LMFDB - Embedded newform 1045.1.w.a.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,1,Mod(284,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6, 5]))

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

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

chi := DirichletCharacter("1045.284");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1045.w (of order $10$, degree $4$, 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:	$0.521522938201$
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:	yes
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.132135025.1

Embedding invariants

Embedding label			949.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	1045.949
Dual form			1045.1.w.a.664.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{8} +(-1.30902 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{8} +(-1.30902 + 0.951057i) q^{9} +0.618034 q^{10} +(-0.809017 + 0.587785i) q^{11} +1.00000 q^{12} +(-0.500000 + 0.363271i) q^{13} +(-0.500000 + 1.53884i) q^{15} +(0.309017 - 0.951057i) q^{18} +(0.309017 + 0.951057i) q^{19} +(0.500000 - 0.363271i) q^{20} +(0.190983 - 0.587785i) q^{22} +(-1.30902 + 0.951057i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.118034 - 0.363271i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.309017 - 0.951057i) q^{30} +1.00000 q^{32} +(1.30902 + 0.951057i) q^{33} +(-0.309017 - 0.951057i) q^{36} +(-0.500000 + 1.53884i) q^{37} +(-0.500000 - 0.363271i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-0.190983 - 0.587785i) q^{44} +1.61803 q^{45} +(-0.809017 - 0.587785i) q^{49} +(-0.500000 - 0.363271i) q^{50} +(-0.118034 - 0.363271i) q^{52} +(-1.61803 + 1.17557i) q^{53} -0.618034 q^{54} +1.00000 q^{55} +(1.30902 - 0.951057i) q^{57} +(-0.809017 - 0.587785i) q^{60} +(1.30902 + 0.951057i) q^{61} +(-0.500000 + 0.363271i) q^{64} +0.618034 q^{65} -1.00000 q^{66} -1.61803 q^{67} +(1.30902 + 0.951057i) q^{72} +(-0.309017 - 0.951057i) q^{74} +(1.30902 - 0.951057i) q^{75} -0.618034 q^{76} -0.618034 q^{78} +(0.809017 + 0.587785i) q^{88} +(-0.809017 + 0.587785i) q^{90} +(0.309017 - 0.951057i) q^{95} +(-0.500000 - 1.53884i) q^{96} +(-0.500000 + 0.363271i) q^{97} +0.618034 q^{98} +(0.500000 - 1.53884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 3 q^{4} - q^{5} + q^{6} + q^{8} - 3 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 3 * q^4 - q^5 + q^6 + q^8 - 3 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 3 q^{4} - q^{5} + q^{6} + q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 2 q^{15} - q^{18} - q^{19} + 2 q^{20} + 3 q^{22} - 3 q^{24} - q^{25} - 4 q^{26} + q^{27} + q^{30} + 4 q^{32} + 3 q^{33} + q^{36} - 2 q^{37} - 2 q^{38} + q^{39} + q^{40} - 3 q^{44} + 2 q^{45} - q^{49} - 2 q^{50} + 4 q^{52} - 2 q^{53} + 2 q^{54} + 4 q^{55} + 3 q^{57} - q^{60} + 3 q^{61} - 2 q^{64} - 2 q^{65} - 4 q^{66} - 2 q^{67} + 3 q^{72} + q^{74} + 3 q^{75} + 2 q^{76} + 2 q^{78} + q^{88} - q^{90} - q^{95} - 2 q^{96} - 2 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 3 * q^4 - q^5 + q^6 + q^8 - 3 * q^9 - 2 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 2 * q^15 - q^18 - q^19 + 2 * q^20 + 3 * q^22 - 3 * q^24 - q^25 - 4 * q^26 + q^27 + q^30 + 4 * q^32 + 3 * q^33 + q^36 - 2 * q^37 - 2 * q^38 + q^39 + q^40 - 3 * q^44 + 2 * q^45 - q^49 - 2 * q^50 + 4 * q^52 - 2 * q^53 + 2 * q^54 + 4 * q^55 + 3 * q^57 - q^60 + 3 * q^61 - 2 * q^64 - 2 * q^65 - 4 * q^66 - 2 * q^67 + 3 * q^72 + q^74 + 3 * q^75 + 2 * q^76 + 2 * q^78 + q^88 - q^90 - q^95 - 2 * q^96 - 2 * q^97 - 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$2$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$3$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$3$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$4$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$5$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$5$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$6$	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
$9$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$10$	0.618034			0.618034
$11$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$11$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$12$	1.00000			1.00000
$13$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$13$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$14$		0			0
$15$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$16$		0			0
$17$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$17$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$18$	0.309017	−	0.951057i	0.309017	−	0.951057i
$19$	0.309017	+	0.951057i	0.309017	+	0.951057i
$19$	0.309017	+	0.951057i	0.309017	+	0.951057i
$20$	0.500000	−	0.363271i	0.500000	−	0.363271i
$21$		0			0
$22$	0.190983	−	0.587785i	0.190983	−	0.587785i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$25$	0.309017	+	0.951057i	0.309017	+	0.951057i
$26$	0.118034	−	0.363271i	0.118034	−	0.363271i
$27$	0.809017	+	0.587785i	0.809017	+	0.587785i
$28$		0			0
$29$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$29$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$30$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$31$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$31$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$32$	1.00000			1.00000
$33$	1.30902	+	0.951057i	1.30902	+	0.951057i
$34$		0			0
$35$		0			0
$36$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$37$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$37$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$38$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$39$	0.809017	+	0.587785i	0.809017	+	0.587785i
$40$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$41$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$41$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$45$	1.61803			1.61803
$46$		0			0
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$50$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$51$		0			0
$52$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$53$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$53$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$54$	−0.618034			−0.618034
$55$	1.00000			1.00000
$56$		0			0
$57$	1.30902	−	0.951057i	1.30902	−	0.951057i
$58$		0			0
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$61$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$61$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$62$		0			0
$63$		0			0
$64$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$65$	0.618034			0.618034
$66$	−1.00000			−1.00000
$67$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$67$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$71$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$72$	1.30902	+	0.951057i	1.30902	+	0.951057i
$73$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$73$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$74$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$75$	1.30902	−	0.951057i	1.30902	−	0.951057i
$76$	−0.618034			−0.618034
$77$		0			0
$78$	−0.618034			−0.618034
$79$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$79$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		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
$87$		0			0
$88$	0.809017	+	0.587785i	0.809017	+	0.587785i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.309017	−	0.951057i	0.309017	−	0.951057i
$96$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$97$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$97$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$98$	0.618034			0.618034
$99$	0.500000	−	1.53884i	0.500000	−	1.53884i
$100$	−0.618034			−0.618034
$101$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$101$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$102$		0			0
$103$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$103$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$104$	0.500000	+	0.363271i	0.500000	+	0.363271i
$105$		0			0
$106$	0.381966	−	1.17557i	0.381966	−	1.17557i
$107$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$107$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$108$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$111$	2.61803			2.61803
$112$		0			0
$113$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$113$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$114$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$115$		0			0
$116$		0			0
$117$	0.309017	−	0.951057i	0.309017	−	0.951057i
$118$		0			0
$119$		0			0
$120$	1.61803			1.61803
$121$	0.309017	−	0.951057i	0.309017	−	0.951057i
$122$	−1.00000			−1.00000
$123$		0			0
$124$		0			0
$125$	0.309017	−	0.951057i	0.309017	−	0.951057i
$126$		0			0
$127$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$127$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$128$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$129$		0			0
$130$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$131$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$131$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$132$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$133$		0			0
$134$	0.809017	−	0.587785i	0.809017	−	0.587785i
$135$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$136$		0			0
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$139$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.190983	−	0.587785i	0.190983	−	0.587785i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$148$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$149$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$149$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$150$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$151$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$151$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$152$	0.809017	−	0.587785i	0.809017	−	0.587785i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$157$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$157$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$158$		0			0
$159$	2.61803	+	1.90211i	2.61803	+	1.90211i
$160$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$161$		0			0
$162$		0			0
$163$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$163$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$164$		0			0
$165$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$166$		0			0
$167$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$167$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$168$		0			0
$169$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$170$		0			0
$171$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$172$		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			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$179$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$180$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$	0.809017	−	2.48990i	0.809017	−	2.48990i
$184$		0			0
$185$	1.30902	−	0.951057i	1.30902	−	0.951057i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.190983	+	0.587785i	0.190983	+	0.587785i
$191$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$191$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$192$	0.809017	+	0.587785i	0.809017	+	0.587785i
$193$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$193$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$194$	0.118034	−	0.363271i	0.118034	−	0.363271i
$195$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$196$	0.500000	−	0.363271i	0.500000	−	0.363271i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.309017	+	0.951057i	0.309017	+	0.951057i
$199$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$199$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$200$	0.809017	−	0.587785i	0.809017	−	0.587785i
$201$	0.809017	+	2.48990i	0.809017	+	2.48990i
$202$	0.118034	−	0.363271i	0.118034	−	0.363271i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	0.118034	+	0.363271i	0.118034	+	0.363271i
$207$		0			0
$208$		0			0
$209$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$210$		0			0
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$	−0.381966	−	1.17557i	−0.381966	−	1.17557i
$213$		0			0
$214$	0.809017	+	0.587785i	0.809017	+	0.587785i
$215$		0			0
$216$	0.309017	−	0.951057i	0.309017	−	0.951057i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$221$		0			0
$222$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$223$	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
$225$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$226$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$227$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$227$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$228$	0.309017	+	0.951057i	0.309017	+	0.951057i
$229$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$229$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$233$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$234$	0.190983	+	0.587785i	0.190983	+	0.587785i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$239$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	0.190983	+	0.587785i	0.190983	+	0.587785i
$243$	1.00000			1.00000
$244$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$245$	0.309017	+	0.951057i	0.309017	+	0.951057i
$246$		0			0
$247$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$248$		0			0
$249$		0			0
$250$	0.190983	+	0.587785i	0.190983	+	0.587785i
$251$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$251$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$252$		0			0
$253$		0			0
$254$	1.23607			1.23607
$255$		0			0
$256$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$257$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$257$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$258$		0			0
$259$		0			0
$260$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$261$		0			0
$262$	0.809017	−	0.587785i	0.809017	−	0.587785i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	0.500000	−	1.53884i	0.500000	−	1.53884i
$265$	2.00000			2.00000
$266$		0			0
$267$		0			0
$268$	0.309017	−	0.951057i	0.309017	−	0.951057i
$269$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$269$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$270$	0.500000	+	0.363271i	0.500000	+	0.363271i
$271$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$271$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$276$		0			0
$277$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$277$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$278$	0.381966	+	1.17557i	0.381966	+	1.17557i
$279$		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			0
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$		0			0
$285$	−1.61803			−1.61803
$286$	0.118034	+	0.363271i	0.118034	+	0.363271i
$287$		0			0
$288$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$289$	0.309017	+	0.951057i	0.309017	+	0.951057i
$290$		0			0
$291$	0.809017	+	0.587785i	0.809017	+	0.587785i
$292$		0			0
$293$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$293$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$294$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$295$		0			0
$296$	1.61803			1.61803
$297$	−1.00000			−1.00000
$298$	1.23607			1.23607
$299$		0			0
$300$	0.309017	+	0.951057i	0.309017	+	0.951057i
$301$		0			0
$302$		0			0
$303$	0.809017	+	0.587785i	0.809017	+	0.587785i
$304$		0			0
$305$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$306$		0			0
$307$	2.00000			2.00000			1.00000			$0$
$307$	2.00000			2.00000			1.00000			$0$
$308$		0			0
$309$	−1.00000			−1.00000
$310$		0			0
$311$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$311$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$312$	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	$0.800000\pi$
$318$	−2.00000			−2.00000
$319$		0			0
$320$	0.618034			0.618034
$321$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	0.809017	+	0.587785i	0.809017	+	0.587785i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$		0			0
$333$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$334$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$335$	1.30902	+	0.951057i	1.30902	+	0.951057i
$336$		0			0
$337$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$337$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$338$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$339$	0.809017	−	0.587785i	0.809017	−	0.587785i
$340$		0			0
$341$		0			0
$342$	1.00000			1.00000
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.00000	−	0.726543i	−1.00000	−	0.726543i
$347$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$347$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$348$		0			0
$349$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$349$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$350$		0			0
$351$	−0.618034			−0.618034
$352$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$359$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$360$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$361$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$362$		0			0
$363$	−1.61803			−1.61803
$364$		0			0
$365$		0			0
$366$	0.500000	+	1.53884i	0.500000	+	1.53884i
$367$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$367$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$368$		0			0
$369$		0			0
$370$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$371$		0			0
$372$		0			0
$373$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$373$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$374$		0			0
$375$	−1.61803			−1.61803
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$379$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$380$	0.500000	+	0.363271i	0.500000	+	0.363271i
$381$	−1.00000	+	3.07768i	−1.00000	+	3.07768i
$382$	0.118034	+	0.363271i	0.118034	+	0.363271i
$383$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$383$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$384$	1.00000			1.00000
$385$		0			0
$386$	−1.00000			−1.00000
$387$		0			0
$388$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$389$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$389$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$390$	0.500000	+	0.363271i	0.500000	+	0.363271i
$391$		0			0
$392$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$393$	0.809017	+	2.48990i	0.809017	+	2.48990i
$394$		0			0
$395$		0			0
$396$	0.809017	+	0.587785i	0.809017	+	0.587785i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	0.809017	−	0.587785i	0.809017	−	0.587785i
$399$		0			0
$400$		0			0
$401$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$401$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$402$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$403$		0			0
$404$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$405$		0			0
$406$		0			0
$407$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$408$		0			0
$409$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$409$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$410$		0			0
$411$		0			0
$412$	0.309017	+	0.224514i	0.309017	+	0.224514i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$417$	−3.23607			−3.23607
$418$	0.618034			0.618034
$419$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$419$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$420$		0			0
$421$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$421$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$422$		0			0
$423$		0			0
$424$	1.61803	+	1.17557i	1.61803	+	1.17557i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.00000			1.00000
$429$	−1.00000			−1.00000
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$		0			0
$433$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$433$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$441$	1.61803			1.61803
$442$		0			0
$443$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$443$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$444$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$445$		0			0
$446$	−1.00000	−	0.726543i	−1.00000	−	0.726543i
$447$	−1.00000	+	3.07768i	−1.00000	+	3.07768i
$448$		0			0
$449$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$449$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$450$	1.00000			1.00000
$451$		0			0
$452$	−0.381966			−0.381966
$453$		0			0
$454$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$455$		0			0
$456$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$457$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$457$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$458$	0.381966	−	1.17557i	0.381966	−	1.17557i
$459$		0			0
$460$		0			0
$461$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$461$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$467$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$468$	0.500000	+	0.363271i	0.500000	+	0.363271i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$476$		0			0
$477$	1.00000	−	3.07768i	1.00000	−	3.07768i
$478$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$479$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$479$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$480$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$481$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$482$		0			0
$483$		0			0
$484$	0.500000	+	0.363271i	0.500000	+	0.363271i
$485$	0.618034			0.618034
$486$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$487$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$487$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$488$	0.500000	−	1.53884i	0.500000	−	1.53884i
$489$		0			0
$490$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$491$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$491$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$492$		0			0
$493$		0			0
$494$	0.381966			0.381966
$495$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$499$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$500$	0.500000	+	0.363271i	0.500000	+	0.363271i
$501$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$502$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$503$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$503$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$504$		0			0
$505$	0.618034			0.618034
$506$		0			0
$507$	1.00000			1.00000
$508$	1.00000	−	0.726543i	1.00000	−	0.726543i
$509$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$509$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$514$	0.118034	+	0.363271i	0.118034	+	0.363271i
$515$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	2.61803	−	1.90211i	2.61803	−	1.90211i
$520$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$		0			0
$523$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$523$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$524$	0.309017	−	0.951057i	0.309017	−	0.951057i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	1.00000			1.00000
$530$	−1.00000	+	0.726543i	−1.00000	+	0.726543i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$536$	0.500000	+	1.53884i	0.500000	+	1.53884i
$537$		0			0
$538$		0			0
$539$	1.00000			1.00000
$540$	0.618034			0.618034
$541$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$541$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$542$	0.118034	+	0.363271i	0.118034	+	0.363271i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$547$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$548$		0			0
$549$	−2.61803			−2.61803
$550$	0.618034			0.618034
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$556$	1.00000	+	0.726543i	1.00000	+	0.726543i
$557$		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
$563$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$563$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$564$		0			0
$565$	0.190983	−	0.587785i	0.190983	−	0.587785i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$569$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$570$	0.809017	−	0.587785i	0.809017	−	0.587785i
$571$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$571$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$572$	0.309017	+	0.224514i	0.309017	+	0.224514i
$573$	−1.00000			−1.00000
$574$		0			0
$575$		0			0
$576$	0.309017	−	0.951057i	0.309017	−	0.951057i
$577$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$577$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$578$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$579$	0.809017	−	2.48990i	0.809017	−	2.48990i
$580$		0			0
$581$		0			0
$582$	−0.618034			−0.618034
$583$	0.618034	−	1.90211i	0.618034	−	1.90211i
$584$		0			0
$585$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$586$	0.118034	+	0.363271i	0.118034	+	0.363271i
$587$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$587$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$588$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	0.500000	−	0.363271i	0.500000	−	0.363271i
$595$		0			0
$596$	1.00000	−	0.726543i	1.00000	−	0.726543i
$597$	0.809017	+	2.48990i	0.809017	+	2.48990i
$598$		0			0
$599$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$599$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$600$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$601$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$601$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$602$		0			0
$603$	2.11803	−	1.53884i	2.11803	−	1.53884i
$604$		0			0
$605$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$606$	−0.618034			−0.618034
$607$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$607$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$608$	0.309017	+	0.951057i	0.309017	+	0.951057i
$609$		0			0
$610$	0.809017	+	0.587785i	0.809017	+	0.587785i
$611$		0			0
$612$		0			0
$613$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$613$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$614$	−1.00000	+	0.726543i	−1.00000	+	0.726543i
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$	0.500000	−	0.363271i	0.500000	−	0.363271i
$619$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$619$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$620$		0			0
$621$		0			0
$622$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$623$		0			0
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$626$		0			0
$627$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$631$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$632$		0			0
$633$		0			0
$634$	0.381966	−	1.17557i	0.381966	−	1.17557i
$635$	0.618034	+	1.90211i	0.618034	+	1.90211i
$636$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$637$	0.618034			0.618034
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.363271i	0.500000	−	0.363271i
$641$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$641$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$642$	0.500000	−	1.53884i	0.500000	−	1.53884i
$643$		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			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$		0			0
$649$		0			0
$650$	0.381966			0.381966
$651$		0			0
$652$		0			0
$653$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$653$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$654$		0			0
$655$	1.30902	+	0.951057i	1.30902	+	0.951057i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$	1.00000			1.00000
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.30902	+	0.951057i	1.30902	+	0.951057i
$667$		0			0
$668$	0.309017	+	0.951057i	0.309017	+	0.951057i
$669$	2.61803	−	1.90211i	2.61803	−	1.90211i
$670$	−1.00000			−1.00000
$671$	−1.61803			−1.61803
$672$		0			0
$673$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$673$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$674$	0.381966	+	1.17557i	0.381966	+	1.17557i
$675$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$676$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$677$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$677$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$678$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$679$		0			0
$680$		0			0
$681$	2.61803			2.61803
$682$		0			0
$683$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$683$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$684$	0.809017	−	0.587785i	0.809017	−	0.587785i
$685$		0			0
$686$		0			0
$687$	2.61803	+	1.90211i	2.61803	+	1.90211i
$688$		0			0
$689$	0.381966	−	1.17557i	0.381966	−	1.17557i
$690$		0			0
$691$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$691$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$692$	−1.23607			−1.23607
$693$		0			0
$694$		0			0
$695$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$696$		0			0
$697$		0			0
$698$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$699$		0			0
$700$		0			0
$701$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$701$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$702$	0.309017	−	0.224514i	0.309017	−	0.224514i
$703$	−1.61803			−1.61803
$704$	0.190983	−	0.587785i	0.190983	−	0.587785i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$709$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$716$		0			0
$717$	0.809017	−	0.587785i	0.809017	−	0.587785i
$718$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$719$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$719$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$720$		0			0
$721$		0			0
$722$	0.190983	−	0.587785i	0.190983	−	0.587785i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.809017	−	0.587785i	0.809017	−	0.587785i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$730$		0			0
$731$		0			0
$732$	1.30902	+	0.951057i	1.30902	+	0.951057i
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$	1.30902	−	0.951057i	1.30902	−	0.951057i
$736$		0			0
$737$	1.30902	−	0.951057i	1.30902	−	0.951057i
$738$		0			0
$739$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$739$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$740$	0.309017	+	0.951057i	0.309017	+	0.951057i
$741$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$742$		0			0
$743$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$743$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$744$		0			0
$745$	0.618034	+	1.90211i	0.618034	+	1.90211i
$746$	0.809017	−	0.587785i	0.809017	−	0.587785i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.809017	−	0.587785i	0.809017	−	0.587785i
$751$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$751$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$752$		0			0
$753$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$754$		0			0
$755$		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
$760$	−1.00000			−1.00000
$761$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$761$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$762$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$763$		0			0
$764$	0.309017	+	0.224514i	0.309017	+	0.224514i
$765$		0			0
$766$	0.381966	−	1.17557i	0.381966	−	1.17557i
$767$		0			0
$768$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$769$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$769$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$770$		0			0
$771$	−1.00000			−1.00000
$772$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$773$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$773$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$774$		0			0
$775$		0			0
$776$	0.500000	+	0.363271i	0.500000	+	0.363271i
$777$		0			0
$778$	0.118034	+	0.363271i	0.118034	+	0.363271i
$779$		0			0
$780$	0.618034			0.618034
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$787$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$787$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.61803			−1.61803
$793$	−1.00000			−1.00000
$794$		0			0
$795$	−1.00000	−	3.07768i	−1.00000	−	3.07768i
$796$	0.309017	−	0.951057i	0.309017	−	0.951057i
$797$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$797$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$798$		0			0
$799$		0			0
$800$	0.309017	+	0.951057i	0.309017	+	0.951057i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−1.61803			−1.61803
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.500000	+	0.363271i	0.500000	+	0.363271i
$809$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$809$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$810$		0			0
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$		0			0
$813$	−1.00000			−1.00000
$814$	0.809017	+	0.587785i	0.809017	+	0.587785i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$821$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$822$		0			0
$823$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$823$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$824$	−0.618034			−0.618034
$825$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$826$		0			0
$827$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$827$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$829$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$830$		0			0
$831$		0			0
$832$	0.118034	−	0.363271i	0.118034	−	0.363271i
$833$		0			0
$834$	1.61803	−	1.17557i	1.61803	−	1.17557i
$835$	−1.61803			−1.61803
$836$	0.500000	−	0.363271i	0.500000	−	0.363271i
$837$		0			0
$838$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$		0			0
$841$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.500000	−	0.363271i	0.500000	−	0.363271i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$853$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$854$		0			0
$855$	0.500000	+	1.53884i	0.500000	+	1.53884i
$856$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$857$	2.00000			2.00000			1.00000			$0$
$857$	2.00000			2.00000			1.00000			$0$
$858$	0.500000	−	0.363271i	0.500000	−	0.363271i
$859$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$859$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$863$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$864$	0.809017	+	0.587785i	0.809017	+	0.587785i
$865$	0.618034	−	1.90211i	0.618034	−	1.90211i
$866$	0.118034	+	0.363271i	0.118034	+	0.363271i
$867$	1.30902	−	0.951057i	1.30902	−	0.951057i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	0.809017	−	0.587785i	0.809017	−	0.587785i
$872$		0			0
$873$	0.309017	−	0.951057i	0.309017	−	0.951057i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$877$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$878$		0			0
$879$	−1.00000			−1.00000
$880$		0			0
$881$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$881$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$882$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$887$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$888$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−1.23607			−1.23607
$893$		0			0
$894$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.809017	−	0.587785i	0.809017	−	0.587785i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.500000	−	0.363271i	0.500000	−	0.363271i
$905$		0			0
$906$		0			0
$907$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$907$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$908$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$909$	0.309017	−	0.951057i	0.309017	−	0.951057i
$910$		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
$915$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$916$	−0.381966	−	1.17557i	−0.381966	−	1.17557i
$917$		0			0
$918$		0			0
$919$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$919$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$920$		0			0
$921$	−1.00000	−	3.07768i	−1.00000	−	3.07768i
$922$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$923$		0			0
$924$		0			0
$925$	−1.61803			−1.61803
$926$		0			0
$927$	0.309017	+	0.951057i	0.309017	+	0.951057i
$928$		0			0
$929$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$929$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$	0.309017	−	0.951057i	0.309017	−	0.951057i
$932$		0			0
$933$	0.809017	−	0.587785i	0.809017	−	0.587785i
$934$		0			0
$935$		0			0
$936$	−1.00000			−1.00000
$937$		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			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$		0			0
$950$	0.190983	−	0.587785i	0.190983	−	0.587785i
$951$	2.61803	+	1.90211i	2.61803	+	1.90211i
$952$		0			0
$953$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$953$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$954$	0.618034	+	1.90211i	0.618034	+	1.90211i
$955$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$956$	−0.381966			−0.381966
$957$		0			0
$958$	0.381966			0.381966
$959$		0			0
$960$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$961$	0.309017	−	0.951057i	0.309017	−	0.951057i
$962$	0.500000	+	0.363271i	0.500000	+	0.363271i
$963$	2.11803	+	1.53884i	2.11803	+	1.53884i
$964$		0			0
$965$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	−1.00000			−1.00000
$969$		0			0
$970$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$971$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$971$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$972$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$973$		0			0
$974$	−1.00000	−	0.726543i	−1.00000	−	0.726543i
$975$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$976$		0			0
$977$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$977$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$978$		0			0
$979$		0			0
$980$	−0.618034			−0.618034
$981$		0			0
$982$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$983$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$983$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.309017	−	0.224514i	0.309017	−	0.224514i
$989$		0			0
$990$	0.309017	−	0.951057i	0.309017	−	0.951057i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.30902	+	0.951057i	1.30902	+	0.951057i
$996$		0			0
$997$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$997$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$998$	0.381966	+	1.17557i	0.381966	+	1.17557i
$999$	−1.30902	+	0.951057i	−1.30902	+	0.951057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.1.w.a.949.1	yes	4
5.4	even	2		1045.1.w.d.949.1	yes	4
11.4	even	5	inner	1045.1.w.a.664.1	✓	4
19.18	odd	2		1045.1.w.d.949.1	yes	4
55.4	even	10		1045.1.w.d.664.1	yes	4
95.94	odd	2	CM	1045.1.w.a.949.1	yes	4
209.37	odd	10		1045.1.w.d.664.1	yes	4
1045.664	odd	10	inner	1045.1.w.a.664.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.1.w.a.664.1	✓	4	11.4	even	5	inner
1045.1.w.a.664.1	✓	4	1045.664	odd	10	inner
1045.1.w.a.949.1	yes	4	1.1	even	1	trivial
1045.1.w.a.949.1	yes	4	95.94	odd	2	CM
1045.1.w.d.664.1	yes	4	55.4	even	10
1045.1.w.d.664.1	yes	4	209.37	odd	10
1045.1.w.d.949.1	yes	4	5.4	even	2
1045.1.w.d.949.1	yes	4	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1045.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{8} +(-1.30902 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.309017 - 0.951057i) q^{8} +(-1.30902 + 0.951057i) q^{9} +0.618034 q^{10} +(-0.809017 + 0.587785i) q^{11} +1.00000 q^{12} +(-0.500000 + 0.363271i) q^{13} +(-0.500000 + 1.53884i) q^{15} +(0.309017 - 0.951057i) q^{18} +(0.309017 + 0.951057i) q^{19} +(0.500000 - 0.363271i) q^{20} +(0.190983 - 0.587785i) q^{22} +(-1.30902 + 0.951057i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.118034 - 0.363271i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.309017 - 0.951057i) q^{30} +1.00000 q^{32} +(1.30902 + 0.951057i) q^{33} +(-0.309017 - 0.951057i) q^{36} +(-0.500000 + 1.53884i) q^{37} +(-0.500000 - 0.363271i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-0.190983 - 0.587785i) q^{44} +1.61803 q^{45} +(-0.809017 - 0.587785i) q^{49} +(-0.500000 - 0.363271i) q^{50} +(-0.118034 - 0.363271i) q^{52} +(-1.61803 + 1.17557i) q^{53} -0.618034 q^{54} +1.00000 q^{55} +(1.30902 - 0.951057i) q^{57} +(-0.809017 - 0.587785i) q^{60} +(1.30902 + 0.951057i) q^{61} +(-0.500000 + 0.363271i) q^{64} +0.618034 q^{65} -1.00000 q^{66} -1.61803 q^{67} +(1.30902 + 0.951057i) q^{72} +(-0.309017 - 0.951057i) q^{74} +(1.30902 - 0.951057i) q^{75} -0.618034 q^{76} -0.618034 q^{78} +(0.809017 + 0.587785i) q^{88} +(-0.809017 + 0.587785i) q^{90} +(0.309017 - 0.951057i) q^{95} +(-0.500000 - 1.53884i) q^{96} +(-0.500000 + 0.363271i) q^{97} +0.618034 q^{98} +(0.500000 - 1.53884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 3 q^{4} - q^{5} + q^{6} + q^{8} - 3 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 3 * q^4 - q^5 + q^6 + q^8 - 3 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 3 q^{4} - q^{5} + q^{6} + q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 2 q^{15} - q^{18} - q^{19} + 2 q^{20} + 3 q^{22} - 3 q^{24} - q^{25} - 4 q^{26} + q^{27} + q^{30} + 4 q^{32} + 3 q^{33} + q^{36} - 2 q^{37} - 2 q^{38} + q^{39} + q^{40} - 3 q^{44} + 2 q^{45} - q^{49} - 2 q^{50} + 4 q^{52} - 2 q^{53} + 2 q^{54} + 4 q^{55} + 3 q^{57} - q^{60} + 3 q^{61} - 2 q^{64} - 2 q^{65} - 4 q^{66} - 2 q^{67} + 3 q^{72} + q^{74} + 3 q^{75} + 2 q^{76} + 2 q^{78} + q^{88} - q^{90} - q^{95} - 2 q^{96} - 2 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 3 * q^4 - q^5 + q^6 + q^8 - 3 * q^9 - 2 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 2 * q^15 - q^18 - q^19 + 2 * q^20 + 3 * q^22 - 3 * q^24 - q^25 - 4 * q^26 + q^27 + q^30 + 4 * q^32 + 3 * q^33 + q^36 - 2 * q^37 - 2 * q^38 + q^39 + q^40 - 3 * q^44 + 2 * q^45 - q^49 - 2 * q^50 + 4 * q^52 - 2 * q^53 + 2 * q^54 + 4 * q^55 + 3 * q^57 - q^60 + 3 * q^61 - 2 * q^64 - 2 * q^65 - 4 * q^66 - 2 * q^67 + 3 * q^72 + q^74 + 3 * q^75 + 2 * q^76 + 2 * q^78 + q^88 - q^90 - q^95 - 2 * q^96 - 2 * q^97 - 2 * q^98 + 2 * q^99

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