LMFDB - Embedded newform 2001.1.bf.d.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			$-0.930874 + 0.365341i$ of defining polynomial
Character	$\chi$	$=$	2001.482
Dual form			2001.1.bf.d.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23137 - 0.430874i) q^{2} +(0.997204 + 0.0747301i) q^{3} +(0.548780 - 0.437637i) q^{4} +(1.26012 - 0.337649i) q^{6} +(-0.206893 + 0.329269i) q^{8} +(0.988831 + 0.149042i) q^{9} +O(q^{10})$	\(q+(1.23137 - 0.430874i) q^{2} +(0.997204 + 0.0747301i) q^{3} +(0.548780 - 0.437637i) q^{4} +(1.26012 - 0.337649i) q^{6} +(-0.206893 + 0.329269i) q^{8} +(0.988831 + 0.149042i) q^{9} +(0.579950 - 0.395403i) q^{12} +(-0.145713 - 0.0332580i) q^{13} +(-0.269079 + 1.17891i) q^{16} +(1.28183 - 0.242536i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-0.230921 + 0.312887i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-0.193756 + 0.0218311i) q^{26} +(0.974928 + 0.222521i) q^{27} +(-0.930874 - 0.365341i) q^{29} +(-0.638050 - 1.82344i) q^{31} +(0.133087 + 1.18118i) q^{32} +(0.607877 - 0.350958i) q^{36} +(-0.142820 - 0.0440542i) q^{39} +(0.0528791 + 0.0528791i) q^{41} +(-0.922474 - 0.922474i) q^{46} +(-1.55215 + 0.975281i) q^{47} +(-0.356427 + 1.15551i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(1.10462 + 0.694076i) q^{50} +(-0.0945192 + 0.0455181i) q^{52} +(1.29637 - 0.146066i) q^{54} +(-1.30366 - 0.0487796i) q^{58} -1.24698i q^{59} +(-1.57135 - 1.97041i) q^{62} +(0.148155 + 0.307647i) q^{64} +(-0.365341 - 0.930874i) q^{69} +(-0.250701 + 1.09839i) q^{71} +(-0.253657 + 0.294755i) q^{72} +(-0.531484 + 1.51889i) q^{73} +(0.563320 + 0.826239i) q^{75} +(-0.194846 + 0.00729061i) q^{78} +(0.955573 + 0.294755i) q^{81} +(0.0878978 + 0.0423294i) q^{82} +(-0.900969 - 0.433884i) q^{87} +(-0.632404 - 0.304550i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(-1.49104 + 1.86971i) q^{94} +(0.0444453 + 1.18783i) q^{96} +(-0.694076 - 1.10462i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.23137	−	0.430874i	1.23137	−	0.430874i	0.365341	−	0.930874i	$-0.380952\pi$
$2$	1.23137	−	0.430874i	1.23137	−	0.430874i	0.866025	+	0.500000i	$0.166667\pi$
$3$	0.997204	+	0.0747301i	0.997204	+	0.0747301i
$3$	0.997204	+	0.0747301i	0.997204	+	0.0747301i
$4$	0.548780	−	0.437637i	0.548780	−	0.437637i
$5$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$5$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$6$	1.26012	−	0.337649i	1.26012	−	0.337649i
$7$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$7$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$8$	−0.206893	+	0.329269i	−0.206893	+	0.329269i
$9$	0.988831	+	0.149042i	0.988831	+	0.149042i
$10$		0			0
$11$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$11$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$12$	0.579950	−	0.395403i	0.579950	−	0.395403i
$13$	−0.145713	−	0.0332580i	−0.145713	−	0.0332580i	0.149042	−	0.988831i	$-0.452381\pi$
$13$	−0.145713	−	0.0332580i	−0.145713	−	0.0332580i	−0.294755	+	0.955573i	$0.595238\pi$
$14$		0			0
$15$		0			0
$16$	−0.269079	+	1.17891i	−0.269079	+	1.17891i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	1.28183	−	0.242536i	1.28183	−	0.242536i
$19$		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
$24$	−0.230921	+	0.312887i	−0.230921	+	0.312887i
$25$	0.623490	+	0.781831i	0.623490	+	0.781831i
$26$	−0.193756	+	0.0218311i	−0.193756	+	0.0218311i
$27$	0.974928	+	0.222521i	0.974928	+	0.222521i
$28$		0			0
$29$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$29$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$30$		0			0
$31$	−0.638050	−	1.82344i	−0.638050	−	1.82344i	−0.563320	−	0.826239i	$-0.690476\pi$
$31$	−0.638050	−	1.82344i	−0.638050	−	1.82344i	−0.0747301	−	0.997204i	$-0.523810\pi$
$32$	0.133087	+	1.18118i	0.133087	+	1.18118i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.607877	−	0.350958i	0.607877	−	0.350958i
$37$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$37$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$38$		0			0
$39$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i
$40$		0			0
$41$	0.0528791	+	0.0528791i	0.0528791	+	0.0528791i	0.733052	−	0.680173i	$-0.238095\pi$
$41$	0.0528791	+	0.0528791i	0.0528791	+	0.0528791i	−0.680173	+	0.733052i	$0.738095\pi$
$42$		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
$46$	−0.922474	−	0.922474i	−0.922474	−	0.922474i
$47$	−1.55215	+	0.975281i	−1.55215	+	0.975281i	−0.563320	+	0.826239i	$0.690476\pi$
$47$	−1.55215	+	0.975281i	−1.55215	+	0.975281i	−0.988831	+	0.149042i	$0.952381\pi$
$48$	−0.356427	+	1.15551i	−0.356427	+	1.15551i
$49$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$50$	1.10462	+	0.694076i	1.10462	+	0.694076i
$51$		0			0
$52$	−0.0945192	+	0.0455181i	−0.0945192	+	0.0455181i
$53$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$53$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$54$	1.29637	−	0.146066i	1.29637	−	0.146066i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−1.30366	−	0.0487796i	−1.30366	−	0.0487796i
$59$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$59$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$60$		0			0
$61$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$61$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$62$	−1.57135	−	1.97041i	−1.57135	−	1.97041i
$63$		0			0
$64$	0.148155	+	0.307647i	0.148155	+	0.307647i
$65$		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
$69$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$70$		0			0
$71$	−0.250701	+	1.09839i	−0.250701	+	1.09839i	0.680173	+	0.733052i	$0.261905\pi$
$71$	−0.250701	+	1.09839i	−0.250701	+	1.09839i	−0.930874	+	0.365341i	$0.880952\pi$
$72$	−0.253657	+	0.294755i	−0.253657	+	0.294755i
$73$	−0.531484	+	1.51889i	−0.531484	+	1.51889i	0.294755	+	0.955573i	$0.404762\pi$
$73$	−0.531484	+	1.51889i	−0.531484	+	1.51889i	−0.826239	+	0.563320i	$0.809524\pi$
$74$		0			0
$75$	0.563320	+	0.826239i	0.563320	+	0.826239i
$76$		0			0
$77$		0			0
$78$	−0.194846	+	0.00729061i	−0.194846	+	0.00729061i
$79$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$79$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$80$		0			0
$81$	0.955573	+	0.294755i	0.955573	+	0.294755i
$82$	0.0878978	+	0.0423294i	0.0878978	+	0.0423294i
$83$		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
$87$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$88$		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
$92$	−0.632404	−	0.304550i	−0.632404	−	0.304550i
$93$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$94$	−1.49104	+	1.86971i	−1.49104	+	1.86971i
$95$		0			0
$96$	0.0444453	+	1.18783i	0.0444453	+	1.18783i
$97$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$97$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$98$	−0.694076	−	1.10462i	−0.694076	−	1.10462i
$99$		0			0
$100$	0.684317	+	0.156191i	0.684317	+	0.156191i
$101$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i	−0.974928	−	0.222521i	$-0.928571\pi$
$101$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i	0.900969	+	0.433884i	$0.142857\pi$
$102$		0			0
$103$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$103$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$104$	0.0410978	−	0.0410978i	0.0410978	−	0.0410978i
$105$		0			0
$106$		0			0
$107$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$107$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$108$	0.632404	−	0.304550i	0.632404	−	0.304550i
$109$		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
$116$	−0.670731	+	0.206893i	−0.670731	+	0.206893i
$117$	−0.139129	−	0.0546039i	−0.139129	−	0.0546039i
$118$	−0.537291	−	1.53549i	−0.537291	−	1.53549i
$119$		0			0
$120$		0			0
$121$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$122$		0			0
$123$	0.0487796	+	0.0566829i	0.0487796	+	0.0566829i
$124$	−1.14816	−	0.721434i	−1.14816	−	0.721434i
$125$		0			0
$126$		0			0
$127$	1.49720	−	0.940755i	1.49720	−	0.940755i	0.500000	−	0.866025i	$-0.333333\pi$
$127$	1.49720	−	0.940755i	1.49720	−	0.940755i	0.997204	−	0.0747301i	$-0.0238095\pi$
$128$	−0.525518	−	0.525518i	−0.525518	−	0.525518i
$129$		0			0
$130$		0			0
$131$	1.43087	+	0.500684i	1.43087	+	0.500684i	0.930874	−	0.365341i	$-0.119048\pi$
$131$	1.43087	+	0.500684i	1.43087	+	0.500684i	0.500000	+	0.866025i	$0.333333\pi$
$132$		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	$0.178571\pi$
$138$	−0.850958	−	0.988831i	−0.850958	−	0.988831i
$139$	−1.01507	+	0.488831i	−1.01507	+	0.488831i	−0.866025	−	0.500000i	$-0.833333\pi$
$139$	−1.01507	+	0.488831i	−1.01507	+	0.488831i	−0.149042	+	0.988831i	$0.547619\pi$
$140$		0			0
$141$	−1.62069	+	0.856562i	−1.62069	+	0.856562i
$142$	0.164564	+	1.46054i	0.164564	+	1.46054i
$143$		0			0
$144$	−0.441781	+	1.12564i	−0.441781	+	1.12564i
$145$		0			0
$146$			2.09932i			2.09932i
$147$	−0.149042	−	0.988831i	−0.149042	−	0.988831i
$148$		0			0
$149$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$149$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$150$	1.04966	+	0.774683i	1.04966	+	0.774683i
$151$	−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
$156$	−0.0976565	+	0.0383273i	−0.0976565	+	0.0383273i
$157$		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
$162$	1.30366	−	0.0487796i	1.30366	−	0.0487796i
$163$	0.975281	+	1.55215i	0.975281	+	1.55215i	0.826239	+	0.563320i	$0.190476\pi$
$163$	0.975281	+	1.55215i	0.975281	+	1.55215i	0.149042	+	0.988831i	$0.452381\pi$
$164$	0.0521609	+	0.00587712i	0.0521609	+	0.00587712i
$165$		0			0
$166$		0			0
$167$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$167$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$168$		0			0
$169$	−0.880843	−	0.424191i	−0.880843	−	0.424191i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$173$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$174$	−1.29637	−	0.146066i	−1.29637	−	0.146066i
$175$		0			0
$176$		0			0
$177$	0.0931869	−	1.24349i	0.0931869	−	1.24349i
$178$		0			0
$179$	−1.72188	−	0.829215i	−1.72188	−	0.829215i	−0.988831	−	0.149042i	$-0.952381\pi$
$179$	−1.72188	−	0.829215i	−1.72188	−	0.829215i	−0.733052	−	0.680173i	$-0.761905\pi$
$180$		0			0
$181$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$181$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$182$		0			0
$183$		0			0
$184$	0.386428	+	0.0435400i	0.386428	+	0.0435400i
$185$		0			0
$186$	−1.41970	−	2.08232i	−1.41970	−	2.08232i
$187$		0			0
$188$	−0.424970	+	1.21449i	−0.424970	+	1.21449i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	0.124750	+	0.317859i	0.124750	+	0.317859i
$193$	−0.132974	+	1.18017i	−0.132974	+	1.18017i	0.733052	+	0.680173i	$0.238095\pi$
$193$	−0.132974	+	1.18017i	−0.132974	+	1.18017i	−0.866025	+	0.500000i	$0.833333\pi$
$194$		0			0
$195$		0			0
$196$	−0.548780	−	0.437637i	−0.548780	−	0.437637i
$197$	0.751509	+	1.56052i	0.751509	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$197$	0.751509	+	1.56052i	0.751509	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$198$		0			0
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	−0.386428	+	0.0435400i	−0.386428	+	0.0435400i
$201$		0			0
$202$			0.292132i			0.292132i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.294755	−	0.955573i	−0.294755	−	0.955573i
$208$	0.0784166	−	0.162834i	0.0784166	−	0.162834i
$209$		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
$213$	−0.332083	+	1.07659i	−0.332083	+	1.07659i
$214$		0			0
$215$		0			0
$216$	−0.274975	+	0.274975i	−0.274975	+	0.274975i
$217$		0			0
$218$		0			0
$219$	−0.643504	+	1.47493i	−0.643504	+	1.47493i
$220$		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
$225$	0.500000	+	0.866025i	0.500000	+	0.866025i
$226$		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
$232$	0.312887	−	0.230921i	0.312887	−	0.230921i
$233$		−	1.46610i		−	1.46610i	−0.680173	−	0.733052i	$-0.738095\pi$
$233$		−	1.46610i		−	1.46610i	0.680173	−	0.733052i	$-0.261905\pi$
$234$	−0.194846	−	0.00729061i	−0.194846	−	0.00729061i
$235$		0			0
$236$	−0.545725	−	0.684317i	−0.545725	−	0.684317i
$237$		0			0
$238$		0			0
$239$	1.06356	+	0.848162i	1.06356	+	0.848162i	0.988831	−	0.149042i	$-0.0476190\pi$
$239$	1.06356	+	0.848162i	1.06356	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$240$		0			0
$241$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$241$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$242$	−0.146066	+	1.29637i	−0.146066	+	1.29637i
$243$	0.930874	+	0.365341i	0.930874	+	0.365341i
$244$		0			0
$245$		0			0
$246$	0.0844888	+	0.0487796i	0.0844888	+	0.0487796i
$247$		0			0
$248$	0.732411	+	0.167168i	0.732411	+	0.167168i
$249$		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
$254$	1.43826	−	1.80352i	1.43826	−	1.80352i
$255$		0			0
$256$	−1.18118	−	0.568828i	−1.18118	−	0.568828i
$257$	1.45557	−	1.16078i	1.45557	−	1.16078i	0.500000	−	0.866025i	$-0.333333\pi$
$257$	1.45557	−	1.16078i	1.45557	−	1.16078i	0.955573	−	0.294755i	$-0.0952381\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$262$	1.97766			1.97766
$263$		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
$269$	0.940755	−	1.49720i	0.940755	−	1.49720i	0.0747301	−	0.997204i	$-0.476190\pi$
$269$	0.940755	−	1.49720i	0.940755	−	1.49720i	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
$276$	−0.607877	−	0.350958i	−0.607877	−	0.350958i
$277$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	0.365341	+	0.930874i	$0.380952\pi$
$277$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	−0.733052	+	0.680173i	$0.761905\pi$
$278$	−1.03930	+	1.03930i	−1.03930	+	1.03930i
$279$	−0.359154	−	1.89817i	−0.359154	−	1.89817i
$280$		0			0
$281$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$281$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$282$	−1.62660	+	1.75306i	−1.62660	+	1.75306i
$283$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$283$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$284$	0.343118	+	0.712492i	0.343118	+	0.712492i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0444453	+	1.18783i	−0.0444453	+	1.18783i
$289$		−	1.00000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	0.373057	+	1.06613i	0.373057	+	1.06613i
$293$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$293$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$294$	−0.609587	−	1.15339i	−0.609587	−	1.15339i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.0332580	+	0.145713i	0.0332580	+	0.145713i
$300$	0.670731	+	0.206893i	0.670731	+	0.206893i
$301$		0			0
$302$	−0.922474	−	0.922474i	−0.922474	−	0.922474i
$303$	−0.0895474	+	0.205245i	−0.0895474	+	0.205245i
$304$		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
$311$	1.66393	+	1.04551i	1.66393	+	1.04551i	0.930874	+	0.365341i	$0.119048\pi$
$311$	1.66393	+	1.04551i	1.66393	+	1.04551i	0.733052	+	0.680173i	$0.238095\pi$
$312$	0.0440542	−	0.0379117i	0.0440542	−	0.0379117i
$313$		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	1.00000			$0$
$317$	0.218169	+	0.623490i	0.218169	+	0.623490i	−0.781831	+	0.623490i	$0.785714\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.653395	−	0.256439i	0.653395	−	0.256439i
$325$	−0.0648483	−	0.134659i	−0.0648483	−	0.134659i
$326$	1.86971	+	1.49104i	1.86971	+	1.49104i
$327$		0			0
$328$	−0.0283518	+	0.00647111i	−0.0283518	+	0.00647111i
$329$		0			0
$330$		0			0
$331$	0.660818	−	0.660818i	0.660818	−	0.660818i	−0.294755	−	0.955573i	$-0.595238\pi$
$331$	0.660818	−	0.660818i	0.660818	−	0.660818i	0.955573	+	0.294755i	$0.0952381\pi$
$332$		0			0
$333$		0			0
$334$	0.776408	−	2.21885i	0.776408	−	2.21885i
$335$		0			0
$336$		0			0
$337$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$337$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$338$	−1.26741	−	0.142803i	−1.26741	−	0.142803i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.548010	+	0.191757i	−0.548010	+	0.191757i
$347$	1.94986			1.94986			0.974928	−	0.222521i	$-0.0714286\pi$
$347$	1.94986			1.94986			0.974928	+	0.222521i	$0.0714286\pi$
$348$	−0.684317	+	0.156191i	−0.684317	+	0.156191i
$349$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$349$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$350$		0			0
$351$	−0.134659	−	0.0648483i	−0.134659	−	0.0648483i
$352$		0			0
$353$	0.531130	+	0.255779i	0.531130	+	0.255779i	0.680173	−	0.733052i	$-0.261905\pi$
$353$	0.531130	+	0.255779i	0.531130	+	0.255779i	−0.149042	+	0.988831i	$0.547619\pi$
$354$	−0.421041	−	1.57135i	−0.421041	−	1.57135i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−2.47756	−	0.279153i	−2.47756	−	0.279153i
$359$		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
$363$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$364$		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	$0.535714\pi$
$368$	1.17891	−	0.269079i	1.17891	−	0.269079i
$369$	0.0444073	+	0.0601697i	0.0444073	+	0.0601697i
$370$		0			0
$371$		0			0
$372$	−1.09103	−	0.805218i	−1.09103	−	0.805218i
$373$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$373$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$374$		0			0
$375$		0			0
$376$		−	0.712854i		−	0.712854i
$377$	0.123490	+	0.0841939i	0.123490	+	0.0841939i
$378$		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
$381$	1.56332	−	0.826239i	1.56332	−	0.826239i
$382$		0			0
$383$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$383$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$384$	−0.484776	−	0.563320i	−0.484776	−	0.563320i
$385$		0			0
$386$	0.344766	+	1.51052i	0.344766	+	1.51052i
$387$		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
$392$	0.367051	+	0.128437i	0.367051	+	0.128437i
$393$	1.38946	+	0.606214i	1.38946	+	0.606214i
$394$	1.59777	+	1.59777i	1.59777	+	1.59777i
$395$		0			0
$396$		0			0
$397$	0.302705	+	1.32624i	0.302705	+	1.32624i	0.866025	+	0.500000i	$0.166667\pi$
$397$	0.302705	+	1.32624i	0.302705	+	1.32624i	−0.563320	+	0.826239i	$0.690476\pi$
$398$		0			0
$399$		0			0
$400$	−1.08948	+	0.524665i	−1.08948	+	0.524665i
$401$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$401$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$402$		0			0
$403$	0.0323281	+	0.286919i	0.0323281	+	0.286919i
$404$	0.0519130	+	0.148359i	0.0519130	+	0.148359i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.0743122	+	0.00837297i	−0.0743122	+	0.00837297i	−0.149042	−	0.988831i	$-0.547619\pi$
$409$	−0.0743122	+	0.00837297i	−0.0743122	+	0.00837297i	0.0747301	+	0.997204i	$0.476190\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.774683	−	1.04966i	−0.774683	−	1.04966i
$415$		0			0
$416$	0.0198913	−	0.176540i	0.0198913	−	0.176540i
$417$	−1.04876	+	0.411608i	−1.04876	+	0.411608i
$418$		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	$0.607143\pi$
$422$	1.79869	+	0.410539i	1.79869	+	0.410539i
$423$	−1.68017	+	0.733052i	−1.68017	+	0.733052i
$424$		0			0
$425$		0			0
$426$	0.0549571	+	1.46876i	0.0549571	+	1.46876i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$431$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$432$	−0.524665	+	1.08948i	−0.524665	+	1.08948i
$433$		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
$438$	−0.156882	+	2.09345i	−0.156882	+	2.09345i
$439$	−1.06356	+	0.848162i	−1.06356	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$439$	−1.06356	+	0.848162i	−1.06356	+	0.848162i	−0.0747301	+	0.997204i	$0.523810\pi$
$440$		0			0
$441$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$442$		0			0
$443$	0.631863	−	1.00560i	0.631863	−	1.00560i	−0.365341	−	0.930874i	$-0.619048\pi$
$443$	0.631863	−	1.00560i	0.631863	−	1.00560i	0.997204	−	0.0747301i	$-0.0238095\pi$
$444$		0			0
$445$		0			0
$446$	−0.308893	−	0.491600i	−0.308893	−	0.491600i
$447$		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	$0.714286\pi$
$450$	0.988831	+	0.850958i	0.988831	+	0.850958i
$451$		0			0
$452$		0			0
$453$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$457$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.928661	−	0.104635i	0.928661	−	0.104635i	0.365341	−	0.930874i	$-0.380952\pi$
$461$	0.928661	−	0.104635i	0.928661	−	0.104635i	0.563320	+	0.826239i	$0.309524\pi$
$462$		0			0
$463$		−	1.80194i		−	1.80194i	−0.433884	−	0.900969i	$-0.642857\pi$
$463$		−	1.80194i		−	1.80194i	0.433884	−	0.900969i	$-0.357143\pi$
$464$	0.681184	−	0.999113i	0.681184	−	0.999113i
$465$		0			0
$466$	−0.631706	−	1.80531i	−0.631706	−	1.80531i
$467$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$467$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$468$	−0.100248	+	0.0309223i	−0.100248	+	0.0309223i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.410591	+	0.257992i	0.410591	+	0.257992i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	1.67508	+	0.586137i	1.67508	+	0.586137i
$479$		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
$484$	0.156191	+	0.684317i	0.156191	+	0.684317i
$485$		0			0
$486$	1.30366	+	0.0487796i	1.30366	+	0.0487796i
$487$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	−0.680173	−	0.733052i	$-0.738095\pi$
$487$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	0.149042	+	0.988831i	$0.452381\pi$
$488$		0			0
$489$	0.856562	+	1.62069i	0.856562	+	1.62069i
$490$		0			0
$491$	0.660096	+	1.88645i	0.660096	+	1.88645i	0.365341	+	0.930874i	$0.380952\pi$
$491$	0.660096	+	1.88645i	0.660096	+	1.88645i	0.294755	+	0.955573i	$0.404762\pi$
$492$	0.0515758	+	0.00975867i	0.0515758	+	0.00975867i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.32136	−	0.261555i	2.32136	−	0.261555i
$497$		0			0
$498$		0			0
$499$	−0.317031	−	0.658322i	−0.317031	−	0.658322i	0.680173	−	0.733052i	$-0.261905\pi$
$499$	−0.317031	−	0.658322i	−0.317031	−	0.658322i	−0.997204	+	0.0747301i	$0.976190\pi$
$500$		0			0
$501$	1.22563	−	1.32091i	1.22563	−	1.32091i
$502$		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
$507$	−0.846680	−	0.488831i	−0.846680	−	0.488831i
$508$	0.409925	−	1.17150i	0.409925	−	1.17150i
$509$	−0.290611	−	0.0663300i	−0.290611	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$509$	−0.290611	−	0.0663300i	−0.290611	−	0.0663300i	−0.365341	+	0.930874i	$0.619048\pi$
$510$		0			0
$511$		0			0
$512$	−0.961042	−	0.108283i	−0.961042	−	0.108283i
$513$		0			0
$514$	1.29219	−	2.05651i	1.29219	−	2.05651i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.443797	−	0.0332580i	−0.443797	−	0.0332580i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−1.28183	−	0.242536i	−1.28183	−	0.242536i
$523$		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
$531$	0.185853	−	1.23305i	0.185853	−	1.23305i
$532$		0			0
$533$	−0.00594652	−	0.00946383i	−0.00594652	−	0.00946383i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.65510	−	0.955573i	−1.65510	−	0.955573i
$538$	0.513309	−	2.24895i	0.513309	−	2.24895i
$539$		0			0
$540$		0			0
$541$	−0.0895474	+	0.794755i	−0.0895474	+	0.794755i	0.866025	+	0.500000i	$0.166667\pi$
$541$	−0.0895474	+	0.794755i	−0.0895474	+	0.794755i	−0.955573	+	0.294755i	$0.904762\pi$
$542$	−2.40099	+	0.548010i	−2.40099	+	0.548010i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.914101	+	1.14625i	0.914101	+	1.14625i	0.988831	+	0.149042i	$0.0476190\pi$
$547$	0.914101	+	1.14625i	0.914101	+	1.14625i	−0.0747301	+	0.997204i	$0.523810\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	0.382094	+	0.0722961i	0.382094	+	0.0722961i
$553$		0			0
$554$	0.241371	+	2.14223i	0.241371	+	2.14223i
$555$		0			0
$556$	−0.343118	+	0.712492i	−0.343118	+	0.712492i
$557$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$557$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$558$	−1.26012	−	2.18260i	−1.26012	−	2.18260i
$559$		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	$0.250000\pi$
$564$	−0.514540	+	1.17934i	−0.514540	+	1.17934i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.309798	−	0.309798i	−0.309798	−	0.309798i
$569$		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
$576$	0.100648	+	0.326292i	0.100648	+	0.326292i
$577$	0.104635	+	0.928661i	0.104635	+	0.928661i	0.930874	+	0.365341i	$0.119048\pi$
$577$	0.104635	+	0.928661i	0.104635	+	0.928661i	−0.826239	+	0.563320i	$0.809524\pi$
$578$	−0.430874	−	1.23137i	−0.430874	−	1.23137i
$579$	−0.220796	+	1.16694i	−0.220796	+	1.16694i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.390163	−	0.489250i	−0.390163	−	0.489250i
$585$		0			0
$586$		0			0
$587$	−0.460898	−	0.367554i	−0.460898	−	0.367554i	0.365341	−	0.930874i	$-0.380952\pi$
$587$	−0.460898	−	0.367554i	−0.460898	−	0.367554i	−0.826239	+	0.563320i	$0.809524\pi$
$588$	−0.514540	−	0.477424i	−0.514540	−	0.477424i
$589$		0			0
$590$		0			0
$591$	0.632789	+	1.61232i	0.632789	+	1.61232i
$592$		0			0
$593$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$593$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.103737	+	0.165096i	0.103737	+	0.165096i
$599$	−1.87590	−	0.211363i	−1.87590	−	0.211363i	−0.900969	−	0.433884i	$-0.857143\pi$
$599$	−1.87590	−	0.211363i	−1.87590	−	0.211363i	−0.974928	+	0.222521i	$0.928571\pi$
$600$	−0.388602	+	0.0145404i	−0.388602	+	0.0145404i
$601$	−0.275400	+	0.438297i	−0.275400	+	0.438297i	−0.955573	−	0.294755i	$-0.904762\pi$
$601$	−0.275400	+	0.438297i	−0.275400	+	0.438297i	0.680173	+	0.733052i	$0.261905\pi$
$602$		0			0
$603$		0			0
$604$	−0.632404	−	0.304550i	−0.632404	−	0.304550i
$605$		0			0
$606$	−0.0218311	+	0.291315i	−0.0218311	+	0.291315i
$607$	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
$611$	0.258604	−	0.0904896i	0.258604	−	0.0904896i
$612$		0			0
$613$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$613$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$614$	−2.33598	−	1.12495i	−2.33598	−	1.12495i
$615$		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
$621$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$622$	2.49939	+	0.570469i	2.49939	+	0.570469i
$623$		0			0
$624$	0.0903659	−	0.156518i	0.0903659	−	0.156518i
$625$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$631$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$632$		0			0
$633$	1.13787	+	0.839789i	1.13787	+	0.839789i
$634$	0.537291	+	0.673741i	0.537291	+	0.673741i
$635$		0			0
$636$		0			0
$637$			0.149460i			0.149460i
$638$		0			0
$639$	−0.411608	+	1.04876i	−0.411608	+	1.04876i
$640$		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
$647$	−0.0663300	−	0.290611i	−0.0663300	−	0.290611i	0.930874	−	0.365341i	$-0.119048\pi$
$647$	−0.0663300	−	0.290611i	−0.0663300	−	0.290611i	−0.997204	+	0.0747301i	$0.976190\pi$
$648$	−0.294755	+	0.253657i	−0.294755	+	0.253657i
$649$		0			0
$650$	−0.137873	−	0.137873i	−0.137873	−	0.137873i
$651$		0			0
$652$	1.21449	+	0.424970i	1.21449	+	0.424970i
$653$	0.488590	+	0.170965i	0.488590	+	0.170965i	0.563320	−	0.826239i	$-0.309524\pi$
$653$	0.488590	+	0.170965i	0.488590	+	0.170965i	−0.0747301	+	0.997204i	$0.523810\pi$
$654$		0			0
$655$		0			0
$656$	−0.0765685	+	0.0481112i	−0.0765685	+	0.0481112i
$657$	−0.751927	+	1.42271i	−0.751927	+	1.42271i
$658$		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	$0.857143\pi$
$662$	0.528980	−	1.09844i	0.528980	−	1.09844i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$668$		−	1.26481i		−	1.26481i
$669$	−0.0663300	−	0.440071i	−0.0663300	−	0.440071i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.255779	−	0.531130i	−0.255779	−	0.531130i	0.733052	−	0.680173i	$-0.238095\pi$
$673$	−0.255779	−	0.531130i	−0.255779	−	0.531130i	−0.988831	+	0.149042i	$0.952381\pi$
$674$		0			0
$675$	0.433884	+	0.900969i	0.433884	+	0.900969i
$676$	−0.669030	+	0.152702i	−0.669030	+	0.152702i
$677$		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
$683$	−1.81507	−	0.414278i	−1.81507	−	0.414278i	−0.826239	−	0.563320i	$-0.809524\pi$
$683$	−1.81507	−	0.414278i	−1.81507	−	0.414278i	−0.988831	+	0.149042i	$0.952381\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.781831	+	0.376510i	0.781831	+	0.376510i	0.781831	−	0.623490i	$-0.214286\pi$
$691$	0.781831	+	0.376510i	0.781831	+	0.376510i			1.00000i	$0.5\pi$
$692$	−0.244230	+	0.194767i	−0.244230	+	0.194767i
$693$		0			0
$694$	2.40099	−	0.840142i	2.40099	−	0.840142i
$695$		0			0
$696$	0.329269	−	0.206893i	0.329269	−	0.206893i
$697$		0			0
$698$	0.899737	−	0.314832i	0.899737	−	0.314832i
$699$	0.109562	−	1.46200i	0.109562	−	1.46200i
$700$		0			0
$701$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$701$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$702$	−0.193756	−	0.0218311i	−0.193756	−	0.0218311i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.764225	+	0.0861074i	0.764225	+	0.0861074i
$707$		0			0
$708$	−0.493060	−	0.723186i	−0.493060	−	0.723186i
$709$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$709$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$714$		0			0
$715$		0			0
$716$	−1.30783	+	0.298504i	−1.30783	+	0.298504i
$717$	0.997204	+	0.925270i	0.997204	+	0.925270i
$718$		0			0
$719$	−0.376510	−	0.781831i	−0.376510	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$719$	−0.376510	−	0.781831i	−0.376510	−	0.781831i	−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	−1.29637	+	0.146066i	−1.29637	+	0.146066i
$723$		0			0
$724$		0			0
$725$	−0.294755	−	0.955573i	−0.294755	−	0.955573i
$726$	−0.242536	+	1.28183i	−0.242536	+	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
$729$	0.900969	+	0.433884i	0.900969	+	0.433884i
$730$		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
$736$	1.00647	−	0.632404i	1.00647	−	0.632404i
$737$		0			0
$738$	0.0806072	+	0.0549571i	0.0806072	+	0.0549571i
$739$	−0.0705858	−	0.0246991i	−0.0705858	−	0.0246991i	0.294755	−	0.955573i	$-0.404762\pi$
$739$	−0.0705858	−	0.0246991i	−0.0705858	−	0.0246991i	−0.365341	+	0.930874i	$0.619048\pi$
$740$		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	$0.821429\pi$
$744$	0.717870	+	0.221434i	0.717870	+	0.221434i
$745$		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	$0.464286\pi$
$752$	−0.732119	−	2.09228i	−0.732119	−	2.09228i
$753$		0			0
$754$	0.188338	+	0.0504651i	0.188338	+	0.0504651i
$755$		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
$761$	1.29196	+	1.03030i	1.29196	+	1.03030i	0.997204	+	0.0747301i	$0.0238095\pi$
$761$	1.29196	+	1.03030i	1.29196	+	1.03030i	0.294755	+	0.955573i	$0.404762\pi$
$762$	1.56902	−	1.69100i	1.56902	−	1.69100i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.0414721	+	0.181701i	−0.0414721	+	0.181701i
$768$	−1.13537	−	0.655507i	−1.13537	−	0.655507i
$769$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$769$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$770$		0			0
$771$	1.53825	−	1.04876i	1.53825	−	1.04876i
$772$	0.443514	+	0.705849i	0.443514	+	0.705849i
$773$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$773$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$774$		0			0
$775$	1.02781	−	1.63575i	1.02781	−	1.63575i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$784$	1.20923			1.20923
$785$		0			0
$786$	1.97213	+	0.147791i	1.97213	+	0.147791i
$787$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$787$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$788$	1.09536	+	0.527496i	1.09536	+	0.527496i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.944183	+	1.50266i	0.944183	+	1.50266i
$795$		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
$800$	−0.840508	+	0.840508i	−0.840508	+	0.840508i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	0.163434	+	0.339374i	0.163434	+	0.339374i
$807$	1.05001	−	1.42271i	1.05001	−	1.42271i
$808$	−0.0542935	−	0.0680819i	−0.0542935	−	0.0680819i
$809$	−1.05737	+	0.119137i	−1.05737	+	0.119137i	−0.623490	−	0.781831i	$-0.714286\pi$
$809$	−1.05737	+	0.119137i	−1.05737	+	0.119137i	−0.433884	+	0.900969i	$0.642857\pi$
$810$		0			0
$811$		−	1.73205i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$811$		−	1.73205i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$812$		0			0
$813$	−1.85486	−	0.350958i	−1.85486	−	0.350958i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.0878978	+	0.0423294i	−0.0878978	+	0.0423294i
$819$		0			0
$820$		0			0
$821$	0.347948	+	1.52446i	0.347948	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$821$	0.347948	+	1.52446i	0.347948	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$822$		0			0
$823$	1.69226	−	1.06332i	1.69226	−	1.06332i	0.826239	−	0.563320i	$-0.190476\pi$
$823$	1.69226	−	1.06332i	1.69226	−	1.06332i	0.866025	−	0.500000i	$-0.166667\pi$
$824$		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	$0.107143\pi$
$828$	−0.579950	−	0.395403i	−0.579950	−	0.395403i
$829$	−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
$831$	−0.487076	+	1.57906i	−0.487076	+	1.57906i
$832$	−0.0113564	−	0.0497555i	−0.0113564	−	0.0497555i
$833$		0			0
$834$	−1.11406	+	0.958723i	−1.11406	+	0.958723i
$835$		0			0
$836$		0			0
$837$	−0.216299	−	1.91970i	−0.216299	−	1.91970i
$838$		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
$841$	0.733052	+	0.680173i	0.733052	+	0.680173i
$842$		0			0
$843$		0			0
$844$	0.986417	−	0.111142i	0.986417	−	0.111142i
$845$		0			0
$846$	−1.75306	+	1.62660i	−1.75306	+	1.62660i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.288914	+	0.736141i	0.288914	+	0.736141i
$853$	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	−0.294755	−	0.955573i	$-0.595238\pi$
$857$	−0.974928	−	0.222521i	−0.974928	−	0.222521i	−0.680173	+	0.733052i	$0.738095\pi$
$858$		0			0
$859$	−1.06332	−	1.69226i	−1.06332	−	1.69226i	−0.563320	−	0.826239i	$-0.690476\pi$
$859$	−1.06332	−	1.69226i	−1.06332	−	1.69226i	−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	−0.365341	−	0.930874i	$-0.619048\pi$
$863$	0.623490	−	0.781831i	0.623490	−	0.781831i	0.988831	+	0.149042i	$0.0476190\pi$
$864$	−0.133087	+	1.18118i	−0.133087	+	1.18118i
$865$		0			0
$866$		0			0
$867$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.292341	+	1.09103i	0.292341	+	1.09103i
$877$	−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	$0.928571\pi$
$878$	−0.944183	+	1.50266i	−0.944183	+	1.50266i
$879$		0			0
$880$		0			0
$881$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$881$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$882$	−0.521689	−	1.19572i	−0.521689	−	1.19572i
$883$	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
$886$	0.344766	−	1.51052i	0.344766	−	1.51052i
$887$	1.25033	−	1.25033i	1.25033	−	1.25033i	0.294755	−	0.955573i	$-0.404762\pi$
$887$	1.25033	−	1.25033i	1.25033	−	1.25033i	0.955573	−	0.294755i	$-0.0952381\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−0.244230	−	0.194767i	−0.244230	−	0.194767i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.0222759	+	0.147791i	0.0222759	+	0.147791i
$898$			2.46273i			2.46273i
$899$	−0.0722342	+	1.93050i	−0.0722342	+	1.93050i
$900$	0.653395	+	0.256439i	0.653395	+	0.256439i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.850958	−	0.988831i	−0.850958	−	0.988831i
$907$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$907$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$908$		0			0
$909$	−0.104635	+	0.197979i	−0.104635	+	0.197979i
$910$		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
$921$	−1.29637	−	1.50641i	−1.29637	−	1.50641i
$922$	1.09844	−	0.528980i	1.09844	−	0.528980i
$923$	0.0730607	−	0.151712i	0.0730607	−	0.151712i
$924$		0			0
$925$		0			0
$926$	−0.776408	−	2.21885i	−0.776408	−	2.21885i
$927$		0			0
$928$	0.307647	−	1.14816i	0.307647	−	1.14816i
$929$		−	0.149460i		−	0.149460i	−0.997204	−	0.0747301i	$-0.976190\pi$
$929$		−	0.149460i		−	0.149460i	0.997204	−	0.0747301i	$-0.0238095\pi$
$930$		0			0
$931$		0			0
$932$	−0.641621	−	0.804568i	−0.641621	−	0.804568i
$933$	1.58114	+	1.16694i	1.58114	+	1.16694i
$934$		0			0
$935$		0			0
$936$	0.0467641	−	0.0345135i	0.0467641	−	0.0345135i
$937$		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
$943$	0.0246991	−	0.0705858i	0.0246991	−	0.0705858i
$944$	1.47008	+	0.335536i	1.47008	+	0.335536i
$945$		0			0
$946$		0			0
$947$	−1.75711	−	0.197979i	−1.75711	−	0.197979i	−0.826239	−	0.563320i	$-0.809524\pi$
$947$	−1.75711	−	0.197979i	−1.75711	−	0.197979i	−0.930874	+	0.365341i	$0.880952\pi$
$948$		0			0
$949$	0.127959	−	0.203646i	0.127959	−	0.203646i
$950$		0			0
$951$	0.170965	+	0.638050i	0.170965	+	0.638050i
$952$		0			0
$953$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$953$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$954$		0			0
$955$		0			0
$956$	0.954848			0.954848
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.13600	+	1.70341i	−2.13600	+	1.70341i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.18017	+	0.132974i	1.18017	+	0.132974i	0.680173	−	0.733052i	$-0.261905\pi$
$967$	1.18017	+	0.132974i	1.18017	+	0.132974i	0.500000	+	0.866025i	$0.333333\pi$
$968$	−0.206893	−	0.329269i	−0.206893	−	0.329269i
$969$		0			0
$970$		0			0
$971$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$971$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$972$	0.670731	−	0.206893i	0.670731	−	0.206893i
$973$		0			0
$974$	−0.543808	+	0.543808i	−0.543808	+	0.543808i
$975$	−0.0546039	−	0.139129i	−0.0546039	−	0.139129i
$976$		0			0
$977$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$977$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$978$	1.75306	+	1.62660i	1.75306	+	1.62660i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.62564	+	2.03849i	1.62564	+	2.03849i
$983$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$983$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$984$	−0.0287561	+	0.00433428i	−0.0287561	+	0.00433428i
$985$		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	$-0.285714\pi$
$992$	2.06890	−	0.996332i	2.06890	−	0.996332i
$993$	0.708353	−	0.609587i	0.708353	−	0.609587i
$994$		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	$-0.0714286\pi$
$998$	−0.674035	−	0.674035i	−0.674035	−	0.674035i
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(1.23137 - 0.430874i) q^{2} +(0.997204 + 0.0747301i) q^{3} +(0.548780 - 0.437637i) q^{4} +(1.26012 - 0.337649i) q^{6} +(-0.206893 + 0.329269i) q^{8} +(0.988831 + 0.149042i) q^{9} +O(q^{10})\)	\(q+(1.23137 - 0.430874i) q^{2} +(0.997204 + 0.0747301i) q^{3} +(0.548780 - 0.437637i) q^{4} +(1.26012 - 0.337649i) q^{6} +(-0.206893 + 0.329269i) q^{8} +(0.988831 + 0.149042i) q^{9} +(0.579950 - 0.395403i) q^{12} +(-0.145713 - 0.0332580i) q^{13} +(-0.269079 + 1.17891i) q^{16} +(1.28183 - 0.242536i) q^{18} +(-0.433884 - 0.900969i) q^{23} +(-0.230921 + 0.312887i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-0.193756 + 0.0218311i) q^{26} +(0.974928 + 0.222521i) q^{27} +(-0.930874 - 0.365341i) q^{29} +(-0.638050 - 1.82344i) q^{31} +(0.133087 + 1.18118i) q^{32} +(0.607877 - 0.350958i) q^{36} +(-0.142820 - 0.0440542i) q^{39} +(0.0528791 + 0.0528791i) q^{41} +(-0.922474 - 0.922474i) q^{46} +(-1.55215 + 0.975281i) q^{47} +(-0.356427 + 1.15551i) q^{48} +(-0.222521 - 0.974928i) q^{49} +(1.10462 + 0.694076i) q^{50} +(-0.0945192 + 0.0455181i) q^{52} +(1.29637 - 0.146066i) q^{54} +(-1.30366 - 0.0487796i) q^{58} -1.24698i q^{59} +(-1.57135 - 1.97041i) q^{62} +(0.148155 + 0.307647i) q^{64} +(-0.365341 - 0.930874i) q^{69} +(-0.250701 + 1.09839i) q^{71} +(-0.253657 + 0.294755i) q^{72} +(-0.531484 + 1.51889i) q^{73} +(0.563320 + 0.826239i) q^{75} +(-0.194846 + 0.00729061i) q^{78} +(0.955573 + 0.294755i) q^{81} +(0.0878978 + 0.0423294i) q^{82} +(-0.900969 - 0.433884i) q^{87} +(-0.632404 - 0.304550i) q^{92} +(-0.500000 - 1.86603i) q^{93} +(-1.49104 + 1.86971i) q^{94} +(0.0444453 + 1.18783i) q^{96} +(-0.694076 - 1.10462i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more