LMFDB - Embedded newform 2001.1.bf.d.827.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,1,Mod(68,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 14, 23]))

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

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

chi := DirichletCharacter("2001.68");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2001.bf (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.998629090279$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{28})$
Coefficient field:	$\Q(\zeta_{84})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 $ x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{84}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{84} - \cdots)$

Embedding invariants

Embedding label			827.2
Root			$0.680173 - 0.733052i$ of defining polynomial
Character	$\chi$	$=$	2001.827
Dual form			2001.1.bf.d.1655.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.132974 + 1.18017i) q^{2} +(-0.149042 - 0.988831i) q^{3} +(-0.400198 + 0.0913425i) q^{4} +(1.14717 - 0.307384i) q^{6} +(0.231237 + 0.660838i) q^{8} +(-0.955573 + 0.294755i) q^{9} +O(q^{10})$	\(q+(0.132974 + 1.18017i) q^{2} +(-0.149042 - 0.988831i) q^{3} +(-0.400198 + 0.0913425i) q^{4} +(1.14717 - 0.307384i) q^{6} +(0.231237 + 0.660838i) q^{8} +(-0.955573 + 0.294755i) q^{9} +(0.149969 + 0.382114i) q^{12} +(0.858075 + 1.78181i) q^{13} +(-1.11899 + 0.538878i) q^{16} +(-0.474928 - 1.08855i) q^{18} +(-0.781831 + 0.623490i) q^{23} +(0.618992 - 0.327147i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-1.98874 + 1.24961i) q^{26} +(0.433884 + 0.900969i) q^{27} +(0.680173 + 0.733052i) q^{29} +(1.91970 - 0.216299i) q^{31} +(-0.412276 - 0.656134i) q^{32} +(0.355494 - 0.205245i) q^{36} +(1.63402 - 1.11406i) q^{39} +(-1.07193 - 1.07193i) q^{41} +(-0.839789 - 0.839789i) q^{46} +(1.88645 + 0.660096i) q^{47} +(0.699637 + 1.02618i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(1.12099 - 0.392253i) q^{50} +(-0.506155 - 0.634698i) q^{52} +(-1.00560 + 0.631863i) q^{54} +(-0.774683 + 0.900198i) q^{58} +0.445042i q^{59} +(0.510540 + 2.23682i) q^{62} +(-0.251496 + 0.200561i) q^{64} +(0.733052 + 0.680173i) q^{69} +(1.67738 - 0.807782i) q^{71} +(-0.415749 - 0.563320i) q^{72} +(-0.928661 - 0.104635i) q^{73} +(-0.930874 + 0.365341i) q^{75} +(1.53206 + 1.78029i) q^{78} +(0.826239 - 0.563320i) q^{81} +(1.12253 - 1.40761i) q^{82} +(0.623490 - 0.781831i) q^{87} +(0.255936 - 0.320934i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(-0.528180 + 2.31411i) q^{94} +(-0.587359 + 0.505463i) q^{96} +(0.392253 - 1.12099i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 14 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9	$ 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9} + 2 q^{12} - 6 q^{16} + 12 q^{18} - 6 q^{24} - 4 q^{25} - 2 q^{26} - 2 q^{31} - 4 q^{32} + 6 q^{36} + 2 q^{39} - 2 q^{41} + 2 q^{46} + 2 q^{47} + 6 q^{48} - 4 q^{49} + 2 q^{50} - 10 q^{52} - 2 q^{54} + 4 q^{58} - 4 q^{62} - 28 q^{64} - 2 q^{69} + 22 q^{72} - 2 q^{73} - 4 q^{78} + 2 q^{81} - 4 q^{82} - 4 q^{87} - 4 q^{92} - 12 q^{93} - 8 q^{94} - 18 q^{96} + 2 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 14 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9 + 2 * q^12 - 6 * q^16 + 12 * q^18 - 6 * q^24 - 4 * q^25 - 2 * q^26 - 2 * q^31 - 4 * q^32 + 6 * q^36 + 2 * q^39 - 2 * q^41 + 2 * q^46 + 2 * q^47 + 6 * q^48 - 4 * q^49 + 2 * q^50 - 10 * q^52 - 2 * q^54 + 4 * q^58 - 4 * q^62 - 28 * q^64 - 2 * q^69 + 22 * q^72 - 2 * q^73 - 4 * q^78 + 2 * q^81 - 4 * q^82 - 4 * q^87 - 4 * q^92 - 12 * q^93 - 8 * q^94 - 18 * q^96 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{27}{28}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.132974	+	1.18017i	0.132974	+	1.18017i	0.866025	+	0.500000i	$0.166667\pi$
$2$	0.132974	+	1.18017i	0.132974	+	1.18017i	−0.733052	+	0.680173i	$0.761905\pi$
$3$	−0.149042	−	0.988831i	−0.149042	−	0.988831i
$3$	−0.149042	−	0.988831i	−0.149042	−	0.988831i
$4$	−0.400198	+	0.0913425i	−0.400198	+	0.0913425i
$5$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$5$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$6$	1.14717	−	0.307384i	1.14717	−	0.307384i
$7$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$7$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$8$	0.231237	+	0.660838i	0.231237	+	0.660838i
$9$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$10$		0			0
$11$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$11$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$12$	0.149969	+	0.382114i	0.149969	+	0.382114i
$13$	0.858075	+	1.78181i	0.858075	+	1.78181i	0.563320	+	0.826239i	$0.309524\pi$
$13$	0.858075	+	1.78181i	0.858075	+	1.78181i	0.294755	+	0.955573i	$0.404762\pi$
$14$		0			0
$15$		0			0
$16$	−1.11899	+	0.538878i	−1.11899	+	0.538878i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	−0.474928	−	1.08855i	−0.474928	−	1.08855i
$19$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$19$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$23$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$24$	0.618992	−	0.327147i	0.618992	−	0.327147i
$25$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$26$	−1.98874	+	1.24961i	−1.98874	+	1.24961i
$27$	0.433884	+	0.900969i	0.433884	+	0.900969i
$28$		0			0
$29$	0.680173	+	0.733052i	0.680173	+	0.733052i
$29$	0.680173	+	0.733052i	0.680173	+	0.733052i
$30$		0			0
$31$	1.91970	−	0.216299i	1.91970	−	0.216299i	0.930874	−	0.365341i	$-0.119048\pi$
$31$	1.91970	−	0.216299i	1.91970	−	0.216299i	0.988831	+	0.149042i	$0.0476190\pi$
$32$	−0.412276	−	0.656134i	−0.412276	−	0.656134i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.355494	−	0.205245i	0.355494	−	0.205245i
$37$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$37$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$38$		0			0
$39$	1.63402	−	1.11406i	1.63402	−	1.11406i
$40$		0			0
$41$	−1.07193	−	1.07193i	−1.07193	−	1.07193i	−0.997204	−	0.0747301i	$-0.976190\pi$
$41$	−1.07193	−	1.07193i	−1.07193	−	1.07193i	−0.0747301	−	0.997204i	$-0.523810\pi$
$42$		0			0
$43$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$43$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$44$		0			0
$45$		0			0
$46$	−0.839789	−	0.839789i	−0.839789	−	0.839789i
$47$	1.88645	+	0.660096i	1.88645	+	0.660096i	0.955573	+	0.294755i	$0.0952381\pi$
$47$	1.88645	+	0.660096i	1.88645	+	0.660096i	0.930874	+	0.365341i	$0.119048\pi$
$48$	0.699637	+	1.02618i	0.699637	+	1.02618i
$49$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$50$	1.12099	−	0.392253i	1.12099	−	0.392253i
$51$		0			0
$52$	−0.506155	−	0.634698i	−0.506155	−	0.634698i
$53$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$53$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$54$	−1.00560	+	0.631863i	−1.00560	+	0.631863i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.774683	+	0.900198i	−0.774683	+	0.900198i
$59$			0.445042i			0.445042i	0.974928	+	0.222521i	$0.0714286\pi$
$59$			0.445042i			0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$60$		0			0
$61$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$61$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$62$	0.510540	+	2.23682i	0.510540	+	2.23682i
$63$		0			0
$64$	−0.251496	+	0.200561i	−0.251496	+	0.200561i
$65$		0			0
$66$		0			0
$67$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$67$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$68$		0			0
$69$	0.733052	+	0.680173i	0.733052	+	0.680173i
$70$		0			0
$71$	1.67738	−	0.807782i	1.67738	−	0.807782i	0.680173	−	0.733052i	$-0.261905\pi$
$71$	1.67738	−	0.807782i	1.67738	−	0.807782i	0.997204	−	0.0747301i	$-0.0238095\pi$
$72$	−0.415749	−	0.563320i	−0.415749	−	0.563320i
$73$	−0.928661	−	0.104635i	−0.928661	−	0.104635i	−0.365341	−	0.930874i	$-0.619048\pi$
$73$	−0.928661	−	0.104635i	−0.928661	−	0.104635i	−0.563320	+	0.826239i	$0.690476\pi$
$74$		0			0
$75$	−0.930874	+	0.365341i	−0.930874	+	0.365341i
$76$		0			0
$77$		0			0
$78$	1.53206	+	1.78029i	1.53206	+	1.78029i
$79$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$79$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$80$		0			0
$81$	0.826239	−	0.563320i	0.826239	−	0.563320i
$82$	1.12253	−	1.40761i	1.12253	−	1.40761i
$83$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$83$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.623490	−	0.781831i	0.623490	−	0.781831i
$88$		0			0
$89$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$89$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$90$		0			0
$91$		0			0
$92$	0.255936	−	0.320934i	0.255936	−	0.320934i
$93$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$94$	−0.528180	+	2.31411i	−0.528180	+	2.31411i
$95$		0			0
$96$	−0.587359	+	0.505463i	−0.587359	+	0.505463i
$97$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$97$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$98$	0.392253	−	1.12099i	0.392253	−	1.12099i
$99$		0			0
$100$	0.178105	+	0.369838i	0.178105	+	0.369838i
$101$	−1.05737	−	0.119137i	−1.05737	−	0.119137i	−0.433884	−	0.900969i	$-0.642857\pi$
$101$	−1.05737	−	0.119137i	−1.05737	−	0.119137i	−0.623490	+	0.781831i	$0.714286\pi$
$102$		0			0
$103$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$103$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$104$	−0.979069	+	0.979069i	−0.979069	+	0.979069i
$105$		0			0
$106$		0			0
$107$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$107$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$108$	−0.255936	−	0.320934i	−0.255936	−	0.320934i
$109$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$109$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$113$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$114$		0			0
$115$		0			0
$116$	−0.339162	−	0.231237i	−0.339162	−	0.231237i
$117$	−1.34515	−	1.44973i	−1.34515	−	1.44973i
$118$	−0.525226	+	0.0591788i	−0.525226	+	0.0591788i
$119$		0			0
$120$		0			0
$121$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$122$		0			0
$123$	−0.900198	+	1.21972i	−0.900198	+	1.21972i
$124$	−0.748504	+	0.261913i	−0.748504	+	0.261913i
$125$		0			0
$126$		0			0
$127$	0.350958	+	0.122805i	0.350958	+	0.122805i	0.500000	−	0.866025i	$-0.333333\pi$
$127$	0.350958	+	0.122805i	0.350958	+	0.122805i	−0.149042	+	0.988831i	$0.547619\pi$
$128$	−0.818082	−	0.818082i	−0.818082	−	0.818082i
$129$		0			0
$130$		0			0
$131$	−0.180173	+	1.59908i	−0.180173	+	1.59908i	0.500000	+	0.866025i	$0.333333\pi$
$131$	−0.180173	+	1.59908i	−0.180173	+	1.59908i	−0.680173	+	0.733052i	$0.738095\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$137$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$138$	−0.705245	+	0.955573i	−0.705245	+	0.955573i
$139$	−1.16078	−	1.45557i	−1.16078	−	1.45557i	−0.866025	−	0.500000i	$-0.833333\pi$
$139$	−1.16078	−	1.45557i	−1.16078	−	1.45557i	−0.294755	−	0.955573i	$-0.595238\pi$
$140$		0			0
$141$	0.371563	−	1.96376i	0.371563	−	1.96376i
$142$	1.17637	+	1.87218i	1.17637	+	1.87218i
$143$		0			0
$144$	0.910442	−	0.844766i	0.910442	−	0.844766i
$145$		0			0
$146$		−	1.10989i		−	1.10989i
$147$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$148$		0			0
$149$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$149$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$150$	−0.554947	−	1.05001i	−0.554947	−	1.05001i
$151$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	−0.930874	−	0.365341i	$-0.880952\pi$
$151$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	0.149042	+	0.988831i	$0.452381\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.552171	+	0.595099i	−0.552171	+	0.595099i
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.774683	+	0.900198i	0.774683	+	0.900198i
$163$	0.660096	−	1.88645i	0.660096	−	1.88645i	0.294755	−	0.955573i	$-0.404762\pi$
$163$	0.660096	−	1.88645i	0.660096	−	1.88645i	0.365341	−	0.930874i	$-0.380952\pi$
$164$	0.526899	+	0.331072i	0.526899	+	0.331072i
$165$		0			0
$166$		0			0
$167$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$167$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$168$		0			0
$169$	−1.81507	+	2.27603i	−1.81507	+	2.27603i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$173$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$174$	1.00560	+	0.631863i	1.00560	+	0.631863i
$175$		0			0
$176$		0			0
$177$	0.440071	−	0.0663300i	0.440071	−	0.0663300i
$178$		0			0
$179$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.0747301	−	0.997204i	$-0.476190\pi$
$179$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.955573	−	0.294755i	$-0.0952381\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$		0			0
$183$		0			0
$184$	−0.592814	−	0.372490i	−0.592814	−	0.372490i
$185$		0			0
$186$	2.13575	−	0.838218i	2.13575	−	0.838218i
$187$		0			0
$188$	−0.815247	−	0.0918562i	−0.815247	−	0.0918562i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	0.235805	+	0.218795i	0.235805	+	0.218795i
$193$	−0.940755	+	1.49720i	−0.940755	+	1.49720i	−0.0747301	+	0.997204i	$0.523810\pi$
$193$	−0.940755	+	1.49720i	−0.940755	+	1.49720i	−0.866025	+	0.500000i	$0.833333\pi$
$194$		0			0
$195$		0			0
$196$	0.400198	+	0.0913425i	0.400198	+	0.0913425i
$197$	1.35417	−	1.07992i	1.35417	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$197$	1.35417	−	1.07992i	1.35417	−	1.07992i	0.988831	−	0.149042i	$-0.0476190\pi$
$198$		0			0
$199$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$199$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$200$	0.592814	−	0.372490i	0.592814	−	0.372490i
$201$		0			0
$202$		−	1.26373i		−	1.26373i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.563320	−	0.826239i	0.563320	−	0.826239i
$208$	−1.92036	−	1.53144i	−1.92036	−	1.53144i
$209$		0			0
$210$		0			0
$211$	1.33485	−	0.467085i	1.33485	−	0.467085i	0.433884	−	0.900969i	$-0.357143\pi$
$211$	1.33485	−	0.467085i	1.33485	−	0.467085i	0.900969	+	0.433884i	$0.142857\pi$
$212$		0			0
$213$	−1.04876	−	1.53825i	−1.04876	−	1.53825i
$214$		0			0
$215$		0			0
$216$	−0.495064	+	0.495064i	−0.495064	+	0.495064i
$217$		0			0
$218$		0			0
$219$	0.0349435	+	0.933884i	0.0349435	+	0.933884i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$223$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$224$		0			0
$225$	0.500000	+	0.866025i	0.500000	+	0.866025i
$226$		0			0
$227$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$227$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$228$		0			0
$229$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$229$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$230$		0			0
$231$		0			0
$232$	−0.327147	+	0.618992i	−0.327147	+	0.618992i
$233$			0.149460i			0.149460i	0.997204	+	0.0747301i	$0.0238095\pi$
$233$			0.149460i			0.149460i	−0.997204	+	0.0747301i	$0.976190\pi$
$234$	1.53206	−	1.78029i	1.53206	−	1.78029i
$235$		0			0
$236$	−0.0406513	−	0.178105i	−0.0406513	−	0.178105i
$237$		0			0
$238$		0			0
$239$	−1.94440	−	0.443797i	−1.94440	−	0.443797i	−0.988831	−	0.149042i	$-0.952381\pi$
$239$	−1.94440	−	0.443797i	−1.94440	−	0.443797i	−0.955573	−	0.294755i	$-0.904762\pi$
$240$		0			0
$241$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$241$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$242$	0.631863	−	1.00560i	0.631863	−	1.00560i
$243$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$244$		0			0
$245$		0			0
$246$	−1.55919	−	0.900198i	−1.55919	−	0.900198i
$247$		0			0
$248$	0.586845	+	1.21860i	0.586845	+	1.21860i
$249$		0			0
$250$		0			0
$251$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$251$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$252$		0			0
$253$		0			0
$254$	−0.0982635	+	0.430521i	−0.0982635	+	0.430521i
$255$		0			0
$256$	0.656134	−	0.822766i	0.656134	−	0.822766i
$257$	1.32624	−	0.302705i	1.32624	−	0.302705i	0.500000	−	0.866025i	$-0.333333\pi$
$257$	1.32624	−	0.302705i	1.32624	−	0.302705i	0.826239	+	0.563320i	$0.190476\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$262$	−1.91115			−1.91115
$263$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$263$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.122805	−	0.350958i	−0.122805	−	0.350958i	0.866025	−	0.500000i	$-0.166667\pi$
$269$	−0.122805	−	0.350958i	−0.122805	−	0.350958i	−0.988831	+	0.149042i	$0.952381\pi$
$270$		0			0
$271$	0.189606	+	0.119137i	0.189606	+	0.119137i	0.623490	−	0.781831i	$-0.285714\pi$
$271$	0.189606	+	0.119137i	0.189606	+	0.119137i	−0.433884	+	0.900969i	$0.642857\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.355494	−	0.205245i	−0.355494	−	0.205245i
$277$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	−0.733052	−	0.680173i	$-0.761905\pi$
$277$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	0.0747301	+	0.997204i	$0.476190\pi$
$278$	1.56347	−	1.56347i	1.56347	−	1.56347i
$279$	−1.77066	+	0.772532i	−1.77066	+	0.772532i
$280$		0			0
$281$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$281$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$282$	2.36698	+	0.177381i	2.36698	+	0.177381i
$283$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$283$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$284$	−0.597498	+	0.476488i	−0.597498	+	0.476488i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.587359	+	0.505463i	0.587359	+	0.505463i
$289$		−	1.00000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	0.381206	−	0.0429516i	0.381206	−	0.0429516i
$293$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$293$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$294$	−1.16694	−	0.220796i	−1.16694	−	0.220796i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.78181	−	0.858075i	−1.78181	−	0.858075i
$300$	0.339162	−	0.231237i	0.339162	−	0.231237i
$301$		0			0
$302$	−0.839789	−	0.839789i	−0.839789	−	0.839789i
$303$	0.0397866	+	1.06332i	0.0397866	+	1.06332i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.19745	+	1.19745i	1.19745	+	1.19745i	0.974928	+	0.222521i	$0.0714286\pi$
$307$	1.19745	+	1.19745i	1.19745	+	1.19745i	0.222521	+	0.974928i	$0.428571\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.754903	+	0.264152i	−0.754903	+	0.264152i	−0.680173	−	0.733052i	$-0.738095\pi$
$311$	−0.754903	+	0.264152i	−0.754903	+	0.264152i	−0.0747301	+	0.997204i	$0.523810\pi$
$312$	1.11406	+	0.822211i	1.11406	+	0.822211i
$313$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$313$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.97493	−	0.222521i	1.97493	−	0.222521i	0.974928	−	0.222521i	$-0.0714286\pi$
$317$	1.97493	−	0.222521i	1.97493	−	0.222521i	1.00000			$0$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.279204	+	0.300910i	−0.279204	+	0.300910i
$325$	1.54620	−	1.23305i	1.54620	−	1.23305i
$326$	2.31411	+	0.528180i	2.31411	+	0.528180i
$327$		0			0
$328$	0.460503	−	0.956245i	0.460503	−	0.956245i
$329$		0			0
$330$		0			0
$331$	1.38956	−	1.38956i	1.38956	−	1.38956i	0.563320	−	0.826239i	$-0.309524\pi$
$331$	1.38956	−	1.38956i	1.38956	−	1.38956i	0.826239	−	0.563320i	$-0.190476\pi$
$332$		0			0
$333$		0			0
$334$	1.47165	+	0.165815i	1.47165	+	0.165815i
$335$		0			0
$336$		0			0
$337$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$337$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$338$	−2.92746	−	1.83944i	−2.92746	−	1.83944i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.239610	−	2.12660i	−0.239610	−	2.12660i
$347$	0.867767			0.867767			0.433884	−	0.900969i	$-0.357143\pi$
$347$	0.867767			0.867767			0.433884	+	0.900969i	$0.357143\pi$
$348$	−0.178105	+	0.369838i	−0.178105	+	0.369838i
$349$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$349$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$350$		0			0
$351$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$352$		0			0
$353$	0.702449	−	0.880843i	0.702449	−	0.880843i	−0.294755	−	0.955573i	$-0.595238\pi$
$353$	0.702449	−	0.880843i	0.702449	−	0.880843i	0.997204	+	0.0747301i	$0.0238095\pi$
$354$	0.136799	+	0.510540i	0.136799	+	0.510540i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.66174	+	1.04414i	1.66174	+	1.04414i
$359$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$359$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$360$		0			0
$361$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$362$		0			0
$363$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$367$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$368$	0.538878	−	1.11899i	0.538878	−	1.11899i
$369$	1.34027	+	0.708353i	1.34027	+	0.708353i
$370$		0			0
$371$		0			0
$372$	0.370546	+	0.701108i	0.370546	+	0.701108i
$373$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$373$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$374$		0			0
$375$		0			0
$376$			1.39927i			1.39927i
$377$	−0.722521	+	1.84095i	−0.722521	+	1.84095i
$378$		0			0
$379$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$379$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$380$		0			0
$381$	0.0691263	−	0.365341i	0.0691263	−	0.365341i
$382$		0			0
$383$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$383$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$384$	−0.687016	+	0.930874i	−0.687016	+	0.930874i
$385$		0			0
$386$	−1.89205	−	0.911166i	−1.89205	−	0.911166i
$387$		0			0
$388$		0			0
$389$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$389$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$390$		0			0
$391$		0			0
$392$	0.0783893	−	0.695724i	0.0783893	−	0.695724i
$393$	1.60807	−	0.0601697i	1.60807	−	0.0601697i
$394$	1.45456	+	1.45456i	1.45456	+	1.45456i
$395$		0			0
$396$		0			0
$397$	1.79690	+	0.865341i	1.79690	+	0.865341i	0.930874	+	0.365341i	$0.119048\pi$
$397$	1.79690	+	0.865341i	1.79690	+	0.865341i	0.866025	+	0.500000i	$0.166667\pi$
$398$		0			0
$399$		0			0
$400$	0.774367	+	0.971025i	0.774367	+	0.971025i
$401$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$401$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$402$		0			0
$403$	2.03265	+	3.23495i	2.03265	+	3.23495i
$404$	0.434041	−	0.0489047i	0.434041	−	0.0489047i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.28359	+	0.806531i	−1.28359	+	0.806531i	−0.988831	−	0.149042i	$-0.952381\pi$
$409$	−1.28359	+	0.806531i	−1.28359	+	0.806531i	−0.294755	+	0.955573i	$0.595238\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	1.05001	+	0.554947i	1.05001	+	0.554947i
$415$		0			0
$416$	0.815343	−	1.29761i	0.815343	−	1.29761i
$417$	−1.26631	+	1.36476i	−1.26631	+	1.36476i
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$		0			0
$421$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$421$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$422$	0.728741	+	1.51325i	0.728741	+	1.51325i
$423$	−1.99720	−	0.0747301i	−1.99720	−	0.0747301i
$424$		0			0
$425$		0			0
$426$	1.67594	−	1.44226i	1.67594	−	1.44226i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$431$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$432$	−0.971025	−	0.774367i	−0.971025	−	0.774367i
$433$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$433$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−1.09750	+	0.165421i	−1.09750	+	0.165421i
$439$	1.94440	−	0.443797i	1.94440	−	0.443797i	0.955573	−	0.294755i	$-0.0952381\pi$
$439$	1.94440	−	0.443797i	1.94440	−	0.443797i	0.988831	−	0.149042i	$-0.0476190\pi$
$440$		0			0
$441$	0.988831	+	0.149042i	0.988831	+	0.149042i
$442$		0			0
$443$	0.584010	+	1.66900i	0.584010	+	1.66900i	0.733052	+	0.680173i	$0.238095\pi$
$443$	0.584010	+	1.66900i	0.584010	+	1.66900i	−0.149042	+	0.988831i	$0.547619\pi$
$444$		0			0
$445$		0			0
$446$	0.706815	−	2.01996i	0.706815	−	2.01996i
$447$		0			0
$448$		0			0
$449$	0.222521	+	0.0250721i	0.222521	+	0.0250721i	0.222521	−	0.974928i	$-0.428571\pi$
$449$	0.222521	+	0.0250721i	0.222521	+	0.0250721i			1.00000i	$0.5\pi$
$450$	−0.955573	+	0.705245i	−0.955573	+	0.705245i
$451$		0			0
$452$		0			0
$453$	0.733052	+	0.680173i	0.733052	+	0.680173i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$457$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.66393	+	1.04551i	−1.66393	+	1.04551i	−0.733052	+	0.680173i	$0.761905\pi$
$461$	−1.66393	+	1.04551i	−1.66393	+	1.04551i	−0.930874	+	0.365341i	$0.880952\pi$
$462$		0			0
$463$			1.24698i			1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$463$			1.24698i			1.24698i	−0.781831	+	0.623490i	$0.785714\pi$
$464$	−1.15613	−	0.453749i	−1.15613	−	0.453749i
$465$		0			0
$466$	−0.176389	+	0.0198742i	−0.176389	+	0.0198742i
$467$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$467$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$468$	0.670749	+	0.457309i	0.670749	+	0.457309i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.294100	+	0.102910i	−0.294100	+	0.102910i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.265203	−	2.35375i	0.265203	−	2.35375i
$479$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$479$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.369838	+	0.178105i	0.369838	+	0.178105i
$485$		0			0
$486$	0.774683	−	0.900198i	0.774683	−	0.900198i
$487$	−0.702449	−	0.880843i	−0.702449	−	0.880843i	0.294755	−	0.955573i	$-0.404762\pi$
$487$	−0.702449	−	0.880843i	−0.702449	−	0.880843i	−0.997204	+	0.0747301i	$0.976190\pi$
$488$		0			0
$489$	−1.96376	−	0.371563i	−1.96376	−	0.371563i
$490$		0			0
$491$	−1.29637	+	0.146066i	−1.29637	+	0.146066i	−0.733052	−	0.680173i	$-0.761905\pi$
$491$	−1.29637	+	0.146066i	−1.29637	+	0.146066i	−0.563320	+	0.826239i	$0.690476\pi$
$492$	0.248844	−	0.570358i	0.248844	−	0.570358i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−2.03158	+	1.27652i	−2.03158	+	1.27652i
$497$		0			0
$498$		0			0
$499$	1.14625	−	0.914101i	1.14625	−	0.914101i	0.149042	−	0.988831i	$-0.452381\pi$
$499$	1.14625	−	0.914101i	1.14625	−	0.914101i	0.997204	+	0.0747301i	$0.0238095\pi$
$500$		0			0
$501$	−1.24349	−	0.0931869i	−1.24349	−	0.0931869i
$502$		0			0
$503$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$503$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.52113	+	1.45557i	2.52113	+	1.45557i
$508$	−0.151670	−	0.0170891i	−0.151670	−	0.0170891i
$509$	−0.255779	−	0.531130i	−0.255779	−	0.531130i	0.733052	−	0.680173i	$-0.238095\pi$
$509$	−0.255779	−	0.531130i	−0.255779	−	0.531130i	−0.988831	+	0.149042i	$0.952381\pi$
$510$		0			0
$511$		0			0
$512$	0.0786427	+	0.0494145i	0.0786427	+	0.0494145i
$513$		0			0
$514$	0.533599	+	1.52494i	0.533599	+	1.52494i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.268565	+	1.78181i	0.268565	+	1.78181i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	0.474928	−	1.08855i	0.474928	−	1.08855i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	−0.0739590	−	0.656405i	−0.0739590	−	0.656405i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.222521	−	0.974928i	0.222521	−	0.974928i
$530$		0			0
$531$	−0.131178	−	0.425270i	−0.131178	−	0.425270i
$532$		0			0
$533$	0.990184	−	2.82978i	0.990184	−	2.82978i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.43109	−	0.826239i	−1.43109	−	0.826239i
$538$	0.397861	−	0.191600i	0.397861	−	0.191600i
$539$		0			0
$540$		0			0
$541$	0.0397866	−	0.0633201i	0.0397866	−	0.0633201i	−0.826239	−	0.563320i	$-0.809524\pi$
$541$	0.0397866	−	0.0633201i	0.0397866	−	0.0633201i	0.866025	+	0.500000i	$0.166667\pi$
$542$	−0.115390	+	0.239610i	−0.115390	+	0.239610i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.0332580	+	0.145713i	0.0332580	+	0.145713i	0.988831	−	0.149042i	$-0.0476190\pi$
$547$	0.0332580	+	0.145713i	0.0332580	+	0.145713i	−0.955573	+	0.294755i	$0.904762\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−0.279975	+	0.641709i	−0.279975	+	0.641709i
$553$		0			0
$554$	−0.461691	−	0.734777i	−0.461691	−	0.734777i
$555$		0			0
$556$	0.597498	+	0.476488i	0.597498	+	0.476488i
$557$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$557$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$558$	−1.14717	−	1.98696i	−1.14717	−	1.98696i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$	0.0306759	+	0.819831i	0.0306759	+	0.819831i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	0.921684	+	0.921684i	0.921684	+	0.921684i
$569$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$569$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$570$		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			0
$575$	0.781831	+	0.623490i	0.781831	+	0.623490i
$576$	0.181206	−	0.265780i	0.181206	−	0.265780i
$577$	−1.04551	−	1.66393i	−1.04551	−	1.66393i	−0.680173	−	0.733052i	$-0.738095\pi$
$577$	−1.04551	−	1.66393i	−1.04551	−	1.66393i	−0.365341	−	0.930874i	$-0.619048\pi$
$578$	1.18017	−	0.132974i	1.18017	−	0.132974i
$579$	1.62069	+	0.707101i	1.62069	+	0.707101i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.145594	−	0.637890i	−0.145594	−	0.637890i
$585$		0			0
$586$		0			0
$587$	−1.09839	−	0.250701i	−1.09839	−	0.250701i	−0.365341	−	0.930874i	$-0.619048\pi$
$587$	−1.09839	−	0.250701i	−1.09839	−	0.250701i	−0.733052	+	0.680173i	$0.761905\pi$
$588$	0.0306759	−	0.409342i	0.0306759	−	0.409342i
$589$		0			0
$590$		0			0
$591$	−1.26968	−	1.17809i	−1.26968	−	1.17809i
$592$		0			0
$593$	0.781831	−	0.376510i	0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$593$	0.781831	−	0.376510i	0.781831	−	0.376510i	0.781831	+	0.623490i	$0.214286\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.775743	−	2.21695i	0.775743	−	2.21695i
$599$	0.189606	+	0.119137i	0.189606	+	0.119137i	0.623490	−	0.781831i	$-0.285714\pi$
$599$	0.189606	+	0.119137i	0.189606	+	0.119137i	−0.433884	+	0.900969i	$0.642857\pi$
$600$	−0.456684	−	0.530676i	−0.456684	−	0.530676i
$601$	0.170965	+	0.488590i	0.170965	+	0.488590i	0.997204	−	0.0747301i	$-0.0238095\pi$
$601$	0.170965	+	0.488590i	0.170965	+	0.488590i	−0.826239	+	0.563320i	$0.809524\pi$
$602$		0			0
$603$		0			0
$604$	0.255936	−	0.320934i	0.255936	−	0.320934i
$605$		0			0
$606$	−1.24961	+	0.188349i	−1.24961	+	0.188349i
$607$	−0.0739590	−	0.656405i	−0.0739590	−	0.656405i	−0.974928	−	0.222521i	$-0.928571\pi$
$607$	−0.0739590	−	0.656405i	−0.0739590	−	0.656405i	0.900969	−	0.433884i	$-0.142857\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.442546	+	3.92770i	0.442546	+	3.92770i
$612$		0			0
$613$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$613$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$614$	−1.25397	+	1.57243i	−1.25397	+	1.57243i
$615$		0			0
$616$		0			0
$617$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$617$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$618$		0			0
$619$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$619$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$620$		0			0
$621$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$622$	−0.412127	−	0.855791i	−0.412127	−	0.855791i
$623$		0			0
$624$	−1.22812	+	2.12716i	−1.22812	+	2.12716i
$625$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$631$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$632$		0			0
$633$	−0.660818	−	1.25033i	−0.660818	−	1.25033i
$634$	0.525226	+	2.30117i	0.525226	+	2.30117i
$635$		0			0
$636$		0			0
$637$		−	1.97766i		−	1.97766i
$638$		0			0
$639$	−1.36476	+	1.26631i	−1.36476	+	1.26631i
$640$		0			0
$641$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$641$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$642$		0			0
$643$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$643$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.531130	−	0.255779i	−0.531130	−	0.255779i	0.149042	−	0.988831i	$-0.452381\pi$
$647$	−0.531130	−	0.255779i	−0.531130	−	0.255779i	−0.680173	+	0.733052i	$0.738095\pi$
$648$	0.563320	+	0.415749i	0.563320	+	0.415749i
$649$		0			0
$650$	1.66082	+	1.66082i	1.66082	+	1.66082i
$651$		0			0
$652$	−0.0918562	+	0.815247i	−0.0918562	+	0.815247i
$653$	0.0579571	−	0.514383i	0.0579571	−	0.514383i	−0.930874	−	0.365341i	$-0.880952\pi$
$653$	0.0579571	−	0.514383i	0.0579571	−	0.514383i	0.988831	−	0.149042i	$-0.0476190\pi$
$654$		0			0
$655$		0			0
$656$	1.77713	+	0.621844i	1.77713	+	0.621844i
$657$	0.918245	−	0.173741i	0.918245	−	0.173741i
$658$		0			0
$659$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$659$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	1.82469	+	1.45514i	1.82469	+	1.45514i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$668$			0.511872i			0.511872i
$669$	−0.531130	+	1.72188i	−0.531130	+	1.72188i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.880843	−	0.702449i	0.880843	−	0.702449i	−0.0747301	−	0.997204i	$-0.523810\pi$
$673$	0.880843	−	0.702449i	0.880843	−	0.702449i	0.955573	+	0.294755i	$0.0952381\pi$
$674$		0			0
$675$	0.781831	−	0.623490i	0.781831	−	0.623490i
$676$	0.518489	−	1.07665i	0.518489	−	1.07665i
$677$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$677$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.590232	+	1.22563i	0.590232	+	1.22563i	0.955573	+	0.294755i	$0.0952381\pi$
$683$	0.590232	+	1.22563i	0.590232	+	1.22563i	−0.365341	+	0.930874i	$0.619048\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.974928	+	1.22252i	−0.974928	+	1.22252i			1.00000i	$0.5\pi$
$691$	−0.974928	+	1.22252i	−0.974928	+	1.22252i	−0.974928	+	0.222521i	$0.928571\pi$
$692$	0.721132	−	0.164594i	0.721132	−	0.164594i
$693$		0			0
$694$	0.115390	+	1.02412i	0.115390	+	1.02412i
$695$		0			0
$696$	0.660838	+	0.231237i	0.660838	+	0.231237i
$697$		0			0
$698$	−0.194953	−	1.73026i	−0.194953	−	1.73026i
$699$	0.147791	−	0.0222759i	0.147791	−	0.0222759i
$700$		0			0
$701$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$701$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$702$	−1.98874	−	1.24961i	−1.98874	−	1.24961i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.13295	+	0.711882i	1.13295	+	0.711882i
$707$		0			0
$708$	−0.170057	+	0.0667424i	−0.170057	+	0.0667424i
$709$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$709$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$714$		0			0
$715$		0			0
$716$	−0.294314	+	0.611150i	−0.294314	+	0.611150i
$717$	−0.149042	+	1.98883i	−0.149042	+	1.98883i
$718$		0			0
$719$	−1.22252	+	0.974928i	−1.22252	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$719$	−1.22252	+	0.974928i	−1.22252	+	0.974928i	−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	1.00560	−	0.631863i	1.00560	−	0.631863i
$723$		0			0
$724$		0			0
$725$	0.563320	−	0.826239i	0.563320	−	0.826239i
$726$	−1.08855	−	0.474928i	−1.08855	−	0.474928i
$727$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$727$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$728$		0			0
$729$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$733$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$734$		0			0
$735$		0			0
$736$	0.731423	+	0.255936i	0.731423	+	0.255936i
$737$		0			0
$738$	−0.657758	+	1.67594i	−0.657758	+	1.67594i
$739$	0.169732	−	1.50641i	0.169732	−	1.50641i	−0.563320	−	0.826239i	$-0.690476\pi$
$739$	0.169732	−	1.50641i	0.169732	−	1.50641i	0.733052	−	0.680173i	$-0.238095\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$743$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$744$	1.11752	−	0.761913i	1.11752	−	0.761913i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$751$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$752$	−2.46663	+	0.277923i	−2.46663	+	0.277923i
$753$		0			0
$754$	−2.26872	−	0.607901i	−2.26872	−	0.607901i
$755$		0			0
$756$		0			0
$757$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$757$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.712362	−	0.162592i	−0.712362	−	0.162592i	−0.149042	−	0.988831i	$-0.547619\pi$
$761$	−0.712362	−	0.162592i	−0.712362	−	0.162592i	−0.563320	+	0.826239i	$0.690476\pi$
$762$	0.440357	+	0.0330002i	0.440357	+	0.0330002i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.792981	+	0.381879i	−0.792981	+	0.381879i
$768$	−0.911368	−	0.526179i	−0.911368	−	0.526179i
$769$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$769$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$770$		0			0
$771$	−0.496990	−	1.26631i	−0.496990	−	1.26631i
$772$	0.239730	−	0.685109i	0.239730	−	0.685109i
$773$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$773$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$774$		0			0
$775$	−0.638050	−	1.82344i	−0.638050	−	1.82344i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$784$	1.24199			1.24199
$785$		0			0
$786$	0.284841	+	1.88980i	0.284841	+	1.88980i
$787$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$787$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$788$	−0.443294	+	0.555874i	−0.443294	+	0.555874i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.782312	+	2.23572i	−0.782312	+	2.23572i
$795$		0			0
$796$		0			0
$797$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$797$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$798$		0			0
$799$		0			0
$800$	−0.547943	+	0.547943i	−0.547943	+	0.547943i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−3.54751	+	2.82905i	−3.54751	+	2.82905i
$807$	−0.328735	+	0.173741i	−0.328735	+	0.173741i
$808$	−0.165773	−	0.726301i	−0.165773	−	0.726301i
$809$	−0.559311	+	0.351438i	−0.559311	+	0.351438i	−0.781831	−	0.623490i	$-0.785714\pi$
$809$	−0.559311	+	0.351438i	−0.559311	+	0.351438i	0.222521	+	0.974928i	$0.428571\pi$
$810$		0			0
$811$		−	1.73205i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$811$		−	1.73205i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$812$		0			0
$813$	0.0895474	−	0.205245i	0.0895474	−	0.205245i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−1.12253	−	1.40761i	−1.12253	−	1.40761i
$819$		0			0
$820$		0			0
$821$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$821$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$822$		0			0
$823$	1.23137	+	0.430874i	1.23137	+	0.430874i	0.866025	−	0.500000i	$-0.166667\pi$
$823$	1.23137	+	0.430874i	1.23137	+	0.430874i	0.365341	+	0.930874i	$0.380952\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$827$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$828$	−0.149969	+	0.382114i	−0.149969	+	0.382114i
$829$	1.40532	+	1.40532i	1.40532	+	1.40532i	0.781831	+	0.623490i	$0.214286\pi$
$829$	1.40532	+	1.40532i	1.40532	+	1.40532i	0.623490	+	0.781831i	$0.285714\pi$
$830$		0			0
$831$	0.411608	+	0.603718i	0.411608	+	0.603718i
$832$	−0.573164	−	0.276021i	−0.573164	−	0.276021i
$833$		0			0
$834$	−1.77904	−	1.31299i	−1.77904	−	1.31299i
$835$		0			0
$836$		0			0
$837$	1.02781	+	1.63575i	1.02781	+	1.63575i
$838$		0			0
$839$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$839$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$840$		0			0
$841$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$842$		0			0
$843$		0			0
$844$	−0.491540	+	0.308855i	−0.491540	+	0.308855i
$845$		0			0
$846$	−0.177381	−	2.36698i	−0.177381	−	2.36698i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.560219	+	0.519807i	0.560219	+	0.519807i
$853$	−0.752407	+	0.752407i	−0.752407	+	0.752407i	−0.974928	−	0.222521i	$-0.928571\pi$
$853$	−0.752407	+	0.752407i	−0.752407	+	0.752407i	0.222521	+	0.974928i	$0.428571\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	−0.997204	−	0.0747301i	$-0.976190\pi$
$857$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	0.563320	−	0.826239i	$-0.309524\pi$
$858$		0			0
$859$	0.430874	−	1.23137i	0.430874	−	1.23137i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.430874	−	1.23137i	0.430874	−	1.23137i	0.930874	−	0.365341i	$-0.119048\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$863$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$864$	0.412276	−	0.656134i	0.412276	−	0.656134i
$865$		0			0
$866$		0			0
$867$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−0.0992876	−	0.370546i	−0.0992876	−	0.370546i
$877$	−0.433884	+	1.90097i	−0.433884	+	1.90097i			1.00000i	$0.5\pi$
$877$	−0.433884	+	1.90097i	−0.433884	+	1.90097i	−0.433884	+	0.900969i	$0.642857\pi$
$878$	0.782312	+	2.23572i	0.782312	+	2.23572i
$879$		0			0
$880$		0			0
$881$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$881$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$882$	−0.0444073	+	1.18681i	−0.0444073	+	1.18681i
$883$	−0.193096	−	0.400969i	−0.193096	−	0.400969i	0.781831	−	0.623490i	$-0.214286\pi$
$883$	−0.193096	−	0.400969i	−0.193096	−	0.400969i	−0.974928	+	0.222521i	$0.928571\pi$
$884$		0			0
$885$		0			0
$886$	−1.89205	+	0.911166i	−1.89205	+	0.911166i
$887$	0.262919	−	0.262919i	0.262919	−	0.262919i	−0.563320	−	0.826239i	$-0.690476\pi$
$887$	0.262919	−	0.262919i	0.262919	−	0.262919i	0.826239	+	0.563320i	$0.190476\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	0.721132	+	0.164594i	0.721132	+	0.164594i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.582926	+	1.88980i	−0.582926	+	1.88980i
$898$			0.265947i			0.265947i
$899$	1.46429	+	1.26012i	1.46429	+	1.26012i
$900$	−0.279204	−	0.300910i	−0.279204	−	0.300910i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.705245	+	0.955573i	−0.705245	+	0.955573i
$907$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$907$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$908$		0			0
$909$	1.04551	−	0.197822i	1.04551	−	0.197822i
$910$		0			0
$911$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$911$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		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			0
$921$	1.00560	−	1.36254i	1.00560	−	1.36254i
$922$	−1.45514	−	1.82469i	−1.45514	−	1.82469i
$923$	2.87863	+	2.29563i	2.87863	+	2.29563i
$924$		0			0
$925$		0			0
$926$	−1.47165	+	0.165815i	−1.47165	+	0.165815i
$927$		0			0
$928$	0.200561	−	0.748504i	0.200561	−	0.748504i
$929$			1.97766i			1.97766i	0.149042	+	0.988831i	$0.452381\pi$
$929$			1.97766i			1.97766i	−0.149042	+	0.988831i	$0.547619\pi$
$930$		0			0
$931$		0			0
$932$	−0.0136521	−	0.0598136i	−0.0136521	−	0.0598136i
$933$	0.373714	+	0.707101i	0.373714	+	0.707101i
$934$		0			0
$935$		0			0
$936$	0.646986	−	1.22416i	0.646986	−	1.22416i
$937$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$937$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$941$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$942$		0			0
$943$	1.50641	+	0.169732i	1.50641	+	0.169732i
$944$	−0.239823	−	0.497998i	−0.239823	−	0.497998i
$945$		0			0
$946$		0			0
$947$	0.314832	+	0.197822i	0.314832	+	0.197822i	0.680173	−	0.733052i	$-0.261905\pi$
$947$	0.314832	+	0.197822i	0.314832	+	0.197822i	−0.365341	+	0.930874i	$0.619048\pi$
$948$		0			0
$949$	−0.610421	−	1.74448i	−0.610421	−	1.74448i
$950$		0			0
$951$	−0.514383	−	1.91970i	−0.514383	−	1.91970i
$952$		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
$956$	0.818684			0.818684
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	2.66355	−	0.607938i	2.66355	−	0.607938i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.49720	+	0.940755i	1.49720	+	0.940755i	0.997204	+	0.0747301i	$0.0238095\pi$
$967$	1.49720	+	0.940755i	1.49720	+	0.940755i	0.500000	+	0.866025i	$0.333333\pi$
$968$	0.231237	−	0.660838i	0.231237	−	0.660838i
$969$		0			0
$970$		0			0
$971$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$971$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$972$	0.339162	+	0.231237i	0.339162	+	0.231237i
$973$		0			0
$974$	0.946139	−	0.946139i	0.946139	−	0.946139i
$975$	−1.44973	−	1.34515i	−1.44973	−	1.34515i
$976$		0			0
$977$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$977$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$978$	0.177381	−	2.36698i	0.177381	−	2.36698i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.344766	−	1.51052i	−0.344766	−	1.51052i
$983$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$983$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$984$	−1.01420	−	0.312839i	−1.01420	−	0.312839i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.678448	+	0.541044i	0.678448	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$991$	0.678448	+	0.541044i	0.678448	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$992$	−0.933370	−	1.17041i	−0.933370	−	1.17041i
$993$	−1.58114	−	1.16694i	−1.58114	−	1.16694i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.211363	+	0.0739590i	0.211363	+	0.0739590i	0.433884	−	0.900969i	$-0.357143\pi$
$997$	0.211363	+	0.0739590i	0.211363	+	0.0739590i	−0.222521	+	0.974928i	$0.571429\pi$
$998$	1.23122	+	1.23122i	1.23122	+	1.23122i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.d.827.2	yes	24
3.2	odd	2		2001.1.bf.c.827.1	✓	24
23.22	odd	2	CM	2001.1.bf.d.827.2	yes	24
29.2	odd	28		2001.1.bf.c.1655.1	yes	24
69.68	even	2		2001.1.bf.c.827.1	✓	24
87.2	even	28	inner	2001.1.bf.d.1655.2	yes	24
667.321	even	28		2001.1.bf.c.1655.1	yes	24
2001.1655	odd	28	inner	2001.1.bf.d.1655.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.827.1	✓	24	3.2	odd	2
2001.1.bf.c.827.1	✓	24	69.68	even	2
2001.1.bf.c.1655.1	yes	24	29.2	odd	28
2001.1.bf.c.1655.1	yes	24	667.321	even	28
2001.1.bf.d.827.2	yes	24	1.1	even	1	trivial
2001.1.bf.d.827.2	yes	24	23.22	odd	2	CM
2001.1.bf.d.1655.2	yes	24	87.2	even	28	inner
2001.1.bf.d.1655.2	yes	24	2001.1655	odd	28	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2001.bf (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.132974 + 1.18017i) q^{2} +(-0.149042 - 0.988831i) q^{3} +(-0.400198 + 0.0913425i) q^{4} +(1.14717 - 0.307384i) q^{6} +(0.231237 + 0.660838i) q^{8} +(-0.955573 + 0.294755i) q^{9} +O(q^{10})\)	\(q+(0.132974 + 1.18017i) q^{2} +(-0.149042 - 0.988831i) q^{3} +(-0.400198 + 0.0913425i) q^{4} +(1.14717 - 0.307384i) q^{6} +(0.231237 + 0.660838i) q^{8} +(-0.955573 + 0.294755i) q^{9} +(0.149969 + 0.382114i) q^{12} +(0.858075 + 1.78181i) q^{13} +(-1.11899 + 0.538878i) q^{16} +(-0.474928 - 1.08855i) q^{18} +(-0.781831 + 0.623490i) q^{23} +(0.618992 - 0.327147i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-1.98874 + 1.24961i) q^{26} +(0.433884 + 0.900969i) q^{27} +(0.680173 + 0.733052i) q^{29} +(1.91970 - 0.216299i) q^{31} +(-0.412276 - 0.656134i) q^{32} +(0.355494 - 0.205245i) q^{36} +(1.63402 - 1.11406i) q^{39} +(-1.07193 - 1.07193i) q^{41} +(-0.839789 - 0.839789i) q^{46} +(1.88645 + 0.660096i) q^{47} +(0.699637 + 1.02618i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(1.12099 - 0.392253i) q^{50} +(-0.506155 - 0.634698i) q^{52} +(-1.00560 + 0.631863i) q^{54} +(-0.774683 + 0.900198i) q^{58} +0.445042i q^{59} +(0.510540 + 2.23682i) q^{62} +(-0.251496 + 0.200561i) q^{64} +(0.733052 + 0.680173i) q^{69} +(1.67738 - 0.807782i) q^{71} +(-0.415749 - 0.563320i) q^{72} +(-0.928661 - 0.104635i) q^{73} +(-0.930874 + 0.365341i) q^{75} +(1.53206 + 1.78029i) q^{78} +(0.826239 - 0.563320i) q^{81} +(1.12253 - 1.40761i) q^{82} +(0.623490 - 0.781831i) q^{87} +(0.255936 - 0.320934i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(-0.528180 + 2.31411i) q^{94} +(-0.587359 + 0.505463i) q^{96} +(0.392253 - 1.12099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 14 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9	\( 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9} + 2 q^{12} - 6 q^{16} + 12 q^{18} - 6 q^{24} - 4 q^{25} - 2 q^{26} - 2 q^{31} - 4 q^{32} + 6 q^{36} + 2 q^{39} - 2 q^{41} + 2 q^{46} + 2 q^{47} + 6 q^{48} - 4 q^{49} + 2 q^{50} - 10 q^{52} - 2 q^{54} + 4 q^{58} - 4 q^{62} - 28 q^{64} - 2 q^{69} + 22 q^{72} - 2 q^{73} - 4 q^{78} + 2 q^{81} - 4 q^{82} - 4 q^{87} - 4 q^{92} - 12 q^{93} - 8 q^{94} - 18 q^{96} + 2 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 14 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9 + 2 * q^12 - 6 * q^16 + 12 * q^18 - 6 * q^24 - 4 * q^25 - 2 * q^26 - 2 * q^31 - 4 * q^32 + 6 * q^36 + 2 * q^39 - 2 * q^41 + 2 * q^46 + 2 * q^47 + 6 * q^48 - 4 * q^49 + 2 * q^50 - 10 * q^52 - 2 * q^54 + 4 * q^58 - 4 * q^62 - 28 * q^64 - 2 * q^69 + 22 * q^72 - 2 * q^73 - 4 * q^78 + 2 * q^81 - 4 * q^82 - 4 * q^87 - 4 * q^92 - 12 * q^93 - 8 * q^94 - 18 * q^96 + 2 * q^98

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