LMFDB - Embedded newform 864.2.bh.b.815.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(47,864)] 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("864.47"); 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([9, 9, 7])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			815.1
Character	$\chi$	$=$	864.815
Dual form			864.2.bh.b.335.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73063 - 0.0701536i) q^{3} +(-0.426624 + 0.155279i) q^{5} +(-1.28150 + 0.225962i) q^{7} +(2.99016 + 0.242820i) q^{9} +(-0.00602720 + 0.0165596i) q^{11} +(1.43581 - 1.71113i) q^{13} +(0.749222 - 0.238801i) q^{15} +(1.27216 + 0.734483i) q^{17} +(-0.677841 - 1.17406i) q^{19} +(2.23365 - 0.301155i) q^{21} +(-0.369486 + 2.09546i) q^{23} +(-3.67233 + 3.08145i) q^{25} +(-5.15782 - 0.630001i) q^{27} +(-5.56933 + 4.67322i) q^{29} +(-8.87753 - 1.56535i) q^{31} +(0.0115926 - 0.0282357i) q^{33} +(0.511630 - 0.295390i) q^{35} +(-4.58718 - 2.64841i) q^{37} +(-2.60490 + 2.86061i) q^{39} +(1.56527 - 1.86542i) q^{41} +(10.1956 + 3.71089i) q^{43} +(-1.31338 + 0.360715i) q^{45} +(0.791397 + 4.48824i) q^{47} +(-4.98668 + 1.81500i) q^{49} +(-2.15011 - 1.36036i) q^{51} -10.4085 q^{53} -0.00800062i q^{55} +(1.09073 + 2.07941i) q^{57} +(3.75319 + 10.3118i) q^{59} +(-8.87057 + 1.56412i) q^{61} +(-3.88674 + 0.364490i) q^{63} +(-0.346849 + 0.952961i) q^{65} +(-3.70041 - 3.10502i) q^{67} +(0.786447 - 3.60054i) q^{69} +(-5.03714 + 8.72458i) q^{71} +(-0.339460 - 0.587962i) q^{73} +(6.57161 - 5.07522i) q^{75} +(0.00398198 - 0.0225829i) q^{77} +(-5.19665 - 6.19313i) q^{79} +(8.88208 + 1.45214i) q^{81} +(-1.29122 - 1.53881i) q^{83} +(-0.656785 - 0.115809i) q^{85} +(9.96629 - 7.69691i) q^{87} +(-0.103744 + 0.0598964i) q^{89} +(-1.45333 + 2.51724i) q^{91} +(15.2539 + 3.33183i) q^{93} +(0.471489 + 0.395626i) q^{95} +(-10.4801 - 3.81446i) q^{97} +(-0.0220433 + 0.0480522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67}+ \cdots + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$-1$

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
$3$	−1.73063	−	0.0701536i	−0.999179	−	0.0405032i
$3$	−1.73063	−	0.0701536i	−0.999179	−	0.0405032i
$4$		0			0
$5$	−0.426624	+	0.155279i	−0.190792	+	0.0694427i	−0.435649	−	0.900116i	$-0.643481\pi$
$5$	−0.426624	+	0.155279i	−0.190792	+	0.0694427i	0.244857	+	0.969559i	$0.421259\pi$
$6$		0			0
$7$	−1.28150	+	0.225962i	−0.484360	+	0.0854057i	−0.410495	−	0.911863i	$-0.634644\pi$
$7$	−1.28150	+	0.225962i	−0.484360	+	0.0854057i	−0.0738642	+	0.997268i	$0.523533\pi$
$8$		0			0
$9$	2.99016	+	0.242820i	0.996719	+	0.0809399i
$10$		0			0
$11$	−0.00602720	+	0.0165596i	−0.00181727	+	0.00499290i	−0.940598	−	0.339522i	$-0.889735\pi$
$11$	−0.00602720	+	0.0165596i	−0.00181727	+	0.00499290i	0.938781	+	0.344515i	$0.111957\pi$
$12$		0			0
$13$	1.43581	−	1.71113i	0.398222	−	0.474582i	−0.529255	−	0.848463i	$-0.677529\pi$
$13$	1.43581	−	1.71113i	0.398222	−	0.474582i	0.927477	+	0.373881i	$0.121973\pi$
$14$		0			0
$15$	0.749222	−	0.238801i	0.193448	−	0.0616580i
$16$		0			0
$17$	1.27216	+	0.734483i	0.308545	+	0.178138i	0.646275	−	0.763105i	$-0.276326\pi$
$17$	1.27216	+	0.734483i	0.308545	+	0.178138i	−0.337730	+	0.941243i	$0.609659\pi$
$18$		0			0
$19$	−0.677841	−	1.17406i	−0.155507	−	0.269347i	0.777736	−	0.628591i	$-0.216368\pi$
$19$	−0.677841	−	1.17406i	−0.155507	−	0.269347i	−0.933244	+	0.359244i	$0.883035\pi$
$20$		0			0
$21$	2.23365	−	0.301155i	0.487421	−	0.0657175i
$22$		0			0
$23$	−0.369486	+	2.09546i	−0.0770432	+	0.436933i	0.921748	+	0.387788i	$0.126761\pi$
$23$	−0.369486	+	2.09546i	−0.0770432	+	0.436933i	−0.998792	+	0.0491452i	$0.984350\pi$
$24$		0			0
$25$	−3.67233	+	3.08145i	−0.734465	+	0.616289i
$26$		0			0
$27$	−5.15782	−	0.630001i	−0.992623	−	0.121244i
$28$		0			0
$29$	−5.56933	+	4.67322i	−1.03420	+	0.867796i	−0.991345	−	0.131286i	$-0.958089\pi$
$29$	−5.56933	+	4.67322i	−1.03420	+	0.867796i	−0.0428540	+	0.999081i	$0.513645\pi$
$30$		0			0
$31$	−8.87753	−	1.56535i	−1.59445	−	0.281145i	−0.695279	−	0.718740i	$-0.744719\pi$
$31$	−8.87753	−	1.56535i	−1.59445	−	0.281145i	−0.899172	+	0.437595i	$0.855830\pi$
$32$		0			0
$33$	0.0115926	−	0.0282357i	0.00201801	−	0.00491520i
$34$		0			0
$35$	0.511630	−	0.295390i	0.0864813	−	0.0499300i
$36$		0			0
$37$	−4.58718	−	2.64841i	−0.754128	−	0.435396i	0.0730557	−	0.997328i	$-0.476725\pi$
$37$	−4.58718	−	2.64841i	−0.754128	−	0.435396i	−0.827183	+	0.561932i	$0.810058\pi$
$38$		0			0
$39$	−2.60490	+	2.86061i	−0.417117	+	0.458064i
$40$		0			0
$41$	1.56527	−	1.86542i	0.244454	−	0.291329i	−0.629841	−	0.776724i	$-0.716880\pi$
$41$	1.56527	−	1.86542i	0.244454	−	0.291329i	0.874295	+	0.485395i	$0.161324\pi$
$42$		0			0
$43$	10.1956	+	3.71089i	1.55481	+	0.565906i	0.969541	−	0.244930i	$-0.0787649\pi$
$43$	10.1956	+	3.71089i	1.55481	+	0.565906i	0.585273	+	0.810836i	$0.300987\pi$
$44$		0			0
$45$	−1.31338	+	0.360715i	−0.195787	+	0.0537722i
$46$		0			0
$47$	0.791397	+	4.48824i	0.115437	+	0.654676i	0.986533	+	0.163563i	$0.0522988\pi$
$47$	0.791397	+	4.48824i	0.115437	+	0.654676i	−0.871096	+	0.491113i	$0.836590\pi$
$48$		0			0
$49$	−4.98668	+	1.81500i	−0.712382	+	0.259286i
$50$		0			0
$51$	−2.15011	−	1.36036i	−0.301076	−	0.190489i
$52$		0			0
$53$	−10.4085			−1.42972			−0.714860	−	0.699267i	$-0.753510\pi$
$53$	−10.4085			−1.42972			−0.714860	+	0.699267i	$0.753510\pi$
$54$		0			0
$55$		−	0.00800062i		−	0.00107880i
$56$		0			0
$57$	1.09073	+	2.07941i	0.144470	+	0.275424i
$58$		0			0
$59$	3.75319	+	10.3118i	0.488624	+	1.34248i	0.901926	+	0.431890i	$0.142153\pi$
$59$	3.75319	+	10.3118i	0.488624	+	1.34248i	−0.413302	+	0.910594i	$0.635625\pi$
$60$		0			0
$61$	−8.87057	+	1.56412i	−1.13576	+	0.200265i	−0.709750	−	0.704453i	$-0.751192\pi$
$61$	−8.87057	+	1.56412i	−1.13576	+	0.200265i	−0.426010	+	0.904718i	$0.640081\pi$
$62$		0			0
$63$	−3.88674	+	0.364490i	−0.489683	+	0.0459214i
$64$		0			0
$65$	−0.346849	+	0.952961i	−0.0430214	+	0.118200i
$66$		0			0
$67$	−3.70041	−	3.10502i	−0.452078	−	0.379338i	0.388129	−	0.921605i	$-0.373122\pi$
$67$	−3.70041	−	3.10502i	−0.452078	−	0.379338i	−0.840206	+	0.542267i	$0.817566\pi$
$68$		0			0
$69$	0.786447	−	3.60054i	0.0946771	−	0.433454i
$70$		0			0
$71$	−5.03714	+	8.72458i	−0.597799	+	1.03542i	0.395347	+	0.918532i	$0.370624\pi$
$71$	−5.03714	+	8.72458i	−0.597799	+	1.03542i	−0.993145	+	0.116886i	$0.962709\pi$
$72$		0			0
$73$	−0.339460	−	0.587962i	−0.0397308	−	0.0688158i	0.845476	−	0.534013i	$-0.179317\pi$
$73$	−0.339460	−	0.587962i	−0.0397308	−	0.0688158i	−0.885207	+	0.465197i	$0.845983\pi$
$74$		0			0
$75$	6.57161	−	5.07522i	0.758824	−	0.586035i
$76$		0			0
$77$	0.00398198	−	0.0225829i	0.000453789	−	0.00257357i
$78$		0			0
$79$	−5.19665	−	6.19313i	−0.584669	−	0.696782i	0.389903	−	0.920856i	$-0.372509\pi$
$79$	−5.19665	−	6.19313i	−0.584669	−	0.696782i	−0.974572	+	0.224074i	$0.928064\pi$
$80$		0			0
$81$	8.88208	+	1.45214i	0.986897	+	0.161349i
$82$		0			0
$83$	−1.29122	−	1.53881i	−0.141729	−	0.168907i	0.690510	−	0.723323i	$-0.257386\pi$
$83$	−1.29122	−	1.53881i	−0.141729	−	0.168907i	−0.832240	+	0.554416i	$0.812942\pi$
$84$		0			0
$85$	−0.656785	−	0.115809i	−0.0712383	−	0.0125612i
$86$		0			0
$87$	9.96629	−	7.69691i	1.06850	−	0.825195i
$88$		0			0
$89$	−0.103744	+	0.0598964i	−0.0109968	+	0.00634901i	−0.505488	−	0.862833i	$-0.668688\pi$
$89$	−0.103744	+	0.0598964i	−0.0109968	+	0.00634901i	0.494492	+	0.869182i	$0.335354\pi$
$90$		0			0
$91$	−1.45333	+	2.51724i	−0.152351	+	0.263879i
$92$		0			0
$93$	15.2539	+	3.33183i	1.58176	+	0.345495i
$94$		0			0
$95$	0.471489	+	0.395626i	0.0483738	+	0.0405904i
$96$		0			0
$97$	−10.4801	−	3.81446i	−1.06410	−	0.387299i	−0.250130	−	0.968212i	$-0.580474\pi$
$97$	−10.4801	−	3.81446i	−1.06410	−	0.387299i	−0.813966	+	0.580913i	$0.802696\pi$
$98$		0			0
$99$	−0.0220433	+	0.0480522i	−0.00221543	+	0.00482943i
$100$		0			0
$101$	2.89743	+	16.4321i	0.288305	+	1.63506i	0.693237	+	0.720710i	$0.256184\pi$
$101$	2.89743	+	16.4321i	0.288305	+	1.63506i	−0.404932	+	0.914347i	$0.632705\pi$
$102$		0			0
$103$	−5.45676	−	14.9923i	−0.537670	−	1.47724i	−0.849753	−	0.527182i	$-0.823249\pi$
$103$	−5.45676	−	14.9923i	−0.537670	−	1.47724i	0.312082	−	0.950055i	$-0.398974\pi$
$104$		0			0
$105$	−0.906165	+	0.475318i	−0.0884326	+	0.0463862i
$106$		0			0
$107$			6.73607i			0.651200i	0.945508	+	0.325600i	$0.105566\pi$
$107$			6.73607i			0.651200i	−0.945508	+	0.325600i	$0.894434\pi$
$108$		0			0
$109$			2.91699i			0.279397i	0.990194	+	0.139699i	$0.0446134\pi$
$109$			2.91699i			0.279397i	−0.990194	+	0.139699i	$0.955387\pi$
$110$		0			0
$111$	7.75291	+	4.90522i	0.735874	+	0.465583i
$112$		0			0
$113$	−6.67148	−	18.3297i	−0.627600	−	1.72432i	−0.687572	−	0.726116i	$-0.741323\pi$
$113$	−6.67148	−	18.3297i	−0.627600	−	1.72432i	0.0599724	−	0.998200i	$-0.480899\pi$
$114$		0			0
$115$	−0.167748	−	0.951347i	−0.0156426	−	0.0887136i
$116$		0			0
$117$	4.70879	−	4.76791i	0.435328	−	0.440793i
$118$		0			0
$119$	−1.79623	−	0.653776i	−0.164661	−	0.0599315i
$120$		0			0
$121$	8.42625	+	7.07046i	0.766023	+	0.642769i
$122$		0			0
$123$	−2.83977	+	3.11853i	−0.256053	+	0.281189i
$124$		0			0
$125$	2.22323	−	3.85075i	0.198852	−	0.344422i
$126$		0			0
$127$	14.9938	−	8.65666i	1.33048	−	0.768154i	0.345108	−	0.938563i	$-0.387842\pi$
$127$	14.9938	−	8.65666i	1.33048	−	0.768154i	0.985373	+	0.170409i	$0.0545088\pi$
$128$		0			0
$129$	−17.3845	−	7.13744i	−1.53062	−	0.628417i
$130$		0			0
$131$	3.03491	+	0.535137i	0.265162	+	0.0467552i	0.304648	−	0.952465i	$-0.401461\pi$
$131$	3.03491	+	0.535137i	0.265162	+	0.0467552i	−0.0394865	+	0.999220i	$0.512572\pi$
$132$		0			0
$133$	1.13394	+	1.35138i	0.0983252	+	0.117179i
$134$		0			0
$135$	2.29828	−	0.532125i	0.197804	−	0.0457980i
$136$		0			0
$137$	7.57425	+	9.02665i	0.647112	+	0.771198i	0.985476	−	0.169817i	$-0.0543177\pi$
$137$	7.57425	+	9.02665i	0.647112	+	0.771198i	−0.338363	+	0.941016i	$0.609873\pi$
$138$		0			0
$139$	0.930383	−	5.27646i	0.0789140	−	0.447544i	−0.919591	−	0.392878i	$-0.871480\pi$
$139$	0.930383	−	5.27646i	0.0789140	−	0.447544i	0.998505	−	0.0546659i	$-0.0174094\pi$
$140$		0			0
$141$	−1.05475	−	7.82299i	−0.0888259	−	0.658815i
$142$		0			0
$143$	0.0196817	+	0.0340897i	0.00164587	+	0.00285073i
$144$		0			0
$145$	1.65036	−	2.85851i	0.137055	−	0.237386i
$146$		0			0
$147$	8.75742	−	2.79126i	0.722300	−	0.230219i
$148$		0			0
$149$	10.9918	+	9.22325i	0.900486	+	0.755598i	0.970285	−	0.241963i	$-0.0777914\pi$
$149$	10.9918	+	9.22325i	0.900486	+	0.755598i	−0.0697991	+	0.997561i	$0.522236\pi$
$150$		0			0
$151$	−4.06790	+	11.1765i	−0.331041	+	0.909528i	0.656800	+	0.754065i	$0.271909\pi$
$151$	−4.06790	+	11.1765i	−0.331041	+	0.909528i	−0.987842	+	0.155464i	$0.950313\pi$
$152$		0			0
$153$	3.62562	+	2.50513i	0.293114	+	0.202527i
$154$		0			0
$155$	4.03044	−	0.710675i	0.323733	−	0.0570828i
$156$		0			0
$157$	−5.75062	−	15.7997i	−0.458950	−	1.26095i	−0.926268	−	0.376865i	$-0.877002\pi$
$157$	−5.75062	−	15.7997i	−0.458950	−	1.26095i	0.467319	−	0.884089i	$-0.345220\pi$
$158$		0			0
$159$	18.0133	+	0.730195i	1.42855	+	0.0579082i
$160$		0			0
$161$		−	2.76881i		−	0.218213i
$162$		0			0
$163$	−10.1776			−0.797169			−0.398585	−	0.917132i	$-0.630498\pi$
$163$	−10.1776			−0.797169			−0.398585	+	0.917132i	$0.630498\pi$
$164$		0			0
$165$	−0.000561272		0.0138461i	−4.36950e−5		0.00107792i
$166$		0			0
$167$	15.0723	−	5.48587i	1.16633	−	0.424509i	0.314975	−	0.949100i	$-0.398004\pi$
$167$	15.0723	−	5.48587i	1.16633	−	0.424509i	0.851355	+	0.524591i	$0.175782\pi$
$168$		0			0
$169$	1.39101	+	7.88879i	0.107000	+	0.606830i
$170$		0			0
$171$	−1.74177	−	3.67520i	−0.133196	−	0.281050i
$172$		0			0
$173$	12.7203	+	4.62982i	0.967109	+	0.351999i	0.776815	−	0.629729i	$-0.216834\pi$
$173$	12.7203	+	4.62982i	0.967109	+	0.351999i	0.190293	+	0.981727i	$0.439056\pi$
$174$		0			0
$175$	4.00978	−	4.77867i	0.303111	−	0.361233i
$176$		0			0
$177$	−5.77198	−	18.1092i	−0.433848	−	1.36117i
$178$		0			0
$179$	−9.84897	−	5.68630i	−0.736146	−	0.425014i	0.0845201	−	0.996422i	$-0.473064\pi$
$179$	−9.84897	−	5.68630i	−0.736146	−	0.425014i	−0.820667	+	0.571407i	$0.806398\pi$
$180$		0			0
$181$	12.8369	−	7.41138i	0.954159	−	0.550884i	0.0597883	−	0.998211i	$-0.480957\pi$
$181$	12.8369	−	7.41138i	0.954159	−	0.550884i	0.894370	+	0.447327i	$0.147624\pi$
$182$		0			0
$183$	15.4614	−	2.08461i	1.14294	−	0.154099i
$184$		0			0
$185$	2.36824	+	0.417585i	0.174117	+	0.0307015i
$186$		0			0
$187$	−0.0198303	+	0.0166396i	−0.00145014	+	0.00121681i
$188$		0			0
$189$	6.75208	−	0.358129i	0.491141	−	0.0260500i
$190$		0			0
$191$	−14.4389	+	12.1157i	−1.04476	+	0.876659i	−0.992533	−	0.121976i	$-0.961077\pi$
$191$	−14.4389	+	12.1157i	−1.04476	+	0.876659i	−0.0522283	+	0.998635i	$0.516632\pi$
$192$		0			0
$193$	−0.366460	+	2.07830i	−0.0263783	+	0.149599i	−0.995152	−	0.0983471i	$-0.968644\pi$
$193$	−0.366460	+	2.07830i	−0.0263783	+	0.149599i	0.968774	+	0.247946i	$0.0797556\pi$
$194$		0			0
$195$	0.667121	−	1.62489i	0.0477735	−	0.116361i
$196$		0			0
$197$	−5.72884	−	9.92264i	−0.408163	−	0.706959i	0.586521	−	0.809934i	$-0.300497\pi$
$197$	−5.72884	−	9.92264i	−0.408163	−	0.706959i	−0.994684	+	0.102975i	$0.967164\pi$
$198$		0			0
$199$	4.92181	+	2.84161i	0.348898	+	0.201436i	0.664200	−	0.747555i	$-0.268772\pi$
$199$	4.92181	+	2.84161i	0.348898	+	0.201436i	−0.315302	+	0.948991i	$0.602106\pi$
$200$		0			0
$201$	6.18622	+	5.63323i	0.436342	+	0.397337i
$202$		0			0
$203$	6.08110	−	7.24717i	0.426809	−	0.508652i
$204$		0			0
$205$	−0.378123	+	1.03889i	−0.0264093	+	0.0725589i
$206$		0			0
$207$	−1.61364	+	6.17603i	−0.112156	+	0.429264i
$208$		0			0
$209$	0.0235273	−	0.00414851i	0.00162742	−	0.000286958i
$210$		0			0
$211$	−15.6412	+	5.69295i	−1.07679	+	0.391919i	−0.818711	−	0.574206i	$-0.805311\pi$
$211$	−15.6412	+	5.69295i	−1.07679	+	0.391919i	−0.258077	+	0.966124i	$0.583089\pi$
$212$		0			0
$213$	9.32948	−	14.7456i	0.639246	−	1.01036i
$214$		0			0
$215$	−4.92591			−0.335945
$216$		0			0
$217$	11.7302			0.796300
$218$		0			0
$219$	0.546232	+	1.04136i	0.0369109	+	0.0703685i
$220$		0			0
$221$	3.08338	−	1.12226i	0.207410	−	0.0754912i
$222$		0			0
$223$	−2.73564	+	0.482367i	−0.183192	+	0.0323017i	−0.264491	−	0.964388i	$-0.585204\pi$
$223$	−2.73564	+	0.482367i	−0.183192	+	0.0323017i	0.0812995	+	0.996690i	$0.474093\pi$
$224$		0			0
$225$	−11.7291	+	8.32230i	−0.781938	+	0.554820i
$226$		0			0
$227$	8.45693	−	23.2352i	0.561306	−	1.54218i	−0.256418	−	0.966566i	$-0.582542\pi$
$227$	8.45693	−	23.2352i	0.561306	−	1.54218i	0.817724	−	0.575611i	$-0.195236\pi$
$228$		0			0
$229$	10.0744	−	12.0062i	0.665736	−	0.793393i	−0.322461	−	0.946583i	$-0.604510\pi$
$229$	10.0744	−	12.0062i	0.665736	−	0.793393i	0.988197	+	0.153190i	$0.0489546\pi$
$230$		0			0
$231$	−0.00847561	+	0.0388034i	−0.000557654	+	0.00255307i
$232$		0			0
$233$	17.5198	+	10.1151i	1.14776	+	0.662659i	0.948340	−	0.317255i	$-0.102761\pi$
$233$	17.5198	+	10.1151i	1.14776	+	0.662659i	0.199419	+	0.979914i	$0.436094\pi$
$234$		0			0
$235$	−1.03456	−	1.79190i	−0.0674870	−	0.116891i
$236$		0			0
$237$	8.55901	+	11.0826i	0.555968	+	0.719891i
$238$		0			0
$239$	1.48780	−	8.43773i	0.0962378	−	0.545791i	−0.898123	−	0.439744i	$-0.855069\pi$
$239$	1.48780	−	8.43773i	0.0962378	−	0.545791i	0.994361	−	0.106048i	$-0.0338196\pi$
$240$		0			0
$241$	11.0727	−	9.29110i	0.713255	−	0.598492i	−0.212255	−	0.977214i	$-0.568081\pi$
$241$	11.0727	−	9.29110i	0.713255	−	0.598492i	0.925510	+	0.378722i	$0.123636\pi$
$242$		0			0
$243$	−15.2697	−	3.13622i	−0.979552	−	0.201189i
$244$		0			0
$245$	1.84561	−	1.54865i	0.117912	−	0.0989395i
$246$		0			0
$247$	−2.98221	−	0.525844i	−0.189754	−	0.0334587i
$248$		0			0
$249$	2.12666	+	2.75370i	0.134772	+	0.174508i
$250$		0			0
$251$	−12.7128	+	7.33976i	−0.802427	+	0.463281i	−0.844319	−	0.535841i	$-0.819995\pi$
$251$	−12.7128	+	7.33976i	−0.802427	+	0.463281i	0.0418921	+	0.999122i	$0.486661\pi$
$252$		0			0
$253$	−0.0324730	−	0.0187483i	−0.00204156	−	0.00117869i
$254$		0			0
$255$	1.12853	+	0.246498i	0.0706711	+	0.0154363i
$256$		0			0
$257$	−14.4703	+	17.2450i	−0.902633	+	1.07572i	0.0941497	+	0.995558i	$0.469987\pi$
$257$	−14.4703	+	17.2450i	−0.902633	+	1.07572i	−0.996782	+	0.0801575i	$0.974458\pi$
$258$		0			0
$259$	6.47689	+	2.35739i	0.402454	+	0.146481i
$260$		0			0
$261$	−17.7879	+	12.6213i	−1.10104	+	0.781240i
$262$		0			0
$263$	3.07511	+	17.4398i	0.189620	+	1.07539i	0.919875	+	0.392212i	$0.128290\pi$
$263$	3.07511	+	17.4398i	0.189620	+	1.07539i	−0.730255	+	0.683175i	$0.760599\pi$
$264$		0			0
$265$	4.44053	−	1.61622i	0.272780	−	0.0992836i
$266$		0			0
$267$	0.183744	−	0.0963806i	0.0112449	−	0.00589839i
$268$		0			0
$269$	−10.2475			−0.624803			−0.312402	−	0.949950i	$-0.601133\pi$
$269$	−10.2475			−0.624803			−0.312402	+	0.949950i	$0.601133\pi$
$270$		0			0
$271$			18.7315i			1.13786i	0.822386	+	0.568929i	$0.192642\pi$
$271$			18.7315i			1.13786i	−0.822386	+	0.568929i	$0.807358\pi$
$272$		0			0
$273$	2.69177	−	4.25446i	0.162913	−	0.257492i
$274$		0			0
$275$	−0.0288937	−	0.0793847i	−0.00174235	−	0.00478708i
$276$		0			0
$277$	−21.4560	+	3.78327i	−1.28917	+	0.227315i	−0.775868	−	0.630895i	$-0.782688\pi$
$277$	−21.4560	+	3.78327i	−1.28917	+	0.227315i	−0.513299	+	0.858210i	$0.671577\pi$
$278$		0			0
$279$	−26.1651	−	6.83628i	−1.56646	−	0.409277i
$280$		0			0
$281$	−3.95262	+	10.8597i	−0.235793	+	0.647837i	0.764203	+	0.644976i	$0.223133\pi$
$281$	−3.95262	+	10.8597i	−0.235793	+	0.647837i	−0.999996	+	0.00286067i	$0.999089\pi$
$282$		0			0
$283$	3.28791	+	2.75888i	0.195446	+	0.163998i	0.735259	−	0.677786i	$-0.237061\pi$
$283$	3.28791	+	2.75888i	0.195446	+	0.163998i	−0.539813	+	0.841785i	$0.681505\pi$
$284$		0			0
$285$	−0.788218	−	0.717759i	−0.0466900	−	0.0425164i
$286$		0			0
$287$	−1.58437	+	2.74421i	−0.0935226	+	0.161986i
$288$		0			0
$289$	−7.42107	−	12.8537i	−0.436533	−	0.756098i
$290$		0			0
$291$	17.8696	+	7.33663i	1.04754	+	0.430081i
$292$		0			0
$293$	2.18285	−	12.3796i	0.127523	−	0.723221i	−0.852254	−	0.523129i	$-0.824765\pi$
$293$	2.18285	−	12.3796i	0.127523	−	0.723221i	0.979777	−	0.200092i	$-0.0641242\pi$
$294$		0			0
$295$	−3.20241	−	3.81648i	−0.186451	−	0.222204i
$296$		0			0
$297$	0.0415197	−	0.0816142i	0.00240922	−	0.00473574i
$298$		0			0
$299$	3.05509	+	3.64092i	0.176681	+	0.210560i
$300$		0			0
$301$	−13.9041	−	2.45167i	−0.801421	−	0.141312i
$302$		0			0
$303$	−3.86160	−	28.6412i	−0.221843	−	1.64539i
$304$		0			0
$305$	3.54153	−	2.04470i	0.202787	−	0.117079i
$306$		0			0
$307$	−7.46768	+	12.9344i	−0.426203	+	0.738205i	−0.996532	−	0.0832113i	$-0.973482\pi$
$307$	−7.46768	+	12.9344i	−0.426203	+	0.738205i	0.570329	+	0.821416i	$0.306816\pi$
$308$		0			0
$309$	8.39186	+	26.3290i	0.477396	+	1.49780i
$310$		0			0
$311$	0.935160	+	0.784692i	0.0530280	+	0.0444958i	0.668916	−	0.743338i	$-0.266758\pi$
$311$	0.935160	+	0.784692i	0.0530280	+	0.0444958i	−0.615888	+	0.787833i	$0.711203\pi$
$312$		0			0
$313$	−3.74180	−	1.36190i	−0.211499	−	0.0769794i	0.234098	−	0.972213i	$-0.424786\pi$
$313$	−3.74180	−	1.36190i	−0.211499	−	0.0769794i	−0.445597	+	0.895234i	$0.647009\pi$
$314$		0			0
$315$	1.60158	−	0.759028i	0.0902389	−	0.0427664i
$316$		0			0
$317$	1.28552	+	7.29053i	0.0722018	+	0.409477i	0.999391	+	0.0348844i	$0.0111063\pi$
$317$	1.28552	+	7.29053i	0.0722018	+	0.409477i	−0.927190	+	0.374593i	$0.877783\pi$
$318$		0			0
$319$	−0.0438192	−	0.120392i	−0.00245340	−	0.00674067i
$320$		0			0
$321$	0.472559	−	11.6576i	0.0263757	−	0.650666i
$322$		0			0
$323$		−	1.99145i		−	0.110807i
$324$		0			0
$325$			10.7082i			0.593984i
$326$		0			0
$327$	0.204638	−	5.04824i	0.0113165	−	0.279168i
$328$		0			0
$329$	−2.02834	−	5.57283i	−0.111826	−	0.307240i
$330$		0			0
$331$	−0.520452	−	2.95163i	−0.0286066	−	0.162236i	0.967158	−	0.254176i	$-0.0818043\pi$
$331$	−0.520452	−	2.95163i	−0.0286066	−	0.162236i	−0.995765	+	0.0919400i	$0.970693\pi$
$332$		0			0
$333$	−13.0733	−	9.03302i	−0.716412	−	0.495006i
$334$		0			0
$335$	2.06083	+	0.750081i	0.112595	+	0.0409813i
$336$		0			0
$337$	−10.0788	−	8.45709i	−0.549025	−	0.460687i	0.325586	−	0.945513i	$-0.394439\pi$
$337$	−10.0788	−	8.45709i	−0.549025	−	0.460687i	−0.874611	+	0.484826i	$0.838883\pi$
$338$		0			0
$339$	10.2600	+	32.1900i	0.557244	+	1.74832i
$340$		0			0
$341$	0.0794281	−	0.137574i	0.00430127	−	0.00745003i
$342$		0			0
$343$	13.8688	−	8.00714i	0.748844	−	0.432345i
$344$		0			0
$345$	0.223570	+	1.65820i	0.0120366	+	0.0892744i
$346$		0			0
$347$	−28.8369	−	5.08472i	−1.54804	−	0.272962i	−0.666660	−	0.745362i	$-0.732277\pi$
$347$	−28.8369	−	5.08472i	−1.54804	−	0.272962i	−0.881385	+	0.472400i	$0.843388\pi$
$348$		0			0
$349$	13.4766	+	16.0608i	0.721385	+	0.859713i	0.994765	−	0.102193i	$-0.0325859\pi$
$349$	13.4766	+	16.0608i	0.721385	+	0.859713i	−0.273380	+	0.961906i	$0.588141\pi$
$350$		0			0
$351$	−8.48366	+	7.92114i	−0.452824	+	0.422799i
$352$		0			0
$353$	2.02760	+	2.41640i	0.107918	+	0.128612i	0.817300	−	0.576213i	$-0.195470\pi$
$353$	2.02760	+	2.41640i	0.107918	+	0.128612i	−0.709381	+	0.704825i	$0.751026\pi$
$354$		0			0
$355$	0.794226	−	4.50428i	0.0421532	−	0.239062i
$356$		0			0
$357$	3.06275	+	1.25746i	0.162098	+	0.0665516i
$358$		0			0
$359$	−15.2950	−	26.4917i	−0.807240	−	1.39818i	−0.914768	−	0.403979i	$-0.867627\pi$
$359$	−15.2950	−	26.4917i	−0.807240	−	1.39818i	0.107529	−	0.994202i	$-0.465706\pi$
$360$		0			0
$361$	8.58106	−	14.8628i	0.451635	−	0.782255i
$362$		0			0
$363$	−14.0867	−	12.8275i	−0.739360	−	0.673268i
$364$		0			0
$365$	0.236120	+	0.198128i	0.0123591	+	0.0103705i
$366$		0			0
$367$	−7.65245	+	21.0249i	−0.399455	+	1.09749i	0.563096	+	0.826391i	$0.309610\pi$
$367$	−7.65245	+	21.0249i	−0.399455	+	1.09749i	−0.962551	+	0.271101i	$0.912612\pi$
$368$		0			0
$369$	5.13336	−	5.19781i	0.267232	−	0.270587i
$370$		0			0
$371$	13.3385	−	2.35193i	0.692499	−	0.122106i
$372$		0			0
$373$	−3.91132	−	10.7463i	−0.202521	−	0.556421i	0.796304	−	0.604897i	$-0.206786\pi$
$373$	−3.91132	−	10.7463i	−0.202521	−	0.556421i	−0.998824	+	0.0484764i	$0.984563\pi$
$374$		0			0
$375$	−4.11773	+	6.50825i	−0.212639	+	0.336085i
$376$		0			0
$377$			16.2397i			0.836387i
$378$		0			0
$379$	21.7004			1.11468			0.557338	−	0.830286i	$-0.311823\pi$
$379$	21.7004			1.11468			0.557338	+	0.830286i	$0.311823\pi$
$380$		0			0
$381$	−26.5560	+	13.9296i	−1.36050	+	0.713635i
$382$		0			0
$383$	31.1726	−	11.3459i	1.59285	−	0.579749i	0.614900	−	0.788605i	$-0.289196\pi$
$383$	31.1726	−	11.3459i	1.59285	−	0.579749i	0.977946	+	0.208856i	$0.0669740\pi$
$384$		0			0
$385$	0.00180784	+	0.0102528i	9.21359e−5	+	0.000522529i
$386$		0			0
$387$	29.5854	+	13.5718i	1.50391	+	0.689896i
$388$		0			0
$389$	−6.54404	−	2.38183i	−0.331796	−	0.120764i	0.170750	−	0.985314i	$-0.445381\pi$
$389$	−6.54404	−	2.38183i	−0.331796	−	0.120764i	−0.502546	+	0.864551i	$0.667603\pi$
$390$		0			0
$391$	−2.00913	+	2.39438i	−0.101606	+	0.121089i
$392$		0			0
$393$	−5.21477	−	1.13903i	−0.263050	−	0.0574567i
$394$		0			0
$395$	3.17868	+	1.83521i	0.159937	+	0.0923395i
$396$		0			0
$397$	31.8597	−	18.3942i	1.59899	−	0.923178i	0.607308	−	0.794466i	$-0.292249\pi$
$397$	31.8597	−	18.3942i	1.59899	−	0.923178i	0.991682	−	0.128712i	$-0.0410841\pi$
$398$		0			0
$399$	−1.86763	−	2.41829i	−0.0934984	−	0.121066i
$400$		0			0
$401$	3.00611	+	0.530059i	0.150118	+	0.0264699i	0.248202	−	0.968708i	$-0.420160\pi$
$401$	3.00611	+	0.530059i	0.150118	+	0.0264699i	−0.0980840	+	0.995178i	$0.531271\pi$
$402$		0			0
$403$	−15.4250	+	12.9431i	−0.768372	+	0.644740i
$404$		0			0
$405$	−4.01480	+	0.759679i	−0.199497	+	0.0377487i
$406$		0			0
$407$	0.0715044	−	0.0599993i	0.00354434	−	0.00297406i
$408$		0			0
$409$	−4.18256	+	23.7205i	−0.206814	+	1.17290i	0.687745	+	0.725952i	$0.258601\pi$
$409$	−4.18256	+	23.7205i	−0.206814	+	1.17290i	−0.894559	+	0.446949i	$0.852511\pi$
$410$		0			0
$411$	−12.4750	−	16.1531i	−0.615345	−	0.796776i
$412$		0			0
$413$	−7.13978	−	12.3665i	−0.351326	−	0.608514i
$414$		0			0
$415$	0.789809	+	0.455997i	0.0387702	+	0.0223840i
$416$		0			0
$417$	−1.98031	+	9.06633i	−0.0969762	+	0.443980i
$418$		0			0
$419$	19.0854	−	22.7451i	0.932383	−	1.11117i	−0.0612068	−	0.998125i	$-0.519495\pi$
$419$	19.0854	−	22.7451i	0.932383	−	1.11117i	0.993590	−	0.113046i	$-0.0360607\pi$
$420$		0			0
$421$	−9.82045	+	26.9815i	−0.478619	+	1.31500i	0.432046	+	0.901851i	$0.357792\pi$
$421$	−9.82045	+	26.9815i	−0.478619	+	1.31500i	−0.910666	+	0.413144i	$0.864430\pi$
$422$		0			0
$423$	1.27657	+	13.6127i	0.0620689	+	0.661872i
$424$		0			0
$425$	−6.93506	+	1.22284i	−0.336400	+	0.0593164i
$426$		0			0
$427$	11.0142	−	4.00883i	0.533013	−	0.194001i
$428$		0			0
$429$	−0.0316702	−	0.0603774i	−0.00152905	−	0.00291505i
$430$		0			0
$431$	−26.5585			−1.27928			−0.639639	−	0.768675i	$-0.720916\pi$
$431$	−26.5585			−1.27928			−0.639639	+	0.768675i	$0.720916\pi$
$432$		0			0
$433$	−1.55270			−0.0746180			−0.0373090	−	0.999304i	$-0.511879\pi$
$433$	−1.55270			−0.0746180			−0.0373090	+	0.999304i	$0.511879\pi$
$434$		0			0
$435$	−3.05670	+	4.83124i	−0.146557	+	0.231640i
$436$		0			0
$437$	2.71064	−	0.986591i	0.129667	−	0.0471951i
$438$		0			0
$439$	1.13120	−	0.199460i	0.0539891	−	0.00951973i	−0.146588	−	0.989198i	$-0.546829\pi$
$439$	1.13120	−	0.199460i	0.0539891	−	0.00951973i	0.200577	+	0.979678i	$0.435718\pi$
$440$		0			0
$441$	−15.3517	+	4.21628i	−0.731032	+	0.200775i
$442$		0			0
$443$	−5.79518	+	15.9221i	−0.275337	+	0.756483i	0.722538	+	0.691331i	$0.242975\pi$
$443$	−5.79518	+	15.9221i	−0.275337	+	0.756483i	−0.997875	+	0.0651518i	$0.979247\pi$
$444$		0			0
$445$	0.0349590	−	0.0416625i	0.00165721	−	0.00197499i
$446$		0			0
$447$	−18.3758	−	16.7331i	−0.869143	−	0.791450i
$448$		0			0
$449$	−26.5725	−	15.3416i	−1.25403	−	0.724017i	−0.282126	−	0.959377i	$-0.591039\pi$
$449$	−26.5725	−	15.3416i	−1.25403	−	0.724017i	−0.971908	+	0.235361i	$0.924373\pi$
$450$		0			0
$451$	0.0214563	+	0.0371634i	0.00101034	+	0.00174996i
$452$		0			0
$453$	7.82410	−	19.0570i	0.367608	−	0.895374i
$454$		0			0
$455$	0.229153	−	1.29959i	0.0107428	−	0.0609257i
$456$		0			0
$457$	5.48725	−	4.60435i	0.256683	−	0.215382i	−0.505361	−	0.862908i	$-0.668641\pi$
$457$	5.48725	−	4.60435i	0.256683	−	0.215382i	0.762044	+	0.647526i	$0.224196\pi$
$458$		0			0
$459$	−6.09886	−	4.58979i	−0.284670	−	0.214233i
$460$		0			0
$461$	−6.34887	+	5.32733i	−0.295696	+	0.248119i	−0.778550	−	0.627582i	$-0.784045\pi$
$461$	−6.34887	+	5.32733i	−0.295696	+	0.248119i	0.482854	+	0.875701i	$0.339600\pi$
$462$		0			0
$463$	0.381159	+	0.0672086i	0.0177140	+	0.00312345i	0.182498	−	0.983206i	$-0.441582\pi$
$463$	0.381159	+	0.0672086i	0.0177140	+	0.00312345i	−0.164784	+	0.986330i	$0.552693\pi$
$464$		0			0
$465$	−7.02505	+	0.947165i	−0.325779	+	0.0439237i
$466$		0			0
$467$	5.76908	−	3.33078i	0.266961	−	0.154130i	−0.360545	−	0.932742i	$-0.617409\pi$
$467$	5.76908	−	3.33078i	0.266961	−	0.154130i	0.627506	+	0.778612i	$0.284076\pi$
$468$		0			0
$469$	5.44368	+	3.14291i	0.251366	+	0.145126i
$470$		0			0
$471$	8.84379	+	27.7469i	0.407500	+	1.27851i
$472$		0			0
$473$	−0.122902	+	0.146469i	−0.00565103	+	0.00673463i
$474$		0			0
$475$	6.10704	+	2.22278i	0.280210	+	0.101988i
$476$		0			0
$477$	−31.1231	−	2.52739i	−1.42503	−	0.115721i
$478$		0			0
$479$	−0.196814	−	1.11619i	−0.00899268	−	0.0510000i	0.979981	−	0.199090i	$-0.0637986\pi$
$479$	−0.196814	−	1.11619i	−0.00899268	−	0.0510000i	−0.988974	+	0.148090i	$0.952687\pi$
$480$		0			0
$481$	−11.1181	+	4.04665i	−0.506941	+	0.184511i
$482$		0			0
$483$	−0.194242	+	4.79179i	−0.00883832	+	0.218034i
$484$		0			0
$485$	5.06338			0.229916
$486$		0			0
$487$			41.9634i			1.90154i	0.309896	+	0.950771i	$0.399706\pi$
$487$			41.9634i			1.90154i	−0.309896	+	0.950771i	$0.600294\pi$
$488$		0			0
$489$	17.6136	+	0.713993i	0.796515	+	0.0322879i
$490$		0			0
$491$	7.04382	+	19.3527i	0.317883	+	0.873377i	0.991003	+	0.133843i	$0.0427317\pi$
$491$	7.04382	+	19.3527i	0.317883	+	0.873377i	−0.673119	+	0.739534i	$0.735046\pi$
$492$		0			0
$493$	−10.5175	+	1.85452i	−0.473684	+	0.0835233i
$494$		0			0
$495$	0.00194271	−	0.0239231i	8.73182e−5	−	0.00107526i
$496$		0			0
$497$	4.48365	−	12.3187i	0.201119	−	0.552570i
$498$		0			0
$499$	−7.68110	−	6.44521i	−0.343853	−	0.288527i	0.454463	−	0.890766i	$-0.349831\pi$
$499$	−7.68110	−	6.44521i	−0.343853	−	0.288527i	−0.798316	+	0.602239i	$0.794276\pi$
$500$		0			0
$501$	−26.4694	+	8.43663i	−1.18257	+	0.376921i
$502$		0			0
$503$	12.3849	−	21.4513i	0.552216	−	0.956466i	−0.445898	−	0.895084i	$-0.647116\pi$
$503$	12.3849	−	21.4513i	0.552216	−	0.956466i	0.998114	−	0.0613824i	$-0.0195509\pi$
$504$		0			0
$505$	−3.78767	−	6.56044i	−0.168549	−	0.291936i
$506$		0			0
$507$	−1.85389	−	13.7502i	−0.0823341	−	0.610666i
$508$		0			0
$509$	5.29018	−	30.0021i	0.234483	−	1.32982i	−0.609217	−	0.793004i	$-0.708516\pi$
$509$	5.29018	−	30.0021i	0.234483	−	1.32982i	0.843700	−	0.536816i	$-0.180373\pi$
$510$		0			0
$511$	0.567874	+	0.676766i	0.0251213	+	0.0299383i
$512$		0			0
$513$	2.75653	+	6.48260i	0.121704	+	0.286214i
$514$		0			0
$515$	4.65597	+	5.54877i	0.205167	+	0.244508i
$516$		0			0
$517$	−0.0790932	−	0.0139463i	−0.00347852	−	0.000613356i
$518$		0			0
$519$	−21.6894	−	8.90488i	−0.952058	−	0.390881i
$520$		0			0
$521$	−2.67309	+	1.54331i	−0.117110	+	0.0676136i	−0.557411	−	0.830237i	$-0.688205\pi$
$521$	−2.67309	+	1.54331i	−0.117110	+	0.0676136i	0.440301	+	0.897850i	$0.354872\pi$
$522$		0			0
$523$	6.24198	−	10.8114i	0.272943	−	0.472750i	−0.696671	−	0.717390i	$-0.745336\pi$
$523$	6.24198	−	10.8114i	0.272943	−	0.472750i	0.969614	+	0.244640i	$0.0786698\pi$
$524$		0			0
$525$	−7.27468	+	7.98880i	−0.317493	+	0.348660i
$526$		0			0
$527$	−10.1439	−	8.51177i	−0.441877	−	0.370779i
$528$		0			0
$529$	17.3585	+	6.31798i	0.754717	+	0.274695i
$530$		0			0
$531$	8.71872	+	31.7453i	0.378360	+	1.37763i
$532$		0			0
$533$	−0.944542	−	5.35676i	−0.0409126	−	0.232027i
$534$		0			0
$535$	−1.04597	−	2.87377i	−0.0452211	−	0.124244i
$536$		0			0
$537$	16.6460	+	10.5318i	0.718328	+	0.454482i
$538$		0			0
$539$		−	0.0935167i		−	0.00402805i
$540$		0			0
$541$			35.0866i			1.50849i	0.656592	+	0.754246i	$0.271997\pi$
$541$			35.0866i			1.50849i	−0.656592	+	0.754246i	$0.728003\pi$
$542$		0			0
$543$	−22.7358	+	11.9258i	−0.975688	+	0.511785i
$544$		0			0
$545$	−0.452947	−	1.24446i	−0.0194021	−	0.0533069i
$546$		0			0
$547$	0.423952	+	2.40435i	0.0181269	+	0.102803i	0.992529	−	0.122010i	$-0.0389340\pi$
$547$	0.423952	+	2.40435i	0.0181269	+	0.102803i	−0.974402	+	0.224813i	$0.927823\pi$
$548$		0			0
$549$	−26.9042	+	2.52302i	−1.14824	+	0.107680i
$550$		0			0
$551$	9.26174	+	3.37100i	0.394563	+	0.143609i
$552$		0			0
$553$	8.05890	+	6.76222i	0.342699	+	0.287559i
$554$		0			0
$555$	−4.06926	−	0.888826i	−0.172730	−	0.0377286i
$556$		0			0
$557$	−3.41195	+	5.90968i	−0.144569	+	0.250401i	−0.929212	−	0.369547i	$-0.879513\pi$
$557$	−3.41195	+	5.90968i	−0.144569	+	0.250401i	0.784643	+	0.619948i	$0.212846\pi$
$558$		0			0
$559$	20.9888	−	12.1179i	0.887730	−	0.512531i
$560$		0			0
$561$	0.0354862	−	0.0274058i	0.00149823	−	0.00115707i
$562$		0			0
$563$	−20.6520	−	3.64150i	−0.870377	−	0.153471i	−0.279415	−	0.960170i	$-0.590141\pi$
$563$	−20.6520	−	3.64150i	−0.870377	−	0.153471i	−0.590962	+	0.806699i	$0.701252\pi$
$564$		0			0
$565$	5.69243	+	6.78397i	0.239482	+	0.285404i
$566$		0			0
$567$	−11.7105	+	0.146105i	−0.491793	+	0.00613585i
$568$		0			0
$569$	−20.8313	−	24.8258i	−0.873295	−	1.04075i	−0.998815	−	0.0486610i	$-0.984505\pi$
$569$	−20.8313	−	24.8258i	−0.873295	−	1.04075i	0.125521	−	0.992091i	$-0.459940\pi$
$570$		0			0
$571$	0.396543	−	2.24891i	0.0165948	−	0.0941139i	−0.975385	−	0.220507i	$-0.929229\pi$
$571$	0.396543	−	2.24891i	0.0165948	−	0.0941139i	0.991980	+	0.126393i	$0.0403400\pi$
$572$		0			0
$573$	25.8383	−	19.9548i	1.07941	−	0.833623i
$574$		0			0
$575$	−5.10017	−	8.83376i	−0.212692	−	0.368393i
$576$		0			0
$577$	−10.7395	+	18.6014i	−0.447092	+	0.774387i	−0.998195	−	0.0600507i	$-0.980874\pi$
$577$	−10.7395	+	18.6014i	−0.447092	+	0.774387i	0.551103	+	0.834437i	$0.314207\pi$
$578$		0			0
$579$	0.780006	−	3.57105i	0.0324159	−	0.148408i
$580$		0			0
$581$	2.00240	+	1.68021i	0.0830736	+	0.0697070i
$582$		0			0
$583$	0.0627342	−	0.172361i	0.00259818	−	0.00713845i
$584$		0			0
$585$	−1.26853	+	2.76528i	−0.0524473	+	0.114330i
$586$		0			0
$587$	−18.6609	+	3.29041i	−0.770216	+	0.135810i	−0.544928	−	0.838483i	$-0.683443\pi$
$587$	−18.6609	+	3.29041i	−0.770216	+	0.135810i	−0.225287	+	0.974292i	$0.572332\pi$
$588$		0			0
$589$	4.17975	+	11.4838i	0.172224	+	0.473180i
$590$		0			0
$591$	9.21839	+	17.5743i	0.379194	+	0.722911i
$592$		0			0
$593$		−	23.6650i		−	0.971804i	−0.874013	−	0.485902i	$-0.838491\pi$
$593$		−	23.6650i		−	0.971804i	0.874013	−	0.485902i	$-0.161509\pi$
$594$		0			0
$595$	0.867835			0.0355778
$596$		0			0
$597$	−8.31848	−	5.26305i	−0.340453	−	0.215402i
$598$		0			0
$599$	8.37844	−	3.04950i	0.342334	−	0.124599i	−0.165131	−	0.986272i	$-0.552805\pi$
$599$	8.37844	−	3.04950i	0.342334	−	0.124599i	0.507465	+	0.861672i	$0.330583\pi$
$600$		0			0
$601$	4.44934	+	25.2334i	0.181492	+	1.02929i	0.930380	+	0.366597i	$0.119477\pi$
$601$	4.44934	+	25.2334i	0.181492	+	1.02929i	−0.748888	+	0.662697i	$0.769412\pi$
$602$		0			0
$603$	−10.3109	−	10.1830i	−0.419891	−	0.414685i
$604$		0			0
$605$	−4.69274	−	1.70802i	−0.190787	−	0.0694407i
$606$		0			0
$607$	8.91382	−	10.6231i	0.361801	−	0.431177i	−0.554182	−	0.832396i	$-0.686969\pi$
$607$	8.91382	−	10.6231i	0.361801	−	0.431177i	0.915982	+	0.401218i	$0.131413\pi$
$608$		0			0
$609$	−11.0325	+	12.1156i	−0.447061	+	0.490947i
$610$		0			0
$611$	8.81625	+	5.09007i	0.356667	+	0.205922i
$612$		0			0
$613$	17.7329	−	10.2381i	0.716224	−	0.413512i	−0.0971374	−	0.995271i	$-0.530969\pi$
$613$	17.7329	−	10.2381i	0.716224	−	0.413512i	0.813361	+	0.581759i	$0.197635\pi$
$614$		0			0
$615$	0.727273	−	1.77140i	0.0293265	−	0.0714297i
$616$		0			0
$617$	45.9610	+	8.10416i	1.85032	+	0.326261i	0.984675	−	0.174399i	$-0.0557983\pi$
$617$	45.9610	+	8.10416i	1.85032	+	0.326261i	0.865644	+	0.500660i	$0.166909\pi$
$618$		0			0
$619$	20.3900	−	17.1092i	0.819542	−	0.687678i	−0.133323	−	0.991073i	$-0.542565\pi$
$619$	20.3900	−	17.1092i	0.819542	−	0.687678i	0.952865	+	0.303395i	$0.0981202\pi$
$620$		0			0
$621$	3.22588	−	10.5752i	0.129450	−	0.424369i
$622$		0			0
$623$	0.119413	−	0.100199i	0.00478417	−	0.00401439i
$624$		0			0
$625$	3.81170	−	21.6172i	0.152468	−	0.864688i
$626$		0			0
$627$	−0.0410081	+	0.00552900i	−0.00163771	+	0.000220807i
$628$		0			0
$629$	−3.89042	−	6.73841i	−0.155121	−	0.268678i
$630$		0			0
$631$	−24.6191	−	14.2138i	−0.980071	−	0.565844i	−0.0777793	−	0.996971i	$-0.524783\pi$
$631$	−24.6191	−	14.2138i	−0.980071	−	0.565844i	−0.902292	+	0.431126i	$0.858116\pi$
$632$		0			0
$633$	27.4686	−	8.75510i	1.09178	−	0.347984i
$634$		0			0
$635$	−5.05252	+	6.02135i	−0.200503	+	0.238950i
$636$		0			0
$637$	−4.05421	+	11.1389i	−0.160634	+	0.441337i
$638$		0			0
$639$	−17.1803	+	24.8648i	−0.679644	+	0.983635i
$640$		0			0
$641$	19.2764	−	3.39896i	0.761373	−	0.134251i	0.220537	−	0.975379i	$-0.429219\pi$
$641$	19.2764	−	3.39896i	0.761373	−	0.134251i	0.540836	+	0.841128i	$0.318108\pi$
$642$		0			0
$643$	10.2317	−	3.72402i	0.403497	−	0.146861i	−0.132296	−	0.991210i	$-0.542235\pi$
$643$	10.2317	−	3.72402i	0.403497	−	0.146861i	0.535793	+	0.844349i	$0.320013\pi$
$644$		0			0
$645$	8.52493	+	0.345571i	0.335669	+	0.0136068i
$646$		0			0
$647$	−19.0202			−0.747763			−0.373881	−	0.927477i	$-0.621973\pi$
$647$	−19.0202			−0.747763			−0.373881	+	0.927477i	$0.621973\pi$
$648$		0			0
$649$	−0.193381			−0.00759085
$650$		0			0
$651$	−20.3007	−	0.822917i	−0.795646	−	0.0322527i
$652$		0			0
$653$	11.7763	−	4.28623i	0.460843	−	0.167733i	−0.101157	−	0.994871i	$-0.532254\pi$
$653$	11.7763	−	4.28623i	0.460843	−	0.167733i	0.562000	+	0.827137i	$0.310032\pi$
$654$		0			0
$655$	−1.37786	+	0.242955i	−0.0538376	+	0.00949302i
$656$		0			0
$657$	−0.872270	−	1.84053i	−0.0340305	−	0.0718058i
$658$		0			0
$659$	−9.65592	+	26.5294i	−0.376141	+	1.03344i	0.596801	+	0.802389i	$0.296438\pi$
$659$	−9.65592	+	26.5294i	−0.376141	+	1.03344i	−0.972942	+	0.231050i	$0.925784\pi$
$660$		0			0
$661$	−10.6735	+	12.7202i	−0.415150	+	0.494757i	−0.932577	−	0.360971i	$-0.882445\pi$
$661$	−10.6735	+	12.7202i	−0.415150	+	0.494757i	0.517427	+	0.855727i	$0.326890\pi$
$662$		0			0
$663$	−5.41491	+	1.72590i	−0.210298	+	0.0670285i
$664$		0			0
$665$	−0.693608	−	0.400455i	−0.0268970	−	0.0155290i
$666$		0			0
$667$	−7.73476	−	13.3970i	−0.299491	−	0.518734i
$668$		0			0
$669$	4.76822	−	0.642884i	0.184350	−	0.0248553i
$670$		0			0
$671$	0.0275635	−	0.156320i	0.00106408	−	0.00603468i
$672$		0			0
$673$	4.64214	−	3.89522i	0.178941	−	0.150150i	−0.548918	−	0.835876i	$-0.684960\pi$
$673$	4.64214	−	3.89522i	0.178941	−	0.150150i	0.727859	+	0.685727i	$0.240516\pi$
$674$		0			0
$675$	20.8825	−	13.5800i	0.803768	−	0.522694i
$676$		0			0
$677$	5.34485	−	4.48486i	0.205419	−	0.172367i	−0.534274	−	0.845311i	$-0.679415\pi$
$677$	5.34485	−	4.48486i	0.205419	−	0.172367i	0.739693	+	0.672944i	$0.234971\pi$
$678$		0			0
$679$	14.2922	+	2.52009i	0.548483	+	0.0967123i
$680$		0			0
$681$	−16.2659	+	39.6183i	−0.623309	+	1.51818i
$682$		0			0
$683$	−25.8624	+	14.9317i	−0.989597	+	0.571344i	−0.905154	−	0.425084i	$-0.860244\pi$
$683$	−25.8624	+	14.9317i	−0.989597	+	0.571344i	−0.0844432	+	0.996428i	$0.526911\pi$
$684$		0			0
$685$	−4.63301	−	2.67487i	−0.177018	−	0.102201i
$686$		0			0
$687$	−18.2773	+	20.0715i	−0.697324	+	0.765777i
$688$		0			0
$689$	−14.9446	+	17.8103i	−0.569346	+	0.678520i
$690$		0			0
$691$	−31.1175	−	11.3259i	−1.18377	−	0.430856i	−0.326236	−	0.945288i	$-0.605780\pi$
$691$	−31.1175	−	11.3259i	−1.18377	−	0.430856i	−0.857531	+	0.514432i	$0.828003\pi$
$692$		0			0
$693$	0.0173903	−	0.0665597i	0.000660604	−	0.00252839i
$694$		0			0
$695$	0.422398	+	2.39554i	0.0160225	+	0.0908679i
$696$		0			0
$697$	3.36139	−	1.22345i	0.127322	−	0.0463414i
$698$		0			0
$699$	−29.6107	−	18.7345i	−1.11998	−	0.708603i
$700$		0			0
$701$	9.68894			0.365946			0.182973	−	0.983118i	$-0.441428\pi$
$701$	9.68894			0.365946			0.182973	+	0.983118i	$0.441428\pi$
$702$		0			0
$703$			7.18080i			0.270829i
$704$		0			0
$705$	1.66473	+	3.17370i	0.0626972	+	0.119528i
$706$		0			0
$707$	−7.42607	−	20.4030i	−0.279286	−	0.767333i
$708$		0			0
$709$	24.6853	−	4.35269i	0.927077	−	0.163469i	0.310329	−	0.950629i	$-0.399561\pi$
$709$	24.6853	−	4.35269i	0.927077	−	0.163469i	0.616748	+	0.787161i	$0.288450\pi$
$710$		0			0
$711$	−14.0350	−	19.7803i	−0.526354	−	0.741819i
$712$		0			0
$713$	6.56025	−	18.0241i	0.245683	−	0.675009i
$714$		0			0
$715$	−0.0136901	−	0.0114874i	−0.000511981	−	0.000429603i
$716$		0			0
$717$	−3.16677	+	14.4982i	−0.118265	+	0.541446i
$718$		0			0
$719$	16.4482	−	28.4892i	0.613415	−	1.06247i	−0.377245	−	0.926113i	$-0.623129\pi$
$719$	16.4482	−	28.4892i	0.613415	−	1.06247i	0.990660	−	0.136353i	$-0.0435381\pi$
$720$		0			0
$721$	10.3805	+	17.9796i	0.386590	+	0.669594i
$722$		0			0
$723$	−19.8145	+	15.3027i	−0.736911	+	0.569112i
$724$		0			0
$725$	6.05210	−	34.3232i	0.224769	−	1.27473i
$726$		0			0
$727$	20.0843	+	23.9355i	0.744884	+	0.887719i	0.996792	−	0.0800327i	$-0.0255025\pi$
$727$	20.0843	+	23.9355i	0.744884	+	0.887719i	−0.251908	+	0.967751i	$0.581058\pi$
$728$		0			0
$729$	26.2062	+	6.49886i	0.970600	+	0.240699i
$730$		0			0
$731$	10.2449	+	12.2094i	0.378920	+	0.451579i
$732$		0			0
$733$	16.2456	+	2.86454i	0.600046	+	0.105804i	0.465417	−	0.885092i	$-0.345904\pi$
$733$	16.2456	+	2.86454i	0.600046	+	0.105804i	0.134630	+	0.990896i	$0.457016\pi$
$734$		0			0
$735$	−3.30271	+	2.55066i	−0.121822	+	0.0940825i
$736$		0			0
$737$	0.0737209	−	0.0425628i	0.00271554	−	0.00156782i
$738$		0			0
$739$	11.5876	−	20.0704i	0.426258	−	0.738301i	−0.570279	−	0.821451i	$-0.693165\pi$
$739$	11.5876	−	20.0704i	0.426258	−	0.738301i	0.996537	+	0.0831501i	$0.0264981\pi$
$740$		0			0
$741$	5.12421	+	1.11925i	0.188243	+	0.0411168i
$742$		0			0
$743$	2.55778	+	2.14623i	0.0938358	+	0.0787376i	0.688499	−	0.725238i	$-0.258270\pi$
$743$	2.55778	+	2.14623i	0.0938358	+	0.0787376i	−0.594663	+	0.803975i	$0.702714\pi$
$744$		0			0
$745$	−6.12156	−	2.22807i	−0.224277	−	0.0816300i
$746$		0			0
$747$	−3.48729	−	4.91482i	−0.127593	−	0.179824i
$748$		0			0
$749$	−1.52210	−	8.63224i	−0.0556162	−	0.315415i
$750$		0			0
$751$	0.701648	+	1.92776i	0.0256035	+	0.0703450i	0.951836	−	0.306608i	$-0.0991940\pi$
$751$	0.701648	+	1.92776i	0.0256035	+	0.0703450i	−0.926232	+	0.376953i	$0.876972\pi$
$752$		0			0
$753$	22.5161	−	11.8106i	0.820533	−	0.430400i
$754$		0			0
$755$		−	5.39982i		−	0.196519i
$756$		0			0
$757$			41.6394i			1.51341i	0.653756	+	0.756705i	$0.273192\pi$
$757$			41.6394i			1.51341i	−0.653756	+	0.756705i	$0.726808\pi$
$758$		0			0
$759$	0.0548834	+	0.0347244i	0.00199214	+	0.00126042i
$760$		0			0
$761$	−14.1101	−	38.7671i	−0.511490	−	1.40531i	−0.879684	−	0.475558i	$-0.842246\pi$
$761$	−14.1101	−	38.7671i	−0.511490	−	1.40531i	0.368195	−	0.929749i	$-0.379976\pi$
$762$		0			0
$763$	−0.659130	−	3.73811i	−0.0238621	−	0.135329i
$764$		0			0
$765$	−1.93577	−	0.505767i	−0.0699879	−	0.0182860i
$766$		0			0
$767$	23.0337	+	8.38359i	0.831700	+	0.302714i
$768$		0			0
$769$	−33.4132	−	28.0370i	−1.20491	−	1.01104i	−0.999476	−	0.0323712i	$-0.989694\pi$
$769$	−33.4132	−	28.0370i	−1.20491	−	1.01104i	−0.205437	−	0.978670i	$-0.565861\pi$
$770$		0			0
$771$	26.2525	−	28.8296i	0.945462	−	1.03827i
$772$		0			0
$773$	3.52468	−	6.10492i	0.126774	−	0.219579i	−0.795651	−	0.605755i	$-0.792871\pi$
$773$	3.52468	−	6.10492i	0.126774	−	0.219579i	0.922425	+	0.386176i	$0.126204\pi$
$774$		0			0
$775$	37.4247	−	21.6072i	1.34434	−	0.776153i
$776$		0			0
$777$	−11.0437	−	4.53415i	−0.396191	−	0.162662i
$778$		0			0
$779$	−3.25111	−	0.573258i	−0.116483	−	0.0205391i
$780$		0			0
$781$	−0.114116	−	0.135998i	−0.00408338	−	0.00486638i
$782$		0			0
$783$	31.6697	−	20.5950i	1.13178	−	0.736004i
$784$		0			0
$785$	4.90671	+	5.84759i	0.175128	+	0.208709i
$786$		0			0
$787$	−8.03739	+	45.5823i	−0.286502	+	1.62483i	0.413369	+	0.910564i	$0.364352\pi$
$787$	−8.03739	+	45.5823i	−0.286502	+	1.62483i	−0.699871	+	0.714270i	$0.746759\pi$
$788$		0			0
$789$	−4.09842	−	30.3976i	−0.145907	−	1.08218i
$790$		0			0
$791$	12.6913	+	21.9820i	0.451250	+	0.781589i
$792$		0			0
$793$	−10.0600	+	17.4245i	−0.357242	+	0.618762i
$794$		0			0
$795$	−7.79830	+	2.48556i	−0.276577	+	0.0881537i
$796$		0			0
$797$	10.7323	+	9.00550i	0.380159	+	0.318991i	0.812765	−	0.582592i	$-0.197961\pi$
$797$	10.7323	+	9.00550i	0.380159	+	0.318991i	−0.432606	+	0.901583i	$0.642406\pi$
$798$		0			0
$799$	−2.28975	+	6.29103i	−0.0810054	+	0.222561i
$800$		0			0
$801$	−0.324754	+	0.153909i	−0.0114746	+	0.00543810i
$802$		0			0
$803$	0.0117824	−	0.00207756i	0.000415792	−	7.33153e-5i
$804$		0			0
$805$	0.429937	+	1.18124i	0.0151533	+	0.0416333i
$806$		0			0
$807$	17.7347	+	0.718901i	0.624290	+	0.0253065i
$808$		0			0
$809$			25.2574i			0.888002i	0.896026	+	0.444001i	$0.146441\pi$
$809$			25.2574i			0.888002i	−0.896026	+	0.444001i	$0.853559\pi$
$810$		0			0
$811$	36.9593			1.29782			0.648908	−	0.760867i	$-0.275226\pi$
$811$	36.9593			1.29782			0.648908	+	0.760867i	$0.275226\pi$
$812$		0			0
$813$	1.31408	−	32.4173i	0.0460869	−	1.13692i
$814$		0			0
$815$	4.34200	−	1.58036i	0.152094	−	0.0553576i
$816$		0			0
$817$	−2.55420	−	14.4856i	−0.0893602	−	0.506787i
$818$		0			0
$819$	−4.95693	+	7.17406i	−0.173209	+	0.250682i
$820$		0			0
$821$	5.42437	+	1.97431i	0.189312	+	0.0689038i	0.434936	−	0.900461i	$-0.356771\pi$
$821$	5.42437	+	1.97431i	0.189312	+	0.0689038i	−0.245625	+	0.969365i	$0.578993\pi$
$822$		0			0
$823$	12.2571	−	14.6074i	0.427254	−	0.509182i	−0.508874	−	0.860841i	$-0.669938\pi$
$823$	12.2571	−	14.6074i	0.427254	−	0.509182i	0.936128	+	0.351659i	$0.114382\pi$
$824$		0			0
$825$	0.0444351	+	0.139412i	0.00154703	+	0.00485372i
$826$		0			0
$827$	23.7503	+	13.7122i	0.825878	+	0.476821i	0.852439	−	0.522826i	$-0.175122\pi$
$827$	23.7503	+	13.7122i	0.825878	+	0.476821i	−0.0265613	+	0.999647i	$0.508456\pi$
$828$		0			0
$829$	23.8710	−	13.7819i	0.829073	−	0.478666i	−0.0244622	−	0.999701i	$-0.507787\pi$
$829$	23.8710	−	13.7819i	0.829073	−	0.478666i	0.853535	+	0.521035i	$0.174454\pi$
$830$		0			0
$831$	37.3978	−	5.04223i	1.29732	−	0.174913i
$832$		0			0
$833$	−7.67695	−	1.35365i	−0.265991	−	0.0469013i
$834$		0			0
$835$	−5.57837	+	4.68081i	−0.193048	+	0.161986i
$836$		0			0
$837$	44.8025	+	13.6666i	1.54860	+	0.472388i
$838$		0			0
$839$	22.7744	−	19.1100i	0.786259	−	0.659750i	−0.158558	−	0.987350i	$-0.550684\pi$
$839$	22.7744	−	19.1100i	0.786259	−	0.659750i	0.944816	+	0.327600i	$0.106240\pi$
$840$		0			0
$841$	4.14263	−	23.4940i	0.142849	−	0.810138i
$842$		0			0
$843$	7.60237	−	18.5169i	0.261839	−	0.637755i
$844$		0			0
$845$	−1.81840	−	3.14956i	−0.0625548	−	0.108348i
$846$		0			0
$847$	−12.3959	−	7.15675i	−0.425927	−	0.245909i
$848$		0			0
$849$	−5.49660	−	5.00526i	−0.188643	−	0.171780i
$850$		0			0
$851$	7.24453	−	8.63370i	0.248339	−	0.295959i
$852$		0			0
$853$	14.9845	−	41.1697i	0.513061	−	1.40962i	−0.364970	−	0.931019i	$-0.618921\pi$
$853$	14.9845	−	41.1697i	0.513061	−	1.40962i	0.878031	−	0.478604i	$-0.158857\pi$
$854$		0			0
$855$	1.31376	+	1.29747i	0.0449297	+	0.0443726i
$856$		0			0
$857$	−12.6966	+	2.23875i	−0.433708	+	0.0764744i	−0.386240	−	0.922398i	$-0.626226\pi$
$857$	−12.6966	+	2.23875i	−0.433708	+	0.0764744i	−0.0474680	+	0.998873i	$0.515115\pi$
$858$		0			0
$859$	26.7551	−	9.73806i	0.912872	−	0.332258i	0.157473	−	0.987523i	$-0.449665\pi$
$859$	26.7551	−	9.73806i	0.912872	−	0.332258i	0.755399	+	0.655265i	$0.227443\pi$
$860$		0			0
$861$	2.93448	−	4.63807i	0.100007	−	0.158065i
$862$		0			0
$863$	46.6170			1.58686			0.793431	−	0.608660i	$-0.208293\pi$
$863$	46.6170			1.58686			0.793431	+	0.608660i	$0.208293\pi$
$864$		0			0
$865$	−6.14571			−0.208961
$866$		0			0
$867$	11.9414	+	22.7656i	0.405551	+	0.773159i
$868$		0			0
$869$	0.133877	−	0.0487272i	0.00454146	−	0.00165296i
$870$		0			0
$871$	−10.6262	+	1.87368i	−0.360054	+	0.0634873i
$872$		0			0
$873$	−30.4110	−	13.9506i	−1.02926	−	0.472157i
$874$		0			0
$875$	−1.97894	+	5.43708i	−0.0669003	+	0.183807i
$876$		0			0
$877$	3.98303	−	4.74679i	0.134497	−	0.160288i	−0.694592	−	0.719404i	$-0.744415\pi$
$877$	3.98303	−	4.74679i	0.134497	−	0.160288i	0.829089	+	0.559116i	$0.188859\pi$
$878$		0			0
$879$	−4.64617	+	21.2713i	−0.156712	+	0.717463i
$880$		0			0
$881$	−21.9173	−	12.6539i	−0.738412	−	0.426322i	0.0830799	−	0.996543i	$-0.473524\pi$
$881$	−21.9173	−	12.6539i	−0.738412	−	0.426322i	−0.821492	+	0.570221i	$0.806858\pi$
$882$		0			0
$883$	−15.7424	−	27.2667i	−0.529775	−	0.917597i	−0.999397	−	0.0347290i	$-0.988943\pi$
$883$	−15.7424	−	27.2667i	−0.529775	−	0.917597i	0.469622	−	0.882868i	$-0.344390\pi$
$884$		0			0
$885$	5.27444	+	6.82958i	0.177298	+	0.229574i
$886$		0			0
$887$	0.0310073	−	0.175851i	0.00104112	−	0.00590451i	−0.984283	−	0.176600i	$-0.943490\pi$
$887$	0.0310073	−	0.175851i	0.00104112	−	0.00590451i	0.985324	+	0.170695i	$0.0546013\pi$
$888$		0			0
$889$	−17.2584	+	14.4815i	−0.578827	+	0.485694i
$890$		0			0
$891$	−0.0775808	+	0.138331i	−0.00259906	+	0.00463427i
$892$		0			0
$893$	4.73299	−	3.97145i	0.158384	−	0.132900i
$894$		0			0
$895$	5.08477	+	0.896582i	0.169965	+	0.0299694i
$896$		0			0
$897$	−5.03181	−	6.51541i	−0.168007	−	0.217543i
$898$		0			0
$899$	56.7571	−	32.7687i	1.89296	−	1.09290i
$900$		0			0
$901$	−13.2413	−	7.64488i	−0.441132	−	0.254688i
$902$		0			0
$903$	23.8909	+	5.21836i	0.795040	+	0.173656i
$904$		0			0
$905$	−4.32570	+	5.15517i	−0.143791	+	0.171364i
$906$		0			0
$907$	18.2575	+	6.64519i	0.606231	+	0.220650i	0.626853	−	0.779137i	$-0.284343\pi$
$907$	18.2575	+	6.64519i	0.606231	+	0.220650i	−0.0206225	+	0.999787i	$0.506565\pi$
$908$		0			0
$909$	4.67372	+	49.8382i	0.155017	+	1.65303i
$910$		0			0
$911$	−0.423720	−	2.40304i	−0.0140385	−	0.0796161i	0.976984	−	0.213314i	$-0.0684258\pi$
$911$	−0.423720	−	2.40304i	−0.0140385	−	0.0796161i	−0.991022	+	0.133698i	$0.957315\pi$
$912$		0			0
$913$	0.0332645	−	0.0121073i	0.00110089	−	0.000400693i
$914$		0			0
$915$	−6.27252	+	3.29017i	−0.207363	+	0.108770i
$916$		0			0
$917$	−4.01015			−0.132427
$918$		0			0
$919$			2.20402i			0.0727038i	0.999339	+	0.0363519i	$0.0115737\pi$
$919$			2.20402i			0.0727038i	−0.999339	+	0.0363519i	$0.988426\pi$
$920$		0			0
$921$	13.8312	−	21.8608i	0.455753	−	0.720337i
$922$		0			0
$923$	7.69653	+	21.1460i	0.253334	+	0.696030i
$924$		0			0
$925$	25.0065	−	4.40933i	0.822210	−	0.144978i
$926$		0			0
$927$	−12.6761	−	46.1544i	−0.416339	−	1.51591i
$928$		0			0
$929$	3.30889	−	9.09111i	0.108561	−	0.298270i	−0.873502	−	0.486820i	$-0.838157\pi$
$929$	3.30889	−	9.09111i	0.108561	−	0.298270i	0.982063	+	0.188551i	$0.0603789\pi$
$930$		0			0
$931$	5.51109	+	4.62435i	0.180619	+	0.151557i
$932$		0			0
$933$	−1.56337	−	1.42362i	−0.0511823	−	0.0466071i
$934$		0			0
$935$	0.00587632	−	0.0101781i	0.000192176	−	0.000332859i
$936$		0			0
$937$	−22.2202	−	38.4864i	−0.725901	−	1.25730i	−0.958602	−	0.284749i	$-0.908090\pi$
$937$	−22.2202	−	38.4864i	−0.725901	−	1.25730i	0.232701	−	0.972548i	$-0.425243\pi$
$938$		0			0
$939$	6.38013	+	2.61945i	0.208208	+	0.0854826i
$940$		0			0
$941$	−7.38960	+	41.9085i	−0.240894	+	1.36618i	0.588944	+	0.808174i	$0.299544\pi$
$941$	−7.38960	+	41.9085i	−0.240894	+	1.36618i	−0.829838	+	0.558004i	$0.811567\pi$
$942$		0			0
$943$	3.33056	+	3.96920i	0.108458	+	0.129255i
$944$		0			0
$945$	−2.82499	+	1.20124i	−0.0918970	+	0.0390763i
$946$		0			0
$947$	−30.3650	−	36.1877i	−0.986731	−	1.17594i	−0.984400	−	0.175943i	$-0.943702\pi$
$947$	−30.3650	−	36.1877i	−0.986731	−	1.17594i	−0.00233119	−	0.999997i	$-0.500742\pi$
$948$		0			0
$949$	−1.49348	−	0.263341i	−0.0484804	−	0.00854841i
$950$		0			0
$951$	−1.71330	−	12.7074i	−0.0555575	−	0.412065i
$952$		0			0
$953$	−23.8540	+	13.7721i	−0.772707	+	0.446123i	−0.833840	−	0.552007i	$-0.813862\pi$
$953$	−23.8540	+	13.7721i	−0.772707	+	0.446123i	0.0611321	+	0.998130i	$0.480529\pi$
$954$		0			0
$955$	4.27868	−	7.41089i	0.138455	−	0.239811i
$956$		0			0
$957$	0.0673888	+	0.211428i	0.00217837	+	0.00683451i
$958$		0			0
$959$	−11.7461	−	9.85611i	−0.379300	−	0.318270i
$960$		0			0
$961$	47.2298	+	17.1902i	1.52354	+	0.554524i
$962$		0			0
$963$	−1.63565	+	20.1419i	−0.0527081	+	0.649064i
$964$		0			0
$965$	−0.166374	−	0.943555i	−0.00535578	−	0.0303741i
$966$		0			0
$967$	−0.543982	−	1.49458i	−0.0174933	−	0.0480624i	0.930639	−	0.365939i	$-0.119252\pi$
$967$	−0.543982	−	1.49458i	−0.0174933	−	0.0480624i	−0.948132	+	0.317877i	$0.897030\pi$
$968$		0			0
$969$	−0.139707	+	3.44646i	−0.00448805	+	0.110716i
$970$		0			0
$971$			9.93969i			0.318980i	0.987200	+	0.159490i	$0.0509849\pi$
$971$			9.93969i			0.318980i	−0.987200	+	0.159490i	$0.949015\pi$
$972$		0			0
$973$			6.97199i			0.223512i
$974$		0			0
$975$	0.751218	−	18.5319i	0.0240582	−	0.593496i
$976$		0			0
$977$	13.5121	+	37.1242i	0.432290	+	1.18771i	0.944403	+	0.328789i	$0.106641\pi$
$977$	13.5121	+	37.1242i	0.432290	+	1.18771i	−0.512113	+	0.858918i	$0.671137\pi$
$978$		0			0
$979$	−0.000366577	−	0.00207896i	−1.17158e−5	−	6.64438e-5i
$980$		0			0
$981$	−0.708304	+	8.72227i	−0.0226144	+	0.278481i
$982$		0			0
$983$	−30.2880	−	11.0239i	−0.966036	−	0.351608i	−0.189640	−	0.981854i	$-0.560732\pi$
$983$	−30.2880	−	11.0239i	−0.966036	−	0.351608i	−0.776396	+	0.630245i	$0.782954\pi$
$984$		0			0
$985$	3.98484	+	3.34368i	0.126967	+	0.106538i
$986$		0			0
$987$	3.11936	+	9.78679i	0.0992902	+	0.311517i
$988$		0			0
$989$	−11.5432	+	19.9933i	−0.367051	+	0.635751i
$990$		0			0
$991$	2.66599	−	1.53921i	0.0846881	−	0.0488947i	−0.457058	−	0.889437i	$-0.651097\pi$
$991$	2.66599	−	1.53921i	0.0846881	−	0.0488947i	0.541746	+	0.840542i	$0.317763\pi$
$992$		0			0
$993$	0.693642	+	5.14469i	0.0220121	+	0.163262i
$994$		0			0
$995$	−2.54100	−	0.448048i	−0.0805553	−	0.0142041i
$996$		0			0
$997$	−27.9424	−	33.3004i	−0.884944	−	1.05464i	−0.998134	−	0.0610619i	$-0.980551\pi$
$997$	−27.9424	−	33.3004i	−0.884944	−	1.05464i	0.113190	−	0.993573i	$-0.463893\pi$
$998$		0			0
$999$	21.9913	+	16.5499i	0.695775	+	0.523617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.815.1		192
4.3	odd	2		216.2.v.b.59.5	yes	192
8.3	odd	2	inner	864.2.bh.b.815.2		192
8.5	even	2		216.2.v.b.59.22	yes	192
12.11	even	2		648.2.v.b.611.28		192
24.5	odd	2		648.2.v.b.611.11		192
27.11	odd	18	inner	864.2.bh.b.335.2		192
108.11	even	18		216.2.v.b.11.22	yes	192
108.43	odd	18		648.2.v.b.35.11		192
216.11	even	18	inner	864.2.bh.b.335.1		192
216.173	odd	18		216.2.v.b.11.5	✓	192
216.205	even	18		648.2.v.b.35.28		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.5	✓	192	216.173	odd	18
216.2.v.b.11.22	yes	192	108.11	even	18
216.2.v.b.59.5	yes	192	4.3	odd	2
216.2.v.b.59.22	yes	192	8.5	even	2
648.2.v.b.35.11		192	108.43	odd	18
648.2.v.b.35.28		192	216.205	even	18
648.2.v.b.611.11		192	24.5	odd	2
648.2.v.b.611.28		192	12.11	even	2
864.2.bh.b.335.1		192	216.11	even	18	inner
864.2.bh.b.335.2		192	27.11	odd	18	inner
864.2.bh.b.815.1		192	1.1	even	1	trivial
864.2.bh.b.815.2		192	8.3	odd	2	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.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73063 - 0.0701536i) q^{3} +(-0.426624 + 0.155279i) q^{5} +(-1.28150 + 0.225962i) q^{7} +(2.99016 + 0.242820i) q^{9} +(-0.00602720 + 0.0165596i) q^{11} +(1.43581 - 1.71113i) q^{13} +(0.749222 - 0.238801i) q^{15} +(1.27216 + 0.734483i) q^{17} +(-0.677841 - 1.17406i) q^{19} +(2.23365 - 0.301155i) q^{21} +(-0.369486 + 2.09546i) q^{23} +(-3.67233 + 3.08145i) q^{25} +(-5.15782 - 0.630001i) q^{27} +(-5.56933 + 4.67322i) q^{29} +(-8.87753 - 1.56535i) q^{31} +(0.0115926 - 0.0282357i) q^{33} +(0.511630 - 0.295390i) q^{35} +(-4.58718 - 2.64841i) q^{37} +(-2.60490 + 2.86061i) q^{39} +(1.56527 - 1.86542i) q^{41} +(10.1956 + 3.71089i) q^{43} +(-1.31338 + 0.360715i) q^{45} +(0.791397 + 4.48824i) q^{47} +(-4.98668 + 1.81500i) q^{49} +(-2.15011 - 1.36036i) q^{51} -10.4085 q^{53} -0.00800062i q^{55} +(1.09073 + 2.07941i) q^{57} +(3.75319 + 10.3118i) q^{59} +(-8.87057 + 1.56412i) q^{61} +(-3.88674 + 0.364490i) q^{63} +(-0.346849 + 0.952961i) q^{65} +(-3.70041 - 3.10502i) q^{67} +(0.786447 - 3.60054i) q^{69} +(-5.03714 + 8.72458i) q^{71} +(-0.339460 - 0.587962i) q^{73} +(6.57161 - 5.07522i) q^{75} +(0.00398198 - 0.0225829i) q^{77} +(-5.19665 - 6.19313i) q^{79} +(8.88208 + 1.45214i) q^{81} +(-1.29122 - 1.53881i) q^{83} +(-0.656785 - 0.115809i) q^{85} +(9.96629 - 7.69691i) q^{87} +(-0.103744 + 0.0598964i) q^{89} +(-1.45333 + 2.51724i) q^{91} +(15.2539 + 3.33183i) q^{93} +(0.471489 + 0.395626i) q^{95} +(-10.4801 - 3.81446i) q^{97} +(-0.0220433 + 0.0480522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67}+ \cdots + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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