LMFDB - Embedded newform 2783.1.f.c.850.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2783,1,Mod(390,2783)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2783, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("2783.390");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2783 = 11^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2783.f (of order $10$, degree $4$, not 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:	$1.38889793016$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.23.1
Artin image:	$C_5\times S_3$
Artin field:	Galois closure of 15.5.20200001513509571303.1

Embedding invariants

Embedding label			850.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	2783.850
Dual form			2783.1.f.c.2138.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{8} +(0.809017 - 0.587785i) q^{13} +(0.809017 + 0.587785i) q^{16} +1.00000 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.309017 - 0.951057i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.309017 + 0.951057i) q^{29} +(0.809017 - 0.587785i) q^{31} +(-0.809017 - 0.587785i) q^{39} +(-0.309017 - 0.951057i) q^{41} +(0.809017 - 0.587785i) q^{46} +(-0.309017 - 0.951057i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} -1.00000 q^{54} +(0.309017 + 0.951057i) q^{58} +(0.618034 - 1.90211i) q^{59} +(0.309017 - 0.951057i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-0.309017 - 0.951057i) q^{69} +(0.809017 + 0.587785i) q^{71} +(-0.309017 + 0.951057i) q^{73} +(0.809017 - 0.587785i) q^{75} -1.00000 q^{78} +(-0.309017 + 0.951057i) q^{81} +(-0.809017 - 0.587785i) q^{82} +1.00000 q^{87} +(-0.809017 - 0.587785i) q^{93} +(-0.809017 - 0.587785i) q^{94} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - q^{6} - q^{8}+O(q^{10}) $ 4 * q + q^2 + q^3 - q^6 - q^8	$ 4 q + q^{2} + q^{3} - q^{6} - q^{8} + q^{13} + q^{16} + 4 q^{23} + q^{24} - q^{25} - q^{26} - q^{27} + q^{29} + q^{31} - q^{39} + q^{41} + q^{46} + q^{47} - q^{48} - q^{49} + q^{50} - 4 q^{54} - q^{58} - 2 q^{59} - q^{62} - q^{64} + q^{69} + q^{71} + q^{73} + q^{75} - 4 q^{78} + q^{81} - q^{82} + 4 q^{87} - q^{93} - q^{94} - 4 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^3 - q^6 - q^8 + q^13 + q^16 + 4 * q^23 + q^24 - q^25 - q^26 - q^27 + q^29 + q^31 - q^39 + q^41 + q^46 + q^47 - q^48 - q^49 + q^50 - 4 * q^54 - q^58 - 2 * q^59 - q^62 - q^64 + q^69 + q^71 + q^73 + q^75 - 4 * q^78 + q^81 - q^82 + 4 * q^87 - q^93 - q^94 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2783\mathbb{Z}\right)^\times$.

$n$	$1937$	$2301$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$2$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$3$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$3$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$4$		0			0
$5$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$5$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$6$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$7$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$7$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$8$	0.309017	+	0.951057i	0.309017	+	0.951057i
$9$		0			0
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$13$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$14$		0			0
$15$		0			0
$16$	0.809017	+	0.587785i	0.809017	+	0.587785i
$17$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$17$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$18$		0			0
$19$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$19$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.00000			1.00000
$23$	1.00000			1.00000
$24$	0.809017	−	0.587785i	0.809017	−	0.587785i
$25$	0.309017	+	0.951057i	0.309017	+	0.951057i
$26$	0.309017	−	0.951057i	0.309017	−	0.951057i
$27$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$28$		0			0
$29$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$29$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$30$		0			0
$31$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$31$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$		0			0
$39$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$40$		0			0
$41$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$41$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$		0			0
$46$	0.809017	−	0.587785i	0.809017	−	0.587785i
$47$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$47$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$48$	0.309017	−	0.951057i	0.309017	−	0.951057i
$49$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$50$	0.809017	+	0.587785i	0.809017	+	0.587785i
$51$		0			0
$52$		0			0
$53$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$53$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$54$	−1.00000			−1.00000
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.309017	+	0.951057i	0.309017	+	0.951057i
$59$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$59$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$60$		0			0
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$	0.309017	−	0.951057i	0.309017	−	0.951057i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$65$		0			0
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$70$		0			0
$71$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$71$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$72$		0			0
$73$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$73$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$74$		0			0
$75$	0.809017	−	0.587785i	0.809017	−	0.587785i
$76$		0			0
$77$		0			0
$78$	−1.00000			−1.00000
$79$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$79$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$80$		0			0
$81$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$82$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$83$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$83$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.00000			1.00000
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$94$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$95$		0			0
$96$		0			0
$97$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$97$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$98$	−1.00000			−1.00000
$99$		0			0
$100$		0			0
$101$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$101$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$102$		0			0
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$	0.809017	+	0.587785i	0.809017	+	0.587785i
$105$		0			0
$106$		0			0
$107$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$107$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$113$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$119$		0			0
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$127$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$128$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$129$		0			0
$130$		0			0
$131$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$131$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$139$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$139$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$140$		0			0
$141$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$142$	1.00000			1.00000
$143$		0			0
$144$		0			0
$145$		0			0
$146$	0.309017	+	0.951057i	0.309017	+	0.951057i
$147$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$148$		0			0
$149$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$149$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$150$	0.309017	−	0.951057i	0.309017	−	0.951057i
$151$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$151$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$157$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.309017	+	0.951057i	0.309017	+	0.951057i
$163$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$163$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$167$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$173$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$174$	0.809017	−	0.587785i	0.809017	−	0.587785i
$175$		0			0
$176$		0			0
$177$	−2.00000			−2.00000
$178$		0			0
$179$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$179$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$180$		0			0
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$		0			0
$184$	0.309017	+	0.951057i	0.309017	+	0.951057i
$185$		0			0
$186$	−1.00000			−1.00000
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$191$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$192$	0.809017	+	0.587785i	0.809017	+	0.587785i
$193$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$193$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$197$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$201$		0			0
$202$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	1.00000			1.00000
$209$		0			0
$210$		0			0
$211$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$211$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$212$		0			0
$213$	0.309017	−	0.951057i	0.309017	−	0.951057i
$214$		0			0
$215$		0			0
$216$	0.309017	−	0.951057i	0.309017	−	0.951057i
$217$		0			0
$218$		0			0
$219$	1.00000			1.00000
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$223$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$227$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$228$		0			0
$229$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$229$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$230$		0			0
$231$		0			0
$232$	−1.00000			−1.00000
$233$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$233$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$239$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$247$		0			0
$248$	0.809017	+	0.587785i	0.809017	+	0.587785i
$249$		0			0
$250$		0			0
$251$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$251$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$252$		0			0
$253$		0			0
$254$	1.00000			1.00000
$255$		0			0
$256$		0			0
$257$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$257$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$269$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$270$		0			0
$271$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$271$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$277$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$278$	0.309017	+	0.951057i	0.309017	+	0.951057i
$279$		0			0
$280$		0			0
$281$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$281$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$282$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.309017	+	0.951057i	0.309017	+	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$293$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$294$	0.309017	+	0.951057i	0.309017	+	0.951057i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.809017	−	0.587785i	0.809017	−	0.587785i
$300$		0			0
$301$		0			0
$302$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$303$	1.61803	+	1.17557i	1.61803	+	1.17557i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.00000			2.00000			1.00000			$0$
$307$	2.00000			2.00000			1.00000			$0$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$311$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$312$	0.309017	−	0.951057i	0.309017	−	0.951057i
$313$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$313$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$317$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	0.809017	+	0.587785i	0.809017	+	0.587785i
$326$	0.309017	−	0.951057i	0.309017	−	0.951057i
$327$		0			0
$328$	0.809017	−	0.587785i	0.809017	−	0.587785i
$329$		0			0
$330$		0			0
$331$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$331$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$		0			0
$334$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$335$		0			0
$336$		0			0
$337$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$337$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.61803	+	1.17557i	1.61803	+	1.17557i
$347$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$347$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$348$		0			0
$349$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$349$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$350$		0			0
$351$	−1.00000			−1.00000
$352$		0			0
$353$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$353$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$354$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$359$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$359$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$360$		0			0
$361$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$367$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$368$	0.809017	+	0.587785i	0.809017	+	0.587785i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$	0.809017	−	0.587785i	0.809017	−	0.587785i
$377$	0.309017	+	0.951057i	0.309017	+	0.951057i
$378$		0			0
$379$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$379$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$380$		0			0
$381$	0.309017	−	0.951057i	0.309017	−	0.951057i
$382$		0			0
$383$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$383$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$384$	1.00000			1.00000
$385$		0			0
$386$	1.00000			1.00000
$387$		0			0
$388$		0			0
$389$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$389$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$390$		0			0
$391$		0			0
$392$	0.309017	−	0.951057i	0.309017	−	0.951057i
$393$	0.309017	+	0.951057i	0.309017	+	0.951057i
$394$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$395$		0			0
$396$		0			0
$397$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$397$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$398$		0			0
$399$		0			0
$400$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$401$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$401$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$402$		0			0
$403$	0.309017	−	0.951057i	0.309017	−	0.951057i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$409$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.00000			1.00000
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$421$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$422$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$433$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$433$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.809017	−	0.587785i	0.809017	−	0.587785i
$439$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$439$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$443$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$444$		0			0
$445$		0			0
$446$	1.61803	+	1.17557i	1.61803	+	1.17557i
$447$		0			0
$448$		0			0
$449$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$449$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$457$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$461$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	2.00000			2.00000			1.00000			$0$
$463$	2.00000			2.00000			1.00000			$0$
$464$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$465$		0			0
$466$	0.309017	−	0.951057i	0.309017	−	0.951057i
$467$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$467$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	2.00000			2.00000
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$479$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$479$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$487$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$488$		0			0
$489$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$490$		0			0
$491$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$491$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	1.00000			1.00000
$497$		0			0
$498$		0			0
$499$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$499$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$500$		0			0
$501$	1.61803	+	1.17557i	1.61803	+	1.17557i
$502$		0			0
$503$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$503$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$509$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$510$		0			0
$511$		0			0
$512$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$513$		0			0
$514$	0.309017	+	0.951057i	0.309017	+	0.951057i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.61803	−	1.17557i	1.61803	−	1.17557i
$520$		0			0
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$		0			0
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	1.00000			1.00000
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$538$	1.00000			1.00000
$539$		0			0
$540$		0			0
$541$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$541$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$542$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$547$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	0.809017	−	0.587785i	0.809017	−	0.587785i
$553$		0			0
$554$	0.309017	−	0.951057i	0.309017	−	0.951057i
$555$		0			0
$556$		0			0
$557$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$557$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$563$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$569$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$569$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.309017	+	0.951057i	0.309017	+	0.951057i
$576$		0			0
$577$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$577$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$578$	0.809017	+	0.587785i	0.809017	+	0.587785i
$579$	0.309017	−	0.951057i	0.309017	−	0.951057i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.00000			−1.00000
$585$		0			0
$586$		0			0
$587$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$587$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	0.309017	+	0.951057i	0.309017	+	0.951057i
$592$		0			0
$593$	2.00000			2.00000			1.00000			$0$
$593$	2.00000			2.00000			1.00000			$0$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.309017	−	0.951057i	0.309017	−	0.951057i
$599$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$599$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$600$	0.809017	+	0.587785i	0.809017	+	0.587785i
$601$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$601$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	2.00000			2.00000
$607$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$607$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$612$		0			0
$613$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$613$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$614$	1.61803	−	1.17557i	1.61803	−	1.17557i
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$619$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$620$		0			0
$621$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$622$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$623$		0			0
$624$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$625$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$631$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$632$		0			0
$633$	1.61803	+	1.17557i	1.61803	+	1.17557i
$634$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$635$		0			0
$636$		0			0
$637$	−1.00000			−1.00000
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$641$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$642$		0			0
$643$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$643$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$647$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$648$	−1.00000			−1.00000
$649$		0			0
$650$	1.00000			1.00000
$651$		0			0
$652$		0			0
$653$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$653$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$654$		0			0
$655$		0			0
$656$	0.309017	−	0.951057i	0.309017	−	0.951057i
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$668$		0			0
$669$	1.61803	−	1.17557i	1.61803	−	1.17557i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$673$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$674$		0			0
$675$	0.309017	−	0.951057i	0.309017	−	0.951057i
$676$		0			0
$677$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$677$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$683$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$691$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$692$		0			0
$693$		0			0
$694$	−2.00000			−2.00000
$695$		0			0
$696$	0.309017	+	0.951057i	0.309017	+	0.951057i
$697$		0			0
$698$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$699$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$700$		0			0
$701$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$701$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$702$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$707$		0			0
$708$		0			0
$709$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$709$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.809017	−	0.587785i	0.809017	−	0.587785i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$718$		0			0
$719$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$719$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$720$		0			0
$721$		0			0
$722$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$723$		0			0
$724$		0			0
$725$	−1.00000			−1.00000
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.309017	+	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$739$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$743$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$744$	0.309017	−	0.951057i	0.309017	−	0.951057i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$751$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$752$	0.309017	−	0.951057i	0.309017	−	0.951057i
$753$		0			0
$754$	0.809017	+	0.587785i	0.809017	+	0.587785i
$755$		0			0
$756$		0			0
$757$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$757$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$761$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$762$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$768$		0			0
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$	1.00000			1.00000
$772$		0			0
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$		0			0
$775$	0.809017	+	0.587785i	0.809017	+	0.587785i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.809017	−	0.587785i	0.809017	−	0.587785i
$784$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$785$		0			0
$786$	0.809017	+	0.587785i	0.809017	+	0.587785i
$787$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$787$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$795$		0			0
$796$		0			0
$797$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$797$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$807$	0.309017	−	0.951057i	0.309017	−	0.951057i
$808$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$809$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$809$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$810$		0			0
$811$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$811$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$812$		0			0
$813$	−2.00000			−2.00000
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.309017	−	0.951057i	0.309017	−	0.951057i
$819$		0			0
$820$		0			0
$821$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$821$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$822$		0			0
$823$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$823$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$827$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$829$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$830$		0			0
$831$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$832$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$833$		0			0
$834$	0.809017	−	0.587785i	0.809017	−	0.587785i
$835$		0			0
$836$		0			0
$837$	−1.00000			−1.00000
$838$		0			0
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$		0			0
$841$		0			0
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$853$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$857$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$859$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$863$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.809017	−	0.587785i	0.809017	−	0.587785i
$868$		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			0
$877$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$877$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$878$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$		0			0
$883$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$883$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$		0			0
$886$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$887$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$887$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$898$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$899$	0.309017	+	0.951057i	0.309017	+	0.951057i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$907$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$907$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$911$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$919$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$920$		0			0
$921$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$922$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$923$	1.00000			1.00000
$924$		0			0
$925$		0			0
$926$	1.61803	−	1.17557i	1.61803	−	1.17557i
$927$		0			0
$928$		0			0
$929$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$929$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$937$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$941$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$944$	1.61803	−	1.17557i	1.61803	−	1.17557i
$945$		0			0
$946$		0			0
$947$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$947$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$	0.309017	+	0.951057i	0.309017	+	0.951057i
$950$		0			0
$951$	1.61803	+	1.17557i	1.61803	+	1.17557i
$952$		0			0
$953$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$953$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$967$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$971$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$972$		0			0
$973$		0			0
$974$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$975$	0.309017	−	0.951057i	0.309017	−	0.951057i
$976$		0			0
$977$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$977$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$978$	−1.00000			−1.00000
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.309017	+	0.951057i	0.309017	+	0.951057i
$983$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$983$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$984$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	2.00000			2.00000			1.00000			$0$
$991$	2.00000			2.00000			1.00000			$0$
$992$		0			0
$993$	0.309017	+	0.951057i	0.309017	+	0.951057i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$997$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$998$	0.309017	+	0.951057i	0.309017	+	0.951057i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2783.1.f.c.850.1		4
11.2	odd	10		2783.1.d.b.1816.1		1
11.3	even	5	inner	2783.1.f.c.390.1		4
11.4	even	5	inner	2783.1.f.c.2138.1		4
11.5	even	5	inner	2783.1.f.c.735.1		4
11.6	odd	10		2783.1.f.a.735.1		4
11.7	odd	10		2783.1.f.a.2138.1		4
11.8	odd	10		2783.1.f.a.390.1		4
11.9	even	5		23.1.b.a.22.1	✓	1
11.10	odd	2		2783.1.f.a.850.1		4
23.22	odd	2	CM	2783.1.f.c.850.1		4
33.20	odd	10		207.1.d.a.91.1		1
44.31	odd	10		368.1.f.a.321.1		1
55.9	even	10		575.1.d.a.551.1		1
55.42	odd	20		575.1.c.a.574.1		2
55.53	odd	20		575.1.c.a.574.2		2
77.9	even	15		1127.1.f.b.459.1		2
77.20	odd	10		1127.1.d.b.344.1		1
77.31	odd	30		1127.1.f.a.275.1		2
77.53	even	15		1127.1.f.b.275.1		2
77.75	odd	30		1127.1.f.a.459.1		2
88.53	even	10		1472.1.f.b.321.1		1
88.75	odd	10		1472.1.f.a.321.1		1
99.20	odd	30		1863.1.f.a.919.1		2
99.31	even	15		1863.1.f.b.298.1		2
99.86	odd	30		1863.1.f.a.298.1		2
99.97	even	15		1863.1.f.b.919.1		2
132.119	even	10		3312.1.c.a.2161.1		1
143.9	even	15		3887.1.h.c.3357.1		2
143.20	odd	60		3887.1.j.e.3403.1		4
143.31	odd	20		3887.1.c.a.3886.2		2
143.42	even	15		3887.1.h.c.22.1		2
143.64	even	10		3887.1.d.b.2874.1		1
143.75	even	30		3887.1.h.a.22.1		2
143.86	odd	20		3887.1.c.a.3886.1		2
143.97	odd	60		3887.1.j.e.3403.2		4
143.108	even	30		3887.1.h.a.3357.1		2
143.119	odd	60		3887.1.j.e.2851.1		4
143.141	odd	60		3887.1.j.e.2851.2		4
253.9	even	55		529.1.d.a.195.1		10
253.20	odd	110		529.1.d.a.359.1		10
253.31	even	55		529.1.d.a.28.1		10
253.42	odd	110		529.1.d.a.352.1		10
253.53	odd	110		529.1.d.a.411.1		10
253.64	even	55		529.1.d.a.274.1		10
253.68	even	10		2783.1.d.b.1816.1		1
253.75	even	55		529.1.d.a.263.1		10
253.86	odd	110		529.1.d.a.263.1		10
253.91	odd	10	inner	2783.1.f.c.390.1		4
253.97	odd	110		529.1.d.a.274.1		10
253.108	even	55		529.1.d.a.411.1		10
253.114	odd	10	inner	2783.1.f.c.2138.1		4
253.119	even	55		529.1.d.a.352.1		10
253.130	odd	110		529.1.d.a.28.1		10
253.137	odd	10	inner	2783.1.f.c.735.1		4
253.141	even	55		529.1.d.a.359.1		10
253.152	odd	110		529.1.d.a.195.1		10
253.160	even	10		2783.1.f.a.735.1		4
253.163	even	55		529.1.d.a.42.1		10
253.174	even	55		529.1.d.a.130.1		10
253.183	even	10		2783.1.f.a.2138.1		4
253.196	even	55		529.1.d.a.63.1		10
253.206	even	10		2783.1.f.a.390.1		4
253.218	odd	110		529.1.d.a.63.1		10
253.229	odd	10		23.1.b.a.22.1	✓	1
253.240	odd	110		529.1.d.a.130.1		10
253.251	odd	110		529.1.d.a.42.1		10
253.252	even	2		2783.1.f.a.850.1		4
759.482	even	10		207.1.d.a.91.1		1
1012.735	even	10		368.1.f.a.321.1		1
1265.229	odd	10		575.1.d.a.551.1		1
1265.482	even	20		575.1.c.a.574.1		2
1265.988	even	20		575.1.c.a.574.2		2
1771.229	even	30		1127.1.f.a.459.1		2
1771.482	even	10		1127.1.d.b.344.1		1
1771.1241	odd	30		1127.1.f.b.459.1		2
1771.1494	even	30		1127.1.f.a.275.1		2
1771.1747	odd	30		1127.1.f.b.275.1		2
2024.229	odd	10		1472.1.f.b.321.1		1
2024.1747	even	10		1472.1.f.a.321.1		1
2277.229	odd	30		1863.1.f.b.298.1		2
2277.482	even	30		1863.1.f.a.298.1		2
2277.988	odd	30		1863.1.f.b.919.1		2
2277.2000	even	30		1863.1.f.a.919.1		2
3036.2759	odd	10		3312.1.c.a.2161.1		1
3289.229	even	20		3887.1.c.a.3886.1		2
3289.735	even	60		3887.1.j.e.3403.1		4
3289.1241	even	60		3887.1.j.e.3403.2		4
3289.1494	odd	10		3887.1.d.b.2874.1		1
3289.1747	even	20		3887.1.c.a.3886.2		2
3289.2000	even	60		3887.1.j.e.2851.2		4
3289.2253	odd	30		3887.1.h.a.3357.1		2
3289.2506	odd	30		3887.1.h.a.22.1		2
3289.2759	odd	30		3887.1.h.c.22.1		2
3289.3012	odd	30		3887.1.h.c.3357.1		2
3289.3265	even	60		3887.1.j.e.2851.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.1.b.a.22.1	✓	1	11.9	even	5
23.1.b.a.22.1	✓	1	253.229	odd	10
207.1.d.a.91.1		1	33.20	odd	10
207.1.d.a.91.1		1	759.482	even	10
368.1.f.a.321.1		1	44.31	odd	10
368.1.f.a.321.1		1	1012.735	even	10
529.1.d.a.28.1		10	253.31	even	55
529.1.d.a.28.1		10	253.130	odd	110
529.1.d.a.42.1		10	253.163	even	55
529.1.d.a.42.1		10	253.251	odd	110
529.1.d.a.63.1		10	253.196	even	55
529.1.d.a.63.1		10	253.218	odd	110
529.1.d.a.130.1		10	253.174	even	55
529.1.d.a.130.1		10	253.240	odd	110
529.1.d.a.195.1		10	253.9	even	55
529.1.d.a.195.1		10	253.152	odd	110
529.1.d.a.263.1		10	253.75	even	55
529.1.d.a.263.1		10	253.86	odd	110
529.1.d.a.274.1		10	253.64	even	55
529.1.d.a.274.1		10	253.97	odd	110
529.1.d.a.352.1		10	253.42	odd	110
529.1.d.a.352.1		10	253.119	even	55
529.1.d.a.359.1		10	253.20	odd	110
529.1.d.a.359.1		10	253.141	even	55
529.1.d.a.411.1		10	253.53	odd	110
529.1.d.a.411.1		10	253.108	even	55
575.1.c.a.574.1		2	55.42	odd	20
575.1.c.a.574.1		2	1265.482	even	20
575.1.c.a.574.2		2	55.53	odd	20
575.1.c.a.574.2		2	1265.988	even	20
575.1.d.a.551.1		1	55.9	even	10
575.1.d.a.551.1		1	1265.229	odd	10
1127.1.d.b.344.1		1	77.20	odd	10
1127.1.d.b.344.1		1	1771.482	even	10
1127.1.f.a.275.1		2	77.31	odd	30
1127.1.f.a.275.1		2	1771.1494	even	30
1127.1.f.a.459.1		2	77.75	odd	30
1127.1.f.a.459.1		2	1771.229	even	30
1127.1.f.b.275.1		2	77.53	even	15
1127.1.f.b.275.1		2	1771.1747	odd	30
1127.1.f.b.459.1		2	77.9	even	15
1127.1.f.b.459.1		2	1771.1241	odd	30
1472.1.f.a.321.1		1	88.75	odd	10
1472.1.f.a.321.1		1	2024.1747	even	10
1472.1.f.b.321.1		1	88.53	even	10
1472.1.f.b.321.1		1	2024.229	odd	10
1863.1.f.a.298.1		2	99.86	odd	30
1863.1.f.a.298.1		2	2277.482	even	30
1863.1.f.a.919.1		2	99.20	odd	30
1863.1.f.a.919.1		2	2277.2000	even	30
1863.1.f.b.298.1		2	99.31	even	15
1863.1.f.b.298.1		2	2277.229	odd	30
1863.1.f.b.919.1		2	99.97	even	15
1863.1.f.b.919.1		2	2277.988	odd	30
2783.1.d.b.1816.1		1	11.2	odd	10
2783.1.d.b.1816.1		1	253.68	even	10
2783.1.f.a.390.1		4	11.8	odd	10
2783.1.f.a.390.1		4	253.206	even	10
2783.1.f.a.735.1		4	11.6	odd	10
2783.1.f.a.735.1		4	253.160	even	10
2783.1.f.a.850.1		4	11.10	odd	2
2783.1.f.a.850.1		4	253.252	even	2
2783.1.f.a.2138.1		4	11.7	odd	10
2783.1.f.a.2138.1		4	253.183	even	10
2783.1.f.c.390.1		4	11.3	even	5	inner
2783.1.f.c.390.1		4	253.91	odd	10	inner
2783.1.f.c.735.1		4	11.5	even	5	inner
2783.1.f.c.735.1		4	253.137	odd	10	inner
2783.1.f.c.850.1		4	1.1	even	1	trivial
2783.1.f.c.850.1		4	23.22	odd	2	CM
2783.1.f.c.2138.1		4	11.4	even	5	inner
2783.1.f.c.2138.1		4	253.114	odd	10	inner
3312.1.c.a.2161.1		1	132.119	even	10
3312.1.c.a.2161.1		1	3036.2759	odd	10
3887.1.c.a.3886.1		2	143.86	odd	20
3887.1.c.a.3886.1		2	3289.229	even	20
3887.1.c.a.3886.2		2	143.31	odd	20
3887.1.c.a.3886.2		2	3289.1747	even	20
3887.1.d.b.2874.1		1	143.64	even	10
3887.1.d.b.2874.1		1	3289.1494	odd	10
3887.1.h.a.22.1		2	143.75	even	30
3887.1.h.a.22.1		2	3289.2506	odd	30
3887.1.h.a.3357.1		2	143.108	even	30
3887.1.h.a.3357.1		2	3289.2253	odd	30
3887.1.h.c.22.1		2	143.42	even	15
3887.1.h.c.22.1		2	3289.2759	odd	30
3887.1.h.c.3357.1		2	143.9	even	15
3887.1.h.c.3357.1		2	3289.3012	odd	30
3887.1.j.e.2851.1		4	143.119	odd	60
3887.1.j.e.2851.1		4	3289.3265	even	60
3887.1.j.e.2851.2		4	143.141	odd	60
3887.1.j.e.2851.2		4	3289.2000	even	60
3887.1.j.e.3403.1		4	143.20	odd	60
3887.1.j.e.3403.1		4	3289.735	even	60
3887.1.j.e.3403.2		4	143.97	odd	60
3887.1.j.e.3403.2		4	3289.1241	even	60

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:	\( N \)	\(=\)	\( 2783 = 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2783.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{8} +(0.809017 - 0.587785i) q^{13} +(0.809017 + 0.587785i) q^{16} +1.00000 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.309017 - 0.951057i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.309017 + 0.951057i) q^{29} +(0.809017 - 0.587785i) q^{31} +(-0.809017 - 0.587785i) q^{39} +(-0.309017 - 0.951057i) q^{41} +(0.809017 - 0.587785i) q^{46} +(-0.309017 - 0.951057i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} -1.00000 q^{54} +(0.309017 + 0.951057i) q^{58} +(0.618034 - 1.90211i) q^{59} +(0.309017 - 0.951057i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-0.309017 - 0.951057i) q^{69} +(0.809017 + 0.587785i) q^{71} +(-0.309017 + 0.951057i) q^{73} +(0.809017 - 0.587785i) q^{75} -1.00000 q^{78} +(-0.309017 + 0.951057i) q^{81} +(-0.809017 - 0.587785i) q^{82} +1.00000 q^{87} +(-0.809017 - 0.587785i) q^{93} +(-0.809017 - 0.587785i) q^{94} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - q^{6} - q^{8}+O(q^{10}) \) 4 * q + q^2 + q^3 - q^6 - q^8	\( 4 q + q^{2} + q^{3} - q^{6} - q^{8} + q^{13} + q^{16} + 4 q^{23} + q^{24} - q^{25} - q^{26} - q^{27} + q^{29} + q^{31} - q^{39} + q^{41} + q^{46} + q^{47} - q^{48} - q^{49} + q^{50} - 4 q^{54} - q^{58} - 2 q^{59} - q^{62} - q^{64} + q^{69} + q^{71} + q^{73} + q^{75} - 4 q^{78} + q^{81} - q^{82} + 4 q^{87} - q^{93} - q^{94} - 4 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^3 - q^6 - q^8 + q^13 + q^16 + 4 * q^23 + q^24 - q^25 - q^26 - q^27 + q^29 + q^31 - q^39 + q^41 + q^46 + q^47 - q^48 - q^49 + q^50 - 4 * q^54 - q^58 - 2 * q^59 - q^62 - q^64 + q^69 + q^71 + q^73 + q^75 - 4 * q^78 + q^81 - q^82 + 4 * q^87 - q^93 - q^94 - 4 * q^98

Introduction

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