LMFDB - Embedded newform 864.2.bf.a.49.28

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			49.28
Character	$\chi$	$=$	864.49
Dual form			864.2.bf.a.529.28

$q$-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	$0.229726\pi$
$5$	1.34230	+	3.68793i	0.600294	+	1.64929i	−0.150386	+	0.988627i	$0.548052\pi$
$6$		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	$-0.744213\pi$
$11$	0.996019	−	2.73654i	0.300311	−	0.825098i	0.994446	−	0.105252i	$-0.0335650\pi$
$12$		0			0
$13$	2.55767	−	3.04812i	0.709371	−	0.845396i	−0.284181	−	0.958771i	$-0.591722\pi$
$13$	2.55767	−	3.04812i	0.709371	−	0.845396i	0.993552	+	0.113375i	$0.0361661\pi$
$14$		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	−0.281720	−	0.959497i	$-0.590905\pi$
$19$	1.78004	−	1.02771i	0.408369	−	0.235772i	0.690089	+	0.723725i	$0.257571\pi$
$20$		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	$-0.952784\pi$
$29$	−5.18495	−	6.17919i	−0.962821	−	1.14745i	0.0261974	−	0.999657i	$-0.491660\pi$
$30$		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	−0.375816	−	0.926694i	$-0.622637\pi$
$37$	−8.31066	−	4.79816i	−1.36626	−	0.788813i	−0.990449	+	0.137881i	$0.955971\pi$
$38$		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	$0.269519\pi$
$43$	−2.14125	+	5.88303i	−0.326537	+	0.897154i	−0.988981	+	0.148042i	$0.952703\pi$
$44$		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	$-0.921780\pi$
$53$		−	3.54207i		−	0.486541i	0.969959	−	0.243270i	$-0.0782202\pi$
$54$		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	$-0.978046\pi$
$59$	−2.13303	−	5.86045i	−0.277697	−	0.762966i	0.719926	−	0.694051i	$-0.244176\pi$
$60$		0			0
$61$	3.22446	−	0.568559i	0.412849	−	0.0727965i	0.0366341	−	0.999329i	$-0.488336\pi$
$61$	3.22446	−	0.568559i	0.412849	−	0.0727965i	0.376215	+	0.926532i	$0.377225\pi$
$62$		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	−0.426275	−	0.904594i	$-0.640174\pi$
$67$	4.40861	−	5.25398i	0.538598	−	0.641876i	0.964873	+	0.262718i	$0.0846188\pi$
$68$		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	$-0.986152\pi$
$83$	−7.91149	−	9.42855i	−0.868399	−	1.03492i	0.130655	−	0.991428i	$-0.458292\pi$
$84$		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	0.0280840	−	0.999606i	$-0.491059\pi$
$101$	3.98336	−	0.702375i	0.396360	−	0.0698889i	0.368276	+	0.929717i	$0.379948\pi$
$102$		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	$-0.924272\pi$
$107$		−	4.87553i		−	0.471335i	0.971834	−	0.235667i	$-0.0757276\pi$
$108$		0			0
$109$			2.52010i			0.241382i	0.992690	+	0.120691i	$0.0385111\pi$
$109$			2.52010i			0.241382i	−0.992690	+	0.120691i	$0.961489\pi$
$110$		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	0.0208660	−	0.999782i	$-0.493358\pi$
$131$	−3.45051	−	0.608417i	−0.301472	−	0.0531577i	−0.322338	+	0.946625i	$0.604469\pi$
$132$		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	0.923268	−	0.384157i	$-0.125508\pi$
$139$	19.5648	+	3.44981i	1.65947	+	0.292609i	0.736199	+	0.676765i	$0.236619\pi$
$140$		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	−0.978630	−	0.205627i	$-0.934077\pi$
$149$	−7.39950	+	8.81838i	−0.606190	+	0.722429i	0.372440	+	0.928056i	$0.378521\pi$
$150$		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	$-0.912560\pi$
$157$	−5.00630	−	13.7547i	−0.399546	−	1.09774i	0.562960	−	0.826484i	$-0.309662\pi$
$158$		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	$0.0747186\pi$
$163$			5.93891i			0.465171i	−0.972576	+	0.232586i	$0.925281\pi$
$164$		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	$0.248690\pi$
$173$	−3.76876	+	10.3546i	−0.286534	+	0.787245i	−0.996545	+	0.0830547i	$0.973532\pi$
$174$		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	0.630628	−	0.776085i	$-0.282797\pi$
$179$	3.66363	+	2.11520i	0.273832	+	0.158097i	−0.356796	+	0.934182i	$0.616131\pi$
$180$		0			0
$181$	16.4676	−	9.50759i	1.22403	−	0.706694i	0.258255	−	0.966077i	$-0.416853\pi$
$181$	16.4676	−	9.50759i	1.22403	−	0.706694i	0.965775	+	0.259383i	$0.0835192\pi$
$182$		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	−0.297071	−	0.954855i	$-0.596010\pi$
$197$	5.35211	−	3.09004i	0.381322	−	0.220156i	0.678393	+	0.734699i	$0.262677\pi$
$198$		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	$-0.902954\pi$
$211$	−6.04444	−	16.6070i	−0.416116	−	1.14327i	0.537767	−	0.843093i	$-0.319268\pi$
$212$		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	$0.419110\pi$
$227$	−8.48739	+	23.3189i	−0.563328	+	1.54773i	−0.814726	+	0.579846i	$0.803113\pi$
$228$		0			0
$229$	−3.58229	+	4.26921i	−0.236724	+	0.282117i	−0.871307	−	0.490738i	$-0.836727\pi$
$229$	−3.58229	+	4.26921i	−0.236724	+	0.282117i	0.634583	+	0.772855i	$0.281172\pi$
$230$		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	$-0.294900\pi$
$251$	25.2441	−	14.5747i	1.59339	−	0.919945i	0.992719	−	0.120450i	$-0.0384337\pi$
$252$		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	$-0.846834\pi$
$269$		−	15.1820i		−	0.925661i	0.886447	−	0.462831i	$-0.153166\pi$
$270$		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	−0.249259	−	0.968437i	$-0.580187\pi$
$277$	−2.53413	+	0.446836i	−0.152261	+	0.0268478i	0.0969979	+	0.995285i	$0.469076\pi$
$278$		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	$0.514540\pi$
$283$	−17.1845	+	20.4797i	−1.02151	+	1.21739i	−0.975851	+	0.218436i	$0.929905\pi$
$284$		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	0.655245	−	0.755416i	$-0.272565\pi$
$293$	17.3330	+	3.05628i	1.01261	+	0.178550i	0.357361	+	0.933966i	$0.383677\pi$
$294$		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	0.179972	−	0.983672i	$-0.442399\pi$
$307$	−10.1962	−	5.88676i	−0.581926	−	0.335975i	−0.761898	+	0.647696i	$0.775732\pi$
$308$		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	−0.321616	−	0.946870i	$-0.604226\pi$
$317$	−5.34112	+	0.941783i	−0.299987	+	0.0528958i	0.0216287	+	0.999766i	$0.493115\pi$
$318$		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	−0.0248795	−	0.999690i	$-0.507920\pi$
$331$	5.34260	−	0.942044i	0.293656	−	0.0517794i	0.318535	+	0.947911i	$0.396809\pi$
$332$		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	−0.306052	−	0.952015i	$-0.599008\pi$
$347$	−17.1238	−	3.01939i	−0.919255	−	0.162089i	−0.613203	+	0.789925i	$0.710119\pi$
$348$		0			0
$349$	−3.38478	−	4.03383i	−0.181183	−	0.215926i	0.667807	−	0.744335i	$-0.267233\pi$
$349$	−3.38478	−	4.03383i	−0.181183	−	0.215926i	−0.848990	+	0.528409i	$0.822789\pi$
$350$		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	0.983030	−	0.183445i	$-0.0587248\pi$
$373$	2.16442	+	5.94669i	0.112069	+	0.307908i	−0.870961	+	0.491353i	$0.836503\pi$
$374$		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	$0.261479\pi$
$379$			28.5066i			1.46428i	−0.681152	+	0.732142i	$0.738521\pi$
$380$		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	−0.969093	−	0.246696i	$-0.920655\pi$
$389$	−1.34416	+	3.69306i	−0.0681518	+	0.187246i	0.900941	+	0.433941i	$0.142877\pi$
$390$		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	−0.878237	−	0.478226i	$-0.841280\pi$
$397$	−17.9961	+	10.3901i	−0.903200	+	0.521463i	−0.0249629	+	0.999688i	$0.507947\pi$
$398$		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	−0.522869	−	0.852413i	$-0.675138\pi$
$419$	8.33906	−	9.93810i	0.407390	−	0.485508i	0.930258	+	0.366905i	$0.119583\pi$
$420$		0			0
$421$	1.49536	−	4.10848i	0.0728795	−	0.200235i	−0.897904	−	0.440191i	$-0.854911\pi$
$421$	1.49536	−	4.10848i	0.0728795	−	0.200235i	0.970784	+	0.239956i	$0.0771330\pi$
$422$		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	$0.366819\pi$
$443$	−10.3614	+	28.4677i	−0.492285	+	1.35254i	−0.898584	+	0.438802i	$0.855403\pi$
$444$		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	$0.0338799\pi$
$461$	19.8885	+	23.7021i	0.926298	+	1.10392i	−0.0680433	+	0.997682i	$0.521676\pi$
$462$		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	−0.519524	−	0.854456i	$-0.673891\pi$
$467$	−0.849394	+	0.490398i	−0.0393052	+	0.0226929i	0.480219	+	0.877149i	$0.340557\pi$
$468$		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	$0.0442679\pi$
$491$	7.10851	+	19.5305i	0.320802	+	0.881398i	−0.669543	+	0.742774i	$0.733510\pi$
$492$		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	−0.426282	−	0.904590i	$-0.640177\pi$
$499$	12.0312	−	14.3382i	0.538588	−	0.641865i	0.964871	+	0.262726i	$0.0846214\pi$
$500$		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	−0.413590	−	0.910463i	$-0.635725\pi$
$509$	−25.1247	−	4.43017i	−1.11363	−	0.196364i	−0.700044	+	0.714099i	$0.746836\pi$
$510$		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	$-0.970959\pi$
$523$	−35.9656	−	20.7647i	−1.57266	−	0.907978i	−0.576824	−	0.816869i	$-0.695708\pi$
$524$		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	$0.0776152\pi$
$541$			11.2309i			0.482852i	−0.970419	+	0.241426i	$0.922385\pi$
$542$		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	−0.581462	−	0.813574i	$-0.697519\pi$
$547$	−19.8704	+	3.50369i	−0.849599	+	0.149807i	−0.268137	+	0.963381i	$0.586408\pi$
$548$		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	0.945094	−	0.326798i	$-0.105970\pi$
$557$	26.7781	+	15.4604i	1.13463	+	0.655076i	0.189532	+	0.981875i	$0.439303\pi$
$558$		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	0.584282	−	0.811551i	$-0.301376\pi$
$563$	20.3052	+	3.58035i	0.855761	+	0.150894i	0.271479	+	0.962444i	$0.412487\pi$
$564$		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	0.0136257	−	0.999907i	$-0.495663\pi$
$571$	−7.54047	−	1.32959i	−0.315559	−	0.0556415i	−0.329184	+	0.944266i	$0.606774\pi$
$572$		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	−0.575532	−	0.817780i	$-0.695205\pi$
$587$	−20.2706	+	3.57425i	−0.836657	+	0.147525i	−0.261126	+	0.965305i	$0.584094\pi$
$588$		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	0.201321	−	0.979525i	$-0.435477\pi$
$613$	28.4795	−	16.4426i	1.15028	−	0.664112i	0.948954	+	0.315414i	$0.102143\pi$
$614$		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	$-0.971778\pi$
$619$	−22.6481	−	26.9910i	−0.910305	−	1.08486i	0.0857667	−	0.996315i	$-0.472666\pi$
$620$		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	$0.226098\pi$
$643$	15.1261	+	41.5587i	0.596517	+	1.63892i	−0.161645	+	0.986849i	$0.551680\pi$
$644$		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	0.954860	−	0.297055i	$-0.0960046\pi$
$653$	0.829258	+	2.27837i	0.0324514	+	0.0891594i	−0.922409	+	0.386215i	$0.873782\pi$
$654$		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	$-0.570695\pi$
$659$	14.7728	−	40.5879i	0.575466	−	1.58108i	0.795738	−	0.605641i	$-0.207083\pi$
$660$		0			0
$661$	−11.3612	+	13.5398i	−0.441901	+	0.526637i	−0.940317	−	0.340301i	$-0.889471\pi$
$661$	−11.3612	+	13.5398i	−0.441901	+	0.526637i	0.498415	+	0.866938i	$0.333915\pi$
$662$		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	0.674592	−	0.738191i	$-0.264320\pi$
$677$	−4.41092	−	5.25673i	−0.169526	−	0.202033i	−0.844118	+	0.536158i	$0.819875\pi$
$678$		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	−0.576743	−	0.816926i	$-0.695677\pi$
$683$	−4.11971	+	2.37852i	−0.157636	+	0.0910113i	0.419107	+	0.907937i	$0.362343\pi$
$684$		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	−0.994523	−	0.104523i	$-0.966669\pi$
$691$	−4.35017	+	11.9520i	−0.165488	+	0.454675i	0.829034	+	0.559198i	$0.188891\pi$
$692$		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	$-0.925573\pi$
$701$		−	12.2688i		−	0.463386i	0.972789	−	0.231693i	$-0.0744265\pi$
$702$		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	−0.638680	−	0.769473i	$-0.720519\pi$
$709$	−25.9792	+	4.58083i	−0.975668	+	0.172037i	−0.336988	+	0.941509i	$0.609408\pi$
$710$		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	0.171738	−	0.985143i	$-0.445062\pi$
$733$	−0.103428	−	0.0182371i	−0.00382018	−	0.000673601i	−0.175558	+	0.984469i	$0.556173\pi$
$734$		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	−0.0703928	−	0.997519i	$-0.522425\pi$
$739$	−26.3545	−	15.2158i	−0.969466	−	0.559722i	−0.899074	+	0.437798i	$0.855759\pi$
$740$		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	$-0.834624\pi$
$757$		−	27.3201i		−	0.992967i	0.868046	−	0.496484i	$-0.165376\pi$
$758$		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	0.909931	−	0.414759i	$-0.136134\pi$
$773$	27.9615	+	16.1436i	1.00571	+	0.580644i	0.0957742	+	0.995403i	$0.469467\pi$
$774$		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	0.827944	−	0.560811i	$-0.189510\pi$
$787$	39.6718	+	6.99522i	1.41415	+	0.249353i	0.586204	+	0.810163i	$0.300622\pi$
$788$		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	−0.806131	−	0.591737i	$-0.798442\pi$
$797$	−2.35451	+	2.80599i	−0.0834009	+	0.0993934i	0.722730	+	0.691130i	$0.242887\pi$
$798$		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	$-0.851252\pi$
$811$		−	25.6578i		−	0.900966i	0.892785	−	0.450483i	$-0.148748\pi$
$812$		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	$-0.744084\pi$
$821$	8.61194	−	23.6611i	0.300559	−	0.825778i	0.994403	−	0.105653i	$-0.0336933\pi$
$822$		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	0.657949	−	0.753062i	$-0.271424\pi$
$827$	9.62668	+	5.55796i	0.334752	+	0.193269i	−0.323197	+	0.946332i	$0.604758\pi$
$828$		0			0
$829$	26.4493	−	15.2705i	0.918621	−	0.530366i	0.0354262	−	0.999372i	$-0.488721\pi$
$829$	26.4493	−	15.2705i	0.918621	−	0.530366i	0.883195	+	0.469006i	$0.155388\pi$
$830$		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	$0.234016\pi$
$853$	−7.52367	+	20.6711i	−0.257605	+	0.707765i	−0.999314	+	0.0370424i	$0.988206\pi$
$854$		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	$-0.995391\pi$
$859$	−7.12897	−	19.5867i	−0.243237	−	0.668289i	0.756658	−	0.653811i	$-0.226831\pi$
$860$		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	−0.769017	−	0.639228i	$-0.779254\pi$
$877$	−0.176559	+	0.210415i	−0.00596198	+	0.00710521i	0.763055	+	0.646333i	$0.223698\pi$
$878$		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	−0.414636	−	0.909987i	$-0.636091\pi$
$883$	4.93626	−	2.84995i	0.166118	−	0.0959085i	0.580754	+	0.814079i	$0.302758\pi$
$884$		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	$0.369866\pi$
$907$	−14.9621	+	41.1081i	−0.496809	+	1.36497i	−0.894342	+	0.447383i	$0.852356\pi$
$908$		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	0.496613	−	0.867972i	$-0.334577\pi$
$941$	20.4427	+	3.60459i	0.666412	+	0.117506i	0.169799	+	0.985479i	$0.445688\pi$
$942$		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	0.539702	−	0.841856i	$-0.318537\pi$
$947$	−11.7887	−	14.0493i	−0.383082	−	0.456540i	−0.922785	+	0.385316i	$0.874092\pi$
$948$		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	$-0.998575\pi$
$971$		−	0.278968i		−	0.00895249i	0.999990	−	0.00447625i	$-0.00142484\pi$
$972$		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	0.446302	−	0.894883i	$-0.352741\pi$
$997$	−16.1819	−	19.2848i	−0.512485	−	0.610756i	−0.958787	+	0.284127i	$0.908296\pi$
$998$		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.49.28		204
4.3	odd	2		216.2.t.a.157.31	yes	204
8.3	odd	2		216.2.t.a.157.17	✓	204
8.5	even	2	inner	864.2.bf.a.49.7		204
12.11	even	2		648.2.t.a.37.4		204
24.11	even	2		648.2.t.a.37.18		204
27.16	even	9	inner	864.2.bf.a.529.7		204
108.11	even	18		648.2.t.a.613.18		204
108.43	odd	18		216.2.t.a.205.17	yes	204
216.11	even	18		648.2.t.a.613.4		204
216.43	odd	18		216.2.t.a.205.31	yes	204
216.205	even	18	inner	864.2.bf.a.529.28		204

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