LMFDB - Embedded newform 2001.1.bf.d.68.1

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			68.1
Root			$-0.563320 + 0.826239i$ of defining polynomial
Character	$\chi$	$=$	2001.68
Dual form			2001.1.bf.d.206.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0397866 - 0.0633201i) q^{2} +(-0.680173 - 0.733052i) q^{3} +(0.431457 - 0.895930i) q^{4} +(-0.0193551 + 0.0722342i) q^{6} +(-0.148209 + 0.0166991i) q^{8} +(-0.0747301 + 0.997204i) q^{9} +O(q^{10})$	\(q+(-0.0397866 - 0.0633201i) q^{2} +(-0.680173 - 0.733052i) q^{3} +(0.431457 - 0.895930i) q^{4} +(-0.0193551 + 0.0722342i) q^{6} +(-0.148209 + 0.0166991i) q^{8} +(-0.0747301 + 0.997204i) q^{9} +(-0.950229 + 0.293107i) q^{12} +(1.14625 - 0.914101i) q^{13} +(-0.613049 - 0.768739i) q^{16} +(0.0661163 - 0.0349435i) q^{18} +(0.974928 - 0.222521i) q^{23} +(0.113049 + 0.0972864i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.103486 - 0.0362114i) q^{26} +(0.781831 - 0.623490i) q^{27} +(-0.563320 - 0.826239i) q^{29} +(0.438297 - 0.275400i) q^{31} +(-0.0735454 + 0.210181i) q^{32} +(0.861182 + 0.497204i) q^{36} +(-1.44973 - 0.218511i) q^{39} +(-1.29621 - 1.29621i) q^{41} +(-0.0528791 - 0.0528791i) q^{46} +(-0.220025 + 1.95278i) q^{47} +(-0.146546 + 0.972272i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.00837297 + 0.0743122i) q^{50} +(-0.324414 - 1.42135i) q^{52} +(-0.0705858 - 0.0246991i) q^{54} +(-0.0299049 + 0.0685427i) q^{58} +1.80194i q^{59} +(-0.0348767 - 0.0167957i) q^{62} +(-0.942367 + 0.215089i) q^{64} +(-0.826239 - 0.563320i) q^{69} +(0.367554 + 0.460898i) q^{71} +(-0.00557677 - 0.149042i) q^{72} +(-1.10462 - 0.694076i) q^{73} +(0.294755 + 0.955573i) q^{75} +(0.0438437 + 0.100491i) q^{78} +(-0.988831 - 0.149042i) q^{81} +(-0.0305044 + 0.133648i) q^{82} +(-0.222521 + 0.974928i) q^{87} +(0.221277 - 0.969476i) q^{92} +(-0.500000 - 0.133975i) q^{93} +(0.132404 - 0.0637624i) q^{94} +(0.204097 - 0.0890466i) q^{96} +(-0.0743122 - 0.00837297i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 14 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9	$ 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9} + 2 q^{12} - 6 q^{16} + 12 q^{18} - 6 q^{24} - 4 q^{25} - 2 q^{26} - 2 q^{31} - 4 q^{32} + 6 q^{36} + 2 q^{39} - 2 q^{41} + 2 q^{46} + 2 q^{47} + 6 q^{48} - 4 q^{49} + 2 q^{50} - 10 q^{52} - 2 q^{54} + 4 q^{58} - 4 q^{62} - 28 q^{64} - 2 q^{69} + 22 q^{72} - 2 q^{73} - 4 q^{78} + 2 q^{81} - 4 q^{82} - 4 q^{87} - 4 q^{92} - 12 q^{93} - 8 q^{94} - 18 q^{96} + 2 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 14 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9 + 2 * q^12 - 6 * q^16 + 12 * q^18 - 6 * q^24 - 4 * q^25 - 2 * q^26 - 2 * q^31 - 4 * q^32 + 6 * q^36 + 2 * q^39 - 2 * q^41 + 2 * q^46 + 2 * q^47 + 6 * q^48 - 4 * q^49 + 2 * q^50 - 10 * q^52 - 2 * q^54 + 4 * q^58 - 4 * q^62 - 28 * q^64 - 2 * q^69 + 22 * q^72 - 2 * q^73 - 4 * q^78 + 2 * q^81 - 4 * q^82 - 4 * q^87 - 4 * q^92 - 12 * q^93 - 8 * q^94 - 18 * q^96 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{23}{28}\right)$	$-1$	$-1$

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 $

$2$	−0.0397866	−	0.0633201i	−0.0397866	−	0.0633201i	0.826239	−	0.563320i	$-0.190476\pi$
$2$	−0.0397866	−	0.0633201i	−0.0397866	−	0.0633201i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$3$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$4$	0.431457	−	0.895930i	0.431457	−	0.895930i
$5$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$5$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$6$	−0.0193551	+	0.0722342i	−0.0193551	+	0.0722342i
$7$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$7$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$8$	−0.148209	+	0.0166991i	−0.148209	+	0.0166991i
$9$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$10$		0			0
$11$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$11$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$12$	−0.950229	+	0.293107i	−0.950229	+	0.293107i
$13$	1.14625	−	0.914101i	1.14625	−	0.914101i	0.149042	−	0.988831i	$-0.452381\pi$
$13$	1.14625	−	0.914101i	1.14625	−	0.914101i	0.997204	+	0.0747301i	$0.0238095\pi$
$14$		0			0
$15$		0			0
$16$	−0.613049	−	0.768739i	−0.613049	−	0.768739i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	0.0661163	−	0.0349435i	0.0661163	−	0.0349435i
$19$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$19$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.974928	−	0.222521i	0.974928	−	0.222521i
$23$	0.974928	−	0.222521i	0.974928	−	0.222521i
$24$	0.113049	+	0.0972864i	0.113049	+	0.0972864i
$25$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$26$	−0.103486	−	0.0362114i	−0.103486	−	0.0362114i
$27$	0.781831	−	0.623490i	0.781831	−	0.623490i
$28$		0			0
$29$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$29$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$30$		0			0
$31$	0.438297	−	0.275400i	0.438297	−	0.275400i	−0.294755	−	0.955573i	$-0.595238\pi$
$31$	0.438297	−	0.275400i	0.438297	−	0.275400i	0.733052	+	0.680173i	$0.238095\pi$
$32$	−0.0735454	+	0.210181i	−0.0735454	+	0.210181i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.861182	+	0.497204i	0.861182	+	0.497204i
$37$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$37$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$38$		0			0
$39$	−1.44973	−	0.218511i	−1.44973	−	0.218511i
$40$		0			0
$41$	−1.29621	−	1.29621i	−1.29621	−	1.29621i	−0.930874	−	0.365341i	$-0.880952\pi$
$41$	−1.29621	−	1.29621i	−1.29621	−	1.29621i	−0.365341	−	0.930874i	$-0.619048\pi$
$42$		0			0
$43$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$43$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$44$		0			0
$45$		0			0
$46$	−0.0528791	−	0.0528791i	−0.0528791	−	0.0528791i
$47$	−0.220025	+	1.95278i	−0.220025	+	1.95278i	0.0747301	+	0.997204i	$0.476190\pi$
$47$	−0.220025	+	1.95278i	−0.220025	+	1.95278i	−0.294755	+	0.955573i	$0.595238\pi$
$48$	−0.146546	+	0.972272i	−0.146546	+	0.972272i
$49$	0.623490	−	0.781831i	0.623490	−	0.781831i
$50$	0.00837297	+	0.0743122i	0.00837297	+	0.0743122i
$51$		0			0
$52$	−0.324414	−	1.42135i	−0.324414	−	1.42135i
$53$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$53$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$54$	−0.0705858	−	0.0246991i	−0.0705858	−	0.0246991i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.0299049	+	0.0685427i	−0.0299049	+	0.0685427i
$59$			1.80194i			1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$59$			1.80194i			1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$60$		0			0
$61$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$61$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$62$	−0.0348767	−	0.0167957i	−0.0348767	−	0.0167957i
$63$		0			0
$64$	−0.942367	+	0.215089i	−0.942367	+	0.215089i
$65$		0			0
$66$		0			0
$67$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$67$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$68$		0			0
$69$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$70$		0			0
$71$	0.367554	+	0.460898i	0.367554	+	0.460898i	0.930874	−	0.365341i	$-0.119048\pi$
$71$	0.367554	+	0.460898i	0.367554	+	0.460898i	−0.563320	+	0.826239i	$0.690476\pi$
$72$	−0.00557677	−	0.149042i	−0.00557677	−	0.149042i
$73$	−1.10462	−	0.694076i	−1.10462	−	0.694076i	−0.149042	−	0.988831i	$-0.547619\pi$
$73$	−1.10462	−	0.694076i	−1.10462	−	0.694076i	−0.955573	+	0.294755i	$0.904762\pi$
$74$		0			0
$75$	0.294755	+	0.955573i	0.294755	+	0.955573i
$76$		0			0
$77$		0			0
$78$	0.0438437	+	0.100491i	0.0438437	+	0.100491i
$79$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$79$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$80$		0			0
$81$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$82$	−0.0305044	+	0.133648i	−0.0305044	+	0.133648i
$83$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$83$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$88$		0			0
$89$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$89$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$90$		0			0
$91$		0			0
$92$	0.221277	−	0.969476i	0.221277	−	0.969476i
$93$	−0.500000	−	0.133975i	−0.500000	−	0.133975i
$94$	0.132404	−	0.0637624i	0.132404	−	0.0637624i
$95$		0			0
$96$	0.204097	−	0.0890466i	0.204097	−	0.0890466i
$97$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$97$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$98$	−0.0743122	−	0.00837297i	−0.0743122	−	0.00837297i
$99$		0			0
$100$	−0.777459	+	0.620003i	−0.777459	+	0.620003i
$101$	−0.559311	−	0.351438i	−0.559311	−	0.351438i	0.222521	−	0.974928i	$-0.428571\pi$
$101$	−0.559311	−	0.351438i	−0.559311	−	0.351438i	−0.781831	+	0.623490i	$0.785714\pi$
$102$		0			0
$103$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$103$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$104$	−0.154619	+	0.154619i	−0.154619	+	0.154619i
$105$		0			0
$106$		0			0
$107$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$107$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$108$	−0.221277	−	0.969476i	−0.221277	−	0.969476i
$109$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$109$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$113$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$114$		0			0
$115$		0			0
$116$	−0.983301	+	0.148209i	−0.983301	+	0.148209i
$117$	0.825886	+	1.21135i	0.825886	+	1.21135i
$118$	0.114099	−	0.0716930i	0.114099	−	0.0716930i
$119$		0			0
$120$		0			0
$121$	0.974928	+	0.222521i	0.974928	+	0.222521i
$122$		0			0
$123$	−0.0685427	+	1.83184i	−0.0685427	+	1.83184i
$124$	−0.0576330	−	0.511507i	−0.0576330	−	0.511507i
$125$		0			0
$126$		0			0
$127$	−0.180173	+	1.59908i	−0.180173	+	1.59908i	0.500000	+	0.866025i	$0.333333\pi$
$127$	−0.180173	+	1.59908i	−0.180173	+	1.59908i	−0.680173	+	0.733052i	$0.738095\pi$
$128$	0.208569	+	0.208569i	0.208569	+	0.208569i
$129$		0			0
$130$		0			0
$131$	1.06332	−	1.69226i	1.06332	−	1.69226i	0.500000	−	0.866025i	$-0.333333\pi$
$131$	1.06332	−	1.69226i	1.06332	−	1.69226i	0.563320	−	0.826239i	$-0.309524\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$137$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$138$	−0.00279620	+	0.0747301i	−0.00279620	+	0.0747301i
$139$	−0.131178	−	0.574730i	−0.131178	−	0.574730i	−0.997204	−	0.0747301i	$-0.976190\pi$
$139$	−0.131178	−	0.574730i	−0.131178	−	0.574730i	0.866025	−	0.500000i	$-0.166667\pi$
$140$		0			0
$141$	1.58114	−	1.16694i	1.58114	−	1.16694i
$142$	0.0145603	−	0.0416111i	0.0145603	−	0.0416111i
$143$		0			0
$144$	0.812403	−	0.553887i	0.812403	−	0.553887i
$145$		0			0
$146$			0.0975592i			0.0975592i
$147$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$148$		0			0
$149$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$149$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$150$	0.0487796	−	0.0566829i	0.0487796	−	0.0566829i
$151$	0.974928	−	0.222521i	0.974928	−	0.222521i	0.294755	−	0.955573i	$-0.404762\pi$
$151$	0.974928	−	0.222521i	0.974928	−	0.222521i	0.680173	+	0.733052i	$0.261905\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.821267	+	1.20458i	−0.821267	+	1.20458i
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.0299049	+	0.0685427i	0.0299049	+	0.0685427i
$163$	1.95278	+	0.220025i	1.95278	+	0.220025i	0.997204	−	0.0747301i	$-0.0238095\pi$
$163$	1.95278	+	0.220025i	1.95278	+	0.220025i	0.955573	+	0.294755i	$0.0952381\pi$
$164$	−1.72058	+	0.602057i	−1.72058	+	0.602057i
$165$		0			0
$166$		0			0
$167$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$167$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$168$		0			0
$169$	0.255779	−	1.12064i	0.255779	−	1.12064i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$173$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$174$	0.0705858	−	0.0246991i	0.0705858	−	0.0246991i
$175$		0			0
$176$		0			0
$177$	1.32091	−	1.22563i	1.32091	−	1.22563i
$178$		0			0
$179$	0.440071	−	1.92808i	0.440071	−	1.92808i	0.0747301	−	0.997204i	$-0.476190\pi$
$179$	0.440071	−	1.92808i	0.440071	−	1.92808i	0.365341	−	0.930874i	$-0.380952\pi$
$180$		0			0
$181$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$181$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$182$		0			0
$183$		0			0
$184$	−0.140777	+	0.0492600i	−0.140777	+	0.0492600i
$185$		0			0
$186$	0.0114100	+	0.0369904i	0.0114100	+	0.0369904i
$187$		0			0
$188$	1.65462	+	1.03967i	1.65462	+	1.03967i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	0.798644	+	0.544506i	0.798644	+	0.544506i
$193$	0.500684	+	1.43087i	0.500684	+	1.43087i	0.866025	+	0.500000i	$0.166667\pi$
$193$	0.500684	+	1.43087i	0.500684	+	1.43087i	−0.365341	+	0.930874i	$0.619048\pi$
$194$		0			0
$195$		0			0
$196$	−0.431457	−	0.895930i	−0.431457	−	0.895930i
$197$	1.68862	−	0.385418i	1.68862	−	0.385418i	0.733052	−	0.680173i	$-0.238095\pi$
$197$	1.68862	−	0.385418i	1.68862	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$198$		0			0
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	0.140777	+	0.0492600i	0.140777	+	0.0492600i
$201$		0			0
$202$			0.0493981i			0.0493981i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.149042	+	0.988831i	0.149042	+	0.988831i
$208$	−1.40541	−	0.320776i	−1.40541	−	0.320776i
$209$		0			0
$210$		0			0
$211$	0.158342	+	1.40532i	0.158342	+	1.40532i	0.781831	+	0.623490i	$0.214286\pi$
$211$	0.158342	+	1.40532i	0.158342	+	1.40532i	−0.623490	+	0.781831i	$0.714286\pi$
$212$		0			0
$213$	0.0878620	−	0.582926i	0.0878620	−	0.582926i
$214$		0			0
$215$		0			0
$216$	−0.105463	+	0.105463i	−0.105463	+	0.105463i
$217$		0			0
$218$		0			0
$219$	0.242536	+	1.28183i	0.242536	+	1.28183i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$223$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$224$		0			0
$225$	0.500000	−	0.866025i	0.500000	−	0.866025i
$226$		0			0
$227$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$227$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$228$		0			0
$229$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$229$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$230$		0			0
$231$		0			0
$232$	0.0972864	+	0.113049i	0.0972864	+	0.113049i
$233$			0.730682i			0.730682i	0.930874	+	0.365341i	$0.119048\pi$
$233$			0.730682i			0.730682i	−0.930874	+	0.365341i	$0.880952\pi$
$234$	0.0438437	−	0.100491i	0.0438437	−	0.100491i
$235$		0			0
$236$	1.61441	+	0.777459i	1.61441	+	0.777459i
$237$		0			0
$238$		0			0
$239$	−0.807782	−	1.67738i	−0.807782	−	1.67738i	−0.733052	−	0.680173i	$-0.761905\pi$
$239$	−0.807782	−	1.67738i	−0.807782	−	1.67738i	−0.0747301	−	0.997204i	$-0.523810\pi$
$240$		0			0
$241$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$241$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$242$	−0.0246991	−	0.0705858i	−0.0246991	−	0.0705858i
$243$	0.563320	+	0.826239i	0.563320	+	0.826239i
$244$		0			0
$245$		0			0
$246$	0.118719	−	0.0685427i	0.118719	−	0.0685427i
$247$		0			0
$248$	−0.0603605	+	0.0481359i	−0.0603605	+	0.0481359i
$249$		0			0
$250$		0			0
$251$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$251$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$252$		0			0
$253$		0			0
$254$	0.108422	−	0.0522133i	0.108422	−	0.0522133i
$255$		0			0
$256$	−0.210181	+	0.920862i	−0.210181	+	0.920862i
$257$	−0.488831	+	1.01507i	−0.488831	+	1.01507i	0.500000	+	0.866025i	$0.333333\pi$
$257$	−0.488831	+	1.01507i	−0.488831	+	1.01507i	−0.988831	+	0.149042i	$0.952381\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.866025	−	0.500000i	0.866025	−	0.500000i
$262$	−0.149460			−0.149460
$263$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$263$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.59908	+	0.180173i	−1.59908	+	0.180173i	−0.866025	−	0.500000i	$-0.833333\pi$
$269$	−1.59908	+	0.180173i	−1.59908	+	0.180173i	−0.733052	+	0.680173i	$0.761905\pi$
$270$		0			0
$271$	−1.00435	+	0.351438i	−1.00435	+	0.351438i	−0.781831	−	0.623490i	$-0.785714\pi$
$271$	−1.00435	+	0.351438i	−1.00435	+	0.351438i	−0.222521	+	0.974928i	$0.571429\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.861182	+	0.497204i	−0.861182	+	0.497204i
$277$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.826239	+	0.563320i	$0.190476\pi$
$277$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.365341	+	0.930874i	$0.380952\pi$
$278$	−0.0311728	+	0.0311728i	−0.0311728	+	0.0311728i
$279$	0.241876	+	0.457652i	0.241876	+	0.457652i
$280$		0			0
$281$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$281$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$282$	−0.136799	−	0.0536895i	−0.136799	−	0.0536895i
$283$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$283$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$284$	0.571516	−	0.130445i	0.571516	−	0.130445i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.204097	−	0.0890466i	−0.204097	−	0.0890466i
$289$		−	1.00000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	−1.09844	+	0.690194i	−1.09844	+	0.690194i
$293$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$293$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$294$	0.0444073	+	0.0601697i	0.0444073	+	0.0601697i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.914101	−	1.14625i	0.914101	−	1.14625i
$300$	0.983301	+	0.148209i	0.983301	+	0.148209i
$301$		0			0
$302$	−0.0528791	−	0.0528791i	−0.0528791	−	0.0528791i
$303$	0.122805	+	0.649042i	0.122805	+	0.649042i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.33485	+	1.33485i	1.33485	+	1.33485i	0.900969	+	0.433884i	$0.142857\pi$
$307$	1.33485	+	1.33485i	1.33485	+	1.33485i	0.433884	+	0.900969i	$0.357143\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.197979	+	1.75711i	0.197979	+	1.75711i	0.563320	+	0.826239i	$0.309524\pi$
$311$	0.197979	+	1.75711i	0.197979	+	1.75711i	−0.365341	+	0.930874i	$0.619048\pi$
$312$	0.218511	+	0.00817612i	0.218511	+	0.00817612i
$313$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$313$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.43388	−	0.900969i	1.43388	−	0.900969i	0.433884	−	0.900969i	$-0.357143\pi$
$317$	1.43388	−	0.900969i	1.43388	−	0.900969i	1.00000			$0$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.560170	+	0.821618i	−0.560170	+	0.821618i
$325$	−1.42935	+	0.326239i	−1.42935	+	0.326239i
$326$	−0.0637624	−	0.132404i	−0.0637624	−	0.132404i
$327$		0			0
$328$	0.213756	+	0.170465i	0.213756	+	0.170465i
$329$		0			0
$330$		0			0
$331$	−0.839789	+	0.839789i	−0.839789	+	0.839789i	−0.988831	−	0.149042i	$-0.952381\pi$
$331$	−0.839789	+	0.839789i	−0.839789	+	0.839789i	0.149042	+	0.988831i	$0.452381\pi$
$332$		0			0
$333$		0			0
$334$	0.0281801	+	0.0177067i	0.0281801	+	0.0177067i
$335$		0			0
$336$		0			0
$337$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$337$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$338$	−0.0811356	+	0.0283906i	−0.0811356	+	0.0283906i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.0496131	−	0.0789588i	−0.0496131	−	0.0789588i
$347$	1.56366			1.56366			0.781831	−	0.623490i	$-0.214286\pi$
$347$	1.56366			1.56366			0.781831	+	0.623490i	$0.214286\pi$
$348$	0.777459	+	0.620003i	0.777459	+	0.620003i
$349$	1.65248			1.65248			0.826239	−	0.563320i	$-0.190476\pi$
$349$	1.65248			1.65248			0.826239	+	0.563320i	$0.190476\pi$
$350$		0			0
$351$	0.326239	−	1.42935i	0.326239	−	1.42935i
$352$		0			0
$353$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i	−0.997204	−	0.0747301i	$-0.976190\pi$
$353$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i	0.930874	+	0.365341i	$0.119048\pi$
$354$	−0.130162	−	0.0348767i	−0.130162	−	0.0348767i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.139595	+	0.0488464i	−0.139595	+	0.0488464i
$359$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$359$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$360$		0			0
$361$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$362$		0			0
$363$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$367$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$368$	−0.768739	−	0.613049i	−0.768739	−	0.613049i
$369$	1.38946	−	1.19572i	1.38946	−	1.19572i
$370$		0			0
$371$		0			0
$372$	−0.335761	+	0.390161i	−0.335761	+	0.390161i
$373$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$373$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$374$		0			0
$375$		0			0
$376$		−	0.293093i		−	0.293093i
$377$	−1.40097	−	0.432142i	−1.40097	−	0.432142i
$378$		0			0
$379$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$379$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$380$		0			0
$381$	1.29476	−	0.955573i	1.29476	−	0.955573i
$382$		0			0
$383$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$383$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$384$	0.0110290	−	0.294755i	0.0110290	−	0.294755i
$385$		0			0
$386$	0.0706825	−	0.0886330i	0.0706825	−	0.0886330i
$387$		0			0
$388$		0			0
$389$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$389$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$390$		0			0
$391$		0			0
$392$	−0.0793508	+	0.126286i	−0.0793508	+	0.126286i
$393$	−1.96376	+	0.371563i	−1.96376	+	0.371563i
$394$	−0.0915893	−	0.0915893i	−0.0915893	−	0.0915893i
$395$		0			0
$396$		0			0
$397$	−1.16078	+	1.45557i	−1.16078	+	1.45557i	−0.294755	+	0.955573i	$0.595238\pi$
$397$	−1.16078	+	1.45557i	−1.16078	+	1.45557i	−0.866025	+	0.500000i	$0.833333\pi$
$398$		0			0
$399$		0			0
$400$	0.218795	+	0.958602i	0.218795	+	0.958602i
$401$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$401$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$402$		0			0
$403$	0.250652	−	0.716324i	0.250652	−	0.716324i
$404$	−0.556183	+	0.349473i	−0.556183	+	0.349473i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.73026	−	0.605443i	−1.73026	−	0.605443i	−0.733052	−	0.680173i	$-0.761905\pi$
$409$	−1.73026	−	0.605443i	−1.73026	−	0.605443i	−0.997204	+	0.0747301i	$0.976190\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.0566829	−	0.0487796i	0.0566829	−	0.0487796i
$415$		0			0
$416$	0.107825	+	0.308147i	0.107825	+	0.308147i
$417$	−0.332083	+	0.487076i	−0.332083	+	0.487076i
$418$		0			0
$419$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$419$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$420$		0			0
$421$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$421$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$422$	0.0826851	−	0.0659392i	0.0826851	−	0.0659392i
$423$	−1.93087	−	0.365341i	−1.93087	−	0.365341i
$424$		0			0
$425$		0			0
$426$	−0.0404066	+	0.0176292i	−0.0404066	+	0.0176292i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$431$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$432$	−0.958602	−	0.218795i	−0.958602	−	0.218795i
$433$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$433$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.0715160	−	0.0663571i	0.0715160	−	0.0663571i
$439$	0.807782	−	1.67738i	0.807782	−	1.67738i	0.0747301	−	0.997204i	$-0.476190\pi$
$439$	0.807782	−	1.67738i	0.807782	−	1.67738i	0.733052	−	0.680173i	$-0.238095\pi$
$440$		0			0
$441$	0.733052	+	0.680173i	0.733052	+	0.680173i
$442$		0			0
$443$	−1.50641	+	0.169732i	−1.50641	+	0.169732i	−0.826239	−	0.563320i	$-0.809524\pi$
$443$	−1.50641	+	0.169732i	−1.50641	+	0.169732i	−0.680173	+	0.733052i	$0.738095\pi$
$444$		0			0
$445$		0			0
$446$	0.0926658	+	0.0104409i	0.0926658	+	0.0104409i
$447$		0			0
$448$		0			0
$449$	0.900969	+	0.566116i	0.900969	+	0.566116i	0.900969	−	0.433884i	$-0.142857\pi$
$449$	0.900969	+	0.566116i	0.900969	+	0.566116i			1.00000i	$0.5\pi$
$450$	−0.0747301	+	0.00279620i	−0.0747301	+	0.00279620i
$451$		0			0
$452$		0			0
$453$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$457$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.12099	+	0.392253i	1.12099	+	0.392253i	0.826239	−	0.563320i	$-0.190476\pi$
$461$	1.12099	+	0.392253i	1.12099	+	0.392253i	0.294755	+	0.955573i	$0.404762\pi$
$462$		0			0
$463$		−	0.445042i		−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$463$		−	0.445042i		−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$464$	−0.289819	+	0.939571i	−0.289819	+	0.939571i
$465$		0			0
$466$	0.0462668	−	0.0290714i	0.0462668	−	0.0290714i
$467$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$467$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$468$	1.44162	−	0.217289i	1.44162	−	0.217289i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.0300908	−	0.267063i	−0.0300908	−	0.267063i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.0740727	+	0.117886i	−0.0740727	+	0.117886i
$479$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$479$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.620003	−	0.777459i	0.620003	−	0.777459i
$485$		0			0
$486$	0.0299049	−	0.0685427i	0.0299049	−	0.0685427i
$487$	0.0663300	+	0.290611i	0.0663300	+	0.290611i	0.997204	−	0.0747301i	$-0.0238095\pi$
$487$	0.0663300	+	0.290611i	0.0663300	+	0.290611i	−0.930874	+	0.365341i	$0.880952\pi$
$488$		0			0
$489$	−1.16694	−	1.58114i	−1.16694	−	1.58114i
$490$		0			0
$491$	0.677197	−	0.425511i	0.677197	−	0.425511i	−0.149042	−	0.988831i	$-0.547619\pi$
$491$	0.677197	−	0.425511i	0.677197	−	0.425511i	0.826239	+	0.563320i	$0.190476\pi$
$492$	1.61163	+	0.851771i	1.61163	+	0.851771i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.480408	−	0.168102i	−0.480408	−	0.168102i
$497$		0			0
$498$		0			0
$499$	1.61105	−	0.367711i	1.61105	−	0.367711i	0.680173	−	0.733052i	$-0.261905\pi$
$499$	1.61105	−	0.367711i	1.61105	−	0.367711i	0.930874	+	0.365341i	$0.119048\pi$
$500$		0			0
$501$	0.414278	+	0.162592i	0.414278	+	0.162592i
$502$		0			0
$503$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$503$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.995462	+	0.574730i	−0.995462	+	0.574730i
$508$	1.35492	+	0.851356i	1.35492	+	0.851356i
$509$	−1.55929	+	1.24349i	−1.55929	+	1.24349i	−0.733052	+	0.680173i	$0.761905\pi$
$509$	−1.55929	+	1.24349i	−1.55929	+	1.24349i	−0.826239	+	0.563320i	$0.809524\pi$
$510$		0			0
$511$		0			0
$512$	0.345081	−	0.120749i	0.345081	−	0.120749i
$513$		0			0
$514$	0.0837231	−	0.00943332i	0.0837231	−	0.00943332i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.848162	−	0.914101i	−0.848162	−	0.914101i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.0661163	−	0.0349435i	−0.0661163	−	0.0349435i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	−1.05737	−	1.68280i	−1.05737	−	1.68280i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.900969	−	0.433884i	0.900969	−	0.433884i
$530$		0			0
$531$	−1.79690	−	0.134659i	−1.79690	−	0.134659i
$532$		0			0
$533$	−2.67065	−	0.300910i	−2.67065	−	0.300910i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.71271	+	0.988831i	−1.71271	+	0.988831i
$538$	0.0750304	+	0.0940852i	0.0750304	+	0.0940852i
$539$		0			0
$540$		0			0
$541$	0.122805	+	0.350958i	0.122805	+	0.350958i	0.988831	−	0.149042i	$-0.0476190\pi$
$541$	0.122805	+	0.350958i	0.122805	+	0.350958i	−0.866025	+	0.500000i	$0.833333\pi$
$542$	0.0622129	+	0.0496131i	0.0622129	+	0.0496131i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.658322	+	0.317031i	0.658322	+	0.317031i	0.733052	−	0.680173i	$-0.238095\pi$
$547$	0.658322	+	0.317031i	0.658322	+	0.317031i	−0.0747301	+	0.997204i	$0.523810\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	0.131863	+	0.0696915i	0.131863	+	0.0696915i
$553$		0			0
$554$	0.0472035	−	0.134900i	0.0472035	−	0.134900i
$555$		0			0
$556$	−0.571516	−	0.130445i	−0.571516	−	0.130445i
$557$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$557$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$558$	0.0193551	−	0.0335240i	0.0193551	−	0.0335240i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$	−0.363298	−	1.92008i	−0.363298	−	1.92008i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.0621713	−	0.0621713i	−0.0621713	−	0.0621713i
$569$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$569$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$570$		0			0
$571$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$571$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$576$	−0.144065	−	0.955806i	−0.144065	−	0.955806i
$577$	−0.392253	+	1.12099i	−0.392253	+	1.12099i	0.563320	+	0.826239i	$0.309524\pi$
$577$	−0.392253	+	1.12099i	−0.392253	+	1.12099i	−0.955573	+	0.294755i	$0.904762\pi$
$578$	−0.0633201	+	0.0397866i	−0.0633201	+	0.0397866i
$579$	0.708353	−	1.34027i	0.708353	−	1.34027i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.175304	+	0.0844220i	0.175304	+	0.0844220i
$585$		0			0
$586$		0			0
$587$	−0.129334	−	0.268565i	−0.129334	−	0.268565i	0.826239	−	0.563320i	$-0.190476\pi$
$587$	−0.129334	−	0.268565i	−0.129334	−	0.268565i	−0.955573	+	0.294755i	$0.904762\pi$
$588$	−0.363298	+	0.925668i	−0.363298	+	0.925668i
$589$		0			0
$590$		0			0
$591$	−1.43109	−	0.975699i	−1.43109	−	0.975699i
$592$		0			0
$593$	−0.974928	−	1.22252i	−0.974928	−	1.22252i	−0.974928	−	0.222521i	$-0.928571\pi$
$593$	−0.974928	−	1.22252i	−0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.108949	−	0.0122756i	−0.108949	−	0.0122756i
$599$	−1.00435	+	0.351438i	−1.00435	+	0.351438i	−0.781831	−	0.623490i	$-0.785714\pi$
$599$	−1.00435	+	0.351438i	−1.00435	+	0.351438i	−0.222521	+	0.974928i	$0.571429\pi$
$600$	−0.0596425	−	0.136702i	−0.0596425	−	0.136702i
$601$	1.91970	−	0.216299i	1.91970	−	0.216299i	0.930874	−	0.365341i	$-0.119048\pi$
$601$	1.91970	−	0.216299i	1.91970	−	0.216299i	0.988831	+	0.149042i	$0.0476190\pi$
$602$		0			0
$603$		0			0
$604$	0.221277	−	0.969476i	0.221277	−	0.969476i
$605$		0			0
$606$	0.0362114	−	0.0335993i	0.0362114	−	0.0335993i
$607$	−1.05737	−	1.68280i	−1.05737	−	1.68280i	−0.623490	−	0.781831i	$-0.714286\pi$
$607$	−1.05737	−	1.68280i	−1.05737	−	1.68280i	−0.433884	−	0.900969i	$-0.642857\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.53283	+	2.43949i	1.53283	+	2.43949i
$612$		0			0
$613$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$613$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$614$	0.0314137	−	0.137632i	0.0314137	−	0.137632i
$615$		0			0
$616$		0			0
$617$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$617$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$618$		0			0
$619$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$619$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$620$		0			0
$621$	0.623490	−	0.781831i	0.623490	−	0.781831i
$622$	0.103384	−	0.0824456i	0.103384	−	0.0824456i
$623$		0			0
$624$	0.720776	+	1.24842i	0.720776	+	1.24842i
$625$	0.623490	+	0.781831i	0.623490	+	0.781831i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$631$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$632$		0			0
$633$	0.922474	−	1.07193i	0.922474	−	1.07193i
$634$	−0.114099	−	0.0549471i	−0.114099	−	0.0549471i
$635$		0			0
$636$		0			0
$637$		−	1.46610i		−	1.46610i
$638$		0			0
$639$	−0.487076	+	0.332083i	−0.487076	+	0.332083i
$640$		0			0
$641$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$641$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$642$		0			0
$643$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$643$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.24349	−	1.55929i	1.24349	−	1.55929i	0.563320	−	0.826239i	$-0.309524\pi$
$647$	1.24349	−	1.55929i	1.24349	−	1.55929i	0.680173	−	0.733052i	$-0.261905\pi$
$648$	0.149042	+	0.00557677i	0.149042	+	0.00557677i
$649$		0			0
$650$	0.0775263	+	0.0775263i	0.0775263	+	0.0775263i
$651$		0			0
$652$	1.03967	−	1.65462i	1.03967	−	1.65462i
$653$	1.02781	−	1.63575i	1.02781	−	1.63575i	0.294755	−	0.955573i	$-0.404762\pi$
$653$	1.02781	−	1.63575i	1.02781	−	1.63575i	0.733052	−	0.680173i	$-0.238095\pi$
$654$		0			0
$655$		0			0
$656$	−0.201808	+	1.79109i	−0.201808	+	1.79109i
$657$	0.774683	−	1.04966i	0.774683	−	1.04966i
$658$		0			0
$659$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$659$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$660$		0			0
$661$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$661$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$662$	0.0865878	+	0.0197631i	0.0865878	+	0.0197631i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$668$			0.442553i			0.442553i
$669$	1.24349	−	0.0931869i	1.24349	−	0.0931869i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.290611	+	0.0663300i	−0.290611	+	0.0663300i	−0.365341	−	0.930874i	$-0.619048\pi$
$673$	−0.290611	+	0.0663300i	−0.290611	+	0.0663300i	0.0747301	+	0.997204i	$0.476190\pi$
$674$		0			0
$675$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$676$	−0.893658	−	0.712669i	−0.893658	−	0.712669i
$677$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$677$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.880843	+	0.702449i	−0.880843	+	0.702449i	−0.955573	−	0.294755i	$-0.904762\pi$
$683$	−0.880843	+	0.702449i	−0.880843	+	0.702449i	0.0747301	+	0.997204i	$0.476190\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.433884	+	1.90097i	−0.433884	+	1.90097i			1.00000i	$0.5\pi$
$691$	−0.433884	+	1.90097i	−0.433884	+	1.90097i	−0.433884	+	0.900969i	$0.642857\pi$
$692$	0.538018	−	1.11721i	0.538018	−	1.11721i
$693$		0			0
$694$	−0.0622129	−	0.0990112i	−0.0622129	−	0.0990112i
$695$		0			0
$696$	0.0166991	−	0.148209i	0.0166991	−	0.148209i
$697$		0			0
$698$	−0.0657465	−	0.104635i	−0.0657465	−	0.104635i
$699$	0.535628	−	0.496990i	0.535628	−	0.496990i
$700$		0			0
$701$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$	−0.103486	+	0.0362114i	−0.103486	+	0.0362114i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.0210406	−	0.00736241i	0.0210406	−	0.00736241i
$707$		0			0
$708$	−0.528160	−	1.71225i	−0.528160	−	1.71225i
$709$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$709$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.366025	−	0.366025i	0.366025	−	0.366025i
$714$		0			0
$715$		0			0
$716$	−1.53755	−	1.22616i	−1.53755	−	1.22616i
$717$	−0.680173	+	1.73305i	−0.680173	+	1.73305i
$718$		0			0
$719$	−1.90097	+	0.433884i	−1.90097	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$719$	−1.90097	+	0.433884i	−1.90097	+	0.433884i	−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.0705858	+	0.0246991i	0.0705858	+	0.0246991i
$723$		0			0
$724$		0			0
$725$	0.149042	+	0.988831i	0.149042	+	0.988831i
$726$	−0.0349435	+	0.0661163i	−0.0349435	+	0.0661163i
$727$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$727$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$728$		0			0
$729$	0.222521	−	0.974928i	0.222521	−	0.974928i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$733$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$734$		0			0
$735$		0			0
$736$	−0.0249319	+	0.221277i	−0.0249319	+	0.221277i
$737$		0			0
$738$	−0.130995	−	0.0404066i	−0.130995	−	0.0404066i
$739$	−0.975281	+	1.55215i	−0.975281	+	1.55215i	−0.149042	+	0.988831i	$0.547619\pi$
$739$	−0.975281	+	1.55215i	−0.975281	+	1.55215i	−0.826239	+	0.563320i	$0.809524\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$743$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$744$	0.0763416	+	0.0115067i	0.0763416	+	0.0115067i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$751$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$752$	1.63606	−	1.02801i	1.63606	−	1.02801i
$753$		0			0
$754$	0.0283766	+	0.105903i	0.0283766	+	0.105903i
$755$		0			0
$756$		0			0
$757$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$757$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.829215	−	1.72188i	−0.829215	−	1.72188i	−0.680173	−	0.733052i	$-0.738095\pi$
$761$	−0.829215	−	1.72188i	−0.829215	−	1.72188i	−0.149042	−	0.988831i	$-0.547619\pi$
$762$	−0.112021	−	0.0439650i	−0.112021	−	0.0439650i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.64715	+	2.06546i	1.64715	+	2.06546i
$768$	0.817999	−	0.472272i	0.817999	−	0.472272i
$769$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$769$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$770$		0			0
$771$	1.07659	−	0.332083i	1.07659	−	0.332083i
$772$	1.49799	+	0.168783i	1.49799	+	0.168783i
$773$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$773$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$774$		0			0
$775$	−0.514383	+	0.0579571i	−0.514383	+	0.0579571i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$784$	−0.983254			−0.983254
$785$		0			0
$786$	0.101659	+	0.109562i	0.101659	+	0.109562i
$787$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$787$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$788$	0.383262	−	1.67918i	0.383262	−	1.67918i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.138351	+	0.0155884i	0.138351	+	0.0155884i
$795$		0			0
$796$		0			0
$797$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$797$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$798$		0			0
$799$		0			0
$800$	0.157456	−	0.157456i	0.157456	−	0.157456i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.0553303	+	0.0126288i	−0.0553303	+	0.0126288i
$807$	1.21972	+	1.04966i	1.21972	+	1.04966i
$808$	0.0887634	+	0.0427462i	0.0887634	+	0.0427462i
$809$	1.87590	+	0.656405i	1.87590	+	0.656405i	0.974928	+	0.222521i	$0.0714286\pi$
$809$	1.87590	+	0.656405i	1.87590	+	0.656405i	0.900969	+	0.433884i	$0.142857\pi$
$810$		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
$813$	0.940755	+	0.497204i	0.940755	+	0.497204i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.0305044	+	0.133648i	0.0305044	+	0.133648i
$819$		0			0
$820$		0			0
$821$	0.541044	−	0.678448i	0.541044	−	0.678448i	−0.433884	−	0.900969i	$-0.642857\pi$
$821$	0.541044	−	0.678448i	0.541044	−	0.678448i	0.974928	+	0.222521i	$0.0714286\pi$
$822$		0			0
$823$	0.0895474	−	0.794755i	0.0895474	−	0.794755i	−0.866025	−	0.500000i	$-0.833333\pi$
$823$	0.0895474	−	0.794755i	0.0895474	−	0.794755i	0.955573	−	0.294755i	$-0.0952381\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$827$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$828$	0.950229	+	0.293107i	0.950229	+	0.293107i
$829$	−1.19745	−	1.19745i	−1.19745	−	1.19745i	−0.974928	−	0.222521i	$-0.928571\pi$
$829$	−1.19745	−	1.19745i	−1.19745	−	1.19745i	−0.222521	−	0.974928i	$-0.571429\pi$
$830$		0			0
$831$	0.284841	−	1.88980i	0.284841	−	1.88980i
$832$	−0.883571	+	1.10796i	−0.883571	+	1.10796i
$833$		0			0
$834$	0.0440542	+	0.00164839i	0.0440542	+	0.00164839i
$835$		0			0
$836$		0			0
$837$	0.170965	−	0.488590i	0.170965	−	0.488590i
$838$		0			0
$839$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$839$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$840$		0			0
$841$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$842$		0			0
$843$		0			0
$844$	1.32739	+	0.464473i	1.32739	+	0.464473i
$845$		0			0
$846$	0.0536895	+	0.136799i	0.0536895	+	0.136799i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.484352	−	0.330226i	−0.484352	−	0.330226i
$853$	0.467085	−	0.467085i	0.467085	−	0.467085i	−0.433884	−	0.900969i	$-0.642857\pi$
$853$	0.467085	−	0.467085i	0.467085	−	0.467085i	0.900969	+	0.433884i	$0.142857\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	−0.930874	−	0.365341i	$-0.880952\pi$
$857$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	0.149042	+	0.988831i	$0.452381\pi$
$858$		0			0
$859$	−0.794755	−	0.0895474i	−0.794755	−	0.0895474i	−0.294755	−	0.955573i	$-0.595238\pi$
$859$	−0.794755	−	0.0895474i	−0.794755	−	0.0895474i	−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$863$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.0747301	+	0.997204i	$0.523810\pi$
$864$	0.0735454	+	0.210181i	0.0735454	+	0.210181i
$865$		0			0
$866$		0			0
$867$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	1.25308	+	0.335761i	1.25308	+	0.335761i
$877$	−0.781831	+	0.376510i	−0.781831	+	0.376510i	−0.781831	−	0.623490i	$-0.785714\pi$
$877$	−0.781831	+	0.376510i	−0.781831	+	0.376510i			1.00000i	$0.5\pi$
$878$	−0.138351	+	0.0155884i	−0.138351	+	0.0155884i
$879$		0			0
$880$		0			0
$881$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$881$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$882$	0.0139029	−	0.0734787i	0.0139029	−	0.0734787i
$883$	−1.40881	+	1.12349i	−1.40881	+	1.12349i	−0.433884	+	0.900969i	$0.642857\pi$
$883$	−1.40881	+	1.12349i	−1.40881	+	1.12349i	−0.974928	+	0.222521i	$0.928571\pi$
$884$		0			0
$885$		0			0
$886$	0.0706825	+	0.0886330i	0.0706825	+	0.0886330i
$887$	−1.13787	+	1.13787i	−1.13787	+	1.13787i	−0.149042	+	0.988831i	$0.547619\pi$
$887$	−1.13787	+	1.13787i	−1.13787	+	1.13787i	−0.988831	+	0.149042i	$0.952381\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	0.538018	+	1.11721i	0.538018	+	1.11721i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1.46200	+	0.109562i	−1.46200	+	0.109562i
$898$		−	0.0795733i		−	0.0795733i
$899$	−0.474448	−	0.206999i	−0.474448	−	0.206999i
$900$	−0.560170	−	0.821618i	−0.560170	−	0.821618i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.00279620	+	0.0747301i	−0.00279620	+	0.0747301i
$907$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$907$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$908$		0			0
$909$	0.392253	−	0.531484i	0.392253	−	0.531484i
$910$		0			0
$911$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$911$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$919$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$920$		0			0
$921$	0.0705858	−	1.88645i	0.0705858	−	1.88645i
$922$	−0.0197631	−	0.0865878i	−0.0197631	−	0.0865878i
$923$	0.842614	+	0.192321i	0.842614	+	0.192321i
$924$		0			0
$925$		0			0
$926$	−0.0281801	+	0.0177067i	−0.0281801	+	0.0177067i
$927$		0			0
$928$	0.215089	−	0.0576330i	0.215089	−	0.0576330i
$929$			1.46610i			1.46610i	0.680173	+	0.733052i	$0.261905\pi$
$929$			1.46610i			1.46610i	−0.680173	+	0.733052i	$0.738095\pi$
$930$		0			0
$931$		0			0
$932$	0.654640	+	0.315258i	0.654640	+	0.315258i
$933$	1.15339	−	1.34027i	1.15339	−	1.34027i
$934$		0			0
$935$		0			0
$936$	−0.142632	−	0.165741i	−0.142632	−	0.165741i
$937$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$937$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$941$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$942$		0			0
$943$	−1.55215	−	0.975281i	−1.55215	−	0.975281i
$944$	1.38522	−	1.10468i	1.38522	−	1.10468i
$945$		0			0
$946$		0			0
$947$	−1.51889	+	0.531484i	−1.51889	+	0.531484i	−0.955573	−	0.294755i	$-0.904762\pi$
$947$	−1.51889	+	0.531484i	−1.51889	+	0.531484i	−0.563320	+	0.826239i	$0.690476\pi$
$948$		0			0
$949$	−1.90062	+	0.214148i	−1.90062	+	0.214148i
$950$		0			0
$951$	−1.63575	−	0.438297i	−1.63575	−	0.438297i
$952$		0			0
$953$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$953$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$954$		0			0
$955$		0			0
$956$	−1.85134			−1.85134
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.317625	+	0.659555i	−0.317625	+	0.659555i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.43087	−	0.500684i	1.43087	−	0.500684i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	1.43087	−	0.500684i	1.43087	−	0.500684i	0.930874	+	0.365341i	$0.119048\pi$
$968$	−0.148209	−	0.0166991i	−0.148209	−	0.0166991i
$969$		0			0
$970$		0			0
$971$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$971$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$972$	0.983301	−	0.148209i	0.983301	−	0.148209i
$973$		0			0
$974$	0.0157625	−	0.0157625i	0.0157625	−	0.0157625i
$975$	1.21135	+	0.825886i	1.21135	+	0.825886i
$976$		0			0
$977$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$977$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$978$	−0.0536895	+	0.136799i	−0.0536895	+	0.136799i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.0538867	−	0.0259505i	−0.0538867	−	0.0259505i
$983$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$983$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$984$	−0.0204315	−	0.272640i	−0.0204315	−	0.272640i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.52446	−	0.347948i	−1.52446	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$991$	−1.52446	−	0.347948i	−1.52446	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$992$	0.0256491	+	0.112376i	0.0256491	+	0.112376i
$993$	1.18681	+	0.0444073i	1.18681	+	0.0444073i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.119137	+	1.05737i	−0.119137	+	1.05737i	0.781831	+	0.623490i	$0.214286\pi$
$997$	−0.119137	+	1.05737i	−0.119137	+	1.05737i	−0.900969	+	0.433884i	$0.857143\pi$
$998$	−0.0873816	−	0.0873816i	−0.0873816	−	0.0873816i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.d.68.1	yes	24
3.2	odd	2		2001.1.bf.c.68.2	✓	24
23.22	odd	2	CM	2001.1.bf.d.68.1	yes	24
29.3	odd	28		2001.1.bf.c.206.2	yes	24
69.68	even	2		2001.1.bf.c.68.2	✓	24
87.32	even	28	inner	2001.1.bf.d.206.1	yes	24
667.206	even	28		2001.1.bf.c.206.2	yes	24
2001.206	odd	28	inner	2001.1.bf.d.206.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.68.2	✓	24	3.2	odd	2
2001.1.bf.c.68.2	✓	24	69.68	even	2
2001.1.bf.c.206.2	yes	24	29.3	odd	28
2001.1.bf.c.206.2	yes	24	667.206	even	28
2001.1.bf.d.68.1	yes	24	1.1	even	1	trivial
2001.1.bf.d.68.1	yes	24	23.22	odd	2	CM
2001.1.bf.d.206.1	yes	24	87.32	even	28	inner
2001.1.bf.d.206.1	yes	24	2001.206	odd	28	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.0397866 - 0.0633201i) q^{2} +(-0.680173 - 0.733052i) q^{3} +(0.431457 - 0.895930i) q^{4} +(-0.0193551 + 0.0722342i) q^{6} +(-0.148209 + 0.0166991i) q^{8} +(-0.0747301 + 0.997204i) q^{9} +O(q^{10})\)	\(q+(-0.0397866 - 0.0633201i) q^{2} +(-0.680173 - 0.733052i) q^{3} +(0.431457 - 0.895930i) q^{4} +(-0.0193551 + 0.0722342i) q^{6} +(-0.148209 + 0.0166991i) q^{8} +(-0.0747301 + 0.997204i) q^{9} +(-0.950229 + 0.293107i) q^{12} +(1.14625 - 0.914101i) q^{13} +(-0.613049 - 0.768739i) q^{16} +(0.0661163 - 0.0349435i) q^{18} +(0.974928 - 0.222521i) q^{23} +(0.113049 + 0.0972864i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.103486 - 0.0362114i) q^{26} +(0.781831 - 0.623490i) q^{27} +(-0.563320 - 0.826239i) q^{29} +(0.438297 - 0.275400i) q^{31} +(-0.0735454 + 0.210181i) q^{32} +(0.861182 + 0.497204i) q^{36} +(-1.44973 - 0.218511i) q^{39} +(-1.29621 - 1.29621i) q^{41} +(-0.0528791 - 0.0528791i) q^{46} +(-0.220025 + 1.95278i) q^{47} +(-0.146546 + 0.972272i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.00837297 + 0.0743122i) q^{50} +(-0.324414 - 1.42135i) q^{52} +(-0.0705858 - 0.0246991i) q^{54} +(-0.0299049 + 0.0685427i) q^{58} +1.80194i q^{59} +(-0.0348767 - 0.0167957i) q^{62} +(-0.942367 + 0.215089i) q^{64} +(-0.826239 - 0.563320i) q^{69} +(0.367554 + 0.460898i) q^{71} +(-0.00557677 - 0.149042i) q^{72} +(-1.10462 - 0.694076i) q^{73} +(0.294755 + 0.955573i) q^{75} +(0.0438437 + 0.100491i) q^{78} +(-0.988831 - 0.149042i) q^{81} +(-0.0305044 + 0.133648i) q^{82} +(-0.222521 + 0.974928i) q^{87} +(0.221277 - 0.969476i) q^{92} +(-0.500000 - 0.133975i) q^{93} +(0.132404 - 0.0637624i) q^{94} +(0.204097 - 0.0890466i) q^{96} +(-0.0743122 - 0.00837297i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 14 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9	\( 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9} + 2 q^{12} - 6 q^{16} + 12 q^{18} - 6 q^{24} - 4 q^{25} - 2 q^{26} - 2 q^{31} - 4 q^{32} + 6 q^{36} + 2 q^{39} - 2 q^{41} + 2 q^{46} + 2 q^{47} + 6 q^{48} - 4 q^{49} + 2 q^{50} - 10 q^{52} - 2 q^{54} + 4 q^{58} - 4 q^{62} - 28 q^{64} - 2 q^{69} + 22 q^{72} - 2 q^{73} - 4 q^{78} + 2 q^{81} - 4 q^{82} - 4 q^{87} - 4 q^{92} - 12 q^{93} - 8 q^{94} - 18 q^{96} + 2 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 14 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9 + 2 * q^12 - 6 * q^16 + 12 * q^18 - 6 * q^24 - 4 * q^25 - 2 * q^26 - 2 * q^31 - 4 * q^32 + 6 * q^36 + 2 * q^39 - 2 * q^41 + 2 * q^46 + 2 * q^47 + 6 * q^48 - 4 * q^49 + 2 * q^50 - 10 * q^52 - 2 * q^54 + 4 * q^58 - 4 * q^62 - 28 * q^64 - 2 * q^69 + 22 * q^72 - 2 * q^73 - 4 * q^78 + 2 * q^81 - 4 * q^82 - 4 * q^87 - 4 * q^92 - 12 * q^93 - 8 * q^94 - 18 * q^96 + 2 * q^98

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