LMFDB - Embedded newform 864.2.bf.a.49.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(49,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	864.49
Dual form			864.2.bf.a.529.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40645 - 1.01088i) q^{3} +(-1.34230 - 3.68793i) q^{5} +(0.499959 + 2.83541i) q^{7} +(0.956226 + 2.84352i) q^{9} +(-0.996019 + 2.73654i) q^{11} +(-2.55767 + 3.04812i) q^{13} +(-1.84019 + 6.54382i) q^{15} +(2.48745 - 4.30839i) q^{17} +(-1.78004 + 1.02771i) q^{19} +(2.16310 - 4.49327i) q^{21} +(-0.165146 + 0.936587i) q^{23} +(-7.96887 + 6.68667i) q^{25} +(1.52959 - 4.96592i) q^{27} +(5.18495 + 6.17919i) q^{29} +(-0.331534 + 1.88022i) q^{31} +(4.16718 - 2.84196i) q^{33} +(9.78570 - 5.64977i) q^{35} +(8.31066 + 4.79816i) q^{37} +(6.67855 - 1.70152i) q^{39} +(0.581151 + 0.487644i) q^{41} +(2.14125 - 5.88303i) q^{43} +(9.20319 - 7.34336i) q^{45} +(-0.932102 - 5.28621i) q^{47} +(-1.21172 + 0.441031i) q^{49} +(-7.85378 + 3.54503i) q^{51} +3.54207i q^{53} +11.4291 q^{55} +(3.54244 + 0.353992i) q^{57} +(2.13303 + 5.86045i) q^{59} +(-3.22446 + 0.568559i) q^{61} +(-7.58447 + 4.13293i) q^{63} +(14.6744 + 5.34105i) q^{65} +(-4.40861 + 5.25398i) q^{67} +(1.17905 - 1.15032i) q^{69} +(-3.83709 + 6.64603i) q^{71} +(3.46824 + 6.00718i) q^{73} +(17.9673 - 1.34890i) q^{75} +(-8.25717 - 1.45596i) q^{77} +(-0.205269 + 0.172241i) q^{79} +(-7.17126 + 5.43811i) q^{81} +(7.91149 + 9.42855i) q^{83} +(-19.2280 - 3.39041i) q^{85} +(-1.04596 - 13.9321i) q^{87} +(-4.11349 - 7.12477i) q^{89} +(-9.92138 - 5.72811i) q^{91} +(2.36698 - 2.30931i) q^{93} +(6.17946 + 5.18518i) q^{95} +(5.06123 + 1.84214i) q^{97} +(-8.73384 - 0.215453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Character values

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

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

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
$3$	−1.40645	−	1.01088i	−0.812017	−	0.583634i
$3$	−1.40645	−	1.01088i	−0.812017	−	0.583634i
$4$		0			0
$5$	−1.34230	−	3.68793i	−0.600294	−	1.64929i	−0.750679	−	0.660667i	$-0.770274\pi$
$5$	−1.34230	−	3.68793i	−0.600294	−	1.64929i	0.150386	−	0.988627i	$-0.451948\pi$
$6$		0			0
$7$	0.499959	+	2.83541i	0.188967	+	1.07168i	0.920752	+	0.390148i	$0.127576\pi$
$7$	0.499959	+	2.83541i	0.188967	+	1.07168i	−0.731786	+	0.681535i	$0.761313\pi$
$8$		0			0
$9$	0.956226	+	2.84352i	0.318742	+	0.947841i
$10$		0			0
$11$	−0.996019	+	2.73654i	−0.300311	+	0.825098i	0.694135	+	0.719845i	$0.255787\pi$
$11$	−0.996019	+	2.73654i	−0.300311	+	0.825098i	−0.994446	+	0.105252i	$0.966435\pi$
$12$		0			0
$13$	−2.55767	+	3.04812i	−0.709371	+	0.845396i	−0.993552	−	0.113375i	$-0.963834\pi$
$13$	−2.55767	+	3.04812i	−0.709371	+	0.845396i	0.284181	+	0.958771i	$0.408278\pi$
$14$		0			0
$15$	−1.84019	+	6.54382i	−0.475136	+	1.68961i
$16$		0			0
$17$	2.48745	−	4.30839i	0.603296	−	1.04494i	−0.389022	−	0.921228i	$-0.627187\pi$
$17$	2.48745	−	4.30839i	0.603296	−	1.04494i	0.992318	−	0.123711i	$-0.0394795\pi$
$18$		0			0
$19$	−1.78004	+	1.02771i	−0.408369	+	0.235772i	−0.690089	−	0.723725i	$-0.742429\pi$
$19$	−1.78004	+	1.02771i	−0.408369	+	0.235772i	0.281720	+	0.959497i	$0.409095\pi$
$20$		0			0
$21$	2.16310	−	4.49327i	0.472027	−	0.980512i
$22$		0			0
$23$	−0.165146	+	0.936587i	−0.0344352	+	0.195292i	−0.997173	−	0.0751465i	$-0.976058\pi$
$23$	−0.165146	+	0.936587i	−0.0344352	+	0.195292i	0.962737	+	0.270438i	$0.0871687\pi$
$24$		0			0
$25$	−7.96887	+	6.68667i	−1.59377	+	1.33733i
$26$		0			0
$27$	1.52959	−	4.96592i	0.294369	−	0.955692i
$28$		0			0
$29$	5.18495	+	6.17919i	0.962821	+	1.14745i	0.989019	+	0.147789i	$0.0472157\pi$
$29$	5.18495	+	6.17919i	0.962821	+	1.14745i	−0.0261974	+	0.999657i	$0.508340\pi$
$30$		0			0
$31$	−0.331534	+	1.88022i	−0.0595453	+	0.337698i	−0.999998	−	0.00222778i	$-0.999291\pi$
$31$	−0.331534	+	1.88022i	−0.0595453	+	0.337698i	0.940452	+	0.339926i	$0.110402\pi$
$32$		0			0
$33$	4.16718	−	2.84196i	0.725413	−	0.494721i
$34$		0			0
$35$	9.78570	−	5.64977i	1.65408	−	0.954986i
$36$		0			0
$37$	8.31066	+	4.79816i	1.36626	+	0.788813i	0.990449	−	0.137881i	$-0.0440293\pi$
$37$	8.31066	+	4.79816i	1.36626	+	0.788813i	0.375816	+	0.926694i	$0.377363\pi$
$38$		0			0
$39$	6.67855	−	1.70152i	1.06942	−	0.272462i
$40$		0			0
$41$	0.581151	+	0.487644i	0.0907605	+	0.0761571i	0.687039	−	0.726621i	$-0.258910\pi$
$41$	0.581151	+	0.487644i	0.0907605	+	0.0761571i	−0.596278	+	0.802778i	$0.703355\pi$
$42$		0			0
$43$	2.14125	−	5.88303i	0.326537	−	0.897154i	−0.662444	−	0.749112i	$-0.730481\pi$
$43$	2.14125	−	5.88303i	0.326537	−	0.897154i	0.988981	−	0.148042i	$-0.0472972\pi$
$44$		0			0
$45$	9.20319	−	7.34336i	1.37193	−	1.09468i
$46$		0			0
$47$	−0.932102	−	5.28621i	−0.135961	−	0.771073i	−0.974186	−	0.225748i	$-0.927517\pi$
$47$	−0.932102	−	5.28621i	−0.135961	−	0.771073i	0.838225	−	0.545325i	$-0.183594\pi$
$48$		0			0
$49$	−1.21172	+	0.441031i	−0.173103	+	0.0630044i
$50$		0			0
$51$	−7.85378	+	3.54503i	−1.09975	+	0.496404i
$52$		0			0
$53$			3.54207i			0.486541i	0.969959	+	0.243270i	$0.0782202\pi$
$53$			3.54207i			0.486541i	−0.969959	+	0.243270i	$0.921780\pi$
$54$		0			0
$55$	11.4291			1.54110
$56$		0			0
$57$	3.54244	+	0.353992i	0.469207	+	0.0468874i
$58$		0			0
$59$	2.13303	+	5.86045i	0.277697	+	0.762966i	0.997623	+	0.0689146i	$0.0219536\pi$
$59$	2.13303	+	5.86045i	0.277697	+	0.762966i	−0.719926	+	0.694051i	$0.755824\pi$
$60$		0			0
$61$	−3.22446	+	0.568559i	−0.412849	+	0.0727965i	−0.376215	−	0.926532i	$-0.622775\pi$
$61$	−3.22446	+	0.568559i	−0.412849	+	0.0727965i	−0.0366341	+	0.999329i	$0.511664\pi$
$62$		0			0
$63$	−7.58447	+	4.13293i	−0.955554	+	0.520701i
$64$		0			0
$65$	14.6744	+	5.34105i	1.82014	+	0.662476i
$66$		0			0
$67$	−4.40861	+	5.25398i	−0.538598	+	0.641876i	−0.964873	−	0.262718i	$-0.915381\pi$
$67$	−4.40861	+	5.25398i	−0.538598	+	0.641876i	0.426275	+	0.904594i	$0.359826\pi$
$68$		0			0
$69$	1.17905	−	1.15032i	0.141941	−	0.138483i
$70$		0			0
$71$	−3.83709	+	6.64603i	−0.455378	+	0.788738i	−0.998710	−	0.0507798i	$-0.983829\pi$
$71$	−3.83709	+	6.64603i	−0.455378	+	0.788738i	0.543332	+	0.839518i	$0.317163\pi$
$72$		0			0
$73$	3.46824	+	6.00718i	0.405927	+	0.703087i	0.994429	−	0.105409i	$-0.0336153\pi$
$73$	3.46824	+	6.00718i	0.405927	+	0.703087i	−0.588502	+	0.808496i	$0.700282\pi$
$74$		0			0
$75$	17.9673	−	1.34890i	2.07468	−	0.155757i
$76$		0			0
$77$	−8.25717	−	1.45596i	−0.940992	−	0.165922i
$78$		0			0
$79$	−0.205269	+	0.172241i	−0.0230945	+	0.0193786i	−0.654262	−	0.756268i	$-0.727021\pi$
$79$	−0.205269	+	0.172241i	−0.0230945	+	0.0193786i	0.631167	+	0.775647i	$0.282576\pi$
$80$		0			0
$81$	−7.17126	+	5.43811i	−0.796807	+	0.604234i
$82$		0			0
$83$	7.91149	+	9.42855i	0.868399	+	1.03492i	0.999054	+	0.0434896i	$0.0138475\pi$
$83$	7.91149	+	9.42855i	0.868399	+	1.03492i	−0.130655	+	0.991428i	$0.541708\pi$
$84$		0			0
$85$	−19.2280	−	3.39041i	−2.08557	−	0.367742i
$86$		0			0
$87$	−1.04596	−	13.9321i	−0.112138	−	1.49368i
$88$		0			0
$89$	−4.11349	−	7.12477i	−0.436029	−	0.755224i	0.561350	−	0.827578i	$-0.310282\pi$
$89$	−4.11349	−	7.12477i	−0.436029	−	0.755224i	−0.997379	+	0.0723541i	$0.976949\pi$
$90$		0			0
$91$	−9.92138	−	5.72811i	−1.04004	−	0.600469i
$92$		0			0
$93$	2.36698	−	2.30931i	0.245444	−	0.239464i
$94$		0			0
$95$	6.17946	+	5.18518i	0.633999	+	0.531988i
$96$		0			0
$97$	5.06123	+	1.84214i	0.513891	+	0.187041i	0.585931	−	0.810361i	$-0.300729\pi$
$97$	5.06123	+	1.84214i	0.513891	+	0.187041i	−0.0720406	+	0.997402i	$0.522951\pi$
$98$		0			0
$99$	−8.73384	−	0.215453i	−0.877784	−	0.0216539i
$100$		0			0
$101$	−3.98336	+	0.702375i	−0.396360	+	0.0698889i	−0.368276	−	0.929717i	$-0.620052\pi$
$101$	−3.98336	+	0.702375i	−0.396360	+	0.0698889i	−0.0280840	+	0.999606i	$0.508941\pi$
$102$		0			0
$103$	−1.07241	+	0.390325i	−0.105668	+	0.0384599i	−0.394313	−	0.918976i	$-0.629017\pi$
$103$	−1.07241	+	0.390325i	−0.105668	+	0.0384599i	0.288645	+	0.957436i	$0.406795\pi$
$104$		0			0
$105$	−19.4744	−	1.94606i	−1.90051	−	0.189916i
$106$		0			0
$107$			4.87553i			0.471335i	0.971834	+	0.235667i	$0.0757276\pi$
$107$			4.87553i			0.471335i	−0.971834	+	0.235667i	$0.924272\pi$
$108$		0			0
$109$		−	2.52010i		−	0.241382i	−0.992690	−	0.120691i	$-0.961489\pi$
$109$		−	2.52010i		−	0.241382i	0.992690	−	0.120691i	$-0.0385111\pi$
$110$		0			0
$111$	−6.83818	−	15.1495i	−0.649051	−	1.43793i
$112$		0			0
$113$	−6.79620	+	2.47361i	−0.639332	+	0.232698i	−0.641288	−	0.767300i	$-0.721600\pi$
$113$	−6.79620	+	2.47361i	−0.639332	+	0.232698i	0.00195583	+	0.999998i	$0.499377\pi$
$114$		0			0
$115$	3.67575	−	0.648133i	0.342765	−	0.0604387i
$116$		0			0
$117$	−11.1131	−	4.35812i	−1.02741	−	0.402908i
$118$		0			0
$119$	13.4597	+	4.89892i	1.23385	+	0.449083i
$120$		0			0
$121$	1.92989	+	1.61937i	0.175445	+	0.147216i
$122$		0			0
$123$	−0.324411	−	1.27332i	−0.0292511	−	0.114812i
$124$		0			0
$125$	18.3625	+	10.6016i	1.64239	+	0.948236i
$126$		0			0
$127$	2.38507	+	4.13106i	0.211641	+	0.366573i	0.952228	−	0.305387i	$-0.0987860\pi$
$127$	2.38507	+	4.13106i	0.211641	+	0.366573i	−0.740587	+	0.671960i	$0.765453\pi$
$128$		0			0
$129$	−8.95864	+	6.10966i	−0.788764	+	0.537926i
$130$		0			0
$131$	3.45051	+	0.608417i	0.301472	+	0.0531577i	0.322338	−	0.946625i	$-0.395531\pi$
$131$	3.45051	+	0.608417i	0.301472	+	0.0531577i	−0.0208660	+	0.999782i	$0.506642\pi$
$132$		0			0
$133$	−3.80391	−	4.53333i	−0.329841	−	0.393089i
$134$		0			0
$135$	−20.3671	+	1.02473i	−1.75292	+	0.0881951i
$136$		0			0
$137$	−12.6574	+	10.6208i	−1.08140	+	0.907400i	−0.996036	−	0.0889501i	$-0.971649\pi$
$137$	−12.6574	+	10.6208i	−1.08140	+	0.907400i	−0.0853611	+	0.996350i	$0.527204\pi$
$138$		0			0
$139$	−19.5648	−	3.44981i	−1.65947	−	0.292609i	−0.736199	−	0.676765i	$-0.763381\pi$
$139$	−19.5648	−	3.44981i	−1.65947	−	0.292609i	−0.923268	+	0.384157i	$0.874492\pi$
$140$		0			0
$141$	−4.03279	+	8.37706i	−0.339622	+	0.705476i
$142$		0			0
$143$	−5.79380	−	10.0352i	−0.484502	−	0.839182i
$144$		0			0
$145$	15.8287	−	27.4161i	1.31450	−	2.27678i
$146$		0			0
$147$	2.15006	+	0.604622i	0.177334	+	0.0498683i
$148$		0			0
$149$	7.39950	−	8.81838i	0.606190	−	0.722429i	−0.372440	−	0.928056i	$-0.621479\pi$
$149$	7.39950	−	8.81838i	0.606190	−	0.722429i	0.978630	+	0.205627i	$0.0659233\pi$
$150$		0			0
$151$	3.42462	+	1.24646i	0.278692	+	0.101436i	0.477585	−	0.878586i	$-0.341512\pi$
$151$	3.42462	+	1.24646i	0.278692	+	0.101436i	−0.198893	+	0.980021i	$0.563735\pi$
$152$		0			0
$153$	14.6296	+	2.95333i	1.18273	+	0.238763i
$154$		0			0
$155$	7.37916	−	1.30114i	0.592708	−	0.104510i
$156$		0			0
$157$	5.00630	+	13.7547i	0.399546	+	1.09774i	0.962506	+	0.271259i	$0.0874402\pi$
$157$	5.00630	+	13.7547i	0.399546	+	1.09774i	−0.562960	+	0.826484i	$0.690338\pi$
$158$		0			0
$159$	3.58062	−	4.98176i	0.283962	−	0.395079i
$160$		0			0
$161$	−2.73817			−0.215798
$162$		0			0
$163$		−	5.93891i		−	0.465171i	−0.972576	−	0.232586i	$-0.925281\pi$
$163$		−	5.93891i		−	0.465171i	0.972576	−	0.232586i	$-0.0747186\pi$
$164$		0			0
$165$	−16.0745	−	11.5535i	−1.25140	−	0.899441i
$166$		0			0
$167$	18.7096	−	6.80974i	1.44779	−	0.526953i	0.505818	−	0.862640i	$-0.331191\pi$
$167$	18.7096	−	6.80974i	1.44779	−	0.526953i	0.941974	+	0.335687i	$0.108968\pi$
$168$		0			0
$169$	−0.491897	−	2.78968i	−0.0378382	−	0.214591i
$170$		0			0
$171$	−4.62443	−	4.07887i	−0.353639	−	0.311919i
$172$		0			0
$173$	3.76876	−	10.3546i	0.286534	−	0.787245i	−0.710011	−	0.704190i	$-0.751310\pi$
$173$	3.76876	−	10.3546i	0.286534	−	0.787245i	0.996545	−	0.0830547i	$-0.0264676\pi$
$174$		0			0
$175$	−22.9435	−	19.2519i	−1.73437	−	1.45531i
$176$		0			0
$177$	2.92423	−	10.3987i	0.219799	−	0.781614i
$178$		0			0
$179$	−3.66363	−	2.11520i	−0.273832	−	0.158097i	0.356796	−	0.934182i	$-0.383869\pi$
$179$	−3.66363	−	2.11520i	−0.273832	−	0.158097i	−0.630628	+	0.776085i	$0.717203\pi$
$180$		0			0
$181$	−16.4676	+	9.50759i	−1.22403	+	0.706694i	−0.965775	−	0.259383i	$-0.916481\pi$
$181$	−16.4676	+	9.50759i	−1.22403	+	0.706694i	−0.258255	+	0.966077i	$0.583147\pi$
$182$		0			0
$183$	5.10980	+	2.45990i	0.377727	+	0.181841i
$184$		0			0
$185$	6.53992	−	37.0897i	0.480825	−	2.72689i
$186$		0			0
$187$	9.31254	+	11.0983i	0.681000	+	0.811585i
$188$		0			0
$189$	14.8451	+	1.85424i	1.07982	+	0.134876i
$190$		0			0
$191$	−6.22796	+	5.22588i	−0.450639	+	0.378131i	−0.839673	−	0.543092i	$-0.817253\pi$
$191$	−6.22796	+	5.22588i	−0.450639	+	0.378131i	0.389034	+	0.921224i	$0.372809\pi$
$192$		0			0
$193$	−2.29037	+	12.9893i	−0.164864	+	0.934993i	0.784340	+	0.620332i	$0.213002\pi$
$193$	−2.29037	+	12.9893i	−0.164864	+	0.934993i	−0.949204	+	0.314661i	$0.898109\pi$
$194$		0			0
$195$	−15.2397	−	22.3461i	−1.09134	−	1.60024i
$196$		0			0
$197$	−5.35211	+	3.09004i	−0.381322	+	0.220156i	−0.678393	−	0.734699i	$-0.737323\pi$
$197$	−5.35211	+	3.09004i	−0.381322	+	0.220156i	0.297071	+	0.954855i	$0.403990\pi$
$198$		0			0
$199$	−4.43708	+	7.68525i	−0.314537	+	0.544793i	−0.979339	−	0.202226i	$-0.935182\pi$
$199$	−4.43708	+	7.68525i	−0.314537	+	0.544793i	0.664802	+	0.747019i	$0.268516\pi$
$200$		0			0
$201$	11.5117	−	2.93289i	0.811971	−	0.206870i
$202$		0			0
$203$	−14.9282	+	17.7908i	−1.04776	+	1.24867i
$204$		0			0
$205$	1.01832	−	2.79781i	0.0711225	−	0.195407i
$206$		0			0
$207$	−2.82113	+	0.425994i	−0.196082	+	0.0296086i
$208$		0			0
$209$	−1.03941	−	5.89477i	−0.0718972	−	0.407750i
$210$		0			0
$211$	6.04444	+	16.6070i	0.416116	+	1.14327i	0.953884	+	0.300177i	$0.0970457\pi$
$211$	6.04444	+	16.6070i	0.416116	+	1.14327i	−0.537767	+	0.843093i	$0.680732\pi$
$212$		0			0
$213$	12.1151	−	5.46848i	0.830110	−	0.374694i
$214$		0			0
$215$	−24.5704			−1.67569
$216$		0			0
$217$	−5.49695			−0.373157
$218$		0			0
$219$	1.19463	−	11.9548i	0.0807258	−	0.807831i
$220$		0			0
$221$	6.77040	+	18.6015i	0.455426	+	1.25127i
$222$		0			0
$223$	4.05080	+	22.9732i	0.271262	+	1.53840i	0.750592	+	0.660767i	$0.229769\pi$
$223$	4.05080	+	22.9732i	0.271262	+	1.53840i	−0.479330	+	0.877635i	$0.659120\pi$
$224$		0			0
$225$	−26.6338	−	16.2657i	−1.77558	−	1.08438i
$226$		0			0
$227$	8.48739	−	23.3189i	0.563328	−	1.54773i	−0.251398	−	0.967884i	$-0.580890\pi$
$227$	8.48739	−	23.3189i	0.563328	−	1.54773i	0.814726	−	0.579846i	$-0.196887\pi$
$228$		0			0
$229$	3.58229	−	4.26921i	0.236724	−	0.282117i	−0.634583	−	0.772855i	$-0.718828\pi$
$229$	3.58229	−	4.26921i	0.236724	−	0.282117i	0.871307	+	0.490738i	$0.163273\pi$
$230$		0			0
$231$	10.1415	+	10.3948i	0.667263	+	0.683927i
$232$		0			0
$233$	−3.32571	+	5.76031i	−0.217875	+	0.377370i	−0.954158	−	0.299303i	$-0.903246\pi$
$233$	−3.32571	+	5.76031i	−0.217875	+	0.377370i	0.736283	+	0.676673i	$0.236579\pi$
$234$		0			0
$235$	−18.2440	+	10.5332i	−1.19011	+	0.687110i
$236$		0			0
$237$	0.462816	−	0.0347460i	0.0300631	−	0.00225699i
$238$		0			0
$239$	4.54329	−	25.7663i	0.293881	−	1.66668i	−0.377836	−	0.925872i	$-0.623332\pi$
$239$	4.54329	−	25.7663i	0.293881	−	1.66668i	0.671717	−	0.740808i	$-0.265557\pi$
$240$		0			0
$241$	−19.2391	+	16.1435i	−1.23930	+	1.03989i	−0.241718	+	0.970347i	$0.577711\pi$
$241$	−19.2391	+	16.1435i	−1.23930	+	1.03989i	−0.997579	+	0.0695464i	$0.977845\pi$
$242$		0			0
$243$	15.5833	−	0.399129i	0.999672	−	0.0256041i
$244$		0			0
$245$	3.25299	+	3.87676i	0.207826	+	0.247677i
$246$		0			0
$247$	1.42019	−	8.05431i	0.0903647	−	0.512484i
$248$		0			0
$249$	−1.59598	−	21.2584i	−0.101141	−	1.34720i
$250$		0			0
$251$	−25.2441	+	14.5747i	−1.59339	+	0.919945i	−0.600672	+	0.799495i	$0.705100\pi$
$251$	−25.2441	+	14.5747i	−1.59339	+	0.919945i	−0.992719	+	0.120450i	$0.961566\pi$
$252$		0			0
$253$	−2.39852	−	1.38479i	−0.150794	−	0.0870608i
$254$		0			0
$255$	23.6159	+	24.2057i	1.47889	+	1.51582i
$256$		0			0
$257$	−5.42626	−	4.55318i	−0.338481	−	0.284019i	0.457664	−	0.889125i	$-0.348686\pi$
$257$	−5.42626	−	4.55318i	−0.338481	−	0.284019i	−0.796145	+	0.605106i	$0.793131\pi$
$258$		0			0
$259$	−9.44975	+	25.9630i	−0.587179	+	1.61326i
$260$		0			0
$261$	−12.6127	+	20.6522i	−0.780705	+	1.27834i
$262$		0			0
$263$	−1.99223	−	11.2985i	−0.122846	−	0.696695i	−0.982564	−	0.185926i	$-0.940472\pi$
$263$	−1.99223	−	11.2985i	−0.122846	−	0.696695i	0.859718	−	0.510770i	$-0.170639\pi$
$264$		0			0
$265$	13.0629	−	4.75451i	0.802449	−	0.292067i
$266$		0			0
$267$	−1.41689	+	14.1789i	−0.0867120	+	0.867736i
$268$		0			0
$269$			15.1820i			0.925661i	0.886447	+	0.462831i	$0.153166\pi$
$269$			15.1820i			0.925661i	−0.886447	+	0.462831i	$0.846834\pi$
$270$		0			0
$271$	−13.2808			−0.806753			−0.403376	−	0.915034i	$-0.632163\pi$
$271$	−13.2808			−0.806753			−0.403376	+	0.915034i	$0.632163\pi$
$272$		0			0
$273$	8.16351	+	18.0857i	0.494078	+	1.09460i
$274$		0			0
$275$	−10.3612	−	28.4672i	−0.624804	−	1.71664i
$276$		0			0
$277$	2.53413	−	0.446836i	0.152261	−	0.0268478i	−0.0969979	−	0.995285i	$-0.530924\pi$
$277$	2.53413	−	0.446836i	0.152261	−	0.0268478i	0.249259	+	0.968437i	$0.419813\pi$
$278$		0			0
$279$	−5.66348	+	0.855194i	−0.339064	+	0.0511991i
$280$		0			0
$281$	25.4277	+	9.25491i	1.51689	+	0.552102i	0.960368	−	0.278734i	$-0.0899147\pi$
$281$	25.4277	+	9.25491i	1.51689	+	0.552102i	0.556518	+	0.830835i	$0.312137\pi$
$282$		0			0
$283$	17.1845	−	20.4797i	1.02151	−	1.21739i	0.0456626	−	0.998957i	$-0.485460\pi$
$283$	17.1845	−	20.4797i	1.02151	−	1.21739i	0.975851	−	0.218436i	$-0.0700955\pi$
$284$		0			0
$285$	−3.44951	−	13.5394i	−0.204331	−	0.802007i
$286$		0			0
$287$	−1.09212	+	1.89160i	−0.0644656	+	0.111658i
$288$		0			0
$289$	−3.87484	−	6.71142i	−0.227932	−	0.394789i
$290$		0			0
$291$	−5.25621	−	7.70721i	−0.308124	−	0.451804i
$292$		0			0
$293$	−17.3330	−	3.05628i	−1.01261	−	0.178550i	−0.357361	−	0.933966i	$-0.616323\pi$
$293$	−17.3330	−	3.05628i	−1.01261	−	0.178550i	−0.655245	+	0.755416i	$0.727435\pi$
$294$		0			0
$295$	18.7498	−	15.7329i	1.09166	−	0.916007i
$296$		0			0
$297$	12.0659	+	9.13192i	0.700137	+	0.529888i
$298$		0			0
$299$	−2.43244	−	2.89887i	−0.140672	−	0.167646i
$300$		0			0
$301$	17.7513	+	3.13004i	1.02317	+	0.180412i
$302$		0			0
$303$	6.31244	+	3.03886i	0.362640	+	0.174578i
$304$		0			0
$305$	6.42499	+	11.1284i	0.367894	+	0.637211i
$306$		0			0
$307$	10.1962	+	5.88676i	0.581926	+	0.335975i	0.761898	−	0.647696i	$-0.224268\pi$
$307$	10.1962	+	5.88676i	0.581926	+	0.335975i	−0.179972	+	0.983672i	$0.557601\pi$
$308$		0			0
$309$	1.90287	+	0.535107i	0.108250	+	0.0304412i
$310$		0			0
$311$	−26.0496	−	21.8582i	−1.47714	−	1.23947i	−0.909175	−	0.416414i	$-0.863287\pi$
$311$	−26.0496	−	21.8582i	−1.47714	−	1.23947i	−0.567965	−	0.823053i	$-0.692269\pi$
$312$		0			0
$313$	6.64081	+	2.41706i	0.375361	+	0.136620i	0.522809	−	0.852450i	$-0.324884\pi$
$313$	6.64081	+	2.41706i	0.375361	+	0.136620i	−0.147449	+	0.989070i	$0.547106\pi$
$314$		0			0
$315$	25.4226	+	22.4234i	1.43240	+	1.26342i
$316$		0			0
$317$	5.34112	−	0.941783i	0.299987	−	0.0528958i	−0.0216287	−	0.999766i	$-0.506885\pi$
$317$	5.34112	−	0.941783i	0.299987	−	0.0528958i	0.321616	+	0.946870i	$0.395774\pi$
$318$		0			0
$319$	−22.0739	+	8.03424i	−1.23590	+	0.449831i
$320$		0			0
$321$	4.92859	−	6.85720i	0.275087	−	0.382732i
$322$		0			0
$323$			10.2255i			0.568961i
$324$		0			0
$325$		−	41.3924i		−	2.29604i
$326$		0			0
$327$	−2.54753	+	3.54441i	−0.140879	+	0.196006i
$328$		0			0
$329$	14.5225	−	5.28577i	0.800654	−	0.291414i
$330$		0			0
$331$	−5.34260	+	0.942044i	−0.293656	+	0.0517794i	−0.318535	−	0.947911i	$-0.603191\pi$
$331$	−5.34260	+	0.942044i	−0.293656	+	0.0517794i	0.0248795	+	0.999690i	$0.492080\pi$
$332$		0			0
$333$	−5.69682	+	28.2197i	−0.312184	+	1.54643i
$334$		0			0
$335$	25.2940	+	9.20627i	1.38196	+	0.502992i
$336$		0			0
$337$	−22.3325	−	18.7392i	−1.21653	−	1.02079i	−0.998999	−	0.0447328i	$-0.985756\pi$
$337$	−22.3325	−	18.7392i	−1.21653	−	1.02079i	−0.217528	−	0.976054i	$-0.569799\pi$
$338$		0			0
$339$	12.0591	+	3.39114i	0.654959	+	0.184182i
$340$		0			0
$341$	−4.81509	−	2.77999i	−0.260752	−	0.150545i
$342$		0			0
$343$	8.22070	+	14.2387i	0.443876	+	0.768816i
$344$		0			0
$345$	−5.82496	−	2.80418i	−0.313605	−	0.150972i
$346$		0			0
$347$	17.1238	+	3.01939i	0.919255	+	0.162089i	0.613203	−	0.789925i	$-0.289881\pi$
$347$	17.1238	+	3.01939i	0.919255	+	0.162089i	0.306052	+	0.952015i	$0.400992\pi$
$348$		0			0
$349$	3.38478	+	4.03383i	0.181183	+	0.215926i	0.848990	−	0.528409i	$-0.177211\pi$
$349$	3.38478	+	4.03383i	0.181183	+	0.215926i	−0.667807	+	0.744335i	$0.732767\pi$
$350$		0			0
$351$	11.2245	+	17.3636i	0.599121	+	0.926799i
$352$		0			0
$353$	−7.22029	+	6.05854i	−0.384297	+	0.322463i	−0.814387	−	0.580323i	$-0.802926\pi$
$353$	−7.22029	+	6.05854i	−0.384297	+	0.322463i	0.430090	+	0.902786i	$0.358482\pi$
$354$		0			0
$355$	29.6606	+	5.22997i	1.57422	+	0.277578i
$356$		0			0
$357$	−13.9782	−	20.4963i	−0.739803	−	1.08478i
$358$		0			0
$359$	8.12377	+	14.0708i	0.428756	+	0.742628i	0.996763	−	0.0803962i	$-0.0256186\pi$
$359$	8.12377	+	14.0708i	0.428756	+	0.742628i	−0.568007	+	0.823024i	$0.692285\pi$
$360$		0			0
$361$	−7.38764	+	12.7958i	−0.388823	+	0.673461i
$362$		0			0
$363$	−1.07731	−	4.22847i	−0.0565440	−	0.221937i
$364$		0			0
$365$	17.4986	−	20.8541i	0.915921	−	1.09155i
$366$		0			0
$367$	−12.0315	−	4.37912i	−0.628042	−	0.228588i	0.00833711	−	0.999965i	$-0.497346\pi$
$367$	−12.0315	−	4.37912i	−0.628042	−	0.228588i	−0.636379	+	0.771377i	$0.719568\pi$
$368$		0			0
$369$	−0.830915	+	2.11881i	−0.0432557	+	0.110301i
$370$		0			0
$371$	−10.0432	+	1.77089i	−0.521417	+	0.0919400i
$372$		0			0
$373$	−2.16442	−	5.94669i	−0.112069	−	0.307908i	0.870961	−	0.491353i	$-0.163497\pi$
$373$	−2.16442	−	5.94669i	−0.112069	−	0.307908i	−0.983030	+	0.183445i	$0.941275\pi$
$374$		0			0
$375$	−15.1090	−	33.4730i	−0.780227	−	1.72854i
$376$		0			0
$377$	−32.0963			−1.65304
$378$		0			0
$379$		−	28.5066i		−	1.46428i	−0.681152	−	0.732142i	$-0.738521\pi$
$379$		−	28.5066i		−	1.46428i	0.681152	−	0.732142i	$-0.261479\pi$
$380$		0			0
$381$	0.821535	−	8.22118i	0.0420885	−	0.421184i
$382$		0			0
$383$	29.5410	−	10.7521i	1.50948	−	0.549405i	0.550983	−	0.834517i	$-0.314253\pi$
$383$	29.5410	−	10.7521i	1.50948	−	0.549405i	0.958494	+	0.285112i	$0.0920308\pi$
$384$		0			0
$385$	5.71409	+	32.4062i	0.291217	+	1.65157i
$386$		0			0
$387$	18.7761	+	0.463183i	0.954441	+	0.0235449i
$388$		0			0
$389$	1.34416	−	3.69306i	0.0681518	−	0.187246i	−0.900941	−	0.433941i	$-0.857123\pi$
$389$	1.34416	−	3.69306i	0.0681518	−	0.187246i	0.969093	+	0.246696i	$0.0793448\pi$
$390$		0			0
$391$	3.62440	+	3.04123i	0.183294	+	0.153802i
$392$		0			0
$393$	−4.23794	−	4.34377i	−0.213776	−	0.219114i
$394$		0			0
$395$	0.910744	+	0.525818i	0.0458245	+	0.0264568i
$396$		0			0
$397$	17.9961	−	10.3901i	0.903200	−	0.521463i	0.0249629	−	0.999688i	$-0.492053\pi$
$397$	17.9961	−	10.3901i	0.903200	−	0.521463i	0.878237	+	0.478226i	$0.158720\pi$
$398$		0			0
$399$	0.767360	+	10.2212i	0.0384161	+	0.511702i
$400$		0			0
$401$	−4.02373	+	22.8197i	−0.200935	+	1.13956i	0.702774	+	0.711413i	$0.251945\pi$
$401$	−4.02373	+	22.8197i	−0.200935	+	1.13956i	−0.903709	+	0.428147i	$0.859166\pi$
$402$		0			0
$403$	−4.88319	−	5.81955i	−0.243249	−	0.289893i
$404$		0			0
$405$	29.6813	+	19.1476i	1.47488	+	0.951451i
$406$		0			0
$407$	−21.4079	+	17.9634i	−1.06115	+	0.890412i
$408$		0			0
$409$	5.07096	−	28.7589i	0.250743	−	1.42203i	−0.556025	−	0.831165i	$-0.687674\pi$
$409$	5.07096	−	28.7589i	0.250743	−	1.42203i	0.806768	−	0.590868i	$-0.201215\pi$
$410$		0			0
$411$	28.5385	−	2.14253i	1.40770	−	0.105683i
$412$		0			0
$413$	−15.5503	+	8.97799i	−0.765182	+	0.441778i
$414$		0			0
$415$	24.1523	−	41.8330i	1.18559	−	2.05350i
$416$		0			0
$417$	24.0297	+	24.6298i	1.17674	+	1.20612i
$418$		0			0
$419$	−8.33906	+	9.93810i	−0.407390	+	0.485508i	−0.930258	−	0.366905i	$-0.880417\pi$
$419$	−8.33906	+	9.93810i	−0.407390	+	0.485508i	0.522869	+	0.852413i	$0.324862\pi$
$420$		0			0
$421$	−1.49536	+	4.10848i	−0.0728795	+	0.200235i	−0.970784	−	0.239956i	$-0.922867\pi$
$421$	−1.49536	+	4.10848i	−0.0728795	+	0.200235i	0.897904	+	0.440191i	$0.145089\pi$
$422$		0			0
$423$	14.1402	−	7.70527i	0.687519	−	0.374643i
$424$		0			0
$425$	8.98665	+	50.9658i	0.435916	+	2.47220i
$426$		0			0
$427$	−3.22419	−	8.85839i	−0.156030	−	0.428688i
$428$		0			0
$429$	−1.99567	+	19.9709i	−0.0963517	+	0.964202i
$430$		0			0
$431$	−1.15854			−0.0558051			−0.0279025	−	0.999611i	$-0.508883\pi$
$431$	−1.15854			−0.0558051			−0.0279025	+	0.999611i	$0.508883\pi$
$432$		0			0
$433$	37.7498			1.81414			0.907069	−	0.420982i	$-0.138314\pi$
$433$	37.7498			1.81414			0.907069	+	0.420982i	$0.138314\pi$
$434$		0			0
$435$	−49.9768	+	22.5585i	−2.39620	+	1.08160i
$436$		0			0
$437$	−0.668571	−	1.83688i	−0.0319821	−	0.0878701i
$438$		0			0
$439$	4.69964	+	26.6530i	0.224301	+	1.27208i	0.864016	+	0.503464i	$0.167941\pi$
$439$	4.69964	+	26.6530i	0.224301	+	1.27208i	−0.639715	+	0.768612i	$0.720948\pi$
$440$		0			0
$441$	−2.41276	−	3.02384i	−0.114894	−	0.143992i
$442$		0			0
$443$	10.3614	−	28.4677i	0.492285	−	1.35254i	−0.406299	−	0.913740i	$-0.633181\pi$
$443$	10.3614	−	28.4677i	0.492285	−	1.35254i	0.898584	−	0.438802i	$-0.144597\pi$
$444$		0			0
$445$	−20.7542	+	24.7338i	−0.983841	+	1.17250i
$446$		0			0
$447$	−19.3214	+	4.92261i	−0.913871	+	0.232831i
$448$		0			0
$449$	−1.70434	+	2.95201i	−0.0804330	+	0.139314i	−0.903436	−	0.428723i	$-0.858964\pi$
$449$	−1.70434	+	2.95201i	−0.0804330	+	0.139314i	0.823003	+	0.568037i	$0.192297\pi$
$450$		0			0
$451$	−1.91329	+	1.10464i	−0.0900934	+	0.0520155i
$452$		0			0
$453$	−3.55655	−	5.21499i	−0.167101	−	0.245021i
$454$		0			0
$455$	−7.80745	+	44.2782i	−0.366019	+	2.07580i
$456$		0			0
$457$	7.27754	−	6.10658i	0.340429	−	0.285654i	−0.456504	−	0.889721i	$-0.650899\pi$
$457$	7.27754	−	6.10658i	0.340429	−	0.285654i	0.796933	+	0.604068i	$0.206454\pi$
$458$		0			0
$459$	−17.5904	−	18.9425i	−0.821048	−	0.884162i
$460$		0			0
$461$	−19.8885	−	23.7021i	−0.926298	−	1.10392i	−0.994341	−	0.106236i	$-0.966120\pi$
$461$	−19.8885	−	23.7021i	−0.926298	−	1.10392i	0.0680433	−	0.997682i	$-0.478324\pi$
$462$		0			0
$463$	4.27095	−	24.2217i	0.198488	−	1.12568i	−0.708876	−	0.705333i	$-0.750797\pi$
$463$	4.27095	−	24.2217i	0.198488	−	1.12568i	0.907364	−	0.420347i	$-0.138092\pi$
$464$		0			0
$465$	−11.6938	−	5.62947i	−0.542285	−	0.261061i
$466$		0			0
$467$	0.849394	−	0.490398i	0.0393052	−	0.0226929i	−0.480219	−	0.877149i	$-0.659443\pi$
$467$	0.849394	−	0.490398i	0.0393052	−	0.0226929i	0.519524	+	0.854456i	$0.326109\pi$
$468$		0			0
$469$	−17.1013	−	9.87344i	−0.789665	−	0.455913i
$470$		0			0
$471$	6.86327	−	24.4061i	0.316243	−	1.12457i
$472$		0			0
$473$	13.9664	+	11.7192i	0.642177	+	0.538851i
$474$		0			0
$475$	7.31297	−	20.0922i	0.335542	−	0.921894i
$476$		0			0
$477$	−10.0720	+	3.38702i	−0.461164	+	0.155081i
$478$		0			0
$479$	1.26087	+	7.15074i	0.0576105	+	0.326726i	0.999969	−	0.00787960i	$-0.00250818\pi$
$479$	1.26087	+	7.15074i	0.0576105	+	0.326726i	−0.942358	+	0.334605i	$0.891397\pi$
$480$		0			0
$481$	−35.8813	+	13.0597i	−1.63605	+	0.595473i
$482$		0			0
$483$	3.85111	+	2.76797i	0.175232	+	0.125947i
$484$		0			0
$485$		−	21.1382i		−	0.959836i
$486$		0			0
$487$	−0.153837			−0.00697103			−0.00348552	−	0.999994i	$-0.501109\pi$
$487$	−0.153837			−0.00697103			−0.00348552	+	0.999994i	$0.501109\pi$
$488$		0			0
$489$	−6.00355	+	8.35280i	−0.271490	+	0.377727i
$490$		0			0
$491$	−7.10851	−	19.5305i	−0.320802	−	0.881398i	−0.990345	−	0.138624i	$-0.955732\pi$
$491$	−7.10851	−	19.5305i	−0.320802	−	0.881398i	0.669543	−	0.742774i	$-0.266490\pi$
$492$		0			0
$493$	39.5197	−	6.96839i	1.77988	−	0.313840i
$494$		0			0
$495$	10.9288	+	32.4990i	0.491215	+	1.46072i
$496$		0			0
$497$	−20.7626	−	7.55696i	−0.931329	−	0.338976i
$498$		0			0
$499$	−12.0312	+	14.3382i	−0.538588	+	0.641865i	−0.964871	−	0.262726i	$-0.915379\pi$
$499$	−12.0312	+	14.3382i	−0.538588	+	0.641865i	0.426282	+	0.904590i	$0.359823\pi$
$500$		0			0
$501$	−33.1980	−	9.33565i	−1.48318	−	0.417086i
$502$		0			0
$503$	−15.2553	+	26.4230i	−0.680200	+	1.17814i	0.294719	+	0.955584i	$0.404774\pi$
$503$	−15.2553	+	26.4230i	−0.680200	+	1.17814i	−0.974919	+	0.222558i	$0.928559\pi$
$504$		0			0
$505$	7.93717	+	13.7476i	0.353200	+	0.611760i
$506$		0			0
$507$	−2.12822	+	4.42081i	−0.0945175	+	0.196335i
$508$		0			0
$509$	25.1247	+	4.43017i	1.11363	+	0.196364i	0.700044	−	0.714099i	$-0.253164\pi$
$509$	25.1247	+	4.43017i	1.11363	+	0.196364i	0.413590	+	0.910463i	$0.364275\pi$
$510$		0			0
$511$	−15.2988	+	12.8372i	−0.676779	+	0.567885i
$512$		0			0
$513$	2.38079	+	10.4115i	0.105114	+	0.459679i
$514$		0			0
$515$	2.87899	+	3.43104i	0.126863	+	0.151190i
$516$		0			0
$517$	15.3943	+	2.71443i	0.677041	+	0.119381i
$518$		0			0
$519$	−15.7679	+	10.7535i	−0.692133	+	0.472025i
$520$		0			0
$521$	−8.58140	−	14.8634i	−0.375958	−	0.651178i	0.614512	−	0.788908i	$-0.289353\pi$
$521$	−8.58140	−	14.8634i	−0.375958	−	0.651178i	−0.990470	+	0.137729i	$0.956020\pi$
$522$		0			0
$523$	35.9656	+	20.7647i	1.57266	+	0.907978i	0.995841	+	0.0911099i	$0.0290415\pi$
$523$	35.9656	+	20.7647i	1.57266	+	0.907978i	0.576824	+	0.816869i	$0.304292\pi$
$524$		0			0
$525$	12.8076	+	50.2702i	0.558969	+	2.19397i
$526$		0			0
$527$	7.27607	+	6.10535i	0.316950	+	0.265953i
$528$		0			0
$529$	20.7630	+	7.55712i	0.902739	+	0.328570i
$530$		0			0
$531$	−14.6247	+	11.6692i	−0.634657	+	0.506402i
$532$		0			0
$533$	−2.97279	+	0.524183i	−0.128766	+	0.0227049i
$534$		0			0
$535$	17.9806	−	6.54441i	0.777370	−	0.282939i
$536$		0			0
$537$	3.01451	+	6.67843i	0.130086	+	0.288196i
$538$		0			0
$539$		−	3.75520i		−	0.161748i
$540$		0			0
$541$		−	11.2309i		−	0.482852i	−0.970419	−	0.241426i	$-0.922385\pi$
$541$		−	11.2309i		−	0.482852i	0.970419	−	0.241426i	$-0.0776152\pi$
$542$		0			0
$543$	32.7720	+	3.27488i	1.40638	+	0.140538i
$544$		0			0
$545$	−9.29398	+	3.38273i	−0.398110	+	0.144900i
$546$		0			0
$547$	19.8704	−	3.50369i	0.849599	−	0.149807i	0.268137	−	0.963381i	$-0.413592\pi$
$547$	19.8704	−	3.50369i	0.849599	−	0.149807i	0.581462	+	0.813574i	$0.302481\pi$
$548$		0			0
$549$	−4.70002	−	8.62515i	−0.200592	−	0.368113i
$550$		0			0
$551$	−15.5798	−	5.67059i	−0.663722	−	0.241575i
$552$		0			0
$553$	−0.590998	−	0.495906i	−0.0251318	−	0.0210881i
$554$		0			0
$555$	−46.6915	+	45.5539i	−1.98194	+	1.93366i
$556$		0			0
$557$	−26.7781	−	15.4604i	−1.13463	−	0.655076i	−0.189532	−	0.981875i	$-0.560697\pi$
$557$	−26.7781	−	15.4604i	−1.13463	−	0.655076i	−0.945094	+	0.326798i	$0.894030\pi$
$558$		0			0
$559$	12.4556	+	21.5737i	0.526814	+	0.912469i
$560$		0			0
$561$	−1.87861	−	25.0231i	−0.0793150	−	1.05648i
$562$		0			0
$563$	−20.3052	−	3.58035i	−0.855761	−	0.150894i	−0.271479	−	0.962444i	$-0.587513\pi$
$563$	−20.3052	−	3.58035i	−0.855761	−	0.150894i	−0.584282	+	0.811551i	$0.698624\pi$
$564$		0			0
$565$	18.2450	+	21.7436i	0.767575	+	0.914760i
$566$		0			0
$567$	−19.0046	−	17.6146i	−0.798117	−	0.739744i
$568$		0			0
$569$	−3.82688	+	3.21114i	−0.160431	+	0.134618i	−0.719469	−	0.694524i	$-0.755615\pi$
$569$	−3.82688	+	3.21114i	−0.160431	+	0.134618i	0.559038	+	0.829142i	$0.311171\pi$
$570$		0			0
$571$	7.54047	+	1.32959i	0.315559	+	0.0556415i	0.329184	−	0.944266i	$-0.393226\pi$
$571$	7.54047	+	1.32959i	0.315559	+	0.0556415i	−0.0136257	+	0.999907i	$0.504337\pi$
$572$		0			0
$573$	14.0421	−	1.05421i	0.586617	−	0.0440404i
$574$		0			0
$575$	−4.94663	−	8.56781i	−0.206289	−	0.357303i
$576$		0			0
$577$	6.53703	−	11.3225i	0.272140	−	0.471361i	−0.697269	−	0.716809i	$-0.745602\pi$
$577$	6.53703	−	11.3225i	0.272140	−	0.471361i	0.969410	+	0.245449i	$0.0789352\pi$
$578$		0			0
$579$	16.3520	−	15.9536i	0.679567	−	0.663009i
$580$		0			0
$581$	−22.7783	+	27.1462i	−0.945005	+	1.12621i
$582$		0			0
$583$	−9.69302	−	3.52797i	−0.401444	−	0.146114i
$584$		0			0
$585$	−1.15535	+	46.8343i	−0.0477677	+	1.93636i
$586$		0			0
$587$	20.2706	−	3.57425i	0.836657	−	0.147525i	0.261126	−	0.965305i	$-0.415906\pi$
$587$	20.2706	−	3.57425i	0.836657	−	0.147525i	0.575532	+	0.817780i	$0.304795\pi$
$588$		0			0
$589$	−1.34217	−	3.68759i	−0.0553033	−	0.151945i
$590$		0			0
$591$	10.6512	+	1.06436i	0.438130	+	0.0437819i
$592$		0			0
$593$	35.4674			1.45647			0.728237	−	0.685326i	$-0.240340\pi$
$593$	35.4674			1.45647			0.728237	+	0.685326i	$0.240340\pi$
$594$		0			0
$595$		−	56.2142i		−	2.30456i
$596$		0			0
$597$	14.0095	−	6.32358i	0.573369	−	0.258807i
$598$		0			0
$599$	−4.95171	+	1.80227i	−0.202321	+	0.0736389i	−0.441193	−	0.897412i	$-0.645445\pi$
$599$	−4.95171	+	1.80227i	−0.202321	+	0.0736389i	0.238872	+	0.971051i	$0.423222\pi$
$600$		0			0
$601$	−6.16086	−	34.9400i	−0.251307	−	1.42523i	−0.805378	−	0.592762i	$-0.798038\pi$
$601$	−6.16086	−	34.9400i	−0.251307	−	1.42523i	0.554071	−	0.832469i	$-0.313074\pi$
$602$		0			0
$603$	−19.1555	−	7.51201i	−0.780071	−	0.305913i
$604$		0			0
$605$	3.38165	−	9.29100i	0.137484	−	0.377733i
$606$		0			0
$607$	6.68660	+	5.61072i	0.271401	+	0.227732i	0.768322	−	0.640063i	$-0.221092\pi$
$607$	6.68660	+	5.61072i	0.271401	+	0.227732i	−0.496922	+	0.867795i	$0.665536\pi$
$608$		0			0
$609$	38.9803	−	9.93120i	1.57956	−	0.402432i
$610$		0			0
$611$	18.4970	+	10.6793i	0.748309	+	0.432036i
$612$		0			0
$613$	−28.4795	+	16.4426i	−1.15028	+	0.664112i	−0.948954	−	0.315414i	$-0.897857\pi$
$613$	−28.4795	+	16.4426i	−1.15028	+	0.664112i	−0.201321	+	0.979525i	$0.564523\pi$
$614$		0			0
$615$	−4.26048	+	2.90559i	−0.171799	+	0.117165i
$616$		0			0
$617$	5.77150	−	32.7318i	0.232352	−	1.31773i	−0.615767	−	0.787928i	$-0.711154\pi$
$617$	5.77150	−	32.7318i	0.232352	−	1.31773i	0.848119	−	0.529805i	$-0.177735\pi$
$618$		0			0
$619$	22.6481	+	26.9910i	0.910305	+	1.08486i	0.996072	+	0.0885446i	$0.0282216\pi$
$619$	22.6481	+	26.9910i	0.910305	+	1.08486i	−0.0857667	+	0.996315i	$0.527334\pi$
$620$		0			0
$621$	4.39841	+	2.25269i	0.176502	+	0.0903974i
$622$		0			0
$623$	18.1451	−	15.2255i	0.726966	−	0.609997i
$624$		0			0
$625$	5.41806	−	30.7273i	0.216722	−	1.22909i
$626$		0			0
$627$	−4.49705	+	9.34144i	−0.179595	+	0.373061i
$628$		0			0
$629$	41.3448	−	23.8704i	1.64852	−	0.951775i
$630$		0			0
$631$	20.3613	−	35.2667i	0.810569	−	1.40395i	−0.101898	−	0.994795i	$-0.532491\pi$
$631$	20.3613	−	35.2667i	0.810569	−	1.40395i	0.912466	−	0.409152i	$-0.134175\pi$
$632$		0			0
$633$	8.28649	−	29.4672i	0.329358	−	1.17121i
$634$		0			0
$635$	12.0336	−	14.3411i	0.477539	−	0.569109i
$636$		0			0
$637$	1.75488	−	4.82149i	0.0695308	−	0.191034i
$638$		0			0
$639$	−22.5673	−	4.55574i	−0.892747	−	0.180222i
$640$		0			0
$641$	−8.76821	−	49.7270i	−0.346323	−	1.96410i	−0.246823	−	0.969061i	$-0.579387\pi$
$641$	−8.76821	−	49.7270i	−0.346323	−	1.96410i	−0.0995006	−	0.995038i	$-0.531725\pi$
$642$		0			0
$643$	−15.1261	−	41.5587i	−0.596517	−	1.63892i	−0.758162	−	0.652067i	$-0.773902\pi$
$643$	−15.1261	−	41.5587i	−0.596517	−	1.63892i	0.161645	−	0.986849i	$-0.448320\pi$
$644$		0			0
$645$	34.5572	+	24.8379i	1.36069	+	0.977990i
$646$		0			0
$647$	−2.96214			−0.116454			−0.0582268	−	0.998303i	$-0.518545\pi$
$647$	−2.96214			−0.116454			−0.0582268	+	0.998303i	$0.518545\pi$
$648$		0			0
$649$	−18.1619			−0.712917
$650$		0			0
$651$	7.73121	+	5.55678i	0.303010	+	0.217787i
$652$		0			0
$653$	−0.829258	−	2.27837i	−0.0324514	−	0.0891594i	0.922409	−	0.386215i	$-0.126218\pi$
$653$	−0.829258	−	2.27837i	−0.0324514	−	0.0891594i	−0.954860	+	0.297055i	$0.903995\pi$
$654$		0			0
$655$	−2.38780	−	13.5419i	−0.0932992	−	0.529126i
$656$		0			0
$657$	−13.7651	+	15.6063i	−0.537029	+	0.608858i
$658$		0			0
$659$	−14.7728	+	40.5879i	−0.575466	+	1.58108i	0.220272	+	0.975438i	$0.429305\pi$
$659$	−14.7728	+	40.5879i	−0.575466	+	1.58108i	−0.795738	+	0.605641i	$0.792917\pi$
$660$		0			0
$661$	11.3612	−	13.5398i	0.441901	−	0.526637i	−0.498415	−	0.866938i	$-0.666085\pi$
$661$	11.3612	−	13.5398i	0.441901	−	0.526637i	0.940317	+	0.340301i	$0.110529\pi$
$662$		0			0
$663$	9.28173	−	33.0063i	0.360472	−	1.28186i
$664$		0			0
$665$	−11.6126	+	20.1137i	−0.450318	+	0.779974i
$666$		0			0
$667$	−6.64362	+	3.83570i	−0.257242	+	0.148519i
$668$		0			0
$669$	17.5260	−	36.4057i	0.677595	−	1.40753i
$670$		0			0
$671$	1.65574	−	9.39015i	0.0639190	−	0.362503i
$672$		0			0
$673$	1.22568	−	1.02847i	0.0472465	−	0.0396445i	−0.618859	−	0.785502i	$-0.712405\pi$
$673$	1.22568	−	1.02847i	0.0472465	−	0.0396445i	0.666105	+	0.745858i	$0.267960\pi$
$674$		0			0
$675$	21.0164	+	49.8006i	0.808923	+	1.91683i
$676$		0			0
$677$	4.41092	+	5.25673i	0.169526	+	0.202033i	0.844118	−	0.536158i	$-0.180125\pi$
$677$	4.41092	+	5.25673i	0.169526	+	0.202033i	−0.674592	+	0.738191i	$0.735680\pi$
$678$		0			0
$679$	−2.69280	+	15.2717i	−0.103340	+	0.586072i
$680$		0			0
$681$	−35.5098	+	24.2172i	−1.36074	+	0.928005i
$682$		0			0
$683$	4.11971	−	2.37852i	0.157636	−	0.0910113i	−0.419107	−	0.907937i	$-0.637657\pi$
$683$	4.11971	−	2.37852i	0.157636	−	0.0910113i	0.576743	+	0.816926i	$0.304323\pi$
$684$		0			0
$685$	56.1590	+	32.4234i	2.14573	+	1.23884i
$686$		0			0
$687$	−9.35400	+	2.38316i	−0.356877	+	0.0909233i
$688$		0			0
$689$	−10.7966	−	9.05946i	−0.411320	−	0.345138i
$690$		0			0
$691$	4.35017	−	11.9520i	0.165488	−	0.454675i	−0.829034	−	0.559198i	$-0.811109\pi$
$691$	4.35017	−	11.9520i	0.165488	−	0.454675i	0.994523	+	0.104523i	$0.0333315\pi$
$692$		0			0
$693$	−3.75566	−	24.8717i	−0.142666	−	0.944798i
$694$		0			0
$695$	13.5392	+	76.7844i	0.513570	+	2.91260i
$696$		0			0
$697$	3.54655	−	1.29084i	0.134335	−	0.0488939i
$698$		0			0
$699$	10.5005	−	4.73969i	0.397164	−	0.179272i
$700$		0			0
$701$			12.2688i			0.463386i	0.972789	+	0.231693i	$0.0744265\pi$
$701$			12.2688i			0.463386i	−0.972789	+	0.231693i	$0.925573\pi$
$702$		0			0
$703$	−19.7244			−0.743921
$704$		0			0
$705$	36.3072	+	3.62815i	1.36741	+	0.136644i
$706$		0			0
$707$	−3.98304	−	10.9433i	−0.149797	−	0.411565i
$708$		0			0
$709$	25.9792	−	4.58083i	0.975668	−	0.172037i	0.336988	−	0.941509i	$-0.390592\pi$
$709$	25.9792	−	4.58083i	0.975668	−	0.172037i	0.638680	+	0.769473i	$0.279481\pi$
$710$		0			0
$711$	−0.686054	−	0.418985i	−0.0257290	−	0.0157132i
$712$		0			0
$713$	−1.70624	−	0.621021i	−0.0638993	−	0.0232574i
$714$		0			0
$715$	−29.2320	+	34.8373i	−1.09321	+	1.30284i
$716$		0			0
$717$	−32.4366	+	31.6463i	−1.21137	+	1.18185i
$718$		0			0
$719$	15.9411	−	27.6108i	0.594502	−	1.02971i	−0.399115	−	0.916901i	$-0.630683\pi$
$719$	15.9411	−	27.6108i	0.594502	−	1.02971i	0.993617	−	0.112807i	$-0.0359841\pi$
$720$		0			0
$721$	−1.64289	−	2.84557i	−0.0611845	−	0.105975i
$722$		0			0
$723$	43.3780	−	3.25661i	1.61325	−	0.121115i
$724$		0			0
$725$	−82.6364	−	14.5710i	−3.06904	−	0.541154i
$726$		0			0
$727$	−30.8679	+	25.9013i	−1.14483	+	0.960625i	−0.999586	−	0.0287706i	$-0.990841\pi$
$727$	−30.8679	+	25.9013i	−1.14483	+	0.960625i	−0.145243	+	0.989396i	$0.546396\pi$
$728$		0			0
$729$	−22.3207	−	15.1916i	−0.826694	−	0.562652i
$730$		0			0
$731$	−20.0202	−	23.8591i	−0.740473	−	0.882461i
$732$		0			0
$733$	0.103428	+	0.0182371i	0.00382018	+	0.000673601i	0.175558	−	0.984469i	$-0.443827\pi$
$733$	0.103428	+	0.0182371i	0.00382018	+	0.000673601i	−0.171738	+	0.985143i	$0.554938\pi$
$734$		0			0
$735$	−0.656222	−	8.74087i	−0.0242051	−	0.322412i
$736$		0			0
$737$	−9.98667	−	17.2974i	−0.367864	−	0.637158i
$738$		0			0
$739$	26.3545	+	15.2158i	0.969466	+	0.559722i	0.899074	−	0.437798i	$-0.144241\pi$
$739$	26.3545	+	15.2158i	0.969466	+	0.559722i	0.0703928	+	0.997519i	$0.477575\pi$
$740$		0			0
$741$	−10.1394	+	9.89237i	−0.372481	+	0.363405i
$742$		0			0
$743$	−12.9183	−	10.8397i	−0.473926	−	0.397671i	0.374298	−	0.927308i	$-0.377884\pi$
$743$	−12.9183	−	10.8397i	−0.473926	−	0.397671i	−0.848224	+	0.529637i	$0.822328\pi$
$744$		0			0
$745$	−42.4539	−	15.4520i	−1.55539	−	0.566116i
$746$		0			0
$747$	−19.2451	+	31.5123i	−0.704143	+	1.15298i
$748$		0			0
$749$	−13.8241	+	2.43756i	−0.505122	+	0.0890666i
$750$		0			0
$751$	−14.6848	+	5.34482i	−0.535855	+	0.195035i	−0.595751	−	0.803169i	$-0.703145\pi$
$751$	−14.6848	+	5.34482i	−0.535855	+	0.195035i	0.0598958	+	0.998205i	$0.480923\pi$
$752$		0			0
$753$	50.2379	+	5.02023i	1.83077	+	0.182947i
$754$		0			0
$755$		−	14.3029i		−	0.520536i
$756$		0			0
$757$			27.3201i			0.992967i	0.868046	+	0.496484i	$0.165376\pi$
$757$			27.3201i			0.992967i	−0.868046	+	0.496484i	$0.834624\pi$
$758$		0			0
$759$	1.97355	+	4.37226i	0.0716353	+	0.158703i
$760$		0			0
$761$	−14.1817	+	5.16172i	−0.514086	+	0.187112i	−0.586019	−	0.810297i	$-0.699306\pi$
$761$	−14.1817	+	5.16172i	−0.514086	+	0.187112i	0.0719327	+	0.997409i	$0.477083\pi$
$762$		0			0
$763$	7.14552	−	1.25995i	0.258685	−	0.0456132i
$764$		0			0
$765$	−8.74558	−	57.9172i	−0.316197	−	2.09400i
$766$		0			0
$767$	−23.3189	−	8.48740i	−0.841998	−	0.306462i
$768$		0			0
$769$	−11.4199	−	9.58242i	−0.411811	−	0.345551i	0.413226	−	0.910628i	$-0.364402\pi$
$769$	−11.4199	−	9.58242i	−0.411811	−	0.345551i	−0.825038	+	0.565077i	$0.808846\pi$
$770$		0			0
$771$	3.02906	+	11.8892i	0.109089	+	0.428178i
$772$		0			0
$773$	−27.9615	−	16.1436i	−1.00571	−	0.580644i	−0.0957742	−	0.995403i	$-0.530533\pi$
$773$	−27.9615	−	16.1436i	−1.00571	−	0.580644i	−0.909931	+	0.414759i	$0.863866\pi$
$774$		0			0
$775$	−9.93049	−	17.2001i	−0.356714	−	0.617846i
$776$		0			0
$777$	39.5362	−	26.9631i	1.41835	−	0.967297i
$778$		0			0
$779$	−1.53563	−	0.270772i	−0.0550195	−	0.00970143i
$780$		0			0
$781$	−14.3653	−	17.1199i	−0.514031	−	0.612598i
$782$		0			0
$783$	38.6162	−	16.2965i	1.38003	−	0.582388i
$784$		0			0
$785$	44.0064	−	36.9258i	1.57066	−	1.31794i
$786$		0			0
$787$	−39.6718	−	6.99522i	−1.41415	−	0.249353i	−0.586204	−	0.810163i	$-0.699378\pi$
$787$	−39.6718	−	6.99522i	−1.41415	−	0.249353i	−0.827944	+	0.560811i	$0.810490\pi$
$788$		0			0
$789$	−8.61949	+	17.9047i	−0.306862	+	0.637425i
$790$		0			0
$791$	−10.4115	−	18.0333i	−0.370191	−	0.641189i
$792$		0			0
$793$	6.51408	−	11.2827i	0.231322	−	0.400661i
$794$		0			0
$795$	−23.1787	−	6.51809i	−0.822062	−	0.231173i
$796$		0			0
$797$	2.35451	−	2.80599i	0.0834009	−	0.0993934i	−0.722730	−	0.691130i	$-0.757113\pi$
$797$	2.35451	−	2.80599i	0.0834009	−	0.0993934i	0.806131	+	0.591737i	$0.201558\pi$
$798$		0			0
$799$	−25.0936	−	9.13334i	−0.887749	−	0.323114i
$800$		0			0
$801$	16.3260	−	18.5097i	0.576852	−	0.654008i
$802$		0			0
$803$	−19.8933	+	3.50773i	−0.702020	+	0.123785i
$804$		0			0
$805$	3.67544	+	10.0982i	0.129542	+	0.355915i
$806$		0			0
$807$	15.3472	−	21.3527i	0.540248	−	0.751652i
$808$		0			0
$809$	−41.2691			−1.45094			−0.725472	−	0.688252i	$-0.758378\pi$
$809$	−41.2691			−1.45094			−0.725472	+	0.688252i	$0.758378\pi$
$810$		0			0
$811$			25.6578i			0.900966i	0.892785	+	0.450483i	$0.148748\pi$
$811$			25.6578i			0.900966i	−0.892785	+	0.450483i	$0.851252\pi$
$812$		0			0
$813$	18.6789	+	13.4254i	0.655097	+	0.470849i
$814$		0			0
$815$	−21.9023	+	7.97178i	−0.767204	+	0.279239i
$816$		0			0
$817$	2.23452	+	12.6726i	0.0781761	+	0.443359i
$818$		0			0
$819$	6.80094	−	33.6891i	0.237644	−	1.17719i
$820$		0			0
$821$	−8.61194	+	23.6611i	−0.300559	+	0.825778i	0.693844	+	0.720125i	$0.255916\pi$
$821$	−8.61194	+	23.6611i	−0.300559	+	0.825778i	−0.994403	+	0.105653i	$0.966307\pi$
$822$		0			0
$823$	−10.3916	−	8.71956i	−0.362227	−	0.303945i	0.443450	−	0.896299i	$-0.353754\pi$
$823$	−10.3916	−	8.71956i	−0.362227	−	0.303945i	−0.805678	+	0.592354i	$0.798199\pi$
$824$		0			0
$825$	−14.2045	+	50.5117i	−0.494536	+	1.75859i
$826$		0			0
$827$	−9.62668	−	5.55796i	−0.334752	−	0.193269i	0.323197	−	0.946332i	$-0.395242\pi$
$827$	−9.62668	−	5.55796i	−0.334752	−	0.193269i	−0.657949	+	0.753062i	$0.728576\pi$
$828$		0			0
$829$	−26.4493	+	15.2705i	−0.918621	+	0.530366i	−0.883195	−	0.469006i	$-0.844612\pi$
$829$	−26.4493	+	15.2705i	−0.918621	+	0.530366i	−0.0354262	+	0.999372i	$0.511279\pi$
$830$		0			0
$831$	−4.01584	−	1.93326i	−0.139308	−	0.0670640i
$832$		0			0
$833$	−1.11397	+	6.31762i	−0.0385967	+	0.218893i
$834$		0			0
$835$	−50.2277	−	59.8590i	−1.73820	−	2.07151i
$836$		0			0
$837$	8.82993	+	4.52233i	0.305207	+	0.156315i
$838$		0			0
$839$	3.67221	−	3.08135i	0.126779	−	0.106380i	−0.577194	−	0.816607i	$-0.695852\pi$
$839$	3.67221	−	3.08135i	0.126779	−	0.106380i	0.703972	+	0.710227i	$0.251408\pi$
$840$		0			0
$841$	−6.26281	+	35.5181i	−0.215959	+	1.22476i
$842$		0			0
$843$	−26.4072	−	38.7210i	−0.909512	−	1.33362i
$844$		0			0
$845$	−9.62790	+	5.55867i	−0.331210	+	0.191224i
$846$		0			0
$847$	−3.62672	+	6.28165i	−0.124615	+	0.215840i
$848$		0			0
$849$	−44.8719	+	11.4322i	−1.54000	+	0.392353i
$850$		0			0
$851$	−5.86637	+	6.99127i	−0.201097	+	0.239657i
$852$		0			0
$853$	7.52367	−	20.6711i	0.257605	−	0.707765i	−0.741708	−	0.670723i	$-0.765984\pi$
$853$	7.52367	−	20.6711i	0.257605	−	0.707765i	0.999314	−	0.0370424i	$-0.0117937\pi$
$854$		0			0
$855$	−8.83523	+	22.5296i	−0.302159	+	0.770498i
$856$		0			0
$857$	−1.54554	−	8.76520i	−0.0527947	−	0.299414i	0.946965	−	0.321337i	$-0.104132\pi$
$857$	−1.54554	−	8.76520i	−0.0527947	−	0.299414i	−0.999760	+	0.0219232i	$0.993021\pi$
$858$		0			0
$859$	7.12897	+	19.5867i	0.243237	+	0.668289i	0.999895	+	0.0144780i	$0.00460866\pi$
$859$	7.12897	+	19.5867i	0.243237	+	0.668289i	−0.756658	+	0.653811i	$0.773169\pi$
$860$		0			0
$861$	3.44820	−	1.55645i	0.117514	−	0.0530436i
$862$		0			0
$863$	21.4666			0.730731			0.365365	−	0.930864i	$-0.380944\pi$
$863$	21.4666			0.730731			0.365365	+	0.930864i	$0.380944\pi$
$864$		0			0
$865$	−43.2459			−1.47040
$866$		0			0
$867$	−1.33468	+	13.3563i	−0.0453282	+	0.453604i
$868$		0			0
$869$	−0.266892	−	0.733280i	−0.00905370	−	0.0248748i
$870$		0			0
$871$	−4.73896	−	26.8760i	−0.160573	−	0.910657i
$872$		0			0
$873$	−0.398481	+	16.1532i	−0.0134866	+	0.546705i
$874$		0			0
$875$	−20.8794	+	57.3655i	−0.705851	+	1.93931i
$876$		0			0
$877$	0.176559	−	0.210415i	0.00596198	−	0.00710521i	−0.763055	−	0.646333i	$-0.776302\pi$
$877$	0.176559	−	0.210415i	0.00596198	−	0.00710521i	0.769017	+	0.639228i	$0.220746\pi$
$878$		0			0
$879$	21.2886	+	21.8202i	0.718045	+	0.735977i
$880$		0			0
$881$	−11.9250	+	20.6547i	−0.401763	+	0.695873i	−0.993939	−	0.109935i	$-0.964936\pi$
$881$	−11.9250	+	20.6547i	−0.401763	+	0.695873i	0.592176	+	0.805809i	$0.298269\pi$
$882$		0			0
$883$	−4.93626	+	2.84995i	−0.166118	+	0.0959085i	−0.580754	−	0.814079i	$-0.697242\pi$
$883$	−4.93626	+	2.84995i	−0.166118	+	0.0959085i	0.414636	+	0.909987i	$0.363909\pi$
$884$		0			0
$885$	−42.2749	+	3.17379i	−1.42106	+	0.106686i
$886$		0			0
$887$	2.98032	−	16.9022i	0.100069	−	0.567521i	−0.893006	−	0.450044i	$-0.851408\pi$
$887$	2.98032	−	16.9022i	0.100069	−	0.567521i	0.993076	−	0.117477i	$-0.0374806\pi$
$888$		0			0
$889$	−10.5208	+	8.82801i	−0.352857	+	0.296082i
$890$		0			0
$891$	−7.73888	−	25.0409i	−0.259262	−	0.838902i
$892$		0			0
$893$	7.09185	+	8.45174i	0.237320	+	0.282827i
$894$		0			0
$895$	−2.88302	+	16.3504i	−0.0963689	+	0.546535i
$896$		0			0
$897$	0.490694	+	6.53604i	0.0163838	+	0.218232i
$898$		0			0
$899$	−13.3372	+	7.70026i	−0.444822	+	0.256818i
$900$		0			0
$901$	15.2606	+	8.81073i	0.508405	+	0.293528i
$902$		0			0
$903$	−21.8023	−	22.3468i	−0.725536	−	0.743655i
$904$		0			0
$905$	57.1678	+	47.9695i	1.90032	+	1.59456i
$906$		0			0
$907$	14.9621	−	41.1081i	0.496809	−	1.36497i	−0.397533	−	0.917588i	$-0.630134\pi$
$907$	14.9621	−	41.1081i	0.496809	−	1.36497i	0.894342	−	0.447383i	$-0.147644\pi$
$908$		0			0
$909$	−5.80622	−	10.6552i	−0.192580	−	0.353410i
$910$		0			0
$911$	−0.448255	−	2.54218i	−0.0148514	−	0.0842262i	0.976481	−	0.215602i	$-0.0691715\pi$
$911$	−0.448255	−	2.54218i	−0.0148514	−	0.0842262i	−0.991333	+	0.131376i	$0.958060\pi$
$912$		0			0
$913$	−33.6816	+	12.2591i	−1.11470	+	0.405717i
$914$		0			0
$915$	2.21308	−	22.1465i	0.0731622	−	0.732141i
$916$		0			0
$917$			10.0878i			0.333127i
$918$		0			0
$919$	59.9068			1.97614			0.988071	−	0.153998i	$-0.0492148\pi$
$919$	59.9068			1.97614			0.988071	+	0.153998i	$0.0492148\pi$
$920$		0			0
$921$	−8.38961	−	18.5866i	−0.276447	−	0.612449i
$922$		0			0
$923$	−10.4439	−	28.6943i	−0.343764	−	0.944483i
$924$		0			0
$925$	−98.3103	+	17.3348i	−3.23242	+	0.569963i
$926$		0			0
$927$	−2.13537	−	2.67618i	−0.0701346	−	0.0878974i
$928$		0			0
$929$	−30.1626	−	10.9783i	−0.989604	−	0.360186i	−0.204037	−	0.978963i	$-0.565406\pi$
$929$	−30.1626	−	10.9783i	−0.989604	−	0.360186i	−0.785567	+	0.618777i	$0.787629\pi$
$930$		0			0
$931$	1.70366	−	2.03035i	0.0558354	−	0.0665420i
$932$		0			0
$933$	14.5415	+	57.0758i	0.476066	+	1.86858i
$934$		0			0
$935$	28.4294	−	49.2412i	0.929741	−	1.61036i
$936$		0			0
$937$	8.40875	+	14.5644i	0.274702	+	0.475797i	0.970060	−	0.242866i	$-0.0780875\pi$
$937$	8.40875	+	14.5644i	0.274702	+	0.475797i	−0.695358	+	0.718663i	$0.744754\pi$
$938$		0			0
$939$	−6.89663	−	10.1126i	−0.225063	−	0.330011i
$940$		0			0
$941$	−20.4427	−	3.60459i	−0.666412	−	0.117506i	−0.169799	−	0.985479i	$-0.554312\pi$
$941$	−20.4427	−	3.60459i	−0.666412	−	0.117506i	−0.496613	+	0.867972i	$0.665423\pi$
$942$		0			0
$943$	−0.552695	+	0.463766i	−0.0179982	+	0.0151023i
$944$		0			0
$945$	−13.0883	−	57.2368i	−0.425761	−	1.86191i
$946$		0			0
$947$	11.7887	+	14.0493i	0.383082	+	0.456540i	0.922785	−	0.385316i	$-0.125908\pi$
$947$	11.7887	+	14.0493i	0.383082	+	0.456540i	−0.539702	+	0.841856i	$0.681463\pi$
$948$		0			0
$949$	−27.1812	−	4.79278i	−0.882340	−	0.155580i
$950$		0			0
$951$	−8.46407	−	4.07468i	−0.274466	−	0.132130i
$952$		0			0
$953$	1.73534	+	3.00570i	0.0562133	+	0.0973643i	0.892763	−	0.450527i	$-0.148764\pi$
$953$	1.73534	+	3.00570i	0.0562133	+	0.0973643i	−0.836549	+	0.547892i	$0.815431\pi$
$954$		0			0
$955$	27.6325	+	15.9536i	0.894166	+	0.516247i
$956$		0			0
$957$	39.1676	+	11.0144i	1.26611	+	0.356044i
$958$		0			0
$959$	−36.4426	−	30.5790i	−1.17679	−	0.987447i
$960$		0			0
$961$	25.7051	+	9.35591i	0.829198	+	0.301803i
$962$		0			0
$963$	−13.8637	+	4.66211i	−0.446751	+	0.150234i
$964$		0			0
$965$	50.9782	−	8.98883i	1.64105	−	0.289361i
$966$		0			0
$967$	29.0536	−	10.5747i	0.934301	−	0.340058i	0.170388	−	0.985377i	$-0.445498\pi$
$967$	29.0536	−	10.5747i	0.934301	−	0.340058i	0.763913	+	0.645319i	$0.223276\pi$
$968$		0			0
$969$	10.3368	−	14.3817i	0.332065	−	0.462006i
$970$		0			0
$971$			0.278968i			0.00895249i	0.999990	+	0.00447625i	$0.00142484\pi$
$971$			0.278968i			0.00895249i	−0.999990	+	0.00447625i	$0.998575\pi$
$972$		0			0
$973$		−	57.1990i		−	1.83372i
$974$		0			0
$975$	−41.8429	+	58.2165i	−1.34005	+	1.86442i
$976$		0			0
$977$	20.1241	−	7.32457i	0.643827	−	0.234334i	0.000588326	−	1.00000i	$-0.499813\pi$
$977$	20.1241	−	7.32457i	0.643827	−	0.234334i	0.643238	+	0.765666i	$0.277591\pi$
$978$		0			0
$979$	23.5943	−	4.16032i	0.754078	−	0.132964i
$980$		0			0
$981$	7.16598	−	2.40979i	0.228792	−	0.0769387i
$982$		0			0
$983$	5.52983	+	2.01269i	0.176374	+	0.0641950i	0.428698	−	0.903448i	$-0.358973\pi$
$983$	5.52983	+	2.01269i	0.176374	+	0.0641950i	−0.252324	+	0.967643i	$0.581195\pi$
$984$		0			0
$985$	18.5800	+	15.5905i	0.592008	+	0.496753i
$986$		0			0
$987$	−25.7686	−	7.24641i	−0.820223	−	0.230656i
$988$		0			0
$989$	5.15636	+	2.97702i	0.163963	+	0.0946639i
$990$		0			0
$991$	−17.5543	−	30.4049i	−0.557631	−	0.965845i	−0.997694	−	0.0678778i	$-0.978377\pi$
$991$	−17.5543	−	30.4049i	−0.557631	−	0.965845i	0.440063	−	0.897967i	$-0.354956\pi$
$992$		0			0
$993$	8.46642	+	4.07581i	0.268674	+	0.129342i
$994$		0			0
$995$	34.2986	+	6.04777i	1.08734	+	0.191727i
$996$		0			0
$997$	16.1819	+	19.2848i	0.512485	+	0.610756i	0.958787	−	0.284127i	$-0.0917036\pi$
$997$	16.1819	+	19.2848i	0.512485	+	0.610756i	−0.446302	+	0.894883i	$0.647259\pi$
$998$		0			0
$999$	36.5392	−	33.9309i	1.15605	−	1.07353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.49.7		204
4.3	odd	2		216.2.t.a.157.17	✓	204
8.3	odd	2		216.2.t.a.157.31	yes	204
8.5	even	2	inner	864.2.bf.a.49.28		204
12.11	even	2		648.2.t.a.37.18		204
24.11	even	2		648.2.t.a.37.4		204
27.16	even	9	inner	864.2.bf.a.529.28		204
108.11	even	18		648.2.t.a.613.4		204
108.43	odd	18		216.2.t.a.205.31	yes	204
216.11	even	18		648.2.t.a.613.18		204
216.43	odd	18		216.2.t.a.205.17	yes	204
216.205	even	18	inner	864.2.bf.a.529.7		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.17	✓	204	4.3	odd	2
216.2.t.a.157.31	yes	204	8.3	odd	2
216.2.t.a.205.17	yes	204	216.43	odd	18
216.2.t.a.205.31	yes	204	108.43	odd	18
648.2.t.a.37.4		204	24.11	even	2
648.2.t.a.37.18		204	12.11	even	2
648.2.t.a.613.4		204	108.11	even	18
648.2.t.a.613.18		204	216.11	even	18
864.2.bf.a.49.7		204	1.1	even	1	trivial
864.2.bf.a.49.28		204	8.5	even	2	inner
864.2.bf.a.529.7		204	216.205	even	18	inner
864.2.bf.a.529.28		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.40645 - 1.01088i) q^{3} +(-1.34230 - 3.68793i) q^{5} +(0.499959 + 2.83541i) q^{7} +(0.956226 + 2.84352i) q^{9} +(-0.996019 + 2.73654i) q^{11} +(-2.55767 + 3.04812i) q^{13} +(-1.84019 + 6.54382i) q^{15} +(2.48745 - 4.30839i) q^{17} +(-1.78004 + 1.02771i) q^{19} +(2.16310 - 4.49327i) q^{21} +(-0.165146 + 0.936587i) q^{23} +(-7.96887 + 6.68667i) q^{25} +(1.52959 - 4.96592i) q^{27} +(5.18495 + 6.17919i) q^{29} +(-0.331534 + 1.88022i) q^{31} +(4.16718 - 2.84196i) q^{33} +(9.78570 - 5.64977i) q^{35} +(8.31066 + 4.79816i) q^{37} +(6.67855 - 1.70152i) q^{39} +(0.581151 + 0.487644i) q^{41} +(2.14125 - 5.88303i) q^{43} +(9.20319 - 7.34336i) q^{45} +(-0.932102 - 5.28621i) q^{47} +(-1.21172 + 0.441031i) q^{49} +(-7.85378 + 3.54503i) q^{51} +3.54207i q^{53} +11.4291 q^{55} +(3.54244 + 0.353992i) q^{57} +(2.13303 + 5.86045i) q^{59} +(-3.22446 + 0.568559i) q^{61} +(-7.58447 + 4.13293i) q^{63} +(14.6744 + 5.34105i) q^{65} +(-4.40861 + 5.25398i) q^{67} +(1.17905 - 1.15032i) q^{69} +(-3.83709 + 6.64603i) q^{71} +(3.46824 + 6.00718i) q^{73} +(17.9673 - 1.34890i) q^{75} +(-8.25717 - 1.45596i) q^{77} +(-0.205269 + 0.172241i) q^{79} +(-7.17126 + 5.43811i) q^{81} +(7.91149 + 9.42855i) q^{83} +(-19.2280 - 3.39041i) q^{85} +(-1.04596 - 13.9321i) q^{87} +(-4.11349 - 7.12477i) q^{89} +(-9.92138 - 5.72811i) q^{91} +(2.36698 - 2.30931i) q^{93} +(6.17946 + 5.18518i) q^{95} +(5.06123 + 1.84214i) q^{97} +(-8.73384 - 0.215453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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