LMFDB - Embedded newform 2001.1.bf.c.896.1

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			896.1
Root			$0.563320 + 0.826239i$ of defining polynomial
Character	$\chi$	$=$	2001.896
Dual form			2001.1.bf.c.1034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69226 - 1.06332i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(1.29922 + 2.69787i) q^{4} +(1.51488 + 1.30366i) q^{6} +(0.446293 - 3.96096i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})$	\(q+(-1.69226 - 1.06332i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(1.29922 + 2.69787i) q^{4} +(1.51488 + 1.30366i) q^{6} +(0.446293 - 3.96096i) q^{8} +(0.955573 + 0.294755i) q^{9} +(-0.882617 - 2.86137i) q^{12} +(-1.14625 - 0.914101i) q^{13} +(-3.10003 + 3.88732i) q^{16} +(-1.30366 - 1.51488i) q^{18} +(0.974928 + 0.222521i) q^{23} +(-1.03166 + 3.85021i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(0.967770 + 2.76573i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-0.563320 + 0.826239i) q^{29} +(1.02781 - 1.63575i) q^{31} +(5.61720 - 1.96554i) q^{32} +(0.446293 + 2.96096i) q^{36} +(0.997204 + 1.07473i) q^{39} +(-0.565533 - 0.565533i) q^{41} +(-1.41322 - 1.41322i) q^{46} +(-0.369485 + 0.0416310i) q^{47} +(3.64478 - 3.38187i) q^{48} +(0.623490 + 0.781831i) q^{49} +(1.98603 + 0.223772i) q^{50} +(0.976892 - 4.28004i) q^{52} +(1.06332 + 1.69226i) q^{54} +(1.83184 - 0.799225i) q^{58} -1.80194i q^{59} +(-3.47864 + 1.67523i) q^{62} +(-6.74838 - 1.54027i) q^{64} +(-0.930874 - 0.365341i) q^{69} +(0.367554 - 0.460898i) q^{71} +(1.59398 - 3.65344i) q^{72} +(-0.806531 - 1.28359i) q^{73} +(0.955573 - 0.294755i) q^{75} +(-0.544750 - 2.87907i) q^{78} +(0.826239 + 0.563320i) q^{81} +(0.355688 + 1.55837i) q^{82} +(0.680173 - 0.733052i) q^{87} +(0.666318 + 2.91933i) q^{92} +(-1.26012 + 1.46429i) q^{93} +(0.669534 + 0.322430i) q^{94} +(-5.84741 + 1.10639i) q^{96} +(-0.223772 - 1.98603i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{19}{28}\right)$	$-1$	$-1$

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 $

$2$	−1.69226	−	1.06332i	−1.69226	−	1.06332i	−0.866025	−	0.500000i	$-0.833333\pi$
$2$	−1.69226	−	1.06332i	−1.69226	−	1.06332i	−0.826239	−	0.563320i	$-0.809524\pi$
$3$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$3$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$4$	1.29922	+	2.69787i	1.29922	+	2.69787i
$5$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$5$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$6$	1.51488	+	1.30366i	1.51488	+	1.30366i
$7$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$7$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$8$	0.446293	−	3.96096i	0.446293	−	3.96096i
$9$	0.955573	+	0.294755i	0.955573	+	0.294755i
$10$		0			0
$11$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$11$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$12$	−0.882617	−	2.86137i	−0.882617	−	2.86137i
$13$	−1.14625	−	0.914101i	−1.14625	−	0.914101i	−0.149042	−	0.988831i	$-0.547619\pi$
$13$	−1.14625	−	0.914101i	−1.14625	−	0.914101i	−0.997204	+	0.0747301i	$0.976190\pi$
$14$		0			0
$15$		0			0
$16$	−3.10003	+	3.88732i	−3.10003	+	3.88732i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	−1.30366	−	1.51488i	−1.30366	−	1.51488i
$19$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$19$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$20$		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
$24$	−1.03166	+	3.85021i	−1.03166	+	3.85021i
$25$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$26$	0.967770	+	2.76573i	0.967770	+	2.76573i
$27$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$28$		0			0
$29$	−0.563320	+	0.826239i	−0.563320	+	0.826239i
$29$	−0.563320	+	0.826239i	−0.563320	+	0.826239i
$30$		0			0
$31$	1.02781	−	1.63575i	1.02781	−	1.63575i	0.294755	−	0.955573i	$-0.404762\pi$
$31$	1.02781	−	1.63575i	1.02781	−	1.63575i	0.733052	−	0.680173i	$-0.238095\pi$
$32$	5.61720	−	1.96554i	5.61720	−	1.96554i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.446293	+	2.96096i	0.446293	+	2.96096i
$37$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$37$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$38$		0			0
$39$	0.997204	+	1.07473i	0.997204	+	1.07473i
$40$		0			0
$41$	−0.565533	−	0.565533i	−0.565533	−	0.565533i	0.365341	−	0.930874i	$-0.380952\pi$
$41$	−0.565533	−	0.565533i	−0.565533	−	0.565533i	−0.930874	+	0.365341i	$0.880952\pi$
$42$		0			0
$43$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$43$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$44$		0			0
$45$		0			0
$46$	−1.41322	−	1.41322i	−1.41322	−	1.41322i
$47$	−0.369485	+	0.0416310i	−0.369485	+	0.0416310i	−0.294755	−	0.955573i	$-0.595238\pi$
$47$	−0.369485	+	0.0416310i	−0.369485	+	0.0416310i	−0.0747301	+	0.997204i	$0.523810\pi$
$48$	3.64478	−	3.38187i	3.64478	−	3.38187i
$49$	0.623490	+	0.781831i	0.623490	+	0.781831i
$50$	1.98603	+	0.223772i	1.98603	+	0.223772i
$51$		0			0
$52$	0.976892	−	4.28004i	0.976892	−	4.28004i
$53$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$53$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$54$	1.06332	+	1.69226i	1.06332	+	1.69226i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.83184	−	0.799225i	1.83184	−	0.799225i
$59$		−	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	$-0.607143\pi$
$61$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$62$	−3.47864	+	1.67523i	−3.47864	+	1.67523i
$63$		0			0
$64$	−6.74838	−	1.54027i	−6.74838	−	1.54027i
$65$		0			0
$66$		0			0
$67$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$67$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$68$		0			0
$69$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$70$		0			0
$71$	0.367554	−	0.460898i	0.367554	−	0.460898i	−0.563320	−	0.826239i	$-0.690476\pi$
$71$	0.367554	−	0.460898i	0.367554	−	0.460898i	0.930874	+	0.365341i	$0.119048\pi$
$72$	1.59398	−	3.65344i	1.59398	−	3.65344i
$73$	−0.806531	−	1.28359i	−0.806531	−	1.28359i	−0.955573	−	0.294755i	$-0.904762\pi$
$73$	−0.806531	−	1.28359i	−0.806531	−	1.28359i	0.149042	−	0.988831i	$-0.452381\pi$
$74$		0			0
$75$	0.955573	−	0.294755i	0.955573	−	0.294755i
$76$		0			0
$77$		0			0
$78$	−0.544750	−	2.87907i	−0.544750	−	2.87907i
$79$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$79$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$80$		0			0
$81$	0.826239	+	0.563320i	0.826239	+	0.563320i
$82$	0.355688	+	1.55837i	0.355688	+	1.55837i
$83$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$83$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.680173	−	0.733052i	0.680173	−	0.733052i
$88$		0			0
$89$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$89$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$90$		0			0
$91$		0			0
$92$	0.666318	+	2.91933i	0.666318	+	2.91933i
$93$	−1.26012	+	1.46429i	−1.26012	+	1.46429i
$94$	0.669534	+	0.322430i	0.669534	+	0.322430i
$95$		0			0
$96$	−5.84741	+	1.10639i	−5.84741	+	1.10639i
$97$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$97$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$98$	−0.223772	−	1.98603i	−0.223772	−	1.98603i
$99$		0			0
$100$	−2.34112	−	1.86698i	−2.34112	−	1.86698i
$101$	−1.00435	−	1.59842i	−1.00435	−	1.59842i	−0.781831	−	0.623490i	$-0.785714\pi$
$101$	−1.00435	−	1.59842i	−1.00435	−	1.59842i	−0.222521	−	0.974928i	$-0.571429\pi$
$102$		0			0
$103$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$103$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$104$	−4.13228	+	4.13228i	−4.13228	+	4.13228i
$105$		0			0
$106$		0			0
$107$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$107$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$108$		−	2.99441i		−	2.99441i
$109$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$109$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$113$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$114$		0			0
$115$		0			0
$116$	−2.96096	−	0.446293i	−2.96096	−	0.446293i
$117$	−0.825886	−	1.21135i	−0.825886	−	1.21135i
$118$	−1.91604	+	3.04935i	−1.91604	+	3.04935i
$119$		0			0
$120$		0			0
$121$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$122$		0			0
$123$	0.474928	+	0.643504i	0.474928	+	0.643504i
$124$	5.74838	+	0.647687i	5.74838	+	0.647687i
$125$		0			0
$126$		0			0
$127$	1.18017	−	0.132974i	1.18017	−	0.132974i	0.500000	−	0.866025i	$-0.333333\pi$
$127$	1.18017	−	0.132974i	1.18017	−	0.132974i	0.680173	+	0.733052i	$0.261905\pi$
$128$	5.57413	+	5.57413i	5.57413	+	5.57413i
$129$		0			0
$130$		0			0
$131$	0.0633201	−	0.0397866i	0.0633201	−	0.0397866i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	0.0633201	−	0.0397866i	0.0633201	−	0.0397866i	0.563320	+	0.826239i	$0.309524\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$137$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$138$	1.18681	+	1.60807i	1.18681	+	1.60807i
$139$	0.131178	−	0.574730i	0.131178	−	0.574730i	−0.866025	−	0.500000i	$-0.833333\pi$
$139$	0.131178	−	0.574730i	0.131178	−	0.574730i	0.997204	−	0.0747301i	$-0.0238095\pi$
$140$		0			0
$141$	0.371563	+	0.0139029i	0.371563	+	0.0139029i
$142$	−1.11208	+	0.389134i	−1.11208	+	0.389134i
$143$		0			0
$144$	−4.10812	+	2.80087i	−4.10812	+	2.80087i
$145$		0			0
$146$			3.02977i			3.02977i
$147$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$148$		0			0
$149$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$149$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$150$	−1.93050	−	0.517276i	−1.93050	−	0.517276i
$151$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.294755	−	0.955573i	$-0.595238\pi$
$151$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.680173	+	0.733052i	$0.738095\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−1.60389	+	4.08664i	−1.60389	+	4.08664i
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.799225	−	1.83184i	−0.799225	−	1.83184i
$163$	−0.0416310	−	0.369485i	−0.0416310	−	0.369485i	−0.997204	−	0.0747301i	$-0.976190\pi$
$163$	−0.0416310	−	0.369485i	−0.0416310	−	0.369485i	0.955573	−	0.294755i	$-0.0952381\pi$
$164$	0.790979	−	2.26049i	0.790979	−	2.26049i
$165$		0			0
$166$		0			0
$167$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$167$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$168$		0			0
$169$	0.255779	+	1.12064i	0.255779	+	1.12064i
$170$		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	$0.714286\pi$
$174$	−1.93050	+	0.517276i	−1.93050	+	0.517276i
$175$		0			0
$176$		0			0
$177$	−0.268565	+	1.78181i	−0.268565	+	1.78181i
$178$		0			0
$179$	−0.440071	−	1.92808i	−0.440071	−	1.92808i	−0.365341	−	0.930874i	$-0.619048\pi$
$179$	−0.440071	−	1.92808i	−0.440071	−	1.92808i	−0.0747301	−	0.997204i	$-0.523810\pi$
$180$		0			0
$181$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$181$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$182$		0			0
$183$		0			0
$184$	1.31650	−	3.76234i	1.31650	−	3.76234i
$185$		0			0
$186$	3.68947	−	1.13805i	3.68947	−	1.13805i
$187$		0			0
$188$	−0.592359	−	0.942734i	−0.592359	−	0.942734i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	6.44344	+	2.52886i	6.44344	+	2.52886i
$193$	−1.23137	−	0.430874i	−1.23137	−	0.430874i	−0.365341	−	0.930874i	$-0.619048\pi$
$193$	−1.23137	−	0.430874i	−1.23137	−	0.430874i	−0.866025	+	0.500000i	$0.833333\pi$
$194$		0			0
$195$		0			0
$196$	−1.29922	+	2.69787i	−1.29922	+	2.69787i
$197$	−1.68862	−	0.385418i	−1.68862	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$197$	−1.68862	−	0.385418i	−1.68862	−	0.385418i	−0.955573	+	0.294755i	$0.904762\pi$
$198$		0			0
$199$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$199$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$200$	1.31650	+	3.76234i	1.31650	+	3.76234i
$201$		0			0
$202$			3.77289i			3.77289i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.866025	+	0.500000i	0.866025	+	0.500000i
$208$	7.10680	−	1.62208i	7.10680	−	1.62208i
$209$		0			0
$210$		0			0
$211$	−1.40532	−	0.158342i	−1.40532	−	0.158342i	−0.623490	−	0.781831i	$-0.714286\pi$
$211$	−1.40532	−	0.158342i	−1.40532	−	0.158342i	−0.781831	+	0.623490i	$0.785714\pi$
$212$		0			0
$213$	−0.432142	+	0.400969i	−0.432142	+	0.400969i
$214$		0			0
$215$		0			0
$216$	−2.12069	+	3.37506i	−2.12069	+	3.37506i
$217$		0			0
$218$		0			0
$219$	0.606214	+	1.38946i	0.606214	+	1.38946i
$220$		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
$225$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$226$		0			0
$227$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$227$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$228$		0			0
$229$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$229$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$230$		0			0
$231$		0			0
$232$	3.02129	+	2.60003i	3.02129	+	2.60003i
$233$		−	0.730682i		−	0.730682i	−0.930874	−	0.365341i	$-0.880952\pi$
$233$		−	0.730682i		−	0.730682i	0.930874	−	0.365341i	$-0.119048\pi$
$234$	0.109562	+	2.92811i	0.109562	+	2.92811i
$235$		0			0
$236$	4.86139	−	2.34112i	4.86139	−	2.34112i
$237$		0			0
$238$		0			0
$239$	0.807782	−	1.67738i	0.807782	−	1.67738i	0.0747301	−	0.997204i	$-0.476190\pi$
$239$	0.807782	−	1.67738i	0.807782	−	1.67738i	0.733052	−	0.680173i	$-0.238095\pi$
$240$		0			0
$241$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$241$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$242$	1.88645	+	0.660096i	1.88645	+	0.660096i
$243$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$244$		0			0
$245$		0			0
$246$	−0.119452	−	1.59398i	−0.119452	−	1.59398i
$247$		0			0
$248$	−6.02042	−	4.80113i	−6.02042	−	4.80113i
$249$		0			0
$250$		0			0
$251$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$251$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$252$		0			0
$253$		0			0
$254$	−2.13856	−	1.02987i	−2.13856	−	1.02987i
$255$		0			0
$256$	−1.96554	−	8.61161i	−1.96554	−	8.61161i
$257$	0.488831	+	1.01507i	0.488831	+	1.01507i	0.988831	+	0.149042i	$0.0476190\pi$
$257$	0.488831	+	1.01507i	0.488831	+	1.01507i	−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
$262$	−0.149460			−0.149460
$263$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$263$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.132974	+	1.18017i	−0.132974	+	1.18017i	0.733052	+	0.680173i	$0.238095\pi$
$269$	−0.132974	+	1.18017i	−0.132974	+	1.18017i	−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	0.559311	−	1.59842i	0.559311	−	1.59842i	−0.222521	−	0.974928i	$-0.571429\pi$
$271$	0.559311	−	1.59842i	0.559311	−	1.59842i	0.781831	−	0.623490i	$-0.214286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.223772	−	2.98603i	−0.223772	−	2.98603i
$277$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.365341	−	0.930874i	$-0.380952\pi$
$277$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.826239	−	0.563320i	$-0.190476\pi$
$278$	−0.833111	+	0.833111i	−0.833111	+	0.833111i
$279$	1.46429	−	1.26012i	1.46429	−	1.26012i
$280$		0			0
$281$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$281$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$282$	−0.614000	−	0.418618i	−0.614000	−	0.418618i
$283$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$283$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$284$	1.72098	+	0.392802i	1.72098	+	0.392802i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	5.94700	−	0.222521i	5.94700	−	0.222521i
$289$		−	1.00000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	2.41508	−	3.84358i	2.41508	−	3.84358i
$293$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$293$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$294$	−0.0747301	+	1.99720i	−0.0747301	+	1.99720i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.914101	−	1.14625i	−0.914101	−	1.14625i
$300$	2.03671	+	2.19506i	2.03671	+	2.19506i
$301$		0			0
$302$	1.41322	+	1.41322i	1.41322	+	1.41322i
$303$	0.754903	+	1.73026i	0.754903	+	1.73026i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.467085	+	0.467085i	0.467085	+	0.467085i	0.900969	−	0.433884i	$-0.142857\pi$
$307$	0.467085	+	0.467085i	0.467085	+	0.467085i	−0.433884	+	0.900969i	$0.642857\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.928661	+	0.104635i	0.928661	+	0.104635i	0.563320	−	0.826239i	$-0.309524\pi$
$311$	0.928661	+	0.104635i	0.928661	+	0.104635i	0.365341	+	0.930874i	$0.380952\pi$
$312$	4.70201	−	3.47024i	4.70201	−	3.47024i
$313$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$313$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.566116	+	0.900969i	−0.566116	+	0.900969i	0.433884	+	0.900969i	$0.357143\pi$
$317$	−0.566116	+	0.900969i	−0.566116	+	0.900969i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.446293	+	2.96096i	−0.446293	+	2.96096i
$325$	1.42935	+	0.326239i	1.42935	+	0.326239i
$326$	−0.322430	+	0.669534i	−0.322430	+	0.669534i
$327$		0			0
$328$	−2.49245	+	1.98766i	−2.49245	+	1.98766i
$329$		0			0
$330$		0			0
$331$	−1.13787	+	1.13787i	−1.13787	+	1.13787i	−0.149042	+	0.988831i	$0.547619\pi$
$331$	−1.13787	+	1.13787i	−1.13787	+	1.13787i	−0.988831	+	0.149042i	$0.952381\pi$
$332$		0			0
$333$		0			0
$334$	−0.473222	−	0.753128i	−0.473222	−	0.753128i
$335$		0			0
$336$		0			0
$337$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$337$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$338$	0.758754	−	2.16840i	0.758754	−	2.16840i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	2.11022	+	1.32594i	2.11022	+	1.32594i
$347$	1.56366			1.56366			0.781831	−	0.623490i	$-0.214286\pi$
$347$	1.56366			1.56366			0.781831	+	0.623490i	$0.214286\pi$
$348$	2.86137	+	0.882617i	2.86137	+	0.882617i
$349$	1.65248			1.65248			0.826239	−	0.563320i	$-0.190476\pi$
$349$	1.65248			1.65248			0.826239	+	0.563320i	$0.190476\pi$
$350$		0			0
$351$	0.636119	+	1.32091i	0.636119	+	1.32091i
$352$		0			0
$353$	−0.0663300	−	0.290611i	−0.0663300	−	0.290611i	0.930874	−	0.365341i	$-0.119048\pi$
$353$	−0.0663300	−	0.290611i	−0.0663300	−	0.290611i	−0.997204	+	0.0747301i	$0.976190\pi$
$354$	2.34912	−	2.72973i	2.34912	−	2.72973i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.30545	+	3.73075i	−1.30545	+	3.73075i
$359$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$359$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$360$		0			0
$361$	0.781831	+	0.623490i	0.781831	+	0.623490i
$362$		0			0
$363$	0.997204	−	0.0747301i	0.997204	−	0.0747301i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$367$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$368$	−3.88732	+	3.10003i	−3.88732	+	3.10003i
$369$	−0.373714	−	0.707101i	−0.373714	−	0.707101i
$370$		0			0
$371$		0			0
$372$	−5.58764	−	1.49720i	−5.58764	−	1.49720i
$373$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$373$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$374$		0			0
$375$		0			0
$376$			1.48210i			1.48210i
$377$	1.40097	−	0.432142i	1.40097	−	0.432142i
$378$		0			0
$379$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$379$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$380$		0			0
$381$	−1.18681	−	0.0444073i	−1.18681	−	0.0444073i
$382$		0			0
$383$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$383$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$384$	−4.68109	−	6.34265i	−4.68109	−	6.34265i
$385$		0			0
$386$	1.62564	+	2.03849i	1.62564	+	2.03849i
$387$		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
$392$	3.37506	−	2.12069i	3.37506	−	2.12069i
$393$	−0.0685427	+	0.0299049i	−0.0685427	+	0.0299049i
$394$	2.44778	+	2.44778i	2.44778	+	2.44778i
$395$		0			0
$396$		0			0
$397$	1.16078	+	1.45557i	1.16078	+	1.45557i	0.866025	+	0.500000i	$0.166667\pi$
$397$	1.16078	+	1.45557i	1.16078	+	1.45557i	0.294755	+	0.955573i	$0.404762\pi$
$398$		0			0
$399$		0			0
$400$	1.10639	−	4.84741i	1.10639	−	4.84741i
$401$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$401$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$402$		0			0
$403$	−2.67336	+	0.935448i	−2.67336	+	0.935448i
$404$	3.00744	−	4.78631i	3.00744	−	4.78631i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.264152	+	0.754903i	0.264152	+	0.754903i	0.997204	+	0.0747301i	$0.0238095\pi$
$409$	0.264152	+	0.754903i	0.264152	+	0.754903i	−0.733052	+	0.680173i	$0.761905\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.933884	−	1.76699i	−0.933884	−	1.76699i
$415$		0			0
$416$	−8.23540	−	2.88169i	−8.23540	−	2.88169i
$417$	−0.215372	+	0.548760i	−0.215372	+	0.548760i
$418$		0			0
$419$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$419$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$420$		0			0
$421$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$421$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$422$	2.20981	+	1.76226i	2.20981	+	1.76226i
$423$	−0.365341	−	0.0691263i	−0.365341	−	0.0691263i
$424$		0			0
$425$		0			0
$426$	1.15766	−	0.219040i	1.15766	−	0.219040i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$431$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$432$	4.47968	−	2.15730i	4.47968	−	2.15730i
$433$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$433$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.451563	−	2.99593i	0.451563	−	2.99593i
$439$	0.807782	+	1.67738i	0.807782	+	1.67738i	0.733052	+	0.680173i	$0.238095\pi$
$439$	0.807782	+	1.67738i	0.807782	+	1.67738i	0.0747301	+	0.997204i	$0.476190\pi$
$440$		0			0
$441$	0.365341	+	0.930874i	0.365341	+	0.930874i
$442$		0			0
$443$	0.146066	−	1.29637i	0.146066	−	1.29637i	−0.680173	−	0.733052i	$-0.738095\pi$
$443$	0.146066	−	1.29637i	0.146066	−	1.29637i	0.826239	−	0.563320i	$-0.190476\pi$
$444$		0			0
$445$		0			0
$446$	0.279040	+	2.47654i	0.279040	+	2.47654i
$447$		0			0
$448$		0			0
$449$	−0.900969	−	1.43388i	−0.900969	−	1.43388i	−0.900969	−	0.433884i	$-0.857143\pi$
$449$	−0.900969	−	1.43388i	−0.900969	−	1.43388i		−	1.00000i	$-0.5\pi$
$450$	1.83184	+	0.799225i	1.83184	+	0.799225i
$451$		0			0
$452$		0			0
$453$	0.930874	+	0.365341i	0.930874	+	0.365341i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$457$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.531484	−	1.51889i	−0.531484	−	1.51889i	−0.826239	−	0.563320i	$-0.809524\pi$
$461$	−0.531484	−	1.51889i	−0.531484	−	1.51889i	0.294755	−	0.955573i	$-0.404762\pi$
$462$		0			0
$463$		−	0.445042i		−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$463$		−	0.445042i		−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$464$	−1.46554	−	4.75117i	−1.46554	−	4.75117i
$465$		0			0
$466$	−0.776949	+	1.23651i	−0.776949	+	1.23651i
$467$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$467$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$468$	2.19506	−	3.80195i	2.19506	−	3.80195i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−7.13741	−	0.804193i	−7.13741	−	0.804193i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−3.15057	+	1.97963i	−3.15057	+	1.97963i
$479$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$479$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.86698	−	2.34112i	−1.86698	−	2.34112i
$485$		0			0
$486$	0.517276	+	1.93050i	0.517276	+	1.93050i
$487$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i	−0.997204	−	0.0747301i	$-0.976190\pi$
$487$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i	0.930874	+	0.365341i	$0.119048\pi$
$488$		0			0
$489$	−0.0139029	+	0.371563i	−0.0139029	+	0.371563i
$490$		0			0
$491$	−0.975281	+	1.55215i	−0.975281	+	1.55215i	−0.149042	+	0.988831i	$0.547619\pi$
$491$	−0.975281	+	1.55215i	−0.975281	+	1.55215i	−0.826239	+	0.563320i	$0.809524\pi$
$492$	−1.11905	+	2.11735i	−1.11905	+	2.11735i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	3.17243	+	9.06628i	3.17243	+	9.06628i
$497$		0			0
$498$		0			0
$499$	−1.61105	−	0.367711i	−1.61105	−	0.367711i	−0.680173	−	0.733052i	$-0.738095\pi$
$499$	−1.61105	−	0.367711i	−1.61105	−	0.367711i	−0.930874	+	0.365341i	$0.880952\pi$
$500$		0			0
$501$	−0.367711	−	0.250701i	−0.367711	−	0.250701i
$502$		0			0
$503$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$503$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0858993	−	1.14625i	−0.0858993	−	1.14625i
$508$	1.89205	+	3.01119i	1.89205	+	3.01119i
$509$	1.55929	+	1.24349i	1.55929	+	1.24349i	0.826239	+	0.563320i	$0.190476\pi$
$509$	1.55929	+	1.24349i	1.55929	+	1.24349i	0.733052	+	0.680173i	$0.238095\pi$
$510$		0			0
$511$		0			0
$512$	−3.22708	+	9.22247i	−3.22708	+	9.22247i
$513$		0			0
$514$	0.252111	−	2.23755i	0.252111	−	2.23755i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.23305	+	0.185853i	1.23305	+	0.185853i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	1.98603	−	0.223772i	1.98603	−	0.223772i
$523$		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
$531$	0.531130	−	1.72188i	0.531130	−	1.72188i
$532$		0			0
$533$	0.131286	+	1.16519i	0.131286	+	1.16519i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.147791	+	1.97213i	0.147791	+	1.97213i
$538$	1.47993	−	1.85577i	1.47993	−	1.85577i
$539$		0			0
$540$		0			0
$541$	1.85486	+	0.649042i	1.85486	+	0.649042i	0.988831	+	0.149042i	$0.0476190\pi$
$541$	1.85486	+	0.649042i	1.85486	+	0.649042i	0.866025	+	0.500000i	$0.166667\pi$
$542$	−2.64613	+	2.11022i	−2.64613	+	2.11022i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.658322	−	0.317031i	0.658322	−	0.317031i	−0.0747301	−	0.997204i	$-0.523810\pi$
$547$	0.658322	−	0.317031i	0.658322	−	0.317031i	0.733052	+	0.680173i	$0.238095\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−1.86254	+	3.52411i	−1.86254	+	3.52411i
$553$		0			0
$554$	−3.60527	+	1.26154i	−3.60527	+	1.26154i
$555$		0			0
$556$	1.72098	−	0.392802i	1.72098	−	0.392802i
$557$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$557$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$558$	−3.81788	+	0.575452i	−3.81788	+	0.575452i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$	0.445236	+	1.02049i	0.445236	+	1.02049i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−1.66156	−	1.66156i	−1.66156	−	1.66156i
$569$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$569$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$570$		0			0
$571$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$571$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$576$	−5.99456	−	3.46096i	−5.99456	−	3.46096i
$577$	−1.51889	+	0.531484i	−1.51889	+	0.531484i	−0.955573	−	0.294755i	$-0.904762\pi$
$577$	−1.51889	+	0.531484i	−1.51889	+	0.531484i	−0.563320	+	0.826239i	$0.690476\pi$
$578$	−1.06332	+	1.69226i	−1.06332	+	1.69226i
$579$	1.15339	+	0.609587i	1.15339	+	0.609587i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−5.44419	+	2.62178i	−5.44419	+	2.62178i
$585$		0			0
$586$		0			0
$587$	0.129334	−	0.268565i	0.129334	−	0.268565i	−0.826239	−	0.563320i	$-0.809524\pi$
$587$	0.129334	−	0.268565i	0.129334	−	0.268565i	0.955573	+	0.294755i	$0.0952381\pi$
$588$	1.68681	−	2.47410i	1.68681	−	2.47410i
$589$		0			0
$590$		0			0
$591$	1.61232	+	0.632789i	1.61232	+	0.632789i
$592$		0			0
$593$	−0.974928	+	1.22252i	−0.974928	+	1.22252i			1.00000i	$0.5\pi$
$593$	−0.974928	+	1.22252i	−0.974928	+	1.22252i	−0.974928	+	0.222521i	$0.928571\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.328073	+	2.91173i	0.328073	+	2.91173i
$599$	−0.559311	+	1.59842i	−0.559311	+	1.59842i	0.222521	+	0.974928i	$0.428571\pi$
$599$	−0.559311	+	1.59842i	−0.559311	+	1.59842i	−0.781831	+	0.623490i	$0.785714\pi$
$600$	−0.741048	−	3.91654i	−0.741048	−	3.91654i
$601$	0.0579571	−	0.514383i	0.0579571	−	0.514383i	−0.930874	−	0.365341i	$-0.880952\pi$
$601$	0.0579571	−	0.514383i	0.0579571	−	0.514383i	0.988831	−	0.149042i	$-0.0476190\pi$
$602$		0			0
$603$		0			0
$604$	−0.666318	−	2.91933i	−0.666318	−	2.91933i
$605$		0			0
$606$	0.562321	−	3.73075i	0.562321	−	3.73075i
$607$	−0.189606	−	0.119137i	−0.189606	−	0.119137i	0.433884	−	0.900969i	$-0.357143\pi$
$607$	−0.189606	−	0.119137i	−0.189606	−	0.119137i	−0.623490	+	0.781831i	$0.714286\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.461576	+	0.290027i	0.461576	+	0.290027i
$612$		0			0
$613$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$613$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$614$	−0.293770	−	1.28709i	−0.293770	−	1.28709i
$615$		0			0
$616$		0			0
$617$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$617$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$618$		0			0
$619$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$619$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$620$		0			0
$621$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$622$	−1.46028	−	1.16453i	−1.46028	−	1.16453i
$623$		0			0
$624$	−7.26919	+	0.544750i	−7.26919	+	0.544750i
$625$	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	$-0.357143\pi$
$631$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$632$		0			0
$633$	1.36603	+	0.366025i	1.36603	+	0.366025i
$634$	1.91604	−	0.922715i	1.91604	−	0.922715i
$635$		0			0
$636$		0			0
$637$		−	1.46610i		−	1.46610i
$638$		0			0
$639$	0.487076	−	0.332083i	0.487076	−	0.332083i
$640$		0			0
$641$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$641$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$642$		0			0
$643$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$643$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.24349	+	1.55929i	1.24349	+	1.55929i	0.680173	+	0.733052i	$0.261905\pi$
$647$	1.24349	+	1.55929i	1.24349	+	1.55929i	0.563320	+	0.826239i	$0.309524\pi$
$648$	2.60003	−	3.02129i	2.60003	−	3.02129i
$649$		0			0
$650$	−2.07193	−	2.07193i	−2.07193	−	2.07193i
$651$		0			0
$652$	0.942734	−	0.592359i	0.942734	−	0.592359i
$653$	−0.438297	+	0.275400i	−0.438297	+	0.275400i	−0.733052	−	0.680173i	$-0.761905\pi$
$653$	−0.438297	+	0.275400i	−0.438297	+	0.275400i	0.294755	+	0.955573i	$0.404762\pi$
$654$		0			0
$655$		0			0
$656$	3.95158	−	0.445236i	3.95158	−	0.445236i
$657$	−0.392355	−	1.46429i	−0.392355	−	1.46429i
$658$		0			0
$659$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$659$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$660$		0			0
$661$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$661$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$662$	3.13551	−	0.715659i	3.13551	−	0.715659i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$668$			1.33264i			1.33264i
$669$	0.623490	+	1.07992i	0.623490	+	1.07992i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.290611	−	0.0663300i	−0.290611	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$673$	−0.290611	−	0.0663300i	−0.290611	−	0.0663300i	−0.365341	+	0.930874i	$0.619048\pi$
$674$		0			0
$675$	1.00000			1.00000
$676$	−2.69103	+	2.14602i	−2.69103	+	2.14602i
$677$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$677$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.880843	+	0.702449i	0.880843	+	0.702449i	0.955573	−	0.294755i	$-0.0952381\pi$
$683$	0.880843	+	0.702449i	0.880843	+	0.702449i	−0.0747301	+	0.997204i	$0.523810\pi$
$684$		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	0.433884	+	0.900969i	$0.357143\pi$
$691$	0.433884	+	1.90097i	0.433884	+	1.90097i			1.00000i	$0.500000\pi$
$692$	−1.62011	−	3.36419i	−1.62011	−	3.36419i
$693$		0			0
$694$	−2.64613	−	1.66267i	−2.64613	−	1.66267i
$695$		0			0
$696$	−2.60003	−	3.02129i	−2.60003	−	3.02129i
$697$		0			0
$698$	−2.79643	−	1.75711i	−2.79643	−	1.75711i
$699$	−0.108903	+	0.722521i	−0.108903	+	0.722521i
$700$		0			0
$701$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$701$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$702$	0.328073	−	2.91173i	0.328073	−	2.91173i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.196764	+	0.562321i	−0.196764	+	0.562321i
$707$		0			0
$708$	−5.15602	+	1.59042i	−5.15602	+	1.59042i
$709$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$709$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.36603	−	1.36603i	1.36603	−	1.36603i
$714$		0			0
$715$		0			0
$716$	4.62995	−	3.69226i	4.62995	−	3.69226i
$717$	−1.04876	+	1.53825i	−1.04876	+	1.53825i
$718$		0			0
$719$	1.90097	+	0.433884i	1.90097	+	0.433884i	1.00000			$0$
$719$	1.90097	+	0.433884i	1.90097	+	0.433884i	0.900969	+	0.433884i	$0.142857\pi$
$720$		0			0
$721$		0			0
$722$	−0.660096	−	1.88645i	−0.660096	−	1.88645i
$723$		0			0
$724$		0			0
$725$	0.149042	−	0.988831i	0.149042	−	0.988831i
$726$	−1.76699	−	0.933884i	−1.76699	−	0.933884i
$727$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$727$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$728$		0			0
$729$	0.623490	+	0.781831i	0.623490	+	0.781831i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$733$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$734$		0			0
$735$		0			0
$736$	5.91374	−	0.666318i	5.91374	−	0.666318i
$737$		0			0
$738$	−0.119452	+	1.59398i	−0.119452	+	1.59398i
$739$	−0.677197	+	0.425511i	−0.677197	+	0.425511i	−0.826239	−	0.563320i	$-0.809524\pi$
$739$	−0.677197	+	0.425511i	−0.677197	+	0.425511i	0.149042	+	0.988831i	$0.452381\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$743$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$744$	5.23761	+	5.64480i	5.23761	+	5.64480i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$751$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$752$	0.983584	−	1.56537i	0.983584	−	1.56537i
$753$		0			0
$754$	−2.83031	−	0.758380i	−2.83031	−	0.758380i
$755$		0			0
$756$		0			0
$757$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$757$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.829215	+	1.72188i	−0.829215	+	1.72188i	−0.149042	+	0.988831i	$0.547619\pi$
$761$	−0.829215	+	1.72188i	−0.829215	+	1.72188i	−0.680173	+	0.733052i	$0.738095\pi$
$762$	1.96118	+	1.33711i	1.96118	+	1.33711i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.64715	+	2.06546i	−1.64715	+	2.06546i
$768$	0.660096	+	8.80837i	0.660096	+	8.80837i
$769$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$769$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$770$		0			0
$771$	−0.332083	−	1.07659i	−0.332083	−	1.07659i
$772$	−0.437381	−	3.88187i	−0.437381	−	3.88187i
$773$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$773$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$774$		0			0
$775$	−0.216299	+	1.91970i	−0.216299	+	1.91970i
$776$		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
$784$	−4.97207			−4.97207
$785$		0			0
$786$	0.147791	+	0.0222759i	0.147791	+	0.0222759i
$787$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$787$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$788$	−1.15410	−	5.05643i	−1.15410	−	5.05643i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.416608	−	3.69749i	−0.416608	−	3.69749i
$795$		0			0
$796$		0			0
$797$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$797$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$798$		0			0
$799$		0			0
$800$	−4.20810	+	4.20810i	−4.20810	+	4.20810i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	5.51870	+	1.25961i	5.51870	+	1.25961i
$807$	0.307384	−	1.14717i	0.307384	−	1.14717i
$808$	−6.77951	+	3.26484i	−6.77951	+	3.26484i
$809$	0.0739590	+	0.211363i	0.0739590	+	0.211363i	0.974928	−	0.222521i	$-0.0714286\pi$
$809$	0.0739590	+	0.211363i	0.0739590	+	0.211363i	−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
$813$	−0.791295	+	1.49720i	−0.791295	+	1.49720i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.355688	−	1.55837i	0.355688	−	1.55837i
$819$		0			0
$820$		0			0
$821$	0.541044	+	0.678448i	0.541044	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$821$	0.541044	+	0.678448i	0.541044	+	0.678448i	−0.433884	+	0.900969i	$0.642857\pi$
$822$		0			0
$823$	1.82160	−	0.205245i	1.82160	−	0.205245i	0.866025	−	0.500000i	$-0.166667\pi$
$823$	1.82160	−	0.205245i	1.82160	−	0.205245i	0.955573	+	0.294755i	$0.0952381\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$827$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$828$	−0.223772	+	2.98603i	−0.223772	+	2.98603i
$829$	0.752407	+	0.752407i	0.752407	+	0.752407i	0.974928	−	0.222521i	$-0.0714286\pi$
$829$	0.752407	+	0.752407i	0.752407	+	0.752407i	−0.222521	+	0.974928i	$0.571429\pi$
$830$		0			0
$831$	−1.40097	+	1.29991i	−1.40097	+	1.29991i
$832$	6.32734	+	7.93423i	6.32734	+	7.93423i
$833$		0			0
$834$	0.947974	−	0.699637i	0.947974	−	0.699637i
$835$		0			0
$836$		0			0
$837$	−1.63575	+	1.02781i	−1.63575	+	1.02781i
$838$		0			0
$839$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$839$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$840$		0			0
$841$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$842$		0			0
$843$		0			0
$844$	−1.39864	−	3.99709i	−1.39864	−	3.99709i
$845$		0			0
$846$	0.544750	+	0.505454i	0.544750	+	0.505454i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−1.64321	−	0.644912i	−1.64321	−	0.644912i
$853$	1.33485	−	1.33485i	1.33485	−	1.33485i	0.433884	−	0.900969i	$-0.357143\pi$
$853$	1.33485	−	1.33485i	1.33485	−	1.33485i	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	$-0.452381\pi$
$857$	−0.781831	−	0.623490i	−0.781831	−	0.623490i	−0.930874	+	0.365341i	$0.880952\pi$
$858$		0			0
$859$	−0.205245	−	1.82160i	−0.205245	−	1.82160i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	−0.205245	−	1.82160i	−0.205245	−	1.82160i	0.294755	−	0.955573i	$-0.404762\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.826239	−	0.563320i	$-0.190476\pi$
$863$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$864$	−5.91374	−	0.666318i	−5.91374	−	0.666318i
$865$		0			0
$866$		0			0
$867$	−0.149042	+	0.988831i	−0.149042	+	0.988831i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−2.96096	+	3.44070i	−2.96096	+	3.44070i
$877$	0.781831	+	0.376510i	0.781831	+	0.376510i	0.781831	−	0.623490i	$-0.214286\pi$
$877$	0.781831	+	0.376510i	0.781831	+	0.376510i			1.00000i	$0.5\pi$
$878$	0.416608	−	3.69749i	0.416608	−	3.69749i
$879$		0			0
$880$		0			0
$881$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$881$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$882$	0.371563	−	1.96376i	0.371563	−	1.96376i
$883$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.974928	+	0.222521i	$0.0714286\pi$
$883$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.433884	+	0.900969i	$0.357143\pi$
$884$		0			0
$885$		0			0
$886$	−1.62564	+	2.03849i	−1.62564	+	2.03849i
$887$	0.839789	−	0.839789i	0.839789	−	0.839789i	−0.149042	−	0.988831i	$-0.547619\pi$
$887$	0.839789	−	0.839789i	0.839789	−	0.839789i	0.988831	+	0.149042i	$0.0476190\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	1.62011	−	3.36419i	1.62011	−	3.36419i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.733052	+	1.26968i	0.733052	+	1.26968i
$898$			3.38453i			3.38453i
$899$	0.772532	+	1.77066i	0.772532	+	1.77066i
$900$	−1.68681	−	2.47410i	−1.68681	−	2.47410i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−1.18681	−	1.60807i	−1.18681	−	1.60807i
$907$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$907$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$908$		0			0
$909$	−0.488590	−	1.82344i	−0.488590	−	1.82344i
$910$		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	$-0.714286\pi$
$919$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$920$		0			0
$921$	−0.392253	−	0.531484i	−0.392253	−	0.531484i
$922$	−0.715659	+	3.13551i	−0.715659	+	3.13551i
$923$	−0.842614	+	0.192321i	−0.842614	+	0.192321i
$924$		0			0
$925$		0			0
$926$	−0.473222	+	0.753128i	−0.473222	+	0.753128i
$927$		0			0
$928$	−1.54027	+	5.74838i	−1.54027	+	5.74838i
$929$		−	1.46610i		−	1.46610i	−0.680173	−	0.733052i	$-0.738095\pi$
$929$		−	1.46610i		−	1.46610i	0.680173	−	0.733052i	$-0.261905\pi$
$930$		0			0
$931$		0			0
$932$	1.97128	−	0.949320i	1.97128	−	0.949320i
$933$	−0.902694	−	0.241876i	−0.902694	−	0.241876i
$934$		0			0
$935$		0			0
$936$	−5.16671	+	2.73068i	−5.16671	+	2.73068i
$937$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$937$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$941$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$942$		0			0
$943$	−0.425511	−	0.677197i	−0.425511	−	0.677197i
$944$	7.00471	+	5.58607i	7.00471	+	5.58607i
$945$		0			0
$946$		0			0
$947$	0.392253	−	1.12099i	0.392253	−	1.12099i	−0.563320	−	0.826239i	$-0.690476\pi$
$947$	0.392253	−	1.12099i	0.392253	−	1.12099i	0.955573	−	0.294755i	$-0.0952381\pi$
$948$		0			0
$949$	−0.248844	+	2.20856i	−0.248844	+	2.20856i
$950$		0			0
$951$	0.694076	−	0.806531i	0.694076	−	0.806531i
$952$		0			0
$953$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$953$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$954$		0			0
$955$		0			0
$956$	5.57483			5.57483
$957$		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
$967$	−0.430874	+	1.23137i	−0.430874	+	1.23137i	0.500000	+	0.866025i	$0.333333\pi$
$967$	−0.430874	+	1.23137i	−0.430874	+	1.23137i	−0.930874	+	0.365341i	$0.880952\pi$
$968$	0.446293	+	3.96096i	0.446293	+	3.96096i
$969$		0			0
$970$		0			0
$971$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$971$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$972$	0.882617	−	2.86137i	0.882617	−	2.86137i
$973$		0			0
$974$	0.421260	−	0.421260i	0.421260	−	0.421260i
$975$	−1.36476	−	0.535628i	−1.36476	−	0.535628i
$976$		0			0
$977$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$977$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$978$	0.418618	−	0.614000i	0.418618	−	0.614000i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	3.30087	−	1.58961i	3.30087	−	1.58961i
$983$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$983$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$984$	2.76085	−	1.59398i	2.76085	−	1.59398i
$985$		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	−0.900969	−	0.433884i	$-0.857143\pi$
$991$	−1.52446	+	0.347948i	−1.52446	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$992$	2.55827	−	11.2085i	2.55827	−	11.2085i
$993$	1.29476	−	0.955573i	1.29476	−	0.955573i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.68280	+	0.189606i	−1.68280	+	0.189606i	−0.900969	−	0.433884i	$-0.857143\pi$
$997$	−1.68280	+	0.189606i	−1.68280	+	0.189606i	−0.781831	+	0.623490i	$0.785714\pi$
$998$	2.33532	+	2.33532i	2.33532	+	2.33532i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.c.896.1	✓	24
3.2	odd	2		2001.1.bf.d.896.2	yes	24
23.22	odd	2	CM	2001.1.bf.c.896.1	✓	24
29.19	odd	28		2001.1.bf.d.1034.2	yes	24
69.68	even	2		2001.1.bf.d.896.2	yes	24
87.77	even	28	inner	2001.1.bf.c.1034.1	yes	24
667.367	even	28		2001.1.bf.d.1034.2	yes	24
2001.1034	odd	28	inner	2001.1.bf.c.1034.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.896.1	✓	24	1.1	even	1	trivial
2001.1.bf.c.896.1	✓	24	23.22	odd	2	CM
2001.1.bf.c.1034.1	yes	24	87.77	even	28	inner
2001.1.bf.c.1034.1	yes	24	2001.1034	odd	28	inner
2001.1.bf.d.896.2	yes	24	3.2	odd	2
2001.1.bf.d.896.2	yes	24	69.68	even	2
2001.1.bf.d.1034.2	yes	24	29.19	odd	28
2001.1.bf.d.1034.2	yes	24	667.367	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)

\(f(q)\)	\(=\)	\(q+(-1.69226 - 1.06332i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(1.29922 + 2.69787i) q^{4} +(1.51488 + 1.30366i) q^{6} +(0.446293 - 3.96096i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})\)	\(q+(-1.69226 - 1.06332i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(1.29922 + 2.69787i) q^{4} +(1.51488 + 1.30366i) q^{6} +(0.446293 - 3.96096i) q^{8} +(0.955573 + 0.294755i) q^{9} +(-0.882617 - 2.86137i) q^{12} +(-1.14625 - 0.914101i) q^{13} +(-3.10003 + 3.88732i) q^{16} +(-1.30366 - 1.51488i) q^{18} +(0.974928 + 0.222521i) q^{23} +(-1.03166 + 3.85021i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(0.967770 + 2.76573i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-0.563320 + 0.826239i) q^{29} +(1.02781 - 1.63575i) q^{31} +(5.61720 - 1.96554i) q^{32} +(0.446293 + 2.96096i) q^{36} +(0.997204 + 1.07473i) q^{39} +(-0.565533 - 0.565533i) q^{41} +(-1.41322 - 1.41322i) q^{46} +(-0.369485 + 0.0416310i) q^{47} +(3.64478 - 3.38187i) q^{48} +(0.623490 + 0.781831i) q^{49} +(1.98603 + 0.223772i) q^{50} +(0.976892 - 4.28004i) q^{52} +(1.06332 + 1.69226i) q^{54} +(1.83184 - 0.799225i) q^{58} -1.80194i q^{59} +(-3.47864 + 1.67523i) q^{62} +(-6.74838 - 1.54027i) q^{64} +(-0.930874 - 0.365341i) q^{69} +(0.367554 - 0.460898i) q^{71} +(1.59398 - 3.65344i) q^{72} +(-0.806531 - 1.28359i) q^{73} +(0.955573 - 0.294755i) q^{75} +(-0.544750 - 2.87907i) q^{78} +(0.826239 + 0.563320i) q^{81} +(0.355688 + 1.55837i) q^{82} +(0.680173 - 0.733052i) q^{87} +(0.666318 + 2.91933i) q^{92} +(-1.26012 + 1.46429i) q^{93} +(0.669534 + 0.322430i) q^{94} +(-5.84741 + 1.10639i) q^{96} +(-0.223772 - 1.98603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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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