LMFDB - Embedded newform 984.1.cj.a.539.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [984,1,Mod(11,984)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(984, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([20, 20, 20, 3]))

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

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

chi := DirichletCharacter("984.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 984 = 2^{3} \cdot 3 \cdot 41 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	984.cj (of order $40$, degree $16$, 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:	$0.491079972431$
Analytic rank:	$0$
Dimension:	$16$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{40}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{40} - \cdots)$

Embedding invariants

Embedding label			539.1
Root			$0.156434 - 0.987688i$ of defining polynomial
Character	$\chi$	$=$	984.539
Dual form			984.1.cj.a.827.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.156434 - 0.987688i) q^{6} +(-0.156434 - 0.987688i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.156434 - 0.987688i) q^{6} +(-0.156434 - 0.987688i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.243950 + 1.01612i) q^{11} +(-0.587785 + 0.809017i) q^{12} +(-0.309017 + 0.951057i) q^{16} +(0.965451 + 1.57547i) q^{17} +(0.987688 - 0.156434i) q^{18} +(-0.987688 - 0.843566i) q^{19} +(0.678671 - 0.794622i) q^{22} +(0.891007 - 0.453990i) q^{24} +(0.951057 + 0.309017i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.707107 - 0.707107i) q^{32} +(-1.04178 + 0.0819895i) q^{33} +(-0.144974 - 1.84206i) q^{34} +(-0.951057 - 0.309017i) q^{36} +(0.497066 + 1.20002i) q^{38} +(-0.987688 - 0.156434i) q^{41} +(-0.863541 + 1.69480i) q^{43} +(-0.965451 + 0.399903i) q^{44} -1.00000 q^{48} +(0.987688 - 0.156434i) q^{49} +(-0.707107 - 0.707107i) q^{50} +(-1.20002 + 1.40505i) q^{51} +(0.453990 + 0.891007i) q^{54} +(0.497066 - 1.20002i) q^{57} +(1.34500 - 0.437016i) q^{59} +(-0.951057 + 0.309017i) q^{64} +(0.965451 + 0.399903i) q^{66} +(-0.108993 - 0.453990i) q^{67} +(-0.707107 + 1.70711i) q^{68} +(0.707107 + 0.707107i) q^{72} +(-0.437016 - 0.437016i) q^{73} +1.00000i q^{75} +(0.101910 - 1.29489i) q^{76} +(0.309017 - 0.951057i) q^{81} +(0.809017 + 0.587785i) q^{82} +1.61803i q^{83} +(1.53884 - 1.11803i) q^{86} +(1.04178 + 0.0819895i) q^{88} +(-0.152583 - 1.93874i) q^{89} +(0.891007 + 0.453990i) q^{96} +(1.47879 - 0.355026i) q^{97} +(-0.951057 - 0.309017i) q^{98} +(-0.399903 - 0.965451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 4 * q^9	$ 16 q - 4 q^{3} - 4 q^{9} + 4 q^{16} + 4 q^{17} + 4 q^{22} - 4 q^{27} - 4 q^{34} - 4 q^{44} - 16 q^{48} + 4 q^{51} + 4 q^{66} - 16 q^{67} + 4 q^{76} - 4 q^{81} + 4 q^{82} + 4 q^{89}+O(q^{100}) $ 16 * q - 4 * q^3 - 4 * q^9 + 4 * q^16 + 4 * q^17 + 4 * q^22 - 4 * q^27 - 4 * q^34 - 4 * q^44 - 16 * q^48 + 4 * q^51 + 4 * q^66 - 16 * q^67 + 4 * q^76 - 4 * q^81 + 4 * q^82 + 4 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/984\mathbb{Z}\right)^\times$.

$n$	$247$	$329$	$457$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{40}\right)$	$-1$

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 $

$2$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$2$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$4$	0.587785	+	0.809017i	0.587785	+	0.809017i
$5$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$5$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$6$	0.156434	−	0.987688i	0.156434	−	0.987688i
$7$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$7$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$8$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$9$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$10$		0			0
$11$	−0.243950	+	1.01612i	−0.243950	+	1.01612i	0.707107	+	0.707107i	$0.250000\pi$
$11$	−0.243950	+	1.01612i	−0.243950	+	1.01612i	−0.951057	+	0.309017i	$0.900000\pi$
$12$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$13$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$13$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$14$		0			0
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$17$	0.965451	+	1.57547i	0.965451	+	1.57547i	0.809017	+	0.587785i	$0.200000\pi$
$17$	0.965451	+	1.57547i	0.965451	+	1.57547i	0.156434	+	0.987688i	$0.450000\pi$
$18$	0.987688	−	0.156434i	0.987688	−	0.156434i
$19$	−0.987688	−	0.843566i	−0.987688	−	0.843566i		−	1.00000i	$-0.5\pi$
$19$	−0.987688	−	0.843566i	−0.987688	−	0.843566i	−0.987688	+	0.156434i	$0.950000\pi$
$20$		0			0
$21$		0			0
$22$	0.678671	−	0.794622i	0.678671	−	0.794622i
$23$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$23$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$24$	0.891007	−	0.453990i	0.891007	−	0.453990i
$25$	0.951057	+	0.309017i	0.951057	+	0.309017i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$28$		0			0
$29$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$29$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$30$		0			0
$31$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$31$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$32$	0.707107	−	0.707107i	0.707107	−	0.707107i
$33$	−1.04178	+	0.0819895i	−1.04178	+	0.0819895i
$34$	−0.144974	−	1.84206i	−0.144974	−	1.84206i
$35$		0			0
$36$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$	0.497066	+	1.20002i	0.497066	+	1.20002i
$39$		0			0
$40$		0			0
$41$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$41$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$42$		0			0
$43$	−0.863541	+	1.69480i	−0.863541	+	1.69480i	−0.156434	+	0.987688i	$0.550000\pi$
$43$	−0.863541	+	1.69480i	−0.863541	+	1.69480i	−0.707107	+	0.707107i	$0.750000\pi$
$44$	−0.965451	+	0.399903i	−0.965451	+	0.399903i
$45$		0			0
$46$		0			0
$47$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$47$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$48$	−1.00000			−1.00000
$49$	0.987688	−	0.156434i	0.987688	−	0.156434i
$50$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$51$	−1.20002	+	1.40505i	−1.20002	+	1.40505i
$52$		0			0
$53$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$53$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$54$	0.453990	+	0.891007i	0.453990	+	0.891007i
$55$		0			0
$56$		0			0
$57$	0.497066	−	1.20002i	0.497066	−	1.20002i
$58$		0			0
$59$	1.34500	−	0.437016i	1.34500	−	0.437016i	0.453990	−	0.891007i	$-0.350000\pi$
$59$	1.34500	−	0.437016i	1.34500	−	0.437016i	0.891007	+	0.453990i	$0.150000\pi$
$60$		0			0
$61$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$61$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$62$		0			0
$63$		0			0
$64$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$65$		0			0
$66$	0.965451	+	0.399903i	0.965451	+	0.399903i
$67$	−0.108993	−	0.453990i	−0.108993	−	0.453990i	0.891007	−	0.453990i	$-0.150000\pi$
$67$	−0.108993	−	0.453990i	−0.108993	−	0.453990i	−1.00000			$\pi$
$68$	−0.707107	+	1.70711i	−0.707107	+	1.70711i
$69$		0			0
$70$		0			0
$71$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$71$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$72$	0.707107	+	0.707107i	0.707107	+	0.707107i
$73$	−0.437016	−	0.437016i	−0.437016	−	0.437016i	0.453990	−	0.891007i	$-0.350000\pi$
$73$	−0.437016	−	0.437016i	−0.437016	−	0.437016i	−0.891007	+	0.453990i	$0.850000\pi$
$74$		0			0
$75$			1.00000i			1.00000i
$76$	0.101910	−	1.29489i	0.101910	−	1.29489i
$77$		0			0
$78$		0			0
$79$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$79$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.309017	−	0.951057i
$82$	0.809017	+	0.587785i	0.809017	+	0.587785i
$83$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$83$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$84$		0			0
$85$		0			0
$86$	1.53884	−	1.11803i	1.53884	−	1.11803i
$87$		0			0
$88$	1.04178	+	0.0819895i	1.04178	+	0.0819895i
$89$	−0.152583	−	1.93874i	−0.152583	−	1.93874i	−0.309017	−	0.951057i	$-0.600000\pi$
$89$	−0.152583	−	1.93874i	−0.152583	−	1.93874i	0.156434	−	0.987688i	$-0.450000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.891007	+	0.453990i	0.891007	+	0.453990i
$97$	1.47879	−	0.355026i	1.47879	−	0.355026i	0.587785	−	0.809017i	$-0.300000\pi$
$97$	1.47879	−	0.355026i	1.47879	−	0.355026i	0.891007	+	0.453990i	$0.150000\pi$
$98$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$99$	−0.399903	−	0.965451i	−0.399903	−	0.965451i
$100$	0.309017	+	0.951057i	0.309017	+	0.951057i
$101$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$101$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$102$	1.70711	−	0.707107i	1.70711	−	0.707107i
$103$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$103$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.363271	−	1.11803i	0.363271	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$107$	0.363271	−	1.11803i	0.363271	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$108$		−	1.00000i		−	1.00000i
$109$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$109$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.44168	+	1.04744i	1.44168	+	1.04744i	0.987688	+	0.156434i	$0.0500000\pi$
$113$	1.44168	+	1.04744i	1.44168	+	1.04744i	0.453990	+	0.891007i	$0.350000\pi$
$114$	−0.987688	+	0.843566i	−0.987688	+	0.843566i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$119$		0			0
$120$		0			0
$121$	−0.0819895	−	0.0417758i	−0.0819895	−	0.0417758i
$122$		0			0
$123$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$127$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$128$	0.987688	+	0.156434i	0.987688	+	0.156434i
$129$	−1.87869	−	0.297556i	−1.87869	−	0.297556i
$130$		0			0
$131$	−0.142040	−	0.896802i	−0.142040	−	0.896802i	−0.951057	−	0.309017i	$-0.900000\pi$
$131$	−0.142040	−	0.896802i	−0.142040	−	0.896802i	0.809017	−	0.587785i	$-0.200000\pi$
$132$	−0.678671	−	0.794622i	−0.678671	−	0.794622i
$133$		0			0
$134$	−0.108993	+	0.453990i	−0.108993	+	0.453990i
$135$		0			0
$136$	1.40505	−	1.20002i	1.40505	−	1.20002i
$137$	−0.707107	−	0.292893i	−0.707107	−	0.292893i		−	1.00000i	$-0.5\pi$
$137$	−0.707107	−	0.292893i	−0.707107	−	0.292893i	−0.707107	+	0.707107i	$0.750000\pi$
$138$		0			0
$139$	0.550672	−	1.69480i	0.550672	−	1.69480i	−0.156434	−	0.987688i	$-0.550000\pi$
$139$	0.550672	−	1.69480i	0.550672	−	1.69480i	0.707107	−	0.707107i	$-0.250000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$145$		0			0
$146$	0.190983	+	0.587785i	0.190983	+	0.587785i
$147$	0.453990	+	0.891007i	0.453990	+	0.891007i
$148$		0			0
$149$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$149$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$150$	0.453990	−	0.891007i	0.453990	−	0.891007i
$151$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$151$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$152$	−0.678671	+	1.10749i	−0.678671	+	1.10749i
$153$	−1.70711	−	0.707107i	−1.70711	−	0.707107i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.0784591	−	0.996917i	$-0.525000\pi$
$157$		0			0		0.0784591	+	0.996917i	$0.475000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$163$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$163$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$164$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$165$		0			0
$166$	0.734572	−	1.44168i	0.734572	−	1.44168i
$167$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$167$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$168$		0			0
$169$	0.156434	−	0.987688i	0.156434	−	0.987688i
$170$		0			0
$171$	1.29489	+	0.101910i	1.29489	+	0.101910i
$172$	−1.87869	+	0.297556i	−1.87869	+	0.297556i
$173$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$173$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$174$		0			0
$175$		0			0
$176$	−0.891007	−	0.546010i	−0.891007	−	0.546010i
$177$	0.831254	+	1.14412i	0.831254	+	1.14412i
$178$	−0.744220	+	1.79671i	−0.744220	+	1.79671i
$179$	−0.398090	−	1.65816i	−0.398090	−	1.65816i	−0.707107	−	0.707107i	$-0.750000\pi$
$179$	−0.398090	−	1.65816i	−0.398090	−	1.65816i	0.309017	−	0.951057i	$-0.400000\pi$
$180$		0			0
$181$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$181$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.83640	+	0.596682i	−1.83640	+	0.596682i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$191$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$192$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$193$	−1.65816	−	1.01612i	−1.65816	−	1.01612i	−0.951057	−	0.309017i	$-0.900000\pi$
$193$	−1.65816	−	1.01612i	−1.65816	−	1.01612i	−0.707107	−	0.707107i	$-0.750000\pi$
$194$	−1.47879	−	0.355026i	−1.47879	−	0.355026i
$195$		0			0
$196$	0.707107	+	0.707107i	0.707107	+	0.707107i
$197$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$197$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$198$	−0.0819895	+	1.04178i	−0.0819895	+	1.04178i
$199$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$199$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$200$	0.156434	−	0.987688i	0.156434	−	0.987688i
$201$	0.398090	−	0.243950i	0.398090	−	0.243950i
$202$		0			0
$203$		0			0
$204$	−1.84206	−	0.144974i	−1.84206	−	0.144974i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.09811	−	0.797826i	1.09811	−	0.797826i
$210$		0			0
$211$	−0.763007	−	0.0600500i	−0.763007	−	0.0600500i	−0.309017	−	0.951057i	$-0.600000\pi$
$211$	−0.763007	−	0.0600500i	−0.763007	−	0.0600500i	−0.453990	+	0.891007i	$0.650000\pi$
$212$		0			0
$213$		0			0
$214$	−0.831254	+	0.831254i	−0.831254	+	0.831254i
$215$		0			0
$216$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$217$		0			0
$218$		0			0
$219$	0.280582	−	0.550672i	0.280582	−	0.550672i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$223$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$224$		0			0
$225$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$226$	−0.809017	−	1.58779i	−0.809017	−	1.58779i
$227$	0.581990	+	0.497066i	0.581990	+	0.497066i	0.891007	−	0.453990i	$-0.150000\pi$
$227$	0.581990	+	0.497066i	0.581990	+	0.497066i	−0.309017	+	0.951057i	$0.600000\pi$
$228$	1.26301	−	0.303221i	1.26301	−	0.303221i
$229$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$229$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.29671	−	1.10749i	1.29671	−	1.10749i	0.309017	−	0.951057i	$-0.400000\pi$
$233$	1.29671	−	1.10749i	1.29671	−	1.10749i	0.987688	−	0.156434i	$-0.0500000\pi$
$234$		0			0
$235$		0			0
$236$	1.14412	+	0.831254i	1.14412	+	0.831254i
$237$		0			0
$238$		0			0
$239$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$239$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$240$		0			0
$241$	1.16110	+	0.183900i	1.16110	+	0.183900i	0.707107	−	0.707107i	$-0.250000\pi$
$241$	1.16110	+	0.183900i	1.16110	+	0.183900i	0.453990	+	0.891007i	$0.350000\pi$
$242$	0.0540874	+	0.0744449i	0.0540874	+	0.0744449i
$243$	1.00000			1.00000
$244$		0			0
$245$		0			0
$246$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$247$		0			0
$248$		0			0
$249$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$250$		0			0
$251$	1.95106	+	0.309017i	1.95106	+	0.309017i	1.00000			$0$
$251$	1.95106	+	0.309017i	1.95106	+	0.309017i	0.951057	+	0.309017i	$0.100000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$257$	0.355026	−	1.47879i	0.355026	−	1.47879i	−0.453990	−	0.891007i	$-0.650000\pi$
$257$	0.355026	−	1.47879i	0.355026	−	1.47879i	0.809017	−	0.587785i	$-0.200000\pi$
$258$	1.53884	+	1.11803i	1.53884	+	1.11803i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.280582	+	0.863541i	−0.280582	+	0.863541i
$263$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$263$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$264$	0.243950	+	1.01612i	0.243950	+	1.01612i
$265$		0			0
$266$		0			0
$267$	1.79671	−	0.744220i	1.79671	−	0.744220i
$268$	0.303221	−	0.355026i	0.303221	−	0.355026i
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$		0			0
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$	−1.79671	+	0.431351i	−1.79671	+	0.431351i
$273$		0			0
$274$	0.497066	+	0.581990i	0.497066	+	0.581990i
$275$	−0.546010	+	0.891007i	−0.546010	+	0.891007i
$276$		0			0
$277$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$277$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$278$	−1.26007	+	1.26007i	−1.26007	+	1.26007i
$279$		0			0
$280$		0			0
$281$	−0.465451	−	0.0366318i	−0.465451	−	0.0366318i	−0.156434	−	0.987688i	$-0.550000\pi$
$281$	−0.465451	−	0.0366318i	−0.465451	−	0.0366318i	−0.309017	+	0.951057i	$0.600000\pi$
$282$		0			0
$283$	1.14412	−	0.831254i	1.14412	−	0.831254i	0.156434	−	0.987688i	$-0.450000\pi$
$283$	1.14412	−	0.831254i	1.14412	−	0.831254i	0.987688	+	0.156434i	$0.0500000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.156434	+	0.987688i	−0.156434	+	0.987688i
$289$	−1.09603	+	2.15108i	−1.09603	+	2.15108i
$290$		0			0
$291$	0.794622	+	1.29671i	0.794622	+	1.29671i
$292$	0.0966818	−	0.610425i	0.0966818	−	0.610425i
$293$		0			0		0.0784591	−	0.996917i	$-0.475000\pi$
$293$		0			0		−0.0784591	+	0.996917i	$0.525000\pi$
$294$		−	1.00000i		−	1.00000i
$295$		0			0
$296$		0			0
$297$	0.794622	−	0.678671i	0.794622	−	0.678671i
$298$		0			0
$299$		0			0
$300$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.10749	−	0.678671i	1.10749	−	0.678671i
$305$		0			0
$306$	1.20002	+	1.40505i	1.20002	+	1.40505i
$307$	−0.809017	+	0.412215i	−0.809017	+	0.412215i	−0.809017	−	0.587785i	$-0.800000\pi$
$307$	−0.809017	+	0.412215i	−0.809017	+	0.412215i			1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$311$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$312$		0			0
$313$	0.398090	+	1.65816i	0.398090	+	1.65816i	0.707107	+	0.707107i	$0.250000\pi$
$313$	0.398090	+	1.65816i	0.398090	+	1.65816i	−0.309017	+	0.951057i	$0.600000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$317$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.17557			1.17557
$322$		0			0
$323$	0.375450	−	2.37050i	0.375450	−	2.37050i
$324$	0.951057	−	0.309017i	0.951057	−	0.309017i
$325$		0			0
$326$	0.533698	−	1.04744i	0.533698	−	1.04744i
$327$		0			0
$328$			1.00000i			1.00000i
$329$		0			0
$330$		0			0
$331$	−0.581990	−	1.40505i	−0.581990	−	1.40505i	−0.891007	−	0.453990i	$-0.850000\pi$
$331$	−0.581990	−	1.40505i	−0.581990	−	1.40505i	0.309017	−	0.951057i	$-0.400000\pi$
$332$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.221232	+	0.221232i	−0.221232	+	0.221232i	−0.809017	−	0.587785i	$-0.800000\pi$
$337$	−0.221232	+	0.221232i	−0.221232	+	0.221232i	0.587785	+	0.809017i	$0.300000\pi$
$338$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$339$	−0.550672	+	1.69480i	−0.550672	+	1.69480i
$340$		0			0
$341$		0			0
$342$	−1.10749	−	0.678671i	−1.10749	−	0.678671i
$343$		0			0
$344$	1.80902	+	0.587785i	1.80902	+	0.587785i
$345$		0			0
$346$		0			0
$347$	−1.26301	+	1.47879i	−1.26301	+	1.47879i	−0.453990	+	0.891007i	$0.650000\pi$
$347$	−1.26301	+	1.47879i	−1.26301	+	1.47879i	−0.809017	+	0.587785i	$0.800000\pi$
$348$		0			0
$349$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$349$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$350$		0			0
$351$		0			0
$352$	0.546010	+	0.891007i	0.546010	+	0.891007i
$353$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$353$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$354$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$355$		0			0
$356$	1.47879	−	1.26301i	1.47879	−	1.26301i
$357$		0			0
$358$	−0.398090	+	1.65816i	−0.398090	+	1.65816i
$359$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$359$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$360$		0			0
$361$	0.107491	+	0.678671i	0.107491	+	0.678671i
$362$		0			0
$363$	0.0143949	−	0.0908861i	0.0143949	−	0.0908861i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$367$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$368$		0			0
$369$	0.891007	−	0.453990i	0.891007	−	0.453990i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$373$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$374$	1.90713	+	0.302060i	1.90713	+	0.302060i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.59811	+	1.16110i	1.59811	+	1.16110i	0.891007	+	0.453990i	$0.150000\pi$
$379$	1.59811	+	1.16110i	1.59811	+	1.16110i	0.707107	+	0.707107i	$0.250000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$383$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$384$	0.156434	+	0.987688i	0.156434	+	0.987688i
$385$		0			0
$386$	1.01612	+	1.65816i	1.01612	+	1.65816i
$387$	−0.297556	−	1.87869i	−0.297556	−	1.87869i
$388$	1.15643	+	0.987688i	1.15643	+	0.987688i
$389$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$389$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$390$		0			0
$391$		0			0
$392$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$393$	0.809017	−	0.412215i	0.809017	−	0.412215i
$394$		0			0
$395$		0			0
$396$	0.546010	−	0.891007i	0.546010	−	0.891007i
$397$		0			0		−0.649448	−	0.760406i	$-0.725000\pi$
$397$		0			0		0.649448	+	0.760406i	$0.275000\pi$
$398$		0			0
$399$		0			0
$400$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$401$	−1.14412	+	1.14412i	−1.14412	+	1.14412i	−0.156434	+	0.987688i	$0.550000\pi$
$401$	−1.14412	+	1.14412i	−1.14412	+	1.14412i	−0.987688	+	0.156434i	$0.950000\pi$
$402$	−0.465451	+	0.0366318i	−0.465451	+	0.0366318i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.57547	+	0.965451i	1.57547	+	0.965451i
$409$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$409$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$410$		0			0
$411$	0.0600500	−	0.763007i	0.0600500	−	0.763007i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.78201			1.78201
$418$	−1.34063	+	0.212335i	−1.34063	+	0.212335i
$419$	−1.34500	−	1.34500i	−1.34500	−	1.34500i	−0.891007	−	0.453990i	$-0.850000\pi$
$419$	−1.34500	−	1.34500i	−1.34500	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$420$		0			0
$421$		0			0		−0.972370	−	0.233445i	$-0.925000\pi$
$421$		0			0		0.972370	+	0.233445i	$0.0750000\pi$
$422$	0.652583	+	0.399903i	0.652583	+	0.399903i
$423$		0			0
$424$		0			0
$425$	0.431351	+	1.79671i	0.431351	+	1.79671i
$426$		0			0
$427$		0			0
$428$	1.11803	−	0.363271i	1.11803	−	0.363271i
$429$		0			0
$430$		0			0
$431$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$431$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$432$	0.809017	−	0.587785i	0.809017	−	0.587785i
$433$	−1.69480	+	0.550672i	−1.69480	+	0.550672i	−0.987688	−	0.156434i	$-0.950000\pi$
$433$	−1.69480	+	0.550672i	−1.69480	+	0.550672i	−0.707107	+	0.707107i	$0.750000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$439$		0			0		−0.852640	−	0.522499i	$-0.825000\pi$
$439$		0			0		0.852640	+	0.522499i	$0.175000\pi$
$440$		0			0
$441$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$442$		0			0
$443$	0.309017	−	0.0489435i	0.309017	−	0.0489435i		−	1.00000i	$-0.5\pi$
$443$	0.309017	−	0.0489435i	0.309017	−	0.0489435i	0.309017	+	0.951057i	$0.400000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.412215	−	0.809017i	0.412215	−	0.809017i	−0.587785	−	0.809017i	$-0.700000\pi$
$449$	0.412215	−	0.809017i	0.412215	−	0.809017i	1.00000			$0$
$450$	0.987688	+	0.156434i	0.987688	+	0.156434i
$451$	0.399903	−	0.965451i	0.399903	−	0.965451i
$452$			1.78201i			1.78201i
$453$		0			0
$454$	−0.292893	−	0.707107i	−0.292893	−	0.707107i
$455$		0			0
$456$	−1.26301	−	0.303221i	−1.26301	−	0.303221i
$457$	−0.465451	−	0.0366318i	−0.465451	−	0.0366318i	−0.156434	−	0.987688i	$-0.550000\pi$
$457$	−0.465451	−	0.0366318i	−0.465451	−	0.0366318i	−0.309017	+	0.951057i	$0.600000\pi$
$458$		0			0
$459$	0.144974	−	1.84206i	0.144974	−	1.84206i
$460$		0			0
$461$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$461$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$462$		0			0
$463$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$463$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$464$		0			0
$465$		0			0
$466$	−1.65816	+	0.398090i	−1.65816	+	0.398090i
$467$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i	0.156434	−	0.987688i	$-0.450000\pi$
$467$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i	−0.453990	+	0.891007i	$0.650000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$473$	−1.51146	−	1.29091i	−1.51146	−	1.29091i
$474$		0			0
$475$	−0.678671	−	1.10749i	−0.678671	−	1.10749i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$479$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$480$		0			0
$481$		0			0
$482$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$483$		0			0
$484$	−0.0143949	−	0.0908861i	−0.0143949	−	0.0908861i
$485$		0			0
$486$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$487$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$487$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$488$		0			0
$489$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$490$		0			0
$491$	−1.97538			−1.97538			−0.987688	−	0.156434i	$-0.950000\pi$
$491$	−1.97538			−1.97538			−0.987688	+	0.156434i	$0.950000\pi$
$492$	0.707107	−	0.707107i	0.707107	−	0.707107i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.59811	+	0.253116i	1.59811	+	0.253116i
$499$	1.93874	−	0.152583i	1.93874	−	0.152583i	0.951057	−	0.309017i	$-0.100000\pi$
$499$	1.93874	−	0.152583i	1.93874	−	0.152583i	0.987688	+	0.156434i	$0.0500000\pi$
$500$		0			0
$501$		0			0
$502$	−1.59811	−	1.16110i	−1.59811	−	1.16110i
$503$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$503$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.987688	−	0.156434i	0.987688	−	0.156434i
$508$		0			0
$509$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$509$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$510$		0			0
$511$		0			0
$512$	0.453990	+	0.891007i	0.453990	+	0.891007i
$513$	0.303221	+	1.26301i	0.303221	+	1.26301i
$514$	−0.987688	+	1.15643i	−0.987688	+	1.15643i
$515$		0			0
$516$	−0.863541	−	1.69480i	−0.863541	−	1.69480i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.891007	+	1.45399i	−0.891007	+	1.45399i			1.00000i	$0.5\pi$
$521$	−0.891007	+	1.45399i	−0.891007	+	1.45399i	−0.891007	+	0.453990i	$0.850000\pi$
$522$		0			0
$523$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$523$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$524$	0.642040	−	0.642040i	0.642040	−	0.642040i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.243950	−	1.01612i	0.243950	−	1.01612i
$529$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$530$		0			0
$531$	−0.831254	+	1.14412i	−0.831254	+	1.14412i
$532$		0			0
$533$		0			0
$534$	−1.93874	−	0.152583i	−1.93874	−	0.152583i
$535$		0			0
$536$	−0.431351	+	0.178671i	−0.431351	+	0.178671i
$537$	1.45399	−	0.891007i	1.45399	−	0.891007i
$538$		0			0
$539$	−0.0819895	+	1.04178i	−0.0819895	+	1.04178i
$540$		0			0
$541$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$541$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$542$		0			0
$543$		0			0
$544$	1.79671	+	0.431351i	1.79671	+	0.431351i
$545$		0			0
$546$		0			0
$547$	−0.581990	+	1.40505i	−0.581990	+	1.40505i	0.309017	+	0.951057i	$0.400000\pi$
$547$	−0.581990	+	1.40505i	−0.581990	+	1.40505i	−0.891007	+	0.453990i	$0.850000\pi$
$548$	−0.178671	−	0.744220i	−0.178671	−	0.744220i
$549$		0			0
$550$	0.891007	−	0.546010i	0.891007	−	0.546010i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.69480	−	0.550672i	1.69480	−	0.550672i
$557$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$557$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.13496	−	1.56213i	−1.13496	−	1.56213i
$562$	0.398090	+	0.243950i	0.398090	+	0.243950i
$563$	1.93874	+	0.465451i	1.93874	+	0.465451i	0.987688	+	0.156434i	$0.0500000\pi$
$563$	1.93874	+	0.465451i	1.93874	+	0.465451i	0.951057	+	0.309017i	$0.100000\pi$
$564$		0			0
$565$		0			0
$566$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$567$		0			0
$568$		0			0
$569$	−0.183900	+	1.16110i	−0.183900	+	1.16110i	0.707107	+	0.707107i	$0.250000\pi$
$569$	−0.183900	+	1.16110i	−0.183900	+	1.16110i	−0.891007	+	0.453990i	$0.850000\pi$
$570$		0			0
$571$	0.144974	−	0.0600500i	0.144974	−	0.0600500i	−0.309017	−	0.951057i	$-0.600000\pi$
$571$	0.144974	−	0.0600500i	0.144974	−	0.0600500i	0.453990	+	0.891007i	$0.350000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.587785	−	0.809017i	0.587785	−	0.809017i
$577$	−0.0600500	−	0.144974i	−0.0600500	−	0.144974i	0.891007	−	0.453990i	$-0.150000\pi$
$577$	−0.0600500	−	0.144974i	−0.0600500	−	0.144974i	−0.951057	+	0.309017i	$0.900000\pi$
$578$	1.95314	−	1.41904i	1.95314	−	1.41904i
$579$	0.453990	−	1.89101i	0.453990	−	1.89101i
$580$		0			0
$581$		0			0
$582$	−0.119322	−	1.51612i	−0.119322	−	1.51612i
$583$		0			0
$584$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$585$		0			0
$586$		0			0
$587$	−0.303221	−	0.355026i	−0.303221	−	0.355026i	0.587785	−	0.809017i	$-0.300000\pi$
$587$	−0.303221	−	0.355026i	−0.303221	−	0.355026i	−0.891007	+	0.453990i	$0.850000\pi$
$588$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.29489	−	1.51612i	1.29489	−	1.51612i	0.587785	−	0.809017i	$-0.300000\pi$
$593$	1.29489	−	1.51612i	1.29489	−	1.51612i	0.707107	−	0.707107i	$-0.250000\pi$
$594$	−1.01612	+	0.243950i	−1.01612	+	0.243950i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	0.987688	−	0.156434i	0.987688	−	0.156434i
$601$	−1.57547	−	0.652583i	−1.57547	−	0.652583i	−0.587785	−	0.809017i	$-0.700000\pi$
$601$	−1.57547	−	0.652583i	−1.57547	−	0.652583i	−0.987688	+	0.156434i	$0.950000\pi$
$602$		0			0
$603$	0.355026	+	0.303221i	0.355026	+	0.303221i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$607$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$608$	−1.29489	+	0.101910i	−1.29489	+	0.101910i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.431351	−	1.79671i	−0.431351	−	1.79671i
$613$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$613$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$614$	0.907981			0.907981
$615$		0			0
$616$		0			0
$617$	−1.76007	−	0.896802i	−1.76007	−	0.896802i	−0.951057	−	0.309017i	$-0.900000\pi$
$617$	−1.76007	−	0.896802i	−1.76007	−	0.896802i	−0.809017	−	0.587785i	$-0.800000\pi$
$618$		0			0
$619$	−1.16110	−	1.59811i	−1.16110	−	1.59811i	−0.707107	−	0.707107i	$-0.750000\pi$
$619$	−1.16110	−	1.59811i	−1.16110	−	1.59811i	−0.453990	−	0.891007i	$-0.650000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.809017	+	0.587785i	0.809017	+	0.587785i
$626$	0.398090	−	1.65816i	0.398090	−	1.65816i
$627$	1.09811	+	0.797826i	1.09811	+	0.797826i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$631$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$632$		0			0
$633$	−0.178671	−	0.744220i	−0.178671	−	0.744220i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.93874	+	0.465451i	−1.93874	+	0.465451i	−0.951057	+	0.309017i	$0.900000\pi$
$641$	−1.93874	+	0.465451i	−1.93874	+	0.465451i	−0.987688	+	0.156434i	$0.950000\pi$
$642$	−1.04744	−	0.533698i	−1.04744	−	0.533698i
$643$	−0.497066	−	0.581990i	−0.497066	−	0.581990i	0.453990	−	0.891007i	$-0.350000\pi$
$643$	−0.497066	−	0.581990i	−0.497066	−	0.581990i	−0.951057	+	0.309017i	$0.900000\pi$
$644$		0			0
$645$		0			0
$646$	−1.41071	+	1.94168i	−1.41071	+	1.94168i
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$649$	0.115951	+	1.47329i	0.115951	+	1.47329i
$650$		0			0
$651$		0			0
$652$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$653$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$653$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$654$		0			0
$655$		0			0
$656$	0.453990	−	0.891007i	0.453990	−	0.891007i
$657$	0.610425	+	0.0966818i	0.610425	+	0.0966818i
$658$		0			0
$659$	−0.707107	+	0.292893i	−0.707107	+	0.292893i	−0.707107	−	0.707107i	$-0.750000\pi$
$659$	−0.707107	+	0.292893i	−0.707107	+	0.292893i			1.00000i	$0.5\pi$
$660$		0			0
$661$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$661$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$662$	−0.119322	+	1.51612i	−0.119322	+	1.51612i
$663$		0			0
$664$	1.59811	−	0.253116i	1.59811	−	0.253116i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.133795	+	0.0819895i	−0.133795	+	0.0819895i	−0.587785	−	0.809017i	$-0.700000\pi$
$673$	−0.133795	+	0.0819895i	−0.133795	+	0.0819895i	0.453990	+	0.891007i	$0.350000\pi$
$674$	0.297556	−	0.0966818i	0.297556	−	0.0966818i
$675$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$676$	0.891007	−	0.453990i	0.891007	−	0.453990i
$677$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$677$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$678$	1.26007	−	1.26007i	1.26007	−	1.26007i
$679$		0			0
$680$		0			0
$681$	−0.292893	+	0.707107i	−0.292893	+	0.707107i
$682$		0			0
$683$	−0.652583	+	1.57547i	−0.652583	+	1.57547i	0.156434	+	0.987688i	$0.450000\pi$
$683$	−0.652583	+	1.57547i	−0.652583	+	1.57547i	−0.809017	+	0.587785i	$0.800000\pi$
$684$	0.678671	+	1.10749i	0.678671	+	1.10749i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.34500	−	1.34500i	−1.34500	−	1.34500i
$689$		0			0
$690$		0			0
$691$	0.0123117	−	0.156434i	0.0123117	−	0.156434i	−0.987688	−	0.156434i	$-0.950000\pi$
$691$	0.0123117	−	0.156434i	0.0123117	−	0.156434i	1.00000			$0$
$692$		0			0
$693$		0			0
$694$	1.79671	−	0.744220i	1.79671	−	0.744220i
$695$		0			0
$696$		0			0
$697$	−0.707107	−	1.70711i	−0.707107	−	1.70711i
$698$		0			0
$699$	1.45399	+	0.891007i	1.45399	+	0.891007i
$700$		0			0
$701$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$701$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$702$		0			0
$703$		0			0
$704$	−0.0819895	−	1.04178i	−0.0819895	−	1.04178i
$705$		0			0
$706$	1.34500	−	1.34500i	1.34500	−	1.34500i
$707$		0			0
$708$	−0.437016	+	1.34500i	−0.437016	+	1.34500i
$709$		0			0		0.522499	−	0.852640i	$-0.325000\pi$
$709$		0			0		−0.522499	+	0.852640i	$0.675000\pi$
$710$		0			0
$711$		0			0
$712$	−1.89101	+	0.453990i	−1.89101	+	0.453990i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.10749	−	1.29671i	1.10749	−	1.29671i
$717$		0			0
$718$		0			0
$719$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$719$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$720$		0			0
$721$		0			0
$722$	0.212335	−	0.653500i	0.212335	−	0.653500i
$723$	0.183900	+	1.16110i	0.183900	+	1.16110i
$724$		0			0
$725$		0			0
$726$	−0.0540874	+	0.0744449i	−0.0540874	+	0.0744449i
$727$		0			0		0.233445	−	0.972370i	$-0.425000\pi$
$727$		0			0		−0.233445	+	0.972370i	$0.575000\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.309017	+	0.951057i
$730$		0			0
$731$	−3.50381	+	0.275756i	−3.50381	+	0.275756i
$732$		0			0
$733$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$733$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.487899			0.487899
$738$	−1.00000			−1.00000
$739$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$739$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$743$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$748$	−1.56213	−	1.13496i	−1.56213	−	1.13496i
$749$		0			0
$750$		0			0
$751$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$751$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$752$		0			0
$753$	0.309017	+	1.95106i	0.309017	+	1.95106i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.760406	−	0.649448i	$-0.775000\pi$
$757$		0			0		0.760406	+	0.649448i	$0.225000\pi$
$758$	−0.896802	−	1.76007i	−0.896802	−	1.76007i
$759$		0			0
$760$		0			0
$761$	0.437016	+	1.34500i	0.437016	+	1.34500i	0.891007	+	0.453990i	$0.150000\pi$
$761$	0.437016	+	1.34500i	0.437016	+	1.34500i	−0.453990	+	0.891007i	$0.650000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.309017	−	0.951057i	0.309017	−	0.951057i
$769$	1.11803	−	1.53884i	1.11803	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$769$	1.11803	−	1.53884i	1.11803	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$770$		0			0
$771$	1.51612	−	0.119322i	1.51612	−	0.119322i
$772$	−0.152583	−	1.93874i	−0.152583	−	1.93874i
$773$		0			0		−0.996917	−	0.0784591i	$-0.975000\pi$
$773$		0			0		0.996917	+	0.0784591i	$0.0250000\pi$
$774$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$775$		0			0
$776$	−0.581990	−	1.40505i	−0.581990	−	1.40505i
$777$		0			0
$778$		0			0
$779$	0.843566	+	0.987688i	0.843566	+	0.987688i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.156434	+	0.987688i	−0.156434	+	0.987688i
$785$		0			0
$786$	−0.907981			−0.907981
$787$	1.95106	−	0.309017i	1.95106	−	0.309017i	0.951057	−	0.309017i	$-0.100000\pi$
$787$	1.95106	−	0.309017i	1.95106	−	0.309017i	1.00000			$0$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.891007	+	0.546010i	−0.891007	+	0.546010i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$797$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$798$		0			0
$799$		0			0
$800$	0.891007	−	0.453990i	0.891007	−	0.453990i
$801$	1.26301	+	1.47879i	1.26301	+	1.47879i
$802$	1.53884	−	0.500000i	1.53884	−	0.500000i
$803$	0.550672	−	0.337452i	0.550672	−	0.337452i
$804$	0.431351	+	0.178671i	0.431351	+	0.178671i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.26301	−	0.303221i	−1.26301	−	0.303221i	−0.453990	−	0.891007i	$-0.650000\pi$
$809$	−1.26301	−	0.303221i	−1.26301	−	0.303221i	−0.809017	+	0.587785i	$0.800000\pi$
$810$		0			0
$811$	−0.221232	−	0.221232i	−0.221232	−	0.221232i	0.587785	−	0.809017i	$-0.300000\pi$
$811$	−0.221232	−	0.221232i	−0.221232	−	0.221232i	−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.965451	−	1.57547i	−0.965451	−	1.57547i
$817$	2.28258	−	0.945476i	2.28258	−	0.945476i
$818$	0.734572	−	1.44168i	0.734572	−	1.44168i
$819$		0			0
$820$		0			0
$821$		0			0			−	1.00000i	$-0.5\pi$
$821$		0			0				1.00000i	$0.5\pi$
$822$	−0.399903	+	0.652583i	−0.399903	+	0.652583i
$823$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$823$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$824$		0			0
$825$	−1.01612	−	0.243950i	−1.01612	−	0.243950i
$826$		0			0
$827$	0.156434	+	1.98769i	0.156434	+	1.98769i	0.156434	+	0.987688i	$0.450000\pi$
$827$	0.156434	+	1.98769i	0.156434	+	1.98769i			1.00000i	$0.500000\pi$
$828$		0			0
$829$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$829$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.20002	+	1.40505i	1.20002	+	1.40505i
$834$	−1.58779	−	0.809017i	−1.58779	−	0.809017i
$835$		0			0
$836$	1.29091	+	0.419442i	1.29091	+	0.419442i
$837$		0			0
$838$	0.587785	+	1.80902i	0.587785	+	1.80902i
$839$		0			0		0.649448	−	0.760406i	$-0.275000\pi$
$839$		0			0		−0.649448	+	0.760406i	$0.725000\pi$
$840$		0			0
$841$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$842$		0			0
$843$	−0.108993	−	0.453990i	−0.108993	−	0.453990i
$844$	−0.399903	−	0.652583i	−0.399903	−	0.652583i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.14412	+	0.831254i	1.14412	+	0.831254i
$850$	0.431351	−	1.79671i	0.431351	−	1.79671i
$851$		0			0
$852$		0			0
$853$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$853$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$854$		0			0
$855$		0			0
$856$	−1.16110	−	0.183900i	−1.16110	−	0.183900i
$857$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$857$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$858$		0			0
$859$	0.278768	+	0.142040i	0.278768	+	0.142040i	0.587785	−	0.809017i	$-0.300000\pi$
$859$	0.278768	+	0.142040i	0.278768	+	0.142040i	−0.309017	+	0.951057i	$0.600000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$863$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$864$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$865$		0			0
$866$	1.76007	+	0.278768i	1.76007	+	0.278768i
$867$	−2.38449	−	0.377666i	−2.38449	−	0.377666i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.987688	+	1.15643i	−0.987688	+	1.15643i
$874$		0			0
$875$		0			0
$876$	0.610425	−	0.0966818i	0.610425	−	0.0966818i
$877$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$877$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.533698	+	1.04744i	0.533698	+	1.04744i	0.987688	+	0.156434i	$0.0500000\pi$
$881$	0.533698	+	1.04744i	0.533698	+	1.04744i	−0.453990	+	0.891007i	$0.650000\pi$
$882$	0.951057	−	0.309017i	0.951057	−	0.309017i
$883$	−0.101910	+	0.119322i	−0.101910	+	0.119322i	−0.809017	−	0.587785i	$-0.800000\pi$
$883$	−0.101910	+	0.119322i	−0.101910	+	0.119322i	0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$		0			0
$886$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i
$887$		0			0		0.972370	−	0.233445i	$-0.0750000\pi$
$887$		0			0		−0.972370	+	0.233445i	$0.925000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.891007	+	0.546010i	0.891007	+	0.546010i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.734572	+	0.533698i	−0.734572	+	0.533698i
$899$		0			0
$900$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$901$		0			0
$902$	−0.794622	+	0.678671i	−0.794622	+	0.678671i
$903$		0			0
$904$	0.809017	−	1.58779i	0.809017	−	1.58779i
$905$		0			0
$906$		0			0
$907$	−0.278768	+	1.76007i	−0.278768	+	1.76007i	0.309017	+	0.951057i	$0.400000\pi$
$907$	−0.278768	+	1.76007i	−0.278768	+	1.76007i	−0.587785	+	0.809017i	$0.700000\pi$
$908$	−0.0600500	+	0.763007i	−0.0600500	+	0.763007i
$909$		0			0
$910$		0			0
$911$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$911$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$912$	0.987688	+	0.843566i	0.987688	+	0.843566i
$913$	−1.64412	−	0.394719i	−1.64412	−	0.394719i
$914$	0.398090	+	0.243950i	0.398090	+	0.243950i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.965451	+	1.57547i	−0.965451	+	1.57547i
$919$		0			0		0.852640	−	0.522499i	$-0.175000\pi$
$919$		0			0		−0.852640	+	0.522499i	$0.825000\pi$
$920$		0			0
$921$	−0.642040	−	0.642040i	−0.642040	−	0.642040i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.292893	+	0.707107i	−0.292893	+	0.707107i	0.707107	+	0.707107i	$0.250000\pi$
$929$	−0.292893	+	0.707107i	−0.292893	+	0.707107i	−1.00000			$\pi$
$930$		0			0
$931$	−1.10749	−	0.678671i	−1.10749	−	0.678671i
$932$	1.65816	+	0.398090i	1.65816	+	0.398090i
$933$		0			0
$934$	0.221232	+	0.221232i	0.221232	+	0.221232i
$935$		0			0
$936$		0			0
$937$	0.144974	−	1.84206i	0.144974	−	1.84206i	−0.309017	−	0.951057i	$-0.600000\pi$
$937$	0.144974	−	1.84206i	0.144974	−	1.84206i	0.453990	−	0.891007i	$-0.350000\pi$
$938$		0			0
$939$	−1.45399	+	0.891007i	−1.45399	+	0.891007i
$940$		0			0
$941$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$941$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$942$		0			0
$943$		0			0
$944$			1.41421i			1.41421i
$945$		0			0
$946$	0.760661	+	1.83640i	0.760661	+	1.83640i
$947$	0.734572	−	0.533698i	0.734572	−	0.533698i	−0.156434	−	0.987688i	$-0.550000\pi$
$947$	0.734572	−	0.533698i	0.734572	−	0.533698i	0.891007	+	0.453990i	$0.150000\pi$
$948$		0			0
$949$		0			0
$950$	0.101910	+	1.29489i	0.101910	+	1.29489i
$951$		0			0
$952$		0			0
$953$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$953$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$962$		0			0
$963$	0.363271	+	1.11803i	0.363271	+	1.11803i
$964$	0.533698	+	1.04744i	0.533698	+	1.04744i
$965$		0			0
$966$		0			0
$967$		0			0		−0.522499	−	0.852640i	$-0.675000\pi$
$967$		0			0		0.522499	+	0.852640i	$0.325000\pi$
$968$	−0.0284354	+	0.0875153i	−0.0284354	+	0.0875153i
$969$	2.37050	−	0.375450i	2.37050	−	0.375450i
$970$		0			0
$971$	0.355026	−	0.303221i	0.355026	−	0.303221i	−0.453990	−	0.891007i	$-0.650000\pi$
$971$	0.355026	−	0.303221i	0.355026	−	0.303221i	0.809017	+	0.587785i	$0.200000\pi$
$972$	0.587785	+	0.809017i	0.587785	+	0.809017i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.98769	−	0.156434i	1.98769	−	0.156434i	0.987688	−	0.156434i	$-0.0500000\pi$
$977$	1.98769	−	0.156434i	1.98769	−	0.156434i	1.00000			$0$
$978$	1.16110	+	0.183900i	1.16110	+	0.183900i
$979$	2.00723	+	0.317914i	2.00723	+	0.317914i
$980$		0			0
$981$		0			0
$982$	1.76007	+	0.896802i	1.76007	+	0.896802i
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.996917	−	0.0784591i	$-0.0250000\pi$
$991$		0			0		−0.996917	+	0.0784591i	$0.975000\pi$
$992$		0			0
$993$	1.15643	−	0.987688i	1.15643	−	0.987688i
$994$		0			0
$995$		0			0
$996$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$997$		0			0		0.760406	−	0.649448i	$-0.225000\pi$
$997$		0			0		−0.760406	+	0.649448i	$0.775000\pi$
$998$	−1.79671	−	0.744220i	−1.79671	−	0.744220i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	984.1.cj.a.539.1	✓	16
3.2	odd	2		984.1.cj.b.539.1	yes	16
4.3	odd	2		3936.1.fx.b.47.1		16
8.3	odd	2	CM	984.1.cj.a.539.1	✓	16
8.5	even	2		3936.1.fx.b.47.1		16
12.11	even	2		3936.1.fx.a.47.1		16
24.5	odd	2		3936.1.fx.a.47.1		16
24.11	even	2		984.1.cj.b.539.1	yes	16
41.7	odd	40		984.1.cj.b.827.1	yes	16
123.89	even	40	inner	984.1.cj.a.827.1	yes	16
164.7	even	40		3936.1.fx.a.335.1		16
328.171	even	40		984.1.cj.b.827.1	yes	16
328.253	odd	40		3936.1.fx.a.335.1		16
492.335	odd	40		3936.1.fx.b.335.1		16
984.581	even	40		3936.1.fx.b.335.1		16
984.827	odd	40	inner	984.1.cj.a.827.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
984.1.cj.a.539.1	✓	16	1.1	even	1	trivial
984.1.cj.a.539.1	✓	16	8.3	odd	2	CM
984.1.cj.a.827.1	yes	16	123.89	even	40	inner
984.1.cj.a.827.1	yes	16	984.827	odd	40	inner
984.1.cj.b.539.1	yes	16	3.2	odd	2
984.1.cj.b.539.1	yes	16	24.11	even	2
984.1.cj.b.827.1	yes	16	41.7	odd	40
984.1.cj.b.827.1	yes	16	328.171	even	40
3936.1.fx.a.47.1		16	12.11	even	2
3936.1.fx.a.47.1		16	24.5	odd	2
3936.1.fx.a.335.1		16	164.7	even	40
3936.1.fx.a.335.1		16	328.253	odd	40
3936.1.fx.b.47.1		16	4.3	odd	2
3936.1.fx.b.47.1		16	8.5	even	2
3936.1.fx.b.335.1		16	492.335	odd	40
3936.1.fx.b.335.1		16	984.581	even	40

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:	\( N \)	\(=\)	\( 984 = 2^{3} \cdot 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	984.cj (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.156434 - 0.987688i) q^{6} +(-0.156434 - 0.987688i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.156434 - 0.987688i) q^{6} +(-0.156434 - 0.987688i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.243950 + 1.01612i) q^{11} +(-0.587785 + 0.809017i) q^{12} +(-0.309017 + 0.951057i) q^{16} +(0.965451 + 1.57547i) q^{17} +(0.987688 - 0.156434i) q^{18} +(-0.987688 - 0.843566i) q^{19} +(0.678671 - 0.794622i) q^{22} +(0.891007 - 0.453990i) q^{24} +(0.951057 + 0.309017i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(0.707107 - 0.707107i) q^{32} +(-1.04178 + 0.0819895i) q^{33} +(-0.144974 - 1.84206i) q^{34} +(-0.951057 - 0.309017i) q^{36} +(0.497066 + 1.20002i) q^{38} +(-0.987688 - 0.156434i) q^{41} +(-0.863541 + 1.69480i) q^{43} +(-0.965451 + 0.399903i) q^{44} -1.00000 q^{48} +(0.987688 - 0.156434i) q^{49} +(-0.707107 - 0.707107i) q^{50} +(-1.20002 + 1.40505i) q^{51} +(0.453990 + 0.891007i) q^{54} +(0.497066 - 1.20002i) q^{57} +(1.34500 - 0.437016i) q^{59} +(-0.951057 + 0.309017i) q^{64} +(0.965451 + 0.399903i) q^{66} +(-0.108993 - 0.453990i) q^{67} +(-0.707107 + 1.70711i) q^{68} +(0.707107 + 0.707107i) q^{72} +(-0.437016 - 0.437016i) q^{73} +1.00000i q^{75} +(0.101910 - 1.29489i) q^{76} +(0.309017 - 0.951057i) q^{81} +(0.809017 + 0.587785i) q^{82} +1.61803i q^{83} +(1.53884 - 1.11803i) q^{86} +(1.04178 + 0.0819895i) q^{88} +(-0.152583 - 1.93874i) q^{89} +(0.891007 + 0.453990i) q^{96} +(1.47879 - 0.355026i) q^{97} +(-0.951057 - 0.309017i) q^{98} +(-0.399903 - 0.965451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 4 * q^9	\( 16 q - 4 q^{3} - 4 q^{9} + 4 q^{16} + 4 q^{17} + 4 q^{22} - 4 q^{27} - 4 q^{34} - 4 q^{44} - 16 q^{48} + 4 q^{51} + 4 q^{66} - 16 q^{67} + 4 q^{76} - 4 q^{81} + 4 q^{82} + 4 q^{89}+O(q^{100}) \) 16 * q - 4 * q^3 - 4 * q^9 + 4 * q^16 + 4 * q^17 + 4 * q^22 - 4 * q^27 - 4 * q^34 - 4 * q^44 - 16 * q^48 + 4 * q^51 + 4 * q^66 - 16 * q^67 + 4 * q^76 - 4 * q^81 + 4 * q^82 + 4 * q^89

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