LMFDB - Embedded newform 864.2.y.a.385.4

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			385.4
Character	$\chi$	$=$	864.385
Dual form			864.2.y.a.193.4

$q$-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	0.170011	−	0.985442i	$-0.445620\pi$
$7$	−2.03971	−	1.71152i	−0.770938	−	0.646894i	−0.940949	+	0.338549i	$0.890064\pi$
$8$		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	$0.341306\pi$
$11$	−0.900636	+	5.10776i	−0.271552	+	1.54005i	−0.749706	+	0.661771i	$0.769805\pi$
$12$		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	−0.966858	−	0.255315i	$-0.917821\pi$
$19$	−1.14343	+	1.98047i	−0.262320	+	0.454351i	0.704538	+	0.709666i	$0.251154\pi$
$20$		0			0
$21$	−2.79218	+	3.67054i	−0.609304	+	0.800977i
$22$		0			0
$23$	1.60649	−	1.34801i	0.334977	−	0.281079i	−0.459747	−	0.888050i	$-0.652060\pi$
$23$	1.60649	−	1.34801i	0.334977	−	0.281079i	0.794724	+	0.606971i	$0.207616\pi$
$24$		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	−0.756036	−	0.654530i	$-0.772866\pi$
$31$	−1.35148	+	1.13403i	−0.242734	+	0.203678i	0.513302	+	0.858208i	$0.328422\pi$
$32$		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	$0.241213\pi$
$43$	−1.25426	+	7.11326i	−0.191273	+	1.08476i	−0.917627	+	0.397442i	$0.869898\pi$
$44$		0			0
$45$	2.45658	+	8.87050i	0.366205	+	1.32234i
$46$		0			0
$47$	0.318115	+	0.266930i	0.0464018	+	0.0389357i	0.665694	−	0.746225i	$-0.268136\pi$
$47$	0.318115	+	0.266930i	0.0464018	+	0.0389357i	−0.619292	+	0.785161i	$0.712580\pi$
$48$		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	$-0.868747\pi$
$59$	−1.47724	−	8.37782i	−0.192320	−	1.09070i	0.723864	−	0.689942i	$-0.242364\pi$
$60$		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	−0.190521	−	0.981683i	$-0.561018\pi$
$67$	−7.91918	−	2.88234i	−0.967482	−	0.352134i	−0.776961	+	0.629549i	$0.783240\pi$
$68$		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	$-0.873037\pi$
$71$	−6.71642	−	11.6332i	−0.797092	−	1.38060i	0.124411	−	0.992231i	$-0.460296\pi$
$72$		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	−0.991412	−	0.130779i	$-0.958252\pi$
$79$	−14.8150	+	5.39221i	−1.66681	+	0.606671i	−0.675402	+	0.737449i	$0.736030\pi$
$80$		0			0
$81$	8.83588	−	1.71094i	0.981764	−	0.190104i
$82$		0			0
$83$	−14.3743	+	5.23180i	−1.57778	+	0.574265i	−0.974720	−	0.223431i	$-0.928274\pi$
$83$	−14.3743	+	5.23180i	−1.57778	+	0.574265i	−0.603060	+	0.797696i	$0.706052\pi$
$84$		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	0.985215	−	0.171323i	$-0.0548042\pi$
$103$	0.00832028	+	0.0471867i	0.000819822	+	0.00464944i	−0.984395	+	0.175972i	$0.943693\pi$
$104$		0			0
$105$	12.5782	+	6.48105i	1.22750	+	0.632485i
$106$		0			0
$107$	14.6768			1.41886			0.709430	−	0.704776i	$-0.248952\pi$
$107$	14.6768			1.41886			0.709430	+	0.704776i	$0.248952\pi$
$108$		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	−0.636804	−	0.771026i	$-0.719744\pi$
$127$	3.93670	−	6.81857i	0.349326	−	0.605050i	0.986130	+	0.165976i	$0.0530773\pi$
$128$		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	$-0.437855\pi$
$131$	13.6635	−	11.4650i	1.19378	−	1.00170i	0.999786	−	0.0207005i	$-0.00658966\pi$
$132$		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	−0.928293	−	0.371851i	$-0.878723\pi$
$139$	−8.52743	+	7.15537i	−0.723288	+	0.606910i	0.205005	+	0.978761i	$0.434279\pi$
$140$		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	$-0.682238\pi$
$151$	3.13116	−	17.7577i	0.254810	−	1.44510i	0.796560	−	0.604559i	$-0.206651\pi$
$152$		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	$-0.220079\pi$
$163$	19.6705			1.54071			0.770356	+	0.637614i	$0.220079\pi$
$164$		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	$-0.948824\pi$
$167$	−1.47684	−	8.37558i	−0.114281	−	0.648121i	0.872822	−	0.488038i	$-0.162287\pi$
$168$		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	$0.0962204\pi$
$179$	9.83560	+	17.0358i	0.735147	+	1.27331i	−0.219511	+	0.975610i	$0.570446\pi$
$180$		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	−0.429510	−	0.903062i	$-0.641314\pi$
$191$	−2.46078	+	0.895652i	−0.178056	+	0.0648071i	0.251454	+	0.967869i	$0.419091\pi$
$192$		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	0.787499	−	0.616316i	$-0.211376\pi$
$199$	−1.97489	−	3.42060i	−0.139996	−	0.242480i	−0.927495	+	0.373836i	$0.878042\pi$
$200$		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	$0.0833592\pi$
$211$	2.13238	+	12.0934i	0.146799	+	0.832541i	−0.819105	+	0.573643i	$0.805530\pi$
$212$		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	−0.154968	−	0.987919i	$-0.549528\pi$
$223$	−17.2447	−	14.4700i	−1.15479	−	0.968983i	−0.999821	+	0.0189364i	$0.993972\pi$
$224$		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	$-0.704483\pi$
$227$	3.58146	−	20.3115i	0.237710	−	1.34812i	0.836831	−	0.547461i	$-0.184406\pi$
$228$		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	−0.533246	−	0.845961i	$-0.679028\pi$
$239$	3.20425	−	2.68869i	0.207266	−	0.173917i	0.740511	+	0.672044i	$0.234583\pi$
$240$		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	−0.960217	−	0.279257i	$-0.909912\pi$
$251$	−3.77483	+	6.53819i	−0.238265	+	0.412687i	0.721952	+	0.691944i	$0.243245\pi$
$252$		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	−0.0969342	−	0.995291i	$-0.530904\pi$
$263$	−17.7407	−	14.8862i	−1.09394	−	0.917922i	−0.997003	+	0.0773688i	$0.975348\pi$
$264$		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	$-0.315466\pi$
$271$	18.0358			1.09560			0.547798	+	0.836611i	$0.315466\pi$
$272$		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	0.613801	−	0.789461i	$-0.289640\pi$
$283$	9.69898	+	3.53014i	0.576545	+	0.209845i	−0.0372566	+	0.999306i	$0.511862\pi$
$284$		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	$-0.825780\pi$
$307$	−15.3776	−	26.6348i	−0.877646	−	1.52013i	−0.0237280	−	0.999718i	$-0.507554\pi$
$308$		0			0
$309$	0.0809475	−	0.0183013i	0.00460494	−	0.00104112i
$310$		0			0
$311$	−5.97071	−	2.17316i	−0.338568	−	0.123229i	0.167140	−	0.985933i	$-0.446547\pi$
$311$	−5.97071	−	2.17316i	−0.338568	−	0.123229i	−0.505709	+	0.862704i	$0.668769\pi$
$312$		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	0.537055	−	0.843547i	$-0.319537\pi$
$331$	−3.64629	−	3.05960i	−0.200418	−	0.168171i	−0.737473	+	0.675376i	$0.763981\pi$
$332$		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	−0.911737	−	0.410774i	$-0.865258\pi$
$347$	−12.3974	+	10.4026i	−0.665525	+	0.558442i	0.246212	+	0.969216i	$0.420814\pi$
$348$		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	$-0.602630\pi$
$359$	12.5614	−	21.7570i	0.662967	−	1.14829i	0.979832	−	0.199822i	$-0.0640363\pi$
$360$		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	$-0.804173\pi$
$367$	2.83795	−	16.0948i	0.148140	−	0.840144i	0.964792	−	0.263013i	$-0.0847163\pi$
$368$		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	$-0.698075\pi$
$379$	−22.6950			−1.16577			−0.582883	+	0.812556i	$0.698075\pi$
$380$		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	$0.0604873\pi$
$383$	2.42329	+	13.7431i	0.123824	+	0.702242i	−0.858175	+	0.513357i	$0.828402\pi$
$384$		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	0.169373	−	0.985552i	$-0.445826\pi$
$419$	−6.84461	−	2.49124i	−0.334381	−	0.121705i	−0.503754	+	0.863847i	$0.668048\pi$
$420$		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	$-0.637159\pi$
$431$	−17.3428			−0.835373			−0.417686	+	0.908591i	$0.637159\pi$
$432$		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	0.652994	−	0.757363i	$-0.273513\pi$
$439$	0.430130	+	0.360922i	0.0205290	+	0.0172259i	−0.632465	+	0.774589i	$0.717957\pi$
$440$		0			0
$441$	−0.0718311	−	0.259376i	−0.00342053	−	0.0123512i
$442$		0			0
$443$	−0.461911	+	2.61963i	−0.0219461	+	0.124462i	−0.993813	−	0.111070i	$-0.964572\pi$
$443$	−0.461911	+	2.61963i	−0.0219461	+	0.124462i	0.971867	+	0.235532i	$0.0756833\pi$
$444$		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	−0.816936	−	0.576729i	$-0.804329\pi$
$463$	−8.40962	+	7.05651i	−0.390828	+	0.327944i	0.426108	+	0.904672i	$0.359884\pi$
$464$		0			0
$465$	5.67622	−	7.46183i	0.263229	−	0.346034i
$466$		0			0
$467$	8.88903	−	15.3963i	0.411335	−	0.712454i	−0.583701	−	0.811969i	$-0.698396\pi$
$467$	8.88903	−	15.3963i	0.411335	−	0.712454i	0.995036	+	0.0995151i	$0.0317291\pi$
$468$		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	0.0119409	−	0.999929i	$-0.496199\pi$
$479$	−21.2453	−	17.8269i	−0.970723	−	0.814533i	−0.982664	+	0.185395i	$0.940643\pi$
$480$		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	$-0.567371\pi$
$487$	−9.27190			−0.420150			−0.210075	+	0.977685i	$0.567371\pi$
$488$		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	$-0.810443\pi$
$491$	−5.35740	−	30.3833i	−0.241776	−	1.37118i	0.586086	−	0.810249i	$-0.300668\pi$
$492$		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	0.190799	−	0.981629i	$-0.438892\pi$
$499$	−6.56790	−	2.39052i	−0.294020	−	0.107014i	−0.484819	+	0.874615i	$0.661114\pi$
$500$		0			0
$501$	−14.3681	+	3.24845i	−0.641918	+	0.145130i
$502$		0			0
$503$	4.24640	+	7.35498i	0.189338	+	0.327942i	0.945030	−	0.326985i	$-0.106033\pi$
$503$	4.24640	+	7.35498i	0.189338	+	0.327942i	−0.755692	+	0.654927i	$0.772699\pi$
$504$		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	0.950469	−	0.310820i	$-0.100603\pi$
$523$	4.71235	+	8.16204i	0.206057	+	0.356901i	−0.744412	+	0.667720i	$0.767270\pi$
$524$		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	0.305331	−	0.952246i	$-0.401233\pi$
$547$	−13.5517	−	11.3712i	−0.579428	−	0.486198i	−0.884759	+	0.466048i	$0.845677\pi$
$548$		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	−0.850450	−	0.526055i	$-0.823670\pi$
$563$	−11.3908	+	9.55804i	−0.480066	+	0.402823i	0.370384	+	0.928879i	$0.379226\pi$
$564$		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	−0.632386	−	0.774653i	$-0.717924\pi$
$571$	0.494303	−	0.414769i	0.0206859	−	0.0173576i	0.653072	+	0.757296i	$0.273480\pi$
$572$		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	$0.0562434\pi$
$587$	32.1865	+	27.0077i	1.32848	+	1.11473i	0.344050	+	0.938951i	$0.388201\pi$
$588$		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	0.974301	−	0.225249i	$-0.0723195\pi$
$599$	−0.447444	−	2.53758i	−0.0182821	−	0.103683i	−0.992583	+	0.121566i	$0.961208\pi$
$600$		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	0.639278	−	0.768976i	$-0.279233\pi$
$607$	15.6374	+	5.69156i	0.634704	+	0.231013i	−0.00457324	+	0.999990i	$0.501456\pi$
$608$		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	−0.530783	−	0.847507i	$-0.678102\pi$
$619$	−9.76827	+	3.55536i	−0.392620	+	0.142902i	0.138164	+	0.990409i	$0.455880\pi$
$620$		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	0.968795	−	0.247864i	$-0.0797286\pi$
$631$	6.77581	+	11.7361i	0.269741	+	0.467205i	−0.699054	+	0.715069i	$0.746395\pi$
$632$		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	$0.230116\pi$
$643$	6.88450	+	39.0439i	0.271498	+	1.53974i	−0.478372	+	0.878158i	$0.658773\pi$
$644$		0			0
$645$	−1.83471	−	38.3402i	−0.0722417	−	1.50964i
$646$		0			0
$647$	19.5044			0.766798			0.383399	−	0.923583i	$-0.374753\pi$
$647$	19.5044			0.766798			0.383399	+	0.923583i	$0.374753\pi$
$648$		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	$-0.839667\pi$
$659$	2.88196	−	16.3444i	0.112265	−	0.636687i	0.988068	−	0.154018i	$-0.0492215\pi$
$660$		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	−0.999796	−	0.0202207i	$-0.993563\pi$
$683$	−12.6068	+	21.8356i	−0.482386	+	0.835517i	0.517409	+	0.855738i	$0.326896\pi$
$684$		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	$0.198241\pi$
$691$	−3.95664	+	22.4392i	−0.150518	+	0.853629i	−0.962770	+	0.270323i	$0.912870\pi$
$692$		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	0.912279	−	0.409569i	$-0.134321\pi$
$719$	2.72008	+	4.71132i	0.101442	+	0.175703i	−0.810837	+	0.585272i	$0.800988\pi$
$720$		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	−0.0123564	−	0.999924i	$-0.503933\pi$
$727$	16.7417	−	6.09349i	0.620917	−	0.225995i	0.633273	+	0.773929i	$0.281711\pi$
$728$		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	0.835746	−	0.549116i	$-0.185035\pi$
$739$	−1.56787	−	2.71563i	−0.0576749	−	0.0998959i	−0.893421	+	0.449220i	$0.851702\pi$
$740$		0			0
$741$	−1.50321	−	1.62675i	−0.0552219	−	0.0597602i
$742$		0			0
$743$	34.7743	+	12.6568i	1.27574	+	0.464333i	0.889023	−	0.457863i	$-0.151385\pi$
$743$	34.7743	+	12.6568i	1.27574	+	0.464333i	0.386722	+	0.922196i	$0.373607\pi$
$744$		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	$-0.782105\pi$
$751$	−7.20695	−	40.8726i	−0.262985	−	1.49146i	0.511726	−	0.859149i	$-0.329006\pi$
$752$		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	−0.737963	−	0.674841i	$-0.764212\pi$
$787$	−5.65334	+	4.74371i	−0.201520	+	0.169095i	0.536443	+	0.843936i	$0.319768\pi$
$788$		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	$-0.661192\pi$
$811$	−27.6255			−0.970063			−0.485031	+	0.874497i	$0.661192\pi$
$812$		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	0.0404023	−	0.999183i	$-0.487136\pi$
$823$	−16.3783	−	5.96120i	−0.570911	−	0.207794i	−0.611313	+	0.791389i	$0.709358\pi$
$824$		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	$-0.796218\pi$
$827$	−26.4085	−	45.7409i	−0.918313	−	1.59057i	−0.116337	−	0.993210i	$-0.537115\pi$
$828$		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	−0.940679	−	0.339298i	$-0.889811\pi$
$839$	−41.8026	+	15.2149i	−1.44318	+	0.525276i	−0.502505	+	0.864574i	$0.667588\pi$
$840$		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	0.949286	−	0.314415i	$-0.101808\pi$
$859$	−1.47386	−	8.35865i	−0.0502873	−	0.285193i	−0.999573	+	0.0292214i	$0.990697\pi$
$860$		0			0
$861$	36.0232	−	23.1618i	1.22767	−	0.789352i
$862$		0			0
$863$	9.56354			0.325547			0.162773	−	0.986663i	$-0.447956\pi$
$863$	9.56354			0.325547			0.162773	+	0.986663i	$0.447956\pi$
$864$		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	−0.665962	−	0.745986i	$-0.731979\pi$
$883$	9.30273	−	16.1128i	0.313062	−	0.542239i	0.979024	+	0.203747i	$0.0653120\pi$
$884$		0			0
$885$	17.4749	+	41.6938i	0.587411	+	1.40152i
$886$		0			0
$887$	7.01393	−	5.88539i	0.235505	−	0.197612i	−0.517396	−	0.855746i	$-0.673098\pi$
$887$	7.01393	−	5.88539i	0.235505	−	0.197612i	0.752901	+	0.658134i	$0.228654\pi$
$888$		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	$-0.638757\pi$
$907$	8.57026	−	48.6044i	0.284571	−	1.61388i	0.706815	−	0.707399i	$-0.250132\pi$
$908$		0			0
$909$	15.0936	+	10.3815i	0.500622	+	0.344333i
$910$		0			0
$911$	−26.3464	−	22.1073i	−0.872895	−	0.732446i	0.0918103	−	0.995777i	$-0.470735\pi$
$911$	−26.3464	−	22.1073i	−0.872895	−	0.732446i	−0.964706	+	0.263330i	$0.915179\pi$
$912$		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	$-0.105022\pi$
$919$	57.3599			1.89213			0.946063	+	0.323981i	$0.105022\pi$
$920$		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	0.410907	−	0.911677i	$-0.365212\pi$
$947$	40.3653	−	14.6918i	1.31170	−	0.477418i	0.900788	+	0.434259i	$0.142990\pi$
$948$		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	$-0.860178\pi$
$967$	−6.22038	−	35.2775i	−0.200034	−	1.13445i	0.705031	−	0.709176i	$-0.250933\pi$
$968$		0			0
$969$	−0.935367	−	19.5465i	−0.0300483	−	0.627923i
$970$		0			0
$971$	47.1246			1.51230			0.756150	−	0.654398i	$-0.227078\pi$
$971$	47.1246			1.51230			0.756150	+	0.654398i	$0.227078\pi$
$972$		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	$0.231735\pi$
$983$	−5.72372	+	32.4608i	−0.182558	+	1.03534i	−0.929053	+	0.369947i	$0.879376\pi$
$984$		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	−0.786350	−	0.617781i	$-0.788032\pi$
$991$	4.46511	−	7.73379i	0.141839	−	0.245672i	0.928189	+	0.372109i	$0.121365\pi$
$992$		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.385.4	yes	48
4.3	odd	2	inner	864.2.y.a.385.5	yes	48
27.4	even	9	inner	864.2.y.a.193.4	✓	48
108.31	odd	18	inner	864.2.y.a.193.5	yes	48

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

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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