LMFDB - Embedded newform 2001.1.bf.c.1448.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2001.68");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1448.2
Root			$-0.680173 - 0.733052i$ of defining polynomial
Character	$\chi$	$=$	2001.1448
Dual form			2001.1.bf.c.275.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59908 + 0.180173i) q^{2} +(0.826239 - 0.563320i) q^{3} +(1.54966 + 0.353699i) q^{4} +(1.42271 - 0.751927i) q^{6} +(0.895403 + 0.313315i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})$	\(q+(1.59908 + 0.180173i) q^{2} +(0.826239 - 0.563320i) q^{3} +(1.54966 + 0.353699i) q^{4} +(1.42271 - 0.751927i) q^{6} +(0.895403 + 0.313315i) q^{8} +(0.365341 - 0.930874i) q^{9} +(1.47963 - 0.580713i) q^{12} +(-0.858075 + 1.78181i) q^{13} +(-0.0567315 - 0.0273204i) q^{16} +(0.751927 - 1.42271i) q^{18} +(-0.781831 - 0.623490i) q^{23} +(0.916313 - 0.245525i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(-1.69316 + 2.69465i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(0.680173 - 0.733052i) q^{29} +(0.0579571 - 0.514383i) q^{31} +(-0.889030 - 0.558615i) q^{32} +(0.895403 - 1.31332i) q^{36} +(0.294755 + 1.95557i) q^{39} +(-0.922474 - 0.922474i) q^{41} +(-1.13787 - 1.13787i) q^{46} +(-0.0246991 - 0.0705858i) q^{47} +(-0.0622639 + 0.00938477i) q^{48} +(-0.900969 + 0.433884i) q^{49} +(-0.531484 + 1.51889i) q^{50} +(-1.95995 + 2.45770i) q^{52} +(-0.180173 - 1.59908i) q^{54} +(1.21972 - 1.04966i) q^{58} -0.445042i q^{59} +(0.185356 - 0.812096i) q^{62} +(-1.27175 - 1.01419i) q^{64} +(-0.997204 - 0.0747301i) q^{69} +(1.67738 + 0.807782i) q^{71} +(0.618784 - 0.719040i) q^{72} +(0.197979 + 1.75711i) q^{73} +(0.365341 + 0.930874i) q^{75} +(0.118995 + 3.18022i) q^{78} +(-0.733052 - 0.680173i) q^{81} +(-1.30890 - 1.64131i) q^{82} +(0.149042 - 0.988831i) q^{87} +(-0.991043 - 1.24273i) q^{92} +(-0.241876 - 0.457652i) q^{93} +(-0.0267781 - 0.117322i) q^{94} +(-1.04923 + 0.0392594i) q^{96} +(-1.51889 + 0.531484i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{15}{28}\right)$	$-1$	$-1$

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 $

$2$	1.59908	+	0.180173i	1.59908	+	0.180173i	0.866025	−	0.500000i	$-0.166667\pi$
$2$	1.59908	+	0.180173i	1.59908	+	0.180173i	0.733052	+	0.680173i	$0.238095\pi$
$3$	0.826239	−	0.563320i	0.826239	−	0.563320i
$3$	0.826239	−	0.563320i	0.826239	−	0.563320i
$4$	1.54966	+	0.353699i	1.54966	+	0.353699i
$5$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$5$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$6$	1.42271	−	0.751927i	1.42271	−	0.751927i
$7$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$7$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$8$	0.895403	+	0.313315i	0.895403	+	0.313315i
$9$	0.365341	−	0.930874i	0.365341	−	0.930874i
$10$		0			0
$11$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$11$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$12$	1.47963	−	0.580713i	1.47963	−	0.580713i
$13$	−0.858075	+	1.78181i	−0.858075	+	1.78181i	−0.294755	+	0.955573i	$0.595238\pi$
$13$	−0.858075	+	1.78181i	−0.858075	+	1.78181i	−0.563320	+	0.826239i	$0.690476\pi$
$14$		0			0
$15$		0			0
$16$	−0.0567315	−	0.0273204i	−0.0567315	−	0.0273204i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	0.751927	−	1.42271i	0.751927	−	1.42271i
$19$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$19$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$23$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$24$	0.916313	−	0.245525i	0.916313	−	0.245525i
$25$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$26$	−1.69316	+	2.69465i	−1.69316	+	2.69465i
$27$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$28$		0			0
$29$	0.680173	−	0.733052i	0.680173	−	0.733052i
$29$	0.680173	−	0.733052i	0.680173	−	0.733052i
$30$		0			0
$31$	0.0579571	−	0.514383i	0.0579571	−	0.514383i	−0.930874	−	0.365341i	$-0.880952\pi$
$31$	0.0579571	−	0.514383i	0.0579571	−	0.514383i	0.988831	−	0.149042i	$-0.0476190\pi$
$32$	−0.889030	−	0.558615i	−0.889030	−	0.558615i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.895403	−	1.31332i	0.895403	−	1.31332i
$37$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$37$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$38$		0			0
$39$	0.294755	+	1.95557i	0.294755	+	1.95557i
$40$		0			0
$41$	−0.922474	−	0.922474i	−0.922474	−	0.922474i	0.0747301	−	0.997204i	$-0.476190\pi$
$41$	−0.922474	−	0.922474i	−0.922474	−	0.922474i	−0.997204	+	0.0747301i	$0.976190\pi$
$42$		0			0
$43$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$43$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$44$		0			0
$45$		0			0
$46$	−1.13787	−	1.13787i	−1.13787	−	1.13787i
$47$	−0.0246991	−	0.0705858i	−0.0246991	−	0.0705858i	0.930874	−	0.365341i	$-0.119048\pi$
$47$	−0.0246991	−	0.0705858i	−0.0246991	−	0.0705858i	−0.955573	+	0.294755i	$0.904762\pi$
$48$	−0.0622639	+	0.00938477i	−0.0622639	+	0.00938477i
$49$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$50$	−0.531484	+	1.51889i	−0.531484	+	1.51889i
$51$		0			0
$52$	−1.95995	+	2.45770i	−1.95995	+	2.45770i
$53$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$53$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$54$	−0.180173	−	1.59908i	−0.180173	−	1.59908i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.21972	−	1.04966i	1.21972	−	1.04966i
$59$		−	0.445042i		−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$59$		−	0.445042i		−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$60$		0			0
$61$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$61$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$62$	0.185356	−	0.812096i	0.185356	−	0.812096i
$63$		0			0
$64$	−1.27175	−	1.01419i	−1.27175	−	1.01419i
$65$		0			0
$66$		0			0
$67$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$67$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$68$		0			0
$69$	−0.997204	−	0.0747301i	−0.997204	−	0.0747301i
$70$		0			0
$71$	1.67738	+	0.807782i	1.67738	+	0.807782i	0.997204	+	0.0747301i	$0.0238095\pi$
$71$	1.67738	+	0.807782i	1.67738	+	0.807782i	0.680173	+	0.733052i	$0.261905\pi$
$72$	0.618784	−	0.719040i	0.618784	−	0.719040i
$73$	0.197979	+	1.75711i	0.197979	+	1.75711i	0.563320	+	0.826239i	$0.309524\pi$
$73$	0.197979	+	1.75711i	0.197979	+	1.75711i	−0.365341	+	0.930874i	$0.619048\pi$
$74$		0			0
$75$	0.365341	+	0.930874i	0.365341	+	0.930874i
$76$		0			0
$77$		0			0
$78$	0.118995	+	3.18022i	0.118995	+	3.18022i
$79$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$79$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$80$		0			0
$81$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$82$	−1.30890	−	1.64131i	−1.30890	−	1.64131i
$83$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$83$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.149042	−	0.988831i	0.149042	−	0.988831i
$88$		0			0
$89$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$89$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$90$		0			0
$91$		0			0
$92$	−0.991043	−	1.24273i	−0.991043	−	1.24273i
$93$	−0.241876	−	0.457652i	−0.241876	−	0.457652i
$94$	−0.0267781	−	0.117322i	−0.0267781	−	0.117322i
$95$		0			0
$96$	−1.04923	+	0.0392594i	−1.04923	+	0.0392594i
$97$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$97$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$98$	−1.51889	+	0.531484i	−1.51889	+	0.531484i
$99$		0			0
$100$	−0.689663	+	1.43210i	−0.689663	+	1.43210i
$101$	0.189606	+	1.68280i	0.189606	+	1.68280i	0.623490	+	0.781831i	$0.285714\pi$
$101$	0.189606	+	1.68280i	0.189606	+	1.68280i	−0.433884	+	0.900969i	$0.642857\pi$
$102$		0			0
$103$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$103$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$104$	−1.32659	+	1.32659i	−1.32659	+	1.32659i
$105$		0			0
$106$		0			0
$107$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$107$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$108$		−	1.58951i		−	1.58951i
$109$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$109$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$113$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$114$		0			0
$115$		0			0
$116$	1.31332	−	0.895403i	1.31332	−	0.895403i
$117$	1.34515	+	1.44973i	1.34515	+	1.44973i
$118$	0.0801844	−	0.711656i	0.0801844	−	0.711656i
$119$		0			0
$120$		0			0
$121$	0.781831	−	0.623490i	0.781831	−	0.623490i
$122$		0			0
$123$	−1.28183	−	0.242536i	−1.28183	−	0.242536i
$124$	0.271751	−	0.776619i	0.271751	−	0.776619i
$125$		0			0
$126$		0			0
$127$	0.649042	+	1.85486i	0.649042	+	1.85486i	0.500000	+	0.866025i	$0.333333\pi$
$127$	0.649042	+	1.85486i	0.649042	+	1.85486i	0.149042	+	0.988831i	$0.452381\pi$
$128$	−1.10846	−	1.10846i	−1.10846	−	1.10846i
$129$		0			0
$130$		0			0
$131$	−1.18017	+	0.132974i	−1.18017	+	0.132974i	−0.680173	−	0.733052i	$-0.738095\pi$
$131$	−1.18017	+	0.132974i	−1.18017	+	0.132974i	−0.500000	+	0.866025i	$0.666667\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$137$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$138$	−1.58114	−	0.299168i	−1.58114	−	0.299168i
$139$	1.16078	−	1.45557i	1.16078	−	1.45557i	0.294755	−	0.955573i	$-0.404762\pi$
$139$	1.16078	−	1.45557i	1.16078	−	1.45557i	0.866025	−	0.500000i	$-0.166667\pi$
$140$		0			0
$141$	−0.0601697	−	0.0444073i	−0.0601697	−	0.0444073i
$142$	2.53671	+	1.59392i	2.53671	+	1.59392i
$143$		0			0
$144$	−0.0461582	+	0.0428286i	−0.0461582	+	0.0428286i
$145$		0			0
$146$			2.84543i			2.84543i
$147$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$148$		0			0
$149$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$149$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$150$	0.416490	+	1.55436i	0.416490	+	1.55436i
$151$	0.781831	+	0.623490i	0.781831	+	0.623490i	0.930874	−	0.365341i	$-0.119048\pi$
$151$	0.781831	+	0.623490i	0.781831	+	0.623490i	−0.149042	+	0.988831i	$0.547619\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.234915	+	3.13472i	−0.234915	+	3.13472i
$157$		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
$162$	−1.04966	−	1.21972i	−1.04966	−	1.21972i
$163$	0.0705858	−	0.0246991i	0.0705858	−	0.0246991i	−0.294755	−	0.955573i	$-0.595238\pi$
$163$	0.0705858	−	0.0246991i	0.0705858	−	0.0246991i	0.365341	+	0.930874i	$0.380952\pi$
$164$	−1.10324	−	1.75580i	−1.10324	−	1.75580i
$165$		0			0
$166$		0			0
$167$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$167$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$168$		0			0
$169$	−1.81507	−	2.27603i	−1.81507	−	2.27603i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$173$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$174$	0.416490	−	1.55436i	0.416490	−	1.55436i
$175$		0			0
$176$		0			0
$177$	−0.250701	−	0.367711i	−0.250701	−	0.367711i
$178$		0			0
$179$	−1.03030	−	1.29196i	−1.03030	−	1.29196i	−0.955573	−	0.294755i	$-0.904762\pi$
$179$	−1.03030	−	1.29196i	−1.03030	−	1.29196i	−0.0747301	−	0.997204i	$-0.523810\pi$
$180$		0			0
$181$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$181$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$182$		0			0
$183$		0			0
$184$	−0.504706	−	0.803234i	−0.504706	−	0.803234i
$185$		0			0
$186$	−0.304322	−	0.775400i	−0.304322	−	0.775400i
$187$		0			0
$188$	−0.0133089	−	0.118120i	−0.0133089	−	0.118120i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	−1.62208	−	0.121558i	−1.62208	−	0.121558i
$193$	0.791295	−	0.497204i	0.791295	−	0.497204i	−0.0747301	−	0.997204i	$-0.523810\pi$
$193$	0.791295	−	0.497204i	0.791295	−	0.497204i	0.866025	+	0.500000i	$0.166667\pi$
$194$		0			0
$195$		0			0
$196$	−1.54966	+	0.353699i	−1.54966	+	0.353699i
$197$	−1.35417	−	1.07992i	−1.35417	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$197$	−1.35417	−	1.07992i	−1.35417	−	1.07992i	−0.365341	−	0.930874i	$-0.619048\pi$
$198$		0			0
$199$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$199$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$200$	−0.504706	+	0.803234i	−0.504706	+	0.803234i
$201$		0			0
$202$			2.72509i			2.72509i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$208$	0.0973598	−	0.0776418i	0.0973598	−	0.0776418i
$209$		0			0
$210$		0			0
$211$	0.467085	−	1.33485i	0.467085	−	1.33485i	−0.433884	−	0.900969i	$-0.642857\pi$
$211$	0.467085	−	1.33485i	0.467085	−	1.33485i	0.900969	−	0.433884i	$-0.142857\pi$
$212$		0			0
$213$	1.84095	−	0.277479i	1.84095	−	0.277479i
$214$		0			0
$215$		0			0
$216$	0.106214	−	0.942673i	0.106214	−	0.942673i
$217$		0			0
$218$		0			0
$219$	1.15339	+	1.34027i	1.15339	+	1.34027i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$223$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−1.00000			$1.00000\pi$
$224$		0			0
$225$	0.826239	+	0.563320i	0.826239	+	0.563320i
$226$		0			0
$227$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$227$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$228$		0			0
$229$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$229$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$230$		0			0
$231$		0			0
$232$	0.838705	−	0.443269i	0.838705	−	0.443269i
$233$		−	0.149460i		−	0.149460i	−0.997204	−	0.0747301i	$-0.976190\pi$
$233$		−	0.149460i		−	0.149460i	0.997204	−	0.0747301i	$-0.0238095\pi$
$234$	1.88980	+	2.56059i	1.88980	+	2.56059i
$235$		0			0
$236$	0.157411	−	0.689663i	0.157411	−	0.689663i
$237$		0			0
$238$		0			0
$239$	1.94440	−	0.443797i	1.94440	−	0.443797i	0.955573	−	0.294755i	$-0.0952381\pi$
$239$	1.94440	−	0.443797i	1.94440	−	0.443797i	0.988831	−	0.149042i	$-0.0476190\pi$
$240$		0			0
$241$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$241$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$242$	1.36254	−	0.856144i	1.36254	−	0.856144i
$243$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$244$		0			0
$245$		0			0
$246$	−2.00605	−	0.618784i	−2.00605	−	0.618784i
$247$		0			0
$248$	0.213059	−	0.442422i	0.213059	−	0.442422i
$249$		0			0
$250$		0			0
$251$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$251$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$252$		0			0
$253$		0			0
$254$	0.703674	+	3.08300i	0.703674	+	3.08300i
$255$		0			0
$256$	−0.558615	−	0.700480i	−0.558615	−	0.700480i
$257$	−1.32624	−	0.302705i	−1.32624	−	0.302705i	−0.500000	−	0.866025i	$-0.666667\pi$
$257$	−1.32624	−	0.302705i	−1.32624	−	0.302705i	−0.826239	+	0.563320i	$0.809524\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$262$	−1.91115			−1.91115
$263$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$263$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.85486	+	0.649042i	1.85486	+	0.649042i	0.988831	+	0.149042i	$0.0476190\pi$
$269$	1.85486	+	0.649042i	1.85486	+	0.649042i	0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	1.05737	+	1.68280i	1.05737	+	1.68280i	0.623490	+	0.781831i	$0.285714\pi$
$271$	1.05737	+	1.68280i	1.05737	+	1.68280i	0.433884	+	0.900969i	$0.357143\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.51889	−	0.468516i	−1.51889	−	0.468516i
$277$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$277$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$278$	2.11843	−	2.11843i	2.11843	−	2.11843i
$279$	−0.457652	−	0.241876i	−0.457652	−	0.241876i
$280$		0			0
$281$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$281$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$282$	−0.0882151	−	0.0818516i	−0.0882151	−	0.0818516i
$283$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$283$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$284$	2.31365	+	1.84507i	2.31365	+	1.84507i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.844799	+	0.623490i	−0.844799	+	0.623490i
$289$		−	1.00000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	−0.314690	+	2.79295i	−0.314690	+	2.79295i
$293$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$293$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$294$	−0.955573	+	1.29476i	−0.955573	+	1.29476i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.78181	−	0.858075i	1.78181	−	0.858075i
$300$	0.236904	+	1.57176i	0.236904	+	1.57176i
$301$		0			0
$302$	1.13787	+	1.13787i	1.13787	+	1.13787i
$303$	1.10462	+	1.28359i	1.10462	+	1.28359i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−0.752407	−	0.752407i	−0.752407	−	0.752407i	0.222521	−	0.974928i	$-0.428571\pi$
$307$	−0.752407	−	0.752407i	−0.752407	−	0.752407i	−0.974928	+	0.222521i	$0.928571\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.605443	+	1.73026i	−0.605443	+	1.73026i	0.0747301	+	0.997204i	$0.476190\pi$
$311$	−0.605443	+	1.73026i	−0.605443	+	1.73026i	−0.680173	+	0.733052i	$0.738095\pi$
$312$	−0.348786	+	1.84338i	−0.348786	+	1.84338i
$313$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$313$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.0250721	+	0.222521i	−0.0250721	+	0.222521i	0.974928	+	0.222521i	$0.0714286\pi$
$317$	−0.0250721	+	0.222521i	−0.0250721	+	0.222521i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.895403	−	1.31332i	−0.895403	−	1.31332i
$325$	−1.54620	−	1.23305i	−1.54620	−	1.23305i
$326$	0.117322	−	0.0267781i	0.117322	−	0.0267781i
$327$		0			0
$328$	−0.536961	−	1.11501i	−0.536961	−	1.11501i
$329$		0			0
$330$		0			0
$331$	0.262919	−	0.262919i	0.262919	−	0.262919i	−0.563320	−	0.826239i	$-0.690476\pi$
$331$	0.262919	−	0.262919i	0.262919	−	0.262919i	0.826239	+	0.563320i	$0.190476\pi$
$332$		0			0
$333$		0			0
$334$	−0.224672	−	1.99402i	−0.224672	−	1.99402i
$335$		0			0
$336$		0			0
$337$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$337$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$338$	−2.49236	−	3.96657i	−2.49236	−	3.96657i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	2.88144	+	0.324660i	2.88144	+	0.324660i
$347$	0.867767			0.867767			0.433884	−	0.900969i	$-0.357143\pi$
$347$	0.867767			0.867767			0.433884	+	0.900969i	$0.357143\pi$
$348$	0.580713	−	1.47963i	0.580713	−	1.47963i
$349$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$349$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$350$		0			0
$351$	1.92808	+	0.440071i	1.92808	+	0.440071i
$352$		0			0
$353$	0.702449	+	0.880843i	0.702449	+	0.880843i	0.997204	−	0.0747301i	$-0.0238095\pi$
$353$	0.702449	+	0.880843i	0.702449	+	0.880843i	−0.294755	+	0.955573i	$0.595238\pi$
$354$	−0.334639	−	0.633168i	−0.334639	−	0.633168i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.41476	−	2.25157i	−1.41476	−	2.25157i
$359$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$359$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$360$		0			0
$361$	0.433884	−	0.900969i	0.433884	−	0.900969i
$362$		0			0
$363$	0.294755	−	0.955573i	0.294755	−	0.955573i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$367$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$368$	0.0273204	+	0.0567315i	0.0273204	+	0.0567315i
$369$	−1.19572	+	0.521689i	−1.19572	+	0.521689i
$370$		0			0
$371$		0			0
$372$	−0.212954	−	0.794755i	−0.212954	−	0.794755i
$373$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$373$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$374$		0			0
$375$		0			0
$376$		−	0.0709414i		−	0.0709414i
$377$	0.722521	+	1.84095i	0.722521	+	1.84095i
$378$		0			0
$379$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$379$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$380$		0			0
$381$	1.58114	+	1.16694i	1.58114	+	1.16694i
$382$		0			0
$383$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$383$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$384$	−1.54027	−	0.291435i	−1.54027	−	0.291435i
$385$		0			0
$386$	1.35492	−	0.652497i	1.35492	−	0.652497i
$387$		0			0
$388$		0			0
$389$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$389$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$390$		0			0
$391$		0			0
$392$	−0.942673	+	0.106214i	−0.942673	+	0.106214i
$393$	−0.900198	+	0.774683i	−0.900198	+	0.774683i
$394$	−1.97085	−	1.97085i	−1.97085	−	1.97085i
$395$		0			0
$396$		0			0
$397$	−1.79690	+	0.865341i	−1.79690	+	0.865341i	−0.866025	+	0.500000i	$0.833333\pi$
$397$	−1.79690	+	0.865341i	−1.79690	+	0.865341i	−0.930874	+	0.365341i	$0.880952\pi$
$398$		0			0
$399$		0			0
$400$	0.0392594	−	0.0492297i	0.0392594	−	0.0492297i
$401$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$401$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$402$		0			0
$403$	0.866803	+	0.544648i	0.866803	+	0.544648i
$404$	−0.301381	+	2.67483i	−0.301381	+	2.67483i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.694076	+	1.10462i	−0.694076	+	1.10462i	0.294755	+	0.955573i	$0.404762\pi$
$409$	−0.694076	+	1.10462i	−0.694076	+	1.10462i	−0.988831	+	0.149042i	$0.952381\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−1.47493	+	0.643504i	−1.47493	+	0.643504i
$415$		0			0
$416$	1.75820	−	1.10475i	1.75820	−	1.10475i
$417$	0.139129	−	1.85654i	0.139129	−	1.85654i
$418$		0			0
$419$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$419$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$420$		0			0
$421$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$421$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$422$	0.987409	−	2.05038i	0.987409	−	2.05038i
$423$	−0.0747301	−	0.00279620i	−0.0747301	−	0.00279620i
$424$		0			0
$425$		0			0
$426$	2.99382	−	0.112021i	2.99382	−	0.112021i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$431$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$432$	−0.0140115	+	0.0613885i	−0.0140115	+	0.0613885i
$433$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$433$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.60289	+	2.35100i	1.60289	+	2.35100i
$439$	1.94440	+	0.443797i	1.94440	+	0.443797i	0.988831	+	0.149042i	$0.0476190\pi$
$439$	1.94440	+	0.443797i	1.94440	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$440$		0			0
$441$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$442$		0			0
$443$	−0.882094	−	0.308658i	−0.882094	−	0.308658i	−0.149042	−	0.988831i	$-0.547619\pi$
$443$	−0.882094	−	0.308658i	−0.882094	−	0.308658i	−0.733052	+	0.680173i	$0.761905\pi$
$444$		0			0
$445$		0			0
$446$	−2.73695	+	0.957700i	−2.73695	+	0.957700i
$447$		0			0
$448$		0			0
$449$	−0.222521	−	1.97493i	−0.222521	−	1.97493i	−0.222521	−	0.974928i	$-0.571429\pi$
$449$	−0.222521	−	1.97493i	−0.222521	−	1.97493i		−	1.00000i	$-0.5\pi$
$450$	1.21972	+	1.04966i	1.21972	+	1.04966i
$451$		0			0
$452$		0			0
$453$	0.997204	+	0.0747301i	0.997204	+	0.0747301i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$457$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.197822	+	0.314832i	−0.197822	+	0.314832i	−0.930874	−	0.365341i	$-0.880952\pi$
$461$	−0.197822	+	0.314832i	−0.197822	+	0.314832i	0.733052	+	0.680173i	$0.238095\pi$
$462$		0			0
$463$			1.24698i			1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$463$			1.24698i			1.24698i	−0.781831	+	0.623490i	$0.785714\pi$
$464$	−0.0586145	+	0.0230045i	−0.0586145	+	0.0230045i
$465$		0			0
$466$	0.0269287	−	0.238998i	0.0269287	−	0.238998i
$467$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$467$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$468$	1.57176	+	2.72236i	1.57176	+	2.72236i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.139438	−	0.398492i	0.139438	−	0.398492i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	3.18921	−	0.359338i	3.18921	−	0.359338i
$479$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$479$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.43210	−	0.689663i	1.43210	−	0.689663i
$485$		0			0
$486$	−1.55436	−	0.416490i	−1.55436	−	0.416490i
$487$	0.702449	−	0.880843i	0.702449	−	0.880843i	−0.294755	−	0.955573i	$-0.595238\pi$
$487$	0.702449	−	0.880843i	0.702449	−	0.880843i	0.997204	+	0.0747301i	$0.0238095\pi$
$488$		0			0
$489$	0.0444073	−	0.0601697i	0.0444073	−	0.0601697i
$490$		0			0
$491$	0.169732	−	1.50641i	0.169732	−	1.50641i	−0.563320	−	0.826239i	$-0.690476\pi$
$491$	0.169732	−	1.50641i	0.169732	−	1.50641i	0.733052	−	0.680173i	$-0.238095\pi$
$492$	−1.90062	−	0.829230i	−1.90062	−	0.829230i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.0173412	+	0.0275983i	−0.0173412	+	0.0275983i
$497$		0			0
$498$		0			0
$499$	−1.14625	−	0.914101i	−1.14625	−	0.914101i	−0.149042	−	0.988831i	$-0.547619\pi$
$499$	−1.14625	−	0.914101i	−1.14625	−	0.914101i	−0.997204	+	0.0747301i	$0.976190\pi$
$500$		0			0
$501$	−0.914101	−	0.848162i	−0.914101	−	0.848162i
$502$		0			0
$503$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$503$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.78181	−	0.858075i	−2.78181	−	0.858075i
$508$	0.349732	+	3.10396i	0.349732	+	3.10396i
$509$	0.255779	−	0.531130i	0.255779	−	0.531130i	−0.733052	−	0.680173i	$-0.761905\pi$
$509$	0.255779	−	0.531130i	0.255779	−	0.531130i	0.988831	+	0.149042i	$0.0476190\pi$
$510$		0			0
$511$		0			0
$512$	0.0669543	+	0.106557i	0.0669543	+	0.106557i
$513$		0			0
$514$	−2.06622	−	0.723001i	−2.06622	−	0.723001i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.48883	−	1.01507i	1.48883	−	1.01507i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.531484	−	1.51889i	−0.531484	−	1.51889i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	−1.87590	−	0.211363i	−1.87590	−	0.211363i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.222521	+	0.974928i	0.222521	+	0.974928i
$530$		0			0
$531$	−0.414278	−	0.162592i	−0.414278	−	0.162592i
$532$		0			0
$533$	2.43523	−	0.852122i	2.43523	−	0.852122i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.57906	−	0.487076i	−1.57906	−	0.487076i
$538$	2.84912	+	1.37206i	2.84912	+	1.37206i
$539$		0			0
$540$		0			0
$541$	−1.69226	+	1.06332i	−1.69226	+	1.06332i	−0.826239	+	0.563320i	$0.809524\pi$
$541$	−1.69226	+	1.06332i	−1.69226	+	1.06332i	−0.866025	+	0.500000i	$0.833333\pi$
$542$	1.38763	+	2.88144i	1.38763	+	2.88144i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.0332580	−	0.145713i	0.0332580	−	0.145713i	−0.955573	−	0.294755i	$-0.904762\pi$
$547$	0.0332580	−	0.145713i	0.0332580	−	0.145713i	0.988831	+	0.149042i	$0.0476190\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−0.869485	−	0.379353i	−0.869485	−	0.379353i
$553$		0			0
$554$	−0.995587	−	0.625569i	−0.995587	−	0.625569i
$555$		0			0
$556$	2.31365	−	1.84507i	2.31365	−	1.84507i
$557$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$557$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$558$	−0.688241	−	0.469235i	−0.688241	−	0.469235i
$559$		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	$0.250000\pi$
$564$	−0.0775357	−	0.0900981i	−0.0775357	−	0.0900981i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	1.24884	+	1.24884i	1.24884	+	1.24884i
$569$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$569$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$570$		0			0
$571$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$571$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.781831	−	0.623490i	0.781831	−	0.623490i
$576$	−1.40870	+	0.813315i	−1.40870	+	0.813315i
$577$	0.314832	+	0.197822i	0.314832	+	0.197822i	0.680173	−	0.733052i	$-0.261905\pi$
$577$	0.314832	+	0.197822i	0.314832	+	0.197822i	−0.365341	+	0.930874i	$0.619048\pi$
$578$	0.180173	−	1.59908i	0.180173	−	1.59908i
$579$	0.373714	−	0.856562i	0.373714	−	0.856562i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.373259	+	1.63535i	−0.373259	+	1.63535i
$585$		0			0
$586$		0			0
$587$	1.09839	−	0.250701i	1.09839	−	0.250701i	0.365341	−	0.930874i	$-0.380952\pi$
$587$	1.09839	−	0.250701i	1.09839	−	0.250701i	0.733052	+	0.680173i	$0.238095\pi$
$588$	−1.08114	+	1.16519i	−1.08114	+	1.16519i
$589$		0			0
$590$		0			0
$591$	−1.72721	−	0.129436i	−1.72721	−	0.129436i
$592$		0			0
$593$	0.781831	+	0.376510i	0.781831	+	0.376510i	0.781831	−	0.623490i	$-0.214286\pi$
$593$	0.781831	+	0.376510i	0.781831	+	0.376510i			1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	3.00386	−	1.05109i	3.00386	−	1.05109i
$599$	−1.05737	−	1.68280i	−1.05737	−	1.68280i	−0.623490	−	0.781831i	$-0.714286\pi$
$599$	−1.05737	−	1.68280i	−1.05737	−	1.68280i	−0.433884	−	0.900969i	$-0.642857\pi$
$600$	0.0354707	+	0.947974i	0.0354707	+	0.947974i
$601$	−1.82344	−	0.638050i	−1.82344	−	0.638050i	−0.997204	−	0.0747301i	$-0.976190\pi$
$601$	−1.82344	−	0.638050i	−1.82344	−	0.638050i	−0.826239	−	0.563320i	$-0.809524\pi$
$602$		0			0
$603$		0			0
$604$	0.991043	+	1.24273i	0.991043	+	1.24273i
$605$		0			0
$606$	1.53510	+	2.25157i	1.53510	+	2.25157i
$607$	1.87590	+	0.211363i	1.87590	+	0.211363i	0.974928	−	0.222521i	$-0.0714286\pi$
$607$	1.87590	+	0.211363i	1.87590	+	0.211363i	0.900969	+	0.433884i	$0.142857\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.146964	+	0.0165589i	0.146964	+	0.0165589i
$612$		0			0
$613$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$613$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$614$	−1.06759	−	1.33872i	−1.06759	−	1.33872i
$615$		0			0
$616$		0			0
$617$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$617$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$618$		0			0
$619$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$619$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$620$		0			0
$621$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$622$	−1.27989	+	2.65773i	−1.27989	+	2.65773i
$623$		0			0
$624$	0.0367052	−	0.118995i	0.0367052	−	0.118995i
$625$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$631$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$632$		0			0
$633$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$634$	−0.0801844	+	0.351311i	−0.0801844	+	0.351311i
$635$		0			0
$636$		0			0
$637$		−	1.97766i		−	1.97766i
$638$		0			0
$639$	1.36476	−	1.26631i	1.36476	−	1.26631i
$640$		0			0
$641$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$641$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$642$		0			0
$643$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$643$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	−0.680173	−	0.733052i	$-0.738095\pi$
$647$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	0.149042	+	0.988831i	$0.452381\pi$
$648$	−0.443269	−	0.838705i	−0.443269	−	0.838705i
$649$		0			0
$650$	−2.25033	−	2.25033i	−2.25033	−	2.25033i
$651$		0			0
$652$	0.118120	−	0.0133089i	0.118120	−	0.0133089i
$653$	−1.91970	+	0.216299i	−1.91970	+	0.216299i	−0.988831	−	0.149042i	$-0.952381\pi$
$653$	−1.91970	+	0.216299i	−1.91970	+	0.216299i	−0.930874	+	0.365341i	$0.880952\pi$
$654$		0			0
$655$		0			0
$656$	0.0271309	+	0.0775357i	0.0271309	+	0.0775357i
$657$	1.70798	+	0.457652i	1.70798	+	0.457652i
$658$		0			0
$659$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$659$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$660$		0			0
$661$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$661$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$662$	0.467798	−	0.373057i	0.467798	−	0.373057i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$668$		−	1.98209i		−	1.98209i
$669$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.880843	+	0.702449i	0.880843	+	0.702449i	0.955573	−	0.294755i	$-0.0952381\pi$
$673$	0.880843	+	0.702449i	0.880843	+	0.702449i	−0.0747301	+	0.997204i	$0.523810\pi$
$674$		0			0
$675$	1.00000			1.00000
$676$	−2.00771	−	4.16905i	−2.00771	−	4.16905i
$677$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$677$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.590232	+	1.22563i	−0.590232	+	1.22563i	0.365341	+	0.930874i	$0.380952\pi$
$683$	−0.590232	+	1.22563i	−0.590232	+	1.22563i	−0.955573	+	0.294755i	$0.904762\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.974928	+	1.22252i	0.974928	+	1.22252i	0.974928	+	0.222521i	$0.0714286\pi$
$691$	0.974928	+	1.22252i	0.974928	+	1.22252i			1.00000i	$0.5\pi$
$692$	2.79239	+	0.637344i	2.79239	+	0.637344i
$693$		0			0
$694$	1.38763	+	0.156348i	1.38763	+	0.156348i
$695$		0			0
$696$	0.443269	−	0.838705i	0.443269	−	0.838705i
$697$		0			0
$698$	−2.34441	−	0.264152i	−2.34441	−	0.264152i
$699$	−0.0841939	−	0.123490i	−0.0841939	−	0.123490i
$700$		0			0
$701$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$701$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$702$	3.00386	+	1.05109i	3.00386	+	1.05109i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.964566	+	1.53510i	0.964566	+	1.53510i
$707$		0			0
$708$	−0.258442	−	0.658499i	−0.258442	−	0.658499i
$709$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$709$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$714$		0			0
$715$		0			0
$716$	−1.13965	−	2.36651i	−1.13965	−	2.36651i
$717$	1.35654	−	1.46200i	1.35654	−	1.46200i
$718$		0			0
$719$	1.22252	+	0.974928i	1.22252	+	0.974928i	1.00000			$0$
$719$	1.22252	+	0.974928i	1.22252	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$720$		0			0
$721$		0			0
$722$	0.856144	−	1.36254i	0.856144	−	1.36254i
$723$		0			0
$724$		0			0
$725$	0.563320	+	0.826239i	0.563320	+	0.826239i
$726$	0.643504	−	1.47493i	0.643504	−	1.47493i
$727$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$727$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$728$		0			0
$729$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$733$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$734$		0			0
$735$		0			0
$736$	0.346781	+	0.991043i	0.346781	+	0.991043i
$737$		0			0
$738$	−2.00605	+	0.618784i	−2.00605	+	0.618784i
$739$	1.29637	−	0.146066i	1.29637	−	0.146066i	0.563320	−	0.826239i	$-0.309524\pi$
$739$	1.29637	−	0.146066i	1.29637	−	0.146066i	0.733052	+	0.680173i	$0.238095\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$743$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$744$	−0.0731873	−	0.485566i	−0.0731873	−	0.485566i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$751$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$752$	−0.000527223		0.00467923i	−0.000527223		0.00467923i
$753$		0			0
$754$	0.823677	+	3.07401i	0.823677	+	3.07401i
$755$		0			0
$756$		0			0
$757$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$757$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.712362	+	0.162592i	−0.712362	+	0.162592i	−0.563320	−	0.826239i	$-0.690476\pi$
$761$	−0.712362	+	0.162592i	−0.712362	+	0.162592i	−0.149042	+	0.988831i	$0.547619\pi$
$762$	2.31812	+	2.15090i	2.31812	+	2.15090i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.792981	+	0.381879i	0.792981	+	0.381879i
$768$	−0.856144	−	0.264085i	−0.856144	−	0.264085i
$769$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$769$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$770$		0			0
$771$	−1.26631	+	0.496990i	−1.26631	+	0.496990i
$772$	1.40210	−	0.490615i	1.40210	−	0.490615i
$773$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$773$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$774$		0			0
$775$	0.488590	+	0.170965i	0.488590	+	0.170965i
$776$		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
$784$	0.0629672			0.0629672
$785$		0			0
$786$	−1.57906	+	1.07659i	−1.57906	+	1.07659i
$787$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$787$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$788$	−1.71654	−	2.15247i	−1.71654	−	2.15247i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−3.02929	+	1.05999i	−3.02929	+	1.05999i
$795$		0			0
$796$		0			0
$797$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$797$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$798$		0			0
$799$		0			0
$800$	0.742437	−	0.742437i	0.742437	−	0.742437i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	1.28795	+	1.02711i	1.28795	+	1.02711i
$807$	1.89817	−	0.508614i	1.89817	−	0.508614i
$808$	−0.357473	+	1.56619i	−0.357473	+	1.56619i
$809$	−1.00435	+	1.59842i	−1.00435	+	1.59842i	−0.222521	+	0.974928i	$0.571429\pi$
$809$	−1.00435	+	1.59842i	−1.00435	+	1.59842i	−0.781831	+	0.623490i	$0.785714\pi$
$810$		0			0
$811$			1.73205i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$811$			1.73205i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$812$		0			0
$813$	1.82160	+	0.794755i	1.82160	+	0.794755i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−1.30890	+	1.64131i	−1.30890	+	1.64131i
$819$		0			0
$820$		0			0
$821$	−1.75676	+	0.846011i	−1.75676	+	0.846011i	−0.781831	+	0.623490i	$0.785714\pi$
$821$	−1.75676	+	0.846011i	−1.75676	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$822$		0			0
$823$	−0.500684	−	1.43087i	−0.500684	−	1.43087i	−0.866025	−	0.500000i	$-0.833333\pi$
$823$	−0.500684	−	1.43087i	−0.500684	−	1.43087i	0.365341	−	0.930874i	$-0.380952\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$827$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$828$	−1.51889	+	0.468516i	−1.51889	+	0.468516i
$829$	−0.158342	−	0.158342i	−0.158342	−	0.158342i	0.623490	−	0.781831i	$-0.285714\pi$
$829$	−0.158342	−	0.158342i	−0.158342	−	0.158342i	−0.781831	+	0.623490i	$0.785714\pi$
$830$		0			0
$831$	−0.722521	+	0.108903i	−0.722521	+	0.108903i
$832$	2.89835	−	1.39577i	2.89835	−	1.39577i
$833$		0			0
$834$	0.556976	−	2.94369i	0.556976	−	2.94369i
$835$		0			0
$836$		0			0
$837$	−0.514383	+	0.0579571i	−0.514383	+	0.0579571i
$838$		0			0
$839$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$839$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$840$		0			0
$841$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$842$		0			0
$843$		0			0
$844$	1.19596	−	1.90336i	1.19596	−	1.90336i
$845$		0			0
$846$	−0.118995	−	0.0179357i	−0.118995	−	0.0179357i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	2.95099	+	0.221146i	2.95099	+	0.221146i
$853$	1.19745	−	1.19745i	1.19745	−	1.19745i	0.222521	−	0.974928i	$-0.428571\pi$
$853$	1.19745	−	1.19745i	1.19745	−	1.19745i	0.974928	−	0.222521i	$-0.0714286\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.433884	+	0.900969i	−0.433884	+	0.900969i	0.563320	+	0.826239i	$0.309524\pi$
$857$	−0.433884	+	0.900969i	−0.433884	+	0.900969i	−0.997204	+	0.0747301i	$0.976190\pi$
$858$		0			0
$859$	−1.43087	+	0.500684i	−1.43087	+	0.500684i	−0.930874	−	0.365341i	$-0.880952\pi$
$859$	−1.43087	+	0.500684i	−1.43087	+	0.500684i	−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.222521	+	0.974928i	0.222521	+	0.974928i	0.955573	+	0.294755i	$0.0952381\pi$
$863$	0.222521	+	0.974928i	0.222521	+	0.974928i	−0.733052	+	0.680173i	$0.761905\pi$
$864$	−0.346781	+	0.991043i	−0.346781	+	0.991043i
$865$		0			0
$866$		0			0
$867$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	1.31332	+	2.48491i	1.31332	+	2.48491i
$877$	0.433884	+	1.90097i	0.433884	+	1.90097i	0.433884	+	0.900969i	$0.357143\pi$
$877$	0.433884	+	1.90097i	0.433884	+	1.90097i			1.00000i	$0.500000\pi$
$878$	3.02929	+	1.05999i	3.02929	+	1.05999i
$879$		0			0
$880$		0			0
$881$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$881$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$882$	−0.0601697	+	1.60807i	−0.0601697	+	1.60807i
$883$	0.193096	−	0.400969i	0.193096	−	0.400969i	−0.781831	−	0.623490i	$-0.785714\pi$
$883$	0.193096	−	0.400969i	0.193096	−	0.400969i	0.974928	+	0.222521i	$0.0714286\pi$
$884$		0			0
$885$		0			0
$886$	−1.35492	−	0.652497i	−1.35492	−	0.652497i
$887$	−1.38956	+	1.38956i	−1.38956	+	1.38956i	−0.563320	+	0.826239i	$0.690476\pi$
$887$	−1.38956	+	1.38956i	−1.38956	+	1.38956i	−0.826239	+	0.563320i	$0.809524\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−2.79239	+	0.637344i	−2.79239	+	0.637344i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.988831	−	1.71271i	0.988831	−	1.71271i
$898$		−	3.19815i		−	3.19815i
$899$	−0.337649	−	0.392355i	−0.337649	−	0.392355i
$900$	1.08114	+	1.16519i	1.08114	+	1.16519i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	1.58114	+	0.299168i	1.58114	+	0.299168i
$907$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$907$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$908$		0			0
$909$	1.63575	+	0.438297i	1.63575	+	0.438297i
$910$		0			0
$911$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$911$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$919$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$920$		0			0
$921$	−1.04551	−	0.197822i	−1.04551	−	0.197822i
$922$	−0.373057	+	0.467798i	−0.373057	+	0.467798i
$923$	−2.87863	+	2.29563i	−2.87863	+	2.29563i
$924$		0			0
$925$		0			0
$926$	−0.224672	+	1.99402i	−0.224672	+	1.99402i
$927$		0			0
$928$	−1.01419	+	0.271751i	−1.01419	+	0.271751i
$929$		−	1.97766i		−	1.97766i	−0.149042	−	0.988831i	$-0.547619\pi$
$929$		−	1.97766i		−	1.97766i	0.149042	−	0.988831i	$-0.452381\pi$
$930$		0			0
$931$		0			0
$932$	0.0528640	−	0.231612i	0.0528640	−	0.231612i
$933$	0.474448	+	1.77066i	0.474448	+	1.77066i
$934$		0			0
$935$		0			0
$936$	0.750231	+	1.71955i	0.750231	+	1.71955i
$937$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$937$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$941$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$942$		0			0
$943$	0.146066	+	1.29637i	0.146066	+	1.29637i
$944$	−0.0121587	+	0.0252479i	−0.0121587	+	0.0252479i
$945$		0			0
$946$		0			0
$947$	1.04551	+	1.66393i	1.04551	+	1.66393i	0.680173	+	0.733052i	$0.261905\pi$
$947$	1.04551	+	1.66393i	1.04551	+	1.66393i	0.365341	+	0.930874i	$0.380952\pi$
$948$		0			0
$949$	−3.30072	−	1.15497i	−3.30072	−	1.15497i
$950$		0			0
$951$	0.104635	+	0.197979i	0.104635	+	0.197979i
$952$		0			0
$953$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$953$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$954$		0			0
$955$		0			0
$956$	3.17013			3.17013
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.713697	+	0.162897i	0.713697	+	0.162897i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.497204	−	0.791295i	−0.497204	−	0.791295i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	−0.497204	−	0.791295i	−0.497204	−	0.791295i	−0.997204	+	0.0747301i	$0.976190\pi$
$968$	0.895403	−	0.313315i	0.895403	−	0.313315i
$969$		0			0
$970$		0			0
$971$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$971$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$972$	−1.47963	−	0.580713i	−1.47963	−	0.580713i
$973$		0			0
$974$	1.28197	−	1.28197i	1.28197	−	1.28197i
$975$	−1.97213	−	0.147791i	−1.97213	−	0.147791i
$976$		0			0
$977$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$977$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$978$	0.0818516	−	0.0882151i	0.0818516	−	0.0882151i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.542829	−	2.37829i	0.542829	−	2.37829i
$983$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$983$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$984$	−1.07177	−	0.618784i	−1.07177	−	0.618784i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.678448	−	0.541044i	0.678448	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$991$	0.678448	−	0.541044i	0.678448	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$992$	−0.338868	+	0.424926i	−0.338868	+	0.424926i
$993$	0.0691263	−	0.365341i	0.0691263	−	0.365341i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.656405	−	1.87590i	−0.656405	−	1.87590i	−0.433884	−	0.900969i	$-0.642857\pi$
$997$	−0.656405	−	1.87590i	−0.656405	−	1.87590i	−0.222521	−	0.974928i	$-0.571429\pi$
$998$	−1.66824	−	1.66824i	−1.66824	−	1.66824i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.c.1448.2	yes	24
3.2	odd	2		2001.1.bf.d.1448.1	yes	24
23.22	odd	2	CM	2001.1.bf.c.1448.2	yes	24
29.14	odd	28		2001.1.bf.d.275.1	yes	24
69.68	even	2		2001.1.bf.d.1448.1	yes	24
87.14	even	28	inner	2001.1.bf.c.275.2	✓	24
667.275	even	28		2001.1.bf.d.275.1	yes	24
2001.275	odd	28	inner	2001.1.bf.c.275.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.275.2	✓	24	87.14	even	28	inner
2001.1.bf.c.275.2	✓	24	2001.275	odd	28	inner
2001.1.bf.c.1448.2	yes	24	1.1	even	1	trivial
2001.1.bf.c.1448.2	yes	24	23.22	odd	2	CM
2001.1.bf.d.275.1	yes	24	29.14	odd	28
2001.1.bf.d.275.1	yes	24	667.275	even	28
2001.1.bf.d.1448.1	yes	24	3.2	odd	2
2001.1.bf.d.1448.1	yes	24	69.68	even	2

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)

\(f(q)\)	\(=\)	\(q+(1.59908 + 0.180173i) q^{2} +(0.826239 - 0.563320i) q^{3} +(1.54966 + 0.353699i) q^{4} +(1.42271 - 0.751927i) q^{6} +(0.895403 + 0.313315i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})\)	\(q+(1.59908 + 0.180173i) q^{2} +(0.826239 - 0.563320i) q^{3} +(1.54966 + 0.353699i) q^{4} +(1.42271 - 0.751927i) q^{6} +(0.895403 + 0.313315i) q^{8} +(0.365341 - 0.930874i) q^{9} +(1.47963 - 0.580713i) q^{12} +(-0.858075 + 1.78181i) q^{13} +(-0.0567315 - 0.0273204i) q^{16} +(0.751927 - 1.42271i) q^{18} +(-0.781831 - 0.623490i) q^{23} +(0.916313 - 0.245525i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(-1.69316 + 2.69465i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(0.680173 - 0.733052i) q^{29} +(0.0579571 - 0.514383i) q^{31} +(-0.889030 - 0.558615i) q^{32} +(0.895403 - 1.31332i) q^{36} +(0.294755 + 1.95557i) q^{39} +(-0.922474 - 0.922474i) q^{41} +(-1.13787 - 1.13787i) q^{46} +(-0.0246991 - 0.0705858i) q^{47} +(-0.0622639 + 0.00938477i) q^{48} +(-0.900969 + 0.433884i) q^{49} +(-0.531484 + 1.51889i) q^{50} +(-1.95995 + 2.45770i) q^{52} +(-0.180173 - 1.59908i) q^{54} +(1.21972 - 1.04966i) q^{58} -0.445042i q^{59} +(0.185356 - 0.812096i) q^{62} +(-1.27175 - 1.01419i) q^{64} +(-0.997204 - 0.0747301i) q^{69} +(1.67738 + 0.807782i) q^{71} +(0.618784 - 0.719040i) q^{72} +(0.197979 + 1.75711i) q^{73} +(0.365341 + 0.930874i) q^{75} +(0.118995 + 3.18022i) q^{78} +(-0.733052 - 0.680173i) q^{81} +(-1.30890 - 1.64131i) q^{82} +(0.149042 - 0.988831i) q^{87} +(-0.991043 - 1.24273i) q^{92} +(-0.241876 - 0.457652i) q^{93} +(-0.0267781 - 0.117322i) q^{94} +(-1.04923 + 0.0392594i) q^{96} +(-1.51889 + 0.531484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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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