LMFDB - Embedded newform 560.2.q.e.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.q (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.2.q.e.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.00000 + 1.73205i) q^{11} +4.00000 q^{13} -1.00000 q^{15} +(3.00000 + 5.19615i) q^{19} +(2.50000 + 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{27} -3.00000 q^{29} +(-1.00000 - 1.73205i) q^{33} +(2.00000 - 1.73205i) q^{35} +(6.00000 + 10.3923i) q^{37} +(-2.00000 + 3.46410i) q^{39} -7.00000 q^{41} +9.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(-6.50000 + 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{53} -2.00000 q^{55} -6.00000 q^{57} +(-5.00000 + 8.66025i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(4.00000 - 3.46410i) q^{63} +(2.00000 + 3.46410i) q^{65} +(5.50000 - 9.52628i) q^{67} -3.00000 q^{69} +10.0000 q^{71} +(4.00000 - 6.92820i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(5.00000 + 1.73205i) q^{77} +(3.00000 + 5.19615i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.00000 q^{83} +(1.50000 - 2.59808i) q^{87} +(-8.50000 - 14.7224i) q^{89} +(-2.00000 - 10.3923i) q^{91} +(-3.00000 + 5.19615i) q^{95} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + q^{5} - q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^3 + q^5 - q^7 + 2 * q^9	$ 2 q - q^{3} + q^{5} - q^{7} + 2 q^{9} - 2 q^{11} + 8 q^{13} - 2 q^{15} + 6 q^{19} + 5 q^{21} + 3 q^{23} - q^{25} - 10 q^{27} - 6 q^{29} - 2 q^{33} + 4 q^{35} + 12 q^{37} - 4 q^{39} - 14 q^{41} + 18 q^{43} - 2 q^{45} - 13 q^{49} + 6 q^{53} - 4 q^{55} - 12 q^{57} - 10 q^{59} - 5 q^{61} + 8 q^{63} + 4 q^{65} + 11 q^{67} - 6 q^{69} + 20 q^{71} + 8 q^{73} - q^{75} + 10 q^{77} + 6 q^{79} - q^{81} + 6 q^{83} + 3 q^{87} - 17 q^{89} - 4 q^{91} - 6 q^{95} - 4 q^{97} - 8 q^{99}+O(q^{100}) $ 2 * q - q^3 + q^5 - q^7 + 2 * q^9 - 2 * q^11 + 8 * q^13 - 2 * q^15 + 6 * q^19 + 5 * q^21 + 3 * q^23 - q^25 - 10 * q^27 - 6 * q^29 - 2 * q^33 + 4 * q^35 + 12 * q^37 - 4 * q^39 - 14 * q^41 + 18 * q^43 - 2 * q^45 - 13 * q^49 + 6 * q^53 - 4 * q^55 - 12 * q^57 - 10 * q^59 - 5 * q^61 + 8 * q^63 + 4 * q^65 + 11 * q^67 - 6 * q^69 + 20 * q^71 + 8 * q^73 - q^75 + 10 * q^77 + 6 * q^79 - q^81 + 6 * q^83 + 3 * q^87 - 17 * q^89 - 4 * q^91 - 6 * q^95 - 4 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		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	$0.591714\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$		0			0
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$		0			0
$35$	2.00000	−	1.73205i	0.338062	−	0.292770i
$36$		0			0
$37$	6.00000	+	10.3923i	0.986394	+	1.70848i	0.635571	+	0.772043i	$0.280765\pi$
$37$	6.00000	+	10.3923i	0.986394	+	1.70848i	0.350823	+	0.936442i	$0.385902\pi$
$38$		0			0
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$		0			0
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$		0			0
$43$	9.00000			1.37249			0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000			1.37249			0.686244	+	0.727372i	$0.259258\pi$
$44$		0			0
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	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
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−6.00000			−0.794719
$58$		0			0
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$	4.00000	−	3.46410i	0.503953	−	0.436436i
$64$		0			0
$65$	2.00000	+	3.46410i	0.248069	+	0.429669i
$66$		0			0
$67$	5.50000	−	9.52628i	0.671932	−	1.16382i	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	5.50000	−	9.52628i	0.671932	−	1.16382i	0.977356	−	0.211604i	$-0.0678686\pi$
$68$		0			0
$69$	−3.00000			−0.361158
$70$		0			0
$71$	10.0000			1.18678			0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000			1.18678			0.593391	+	0.804914i	$0.297789\pi$
$72$		0			0
$73$	4.00000	−	6.92820i	0.468165	−	0.810885i	−0.531174	−	0.847263i	$-0.678249\pi$
$73$	4.00000	−	6.92820i	0.468165	−	0.810885i	0.999338	+	0.0363782i	$0.0115821\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	5.00000	+	1.73205i	0.569803	+	0.197386i
$78$		0			0
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	3.00000			0.329293			0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000			0.329293			0.164646	+	0.986353i	$0.447352\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	−8.50000	−	14.7224i	−0.900998	−	1.56057i	−0.826201	−	0.563376i	$-0.809502\pi$
$89$	−8.50000	−	14.7224i	−0.900998	−	1.56057i	−0.0747975	−	0.997199i	$-0.523831\pi$
$90$		0			0
$91$	−2.00000	−	10.3923i	−0.209657	−	1.08941i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	8.50000	−	14.7224i	0.845782	−	1.46494i	−0.0391591	−	0.999233i	$-0.512468\pi$
$101$	8.50000	−	14.7224i	0.845782	−	1.46494i	0.884941	−	0.465704i	$-0.154199\pi$
$102$		0			0
$103$	−7.50000	−	12.9904i	−0.738997	−	1.27998i	−0.952947	−	0.303136i	$-0.901966\pi$
$103$	−7.50000	−	12.9904i	−0.738997	−	1.27998i	0.213950	−	0.976845i	$-0.431367\pi$
$104$		0			0
$105$	0.500000	+	2.59808i	0.0487950	+	0.253546i
$106$		0			0
$107$	−0.500000	−	0.866025i	−0.0483368	−	0.0837218i	0.840845	−	0.541276i	$-0.182059\pi$
$107$	−0.500000	−	0.866025i	−0.0483368	−	0.0837218i	−0.889182	+	0.457555i	$0.848725\pi$
$108$		0			0
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	−0.721102	−	0.692829i	$-0.756364\pi$
$109$	2.50000	−	4.33013i	0.239457	−	0.414751i	0.960558	+	0.278078i	$0.0896974\pi$
$110$		0			0
$111$	−12.0000			−1.13899
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$		0			0
$117$	4.00000	+	6.92820i	0.369800	+	0.640513i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	3.50000	−	6.06218i	0.315584	−	0.546608i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$	−4.50000	+	7.79423i	−0.396203	+	0.686244i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	12.0000	−	10.3923i	1.04053	−	0.901127i
$134$		0			0
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$		0			0
$137$	2.00000	−	3.46410i	0.170872	−	0.295958i	−0.767853	−	0.640626i	$-0.778675\pi$
$137$	2.00000	−	3.46410i	0.170872	−	0.295958i	0.938725	+	0.344668i	$0.112008\pi$
$138$		0			0
$139$	−18.0000			−1.52674			−0.763370	−	0.645961i	$-0.776457\pi$
$139$	−18.0000			−1.52674			−0.763370	+	0.645961i	$0.776457\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.00000	+	6.92820i	−0.334497	+	0.579365i
$144$		0			0
$145$	−1.50000	−	2.59808i	−0.124568	−	0.215758i
$146$		0			0
$147$	1.00000	−	6.92820i	0.0824786	−	0.571429i
$148$		0			0
$149$	8.50000	+	14.7224i	0.696347	+	1.20611i	0.969724	+	0.244202i	$0.0785259\pi$
$149$	8.50000	+	14.7224i	0.696347	+	1.20611i	−0.273377	+	0.961907i	$0.588141\pi$
$150$		0			0
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	−0.0964061	−	0.995342i	$-0.530735\pi$
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	0.910195	−	0.414181i	$-0.135932\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$		0			0
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$		0			0
$161$	6.00000	−	5.19615i	0.472866	−	0.409514i
$162$		0			0
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	0.529454	−	0.848339i	$-0.322397\pi$
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	−0.999410	+	0.0343508i	$0.989064\pi$
$164$		0			0
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$		0			0
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−6.00000	+	10.3923i	−0.458831	+	0.794719i
$172$		0			0
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	0.977064	−	0.212947i	$-0.0683062\pi$
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	−0.672949	+	0.739689i	$0.734973\pi$
$174$		0			0
$175$	2.50000	+	0.866025i	0.188982	+	0.0654654i
$176$		0			0
$177$	−5.00000	−	8.66025i	−0.375823	−	0.650945i
$178$		0			0
$179$	−4.00000	+	6.92820i	−0.298974	+	0.517838i	−0.975901	−	0.218212i	$-0.929978\pi$
$179$	−4.00000	+	6.92820i	−0.298974	+	0.517838i	0.676927	+	0.736050i	$0.263311\pi$
$180$		0			0
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$		0			0
$183$	5.00000			0.369611
$184$		0			0
$185$	−6.00000	+	10.3923i	−0.441129	+	0.764057i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.50000	+	12.9904i	0.181848	+	0.944911i
$190$		0			0
$191$	7.00000	+	12.1244i	0.506502	+	0.877288i	0.999972	+	0.00752447i	$0.00239513\pi$
$191$	7.00000	+	12.1244i	0.506502	+	0.877288i	−0.493469	+	0.869763i	$0.664272\pi$
$192$		0			0
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	−0.133056	−	0.991109i	$-0.542479\pi$
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	0.924853	−	0.380325i	$-0.124188\pi$
$194$		0			0
$195$	−4.00000			−0.286446
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	6.00000	−	10.3923i	0.425329	−	0.736691i	−0.571122	−	0.820865i	$-0.693492\pi$
$199$	6.00000	−	10.3923i	0.425329	−	0.736691i	0.996451	+	0.0841740i	$0.0268252\pi$
$200$		0			0
$201$	5.50000	+	9.52628i	0.387940	+	0.671932i
$202$		0			0
$203$	1.50000	+	7.79423i	0.105279	+	0.547048i
$204$		0			0
$205$	−3.50000	−	6.06218i	−0.244451	−	0.423401i
$206$		0			0
$207$	−3.00000	+	5.19615i	−0.208514	+	0.361158i
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$		0			0
$213$	−5.00000	+	8.66025i	−0.342594	+	0.593391i
$214$		0			0
$215$	4.50000	+	7.79423i	0.306897	+	0.531562i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$		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	$0.209046\pi$
$228$		0			0
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	0.897173	−	0.441679i	$-0.145617\pi$
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	−0.831092	+	0.556136i	$0.812283\pi$
$230$		0			0
$231$	−4.00000	+	3.46410i	−0.263181	+	0.227921i
$232$		0			0
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	0.924072	−	0.382219i	$-0.124840\pi$
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	−0.793047	+	0.609160i	$0.791507\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.00000			−0.389742
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$		0			0
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$		0			0
$245$	−5.50000	−	4.33013i	−0.351382	−	0.276642i
$246$		0			0
$247$	12.0000	+	20.7846i	0.763542	+	1.32249i
$248$		0			0
$249$	−1.50000	+	2.59808i	−0.0950586	+	0.164646i
$250$		0			0
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.0000	−	20.7846i	−0.748539	−	1.29651i	−0.948523	−	0.316709i	$-0.897422\pi$
$257$	−12.0000	−	20.7846i	−0.748539	−	1.29651i	0.199983	−	0.979799i	$-0.435911\pi$
$258$		0			0
$259$	24.0000	−	20.7846i	1.49129	−	1.29149i
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	−0.336270	−	0.941766i	$-0.609166\pi$
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	0.983728	−	0.179664i	$-0.0575011\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	17.0000			1.04038
$268$		0			0
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.189404	+	0.981899i	$0.560656\pi$
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.755648	+	0.654978i	$0.772678\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$		0			0
$273$	10.0000	+	3.46410i	0.605228	+	0.209657i
$274$		0			0
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$		0			0
$285$	−3.00000	−	5.19615i	−0.177705	−	0.307794i
$286$		0			0
$287$	3.50000	+	18.1865i	0.206598	+	1.07352i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$		0			0
$293$	−4.00000			−0.233682			−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000			−0.233682			−0.116841	+	0.993151i	$0.537277\pi$
$294$		0			0
$295$	−10.0000			−0.582223
$296$		0			0
$297$	5.00000	−	8.66025i	0.290129	−	0.502519i
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	−4.50000	−	23.3827i	−0.259376	−	1.34776i
$302$		0			0
$303$	8.50000	+	14.7224i	0.488312	+	0.845782i
$304$		0			0
$305$	2.50000	−	4.33013i	0.143150	−	0.247942i
$306$		0			0
$307$	21.0000			1.19853			0.599267	−	0.800549i	$-0.295459\pi$
$307$	21.0000			1.19853			0.599267	+	0.800549i	$0.295459\pi$
$308$		0			0
$309$	15.0000			0.853320
$310$		0			0
$311$	5.00000	−	8.66025i	0.283524	−	0.491078i	−0.688726	−	0.725022i	$-0.741830\pi$
$311$	5.00000	−	8.66025i	0.283524	−	0.491078i	0.972250	+	0.233944i	$0.0751631\pi$
$312$		0			0
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	0.998522	−	0.0543564i	$-0.0173107\pi$
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	−0.546335	+	0.837567i	$0.683977\pi$
$314$		0			0
$315$	5.00000	+	1.73205i	0.281718	+	0.0975900i
$316$		0			0
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$		0			0
$321$	1.00000			0.0558146
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−2.00000	+	3.46410i	−0.110940	+	0.192154i
$326$		0			0
$327$	2.50000	+	4.33013i	0.138250	+	0.239457i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$		0			0
$333$	−12.0000	+	20.7846i	−0.657596	+	1.13899i
$334$		0			0
$335$	11.0000			0.600994
$336$		0			0
$337$	10.0000			0.544735			0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000			0.544735			0.272367	+	0.962193i	$0.412193\pi$
$338$		0			0
$339$	9.00000	−	15.5885i	0.488813	−	0.846649i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	−1.50000	−	2.59808i	−0.0807573	−	0.139876i
$346$		0			0
$347$	−12.5000	+	21.6506i	−0.671035	+	1.16227i	0.306576	+	0.951846i	$0.400817\pi$
$347$	−12.5000	+	21.6506i	−0.671035	+	1.16227i	−0.977611	+	0.210421i	$0.932517\pi$
$348$		0			0
$349$	17.0000			0.909989			0.454995	−	0.890494i	$-0.349641\pi$
$349$	17.0000			0.909989			0.454995	+	0.890494i	$0.349641\pi$
$350$		0			0
$351$	−20.0000			−1.06752
$352$		0			0
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$	5.00000	+	8.66025i	0.265372	+	0.459639i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$	8.00000			0.418739
$366$		0			0
$367$	6.50000	−	11.2583i	0.339297	−	0.587680i	−0.645003	−	0.764180i	$-0.723144\pi$
$367$	6.50000	−	11.2583i	0.339297	−	0.587680i	0.984301	+	0.176500i	$0.0564774\pi$
$368$		0			0
$369$	−7.00000	−	12.1244i	−0.364405	−	0.631169i
$370$		0			0
$371$	−15.0000	−	5.19615i	−0.778761	−	0.269771i
$372$		0			0
$373$	−18.0000	−	31.1769i	−0.932005	−	1.61428i	−0.779890	−	0.625917i	$-0.784725\pi$
$373$	−18.0000	−	31.1769i	−0.932005	−	1.61428i	−0.152115	−	0.988363i	$-0.548608\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$		0			0
$381$	4.00000	−	6.92820i	0.204926	−	0.354943i
$382$		0			0
$383$	−16.5000	−	28.5788i	−0.843111	−	1.46031i	−0.887252	−	0.461285i	$-0.847389\pi$
$383$	−16.5000	−	28.5788i	−0.843111	−	1.46031i	0.0441413	−	0.999025i	$-0.485945\pi$
$384$		0			0
$385$	1.00000	+	5.19615i	0.0509647	+	0.264820i
$386$		0			0
$387$	9.00000	+	15.5885i	0.457496	+	0.792406i
$388$		0			0
$389$	7.00000	−	12.1244i	0.354914	−	0.614729i	−0.632189	−	0.774814i	$-0.717843\pi$
$389$	7.00000	−	12.1244i	0.354914	−	0.614729i	0.987103	+	0.160085i	$0.0511768\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.00000	+	5.19615i	−0.150946	+	0.261447i
$396$		0			0
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	0.890028	−	0.455905i	$-0.150684\pi$
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	−0.839840	+	0.542834i	$0.817351\pi$
$398$		0			0
$399$	3.00000	+	15.5885i	0.150188	+	0.780399i
$400$		0			0
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	0.902703	+	0.430263i	$0.141579\pi$
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	−0.0787327	+	0.996896i	$0.525087\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	−0.659374	−	0.751815i	$-0.729178\pi$
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	0.980778	+	0.195127i	$0.0625118\pi$
$410$		0			0
$411$	2.00000	+	3.46410i	0.0986527	+	0.170872i
$412$		0			0
$413$	25.0000	+	8.66025i	1.23017	+	0.426143i
$414$		0			0
$415$	1.50000	+	2.59808i	0.0736321	+	0.127535i
$416$		0			0
$417$	9.00000	−	15.5885i	0.440732	−	0.763370i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−31.0000			−1.51085			−0.755424	−	0.655237i	$-0.772569\pi$
$421$	−31.0000			−1.51085			−0.755424	+	0.655237i	$0.772569\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−10.0000	+	8.66025i	−0.483934	+	0.419099i
$428$		0			0
$429$	−4.00000	−	6.92820i	−0.193122	−	0.334497i
$430$		0			0
$431$	−11.0000	+	19.0526i	−0.529851	+	0.917729i	0.469542	+	0.882910i	$0.344419\pi$
$431$	−11.0000	+	19.0526i	−0.529851	+	0.917729i	−0.999394	+	0.0348195i	$0.988914\pi$
$432$		0			0
$433$	18.0000			0.865025			0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000			0.865025			0.432512	+	0.901628i	$0.357627\pi$
$434$		0			0
$435$	3.00000			0.143839
$436$		0			0
$437$	−9.00000	+	15.5885i	−0.430528	+	0.745697i
$438$		0			0
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	0.814344	−	0.580383i	$-0.197097\pi$
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	−0.909798	+	0.415051i	$0.863764\pi$
$440$		0			0
$441$	−11.0000	−	8.66025i	−0.523810	−	0.412393i
$442$		0			0
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	0.501129	−	0.865373i	$-0.332918\pi$
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	−0.999999	+	0.00130426i	$0.999585\pi$
$444$		0			0
$445$	8.50000	−	14.7224i	0.402939	−	0.697910i
$446$		0			0
$447$	−17.0000			−0.804072
$448$		0			0
$449$	39.0000			1.84052			0.920262	−	0.391303i	$-0.127976\pi$
$449$	39.0000			1.84052			0.920262	+	0.391303i	$0.127976\pi$
$450$		0			0
$451$	7.00000	−	12.1244i	0.329617	−	0.570914i
$452$		0			0
$453$	10.0000	+	17.3205i	0.469841	+	0.813788i
$454$		0			0
$455$	8.00000	−	6.92820i	0.375046	−	0.324799i
$456$		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
$459$		0			0
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	−29.0000			−1.34774			−0.673872	−	0.738848i	$-0.735370\pi$
$463$	−29.0000			−1.34774			−0.673872	+	0.738848i	$0.735370\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−16.5000	−	28.5788i	−0.763529	−	1.32247i	−0.941021	−	0.338349i	$-0.890132\pi$
$467$	−16.5000	−	28.5788i	−0.763529	−	1.32247i	0.177492	−	0.984122i	$-0.443202\pi$
$468$		0			0
$469$	−27.5000	−	9.52628i	−1.26983	−	0.439883i
$470$		0			0
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$		0			0
$473$	−9.00000	+	15.5885i	−0.413820	+	0.716758i
$474$		0			0
$475$	−6.00000			−0.275299
$476$		0			0
$477$	12.0000			0.549442
$478$		0			0
$479$	18.0000	−	31.1769i	0.822441	−	1.42451i	−0.0814184	−	0.996680i	$-0.525945\pi$
$479$	18.0000	−	31.1769i	0.822441	−	1.42451i	0.903859	−	0.427830i	$-0.140722\pi$
$480$		0			0
$481$	24.0000	+	41.5692i	1.09431	+	1.89539i
$482$		0			0
$483$	1.50000	+	7.79423i	0.0682524	+	0.354650i
$484$		0			0
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$		0			0
$487$	16.0000	−	27.7128i	0.725029	−	1.25579i	−0.233933	−	0.972253i	$-0.575160\pi$
$487$	16.0000	−	27.7128i	0.725029	−	1.25579i	0.958962	−	0.283535i	$-0.0915071\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−2.00000	−	3.46410i	−0.0898933	−	0.155700i
$496$		0			0
$497$	−5.00000	−	25.9808i	−0.224281	−	1.16540i
$498$		0			0
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$		0			0
$503$	37.0000			1.64975			0.824874	−	0.565316i	$-0.191246\pi$
$503$	37.0000			1.64975			0.824874	+	0.565316i	$0.191246\pi$
$504$		0			0
$505$	17.0000			0.756490
$506$		0			0
$507$	−1.50000	+	2.59808i	−0.0666173	+	0.115385i
$508$		0			0
$509$	−10.5000	−	18.1865i	−0.465404	−	0.806104i	0.533815	−	0.845601i	$-0.320758\pi$
$509$	−10.5000	−	18.1865i	−0.465404	−	0.806104i	−0.999220	+	0.0394971i	$0.987424\pi$
$510$		0			0
$511$	−20.0000	−	6.92820i	−0.884748	−	0.306486i
$512$		0			0
$513$	−15.0000	−	25.9808i	−0.662266	−	1.14708i
$514$		0			0
$515$	7.50000	−	12.9904i	0.330489	−	0.572425i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−8.00000			−0.351161
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$		0			0
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	0.990873	+	0.134801i	$0.0430394\pi$
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	−0.378695	+	0.925521i	$0.623627\pi$
$524$		0			0
$525$	−2.00000	+	1.73205i	−0.0872872	+	0.0755929i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	−20.0000			−0.867926
$532$		0			0
$533$	−28.0000			−1.21281
$534$		0			0
$535$	0.500000	−	0.866025i	0.0216169	−	0.0374415i
$536$		0			0
$537$	−4.00000	−	6.92820i	−0.172613	−	0.298974i
$538$		0			0
$539$	2.00000	−	13.8564i	0.0861461	−	0.596838i
$540$		0			0
$541$	−19.5000	−	33.7750i	−0.838370	−	1.45210i	−0.891256	−	0.453500i	$-0.850175\pi$
$541$	−19.5000	−	33.7750i	−0.838370	−	1.45210i	0.0528859	−	0.998601i	$-0.483158\pi$
$542$		0			0
$543$	2.50000	−	4.33013i	0.107285	−	0.185824i
$544$		0			0
$545$	5.00000			0.214176
$546$		0			0
$547$	13.0000			0.555840			0.277920	−	0.960604i	$-0.410355\pi$
$547$	13.0000			0.555840			0.277920	+	0.960604i	$0.410355\pi$
$548$		0			0
$549$	5.00000	−	8.66025i	0.213395	−	0.369611i
$550$		0			0
$551$	−9.00000	−	15.5885i	−0.383413	−	0.664091i
$552$		0			0
$553$	12.0000	−	10.3923i	0.510292	−	0.441926i
$554$		0			0
$555$	−6.00000	−	10.3923i	−0.254686	−	0.441129i
$556$		0			0
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	0.350824	+	0.936442i	$0.385902\pi$
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$558$		0			0
$559$	36.0000			1.52264
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.50000	+	9.52628i	−0.231797	+	0.401485i	−0.958337	−	0.285640i	$-0.907794\pi$
$563$	−5.50000	+	9.52628i	−0.231797	+	0.401485i	0.726540	+	0.687124i	$0.241127\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$		0			0
$567$	2.50000	+	0.866025i	0.104990	+	0.0363696i
$568$		0			0
$569$	−11.0000	−	19.0526i	−0.461144	−	0.798725i	0.537874	−	0.843025i	$-0.319228\pi$
$569$	−11.0000	−	19.0526i	−0.461144	−	0.798725i	−0.999018	+	0.0443003i	$0.985894\pi$
$570$		0			0
$571$	−9.00000	+	15.5885i	−0.376638	+	0.652357i	−0.990571	−	0.137002i	$-0.956253\pi$
$571$	−9.00000	+	15.5885i	−0.376638	+	0.652357i	0.613933	+	0.789359i	$0.289587\pi$
$572$		0			0
$573$	−14.0000			−0.584858
$574$		0			0
$575$	−3.00000			−0.125109
$576$		0			0
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$		0			0
$579$	11.0000	+	19.0526i	0.457144	+	0.791797i
$580$		0			0
$581$	−1.50000	−	7.79423i	−0.0622305	−	0.323359i
$582$		0			0
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$		0			0
$585$	−4.00000	+	6.92820i	−0.165380	+	0.286446i
$586$		0			0
$587$	−20.0000			−0.825488			−0.412744	−	0.910847i	$-0.635430\pi$
$587$	−20.0000			−0.825488			−0.412744	+	0.910847i	$0.635430\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$		0			0
$593$	5.00000	+	8.66025i	0.205325	+	0.355634i	0.950236	−	0.311530i	$-0.100841\pi$
$593$	5.00000	+	8.66025i	0.205325	+	0.355634i	−0.744911	+	0.667164i	$0.767508\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	6.00000	+	10.3923i	0.245564	+	0.425329i
$598$		0			0
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$		0			0
$603$	22.0000			0.895909
$604$		0			0
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	0.786212	−	0.617957i	$-0.212039\pi$
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	−0.928272	+	0.371901i	$0.878706\pi$
$608$		0			0
$609$	−7.50000	−	2.59808i	−0.303915	−	0.105279i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	−0.935428	−	0.353518i	$-0.884985\pi$
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	0.773869	+	0.633345i	$0.218319\pi$
$614$		0			0
$615$	7.00000			0.282267
$616$		0			0
$617$	−20.0000			−0.805170			−0.402585	−	0.915383i	$-0.631888\pi$
$617$	−20.0000			−0.805170			−0.402585	+	0.915383i	$0.631888\pi$
$618$		0			0
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	−0.477143	−	0.878826i	$-0.658328\pi$
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	0.999657	−	0.0261952i	$-0.00833914\pi$
$620$		0			0
$621$	−7.50000	−	12.9904i	−0.300965	−	0.521286i
$622$		0			0
$623$	−34.0000	+	29.4449i	−1.36218	+	1.17968i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	6.00000	−	10.3923i	0.239617	−	0.415029i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	6.00000			0.238856			0.119428	−	0.992843i	$-0.461894\pi$
$631$	6.00000			0.238856			0.119428	+	0.992843i	$0.461894\pi$
$632$		0			0
$633$	−7.00000	+	12.1244i	−0.278225	+	0.481900i
$634$		0			0
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$	−26.0000	+	10.3923i	−1.03016	+	0.411758i
$638$		0			0
$639$	10.0000	+	17.3205i	0.395594	+	0.685189i
$640$		0			0
$641$	−6.50000	+	11.2583i	−0.256735	+	0.444677i	−0.965365	−	0.260902i	$-0.915980\pi$
$641$	−6.50000	+	11.2583i	−0.256735	+	0.444677i	0.708631	+	0.705580i	$0.249313\pi$
$642$		0			0
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	−9.00000			−0.354375
$646$		0			0
$647$	22.5000	−	38.9711i	0.884566	−	1.53211i	0.0383563	−	0.999264i	$-0.487788\pi$
$647$	22.5000	−	38.9711i	0.884566	−	1.53211i	0.846210	−	0.532850i	$-0.178879\pi$
$648$		0			0
$649$	−10.0000	−	17.3205i	−0.392534	−	0.679889i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	16.0000			0.624219
$658$		0			0
$659$	46.0000			1.79191			0.895953	−	0.444149i	$-0.146494\pi$
$659$	46.0000			1.79191			0.895953	+	0.444149i	$0.146494\pi$
$660$		0			0
$661$	3.50000	−	6.06218i	0.136134	−	0.235791i	−0.789896	−	0.613241i	$-0.789865\pi$
$661$	3.50000	−	6.06218i	0.136134	−	0.235791i	0.926030	+	0.377450i	$0.123199\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	15.0000	+	5.19615i	0.581675	+	0.201498i
$666$		0			0
$667$	−4.50000	−	7.79423i	−0.174241	−	0.301794i
$668$		0			0
$669$	−2.00000	+	3.46410i	−0.0773245	+	0.133930i
$670$		0			0
$671$	10.0000			0.386046
$672$		0			0
$673$	−16.0000			−0.616755			−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000			−0.616755			−0.308377	+	0.951264i	$0.599786\pi$
$674$		0			0
$675$	2.50000	−	4.33013i	0.0962250	−	0.166667i
$676$		0			0
$677$	18.0000	+	31.1769i	0.691796	+	1.19823i	0.971249	+	0.238067i	$0.0765137\pi$
$677$	18.0000	+	31.1769i	0.691796	+	1.19823i	−0.279453	+	0.960159i	$0.590153\pi$
$678$		0			0
$679$	1.00000	+	5.19615i	0.0383765	+	0.199410i
$680$		0			0
$681$	−2.00000	−	3.46410i	−0.0766402	−	0.132745i
$682$		0			0
$683$	3.50000	−	6.06218i	0.133924	−	0.231963i	−0.791262	−	0.611477i	$-0.790576\pi$
$683$	3.50000	−	6.06218i	0.133924	−	0.231963i	0.925186	+	0.379514i	$0.123909\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$	−2.00000			−0.0763048
$688$		0			0
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	−5.00000	−	8.66025i	−0.190209	−	0.329452i	0.755110	−	0.655598i	$-0.227583\pi$
$691$	−5.00000	−	8.66025i	−0.190209	−	0.329452i	−0.945319	+	0.326146i	$0.894250\pi$
$692$		0			0
$693$	2.00000	+	10.3923i	0.0759737	+	0.394771i
$694$		0			0
$695$	−9.00000	−	15.5885i	−0.341389	−	0.591304i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−4.00000			−0.151294
$700$		0			0
$701$	45.0000			1.69963			0.849813	−	0.527084i	$-0.176715\pi$
$701$	45.0000			1.69963			0.849813	+	0.527084i	$0.176715\pi$
$702$		0			0
$703$	−36.0000	+	62.3538i	−1.35777	+	2.35172i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−42.5000	−	14.7224i	−1.59838	−	0.553694i
$708$		0			0
$709$	−0.500000	−	0.866025i	−0.0187779	−	0.0325243i	0.856484	−	0.516174i	$-0.172644\pi$
$709$	−0.500000	−	0.866025i	−0.0187779	−	0.0325243i	−0.875262	+	0.483650i	$0.839311\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−8.00000			−0.299183
$716$		0			0
$717$	10.0000	−	17.3205i	0.373457	−	0.646846i
$718$		0			0
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	0.999848	−	0.0174426i	$-0.00555244\pi$
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	−0.515030	+	0.857172i	$0.672219\pi$
$720$		0			0
$721$	−30.0000	+	25.9808i	−1.11726	+	0.967574i
$722$		0			0
$723$	−9.00000	−	15.5885i	−0.334714	−	0.579741i
$724$		0			0
$725$	1.50000	−	2.59808i	0.0557086	−	0.0964901i
$726$		0			0
$727$	13.0000			0.482143			0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000			0.482143			0.241072	+	0.970507i	$0.422501\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$		0			0
$735$	6.50000	−	2.59808i	0.239756	−	0.0958315i
$736$		0			0
$737$	11.0000	+	19.0526i	0.405190	+	0.701810i
$738$		0			0
$739$	−5.00000	+	8.66025i	−0.183928	+	0.318573i	−0.943215	−	0.332184i	$-0.892215\pi$
$739$	−5.00000	+	8.66025i	−0.183928	+	0.318573i	0.759287	+	0.650756i	$0.225548\pi$
$740$		0			0
$741$	−24.0000			−0.881662
$742$		0			0
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$		0			0
$745$	−8.50000	+	14.7224i	−0.311416	+	0.539388i
$746$		0			0
$747$	3.00000	+	5.19615i	0.109764	+	0.190117i
$748$		0			0
$749$	−2.00000	+	1.73205i	−0.0730784	+	0.0632878i
$750$		0			0
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	0.999921	+	0.0125942i	$0.00400897\pi$
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	−0.489053	+	0.872254i	$0.662658\pi$
$752$		0			0
$753$	−2.00000	+	3.46410i	−0.0728841	+	0.126239i
$754$		0			0
$755$	20.0000			0.727875
$756$		0			0
$757$	20.0000			0.726912			0.363456	−	0.931611i	$-0.381597\pi$
$757$	20.0000			0.726912			0.363456	+	0.931611i	$0.381597\pi$
$758$		0			0
$759$	3.00000	−	5.19615i	0.108893	−	0.188608i
$760$		0			0
$761$	11.0000	+	19.0526i	0.398750	+	0.690655i	0.993572	−	0.113203i	$-0.0361109\pi$
$761$	11.0000	+	19.0526i	0.398750	+	0.690655i	−0.594822	+	0.803857i	$0.702778\pi$
$762$		0			0
$763$	−12.5000	−	4.33013i	−0.452530	−	0.156761i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−20.0000	+	34.6410i	−0.722158	+	1.25081i
$768$		0			0
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$		0			0
$773$	−2.00000	+	3.46410i	−0.0719350	+	0.124595i	−0.899749	−	0.436407i	$-0.856251\pi$
$773$	−2.00000	+	3.46410i	−0.0719350	+	0.124595i	0.827814	+	0.561002i	$0.189584\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	6.00000	+	31.1769i	0.215249	+	1.11847i
$778$		0			0
$779$	−21.0000	−	36.3731i	−0.752403	−	1.30320i
$780$		0			0
$781$	−10.0000	+	17.3205i	−0.357828	+	0.619777i
$782$		0			0
$783$	15.0000			0.536056
$784$		0			0
$785$	14.0000			0.499681
$786$		0			0
$787$	−18.5000	+	32.0429i	−0.659454	+	1.14221i	0.321303	+	0.946976i	$0.395879\pi$
$787$	−18.5000	+	32.0429i	−0.659454	+	1.14221i	−0.980757	+	0.195231i	$0.937454\pi$
$788$		0			0
$789$	10.5000	+	18.1865i	0.373810	+	0.647458i
$790$		0			0
$791$	9.00000	+	46.7654i	0.320003	+	1.66279i
$792$		0			0
$793$	−10.0000	−	17.3205i	−0.355110	−	0.615069i
$794$		0			0
$795$	−3.00000	+	5.19615i	−0.106399	+	0.184289i
$796$		0			0
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	17.0000	−	29.4449i	0.600665	−	1.04038i
$802$		0			0
$803$	8.00000	+	13.8564i	0.282314	+	0.488982i
$804$		0			0
$805$	7.50000	+	2.59808i	0.264340	+	0.0915702i
$806$		0			0
$807$	−15.5000	−	26.8468i	−0.545626	−	0.945052i
$808$		0			0
$809$	5.50000	−	9.52628i	0.193370	−	0.334926i	−0.752995	−	0.658026i	$-0.771392\pi$
$809$	5.50000	−	9.52628i	0.193370	−	0.334926i	0.946365	+	0.323100i	$0.104725\pi$
$810$		0			0
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		0			0
$813$	2.00000			0.0701431
$814$		0			0
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$		0			0
$817$	27.0000	+	46.7654i	0.944610	+	1.63611i
$818$		0			0
$819$	16.0000	−	13.8564i	0.559085	−	0.484182i
$820$		0			0
$821$	17.0000	+	29.4449i	0.593304	+	1.02763i	0.993784	+	0.111327i	$0.0355102\pi$
$821$	17.0000	+	29.4449i	0.593304	+	1.02763i	−0.400480	+	0.916306i	$0.631157\pi$
$822$		0			0
$823$	−6.50000	+	11.2583i	−0.226576	+	0.392441i	−0.956791	−	0.290776i	$-0.906086\pi$
$823$	−6.50000	+	11.2583i	−0.226576	+	0.392441i	0.730215	+	0.683217i	$0.239420\pi$
$824$		0			0
$825$	2.00000			0.0696311
$826$		0			0
$827$	31.0000			1.07798			0.538988	−	0.842314i	$-0.318807\pi$
$827$	31.0000			1.07798			0.538988	+	0.842314i	$0.318807\pi$
$828$		0			0
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−46.0000			−1.58810			−0.794048	−	0.607855i	$-0.792030\pi$
$839$	−46.0000			−1.58810			−0.794048	+	0.607855i	$0.792030\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$	−13.0000	+	22.5167i	−0.447744	+	0.775515i
$844$		0			0
$845$	1.50000	+	2.59808i	0.0516016	+	0.0893765i
$846$		0			0
$847$	14.0000	−	12.1244i	0.481046	−	0.416598i
$848$		0			0
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$		0			0
$851$	−18.0000	+	31.1769i	−0.617032	+	1.06873i
$852$		0			0
$853$	34.0000			1.16414			0.582069	−	0.813139i	$-0.302243\pi$
$853$	34.0000			1.16414			0.582069	+	0.813139i	$0.302243\pi$
$854$		0			0
$855$	−12.0000			−0.410391
$856$		0			0
$857$	13.0000	−	22.5167i	0.444072	−	0.769154i	−0.553915	−	0.832573i	$-0.686867\pi$
$857$	13.0000	−	22.5167i	0.444072	−	0.769154i	0.997987	+	0.0634184i	$0.0202003\pi$
$858$		0			0
$859$	28.0000	+	48.4974i	0.955348	+	1.65471i	0.733571	+	0.679613i	$0.237852\pi$
$859$	28.0000	+	48.4974i	0.955348	+	1.65471i	0.221777	+	0.975097i	$0.428814\pi$
$860$		0			0
$861$	−17.5000	−	6.06218i	−0.596398	−	0.206598i
$862$		0			0
$863$	−21.5000	−	37.2391i	−0.731869	−	1.26763i	−0.956084	−	0.293094i	$-0.905315\pi$
$863$	−21.5000	−	37.2391i	−0.731869	−	1.26763i	0.224215	−	0.974540i	$-0.428018\pi$
$864$		0			0
$865$	−4.00000	+	6.92820i	−0.136004	+	0.235566i
$866$		0			0
$867$	−17.0000			−0.577350
$868$		0			0
$869$	−12.0000			−0.407072
$870$		0			0
$871$	22.0000	−	38.1051i	0.745442	−	1.29114i
$872$		0			0
$873$	−2.00000	−	3.46410i	−0.0676897	−	0.117242i
$874$		0			0
$875$	0.500000	+	2.59808i	0.0169031	+	0.0878310i
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$		0			0
$879$	2.00000	−	3.46410i	0.0674583	−	0.116841i
$880$		0			0
$881$	41.0000			1.38133			0.690663	−	0.723177i	$-0.257319\pi$
$881$	41.0000			1.38133			0.690663	+	0.723177i	$0.257319\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	5.00000	−	8.66025i	0.168073	−	0.291111i
$886$		0			0
$887$	18.5000	+	32.0429i	0.621169	+	1.07590i	0.989268	+	0.146110i	$0.0466754\pi$
$887$	18.5000	+	32.0429i	0.621169	+	1.07590i	−0.368099	+	0.929787i	$0.619991\pi$
$888$		0			0
$889$	4.00000	+	20.7846i	0.134156	+	0.697093i
$890$		0			0
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−8.00000			−0.267411
$896$		0			0
$897$	−12.0000			−0.400668
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	22.5000	+	7.79423i	0.748753	+	0.259376i
$904$		0			0
$905$	−2.50000	−	4.33013i	−0.0831028	−	0.143938i
$906$		0			0
$907$	4.50000	−	7.79423i	0.149420	−	0.258803i	−0.781593	−	0.623788i	$-0.785593\pi$
$907$	4.50000	−	7.79423i	0.149420	−	0.258803i	0.931013	+	0.364985i	$0.118926\pi$
$908$		0			0
$909$	34.0000			1.12771
$910$		0			0
$911$	34.0000			1.12647			0.563235	−	0.826297i	$-0.309557\pi$
$911$	34.0000			1.12647			0.563235	+	0.826297i	$0.309557\pi$
$912$		0			0
$913$	−3.00000	+	5.19615i	−0.0992855	+	0.171968i
$914$		0			0
$915$	2.50000	+	4.33013i	0.0826475	+	0.143150i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	0.997429	+	0.0716652i	$0.0228313\pi$
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	−0.436650	+	0.899631i	$0.643835\pi$
$920$		0			0
$921$	−10.5000	+	18.1865i	−0.345987	+	0.599267i
$922$		0			0
$923$	40.0000			1.31662
$924$		0			0
$925$	−12.0000			−0.394558
$926$		0			0
$927$	15.0000	−	25.9808i	0.492665	−	0.853320i
$928$		0			0
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		0			0
$931$	−33.0000	−	25.9808i	−1.08153	−	0.851485i
$932$		0			0
$933$	5.00000	+	8.66025i	0.163693	+	0.283524i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	4.00000			0.130674			0.0653372	−	0.997863i	$-0.479188\pi$
$937$	4.00000			0.130674			0.0653372	+	0.997863i	$0.479188\pi$
$938$		0			0
$939$	−16.0000			−0.522140
$940$		0			0
$941$	19.0000	−	32.9090i	0.619382	−	1.07280i	−0.370216	−	0.928946i	$-0.620716\pi$
$941$	19.0000	−	32.9090i	0.619382	−	1.07280i	0.989599	−	0.143856i	$-0.0459502\pi$
$942$		0			0
$943$	−10.5000	−	18.1865i	−0.341927	−	0.592235i
$944$		0			0
$945$	−10.0000	+	8.66025i	−0.325300	+	0.281718i
$946$		0			0
$947$	−6.50000	−	11.2583i	−0.211222	−	0.365847i	0.740875	−	0.671642i	$-0.234411\pi$
$947$	−6.50000	−	11.2583i	−0.211222	−	0.365847i	−0.952097	+	0.305796i	$0.901078\pi$
$948$		0			0
$949$	16.0000	−	27.7128i	0.519382	−	0.899596i
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$	−28.0000			−0.907009			−0.453504	−	0.891254i	$-0.649826\pi$
$953$	−28.0000			−0.907009			−0.453504	+	0.891254i	$0.649826\pi$
$954$		0			0
$955$	−7.00000	+	12.1244i	−0.226515	+	0.392335i
$956$		0			0
$957$	3.00000	+	5.19615i	0.0969762	+	0.167968i
$958$		0			0
$959$	−10.0000	−	3.46410i	−0.322917	−	0.111862i
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$		0			0
$963$	1.00000	−	1.73205i	0.0322245	−	0.0558146i
$964$		0			0
$965$	22.0000			0.708205
$966$		0			0
$967$	−13.0000			−0.418052			−0.209026	−	0.977910i	$-0.567029\pi$
$967$	−13.0000			−0.418052			−0.209026	+	0.977910i	$0.567029\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	0.985024	+	0.172418i	$0.0551581\pi$
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	−0.343193	+	0.939265i	$0.611509\pi$
$972$		0			0
$973$	9.00000	+	46.7654i	0.288527	+	1.49923i
$974$		0			0
$975$	−2.00000	−	3.46410i	−0.0640513	−	0.110940i
$976$		0			0
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$	34.0000			1.08664
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	−0.785295	−	0.619122i	$-0.787489\pi$
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	0.928823	+	0.370525i	$0.120822\pi$
$984$		0			0
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	13.5000	+	23.3827i	0.429275	+	0.743526i
$990$		0			0
$991$	10.0000	−	17.3205i	0.317660	−	0.550204i	−0.662339	−	0.749204i	$-0.730436\pi$
$991$	10.0000	−	17.3205i	0.317660	−	0.550204i	0.979999	+	0.199000i	$0.0637695\pi$
$992$		0			0
$993$	−4.00000			−0.126936
$994$		0			0
$995$	12.0000			0.380426
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$		0			0
$999$	−30.0000	−	51.9615i	−0.949158	−	1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.e.81.1		2
4.3	odd	2		280.2.q.b.81.1	✓	2
7.2	even	3	inner	560.2.q.e.401.1		2
7.3	odd	6		3920.2.a.q.1.1		1
7.4	even	3		3920.2.a.v.1.1		1
12.11	even	2		2520.2.bi.d.361.1		2
20.3	even	4		1400.2.bh.c.249.2		4
20.7	even	4		1400.2.bh.c.249.1		4
20.19	odd	2		1400.2.q.c.1201.1		2
28.3	even	6		1960.2.a.l.1.1		1
28.11	odd	6		1960.2.a.c.1.1		1
28.19	even	6		1960.2.q.d.961.1		2
28.23	odd	6		280.2.q.b.121.1	yes	2
28.27	even	2		1960.2.q.d.361.1		2
84.23	even	6		2520.2.bi.d.1801.1		2
140.23	even	12		1400.2.bh.c.849.1		4
140.39	odd	6		9800.2.a.z.1.1		1
140.59	even	6		9800.2.a.o.1.1		1
140.79	odd	6		1400.2.q.c.401.1		2
140.107	even	12		1400.2.bh.c.849.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.b.81.1	✓	2	4.3	odd	2
280.2.q.b.121.1	yes	2	28.23	odd	6
560.2.q.e.81.1		2	1.1	even	1	trivial
560.2.q.e.401.1		2	7.2	even	3	inner
1400.2.q.c.401.1		2	140.79	odd	6
1400.2.q.c.1201.1		2	20.19	odd	2
1400.2.bh.c.249.1		4	20.7	even	4
1400.2.bh.c.249.2		4	20.3	even	4
1400.2.bh.c.849.1		4	140.23	even	12
1400.2.bh.c.849.2		4	140.107	even	12
1960.2.a.c.1.1		1	28.11	odd	6
1960.2.a.l.1.1		1	28.3	even	6
1960.2.q.d.361.1		2	28.27	even	2
1960.2.q.d.961.1		2	28.19	even	6
2520.2.bi.d.361.1		2	12.11	even	2
2520.2.bi.d.1801.1		2	84.23	even	6
3920.2.a.q.1.1		1	7.3	odd	6
3920.2.a.v.1.1		1	7.4	even	3
9800.2.a.o.1.1		1	140.59	even	6
9800.2.a.z.1.1		1	140.39	odd	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.00000 + 1.73205i) q^{11} +4.00000 q^{13} -1.00000 q^{15} +(3.00000 + 5.19615i) q^{19} +(2.50000 + 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{27} -3.00000 q^{29} +(-1.00000 - 1.73205i) q^{33} +(2.00000 - 1.73205i) q^{35} +(6.00000 + 10.3923i) q^{37} +(-2.00000 + 3.46410i) q^{39} -7.00000 q^{41} +9.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(-6.50000 + 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{53} -2.00000 q^{55} -6.00000 q^{57} +(-5.00000 + 8.66025i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(4.00000 - 3.46410i) q^{63} +(2.00000 + 3.46410i) q^{65} +(5.50000 - 9.52628i) q^{67} -3.00000 q^{69} +10.0000 q^{71} +(4.00000 - 6.92820i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(5.00000 + 1.73205i) q^{77} +(3.00000 + 5.19615i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.00000 q^{83} +(1.50000 - 2.59808i) q^{87} +(-8.50000 - 14.7224i) q^{89} +(-2.00000 - 10.3923i) q^{91} +(-3.00000 + 5.19615i) q^{95} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + q^{5} - q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^3 + q^5 - q^7 + 2 * q^9	\( 2 q - q^{3} + q^{5} - q^{7} + 2 q^{9} - 2 q^{11} + 8 q^{13} - 2 q^{15} + 6 q^{19} + 5 q^{21} + 3 q^{23} - q^{25} - 10 q^{27} - 6 q^{29} - 2 q^{33} + 4 q^{35} + 12 q^{37} - 4 q^{39} - 14 q^{41} + 18 q^{43} - 2 q^{45} - 13 q^{49} + 6 q^{53} - 4 q^{55} - 12 q^{57} - 10 q^{59} - 5 q^{61} + 8 q^{63} + 4 q^{65} + 11 q^{67} - 6 q^{69} + 20 q^{71} + 8 q^{73} - q^{75} + 10 q^{77} + 6 q^{79} - q^{81} + 6 q^{83} + 3 q^{87} - 17 q^{89} - 4 q^{91} - 6 q^{95} - 4 q^{97} - 8 q^{99}+O(q^{100}) \) 2 * q - q^3 + q^5 - q^7 + 2 * q^9 - 2 * q^11 + 8 * q^13 - 2 * q^15 + 6 * q^19 + 5 * q^21 + 3 * q^23 - q^25 - 10 * q^27 - 6 * q^29 - 2 * q^33 + 4 * q^35 + 12 * q^37 - 4 * q^39 - 14 * q^41 + 18 * q^43 - 2 * q^45 - 13 * q^49 + 6 * q^53 - 4 * q^55 - 12 * q^57 - 10 * q^59 - 5 * q^61 + 8 * q^63 + 4 * q^65 + 11 * q^67 - 6 * q^69 + 20 * q^71 + 8 * q^73 - q^75 + 10 * q^77 + 6 * q^79 - q^81 + 6 * q^83 + 3 * q^87 - 17 * q^89 - 4 * q^91 - 6 * q^95 - 4 * q^97 - 8 * q^99

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