.207912i
$971$	−1.98904	−	0.209057i	−1.98904	−	0.209057i	−0.994522	−	0.104528i	$-0.966667\pi$
$971$	−1.98904	−	0.209057i	−1.98904	−	0.209057i	−0.994522	−	0.104528i	$-0.966667\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.14412	−	0.831254i	1.14412	−	0.831254i
$977$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$977$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$978$	−0.0523360	+	0.998630i	−0.0523360	+	0.998630i
$979$		0			0
$980$		0			0
$981$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$982$	−0.147826	+	1.40647i	−0.147826	+	1.40647i
$983$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$983$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$984$	0.453990	+	0.891007i	0.453990	+	0.891007i
$985$	−1.38331	−	0.294032i	−1.38331	−	0.294032i
$986$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$991$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$992$		0			0
$993$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$994$	0.809017	+	0.587785i	0.809017	+	0.587785i
$995$		0			0
$996$		0			0
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$998$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2883.1.o.e.2738.2		32
3.2	odd	2	inner	2883.1.o.e.2738.3		32
31.2	even	5	inner	2883.1.o.e.2768.2		32
31.3	odd	30	inner	2883.1.o.e.338.4		32
31.4	even	5		2883.1.h.c.1400.1		8
31.5	even	3		2883.1.l.d.374.2		16
31.6	odd	6	inner	2883.1.o.e.2654.2		32
31.7	even	15		2883.1.h.c.521.2		8
31.8	even	5	inner	2883.1.o.e.1508.3		32
31.9	even	15		2883.1.l.d.2453.4		16
31.10	even	15		2883.1.l.d.1589.1		16
31.11	odd	30		2883.1.b.c.962.2	yes	4
31.12	odd	30	inner	2883.1.o.e.1409.1		32
31.13	odd	30		2883.1.l.d.1349.3		16
31.14	even	15	inner	2883.1.o.e.1805.4		32
31.15	odd	10	inner	2883.1.o.e.1196.4		32
31.16	even	5	inner	2883.1.o.e.1196.3		32
31.17	odd	30	inner	2883.1.o.e.1805.3		32
31.18	even	15		2883.1.l.d.1349.4		16
31.19	even	15	inner	2883.1.o.e.1409.2		32
31.20	even	15		2883.1.b.c.962.1	✓	4
31.21	odd	30		2883.1.l.d.1589.2		16
31.22	odd	30		2883.1.l.d.2453.3		16
31.23	odd	10	inner	2883.1.o.e.1508.4		32
31.24	odd	30		2883.1.h.c.521.1		8
31.25	even	3	inner	2883.1.o.e.2654.1		32
31.26	odd	6		2883.1.l.d.374.1		16
31.27	odd	10		2883.1.h.c.1400.2		8
31.28	even	15	inner	2883.1.o.e.338.3		32
31.29	odd	10	inner	2883.1.o.e.2768.1		32
31.30	odd	2	inner	2883.1.o.e.2738.1		32
93.2	odd	10	inner	2883.1.o.e.2768.4		32
93.5	odd	6		2883.1.l.d.374.4		16
93.8	odd	10	inner	2883.1.o.e.1508.2		32
93.11	even	30		2883.1.b.c.962.4	yes	4
93.14	odd	30	inner	2883.1.o.e.1805.2		32
93.17	even	30	inner	2883.1.o.e.1805.1		32
93.20	odd	30		2883.1.b.c.962.3	yes	4
93.23	even	10	inner	2883.1.o.e.1508.1		32
93.26	even	6		2883.1.l.d.374.3		16
93.29	even	10	inner	2883.1.o.e.2768.3		32
93.35	odd	10		2883.1.h.c.1400.4		8
93.38	odd	30		2883.1.h.c.521.3		8
93.41	odd	30		2883.1.l.d.1589.4		16
93.44	even	30		2883.1.l.d.1349.1		16
93.47	odd	10	inner	2883.1.o.e.1196.1		32
93.50	odd	30	inner	2883.1.o.e.1409.3		32
93.53	even	30		2883.1.l.d.2453.2		16
93.56	odd	6	inner	2883.1.o.e.2654.3		32
93.59	odd	30	inner	2883.1.o.e.338.2		32
93.65	even	30	inner	2883.1.o.e.338.1		32
93.68	even	6	inner	2883.1.o.e.2654.4		32
93.71	odd	30		2883.1.l.d.2453.1		16
93.74	even	30	inner	2883.1.o.e.1409.4		32
93.77	even	10	inner	2883.1.o.e.1196.2		32
93.80	odd	30		2883.1.l.d.1349.2		16
93.83	even	30		2883.1.l.d.1589.3		16
93.86	even	30		2883.1.h.c.521.4		8
93.89	even	10		2883.1.h.c.1400.3		8
93.92	even	2	inner	2883.1.o.e.2738.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2883.1.b.c.962.1	✓	4	31.20	even	15
2883.1.b.c.962.2	yes	4	31.11	odd	30
2883.1.b.c.962.3	yes	4	93.20	odd	30
2883.1.b.c.962.4	yes	4	93.11	even	30
2883.1.h.c.521.1		8	31.24	odd	30
2883.1.h.c.521.2		8	31.7	even	15
2883.1.h.c.521.3		8	93.38	odd	30
2883.1.h.c.521.4		8	93.86	even	30
2883.1.h.c.1400.1		8	31.4	even	5
2883.1.h.c.1400.2		8	31.27	odd	10
2883.1.h.c.1400.3		8	93.89	even	10
2883.1.h.c.1400.4		8	93.35	odd	10
2883.1.l.d.374.1		16	31.26	odd	6
2883.1.l.d.374.2		16	31.5	even	3
2883.1.l.d.374.3		16	93.26	even	6
2883.1.l.d.374.4		16	93.5	odd	6
2883.1.l.d.1349.1		16	93.44	even	30
2883.1.l.d.1349.2		16	93.80	odd	30
2883.1.l.d.1349.3		16	31.13	odd	30
2883.1.l.d.1349.4		16	31.18	even	15
2883.1.l.d.1589.1		16	31.10	even	15
2883.1.l.d.1589.2		16	31.21	odd	30
2883.1.l.d.1589.3		16	93.83	even	30
2883.1.l.d.1589.4		16	93.41	odd	30
2883.1.l.d.2453.1		16	93.71	odd	30
2883.1.l.d.2453.2		16	93.53	even	30
2883.1.l.d.2453.3		16	31.22	odd	30
2883.1.l.d.2453.4		16	31.9	even	15
2883.1.o.e.338.1		32	93.65	even	30	inner
2883.1.o.e.338.2		32	93.59	odd	30	inner
2883.1.o.e.338.3		32	31.28	even	15	inner
2883.1.o.e.338.4		32	31.3	odd	30	inner
2883.1.o.e.1196.1		32	93.47	odd	10	inner
2883.1.o.e.1196.2		32	93.77	even	10	inner
2883.1.o.e.1196.3		32	31.16	even	5	inner
2883.1.o.e.1196.4		32	31.15	odd	10	inner
2883.1.o.e.1409.1		32	31.12	odd	30	inner
2883.1.o.e.1409.2		32	31.19	even	15	inner
2883.1.o.e.1409.3		32	93.50	odd	30	inner
2883.1.o.e.1409.4		32	93.74	even	30	inner
2883.1.o.e.1508.1		32	93.23	even	10	inner
2883.1.o.e.1508.2		32	93.8	odd	10	inner
2883.1.o.e.1508.3		32	31.8	even	5	inner
2883.1.o.e.1508.4		32	31.23	odd	10	inner
2883.1.o.e.1805.1		32	93.17	even	30	inner
2883.1.o.e.1805.2		32	93.14	odd	30	inner
2883.1.o.e.1805.3		32	31.17	odd	30	inner
2883.1.o.e.1805.4		32	31.14	even	15	inner
2883.1.o.e.2654.1		32	31.25	even	3	inner
2883.1.o.e.2654.2		32	31.6	odd	6	inner
2883.1.o.e.2654.3		32	93.56	odd	6	inner
2883.1.o.e.2654.4		32	93.68	even	6	inner
2883.1.o.e.2738.1		32	31.30	odd	2	inner
2883.1.o.e.2738.2		32	1.1	even	1	trivial
2883.1.o.e.2738.3		32	3.2	odd	2	inner
2883.1.o.e.2738.4		32	93.92	even	2	inner
2883.1.o.e.2768.1		32	31.29	odd	10	inner
2883.1.o.e.2768.2		32	31.2	even	5	inner
2883.1.o.e.2768.3		32	93.29	even	10	inner
2883.1.o.e.2768.4		32	93.2	odd	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2883 = 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2883.o (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.777146 + 0.629320i) q^{3} +(0.866025 - 0.500000i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.978148 + 0.207912i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.207912 + 0.978148i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-0.743145 + 0.669131i) q^{14} +(0.987688 + 0.156434i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.05097 + 0.946294i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(0.913545 - 0.406737i) q^{19} +(0.629320 + 0.777146i) q^{21} +(-0.544639 - 0.838671i) q^{24} +(-0.453990 + 0.891007i) q^{27} +(0.831254 - 1.14412i) q^{29} +(-0.707107 + 0.707107i) q^{30} +(-0.147826 - 1.40647i) q^{34} +(0.951057 - 0.309017i) q^{35} +(-0.207912 + 0.978148i) q^{38} +(-0.978148 + 0.207912i) q^{40} +(-0.994522 - 0.104528i) q^{41} +(-0.998630 + 0.0523360i) q^{42} +(-1.29195 + 0.575212i) q^{43} +(0.669131 + 0.743145i) q^{45} +(0.998630 + 0.0523360i) q^{48} +(-1.41228 + 0.0740142i) q^{51} +(-0.453990 - 0.891007i) q^{54} +(-0.866025 - 0.500000i) q^{56} +(0.965926 + 0.258819i) q^{57} +(0.437016 + 1.34500i) q^{58} +(0.994522 - 0.104528i) q^{59} +1.41421 q^{61} +1.00000i q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.309017 + 0.951057i) q^{70} +(-0.207912 - 0.978148i) q^{71} +(0.104528 - 0.994522i) q^{72} +(0.406737 - 0.913545i) q^{80} +(-0.913545 + 0.406737i) q^{81} +(0.669131 - 0.743145i) q^{82} +(-1.40647 - 0.147826i) q^{83} +(-0.437016 + 1.34500i) q^{85} +(0.294032 - 1.38331i) q^{86} +(1.36603 - 0.366025i) q^{87} +(-0.994522 + 0.104528i) q^{90} +(0.587785 - 0.809017i) q^{95} +(-0.309017 - 0.951057i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7} + 4 q^{10} + 8 q^{16} - 4 q^{18} + 4 q^{19} + 4 q^{40} + 4 q^{45} - 4 q^{51} + 8 q^{64} + 8 q^{70} - 4 q^{72} - 4 q^{81} + 4 q^{82} + 16 q^{87} + 8 q^{97}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 + 8 * q^16 - 4 * q^18 + 4 * q^19 + 4 * q^40 + 4 * q^45 - 4 * q^51 + 8 * q^64 + 8 * q^70 - 4 * q^72 - 4 * q^81 + 4 * q^82 + 16 * q^87 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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