LMFDB - Embedded newform 864.2.bf.a.49.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(49,864)]

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, 9, 14]))

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

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

chi := DirichletCharacter("864.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: 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:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.9
Character	$\chi$	$=$	864.49
Dual form			864.2.bf.a.529.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21028 + 1.23904i) q^{3} +(-0.405536 - 1.11420i) q^{5} +(-0.0413952 - 0.234764i) q^{7} +(-0.0704471 - 2.99917i) q^{9} +O(q^{10})$	\(q+(-1.21028 + 1.23904i) q^{3} +(-0.405536 - 1.11420i) q^{5} +(-0.0413952 - 0.234764i) q^{7} +(-0.0704471 - 2.99917i) q^{9} +(-1.06877 + 2.93642i) q^{11} +(0.138720 - 0.165320i) q^{13} +(1.87135 + 0.846019i) q^{15} +(0.713116 - 1.23515i) q^{17} +(0.444108 - 0.256406i) q^{19} +(0.340982 + 0.232839i) q^{21} +(1.00003 - 5.67143i) q^{23} +(2.75324 - 2.31024i) q^{25} +(3.80136 + 3.54255i) q^{27} +(-5.88571 - 7.01432i) q^{29} +(0.723390 - 4.10255i) q^{31} +(-2.34484 - 4.87814i) q^{33} +(-0.244787 + 0.141328i) q^{35} +(4.45075 + 2.56964i) q^{37} +(0.0369484 + 0.371963i) q^{39} +(8.81242 + 7.39450i) q^{41} +(1.90966 - 5.24675i) q^{43} +(-3.31311 + 1.29477i) q^{45} +(-0.360171 - 2.04263i) q^{47} +(6.52445 - 2.37470i) q^{49} +(0.667336 + 2.37846i) q^{51} +6.45988i q^{53} +3.70519 q^{55} +(-0.219797 + 0.860591i) q^{57} +(-1.81520 - 4.98722i) q^{59} +(13.4019 - 2.36311i) q^{61} +(-0.701181 + 0.140690i) q^{63} +(-0.240456 - 0.0875188i) q^{65} +(5.99107 - 7.13987i) q^{67} +(5.81682 + 8.10308i) q^{69} +(3.31534 - 5.74233i) q^{71} +(0.552466 + 0.956899i) q^{73} +(-0.469703 + 6.20741i) q^{75} +(0.733607 + 0.129355i) q^{77} +(-9.54970 + 8.01315i) q^{79} +(-8.99007 + 0.422566i) q^{81} +(0.311211 + 0.370887i) q^{83} +(-1.66540 - 0.293656i) q^{85} +(15.8144 + 1.19665i) q^{87} +(-6.83971 - 11.8467i) q^{89} +(-0.0445535 - 0.0257230i) q^{91} +(4.20772 + 5.86154i) q^{93} +(-0.465790 - 0.390844i) q^{95} +(-3.49625 - 1.27253i) q^{97} +(8.88213 + 2.99856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) $ 204 * q + 12 * q^7 - 12 * q^9	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.21028	+	1.23904i	−0.698755	+	0.715361i
$3$	−1.21028	+	1.23904i	−0.698755	+	0.715361i
$4$		0			0
$5$	−0.405536	−	1.11420i	−0.181361	−	0.498286i	0.815382	−	0.578923i	$-0.196527\pi$
$5$	−0.405536	−	1.11420i	−0.181361	−	0.498286i	−0.996744	+	0.0806369i	$0.974305\pi$
$6$		0			0
$7$	−0.0413952	−	0.234764i	−0.0156459	−	0.0887324i	0.975985	−	0.217838i	$-0.0699005\pi$
$7$	−0.0413952	−	0.234764i	−0.0156459	−	0.0887324i	−0.991631	+	0.129106i	$0.958789\pi$
$8$		0			0
$9$	−0.0704471	−	2.99917i	−0.0234824	−	0.999724i
$10$		0			0
$11$	−1.06877	+	2.93642i	−0.322246	+	0.885364i	0.667764	+	0.744373i	$0.267251\pi$
$11$	−1.06877	+	2.93642i	−0.322246	+	0.885364i	−0.990011	+	0.140992i	$0.954971\pi$
$12$		0			0
$13$	0.138720	−	0.165320i	0.0384740	−	0.0458515i	−0.746464	−	0.665425i	$-0.768250\pi$
$13$	0.138720	−	0.165320i	0.0384740	−	0.0458515i	0.784938	+	0.619574i	$0.212695\pi$
$14$		0			0
$15$	1.87135	+	0.846019i	0.483181	+	0.218441i
$16$		0			0
$17$	0.713116	−	1.23515i	0.172956	−	0.299569i	−0.766496	−	0.642249i	$-0.778001\pi$
$17$	0.713116	−	1.23515i	0.172956	−	0.299569i	0.939452	+	0.342680i	$0.111335\pi$
$18$		0			0
$19$	0.444108	−	0.256406i	0.101885	−	0.0588236i	−0.448191	−	0.893938i	$-0.647932\pi$
$19$	0.444108	−	0.256406i	0.101885	−	0.0588236i	0.550077	+	0.835114i	$0.314598\pi$
$20$		0			0
$21$	0.340982	+	0.232839i	0.0744083	+	0.0508097i
$22$		0			0
$23$	1.00003	−	5.67143i	0.208520	−	1.18257i	−0.683284	−	0.730152i	$-0.739449\pi$
$23$	1.00003	−	5.67143i	0.208520	−	1.18257i	0.891804	−	0.452422i	$-0.149440\pi$
$24$		0			0
$25$	2.75324	−	2.31024i	0.550647	−	0.462048i
$26$		0			0
$27$	3.80136	+	3.54255i	0.731572	+	0.681764i
$28$		0			0
$29$	−5.88571	−	7.01432i	−1.09295	−	1.30253i	−0.949811	−	0.312824i	$-0.898725\pi$
$29$	−5.88571	−	7.01432i	−1.09295	−	1.30253i	−0.143139	−	0.989703i	$-0.545719\pi$
$30$		0			0
$31$	0.723390	−	4.10255i	0.129925	−	0.736840i	−0.848336	−	0.529459i	$-0.822395\pi$
$31$	0.723390	−	4.10255i	0.129925	−	0.736840i	0.978260	−	0.207381i	$-0.0664939\pi$
$32$		0			0
$33$	−2.34484	−	4.87814i	−0.408184	−	0.849175i
$34$		0			0
$35$	−0.244787	+	0.141328i	−0.0413765	+	0.0238888i
$36$		0			0
$37$	4.45075	+	2.56964i	0.731698	+	0.422446i	0.819043	−	0.573732i	$-0.194505\pi$
$37$	4.45075	+	2.56964i	0.731698	+	0.422446i	−0.0873450	+	0.996178i	$0.527838\pi$
$38$		0			0
$39$	0.0369484	+	0.371963i	0.00591648	+	0.0595618i
$40$		0			0
$41$	8.81242	+	7.39450i	1.37627	+	1.15483i	0.970570	+	0.240821i	$0.0774166\pi$
$41$	8.81242	+	7.39450i	1.37627	+	1.15483i	0.405700	+	0.914006i	$0.367028\pi$
$42$		0			0
$43$	1.90966	−	5.24675i	0.291220	−	0.800121i	−0.704668	−	0.709537i	$-0.748904\pi$
$43$	1.90966	−	5.24675i	0.291220	−	0.800121i	0.995889	−	0.0905846i	$-0.0288736\pi$
$44$		0			0
$45$	−3.31311	+	1.29477i	−0.493890	+	0.193012i
$46$		0			0
$47$	−0.360171	−	2.04263i	−0.0525363	−	0.297948i	0.947207	−	0.320624i	$-0.103893\pi$
$47$	−0.360171	−	2.04263i	−0.0525363	−	0.297948i	−0.999743	+	0.0226758i	$0.992781\pi$
$48$		0			0
$49$	6.52445	−	2.37470i	0.932064	−	0.339244i
$50$		0			0
$51$	0.667336	+	2.37846i	0.0934457	+	0.333051i
$52$		0			0
$53$			6.45988i			0.887333i	0.896192	+	0.443666i	$0.146322\pi$
$53$			6.45988i			0.887333i	−0.896192	+	0.443666i	$0.853678\pi$
$54$		0			0
$55$	3.70519			0.499608
$56$		0			0
$57$	−0.219797	+	0.860591i	−0.0291129	+	0.113988i
$58$		0			0
$59$	−1.81520	−	4.98722i	−0.236319	−	0.649281i	−0.999993	−	0.00367917i	$-0.998829\pi$
$59$	−1.81520	−	4.98722i	−0.236319	−	0.649281i	0.763674	−	0.645602i	$-0.223393\pi$
$60$		0			0
$61$	13.4019	−	2.36311i	1.71594	−	0.302566i	0.772720	−	0.634747i	$-0.218896\pi$
$61$	13.4019	−	2.36311i	1.71594	−	0.302566i	0.943216	+	0.332181i	$0.107785\pi$
$62$		0			0
$63$	−0.701181	+	0.140690i	−0.0883405	+	0.0177252i
$64$		0			0
$65$	−0.240456	−	0.0875188i	−0.0298249	−	0.0108554i
$66$		0			0
$67$	5.99107	−	7.13987i	0.731925	−	0.872274i	−0.263806	−	0.964576i	$-0.584978\pi$
$67$	5.99107	−	7.13987i	0.731925	−	0.872274i	0.995731	+	0.0923014i	$0.0294223\pi$
$68$		0			0
$69$	5.81682	+	8.10308i	0.700263	+	0.975497i
$70$		0			0
$71$	3.31534	−	5.74233i	0.393458	−	0.681489i	−0.599445	−	0.800416i	$-0.704612\pi$
$71$	3.31534	−	5.74233i	0.393458	−	0.681489i	0.992903	+	0.118927i	$0.0379454\pi$
$72$		0			0
$73$	0.552466	+	0.956899i	0.0646612	+	0.111997i	0.896544	−	0.442955i	$-0.146070\pi$
$73$	0.552466	+	0.956899i	0.0646612	+	0.111997i	−0.831882	+	0.554952i	$0.812737\pi$
$74$		0			0
$75$	−0.469703	+	6.20741i	−0.0542366	+	0.716770i
$76$		0			0
$77$	0.733607	+	0.129355i	0.0836023	+	0.0147413i
$78$		0			0
$79$	−9.54970	+	8.01315i	−1.07443	+	0.901550i	−0.995446	−	0.0953262i	$-0.969611\pi$
$79$	−9.54970	+	8.01315i	−1.07443	+	0.901550i	−0.0789794	+	0.996876i	$0.525166\pi$
$80$		0			0
$81$	−8.99007	+	0.422566i	−0.998897	+	0.0469518i
$82$		0			0
$83$	0.311211	+	0.370887i	0.0341599	+	0.0407102i	0.782854	−	0.622206i	$-0.213763\pi$
$83$	0.311211	+	0.370887i	0.0341599	+	0.0407102i	−0.748694	+	0.662916i	$0.769319\pi$
$84$		0			0
$85$	−1.66540	−	0.293656i	−0.180638	−	0.0318514i
$86$		0			0
$87$	15.8144	+	1.19665i	1.69548	+	0.128294i
$88$		0			0
$89$	−6.83971	−	11.8467i	−0.725008	−	1.25575i	−0.958971	−	0.283505i	$-0.908503\pi$
$89$	−6.83971	−	11.8467i	−0.725008	−	1.25575i	0.233963	−	0.972245i	$-0.424830\pi$
$90$		0			0
$91$	−0.0445535	−	0.0257230i	−0.00467048	−	0.00269650i
$92$		0			0
$93$	4.20772	+	5.86154i	0.436321	+	0.607814i
$94$		0			0
$95$	−0.465790	−	0.390844i	−0.0477890	−	0.0400998i
$96$		0			0
$97$	−3.49625	−	1.27253i	−0.354990	−	0.129206i	0.158368	−	0.987380i	$-0.449377\pi$
$97$	−3.49625	−	1.27253i	−0.354990	−	0.129206i	−0.513359	+	0.858174i	$0.671599\pi$
$98$		0			0
$99$	8.88213	+	2.99856i	0.892687	+	0.301367i
$100$		0			0
$101$	−9.92883	+	1.75072i	−0.987955	+	0.174203i	−0.644201	−	0.764856i	$-0.722810\pi$
$101$	−9.92883	+	1.75072i	−0.987955	+	0.174203i	−0.343754	+	0.939060i	$0.611699\pi$
$102$		0			0
$103$	−0.422913	+	0.153928i	−0.0416709	+	0.0151670i	−0.362772	−	0.931878i	$-0.618169\pi$
$103$	−0.422913	+	0.153928i	−0.0416709	+	0.0151670i	0.321101	+	0.947045i	$0.395947\pi$
$104$		0			0
$105$	0.121150	−	0.474347i	0.0118230	−	0.0462916i
$106$		0			0
$107$		−	12.7048i		−	1.22822i	−0.789221	−	0.614110i	$-0.789515\pi$
$107$		−	12.7048i		−	1.22822i	0.789221	−	0.614110i	$-0.210485\pi$
$108$		0			0
$109$		−	4.56634i		−	0.437376i	−0.975795	−	0.218688i	$-0.929822\pi$
$109$		−	4.56634i		−	0.437376i	0.975795	−	0.218688i	$-0.0701776\pi$
$110$		0			0
$111$	−8.57054	+	2.40468i	−0.813479	+	0.228242i
$112$		0			0
$113$	−2.54320	+	0.925647i	−0.239244	+	0.0870776i	−0.458859	−	0.888509i	$-0.651742\pi$
$113$	−2.54320	+	0.925647i	−0.239244	+	0.0870776i	0.219616	+	0.975586i	$0.429520\pi$
$114$		0			0
$115$	−6.72466	+	1.18574i	−0.627078	+	0.110571i
$116$		0			0
$117$	−0.505596	−	0.404399i	−0.0467424	−	0.0373867i
$118$		0			0
$119$	−0.319489	−	0.116284i	−0.0292875	−	0.0106598i
$120$		0			0
$121$	0.946186	+	0.793944i	0.0860169	+	0.0721767i
$122$		0			0
$123$	−19.8276	+	1.96954i	−1.78779	+	0.177588i
$124$		0			0
$125$	−8.82488	−	5.09505i	−0.789321	−	0.455715i
$126$		0			0
$127$	8.58707	+	14.8732i	0.761980	+	1.31979i	0.941829	+	0.336093i	$0.109106\pi$
$127$	8.58707	+	14.8732i	0.761980	+	1.31979i	−0.179849	+	0.983694i	$0.557561\pi$
$128$		0			0
$129$	4.18971	+	8.71618i	0.368884	+	0.767417i
$130$		0			0
$131$	−15.9220	−	2.80749i	−1.39112	−	0.245291i	−0.572628	−	0.819815i	$-0.694076\pi$
$131$	−15.9220	−	2.80749i	−1.39112	−	0.245291i	−0.818488	+	0.574524i	$0.805187\pi$
$132$		0			0
$133$	−0.0785788	−	0.0936466i	−0.00681365	−	0.00812019i
$134$		0			0
$135$	2.40553	−	5.67211i	0.207035	−	0.488178i
$136$		0			0
$137$	−11.4434	+	9.60213i	−0.977673	+	0.820365i	−0.983737	−	0.179616i	$-0.942514\pi$
$137$	−11.4434	+	9.60213i	−0.977673	+	0.820365i	0.00606337	+	0.999982i	$0.498070\pi$
$138$		0			0
$139$	19.8936	+	3.50777i	1.68735	+	0.297525i	0.933248	−	0.359233i	$-0.116962\pi$
$139$	19.8936	+	3.50777i	1.68735	+	0.297525i	0.754101	+	0.656758i	$0.228073\pi$
$140$		0			0
$141$	2.96681	+	2.02589i	0.249850	+	0.170610i
$142$		0			0
$143$	0.337190	+	0.584030i	0.0281972	+	0.0488390i
$144$		0			0
$145$	−5.42850	+	9.40243i	−0.450812	+	0.780829i
$146$		0			0
$147$	−4.95405	+	10.9581i	−0.408603	+	0.903810i
$148$		0			0
$149$	−5.63155	+	6.71142i	−0.461355	+	0.549821i	−0.945694	−	0.325059i	$-0.894616\pi$
$149$	−5.63155	+	6.71142i	−0.461355	+	0.549821i	0.484339	+	0.874880i	$0.339060\pi$
$150$		0			0
$151$	−10.9766	−	3.99514i	−0.893260	−	0.325120i	−0.145711	−	0.989327i	$-0.546547\pi$
$151$	−10.9766	−	3.99514i	−0.893260	−	0.325120i	−0.747549	+	0.664207i	$0.768769\pi$
$152$		0			0
$153$	−3.75467	−	2.05174i	−0.303547	−	0.165874i
$154$		0			0
$155$	−4.86443	+	0.857730i	−0.390720	+	0.0688945i
$156$		0			0
$157$	−4.94482	−	13.5858i	−0.394640	−	1.08426i	−0.964858	−	0.262771i	$-0.915364\pi$
$157$	−4.94482	−	13.5858i	−0.394640	−	1.08426i	0.570219	−	0.821493i	$-0.306858\pi$
$158$		0			0
$159$	−8.00406	−	7.81826i	−0.634763	−	0.620028i
$160$		0			0
$161$	−1.37284			−0.108195
$162$		0			0
$163$		−	16.3296i		−	1.27903i	−0.768779	−	0.639515i	$-0.779135\pi$
$163$		−	16.3296i		−	1.27903i	0.768779	−	0.639515i	$-0.220865\pi$
$164$		0			0
$165$	−4.48432	+	4.59088i	−0.349103	+	0.357400i
$166$		0			0
$167$	17.9403	−	6.52973i	1.38826	−	0.505286i	0.463590	−	0.886050i	$-0.346561\pi$
$167$	17.9403	−	6.52973i	1.38826	−	0.505286i	0.924672	+	0.380764i	$0.124339\pi$
$168$		0			0
$169$	2.24934	+	12.7566i	0.173026	+	0.981280i
$170$		0			0
$171$	−0.800292	−	1.31389i	−0.0611999	−	0.100476i
$172$		0			0
$173$	4.98866	−	13.7062i	0.379281	−	1.04207i	−0.592374	−	0.805663i	$-0.701809\pi$
$173$	4.98866	−	13.7062i	0.379281	−	1.04207i	0.971655	−	0.236403i	$-0.0759686\pi$
$174$		0			0
$175$	−0.656332	−	0.550728i	−0.0496140	−	0.0416311i
$176$		0			0
$177$	8.37627	+	3.78682i	0.629599	+	0.284635i
$178$		0			0
$179$	−0.145083	−	0.0837640i	−0.0108440	−	0.00626081i	0.494568	−	0.869139i	$-0.335326\pi$
$179$	−0.145083	−	0.0837640i	−0.0108440	−	0.00626081i	−0.505412	+	0.862878i	$0.668660\pi$
$180$		0			0
$181$	−11.9270	+	6.88607i	−0.886529	+	0.511838i	−0.872805	−	0.488068i	$-0.837702\pi$
$181$	−11.9270	+	6.88607i	−0.886529	+	0.511838i	−0.0137232	+	0.999906i	$0.504368\pi$
$182$		0			0
$183$	−13.2920	+	19.4655i	−0.982575	+	1.43893i
$184$		0			0
$185$	1.05816	−	6.00111i	0.0777973	−	0.441210i
$186$		0			0
$187$	2.86477	+	3.41410i	0.209493	+	0.249664i
$188$		0			0
$189$	0.674305	−	1.03907i	0.0490484	−	0.0755809i
$190$		0			0
$191$	−19.3252	+	16.2157i	−1.39832	+	1.17333i	−0.436481	+	0.899713i	$0.643776\pi$
$191$	−19.3252	+	16.2157i	−1.39832	+	1.17333i	−0.961839	+	0.273617i	$0.911780\pi$
$192$		0			0
$193$	2.61893	−	14.8527i	0.188515	−	1.06912i	−0.732841	−	0.680400i	$-0.761806\pi$
$193$	2.61893	−	14.8527i	0.188515	−	1.06912i	0.921356	−	0.388721i	$-0.127083\pi$
$194$		0			0
$195$	0.399458	−	0.192013i	0.0286058	−	0.0137503i
$196$		0			0
$197$	−2.26349	+	1.30682i	−0.161267	+	0.0931074i	−0.578461	−	0.815710i	$-0.696347\pi$
$197$	−2.26349	+	1.30682i	−0.161267	+	0.0931074i	0.417195	+	0.908817i	$0.363013\pi$
$198$		0			0
$199$	−4.49498	+	7.78553i	−0.318641	+	0.551902i	−0.980205	−	0.197987i	$-0.936560\pi$
$199$	−4.49498	+	7.78553i	−0.318641	+	0.551902i	0.661564	+	0.749889i	$0.269893\pi$
$200$		0			0
$201$	1.59574	+	16.0644i	0.112554	+	1.13310i
$202$		0			0
$203$	−1.40307	+	1.67211i	−0.0984761	+	0.117359i
$204$		0			0
$205$	4.66521	−	12.8176i	0.325832	−	0.895217i
$206$		0			0
$207$	−17.0800	−	2.59971i	−1.18714	−	0.180693i
$208$		0			0
$209$	0.278267	+	1.57813i	0.0192481	+	0.109161i
$210$		0			0
$211$	4.05109	+	11.1303i	0.278888	+	0.766240i	0.997489	+	0.0708169i	$0.0225606\pi$
$211$	4.05109	+	11.1303i	0.278888	+	0.766240i	−0.718601	+	0.695423i	$0.755217\pi$
$212$		0			0
$213$	3.10250	+	11.0577i	0.212580	+	0.757658i
$214$		0			0
$215$	−6.62037			−0.451505
$216$		0			0
$217$	−0.993075			−0.0674143
$218$		0			0
$219$	−1.85427	−	0.473587i	−0.125300	−	0.0320020i
$220$		0			0
$221$	−0.105272	−	0.289233i	−0.00708137	−	0.0194559i
$222$		0			0
$223$	−3.12760	−	17.7375i	−0.209440	−	1.18779i	−0.890299	−	0.455377i	$-0.849504\pi$
$223$	−3.12760	−	17.7375i	−0.209440	−	1.18779i	0.680859	−	0.732414i	$-0.261607\pi$
$224$		0			0
$225$	−7.12277	−	8.09468i	−0.474851	−	0.539646i
$226$		0			0
$227$	−1.45106	+	3.98676i	−0.0963105	+	0.264611i	−0.978487	−	0.206308i	$-0.933855\pi$
$227$	−1.45106	+	3.98676i	−0.0963105	+	0.264611i	0.882177	+	0.470919i	$0.156077\pi$
$228$		0			0
$229$	3.74408	−	4.46202i	0.247416	−	0.294859i	−0.628016	−	0.778201i	$-0.716133\pi$
$229$	3.74408	−	4.46202i	0.247416	−	0.294859i	0.875432	+	0.483342i	$0.160577\pi$
$230$		0			0
$231$	−1.04815	+	0.752415i	−0.0689629	+	0.0495052i
$232$		0			0
$233$	6.87852	−	11.9139i	0.450627	−	0.780509i	−0.547798	−	0.836611i	$-0.684534\pi$
$233$	6.87852	−	11.9139i	0.450627	−	0.780509i	0.998425	+	0.0561019i	$0.0178672\pi$
$234$		0			0
$235$	−2.12984	+	1.22966i	−0.138935	+	0.0802144i
$236$		0			0
$237$	1.62918	−	21.5306i	0.105827	−	1.39856i
$238$		0			0
$239$	−4.92212	+	27.9147i	−0.318385	+	1.80565i	0.234191	+	0.972191i	$0.424756\pi$
$239$	−4.92212	+	27.9147i	−0.318385	+	1.80565i	−0.552576	+	0.833462i	$0.686355\pi$
$240$		0			0
$241$	−14.6647	+	12.3052i	−0.944638	+	0.792645i	−0.978386	−	0.206785i	$-0.933700\pi$
$241$	−14.6647	+	12.3052i	−0.944638	+	0.792645i	0.0337487	+	0.999430i	$0.489255\pi$
$242$		0			0
$243$	10.3569	−	11.6505i	0.664397	−	0.747380i
$244$		0			0
$245$	−5.29180	−	6.30652i	−0.338081	−	0.402909i
$246$		0			0
$247$	0.0192176	−	0.108989i	0.00122279	−	0.00693478i
$248$		0			0
$249$	−0.836197	−	0.0632735i	−0.0529919	−	0.00400979i
$250$		0			0
$251$	1.18008	−	0.681320i	0.0744860	−	0.0430045i	−0.462294	−	0.886726i	$-0.652974\pi$
$251$	1.18008	−	0.681320i	0.0744860	−	0.0430045i	0.536780	+	0.843722i	$0.319640\pi$
$252$		0			0
$253$	15.5849	+	8.99795i	0.979814	+	0.565696i
$254$		0			0
$255$	2.37945	−	1.70810i	0.149007	−	0.106965i
$256$		0			0
$257$	16.1382	+	13.5415i	1.00667	+	0.844698i	0.987895	−	0.155126i	$-0.0495784\pi$
$257$	16.1382	+	13.5415i	1.00667	+	0.844698i	0.0187768	+	0.999824i	$0.494023\pi$
$258$		0			0
$259$	0.419019	−	1.15124i	0.0260366	−	0.0715349i
$260$		0			0
$261$	−20.6225	+	18.1464i	−1.27650	+	1.12323i
$262$		0			0
$263$	1.23938	+	7.02885i	0.0764232	+	0.433418i	0.998880	+	0.0473170i	$0.0150671\pi$
$263$	1.23938	+	7.02885i	0.0764232	+	0.433418i	−0.922457	+	0.386101i	$0.873822\pi$
$264$		0			0
$265$	7.19761	−	2.61971i	0.442145	−	0.160928i
$266$		0			0
$267$	22.9565	+	5.86316i	1.40492	+	0.358820i
$268$		0			0
$269$		−	2.68764i		−	0.163868i	−0.996638	−	0.0819341i	$-0.973890\pi$
$269$		−	2.68764i		−	0.163868i	0.996638	−	0.0819341i	$-0.0261097\pi$
$270$		0			0
$271$	27.8912			1.69427			0.847133	−	0.531380i	$-0.178326\pi$
$271$	27.8912			1.69427			0.847133	+	0.531380i	$0.178326\pi$
$272$		0			0
$273$	0.0857940	−	0.0240716i	0.00519249	−	0.00145688i
$274$		0			0
$275$	3.84126	+	10.5538i	0.231637	+	0.636417i
$276$		0			0
$277$	9.03501	−	1.59312i	0.542861	−	0.0957211i	0.104508	−	0.994524i	$-0.466673\pi$
$277$	9.03501	−	1.59312i	0.542861	−	0.0957211i	0.438353	+	0.898803i	$0.355562\pi$
$278$		0			0
$279$	−12.3552	−	1.88056i	−0.739687	−	0.112586i
$280$		0			0
$281$	2.39035	+	0.870016i	0.142596	+	0.0519008i	0.412332	−	0.911033i	$-0.364714\pi$
$281$	2.39035	+	0.870016i	0.142596	+	0.0519008i	−0.269736	+	0.962934i	$0.586936\pi$
$282$		0			0
$283$	−8.22590	+	9.80324i	−0.488979	+	0.582742i	−0.952957	−	0.303104i	$-0.901977\pi$
$283$	−8.22590	+	9.80324i	−0.488979	+	0.582742i	0.463979	+	0.885846i	$0.346421\pi$
$284$		0			0
$285$	1.04801	−	0.104102i	0.0620786	−	0.00616649i
$286$		0			0
$287$	1.37117	−	2.37493i	0.0809376	−	0.140188i
$288$		0			0
$289$	7.48293	+	12.9608i	0.440172	+	0.762401i
$290$		0			0
$291$	5.80816	−	2.79188i	0.340480	−	0.163663i
$292$		0			0
$293$	18.7541	+	3.30685i	1.09563	+	0.193188i	0.692116	−	0.721787i	$-0.256679\pi$
$293$	18.7541	+	3.30685i	1.09563	+	0.193188i	0.403510	+	0.914975i	$0.367790\pi$
$294$		0			0
$295$	−4.82064	+	4.04500i	−0.280668	+	0.235509i
$296$		0			0
$297$	−14.4652	+	7.37622i	−0.839356	+	0.428012i
$298$		0			0
$299$	−0.798877	−	0.952065i	−0.0462003	−	0.0550593i
$300$		0			0
$301$	−1.31080	−	0.231129i	−0.0755531	−	0.0133220i
$302$		0			0
$303$	9.84744	−	14.4211i	0.565721	−	0.828470i
$304$		0			0
$305$	−8.06793	−	13.9741i	−0.461968	−	0.800153i
$306$		0			0
$307$	10.1675	+	5.87019i	0.580288	+	0.335029i	0.761248	−	0.648461i	$-0.224587\pi$
$307$	10.1675	+	5.87019i	0.580288	+	0.335029i	−0.180960	+	0.983490i	$0.557920\pi$
$308$		0			0
$309$	0.321120	−	0.710303i	0.0182679	−	0.0404077i
$310$		0			0
$311$	2.30115	+	1.93090i	0.130486	+	0.109491i	0.705695	−	0.708515i	$-0.250635\pi$
$311$	2.30115	+	1.93090i	0.130486	+	0.109491i	−0.575209	+	0.818007i	$0.695079\pi$
$312$		0			0
$313$	−29.3835	−	10.6947i	−1.66085	−	0.604501i	−0.670356	−	0.742040i	$-0.733858\pi$
$313$	−29.3835	−	10.6947i	−1.66085	−	0.604501i	−0.990496	+	0.137539i	$0.956081\pi$
$314$		0			0
$315$	0.441111	+	0.724202i	0.0248538	+	0.0408042i
$316$		0			0
$317$	15.2754	−	2.69346i	0.857952	−	0.151280i	0.272668	−	0.962108i	$-0.412094\pi$
$317$	15.2754	−	2.69346i	0.857952	−	0.151280i	0.585284	+	0.810828i	$0.300983\pi$
$318$		0			0
$319$	26.8875	−	9.78624i	1.50541	−	0.547924i
$320$		0			0
$321$	15.7418	+	15.3764i	0.878620	+	0.858225i
$322$		0			0
$323$		−	0.731389i		−	0.0406956i
$324$		0			0
$325$		−	0.775642i		−	0.0430249i
$326$		0			0
$327$	5.65788	+	5.52654i	0.312881	+	0.305618i
$328$		0			0
$329$	−0.464626	+	0.169110i	−0.0256157	+	0.00932334i
$330$		0			0
$331$	−16.8366	+	2.96874i	−0.925422	+	0.163177i	−0.615998	−	0.787748i	$-0.711247\pi$
$331$	−16.8366	+	2.96874i	−0.925422	+	0.163177i	−0.309423	+	0.950924i	$0.600136\pi$
$332$		0			0
$333$	7.39325	−	13.5296i	0.405148	−	0.741416i
$334$		0			0
$335$	−10.3848	−	3.77978i	−0.567385	−	0.206511i
$336$		0			0
$337$	−8.15001	−	6.83867i	−0.443959	−	0.372526i	0.393229	−	0.919440i	$-0.371358\pi$
$337$	−8.15001	−	6.83867i	−0.443959	−	0.372526i	−0.837189	+	0.546914i	$0.815802\pi$
$338$		0			0
$339$	1.93106	−	4.27142i	0.104881	−	0.231992i
$340$		0			0
$341$	11.2737	+	6.50886i	0.610504	+	0.352475i
$342$		0			0
$343$	−1.66192	−	2.87854i	−0.0897355	−	0.155426i
$344$		0			0
$345$	6.66954	−	9.76720i	0.359076	−	0.525849i
$346$		0			0
$347$	−12.4691	−	2.19864i	−0.669378	−	0.118029i	−0.171377	−	0.985206i	$-0.554821\pi$
$347$	−12.4691	−	2.19864i	−0.669378	−	0.118029i	−0.498002	+	0.867176i	$0.665933\pi$
$348$		0			0
$349$	−19.3979	−	23.1175i	−1.03834	−	1.23745i	−0.970839	−	0.239731i	$-0.922941\pi$
$349$	−19.3979	−	23.1175i	−1.03834	−	1.23745i	−0.0675040	−	0.997719i	$-0.521504\pi$
$350$		0			0
$351$	1.11298	−	0.137018i	0.0594064	−	0.00731350i
$352$		0			0
$353$	−1.46184	+	1.22663i	−0.0778058	+	0.0652868i	−0.680861	−	0.732413i	$-0.738394\pi$
$353$	−1.46184	+	1.22663i	−0.0778058	+	0.0652868i	0.603055	+	0.797699i	$0.293950\pi$
$354$		0			0
$355$	−7.74260	−	1.36523i	−0.410935	−	0.0724588i
$356$		0			0
$357$	0.530752	−	0.255123i	0.0280904	−	0.0135026i
$358$		0			0
$359$	−11.0996	−	19.2251i	−0.585816	−	1.01466i	−0.994773	−	0.102109i	$-0.967441\pi$
$359$	−11.0996	−	19.2251i	−0.585816	−	1.01466i	0.408957	−	0.912554i	$-0.365893\pi$
$360$		0			0
$361$	−9.36851	+	16.2267i	−0.493080	+	0.854039i
$362$		0			0
$363$	−2.12888	+	0.211469i	−0.111737	+	0.0110992i
$364$		0			0
$365$	0.842133	−	1.00361i	0.0440793	−	0.0525316i
$366$		0			0
$367$	8.72294	+	3.17489i	0.455334	+	0.165728i	0.559497	−	0.828832i	$-0.310994\pi$
$367$	8.72294	+	3.17489i	0.455334	+	0.165728i	−0.104163	+	0.994560i	$0.533217\pi$
$368$		0			0
$369$	21.5566	−	26.9509i	1.12219	−	1.40301i
$370$		0			0
$371$	1.51655	−	0.267408i	0.0787351	−	0.0138831i
$372$		0			0
$373$	9.68526	+	26.6100i	0.501484	+	1.37782i	0.889826	+	0.456300i	$0.150826\pi$
$373$	9.68526	+	26.6100i	0.501484	+	1.37782i	−0.388342	+	0.921515i	$0.626952\pi$
$374$		0			0
$375$	16.9935	−	4.76796i	0.877543	−	0.246216i
$376$		0			0
$377$	−1.97607			−0.101773
$378$		0			0
$379$		−	19.6262i		−	1.00813i	−0.863665	−	0.504066i	$-0.831837\pi$
$379$		−	19.6262i		−	1.00813i	0.863665	−	0.504066i	$-0.168163\pi$
$380$		0			0
$381$	−28.8213	−	7.36105i	−1.47656	−	0.377118i
$382$		0			0
$383$	27.5144	−	10.0144i	1.40592	−	0.511713i	0.475991	−	0.879450i	$-0.342090\pi$
$383$	27.5144	−	10.0144i	1.40592	−	0.511713i	0.929930	+	0.367737i	$0.119867\pi$
$384$		0			0
$385$	−0.153377	−	0.869845i	−0.00781682	−	0.0443314i
$386$		0			0
$387$	−15.8704	−	5.35778i	−0.806739	−	0.272351i
$388$		0			0
$389$	−5.85172	+	16.0775i	−0.296694	+	0.815161i	0.698353	+	0.715754i	$0.253917\pi$
$389$	−5.85172	+	16.0775i	−0.296694	+	0.815161i	−0.995047	+	0.0994068i	$0.968305\pi$
$390$		0			0
$391$	−6.29194	−	5.27957i	−0.318197	−	0.266999i
$392$		0			0
$393$	22.7487	−	16.3302i	1.14752	−	0.823751i
$394$		0			0
$395$	12.8010	+	7.39067i	0.644089	+	0.371865i
$396$		0			0
$397$	−16.4242	+	9.48249i	−0.824305	+	0.475913i	−0.851899	−	0.523707i	$-0.824549\pi$
$397$	−16.4242	+	9.48249i	−0.824305	+	0.475913i	0.0275939	+	0.999619i	$0.491215\pi$
$398$		0			0
$399$	0.211134	+	0.0159761i	0.0105699	+	0.000799807i
$400$		0			0
$401$	3.45976	−	19.6213i	0.172772	−	0.979839i	−0.767912	−	0.640555i	$-0.778704\pi$
$401$	3.45976	−	19.6213i	0.172772	−	0.979839i	0.940684	−	0.339284i	$-0.110185\pi$
$402$		0			0
$403$	−0.577885	−	0.688697i	−0.0287865	−	0.0343064i
$404$		0			0
$405$	4.11662	+	9.84539i	0.204557	+	0.489221i
$406$		0			0
$407$	−12.3024	+	10.3229i	−0.609806	+	0.511688i
$408$		0			0
$409$	4.21976	−	23.9314i	0.208654	−	1.18333i	−0.682932	−	0.730482i	$-0.739296\pi$
$409$	4.21976	−	23.9314i	0.208654	−	1.18333i	0.891586	−	0.452851i	$-0.149593\pi$
$410$		0			0
$411$	1.95224	−	25.8001i	0.0962971	−	1.27262i
$412$		0			0
$413$	−1.09568	+	0.632590i	−0.0539148	+	0.0311277i
$414$		0			0
$415$	0.287036	−	0.497160i	0.0140900	−	0.0244046i
$416$		0			0
$417$	−28.4230	+	20.4036i	−1.39188	+	0.999166i
$418$		0			0
$419$	−2.59476	+	3.09232i	−0.126762	+	0.151070i	−0.825693	−	0.564120i	$-0.809215\pi$
$419$	−2.59476	+	3.09232i	−0.126762	+	0.151070i	0.698930	+	0.715190i	$0.253660\pi$
$420$		0			0
$421$	−9.46503	+	26.0049i	−0.461297	+	1.26740i	0.463213	+	0.886247i	$0.346696\pi$
$421$	−9.46503	+	26.0049i	−0.461297	+	1.26740i	−0.924510	+	0.381157i	$0.875526\pi$
$422$		0			0
$423$	−6.10083	+	1.22411i	−0.296632	+	0.0595183i
$424$		0			0
$425$	−0.890123	−	5.04814i	−0.0431773	−	0.244871i
$426$		0			0
$427$	−1.10955	−	3.04846i	−0.0536948	−	0.147525i
$428$		0			0
$429$	−1.13173	−	0.289047i	−0.0546405	−	0.0139553i
$430$		0			0
$431$	12.0774			0.581746			0.290873	−	0.956762i	$-0.406054\pi$
$431$	12.0774			0.581746			0.290873	+	0.956762i	$0.406054\pi$
$432$		0			0
$433$	26.9197			1.29368			0.646838	−	0.762627i	$-0.276091\pi$
$433$	26.9197			1.29368			0.646838	+	0.762627i	$0.276091\pi$
$434$		0			0
$435$	−5.08000	−	18.1057i	−0.243568	−	0.868102i
$436$		0			0
$437$	−1.01007	−	2.77514i	−0.0483181	−	0.132753i
$438$		0			0
$439$	−1.30866	−	7.42181i	−0.0624592	−	0.354224i	−0.999980	−	0.00629488i	$-0.997996\pi$
$439$	−1.30866	−	7.42181i	−0.0624592	−	0.354224i	0.937521	−	0.347929i	$-0.113115\pi$
$440$		0			0
$441$	−7.58178	−	19.4007i	−0.361037	−	0.923841i
$442$		0			0
$443$	4.49687	−	12.3550i	0.213653	−	0.587006i	−0.785854	−	0.618412i	$-0.787776\pi$
$443$	4.49687	−	12.3550i	0.213653	−	0.587006i	0.999507	+	0.0314063i	$0.00999858\pi$
$444$		0			0
$445$	−10.4259	+	12.4251i	−0.494234	+	0.589006i
$446$		0			0
$447$	−1.49998	−	15.1004i	−0.0709465	−	0.714225i
$448$		0			0
$449$	1.92088	−	3.32707i	0.0906521	−	0.157014i	−0.817134	−	0.576448i	$-0.804438\pi$
$449$	1.92088	−	3.32707i	0.0906521	−	0.157014i	0.907786	+	0.419434i	$0.137772\pi$
$450$		0			0
$451$	−31.1318	+	17.9740i	−1.46594	+	0.846361i
$452$		0			0
$453$	18.2349	−	8.76518i	0.856748	−	0.411824i
$454$		0			0
$455$	−0.0105925	+	0.0600732i	−0.000496585	+	0.00281627i
$456$		0			0
$457$	6.71833	−	5.63735i	0.314270	−	0.263704i	−0.471984	−	0.881607i	$-0.656462\pi$
$457$	6.71833	−	5.63735i	0.314270	−	0.263704i	0.786254	+	0.617903i	$0.212018\pi$
$458$		0			0
$459$	7.08640	−	2.16901i	0.330765	−	0.101241i
$460$		0			0
$461$	8.50044	+	10.1304i	0.395905	+	0.471821i	0.926767	−	0.375637i	$-0.122576\pi$
$461$	8.50044	+	10.1304i	0.395905	+	0.471821i	−0.530862	+	0.847458i	$0.678132\pi$
$462$		0			0
$463$	4.30874	−	24.4361i	0.200244	−	1.13564i	−0.704506	−	0.709698i	$-0.748831\pi$
$463$	4.30874	−	24.4361i	0.200244	−	1.13564i	0.904750	−	0.425943i	$-0.140058\pi$
$464$		0			0
$465$	4.82455	−	7.06532i	0.223733	−	0.327646i
$466$		0			0
$467$	21.4143	−	12.3636i	0.990937	−	0.572118i	0.0853826	−	0.996348i	$-0.472789\pi$
$467$	21.4143	−	12.3636i	0.990937	−	0.572118i	0.905554	+	0.424231i	$0.139455\pi$
$468$		0			0
$469$	−1.92419	−	1.11093i	−0.0888506	−	0.0512979i
$470$		0			0
$471$	22.8180	+	10.3158i	1.05140	+	0.475325i
$472$		0			0
$473$	13.3657	+	11.2151i	0.614554	+	0.515672i
$474$		0			0
$475$	0.630376	−	1.73194i	0.0289236	−	0.0794670i
$476$		0			0
$477$	19.3743	−	0.455080i	0.887088	−	0.0208367i
$478$		0			0
$479$	3.21952	+	18.2588i	0.147104	+	0.834266i	0.965654	+	0.259831i	$0.0836669\pi$
$479$	3.21952	+	18.2588i	0.147104	+	0.834266i	−0.818550	+	0.574435i	$0.805222\pi$
$480$		0			0
$481$	1.04222	−	0.379337i	0.0475212	−	0.0172963i
$482$		0			0
$483$	1.66152	−	1.70101i	0.0756019	−	0.0773985i
$484$		0			0
$485$			4.41158i			0.200320i
$486$		0			0
$487$	−22.5854			−1.02344			−0.511721	−	0.859152i	$-0.670992\pi$
$487$	−22.5854			−1.02344			−0.511721	+	0.859152i	$0.670992\pi$
$488$		0			0
$489$	20.2330	+	19.7633i	0.914968	+	0.893728i
$490$		0			0
$491$	10.7393	+	29.5059i	0.484656	+	1.33158i	0.905460	+	0.424431i	$0.139526\pi$
$491$	10.7393	+	29.5059i	0.484656	+	1.33158i	−0.420804	+	0.907151i	$0.638252\pi$
$492$		0			0
$493$	−12.8610	+	2.26773i	−0.579228	+	0.102134i
$494$		0			0
$495$	−0.261020	−	11.1125i	−0.0117320	−	0.499470i
$496$		0			0
$497$	−1.48533	−	0.540616i	−0.0666262	−	0.0242499i
$498$		0			0
$499$	−3.98932	+	4.75429i	−0.178587	+	0.212831i	−0.847910	−	0.530140i	$-0.822139\pi$
$499$	−3.98932	+	4.75429i	−0.178587	+	0.212831i	0.669324	+	0.742971i	$0.266584\pi$
$500$		0			0
$501$	−13.6222	+	30.1316i	−0.608593	+	1.34618i
$502$		0			0
$503$	16.7341	−	28.9843i	0.746135	−	1.29234i	−0.203527	−	0.979069i	$-0.565241\pi$
$503$	16.7341	−	28.9843i	0.746135	−	1.29234i	0.949663	−	0.313275i	$-0.101426\pi$
$504$		0			0
$505$	5.97715	+	10.3527i	0.265980	+	0.460691i
$506$		0			0
$507$	−18.5283	−	12.6521i	−0.822872	−	0.561898i
$508$		0			0
$509$	15.8720	+	2.79867i	0.703516	+	0.124049i	0.513951	−	0.857819i	$-0.328181\pi$
$509$	15.8720	+	2.79867i	0.703516	+	0.124049i	0.189565	+	0.981868i	$0.439292\pi$
$510$		0			0
$511$	0.201776	−	0.169310i	0.00892603	−	0.00748983i
$512$		0			0
$513$	2.59655	+	0.598584i	0.114640	+	0.0264281i
$514$		0			0
$515$	0.343013	+	0.408787i	0.0151150	+	0.0180133i
$516$		0			0
$517$	6.38296	+	1.12549i	0.280722	+	0.0494989i
$518$		0			0
$519$	10.9449	+	22.7695i	0.480429	+	0.999472i
$520$		0			0
$521$	3.02471	+	5.23895i	0.132515	+	0.229523i	0.924645	−	0.380829i	$-0.124361\pi$
$521$	3.02471	+	5.23895i	0.132515	+	0.229523i	−0.792130	+	0.610352i	$0.791028\pi$
$522$		0			0
$523$	24.9776	+	14.4208i	1.09219	+	0.630578i	0.934160	−	0.356855i	$-0.116151\pi$
$523$	24.9776	+	14.4208i	1.09219	+	0.630578i	0.158034	+	0.987434i	$0.449484\pi$
$524$		0			0
$525$	1.47672	−	0.146688i	0.0644493	−	0.00640198i
$526$		0			0
$527$	−4.55142	−	3.81909i	−0.198263	−	0.166362i
$528$		0			0
$529$	−9.55209	−	3.47668i	−0.415308	−	0.151160i
$530$		0			0
$531$	−14.8297	+	5.79543i	−0.643552	+	0.251500i
$532$		0			0
$533$	2.44492	−	0.431105i	0.105901	−	0.0186732i
$534$		0			0
$535$	−14.1557	+	5.15226i	−0.612004	+	0.222751i
$536$		0			0
$537$	0.279379	−	0.0783866i	0.0120561	−	0.00338263i
$538$		0			0
$539$			21.6965i			0.934536i
$540$		0			0
$541$		−	13.1657i		−	0.566037i	−0.959115	−	0.283018i	$-0.908664\pi$
$541$		−	13.1657i		−	0.566037i	0.959115	−	0.283018i	$-0.0913357\pi$
$542$		0			0
$543$	5.90291	−	23.1121i	0.253318	−	0.991837i
$544$		0			0
$545$	−5.08782	+	1.85181i	−0.217938	+	0.0793230i
$546$		0			0
$547$	9.84274	−	1.73554i	0.420845	−	0.0742064i	0.0407846	−	0.999168i	$-0.487014\pi$
$547$	9.84274	−	1.73554i	0.420845	−	0.0742064i	0.380061	+	0.924962i	$0.375903\pi$
$548$		0			0
$549$	−8.03151	−	40.0281i	−0.342777	−	1.70836i
$550$		0			0
$551$	−4.41241	−	1.60599i	−0.187975	−	0.0684173i
$552$		0			0
$553$	2.27651	+	1.91022i	0.0968070	+	0.0812308i
$554$		0			0
$555$	6.15496	+	8.57412i	0.261263	+	0.363951i
$556$		0			0
$557$	7.31847	+	4.22532i	0.310093	+	0.179032i	0.646968	−	0.762517i	$-0.276037\pi$
$557$	7.31847	+	4.22532i	0.310093	+	0.179032i	−0.336875	+	0.941549i	$0.609370\pi$
$558$		0			0
$559$	−0.602485	−	1.04353i	−0.0254824	−	0.0441368i
$560$		0			0
$561$	−7.69739	−	0.582447i	−0.324984	−	0.0245909i
$562$		0			0
$563$	25.3901	+	4.47697i	1.07007	+	0.188682i	0.680819	−	0.732451i	$-0.261624\pi$
$563$	25.3901	+	4.47697i	1.07007	+	0.188682i	0.389248	+	0.921133i	$0.372735\pi$
$564$		0			0
$565$	2.06272	+	2.45825i	0.0867791	+	0.103419i
$566$		0			0
$567$	0.471349	+	2.09305i	0.0197948	+	0.0878999i
$568$		0			0
$569$	−8.71855	+	7.31573i	−0.365500	+	0.306691i	−0.806979	−	0.590581i	$-0.798899\pi$
$569$	−8.71855	+	7.31573i	−0.365500	+	0.306691i	0.441478	+	0.897272i	$0.354454\pi$
$570$		0			0
$571$	−26.6143	−	4.69281i	−1.11377	−	0.196388i	−0.413667	−	0.910428i	$-0.635752\pi$
$571$	−26.6143	−	4.69281i	−1.11377	−	0.196388i	−0.700105	+	0.714040i	$0.746863\pi$
$572$		0			0
$573$	3.29688	−	43.5703i	0.137729	−	1.82017i
$574$		0			0
$575$	−10.3490	−	17.9251i	−0.431585	−	0.747527i
$576$		0			0
$577$	12.3559	−	21.4010i	0.514381	−	0.890934i	−0.485480	−	0.874248i	$-0.661355\pi$
$577$	12.3559	−	21.4010i	0.514381	−	0.890934i	0.999861	−	0.0166860i	$-0.00531156\pi$
$578$		0			0
$579$	15.2335	+	21.2209i	0.633082	+	0.881910i
$580$		0			0
$581$	0.0741883	−	0.0884141i	0.00307785	−	0.00366804i
$582$		0			0
$583$	−18.9689	−	6.90413i	−0.785613	−	0.285940i
$584$		0			0
$585$	−0.245544	+	0.727334i	−0.0101520	+	0.0300716i
$586$		0			0
$587$	23.8213	−	4.20034i	0.983211	−	0.173367i	0.341140	−	0.940012i	$-0.389187\pi$
$587$	23.8213	−	4.20034i	0.983211	−	0.173367i	0.642070	+	0.766646i	$0.278076\pi$
$588$		0			0
$589$	−0.730655	−	2.00746i	−0.0301061	−	0.0827159i
$590$		0			0
$591$	1.12024	−	4.38618i	0.0460806	−	0.180423i
$592$		0			0
$593$	−17.3047			−0.710619			−0.355309	−	0.934749i	$-0.615624\pi$
$593$	−17.3047			−0.710619			−0.355309	+	0.934749i	$0.615624\pi$
$594$		0			0
$595$			0.403132i			0.0165268i
$596$		0			0
$597$	−4.20642	−	14.9921i	−0.172157	−	0.613587i
$598$		0			0
$599$	27.4599	−	9.99460i	1.12198	−	0.408368i	0.286607	−	0.958048i	$-0.407472\pi$
$599$	27.4599	−	9.99460i	1.12198	−	0.408368i	0.835375	+	0.549680i	$0.185250\pi$
$600$		0			0
$601$	−2.89901	−	16.4411i	−0.118253	−	0.670648i	−0.985088	−	0.172052i	$-0.944960\pi$
$601$	−2.89901	−	16.4411i	−0.118253	−	0.670648i	0.866835	−	0.498596i	$-0.166151\pi$
$602$		0			0
$603$	−21.8358	−	17.4653i	−0.889221	−	0.711240i
$604$		0			0
$605$	0.500901	−	1.37621i	0.0203645	−	0.0559511i
$606$		0			0
$607$	12.1597	+	10.2032i	0.493546	+	0.414134i	0.855295	−	0.518141i	$-0.173376\pi$
$607$	12.1597	+	10.2032i	0.493546	+	0.414134i	−0.361749	+	0.932276i	$0.617820\pi$
$608$		0			0
$609$	−0.373711	−	3.76218i	−0.0151435	−	0.152451i
$610$		0			0
$611$	−0.387651	−	0.223810i	−0.0156827	−	0.00905439i
$612$		0			0
$613$	−32.1513	+	18.5625i	−1.29858	+	0.749734i	−0.980158	−	0.198216i	$-0.936485\pi$
$613$	−32.1513	+	18.5625i	−1.29858	+	0.749734i	−0.318419	+	0.947950i	$0.603152\pi$
$614$		0			0
$615$	10.2353	+	21.2932i	0.412726	+	0.858625i
$616$		0			0
$617$	−2.58978	+	14.6874i	−0.104261	+	0.591292i	0.887252	+	0.461285i	$0.152611\pi$
$617$	−2.58978	+	14.6874i	−0.104261	+	0.591292i	−0.991513	+	0.130008i	$0.958500\pi$
$618$		0			0
$619$	14.3227	+	17.0691i	0.575677	+	0.686065i	0.972786	−	0.231707i	$-0.0744309\pi$
$619$	14.3227	+	17.0691i	0.575677	+	0.686065i	−0.397109	+	0.917771i	$0.629986\pi$
$620$		0			0
$621$	23.8928	−	18.0165i	0.958784	−	0.722977i
$622$		0			0
$623$	−2.49805	+	2.09611i	−0.100082	+	0.0839790i
$624$		0			0
$625$	1.02244	−	5.79855i	0.0408976	−	0.231942i
$626$		0			0
$627$	−2.29215	−	1.56519i	−0.0915395	−	0.0625078i
$628$		0			0
$629$	6.34779	−	3.66490i	0.253103	−	0.146129i
$630$		0			0
$631$	−16.9281	+	29.3204i	−0.673898	+	1.16723i	0.302892	+	0.953025i	$0.402048\pi$
$631$	−16.9281	+	29.3204i	−0.673898	+	1.16723i	−0.976790	+	0.214201i	$0.931285\pi$
$632$		0			0
$633$	−18.6938	−	8.45128i	−0.743013	−	0.335908i
$634$		0			0
$635$	13.0894	−	15.5994i	0.519438	−	0.619042i
$636$		0			0
$637$	0.512485	−	1.40804i	0.0203054	−	0.0557886i
$638$		0			0
$639$	−17.4558	−	9.53873i	−0.690541	−	0.377346i
$640$		0			0
$641$	4.34643	+	24.6498i	0.171674	+	0.973609i	0.941914	+	0.335855i	$0.109025\pi$
$641$	4.34643	+	24.6498i	0.171674	+	0.973609i	−0.770240	+	0.637754i	$0.779864\pi$
$642$		0			0
$643$	1.25058	+	3.43594i	0.0493181	+	0.135500i	0.961906	−	0.273380i	$-0.0881416\pi$
$643$	1.25058	+	3.43594i	0.0493181	+	0.135500i	−0.912588	+	0.408880i	$0.865919\pi$
$644$		0			0
$645$	8.01250	−	8.20291i	0.315492	−	0.322989i
$646$		0			0
$647$	−1.80647			−0.0710199			−0.0355099	−	0.999369i	$-0.511306\pi$
$647$	−1.80647			−0.0710199			−0.0355099	+	0.999369i	$0.511306\pi$
$648$		0			0
$649$	16.5846			0.651003
$650$		0			0
$651$	1.20190	−	1.23046i	0.0471061	−	0.0482256i
$652$		0			0
$653$	3.15885	+	8.67887i	0.123615	+	0.339630i	0.986029	−	0.166574i	$-0.0532704\pi$
$653$	3.15885	+	8.67887i	0.123615	+	0.339630i	−0.862414	+	0.506204i	$0.831048\pi$
$654$		0			0
$655$	3.32886	+	18.8789i	0.130069	+	0.737660i
$656$		0			0
$657$	2.83098	−	1.72435i	0.110447	−	0.0672733i
$658$		0			0
$659$	0.0418647	−	0.115022i	0.00163082	−	0.00448063i	−0.938875	−	0.344259i	$-0.888130\pi$
$659$	0.0418647	−	0.115022i	0.00163082	−	0.00448063i	0.940505	+	0.339779i	$0.110352\pi$
$660$		0			0
$661$	14.2244	−	16.9520i	0.553266	−	0.659357i	−0.414841	−	0.909894i	$-0.636163\pi$
$661$	14.2244	−	16.9520i	0.553266	−	0.659357i	0.968107	+	0.250537i	$0.0806073\pi$
$662$		0			0
$663$	0.485780	+	0.219616i	0.0188661	+	0.00852918i
$664$		0			0
$665$	−0.0724746	+	0.125530i	−0.00281044	+	0.00486783i
$666$		0			0
$667$	−45.6671	+	26.3659i	−1.76824	+	1.02089i
$668$		0			0
$669$	25.7628	+	17.5921i	0.996047	+	0.680151i
$670$		0			0
$671$	−7.38443	+	41.8792i	−0.285073	+	1.61673i
$672$		0			0
$673$	−7.84571	+	6.58333i	−0.302430	+	0.253769i	−0.781355	−	0.624087i	$-0.785471\pi$
$673$	−7.84571	+	6.58333i	−0.302430	+	0.253769i	0.478925	+	0.877856i	$0.341027\pi$
$674$		0			0
$675$	18.6502	+	0.971427i	0.717846	+	0.0373902i
$676$		0			0
$677$	14.8248	+	17.6675i	0.569762	+	0.679016i	0.971582	−	0.236703i	$-0.0760667\pi$
$677$	14.8248	+	17.6675i	0.569762	+	0.679016i	−0.401820	+	0.915719i	$0.631622\pi$
$678$		0			0
$679$	−0.154016	+	0.873469i	−0.00591060	+	0.0335207i
$680$		0			0
$681$	−3.18357	−	6.62303i	−0.121995	−	0.253795i
$682$		0			0
$683$	6.81614	−	3.93530i	0.260812	−	0.150580i	−0.363893	−	0.931441i	$-0.618553\pi$
$683$	6.81614	−	3.93530i	0.260812	−	0.150580i	0.624705	+	0.780861i	$0.285219\pi$
$684$		0			0
$685$	15.3394	+	8.85621i	0.586089	+	0.338378i
$686$		0			0
$687$	0.997245	+	10.0394i	0.0380473	+	0.383026i
$688$		0			0
$689$	1.06795	+	0.896115i	0.0406856	+	0.0341392i
$690$		0			0
$691$	0.592529	−	1.62796i	0.0225408	−	0.0619305i	−0.927912	−	0.372800i	$-0.878398\pi$
$691$	0.592529	−	1.62796i	0.0225408	−	0.0619305i	0.950453	+	0.310869i	$0.100620\pi$
$692$		0			0
$693$	0.336277	−	2.20933i	0.0127741	−	0.0839254i
$694$		0			0
$695$	−4.15919	−	23.5880i	−0.157767	−	0.894742i
$696$		0			0
$697$	15.4176	−	5.61155i	0.583984	−	0.212553i
$698$		0			0
$699$	6.43694	+	22.9420i	0.243467	+	0.867745i
$700$		0			0
$701$		−	30.8677i		−	1.16586i	−0.812524	−	0.582928i	$-0.801907\pi$
$701$		−	30.8677i		−	1.16586i	0.812524	−	0.582928i	$-0.198093\pi$
$702$		0			0
$703$	2.63548			0.0993991
$704$		0			0
$705$	1.05410	−	4.12719i	0.0396996	−	0.155439i
$706$		0			0
$707$	0.822011	+	2.25846i	0.0309149	+	0.0849381i
$708$		0			0
$709$	−37.7208	+	6.65119i	−1.41663	+	0.249791i	−0.828960	−	0.559307i	$-0.811067\pi$
$709$	−37.7208	+	6.65119i	−1.41663	+	0.249791i	−0.587674	+	0.809098i	$0.699956\pi$
$710$		0			0
$711$	24.7056	+	28.0767i	0.926532	+	1.05296i
$712$		0			0
$713$	−22.5439	−	8.20531i	−0.844276	−	0.307291i
$714$		0			0
$715$	0.513984	−	0.612542i	0.0192219	−	0.0229078i
$716$		0			0
$717$	−28.6304	−	39.8833i	−1.06922	−	1.48947i
$718$		0			0
$719$	−18.7935	+	32.5513i	−0.700880	+	1.21396i	0.267278	+	0.963619i	$0.413876\pi$
$719$	−18.7935	+	32.5513i	−0.700880	+	1.21396i	−0.968158	+	0.250340i	$0.919457\pi$
$720$		0			0
$721$	0.0536433	+	0.0929129i	0.00199778	+	0.00346026i
$722$		0			0
$723$	2.50181	−	33.0629i	0.0930432	−	1.22962i
$724$		0			0
$725$	−32.4095	−	5.71468i	−1.20366	−	0.212238i
$726$		0			0
$727$	−36.9916	+	31.0397i	−1.37194	+	1.15120i	−0.399857	+	0.916578i	$0.630940\pi$
$727$	−36.9916	+	31.0397i	−1.37194	+	1.15120i	−0.972087	+	0.234620i	$0.924615\pi$
$728$		0			0
$729$	1.90067	+	26.9330i	0.0703953	+	0.997519i
$730$		0			0
$731$	−5.11873	−	6.10026i	−0.189323	−	0.225626i
$732$		0			0
$733$	11.7017	+	2.06332i	0.432212	+	0.0762106i	0.385522	−	0.922699i	$-0.374022\pi$
$733$	11.7017	+	2.06332i	0.432212	+	0.0762106i	0.0466902	+	0.998909i	$0.485133\pi$
$734$		0			0
$735$	14.2186	+	1.07589i	0.524461	+	0.0396850i
$736$		0			0
$737$	14.5626	+	25.2232i	0.536421	+	0.929108i
$738$		0			0
$739$	5.18963	+	2.99624i	0.190904	+	0.110218i	0.592406	−	0.805640i	$-0.298178\pi$
$739$	5.18963	+	2.99624i	0.190904	+	0.110218i	−0.401502	+	0.915858i	$0.631512\pi$
$740$		0			0
$741$	0.111783	+	0.155718i	0.00410644	+	0.00572045i
$742$		0			0
$743$	−15.4252	−	12.9432i	−0.565894	−	0.474841i	0.314387	−	0.949295i	$-0.398201\pi$
$743$	−15.4252	−	12.9432i	−0.565894	−	0.474841i	−0.880280	+	0.474454i	$0.842646\pi$
$744$		0			0
$745$	9.76167	+	3.55296i	0.357640	+	0.130170i
$746$		0			0
$747$	1.09043	−	0.959505i	0.0398968	−	0.0351064i
$748$		0			0
$749$	−2.98263	+	0.525918i	−0.108983	+	0.0192166i
$750$		0			0
$751$	6.57228	−	2.39211i	0.239826	−	0.0872894i	−0.219311	−	0.975655i	$-0.570381\pi$
$751$	6.57228	−	2.39211i	0.239826	−	0.0872894i	0.459137	+	0.888366i	$0.348159\pi$
$752$		0			0
$753$	−0.584044	+	2.28676i	−0.0212837	+	0.0833340i
$754$		0			0
$755$			13.8503i			0.504063i
$756$		0			0
$757$		−	45.7941i		−	1.66441i	−0.554465	−	0.832207i	$-0.687077\pi$
$757$		−	45.7941i		−	1.66441i	0.554465	−	0.832207i	$-0.312923\pi$
$758$		0			0
$759$	−30.0109	+	8.42031i	−1.08933	+	0.305638i
$760$		0			0
$761$	4.48572	−	1.63267i	0.162607	−	0.0591842i	−0.259434	−	0.965761i	$-0.583536\pi$
$761$	4.48572	−	1.63267i	0.162607	−	0.0591842i	0.422041	+	0.906577i	$0.361314\pi$
$762$		0			0
$763$	−1.07201	+	0.189024i	−0.0388094	+	0.00684314i
$764$		0			0
$765$	−0.763401	+	5.01552i	−0.0276008	+	0.181336i
$766$		0			0
$767$	−1.07629	−	0.391738i	−0.0388627	−	0.0141449i
$768$		0			0
$769$	−7.11042	−	5.96635i	−0.256408	−	0.215152i	0.505518	−	0.862816i	$-0.331302\pi$
$769$	−7.11042	−	5.96635i	−0.256408	−	0.215152i	−0.761926	+	0.647664i	$0.775746\pi$
$770$		0			0
$771$	−36.3102	+	3.60682i	−1.30768	+	0.129897i
$772$		0			0
$773$	28.1267	+	16.2390i	1.01165	+	0.584075i	0.911674	−	0.410915i	$-0.134791\pi$
$773$	28.1267	+	16.2390i	1.01165	+	0.584075i	0.0999739	+	0.994990i	$0.468124\pi$
$774$		0			0
$775$	−7.48621	−	12.9665i	−0.268913	−	0.465770i
$776$		0			0
$777$	0.919310	+	1.91251i	0.0329801	+	0.0686109i
$778$		0			0
$779$	5.80966	+	1.02440i	0.208153	+	0.0367030i
$780$		0			0
$781$	13.3186	+	15.8725i	0.476576	+	0.567961i
$782$		0			0
$783$	2.47487	−	47.5144i	0.0884446	−	1.69803i
$784$		0			0
$785$	−13.1320	+	11.0191i	−0.468701	+	0.393287i
$786$		0			0
$787$	−5.13648	−	0.905700i	−0.183096	−	0.0322847i	0.0813484	−	0.996686i	$-0.474077\pi$
$787$	−5.13648	−	0.905700i	−0.183096	−	0.0322847i	−0.264444	+	0.964401i	$0.585188\pi$
$788$		0			0
$789$	−10.2090	−	6.97124i	−0.363451	−	0.248183i
$790$		0			0
$791$	0.322585	+	0.558733i	0.0114698	+	0.0198663i
$792$		0			0
$793$	1.46844	−	2.54341i	0.0521458	−	0.0903192i
$794$		0			0
$795$	−5.46518	+	12.0887i	−0.193830	+	0.428743i
$796$		0			0
$797$	−29.4836	+	35.1372i	−1.04436	+	1.24462i	−0.0754670	+	0.997148i	$0.524045\pi$
$797$	−29.4836	+	35.1372i	−1.04436	+	1.24462i	−0.968895	+	0.247473i	$0.920400\pi$
$798$		0			0
$799$	−2.77980	−	1.01177i	−0.0983424	−	0.0357937i
$800$		0			0
$801$	−35.0485	+	21.3480i	−1.23838	+	0.754296i
$802$		0			0
$803$	−3.40032	+	0.599568i	−0.119995	+	0.0211583i
$804$		0			0
$805$	0.556737	+	1.52962i	0.0196224	+	0.0539121i
$806$		0			0
$807$	3.33010	+	3.25280i	0.117225	+	0.114504i
$808$		0			0
$809$	0.0690265			0.00242684			0.00121342	−	0.999999i	$-0.499614\pi$
$809$	0.0690265			0.00242684			0.00121342	+	0.999999i	$0.499614\pi$
$810$		0			0
$811$		−	13.7552i		−	0.483012i	−0.970399	−	0.241506i	$-0.922359\pi$
$811$		−	13.7552i		−	0.483012i	0.970399	−	0.241506i	$-0.0776414\pi$
$812$		0			0
$813$	−33.7561	+	34.5583i	−1.18388	+	1.21201i
$814$		0			0
$815$	−18.1944	+	6.62222i	−0.637322	+	0.231966i
$816$		0			0
$817$	−0.497202	−	2.81977i	−0.0173949	−	0.0986513i
$818$		0			0
$819$	−0.0740090	+	0.135436i	−0.00258608	+	0.00473251i
$820$		0			0
$821$	−5.93627	+	16.3098i	−0.207177	+	0.569215i	−0.999145	−	0.0413482i	$-0.986835\pi$
$821$	−5.93627	+	16.3098i	−0.207177	+	0.569215i	0.791967	+	0.610563i	$0.209057\pi$
$822$		0			0
$823$	−19.0763	−	16.0069i	−0.664956	−	0.557965i	0.246611	−	0.969114i	$-0.420683\pi$
$823$	−19.0763	−	16.0069i	−0.664956	−	0.557965i	−0.911568	+	0.411150i	$0.865127\pi$
$824$		0			0
$825$	−17.7256	−	8.01354i	−0.617125	−	0.278996i
$826$		0			0
$827$	−15.0563	−	8.69274i	−0.523558	−	0.302276i	0.214831	−	0.976651i	$-0.431080\pi$
$827$	−15.0563	−	8.69274i	−0.523558	−	0.302276i	−0.738389	+	0.674375i	$0.764413\pi$
$828$		0			0
$829$	−9.68727	+	5.59295i	−0.336453	+	0.194251i	−0.658702	−	0.752404i	$-0.728894\pi$
$829$	−9.68727	+	5.59295i	−0.336453	+	0.194251i	0.322250	+	0.946655i	$0.395561\pi$
$830$		0			0
$831$	−8.96096	+	13.1229i	−0.310852	+	0.455227i
$832$		0			0
$833$	1.71956	−	9.75213i	0.0595793	−	0.337891i
$834$		0			0
$835$	−14.5509	−	17.3411i	−0.503554	−	0.600112i
$836$		0			0
$837$	17.2834	−	13.0326i	0.597400	−	0.450473i
$838$		0			0
$839$	33.9566	−	28.4930i	1.17231	−	0.983687i	0.172313	−	0.985042i	$-0.444876\pi$
$839$	33.9566	−	28.4930i	1.17231	−	0.983687i	0.999999	+	0.00135535i	$0.000431423\pi$
$840$		0			0
$841$	−9.52327	+	54.0092i	−0.328389	+	1.86238i
$842$		0			0
$843$	−3.97098	+	1.90878i	−0.136768	+	0.0657418i
$844$		0			0
$845$	13.3013	−	7.67949i	0.457578	−	0.264183i
$846$		0			0
$847$	0.147222	−	0.254996i	0.00505860	−	0.00876175i
$848$		0			0
$849$	−2.19099	−	22.0569i	−0.0751945	−	0.756991i
$850$		0			0
$851$	19.0244	−	22.6724i	0.652147	−	0.777199i
$852$		0			0
$853$	−8.35486	+	22.9548i	−0.286065	+	0.785957i	0.710542	+	0.703654i	$0.248450\pi$
$853$	−8.35486	+	22.9548i	−0.286065	+	0.785957i	−0.996607	+	0.0823028i	$0.973773\pi$
$854$		0			0
$855$	−1.13940	+	1.42452i	−0.0389665	+	0.0487175i
$856$		0			0
$857$	5.82802	+	33.0524i	0.199081	+	1.12905i	0.906485	+	0.422237i	$0.138755\pi$
$857$	5.82802	+	33.0524i	0.199081	+	1.12905i	−0.707404	+	0.706810i	$0.750134\pi$
$858$		0			0
$859$	−9.67956	−	26.5944i	−0.330262	−	0.907389i	−0.988043	−	0.154179i	$-0.950727\pi$
$859$	−9.67956	−	26.5944i	−0.330262	−	0.907389i	0.657780	−	0.753210i	$-0.271495\pi$
$860$		0			0
$861$	1.28314	+	4.57327i	0.0437294	+	0.155857i
$862$		0			0
$863$	−19.9690			−0.679754			−0.339877	−	0.940470i	$-0.610385\pi$
$863$	−19.9690			−0.679754			−0.339877	+	0.940470i	$0.610385\pi$
$864$		0			0
$865$	−17.2946			−0.588034
$866$		0			0
$867$	−25.1154	−	6.41455i	−0.852965	−	0.217850i
$868$		0			0
$869$	−13.3236	−	36.6062i	−0.451971	−	1.24178i
$870$		0			0
$871$	−0.349284	−	1.98089i	−0.0118350	−	0.0671198i
$872$		0			0
$873$	−3.57024	+	10.5755i	−0.120834	+	0.357926i
$874$		0			0
$875$	−0.830825	+	2.28267i	−0.0280870	+	0.0771684i
$876$		0			0
$877$	−27.9807	+	33.3462i	−0.944843	+	1.12602i	0.0470437	+	0.998893i	$0.485020\pi$
$877$	−27.9807	+	33.3462i	−0.944843	+	1.12602i	−0.991886	+	0.127127i	$0.959424\pi$
$878$		0			0
$879$	−26.7950	+	19.2349i	−0.903774	+	0.648777i
$880$		0			0
$881$	−5.97531	+	10.3495i	−0.201313	+	0.348685i	−0.948952	−	0.315421i	$-0.897854\pi$
$881$	−5.97531	+	10.3495i	−0.201313	+	0.348685i	0.747638	+	0.664106i	$0.231188\pi$
$882$		0			0
$883$	−12.4134	+	7.16688i	−0.417744	+	0.241185i	−0.694112	−	0.719867i	$-0.744203\pi$
$883$	−12.4134	+	7.16688i	−0.417744	+	0.241185i	0.276367	+	0.961052i	$0.410869\pi$
$884$		0			0
$885$	0.822403	−	10.8685i	0.0276448	−	0.365342i
$886$		0			0
$887$	−1.08261	+	6.13976i	−0.0363503	+	0.206153i	−0.997574	−	0.0696179i	$-0.977822\pi$
$887$	−1.08261	+	6.13976i	−0.0363503	+	0.206153i	0.961223	+	0.275771i	$0.0889331\pi$
$888$		0			0
$889$	3.13624	−	2.63161i	0.105186	−	0.0882615i
$890$		0			0
$891$	8.36749	−	26.8503i	0.280321	−	0.899518i
$892$		0			0
$893$	−0.683697	−	0.814799i	−0.0228791	−	0.0272662i
$894$		0			0
$895$	−0.0344934	+	0.195622i	−0.00115299	+	0.00653891i
$896$		0			0
$897$	2.14651	+	0.162423i	0.0716699	+	0.00542313i
$898$		0			0
$899$	−33.0343	+	19.0723i	−1.10175	+	0.636098i
$900$		0			0
$901$	7.97894	+	4.60664i	0.265817	+	0.153470i
$902$		0			0
$903$	1.87281	−	1.34440i	0.0623232	−	0.0447389i
$904$		0			0
$905$	12.5093	+	10.4966i	0.415823	+	0.348917i
$906$		0			0
$907$	7.56961	−	20.7973i	0.251345	−	0.690564i	−0.748286	−	0.663377i	$-0.769123\pi$
$907$	7.56961	−	20.7973i	0.251345	−	0.690564i	0.999630	−	0.0271874i	$-0.00865508\pi$
$908$		0			0
$909$	5.95017	+	29.6549i	0.197355	+	0.983592i
$910$		0			0
$911$	5.43254	+	30.8094i	0.179988	+	1.02076i	0.932228	+	0.361873i	$0.117862\pi$
$911$	5.43254	+	30.8094i	0.179988	+	1.02076i	−0.752240	+	0.658890i	$0.771026\pi$
$912$		0			0
$913$	−1.42169	+	0.517455i	−0.0470512	+	0.0171252i
$914$		0			0
$915$	27.0789	+	6.91603i	0.895201	+	0.228637i
$916$		0			0
$917$			3.85414i			0.127275i
$918$		0			0
$919$	15.8895			0.524145			0.262073	−	0.965048i	$-0.415594\pi$
$919$	15.8895			0.524145			0.262073	+	0.965048i	$0.415594\pi$
$920$		0			0
$921$	−19.5789	+	5.49334i	−0.645146	+	0.181012i
$922$		0			0
$923$	−0.489419	−	1.34467i	−0.0161094	−	0.0442603i
$924$		0			0
$925$	18.1904	−	3.20747i	0.598098	−	0.105461i
$926$		0			0
$927$	0.491449	+	1.25755i	0.0161413	+	0.0413032i
$928$		0			0
$929$	−7.73697	−	2.81603i	−0.253842	−	0.0923908i	0.211965	−	0.977277i	$-0.432014\pi$
$929$	−7.73697	−	2.81603i	−0.253842	−	0.0923908i	−0.465807	+	0.884886i	$0.654236\pi$
$930$		0			0
$931$	2.28867	−	2.72753i	0.0750082	−	0.0893913i
$932$		0			0
$933$	−5.17750	+	0.514299i	−0.169504	+	0.0168374i
$934$		0			0
$935$	2.64223	−	4.57648i	0.0864102	−	0.149667i
$936$		0			0
$937$	−20.2128	−	35.0096i	−0.660323	−	1.14371i	−0.980531	−	0.196366i	$-0.937086\pi$
$937$	−20.2128	−	35.0096i	−0.660323	−	1.14371i	0.320207	−	0.947348i	$-0.396247\pi$
$938$		0			0
$939$	48.8134	−	23.4637i	1.59296	−	0.765710i
$940$		0			0
$941$	3.90263	+	0.688139i	0.127222	+	0.0224327i	0.236897	−	0.971535i	$-0.423870\pi$
$941$	3.90263	+	0.688139i	0.127222	+	0.0224327i	−0.109674	+	0.993968i	$0.534981\pi$
$942$		0			0
$943$	50.7500	−	42.5843i	1.65265	−	1.38674i
$944$		0			0
$945$	−1.43118	−	0.329932i	−0.0465564	−	0.0107327i
$946$		0			0
$947$	−10.2845	−	12.2566i	−0.334203	−	0.398287i	0.572605	−	0.819831i	$-0.305933\pi$
$947$	−10.2845	−	12.2566i	−0.334203	−	0.398287i	−0.906808	+	0.421544i	$0.861488\pi$
$948$		0			0
$949$	0.234833	+	0.0414073i	0.00762299	+	0.00134414i
$950$		0			0
$951$	−15.1502	+	22.1867i	−0.491278	+	0.719453i
$952$		0			0
$953$	−2.31775	−	4.01447i	−0.0750794	−	0.130041i	0.826041	−	0.563609i	$-0.190588\pi$
$953$	−2.31775	−	4.01447i	−0.0750794	−	0.130041i	−0.901121	+	0.433568i	$0.857254\pi$
$954$		0			0
$955$	25.9047	+	14.9561i	0.838255	+	0.483967i
$956$		0			0
$957$	−20.4158	+	45.1588i	−0.659949	+	1.45978i
$958$		0			0
$959$	2.72793	+	2.28901i	0.0880896	+	0.0739159i
$960$		0			0
$961$	12.8228	+	4.66713i	0.413640	+	0.150553i
$962$		0			0
$963$	−38.1039	+	0.895016i	−1.22788	+	0.0288415i
$964$		0			0
$965$	−17.6110	+	3.10529i	−0.566917	+	0.0999628i
$966$		0			0
$967$	−12.2913	+	4.47367i	−0.395262	+	0.143864i	−0.532001	−	0.846743i	$-0.678560\pi$
$967$	−12.2913	+	4.47367i	−0.395262	+	0.143864i	0.136740	+	0.990607i	$0.456338\pi$
$968$		0			0
$969$	0.906221	+	0.885185i	0.0291120	+	0.0284362i
$970$		0			0
$971$			39.8563i			1.27905i	0.768771	+	0.639524i	$0.220869\pi$
$971$			39.8563i			1.27905i	−0.768771	+	0.639524i	$0.779131\pi$
$972$		0			0
$973$		−	4.81549i		−	0.154378i
$974$		0			0
$975$	0.961052	+	0.938744i	0.0307783	+	0.0300639i
$976$		0			0
$977$	−30.2576	+	11.0129i	−0.968026	+	0.352333i	−0.777174	−	0.629286i	$-0.783347\pi$
$977$	−30.2576	+	11.0129i	−0.968026	+	0.352333i	−0.190852	+	0.981619i	$0.561125\pi$
$978$		0			0
$979$	42.0970	−	7.42285i	1.34543	−	0.237235i
$980$		0			0
$981$	−13.6952	+	0.321685i	−0.437255	+	0.0102706i
$982$		0			0
$983$	10.6134	+	3.86297i	0.338516	+	0.123210i	0.505684	−	0.862719i	$-0.331240\pi$
$983$	10.6134	+	3.86297i	0.338516	+	0.123210i	−0.167168	+	0.985928i	$0.553462\pi$
$984$		0			0
$985$	2.37399	+	1.99202i	0.0756417	+	0.0634709i
$986$		0			0
$987$	0.352793	−	0.780362i	0.0112295	−	0.0248392i
$988$		0			0
$989$	−27.8468	−	16.0774i	−0.885478	−	0.511231i
$990$		0			0
$991$	3.48999	+	6.04483i	0.110863	+	0.192020i	0.916118	−	0.400908i	$-0.131305\pi$
$991$	3.48999	+	6.04483i	0.110863	+	0.192020i	−0.805255	+	0.592928i	$0.797972\pi$
$992$		0			0
$993$	16.6986	−	24.4542i	0.529913	−	0.776031i
$994$		0			0
$995$	10.4975	+	1.85100i	0.332794	+	0.0586806i
$996$		0			0
$997$	20.4979	+	24.4285i	0.649176	+	0.773658i	0.985790	−	0.167985i	$-0.0537261\pi$
$997$	20.4979	+	24.4285i	0.649176	+	0.773658i	−0.336614	+	0.941643i	$0.609282\pi$
$998$		0			0
$999$	7.81581	+	25.5351i	0.247281	+	0.807895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.49.9		204
4.3	odd	2		216.2.t.a.157.8	✓	204
8.3	odd	2		216.2.t.a.157.23	yes	204
8.5	even	2	inner	864.2.bf.a.49.26		204
12.11	even	2		648.2.t.a.37.27		204
24.11	even	2		648.2.t.a.37.12		204
27.16	even	9	inner	864.2.bf.a.529.26		204
108.11	even	18		648.2.t.a.613.12		204
108.43	odd	18		216.2.t.a.205.23	yes	204
216.11	even	18		648.2.t.a.613.27		204
216.43	odd	18		216.2.t.a.205.8	yes	204
216.205	even	18	inner	864.2.bf.a.529.9		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.8	✓	204	4.3	odd	2
216.2.t.a.157.23	yes	204	8.3	odd	2
216.2.t.a.205.8	yes	204	216.43	odd	18
216.2.t.a.205.23	yes	204	108.43	odd	18
648.2.t.a.37.12		204	24.11	even	2
648.2.t.a.37.27		204	12.11	even	2
648.2.t.a.613.12		204	108.11	even	18
648.2.t.a.613.27		204	216.11	even	18
864.2.bf.a.49.9		204	1.1	even	1	trivial
864.2.bf.a.49.26		204	8.5	even	2	inner
864.2.bf.a.529.9		204	216.205	even	18	inner
864.2.bf.a.529.26		204	27.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.21028 + 1.23904i) q^{3} +(-0.405536 - 1.11420i) q^{5} +(-0.0413952 - 0.234764i) q^{7} +(-0.0704471 - 2.99917i) q^{9} +O(q^{10})\)	\(q+(-1.21028 + 1.23904i) q^{3} +(-0.405536 - 1.11420i) q^{5} +(-0.0413952 - 0.234764i) q^{7} +(-0.0704471 - 2.99917i) q^{9} +(-1.06877 + 2.93642i) q^{11} +(0.138720 - 0.165320i) q^{13} +(1.87135 + 0.846019i) q^{15} +(0.713116 - 1.23515i) q^{17} +(0.444108 - 0.256406i) q^{19} +(0.340982 + 0.232839i) q^{21} +(1.00003 - 5.67143i) q^{23} +(2.75324 - 2.31024i) q^{25} +(3.80136 + 3.54255i) q^{27} +(-5.88571 - 7.01432i) q^{29} +(0.723390 - 4.10255i) q^{31} +(-2.34484 - 4.87814i) q^{33} +(-0.244787 + 0.141328i) q^{35} +(4.45075 + 2.56964i) q^{37} +(0.0369484 + 0.371963i) q^{39} +(8.81242 + 7.39450i) q^{41} +(1.90966 - 5.24675i) q^{43} +(-3.31311 + 1.29477i) q^{45} +(-0.360171 - 2.04263i) q^{47} +(6.52445 - 2.37470i) q^{49} +(0.667336 + 2.37846i) q^{51} +6.45988i q^{53} +3.70519 q^{55} +(-0.219797 + 0.860591i) q^{57} +(-1.81520 - 4.98722i) q^{59} +(13.4019 - 2.36311i) q^{61} +(-0.701181 + 0.140690i) q^{63} +(-0.240456 - 0.0875188i) q^{65} +(5.99107 - 7.13987i) q^{67} +(5.81682 + 8.10308i) q^{69} +(3.31534 - 5.74233i) q^{71} +(0.552466 + 0.956899i) q^{73} +(-0.469703 + 6.20741i) q^{75} +(0.733607 + 0.129355i) q^{77} +(-9.54970 + 8.01315i) q^{79} +(-8.99007 + 0.422566i) q^{81} +(0.311211 + 0.370887i) q^{83} +(-1.66540 - 0.293656i) q^{85} +(15.8144 + 1.19665i) q^{87} +(-6.83971 - 11.8467i) q^{89} +(-0.0445535 - 0.0257230i) q^{91} +(4.20772 + 5.86154i) q^{93} +(-0.465790 - 0.390844i) q^{95} +(-3.49625 - 1.27253i) q^{97} +(8.88213 + 2.99856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 204 * q + 12 * q^7 - 12 * q^9	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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