LMFDB - Embedded newform 539.2.e.f.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(67,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, 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("539.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.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:	$4.30393666895$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	539.67
Dual form			539.2.e.f.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.00000 - 5.19615i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-3.00000 - 5.19615i) q^{12} -4.00000 q^{13} +3.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{19} +2.00000 q^{20} +(2.50000 + 4.33013i) q^{23} +(2.00000 - 3.46410i) q^{25} -9.00000 q^{27} +10.0000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-1.50000 - 2.59808i) q^{33} -12.0000 q^{36} +(2.50000 + 4.33013i) q^{37} +(-6.00000 + 10.3923i) q^{39} -2.00000 q^{41} -8.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(3.00000 - 5.19615i) q^{45} +(-4.00000 - 6.92820i) q^{47} -12.0000 q^{48} +(3.00000 + 5.19615i) q^{51} +(-4.00000 + 6.92820i) q^{52} +(3.00000 - 5.19615i) q^{53} +1.00000 q^{55} +18.0000 q^{57} +(-1.50000 + 2.59808i) q^{59} +(3.00000 - 5.19615i) q^{60} +(1.00000 + 1.73205i) q^{61} -8.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(1.50000 - 2.59808i) q^{67} +(2.00000 + 3.46410i) q^{68} +15.0000 q^{69} +1.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(-6.00000 - 10.3923i) q^{75} +12.0000 q^{76} +(-3.00000 - 5.19615i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +12.0000 q^{83} -2.00000 q^{85} +(15.0000 - 25.9808i) q^{87} +(7.50000 + 12.9904i) q^{89} +10.0000 q^{92} +(1.50000 + 2.59808i) q^{93} +(-3.00000 + 5.19615i) q^{95} -5.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 2 q^{4} + q^{5} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 2 * q^4 + q^5 - 6 * q^9	$ 2 q + 3 q^{3} + 2 q^{4} + q^{5} - 6 q^{9} + q^{11} - 6 q^{12} - 8 q^{13} + 6 q^{15} - 4 q^{16} - 2 q^{17} + 6 q^{19} + 4 q^{20} + 5 q^{23} + 4 q^{25} - 18 q^{27} + 20 q^{29} - q^{31} - 3 q^{33} - 24 q^{36} + 5 q^{37} - 12 q^{39} - 4 q^{41} - 16 q^{43} - 2 q^{44} + 6 q^{45} - 8 q^{47} - 24 q^{48} + 6 q^{51} - 8 q^{52} + 6 q^{53} + 2 q^{55} + 36 q^{57} - 3 q^{59} + 6 q^{60} + 2 q^{61} - 16 q^{64} - 4 q^{65} + 3 q^{67} + 4 q^{68} + 30 q^{69} + 2 q^{71} - 10 q^{73} - 12 q^{75} + 24 q^{76} - 6 q^{79} + 4 q^{80} - 9 q^{81} + 24 q^{83} - 4 q^{85} + 30 q^{87} + 15 q^{89} + 20 q^{92} + 3 q^{93} - 6 q^{95} - 10 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 2 * q^4 + q^5 - 6 * q^9 + q^11 - 6 * q^12 - 8 * q^13 + 6 * q^15 - 4 * q^16 - 2 * q^17 + 6 * q^19 + 4 * q^20 + 5 * q^23 + 4 * q^25 - 18 * q^27 + 20 * q^29 - q^31 - 3 * q^33 - 24 * q^36 + 5 * q^37 - 12 * q^39 - 4 * q^41 - 16 * q^43 - 2 * q^44 + 6 * q^45 - 8 * q^47 - 24 * q^48 + 6 * q^51 - 8 * q^52 + 6 * q^53 + 2 * q^55 + 36 * q^57 - 3 * q^59 + 6 * q^60 + 2 * q^61 - 16 * q^64 - 4 * q^65 + 3 * q^67 + 4 * q^68 + 30 * q^69 + 2 * q^71 - 10 * q^73 - 12 * q^75 + 24 * q^76 - 6 * q^79 + 4 * q^80 - 9 * q^81 + 24 * q^83 - 4 * q^85 + 30 * q^87 + 15 * q^89 + 20 * q^92 + 3 * q^93 - 6 * q^95 - 10 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−3.00000	−	5.19615i	−0.866025	−	1.50000i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−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	$0.244646\pi$
$18$		0			0
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$		0			0
$23$	2.50000	+	4.33013i	0.521286	+	0.902894i	0.999694	+	0.0247559i	$0.00788087\pi$
$23$	2.50000	+	4.33013i	0.521286	+	0.902894i	−0.478407	+	0.878138i	$0.658786\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$		0			0
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$		0			0
$35$		0			0
$36$	−12.0000			−2.00000
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	0.994999	−	0.0998840i	$-0.0318472\pi$
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	−0.584002	+	0.811752i	$0.698514\pi$
$38$		0			0
$39$	−6.00000	+	10.3923i	−0.960769	+	1.66410i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	3.00000	−	5.19615i	0.447214	−	0.774597i
$46$		0			0
$47$	−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	$-0.364968\pi$
$48$	−12.0000			−1.73205
$49$		0			0
$50$		0			0
$51$	3.00000	+	5.19615i	0.420084	+	0.727607i
$52$	−4.00000	+	6.92820i	−0.554700	+	0.960769i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$		0			0
$57$	18.0000			2.38416
$58$		0			0
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$	3.00000	−	5.19615i	0.387298	−	0.670820i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$	15.0000			1.80579
$70$		0			0
$71$	1.00000			0.118678			0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000			0.118678			0.0593391	+	0.998238i	$0.481101\pi$
$72$		0			0
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$	−6.00000	−	10.3923i	−0.692820	−	1.20000i
$76$	12.0000			1.37649
$77$		0			0
$78$		0			0
$79$	−3.00000	−	5.19615i	−0.337526	−	0.584613i	0.646440	−	0.762964i	$-0.276257\pi$
$79$	−3.00000	−	5.19615i	−0.337526	−	0.584613i	−0.983967	+	0.178352i	$0.942924\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$		0			0
$87$	15.0000	−	25.9808i	1.60817	−	2.78543i
$88$		0			0
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	0.922840	+	0.385183i	$0.125862\pi$
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	−0.127842	+	0.991795i	$0.540805\pi$
$90$		0			0
$91$		0			0
$92$	10.0000			1.04257
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	−5.00000			−0.507673			−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000			−0.507673			−0.253837	+	0.967247i	$0.581693\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$	−4.00000	−	6.92820i	−0.400000	−	0.692820i
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$		0			0
$103$	6.00000	+	10.3923i	0.591198	+	1.02398i	0.994071	+	0.108729i	$0.0346780\pi$
$103$	6.00000	+	10.3923i	0.591198	+	1.02398i	−0.402874	+	0.915255i	$0.631989\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.00000	+	8.66025i	0.483368	+	0.837218i	0.999818	−	0.0190994i	$-0.00607989\pi$
$107$	5.00000	+	8.66025i	0.483368	+	0.837218i	−0.516449	+	0.856318i	$0.672747\pi$
$108$	−9.00000	+	15.5885i	−0.866025	+	1.50000i
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	−0.945769	−	0.324840i	$-0.894690\pi$
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	0.754204	+	0.656640i	$0.228023\pi$
$110$		0			0
$111$	15.0000			1.42374
$112$		0			0
$113$	−19.0000			−1.78737			−0.893685	−	0.448695i	$-0.851889\pi$
$113$	−19.0000			−1.78737			−0.893685	+	0.448695i	$0.851889\pi$
$114$		0			0
$115$	−2.50000	+	4.33013i	−0.233126	+	0.403786i
$116$	10.0000	−	17.3205i	0.928477	−	1.60817i
$117$	12.0000	+	20.7846i	1.10940	+	1.92154i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	9.00000			0.804984
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$	−12.0000	+	20.7846i	−1.05654	+	1.82998i
$130$		0			0
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$		0			0
$135$	−4.50000	−	7.79423i	−0.387298	−	0.670820i
$136$		0			0
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	−24.0000			−2.02116
$142$		0			0
$143$	−2.00000	+	3.46410i	−0.167248	+	0.289683i
$144$	−12.0000	+	20.7846i	−1.00000	+	1.73205i
$145$	5.00000	+	8.66025i	0.415227	+	0.719195i
$146$		0			0
$147$		0			0
$148$	10.0000			0.821995
$149$	11.0000	+	19.0526i	0.901155	+	1.56085i	0.825997	+	0.563675i	$0.190613\pi$
$149$	11.0000	+	19.0526i	0.901155	+	1.56085i	0.0751583	+	0.997172i	$0.476054\pi$
$150$		0			0
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	−0.961888	−	0.273442i	$-0.911838\pi$
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	0.717752	+	0.696299i	$0.245171\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	−1.00000			−0.0803219
$156$	12.0000	+	20.7846i	0.960769	+	1.66410i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$		0			0
$159$	−9.00000	−	15.5885i	−0.713746	−	1.23625i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−2.00000	+	3.46410i	−0.156174	+	0.270501i
$165$	1.50000	−	2.59808i	0.116775	−	0.202260i
$166$		0			0
$167$	−2.00000			−0.154765			−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000			−0.154765			−0.0773823	+	0.997001i	$0.524656\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	18.0000	−	31.1769i	1.37649	−	2.38416i
$172$	−8.00000	+	13.8564i	−0.609994	+	1.05654i
$173$	−8.00000	−	13.8564i	−0.608229	−	1.05348i	−0.991532	−	0.129861i	$-0.958547\pi$
$173$	−8.00000	−	13.8564i	−0.608229	−	1.05348i	0.383304	−	0.923622i	$-0.374786\pi$
$174$		0			0
$175$		0			0
$176$	−4.00000			−0.301511
$177$	4.50000	+	7.79423i	0.338241	+	0.585850i
$178$		0			0
$179$	−0.500000	+	0.866025i	−0.0373718	+	0.0647298i	−0.884106	−	0.467286i	$-0.845232\pi$
$179$	−0.500000	+	0.866025i	−0.0373718	+	0.0647298i	0.846735	+	0.532016i	$0.178565\pi$
$180$	−6.00000	−	10.3923i	−0.447214	−	0.774597i
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		0			0
$183$	6.00000			0.443533
$184$		0			0
$185$	−2.50000	+	4.33013i	−0.183804	+	0.318357i
$186$		0			0
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	−16.0000			−1.16692
$189$		0			0
$190$		0			0
$191$	−2.50000	−	4.33013i	−0.180894	−	0.313317i	0.761291	−	0.648410i	$-0.224566\pi$
$191$	−2.50000	−	4.33013i	−0.180894	−	0.313317i	−0.942185	+	0.335093i	$0.891232\pi$
$192$	−12.0000	+	20.7846i	−0.866025	+	1.50000i
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$		0			0
$195$	−12.0000			−0.859338
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$		0			0
$201$	−4.50000	−	7.79423i	−0.317406	−	0.549762i
$202$		0			0
$203$		0			0
$204$	12.0000			0.840168
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$		0			0
$207$	15.0000	−	25.9808i	1.04257	−	1.80579i
$208$	8.00000	+	13.8564i	0.554700	+	0.960769i
$209$	6.00000			0.415029
$210$		0			0
$211$	−2.00000			−0.137686			−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$	1.50000	−	2.59808i	0.102778	−	0.178017i
$214$		0			0
$215$	−4.00000	−	6.92820i	−0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	15.0000	+	25.9808i	1.01361	+	1.75562i
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	4.00000	−	6.92820i	0.269069	−	0.466041i
$222$		0			0
$223$	1.00000			0.0669650			0.0334825	−	0.999439i	$-0.489340\pi$
$223$	1.00000			0.0669650			0.0334825	+	0.999439i	$0.489340\pi$
$224$		0			0
$225$	−24.0000			−1.60000
$226$		0			0
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$	18.0000	−	31.1769i	1.19208	−	2.06474i
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	−18.0000			−1.16923
$238$		0			0
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	−6.00000	−	10.3923i	−0.387298	−	0.670820i
$241$	6.00000	−	10.3923i	0.386494	−	0.669427i	−0.605481	−	0.795860i	$-0.707019\pi$
$241$	6.00000	−	10.3923i	0.386494	−	0.669427i	0.991975	+	0.126432i	$0.0403527\pi$
$242$		0			0
$243$		0			0
$244$	4.00000			0.256074
$245$		0			0
$246$		0			0
$247$	−12.0000	−	20.7846i	−0.763542	−	1.32249i
$248$		0			0
$249$	18.0000	−	31.1769i	1.14070	−	1.97576i
$250$		0			0
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$		0			0
$253$	5.00000			0.314347
$254$		0			0
$255$	−3.00000	+	5.19615i	−0.187867	+	0.325396i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$		0			0
$260$	−8.00000			−0.496139
$261$	−30.0000	−	51.9615i	−1.85695	−	3.21634i
$262$		0			0
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	45.0000			2.75396
$268$	−3.00000	−	5.19615i	−0.183254	−	0.317406i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$		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	$0.994865\pi$
$272$	8.00000			0.485071
$273$		0			0
$274$		0			0
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$	15.0000	−	25.9808i	0.902894	−	1.56386i
$277$	−12.0000	+	20.7846i	−0.721010	+	1.24883i	0.239585	+	0.970875i	$0.422989\pi$
$277$	−12.0000	+	20.7846i	−0.721010	+	1.24883i	−0.960595	+	0.277951i	$0.910345\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$		0			0
$283$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$283$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$	9.00000	+	15.5885i	0.533114	+	0.923381i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−7.50000	+	12.9904i	−0.439658	+	0.761510i
$292$	10.0000	+	17.3205i	0.585206	+	1.01361i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	−3.00000			−0.174667
$296$		0			0
$297$	−4.50000	+	7.79423i	−0.261116	+	0.452267i
$298$		0			0
$299$	−10.0000	−	17.3205i	−0.578315	−	1.00167i
$300$	−24.0000			−1.38564
$301$		0			0
$302$		0			0
$303$	−18.0000	−	31.1769i	−1.03407	−	1.79107i
$304$	12.0000	−	20.7846i	0.688247	−	1.19208i
$305$	−1.00000	+	1.73205i	−0.0572598	+	0.0991769i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	36.0000			2.04797
$310$		0			0
$311$	−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
$313$	11.5000	+	19.9186i	0.650018	+	1.12586i	0.983118	+	0.182973i	$0.0585722\pi$
$313$	11.5000	+	19.9186i	0.650018	+	1.12586i	−0.333099	+	0.942892i	$0.608094\pi$
$314$		0			0
$315$		0			0
$316$	−12.0000			−0.675053
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	0.711535	−	0.702650i	$-0.248000\pi$
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	−0.964281	+	0.264883i	$0.914667\pi$
$318$		0			0
$319$	5.00000	−	8.66025i	0.279946	−	0.484881i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$	30.0000			1.67444
$322$		0			0
$323$	−12.0000			−0.667698
$324$	9.00000	+	15.5885i	0.500000	+	0.866025i
$325$	−8.00000	+	13.8564i	−0.443760	+	0.768615i
$326$		0			0
$327$	6.00000	+	10.3923i	0.331801	+	0.574696i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	0.999298	−	0.0374662i	$-0.0119287\pi$
$331$	8.50000	+	14.7224i	0.467202	+	0.809218i	−0.532096	+	0.846684i	$0.678595\pi$
$332$	12.0000	−	20.7846i	0.658586	−	1.14070i
$333$	15.0000	−	25.9808i	0.821995	−	1.42374i
$334$		0			0
$335$	3.00000			0.163908
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$	−28.5000	+	49.3634i	−1.54791	+	2.68105i
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$	0.500000	+	0.866025i	0.0270765	+	0.0468979i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	7.50000	+	12.9904i	0.403786	+	0.699379i
$346$		0			0
$347$	−7.00000	+	12.1244i	−0.375780	+	0.650870i	−0.990443	−	0.137920i	$-0.955958\pi$
$347$	−7.00000	+	12.1244i	−0.375780	+	0.650870i	0.614664	+	0.788789i	$0.289292\pi$
$348$	−30.0000	−	51.9615i	−1.60817	−	2.78543i
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$		0			0
$351$	36.0000			1.92154
$352$		0			0
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	−0.960574	−	0.278024i	$-0.910320\pi$
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	0.721063	+	0.692869i	$0.243654\pi$
$354$		0			0
$355$	0.500000	+	0.866025i	0.0265372	+	0.0459639i
$356$	30.0000			1.59000
$357$		0			0
$358$		0			0
$359$	−4.00000	−	6.92820i	−0.211112	−	0.365657i	0.740951	−	0.671559i	$-0.234375\pi$
$359$	−4.00000	−	6.92820i	−0.211112	−	0.365657i	−0.952063	+	0.305903i	$0.901042\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$		0			0
$363$	−3.00000			−0.157459
$364$		0			0
$365$	−10.0000			−0.523424
$366$		0			0
$367$	5.50000	−	9.52628i	0.287098	−	0.497268i	−0.686018	−	0.727585i	$-0.740643\pi$
$367$	5.50000	−	9.52628i	0.287098	−	0.497268i	0.973116	+	0.230317i	$0.0739762\pi$
$368$	10.0000	−	17.3205i	0.521286	−	0.902894i
$369$	6.00000	+	10.3923i	0.312348	+	0.541002i
$370$		0			0
$371$		0			0
$372$	6.00000			0.311086
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	13.5000	−	23.3827i	0.697137	−	1.20748i
$376$		0			0
$377$	−40.0000			−2.06010
$378$		0			0
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$	6.00000	+	10.3923i	0.307794	+	0.533114i
$381$	3.00000	−	5.19615i	0.153695	−	0.266207i
$382$		0			0
$383$	−8.50000	−	14.7224i	−0.434330	−	0.752281i	0.562911	−	0.826518i	$-0.309681\pi$
$383$	−8.50000	−	14.7224i	−0.434330	−	0.752281i	−0.997241	+	0.0742364i	$0.976348\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	24.0000	+	41.5692i	1.21999	+	2.11308i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	−0.957263	−	0.289220i	$-0.906604\pi$
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	0.729103	+	0.684403i	$0.239937\pi$
$390$		0			0
$391$	−10.0000			−0.505722
$392$		0			0
$393$	−54.0000			−2.72394
$394$		0			0
$395$	3.00000	−	5.19615i	0.150946	−	0.261447i
$396$	−6.00000	+	10.3923i	−0.301511	+	0.522233i
$397$	−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	$0.982515\pi$
$398$		0			0
$399$		0			0
$400$	−16.0000			−0.800000
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$		0			0
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	−12.0000	−	20.7846i	−0.597022	−	1.03407i
$405$	−9.00000			−0.447214
$406$		0			0
$407$	5.00000			0.247841
$408$		0			0
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$		0			0
$411$	−4.50000	−	7.79423i	−0.221969	−	0.384461i
$412$	24.0000			1.18240
$413$		0			0
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$		0			0
$417$	−15.0000	+	25.9808i	−0.734553	+	1.27228i
$418$		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	$0.319894\pi$
$422$		0			0
$423$	−24.0000	+	41.5692i	−1.16692	+	2.02116i
$424$		0			0
$425$	4.00000	+	6.92820i	0.194029	+	0.336067i
$426$		0			0
$427$		0			0
$428$	20.0000			0.966736
$429$	6.00000	+	10.3923i	0.289683	+	0.501745i
$430$		0			0
$431$	10.0000	−	17.3205i	0.481683	−	0.834300i	−0.518096	−	0.855323i	$-0.673359\pi$
$431$	10.0000	−	17.3205i	0.481683	−	0.834300i	0.999779	+	0.0210230i	$0.00669232\pi$
$432$	18.0000	+	31.1769i	0.866025	+	1.50000i
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$		0			0
$435$	30.0000			1.43839
$436$	4.00000	+	6.92820i	0.191565	+	0.331801i
$437$	−15.0000	+	25.9808i	−0.717547	+	1.24283i
$438$		0			0
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	19.5000	+	33.7750i	0.926473	+	1.60470i	0.789175	+	0.614168i	$0.210508\pi$
$443$	19.5000	+	33.7750i	0.926473	+	1.60470i	0.137298	+	0.990530i	$0.456158\pi$
$444$	15.0000	−	25.9808i	0.711868	−	1.23299i
$445$	−7.50000	+	12.9904i	−0.355534	+	0.615803i
$446$		0			0
$447$	66.0000			3.12169
$448$		0			0
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$	−1.00000	+	1.73205i	−0.0470882	+	0.0815591i
$452$	−19.0000	+	32.9090i	−0.893685	+	1.54791i
$453$	9.00000	+	15.5885i	0.422857	+	0.732410i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.00000	−	6.92820i	−0.187112	−	0.324088i	0.757174	−	0.653213i	$-0.226579\pi$
$457$	−4.00000	−	6.92820i	−0.187112	−	0.324088i	−0.944286	+	0.329125i	$0.893246\pi$
$458$		0			0
$459$	9.00000	−	15.5885i	0.420084	−	0.727607i
$460$	5.00000	+	8.66025i	0.233126	+	0.403786i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	13.0000			0.604161			0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000			0.604161			0.302081	+	0.953282i	$0.402319\pi$
$464$	−20.0000	−	34.6410i	−0.928477	−	1.60817i
$465$	−1.50000	+	2.59808i	−0.0695608	+	0.120483i
$466$		0			0
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	0.829231	−	0.558906i	$-0.188779\pi$
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	−0.898642	+	0.438682i	$0.855446\pi$
$468$	48.0000			2.21880
$469$		0			0
$470$		0			0
$471$	10.5000	+	18.1865i	0.483814	+	0.837991i
$472$		0			0
$473$	−4.00000	+	6.92820i	−0.183920	+	0.318559i
$474$		0			0
$475$	24.0000			1.10120
$476$		0			0
$477$	−36.0000			−1.64833
$478$		0			0
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$		0			0
$481$	−10.0000	−	17.3205i	−0.455961	−	0.789747i
$482$		0			0
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−2.50000	−	4.33013i	−0.113519	−	0.196621i
$486$		0			0
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	−0.680335	−	0.732901i	$-0.738166\pi$
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	0.974879	+	0.222737i	$0.0714992\pi$
$488$		0			0
$489$	−12.0000			−0.542659
$490$		0			0
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$	6.00000	+	10.3923i	0.270501	+	0.468521i
$493$	−10.0000	+	17.3205i	−0.450377	+	0.780076i
$494$		0			0
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$	4.00000			0.179605
$497$		0			0
$498$		0			0
$499$	−22.0000	−	38.1051i	−0.984855	−	1.70582i	−0.642578	−	0.766220i	$-0.722135\pi$
$499$	−22.0000	−	38.1051i	−0.984855	−	1.70582i	−0.342277	−	0.939599i	$-0.611198\pi$
$500$	9.00000	−	15.5885i	0.402492	−	0.697137i
$501$	−3.00000	+	5.19615i	−0.134030	+	0.232147i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$		0			0
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$	2.00000	−	3.46410i	0.0887357	−	0.153695i
$509$	15.5000	+	26.8468i	0.687025	+	1.18996i	0.972796	+	0.231665i	$0.0744172\pi$
$509$	15.5000	+	26.8468i	0.687025	+	1.18996i	−0.285770	+	0.958298i	$0.592249\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−27.0000	−	46.7654i	−1.19208	−	2.06474i
$514$		0			0
$515$	−6.00000	+	10.3923i	−0.264392	+	0.457940i
$516$	24.0000	+	41.5692i	1.05654	+	1.82998i
$517$	−8.00000			−0.351840
$518$		0			0
$519$	−48.0000			−2.10697
$520$		0			0
$521$	−3.50000	+	6.06218i	−0.153338	+	0.265589i	−0.932453	−	0.361293i	$-0.882336\pi$
$521$	−3.50000	+	6.06218i	−0.153338	+	0.265589i	0.779115	+	0.626881i	$0.215669\pi$
$522$		0			0
$523$	−16.0000	−	27.7128i	−0.699631	−	1.21180i	−0.968594	−	0.248646i	$-0.920014\pi$
$523$	−16.0000	−	27.7128i	−0.699631	−	1.21180i	0.268963	−	0.963150i	$-0.413319\pi$
$524$	−36.0000			−1.57267
$525$		0			0
$526$		0			0
$527$	−1.00000	−	1.73205i	−0.0435607	−	0.0754493i
$528$	−6.00000	+	10.3923i	−0.261116	+	0.452267i
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$		0			0
$531$	18.0000			0.781133
$532$		0			0
$533$	8.00000			0.346518
$534$		0			0
$535$	−5.00000	+	8.66025i	−0.216169	+	0.374415i
$536$		0			0
$537$	1.50000	+	2.59808i	0.0647298	+	0.112115i
$538$		0			0
$539$		0			0
$540$	−18.0000			−0.774597
$541$	−16.0000	−	27.7128i	−0.687894	−	1.19147i	−0.972518	−	0.232828i	$-0.925202\pi$
$541$	−16.0000	−	27.7128i	−0.687894	−	1.19147i	0.284624	−	0.958639i	$-0.408131\pi$
$542$		0			0
$543$	7.50000	−	12.9904i	0.321856	−	0.557471i
$544$		0			0
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−24.0000			−1.02617			−0.513083	−	0.858339i	$-0.671497\pi$
$547$	−24.0000			−1.02617			−0.513083	+	0.858339i	$0.671497\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$	6.00000	−	10.3923i	0.256074	−	0.443533i
$550$		0			0
$551$	30.0000	+	51.9615i	1.27804	+	2.21364i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	7.50000	+	12.9904i	0.318357	+	0.551411i
$556$	−10.0000	+	17.3205i	−0.424094	+	0.734553i
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	−0.975356	−	0.220638i	$-0.929186\pi$
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	0.678756	+	0.734364i	$0.262519\pi$
$558$		0			0
$559$	32.0000			1.35346
$560$		0			0
$561$	6.00000			0.253320
$562$		0			0
$563$	−10.0000	+	17.3205i	−0.421450	+	0.729972i	−0.996082	−	0.0884397i	$-0.971812\pi$
$563$	−10.0000	+	17.3205i	−0.421450	+	0.729972i	0.574632	+	0.818412i	$0.305145\pi$
$564$	−24.0000	+	41.5692i	−1.01058	+	1.75038i
$565$	−9.50000	−	16.4545i	−0.399668	−	0.692245i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$	4.00000	+	6.92820i	0.167248	+	0.289683i
$573$	−15.0000			−0.626634
$574$		0			0
$575$	20.0000			0.834058
$576$	24.0000	+	41.5692i	1.00000	+	1.73205i
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	−0.479337	−	0.877631i	$-0.659123\pi$
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	0.999719	−	0.0236970i	$-0.00754370\pi$
$578$		0			0
$579$	21.0000	+	36.3731i	0.872730	+	1.51161i
$580$	20.0000			0.830455
$581$		0			0
$582$		0			0
$583$	−3.00000	−	5.19615i	−0.124247	−	0.215203i
$584$		0			0
$585$	−12.0000	+	20.7846i	−0.496139	+	0.859338i
$586$		0			0
$587$	36.0000			1.48588			0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000			1.48588			0.742940	+	0.669359i	$0.233431\pi$
$588$		0			0
$589$	−6.00000			−0.247226
$590$		0			0
$591$	27.0000	−	46.7654i	1.11063	−	1.92367i
$592$	10.0000	−	17.3205i	0.410997	−	0.711868i
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	−0.990212	−	0.139569i	$-0.955428\pi$
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	0.374236	−	0.927333i	$-0.377905\pi$
$594$		0			0
$595$		0			0
$596$	44.0000			1.80231
$597$	−12.0000	−	20.7846i	−0.491127	−	0.850657i
$598$		0			0
$599$	24.0000	−	41.5692i	0.980613	−	1.69847i	0.320607	−	0.947212i	$-0.396113\pi$
$599$	24.0000	−	41.5692i	0.980613	−	1.69847i	0.660006	−	0.751260i	$-0.270554\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$	−18.0000			−0.733017
$604$	6.00000	+	10.3923i	0.244137	+	0.422857i
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$		0			0
$607$	5.00000	+	8.66025i	0.202944	+	0.351509i	0.949476	−	0.313841i	$-0.101616\pi$
$607$	5.00000	+	8.66025i	0.202944	+	0.351509i	−0.746532	+	0.665350i	$0.768282\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.0000	+	27.7128i	0.647291	+	1.12114i
$612$	12.0000	−	20.7846i	0.485071	−	0.840168i
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	−0.981129	−	0.193352i	$-0.938064\pi$
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	0.658012	+	0.753007i	$0.271397\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	0.643094	+	0.765787i	$0.277650\pi$
$620$	−1.00000	+	1.73205i	−0.0401610	+	0.0695608i
$621$	−22.5000	−	38.9711i	−0.902894	−	1.56386i
$622$		0			0
$623$		0			0
$624$	48.0000			1.92154
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	9.00000	−	15.5885i	0.359425	−	0.622543i
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$	−10.0000			−0.398726
$630$		0			0
$631$	27.0000			1.07485			0.537427	−	0.843311i	$-0.319397\pi$
$631$	27.0000			1.07485			0.537427	+	0.843311i	$0.319397\pi$
$632$		0			0
$633$	−3.00000	+	5.19615i	−0.119239	+	0.206529i
$634$		0			0
$635$	1.00000	+	1.73205i	0.0396838	+	0.0687343i
$636$	−36.0000			−1.42749
$637$		0			0
$638$		0			0
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$		0			0
$641$	−7.50000	+	12.9904i	−0.296232	+	0.513089i	−0.975271	−	0.221013i	$-0.929064\pi$
$641$	−7.50000	+	12.9904i	−0.296232	+	0.513089i	0.679039	+	0.734103i	$0.262397\pi$
$642$		0			0
$643$	−29.0000			−1.14365			−0.571824	−	0.820376i	$-0.693764\pi$
$643$	−29.0000			−1.14365			−0.571824	+	0.820376i	$0.693764\pi$
$644$		0			0
$645$	−24.0000			−0.944999
$646$		0			0
$647$	10.5000	−	18.1865i	0.412798	−	0.714986i	−0.582397	−	0.812905i	$-0.697885\pi$
$647$	10.5000	−	18.1865i	0.412798	−	0.714986i	0.995194	+	0.0979182i	$0.0312184\pi$
$648$		0			0
$649$	1.50000	+	2.59808i	0.0588802	+	0.101983i
$650$		0			0
$651$		0			0
$652$	−8.00000			−0.313304
$653$	8.50000	+	14.7224i	0.332631	+	0.576133i	0.983027	−	0.183462i	$-0.0587304\pi$
$653$	8.50000	+	14.7224i	0.332631	+	0.576133i	−0.650396	+	0.759595i	$0.725397\pi$
$654$		0			0
$655$	9.00000	−	15.5885i	0.351659	−	0.609091i
$656$	4.00000	+	6.92820i	0.156174	+	0.270501i
$657$	60.0000			2.34082
$658$		0			0
$659$	−2.00000			−0.0779089			−0.0389545	−	0.999241i	$-0.512403\pi$
$659$	−2.00000			−0.0779089			−0.0389545	+	0.999241i	$0.512403\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	0.294105	+	0.955773i	$0.404978\pi$
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	−0.974776	+	0.223184i	$0.928355\pi$
$662$		0			0
$663$	−12.0000	−	20.7846i	−0.466041	−	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	25.0000	+	43.3013i	0.968004	+	1.67663i
$668$	−2.00000	+	3.46410i	−0.0773823	+	0.134030i
$669$	1.50000	−	2.59808i	0.0579934	−	0.100447i
$670$		0			0
$671$	2.00000			0.0772091
$672$		0			0
$673$	4.00000			0.154189			0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000			0.154189			0.0770943	+	0.997024i	$0.475436\pi$
$674$		0			0
$675$	−18.0000	+	31.1769i	−0.692820	+	1.20000i
$676$	3.00000	−	5.19615i	0.115385	−	0.199852i
$677$	−19.0000	−	32.9090i	−0.730229	−	1.26479i	−0.956785	−	0.290796i	$-0.906080\pi$
$677$	−19.0000	−	32.9090i	−0.730229	−	1.26479i	0.226556	−	0.973998i	$-0.427253\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$		0			0
$683$	−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	$0.240403\pi$
$684$	−36.0000	−	62.3538i	−1.37649	−	2.38416i
$685$	3.00000			0.114624
$686$		0			0
$687$	21.0000			0.801200
$688$	16.0000	+	27.7128i	0.609994	+	1.05654i
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$	−7.50000	−	12.9904i	−0.285313	−	0.494177i	0.687372	−	0.726306i	$-0.258764\pi$
$691$	−7.50000	−	12.9904i	−0.285313	−	0.494177i	−0.972685	+	0.232128i	$0.925431\pi$
$692$	−32.0000			−1.21646
$693$		0			0
$694$		0			0
$695$	−5.00000	−	8.66025i	−0.189661	−	0.328502i
$696$		0			0
$697$	2.00000	−	3.46410i	0.0757554	−	0.131212i
$698$		0			0
$699$	−18.0000			−0.680823
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−15.0000	+	25.9808i	−0.565736	+	0.979883i
$704$	−4.00000	+	6.92820i	−0.150756	+	0.261116i
$705$	−12.0000	−	20.7846i	−0.451946	−	0.782794i
$706$		0			0
$707$		0			0
$708$	18.0000			0.676481
$709$	−19.5000	−	33.7750i	−0.732338	−	1.26845i	−0.955882	−	0.293752i	$-0.905096\pi$
$709$	−19.5000	−	33.7750i	−0.732338	−	1.26845i	0.223544	−	0.974694i	$-0.428237\pi$
$710$		0			0
$711$	−18.0000	+	31.1769i	−0.675053	+	1.16923i
$712$		0			0
$713$	−5.00000			−0.187251
$714$		0			0
$715$	−4.00000			−0.149592
$716$	1.00000	+	1.73205i	0.0373718	+	0.0647298i
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$		0			0
$719$	5.50000	+	9.52628i	0.205115	+	0.355270i	0.950169	−	0.311734i	$-0.100910\pi$
$719$	5.50000	+	9.52628i	0.205115	+	0.355270i	−0.745054	+	0.667004i	$0.767576\pi$
$720$	−24.0000			−0.894427
$721$		0			0
$722$		0			0
$723$	−18.0000	−	31.1769i	−0.669427	−	1.15948i
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	20.0000	−	34.6410i	0.742781	−	1.28654i
$726$		0			0
$727$	−19.0000			−0.704671			−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000			−0.704671			−0.352335	+	0.935874i	$0.614612\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	8.00000	−	13.8564i	0.295891	−	0.512498i
$732$	6.00000	−	10.3923i	0.221766	−	0.384111i
$733$	2.00000	+	3.46410i	0.0738717	+	0.127950i	0.900595	−	0.434659i	$-0.143131\pi$
$733$	2.00000	+	3.46410i	0.0738717	+	0.127950i	−0.826723	+	0.562609i	$0.809798\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.50000	−	2.59808i	−0.0552532	−	0.0957014i
$738$		0			0
$739$	9.00000	−	15.5885i	0.331070	−	0.573431i	−0.651652	−	0.758518i	$-0.725924\pi$
$739$	9.00000	−	15.5885i	0.331070	−	0.573431i	0.982722	+	0.185088i	$0.0592569\pi$
$740$	5.00000	+	8.66025i	0.183804	+	0.318357i
$741$	−72.0000			−2.64499
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	−11.0000	+	19.0526i	−0.403009	+	0.698032i
$746$		0			0
$747$	−36.0000	−	62.3538i	−1.31717	−	2.28141i
$748$	4.00000			0.146254
$749$		0			0
$750$		0			0
$751$	11.5000	+	19.9186i	0.419641	+	0.726839i	0.995903	−	0.0904254i	$-0.0288227\pi$
$751$	11.5000	+	19.9186i	0.419641	+	0.726839i	−0.576262	+	0.817265i	$0.695489\pi$
$752$	−16.0000	+	27.7128i	−0.583460	+	1.01058i
$753$	−31.5000	+	54.5596i	−1.14792	+	1.98826i
$754$		0			0
$755$	−6.00000			−0.218362
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$		0			0
$759$	7.50000	−	12.9904i	0.272233	−	0.471521i
$760$		0			0
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.861996	+	0.506915i	$0.169214\pi$
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.00800331	+	0.999968i	$0.497452\pi$
$762$		0			0
$763$		0			0
$764$	−10.0000			−0.361787
$765$	6.00000	+	10.3923i	0.216930	+	0.375735i
$766$		0			0
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$	24.0000	+	41.5692i	0.866025	+	1.50000i
$769$	40.0000			1.44244			0.721218	−	0.692708i	$-0.243582\pi$
$769$	40.0000			1.44244			0.721218	+	0.692708i	$0.243582\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	14.0000	+	24.2487i	0.503871	+	0.872730i
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$		0			0
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$	−12.0000	+	20.7846i	−0.429669	+	0.744208i
$781$	0.500000	−	0.866025i	0.0178914	−	0.0309888i
$782$		0			0
$783$	−90.0000			−3.21634
$784$		0			0
$785$	−7.00000			−0.249841
$786$		0			0
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	−0.600620	−	0.799535i	$-0.705079\pi$
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	0.992727	+	0.120384i	$0.0384127\pi$
$788$	18.0000	−	31.1769i	0.641223	−	1.11063i
$789$	27.0000	+	46.7654i	0.961225	+	1.66489i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−4.00000	−	6.92820i	−0.142044	−	0.246028i
$794$		0			0
$795$	9.00000	−	15.5885i	0.319197	−	0.552866i
$796$	−8.00000	−	13.8564i	−0.283552	−	0.491127i
$797$	23.0000			0.814702			0.407351	−	0.913272i	$-0.366453\pi$
$797$	23.0000			0.814702			0.407351	+	0.913272i	$0.366453\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$		0			0
$801$	45.0000	−	77.9423i	1.59000	−	2.75396i
$802$		0			0
$803$	5.00000	+	8.66025i	0.176446	+	0.305614i
$804$	−18.0000			−0.634811
$805$		0			0
$806$		0			0
$807$	−27.0000	−	46.7654i	−0.950445	−	1.64622i
$808$		0			0
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$		0			0
$811$	−22.0000			−0.772524			−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000			−0.772524			−0.386262	+	0.922389i	$0.626234\pi$
$812$		0			0
$813$	−48.0000			−1.68343
$814$		0			0
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$	12.0000	−	20.7846i	0.420084	−	0.727607i
$817$	−24.0000	−	41.5692i	−0.839654	−	1.45432i
$818$		0			0
$819$		0			0
$820$	−4.00000			−0.139686
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	12.5000	−	21.6506i	0.435723	−	0.754694i	−0.561632	−	0.827387i	$-0.689826\pi$
$823$	12.5000	−	21.6506i	0.435723	−	0.754694i	0.997354	+	0.0726937i	$0.0231595\pi$
$824$		0			0
$825$	−12.0000			−0.417786
$826$		0			0
$827$	20.0000			0.695468			0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000			0.695468			0.347734	+	0.937593i	$0.386951\pi$
$828$	−30.0000	−	51.9615i	−1.04257	−	1.80579i
$829$	14.5000	−	25.1147i	0.503606	−	0.872271i	−0.496385	−	0.868102i	$-0.665340\pi$
$829$	14.5000	−	25.1147i	0.503606	−	0.872271i	0.999991	−	0.00416865i	$-0.00132693\pi$
$830$		0			0
$831$	36.0000	+	62.3538i	1.24883	+	2.16303i
$832$	32.0000			1.10940
$833$		0			0
$834$		0			0
$835$	−1.00000	−	1.73205i	−0.0346064	−	0.0599401i
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$	4.50000	−	7.79423i	0.155543	−	0.269408i
$838$		0			0
$839$	45.0000			1.55357			0.776786	−	0.629764i	$-0.216849\pi$
$839$	45.0000			1.55357			0.776786	+	0.629764i	$0.216849\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$		0			0
$843$	−6.00000	+	10.3923i	−0.206651	+	0.357930i
$844$	−2.00000	+	3.46410i	−0.0688428	+	0.119239i
$845$	1.50000	+	2.59808i	0.0516016	+	0.0893765i
$846$		0			0
$847$		0			0
$848$	−24.0000			−0.824163
$849$		0			0
$850$		0			0
$851$	−12.5000	+	21.6506i	−0.428494	+	0.742174i
$852$	−3.00000	−	5.19615i	−0.102778	−	0.178017i
$853$	−34.0000			−1.16414			−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000			−1.16414			−0.582069	+	0.813139i	$0.697757\pi$
$854$		0			0
$855$	36.0000			1.23117
$856$		0			0
$857$	14.0000	−	24.2487i	0.478231	−	0.828320i	−0.521458	−	0.853277i	$-0.674612\pi$
$857$	14.0000	−	24.2487i	0.478231	−	0.828320i	0.999689	+	0.0249570i	$0.00794488\pi$
$858$		0			0
$859$	−27.5000	−	47.6314i	−0.938288	−	1.62516i	−0.768663	−	0.639654i	$-0.779078\pi$
$859$	−27.5000	−	47.6314i	−0.938288	−	1.62516i	−0.169625	−	0.985509i	$-0.554255\pi$
$860$	−16.0000			−0.545595
$861$		0			0
$862$		0			0
$863$	−26.0000	−	45.0333i	−0.885050	−	1.53295i	−0.845656	−	0.533728i	$-0.820790\pi$
$863$	−26.0000	−	45.0333i	−0.885050	−	1.53295i	−0.0393943	−	0.999224i	$-0.512543\pi$
$864$		0			0
$865$	8.00000	−	13.8564i	0.272008	−	0.471132i
$866$		0			0
$867$	39.0000			1.32451
$868$		0			0
$869$	−6.00000			−0.203536
$870$		0			0
$871$	−6.00000	+	10.3923i	−0.203302	+	0.352130i
$872$		0			0
$873$	15.0000	+	25.9808i	0.507673	+	0.879316i
$874$		0			0
$875$		0			0
$876$	60.0000			2.02721
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	0.985079	+	0.172102i	$0.0550559\pi$
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	−0.343495	+	0.939155i	$0.611611\pi$
$878$		0			0
$879$	−9.00000	+	15.5885i	−0.303562	+	0.525786i
$880$	−2.00000	−	3.46410i	−0.0674200	−	0.116775i
$881$	27.0000			0.909653			0.454827	−	0.890580i	$-0.349701\pi$
$881$	27.0000			0.909653			0.454827	+	0.890580i	$0.349701\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	−8.00000	−	13.8564i	−0.269069	−	0.466041i
$885$	−4.50000	+	7.79423i	−0.151266	+	0.262000i
$886$		0			0
$887$	1.00000	+	1.73205i	0.0335767	+	0.0581566i	0.882325	−	0.470640i	$-0.155977\pi$
$887$	1.00000	+	1.73205i	0.0335767	+	0.0581566i	−0.848749	+	0.528796i	$0.822644\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.50000	+	7.79423i	0.150756	+	0.261116i
$892$	1.00000	−	1.73205i	0.0334825	−	0.0579934i
$893$	24.0000	−	41.5692i	0.803129	−	1.39106i
$894$		0			0
$895$	−1.00000			−0.0334263
$896$		0			0
$897$	−60.0000			−2.00334
$898$		0			0
$899$	−5.00000	+	8.66025i	−0.166759	+	0.288836i
$900$	−24.0000	+	41.5692i	−0.800000	+	1.38564i
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.50000	+	4.33013i	0.0831028	+	0.143938i
$906$		0			0
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	0.979531	−	0.201291i	$-0.0645138\pi$
$908$	4.00000	+	6.92820i	0.132745	+	0.229920i
$909$	−72.0000			−2.38809
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−36.0000	−	62.3538i	−1.19208	−	2.06474i
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$		0			0
$915$	3.00000	+	5.19615i	0.0991769	+	0.171780i
$916$	14.0000			0.462573
$917$		0			0
$918$		0			0
$919$	−24.0000	−	41.5692i	−0.791687	−	1.37124i	−0.924922	−	0.380158i	$-0.875870\pi$
$919$	−24.0000	−	41.5692i	−0.791687	−	1.37124i	0.133235	−	0.991084i	$-0.457464\pi$
$920$		0			0
$921$	−42.0000	+	72.7461i	−1.38395	+	2.39707i
$922$		0			0
$923$	−4.00000			−0.131662
$924$		0			0
$925$	20.0000			0.657596
$926$		0			0
$927$	36.0000	−	62.3538i	1.18240	−	2.04797i
$928$		0			0
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		0			0
$931$		0			0
$932$	−12.0000			−0.393073
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$		0			0
$935$	−1.00000	+	1.73205i	−0.0327035	+	0.0566441i
$936$		0			0
$937$	36.0000			1.17607			0.588034	−	0.808836i	$-0.299902\pi$
$937$	36.0000			1.17607			0.588034	+	0.808836i	$0.299902\pi$
$938$		0			0
$939$	69.0000			2.25173
$940$	−8.00000	−	13.8564i	−0.260931	−	0.451946i
$941$	−29.0000	+	50.2295i	−0.945373	+	1.63743i	−0.190370	+	0.981712i	$0.560969\pi$
$941$	−29.0000	+	50.2295i	−0.945373	+	1.63743i	−0.755003	+	0.655722i	$0.772364\pi$
$942$		0			0
$943$	−5.00000	−	8.66025i	−0.162822	−	0.282017i
$944$	12.0000			0.390567
$945$		0			0
$946$		0			0
$947$	−2.50000	−	4.33013i	−0.0812391	−	0.140710i	0.822543	−	0.568702i	$-0.192554\pi$
$947$	−2.50000	−	4.33013i	−0.0812391	−	0.140710i	−0.903782	+	0.427992i	$0.859221\pi$
$948$	−18.0000	+	31.1769i	−0.584613	+	1.01258i
$949$	20.0000	−	34.6410i	0.649227	−	1.12449i
$950$		0			0
$951$	−27.0000			−0.875535
$952$		0			0
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$		0			0
$955$	2.50000	−	4.33013i	0.0808981	−	0.140120i
$956$	4.00000	−	6.92820i	0.129369	−	0.224074i
$957$	−15.0000	−	25.9808i	−0.484881	−	0.839839i
$958$		0			0
$959$		0			0
$960$	−24.0000			−0.774597
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$	30.0000	−	51.9615i	0.966736	−	1.67444i
$964$	−12.0000	−	20.7846i	−0.386494	−	0.669427i
$965$	−14.0000			−0.450676
$966$		0			0
$967$	−34.0000			−1.09337			−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000			−1.09337			−0.546683	+	0.837340i	$0.684110\pi$
$968$		0			0
$969$	−18.0000	+	31.1769i	−0.578243	+	1.00155i
$970$		0			0
$971$	−14.5000	−	25.1147i	−0.465327	−	0.805970i	0.533889	−	0.845555i	$-0.320730\pi$
$971$	−14.5000	−	25.1147i	−0.465327	−	0.805970i	−0.999216	+	0.0395843i	$0.987397\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	24.0000	+	41.5692i	0.768615	+	1.33128i
$976$	4.00000	−	6.92820i	0.128037	−	0.221766i
$977$	15.5000	−	26.8468i	0.495889	−	0.858905i	−0.504100	−	0.863645i	$-0.668176\pi$
$977$	15.5000	−	26.8468i	0.495889	−	0.858905i	0.999989	+	0.00474056i	$0.00150897\pi$
$978$		0			0
$979$	15.0000			0.479402
$980$		0			0
$981$	24.0000			0.766261
$982$		0			0
$983$	13.5000	−	23.3827i	0.430583	−	0.745792i	−0.566340	−	0.824171i	$-0.691641\pi$
$983$	13.5000	−	23.3827i	0.430583	−	0.745792i	0.996924	+	0.0783795i	$0.0249746\pi$
$984$		0			0
$985$	9.00000	+	15.5885i	0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$	−48.0000			−1.52708
$989$	−20.0000	−	34.6410i	−0.635963	−	1.10152i
$990$		0			0
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	−0.491698	−	0.870766i	$-0.663623\pi$
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	0.999954	−	0.00956046i	$-0.00304324\pi$
$992$		0			0
$993$	51.0000			1.61844
$994$		0			0
$995$	8.00000			0.253617
$996$	−36.0000	−	62.3538i	−1.14070	−	1.97576i
$997$	6.00000	−	10.3923i	0.190022	−	0.329128i	−0.755235	−	0.655454i	$-0.772477\pi$
$997$	6.00000	−	10.3923i	0.190022	−	0.329128i	0.945257	+	0.326326i	$0.105811\pi$
$998$		0			0
$999$	−22.5000	−	38.9711i	−0.711868	−	1.23299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.e.f.67.1		2
7.2	even	3	inner	539.2.e.f.177.1		2
7.3	odd	6		539.2.a.c.1.1		1
7.4	even	3		77.2.a.a.1.1	✓	1
7.5	odd	6		539.2.e.c.177.1		2
7.6	odd	2		539.2.e.c.67.1		2
21.11	odd	6		693.2.a.c.1.1		1
21.17	even	6		4851.2.a.j.1.1		1
28.3	even	6		8624.2.a.a.1.1		1
28.11	odd	6		1232.2.a.l.1.1		1
35.4	even	6		1925.2.a.h.1.1		1
35.18	odd	12		1925.2.b.e.1849.1		2
35.32	odd	12		1925.2.b.e.1849.2		2
56.11	odd	6		4928.2.a.a.1.1		1
56.53	even	6		4928.2.a.bj.1.1		1
77.4	even	15		847.2.f.i.148.1		4
77.10	even	6		5929.2.a.f.1.1		1
77.18	odd	30		847.2.f.h.148.1		4
77.25	even	15		847.2.f.i.372.1		4
77.32	odd	6		847.2.a.b.1.1		1
77.39	odd	30		847.2.f.h.729.1		4
77.46	odd	30		847.2.f.h.323.1		4
77.53	even	15		847.2.f.i.323.1		4
77.60	even	15		847.2.f.i.729.1		4
77.74	odd	30		847.2.f.h.372.1		4
231.32	even	6		7623.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.a.1.1	✓	1	7.4	even	3
539.2.a.c.1.1		1	7.3	odd	6
539.2.e.c.67.1		2	7.6	odd	2
539.2.e.c.177.1		2	7.5	odd	6
539.2.e.f.67.1		2	1.1	even	1	trivial
539.2.e.f.177.1		2	7.2	even	3	inner
693.2.a.c.1.1		1	21.11	odd	6
847.2.a.b.1.1		1	77.32	odd	6
847.2.f.h.148.1		4	77.18	odd	30
847.2.f.h.323.1		4	77.46	odd	30
847.2.f.h.372.1		4	77.74	odd	30
847.2.f.h.729.1		4	77.39	odd	30
847.2.f.i.148.1		4	77.4	even	15
847.2.f.i.323.1		4	77.53	even	15
847.2.f.i.372.1		4	77.25	even	15
847.2.f.i.729.1		4	77.60	even	15
1232.2.a.l.1.1		1	28.11	odd	6
1925.2.a.h.1.1		1	35.4	even	6
1925.2.b.e.1849.1		2	35.18	odd	12
1925.2.b.e.1849.2		2	35.32	odd	12
4851.2.a.j.1.1		1	21.17	even	6
4928.2.a.a.1.1		1	56.11	odd	6
4928.2.a.bj.1.1		1	56.53	even	6
5929.2.a.f.1.1		1	77.10	even	6
7623.2.a.j.1.1		1	231.32	even	6
8624.2.a.a.1.1		1	28.3	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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-3.00000 - 5.19615i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-3.00000 - 5.19615i) q^{12} -4.00000 q^{13} +3.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{19} +2.00000 q^{20} +(2.50000 + 4.33013i) q^{23} +(2.00000 - 3.46410i) q^{25} -9.00000 q^{27} +10.0000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-1.50000 - 2.59808i) q^{33} -12.0000 q^{36} +(2.50000 + 4.33013i) q^{37} +(-6.00000 + 10.3923i) q^{39} -2.00000 q^{41} -8.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(3.00000 - 5.19615i) q^{45} +(-4.00000 - 6.92820i) q^{47} -12.0000 q^{48} +(3.00000 + 5.19615i) q^{51} +(-4.00000 + 6.92820i) q^{52} +(3.00000 - 5.19615i) q^{53} +1.00000 q^{55} +18.0000 q^{57} +(-1.50000 + 2.59808i) q^{59} +(3.00000 - 5.19615i) q^{60} +(1.00000 + 1.73205i) q^{61} -8.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(1.50000 - 2.59808i) q^{67} +(2.00000 + 3.46410i) q^{68} +15.0000 q^{69} +1.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(-6.00000 - 10.3923i) q^{75} +12.0000 q^{76} +(-3.00000 - 5.19615i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +12.0000 q^{83} -2.00000 q^{85} +(15.0000 - 25.9808i) q^{87} +(7.50000 + 12.9904i) q^{89} +10.0000 q^{92} +(1.50000 + 2.59808i) q^{93} +(-3.00000 + 5.19615i) q^{95} -5.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 2 q^{4} + q^{5} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 2 * q^4 + q^5 - 6 * q^9	\( 2 q + 3 q^{3} + 2 q^{4} + q^{5} - 6 q^{9} + q^{11} - 6 q^{12} - 8 q^{13} + 6 q^{15} - 4 q^{16} - 2 q^{17} + 6 q^{19} + 4 q^{20} + 5 q^{23} + 4 q^{25} - 18 q^{27} + 20 q^{29} - q^{31} - 3 q^{33} - 24 q^{36} + 5 q^{37} - 12 q^{39} - 4 q^{41} - 16 q^{43} - 2 q^{44} + 6 q^{45} - 8 q^{47} - 24 q^{48} + 6 q^{51} - 8 q^{52} + 6 q^{53} + 2 q^{55} + 36 q^{57} - 3 q^{59} + 6 q^{60} + 2 q^{61} - 16 q^{64} - 4 q^{65} + 3 q^{67} + 4 q^{68} + 30 q^{69} + 2 q^{71} - 10 q^{73} - 12 q^{75} + 24 q^{76} - 6 q^{79} + 4 q^{80} - 9 q^{81} + 24 q^{83} - 4 q^{85} + 30 q^{87} + 15 q^{89} + 20 q^{92} + 3 q^{93} - 6 q^{95} - 10 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 2 * q^4 + q^5 - 6 * q^9 + q^11 - 6 * q^12 - 8 * q^13 + 6 * q^15 - 4 * q^16 - 2 * q^17 + 6 * q^19 + 4 * q^20 + 5 * q^23 + 4 * q^25 - 18 * q^27 + 20 * q^29 - q^31 - 3 * q^33 - 24 * q^36 + 5 * q^37 - 12 * q^39 - 4 * q^41 - 16 * q^43 - 2 * q^44 + 6 * q^45 - 8 * q^47 - 24 * q^48 + 6 * q^51 - 8 * q^52 + 6 * q^53 + 2 * q^55 + 36 * q^57 - 3 * q^59 + 6 * q^60 + 2 * q^61 - 16 * q^64 - 4 * q^65 + 3 * q^67 + 4 * q^68 + 30 * q^69 + 2 * q^71 - 10 * q^73 - 12 * q^75 + 24 * q^76 - 6 * q^79 + 4 * q^80 - 9 * q^81 + 24 * q^83 - 4 * q^85 + 30 * q^87 + 15 * q^89 + 20 * q^92 + 3 * q^93 - 6 * q^95 - 10 * q^97 - 12 * q^99

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