LMFDB - Embedded newform 2001.1.bf.d.1034.1

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			1034.1
Root			$-0.997204 - 0.0747301i$ of defining polynomial
Character	$\chi$	$=$	2001.1034
Dual form			2001.1.bf.d.896.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.791295 + 0.497204i) q^{2} +(0.294755 - 0.955573i) q^{3} +(-0.0549471 + 0.114099i) q^{4} +(0.241876 + 0.902694i) q^{6} +(-0.117886 - 1.04627i) q^{8} +(-0.826239 - 0.563320i) q^{9} +O(q^{10})$	\(q+(-0.791295 + 0.497204i) q^{2} +(0.294755 - 0.955573i) q^{3} +(-0.0549471 + 0.114099i) q^{4} +(0.241876 + 0.902694i) q^{6} +(-0.117886 - 1.04627i) q^{8} +(-0.826239 - 0.563320i) q^{9} +(0.0928338 + 0.0861372i) q^{12} +(1.49419 - 1.19158i) q^{13} +(0.534532 + 0.670281i) q^{16} +(0.933884 + 0.0349435i) q^{18} +(-0.974928 + 0.222521i) q^{23} +(-1.03453 - 0.195744i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.589891 + 1.68581i) q^{26} +(-0.781831 + 0.623490i) q^{27} +(-0.997204 + 0.0747301i) q^{29} +(-0.275400 - 0.438297i) q^{31} +(0.237564 + 0.0831272i) q^{32} +(0.109674 - 0.0633201i) q^{36} +(-0.698220 - 1.77904i) q^{39} +(0.839789 - 0.839789i) q^{41} +(0.660818 - 0.660818i) q^{46} +(1.50641 + 0.169732i) q^{47} +(0.798059 - 0.313215i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.928661 - 0.104635i) q^{50} +(0.0538562 + 0.235960i) q^{52} +(0.308658 - 0.882094i) q^{54} +(0.751927 - 0.554947i) q^{58} -1.80194i q^{59} +(0.435846 + 0.209892i) q^{62} +(-1.06514 + 0.243112i) q^{64} +(-0.0747301 + 0.997204i) q^{69} +(-0.848162 - 1.06356i) q^{71} +(-0.491981 + 0.930874i) q^{72} +(-0.197822 + 0.314832i) q^{73} +(-0.680173 + 0.733052i) q^{75} +(1.43704 + 1.06058i) q^{78} +(0.365341 + 0.930874i) q^{81} +(-0.246975 + 1.08207i) q^{82} +(-0.222521 + 0.974928i) q^{87} +(0.0281801 - 0.123465i) q^{92} +(-0.500000 + 0.133975i) q^{93} +(-1.27641 + 0.614686i) q^{94} +(0.149457 - 0.202507i) q^{96} +(-0.104635 + 0.928661i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{9}{28}\right)$	$-1$	$-1$

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 $

$2$	−0.791295	+	0.497204i	−0.791295	+	0.497204i	−0.866025	−	0.500000i	$-0.833333\pi$
$2$	−0.791295	+	0.497204i	−0.791295	+	0.497204i	0.0747301	+	0.997204i	$0.476190\pi$
$3$	0.294755	−	0.955573i	0.294755	−	0.955573i
$3$	0.294755	−	0.955573i	0.294755	−	0.955573i
$4$	−0.0549471	+	0.114099i	−0.0549471	+	0.114099i
$5$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$5$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$6$	0.241876	+	0.902694i	0.241876	+	0.902694i
$7$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$7$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$8$	−0.117886	−	1.04627i	−0.117886	−	1.04627i
$9$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$10$		0			0
$11$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$11$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$12$	0.0928338	+	0.0861372i	0.0928338	+	0.0861372i
$13$	1.49419	−	1.19158i	1.49419	−	1.19158i	0.563320	−	0.826239i	$-0.309524\pi$
$13$	1.49419	−	1.19158i	1.49419	−	1.19158i	0.930874	−	0.365341i	$-0.119048\pi$
$14$		0			0
$15$		0			0
$16$	0.534532	+	0.670281i	0.534532	+	0.670281i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	0.933884	+	0.0349435i	0.933884	+	0.0349435i
$19$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$19$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$23$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$24$	−1.03453	−	0.195744i	−1.03453	−	0.195744i
$25$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$26$	−0.589891	+	1.68581i	−0.589891	+	1.68581i
$27$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$28$		0			0
$29$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$29$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$30$		0			0
$31$	−0.275400	−	0.438297i	−0.275400	−	0.438297i	0.680173	−	0.733052i	$-0.261905\pi$
$31$	−0.275400	−	0.438297i	−0.275400	−	0.438297i	−0.955573	+	0.294755i	$0.904762\pi$
$32$	0.237564	+	0.0831272i	0.237564	+	0.0831272i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.109674	−	0.0633201i	0.109674	−	0.0633201i
$37$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$37$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$38$		0			0
$39$	−0.698220	−	1.77904i	−0.698220	−	1.77904i
$40$		0			0
$41$	0.839789	−	0.839789i	0.839789	−	0.839789i	−0.149042	−	0.988831i	$-0.547619\pi$
$41$	0.839789	−	0.839789i	0.839789	−	0.839789i	0.988831	+	0.149042i	$0.0476190\pi$
$42$		0			0
$43$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$43$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$44$		0			0
$45$		0			0
$46$	0.660818	−	0.660818i	0.660818	−	0.660818i
$47$	1.50641	+	0.169732i	1.50641	+	0.169732i	0.826239	−	0.563320i	$-0.190476\pi$
$47$	1.50641	+	0.169732i	1.50641	+	0.169732i	0.680173	+	0.733052i	$0.261905\pi$
$48$	0.798059	−	0.313215i	0.798059	−	0.313215i
$49$	0.623490	−	0.781831i	0.623490	−	0.781831i
$50$	0.928661	−	0.104635i	0.928661	−	0.104635i
$51$		0			0
$52$	0.0538562	+	0.235960i	0.0538562	+	0.235960i
$53$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$53$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$54$	0.308658	−	0.882094i	0.308658	−	0.882094i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.751927	−	0.554947i	0.751927	−	0.554947i
$59$		−	1.80194i		−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$59$		−	1.80194i		−	1.80194i	0.433884	−	0.900969i	$-0.357143\pi$
$60$		0			0
$61$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$61$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$62$	0.435846	+	0.209892i	0.435846	+	0.209892i
$63$		0			0
$64$	−1.06514	+	0.243112i	−1.06514	+	0.243112i
$65$		0			0
$66$		0			0
$67$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$67$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$68$		0			0
$69$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$70$		0			0
$71$	−0.848162	−	1.06356i	−0.848162	−	1.06356i	−0.997204	−	0.0747301i	$-0.976190\pi$
$71$	−0.848162	−	1.06356i	−0.848162	−	1.06356i	0.149042	−	0.988831i	$-0.452381\pi$
$72$	−0.491981	+	0.930874i	−0.491981	+	0.930874i
$73$	−0.197822	+	0.314832i	−0.197822	+	0.314832i	−0.930874	−	0.365341i	$-0.880952\pi$
$73$	−0.197822	+	0.314832i	−0.197822	+	0.314832i	0.733052	+	0.680173i	$0.238095\pi$
$74$		0			0
$75$	−0.680173	+	0.733052i	−0.680173	+	0.733052i
$76$		0			0
$77$		0			0
$78$	1.43704	+	1.06058i	1.43704	+	1.06058i
$79$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$79$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$80$		0			0
$81$	0.365341	+	0.930874i	0.365341	+	0.930874i
$82$	−0.246975	+	1.08207i	−0.246975	+	1.08207i
$83$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$83$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$88$		0			0
$89$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$89$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$90$		0			0
$91$		0			0
$92$	0.0281801	−	0.123465i	0.0281801	−	0.123465i
$93$	−0.500000	+	0.133975i	−0.500000	+	0.133975i
$94$	−1.27641	+	0.614686i	−1.27641	+	0.614686i
$95$		0			0
$96$	0.149457	−	0.202507i	0.149457	−	0.202507i
$97$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$97$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$98$	−0.104635	+	0.928661i	−0.104635	+	0.928661i
$99$		0			0
$100$	0.0990112	−	0.0789588i	0.0990112	−	0.0789588i
$101$	1.00435	−	1.59842i	1.00435	−	1.59842i	0.222521	−	0.974928i	$-0.428571\pi$
$101$	1.00435	−	1.59842i	1.00435	−	1.59842i	0.781831	−	0.623490i	$-0.214286\pi$
$102$		0			0
$103$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$103$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$104$	−1.42285	−	1.42285i	−1.42285	−	1.42285i
$105$		0			0
$106$		0			0
$107$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$107$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$108$	−0.0281801	−	0.123465i	−0.0281801	−	0.123465i
$109$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$109$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$113$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$114$		0			0
$115$		0			0
$116$	0.0462668	−	0.117886i	0.0462668	−	0.117886i
$117$	−1.90580	+	0.142820i	−1.90580	+	0.142820i
$118$	0.895930	+	1.42586i	0.895930	+	1.42586i
$119$		0			0
$120$		0			0
$121$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$122$		0			0
$123$	−0.554947	−	1.05001i	−0.554947	−	1.05001i
$124$	0.0651416	−	0.00733969i	0.0651416	−	0.00733969i
$125$		0			0
$126$		0			0
$127$	0.794755	+	0.0895474i	0.794755	+	0.0895474i	0.500000	−	0.866025i	$-0.333333\pi$
$127$	0.794755	+	0.0895474i	0.794755	+	0.0895474i	0.294755	+	0.955573i	$0.404762\pi$
$128$	0.543995	−	0.543995i	0.543995	−	0.543995i
$129$		0			0
$130$		0			0
$131$	1.49720	+	0.940755i	1.49720	+	0.940755i	0.997204	+	0.0747301i	$0.0238095\pi$
$131$	1.49720	+	0.940755i	1.49720	+	0.940755i	0.500000	+	0.866025i	$0.333333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$137$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$138$	−0.436680	−	0.826239i	−0.436680	−	0.826239i
$139$	0.302705	+	1.32624i	0.302705	+	1.32624i	0.866025	+	0.500000i	$0.166667\pi$
$139$	0.302705	+	1.32624i	0.302705	+	1.32624i	−0.563320	+	0.826239i	$0.690476\pi$
$140$		0			0
$141$	0.606214	−	1.38946i	0.606214	−	1.38946i
$142$	1.19995	+	0.419882i	1.19995	+	0.419882i
$143$		0			0
$144$	−0.0640678	−	0.854925i	−0.0640678	−	0.854925i
$145$		0			0
$146$		−	0.347483i		−	0.347483i
$147$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$148$		0			0
$149$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$149$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$150$	0.173741	−	0.918245i	0.173741	−	0.918245i
$151$	−0.974928	+	0.222521i	−0.974928	+	0.222521i	−0.680173	−	0.733052i	$-0.738095\pi$
$151$	−0.974928	+	0.222521i	−0.974928	+	0.222521i	−0.294755	+	0.955573i	$0.595238\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.241351	+	0.0180868i	0.241351	+	0.0180868i
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.751927	−	0.554947i	−0.751927	−	0.554947i
$163$	−0.169732	+	1.50641i	−0.169732	+	1.50641i	0.563320	+	0.826239i	$0.309524\pi$
$163$	−0.169732	+	1.50641i	−0.169732	+	1.50641i	−0.733052	+	0.680173i	$0.761905\pi$
$164$	0.0496749	+	0.141963i	0.0496749	+	0.141963i
$165$		0			0
$166$		0			0
$167$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$167$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$168$		0			0
$169$	0.590232	−	2.58597i	0.590232	−	2.58597i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$173$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$174$	−0.308658	−	0.882094i	−0.308658	−	0.882094i
$175$		0			0
$176$		0			0
$177$	−1.72188	−	0.531130i	−1.72188	−	0.531130i
$178$		0			0
$179$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	0.826239	+	0.563320i	$0.190476\pi$
$179$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	−0.988831	+	0.149042i	$0.952381\pi$
$180$		0			0
$181$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$181$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$182$		0			0
$183$		0			0
$184$	0.347747	+	0.993803i	0.347747	+	0.993803i
$185$		0			0
$186$	0.329035	−	0.354615i	0.329035	−	0.354615i
$187$		0			0
$188$	−0.102139	+	0.162553i	−0.102139	+	0.162553i
$189$		0			0
$190$		0			0
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	−0.0816451	+	1.08948i	−0.0816451	+	1.08948i
$193$	1.85486	−	0.649042i	1.85486	−	0.649042i	0.866025	−	0.500000i	$-0.166667\pi$
$193$	1.85486	−	0.649042i	1.85486	−	0.649042i	0.988831	−	0.149042i	$-0.0476190\pi$
$194$		0			0
$195$		0			0
$196$	0.0549471	+	0.114099i	0.0549471	+	0.114099i
$197$	−1.68862	+	0.385418i	−1.68862	+	0.385418i	−0.955573	−	0.294755i	$-0.904762\pi$
$197$	−1.68862	+	0.385418i	−1.68862	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$198$		0			0
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	−0.347747	+	0.993803i	−0.347747	+	0.993803i
$201$		0			0
$202$			1.76419i			1.76419i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.930874	+	0.365341i	0.930874	+	0.365341i
$208$	1.59739	+	0.364593i	1.59739	+	0.364593i
$209$		0			0
$210$		0			0
$211$	−1.40532	+	0.158342i	−1.40532	+	0.158342i	−0.781831	−	0.623490i	$-0.785714\pi$
$211$	−1.40532	+	0.158342i	−1.40532	+	0.158342i	−0.623490	+	0.781831i	$0.714286\pi$
$212$		0			0
$213$	−1.26631	+	0.496990i	−1.26631	+	0.496990i
$214$		0			0
$215$		0			0
$216$	0.744504	+	0.744504i	0.744504	+	0.744504i
$217$		0			0
$218$		0			0
$219$	0.242536	+	0.281831i	0.242536	+	0.281831i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$223$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$224$		0			0
$225$	0.500000	+	0.866025i	0.500000	+	0.866025i
$226$		0			0
$227$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$227$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$228$		0			0
$229$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$229$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$230$		0			0
$231$		0			0
$232$	0.195744	+	1.03453i	0.195744	+	1.03453i
$233$			1.97766i			1.97766i	0.149042	+	0.988831i	$0.452381\pi$
$233$			1.97766i			1.97766i	−0.149042	+	0.988831i	$0.547619\pi$
$234$	1.43704	−	1.06058i	1.43704	−	1.06058i
$235$		0			0
$236$	0.205599	+	0.0990112i	0.205599	+	0.0990112i
$237$		0			0
$238$		0			0
$239$	0.129334	+	0.268565i	0.129334	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$239$	0.129334	+	0.268565i	0.129334	+	0.268565i	−0.826239	+	0.563320i	$0.809524\pi$
$240$		0			0
$241$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$241$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$242$	0.882094	−	0.308658i	0.882094	−	0.308658i
$243$	0.997204	−	0.0747301i	0.997204	−	0.0747301i
$244$		0			0
$245$		0			0
$246$	0.961197	+	0.554947i	0.961197	+	0.554947i
$247$		0			0
$248$	−0.426109	+	0.339811i	−0.426109	+	0.339811i
$249$		0			0
$250$		0			0
$251$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$251$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$252$		0			0
$253$		0			0
$254$	−0.673409	+	0.324297i	−0.673409	+	0.324297i
$255$		0			0
$256$	0.0831272	−	0.364204i	0.0831272	−	0.364204i
$257$	0.865341	−	1.79690i	0.865341	−	1.79690i	0.365341	−	0.930874i	$-0.380952\pi$
$257$	0.865341	−	1.79690i	0.865341	−	1.79690i	0.500000	−	0.866025i	$-0.333333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.866025	+	0.500000i	0.866025	+	0.500000i
$262$	−1.65248			−1.65248
$263$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$263$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.0895474	+	0.794755i	0.0895474	+	0.794755i	0.955573	+	0.294755i	$0.0952381\pi$
$269$	0.0895474	+	0.794755i	0.0895474	+	0.794755i	−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	0.559311	+	1.59842i	0.559311	+	1.59842i	0.781831	+	0.623490i	$0.214286\pi$
$271$	0.559311	+	1.59842i	0.559311	+	1.59842i	−0.222521	+	0.974928i	$0.571429\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.109674	−	0.0633201i	−0.109674	−	0.0633201i
$277$	−0.914101	−	1.14625i	−0.914101	−	1.14625i	−0.988831	−	0.149042i	$-0.952381\pi$
$277$	−0.914101	−	1.14625i	−0.914101	−	1.14625i	0.0747301	−	0.997204i	$-0.476190\pi$
$278$	−0.898940	−	0.898940i	−0.898940	−	0.898940i
$279$	−0.0193551	+	0.517276i	−0.0193551	+	0.517276i
$280$		0			0
$281$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$281$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$282$	0.211149	+	1.40088i	0.211149	+	1.40088i
$283$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$283$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$284$	0.167955	−	0.0383346i	0.167955	−	0.0383346i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.149457	−	0.202507i	−0.149457	−	0.202507i
$289$			1.00000i			1.00000i
$290$		0			0
$291$		0			0
$292$	−0.0250522	−	0.0398703i	−0.0250522	−	0.0398703i
$293$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$293$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$294$	0.856562	+	0.373714i	0.856562	+	0.373714i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.19158	+	1.49419i	−1.19158	+	1.49419i
$300$	−0.0462668	−	0.117886i	−0.0462668	−	0.117886i
$301$		0			0
$302$	0.660818	−	0.660818i	0.660818	−	0.660818i
$303$	−1.23137	−	1.43087i	−1.23137	−	1.43087i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.467085	−	0.467085i	0.467085	−	0.467085i	−0.433884	−	0.900969i	$-0.642857\pi$
$307$	0.467085	−	0.467085i	0.467085	−	0.467085i	0.900969	+	0.433884i	$0.142857\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.98603	−	0.223772i	1.98603	−	0.223772i	0.988831	−	0.149042i	$-0.0476190\pi$
$311$	1.98603	−	0.223772i	1.98603	−	0.223772i	0.997204	−	0.0747301i	$-0.0238095\pi$
$312$	−1.77904	+	0.940248i	−1.77904	+	0.940248i
$313$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$313$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.566116	+	0.900969i	0.566116	+	0.900969i	1.00000			$0$
$317$	0.566116	+	0.900969i	0.566116	+	0.900969i	−0.433884	+	0.900969i	$0.642857\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.126286	−	0.00946383i	−0.126286	−	0.00946383i
$325$	−1.86323	+	0.425270i	−1.86323	+	0.425270i
$326$	−0.614686	−	1.27641i	−0.614686	−	1.27641i
$327$		0			0
$328$	−0.977642	−	0.779644i	−0.977642	−	0.779644i
$329$		0			0
$330$		0			0
$331$	1.29621	+	1.29621i	1.29621	+	1.29621i	0.930874	+	0.365341i	$0.119048\pi$
$331$	1.29621	+	1.29621i	1.29621	+	1.29621i	0.365341	+	0.930874i	$0.380952\pi$
$332$		0			0
$333$		0			0
$334$	0.221277	−	0.352160i	0.221277	−	0.352160i
$335$		0			0
$336$		0			0
$337$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$337$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$338$	0.818709	+	2.33973i	0.818709	+	2.33973i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.986729	+	0.620003i	−0.986729	+	0.620003i
$347$	−1.56366			−1.56366			−0.781831	−	0.623490i	$-0.785714\pi$
$347$	−1.56366			−1.56366			−0.781831	+	0.623490i	$0.785714\pi$
$348$	−0.0990112	−	0.0789588i	−0.0990112	−	0.0789588i
$349$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$349$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$350$		0			0
$351$	−0.425270	+	1.86323i	−0.425270	+	1.86323i
$352$		0			0
$353$	−0.414278	+	1.81507i	−0.414278	+	1.81507i	0.149042	+	0.988831i	$0.452381\pi$
$353$	−0.414278	+	1.81507i	−0.414278	+	1.81507i	−0.563320	+	0.826239i	$0.690476\pi$
$354$	1.62660	−	0.435846i	1.62660	−	0.435846i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.225531	−	0.644530i	−0.225531	−	0.644530i
$359$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$359$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$360$		0			0
$361$	0.781831	−	0.623490i	0.781831	−	0.623490i
$362$		0			0
$363$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$367$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$368$	−0.670281	−	0.534532i	−0.670281	−	0.534532i
$369$	−1.16694	+	0.220796i	−1.16694	+	0.220796i
$370$		0			0
$371$		0			0
$372$	0.0121872	−	0.0644109i	0.0121872	−	0.0644109i
$373$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$373$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$374$		0			0
$375$		0			0
$376$		−	1.59612i		−	1.59612i
$377$	−1.40097	+	1.29991i	−1.40097	+	1.29991i
$378$		0			0
$379$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$379$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$380$		0			0
$381$	0.319827	−	0.733052i	0.319827	−	0.733052i
$382$		0			0
$383$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$383$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$384$	−0.359482	−	0.680173i	−0.359482	−	0.680173i
$385$		0			0
$386$	−1.14503	+	1.43583i	−1.14503	+	1.43583i
$387$		0			0
$388$		0			0
$389$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$389$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$390$		0			0
$391$		0			0
$392$	−0.891505	−	0.560170i	−0.891505	−	0.560170i
$393$	1.34027	−	1.15339i	1.34027	−	1.15339i
$394$	1.14457	−	1.14457i	1.14457	−	1.14457i
$395$		0			0
$396$		0			0
$397$	−0.185853	+	0.233052i	−0.185853	+	0.233052i	−0.866025	−	0.500000i	$-0.833333\pi$
$397$	−0.185853	+	0.233052i	−0.185853	+	0.233052i	0.680173	+	0.733052i	$0.261905\pi$
$398$		0			0
$399$		0			0
$400$	−0.190772	−	0.835827i	−0.190772	−	0.835827i
$401$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$401$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$402$		0			0
$403$	−0.933767	−	0.326739i	−0.933767	−	0.326739i
$404$	0.127191	+	0.202424i	0.127191	+	0.202424i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.392253	−	1.12099i	0.392253	−	1.12099i	−0.563320	−	0.826239i	$-0.690476\pi$
$409$	0.392253	−	1.12099i	0.392253	−	1.12099i	0.955573	−	0.294755i	$-0.0952381\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.918245	+	0.173741i	−0.918245	+	0.173741i
$415$		0			0
$416$	0.454019	−	0.158868i	0.454019	−	0.158868i
$417$	1.35654	+	0.101659i	1.35654	+	0.101659i
$418$		0			0
$419$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$419$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$420$		0			0
$421$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$421$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$422$	1.03330	−	0.824026i	1.03330	−	0.824026i
$423$	−1.14904	−	0.988831i	−1.14904	−	0.988831i
$424$		0			0
$425$		0			0
$426$	0.754920	−	1.02288i	0.754920	−	1.02288i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$431$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$432$	−0.835827	−	0.190772i	−0.835827	−	0.190772i
$433$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$433$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.332045	−	0.102422i	−0.332045	−	0.102422i
$439$	−0.129334	+	0.268565i	−0.129334	+	0.268565i	−0.955573	−	0.294755i	$-0.904762\pi$
$439$	−0.129334	+	0.268565i	−0.129334	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$440$		0			0
$441$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$442$		0			0
$443$	0.220025	+	1.95278i	0.220025	+	1.95278i	0.294755	+	0.955573i	$0.404762\pi$
$443$	0.220025	+	1.95278i	0.220025	+	1.95278i	−0.0747301	+	0.997204i	$0.523810\pi$
$444$		0			0
$445$		0			0
$446$	0.130478	−	1.15802i	0.130478	−	1.15802i
$447$		0			0
$448$		0			0
$449$	0.900969	−	1.43388i	0.900969	−	1.43388i		−	1.00000i	$-0.5\pi$
$449$	0.900969	−	1.43388i	0.900969	−	1.43388i	0.900969	−	0.433884i	$-0.142857\pi$
$450$	−0.826239	−	0.436680i	−0.826239	−	0.436680i
$451$		0			0
$452$		0			0
$453$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$457$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.605443	+	1.73026i	−0.605443	+	1.73026i	0.0747301	+	0.997204i	$0.476190\pi$
$461$	−0.605443	+	1.73026i	−0.605443	+	1.73026i	−0.680173	+	0.733052i	$0.738095\pi$
$462$		0			0
$463$			0.445042i			0.445042i	0.974928	+	0.222521i	$0.0714286\pi$
$463$			0.445042i			0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$464$	−0.583127	−	0.628462i	−0.583127	−	0.628462i
$465$		0			0
$466$	−0.983301	−	1.56491i	−0.983301	−	1.56491i
$467$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$467$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$468$	0.0884226	−	0.225297i	0.0884226	−	0.225297i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.88531	+	0.212423i	−1.88531	+	0.212423i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.235873	−	0.148209i	−0.235873	−	0.148209i
$479$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$479$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.0789588	−	0.0990112i	0.0789588	−	0.0990112i
$485$		0			0
$486$	−0.751927	+	0.554947i	−0.751927	+	0.554947i
$487$	0.414278	+	1.81507i	0.414278	+	1.81507i	0.563320	+	0.826239i	$0.309524\pi$
$487$	0.414278	+	1.81507i	0.414278	+	1.81507i	−0.149042	+	0.988831i	$0.547619\pi$
$488$		0			0
$489$	1.38946	+	0.606214i	1.38946	+	0.606214i
$490$		0			0
$491$	−0.856144	−	1.36254i	−0.856144	−	1.36254i	−0.930874	−	0.365341i	$-0.880952\pi$
$491$	−0.856144	−	1.36254i	−0.856144	−	1.36254i	0.0747301	−	0.997204i	$-0.476190\pi$
$492$	0.150298	−	0.00562374i	0.150298	−	0.00562374i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.146572	−	0.418879i	0.146572	−	0.418879i
$497$		0			0
$498$		0			0
$499$	−0.145713	+	0.0332580i	−0.145713	+	0.0332580i	−0.294755	−	0.955573i	$-0.595238\pi$
$499$	−0.145713	+	0.0332580i	−0.145713	+	0.0332580i	0.149042	+	0.988831i	$0.452381\pi$
$500$		0			0
$501$	0.0663300	+	0.440071i	0.0663300	+	0.440071i
$502$		0			0
$503$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$503$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.29711	−	1.32624i	−2.29711	−	1.32624i
$508$	−0.0538867	+	0.0857602i	−0.0538867	+	0.0857602i
$509$	0.880843	−	0.702449i	0.880843	−	0.702449i	−0.0747301	−	0.997204i	$-0.523810\pi$
$509$	0.880843	−	0.702449i	0.880843	−	0.702449i	0.955573	+	0.294755i	$0.0952381\pi$
$510$		0			0
$511$		0			0
$512$	0.369398	+	1.05568i	0.369398	+	1.05568i
$513$		0			0
$514$	0.208685	+	1.85213i	0.208685	+	1.85213i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.367554	−	1.19158i	0.367554	−	1.19158i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.933884	+	0.0349435i	−0.933884	+	0.0349435i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	−0.189606	+	0.119137i	−0.189606	+	0.119137i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.900969	−	0.433884i	0.900969	−	0.433884i
$530$		0			0
$531$	−1.01507	+	1.48883i	−1.01507	+	1.48883i
$532$		0			0
$533$	0.254132	−	2.25548i	0.254132	−	2.25548i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.632789	+	0.365341i	0.632789	+	0.365341i
$538$	−0.466014	−	0.584363i	−0.466014	−	0.584363i
$539$		0			0
$540$		0			0
$541$	−1.23137	+	0.430874i	−1.23137	+	0.430874i	−0.866025	−	0.500000i	$-0.833333\pi$
$541$	−1.23137	+	0.430874i	−1.23137	+	0.430874i	−0.365341	+	0.930874i	$0.619048\pi$
$542$	−1.23732	−	0.986729i	−1.23732	−	0.986729i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.78181	−	0.858075i	−1.78181	−	0.858075i	−0.955573	−	0.294755i	$-0.904762\pi$
$547$	−1.78181	−	0.858075i	−1.78181	−	0.858075i	−0.826239	−	0.563320i	$-0.809524\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	1.05215	−	0.0393687i	1.05215	−	0.0393687i
$553$		0			0
$554$	1.29324	+	0.452525i	1.29324	+	0.452525i
$555$		0			0
$556$	−0.167955	−	0.0383346i	−0.167955	−	0.0383346i
$557$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$557$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$558$	−0.241876	−	0.418942i	−0.241876	−	0.418942i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$563$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$564$	0.125226	+	0.145515i	0.125226	+	0.145515i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−1.01278	+	1.01278i	−1.01278	+	1.01278i
$569$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$569$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$570$		0			0
$571$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$571$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.974928	+	0.222521i	0.974928	+	0.222521i
$576$	1.01701	+	0.399147i	1.01701	+	0.399147i
$577$	1.73026	+	0.605443i	1.73026	+	0.605443i	0.997204	−	0.0747301i	$-0.0238095\pi$
$577$	1.73026	+	0.605443i	1.73026	+	0.605443i	0.733052	+	0.680173i	$0.238095\pi$
$578$	−0.497204	−	0.791295i	−0.497204	−	0.791295i
$579$	−0.0734787	−	1.96376i	−0.0734787	−	1.96376i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.352718	+	0.169860i	0.352718	+	0.169860i
$585$		0			0
$586$		0			0
$587$	0.807782	+	1.67738i	0.807782	+	1.67738i	0.733052	+	0.680173i	$0.238095\pi$
$587$	0.807782	+	1.67738i	0.807782	+	1.67738i	0.0747301	+	0.997204i	$0.476190\pi$
$588$	0.125226	−	0.0188747i	0.125226	−	0.0188747i
$589$		0			0
$590$		0			0
$591$	−0.129436	+	1.72721i	−0.129436	+	1.72721i
$592$		0			0
$593$	0.974928	+	1.22252i	0.974928	+	1.22252i	0.974928	+	0.222521i	$0.0714286\pi$
$593$	0.974928	+	1.22252i	0.974928	+	1.22252i			1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.199973	−	1.77481i	0.199973	−	1.77481i
$599$	0.559311	+	1.59842i	0.559311	+	1.59842i	0.781831	+	0.623490i	$0.214286\pi$
$599$	0.559311	+	1.59842i	0.559311	+	1.59842i	−0.222521	+	0.974928i	$0.571429\pi$
$600$	0.847151	+	0.625226i	0.847151	+	0.625226i
$601$	−0.216299	−	1.91970i	−0.216299	−	1.91970i	−0.365341	−	0.930874i	$-0.619048\pi$
$601$	−0.216299	−	1.91970i	−0.216299	−	1.91970i	0.149042	−	0.988831i	$-0.452381\pi$
$602$		0			0
$603$		0			0
$604$	0.0281801	−	0.123465i	0.0281801	−	0.123465i
$605$		0			0
$606$	1.68581	+	0.520004i	1.68581	+	0.520004i
$607$	−0.189606	+	0.119137i	−0.189606	+	0.119137i	−0.623490	−	0.781831i	$-0.714286\pi$
$607$	−0.189606	+	0.119137i	−0.189606	+	0.119137i	0.433884	+	0.900969i	$0.357143\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.45312	−	1.54140i	2.45312	−	1.54140i
$612$		0			0
$613$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$613$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$614$	−0.137366	+	0.601839i	−0.137366	+	0.601839i
$615$		0			0
$616$		0			0
$617$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$617$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$618$		0			0
$619$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$619$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$620$		0			0
$621$	0.623490	−	0.781831i	0.623490	−	0.781831i
$622$	−1.46028	+	1.16453i	−1.46028	+	1.16453i
$623$		0			0
$624$	0.819234	−	1.41895i	0.819234	−	1.41895i
$625$	0.623490	+	0.781831i	0.623490	+	0.781831i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$631$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$632$		0			0
$633$	−0.262919	+	1.38956i	−0.262919	+	1.38956i
$634$	−0.895930	−	0.431457i	−0.895930	−	0.431457i
$635$		0			0
$636$		0			0
$637$		−	1.91115i		−	1.91115i
$638$		0			0
$639$	0.101659	+	1.35654i	0.101659	+	1.35654i
$640$		0			0
$641$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$641$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$642$		0			0
$643$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$643$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.702449	−	0.880843i	0.702449	−	0.880843i	−0.294755	−	0.955573i	$-0.595238\pi$
$647$	0.702449	−	0.880843i	0.702449	−	0.880843i	0.997204	+	0.0747301i	$0.0238095\pi$
$648$	0.930874	−	0.491981i	0.930874	−	0.491981i
$649$		0			0
$650$	1.26292	−	1.26292i	1.26292	−	1.26292i
$651$		0			0
$652$	−0.162553	−	0.102139i	−0.162553	−	0.102139i
$653$	−1.63575	−	1.02781i	−1.63575	−	1.02781i	−0.955573	−	0.294755i	$-0.904762\pi$
$653$	−1.63575	−	1.02781i	−1.63575	−	1.02781i	−0.680173	−	0.733052i	$-0.738095\pi$
$654$		0			0
$655$		0			0
$656$	1.01179	+	0.114001i	1.01179	+	0.114001i
$657$	0.340799	−	0.148689i	0.340799	−	0.148689i
$658$		0			0
$659$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$659$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$660$		0			0
$661$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$661$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$662$	−1.67017	−	0.381206i	−1.67017	−	0.381206i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.955573	−	0.294755i	0.955573	−	0.294755i
$668$		−	0.0563602i		−	0.0563602i
$669$	0.702449	+	1.03030i	0.702449	+	1.03030i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.81507	−	0.414278i	1.81507	−	0.414278i	0.826239	−	0.563320i	$-0.190476\pi$
$673$	1.81507	−	0.414278i	1.81507	−	0.414278i	0.988831	+	0.149042i	$0.0476190\pi$
$674$		0			0
$675$	0.974928	−	0.222521i	0.974928	−	0.222521i
$676$	0.262625	+	0.209436i	0.262625	+	0.209436i
$677$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$677$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.55929	−	1.24349i	1.55929	−	1.24349i	0.733052	−	0.680173i	$-0.238095\pi$
$683$	1.55929	−	1.24349i	1.55929	−	1.24349i	0.826239	−	0.563320i	$-0.190476\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$691$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$692$	−0.0685179	+	0.142279i	−0.0685179	+	0.142279i
$693$		0			0
$694$	1.23732	−	0.777459i	1.23732	−	0.777459i
$695$		0			0
$696$	1.04627	+	0.117886i	1.04627	+	0.117886i
$697$		0			0
$698$	−0.118267	+	0.0743122i	−0.118267	+	0.0743122i
$699$	1.88980	+	0.582926i	1.88980	+	0.582926i
$700$		0			0
$701$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$	−0.589891	−	1.68581i	−0.589891	−	1.68581i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.574643	−	1.64224i	−0.574643	−	1.64224i
$707$		0			0
$708$	0.155214	−	0.167281i	0.155214	−	0.167281i
$709$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$709$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.366025	+	0.366025i	0.366025	+	0.366025i
$714$		0			0
$715$		0			0
$716$	−0.0723457	−	0.0576938i	−0.0723457	−	0.0576938i
$717$	0.294755	−	0.0444272i	0.294755	−	0.0444272i
$718$		0			0
$719$	−1.90097	+	0.433884i	−1.90097	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$719$	−1.90097	+	0.433884i	−1.90097	+	0.433884i	−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	−0.308658	+	0.882094i	−0.308658	+	0.882094i
$723$		0			0
$724$		0			0
$725$	0.930874	+	0.365341i	0.930874	+	0.365341i
$726$	−0.0349435	−	0.933884i	−0.0349435	−	0.933884i
$727$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$727$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$728$		0			0
$729$	0.222521	−	0.974928i	0.222521	−	0.974928i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$733$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$734$		0			0
$735$		0			0
$736$	−0.250105	−	0.0281801i	−0.250105	−	0.0281801i
$737$		0			0
$738$	0.813610	−	0.754920i	0.813610	−	0.754920i
$739$	−1.00560	−	0.631863i	−1.00560	−	0.631863i	−0.0747301	−	0.997204i	$-0.523810\pi$
$739$	−1.00560	−	0.631863i	−1.00560	−	0.631863i	−0.930874	+	0.365341i	$0.880952\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$743$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$744$	0.199116	+	0.507340i	0.199116	+	0.507340i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$751$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$752$	0.691457	+	1.10045i	0.691457	+	1.10045i
$753$		0			0
$754$	0.462260	−	1.72518i	0.462260	−	1.72518i
$755$		0			0
$756$		0			0
$757$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$757$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.636119	−	1.32091i	−0.636119	−	1.32091i	−0.930874	−	0.365341i	$-0.880952\pi$
$761$	−0.636119	−	1.32091i	−0.636119	−	1.32091i	0.294755	−	0.955573i	$-0.404762\pi$
$762$	0.111398	+	0.739080i	0.111398	+	0.739080i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.14715	−	2.69244i	−2.14715	−	2.69244i
$768$	−0.323521	−	0.186785i	−0.323521	−	0.186785i
$769$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$769$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$770$		0			0
$771$	−1.46200	−	1.35654i	−1.46200	−	1.35654i
$772$	−0.0278640	+	0.247300i	−0.0278640	+	0.247300i
$773$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$773$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$774$		0			0
$775$	0.0579571	+	0.514383i	0.0579571	+	0.514383i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.733052	−	0.680173i	0.733052	−	0.680173i
$784$	0.857322			0.857322
$785$		0			0
$786$	−0.487076	+	1.57906i	−0.487076	+	1.57906i
$787$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$787$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$788$	0.0488093	−	0.213848i	0.0488093	−	0.213848i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.0311901	−	0.276820i	0.0311901	−	0.276820i
$795$		0			0
$796$		0			0
$797$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$797$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$798$		0			0
$799$		0			0
$800$	−0.177970	−	0.177970i	−0.177970	−	0.177970i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	0.901341	−	0.205725i	0.901341	−	0.205725i
$807$	0.785841	+	0.148689i	0.785841	+	0.148689i
$808$	−1.79077	−	0.862390i	−1.79077	−	0.862390i
$809$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i	−0.974928	−	0.222521i	$-0.928571\pi$
$809$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i	0.900969	+	0.433884i	$0.142857\pi$
$810$		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
$813$	1.69226	−	0.0633201i	1.69226	−	0.0633201i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.246975	+	1.08207i	0.246975	+	1.08207i
$819$		0			0
$820$		0			0
$821$	−0.541044	+	0.678448i	−0.541044	+	0.678448i	−0.974928	−	0.222521i	$-0.928571\pi$
$821$	−0.541044	+	0.678448i	−0.541044	+	0.678448i	0.433884	+	0.900969i	$0.357143\pi$
$822$		0			0
$823$	−1.59908	−	0.180173i	−1.59908	−	0.180173i	−0.733052	−	0.680173i	$-0.761905\pi$
$823$	−1.59908	−	0.180173i	−1.59908	−	0.180173i	−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$827$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$828$	−0.0928338	+	0.0861372i	−0.0928338	+	0.0861372i
$829$	0.752407	−	0.752407i	0.752407	−	0.752407i	−0.222521	−	0.974928i	$-0.571429\pi$
$829$	0.752407	−	0.752407i	0.752407	−	0.752407i	0.974928	+	0.222521i	$0.0714286\pi$
$830$		0			0
$831$	−1.36476	+	0.535628i	−1.36476	+	0.535628i
$832$	−1.30184	+	1.63246i	−1.30184	+	1.63246i
$833$		0			0
$834$	−1.12397	+	0.594036i	−1.12397	+	0.594036i
$835$		0			0
$836$		0			0
$837$	0.488590	+	0.170965i	0.488590	+	0.170965i
$838$		0			0
$839$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$839$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$840$		0			0
$841$	0.988831	−	0.149042i	0.988831	−	0.149042i
$842$		0			0
$843$		0			0
$844$	0.0591517	−	0.169046i	0.0591517	−	0.169046i
$845$		0			0
$846$	1.40088	+	0.211149i	1.40088	+	0.211149i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.0128741	−	0.171793i	0.0128741	−	0.171793i
$853$	1.33485	+	1.33485i	1.33485	+	1.33485i	0.900969	+	0.433884i	$0.142857\pi$
$853$	1.33485	+	1.33485i	1.33485	+	1.33485i	0.433884	+	0.900969i	$0.357143\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.781831	−	0.623490i	0.781831	−	0.623490i	−0.149042	−	0.988831i	$-0.547619\pi$
$857$	0.781831	−	0.623490i	0.781831	−	0.623490i	0.930874	+	0.365341i	$0.119048\pi$
$858$		0			0
$859$	0.180173	−	1.59908i	0.180173	−	1.59908i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.180173	−	1.59908i	0.180173	−	1.59908i	0.680173	−	0.733052i	$-0.261905\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$863$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.0747301	+	0.997204i	$0.523810\pi$
$864$	−0.237564	+	0.0831272i	−0.237564	+	0.0831272i
$865$		0			0
$866$		0			0
$867$	0.955573	+	0.294755i	0.955573	+	0.294755i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−0.0454833	+	0.0121872i	−0.0454833	+	0.0121872i
$877$	0.781831	−	0.376510i	0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$877$	0.781831	−	0.376510i	0.781831	−	0.376510i	0.781831	+	0.623490i	$0.214286\pi$
$878$	−0.0311901	−	0.276820i	−0.0311901	−	0.276820i
$879$		0			0
$880$		0			0
$881$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$881$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$882$	0.609587	−	0.708353i	0.609587	−	0.708353i
$883$	1.40881	−	1.12349i	1.40881	−	1.12349i	0.433884	−	0.900969i	$-0.357143\pi$
$883$	1.40881	−	1.12349i	1.40881	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$884$		0			0
$885$		0			0
$886$	−1.14503	−	1.43583i	−1.14503	−	1.43583i
$887$	−0.565533	−	0.565533i	−0.565533	−	0.565533i	0.365341	−	0.930874i	$-0.380952\pi$
$887$	−0.565533	−	0.565533i	−0.565533	−	0.565533i	−0.930874	+	0.365341i	$0.880952\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−0.0685179	−	0.142279i	−0.0685179	−	0.142279i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.07659	+	1.57906i	1.07659	+	1.57906i
$898$			1.58259i			1.58259i
$899$	0.307384	+	0.416490i	0.307384	+	0.416490i
$900$	−0.126286	+	0.00946383i	−0.126286	+	0.00946383i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.436680	−	0.826239i	−0.436680	−	0.826239i
$907$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$907$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$908$		0			0
$909$	−1.73026	+	0.754903i	−1.73026	+	0.754903i
$910$		0			0
$911$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$911$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$919$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$920$		0			0
$921$	−0.308658	−	0.584010i	−0.308658	−	0.584010i
$922$	−0.381206	−	1.67017i	−0.381206	−	1.67017i
$923$	−2.53464	−	0.578514i	−2.53464	−	0.578514i
$924$		0			0
$925$		0			0
$926$	−0.221277	−	0.352160i	−0.221277	−	0.352160i
$927$		0			0
$928$	−0.243112	−	0.0651416i	−0.243112	−	0.0651416i
$929$			1.91115i			1.91115i	0.294755	+	0.955573i	$0.404762\pi$
$929$			1.91115i			1.91115i	−0.294755	+	0.955573i	$0.595238\pi$
$930$		0			0
$931$		0			0
$932$	−0.225649	−	0.108667i	−0.225649	−	0.108667i
$933$	0.371563	−	1.96376i	0.371563	−	1.96376i
$934$		0			0
$935$		0			0
$936$	0.374095	+	1.97714i	0.374095	+	1.97714i
$937$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$937$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$941$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$942$		0			0
$943$	−0.631863	+	1.00560i	−0.631863	+	1.00560i
$944$	1.20781	−	0.963193i	1.20781	−	0.963193i
$945$		0			0
$946$		0			0
$947$	−0.264152	−	0.754903i	−0.264152	−	0.754903i	−0.997204	−	0.0747301i	$-0.976190\pi$
$947$	−0.264152	−	0.754903i	−0.264152	−	0.754903i	0.733052	−	0.680173i	$-0.238095\pi$
$948$		0			0
$949$	0.0795629	+	0.706140i	0.0795629	+	0.706140i
$950$		0			0
$951$	1.02781	−	0.275400i	1.02781	−	0.275400i
$952$		0			0
$953$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$953$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$954$		0			0
$955$		0			0
$956$	−0.0377495			−0.0377495
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.317625	−	0.659555i	0.317625	−	0.659555i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.649042	+	1.85486i	0.649042	+	1.85486i	0.500000	+	0.866025i	$0.333333\pi$
$967$	0.649042	+	1.85486i	0.649042	+	1.85486i	0.149042	+	0.988831i	$0.452381\pi$
$968$	−0.117886	+	1.04627i	−0.117886	+	1.04627i
$969$		0			0
$970$		0			0
$971$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$971$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$972$	−0.0462668	+	0.117886i	−0.0462668	+	0.117886i
$973$		0			0
$974$	−1.23028	−	1.23028i	−1.23028	−	1.23028i
$975$	−0.142820	+	1.90580i	−0.142820	+	1.90580i
$976$		0			0
$977$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$977$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$978$	−1.40088	+	0.211149i	−1.40088	+	0.211149i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.35492	+	0.652497i	1.35492	+	0.652497i
$983$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$983$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$984$	−1.03317	+	0.704404i	−1.03317	+	0.704404i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.52446	−	0.347948i	−1.52446	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$991$	−1.52446	−	0.347948i	−1.52446	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$992$	−0.0289907	−	0.127017i	−0.0289907	−	0.127017i
$993$	1.62069	−	0.856562i	1.62069	−	0.856562i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.68280	−	0.189606i	−1.68280	−	0.189606i	−0.781831	−	0.623490i	$-0.785714\pi$
$997$	−1.68280	−	0.189606i	−1.68280	−	0.189606i	−0.900969	+	0.433884i	$0.857143\pi$
$998$	0.0987659	−	0.0987659i	0.0987659	−	0.0987659i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.d.1034.1	yes	24
3.2	odd	2		2001.1.bf.c.1034.2	yes	24
23.22	odd	2	CM	2001.1.bf.d.1034.1	yes	24
29.26	odd	28		2001.1.bf.c.896.2	✓	24
69.68	even	2		2001.1.bf.c.1034.2	yes	24
87.26	even	28	inner	2001.1.bf.d.896.1	yes	24
667.229	even	28		2001.1.bf.c.896.2	✓	24
2001.896	odd	28	inner	2001.1.bf.d.896.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.896.2	✓	24	29.26	odd	28
2001.1.bf.c.896.2	✓	24	667.229	even	28
2001.1.bf.c.1034.2	yes	24	3.2	odd	2
2001.1.bf.c.1034.2	yes	24	69.68	even	2
2001.1.bf.d.896.1	yes	24	87.26	even	28	inner
2001.1.bf.d.896.1	yes	24	2001.896	odd	28	inner
2001.1.bf.d.1034.1	yes	24	1.1	even	1	trivial
2001.1.bf.d.1034.1	yes	24	23.22	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(-0.791295 + 0.497204i) q^{2} +(0.294755 - 0.955573i) q^{3} +(-0.0549471 + 0.114099i) q^{4} +(0.241876 + 0.902694i) q^{6} +(-0.117886 - 1.04627i) q^{8} +(-0.826239 - 0.563320i) q^{9} +O(q^{10})\)	\(q+(-0.791295 + 0.497204i) q^{2} +(0.294755 - 0.955573i) q^{3} +(-0.0549471 + 0.114099i) q^{4} +(0.241876 + 0.902694i) q^{6} +(-0.117886 - 1.04627i) q^{8} +(-0.826239 - 0.563320i) q^{9} +(0.0928338 + 0.0861372i) q^{12} +(1.49419 - 1.19158i) q^{13} +(0.534532 + 0.670281i) q^{16} +(0.933884 + 0.0349435i) q^{18} +(-0.974928 + 0.222521i) q^{23} +(-1.03453 - 0.195744i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.589891 + 1.68581i) q^{26} +(-0.781831 + 0.623490i) q^{27} +(-0.997204 + 0.0747301i) q^{29} +(-0.275400 - 0.438297i) q^{31} +(0.237564 + 0.0831272i) q^{32} +(0.109674 - 0.0633201i) q^{36} +(-0.698220 - 1.77904i) q^{39} +(0.839789 - 0.839789i) q^{41} +(0.660818 - 0.660818i) q^{46} +(1.50641 + 0.169732i) q^{47} +(0.798059 - 0.313215i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.928661 - 0.104635i) q^{50} +(0.0538562 + 0.235960i) q^{52} +(0.308658 - 0.882094i) q^{54} +(0.751927 - 0.554947i) q^{58} -1.80194i q^{59} +(0.435846 + 0.209892i) q^{62} +(-1.06514 + 0.243112i) q^{64} +(-0.0747301 + 0.997204i) q^{69} +(-0.848162 - 1.06356i) q^{71} +(-0.491981 + 0.930874i) q^{72} +(-0.197822 + 0.314832i) q^{73} +(-0.680173 + 0.733052i) q^{75} +(1.43704 + 1.06058i) q^{78} +(0.365341 + 0.930874i) q^{81} +(-0.246975 + 1.08207i) q^{82} +(-0.222521 + 0.974928i) q^{87} +(0.0281801 - 0.123465i) q^{92} +(-0.500000 + 0.133975i) q^{93} +(-1.27641 + 0.614686i) q^{94} +(0.149457 - 0.202507i) q^{96} +(-0.104635 + 0.928661i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 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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