LMFDB - Embedded newform 1045.1.w.f.284.1

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{20}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{20} + \cdots)$

Embedding invariants

Embedding label			284.1
Root			$-0.453990 + 0.891007i$ of defining polynomial
Character	$\chi$	$=$	1045.284
Dual form			1045.1.w.f.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.610425 + 1.87869i) q^{2} +(-0.734572 + 0.533698i) q^{3} +(-2.34786 - 1.70582i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.554254 - 1.70582i) q^{6} +(3.03979 - 2.20854i) q^{8} +(-0.0542543 + 0.166977i) q^{9} +O(q^{10})$	\(q+(-0.610425 + 1.87869i) q^{2} +(-0.734572 + 0.533698i) q^{3} +(-2.34786 - 1.70582i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.554254 - 1.70582i) q^{6} +(3.03979 - 2.20854i) q^{8} +(-0.0542543 + 0.166977i) q^{9} +1.97538 q^{10} +(0.951057 + 0.309017i) q^{11} +2.63506 q^{12} +(-0.0966818 + 0.297556i) q^{13} +(0.734572 + 0.533698i) q^{15} +(1.39680 + 4.29892i) q^{16} +(-0.280582 - 0.203854i) q^{18} +(0.809017 - 0.587785i) q^{19} +(-0.896802 + 2.76007i) q^{20} +(-1.16110 + 1.59811i) q^{22} +(-1.05425 + 3.24466i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.500000 - 0.363271i) q^{26} +(-0.329843 - 1.01515i) q^{27} +(-1.45106 + 1.05425i) q^{30} -5.17160 q^{32} +(-0.863541 + 0.280582i) q^{33} +(0.412215 - 0.299492i) q^{36} +(1.44168 + 1.04744i) q^{37} +(0.610425 + 1.87869i) q^{38} +(-0.0877853 - 0.270175i) q^{39} +(-3.03979 - 2.20854i) q^{40} +(-1.70582 - 2.34786i) q^{44} +0.175571 q^{45} +(-3.32037 - 2.41239i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.610425 - 1.87869i) q^{50} +(0.734572 - 0.533698i) q^{52} +(-0.437016 + 1.34500i) q^{53} +2.10851 q^{54} -1.00000i q^{55} +(-0.280582 + 0.863541i) q^{57} +(-0.814279 - 2.50609i) q^{60} +(0.587785 + 1.80902i) q^{61} +(1.76007 - 5.41695i) q^{64} +0.312869 q^{65} -1.79360i q^{66} +1.78201 q^{67} +(0.203854 + 0.627399i) q^{72} +(-2.84786 + 2.06909i) q^{74} +(0.280582 - 0.863541i) q^{75} -2.90211 q^{76} +0.561163 q^{78} +(3.65688 - 2.65688i) q^{80} +(0.642040 + 0.466469i) q^{81} +(3.57349 - 1.16110i) q^{88} +(-0.107173 + 0.329843i) q^{90} +(-0.809017 - 0.587785i) q^{95} +(3.79892 - 2.76007i) q^{96} +(0.610425 - 1.87869i) q^{97} -1.97538 q^{98} +(-0.103198 + 0.142040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 4 q^{5} - 12 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 + 4 * q^5 - 12 * q^6 - 4 * q^9	$ 16 q - 4 q^{4} + 4 q^{5} - 12 q^{6} - 4 q^{9} + 4 q^{16} + 4 q^{19} + 4 q^{20} - 20 q^{24} - 4 q^{25} - 8 q^{26} - 8 q^{30} + 16 q^{36} + 8 q^{39} - 16 q^{45} - 4 q^{49} + 40 q^{54} + 4 q^{64} - 12 q^{74} - 16 q^{76} + 16 q^{80} + 4 q^{81} - 4 q^{95} + 12 q^{96} - 20 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 + 4 * q^5 - 12 * q^6 - 4 * q^9 + 4 * q^16 + 4 * q^19 + 4 * q^20 - 20 * q^24 - 4 * q^25 - 8 * q^26 - 8 * q^30 + 16 * q^36 + 8 * q^39 - 16 * q^45 - 4 * q^49 + 40 * q^54 + 4 * q^64 - 12 * q^74 - 16 * q^76 + 16 * q^80 + 4 * q^81 - 4 * q^95 + 12 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−0.610425	+	1.87869i	−0.610425	+	1.87869i	−0.156434	+	0.987688i	$0.550000\pi$
$2$	−0.610425	+	1.87869i	−0.610425	+	1.87869i	−0.453990	+	0.891007i	$0.650000\pi$
$3$	−0.734572	+	0.533698i	−0.734572	+	0.533698i	−0.891007	−	0.453990i	$-0.850000\pi$
$3$	−0.734572	+	0.533698i	−0.734572	+	0.533698i	0.156434	+	0.987688i	$0.450000\pi$
$4$	−2.34786	−	1.70582i	−2.34786	−	1.70582i
$5$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$5$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$6$	−0.554254	−	1.70582i	−0.554254	−	1.70582i
$7$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$7$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$8$	3.03979	−	2.20854i	3.03979	−	2.20854i
$9$	−0.0542543	+	0.166977i	−0.0542543	+	0.166977i
$10$	1.97538			1.97538
$11$	0.951057	+	0.309017i	0.951057	+	0.309017i
$11$	0.951057	+	0.309017i	0.951057	+	0.309017i
$12$	2.63506			2.63506
$13$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i	−0.987688	−	0.156434i	$-0.950000\pi$
$13$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i	0.891007	+	0.453990i	$0.150000\pi$
$14$		0			0
$15$	0.734572	+	0.533698i	0.734572	+	0.533698i
$16$	1.39680	+	4.29892i	1.39680	+	4.29892i
$17$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$17$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$18$	−0.280582	−	0.203854i	−0.280582	−	0.203854i
$19$	0.809017	−	0.587785i	0.809017	−	0.587785i
$19$	0.809017	−	0.587785i	0.809017	−	0.587785i
$20$	−0.896802	+	2.76007i	−0.896802	+	2.76007i
$21$		0			0
$22$	−1.16110	+	1.59811i	−1.16110	+	1.59811i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−1.05425	+	3.24466i	−1.05425	+	3.24466i
$25$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$26$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$27$	−0.329843	−	1.01515i	−0.329843	−	1.01515i
$28$		0			0
$29$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$29$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$30$	−1.45106	+	1.05425i	−1.45106	+	1.05425i
$31$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$31$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$32$	−5.17160			−5.17160
$33$	−0.863541	+	0.280582i	−0.863541	+	0.280582i
$34$		0			0
$35$		0			0
$36$	0.412215	−	0.299492i	0.412215	−	0.299492i
$37$	1.44168	+	1.04744i	1.44168	+	1.04744i	0.987688	+	0.156434i	$0.0500000\pi$
$37$	1.44168	+	1.04744i	1.44168	+	1.04744i	0.453990	+	0.891007i	$0.350000\pi$
$38$	0.610425	+	1.87869i	0.610425	+	1.87869i
$39$	−0.0877853	−	0.270175i	−0.0877853	−	0.270175i
$40$	−3.03979	−	2.20854i	−3.03979	−	2.20854i
$41$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$41$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−1.70582	−	2.34786i	−1.70582	−	2.34786i
$45$	0.175571			0.175571
$46$		0			0
$47$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$47$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$48$	−3.32037	−	2.41239i	−3.32037	−	2.41239i
$49$	0.309017	+	0.951057i	0.309017	+	0.951057i
$50$	−0.610425	−	1.87869i	−0.610425	−	1.87869i
$51$		0			0
$52$	0.734572	−	0.533698i	0.734572	−	0.533698i
$53$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	0.453990	+	0.891007i	$0.350000\pi$
$53$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	−0.891007	+	0.453990i	$0.850000\pi$
$54$	2.10851			2.10851
$55$		−	1.00000i		−	1.00000i
$56$		0			0
$57$	−0.280582	+	0.863541i	−0.280582	+	0.863541i
$58$		0			0
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$	−0.814279	−	2.50609i	−0.814279	−	2.50609i
$61$	0.587785	+	1.80902i	0.587785	+	1.80902i	0.587785	+	0.809017i	$0.300000\pi$
$61$	0.587785	+	1.80902i	0.587785	+	1.80902i			1.00000i	$0.5\pi$
$62$		0			0
$63$		0			0
$64$	1.76007	−	5.41695i	1.76007	−	5.41695i
$65$	0.312869			0.312869
$66$		−	1.79360i		−	1.79360i
$67$	1.78201			1.78201			0.891007	−	0.453990i	$-0.150000\pi$
$67$	1.78201			1.78201			0.891007	+	0.453990i	$0.150000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$71$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$72$	0.203854	+	0.627399i	0.203854	+	0.627399i
$73$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$73$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$74$	−2.84786	+	2.06909i	−2.84786	+	2.06909i
$75$	0.280582	−	0.863541i	0.280582	−	0.863541i
$76$	−2.90211			−2.90211
$77$		0			0
$78$	0.561163			0.561163
$79$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$79$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$80$	3.65688	−	2.65688i	3.65688	−	2.65688i
$81$	0.642040	+	0.466469i	0.642040	+	0.466469i
$82$		0			0
$83$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$83$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	3.57349	−	1.16110i	3.57349	−	1.16110i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−0.107173	+	0.329843i	−0.107173	+	0.329843i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$96$	3.79892	−	2.76007i	3.79892	−	2.76007i
$97$	0.610425	−	1.87869i	0.610425	−	1.87869i	0.156434	−	0.987688i	$-0.450000\pi$
$97$	0.610425	−	1.87869i	0.610425	−	1.87869i	0.453990	−	0.891007i	$-0.350000\pi$
$98$	−1.97538			−1.97538
$99$	−0.103198	+	0.142040i	−0.103198	+	0.142040i
$100$	2.90211			2.90211
$101$	0.363271	−	1.11803i	0.363271	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$101$	0.363271	−	1.11803i	0.363271	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$102$		0			0
$103$	0.253116	+	0.183900i	0.253116	+	0.183900i	0.707107	−	0.707107i	$-0.250000\pi$
$103$	0.253116	+	0.183900i	0.253116	+	0.183900i	−0.453990	+	0.891007i	$0.650000\pi$
$104$	0.363271	+	1.11803i	0.363271	+	1.11803i
$105$		0			0
$106$	−2.26007	−	1.64204i	−2.26007	−	1.64204i
$107$	−1.44168	+	1.04744i	−1.44168	+	1.04744i	−0.453990	+	0.891007i	$0.650000\pi$
$107$	−1.44168	+	1.04744i	−1.44168	+	1.04744i	−0.987688	+	0.156434i	$0.950000\pi$
$108$	−0.957243	+	2.94609i	−0.957243	+	2.94609i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	1.87869	+	0.610425i	1.87869	+	0.610425i
$111$	−1.61803			−1.61803
$112$		0			0
$113$	0.253116	−	0.183900i	0.253116	−	0.183900i	−0.453990	−	0.891007i	$-0.650000\pi$
$113$	0.253116	−	0.183900i	0.253116	−	0.183900i	0.707107	+	0.707107i	$0.250000\pi$
$114$	−1.45106	−	1.05425i	−1.45106	−	1.05425i
$115$		0			0
$116$		0			0
$117$	−0.0444398	−	0.0322874i	−0.0444398	−	0.0322874i
$118$		0			0
$119$		0			0
$120$	3.41164			3.41164
$121$	0.809017	+	0.587785i	0.809017	+	0.587785i
$122$	−3.75739			−3.75739
$123$		0			0
$124$		0			0
$125$	0.809017	+	0.587785i	0.809017	+	0.587785i
$126$		0			0
$127$	−0.437016	−	1.34500i	−0.437016	−	1.34500i	−0.891007	−	0.453990i	$-0.850000\pi$
$127$	−0.437016	−	1.34500i	−0.437016	−	1.34500i	0.453990	−	0.891007i	$-0.350000\pi$
$128$	4.91849	+	3.57349i	4.91849	+	3.57349i
$129$		0			0
$130$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$131$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$131$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$132$	2.50609	+	0.814279i	2.50609	+	0.814279i
$133$		0			0
$134$	−1.08779	+	3.34786i	−1.08779	+	3.34786i
$135$	−0.863541	+	0.627399i	−0.863541	+	0.627399i
$136$		0			0
$137$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$137$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$138$		0			0
$139$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$139$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.183900	+	0.253116i	−0.183900	+	0.253116i
$144$	−0.793604			−0.793604
$145$		0			0
$146$		0			0
$147$	−0.734572	−	0.533698i	−0.734572	−	0.533698i
$148$	−1.59811	−	4.91849i	−1.59811	−	4.91849i
$149$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$149$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$150$	1.45106	+	1.05425i	1.45106	+	1.05425i
$151$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$151$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$152$	1.16110	−	3.57349i	1.16110	−	3.57349i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.254763	+	0.784079i	−0.254763	+	0.784079i
$157$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$157$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$158$		0			0
$159$	−0.396802	−	1.22123i	−0.396802	−	1.22123i
$160$	1.59811	+	4.91849i	1.59811	+	4.91849i
$161$		0			0
$162$	−1.26827	+	0.921452i	−1.26827	+	0.921452i
$163$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$163$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$164$		0			0
$165$	0.533698	+	0.734572i	0.533698	+	0.734572i
$166$		0			0
$167$	0.280582	−	0.863541i	0.280582	−	0.863541i	−0.707107	−	0.707107i	$-0.750000\pi$
$167$	0.280582	−	0.863541i	0.280582	−	0.863541i	0.987688	−	0.156434i	$-0.0500000\pi$
$168$		0			0
$169$	0.729825	+	0.530249i	0.729825	+	0.530249i
$170$		0			0
$171$	0.0542543	+	0.166977i	0.0542543	+	0.166977i
$172$		0			0
$173$	−1.14412	+	0.831254i	−1.14412	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$173$	−1.14412	+	0.831254i	−1.14412	+	0.831254i	−0.156434	+	0.987688i	$0.550000\pi$
$174$		0			0
$175$		0			0
$176$			4.52015i			4.52015i
$177$		0			0
$178$		0			0
$179$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$179$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$180$	−0.412215	−	0.299492i	−0.412215	−	0.299492i
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$		0			0
$183$	−1.39724	−	1.01515i	−1.39724	−	1.01515i
$184$		0			0
$185$	0.550672	−	1.69480i	0.550672	−	1.69480i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	1.59811	−	1.16110i	1.59811	−	1.16110i
$191$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$191$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$192$	1.59811	+	4.91849i	1.59811	+	4.91849i
$193$	0.280582	+	0.863541i	0.280582	+	0.863541i	0.987688	+	0.156434i	$0.0500000\pi$
$193$	0.280582	+	0.863541i	0.280582	+	0.863541i	−0.707107	+	0.707107i	$0.750000\pi$
$194$	3.15688	+	2.29360i	3.15688	+	2.29360i
$195$	−0.229825	+	0.166977i	−0.229825	+	0.166977i
$196$	0.896802	−	2.76007i	0.896802	−	2.76007i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−0.203854	−	0.280582i	−0.203854	−	0.280582i
$199$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$199$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$200$	−1.16110	+	3.57349i	−1.16110	+	3.57349i
$201$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$202$	1.87869	+	1.36495i	1.87869	+	1.36495i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$207$		0			0
$208$	−1.41421			−1.41421
$209$	0.951057	−	0.309017i	0.951057	−	0.309017i
$210$		0			0
$211$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$211$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$212$	3.32037	−	2.41239i	3.32037	−	2.41239i
$213$		0			0
$214$	−1.08779	−	3.34786i	−1.08779	−	3.34786i
$215$		0			0
$216$	−3.24466	−	2.35738i	−3.24466	−	2.35738i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−1.70582	+	2.34786i	−1.70582	+	2.34786i
$221$		0			0
$222$	0.987688	−	3.03979i	0.987688	−	3.03979i
$223$	1.14412	−	0.831254i	1.14412	−	0.831254i	0.156434	−	0.987688i	$-0.450000\pi$
$223$	1.14412	−	0.831254i	1.14412	−	0.831254i	0.987688	+	0.156434i	$0.0500000\pi$
$224$		0			0
$225$	−0.0542543	−	0.166977i	−0.0542543	−	0.166977i
$226$	0.190983	+	0.587785i	0.190983	+	0.587785i
$227$	0.734572	+	0.533698i	0.734572	+	0.533698i	0.891007	−	0.453990i	$-0.150000\pi$
$227$	0.734572	+	0.533698i	0.734572	+	0.533698i	−0.156434	+	0.987688i	$0.550000\pi$
$228$	2.13181	−	1.54885i	2.13181	−	1.54885i
$229$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$229$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$233$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$234$	0.0877853	−	0.0637797i	0.0877853	−	0.0637797i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$239$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$240$	−1.26827	+	3.90333i	−1.26827	+	3.90333i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−1.59811	+	1.16110i	−1.59811	+	1.16110i
$243$	0.346818			0.346818
$244$	1.70582	−	5.24997i	1.70582	−	5.24997i
$245$	0.809017	−	0.587785i	0.809017	−	0.587785i
$246$		0			0
$247$	0.0966818	+	0.297556i	0.0966818	+	0.297556i
$248$		0			0
$249$		0			0
$250$	−1.59811	+	1.16110i	−1.59811	+	1.16110i
$251$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$251$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$252$		0			0
$253$		0			0
$254$	2.79360			2.79360
$255$		0			0
$256$	−5.10793	+	3.71113i	−5.10793	+	3.71113i
$257$	−0.253116	−	0.183900i	−0.253116	−	0.183900i	0.453990	−	0.891007i	$-0.350000\pi$
$257$	−0.253116	−	0.183900i	−0.253116	−	0.183900i	−0.707107	+	0.707107i	$0.750000\pi$
$258$		0			0
$259$		0			0
$260$	−0.734572	−	0.533698i	−0.734572	−	0.533698i
$261$		0			0
$262$	−0.377263	+	1.16110i	−0.377263	+	1.16110i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	−2.00531	+	2.76007i	−2.00531	+	2.76007i
$265$	1.41421			1.41421
$266$		0			0
$267$		0			0
$268$	−4.18391	−	3.03979i	−4.18391	−	3.03979i
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$	−0.651565	−	2.00531i	−0.651565	−	2.00531i
$271$	−0.951057	−	0.690983i	−0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$271$	−0.951057	−	0.690983i	−0.951057	−	0.690983i	−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$276$		0			0
$277$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$277$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$281$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$282$		0			0
$283$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$283$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$284$		0			0
$285$	0.907981			0.907981
$286$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$287$		0			0
$288$	0.280582	−	0.863541i	0.280582	−	0.863541i
$289$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$290$		0			0
$291$	0.554254	+	1.70582i	0.554254	+	1.70582i
$292$		0			0
$293$	−1.59811	−	1.16110i	−1.59811	−	1.16110i	−0.891007	−	0.453990i	$-0.850000\pi$
$293$	−1.59811	−	1.16110i	−1.59811	−	1.16110i	−0.707107	−	0.707107i	$-0.750000\pi$
$294$	1.45106	−	1.05425i	1.45106	−	1.05425i
$295$		0			0
$296$	6.69572			6.69572
$297$		−	1.06740i		−	1.06740i
$298$		0			0
$299$		0			0
$300$	−2.13181	+	1.54885i	−2.13181	+	1.54885i
$301$		0			0
$302$		0			0
$303$	0.329843	+	1.01515i	0.329843	+	1.01515i
$304$	3.65688	+	2.65688i	3.65688	+	2.65688i
$305$	1.53884	−	1.11803i	1.53884	−	1.11803i
$306$		0			0
$307$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$307$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$308$		0			0
$309$	−0.284079			−0.284079
$310$		0			0
$311$	−0.951057	+	0.690983i	−0.951057	+	0.690983i	−0.951057	−	0.309017i	$-0.900000\pi$
$311$	−0.951057	+	0.690983i	−0.951057	+	0.690983i			1.00000i	$0.5\pi$
$312$	−0.863541	−	0.627399i	−0.863541	−	0.627399i
$313$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$313$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.437016	−	1.34500i	0.437016	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$317$	0.437016	−	1.34500i	0.437016	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$318$	2.53654			2.53654
$319$		0			0
$320$	−5.69572			−5.69572
$321$	0.500000	−	1.53884i	0.500000	−	1.53884i
$322$		0			0
$323$		0			0
$324$	−0.711706	−	2.19041i	−0.711706	−	2.19041i
$325$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−1.70582	+	0.554254i	−1.70582	+	0.554254i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$		0			0
$333$	−0.253116	+	0.183900i	−0.253116	+	0.183900i
$334$	1.45106	+	1.05425i	1.45106	+	1.05425i
$335$	−0.550672	−	1.69480i	−0.550672	−	1.69480i
$336$		0			0
$337$	−1.14412	−	0.831254i	−1.14412	−	0.831254i	−0.156434	−	0.987688i	$-0.550000\pi$
$337$	−1.14412	−	0.831254i	−1.14412	−	0.831254i	−0.987688	+	0.156434i	$0.950000\pi$
$338$	−1.44168	+	1.04744i	−1.44168	+	1.04744i
$339$	−0.0877853	+	0.270175i	−0.0877853	+	0.270175i
$340$		0			0
$341$		0			0
$342$	−0.346818			−0.346818
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.863271	−	2.65688i	−0.863271	−	2.65688i
$347$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$347$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$348$		0			0
$349$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$349$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$350$		0			0
$351$	0.333955			0.333955
$352$	−4.91849	−	1.59811i	−4.91849	−	1.59811i
$353$		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
$359$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$359$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$360$	0.533698	−	0.387754i	0.533698	−	0.387754i
$361$	0.309017	−	0.951057i	0.309017	−	0.951057i
$362$		0			0
$363$	−0.907981			−0.907981
$364$		0			0
$365$		0			0
$366$	2.76007	−	2.00531i	2.76007	−	2.00531i
$367$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$367$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$368$		0			0
$369$		0			0
$370$	2.84786	+	2.06909i	2.84786	+	2.06909i
$371$		0			0
$372$		0			0
$373$	−1.78201			−1.78201			−0.891007	−	0.453990i	$-0.850000\pi$
$373$	−1.78201			−1.78201			−0.891007	+	0.453990i	$0.850000\pi$
$374$		0			0
$375$	−0.907981			−0.907981
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$379$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$380$	0.896802	+	2.76007i	0.896802	+	2.76007i
$381$	1.03884	+	0.754763i	1.03884	+	0.754763i
$382$	2.58580	−	1.87869i	2.58580	−	1.87869i
$383$	0.437016	−	1.34500i	0.437016	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$383$	0.437016	−	1.34500i	0.437016	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$384$	−5.52015			−5.52015
$385$		0			0
$386$	−1.79360			−1.79360
$387$		0			0
$388$	−4.63791	+	3.36964i	−4.63791	+	3.36964i
$389$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$389$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$390$	−0.173409	−	0.533698i	−0.173409	−	0.533698i
$391$		0			0
$392$	3.03979	+	2.20854i	3.03979	+	2.20854i
$393$	−0.453990	+	0.329843i	−0.453990	+	0.329843i
$394$		0			0
$395$		0			0
$396$	0.484587	−	0.157452i	0.484587	−	0.157452i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	0.377263	−	1.16110i	0.377263	−	1.16110i
$399$		0			0
$400$	−3.65688	−	2.65688i	−3.65688	−	2.65688i
$401$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$401$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$402$	−0.987688	−	3.03979i	−0.987688	−	3.03979i
$403$		0			0
$404$	−2.76007	+	2.00531i	−2.76007	+	2.00531i
$405$	0.245237	−	0.754763i	0.245237	−	0.754763i
$406$		0			0
$407$	1.04744	+	1.44168i	1.04744	+	1.44168i
$408$		0			0
$409$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$409$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$410$		0			0
$411$		0			0
$412$	−0.280582	−	0.863541i	−0.280582	−	0.863541i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.500000	−	1.53884i	0.500000	−	1.53884i
$417$		0			0
$418$			1.97538i			1.97538i
$419$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$419$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$420$		0			0
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$		0			0
$424$	1.64204	+	5.05368i	1.64204	+	5.05368i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	5.17160			5.17160
$429$		−	0.284079i		−	0.284079i
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$	3.90333	−	2.83594i	3.90333	−	2.83594i
$433$	1.59811	+	1.16110i	1.59811	+	1.16110i	0.891007	+	0.453990i	$0.150000\pi$
$433$	1.59811	+	1.16110i	1.59811	+	1.16110i	0.707107	+	0.707107i	$0.250000\pi$
$434$		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			$\pi$
$440$	−2.20854	−	3.03979i	−2.20854	−	3.03979i
$441$	−0.175571			−0.175571
$442$		0			0
$443$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$443$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$444$	3.79892	+	2.76007i	3.79892	+	2.76007i
$445$		0			0
$446$	0.863271	+	2.65688i	0.863271	+	2.65688i
$447$		0			0
$448$		0			0
$449$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$449$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$450$	0.346818			0.346818
$451$		0			0
$452$	−0.907981			−0.907981
$453$		0			0
$454$	−1.45106	+	1.05425i	−1.45106	+	1.05425i
$455$		0			0
$456$	1.05425	+	3.24466i	1.05425	+	3.24466i
$457$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$457$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$461$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$462$		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		−0.309017	−	0.951057i	$-0.600000\pi$
$467$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$468$	0.0492618	+	0.151612i	0.0492618	+	0.151612i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$476$		0			0
$477$	−0.200874	−	0.145944i	−0.200874	−	0.145944i
$478$	0.987688	+	3.03979i	0.987688	+	3.03979i
$479$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$479$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$480$	−3.79892	−	2.76007i	−3.79892	−	2.76007i
$481$	−0.451057	+	0.327712i	−0.451057	+	0.327712i
$482$		0			0
$483$		0			0
$484$	−0.896802	−	2.76007i	−0.896802	−	2.76007i
$485$	−1.97538			−1.97538
$486$	−0.211706	+	0.651565i	−0.211706	+	0.651565i
$487$	−1.14412	+	0.831254i	−1.14412	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$487$	−1.14412	+	0.831254i	−1.14412	+	0.831254i	−0.156434	+	0.987688i	$0.550000\pi$
$488$	5.78203	+	4.20089i	5.78203	+	4.20089i
$489$		0			0
$490$	0.610425	+	1.87869i	0.610425	+	1.87869i
$491$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$491$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$		0			0
$494$	−0.618034			−0.618034
$495$	0.166977	+	0.0542543i	0.166977	+	0.0542543i
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$499$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$500$	−0.896802	−	2.76007i	−0.896802	−	2.76007i
$501$	0.254763	+	0.784079i	0.254763	+	0.784079i
$502$	−0.987688	−	0.717598i	−0.987688	−	0.717598i
$503$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$503$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$504$		0			0
$505$	−1.17557			−1.17557
$506$		0			0
$507$	−0.819101			−0.819101
$508$	−1.26827	+	3.90333i	−1.26827	+	3.90333i
$509$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$509$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	−1.97538	−	6.07958i	−1.97538	−	6.07958i
$513$	−0.863541	−	0.627399i	−0.863541	−	0.627399i
$514$	0.500000	−	0.363271i	0.500000	−	0.363271i
$515$	0.0966818	−	0.297556i	0.0966818	−	0.297556i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.396802	−	1.22123i	0.396802	−	1.22123i
$520$	0.951057	−	0.690983i	0.951057	−	0.690983i
$521$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$521$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$522$		0			0
$523$	0.0966818	+	0.297556i	0.0966818	+	0.297556i	0.987688	−	0.156434i	$-0.0500000\pi$
$523$	0.0966818	+	0.297556i	0.0966818	+	0.297556i	−0.891007	+	0.453990i	$0.850000\pi$
$524$	−1.45106	−	1.05425i	−1.45106	−	1.05425i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−2.41239	−	3.32037i	−2.41239	−	3.32037i
$529$	1.00000			1.00000
$530$	−0.863271	+	2.65688i	−0.863271	+	2.65688i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.44168	+	1.04744i	1.44168	+	1.04744i
$536$	5.41695	−	3.93564i	5.41695	−	3.93564i
$537$		0			0
$538$		0			0
$539$			1.00000i			1.00000i
$540$	3.09770			3.09770
$541$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$541$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$542$	1.87869	−	1.36495i	1.87869	−	1.36495i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.734572	+	0.533698i	−0.734572	+	0.533698i	−0.891007	−	0.453990i	$-0.850000\pi$
$547$	−0.734572	+	0.533698i	−0.734572	+	0.533698i	0.156434	+	0.987688i	$0.450000\pi$
$548$		0			0
$549$	−0.333955			−0.333955
$550$		−	1.97538i		−	1.97538i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.500000	+	1.53884i	0.500000	+	1.53884i
$556$		0			0
$557$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$557$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.610425	−	1.87869i	0.610425	−	1.87869i	0.156434	−	0.987688i	$-0.450000\pi$
$563$	0.610425	−	1.87869i	0.610425	−	1.87869i	0.453990	−	0.891007i	$-0.350000\pi$
$564$		0			0
$565$	−0.253116	−	0.183900i	−0.253116	−	0.183900i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$569$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$570$	−0.554254	+	1.70582i	−0.554254	+	1.70582i
$571$	−1.17557			−1.17557			−0.587785	−	0.809017i	$-0.700000\pi$
$571$	−1.17557			−1.17557			−0.587785	+	0.809017i	$0.700000\pi$
$572$	0.863541	−	0.280582i	0.863541	−	0.280582i
$573$	1.46914			1.46914
$574$		0			0
$575$		0			0
$576$	0.809017	+	0.587785i	0.809017	+	0.587785i
$577$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$577$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$578$	−0.610425	−	1.87869i	−0.610425	−	1.87869i
$579$	−0.666977	−	0.484587i	−0.666977	−	0.484587i
$580$		0			0
$581$		0			0
$582$	−3.54304			−3.54304
$583$	−0.831254	+	1.14412i	−0.831254	+	1.14412i
$584$		0			0
$585$	−0.0169745	+	0.0522421i	−0.0169745	+	0.0522421i
$586$	3.15688	−	2.29360i	3.15688	−	2.29360i
$587$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$587$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$588$	0.814279	+	2.50609i	0.814279	+	2.50609i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−2.48912	+	7.66072i	−2.48912	+	7.66072i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	2.00531	+	0.651565i	2.00531	+	0.651565i
$595$		0			0
$596$		0			0
$597$	0.453990	−	0.329843i	0.453990	−	0.329843i
$598$		0			0
$599$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$599$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$600$	−1.05425	−	3.24466i	−1.05425	−	3.24466i
$601$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$601$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$602$		0			0
$603$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i
$604$		0			0
$605$	0.309017	−	0.951057i	0.309017	−	0.951057i
$606$	−2.10851			−2.10851
$607$	−0.280582	+	0.863541i	−0.280582	+	0.863541i	0.707107	+	0.707107i	$0.250000\pi$
$607$	−0.280582	+	0.863541i	−0.280582	+	0.863541i	−0.987688	+	0.156434i	$0.950000\pi$
$608$	−4.18391	+	3.03979i	−4.18391	+	3.03979i
$609$		0			0
$610$	1.16110	+	3.57349i	1.16110	+	3.57349i
$611$		0			0
$612$		0			0
$613$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$613$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$614$	−0.863271	+	2.65688i	−0.863271	+	2.65688i
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$	0.173409	−	0.533698i	0.173409	−	0.533698i
$619$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$619$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$620$		0			0
$621$		0			0
$622$	−0.717598	−	2.20854i	−0.717598	−	2.20854i
$623$		0			0
$624$	1.03884	−	0.754763i	1.03884	−	0.754763i
$625$	0.309017	−	0.951057i	0.309017	−	0.951057i
$626$		0			0
$627$	−0.533698	+	0.734572i	−0.533698	+	0.734572i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.951057	−	0.690983i	−0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$631$	−0.951057	−	0.690983i	−0.951057	−	0.690983i	−0.951057	+	0.309017i	$0.900000\pi$
$632$		0			0
$633$		0			0
$634$	2.26007	+	1.64204i	2.26007	+	1.64204i
$635$	−1.14412	+	0.831254i	−1.14412	+	0.831254i
$636$	−1.15156	+	3.54415i	−1.15156	+	3.54415i
$637$	−0.312869			−0.312869
$638$		0			0
$639$		0			0
$640$	1.87869	−	5.78203i	1.87869	−	5.78203i
$641$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$641$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$642$	2.58580	+	1.87869i	2.58580	+	1.87869i
$643$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$643$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$	2.98188			2.98188
$649$		0			0
$650$	0.618034			0.618034
$651$		0			0
$652$		0			0
$653$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$653$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$654$		0			0
$655$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		−	2.63506i		−	2.63506i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$667$		0			0
$668$	−2.13181	+	1.54885i	−2.13181	+	1.54885i
$669$	−0.396802	+	1.22123i	−0.396802	+	1.22123i
$670$	3.52015			3.52015
$671$			1.90211i			1.90211i
$672$		0			0
$673$	0.550672	−	1.69480i	0.550672	−	1.69480i	−0.156434	−	0.987688i	$-0.550000\pi$
$673$	0.550672	−	1.69480i	0.550672	−	1.69480i	0.707107	−	0.707107i	$-0.250000\pi$
$674$	2.26007	−	1.64204i	2.26007	−	1.64204i
$675$	0.863541	+	0.627399i	0.863541	+	0.627399i
$676$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$677$	0.280582	+	0.863541i	0.280582	+	0.863541i	0.987688	+	0.156434i	$0.0500000\pi$
$677$	0.280582	+	0.863541i	0.280582	+	0.863541i	−0.707107	+	0.707107i	$0.750000\pi$
$678$	−0.453990	−	0.329843i	−0.453990	−	0.329843i
$679$		0			0
$680$		0			0
$681$	−0.824429			−0.824429
$682$		0			0
$683$	1.97538			1.97538			0.987688	−	0.156434i	$-0.0500000\pi$
$683$	1.97538			1.97538			0.987688	+	0.156434i	$0.0500000\pi$
$684$	0.157452	−	0.484587i	0.157452	−	0.484587i
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.357960	−	0.260074i	−0.357960	−	0.260074i
$690$		0			0
$691$	0.363271	−	1.11803i	0.363271	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$691$	0.363271	−	1.11803i	0.363271	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$692$	4.10421			4.10421
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.987688	−	3.03979i	−0.987688	−	3.03979i
$699$		0			0
$700$		0			0
$701$	0.951057	−	0.690983i	0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$701$	0.951057	−	0.690983i	0.951057	−	0.690983i	0.951057	+	0.309017i	$0.100000\pi$
$702$	−0.203854	+	0.627399i	−0.203854	+	0.627399i
$703$	1.78201			1.78201
$704$	3.34786	−	4.60793i	3.34786	−	4.60793i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$709$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	0.297556	+	0.0966818i	0.297556	+	0.0966818i
$716$		0			0
$717$	−0.453990	+	1.39724i	−0.453990	+	1.39724i
$718$	3.03979	−	2.20854i	3.03979	−	2.20854i
$719$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$719$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$720$	0.245237	+	0.754763i	0.245237	+	0.754763i
$721$		0			0
$722$	1.59811	+	1.16110i	1.59811	+	1.16110i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.554254	−	1.70582i	0.554254	−	1.70582i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−0.896802	+	0.651565i	−0.896802	+	0.651565i
$730$		0			0
$731$		0			0
$732$	1.54885	+	4.76687i	1.54885	+	4.76687i
$733$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$733$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$734$		0			0
$735$	−0.280582	+	0.863541i	−0.280582	+	0.863541i
$736$		0			0
$737$	1.69480	+	0.550672i	1.69480	+	0.550672i
$738$		0			0
$739$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$739$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$740$	−4.18391	+	3.03979i	−4.18391	+	3.03979i
$741$	−0.229825	−	0.166977i	−0.229825	−	0.166977i
$742$		0			0
$743$	0.610425	+	1.87869i	0.610425	+	1.87869i	0.453990	+	0.891007i	$0.350000\pi$
$743$	0.610425	+	1.87869i	0.610425	+	1.87869i	0.156434	+	0.987688i	$0.450000\pi$
$744$		0			0
$745$		0			0
$746$	1.08779	−	3.34786i	1.08779	−	3.34786i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.554254	−	1.70582i	0.554254	−	1.70582i
$751$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$751$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$752$		0			0
$753$	−0.173409	−	0.533698i	−0.173409	−	0.533698i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$757$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$758$		0			0
$759$		0			0
$760$	−3.75739			−3.75739
$761$	0.587785	−	1.80902i	0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$761$	0.587785	−	1.80902i	0.587785	−	1.80902i	0.587785	−	0.809017i	$-0.300000\pi$
$762$	−2.05210	+	1.49094i	−2.05210	+	1.49094i
$763$		0			0
$764$	1.45106	+	4.46589i	1.45106	+	4.46589i
$765$		0			0
$766$	2.26007	+	1.64204i	2.26007	+	1.64204i
$767$		0			0
$768$	1.77152	−	5.45218i	1.77152	−	5.45218i
$769$	−1.90211			−1.90211			−0.951057	−	0.309017i	$-0.900000\pi$
$769$	−1.90211			−1.90211			−0.951057	+	0.309017i	$0.900000\pi$
$770$		0			0
$771$	0.284079			0.284079
$772$	0.814279	−	2.50609i	0.814279	−	2.50609i
$773$	0.734572	−	0.533698i	0.734572	−	0.533698i	−0.156434	−	0.987688i	$-0.550000\pi$
$773$	0.734572	−	0.533698i	0.734572	−	0.533698i	0.891007	+	0.453990i	$0.150000\pi$
$774$		0			0
$775$		0			0
$776$	−2.29360	−	7.05899i	−2.29360	−	7.05899i
$777$		0			0
$778$	−2.58580	+	1.87869i	−2.58580	+	1.87869i
$779$		0			0
$780$	0.824429			0.824429
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−3.65688	+	2.65688i	−3.65688	+	2.65688i
$785$		0			0
$786$	−0.342548	−	1.05425i	−0.342548	−	1.05425i
$787$	−0.550672	−	1.69480i	−0.550672	−	1.69480i	−0.707107	−	0.707107i	$-0.750000\pi$
$787$	−0.550672	−	1.69480i	−0.550672	−	1.69480i	0.156434	−	0.987688i	$-0.450000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$			0.659687i			0.659687i
$793$	−0.595112			−0.595112
$794$		0			0
$795$	−1.03884	+	0.754763i	−1.03884	+	0.754763i
$796$	1.45106	+	1.05425i	1.45106	+	1.05425i
$797$	0.610425	+	1.87869i	0.610425	+	1.87869i	0.453990	+	0.891007i	$0.350000\pi$
$797$	0.610425	+	1.87869i	0.610425	+	1.87869i	0.156434	+	0.987688i	$0.450000\pi$
$798$		0			0
$799$		0			0
$800$	4.18391	−	3.03979i	4.18391	−	3.03979i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	4.69572			4.69572
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.36495	−	4.20089i	−1.36495	−	4.20089i
$809$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$809$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$810$	1.26827	+	0.921452i	1.26827	+	0.921452i
$811$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$811$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$	1.06740			1.06740
$814$	−3.34786	+	1.08779i	−3.34786	+	1.08779i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$821$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$822$		0			0
$823$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$823$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$824$	1.17557			1.17557
$825$	0.533698	−	0.734572i	0.533698	−	0.734572i
$826$		0			0
$827$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	0.453990	+	0.891007i	$0.350000\pi$
$827$	−0.437016	+	1.34500i	−0.437016	+	1.34500i	−0.891007	+	0.453990i	$0.850000\pi$
$828$		0			0
$829$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$829$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$830$		0			0
$831$		0			0
$832$	1.44168	+	1.04744i	1.44168	+	1.04744i
$833$		0			0
$834$		0			0
$835$	−0.907981			−0.907981
$836$	−2.76007	−	0.896802i	−2.76007	−	0.896802i
$837$		0			0
$838$	0.987688	−	3.03979i	0.987688	−	3.03979i
$839$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$839$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$840$		0			0
$841$	0.309017	+	0.951057i	0.309017	+	0.951057i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.278768	−	0.857960i	0.278768	−	0.857960i
$846$		0			0
$847$		0			0
$848$	−6.39245			−6.39245
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$853$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$854$		0			0
$855$	0.142040	−	0.103198i	0.142040	−	0.103198i
$856$	−2.06909	+	6.36801i	−2.06909	+	6.36801i
$857$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$857$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$858$	0.533698	+	0.173409i	0.533698	+	0.173409i
$859$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$859$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.0966818	+	0.297556i	0.0966818	+	0.297556i	0.987688	−	0.156434i	$-0.0500000\pi$
$863$	0.0966818	+	0.297556i	0.0966818	+	0.297556i	−0.891007	+	0.453990i	$0.850000\pi$
$864$	1.70582	+	5.24997i	1.70582	+	5.24997i
$865$	1.14412	+	0.831254i	1.14412	+	0.831254i
$866$	−3.15688	+	2.29360i	−3.15688	+	2.29360i
$867$	0.280582	−	0.863541i	0.280582	−	0.863541i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−0.172288	+	0.530249i	−0.172288	+	0.530249i
$872$		0			0
$873$	0.280582	+	0.203854i	0.280582	+	0.203854i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	−0.707107	−	0.707107i	$-0.750000\pi$
$877$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	0.453990	+	0.891007i	$0.350000\pi$
$878$		0			0
$879$	1.79360			1.79360
$880$	4.29892	−	1.39680i	4.29892	−	1.39680i
$881$	1.90211			1.90211			0.951057	−	0.309017i	$-0.100000\pi$
$881$	1.90211			1.90211			0.951057	+	0.309017i	$0.100000\pi$
$882$	0.107173	−	0.329843i	0.107173	−	0.329843i
$883$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$883$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.253116	+	0.183900i	0.253116	+	0.183900i	0.707107	−	0.707107i	$-0.250000\pi$
$887$	0.253116	+	0.183900i	0.253116	+	0.183900i	−0.453990	+	0.891007i	$0.650000\pi$
$888$	−4.91849	+	3.57349i	−4.91849	+	3.57349i
$889$		0			0
$890$		0			0
$891$	0.466469	+	0.642040i	0.466469	+	0.642040i
$892$	−4.10421			−4.10421
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.157452	+	0.484587i	−0.157452	+	0.484587i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.363271	−	1.11803i	0.363271	−	1.11803i
$905$		0			0
$906$		0			0
$907$	0.437016	+	1.34500i	0.437016	+	1.34500i	0.891007	+	0.453990i	$0.150000\pi$
$907$	0.437016	+	1.34500i	0.437016	+	1.34500i	−0.453990	+	0.891007i	$0.650000\pi$
$908$	−0.814279	−	2.50609i	−0.814279	−	2.50609i
$909$	0.166977	+	0.121316i	0.166977	+	0.121316i
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$	−4.10421			−4.10421
$913$		0			0
$914$		0			0
$915$	−0.533698	+	1.64255i	−0.533698	+	1.64255i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$919$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$920$		0			0
$921$	−1.03884	+	0.754763i	−1.03884	+	0.754763i
$922$	0.987688	−	3.03979i	0.987688	−	3.03979i
$923$		0			0
$924$		0			0
$925$	−1.78201			−1.78201
$926$		0			0
$927$	−0.0444398	+	0.0322874i	−0.0444398	+	0.0322874i
$928$		0			0
$929$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$929$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$930$		0			0
$931$	0.809017	+	0.587785i	0.809017	+	0.587785i
$932$		0			0
$933$	0.329843	−	1.01515i	0.329843	−	1.01515i
$934$		0			0
$935$		0			0
$936$	−0.206396			−0.206396
$937$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$937$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$941$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$942$		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
$950$	−1.59811	−	1.16110i	−1.59811	−	1.16110i
$951$	0.396802	+	1.22123i	0.396802	+	1.22123i
$952$		0			0
$953$	−0.734572	−	0.533698i	−0.734572	−	0.533698i	0.156434	−	0.987688i	$-0.450000\pi$
$953$	−0.734572	−	0.533698i	−0.734572	−	0.533698i	−0.891007	+	0.453990i	$0.850000\pi$
$954$	0.396802	−	0.288294i	0.396802	−	0.288294i
$955$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$956$	−4.69572			−4.69572
$957$		0			0
$958$	2.32219			2.32219
$959$		0			0
$960$	4.18391	−	3.03979i	4.18391	−	3.03979i
$961$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$962$	−0.340334	−	1.04744i	−0.340334	−	1.04744i
$963$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i
$964$		0			0
$965$	0.734572	−	0.533698i	0.734572	−	0.533698i
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	3.75739			3.75739
$969$		0			0
$970$	1.20582	−	3.71113i	1.20582	−	3.71113i
$971$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$971$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$972$	−0.814279	−	0.591609i	−0.814279	−	0.591609i
$973$		0			0
$974$	−0.863271	−	2.65688i	−0.863271	−	2.65688i
$975$	0.229825	+	0.166977i	0.229825	+	0.166977i
$976$	−6.95579	+	5.05368i	−6.95579	+	5.05368i
$977$	−0.610425	+	1.87869i	−0.610425	+	1.87869i	−0.156434	+	0.987688i	$0.550000\pi$
$977$	−0.610425	+	1.87869i	−0.610425	+	1.87869i	−0.453990	+	0.891007i	$0.650000\pi$
$978$		0			0
$979$		0			0
$980$	−2.90211			−2.90211
$981$		0			0
$982$	−0.987688	+	0.717598i	−0.987688	+	0.717598i
$983$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.987688	−	0.156434i	$-0.950000\pi$
$983$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.453990	−	0.891007i	$-0.650000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.280582	−	0.863541i	0.280582	−	0.863541i
$989$		0			0
$990$	−0.203854	+	0.280582i	−0.203854	+	0.280582i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.190983	+	0.587785i	0.190983	+	0.587785i
$996$		0			0
$997$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$997$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$998$		0			0
$999$	0.587785	−	1.80902i	0.587785	−	1.80902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.1.w.f.284.1	✓	16
5.4	even	2	inner	1045.1.w.f.284.4	yes	16
11.5	even	5	inner	1045.1.w.f.379.1	yes	16
19.18	odd	2	inner	1045.1.w.f.284.4	yes	16
55.49	even	10	inner	1045.1.w.f.379.4	yes	16
95.94	odd	2	CM	1045.1.w.f.284.1	✓	16
209.170	odd	10	inner	1045.1.w.f.379.4	yes	16
1045.379	odd	10	inner	1045.1.w.f.379.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.1.w.f.284.1	✓	16	1.1	even	1	trivial
1045.1.w.f.284.1	✓	16	95.94	odd	2	CM
1045.1.w.f.284.4	yes	16	5.4	even	2	inner
1045.1.w.f.284.4	yes	16	19.18	odd	2	inner
1045.1.w.f.379.1	yes	16	11.5	even	5	inner
1045.1.w.f.379.1	yes	16	1045.379	odd	10	inner
1045.1.w.f.379.4	yes	16	55.49	even	10	inner
1045.1.w.f.379.4	yes	16	209.170	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.610425 + 1.87869i) q^{2} +(-0.734572 + 0.533698i) q^{3} +(-2.34786 - 1.70582i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.554254 - 1.70582i) q^{6} +(3.03979 - 2.20854i) q^{8} +(-0.0542543 + 0.166977i) q^{9} +O(q^{10})\)	\(q+(-0.610425 + 1.87869i) q^{2} +(-0.734572 + 0.533698i) q^{3} +(-2.34786 - 1.70582i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.554254 - 1.70582i) q^{6} +(3.03979 - 2.20854i) q^{8} +(-0.0542543 + 0.166977i) q^{9} +1.97538 q^{10} +(0.951057 + 0.309017i) q^{11} +2.63506 q^{12} +(-0.0966818 + 0.297556i) q^{13} +(0.734572 + 0.533698i) q^{15} +(1.39680 + 4.29892i) q^{16} +(-0.280582 - 0.203854i) q^{18} +(0.809017 - 0.587785i) q^{19} +(-0.896802 + 2.76007i) q^{20} +(-1.16110 + 1.59811i) q^{22} +(-1.05425 + 3.24466i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.500000 - 0.363271i) q^{26} +(-0.329843 - 1.01515i) q^{27} +(-1.45106 + 1.05425i) q^{30} -5.17160 q^{32} +(-0.863541 + 0.280582i) q^{33} +(0.412215 - 0.299492i) q^{36} +(1.44168 + 1.04744i) q^{37} +(0.610425 + 1.87869i) q^{38} +(-0.0877853 - 0.270175i) q^{39} +(-3.03979 - 2.20854i) q^{40} +(-1.70582 - 2.34786i) q^{44} +0.175571 q^{45} +(-3.32037 - 2.41239i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.610425 - 1.87869i) q^{50} +(0.734572 - 0.533698i) q^{52} +(-0.437016 + 1.34500i) q^{53} +2.10851 q^{54} -1.00000i q^{55} +(-0.280582 + 0.863541i) q^{57} +(-0.814279 - 2.50609i) q^{60} +(0.587785 + 1.80902i) q^{61} +(1.76007 - 5.41695i) q^{64} +0.312869 q^{65} -1.79360i q^{66} +1.78201 q^{67} +(0.203854 + 0.627399i) q^{72} +(-2.84786 + 2.06909i) q^{74} +(0.280582 - 0.863541i) q^{75} -2.90211 q^{76} +0.561163 q^{78} +(3.65688 - 2.65688i) q^{80} +(0.642040 + 0.466469i) q^{81} +(3.57349 - 1.16110i) q^{88} +(-0.107173 + 0.329843i) q^{90} +(-0.809017 - 0.587785i) q^{95} +(3.79892 - 2.76007i) q^{96} +(0.610425 - 1.87869i) q^{97} -1.97538 q^{98} +(-0.103198 + 0.142040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 4 q^{5} - 12 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 + 4 * q^5 - 12 * q^6 - 4 * q^9	\( 16 q - 4 q^{4} + 4 q^{5} - 12 q^{6} - 4 q^{9} + 4 q^{16} + 4 q^{19} + 4 q^{20} - 20 q^{24} - 4 q^{25} - 8 q^{26} - 8 q^{30} + 16 q^{36} + 8 q^{39} - 16 q^{45} - 4 q^{49} + 40 q^{54} + 4 q^{64} - 12 q^{74} - 16 q^{76} + 16 q^{80} + 4 q^{81} - 4 q^{95} + 12 q^{96} - 20 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 + 4 * q^5 - 12 * q^6 - 4 * q^9 + 4 * q^16 + 4 * q^19 + 4 * q^20 - 20 * q^24 - 4 * q^25 - 8 * q^26 - 8 * q^30 + 16 * q^36 + 8 * q^39 - 16 * q^45 - 4 * q^49 + 40 * q^54 + 4 * q^64 - 12 * q^74 - 16 * q^76 + 16 * q^80 + 4 * q^81 - 4 * q^95 + 12 * q^96 - 20 * q^99

Introduction

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