LMFDB - Embedded newform 2001.1.bf.d.827.1

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			827.1
Root			$0.294755 + 0.955573i$ of defining polynomial
Character	$\chi$	$=$	2001.827
Dual form			2001.1.bf.d.1655.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0895474 + 0.794755i) q^{2} +(0.930874 + 0.365341i) q^{3} +(0.351311 - 0.0801844i) q^{4} +(-0.206999 + 0.772532i) q^{6} +(0.359338 + 1.02693i) q^{8} +(0.733052 + 0.680173i) q^{9} +O(q^{10})$	\(q+(0.0895474 + 0.794755i) q^{2} +(0.930874 + 0.365341i) q^{3} +(0.351311 - 0.0801844i) q^{4} +(-0.206999 + 0.772532i) q^{6} +(0.359338 + 1.02693i) q^{8} +(0.733052 + 0.680173i) q^{9} +(0.356321 + 0.0537067i) q^{12} +(-0.317031 - 0.658322i) q^{13} +(-0.459319 + 0.221196i) q^{16} +(-0.474928 + 0.643504i) q^{18} +(-0.781831 + 0.623490i) q^{23} +(-0.0406810 + 1.08722i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.494815 - 0.310913i) q^{26} +(0.433884 + 0.900969i) q^{27} +(0.294755 - 0.955573i) q^{29} +(-0.514383 + 0.0579571i) q^{31} +(0.361914 + 0.575983i) q^{32} +(0.312068 + 0.180173i) q^{36} +(-0.0546039 - 0.728639i) q^{39} +(-0.262919 - 0.262919i) q^{41} +(-0.565533 - 0.565533i) q^{46} +(-0.882094 - 0.308658i) q^{47} +(-0.508380 + 0.0380978i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(0.754903 - 0.264152i) q^{50} +(-0.164164 - 0.205855i) q^{52} +(-0.677197 + 0.425511i) q^{54} +(0.785841 + 0.148689i) q^{58} +0.445042i q^{59} +(-0.0921234 - 0.403619i) q^{62} +(-0.823939 + 0.657069i) q^{64} +(-0.955573 + 0.294755i) q^{69} +(-0.268565 + 0.129334i) q^{71} +(-0.435076 + 0.997204i) q^{72} +(1.98603 + 0.223772i) q^{73} +(0.149042 - 0.988831i) q^{75} +(0.574200 - 0.108644i) q^{78} +(0.0747301 + 0.997204i) q^{81} +(0.185412 - 0.232500i) q^{82} +(0.623490 - 0.781831i) q^{87} +(-0.224672 + 0.281729i) q^{92} +(-0.500000 - 0.133975i) q^{93} +(0.166318 - 0.728688i) q^{94} +(0.126466 + 0.668389i) q^{96} +(0.264152 - 0.754903i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times$.

$n$	$553$	$668$	$1132$
$\chi(n)$	$e\left(\frac{27}{28}\right)$	$-1$	$-1$

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 $

$2$	0.0895474	+	0.794755i	0.0895474	+	0.794755i	0.955573	+	0.294755i	$0.0952381\pi$
$2$	0.0895474	+	0.794755i	0.0895474	+	0.794755i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	0.930874	+	0.365341i	0.930874	+	0.365341i
$3$	0.930874	+	0.365341i	0.930874	+	0.365341i
$4$	0.351311	−	0.0801844i	0.351311	−	0.0801844i
$5$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$5$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$6$	−0.206999	+	0.772532i	−0.206999	+	0.772532i
$7$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$7$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$8$	0.359338	+	1.02693i	0.359338	+	1.02693i
$9$	0.733052	+	0.680173i	0.733052	+	0.680173i
$10$		0			0
$11$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$11$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$12$	0.356321	+	0.0537067i	0.356321	+	0.0537067i
$13$	−0.317031	−	0.658322i	−0.317031	−	0.658322i	0.680173	−	0.733052i	$-0.261905\pi$
$13$	−0.317031	−	0.658322i	−0.317031	−	0.658322i	−0.997204	+	0.0747301i	$0.976190\pi$
$14$		0			0
$15$		0			0
$16$	−0.459319	+	0.221196i	−0.459319	+	0.221196i
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	−0.474928	+	0.643504i	−0.474928	+	0.643504i
$19$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$19$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$23$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$24$	−0.0406810	+	1.08722i	−0.0406810	+	1.08722i
$25$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$26$	0.494815	−	0.310913i	0.494815	−	0.310913i
$27$	0.433884	+	0.900969i	0.433884	+	0.900969i
$28$		0			0
$29$	0.294755	−	0.955573i	0.294755	−	0.955573i
$29$	0.294755	−	0.955573i	0.294755	−	0.955573i
$30$		0			0
$31$	−0.514383	+	0.0579571i	−0.514383	+	0.0579571i	−0.365341	−	0.930874i	$-0.619048\pi$
$31$	−0.514383	+	0.0579571i	−0.514383	+	0.0579571i	−0.149042	+	0.988831i	$0.547619\pi$
$32$	0.361914	+	0.575983i	0.361914	+	0.575983i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.312068	+	0.180173i	0.312068	+	0.180173i
$37$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$37$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$38$		0			0
$39$	−0.0546039	−	0.728639i	−0.0546039	−	0.728639i
$40$		0			0
$41$	−0.262919	−	0.262919i	−0.262919	−	0.262919i	0.563320	−	0.826239i	$-0.309524\pi$
$41$	−0.262919	−	0.262919i	−0.262919	−	0.262919i	−0.826239	+	0.563320i	$0.809524\pi$
$42$		0			0
$43$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$43$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$44$		0			0
$45$		0			0
$46$	−0.565533	−	0.565533i	−0.565533	−	0.565533i
$47$	−0.882094	−	0.308658i	−0.882094	−	0.308658i	−0.149042	−	0.988831i	$-0.547619\pi$
$47$	−0.882094	−	0.308658i	−0.882094	−	0.308658i	−0.733052	+	0.680173i	$0.761905\pi$
$48$	−0.508380	+	0.0380978i	−0.508380	+	0.0380978i
$49$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$50$	0.754903	−	0.264152i	0.754903	−	0.264152i
$51$		0			0
$52$	−0.164164	−	0.205855i	−0.164164	−	0.205855i
$53$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$53$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$54$	−0.677197	+	0.425511i	−0.677197	+	0.425511i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.785841	+	0.148689i	0.785841	+	0.148689i
$59$			0.445042i			0.445042i	0.974928	+	0.222521i	$0.0714286\pi$
$59$			0.445042i			0.445042i	−0.974928	+	0.222521i	$0.928571\pi$
$60$		0			0
$61$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$61$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$62$	−0.0921234	−	0.403619i	−0.0921234	−	0.403619i
$63$		0			0
$64$	−0.823939	+	0.657069i	−0.823939	+	0.657069i
$65$		0			0
$66$		0			0
$67$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$67$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$68$		0			0
$69$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$70$		0			0
$71$	−0.268565	+	0.129334i	−0.268565	+	0.129334i	−0.563320	−	0.826239i	$-0.690476\pi$
$71$	−0.268565	+	0.129334i	−0.268565	+	0.129334i	0.294755	+	0.955573i	$0.404762\pi$
$72$	−0.435076	+	0.997204i	−0.435076	+	0.997204i
$73$	1.98603	+	0.223772i	1.98603	+	0.223772i	0.997204	+	0.0747301i	$0.0238095\pi$
$73$	1.98603	+	0.223772i	1.98603	+	0.223772i	0.988831	+	0.149042i	$0.0476190\pi$
$74$		0			0
$75$	0.149042	−	0.988831i	0.149042	−	0.988831i
$76$		0			0
$77$		0			0
$78$	0.574200	−	0.108644i	0.574200	−	0.108644i
$79$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$79$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$80$		0			0
$81$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$82$	0.185412	−	0.232500i	0.185412	−	0.232500i
$83$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$83$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.623490	−	0.781831i	0.623490	−	0.781831i
$88$		0			0
$89$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$89$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$90$		0			0
$91$		0			0
$92$	−0.224672	+	0.281729i	−0.224672	+	0.281729i
$93$	−0.500000	−	0.133975i	−0.500000	−	0.133975i
$94$	0.166318	−	0.728688i	0.166318	−	0.728688i
$95$		0			0
$96$	0.126466	+	0.668389i	0.126466	+	0.668389i
$97$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$97$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$98$	0.264152	−	0.754903i	0.264152	−	0.754903i
$99$		0			0
$100$	−0.156348	−	0.324660i	−0.156348	−	0.324660i
$101$	−1.05737	−	0.119137i	−1.05737	−	0.119137i	−0.433884	−	0.900969i	$-0.642857\pi$
$101$	−1.05737	−	0.119137i	−1.05737	−	0.119137i	−0.623490	+	0.781831i	$0.714286\pi$
$102$		0			0
$103$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$103$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$104$	0.562128	−	0.562128i	0.562128	−	0.562128i
$105$		0			0
$106$		0			0
$107$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$107$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$108$	0.224672	+	0.281729i	0.224672	+	0.281729i
$109$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$109$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$113$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$114$		0			0
$115$		0			0
$116$	0.0269287	−	0.359338i	0.0269287	−	0.359338i
$117$	0.215372	−	0.698220i	0.215372	−	0.698220i
$118$	−0.353699	+	0.0398523i	−0.353699	+	0.0398523i
$119$		0			0
$120$		0			0
$121$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$122$		0			0
$123$	−0.148689	−	0.340799i	−0.148689	−	0.340799i
$124$	−0.176061	+	0.0616065i	−0.176061	+	0.0616065i
$125$		0			0
$126$		0			0
$127$	1.43087	+	0.500684i	1.43087	+	0.500684i	0.930874	−	0.365341i	$-0.119048\pi$
$127$	1.43087	+	0.500684i	1.43087	+	0.500684i	0.500000	+	0.866025i	$0.333333\pi$
$128$	−0.114983	−	0.114983i	−0.114983	−	0.114983i
$129$		0			0
$130$		0			0
$131$	0.205245	−	1.82160i	0.205245	−	1.82160i	−0.294755	−	0.955573i	$-0.595238\pi$
$131$	0.205245	−	1.82160i	0.205245	−	1.82160i	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		0.943883	−	0.330279i	$-0.107143\pi$
$137$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$138$	−0.319827	−	0.733052i	−0.319827	−	0.733052i
$139$	0.185853	+	0.233052i	0.185853	+	0.233052i	0.866025	−	0.500000i	$-0.166667\pi$
$139$	0.185853	+	0.233052i	0.185853	+	0.233052i	−0.680173	+	0.733052i	$0.738095\pi$
$140$		0			0
$141$	−0.708353	−	0.609587i	−0.708353	−	0.609587i
$142$	−0.126838	−	0.201862i	−0.126838	−	0.201862i
$143$		0			0
$144$	−0.487156	−	0.150268i	−0.487156	−	0.150268i
$145$		0			0
$146$			1.59845i			1.59845i
$147$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$148$		0			0
$149$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$149$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$150$	0.799225	+	0.0299049i	0.799225	+	0.0299049i
$151$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	−0.930874	−	0.365341i	$-0.880952\pi$
$151$	−0.781831	+	0.623490i	−0.781831	+	0.623490i	0.149042	+	0.988831i	$0.452381\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.0776084	−	0.251600i	−0.0776084	−	0.251600i
$157$		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
$162$	−0.785841	+	0.148689i	−0.785841	+	0.148689i
$163$	−0.308658	+	0.882094i	−0.308658	+	0.882094i	0.680173	+	0.733052i	$0.261905\pi$
$163$	−0.308658	+	0.882094i	−0.308658	+	0.882094i	−0.988831	+	0.149042i	$0.952381\pi$
$164$	−0.113448	−	0.0712842i	−0.113448	−	0.0712842i
$165$		0			0
$166$		0			0
$167$	0.277479	−	1.21572i	0.277479	−	1.21572i	−0.623490	−	0.781831i	$-0.714286\pi$
$167$	0.277479	−	1.21572i	0.277479	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$168$		0			0
$169$	0.290611	−	0.364415i	0.290611	−	0.364415i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$173$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$174$	0.677197	+	0.425511i	0.677197	+	0.425511i
$175$		0			0
$176$		0			0
$177$	−0.162592	+	0.414278i	−0.162592	+	0.414278i
$178$		0			0
$179$	0.0931869	−	0.116853i	0.0931869	−	0.116853i	−0.733052	−	0.680173i	$-0.761905\pi$
$179$	0.0931869	−	0.116853i	0.0931869	−	0.116853i	0.826239	+	0.563320i	$0.190476\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$		0			0
$183$		0			0
$184$	−0.921221	−	0.578842i	−0.921221	−	0.578842i
$185$		0			0
$186$	0.0617033	−	0.409375i	0.0617033	−	0.409375i
$187$		0			0
$188$	−0.334639	−	0.0377047i	−0.334639	−	0.0377047i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	−1.00704	+	0.310630i	−1.00704	+	0.310630i
$193$	0.0397866	−	0.0633201i	0.0397866	−	0.0633201i	−0.826239	−	0.563320i	$-0.809524\pi$
$193$	0.0397866	−	0.0633201i	0.0397866	−	0.0633201i	0.866025	+	0.500000i	$0.166667\pi$
$194$		0			0
$195$		0			0
$196$	−0.351311	−	0.0801844i	−0.351311	−	0.0801844i
$197$	−1.35417	+	1.07992i	−1.35417	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$197$	−1.35417	+	1.07992i	−1.35417	+	1.07992i	−0.988831	+	0.149042i	$0.952381\pi$
$198$		0			0
$199$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$199$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$200$	0.921221	−	0.578842i	0.921221	−	0.578842i
$201$		0			0
$202$		−	0.851022i		−	0.851022i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.997204	−	0.0747301i	−0.997204	−	0.0747301i
$208$	0.291237	+	0.232254i	0.291237	+	0.232254i
$209$		0			0
$210$		0			0
$211$	1.33485	−	0.467085i	1.33485	−	0.467085i	0.433884	−	0.900969i	$-0.357143\pi$
$211$	1.33485	−	0.467085i	1.33485	−	0.467085i	0.900969	+	0.433884i	$0.142857\pi$
$212$		0			0
$213$	−0.297251	+	0.0222759i	−0.297251	+	0.0222759i
$214$		0			0
$215$		0			0
$216$	−0.769320	+	0.769320i	−0.769320	+	0.769320i
$217$		0			0
$218$		0			0
$219$	1.76699	+	0.933884i	1.76699	+	0.933884i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$223$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$224$		0			0
$225$	0.500000	−	0.866025i	0.500000	−	0.866025i
$226$		0			0
$227$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$227$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$228$		0			0
$229$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$229$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$230$		0			0
$231$		0			0
$232$	1.08722	−	0.0406810i	1.08722	−	0.0406810i
$233$			1.65248i			1.65248i	0.563320	+	0.826239i	$0.309524\pi$
$233$			1.65248i			1.65248i	−0.563320	+	0.826239i	$0.690476\pi$
$234$	0.574200	+	0.108644i	0.574200	+	0.108644i
$235$		0			0
$236$	0.0356854	+	0.156348i	0.0356854	+	0.156348i
$237$		0			0
$238$		0			0
$239$	1.09839	+	0.250701i	1.09839	+	0.250701i	0.733052	−	0.680173i	$-0.238095\pi$
$239$	1.09839	+	0.250701i	1.09839	+	0.250701i	0.365341	+	0.930874i	$0.380952\pi$
$240$		0			0
$241$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$241$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$242$	0.425511	−	0.677197i	0.425511	−	0.677197i
$243$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$244$		0			0
$245$		0			0
$246$	0.257537	−	0.148689i	0.257537	−	0.148689i
$247$		0			0
$248$	−0.244355	−	0.507409i	−0.244355	−	0.507409i
$249$		0			0
$250$		0			0
$251$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$251$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$252$		0			0
$253$		0			0
$254$	−0.269790	+	1.18203i	−0.269790	+	1.18203i
$255$		0			0
$256$	−0.575983	+	0.722259i	−0.575983	+	0.722259i
$257$	0.574730	−	0.131178i	0.574730	−	0.131178i	0.0747301	−	0.997204i	$-0.476190\pi$
$257$	0.574730	−	0.131178i	0.574730	−	0.131178i	0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.866025	−	0.500000i	0.866025	−	0.500000i
$262$	1.46610			1.46610
$263$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$263$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.500684	−	1.43087i	−0.500684	−	1.43087i	−0.866025	−	0.500000i	$-0.833333\pi$
$269$	−0.500684	−	1.43087i	−0.500684	−	1.43087i	0.365341	−	0.930874i	$-0.380952\pi$
$270$		0			0
$271$	0.189606	+	0.119137i	0.189606	+	0.119137i	0.623490	−	0.781831i	$-0.285714\pi$
$271$	0.189606	+	0.119137i	0.189606	+	0.119137i	−0.433884	+	0.900969i	$0.642857\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.312068	+	0.180173i	−0.312068	+	0.180173i
$277$	1.78181	−	0.858075i	1.78181	−	0.858075i	0.826239	−	0.563320i	$-0.190476\pi$
$277$	1.78181	−	0.858075i	1.78181	−	0.858075i	0.955573	−	0.294755i	$-0.0952381\pi$
$278$	−0.168577	+	0.168577i	−0.168577	+	0.168577i
$279$	−0.416490	−	0.307384i	−0.416490	−	0.307384i
$280$		0			0
$281$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$281$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$282$	0.421041	−	0.617554i	0.421041	−	0.617554i
$283$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$283$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$284$	−0.0839792	+	0.0669712i	−0.0839792	+	0.0669712i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.126466	+	0.668389i	−0.126466	+	0.668389i
$289$		−	1.00000i		−	1.00000i
$290$		0			0
$291$		0			0
$292$	0.715659	−	0.0806354i	0.715659	−	0.0806354i
$293$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$293$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$294$	0.521689	−	0.606214i	0.521689	−	0.606214i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.658322	+	0.317031i	0.658322	+	0.317031i
$300$	−0.0269287	−	0.359338i	−0.0269287	−	0.359338i
$301$		0			0
$302$	−0.565533	−	0.565533i	−0.565533	−	0.565533i
$303$	−0.940755	−	0.497204i	−0.940755	−	0.497204i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.19745	+	1.19745i	1.19745	+	1.19745i	0.974928	+	0.222521i	$0.0714286\pi$
$307$	1.19745	+	1.19745i	1.19745	+	1.19745i	0.222521	+	0.974928i	$0.428571\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.12099	+	0.392253i	−1.12099	+	0.392253i	−0.826239	−	0.563320i	$-0.809524\pi$
$311$	−1.12099	+	0.392253i	−1.12099	+	0.392253i	−0.294755	+	0.955573i	$0.595238\pi$
$312$	0.728639	−	0.317902i	0.728639	−	0.317902i
$313$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$313$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.97493	−	0.222521i	1.97493	−	0.222521i	0.974928	−	0.222521i	$-0.0714286\pi$
$317$	1.97493	−	0.222521i	1.97493	−	0.222521i	1.00000			$0$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.106214	+	0.344336i	0.106214	+	0.344336i
$325$	−0.571270	+	0.455573i	−0.571270	+	0.455573i
$326$	−0.728688	−	0.166318i	−0.728688	−	0.166318i
$327$		0			0
$328$	0.175522	−	0.364475i	0.175522	−	0.364475i
$329$		0			0
$330$		0			0
$331$	−0.922474	+	0.922474i	−0.922474	+	0.922474i	−0.997204	−	0.0747301i	$-0.976190\pi$
$331$	−0.922474	+	0.922474i	−0.922474	+	0.922474i	0.0747301	+	0.997204i	$0.476190\pi$
$332$		0			0
$333$		0			0
$334$	0.991043	+	0.111664i	0.991043	+	0.111664i
$335$		0			0
$336$		0			0
$337$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$337$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$338$	0.315644	+	0.198332i	0.315644	+	0.198332i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.161359	−	1.43210i	−0.161359	−	1.43210i
$347$	0.867767			0.867767			0.433884	−	0.900969i	$-0.357143\pi$
$347$	0.867767			0.867767			0.433884	+	0.900969i	$0.357143\pi$
$348$	0.156348	−	0.324660i	0.156348	−	0.324660i
$349$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$349$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$350$		0			0
$351$	0.455573	−	0.571270i	0.455573	−	0.571270i
$352$		0			0
$353$	−1.24349	+	1.55929i	−1.24349	+	1.55929i	−0.563320	+	0.826239i	$0.690476\pi$
$353$	−1.24349	+	1.55929i	−1.24349	+	1.55929i	−0.680173	+	0.733052i	$0.738095\pi$
$354$	−0.343809	−	0.0921234i	−0.343809	−	0.0921234i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.101214	+	0.0635969i	0.101214	+	0.0635969i
$359$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$359$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$360$		0			0
$361$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$362$		0			0
$363$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$367$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$368$	0.221196	−	0.459319i	0.221196	−	0.459319i
$369$	−0.0139029	−	0.371563i	−0.0139029	−	0.371563i
$370$		0			0
$371$		0			0
$372$	−0.186398	−	0.00697453i	−0.186398	−	0.00697453i
$373$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$373$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$374$		0			0
$375$		0			0
$376$		−	1.01676i		−	1.01676i
$377$	−0.722521	+	0.108903i	−0.722521	+	0.108903i
$378$		0			0
$379$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$379$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$380$		0			0
$381$	1.14904	+	0.988831i	1.14904	+	0.988831i
$382$		0			0
$383$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$383$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$384$	−0.0650265	−	0.149042i	−0.0650265	−	0.149042i
$385$		0			0
$386$	0.0538867	+	0.0259505i	0.0538867	+	0.0259505i
$387$		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
$392$	0.121815	−	1.08114i	0.121815	−	1.08114i
$393$	0.856562	−	1.62069i	0.856562	−	1.62069i
$394$	−0.979531	−	0.979531i	−0.979531	−	0.979531i
$395$		0			0
$396$		0			0
$397$	−1.01507	−	0.488831i	−1.01507	−	0.488831i	−0.149042	−	0.988831i	$-0.547619\pi$
$397$	−1.01507	−	0.488831i	−1.01507	−	0.488831i	−0.866025	+	0.500000i	$0.833333\pi$
$398$		0			0
$399$		0			0
$400$	0.317859	+	0.398582i	0.317859	+	0.398582i
$401$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$401$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$402$		0			0
$403$	0.201230	+	0.320256i	0.201230	+	0.320256i
$404$	−0.381020	+	0.0429306i	−0.381020	+	0.0429306i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.314832	+	0.197822i	−0.314832	+	0.197822i	−0.680173	−	0.733052i	$-0.738095\pi$
$409$	−0.314832	+	0.197822i	−0.314832	+	0.197822i	0.365341	+	0.930874i	$0.380952\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.0299049	−	0.799225i	−0.0299049	−	0.799225i
$415$		0			0
$416$	0.264444	−	0.420860i	0.264444	−	0.420860i
$417$	0.0878620	+	0.284841i	0.0878620	+	0.284841i
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$		0			0
$421$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$421$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$422$	0.490751	+	1.01905i	0.490751	+	1.01905i
$423$	−0.436680	−	0.826239i	−0.436680	−	0.826239i
$424$		0			0
$425$		0			0
$426$	−0.0443219	−	0.234247i	−0.0443219	−	0.234247i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$431$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$432$	−0.398582	−	0.317859i	−0.398582	−	0.317859i
$433$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$433$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.583979	+	1.48795i	−0.583979	+	1.48795i
$439$	−1.09839	+	0.250701i	−1.09839	+	0.250701i	−0.733052	−	0.680173i	$-0.761905\pi$
$439$	−1.09839	+	0.250701i	−1.09839	+	0.250701i	−0.365341	+	0.930874i	$0.619048\pi$
$440$		0			0
$441$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$442$		0			0
$443$	−0.0246991	−	0.0705858i	−0.0246991	−	0.0705858i	0.930874	−	0.365341i	$-0.119048\pi$
$443$	−0.0246991	−	0.0705858i	−0.0246991	−	0.0705858i	−0.955573	+	0.294755i	$0.904762\pi$
$444$		0			0
$445$		0			0
$446$	0.475985	−	1.36029i	0.475985	−	1.36029i
$447$		0			0
$448$		0			0
$449$	0.222521	+	0.0250721i	0.222521	+	0.0250721i	0.222521	−	0.974928i	$-0.428571\pi$
$449$	0.222521	+	0.0250721i	0.222521	+	0.0250721i			1.00000i	$0.5\pi$
$450$	0.733052	+	0.319827i	0.733052	+	0.319827i
$451$		0			0
$452$		0			0
$453$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$457$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.10462	−	0.694076i	1.10462	−	0.694076i	0.149042	−	0.988831i	$-0.452381\pi$
$461$	1.10462	−	0.694076i	1.10462	−	0.694076i	0.955573	+	0.294755i	$0.0952381\pi$
$462$		0			0
$463$			1.24698i			1.24698i	0.781831	+	0.623490i	$0.214286\pi$
$463$			1.24698i			1.24698i	−0.781831	+	0.623490i	$0.785714\pi$
$464$	0.0759826	+	0.504112i	0.0759826	+	0.504112i
$465$		0			0
$466$	−1.31332	+	0.147975i	−1.31332	+	0.147975i
$467$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$467$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$468$	0.0196763	−	0.262562i	0.0196763	−	0.262562i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.457026	+	0.159920i	−0.457026	+	0.159920i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.100888	+	0.895403i	−0.100888	+	0.895403i
$479$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$479$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.324660	−	0.156348i	−0.324660	−	0.156348i
$485$		0			0
$486$	−0.785841	−	0.148689i	−0.785841	−	0.148689i
$487$	1.24349	+	1.55929i	1.24349	+	1.55929i	0.680173	+	0.733052i	$0.261905\pi$
$487$	1.24349	+	1.55929i	1.24349	+	1.55929i	0.563320	+	0.826239i	$0.309524\pi$
$488$		0			0
$489$	−0.609587	+	0.708353i	−0.609587	+	0.708353i
$490$		0			0
$491$	1.95278	−	0.220025i	1.95278	−	0.220025i	0.955573	−	0.294755i	$-0.0952381\pi$
$491$	1.95278	−	0.220025i	1.95278	−	0.220025i	0.997204	+	0.0747301i	$0.0238095\pi$
$492$	−0.0795629	−	0.107804i	−0.0795629	−	0.107804i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.223446	−	0.140401i	0.223446	−	0.140401i
$497$		0			0
$498$		0			0
$499$	−1.49419	+	1.19158i	−1.49419	+	1.19158i	−0.563320	+	0.826239i	$0.690476\pi$
$499$	−1.49419	+	1.19158i	−1.49419	+	1.19158i	−0.930874	+	0.365341i	$0.880952\pi$
$500$		0			0
$501$	0.702449	−	1.03030i	0.702449	−	1.03030i
$502$		0			0
$503$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$503$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.403658	−	0.233052i	0.403658	−	0.233052i
$508$	0.542829	+	0.0611621i	0.542829	+	0.0611621i
$509$	−0.590232	−	1.22563i	−0.590232	−	1.22563i	−0.955573	−	0.294755i	$-0.904762\pi$
$509$	−0.590232	−	1.22563i	−0.590232	−	1.22563i	0.365341	−	0.930874i	$-0.380952\pi$
$510$		0			0
$511$		0			0
$512$	−0.763283	−	0.479602i	−0.763283	−	0.479602i
$513$		0			0
$514$	0.155720	+	0.445023i	0.155720	+	0.445023i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.67738	−	0.658322i	−1.67738	−	0.658322i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	0.474928	+	0.643504i	0.474928	+	0.643504i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	−0.0739590	−	0.656405i	−0.0739590	−	0.656405i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.222521	−	0.974928i	0.222521	−	0.974928i
$530$		0			0
$531$	−0.302705	+	0.326239i	−0.302705	+	0.326239i
$532$		0			0
$533$	−0.0897317	+	0.256439i	−0.0897317	+	0.256439i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.129436	−	0.0747301i	0.129436	−	0.0747301i
$538$	1.09236	−	0.526053i	1.09236	−	0.526053i
$539$		0			0
$540$		0			0
$541$	−0.940755	+	1.49720i	−0.940755	+	1.49720i	−0.0747301	+	0.997204i	$0.523810\pi$
$541$	−0.940755	+	1.49720i	−0.940755	+	1.49720i	−0.866025	+	0.500000i	$0.833333\pi$
$542$	−0.0777063	+	0.161359i	−0.0777063	+	0.161359i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.367711	+	1.61105i	0.367711	+	1.61105i	0.733052	+	0.680173i	$0.238095\pi$
$547$	0.367711	+	1.61105i	0.367711	+	1.61105i	−0.365341	+	0.930874i	$0.619048\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−0.646066	−	0.875388i	−0.646066	−	0.875388i
$553$		0			0
$554$	0.841516	+	1.33927i	0.841516	+	1.33927i
$555$		0			0
$556$	0.0839792	+	0.0669712i	0.0839792	+	0.0669712i
$557$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$557$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$558$	0.206999	−	0.358533i	0.206999	−	0.358533i
$559$		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	$0.250000\pi$
$564$	−0.297731	−	0.157356i	−0.297731	−	0.157356i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.229322	−	0.229322i	−0.229322	−	0.229322i
$569$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$569$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$570$		0			0
$571$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$571$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.781831	+	0.623490i	0.781831	+	0.623490i
$576$	−1.05091	−	0.0787549i	−1.05091	−	0.0787549i
$577$	0.694076	+	1.10462i	0.694076	+	1.10462i	0.988831	+	0.149042i	$0.0476190\pi$
$577$	0.694076	+	1.10462i	0.694076	+	1.10462i	−0.294755	+	0.955573i	$0.595238\pi$
$578$	0.794755	−	0.0895474i	0.794755	−	0.0895474i
$579$	0.0601697	−	0.0444073i	0.0601697	−	0.0444073i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.483859	+	2.11993i	0.483859	+	2.11993i
$585$		0			0
$586$		0			0
$587$	1.94440	+	0.443797i	1.94440	+	0.443797i	0.988831	+	0.149042i	$0.0476190\pi$
$587$	1.94440	+	0.443797i	1.94440	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$588$	−0.297731	−	0.202990i	−0.297731	−	0.202990i
$589$		0			0
$590$		0			0
$591$	−1.65510	+	0.510531i	−1.65510	+	0.510531i
$592$		0			0
$593$	0.781831	−	0.376510i	0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$593$	0.781831	−	0.376510i	0.781831	−	0.376510i	0.781831	+	0.623490i	$0.214286\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.193011	+	0.551594i	−0.193011	+	0.551594i
$599$	0.189606	+	0.119137i	0.189606	+	0.119137i	0.623490	−	0.781831i	$-0.285714\pi$
$599$	0.189606	+	0.119137i	0.189606	+	0.119137i	−0.433884	+	0.900969i	$0.642857\pi$
$600$	1.06902	−	0.202269i	1.06902	−	0.202269i
$601$	−0.638050	−	1.82344i	−0.638050	−	1.82344i	−0.563320	−	0.826239i	$-0.690476\pi$
$601$	−0.638050	−	1.82344i	−0.638050	−	1.82344i	−0.0747301	−	0.997204i	$-0.523810\pi$
$602$		0			0
$603$		0			0
$604$	−0.224672	+	0.281729i	−0.224672	+	0.281729i
$605$		0			0
$606$	0.310913	−	0.792194i	0.310913	−	0.792194i
$607$	−0.0739590	−	0.656405i	−0.0739590	−	0.656405i	−0.974928	−	0.222521i	$-0.928571\pi$
$607$	−0.0739590	−	0.656405i	−0.0739590	−	0.656405i	0.900969	−	0.433884i	$-0.142857\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0764549	+	0.678556i	0.0764549	+	0.678556i
$612$		0			0
$613$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$613$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$614$	−0.844450	+	1.05891i	−0.844450	+	1.05891i
$615$		0			0
$616$		0			0
$617$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$617$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$618$		0			0
$619$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$619$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$620$		0			0
$621$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$622$	−0.412127	−	0.855791i	−0.412127	−	0.855791i
$623$		0			0
$624$	0.186253	+	0.322600i	0.186253	+	0.322600i
$625$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$631$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$632$		0			0
$633$	1.41322	+	0.0528791i	1.41322	+	0.0528791i
$634$	0.353699	+	1.54966i	0.353699	+	1.54966i
$635$		0			0
$636$		0			0
$637$			0.730682i			0.730682i
$638$		0			0
$639$	−0.284841	−	0.0878620i	−0.284841	−	0.0878620i
$640$		0			0
$641$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$641$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$642$		0			0
$643$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$643$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.22563	−	0.590232i	−1.22563	−	0.590232i	−0.294755	−	0.955573i	$-0.595238\pi$
$647$	−1.22563	−	0.590232i	−1.22563	−	0.590232i	−0.930874	+	0.365341i	$0.880952\pi$
$648$	−0.997204	+	0.435076i	−0.997204	+	0.435076i
$649$		0			0
$650$	−0.413225	−	0.413225i	−0.413225	−	0.413225i
$651$		0			0
$652$	−0.0377047	+	0.334639i	−0.0377047	+	0.334639i
$653$	−0.216299	+	1.91970i	−0.216299	+	1.91970i	0.149042	+	0.988831i	$0.452381\pi$
$653$	−0.216299	+	1.91970i	−0.216299	+	1.91970i	−0.365341	+	0.930874i	$0.619048\pi$
$654$		0			0
$655$		0			0
$656$	0.178920	+	0.0626069i	0.178920	+	0.0626069i
$657$	1.30366	+	1.51488i	1.30366	+	1.51488i
$658$		0			0
$659$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$659$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	−0.815746	−	0.650536i	−0.815746	−	0.650536i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.365341	+	0.930874i	0.365341	+	0.930874i
$668$		−	0.449343i		−	0.449343i
$669$	−1.22563	−	1.32091i	−1.22563	−	1.32091i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.55929	+	1.24349i	−1.55929	+	1.24349i	−0.733052	+	0.680173i	$0.761905\pi$
$673$	−1.55929	+	1.24349i	−1.55929	+	1.24349i	−0.826239	+	0.563320i	$0.809524\pi$
$674$		0			0
$675$	0.781831	−	0.623490i	0.781831	−	0.623490i
$676$	0.0728744	−	0.151325i	0.0728744	−	0.151325i
$677$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$677$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.255779	+	0.531130i	0.255779	+	0.531130i	0.988831	−	0.149042i	$-0.0476190\pi$
$683$	0.255779	+	0.531130i	0.255779	+	0.531130i	−0.733052	+	0.680173i	$0.761905\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.974928	+	1.22252i	−0.974928	+	1.22252i			1.00000i	$0.5\pi$
$691$	−0.974928	+	1.22252i	−0.974928	+	1.22252i	−0.974928	+	0.222521i	$0.928571\pi$
$692$	−0.633040	+	0.144487i	−0.633040	+	0.144487i
$693$		0			0
$694$	0.0777063	+	0.689663i	0.0777063	+	0.689663i
$695$		0			0
$696$	1.02693	+	0.359338i	1.02693	+	0.359338i
$697$		0			0
$698$	0.171138	+	1.51889i	0.171138	+	1.51889i
$699$	−0.603718	+	1.53825i	−0.603718	+	1.53825i
$700$		0			0
$701$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$701$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$702$	0.494815	+	0.310913i	0.494815	+	0.310913i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−1.35061	−	0.848642i	−1.35061	−	0.848642i
$707$		0			0
$708$	−0.0239017	+	0.158578i	−0.0239017	+	0.158578i
$709$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$709$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.366025	−	0.366025i	0.366025	−	0.366025i
$714$		0			0
$715$		0			0
$716$	0.0233678	−	0.0485238i	0.0233678	−	0.0485238i
$717$	0.930874	+	0.634659i	0.930874	+	0.634659i
$718$		0			0
$719$	−1.22252	+	0.974928i	−1.22252	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$719$	−1.22252	+	0.974928i	−1.22252	+	0.974928i	−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.677197	−	0.425511i	0.677197	−	0.425511i
$723$		0			0
$724$		0			0
$725$	−0.997204	−	0.0747301i	−0.997204	−	0.0747301i
$726$	0.643504	−	0.474928i	0.643504	−	0.474928i
$727$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$727$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$728$		0			0
$729$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$733$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$734$		0			0
$735$		0			0
$736$	−0.642075	−	0.224672i	−0.642075	−	0.224672i
$737$		0			0
$738$	0.294057	−	0.0443219i	0.294057	−	0.0443219i
$739$	0.0416310	−	0.369485i	0.0416310	−	0.369485i	−0.955573	−	0.294755i	$-0.904762\pi$
$739$	0.0416310	−	0.369485i	0.0416310	−	0.369485i	0.997204	−	0.0747301i	$-0.0238095\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$743$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$744$	−0.0420866	−	0.561606i	−0.0420866	−	0.561606i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$751$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$752$	0.473437	−	0.0533435i	0.473437	−	0.0533435i
$753$		0			0
$754$	−0.151251	−	0.564475i	−0.151251	−	0.564475i
$755$		0			0
$756$		0			0
$757$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$757$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.92808	+	0.440071i	1.92808	+	0.440071i	0.997204	+	0.0747301i	$0.0238095\pi$
$761$	1.92808	+	0.440071i	1.92808	+	0.440071i	0.930874	+	0.365341i	$0.119048\pi$
$762$	−0.682985	+	1.00175i	−0.682985	+	1.00175i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.292981	−	0.141092i	0.292981	−	0.141092i
$768$	−0.800038	+	0.461902i	−0.800038	+	0.461902i
$769$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$769$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$770$		0			0
$771$	0.582926	+	0.0878620i	0.582926	+	0.0878620i
$772$	0.00890019	−	0.0254353i	0.00890019	−	0.0254353i
$773$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$773$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$774$		0			0
$775$	0.170965	+	0.488590i	0.170965	+	0.488590i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.988831	−	0.149042i	0.988831	−	0.149042i
$784$	0.509806			0.509806
$785$		0			0
$786$	1.36476	+	0.535628i	1.36476	+	0.535628i
$787$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$787$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$788$	−0.389143	+	0.487970i	−0.389143	+	0.487970i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.297604	−	0.850504i	0.297604	−	0.850504i
$795$		0			0
$796$		0			0
$797$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$797$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$798$		0			0
$799$		0			0
$800$	0.481008	−	0.481008i	0.481008	−	0.481008i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.236505	+	0.188607i	−0.236505	+	0.188607i
$807$	0.0566829	−	1.51488i	0.0566829	−	1.51488i
$808$	−0.257609	−	1.12866i	−0.257609	−	1.12866i
$809$	−0.559311	+	0.351438i	−0.559311	+	0.351438i	−0.781831	−	0.623490i	$-0.785714\pi$
$809$	−0.559311	+	0.351438i	−0.559311	+	0.351438i	0.222521	+	0.974928i	$0.428571\pi$
$810$		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
$813$	0.132974	+	0.180173i	0.132974	+	0.180173i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.185412	−	0.232500i	−0.185412	−	0.232500i
$819$		0			0
$820$		0			0
$821$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$821$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$822$		0			0
$823$	−1.85486	−	0.649042i	−1.85486	−	0.649042i	−0.988831	−	0.149042i	$-0.952381\pi$
$823$	−1.85486	−	0.649042i	−1.85486	−	0.649042i	−0.866025	−	0.500000i	$-0.833333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$827$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$828$	−0.356321	+	0.0537067i	−0.356321	+	0.0537067i
$829$	1.40532	+	1.40532i	1.40532	+	1.40532i	0.781831	+	0.623490i	$0.214286\pi$
$829$	1.40532	+	1.40532i	1.40532	+	1.40532i	0.623490	+	0.781831i	$0.285714\pi$
$830$		0			0
$831$	1.97213	−	0.147791i	1.97213	−	0.147791i
$832$	0.693777	+	0.334105i	0.693777	+	0.334105i
$833$		0			0
$834$	−0.218511	+	0.0953356i	−0.218511	+	0.0953356i
$835$		0			0
$836$		0			0
$837$	−0.275400	−	0.438297i	−0.275400	−	0.438297i
$838$		0			0
$839$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$839$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$840$		0			0
$841$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$842$		0			0
$843$		0			0
$844$	0.431495	−	0.271126i	0.431495	−	0.271126i
$845$		0			0
$846$	0.617554	−	0.421041i	0.617554	−	0.421041i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.102641	+	0.0316607i	−0.102641	+	0.0316607i
$853$	−0.752407	+	0.752407i	−0.752407	+	0.752407i	−0.974928	−	0.222521i	$-0.928571\pi$
$853$	−0.752407	+	0.752407i	−0.752407	+	0.752407i	0.222521	+	0.974928i	$0.428571\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	−0.997204	−	0.0747301i	$-0.976190\pi$
$857$	−0.433884	−	0.900969i	−0.433884	−	0.900969i	0.563320	−	0.826239i	$-0.309524\pi$
$858$		0			0
$859$	−0.649042	+	1.85486i	−0.649042	+	1.85486i	−0.149042	+	0.988831i	$0.547619\pi$
$859$	−0.649042	+	1.85486i	−0.649042	+	1.85486i	−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$863$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$864$	−0.361914	+	0.575983i	−0.361914	+	0.575983i
$865$		0			0
$866$		0			0
$867$	0.365341	−	0.930874i	0.365341	−	0.930874i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.695647	+	0.186398i	0.695647	+	0.186398i
$877$	−0.433884	+	1.90097i	−0.433884	+	1.90097i			1.00000i	$0.5\pi$
$877$	−0.433884	+	1.90097i	−0.433884	+	1.90097i	−0.433884	+	0.900969i	$0.642857\pi$
$878$	−0.297604	−	0.850504i	−0.297604	−	0.850504i
$879$		0			0
$880$		0			0
$881$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$881$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$882$	0.707101	−	0.373714i	0.707101	−	0.373714i
$883$	−0.193096	−	0.400969i	−0.193096	−	0.400969i	0.781831	−	0.623490i	$-0.214286\pi$
$883$	−0.193096	−	0.400969i	−0.193096	−	0.400969i	−0.974928	+	0.222521i	$0.928571\pi$
$884$		0			0
$885$		0			0
$886$	0.0538867	−	0.0259505i	0.0538867	−	0.0259505i
$887$	1.07193	−	1.07193i	1.07193	−	1.07193i	0.0747301	−	0.997204i	$-0.476190\pi$
$887$	1.07193	−	1.07193i	1.07193	−	1.07193i	0.997204	−	0.0747301i	$-0.0238095\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−0.633040	−	0.144487i	−0.633040	−	0.144487i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.496990	+	0.535628i	0.496990	+	0.535628i
$898$			0.179095i			0.179095i
$899$	−0.0962349	+	0.508614i	−0.0962349	+	0.508614i
$900$	0.106214	−	0.344336i	0.106214	−	0.344336i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.319827	−	0.733052i	−0.319827	−	0.733052i
$907$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$907$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$908$		0			0
$909$	−0.694076	−	0.806531i	−0.694076	−	0.806531i
$910$		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		−0.900969	−	0.433884i	$-0.857143\pi$
$919$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$920$		0			0
$921$	0.677197	+	1.55215i	0.677197	+	1.55215i
$922$	0.650536	+	0.815746i	0.650536	+	0.815746i
$923$	0.170287	+	0.135799i	0.170287	+	0.135799i
$924$		0			0
$925$		0			0
$926$	−0.991043	+	0.111664i	−0.991043	+	0.111664i
$927$		0			0
$928$	0.657069	−	0.176061i	0.657069	−	0.176061i
$929$		−	0.730682i		−	0.730682i	−0.930874	−	0.365341i	$-0.880952\pi$
$929$		−	0.730682i		−	0.730682i	0.930874	−	0.365341i	$-0.119048\pi$
$930$		0			0
$931$		0			0
$932$	0.132503	+	0.580533i	0.132503	+	0.580533i
$933$	−1.18681	−	0.0444073i	−1.18681	−	0.0444073i
$934$		0			0
$935$		0			0
$936$	0.794413	−	0.0297249i	0.794413	−	0.0297249i
$937$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$937$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$941$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$942$		0			0
$943$	0.369485	+	0.0416310i	0.369485	+	0.0416310i
$944$	−0.0984417	−	0.204416i	−0.0984417	−	0.204416i
$945$		0			0
$946$		0			0
$947$	1.28359	+	0.806531i	1.28359	+	0.806531i	0.988831	−	0.149042i	$-0.0476190\pi$
$947$	1.28359	+	0.806531i	1.28359	+	0.806531i	0.294755	+	0.955573i	$0.404762\pi$
$948$		0			0
$949$	−0.482320	−	1.37839i	−0.482320	−	1.37839i
$950$		0			0
$951$	1.91970	+	0.514383i	1.91970	+	0.514383i
$952$		0			0
$953$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$953$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$954$		0			0
$955$		0			0
$956$	0.405980			0.405980
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.713697	+	0.162897i	−0.713697	+	0.162897i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.0633201	−	0.0397866i	−0.0633201	−	0.0397866i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	−0.0633201	−	0.0397866i	−0.0633201	−	0.0397866i	−0.563320	+	0.826239i	$0.690476\pi$
$968$	0.359338	−	1.02693i	0.359338	−	1.02693i
$969$		0			0
$970$		0			0
$971$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$971$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$972$	−0.0269287	+	0.359338i	−0.0269287	+	0.359338i
$973$		0			0
$974$	−1.12790	+	1.12790i	−1.12790	+	1.12790i
$975$	−0.698220	+	0.215372i	−0.698220	+	0.215372i
$976$		0			0
$977$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$977$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$978$	−0.617554	−	0.421041i	−0.617554	−	0.421041i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.349732	+	1.53228i	0.349732	+	1.53228i
$983$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$983$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$984$	0.296547	−	0.275155i	0.296547	−	0.275155i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.678448	+	0.541044i	0.678448	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$991$	0.678448	+	0.541044i	0.678448	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$992$	−0.219545	−	0.275300i	−0.219545	−	0.275300i
$993$	−1.19572	+	0.521689i	−1.19572	+	0.521689i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.211363	+	0.0739590i	0.211363	+	0.0739590i	0.433884	−	0.900969i	$-0.357143\pi$
$997$	0.211363	+	0.0739590i	0.211363	+	0.0739590i	−0.222521	+	0.974928i	$0.571429\pi$
$998$	−1.08082	−	1.08082i	−1.08082	−	1.08082i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.1.bf.d.827.1	yes	24
3.2	odd	2		2001.1.bf.c.827.2	✓	24
23.22	odd	2	CM	2001.1.bf.d.827.1	yes	24
29.2	odd	28		2001.1.bf.c.1655.2	yes	24
69.68	even	2		2001.1.bf.c.827.2	✓	24
87.2	even	28	inner	2001.1.bf.d.1655.1	yes	24
667.321	even	28		2001.1.bf.c.1655.2	yes	24
2001.1655	odd	28	inner	2001.1.bf.d.1655.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.1.bf.c.827.2	✓	24	3.2	odd	2
2001.1.bf.c.827.2	✓	24	69.68	even	2
2001.1.bf.c.1655.2	yes	24	29.2	odd	28
2001.1.bf.c.1655.2	yes	24	667.321	even	28
2001.1.bf.d.827.1	yes	24	1.1	even	1	trivial
2001.1.bf.d.827.1	yes	24	23.22	odd	2	CM
2001.1.bf.d.1655.1	yes	24	87.2	even	28	inner
2001.1.bf.d.1655.1	yes	24	2001.1655	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)

\(f(q)\)	\(=\)	\(q+(0.0895474 + 0.794755i) q^{2} +(0.930874 + 0.365341i) q^{3} +(0.351311 - 0.0801844i) q^{4} +(-0.206999 + 0.772532i) q^{6} +(0.359338 + 1.02693i) q^{8} +(0.733052 + 0.680173i) q^{9} +O(q^{10})\)	\(q+(0.0895474 + 0.794755i) q^{2} +(0.930874 + 0.365341i) q^{3} +(0.351311 - 0.0801844i) q^{4} +(-0.206999 + 0.772532i) q^{6} +(0.359338 + 1.02693i) q^{8} +(0.733052 + 0.680173i) q^{9} +(0.356321 + 0.0537067i) q^{12} +(-0.317031 - 0.658322i) q^{13} +(-0.459319 + 0.221196i) q^{16} +(-0.474928 + 0.643504i) q^{18} +(-0.781831 + 0.623490i) q^{23} +(-0.0406810 + 1.08722i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.494815 - 0.310913i) q^{26} +(0.433884 + 0.900969i) q^{27} +(0.294755 - 0.955573i) q^{29} +(-0.514383 + 0.0579571i) q^{31} +(0.361914 + 0.575983i) q^{32} +(0.312068 + 0.180173i) q^{36} +(-0.0546039 - 0.728639i) q^{39} +(-0.262919 - 0.262919i) q^{41} +(-0.565533 - 0.565533i) q^{46} +(-0.882094 - 0.308658i) q^{47} +(-0.508380 + 0.0380978i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(0.754903 - 0.264152i) q^{50} +(-0.164164 - 0.205855i) q^{52} +(-0.677197 + 0.425511i) q^{54} +(0.785841 + 0.148689i) q^{58} +0.445042i q^{59} +(-0.0921234 - 0.403619i) q^{62} +(-0.823939 + 0.657069i) q^{64} +(-0.955573 + 0.294755i) q^{69} +(-0.268565 + 0.129334i) q^{71} +(-0.435076 + 0.997204i) q^{72} +(1.98603 + 0.223772i) q^{73} +(0.149042 - 0.988831i) q^{75} +(0.574200 - 0.108644i) q^{78} +(0.0747301 + 0.997204i) q^{81} +(0.185412 - 0.232500i) q^{82} +(0.623490 - 0.781831i) q^{87} +(-0.224672 + 0.281729i) q^{92} +(-0.500000 - 0.133975i) q^{93} +(0.166318 - 0.728688i) q^{94} +(0.126466 + 0.668389i) q^{96} +(0.264152 - 0.754903i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 14 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 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