LMFDB - Embedded newform 2380.1.bi.c.1427.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2380,1,Mod(1427,2380)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2380.1427"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2380, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 2, 2])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2380.bi (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.18777473007$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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:	$\Z[a_1, \ldots, a_{5}]$
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			1427.2
Root			$0.156434 - 0.987688i$ of defining polynomial
Character	$\chi$	$=$	2380.1427
Dual form			2380.1.bi.c.1903.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.34500 + 1.34500i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.156434 + 0.987688i) q^{5} +(-0.863541 - 1.69480i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.587785 - 0.809017i) q^{8} +2.61803i q^{9} +(0.156434 - 0.987688i) q^{10} +(0.297556 + 1.87869i) q^{12} +(-0.891007 + 0.453990i) q^{14} +(-1.11803 + 1.53884i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.707107 - 0.707107i) q^{17} +(0.809017 - 2.48990i) q^{18} +(-0.453990 + 0.891007i) q^{20} +1.90211 q^{21} +(0.297556 - 1.87869i) q^{24} +(-0.951057 + 0.309017i) q^{25} +(-2.17625 + 2.17625i) q^{27} +(0.987688 - 0.156434i) q^{28} +(1.53884 - 1.11803i) q^{30} +0.312869i q^{31} -1.00000i q^{32} +(0.453990 + 0.891007i) q^{34} +(0.809017 + 0.587785i) q^{35} +(-1.53884 + 2.11803i) q^{36} +(0.707107 - 0.707107i) q^{40} -1.78201 q^{41} +(-1.80902 - 0.587785i) q^{42} +(1.26007 + 1.26007i) q^{43} +(-2.58580 + 0.409551i) q^{45} +(-0.863541 + 1.69480i) q^{48} -1.00000i q^{49} +1.00000 q^{50} -1.90211i q^{51} +(1.39680 - 1.39680i) q^{53} +(2.74224 - 1.39724i) q^{54} +(-0.987688 - 0.156434i) q^{56} +(-1.80902 + 0.587785i) q^{60} +0.907981 q^{61} +(0.0966818 - 0.297556i) q^{62} +(1.85123 + 1.85123i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.221232 + 0.221232i) q^{67} +(-0.156434 - 0.987688i) q^{68} +(-0.587785 - 0.809017i) q^{70} +(2.11803 - 1.53884i) q^{72} +(1.34500 - 1.34500i) q^{73} +(-1.69480 - 0.863541i) q^{75} +(-0.891007 + 0.453990i) q^{80} -3.23607 q^{81} +(1.69480 + 0.550672i) q^{82} +(1.53884 + 1.11803i) q^{84} +(0.587785 - 0.809017i) q^{85} +(-0.809017 - 1.58779i) q^{86} +(2.58580 + 0.409551i) q^{90} +(-0.420808 + 0.420808i) q^{93} +(1.34500 - 1.34500i) q^{96} +(-0.831254 - 0.831254i) q^{97} +(-0.309017 + 0.951057i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{16} + 4 q^{18} + 4 q^{35} - 20 q^{42} - 4 q^{43} + 16 q^{50} + 4 q^{53} - 20 q^{60} + 4 q^{64} - 4 q^{67} + 16 q^{72} - 16 q^{81} - 4 q^{86} + 4 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^16 + 4 * q^18 + 4 * q^35 - 20 * q^42 - 4 * q^43 + 16 * q^50 + 4 * q^53 - 20 * q^60 + 4 * q^64 - 4 * q^67 + 16 * q^72 - 16 * q^81 - 4 * q^86 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2380\mathbb{Z}\right)^\times$.

$n$	$477$	$1191$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$2$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$3$	1.34500	+	1.34500i	1.34500	+	1.34500i	0.891007	+	0.453990i	$0.150000\pi$
$3$	1.34500	+	1.34500i	1.34500	+	1.34500i	0.453990	+	0.891007i	$0.350000\pi$
$4$	0.809017	+	0.587785i	0.809017	+	0.587785i
$5$	0.156434	+	0.987688i	0.156434	+	0.987688i
$5$	0.156434	+	0.987688i	0.156434	+	0.987688i
$6$	−0.863541	−	1.69480i	−0.863541	−	1.69480i
$7$	0.707107	−	0.707107i	0.707107	−	0.707107i
$7$	0.707107	−	0.707107i	0.707107	−	0.707107i
$8$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$9$			2.61803i			2.61803i
$10$	0.156434	−	0.987688i	0.156434	−	0.987688i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	0.297556	+	1.87869i	0.297556	+	1.87869i
$13$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$13$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$14$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$15$	−1.11803	+	1.53884i	−1.11803	+	1.53884i
$16$	0.309017	+	0.951057i	0.309017	+	0.951057i
$17$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$17$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$18$	0.809017	−	2.48990i	0.809017	−	2.48990i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$21$	1.90211			1.90211
$22$		0			0
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	0.297556	−	1.87869i	0.297556	−	1.87869i
$25$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$26$		0			0
$27$	−2.17625	+	2.17625i	−2.17625	+	2.17625i
$28$	0.987688	−	0.156434i	0.987688	−	0.156434i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	1.53884	−	1.11803i	1.53884	−	1.11803i
$31$			0.312869i			0.312869i	0.987688	+	0.156434i	$0.0500000\pi$
$31$			0.312869i			0.312869i	−0.987688	+	0.156434i	$0.950000\pi$
$32$		−	1.00000i		−	1.00000i
$33$		0			0
$34$	0.453990	+	0.891007i	0.453990	+	0.891007i
$35$	0.809017	+	0.587785i	0.809017	+	0.587785i
$36$	−1.53884	+	2.11803i	−1.53884	+	2.11803i
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$		0			0
$39$		0			0
$40$	0.707107	−	0.707107i	0.707107	−	0.707107i
$41$	−1.78201			−1.78201			−0.891007	−	0.453990i	$-0.850000\pi$
$41$	−1.78201			−1.78201			−0.891007	+	0.453990i	$0.850000\pi$
$42$	−1.80902	−	0.587785i	−1.80902	−	0.587785i
$43$	1.26007	+	1.26007i	1.26007	+	1.26007i	0.951057	+	0.309017i	$0.100000\pi$
$43$	1.26007	+	1.26007i	1.26007	+	1.26007i	0.309017	+	0.951057i	$0.400000\pi$
$44$		0			0
$45$	−2.58580	+	0.409551i	−2.58580	+	0.409551i
$46$		0			0
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$	−0.863541	+	1.69480i	−0.863541	+	1.69480i
$49$		−	1.00000i		−	1.00000i
$50$	1.00000			1.00000
$51$		−	1.90211i		−	1.90211i
$52$		0			0
$53$	1.39680	−	1.39680i	1.39680	−	1.39680i	0.587785	−	0.809017i	$-0.300000\pi$
$53$	1.39680	−	1.39680i	1.39680	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$54$	2.74224	−	1.39724i	2.74224	−	1.39724i
$55$		0			0
$56$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$57$		0			0
$58$		0			0
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$	−1.80902	+	0.587785i	−1.80902	+	0.587785i
$61$	0.907981			0.907981			0.453990	−	0.891007i	$-0.350000\pi$
$61$	0.907981			0.907981			0.453990	+	0.891007i	$0.350000\pi$
$62$	0.0966818	−	0.297556i	0.0966818	−	0.297556i
$63$	1.85123	+	1.85123i	1.85123	+	1.85123i
$64$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$65$		0			0
$66$		0			0
$67$	−0.221232	+	0.221232i	−0.221232	+	0.221232i	−0.809017	−	0.587785i	$-0.800000\pi$
$67$	−0.221232	+	0.221232i	−0.221232	+	0.221232i	0.587785	+	0.809017i	$0.300000\pi$
$68$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$69$		0			0
$70$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	2.11803	−	1.53884i	2.11803	−	1.53884i
$73$	1.34500	−	1.34500i	1.34500	−	1.34500i	0.453990	−	0.891007i	$-0.350000\pi$
$73$	1.34500	−	1.34500i	1.34500	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$74$		0			0
$75$	−1.69480	−	0.863541i	−1.69480	−	0.863541i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$81$	−3.23607			−3.23607
$82$	1.69480	+	0.550672i	1.69480	+	0.550672i
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$	1.53884	+	1.11803i	1.53884	+	1.11803i
$85$	0.587785	−	0.809017i	0.587785	−	0.809017i
$86$	−0.809017	−	1.58779i	−0.809017	−	1.58779i
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	2.58580	+	0.409551i	2.58580	+	0.409551i
$91$		0			0
$92$		0			0
$93$	−0.420808	+	0.420808i	−0.420808	+	0.420808i
$94$		0			0
$95$		0			0
$96$	1.34500	−	1.34500i	1.34500	−	1.34500i
$97$	−0.831254	−	0.831254i	−0.831254	−	0.831254i	0.156434	−	0.987688i	$-0.450000\pi$
$97$	−0.831254	−	0.831254i	−0.831254	−	0.831254i	−0.987688	+	0.156434i	$0.950000\pi$
$98$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$99$		0			0
$100$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$103$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$103$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$104$		0			0
$105$	0.297556	+	1.87869i	0.297556	+	1.87869i
$106$	−1.76007	+	0.896802i	−1.76007	+	0.896802i
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$	−3.03979	+	0.481456i	−3.03979	+	0.481456i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	0.891007	+	0.453990i	0.891007	+	0.453990i
$113$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$113$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.00000			−1.00000
$120$	1.90211			1.90211
$121$	−1.00000			−1.00000
$122$	−0.863541	−	0.280582i	−0.863541	−	0.280582i
$123$	−2.39680	−	2.39680i	−2.39680	−	2.39680i
$124$	−0.183900	+	0.253116i	−0.183900	+	0.253116i
$125$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$126$	−1.18856	−	2.33269i	−1.18856	−	2.33269i
$127$	1.39680	−	1.39680i	1.39680	−	1.39680i	0.587785	−	0.809017i	$-0.300000\pi$
$127$	1.39680	−	1.39680i	1.39680	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$128$	0.587785	−	0.809017i	0.587785	−	0.809017i
$129$			3.38959i			3.38959i
$130$		0			0
$131$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$131$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$132$		0			0
$133$		0			0
$134$	0.278768	−	0.142040i	0.278768	−	0.142040i
$135$	−2.48990	−	1.80902i	−2.48990	−	1.80902i
$136$	−0.156434	+	0.987688i	−0.156434	+	0.987688i
$137$	−0.642040	−	0.642040i	−0.642040	−	0.642040i	0.309017	−	0.951057i	$-0.400000\pi$
$137$	−0.642040	−	0.642040i	−0.642040	−	0.642040i	−0.951057	+	0.309017i	$0.900000\pi$
$138$		0			0
$139$	−1.97538			−1.97538			−0.987688	−	0.156434i	$-0.950000\pi$
$139$	−1.97538			−1.97538			−0.987688	+	0.156434i	$0.950000\pi$
$140$	0.309017	+	0.951057i	0.309017	+	0.951057i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$145$		0			0
$146$	−1.69480	+	0.863541i	−1.69480	+	0.863541i
$147$	1.34500	−	1.34500i	1.34500	−	1.34500i
$148$		0			0
$149$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$149$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$150$	1.34500	+	1.34500i	1.34500	+	1.34500i
$151$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$151$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$152$		0			0
$153$	1.85123	−	1.85123i	1.85123	−	1.85123i
$154$		0			0
$155$	−0.309017	+	0.0489435i	−0.309017	+	0.0489435i
$156$		0			0
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$	3.75739			3.75739
$160$	0.987688	−	0.156434i	0.987688	−	0.156434i
$161$		0			0
$162$	3.07768	+	1.00000i	3.07768	+	1.00000i
$163$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$163$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$164$	−1.44168	−	1.04744i	−1.44168	−	1.04744i
$165$		0			0
$166$		0			0
$167$	0.437016	−	0.437016i	0.437016	−	0.437016i	−0.453990	−	0.891007i	$-0.650000\pi$
$167$	0.437016	−	0.437016i	0.437016	−	0.437016i	0.891007	+	0.453990i	$0.150000\pi$
$168$	−1.11803	−	1.53884i	−1.11803	−	1.53884i
$169$		−	1.00000i		−	1.00000i
$170$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$171$		0			0
$172$	0.278768	+	1.76007i	0.278768	+	1.76007i
$173$	−1.34500	+	1.34500i	−1.34500	+	1.34500i	−0.453990	+	0.891007i	$0.650000\pi$
$173$	−1.34500	+	1.34500i	−1.34500	+	1.34500i	−0.891007	+	0.453990i	$0.850000\pi$
$174$		0			0
$175$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$179$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$180$	−2.33269	−	1.18856i	−2.33269	−	1.18856i
$181$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$181$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$182$		0			0
$183$	1.22123	+	1.22123i	1.22123	+	1.22123i
$184$		0			0
$185$		0			0
$186$	0.530249	−	0.270175i	0.530249	−	0.270175i
$187$		0			0
$188$		0			0
$189$			3.07768i			3.07768i
$190$		0			0
$191$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$191$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$192$	−1.69480	+	0.863541i	−1.69480	+	0.863541i
$193$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$193$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$194$	0.533698	+	1.04744i	0.533698	+	1.04744i
$195$		0			0
$196$	0.587785	−	0.809017i	0.587785	−	0.809017i
$197$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$197$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$198$		0			0
$199$	−0.907981			−0.907981			−0.453990	−	0.891007i	$-0.650000\pi$
$199$	−0.907981			−0.907981			−0.453990	+	0.891007i	$0.650000\pi$
$200$	0.809017	+	0.587785i	0.809017	+	0.587785i
$201$	−0.595112			−0.595112
$202$		0			0
$203$		0			0
$204$	1.11803	−	1.53884i	1.11803	−	1.53884i
$205$	−0.278768	−	1.76007i	−0.278768	−	1.76007i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$	0.297556	−	1.87869i	0.297556	−	1.87869i
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	1.95106	−	0.309017i	1.95106	−	0.309017i
$213$		0			0
$214$		0			0
$215$	−1.04744	+	1.44168i	−1.04744	+	1.44168i
$216$	3.03979	+	0.481456i	3.03979	+	0.481456i
$217$	0.221232	+	0.221232i	0.221232	+	0.221232i
$218$		0			0
$219$	3.61803			3.61803
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$225$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$226$		0			0
$227$	1.14412	−	1.14412i	1.14412	−	1.14412i	0.156434	−	0.987688i	$-0.450000\pi$
$227$	1.14412	−	1.14412i	1.14412	−	1.14412i	0.987688	−	0.156434i	$-0.0500000\pi$
$228$		0			0
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$233$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	0.951057	+	0.309017i	0.951057	+	0.309017i
$239$	1.90211			1.90211			0.951057	−	0.309017i	$-0.100000\pi$
$239$	1.90211			1.90211			0.951057	+	0.309017i	$0.100000\pi$
$240$	−1.80902	−	0.587785i	−1.80902	−	0.587785i
$241$	−0.312869			−0.312869			−0.156434	−	0.987688i	$-0.550000\pi$
$241$	−0.312869			−0.312869			−0.156434	+	0.987688i	$0.550000\pi$
$242$	0.951057	+	0.309017i	0.951057	+	0.309017i
$243$	−2.17625	−	2.17625i	−2.17625	−	2.17625i
$244$	0.734572	+	0.533698i	0.734572	+	0.533698i
$245$	0.987688	−	0.156434i	0.987688	−	0.156434i
$246$	1.53884	+	3.02015i	1.53884	+	3.02015i
$247$		0			0
$248$	0.253116	−	0.183900i	0.253116	−	0.183900i
$249$		0			0
$250$	0.156434	+	0.987688i	0.156434	+	0.987688i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	0.409551	+	2.58580i	0.409551	+	2.58580i
$253$		0			0
$254$	−1.76007	+	0.896802i	−1.76007	+	0.896802i
$255$	1.87869	−	0.297556i	1.87869	−	0.297556i
$256$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$257$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$257$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$258$	1.04744	−	3.22369i	1.04744	−	3.22369i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.437016	−	1.34500i	0.437016	−	1.34500i
$263$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$263$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$264$		0			0
$265$	1.59811	+	1.16110i	1.59811	+	1.16110i
$266$		0			0
$267$		0			0
$268$	−0.309017	+	0.0489435i	−0.309017	+	0.0489435i
$269$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$269$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$270$	1.80902	+	2.48990i	1.80902	+	2.48990i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	0.453990	−	0.891007i	0.453990	−	0.891007i
$273$		0			0
$274$	0.412215	+	0.809017i	0.412215	+	0.809017i
$275$		0			0
$276$		0			0
$277$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$277$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$278$	1.87869	+	0.610425i	1.87869	+	0.610425i
$279$	−0.819101			−0.819101
$280$		−	1.00000i		−	1.00000i
$281$	−1.17557			−1.17557			−0.587785	−	0.809017i	$-0.700000\pi$
$281$	−1.17557			−1.17557			−0.587785	+	0.809017i	$0.700000\pi$
$282$		0			0
$283$	−1.14412	−	1.14412i	−1.14412	−	1.14412i	−0.987688	−	0.156434i	$-0.950000\pi$
$283$	−1.14412	−	1.14412i	−1.14412	−	1.14412i	−0.156434	−	0.987688i	$-0.550000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.26007	+	1.26007i	−1.26007	+	1.26007i
$288$	2.61803			2.61803
$289$			1.00000i			1.00000i
$290$		0			0
$291$		−	2.23607i		−	2.23607i
$292$	1.87869	−	0.297556i	1.87869	−	0.297556i
$293$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$	−1.69480	+	0.863541i	−1.69480	+	0.863541i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$299$		0			0
$300$	−0.863541	−	1.69480i	−0.863541	−	1.69480i
$301$	1.78201			1.78201
$302$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$303$		0			0
$304$		0			0
$305$	0.142040	+	0.896802i	0.142040	+	0.896802i
$306$	−2.33269	+	1.18856i	−2.33269	+	1.18856i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		0			0
$310$	0.309017	+	0.0489435i	0.309017	+	0.0489435i
$311$			1.97538i			1.97538i	0.156434	+	0.987688i	$0.450000\pi$
$311$			1.97538i			1.97538i	−0.156434	+	0.987688i	$0.550000\pi$
$312$		0			0
$313$	−1.14412	+	1.14412i	−1.14412	+	1.14412i	−0.156434	+	0.987688i	$0.550000\pi$
$313$	−1.14412	+	1.14412i	−1.14412	+	1.14412i	−0.987688	+	0.156434i	$0.950000\pi$
$314$		0			0
$315$	−1.53884	+	2.11803i	−1.53884	+	2.11803i
$316$		0			0
$317$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$317$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$318$	−3.57349	−	1.16110i	−3.57349	−	1.16110i
$319$		0			0
$320$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−2.61803	−	1.90211i	−2.61803	−	1.90211i
$325$		0			0
$326$		0			0
$327$		0			0
$328$	1.04744	+	1.44168i	1.04744	+	1.44168i
$329$		0			0
$330$		0			0
$331$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$331$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$332$		0			0
$333$		0			0
$334$	−0.550672	+	0.280582i	−0.550672	+	0.280582i
$335$	−0.253116	−	0.183900i	−0.253116	−	0.183900i
$336$	0.587785	+	1.80902i	0.587785	+	1.80902i
$337$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$337$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$338$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$339$		0			0
$340$	0.951057	−	0.309017i	0.951057	−	0.309017i
$341$		0			0
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$344$	0.278768	−	1.76007i	0.278768	−	1.76007i
$345$		0			0
$346$	1.69480	−	0.863541i	1.69480	−	0.863541i
$347$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$347$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	0.707107	−	0.707107i	0.707107	−	0.707107i
$351$		0			0
$352$		0			0
$353$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$353$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.34500	−	1.34500i	−1.34500	−	1.34500i
$358$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$359$	1.17557			1.17557			0.587785	−	0.809017i	$-0.300000\pi$
$359$	1.17557			1.17557			0.587785	+	0.809017i	$0.300000\pi$
$360$	1.85123	+	1.85123i	1.85123	+	1.85123i
$361$	1.00000			1.00000
$362$	−1.34500	−	0.437016i	−1.34500	−	0.437016i
$363$	−1.34500	−	1.34500i	−1.34500	−	1.34500i
$364$		0			0
$365$	1.53884	+	1.11803i	1.53884	+	1.11803i
$366$	−0.784079	−	1.53884i	−0.784079	−	1.53884i
$367$	−0.437016	+	0.437016i	−0.437016	+	0.437016i	−0.891007	−	0.453990i	$-0.850000\pi$
$367$	−0.437016	+	0.437016i	−0.437016	+	0.437016i	0.453990	+	0.891007i	$0.350000\pi$
$368$		0			0
$369$		−	4.66537i		−	4.66537i
$370$		0			0
$371$		−	1.97538i		−	1.97538i
$372$	−0.587785	+	0.0930960i	−0.587785	+	0.0930960i
$373$	1.26007	−	1.26007i	1.26007	−	1.26007i	0.309017	−	0.951057i	$-0.400000\pi$
$373$	1.26007	−	1.26007i	1.26007	−	1.26007i	0.951057	−	0.309017i	$-0.100000\pi$
$374$		0			0
$375$	0.587785	−	1.80902i	0.587785	−	1.80902i
$376$		0			0
$377$		0			0
$378$	0.951057	−	2.92705i	0.951057	−	2.92705i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	3.75739			3.75739
$382$	0.500000	−	1.53884i	0.500000	−	1.53884i
$383$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$383$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$384$	1.87869	−	0.297556i	1.87869	−	0.297556i
$385$		0			0
$386$		0			0
$387$	−3.29892	+	3.29892i	−3.29892	+	3.29892i
$388$	−0.183900	−	1.16110i	−0.183900	−	1.16110i
$389$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$389$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$390$		0			0
$391$		0			0
$392$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$393$	−1.90211	+	1.90211i	−1.90211	+	1.90211i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.14412	−	1.14412i	−1.14412	−	1.14412i	−0.987688	−	0.156434i	$-0.950000\pi$
$397$	−1.14412	−	1.14412i	−1.14412	−	1.14412i	−0.156434	−	0.987688i	$-0.550000\pi$
$398$	0.863541	+	0.280582i	0.863541	+	0.280582i
$399$		0			0
$400$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$	0.565985	+	0.183900i	0.565985	+	0.183900i
$403$		0			0
$404$		0			0
$405$	−0.506233	−	3.19623i	−0.506233	−	3.19623i
$406$		0			0
$407$		0			0
$408$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$	−0.278768	+	1.76007i	−0.278768	+	1.76007i
$411$		−	1.72708i		−	1.72708i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.65688	−	2.65688i	−2.65688	−	2.65688i
$418$		0			0
$419$	0.312869			0.312869			0.156434	−	0.987688i	$-0.450000\pi$
$419$	0.312869			0.312869			0.156434	+	0.987688i	$0.450000\pi$
$420$	−0.863541	+	1.69480i	−0.863541	+	1.69480i
$421$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$421$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$422$		0			0
$423$		0			0
$424$	−1.95106	−	0.309017i	−1.95106	−	0.309017i
$425$	0.891007	+	0.453990i	0.891007	+	0.453990i
$426$		0			0
$427$	0.642040	−	0.642040i	0.642040	−	0.642040i
$428$		0			0
$429$		0			0
$430$	1.44168	−	1.04744i	1.44168	−	1.04744i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−2.74224	−	1.39724i	−2.74224	−	1.39724i
$433$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$433$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$434$	−0.142040	−	0.278768i	−0.142040	−	0.278768i
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−3.44095	−	1.11803i	−3.44095	−	1.11803i
$439$	−1.78201			−1.78201			−0.891007	−	0.453990i	$-0.850000\pi$
$439$	−1.78201			−1.78201			−0.891007	+	0.453990i	$0.850000\pi$
$440$		0			0
$441$	2.61803			2.61803
$442$		0			0
$443$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$443$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.831254	−	0.831254i	0.831254	−	0.831254i
$448$	0.453990	+	0.891007i	0.453990	+	0.891007i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$			2.61803i			2.61803i
$451$		0			0
$452$		0			0
$453$	0.831254	−	0.831254i	0.831254	−	0.831254i
$454$	−1.44168	+	0.734572i	−1.44168	+	0.734572i
$455$		0			0
$456$		0			0
$457$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$457$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.587785	+	0.809017i	$0.300000\pi$
$458$		0			0
$459$	3.07768			3.07768
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	−0.642040	−	0.642040i	−0.642040	−	0.642040i	0.309017	−	0.951057i	$-0.400000\pi$
$463$	−0.642040	−	0.642040i	−0.642040	−	0.642040i	−0.951057	+	0.309017i	$0.900000\pi$
$464$		0			0
$465$	−0.481456	−	0.349798i	−0.481456	−	0.349798i
$466$		0			0
$467$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$467$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$468$		0			0
$469$			0.312869i			0.312869i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$477$	3.65688	+	3.65688i	3.65688	+	3.65688i
$478$	−1.80902	−	0.587785i	−1.80902	−	0.587785i
$479$	−1.78201			−1.78201			−0.891007	−	0.453990i	$-0.850000\pi$
$479$	−1.78201			−1.78201			−0.891007	+	0.453990i	$0.850000\pi$
$480$	1.53884	+	1.11803i	1.53884	+	1.11803i
$481$		0			0
$482$	0.297556	+	0.0966818i	0.297556	+	0.0966818i
$483$		0			0
$484$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$485$	0.690983	−	0.951057i	0.690983	−	0.951057i
$486$	1.39724	+	2.74224i	1.39724	+	2.74224i
$487$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$487$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$488$	−0.533698	−	0.734572i	−0.533698	−	0.734572i
$489$		0			0
$490$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$491$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$491$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$492$	−0.530249	−	3.34786i	−0.530249	−	3.34786i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.297556	+	0.0966818i	−0.297556	+	0.0966818i
$497$		0			0
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	0.156434	−	0.987688i	0.156434	−	0.987688i
$501$	1.17557			1.17557
$502$		0			0
$503$	0.831254	+	0.831254i	0.831254	+	0.831254i	0.987688	−	0.156434i	$-0.0500000\pi$
$503$	0.831254	+	0.831254i	0.831254	+	0.831254i	−0.156434	+	0.987688i	$0.550000\pi$
$504$	0.409551	−	2.58580i	0.409551	−	2.58580i
$505$		0			0
$506$		0			0
$507$	1.34500	−	1.34500i	1.34500	−	1.34500i
$508$	1.95106	−	0.309017i	1.95106	−	0.309017i
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$	−1.87869	−	0.297556i	−1.87869	−	0.297556i
$511$		−	1.90211i		−	1.90211i
$512$	0.951057	−	0.309017i	0.951057	−	0.309017i
$513$		0			0
$514$		0			0
$515$		0			0
$516$	−1.99235	+	2.74224i	−1.99235	+	2.74224i
$517$		0			0
$518$		0			0
$519$	−3.61803			−3.61803
$520$		0			0
$521$	−0.907981			−0.907981			−0.453990	−	0.891007i	$-0.650000\pi$
$521$	−0.907981			−0.907981			−0.453990	+	0.891007i	$0.650000\pi$
$522$		0			0
$523$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$523$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$524$	−0.831254	+	1.14412i	−0.831254	+	1.14412i
$525$	−1.80902	+	0.587785i	−1.80902	+	0.587785i
$526$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$527$	0.221232	−	0.221232i	0.221232	−	0.221232i
$528$		0			0
$529$			1.00000i			1.00000i
$530$	−1.16110	−	1.59811i	−1.16110	−	1.59811i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.309017	+	0.0489435i	0.309017	+	0.0489435i
$537$	0.831254	+	0.831254i	0.831254	+	0.831254i
$538$	−0.437016	+	1.34500i	−0.437016	+	1.34500i
$539$		0			0
$540$	−0.951057	−	2.92705i	−0.951057	−	2.92705i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	1.90211	+	1.90211i	1.90211	+	1.90211i
$544$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$545$		0			0
$546$		0			0
$547$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$547$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$548$	−0.142040	−	0.896802i	−0.142040	−	0.896802i
$549$			2.37713i			2.37713i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.59811	−	1.16110i	−1.59811	−	1.16110i
$557$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$557$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$558$	0.779012	+	0.253116i	0.779012	+	0.253116i
$559$		0			0
$560$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$561$		0			0
$562$	1.11803	+	0.363271i	1.11803	+	0.363271i
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$		0			0
$565$		0			0
$566$	0.734572	+	1.44168i	0.734572	+	1.44168i
$567$	−2.28825	+	2.28825i	−2.28825	+	2.28825i
$568$		0			0
$569$			1.90211i			1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$569$			1.90211i			1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	−2.17625	+	2.17625i	−2.17625	+	2.17625i
$574$	1.58779	−	0.809017i	1.58779	−	0.809017i
$575$		0			0
$576$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$577$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$577$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$578$	0.309017	−	0.951057i	0.309017	−	0.951057i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	−0.690983	+	2.12663i	−0.690983	+	2.12663i
$583$		0			0
$584$	−1.87869	−	0.297556i	−1.87869	−	0.297556i
$585$		0			0
$586$		0			0
$587$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$587$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$588$	1.87869	−	0.297556i	1.87869	−	0.297556i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$596$	0.363271	−	0.500000i	0.363271	−	0.500000i
$597$	−1.22123	−	1.22123i	−1.22123	−	1.22123i
$598$		0			0
$599$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$599$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$600$	0.297556	+	1.87869i	0.297556	+	1.87869i
$601$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$601$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$602$	−1.69480	−	0.550672i	−1.69480	−	0.550672i
$603$	−0.579192	−	0.579192i	−0.579192	−	0.579192i
$604$	0.363271	−	0.500000i	0.363271	−	0.500000i
$605$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$606$		0			0
$607$	0.831254	−	0.831254i	0.831254	−	0.831254i	−0.156434	−	0.987688i	$-0.550000\pi$
$607$	0.831254	−	0.831254i	0.831254	−	0.831254i	0.987688	+	0.156434i	$0.0500000\pi$
$608$		0			0
$609$		0			0
$610$	0.142040	−	0.896802i	0.142040	−	0.896802i
$611$		0			0
$612$	2.58580	−	0.409551i	2.58580	−	0.409551i
$613$	−0.221232	+	0.221232i	−0.221232	+	0.221232i	−0.809017	−	0.587785i	$-0.800000\pi$
$613$	−0.221232	+	0.221232i	−0.221232	+	0.221232i	0.587785	+	0.809017i	$0.300000\pi$
$614$		0			0
$615$	1.99235	−	2.74224i	1.99235	−	2.74224i
$616$		0			0
$617$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$617$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$618$		0			0
$619$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$619$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$620$	−0.278768	−	0.142040i	−0.278768	−	0.142040i
$621$		0			0
$622$	0.610425	−	1.87869i	0.610425	−	1.87869i
$623$		0			0
$624$		0			0
$625$	0.809017	−	0.587785i	0.809017	−	0.587785i
$626$	1.44168	−	0.734572i	1.44168	−	0.734572i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	2.11803	−	1.53884i	2.11803	−	1.53884i
$631$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$631$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.59811	+	1.16110i	1.59811	+	1.16110i
$636$	3.03979	+	2.20854i	3.03979	+	2.20854i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.891007	+	0.453990i	0.891007	+	0.453990i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		0			0
$643$	0.437016	+	0.437016i	0.437016	+	0.437016i	0.891007	−	0.453990i	$-0.150000\pi$
$643$	0.437016	+	0.437016i	0.437016	+	0.437016i	−0.453990	+	0.891007i	$0.650000\pi$
$644$		0			0
$645$	−3.34786	+	0.530249i	−3.34786	+	0.530249i
$646$		0			0
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	1.90211	+	2.61803i	1.90211	+	2.61803i
$649$		0			0
$650$		0			0
$651$			0.595112i			0.595112i
$652$		0			0
$653$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$653$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$654$		0			0
$655$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$656$	−0.550672	−	1.69480i	−0.550672	−	1.69480i
$657$	3.52125	+	3.52125i	3.52125	+	3.52125i
$658$		0			0
$659$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$659$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	0.363271	−	1.11803i	0.363271	−	1.11803i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.610425	−	0.0966818i	0.610425	−	0.0966818i
$669$		0			0
$670$	0.183900	+	0.253116i	0.183900	+	0.253116i
$671$		0			0
$672$		−	1.90211i		−	1.90211i
$673$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$673$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$674$		0			0
$675$	1.39724	−	2.74224i	1.39724	−	2.74224i
$676$	0.587785	−	0.809017i	0.587785	−	0.809017i
$677$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$677$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$678$		0			0
$679$	−1.17557			−1.17557
$680$	−1.00000			−1.00000
$681$	3.07768			3.07768
$682$		0			0
$683$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$683$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$684$		0			0
$685$	0.533698	−	0.734572i	0.533698	−	0.734572i
$686$	0.453990	+	0.891007i	0.453990	+	0.891007i
$687$		0			0
$688$	−0.809017	+	1.58779i	−0.809017	+	1.58779i
$689$		0			0
$690$		0			0
$691$			1.78201i			1.78201i	0.453990	+	0.891007i	$0.350000\pi$
$691$			1.78201i			1.78201i	−0.453990	+	0.891007i	$0.650000\pi$
$692$	−1.87869	+	0.297556i	−1.87869	+	0.297556i
$693$		0			0
$694$		0			0
$695$	−0.309017	−	1.95106i	−0.309017	−	1.95106i
$696$		0			0
$697$	1.26007	+	1.26007i	1.26007	+	1.26007i
$698$		0			0
$699$		0			0
$700$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$	0.863541	+	1.69480i	0.863541	+	1.69480i
$715$		0			0
$716$	0.500000	+	0.363271i	0.500000	+	0.363271i
$717$	2.55834	+	2.55834i	2.55834	+	2.55834i
$718$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$719$	0.907981			0.907981			0.453990	−	0.891007i	$-0.350000\pi$
$719$	0.907981			0.907981			0.453990	+	0.891007i	$0.350000\pi$
$720$	−1.18856	−	2.33269i	−1.18856	−	2.33269i
$721$		0			0
$722$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$723$	−0.420808	−	0.420808i	−0.420808	−	0.420808i
$724$	1.14412	+	0.831254i	1.14412	+	0.831254i
$725$		0			0
$726$	0.863541	+	1.69480i	0.863541	+	1.69480i
$727$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$727$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$728$		0			0
$729$		−	2.61803i		−	2.61803i
$730$	−1.11803	−	1.53884i	−1.11803	−	1.53884i
$731$		−	1.78201i		−	1.78201i
$732$	0.270175	+	1.70582i	0.270175	+	1.70582i
$733$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$733$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$734$	0.550672	−	0.280582i	0.550672	−	0.280582i
$735$	1.53884	+	1.11803i	1.53884	+	1.11803i
$736$		0			0
$737$		0			0
$738$	−1.44168	+	4.43703i	−1.44168	+	4.43703i
$739$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$739$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$740$		0			0
$741$		0			0
$742$	−0.610425	+	1.87869i	−0.610425	+	1.87869i
$743$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$743$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$744$	0.587785	+	0.0930960i	0.587785	+	0.0930960i
$745$	0.610425	−	0.0966818i	0.610425	−	0.0966818i
$746$	−1.58779	+	0.809017i	−1.58779	+	0.809017i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−1.11803	+	1.53884i	−1.11803	+	1.53884i
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.610425	−	0.0966818i	0.610425	−	0.0966818i
$756$	−1.80902	+	2.48990i	−1.80902	+	2.48990i
$757$	0.642040	+	0.642040i	0.642040	+	0.642040i	0.951057	−	0.309017i	$-0.100000\pi$
$757$	0.642040	+	0.642040i	0.642040	+	0.642040i	−0.309017	+	0.951057i	$0.600000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$	−3.57349	−	1.16110i	−3.57349	−	1.16110i
$763$		0			0
$764$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$765$	2.11803	+	1.53884i	2.11803	+	1.53884i
$766$		0			0
$767$		0			0
$768$	−1.87869	−	0.297556i	−1.87869	−	0.297556i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$773$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$774$	4.15688	−	2.11803i	4.15688	−	2.11803i
$775$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i
$776$	−0.183900	+	1.16110i	−0.183900	+	1.16110i
$777$		0			0
$778$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.951057	−	0.309017i	0.951057	−	0.309017i
$785$		0			0
$786$	2.39680	−	1.22123i	2.39680	−	1.22123i
$787$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$787$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$788$		0			0
$789$			2.68999i			2.68999i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.734572	+	1.44168i	0.734572	+	1.44168i
$795$	0.587785	+	3.71113i	0.587785	+	3.71113i
$796$	−0.734572	−	0.533698i	−0.734572	−	0.533698i
$797$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$797$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$798$		0			0
$799$		0			0
$800$	0.309017	+	0.951057i	0.309017	+	0.951057i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−0.481456	−	0.349798i	−0.481456	−	0.349798i
$805$		0			0
$806$		0			0
$807$	1.90211	−	1.90211i	1.90211	−	1.90211i
$808$		0			0
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$	−0.506233	+	3.19623i	−0.506233	+	3.19623i
$811$		−	0.907981i		−	0.907981i	−0.891007	−	0.453990i	$-0.850000\pi$
$811$		−	0.907981i		−	0.907981i	0.891007	−	0.453990i	$-0.150000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.80902	−	0.587785i	1.80902	−	0.587785i
$817$		0			0
$818$		0			0
$819$		0			0
$820$	0.809017	−	1.58779i	0.809017	−	1.58779i
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−0.533698	+	1.64255i	−0.533698	+	1.64255i
$823$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$823$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$		0			0			−	1.00000i	$-0.5\pi$
$829$		0			0				1.00000i	$0.5\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$834$	1.70582	+	3.34786i	1.70582	+	3.34786i
$835$	0.500000	+	0.363271i	0.500000	+	0.363271i
$836$		0			0
$837$	−0.680881	−	0.680881i	−0.680881	−	0.680881i
$838$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i
$839$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$839$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$840$	1.34500	−	1.34500i	1.34500	−	1.34500i
$841$	−1.00000			−1.00000
$842$	0.587785	+	0.190983i	0.587785	+	0.190983i
$843$	−1.58114	−	1.58114i	−1.58114	−	1.58114i
$844$		0			0
$845$	0.987688	−	0.156434i	0.987688	−	0.156434i
$846$		0			0
$847$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$848$	1.76007	+	0.896802i	1.76007	+	0.896802i
$849$		−	3.07768i		−	3.07768i
$850$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$851$		0			0
$852$		0			0
$853$	−1.41421	+	1.41421i	−1.41421	+	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$853$	−1.41421	+	1.41421i	−1.41421	+	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$854$	−0.809017	+	0.412215i	−0.809017	+	0.412215i
$855$		0			0
$856$		0			0
$857$	−1.14412	−	1.14412i	−1.14412	−	1.14412i	−0.987688	−	0.156434i	$-0.950000\pi$
$857$	−1.14412	−	1.14412i	−1.14412	−	1.14412i	−0.156434	−	0.987688i	$-0.550000\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$	−1.69480	+	0.550672i	−1.69480	+	0.550672i
$861$	−3.38959			−3.38959
$862$		0			0
$863$	−1.39680	−	1.39680i	−1.39680	−	1.39680i	−0.809017	−	0.587785i	$-0.800000\pi$
$863$	−1.39680	−	1.39680i	−1.39680	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$864$	2.17625	+	2.17625i	2.17625	+	2.17625i
$865$	−1.53884	−	1.11803i	−1.53884	−	1.11803i
$866$		0			0
$867$	−1.34500	+	1.34500i	−1.34500	+	1.34500i
$868$	0.0489435	+	0.309017i	0.0489435	+	0.309017i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	2.17625	−	2.17625i	2.17625	−	2.17625i
$874$		0			0
$875$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$876$	2.92705	+	2.12663i	2.92705	+	2.12663i
$877$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$877$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$878$	1.69480	+	0.550672i	1.69480	+	0.550672i
$879$		0			0
$880$		0			0
$881$	1.97538			1.97538			0.987688	−	0.156434i	$-0.0500000\pi$
$881$	1.97538			1.97538			0.987688	+	0.156434i	$0.0500000\pi$
$882$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$883$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$883$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.587785	+	0.809017i	$0.300000\pi$
$884$		0			0
$885$		0			0
$886$	0.642040	+	1.26007i	0.642040	+	1.26007i
$887$	−1.14412	+	1.14412i	−1.14412	+	1.14412i	−0.156434	+	0.987688i	$0.550000\pi$
$887$	−1.14412	+	1.14412i	−1.14412	+	1.14412i	−0.987688	+	0.156434i	$0.950000\pi$
$888$		0			0
$889$		−	1.97538i		−	1.97538i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	−1.04744	+	0.533698i	−1.04744	+	0.533698i
$895$	0.0966818	+	0.610425i	0.0966818	+	0.610425i
$896$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.809017	−	2.48990i	0.809017	−	2.48990i
$901$	−1.97538			−1.97538
$902$		0			0
$903$	2.39680	+	2.39680i	2.39680	+	2.39680i
$904$		0			0
$905$	0.221232	+	1.39680i	0.221232	+	1.39680i
$906$	−1.04744	+	0.533698i	−1.04744	+	0.533698i
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$	1.59811	−	0.253116i	1.59811	−	0.253116i
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$	−0.896802	−	1.76007i	−0.896802	−	1.76007i
$915$	−1.01515	+	1.39724i	−1.01515	+	1.39724i
$916$		0			0
$917$	1.00000	+	1.00000i	1.00000	+	1.00000i
$918$	−2.92705	−	0.951057i	−2.92705	−	0.951057i
$919$	−1.90211			−1.90211			−0.951057	−	0.309017i	$-0.900000\pi$
$919$	−1.90211			−1.90211			−0.951057	+	0.309017i	$0.900000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.412215	+	0.809017i	0.412215	+	0.809017i
$927$		0			0
$928$		0			0
$929$		−	0.312869i		−	0.312869i	−0.987688	−	0.156434i	$-0.950000\pi$
$929$		−	0.312869i		−	0.312869i	0.987688	−	0.156434i	$-0.0500000\pi$
$930$	0.349798	+	0.481456i	0.349798	+	0.481456i
$931$		0			0
$932$		0			0
$933$	−2.65688	+	2.65688i	−2.65688	+	2.65688i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$937$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$938$	0.0966818	−	0.297556i	0.0966818	−	0.297556i
$939$	−3.07768			−3.07768
$940$		0			0
$941$	0.907981			0.907981			0.453990	−	0.891007i	$-0.350000\pi$
$941$	0.907981			0.907981			0.453990	+	0.891007i	$0.350000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−3.03979	+	0.481456i	−3.03979	+	0.481456i
$946$		0			0
$947$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$947$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.587785	+	0.809017i	0.587785	+	0.809017i
$953$	0.221232	−	0.221232i	0.221232	−	0.221232i	−0.587785	−	0.809017i	$-0.700000\pi$
$953$	0.221232	−	0.221232i	0.221232	−	0.221232i	0.809017	+	0.587785i	$0.200000\pi$
$954$	−2.34786	−	4.60793i	−2.34786	−	4.60793i
$955$	−1.59811	+	0.253116i	−1.59811	+	0.253116i
$956$	1.53884	+	1.11803i	1.53884	+	1.11803i
$957$		0			0
$958$	1.69480	+	0.550672i	1.69480	+	0.550672i
$959$	−0.907981			−0.907981
$960$	−1.11803	−	1.53884i	−1.11803	−	1.53884i
$961$	0.902113			0.902113
$962$		0			0
$963$		0			0
$964$	−0.253116	−	0.183900i	−0.253116	−	0.183900i
$965$		0			0
$966$		0			0
$967$	−0.642040	+	0.642040i	−0.642040	+	0.642040i	−0.951057	−	0.309017i	$-0.900000\pi$
$967$	−0.642040	+	0.642040i	−0.642040	+	0.642040i	0.309017	+	0.951057i	$0.400000\pi$
$968$	0.587785	+	0.809017i	0.587785	+	0.809017i
$969$		0			0
$970$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	−0.481456	−	3.03979i	−0.481456	−	3.03979i
$973$	−1.39680	+	1.39680i	−1.39680	+	1.39680i
$974$		0			0
$975$		0			0
$976$	0.280582	+	0.863541i	0.280582	+	0.863541i
$977$	−0.221232	−	0.221232i	−0.221232	−	0.221232i	0.587785	−	0.809017i	$-0.300000\pi$
$977$	−0.221232	−	0.221232i	−0.221232	−	0.221232i	−0.809017	+	0.587785i	$0.800000\pi$
$978$		0			0
$979$		0			0
$980$	0.891007	+	0.453990i	0.891007	+	0.453990i
$981$		0			0
$982$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$983$	0.831254	+	0.831254i	0.831254	+	0.831254i	0.987688	−	0.156434i	$-0.0500000\pi$
$983$	0.831254	+	0.831254i	0.831254	+	0.831254i	−0.156434	+	0.987688i	$0.550000\pi$
$984$	−0.530249	+	3.34786i	−0.530249	+	3.34786i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$	0.312869			0.312869
$993$	−1.58114	+	1.58114i	−1.58114	+	1.58114i
$994$		0			0
$995$	−0.142040	−	0.896802i	−0.142040	−	0.896802i
$996$		0			0
$997$	−0.437016	−	0.437016i	−0.437016	−	0.437016i	0.453990	−	0.891007i	$-0.350000\pi$
$997$	−0.437016	−	0.437016i	−0.437016	−	0.437016i	−0.891007	+	0.453990i	$0.850000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2380.1.bi.c.1427.2	yes	16
4.3	odd	2		2380.1.bi.d.1427.1	yes	16
5.3	odd	4		2380.1.bi.d.1903.3	yes	16
7.6	odd	2	inner	2380.1.bi.c.1427.1	✓	16
17.16	even	2	inner	2380.1.bi.c.1427.1	✓	16
20.3	even	4	inner	2380.1.bi.c.1903.2	yes	16
28.27	even	2		2380.1.bi.d.1427.2	yes	16
35.13	even	4		2380.1.bi.d.1903.4	yes	16
68.67	odd	2		2380.1.bi.d.1427.2	yes	16
85.33	odd	4		2380.1.bi.d.1903.4	yes	16
119.118	odd	2	CM	2380.1.bi.c.1427.2	yes	16
140.83	odd	4	inner	2380.1.bi.c.1903.1	yes	16
340.203	even	4	inner	2380.1.bi.c.1903.1	yes	16
476.475	even	2		2380.1.bi.d.1427.1	yes	16
595.118	even	4		2380.1.bi.d.1903.3	yes	16
2380.1903	odd	4	inner	2380.1.bi.c.1903.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2380.1.bi.c.1427.1	✓	16	7.6	odd	2	inner
2380.1.bi.c.1427.1	✓	16	17.16	even	2	inner
2380.1.bi.c.1427.2	yes	16	1.1	even	1	trivial
2380.1.bi.c.1427.2	yes	16	119.118	odd	2	CM
2380.1.bi.c.1903.1	yes	16	140.83	odd	4	inner
2380.1.bi.c.1903.1	yes	16	340.203	even	4	inner
2380.1.bi.c.1903.2	yes	16	20.3	even	4	inner
2380.1.bi.c.1903.2	yes	16	2380.1903	odd	4	inner
2380.1.bi.d.1427.1	yes	16	4.3	odd	2
2380.1.bi.d.1427.1	yes	16	476.475	even	2
2380.1.bi.d.1427.2	yes	16	28.27	even	2
2380.1.bi.d.1427.2	yes	16	68.67	odd	2
2380.1.bi.d.1903.3	yes	16	5.3	odd	4
2380.1.bi.d.1903.3	yes	16	595.118	even	4
2380.1.bi.d.1903.4	yes	16	35.13	even	4
2380.1.bi.d.1903.4	yes	16	85.33	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2380.bi (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.34500 + 1.34500i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.156434 + 0.987688i) q^{5} +(-0.863541 - 1.69480i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-0.587785 - 0.809017i) q^{8} +2.61803i q^{9} +(0.156434 - 0.987688i) q^{10} +(0.297556 + 1.87869i) q^{12} +(-0.891007 + 0.453990i) q^{14} +(-1.11803 + 1.53884i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.707107 - 0.707107i) q^{17} +(0.809017 - 2.48990i) q^{18} +(-0.453990 + 0.891007i) q^{20} +1.90211 q^{21} +(0.297556 - 1.87869i) q^{24} +(-0.951057 + 0.309017i) q^{25} +(-2.17625 + 2.17625i) q^{27} +(0.987688 - 0.156434i) q^{28} +(1.53884 - 1.11803i) q^{30} +0.312869i q^{31} -1.00000i q^{32} +(0.453990 + 0.891007i) q^{34} +(0.809017 + 0.587785i) q^{35} +(-1.53884 + 2.11803i) q^{36} +(0.707107 - 0.707107i) q^{40} -1.78201 q^{41} +(-1.80902 - 0.587785i) q^{42} +(1.26007 + 1.26007i) q^{43} +(-2.58580 + 0.409551i) q^{45} +(-0.863541 + 1.69480i) q^{48} -1.00000i q^{49} +1.00000 q^{50} -1.90211i q^{51} +(1.39680 - 1.39680i) q^{53} +(2.74224 - 1.39724i) q^{54} +(-0.987688 - 0.156434i) q^{56} +(-1.80902 + 0.587785i) q^{60} +0.907981 q^{61} +(0.0966818 - 0.297556i) q^{62} +(1.85123 + 1.85123i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.221232 + 0.221232i) q^{67} +(-0.156434 - 0.987688i) q^{68} +(-0.587785 - 0.809017i) q^{70} +(2.11803 - 1.53884i) q^{72} +(1.34500 - 1.34500i) q^{73} +(-1.69480 - 0.863541i) q^{75} +(-0.891007 + 0.453990i) q^{80} -3.23607 q^{81} +(1.69480 + 0.550672i) q^{82} +(1.53884 + 1.11803i) q^{84} +(0.587785 - 0.809017i) q^{85} +(-0.809017 - 1.58779i) q^{86} +(2.58580 + 0.409551i) q^{90} +(-0.420808 + 0.420808i) q^{93} +(1.34500 - 1.34500i) q^{96} +(-0.831254 - 0.831254i) q^{97} +(-0.309017 + 0.951057i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{16} + 4 q^{18} + 4 q^{35} - 20 q^{42} - 4 q^{43} + 16 q^{50} + 4 q^{53} - 20 q^{60} + 4 q^{64} - 4 q^{67} + 16 q^{72} - 16 q^{81} - 4 q^{86} + 4 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^16 + 4 * q^18 + 4 * q^35 - 20 * q^42 - 4 * q^43 + 16 * q^50 + 4 * q^53 - 20 * q^60 + 4 * q^64 - 4 * q^67 + 16 * q^72 - 16 * q^81 - 4 * q^86 + 4 * q^98

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