LMFDB - Embedded newform 864.2.y.d.97.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(97,864)] 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("864.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,0,0,0,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.6
Character	$\chi$	$=$	864.97
Dual form			864.2.y.d.481.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.523054 - 1.65119i) q^{3} +(-0.117882 - 0.0429055i) q^{5} +(-0.455772 + 2.58481i) q^{7} +(-2.45283 - 1.72732i) q^{9} +(-3.45559 + 1.25773i) q^{11} +(-3.57220 + 2.99743i) q^{13} +(-0.132504 + 0.172203i) q^{15} +(-2.83754 - 4.91477i) q^{17} +(-3.93671 + 6.81859i) q^{19} +(4.02961 + 2.10456i) q^{21} +(0.231664 + 1.31383i) q^{23} +(-3.81817 - 3.20382i) q^{25} +(-4.13509 + 3.14660i) q^{27} +(2.22400 + 1.86616i) q^{29} +(-1.05452 - 5.98046i) q^{31} +(0.269289 + 6.36368i) q^{33} +(0.164630 - 0.285147i) q^{35} +(-4.35763 - 7.54764i) q^{37} +(3.08087 + 7.46619i) q^{39} +(4.50075 - 3.77658i) q^{41} +(2.69227 - 0.979908i) q^{43} +(0.215033 + 0.308859i) q^{45} +(-0.997043 + 5.65451i) q^{47} +(0.104320 + 0.0379694i) q^{49} +(-9.59938 + 2.11462i) q^{51} +11.4363 q^{53} +0.461315 q^{55} +(9.19964 + 10.0667i) q^{57} +(-11.1792 - 4.06891i) q^{59} +(-1.96285 + 11.1319i) q^{61} +(5.58273 - 5.55284i) q^{63} +(0.549705 - 0.200076i) q^{65} +(-4.89304 + 4.10575i) q^{67} +(2.29055 + 0.304684i) q^{69} +(0.759192 + 1.31496i) q^{71} +(-1.02736 + 1.77944i) q^{73} +(-7.28721 + 4.62873i) q^{75} +(-1.67604 - 9.50529i) q^{77} +(4.69802 + 3.94211i) q^{79} +(3.03274 + 8.47363i) q^{81} +(5.85437 + 4.91240i) q^{83} +(0.123624 + 0.701108i) q^{85} +(4.24464 - 2.69613i) q^{87} +(4.62241 - 8.00624i) q^{89} +(-6.11970 - 10.5996i) q^{91} +(-10.4264 - 1.38690i) q^{93} +(0.756622 - 0.634881i) q^{95} +(-4.70296 + 1.71174i) q^{97} +(10.6485 + 2.88390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77}+ \cdots + 12 q^{97}+O(q^{100}) $ 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.523054	−	1.65119i	0.301985	−	0.953313i
$3$	0.523054	−	1.65119i	0.301985	−	0.953313i
$4$		0			0
$5$	−0.117882	−	0.0429055i	−0.0527184	−	0.0191879i	0.315526	−	0.948917i	$-0.397819\pi$
$5$	−0.117882	−	0.0429055i	−0.0527184	−	0.0191879i	−0.368245	+	0.929729i	$0.620041\pi$
$6$		0			0
$7$	−0.455772	+	2.58481i	−0.172266	+	0.976967i	0.768987	+	0.639264i	$0.220761\pi$
$7$	−0.455772	+	2.58481i	−0.172266	+	0.976967i	−0.941253	+	0.337703i	$0.890350\pi$
$8$		0			0
$9$	−2.45283	−	1.72732i	−0.817610	−	0.575773i
$10$		0			0
$11$	−3.45559	+	1.25773i	−1.04190	+	0.379220i	−0.805600	−	0.592460i	$-0.798157\pi$
$11$	−3.45559	+	1.25773i	−1.04190	+	0.379220i	−0.236299	+	0.971680i	$0.575935\pi$
$12$		0			0
$13$	−3.57220	+	2.99743i	−0.990751	+	0.831339i	−0.985676	−	0.168648i	$-0.946060\pi$
$13$	−3.57220	+	2.99743i	−0.990751	+	0.831339i	−0.00507477	+	0.999987i	$0.501615\pi$
$14$		0			0
$15$	−0.132504	+	0.172203i	−0.0342123	+	0.0444626i
$16$		0			0
$17$	−2.83754	−	4.91477i	−0.688205	−	1.19201i	−0.972418	−	0.233245i	$-0.925066\pi$
$17$	−2.83754	−	4.91477i	−0.688205	−	1.19201i	0.284213	−	0.958761i	$-0.408268\pi$
$18$		0			0
$19$	−3.93671	+	6.81859i	−0.903144	+	1.56429i	−0.0797544	+	0.996815i	$0.525414\pi$
$19$	−3.93671	+	6.81859i	−0.903144	+	1.56429i	−0.823390	+	0.567477i	$0.807920\pi$
$20$		0			0
$21$	4.02961	+	2.10456i	0.879334	+	0.459253i
$22$		0			0
$23$	0.231664	+	1.31383i	0.0483052	+	0.273952i	0.999388	−	0.0349841i	$-0.0111381\pi$
$23$	0.231664	+	1.31383i	0.0483052	+	0.273952i	−0.951083	+	0.308936i	$0.900027\pi$
$24$		0			0
$25$	−3.81817	−	3.20382i	−0.763633	−	0.640764i
$26$		0			0
$27$	−4.13509	+	3.14660i	−0.795798	+	0.605563i
$28$		0			0
$29$	2.22400	+	1.86616i	0.412986	+	0.346537i	0.825487	−	0.564420i	$-0.190900\pi$
$29$	2.22400	+	1.86616i	0.412986	+	0.346537i	−0.412501	+	0.910957i	$0.635345\pi$
$30$		0			0
$31$	−1.05452	−	5.98046i	−0.189397	−	1.07412i	−0.920175	−	0.391507i	$-0.871954\pi$
$31$	−1.05452	−	5.98046i	−0.189397	−	1.07412i	0.730778	−	0.682615i	$-0.239157\pi$
$32$		0			0
$33$	0.269289	+	6.36368i	0.0468772	+	1.10777i
$34$		0			0
$35$	0.164630	−	0.285147i	0.0278275	−	0.0481987i
$36$		0			0
$37$	−4.35763	−	7.54764i	−0.716390	−	1.24082i	−0.962421	−	0.271562i	$-0.912460\pi$
$37$	−4.35763	−	7.54764i	−0.716390	−	1.24082i	0.246031	−	0.969262i	$-0.420873\pi$
$38$		0			0
$39$	3.08087	+	7.46619i	0.493333	+	1.19555i
$40$		0			0
$41$	4.50075	−	3.77658i	0.702900	−	0.589803i	−0.219697	−	0.975568i	$-0.570507\pi$
$41$	4.50075	−	3.77658i	0.702900	−	0.589803i	0.922597	+	0.385765i	$0.126062\pi$
$42$		0			0
$43$	2.69227	−	0.979908i	0.410568	−	0.149434i	−0.128475	−	0.991713i	$-0.541008\pi$
$43$	2.69227	−	0.979908i	0.410568	−	0.149434i	0.539043	+	0.842278i	$0.318786\pi$
$44$		0			0
$45$	0.215033	+	0.308859i	0.0320552	+	0.0460420i
$46$		0			0
$47$	−0.997043	+	5.65451i	−0.145434	+	0.824795i	0.821584	+	0.570087i	$0.193091\pi$
$47$	−0.997043	+	5.65451i	−0.145434	+	0.824795i	−0.967018	+	0.254708i	$0.918021\pi$
$48$		0			0
$49$	0.104320	+	0.0379694i	0.0149029	+	0.00542420i
$50$		0			0
$51$	−9.59938	+	2.11462i	−1.34418	+	0.296106i
$52$		0			0
$53$	11.4363			1.57090			0.785449	−	0.618927i	$-0.212432\pi$
$53$	11.4363			1.57090			0.785449	+	0.618927i	$0.212432\pi$
$54$		0			0
$55$	0.461315			0.0622037
$56$		0			0
$57$	9.19964	+	10.0667i	1.21852	+	1.33337i
$58$		0			0
$59$	−11.1792	−	4.06891i	−1.45541	−	0.529727i	−0.511315	−	0.859393i	$-0.670841\pi$
$59$	−11.1792	−	4.06891i	−1.45541	−	0.529727i	−0.944097	+	0.329667i	$0.893064\pi$
$60$		0			0
$61$	−1.96285	+	11.1319i	−0.251318	+	1.42529i	0.554033	+	0.832495i	$0.313088\pi$
$61$	−1.96285	+	11.1319i	−0.251318	+	1.42529i	−0.805351	+	0.592799i	$0.798023\pi$
$62$		0			0
$63$	5.58273	−	5.55284i	0.703357	−	0.699592i
$64$		0			0
$65$	0.549705	−	0.200076i	0.0681825	−	0.0248164i
$66$		0			0
$67$	−4.89304	+	4.10575i	−0.597780	+	0.501597i	−0.890731	−	0.454531i	$-0.849807\pi$
$67$	−4.89304	+	4.10575i	−0.597780	+	0.501597i	0.292951	+	0.956127i	$0.405363\pi$
$68$		0			0
$69$	2.29055	+	0.304684i	0.275750	+	0.0366796i
$70$		0			0
$71$	0.759192	+	1.31496i	0.0900995	+	0.156057i	0.907553	−	0.419938i	$-0.137948\pi$
$71$	0.759192	+	1.31496i	0.0900995	+	0.156057i	−0.817453	+	0.575995i	$0.804615\pi$
$72$		0			0
$73$	−1.02736	+	1.77944i	−0.120243	+	0.208267i	−0.919863	−	0.392239i	$-0.871701\pi$
$73$	−1.02736	+	1.77944i	−0.120243	+	0.208267i	0.799620	+	0.600506i	$0.205034\pi$
$74$		0			0
$75$	−7.28721	+	4.62873i	−0.841455	+	0.534480i
$76$		0			0
$77$	−1.67604	−	9.50529i	−0.191002	−	1.08323i
$78$		0			0
$79$	4.69802	+	3.94211i	0.528568	+	0.443522i	0.867607	−	0.497251i	$-0.165657\pi$
$79$	4.69802	+	3.94211i	0.528568	+	0.443522i	−0.339038	+	0.940773i	$0.610102\pi$
$80$		0			0
$81$	3.03274	+	8.47363i	0.336971	+	0.941515i
$82$		0			0
$83$	5.85437	+	4.91240i	0.642600	+	0.539206i	0.904816	−	0.425804i	$-0.140009\pi$
$83$	5.85437	+	4.91240i	0.642600	+	0.539206i	−0.262215	+	0.965009i	$0.584453\pi$
$84$		0			0
$85$	0.123624	+	0.701108i	0.0134089	+	0.0760459i
$86$		0			0
$87$	4.24464	−	2.69613i	0.455073	−	0.289056i
$88$		0			0
$89$	4.62241	−	8.00624i	0.489974	−	0.848660i	−0.509959	−	0.860199i	$-0.670340\pi$
$89$	4.62241	−	8.00624i	0.489974	−	0.848660i	0.999933	+	0.0115384i	$0.00367286\pi$
$90$		0			0
$91$	−6.11970	−	10.5996i	−0.641519	−	1.11114i
$92$		0			0
$93$	−10.4264	−	1.38690i	−1.08117	−	0.143815i
$94$		0			0
$95$	0.756622	−	0.634881i	0.0776278	−	0.0651374i
$96$		0			0
$97$	−4.70296	+	1.71174i	−0.477514	+	0.173801i	−0.569553	−	0.821955i	$-0.692884\pi$
$97$	−4.70296	+	1.71174i	−0.477514	+	0.173801i	0.0920394	+	0.995755i	$0.470661\pi$
$98$		0			0
$99$	10.6485	+	2.88390i	1.07021	+	0.289843i
$100$		0			0
$101$	0.482279	−	2.73514i	0.0479885	−	0.272157i	−0.951367	−	0.308061i	$-0.900320\pi$
$101$	0.482279	−	2.73514i	0.0479885	−	0.272157i	0.999355	+	0.0359042i	$0.0114311\pi$
$102$		0			0
$103$	4.49064	+	1.63446i	0.442476	+	0.161048i	0.553644	−	0.832754i	$-0.313237\pi$
$103$	4.49064	+	1.63446i	0.442476	+	0.161048i	−0.111168	+	0.993802i	$0.535459\pi$
$104$		0			0
$105$	−0.384721	−	0.420982i	−0.0375449	−	0.0410837i
$106$		0			0
$107$	8.29504			0.801912			0.400956	−	0.916097i	$-0.368678\pi$
$107$	8.29504			0.801912			0.400956	+	0.916097i	$0.368678\pi$
$108$		0			0
$109$	−9.97414			−0.955350			−0.477675	−	0.878537i	$-0.658520\pi$
$109$	−9.97414			−0.955350			−0.477675	+	0.878537i	$0.658520\pi$
$110$		0			0
$111$	−14.7418	+	3.24744i	−1.39923	+	0.308233i
$112$		0			0
$113$	−5.92458	−	2.15637i	−0.557338	−	0.202854i	0.0479658	−	0.998849i	$-0.484726\pi$
$113$	−5.92458	−	2.15637i	−0.557338	−	0.202854i	−0.605304	+	0.795995i	$0.706948\pi$
$114$		0			0
$115$	0.0290616	−	0.164816i	0.00271000	−	0.0153692i
$116$		0			0
$117$	13.9395	−	1.18186i	1.28871	−	0.109263i
$118$		0			0
$119$	13.9970	−	5.09450i	1.28311	−	0.467012i
$120$		0			0
$121$	1.93272	−	1.62174i	0.175702	−	0.147431i
$122$		0			0
$123$	−3.88170	−	9.40694i	−0.350001	−	0.848195i
$124$		0			0
$125$	0.626249	+	1.08470i	0.0560134	+	0.0970181i
$126$		0			0
$127$	−1.28090	+	2.21858i	−0.113661	+	0.196867i	−0.917244	−	0.398326i	$-0.869591\pi$
$127$	−1.28090	+	2.21858i	−0.113661	+	0.196867i	0.803583	+	0.595193i	$0.202925\pi$
$128$		0			0
$129$	−0.209805	−	4.95799i	−0.0184723	−	0.436527i
$130$		0			0
$131$	1.82308	+	10.3392i	0.159284	+	0.903342i	0.954764	+	0.297364i	$0.0961073\pi$
$131$	1.82308	+	10.3392i	0.159284	+	0.903342i	−0.795481	+	0.605979i	$0.792782\pi$
$132$		0			0
$133$	−15.8305	−	13.2834i	−1.37268	−	1.15182i
$134$		0			0
$135$	0.622458	−	0.193509i	0.0535727	−	0.0166546i
$136$		0			0
$137$	−6.76805	−	5.67906i	−0.578233	−	0.485195i	0.306133	−	0.951989i	$-0.400965\pi$
$137$	−6.76805	−	5.67906i	−0.578233	−	0.485195i	−0.884366	+	0.466793i	$0.845409\pi$
$138$		0			0
$139$	−2.60077	−	14.7497i	−0.220594	−	1.25105i	−0.870931	−	0.491406i	$-0.836483\pi$
$139$	−2.60077	−	14.7497i	−0.220594	−	1.25105i	0.650337	−	0.759646i	$-0.274628\pi$
$140$		0			0
$141$	8.81514	+	4.60392i	0.742369	+	0.387720i
$142$		0			0
$143$	8.57410	−	14.8508i	0.717002	−	1.24188i
$144$		0			0
$145$	−0.182101	−	0.315408i	−0.0151226	−	0.0261932i
$146$		0			0
$147$	0.117260	−	0.152392i	0.00967140	−	0.0125691i
$148$		0			0
$149$	−0.793694	+	0.665988i	−0.0650220	+	0.0545599i	−0.674719	−	0.738074i	$-0.735735\pi$
$149$	−0.793694	+	0.665988i	−0.0650220	+	0.0545599i	0.609697	+	0.792634i	$0.291291\pi$
$150$		0			0
$151$	2.53909	−	0.924153i	0.206628	−	0.0752065i	−0.236633	−	0.971599i	$-0.576044\pi$
$151$	2.53909	−	0.924153i	0.206628	−	0.0752065i	0.443261	+	0.896393i	$0.353822\pi$
$152$		0			0
$153$	−1.52936	+	16.9564i	−0.123642	+	1.37085i
$154$		0			0
$155$	−0.132286	+	0.750232i	−0.0106255	+	0.0602601i
$156$		0			0
$157$	−14.8884	−	5.41894i	−1.18822	−	0.432478i	−0.329125	−	0.944286i	$-0.606754\pi$
$157$	−14.8884	−	5.41894i	−1.18822	−	0.432478i	−0.859100	+	0.511808i	$0.828976\pi$
$158$		0			0
$159$	5.98180	−	18.8835i	0.474388	−	1.49756i
$160$		0			0
$161$	−3.50159			−0.275964
$162$		0			0
$163$	−9.96542			−0.780552			−0.390276	−	0.920698i	$-0.627620\pi$
$163$	−9.96542			−0.780552			−0.390276	+	0.920698i	$0.627620\pi$
$164$		0			0
$165$	0.241293	−	0.761717i	0.0187846	−	0.0592996i
$166$		0			0
$167$	−19.7675	−	7.19478i	−1.52966	−	0.556749i	−0.566118	−	0.824324i	$-0.691555\pi$
$167$	−19.7675	−	7.19478i	−1.52966	−	0.556749i	−0.963537	+	0.267575i	$0.913778\pi$
$168$		0			0
$169$	1.51860	−	8.61240i	0.116815	−	0.662492i
$170$		0			0
$171$	21.4340	−	9.92487i	1.63910	−	0.758974i
$172$		0			0
$173$	21.2829	−	7.74634i	1.61811	−	0.588943i	0.635088	−	0.772440i	$-0.280964\pi$
$173$	21.2829	−	7.74634i	1.61811	−	0.588943i	0.983020	+	0.183496i	$0.0587416\pi$
$174$		0			0
$175$	10.0215	−	8.40903i	0.757554	−	0.635663i
$176$		0			0
$177$	−12.5659	+	16.3307i	−0.944508	+	1.22749i
$178$		0			0
$179$	−10.8603	−	18.8105i	−0.811734	−	1.40597i	−0.911649	−	0.410969i	$-0.865190\pi$
$179$	−10.8603	−	18.8105i	−0.811734	−	1.40597i	0.0999149	−	0.994996i	$-0.468143\pi$
$180$		0			0
$181$	−12.0198	+	20.8189i	−0.893427	+	1.54746i	−0.0576866	+	0.998335i	$0.518372\pi$
$181$	−12.0198	+	20.8189i	−0.893427	+	1.54746i	−0.835740	+	0.549125i	$0.814961\pi$
$182$		0			0
$183$	17.3542	+	9.06362i	1.28286	+	0.670002i
$184$		0			0
$185$	0.189851	+	1.07670i	0.0139581	+	0.0791603i
$186$		0			0
$187$	15.9868	+	13.4146i	1.16907	+	0.980969i
$188$		0			0
$189$	−6.24870	−	12.1226i	−0.454526	−	0.881786i
$190$		0			0
$191$	12.5068	+	10.4945i	0.904962	+	0.759353i	0.971154	−	0.238454i	$-0.0766405\pi$
$191$	12.5068	+	10.4945i	0.904962	+	0.759353i	−0.0661920	+	0.997807i	$0.521085\pi$
$192$		0			0
$193$	−1.38739	−	7.86827i	−0.0998664	−	0.566370i	−0.993147	−	0.116871i	$-0.962714\pi$
$193$	−1.38739	−	7.86827i	−0.0998664	−	0.566370i	0.893281	−	0.449499i	$-0.148398\pi$
$194$		0			0
$195$	−0.0428377	−	1.01231i	−0.00306767	−	0.0724934i
$196$		0			0
$197$	−2.90861	+	5.03786i	−0.207230	+	0.358933i	−0.950841	−	0.309680i	$-0.899778\pi$
$197$	−2.90861	+	5.03786i	−0.207230	+	0.358933i	0.743611	+	0.668613i	$0.233111\pi$
$198$		0			0
$199$	13.0439	+	22.5927i	0.924659	+	1.60156i	0.792109	+	0.610380i	$0.208983\pi$
$199$	13.0439	+	22.5927i	0.924659	+	1.60156i	0.132550	+	0.991176i	$0.457684\pi$
$200$		0			0
$201$	4.22003	+	10.2268i	0.297658	+	0.721346i
$202$		0			0
$203$	−5.83730	+	4.89808i	−0.409698	+	0.343778i
$204$		0			0
$205$	−0.692594	+	0.252083i	−0.0483728	+	0.0176063i
$206$		0			0
$207$	1.70117	−	3.62275i	0.118240	−	0.251799i
$208$		0			0
$209$	5.02771	−	28.5136i	0.347774	−	1.97232i
$210$		0			0
$211$	7.63350	+	2.77837i	0.525512	+	0.191271i	0.591133	−	0.806574i	$-0.298681\pi$
$211$	7.63350	+	2.77837i	0.525512	+	0.191271i	−0.0656213	+	0.997845i	$0.520903\pi$
$212$		0			0
$213$	2.56834	−	0.565772i	0.175980	−	0.0387661i
$214$		0			0
$215$	−0.359414			−0.0245118
$216$		0			0
$217$	15.9390			1.08201
$218$		0			0
$219$	2.40082	+	2.62710i	0.162232	+	0.177523i
$220$		0			0
$221$	24.8680	+	9.05120i	1.67280	+	0.608850i
$222$		0			0
$223$	0.277312	−	1.57271i	0.0185702	−	0.105317i	−0.974114	−	0.226058i	$-0.927416\pi$
$223$	0.277312	−	1.57271i	0.0185702	−	0.105317i	0.992684	+	0.120741i	$0.0385272\pi$
$224$		0			0
$225$	3.83129	+	14.4536i	0.255419	+	0.963575i
$226$		0			0
$227$	−15.8536	+	5.77025i	−1.05224	+	0.382985i	−0.809508	−	0.587108i	$-0.800266\pi$
$227$	−15.8536	+	5.77025i	−1.05224	+	0.382985i	−0.242734	+	0.970093i	$0.578044\pi$
$228$		0			0
$229$	−6.62459	+	5.55869i	−0.437765	+	0.367329i	−0.834872	−	0.550444i	$-0.814459\pi$
$229$	−6.62459	+	5.55869i	−0.437765	+	0.367329i	0.397107	+	0.917772i	$0.370014\pi$
$230$		0			0
$231$	−16.5717	−	2.20433i	−1.09034	−	0.145034i
$232$		0			0
$233$	−1.48885	−	2.57876i	−0.0975375	−	0.168940i	0.813127	−	0.582086i	$-0.197763\pi$
$233$	−1.48885	−	2.57876i	−0.0975375	−	0.168940i	−0.910665	+	0.413146i	$0.864430\pi$
$234$		0			0
$235$	0.360143	−	0.623786i	0.0234931	−	0.0406913i
$236$		0			0
$237$	8.96647	−	5.69537i	0.582435	−	0.369954i
$238$		0			0
$239$	−4.73071	−	26.8292i	−0.306004	−	1.73543i	−0.618741	−	0.785595i	$-0.712357\pi$
$239$	−4.73071	−	26.8292i	−0.306004	−	1.73543i	0.312737	−	0.949840i	$-0.398754\pi$
$240$		0			0
$241$	14.9225	+	12.5215i	0.961245	+	0.806580i	0.981155	−	0.193222i	$-0.0618937\pi$
$241$	14.9225	+	12.5215i	0.961245	+	0.806580i	−0.0199104	+	0.999802i	$0.506338\pi$
$242$		0			0
$243$	15.5778	−	0.575450i	0.999318	−	0.0369152i
$244$		0			0
$245$	−0.0106683	−	0.00895180i	−0.000681576	−	0.000571910i
$246$		0			0
$247$	−6.37553	−	36.1574i	−0.405665	−	2.30064i
$248$		0			0
$249$	11.1734	−	7.09720i	0.708087	−	0.449767i
$250$		0			0
$251$	12.9577	−	22.4434i	0.817882	−	1.41661i	−0.0893580	−	0.996000i	$-0.528482\pi$
$251$	12.9577	−	22.4434i	0.817882	−	1.41661i	0.907240	−	0.420614i	$-0.138185\pi$
$252$		0			0
$253$	−2.45298	−	4.24868i	−0.154217	−	0.267112i
$254$		0			0
$255$	1.22232	+	0.162591i	0.0765448	+	0.0101818i
$256$		0			0
$257$	5.14225	−	4.31486i	0.320765	−	0.269153i	−0.468160	−	0.883644i	$-0.655083\pi$
$257$	5.14225	−	4.31486i	0.320765	−	0.269153i	0.788924	+	0.614490i	$0.210638\pi$
$258$		0			0
$259$	21.4953	−	7.82365i	1.33565	−	0.486138i
$260$		0			0
$261$	−2.23164	−	8.41892i	−0.138135	−	0.521118i
$262$		0			0
$263$	−3.68337	+	20.8894i	−0.227126	+	1.28810i	0.631453	+	0.775414i	$0.282459\pi$
$263$	−3.68337	+	20.8894i	−0.227126	+	1.28810i	−0.858579	+	0.512682i	$0.828652\pi$
$264$		0			0
$265$	−1.34813	−	0.490680i	−0.0828152	−	0.0301423i
$266$		0			0
$267$	−10.8020	−	11.8202i	−0.661073	−	0.723381i
$268$		0			0
$269$	−16.8927			−1.02997			−0.514985	−	0.857199i	$-0.672202\pi$
$269$	−16.8927			−1.02997			−0.514985	+	0.857199i	$0.672202\pi$
$270$		0			0
$271$	−32.3213			−1.96338			−0.981690	−	0.190484i	$-0.938994\pi$
$271$	−32.3213			−1.96338			−0.981690	+	0.190484i	$0.938994\pi$
$272$		0			0
$273$	−20.7029	+	4.56058i	−1.25300	+	0.276019i
$274$		0			0
$275$	17.2236	+	6.26887i	1.03862	+	0.378027i
$276$		0			0
$277$	1.54560	−	8.76555i	0.0928662	−	0.526671i	−0.902514	−	0.430660i	$-0.858281\pi$
$277$	1.54560	−	8.76555i	0.0928662	−	0.526671i	0.995380	−	0.0960103i	$-0.0306082\pi$
$278$		0			0
$279$	−7.74361	+	16.4905i	−0.463598	+	0.987262i
$280$		0			0
$281$	−23.0981	+	8.40702i	−1.37792	+	0.501521i	−0.921546	−	0.388268i	$-0.873073\pi$
$281$	−23.0981	+	8.40702i	−1.37792	+	0.501521i	−0.456371	+	0.889789i	$0.650851\pi$
$282$		0			0
$283$	2.17943	−	1.82876i	0.129554	−	0.108709i	−0.575708	−	0.817655i	$-0.695274\pi$
$283$	2.17943	−	1.82876i	0.129554	−	0.108709i	0.705262	+	0.708946i	$0.250829\pi$
$284$		0			0
$285$	−0.652553	−	1.58140i	−0.0386539	−	0.0936741i
$286$		0			0
$287$	7.71044	+	13.3549i	0.455133	+	0.788313i
$288$		0			0
$289$	−7.60329	+	13.1693i	−0.447252	+	0.774664i
$290$		0			0
$291$	0.366495	+	8.66080i	0.0214843	+	0.507705i
$292$		0			0
$293$	2.77310	+	15.7270i	0.162006	+	0.918783i	0.952098	+	0.305794i	$0.0989219\pi$
$293$	2.77310	+	15.7270i	0.162006	+	0.918783i	−0.790091	+	0.612989i	$0.789967\pi$
$294$		0			0
$295$	1.14325	+	0.959301i	0.0665626	+	0.0558527i
$296$		0			0
$297$	10.3316	−	16.0742i	0.599499	−	0.932718i
$298$		0			0
$299$	−4.76567	−	3.99887i	−0.275606	−	0.231261i
$300$		0			0
$301$	1.30581	+	7.40564i	0.0752659	+	0.426854i
$302$		0			0
$303$	−4.26397	−	2.22696i	−0.244958	−	0.127935i
$304$		0			0
$305$	0.709005	−	1.22803i	0.0405975	−	0.0703169i
$306$		0			0
$307$	0.0866822	+	0.150138i	0.00494721	+	0.00856882i	0.868488	−	0.495709i	$-0.165092\pi$
$307$	0.0866822	+	0.150138i	0.00494721	+	0.00856882i	−0.863541	+	0.504278i	$0.831759\pi$
$308$		0			0
$309$	5.04764	−	6.55997i	0.287150	−	0.373184i
$310$		0			0
$311$	−5.47840	+	4.59693i	−0.310652	+	0.260668i	−0.784761	−	0.619798i	$-0.787215\pi$
$311$	−5.47840	+	4.59693i	−0.310652	+	0.260668i	0.474110	+	0.880466i	$0.342770\pi$
$312$		0			0
$313$	10.8880	−	3.96291i	0.615427	−	0.223997i	−0.0154491	−	0.999881i	$-0.504918\pi$
$313$	10.8880	−	3.96291i	0.615427	−	0.223997i	0.630876	+	0.775883i	$0.282696\pi$
$314$		0			0
$315$	−0.896350	+	0.415050i	−0.0505036	+	0.0233854i
$316$		0			0
$317$	−3.23751	+	18.3609i	−0.181837	+	1.03125i	0.748115	+	0.663569i	$0.230959\pi$
$317$	−3.23751	+	18.3609i	−0.181837	+	1.03125i	−0.929952	+	0.367680i	$0.880152\pi$
$318$		0			0
$319$	−10.0324	−	3.65148i	−0.561704	−	0.204443i
$320$		0			0
$321$	4.33875	−	13.6967i	0.242166	−	0.764473i
$322$		0			0
$323$	44.6824			2.48619
$324$		0			0
$325$	23.2425			1.28926
$326$		0			0
$327$	−5.21702	+	16.4692i	−0.288502	+	0.910747i
$328$		0			0
$329$	−14.1614	−	5.15434i	−0.780745	−	0.284168i
$330$		0			0
$331$	−1.18216	+	6.70438i	−0.0649776	+	0.368506i	0.934929	+	0.354835i	$0.115463\pi$
$331$	−1.18216	+	6.70438i	−0.0649776	+	0.368506i	−0.999907	+	0.0136713i	$0.995648\pi$
$332$		0			0
$333$	−2.34865	+	26.0401i	−0.128705	+	1.42699i
$334$		0			0
$335$	0.752960	−	0.274055i	0.0411386	−	0.0149732i
$336$		0			0
$337$	10.9514	−	9.18930i	0.596559	−	0.500573i	−0.293778	−	0.955874i	$-0.594913\pi$
$337$	10.9514	−	9.18930i	0.596559	−	0.500573i	0.890338	+	0.455301i	$0.150468\pi$
$338$		0			0
$339$	−6.65945	+	8.65469i	−0.361692	+	0.470058i
$340$		0			0
$341$	11.1658	+	19.3397i	0.604661	+	1.04730i
$342$		0			0
$343$	−9.33210	+	16.1637i	−0.503886	+	0.872756i
$344$		0			0
$345$	−0.256942	−	0.134194i	−0.0138333	−	0.00722475i
$346$		0			0
$347$	−1.57751	−	8.94648i	−0.0846850	−	0.480272i	−0.997424	−	0.0717295i	$-0.977148\pi$
$347$	−1.57751	−	8.94648i	−0.0846850	−	0.480272i	0.912739	−	0.408543i	$-0.133963\pi$
$348$		0			0
$349$	23.3195	+	19.5674i	1.24826	+	1.04742i	0.996832	+	0.0795420i	$0.0253458\pi$
$349$	23.3195	+	19.5674i	1.24826	+	1.04742i	0.251432	+	0.967875i	$0.419099\pi$
$350$		0			0
$351$	5.33965	−	23.6349i	0.285010	−	1.26154i
$352$		0			0
$353$	14.5816	+	12.2355i	0.776103	+	0.651227i	0.942264	−	0.334871i	$-0.108693\pi$
$353$	14.5816	+	12.2355i	0.776103	+	0.651227i	−0.166161	+	0.986099i	$0.553137\pi$
$354$		0			0
$355$	−0.0330760	−	0.187583i	−0.00175549	−	0.00995589i
$356$		0			0
$357$	−1.09077	−	25.7764i	−0.0577295	−	1.36423i
$358$		0			0
$359$	−6.58484	+	11.4053i	−0.347534	+	0.601947i	−0.985811	−	0.167860i	$-0.946314\pi$
$359$	−6.58484	+	11.4053i	−0.347534	+	0.601947i	0.638276	+	0.769807i	$0.279648\pi$
$360$		0			0
$361$	−21.4954	−	37.2312i	−1.13134	−	1.95953i
$362$		0			0
$363$	−1.66689	−	4.03954i	−0.0874888	−	0.212021i
$364$		0			0
$365$	0.197454	−	0.165684i	0.0103352	−	0.00867229i
$366$		0			0
$367$	−3.36806	+	1.22587i	−0.175811	+	0.0639900i	−0.428426	−	0.903577i	$-0.640932\pi$
$367$	−3.36806	+	1.22587i	−0.175811	+	0.0639900i	0.252615	+	0.967567i	$0.418709\pi$
$368$		0			0
$369$	−17.5629	+	1.48907i	−0.914290	+	0.0775180i
$370$		0			0
$371$	−5.21235	+	29.5607i	−0.270612	+	1.53472i
$372$		0			0
$373$	−3.51431	−	1.27911i	−0.181964	−	0.0662296i	0.249431	−	0.968393i	$-0.419756\pi$
$373$	−3.51431	−	1.27911i	−0.181964	−	0.0662296i	−0.431395	+	0.902163i	$0.641979\pi$
$374$		0			0
$375$	2.11860	−	0.466700i	0.109404	−	0.0241003i
$376$		0			0
$377$	−13.5383			−0.697256
$378$		0			0
$379$	−21.1965			−1.08879			−0.544396	−	0.838829i	$-0.683241\pi$
$379$	−21.1965			−1.08879			−0.544396	+	0.838829i	$0.683241\pi$
$380$		0			0
$381$	2.99331	+	3.27544i	0.153352	+	0.167806i
$382$		0			0
$383$	−30.2931	−	11.0258i	−1.54791	−	0.563392i	−0.579981	−	0.814630i	$-0.696940\pi$
$383$	−30.2931	−	11.0258i	−1.54791	−	0.563392i	−0.967925	+	0.251238i	$0.919162\pi$
$384$		0			0
$385$	−0.210255	+	1.19241i	−0.0107156	+	0.0607710i
$386$		0			0
$387$	−8.29630	−	2.24687i	−0.421725	−	0.114215i
$388$		0			0
$389$	−8.45310	+	3.07668i	−0.428589	+	0.155994i	−0.547302	−	0.836935i	$-0.684345\pi$
$389$	−8.45310	+	3.07668i	−0.428589	+	0.155994i	0.118713	+	0.992929i	$0.462123\pi$
$390$		0			0
$391$	5.79981	−	4.86662i	0.293309	−	0.246115i
$392$		0			0
$393$	18.0256	+	2.39772i	0.909269	+	0.120949i
$394$		0			0
$395$	−0.384673	−	0.666274i	−0.0193550	−	0.0335239i
$396$		0			0
$397$	−2.88536	+	4.99759i	−0.144812	+	0.250822i	−0.929303	−	0.369319i	$-0.879591\pi$
$397$	−2.88536	+	4.99759i	−0.144812	+	0.250822i	0.784491	+	0.620140i	$0.212924\pi$
$398$		0			0
$399$	−30.2136	+	19.1912i	−1.51257	+	0.960762i
$400$		0			0
$401$	−3.00980	−	17.0694i	−0.150302	−	0.852405i	−0.962956	−	0.269659i	$-0.913089\pi$
$401$	−3.00980	−	17.0694i	−0.150302	−	0.852405i	0.812654	−	0.582747i	$-0.198022\pi$
$402$		0			0
$403$	21.6930	+	18.2026i	1.08060	+	0.906734i
$404$		0			0
$405$	0.00606030	−	1.12901i	0.000301138	−	0.0561009i
$406$		0			0
$407$	24.5511	+	20.6008i	1.21695	+	1.02114i
$408$		0			0
$409$	0.738521	+	4.18836i	0.0365175	+	0.207101i	0.997607	−	0.0691351i	$-0.0220239\pi$
$409$	0.738521	+	4.18836i	0.0365175	+	0.207101i	−0.961090	+	0.276236i	$0.910913\pi$
$410$		0			0
$411$	−12.9172	+	8.20484i	−0.637161	+	0.404715i
$412$		0			0
$413$	15.6126	−	27.0417i	0.768243	−	1.33064i
$414$		0			0
$415$	−0.479355	−	0.830267i	−0.0235306	−	0.0407562i
$416$		0			0
$417$	−25.7148	−	3.42053i	−1.25926	−	0.167504i
$418$		0			0
$419$	−25.5356	+	21.4269i	−1.24749	+	1.04677i	−0.250595	+	0.968092i	$0.580626\pi$
$419$	−25.5356	+	21.4269i	−1.24749	+	1.04677i	−0.996900	+	0.0786806i	$0.974929\pi$
$420$		0			0
$421$	−26.0334	+	9.47538i	−1.26879	+	0.461802i	−0.886709	−	0.462327i	$-0.847014\pi$
$421$	−26.0334	+	9.47538i	−1.26879	+	0.461802i	−0.382080	+	0.924129i	$0.624792\pi$
$422$		0			0
$423$	12.2127	−	12.1473i	0.593803	−	0.590624i
$424$		0			0
$425$	−4.91183	+	27.8564i	−0.238259	+	1.35123i
$426$		0			0
$427$	−27.8793	−	10.1472i	−1.34917	−	0.491058i
$428$		0			0
$429$	−20.0367	−	21.9252i	−0.967380	−	1.05856i
$430$		0			0
$431$	−36.9630			−1.78045			−0.890223	−	0.455525i	$-0.849452\pi$
$431$	−36.9630			−1.78045			−0.890223	+	0.455525i	$0.849452\pi$
$432$		0			0
$433$	22.1282			1.06341			0.531706	−	0.846929i	$-0.321551\pi$
$433$	22.1282			1.06341			0.531706	+	0.846929i	$0.321551\pi$
$434$		0			0
$435$	−0.616046	+	0.135707i	−0.0295371	+	0.00650665i
$436$		0			0
$437$	−9.87045	−	3.59255i	−0.472168	−	0.171855i
$438$		0			0
$439$	−5.49575	+	31.1679i	−0.262298	+	1.48756i	0.514323	+	0.857597i	$0.328043\pi$
$439$	−5.49575	+	31.1679i	−0.262298	+	1.48756i	−0.776621	+	0.629968i	$0.783068\pi$
$440$		0			0
$441$	−0.190294	−	0.273326i	−0.00906162	−	0.0130155i
$442$		0			0
$443$	17.9064	−	6.51739i	0.850757	−	0.309650i	0.120408	−	0.992724i	$-0.461580\pi$
$443$	17.9064	−	6.51739i	0.850757	−	0.309650i	0.730349	+	0.683074i	$0.239357\pi$
$444$		0			0
$445$	−0.888410	+	0.745465i	−0.0421147	+	0.0353384i
$446$		0			0
$447$	0.684526	+	1.65888i	0.0323770	+	0.0784625i
$448$		0			0
$449$	0.914818	+	1.58451i	0.0431729	+	0.0747777i	0.886804	−	0.462145i	$-0.152920\pi$
$449$	0.914818	+	1.58451i	0.0431729	+	0.0747777i	−0.843631	+	0.536923i	$0.819587\pi$
$450$		0			0
$451$	−10.8028	+	18.7111i	−0.508686	+	0.881069i
$452$		0			0
$453$	−0.197867	−	4.67589i	−0.00929662	−	0.219692i
$454$		0			0
$455$	0.266619	+	1.51207i	0.0124993	+	0.0708871i
$456$		0			0
$457$	4.83748	+	4.05913i	0.226288	+	0.189878i	0.748882	−	0.662704i	$-0.230591\pi$
$457$	4.83748	+	4.05913i	0.226288	+	0.189878i	−0.522594	+	0.852582i	$0.675036\pi$
$458$		0			0
$459$	27.1983	+	11.3944i	1.26951	+	0.531844i
$460$		0			0
$461$	−17.6337	−	14.7965i	−0.821284	−	0.689139i	0.131988	−	0.991251i	$-0.457864\pi$
$461$	−17.6337	−	14.7965i	−0.821284	−	0.689139i	−0.953272	+	0.302112i	$0.902308\pi$
$462$		0			0
$463$	−0.792160	−	4.49256i	−0.0368148	−	0.208787i	0.960852	−	0.277063i	$-0.0893612\pi$
$463$	−0.792160	−	4.49256i	−0.0368148	−	0.208787i	−0.997666	+	0.0682762i	$0.978250\pi$
$464$		0			0
$465$	1.16958	+	0.610841i	0.0542380	+	0.0283271i
$466$		0			0
$467$	9.33506	−	16.1688i	0.431975	−	0.748203i	−0.565068	−	0.825044i	$-0.691150\pi$
$467$	9.33506	−	16.1688i	0.431975	−	0.748203i	0.997043	+	0.0768415i	$0.0244836\pi$
$468$		0			0
$469$	−8.38247	−	14.5189i	−0.387067	−	0.670419i
$470$		0			0
$471$	−16.7351	+	21.7491i	−0.771114	+	1.00215i
$472$		0			0
$473$	−8.07093	+	6.77232i	−0.371102	+	0.311391i
$474$		0			0
$475$	36.8766	−	13.4220i	1.69201	−	0.615842i
$476$		0			0
$477$	−28.0513	−	19.7541i	−1.28438	−	0.904480i
$478$		0			0
$479$	3.27407	−	18.5682i	0.149596	−	0.848402i	−0.813965	−	0.580914i	$-0.802695\pi$
$479$	3.27407	−	18.5682i	0.149596	−	0.848402i	0.963561	−	0.267488i	$-0.0861935\pi$
$480$		0			0
$481$	38.1899	+	13.9000i	1.74131	+	0.633785i
$482$		0			0
$483$	−1.83152	+	5.78177i	−0.0833370	+	0.263080i
$484$		0			0
$485$	0.627837			0.0285086
$486$		0			0
$487$	7.06379			0.320091			0.160046	−	0.987110i	$-0.448836\pi$
$487$	7.06379			0.320091			0.160046	+	0.987110i	$0.448836\pi$
$488$		0			0
$489$	−5.21245	+	16.4548i	−0.235715	+	0.744110i
$490$		0			0
$491$	−12.8004	−	4.65896i	−0.577673	−	0.210256i	0.0366260	−	0.999329i	$-0.488339\pi$
$491$	−12.8004	−	4.65896i	−0.577673	−	0.210256i	−0.614299	+	0.789073i	$0.710561\pi$
$492$		0			0
$493$	2.86103	−	16.2257i	0.128855	−	0.730770i
$494$		0			0
$495$	−1.13153	−	0.796838i	−0.0508584	−	0.0358152i
$496$		0			0
$497$	−3.74494	+	1.36305i	−0.167984	+	0.0611410i
$498$		0			0
$499$	1.61381	−	1.35415i	0.0722441	−	0.0606200i	−0.605951	−	0.795502i	$-0.707207\pi$
$499$	1.61381	−	1.35415i	0.0722441	−	0.0606200i	0.678195	+	0.734882i	$0.262763\pi$
$500$		0			0
$501$	−22.2194	+	28.8766i	−0.992689	+	1.29011i
$502$		0			0
$503$	−6.75516	−	11.7003i	−0.301198	−	0.521689i	0.675210	−	0.737626i	$-0.264053\pi$
$503$	−6.75516	−	11.7003i	−0.301198	−	0.521689i	−0.976407	+	0.215936i	$0.930720\pi$
$504$		0			0
$505$	−0.174204	+	0.301731i	−0.00775200	+	0.0134269i
$506$		0			0
$507$	−13.4264	−	7.01223i	−0.596285	−	0.311424i
$508$		0			0
$509$	3.85780	+	21.8787i	0.170994	+	0.969756i	0.942667	+	0.333736i	$0.108309\pi$
$509$	3.85780	+	21.8787i	0.170994	+	0.969756i	−0.771672	+	0.636020i	$0.780580\pi$
$510$		0			0
$511$	−4.13127	−	3.46654i	−0.182756	−	0.153351i
$512$		0			0
$513$	−5.17669	−	40.5827i	−0.228556	−	1.79177i
$514$		0			0
$515$	−0.459238	−	0.385346i	−0.0202364	−	0.0169804i
$516$		0			0
$517$	−3.66649	−	20.7937i	−0.161252	−	0.914505i
$518$		0			0
$519$	−1.65854	−	39.1938i	−0.0728020	−	1.72042i
$520$		0			0
$521$	−21.8341	+	37.8178i	−0.956570	+	1.65683i	−0.225836	+	0.974165i	$0.572511\pi$
$521$	−21.8341	+	37.8178i	−0.956570	+	1.65683i	−0.730734	+	0.682663i	$0.760822\pi$
$522$		0			0
$523$	−12.7312	−	22.0511i	−0.556698	−	0.964229i	−0.997769	−	0.0667568i	$-0.978735\pi$
$523$	−12.7312	−	22.0511i	−0.556698	−	0.964229i	0.441072	−	0.897472i	$-0.354598\pi$
$524$		0			0
$525$	−8.64309	−	20.9457i	−0.377216	−	0.914147i
$526$		0			0
$527$	−26.4003	+	22.1525i	−1.15002	+	0.964978i
$528$		0			0
$529$	19.9405	−	7.25773i	0.866976	−	0.315554i
$530$		0			0
$531$	20.3924	+	29.2904i	0.884957	+	1.27110i
$532$		0			0
$533$	−4.75756	+	26.9814i	−0.206073	+	1.16870i
$534$		0			0
$535$	−0.977835	−	0.355903i	−0.0422755	−	0.0153870i
$536$		0			0
$537$	−36.7402	+	8.09339i	−1.58546	+	0.349256i
$538$		0			0
$539$	−0.408242			−0.0175842
$540$		0			0
$541$	33.2229			1.42836			0.714182	−	0.699960i	$-0.246799\pi$
$541$	33.2229			1.42836			0.714182	+	0.699960i	$0.246799\pi$
$542$		0			0
$543$	28.0889	+	30.7364i	1.20541	+	1.31903i
$544$		0			0
$545$	1.17577	+	0.427946i	0.0503645	+	0.0183312i
$546$		0			0
$547$	1.77507	−	10.0669i	0.0758963	−	0.430429i	−0.923056	−	0.384666i	$-0.874317\pi$
$547$	1.77507	−	10.0669i	0.0758963	−	0.430429i	0.998952	−	0.0457638i	$-0.0145722\pi$
$548$		0			0
$549$	24.0429	−	23.9142i	1.02613	−	1.02063i
$550$		0			0
$551$	−21.4798	+	7.81801i	−0.915070	+	0.333058i
$552$		0			0
$553$	−12.3308	+	10.3468i	−0.524360	+	0.439991i
$554$		0			0
$555$	1.87713	+	0.249692i	0.0796796	+	0.0105988i
$556$		0			0
$557$	−6.32377	−	10.9531i	−0.267947	−	0.464097i	0.700385	−	0.713766i	$-0.253012\pi$
$557$	−6.32377	−	10.9531i	−0.267947	−	0.464097i	−0.968331	+	0.249668i	$0.919678\pi$
$558$		0			0
$559$	−6.68014	+	11.5703i	−0.282540	+	0.489373i
$560$		0			0
$561$	30.5119	−	19.3807i	1.28821	−	0.818254i
$562$		0			0
$563$	0.446820	+	2.53404i	0.0188312	+	0.106797i	0.992775	−	0.119994i	$-0.0382876\pi$
$563$	0.446820	+	2.53404i	0.0188312	+	0.106797i	−0.973943	+	0.226791i	$0.927176\pi$
$564$		0			0
$565$	0.605881	+	0.508394i	0.0254896	+	0.0213883i
$566$		0			0
$567$	−23.2850	+	3.97702i	−0.977878	+	0.167019i
$568$		0			0
$569$	11.5057	+	9.65440i	0.482343	+	0.404733i	0.851273	−	0.524724i	$-0.175831\pi$
$569$	11.5057	+	9.65440i	0.482343	+	0.404733i	−0.368930	+	0.929457i	$0.620276\pi$
$570$		0			0
$571$	8.05115	+	45.6603i	0.336930	+	1.91082i	0.407282	+	0.913303i	$0.366477\pi$
$571$	8.05115	+	45.6603i	0.336930	+	1.91082i	−0.0703518	+	0.997522i	$0.522412\pi$
$572$		0			0
$573$	23.8701	−	15.1619i	0.997186	−	0.633398i
$574$		0			0
$575$	3.32475	−	5.75863i	0.138651	−	0.240151i
$576$		0			0
$577$	11.3387	+	19.6392i	0.472037	+	0.817591i	0.999488	−	0.0319938i	$-0.0101857\pi$
$577$	11.3387	+	19.6392i	0.472037	+	0.817591i	−0.527451	+	0.849585i	$0.676852\pi$
$578$		0			0
$579$	−13.7177	−	1.82469i	−0.570086	−	0.0758317i
$580$		0			0
$581$	−15.3659	+	12.8935i	−0.637484	+	0.534913i
$582$		0			0
$583$	−39.5192	+	14.3838i	−1.63672	+	0.595716i
$584$		0			0
$585$	−1.69393	−	0.458762i	−0.0700352	−	0.0189675i
$586$		0			0
$587$	−2.44425	+	13.8620i	−0.100885	+	0.572148i	0.891899	+	0.452234i	$0.149373\pi$
$587$	−2.44425	+	13.8620i	−0.100885	+	0.572148i	−0.992784	+	0.119914i	$0.961738\pi$
$588$		0			0
$589$	44.9296	+	16.3530i	1.85129	+	0.673815i
$590$		0			0
$591$	6.79709	+	7.43773i	0.279595	+	0.305947i
$592$		0			0
$593$	20.7559			0.852342			0.426171	−	0.904643i	$-0.359862\pi$
$593$	20.7559			0.852342			0.426171	+	0.904643i	$0.359862\pi$
$594$		0			0
$595$	−1.86858			−0.0766042
$596$		0			0
$597$	44.1275	−	9.72072i	1.80602	−	0.397842i
$598$		0			0
$599$	20.5730	+	7.48796i	0.840590	+	0.305950i	0.726198	−	0.687486i	$-0.241286\pi$
$599$	20.5730	+	7.48796i	0.840590	+	0.305950i	0.114392	+	0.993436i	$0.463508\pi$
$600$		0			0
$601$	−0.604738	+	3.42964i	−0.0246678	+	0.139898i	−0.994654	−	0.103261i	$-0.967072\pi$
$601$	−0.604738	+	3.42964i	−0.0246678	+	0.139898i	0.969987	+	0.243159i	$0.0781836\pi$
$602$		0			0
$603$	19.0937	−	1.61886i	0.777556	−	0.0659250i
$604$		0			0
$605$	−0.297415	+	0.108250i	−0.0120916	+	0.00440099i
$606$		0			0
$607$	25.1901	−	21.1370i	1.02243	−	0.857925i	0.0325032	−	0.999472i	$-0.489652\pi$
$607$	25.1901	−	21.1370i	1.02243	−	0.857925i	0.989932	+	0.141547i	$0.0452076\pi$
$608$		0			0
$609$	5.03441	+	12.2004i	0.204005	+	0.494386i
$610$		0			0
$611$	−13.3874	−	23.1876i	−0.541596	−	0.938072i
$612$		0			0
$613$	−3.84685	+	6.66293i	−0.155373	+	0.269113i	−0.933195	−	0.359371i	$-0.882991\pi$
$613$	−3.84685	+	6.66293i	−0.155373	+	0.269113i	0.777822	+	0.628485i	$0.216324\pi$
$614$		0			0
$615$	0.0539728	+	1.27545i	0.00217639	+	0.0514313i
$616$		0			0
$617$	2.72419	+	15.4496i	0.109672	+	0.621979i	0.989251	+	0.146227i	$0.0467130\pi$
$617$	2.72419	+	15.4496i	0.109672	+	0.621979i	−0.879579	+	0.475752i	$0.842176\pi$
$618$		0			0
$619$	−0.0947545	−	0.0795085i	−0.00380851	−	0.00319572i	0.640881	−	0.767640i	$-0.278569\pi$
$619$	−0.0947545	−	0.0795085i	−0.00380851	−	0.00319572i	−0.644690	+	0.764444i	$0.723013\pi$
$620$		0			0
$621$	−5.09204	−	4.70384i	−0.204336	−	0.188759i
$622$		0			0
$623$	18.5879	+	15.5971i	0.744708	+	0.624884i
$624$		0			0
$625$	4.30026	+	24.3880i	0.172010	+	0.975519i
$626$		0			0
$627$	−44.4514	−	23.2158i	−1.77522	−	0.927150i
$628$		0			0
$629$	−24.7299	+	42.8335i	−0.986046	+	1.70788i
$630$		0			0
$631$	2.58465	+	4.47675i	0.102893	+	0.178216i	0.912876	−	0.408238i	$-0.133857\pi$
$631$	2.58465	+	4.47675i	0.102893	+	0.178216i	−0.809982	+	0.586454i	$0.800523\pi$
$632$		0			0
$633$	8.58034	−	11.1511i	0.341038	−	0.443216i
$634$		0			0
$635$	0.246184	−	0.206573i	0.00976951	−	0.00819759i
$636$		0			0
$637$	−0.486463	+	0.177058i	−0.0192744	+	0.00701530i
$638$		0			0
$639$	0.409185	−	4.53673i	0.0161871	−	0.179470i
$640$		0			0
$641$	5.97504	−	33.8862i	0.236000	−	1.33842i	−0.604497	−	0.796607i	$-0.706626\pi$
$641$	5.97504	−	33.8862i	0.236000	−	1.33842i	0.840497	−	0.541816i	$-0.182263\pi$
$642$		0			0
$643$	15.4892	+	5.63762i	0.610835	+	0.222326i	0.628869	−	0.777512i	$-0.283518\pi$
$643$	15.4892	+	5.63762i	0.610835	+	0.222326i	−0.0180334	+	0.999837i	$0.505741\pi$
$644$		0			0
$645$	−0.187993	+	0.593459i	−0.00740221	+	0.0233674i
$646$		0			0
$647$	29.2900			1.15151			0.575754	−	0.817623i	$-0.304708\pi$
$647$	29.2900			1.15151			0.575754	+	0.817623i	$0.304708\pi$
$648$		0			0
$649$	43.7484			1.71728
$650$		0			0
$651$	8.33695	−	26.3182i	0.326751	−	1.03149i
$652$		0			0
$653$	−22.1954	−	8.07847i	−0.868573	−	0.316135i	−0.130984	−	0.991384i	$-0.541814\pi$
$653$	−22.1954	−	8.07847i	−0.868573	−	0.316135i	−0.737589	+	0.675250i	$0.764036\pi$
$654$		0			0
$655$	0.228701	−	1.29703i	0.00893609	−	0.0506791i
$656$		0			0
$657$	5.59358	−	2.59008i	0.218227	−	0.101049i
$658$		0			0
$659$	−22.1475	+	8.06105i	−0.862746	+	0.314014i	−0.735226	−	0.677822i	$-0.762924\pi$
$659$	−22.1475	+	8.06105i	−0.862746	+	0.314014i	−0.127520	+	0.991836i	$0.540702\pi$
$660$		0			0
$661$	29.6781	−	24.9029i	1.15435	−	0.968611i	0.154533	−	0.987988i	$-0.450613\pi$
$661$	29.6781	−	24.9029i	1.15435	−	0.968611i	0.999812	+	0.0193771i	$0.00616831\pi$
$662$		0			0
$663$	27.9525	−	36.3274i	1.08559	−	1.41084i
$664$		0			0
$665$	1.29620	+	2.24509i	0.0502646	+	0.0870608i
$666$		0			0
$667$	−1.93659	+	3.35427i	−0.0749851	+	0.129878i
$668$		0			0
$669$	−2.45179	−	1.28051i	−0.0947918	−	0.0495073i
$670$		0			0
$671$	−7.21812	−	40.9360i	−0.278653	−	1.58032i
$672$		0			0
$673$	−19.8822	−	16.6832i	−0.766403	−	0.643088i	0.173382	−	0.984855i	$-0.444530\pi$
$673$	−19.8822	−	16.6832i	−0.766403	−	0.643088i	−0.939785	+	0.341766i	$0.888975\pi$
$674$		0			0
$675$	25.8696	+	1.23385i	0.995721	+	0.0474911i
$676$		0			0
$677$	10.7443	+	9.01554i	0.412937	+	0.346495i	0.825469	−	0.564448i	$-0.190911\pi$
$677$	10.7443	+	9.01554i	0.412937	+	0.346495i	−0.412532	+	0.910943i	$0.635355\pi$
$678$		0			0
$679$	−2.28104	−	12.9364i	−0.0875384	−	0.496455i
$680$		0			0
$681$	1.23545	+	29.1954i	0.0473425	+	1.11877i
$682$		0			0
$683$	3.03884	−	5.26342i	0.116278	−	0.201399i	−0.802012	−	0.597308i	$-0.796237\pi$
$683$	3.03884	−	5.26342i	0.116278	−	0.201399i	0.918290	+	0.395909i	$0.129570\pi$
$684$		0			0
$685$	0.554167	+	0.959845i	0.0211736	+	0.0366738i
$686$		0			0
$687$	5.71342	+	13.8459i	0.217980	+	0.528255i
$688$		0			0
$689$	−40.8528	+	34.2796i	−1.55637	+	1.30595i
$690$		0			0
$691$	−19.7802	+	7.19942i	−0.752476	+	0.273879i	−0.689647	−	0.724146i	$-0.742234\pi$
$691$	−19.7802	+	7.19942i	−0.752476	+	0.273879i	−0.0628286	+	0.998024i	$0.520012\pi$
$692$		0			0
$693$	−12.3076	+	26.2099i	−0.467528	+	0.995632i
$694$		0			0
$695$	−0.326259	+	1.85031i	−0.0123757	+	0.0701862i
$696$		0			0
$697$	−31.3321	−	11.4040i	−1.18679	−	0.431955i
$698$		0			0
$699$	−5.03675	+	1.10953i	−0.190507	+	0.0419663i
$700$		0			0
$701$	30.2155			1.14122			0.570611	−	0.821220i	$-0.306706\pi$
$701$	30.2155			1.14122			0.570611	+	0.821220i	$0.306706\pi$
$702$		0			0
$703$	68.6189			2.58801
$704$		0			0
$705$	−0.841612	−	0.920937i	−0.0316970	−	0.0346845i
$706$		0			0
$707$	6.85001	+	2.49320i	0.257621	+	0.0937665i
$708$		0			0
$709$	0.728477	−	4.13140i	0.0273585	−	0.155158i	−0.968068	−	0.250687i	$-0.919343\pi$
$709$	0.728477	−	4.13140i	0.0273585	−	0.155158i	0.995427	+	0.0955296i	$0.0304545\pi$
$710$		0			0
$711$	−4.71417	−	17.7843i	−0.176795	−	0.666963i
$712$		0			0
$713$	7.61300	−	2.77091i	0.285109	−	0.103771i
$714$		0			0
$715$	−1.64791	+	1.38276i	−0.0616284	+	0.0517124i
$716$		0			0
$717$	−46.7744	−	6.22183i	−1.74682	−	0.232358i
$718$		0			0
$719$	6.47407	+	11.2134i	0.241442	+	0.418190i	0.961125	−	0.276112i	$-0.0890462\pi$
$719$	6.47407	+	11.2134i	0.241442	+	0.418190i	−0.719683	+	0.694303i	$0.755713\pi$
$720$		0			0
$721$	−6.27148	+	10.8625i	−0.233562	+	0.404541i
$722$		0			0
$723$	28.4806	−	18.0905i	1.05920	−	0.672791i
$724$		0			0
$725$	−2.51276	−	14.2506i	−0.0933217	−	0.529254i
$726$		0			0
$727$	6.89220	+	5.78325i	0.255618	+	0.214489i	0.761587	−	0.648063i	$-0.224421\pi$
$727$	6.89220	+	5.78325i	0.255618	+	0.214489i	−0.505969	+	0.862552i	$0.668865\pi$
$728$		0			0
$729$	7.19787	−	26.0229i	0.266588	−	0.963811i
$730$		0			0
$731$	−12.4555	−	10.4514i	−0.460682	−	0.386558i
$732$		0			0
$733$	4.08103	+	23.1447i	0.150736	+	0.854869i	0.962581	+	0.270995i	$0.0873526\pi$
$733$	4.08103	+	23.1447i	0.150736	+	0.854869i	−0.811844	+	0.583874i	$0.801536\pi$
$734$		0			0
$735$	−0.0203612	+	0.0129331i	−0.000751035	+	0.000477046i
$736$		0			0
$737$	11.7444	−	20.3419i	0.432611	−	0.749304i
$738$		0			0
$739$	−8.97888	−	15.5519i	−0.330293	−	0.572085i	0.652276	−	0.757982i	$-0.273814\pi$
$739$	−8.97888	−	15.5519i	−0.330293	−	0.572085i	−0.982569	+	0.185897i	$0.940481\pi$
$740$		0			0
$741$	−63.0374	−	8.38510i	−2.31574	−	0.308034i
$742$		0			0
$743$	30.4147	−	25.5210i	1.11581	−	0.936273i	0.117422	−	0.993082i	$-0.462537\pi$
$743$	30.4147	−	25.5210i	1.11581	−	0.936273i	0.998385	+	0.0568090i	$0.0180926\pi$
$744$		0			0
$745$	0.122137	−	0.0444541i	0.00447474	−	0.00162867i
$746$		0			0
$747$	−5.87449	−	22.1616i	−0.214936	−	0.810851i
$748$		0			0
$749$	−3.78065	+	21.4411i	−0.138142	+	0.783442i
$750$		0			0
$751$	−39.8431	−	14.5017i	−1.45390	−	0.529175i	−0.510220	−	0.860044i	$-0.670436\pi$
$751$	−39.8431	−	14.5017i	−1.45390	−	0.529175i	−0.943677	+	0.330869i	$0.892658\pi$
$752$		0			0
$753$	−30.2806	−	33.1346i	−1.10349	−	1.20749i
$754$		0			0
$755$	−0.338964			−0.0123362
$756$		0			0
$757$	21.1986			0.770477			0.385238	−	0.922817i	$-0.374119\pi$
$757$	21.1986			0.770477			0.385238	+	0.922817i	$0.374119\pi$
$758$		0			0
$759$	−8.29841	+	1.82803i	−0.301213	+	0.0663534i
$760$		0			0
$761$	14.9591	+	5.44467i	0.542267	+	0.197369i	0.598607	−	0.801043i	$-0.295721\pi$
$761$	14.9591	+	5.44467i	0.542267	+	0.197369i	−0.0563405	+	0.998412i	$0.517943\pi$
$762$		0			0
$763$	4.54594	−	25.7813i	0.164574	−	0.933346i
$764$		0			0
$765$	0.907808	−	1.93324i	0.0328219	−	0.0698963i
$766$		0			0
$767$	52.1308	−	18.9741i	1.88233	−	0.685113i
$768$		0			0
$769$	2.02994	−	1.70333i	0.0732017	−	0.0614235i	−0.605453	−	0.795881i	$-0.707008\pi$
$769$	2.02994	−	1.70333i	0.0732017	−	0.0614235i	0.678654	+	0.734458i	$0.262563\pi$
$770$		0			0
$771$	−4.43496	−	10.7477i	−0.159721	−	0.387069i
$772$		0			0
$773$	−13.8605	−	24.0070i	−0.498526	−	0.863473i	0.501472	−	0.865174i	$-0.332792\pi$
$773$	−13.8605	−	24.0070i	−0.498526	−	0.863473i	−0.999999	+	0.00170080i	$0.999459\pi$
$774$		0			0
$775$	−15.1340	+	26.2129i	−0.543629	+	0.941594i
$776$		0			0
$777$	−1.67510	−	39.5849i	−0.0600938	−	1.42010i
$778$		0			0
$779$	8.03277	+	45.5561i	0.287804	+	1.63222i
$780$		0			0
$781$	−4.27732	−	3.58910i	−0.153055	−	0.128428i
$782$		0			0
$783$	−15.0685	−	0.718693i	−0.538503	−	0.0256840i
$784$		0			0
$785$	1.52257	+	1.27759i	0.0543429	+	0.0455991i
$786$		0			0
$787$	−6.12354	−	34.7283i	−0.218281	−	1.23793i	−0.875122	−	0.483902i	$-0.839219\pi$
$787$	−6.12354	−	34.7283i	−0.218281	−	1.23793i	0.656842	−	0.754029i	$-0.271892\pi$
$788$		0			0
$789$	32.5657	+	17.0082i	1.15937	+	0.605508i
$790$		0			0
$791$	8.27408	−	14.3311i	0.294192	−	0.509556i
$792$		0			0
$793$	−26.3554	−	45.6489i	−0.935909	−	1.62104i
$794$		0			0
$795$	−1.51535	+	1.96937i	−0.0537440	+	0.0698462i
$796$		0			0
$797$	32.8151	−	27.5351i	1.16237	−	0.975344i	0.162435	−	0.986719i	$-0.448065\pi$
$797$	32.8151	−	27.5351i	1.16237	−	0.975344i	0.999935	+	0.0113750i	$0.00362085\pi$
$798$		0			0
$799$	30.6198	−	11.1447i	1.08325	−	0.394270i
$800$		0			0
$801$	−25.1673	+	11.6536i	−0.889243	+	0.411759i
$802$		0			0
$803$	1.31207	−	7.44114i	0.0463021	−	0.262592i
$804$		0			0
$805$	0.412774	+	0.150237i	0.0145484	+	0.00529517i
$806$		0			0
$807$	−8.83582	+	27.8931i	−0.311036	+	0.981882i
$808$		0			0
$809$	6.44196			0.226487			0.113244	−	0.993567i	$-0.463876\pi$
$809$	6.44196			0.226487			0.113244	+	0.993567i	$0.463876\pi$
$810$		0			0
$811$	−36.4969			−1.28158			−0.640790	−	0.767716i	$-0.721393\pi$
$811$	−36.4969			−1.28158			−0.640790	+	0.767716i	$0.721393\pi$
$812$		0			0
$813$	−16.9058	+	53.3685i	−0.592912	+	1.87172i
$814$		0			0
$815$	1.17474	+	0.427571i	0.0411494	+	0.0149772i
$816$		0			0
$817$	−3.91712	+	22.2151i	−0.137043	+	0.777209i
$818$		0			0
$819$	−3.29836	+	36.5697i	−0.115254	+	1.27785i
$820$		0			0
$821$	−8.15624	+	2.96863i	−0.284655	+	0.103606i	−0.480402	−	0.877049i	$-0.659509\pi$
$821$	−8.15624	+	2.96863i	−0.284655	+	0.103606i	0.195747	+	0.980654i	$0.437287\pi$
$822$		0			0
$823$	40.9518	−	34.3626i	1.42749	−	1.19781i	0.480312	−	0.877098i	$-0.340524\pi$
$823$	40.9518	−	34.3626i	1.42749	−	1.19781i	0.947178	−	0.320708i	$-0.103921\pi$
$824$		0			0
$825$	19.3599	−	25.1604i	0.674026	−	0.875971i
$826$		0			0
$827$	12.8831	+	22.3142i	0.447989	+	0.775939i	0.998255	−	0.0590499i	$-0.0188071\pi$
$827$	12.8831	+	22.3142i	0.447989	+	0.775939i	−0.550266	+	0.834989i	$0.685474\pi$
$828$		0			0
$829$	−24.4963	+	42.4288i	−0.850791	+	1.47361i	0.0297037	+	0.999559i	$0.490544\pi$
$829$	−24.4963	+	42.4288i	−0.850791	+	1.47361i	−0.880495	+	0.474055i	$0.842790\pi$
$830$		0			0
$831$	−13.6651	−	7.13693i	−0.474037	−	0.247577i
$832$		0			0
$833$	−0.109402	−	0.620448i	−0.00379055	−	0.0214973i
$834$		0			0
$835$	2.02153	+	1.69627i	0.0699581	+	0.0587018i
$836$		0			0
$837$	23.1786	+	21.4116i	0.801169	+	0.740092i
$838$		0			0
$839$	2.47353	+	2.07554i	0.0853958	+	0.0716556i	0.684486	−	0.729026i	$-0.260027\pi$
$839$	2.47353	+	2.07554i	0.0853958	+	0.0716556i	−0.599090	+	0.800681i	$0.704471\pi$
$840$		0			0
$841$	−3.57217	−	20.2588i	−0.123178	−	0.698578i
$842$		0			0
$843$	1.80000	+	42.5366i	0.0619953	+	1.46504i
$844$		0			0
$845$	−0.548534	+	0.950089i	−0.0188702	+	0.0326841i
$846$		0			0
$847$	3.31103	+	5.73487i	0.113768	+	0.197052i
$848$		0			0
$849$	−1.87966	−	4.55519i	−0.0645099	−	0.156334i
$850$		0			0
$851$	8.90680	−	7.47369i	0.305321	−	0.256195i
$852$		0			0
$853$	36.5216	−	13.2928i	1.25047	−	0.455135i	0.369912	−	0.929067i	$-0.379388\pi$
$853$	36.5216	−	13.2928i	1.25047	−	0.455135i	0.880562	+	0.473931i	$0.157165\pi$
$854$		0			0
$855$	−2.95251	+	0.250328i	−0.100974	+	0.00856103i
$856$		0			0
$857$	0.614400	−	3.48443i	0.0209875	−	0.119026i	−0.972514	−	0.232844i	$-0.925197\pi$
$857$	0.614400	−	3.48443i	0.0209875	−	0.119026i	0.993502	+	0.113818i	$0.0363080\pi$
$858$		0			0
$859$	−15.4016	−	5.60573i	−0.525497	−	0.191265i	0.0656297	−	0.997844i	$-0.479094\pi$
$859$	−15.4016	−	5.60573i	−0.525497	−	0.191265i	−0.591126	+	0.806579i	$0.701317\pi$
$860$		0			0
$861$	26.0843	−	5.74605i	0.888952	−	0.195825i
$862$		0			0
$863$	10.7841			0.367095			0.183548	−	0.983011i	$-0.441242\pi$
$863$	10.7841			0.367095			0.183548	+	0.983011i	$0.441242\pi$
$864$		0			0
$865$	−2.84123			−0.0966047
$866$		0			0
$867$	17.7680	+	19.4427i	0.603433	+	0.660308i
$868$		0			0
$869$	−21.1925	−	7.71345i	−0.718908	−	0.261661i
$870$		0			0
$871$	5.17222	−	29.3331i	0.175254	−	0.993915i
$872$		0			0
$873$	14.4923	+	3.92491i	0.490489	+	0.132838i
$874$		0			0
$875$	−3.08916	+	1.12436i	−0.104433	+	0.0380104i
$876$		0			0
$877$	15.8353	−	13.2874i	0.534719	−	0.448683i	−0.335008	−	0.942215i	$-0.608739\pi$
$877$	15.8353	−	13.2874i	0.534719	−	0.448683i	0.869727	+	0.493533i	$0.164295\pi$
$878$		0			0
$879$	27.4187	+	3.64718i	0.924811	+	0.123016i
$880$		0			0
$881$	16.2188	+	28.0917i	0.546424	+	0.946434i	0.998516	+	0.0544629i	$0.0173447\pi$
$881$	16.2188	+	28.0917i	0.546424	+	0.946434i	−0.452092	+	0.891972i	$0.649322\pi$
$882$		0			0
$883$	22.6736	−	39.2718i	0.763027	−	1.32160i	−0.178256	−	0.983984i	$-0.557046\pi$
$883$	22.6736	−	39.2718i	0.763027	−	1.32160i	0.941283	−	0.337618i	$-0.109621\pi$
$884$		0			0
$885$	2.18197	−	1.38595i	0.0733460	−	0.0465883i
$886$		0			0
$887$	−2.34480	−	13.2980i	−0.0787308	−	0.446505i	−0.998534	−	0.0541251i	$-0.982763\pi$
$887$	−2.34480	−	13.2980i	−0.0787308	−	0.446505i	0.919803	−	0.392380i	$-0.128348\pi$
$888$		0			0
$889$	−5.15082	−	4.32205i	−0.172753	−	0.144957i
$890$		0			0
$891$	−21.1375	−	25.4670i	−0.708132	−	0.853178i
$892$		0			0
$893$	−34.6307	−	29.0586i	−1.15887	−	0.972409i
$894$		0			0
$895$	0.473153	+	2.68339i	0.0158158	+	0.0896957i
$896$		0			0
$897$	−9.09558	+	5.77738i	−0.303692	+	0.192901i
$898$		0			0
$899$	8.81523	−	15.2684i	0.294004	−	0.509230i
$900$		0			0
$901$	−32.4510	−	56.2068i	−1.08110	−	1.87252i
$902$		0			0
$903$	12.9111	+	1.71741i	0.429654	+	0.0571517i
$904$		0			0
$905$	2.31017	−	1.93846i	0.0767925	−	0.0644366i
$906$		0			0
$907$	29.6409	−	10.7884i	0.984209	−	0.358223i	0.200734	−	0.979646i	$-0.435667\pi$
$907$	29.6409	−	10.7884i	0.984209	−	0.358223i	0.783475	+	0.621423i	$0.213445\pi$
$908$		0			0
$909$	−5.90741	+	5.87578i	−0.195936	+	0.194887i
$910$		0			0
$911$	−1.53316	+	8.69498i	−0.0507958	+	0.288078i	−0.999615	−	0.0277420i	$-0.991168\pi$
$911$	−1.53316	+	8.69498i	−0.0507958	+	0.288078i	0.948819	+	0.315820i	$0.102279\pi$
$912$		0			0
$913$	−26.4088	−	9.61200i	−0.874002	−	0.318111i
$914$		0			0
$915$	−1.65686	−	1.81303i	−0.0547741	−	0.0599368i
$916$		0			0
$917$	−27.5559			−0.909975
$918$		0			0
$919$	−1.42034			−0.0468527			−0.0234263	−	0.999726i	$-0.507458\pi$
$919$	−1.42034			−0.0468527			−0.0234263	+	0.999726i	$0.507458\pi$
$920$		0			0
$921$	0.293245	−	0.0645981i	0.00966275	−	0.00212858i
$922$		0			0
$923$	−6.65349	−	2.42167i	−0.219002	−	0.0797103i
$924$		0			0
$925$	−7.54313	+	42.7792i	−0.248017	+	1.40657i
$926$		0			0
$927$	−8.19154	−	11.7658i	−0.269045	−	0.386440i
$928$		0			0
$929$	−47.1069	+	17.1455i	−1.54553	+	0.562526i	−0.967363	−	0.253395i	$-0.918453\pi$
$929$	−47.1069	+	17.1455i	−1.54553	+	0.562526i	−0.578164	+	0.815921i	$0.696231\pi$
$930$		0			0
$931$	−0.669576	+	0.561841i	−0.0219445	+	0.0184136i
$932$		0			0
$933$	4.72488	+	11.4503i	0.154686	+	0.374866i
$934$		0			0
$935$	−1.30900	−	2.26726i	−0.0428089	−	0.0741472i
$936$		0			0
$937$	−28.4431	+	49.2649i	−0.929195	+	1.60941i	−0.144524	+	0.989501i	$0.546165\pi$
$937$	−28.4431	+	49.2649i	−0.929195	+	1.60941i	−0.784671	+	0.619912i	$0.787168\pi$
$938$		0			0
$939$	−0.848487	−	20.0510i	−0.0276893	−	0.654338i
$940$		0			0
$941$	−4.19352	−	23.7826i	−0.136705	−	0.775292i	−0.973657	−	0.228016i	$-0.926776\pi$
$941$	−4.19352	−	23.7826i	−0.136705	−	0.775292i	0.836952	−	0.547276i	$-0.184335\pi$
$942$		0			0
$943$	6.00444	+	5.03833i	0.195532	+	0.164070i
$944$		0			0
$945$	0.216485	+	1.69713i	0.00704225	+	0.0552077i
$946$		0			0
$947$	−40.9796	−	34.3860i	−1.33166	−	1.11739i	−0.983687	−	0.179889i	$-0.942426\pi$
$947$	−40.9796	−	34.3860i	−1.33166	−	1.11739i	−0.347971	−	0.937505i	$-0.613129\pi$
$948$		0			0
$949$	−1.66381	−	9.43594i	−0.0540096	−	0.306304i
$950$		0			0
$951$	28.6238	+	14.9495i	0.928190	+	0.484769i
$952$		0			0
$953$	−7.85157	+	13.5993i	−0.254337	+	0.440525i	−0.964715	−	0.263295i	$-0.915191\pi$
$953$	−7.85157	+	13.5993i	−0.254337	+	0.440525i	0.710378	+	0.703820i	$0.248524\pi$
$954$		0			0
$955$	−1.02406	−	1.77372i	−0.0331377	−	0.0573962i
$956$		0			0
$957$	−11.2767	+	14.6554i	−0.364525	+	0.473740i
$958$		0			0
$959$	17.7640	−	14.9058i	0.573630	−	0.481332i
$960$		0			0
$961$	−5.52339	+	2.01035i	−0.178174	+	0.0648499i
$962$		0			0
$963$	−20.3463	−	14.3282i	−0.655651	−	0.461719i
$964$		0			0
$965$	−0.174044	+	0.987053i	−0.00560268	+	0.0317744i
$966$		0			0
$967$	25.1121	+	9.14006i	0.807551	+	0.293924i	0.712612	−	0.701559i	$-0.247512\pi$
$967$	25.1121	+	9.14006i	0.807551	+	0.293924i	0.0949391	+	0.995483i	$0.469734\pi$
$968$		0			0
$969$	23.3713	−	73.7789i	0.750794	−	2.37012i
$970$		0			0
$971$	−2.58426			−0.0829328			−0.0414664	−	0.999140i	$-0.513203\pi$
$971$	−2.58426			−0.0829328			−0.0414664	+	0.999140i	$0.513203\pi$
$972$		0			0
$973$	39.3105			1.26024
$974$		0			0
$975$	12.1571	−	38.3777i	0.389339	−	1.22907i
$976$		0			0
$977$	52.1656	+	18.9867i	1.66893	+	0.607439i	0.991727	−	0.128362i	$-0.0409720\pi$
$977$	52.1656	+	18.9867i	1.66893	+	0.607439i	0.677198	+	0.735801i	$0.263194\pi$
$978$		0			0
$979$	−5.90343	+	33.4800i	−0.188675	+	1.07003i
$980$		0			0
$981$	24.4649	+	17.2285i	0.781103	+	0.550064i
$982$		0			0
$983$	0.457913	−	0.166667i	0.0146052	−	0.00531584i	−0.334707	−	0.942322i	$-0.608637\pi$
$983$	0.457913	−	0.166667i	0.0146052	−	0.00531584i	0.349312	+	0.937006i	$0.386415\pi$
$984$		0			0
$985$	0.559025	−	0.469077i	0.0178120	−	0.0149460i
$986$		0			0
$987$	−15.9180	+	20.6872i	−0.506674	+	0.658479i
$988$		0			0
$989$	1.91113	+	3.31018i	0.0607705	+	0.105258i
$990$		0			0
$991$	11.1229	−	19.2654i	0.353330	−	0.611986i	−0.633500	−	0.773742i	$-0.718382\pi$
$991$	11.1229	−	19.2654i	0.353330	−	0.611986i	0.986831	+	0.161756i	$0.0517158\pi$
$992$		0			0
$993$	10.4518	+	5.45873i	0.331679	+	0.173227i
$994$		0			0
$995$	−0.568289	−	3.22293i	−0.0180160	−	0.102174i
$996$		0			0
$997$	14.2775	+	11.9803i	0.452173	+	0.379419i	0.840242	−	0.542212i	$-0.182413\pi$
$997$	14.2775	+	11.9803i	0.452173	+	0.379419i	−0.388068	+	0.921631i	$0.626858\pi$
$998$		0			0
$999$	41.7685	+	17.4984i	1.32150	+	0.553626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.97.6	yes	60
4.3	odd	2	inner	864.2.y.d.97.5	✓	60
27.22	even	9	inner	864.2.y.d.481.6	yes	60
108.103	odd	18	inner	864.2.y.d.481.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.97.5	✓	60	4.3	odd	2	inner
864.2.y.d.97.6	yes	60	1.1	even	1	trivial
864.2.y.d.481.5	yes	60	108.103	odd	18	inner
864.2.y.d.481.6	yes	60	27.22	even	9	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.523054 - 1.65119i) q^{3} +(-0.117882 - 0.0429055i) q^{5} +(-0.455772 + 2.58481i) q^{7} +(-2.45283 - 1.72732i) q^{9} +(-3.45559 + 1.25773i) q^{11} +(-3.57220 + 2.99743i) q^{13} +(-0.132504 + 0.172203i) q^{15} +(-2.83754 - 4.91477i) q^{17} +(-3.93671 + 6.81859i) q^{19} +(4.02961 + 2.10456i) q^{21} +(0.231664 + 1.31383i) q^{23} +(-3.81817 - 3.20382i) q^{25} +(-4.13509 + 3.14660i) q^{27} +(2.22400 + 1.86616i) q^{29} +(-1.05452 - 5.98046i) q^{31} +(0.269289 + 6.36368i) q^{33} +(0.164630 - 0.285147i) q^{35} +(-4.35763 - 7.54764i) q^{37} +(3.08087 + 7.46619i) q^{39} +(4.50075 - 3.77658i) q^{41} +(2.69227 - 0.979908i) q^{43} +(0.215033 + 0.308859i) q^{45} +(-0.997043 + 5.65451i) q^{47} +(0.104320 + 0.0379694i) q^{49} +(-9.59938 + 2.11462i) q^{51} +11.4363 q^{53} +0.461315 q^{55} +(9.19964 + 10.0667i) q^{57} +(-11.1792 - 4.06891i) q^{59} +(-1.96285 + 11.1319i) q^{61} +(5.58273 - 5.55284i) q^{63} +(0.549705 - 0.200076i) q^{65} +(-4.89304 + 4.10575i) q^{67} +(2.29055 + 0.304684i) q^{69} +(0.759192 + 1.31496i) q^{71} +(-1.02736 + 1.77944i) q^{73} +(-7.28721 + 4.62873i) q^{75} +(-1.67604 - 9.50529i) q^{77} +(4.69802 + 3.94211i) q^{79} +(3.03274 + 8.47363i) q^{81} +(5.85437 + 4.91240i) q^{83} +(0.123624 + 0.701108i) q^{85} +(4.24464 - 2.69613i) q^{87} +(4.62241 - 8.00624i) q^{89} +(-6.11970 - 10.5996i) q^{91} +(-10.4264 - 1.38690i) q^{93} +(0.756622 - 0.634881i) q^{95} +(-4.70296 + 1.71174i) q^{97} +(10.6485 + 2.88390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77}+ \cdots + 12 q^{97}+O(q^{100}) \) 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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