LMFDB - Embedded newform 1280.2.n.i.1023.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(767,1280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1280.767"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1280, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,2,0,-4,0,-2,0,0,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 320)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1023.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1280.1023
Dual form			1280.2.n.i.767.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} +1.00000i q^{9} +4.00000i q^{11} +(3.00000 + 3.00000i) q^{13} +(-3.00000 + 1.00000i) q^{15} +(-3.00000 + 3.00000i) q^{17} +6.00000 q^{19} -2.00000 q^{21} +(-3.00000 + 3.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} -2.00000i q^{29} -6.00000i q^{31} +(4.00000 + 4.00000i) q^{33} +(1.00000 + 3.00000i) q^{35} +(3.00000 - 3.00000i) q^{37} +6.00000 q^{39} -6.00000 q^{41} +(3.00000 - 3.00000i) q^{43} +(1.00000 - 2.00000i) q^{45} +(9.00000 + 9.00000i) q^{47} -5.00000i q^{49} +6.00000i q^{51} +(5.00000 + 5.00000i) q^{53} +(4.00000 - 8.00000i) q^{55} +(6.00000 - 6.00000i) q^{57} +10.0000 q^{59} -12.0000 q^{61} +(1.00000 - 1.00000i) q^{63} +(-3.00000 - 9.00000i) q^{65} +(9.00000 + 9.00000i) q^{67} +6.00000i q^{69} +6.00000i q^{71} +(-5.00000 - 5.00000i) q^{73} +(7.00000 + 1.00000i) q^{75} +(4.00000 - 4.00000i) q^{77} +5.00000 q^{81} +(-3.00000 + 3.00000i) q^{83} +(9.00000 - 3.00000i) q^{85} +(-2.00000 - 2.00000i) q^{87} -6.00000i q^{91} +(-6.00000 - 6.00000i) q^{93} +(-12.0000 - 6.00000i) q^{95} +(-7.00000 + 7.00000i) q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 6 q^{13} - 6 q^{15} - 6 q^{17} + 12 q^{19} - 4 q^{21} - 6 q^{23} + 6 q^{25} + 8 q^{27} + 8 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} - 12 q^{41} + 6 q^{43} + 2 q^{45}+ \cdots - 8 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 6 * q^13 - 6 * q^15 - 6 * q^17 + 12 * q^19 - 4 * q^21 - 6 * q^23 + 6 * q^25 + 8 * q^27 + 8 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 - 12 * q^41 + 6 * q^43 + 2 * q^45 + 18 * q^47 + 10 * q^53 + 8 * q^55 + 12 * q^57 + 20 * q^59 - 24 * q^61 + 2 * q^63 - 6 * q^65 + 18 * q^67 - 10 * q^73 + 14 * q^75 + 8 * q^77 + 10 * q^81 - 6 * q^83 + 18 * q^85 - 4 * q^87 - 12 * q^93 - 24 * q^95 - 14 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	0.934172	+	0.356822i	$0.116140\pi$
$4$		0			0
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			4.00000i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$11$			4.00000i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$12$		0			0
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	0.987797	−	0.155747i	$-0.0497784\pi$
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	−0.155747	+	0.987797i	$0.549778\pi$
$14$		0			0
$15$	−3.00000	+	1.00000i	−0.774597	+	0.258199i
$16$		0			0
$17$	−3.00000	+	3.00000i	−0.727607	+	0.727607i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−3.00000	+	3.00000i	−0.727607	+	0.727607i	0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$		0			0
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	−0.946943	−	0.321400i	$-0.895847\pi$
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	0.321400	+	0.946943i	$0.395847\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$	4.00000	+	4.00000i	0.769800	+	0.769800i
$28$		0			0
$29$		−	2.00000i		−	0.371391i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		0			0
$31$		−	6.00000i		−	1.07763i	−0.842424	−	0.538816i	$-0.818872\pi$
$31$		−	6.00000i		−	1.07763i	0.842424	−	0.538816i	$-0.181128\pi$
$32$		0			0
$33$	4.00000	+	4.00000i	0.696311	+	0.696311i
$34$		0			0
$35$	1.00000	+	3.00000i	0.169031	+	0.507093i
$36$		0			0
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$		0			0
$39$	6.00000			0.960769
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$		0			0
$45$	1.00000	−	2.00000i	0.149071	−	0.298142i
$46$		0			0
$47$	9.00000	+	9.00000i	1.31278	+	1.31278i	0.919354	+	0.393431i	$0.128712\pi$
$47$	9.00000	+	9.00000i	1.31278	+	1.31278i	0.393431	+	0.919354i	$0.371288\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$			6.00000i			0.840168i
$52$		0			0
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	4.00000	−	8.00000i	0.539360	−	1.07872i
$56$		0			0
$57$	6.00000	−	6.00000i	0.794719	−	0.794719i
$58$		0			0
$59$	10.0000			1.30189			0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000			1.30189			0.650945	+	0.759125i	$0.274373\pi$
$60$		0			0
$61$	−12.0000			−1.53644			−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000			−1.53644			−0.768221	+	0.640184i	$0.778858\pi$
$62$		0			0
$63$	1.00000	−	1.00000i	0.125988	−	0.125988i
$64$		0			0
$65$	−3.00000	−	9.00000i	−0.372104	−	1.11631i
$66$		0			0
$67$	9.00000	+	9.00000i	1.09952	+	1.09952i	0.994466	+	0.105059i	$0.0335031\pi$
$67$	9.00000	+	9.00000i	1.09952	+	1.09952i	0.105059	+	0.994466i	$0.466497\pi$
$68$		0			0
$69$			6.00000i			0.722315i
$70$		0			0
$71$			6.00000i			0.712069i	0.934473	+	0.356034i	$0.115871\pi$
$71$			6.00000i			0.712069i	−0.934473	+	0.356034i	$0.884129\pi$
$72$		0			0
$73$	−5.00000	−	5.00000i	−0.585206	−	0.585206i	0.351123	−	0.936329i	$-0.385800\pi$
$73$	−5.00000	−	5.00000i	−0.585206	−	0.585206i	−0.936329	+	0.351123i	$0.885800\pi$
$74$		0			0
$75$	7.00000	+	1.00000i	0.808290	+	0.115470i
$76$		0			0
$77$	4.00000	−	4.00000i	0.455842	−	0.455842i
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	−3.00000	+	3.00000i	−0.329293	+	0.329293i	−0.852318	−	0.523025i	$-0.824804\pi$
$83$	−3.00000	+	3.00000i	−0.329293	+	0.329293i	0.523025	+	0.852318i	$0.324804\pi$
$84$		0			0
$85$	9.00000	−	3.00000i	0.976187	−	0.325396i
$86$		0			0
$87$	−2.00000	−	2.00000i	−0.214423	−	0.214423i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$		−	6.00000i		−	0.628971i
$92$		0			0
$93$	−6.00000	−	6.00000i	−0.622171	−	0.622171i
$94$		0			0
$95$	−12.0000	−	6.00000i	−1.23117	−	0.615587i
$96$		0			0
$97$	−7.00000	+	7.00000i	−0.710742	+	0.710742i	−0.966691	−	0.255948i	$-0.917612\pi$
$97$	−7.00000	+	7.00000i	−0.710742	+	0.710742i	0.255948	+	0.966691i	$0.417612\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	−8.00000			−0.796030			−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000			−0.796030			−0.398015	+	0.917379i	$0.630301\pi$
$102$		0			0
$103$	−11.0000	+	11.0000i	−1.08386	+	1.08386i	−0.0877167	+	0.996145i	$0.527957\pi$
$103$	−11.0000	+	11.0000i	−1.08386	+	1.08386i	−0.996145	+	0.0877167i	$0.972043\pi$
$104$		0			0
$105$	4.00000	+	2.00000i	0.390360	+	0.195180i
$106$		0			0
$107$	3.00000	+	3.00000i	0.290021	+	0.290021i	0.837088	−	0.547068i	$-0.184256\pi$
$107$	3.00000	+	3.00000i	0.290021	+	0.290021i	−0.547068	+	0.837088i	$0.684256\pi$
$108$		0			0
$109$			18.0000i			1.72409i	0.506834	+	0.862044i	$0.330816\pi$
$109$			18.0000i			1.72409i	−0.506834	+	0.862044i	$0.669184\pi$
$110$		0			0
$111$		−	6.00000i		−	0.569495i
$112$		0			0
$113$	−3.00000	−	3.00000i	−0.282216	−	0.282216i	0.551776	−	0.833992i	$-0.313950\pi$
$113$	−3.00000	−	3.00000i	−0.282216	−	0.282216i	−0.833992	+	0.551776i	$0.813950\pi$
$114$		0			0
$115$	9.00000	−	3.00000i	0.839254	−	0.279751i
$116$		0			0
$117$	−3.00000	+	3.00000i	−0.277350	+	0.277350i
$118$		0			0
$119$	6.00000			0.550019
$120$		0			0
$121$	−5.00000			−0.454545
$122$		0			0
$123$	−6.00000	+	6.00000i	−0.541002	+	0.541002i
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	5.00000	+	5.00000i	0.443678	+	0.443678i	0.893246	−	0.449568i	$-0.148422\pi$
$127$	5.00000	+	5.00000i	0.443678	+	0.443678i	−0.449568	+	0.893246i	$0.648422\pi$
$128$		0			0
$129$		−	6.00000i		−	0.528271i
$130$		0			0
$131$		−	4.00000i		−	0.349482i	−0.984614	−	0.174741i	$-0.944091\pi$
$131$		−	4.00000i		−	0.349482i	0.984614	−	0.174741i	$-0.0559088\pi$
$132$		0			0
$133$	−6.00000	−	6.00000i	−0.520266	−	0.520266i
$134$		0			0
$135$	−4.00000	−	12.0000i	−0.344265	−	1.03280i
$136$		0			0
$137$	3.00000	−	3.00000i	0.256307	−	0.256307i	−0.567243	−	0.823550i	$-0.691990\pi$
$137$	3.00000	−	3.00000i	0.256307	−	0.256307i	0.823550	+	0.567243i	$0.191990\pi$
$138$		0			0
$139$	−6.00000			−0.508913			−0.254457	−	0.967084i	$-0.581897\pi$
$139$	−6.00000			−0.508913			−0.254457	+	0.967084i	$0.581897\pi$
$140$		0			0
$141$	18.0000			1.51587
$142$		0			0
$143$	−12.0000	+	12.0000i	−1.00349	+	1.00349i
$144$		0			0
$145$	−2.00000	+	4.00000i	−0.166091	+	0.332182i
$146$		0			0
$147$	−5.00000	−	5.00000i	−0.412393	−	0.412393i
$148$		0			0
$149$		−	2.00000i		−	0.163846i	−0.996639	−	0.0819232i	$-0.973894\pi$
$149$		−	2.00000i		−	0.163846i	0.996639	−	0.0819232i	$-0.0261062\pi$
$150$		0			0
$151$		−	10.0000i		−	0.813788i	−0.913475	−	0.406894i	$-0.866612\pi$
$151$		−	10.0000i		−	0.813788i	0.913475	−	0.406894i	$-0.133388\pi$
$152$		0			0
$153$	−3.00000	−	3.00000i	−0.242536	−	0.242536i
$154$		0			0
$155$	−6.00000	+	12.0000i	−0.481932	+	0.963863i
$156$		0			0
$157$	−3.00000	+	3.00000i	−0.239426	+	0.239426i	−0.816612	−	0.577186i	$-0.804151\pi$
$157$	−3.00000	+	3.00000i	−0.239426	+	0.239426i	0.577186	+	0.816612i	$0.304151\pi$
$158$		0			0
$159$	10.0000			0.793052
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	9.00000	−	9.00000i	0.704934	−	0.704934i	−0.260531	−	0.965465i	$-0.583898\pi$
$163$	9.00000	−	9.00000i	0.704934	−	0.704934i	0.965465	+	0.260531i	$0.0838976\pi$
$164$		0			0
$165$	−4.00000	−	12.0000i	−0.311400	−	0.934199i
$166$		0			0
$167$	3.00000	+	3.00000i	0.232147	+	0.232147i	0.813588	−	0.581441i	$-0.197511\pi$
$167$	3.00000	+	3.00000i	0.232147	+	0.232147i	−0.581441	+	0.813588i	$0.697511\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$			6.00000i			0.458831i
$172$		0			0
$173$	15.0000	+	15.0000i	1.14043	+	1.14043i	0.988372	+	0.152057i	$0.0485898\pi$
$173$	15.0000	+	15.0000i	1.14043	+	1.14043i	0.152057	+	0.988372i	$0.451410\pi$
$174$		0			0
$175$	1.00000	−	7.00000i	0.0755929	−	0.529150i
$176$		0			0
$177$	10.0000	−	10.0000i	0.751646	−	0.751646i
$178$		0			0
$179$	−2.00000			−0.149487			−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000			−0.149487			−0.0747435	+	0.997203i	$0.523814\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	−12.0000	+	12.0000i	−0.887066	+	0.887066i
$184$		0			0
$185$	−9.00000	+	3.00000i	−0.661693	+	0.220564i
$186$		0			0
$187$	−12.0000	−	12.0000i	−0.877527	−	0.877527i
$188$		0			0
$189$		−	8.00000i		−	0.581914i
$190$		0			0
$191$		−	6.00000i		−	0.434145i	−0.976156	−	0.217072i	$-0.930349\pi$
$191$		−	6.00000i		−	0.434145i	0.976156	−	0.217072i	$-0.0696508\pi$
$192$		0			0
$193$	5.00000	+	5.00000i	0.359908	+	0.359908i	0.863779	−	0.503871i	$-0.168091\pi$
$193$	5.00000	+	5.00000i	0.359908	+	0.359908i	−0.503871	+	0.863779i	$0.668091\pi$
$194$		0			0
$195$	−12.0000	−	6.00000i	−0.859338	−	0.429669i
$196$		0			0
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	−0.862423	−	0.506188i	$-0.831054\pi$
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	0.506188	+	0.862423i	$0.331054\pi$
$198$		0			0
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$		0			0
$201$	18.0000			1.26962
$202$		0			0
$203$	−2.00000	+	2.00000i	−0.140372	+	0.140372i
$204$		0			0
$205$	12.0000	+	6.00000i	0.838116	+	0.419058i
$206$		0			0
$207$	−3.00000	−	3.00000i	−0.208514	−	0.208514i
$208$		0			0
$209$			24.0000i			1.66011i
$210$		0			0
$211$		−	12.0000i		−	0.826114i	−0.910705	−	0.413057i	$-0.864461\pi$
$211$		−	12.0000i		−	0.826114i	0.910705	−	0.413057i	$-0.135539\pi$
$212$		0			0
$213$	6.00000	+	6.00000i	0.411113	+	0.411113i
$214$		0			0
$215$	−9.00000	+	3.00000i	−0.613795	+	0.204598i
$216$		0			0
$217$	−6.00000	+	6.00000i	−0.407307	+	0.407307i
$218$		0			0
$219$	−10.0000			−0.675737
$220$		0			0
$221$	−18.0000			−1.21081
$222$		0			0
$223$	−13.0000	+	13.0000i	−0.870544	+	0.870544i	−0.992532	−	0.121987i	$-0.961073\pi$
$223$	−13.0000	+	13.0000i	−0.870544	+	0.870544i	0.121987	+	0.992532i	$0.461073\pi$
$224$		0			0
$225$	−4.00000	+	3.00000i	−0.266667	+	0.200000i
$226$		0			0
$227$	−11.0000	−	11.0000i	−0.730096	−	0.730096i	0.240543	−	0.970639i	$-0.422675\pi$
$227$	−11.0000	−	11.0000i	−0.730096	−	0.730096i	−0.970639	+	0.240543i	$0.922675\pi$
$228$		0			0
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		0			0
$231$		−	8.00000i		−	0.526361i
$232$		0			0
$233$	15.0000	+	15.0000i	0.982683	+	0.982683i	0.999853	−	0.0171699i	$-0.00546562\pi$
$233$	15.0000	+	15.0000i	0.982683	+	0.982683i	−0.0171699	+	0.999853i	$0.505466\pi$
$234$		0			0
$235$	−9.00000	−	27.0000i	−0.587095	−	1.76129i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		0			0
$243$	−7.00000	+	7.00000i	−0.449050	+	0.449050i
$244$		0			0
$245$	−5.00000	+	10.0000i	−0.319438	+	0.638877i
$246$		0			0
$247$	18.0000	+	18.0000i	1.14531	+	1.14531i
$248$		0			0
$249$			6.00000i			0.380235i
$250$		0			0
$251$		−	4.00000i		−	0.252478i	−0.992000	−	0.126239i	$-0.959709\pi$
$251$		−	4.00000i		−	0.252478i	0.992000	−	0.126239i	$-0.0402906\pi$
$252$		0			0
$253$	−12.0000	−	12.0000i	−0.754434	−	0.754434i
$254$		0			0
$255$	6.00000	−	12.0000i	0.375735	−	0.751469i
$256$		0			0
$257$	−3.00000	+	3.00000i	−0.187135	+	0.187135i	−0.794456	−	0.607321i	$-0.792244\pi$
$257$	−3.00000	+	3.00000i	−0.187135	+	0.187135i	0.607321	+	0.794456i	$0.292244\pi$
$258$		0			0
$259$	−6.00000			−0.372822
$260$		0			0
$261$	2.00000			0.123797
$262$		0			0
$263$	9.00000	−	9.00000i	0.554964	−	0.554964i	−0.372906	−	0.927869i	$-0.621638\pi$
$263$	9.00000	−	9.00000i	0.554964	−	0.554964i	0.927869	+	0.372906i	$0.121638\pi$
$264$		0			0
$265$	−5.00000	−	15.0000i	−0.307148	−	0.921443i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	14.0000i		−	0.853595i	−0.904347	−	0.426798i	$-0.859642\pi$
$269$		−	14.0000i		−	0.853595i	0.904347	−	0.426798i	$-0.140358\pi$
$270$		0			0
$271$			2.00000i			0.121491i	0.998153	+	0.0607457i	$0.0193479\pi$
$271$			2.00000i			0.121491i	−0.998153	+	0.0607457i	$0.980652\pi$
$272$		0			0
$273$	−6.00000	−	6.00000i	−0.363137	−	0.363137i
$274$		0			0
$275$	−16.0000	+	12.0000i	−0.964836	+	0.723627i
$276$		0			0
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	−0.0942828	−	0.995545i	$-0.530056\pi$
$277$	15.0000	−	15.0000i	0.901263	−	0.901263i	0.995545	+	0.0942828i	$0.0300558\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	15.0000	−	15.0000i	0.891657	−	0.891657i	−0.103022	−	0.994679i	$-0.532851\pi$
$283$	15.0000	−	15.0000i	0.891657	−	0.891657i	0.994679	+	0.103022i	$0.0328511\pi$
$284$		0			0
$285$	−18.0000	+	6.00000i	−1.06623	+	0.355409i
$286$		0			0
$287$	6.00000	+	6.00000i	0.354169	+	0.354169i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$		0			0
$291$			14.0000i			0.820695i
$292$		0			0
$293$	1.00000	+	1.00000i	0.0584206	+	0.0584206i	0.735714	−	0.677293i	$-0.236847\pi$
$293$	1.00000	+	1.00000i	0.0584206	+	0.0584206i	−0.677293	+	0.735714i	$0.736847\pi$
$294$		0			0
$295$	−20.0000	−	10.0000i	−1.16445	−	0.582223i
$296$		0			0
$297$	−16.0000	+	16.0000i	−0.928414	+	0.928414i
$298$		0			0
$299$	−18.0000			−1.04097
$300$		0			0
$301$	−6.00000			−0.345834
$302$		0			0
$303$	−8.00000	+	8.00000i	−0.459588	+	0.459588i
$304$		0			0
$305$	24.0000	+	12.0000i	1.37424	+	0.687118i
$306$		0			0
$307$	−15.0000	−	15.0000i	−0.856095	−	0.856095i	0.134780	−	0.990876i	$-0.456967\pi$
$307$	−15.0000	−	15.0000i	−0.856095	−	0.856095i	−0.990876	+	0.134780i	$0.956967\pi$
$308$		0			0
$309$			22.0000i			1.25154i
$310$		0			0
$311$		−	18.0000i		−	1.02069i	−0.859971	−	0.510343i	$-0.829518\pi$
$311$		−	18.0000i		−	1.02069i	0.859971	−	0.510343i	$-0.170482\pi$
$312$		0			0
$313$	−1.00000	−	1.00000i	−0.0565233	−	0.0565233i	0.678280	−	0.734803i	$-0.262726\pi$
$313$	−1.00000	−	1.00000i	−0.0565233	−	0.0565233i	−0.734803	+	0.678280i	$0.762726\pi$
$314$		0			0
$315$	−3.00000	+	1.00000i	−0.169031	+	0.0563436i
$316$		0			0
$317$	−3.00000	+	3.00000i	−0.168497	+	0.168497i	−0.786318	−	0.617822i	$-0.788015\pi$
$317$	−3.00000	+	3.00000i	−0.168497	+	0.168497i	0.617822	+	0.786318i	$0.288015\pi$
$318$		0			0
$319$	8.00000			0.447914
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$	−18.0000	+	18.0000i	−1.00155	+	1.00155i
$324$		0			0
$325$	−3.00000	+	21.0000i	−0.166410	+	1.16487i
$326$		0			0
$327$	18.0000	+	18.0000i	0.995402	+	0.995402i
$328$		0			0
$329$		−	18.0000i		−	0.992372i
$330$		0			0
$331$		−	12.0000i		−	0.659580i	−0.944054	−	0.329790i	$-0.893022\pi$
$331$		−	12.0000i		−	0.659580i	0.944054	−	0.329790i	$-0.106978\pi$
$332$		0			0
$333$	3.00000	+	3.00000i	0.164399	+	0.164399i
$334$		0			0
$335$	−9.00000	−	27.0000i	−0.491723	−	1.47517i
$336$		0			0
$337$	25.0000	−	25.0000i	1.36184	−	1.36184i	0.490261	−	0.871576i	$-0.336901\pi$
$337$	25.0000	−	25.0000i	1.36184	−	1.36184i	0.871576	−	0.490261i	$-0.163099\pi$
$338$		0			0
$339$	−6.00000			−0.325875
$340$		0			0
$341$	24.0000			1.29967
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$	6.00000	−	12.0000i	0.323029	−	0.646058i
$346$		0			0
$347$	−17.0000	−	17.0000i	−0.912608	−	0.912608i	0.0838690	−	0.996477i	$-0.473272\pi$
$347$	−17.0000	−	17.0000i	−0.912608	−	0.912608i	−0.996477	+	0.0838690i	$0.973272\pi$
$348$		0			0
$349$		−	18.0000i		−	0.963518i	−0.876304	−	0.481759i	$-0.839998\pi$
$349$		−	18.0000i		−	0.963518i	0.876304	−	0.481759i	$-0.160002\pi$
$350$		0			0
$351$			24.0000i			1.28103i
$352$		0			0
$353$	−15.0000	−	15.0000i	−0.798369	−	0.798369i	0.184469	−	0.982838i	$-0.440943\pi$
$353$	−15.0000	−	15.0000i	−0.798369	−	0.798369i	−0.982838	+	0.184469i	$0.940943\pi$
$354$		0			0
$355$	6.00000	−	12.0000i	0.318447	−	0.636894i
$356$		0			0
$357$	6.00000	−	6.00000i	0.317554	−	0.317554i
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$		0			0
$363$	−5.00000	+	5.00000i	−0.262432	+	0.262432i
$364$		0			0
$365$	5.00000	+	15.0000i	0.261712	+	0.785136i
$366$		0			0
$367$	−11.0000	−	11.0000i	−0.574195	−	0.574195i	0.359103	−	0.933298i	$-0.383083\pi$
$367$	−11.0000	−	11.0000i	−0.574195	−	0.574195i	−0.933298	+	0.359103i	$0.883083\pi$
$368$		0			0
$369$		−	6.00000i		−	0.312348i
$370$		0			0
$371$		−	10.0000i		−	0.519174i
$372$		0			0
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	0.625161	−	0.780496i	$-0.285033\pi$
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	−0.780496	+	0.625161i	$0.785033\pi$
$374$		0			0
$375$	−13.0000	−	9.00000i	−0.671317	−	0.464758i
$376$		0			0
$377$	6.00000	−	6.00000i	0.309016	−	0.309016i
$378$		0			0
$379$	18.0000			0.924598			0.462299	−	0.886724i	$-0.347025\pi$
$379$	18.0000			0.924598			0.462299	+	0.886724i	$0.347025\pi$
$380$		0			0
$381$	10.0000			0.512316
$382$		0			0
$383$	−21.0000	+	21.0000i	−1.07305	+	1.07305i	−0.0759373	+	0.997113i	$0.524195\pi$
$383$	−21.0000	+	21.0000i	−1.07305	+	1.07305i	−0.997113	+	0.0759373i	$0.975805\pi$
$384$		0			0
$385$	−12.0000	+	4.00000i	−0.611577	+	0.203859i
$386$		0			0
$387$	3.00000	+	3.00000i	0.152499	+	0.152499i
$388$		0			0
$389$		−	26.0000i		−	1.31825i	−0.752032	−	0.659126i	$-0.770926\pi$
$389$		−	26.0000i		−	1.31825i	0.752032	−	0.659126i	$-0.229074\pi$
$390$		0			0
$391$		−	18.0000i		−	0.910299i
$392$		0			0
$393$	−4.00000	−	4.00000i	−0.201773	−	0.201773i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.00000	−	9.00000i	0.451697	−	0.451697i	−0.444220	−	0.895918i	$-0.646519\pi$
$397$	9.00000	−	9.00000i	0.451697	−	0.451697i	0.895918	+	0.444220i	$0.146519\pi$
$398$		0			0
$399$	−12.0000			−0.600751
$400$		0			0
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$		0			0
$403$	18.0000	−	18.0000i	0.896644	−	0.896644i
$404$		0			0
$405$	−10.0000	−	5.00000i	−0.496904	−	0.248452i
$406$		0			0
$407$	12.0000	+	12.0000i	0.594818	+	0.594818i
$408$		0			0
$409$		−	12.0000i		−	0.593362i	−0.954977	−	0.296681i	$-0.904120\pi$
$409$		−	12.0000i		−	0.593362i	0.954977	−	0.296681i	$-0.0958798\pi$
$410$		0			0
$411$		−	6.00000i		−	0.295958i
$412$		0			0
$413$	−10.0000	−	10.0000i	−0.492068	−	0.492068i
$414$		0			0
$415$	9.00000	−	3.00000i	0.441793	−	0.147264i
$416$		0			0
$417$	−6.00000	+	6.00000i	−0.293821	+	0.293821i
$418$		0			0
$419$	−10.0000			−0.488532			−0.244266	−	0.969708i	$-0.578547\pi$
$419$	−10.0000			−0.488532			−0.244266	+	0.969708i	$0.578547\pi$
$420$		0			0
$421$	−12.0000			−0.584844			−0.292422	−	0.956289i	$-0.594461\pi$
$421$	−12.0000			−0.584844			−0.292422	+	0.956289i	$0.594461\pi$
$422$		0			0
$423$	−9.00000	+	9.00000i	−0.437595	+	0.437595i
$424$		0			0
$425$	−21.0000	−	3.00000i	−1.01865	−	0.145521i
$426$		0			0
$427$	12.0000	+	12.0000i	0.580721	+	0.580721i
$428$		0			0
$429$			24.0000i			1.15873i
$430$		0			0
$431$		−	30.0000i		−	1.44505i	−0.691345	−	0.722525i	$-0.742982\pi$
$431$		−	30.0000i		−	1.44505i	0.691345	−	0.722525i	$-0.257018\pi$
$432$		0			0
$433$	−7.00000	−	7.00000i	−0.336399	−	0.336399i	0.518611	−	0.855010i	$-0.326449\pi$
$433$	−7.00000	−	7.00000i	−0.336399	−	0.336399i	−0.855010	+	0.518611i	$0.826449\pi$
$434$		0			0
$435$	2.00000	+	6.00000i	0.0958927	+	0.287678i
$436$		0			0
$437$	−18.0000	+	18.0000i	−0.861057	+	0.861057i
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$	5.00000			0.238095
$442$		0			0
$443$	−25.0000	+	25.0000i	−1.18779	+	1.18779i	−0.210108	+	0.977678i	$0.567381\pi$
$443$	−25.0000	+	25.0000i	−1.18779	+	1.18779i	−0.977678	+	0.210108i	$0.932619\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−2.00000	−	2.00000i	−0.0945968	−	0.0945968i
$448$		0			0
$449$		−	12.0000i		−	0.566315i	−0.959073	−	0.283158i	$-0.908618\pi$
$449$		−	12.0000i		−	0.566315i	0.959073	−	0.283158i	$-0.0913819\pi$
$450$		0			0
$451$		−	24.0000i		−	1.13012i
$452$		0			0
$453$	−10.0000	−	10.0000i	−0.469841	−	0.469841i
$454$		0			0
$455$	−6.00000	+	12.0000i	−0.281284	+	0.562569i
$456$		0			0
$457$	−17.0000	+	17.0000i	−0.795226	+	0.795226i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$	−17.0000	+	17.0000i	−0.795226	+	0.795226i	0.187112	+	0.982339i	$0.440087\pi$
$458$		0			0
$459$	−24.0000			−1.12022
$460$		0			0
$461$	40.0000			1.86299			0.931493	−	0.363760i	$-0.118507\pi$
$461$	40.0000			1.86299			0.931493	+	0.363760i	$0.118507\pi$
$462$		0			0
$463$	−1.00000	+	1.00000i	−0.0464739	+	0.0464739i	−0.729962	−	0.683488i	$-0.760462\pi$
$463$	−1.00000	+	1.00000i	−0.0464739	+	0.0464739i	0.683488	+	0.729962i	$0.260462\pi$
$464$		0			0
$465$	6.00000	+	18.0000i	0.278243	+	0.834730i
$466$		0			0
$467$	21.0000	+	21.0000i	0.971764	+	0.971764i	0.999612	−	0.0278481i	$-0.00886546\pi$
$467$	21.0000	+	21.0000i	0.971764	+	0.971764i	−0.0278481	+	0.999612i	$0.508865\pi$
$468$		0			0
$469$		−	18.0000i		−	0.831163i
$470$		0			0
$471$			6.00000i			0.276465i
$472$		0			0
$473$	12.0000	+	12.0000i	0.551761	+	0.551761i
$474$		0			0
$475$	18.0000	+	24.0000i	0.825897	+	1.10120i
$476$		0			0
$477$	−5.00000	+	5.00000i	−0.228934	+	0.228934i
$478$		0			0
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$		0			0
$481$	18.0000			0.820729
$482$		0			0
$483$	6.00000	−	6.00000i	0.273009	−	0.273009i
$484$		0			0
$485$	21.0000	−	7.00000i	0.953561	−	0.317854i
$486$		0			0
$487$	−1.00000	−	1.00000i	−0.0453143	−	0.0453143i	0.684087	−	0.729401i	$-0.260201\pi$
$487$	−1.00000	−	1.00000i	−0.0453143	−	0.0453143i	−0.729401	+	0.684087i	$0.760201\pi$
$488$		0			0
$489$		−	18.0000i		−	0.813988i
$490$		0			0
$491$			20.0000i			0.902587i	0.892375	+	0.451294i	$0.149037\pi$
$491$			20.0000i			0.902587i	−0.892375	+	0.451294i	$0.850963\pi$
$492$		0			0
$493$	6.00000	+	6.00000i	0.270226	+	0.270226i
$494$		0			0
$495$	8.00000	+	4.00000i	0.359573	+	0.179787i
$496$		0			0
$497$	6.00000	−	6.00000i	0.269137	−	0.269137i
$498$		0			0
$499$	6.00000			0.268597			0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000			0.268597			0.134298	+	0.990941i	$0.457122\pi$
$500$		0			0
$501$	6.00000			0.268060
$502$		0			0
$503$	21.0000	−	21.0000i	0.936344	−	0.936344i	−0.0617480	−	0.998092i	$-0.519668\pi$
$503$	21.0000	−	21.0000i	0.936344	−	0.936344i	0.998092	+	0.0617480i	$0.0196675\pi$
$504$		0			0
$505$	16.0000	+	8.00000i	0.711991	+	0.355995i
$506$		0			0
$507$	5.00000	+	5.00000i	0.222058	+	0.222058i
$508$		0			0
$509$			14.0000i			0.620539i	0.950649	+	0.310270i	$0.100419\pi$
$509$			14.0000i			0.620539i	−0.950649	+	0.310270i	$0.899581\pi$
$510$		0			0
$511$			10.0000i			0.442374i
$512$		0			0
$513$	24.0000	+	24.0000i	1.05963	+	1.05963i
$514$		0			0
$515$	33.0000	−	11.0000i	1.45415	−	0.484718i
$516$		0			0
$517$	−36.0000	+	36.0000i	−1.58328	+	1.58328i
$518$		0			0
$519$	30.0000			1.31685
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	15.0000	−	15.0000i	0.655904	−	0.655904i	−0.298504	−	0.954408i	$-0.596488\pi$
$523$	15.0000	−	15.0000i	0.655904	−	0.655904i	0.954408	+	0.298504i	$0.0964877\pi$
$524$		0			0
$525$	−6.00000	−	8.00000i	−0.261861	−	0.349149i
$526$		0			0
$527$	18.0000	+	18.0000i	0.784092	+	0.784092i
$528$		0			0
$529$			5.00000i			0.217391i
$530$		0			0
$531$			10.0000i			0.433963i
$532$		0			0
$533$	−18.0000	−	18.0000i	−0.779667	−	0.779667i
$534$		0			0
$535$	−3.00000	−	9.00000i	−0.129701	−	0.389104i
$536$		0			0
$537$	−2.00000	+	2.00000i	−0.0863064	+	0.0863064i
$538$		0			0
$539$	20.0000			0.861461
$540$		0			0
$541$	24.0000			1.03184			0.515920	−	0.856637i	$-0.327450\pi$
$541$	24.0000			1.03184			0.515920	+	0.856637i	$0.327450\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	18.0000	−	36.0000i	0.771035	−	1.54207i
$546$		0			0
$547$	−3.00000	−	3.00000i	−0.128271	−	0.128271i	0.640057	−	0.768328i	$-0.278911\pi$
$547$	−3.00000	−	3.00000i	−0.128271	−	0.128271i	−0.768328	+	0.640057i	$0.778911\pi$
$548$		0			0
$549$		−	12.0000i		−	0.512148i
$550$		0			0
$551$		−	12.0000i		−	0.511217i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−6.00000	+	12.0000i	−0.254686	+	0.509372i
$556$		0			0
$557$	−31.0000	+	31.0000i	−1.31351	+	1.31351i	−0.394704	+	0.918808i	$0.629153\pi$
$557$	−31.0000	+	31.0000i	−1.31351	+	1.31351i	−0.918808	+	0.394704i	$0.870847\pi$
$558$		0			0
$559$	18.0000			0.761319
$560$		0			0
$561$	−24.0000			−1.01328
$562$		0			0
$563$	1.00000	−	1.00000i	0.0421450	−	0.0421450i	−0.685720	−	0.727865i	$-0.740513\pi$
$563$	1.00000	−	1.00000i	0.0421450	−	0.0421450i	0.727865	+	0.685720i	$0.240513\pi$
$564$		0			0
$565$	3.00000	+	9.00000i	0.126211	+	0.378633i
$566$		0			0
$567$	−5.00000	−	5.00000i	−0.209980	−	0.209980i
$568$		0			0
$569$			12.0000i			0.503066i	0.967849	+	0.251533i	$0.0809347\pi$
$569$			12.0000i			0.503066i	−0.967849	+	0.251533i	$0.919065\pi$
$570$		0			0
$571$		−	12.0000i		−	0.502184i	−0.967963	−	0.251092i	$-0.919210\pi$
$571$		−	12.0000i		−	0.502184i	0.967963	−	0.251092i	$-0.0807897\pi$
$572$		0			0
$573$	−6.00000	−	6.00000i	−0.250654	−	0.250654i
$574$		0			0
$575$	−21.0000	−	3.00000i	−0.875761	−	0.125109i
$576$		0			0
$577$	−19.0000	+	19.0000i	−0.790980	+	0.790980i	−0.981654	−	0.190673i	$-0.938933\pi$
$577$	−19.0000	+	19.0000i	−0.790980	+	0.790980i	0.190673	+	0.981654i	$0.438933\pi$
$578$		0			0
$579$	10.0000			0.415586
$580$		0			0
$581$	6.00000			0.248922
$582$		0			0
$583$	−20.0000	+	20.0000i	−0.828315	+	0.828315i
$584$		0			0
$585$	9.00000	−	3.00000i	0.372104	−	0.124035i
$586$		0			0
$587$	15.0000	+	15.0000i	0.619116	+	0.619116i	0.945305	−	0.326188i	$-0.105764\pi$
$587$	15.0000	+	15.0000i	0.619116	+	0.619116i	−0.326188	+	0.945305i	$0.605764\pi$
$588$		0			0
$589$		−	36.0000i		−	1.48335i
$590$		0			0
$591$			10.0000i			0.411345i
$592$		0			0
$593$	−15.0000	−	15.0000i	−0.615976	−	0.615976i	0.328521	−	0.944497i	$-0.393450\pi$
$593$	−15.0000	−	15.0000i	−0.615976	−	0.615976i	−0.944497	+	0.328521i	$0.893450\pi$
$594$		0			0
$595$	−12.0000	−	6.00000i	−0.491952	−	0.245976i
$596$		0			0
$597$	16.0000	−	16.0000i	0.654836	−	0.654836i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	−9.00000	+	9.00000i	−0.366508	+	0.366508i
$604$		0			0
$605$	10.0000	+	5.00000i	0.406558	+	0.203279i
$606$		0			0
$607$	−7.00000	−	7.00000i	−0.284121	−	0.284121i	0.550629	−	0.834750i	$-0.314388\pi$
$607$	−7.00000	−	7.00000i	−0.284121	−	0.284121i	−0.834750	+	0.550629i	$0.814388\pi$
$608$		0			0
$609$			4.00000i			0.162088i
$610$		0			0
$611$			54.0000i			2.18461i
$612$		0			0
$613$	9.00000	+	9.00000i	0.363507	+	0.363507i	0.865102	−	0.501596i	$-0.167253\pi$
$613$	9.00000	+	9.00000i	0.363507	+	0.363507i	−0.501596	+	0.865102i	$0.667253\pi$
$614$		0			0
$615$	18.0000	−	6.00000i	0.725830	−	0.241943i
$616$		0			0
$617$	15.0000	−	15.0000i	0.603877	−	0.603877i	−0.337462	−	0.941339i	$-0.609568\pi$
$617$	15.0000	−	15.0000i	0.603877	−	0.603877i	0.941339	+	0.337462i	$0.109568\pi$
$618$		0			0
$619$	42.0000			1.68812			0.844061	−	0.536247i	$-0.180158\pi$
$619$	42.0000			1.68812			0.844061	+	0.536247i	$0.180158\pi$
$620$		0			0
$621$	−24.0000			−0.963087
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	24.0000	+	24.0000i	0.958468	+	0.958468i
$628$		0			0
$629$			18.0000i			0.717707i
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$		0			0
$633$	−12.0000	−	12.0000i	−0.476957	−	0.476957i
$634$		0			0
$635$	−5.00000	−	15.0000i	−0.198419	−	0.595257i
$636$		0			0
$637$	15.0000	−	15.0000i	0.594322	−	0.594322i
$638$		0			0
$639$	−6.00000			−0.237356
$640$		0			0
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$	−3.00000	+	3.00000i	−0.118308	+	0.118308i	−0.763782	−	0.645474i	$-0.776660\pi$
$643$	−3.00000	+	3.00000i	−0.118308	+	0.118308i	0.645474	+	0.763782i	$0.276660\pi$
$644$		0			0
$645$	−6.00000	+	12.0000i	−0.236250	+	0.472500i
$646$		0			0
$647$	−9.00000	−	9.00000i	−0.353827	−	0.353827i	0.507705	−	0.861531i	$-0.330494\pi$
$647$	−9.00000	−	9.00000i	−0.353827	−	0.353827i	−0.861531	+	0.507705i	$0.830494\pi$
$648$		0			0
$649$			40.0000i			1.57014i
$650$		0			0
$651$			12.0000i			0.470317i
$652$		0			0
$653$	−33.0000	−	33.0000i	−1.29139	−	1.29139i	−0.933928	−	0.357462i	$-0.883642\pi$
$653$	−33.0000	−	33.0000i	−1.29139	−	1.29139i	−0.357462	−	0.933928i	$-0.616358\pi$
$654$		0			0
$655$	−4.00000	+	8.00000i	−0.156293	+	0.312586i
$656$		0			0
$657$	5.00000	−	5.00000i	0.195069	−	0.195069i
$658$		0			0
$659$	22.0000			0.856998			0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000			0.856998			0.428499	+	0.903542i	$0.359042\pi$
$660$		0			0
$661$	12.0000			0.466746			0.233373	−	0.972387i	$-0.425024\pi$
$661$	12.0000			0.466746			0.233373	+	0.972387i	$0.425024\pi$
$662$		0			0
$663$	−18.0000	+	18.0000i	−0.699062	+	0.699062i
$664$		0			0
$665$	6.00000	+	18.0000i	0.232670	+	0.698010i
$666$		0			0
$667$	6.00000	+	6.00000i	0.232321	+	0.232321i
$668$		0			0
$669$			26.0000i			1.00522i
$670$		0			0
$671$		−	48.0000i		−	1.85302i
$672$		0			0
$673$	25.0000	+	25.0000i	0.963679	+	0.963679i	0.999363	−	0.0356839i	$-0.0113610\pi$
$673$	25.0000	+	25.0000i	0.963679	+	0.963679i	−0.0356839	+	0.999363i	$0.511361\pi$
$674$		0			0
$675$	−4.00000	+	28.0000i	−0.153960	+	1.07772i
$676$		0			0
$677$	27.0000	−	27.0000i	1.03769	−	1.03769i	0.0384331	−	0.999261i	$-0.487763\pi$
$677$	27.0000	−	27.0000i	1.03769	−	1.03769i	0.999261	−	0.0384331i	$-0.0122367\pi$
$678$		0			0
$679$	14.0000			0.537271
$680$		0			0
$681$	−22.0000			−0.843042
$682$		0			0
$683$	27.0000	−	27.0000i	1.03313	−	1.03313i	0.0336941	−	0.999432i	$-0.489273\pi$
$683$	27.0000	−	27.0000i	1.03313	−	1.03313i	0.999432	−	0.0336941i	$-0.0107272\pi$
$684$		0			0
$685$	−9.00000	+	3.00000i	−0.343872	+	0.114624i
$686$		0			0
$687$	−6.00000	−	6.00000i	−0.228914	−	0.228914i
$688$		0			0
$689$			30.0000i			1.14291i
$690$		0			0
$691$		−	12.0000i		−	0.456502i	−0.973602	−	0.228251i	$-0.926699\pi$
$691$		−	12.0000i		−	0.456502i	0.973602	−	0.228251i	$-0.0733006\pi$
$692$		0			0
$693$	4.00000	+	4.00000i	0.151947	+	0.151947i
$694$		0			0
$695$	12.0000	+	6.00000i	0.455186	+	0.227593i
$696$		0			0
$697$	18.0000	−	18.0000i	0.681799	−	0.681799i
$698$		0			0
$699$	30.0000			1.13470
$700$		0			0
$701$	−20.0000			−0.755390			−0.377695	−	0.925930i	$-0.623283\pi$
$701$	−20.0000			−0.755390			−0.377695	+	0.925930i	$0.623283\pi$
$702$		0			0
$703$	18.0000	−	18.0000i	0.678883	−	0.678883i
$704$		0			0
$705$	−36.0000	−	18.0000i	−1.35584	−	0.677919i
$706$		0			0
$707$	8.00000	+	8.00000i	0.300871	+	0.300871i
$708$		0			0
$709$			42.0000i			1.57734i	0.614815	+	0.788672i	$0.289231\pi$
$709$			42.0000i			1.57734i	−0.614815	+	0.788672i	$0.710769\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	18.0000	+	18.0000i	0.674105	+	0.674105i
$714$		0			0
$715$	36.0000	−	12.0000i	1.34632	−	0.448775i
$716$		0			0
$717$	24.0000	−	24.0000i	0.896296	−	0.896296i
$718$		0			0
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$	22.0000			0.819323
$722$		0			0
$723$	−18.0000	+	18.0000i	−0.669427	+	0.669427i
$724$		0			0
$725$	8.00000	−	6.00000i	0.297113	−	0.222834i
$726$		0			0
$727$	−25.0000	−	25.0000i	−0.927199	−	0.927199i	0.0703254	−	0.997524i	$-0.477596\pi$
$727$	−25.0000	−	25.0000i	−0.927199	−	0.927199i	−0.997524	+	0.0703254i	$0.977596\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$		0			0
$731$			18.0000i			0.665754i
$732$		0			0
$733$	15.0000	+	15.0000i	0.554038	+	0.554038i	0.927604	−	0.373566i	$-0.121865\pi$
$733$	15.0000	+	15.0000i	0.554038	+	0.554038i	−0.373566	+	0.927604i	$0.621865\pi$
$734$		0			0
$735$	5.00000	+	15.0000i	0.184428	+	0.553283i
$736$		0			0
$737$	−36.0000	+	36.0000i	−1.32608	+	1.32608i
$738$		0			0
$739$	30.0000			1.10357			0.551784	−	0.833987i	$-0.313947\pi$
$739$	30.0000			1.10357			0.551784	+	0.833987i	$0.313947\pi$
$740$		0			0
$741$	36.0000			1.32249
$742$		0			0
$743$	9.00000	−	9.00000i	0.330178	−	0.330178i	−0.522476	−	0.852654i	$-0.674992\pi$
$743$	9.00000	−	9.00000i	0.330178	−	0.330178i	0.852654	+	0.522476i	$0.174992\pi$
$744$		0			0
$745$	−2.00000	+	4.00000i	−0.0732743	+	0.146549i
$746$		0			0
$747$	−3.00000	−	3.00000i	−0.109764	−	0.109764i
$748$		0			0
$749$		−	6.00000i		−	0.219235i
$750$		0			0
$751$			42.0000i			1.53260i	0.642482	+	0.766301i	$0.277905\pi$
$751$			42.0000i			1.53260i	−0.642482	+	0.766301i	$0.722095\pi$
$752$		0			0
$753$	−4.00000	−	4.00000i	−0.145768	−	0.145768i
$754$		0			0
$755$	−10.0000	+	20.0000i	−0.363937	+	0.727875i
$756$		0			0
$757$	−9.00000	+	9.00000i	−0.327111	+	0.327111i	−0.851487	−	0.524376i	$-0.824299\pi$
$757$	−9.00000	+	9.00000i	−0.327111	+	0.327111i	0.524376	+	0.851487i	$0.324299\pi$
$758$		0			0
$759$	−24.0000			−0.871145
$760$		0			0
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$		0			0
$763$	18.0000	−	18.0000i	0.651644	−	0.651644i
$764$		0			0
$765$	3.00000	+	9.00000i	0.108465	+	0.325396i
$766$		0			0
$767$	30.0000	+	30.0000i	1.08324	+	1.08324i
$768$		0			0
$769$		−	40.0000i		−	1.44244i	−0.692708	−	0.721218i	$-0.743582\pi$
$769$		−	40.0000i		−	1.44244i	0.692708	−	0.721218i	$-0.256418\pi$
$770$		0			0
$771$			6.00000i			0.216085i
$772$		0			0
$773$	9.00000	+	9.00000i	0.323708	+	0.323708i	0.850188	−	0.526480i	$-0.176489\pi$
$773$	9.00000	+	9.00000i	0.323708	+	0.323708i	−0.526480	+	0.850188i	$0.676489\pi$
$774$		0			0
$775$	24.0000	−	18.0000i	0.862105	−	0.646579i
$776$		0			0
$777$	−6.00000	+	6.00000i	−0.215249	+	0.215249i
$778$		0			0
$779$	−36.0000			−1.28983
$780$		0			0
$781$	−24.0000			−0.858788
$782$		0			0
$783$	8.00000	−	8.00000i	0.285897	−	0.285897i
$784$		0			0
$785$	9.00000	−	3.00000i	0.321224	−	0.107075i
$786$		0			0
$787$	−15.0000	−	15.0000i	−0.534692	−	0.534692i	0.387273	−	0.921965i	$-0.373417\pi$
$787$	−15.0000	−	15.0000i	−0.534692	−	0.534692i	−0.921965	+	0.387273i	$0.873417\pi$
$788$		0			0
$789$		−	18.0000i		−	0.640817i
$790$		0			0
$791$			6.00000i			0.213335i
$792$		0			0
$793$	−36.0000	−	36.0000i	−1.27840	−	1.27840i
$794$		0			0
$795$	−20.0000	−	10.0000i	−0.709327	−	0.354663i
$796$		0			0
$797$	−3.00000	+	3.00000i	−0.106265	+	0.106265i	−0.758240	−	0.651975i	$-0.773941\pi$
$797$	−3.00000	+	3.00000i	−0.106265	+	0.106265i	0.651975	+	0.758240i	$0.273941\pi$
$798$		0			0
$799$	−54.0000			−1.91038
$800$		0			0
$801$		0			0
$802$		0			0
$803$	20.0000	−	20.0000i	0.705785	−	0.705785i
$804$		0			0
$805$	−12.0000	−	6.00000i	−0.422944	−	0.211472i
$806$		0			0
$807$	−14.0000	−	14.0000i	−0.492823	−	0.492823i
$808$		0			0
$809$		−	48.0000i		−	1.68759i	−0.536666	−	0.843795i	$-0.680316\pi$
$809$		−	48.0000i		−	1.68759i	0.536666	−	0.843795i	$-0.319684\pi$
$810$		0			0
$811$			12.0000i			0.421377i	0.977553	+	0.210688i	$0.0675706\pi$
$811$			12.0000i			0.421377i	−0.977553	+	0.210688i	$0.932429\pi$
$812$		0			0
$813$	2.00000	+	2.00000i	0.0701431	+	0.0701431i
$814$		0			0
$815$	−27.0000	+	9.00000i	−0.945769	+	0.315256i
$816$		0			0
$817$	18.0000	−	18.0000i	0.629740	−	0.629740i
$818$		0			0
$819$	6.00000			0.209657
$820$		0			0
$821$	−52.0000			−1.81481			−0.907406	−	0.420255i	$-0.861941\pi$
$821$	−52.0000			−1.81481			−0.907406	+	0.420255i	$0.861941\pi$
$822$		0			0
$823$	5.00000	−	5.00000i	0.174289	−	0.174289i	−0.614572	−	0.788861i	$-0.710671\pi$
$823$	5.00000	−	5.00000i	0.174289	−	0.174289i	0.788861	+	0.614572i	$0.210671\pi$
$824$		0			0
$825$	−4.00000	+	28.0000i	−0.139262	+	0.974835i
$826$		0			0
$827$	23.0000	+	23.0000i	0.799788	+	0.799788i	0.983062	−	0.183274i	$-0.0586694\pi$
$827$	23.0000	+	23.0000i	0.799788	+	0.799788i	−0.183274	+	0.983062i	$0.558669\pi$
$828$		0			0
$829$		−	30.0000i		−	1.04194i	−0.853574	−	0.520972i	$-0.825570\pi$
$829$		−	30.0000i		−	1.04194i	0.853574	−	0.520972i	$-0.174430\pi$
$830$		0			0
$831$		−	30.0000i		−	1.04069i
$832$		0			0
$833$	15.0000	+	15.0000i	0.519719	+	0.519719i
$834$		0			0
$835$	−3.00000	−	9.00000i	−0.103819	−	0.311458i
$836$		0			0
$837$	24.0000	−	24.0000i	0.829561	−	0.829561i
$838$		0			0
$839$	−48.0000			−1.65714			−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000			−1.65714			−0.828572	+	0.559883i	$0.810846\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$		0			0
$843$	−6.00000	+	6.00000i	−0.206651	+	0.206651i
$844$		0			0
$845$	5.00000	−	10.0000i	0.172005	−	0.344010i
$846$		0			0
$847$	5.00000	+	5.00000i	0.171802	+	0.171802i
$848$		0			0
$849$		−	30.0000i		−	1.02960i
$850$		0			0
$851$			18.0000i			0.617032i
$852$		0			0
$853$	9.00000	+	9.00000i	0.308154	+	0.308154i	0.844193	−	0.536039i	$-0.180080\pi$
$853$	9.00000	+	9.00000i	0.308154	+	0.308154i	−0.536039	+	0.844193i	$0.680080\pi$
$854$		0			0
$855$	6.00000	−	12.0000i	0.205196	−	0.410391i
$856$		0			0
$857$	27.0000	−	27.0000i	0.922302	−	0.922302i	−0.0748894	−	0.997192i	$-0.523860\pi$
$857$	27.0000	−	27.0000i	0.922302	−	0.922302i	0.997192	+	0.0748894i	$0.0238604\pi$
$858$		0			0
$859$	−6.00000			−0.204717			−0.102359	−	0.994748i	$-0.532639\pi$
$859$	−6.00000			−0.204717			−0.102359	+	0.994748i	$0.532639\pi$
$860$		0			0
$861$	12.0000			0.408959
$862$		0			0
$863$	15.0000	−	15.0000i	0.510606	−	0.510606i	−0.404106	−	0.914712i	$-0.632417\pi$
$863$	15.0000	−	15.0000i	0.510606	−	0.510606i	0.914712	+	0.404106i	$0.132417\pi$
$864$		0			0
$865$	−15.0000	−	45.0000i	−0.510015	−	1.53005i
$866$		0			0
$867$	−1.00000	−	1.00000i	−0.0339618	−	0.0339618i
$868$		0			0
$869$		0			0
$870$		0			0
$871$			54.0000i			1.82972i
$872$		0			0
$873$	−7.00000	−	7.00000i	−0.236914	−	0.236914i
$874$		0			0
$875$	−9.00000	+	13.0000i	−0.304256	+	0.439480i
$876$		0			0
$877$	−27.0000	+	27.0000i	−0.911725	+	0.911725i	−0.996408	−	0.0846827i	$-0.973012\pi$
$877$	−27.0000	+	27.0000i	−0.911725	+	0.911725i	0.0846827	+	0.996408i	$0.473012\pi$
$878$		0			0
$879$	2.00000			0.0674583
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	9.00000	−	9.00000i	0.302874	−	0.302874i	−0.539263	−	0.842137i	$-0.681297\pi$
$883$	9.00000	−	9.00000i	0.302874	−	0.302874i	0.842137	+	0.539263i	$0.181297\pi$
$884$		0			0
$885$	−30.0000	+	10.0000i	−1.00844	+	0.336146i
$886$		0			0
$887$	−9.00000	−	9.00000i	−0.302190	−	0.302190i	0.539680	−	0.841870i	$-0.318545\pi$
$887$	−9.00000	−	9.00000i	−0.302190	−	0.302190i	−0.841870	+	0.539680i	$0.818545\pi$
$888$		0			0
$889$		−	10.0000i		−	0.335389i
$890$		0			0
$891$			20.0000i			0.670025i
$892$		0			0
$893$	54.0000	+	54.0000i	1.80704	+	1.80704i
$894$		0			0
$895$	4.00000	+	2.00000i	0.133705	+	0.0668526i
$896$		0			0
$897$	−18.0000	+	18.0000i	−0.601003	+	0.601003i
$898$		0			0
$899$	−12.0000			−0.400222
$900$		0			0
$901$	−30.0000			−0.999445
$902$		0			0
$903$	−6.00000	+	6.00000i	−0.199667	+	0.199667i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	3.00000	+	3.00000i	0.0996134	+	0.0996134i	0.755157	−	0.655544i	$-0.227561\pi$
$907$	3.00000	+	3.00000i	0.0996134	+	0.0996134i	−0.655544	+	0.755157i	$0.727561\pi$
$908$		0			0
$909$		−	8.00000i		−	0.265343i
$910$		0			0
$911$		−	6.00000i		−	0.198789i	−0.995048	−	0.0993944i	$-0.968309\pi$
$911$		−	6.00000i		−	0.198789i	0.995048	−	0.0993944i	$-0.0316906\pi$
$912$		0			0
$913$	−12.0000	−	12.0000i	−0.397142	−	0.397142i
$914$		0			0
$915$	36.0000	−	12.0000i	1.19012	−	0.396708i
$916$		0			0
$917$	−4.00000	+	4.00000i	−0.132092	+	0.132092i
$918$		0			0
$919$	48.0000			1.58337			0.791687	−	0.610927i	$-0.209203\pi$
$919$	48.0000			1.58337			0.791687	+	0.610927i	$0.209203\pi$
$920$		0			0
$921$	−30.0000			−0.988534
$922$		0			0
$923$	−18.0000	+	18.0000i	−0.592477	+	0.592477i
$924$		0			0
$925$	21.0000	+	3.00000i	0.690476	+	0.0986394i
$926$		0			0
$927$	−11.0000	−	11.0000i	−0.361287	−	0.361287i
$928$		0			0
$929$			12.0000i			0.393707i	0.980433	+	0.196854i	$0.0630724\pi$
$929$			12.0000i			0.393707i	−0.980433	+	0.196854i	$0.936928\pi$
$930$		0			0
$931$		−	30.0000i		−	0.983210i
$932$		0			0
$933$	−18.0000	−	18.0000i	−0.589294	−	0.589294i
$934$		0			0
$935$	12.0000	+	36.0000i	0.392442	+	1.17733i
$936$		0			0
$937$	23.0000	−	23.0000i	0.751377	−	0.751377i	−0.223359	−	0.974736i	$-0.571702\pi$
$937$	23.0000	−	23.0000i	0.751377	−	0.751377i	0.974736	+	0.223359i	$0.0717022\pi$
$938$		0			0
$939$	−2.00000			−0.0652675
$940$		0			0
$941$	−32.0000			−1.04317			−0.521585	−	0.853199i	$-0.674659\pi$
$941$	−32.0000			−1.04317			−0.521585	+	0.853199i	$0.674659\pi$
$942$		0			0
$943$	18.0000	−	18.0000i	0.586161	−	0.586161i
$944$		0			0
$945$	−8.00000	+	16.0000i	−0.260240	+	0.520480i
$946$		0			0
$947$	−7.00000	−	7.00000i	−0.227469	−	0.227469i	0.584165	−	0.811635i	$-0.301422\pi$
$947$	−7.00000	−	7.00000i	−0.227469	−	0.227469i	−0.811635	+	0.584165i	$0.801422\pi$
$948$		0			0
$949$		−	30.0000i		−	0.973841i
$950$		0			0
$951$			6.00000i			0.194563i
$952$		0			0
$953$	−9.00000	−	9.00000i	−0.291539	−	0.291539i	0.546149	−	0.837688i	$-0.316093\pi$
$953$	−9.00000	−	9.00000i	−0.291539	−	0.291539i	−0.837688	+	0.546149i	$0.816093\pi$
$954$		0			0
$955$	−6.00000	+	12.0000i	−0.194155	+	0.388311i
$956$		0			0
$957$	8.00000	−	8.00000i	0.258603	−	0.258603i
$958$		0			0
$959$	−6.00000			−0.193750
$960$		0			0
$961$	−5.00000			−0.161290
$962$		0			0
$963$	−3.00000	+	3.00000i	−0.0966736	+	0.0966736i
$964$		0			0
$965$	−5.00000	−	15.0000i	−0.160956	−	0.482867i
$966$		0			0
$967$	−5.00000	−	5.00000i	−0.160789	−	0.160789i	0.622127	−	0.782916i	$-0.286269\pi$
$967$	−5.00000	−	5.00000i	−0.160789	−	0.160789i	−0.782916	+	0.622127i	$0.786269\pi$
$968$		0			0
$969$			36.0000i			1.15649i
$970$		0			0
$971$		−	20.0000i		−	0.641831i	−0.947108	−	0.320915i	$-0.896010\pi$
$971$		−	20.0000i		−	0.641831i	0.947108	−	0.320915i	$-0.103990\pi$
$972$		0			0
$973$	6.00000	+	6.00000i	0.192351	+	0.192351i
$974$		0			0
$975$	18.0000	+	24.0000i	0.576461	+	0.768615i
$976$		0			0
$977$	9.00000	−	9.00000i	0.287936	−	0.287936i	−0.548328	−	0.836263i	$-0.684735\pi$
$977$	9.00000	−	9.00000i	0.287936	−	0.287936i	0.836263	+	0.548328i	$0.184735\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−18.0000			−0.574696
$982$		0			0
$983$	33.0000	−	33.0000i	1.05254	−	1.05254i	0.0539954	−	0.998541i	$-0.482804\pi$
$983$	33.0000	−	33.0000i	1.05254	−	1.05254i	0.998541	−	0.0539954i	$-0.0171956\pi$
$984$		0			0
$985$	15.0000	−	5.00000i	0.477940	−	0.159313i
$986$		0			0
$987$	−18.0000	−	18.0000i	−0.572946	−	0.572946i
$988$		0			0
$989$			18.0000i			0.572367i
$990$		0			0
$991$			2.00000i			0.0635321i	0.999495	+	0.0317660i	$0.0101131\pi$
$991$			2.00000i			0.0635321i	−0.999495	+	0.0317660i	$0.989887\pi$
$992$		0			0
$993$	−12.0000	−	12.0000i	−0.380808	−	0.380808i
$994$		0			0
$995$	−32.0000	−	16.0000i	−1.01447	−	0.507234i
$996$		0			0
$997$	−9.00000	+	9.00000i	−0.285033	+	0.285033i	−0.835112	−	0.550079i	$-0.814597\pi$
$997$	−9.00000	+	9.00000i	−0.285033	+	0.285033i	0.550079	+	0.835112i	$0.314597\pi$
$998$		0			0
$999$	24.0000			0.759326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.n.i.1023.1		2
4.3	odd	2		1280.2.n.c.1023.1		2
5.2	odd	4		1280.2.n.c.767.1		2
8.3	odd	2		1280.2.n.j.1023.1		2
8.5	even	2		1280.2.n.d.1023.1		2
16.3	odd	4		320.2.o.a.223.1	✓	2
16.5	even	4		320.2.o.b.223.1	yes	2
16.11	odd	4		320.2.o.d.223.1	yes	2
16.13	even	4		320.2.o.c.223.1	yes	2
20.7	even	4	inner	1280.2.n.i.767.1		2
40.27	even	4		1280.2.n.d.767.1		2
40.37	odd	4		1280.2.n.j.767.1		2
80.3	even	4		1600.2.o.c.607.1		2
80.13	odd	4		1600.2.o.b.607.1		2
80.19	odd	4		1600.2.o.d.543.1		2
80.27	even	4		320.2.o.c.287.1	yes	2
80.29	even	4		1600.2.o.a.543.1		2
80.37	odd	4		320.2.o.a.287.1	yes	2
80.43	even	4		1600.2.o.a.607.1		2
80.53	odd	4		1600.2.o.d.607.1		2
80.59	odd	4		1600.2.o.b.543.1		2
80.67	even	4		320.2.o.b.287.1	yes	2
80.69	even	4		1600.2.o.c.543.1		2
80.77	odd	4		320.2.o.d.287.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
320.2.o.a.223.1	✓	2	16.3	odd	4
320.2.o.a.287.1	yes	2	80.37	odd	4
320.2.o.b.223.1	yes	2	16.5	even	4
320.2.o.b.287.1	yes	2	80.67	even	4
320.2.o.c.223.1	yes	2	16.13	even	4
320.2.o.c.287.1	yes	2	80.27	even	4
320.2.o.d.223.1	yes	2	16.11	odd	4
320.2.o.d.287.1	yes	2	80.77	odd	4
1280.2.n.c.767.1		2	5.2	odd	4
1280.2.n.c.1023.1		2	4.3	odd	2
1280.2.n.d.767.1		2	40.27	even	4
1280.2.n.d.1023.1		2	8.5	even	2
1280.2.n.i.767.1		2	20.7	even	4	inner
1280.2.n.i.1023.1		2	1.1	even	1	trivial
1280.2.n.j.767.1		2	40.37	odd	4
1280.2.n.j.1023.1		2	8.3	odd	2
1600.2.o.a.543.1		2	80.29	even	4
1600.2.o.a.607.1		2	80.43	even	4
1600.2.o.b.543.1		2	80.59	odd	4
1600.2.o.b.607.1		2	80.13	odd	4
1600.2.o.c.543.1		2	80.69	even	4
1600.2.o.c.607.1		2	80.3	even	4
1600.2.o.d.543.1		2	80.19	odd	4
1600.2.o.d.607.1		2	80.53	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} +1.00000i q^{9} +4.00000i q^{11} +(3.00000 + 3.00000i) q^{13} +(-3.00000 + 1.00000i) q^{15} +(-3.00000 + 3.00000i) q^{17} +6.00000 q^{19} -2.00000 q^{21} +(-3.00000 + 3.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} -2.00000i q^{29} -6.00000i q^{31} +(4.00000 + 4.00000i) q^{33} +(1.00000 + 3.00000i) q^{35} +(3.00000 - 3.00000i) q^{37} +6.00000 q^{39} -6.00000 q^{41} +(3.00000 - 3.00000i) q^{43} +(1.00000 - 2.00000i) q^{45} +(9.00000 + 9.00000i) q^{47} -5.00000i q^{49} +6.00000i q^{51} +(5.00000 + 5.00000i) q^{53} +(4.00000 - 8.00000i) q^{55} +(6.00000 - 6.00000i) q^{57} +10.0000 q^{59} -12.0000 q^{61} +(1.00000 - 1.00000i) q^{63} +(-3.00000 - 9.00000i) q^{65} +(9.00000 + 9.00000i) q^{67} +6.00000i q^{69} +6.00000i q^{71} +(-5.00000 - 5.00000i) q^{73} +(7.00000 + 1.00000i) q^{75} +(4.00000 - 4.00000i) q^{77} +5.00000 q^{81} +(-3.00000 + 3.00000i) q^{83} +(9.00000 - 3.00000i) q^{85} +(-2.00000 - 2.00000i) q^{87} -6.00000i q^{91} +(-6.00000 - 6.00000i) q^{93} +(-12.0000 - 6.00000i) q^{95} +(-7.00000 + 7.00000i) q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 6 q^{13} - 6 q^{15} - 6 q^{17} + 12 q^{19} - 4 q^{21} - 6 q^{23} + 6 q^{25} + 8 q^{27} + 8 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} - 12 q^{41} + 6 q^{43} + 2 q^{45}+ \cdots - 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 6 * q^13 - 6 * q^15 - 6 * q^17 + 12 * q^19 - 4 * q^21 - 6 * q^23 + 6 * q^25 + 8 * q^27 + 8 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 - 12 * q^41 + 6 * q^43 + 2 * q^45 + 18 * q^47 + 10 * q^53 + 8 * q^55 + 12 * q^57 + 20 * q^59 - 24 * q^61 + 2 * q^63 - 6 * q^65 + 18 * q^67 - 10 * q^73 + 14 * q^75 + 8 * q^77 + 10 * q^81 - 6 * q^83 + 18 * q^85 - 4 * q^87 - 12 * q^93 - 24 * q^95 - 14 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more