LMFDB - Embedded newform 2001.1.bf.c.68.1

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			68.1
Root			$0.997204 + 0.0747301i$ of defining polynomial
Character	$\chi$	$=$	2001.68
Dual form			2001.1.bf.c.206.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.940755 - 1.49720i) q^{2} +(0.365341 - 0.930874i) q^{3} +(-0.922715 + 1.91604i) q^{4} +(-1.73740 + 0.328735i) q^{6} +(1.97963 - 0.223051i) q^{8} +(-0.733052 - 0.680173i) q^{9} +O(q^{10})$	\(q+(-0.940755 - 1.49720i) q^{2} +(0.365341 - 0.930874i) q^{3} +(-0.922715 + 1.91604i) q^{4} +(-1.73740 + 0.328735i) q^{6} +(1.97963 - 0.223051i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(1.44648 + 1.55894i) q^{12} +(-1.49419 + 1.19158i) q^{13} +(-0.870366 - 1.09140i) q^{16} +(-0.328735 + 1.73740i) q^{18} +(-0.974928 + 0.222521i) q^{23} +(0.515609 - 1.92428i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(3.18971 + 1.11613i) q^{26} +(-0.900969 + 0.433884i) q^{27} +(-0.997204 + 0.0747301i) q^{29} +(-1.63575 + 1.02781i) q^{31} +(-0.157284 + 0.449493i) q^{32} +(1.97963 - 0.776949i) q^{36} +(0.563320 + 1.82624i) q^{39} +(-1.13787 - 1.13787i) q^{41} +(1.25033 + 1.25033i) q^{46} +(-0.146066 + 1.29637i) q^{47} +(-1.33394 + 0.411466i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.197979 + 1.75711i) q^{50} +(-0.904396 - 3.96242i) q^{52} +(1.49720 + 0.940755i) q^{54} +(1.05001 + 1.42271i) q^{58} -1.80194i q^{59} +(3.07767 + 1.48213i) q^{62} +(-0.540010 + 0.123254i) q^{64} +(-0.149042 + 0.988831i) q^{69} +(-0.848162 - 1.06356i) q^{71} +(-1.60289 - 1.18298i) q^{72} +(1.66393 + 1.04551i) q^{73} +(-0.733052 + 0.680173i) q^{75} +(2.20431 - 2.56145i) q^{78} +(0.0747301 + 0.997204i) q^{81} +(-0.633168 + 2.77409i) q^{82} +(-0.294755 + 0.955573i) q^{87} +(0.473222 - 2.07332i) q^{92} +(0.359154 + 1.89817i) q^{93} +(2.07835 - 1.00088i) q^{94} +(0.360958 + 0.310630i) q^{96} +(-1.75711 - 0.197979i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 2 * q^3 + 14 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9	$ 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 6 q^{12} - 6 q^{16} + 4 q^{18} - 6 q^{24} - 4 q^{25} + 2 q^{26} - 4 q^{27} - 2 q^{31} + 4 q^{32} + 6 q^{36} + 2 q^{41} + 2 q^{46} - 2 q^{47} - 4 q^{48} - 4 q^{49} - 2 q^{50} - 10 q^{52} + 12 q^{54} + 4 q^{58} + 4 q^{62} - 28 q^{64} + 14 q^{72} - 2 q^{73} + 2 q^{75} + 10 q^{78} + 2 q^{81} - 4 q^{82} + 4 q^{92} - 2 q^{93} - 8 q^{94} - 24 q^{96} - 2 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 2 * q^3 + 14 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 6 * q^12 - 6 * q^16 + 4 * q^18 - 6 * q^24 - 4 * q^25 + 2 * q^26 - 4 * q^27 - 2 * q^31 + 4 * q^32 + 6 * q^36 + 2 * q^41 + 2 * q^46 - 2 * q^47 - 4 * q^48 - 4 * q^49 - 2 * q^50 - 10 * q^52 + 12 * q^54 + 4 * q^58 + 4 * q^62 - 28 * q^64 + 14 * q^72 - 2 * q^73 + 2 * q^75 + 10 * q^78 + 2 * q^81 - 4 * q^82 + 4 * q^92 - 2 * q^93 - 8 * q^94 - 24 * q^96 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{23}{28}\right)$	$-1$	$-1$

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 $

$2$	−0.940755	−	1.49720i	−0.940755	−	1.49720i	−0.866025	−	0.500000i	$-0.833333\pi$
$2$	−0.940755	−	1.49720i	−0.940755	−	1.49720i	−0.0747301	−	0.997204i	$-0.523810\pi$
$3$	0.365341	−	0.930874i	0.365341	−	0.930874i
$3$	0.365341	−	0.930874i	0.365341	−	0.930874i
$4$	−0.922715	+	1.91604i	−0.922715	+	1.91604i
$5$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$5$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$6$	−1.73740	+	0.328735i	−1.73740	+	0.328735i
$7$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$7$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$8$	1.97963	−	0.223051i	1.97963	−	0.223051i
$9$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$10$		0			0
$11$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$11$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$12$	1.44648	+	1.55894i	1.44648	+	1.55894i
$13$	−1.49419	+	1.19158i	−1.49419	+	1.19158i	−0.563320	+	0.826239i	$0.690476\pi$
$13$	−1.49419	+	1.19158i	−1.49419	+	1.19158i	−0.930874	+	0.365341i	$0.880952\pi$
$14$		0			0
$15$		0			0
$16$	−0.870366	−	1.09140i	−0.870366	−	1.09140i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	−0.328735	+	1.73740i	−0.328735	+	1.73740i
$19$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$19$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$20$		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
$24$	0.515609	−	1.92428i	0.515609	−	1.92428i
$25$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$26$	3.18971	+	1.11613i	3.18971	+	1.11613i
$27$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$28$		0			0
$29$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$29$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$30$		0			0
$31$	−1.63575	+	1.02781i	−1.63575	+	1.02781i	−0.680173	+	0.733052i	$0.738095\pi$
$31$	−1.63575	+	1.02781i	−1.63575	+	1.02781i	−0.955573	+	0.294755i	$0.904762\pi$
$32$	−0.157284	+	0.449493i	−0.157284	+	0.449493i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.97963	−	0.776949i	1.97963	−	0.776949i
$37$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$37$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$38$		0			0
$39$	0.563320	+	1.82624i	0.563320	+	1.82624i
$40$		0			0
$41$	−1.13787	−	1.13787i	−1.13787	−	1.13787i	−0.988831	−	0.149042i	$-0.952381\pi$
$41$	−1.13787	−	1.13787i	−1.13787	−	1.13787i	−0.149042	−	0.988831i	$-0.547619\pi$
$42$		0			0
$43$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$43$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$44$		0			0
$45$		0			0
$46$	1.25033	+	1.25033i	1.25033	+	1.25033i
$47$	−0.146066	+	1.29637i	−0.146066	+	1.29637i	0.680173	+	0.733052i	$0.261905\pi$
$47$	−0.146066	+	1.29637i	−0.146066	+	1.29637i	−0.826239	+	0.563320i	$0.809524\pi$
$48$	−1.33394	+	0.411466i	−1.33394	+	0.411466i
$49$	0.623490	−	0.781831i	0.623490	−	0.781831i
$50$	0.197979	+	1.75711i	0.197979	+	1.75711i
$51$		0			0
$52$	−0.904396	−	3.96242i	−0.904396	−	3.96242i
$53$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$53$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$54$	1.49720	+	0.940755i	1.49720	+	0.940755i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.05001	+	1.42271i	1.05001	+	1.42271i
$59$		−	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		−0.943883	−	0.330279i	$-0.892857\pi$
$61$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$62$	3.07767	+	1.48213i	3.07767	+	1.48213i
$63$		0			0
$64$	−0.540010	+	0.123254i	−0.540010	+	0.123254i
$65$		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
$69$	−0.149042	+	0.988831i	−0.149042	+	0.988831i
$70$		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	$-0.452381\pi$
$72$	−1.60289	−	1.18298i	−1.60289	−	1.18298i
$73$	1.66393	+	1.04551i	1.66393	+	1.04551i	0.930874	+	0.365341i	$0.119048\pi$
$73$	1.66393	+	1.04551i	1.66393	+	1.04551i	0.733052	+	0.680173i	$0.238095\pi$
$74$		0			0
$75$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$76$		0			0
$77$		0			0
$78$	2.20431	−	2.56145i	2.20431	−	2.56145i
$79$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$79$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$80$		0			0
$81$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$82$	−0.633168	+	2.77409i	−0.633168	+	2.77409i
$83$		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
$87$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$88$		0			0
$89$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$89$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$90$		0			0
$91$		0			0
$92$	0.473222	−	2.07332i	0.473222	−	2.07332i
$93$	0.359154	+	1.89817i	0.359154	+	1.89817i
$94$	2.07835	−	1.00088i	2.07835	−	1.00088i
$95$		0			0
$96$	0.360958	+	0.310630i	0.360958	+	0.310630i
$97$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$97$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$98$	−1.75711	−	0.197979i	−1.75711	−	0.197979i
$99$		0			0
$100$	1.66267	−	1.32594i	1.66267	−	1.32594i
$101$	0.559311	+	0.351438i	0.559311	+	0.351438i	0.781831	−	0.623490i	$-0.214286\pi$
$101$	0.559311	+	0.351438i	0.559311	+	0.351438i	−0.222521	+	0.974928i	$0.571429\pi$
$102$		0			0
$103$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$103$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$104$	−2.69217	+	2.69217i	−2.69217	+	2.69217i
$105$		0			0
$106$		0			0
$107$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$107$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$108$		−	2.12664i		−	2.12664i
$109$		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		−0.943883	−	0.330279i	$-0.892857\pi$
$113$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$114$		0			0
$115$		0			0
$116$	0.776949	−	1.97963i	0.776949	−	1.97963i
$117$	1.90580	+	0.142820i	1.90580	+	0.142820i
$118$	−2.69787	+	1.69518i	−2.69787	+	1.69518i
$119$		0			0
$120$		0			0
$121$	0.974928	+	0.222521i	0.974928	+	0.222521i
$122$		0			0
$123$	−1.47493	+	0.643504i	−1.47493	+	0.643504i
$124$	−0.459990	−	4.08252i	−0.459990	−	4.08252i
$125$		0			0
$126$		0			0
$127$	0.205245	−	1.82160i	0.205245	−	1.82160i	−0.294755	−	0.955573i	$-0.595238\pi$
$127$	0.205245	−	1.82160i	0.205245	−	1.82160i	0.500000	−	0.866025i	$-0.333333\pi$
$128$	1.02929	+	1.02929i	1.02929	+	1.02929i
$129$		0			0
$130$		0			0
$131$	0.497204	−	0.791295i	0.497204	−	0.791295i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	0.497204	−	0.791295i	0.497204	−	0.791295i	0.997204	+	0.0747301i	$0.0238095\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$137$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$138$	1.62069	−	0.707101i	1.62069	−	0.707101i
$139$	−0.302705	−	1.32624i	−0.302705	−	1.32624i	−0.866025	−	0.500000i	$-0.833333\pi$
$139$	−0.302705	−	1.32624i	−0.302705	−	1.32624i	0.563320	−	0.826239i	$-0.309524\pi$
$140$		0			0
$141$	1.15339	+	0.609587i	1.15339	+	0.609587i
$142$	−0.794455	+	2.27042i	−0.794455	+	2.27042i
$143$		0			0
$144$	−0.104320	+	1.39205i	−0.104320	+	1.39205i
$145$		0			0
$146$		−	3.47481i		−	3.47481i
$147$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$148$		0			0
$149$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$149$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$150$	1.70798	+	0.457652i	1.70798	+	0.457652i
$151$	0.974928	−	0.222521i	0.974928	−	0.222521i	0.294755	−	0.955573i	$-0.404762\pi$
$151$	0.974928	−	0.222521i	0.974928	−	0.222521i	0.680173	+	0.733052i	$0.261905\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−4.01892	−	0.605755i	−4.01892	−	0.605755i
$157$		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
$162$	1.42271	−	1.05001i	1.42271	−	1.05001i
$163$	−1.29637	−	0.146066i	−1.29637	−	0.146066i	−0.563320	−	0.826239i	$-0.690476\pi$
$163$	−1.29637	−	0.146066i	−1.29637	−	0.146066i	−0.733052	+	0.680173i	$0.761905\pi$
$164$	3.23014	−	1.13027i	3.23014	−	1.13027i
$165$		0			0
$166$		0			0
$167$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$167$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$168$		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	$-0.714286\pi$
$173$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$174$	1.70798	−	0.457652i	1.70798	−	0.457652i
$175$		0			0
$176$		0			0
$177$	−1.67738	−	0.658322i	−1.67738	−	0.658322i
$178$		0			0
$179$	0.162592	−	0.712362i	0.162592	−	0.712362i	−0.826239	−	0.563320i	$-0.809524\pi$
$179$	0.162592	−	0.712362i	0.162592	−	0.712362i	0.988831	−	0.149042i	$-0.0476190\pi$
$180$		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
$184$	−1.88037	+	0.657969i	−1.88037	+	0.657969i
$185$		0			0
$186$	2.50408	−	2.32344i	2.50408	−	2.32344i
$187$		0			0
$188$	−2.34912	−	1.47605i	−2.34912	−	1.47605i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	−0.0825542	+	0.547711i	−0.0825542	+	0.547711i
$193$	0.122805	+	0.350958i	0.122805	+	0.350958i	0.988831	−	0.149042i	$-0.0476190\pi$
$193$	0.122805	+	0.350958i	0.122805	+	0.350958i	−0.866025	+	0.500000i	$0.833333\pi$
$194$		0			0
$195$		0			0
$196$	0.922715	+	1.91604i	0.922715	+	1.91604i
$197$	1.68862	−	0.385418i	1.68862	−	0.385418i	0.733052	−	0.680173i	$-0.238095\pi$
$197$	1.68862	−	0.385418i	1.68862	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$198$		0			0
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	−1.88037	−	0.657969i	−1.88037	−	0.657969i
$201$		0			0
$202$		−	1.16802i		−	1.16802i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.866025	+	0.500000i	0.866025	+	0.500000i
$208$	2.60099	+	0.593659i	2.60099	+	0.593659i
$209$		0			0
$210$		0			0
$211$	0.158342	+	1.40532i	0.158342	+	1.40532i	0.781831	+	0.623490i	$0.214286\pi$
$211$	0.158342	+	1.40532i	0.158342	+	1.40532i	−0.623490	+	0.781831i	$0.714286\pi$
$212$		0			0
$213$	−1.29991	+	0.400969i	−1.29991	+	0.400969i
$214$		0			0
$215$		0			0
$216$	−1.68681	+	1.05989i	−1.68681	+	1.05989i
$217$		0			0
$218$		0			0
$219$	1.58114	−	1.16694i	1.58114	−	1.16694i
$220$		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
$225$	0.365341	+	0.930874i	0.365341	+	0.930874i
$226$		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		0.330279	−	0.943883i	$-0.392857\pi$
$229$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$230$		0			0
$231$		0			0
$232$	−1.95743	+	0.370366i	−1.95743	+	0.370366i
$233$			1.97766i			1.97766i	0.149042	+	0.988831i	$0.452381\pi$
$233$			1.97766i			1.97766i	−0.149042	+	0.988831i	$0.547619\pi$
$234$	−1.57906	−	2.98773i	−1.57906	−	2.98773i
$235$		0			0
$236$	3.45258	+	1.66267i	3.45258	+	1.66267i
$237$		0			0
$238$		0			0
$239$	−0.129334	−	0.268565i	−0.129334	−	0.268565i	0.826239	−	0.563320i	$-0.190476\pi$
$239$	−0.129334	−	0.268565i	−0.129334	−	0.268565i	−0.955573	+	0.294755i	$0.904762\pi$
$240$		0			0
$241$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$241$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$242$	−0.584010	−	1.66900i	−0.584010	−	1.66900i
$243$	0.955573	+	0.294755i	0.955573	+	0.294755i
$244$		0			0
$245$		0			0
$246$	2.35100	+	1.60289i	2.35100	+	1.60289i
$247$		0			0
$248$	−3.00892	+	2.39954i	−3.00892	+	2.39954i
$249$		0			0
$250$		0			0
$251$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$251$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$252$		0			0
$253$		0			0
$254$	−2.92039	+	1.40639i	−2.92039	+	1.40639i
$255$		0			0
$256$	0.449493	−	1.96936i	0.449493	−	1.96936i
$257$	−0.865341	+	1.79690i	−0.865341	+	1.79690i	−0.365341	+	0.930874i	$0.619048\pi$
$257$	−0.865341	+	1.79690i	−0.865341	+	1.79690i	−0.500000	+	0.866025i	$0.666667\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.781831	+	0.623490i	0.781831	+	0.623490i
$262$	−1.65248			−1.65248
$263$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$263$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.82160	+	0.205245i	−1.82160	+	0.205245i	−0.955573	−	0.294755i	$-0.904762\pi$
$269$	−1.82160	+	0.205245i	−1.82160	+	0.205245i	−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	−1.00435	+	0.351438i	−1.00435	+	0.351438i	−0.781831	−	0.623490i	$-0.785714\pi$
$271$	−1.00435	+	0.351438i	−1.00435	+	0.351438i	−0.222521	+	0.974928i	$0.571429\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.75711	−	1.19798i	−1.75711	−	1.19798i
$277$	−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	$-0.476190\pi$
$278$	−1.70088	+	1.70088i	−1.70088	+	1.70088i
$279$	1.89817	+	0.359154i	1.89817	+	0.359154i
$280$		0			0
$281$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$281$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$282$	−0.172387	−	2.30034i	−0.172387	−	2.30034i
$283$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$283$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$284$	2.82043	−	0.643745i	2.82043	−	0.643745i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.421030	−	0.222521i	0.421030	−	0.222521i
$289$		−	1.00000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	−3.53857	+	2.22343i	−3.53857	+	2.22343i
$293$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$293$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$294$	−0.826239	+	1.56332i	−0.826239	+	1.56332i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.19158	−	1.49419i	1.19158	−	1.49419i
$300$	−0.626838	−	2.03216i	−0.626838	−	2.03216i
$301$		0			0
$302$	−1.25033	−	1.25033i	−1.25033	−	1.25033i
$303$	0.531484	−	0.392253i	0.531484	−	0.392253i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.33485	+	1.33485i	1.33485	+	1.33485i	0.900969	+	0.433884i	$0.142857\pi$
$307$	1.33485	+	1.33485i	1.33485	+	1.33485i	0.433884	+	0.900969i	$0.357143\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.00837297	+	0.0743122i	0.00837297	+	0.0743122i	0.997204	−	0.0747301i	$-0.0238095\pi$
$311$	0.00837297	+	0.0743122i	0.00837297	+	0.0743122i	−0.988831	+	0.149042i	$0.952381\pi$
$312$	1.52251	+	3.48963i	1.52251	+	3.48963i
$313$		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
$317$	−1.43388	+	0.900969i	−1.43388	+	0.900969i	−0.433884	+	0.900969i	$0.642857\pi$
$317$	−1.43388	+	0.900969i	−1.43388	+	0.900969i	−1.00000			$1.00000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.97963	−	0.776949i	−1.97963	−	0.776949i
$325$	1.86323	−	0.425270i	1.86323	−	0.425270i
$326$	1.00088	+	2.07835i	1.00088	+	2.07835i
$327$		0			0
$328$	−2.50638	−	1.99877i	−2.50638	−	1.99877i
$329$		0			0
$330$		0			0
$331$	−0.565533	+	0.565533i	−0.565533	+	0.565533i	−0.930874	−	0.365341i	$-0.880952\pi$
$331$	−0.565533	+	0.565533i	−0.565533	+	0.565533i	0.365341	+	0.930874i	$0.380952\pi$
$332$		0			0
$333$		0			0
$334$	−0.666318	−	0.418676i	−0.666318	−	0.418676i
$335$		0			0
$336$		0			0
$337$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$337$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$338$	−4.42699	+	1.54907i	−4.42699	+	1.54907i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.17310	+	1.86698i	1.17310	+	1.86698i
$347$	−1.56366			−1.56366			−0.781831	−	0.623490i	$-0.785714\pi$
$347$	−1.56366			−1.56366			−0.781831	+	0.623490i	$0.785714\pi$
$348$	−1.55894	−	1.44648i	−1.55894	−	1.44648i
$349$	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
$351$	0.829215	−	1.72188i	0.829215	−	1.72188i
$352$		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	$0.690476\pi$
$354$	0.592359	+	3.13069i	0.592359	+	3.13069i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.21951	+	0.426725i	−1.21951	+	0.426725i
$359$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$359$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$360$		0			0
$361$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$362$		0			0
$363$	0.563320	−	0.826239i	0.563320	−	0.826239i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$367$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$368$	1.09140	+	0.870366i	1.09140	+	0.870366i
$369$	0.0601697	+	1.60807i	0.0601697	+	1.60807i
$370$		0			0
$371$		0			0
$372$	−3.96836	−	1.06332i	−3.96836	−	1.06332i
$373$		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
$376$			2.59892i			2.59892i
$377$	1.40097	−	1.29991i	1.40097	−	1.29991i
$378$		0			0
$379$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$379$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$380$		0			0
$381$	−1.62069	−	0.856562i	−1.62069	−	0.856562i
$382$		0			0
$383$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$383$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$384$	1.33418	−	0.582097i	1.33418	−	0.582097i
$385$		0			0
$386$	0.409925	−	0.514030i	0.409925	−	0.514030i
$387$		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
$392$	1.05989	−	1.68681i	1.05989	−	1.68681i
$393$	−0.554947	−	0.751927i	−0.554947	−	0.751927i
$394$	−2.16563	−	2.16563i	−2.16563	−	2.16563i
$395$		0			0
$396$		0			0
$397$	0.185853	−	0.233052i	0.185853	−	0.233052i	−0.680173	−	0.733052i	$-0.738095\pi$
$397$	0.185853	−	0.233052i	0.185853	−	0.233052i	0.866025	+	0.500000i	$0.166667\pi$
$398$		0			0
$399$		0			0
$400$	0.310630	+	1.36096i	0.310630	+	1.36096i
$401$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$401$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$402$		0			0
$403$	1.21941	−	3.48486i	1.21941	−	3.48486i
$404$	−1.18945	+	0.747382i	−1.18945	+	0.747382i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.51889	+	0.531484i	1.51889	+	0.531484i	0.955573	−	0.294755i	$-0.0952381\pi$
$409$	1.51889	+	0.531484i	1.51889	+	0.531484i	0.563320	+	0.826239i	$0.309524\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.0661163	−	1.76699i	−0.0661163	−	1.76699i
$415$		0			0
$416$	−0.300593	−	0.859046i	−0.300593	−	0.859046i
$417$	−1.34515	−	0.202749i	−1.34515	−	0.202749i
$418$		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		−0.846724	−	0.532032i	$-0.821429\pi$
$421$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$422$	1.95509	−	1.55913i	1.95509	−	1.55913i
$423$	0.988831	−	0.850958i	0.988831	−	0.850958i
$424$		0			0
$425$		0			0
$426$	1.82323	+	1.56902i	1.82323	+	1.56902i
$427$		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	$0.642857\pi$
$432$	1.25771	+	0.605684i	1.25771	+	0.605684i
$433$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$433$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−3.23461	−	1.26949i	−3.23461	−	1.26949i
$439$	−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
$441$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$442$		0			0
$443$	0.369485	−	0.0416310i	0.369485	−	0.0416310i	0.0747301	−	0.997204i	$-0.476190\pi$
$443$	0.369485	−	0.0416310i	0.369485	−	0.0416310i	0.294755	+	0.955573i	$0.404762\pi$
$444$		0			0
$445$		0			0
$446$	2.19108	+	0.246876i	2.19108	+	0.246876i
$447$		0			0
$448$		0			0
$449$	−0.900969	−	0.566116i	−0.900969	−	0.566116i		−	1.00000i	$-0.5\pi$
$449$	−0.900969	−	0.566116i	−0.900969	−	0.566116i	−0.900969	+	0.433884i	$0.857143\pi$
$450$	1.05001	−	1.42271i	1.05001	−	1.42271i
$451$		0			0
$452$		0			0
$453$	0.149042	−	0.988831i	0.149042	−	0.988831i
$454$		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
$461$	−0.754903	−	0.264152i	−0.754903	−	0.264152i	−0.0747301	−	0.997204i	$-0.523810\pi$
$461$	−0.754903	−	0.264152i	−0.754903	−	0.264152i	−0.680173	+	0.733052i	$0.738095\pi$
$462$		0			0
$463$		−	0.445042i		−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$463$		−	0.445042i		−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$464$	0.949493	+	1.02331i	0.949493	+	1.02331i
$465$		0			0
$466$	2.96096	−	1.86050i	2.96096	−	1.86050i
$467$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$467$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$468$	−2.03216	+	3.51980i	−2.03216	+	3.51980i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.401924	−	3.56718i	−0.401924	−	3.56718i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.280425	+	0.446293i	−0.280425	+	0.446293i
$479$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$479$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.32594	+	1.66267i	−1.32594	+	1.66267i
$485$		0			0
$486$	−0.457652	−	1.70798i	−0.457652	−	1.70798i
$487$	−0.414278	−	1.81507i	−0.414278	−	1.81507i	−0.563320	−	0.826239i	$-0.690476\pi$
$487$	−0.414278	−	1.81507i	−0.414278	−	1.81507i	0.149042	−	0.988831i	$-0.452381\pi$
$488$		0			0
$489$	−0.609587	+	1.15339i	−0.609587	+	1.15339i
$490$		0			0
$491$	−1.00560	+	0.631863i	−1.00560	+	0.631863i	−0.930874	−	0.365341i	$-0.880952\pi$
$491$	−1.00560	+	0.631863i	−1.00560	+	0.631863i	−0.0747301	+	0.997204i	$0.523810\pi$
$492$	0.127959	−	3.41979i	0.127959	−	3.41979i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.54545	+	0.890691i	2.54545	+	0.890691i
$497$		0			0
$498$		0			0
$499$	0.145713	−	0.0332580i	0.145713	−	0.0332580i	−0.149042	−	0.988831i	$-0.547619\pi$
$499$	0.145713	−	0.0332580i	0.145713	−	0.0332580i	0.294755	+	0.955573i	$0.404762\pi$
$500$		0			0
$501$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i
$502$		0			0
$503$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$503$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.19158	−	1.49419i	−2.19158	−	1.49419i
$508$	3.30087	+	2.07407i	3.30087	+	2.07407i
$509$	−0.880843	+	0.702449i	−0.880843	+	0.702449i	−0.955573	−	0.294755i	$-0.904762\pi$
$509$	−0.880843	+	0.702449i	−0.880843	+	0.702449i	0.0747301	+	0.997204i	$0.476190\pi$
$510$		0			0
$511$		0			0
$512$	−1.99744	+	0.698934i	−1.99744	+	0.698934i
$513$		0			0
$514$	3.50440	−	0.394851i	3.50440	−	0.394851i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.455573	+	1.16078i	−0.455573	+	1.16078i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	0.197979	−	1.75711i	0.197979	−	1.75711i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	1.05737	+	1.68280i	1.05737	+	1.68280i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.900969	−	0.433884i	0.900969	−	0.433884i
$530$		0			0
$531$	−1.22563	+	1.32091i	−1.22563	+	1.32091i
$532$		0			0
$533$	3.05607	+	0.344336i	3.05607	+	0.344336i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.603718	−	0.411608i	−0.603718	−	0.411608i
$538$	2.02097	+	2.53422i	2.02097	+	2.53422i
$539$		0			0
$540$		0			0
$541$	0.500684	+	1.43087i	0.500684	+	1.43087i	0.866025	+	0.500000i	$0.166667\pi$
$541$	0.500684	+	1.43087i	0.500684	+	1.43087i	−0.365341	+	0.930874i	$0.619048\pi$
$542$	1.47102	+	1.17310i	1.47102	+	1.17310i
$543$		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
$552$	−0.0744892	+	1.99077i	−0.0744892	+	1.99077i
$553$		0			0
$554$	−0.856219	+	2.44693i	−0.856219	+	2.44693i
$555$		0			0
$556$	2.82043	+	0.643745i	2.82043	+	0.643745i
$557$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$557$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$558$	−1.24799	−	3.17983i	−1.24799	−	3.17983i
$559$		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	$0.250000\pi$
$564$	−2.23224	+	1.64747i	−2.23224	+	1.64747i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−1.91628	−	1.91628i	−1.91628	−	1.91628i
$569$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$569$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$570$		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
$576$	0.479690	+	0.276949i	0.479690	+	0.276949i
$577$	−0.264152	+	0.754903i	−0.264152	+	0.754903i	0.733052	+	0.680173i	$0.238095\pi$
$577$	−0.264152	+	0.754903i	−0.264152	+	0.754903i	−0.997204	+	0.0747301i	$0.976190\pi$
$578$	−1.49720	+	0.940755i	−1.49720	+	0.940755i
$579$	0.371563	+	0.0139029i	0.371563	+	0.0139029i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	3.52717	+	1.69859i	3.52717	+	1.69859i
$585$		0			0
$586$		0			0
$587$	−0.807782	−	1.67738i	−0.807782	−	1.67738i	−0.733052	−	0.680173i	$-0.761905\pi$
$587$	−0.807782	−	1.67738i	−0.807782	−	1.67738i	−0.0747301	−	0.997204i	$-0.523810\pi$
$588$	2.12069	−	0.158924i	2.12069	−	0.158924i
$589$		0			0
$590$		0			0
$591$	0.258149	−	1.71271i	0.258149	−	1.71271i
$592$		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
$598$	−3.35810	−	0.378367i	−3.35810	−	0.378367i
$599$	1.00435	−	0.351438i	1.00435	−	0.351438i	0.222521	−	0.974928i	$-0.428571\pi$
$599$	1.00435	−	0.351438i	1.00435	−	0.351438i	0.781831	+	0.623490i	$0.214286\pi$
$600$	−1.29946	+	1.51000i	−1.29946	+	1.51000i
$601$	−0.514383	+	0.0579571i	−0.514383	+	0.0579571i	−0.365341	−	0.930874i	$-0.619048\pi$
$601$	−0.514383	+	0.0579571i	−0.514383	+	0.0579571i	−0.149042	+	0.988831i	$0.547619\pi$
$602$		0			0
$603$		0			0
$604$	−0.473222	+	2.07332i	−0.473222	+	2.07332i
$605$		0			0
$606$	−1.08728	−	0.426725i	−1.08728	−	0.426725i
$607$	−1.05737	−	1.68280i	−1.05737	−	1.68280i	−0.623490	−	0.781831i	$-0.714286\pi$
$607$	−1.05737	−	1.68280i	−1.05737	−	1.68280i	−0.433884	−	0.900969i	$-0.642857\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.32648	−	2.11108i	−1.32648	−	2.11108i
$612$		0			0
$613$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$613$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$614$	0.742776	−	3.25432i	0.742776	−	3.25432i
$615$		0			0
$616$		0			0
$617$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$617$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$618$		0			0
$619$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$619$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$620$		0			0
$621$	0.781831	−	0.623490i	0.781831	−	0.623490i
$622$	0.103384	−	0.0824456i	0.103384	−	0.0824456i
$623$		0			0
$624$	1.50287	−	2.20431i	1.50287	−	2.20431i
$625$	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
$633$	1.36603	+	0.366025i	1.36603	+	0.366025i
$634$	2.69787	+	1.29922i	2.69787	+	1.29922i
$635$		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		0.330279	−	0.943883i	$-0.392857\pi$
$641$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$642$		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	$0.0238095\pi$
$648$	0.370366	+	1.95743i	0.370366	+	1.95743i
$649$		0			0
$650$	−2.38956	−	2.38956i	−2.38956	−	2.38956i
$651$		0			0
$652$	1.47605	−	2.34912i	1.47605	−	2.34912i
$653$	0.275400	−	0.438297i	0.275400	−	0.438297i	−0.680173	−	0.733052i	$-0.738095\pi$
$653$	0.275400	−	0.438297i	0.275400	−	0.438297i	0.955573	+	0.294755i	$0.0952381\pi$
$654$		0			0
$655$		0			0
$656$	−0.251514	+	2.23224i	−0.251514	+	2.23224i
$657$	−0.508614	−	1.89817i	−0.508614	−	1.89817i
$658$		0			0
$659$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$659$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$660$		0			0
$661$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$661$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$662$	1.37875	+	0.314690i	1.37875	+	0.314690i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.955573	−	0.294755i	0.955573	−	0.294755i
$668$			0.946444i			0.946444i
$669$	0.623490	+	1.07992i	0.623490	+	1.07992i
$670$		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
$675$	1.00000			1.00000
$676$	4.41021	+	3.51702i	4.41021	+	3.51702i
$677$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$677$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$678$		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	$0.761905\pi$
$683$	−1.55929	+	1.24349i	−1.55929	+	1.24349i	−0.826239	+	0.563320i	$0.809524\pi$
$684$		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	$0.642857\pi$
$692$	1.15061	−	2.38926i	1.15061	−	2.38926i
$693$		0			0
$694$	1.47102	+	2.34112i	1.47102	+	2.34112i
$695$		0			0
$696$	−0.370366	+	1.95743i	−0.370366	+	1.95743i
$697$		0			0
$698$	−0.140605	−	0.223772i	−0.140605	−	0.223772i
$699$	1.84095	+	0.722521i	1.84095	+	0.722521i
$700$		0			0
$701$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$	−3.35810	+	0.378367i	−3.35810	+	0.378367i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	3.10726	−	1.08728i	3.10726	−	1.08728i
$707$		0			0
$708$	2.80911	−	2.60647i	2.80911	−	2.60647i
$709$		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
$713$	1.36603	−	1.36603i	1.36603	−	1.36603i
$714$		0			0
$715$		0			0
$716$	1.21489	+	0.968839i	1.21489	+	0.968839i
$717$	−0.297251	+	0.0222759i	−0.297251	+	0.0222759i
$718$		0			0
$719$	1.90097	−	0.433884i	1.90097	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$719$	1.90097	−	0.433884i	1.90097	−	0.433884i	1.00000			$0$
$720$		0			0
$721$		0			0
$722$	1.66900	+	0.584010i	1.66900	+	0.584010i
$723$		0			0
$724$		0			0
$725$	0.930874	+	0.365341i	0.930874	+	0.365341i
$726$	−1.76699	−	0.0661163i	−1.76699	−	0.0661163i
$727$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$727$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$728$		0			0
$729$	0.623490	−	0.781831i	0.623490	−	0.781831i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$733$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$734$		0			0
$735$		0			0
$736$	0.0533193	−	0.473222i	0.0533193	−	0.473222i
$737$		0			0
$738$	2.35100	−	1.60289i	2.35100	−	1.60289i
$739$	0.856144	−	1.36254i	0.856144	−	1.36254i	−0.0747301	−	0.997204i	$-0.523810\pi$
$739$	0.856144	−	1.36254i	0.856144	−	1.36254i	0.930874	−	0.365341i	$-0.119048\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$743$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$744$	1.13438	+	3.67758i	1.13438	+	3.67758i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$751$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$752$	1.54200	−	0.968901i	1.54200	−	0.968901i
$753$		0			0
$754$	−3.26420	−	0.874639i	−3.26420	−	0.874639i
$755$		0			0
$756$		0			0
$757$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$757$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$758$		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	$-0.404762\pi$
$762$	0.242229	+	3.23232i	0.242229	+	3.23232i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.14715	+	2.69244i	2.14715	+	2.69244i
$768$	−1.66900	−	1.13791i	−1.66900	−	1.13791i
$769$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$769$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$770$		0			0
$771$	1.35654	+	1.46200i	1.35654	+	1.46200i
$772$	−0.785762	−	0.0885341i	−0.785762	−	0.0885341i
$773$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$773$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$774$		0			0
$775$	1.91970	−	0.216299i	1.91970	−	0.216299i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.866025	−	0.500000i	0.866025	−	0.500000i
$784$	−1.39596			−1.39596
$785$		0			0
$786$	−0.603718	+	1.53825i	−0.603718	+	1.53825i
$787$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$787$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$788$	−0.819644	+	3.59110i	−0.819644	+	3.59110i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.523768	−	0.0590145i	−0.523768	−	0.0590145i
$795$		0			0
$796$		0			0
$797$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$797$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$798$		0			0
$799$		0			0
$800$	0.336736	−	0.336736i	0.336736	−	0.336736i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−6.36472	+	1.45270i	−6.36472	+	1.45270i
$807$	−0.474448	+	1.77066i	−0.474448	+	1.77066i
$808$	1.18562	+	0.570964i	1.18562	+	0.570964i
$809$	−1.87590	−	0.656405i	−1.87590	−	0.656405i	−0.974928	−	0.222521i	$-0.928571\pi$
$809$	−1.87590	−	0.656405i	−1.87590	−	0.656405i	−0.900969	−	0.433884i	$-0.857143\pi$
$810$		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
$813$	−0.0397866	+	1.06332i	−0.0397866	+	1.06332i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.633168	−	2.77409i	−0.633168	−	2.77409i
$819$		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
$823$	0.132974	−	1.18017i	0.132974	−	1.18017i	−0.733052	−	0.680173i	$-0.761905\pi$
$823$	0.132974	−	1.18017i	0.132974	−	1.18017i	0.866025	−	0.500000i	$-0.166667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$827$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$828$	−1.75711	+	1.19798i	−1.75711	+	1.19798i
$829$	−1.19745	−	1.19745i	−1.19745	−	1.19745i	−0.974928	−	0.222521i	$-0.928571\pi$
$829$	−1.19745	−	1.19745i	−1.19745	−	1.19745i	−0.222521	−	0.974928i	$-0.571429\pi$
$830$		0			0
$831$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$832$	0.660013	−	0.827631i	0.660013	−	0.827631i
$833$		0			0
$834$	0.961902	+	2.20470i	0.961902	+	2.20470i
$835$		0			0
$836$		0			0
$837$	1.02781	−	1.63575i	1.02781	−	1.63575i
$838$		0			0
$839$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$839$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$840$		0			0
$841$	0.988831	−	0.149042i	0.988831	−	0.149042i
$842$		0			0
$843$		0			0
$844$	−2.83875	−	0.993322i	−2.83875	−	0.993322i
$845$		0			0
$846$	−2.20431	−	0.679938i	−2.20431	−	0.679938i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.431174	−	2.86065i	0.431174	−	2.86065i
$853$	0.467085	−	0.467085i	0.467085	−	0.467085i	−0.433884	−	0.900969i	$-0.642857\pi$
$853$	0.467085	−	0.467085i	0.467085	−	0.467085i	0.900969	+	0.433884i	$0.142857\pi$
$854$		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
$859$	−1.18017	−	0.132974i	−1.18017	−	0.132974i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	−1.18017	−	0.132974i	−1.18017	−	0.132974i	−0.680173	+	0.733052i	$0.738095\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.900969	−	0.433884i	0.900969	−	0.433884i	0.0747301	−	0.997204i	$-0.476190\pi$
$863$	0.900969	−	0.433884i	0.900969	−	0.433884i	0.826239	+	0.563320i	$0.190476\pi$
$864$	−0.0533193	−	0.473222i	−0.0533193	−	0.473222i
$865$		0			0
$866$		0			0
$867$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.776949	+	4.10627i	0.776949	+	4.10627i
$877$	−0.781831	+	0.376510i	−0.781831	+	0.376510i	−0.781831	−	0.623490i	$-0.785714\pi$
$877$	−0.781831	+	0.376510i	−0.781831	+	0.376510i			1.00000i	$0.5\pi$
$878$	0.523768	−	0.0590145i	0.523768	−	0.0590145i
$879$		0			0
$880$		0			0
$881$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$881$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$882$	1.15339	+	1.34027i	1.15339	+	1.34027i
$883$	−1.40881	+	1.12349i	−1.40881	+	1.12349i	−0.433884	+	0.900969i	$0.642857\pi$
$883$	−1.40881	+	1.12349i	−1.40881	+	1.12349i	−0.974928	+	0.222521i	$0.928571\pi$
$884$		0			0
$885$		0			0
$886$	−0.409925	−	0.514030i	−0.409925	−	0.514030i
$887$	−1.29621	+	1.29621i	−1.29621	+	1.29621i	−0.365341	+	0.930874i	$0.619048\pi$
$887$	−1.29621	+	1.29621i	−1.29621	+	1.29621i	−0.930874	+	0.365341i	$0.880952\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−1.15061	−	2.38926i	−1.15061	−	2.38926i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.955573	−	1.65510i	−0.955573	−	1.65510i
$898$			1.88151i			1.88151i
$899$	1.55436	−	1.14717i	1.55436	−	1.14717i
$900$	−2.12069	−	0.158924i	−2.12069	−	0.158924i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−1.62069	+	0.707101i	−1.62069	+	0.707101i
$907$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$907$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$908$		0			0
$909$	−0.170965	−	0.638050i	−0.170965	−	0.638050i
$910$		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		0.623490	−	0.781831i	$-0.285714\pi$
$919$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$920$		0			0
$921$	1.73026	−	0.754903i	1.73026	−	0.754903i
$922$	0.314690	+	1.37875i	0.314690	+	1.37875i
$923$	2.53464	+	0.578514i	2.53464	+	0.578514i
$924$		0			0
$925$		0			0
$926$	−0.666318	+	0.418676i	−0.666318	+	0.418676i
$927$		0			0
$928$	0.123254	−	0.459990i	0.123254	−	0.459990i
$929$			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
$932$	−3.78927	−	1.82482i	−3.78927	−	1.82482i
$933$	0.0722342	+	0.0193551i	0.0722342	+	0.0193551i
$934$		0			0
$935$		0			0
$936$	3.80464	−	0.142360i	3.80464	−	0.142360i
$937$		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
$943$	1.36254	+	0.856144i	1.36254	+	0.856144i
$944$	−1.96664	+	1.56834i	−1.96664	+	1.56834i
$945$		0			0
$946$		0			0
$947$	−1.73026	+	0.605443i	−1.73026	+	0.605443i	−0.997204	−	0.0747301i	$-0.976190\pi$
$947$	−1.73026	+	0.605443i	−1.73026	+	0.605443i	−0.733052	+	0.680173i	$0.761905\pi$
$948$		0			0
$949$	−3.73204	+	0.420500i	−3.73204	+	0.420500i
$950$		0			0
$951$	0.314832	+	1.66393i	0.314832	+	1.66393i
$952$		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
$956$	0.633919			0.633919
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.18539	−	2.46149i	1.18539	−	2.46149i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.350958	−	0.122805i	0.350958	−	0.122805i	−0.149042	−	0.988831i	$-0.547619\pi$
$967$	0.350958	−	0.122805i	0.350958	−	0.122805i	0.500000	+	0.866025i	$0.333333\pi$
$968$	1.97963	+	0.223051i	1.97963	+	0.223051i
$969$		0			0
$970$		0			0
$971$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$971$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$972$	−1.44648	+	1.55894i	−1.44648	+	1.55894i
$973$		0			0
$974$	−2.32779	+	2.32779i	−2.32779	+	2.32779i
$975$	0.284841	−	1.88980i	0.284841	−	1.88980i
$976$		0			0
$977$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$977$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$978$	2.30034	−	0.172387i	2.30034	−	0.172387i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.89205	+	0.911166i	1.89205	+	0.911166i
$983$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$983$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$984$	−2.77628	+	1.60289i	−2.77628	+	1.60289i
$985$		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	$0.857143\pi$
$992$	−0.204715	−	0.896913i	−0.204715	−	0.896913i
$993$	0.319827	+	0.733052i	0.319827	+	0.733052i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.119137	+	1.05737i	−0.119137	+	1.05737i	0.781831	+	0.623490i	$0.214286\pi$
$997$	−0.119137	+	1.05737i	−0.119137	+	1.05737i	−0.900969	+	0.433884i	$0.857143\pi$
$998$	−0.186874	−	0.186874i	−0.186874	−	0.186874i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.c.68.1	✓	24
3.2	odd	2		2001.1.bf.d.68.2	yes	24
23.22	odd	2	CM	2001.1.bf.c.68.1	✓	24
29.3	odd	28		2001.1.bf.d.206.2	yes	24
69.68	even	2		2001.1.bf.d.68.2	yes	24
87.32	even	28	inner	2001.1.bf.c.206.1	yes	24
667.206	even	28		2001.1.bf.d.206.2	yes	24
2001.206	odd	28	inner	2001.1.bf.c.206.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.68.1	✓	24	1.1	even	1	trivial
2001.1.bf.c.68.1	✓	24	23.22	odd	2	CM
2001.1.bf.c.206.1	yes	24	87.32	even	28	inner
2001.1.bf.c.206.1	yes	24	2001.206	odd	28	inner
2001.1.bf.d.68.2	yes	24	3.2	odd	2
2001.1.bf.d.68.2	yes	24	69.68	even	2
2001.1.bf.d.206.2	yes	24	29.3	odd	28
2001.1.bf.d.206.2	yes	24	667.206	even	28

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)

\(f(q)\)	\(=\)	\(q+(-0.940755 - 1.49720i) q^{2} +(0.365341 - 0.930874i) q^{3} +(-0.922715 + 1.91604i) q^{4} +(-1.73740 + 0.328735i) q^{6} +(1.97963 - 0.223051i) q^{8} +(-0.733052 - 0.680173i) q^{9} +O(q^{10})\)	\(q+(-0.940755 - 1.49720i) q^{2} +(0.365341 - 0.930874i) q^{3} +(-0.922715 + 1.91604i) q^{4} +(-1.73740 + 0.328735i) q^{6} +(1.97963 - 0.223051i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(1.44648 + 1.55894i) q^{12} +(-1.49419 + 1.19158i) q^{13} +(-0.870366 - 1.09140i) q^{16} +(-0.328735 + 1.73740i) q^{18} +(-0.974928 + 0.222521i) q^{23} +(0.515609 - 1.92428i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(3.18971 + 1.11613i) q^{26} +(-0.900969 + 0.433884i) q^{27} +(-0.997204 + 0.0747301i) q^{29} +(-1.63575 + 1.02781i) q^{31} +(-0.157284 + 0.449493i) q^{32} +(1.97963 - 0.776949i) q^{36} +(0.563320 + 1.82624i) q^{39} +(-1.13787 - 1.13787i) q^{41} +(1.25033 + 1.25033i) q^{46} +(-0.146066 + 1.29637i) q^{47} +(-1.33394 + 0.411466i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.197979 + 1.75711i) q^{50} +(-0.904396 - 3.96242i) q^{52} +(1.49720 + 0.940755i) q^{54} +(1.05001 + 1.42271i) q^{58} -1.80194i q^{59} +(3.07767 + 1.48213i) q^{62} +(-0.540010 + 0.123254i) q^{64} +(-0.149042 + 0.988831i) q^{69} +(-0.848162 - 1.06356i) q^{71} +(-1.60289 - 1.18298i) q^{72} +(1.66393 + 1.04551i) q^{73} +(-0.733052 + 0.680173i) q^{75} +(2.20431 - 2.56145i) q^{78} +(0.0747301 + 0.997204i) q^{81} +(-0.633168 + 2.77409i) q^{82} +(-0.294755 + 0.955573i) q^{87} +(0.473222 - 2.07332i) q^{92} +(0.359154 + 1.89817i) q^{93} +(2.07835 - 1.00088i) q^{94} +(0.360958 + 0.310630i) q^{96} +(-1.75711 - 0.197979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 2 * q^3 + 14 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 6 q^{12} - 6 q^{16} + 4 q^{18} - 6 q^{24} - 4 q^{25} + 2 q^{26} - 4 q^{27} - 2 q^{31} + 4 q^{32} + 6 q^{36} + 2 q^{41} + 2 q^{46} - 2 q^{47} - 4 q^{48} - 4 q^{49} - 2 q^{50} - 10 q^{52} + 12 q^{54} + 4 q^{58} + 4 q^{62} - 28 q^{64} + 14 q^{72} - 2 q^{73} + 2 q^{75} + 10 q^{78} + 2 q^{81} - 4 q^{82} + 4 q^{92} - 2 q^{93} - 8 q^{94} - 24 q^{96} - 2 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 2 * q^3 + 14 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 6 * q^12 - 6 * q^16 + 4 * q^18 - 6 * q^24 - 4 * q^25 + 2 * q^26 - 4 * q^27 - 2 * q^31 + 4 * q^32 + 6 * q^36 + 2 * q^41 + 2 * q^46 - 2 * q^47 - 4 * q^48 - 4 * q^49 - 2 * q^50 - 10 * q^52 + 12 * q^54 + 4 * q^58 + 4 * q^62 - 28 * q^64 + 14 * q^72 - 2 * q^73 + 2 * q^75 + 10 * q^78 + 2 * q^81 - 4 * q^82 + 4 * q^92 - 2 * q^93 - 8 * q^94 - 24 * q^96 - 2 * q^98

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