LMFDB - Embedded newform 2001.1.bf.c.482.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2001.68");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			482.2
Root			$0.149042 - 0.988831i$ of defining polynomial
Character	$\chi$	$=$	2001.482
Dual form			2001.1.bf.c.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85486 - 0.649042i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(2.23740 - 1.78427i) q^{4} +(-1.80117 - 0.785841i) q^{6} +(1.94648 - 3.09781i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})$	\(q+(1.85486 - 0.649042i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(2.23740 - 1.78427i) q^{4} +(-1.80117 - 0.785841i) q^{6} +(1.94648 - 3.09781i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(-2.85375 - 0.213859i) q^{12} +(-1.61105 - 0.367711i) q^{13} +(0.963038 - 4.21934i) q^{16} +(0.785841 + 1.80117i) q^{18} +(0.433884 + 0.900969i) q^{23} +(-3.53392 + 0.946911i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-3.22692 + 0.363587i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.149042 - 0.988831i) q^{29} +(0.170965 + 0.488590i) q^{31} +(-0.542605 - 4.81575i) q^{32} +(1.94648 + 2.09781i) q^{36} +(0.930874 + 1.36534i) q^{39} +(1.25033 + 1.25033i) q^{41} +(1.38956 + 1.38956i) q^{46} +(-1.36254 + 0.856144i) q^{47} +(-3.57584 + 2.43797i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(1.66393 + 1.04551i) q^{50} +(-4.26066 + 2.05182i) q^{52} +(0.649042 - 1.85486i) q^{54} +(-0.918245 - 1.73740i) q^{58} +1.24698i q^{59} +(0.634231 + 0.795301i) q^{62} +(-2.25429 - 4.68109i) q^{64} +(0.294755 - 0.955573i) q^{69} +(-0.443797 + 1.94440i) q^{71} +(3.23461 + 1.70954i) q^{72} +(0.605443 - 1.73026i) q^{73} +(0.0747301 - 0.997204i) q^{75} +(2.61280 + 1.92833i) q^{78} +(-0.988831 + 0.149042i) q^{81} +(3.13069 + 1.50766i) q^{82} +(-0.563320 + 0.826239i) q^{87} +(2.57835 + 1.24167i) q^{92} +(0.206999 - 0.474448i) q^{93} +(-1.97165 + 2.47237i) q^{94} +(-2.87778 + 3.89926i) q^{96} +(-1.04551 - 1.66393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{11}{28}\right)$	$-1$	$-1$

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 $

$2$	1.85486	−	0.649042i	1.85486	−	0.649042i	0.866025	−	0.500000i	$-0.166667\pi$
$2$	1.85486	−	0.649042i	1.85486	−	0.649042i	0.988831	−	0.149042i	$-0.0476190\pi$
$3$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$3$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$4$	2.23740	−	1.78427i	2.23740	−	1.78427i
$5$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$5$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$6$	−1.80117	−	0.785841i	−1.80117	−	0.785841i
$7$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$7$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$8$	1.94648	−	3.09781i	1.94648	−	3.09781i
$9$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$10$		0			0
$11$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$11$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$12$	−2.85375	−	0.213859i	−2.85375	−	0.213859i
$13$	−1.61105	−	0.367711i	−1.61105	−	0.367711i	−0.680173	−	0.733052i	$-0.738095\pi$
$13$	−1.61105	−	0.367711i	−1.61105	−	0.367711i	−0.930874	+	0.365341i	$0.880952\pi$
$14$		0			0
$15$		0			0
$16$	0.963038	−	4.21934i	0.963038	−	4.21934i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	0.785841	+	1.80117i	0.785841	+	1.80117i
$19$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$19$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$20$		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
$24$	−3.53392	+	0.946911i	−3.53392	+	0.946911i
$25$	0.623490	+	0.781831i	0.623490	+	0.781831i
$26$	−3.22692	+	0.363587i	−3.22692	+	0.363587i
$27$	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
$31$	0.170965	+	0.488590i	0.170965	+	0.488590i	0.997204	−	0.0747301i	$-0.0238095\pi$
$31$	0.170965	+	0.488590i	0.170965	+	0.488590i	−0.826239	+	0.563320i	$0.809524\pi$
$32$	−0.542605	−	4.81575i	−0.542605	−	4.81575i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.94648	+	2.09781i	1.94648	+	2.09781i
$37$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$37$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$38$		0			0
$39$	0.930874	+	1.36534i	0.930874	+	1.36534i
$40$		0			0
$41$	1.25033	+	1.25033i	1.25033	+	1.25033i	0.955573	+	0.294755i	$0.0952381\pi$
$41$	1.25033	+	1.25033i	1.25033	+	1.25033i	0.294755	+	0.955573i	$0.404762\pi$
$42$		0			0
$43$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$43$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$44$		0			0
$45$		0			0
$46$	1.38956	+	1.38956i	1.38956	+	1.38956i
$47$	−1.36254	+	0.856144i	−1.36254	+	0.856144i	−0.997204	−	0.0747301i	$-0.976190\pi$
$47$	−1.36254	+	0.856144i	−1.36254	+	0.856144i	−0.365341	+	0.930874i	$0.619048\pi$
$48$	−3.57584	+	2.43797i	−3.57584	+	2.43797i
$49$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$50$	1.66393	+	1.04551i	1.66393	+	1.04551i
$51$		0			0
$52$	−4.26066	+	2.05182i	−4.26066	+	2.05182i
$53$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$53$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$54$	0.649042	−	1.85486i	0.649042	−	1.85486i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.918245	−	1.73740i	−0.918245	−	1.73740i
$59$			1.24698i			1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$59$			1.24698i			1.24698i	−0.781831	+	0.623490i	$0.785714\pi$
$60$		0			0
$61$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$61$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$62$	0.634231	+	0.795301i	0.634231	+	0.795301i
$63$		0			0
$64$	−2.25429	−	4.68109i	−2.25429	−	4.68109i
$65$		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	$0.547619\pi$
$71$	−0.443797	+	1.94440i	−0.443797	+	1.94440i	−0.294755	+	0.955573i	$0.595238\pi$
$72$	3.23461	+	1.70954i	3.23461	+	1.70954i
$73$	0.605443	−	1.73026i	0.605443	−	1.73026i	−0.0747301	−	0.997204i	$-0.523810\pi$
$73$	0.605443	−	1.73026i	0.605443	−	1.73026i	0.680173	−	0.733052i	$-0.261905\pi$
$74$		0			0
$75$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$76$		0			0
$77$		0			0
$78$	2.61280	+	1.92833i	2.61280	+	1.92833i
$79$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$79$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$80$		0			0
$81$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$82$	3.13069	+	1.50766i	3.13069	+	1.50766i
$83$		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		0.943883	−	0.330279i	$-0.107143\pi$
$89$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$90$		0			0
$91$		0			0
$92$	2.57835	+	1.24167i	2.57835	+	1.24167i
$93$	0.206999	−	0.474448i	0.206999	−	0.474448i
$94$	−1.97165	+	2.47237i	−1.97165	+	2.47237i
$95$		0			0
$96$	−2.87778	+	3.89926i	−2.87778	+	3.89926i
$97$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$97$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$98$	−1.04551	−	1.66393i	−1.04551	−	1.66393i
$99$		0			0
$100$	2.79000	+	0.636799i	2.79000	+	0.636799i
$101$	0.0739590	−	0.211363i	0.0739590	−	0.211363i	−0.900969	−	0.433884i	$-0.857143\pi$
$101$	0.0739590	−	0.211363i	0.0739590	−	0.211363i	0.974928	+	0.222521i	$0.0714286\pi$
$102$		0			0
$103$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$103$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$104$	−4.27497	+	4.27497i	−4.27497	+	4.27497i
$105$		0			0
$106$		0			0
$107$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$107$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$108$		−	2.86175i		−	2.86175i
$109$		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		0.993712	−	0.111964i	$-0.0357143\pi$
$113$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$114$		0			0
$115$		0			0
$116$	−2.09781	−	1.94648i	−2.09781	−	1.94648i
$117$	0.246289	−	1.63402i	0.246289	−	1.63402i
$118$	0.809342	+	2.31297i	0.809342	+	2.31297i
$119$		0			0
$120$		0			0
$121$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$122$		0			0
$123$	−0.0661163	−	1.76699i	−0.0661163	−	1.76699i
$124$	1.25429	+	0.788125i	1.25429	+	0.788125i
$125$		0			0
$126$		0			0
$127$	−0.0633201	+	0.0397866i	−0.0633201	+	0.0397866i	−0.563320	−	0.826239i	$-0.690476\pi$
$127$	−0.0633201	+	0.0397866i	−0.0633201	+	0.0397866i	0.500000	+	0.866025i	$0.333333\pi$
$128$	−3.79282	−	3.79282i	−3.79282	−	3.79282i
$129$		0			0
$130$		0			0
$131$	−0.350958	−	0.122805i	−0.350958	−	0.122805i	0.149042	−	0.988831i	$-0.452381\pi$
$131$	−0.350958	−	0.122805i	−0.350958	−	0.122805i	−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		−0.846724	−	0.532032i	$-0.821429\pi$
$137$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$138$	−0.0734787	−	1.96376i	−0.0734787	−	1.96376i
$139$	1.79690	−	0.865341i	1.79690	−	0.865341i	0.866025	−	0.500000i	$-0.166667\pi$
$139$	1.79690	−	0.865341i	1.79690	−	0.865341i	0.930874	−	0.365341i	$-0.119048\pi$
$140$		0			0
$141$	1.58114	+	0.299168i	1.58114	+	0.299168i
$142$	0.438820	+	3.89463i	0.438820	+	3.89463i
$143$		0			0
$144$	4.27951	+	0.645033i	4.27951	+	0.645033i
$145$		0			0
$146$		−	3.60233i		−	3.60233i
$147$	−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	$0.285714\pi$
$150$	−0.508614	−	1.89817i	−0.508614	−	1.89817i
$151$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	−0.997204	−	0.0747301i	$-0.976190\pi$
$151$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	0.563320	−	0.826239i	$-0.309524\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	4.51888	+	1.39389i	4.51888	+	1.39389i
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.73740	+	0.918245i	−1.73740	+	0.918245i
$163$	−0.856144	−	1.36254i	−0.856144	−	1.36254i	−0.930874	−	0.365341i	$-0.880952\pi$
$163$	−0.856144	−	1.36254i	−0.856144	−	1.36254i	0.0747301	−	0.997204i	$-0.476190\pi$
$164$	5.02841	+	0.566566i	5.02841	+	0.566566i
$165$		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	$0.428571\pi$
$174$	−0.508614	+	1.89817i	−0.508614	+	1.89817i
$175$		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
$184$	3.63558	+	0.409631i	3.63558	+	0.409631i
$185$		0			0
$186$	0.0760175	−	1.01438i	0.0760175	−	1.01438i
$187$		0			0
$188$	−1.52097	+	4.34669i	−1.52097	+	4.34669i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	−1.53144	+	4.96479i	−1.53144	+	4.96479i
$193$	−0.0895474	+	0.794755i	−0.0895474	+	0.794755i	0.866025	+	0.500000i	$0.166667\pi$
$193$	−0.0895474	+	0.794755i	−0.0895474	+	0.794755i	−0.955573	+	0.294755i	$0.904762\pi$
$194$		0			0
$195$		0			0
$196$	−2.23740	−	1.78427i	−2.23740	−	1.78427i
$197$	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	$0.285714\pi$
$200$	3.63558	−	0.409631i	3.63558	−	0.409631i
$201$		0			0
$202$		−	0.440050i		−	0.440050i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$208$	−3.10300	+	6.44344i	−3.10300	+	6.44344i
$209$		0			0
$210$		0			0
$211$	1.19745	+	0.752407i	1.19745	+	0.752407i	0.974928	−	0.222521i	$-0.0714286\pi$
$211$	1.19745	+	0.752407i	1.19745	+	0.752407i	0.222521	+	0.974928i	$0.428571\pi$
$212$		0			0
$213$	1.64786	−	1.12349i	1.64786	−	1.12349i
$214$		0			0
$215$		0			0
$216$	−1.20835	−	3.45327i	−1.20835	−	3.45327i
$217$		0			0
$218$		0			0
$219$	−1.62069	+	0.856562i	−1.62069	+	0.856562i
$220$		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		−0.111964	−	0.993712i	$-0.535714\pi$
$229$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$230$		0			0
$231$		0			0
$232$	−3.35332	−	1.46304i	−3.35332	−	1.46304i
$233$		−	1.91115i		−	1.91115i	−0.294755	−	0.955573i	$-0.595238\pi$
$233$		−	1.91115i		−	1.91115i	0.294755	−	0.955573i	$-0.404762\pi$
$234$	−0.603718	−	3.19073i	−0.603718	−	3.19073i
$235$		0			0
$236$	2.22495	+	2.79000i	2.22495	+	2.79000i
$237$		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	$0.928571\pi$
$242$	−0.220025	+	1.95278i	−0.220025	+	1.95278i
$243$	0.826239	+	0.563320i	0.826239	+	0.563320i
$244$		0			0
$245$		0			0
$246$	−1.26949	−	3.23461i	−1.26949	−	3.23461i
$247$		0			0
$248$	1.84634	+	0.421415i	1.84634	+	0.421415i
$249$		0			0
$250$		0			0
$251$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$251$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$252$		0			0
$253$		0			0
$254$	−0.0916264	+	0.114896i	−0.0916264	+	0.114896i
$255$		0			0
$256$	−4.81575	−	2.31914i	−4.81575	−	2.31914i
$257$	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		0.943883	−	0.330279i	$-0.107143\pi$
$263$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.0397866	−	0.0633201i	0.0397866	−	0.0633201i	−0.826239	−	0.563320i	$-0.809524\pi$
$269$	0.0397866	−	0.0633201i	0.0397866	−	0.0633201i	0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−1.87590	−	0.211363i	−1.87590	−	0.211363i	−0.900969	−	0.433884i	$-0.857143\pi$
$271$	−1.87590	−	0.211363i	−1.87590	−	0.211363i	−0.974928	+	0.222521i	$0.928571\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.04551	−	2.66393i	−1.04551	−	2.66393i
$277$	−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	$0.0952381\pi$
$278$	2.77135	−	2.77135i	2.77135	−	2.77135i
$279$	−0.474448	+	0.206999i	−0.474448	+	0.206999i
$280$		0			0
$281$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$281$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$282$	3.12696	−	0.471314i	3.12696	−	0.471314i
$283$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$283$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$284$	2.47639	+	5.14227i	2.47639	+	5.14227i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	4.76173	−	0.900969i	4.76173	−	0.900969i
$289$		−	1.00000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	−1.73262	−	4.95155i	−1.73262	−	4.95155i
$293$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$293$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$294$	−0.365341	+	1.93087i	−0.365341	+	1.93087i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$300$	−1.61208	−	2.36449i	−1.61208	−	2.36449i
$301$		0			0
$302$	−1.38956	−	1.38956i	−1.38956	−	1.38956i
$303$	−0.197979	+	0.104635i	−0.197979	+	0.104635i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.40532	−	1.40532i	−1.40532	−	1.40532i	−0.781831	−	0.623490i	$-0.785714\pi$
$307$	−1.40532	−	1.40532i	−1.40532	−	1.40532i	−0.623490	−	0.781831i	$-0.714286\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.10462	+	0.694076i	1.10462	+	0.694076i	0.955573	−	0.294755i	$-0.0952381\pi$
$311$	1.10462	+	0.694076i	1.10462	+	0.694076i	0.149042	+	0.988831i	$0.452381\pi$
$312$	6.04150	−	0.226057i	6.04150	−	0.226057i
$313$		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
$317$	−0.218169	−	0.623490i	−0.218169	−	0.623490i	0.781831	−	0.623490i	$-0.214286\pi$
$317$	−0.218169	−	0.623490i	−0.218169	−	0.623490i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.94648	+	2.09781i	−1.94648	+	2.09781i
$325$	−0.716983	−	1.48883i	−0.716983	−	1.48883i
$326$	−2.47237	−	1.97165i	−2.47237	−	1.97165i
$327$		0			0
$328$	6.30702	−	1.43954i	6.30702	−	1.43954i
$329$		0			0
$330$		0			0
$331$	−1.41322	+	1.41322i	−1.41322	+	1.41322i	−0.680173	+	0.733052i	$0.738095\pi$
$331$	−1.41322	+	1.41322i	−1.41322	+	1.41322i	−0.733052	+	0.680173i	$0.761905\pi$
$332$		0			0
$333$		0			0
$334$	−1.16953	+	3.34234i	−1.16953	+	3.34234i
$335$		0			0
$336$		0			0
$337$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$337$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$338$	3.37964	+	0.380793i	3.37964	+	0.380793i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.825489	−	0.288851i	0.825489	−	0.288851i
$347$	−1.94986			−1.94986			−0.974928	−	0.222521i	$-0.928571\pi$
$347$	−1.94986			−1.94986			−0.974928	+	0.222521i	$0.928571\pi$
$348$	0.213859	+	2.85375i	0.213859	+	2.85375i
$349$	−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	−0.294755	−	0.955573i	$-0.595238\pi$
$353$	−1.22563	−	0.590232i	−1.22563	−	0.590232i	−0.930874	+	0.365341i	$0.880952\pi$
$354$	0.979928	−	2.24602i	0.979928	−	2.24602i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−2.86297	−	0.322580i	−2.86297	−	0.322580i
$359$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$359$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$360$		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		0.111964	−	0.993712i	$-0.464286\pi$
$367$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$368$	4.21934	−	0.963038i	4.21934	−	0.963038i
$369$	−1.15339	+	1.34027i	−1.15339	+	1.34027i
$370$		0			0
$371$		0			0
$372$	−0.383401	−	1.43087i	−0.383401	−	1.43087i
$373$		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
$376$			5.88737i			5.88737i
$377$	−0.123490	+	1.64786i	−0.123490	+	1.64786i
$378$		0			0
$379$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$379$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$380$		0			0
$381$	0.0734787	+	0.0139029i	0.0734787	+	0.0139029i
$382$		0			0
$383$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$383$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$384$	0.200561	+	5.36011i	0.200561	+	5.36011i
$385$		0			0
$386$	0.349732	+	1.53228i	0.349732	+	1.53228i
$387$		0			0
$388$		0			0
$389$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$389$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$390$		0			0
$391$		0			0
$392$	−3.45327	−	1.20835i	−3.45327	−	1.20835i
$393$	0.173741	+	0.328735i	0.173741	+	0.328735i
$394$	2.40679	+	2.40679i	2.40679	+	2.40679i
$395$		0			0
$396$		0			0
$397$	0.131178	+	0.574730i	0.131178	+	0.574730i	0.997204	+	0.0747301i	$0.0238095\pi$
$397$	0.131178	+	0.574730i	0.131178	+	0.574730i	−0.866025	+	0.500000i	$0.833333\pi$
$398$		0			0
$399$		0			0
$400$	3.89926	−	1.87778i	3.89926	−	1.87778i
$401$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$401$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$402$		0			0
$403$	−0.0957728	−	0.850007i	−0.0957728	−	0.850007i
$404$	−0.211652	−	0.604867i	−0.211652	−	0.604867i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.75711	−	0.197979i	1.75711	−	0.197979i	0.826239	−	0.563320i	$-0.190476\pi$
$409$	1.75711	−	0.197979i	1.75711	−	0.197979i	0.930874	+	0.365341i	$0.119048\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−1.28183	+	1.48952i	−1.28183	+	1.48952i
$415$		0			0
$416$	−0.896642	+	7.95792i	−0.896642	+	7.95792i
$417$	−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		0.330279	−	0.943883i	$-0.392857\pi$
$421$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$422$	2.70944	+	0.618412i	2.70944	+	0.618412i
$423$	−0.955573	−	1.29476i	−0.955573	−	1.29476i
$424$		0			0
$425$		0			0
$426$	2.32735	−	3.15344i	2.32735	−	3.15344i
$427$		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	$0.785714\pi$
$432$	−2.69837	−	3.38365i	−2.69837	−	3.38365i
$433$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$433$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−2.45021	+	2.64070i	−2.45021	+	2.64070i
$439$	−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
$443$	−0.425511	+	0.677197i	−0.425511	+	0.677197i	−0.988831	−	0.149042i	$-0.952381\pi$
$443$	−0.425511	+	0.677197i	−0.425511	+	0.677197i	0.563320	+	0.826239i	$0.309524\pi$
$444$		0			0
$445$		0			0
$446$	−0.465297	−	0.740517i	−0.465297	−	0.740517i
$447$		0			0
$448$		0			0
$449$	0.623490	−	1.78183i	0.623490	−	1.78183i		−	1.00000i	$-0.5\pi$
$449$	0.623490	−	1.78183i	0.623490	−	1.78183i	0.623490	−	0.781831i	$-0.285714\pi$
$450$	−0.918245	+	1.73740i	−0.918245	+	1.73740i
$451$		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
$461$	1.98603	−	0.223772i	1.98603	−	0.223772i	0.988831	−	0.149042i	$-0.0476190\pi$
$461$	1.98603	−	0.223772i	1.98603	−	0.223772i	0.997204	−	0.0747301i	$-0.0238095\pi$
$462$		0			0
$463$		−	1.80194i		−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$463$		−	1.80194i		−	1.80194i	0.433884	−	0.900969i	$-0.357143\pi$
$464$	−4.31575	−	0.323421i	−4.31575	−	0.323421i
$465$		0			0
$466$	−1.24041	−	3.54490i	−1.24041	−	3.54490i
$467$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$467$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$468$	−2.36449	−	4.09541i	−2.36449	−	4.09541i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	3.86291	+	2.42722i	3.86291	+	2.42722i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.09346	−	0.382617i	−1.09346	−	0.382617i
$479$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$479$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.636799	+	2.79000i	0.636799	+	2.79000i
$485$		0			0
$486$	1.89817	+	0.508614i	1.89817	+	0.508614i
$487$	−1.22563	+	0.590232i	−1.22563	+	0.590232i	−0.930874	−	0.365341i	$-0.880952\pi$
$487$	−1.22563	+	0.590232i	−1.22563	+	0.590232i	−0.294755	+	0.955573i	$0.595238\pi$
$488$		0			0
$489$	−0.299168	+	1.58114i	−0.299168	+	1.58114i
$490$		0			0
$491$	0.308658	+	0.882094i	0.308658	+	0.882094i	0.988831	+	0.149042i	$0.0476190\pi$
$491$	0.308658	+	0.882094i	0.308658	+	0.882094i	−0.680173	+	0.733052i	$0.738095\pi$
$492$	−3.30072	−	3.83551i	−3.30072	−	3.83551i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.22617	−	0.250830i	2.22617	−	0.250830i
$497$		0			0
$498$		0			0
$499$	0.858075	+	1.78181i	0.858075	+	1.78181i	0.563320	+	0.826239i	$0.309524\pi$
$499$	0.858075	+	1.78181i	0.858075	+	1.78181i	0.294755	+	0.955573i	$0.404762\pi$
$500$		0			0
$501$	1.78181	−	0.268565i	1.78181	−	0.268565i
$502$		0			0
$503$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$503$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.632289	−	1.61105i	−0.632289	−	1.61105i
$508$	−0.0706825	+	0.201999i	−0.0706825	+	0.201999i
$509$	−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
$512$	−5.10761	−	0.575490i	−5.10761	−	0.575490i
$513$		0			0
$514$	0.311651	−	0.495990i	0.311651	−	0.495990i
$515$		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			$\pi$
$522$	1.66393	−	1.04551i	1.66393	−	1.04551i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	−1.00435	+	0.351438i	−1.00435	+	0.351438i
$525$		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
$533$	−1.55458	−	2.47410i	−1.55458	−	2.47410i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.535628	+	1.36476i	0.535628	+	1.36476i
$538$	0.0327011	−	0.143273i	0.0327011	−	0.143273i
$539$		0			0
$540$		0			0
$541$	−0.132974	+	1.18017i	−0.132974	+	1.18017i	0.733052	+	0.680173i	$0.238095\pi$
$541$	−0.132974	+	1.18017i	−0.132974	+	1.18017i	−0.866025	+	0.500000i	$0.833333\pi$
$542$	−3.61670	+	0.825489i	−3.61670	+	0.825489i
$543$		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
$552$	−2.38645	−	2.77310i	−2.38645	−	2.77310i
$553$		0			0
$554$	0.0328850	+	0.291862i	0.0328850	+	0.291862i
$555$		0			0
$556$	2.47639	−	5.14227i	2.47639	−	5.14227i
$557$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$557$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$558$	−0.745681	+	0.691891i	−0.745681	+	0.691891i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$	4.07145	−	2.15182i	4.07145	−	2.15182i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	5.15955	+	5.15955i	5.15955	+	5.15955i
$569$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$569$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$570$		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
$576$	4.49954	−	2.59781i	4.49954	−	2.59781i
$577$	−0.223772	−	1.98603i	−0.223772	−	1.98603i	−0.149042	−	0.988831i	$-0.547619\pi$
$577$	−0.223772	−	1.98603i	−0.223772	−	1.98603i	−0.0747301	−	0.997204i	$-0.523810\pi$
$578$	−0.649042	−	1.85486i	−0.649042	−	1.85486i
$579$	0.606214	−	0.521689i	0.606214	−	0.521689i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−4.18152	−	5.24346i	−4.18152	−	5.24346i
$585$		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	$0.476190\pi$
$588$	0.426521	+	2.82978i	0.426521	+	2.82978i
$589$		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	$0.642857\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−1.72769	−	2.74960i	−1.72769	−	2.74960i
$599$	1.87590	+	0.211363i	1.87590	+	0.211363i	0.974928	−	0.222521i	$-0.0714286\pi$
$599$	1.87590	+	0.211363i	1.87590	+	0.211363i	0.900969	+	0.433884i	$0.142857\pi$
$600$	−2.94369	−	2.17254i	−2.94369	−	2.17254i
$601$	1.02781	−	1.63575i	1.02781	−	1.63575i	0.294755	−	0.955573i	$-0.404762\pi$
$601$	1.02781	−	1.63575i	1.02781	−	1.63575i	0.733052	−	0.680173i	$-0.238095\pi$
$602$		0			0
$603$		0			0
$604$	−2.57835	−	1.24167i	−2.57835	−	1.24167i
$605$		0			0
$606$	−0.299310	+	0.322580i	−0.299310	+	0.322580i
$607$	1.00435	−	0.351438i	1.00435	−	0.351438i	0.222521	−	0.974928i	$-0.428571\pi$
$607$	1.00435	−	0.351438i	1.00435	−	0.351438i	0.781831	+	0.623490i	$0.214286\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.50994	−	0.878265i	2.50994	−	0.878265i
$612$		0			0
$613$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$613$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$614$	−3.51878	−	1.69456i	−3.51878	−	1.69456i
$615$		0			0
$616$		0			0
$617$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$617$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$618$		0			0
$619$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$619$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$620$		0			0
$621$	0.974928	+	0.222521i	0.974928	+	0.222521i
$622$	2.49939	+	0.570469i	2.49939	+	0.570469i
$623$		0			0
$624$	6.65731	−	2.61280i	6.65731	−	2.61280i
$625$	−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
$633$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$634$	−0.809342	−	1.01488i	−0.809342	−	1.01488i
$635$		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		−0.111964	−	0.993712i	$-0.535714\pi$
$641$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$642$		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	$-0.690476\pi$
$647$	−0.414278	−	1.81507i	−0.414278	−	1.81507i	0.149042	−	0.988831i	$-0.452381\pi$
$648$	−1.46304	+	3.35332i	−1.46304	+	3.35332i
$649$		0			0
$650$	−2.29621	−	2.29621i	−2.29621	−	2.29621i
$651$		0			0
$652$	−4.34669	−	1.52097i	−4.34669	−	1.52097i
$653$	1.82344	+	0.638050i	1.82344	+	0.638050i	0.997204	+	0.0747301i	$0.0238095\pi$
$653$	1.82344	+	0.638050i	1.82344	+	0.638050i	0.826239	+	0.563320i	$0.190476\pi$
$654$		0			0
$655$		0			0
$656$	6.47968	−	4.07145i	6.47968	−	4.07145i
$657$	1.77066	+	0.474448i	1.77066	+	0.474448i
$658$		0			0
$659$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$659$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$660$		0			0
$661$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$661$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$662$	−1.70409	+	3.53857i	−1.70409	+	3.53857i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.826239	−	0.563320i	0.826239	−	0.563320i
$668$			5.15669i			5.15669i
$669$	−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
$676$	4.82860	−	1.10210i	4.82860	−	1.10210i
$677$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$677$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$678$		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	0.781831	−	0.623490i	$-0.214286\pi$
$691$	0.781831	+	0.376510i	0.781831	+	0.376510i			1.00000i	$0.5\pi$
$692$	0.995739	−	0.794075i	0.995739	−	0.794075i
$693$		0			0
$694$	−3.61670	+	1.26554i	−3.61670	+	1.26554i
$695$		0			0
$696$	1.46304	+	3.35332i	1.46304	+	3.35332i
$697$		0			0
$698$	−3.66828	+	1.28359i	−3.66828	+	1.28359i
$699$	−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	$0.142857\pi$
$702$	−1.72769	+	2.74960i	−1.72769	+	2.74960i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−2.65645	−	0.299310i	−2.65645	−	0.299310i
$707$		0			0
$708$	0.266677	−	3.55856i	0.266677	−	3.55856i
$709$		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
$713$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$714$		0			0
$715$		0			0
$716$	−4.09043	+	0.933613i	−4.09043	+	0.933613i
$717$	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
$722$	−1.95278	+	0.220025i	−1.95278	+	0.220025i
$723$		0			0
$724$		0			0
$725$	0.680173	−	0.733052i	0.680173	−	0.733052i
$726$	1.48952	−	1.28183i	1.48952	−	1.28183i
$727$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$727$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$728$		0			0
$729$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$733$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$734$		0			0
$735$		0			0
$736$	4.10341	−	2.57835i	4.10341	−	2.57835i
$737$		0			0
$738$	−1.26949	+	3.23461i	−1.26949	+	3.23461i
$739$	1.66900	+	0.584010i	1.66900	+	0.584010i	0.988831	−	0.149042i	$-0.0476190\pi$
$739$	1.66900	+	0.584010i	1.66900	+	0.584010i	0.680173	+	0.733052i	$0.261905\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$743$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$744$	−1.06683	−	1.56475i	−1.06683	−	1.56475i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$751$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$752$	2.30018	+	6.57354i	2.30018	+	6.57354i
$753$		0			0
$754$	0.840473	+	3.13669i	0.840473	+	3.13669i
$755$		0			0
$756$		0			0
$757$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$757$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.116853	−	0.0931869i	−0.116853	−	0.0931869i	0.563320	−	0.826239i	$-0.309524\pi$
$761$	−0.116853	−	0.0931869i	−0.116853	−	0.0931869i	−0.680173	+	0.733052i	$0.738095\pi$
$762$	0.145316	−	0.0219029i	0.145316	−	0.0219029i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.458528	−	2.00894i	0.458528	−	2.00894i
$768$	1.95278	+	4.97559i	1.95278	+	4.97559i
$769$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$769$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$770$		0			0
$771$	−0.297251	−	0.0222759i	−0.297251	−	0.0222759i
$772$	1.21770	+	1.93797i	1.21770	+	1.93797i
$773$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$773$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$774$		0			0
$775$	−0.275400	+	0.438297i	−0.275400	+	0.438297i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$784$	−4.32785			−4.32785
$785$		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	$0.785714\pi$
$788$	4.46583	+	2.15063i	4.46583	+	2.15063i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.616341	+	0.980901i	0.616341	+	0.980901i
$795$		0			0
$796$		0			0
$797$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$797$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$798$		0			0
$799$		0			0
$800$	3.42680	−	3.42680i	3.42680	−	3.42680i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.729335	−	1.51448i	−0.729335	−	1.51448i
$807$	−0.0722342	+	0.0193551i	−0.0722342	+	0.0193551i
$808$	−0.510802	−	0.640525i	−0.510802	−	0.640525i
$809$	1.05737	−	0.119137i	1.05737	−	0.119137i	0.433884	−	0.900969i	$-0.357143\pi$
$809$	1.05737	−	0.119137i	1.05737	−	0.119137i	0.623490	+	0.781831i	$0.285714\pi$
$810$		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
$813$	1.23137	+	1.43087i	1.23137	+	1.43087i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	3.13069	−	1.50766i	3.13069	−	1.50766i
$819$		0			0
$820$		0			0
$821$	−0.347948	−	1.52446i	−0.347948	−	1.52446i	−0.781831	−	0.623490i	$-0.785714\pi$
$821$	−0.347948	−	1.52446i	−0.347948	−	1.52446i	0.433884	−	0.900969i	$-0.357143\pi$
$822$		0			0
$823$	−0.791295	+	0.497204i	−0.791295	+	0.497204i	−0.866025	−	0.500000i	$-0.833333\pi$
$823$	−0.791295	+	0.497204i	−0.791295	+	0.497204i	0.0747301	+	0.997204i	$0.476190\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$827$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$828$	−1.04551	+	2.66393i	−1.04551	+	2.66393i
$829$	−0.467085	−	0.467085i	−0.467085	−	0.467085i	0.433884	−	0.900969i	$-0.357143\pi$
$829$	−0.467085	−	0.467085i	−0.467085	−	0.467085i	−0.900969	+	0.433884i	$0.857143\pi$
$830$		0			0
$831$	0.123490	−	0.0841939i	0.123490	−	0.0841939i
$832$	1.91049	+	8.37038i	1.91049	+	8.37038i
$833$		0			0
$834$	−3.91654	+	0.146546i	−3.91654	+	0.146546i
$835$		0			0
$836$		0			0
$837$	0.488590	+	0.170965i	0.488590	+	0.170965i
$838$		0			0
$839$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$839$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$840$		0			0
$841$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$842$		0			0
$843$		0			0
$844$	4.02167	−	0.453134i	4.02167	−	0.453134i
$845$		0			0
$846$	−2.61280	−	1.78138i	−2.61280	−	1.78138i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	1.68231	−	5.45392i	1.68231	−	5.45392i
$853$	0.158342	−	0.158342i	0.158342	−	0.158342i	−0.623490	−	0.781831i	$-0.714286\pi$
$853$	0.158342	−	0.158342i	0.158342	−	0.158342i	0.781831	+	0.623490i	$0.214286\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.974928	+	0.222521i	0.974928	+	0.222521i	0.680173	−	0.733052i	$-0.261905\pi$
$857$	0.974928	+	0.222521i	0.974928	+	0.222521i	0.294755	+	0.955573i	$0.404762\pi$
$858$		0			0
$859$	0.497204	+	0.791295i	0.497204	+	0.791295i	0.997204	−	0.0747301i	$-0.0238095\pi$
$859$	0.497204	+	0.791295i	0.497204	+	0.791295i	−0.500000	+	0.866025i	$0.666667\pi$
$860$		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	$0.380952\pi$
$864$	−4.10341	−	2.57835i	−4.10341	−	2.57835i
$865$		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
$876$	−2.09781	+	4.80823i	−2.09781	+	4.80823i
$877$	−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	$0.928571\pi$
$878$	−0.616341	+	0.980901i	−0.616341	+	0.980901i
$879$		0			0
$880$		0			0
$881$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$881$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$882$	1.58114	−	1.16694i	1.58114	−	1.16694i
$883$	1.21572	+	0.277479i	1.21572	+	0.277479i	0.781831	−	0.623490i	$-0.214286\pi$
$883$	1.21572	+	0.277479i	1.21572	+	0.277479i	0.433884	+	0.900969i	$0.357143\pi$
$884$		0			0
$885$		0			0
$886$	−0.349732	+	1.53228i	−0.349732	+	1.53228i
$887$	0.0528791	−	0.0528791i	0.0528791	−	0.0528791i	−0.680173	−	0.733052i	$-0.738095\pi$
$887$	0.0528791	−	0.0528791i	0.0528791	−	0.0528791i	0.733052	+	0.680173i	$0.238095\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−0.995739	−	0.794075i	−0.995739	−	0.794075i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$898$		−	3.70971i		−	3.70971i
$899$	0.457652	−	0.241876i	0.457652	−	0.241876i
$900$	−0.426521	+	2.82978i	−0.426521	+	2.82978i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.0734787	+	1.96376i	0.0734787	+	1.96376i
$907$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$907$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$908$		0			0
$909$	0.216299	+	0.0579571i	0.216299	+	0.0579571i
$910$		0			0
$911$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$911$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$919$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$920$		0			0
$921$	0.0743122	+	1.98603i	0.0743122	+	1.98603i
$922$	3.53857	−	1.70409i	3.53857	−	1.70409i
$923$	1.42996	−	2.96934i	1.42996	−	2.96934i
$924$		0			0
$925$		0			0
$926$	−1.16953	−	3.34234i	−1.16953	−	3.34234i
$927$		0			0
$928$	−4.68109	+	1.25429i	−4.68109	+	1.25429i
$929$			1.65248i			1.65248i	0.563320	+	0.826239i	$0.309524\pi$
$929$			1.65248i			1.65248i	−0.563320	+	0.826239i	$0.690476\pi$
$930$		0			0
$931$		0			0
$932$	−3.41000	−	4.27601i	−3.41000	−	4.27601i
$933$	−0.337649	−	1.26012i	−0.337649	−	1.26012i
$934$		0			0
$935$		0			0
$936$	−4.58249	−	3.94355i	−4.58249	−	3.94355i
$937$		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
$943$	−0.584010	+	1.66900i	−0.584010	+	1.66900i
$944$	5.26143	+	1.20089i	5.26143	+	1.20089i
$945$		0			0
$946$		0			0
$947$	−0.0743122	−	0.00837297i	−0.0743122	−	0.00837297i	0.0747301	−	0.997204i	$-0.476190\pi$
$947$	−0.0743122	−	0.00837297i	−0.0743122	−	0.00837297i	−0.149042	+	0.988831i	$0.547619\pi$
$948$		0			0
$949$	−1.61163	+	2.56489i	−1.61163	+	2.56489i
$950$		0			0
$951$	−0.264152	+	0.605443i	−0.264152	+	0.605443i
$952$		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
$956$	−1.68703			−1.68703
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.572340	−	0.456426i	0.572340	−	0.456426i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.794755	+	0.0895474i	0.794755	+	0.0895474i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	0.794755	+	0.0895474i	0.794755	+	0.0895474i	0.294755	+	0.955573i	$0.404762\pi$
$968$	1.94648	+	3.09781i	1.94648	+	3.09781i
$969$		0			0
$970$		0			0
$971$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$971$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$972$	2.85375	−	0.213859i	2.85375	−	0.213859i
$973$		0			0
$974$	−1.89028	+	1.89028i	−1.89028	+	1.89028i
$975$	−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	$0.928571\pi$
$978$	0.471314	+	3.12696i	0.471314	+	3.12696i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.14503	+	1.43583i	1.14503	+	1.43583i
$983$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$983$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$984$	−5.60251	−	3.23461i	−5.60251	−	3.23461i
$985$		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	$-0.285714\pi$
$992$	2.26016	−	1.08844i	2.26016	−	1.08844i
$993$	1.99720	−	0.0747301i	1.99720	−	0.0747301i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.59842	−	1.00435i	1.59842	−	1.00435i	0.623490	−	0.781831i	$-0.285714\pi$
$997$	1.59842	−	1.00435i	1.59842	−	1.00435i	0.974928	−	0.222521i	$-0.0714286\pi$
$998$	2.74808	+	2.74808i	2.74808	+	2.74808i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.c.482.2	yes	24
3.2	odd	2		2001.1.bf.d.482.1	yes	24
23.22	odd	2	CM	2001.1.bf.c.482.2	yes	24
29.21	odd	28		2001.1.bf.d.137.1	yes	24
69.68	even	2		2001.1.bf.d.482.1	yes	24
87.50	even	28	inner	2001.1.bf.c.137.2	✓	24
667.137	even	28		2001.1.bf.d.137.1	yes	24
2001.137	odd	28	inner	2001.1.bf.c.137.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.137.2	✓	24	87.50	even	28	inner
2001.1.bf.c.137.2	✓	24	2001.137	odd	28	inner
2001.1.bf.c.482.2	yes	24	1.1	even	1	trivial
2001.1.bf.c.482.2	yes	24	23.22	odd	2	CM
2001.1.bf.d.137.1	yes	24	29.21	odd	28
2001.1.bf.d.137.1	yes	24	667.137	even	28
2001.1.bf.d.482.1	yes	24	3.2	odd	2
2001.1.bf.d.482.1	yes	24	69.68	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.85486 - 0.649042i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(2.23740 - 1.78427i) q^{4} +(-1.80117 - 0.785841i) q^{6} +(1.94648 - 3.09781i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})\)	\(q+(1.85486 - 0.649042i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(2.23740 - 1.78427i) q^{4} +(-1.80117 - 0.785841i) q^{6} +(1.94648 - 3.09781i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(-2.85375 - 0.213859i) q^{12} +(-1.61105 - 0.367711i) q^{13} +(0.963038 - 4.21934i) q^{16} +(0.785841 + 1.80117i) q^{18} +(0.433884 + 0.900969i) q^{23} +(-3.53392 + 0.946911i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-3.22692 + 0.363587i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.149042 - 0.988831i) q^{29} +(0.170965 + 0.488590i) q^{31} +(-0.542605 - 4.81575i) q^{32} +(1.94648 + 2.09781i) q^{36} +(0.930874 + 1.36534i) q^{39} +(1.25033 + 1.25033i) q^{41} +(1.38956 + 1.38956i) q^{46} +(-1.36254 + 0.856144i) q^{47} +(-3.57584 + 2.43797i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(1.66393 + 1.04551i) q^{50} +(-4.26066 + 2.05182i) q^{52} +(0.649042 - 1.85486i) q^{54} +(-0.918245 - 1.73740i) q^{58} +1.24698i q^{59} +(0.634231 + 0.795301i) q^{62} +(-2.25429 - 4.68109i) q^{64} +(0.294755 - 0.955573i) q^{69} +(-0.443797 + 1.94440i) q^{71} +(3.23461 + 1.70954i) q^{72} +(0.605443 - 1.73026i) q^{73} +(0.0747301 - 0.997204i) q^{75} +(2.61280 + 1.92833i) q^{78} +(-0.988831 + 0.149042i) q^{81} +(3.13069 + 1.50766i) q^{82} +(-0.563320 + 0.826239i) q^{87} +(2.57835 + 1.24167i) q^{92} +(0.206999 - 0.474448i) q^{93} +(-1.97165 + 2.47237i) q^{94} +(-2.87778 + 3.89926i) q^{96} +(-1.04551 - 1.66393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{3} + 14 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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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