LMFDB - Embedded newform 864.2.bf.a.241.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(49,864)] 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("864.49"); 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, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			241.34
Character	$\chi$	$=$	864.241
Dual form			864.2.bf.a.337.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73179 - 0.0302651i) q^{3} +(0.721676 + 0.860059i) q^{5} +(-1.31793 + 0.479686i) q^{7} +(2.99817 - 0.104825i) q^{9} +(1.05816 - 1.26106i) q^{11} +(0.671077 - 0.118329i) q^{13} +(1.27582 + 1.46760i) q^{15} +(0.907443 + 1.57174i) q^{17} +(2.96777 + 1.71344i) q^{19} +(-2.26785 + 0.870601i) q^{21} +(3.62278 + 1.31858i) q^{23} +(0.649354 - 3.68267i) q^{25} +(5.18901 - 0.272275i) q^{27} +(-3.92395 - 0.691898i) q^{29} +(6.21468 + 2.26196i) q^{31} +(1.79434 - 2.21592i) q^{33} +(-1.36367 - 0.787317i) q^{35} +(-3.83532 + 2.21432i) q^{37} +(1.15858 - 0.225231i) q^{39} +(0.952217 + 5.40029i) q^{41} +(-7.26017 + 8.65234i) q^{43} +(2.25386 + 2.50295i) q^{45} +(11.5469 - 4.20273i) q^{47} +(-3.85548 + 3.23513i) q^{49} +(1.61907 + 2.69445i) q^{51} -6.89741i q^{53} +1.84824 q^{55} +(5.19140 + 2.87750i) q^{57} +(-6.78921 - 8.09106i) q^{59} +(-1.24084 - 3.40917i) q^{61} +(-3.90108 + 1.57633i) q^{63} +(0.586070 + 0.491771i) q^{65} +(-11.9425 + 2.10578i) q^{67} +(6.31378 + 2.17386i) q^{69} +(-6.80355 - 11.7841i) q^{71} +(4.73823 - 8.20685i) q^{73} +(1.01309 - 6.39725i) q^{75} +(-0.789660 + 2.16957i) q^{77} +(-1.59290 + 9.03380i) q^{79} +(8.97802 - 0.628568i) q^{81} +(1.29853 + 0.228966i) q^{83} +(-0.696908 + 1.91474i) q^{85} +(-6.81638 - 1.07946i) q^{87} +(-3.52339 + 6.10270i) q^{89} +(-0.827669 + 0.477855i) q^{91} +(10.8310 + 3.72914i) q^{93} +(0.668104 + 3.78901i) q^{95} +(-6.33275 - 5.31381i) q^{97} +(3.04035 - 3.89180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$1$

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
$3$	1.73179	−	0.0302651i	0.999847	−	0.0174736i
$3$	1.73179	−	0.0302651i	0.999847	−	0.0174736i
$4$		0			0
$5$	0.721676	+	0.860059i	0.322743	+	0.384630i	0.902883	−	0.429887i	$-0.141447\pi$
$5$	0.721676	+	0.860059i	0.322743	+	0.384630i	−0.580140	+	0.814517i	$0.697002\pi$
$6$		0			0
$7$	−1.31793	+	0.479686i	−0.498129	+	0.181304i	−0.578852	−	0.815432i	$-0.696499\pi$
$7$	−1.31793	+	0.479686i	−0.498129	+	0.181304i	0.0807232	+	0.996737i	$0.474277\pi$
$8$		0			0
$9$	2.99817	−	0.104825i	0.999389	−	0.0349418i
$10$		0			0
$11$	1.05816	−	1.26106i	0.319047	−	0.380225i	−0.582556	−	0.812791i	$-0.697947\pi$
$11$	1.05816	−	1.26106i	0.319047	−	0.380225i	0.901602	+	0.432566i	$0.142392\pi$
$12$		0			0
$13$	0.671077	−	0.118329i	0.186123	−	0.0328186i	−0.0798095	−	0.996810i	$-0.525431\pi$
$13$	0.671077	−	0.118329i	0.186123	−	0.0328186i	0.265933	+	0.963992i	$0.414320\pi$
$14$		0			0
$15$	1.27582	+	1.46760i	0.329415	+	0.378932i
$16$		0			0
$17$	0.907443	+	1.57174i	0.220087	+	0.381202i	0.954834	−	0.297139i	$-0.0960324\pi$
$17$	0.907443	+	1.57174i	0.220087	+	0.381202i	−0.734747	+	0.678341i	$0.762699\pi$
$18$		0			0
$19$	2.96777	+	1.71344i	0.680853	+	0.393091i	0.800176	−	0.599765i	$-0.204739\pi$
$19$	2.96777	+	1.71344i	0.680853	+	0.393091i	−0.119323	+	0.992855i	$0.538073\pi$
$20$		0			0
$21$	−2.26785	+	0.870601i	−0.494885	+	0.189981i
$22$		0			0
$23$	3.62278	+	1.31858i	0.755401	+	0.274944i	0.690877	−	0.722973i	$-0.257225\pi$
$23$	3.62278	+	1.31858i	0.755401	+	0.274944i	0.0645244	+	0.997916i	$0.479447\pi$
$24$		0			0
$25$	0.649354	−	3.68267i	0.129871	−	0.736534i
$26$		0			0
$27$	5.18901	−	0.272275i	0.998626	−	0.0523993i
$28$		0			0
$29$	−3.92395	−	0.691898i	−0.728659	−	0.128482i	−0.203001	−	0.979179i	$-0.565070\pi$
$29$	−3.92395	−	0.691898i	−0.728659	−	0.128482i	−0.525657	+	0.850696i	$0.676181\pi$
$30$		0			0
$31$	6.21468	+	2.26196i	1.11619	+	0.406260i	0.833260	−	0.552881i	$-0.186471\pi$
$31$	6.21468	+	2.26196i	1.11619	+	0.406260i	0.282930	+	0.959141i	$0.408694\pi$
$32$		0			0
$33$	1.79434	−	2.21592i	0.312354	−	0.385742i
$34$		0			0
$35$	−1.36367	−	0.787317i	−0.230503	−	0.133081i
$36$		0			0
$37$	−3.83532	+	2.21432i	−0.630522	+	0.364032i	−0.780954	−	0.624588i	$-0.785267\pi$
$37$	−3.83532	+	2.21432i	−0.630522	+	0.364032i	0.150432	+	0.988620i	$0.451934\pi$
$38$		0			0
$39$	1.15858	−	0.225231i	0.185521	−	0.0360658i
$40$		0			0
$41$	0.952217	+	5.40029i	0.148711	+	0.843384i	0.964312	+	0.264769i	$0.0852956\pi$
$41$	0.952217	+	5.40029i	0.148711	+	0.843384i	−0.815601	+	0.578615i	$0.803593\pi$
$42$		0			0
$43$	−7.26017	+	8.65234i	−1.10717	+	1.31947i	−0.164257	+	0.986418i	$0.552523\pi$
$43$	−7.26017	+	8.65234i	−1.10717	+	1.31947i	−0.942909	+	0.333051i	$0.891922\pi$
$44$		0			0
$45$	2.25386	+	2.50295i	0.335986	+	0.373118i
$46$		0			0
$47$	11.5469	−	4.20273i	1.68429	−	0.613031i	0.690402	−	0.723426i	$-0.257434\pi$
$47$	11.5469	−	4.20273i	1.68429	−	0.613031i	0.993888	+	0.110395i	$0.0352116\pi$
$48$		0			0
$49$	−3.85548	+	3.23513i	−0.550783	+	0.462162i
$50$		0			0
$51$	1.61907	+	2.69445i	0.226715	+	0.377298i
$52$		0			0
$53$		−	6.89741i		−	0.947432i	−0.880678	−	0.473716i	$-0.842912\pi$
$53$		−	6.89741i		−	0.947432i	0.880678	−	0.473716i	$-0.157088\pi$
$54$		0			0
$55$	1.84824			0.249216
$56$		0			0
$57$	5.19140	+	2.87750i	0.687618	+	0.381134i
$58$		0			0
$59$	−6.78921	−	8.09106i	−0.883880	−	1.05337i	−0.998203	−	0.0599230i	$-0.980914\pi$
$59$	−6.78921	−	8.09106i	−0.883880	−	1.05337i	0.114323	−	0.993444i	$-0.463530\pi$
$60$		0			0
$61$	−1.24084	−	3.40917i	−0.158873	−	0.436499i	0.834560	−	0.550917i	$-0.185722\pi$
$61$	−1.24084	−	3.40917i	−0.158873	−	0.436499i	−0.993433	+	0.114418i	$0.963500\pi$
$62$		0			0
$63$	−3.90108	+	1.57633i	−0.491490	+	0.198599i
$64$		0			0
$65$	0.586070	+	0.491771i	0.0726930	+	0.0609967i
$66$		0			0
$67$	−11.9425	+	2.10578i	−1.45901	+	0.257263i	−0.846156	−	0.532935i	$-0.821089\pi$
$67$	−11.9425	+	2.10578i	−1.45901	+	0.257263i	−0.612852	+	0.790198i	$0.709978\pi$
$68$		0			0
$69$	6.31378	+	2.17386i	0.760090	+	0.261702i
$70$		0			0
$71$	−6.80355	−	11.7841i	−0.807432	−	1.39851i	−0.914637	−	0.404277i	$-0.867523\pi$
$71$	−6.80355	−	11.7841i	−0.807432	−	1.39851i	0.107204	−	0.994237i	$-0.465810\pi$
$72$		0			0
$73$	4.73823	−	8.20685i	0.554567	−	0.960539i	−0.443370	−	0.896339i	$-0.646217\pi$
$73$	4.73823	−	8.20685i	0.554567	−	0.960539i	0.997937	−	0.0642000i	$-0.0204496\pi$
$74$		0			0
$75$	1.01309	−	6.39725i	0.116981	−	0.738691i
$76$		0			0
$77$	−0.789660	+	2.16957i	−0.0899901	+	0.247246i
$78$		0			0
$79$	−1.59290	+	9.03380i	−0.179215	+	1.01638i	0.753949	+	0.656933i	$0.228146\pi$
$79$	−1.59290	+	9.03380i	−0.179215	+	1.01638i	−0.933165	+	0.359449i	$0.882965\pi$
$80$		0			0
$81$	8.97802	−	0.628568i	0.997558	−	0.0698409i
$82$		0			0
$83$	1.29853	+	0.228966i	0.142532	+	0.0251322i	0.244459	−	0.969660i	$-0.421390\pi$
$83$	1.29853	+	0.228966i	0.142532	+	0.0251322i	−0.101927	+	0.994792i	$0.532501\pi$
$84$		0			0
$85$	−0.696908	+	1.91474i	−0.0755903	+	0.207683i
$86$		0			0
$87$	−6.81638	−	1.07946i	−0.730792	−	0.115730i
$88$		0			0
$89$	−3.52339	+	6.10270i	−0.373479	+	0.646884i	−0.990098	−	0.140377i	$-0.955168\pi$
$89$	−3.52339	+	6.10270i	−0.373479	+	0.646884i	0.616619	+	0.787262i	$0.288502\pi$
$90$		0			0
$91$	−0.827669	+	0.477855i	−0.0867633	+	0.0500928i
$92$		0			0
$93$	10.8310	+	3.72914i	1.12312	+	0.386694i
$94$		0			0
$95$	0.668104	+	3.78901i	0.0685460	+	0.388744i
$96$		0			0
$97$	−6.33275	−	5.31381i	−0.642993	−	0.539535i	0.261943	−	0.965083i	$-0.415637\pi$
$97$	−6.33275	−	5.31381i	−0.642993	−	0.539535i	−0.904936	+	0.425548i	$0.860081\pi$
$98$		0			0
$99$	3.04035	−	3.89180i	0.305566	−	0.391141i
$100$		0			0
$101$	−6.04137	−	16.5985i	−0.601139	−	1.65162i	−0.748971	−	0.662603i	$-0.769452\pi$
$101$	−6.04137	−	16.5985i	−0.601139	−	1.65162i	0.147832	−	0.989012i	$-0.452770\pi$
$102$		0			0
$103$	2.98038	−	2.50084i	0.293666	−	0.246415i	−0.484036	−	0.875048i	$-0.660830\pi$
$103$	2.98038	−	2.50084i	0.293666	−	0.246415i	0.777702	+	0.628633i	$0.216385\pi$
$104$		0			0
$105$	−2.38542	−	1.32219i	−0.232793	−	0.129033i
$106$		0			0
$107$		−	4.16409i		−	0.402558i	−0.979534	−	0.201279i	$-0.935490\pi$
$107$		−	4.16409i		−	0.402558i	0.979534	−	0.201279i	$-0.0645098\pi$
$108$		0			0
$109$			20.6082i			1.97391i	0.161002	+	0.986954i	$0.448527\pi$
$109$			20.6082i			1.97391i	−0.161002	+	0.986954i	$0.551473\pi$
$110$		0			0
$111$	−6.57493	+	3.95081i	−0.624065	+	0.374994i
$112$		0			0
$113$	2.03205	−	1.70510i	0.191160	−	0.160402i	−0.542185	−	0.840259i	$-0.682403\pi$
$113$	2.03205	−	1.70510i	0.191160	−	0.160402i	0.733344	+	0.679857i	$0.237958\pi$
$114$		0			0
$115$	1.48041	+	4.06739i	0.138049	+	0.379286i
$116$		0			0
$117$	1.99960	−	0.425116i	0.184863	−	0.0393020i
$118$		0			0
$119$	−1.94988	−	1.63615i	−0.178745	−	0.149985i
$120$		0			0
$121$	1.43955	+	8.16407i	0.130868	+	0.742188i
$122$		0			0
$123$	1.81248	+	9.32333i	0.163426	+	0.840656i
$124$		0			0
$125$	8.49749	−	4.90603i	0.760039	−	0.438809i
$126$		0			0
$127$	2.14785	−	3.72019i	0.190591	−	0.330113i	−0.754855	−	0.655891i	$-0.772293\pi$
$127$	2.14785	−	3.72019i	0.190591	−	0.330113i	0.945446	+	0.325778i	$0.105626\pi$
$128$		0			0
$129$	−12.3112	+	15.2037i	−1.08394	+	1.33861i
$130$		0			0
$131$	2.70846	−	7.44142i	0.236639	−	0.650160i	−0.763352	−	0.645982i	$-0.776448\pi$
$131$	2.70846	−	7.44142i	0.236639	−	0.650160i	0.999991	−	0.00417788i	$-0.00132986\pi$
$132$		0			0
$133$	−4.73321	−	0.834593i	−0.410422	−	0.0723684i
$134$		0			0
$135$	3.97896	+	4.26637i	0.342454	+	0.367190i
$136$		0			0
$137$	2.73472	−	15.5094i	0.233643	−	1.32506i	−0.611809	−	0.791006i	$-0.709558\pi$
$137$	2.73472	−	15.5094i	0.233643	−	1.32506i	0.845452	−	0.534051i	$-0.179331\pi$
$138$		0			0
$139$	0.133147	−	0.365819i	0.0112934	−	0.0310283i	−0.933918	−	0.357488i	$-0.883633\pi$
$139$	0.133147	−	0.365819i	0.0112934	−	0.0310283i	0.945211	+	0.326459i	$0.105856\pi$
$140$		0			0
$141$	19.8696	−	7.62770i	1.67332	−	0.642368i
$142$		0			0
$143$	0.560885	−	0.971482i	0.0469036	−	0.0812394i
$144$		0			0
$145$	−2.23674	−	3.87415i	−0.185751	−	0.321731i
$146$		0			0
$147$	−6.57896	+	5.71924i	−0.542623	+	0.471715i
$148$		0			0
$149$	−11.6562	+	2.05530i	−0.954913	+	0.168377i	−0.629331	−	0.777137i	$-0.716671\pi$
$149$	−11.6562	+	2.05530i	−0.954913	+	0.168377i	−0.325581	+	0.945514i	$0.605560\pi$
$150$		0			0
$151$	−7.05111	−	5.91658i	−0.573811	−	0.481485i	0.309097	−	0.951031i	$-0.399973\pi$
$151$	−7.05111	−	5.91658i	−0.573811	−	0.481485i	−0.882908	+	0.469546i	$0.844418\pi$
$152$		0			0
$153$	2.88542	+	4.61721i	0.233273	+	0.373279i
$154$		0			0
$155$	2.53957	+	6.97740i	0.203983	+	0.560438i
$156$		0			0
$157$	8.84016	+	10.5353i	0.705521	+	0.840807i	0.993139	−	0.116938i	$-0.0373078\pi$
$157$	8.84016	+	10.5353i	0.705521	+	0.840807i	−0.287618	+	0.957745i	$0.592863\pi$
$158$		0			0
$159$	−0.208751	−	11.9448i	−0.0165550	−	0.947288i
$160$		0			0
$161$	−5.40706			−0.426136
$162$		0			0
$163$		−	12.7196i		−	0.996272i	−0.867099	−	0.498136i	$-0.834018\pi$
$163$		−	12.7196i		−	0.996272i	0.867099	−	0.498136i	$-0.165982\pi$
$164$		0			0
$165$	3.20075	−	0.0559371i	0.249178	−	0.00435470i
$166$		0			0
$167$	−15.1696	+	12.7288i	−1.17386	+	0.984986i	−0.173861	+	0.984770i	$0.555624\pi$
$167$	−15.1696	+	12.7288i	−1.17386	+	0.984986i	−1.00000		0.000215714i	$0.999931\pi$
$168$		0			0
$169$	−11.7797	+	4.28745i	−0.906128	+	0.329804i
$170$		0			0
$171$	9.07748	+	4.82609i	0.694172	+	0.369060i
$172$		0			0
$173$	3.14984	−	3.75384i	0.239478	−	0.285399i	−0.632897	−	0.774236i	$-0.718134\pi$
$173$	3.14984	−	3.75384i	0.239478	−	0.285399i	0.872375	+	0.488837i	$0.162579\pi$
$174$		0			0
$175$	0.910724	+	5.16497i	0.0688443	+	0.390435i
$176$		0			0
$177$	−12.0023	−	13.8065i	−0.902151	−	1.03776i
$178$		0			0
$179$	−3.21176	+	1.85431i	−0.240058	+	0.138598i	−0.615204	−	0.788368i	$-0.710926\pi$
$179$	−3.21176	+	1.85431i	−0.240058	+	0.138598i	0.375145	+	0.926966i	$0.377593\pi$
$180$		0			0
$181$	−14.1322	−	8.15921i	−1.05044	−	0.606470i	−0.127665	−	0.991817i	$-0.540748\pi$
$181$	−14.1322	−	8.15921i	−1.05044	−	0.606470i	−0.922771	+	0.385348i	$0.874081\pi$
$182$		0			0
$183$	−2.25204	−	5.86640i	−0.166476	−	0.433657i
$184$		0			0
$185$	−4.67230	−	1.70058i	−0.343515	−	0.125029i
$186$		0			0
$187$	2.94228	+	0.518804i	0.215161	+	0.0379387i
$188$		0			0
$189$	−6.70813	+	2.84793i	−0.487945	+	0.207157i
$190$		0			0
$191$	−1.19811	+	6.79482i	−0.0866922	+	0.491656i	0.910286	+	0.413979i	$0.135861\pi$
$191$	−1.19811	+	6.79482i	−0.0866922	+	0.491656i	−0.996979	+	0.0776767i	$0.975250\pi$
$192$		0			0
$193$	8.95564	+	3.25959i	0.644641	+	0.234630i	0.643591	−	0.765369i	$-0.277444\pi$
$193$	8.95564	+	3.25959i	0.644641	+	0.234630i	0.00104978	+	0.999999i	$0.499666\pi$
$194$		0			0
$195$	1.02983	+	0.833905i	0.0737477	+	0.0597172i
$196$		0			0
$197$	−1.74001	−	1.00460i	−0.123971	−	0.0715746i	0.436732	−	0.899592i	$-0.356136\pi$
$197$	−1.74001	−	1.00460i	−0.123971	−	0.0715746i	−0.560703	+	0.828017i	$0.689469\pi$
$198$		0			0
$199$	−10.6564	−	18.4573i	−0.755409	−	1.30841i	−0.945171	−	0.326576i	$-0.894105\pi$
$199$	−10.6564	−	18.4573i	−0.755409	−	1.30841i	0.189762	−	0.981830i	$-0.439228\pi$
$200$		0			0
$201$	−20.6181	+	4.00821i	−1.45429	+	0.282717i
$202$		0			0
$203$	5.50336	−	0.970392i	0.386260	−	0.0681081i
$204$		0			0
$205$	−3.95738	+	4.71622i	−0.276395	+	0.329395i
$206$		0			0
$207$	10.9999	+	3.57357i	0.764547	+	0.248381i
$208$		0			0
$209$	5.30113	−	1.92945i	0.366687	−	0.133463i
$210$		0			0
$211$	5.98817	+	7.13642i	0.412242	+	0.491291i	0.931712	−	0.363197i	$-0.118315\pi$
$211$	5.98817	+	7.13642i	0.412242	+	0.491291i	−0.519470	+	0.854489i	$0.673870\pi$
$212$		0			0
$213$	−12.1389	−	20.2016i	−0.831746	−	1.38419i
$214$		0			0
$215$	−12.6810			−0.864838
$216$		0			0
$217$	−9.27552			−0.629664
$218$		0			0
$219$	7.95721	−	14.3559i	0.537699	−	0.970083i
$220$		0			0
$221$	0.794946	+	0.947380i	0.0534739	+	0.0637277i
$222$		0			0
$223$	−23.1313	+	8.41909i	−1.54898	+	0.563784i	−0.968179	−	0.250259i	$-0.919484\pi$
$223$	−23.1313	+	8.41909i	−1.54898	+	0.563784i	−0.580805	+	0.814043i	$0.697262\pi$
$224$		0			0
$225$	1.56084	−	11.1093i	0.104056	−	0.740622i
$226$		0			0
$227$	2.62591	−	3.12944i	0.174288	−	0.207708i	−0.671828	−	0.740707i	$-0.734491\pi$
$227$	2.62591	−	3.12944i	0.174288	−	0.207708i	0.846116	+	0.532999i	$0.178935\pi$
$228$		0			0
$229$	−12.4279	+	2.19138i	−0.821261	+	0.144810i	−0.568463	−	0.822709i	$-0.692462\pi$
$229$	−12.4279	+	2.19138i	−0.821261	+	0.144810i	−0.252798	+	0.967519i	$0.581351\pi$
$230$		0			0
$231$	−1.30186	+	3.78114i	−0.0856561	+	0.248781i
$232$		0			0
$233$	−12.2882	−	21.2839i	−0.805030	−	1.39435i	−0.916271	−	0.400559i	$-0.868816\pi$
$233$	−12.2882	−	21.2839i	−0.805030	−	1.39435i	0.111241	−	0.993793i	$-0.464517\pi$
$234$		0			0
$235$	11.9477	+	6.89802i	0.779383	+	0.449977i
$236$		0			0
$237$	−2.48516	+	15.6928i	−0.161428	+	1.01936i
$238$		0			0
$239$	10.1778	+	3.70441i	0.658346	+	0.239618i	0.649522	−	0.760343i	$-0.274969\pi$
$239$	10.1778	+	3.70441i	0.658346	+	0.239618i	0.00882395	+	0.999961i	$0.497191\pi$
$240$		0			0
$241$	−2.29103	+	12.9931i	−0.147579	+	0.836959i	0.817682	+	0.575670i	$0.195259\pi$
$241$	−2.29103	+	12.9931i	−0.147579	+	0.836959i	−0.965261	+	0.261289i	$0.915852\pi$
$242$		0			0
$243$	15.5290	−	1.36027i	0.996185	−	0.0872611i
$244$		0			0
$245$	−5.56481	−	0.981227i	−0.355523	−	0.0626883i
$246$		0			0
$247$	2.19435	+	0.798678i	0.139623	+	0.0508187i
$248$		0			0
$249$	2.25570	+	0.357219i	0.142949	+	0.0226379i
$250$		0			0
$251$	−17.6367	−	10.1826i	−1.11322	−	0.642717i	−0.173558	−	0.984824i	$-0.555526\pi$
$251$	−17.6367	−	10.1826i	−1.11322	−	0.642717i	−0.939661	+	0.342106i	$0.888860\pi$
$252$		0			0
$253$	5.49629	−	3.17328i	0.345549	−	0.199503i
$254$		0			0
$255$	−1.14895	+	3.33701i	−0.0719498	+	0.208972i
$256$		0			0
$257$	2.07937	+	11.7927i	0.129707	+	0.735606i	0.978400	+	0.206720i	$0.0662790\pi$
$257$	2.07937	+	11.7927i	0.129707	+	0.735606i	−0.848693	+	0.528886i	$0.822610\pi$
$258$		0			0
$259$	3.99249	−	4.75806i	0.248081	−	0.295651i
$260$		0			0
$261$	−11.8372	−	1.66310i	−0.732703	−	0.102943i
$262$		0			0
$263$	9.28725	−	3.38028i	0.572677	−	0.208437i	−0.0394166	−	0.999223i	$-0.512550\pi$
$263$	9.28725	−	3.38028i	0.572677	−	0.208437i	0.612093	+	0.790786i	$0.290328\pi$
$264$		0			0
$265$	5.93218	−	4.97769i	0.364411	−	0.305777i
$266$		0			0
$267$	−5.91706	+	10.6752i	−0.362118	+	0.653312i
$268$		0			0
$269$			5.38944i			0.328600i	0.986410	+	0.164300i	$0.0525365\pi$
$269$			5.38944i			0.328600i	−0.986410	+	0.164300i	$0.947463\pi$
$270$		0			0
$271$	6.24978			0.379647			0.189823	−	0.981818i	$-0.439208\pi$
$271$	6.24978			0.379647			0.189823	+	0.981818i	$0.439208\pi$
$272$		0			0
$273$	−1.41888	+	0.852592i	−0.0858747	+	0.0516012i
$274$		0			0
$275$	−3.95697	−	4.71573i	−0.238614	−	0.284369i
$276$		0			0
$277$	−4.85450	−	13.3376i	−0.291679	−	0.801381i	−0.995821	−	0.0913223i	$-0.970891\pi$
$277$	−4.85450	−	13.3376i	−0.291679	−	0.801381i	0.704143	−	0.710059i	$-0.251332\pi$
$278$		0			0
$279$	18.8698	+	6.13028i	1.12970	+	0.367010i
$280$		0			0
$281$	21.3543	+	17.9184i	1.27389	+	1.06892i	0.994055	+	0.108875i	$0.0347249\pi$
$281$	21.3543	+	17.9184i	1.27389	+	1.06892i	0.279837	+	0.960047i	$0.409720\pi$
$282$		0			0
$283$	−22.0316	+	3.88476i	−1.30964	+	0.230925i	−0.784521	−	0.620102i	$-0.787091\pi$
$283$	−22.0316	+	3.88476i	−1.30964	+	0.230925i	−0.525121	+	0.851027i	$0.675980\pi$
$284$		0			0
$285$	1.27169	+	6.54153i	0.0753283	+	0.387487i
$286$		0			0
$287$	−3.84539	−	6.66042i	−0.226986	−	0.393152i
$288$		0			0
$289$	6.85309	−	11.8699i	0.403123	−	0.698230i
$290$		0			0
$291$	−11.1278	−	9.01072i	−0.652323	−	0.528218i
$292$		0			0
$293$	0.130208	−	0.357742i	0.00760680	−	0.0208995i	−0.935831	−	0.352449i	$-0.885349\pi$
$293$	0.130208	−	0.357742i	0.00760680	−	0.0208995i	0.943438	+	0.331549i	$0.107571\pi$
$294$		0			0
$295$	2.05919	−	11.6782i	0.119891	−	0.679934i
$296$		0			0
$297$	5.14744	−	6.83179i	0.298685	−	0.396421i
$298$		0			0
$299$	2.58719	+	0.456191i	0.149621	+	0.0263822i
$300$		0			0
$301$	5.41797	−	14.8857i	0.312286	−	0.858000i
$302$		0			0
$303$	−10.9647	−	28.5623i	−0.629907	−	1.64086i
$304$		0			0
$305$	2.03661	−	3.52751i	0.116616	−	0.201984i
$306$		0			0
$307$	−9.47107	+	5.46813i	−0.540543	+	0.312083i	−0.745299	−	0.666731i	$-0.767693\pi$
$307$	−9.47107	+	5.46813i	−0.540543	+	0.312083i	0.204756	+	0.978813i	$0.434360\pi$
$308$		0			0
$309$	5.08570	−	4.42112i	0.289315	−	0.251509i
$310$		0			0
$311$	3.17033	+	17.9798i	0.179773	+	1.01954i	0.932490	+	0.361197i	$0.117632\pi$
$311$	3.17033	+	17.9798i	0.179773	+	1.01954i	−0.752717	+	0.658344i	$0.771257\pi$
$312$		0			0
$313$	2.49125	+	2.09041i	0.140814	+	0.118157i	0.710474	−	0.703724i	$-0.248481\pi$
$313$	2.49125	+	2.09041i	0.140814	+	0.118157i	−0.569660	+	0.821880i	$0.692925\pi$
$314$		0			0
$315$	−4.17105	−	2.21756i	−0.235012	−	0.124945i
$316$		0			0
$317$	5.82505	+	16.0042i	0.327167	+	0.898885i	0.988825	+	0.149079i	$0.0476309\pi$
$317$	5.82505	+	16.0042i	0.327167	+	0.898885i	−0.661658	+	0.749806i	$0.730147\pi$
$318$		0			0
$319$	−5.02469	+	4.21621i	−0.281328	+	0.236063i
$320$		0			0
$321$	−0.126027	−	7.21132i	−0.00703412	−	0.402497i
$322$		0			0
$323$			6.21940i			0.346057i
$324$		0			0
$325$		−	2.54819i		−	0.141348i
$326$		0			0
$327$	0.623709	+	35.6890i	0.0344912	+	1.97361i
$328$		0			0
$329$	−13.2020	+	11.0778i	−0.727849	+	0.610737i
$330$		0			0
$331$	1.92215	+	5.28106i	0.105651	+	0.290273i	0.981242	−	0.192780i	$-0.0617502\pi$
$331$	1.92215	+	5.28106i	0.105651	+	0.290273i	−0.875591	+	0.483053i	$0.839528\pi$
$332$		0			0
$333$	−11.2668	+	7.04095i	−0.617417	+	0.385841i
$334$		0			0
$335$	−10.4297	−	8.75156i	−0.569836	−	0.478149i
$336$		0			0
$337$	3.30062	+	18.7188i	0.179796	+	1.01968i	0.932461	+	0.361271i	$0.117657\pi$
$337$	3.30062	+	18.7188i	0.179796	+	1.01968i	−0.752665	+	0.658404i	$0.771232\pi$
$338$		0			0
$339$	3.46748	−	3.01436i	0.188328	−	0.163718i
$340$		0			0
$341$	9.42860	−	5.44360i	0.510587	−	0.294788i
$342$		0			0
$343$	8.43817	−	14.6153i	0.455618	−	0.789154i
$344$		0			0
$345$	2.68685	+	6.99905i	0.144655	+	0.376816i
$346$		0			0
$347$	3.17358	−	8.71933i	0.170366	−	0.468078i	−0.824898	−	0.565282i	$-0.808768\pi$
$347$	3.17358	−	8.71933i	0.170366	−	0.468078i	0.995265	+	0.0972035i	$0.0309898\pi$
$348$		0			0
$349$	7.31028	+	1.28900i	0.391310	+	0.0689985i	0.365842	−	0.930677i	$-0.380781\pi$
$349$	7.31028	+	1.28900i	0.391310	+	0.0689985i	0.0254684	+	0.999676i	$0.491892\pi$
$350$		0			0
$351$	3.45001	−	0.796728i	0.184148	−	0.0425262i
$352$		0			0
$353$	4.91102	−	27.8518i	0.261387	−	1.48240i	−0.517742	−	0.855537i	$-0.673227\pi$
$353$	4.91102	−	27.8518i	0.261387	−	1.48240i	0.779129	−	0.626864i	$-0.215662\pi$
$354$		0			0
$355$	5.22506	−	14.3557i	0.277318	−	0.761924i
$356$		0			0
$357$	−3.42630	−	2.77444i	−0.181339	−	0.146839i
$358$		0			0
$359$	−8.47821	+	14.6847i	−0.447463	+	0.775029i	−0.998220	−	0.0596369i	$-0.981006\pi$
$359$	−8.47821	+	14.6847i	−0.447463	+	0.775029i	0.550757	+	0.834666i	$0.314339\pi$
$360$		0			0
$361$	−3.62823	−	6.28428i	−0.190960	−	0.330752i
$362$		0			0
$363$	2.74007	+	14.0949i	0.143817	+	0.739788i
$364$		0			0
$365$	10.4778	−	1.84753i	0.548435	−	0.0967039i
$366$		0			0
$367$	−6.19539	−	5.19855i	−0.323397	−	0.271362i	0.466606	−	0.884465i	$-0.345477\pi$
$367$	−6.19539	−	5.19855i	−0.323397	−	0.271362i	−0.790003	+	0.613103i	$0.789921\pi$
$368$		0			0
$369$	3.42099	+	16.0912i	0.178090	+	0.837673i
$370$		0			0
$371$	3.30859	+	9.09028i	0.171773	+	0.471944i
$372$		0			0
$373$	14.1644	+	16.8805i	0.733405	+	0.874038i	0.995859	−	0.0909062i	$-0.0289763\pi$
$373$	14.1644	+	16.8805i	0.733405	+	0.874038i	−0.262454	+	0.964944i	$0.584532\pi$
$374$		0			0
$375$	14.5674	−	8.75337i	0.752255	−	0.452022i
$376$		0			0
$377$	−2.71514			−0.139837
$378$		0			0
$379$		−	9.42240i		−	0.483996i	−0.970277	−	0.241998i	$-0.922197\pi$
$379$		−	9.42240i		−	0.483996i	0.970277	−	0.241998i	$-0.0778027\pi$
$380$		0			0
$381$	3.60703	−	6.50757i	0.184794	−	0.333393i
$382$		0			0
$383$	13.2473	−	11.1158i	0.676904	−	0.567989i	−0.238196	−	0.971217i	$-0.576556\pi$
$383$	13.2473	−	11.1158i	0.676904	−	0.567989i	0.915100	+	0.403228i	$0.132112\pi$
$384$		0			0
$385$	−2.43584	+	0.886573i	−0.124142	+	0.0451840i
$386$		0			0
$387$	−20.8602	+	26.7022i	−1.06039	+	1.35735i
$388$		0			0
$389$	−15.9667	+	19.0284i	−0.809546	+	0.964780i	−0.999856	−	0.0169443i	$-0.994606\pi$
$389$	−15.9667	+	19.0284i	−0.809546	+	0.964780i	0.190310	+	0.981724i	$0.439051\pi$
$390$		0			0
$391$	1.21500	+	6.89059i	0.0614451	+	0.348472i
$392$		0			0
$393$	4.46525	−	12.9689i	0.225242	−	0.654196i
$394$		0			0
$395$	−8.91916	+	5.14948i	−0.448772	+	0.259098i
$396$		0			0
$397$	5.94466	+	3.43215i	0.298354	+	0.172255i	0.641703	−	0.766953i	$-0.278228\pi$
$397$	5.94466	+	3.43215i	0.298354	+	0.172255i	−0.343349	+	0.939208i	$0.611561\pi$
$398$		0			0
$399$	−8.22217	−	1.30209i	−0.411624	−	0.0651858i
$400$		0			0
$401$	11.8463	+	4.31169i	0.591574	+	0.215315i	0.620422	−	0.784268i	$-0.286961\pi$
$401$	11.8463	+	4.31169i	0.591574	+	0.215315i	−0.0288475	+	0.999584i	$0.509184\pi$
$402$		0			0
$403$	4.43819	+	0.782572i	0.221082	+	0.0389827i
$404$		0			0
$405$	7.01983	+	7.26801i	0.348818	+	0.361150i
$406$		0			0
$407$	−1.26597	+	7.17969i	−0.0627519	+	0.355884i
$408$		0			0
$409$	32.0334	+	11.6592i	1.58395	+	0.576510i	0.976058	−	0.217510i	$-0.0697935\pi$
$409$	32.0334	+	11.6592i	1.58395	+	0.576510i	0.607891	+	0.794020i	$0.292016\pi$
$410$		0			0
$411$	4.26657	−	26.9417i	0.210454	−	1.32894i
$412$		0			0
$413$	12.8288	+	7.40673i	0.631266	+	0.364462i
$414$		0			0
$415$	0.740192	+	1.28205i	0.0363346	+	0.0629334i
$416$		0			0
$417$	0.219511	−	0.637549i	0.0107495	−	0.0312209i
$418$		0			0
$419$	−10.9419	+	1.92935i	−0.534545	+	0.0942547i	−0.434403	−	0.900718i	$-0.643041\pi$
$419$	−10.9419	+	1.92935i	−0.534545	+	0.0942547i	−0.100142	+	0.994973i	$0.531930\pi$
$420$		0			0
$421$	12.6851	−	15.1175i	0.618232	−	0.736780i	−0.362533	−	0.931971i	$-0.618088\pi$
$421$	12.6851	−	15.1175i	0.618232	−	0.736780i	0.980765	+	0.195190i	$0.0625325\pi$
$422$		0			0
$423$	34.1790	−	13.8109i	1.66184	−	0.671509i
$424$		0			0
$425$	6.37744	−	2.32120i	0.309352	−	0.112595i
$426$		0			0
$427$	3.27066	+	3.89782i	0.158278	+	0.188629i
$428$		0			0
$429$	0.941932	−	1.69937i	0.0454769	−	0.0820466i
$430$		0			0
$431$	0.293057			0.0141161			0.00705803	−	0.999975i	$-0.497753\pi$
$431$	0.293057			0.0141161			0.00705803	+	0.999975i	$0.497753\pi$
$432$		0			0
$433$	18.2482			0.876954			0.438477	−	0.898742i	$-0.355518\pi$
$433$	18.2482			0.876954			0.438477	+	0.898742i	$0.355518\pi$
$434$		0			0
$435$	−3.99081	−	6.64151i	−0.191345	−	0.318436i
$436$		0			0
$437$	8.49225	+	10.1207i	0.406239	+	0.484137i
$438$		0			0
$439$	−0.920498	+	0.335034i	−0.0439330	+	0.0159903i	−0.363893	−	0.931441i	$-0.618553\pi$
$439$	−0.920498	+	0.335034i	−0.0439330	+	0.0159903i	0.319960	+	0.947431i	$0.396330\pi$
$440$		0			0
$441$	−11.2203	+	10.1036i	−0.534298	+	0.481125i
$442$		0			0
$443$	−3.31318	+	3.94849i	−0.157414	+	0.187599i	−0.838987	−	0.544151i	$-0.816852\pi$
$443$	−3.31318	+	3.94849i	−0.157414	+	0.187599i	0.681573	+	0.731750i	$0.261296\pi$
$444$		0			0
$445$	−7.79143	+	1.37384i	−0.369349	+	0.0651262i
$446$		0			0
$447$	−20.1238	+	3.91212i	−0.951825	+	0.185037i
$448$		0			0
$449$	−6.21921	−	10.7720i	−0.293503	−	0.508362i	0.681133	−	0.732160i	$-0.261488\pi$
$449$	−6.21921	−	10.7720i	−0.293503	−	0.508362i	−0.974635	+	0.223798i	$0.928154\pi$
$450$		0			0
$451$	7.81771	+	4.51356i	0.368122	+	0.212535i
$452$		0			0
$453$	−12.3901	−	10.0329i	−0.582137	−	0.471385i
$454$		0			0
$455$	−1.00829	−	0.366988i	−0.0472695	−	0.0172047i
$456$		0			0
$457$	−4.18789	+	23.7507i	−0.195901	+	1.11101i	0.715228	+	0.698891i	$0.246323\pi$
$457$	−4.18789	+	23.7507i	−0.195901	+	1.11101i	−0.911129	+	0.412121i	$0.864788\pi$
$458$		0			0
$459$	5.13668	+	7.90869i	0.239760	+	0.369146i
$460$		0			0
$461$	36.0117	+	6.34983i	1.67723	+	0.295741i	0.929654	−	0.368434i	$-0.120106\pi$
$461$	36.0117	+	6.34983i	1.67723	+	0.295741i	0.747577	+	0.664175i	$0.231217\pi$
$462$		0			0
$463$	21.2745	+	7.74329i	0.988711	+	0.359861i	0.785221	−	0.619216i	$-0.212549\pi$
$463$	21.2745	+	7.74329i	0.988711	+	0.359861i	0.203490	+	0.979077i	$0.434772\pi$
$464$		0			0
$465$	4.60916	+	12.0065i	0.213744	+	0.556788i
$466$		0			0
$467$	20.1982	+	11.6614i	0.934662	+	0.539628i	0.888283	−	0.459296i	$-0.151898\pi$
$467$	20.1982	+	11.6614i	0.934662	+	0.539628i	0.0463792	+	0.998924i	$0.485232\pi$
$468$		0			0
$469$	14.7292	−	8.50392i	0.680132	−	0.392674i
$470$		0			0
$471$	15.6281	+	17.9773i	0.720105	+	0.828351i
$472$		0			0
$473$	3.22874	+	18.3111i	0.148458	+	0.841945i
$474$		0			0
$475$	8.23718	−	9.81669i	0.377948	−	0.450420i
$476$		0			0
$477$	−0.723024	−	20.6796i	−0.0331050	−	0.946854i
$478$		0			0
$479$	37.4812	−	13.6420i	1.71256	−	0.623320i	0.715405	−	0.698710i	$-0.246242\pi$
$479$	37.4812	−	13.6420i	1.71256	−	0.623320i	0.997154	+	0.0753898i	$0.0240201\pi$
$480$		0			0
$481$	−2.31177	+	1.93981i	−0.105408	+	0.0884477i
$482$		0			0
$483$	−9.36387	+	0.163645i	−0.426071	+	0.00744611i
$484$		0			0
$485$		−	9.28139i		−	0.421446i
$486$		0			0
$487$	32.0323			1.45152			0.725762	−	0.687946i	$-0.241488\pi$
$487$	32.0323			1.45152			0.725762	+	0.687946i	$0.241488\pi$
$488$		0			0
$489$	−0.384959	−	22.0276i	−0.0174084	−	0.996120i
$490$		0			0
$491$	16.9415	+	20.1901i	0.764559	+	0.911166i	0.998127	−	0.0611743i	$-0.0194845\pi$
$491$	16.9415	+	20.1901i	0.764559	+	0.911166i	−0.233568	+	0.972341i	$0.575040\pi$
$492$		0			0
$493$	−2.47328	−	6.79527i	−0.111391	−	0.306044i
$494$		0			0
$495$	5.54133	−	0.193742i	0.249064	−	0.00870806i
$496$		0			0
$497$	14.6192	+	12.2670i	0.655762	+	0.550250i
$498$		0			0
$499$	0.796549	−	0.140453i	0.0356584	−	0.00628755i	−0.155790	−	0.987790i	$-0.549792\pi$
$499$	0.796549	−	0.140453i	0.0356584	−	0.00628755i	0.191449	+	0.981503i	$0.438681\pi$
$500$		0			0
$501$	−25.8853	+	22.5027i	−1.15647	+	1.00535i
$502$		0			0
$503$	0.838775	+	1.45280i	0.0373991	+	0.0647772i	0.884119	−	0.467262i	$-0.154759\pi$
$503$	0.838775	+	1.45280i	0.0373991	+	0.0647772i	−0.846720	+	0.532039i	$0.821426\pi$
$504$		0			0
$505$	9.91581	−	17.1747i	0.441248	−	0.764264i
$506$		0			0
$507$	−20.2701	+	7.78145i	−0.900227	+	0.345586i
$508$		0			0
$509$	−2.89525	+	7.95462i	−0.128330	+	0.352583i	−0.987173	−	0.159656i	$-0.948961\pi$
$509$	−2.89525	+	7.95462i	−0.128330	+	0.352583i	0.858843	+	0.512239i	$0.171184\pi$
$510$		0			0
$511$	−2.30792	+	13.0889i	−0.102096	+	0.579018i
$512$		0			0
$513$	15.8663	+	8.08303i	0.700515	+	0.356874i
$514$		0			0
$515$	4.30174	+	0.758513i	0.189557	+	0.0334241i
$516$		0			0
$517$	6.91855	−	19.0085i	0.304277	−	0.835995i
$518$		0			0
$519$	5.34124	−	6.59617i	0.234455	−	0.289540i
$520$		0			0
$521$	1.96303	−	3.40007i	0.0860020	−	0.148960i	−0.819816	−	0.572627i	$-0.805924\pi$
$521$	1.96303	−	3.40007i	0.0860020	−	0.148960i	0.905818	+	0.423668i	$0.139258\pi$
$522$		0			0
$523$	14.9783	−	8.64774i	0.654956	−	0.378139i	−0.135396	−	0.990792i	$-0.543231\pi$
$523$	14.9783	−	8.64774i	0.654956	−	0.378139i	0.790353	+	0.612652i	$0.209897\pi$
$524$		0			0
$525$	1.73350	+	8.91707i	0.0756561	+	0.389173i
$526$		0			0
$527$	2.08426	+	11.8205i	0.0907920	+	0.514907i
$528$		0			0
$529$	−6.23317	−	5.23025i	−0.271008	−	0.227402i
$530$		0			0
$531$	−21.2033	−	23.5467i	−0.920146	−	1.02184i
$532$		0			0
$533$	1.27802	+	3.51134i	0.0553573	+	0.152093i
$534$		0			0
$535$	3.58137	−	3.00512i	0.154836	−	0.129923i
$536$		0			0
$537$	−5.50597	+	3.30848i	−0.237600	+	0.142771i
$538$		0			0
$539$			8.28529i			0.356873i
$540$		0			0
$541$		−	11.4118i		−	0.490630i	−0.969443	−	0.245315i	$-0.921109\pi$
$541$		−	11.4118i		−	0.490630i	0.969443	−	0.245315i	$-0.0788914\pi$
$542$		0			0
$543$	−24.7208	−	13.7023i	−1.06087	−	0.588022i
$544$		0			0
$545$	−17.7243	+	14.8724i	−0.759225	+	0.637065i
$546$		0			0
$547$	−4.84214	−	13.3037i	−0.207035	−	0.568824i	0.792101	−	0.610390i	$-0.208987\pi$
$547$	−4.84214	−	13.3037i	−0.207035	−	0.568824i	−0.999136	+	0.0415665i	$0.986765\pi$
$548$		0			0
$549$	−4.07760	−	10.0912i	−0.174028	−	0.430681i
$550$		0			0
$551$	−10.4598	−	8.77685i	−0.445604	−	0.373906i
$552$		0			0
$553$	−2.23406	−	12.6700i	−0.0950018	−	0.538782i
$554$		0			0
$555$	−8.14290	−	2.80363i	−0.345647	−	0.119008i
$556$		0			0
$557$	−29.6837	+	17.1379i	−1.25774	+	0.726155i	−0.972634	−	0.232342i	$-0.925361\pi$
$557$	−29.6837	+	17.1379i	−1.25774	+	0.726155i	−0.285103	+	0.958497i	$0.592028\pi$
$558$		0			0
$559$	−3.84831	+	6.66547i	−0.162766	+	0.281919i
$560$		0			0
$561$	5.11110	+	0.809409i	0.215791	+	0.0341733i
$562$		0			0
$563$	−11.1729	+	30.6973i	−0.470882	+	1.29374i	0.446162	+	0.894952i	$0.352790\pi$
$563$	−11.1729	+	30.6973i	−0.470882	+	1.29374i	−0.917044	+	0.398786i	$0.869432\pi$
$564$		0			0
$565$	2.93297	+	0.517161i	0.123391	+	0.0217571i
$566$		0			0
$567$	−11.5309	+	5.13504i	−0.484250	+	0.215651i
$568$		0			0
$569$	4.57663	−	25.9553i	0.191862	−	1.08810i	−0.724955	−	0.688797i	$-0.758139\pi$
$569$	4.57663	−	25.9553i	0.191862	−	1.08810i	0.916817	−	0.399308i	$-0.130750\pi$
$570$		0			0
$571$	14.3103	−	39.3171i	0.598865	−	1.64537i	−0.154673	−	0.987966i	$-0.549432\pi$
$571$	14.3103	−	39.3171i	0.598865	−	1.64537i	0.753539	−	0.657404i	$-0.228345\pi$
$572$		0			0
$573$	−1.86922	+	11.8034i	−0.0780880	+	0.493095i
$574$		0			0
$575$	7.20837	−	12.4853i	0.300610	−	0.520672i
$576$		0			0
$577$	−6.39933	−	11.0840i	−0.266408	−	0.461431i	0.701524	−	0.712646i	$-0.252503\pi$
$577$	−6.39933	−	11.0840i	−0.266408	−	0.461431i	−0.967931	+	0.251215i	$0.919170\pi$
$578$		0			0
$579$	15.6079	+	5.37387i	0.648643	+	0.223330i
$580$		0			0
$581$	−1.82120	+	0.321126i	−0.0755560	+	0.0133226i
$582$		0			0
$583$	−8.69808	−	7.29856i	−0.360238	−	0.302275i
$584$		0			0
$585$	1.80869	+	1.41298i	0.0747800	+	0.0584194i
$586$		0			0
$587$	4.86117	+	13.3560i	0.200642	+	0.551260i	0.998681	−	0.0513464i	$-0.0163513\pi$
$587$	4.86117	+	13.3560i	0.200642	+	0.551260i	−0.798039	+	0.602606i	$0.794129\pi$
$588$		0			0
$589$	14.5680	+	17.3615i	0.600264	+	0.715367i
$590$		0			0
$591$	−3.04374	−	1.68709i	−0.125203	−	0.0693975i
$592$		0			0
$593$	−22.4225			−0.920782			−0.460391	−	0.887716i	$-0.652291\pi$
$593$	−22.4225			−0.920782			−0.460391	+	0.887716i	$0.652291\pi$
$594$		0			0
$595$		−	2.85778i		−	0.117158i
$596$		0			0
$597$	−19.0131	−	31.6417i	−0.778156	−	1.29501i
$598$		0			0
$599$	−3.21966	+	2.70162i	−0.131552	+	0.110385i	−0.706190	−	0.708023i	$-0.749587\pi$
$599$	−3.21966	+	2.70162i	−0.131552	+	0.110385i	0.574638	+	0.818408i	$0.305143\pi$
$600$		0			0
$601$	−12.5218	+	4.55756i	−0.510775	+	0.185907i	−0.584534	−	0.811369i	$-0.698723\pi$
$601$	−12.5218	+	4.55756i	−0.510775	+	0.185907i	0.0737590	+	0.997276i	$0.476500\pi$
$602$		0			0
$603$	−35.5849	+	7.56537i	−1.44913	+	0.308086i
$604$		0			0
$605$	−5.98270	+	7.12991i	−0.243231	+	0.289872i
$606$		0			0
$607$	5.79180	+	32.8469i	0.235082	+	1.33322i	0.842441	+	0.538789i	$0.181118\pi$
$607$	5.79180	+	32.8469i	0.235082	+	1.33322i	−0.607359	+	0.794428i	$0.707771\pi$
$608$		0			0
$609$	9.50128	−	1.84707i	0.385011	−	0.0748471i
$610$		0			0
$611$	7.25156	−	4.18669i	0.293367	−	0.169375i
$612$		0			0
$613$	−11.1640	−	6.44552i	−0.450908	−	0.260332i	0.257305	−	0.966330i	$-0.417165\pi$
$613$	−11.1640	−	6.44552i	−0.450908	−	0.260332i	−0.708214	+	0.705998i	$0.750499\pi$
$614$		0			0
$615$	−6.71060	+	8.28726i	−0.270597	+	0.334174i
$616$		0			0
$617$	20.7471	+	7.55132i	0.835246	+	0.304005i	0.724010	−	0.689789i	$-0.242297\pi$
$617$	20.7471	+	7.55132i	0.835246	+	0.304005i	0.111236	+	0.993794i	$0.464519\pi$
$618$		0			0
$619$	0.110454	+	0.0194760i	0.00443952	+	0.000782807i	0.175867	−	0.984414i	$-0.443727\pi$
$619$	0.110454	+	0.0194760i	0.00443952	+	0.000782807i	−0.171428	+	0.985197i	$0.554838\pi$
$620$		0			0
$621$	19.1577	+	5.85575i	0.768770	+	0.234983i
$622$		0			0
$623$	1.71619	−	9.73302i	0.0687579	−	0.389945i
$624$		0			0
$625$	−7.21791	−	2.62710i	−0.288716	−	0.105084i
$626$		0			0
$627$	9.12203	−	3.50184i	0.364299	−	0.139850i
$628$		0			0
$629$	−6.96066	−	4.01874i	−0.277540	−	0.160238i
$630$		0			0
$631$	7.25883	+	12.5727i	0.288970	+	0.500510i	0.973564	−	0.228414i	$-0.0733540\pi$
$631$	7.25883	+	12.5727i	0.288970	+	0.500510i	−0.684595	+	0.728924i	$0.740021\pi$
$632$		0			0
$633$	10.5862	+	12.1775i	0.420764	+	0.484013i
$634$		0			0
$635$	4.74963	−	0.837488i	0.188483	−	0.0332347i
$636$		0			0
$637$	−2.20451	+	2.62724i	−0.0873460	+	0.104095i
$638$		0			0
$639$	−21.6334	−	34.6175i	−0.855806	−	1.36945i
$640$		0			0
$641$	−26.9693	+	9.81603i	−1.06522	+	0.387710i	−0.814389	−	0.580320i	$-0.802928\pi$
$641$	−26.9693	+	9.81603i	−1.06522	+	0.387710i	−0.250835	+	0.968030i	$0.580705\pi$
$642$		0			0
$643$	16.9076	+	20.1497i	0.666772	+	0.794628i	0.988341	−	0.152258i	$-0.0486546\pi$
$643$	16.9076	+	20.1497i	0.666772	+	0.794628i	−0.321569	+	0.946886i	$0.604210\pi$
$644$		0			0
$645$	−21.9608	+	0.383792i	−0.864706	+	0.0151118i
$646$		0			0
$647$	−31.9679			−1.25679			−0.628394	−	0.777895i	$-0.716287\pi$
$647$	−31.9679			−1.25679			−0.628394	+	0.777895i	$0.716287\pi$
$648$		0			0
$649$	−17.3874			−0.682516
$650$		0			0
$651$	−16.0632	+	0.280725i	−0.629567	+	0.0110025i
$652$		0			0
$653$	−24.4383	−	29.1244i	−0.956344	−	1.13973i	−0.990109	−	0.140297i	$-0.955194\pi$
$653$	−24.4383	−	29.1244i	−0.956344	−	1.13973i	0.0337653	−	0.999430i	$-0.489250\pi$
$654$		0			0
$655$	8.35469	−	3.04086i	0.326445	−	0.118816i
$656$		0			0
$657$	13.3457	−	25.1022i	0.520666	−	0.979330i
$658$		0			0
$659$	13.8230	−	16.4736i	0.538469	−	0.641722i	−0.426375	−	0.904546i	$-0.640210\pi$
$659$	13.8230	−	16.4736i	0.538469	−	0.641722i	0.964844	+	0.262825i	$0.0846540\pi$
$660$		0			0
$661$	−40.0325	+	7.05881i	−1.55708	+	0.274556i	−0.884883	−	0.465813i	$-0.845762\pi$
$661$	−40.0325	+	7.05881i	−1.55708	+	0.274556i	−0.672201	+	0.740369i	$0.734651\pi$
$662$		0			0
$663$	1.40535	+	1.61660i	0.0545793	+	0.0627836i
$664$		0			0
$665$	−2.69804	−	4.67315i	−0.104626	−	0.181217i
$666$		0			0
$667$	−13.3033	−	7.68064i	−0.515104	−	0.297396i
$668$		0			0
$669$	−39.8036	+	15.2801i	−1.53890	+	0.590764i
$670$		0			0
$671$	−5.61218	−	2.04267i	−0.216656	−	0.0788563i
$672$		0			0
$673$	7.13129	−	40.4435i	0.274891	−	1.55898i	−0.464417	−	0.885616i	$-0.653736\pi$
$673$	7.13129	−	40.4435i	0.274891	−	1.55898i	0.739308	−	0.673367i	$-0.235153\pi$
$674$		0			0
$675$	2.36681	−	19.2862i	0.0910985	−	0.742328i
$676$		0			0
$677$	−17.2637	−	3.04406i	−0.663499	−	0.116993i	−0.168251	−	0.985744i	$-0.553812\pi$
$677$	−17.2637	−	3.04406i	−0.663499	−	0.116993i	−0.495248	+	0.868752i	$0.664923\pi$
$678$		0			0
$679$	10.8951	+	3.96547i	0.418114	+	0.152181i
$680$		0			0
$681$	4.45280	−	5.49899i	0.170632	−	0.210722i
$682$		0			0
$683$	34.2463	+	19.7721i	1.31040	+	0.756558i	0.982162	−	0.188038i	$-0.0602127\pi$
$683$	34.2463	+	19.7721i	1.31040	+	0.756558i	0.328235	+	0.944596i	$0.393546\pi$
$684$		0			0
$685$	15.3126	−	8.84073i	0.585064	−	0.337787i
$686$		0			0
$687$	−21.4562	+	4.17113i	−0.818605	+	0.159139i
$688$		0			0
$689$	−0.816164	−	4.62869i	−0.0310934	−	0.176339i
$690$		0			0
$691$	13.9569	−	16.6332i	0.530946	−	0.632757i	−0.432186	−	0.901784i	$-0.642258\pi$
$691$	13.9569	−	16.6332i	0.530946	−	0.632757i	0.963133	+	0.269027i	$0.0867022\pi$
$692$		0			0
$693$	−2.14011	+	6.58752i	−0.0812960	+	0.250239i
$694$		0			0
$695$	0.410715	−	0.149488i	0.0155793	−	0.00567040i
$696$		0			0
$697$	−7.62376	+	6.39709i	−0.288770	+	0.242307i
$698$		0			0
$699$	−21.9248	−	36.4872i	−0.829271	−	1.38007i
$700$		0			0
$701$			24.5820i			0.928448i	0.885718	+	0.464224i	$0.153667\pi$
$701$			24.5820i			0.928448i	−0.885718	+	0.464224i	$0.846333\pi$
$702$		0			0
$703$	−15.1764			−0.572390
$704$		0			0
$705$	20.8997	+	11.5843i	0.787127	+	0.436290i
$706$		0			0
$707$	15.9242	+	18.9777i	0.598889	+	0.713729i
$708$		0			0
$709$	14.8834	+	40.8919i	0.558959	+	1.53573i	0.821151	+	0.570711i	$0.193332\pi$
$709$	14.8834	+	40.8919i	0.558959	+	1.53573i	−0.262193	+	0.965016i	$0.584446\pi$
$710$		0			0
$711$	−3.82882	+	27.2518i	−0.143592	+	1.02202i
$712$		0			0
$713$	19.5318	+	16.3891i	0.731473	+	0.613778i
$714$		0			0
$715$	1.24031	−	0.218700i	0.0463850	−	0.00817892i
$716$		0			0
$717$	17.7379	+	6.10722i	0.662433	+	0.228078i
$718$		0			0
$719$	−2.30085	−	3.98520i	−0.0858074	−	0.148623i	0.819928	−	0.572467i	$-0.194014\pi$
$719$	−2.30085	−	3.98520i	−0.0858074	−	0.148623i	−0.905735	+	0.423844i	$0.860680\pi$
$720$		0			0
$721$	−2.72831	+	4.72557i	−0.101607	+	0.175989i
$722$		0			0
$723$	−3.57434	+	22.5706i	−0.132931	+	0.839410i
$724$		0			0
$725$	−5.09606	+	14.0013i	−0.189263	+	0.519996i
$726$		0			0
$727$	0.922052	−	5.22921i	0.0341970	−	0.193941i	−0.962923	−	0.269775i	$-0.913051\pi$
$727$	0.922052	−	5.22921i	0.0341970	−	0.193941i	0.997120	+	0.0758339i	$0.0241619\pi$
$728$		0			0
$729$	26.8517	−	2.82568i	0.994509	−	0.104655i
$730$		0			0
$731$	−20.1874	−	3.55958i	−0.746658	−	0.131656i
$732$		0			0
$733$	17.7690	−	48.8201i	0.656315	−	1.80321i	0.0633350	−	0.997992i	$-0.479826\pi$
$733$	17.7690	−	48.8201i	0.656315	−	1.80321i	0.592980	−	0.805217i	$-0.297951\pi$
$734$		0			0
$735$	−9.66676	−	1.53086i	−0.356564	−	0.0564664i
$736$		0			0
$737$	−9.98153	+	17.2885i	−0.367674	+	0.636831i
$738$		0			0
$739$	−8.21344	+	4.74203i	−0.302136	+	0.174439i	−0.643402	−	0.765528i	$-0.722478\pi$
$739$	−8.21344	+	4.74203i	−0.302136	+	0.174439i	0.341266	+	0.939967i	$0.389144\pi$
$740$		0			0
$741$	3.82432	+	1.31673i	0.140490	+	0.0483712i
$742$		0			0
$743$	−1.45201	−	8.23477i	−0.0532691	−	0.302104i	0.946520	−	0.322646i	$-0.104572\pi$
$743$	−1.45201	−	8.23477i	−0.0532691	−	0.302104i	−0.999789	+	0.0205412i	$0.993461\pi$
$744$		0			0
$745$	−10.1797	−	8.54176i	−0.372954	−	0.312946i
$746$		0			0
$747$	3.91721	+	0.550359i	0.143323	+	0.0201366i
$748$		0			0
$749$	1.99746	+	5.48797i	0.0729855	+	0.200526i
$750$		0			0
$751$	−36.5089	+	30.6346i	−1.33223	+	1.11787i	−0.348680	+	0.937242i	$0.613370\pi$
$751$	−36.5089	+	30.6346i	−1.33223	+	1.11787i	−0.983551	+	0.180632i	$0.942186\pi$
$752$		0			0
$753$	−30.8512	−	17.1002i	−1.12428	−	0.623167i
$754$		0			0
$755$		−	10.3342i		−	0.376101i
$756$		0			0
$757$		−	22.8271i		−	0.829666i	−0.909898	−	0.414833i	$-0.863840\pi$
$757$		−	22.8271i		−	0.829666i	0.909898	−	0.414833i	$-0.136160\pi$
$758$		0			0
$759$	9.42236	−	5.66180i	0.342010	−	0.205510i
$760$		0			0
$761$	−9.00453	+	7.55570i	−0.326414	+	0.273894i	−0.791237	−	0.611510i	$-0.790562\pi$
$761$	−9.00453	+	7.55570i	−0.326414	+	0.273894i	0.464823	+	0.885404i	$0.346118\pi$
$762$		0			0
$763$	−9.88546	−	27.1601i	−0.357878	−	0.983261i
$764$		0			0
$765$	−1.88873	+	5.81376i	−0.0682873	+	0.210197i
$766$		0			0
$767$	−5.51349	−	4.62637i	−0.199081	−	0.167048i
$768$		0			0
$769$	−3.03895	−	17.2347i	−0.109587	−	0.621501i	−0.989288	−	0.145974i	$-0.953369\pi$
$769$	−3.03895	−	17.2347i	−0.109587	−	0.621501i	0.879701	−	0.475527i	$-0.157743\pi$
$770$		0			0
$771$	3.95792	+	20.3594i	0.142541	+	0.733228i
$772$		0			0
$773$	20.9933	−	12.1205i	0.755076	−	0.435943i	−0.0724491	−	0.997372i	$-0.523081\pi$
$773$	20.9933	−	12.1205i	0.755076	−	0.435943i	0.827525	+	0.561429i	$0.189748\pi$
$774$		0			0
$775$	12.3656	−	21.4178i	0.444185	−	0.769351i
$776$		0			0
$777$	6.77013	−	8.36077i	0.242877	−	0.299941i
$778$		0			0
$779$	−6.42713	+	17.6584i	−0.230276	+	0.632677i
$780$		0			0
$781$	−22.0597	−	3.88972i	−0.789359	−	0.139185i
$782$		0			0
$783$	−20.5498	−	2.52187i	−0.734390	−	0.0901244i
$784$		0			0
$785$	−2.68125	+	15.2061i	−0.0956979	+	0.542730i
$786$		0			0
$787$	2.60184	−	7.14850i	0.0927457	−	0.254817i	−0.884642	−	0.466270i	$-0.845597\pi$
$787$	2.60184	−	7.14850i	0.0927457	−	0.254817i	0.977388	+	0.211454i	$0.0678197\pi$
$788$		0			0
$789$	15.9812	−	6.13501i	0.568947	−	0.218412i
$790$		0			0
$791$	−1.86019	+	3.22194i	−0.0661406	+	0.114559i
$792$		0			0
$793$	−1.23610	−	2.14099i	−0.0438952	−	0.0760287i
$794$		0			0
$795$	10.1226	−	8.79984i	0.359012	−	0.312098i
$796$		0			0
$797$	13.7809	−	2.42995i	0.488146	−	0.0860733i	0.0758424	−	0.997120i	$-0.475835\pi$
$797$	13.7809	−	2.42995i	0.488146	−	0.0860733i	0.412304	+	0.911047i	$0.364724\pi$
$798$		0			0
$799$	17.0837	+	14.3350i	0.604380	+	0.507135i
$800$		0			0
$801$	−9.92401	+	18.6662i	−0.350648	+	0.659539i
$802$		0			0
$803$	−5.33557	−	14.6594i	−0.188288	−	0.517317i
$804$		0			0
$805$	−3.90214	−	4.65039i	−0.137532	−	0.163905i
$806$		0			0
$807$	0.163112	+	9.33336i	0.00574181	+	0.328550i
$808$		0			0
$809$	−20.7183			−0.728415			−0.364208	−	0.931318i	$-0.618660\pi$
$809$	−20.7183			−0.728415			−0.364208	+	0.931318i	$0.618660\pi$
$810$		0			0
$811$			43.7615i			1.53668i	0.640045	+	0.768338i	$0.278916\pi$
$811$			43.7615i			1.53668i	−0.640045	+	0.768338i	$0.721084\pi$
$812$		0			0
$813$	10.8233	−	0.189150i	0.379589	−	0.00663378i
$814$		0			0
$815$	10.9396	−	9.17939i	0.383197	−	0.321540i
$816$		0			0
$817$	−36.3718	+	13.2382i	−1.27249	+	0.463148i
$818$		0			0
$819$	−2.43140	+	1.51945i	−0.0849600	+	0.0530939i
$820$		0			0
$821$	12.4887	−	14.8834i	0.435858	−	0.519435i	−0.502745	−	0.864435i	$-0.667677\pi$
$821$	12.4887	−	14.8834i	0.435858	−	0.519435i	0.938603	+	0.345000i	$0.112121\pi$
$822$		0			0
$823$	−6.24682	−	35.4275i	−0.217750	−	1.23492i	−0.876069	−	0.482185i	$-0.839843\pi$
$823$	−6.24682	−	35.4275i	−0.217750	−	1.23492i	0.658319	−	0.752739i	$-0.271268\pi$
$824$		0			0
$825$	−6.99534	−	8.04688i	−0.243547	−	0.280156i
$826$		0			0
$827$	35.6157	−	20.5627i	1.23848	−	0.715037i	0.269697	−	0.962945i	$-0.413077\pi$
$827$	35.6157	−	20.5627i	1.23848	−	0.715037i	0.968783	+	0.247909i	$0.0797433\pi$
$828$		0			0
$829$	43.3862	+	25.0490i	1.50687	+	0.869989i	0.999968	+	0.00798294i	$0.00254108\pi$
$829$	43.3862	+	25.0490i	1.50687	+	0.869989i	0.506897	+	0.862006i	$0.330792\pi$
$830$		0			0
$831$	−8.81063	−	22.9510i	−0.305637	−	0.796162i
$832$		0			0
$833$	−8.58341	−	3.12411i	−0.297397	−	0.108244i
$834$		0			0
$835$	−21.8951	−	3.86070i	−0.757711	−	0.133605i
$836$		0			0
$837$	32.8640	+	10.0452i	1.13594	+	0.347214i
$838$		0			0
$839$	−2.93816	+	16.6631i	−0.101436	+	0.575275i	0.891148	+	0.453714i	$0.149901\pi$
$839$	−2.93816	+	16.6631i	−0.101436	+	0.575275i	−0.992584	+	0.121561i	$0.961210\pi$
$840$		0			0
$841$	−12.3325	−	4.48865i	−0.425257	−	0.154781i
$842$		0			0
$843$	37.5234	+	30.3846i	1.29238	+	1.04650i
$844$		0			0
$845$	−12.1886	−	7.03706i	−0.419299	−	0.242082i
$846$		0			0
$847$	−5.81341	−	10.0691i	−0.199751	−	0.345979i
$848$		0			0
$849$	−38.0364	+	7.39437i	−1.30541	+	0.253774i
$850$		0			0
$851$	−16.8143	+	2.96481i	−0.576385	+	0.101632i
$852$		0			0
$853$	16.8126	−	20.0365i	0.575653	−	0.686037i	−0.397128	−	0.917763i	$-0.629993\pi$
$853$	16.8126	−	20.0365i	0.575653	−	0.686037i	0.972781	+	0.231726i	$0.0744374\pi$
$854$		0			0
$855$	2.40027	+	11.2900i	0.0820876	+	0.386111i
$856$		0			0
$857$	−39.5672	+	14.4013i	−1.35159	+	0.491938i	−0.913444	−	0.406965i	$-0.866587\pi$
$857$	−39.5672	+	14.4013i	−1.35159	+	0.491938i	−0.438146	+	0.898904i	$0.644365\pi$
$858$		0			0
$859$	27.7503	+	33.0715i	0.946827	+	1.12838i	0.991594	+	0.129387i	$0.0413011\pi$
$859$	27.7503	+	33.0715i	0.946827	+	1.12838i	−0.0447668	+	0.998997i	$0.514254\pi$
$860$		0			0
$861$	−6.86098	−	11.4180i	−0.233822	−	0.389126i
$862$		0			0
$863$	31.5239			1.07308			0.536542	−	0.843873i	$-0.319730\pi$
$863$	31.5239			1.07308			0.536542	+	0.843873i	$0.319730\pi$
$864$		0			0
$865$	5.50169			0.187063
$866$		0			0
$867$	11.5089	−	20.7636i	0.390861	−	0.705167i
$868$		0			0
$869$	9.70666	+	11.5679i	0.329276	+	0.392416i
$870$		0			0
$871$	−7.76516	+	2.82629i	−0.263112	+	0.0957651i
$872$		0			0
$873$	−19.5437	−	15.2679i	−0.661453	−	0.516739i
$874$		0			0
$875$	−8.84571	+	10.5419i	−0.299040	+	0.356382i
$876$		0			0
$877$	−22.1917	+	3.91299i	−0.749360	+	0.132132i	−0.535269	−	0.844681i	$-0.679790\pi$
$877$	−22.1917	+	3.91299i	−0.749360	+	0.132132i	−0.214091	+	0.976814i	$0.568679\pi$
$878$		0			0
$879$	0.214665	−	0.623474i	0.00724045	−	0.0210293i
$880$		0			0
$881$	15.0315	+	26.0353i	0.506424	+	0.877153i	0.999972	+	0.00743425i	$0.00236642\pi$
$881$	15.0315	+	26.0353i	0.506424	+	0.877153i	−0.493548	+	0.869719i	$0.664300\pi$
$882$		0			0
$883$	−11.7757	−	6.79869i	−0.396283	−	0.228794i	0.288596	−	0.957451i	$-0.406812\pi$
$883$	−11.7757	−	6.79869i	−0.396283	−	0.228794i	−0.684879	+	0.728657i	$0.740145\pi$
$884$		0			0
$885$	3.21263	−	20.2865i	0.107991	−	0.681925i
$886$		0			0
$887$	−34.6577	−	12.6144i	−1.16369	−	0.423549i	−0.313277	−	0.949662i	$-0.601427\pi$
$887$	−34.6577	−	12.6144i	−1.16369	−	0.423549i	−0.850415	+	0.526112i	$0.823649\pi$
$888$		0			0
$889$	−1.04619	+	5.93322i	−0.0350880	+	0.198994i
$890$		0			0
$891$	8.70751	−	11.9870i	0.291713	−	0.401579i
$892$		0			0
$893$	41.4697	+	7.31222i	1.38773	+	0.244694i
$894$		0			0
$895$	−3.91267	−	1.42409i	−0.130786	−	0.0476022i
$896$		0			0
$897$	4.49426	+	0.711724i	0.150059	+	0.0237638i
$898$		0			0
$899$	−22.8210	−	13.1757i	−0.761124	−	0.439435i
$900$		0			0
$901$	10.8409	−	6.25901i	0.361163	−	0.208518i
$902$		0			0
$903$	8.93224	−	25.9429i	0.297246	−	0.863326i
$904$		0			0
$905$	−3.18143	−	18.0428i	−0.105754	−	0.599763i
$906$		0			0
$907$	2.75537	−	3.28372i	0.0914905	−	0.109034i	−0.718357	−	0.695675i	$-0.755105\pi$
$907$	2.75537	−	3.28372i	0.0914905	−	0.109034i	0.809847	+	0.586641i	$0.199550\pi$
$908$		0			0
$909$	−19.8530	−	49.1319i	−0.658482	−	1.62960i
$910$		0			0
$911$	26.1940	−	9.53385i	0.867847	−	0.315871i	0.130552	−	0.991441i	$-0.458325\pi$
$911$	26.1940	−	9.53385i	0.867847	−	0.315871i	0.737295	+	0.675571i	$0.236103\pi$
$912$		0			0
$913$	1.66279	−	1.39525i	0.0550303	−	0.0461759i
$914$		0			0
$915$	3.42021	−	6.17053i	0.113069	−	0.203991i
$916$		0			0
$917$			11.1065i			0.366767i
$918$		0			0
$919$	−54.1746			−1.78705			−0.893527	−	0.449009i	$-0.851777\pi$
$919$	−54.1746			−1.78705			−0.893527	+	0.449009i	$0.851777\pi$
$920$		0			0
$921$	−16.2364	+	9.75627i	−0.535007	+	0.321480i
$922$		0			0
$923$	−5.96010	−	7.10297i	−0.196179	−	0.233797i
$924$		0			0
$925$	5.66414	+	15.5621i	0.186236	+	0.511678i
$926$		0			0
$927$	8.67354	−	7.81035i	0.284876	−	0.256526i
$928$		0			0
$929$	−26.4712	−	22.2120i	−0.868491	−	0.728751i	0.0952887	−	0.995450i	$-0.469623\pi$
$929$	−26.4712	−	22.2120i	−0.868491	−	0.728751i	−0.963780	+	0.266699i	$0.914067\pi$
$930$		0			0
$931$	−16.9854	+	2.99498i	−0.556674	+	0.0981566i
$932$		0			0
$933$	6.03449	+	31.0412i	0.197560	+	1.01624i
$934$		0			0
$935$	1.67717	+	2.90494i	0.0548493	+	0.0950018i
$936$		0			0
$937$	−13.1443	+	22.7665i	−0.429404	+	0.743750i	−0.996820	−	0.0796811i	$-0.974610\pi$
$937$	−13.1443	+	22.7665i	−0.429404	+	0.743750i	0.567416	+	0.823431i	$0.307943\pi$
$938$		0			0
$939$	4.37758	+	3.54474i	0.142857	+	0.115678i
$940$		0			0
$941$	13.8588	−	38.0767i	0.451784	−	1.24127i	−0.479683	−	0.877442i	$-0.659248\pi$
$941$	13.8588	−	38.0767i	0.451784	−	1.24127i	0.931467	−	0.363825i	$-0.118529\pi$
$942$		0			0
$943$	−3.67106	+	20.8196i	−0.119546	+	0.677980i
$944$		0			0
$945$	−7.29049	−	3.71411i	−0.237160	−	0.120820i
$946$		0			0
$947$	−38.4009	−	6.77112i	−1.24786	−	0.220032i	−0.489580	−	0.871958i	$-0.662850\pi$
$947$	−38.4009	−	6.77112i	−1.24786	−	0.220032i	−0.758282	+	0.651926i	$0.773961\pi$
$948$		0			0
$949$	2.20861	−	6.06810i	0.0716944	−	0.196979i
$950$		0			0
$951$	10.5721	+	27.5395i	0.342824	+	0.893031i
$952$		0			0
$953$	12.7586	−	22.0985i	0.413291	−	0.715842i	−0.581956	−	0.813220i	$-0.697712\pi$
$953$	12.7586	−	22.0985i	0.413291	−	0.715842i	0.995247	+	0.0973785i	$0.0310458\pi$
$954$		0			0
$955$	−6.70859	+	3.87321i	−0.217085	+	0.125334i
$956$		0			0
$957$	−8.57408	+	7.45365i	−0.277161	+	0.240942i
$958$		0			0
$959$	3.83547	+	21.7520i	0.123854	+	0.702410i
$960$		0			0
$961$	9.75845	+	8.18831i	0.314789	+	0.264139i
$962$		0			0
$963$	−0.436503	−	12.4847i	−0.0140661	−	0.402312i
$964$		0			0
$965$	3.65963	+	10.0547i	0.117808	+	0.323674i
$966$		0			0
$967$	35.3489	−	29.6612i	1.13674	−	0.953841i	0.137416	−	0.990513i	$-0.456120\pi$
$967$	35.3489	−	29.6612i	1.13674	−	0.953841i	0.999327	+	0.0366729i	$0.0116760\pi$
$968$		0			0
$969$	0.188231	+	10.7707i	0.00604685	+	0.346004i
$970$		0			0
$971$			1.40859i			0.0452039i	0.999745	+	0.0226020i	$0.00719504\pi$
$971$			1.40859i			0.0452039i	−0.999745	+	0.0226020i	$0.992805\pi$
$972$		0			0
$973$			0.545991i			0.0175037i
$974$		0			0
$975$	−0.0771213	−	4.41293i	−0.00246986	−	0.141327i
$976$		0			0
$977$	36.5361	−	30.6574i	1.16889	−	0.980817i	0.168904	−	0.985633i	$-0.445977\pi$
$977$	36.5361	−	30.6574i	1.16889	−	0.980817i	0.999988	+	0.00481536i	$0.00153278\pi$
$978$		0			0
$979$	3.96758	+	10.9008i	0.126805	+	0.348393i
$980$		0			0
$981$	2.16026	+	61.7869i	0.0689719	+	1.97270i
$982$		0			0
$983$	−13.2755	−	11.1394i	−0.423421	−	0.355293i	0.406041	−	0.913855i	$-0.366909\pi$
$983$	−13.2755	−	11.1394i	−0.423421	−	0.355293i	−0.829463	+	0.558562i	$0.811353\pi$
$984$		0			0
$985$	−0.391712	−	2.22151i	−0.0124810	−	0.0707832i
$986$		0			0
$987$	−22.5277	+	19.5839i	−0.717066	+	0.623362i
$988$		0			0
$989$	−37.7108	+	21.7723i	−1.19913	+	0.692320i
$990$		0			0
$991$	−16.1511	+	27.9745i	−0.513056	+	0.888638i	0.486830	+	0.873497i	$0.338153\pi$
$991$	−16.1511	+	27.9745i	−0.513056	+	0.888638i	−0.999885	+	0.0151416i	$0.995180\pi$
$992$		0			0
$993$	3.48858	+	9.08749i	0.110707	+	0.288383i
$994$		0			0
$995$	8.18398	−	22.4853i	0.259450	−	0.712832i
$996$		0			0
$997$	24.1513	+	4.25852i	0.764879	+	0.134869i	0.542459	−	0.840082i	$-0.317493\pi$
$997$	24.1513	+	4.25852i	0.764879	+	0.134869i	0.222420	+	0.974951i	$0.428604\pi$
$998$		0			0
$999$	−19.2986	+	12.5344i	−0.610581	+	0.396571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.241.34		204
4.3	odd	2		216.2.t.a.133.34	yes	204
8.3	odd	2		216.2.t.a.133.4	yes	204
8.5	even	2	inner	864.2.bf.a.241.1		204
12.11	even	2		648.2.t.a.397.1		204
24.11	even	2		648.2.t.a.397.31		204
27.13	even	9	inner	864.2.bf.a.337.1		204
108.67	odd	18		216.2.t.a.13.4	✓	204
108.95	even	18		648.2.t.a.253.31		204
216.13	even	18	inner	864.2.bf.a.337.34		204
216.67	odd	18		216.2.t.a.13.34	yes	204
216.203	even	18		648.2.t.a.253.1		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.4	✓	204	108.67	odd	18
216.2.t.a.13.34	yes	204	216.67	odd	18
216.2.t.a.133.4	yes	204	8.3	odd	2
216.2.t.a.133.34	yes	204	4.3	odd	2
648.2.t.a.253.1		204	216.203	even	18
648.2.t.a.253.31		204	108.95	even	18
648.2.t.a.397.1		204	12.11	even	2
648.2.t.a.397.31		204	24.11	even	2
864.2.bf.a.241.1		204	8.5	even	2	inner
864.2.bf.a.241.34		204	1.1	even	1	trivial
864.2.bf.a.337.1		204	27.13	even	9	inner
864.2.bf.a.337.34		204	216.13	even	18	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.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73179 - 0.0302651i) q^{3} +(0.721676 + 0.860059i) q^{5} +(-1.31793 + 0.479686i) q^{7} +(2.99817 - 0.104825i) q^{9} +(1.05816 - 1.26106i) q^{11} +(0.671077 - 0.118329i) q^{13} +(1.27582 + 1.46760i) q^{15} +(0.907443 + 1.57174i) q^{17} +(2.96777 + 1.71344i) q^{19} +(-2.26785 + 0.870601i) q^{21} +(3.62278 + 1.31858i) q^{23} +(0.649354 - 3.68267i) q^{25} +(5.18901 - 0.272275i) q^{27} +(-3.92395 - 0.691898i) q^{29} +(6.21468 + 2.26196i) q^{31} +(1.79434 - 2.21592i) q^{33} +(-1.36367 - 0.787317i) q^{35} +(-3.83532 + 2.21432i) q^{37} +(1.15858 - 0.225231i) q^{39} +(0.952217 + 5.40029i) q^{41} +(-7.26017 + 8.65234i) q^{43} +(2.25386 + 2.50295i) q^{45} +(11.5469 - 4.20273i) q^{47} +(-3.85548 + 3.23513i) q^{49} +(1.61907 + 2.69445i) q^{51} -6.89741i q^{53} +1.84824 q^{55} +(5.19140 + 2.87750i) q^{57} +(-6.78921 - 8.09106i) q^{59} +(-1.24084 - 3.40917i) q^{61} +(-3.90108 + 1.57633i) q^{63} +(0.586070 + 0.491771i) q^{65} +(-11.9425 + 2.10578i) q^{67} +(6.31378 + 2.17386i) q^{69} +(-6.80355 - 11.7841i) q^{71} +(4.73823 - 8.20685i) q^{73} +(1.01309 - 6.39725i) q^{75} +(-0.789660 + 2.16957i) q^{77} +(-1.59290 + 9.03380i) q^{79} +(8.97802 - 0.628568i) q^{81} +(1.29853 + 0.228966i) q^{83} +(-0.696908 + 1.91474i) q^{85} +(-6.81638 - 1.07946i) q^{87} +(-3.52339 + 6.10270i) q^{89} +(-0.827669 + 0.477855i) q^{91} +(10.8310 + 3.72914i) q^{93} +(0.668104 + 3.78901i) q^{95} +(-6.33275 - 5.31381i) q^{97} +(3.04035 - 3.89180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more