LMFDB - Embedded newform 2001.1.bf.c.275.1

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			275.1
Root			$-0.294755 - 0.955573i$ of defining polynomial
Character	$\chi$	$=$	2001.275
Dual form			2001.1.bf.c.1448.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82160 + 0.205245i) q^{2} +(0.0747301 - 0.997204i) q^{3} +(2.30117 - 0.525226i) q^{4} +(0.0685427 + 1.83184i) q^{6} +(-2.35375 + 0.823611i) q^{8} +(-0.988831 - 0.149042i) q^{9} +O(q^{10})$	\(q+(-1.82160 + 0.205245i) q^{2} +(0.0747301 - 0.997204i) q^{3} +(2.30117 - 0.525226i) q^{4} +(0.0685427 + 1.83184i) q^{6} +(-2.35375 + 0.823611i) q^{8} +(-0.988831 - 0.149042i) q^{9} +(-0.351791 - 2.33398i) q^{12} +(0.317031 + 0.658322i) q^{13} +(1.99194 - 0.959267i) q^{16} +(1.83184 + 0.0685427i) q^{18} +(-0.781831 + 0.623490i) q^{23} +(0.645413 + 2.40871i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.712620 - 1.13413i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(0.294755 - 0.955573i) q^{29} +(-0.216299 - 1.91970i) q^{31} +(-1.32017 + 0.829515i) q^{32} +(-2.35375 + 0.176389i) q^{36} +(0.680173 - 0.266948i) q^{39} +(1.38956 - 1.38956i) q^{41} +(1.29621 - 1.29621i) q^{46} +(0.584010 - 1.66900i) q^{47} +(-0.807727 - 2.05806i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(0.605443 + 1.73026i) q^{50} +(1.07531 + 1.34840i) q^{52} +(0.205245 - 1.82160i) q^{54} +(-0.340799 + 1.80117i) q^{58} +0.445042i q^{59} +(0.788019 + 3.45254i) q^{62} +(0.506019 - 0.403537i) q^{64} +(0.563320 + 0.826239i) q^{69} +(-0.268565 + 0.129334i) q^{71} +(2.45021 - 0.463605i) q^{72} +(-0.00837297 + 0.0743122i) q^{73} +(-0.988831 + 0.149042i) q^{75} +(-1.18421 + 0.625874i) q^{78} +(0.955573 + 0.294755i) q^{81} +(-2.24602 + 2.81642i) q^{82} +(-0.930874 - 0.365341i) q^{87} +(-1.47165 + 1.84539i) q^{92} +(-1.93050 + 0.0722342i) q^{93} +(-0.721277 + 3.16012i) q^{94} +(0.728540 + 1.37846i) q^{96} +(1.73026 + 0.605443i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$-1$	$-1$

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 $

$2$	−1.82160	+	0.205245i	−1.82160	+	0.205245i	−0.955573	−	0.294755i	$-0.904762\pi$
$2$	−1.82160	+	0.205245i	−1.82160	+	0.205245i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$3$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$4$	2.30117	−	0.525226i	2.30117	−	0.525226i
$5$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$5$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$6$	0.0685427	+	1.83184i	0.0685427	+	1.83184i
$7$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$7$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$8$	−2.35375	+	0.823611i	−2.35375	+	0.823611i
$9$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$10$		0			0
$11$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$11$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$12$	−0.351791	−	2.33398i	−0.351791	−	2.33398i
$13$	0.317031	+	0.658322i	0.317031	+	0.658322i	0.997204	−	0.0747301i	$-0.0238095\pi$
$13$	0.317031	+	0.658322i	0.317031	+	0.658322i	−0.680173	+	0.733052i	$0.738095\pi$
$14$		0			0
$15$		0			0
$16$	1.99194	−	0.959267i	1.99194	−	0.959267i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	1.83184	+	0.0685427i	1.83184	+	0.0685427i
$19$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$19$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$20$		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
$24$	0.645413	+	2.40871i	0.645413	+	2.40871i
$25$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$26$	−0.712620	−	1.13413i	−0.712620	−	1.13413i
$27$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$28$		0			0
$29$	0.294755	−	0.955573i	0.294755	−	0.955573i
$29$	0.294755	−	0.955573i	0.294755	−	0.955573i
$30$		0			0
$31$	−0.216299	−	1.91970i	−0.216299	−	1.91970i	−0.365341	−	0.930874i	$-0.619048\pi$
$31$	−0.216299	−	1.91970i	−0.216299	−	1.91970i	0.149042	−	0.988831i	$-0.452381\pi$
$32$	−1.32017	+	0.829515i	−1.32017	+	0.829515i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.35375	+	0.176389i	−2.35375	+	0.176389i
$37$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$37$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$38$		0			0
$39$	0.680173	−	0.266948i	0.680173	−	0.266948i
$40$		0			0
$41$	1.38956	−	1.38956i	1.38956	−	1.38956i	0.563320	−	0.826239i	$-0.309524\pi$
$41$	1.38956	−	1.38956i	1.38956	−	1.38956i	0.826239	−	0.563320i	$-0.190476\pi$
$42$		0			0
$43$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$43$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$44$		0			0
$45$		0			0
$46$	1.29621	−	1.29621i	1.29621	−	1.29621i
$47$	0.584010	−	1.66900i	0.584010	−	1.66900i	−0.149042	−	0.988831i	$-0.547619\pi$
$47$	0.584010	−	1.66900i	0.584010	−	1.66900i	0.733052	−	0.680173i	$-0.238095\pi$
$48$	−0.807727	−	2.05806i	−0.807727	−	2.05806i
$49$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$50$	0.605443	+	1.73026i	0.605443	+	1.73026i
$51$		0			0
$52$	1.07531	+	1.34840i	1.07531	+	1.34840i
$53$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$53$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$54$	0.205245	−	1.82160i	0.205245	−	1.82160i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.340799	+	1.80117i	−0.340799	+	1.80117i
$59$			0.445042i			0.445042i	0.974928	+	0.222521i	$0.0714286\pi$
$59$			0.445042i			0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$60$		0			0
$61$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$61$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$62$	0.788019	+	3.45254i	0.788019	+	3.45254i
$63$		0			0
$64$	0.506019	−	0.403537i	0.506019	−	0.403537i
$65$		0			0
$66$		0			0
$67$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$67$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$68$		0			0
$69$	0.563320	+	0.826239i	0.563320	+	0.826239i
$70$		0			0
$71$	−0.268565	+	0.129334i	−0.268565	+	0.129334i	−0.563320	−	0.826239i	$-0.690476\pi$
$71$	−0.268565	+	0.129334i	−0.268565	+	0.129334i	0.294755	+	0.955573i	$0.404762\pi$
$72$	2.45021	−	0.463605i	2.45021	−	0.463605i
$73$	−0.00837297	+	0.0743122i	−0.00837297	+	0.0743122i	−0.997204	−	0.0747301i	$-0.976190\pi$
$73$	−0.00837297	+	0.0743122i	−0.00837297	+	0.0743122i	0.988831	+	0.149042i	$0.0476190\pi$
$74$		0			0
$75$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$76$		0			0
$77$		0			0
$78$	−1.18421	+	0.625874i	−1.18421	+	0.625874i
$79$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$79$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$80$		0			0
$81$	0.955573	+	0.294755i	0.955573	+	0.294755i
$82$	−2.24602	+	2.81642i	−2.24602	+	2.81642i
$83$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$83$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$88$		0			0
$89$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$89$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$90$		0			0
$91$		0			0
$92$	−1.47165	+	1.84539i	−1.47165	+	1.84539i
$93$	−1.93050	+	0.0722342i	−1.93050	+	0.0722342i
$94$	−0.721277	+	3.16012i	−0.721277	+	3.16012i
$95$		0			0
$96$	0.728540	+	1.37846i	0.728540	+	1.37846i
$97$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$97$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$98$	1.73026	+	0.605443i	1.73026	+	0.605443i
$99$		0			0
$100$	−1.02412	−	2.12660i	−1.02412	−	2.12660i
$101$	0.189606	−	1.68280i	0.189606	−	1.68280i	−0.433884	−	0.900969i	$-0.642857\pi$
$101$	0.189606	−	1.68280i	0.189606	−	1.68280i	0.623490	−	0.781831i	$-0.285714\pi$
$102$		0			0
$103$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$103$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$104$	−1.28841	−	1.28841i	−1.28841	−	1.28841i
$105$		0			0
$106$		0			0
$107$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$107$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$108$			2.36035i			2.36035i
$109$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$109$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$113$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$114$		0			0
$115$		0			0
$116$	0.176389	−	2.35375i	0.176389	−	2.35375i
$117$	−0.215372	−	0.698220i	−0.215372	−	0.698220i
$118$	−0.0913425	−	0.810687i	−0.0913425	−	0.810687i
$119$		0			0
$120$		0			0
$121$	0.781831	+	0.623490i	0.781831	+	0.623490i
$122$		0			0
$123$	−1.28183	−	1.48952i	−1.28183	−	1.48952i
$124$	−1.50602	−	4.30395i	−1.50602	−	4.30395i
$125$		0			0
$126$		0			0
$127$	−0.430874	+	1.23137i	−0.430874	+	1.23137i	0.500000	+	0.866025i	$0.333333\pi$
$127$	−0.430874	+	1.23137i	−0.430874	+	1.23137i	−0.930874	+	0.365341i	$0.880952\pi$
$128$	0.263543	−	0.263543i	0.263543	−	0.263543i
$129$		0			0
$130$		0			0
$131$	−0.794755	−	0.0895474i	−0.794755	−	0.0895474i	−0.294755	−	0.955573i	$-0.595238\pi$
$131$	−0.794755	−	0.0895474i	−0.794755	−	0.0895474i	−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	$-0.607143\pi$
$137$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$138$	−1.19572	−	1.38946i	−1.19572	−	1.38946i
$139$	−0.185853	−	0.233052i	−0.185853	−	0.233052i	0.680173	−	0.733052i	$-0.261905\pi$
$139$	−0.185853	−	0.233052i	−0.185853	−	0.233052i	−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$	−1.62069	−	0.707101i	−1.62069	−	0.707101i
$142$	0.462672	−	0.290716i	0.462672	−	0.290716i
$143$		0			0
$144$	−2.11266	+	0.651670i	−2.11266	+	0.651670i
$145$		0			0
$146$		−	0.137085i		−	0.137085i
$147$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$148$		0			0
$149$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$149$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$150$	1.77066	−	0.474448i	1.77066	−	0.474448i
$151$	0.781831	−	0.623490i	0.781831	−	0.623490i	−0.149042	−	0.988831i	$-0.547619\pi$
$151$	0.781831	−	0.623490i	0.781831	−	0.623490i	0.930874	+	0.365341i	$0.119048\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	1.42498	−	0.971537i	1.42498	−	0.971537i
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.80117	−	0.340799i	−1.80117	−	0.340799i
$163$	−1.66900	−	0.584010i	−1.66900	−	0.584010i	−0.680173	−	0.733052i	$-0.738095\pi$
$163$	−1.66900	−	0.584010i	−1.66900	−	0.584010i	−0.988831	+	0.149042i	$0.952381\pi$
$164$	2.46777	−	3.92744i	2.46777	−	3.92744i
$165$		0			0
$166$		0			0
$167$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$167$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$168$		0			0
$169$	0.290611	−	0.364415i	0.290611	−	0.364415i
$170$		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	$0.142857\pi$
$174$	1.77066	+	0.474448i	1.77066	+	0.474448i
$175$		0			0
$176$		0			0
$177$	0.443797	+	0.0332580i	0.443797	+	0.0332580i
$178$		0			0
$179$	−0.0931869	+	0.116853i	−0.0931869	+	0.116853i	−0.826239	−	0.563320i	$-0.809524\pi$
$179$	−0.0931869	+	0.116853i	−0.0931869	+	0.116853i	0.733052	+	0.680173i	$0.238095\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$		0			0
$183$		0			0
$184$	1.32672	−	2.11146i	1.32672	−	2.11146i
$185$		0			0
$186$	3.50177	−	0.527807i	3.50177	−	0.527807i
$187$		0			0
$188$	0.467299	−	4.14739i	0.467299	−	4.14739i
$189$		0			0
$190$		0			0
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	−0.364593	−	0.534760i	−0.364593	−	0.534760i
$193$	−1.69226	−	1.06332i	−1.69226	−	1.06332i	−0.866025	−	0.500000i	$-0.833333\pi$
$193$	−1.69226	−	1.06332i	−1.69226	−	1.06332i	−0.826239	−	0.563320i	$-0.809524\pi$
$194$		0			0
$195$		0			0
$196$	−2.30117	−	0.525226i	−2.30117	−	0.525226i
$197$	1.35417	−	1.07992i	1.35417	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$197$	1.35417	−	1.07992i	1.35417	−	1.07992i	0.988831	−	0.149042i	$-0.0476190\pi$
$198$		0			0
$199$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$199$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$200$	1.32672	+	2.11146i	1.32672	+	2.11146i
$201$		0			0
$202$			3.10430i			3.10430i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.866025	−	0.500000i	0.866025	−	0.500000i
$208$	1.26301	+	1.00722i	1.26301	+	1.00722i
$209$		0			0
$210$		0			0
$211$	0.467085	+	1.33485i	0.467085	+	1.33485i	0.900969	+	0.433884i	$0.142857\pi$
$211$	0.467085	+	1.33485i	0.467085	+	1.33485i	−0.433884	+	0.900969i	$0.642857\pi$
$212$		0			0
$213$	0.108903	+	0.277479i	0.108903	+	0.277479i
$214$		0			0
$215$		0			0
$216$	−0.279204	−	2.47800i	−0.279204	−	2.47800i
$217$		0			0
$218$		0			0
$219$	0.0734787	+	0.0139029i	0.0734787	+	0.0139029i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$223$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$224$		0			0
$225$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$226$		0			0
$227$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$227$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$228$		0			0
$229$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$229$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$230$		0			0
$231$		0			0
$232$	0.0932418	+	2.49194i	0.0932418	+	2.49194i
$233$			1.65248i			1.65248i	0.563320	+	0.826239i	$0.309524\pi$
$233$			1.65248i			1.65248i	−0.563320	+	0.826239i	$0.690476\pi$
$234$	0.535628	+	1.22767i	0.535628	+	1.22767i
$235$		0			0
$236$	0.233748	+	1.02412i	0.233748	+	1.02412i
$237$		0			0
$238$		0			0
$239$	−1.09839	−	0.250701i	−1.09839	−	0.250701i	−0.365341	−	0.930874i	$-0.619048\pi$
$239$	−1.09839	−	0.250701i	−1.09839	−	0.250701i	−0.733052	+	0.680173i	$0.761905\pi$
$240$		0			0
$241$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$241$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$242$	−1.55215	−	0.975281i	−1.55215	−	0.975281i
$243$	0.365341	−	0.930874i	0.365341	−	0.930874i
$244$		0			0
$245$		0			0
$246$	2.64070	+	2.45021i	2.64070	+	2.45021i
$247$		0			0
$248$	2.09020	+	4.34035i	2.09020	+	4.34035i
$249$		0			0
$250$		0			0
$251$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$251$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$252$		0			0
$253$		0			0
$254$	0.532147	−	2.33149i	0.532147	−	2.33149i
$255$		0			0
$256$	−0.829515	+	1.04018i	−0.829515	+	1.04018i
$257$	−0.574730	+	0.131178i	−0.574730	+	0.131178i	−0.500000	−	0.866025i	$-0.666667\pi$
$257$	−0.574730	+	0.131178i	−0.574730	+	0.131178i	−0.0747301	+	0.997204i	$0.523810\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$262$	1.46610			1.46610
$263$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$263$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.23137	+	0.430874i	−1.23137	+	0.430874i	−0.866025	−	0.500000i	$-0.833333\pi$
$269$	−1.23137	+	0.430874i	−1.23137	+	0.430874i	−0.365341	+	0.930874i	$0.619048\pi$
$270$		0			0
$271$	1.05737	−	1.68280i	1.05737	−	1.68280i	0.433884	−	0.900969i	$-0.357143\pi$
$271$	1.05737	−	1.68280i	1.05737	−	1.68280i	0.623490	−	0.781831i	$-0.285714\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	1.73026	+	1.60544i	1.73026	+	1.60544i
$277$	1.78181	−	0.858075i	1.78181	−	0.858075i	0.826239	−	0.563320i	$-0.190476\pi$
$277$	1.78181	−	0.858075i	1.78181	−	0.858075i	0.955573	−	0.294755i	$-0.0952381\pi$
$278$	0.386382	+	0.386382i	0.386382	+	0.386382i
$279$	−0.0722342	+	1.93050i	−0.0722342	+	1.93050i
$280$		0			0
$281$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$281$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$282$	3.09738	+	0.955416i	3.09738	+	0.955416i
$283$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$283$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$284$	−0.550083	+	0.438676i	−0.550083	+	0.438676i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.42905	−	0.623490i	1.42905	−	0.623490i
$289$			1.00000i			1.00000i
$290$		0			0
$291$		0			0
$292$	0.0197631	+	0.175402i	0.0197631	+	0.175402i
$293$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$293$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$294$	0.733052	−	1.68017i	0.733052	−	1.68017i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.658322	−	0.317031i	−0.658322	−	0.317031i
$300$	−2.19718	+	0.862331i	−2.19718	+	0.862331i
$301$		0			0
$302$	−1.29621	+	1.29621i	−1.29621	+	1.29621i
$303$	−1.66393	−	0.314832i	−1.66393	−	0.314832i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−0.752407	+	0.752407i	−0.752407	+	0.752407i	−0.974928	−	0.222521i	$-0.928571\pi$
$307$	−0.752407	+	0.752407i	−0.752407	+	0.752407i	0.222521	+	0.974928i	$0.428571\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.531484	+	1.51889i	0.531484	+	1.51889i	0.826239	+	0.563320i	$0.190476\pi$
$311$	0.531484	+	1.51889i	0.531484	+	1.51889i	−0.294755	+	0.955573i	$0.595238\pi$
$312$	−1.38109	+	1.18853i	−1.38109	+	1.18853i
$313$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$313$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−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
$324$	2.35375	+	0.176389i	2.35375	+	0.176389i
$325$	0.571270	−	0.455573i	0.571270	−	0.455573i
$326$	3.16012	+	0.721277i	3.16012	+	0.721277i
$327$		0			0
$328$	−2.12621	+	4.41512i	−2.12621	+	4.41512i
$329$		0			0
$330$		0			0
$331$	1.07193	+	1.07193i	1.07193	+	1.07193i	0.997204	+	0.0747301i	$0.0238095\pi$
$331$	1.07193	+	1.07193i	1.07193	+	1.07193i	0.0747301	+	0.997204i	$0.476190\pi$
$332$		0			0
$333$		0			0
$334$	0.255936	−	2.27150i	0.255936	−	2.27150i
$335$		0			0
$336$		0			0
$337$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$337$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$338$	−0.454582	+	0.723463i	−0.454582	+	0.723463i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−3.28241	+	0.369838i	−3.28241	+	0.369838i
$347$	0.867767			0.867767			0.433884	−	0.900969i	$-0.357143\pi$
$347$	0.867767			0.867767			0.433884	+	0.900969i	$0.357143\pi$
$348$	−2.33398	−	0.351791i	−2.33398	−	0.351791i
$349$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$349$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$350$		0			0
$351$	−0.712362	+	0.162592i	−0.712362	+	0.162592i
$352$		0			0
$353$	−1.24349	+	1.55929i	−1.24349	+	1.55929i	−0.563320	+	0.826239i	$0.690476\pi$
$353$	−1.24349	+	1.55929i	−1.24349	+	1.55929i	−0.680173	+	0.733052i	$0.738095\pi$
$354$	−0.815247	+	0.0305044i	−0.815247	+	0.0305044i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.145766	−	0.231985i	0.145766	−	0.231985i
$359$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$359$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$360$		0			0
$361$	0.433884	+	0.900969i	0.433884	+	0.900969i
$362$		0			0
$363$	0.680173	−	0.733052i	0.680173	−	0.733052i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$367$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$368$	−0.959267	+	1.99194i	−0.959267	+	1.99194i
$369$	−1.58114	+	1.16694i	−1.58114	+	1.16694i
$370$		0			0
$371$		0			0
$372$	−4.40446	+	1.18017i	−4.40446	+	1.18017i
$373$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$373$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$374$		0			0
$375$		0			0
$376$			4.40941i			4.40941i
$377$	0.722521	−	0.108903i	0.722521	−	0.108903i
$378$		0			0
$379$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$379$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$380$		0			0
$381$	1.19572	+	0.521689i	1.19572	+	0.521689i
$382$		0			0
$383$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$383$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$384$	−0.243112	−	0.282501i	−0.243112	−	0.282501i
$385$		0			0
$386$	3.30087	+	1.58961i	3.30087	+	1.58961i
$387$		0			0
$388$		0			0
$389$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$389$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$390$		0			0
$391$		0			0
$392$	2.47800	+	0.279204i	2.47800	+	0.279204i
$393$	−0.148689	+	0.785841i	−0.148689	+	0.785841i
$394$	−2.24511	+	2.24511i	−2.24511	+	2.24511i
$395$		0			0
$396$		0			0
$397$	1.01507	+	0.488831i	1.01507	+	0.488831i	0.866025	−	0.500000i	$-0.166667\pi$
$397$	1.01507	+	0.488831i	1.01507	+	0.488831i	0.149042	+	0.988831i	$0.452381\pi$
$398$		0			0
$399$		0			0
$400$	−1.37846	−	1.72854i	−1.37846	−	1.72854i
$401$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$401$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$402$		0			0
$403$	1.19521	−	0.751000i	1.19521	−	0.751000i
$404$	−0.447536	−	3.97199i	−0.447536	−	3.97199i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.04551	+	1.66393i	1.04551	+	1.66393i	0.680173	+	0.733052i	$0.261905\pi$
$409$	1.04551	+	1.66393i	1.04551	+	1.66393i	0.365341	+	0.930874i	$0.380952\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−1.47493	+	1.08855i	−1.47493	+	1.08855i
$415$		0			0
$416$	−0.964622	−	0.606112i	−0.964622	−	0.606112i
$417$	−0.246289	+	0.167917i	−0.246289	+	0.167917i
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$		0			0
$421$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$421$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$422$	−1.12481	−	2.33570i	−1.12481	−	2.33570i
$423$	−0.826239	+	1.56332i	−0.826239	+	1.56332i
$424$		0			0
$425$		0			0
$426$	−0.255328	−	0.483104i	−0.255328	−	0.483104i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$431$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$432$	0.491968	+	2.15545i	0.491968	+	2.15545i
$433$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$433$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.136702	−	0.0102444i	−0.136702	−	0.0102444i
$439$	−1.09839	+	0.250701i	−1.09839	+	0.250701i	−0.733052	−	0.680173i	$-0.761905\pi$
$439$	−1.09839	+	0.250701i	−1.09839	+	0.250701i	−0.365341	+	0.930874i	$0.619048\pi$
$440$		0			0
$441$	0.826239	+	0.563320i	0.826239	+	0.563320i
$442$		0			0
$443$	1.88645	−	0.660096i	1.88645	−	0.660096i	0.930874	−	0.365341i	$-0.119048\pi$
$443$	1.88645	−	0.660096i	1.88645	−	0.660096i	0.955573	−	0.294755i	$-0.0952381\pi$
$444$		0			0
$445$		0			0
$446$	3.11781	+	1.09097i	3.11781	+	1.09097i
$447$		0			0
$448$		0			0
$449$	−0.222521	+	1.97493i	−0.222521	+	1.97493i			1.00000i	$0.5\pi$
$449$	−0.222521	+	1.97493i	−0.222521	+	1.97493i	−0.222521	+	0.974928i	$0.571429\pi$
$450$	−0.340799	−	1.80117i	−0.340799	−	1.80117i
$451$		0			0
$452$		0			0
$453$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$457$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.806531	−	1.28359i	−0.806531	−	1.28359i	−0.955573	−	0.294755i	$-0.904762\pi$
$461$	−0.806531	−	1.28359i	−0.806531	−	1.28359i	0.149042	−	0.988831i	$-0.452381\pi$
$462$		0			0
$463$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$463$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$464$	−0.329515	−	2.18619i	−0.329515	−	2.18619i
$465$		0			0
$466$	−0.339162	−	3.01015i	−0.339162	−	3.01015i
$467$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$467$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$468$	−0.862331	−	1.49360i	−0.862331	−	1.49360i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.366541	−	1.04752i	−0.366541	−	1.04752i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	2.05229	+	0.231237i	2.05229	+	0.231237i
$479$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$479$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	2.12660	+	1.02412i	2.12660	+	1.02412i
$485$		0			0
$486$	−0.474448	+	1.77066i	−0.474448	+	1.77066i
$487$	−1.24349	−	1.55929i	−1.24349	−	1.55929i	−0.680173	−	0.733052i	$-0.738095\pi$
$487$	−1.24349	−	1.55929i	−1.24349	−	1.55929i	−0.563320	−	0.826239i	$-0.690476\pi$
$488$		0			0
$489$	−0.707101	+	1.62069i	−0.707101	+	1.62069i
$490$		0			0
$491$	0.0416310	+	0.369485i	0.0416310	+	0.369485i	0.997204	+	0.0747301i	$0.0238095\pi$
$491$	0.0416310	+	0.369485i	0.0416310	+	0.369485i	−0.955573	+	0.294755i	$0.904762\pi$
$492$	−3.73204	−	2.75437i	−3.73204	−	2.75437i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−2.27236	−	3.61645i	−2.27236	−	3.61645i
$497$		0			0
$498$		0			0
$499$	1.49419	−	1.19158i	1.49419	−	1.19158i	0.563320	−	0.826239i	$-0.309524\pi$
$499$	1.49419	−	1.19158i	1.49419	−	1.19158i	0.930874	−	0.365341i	$-0.119048\pi$
$500$		0			0
$501$	1.19158	+	0.367554i	1.19158	+	0.367554i
$502$		0			0
$503$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$503$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.341678	−	0.317031i	−0.341678	−	0.317031i
$508$	−0.344766	+	3.05989i	−0.344766	+	3.05989i
$509$	0.590232	+	1.22563i	0.590232	+	1.22563i	0.955573	+	0.294755i	$0.0952381\pi$
$509$	0.590232	+	1.22563i	0.590232	+	1.22563i	−0.365341	+	0.930874i	$0.619048\pi$
$510$		0			0
$511$		0			0
$512$	1.09926	−	1.74946i	1.09926	−	1.74946i
$513$		0			0
$514$	1.02000	−	0.356915i	1.02000	−	0.356915i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.134659	−	1.79690i	0.134659	−	1.79690i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	0.605443	−	1.73026i	0.605443	−	1.73026i
$523$		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
$531$	0.0663300	−	0.440071i	0.0663300	−	0.440071i
$532$		0			0
$533$	1.35531	+	0.474244i	1.35531	+	0.474244i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.109562	+	0.101659i	0.109562	+	0.101659i
$538$	2.15462	−	1.03761i	2.15462	−	1.03761i
$539$		0			0
$540$		0			0
$541$	0.791295	+	0.497204i	0.791295	+	0.497204i	0.866025	−	0.500000i	$-0.166667\pi$
$541$	0.791295	+	0.497204i	0.791295	+	0.497204i	−0.0747301	+	0.997204i	$0.523810\pi$
$542$	−1.58072	+	3.28241i	−1.58072	+	3.28241i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.367711	+	1.61105i	0.367711	+	1.61105i	0.733052	+	0.680173i	$0.238095\pi$
$547$	0.367711	+	1.61105i	0.367711	+	1.61105i	−0.365341	+	0.930874i	$0.619048\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−2.00641	−	1.48080i	−2.00641	−	1.48080i
$553$		0			0
$554$	−3.06963	+	1.92878i	−3.06963	+	1.92878i
$555$		0			0
$556$	−0.550083	−	0.438676i	−0.550083	−	0.438676i
$557$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$557$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$558$	−0.264644	−	3.53142i	−0.264644	−	3.53142i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$563$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$564$	−4.10087	−	0.775927i	−4.10087	−	0.775927i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	0.525612	−	0.525612i	0.525612	−	0.525612i
$569$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$569$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$570$		0			0
$571$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$571$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.781831	+	0.623490i	0.781831	+	0.623490i
$576$	−0.560511	+	0.323611i	−0.560511	+	0.323611i
$577$	1.28359	−	0.806531i	1.28359	−	0.806531i	0.294755	−	0.955573i	$-0.404762\pi$
$577$	1.28359	−	0.806531i	1.28359	−	0.806531i	0.988831	+	0.149042i	$0.0476190\pi$
$578$	−0.205245	−	1.82160i	−0.205245	−	1.82160i
$579$	−1.18681	+	1.60807i	−1.18681	+	1.60807i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.0414965	−	0.181808i	−0.0414965	−	0.181808i
$585$		0			0
$586$		0			0
$587$	−1.94440	−	0.443797i	−1.94440	−	0.443797i	−0.988831	−	0.149042i	$-0.952381\pi$
$587$	−1.94440	−	0.443797i	−1.94440	−	0.443797i	−0.955573	−	0.294755i	$-0.904762\pi$
$588$	−0.695724	+	2.25548i	−0.695724	+	2.25548i
$589$		0			0
$590$		0			0
$591$	−0.975699	−	1.43109i	−0.975699	−	1.43109i
$592$		0			0
$593$	0.781831	−	0.376510i	0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$593$	0.781831	−	0.376510i	0.781831	−	0.376510i	0.781831	+	0.623490i	$0.214286\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	1.26427	+	0.442386i	1.26427	+	0.442386i
$599$	−1.05737	+	1.68280i	−1.05737	+	1.68280i	−0.433884	+	0.900969i	$0.642857\pi$
$599$	−1.05737	+	1.68280i	−1.05737	+	1.68280i	−0.623490	+	0.781831i	$0.714286\pi$
$600$	2.20470	−	1.16522i	2.20470	−	1.16522i
$601$	0.488590	−	0.170965i	0.488590	−	0.170965i	−0.0747301	−	0.997204i	$-0.523810\pi$
$601$	0.488590	−	0.170965i	0.488590	−	0.170965i	0.563320	+	0.826239i	$0.309524\pi$
$602$		0			0
$603$		0			0
$604$	1.47165	−	1.84539i	1.47165	−	1.84539i
$605$		0			0
$606$	3.09562	+	0.231985i	3.09562	+	0.231985i
$607$	1.87590	−	0.211363i	1.87590	−	0.211363i	0.900969	−	0.433884i	$-0.142857\pi$
$607$	1.87590	−	0.211363i	1.87590	−	0.211363i	0.974928	+	0.222521i	$0.0714286\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.28389	−	0.144660i	1.28389	−	0.144660i
$612$		0			0
$613$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$613$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$614$	1.21616	−	1.52501i	1.21616	−	1.52501i
$615$		0			0
$616$		0			0
$617$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$617$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$618$		0			0
$619$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$619$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$620$		0			0
$621$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$622$	−1.27989	−	2.65773i	−1.27989	−	2.65773i
$623$		0			0
$624$	1.09879	−	1.18421i	1.09879	−	1.18421i
$625$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$631$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$632$		0			0
$633$	1.36603	−	0.366025i	1.36603	−	0.366025i
$634$	0.0913425	+	0.400198i	0.0913425	+	0.400198i
$635$		0			0
$636$		0			0
$637$		−	0.730682i		−	0.730682i
$638$		0			0
$639$	0.284841	−	0.0878620i	0.284841	−	0.0878620i
$640$		0			0
$641$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$641$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$642$		0			0
$643$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$643$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.22563	−	0.590232i	−1.22563	−	0.590232i	−0.294755	−	0.955573i	$-0.595238\pi$
$647$	−1.22563	−	0.590232i	−1.22563	−	0.590232i	−0.930874	+	0.365341i	$0.880952\pi$
$648$	−2.49194	+	0.0932418i	−2.49194	+	0.0932418i
$649$		0			0
$650$	−0.947121	+	0.947121i	−0.947121	+	0.947121i
$651$		0			0
$652$	−4.14739	−	0.467299i	−4.14739	−	0.467299i
$653$	0.514383	+	0.0579571i	0.514383	+	0.0579571i	0.365341	−	0.930874i	$-0.380952\pi$
$653$	0.514383	+	0.0579571i	0.514383	+	0.0579571i	0.149042	+	0.988831i	$0.452381\pi$
$654$		0			0
$655$		0			0
$656$	1.43496	−	4.10087i	1.43496	−	4.10087i
$657$	0.0193551	−	0.0722342i	0.0193551	−	0.0722342i
$658$		0			0
$659$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$659$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	−2.17264	−	1.73262i	−2.17264	−	1.73262i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.365341	+	0.930874i	0.365341	+	0.930874i
$668$			2.94330i			2.94330i
$669$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.55929	+	1.24349i	−1.55929	+	1.24349i	−0.733052	+	0.680173i	$0.761905\pi$
$673$	−1.55929	+	1.24349i	−1.55929	+	1.24349i	−0.826239	+	0.563320i	$0.809524\pi$
$674$		0			0
$675$	1.00000			1.00000
$676$	0.477344	−	0.991215i	0.477344	−	0.991215i
$677$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$677$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.255779	−	0.531130i	−0.255779	−	0.531130i	0.733052	−	0.680173i	$-0.238095\pi$
$683$	−0.255779	−	0.531130i	−0.255779	−	0.531130i	−0.988831	+	0.149042i	$0.952381\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$691$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$692$	4.14656	−	0.946425i	4.14656	−	0.946425i
$693$		0			0
$694$	−1.58072	+	0.178105i	−1.58072	+	0.178105i
$695$		0			0
$696$	2.49194	+	0.0932418i	2.49194	+	0.0932418i
$697$		0			0
$698$	−3.48134	+	0.392253i	−3.48134	+	0.392253i
$699$	1.64786	+	0.123490i	1.64786	+	0.123490i
$700$		0			0
$701$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$701$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$702$	1.26427	−	0.442386i	1.26427	−	0.442386i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.94511	−	3.09562i	1.94511	−	3.09562i
$707$		0			0
$708$	1.03872	−	0.156562i	1.03872	−	0.156562i
$709$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$709$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.36603	+	1.36603i	1.36603	+	1.36603i
$714$		0			0
$715$		0			0
$716$	−0.153064	+	0.317842i	−0.153064	+	0.317842i
$717$	−0.332083	+	1.07659i	−0.332083	+	1.07659i
$718$		0			0
$719$	1.22252	−	0.974928i	1.22252	−	0.974928i	0.222521	−	0.974928i	$-0.428571\pi$
$719$	1.22252	−	0.974928i	1.22252	−	0.974928i	1.00000			$0$
$720$		0			0
$721$		0			0
$722$	−0.975281	−	1.55215i	−0.975281	−	1.55215i
$723$		0			0
$724$		0			0
$725$	−0.997204	−	0.0747301i	−0.997204	−	0.0747301i
$726$	−1.08855	+	1.47493i	−1.08855	+	1.47493i
$727$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$727$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$728$		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	$-0.607143\pi$
$733$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$734$		0			0
$735$		0			0
$736$	0.514953	−	1.47165i	0.514953	−	1.47165i
$737$		0			0
$738$	2.64070	−	2.45021i	2.64070	−	2.45021i
$739$	−1.95278	−	0.220025i	−1.95278	−	0.220025i	−0.955573	−	0.294755i	$-0.904762\pi$
$739$	−1.95278	−	0.220025i	−1.95278	−	0.220025i	−0.997204	+	0.0747301i	$0.976190\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$743$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$744$	4.48441	−	1.76000i	4.48441	−	1.76000i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$751$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$752$	−0.437709	−	3.88477i	−0.437709	−	3.88477i
$753$		0			0
$754$	−1.29379	+	0.346670i	−1.29379	+	0.346670i
$755$		0			0
$756$		0			0
$757$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$757$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.92808	+	0.440071i	1.92808	+	0.440071i	0.997204	+	0.0747301i	$0.0238095\pi$
$761$	1.92808	+	0.440071i	1.92808	+	0.440071i	0.930874	+	0.365341i	$0.119048\pi$
$762$	−2.28520	−	0.704892i	−2.28520	−	0.704892i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.292981	+	0.141092i	−0.292981	+	0.141092i
$768$	0.975281	+	0.904929i	0.975281	+	0.904929i
$769$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$769$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$770$		0			0
$771$	0.0878620	+	0.582926i	0.0878620	+	0.582926i
$772$	−4.45267	−	1.55806i	−4.45267	−	1.55806i
$773$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$773$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$774$		0			0
$775$	−1.82344	+	0.638050i	−1.82344	+	0.638050i
$776$		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
$784$	−2.21089			−2.21089
$785$		0			0
$786$	0.109562	−	1.46200i	0.109562	−	1.46200i
$787$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$787$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$788$	2.54897	−	3.19631i	2.54897	−	3.19631i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−1.94938	−	0.682116i	−1.94938	−	0.682116i
$795$		0			0
$796$		0			0
$797$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$797$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$798$		0			0
$799$		0			0
$800$	1.10248	+	1.10248i	1.10248	+	1.10248i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−2.02305	+	1.61333i	−2.02305	+	1.61333i
$807$	0.337649	+	1.26012i	0.337649	+	1.26012i
$808$	0.939689	+	4.11705i	0.939689	+	4.11705i
$809$	−1.00435	−	1.59842i	−1.00435	−	1.59842i	−0.781831	−	0.623490i	$-0.785714\pi$
$809$	−1.00435	−	1.59842i	−1.00435	−	1.59842i	−0.222521	−	0.974928i	$-0.571429\pi$
$810$		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
$813$	−1.59908	−	1.18017i	−1.59908	−	1.18017i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−2.24602	−	2.81642i	−2.24602	−	2.81642i
$819$		0			0
$820$		0			0
$821$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$821$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$822$		0			0
$823$	−0.122805	+	0.350958i	−0.122805	+	0.350958i	−0.988831	−	0.149042i	$-0.952381\pi$
$823$	−0.122805	+	0.350958i	−0.122805	+	0.350958i	0.866025	+	0.500000i	$0.166667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$827$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$828$	1.73026	−	1.60544i	1.73026	−	1.60544i
$829$	−0.158342	+	0.158342i	−0.158342	+	0.158342i	−0.781831	−	0.623490i	$-0.785714\pi$
$829$	−0.158342	+	0.158342i	−0.158342	+	0.158342i	0.623490	+	0.781831i	$0.285714\pi$
$830$		0			0
$831$	−0.722521	−	1.84095i	−0.722521	−	1.84095i
$832$	0.426081	+	0.205190i	0.426081	+	0.205190i
$833$		0			0
$834$	0.414176	−	0.356427i	0.414176	−	0.356427i
$835$		0			0
$836$		0			0
$837$	1.91970	+	0.216299i	1.91970	+	0.216299i
$838$		0			0
$839$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$839$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$840$		0			0
$841$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$842$		0			0
$843$		0			0
$844$	1.77594	+	2.82639i	1.77594	+	2.82639i
$845$		0			0
$846$	1.18421	−	3.01732i	1.18421	−	3.01732i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.396342	+	0.581327i	0.396342	+	0.581327i
$853$	1.19745	+	1.19745i	1.19745	+	1.19745i	0.974928	+	0.222521i	$0.0714286\pi$
$853$	1.19745	+	1.19745i	1.19745	+	1.19745i	0.222521	+	0.974928i	$0.428571\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	−0.997204	−	0.0747301i	$-0.976190\pi$
$857$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	0.563320	−	0.826239i	$-0.309524\pi$
$858$		0			0
$859$	−0.350958	−	0.122805i	−0.350958	−	0.122805i	0.149042	−	0.988831i	$-0.452381\pi$
$859$	−0.350958	−	0.122805i	−0.350958	−	0.122805i	−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	−0.733052	−	0.680173i	$-0.761905\pi$
$863$	0.222521	−	0.974928i	0.222521	−	0.974928i	0.955573	−	0.294755i	$-0.0952381\pi$
$864$	−0.514953	−	1.47165i	−0.514953	−	1.47165i
$865$		0			0
$866$		0			0
$867$	0.997204	+	0.0747301i	0.997204	+	0.0747301i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.176389	−	0.00660000i	0.176389	−	0.00660000i
$877$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$877$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$878$	1.94938	−	0.682116i	1.94938	−	0.682116i
$879$		0			0
$880$		0			0
$881$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$881$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$882$	−1.62069	−	0.856562i	−1.62069	−	0.856562i
$883$	0.193096	+	0.400969i	0.193096	+	0.400969i	0.974928	−	0.222521i	$-0.0714286\pi$
$883$	0.193096	+	0.400969i	0.193096	+	0.400969i	−0.781831	+	0.623490i	$0.785714\pi$
$884$		0			0
$885$		0			0
$886$	−3.30087	+	1.58961i	−3.30087	+	1.58961i
$887$	0.922474	+	0.922474i	0.922474	+	0.922474i	0.997204	−	0.0747301i	$-0.0238095\pi$
$887$	0.922474	+	0.922474i	0.922474	+	0.922474i	−0.0747301	+	0.997204i	$0.523810\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−4.14656	−	0.946425i	−4.14656	−	0.946425i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$898$		−	3.64320i		−	3.64320i
$899$	−1.89817	−	0.359154i	−1.89817	−	0.359154i
$900$	0.695724	+	2.25548i	0.695724	+	2.25548i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	1.19572	+	1.38946i	1.19572	+	1.38946i
$907$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$907$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$908$		0			0
$909$	−0.438297	+	1.63575i	−0.438297	+	1.63575i
$910$		0			0
$911$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$911$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$919$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$920$		0			0
$921$	0.694076	+	0.806531i	0.694076	+	0.806531i
$922$	1.73262	+	2.17264i	1.73262	+	2.17264i
$923$	−0.170287	−	0.135799i	−0.170287	−	0.135799i
$924$		0			0
$925$		0			0
$926$	0.255936	+	2.27150i	0.255936	+	2.27150i
$927$		0			0
$928$	0.403537	+	1.50602i	0.403537	+	1.50602i
$929$		−	0.730682i		−	0.730682i	−0.930874	−	0.365341i	$-0.880952\pi$
$929$		−	0.730682i		−	0.730682i	0.930874	−	0.365341i	$-0.119048\pi$
$930$		0			0
$931$		0			0
$932$	0.867925	+	3.80263i	0.867925	+	3.80263i
$933$	1.55436	−	0.416490i	1.55436	−	0.416490i
$934$		0			0
$935$		0			0
$936$	1.08199	+	1.46605i	1.08199	+	1.46605i
$937$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$937$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$941$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$942$		0			0
$943$	−0.220025	+	1.95278i	−0.220025	+	1.95278i
$944$	0.426914	+	0.886496i	0.426914	+	0.886496i
$945$		0			0
$946$		0			0
$947$	−0.694076	+	1.10462i	−0.694076	+	1.10462i	0.294755	+	0.955573i	$0.404762\pi$
$947$	−0.694076	+	1.10462i	−0.694076	+	1.10462i	−0.988831	+	0.149042i	$0.952381\pi$
$948$		0			0
$949$	−0.0515758	+	0.0180472i	−0.0515758	+	0.0180472i
$950$		0			0
$951$	−0.223772	+	0.00837297i	−0.223772	+	0.00837297i
$952$		0			0
$953$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$953$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$954$		0			0
$955$		0			0
$956$	−2.65926			−2.65926
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.66355	+	0.607938i	−2.66355	+	0.607938i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.06332	−	1.69226i	1.06332	−	1.69226i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	1.06332	−	1.69226i	1.06332	−	1.69226i	0.563320	−	0.826239i	$-0.309524\pi$
$968$	−2.35375	−	0.823611i	−2.35375	−	0.823611i
$969$		0			0
$970$		0			0
$971$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$971$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$972$	0.351791	−	2.33398i	0.351791	−	2.33398i
$973$		0			0
$974$	2.58518	+	2.58518i	2.58518	+	2.58518i
$975$	−0.411608	−	0.603718i	−0.411608	−	0.603718i
$976$		0			0
$977$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$977$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$978$	0.955416	−	3.09738i	0.955416	−	3.09738i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.151670	−	0.664509i	−0.151670	−	0.664509i
$983$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$983$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$984$	4.24389	+	2.45021i	4.24389	+	2.45021i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.678448	+	0.541044i	0.678448	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$991$	0.678448	+	0.541044i	0.678448	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$992$	1.87797	+	2.35491i	1.87797	+	2.35491i
$993$	1.14904	−	0.988831i	1.14904	−	0.988831i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.656405	+	1.87590i	−0.656405	+	1.87590i	−0.222521	+	0.974928i	$0.571429\pi$
$997$	−0.656405	+	1.87590i	−0.656405	+	1.87590i	−0.433884	+	0.900969i	$0.642857\pi$
$998$	−2.47726	+	2.47726i	−2.47726	+	2.47726i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.c.275.1	✓	24
3.2	odd	2		2001.1.bf.d.275.2	yes	24
23.22	odd	2	CM	2001.1.bf.c.275.1	✓	24
29.27	odd	28		2001.1.bf.d.1448.2	yes	24
69.68	even	2		2001.1.bf.d.275.2	yes	24
87.56	even	28	inner	2001.1.bf.c.1448.1	yes	24
667.114	even	28		2001.1.bf.d.1448.2	yes	24
2001.1448	odd	28	inner	2001.1.bf.c.1448.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.275.1	✓	24	1.1	even	1	trivial
2001.1.bf.c.275.1	✓	24	23.22	odd	2	CM
2001.1.bf.c.1448.1	yes	24	87.56	even	28	inner
2001.1.bf.c.1448.1	yes	24	2001.1448	odd	28	inner
2001.1.bf.d.275.2	yes	24	3.2	odd	2
2001.1.bf.d.275.2	yes	24	69.68	even	2
2001.1.bf.d.1448.2	yes	24	29.27	odd	28
2001.1.bf.d.1448.2	yes	24	667.114	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)

\(f(q)\)	\(=\)	\(q+(-1.82160 + 0.205245i) q^{2} +(0.0747301 - 0.997204i) q^{3} +(2.30117 - 0.525226i) q^{4} +(0.0685427 + 1.83184i) q^{6} +(-2.35375 + 0.823611i) q^{8} +(-0.988831 - 0.149042i) q^{9} +O(q^{10})\)	\(q+(-1.82160 + 0.205245i) q^{2} +(0.0747301 - 0.997204i) q^{3} +(2.30117 - 0.525226i) q^{4} +(0.0685427 + 1.83184i) q^{6} +(-2.35375 + 0.823611i) q^{8} +(-0.988831 - 0.149042i) q^{9} +(-0.351791 - 2.33398i) q^{12} +(0.317031 + 0.658322i) q^{13} +(1.99194 - 0.959267i) q^{16} +(1.83184 + 0.0685427i) q^{18} +(-0.781831 + 0.623490i) q^{23} +(0.645413 + 2.40871i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.712620 - 1.13413i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(0.294755 - 0.955573i) q^{29} +(-0.216299 - 1.91970i) q^{31} +(-1.32017 + 0.829515i) q^{32} +(-2.35375 + 0.176389i) q^{36} +(0.680173 - 0.266948i) q^{39} +(1.38956 - 1.38956i) q^{41} +(1.29621 - 1.29621i) q^{46} +(0.584010 - 1.66900i) q^{47} +(-0.807727 - 2.05806i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(0.605443 + 1.73026i) q^{50} +(1.07531 + 1.34840i) q^{52} +(0.205245 - 1.82160i) q^{54} +(-0.340799 + 1.80117i) q^{58} +0.445042i q^{59} +(0.788019 + 3.45254i) q^{62} +(0.506019 - 0.403537i) q^{64} +(0.563320 + 0.826239i) q^{69} +(-0.268565 + 0.129334i) q^{71} +(2.45021 - 0.463605i) q^{72} +(-0.00837297 + 0.0743122i) q^{73} +(-0.988831 + 0.149042i) q^{75} +(-1.18421 + 0.625874i) q^{78} +(0.955573 + 0.294755i) q^{81} +(-2.24602 + 2.81642i) q^{82} +(-0.930874 - 0.365341i) q^{87} +(-1.47165 + 1.84539i) q^{92} +(-1.93050 + 0.0722342i) q^{93} +(-0.721277 + 3.16012i) q^{94} +(0.728540 + 1.37846i) q^{96} +(1.73026 + 0.605443i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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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