LMFDB - Embedded newform 864.2.y.a.385.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			385.5
Character	$\chi$	$=$	864.385
Dual form			864.2.y.a.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0827900 + 1.73007i) q^{3} +(-0.532774 - 3.02151i) q^{5} +(2.03971 + 1.71152i) q^{7} +(-2.98629 + 0.286465i) q^{9} +O(q^{10})$	\(q+(0.0827900 + 1.73007i) q^{3} +(-0.532774 - 3.02151i) q^{5} +(2.03971 + 1.71152i) q^{7} +(-2.98629 + 0.286465i) q^{9} +(0.900636 - 5.10776i) q^{11} +(-0.525472 - 0.191256i) q^{13} +(5.18332 - 1.17189i) q^{15} +(-2.47022 - 4.27855i) q^{17} +(1.14343 - 1.98047i) q^{19} +(-2.79218 + 3.67054i) q^{21} +(-1.60649 + 1.34801i) q^{23} +(-4.14723 + 1.50947i) q^{25} +(-0.742840 - 5.14278i) q^{27} +(7.83081 - 2.85018i) q^{29} +(1.35148 - 1.13403i) q^{31} +(8.91135 + 1.13529i) q^{33} +(4.08467 - 7.07486i) q^{35} +(3.54909 + 6.14721i) q^{37} +(0.287383 - 0.924938i) q^{39} +(-8.72625 - 3.17609i) q^{41} +(1.25426 - 7.11326i) q^{43} +(2.45658 + 8.87050i) q^{45} +(-0.318115 - 0.266930i) q^{47} +(0.0155785 + 0.0883500i) q^{49} +(7.19769 - 4.62788i) q^{51} +4.35868 q^{53} -15.9130 q^{55} +(3.52102 + 1.81424i) q^{57} +(1.47724 + 8.37782i) q^{59} +(-7.90191 - 6.63049i) q^{61} +(-6.58146 - 4.52679i) q^{63} +(-0.297925 + 1.68962i) q^{65} +(7.91918 + 2.88234i) q^{67} +(-2.46515 - 2.66774i) q^{69} +(6.71642 + 11.6332i) q^{71} +(-1.03573 + 1.79394i) q^{73} +(-2.95483 - 7.05003i) q^{75} +(10.5791 - 8.87689i) q^{77} +(14.8150 - 5.39221i) q^{79} +(8.83588 - 1.71094i) q^{81} +(14.3743 - 5.23180i) q^{83} +(-11.6116 + 9.74332i) q^{85} +(5.57933 + 13.3119i) q^{87} +(4.58615 - 7.94345i) q^{89} +(-0.744472 - 1.28946i) q^{91} +(2.07384 + 2.24428i) q^{93} +(-6.59321 - 2.39973i) q^{95} +(-0.972374 + 5.51461i) q^{97} +(-1.22637 + 15.5113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{9}+O(q^{10}) $ 48 * q - 12 * q^9	$ 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) $ 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	0.0827900	+	1.73007i	0.0477988	+	0.998857i
$3$	0.0827900	+	1.73007i	0.0477988	+	0.998857i
$4$		0			0
$5$	−0.532774	−	3.02151i	−0.238264	−	1.35126i	−0.835630	−	0.549293i	$-0.814897\pi$
$5$	−0.532774	−	3.02151i	−0.238264	−	1.35126i	0.597366	−	0.801969i	$-0.296214\pi$
$6$		0			0
$7$	2.03971	+	1.71152i	0.770938	+	0.646894i	0.940949	−	0.338549i	$-0.109936\pi$
$7$	2.03971	+	1.71152i	0.770938	+	0.646894i	−0.170011	+	0.985442i	$0.554380\pi$
$8$		0			0
$9$	−2.98629	+	0.286465i	−0.995431	+	0.0954883i
$10$		0			0
$11$	0.900636	−	5.10776i	0.271552	−	1.54005i	−0.478154	−	0.878276i	$-0.658694\pi$
$11$	0.900636	−	5.10776i	0.271552	−	1.54005i	0.749706	−	0.661771i	$-0.230195\pi$
$12$		0			0
$13$	−0.525472	−	0.191256i	−0.145740	−	0.0530449i	0.268120	−	0.963385i	$-0.413598\pi$
$13$	−0.525472	−	0.191256i	−0.145740	−	0.0530449i	−0.413860	+	0.910340i	$0.635820\pi$
$14$		0			0
$15$	5.18332	−	1.17189i	1.33833	−	0.302580i
$16$		0			0
$17$	−2.47022	−	4.27855i	−0.599117	−	1.03770i	−0.992952	−	0.118520i	$-0.962185\pi$
$17$	−2.47022	−	4.27855i	−0.599117	−	1.03770i	0.393834	−	0.919181i	$-0.371148\pi$
$18$		0			0
$19$	1.14343	−	1.98047i	0.262320	−	0.454351i	−0.704538	−	0.709666i	$-0.748846\pi$
$19$	1.14343	−	1.98047i	0.262320	−	0.454351i	0.966858	+	0.255315i	$0.0821791\pi$
$20$		0			0
$21$	−2.79218	+	3.67054i	−0.609304	+	0.800977i
$22$		0			0
$23$	−1.60649	+	1.34801i	−0.334977	+	0.281079i	−0.794724	−	0.606971i	$-0.792384\pi$
$23$	−1.60649	+	1.34801i	−0.334977	+	0.281079i	0.459747	+	0.888050i	$0.347940\pi$
$24$		0			0
$25$	−4.14723	+	1.50947i	−0.829446	+	0.301893i
$26$		0			0
$27$	−0.742840	−	5.14278i	−0.142960	−	0.989729i
$28$		0			0
$29$	7.83081	−	2.85018i	1.45414	−	0.529265i	0.510399	−	0.859938i	$-0.329498\pi$
$29$	7.83081	−	2.85018i	1.45414	−	0.529265i	0.943746	+	0.330672i	$0.107275\pi$
$30$		0			0
$31$	1.35148	−	1.13403i	0.242734	−	0.203678i	−0.513302	−	0.858208i	$-0.671578\pi$
$31$	1.35148	−	1.13403i	0.242734	−	0.203678i	0.756036	+	0.654530i	$0.227134\pi$
$32$		0			0
$33$	8.91135	+	1.13529i	1.55127	+	0.197629i
$34$		0			0
$35$	4.08467	−	7.07486i	0.690436	−	1.19587i
$36$		0			0
$37$	3.54909	+	6.14721i	0.583468	+	1.01060i	0.995065	+	0.0992295i	$0.0316378\pi$
$37$	3.54909	+	6.14721i	0.583468	+	1.01060i	−0.411597	+	0.911366i	$0.635029\pi$
$38$		0			0
$39$	0.287383	−	0.924938i	0.0460181	−	0.148109i
$40$		0			0
$41$	−8.72625	−	3.17609i	−1.36281	−	0.496023i	−0.445888	−	0.895089i	$-0.647112\pi$
$41$	−8.72625	−	3.17609i	−1.36281	−	0.496023i	−0.916922	+	0.399066i	$0.869334\pi$
$42$		0			0
$43$	1.25426	−	7.11326i	0.191273	−	1.08476i	−0.726355	−	0.687320i	$-0.758787\pi$
$43$	1.25426	−	7.11326i	0.191273	−	1.08476i	0.917627	−	0.397442i	$-0.130102\pi$
$44$		0			0
$45$	2.45658	+	8.87050i	0.366205	+	1.32234i
$46$		0			0
$47$	−0.318115	−	0.266930i	−0.0464018	−	0.0389357i	0.619292	−	0.785161i	$-0.287420\pi$
$47$	−0.318115	−	0.266930i	−0.0464018	−	0.0389357i	−0.665694	+	0.746225i	$0.731864\pi$
$48$		0			0
$49$	0.0155785	+	0.0883500i	0.00222550	+	0.0126214i
$50$		0			0
$51$	7.19769	−	4.62788i	1.00788	−	0.648033i
$52$		0			0
$53$	4.35868			0.598711			0.299356	−	0.954142i	$-0.403228\pi$
$53$	4.35868			0.598711			0.299356	+	0.954142i	$0.403228\pi$
$54$		0			0
$55$	−15.9130			−2.14571
$56$		0			0
$57$	3.52102	+	1.81424i	0.466371	+	0.240303i
$58$		0			0
$59$	1.47724	+	8.37782i	0.192320	+	1.09070i	0.916184	+	0.400757i	$0.131253\pi$
$59$	1.47724	+	8.37782i	0.192320	+	1.09070i	−0.723864	+	0.689942i	$0.757636\pi$
$60$		0			0
$61$	−7.90191	−	6.63049i	−1.01174	−	0.848947i	−0.0231695	−	0.999732i	$-0.507376\pi$
$61$	−7.90191	−	6.63049i	−1.01174	−	0.848947i	−0.988567	+	0.150784i	$0.951820\pi$
$62$		0			0
$63$	−6.58146	−	4.52679i	−0.829186	−	0.570322i
$64$		0			0
$65$	−0.297925	+	1.68962i	−0.0369531	+	0.209571i
$66$		0			0
$67$	7.91918	+	2.88234i	0.967482	+	0.352134i	0.776961	−	0.629549i	$-0.216760\pi$
$67$	7.91918	+	2.88234i	0.967482	+	0.352134i	0.190521	+	0.981683i	$0.438982\pi$
$68$		0			0
$69$	−2.46515	−	2.66774i	−0.296769	−	0.321159i
$70$		0			0
$71$	6.71642	+	11.6332i	0.797092	+	1.38060i	0.921502	+	0.388373i	$0.126963\pi$
$71$	6.71642	+	11.6332i	0.797092	+	1.38060i	−0.124411	+	0.992231i	$0.539704\pi$
$72$		0			0
$73$	−1.03573	+	1.79394i	−0.121223	+	0.209964i	−0.920250	−	0.391330i	$-0.872015\pi$
$73$	−1.03573	+	1.79394i	−0.121223	+	0.209964i	0.799027	+	0.601295i	$0.205348\pi$
$74$		0			0
$75$	−2.95483	−	7.05003i	−0.341195	−	0.814067i
$76$		0			0
$77$	10.5791	−	8.87689i	1.20560	−	1.01162i
$78$		0			0
$79$	14.8150	−	5.39221i	1.66681	−	0.606671i	0.675402	−	0.737449i	$-0.263970\pi$
$79$	14.8150	−	5.39221i	1.66681	−	0.606671i	0.991412	+	0.130779i	$0.0417478\pi$
$80$		0			0
$81$	8.83588	−	1.71094i	0.981764	−	0.190104i
$82$		0			0
$83$	14.3743	−	5.23180i	1.57778	−	0.574265i	0.603060	−	0.797696i	$-0.293948\pi$
$83$	14.3743	−	5.23180i	1.57778	−	0.574265i	0.974720	+	0.223431i	$0.0717259\pi$
$84$		0			0
$85$	−11.6116	+	9.74332i	−1.25946	+	1.05681i
$86$		0			0
$87$	5.57933	+	13.3119i	0.598167	+	1.42718i
$88$		0			0
$89$	4.58615	−	7.94345i	0.486131	−	0.842004i	−0.513742	−	0.857945i	$-0.671741\pi$
$89$	4.58615	−	7.94345i	0.486131	−	0.842004i	0.999873	+	0.0159407i	$0.00507430\pi$
$90$		0			0
$91$	−0.744472	−	1.28946i	−0.0780418	−	0.135172i
$92$		0			0
$93$	2.07384	+	2.24428i	0.215047	+	0.232721i
$94$		0			0
$95$	−6.59321	−	2.39973i	−0.676449	−	0.246207i
$96$		0			0
$97$	−0.972374	+	5.51461i	−0.0987297	+	0.559924i	0.894811	+	0.446445i	$0.147310\pi$
$97$	−0.972374	+	5.51461i	−0.0987297	+	0.559924i	−0.993540	+	0.113478i	$0.963801\pi$
$98$		0			0
$99$	−1.22637	+	15.5113i	−0.123254	+	1.55894i
$100$		0			0
$101$	−4.67776	−	3.92511i	−0.465455	−	0.390563i	0.379678	−	0.925119i	$-0.376035\pi$
$101$	−4.67776	−	3.92511i	−0.465455	−	0.390563i	−0.845133	+	0.534555i	$0.820479\pi$
$102$		0			0
$103$	−0.00832028	−	0.0471867i	−0.000819822	−	0.00464944i	0.984395	−	0.175972i	$-0.0563070\pi$
$103$	−0.00832028	−	0.0471867i	−0.000819822	−	0.00464944i	−0.985215	+	0.171323i	$0.945196\pi$
$104$		0			0
$105$	12.5782	+	6.48105i	1.22750	+	0.632485i
$106$		0			0
$107$	−14.6768			−1.41886			−0.709430	−	0.704776i	$-0.751048\pi$
$107$	−14.6768			−1.41886			−0.709430	+	0.704776i	$0.751048\pi$
$108$		0			0
$109$	−15.6691			−1.50083			−0.750415	−	0.660967i	$-0.770146\pi$
$109$	−15.6691			−1.50083			−0.750415	+	0.660967i	$0.770146\pi$
$110$		0			0
$111$	−10.3413	+	6.64911i	−0.981551	+	0.631106i
$112$		0			0
$113$	3.01820	+	17.1170i	0.283928	+	1.61024i	0.709090	+	0.705118i	$0.249106\pi$
$113$	3.01820	+	17.1170i	0.283928	+	1.61024i	−0.425162	+	0.905117i	$0.639783\pi$
$114$		0			0
$115$	4.92892	+	4.13585i	0.459624	+	0.385670i
$116$		0			0
$117$	1.62400	+	0.420618i	0.150139	+	0.0388861i
$118$		0			0
$119$	2.28429	−	12.9548i	0.209400	−	1.18757i
$120$		0			0
$121$	−14.9414	−	5.43824i	−1.35831	−	0.494385i
$122$		0			0
$123$	4.77242	−	15.3600i	0.430315	−	1.38496i
$124$		0			0
$125$	−0.899900	−	1.55867i	−0.0804895	−	0.139412i
$126$		0			0
$127$	−3.93670	+	6.81857i	−0.349326	+	0.605050i	−0.986130	−	0.165976i	$-0.946923\pi$
$127$	−3.93670	+	6.81857i	−0.349326	+	0.605050i	0.636804	+	0.771026i	$0.280256\pi$
$128$		0			0
$129$	12.4103	+	1.58105i	1.09266	+	0.139204i
$130$		0			0
$131$	−13.6635	+	11.4650i	−1.19378	+	1.00170i	−0.193997	+	0.981002i	$0.562145\pi$
$131$	−13.6635	+	11.4650i	−1.19378	+	1.00170i	−0.999786	+	0.0207005i	$0.993410\pi$
$132$		0			0
$133$	5.72187	−	2.08259i	0.496149	−	0.180584i
$134$		0			0
$135$	−15.1432	+	4.98444i	−1.30332	+	0.428992i
$136$		0			0
$137$	−5.71051	+	2.07845i	−0.487881	+	0.177574i	−0.574235	−	0.818690i	$-0.694701\pi$
$137$	−5.71051	+	2.07845i	−0.487881	+	0.177574i	0.0863540	+	0.996265i	$0.472478\pi$
$138$		0			0
$139$	8.52743	−	7.15537i	0.723288	−	0.606910i	−0.205005	−	0.978761i	$-0.565721\pi$
$139$	8.52743	−	7.15537i	0.723288	−	0.606910i	0.928293	+	0.371851i	$0.121277\pi$
$140$		0			0
$141$	0.435471	−	0.572460i	0.0366733	−	0.0482098i
$142$		0			0
$143$	−1.45015	+	2.51173i	−0.121268	+	0.210042i
$144$		0			0
$145$	−12.7839	−	22.1424i	−1.06165	−	1.83883i
$146$		0			0
$147$	−0.151562	+	0.0342664i	−0.0125006	+	0.00282624i
$148$		0			0
$149$	−8.28459	−	3.01534i	−0.678700	−	0.247027i	−0.0204107	−	0.999792i	$-0.506497\pi$
$149$	−8.28459	−	3.01534i	−0.678700	−	0.247027i	−0.658289	+	0.752765i	$0.728720\pi$
$150$		0			0
$151$	−3.13116	+	17.7577i	−0.254810	+	1.44510i	0.541750	+	0.840540i	$0.317762\pi$
$151$	−3.13116	+	17.7577i	−0.254810	+	1.44510i	−0.796560	+	0.604559i	$0.793349\pi$
$152$		0			0
$153$	8.60246	+	12.0694i	0.695468	+	0.975751i
$154$		0			0
$155$	−4.14652	−	3.47934i	−0.333057	−	0.279468i
$156$		0			0
$157$	1.20456	+	6.83139i	0.0961343	+	0.545205i	0.994394	+	0.105739i	$0.0337209\pi$
$157$	1.20456	+	6.83139i	0.0961343	+	0.545205i	−0.898260	+	0.439465i	$0.855168\pi$
$158$		0			0
$159$	0.360855	+	7.54083i	0.0286177	+	0.598027i
$160$		0			0
$161$	−5.58392			−0.440074
$162$		0			0
$163$	−19.6705			−1.54071			−0.770356	−	0.637614i	$-0.779921\pi$
$163$	−19.6705			−1.54071			−0.770356	+	0.637614i	$0.779921\pi$
$164$		0			0
$165$	−1.31744	−	27.5306i	−0.102562	−	2.14325i
$166$		0			0
$167$	1.47684	+	8.37558i	0.114281	+	0.648121i	0.987104	+	0.160083i	$0.0511763\pi$
$167$	1.47684	+	8.37558i	0.114281	+	0.648121i	−0.872822	+	0.488038i	$0.837713\pi$
$168$		0			0
$169$	−9.71904	−	8.15524i	−0.747618	−	0.627326i
$170$		0			0
$171$	−2.84727	+	6.24182i	−0.217736	+	0.477324i
$172$		0			0
$173$	2.77597	−	15.7433i	0.211053	−	1.19694i	−0.676572	−	0.736376i	$-0.736535\pi$
$173$	2.77597	−	15.7433i	0.211053	−	1.19694i	0.887625	−	0.460566i	$-0.152354\pi$
$174$		0			0
$175$	−11.0426	−	4.01919i	−0.834744	−	0.303822i
$176$		0			0
$177$	−14.3719	+	3.24932i	−1.08026	+	0.244234i
$178$		0			0
$179$	−9.83560	−	17.0358i	−0.735147	−	1.27331i	−0.954659	−	0.297703i	$-0.903780\pi$
$179$	−9.83560	−	17.0358i	−0.735147	−	1.27331i	0.219511	−	0.975610i	$-0.429554\pi$
$180$		0			0
$181$	−5.55489	+	9.62135i	−0.412892	+	0.715149i	−0.995205	−	0.0978154i	$-0.968815\pi$
$181$	−5.55489	+	9.62135i	−0.412892	+	0.715149i	0.582313	+	0.812965i	$0.302148\pi$
$182$		0			0
$183$	10.8170	−	14.2198i	0.799617	−	1.05116i
$184$		0			0
$185$	16.6830	−	13.9987i	1.22656	−	1.02921i
$186$		0			0
$187$	−24.0786	+	8.76389i	−1.76080	+	0.640879i
$188$		0			0
$189$	7.28679	−	11.7612i	0.530036	−	0.855499i
$190$		0			0
$191$	2.46078	−	0.895652i	0.178056	−	0.0648071i	−0.251454	−	0.967869i	$-0.580909\pi$
$191$	2.46078	−	0.895652i	0.178056	−	0.0648071i	0.429510	+	0.903062i	$0.358686\pi$
$192$		0			0
$193$	2.35123	−	1.97292i	0.169245	−	0.142014i	−0.554231	−	0.832363i	$-0.686988\pi$
$193$	2.35123	−	1.97292i	0.169245	−	0.142014i	0.723476	+	0.690349i	$0.242543\pi$
$194$		0			0
$195$	−2.94782	−	0.375548i	−0.211098	−	0.0268936i
$196$		0			0
$197$	8.74770	−	15.1515i	0.623248	−	1.07950i	−0.365629	−	0.930761i	$-0.619146\pi$
$197$	8.74770	−	15.1515i	0.623248	−	1.07950i	0.988877	−	0.148737i	$-0.0475206\pi$
$198$		0			0
$199$	1.97489	+	3.42060i	0.139996	+	0.242480i	0.927495	−	0.373836i	$-0.121958\pi$
$199$	1.97489	+	3.42060i	0.139996	+	0.242480i	−0.787499	+	0.616316i	$0.788624\pi$
$200$		0			0
$201$	−4.33103	+	13.9394i	−0.305488	+	0.983207i
$202$		0			0
$203$	20.8507	+	7.58904i	1.46343	+	0.532646i
$204$		0			0
$205$	−4.94749	+	28.0586i	−0.345548	+	1.95970i
$206$		0			0
$207$	4.41130	−	4.48575i	0.306606	−	0.311781i
$208$		0			0
$209$	−9.08596	−	7.62403i	−0.628489	−	0.527365i
$210$		0			0
$211$	−2.13238	−	12.0934i	−0.146799	−	0.832541i	−0.965905	−	0.258898i	$-0.916641\pi$
$211$	−2.13238	−	12.0934i	−0.146799	−	0.832541i	0.819105	−	0.573643i	$-0.194470\pi$
$212$		0			0
$213$	−19.5702	+	12.5830i	−1.34093	+	0.862172i
$214$		0			0
$215$	−22.1610			−1.51137
$216$		0			0
$217$	4.69755			0.318890
$218$		0			0
$219$	−3.18939	−	1.64337i	−0.215519	−	0.111048i
$220$		0			0
$221$	0.479734	+	2.72071i	0.0322704	+	0.183015i
$222$		0			0
$223$	17.2447	+	14.4700i	1.15479	+	0.968983i	0.999821	−	0.0189364i	$-0.00602802\pi$
$223$	17.2447	+	14.4700i	1.15479	+	0.968983i	0.154968	+	0.987919i	$0.450472\pi$
$224$		0			0
$225$	11.9524	−	5.69575i	0.796828	−	0.379716i
$226$		0			0
$227$	−3.58146	+	20.3115i	−0.237710	+	1.34812i	0.599122	+	0.800658i	$0.295517\pi$
$227$	−3.58146	+	20.3115i	−0.237710	+	1.34812i	−0.836831	+	0.547461i	$0.815594\pi$
$228$		0			0
$229$	19.0027	+	6.91642i	1.25573	+	0.457050i	0.882336	−	0.470621i	$-0.155970\pi$
$229$	19.0027	+	6.91642i	1.25573	+	0.457050i	0.373399	+	0.927671i	$0.378192\pi$
$230$		0			0
$231$	16.2335	+	17.5676i	1.06808	+	1.15586i
$232$		0			0
$233$	4.10859	+	7.11628i	0.269163	+	0.466203i	0.968646	−	0.248446i	$-0.0799198\pi$
$233$	4.10859	+	7.11628i	0.269163	+	0.466203i	−0.699483	+	0.714649i	$0.746586\pi$
$234$		0			0
$235$	−0.637049	+	1.10340i	−0.0415565	+	0.0719779i
$236$		0			0
$237$	10.5554	+	25.1845i	0.685649	+	1.63591i
$238$		0			0
$239$	−3.20425	+	2.68869i	−0.207266	+	0.173917i	−0.740511	−	0.672044i	$-0.765417\pi$
$239$	−3.20425	+	2.68869i	−0.207266	+	0.173917i	0.533246	+	0.845961i	$0.320972\pi$
$240$		0			0
$241$	17.2957	−	6.29514i	1.11412	−	0.405505i	0.281615	−	0.959528i	$-0.409130\pi$
$241$	17.2957	−	6.29514i	1.11412	−	0.405505i	0.832502	+	0.554022i	$0.186908\pi$
$242$		0			0
$243$	3.69156	+	15.1450i	0.236814	+	0.971555i
$244$		0			0
$245$	0.258651	−	0.0941412i	0.0165246	−	0.00601446i
$246$		0			0
$247$	−0.979616	+	0.821995i	−0.0623315	+	0.0523023i
$248$		0			0
$249$	10.2414	+	24.4353i	0.649024	+	1.54853i
$250$		0			0
$251$	3.77483	−	6.53819i	0.238265	−	0.412687i	−0.721952	−	0.691944i	$-0.756755\pi$
$251$	3.77483	−	6.53819i	0.238265	−	0.412687i	0.960217	+	0.279257i	$0.0900880\pi$
$252$		0			0
$253$	5.43843	+	9.41964i	0.341911	+	0.592207i
$254$		0			0
$255$	−17.8180	−	19.2823i	−1.11580	−	1.20750i
$256$		0			0
$257$	−8.31085	−	3.02490i	−0.518417	−	0.188688i	0.0695423	−	0.997579i	$-0.477846\pi$
$257$	−8.31085	−	3.02490i	−0.518417	−	0.188688i	−0.587959	+	0.808891i	$0.700068\pi$
$258$		0			0
$259$	−3.28195	+	18.6129i	−0.203931	+	1.15655i
$260$		0			0
$261$	−22.5686	+	10.7547i	−1.39696	+	0.665701i
$262$		0			0
$263$	17.7407	+	14.8862i	1.09394	+	0.917922i	0.997003	−	0.0773688i	$-0.0246519\pi$
$263$	17.7407	+	14.8862i	1.09394	+	0.917922i	0.0969342	+	0.995291i	$0.469096\pi$
$264$		0			0
$265$	−2.32219	−	13.1698i	−0.142651	−	0.809016i
$266$		0			0
$267$	14.1224	+	7.27673i	0.864278	+	0.445329i
$268$		0			0
$269$	−1.10407			−0.0673162			−0.0336581	−	0.999433i	$-0.510716\pi$
$269$	−1.10407			−0.0673162			−0.0336581	+	0.999433i	$0.510716\pi$
$270$		0			0
$271$	−18.0358			−1.09560			−0.547798	−	0.836611i	$-0.684534\pi$
$271$	−18.0358			−1.09560			−0.547798	+	0.836611i	$0.684534\pi$
$272$		0			0
$273$	2.16923	−	1.39474i	0.131288	−	0.0844137i
$274$		0			0
$275$	3.97485	+	22.5425i	0.239693	+	1.35936i
$276$		0			0
$277$	16.1340	+	13.5381i	0.969400	+	0.813424i	0.982457	−	0.186491i	$-0.0597116\pi$
$277$	16.1340	+	13.5381i	0.969400	+	0.813424i	−0.0130562	+	0.999915i	$0.504156\pi$
$278$		0			0
$279$	−3.71107	+	3.77370i	−0.222176	+	0.225925i
$280$		0			0
$281$	1.68697	−	9.56727i	0.100636	−	0.570735i	−0.892238	−	0.451566i	$-0.850866\pi$
$281$	1.68697	−	9.56727i	0.100636	−	0.570735i	0.992874	−	0.119170i	$-0.0380233\pi$
$282$		0			0
$283$	−9.69898	−	3.53014i	−0.576545	−	0.209845i	0.0372566	−	0.999306i	$-0.488138\pi$
$283$	−9.69898	−	3.53014i	−0.576545	−	0.209845i	−0.613801	+	0.789461i	$0.710360\pi$
$284$		0			0
$285$	3.60585	−	11.6054i	0.213592	−	0.687444i
$286$		0			0
$287$	−12.3631	−	21.4134i	−0.729768	−	1.26400i
$288$		0			0
$289$	−3.70401	+	6.41554i	−0.217883	+	0.377385i
$290$		0			0
$291$	−9.62117	−	1.22572i	−0.564003	−	0.0718531i
$292$		0			0
$293$	8.64392	−	7.25311i	0.504983	−	0.423731i	−0.354376	−	0.935103i	$-0.615307\pi$
$293$	8.64392	−	7.25311i	0.504983	−	0.423731i	0.859360	+	0.511372i	$0.170862\pi$
$294$		0			0
$295$	24.5267	−	8.92698i	1.42800	−	0.519749i
$296$		0			0
$297$	−26.9371	−	0.837525i	−1.56305	−	0.0485981i
$298$		0			0
$299$	1.10198	−	0.401089i	0.0637292	−	0.0231955i
$300$		0			0
$301$	14.7328	−	12.3623i	0.849185	−	0.712550i
$302$		0			0
$303$	6.40345	−	8.41783i	0.367869	−	0.483591i
$304$		0			0
$305$	−15.8242	+	27.4083i	−0.906090	+	1.56939i
$306$		0			0
$307$	15.3776	+	26.6348i	0.877646	+	1.52013i	0.853918	+	0.520408i	$0.174220\pi$
$307$	15.3776	+	26.6348i	0.877646	+	1.52013i	0.0237280	+	0.999718i	$0.492446\pi$
$308$		0			0
$309$	0.0809475	−	0.0183013i	0.00460494	−	0.00104112i
$310$		0			0
$311$	5.97071	+	2.17316i	0.338568	+	0.123229i	0.505709	−	0.862704i	$-0.331231\pi$
$311$	5.97071	+	2.17316i	0.338568	+	0.123229i	−0.167140	+	0.985933i	$0.553453\pi$
$312$		0			0
$313$	0.271566	−	1.54013i	0.0153498	−	0.0870532i	−0.976170	−	0.217005i	$-0.930371\pi$
$313$	0.271566	−	1.54013i	0.0153498	−	0.0870532i	0.991520	+	0.129952i	$0.0414823\pi$
$314$		0			0
$315$	−10.1713	+	22.2977i	−0.573089	+	1.25633i
$316$		0			0
$317$	15.4451	+	12.9600i	0.867482	+	0.727903i	0.963566	−	0.267470i	$-0.0861875\pi$
$317$	15.4451	+	12.9600i	0.867482	+	0.727903i	−0.0960847	+	0.995373i	$0.530632\pi$
$318$		0			0
$319$	−7.50533	−	42.5649i	−0.420218	−	2.38317i
$320$		0			0
$321$	−1.21509	−	25.3919i	−0.0678198	−	1.41724i
$322$		0			0
$323$	−11.2981			−0.628641
$324$		0			0
$325$	2.46795			0.136897
$326$		0			0
$327$	−1.29725	−	27.1087i	−0.0717378	−	1.49911i
$328$		0			0
$329$	−0.192006	−	1.08892i	−0.0105856	−	0.0600340i
$330$		0			0
$331$	3.64629	+	3.05960i	0.200418	+	0.168171i	0.737473	−	0.675376i	$-0.236019\pi$
$331$	3.64629	+	3.05960i	0.200418	+	0.168171i	−0.537055	+	0.843547i	$0.680463\pi$
$332$		0			0
$333$	−12.3596	−	17.3407i	−0.677302	−	0.950263i
$334$		0			0
$335$	4.48991	−	25.4635i	0.245310	−	1.39122i
$336$		0			0
$337$	2.05863	+	0.749279i	0.112141	+	0.0408158i	0.397481	−	0.917610i	$-0.369884\pi$
$337$	2.05863	+	0.749279i	0.112141	+	0.0408158i	−0.285340	+	0.958426i	$0.592107\pi$
$338$		0			0
$339$	−29.3638	+	6.63881i	−1.59482	+	0.360571i
$340$		0			0
$341$	−4.57516	−	7.92440i	−0.247759	−	0.429130i
$342$		0			0
$343$	9.19984	−	15.9346i	0.496745	−	0.860387i
$344$		0			0
$345$	−6.74725	+	8.86978i	−0.363260	+	0.477533i
$346$		0			0
$347$	12.3974	−	10.4026i	0.665525	−	0.558442i	−0.246212	−	0.969216i	$-0.579186\pi$
$347$	12.3974	−	10.4026i	0.665525	−	0.558442i	0.911737	+	0.410774i	$0.134742\pi$
$348$		0			0
$349$	−7.64114	+	2.78115i	−0.409021	+	0.148871i	−0.538332	−	0.842733i	$-0.680946\pi$
$349$	−7.64114	+	2.78115i	−0.409021	+	0.148871i	0.129311	+	0.991604i	$0.458723\pi$
$350$		0			0
$351$	−0.593247	+	2.84446i	−0.0316652	+	0.151826i
$352$		0			0
$353$	−12.6117	+	4.59029i	−0.671254	+	0.244317i	−0.655088	−	0.755553i	$-0.727368\pi$
$353$	−12.6117	+	4.59029i	−0.671254	+	0.244317i	−0.0161666	+	0.999869i	$0.505146\pi$
$354$		0			0
$355$	31.5714	−	26.4916i	1.67564	−	1.40603i
$356$		0			0
$357$	22.6019	+	2.87945i	1.19622	+	0.152397i
$358$		0			0
$359$	−12.5614	+	21.7570i	−0.662967	+	1.14829i	0.316866	+	0.948470i	$0.397370\pi$
$359$	−12.5614	+	21.7570i	−0.662967	+	1.14829i	−0.979832	+	0.199822i	$0.935964\pi$
$360$		0			0
$361$	6.88516	+	11.9254i	0.362377	+	0.627655i
$362$		0			0
$363$	8.17153	−	26.3000i	0.428894	−	1.38039i
$364$		0			0
$365$	5.97221	+	2.17371i	0.312600	+	0.113777i
$366$		0			0
$367$	−2.83795	+	16.0948i	−0.148140	+	0.840144i	0.816652	+	0.577130i	$0.195827\pi$
$367$	−2.83795	+	16.0948i	−0.148140	+	0.840144i	−0.964792	+	0.263013i	$0.915284\pi$
$368$		0			0
$369$	26.9690	+	6.98498i	1.40395	+	0.363623i
$370$		0			0
$371$	8.89045	+	7.45997i	0.461569	+	0.387302i
$372$		0			0
$373$	0.483980	+	2.74478i	0.0250595	+	0.142120i	0.994770	−	0.102136i	$-0.0325676\pi$
$373$	0.483980	+	2.74478i	0.0250595	+	0.142120i	−0.969711	+	0.244255i	$0.921457\pi$
$374$		0			0
$375$	2.62211	−	1.68593i	0.135405	−	0.0870612i
$376$		0			0
$377$	−4.65999			−0.240002
$378$		0			0
$379$	22.6950			1.16577			0.582883	−	0.812556i	$-0.301925\pi$
$379$	22.6950			1.16577			0.582883	+	0.812556i	$0.301925\pi$
$380$		0			0
$381$	−12.1225	−	6.24626i	−0.621056	−	0.320006i
$382$		0			0
$383$	−2.42329	−	13.7431i	−0.123824	−	0.702242i	−0.981999	−	0.188885i	$-0.939513\pi$
$383$	−2.42329	−	13.7431i	−0.123824	−	0.702242i	0.858175	−	0.513357i	$-0.171598\pi$
$384$		0			0
$385$	−32.4579	−	27.2354i	−1.65421	−	1.38804i
$386$		0			0
$387$	−1.70788	+	21.6016i	−0.0868166	+	1.09807i
$388$		0			0
$389$	0.00646381	−	0.0366581i	0.000327728	−	0.00185864i	−0.984643	−	0.174577i	$-0.944144\pi$
$389$	0.00646381	−	0.0366581i	0.000327728	−	0.00185864i	0.984971	+	0.172719i	$0.0552552\pi$
$390$		0			0
$391$	9.73591	+	3.54358i	0.492366	+	0.179207i
$392$		0			0
$393$	−20.9665	−	22.6896i	−1.05762	−	1.14454i
$394$		0			0
$395$	−24.1857	−	41.8908i	−1.21691	−	2.10775i
$396$		0			0
$397$	18.4223	−	31.9084i	0.924591	−	1.60144i	0.132374	−	0.991200i	$-0.457740\pi$
$397$	18.4223	−	31.9084i	0.924591	−	1.60144i	0.792217	−	0.610239i	$-0.208927\pi$
$398$		0			0
$399$	4.07674	+	9.72683i	0.204092	+	0.486950i
$400$		0			0
$401$	−2.48227	+	2.08287i	−0.123959	+	0.104014i	−0.702660	−	0.711526i	$-0.748004\pi$
$401$	−2.48227	+	2.08287i	−0.123959	+	0.104014i	0.578701	+	0.815540i	$0.303560\pi$
$402$		0			0
$403$	−0.927058	+	0.337421i	−0.0461800	+	0.0168082i
$404$		0			0
$405$	−9.87714	−	25.7862i	−0.490799	−	1.28132i
$406$		0			0
$407$	34.5949	−	12.5915i	1.71481	−	0.624138i
$408$		0			0
$409$	9.18837	−	7.70996i	0.454336	−	0.381233i	−0.386706	−	0.922203i	$-0.626387\pi$
$409$	9.18837	−	7.70996i	0.454336	−	0.381233i	0.841042	+	0.540970i	$0.181943\pi$
$410$		0			0
$411$	−4.06865	−	9.70751i	−0.200691	−	0.478836i
$412$		0			0
$413$	−11.3257	+	19.6166i	−0.557300	+	0.965272i
$414$		0			0
$415$	−23.4662	−	40.6446i	−1.15191	−	1.99517i
$416$		0			0
$417$	13.0853	+	14.1607i	0.640789	+	0.693451i
$418$		0			0
$419$	6.84461	+	2.49124i	0.334381	+	0.121705i	0.503754	−	0.863847i	$-0.331952\pi$
$419$	6.84461	+	2.49124i	0.334381	+	0.121705i	−0.169373	+	0.985552i	$0.554174\pi$
$420$		0			0
$421$	−2.14577	+	12.1693i	−0.104578	+	0.593093i	0.886810	+	0.462135i	$0.152917\pi$
$421$	−2.14577	+	12.1693i	−0.104578	+	0.593093i	−0.991388	+	0.130958i	$0.958195\pi$
$422$		0			0
$423$	1.02645	+	0.706002i	0.0499077	+	0.0343270i
$424$		0			0
$425$	16.7029	+	14.0154i	0.810211	+	0.679847i
$426$		0			0
$427$	−4.76939	−	27.0486i	−0.230807	−	1.30897i
$428$		0			0
$429$	−4.46553	−	2.30092i	−0.215598	−	0.111089i
$430$		0			0
$431$	17.3428			0.835373			0.417686	−	0.908591i	$-0.362841\pi$
$431$	17.3428			0.835373			0.417686	+	0.908591i	$0.362841\pi$
$432$		0			0
$433$	18.6172			0.894683			0.447342	−	0.894363i	$-0.352371\pi$
$433$	18.6172			0.894683			0.447342	+	0.894363i	$0.352371\pi$
$434$		0			0
$435$	37.2495	−	23.9502i	1.78598	−	1.14833i
$436$		0			0
$437$	0.832785	+	4.72296i	0.0398375	+	0.225930i
$438$		0			0
$439$	−0.430130	−	0.360922i	−0.0205290	−	0.0172259i	0.632465	−	0.774589i	$-0.282043\pi$
$439$	−0.430130	−	0.360922i	−0.0205290	−	0.0172259i	−0.652994	+	0.757363i	$0.726487\pi$
$440$		0			0
$441$	−0.0718311	−	0.259376i	−0.00342053	−	0.0123512i
$442$		0			0
$443$	0.461911	−	2.61963i	0.0219461	−	0.124462i	−0.971867	−	0.235532i	$-0.924317\pi$
$443$	0.461911	−	2.61963i	0.0219461	−	0.124462i	0.993813	+	0.111070i	$0.0354278\pi$
$444$		0			0
$445$	−26.4446	−	9.62506i	−1.25360	−	0.456271i
$446$		0			0
$447$	4.53088	−	14.5826i	0.214303	−	0.689732i
$448$		0			0
$449$	6.46856	+	11.2039i	0.305270	+	0.528743i	0.977321	−	0.211761i	$-0.0679200\pi$
$449$	6.46856	+	11.2039i	0.305270	+	0.528743i	−0.672051	+	0.740504i	$0.734587\pi$
$450$		0			0
$451$	−24.0819	+	41.7110i	−1.13397	+	1.96410i
$452$		0			0
$453$	−30.9813	−	3.94697i	−1.45563	−	0.185445i
$454$		0			0
$455$	−3.49949	+	2.93642i	−0.164059	+	0.137662i
$456$		0			0
$457$	36.6300	−	13.3322i	1.71348	−	0.623655i	0.716236	−	0.697858i	$-0.245863\pi$
$457$	36.6300	−	13.3322i	1.71348	−	0.623655i	0.997243	+	0.0742028i	$0.0236412\pi$
$458$		0			0
$459$	−20.1687	+	15.8821i	−0.941393	+	0.741313i
$460$		0			0
$461$	−2.23220	+	0.812453i	−0.103964	+	0.0378397i	−0.393478	−	0.919334i	$-0.628728\pi$
$461$	−2.23220	+	0.812453i	−0.103964	+	0.0378397i	0.289515	+	0.957174i	$0.406506\pi$
$462$		0			0
$463$	8.40962	−	7.05651i	0.390828	−	0.327944i	−0.426108	−	0.904672i	$-0.640116\pi$
$463$	8.40962	−	7.05651i	0.390828	−	0.327944i	0.816936	+	0.576729i	$0.195671\pi$
$464$		0			0
$465$	5.67622	−	7.46183i	0.263229	−	0.346034i
$466$		0			0
$467$	−8.88903	+	15.3963i	−0.411335	+	0.712454i	−0.995036	−	0.0995151i	$-0.968271\pi$
$467$	−8.88903	+	15.3963i	−0.411335	+	0.712454i	0.583701	+	0.811969i	$0.301604\pi$
$468$		0			0
$469$	11.2196	+	19.4330i	0.518074	+	0.897331i
$470$		0			0
$471$	−11.7191	+	2.64954i	−0.539986	+	0.122085i
$472$		0			0
$473$	−35.2032	−	12.8129i	−1.61864	−	0.589138i
$474$		0			0
$475$	−1.75259	+	9.93943i	−0.0804143	+	0.456052i
$476$		0			0
$477$	−13.0163	+	1.24861i	−0.595975	+	0.0571699i
$478$		0			0
$479$	21.2453	+	17.8269i	0.970723	+	0.814533i	0.982664	−	0.185395i	$-0.0593566\pi$
$479$	21.2453	+	17.8269i	0.970723	+	0.814533i	−0.0119409	+	0.999929i	$0.503801\pi$
$480$		0			0
$481$	−0.689258	−	3.90898i	−0.0314275	−	0.178234i
$482$		0			0
$483$	−0.462292	−	9.66057i	−0.0210350	−	0.439571i
$484$		0			0
$485$	17.1805			0.780127
$486$		0			0
$487$	9.27190			0.420150			0.210075	−	0.977685i	$-0.432629\pi$
$487$	9.27190			0.420150			0.210075	+	0.977685i	$0.432629\pi$
$488$		0			0
$489$	−1.62852	−	34.0313i	−0.0736442	−	1.53895i
$490$		0			0
$491$	5.35740	+	30.3833i	0.241776	+	1.37118i	0.827862	+	0.560932i	$0.189557\pi$
$491$	5.35740	+	30.3833i	0.241776	+	1.37118i	−0.586086	+	0.810249i	$0.699332\pi$
$492$		0			0
$493$	−31.5385	−	26.4639i	−1.42042	−	1.19188i
$494$		0			0
$495$	47.5208	−	4.55851i	2.13590	−	0.204890i
$496$		0			0
$497$	−6.21087	+	35.2236i	−0.278595	+	1.57999i
$498$		0			0
$499$	6.56790	+	2.39052i	0.294020	+	0.107014i	0.484819	−	0.874615i	$-0.338886\pi$
$499$	6.56790	+	2.39052i	0.294020	+	0.107014i	−0.190799	+	0.981629i	$0.561108\pi$
$500$		0			0
$501$	−14.3681	+	3.24845i	−0.641918	+	0.145130i
$502$		0			0
$503$	−4.24640	−	7.35498i	−0.189338	−	0.327942i	0.755692	−	0.654927i	$-0.227301\pi$
$503$	−4.24640	−	7.35498i	−0.189338	−	0.327942i	−0.945030	+	0.326985i	$0.893967\pi$
$504$		0			0
$505$	−9.36758	+	16.2251i	−0.416852	+	0.722009i
$506$		0			0
$507$	13.3045	−	17.4898i	0.590874	−	0.776749i
$508$		0			0
$509$	−29.3394	+	24.6187i	−1.30045	+	1.09121i	−0.310380	+	0.950613i	$0.600456\pi$
$509$	−29.3394	+	24.6187i	−1.30045	+	1.09121i	−0.990068	+	0.140592i	$0.955099\pi$
$510$		0			0
$511$	−5.18295	+	1.88644i	−0.229280	+	0.0834511i
$512$		0			0
$513$	−11.0345	−	4.40921i	−0.487186	−	0.194672i
$514$		0			0
$515$	−0.138142	+	0.0502797i	−0.00608728	+	0.00221559i
$516$		0			0
$517$	−1.64992	+	1.38445i	−0.0725633	+	0.0608879i
$518$		0			0
$519$	27.4669	+	3.49924i	1.20566	+	0.153600i
$520$		0			0
$521$	−6.00838	+	10.4068i	−0.263232	+	0.455931i	−0.967099	−	0.254401i	$-0.918122\pi$
$521$	−6.00838	+	10.4068i	−0.263232	+	0.455931i	0.703867	+	0.710332i	$0.251455\pi$
$522$		0			0
$523$	−4.71235	−	8.16204i	−0.206057	−	0.356901i	0.744412	−	0.667720i	$-0.232730\pi$
$523$	−4.71235	−	8.16204i	−0.206057	−	0.356901i	−0.950469	+	0.310820i	$0.899397\pi$
$524$		0			0
$525$	6.03926	−	19.4373i	0.263575	−	0.848312i
$526$		0			0
$527$	−8.19048	−	2.98109i	−0.356783	−	0.129858i
$528$		0			0
$529$	−3.23021	+	18.3195i	−0.140444	+	0.796498i
$530$		0			0
$531$	−6.81141	−	24.5954i	−0.295590	−	1.06735i
$532$		0			0
$533$	3.97795	+	3.33790i	0.172304	+	0.144580i
$534$		0			0
$535$	7.81942	+	44.3462i	0.338063	+	1.91725i
$536$		0			0
$537$	28.6588	−	18.4267i	1.23672	−	0.795170i
$538$		0			0
$539$	0.465301			0.0200419
$540$		0			0
$541$	−14.1872			−0.609956			−0.304978	−	0.952359i	$-0.598649\pi$
$541$	−14.1872			−0.609956			−0.304978	+	0.952359i	$0.598649\pi$
$542$		0			0
$543$	−17.1055	−	8.81380i	−0.734068	−	0.378236i
$544$		0			0
$545$	8.34810	+	47.3444i	0.357593	+	2.02801i
$546$		0			0
$547$	13.5517	+	11.3712i	0.579428	+	0.486198i	0.884759	−	0.466048i	$-0.154323\pi$
$547$	13.5517	+	11.3712i	0.579428	+	0.486198i	−0.305331	+	0.952246i	$0.598767\pi$
$548$		0			0
$549$	25.4968	+	17.5370i	1.08818	+	0.748459i
$550$		0			0
$551$	3.30925	−	18.7677i	0.140979	−	0.799529i
$552$		0			0
$553$	39.4471	+	14.3576i	1.67746	+	0.610546i
$554$		0			0
$555$	25.5999	+	27.7038i	1.08666	+	1.17596i
$556$		0			0
$557$	4.84820	+	8.39732i	0.205425	+	0.355806i	0.950268	−	0.311433i	$-0.100809\pi$
$557$	4.84820	+	8.39732i	0.205425	+	0.355806i	−0.744843	+	0.667239i	$0.767476\pi$
$558$		0			0
$559$	−2.01953	+	3.49793i	−0.0854171	+	0.147947i
$560$		0			0
$561$	−17.1556	−	40.9321i	−0.724311	−	1.72815i
$562$		0			0
$563$	11.3908	−	9.55804i	0.480066	−	0.402823i	−0.370384	−	0.928879i	$-0.620774\pi$
$563$	11.3908	−	9.55804i	0.480066	−	0.402823i	0.850450	+	0.526055i	$0.176330\pi$
$564$		0			0
$565$	50.1113	−	18.2390i	2.10820	−	0.767322i
$566$		0			0
$567$	20.9509	+	11.6330i	0.879856	+	0.488538i
$568$		0			0
$569$	17.0880	−	6.21952i	0.716365	−	0.260736i	0.0419833	−	0.999118i	$-0.486632\pi$
$569$	17.0880	−	6.21952i	0.716365	−	0.260736i	0.674382	+	0.738383i	$0.264410\pi$
$570$		0			0
$571$	−0.494303	+	0.414769i	−0.0206859	+	0.0173576i	−0.653072	−	0.757296i	$-0.726520\pi$
$571$	−0.494303	+	0.414769i	−0.0206859	+	0.0173576i	0.632386	+	0.774653i	$0.282076\pi$
$572$		0			0
$573$	1.75327	+	4.18318i	0.0732439	+	0.174755i
$574$		0			0
$575$	4.62772	−	8.01544i	0.192989	−	0.334267i
$576$		0			0
$577$	−19.8016	−	34.2974i	−0.824351	−	1.42782i	−0.902414	−	0.430869i	$-0.858207\pi$
$577$	−19.8016	−	34.2974i	−0.824351	−	1.42782i	0.0780633	−	0.996948i	$-0.475126\pi$
$578$		0			0
$579$	3.60795	+	3.90446i	0.149941	+	0.162264i
$580$		0			0
$581$	38.2736	+	13.9305i	1.58786	+	0.577933i
$582$		0			0
$583$	3.92559	−	22.2631i	0.162581	−	0.922043i
$584$		0			0
$585$	0.405675	−	5.13104i	0.0167726	−	0.212142i
$586$		0			0
$587$	−32.1865	−	27.0077i	−1.32848	−	1.11473i	−0.984430	−	0.175776i	$-0.943757\pi$
$587$	−32.1865	−	27.0077i	−1.32848	−	1.11473i	−0.344050	−	0.938951i	$-0.611799\pi$
$588$		0			0
$589$	−0.700592	−	3.97326i	−0.0288674	−	0.163715i
$590$		0			0
$591$	26.9373	+	13.8798i	1.10805	+	0.570937i
$592$		0			0
$593$	−1.58469			−0.0650756			−0.0325378	−	0.999471i	$-0.510359\pi$
$593$	−1.58469			−0.0650756			−0.0325378	+	0.999471i	$0.510359\pi$
$594$		0			0
$595$	−40.3602			−1.65461
$596$		0			0
$597$	−5.75439	+	3.69988i	−0.235511	+	0.151426i
$598$		0			0
$599$	0.447444	+	2.53758i	0.0182821	+	0.103683i	0.992583	−	0.121566i	$-0.0387916\pi$
$599$	0.447444	+	2.53758i	0.0182821	+	0.103683i	−0.974301	+	0.225249i	$0.927681\pi$
$600$		0			0
$601$	11.6975	+	9.81540i	0.477152	+	0.400378i	0.849396	−	0.527757i	$-0.176967\pi$
$601$	11.6975	+	9.81540i	0.477152	+	0.400378i	−0.372243	+	0.928135i	$0.621411\pi$
$602$		0			0
$603$	−24.4747	−	6.33896i	−0.996685	−	0.258142i
$604$		0			0
$605$	−8.47129	+	48.0431i	−0.344407	+	1.95323i
$606$		0			0
$607$	−15.6374	−	5.69156i	−0.634704	−	0.231013i	0.00457324	−	0.999990i	$-0.498544\pi$
$607$	−15.6374	−	5.69156i	−0.634704	−	0.231013i	−0.639278	+	0.768976i	$0.720767\pi$
$608$		0			0
$609$	−11.4033	+	36.7015i	−0.462087	+	1.48722i
$610$		0			0
$611$	0.116108	+	0.201106i	0.00469724	+	0.00813586i
$612$		0			0
$613$	22.0896	−	38.2603i	0.892190	−	1.54532i	0.0549457	−	0.998489i	$-0.482501\pi$
$613$	22.0896	−	38.2603i	0.892190	−	1.54532i	0.837244	−	0.546829i	$-0.184165\pi$
$614$		0			0
$615$	−48.9530	−	6.23654i	−1.97397	−	0.251481i
$616$		0			0
$617$	−7.32615	+	6.14737i	−0.294940	+	0.247484i	−0.778234	−	0.627974i	$-0.783884\pi$
$617$	−7.32615	+	6.14737i	−0.294940	+	0.247484i	0.483295	+	0.875458i	$0.339440\pi$
$618$		0			0
$619$	9.76827	−	3.55536i	0.392620	−	0.142902i	−0.138164	−	0.990409i	$-0.544120\pi$
$619$	9.76827	−	3.55536i	0.392620	−	0.142902i	0.530783	+	0.847507i	$0.321898\pi$
$620$		0			0
$621$	8.12587	+	7.26048i	0.326080	+	0.291353i
$622$		0			0
$623$	22.9498	−	8.35304i	0.919464	−	0.334658i
$624$		0			0
$625$	−21.1344	+	17.7338i	−0.845374	+	0.709353i
$626$		0			0
$627$	12.4379	−	16.3505i	0.496721	−	0.652978i
$628$		0			0
$629$	17.5341	−	30.3700i	0.699131	−	1.21093i
$630$		0			0
$631$	−6.77581	−	11.7361i	−0.269741	−	0.467205i	0.699054	−	0.715069i	$-0.253605\pi$
$631$	−6.77581	−	11.7361i	−0.269741	−	0.467205i	−0.968795	+	0.247864i	$0.920271\pi$
$632$		0			0
$633$	20.7458	−	4.69038i	0.824572	−	0.186426i
$634$		0			0
$635$	22.6998	+	8.26204i	0.900812	+	0.327869i
$636$		0			0
$637$	0.00871143	−	0.0494050i	0.000345159	−	0.00195750i
$638$		0			0
$639$	−23.3897	−	32.8160i	−0.925281	−	1.29818i
$640$		0			0
$641$	−7.27616	−	6.10542i	−0.287391	−	0.241150i	0.487682	−	0.873021i	$-0.337843\pi$
$641$	−7.27616	−	6.10542i	−0.287391	−	0.241150i	−0.775073	+	0.631872i	$0.782287\pi$
$642$		0			0
$643$	−6.88450	−	39.0439i	−0.271498	−	1.53974i	−0.749870	−	0.661585i	$-0.769884\pi$
$643$	−6.88450	−	39.0439i	−0.271498	−	1.53974i	0.478372	−	0.878158i	$-0.341227\pi$
$644$		0			0
$645$	−1.83471	−	38.3402i	−0.0722417	−	1.50964i
$646$		0			0
$647$	−19.5044			−0.766798			−0.383399	−	0.923583i	$-0.625247\pi$
$647$	−19.5044			−0.766798			−0.383399	+	0.923583i	$0.625247\pi$
$648$		0			0
$649$	44.1223			1.73195
$650$		0			0
$651$	0.388910	+	8.12709i	0.0152426	+	0.318526i
$652$		0			0
$653$	−1.18031	−	6.69386i	−0.0461890	−	0.261951i	0.952965	−	0.303081i	$-0.0980153\pi$
$653$	−1.18031	−	6.69386i	−0.0461890	−	0.261951i	−0.999154	+	0.0411302i	$0.986904\pi$
$654$		0			0
$655$	41.9212	+	35.1761i	1.63800	+	1.37444i
$656$		0			0
$657$	2.57909	−	5.65392i	0.100620	−	0.220580i
$658$		0			0
$659$	−2.88196	+	16.3444i	−0.112265	+	0.636687i	0.875803	+	0.482669i	$0.160333\pi$
$659$	−2.88196	+	16.3444i	−0.112265	+	0.636687i	−0.988068	+	0.154018i	$0.950779\pi$
$660$		0			0
$661$	−5.88894	−	2.14340i	−0.229053	−	0.0833686i	0.224944	−	0.974372i	$-0.427780\pi$
$661$	−5.88894	−	2.14340i	−0.229053	−	0.0833686i	−0.453997	+	0.891003i	$0.650002\pi$
$662$		0			0
$663$	−4.66730	+	1.05522i	−0.181263	+	0.0409814i
$664$		0			0
$665$	−9.34104	−	16.1792i	−0.362230	−	0.627401i
$666$		0			0
$667$	−8.73807	+	15.1348i	−0.338339	+	0.586021i
$668$		0			0
$669$	−23.6064	+	31.0325i	−0.912678	+	1.19979i
$670$		0			0
$671$	−40.9837	+	34.3894i	−1.58216	+	1.32759i
$672$		0			0
$673$	23.8172	−	8.66874i	0.918084	−	0.334155i	0.160608	−	0.987018i	$-0.448654\pi$
$673$	23.8172	−	8.66874i	0.918084	−	0.334155i	0.757476	+	0.652863i	$0.226432\pi$
$674$		0			0
$675$	10.8436	+	20.2070i	0.417370	+	0.777767i
$676$		0			0
$677$	−22.3294	+	8.12724i	−0.858189	+	0.312355i	−0.733375	−	0.679825i	$-0.762056\pi$
$677$	−22.3294	+	8.12724i	−0.858189	+	0.312355i	−0.124815	+	0.992180i	$0.539834\pi$
$678$		0			0
$679$	−11.4217	+	9.58396i	−0.438325	+	0.367799i
$680$		0			0
$681$	−35.4368	−	4.51459i	−1.35794	−	0.173000i
$682$		0			0
$683$	12.6068	−	21.8356i	0.482386	−	0.835517i	−0.517409	−	0.855738i	$-0.673104\pi$
$683$	12.6068	−	21.8356i	0.482386	−	0.835517i	0.999796	+	0.0202207i	$0.00643690\pi$
$684$		0			0
$685$	9.32249	+	16.1470i	0.356194	+	0.616946i
$686$		0			0
$687$	−10.3927	+	33.4486i	−0.396505	+	1.27615i
$688$		0			0
$689$	−2.29037	−	0.833625i	−0.0872560	−	0.0317586i
$690$		0			0
$691$	3.95664	−	22.4392i	0.150518	−	0.853629i	−0.812252	−	0.583307i	$-0.801759\pi$
$691$	3.95664	−	22.4392i	0.150518	−	0.853629i	0.962770	−	0.270323i	$-0.0871303\pi$
$692$		0			0
$693$	−29.0492	+	29.5395i	−1.10349	+	1.12211i
$694$		0			0
$695$	−26.1632	−	21.9536i	−0.992428	−	0.832746i
$696$		0			0
$697$	7.96669	+	45.1814i	0.301760	+	1.71137i
$698$		0			0
$699$	−11.9715	+	7.69731i	−0.452805	+	0.291139i
$700$		0			0
$701$	−8.53279			−0.322279			−0.161140	−	0.986932i	$-0.551517\pi$
$701$	−8.53279			−0.322279			−0.161140	+	0.986932i	$0.551517\pi$
$702$		0			0
$703$	16.2325			0.612221
$704$		0			0
$705$	−1.96170	−	1.01079i	−0.0738820	−	0.0380685i
$706$		0			0
$707$	−2.82338	−	16.0122i	−0.106184	−	0.602200i
$708$		0			0
$709$	−15.7053	−	13.1783i	−0.589825	−	0.494922i	0.298332	−	0.954462i	$-0.403570\pi$
$709$	−15.7053	−	13.1783i	−0.589825	−	0.494922i	−0.888157	+	0.459541i	$0.848014\pi$
$710$		0			0
$711$	−42.6971	+	20.3467i	−1.60127	+	0.763060i
$712$		0			0
$713$	−0.642469	+	3.64362i	−0.0240606	+	0.136455i
$714$		0			0
$715$	8.36183	+	3.04346i	0.312715	+	0.113819i
$716$		0			0
$717$	−4.91690	−	5.32099i	−0.183625	−	0.198716i
$718$		0			0
$719$	−2.72008	−	4.71132i	−0.101442	−	0.175703i	0.810837	−	0.585272i	$-0.199012\pi$
$719$	−2.72008	−	4.71132i	−0.101442	−	0.175703i	−0.912279	+	0.409569i	$0.865679\pi$
$720$		0			0
$721$	0.0637900	−	0.110487i	0.00237566	−	0.00411477i
$722$		0			0
$723$	12.3229	+	29.4017i	0.458295	+	1.09346i
$724$		0			0
$725$	−28.1739	+	23.6407i	−1.04635	+	0.877994i
$726$		0			0
$727$	−16.7417	+	6.09349i	−0.620917	+	0.225995i	−0.633273	−	0.773929i	$-0.718289\pi$
$727$	−16.7417	+	6.09349i	−0.620917	+	0.225995i	0.0123564	+	0.999924i	$0.496067\pi$
$728$		0			0
$729$	−25.8964	+	7.64052i	−0.959125	+	0.282982i
$730$		0			0
$731$	−33.5328	+	12.2049i	−1.24025	+	0.451415i
$732$		0			0
$733$	6.10760	−	5.12488i	0.225589	−	0.189292i	−0.522987	−	0.852341i	$-0.675182\pi$
$733$	6.10760	−	5.12488i	0.225589	−	0.189292i	0.748576	+	0.663049i	$0.230738\pi$
$734$		0			0
$735$	0.184285	+	0.439690i	0.00679744	+	0.0162182i
$736$		0			0
$737$	21.8546	−	37.8533i	0.805025	−	1.39434i
$738$		0			0
$739$	1.56787	+	2.71563i	0.0576749	+	0.0998959i	0.893421	−	0.449220i	$-0.148298\pi$
$739$	1.56787	+	2.71563i	0.0576749	+	0.0998959i	−0.835746	+	0.549116i	$0.814965\pi$
$740$		0			0
$741$	−1.50321	−	1.62675i	−0.0552219	−	0.0597602i
$742$		0			0
$743$	−34.7743	−	12.6568i	−1.27574	−	0.464333i	−0.386722	−	0.922196i	$-0.626393\pi$
$743$	−34.7743	−	12.6568i	−1.27574	−	0.464333i	−0.889023	+	0.457863i	$0.848615\pi$
$744$		0			0
$745$	−4.69708	+	26.6385i	−0.172088	+	0.975959i
$746$		0			0
$747$	−41.4270	+	19.7414i	−1.51573	+	0.722300i
$748$		0			0
$749$	−29.9364	−	25.1196i	−1.09385	−	0.917852i
$750$		0			0
$751$	7.20695	+	40.8726i	0.262985	+	1.49146i	0.774711	+	0.632315i	$0.217895\pi$
$751$	7.20695	+	40.8726i	0.262985	+	1.49146i	−0.511726	+	0.859149i	$0.670994\pi$
$752$		0			0
$753$	11.6241	+	5.98942i	0.423604	+	0.218267i
$754$		0			0
$755$	55.3232			2.01342
$756$		0			0
$757$	12.5894			0.457571			0.228786	−	0.973477i	$-0.426525\pi$
$757$	12.5894			0.457571			0.228786	+	0.973477i	$0.426525\pi$
$758$		0			0
$759$	−15.8464	+	10.1887i	−0.575188	+	0.369827i
$760$		0			0
$761$	−2.38353	−	13.5177i	−0.0864029	−	0.490015i	−0.997045	−	0.0768194i	$-0.975524\pi$
$761$	−2.38353	−	13.5177i	−0.0864029	−	0.490015i	0.910642	−	0.413196i	$-0.135588\pi$
$762$		0			0
$763$	−31.9604	−	26.8180i	−1.15705	−	0.970877i
$764$		0			0
$765$	31.8846	−	32.4227i	1.15279	−	1.17225i
$766$		0			0
$767$	0.826064	−	4.68484i	0.0298275	−	0.169160i
$768$		0			0
$769$	20.8589	+	7.59201i	0.752190	+	0.273775i	0.689527	−	0.724260i	$-0.257818\pi$
$769$	20.8589	+	7.59201i	0.752190	+	0.273775i	0.0626629	+	0.998035i	$0.480041\pi$
$770$		0			0
$771$	4.54524	−	14.6288i	0.163693	−	0.526843i
$772$		0			0
$773$	11.4098	+	19.7623i	0.410381	+	0.710800i	0.994931	−	0.100557i	$-0.0320625\pi$
$773$	11.4098	+	19.7623i	0.410381	+	0.710800i	−0.584550	+	0.811357i	$0.698729\pi$
$774$		0			0
$775$	−3.89313	+	6.74310i	−0.139845	+	0.242219i
$776$		0			0
$777$	−32.4733	−	4.13705i	−1.16497	−	0.148416i
$778$		0			0
$779$	−16.2680	+	13.6505i	−0.582861	+	0.489078i
$780$		0			0
$781$	65.4685	−	23.8286i	2.34265	−	0.852653i
$782$		0			0
$783$	−20.4749	−	38.1549i	−0.731713	−	1.36354i
$784$		0			0
$785$	19.9994	−	7.27918i	0.713809	−	0.259805i
$786$		0			0
$787$	5.65334	−	4.74371i	0.201520	−	0.169095i	−0.536443	−	0.843936i	$-0.680232\pi$
$787$	5.65334	−	4.74371i	0.201520	−	0.169095i	0.737963	+	0.674841i	$0.235788\pi$
$788$		0			0
$789$	−24.2854	+	31.9251i	−0.864584	+	1.13656i
$790$		0			0
$791$	−23.1399	+	40.0795i	−0.822760	+	1.42506i
$792$		0			0
$793$	2.88411	+	4.99543i	0.102418	+	0.177393i
$794$		0			0
$795$	22.5925	−	5.10789i	0.801272	−	0.181158i
$796$		0			0
$797$	33.4935	+	12.1906i	1.18640	+	0.431815i	0.858459	−	0.512883i	$-0.171422\pi$
$797$	33.4935	+	12.1906i	1.18640	+	0.431815i	0.327943	+	0.944698i	$0.393645\pi$
$798$		0			0
$799$	−0.356259	+	2.02045i	−0.0126035	+	0.0714783i
$800$		0			0
$801$	−11.4201	+	25.0352i	−0.403508	+	0.884577i
$802$		0			0
$803$	8.23018	+	6.90594i	0.290437	+	0.243705i
$804$		0			0
$805$	2.97497	+	16.8719i	0.104854	+	0.594655i
$806$		0			0
$807$	−0.0914057	−	1.91011i	−0.00321763	−	0.0672392i
$808$		0			0
$809$	−1.09426			−0.0384721			−0.0192360	−	0.999815i	$-0.506123\pi$
$809$	−1.09426			−0.0384721			−0.0192360	+	0.999815i	$0.506123\pi$
$810$		0			0
$811$	27.6255			0.970063			0.485031	−	0.874497i	$-0.338808\pi$
$811$	27.6255			0.970063			0.485031	+	0.874497i	$0.338808\pi$
$812$		0			0
$813$	−1.49318	−	31.2032i	−0.0523681	−	1.09434i
$814$		0			0
$815$	10.4799	+	59.4346i	0.367096	+	2.08190i
$816$		0			0
$817$	−12.6535	−	10.6175i	−0.442688	−	0.371460i
$818$		0			0
$819$	2.59260	+	3.63745i	0.0905926	+	0.127103i
$820$		0			0
$821$	6.69214	−	37.9530i	0.233557	−	1.32457i	−0.612073	−	0.790801i	$-0.709664\pi$
$821$	6.69214	−	37.9530i	0.233557	−	1.32457i	0.845631	−	0.533769i	$-0.179225\pi$
$822$		0			0
$823$	16.3783	+	5.96120i	0.570911	+	0.207794i	0.611313	−	0.791389i	$-0.290642\pi$
$823$	16.3783	+	5.96120i	0.570911	+	0.207794i	−0.0404023	+	0.999183i	$0.512864\pi$
$824$		0			0
$825$	−38.6711	+	8.74307i	−1.34635	+	0.304395i
$826$		0			0
$827$	26.4085	+	45.7409i	0.918313	+	1.59057i	0.801976	+	0.597356i	$0.203782\pi$
$827$	26.4085	+	45.7409i	0.918313	+	1.59057i	0.116337	+	0.993210i	$0.462885\pi$
$828$		0			0
$829$	−15.4297	+	26.7250i	−0.535895	+	0.928197i	0.463225	+	0.886241i	$0.346692\pi$
$829$	−15.4297	+	26.7250i	−0.535895	+	0.928197i	−0.999119	+	0.0419562i	$0.986641\pi$
$830$		0			0
$831$	−22.0861	+	29.0338i	−0.766158	+	1.00717i
$832$		0			0
$833$	0.339528	−	0.284898i	0.0117639	−	0.00987112i
$834$		0			0
$835$	24.5201	−	8.92458i	0.848553	−	0.308848i
$836$		0			0
$837$	−6.83600	−	6.10798i	−0.236287	−	0.211123i
$838$		0			0
$839$	41.8026	−	15.2149i	1.44318	−	0.525276i	0.502505	−	0.864574i	$-0.332412\pi$
$839$	41.8026	−	15.2149i	1.44318	−	0.525276i	0.940679	+	0.339298i	$0.110189\pi$
$840$		0			0
$841$	30.9827	−	25.9976i	1.06837	−	0.896469i
$842$		0			0
$843$	16.6917	+	2.12650i	0.574893	+	0.0732406i
$844$		0			0
$845$	−19.4631	+	33.7111i	−0.669551	+	1.15970i
$846$		0			0
$847$	−21.1685	−	36.6650i	−0.727359	−	1.25982i
$848$		0			0
$849$	5.30442	−	17.0722i	0.182047	−	0.585916i
$850$		0			0
$851$	−13.9881	−	5.09124i	−0.479505	−	0.174526i
$852$		0			0
$853$	−3.75590	+	21.3007i	−0.128599	+	0.729324i	0.850505	+	0.525967i	$0.176296\pi$
$853$	−3.75590	+	21.3007i	−0.128599	+	0.729324i	−0.979105	+	0.203357i	$0.934815\pi$
$854$		0			0
$855$	20.3767	+	5.27757i	0.696868	+	0.180489i
$856$		0			0
$857$	−4.87094	−	4.08720i	−0.166388	−	0.139616i	0.555792	−	0.831322i	$-0.312415\pi$
$857$	−4.87094	−	4.08720i	−0.166388	−	0.139616i	−0.722180	+	0.691705i	$0.756860\pi$
$858$		0			0
$859$	1.47386	+	8.35865i	0.0502873	+	0.285193i	0.999573	−	0.0292214i	$-0.00930280\pi$
$859$	1.47386	+	8.35865i	0.0502873	+	0.285193i	−0.949286	+	0.314415i	$0.898192\pi$
$860$		0			0
$861$	36.0232	−	23.1618i	1.22767	−	0.789352i
$862$		0			0
$863$	−9.56354			−0.325547			−0.162773	−	0.986663i	$-0.552044\pi$
$863$	−9.56354			−0.325547			−0.162773	+	0.986663i	$0.552044\pi$
$864$		0			0
$865$	−49.0476			−1.66767
$866$		0			0
$867$	−11.4060	−	5.87706i	−0.387368	−	0.199596i
$868$		0			0
$869$	−14.1992	−	80.5277i	−0.481675	−	2.73171i
$870$		0			0
$871$	−3.61004	−	3.02918i	−0.122322	−	0.102640i
$872$		0			0
$873$	1.32405	−	16.7468i	0.0448123	−	0.566793i
$874$		0			0
$875$	0.832164	−	4.71944i	0.0281323	−	0.159546i
$876$		0			0
$877$	1.10266	+	0.401336i	0.0372343	+	0.0135522i	0.360570	−	0.932732i	$-0.382582\pi$
$877$	1.10266	+	0.401336i	0.0372343	+	0.0135522i	−0.323336	+	0.946284i	$0.604804\pi$
$878$		0			0
$879$	13.2640	+	14.3541i	0.447385	+	0.484152i
$880$		0			0
$881$	2.60086	+	4.50483i	0.0876253	+	0.151772i	0.906507	−	0.422191i	$-0.138739\pi$
$881$	2.60086	+	4.50483i	0.0876253	+	0.151772i	−0.818882	+	0.573963i	$0.805406\pi$
$882$		0			0
$883$	−9.30273	+	16.1128i	−0.313062	+	0.542239i	−0.979024	−	0.203747i	$-0.934688\pi$
$883$	−9.30273	+	16.1128i	−0.313062	+	0.542239i	0.665962	+	0.745986i	$0.268021\pi$
$884$		0			0
$885$	17.4749	+	41.6938i	0.587411	+	1.40152i
$886$		0			0
$887$	−7.01393	+	5.88539i	−0.235505	+	0.197612i	−0.752901	−	0.658134i	$-0.771346\pi$
$887$	−7.01393	+	5.88539i	−0.235505	+	0.197612i	0.517396	+	0.855746i	$0.326902\pi$
$888$		0			0
$889$	−19.6998	+	7.17015i	−0.660711	+	0.240479i
$890$		0			0
$891$	−0.781144	−	46.6724i	−0.0261693	−	1.56359i
$892$		0			0
$893$	−0.892387	+	0.324802i	−0.0298626	+	0.0108691i
$894$		0			0
$895$	−46.2336	+	38.7946i	−1.54542	+	1.29676i
$896$		0			0
$897$	0.785145	+	1.87330i	0.0262152	+	0.0625477i
$898$		0			0
$899$	7.35102	−	12.7323i	0.245170	−	0.424648i
$900$		0			0
$901$	−10.7669	−	18.6489i	−0.358698	−	0.621284i
$902$		0			0
$903$	22.6074	+	24.4653i	0.752326	+	0.814155i
$904$		0			0
$905$	32.0305	+	11.6582i	1.06473	+	0.387530i
$906$		0			0
$907$	−8.57026	+	48.6044i	−0.284571	+	1.61388i	0.422244	+	0.906482i	$0.361243\pi$
$907$	−8.57026	+	48.6044i	−0.284571	+	1.61388i	−0.706815	+	0.707399i	$0.749868\pi$
$908$		0			0
$909$	15.0936	+	10.3815i	0.500622	+	0.344333i
$910$		0			0
$911$	26.3464	+	22.1073i	0.872895	+	0.732446i	0.964706	−	0.263330i	$-0.0848209\pi$
$911$	26.3464	+	22.1073i	0.872895	+	0.732446i	−0.0918103	+	0.995777i	$0.529265\pi$
$912$		0			0
$913$	−13.7768	−	78.1322i	−0.455946	−	2.58580i
$914$		0			0
$915$	−48.7284	−	25.1078i	−1.61091	−	0.830039i
$916$		0			0
$917$	−47.4921			−1.56833
$918$		0			0
$919$	−57.3599			−1.89213			−0.946063	−	0.323981i	$-0.894978\pi$
$919$	−57.3599			−1.89213			−0.946063	+	0.323981i	$0.894978\pi$
$920$		0			0
$921$	−44.8069	+	28.8094i	−1.47644	+	0.949303i
$922$		0			0
$923$	−1.30437	−	7.39746i	−0.0429339	−	0.243491i
$924$		0			0
$925$	−23.9979	−	20.1366i	−0.789047	−	0.662089i
$926$		0			0
$927$	0.0383641	+	0.138530i	0.00126004	+	0.00454991i
$928$		0			0
$929$	3.83992	−	21.7773i	0.125984	−	0.714490i	−0.854735	−	0.519065i	$-0.826280\pi$
$929$	3.83992	−	21.7773i	0.125984	−	0.714490i	0.980719	−	0.195425i	$-0.0626086\pi$
$930$		0			0
$931$	0.192788	+	0.0701689i	0.00631836	+	0.00229969i
$932$		0			0
$933$	−3.26541	+	10.5097i	−0.106905	+	0.344071i
$934$		0			0
$935$	39.3087	+	68.0846i	1.28553	+	2.22660i
$936$		0			0
$937$	4.37383	−	7.57569i	0.142887	−	0.247487i	−0.785696	−	0.618613i	$-0.787695\pi$
$937$	4.37383	−	7.57569i	0.142887	−	0.247487i	0.928583	+	0.371126i	$0.121028\pi$
$938$		0			0
$939$	2.68701	+	0.342322i	0.0876874	+	0.0111712i
$940$		0			0
$941$	−41.9702	+	35.2172i	−1.36819	+	1.14805i	−0.394833	+	0.918753i	$0.629197\pi$
$941$	−41.9702	+	35.2172i	−1.36819	+	1.14805i	−0.973357	+	0.229295i	$0.926358\pi$
$942$		0			0
$943$	18.3000	−	6.66067i	0.595931	−	0.216901i
$944$		0			0
$945$	−39.4187	−	15.7511i	−1.28229	−	0.512383i
$946$		0			0
$947$	−40.3653	+	14.6918i	−1.31170	+	0.477418i	−0.900788	−	0.434259i	$-0.857010\pi$
$947$	−40.3653	+	14.6918i	−1.31170	+	0.477418i	−0.410907	+	0.911677i	$0.634788\pi$
$948$		0			0
$949$	0.887349	−	0.744574i	0.0288046	−	0.0241699i
$950$		0			0
$951$	−21.1429	+	27.7940i	−0.685607	+	0.901283i
$952$		0			0
$953$	1.95900	−	3.39309i	0.0634583	−	0.109913i	−0.832551	−	0.553949i	$-0.813120\pi$
$953$	1.95900	−	3.39309i	0.0634583	−	0.109913i	0.896009	+	0.444036i	$0.146454\pi$
$954$		0			0
$955$	−4.01727	−	6.95811i	−0.129996	−	0.225159i
$956$		0			0
$957$	73.0189	−	16.5087i	2.36036	−	0.533650i
$958$		0			0
$959$	−15.2051	−	5.53420i	−0.490998	−	0.178709i
$960$		0			0
$961$	−4.84261	+	27.4638i	−0.156213	+	0.885929i
$962$		0			0
$963$	43.8292	−	4.20439i	1.41238	−	0.135485i
$964$		0			0
$965$	−7.21388	−	6.05316i	−0.232223	−	0.194858i
$966$		0			0
$967$	6.22038	+	35.2775i	0.200034	+	1.13445i	0.905065	+	0.425273i	$0.139822\pi$
$967$	6.22038	+	35.2775i	0.200034	+	1.13445i	−0.705031	+	0.709176i	$0.749067\pi$
$968$		0			0
$969$	−0.935367	−	19.5465i	−0.0300483	−	0.627923i
$970$		0			0
$971$	−47.1246			−1.51230			−0.756150	−	0.654398i	$-0.772922\pi$
$971$	−47.1246			−1.51230			−0.756150	+	0.654398i	$0.772922\pi$
$972$		0			0
$973$	29.6400			0.950216
$974$		0			0
$975$	0.204321	+	4.26973i	0.00654352	+	0.136741i
$976$		0			0
$977$	−7.15880	−	40.5996i	−0.229030	−	1.29890i	−0.854828	−	0.518911i	$-0.826338\pi$
$977$	−7.15880	−	40.5996i	−0.229030	−	1.29890i	0.625798	−	0.779985i	$-0.284773\pi$
$978$		0			0
$979$	−36.4428	−	30.5791i	−1.16472	−	0.977313i
$980$		0			0
$981$	46.7926	−	4.48865i	1.49397	−	0.143312i
$982$		0			0
$983$	5.72372	−	32.4608i	0.182558	−	1.03534i	−0.746494	−	0.665392i	$-0.768265\pi$
$983$	5.72372	−	32.4608i	0.182558	−	1.03534i	0.929053	−	0.369947i	$-0.120624\pi$
$984$		0			0
$985$	−50.4409	−	18.3590i	−1.60718	−	0.584966i
$986$		0			0
$987$	1.86801	−	0.422335i	0.0594594	−	0.0134431i
$988$		0			0
$989$	7.57376	+	13.1181i	0.240832	+	0.417133i
$990$		0			0
$991$	−4.46511	+	7.73379i	−0.141839	+	0.245672i	−0.928189	−	0.372109i	$-0.878635\pi$
$991$	−4.46511	+	7.73379i	−0.141839	+	0.245672i	0.786350	+	0.617781i	$0.211968\pi$
$992$		0			0
$993$	−4.99145	+	6.56165i	−0.158399	+	0.208228i
$994$		0			0
$995$	9.28323	−	7.78955i	0.294298	−	0.246945i
$996$		0			0
$997$	−34.4876	+	12.5525i	−1.09223	+	0.397541i	−0.824448	−	0.565937i	$-0.808514\pi$
$997$	−34.4876	+	12.5525i	−1.09223	+	0.397541i	−0.267786	+	0.963478i	$0.586292\pi$
$998$		0			0
$999$	28.9774	−	22.8186i	0.916803	−	0.721949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.a.385.5	yes	48
4.3	odd	2	inner	864.2.y.a.385.4	yes	48
27.4	even	9	inner	864.2.y.a.193.5	yes	48
108.31	odd	18	inner	864.2.y.a.193.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.a.193.4	✓	48	108.31	odd	18	inner
864.2.y.a.193.5	yes	48	27.4	even	9	inner
864.2.y.a.385.4	yes	48	4.3	odd	2	inner
864.2.y.a.385.5	yes	48	1.1	even	1	trivial

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.0827900 + 1.73007i) q^{3} +(-0.532774 - 3.02151i) q^{5} +(2.03971 + 1.71152i) q^{7} +(-2.98629 + 0.286465i) q^{9} +O(q^{10})\)	\(q+(0.0827900 + 1.73007i) q^{3} +(-0.532774 - 3.02151i) q^{5} +(2.03971 + 1.71152i) q^{7} +(-2.98629 + 0.286465i) q^{9} +(0.900636 - 5.10776i) q^{11} +(-0.525472 - 0.191256i) q^{13} +(5.18332 - 1.17189i) q^{15} +(-2.47022 - 4.27855i) q^{17} +(1.14343 - 1.98047i) q^{19} +(-2.79218 + 3.67054i) q^{21} +(-1.60649 + 1.34801i) q^{23} +(-4.14723 + 1.50947i) q^{25} +(-0.742840 - 5.14278i) q^{27} +(7.83081 - 2.85018i) q^{29} +(1.35148 - 1.13403i) q^{31} +(8.91135 + 1.13529i) q^{33} +(4.08467 - 7.07486i) q^{35} +(3.54909 + 6.14721i) q^{37} +(0.287383 - 0.924938i) q^{39} +(-8.72625 - 3.17609i) q^{41} +(1.25426 - 7.11326i) q^{43} +(2.45658 + 8.87050i) q^{45} +(-0.318115 - 0.266930i) q^{47} +(0.0155785 + 0.0883500i) q^{49} +(7.19769 - 4.62788i) q^{51} +4.35868 q^{53} -15.9130 q^{55} +(3.52102 + 1.81424i) q^{57} +(1.47724 + 8.37782i) q^{59} +(-7.90191 - 6.63049i) q^{61} +(-6.58146 - 4.52679i) q^{63} +(-0.297925 + 1.68962i) q^{65} +(7.91918 + 2.88234i) q^{67} +(-2.46515 - 2.66774i) q^{69} +(6.71642 + 11.6332i) q^{71} +(-1.03573 + 1.79394i) q^{73} +(-2.95483 - 7.05003i) q^{75} +(10.5791 - 8.87689i) q^{77} +(14.8150 - 5.39221i) q^{79} +(8.83588 - 1.71094i) q^{81} +(14.3743 - 5.23180i) q^{83} +(-11.6116 + 9.74332i) q^{85} +(5.57933 + 13.3119i) q^{87} +(4.58615 - 7.94345i) q^{89} +(-0.744472 - 1.28946i) q^{91} +(2.07384 + 2.24428i) q^{93} +(-6.59321 - 2.39973i) q^{95} +(-0.972374 + 5.51461i) q^{97} +(-1.22637 + 15.5113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{9}+O(q^{10}) \) 48 * q - 12 * q^9	\( 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) \) 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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