LMFDB - Embedded newform 864.2.bf.a.241.17

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			241.17
Character	$\chi$	$=$	864.241
Dual form			864.2.bf.a.337.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0518114 - 1.73128i) q^{3} +(1.55117 + 1.84861i) q^{5} +(1.49685 - 0.544810i) q^{7} +(-2.99463 + 0.179400i) q^{9} +(0.102391 - 0.122025i) q^{11} +(3.39140 - 0.597995i) q^{13} +(3.12009 - 2.78128i) q^{15} +(-1.43581 - 2.48690i) q^{17} +(3.75621 + 2.16865i) q^{19} +(-1.02077 - 2.56324i) q^{21} +(-2.14748 - 0.781619i) q^{23} +(-0.142997 + 0.810974i) q^{25} +(0.465746 + 5.17524i) q^{27} +(8.60509 + 1.51731i) q^{29} +(6.69129 + 2.43543i) q^{31} +(-0.216565 - 0.170946i) q^{33} +(3.32901 + 1.92201i) q^{35} +(-5.14590 + 2.97099i) q^{37} +(-1.21101 - 5.84046i) q^{39} +(-1.74706 - 9.90807i) q^{41} +(7.59829 - 9.05529i) q^{43} +(-4.97682 - 5.25763i) q^{45} +(-3.66367 + 1.33347i) q^{47} +(-3.41856 + 2.86851i) q^{49} +(-4.23112 + 2.61464i) q^{51} +9.80805i q^{53} +0.384404 q^{55} +(3.55991 - 6.61539i) q^{57} +(-1.72220 - 2.05244i) q^{59} +(-0.492702 - 1.35369i) q^{61} +(-4.38478 + 1.90004i) q^{63} +(6.36609 + 5.34178i) q^{65} +(-0.225321 + 0.0397302i) q^{67} +(-1.24193 + 3.75838i) q^{69} +(-2.82317 - 4.88987i) q^{71} +(7.14574 - 12.3768i) q^{73} +(1.41143 + 0.205549i) q^{75} +(0.0867843 - 0.238438i) q^{77} +(2.18269 - 12.3786i) q^{79} +(8.93563 - 1.07447i) q^{81} +(-11.1079 - 1.95862i) q^{83} +(2.37013 - 6.51187i) q^{85} +(2.18104 - 14.9764i) q^{87} +(-3.73417 + 6.46777i) q^{89} +(4.75063 - 2.74278i) q^{91} +(3.86972 - 11.7107i) q^{93} +(1.81753 + 10.3077i) q^{95} +(5.17680 + 4.34385i) q^{97} +(-0.284733 + 0.383790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.0518114	−	1.73128i	−0.0299133	−	0.999552i
$3$	−0.0518114	−	1.73128i	−0.0299133	−	0.999552i
$4$		0			0
$5$	1.55117	+	1.84861i	0.693704	+	0.826724i	0.991798	−	0.127812i	$-0.0407956\pi$
$5$	1.55117	+	1.84861i	0.693704	+	0.826724i	−0.298095	+	0.954536i	$0.596351\pi$
$6$		0			0
$7$	1.49685	−	0.544810i	0.565757	−	0.205919i	−0.0432765	−	0.999063i	$-0.513780\pi$
$7$	1.49685	−	0.544810i	0.565757	−	0.205919i	0.609034	+	0.793144i	$0.291557\pi$
$8$		0			0
$9$	−2.99463	+	0.179400i	−0.998210	+	0.0597999i
$10$		0			0
$11$	0.102391	−	0.122025i	0.0308722	−	0.0367920i	−0.750387	−	0.660998i	$-0.770133\pi$
$11$	0.102391	−	0.122025i	0.0308722	−	0.0367920i	0.781260	+	0.624206i	$0.214577\pi$
$12$		0			0
$13$	3.39140	−	0.597995i	0.940604	−	0.165854i	0.317735	−	0.948180i	$-0.397078\pi$
$13$	3.39140	−	0.597995i	0.940604	−	0.165854i	0.622869	+	0.782326i	$0.285967\pi$
$14$		0			0
$15$	3.12009	−	2.78128i	0.805603	−	0.718123i
$16$		0			0
$17$	−1.43581	−	2.48690i	−0.348236	−	0.603163i	0.637700	−	0.770285i	$-0.279886\pi$
$17$	−1.43581	−	2.48690i	−0.348236	−	0.603163i	−0.985936	+	0.167122i	$0.946553\pi$
$18$		0			0
$19$	3.75621	+	2.16865i	0.861733	+	0.497522i	0.864592	−	0.502474i	$-0.167577\pi$
$19$	3.75621	+	2.16865i	0.861733	+	0.497522i	−0.00285908	+	0.999996i	$0.500910\pi$
$20$		0			0
$21$	−1.02077	−	2.56324i	−0.222750	−	0.559344i
$22$		0			0
$23$	−2.14748	−	0.781619i	−0.447781	−	0.162979i	0.108280	−	0.994120i	$-0.465466\pi$
$23$	−2.14748	−	0.781619i	−0.447781	−	0.162979i	−0.556061	+	0.831142i	$0.687688\pi$
$24$		0			0
$25$	−0.142997	+	0.810974i	−0.0285993	+	0.162195i
$26$		0			0
$27$	0.465746	+	5.17524i	0.0896329	+	0.995975i
$28$		0			0
$29$	8.60509	+	1.51731i	1.59793	+	0.281757i	0.900486	−	0.434886i	$-0.143211\pi$
$29$	8.60509	+	1.51731i	1.59793	+	0.281757i	0.697440	+	0.716643i	$0.254322\pi$
$30$		0			0
$31$	6.69129	+	2.43543i	1.20179	+	0.437416i	0.863849	−	0.503751i	$-0.168047\pi$
$31$	6.69129	+	2.43543i	1.20179	+	0.437416i	0.337942	+	0.941167i	$0.390269\pi$
$32$		0			0
$33$	−0.216565	−	0.170946i	−0.0376991	−	0.0297578i
$34$		0			0
$35$	3.32901	+	1.92201i	0.562706	+	0.324878i
$36$		0			0
$37$	−5.14590	+	2.97099i	−0.845981	+	0.488427i	−0.859293	−	0.511484i	$-0.829096\pi$
$37$	−5.14590	+	2.97099i	−0.845981	+	0.488427i	0.0133118	+	0.999911i	$0.495763\pi$
$38$		0			0
$39$	−1.21101	−	5.84046i	−0.193916	−	0.935222i
$40$		0			0
$41$	−1.74706	−	9.90807i	−0.272845	−	1.54738i	−0.745725	−	0.666254i	$-0.767897\pi$
$41$	−1.74706	−	9.90807i	−0.272845	−	1.54738i	0.472880	−	0.881127i	$-0.343214\pi$
$42$		0			0
$43$	7.59829	−	9.05529i	1.15873	−	1.38092i	0.247567	−	0.968871i	$-0.420369\pi$
$43$	7.59829	−	9.05529i	1.15873	−	1.38092i	0.911162	−	0.412048i	$-0.135187\pi$
$44$		0			0
$45$	−4.97682	−	5.25763i	−0.741900	−	0.783761i
$46$		0			0
$47$	−3.66367	+	1.33347i	−0.534402	+	0.194506i	−0.595103	−	0.803650i	$-0.702889\pi$
$47$	−3.66367	+	1.33347i	−0.534402	+	0.194506i	0.0607009	+	0.998156i	$0.480666\pi$
$48$		0			0
$49$	−3.41856	+	2.86851i	−0.488366	+	0.409788i
$50$		0			0
$51$	−4.23112	+	2.61464i	−0.592476	+	0.366123i
$52$		0			0
$53$			9.80805i			1.34724i	0.739078	+	0.673620i	$0.235262\pi$
$53$			9.80805i			1.34724i	−0.739078	+	0.673620i	$0.764738\pi$
$54$		0			0
$55$	0.384404			0.0518330
$56$		0			0
$57$	3.55991	−	6.61539i	0.471522	−	0.876230i
$58$		0			0
$59$	−1.72220	−	2.05244i	−0.224212	−	0.267205i	0.642198	−	0.766539i	$-0.278023\pi$
$59$	−1.72220	−	2.05244i	−0.224212	−	0.267205i	−0.866410	+	0.499334i	$0.833578\pi$
$60$		0			0
$61$	−0.492702	−	1.35369i	−0.0630841	−	0.173322i	0.904146	−	0.427224i	$-0.140508\pi$
$61$	−0.492702	−	1.35369i	−0.0630841	−	0.173322i	−0.967230	+	0.253902i	$0.918286\pi$
$62$		0			0
$63$	−4.38478	+	1.90004i	−0.552431	+	0.239382i
$64$		0			0
$65$	6.36609	+	5.34178i	0.789616	+	0.662566i
$66$		0			0
$67$	−0.225321	+	0.0397302i	−0.0275273	+	0.00485381i	−0.187395	−	0.982285i	$-0.560004\pi$
$67$	−0.225321	+	0.0397302i	−0.0275273	+	0.00485381i	0.159868	+	0.987138i	$0.448893\pi$
$68$		0			0
$69$	−1.24193	+	3.75838i	−0.149511	+	0.452456i
$70$		0			0
$71$	−2.82317	−	4.88987i	−0.335048	−	0.580320i	0.648446	−	0.761261i	$-0.275419\pi$
$71$	−2.82317	−	4.88987i	−0.335048	−	0.580320i	−0.983494	+	0.180940i	$0.942086\pi$
$72$		0			0
$73$	7.14574	−	12.3768i	0.836346	−	1.44859i	−0.0565836	−	0.998398i	$-0.518021\pi$
$73$	7.14574	−	12.3768i	0.836346	−	1.44859i	0.892930	−	0.450196i	$-0.148646\pi$
$74$		0			0
$75$	1.41143	+	0.205549i	0.162978	+	0.0237347i
$76$		0			0
$77$	0.0867843	−	0.238438i	0.00988999	−	0.0271725i
$78$		0			0
$79$	2.18269	−	12.3786i	0.245572	−	1.39271i	−0.573590	−	0.819143i	$-0.694450\pi$
$79$	2.18269	−	12.3786i	0.245572	−	1.39271i	0.819161	−	0.573563i	$-0.194439\pi$
$80$		0			0
$81$	8.93563	−	1.07447i	0.992848	−	0.119386i
$82$		0			0
$83$	−11.1079	−	1.95862i	−1.21925	−	0.214987i	−0.473248	−	0.880929i	$-0.656919\pi$
$83$	−11.1079	−	1.95862i	−1.21925	−	0.214987i	−0.746003	+	0.665942i	$0.768030\pi$
$84$		0			0
$85$	2.37013	−	6.51187i	0.257076	−	0.706311i
$86$		0			0
$87$	2.18104	−	14.9764i	0.233832	−	1.60564i
$88$		0			0
$89$	−3.73417	+	6.46777i	−0.395821	+	0.685582i	−0.993206	−	0.116373i	$-0.962873\pi$
$89$	−3.73417	+	6.46777i	−0.395821	+	0.685582i	0.597385	+	0.801955i	$0.296207\pi$
$90$		0			0
$91$	4.75063	−	2.74278i	0.498001	−	0.287521i
$92$		0			0
$93$	3.86972	−	11.7107i	0.401271	−	1.21434i
$94$		0			0
$95$	1.81753	+	10.3077i	0.186474	+	1.05755i
$96$		0			0
$97$	5.17680	+	4.34385i	0.525624	+	0.441051i	0.866587	−	0.499026i	$-0.166309\pi$
$97$	5.17680	+	4.34385i	0.525624	+	0.441051i	−0.340963	+	0.940077i	$0.610753\pi$
$98$		0			0
$99$	−0.284733	+	0.383790i	−0.0286168	+	0.0385724i
$100$		0			0
$101$	0.582767	+	1.60114i	0.0579875	+	0.159319i	0.965304	−	0.261129i	$-0.0840949\pi$
$101$	0.582767	+	1.60114i	0.0579875	+	0.159319i	−0.907316	+	0.420449i	$0.861873\pi$
$102$		0			0
$103$	−9.82235	+	8.24193i	−0.967825	+	0.812102i	−0.982208	−	0.187795i	$-0.939866\pi$
$103$	−9.82235	+	8.24193i	−0.967825	+	0.812102i	0.0143832	+	0.999897i	$0.495422\pi$
$104$		0			0
$105$	3.15504	−	5.86302i	0.307901	−	0.572172i
$106$		0			0
$107$			15.7558i			1.52317i	0.648065	+	0.761585i	$0.275579\pi$
$107$			15.7558i			1.52317i	−0.648065	+	0.761585i	$0.724421\pi$
$108$		0			0
$109$		−	4.23854i		−	0.405978i	−0.979181	−	0.202989i	$-0.934934\pi$
$109$		−	4.23854i		−	0.405978i	0.979181	−	0.202989i	$-0.0650656\pi$
$110$		0			0
$111$	5.41021	+	8.75504i	0.513515	+	0.830992i
$112$		0			0
$113$	−5.72871	+	4.80696i	−0.538912	+	0.452201i	−0.871166	−	0.490989i	$-0.836635\pi$
$113$	−5.72871	+	4.80696i	−0.538912	+	0.452201i	0.332254	+	0.943190i	$0.392191\pi$
$114$		0			0
$115$	−1.88620	−	5.18228i	−0.175889	−	0.483250i
$116$		0			0
$117$	−10.0487	+	2.39919i	−0.929003	+	0.221805i
$118$		0			0
$119$	−3.50409	−	2.94028i	−0.321220	−	0.269535i
$120$		0			0
$121$	1.90572	+	10.8079i	0.173248	+	0.982536i
$122$		0			0
$123$	−17.0631	+	3.53799i	−1.53853	+	0.319010i
$124$		0			0
$125$	8.72843	−	5.03936i	0.780695	−	0.450734i
$126$		0			0
$127$	−6.92735	+	11.9985i	−0.614703	+	1.06470i	0.375734	+	0.926728i	$0.377391\pi$
$127$	−6.92735	+	11.9985i	−0.614703	+	1.06470i	−0.990437	+	0.137969i	$0.955943\pi$
$128$		0			0
$129$	−16.0709	−	12.6856i	−1.41496	−	1.11690i
$130$		0			0
$131$	1.76657	−	4.85361i	0.154346	−	0.424061i	−0.838286	−	0.545231i	$-0.816442\pi$
$131$	1.76657	−	4.85361i	0.154346	−	0.424061i	0.992632	+	0.121169i	$0.0386643\pi$
$132$		0			0
$133$	6.80399	+	1.19973i	0.589981	+	0.104030i
$134$		0			0
$135$	−8.84455	+	8.88865i	−0.761217	+	0.765013i
$136$		0			0
$137$	−3.27446	+	18.5704i	−0.279756	+	1.58658i	0.443680	+	0.896185i	$0.353673\pi$
$137$	−3.27446	+	18.5704i	−0.279756	+	1.58658i	−0.723436	+	0.690391i	$0.757438\pi$
$138$		0			0
$139$	5.53623	−	15.2107i	0.469577	−	1.29015i	−0.448512	−	0.893777i	$-0.648046\pi$
$139$	5.53623	−	15.2107i	0.469577	−	1.29015i	0.918089	−	0.396375i	$-0.129732\pi$
$140$		0			0
$141$	2.49842	+	6.27374i	0.210405	+	0.528344i
$142$		0			0
$143$	0.274279	−	0.475066i	0.0229364	−	0.0397270i
$144$		0			0
$145$	10.5430	+	18.2611i	0.875551	+	1.51650i
$146$		0			0
$147$	5.14331	+	5.76985i	0.424213	+	0.475889i
$148$		0			0
$149$	−12.7731	+	2.25224i	−1.04641	+	0.184511i	−0.670321	−	0.742071i	$-0.733843\pi$
$149$	−12.7731	+	2.25224i	−1.04641	+	0.184511i	−0.376092	+	0.926582i	$0.622732\pi$
$150$		0			0
$151$	−2.57721	−	2.16253i	−0.209730	−	0.175985i	0.531871	−	0.846825i	$-0.321489\pi$
$151$	−2.57721	−	2.16253i	−0.209730	−	0.175985i	−0.741602	+	0.670841i	$0.765933\pi$
$152$		0			0
$153$	4.74588	+	7.18977i	0.383682	+	0.581259i
$154$		0			0
$155$	5.87716	+	16.1474i	0.472065	+	1.29699i
$156$		0			0
$157$	−0.320529	−	0.381992i	−0.0255810	−	0.0304863i	0.753102	−	0.657903i	$-0.228557\pi$
$157$	−0.320529	−	0.381992i	−0.0255810	−	0.0304863i	−0.778683	+	0.627417i	$0.784112\pi$
$158$		0			0
$159$	16.9804	−	0.508169i	1.34664	−	0.0403004i
$160$		0			0
$161$	−3.64030			−0.286896
$162$		0			0
$163$			11.3041i			0.885405i	0.896669	+	0.442703i	$0.145980\pi$
$163$			11.3041i			0.885405i	−0.896669	+	0.442703i	$0.854020\pi$
$164$		0			0
$165$	−0.0199165	−	0.665509i	−0.00155050	−	0.0518098i
$166$		0			0
$167$	−10.0898	+	8.46632i	−0.780770	+	0.655144i	−0.943442	−	0.331536i	$-0.892433\pi$
$167$	−10.0898	+	8.46632i	−0.780770	+	0.655144i	0.162673	+	0.986680i	$0.447989\pi$
$168$		0			0
$169$	−1.07204	+	0.390189i	−0.0824644	+	0.0300146i
$170$		0			0
$171$	−11.6375	−	5.82044i	−0.889943	−	0.445100i
$172$		0			0
$173$	−10.5281	+	12.5470i	−0.800440	+	0.953928i	−0.999661	−	0.0260269i	$-0.991714\pi$
$173$	−10.5281	+	12.5470i	−0.800440	+	0.953928i	0.199221	+	0.979955i	$0.436159\pi$
$174$		0			0
$175$	0.227782	+	1.29182i	0.0172187	+	0.0976521i
$176$		0			0
$177$	−3.46411	+	3.08795i	−0.260379	+	0.232104i
$178$		0			0
$179$	5.13398	−	2.96410i	0.383731	−	0.221547i	−0.295709	−	0.955278i	$-0.595556\pi$
$179$	5.13398	−	2.96410i	0.383731	−	0.221547i	0.679441	+	0.733731i	$0.262223\pi$
$180$		0			0
$181$	1.50802	+	0.870656i	0.112090	+	0.0647154i	0.554997	−	0.831852i	$-0.312719\pi$
$181$	1.50802	+	0.870656i	0.112090	+	0.0647154i	−0.442907	+	0.896568i	$0.646053\pi$
$182$		0			0
$183$	−2.31808	+	0.923140i	−0.171357	+	0.0682405i
$184$		0			0
$185$	−13.4744	−	4.90427i	−0.990655	−	0.360569i
$186$		0			0
$187$	−0.450481	−	0.0794319i	−0.0329424	−	0.00580863i
$188$		0			0
$189$	3.51667	+	7.49283i	0.255800	+	0.545023i
$190$		0			0
$191$	−1.88621	+	10.6972i	−0.136481	+	0.774023i	0.837336	+	0.546689i	$0.184112\pi$
$191$	−1.88621	+	10.6972i	−0.136481	+	0.774023i	−0.973817	+	0.227334i	$0.926999\pi$
$192$		0			0
$193$	−13.6021	−	4.95075i	−0.979100	−	0.356363i	−0.197609	−	0.980281i	$-0.563318\pi$
$193$	−13.6021	−	4.95075i	−0.979100	−	0.356363i	−0.781490	+	0.623918i	$0.785540\pi$
$194$		0			0
$195$	8.91826	−	11.2982i	0.638650	−	0.809082i
$196$		0			0
$197$	7.36911	+	4.25456i	0.525027	+	0.303125i	0.738989	−	0.673717i	$-0.235303\pi$
$197$	7.36911	+	4.25456i	0.525027	+	0.303125i	−0.213962	+	0.976842i	$0.568637\pi$
$198$		0			0
$199$	6.17939	+	10.7030i	0.438045	+	0.758716i	0.997539	−	0.0701183i	$-0.0223377\pi$
$199$	6.17939	+	10.7030i	0.438045	+	0.758716i	−0.559494	+	0.828835i	$0.689004\pi$
$200$		0			0
$201$	0.0804581	+	0.388034i	0.00567508	+	0.0273698i
$202$		0			0
$203$	13.7072	−	2.41695i	0.962057	−	0.169637i
$204$		0			0
$205$	15.6062	−	18.5987i	1.08998	−	1.29899i
$206$		0			0
$207$	6.57114	+	1.95540i	0.456726	+	0.135910i
$208$		0			0
$209$	0.649234	−	0.236302i	0.0449084	−	0.0163453i
$210$		0			0
$211$	−1.13641	−	1.35433i	−0.0782339	−	0.0932356i	0.725508	−	0.688214i	$-0.241605\pi$
$211$	−1.13641	−	1.35433i	−0.0782339	−	0.0932356i	−0.803742	+	0.594978i	$0.797161\pi$
$212$		0			0
$213$	−8.31943	+	5.14103i	−0.570038	+	0.352257i
$214$		0			0
$215$	28.5259			1.94545
$216$		0			0
$217$	11.3427			0.769994
$218$		0			0
$219$	−21.7979	−	11.7300i	−1.47296	−	0.792640i
$220$		0			0
$221$	−6.35657	−	7.57546i	−0.427589	−	0.509581i
$222$		0			0
$223$	2.82725	−	1.02903i	0.189327	−	0.0689092i	−0.245617	−	0.969367i	$-0.578991\pi$
$223$	2.82725	−	1.02903i	0.189327	−	0.0689092i	0.434944	+	0.900458i	$0.356768\pi$
$224$		0			0
$225$	0.282734	−	2.45422i	0.0188489	−	0.163615i
$226$		0			0
$227$	−3.65533	+	4.35626i	−0.242613	+	0.289135i	−0.873586	−	0.486670i	$-0.838211\pi$
$227$	−3.65533	+	4.35626i	−0.242613	+	0.289135i	0.630973	+	0.775805i	$0.282656\pi$
$228$		0			0
$229$	−21.4459	+	3.78149i	−1.41718	+	0.249888i	−0.829185	−	0.558974i	$-0.811195\pi$
$229$	−21.4459	+	3.78149i	−1.41718	+	0.249888i	−0.587998	+	0.808862i	$0.700084\pi$
$230$		0			0
$231$	−0.417298	−	0.137894i	−0.0274562	−	0.00907275i
$232$		0			0
$233$	−11.7482	−	20.3485i	−0.769650	−	1.33307i	−0.937753	−	0.347303i	$-0.887097\pi$
$233$	−11.7482	−	20.3485i	−0.769650	−	1.33307i	0.168103	−	0.985769i	$-0.446236\pi$
$234$		0			0
$235$	−8.14804	−	4.70427i	−0.531520	−	0.306873i
$236$		0			0
$237$	−21.5439	−	3.13748i	−1.39943	−	0.203801i
$238$		0			0
$239$	−21.9880	−	8.00297i	−1.42228	−	0.517669i	−0.487574	−	0.873082i	$-0.662118\pi$
$239$	−21.9880	−	8.00297i	−1.42228	−	0.517669i	−0.934710	+	0.355413i	$0.884340\pi$
$240$		0			0
$241$	0.682320	−	3.86963i	0.0439521	−	0.249265i	−0.954913	−	0.296884i	$-0.904052\pi$
$241$	0.682320	−	3.86963i	0.0439521	−	0.249265i	0.998866	+	0.0476196i	$0.0151635\pi$
$242$		0			0
$243$	−2.32317	−	15.4144i	−0.149032	−	0.988832i
$244$		0			0
$245$	−10.6055	−	1.87004i	−0.677562	−	0.119472i
$246$		0			0
$247$	14.0356	+	5.10855i	0.893066	+	0.325049i
$248$		0			0
$249$	−2.81540	+	19.3323i	−0.178419	+	1.22514i
$250$		0			0
$251$	−0.431970	−	0.249398i	−0.0272657	−	0.0157419i	0.486305	−	0.873789i	$-0.338344\pi$
$251$	−0.431970	−	0.249398i	−0.0272657	−	0.0157419i	−0.513571	+	0.858047i	$0.671678\pi$
$252$		0			0
$253$	−0.315261	+	0.182016i	−0.0198203	+	0.0114433i
$254$		0			0
$255$	−11.3966	−	3.76595i	−0.713685	−	0.235833i
$256$		0			0
$257$	0.156179	+	0.885735i	0.00974218	+	0.0552506i	0.989291	−	0.145955i	$-0.0466253\pi$
$257$	0.156179	+	0.885735i	0.00974218	+	0.0552506i	−0.979549	+	0.201205i	$0.935514\pi$
$258$		0			0
$259$	−6.08403	+	7.25067i	−0.378043	+	0.450535i
$260$		0			0
$261$	−26.0413	−	3.00003i	−1.61191	−	0.185697i
$262$		0			0
$263$	9.42004	−	3.42861i	0.580864	−	0.211417i	−0.0348423	−	0.999393i	$-0.511093\pi$
$263$	9.42004	−	3.42861i	0.580864	−	0.211417i	0.615707	+	0.787976i	$0.288871\pi$
$264$		0			0
$265$	−18.1313	+	15.2139i	−1.11380	+	0.934585i
$266$		0			0
$267$	11.3910	+	6.12977i	0.697115	+	0.375136i
$268$		0			0
$269$		−	1.04059i		−	0.0634460i	−0.999497	−	0.0317230i	$-0.989901\pi$
$269$		−	1.04059i		−	0.0634460i	0.999497	−	0.0317230i	$-0.0100994\pi$
$270$		0			0
$271$	30.0408			1.82485			0.912423	−	0.409248i	$-0.134209\pi$
$271$	30.0408			1.82485			0.912423	+	0.409248i	$0.134209\pi$
$272$		0			0
$273$	−4.99464	−	8.08254i	−0.302289	−	0.489178i
$274$		0			0
$275$	0.0843178	+	0.100486i	0.00508456	+	0.00605954i
$276$		0			0
$277$	6.71914	+	18.4607i	0.403714	+	1.10920i	0.960437	+	0.278497i	$0.0898363\pi$
$277$	6.71914	+	18.4607i	0.403714	+	1.10920i	−0.556723	+	0.830698i	$0.687941\pi$
$278$		0			0
$279$	−20.4749	−	6.09280i	−1.22580	−	0.364767i
$280$		0			0
$281$	21.2698	+	17.8475i	1.26885	+	1.06469i	0.994681	+	0.103008i	$0.0328467\pi$
$281$	21.2698	+	17.8475i	1.26885	+	1.06469i	0.274167	+	0.961682i	$0.411598\pi$
$282$		0			0
$283$	−24.5768	+	4.33356i	−1.46094	+	0.257603i	−0.846934	−	0.531698i	$-0.821554\pi$
$283$	−24.5768	+	4.33356i	−1.46094	+	0.257603i	−0.614007	+	0.789301i	$0.710443\pi$
$284$		0			0
$285$	17.7513	−	3.68070i	1.05150	−	0.218026i
$286$		0			0
$287$	−8.01310	−	13.8791i	−0.472999	−	0.819258i
$288$		0			0
$289$	4.37687	−	7.58097i	0.257463	−	0.445939i
$290$		0			0
$291$	7.25219	−	9.18753i	0.425131	−	0.538582i
$292$		0			0
$293$	2.79279	−	7.67312i	0.163156	−	0.448268i	−0.830993	−	0.556283i	$-0.812227\pi$
$293$	2.79279	−	7.67312i	0.163156	−	0.448268i	0.994149	+	0.108015i	$0.0344493\pi$
$294$		0			0
$295$	1.12274	−	6.36736i	0.0653683	−	0.370722i
$296$		0			0
$297$	0.679199	+	0.473067i	0.0394111	+	0.0274501i
$298$		0			0
$299$	−7.75036	−	1.36660i	−0.448215	−	0.0790324i
$300$		0			0
$301$	6.44011	−	17.6941i	0.371202	−	1.01987i
$302$		0			0
$303$	2.74182	−	1.09189i	0.157513	−	0.0627273i
$304$		0			0
$305$	1.73818	−	3.01061i	0.0995278	−	0.172387i
$306$		0			0
$307$	−16.1236	+	9.30896i	−0.920222	+	0.531290i	−0.883706	−	0.468043i	$-0.844959\pi$
$307$	−16.1236	+	9.30896i	−0.920222	+	0.531290i	−0.0365160	+	0.999333i	$0.511626\pi$
$308$		0			0
$309$	14.7780	+	16.5782i	0.840689	+	0.943099i
$310$		0			0
$311$	0.851609	+	4.82971i	0.0482903	+	0.273868i	0.999386	−	0.0350274i	$-0.0111518\pi$
$311$	0.851609	+	4.82971i	0.0482903	+	0.273868i	−0.951096	+	0.308895i	$0.900041\pi$
$312$		0			0
$313$	−7.88890	−	6.61958i	−0.445907	−	0.374161i	0.392007	−	0.919962i	$-0.371781\pi$
$313$	−7.88890	−	6.61958i	−0.445907	−	0.374161i	−0.837914	+	0.545802i	$0.816225\pi$
$314$		0			0
$315$	−10.3140	−	5.15848i	−0.581126	−	0.290647i
$316$		0			0
$317$	−7.72259	−	21.2177i	−0.433744	−	1.19170i	−0.943497	−	0.331381i	$-0.892485\pi$
$317$	−7.72259	−	21.2177i	−0.433744	−	1.19170i	0.509753	−	0.860321i	$-0.329737\pi$
$318$		0			0
$319$	1.06624	−	0.894680i	0.0596979	−	0.0500925i
$320$		0			0
$321$	27.2776	−	0.816330i	1.52249	−	0.0455631i
$322$		0			0
$323$		−	12.4551i		−	0.693020i
$324$		0			0
$325$			2.83585i			0.157304i
$326$		0			0
$327$	−7.33808	+	0.219605i	−0.405797	+	0.0121442i
$328$		0			0
$329$	−4.75749	+	3.99201i	−0.262289	+	0.220087i
$330$		0			0
$331$	8.06296	+	22.1528i	0.443180	+	1.21763i	0.937389	+	0.348284i	$0.113236\pi$
$331$	8.06296	+	22.1528i	0.443180	+	1.21763i	−0.494209	+	0.869343i	$0.664542\pi$
$332$		0			0
$333$	14.8771	−	9.82018i	0.815259	−	0.538143i
$334$		0			0
$335$	−0.422957	−	0.354903i	−0.0231086	−	0.0193904i
$336$		0			0
$337$	−5.70981	−	32.3820i	−0.311033	−	1.76396i	−0.593649	−	0.804724i	$-0.702313\pi$
$337$	−5.70981	−	32.3820i	−0.311033	−	1.76396i	0.282615	−	0.959233i	$-0.408798\pi$
$338$		0			0
$339$	8.61898	+	9.66892i	0.468119	+	0.525144i
$340$		0			0
$341$	0.982316	−	0.567140i	0.0531954	−	0.0307124i
$342$		0			0
$343$	−9.12950	+	15.8128i	−0.492947	+	0.853809i
$344$		0			0
$345$	−8.87423	+	3.53403i	−0.477772	+	0.190266i
$346$		0			0
$347$	−0.288638	+	0.793027i	−0.0154949	+	0.0425719i	−0.947199	−	0.320646i	$-0.896100\pi$
$347$	−0.288638	+	0.793027i	−0.0154949	+	0.0425719i	0.931704	+	0.363218i	$0.118322\pi$
$348$		0			0
$349$	13.8072	+	2.43459i	0.739085	+	0.130321i	0.530501	−	0.847684i	$-0.322004\pi$
$349$	13.8072	+	2.43459i	0.739085	+	0.130321i	0.208583	+	0.978005i	$0.433115\pi$
$350$		0			0
$351$	4.67429	+	17.2728i	0.249495	+	0.921952i
$352$		0			0
$353$	4.09441	−	23.2205i	0.217923	−	1.23590i	−0.657838	−	0.753159i	$-0.728529\pi$
$353$	4.09441	−	23.2205i	0.217923	−	1.23590i	0.875761	−	0.482744i	$-0.160360\pi$
$354$		0			0
$355$	4.66025	−	12.8039i	0.247341	−	0.679562i
$356$		0			0
$357$	−4.90889	+	6.21889i	−0.259806	+	0.329139i
$358$		0			0
$359$	13.4957	−	23.3753i	0.712277	−	1.23370i	−0.251724	−	0.967799i	$-0.580997\pi$
$359$	13.4957	−	23.3753i	0.712277	−	1.23370i	0.964001	−	0.265900i	$-0.0856692\pi$
$360$		0			0
$361$	−0.0939335	−	0.162698i	−0.00494387	−	0.00856303i
$362$		0			0
$363$	18.6127	−	3.85931i	0.976914	−	0.202561i
$364$		0			0
$365$	33.9641	−	5.98879i	1.77776	−	0.313468i
$366$		0			0
$367$	−22.3181	−	18.7271i	−1.16500	−	0.977547i	−0.165033	−	0.986288i	$-0.552773\pi$
$367$	−22.3181	−	18.7271i	−1.16500	−	0.977547i	−0.999962	+	0.00874090i	$0.997218\pi$
$368$		0			0
$369$	7.00930	+	29.3576i	0.364890	+	1.52829i
$370$		0			0
$371$	5.34353	+	14.6812i	0.277422	+	0.762211i
$372$		0			0
$373$	−0.738799	−	0.880467i	−0.0382536	−	0.0455888i	0.746578	−	0.665297i	$-0.231695\pi$
$373$	−0.738799	−	0.880467i	−0.0382536	−	0.0455888i	−0.784832	+	0.619709i	$0.787251\pi$
$374$		0			0
$375$	−9.17676	−	14.8502i	−0.473886	−	0.766862i
$376$		0			0
$377$	30.0906			1.54975
$378$		0			0
$379$			16.9124i			0.868731i	0.900737	+	0.434365i	$0.143027\pi$
$379$			16.9124i			0.868731i	−0.900737	+	0.434365i	$0.856973\pi$
$380$		0			0
$381$	21.1317	+	11.3715i	1.08261	+	0.582579i
$382$		0			0
$383$	−15.4572	+	12.9701i	−0.789826	+	0.662743i	−0.945702	−	0.325034i	$-0.894624\pi$
$383$	−15.4572	+	12.9701i	−0.789826	+	0.662743i	0.155876	+	0.987777i	$0.450180\pi$
$384$		0			0
$385$	0.575396	−	0.209427i	0.0293249	−	0.0106734i
$386$		0			0
$387$	−21.1296	+	28.4804i	−1.07408	+	1.44774i
$388$		0			0
$389$	−18.7454	+	22.3399i	−0.950428	+	1.13268i	0.0406204	+	0.999175i	$0.487067\pi$
$389$	−18.7454	+	22.3399i	−0.950428	+	1.13268i	−0.991049	+	0.133502i	$0.957378\pi$
$390$		0			0
$391$	1.13957	+	6.46284i	0.0576307	+	0.326840i
$392$		0			0
$393$	−8.49446	−	2.80694i	−0.428489	−	0.141592i
$394$		0			0
$395$	26.2690	−	15.1664i	1.32174	−	0.763105i
$396$		0			0
$397$	10.3158	+	5.95584i	0.517736	+	0.298915i	0.736008	−	0.676973i	$-0.236709\pi$
$397$	10.3158	+	5.95584i	0.517736	+	0.298915i	−0.218272	+	0.975888i	$0.570042\pi$
$398$		0			0
$399$	1.72453	−	11.8417i	0.0863347	−	0.592829i
$400$		0			0
$401$	2.23681	+	0.814132i	0.111701	+	0.0406558i	0.397266	−	0.917704i	$-0.369959\pi$
$401$	2.23681	+	0.814132i	0.111701	+	0.0406558i	−0.285565	+	0.958359i	$0.592181\pi$
$402$		0			0
$403$	24.1492	+	4.25815i	1.20296	+	0.212114i
$404$		0			0
$405$	15.8469	+	14.8518i	0.787441	+	0.737993i
$406$		0			0
$407$	−0.164360	+	0.932134i	−0.00814705	+	0.0462042i
$408$		0			0
$409$	12.0885	+	4.39986i	0.597739	+	0.217559i	0.623130	−	0.782119i	$-0.285861\pi$
$409$	12.0885	+	4.39986i	0.597739	+	0.217559i	−0.0253911	+	0.999678i	$0.508083\pi$
$410$		0			0
$411$	32.3201	+	4.70684i	1.59424	+	0.232171i
$412$		0			0
$413$	−3.69607	−	2.13393i	−0.181872	−	0.105004i
$414$		0			0
$415$	−13.6095	−	23.5724i	−0.668064	−	1.15712i
$416$		0			0
$417$	−26.6207	−	8.79666i	−1.30362	−	0.430774i
$418$		0			0
$419$	−7.38244	+	1.30172i	−0.360656	+	0.0635933i	−0.351040	−	0.936360i	$-0.614172\pi$
$419$	−7.38244	+	1.30172i	−0.360656	+	0.0635933i	−0.00961568	+	0.999954i	$0.503061\pi$
$420$		0			0
$421$	−5.15270	+	6.14075i	−0.251127	+	0.299282i	−0.876850	−	0.480763i	$-0.840360\pi$
$421$	−5.15270	+	6.14075i	−0.251127	+	0.299282i	0.625723	+	0.780045i	$0.284804\pi$
$422$		0			0
$423$	10.7321	−	4.65051i	0.521814	−	0.226115i
$424$		0			0
$425$	2.22213	−	0.808790i	0.107789	−	0.0392321i
$426$		0			0
$427$	−1.47501	−	1.75784i	−0.0713805	−	0.0850680i
$428$		0			0
$429$	−0.836681	−	0.450240i	−0.0403953	−	0.0217378i
$430$		0			0
$431$	4.63698			0.223356			0.111678	−	0.993744i	$-0.464378\pi$
$431$	4.63698			0.223356			0.111678	+	0.993744i	$0.464378\pi$
$432$		0			0
$433$	−0.0678381			−0.00326009			−0.00163005	−	0.999999i	$-0.500519\pi$
$433$	−0.0678381			−0.00326009			−0.00163005	+	0.999999i	$0.500519\pi$
$434$		0			0
$435$	31.0687	−	19.1990i	1.48963	−	0.920523i
$436$		0			0
$437$	−6.37133	−	7.59305i	−0.304782	−	0.363225i
$438$		0			0
$439$	−12.9530	+	4.71449i	−0.618211	+	0.225010i	−0.632092	−	0.774893i	$-0.717804\pi$
$439$	−12.9530	+	4.71449i	−0.618211	+	0.225010i	0.0138813	+	0.999904i	$0.495581\pi$
$440$		0			0
$441$	9.72272	−	9.20343i	0.462987	−	0.438258i
$442$		0			0
$443$	8.58044	−	10.2258i	0.407669	−	0.485841i	−0.522673	−	0.852533i	$-0.675065\pi$
$443$	8.58044	−	10.2258i	0.407669	−	0.485841i	0.930342	+	0.366692i	$0.119510\pi$
$444$		0			0
$445$	−17.7487	+	3.12957i	−0.841369	+	0.148356i
$446$		0			0
$447$	4.56104	+	21.9971i	0.215730	+	1.04043i
$448$		0			0
$449$	6.26480	+	10.8509i	0.295654	+	0.512088i	0.975137	−	0.221604i	$-0.0711291\pi$
$449$	6.26480	+	10.8509i	0.295654	+	0.512088i	−0.679483	+	0.733692i	$0.737796\pi$
$450$		0			0
$451$	−1.38792	−	0.801316i	−0.0653546	−	0.0377325i
$452$		0			0
$453$	−3.61041	+	4.57390i	−0.169632	+	0.214901i
$454$		0			0
$455$	12.4393	+	4.52755i	0.583166	+	0.212255i
$456$		0			0
$457$	3.14504	−	17.8364i	0.147119	−	0.834352i	−0.818523	−	0.574474i	$-0.805207\pi$
$457$	3.14504	−	17.8364i	0.147119	−	0.834352i	0.965642	−	0.259878i	$-0.0836822\pi$
$458$		0			0
$459$	12.2016	−	8.58894i	0.569521	−	0.400898i
$460$		0			0
$461$	6.87340	+	1.21197i	0.320126	+	0.0564469i	0.331402	−	0.943490i	$-0.392478\pi$
$461$	6.87340	+	1.21197i	0.320126	+	0.0564469i	−0.0112760	+	0.999936i	$0.503589\pi$
$462$		0			0
$463$	−26.8210	−	9.76206i	−1.24648	−	0.453681i	−0.367269	−	0.930115i	$-0.619707\pi$
$463$	−26.8210	−	9.76206i	−1.24648	−	0.453681i	−0.879210	+	0.476434i	$0.841929\pi$
$464$		0			0
$465$	27.6510	−	11.0116i	1.28229	−	0.510651i
$466$		0			0
$467$	−0.471619	−	0.272289i	−0.0218239	−	0.0126000i	0.489048	−	0.872257i	$-0.337344\pi$
$467$	−0.471619	−	0.272289i	−0.0218239	−	0.0126000i	−0.510872	+	0.859657i	$0.670677\pi$
$468$		0			0
$469$	−0.315627	+	0.182227i	−0.0145743	+	0.00841448i
$470$		0			0
$471$	−0.644726	+	0.574716i	−0.0297074	+	0.0264815i
$472$		0			0
$473$	−0.326975	−	1.85437i	−0.0150343	−	0.0852640i
$474$		0			0
$475$	−2.29584	+	2.73608i	−0.105340	+	0.125540i
$476$		0			0
$477$	−1.75956	−	29.3715i	−0.0805647	−	1.34483i
$478$		0			0
$479$	−7.93244	+	2.88717i	−0.362442	+	0.131918i	−0.516821	−	0.856094i	$-0.672885\pi$
$479$	−7.93244	+	2.88717i	−0.362442	+	0.131918i	0.154379	+	0.988012i	$0.450662\pi$
$480$		0			0
$481$	−15.6752	+	13.1530i	−0.714725	+	0.599726i
$482$		0			0
$483$	0.188609	+	6.30236i	0.00858200	+	0.286767i
$484$		0			0
$485$			16.3079i			0.740505i
$486$		0			0
$487$	15.0013			0.679775			0.339888	−	0.940466i	$-0.389611\pi$
$487$	15.0013			0.679775			0.339888	+	0.940466i	$0.389611\pi$
$488$		0			0
$489$	19.5705	−	0.585681i	0.885009	−	0.0264854i
$490$		0			0
$491$	−9.43399	−	11.2430i	−0.425750	−	0.507389i	0.509941	−	0.860209i	$-0.329667\pi$
$491$	−9.43399	−	11.2430i	−0.425750	−	0.507389i	−0.935691	+	0.352820i	$0.885223\pi$
$492$		0			0
$493$	−8.58191	−	23.5786i	−0.386510	−	1.06193i
$494$		0			0
$495$	−1.15115	+	0.0689619i	−0.0517402	+	0.00309961i
$496$		0			0
$497$	−6.88991	−	5.78132i	−0.309055	−	0.259328i
$498$		0			0
$499$	−17.0588	+	3.00792i	−0.763655	+	0.134653i	−0.541892	−	0.840448i	$-0.682292\pi$
$499$	−17.0588	+	3.00792i	−0.763655	+	0.134653i	−0.221762	+	0.975101i	$0.571181\pi$
$500$		0			0
$501$	15.1803	+	17.0295i	0.678206	+	0.760823i
$502$		0			0
$503$	2.40445	+	4.16463i	0.107209	+	0.185692i	0.914639	−	0.404272i	$-0.132475\pi$
$503$	2.40445	+	4.16463i	0.107209	+	0.185692i	−0.807429	+	0.589964i	$0.799142\pi$
$504$		0			0
$505$	−2.05591	+	3.56095i	−0.0914870	+	0.158460i
$506$		0			0
$507$	0.731069	+	1.83577i	0.0324679	+	0.0815296i
$508$		0			0
$509$	10.1785	−	27.9653i	0.451155	−	1.23954i	−0.480757	−	0.876854i	$-0.659638\pi$
$509$	10.1785	−	27.9653i	0.451155	−	1.23954i	0.931912	−	0.362685i	$-0.118140\pi$
$510$		0			0
$511$	3.95313	−	22.4193i	0.174876	−	0.991772i
$512$		0			0
$513$	−9.47383	+	20.4493i	−0.418280	+	0.902859i
$514$		0			0
$515$	−30.4722	−	5.37308i	−1.34277	−	0.236766i
$516$		0			0
$517$	−0.212412	+	0.583597i	−0.00934187	+	0.0256666i
$518$		0			0
$519$	22.2677	+	17.5771i	0.977445	+	0.771547i
$520$		0			0
$521$	15.3931	−	26.6615i	0.674382	−	1.16806i	−0.302267	−	0.953223i	$-0.597744\pi$
$521$	15.3931	−	26.6615i	0.674382	−	1.16806i	0.976649	−	0.214840i	$-0.0689231\pi$
$522$		0			0
$523$	20.1716	−	11.6461i	0.882042	−	0.509247i	0.0107111	−	0.999943i	$-0.496590\pi$
$523$	20.1716	−	11.6461i	0.882042	−	0.509247i	0.871331	+	0.490695i	$0.163257\pi$
$524$		0			0
$525$	2.22469	−	0.461284i	0.0970933	−	0.0201321i
$526$		0			0
$527$	−3.55077	−	20.1374i	−0.154674	−	0.877200i
$528$		0			0
$529$	−13.6183	−	11.4271i	−0.592099	−	0.496830i
$530$		0			0
$531$	5.52557	+	5.83734i	0.239789	+	0.253319i
$532$		0			0
$533$	−11.8499	−	32.5574i	−0.513278	−	1.41022i
$534$		0			0
$535$	−29.1263	+	24.4399i	−1.25924	+	1.05663i
$536$		0			0
$537$	−5.39768	−	8.73475i	−0.232927	−	0.376932i
$538$		0			0
$539$			0.710862i			0.0306190i
$540$		0			0
$541$			29.0030i			1.24694i	0.781848	+	0.623469i	$0.214277\pi$
$541$			29.0030i			1.24694i	−0.781848	+	0.623469i	$0.785723\pi$
$542$		0			0
$543$	1.42921	−	2.65591i	0.0613334	−	0.113976i
$544$		0			0
$545$	7.83541	−	6.57469i	0.335632	−	0.281629i
$546$		0			0
$547$	−3.84045	−	10.5516i	−0.164206	−	0.451152i	0.830113	−	0.557596i	$-0.188276\pi$
$547$	−3.84045	−	10.5516i	−0.164206	−	0.451152i	−0.994319	+	0.106443i	$0.966054\pi$
$548$		0			0
$549$	1.71831	+	3.96541i	0.0733358	+	0.169239i
$550$		0			0
$551$	29.0320	+	24.3607i	1.23681	+	1.03780i
$552$		0			0
$553$	−3.47684	−	19.7182i	−0.147850	−	0.838501i
$554$		0			0
$555$	−7.79251	+	23.5819i	−0.330774	+	1.00100i
$556$		0			0
$557$	2.53413	−	1.46308i	0.107374	−	0.0619927i	−0.445351	−	0.895356i	$-0.646921\pi$
$557$	2.53413	−	1.46308i	0.107374	−	0.0619927i	0.552726	+	0.833363i	$0.313588\pi$
$558$		0			0
$559$	20.3538	−	35.2538i	0.860874	−	1.49108i
$560$		0			0
$561$	−0.114178	+	0.784021i	−0.00482062	+	0.0331014i
$562$		0			0
$563$	2.96778	−	8.15390i	0.125077	−	0.343646i	−0.861312	−	0.508077i	$-0.830357\pi$
$563$	2.96778	−	8.15390i	0.125077	−	0.343646i	0.986389	+	0.164431i	$0.0525788\pi$
$564$		0			0
$565$	−17.7724	−	3.13375i	−0.747690	−	0.131838i
$566$		0			0
$567$	12.7899	−	6.47655i	0.537127	−	0.271989i
$568$		0			0
$569$	−1.80356	+	10.2285i	−0.0756093	+	0.428802i	0.923381	+	0.383884i	$0.125414\pi$
$569$	−1.80356	+	10.2285i	−0.0756093	+	0.428802i	−0.998991	+	0.0449179i	$0.985697\pi$
$570$		0			0
$571$	−1.71537	+	4.71295i	−0.0717862	+	0.197231i	−0.970397	−	0.241516i	$-0.922355\pi$
$571$	−1.71537	+	4.71295i	−0.0717862	+	0.197231i	0.898611	+	0.438747i	$0.144578\pi$
$572$		0			0
$573$	18.6175	+	2.71131i	0.777759	+	0.113266i
$574$		0			0
$575$	0.940956	−	1.62978i	0.0392406	−	0.0679667i
$576$		0			0
$577$	4.43057	+	7.67398i	0.184447	+	0.319472i	0.943390	−	0.331685i	$-0.107617\pi$
$577$	4.43057	+	7.67398i	0.184447	+	0.319472i	−0.758943	+	0.651157i	$0.774284\pi$
$578$		0			0
$579$	−7.86638	+	23.8055i	−0.326915	+	0.989321i
$580$		0			0
$581$	−17.6940	+	3.11993i	−0.734070	+	0.129436i
$582$		0			0
$583$	1.19683	+	1.00426i	0.0495677	+	0.0415922i
$584$		0			0
$585$	−20.0224	−	14.8546i	−0.827824	−	0.614162i
$586$		0			0
$587$	0.553940	+	1.52194i	0.0228636	+	0.0628171i	0.950599	−	0.310420i	$-0.100470\pi$
$587$	0.553940	+	1.52194i	0.0228636	+	0.0628171i	−0.927736	+	0.373238i	$0.878248\pi$
$588$		0			0
$589$	19.8523	+	23.6590i	0.817999	+	0.974854i
$590$		0			0
$591$	6.98401	−	12.9784i	0.287284	−	0.533860i
$592$		0			0
$593$	−16.7535			−0.687984			−0.343992	−	0.938973i	$-0.611779\pi$
$593$	−16.7535			−0.687984			−0.343992	+	0.938973i	$0.611779\pi$
$594$		0			0
$595$		−	11.0386i		−	0.452538i
$596$		0			0
$597$	18.2097	−	11.2528i	0.745273	−	0.460545i
$598$		0			0
$599$	31.3875	−	26.3372i	1.28246	−	1.07611i	0.289557	−	0.957161i	$-0.406492\pi$
$599$	31.3875	−	26.3372i	1.28246	−	1.07611i	0.992900	−	0.118949i	$-0.0379524\pi$
$600$		0			0
$601$	−8.03176	+	2.92332i	−0.327622	+	0.119245i	−0.500594	−	0.865682i	$-0.666885\pi$
$601$	−8.03176	+	2.92332i	−0.327622	+	0.119245i	0.172972	+	0.984927i	$0.444663\pi$
$602$		0			0
$603$	0.667626	−	0.159400i	0.0271878	−	0.00649126i
$604$		0			0
$605$	−17.0235	+	20.2878i	−0.692103	+	0.824817i
$606$		0			0
$607$	−4.22098	−	23.9383i	−0.171324	−	0.971627i	−0.942302	−	0.334765i	$-0.891343\pi$
$607$	−4.22098	−	23.9383i	−0.171324	−	0.971627i	0.770978	−	0.636862i	$-0.219768\pi$
$608$		0			0
$609$	−4.89460	−	23.6057i	−0.198339	−	0.956552i
$610$		0			0
$611$	−11.6276	+	6.71318i	−0.470401	+	0.271586i
$612$		0			0
$613$	14.3628	+	8.29237i	0.580108	+	0.334926i	0.761176	−	0.648545i	$-0.224622\pi$
$613$	14.3628	+	8.29237i	0.580108	+	0.334926i	−0.181068	+	0.983471i	$0.557955\pi$
$614$		0			0
$615$	−33.0081	−	26.0550i	−1.33101	−	1.05064i
$616$		0			0
$617$	−17.6023	−	6.40672i	−0.708642	−	0.257925i	−0.0375461	−	0.999295i	$-0.511954\pi$
$617$	−17.6023	−	6.40672i	−0.708642	−	0.257925i	−0.671096	+	0.741370i	$0.734176\pi$
$618$		0			0
$619$	4.87939	+	0.860368i	0.196119	+	0.0345811i	0.270845	−	0.962623i	$-0.412697\pi$
$619$	4.87939	+	0.860368i	0.196119	+	0.0345811i	−0.0747256	+	0.997204i	$0.523808\pi$
$620$		0			0
$621$	3.04488	−	11.4778i	0.122187	−	0.460587i
$622$		0			0
$623$	−2.06579	+	11.7157i	−0.0827643	+	0.469380i
$624$		0			0
$625$	26.7242	+	9.72681i	1.06897	+	0.389072i
$626$		0			0
$627$	−0.442741	−	1.11176i	−0.0176814	−	0.0443994i
$628$		0			0
$629$	14.7771	+	8.53157i	0.589202	+	0.340176i
$630$		0			0
$631$	2.46788	+	4.27449i	0.0982447	+	0.170165i	0.910958	−	0.412499i	$-0.135344\pi$
$631$	2.46788	+	4.27449i	0.0982447	+	0.170165i	−0.812713	+	0.582664i	$0.802011\pi$
$632$		0			0
$633$	−2.28583	+	2.03761i	−0.0908536	+	0.0809879i
$634$		0			0
$635$	−32.9261	+	5.80576i	−1.30663	+	0.230394i
$636$		0			0
$637$	−9.87834	+	11.7725i	−0.391394	+	0.466445i
$638$		0			0
$639$	9.33158	+	14.1369i	0.369152	+	0.559246i
$640$		0			0
$641$	1.74409	−	0.634798i	0.0688875	−	0.0250730i	−0.307347	−	0.951598i	$-0.599441\pi$
$641$	1.74409	−	0.634798i	0.0688875	−	0.0250730i	0.376234	+	0.926525i	$0.377219\pi$
$642$		0			0
$643$	21.2761	+	25.3559i	0.839048	+	0.999938i	0.999916	+	0.0129623i	$0.00412614\pi$
$643$	21.2761	+	25.3559i	0.839048	+	0.999938i	−0.160868	+	0.986976i	$0.551429\pi$
$644$		0			0
$645$	−1.47797	−	49.3863i	−0.0581949	−	1.94458i
$646$		0			0
$647$	−8.85391			−0.348083			−0.174042	−	0.984738i	$-0.555683\pi$
$647$	−8.85391			−0.348083			−0.174042	+	0.984738i	$0.555683\pi$
$648$		0			0
$649$	−0.426789			−0.0167529
$650$		0			0
$651$	−0.587682	−	19.6374i	−0.0230331	−	0.769650i
$652$		0			0
$653$	−6.38975	−	7.61501i	−0.250050	−	0.297998i	0.626389	−	0.779511i	$-0.284532\pi$
$653$	−6.38975	−	7.61501i	−0.250050	−	0.297998i	−0.876439	+	0.481512i	$0.840088\pi$
$654$		0			0
$655$	11.7127	−	4.26306i	0.457652	−	0.166572i
$656$		0			0
$657$	−19.1785	+	38.3459i	−0.748224	+	1.49601i
$658$		0			0
$659$	27.1973	−	32.4125i	1.05946	−	1.26261i	0.0958197	−	0.995399i	$-0.469453\pi$
$659$	27.1973	−	32.4125i	1.05946	−	1.26261i	0.963637	−	0.267213i	$-0.0861028\pi$
$660$		0			0
$661$	−49.7307	+	8.76886i	−1.93430	+	0.341069i	−0.999886	−	0.0151198i	$-0.995187\pi$
$661$	−49.7307	+	8.76886i	−1.93430	+	0.341069i	−0.934414	+	0.356189i	$0.884076\pi$
$662$		0			0
$663$	−12.7859	+	11.3975i	−0.496562	+	0.442641i
$664$		0			0
$665$	8.33631	+	14.4389i	0.323268	+	0.559917i
$666$		0			0
$667$	−17.2933	−	9.98430i	−0.669600	−	0.386594i
$668$		0			0
$669$	−1.92803	−	4.84143i	−0.0745418	−	0.187181i
$670$		0			0
$671$	−0.215633	−	0.0784840i	−0.00832442	−	0.00302984i
$672$		0			0
$673$	2.52619	−	14.3267i	0.0973775	−	0.552255i	−0.896615	−	0.442810i	$-0.853981\pi$
$673$	2.52619	−	14.3267i	0.0973775	−	0.552255i	0.993993	−	0.109445i	$-0.0349074\pi$
$674$		0			0
$675$	−4.26358	−	0.362334i	−0.164105	−	0.0139462i
$676$		0			0
$677$	39.3485	+	6.93820i	1.51229	+	0.266657i	0.867396	−	0.497619i	$-0.165792\pi$
$677$	39.3485	+	6.93820i	1.51229	+	0.266657i	0.644890	+	0.764276i	$0.276903\pi$
$678$		0			0
$679$	10.1155	+	3.68173i	0.388197	+	0.141292i
$680$		0			0
$681$	7.73127	+	6.10268i	0.296263	+	0.233855i
$682$		0			0
$683$	−16.3031	−	9.41260i	−0.623821	−	0.360163i	0.154534	−	0.987987i	$-0.450612\pi$
$683$	−16.3031	−	9.41260i	−0.623821	−	0.360163i	−0.778355	+	0.627824i	$0.783946\pi$
$684$		0			0
$685$	−39.4087	+	22.7526i	−1.50573	+	0.869333i
$686$		0			0
$687$	7.65794	+	36.9328i	0.292168	+	1.40907i
$688$		0			0
$689$	5.86516	+	33.2630i	0.223445	+	1.26722i
$690$		0			0
$691$	7.33473	−	8.74119i	0.279026	−	0.332531i	−0.608270	−	0.793730i	$-0.708136\pi$
$691$	7.33473	−	8.74119i	0.279026	−	0.332531i	0.887297	+	0.461199i	$0.152581\pi$
$692$		0			0
$693$	−0.217111	+	0.729603i	−0.00824738	+	0.0277153i
$694$		0			0
$695$	36.7062	−	13.3600i	1.39235	−	0.506773i
$696$		0			0
$697$	−22.1320	+	18.5709i	−0.838307	+	0.703423i
$698$		0			0
$699$	−34.6201	+	21.3937i	−1.30945	+	0.809182i
$700$		0			0
$701$		−	29.8398i		−	1.12704i	−0.826104	−	0.563518i	$-0.809448\pi$
$701$		−	29.8398i		−	1.12704i	0.826104	−	0.563518i	$-0.190552\pi$
$702$		0			0
$703$	−25.7721			−0.972013
$704$		0			0
$705$	−7.72223	+	14.3502i	−0.290836	+	0.540461i
$706$		0			0
$707$	1.74463	+	2.07917i	0.0656137	+	0.0781954i
$708$		0			0
$709$	−0.897749	−	2.46655i	−0.0337157	−	0.0926331i	0.921693	−	0.387921i	$-0.126807\pi$
$709$	−0.897749	−	2.46655i	−0.0337157	−	0.0926331i	−0.955408	+	0.295288i	$0.904584\pi$
$710$		0			0
$711$	−4.31562	+	37.4610i	−0.161849	+	1.40490i
$712$		0			0
$713$	−12.4658	−	10.4601i	−0.466849	−	0.391733i
$714$		0			0
$715$	1.30367	−	0.229871i	0.0487543	−	0.00859670i
$716$		0			0
$717$	−12.7161	+	38.4819i	−0.474892	+	1.43713i
$718$		0			0
$719$	6.54404	+	11.3346i	0.244051	+	0.422709i	0.961864	−	0.273526i	$-0.0881901\pi$
$719$	6.54404	+	11.3346i	0.244051	+	0.422709i	−0.717813	+	0.696236i	$0.754857\pi$
$720$		0			0
$721$	−10.2123	+	17.6883i	−0.380327	+	0.658746i
$722$		0			0
$723$	−6.73475	−	0.980794i	−0.250468	−	0.0364761i
$724$		0			0
$725$	−2.46100	+	6.76154i	−0.0913992	+	0.251117i
$726$		0			0
$727$	−6.97054	+	39.5319i	−0.258523	+	1.46616i	0.528342	+	0.849031i	$0.322814\pi$
$727$	−6.97054	+	39.5319i	−0.258523	+	1.46616i	−0.786865	+	0.617125i	$0.788297\pi$
$728$		0			0
$729$	−26.5662	+	4.82069i	−0.983932	+	0.178544i
$730$		0			0
$731$	−33.4294	−	5.89450i	−1.23643	−	0.218016i
$732$		0			0
$733$	0.696450	−	1.91348i	0.0257240	−	0.0706760i	−0.926166	−	0.377116i	$-0.876916\pi$
$733$	0.696450	−	1.91348i	0.0257240	−	0.0706760i	0.951890	+	0.306440i	$0.0991380\pi$
$734$		0			0
$735$	−2.68807	+	18.4580i	−0.0991509	+	0.680833i
$736$		0			0
$737$	−0.0182229	+	0.0315629i	−0.000671248	+	0.00116264i
$738$		0			0
$739$	−30.6990	+	17.7241i	−1.12928	+	0.651990i	−0.943754	−	0.330649i	$-0.892732\pi$
$739$	−30.6990	+	17.7241i	−1.12928	+	0.651990i	−0.185526	+	0.982639i	$0.559399\pi$
$740$		0			0
$741$	8.11710	−	24.5642i	0.298189	−	0.902389i
$742$		0			0
$743$	−9.22773	−	52.3330i	−0.338532	−	1.91991i	−0.389106	−	0.921193i	$-0.627216\pi$
$743$	−9.22773	−	52.3330i	−0.338532	−	1.91991i	0.0505739	−	0.998720i	$-0.483895\pi$
$744$		0			0
$745$	−23.9767	−	20.1189i	−0.878440	−	0.737099i
$746$		0			0
$747$	33.6155	+	3.87260i	1.22993	+	0.141691i
$748$		0			0
$749$	8.58392	+	23.5841i	0.313649	+	0.861745i
$750$		0			0
$751$	−6.58894	+	5.52878i	−0.240434	+	0.201748i	−0.755040	−	0.655679i	$-0.772383\pi$
$751$	−6.58894	+	5.52878i	−0.240434	+	0.201748i	0.514606	+	0.857427i	$0.327938\pi$
$752$		0			0
$753$	−0.409396	+	0.760782i	−0.0149192	+	0.0277244i
$754$		0			0
$755$		−	8.11871i		−	0.295470i
$756$		0			0
$757$			21.7216i			0.789484i	0.918792	+	0.394742i	$0.129166\pi$
$757$			21.7216i			0.789484i	−0.918792	+	0.394742i	$0.870834\pi$
$758$		0			0
$759$	0.331454	+	0.536373i	0.0120310	+	0.0194691i
$760$		0			0
$761$	−0.341041	+	0.286168i	−0.0123627	+	0.0103736i	−0.648948	−	0.760833i	$-0.724791\pi$
$761$	−0.341041	+	0.286168i	−0.0123627	+	0.0103736i	0.636585	+	0.771206i	$0.280346\pi$
$762$		0			0
$763$	−2.30920	−	6.34447i	−0.0835986	−	0.229685i
$764$		0			0
$765$	−5.92943	+	19.9258i	−0.214379	+	0.720420i
$766$		0			0
$767$	−7.06802	−	5.93077i	−0.255211	−	0.214148i
$768$		0			0
$769$	3.22004	+	18.2618i	0.116118	+	0.658536i	0.986191	+	0.165614i	$0.0529604\pi$
$769$	3.22004	+	18.2618i	0.116118	+	0.658536i	−0.870073	+	0.492923i	$0.835928\pi$
$770$		0			0
$771$	1.52536	−	0.316280i	0.0549345	−	0.0113905i
$772$		0			0
$773$	1.50501	−	0.868919i	0.0541315	−	0.0312528i	−0.472690	−	0.881229i	$-0.656717\pi$
$773$	1.50501	−	0.868919i	0.0541315	−	0.0312528i	0.526822	+	0.849976i	$0.323384\pi$
$774$		0			0
$775$	−2.93190	+	5.07821i	−0.105317	+	0.182415i
$776$		0			0
$777$	12.8681	+	10.1575i	0.461642	+	0.364397i
$778$		0			0
$779$	14.9248	−	41.0055i	0.534736	−	1.46918i
$780$		0			0
$781$	−0.885756	−	0.156183i	−0.0316948	−	0.00558865i
$782$		0			0
$783$	−3.84465	+	45.2401i	−0.137397	+	1.61675i
$784$		0			0
$785$	0.208959	−	1.18507i	0.00745808	−	0.0422969i
$786$		0			0
$787$	12.6576	−	34.7764i	0.451193	−	1.23964i	−0.480692	−	0.876890i	$-0.659614\pi$
$787$	12.6576	−	34.7764i	0.451193	−	1.23964i	0.931885	−	0.362754i	$-0.118163\pi$
$788$		0			0
$789$	−6.42394	−	16.1310i	−0.228698	−	0.574280i
$790$		0			0
$791$	−5.95616	+	10.3164i	−0.211777	+	0.366808i
$792$		0			0
$793$	−2.48045	−	4.29626i	−0.0880833	−	0.152565i
$794$		0			0
$795$	27.2789	+	30.6020i	0.967484	+	1.08534i
$796$		0			0
$797$	11.7114	−	2.06503i	0.414837	−	0.0731470i	0.0376658	−	0.999290i	$-0.488008\pi$
$797$	11.7114	−	2.06503i	0.414837	−	0.0731470i	0.377172	+	0.926143i	$0.376897\pi$
$798$		0			0
$799$	8.57656	+	7.19659i	0.303417	+	0.254597i
$800$		0			0
$801$	10.0221	−	20.0385i	0.354115	−	0.708025i
$802$		0			0
$803$	−0.778620	−	2.13924i	−0.0274769	−	0.0754922i
$804$		0			0
$805$	−5.64671	−	6.72949i	−0.199021	−	0.237183i
$806$		0			0
$807$	−1.80155	+	0.0539145i	−0.0634176	+	0.00189788i
$808$		0			0
$809$	13.6067			0.478385			0.239192	−	0.970972i	$-0.423117\pi$
$809$	13.6067			0.478385			0.239192	+	0.970972i	$0.423117\pi$
$810$		0			0
$811$			23.1998i			0.814656i	0.913282	+	0.407328i	$0.133539\pi$
$811$			23.1998i			0.814656i	−0.913282	+	0.407328i	$0.866461\pi$
$812$		0			0
$813$	−1.55645	−	52.0088i	−0.0545872	−	1.82403i
$814$		0			0
$815$	−20.8969	+	17.5346i	−0.731985	+	0.614209i
$816$		0			0
$817$	48.1785	−	17.5355i	1.68555	−	0.613491i
$818$		0			0
$819$	−13.7343	+	9.06586i	−0.479916	+	0.316787i
$820$		0			0
$821$	18.9516	−	22.5856i	0.661414	−	0.788243i	−0.326174	−	0.945310i	$-0.605759\pi$
$821$	18.9516	−	22.5856i	0.661414	−	0.788243i	0.987588	+	0.157067i	$0.0502039\pi$
$822$		0			0
$823$	−2.95142	−	16.7383i	−0.102880	−	0.583462i	−0.992046	−	0.125877i	$-0.959826\pi$
$823$	−2.95142	−	16.7383i	−0.102880	−	0.583462i	0.889166	−	0.457585i	$-0.151285\pi$
$824$		0			0
$825$	0.169600	−	0.151184i	0.00590473	−	0.00526354i
$826$		0			0
$827$	−44.0488	+	25.4316i	−1.53173	+	0.884343i	−0.532444	+	0.846465i	$0.678726\pi$
$827$	−44.0488	+	25.4316i	−1.53173	+	0.884343i	−0.999282	+	0.0378772i	$0.987940\pi$
$828$		0			0
$829$	−41.8595	−	24.1676i	−1.45384	−	0.839374i	−0.455143	−	0.890418i	$-0.650412\pi$
$829$	−41.8595	−	24.1676i	−1.45384	−	0.839374i	−0.998696	+	0.0510440i	$0.983745\pi$
$830$		0			0
$831$	31.6124	−	12.5892i	1.09662	−	0.436713i
$832$		0			0
$833$	12.0421	+	4.38298i	0.417235	+	0.151861i
$834$		0			0
$835$	−31.3019	−	5.51936i	−1.08325	−	0.191005i
$836$		0			0
$837$	−9.48749	+	35.7633i	−0.327936	+	1.23616i
$838$		0			0
$839$	−4.93028	+	27.9610i	−0.170212	+	0.965321i	0.773314	+	0.634023i	$0.218598\pi$
$839$	−4.93028	+	27.9610i	−0.170212	+	0.965321i	−0.943526	+	0.331298i	$0.892514\pi$
$840$		0			0
$841$	44.4943	+	16.1946i	1.53429	+	0.558434i
$842$		0			0
$843$	29.7968	−	37.7485i	1.02626	−	1.30013i
$844$		0			0
$845$	−2.38422	−	1.37653i	−0.0820196	−	0.0473540i
$846$		0			0
$847$	8.74084	+	15.1396i	0.300339	+	0.520202i
$848$		0			0
$849$	8.77594	+	42.3247i	0.301190	+	1.45258i
$850$		0			0
$851$	13.3729	−	2.35800i	0.458417	−	0.0808313i
$852$		0			0
$853$	−17.3921	+	20.7271i	−0.595495	+	0.709684i	−0.976652	−	0.214827i	$-0.931081\pi$
$853$	−17.3921	+	20.7271i	−0.595495	+	0.709684i	0.381157	+	0.924510i	$0.375526\pi$
$854$		0			0
$855$	−7.29202	−	30.5417i	−0.249382	−	1.04450i
$856$		0			0
$857$	1.73329	−	0.630867i	0.0592082	−	0.0215500i	−0.312246	−	0.950001i	$-0.601081\pi$
$857$	1.73329	−	0.630867i	0.0592082	−	0.0215500i	0.371454	+	0.928451i	$0.378859\pi$
$858$		0			0
$859$	11.6792	+	13.9187i	0.398489	+	0.474901i	0.927559	−	0.373678i	$-0.121903\pi$
$859$	11.6792	+	13.9187i	0.398489	+	0.474901i	−0.529070	+	0.848578i	$0.677459\pi$
$860$		0			0
$861$	−23.6134	+	14.5920i	−0.804742	+	0.497294i
$862$		0			0
$863$	−49.6695			−1.69077			−0.845385	−	0.534157i	$-0.820629\pi$
$863$	−49.6695			−1.69077			−0.845385	+	0.534157i	$0.820629\pi$
$864$		0			0
$865$	−39.5254			−1.34390
$866$		0			0
$867$	−13.3515	−	7.18480i	−0.453441	−	0.244008i
$868$		0			0
$869$	−1.28702	−	1.53381i	−0.0436592	−	0.0520310i
$870$		0			0
$871$	−0.740394	+	0.269482i	−0.0250873	+	0.00913103i
$872$		0			0
$873$	−16.2819	−	12.0795i	−0.551059	−	0.408830i
$874$		0			0
$875$	10.3197	−	12.2985i	0.348869	−	0.415766i
$876$		0			0
$877$	22.9919	−	4.05410i	0.776382	−	0.136897i	0.228603	−	0.973520i	$-0.426584\pi$
$877$	22.9919	−	4.05410i	0.776382	−	0.136897i	0.547779	+	0.836623i	$0.315473\pi$
$878$		0			0
$879$	−13.4290	−	4.43753i	−0.452948	−	0.149674i
$880$		0			0
$881$	−15.9640	−	27.6505i	−0.537842	−	0.931569i	−0.999020	−	0.0442614i	$-0.985907\pi$
$881$	−15.9640	−	27.6505i	−0.537842	−	0.931569i	0.461178	−	0.887307i	$-0.347427\pi$
$882$		0			0
$883$	40.1101	+	23.1576i	1.34981	+	0.779315i	0.988223	−	0.153023i	$-0.0489007\pi$
$883$	40.1101	+	23.1576i	1.34981	+	0.779315i	0.361590	+	0.932337i	$0.382234\pi$
$884$		0			0
$885$	−11.0818	−	1.61387i	−0.372512	−	0.0542496i
$886$		0			0
$887$	32.0649	+	11.6707i	1.07663	+	0.391863i	0.818654	−	0.574288i	$-0.194721\pi$
$887$	32.0649	+	11.6707i	1.07663	+	0.391863i	0.257980	+	0.966150i	$0.416943\pi$
$888$		0			0
$889$	−3.83231	+	21.7341i	−0.128532	+	0.728939i
$890$		0			0
$891$	0.783820	−	1.20039i	0.0262589	−	0.0402146i
$892$		0			0
$893$	−16.6533	−	2.93643i	−0.557283	−	0.0982640i
$894$		0			0
$895$	13.4431	+	4.89290i	0.449354	+	0.163552i
$896$		0			0
$897$	−1.96440	+	13.4888i	−0.0655894	+	0.450379i
$898$		0			0
$899$	53.8839	+	31.1099i	1.79713	+	1.03757i
$900$		0			0
$901$	24.3917	−	14.0825i	0.812605	−	0.469158i
$902$		0			0
$903$	−30.9670	−	10.2329i	−1.03052	−	0.340528i
$904$		0			0
$905$	0.729690	+	4.13828i	0.0242557	+	0.137561i
$906$		0			0
$907$	−0.685743	+	0.817237i	−0.0227697	+	0.0271359i	−0.777309	−	0.629119i	$-0.783416\pi$
$907$	−0.685743	+	0.817237i	−0.0227697	+	0.0271359i	0.754539	+	0.656255i	$0.227860\pi$
$908$		0			0
$909$	−2.03242	−	4.69028i	−0.0674110	−	0.155567i
$910$		0			0
$911$	−2.39685	+	0.872383i	−0.0794113	+	0.0289033i	−0.381420	−	0.924402i	$-0.624565\pi$
$911$	−2.39685	+	0.872383i	−0.0794113	+	0.0289033i	0.302009	+	0.953305i	$0.402343\pi$
$912$		0			0
$913$	−1.37636	+	1.15490i	−0.0455508	+	0.0382216i
$914$		0			0
$915$	−5.30226	−	2.85328i	−0.175287	−	0.0943266i
$916$		0			0
$917$		−	8.22758i		−	0.271699i
$918$		0			0
$919$	−3.85703			−0.127232			−0.0636159	−	0.997974i	$-0.520263\pi$
$919$	−3.85703			−0.127232			−0.0636159	+	0.997974i	$0.520263\pi$
$920$		0			0
$921$	16.9518	+	27.4321i	0.558579	+	0.903917i
$922$		0			0
$923$	−12.4986	−	14.8952i	−0.411396	−	0.490283i
$924$		0			0
$925$	−1.67355	−	4.59804i	−0.0550259	−	0.151182i
$926$		0			0
$927$	27.9357	−	26.4437i	0.917530	−	0.868524i
$928$		0			0
$929$	23.6191	+	19.8188i	0.774919	+	0.650234i	0.941964	−	0.335715i	$-0.108978\pi$
$929$	23.6191	+	19.8188i	0.774919	+	0.650234i	−0.167045	+	0.985949i	$0.553422\pi$
$930$		0			0
$931$	−19.0616	+	3.36108i	−0.624719	+	0.110155i
$932$		0			0
$933$	8.31744	−	1.72460i	0.272301	−	0.0564610i
$934$		0			0
$935$	−0.551933	−	0.955975i	−0.0180501	−	0.0312637i
$936$		0			0
$937$	3.69048	−	6.39210i	0.120563	−	0.208821i	−0.799427	−	0.600763i	$-0.794863\pi$
$937$	3.69048	−	6.39210i	0.120563	−	0.208821i	0.919990	+	0.391942i	$0.128197\pi$
$938$		0			0
$939$	−11.0516	+	14.0008i	−0.360655	+	0.456900i
$940$		0			0
$941$	−13.1119	+	36.0246i	−0.427435	+	1.17437i	0.519929	+	0.854209i	$0.325958\pi$
$941$	−13.1119	+	36.0246i	−0.427435	+	1.17437i	−0.947364	+	0.320158i	$0.896264\pi$
$942$		0			0
$943$	−3.99256	+	22.6429i	−0.130016	+	0.737355i
$944$		0			0
$945$	−8.39636	+	18.1236i	−0.273134	+	0.589561i
$946$		0			0
$947$	21.8272	+	3.84873i	0.709289	+	0.125067i	0.516642	−	0.856201i	$-0.327182\pi$
$947$	21.8272	+	3.84873i	0.709289	+	0.125067i	0.192647	+	0.981268i	$0.438293\pi$
$948$		0			0
$949$	16.8328	−	46.2477i	0.546416	−	1.50126i
$950$		0			0
$951$	−36.3335	+	14.4693i	−1.17819	+	0.469198i
$952$		0			0
$953$	22.3908	−	38.7819i	0.725308	−	1.25627i	−0.233540	−	0.972347i	$-0.575031\pi$
$953$	22.3908	−	38.7819i	0.725308	−	1.25627i	0.958847	−	0.283922i	$-0.0916358\pi$
$954$		0			0
$955$	−22.7008	+	13.1063i	−0.734580	+	0.424110i
$956$		0			0
$957$	−1.60418	−	1.79960i	−0.0518558	−	0.0581727i
$958$		0			0
$959$	5.21595	+	29.5811i	0.168432	+	0.955224i
$960$		0			0
$961$	15.0947	+	12.6659i	0.486925	+	0.408579i
$962$		0			0
$963$	−2.82658	−	47.1828i	−0.0910854	−	1.52044i
$964$		0			0
$965$	−11.9471	−	32.8244i	−0.384591	−	1.05666i
$966$		0			0
$967$	−32.4852	+	27.2583i	−1.04465	+	0.876567i	−0.992521	−	0.122073i	$-0.961046\pi$
$967$	−32.4852	+	27.2583i	−1.04465	+	0.876567i	−0.0521310	+	0.998640i	$0.516601\pi$
$968$		0			0
$969$	−21.5632	+	0.645316i	−0.692710	+	0.0207305i
$970$		0			0
$971$			9.33492i			0.299572i	0.988718	+	0.149786i	$0.0478584\pi$
$971$			9.33492i			0.299572i	−0.988718	+	0.149786i	$0.952142\pi$
$972$		0			0
$973$		−	25.7843i		−	0.826608i
$974$		0			0
$975$	4.90963	−	0.146929i	0.157234	−	0.00470550i
$976$		0			0
$977$	0.274142	−	0.230032i	0.00877057	−	0.00735938i	−0.638392	−	0.769712i	$-0.720400\pi$
$977$	0.274142	−	0.230032i	0.00877057	−	0.00735938i	0.647162	+	0.762352i	$0.275956\pi$
$978$		0			0
$979$	0.406885	+	1.11791i	0.0130041	+	0.0357285i
$980$		0			0
$981$	0.760392	+	12.6929i	0.0242774	+	0.405252i
$982$		0			0
$983$	6.53130	+	5.48041i	0.208316	+	0.174798i	0.740976	−	0.671531i	$-0.234363\pi$
$983$	6.53130	+	5.48041i	0.208316	+	0.174798i	−0.532660	+	0.846329i	$0.678808\pi$
$984$		0			0
$985$	3.56571	+	20.2221i	0.113613	+	0.644331i
$986$		0			0
$987$	7.15777	+	8.02970i	0.227834	+	0.255588i
$988$		0			0
$989$	−23.3950	+	13.5071i	−0.743917	+	0.429501i
$990$		0			0
$991$	25.9790	−	44.9969i	0.825249	−	1.42937i	−0.0764798	−	0.997071i	$-0.524368\pi$
$991$	25.9790	−	44.9969i	0.825249	−	1.42937i	0.901729	−	0.432302i	$-0.142299\pi$
$992$		0			0
$993$	37.9348	−	15.1070i	1.20383	−	0.479405i
$994$		0			0
$995$	−10.2004	+	28.0255i	−0.323375	+	0.888467i
$996$		0			0
$997$	44.7921	+	7.89805i	1.41858	+	0.250134i	0.829755	−	0.558128i	$-0.188480\pi$
$997$	44.7921	+	7.89805i	1.41858	+	0.250134i	0.588824	+	0.808262i	$0.299591\pi$
$998$		0			0
$999$	−17.7722	−	25.2475i	−0.562289	−	0.798797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.241.17		204
4.3	odd	2		216.2.t.a.133.31	yes	204
8.3	odd	2		216.2.t.a.133.9	yes	204
8.5	even	2	inner	864.2.bf.a.241.18		204
12.11	even	2		648.2.t.a.397.4		204
24.11	even	2		648.2.t.a.397.26		204
27.13	even	9	inner	864.2.bf.a.337.18		204
108.67	odd	18		216.2.t.a.13.9	✓	204
108.95	even	18		648.2.t.a.253.26		204
216.13	even	18	inner	864.2.bf.a.337.17		204
216.67	odd	18		216.2.t.a.13.31	yes	204
216.203	even	18		648.2.t.a.253.4		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.9	✓	204	108.67	odd	18
216.2.t.a.13.31	yes	204	216.67	odd	18
216.2.t.a.133.9	yes	204	8.3	odd	2
216.2.t.a.133.31	yes	204	4.3	odd	2
648.2.t.a.253.4		204	216.203	even	18
648.2.t.a.253.26		204	108.95	even	18
648.2.t.a.397.4		204	12.11	even	2
648.2.t.a.397.26		204	24.11	even	2
864.2.bf.a.241.17		204	1.1	even	1	trivial
864.2.bf.a.241.18		204	8.5	even	2	inner
864.2.bf.a.337.17		204	216.13	even	18	inner
864.2.bf.a.337.18		204	27.13	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.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0518114 - 1.73128i) q^{3} +(1.55117 + 1.84861i) q^{5} +(1.49685 - 0.544810i) q^{7} +(-2.99463 + 0.179400i) q^{9} +(0.102391 - 0.122025i) q^{11} +(3.39140 - 0.597995i) q^{13} +(3.12009 - 2.78128i) q^{15} +(-1.43581 - 2.48690i) q^{17} +(3.75621 + 2.16865i) q^{19} +(-1.02077 - 2.56324i) q^{21} +(-2.14748 - 0.781619i) q^{23} +(-0.142997 + 0.810974i) q^{25} +(0.465746 + 5.17524i) q^{27} +(8.60509 + 1.51731i) q^{29} +(6.69129 + 2.43543i) q^{31} +(-0.216565 - 0.170946i) q^{33} +(3.32901 + 1.92201i) q^{35} +(-5.14590 + 2.97099i) q^{37} +(-1.21101 - 5.84046i) q^{39} +(-1.74706 - 9.90807i) q^{41} +(7.59829 - 9.05529i) q^{43} +(-4.97682 - 5.25763i) q^{45} +(-3.66367 + 1.33347i) q^{47} +(-3.41856 + 2.86851i) q^{49} +(-4.23112 + 2.61464i) q^{51} +9.80805i q^{53} +0.384404 q^{55} +(3.55991 - 6.61539i) q^{57} +(-1.72220 - 2.05244i) q^{59} +(-0.492702 - 1.35369i) q^{61} +(-4.38478 + 1.90004i) q^{63} +(6.36609 + 5.34178i) q^{65} +(-0.225321 + 0.0397302i) q^{67} +(-1.24193 + 3.75838i) q^{69} +(-2.82317 - 4.88987i) q^{71} +(7.14574 - 12.3768i) q^{73} +(1.41143 + 0.205549i) q^{75} +(0.0867843 - 0.238438i) q^{77} +(2.18269 - 12.3786i) q^{79} +(8.93563 - 1.07447i) q^{81} +(-11.1079 - 1.95862i) q^{83} +(2.37013 - 6.51187i) q^{85} +(2.18104 - 14.9764i) q^{87} +(-3.73417 + 6.46777i) q^{89} +(4.75063 - 2.74278i) q^{91} +(3.86972 - 11.7107i) q^{93} +(1.81753 + 10.3077i) q^{95} +(5.17680 + 4.34385i) q^{97} +(-0.284733 + 0.383790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 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