LMFDB - Embedded newform 900.2.i.e.301.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(301,900)] 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("900.301"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.142635249.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 3x^{6} + 3x^{5} - 11x^{4} + 6x^{3} + 12x^{2} - 24x + 16 $ x^8 - 3x^7 + 3x^6 + 3x^5 - 11x^4 + 6x^3 + 12x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.2
Root			$-1.32841 + 0.485097i$ of defining polynomial
Character	$\chi$	$=$	900.301
Dual form			900.2.i.e.601.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02936 - 1.39299i) q^{3} +(0.340213 + 0.589266i) q^{7} +(-0.880830 + 2.86778i) q^{9} +(0.840213 + 1.45529i) q^{11} +(2.57251 - 4.45572i) q^{13} +1.31957 q^{17} -0.324642 q^{19} +(0.470639 - 1.08048i) q^{21} +(1.89462 - 3.28158i) q^{23} +(4.90147 - 1.72499i) q^{27} +(4.32292 + 7.48751i) q^{29} +(2.07251 - 3.58970i) q^{31} +(1.16232 - 2.66843i) q^{33} -1.35578 q^{37} +(-8.85481 + 1.00307i) q^{39} +(3.57505 - 6.19216i) q^{41} +(-3.64503 - 6.31337i) q^{43} +(-6.48270 - 11.2284i) q^{47} +(3.26851 - 5.66123i) q^{49} +(-1.35832 - 1.83815i) q^{51} +8.83052 q^{53} +(0.334174 + 0.452222i) q^{57} +(-4.40766 + 7.63429i) q^{59} +(-4.98524 - 8.63469i) q^{61} +(-1.98955 + 0.456611i) q^{63} +(-2.08808 + 3.61667i) q^{67} +(-6.52145 + 0.738747i) q^{69} -0.891185 q^{71} +7.82038 q^{73} +(-0.571703 + 0.990219i) q^{77} +(-4.82799 - 8.36232i) q^{79} +(-7.44828 - 5.05205i) q^{81} +(2.42830 + 4.20593i) q^{83} +(5.98017 - 13.7291i) q^{87} +17.4764 q^{89} +3.50081 q^{91} +(-7.13377 + 0.808111i) q^{93} +(4.46713 + 7.73730i) q^{97} +(-4.91354 + 1.12768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - q^{7} + 5 q^{9} + 3 q^{11} + 2 q^{13} + 18 q^{17} - 8 q^{19} + 13 q^{21} + 3 q^{23} + 16 q^{27} - 9 q^{29} - 2 q^{31} + 12 q^{33} + 2 q^{37} - 17 q^{39} + 9 q^{41} + 8 q^{43} - 12 q^{47}+ \cdots + 33 q^{99}+O(q^{100}) $ 8 * q + q^3 - q^7 + 5 * q^9 + 3 * q^11 + 2 * q^13 + 18 * q^17 - 8 * q^19 + 13 * q^21 + 3 * q^23 + 16 * q^27 - 9 * q^29 - 2 * q^31 + 12 * q^33 + 2 * q^37 - 17 * q^39 + 9 * q^41 + 8 * q^43 - 12 * q^47 - 9 * q^49 + 3 * q^51 + 24 * q^53 - 40 * q^57 - 15 * q^59 + q^61 + 35 * q^63 + 11 * q^67 + 9 * q^69 - 24 * q^71 + 20 * q^73 - 36 * q^77 + 7 * q^79 - 31 * q^81 - 12 * q^83 + 9 * q^87 + 6 * q^89 - 22 * q^91 - 19 * q^93 + 5 * q^97 + 33 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−1.02936	−	1.39299i	−0.594302	−	0.804242i
$3$	−1.02936	−	1.39299i	−0.594302	−	0.804242i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.340213	+	0.589266i	0.128588	+	0.222722i	0.923130	−	0.384488i	$-0.125622\pi$
$7$	0.340213	+	0.589266i	0.128588	+	0.222722i	−0.794541	+	0.607210i	$0.792289\pi$
$8$		0			0
$9$	−0.880830	+	2.86778i	−0.293610	+	0.955925i
$10$		0			0
$11$	0.840213	+	1.45529i	0.253334	+	0.438787i	0.964442	−	0.264296i	$-0.0851396\pi$
$11$	0.840213	+	1.45529i	0.253334	+	0.438787i	−0.711108	+	0.703083i	$0.751806\pi$
$12$		0			0
$13$	2.57251	−	4.45572i	0.713487	−	1.23580i	−0.250054	−	0.968232i	$-0.580448\pi$
$13$	2.57251	−	4.45572i	0.713487	−	1.23580i	0.963540	−	0.267563i	$-0.0862184\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.31957			0.320044			0.160022	−	0.987113i	$-0.448844\pi$
$17$	1.31957			0.320044			0.160022	+	0.987113i	$0.448844\pi$
$18$		0			0
$19$	−0.324642			−0.0744779			−0.0372390	−	0.999306i	$-0.511856\pi$
$19$	−0.324642			−0.0744779			−0.0372390	+	0.999306i	$0.511856\pi$
$20$		0			0
$21$	0.470639	−	1.08048i	0.102702	−	0.235780i
$22$		0			0
$23$	1.89462	−	3.28158i	0.395056	−	0.684257i	−0.598053	−	0.801457i	$-0.704059\pi$
$23$	1.89462	−	3.28158i	0.395056	−	0.684257i	0.993108	+	0.117200i	$0.0373920\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.90147	−	1.72499i	0.943288	−	0.331975i
$28$		0			0
$29$	4.32292	+	7.48751i	0.802746	+	1.39040i	0.917802	+	0.397037i	$0.129962\pi$
$29$	4.32292	+	7.48751i	0.802746	+	1.39040i	−0.115057	+	0.993359i	$0.536705\pi$
$30$		0			0
$31$	2.07251	−	3.58970i	0.372234	−	0.644729i	−0.617675	−	0.786434i	$-0.711925\pi$
$31$	2.07251	−	3.58970i	0.372234	−	0.644729i	0.989909	+	0.141705i	$0.0452585\pi$
$32$		0			0
$33$	1.16232	−	2.66843i	0.202334	−	0.464514i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.35578			−0.222890			−0.111445	−	0.993771i	$-0.535548\pi$
$37$	−1.35578			−0.222890			−0.111445	+	0.993771i	$0.535548\pi$
$38$		0			0
$39$	−8.85481	+	1.00307i	−1.41790	+	0.160620i
$40$		0			0
$41$	3.57505	−	6.19216i	0.558328	−	0.967053i	−0.439308	−	0.898337i	$-0.644776\pi$
$41$	3.57505	−	6.19216i	0.558328	−	0.967053i	0.997636	−	0.0687167i	$-0.0218904\pi$
$42$		0			0
$43$	−3.64503	−	6.31337i	−0.555861	−	0.962780i	−0.997836	−	0.0657523i	$-0.979055\pi$
$43$	−3.64503	−	6.31337i	−0.555861	−	0.962780i	0.441975	−	0.897027i	$-0.354278\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.48270	−	11.2284i	−0.945600	−	1.63783i	−0.754546	−	0.656247i	$-0.772143\pi$
$47$	−6.48270	−	11.2284i	−0.945600	−	1.63783i	−0.191054	−	0.981580i	$-0.561190\pi$
$48$		0			0
$49$	3.26851	−	5.66123i	0.466930	−	0.808747i
$50$		0			0
$51$	−1.35832	−	1.83815i	−0.190203	−	0.257393i
$52$		0			0
$53$	8.83052			1.21297			0.606483	−	0.795097i	$-0.292580\pi$
$53$	8.83052			1.21297			0.606483	+	0.795097i	$0.292580\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.334174	+	0.452222i	0.0442624	+	0.0598983i
$58$		0			0
$59$	−4.40766	+	7.63429i	−0.573828	+	0.993900i	0.422340	+	0.906438i	$0.361209\pi$
$59$	−4.40766	+	7.63429i	−0.573828	+	0.993900i	−0.996168	+	0.0874619i	$0.972124\pi$
$60$		0			0
$61$	−4.98524	−	8.63469i	−0.638294	−	1.10556i	−0.985807	−	0.167883i	$-0.946307\pi$
$61$	−4.98524	−	8.63469i	−0.638294	−	1.10556i	0.347513	−	0.937675i	$-0.387026\pi$
$62$		0			0
$63$	−1.98955	+	0.456611i	−0.250660	+	0.0575276i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.08808	+	3.61667i	−0.255100	+	0.441846i	−0.964923	−	0.262534i	$-0.915442\pi$
$67$	−2.08808	+	3.61667i	−0.255100	+	0.441846i	0.709823	+	0.704380i	$0.248775\pi$
$68$		0			0
$69$	−6.52145	+	0.738747i	−0.785090	+	0.0889347i
$70$		0			0
$71$	−0.891185			−0.105764			−0.0528821	−	0.998601i	$-0.516841\pi$
$71$	−0.891185			−0.105764			−0.0528821	+	0.998601i	$0.516841\pi$
$72$		0			0
$73$	7.82038			0.915307			0.457653	−	0.889131i	$-0.348690\pi$
$73$	7.82038			0.915307			0.457653	+	0.889131i	$0.348690\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.571703	+	0.990219i	−0.0651516	+	0.112846i
$78$		0			0
$79$	−4.82799	−	8.36232i	−0.543191	−	0.940834i	−0.998718	−	0.0506124i	$-0.983883\pi$
$79$	−4.82799	−	8.36232i	−0.543191	−	0.940834i	0.455528	−	0.890222i	$-0.349451\pi$
$80$		0			0
$81$	−7.44828	−	5.05205i	−0.827586	−	0.561339i
$82$		0			0
$83$	2.42830	+	4.20593i	0.266540	+	0.461661i	0.967966	−	0.251081i	$-0.0807861\pi$
$83$	2.42830	+	4.20593i	0.266540	+	0.461661i	−0.701426	+	0.712743i	$0.747453\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.98017	−	13.7291i	0.641142	−	1.47192i
$88$		0			0
$89$	17.4764			1.85249			0.926245	−	0.376922i	$-0.123018\pi$
$89$	17.4764			1.85249			0.926245	+	0.376922i	$0.123018\pi$
$90$		0			0
$91$	3.50081			0.366985
$92$		0			0
$93$	−7.13377	+	0.808111i	−0.739737	+	0.0837972i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.46713	+	7.73730i	0.453569	+	0.785604i	0.998605	−	0.0528087i	$-0.0168173\pi$
$97$	4.46713	+	7.73730i	0.453569	+	0.785604i	−0.545036	+	0.838413i	$0.683484\pi$
$98$		0			0
$99$	−4.91354	+	1.12768i	−0.493829	+	0.113336i
$100$		0			0
$101$	5.42830	+	9.40209i	0.540136	+	0.935543i	0.998896	+	0.0469823i	$0.0149604\pi$
$101$	5.42830	+	9.40209i	0.540136	+	0.935543i	−0.458760	+	0.888560i	$0.651706\pi$
$102$		0			0
$103$	5.84102	−	10.1169i	0.575533	−	0.996853i	−0.420450	−	0.907316i	$-0.638128\pi$
$103$	5.84102	−	10.1169i	0.575533	−	0.996853i	0.995983	−	0.0895370i	$-0.0285387\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.11550			−0.494534			−0.247267	−	0.968947i	$-0.579533\pi$
$107$	−5.11550			−0.494534			−0.247267	+	0.968947i	$0.579533\pi$
$108$		0			0
$109$	7.17110			0.686867			0.343433	−	0.939177i	$-0.388410\pi$
$109$	7.17110			0.686867			0.343433	+	0.939177i	$0.388410\pi$
$110$		0			0
$111$	1.39559	+	1.88859i	0.132464	+	0.179257i
$112$		0			0
$113$	−8.82292	+	15.2817i	−0.829990	+	1.43759i	0.0680547	+	0.997682i	$0.478321\pi$
$113$	−8.82292	+	15.2817i	−0.829990	+	1.43759i	−0.898045	+	0.439904i	$0.855013\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	10.5121	+	11.3021i	0.971841	+	1.04488i
$118$		0			0
$119$	0.448936	+	0.777580i	0.0411539	+	0.0712807i
$120$		0			0
$121$	4.08808	−	7.08077i	0.371644	−	0.643706i
$122$		0			0
$123$	−12.3056	+	1.39398i	−1.10956	+	0.125691i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.13489			−0.278176			−0.139088	−	0.990280i	$-0.544417\pi$
$127$	−3.13489			−0.278176			−0.139088	+	0.990280i	$0.544417\pi$
$128$		0			0
$129$	−5.04240	+	11.5762i	−0.443958	+	1.01923i
$130$		0			0
$131$	−4.05775	+	7.02823i	−0.354527	+	0.614059i	−0.987037	−	0.160493i	$-0.948692\pi$
$131$	−4.05775	+	7.02823i	−0.354527	+	0.614059i	0.632510	+	0.774553i	$0.282025\pi$
$132$		0			0
$133$	−0.110447	−	0.191300i	−0.00957700	−	0.0165879i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.44559	−	5.96794i	−0.294377	−	0.509876i	0.680463	−	0.732783i	$-0.261779\pi$
$137$	−3.44559	−	5.96794i	−0.294377	−	0.509876i	−0.974840	+	0.222907i	$0.928445\pi$
$138$		0			0
$139$	10.1277	−	17.5417i	0.859023	−	1.48787i	−0.0138392	−	0.999904i	$-0.504405\pi$
$139$	10.1277	−	17.5417i	0.859023	−	1.48787i	0.872862	−	0.487967i	$-0.162261\pi$
$140$		0			0
$141$	−8.96794	+	20.5884i	−0.755237	+	1.73385i
$142$		0			0
$143$	8.64584			0.723001
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−11.2505	+	1.27445i	−0.927925	+	0.105115i
$148$		0			0
$149$	−5.03368	+	8.71858i	−0.412375	+	0.714254i	−0.995149	−	0.0983800i	$-0.968634\pi$
$149$	−5.03368	+	8.71858i	−0.412375	+	0.714254i	0.582774	+	0.812634i	$0.301967\pi$
$150$		0			0
$151$	9.39543	+	16.2734i	0.764589	+	1.32431i	0.940463	+	0.339895i	$0.110391\pi$
$151$	9.39543	+	16.2734i	0.764589	+	1.32431i	−0.175874	+	0.984413i	$0.556275\pi$
$152$		0			0
$153$	−1.16232	+	3.78424i	−0.0939681	+	0.305938i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.74071	+	16.8714i	−0.777393	+	1.34648i	0.156046	+	0.987750i	$0.450125\pi$
$157$	−9.74071	+	16.8714i	−0.777393	+	1.34648i	−0.933439	+	0.358735i	$0.883208\pi$
$158$		0			0
$159$	−9.08980	−	12.3008i	−0.720868	−	0.975517i
$160$		0			0
$161$	2.57830			0.203198
$162$		0			0
$163$	−12.2640			−0.960589			−0.480294	−	0.877107i	$-0.659470\pi$
$163$	−12.2640			−0.960589			−0.480294	+	0.877107i	$0.659470\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.75547	+	11.7008i	−0.522754	+	0.905437i	0.476895	+	0.878960i	$0.341762\pi$
$167$	−6.75547	+	11.7008i	−0.522754	+	0.905437i	−0.999649	+	0.0264767i	$0.991571\pi$
$168$		0			0
$169$	−6.73564	−	11.6665i	−0.518126	−	0.897421i
$170$		0			0
$171$	0.285954	−	0.931000i	0.0218675	−	0.0711953i
$172$		0			0
$173$	0.877325	+	1.51957i	0.0667018	+	0.115531i	0.897448	−	0.441121i	$-0.145419\pi$
$173$	0.877325	+	1.51957i	0.0667018	+	0.115531i	−0.830746	+	0.556652i	$0.812086\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	15.1715	−	1.71863i	1.14036	−	0.129180i
$178$		0			0
$179$	22.9393			1.71457			0.857283	−	0.514845i	$-0.172151\pi$
$179$	22.9393			1.71457			0.857283	+	0.514845i	$0.172151\pi$
$180$		0			0
$181$	−12.4452			−0.925045			−0.462523	−	0.886607i	$-0.653056\pi$
$181$	−12.4452			−0.925045			−0.462523	+	0.886607i	$0.653056\pi$
$182$		0			0
$183$	−6.89640	+	15.8326i	−0.509797	+	1.17038i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.10872	+	1.92036i	0.0810779	+	0.140431i
$188$		0			0
$189$	2.68402	+	2.30141i	0.195234	+	0.167403i
$190$		0			0
$191$	8.28924	+	14.3574i	0.599788	+	1.03886i	0.992852	+	0.119353i	$0.0380819\pi$
$191$	8.28924	+	14.3574i	0.599788	+	1.03886i	−0.393063	+	0.919511i	$0.628585\pi$
$192$		0			0
$193$	−7.80735	+	13.5227i	−0.561985	+	0.973387i	0.435338	+	0.900267i	$0.356629\pi$
$193$	−7.80735	+	13.5227i	−0.561985	+	0.973387i	−0.997323	+	0.0731197i	$0.976704\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.8153			1.26929			0.634644	−	0.772804i	$-0.281147\pi$
$197$	17.8153			1.26929			0.634644	+	0.772804i	$0.281147\pi$
$198$		0			0
$199$	8.07749			0.572598			0.286299	−	0.958140i	$-0.407575\pi$
$199$	8.07749			0.572598			0.286299	+	0.958140i	$0.407575\pi$
$200$		0			0
$201$	7.18737	−	0.814182i	0.506958	−	0.0574280i
$202$		0			0
$203$	−2.94143	+	5.09470i	−0.206448	+	0.357578i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.74199	+	8.32386i	0.538106	+	0.578548i
$208$		0			0
$209$	−0.272768	−	0.472449i	−0.0188678	−	0.0326799i
$210$		0			0
$211$	−7.19436	+	12.4610i	−0.495281	+	0.857851i	−0.999985	−	0.00544105i	$-0.998268\pi$
$211$	−7.19436	+	12.4610i	−0.495281	+	0.857851i	0.504705	+	0.863292i	$0.331601\pi$
$212$		0			0
$213$	0.917351	+	1.24141i	0.0628559	+	0.0850600i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.82038			0.191460
$218$		0			0
$219$	−8.05000	−	10.8937i	−0.543969	−	0.736128i
$220$		0			0
$221$	3.39462	−	5.87966i	0.228347	−	0.395508i
$222$		0			0
$223$	−1.01811	−	1.76341i	−0.0681774	−	0.118087i	0.829922	−	0.557880i	$-0.188385\pi$
$223$	−1.01811	−	1.76341i	−0.0681774	−	0.118087i	−0.898099	+	0.439793i	$0.855052\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.6838	−	23.7010i	−0.908224	−	1.57309i	−0.816530	−	0.577302i	$-0.804105\pi$
$227$	−13.6838	−	23.7010i	−0.908224	−	1.57309i	−0.0916932	−	0.995787i	$-0.529228\pi$
$228$		0			0
$229$	4.71500	−	8.16663i	0.311576	−	0.539666i	−0.667128	−	0.744944i	$-0.732476\pi$
$229$	4.71500	−	8.16663i	0.311576	−	0.539666i	0.978704	+	0.205278i	$0.0658097\pi$
$230$		0			0
$231$	1.96785	−	0.222917i	0.129475	−	0.0146669i
$232$		0			0
$233$	−0.191372			−0.0125372			−0.00626859	−	0.999980i	$-0.501995\pi$
$233$	−0.191372			−0.0125372			−0.00626859	+	0.999980i	$0.501995\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.67886	+	15.3332i	−0.433839	+	0.995996i
$238$		0			0
$239$	−1.10538	+	1.91457i	−0.0715011	+	0.123843i	−0.899559	−	0.436799i	$-0.856112\pi$
$239$	−1.10538	+	1.91457i	−0.0715011	+	0.123843i	0.828058	+	0.560642i	$0.189446\pi$
$240$		0			0
$241$	−11.2537	−	19.4921i	−0.724918	−	1.25559i	−0.959008	−	0.283379i	$-0.908544\pi$
$241$	−11.2537	−	19.4921i	−0.724918	−	1.25559i	0.234090	−	0.972215i	$-0.424789\pi$
$242$		0			0
$243$	0.629524	+	15.5757i	0.0403840	+	0.999184i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.835145	+	1.44651i	−0.0531390	+	0.0920395i
$248$		0			0
$249$	3.35922	−	7.71201i	0.212882	−	0.488729i
$250$		0			0
$251$	−24.9654			−1.57580			−0.787901	−	0.615802i	$-0.788832\pi$
$251$	−24.9654			−1.57580			−0.787901	+	0.615802i	$0.788832\pi$
$252$		0			0
$253$	6.36754			0.400324
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.15979	+	14.1332i	−0.508994	+	0.881603i	0.490952	+	0.871186i	$0.336649\pi$
$257$	−8.15979	+	14.1332i	−0.508994	+	0.881603i	−0.999946	+	0.0104161i	$0.996684\pi$
$258$		0			0
$259$	−0.461256	−	0.798918i	−0.0286610	−	0.0496424i
$260$		0			0
$261$	−25.2803	+	5.80193i	−1.56481	+	0.359130i
$262$		0			0
$263$	8.34356	+	14.4515i	0.514486	+	0.891115i	0.999859	+	0.0168083i	$0.00535049\pi$
$263$	8.34356	+	14.4515i	0.514486	+	0.891115i	−0.485373	+	0.874307i	$0.661316\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−17.9895	−	24.3444i	−1.10094	−	1.48985i
$268$		0			0
$269$	3.36085			0.204915			0.102457	−	0.994737i	$-0.467329\pi$
$269$	3.36085			0.204915			0.102457	+	0.994737i	$0.467329\pi$
$270$		0			0
$271$	20.0498			1.21794			0.608968	−	0.793195i	$-0.291584\pi$
$271$	20.0498			1.21794			0.608968	+	0.793195i	$0.291584\pi$
$272$		0			0
$273$	−3.60360	−	4.87659i	−0.218100	−	0.295144i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.10619	−	7.11213i	−0.246717	−	0.427326i	0.715896	−	0.698207i	$-0.246018\pi$
$277$	−4.10619	−	7.11213i	−0.246717	−	0.427326i	−0.962613	+	0.270881i	$0.912685\pi$
$278$		0			0
$279$	8.46891	+	9.10542i	0.507021	+	0.545127i
$280$		0			0
$281$	−0.188028	−	0.325674i	−0.0112168	−	0.0194281i	0.860363	−	0.509683i	$-0.170237\pi$
$281$	−0.188028	−	0.325674i	−0.0112168	−	0.0194281i	−0.871579	+	0.490255i	$0.836904\pi$
$282$		0			0
$283$	0.352441	−	0.610445i	0.0209504	−	0.0362872i	−0.855360	−	0.518034i	$-0.826664\pi$
$283$	0.352441	−	0.610445i	0.0209504	−	0.0362872i	0.876311	+	0.481747i	$0.159997\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.86511			0.287178
$288$		0			0
$289$	−15.2587			−0.897572
$290$		0			0
$291$	6.17967	−	14.1871i	0.362259	−	0.831665i
$292$		0			0
$293$	−9.09569	+	15.7542i	−0.531376	+	0.920370i	0.467954	+	0.883753i	$0.344991\pi$
$293$	−9.09569	+	15.7542i	−0.531376	+	0.920370i	−0.999329	+	0.0366167i	$0.988342\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	6.62864	+	5.68371i	0.384633	+	0.329802i
$298$		0			0
$299$	−9.74787	−	16.8838i	−0.563734	−	0.976416i
$300$		0			0
$301$	2.48017	−	4.29578i	0.142955	−	0.247605i
$302$		0			0
$303$	7.50931	−	17.2397i	0.431399	−	0.990395i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−4.04128			−0.230648			−0.115324	−	0.993328i	$-0.536791\pi$
$307$	−4.04128			−0.230648			−0.115324	+	0.993328i	$0.536791\pi$
$308$		0			0
$309$	−20.1053	+	2.27752i	−1.14375	+	0.129564i
$310$		0			0
$311$	4.58474	−	7.94100i	0.259977	−	0.450293i	−0.706259	−	0.707954i	$-0.749618\pi$
$311$	4.58474	−	7.94100i	0.259977	−	0.450293i	0.966235	+	0.257661i	$0.0829518\pi$
$312$		0			0
$313$	8.61126	+	14.9151i	0.486737	+	0.843053i	0.999884	−	0.0152476i	$-0.00485366\pi$
$313$	8.61126	+	14.9151i	0.486737	+	0.843053i	−0.513147	+	0.858301i	$0.671520\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.23149	−	7.32916i	−0.237664	−	0.411646i	0.722379	−	0.691497i	$-0.243048\pi$
$317$	−4.23149	−	7.32916i	−0.237664	−	0.411646i	−0.960044	+	0.279851i	$0.909715\pi$
$318$		0			0
$319$	−7.26434	+	12.5822i	−0.406725	+	0.704469i
$320$		0			0
$321$	5.26570	+	7.12583i	0.293903	+	0.397725i
$322$		0			0
$323$	−0.428389			−0.0238362
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.38165	−	9.98926i	−0.408206	−	0.552407i
$328$		0			0
$329$	4.41100	−	7.64008i	0.243186	−	0.421211i
$330$		0			0
$331$	3.51892	+	6.09494i	0.193417	+	0.335008i	0.946380	−	0.323054i	$-0.104710\pi$
$331$	3.51892	+	6.09494i	0.193417	+	0.335008i	−0.752963	+	0.658062i	$0.771376\pi$
$332$		0			0
$333$	1.19422	−	3.88809i	0.0654426	−	0.213066i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	12.2744	−	21.2599i	0.668629	−	1.15810i	−0.309659	−	0.950848i	$-0.600215\pi$
$337$	12.2744	−	21.2599i	0.668629	−	1.15810i	0.978288	−	0.207251i	$-0.0664517\pi$
$338$		0			0
$339$	30.3693	−	3.44022i	1.64943	−	0.186847i
$340$		0			0
$341$	6.96541			0.377198
$342$		0			0
$343$	9.21094			0.497344
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.6631	+	21.9332i	−0.679792	+	1.17744i	0.295251	+	0.955420i	$0.404597\pi$
$347$	−12.6631	+	21.9332i	−0.679792	+	1.17744i	−0.975043	+	0.222015i	$0.928737\pi$
$348$		0			0
$349$	5.44396	+	9.42922i	0.291409	+	0.504734i	0.974143	−	0.225932i	$-0.0725428\pi$
$349$	5.44396	+	9.42922i	0.291409	+	0.504734i	−0.682735	+	0.730667i	$0.739209\pi$
$350$		0			0
$351$	4.92301	−	26.2772i	0.262771	−	1.40257i
$352$		0			0
$353$	−13.2306	−	22.9160i	−0.704192	−	1.21970i	−0.966982	−	0.254844i	$-0.917976\pi$
$353$	−13.2306	−	22.9160i	−0.704192	−	1.21970i	0.262790	−	0.964853i	$-0.415357\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.621042	−	1.42577i	0.0328691	−	0.0754600i
$358$		0			0
$359$	−24.7007			−1.30365			−0.651826	−	0.758369i	$-0.725997\pi$
$359$	−24.7007			−1.30365			−0.651826	+	0.758369i	$0.725997\pi$
$360$		0			0
$361$	−18.8946			−0.994453
$362$		0			0
$363$	−14.0715	+	1.59402i	−0.738564	+	0.0836643i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.56744	+	13.1072i	0.395017	+	0.684190i	0.993103	−	0.117242i	$-0.0374052\pi$
$367$	7.56744	+	13.1072i	0.395017	+	0.684190i	−0.598086	+	0.801432i	$0.704072\pi$
$368$		0			0
$369$	14.6087	+	15.7067i	0.760500	+	0.817657i
$370$		0			0
$371$	3.00426	+	5.20353i	0.155973	+	0.270154i
$372$		0			0
$373$	4.47474	−	7.75047i	0.231693	−	0.401304i	−0.726613	−	0.687047i	$-0.758907\pi$
$373$	4.47474	−	7.75047i	0.231693	−	0.401304i	0.958306	+	0.285742i	$0.0922402\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	44.4830			2.29099
$378$		0			0
$379$	7.22270			0.371005			0.185503	−	0.982644i	$-0.440609\pi$
$379$	7.22270			0.371005			0.185503	+	0.982644i	$0.440609\pi$
$380$		0			0
$381$	3.22693	+	4.36686i	0.165321	+	0.223721i
$382$		0			0
$383$	17.8634	−	30.9403i	0.912776	−	1.58097i	0.102650	−	0.994718i	$-0.467268\pi$
$383$	17.8634	−	30.9403i	0.912776	−	1.58097i	0.810126	−	0.586256i	$-0.199399\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	21.3160	−	4.89211i	1.08355	−	0.248680i
$388$		0			0
$389$	−0.353250	−	0.611848i	−0.0179105	−	0.0310219i	0.856931	−	0.515431i	$-0.172368\pi$
$389$	−0.353250	−	0.611848i	−0.0179105	−	0.0310219i	−0.874842	+	0.484409i	$0.839035\pi$
$390$		0			0
$391$	2.50009	−	4.33029i	0.126435	−	0.218992i
$392$		0			0
$393$	13.9671	−	1.58219i	0.704549	−	0.0798110i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−6.44014			−0.323222			−0.161611	−	0.986855i	$-0.551669\pi$
$397$	−6.44014			−0.323222			−0.161611	+	0.986855i	$0.551669\pi$
$398$		0			0
$399$	−0.152789	+	0.350769i	−0.00764902	+	0.0175604i
$400$		0			0
$401$	13.3600	−	23.1403i	0.667168	−	1.15557i	−0.311525	−	0.950238i	$-0.600840\pi$
$401$	13.3600	−	23.1403i	0.667168	−	1.15557i	0.978693	−	0.205331i	$-0.0658270\pi$
$402$		0			0
$403$	−10.6631	−	18.4691i	−0.531168	−	0.920011i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.13915	−	1.97306i	−0.0564655	−	0.0978010i
$408$		0			0
$409$	−12.0463	+	20.8649i	−0.595653	+	1.03170i	0.397802	+	0.917471i	$0.369773\pi$
$409$	−12.0463	+	20.8649i	−0.595653	+	1.03170i	−0.993454	+	0.114230i	$0.963560\pi$
$410$		0			0
$411$	−4.76651	+	10.9428i	−0.235115	+	0.539770i
$412$		0			0
$413$	−5.99817			−0.295151
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−34.8605	+	3.94899i	−1.70713	+	0.193383i
$418$		0			0
$419$	−11.9566	+	20.7095i	−0.584120	+	1.01172i	0.410865	+	0.911696i	$0.365227\pi$
$419$	−11.9566	+	20.7095i	−0.584120	+	1.01172i	−0.994985	+	0.100029i	$0.968107\pi$
$420$		0			0
$421$	4.75466	+	8.23532i	0.231728	+	0.401365i	0.958317	−	0.285708i	$-0.0922287\pi$
$421$	4.75466	+	8.23532i	0.231728	+	0.401365i	−0.726589	+	0.687073i	$0.758895\pi$
$422$		0			0
$423$	37.9106	−	8.70065i	1.84328	−	0.423040i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.39209	−	5.87527i	0.164155	−	0.284324i
$428$		0			0
$429$	−8.89969	−	12.0435i	−0.429681	−	0.581468i
$430$		0			0
$431$	−29.8287			−1.43680			−0.718399	−	0.695632i	$-0.755125\pi$
$431$	−29.8287			−1.43680			−0.718399	+	0.695632i	$0.755125\pi$
$432$		0			0
$433$	−14.2385			−0.684256			−0.342128	−	0.939653i	$-0.611148\pi$
$433$	−14.2385			−0.684256			−0.342128	+	0.939653i	$0.611148\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.615073	+	1.06534i	−0.0294229	+	0.0509620i
$438$		0			0
$439$	16.4764	+	28.5379i	0.786374	+	1.36204i	0.928175	+	0.372144i	$0.121377\pi$
$439$	16.4764	+	28.5379i	0.786374	+	1.36204i	−0.141802	+	0.989895i	$0.545290\pi$
$440$		0			0
$441$	13.3561	+	14.3599i	0.636006	+	0.683806i
$442$		0			0
$443$	−17.2112	−	29.8107i	−0.817728	−	1.41635i	−0.907352	−	0.420371i	$-0.861900\pi$
$443$	−17.2112	−	29.8107i	−0.817728	−	1.41635i	0.0896240	−	0.995976i	$-0.471433\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	17.3264	−	1.96272i	0.819508	−	0.0928336i
$448$		0			0
$449$	−2.91326			−0.137485			−0.0687426	−	0.997634i	$-0.521899\pi$
$449$	−2.91326			−0.137485			−0.0687426	+	0.997634i	$0.521899\pi$
$450$		0			0
$451$	12.0152			0.565774
$452$		0			0
$453$	12.9973	−	29.8389i	0.610667	−	1.40195i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.9144	−	20.6364i	−0.557334	−	0.965331i	−0.997718	−	0.0675210i	$-0.978491\pi$
$457$	−11.9144	−	20.6364i	−0.557334	−	0.965331i	0.440384	−	0.897810i	$-0.354842\pi$
$458$		0			0
$459$	6.46785	−	2.27625i	0.301893	−	0.106246i
$460$		0			0
$461$	−3.16322	−	5.47886i	−0.147326	−	0.255176i	0.782912	−	0.622132i	$-0.213733\pi$
$461$	−3.16322	−	5.47886i	−0.147326	−	0.255176i	−0.930238	+	0.366956i	$0.880400\pi$
$462$		0			0
$463$	−2.15889	+	3.73930i	−0.100332	+	0.173780i	−0.911821	−	0.410587i	$-0.865324\pi$
$463$	−2.15889	+	3.73930i	−0.100332	+	0.173780i	0.811490	+	0.584367i	$0.198657\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.352336			−0.0163042			−0.00815208	−	0.999967i	$-0.502595\pi$
$467$	−0.352336			−0.0163042			−0.00815208	+	0.999967i	$0.502595\pi$
$468$		0			0
$469$	−2.84157			−0.131212
$470$		0			0
$471$	33.5284	−	3.79808i	1.54491	−	0.175006i
$472$		0			0
$473$	6.12520	−	10.6092i	0.281637	−	0.487809i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.77819	+	25.3239i	−0.356139	+	1.15950i
$478$		0			0
$479$	−14.0370	−	24.3128i	−0.641368	−	1.11088i	−0.985128	−	0.171824i	$-0.945034\pi$
$479$	−14.0370	−	24.3128i	−0.641368	−	1.11088i	0.343760	−	0.939058i	$-0.388299\pi$
$480$		0			0
$481$	−3.48777	+	6.04100i	−0.159029	+	0.275446i
$482$		0			0
$483$	−2.65400	−	3.59154i	−0.120761	−	0.163421i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	27.9426			1.26620			0.633099	−	0.774070i	$-0.281782\pi$
$487$	27.9426			1.26620			0.633099	+	0.774070i	$0.281782\pi$
$488$		0			0
$489$	12.6241	+	17.0836i	0.570880	+	0.772546i
$490$		0			0
$491$	6.26517	−	10.8516i	0.282743	−	0.489725i	−0.689316	−	0.724460i	$-0.742089\pi$
$491$	6.26517	−	10.8516i	0.282743	−	0.489725i	0.972059	+	0.234735i	$0.0754223\pi$
$492$		0			0
$493$	5.70441	+	9.88033i	0.256914	+	0.444988i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.303193	−	0.525145i	−0.0136001	−	0.0235560i
$498$		0			0
$499$	−21.4350	+	37.1265i	−0.959562	+	1.66201i	−0.235996	+	0.971754i	$0.575835\pi$
$499$	−21.4350	+	37.1265i	−0.959562	+	1.66201i	−0.723566	+	0.690256i	$0.757498\pi$
$500$		0			0
$501$	23.2529	−	2.63408i	1.03886	−	0.117682i
$502$		0			0
$503$	12.8635			0.573554			0.286777	−	0.957997i	$-0.407416\pi$
$503$	12.8635			0.573554			0.286777	+	0.957997i	$0.407416\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.31785	+	21.3917i	−0.413820	+	0.950038i
$508$		0			0
$509$	−6.82635	+	11.8236i	−0.302573	+	0.524071i	−0.976718	−	0.214527i	$-0.931179\pi$
$509$	−6.82635	+	11.8236i	−0.302573	+	0.524071i	0.674145	+	0.738599i	$0.264512\pi$
$510$		0			0
$511$	2.66060	+	4.60829i	0.117698	+	0.203859i
$512$		0			0
$513$	−1.59122	+	0.560004i	−0.0702542	+	0.0247248i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	10.8937	−	18.8685i	0.479105	−	0.829834i
$518$		0			0
$519$	1.21366	−	2.78629i	0.0532738	−	0.122305i
$520$		0			0
$521$	32.8962			1.44121			0.720605	−	0.693346i	$-0.243864\pi$
$521$	32.8962			1.44121			0.720605	+	0.693346i	$0.243864\pi$
$522$		0			0
$523$	−18.0641			−0.789887			−0.394944	−	0.918705i	$-0.629236\pi$
$523$	−18.0641			−0.789887			−0.394944	+	0.918705i	$0.629236\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.73483	−	4.73687i	0.119131	−	0.206341i
$528$		0			0
$529$	4.32083	+	7.48389i	0.187862	+	0.325387i
$530$		0			0
$531$	−18.0110	−	19.3647i	−0.781612	−	0.840356i
$532$		0			0
$533$	−18.3937	−	31.8588i	−0.796720	−	1.37996i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−23.6129	−	31.9542i	−1.01897	−	1.37893i
$538$		0			0
$539$	10.9850			0.473157
$540$		0			0
$541$	−2.25204			−0.0968226			−0.0484113	−	0.998827i	$-0.515416\pi$
$541$	−2.25204			−0.0968226			−0.0484113	+	0.998827i	$0.515416\pi$
$542$		0			0
$543$	12.8106	+	17.3360i	0.549756	+	0.743960i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.39715	−	7.61610i	−0.188009	−	0.325641i	0.756578	−	0.653904i	$-0.226870\pi$
$547$	−4.39715	−	7.61610i	−0.188009	−	0.325641i	−0.944586	+	0.328263i	$0.893537\pi$
$548$		0			0
$549$	29.1535	−	6.69085i	1.24424	−	0.285559i
$550$		0			0
$551$	−1.40340	−	2.43076i	−0.0597868	−	0.103554i
$552$		0			0
$553$	3.28509	−	5.68994i	0.139696	−	0.241961i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.4199			1.03470			0.517352	−	0.855773i	$-0.326918\pi$
$557$	24.4199			1.03470			0.517352	+	0.855773i	$0.326918\pi$
$558$		0			0
$559$	−37.5075			−1.58640
$560$		0			0
$561$	1.53377	−	3.52119i	0.0647557	−	0.148665i
$562$		0			0
$563$	−5.07839	+	8.79603i	−0.214029	+	0.370708i	−0.952972	−	0.303059i	$-0.901992\pi$
$563$	−5.07839	+	8.79603i	−0.214029	+	0.370708i	0.738943	+	0.673768i	$0.235325\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.443002	−	6.10779i	0.0186043	−	0.256503i
$568$		0			0
$569$	−22.8537	−	39.5837i	−0.958076	−	1.65944i	−0.727166	−	0.686461i	$-0.759163\pi$
$569$	−22.8537	−	39.5837i	−0.958076	−	1.65944i	−0.230910	−	0.972975i	$-0.574170\pi$
$570$		0			0
$571$	−5.36629	+	9.29468i	−0.224572	+	0.388970i	−0.956191	−	0.292744i	$-0.905432\pi$
$571$	−5.36629	+	9.29468i	−0.224572	+	0.388970i	0.731619	+	0.681714i	$0.238765\pi$
$572$		0			0
$573$	11.4670	−	26.3258i	0.479043	−	1.09977i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−15.9857			−0.665493			−0.332746	−	0.943016i	$-0.607975\pi$
$577$	−15.9857			−0.665493			−0.332746	+	0.943016i	$0.607975\pi$
$578$		0			0
$579$	26.8736	−	3.04423i	1.11683	−	0.126514i
$580$		0			0
$581$	−1.65228	+	2.86183i	−0.0685480	+	0.118729i
$582$		0			0
$583$	7.41952	+	12.8510i	0.307285	+	0.532233i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.1733	+	31.4770i	0.750090	+	1.29919i	0.947778	+	0.318930i	$0.103323\pi$
$587$	18.1733	+	31.4770i	0.750090	+	1.29919i	−0.197688	+	0.980265i	$0.563343\pi$
$588$		0			0
$589$	−0.672824	+	1.16537i	−0.0277232	+	0.0480181i
$590$		0			0
$591$	−18.3384	−	24.8165i	−0.754341	−	1.02082i
$592$		0			0
$593$	9.27142			0.380732			0.190366	−	0.981713i	$-0.439033\pi$
$593$	9.27142			0.380732			0.190366	+	0.981713i	$0.439033\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.31465	−	11.2518i	−0.340296	−	0.460507i
$598$		0			0
$599$	−8.11642	+	14.0580i	−0.331628	+	0.574396i	−0.982831	−	0.184507i	$-0.940931\pi$
$599$	−8.11642	+	14.0580i	−0.331628	+	0.574396i	0.651203	+	0.758903i	$0.274264\pi$
$600$		0			0
$601$	−7.69427	−	13.3269i	−0.313856	−	0.543614i	0.665338	−	0.746543i	$-0.268288\pi$
$601$	−7.69427	−	13.3269i	−0.313856	−	0.543614i	−0.979194	+	0.202928i	$0.934954\pi$
$602$		0			0
$603$	−8.53254	−	9.17383i	−0.347472	−	0.373587i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	4.82038	−	8.34915i	0.195653	−	0.338882i	−0.751461	−	0.659777i	$-0.770651\pi$
$607$	4.82038	−	8.34915i	0.195653	−	0.338882i	0.947115	+	0.320896i	$0.103984\pi$
$608$		0			0
$609$	10.1246	−	1.14692i	0.410271	−	0.0464754i
$610$		0			0
$611$	−66.7074			−2.69869
$612$		0			0
$613$	40.2967			1.62757			0.813785	−	0.581166i	$-0.197403\pi$
$613$	40.2967			1.62757			0.813785	+	0.581166i	$0.197403\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.63480	+	13.2239i	−0.307365	+	0.532372i	−0.977785	−	0.209610i	$-0.932781\pi$
$617$	−7.63480	+	13.2239i	−0.307365	+	0.532372i	0.670420	+	0.741982i	$0.266114\pi$
$618$		0			0
$619$	13.0042	+	22.5240i	0.522685	+	0.905317i	0.999652	+	0.0263952i	$0.00840284\pi$
$619$	13.0042	+	22.5240i	0.522685	+	0.905317i	−0.476967	+	0.878921i	$0.658264\pi$
$620$		0			0
$621$	3.62573	−	19.3528i	0.145496	−	0.776600i
$622$		0			0
$623$	5.94568	+	10.2982i	0.238209	+	0.412590i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.377338	+	0.866283i	−0.0150694	+	0.0345960i
$628$		0			0
$629$	−1.78906			−0.0713344
$630$		0			0
$631$	−4.84484			−0.192870			−0.0964350	−	0.995339i	$-0.530744\pi$
$631$	−4.84484			−0.192870			−0.0964350	+	0.995339i	$0.530744\pi$
$632$		0			0
$633$	24.7636	−	2.80521i	0.984266	−	0.111497i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−16.8166	−	29.1271i	−0.666297	−	1.15406i
$638$		0			0
$639$	0.784983	−	2.55572i	0.0310534	−	0.101103i
$640$		0			0
$641$	−6.66313	−	11.5409i	−0.263178	−	0.455837i	0.703907	−	0.710292i	$-0.251437\pi$
$641$	−6.66313	−	11.5409i	−0.263178	−	0.455837i	−0.967085	+	0.254455i	$0.918104\pi$
$642$		0			0
$643$	−18.0101	+	31.1944i	−0.710250	+	1.23019i	0.254513	+	0.967069i	$0.418085\pi$
$643$	−18.0101	+	31.1944i	−0.710250	+	1.23019i	−0.964763	+	0.263120i	$0.915249\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.82219			0.189580			0.0947899	−	0.995497i	$-0.469782\pi$
$647$	4.82219			0.189580			0.0947899	+	0.995497i	$0.469782\pi$
$648$		0			0
$649$	−14.8135			−0.581480
$650$		0			0
$651$	−2.90319	−	3.92876i	−0.113785	−	0.153980i
$652$		0			0
$653$	−21.1361	+	36.6089i	−0.827121	+	1.43262i	0.0731662	+	0.997320i	$0.476690\pi$
$653$	−21.1361	+	36.6089i	−0.827121	+	1.43262i	−0.900287	+	0.435296i	$0.856644\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−6.88843	+	22.4271i	−0.268743	+	0.874965i
$658$		0			0
$659$	−18.7546	−	32.4838i	−0.730574	−	1.26539i	−0.956638	−	0.291279i	$-0.905919\pi$
$659$	−18.7546	−	32.4838i	−0.730574	−	1.26539i	0.226064	−	0.974112i	$-0.427414\pi$
$660$		0			0
$661$	3.17952	−	5.50710i	0.123669	−	0.214201i	−0.797543	−	0.603262i	$-0.793867\pi$
$661$	3.17952	−	5.50710i	0.123669	−	0.214201i	0.921212	+	0.389061i	$0.127201\pi$
$662$		0			0
$663$	−11.6846	+	1.32362i	−0.453791	+	0.0514053i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	32.7612			1.26852
$668$		0			0
$669$	−1.40841	+	3.23339i	−0.0544523	+	0.125010i
$670$		0			0
$671$	8.37733	−	14.5100i	0.323403	−	0.560151i
$672$		0			0
$673$	0.449838	+	0.779142i	0.0173400	+	0.0300337i	0.874565	−	0.484908i	$-0.161147\pi$
$673$	0.449838	+	0.779142i	0.0173400	+	0.0300337i	−0.857225	+	0.514942i	$0.827814\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.0144	−	27.7377i	−0.615483	−	1.06605i	−0.990300	−	0.138948i	$-0.955628\pi$
$677$	−16.0144	−	27.7377i	−0.615483	−	1.06605i	0.374817	−	0.927099i	$-0.377706\pi$
$678$		0			0
$679$	−3.03955	+	5.26466i	−0.116647	+	0.202039i
$680$		0			0
$681$	−18.9296	+	43.4582i	−0.725385	+	1.66532i
$682$		0			0
$683$	−14.7371			−0.563899			−0.281950	−	0.959429i	$-0.590981\pi$
$683$	−14.7371			−0.563899			−0.281950	+	0.959429i	$0.590981\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−16.2295	+	1.83847i	−0.619192	+	0.0701419i
$688$		0			0
$689$	22.7166	−	39.3463i	0.865434	−	1.49898i
$690$		0			0
$691$	11.2719	+	19.5234i	0.428802	+	0.742706i	0.996767	−	0.0803463i	$-0.0256026\pi$
$691$	11.2719	+	19.5234i	0.428802	+	0.742706i	−0.567965	+	0.823052i	$0.692269\pi$
$692$		0			0
$693$	−2.33615	−	2.51173i	−0.0887430	−	0.0954128i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.71754	−	8.17102i	0.178689	−	0.309499i
$698$		0			0
$699$	0.196991	+	0.266579i	0.00745087	+	0.0100829i
$700$		0			0
$701$	19.9984			0.755327			0.377664	−	0.925943i	$-0.376728\pi$
$701$	19.9984			0.755327			0.377664	+	0.925943i	$0.376728\pi$
$702$		0			0
$703$	0.440144			0.0166004
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.69356	+	6.39743i	−0.138910	+	0.240600i
$708$		0			0
$709$	−7.50850	−	13.0051i	−0.281988	−	0.488417i	0.689886	−	0.723918i	$-0.257660\pi$
$709$	−7.50850	−	13.0051i	−0.281988	−	0.488417i	−0.971874	+	0.235500i	$0.924327\pi$
$710$		0			0
$711$	28.2339	−	6.47980i	1.05885	−	0.243011i
$712$		0			0
$713$	−7.85325	−	13.6022i	−0.294107	−	0.509407i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.80481	−	0.431008i	0.142093	−	0.0160963i
$718$		0			0
$719$	−25.8289			−0.963254			−0.481627	−	0.876376i	$-0.659954\pi$
$719$	−25.8289			−0.963254			−0.481627	+	0.876376i	$0.659954\pi$
$720$		0			0
$721$	7.94877			0.296028
$722$		0			0
$723$	−15.5680	+	35.7407i	−0.578981	+	1.32921i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	5.31332	+	9.20293i	0.197060	+	0.341318i	0.947574	−	0.319537i	$-0.103527\pi$
$727$	5.31332	+	9.20293i	0.197060	+	0.341318i	−0.750514	+	0.660855i	$0.770194\pi$
$728$		0			0
$729$	21.0488	−	16.9100i	0.779586	−	0.626296i
$730$		0			0
$731$	−4.80988	−	8.33096i	−0.177900	−	0.308132i
$732$		0			0
$733$	−20.8807	+	36.1664i	−0.771245	+	1.33584i	0.165636	+	0.986187i	$0.447032\pi$
$733$	−20.8807	+	36.1664i	−0.771245	+	1.33584i	−0.936881	+	0.349649i	$0.886301\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.01774			−0.258502
$738$		0			0
$739$	49.1030			1.80628			0.903141	−	0.429343i	$-0.141255\pi$
$739$	49.1030			1.80628			0.903141	+	0.429343i	$0.141255\pi$
$740$		0			0
$741$	2.87464	−	0.325638i	0.105603	−	0.0119626i
$742$		0			0
$743$	9.65553	−	16.7239i	0.354227	−	0.613539i	−0.632758	−	0.774349i	$-0.718077\pi$
$743$	9.65553	−	16.7239i	0.354227	−	0.613539i	0.986985	+	0.160810i	$0.0514107\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−14.2006	+	3.25910i	−0.519573	+	0.119244i
$748$		0			0
$749$	−1.74036	−	3.01439i	−0.0635914	−	0.110144i
$750$		0			0
$751$	−4.15725	+	7.20057i	−0.151700	+	0.262753i	−0.931853	−	0.362837i	$-0.881808\pi$
$751$	−4.15725	+	7.20057i	−0.151700	+	0.262753i	0.780152	+	0.625590i	$0.215142\pi$
$752$		0			0
$753$	25.6984	+	34.7765i	0.936503	+	1.26733i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−33.8667			−1.23091			−0.615453	−	0.788173i	$-0.711027\pi$
$757$	−33.8667			−1.23091			−0.615453	+	0.788173i	$0.711027\pi$
$758$		0			0
$759$	−6.55450	−	8.86991i	−0.237913	−	0.321957i
$760$		0			0
$761$	−9.52407	+	16.4962i	−0.345247	+	0.597986i	−0.985399	−	0.170263i	$-0.945538\pi$
$761$	−9.52407	+	16.4962i	−0.345247	+	0.597986i	0.640151	+	0.768249i	$0.278872\pi$
$762$		0			0
$763$	2.43970	+	4.22569i	0.0883231	+	0.152980i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	22.6775	+	39.2786i	0.818837	+	1.41827i
$768$		0			0
$769$	−16.8313	+	29.1527i	−0.606953	+	1.05127i	0.384786	+	0.923006i	$0.374275\pi$
$769$	−16.8313	+	29.1527i	−0.606953	+	1.05127i	−0.991740	+	0.128268i	$0.959058\pi$
$770$		0			0
$771$	28.0867	−	3.18165i	1.01152	−	0.114584i
$772$		0			0
$773$	−23.5354			−0.846509			−0.423254	−	0.906011i	$-0.639112\pi$
$773$	−23.5354			−0.846509			−0.423254	+	0.906011i	$0.639112\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.638085	+	1.46490i	−0.0228912	+	0.0525529i
$778$		0			0
$779$	−1.16061	+	2.01023i	−0.0415832	+	0.0720241i
$780$		0			0
$781$	−0.748785	−	1.29693i	−0.0267936	−	0.0464080i
$782$		0			0
$783$	34.1045	+	29.2428i	1.21880	+	1.04505i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−11.7661	+	20.3794i	−0.419415	+	0.726448i	−0.995881	−	0.0906732i	$-0.971098\pi$
$787$	−11.7661	+	20.3794i	−0.419415	+	0.726448i	0.576466	+	0.817121i	$0.304431\pi$
$788$		0			0
$789$	11.5422	−	26.4983i	0.410912	−	0.943363i
$790$		0			0
$791$	−12.0067			−0.426909
$792$		0			0
$793$	−51.2984			−1.82166
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.26526	+	2.19149i	−0.0448177	+	0.0776266i	−0.887564	−	0.460684i	$-0.847604\pi$
$797$	−1.26526	+	2.19149i	−0.0448177	+	0.0776266i	0.842746	+	0.538311i	$0.180937\pi$
$798$		0			0
$799$	−8.55441	−	14.8167i	−0.302633	−	0.524176i
$800$		0			0
$801$	−15.3937	+	50.1183i	−0.543910	+	1.77084i
$802$		0			0
$803$	6.57079	+	11.3809i	0.231878	+	0.401625i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.45953	−	4.68163i	−0.121781	−	0.164801i
$808$		0			0
$809$	−21.5178			−0.756526			−0.378263	−	0.925698i	$-0.623479\pi$
$809$	−21.5178			−0.756526			−0.378263	+	0.925698i	$0.623479\pi$
$810$		0			0
$811$	−45.0566			−1.58215			−0.791076	−	0.611717i	$-0.790479\pi$
$811$	−45.0566			−1.58215			−0.791076	+	0.611717i	$0.790479\pi$
$812$		0			0
$813$	−20.6385	−	27.9291i	−0.723822	−	0.979516i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.18333	+	2.04958i	0.0413994	+	0.0717059i
$818$		0			0
$819$	−3.08362	+	10.0395i	−0.107750	+	0.350810i
$820$		0			0
$821$	14.9047	+	25.8158i	0.520179	+	0.900977i	0.999725	+	0.0234598i	$0.00746816\pi$
$821$	14.9047	+	25.8158i	0.520179	+	0.900977i	−0.479546	+	0.877517i	$0.659199\pi$
$822$		0			0
$823$	6.45610	−	11.1823i	0.225045	−	0.389790i	−0.731288	−	0.682069i	$-0.761080\pi$
$823$	6.45610	−	11.1823i	0.225045	−	0.389790i	0.956333	+	0.292279i	$0.0944136\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	8.92395			0.310316			0.155158	−	0.987890i	$-0.450411\pi$
$827$	8.92395			0.310316			0.155158	+	0.987890i	$0.450411\pi$
$828$		0			0
$829$	23.2259			0.806670			0.403335	−	0.915052i	$-0.367851\pi$
$829$	23.2259			0.806670			0.403335	+	0.915052i	$0.367851\pi$
$830$		0			0
$831$	−5.68036	+	13.0408i	−0.197049	+	0.452381i
$832$		0			0
$833$	4.31304	−	7.47041i	0.149438	−	0.258834i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.96616	−	21.1699i	0.137091	−	0.731737i
$838$		0			0
$839$	13.1839	+	22.8351i	0.455157	+	0.788356i	0.998697	−	0.0510276i	$-0.0162496\pi$
$839$	13.1839	+	22.8351i	0.455157	+	0.788356i	−0.543540	+	0.839383i	$0.682916\pi$
$840$		0			0
$841$	−22.8752	+	39.6211i	−0.788801	+	1.36624i
$842$		0			0
$843$	−0.260111	+	0.597157i	−0.00895871	+	0.0205672i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.56328			0.191157
$848$		0			0
$849$	−1.21313	+	0.137423i	−0.0416346	+	0.00471635i
$850$		0			0
$851$	−2.56870	+	4.44911i	−0.0880538	+	0.152514i
$852$		0			0
$853$	27.4612	+	47.5641i	0.940252	+	1.62856i	0.764990	+	0.644042i	$0.222744\pi$
$853$	27.4612	+	47.5641i	0.940252	+	1.62856i	0.175262	+	0.984522i	$0.443923\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.96967	−	6.87567i	−0.135601	−	0.234868i	0.790226	−	0.612816i	$-0.209963\pi$
$857$	−3.96967	−	6.87567i	−0.135601	−	0.234868i	−0.925827	+	0.377948i	$0.876630\pi$
$858$		0			0
$859$	9.43843	−	16.3478i	0.322035	−	0.557781i	−0.658873	−	0.752254i	$-0.728966\pi$
$859$	9.43843	−	16.3478i	0.322035	−	0.557781i	0.980908	+	0.194473i	$0.0622997\pi$
$860$		0			0
$861$	−5.00796	−	6.77704i	−0.170671	−	0.230961i
$862$		0			0
$863$	−19.4215			−0.661116			−0.330558	−	0.943786i	$-0.607237\pi$
$863$	−19.4215			−0.661116			−0.330558	+	0.943786i	$0.607237\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	15.7067	+	21.2552i	0.533429	+	0.721865i
$868$		0			0
$869$	8.11307	−	14.0523i	0.275217	−	0.476690i
$870$		0			0
$871$	10.7432	+	18.6078i	0.364021	+	0.630503i
$872$		0			0
$873$	−26.1236	+	5.99549i	−0.884151	+	0.202916i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.19055	+	10.7223i	−0.209040	+	0.362068i	−0.951412	−	0.307920i	$-0.900367\pi$
$877$	−6.19055	+	10.7223i	−0.209040	+	0.362068i	0.742372	+	0.669987i	$0.233701\pi$
$878$		0			0
$879$	31.3081	−	3.54657i	1.05600	−	0.119623i
$880$		0			0
$881$	16.8910			0.569072			0.284536	−	0.958665i	$-0.408160\pi$
$881$	16.8910			0.569072			0.284536	+	0.958665i	$0.408160\pi$
$882$		0			0
$883$	−17.8457			−0.600556			−0.300278	−	0.953852i	$-0.597079\pi$
$883$	−17.8457			−0.600556			−0.300278	+	0.953852i	$0.597079\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.49365	+	6.05118i	−0.117305	+	0.203179i	−0.918699	−	0.394959i	$-0.870759\pi$
$887$	−3.49365	+	6.05118i	−0.117305	+	0.203179i	0.801394	+	0.598137i	$0.204092\pi$
$888$		0			0
$889$	−1.06653	−	1.84728i	−0.0357703	−	0.0619559i
$890$		0			0
$891$	1.09407	−	15.0842i	0.0366526	−	0.505340i
$892$		0			0
$893$	2.10456	+	3.64520i	0.0704263	+	0.121982i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−13.4849	+	30.9582i	−0.450246	+	1.03366i
$898$		0			0
$899$	35.8372			1.19524
$900$		0			0
$901$	11.6525			0.388202
$902$		0			0
$903$	−8.53696	+	0.967064i	−0.284092	+	0.0321819i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	18.0042	+	31.1843i	0.597821	+	1.03546i	0.993142	+	0.116914i	$0.0373000\pi$
$907$	18.0042	+	31.1843i	0.597821	+	1.03546i	−0.395321	+	0.918543i	$0.629367\pi$
$908$		0			0
$909$	−31.7445	+	7.28549i	−1.05290	+	0.241645i
$910$		0			0
$911$	4.70994	+	8.15785i	0.156047	+	0.270282i	0.933440	−	0.358734i	$-0.116791\pi$
$911$	4.70994	+	8.15785i	0.156047	+	0.270282i	−0.777393	+	0.629016i	$0.783458\pi$
$912$		0			0
$913$	−4.08057	+	7.06776i	−0.135047	+	0.233909i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.52200			−0.182353
$918$		0			0
$919$	−9.54389			−0.314824			−0.157412	−	0.987533i	$-0.550315\pi$
$919$	−9.54389			−0.314824			−0.157412	+	0.987533i	$0.550315\pi$
$920$		0			0
$921$	4.15994	+	5.62945i	0.137075	+	0.185497i
$922$		0			0
$923$	−2.29258	+	3.97087i	−0.0754613	+	0.130703i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	23.8682	+	25.6621i	0.783934	+	0.842853i
$928$		0			0
$929$	4.00969	+	6.94499i	0.131554	+	0.227858i	0.924276	−	0.381726i	$-0.124670\pi$
$929$	4.00969	+	6.94499i	0.131554	+	0.227858i	−0.792722	+	0.609583i	$0.791337\pi$
$930$		0			0
$931$	−1.06109	+	1.83787i	−0.0347760	+	0.0602338i
$932$		0			0
$933$	−15.7811	+	1.78767i	−0.516649	+	0.0585258i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	36.1070			1.17956			0.589782	−	0.807563i	$-0.299214\pi$
$937$	36.1070			1.17956			0.589782	+	0.807563i	$0.299214\pi$
$938$		0			0
$939$	11.9125	−	27.3484i	0.388750	−	0.892483i
$940$		0			0
$941$	−10.4077	+	18.0266i	−0.339280	+	0.587650i	−0.984297	−	0.176518i	$-0.943517\pi$
$941$	−10.4077	+	18.0266i	−0.339280	+	0.587650i	0.645018	+	0.764168i	$0.276850\pi$
$942$		0			0
$943$	−13.5467	−	23.4636i	−0.441142	−	0.764080i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.46207	−	4.26442i	−0.0800064	−	0.138575i	0.823246	−	0.567685i	$-0.192161\pi$
$947$	−2.46207	−	4.26442i	−0.0800064	−	0.138575i	−0.903252	+	0.429110i	$0.858827\pi$
$948$		0			0
$949$	20.1180	−	34.8455i	0.653059	−	1.13113i
$950$		0			0
$951$	−5.85369	+	13.4388i	−0.189819	+	0.435782i
$952$		0			0
$953$	6.23702			0.202037			0.101018	−	0.994885i	$-0.467790\pi$
$953$	6.23702			0.202037			0.101018	+	0.994885i	$0.467790\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	25.0045	−	2.83250i	0.808281	−	0.0915617i
$958$		0			0
$959$	2.34447	−	4.06074i	0.0757069	−	0.131128i
$960$		0			0
$961$	6.90938	+	11.9674i	0.222883	+	0.386045i
$962$		0			0
$963$	4.50589	−	14.6701i	0.145200	−	0.472738i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	8.88239	−	15.3848i	0.285639	−	0.494740i	−0.687125	−	0.726539i	$-0.741128\pi$
$967$	8.88239	−	15.3848i	0.285639	−	0.494740i	0.972764	+	0.231799i	$0.0744610\pi$
$968$		0			0
$969$	0.440967	+	0.596740i	0.0141659	+	0.0191701i
$970$		0			0
$971$	9.98061			0.320293			0.160147	−	0.987093i	$-0.448803\pi$
$971$	9.98061			0.320293			0.160147	+	0.987093i	$0.448803\pi$
$972$		0			0
$973$	13.7823			0.441842
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.26642	+	14.3179i	−0.264466	+	0.458069i	−0.967424	−	0.253163i	$-0.918529\pi$
$977$	−8.26642	+	14.3179i	−0.264466	+	0.458069i	0.702957	+	0.711232i	$0.251862\pi$
$978$		0			0
$979$	14.6839	+	25.4332i	0.469298	+	0.812848i
$980$		0			0
$981$	−6.31652	+	20.5651i	−0.201671	+	0.656593i
$982$		0			0
$983$	28.7209	+	49.7460i	0.916054	+	1.58665i	0.805351	+	0.592798i	$0.201977\pi$
$983$	28.7209	+	49.7460i	0.916054	+	1.58665i	0.110703	+	0.993854i	$0.464690\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−15.1831	+	1.71993i	−0.483282	+	0.0547460i
$988$		0			0
$989$	−27.6238			−0.878384
$990$		0			0
$991$	55.5294			1.76395			0.881975	−	0.471297i	$-0.156214\pi$
$991$	55.5294			1.76395			0.881975	+	0.471297i	$0.156214\pi$
$992$		0			0
$993$	4.86794	−	11.1757i	0.154479	−	0.354650i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.05984	−	7.03185i	−0.128577	−	0.222701i	0.794549	−	0.607200i	$-0.207707\pi$
$997$	−4.05984	−	7.03185i	−0.128577	−	0.222701i	−0.923125	+	0.384499i	$0.874374\pi$
$998$		0			0
$999$	−6.64534	+	2.33872i	−0.210249	+	0.0739937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.i.e.301.2	yes	8
3.2	odd	2		2700.2.i.d.901.3		8
5.2	odd	4		900.2.s.d.49.1		16
5.3	odd	4		900.2.s.d.49.8		16
5.4	even	2		900.2.i.d.301.3	✓	8
9.2	odd	6		2700.2.i.d.1801.3		8
9.4	even	3		8100.2.a.z.1.2		4
9.5	odd	6		8100.2.a.ba.1.2		4
9.7	even	3	inner	900.2.i.e.601.2	yes	8
15.2	even	4		2700.2.s.d.1549.3		16
15.8	even	4		2700.2.s.d.1549.6		16
15.14	odd	2		2700.2.i.e.901.2		8
45.2	even	12		2700.2.s.d.2449.6		16
45.4	even	6		8100.2.a.x.1.3		4
45.7	odd	12		900.2.s.d.349.8		16
45.13	odd	12		8100.2.d.q.649.6		8
45.14	odd	6		8100.2.a.y.1.3		4
45.22	odd	12		8100.2.d.q.649.3		8
45.23	even	12		8100.2.d.s.649.6		8
45.29	odd	6		2700.2.i.e.1801.2		8
45.32	even	12		8100.2.d.s.649.3		8
45.34	even	6		900.2.i.d.601.3	yes	8
45.38	even	12		2700.2.s.d.2449.3		16
45.43	odd	12		900.2.s.d.349.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.i.d.301.3	✓	8	5.4	even	2
900.2.i.d.601.3	yes	8	45.34	even	6
900.2.i.e.301.2	yes	8	1.1	even	1	trivial
900.2.i.e.601.2	yes	8	9.7	even	3	inner
900.2.s.d.49.1		16	5.2	odd	4
900.2.s.d.49.8		16	5.3	odd	4
900.2.s.d.349.1		16	45.43	odd	12
900.2.s.d.349.8		16	45.7	odd	12
2700.2.i.d.901.3		8	3.2	odd	2
2700.2.i.d.1801.3		8	9.2	odd	6
2700.2.i.e.901.2		8	15.14	odd	2
2700.2.i.e.1801.2		8	45.29	odd	6
2700.2.s.d.1549.3		16	15.2	even	4
2700.2.s.d.1549.6		16	15.8	even	4
2700.2.s.d.2449.3		16	45.38	even	12
2700.2.s.d.2449.6		16	45.2	even	12
8100.2.a.x.1.3		4	45.4	even	6
8100.2.a.y.1.3		4	45.14	odd	6
8100.2.a.z.1.2		4	9.4	even	3
8100.2.a.ba.1.2		4	9.5	odd	6
8100.2.d.q.649.3		8	45.22	odd	12
8100.2.d.q.649.6		8	45.13	odd	12
8100.2.d.s.649.3		8	45.32	even	12
8100.2.d.s.649.6		8	45.23	even	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02936 - 1.39299i) q^{3} +(0.340213 + 0.589266i) q^{7} +(-0.880830 + 2.86778i) q^{9} +(0.840213 + 1.45529i) q^{11} +(2.57251 - 4.45572i) q^{13} +1.31957 q^{17} -0.324642 q^{19} +(0.470639 - 1.08048i) q^{21} +(1.89462 - 3.28158i) q^{23} +(4.90147 - 1.72499i) q^{27} +(4.32292 + 7.48751i) q^{29} +(2.07251 - 3.58970i) q^{31} +(1.16232 - 2.66843i) q^{33} -1.35578 q^{37} +(-8.85481 + 1.00307i) q^{39} +(3.57505 - 6.19216i) q^{41} +(-3.64503 - 6.31337i) q^{43} +(-6.48270 - 11.2284i) q^{47} +(3.26851 - 5.66123i) q^{49} +(-1.35832 - 1.83815i) q^{51} +8.83052 q^{53} +(0.334174 + 0.452222i) q^{57} +(-4.40766 + 7.63429i) q^{59} +(-4.98524 - 8.63469i) q^{61} +(-1.98955 + 0.456611i) q^{63} +(-2.08808 + 3.61667i) q^{67} +(-6.52145 + 0.738747i) q^{69} -0.891185 q^{71} +7.82038 q^{73} +(-0.571703 + 0.990219i) q^{77} +(-4.82799 - 8.36232i) q^{79} +(-7.44828 - 5.05205i) q^{81} +(2.42830 + 4.20593i) q^{83} +(5.98017 - 13.7291i) q^{87} +17.4764 q^{89} +3.50081 q^{91} +(-7.13377 + 0.808111i) q^{93} +(4.46713 + 7.73730i) q^{97} +(-4.91354 + 1.12768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - q^{7} + 5 q^{9} + 3 q^{11} + 2 q^{13} + 18 q^{17} - 8 q^{19} + 13 q^{21} + 3 q^{23} + 16 q^{27} - 9 q^{29} - 2 q^{31} + 12 q^{33} + 2 q^{37} - 17 q^{39} + 9 q^{41} + 8 q^{43} - 12 q^{47}+ \cdots + 33 q^{99}+O(q^{100}) \) 8 * q + q^3 - q^7 + 5 * q^9 + 3 * q^11 + 2 * q^13 + 18 * q^17 - 8 * q^19 + 13 * q^21 + 3 * q^23 + 16 * q^27 - 9 * q^29 - 2 * q^31 + 12 * q^33 + 2 * q^37 - 17 * q^39 + 9 * q^41 + 8 * q^43 - 12 * q^47 - 9 * q^49 + 3 * q^51 + 24 * q^53 - 40 * q^57 - 15 * q^59 + q^61 + 35 * q^63 + 11 * q^67 + 9 * q^69 - 24 * q^71 + 20 * q^73 - 36 * q^77 + 7 * q^79 - 31 * q^81 - 12 * q^83 + 9 * q^87 + 6 * q^89 - 22 * q^91 - 19 * q^93 + 5 * q^97 + 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more