LMFDB - Embedded newform 2001.1.bf.c.620.1

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			620.1
Root			$-0.149042 + 0.988831i$ of defining polynomial
Character	$\chi$	$=$	2001.620
Dual form			2001.1.bf.c.965.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.122805 + 0.350958i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.673741 - 0.537291i) q^{4} +(0.148689 - 0.340799i) q^{6} +(0.586137 + 0.368294i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})$	\(q+(0.122805 + 0.350958i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.673741 - 0.537291i) q^{4} +(0.148689 - 0.340799i) q^{6} +(0.586137 + 0.368294i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(-0.859338 - 0.0643985i) q^{12} +(1.61105 + 0.367711i) q^{13} +(0.134482 - 0.589204i) q^{16} +(-0.340799 + 0.148689i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-0.179165 - 0.668653i) q^{24} +(0.623490 + 0.781831i) q^{25} +(0.0687943 + 0.610566i) q^{26} +(0.623490 - 0.781831i) q^{27} +(0.149042 + 0.988831i) q^{29} +(-1.82344 + 0.638050i) q^{31} +(0.911189 - 0.102666i) q^{32} +(0.586137 + 0.631706i) q^{36} +(-0.930874 - 1.36534i) q^{39} +(0.660818 - 0.660818i) q^{41} +(0.262919 - 0.262919i) q^{46} +(0.631863 + 1.00560i) q^{47} +(-0.499343 + 0.340446i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(-0.197822 + 0.314832i) q^{50} +(1.28300 - 0.617858i) q^{52} +(0.350958 + 0.122805i) q^{54} +(-0.328735 + 0.173741i) q^{58} -1.24698i q^{59} +(-0.447857 - 0.561595i) q^{62} +(-0.114290 - 0.237325i) q^{64} +(-0.294755 + 0.955573i) q^{69} +(0.443797 - 1.94440i) q^{71} +(-0.323462 + 0.612021i) q^{72} +(-0.754903 - 0.264152i) q^{73} +(0.0747301 - 0.997204i) q^{75} +(0.364861 - 0.494369i) q^{78} +(-0.988831 + 0.149042i) q^{81} +(0.313071 + 0.150767i) q^{82} +(0.563320 - 0.826239i) q^{87} +(-0.776408 - 0.373898i) q^{92} +(1.77066 + 0.772532i) q^{93} +(-0.275328 + 0.345251i) q^{94} +(-0.737780 - 0.544506i) q^{96} +(0.314832 - 0.197822i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{25}{28}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.122805	+	0.350958i	0.122805	+	0.350958i	0.988831	−	0.149042i	$-0.0476190\pi$
$2$	0.122805	+	0.350958i	0.122805	+	0.350958i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$3$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$4$	0.673741	−	0.537291i	0.673741	−	0.537291i
$5$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$5$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$6$	0.148689	−	0.340799i	0.148689	−	0.340799i
$7$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$7$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$8$	0.586137	+	0.368294i	0.586137	+	0.368294i
$9$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$10$		0			0
$11$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$11$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$12$	−0.859338	−	0.0643985i	−0.859338	−	0.0643985i
$13$	1.61105	+	0.367711i	1.61105	+	0.367711i	0.930874	−	0.365341i	$-0.119048\pi$
$13$	1.61105	+	0.367711i	1.61105	+	0.367711i	0.680173	+	0.733052i	$0.261905\pi$
$14$		0			0
$15$		0			0
$16$	0.134482	−	0.589204i	0.134482	−	0.589204i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	−0.340799	+	0.148689i	−0.340799	+	0.148689i
$19$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$19$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$23$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$24$	−0.179165	−	0.668653i	−0.179165	−	0.668653i
$25$	0.623490	+	0.781831i	0.623490	+	0.781831i
$26$	0.0687943	+	0.610566i	0.0687943	+	0.610566i
$27$	0.623490	−	0.781831i	0.623490	−	0.781831i
$28$		0			0
$29$	0.149042	+	0.988831i	0.149042	+	0.988831i
$29$	0.149042	+	0.988831i	0.149042	+	0.988831i
$30$		0			0
$31$	−1.82344	+	0.638050i	−1.82344	+	0.638050i	−0.826239	+	0.563320i	$0.809524\pi$
$31$	−1.82344	+	0.638050i	−1.82344	+	0.638050i	−0.997204	+	0.0747301i	$0.976190\pi$
$32$	0.911189	−	0.102666i	0.911189	−	0.102666i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.586137	+	0.631706i	0.586137	+	0.631706i
$37$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$37$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$38$		0			0
$39$	−0.930874	−	1.36534i	−0.930874	−	1.36534i
$40$		0			0
$41$	0.660818	−	0.660818i	0.660818	−	0.660818i	−0.294755	−	0.955573i	$-0.595238\pi$
$41$	0.660818	−	0.660818i	0.660818	−	0.660818i	0.955573	+	0.294755i	$0.0952381\pi$
$42$		0			0
$43$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$43$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$44$		0			0
$45$		0			0
$46$	0.262919	−	0.262919i	0.262919	−	0.262919i
$47$	0.631863	+	1.00560i	0.631863	+	1.00560i	0.997204	+	0.0747301i	$0.0238095\pi$
$47$	0.631863	+	1.00560i	0.631863	+	1.00560i	−0.365341	+	0.930874i	$0.619048\pi$
$48$	−0.499343	+	0.340446i	−0.499343	+	0.340446i
$49$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$50$	−0.197822	+	0.314832i	−0.197822	+	0.314832i
$51$		0			0
$52$	1.28300	−	0.617858i	1.28300	−	0.617858i
$53$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$53$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$54$	0.350958	+	0.122805i	0.350958	+	0.122805i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.328735	+	0.173741i	−0.328735	+	0.173741i
$59$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$59$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$60$		0			0
$61$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$61$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$62$	−0.447857	−	0.561595i	−0.447857	−	0.561595i
$63$		0			0
$64$	−0.114290	−	0.237325i	−0.114290	−	0.237325i
$65$		0			0
$66$		0			0
$67$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$67$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$68$		0			0
$69$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$70$		0			0
$71$	0.443797	−	1.94440i	0.443797	−	1.94440i	0.149042	−	0.988831i	$-0.452381\pi$
$71$	0.443797	−	1.94440i	0.443797	−	1.94440i	0.294755	−	0.955573i	$-0.404762\pi$
$72$	−0.323462	+	0.612021i	−0.323462	+	0.612021i
$73$	−0.754903	−	0.264152i	−0.754903	−	0.264152i	−0.0747301	−	0.997204i	$-0.523810\pi$
$73$	−0.754903	−	0.264152i	−0.754903	−	0.264152i	−0.680173	+	0.733052i	$0.738095\pi$
$74$		0			0
$75$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$76$		0			0
$77$		0			0
$78$	0.364861	−	0.494369i	0.364861	−	0.494369i
$79$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$79$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$80$		0			0
$81$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$82$	0.313071	+	0.150767i	0.313071	+	0.150767i
$83$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$83$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.563320	−	0.826239i	0.563320	−	0.826239i
$88$		0			0
$89$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$89$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$90$		0			0
$91$		0			0
$92$	−0.776408	−	0.373898i	−0.776408	−	0.373898i
$93$	1.77066	+	0.772532i	1.77066	+	0.772532i
$94$	−0.275328	+	0.345251i	−0.275328	+	0.345251i
$95$		0			0
$96$	−0.737780	−	0.544506i	−0.737780	−	0.544506i
$97$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$97$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$98$	0.314832	−	0.197822i	0.314832	−	0.197822i
$99$		0			0
$100$	0.840142	+	0.191757i	0.840142	+	0.191757i
$101$	−1.87590	−	0.656405i	−1.87590	−	0.656405i	−0.974928	−	0.222521i	$-0.928571\pi$
$101$	−1.87590	−	0.656405i	−1.87590	−	0.656405i	−0.900969	−	0.433884i	$-0.857143\pi$
$102$		0			0
$103$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$103$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$104$	0.808868	+	0.808868i	0.808868	+	0.808868i
$105$		0			0
$106$		0			0
$107$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$107$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$108$		−	0.861747i		−	0.861747i
$109$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$109$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$113$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$114$		0			0
$115$		0			0
$116$	0.631706	+	0.586137i	0.631706	+	0.586137i
$117$	−0.246289	+	1.63402i	−0.246289	+	1.63402i
$118$	0.437637	−	0.153136i	0.437637	−	0.153136i
$119$		0			0
$120$		0			0
$121$	0.433884	−	0.900969i	0.433884	−	0.900969i
$122$		0			0
$123$	−0.933884	+	0.0349435i	−0.933884	+	0.0349435i
$124$	−0.885710	+	1.40960i	−0.885710	+	1.40960i
$125$		0			0
$126$		0			0
$127$	1.06332	+	1.69226i	1.06332	+	1.69226i	0.563320	+	0.826239i	$0.309524\pi$
$127$	1.06332	+	1.69226i	1.06332	+	1.69226i	0.500000	+	0.866025i	$0.333333\pi$
$128$	0.717641	−	0.717641i	0.717641	−	0.717641i
$129$		0			0
$130$		0			0
$131$	−0.649042	+	1.85486i	−0.649042	+	1.85486i	−0.149042	+	0.988831i	$0.547619\pi$
$131$	−0.649042	+	1.85486i	−0.649042	+	1.85486i	−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		0.532032	−	0.846724i	$-0.321429\pi$
$137$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$138$	−0.371563	+	0.0139029i	−0.371563	+	0.0139029i
$139$	−1.79690	+	0.865341i	−1.79690	+	0.865341i	−0.866025	+	0.500000i	$0.833333\pi$
$139$	−1.79690	+	0.865341i	−1.79690	+	0.865341i	−0.930874	+	0.365341i	$0.880952\pi$
$140$		0			0
$141$	0.220796	−	1.16694i	0.220796	−	1.16694i
$142$	0.736904	−	0.0830292i	0.736904	−	0.0830292i
$143$		0			0
$144$	0.597606	+	0.0900746i	0.597606	+	0.0900746i
$145$		0			0
$146$		−	0.297378i		−	0.297378i
$147$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$148$		0			0
$149$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$149$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$150$	0.359154	−	0.0962349i	0.359154	−	0.0962349i
$151$	0.433884	+	0.900969i	0.433884	+	0.900969i	0.997204	+	0.0747301i	$0.0238095\pi$
$151$	0.433884	+	0.900969i	0.433884	+	0.900969i	−0.563320	+	0.826239i	$0.690476\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−1.36075	−	0.419737i	−1.36075	−	0.419737i
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.173741	−	0.328735i	−0.173741	−	0.328735i
$163$	1.00560	−	0.631863i	1.00560	−	0.631863i	0.0747301	−	0.997204i	$-0.476190\pi$
$163$	1.00560	−	0.631863i	1.00560	−	0.631863i	0.930874	+	0.365341i	$0.119048\pi$
$164$	0.0901689	−	0.800271i	0.0901689	−	0.800271i
$165$		0			0
$166$		0			0
$167$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$167$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$168$		0			0
$169$	1.55929	+	0.750915i	1.55929	+	0.750915i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$173$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$174$	0.359154	+	0.0962349i	0.359154	+	0.0962349i
$175$		0			0
$176$		0			0
$177$	−0.848162	+	0.914101i	−0.848162	+	0.914101i
$178$		0			0
$179$	−1.32091	−	0.636119i	−1.32091	−	0.636119i	−0.365341	−	0.930874i	$-0.619048\pi$
$179$	−1.32091	−	0.636119i	−1.32091	−	0.636119i	−0.955573	+	0.294755i	$0.904762\pi$
$180$		0			0
$181$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$181$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$182$		0			0
$183$		0			0
$184$	0.0775064	−	0.687888i	0.0775064	−	0.687888i
$185$		0			0
$186$	−0.0536792	+	0.716299i	−0.0536792	+	0.716299i
$187$		0			0
$188$	0.966014	+	0.338023i	0.966014	+	0.338023i
$189$		0			0
$190$		0			0
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	−0.0776418	+	0.251709i	−0.0776418	+	0.251709i
$193$	−1.82160	−	0.205245i	−1.82160	−	0.205245i	−0.866025	−	0.500000i	$-0.833333\pi$
$193$	−1.82160	−	0.205245i	−1.82160	−	0.205245i	−0.955573	+	0.294755i	$0.904762\pi$
$194$		0			0
$195$		0			0
$196$	−0.673741	−	0.537291i	−0.673741	−	0.537291i
$197$	0.751509	+	1.56052i	0.751509	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$197$	0.751509	+	1.56052i	0.751509	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$198$		0			0
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	0.0775064	+	0.687888i	0.0775064	+	0.687888i
$201$		0			0
$202$		−	0.738971i		−	0.738971i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.866025	−	0.500000i	0.866025	−	0.500000i
$208$	0.433313	−	0.899784i	0.433313	−	0.899784i
$209$		0			0
$210$		0			0
$211$	−0.752407	+	1.19745i	−0.752407	+	1.19745i	0.222521	+	0.974928i	$0.428571\pi$
$211$	−0.752407	+	1.19745i	−0.752407	+	1.19745i	−0.974928	+	0.222521i	$0.928571\pi$
$212$		0			0
$213$	−1.64786	+	1.12349i	−1.64786	+	1.12349i
$214$		0			0
$215$		0			0
$216$	0.653395	−	0.228633i	0.653395	−	0.228633i
$217$		0			0
$218$		0			0
$219$	0.373714	+	0.707101i	0.373714	+	0.707101i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$223$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	−1.00000			$\pi$
$224$		0			0
$225$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$226$		0			0
$227$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$227$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$228$		0			0
$229$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$229$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$230$		0			0
$231$		0			0
$232$	−0.276822	+	0.634482i	−0.276822	+	0.634482i
$233$			1.91115i			1.91115i	0.294755	+	0.955573i	$0.404762\pi$
$233$			1.91115i			1.91115i	−0.294755	+	0.955573i	$0.595238\pi$
$234$	−0.603718	+	0.114230i	−0.603718	+	0.114230i
$235$		0			0
$236$	−0.669991	−	0.840142i	−0.669991	−	0.840142i
$237$		0			0
$238$		0			0
$239$	−0.460898	−	0.367554i	−0.460898	−	0.367554i	0.365341	−	0.930874i	$-0.380952\pi$
$239$	−0.460898	−	0.367554i	−0.460898	−	0.367554i	−0.826239	+	0.563320i	$0.809524\pi$
$240$		0			0
$241$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$241$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$242$	0.369485	+	0.0416310i	0.369485	+	0.0416310i
$243$	0.826239	+	0.563320i	0.826239	+	0.563320i
$244$		0			0
$245$		0			0
$246$	−0.126950	−	0.323462i	−0.126950	−	0.323462i
$247$		0			0
$248$	−1.30378	−	0.297579i	−1.30378	−	0.297579i
$249$		0			0
$250$		0			0
$251$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$251$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$252$		0			0
$253$		0			0
$254$	−0.463332	+	0.581000i	−0.463332	+	0.581000i
$255$		0			0
$256$	0.102666	+	0.0494415i	0.102666	+	0.0494415i
$257$	0.233052	−	0.185853i	0.233052	−	0.185853i	−0.500000	−	0.866025i	$-0.666667\pi$
$257$	0.233052	−	0.185853i	0.233052	−	0.185853i	0.733052	+	0.680173i	$0.238095\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$262$	−0.730682			−0.730682
$263$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$263$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.69226	−	1.06332i	−1.69226	−	1.06332i	−0.866025	−	0.500000i	$-0.833333\pi$
$269$	−1.69226	−	1.06332i	−1.69226	−	1.06332i	−0.826239	−	0.563320i	$-0.809524\pi$
$270$		0			0
$271$	0.0739590	−	0.656405i	0.0739590	−	0.656405i	−0.900969	−	0.433884i	$-0.857143\pi$
$271$	0.0739590	−	0.656405i	0.0739590	−	0.656405i	0.974928	−	0.222521i	$-0.0714286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.314832	+	0.802178i	0.314832	+	0.802178i
$277$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	−0.988831	−	0.149042i	$-0.952381\pi$
$277$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	0.955573	+	0.294755i	$0.0952381\pi$
$278$	−0.524367	−	0.524367i	−0.524367	−	0.524367i
$279$	−0.772532	−	1.77066i	−0.772532	−	1.77066i
$280$		0			0
$281$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$281$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$282$	0.436660	−	0.0658159i	0.436660	−	0.0658159i
$283$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$283$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$284$	−0.745705	−	1.54847i	−0.745705	−	1.54847i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.170473	+	0.900969i	0.170473	+	0.900969i
$289$			1.00000i			1.00000i
$290$		0			0
$291$		0			0
$292$	−0.650536	+	0.227632i	−0.650536	+	0.227632i
$293$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$293$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$294$	−0.365341	−	0.0691263i	−0.365341	−	0.0691263i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$300$	−0.485440	−	0.712009i	−0.485440	−	0.712009i
$301$		0			0
$302$	−0.262919	+	0.262919i	−0.262919	+	0.262919i
$303$	0.928661	+	1.75711i	0.928661	+	1.75711i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.158342	−	0.158342i	0.158342	−	0.158342i	−0.623490	−	0.781831i	$-0.714286\pi$
$307$	0.158342	−	0.158342i	0.158342	−	0.158342i	0.781831	+	0.623490i	$0.214286\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.806531	−	1.28359i	0.806531	−	1.28359i	−0.149042	−	0.988831i	$-0.547619\pi$
$311$	0.806531	−	1.28359i	0.806531	−	1.28359i	0.955573	−	0.294755i	$-0.0952381\pi$
$312$	−0.0427723	−	1.14311i	−0.0427723	−	1.14311i
$313$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$313$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.78183	+	0.623490i	−1.78183	+	0.623490i	−0.781831	+	0.623490i	$0.785714\pi$
$317$	−1.78183	+	0.623490i	−1.78183	+	0.623490i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.586137	+	0.631706i	−0.586137	+	0.631706i
$325$	0.716983	+	1.48883i	0.716983	+	1.48883i
$326$	0.345251	+	0.275328i	0.345251	+	0.275328i
$327$		0			0
$328$	0.630705	−	0.143954i	0.630705	−	0.143954i
$329$		0			0
$330$		0			0
$331$	−0.0528791	−	0.0528791i	−0.0528791	−	0.0528791i	0.680173	−	0.733052i	$-0.261905\pi$
$331$	−0.0528791	−	0.0528791i	−0.0528791	−	0.0528791i	−0.733052	+	0.680173i	$0.761905\pi$
$332$		0			0
$333$		0			0
$334$	−0.632404	−	0.221288i	−0.632404	−	0.221288i
$335$		0			0
$336$		0			0
$337$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$337$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$338$	−0.0720500	+	0.639462i	−0.0720500	+	0.639462i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.0546536	+	0.156191i	0.0546536	+	0.156191i
$347$	1.94986			1.94986			0.974928	−	0.222521i	$-0.0714286\pi$
$347$	1.94986			1.94986			0.974928	+	0.222521i	$0.0714286\pi$
$348$	−0.0643985	−	0.859338i	−0.0643985	−	0.859338i
$349$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$349$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$350$		0			0
$351$	1.29196	−	1.03030i	1.29196	−	1.03030i
$352$		0			0
$353$	1.22563	+	0.590232i	1.22563	+	0.590232i	0.930874	−	0.365341i	$-0.119048\pi$
$353$	1.22563	+	0.590232i	1.22563	+	0.590232i	0.294755	+	0.955573i	$0.404762\pi$
$354$	−0.424970	−	0.185412i	−0.424970	−	0.185412i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0610354	−	0.541704i	0.0610354	−	0.541704i
$359$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$359$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$360$		0			0
$361$	0.974928	+	0.222521i	0.974928	+	0.222521i
$362$		0			0
$363$	−0.930874	+	0.365341i	−0.930874	+	0.365341i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$367$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$368$	−0.589204	+	0.134482i	−0.589204	+	0.134482i
$369$	0.708353	+	0.609587i	0.708353	+	0.609587i
$370$		0			0
$371$		0			0
$372$	1.60804	−	0.430874i	1.60804	−	0.430874i
$373$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$373$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$374$		0			0
$375$		0			0
$376$			0.822133i			0.822133i
$377$	−0.123490	+	1.64786i	−0.123490	+	1.64786i
$378$		0			0
$379$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$379$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$380$		0			0
$381$	0.371563	−	1.96376i	0.371563	−	1.96376i
$382$		0			0
$383$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$383$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$384$	−1.01419	+	0.0379482i	−1.01419	+	0.0379482i
$385$		0			0
$386$	−0.151670	−	0.664509i	−0.151670	−	0.664509i
$387$		0			0
$388$		0			0
$389$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$389$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$390$		0			0
$391$		0			0
$392$	0.228633	−	0.653395i	0.228633	−	0.653395i
$393$	1.73740	−	0.918245i	1.73740	−	0.918245i
$394$	−0.455389	+	0.455389i	−0.455389	+	0.455389i
$395$		0			0
$396$		0			0
$397$	−0.131178	−	0.574730i	−0.131178	−	0.574730i	−0.997204	−	0.0747301i	$-0.976190\pi$
$397$	−0.131178	−	0.574730i	−0.131178	−	0.574730i	0.866025	−	0.500000i	$-0.166667\pi$
$398$		0			0
$399$		0			0
$400$	0.544506	−	0.262220i	0.544506	−	0.262220i
$401$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$401$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$402$		0			0
$403$	−3.17227	+	0.357429i	−3.17227	+	0.357429i
$404$	−1.61655	+	0.565655i	−1.61655	+	0.565655i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.104635	−	0.928661i	−0.104635	−	0.928661i	−0.930874	−	0.365341i	$-0.880952\pi$
$409$	−0.104635	−	0.928661i	−0.104635	−	0.928661i	0.826239	−	0.563320i	$-0.190476\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.281831	+	0.242536i	0.281831	+	0.242536i
$415$		0			0
$416$	1.50572	+	0.169654i	1.50572	+	0.169654i
$417$	1.90580	+	0.587862i	1.90580	+	0.587862i
$418$		0			0
$419$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$419$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$420$		0			0
$421$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$421$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$422$	−0.512654	−	0.117010i	−0.512654	−	0.117010i
$423$	−0.955573	+	0.705245i	−0.955573	+	0.705245i
$424$		0			0
$425$		0			0
$426$	−0.596663	−	0.440357i	−0.596663	−	0.440357i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$431$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$432$	−0.376810	−	0.472505i	−0.376810	−	0.472505i
$433$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$433$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.202269	+	0.217994i	−0.202269	+	0.217994i
$439$	−0.460898	+	0.367554i	−0.460898	+	0.367554i	−0.826239	−	0.563320i	$-0.809524\pi$
$439$	−0.460898	+	0.367554i	−0.460898	+	0.367554i	0.365341	+	0.930874i	$0.380952\pi$
$440$		0			0
$441$	0.955573	−	0.294755i	0.955573	−	0.294755i
$442$		0			0
$443$	−1.55215	−	0.975281i	−1.55215	−	0.975281i	−0.988831	−	0.149042i	$-0.952381\pi$
$443$	−1.55215	−	0.975281i	−1.55215	−	0.975281i	−0.563320	−	0.826239i	$-0.690476\pi$
$444$		0			0
$445$		0			0
$446$	0.140113	−	0.0880390i	0.140113	−	0.0880390i
$447$		0			0
$448$		0			0
$449$	0.623490	+	0.218169i	0.623490	+	0.218169i	0.623490	−	0.781831i	$-0.285714\pi$
$449$	0.623490	+	0.218169i	0.623490	+	0.218169i			1.00000i	$0.5\pi$
$450$	−0.328735	−	0.173741i	−0.328735	−	0.173741i
$451$		0			0
$452$		0			0
$453$	0.294755	−	0.955573i	0.294755	−	0.955573i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$457$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.00837297	−	0.0743122i	−0.00837297	−	0.0743122i	0.988831	−	0.149042i	$-0.0476190\pi$
$461$	−0.00837297	−	0.0743122i	−0.00837297	−	0.0743122i	−0.997204	+	0.0747301i	$0.976190\pi$
$462$		0			0
$463$			1.80194i			1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$463$			1.80194i			1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$464$	0.602666	+	0.0451636i	0.602666	+	0.0451636i
$465$		0			0
$466$	−0.670731	+	0.234699i	−0.670731	+	0.234699i
$467$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$467$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$468$	0.712009	+	1.23324i	0.712009	+	1.23324i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.459256	−	0.730901i	0.459256	−	0.730901i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.0723951	−	0.206893i	0.0723951	−	0.206893i
$479$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$479$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.191757	−	0.840142i	−0.191757	−	0.840142i
$485$		0			0
$486$	−0.0962349	+	0.359154i	−0.0962349	+	0.359154i
$487$	1.22563	−	0.590232i	1.22563	−	0.590232i	0.294755	−	0.955573i	$-0.404762\pi$
$487$	1.22563	−	0.590232i	1.22563	−	0.590232i	0.930874	+	0.365341i	$0.119048\pi$
$488$		0			0
$489$	−1.16694	−	0.220796i	−1.16694	−	0.220796i
$490$		0			0
$491$	1.66900	−	0.584010i	1.66900	−	0.584010i	0.680173	−	0.733052i	$-0.261905\pi$
$491$	1.66900	−	0.584010i	1.66900	−	0.584010i	0.988831	+	0.149042i	$0.0476190\pi$
$492$	−0.610421	+	0.525310i	−0.610421	+	0.525310i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.130722	+	1.16019i	0.130722	+	1.16019i
$497$		0			0
$498$		0			0
$499$	−0.858075	−	1.78181i	−0.858075	−	1.78181i	−0.563320	−	0.826239i	$-0.690476\pi$
$499$	−0.858075	−	1.78181i	−0.858075	−	1.78181i	−0.294755	−	0.955573i	$-0.595238\pi$
$500$		0			0
$501$	1.78181	−	0.268565i	1.78181	−	0.268565i
$502$		0			0
$503$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$503$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.632289	−	1.61105i	−0.632289	−	1.61105i
$508$	1.62564	+	0.568836i	1.62564	+	0.568836i
$509$	−1.81507	−	0.414278i	−1.81507	−	0.414278i	−0.826239	−	0.563320i	$-0.809524\pi$
$509$	−1.81507	−	0.414278i	−1.81507	−	0.414278i	−0.988831	+	0.149042i	$0.952381\pi$
$510$		0			0
$511$		0			0
$512$	0.108889	−	0.966412i	0.108889	−	0.966412i
$513$		0			0
$514$	0.0938465	+	0.0589676i	0.0938465	+	0.0589676i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.326239	−	0.302705i	−0.326239	−	0.302705i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.197822	−	0.314832i	−0.197822	−	0.314832i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	0.559311	+	1.59842i	0.559311	+	1.59842i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$530$		0			0
$531$	1.24349	−	0.0931869i	1.24349	−	0.0931869i
$532$		0			0
$533$	1.30760	−	0.821618i	1.30760	−	0.821618i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.535628	+	1.36476i	0.535628	+	1.36476i
$538$	0.165361	−	0.724495i	0.165361	−	0.724495i
$539$		0			0
$540$		0			0
$541$	1.59908	+	0.180173i	1.59908	+	0.180173i	0.866025	−	0.500000i	$-0.166667\pi$
$541$	1.59908	+	0.180173i	1.59908	+	0.180173i	0.733052	+	0.680173i	$0.238095\pi$
$542$	0.239453	−	0.0546536i	0.239453	−	0.0546536i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.19158	−	1.49419i	−1.19158	−	1.49419i	−0.826239	−	0.563320i	$-0.809524\pi$
$547$	−1.19158	−	1.49419i	−1.19158	−	1.49419i	−0.365341	−	0.930874i	$-0.619048\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−0.524699	+	0.451540i	−0.524699	+	0.451540i
$553$		0			0
$554$	−0.0552233	+	0.00622218i	−0.0552233	+	0.00622218i
$555$		0			0
$556$	−0.745705	+	1.54847i	−0.745705	+	1.54847i
$557$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$557$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$558$	0.526557	−	0.488573i	0.526557	−	0.488573i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$563$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$564$	−0.478224	−	0.904844i	−0.478224	−	0.904844i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	0.976239	−	0.976239i	0.976239	−	0.976239i
$569$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$569$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$570$		0			0
$571$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$571$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.433884	−	0.900969i	0.433884	−	0.900969i
$576$	0.228121	−	0.131706i	0.228121	−	0.131706i
$577$	0.0743122	−	0.00837297i	0.0743122	−	0.00837297i	−0.0747301	−	0.997204i	$-0.523810\pi$
$577$	0.0743122	−	0.00837297i	0.0743122	−	0.00837297i	0.149042	+	0.988831i	$0.452381\pi$
$578$	−0.350958	+	0.122805i	−0.350958	+	0.122805i
$579$	1.19572	+	1.38946i	1.19572	+	1.38946i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.345191	−	0.432856i	−0.345191	−	0.432856i
$585$		0			0
$586$		0			0
$587$	1.06356	+	0.848162i	1.06356	+	0.848162i	0.988831	−	0.149042i	$-0.0476190\pi$
$587$	1.06356	+	0.848162i	1.06356	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$588$	0.128437	+	0.852122i	0.128437	+	0.852122i
$589$		0			0
$590$		0			0
$591$	0.510531	−	1.65510i	0.510531	−	1.65510i
$592$		0			0
$593$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$593$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.520252	−	0.326896i	0.520252	−	0.326896i
$599$	−0.0739590	+	0.656405i	−0.0739590	+	0.656405i	0.900969	+	0.433884i	$0.142857\pi$
$599$	−0.0739590	+	0.656405i	−0.0739590	+	0.656405i	−0.974928	+	0.222521i	$0.928571\pi$
$600$	0.411067	−	0.556976i	0.411067	−	0.556976i
$601$	0.438297	+	0.275400i	0.438297	+	0.275400i	0.733052	−	0.680173i	$-0.238095\pi$
$601$	0.438297	+	0.275400i	0.438297	+	0.275400i	−0.294755	+	0.955573i	$0.595238\pi$
$602$		0			0
$603$		0			0
$604$	0.776408	+	0.373898i	0.776408	+	0.373898i
$605$		0			0
$606$	−0.502628	+	0.541704i	−0.502628	+	0.541704i
$607$	−0.559311	−	1.59842i	−0.559311	−	1.59842i	−0.781831	−	0.623490i	$-0.785714\pi$
$607$	−0.559311	−	1.59842i	−0.559311	−	1.59842i	0.222521	−	0.974928i	$-0.428571\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.648189	+	1.85242i	0.648189	+	1.85242i
$612$		0			0
$613$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$613$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$614$	0.0750165	+	0.0361260i	0.0750165	+	0.0361260i
$615$		0			0
$616$		0			0
$617$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$617$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$618$		0			0
$619$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$619$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$620$		0			0
$621$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$622$	0.549531	+	0.125427i	0.549531	+	0.125427i
$623$		0			0
$624$	−0.929650	+	0.364861i	−0.929650	+	0.364861i
$625$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$631$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$632$		0			0
$633$	1.36603	−	0.366025i	1.36603	−	0.366025i
$634$	−0.437637	−	0.548780i	−0.437637	−	0.548780i
$635$		0			0
$636$		0			0
$637$		−	1.65248i		−	1.65248i
$638$		0			0
$639$	1.97213	+	0.297251i	1.97213	+	0.297251i
$640$		0			0
$641$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$641$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$642$		0			0
$643$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$643$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.414278	+	1.81507i	0.414278	+	1.81507i	0.563320	+	0.826239i	$0.309524\pi$
$647$	0.414278	+	1.81507i	0.414278	+	1.81507i	−0.149042	+	0.988831i	$0.547619\pi$
$648$	−0.634482	−	0.276822i	−0.634482	−	0.276822i
$649$		0			0
$650$	−0.434467	+	0.434467i	−0.434467	+	0.434467i
$651$		0			0
$652$	0.338023	−	0.966014i	0.338023	−	0.966014i
$653$	−0.170965	+	0.488590i	−0.170965	+	0.488590i	−0.997204	−	0.0747301i	$-0.976190\pi$
$653$	−0.170965	+	0.488590i	−0.170965	+	0.488590i	0.826239	+	0.563320i	$0.190476\pi$
$654$		0			0
$655$		0			0
$656$	−0.300488	−	0.478224i	−0.300488	−	0.478224i
$657$	0.206999	−	0.772532i	0.206999	−	0.772532i
$658$		0			0
$659$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$659$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$660$		0			0
$661$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$661$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$662$	0.0120645	−	0.0250522i	0.0120645	−	0.0250522i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.826239	−	0.563320i	0.826239	−	0.563320i
$668$			1.55282i			1.55282i
$669$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.590232	−	1.22563i	−0.590232	−	1.22563i	−0.955573	−	0.294755i	$-0.904762\pi$
$673$	−0.590232	−	1.22563i	−0.590232	−	1.22563i	0.365341	−	0.930874i	$-0.380952\pi$
$674$		0			0
$675$	1.00000			1.00000
$676$	1.45402	−	0.331870i	1.45402	−	0.331870i
$677$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$677$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.290611	−	0.0663300i	−0.290611	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$683$	−0.290611	−	0.0663300i	−0.290611	−	0.0663300i	−0.365341	+	0.930874i	$0.619048\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.781831	−	0.376510i	−0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$691$	−0.781831	−	0.376510i	−0.781831	−	0.376510i	−0.781831	+	0.623490i	$0.785714\pi$
$692$	0.299843	−	0.239117i	0.299843	−	0.239117i
$693$		0			0
$694$	0.239453	+	0.684317i	0.239453	+	0.684317i
$695$		0			0
$696$	0.634482	−	0.276822i	0.634482	−	0.276822i
$697$		0			0
$698$	−0.242868	−	0.694076i	−0.242868	−	0.694076i
$699$	1.29991	−	1.40097i	1.29991	−	1.40097i
$700$		0			0
$701$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$701$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$702$	0.520252	+	0.326896i	0.520252	+	0.326896i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.0566325	+	0.502628i	−0.0566325	+	0.502628i
$707$		0			0
$708$	−0.0803036	+	1.07158i	−0.0803036	+	1.07158i
$709$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$709$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.36603	+	1.36603i	1.36603	+	1.36603i
$714$		0			0
$715$		0			0
$716$	−1.23173	+	0.281135i	−1.23173	+	0.281135i
$717$	0.0878620	+	0.582926i	0.0878620	+	0.582926i
$718$		0			0
$719$	0.376510	+	0.781831i	0.376510	+	0.781831i	1.00000			$0$
$719$	0.376510	+	0.781831i	0.376510	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$720$		0			0
$721$		0			0
$722$	0.0416310	+	0.369485i	0.0416310	+	0.369485i
$723$		0			0
$724$		0			0
$725$	−0.680173	+	0.733052i	−0.680173	+	0.733052i
$726$	−0.242536	−	0.281831i	−0.242536	−	0.281831i
$727$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$727$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$728$		0			0
$729$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$733$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$734$		0			0
$735$		0			0
$736$	−0.487849	−	0.776408i	−0.487849	−	0.776408i
$737$		0			0
$738$	−0.126950	+	0.323462i	−0.126950	+	0.323462i
$739$	0.308658	−	0.882094i	0.308658	−	0.882094i	−0.680173	−	0.733052i	$-0.738095\pi$
$739$	0.308658	−	0.882094i	0.308658	−	0.882094i	0.988831	−	0.149042i	$-0.0476190\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$743$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$744$	0.753332	+	1.10493i	0.753332	+	1.10493i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$751$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$752$	0.677480	−	0.237060i	0.677480	−	0.237060i
$753$		0			0
$754$	−0.593493	+	0.159026i	−0.593493	+	0.159026i
$755$		0			0
$756$		0			0
$757$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$757$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.116853	+	0.0931869i	0.116853	+	0.0931869i	0.680173	−	0.733052i	$-0.261905\pi$
$761$	0.116853	+	0.0931869i	0.116853	+	0.0931869i	−0.563320	+	0.826239i	$0.690476\pi$
$762$	0.734826	−	0.110757i	0.734826	−	0.110757i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.458528	−	2.00894i	0.458528	−	2.00894i
$768$	−0.0416310	−	0.106074i	−0.0416310	−	0.106074i
$769$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$769$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$770$		0			0
$771$	−0.297251	−	0.0222759i	−0.297251	−	0.0222759i
$772$	−1.33756	+	0.840446i	−1.33756	+	0.840446i
$773$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$773$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$774$		0			0
$775$	−1.63575	−	1.02781i	−1.63575	−	1.02781i
$776$		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
$784$	−0.604356			−0.604356
$785$		0			0
$786$	0.535628	+	0.496990i	0.535628	+	0.496990i
$787$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$787$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$788$	1.34478	+	0.647611i	1.34478	+	0.647611i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.185597	−	0.116618i	0.185597	−	0.116618i
$795$		0			0
$796$		0			0
$797$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$797$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$798$		0			0
$799$		0			0
$800$	0.648385	+	0.648385i	0.648385	+	0.648385i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.515014	−	1.06944i	−0.515014	−	1.06944i
$807$	0.517276	+	1.93050i	0.517276	+	1.93050i
$808$	−0.857783	−	1.07563i	−0.857783	−	1.07563i
$809$	0.189606	+	1.68280i	0.189606	+	1.68280i	0.623490	+	0.781831i	$0.285714\pi$
$809$	0.189606	+	1.68280i	0.189606	+	1.68280i	−0.433884	+	0.900969i	$0.642857\pi$
$810$		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
$813$	−0.500684	+	0.430874i	−0.500684	+	0.430874i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.313071	−	0.150767i	0.313071	−	0.150767i
$819$		0			0
$820$		0			0
$821$	0.347948	+	1.52446i	0.347948	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$821$	0.347948	+	1.52446i	0.347948	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$822$		0			0
$823$	0.940755	+	1.49720i	0.940755	+	1.49720i	0.866025	+	0.500000i	$0.166667\pi$
$823$	0.940755	+	1.49720i	0.940755	+	1.49720i	0.0747301	+	0.997204i	$0.476190\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$827$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$828$	0.314832	−	0.802178i	0.314832	−	0.802178i
$829$	−1.33485	+	1.33485i	−1.33485	+	1.33485i	−0.433884	+	0.900969i	$0.642857\pi$
$829$	−1.33485	+	1.33485i	−1.33485	+	1.33485i	−0.900969	+	0.433884i	$0.857143\pi$
$830$		0			0
$831$	0.123490	−	0.0841939i	0.123490	−	0.0841939i
$832$	−0.0968592	−	0.424368i	−0.0968592	−	0.424368i
$833$		0			0
$834$	0.0277281	+	0.741048i	0.0277281	+	0.741048i
$835$		0			0
$836$		0			0
$837$	−0.638050	+	1.82344i	−0.638050	+	1.82344i
$838$		0			0
$839$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$839$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$840$		0			0
$841$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$842$		0			0
$843$		0			0
$844$	0.136451	+	1.21103i	0.136451	+	1.21103i
$845$		0			0
$846$	−0.364861	−	0.248758i	−0.364861	−	0.248758i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.506589	+	1.64232i	−0.506589	+	1.64232i
$853$	−1.40532	−	1.40532i	−1.40532	−	1.40532i	−0.781831	−	0.623490i	$-0.785714\pi$
$853$	−1.40532	−	1.40532i	−1.40532	−	1.40532i	−0.623490	−	0.781831i	$-0.714286\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.294755	−	0.955573i	$-0.595238\pi$
$857$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.680173	+	0.733052i	$0.738095\pi$
$858$		0			0
$859$	−1.49720	+	0.940755i	−1.49720	+	0.940755i	−0.500000	+	0.866025i	$0.666667\pi$
$859$	−1.49720	+	0.940755i	−1.49720	+	0.940755i	−0.997204	+	0.0747301i	$0.976190\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	−0.988831	−	0.149042i	$-0.952381\pi$
$863$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$864$	0.487849	−	0.776408i	0.487849	−	0.776408i
$865$		0			0
$866$		0			0
$867$	0.680173	−	0.733052i	0.680173	−	0.733052i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.631706	+	0.275610i	0.631706	+	0.275610i
$877$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$877$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$878$	−0.185597	−	0.116618i	−0.185597	−	0.116618i
$879$		0			0
$880$		0			0
$881$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$881$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$882$	0.220796	+	0.299168i	0.220796	+	0.299168i
$883$	−1.21572	−	0.277479i	−1.21572	−	0.277479i	−0.433884	−	0.900969i	$-0.642857\pi$
$883$	−1.21572	−	0.277479i	−1.21572	−	0.277479i	−0.781831	+	0.623490i	$0.785714\pi$
$884$		0			0
$885$		0			0
$886$	0.151670	−	0.664509i	0.151670	−	0.664509i
$887$	1.41322	+	1.41322i	1.41322	+	1.41322i	0.733052	+	0.680173i	$0.238095\pi$
$887$	1.41322	+	1.41322i	1.41322	+	1.41322i	0.680173	+	0.733052i	$0.261905\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−0.299843	−	0.239117i	−0.299843	−	0.239117i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$898$			0.245611i			0.245611i
$899$	−0.902694	−	1.70798i	−0.902694	−	1.70798i
$900$	−0.128437	+	0.852122i	−0.128437	+	0.852122i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.371563	−	0.0139029i	0.371563	−	0.0139029i
$907$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$907$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$908$		0			0
$909$	0.514383	−	1.91970i	0.514383	−	1.91970i
$910$		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		−0.222521	−	0.974928i	$-0.571429\pi$
$919$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$920$		0			0
$921$	−0.223772	+	0.00837297i	−0.223772	+	0.00837297i
$922$	0.0250522	−	0.0120645i	0.0250522	−	0.0120645i
$923$	1.42996	−	2.96934i	1.42996	−	2.96934i
$924$		0			0
$925$		0			0
$926$	−0.632404	+	0.221288i	−0.632404	+	0.221288i
$927$		0			0
$928$	0.237325	+	0.885710i	0.237325	+	0.885710i
$929$		−	1.65248i		−	1.65248i	−0.563320	−	0.826239i	$-0.690476\pi$
$929$		−	1.65248i		−	1.65248i	0.563320	−	0.826239i	$-0.309524\pi$
$930$		0			0
$931$		0			0
$932$	1.02684	+	1.28762i	1.02684	+	1.28762i
$933$	−1.46429	+	0.392355i	−1.46429	+	0.392355i
$934$		0			0
$935$		0			0
$936$	−0.746160	+	0.867053i	−0.746160	+	0.867053i
$937$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$937$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$941$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$942$		0			0
$943$	−0.882094	−	0.308658i	−0.882094	−	0.308658i
$944$	−0.734725	−	0.167696i	−0.734725	−	0.167696i
$945$		0			0
$946$		0			0
$947$	0.223772	−	1.98603i	0.223772	−	1.98603i	0.0747301	−	0.997204i	$-0.476190\pi$
$947$	0.223772	−	1.98603i	0.223772	−	1.98603i	0.149042	−	0.988831i	$-0.452381\pi$
$948$		0			0
$949$	−1.11905	−	0.703147i	−1.11905	−	0.703147i
$950$		0			0
$951$	1.73026	+	0.754903i	1.73026	+	0.754903i
$952$		0			0
$953$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$953$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$954$		0			0
$955$		0			0
$956$	−0.508009			−0.508009
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	2.13600	−	1.70341i	2.13600	−	1.70341i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.205245	−	1.82160i	0.205245	−	1.82160i	−0.294755	−	0.955573i	$-0.595238\pi$
$967$	0.205245	−	1.82160i	0.205245	−	1.82160i	0.500000	−	0.866025i	$-0.333333\pi$
$968$	0.586137	−	0.368294i	0.586137	−	0.368294i
$969$		0			0
$970$		0			0
$971$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$971$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$972$	0.859338	−	0.0643985i	0.859338	−	0.0643985i
$973$		0			0
$974$	0.357660	+	0.357660i	0.357660	+	0.357660i
$975$	0.487076	−	1.57906i	0.487076	−	1.57906i
$976$		0			0
$977$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$977$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$978$	−0.0658159	−	0.436660i	−0.0658159	−	0.436660i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.409925	+	0.514030i	0.409925	+	0.514030i
$983$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$983$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$984$	−0.560253	−	0.323462i	−0.560253	−	0.323462i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.846011	−	1.75676i	0.846011	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$991$	0.846011	−	1.75676i	0.846011	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$992$	−1.59599	+	0.768590i	−1.59599	+	0.768590i
$993$	0.00279620	+	0.0747301i	0.00279620	+	0.0747301i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.351438	−	0.559311i	−0.351438	−	0.559311i	0.623490	−	0.781831i	$-0.285714\pi$
$997$	−0.351438	−	0.559311i	−0.351438	−	0.559311i	−0.974928	+	0.222521i	$0.928571\pi$
$998$	0.519964	−	0.519964i	0.519964	−	0.519964i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.c.620.1	✓	24
3.2	odd	2		2001.1.bf.d.620.2	yes	24
23.22	odd	2	CM	2001.1.bf.c.620.1	✓	24
29.8	odd	28		2001.1.bf.d.965.2	yes	24
69.68	even	2		2001.1.bf.d.620.2	yes	24
87.8	even	28	inner	2001.1.bf.c.965.1	yes	24
667.298	even	28		2001.1.bf.d.965.2	yes	24
2001.965	odd	28	inner	2001.1.bf.c.965.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.620.1	✓	24	1.1	even	1	trivial
2001.1.bf.c.620.1	✓	24	23.22	odd	2	CM
2001.1.bf.c.965.1	yes	24	87.8	even	28	inner
2001.1.bf.c.965.1	yes	24	2001.965	odd	28	inner
2001.1.bf.d.620.2	yes	24	3.2	odd	2
2001.1.bf.d.620.2	yes	24	69.68	even	2
2001.1.bf.d.965.2	yes	24	29.8	odd	28
2001.1.bf.d.965.2	yes	24	667.298	even	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.122805 + 0.350958i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.673741 - 0.537291i) q^{4} +(0.148689 - 0.340799i) q^{6} +(0.586137 + 0.368294i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})\)	\(q+(0.122805 + 0.350958i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.673741 - 0.537291i) q^{4} +(0.148689 - 0.340799i) q^{6} +(0.586137 + 0.368294i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(-0.859338 - 0.0643985i) q^{12} +(1.61105 + 0.367711i) q^{13} +(0.134482 - 0.589204i) q^{16} +(-0.340799 + 0.148689i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-0.179165 - 0.668653i) q^{24} +(0.623490 + 0.781831i) q^{25} +(0.0687943 + 0.610566i) q^{26} +(0.623490 - 0.781831i) q^{27} +(0.149042 + 0.988831i) q^{29} +(-1.82344 + 0.638050i) q^{31} +(0.911189 - 0.102666i) q^{32} +(0.586137 + 0.631706i) q^{36} +(-0.930874 - 1.36534i) q^{39} +(0.660818 - 0.660818i) q^{41} +(0.262919 - 0.262919i) q^{46} +(0.631863 + 1.00560i) q^{47} +(-0.499343 + 0.340446i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(-0.197822 + 0.314832i) q^{50} +(1.28300 - 0.617858i) q^{52} +(0.350958 + 0.122805i) q^{54} +(-0.328735 + 0.173741i) q^{58} -1.24698i q^{59} +(-0.447857 - 0.561595i) q^{62} +(-0.114290 - 0.237325i) q^{64} +(-0.294755 + 0.955573i) q^{69} +(0.443797 - 1.94440i) q^{71} +(-0.323462 + 0.612021i) q^{72} +(-0.754903 - 0.264152i) q^{73} +(0.0747301 - 0.997204i) q^{75} +(0.364861 - 0.494369i) q^{78} +(-0.988831 + 0.149042i) q^{81} +(0.313071 + 0.150767i) q^{82} +(0.563320 - 0.826239i) q^{87} +(-0.776408 - 0.373898i) q^{92} +(1.77066 + 0.772532i) q^{93} +(-0.275328 + 0.345251i) q^{94} +(-0.737780 - 0.544506i) q^{96} +(0.314832 - 0.197822i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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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