LMFDB - Embedded newform 1078.2.e.b.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1078.67
Dual form			1078.2.e.b.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(1.50000 - 2.59808i) q^{18} +2.00000 q^{20} -1.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -2.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +2.00000 q^{34} -3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{40} +10.0000 q^{41} +4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(3.00000 - 5.19615i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-4.00000 - 6.92820i) q^{47} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} -2.00000 q^{55} +(1.00000 + 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(6.00000 - 10.3923i) q^{67} +(-1.00000 - 1.73205i) q^{68} +16.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-5.00000 - 8.66025i) q^{82} +4.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} -6.00000 q^{90} -8.00000 q^{92} +(-4.00000 + 6.92820i) q^{94} +10.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9} - 2 q^{10} + q^{11} + 4 q^{13} - q^{16} - 2 q^{17} + 3 q^{18} + 4 q^{20} - 2 q^{22} + 8 q^{23} + q^{25} - 2 q^{26} - 4 q^{29} + 8 q^{31} - q^{32} + 4 q^{34} - 6 q^{36} + 2 q^{37} - 2 q^{40} + 20 q^{41} + 8 q^{43} + q^{44} + 6 q^{45} + 8 q^{46} - 8 q^{47} - 2 q^{50} - 2 q^{52} - 6 q^{53} - 4 q^{55} + 2 q^{58} - 10 q^{61} - 16 q^{62} + 2 q^{64} - 4 q^{65} + 12 q^{67} - 2 q^{68} + 32 q^{71} + 3 q^{72} + 14 q^{73} + 2 q^{74} - 2 q^{80} - 9 q^{81} - 10 q^{82} + 8 q^{85} - 4 q^{86} + q^{88} + 6 q^{89} - 12 q^{90} - 16 q^{92} - 8 q^{94} + 20 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9 - 2 * q^10 + q^11 + 4 * q^13 - q^16 - 2 * q^17 + 3 * q^18 + 4 * q^20 - 2 * q^22 + 8 * q^23 + q^25 - 2 * q^26 - 4 * q^29 + 8 * q^31 - q^32 + 4 * q^34 - 6 * q^36 + 2 * q^37 - 2 * q^40 + 20 * q^41 + 8 * q^43 + q^44 + 6 * q^45 + 8 * q^46 - 8 * q^47 - 2 * q^50 - 2 * q^52 - 6 * q^53 - 4 * q^55 + 2 * q^58 - 10 * q^61 - 16 * q^62 + 2 * q^64 - 4 * q^65 + 12 * q^67 - 2 * q^68 + 32 * q^71 + 3 * q^72 + 14 * q^73 + 2 * q^74 - 2 * q^80 - 9 * q^81 - 10 * q^82 + 8 * q^85 - 4 * q^86 + q^88 + 6 * q^89 - 12 * q^90 - 16 * q^92 - 8 * q^94 + 20 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	−1.00000			−0.213201
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		0			0
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	2.00000			0.342997
$35$		0			0
$36$	−3.00000			−0.500000
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$		0			0
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	3.00000	−	5.19615i	0.447214	−	0.774597i
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$		0			0
$49$		0			0
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$		0			0
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$		0			0
$71$	16.0000			1.89885			0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000			1.89885			0.949425	+	0.313993i	$0.101667\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−5.00000	−	8.66025i	−0.552158	−	0.956365i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$	−8.00000			−0.834058
$93$		0			0
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$		0			0
$96$		0			0
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$		0			0
$99$	3.00000			0.301511
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	6.00000			0.582772
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$		0			0
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$	8.00000	−	13.8564i	0.746004	−	1.29212i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$		0			0
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000			−1.03664
$135$		0			0
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$		0			0
$142$	−8.00000	−	13.8564i	−0.671345	−	1.16280i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	2.00000	+	3.46410i	0.166091	+	0.287678i
$146$	−14.0000			−1.15865
$147$		0			0
$148$	−2.00000			−0.164399
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$		0			0
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$		0			0
$159$		0			0
$160$	2.00000			0.158114
$161$		0			0
$162$	9.00000			0.707107
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$	−5.00000	+	8.66025i	−0.390434	+	0.676252i
$165$		0			0
$166$		0			0
$167$	16.0000			1.23812			0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000			1.23812			0.619059	+	0.785345i	$0.287514\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−2.00000	−	3.46410i	−0.153393	−	0.265684i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		0			0
$175$		0			0
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$	3.00000	+	5.19615i	0.223607	+	0.387298i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$		0			0
$184$	4.00000	+	6.92820i	0.294884	+	0.510754i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	8.00000			0.583460
$189$		0			0
$190$		0			0
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	18.0000			1.26648
$203$		0			0
$204$		0			0
$205$	−10.0000	−	17.3205i	−0.698430	−	1.20972i
$206$		0			0
$207$	−12.0000	+	20.7846i	−0.834058	+	1.44463i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$		0			0
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	−4.00000	−	6.92820i	−0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$	−2.00000			−0.135457
$219$		0			0
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	−1.00000	−	1.73205i	−0.0665190	−	0.115214i
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	0.468368	+	0.883534i	$0.344842\pi$
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	−0.999346	+	0.0361484i	$0.988491\pi$
$228$		0			0
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	−16.0000			−1.05501
$231$		0			0
$232$	−2.00000			−0.131306
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	−8.00000	+	13.8564i	−0.521862	+	0.903892i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$		0			0
$244$	10.0000			0.640184
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$		0			0
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.773427	+	0.633885i	$0.218541\pi$
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.162247	+	0.986750i	$0.448126\pi$
$258$		0			0
$259$		0			0
$260$	4.00000			0.248069
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$		0			0
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$		0			0
$277$	−15.0000	+	25.9808i	−0.901263	+	1.56103i	−0.0754058	+	0.997153i	$0.524025\pi$
$277$	−15.0000	+	25.9808i	−0.901263	+	1.56103i	−0.825857	+	0.563880i	$0.809308\pi$
$278$	8.00000	+	13.8564i	0.479808	+	0.831052i
$279$	24.0000			1.43684
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$		0			0
$283$	12.0000	−	20.7846i	0.713326	−	1.23552i	−0.250276	−	0.968175i	$-0.580521\pi$
$283$	12.0000	−	20.7846i	0.713326	−	1.23552i	0.963602	−	0.267342i	$-0.0861454\pi$
$284$	−8.00000	+	13.8564i	−0.474713	+	0.822226i
$285$		0			0
$286$	−2.00000			−0.118262
$287$		0			0
$288$	−3.00000			−0.176777
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	2.00000	−	3.46410i	0.117444	−	0.203419i
$291$		0			0
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	−30.0000			−1.75262			−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000			−1.75262			−0.876309	+	0.481749i	$0.840002\pi$
$294$		0			0
$295$		0			0
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$		0			0
$298$	−7.00000	+	12.1244i	−0.405499	+	0.702345i
$299$	8.00000	+	13.8564i	0.462652	+	0.801337i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.0000	+	17.3205i	−0.572598	+	0.991769i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$		0			0
$309$		0			0
$310$	8.00000	+	13.8564i	0.454369	+	0.786991i
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$		0			0
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$		0			0
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		0			0
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$	−1.00000	−	1.73205i	−0.0559017	−	0.0968246i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	1.00000	−	1.73205i	0.0554700	−	0.0960769i
$326$	10.0000	−	17.3205i	0.553849	−	0.959294i
$327$		0			0
$328$	10.0000			0.552158
$329$		0			0
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$		0			0
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$	−8.00000	−	13.8564i	−0.437741	−	0.758189i
$335$	−24.0000			−1.31126
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$	−4.00000	−	6.92820i	−0.216612	−	0.375183i
$342$		0			0
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	7.00000	−	12.1244i	0.376322	−	0.651809i
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	−0.195507	−	0.980702i	$-0.562635\pi$
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	0.947067	−	0.321037i	$-0.104031\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$	−16.0000	−	27.7128i	−0.849192	−	1.47084i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	4.00000			0.211407
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	−0.886100	−	0.463494i	$-0.846596\pi$
$359$	−16.0000	−	27.7128i	−0.844448	−	1.46263i	0.0416523	−	0.999132i	$-0.486738\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	11.0000	+	19.0526i	0.578147	+	1.00138i
$363$		0			0
$364$		0			0
$365$	−28.0000			−1.46559
$366$		0			0
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$	4.00000	−	6.92820i	0.208514	−	0.361158i
$369$	15.0000	+	25.9808i	0.780869	+	1.35250i
$370$	−4.00000			−0.207950
$371$		0			0
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$	1.00000	−	1.73205i	0.0517088	−	0.0895622i
$375$		0			0
$376$	−4.00000	−	6.92820i	−0.206284	−	0.357295i
$377$	−4.00000			−0.206010
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$		0			0
$381$		0			0
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	−4.00000	−	6.92820i	−0.204390	−	0.354015i	0.745548	−	0.666452i	$-0.232188\pi$
$383$	−4.00000	−	6.92820i	−0.204390	−	0.354015i	−0.949938	+	0.312437i	$0.898855\pi$
$384$		0			0
$385$		0			0
$386$	2.00000			0.101797
$387$	6.00000	+	10.3923i	0.304997	+	0.528271i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	−9.00000	−	15.5885i	−0.451697	−	0.782362i	0.546795	−	0.837267i	$-0.315848\pi$
$397$	−9.00000	−	15.5885i	−0.451697	−	0.782362i	−0.998492	+	0.0549046i	$0.982515\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	8.00000	−	13.8564i	0.398508	−	0.690237i
$404$	−9.00000	−	15.5885i	−0.447767	−	0.775555i
$405$	18.0000			0.894427
$406$		0			0
$407$	2.00000			0.0991363
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	−10.0000	+	17.3205i	−0.493865	+	0.855399i
$411$		0			0
$412$		0			0
$413$		0			0
$414$	24.0000			1.17954
$415$		0			0
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		0			0
$418$		0			0
$419$	16.0000			0.781651			0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000			0.781651			0.390826	+	0.920465i	$0.372190\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	12.0000	−	20.7846i	0.583460	−	1.01058i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$	−4.00000			−0.193347
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	4.00000	−	6.92820i	0.192673	−	0.333720i	−0.753462	−	0.657491i	$-0.771618\pi$
$431$	4.00000	−	6.92820i	0.192673	−	0.333720i	0.946135	+	0.323772i	$0.104951\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$		0			0
$438$		0			0
$439$	−20.0000	−	34.6410i	−0.954548	−	1.65333i	−0.735399	−	0.677634i	$-0.763005\pi$
$439$	−20.0000	−	34.6410i	−0.954548	−	1.65333i	−0.219149	−	0.975691i	$-0.570328\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$	4.00000			0.190261
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	−1.50000	−	2.59808i	−0.0707107	−	0.122474i
$451$	5.00000	−	8.66025i	0.235441	−	0.407795i
$452$	−1.00000	+	1.73205i	−0.0470360	+	0.0814688i
$453$		0			0
$454$	16.0000			0.750917
$455$		0			0
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$		0			0
$460$	8.00000	+	13.8564i	0.373002	+	0.646058i
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−12.0000	−	20.7846i	−0.555294	−	0.961797i	−0.997881	−	0.0650714i	$-0.979272\pi$
$467$	−12.0000	−	20.7846i	−0.555294	−	0.961797i	0.442587	−	0.896726i	$-0.354061\pi$
$468$	−6.00000			−0.277350
$469$		0			0
$470$	16.0000			0.738025
$471$		0			0
$472$		0			0
$473$	2.00000	−	3.46410i	0.0919601	−	0.159280i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−18.0000			−0.824163
$478$	4.00000	+	6.92820i	0.182956	+	0.316889i
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	−0.942821	−	0.333300i	$-0.891838\pi$
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	0.760056	+	0.649857i	$0.225171\pi$
$480$		0			0
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	18.0000			0.819878
$483$		0			0
$484$	1.00000			0.0454545
$485$	−10.0000	−	17.3205i	−0.454077	−	0.786484i
$486$		0			0
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.0871056	−	0.996199i	$-0.472238\pi$
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.819181	−	0.573535i	$-0.194428\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$		0			0
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	2.00000	−	3.46410i	0.0900755	−	0.156015i
$494$		0			0
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$	−8.00000			−0.359211
$497$		0			0
$498$		0			0
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	0.988204	+	0.153141i	$0.0489388\pi$
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	−0.361478	+	0.932381i	$0.617728\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$		0			0
$502$	−12.0000	−	20.7846i	−0.535586	−	0.927663i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$	−4.00000	−	6.92820i	−0.177822	−	0.307996i
$507$		0			0
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	0.843012	−	0.537895i	$-0.180780\pi$
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	−0.887336	+	0.461123i	$0.847447\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	15.0000	−	25.9808i	0.661622	−	1.14596i
$515$		0			0
$516$		0			0
$517$	−8.00000			−0.351840
$518$		0			0
$519$		0			0
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	−17.0000	+	29.4449i	−0.744784	+	1.29000i	0.205512	+	0.978655i	$0.434114\pi$
$521$	−17.0000	+	29.4449i	−0.744784	+	1.29000i	−0.950296	+	0.311348i	$0.899219\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	−0.940129	+	0.340818i	$0.889296\pi$
$524$		0			0
$525$		0			0
$526$	−24.0000			−1.04645
$527$	8.00000	+	13.8564i	0.348485	+	0.603595i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$		0			0
$532$		0			0
$533$	20.0000			0.866296
$534$		0			0
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$		0			0
$538$	18.0000			0.776035
$539$		0			0
$540$		0			0
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	−0.907975	−	0.419025i	$-0.862372\pi$
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	0.0911008	−	0.995842i	$-0.470961\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$		0			0
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−36.0000			−1.53925			−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000			−1.53925			−0.769624	+	0.638497i	$0.779557\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	30.0000			1.27458
$555$		0			0
$556$	8.00000	−	13.8564i	0.339276	−	0.587643i
$557$	5.00000	−	8.66025i	0.211857	−	0.366947i	−0.740439	−	0.672124i	$-0.765382\pi$
$557$	5.00000	−	8.66025i	0.211857	−	0.366947i	0.952296	+	0.305177i	$0.0987156\pi$
$558$	−12.0000	−	20.7846i	−0.508001	−	0.879883i
$559$	8.00000			0.338364
$560$		0			0
$561$		0			0
$562$	11.0000	+	19.0526i	0.464007	+	0.803684i
$563$	−4.00000	+	6.92820i	−0.168580	+	0.291989i	−0.937921	−	0.346850i	$-0.887251\pi$
$563$	−4.00000	+	6.92820i	−0.168580	+	0.291989i	0.769341	+	0.638838i	$0.220585\pi$
$564$		0			0
$565$	−2.00000	−	3.46410i	−0.0841406	−	0.145736i
$566$	−24.0000			−1.00880
$567$		0			0
$568$	16.0000			0.671345
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.122292	−	0.992494i	$-0.460975\pi$
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.798379	−	0.602155i	$-0.205691\pi$
$572$	1.00000	+	1.73205i	0.0418121	+	0.0724207i
$573$		0			0
$574$		0			0
$575$	8.00000			0.333623
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$		0			0
$580$	−4.00000			−0.166091
$581$		0			0
$582$		0			0
$583$	3.00000	+	5.19615i	0.124247	+	0.215203i
$584$	7.00000	−	12.1244i	0.289662	−	0.501709i
$585$	6.00000	−	10.3923i	0.248069	−	0.429669i
$586$	15.0000	+	25.9808i	0.619644	+	1.07326i
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−21.0000	−	36.3731i	−0.862367	−	1.49366i	−0.869638	−	0.493689i	$-0.835648\pi$
$593$	−21.0000	−	36.3731i	−0.862367	−	1.49366i	0.00727173	−	0.999974i	$-0.497685\pi$
$594$		0			0
$595$		0			0
$596$	14.0000			0.573462
$597$		0			0
$598$	8.00000	−	13.8564i	0.327144	−	0.566631i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−46.0000			−1.87638			−0.938190	−	0.346122i	$-0.887498\pi$
$601$	−46.0000			−1.87638			−0.938190	+	0.346122i	$0.887498\pi$
$602$		0			0
$603$	36.0000			1.46603
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$		0			0
$609$		0			0
$610$	20.0000			0.809776
$611$	−8.00000	−	13.8564i	−0.323645	−	0.560570i
$612$	3.00000	−	5.19615i	0.121268	−	0.210042i
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	−0.998002	−	0.0631797i	$-0.979876\pi$
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	0.553716	+	0.832705i	$0.313209\pi$
$614$	8.00000	+	13.8564i	0.322854	+	0.559199i
$615$		0			0
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	8.00000	−	13.8564i	0.321547	−	0.556936i	−0.659260	−	0.751915i	$-0.729130\pi$
$619$	8.00000	−	13.8564i	0.321547	−	0.556936i	0.980807	+	0.194979i	$0.0624638\pi$
$620$	8.00000	−	13.8564i	0.321288	−	0.556487i
$621$		0			0
$622$	8.00000			0.320771
$623$		0			0
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$		0			0
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$	−4.00000			−0.159490
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$		0			0
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	−8.00000	−	13.8564i	−0.317470	−	0.549875i
$636$		0			0
$637$		0			0
$638$	2.00000			0.0791808
$639$	24.0000	+	41.5692i	0.949425	+	1.64445i
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$		0			0
$643$	−32.0000			−1.26196			−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000			−1.26196			−0.630978	+	0.775800i	$0.717346\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$		0			0
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	−20.0000			−0.783260
$653$	13.0000	+	22.5167i	0.508729	+	0.881145i	0.999949	+	0.0101092i	$0.00321793\pi$
$653$	13.0000	+	22.5167i	0.508729	+	0.881145i	−0.491220	+	0.871036i	$0.663449\pi$
$654$		0			0
$655$		0			0
$656$	−5.00000	−	8.66025i	−0.195217	−	0.338126i
$657$	42.0000			1.63858
$658$		0			0
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$		0			0
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	6.00000			0.232495
$667$	−8.00000	−	13.8564i	−0.309761	−	0.536522i
$668$	−8.00000	+	13.8564i	−0.309529	+	0.536120i
$669$		0			0
$670$	12.0000	+	20.7846i	0.463600	+	0.802980i
$671$	−10.0000			−0.386046
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	−9.00000	−	15.5885i	−0.346667	−	0.600445i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−13.0000	−	22.5167i	−0.499631	−	0.865386i	0.500369	−	0.865812i	$-0.333198\pi$
$677$	−13.0000	−	22.5167i	−0.499631	−	0.865386i	−1.00000		0.000426509i	$0.999864\pi$
$678$		0			0
$679$		0			0
$680$	4.00000			0.153393
$681$		0			0
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	−12.0000	−	20.7846i	−0.456502	−	0.790684i	0.542272	−	0.840203i	$-0.317564\pi$
$691$	−12.0000	−	20.7846i	−0.456502	−	0.790684i	−0.998773	+	0.0495194i	$0.984231\pi$
$692$	−14.0000			−0.532200
$693$		0			0
$694$	−28.0000			−1.06287
$695$	16.0000	+	27.7128i	0.606915	+	1.05121i
$696$		0			0
$697$	−10.0000	+	17.3205i	−0.378777	+	0.656061i
$698$	−1.00000	−	1.73205i	−0.0378506	−	0.0655591i
$699$		0			0
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$		0			0
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	18.0000			0.677439
$707$		0			0
$708$		0			0
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	−0.997202	−	0.0747503i	$-0.976184\pi$
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	0.433865	−	0.900978i	$-0.357149\pi$
$710$	−16.0000	+	27.7128i	−0.600469	+	1.04004i
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	64.0000			2.39682
$714$		0			0
$715$	−4.00000			−0.149592
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$		0			0
$718$	−16.0000	+	27.7128i	−0.597115	+	1.03423i
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	0.930923	−	0.365216i	$-0.119005\pi$
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	−0.781748	+	0.623595i	$0.785672\pi$
$720$	−6.00000			−0.223607
$721$		0			0
$722$	−19.0000			−0.707107
$723$		0			0
$724$	11.0000	−	19.0526i	0.408812	−	0.708083i
$725$	−1.00000	+	1.73205i	−0.0371391	+	0.0643268i
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	14.0000	+	24.2487i	0.518163	+	0.897485i
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	16.0000			0.590571
$735$		0			0
$736$	−8.00000			−0.294884
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	15.0000	−	25.9808i	0.552158	−	0.956365i
$739$	−6.00000	+	10.3923i	−0.220714	+	0.382287i	−0.955025	−	0.296526i	$-0.904172\pi$
$739$	−6.00000	+	10.3923i	−0.220714	+	0.382287i	0.734311	+	0.678813i	$0.237505\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$	−14.0000	+	24.2487i	−0.512920	+	0.888404i
$746$	−7.00000	+	12.1244i	−0.256288	+	0.443904i
$747$		0			0
$748$	−2.00000			−0.0731272
$749$		0			0
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$		0			0
$754$	2.00000	+	3.46410i	0.0728357	+	0.126155i
$755$		0			0
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−2.00000	−	3.46410i	−0.0726433	−	0.125822i
$759$		0			0
$760$		0			0
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	0.915264	−	0.402854i	$-0.131982\pi$
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	−0.806514	+	0.591215i	$0.798649\pi$
$762$		0			0
$763$		0			0
$764$	8.00000			0.289430
$765$	6.00000	+	10.3923i	0.216930	+	0.375735i
$766$	−4.00000	+	6.92820i	−0.144526	+	0.250326i
$767$		0			0
$768$		0			0
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$	6.00000	−	10.3923i	0.215666	−	0.373544i
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$	10.0000			0.358979
$777$		0			0
$778$	−18.0000			−0.645331
$779$		0			0
$780$		0			0
$781$	8.00000	−	13.8564i	0.286263	−	0.495821i
$782$	8.00000	+	13.8564i	0.286079	+	0.495504i
$783$		0			0
$784$		0			0
$785$	−28.0000			−0.999363
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	3.00000			0.106600
$793$	−10.0000	−	17.3205i	−0.355110	−	0.615069i
$794$	−9.00000	+	15.5885i	−0.319398	+	0.553214i
$795$		0			0
$796$	−8.00000	−	13.8564i	−0.283552	−	0.491127i
$797$	2.00000			0.0708436			0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000			0.0708436			0.0354218	+	0.999372i	$0.488723\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	−7.00000	−	12.1244i	−0.247025	−	0.427859i
$804$		0			0
$805$		0			0
$806$	−16.0000			−0.563576
$807$		0			0
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	0.214930	+	0.976629i	$0.431048\pi$
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	−0.953251	+	0.302180i	$0.902286\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$		0			0
$813$		0			0
$814$	−1.00000	−	1.73205i	−0.0350500	−	0.0607083i
$815$	20.0000	−	34.6410i	0.700569	−	1.21342i
$816$		0			0
$817$		0			0
$818$	10.0000			0.349642
$819$		0			0
$820$	20.0000			0.698430
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		0			0
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−52.0000			−1.80822			−0.904109	−	0.427303i	$-0.859464\pi$
$827$	−52.0000			−1.80822			−0.904109	+	0.427303i	$0.859464\pi$
$828$	−12.0000	−	20.7846i	−0.417029	−	0.722315i
$829$	19.0000	−	32.9090i	0.659897	−	1.14298i	−0.320745	−	0.947166i	$-0.603933\pi$
$829$	19.0000	−	32.9090i	0.659897	−	1.14298i	0.980642	−	0.195810i	$-0.0627335\pi$
$830$		0			0
$831$		0			0
$832$	2.00000			0.0693375
$833$		0			0
$834$		0			0
$835$	−16.0000	−	27.7128i	−0.553703	−	0.959041i
$836$		0			0
$837$		0			0
$838$	−8.00000	−	13.8564i	−0.276355	−	0.478662i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−11.0000	−	19.0526i	−0.379085	−	0.656595i
$843$		0			0
$844$	−2.00000	+	3.46410i	−0.0688428	+	0.119239i
$845$	9.00000	+	15.5885i	0.309609	+	0.536259i
$846$	−24.0000			−0.825137
$847$		0			0
$848$	6.00000			0.206041
$849$		0			0
$850$	1.00000	−	1.73205i	0.0342997	−	0.0594089i
$851$	−8.00000	+	13.8564i	−0.274236	+	0.474991i
$852$		0			0
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$		0			0
$855$		0			0
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	11.0000	−	19.0526i	0.375753	−	0.650823i	−0.614687	−	0.788771i	$-0.710717\pi$
$857$	11.0000	−	19.0526i	0.375753	−	0.650823i	0.990439	+	0.137948i	$0.0440508\pi$
$858$		0			0
$859$	28.0000	+	48.4974i	0.955348	+	1.65471i	0.733571	+	0.679613i	$0.237852\pi$
$859$	28.0000	+	48.4974i	0.955348	+	1.65471i	0.221777	+	0.975097i	$0.428814\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$	−8.00000			−0.272481
$863$	−20.0000	−	34.6410i	−0.680808	−	1.17919i	−0.974735	−	0.223366i	$-0.928296\pi$
$863$	−20.0000	−	34.6410i	−0.680808	−	1.17919i	0.293927	−	0.955828i	$-0.405038\pi$
$864$		0			0
$865$	14.0000	−	24.2487i	0.476014	−	0.824481i
$866$	−13.0000	−	22.5167i	−0.441758	−	0.765147i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	12.0000	−	20.7846i	0.406604	−	0.704260i
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$	15.0000	+	25.9808i	0.507673	+	0.879316i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	0.882415	−	0.470471i	$-0.155916\pi$
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	−0.848648	+	0.528958i	$0.822583\pi$
$878$	−20.0000	+	34.6410i	−0.674967	+	1.16908i
$879$		0			0
$880$	1.00000	+	1.73205i	0.0337100	+	0.0583874i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−2.00000	−	3.46410i	−0.0672673	−	0.116510i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	16.0000	+	27.7128i	0.537227	+	0.930505i	0.999052	+	0.0435339i	$0.0138616\pi$
$887$	16.0000	+	27.7128i	0.537227	+	0.930505i	−0.461825	+	0.886971i	$0.652805\pi$
$888$		0			0
$889$		0			0
$890$	−12.0000			−0.402241
$891$	4.50000	+	7.79423i	0.150756	+	0.261116i
$892$	−8.00000	+	13.8564i	−0.267860	+	0.463947i
$893$		0			0
$894$		0			0
$895$	8.00000			0.267411
$896$		0			0
$897$		0			0
$898$	15.0000	+	25.9808i	0.500556	+	0.866989i
$899$	−8.00000	+	13.8564i	−0.266815	+	0.462137i
$900$	−1.50000	+	2.59808i	−0.0500000	+	0.0866025i
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$	−10.0000			−0.332964
$903$		0			0
$904$	2.00000			0.0665190
$905$	22.0000	+	38.1051i	0.731305	+	1.26666i
$906$		0			0
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	−0.830909	−	0.556408i	$-0.812179\pi$
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	0.897318	+	0.441384i	$0.145512\pi$
$908$	−8.00000	−	13.8564i	−0.265489	−	0.459841i
$909$	−54.0000			−1.79107
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$		0			0
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$		0			0
$916$	−22.0000			−0.726900
$917$		0			0
$918$		0			0
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$	8.00000	−	13.8564i	0.263752	−	0.456832i
$921$		0			0
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$	32.0000			1.05329
$924$		0			0
$925$	2.00000			0.0657596
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$		0			0
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$		0			0
$932$	−6.00000			−0.196537
$933$		0			0
$934$	−12.0000	+	20.7846i	−0.392652	+	0.680093i
$935$	2.00000	−	3.46410i	0.0654070	−	0.113288i
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$		0			0
$939$		0			0
$940$	−8.00000	−	13.8564i	−0.260931	−	0.451946i
$941$	19.0000	−	32.9090i	0.619382	−	1.07280i	−0.370216	−	0.928946i	$-0.620716\pi$
$941$	19.0000	−	32.9090i	0.619382	−	1.07280i	0.989599	−	0.143856i	$-0.0459502\pi$
$942$		0			0
$943$	40.0000	+	69.2820i	1.30258	+	2.25613i
$944$		0			0
$945$		0			0
$946$	−4.00000			−0.130051
$947$	26.0000	+	45.0333i	0.844886	+	1.46339i	0.885720	+	0.464220i	$0.153665\pi$
$947$	26.0000	+	45.0333i	0.844886	+	1.46339i	−0.0408333	+	0.999166i	$0.513001\pi$
$948$		0			0
$949$	14.0000	−	24.2487i	0.454459	−	0.787146i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$	9.00000	+	15.5885i	0.291386	+	0.504695i
$955$	−8.00000	+	13.8564i	−0.258874	+	0.448383i
$956$	4.00000	−	6.92820i	0.129369	−	0.224074i
$957$		0			0
$958$	8.00000			0.258468
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	−9.00000	−	15.5885i	−0.289870	−	0.502070i
$965$	4.00000			0.128765
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$		0			0
$970$	−10.0000	+	17.3205i	−0.321081	+	0.556128i
$971$	8.00000	+	13.8564i	0.256732	+	0.444673i	0.965365	−	0.260905i	$-0.0840208\pi$
$971$	8.00000	+	13.8564i	0.256732	+	0.444673i	−0.708632	+	0.705578i	$0.750687\pi$
$972$		0			0
$973$		0			0
$974$	−40.0000			−1.28168
$975$		0			0
$976$	−5.00000	+	8.66025i	−0.160046	+	0.277208i
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	−0.881579	−	0.472037i	$-0.843519\pi$
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	0.849586	+	0.527451i	$0.176852\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	6.00000			0.191565
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$		0			0
$985$	18.0000	+	31.1769i	0.573528	+	0.993379i
$986$	−4.00000			−0.127386
$987$		0			0
$988$		0			0
$989$	16.0000	+	27.7128i	0.508770	+	0.881216i
$990$	−3.00000	+	5.19615i	−0.0953463	+	0.165145i
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$		0			0
$995$	32.0000			1.01447
$996$		0			0
$997$	15.0000	−	25.9808i	0.475055	−	0.822819i	−0.524537	−	0.851388i	$-0.675762\pi$
$997$	15.0000	−	25.9808i	0.475055	−	0.822819i	0.999592	+	0.0285686i	$0.00909491\pi$
$998$	14.0000	−	24.2487i	0.443162	−	0.767580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.b.67.1		2
7.2	even	3	inner	1078.2.e.b.177.1		2
7.3	odd	6		1078.2.a.j.1.1		1
7.4	even	3		154.2.a.c.1.1	✓	1
7.5	odd	6		1078.2.e.c.177.1		2
7.6	odd	2		1078.2.e.c.67.1		2
21.11	odd	6		1386.2.a.b.1.1		1
21.17	even	6		9702.2.a.v.1.1		1
28.3	even	6		8624.2.a.o.1.1		1
28.11	odd	6		1232.2.a.h.1.1		1
35.4	even	6		3850.2.a.f.1.1		1
35.18	odd	12		3850.2.c.l.1849.1		2
35.32	odd	12		3850.2.c.l.1849.2		2
56.11	odd	6		4928.2.a.o.1.1		1
56.53	even	6		4928.2.a.n.1.1		1
77.32	odd	6		1694.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.a.c.1.1	✓	1	7.4	even	3
1078.2.a.j.1.1		1	7.3	odd	6
1078.2.e.b.67.1		2	1.1	even	1	trivial
1078.2.e.b.177.1		2	7.2	even	3	inner
1078.2.e.c.67.1		2	7.6	odd	2
1078.2.e.c.177.1		2	7.5	odd	6
1232.2.a.h.1.1		1	28.11	odd	6
1386.2.a.b.1.1		1	21.11	odd	6
1694.2.a.c.1.1		1	77.32	odd	6
3850.2.a.f.1.1		1	35.4	even	6
3850.2.c.l.1849.1		2	35.18	odd	12
3850.2.c.l.1849.2		2	35.32	odd	12
4928.2.a.n.1.1		1	56.53	even	6
4928.2.a.o.1.1		1	56.11	odd	6
8624.2.a.o.1.1		1	28.3	even	6
9702.2.a.v.1.1		1	21.17	even	6

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(1.50000 - 2.59808i) q^{18} +2.00000 q^{20} -1.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -2.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +2.00000 q^{34} -3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{40} +10.0000 q^{41} +4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(3.00000 - 5.19615i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-4.00000 - 6.92820i) q^{47} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} -2.00000 q^{55} +(1.00000 + 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(6.00000 - 10.3923i) q^{67} +(-1.00000 - 1.73205i) q^{68} +16.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +(7.00000 - 12.1244i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-5.00000 - 8.66025i) q^{82} +4.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} -6.00000 q^{90} -8.00000 q^{92} +(-4.00000 + 6.92820i) q^{94} +10.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{8} + 3 q^{9} - 2 q^{10} + q^{11} + 4 q^{13} - q^{16} - 2 q^{17} + 3 q^{18} + 4 q^{20} - 2 q^{22} + 8 q^{23} + q^{25} - 2 q^{26} - 4 q^{29} + 8 q^{31} - q^{32} + 4 q^{34} - 6 q^{36} + 2 q^{37} - 2 q^{40} + 20 q^{41} + 8 q^{43} + q^{44} + 6 q^{45} + 8 q^{46} - 8 q^{47} - 2 q^{50} - 2 q^{52} - 6 q^{53} - 4 q^{55} + 2 q^{58} - 10 q^{61} - 16 q^{62} + 2 q^{64} - 4 q^{65} + 12 q^{67} - 2 q^{68} + 32 q^{71} + 3 q^{72} + 14 q^{73} + 2 q^{74} - 2 q^{80} - 9 q^{81} - 10 q^{82} + 8 q^{85} - 4 q^{86} + q^{88} + 6 q^{89} - 12 q^{90} - 16 q^{92} - 8 q^{94} + 20 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^8 + 3 * q^9 - 2 * q^10 + q^11 + 4 * q^13 - q^16 - 2 * q^17 + 3 * q^18 + 4 * q^20 - 2 * q^22 + 8 * q^23 + q^25 - 2 * q^26 - 4 * q^29 + 8 * q^31 - q^32 + 4 * q^34 - 6 * q^36 + 2 * q^37 - 2 * q^40 + 20 * q^41 + 8 * q^43 + q^44 + 6 * q^45 + 8 * q^46 - 8 * q^47 - 2 * q^50 - 2 * q^52 - 6 * q^53 - 4 * q^55 + 2 * q^58 - 10 * q^61 - 16 * q^62 + 2 * q^64 - 4 * q^65 + 12 * q^67 - 2 * q^68 + 32 * q^71 + 3 * q^72 + 14 * q^73 + 2 * q^74 - 2 * q^80 - 9 * q^81 - 10 * q^82 + 8 * q^85 - 4 * q^86 + q^88 + 6 * q^89 - 12 * q^90 - 16 * q^92 - 8 * q^94 + 20 * q^97 + 6 * q^99

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