LMFDB - Embedded newform 432.2.be.a.239.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.4
Character	$\chi$	$=$	432.239
Dual form			432.2.be.a.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.340461 - 1.69826i) q^{3} +(1.68195 + 0.296574i) q^{5} +(-0.981328 - 1.16950i) q^{7} +(-2.76817 - 1.15638i) q^{9} +O(q^{10})$	\(q+(0.340461 - 1.69826i) q^{3} +(1.68195 + 0.296574i) q^{5} +(-0.981328 - 1.16950i) q^{7} +(-2.76817 - 1.15638i) q^{9} +(-0.602821 - 3.41877i) q^{11} +(2.74648 - 0.999638i) q^{13} +(1.07630 - 2.75542i) q^{15} +(0.812691 + 0.469208i) q^{17} +(1.51710 - 0.875899i) q^{19} +(-2.32022 + 1.26838i) q^{21} +(0.0294832 + 0.0247394i) q^{23} +(-1.95745 - 0.712454i) q^{25} +(-2.90629 + 4.30738i) q^{27} +(-1.84729 + 5.07538i) q^{29} +(4.26730 - 5.08557i) q^{31} +(-6.01119 - 0.140209i) q^{33} +(-1.30371 - 2.25808i) q^{35} +(3.09995 - 5.36926i) q^{37} +(-0.762576 - 5.00458i) q^{39} +(1.60794 + 4.41779i) q^{41} +(-8.03174 + 1.41621i) q^{43} +(-4.31299 - 2.76595i) q^{45} +(6.29137 - 5.27909i) q^{47} +(0.810809 - 4.59833i) q^{49} +(1.07353 - 1.22041i) q^{51} +12.6923i q^{53} -5.92899i q^{55} +(-0.970991 - 2.87464i) q^{57} +(-2.57645 + 14.6118i) q^{59} +(10.6194 - 8.91077i) q^{61} +(1.36410 + 4.37217i) q^{63} +(4.91592 - 0.866810i) q^{65} +(4.52189 + 12.4238i) q^{67} +(0.0520517 - 0.0416474i) q^{69} +(-1.81864 + 3.14997i) q^{71} +(-2.02246 - 3.50300i) q^{73} +(-1.87637 + 3.08170i) q^{75} +(-3.40669 + 4.05993i) q^{77} +(-4.29234 + 11.7931i) q^{79} +(6.32557 + 6.40213i) q^{81} +(3.42314 + 1.24592i) q^{83} +(1.22775 + 1.03021i) q^{85} +(7.99038 + 4.86514i) q^{87} +(7.61727 - 4.39783i) q^{89} +(-3.86428 - 2.23104i) q^{91} +(-7.18377 - 8.97842i) q^{93} +(2.81146 - 1.02329i) q^{95} +(0.737508 + 4.18262i) q^{97} +(-2.28469 + 10.1608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^5 - 12 * q^9	$ 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) $ 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.340461	−	1.69826i	0.196565	−	0.980491i
$3$	0.340461	−	1.69826i	0.196565	−	0.980491i
$4$		0			0
$5$	1.68195	+	0.296574i	0.752193	+	0.132632i	0.536583	−	0.843848i	$-0.319715\pi$
$5$	1.68195	+	0.296574i	0.752193	+	0.132632i	0.215610	+	0.976480i	$0.430826\pi$
$6$		0			0
$7$	−0.981328	−	1.16950i	−0.370907	−	0.442030i	0.548015	−	0.836468i	$-0.315384\pi$
$7$	−0.981328	−	1.16950i	−0.370907	−	0.442030i	−0.918922	+	0.394438i	$0.870939\pi$
$8$		0			0
$9$	−2.76817	−	1.15638i	−0.922724	−	0.385460i
$10$		0			0
$11$	−0.602821	−	3.41877i	−0.181757	−	1.03080i	−0.930051	−	0.367430i	$-0.880238\pi$
$11$	−0.602821	−	3.41877i	−0.181757	−	1.03080i	0.748294	−	0.663368i	$-0.230873\pi$
$12$		0			0
$13$	2.74648	−	0.999638i	0.761737	−	0.277250i	0.0682011	−	0.997672i	$-0.478274\pi$
$13$	2.74648	−	0.999638i	0.761737	−	0.277250i	0.693536	+	0.720422i	$0.256052\pi$
$14$		0			0
$15$	1.07630	−	2.75542i	0.277899	−	0.711447i
$16$		0			0
$17$	0.812691	+	0.469208i	0.197107	+	0.113800i	0.595305	−	0.803500i	$-0.297031\pi$
$17$	0.812691	+	0.469208i	0.197107	+	0.113800i	−0.398199	+	0.917299i	$0.630365\pi$
$18$		0			0
$19$	1.51710	−	0.875899i	0.348047	−	0.200945i	−0.315778	−	0.948833i	$-0.602265\pi$
$19$	1.51710	−	0.875899i	0.348047	−	0.200945i	0.663825	+	0.747888i	$0.268932\pi$
$20$		0			0
$21$	−2.32022	+	1.26838i	−0.506314	+	0.276783i
$22$		0			0
$23$	0.0294832	+	0.0247394i	0.00614768	+	0.00515851i	0.645856	−	0.763459i	$-0.276501\pi$
$23$	0.0294832	+	0.0247394i	0.00614768	+	0.00515851i	−0.639709	+	0.768618i	$0.720945\pi$
$24$		0			0
$25$	−1.95745	−	0.712454i	−0.391490	−	0.142491i
$26$		0			0
$27$	−2.90629	+	4.30738i	−0.559316	+	0.828955i
$28$		0			0
$29$	−1.84729	+	5.07538i	−0.343032	+	0.942474i	0.641477	+	0.767142i	$0.278322\pi$
$29$	−1.84729	+	5.07538i	−0.343032	+	0.942474i	−0.984509	+	0.175331i	$0.943900\pi$
$30$		0			0
$31$	4.26730	−	5.08557i	0.766430	−	0.913396i	−0.231806	−	0.972762i	$-0.574464\pi$
$31$	4.26730	−	5.08557i	0.766430	−	0.913396i	0.998236	+	0.0593663i	$0.0189080\pi$
$32$		0			0
$33$	−6.01119	−	0.140209i	−1.04641	−	0.0244072i
$34$		0			0
$35$	−1.30371	−	2.25808i	−0.220366	−	0.381686i
$36$		0			0
$37$	3.09995	−	5.36926i	0.509628	−	0.882702i	−0.490310	−	0.871548i	$-0.663116\pi$
$37$	3.09995	−	5.36926i	0.509628	−	0.882702i	0.999938	−	0.0111534i	$-0.00355030\pi$
$38$		0			0
$39$	−0.762576	−	5.00458i	−0.122110	−	0.801374i
$40$		0			0
$41$	1.60794	+	4.41779i	0.251119	+	0.689943i	0.999640	+	0.0268321i	$0.00854194\pi$
$41$	1.60794	+	4.41779i	0.251119	+	0.689943i	−0.748521	+	0.663111i	$0.769236\pi$
$42$		0			0
$43$	−8.03174	+	1.41621i	−1.22483	+	0.215970i	−0.748403	−	0.663244i	$-0.769179\pi$
$43$	−8.03174	+	1.41621i	−1.22483	+	0.215970i	−0.476426	+	0.879215i	$0.658068\pi$
$44$		0			0
$45$	−4.31299	−	2.76595i	−0.642942	−	0.412323i
$46$		0			0
$47$	6.29137	−	5.27909i	0.917691	−	0.770034i	−0.0558757	−	0.998438i	$-0.517795\pi$
$47$	6.29137	−	5.27909i	0.917691	−	0.770034i	0.973567	+	0.228404i	$0.0733506\pi$
$48$		0			0
$49$	0.810809	−	4.59833i	0.115830	−	0.656904i
$50$		0			0
$51$	1.07353	−	1.22041i	0.150324	−	0.170892i
$52$		0			0
$53$			12.6923i			1.74342i	0.490020	+	0.871711i	$0.336989\pi$
$53$			12.6923i			1.74342i	−0.490020	+	0.871711i	$0.663011\pi$
$54$		0			0
$55$		−	5.92899i		−	0.799465i
$56$		0			0
$57$	−0.970991	−	2.87464i	−0.128611	−	0.380756i
$58$		0			0
$59$	−2.57645	+	14.6118i	−0.335425	+	1.90229i	0.0875717	+	0.996158i	$0.472089\pi$
$59$	−2.57645	+	14.6118i	−0.335425	+	1.90229i	−0.422997	+	0.906131i	$0.639022\pi$
$60$		0			0
$61$	10.6194	−	8.91077i	1.35968	−	1.14091i	0.383600	−	0.923499i	$-0.374684\pi$
$61$	10.6194	−	8.91077i	1.35968	−	1.14091i	0.976081	−	0.217408i	$-0.0697602\pi$
$62$		0			0
$63$	1.36410	+	4.37217i	0.171860	+	0.550842i
$64$		0			0
$65$	4.91592	−	0.866810i	0.609745	−	0.107515i
$66$		0			0
$67$	4.52189	+	12.4238i	0.552437	+	1.51781i	0.830373	+	0.557208i	$0.188127\pi$
$67$	4.52189	+	12.4238i	0.552437	+	1.51781i	−0.277937	+	0.960599i	$0.589651\pi$
$68$		0			0
$69$	0.0520517	−	0.0416474i	0.00626629	−	0.00501376i
$70$		0			0
$71$	−1.81864	+	3.14997i	−0.215832	+	0.373833i	−0.953530	−	0.301299i	$-0.902580\pi$
$71$	−1.81864	+	3.14997i	−0.215832	+	0.373833i	0.737697	+	0.675132i	$0.235913\pi$
$72$		0			0
$73$	−2.02246	−	3.50300i	−0.236711	−	0.409996i	0.723058	−	0.690788i	$-0.242736\pi$
$73$	−2.02246	−	3.50300i	−0.236711	−	0.409996i	−0.959769	+	0.280792i	$0.909403\pi$
$74$		0			0
$75$	−1.87637	+	3.08170i	−0.216664	+	0.355844i
$76$		0			0
$77$	−3.40669	+	4.05993i	−0.388228	+	0.462672i
$78$		0			0
$79$	−4.29234	+	11.7931i	−0.482926	+	1.32683i	0.424047	+	0.905640i	$0.360609\pi$
$79$	−4.29234	+	11.7931i	−0.482926	+	1.32683i	−0.906973	+	0.421188i	$0.861613\pi$
$80$		0			0
$81$	6.32557	+	6.40213i	0.702841	+	0.711347i
$82$		0			0
$83$	3.42314	+	1.24592i	0.375739	+	0.136758i	0.522984	−	0.852342i	$-0.324819\pi$
$83$	3.42314	+	1.24592i	0.375739	+	0.136758i	−0.147246	+	0.989100i	$0.547041\pi$
$84$		0			0
$85$	1.22775	+	1.03021i	0.133169	+	0.111742i
$86$		0			0
$87$	7.99038	+	4.86514i	0.856659	+	0.521597i
$88$		0			0
$89$	7.61727	−	4.39783i	0.807429	−	0.466169i	−0.0386332	−	0.999253i	$-0.512300\pi$
$89$	7.61727	−	4.39783i	0.807429	−	0.466169i	0.846062	+	0.533084i	$0.178967\pi$
$90$		0			0
$91$	−3.86428	−	2.23104i	−0.405086	−	0.233877i
$92$		0			0
$93$	−7.18377	−	8.97842i	−0.744923	−	0.931019i
$94$		0			0
$95$	2.81146	−	1.02329i	0.288450	−	0.104987i
$96$		0			0
$97$	0.737508	+	4.18262i	0.0748826	+	0.424680i	0.999085	+	0.0427765i	$0.0136203\pi$
$97$	0.737508	+	4.18262i	0.0748826	+	0.424680i	−0.924202	+	0.381904i	$0.875269\pi$
$98$		0			0
$99$	−2.28469	+	10.1608i	−0.229620	+	1.02120i
$100$		0			0
$101$	4.83655	+	5.76397i	0.481254	+	0.573537i	0.950971	−	0.309281i	$-0.100088\pi$
$101$	4.83655	+	5.76397i	0.481254	+	0.573537i	−0.469716	+	0.882817i	$0.655644\pi$
$102$		0			0
$103$	12.3823	+	2.18334i	1.22007	+	0.215131i	0.746355	−	0.665548i	$-0.231802\pi$
$103$	12.3823	+	2.18334i	1.22007	+	0.215131i	0.473713	+	0.880679i	$0.342913\pi$
$104$		0			0
$105$	−4.27867	+	1.44524i	−0.417556	+	0.141041i
$106$		0			0
$107$	−19.0430			−1.84096			−0.920478	−	0.390794i	$-0.872201\pi$
$107$	−19.0430			−1.84096			−0.920478	+	0.390794i	$0.872201\pi$
$108$		0			0
$109$	4.46704			0.427865			0.213933	−	0.976848i	$-0.431373\pi$
$109$	4.46704			0.427865			0.213933	+	0.976848i	$0.431373\pi$
$110$		0			0
$111$	−8.06300	−	7.09254i	−0.765306	−	0.673194i
$112$		0			0
$113$	−1.78707	−	0.315108i	−0.168113	−	0.0296428i	0.0889580	−	0.996035i	$-0.471646\pi$
$113$	−1.78707	−	0.315108i	−0.168113	−	0.0296428i	−0.257071	+	0.966393i	$0.582757\pi$
$114$		0			0
$115$	0.0422524	+	0.0503544i	0.00394005	+	0.00469557i
$116$		0			0
$117$	−8.75870	−	0.408809i	−0.809742	−	0.0377944i
$118$		0			0
$119$	−0.248778	−	1.41089i	−0.0228054	−	0.129336i
$120$		0			0
$121$	−0.987967	+	0.359591i	−0.0898152	+	0.0326901i
$122$		0			0
$123$	8.05000	−	1.22662i	0.725844	−	0.110601i
$124$		0			0
$125$	−10.4765	−	6.04859i	−0.937044	−	0.541003i
$126$		0			0
$127$	6.27879	−	3.62506i	0.557153	−	0.321672i	−0.194849	−	0.980833i	$-0.562422\pi$
$127$	6.27879	−	3.62506i	0.557153	−	0.321672i	0.752002	+	0.659161i	$0.229088\pi$
$128$		0			0
$129$	−0.329394	+	14.1221i	−0.0290015	+	1.24339i
$130$		0			0
$131$	13.3886	+	11.2343i	1.16976	+	0.981548i	0.999992	−	0.00393578i	$-0.00125280\pi$
$131$	13.3886	+	11.2343i	1.16976	+	0.981548i	0.169771	+	0.985484i	$0.445697\pi$
$132$		0			0
$133$	−2.51314	−	0.914708i	−0.217917	−	0.0793152i
$134$		0			0
$135$	−6.16570	+	6.38288i	−0.530659	+	0.549351i
$136$		0			0
$137$	1.81753	−	4.99361i	0.155282	−	0.426633i	−0.837519	−	0.546408i	$-0.815995\pi$
$137$	1.81753	−	4.99361i	0.155282	−	0.426633i	0.992801	+	0.119774i	$0.0382172\pi$
$138$		0			0
$139$	−7.75657	+	9.24392i	−0.657904	+	0.784059i	−0.987083	−	0.160208i	$-0.948783\pi$
$139$	−7.75657	+	9.24392i	−0.657904	+	0.784059i	0.329179	+	0.944267i	$0.393228\pi$
$140$		0			0
$141$	−6.82330	−	12.4817i	−0.574625	−	1.05115i
$142$		0			0
$143$	−5.07317	−	8.78699i	−0.424240	−	0.734805i
$144$		0			0
$145$	−4.61227	+	7.98869i	−0.383028	+	0.663425i
$146$		0			0
$147$	−7.53310	−	2.94251i	−0.621320	−	0.242694i
$148$		0			0
$149$	0.380050	+	1.04418i	0.0311349	+	0.0855425i	0.954286	−	0.298894i	$-0.0966179\pi$
$149$	0.380050	+	1.04418i	0.0311349	+	0.0855425i	−0.923151	+	0.384437i	$0.874396\pi$
$150$		0			0
$151$	−8.54782	+	1.50721i	−0.695612	+	0.122655i	−0.510264	−	0.860018i	$-0.670452\pi$
$151$	−8.54782	+	1.50721i	−0.695612	+	0.122655i	−0.185348	+	0.982673i	$0.559341\pi$
$152$		0			0
$153$	−1.70709	−	2.23863i	−0.138010	−	0.180982i
$154$		0			0
$155$	8.68565	−	7.28813i	0.697648	−	0.585396i
$156$		0			0
$157$	0.0313604	−	0.177853i	0.00250283	−	0.0141943i	−0.983531	−	0.180741i	$-0.942150\pi$
$157$	0.0313604	−	0.177853i	0.00250283	−	0.0141943i	0.986034	+	0.166547i	$0.0532616\pi$
$158$		0			0
$159$	21.5548	+	4.32123i	1.70941	+	0.342696i
$160$		0			0
$161$		−	0.0587581i		−	0.00463079i
$162$		0			0
$163$		−	21.6854i		−	1.69853i	−0.527967	−	0.849265i	$-0.677045\pi$
$163$		−	21.6854i		−	1.69853i	0.527967	−	0.849265i	$-0.322955\pi$
$164$		0			0
$165$	−10.0690	−	2.01859i	−0.783868	−	0.157147i
$166$		0			0
$167$	−0.444010	+	2.51811i	−0.0343585	+	0.194857i	−0.997156	−	0.0753678i	$-0.975987\pi$
$167$	−0.444010	+	2.51811i	−0.0343585	+	0.194857i	0.962797	+	0.270225i	$0.0870980\pi$
$168$		0			0
$169$	−3.41469	+	2.86526i	−0.262668	+	0.220405i
$170$		0			0
$171$	−5.21247	+	0.670293i	−0.398608	+	0.0512586i
$172$		0			0
$173$	−11.1824	+	1.97176i	−0.850183	+	0.149910i	−0.581730	−	0.813382i	$-0.697624\pi$
$173$	−11.1824	+	1.97176i	−0.850183	+	0.149910i	−0.268454	+	0.963293i	$0.586513\pi$
$174$		0			0
$175$	1.08769	+	2.98839i	0.0822213	+	0.225901i
$176$		0			0
$177$	23.9374	+	9.35021i	1.79924	+	0.702805i
$178$		0			0
$179$	−2.60767	+	4.51662i	−0.194907	+	0.337588i	−0.946870	−	0.321617i	$-0.895774\pi$
$179$	−2.60767	+	4.51662i	−0.194907	+	0.337588i	0.751963	+	0.659205i	$0.229107\pi$
$180$		0			0
$181$	5.98011	+	10.3579i	0.444498	+	0.769893i	0.998017	−	0.0629432i	$-0.0200487\pi$
$181$	5.98011	+	10.3579i	0.444498	+	0.769893i	−0.553519	+	0.832837i	$0.686715\pi$
$182$		0			0
$183$	−11.5173	−	21.0683i	−0.851384	−	1.55742i
$184$		0			0
$185$	6.80635	−	8.11149i	0.500413	−	0.596369i
$186$		0			0
$187$	1.11420	−	3.06125i	0.0814787	−	0.223861i
$188$		0			0
$189$	7.88950	−	0.828040i	0.573877	−	0.0602310i
$190$		0			0
$191$	10.3596	+	3.77059i	0.749595	+	0.272830i	0.688435	−	0.725298i	$-0.258298\pi$
$191$	10.3596	+	3.77059i	0.749595	+	0.272830i	0.0611596	+	0.998128i	$0.480520\pi$
$192$		0			0
$193$	−6.58102	−	5.52213i	−0.473712	−	0.397492i	0.374434	−	0.927253i	$-0.377837\pi$
$193$	−6.58102	−	5.52213i	−0.473712	−	0.397492i	−0.848146	+	0.529762i	$0.822281\pi$
$194$		0			0
$195$	0.201609	−	8.64363i	0.0144375	−	0.618983i
$196$		0			0
$197$	15.1886	−	8.76915i	1.08214	−	0.624776i	0.150670	−	0.988584i	$-0.451857\pi$
$197$	15.1886	−	8.76915i	1.08214	−	0.624776i	0.931474	+	0.363808i	$0.118524\pi$
$198$		0			0
$199$	−15.6687	−	9.04633i	−1.11073	−	0.641278i	−0.171708	−	0.985148i	$-0.554929\pi$
$199$	−15.6687	−	9.04633i	−1.11073	−	0.641278i	−0.939017	+	0.343870i	$0.888262\pi$
$200$		0			0
$201$	22.6383	−	3.44953i	1.59679	−	0.243311i
$202$		0			0
$203$	7.74845	−	2.82021i	0.543835	−	0.197940i
$204$		0			0
$205$	1.39429	+	7.90739i	0.0973812	+	0.552276i
$206$		0			0
$207$	−0.0530065	−	0.102577i	−0.00368421	−	0.00712957i
$208$		0			0
$209$	−3.90904	−	4.65861i	−0.270394	−	0.322243i
$210$		0			0
$211$	15.8844	+	2.80084i	1.09352	+	0.192818i	0.691188	−	0.722675i	$-0.257087\pi$
$211$	15.8844	+	2.80084i	1.09352	+	0.192818i	0.402335	+	0.915492i	$0.368199\pi$
$212$		0			0
$213$	4.73029	+	4.16096i	0.324114	+	0.285104i
$214$		0			0
$215$	−13.9290			−0.949952
$216$		0			0
$217$	−10.1352			−0.688023
$218$		0			0
$219$	−6.63758	+	2.24203i	−0.448526	+	0.151502i
$220$		0			0
$221$	2.70108	+	0.476273i	0.181694	+	0.0320376i
$222$		0			0
$223$	−1.67593	−	1.99730i	−0.112229	−	0.133749i	0.707005	−	0.707208i	$-0.250046\pi$
$223$	−1.67593	−	1.99730i	−0.112229	−	0.133749i	−0.819234	+	0.573459i	$0.805601\pi$
$224$		0			0
$225$	4.59469	+	4.23575i	0.306313	+	0.282384i
$226$		0			0
$227$	−3.97284	−	22.5311i	−0.263686	−	1.49544i	−0.772750	−	0.634711i	$-0.781119\pi$
$227$	−3.97284	−	22.5311i	−0.263686	−	1.49544i	0.509063	−	0.860729i	$-0.329992\pi$
$228$		0			0
$229$	0.564600	−	0.205498i	0.0373098	−	0.0135797i	−0.323298	−	0.946297i	$-0.604792\pi$
$229$	0.564600	−	0.205498i	0.0373098	−	0.0135797i	0.360608	+	0.932718i	$0.382569\pi$
$230$		0			0
$231$	5.73498	+	7.16769i	0.377334	+	0.471599i
$232$		0			0
$233$	−25.8951	−	14.9505i	−1.69644	−	0.979441i	−0.949086	−	0.315016i	$-0.897990\pi$
$233$	−25.8951	−	14.9505i	−1.69644	−	0.979441i	−0.747355	−	0.664425i	$-0.768676\pi$
$234$		0			0
$235$	12.1474	−	7.01332i	0.792411	−	0.457499i
$236$		0			0
$237$	18.5664	+	11.3046i	1.20602	+	0.734313i
$238$		0			0
$239$	−0.533039	−	0.447273i	−0.0344794	−	0.0289317i	0.625385	−	0.780316i	$-0.284942\pi$
$239$	−0.533039	−	0.447273i	−0.0344794	−	0.0289317i	−0.659865	+	0.751385i	$0.729386\pi$
$240$		0			0
$241$	−14.8422	−	5.40211i	−0.956069	−	0.347981i	−0.183577	−	0.983005i	$-0.558768\pi$
$241$	−14.8422	−	5.40211i	−0.956069	−	0.347981i	−0.772492	+	0.635024i	$0.780990\pi$
$242$		0			0
$243$	13.0261	−	8.56278i	0.835623	−	0.549303i
$244$		0			0
$245$	2.72749	−	7.49371i	0.174253	−	0.478755i
$246$		0			0
$247$	3.29111	−	3.92219i	0.209408	−	0.249563i
$248$		0			0
$249$	3.28134	−	5.38920i	0.207947	−	0.341527i
$250$		0			0
$251$	−11.0929	−	19.2135i	−0.700180	−	1.21275i	−0.968403	−	0.249391i	$-0.919770\pi$
$251$	−11.0929	−	19.2135i	−0.700180	−	1.21275i	0.268223	−	0.963357i	$-0.413564\pi$
$252$		0			0
$253$	0.0668050	−	0.115710i	0.00420000	−	0.00727461i
$254$		0			0
$255$	2.16756	−	1.73430i	0.135738	−	0.108606i
$256$		0			0
$257$	−7.17758	−	19.7202i	−0.447725	−	1.23012i	−0.934304	−	0.356478i	$-0.883977\pi$
$257$	−7.17758	−	19.7202i	−0.447725	−	1.23012i	0.486578	−	0.873637i	$-0.338245\pi$
$258$		0			0
$259$	−9.32143	+	1.64362i	−0.579205	+	0.102130i
$260$		0			0
$261$	10.9827	−	11.9134i	0.679810	−	0.737418i
$262$		0			0
$263$	6.15049	−	5.16087i	0.379256	−	0.318233i	−0.433155	−	0.901320i	$-0.642600\pi$
$263$	6.15049	−	5.16087i	0.379256	−	0.318233i	0.812410	+	0.583086i	$0.198155\pi$
$264$		0			0
$265$	−3.76421	+	21.3479i	−0.231233	+	1.31139i
$266$		0			0
$267$	−4.87528	−	14.4334i	−0.298363	−	0.883309i
$268$		0			0
$269$			26.1874i			1.59668i	0.602209	+	0.798338i	$0.294287\pi$
$269$			26.1874i			1.59668i	−0.602209	+	0.798338i	$0.705713\pi$
$270$		0			0
$271$		−	14.9170i		−	0.906140i	−0.891475	−	0.453070i	$-0.850329\pi$
$271$		−	14.9170i		−	0.906140i	0.891475	−	0.453070i	$-0.149671\pi$
$272$		0			0
$273$	−5.10452	+	5.80297i	−0.308940	+	0.351212i
$274$		0			0
$275$	−1.25572	+	7.12155i	−0.0757229	+	0.429446i
$276$		0			0
$277$	−14.2963	+	11.9960i	−0.858983	+	0.720772i	−0.961749	−	0.273933i	$-0.911675\pi$
$277$	−14.2963	+	11.9960i	−0.858983	+	0.720772i	0.102766	+	0.994706i	$0.467231\pi$
$278$		0			0
$279$	−17.6935	+	9.14312i	−1.05928	+	0.547384i
$280$		0			0
$281$	−4.14342	+	0.730597i	−0.247176	+	0.0435838i	−0.295863	−	0.955230i	$-0.595607\pi$
$281$	−4.14342	+	0.730597i	−0.247176	+	0.0435838i	0.0486874	+	0.998814i	$0.484496\pi$
$282$		0			0
$283$	−0.667465	−	1.83384i	−0.0396766	−	0.109011i	0.918272	−	0.395950i	$-0.129585\pi$
$283$	−0.667465	−	1.83384i	−0.0396766	−	0.109011i	−0.957949	+	0.286939i	$0.907362\pi$
$284$		0			0
$285$	−0.780618	−	5.12298i	−0.0462398	−	0.303459i
$286$		0			0
$287$	3.58869	−	6.21579i	0.211834	−	0.366907i
$288$		0			0
$289$	−8.05969	−	13.9598i	−0.474099	−	0.821164i
$290$		0			0
$291$	7.35426	+	0.171535i	0.431114	+	0.0100556i
$292$		0			0
$293$	−5.47915	+	6.52979i	−0.320095	+	0.381474i	−0.901966	−	0.431806i	$-0.857876\pi$
$293$	−5.47915	+	6.52979i	−0.320095	+	0.381474i	0.581871	+	0.813281i	$0.302321\pi$
$294$		0			0
$295$	−8.66693	+	23.8122i	−0.504608	+	1.38640i
$296$		0			0
$297$	16.4779	+	7.33935i	0.956144	+	0.425872i
$298$		0			0
$299$	0.105706	+	0.0384737i	0.00611311	+	0.00222499i
$300$		0			0
$301$	9.53804	+	8.00336i	0.549763	+	0.461306i
$302$		0			0
$303$	11.4354	−	6.25131i	0.656945	−	0.359128i
$304$		0			0
$305$	20.5041	−	11.8381i	1.17406	−	0.677845i
$306$		0			0
$307$	8.57163	+	4.94883i	0.489209	+	0.282445i	0.724246	−	0.689542i	$-0.242188\pi$
$307$	8.57163	+	4.94883i	0.489209	+	0.282445i	−0.235037	+	0.971986i	$0.575521\pi$
$308$		0			0
$309$	7.92358	−	20.2851i	0.450756	−	1.15398i
$310$		0			0
$311$	−22.5915	+	8.22263i	−1.28105	+	0.466262i	−0.890778	−	0.454439i	$-0.849840\pi$
$311$	−22.5915	+	8.22263i	−1.28105	+	0.466262i	−0.390267	+	0.920702i	$0.627617\pi$
$312$		0			0
$313$	0.300476	+	1.70409i	0.0169839	+	0.0963207i	0.992121	−	0.125280i	$-0.0399829\pi$
$313$	0.300476	+	1.70409i	0.0169839	+	0.0963207i	−0.975137	+	0.221601i	$0.928872\pi$
$314$		0			0
$315$	0.997677	+	7.75835i	0.0562127	+	0.437133i
$316$		0			0
$317$	−11.5341	−	13.7458i	−0.647819	−	0.772040i	0.337765	−	0.941231i	$-0.390329\pi$
$317$	−11.5341	−	13.7458i	−0.647819	−	0.772040i	−0.985583	+	0.169190i	$0.945885\pi$
$318$		0			0
$319$	18.4651	+	3.25590i	1.03385	+	0.182295i
$320$		0			0
$321$	−6.48339	+	32.3400i	−0.361868	+	1.80504i
$322$		0			0
$323$	1.64391			0.0914698
$324$		0			0
$325$	−6.08830			−0.337718
$326$		0			0
$327$	1.52085	−	7.58620i	0.0841033	−	0.419518i
$328$		0			0
$329$	−12.3478	−	2.17725i	−0.680756	−	0.120036i
$330$		0			0
$331$	−6.23357	−	7.42888i	−0.342628	−	0.408328i	0.567023	−	0.823702i	$-0.308095\pi$
$331$	−6.23357	−	7.42888i	−0.342628	−	0.408328i	−0.909651	+	0.415374i	$0.863651\pi$
$332$		0			0
$333$	−14.7901	+	11.2783i	−0.810493	+	0.618049i
$334$		0			0
$335$	3.92104	+	22.2373i	0.214229	+	1.21495i
$336$		0			0
$337$	−25.7092	+	9.35737i	−1.40047	+	0.509728i	−0.928317	−	0.371790i	$-0.878744\pi$
$337$	−25.7092	+	9.35737i	−1.40047	+	0.509728i	−0.472150	+	0.881518i	$0.656522\pi$
$338$		0			0
$339$	−1.14356	+	2.92762i	−0.0621097	+	0.159006i
$340$		0			0
$341$	−19.9588	−	11.5232i	−1.08083	−	0.624018i
$342$		0			0
$343$	−15.4284	+	8.90759i	−0.833055	+	0.480965i
$344$		0			0
$345$	0.0999001	−	0.0546118i	0.00537844	−	0.00294020i
$346$		0			0
$347$	19.6703	+	16.5053i	1.05596	+	0.886052i	0.993707	−	0.112008i	$-0.0357283\pi$
$347$	19.6703	+	16.5053i	1.05596	+	0.886052i	0.0622488	+	0.998061i	$0.480173\pi$
$348$		0			0
$349$	20.8555	+	7.59080i	1.11637	+	0.406326i	0.833327	−	0.552780i	$-0.186433\pi$
$349$	20.8555	+	7.59080i	1.11637	+	0.406326i	0.283045	+	0.959107i	$0.408655\pi$
$350$		0			0
$351$	−3.67626	+	14.7354i	−0.196224	+	0.786516i
$352$		0			0
$353$	6.49361	−	17.8410i	0.345620	−	0.949583i	−0.638113	−	0.769943i	$-0.720285\pi$
$353$	6.49361	−	17.8410i	0.345620	−	0.949583i	0.983732	−	0.179640i	$-0.0574932\pi$
$354$		0			0
$355$	−3.99306	+	4.75874i	−0.211930	+	0.252568i
$356$		0			0
$357$	−2.48076	−	0.0578627i	−0.131296	−	0.00306242i
$358$		0			0
$359$	11.3488	+	19.6567i	0.598968	+	1.03744i	0.992974	+	0.118335i	$0.0377556\pi$
$359$	11.3488	+	19.6567i	0.598968	+	1.03744i	−0.394006	+	0.919108i	$0.628911\pi$
$360$		0			0
$361$	−7.96560	+	13.7968i	−0.419242	+	0.726149i
$362$		0			0
$363$	0.274315	+	1.80025i	0.0143978	+	0.0944887i
$364$		0			0
$365$	−2.36278	−	6.49170i	−0.123674	−	0.339791i
$366$		0			0
$367$	−7.82713	+	1.38013i	−0.408573	+	0.0720424i	−0.374157	−	0.927365i	$-0.622068\pi$
$367$	−7.82713	+	1.38013i	−0.408573	+	0.0720424i	−0.0344155	+	0.999408i	$0.510957\pi$
$368$		0			0
$369$	0.657580	−	14.0886i	0.0342323	−	0.733423i
$370$		0			0
$371$	14.8437	−	12.4553i	0.770645	−	0.646648i
$372$		0			0
$373$	0.275405	−	1.56190i	0.0142599	−	0.0808721i	−0.976847	−	0.213938i	$-0.931371\pi$
$373$	0.275405	−	1.56190i	0.0142599	−	0.0808721i	0.991107	+	0.133066i	$0.0424821\pi$
$374$		0			0
$375$	−13.8389	+	15.7325i	−0.714638	+	0.812421i
$376$		0			0
$377$			15.7860i			0.813023i
$378$		0			0
$379$			24.0092i			1.23327i	0.787249	+	0.616635i	$0.211505\pi$
$379$			24.0092i			1.23327i	−0.787249	+	0.616635i	$0.788495\pi$
$380$		0			0
$381$	−4.01862	−	11.8972i	−0.205880	−	0.609512i
$382$		0			0
$383$	0.226558	−	1.28488i	0.0115766	−	0.0656541i	−0.978472	−	0.206379i	$-0.933832\pi$
$383$	0.226558	−	1.28488i	0.0115766	−	0.0656541i	0.990049	+	0.140725i	$0.0449432\pi$
$384$		0			0
$385$	−6.93396	+	5.81829i	−0.353388	+	0.296527i
$386$		0			0
$387$	23.8709	+	5.36743i	1.21343	+	0.272842i
$388$		0			0
$389$	15.0139	−	2.64735i	0.761234	−	0.134226i	0.220462	−	0.975396i	$-0.429243\pi$
$389$	15.0139	−	2.64735i	0.761234	−	0.134226i	0.540772	+	0.841169i	$0.318132\pi$
$390$		0			0
$391$	0.0123529	+	0.0339392i	0.000624711	+	0.00171638i
$392$		0			0
$393$	23.6371	−	18.9124i	1.19233	−	0.954004i
$394$		0			0
$395$	−10.7170	+	18.5625i	−0.539233	+	0.933979i
$396$		0			0
$397$	7.08632	+	12.2739i	0.355652	+	0.616008i	0.987229	−	0.159305i	$-0.0509254\pi$
$397$	7.08632	+	12.2739i	0.355652	+	0.616008i	−0.631577	+	0.775313i	$0.717592\pi$
$398$		0			0
$399$	−2.40904	+	3.95654i	−0.120603	+	0.198075i
$400$		0			0
$401$	19.9488	−	23.7741i	0.996197	−	1.18722i	0.0138970	−	0.999903i	$-0.495576\pi$
$401$	19.9488	−	23.7741i	0.996197	−	1.18722i	0.982299	−	0.187317i	$-0.0599793\pi$
$402$		0			0
$403$	6.63634	−	18.2332i	0.330580	−	0.908260i
$404$		0			0
$405$	8.74061	+	12.6441i	0.434324	+	0.628289i
$406$		0			0
$407$	−20.2250	−	7.36129i	−1.00252	−	0.364886i
$408$		0			0
$409$	6.87431	+	5.76823i	0.339913	+	0.285221i	0.796725	−	0.604343i	$-0.206564\pi$
$409$	6.87431	+	5.76823i	0.339913	+	0.285221i	−0.456812	+	0.889563i	$0.651009\pi$
$410$		0			0
$411$	−7.86166	−	4.78676i	−0.387787	−	0.236114i
$412$		0			0
$413$	19.6168	−	11.3258i	0.965280	−	0.557305i
$414$		0			0
$415$	5.38806	+	3.11080i	0.264489	+	0.152703i
$416$		0			0
$417$	13.0578	+	16.3199i	0.639442	+	0.799187i
$418$		0			0
$419$	−8.46849	+	3.08228i	−0.413713	+	0.150579i	−0.540487	−	0.841352i	$-0.681760\pi$
$419$	−8.46849	+	3.08228i	−0.413713	+	0.150579i	0.126774	+	0.991932i	$0.459538\pi$
$420$		0			0
$421$	−2.46690	−	13.9905i	−0.120229	−	0.681855i	−0.984027	−	0.178017i	$-0.943032\pi$
$421$	−2.46690	−	13.9905i	−0.120229	−	0.681855i	0.863798	−	0.503838i	$-0.168079\pi$
$422$		0			0
$423$	−23.5202	+	7.33821i	−1.14359	+	0.356796i
$424$		0			0
$425$	−1.25651	−	1.49746i	−0.0609499	−	0.0726373i
$426$		0			0
$427$	−20.8423	−	3.67506i	−1.00863	−	0.177849i
$428$		0			0
$429$	−16.6498	+	5.62394i	−0.803860	+	0.271526i
$430$		0			0
$431$	26.9626			1.29874			0.649372	−	0.760471i	$-0.275032\pi$
$431$	26.9626			1.29874			0.649372	+	0.760471i	$0.275032\pi$
$432$		0			0
$433$	3.92105			0.188434			0.0942169	−	0.995552i	$-0.469965\pi$
$433$	3.92105			0.188434			0.0942169	+	0.995552i	$0.469965\pi$
$434$		0			0
$435$	11.9966	+	10.5527i	0.575192	+	0.505962i
$436$		0			0
$437$	0.0663982	+	0.0117078i	0.00317626	+	0.000560060i
$438$		0			0
$439$	12.3057	+	14.6654i	0.587320	+	0.699941i	0.975089	−	0.221816i	$-0.0711985\pi$
$439$	12.3057	+	14.6654i	0.587320	+	0.699941i	−0.387769	+	0.921757i	$0.626754\pi$
$440$		0			0
$441$	−7.56187	+	11.7914i	−0.360089	+	0.561493i
$442$		0			0
$443$	−3.58423	−	20.3272i	−0.170292	−	0.965772i	−0.943439	−	0.331546i	$-0.892430\pi$
$443$	−3.58423	−	20.3272i	−0.170292	−	0.965772i	0.773147	−	0.634226i	$-0.218681\pi$
$444$		0			0
$445$	14.1162	−	5.13787i	0.669171	−	0.243558i
$446$		0			0
$447$	1.90268	−	0.289922i	0.0899936	−	0.0137128i
$448$		0			0
$449$	−12.2207	−	7.05561i	−0.576730	−	0.332975i	0.183103	−	0.983094i	$-0.441386\pi$
$449$	−12.2207	−	7.05561i	−0.576730	−	0.332975i	−0.759833	+	0.650119i	$0.774719\pi$
$450$		0			0
$451$	14.1341	−	8.16033i	0.665549	−	0.384255i
$452$		0			0
$453$	−0.350559	+	15.0296i	−0.0164707	+	0.706151i
$454$		0			0
$455$	−5.83787	−	4.89855i	−0.273684	−	0.229648i
$456$		0			0
$457$	13.0602	+	4.75353i	0.610932	+	0.222361i	0.628911	−	0.777477i	$-0.283501\pi$
$457$	13.0602	+	4.75353i	0.610932	+	0.222361i	−0.0179791	+	0.999838i	$0.505723\pi$
$458$		0			0
$459$	−4.38297	+	2.13691i	−0.204579	+	0.0997426i
$460$		0			0
$461$	−11.4525	+	31.4654i	−0.533394	+	1.46549i	0.321613	+	0.946871i	$0.395775\pi$
$461$	−11.4525	+	31.4654i	−0.533394	+	1.46549i	−0.855007	+	0.518617i	$0.826447\pi$
$462$		0			0
$463$	12.5926	−	15.0072i	0.585226	−	0.697445i	−0.389455	−	0.921046i	$-0.627337\pi$
$463$	12.5926	−	15.0072i	0.585226	−	0.697445i	0.974681	+	0.223600i	$0.0717810\pi$
$464$		0			0
$465$	−9.42001	−	17.2318i	−0.436843	−	0.799106i
$466$		0			0
$467$	6.24674	+	10.8197i	0.289065	+	0.500675i	0.973587	−	0.228317i	$-0.0733224\pi$
$467$	6.24674	+	10.8197i	0.289065	+	0.500675i	−0.684522	+	0.728992i	$0.739989\pi$
$468$		0			0
$469$	10.0922	−	17.4802i	0.466013	−	0.807159i
$470$		0			0
$471$	−0.291364	−	0.113810i	−0.0134254	−	0.00524409i
$472$		0			0
$473$	9.68341	+	26.6049i	0.445244	+	1.22330i
$474$		0			0
$475$	−3.59369	+	0.633664i	−0.164890	+	0.0290745i
$476$		0			0
$477$	14.6771	−	35.1345i	0.672020	−	1.60870i
$478$		0			0
$479$	−29.6447	+	24.8749i	−1.35450	+	1.13656i	−0.376864	+	0.926269i	$0.622998\pi$
$479$	−29.6447	+	24.8749i	−1.35450	+	1.13656i	−0.977638	+	0.210294i	$0.932558\pi$
$480$		0			0
$481$	3.14663	−	17.8454i	0.143474	−	0.813681i
$482$		0			0
$483$	−0.0997865	−	0.0200048i	−0.00454044	−	0.000910250i
$484$		0			0
$485$			7.25369i			0.329373i
$486$		0			0
$487$			20.1282i			0.912096i	0.889955	+	0.456048i	$0.150736\pi$
$487$			20.1282i			0.912096i	−0.889955	+	0.456048i	$0.849264\pi$
$488$		0			0
$489$	−36.8274	−	7.38302i	−1.66539	−	0.333872i
$490$		0			0
$491$	1.32914	−	7.53795i	0.0599834	−	0.340183i	−0.940016	−	0.341130i	$-0.889190\pi$
$491$	1.32914	−	7.53795i	0.0599834	−	0.340183i	1.00000		0.000947128i	$0.000301480\pi$
$492$		0			0
$493$	−3.88268	+	3.25795i	−0.174867	+	0.146731i
$494$		0			0
$495$	−6.85617	+	16.4125i	−0.308162	+	0.737686i
$496$		0			0
$497$	5.46857	−	0.964257i	0.245299	−	0.0432528i
$498$		0			0
$499$	4.53447	+	12.4584i	0.202991	+	0.557713i	0.998859	−	0.0477573i	$-0.0152074\pi$
$499$	4.53447	+	12.4584i	0.202991	+	0.557713i	−0.795868	+	0.605470i	$0.792985\pi$
$500$		0			0
$501$	4.12523	+	1.61136i	0.184302	+	0.0719903i
$502$		0			0
$503$	6.64136	−	11.5032i	0.296124	−	0.512902i	−0.679122	−	0.734026i	$-0.737639\pi$
$503$	6.64136	−	11.5032i	0.296124	−	0.512902i	0.975246	+	0.221124i	$0.0709726\pi$
$504$		0			0
$505$	6.42540	+	11.1291i	0.285927	+	0.495240i
$506$		0			0
$507$	3.70340	+	6.77454i	0.164474	+	0.300868i
$508$		0			0
$509$	−24.3879	+	29.0644i	−1.08097	+	1.28826i	−0.125851	+	0.992049i	$0.540166\pi$
$509$	−24.3879	+	29.0644i	−1.08097	+	1.28826i	−0.955124	+	0.296206i	$0.904278\pi$
$510$		0			0
$511$	−2.11207	+	5.80287i	−0.0934325	+	0.256704i
$512$		0			0
$513$	−0.636310	+	9.08034i	−0.0280938	+	0.400907i
$514$		0			0
$515$	20.1790	+	7.34455i	0.889193	+	0.323640i
$516$		0			0
$517$	−21.8405	−	18.3264i	−0.960546	−	0.805994i
$518$		0			0
$519$	−0.458608	+	19.6620i	−0.0201306	+	0.863064i
$520$		0			0
$521$	17.1443	−	9.89824i	0.751103	−	0.433650i	−0.0749891	−	0.997184i	$-0.523892\pi$
$521$	17.1443	−	9.89824i	0.751103	−	0.433650i	0.826092	+	0.563535i	$0.190559\pi$
$522$		0			0
$523$	20.9712	+	12.1077i	0.917007	+	0.529434i	0.882679	−	0.469976i	$-0.155738\pi$
$523$	20.9712	+	12.1077i	0.917007	+	0.529434i	0.0343279	+	0.999411i	$0.489071\pi$
$524$		0			0
$525$	5.44538	−	0.829744i	0.237656	−	0.0362130i
$526$		0			0
$527$	5.85419	−	2.13075i	0.255012	−	0.0928169i
$528$		0			0
$529$	−3.99365	−	22.6491i	−0.173637	−	0.984744i
$530$		0			0
$531$	24.0288	−	37.4685i	1.04276	−	1.62600i
$532$		0			0
$533$	8.83238	+	10.5260i	0.382573	+	0.455933i
$534$		0			0
$535$	−32.0294	−	5.64766i	−1.38475	−	0.244169i
$536$		0			0
$537$	6.78259	+	5.96624i	0.292690	+	0.257462i
$538$		0			0
$539$	−16.2094			−0.698188
$540$		0			0
$541$	−6.77906			−0.291454			−0.145727	−	0.989325i	$-0.546552\pi$
$541$	−6.77906			−0.291454			−0.145727	+	0.989325i	$0.546552\pi$
$542$		0			0
$543$	19.6263	−	6.62934i	0.842246	−	0.284492i
$544$		0			0
$545$	7.51336	+	1.32481i	0.321837	+	0.0567485i
$546$		0			0
$547$	−16.7637	−	19.9782i	−0.716765	−	0.854207i	0.277548	−	0.960712i	$-0.410478\pi$
$547$	−16.7637	−	19.9782i	−0.716765	−	0.854207i	−0.994312	+	0.106505i	$0.966034\pi$
$548$		0			0
$549$	−39.7007	+	12.3864i	−1.69439	+	0.528640i
$550$		0			0
$551$	1.64300	+	9.31790i	0.0699940	+	0.396956i
$552$		0			0
$553$	18.0043	−	6.55301i	0.765619	−	0.278662i
$554$		0			0
$555$	−11.4581	−	14.3206i	−0.486370	−	0.607875i
$556$		0			0
$557$	−24.8803	−	14.3647i	−1.05421	−	0.608650i	−0.130387	−	0.991463i	$-0.541622\pi$
$557$	−24.8803	−	14.3647i	−1.05421	−	0.608650i	−0.923826	+	0.382813i	$0.874955\pi$
$558$		0			0
$559$	−20.6433	+	11.9184i	−0.873120	+	0.504096i
$560$		0			0
$561$	−4.81946	−	2.93444i	−0.203478	−	0.123892i
$562$		0			0
$563$	−16.0134	−	13.4368i	−0.674885	−	0.566296i	0.239622	−	0.970866i	$-0.422977\pi$
$563$	−16.0134	−	13.4368i	−0.674885	−	0.566296i	−0.914507	+	0.404571i	$0.867421\pi$
$564$		0			0
$565$	−2.91231	−	1.05999i	−0.122522	−	0.0445943i
$566$		0			0
$567$	1.27984	−	13.6803i	0.0537482	−	0.574520i
$568$		0			0
$569$	−9.78377	+	26.8807i	−0.410157	+	1.12690i	0.546951	+	0.837165i	$0.315788\pi$
$569$	−9.78377	+	26.8807i	−0.410157	+	1.12690i	−0.957108	+	0.289732i	$0.906434\pi$
$570$		0			0
$571$	6.24820	−	7.44632i	0.261479	−	0.311619i	−0.619292	−	0.785161i	$-0.712580\pi$
$571$	6.24820	−	7.44632i	0.261479	−	0.311619i	0.880771	+	0.473542i	$0.157025\pi$
$572$		0			0
$573$	9.93048	−	16.3096i	0.414852	−	0.681342i
$574$		0			0
$575$	−0.0400863	−	0.0694315i	−0.00167171	−	0.00289549i
$576$		0			0
$577$	−3.09107	+	5.35388i	−0.128683	+	0.222885i	−0.923166	−	0.384400i	$-0.874408\pi$
$577$	−3.09107	+	5.35388i	−0.128683	+	0.222885i	0.794484	+	0.607285i	$0.207742\pi$
$578$		0			0
$579$	−11.6186	+	9.29621i	−0.482852	+	0.386337i
$580$		0			0
$581$	−1.90212	−	5.22603i	−0.0789132	−	0.216812i
$582$		0			0
$583$	43.3921	−	7.65119i	1.79712	−	0.316880i
$584$		0			0
$585$	−14.6105	−	3.28520i	−0.604069	−	0.135826i
$586$		0			0
$587$	−4.60609	+	3.86497i	−0.190114	+	0.159524i	−0.732877	−	0.680362i	$-0.761823\pi$
$587$	−4.60609	+	3.86497i	−0.190114	+	0.159524i	0.542763	+	0.839886i	$0.317378\pi$
$588$		0			0
$589$	2.01948	−	11.4531i	0.0832113	−	0.471915i
$590$		0			0
$591$	−9.72117	−	28.7798i	−0.399875	−	1.18384i
$592$		0			0
$593$			45.9763i			1.88802i	0.329915	+	0.944011i	$0.392980\pi$
$593$			45.9763i			1.88802i	−0.329915	+	0.944011i	$0.607020\pi$
$594$		0			0
$595$		−	2.44683i		−	0.100310i
$596$		0			0
$597$	−20.6976	+	23.5296i	−0.847096	+	0.963003i
$598$		0			0
$599$	4.50094	−	25.5261i	0.183903	−	1.04297i	−0.743453	−	0.668788i	$-0.766813\pi$
$599$	4.50094	−	25.5261i	0.183903	−	1.04297i	0.927356	−	0.374180i	$-0.122076\pi$
$600$		0			0
$601$	6.44957	−	5.41183i	0.263084	−	0.220753i	−0.501698	−	0.865043i	$-0.667291\pi$
$601$	6.44957	−	5.41183i	0.263084	−	0.220753i	0.764782	+	0.644289i	$0.222847\pi$
$602$		0			0
$603$	1.84926	−	39.6202i	0.0753077	−	1.61346i
$604$		0			0
$605$	−1.76836	+	0.311810i	−0.0718941	+	0.0126769i
$606$		0			0
$607$	−5.71034	−	15.6890i	−0.231776	−	0.636798i	0.768219	−	0.640188i	$-0.221143\pi$
$607$	−5.71034	−	15.6890i	−0.231776	−	0.636798i	−0.999994	+	0.00338920i	$0.998921\pi$
$608$		0			0
$609$	−2.15140	−	14.1191i	−0.0871791	−	0.572133i
$610$		0			0
$611$	12.0020	−	20.7880i	0.485548	−	0.840993i
$612$		0			0
$613$	−12.4645	−	21.5892i	−0.503437	−	0.871979i	−0.999992	−	0.00397384i	$-0.998735\pi$
$613$	−12.4645	−	21.5892i	−0.503437	−	0.871979i	0.496555	−	0.868005i	$-0.334598\pi$
$614$		0			0
$615$	13.9035	+	0.324294i	0.560643	+	0.0130768i
$616$		0			0
$617$	−5.56720	+	6.63473i	−0.224127	+	0.267104i	−0.866376	−	0.499392i	$-0.833557\pi$
$617$	−5.56720	+	6.63473i	−0.224127	+	0.267104i	0.642249	+	0.766496i	$0.278001\pi$
$618$		0			0
$619$	6.19615	−	17.0238i	0.249044	−	0.684244i	−0.750678	−	0.660669i	$-0.770273\pi$
$619$	6.19615	−	17.0238i	0.249044	−	0.684244i	0.999722	−	0.0235754i	$-0.00750497\pi$
$620$		0			0
$621$	−0.192248	+	0.0550956i	−0.00771466	+	0.00221091i
$622$		0			0
$623$	−12.6183	−	4.59269i	−0.505542	−	0.184002i
$624$		0			0
$625$	−7.84845	−	6.58563i	−0.313938	−	0.263425i
$626$		0			0
$627$	−9.24240	+	5.05249i	−0.369106	+	0.201777i
$628$		0			0
$629$	5.03860	−	2.90904i	0.200902	−	0.115991i
$630$		0			0
$631$	−39.2093	−	22.6375i	−1.56090	−	0.901185i	−0.997166	−	0.0752273i	$-0.976032\pi$
$631$	−39.2093	−	22.6375i	−1.56090	−	0.901185i	−0.563732	−	0.825958i	$-0.690635\pi$
$632$		0			0
$633$	10.1645	−	26.0222i	0.404005	−	1.03429i
$634$		0			0
$635$	11.6357	−	4.23506i	0.461750	−	0.168063i
$636$		0			0
$637$	−2.36979	−	13.4397i	−0.0938944	−	0.532502i
$638$		0			0
$639$	8.67687	−	6.61663i	0.343252	−	0.261750i
$640$		0			0
$641$	9.21101	+	10.9773i	0.363813	+	0.433576i	0.916636	−	0.399723i	$-0.130894\pi$
$641$	9.21101	+	10.9773i	0.363813	+	0.433576i	−0.552823	+	0.833299i	$0.686449\pi$
$642$		0			0
$643$	−24.8469	−	4.38119i	−0.979867	−	0.172777i	−0.339299	−	0.940678i	$-0.610190\pi$
$643$	−24.8469	−	4.38119i	−0.979867	−	0.172777i	−0.640568	+	0.767901i	$0.721301\pi$
$644$		0			0
$645$	−4.74228	+	23.6551i	−0.186727	+	0.931419i
$646$		0			0
$647$	36.8495			1.44870			0.724352	−	0.689430i	$-0.242139\pi$
$647$	36.8495			1.44870			0.724352	+	0.689430i	$0.242139\pi$
$648$		0			0
$649$	51.5074			2.02184
$650$		0			0
$651$	−3.45064	+	17.2122i	−0.135241	+	0.674600i
$652$		0			0
$653$	31.3576	+	5.52920i	1.22712	+	0.216374i	0.749387	−	0.662132i	$-0.230348\pi$
$653$	31.3576	+	5.52920i	1.22712	+	0.216374i	0.477732	+	0.878506i	$0.341459\pi$
$654$		0			0
$655$	19.1871	+	22.8663i	0.749703	+	0.893461i
$656$		0			0
$657$	1.54771	+	12.0357i	0.0603820	+	0.469556i
$658$		0			0
$659$	2.52273	+	14.3071i	0.0982717	+	0.557326i	0.993696	+	0.112112i	$0.0357615\pi$
$659$	2.52273	+	14.3071i	0.0982717	+	0.557326i	−0.895424	+	0.445215i	$0.853127\pi$
$660$		0			0
$661$	6.12471	−	2.22921i	0.238224	−	0.0867063i	−0.220150	−	0.975466i	$-0.570655\pi$
$661$	6.12471	−	2.22921i	0.238224	−	0.0867063i	0.458373	+	0.888760i	$0.348432\pi$
$662$		0			0
$663$	1.72845	−	4.42498i	0.0671273	−	0.171852i
$664$		0			0
$665$	−3.95571	−	2.28383i	−0.153396	−	0.0885630i
$666$		0			0
$667$	−0.180025	+	0.103938i	−0.00697061	+	0.00402449i
$668$		0			0
$669$	−3.96252	+	2.16617i	−0.153200	+	0.0837489i
$670$		0			0
$671$	−36.8655	−	30.9338i	−1.42318	−	1.19419i
$672$		0			0
$673$	17.8218	+	6.48661i	0.686980	+	0.250040i	0.661842	−	0.749644i	$-0.269775\pi$
$673$	17.8218	+	6.48661i	0.686980	+	0.250040i	0.0251385	+	0.999684i	$0.491997\pi$
$674$		0			0
$675$	8.75772	−	6.36088i	0.337085	−	0.244830i
$676$		0			0
$677$	9.86289	−	27.0981i	0.379062	−	1.04146i	−0.592684	−	0.805435i	$-0.701932\pi$
$677$	9.86289	−	27.0981i	0.379062	−	1.04146i	0.971746	−	0.236029i	$-0.0758459\pi$
$678$		0			0
$679$	4.16784	−	4.96703i	0.159947	−	0.190617i
$680$		0			0
$681$	−39.6162	−	0.924033i	−1.51810	−	0.0354090i
$682$		0			0
$683$	0.473868	+	0.820764i	0.0181321	+	0.0314057i	0.874949	−	0.484215i	$-0.160895\pi$
$683$	0.473868	+	0.820764i	0.0181321	+	0.0314057i	−0.856817	+	0.515621i	$0.827561\pi$
$684$		0			0
$685$	4.53797	−	7.86000i	0.173387	−	0.300315i
$686$		0			0
$687$	−0.156764	−	1.02880i	−0.00598094	−	0.0392513i
$688$		0			0
$689$	12.6877	+	34.8592i	0.483363	+	1.32803i
$690$		0			0
$691$	21.8003	−	3.84398i	0.829321	−	0.146232i	0.257156	−	0.966370i	$-0.417215\pi$
$691$	21.8003	−	3.84398i	0.829321	−	0.146232i	0.572165	+	0.820138i	$0.306104\pi$
$692$		0			0
$693$	14.1251	−	7.29917i	0.536570	−	0.277273i
$694$		0			0
$695$	−15.7877	+	13.2475i	−0.598862	+	0.502505i
$696$		0			0
$697$	−0.766098	+	4.34476i	−0.0290180	+	0.164569i
$698$		0			0
$699$	−34.2061	+	38.8865i	−1.29379	+	1.47082i
$700$		0			0
$701$			37.6486i			1.42197i	0.703209	+	0.710983i	$0.251750\pi$
$701$			37.6486i			1.42197i	−0.703209	+	0.710983i	$0.748250\pi$
$702$		0			0
$703$		−	10.8610i		−	0.409629i
$704$		0			0
$705$	−7.77473	−	23.0173i	−0.292813	−	0.866880i
$706$		0			0
$707$	1.99473	−	11.3127i	0.0750197	−	0.425458i
$708$		0			0
$709$	24.0912	−	20.2150i	0.904766	−	0.759189i	−0.0663503	−	0.997796i	$-0.521135\pi$
$709$	24.0912	−	20.2150i	0.904766	−	0.759189i	0.971116	+	0.238608i	$0.0766911\pi$
$710$		0			0
$711$	25.5193	−	27.6818i	0.957048	−	1.03815i
$712$		0			0
$713$	0.251628	−	0.0443687i	0.00942353	−	0.00166162i
$714$		0			0
$715$	−5.92684	−	16.2839i	−0.221651	−	0.608982i
$716$		0			0
$717$	−0.941064	+	0.752960i	−0.0351447	+	0.0281198i
$718$		0			0
$719$	10.2799	−	17.8053i	0.383375	−	0.664025i	−0.608167	−	0.793809i	$-0.708095\pi$
$719$	10.2799	−	17.8053i	0.383375	−	0.664025i	0.991542	+	0.129784i	$0.0414283\pi$
$720$		0			0
$721$	−9.59772	−	16.6237i	−0.357438	−	0.619100i
$722$		0			0
$723$	−14.2274	+	23.3667i	−0.529122	+	0.869016i
$724$		0			0
$725$	7.23194	−	8.61869i	0.268588	−	0.320090i
$726$		0			0
$727$	16.7919	−	46.1353i	0.622776	−	1.71106i	−0.0773130	−	0.997007i	$-0.524634\pi$
$727$	16.7919	−	46.1353i	0.622776	−	1.71106i	0.700089	−	0.714056i	$-0.253144\pi$
$728$		0			0
$729$	−10.1070	−	25.0370i	−0.374332	−	0.927295i
$730$		0			0
$731$	−7.19182	−	2.61761i	−0.265999	−	0.0968158i
$732$		0			0
$733$	31.2847	+	26.2510i	1.15553	+	0.969603i	0.999834	−	0.0182021i	$-0.00579423\pi$
$733$	31.2847	+	26.2510i	1.15553	+	0.969603i	0.155694	+	0.987805i	$0.450239\pi$
$734$		0			0
$735$	−11.7977	−	7.18329i	−0.435163	−	0.264960i
$736$		0			0
$737$	39.7482	−	22.9486i	1.46414	−	0.845323i
$738$		0			0
$739$	34.5124	+	19.9257i	1.26956	+	0.732981i	0.974905	−	0.222623i	$-0.0714619\pi$
$739$	34.5124	+	19.9257i	1.26956	+	0.732981i	0.294655	+	0.955604i	$0.404795\pi$
$740$		0			0
$741$	−5.54041	−	6.92451i	−0.203532	−	0.254378i
$742$		0			0
$743$	24.8926	−	9.06017i	0.913221	−	0.332385i	0.157683	−	0.987490i	$-0.449598\pi$
$743$	24.8926	−	9.06017i	0.913221	−	0.332385i	0.755538	+	0.655104i	$0.227375\pi$
$744$		0			0
$745$	0.329550	+	1.86897i	0.0120738	+	0.0684739i
$746$		0			0
$747$	−8.03509	−	7.40738i	−0.293989	−	0.271022i
$748$		0			0
$749$	18.6874	+	22.2708i	0.682824	+	0.813758i
$750$		0			0
$751$	6.30283	+	1.11136i	0.229994	+	0.0405541i	0.287457	−	0.957794i	$-0.407190\pi$
$751$	6.30283	+	1.11136i	0.229994	+	0.0405541i	−0.0574634	+	0.998348i	$0.518301\pi$
$752$		0			0
$753$	−36.4063	+	12.2972i	−1.32672	+	0.448136i
$754$		0			0
$755$	−14.8240			−0.539502
$756$		0			0
$757$	−23.3500			−0.848671			−0.424336	−	0.905505i	$-0.639492\pi$
$757$	−23.3500			−0.848671			−0.424336	+	0.905505i	$0.639492\pi$
$758$		0			0
$759$	−0.173761	−	0.152847i	−0.00630711	−	0.00554799i
$760$		0			0
$761$	−46.5181	−	8.20240i	−1.68628	−	0.297337i	−0.753411	−	0.657550i	$-0.771593\pi$
$761$	−46.5181	−	8.20240i	−1.68628	−	0.297337i	−0.932870	+	0.360213i	$0.882704\pi$
$762$		0			0
$763$	−4.38363	−	5.22421i	−0.158698	−	0.189129i
$764$		0			0
$765$	−2.20732	−	4.27155i	−0.0798060	−	0.154438i
$766$		0			0
$767$	7.53030	+	42.7065i	0.271903	+	1.54204i
$768$		0			0
$769$	22.1294	−	8.05443i	0.798006	−	0.290450i	0.0893459	−	0.996001i	$-0.471522\pi$
$769$	22.1294	−	8.05443i	0.798006	−	0.290450i	0.708660	+	0.705550i	$0.249300\pi$
$770$		0			0
$771$	−35.9338	+	5.47543i	−1.29412	+	0.197193i
$772$		0			0
$773$	12.0923	+	6.98148i	0.434929	+	0.251106i	0.701444	−	0.712724i	$-0.252539\pi$
$773$	12.0923	+	6.98148i	0.434929	+	0.251106i	−0.266515	+	0.963831i	$0.585872\pi$
$774$		0			0
$775$	−11.9763	+	6.91450i	−0.430200	+	0.248376i
$776$		0			0
$777$	−0.382286	+	16.3898i	−0.0137144	+	0.587980i
$778$		0			0
$779$	6.30895	+	5.29384i	0.226042	+	0.189671i
$780$		0			0
$781$	11.8653	+	4.31863i	0.424575	+	0.154533i
$782$		0			0
$783$	−16.4928	−	22.7075i	−0.589405	−	0.811498i
$784$		0			0
$785$	0.105493	−	0.289841i	0.00376522	−	0.0103449i
$786$		0			0
$787$	−33.1852	+	39.5486i	−1.18292	+	1.40975i	−0.291508	+	0.956568i	$0.594157\pi$
$787$	−33.1852	+	39.5486i	−1.18292	+	1.40975i	−0.891416	+	0.453186i	$0.850287\pi$
$788$		0			0
$789$	−6.67051	−	12.2022i	−0.237476	−	0.434410i
$790$		0			0
$791$	1.38518	+	2.39920i	0.0492513	+	0.0853057i
$792$		0			0
$793$	20.2586	−	35.0889i	0.719403	−	1.24604i
$794$		0			0
$795$	34.9727	+	13.6607i	1.24035	+	0.484495i
$796$		0			0
$797$	−12.4781	−	34.2834i	−0.441998	−	1.21438i	−0.938176	−	0.346159i	$-0.887486\pi$
$797$	−12.4781	−	34.2834i	−0.441998	−	1.21438i	0.496178	−	0.868221i	$-0.334736\pi$
$798$		0			0
$799$	7.58993	−	1.33831i	0.268512	−	0.0473460i
$800$		0			0
$801$	−26.1715	+	3.36550i	−0.924724	+	0.118914i
$802$		0			0
$803$	−10.7568	+	9.02601i	−0.379598	+	0.318521i
$804$		0			0
$805$	0.0174261	−	0.0988284i	0.000614190	−	0.00348324i
$806$		0			0
$807$	44.4731	+	8.91579i	1.56553	+	0.313851i
$808$		0			0
$809$			40.9070i			1.43821i	0.694899	+	0.719107i	$0.255449\pi$
$809$			40.9070i			1.43821i	−0.694899	+	0.719107i	$0.744551\pi$
$810$		0			0
$811$			39.1807i			1.37582i	0.725795	+	0.687911i	$0.241472\pi$
$811$			39.1807i			1.37582i	−0.725795	+	0.687911i	$0.758528\pi$
$812$		0			0
$813$	−25.3329	−	5.07863i	−0.888462	−	0.178115i
$814$		0			0
$815$	6.43132	−	36.4738i	0.225279	−	1.27762i
$816$		0			0
$817$	−10.9445	+	9.18353i	−0.382900	+	0.321291i
$818$		0			0
$819$	8.11706	+	10.6445i	0.283633	+	0.371949i
$820$		0			0
$821$	−7.39112	+	1.30325i	−0.257952	+	0.0454839i	−0.301129	−	0.953584i	$-0.597363\pi$
$821$	−7.39112	+	1.30325i	−0.257952	+	0.0454839i	0.0431766	+	0.999067i	$0.486252\pi$
$822$		0			0
$823$	−9.86470	−	27.1030i	−0.343862	−	0.944753i	−0.984263	−	0.176712i	$-0.943454\pi$
$823$	−9.86470	−	27.1030i	−0.343862	−	0.944753i	0.640401	−	0.768041i	$-0.278768\pi$
$824$		0			0
$825$	11.6667	+	4.55715i	0.406183	+	0.158660i
$826$		0			0
$827$	−20.3147	+	35.1861i	−0.706411	+	1.22354i	0.259769	+	0.965671i	$0.416354\pi$
$827$	−20.3147	+	35.1861i	−0.706411	+	1.22354i	−0.966180	+	0.257869i	$0.916980\pi$
$828$		0			0
$829$	8.83592	+	15.3043i	0.306884	+	0.531539i	0.977679	−	0.210104i	$-0.0673802\pi$
$829$	8.83592	+	15.3043i	0.306884	+	0.531539i	−0.670795	+	0.741643i	$0.734047\pi$
$830$		0			0
$831$	15.5051	+	28.3630i	0.537864	+	0.983903i
$832$		0			0
$833$	2.81651	−	3.35658i	0.0975862	−	0.116299i
$834$		0			0
$835$	−1.49361	+	4.10366i	−0.0516885	+	0.142013i
$836$		0			0
$837$	9.50345	+	33.1610i	0.328487	+	1.14621i
$838$		0			0
$839$	−11.2749	−	4.10375i	−0.389254	−	0.141677i	0.139977	−	0.990155i	$-0.455297\pi$
$839$	−11.2749	−	4.10375i	−0.389254	−	0.141677i	−0.529231	+	0.848478i	$0.677520\pi$
$840$		0			0
$841$	−0.131685	−	0.110497i	−0.00454086	−	0.00381023i
$842$		0			0
$843$	−0.169928	+	7.28535i	−0.00585263	+	0.250921i
$844$		0			0
$845$	−6.59311	+	3.80653i	−0.226810	+	0.130949i
$846$		0			0
$847$	1.39006	+	0.802553i	0.0477631	+	0.0275760i
$848$		0			0
$849$	−3.34159	+	0.509177i	−0.114683	+	0.0174749i
$850$		0			0
$851$	0.224229	−	0.0816125i	0.00768646	−	0.00279764i
$852$		0			0
$853$	2.26964	+	12.8718i	0.0777110	+	0.440721i	0.998693	+	0.0511152i	$0.0162776\pi$
$853$	2.26964	+	12.8718i	0.0777110	+	0.440721i	−0.920982	+	0.389606i	$0.872611\pi$
$854$		0			0
$855$	−8.96593	−	0.418482i	−0.306628	−	0.0143118i
$856$		0			0
$857$	−11.7920	−	14.0531i	−0.402807	−	0.480046i	0.526067	−	0.850443i	$-0.323666\pi$
$857$	−11.7920	−	14.0531i	−0.402807	−	0.480046i	−0.928874	+	0.370397i	$0.879222\pi$
$858$		0			0
$859$	−44.0233	−	7.76250i	−1.50206	−	0.264853i	−0.638704	−	0.769453i	$-0.720529\pi$
$859$	−44.0233	−	7.76250i	−1.50206	−	0.264853i	−0.863353	+	0.504600i	$0.831640\pi$
$860$		0			0
$861$	−9.33423	−	8.21076i	−0.318110	−	0.279822i
$862$		0			0
$863$	56.2127			1.91350			0.956751	−	0.290908i	$-0.0939572\pi$
$863$	56.2127			1.91350			0.956751	+	0.290908i	$0.0939572\pi$
$864$		0			0
$865$	−19.3931			−0.659385
$866$		0			0
$867$	−26.4514	+	8.93469i	−0.898335	+	0.303438i
$868$		0			0
$869$	42.9054	+	7.56539i	1.45547	+	0.256638i
$870$		0			0
$871$	24.8386	+	29.6015i	0.841623	+	1.00301i
$872$		0			0
$873$	2.79515	−	12.4310i	0.0946014	−	0.420727i
$874$		0			0
$875$	3.20702	+	18.1879i	0.108417	+	0.614863i
$876$		0			0
$877$	−49.6889	+	18.0853i	−1.67788	+	0.610697i	−0.993016	−	0.117977i	$-0.962359\pi$
$877$	−49.6889	+	18.0853i	−1.67788	+	0.610697i	−0.684860	+	0.728675i	$0.740137\pi$
$878$		0			0
$879$	9.22385	+	11.5281i	0.311113	+	0.388835i
$880$		0			0
$881$	−17.9275	−	10.3504i	−0.603992	−	0.348715i	0.166618	−	0.986021i	$-0.446715\pi$
$881$	−17.9275	−	10.3504i	−0.603992	−	0.348715i	−0.770610	+	0.637306i	$0.780049\pi$
$882$		0			0
$883$	−15.8565	+	9.15473i	−0.533612	+	0.308081i	−0.742486	−	0.669861i	$-0.766354\pi$
$883$	−15.8565	+	9.15473i	−0.533612	+	0.308081i	0.208874	+	0.977943i	$0.433020\pi$
$884$		0			0
$885$	37.4886	+	22.8258i	1.26016	+	0.767282i
$886$		0			0
$887$	−14.9691	−	12.5606i	−0.502615	−	0.421744i	0.355907	−	0.934521i	$-0.384172\pi$
$887$	−14.9691	−	12.5606i	−0.502615	−	0.421744i	−0.858521	+	0.512778i	$0.828616\pi$
$888$		0			0
$889$	−10.4011	−	3.78568i	−0.348841	−	0.126968i
$890$		0			0
$891$	18.0742	−	25.4850i	0.605509	−	0.853779i
$892$		0			0
$893$	4.92070	−	13.5195i	0.164665	−	0.452413i
$894$		0			0
$895$	−5.72550	+	6.82338i	−0.191382	+	0.228081i
$896$		0			0
$897$	0.101327	−	0.166417i	0.00338321	−	0.00555649i
$898$		0			0
$899$	17.9283	+	31.0527i	0.597941	+	1.03566i
$900$		0			0
$901$	−5.95533	+	10.3149i	−0.198401	+	0.343640i
$902$		0			0
$903$	16.8391	−	13.4732i	0.560371	−	0.448361i
$904$		0			0
$905$	6.98640	+	19.1950i	0.232236	+	0.638063i
$906$		0			0
$907$	39.2190	−	6.91536i	1.30224	−	0.229621i	0.520845	−	0.853651i	$-0.325617\pi$
$907$	39.2190	−	6.91536i	1.30224	−	0.229621i	0.781400	+	0.624030i	$0.214506\pi$
$908$		0			0
$909$	−6.72305	−	21.5486i	−0.222990	−	0.714721i
$910$		0			0
$911$	−36.5751	+	30.6901i	−1.21179	+	1.01681i	−0.212572	+	0.977145i	$0.568184\pi$
$911$	−36.5751	+	30.6901i	−1.21179	+	1.01681i	−0.999213	+	0.0396634i	$0.987371\pi$
$912$		0			0
$913$	2.19598	−	12.4540i	0.0726762	−	0.412167i
$914$		0			0
$915$	−13.1233	−	38.8517i	−0.433841	−	1.28440i
$916$		0			0
$917$		−	26.6825i		−	0.881133i
$918$		0			0
$919$			45.4710i			1.49995i	0.661466	+	0.749975i	$0.269934\pi$
$919$			45.4710i			1.49995i	−0.661466	+	0.749975i	$0.730066\pi$
$920$		0			0
$921$	11.3227	−	12.8720i	0.373096	−	0.424146i
$922$		0			0
$923$	−1.84602	+	10.4693i	−0.0607626	+	0.344602i
$924$		0			0
$925$	−9.89334	+	8.30150i	−0.325291	+	0.272952i
$926$		0			0
$927$	−31.7517	−	20.3626i	−1.04286	−	0.668794i
$928$		0			0
$929$	−28.7888	+	5.07625i	−0.944531	+	0.166546i	−0.624644	−	0.780909i	$-0.714756\pi$
$929$	−28.7888	+	5.07625i	−0.944531	+	0.166546i	−0.319887	+	0.947456i	$0.603645\pi$
$930$		0			0
$931$	−2.79759	−	7.68631i	−0.0916873	−	0.251909i
$932$		0			0
$933$	6.27265	+	41.1657i	0.205357	+	1.34770i
$934$		0			0
$935$	2.78193	−	4.81844i	0.0909788	−	0.157580i
$936$		0			0
$937$	1.92824	+	3.33982i	0.0629930	+	0.109107i	0.895802	−	0.444453i	$-0.146602\pi$
$937$	1.92824	+	3.33982i	0.0629930	+	0.109107i	−0.832809	+	0.553560i	$0.813269\pi$
$938$		0			0
$939$	2.99628	+	0.0698872i	0.0977800	+	0.00228068i
$940$		0			0
$941$	−6.70135	+	7.98635i	−0.218458	+	0.260348i	−0.864132	−	0.503265i	$-0.832132\pi$
$941$	−6.70135	+	7.98635i	−0.218458	+	0.260348i	0.645674	+	0.763613i	$0.276576\pi$
$942$		0			0
$943$	−0.0618859	+	0.170030i	−0.00201528	+	0.00553694i
$944$		0			0
$945$	13.5154	+	0.947096i	0.439655	+	0.0308090i
$946$		0			0
$947$	−20.2753	−	7.37959i	−0.658858	−	0.239805i	−0.00911453	−	0.999958i	$-0.502901\pi$
$947$	−20.2753	−	7.37959i	−0.658858	−	0.239805i	−0.649743	+	0.760154i	$0.725124\pi$
$948$		0			0
$949$	−9.05639	−	7.59921i	−0.293983	−	0.246681i
$950$		0			0
$951$	−27.2708	+	14.9080i	−0.884317	+	0.483424i
$952$		0			0
$953$	−30.4831	+	17.5994i	−0.987446	+	0.570102i	−0.904510	−	0.426453i	$-0.859763\pi$
$953$	−30.4831	+	17.5994i	−0.987446	+	0.570102i	−0.0829360	+	0.996555i	$0.526430\pi$
$954$		0			0
$955$	16.3061	+	9.41434i	0.527654	+	0.304641i
$956$		0			0
$957$	11.8160	−	30.2501i	0.381957	−	0.977846i
$958$		0			0
$959$	−7.62363	+	2.77477i	−0.246180	+	0.0896021i
$960$		0			0
$961$	−2.27009	−	12.8743i	−0.0732285	−	0.415300i
$962$		0			0
$963$	52.7143	+	22.0210i	1.69870	+	0.709616i
$964$		0			0
$965$	−9.43125	−	11.2397i	−0.303603	−	0.361820i
$966$		0			0
$967$	10.0342	+	1.76930i	0.322678	+	0.0568968i	0.332641	−	0.943054i	$-0.392060\pi$
$967$	10.0342	+	1.76930i	0.322678	+	0.0568968i	−0.00996311	+	0.999950i	$0.503171\pi$
$968$		0			0
$969$	0.559688	−	2.79179i	0.0179798	−	0.0896853i
$970$		0			0
$971$	9.24359			0.296641			0.148321	−	0.988939i	$-0.452613\pi$
$971$	9.24359			0.296641			0.148321	+	0.988939i	$0.452613\pi$
$972$		0			0
$973$	18.4225			0.590599
$974$		0			0
$975$	−2.07283	+	10.3395i	−0.0663836	+	0.331130i
$976$		0			0
$977$	−6.13934	−	1.08253i	−0.196415	−	0.0346332i	0.0745752	−	0.997215i	$-0.476240\pi$
$977$	−6.13934	−	1.08253i	−0.196415	−	0.0346332i	−0.270990	+	0.962582i	$0.587351\pi$
$978$		0			0
$979$	−19.6270	−	23.3906i	−0.627283	−	0.747566i
$980$		0			0
$981$	−12.3655	−	5.16560i	−0.394802	−	0.164925i
$982$		0			0
$983$	−2.20795	−	12.5219i	−0.0704228	−	0.399388i	−0.999560	−	0.0296531i	$-0.990560\pi$
$983$	−2.20795	−	12.5219i	−0.0704228	−	0.399388i	0.929137	−	0.369735i	$-0.120551\pi$
$984$		0			0
$985$	28.1472	−	10.2448i	0.896846	−	0.326425i
$986$		0			0
$987$	−7.90148	+	20.2285i	−0.251507	+	0.643880i
$988$		0			0
$989$	−0.271838	−	0.156946i	−0.00864394	−	0.00499058i
$990$		0			0
$991$	−5.84640	+	3.37542i	−0.185717	+	0.107224i	−0.589976	−	0.807421i	$-0.700863\pi$
$991$	−5.84640	+	3.37542i	−0.185717	+	0.107224i	0.404259	+	0.914645i	$0.367529\pi$
$992$		0			0
$993$	−14.7385	+	8.05698i	−0.467711	+	0.255681i
$994$		0			0
$995$	−23.6711	−	19.8624i	−0.750425	−	0.629682i
$996$		0			0
$997$	−54.9552	−	20.0021i	−1.74045	−	0.633472i	−0.741166	−	0.671322i	$-0.765727\pi$
$997$	−54.9552	−	20.0021i	−1.74045	−	0.633472i	−0.999283	+	0.0378501i	$0.987949\pi$
$998$		0			0
$999$	14.1181	+	28.9573i	0.446677	+	0.916167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.239.4	yes	36
4.3	odd	2	inner	432.2.be.a.239.3	yes	36
27.20	odd	18	inner	432.2.be.a.47.3	✓	36
108.47	even	18	inner	432.2.be.a.47.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.47.3	✓	36	27.20	odd	18	inner
432.2.be.a.47.4	yes	36	108.47	even	18	inner
432.2.be.a.239.3	yes	36	4.3	odd	2	inner
432.2.be.a.239.4	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.340461 - 1.69826i) q^{3} +(1.68195 + 0.296574i) q^{5} +(-0.981328 - 1.16950i) q^{7} +(-2.76817 - 1.15638i) q^{9} +O(q^{10})\)	\(q+(0.340461 - 1.69826i) q^{3} +(1.68195 + 0.296574i) q^{5} +(-0.981328 - 1.16950i) q^{7} +(-2.76817 - 1.15638i) q^{9} +(-0.602821 - 3.41877i) q^{11} +(2.74648 - 0.999638i) q^{13} +(1.07630 - 2.75542i) q^{15} +(0.812691 + 0.469208i) q^{17} +(1.51710 - 0.875899i) q^{19} +(-2.32022 + 1.26838i) q^{21} +(0.0294832 + 0.0247394i) q^{23} +(-1.95745 - 0.712454i) q^{25} +(-2.90629 + 4.30738i) q^{27} +(-1.84729 + 5.07538i) q^{29} +(4.26730 - 5.08557i) q^{31} +(-6.01119 - 0.140209i) q^{33} +(-1.30371 - 2.25808i) q^{35} +(3.09995 - 5.36926i) q^{37} +(-0.762576 - 5.00458i) q^{39} +(1.60794 + 4.41779i) q^{41} +(-8.03174 + 1.41621i) q^{43} +(-4.31299 - 2.76595i) q^{45} +(6.29137 - 5.27909i) q^{47} +(0.810809 - 4.59833i) q^{49} +(1.07353 - 1.22041i) q^{51} +12.6923i q^{53} -5.92899i q^{55} +(-0.970991 - 2.87464i) q^{57} +(-2.57645 + 14.6118i) q^{59} +(10.6194 - 8.91077i) q^{61} +(1.36410 + 4.37217i) q^{63} +(4.91592 - 0.866810i) q^{65} +(4.52189 + 12.4238i) q^{67} +(0.0520517 - 0.0416474i) q^{69} +(-1.81864 + 3.14997i) q^{71} +(-2.02246 - 3.50300i) q^{73} +(-1.87637 + 3.08170i) q^{75} +(-3.40669 + 4.05993i) q^{77} +(-4.29234 + 11.7931i) q^{79} +(6.32557 + 6.40213i) q^{81} +(3.42314 + 1.24592i) q^{83} +(1.22775 + 1.03021i) q^{85} +(7.99038 + 4.86514i) q^{87} +(7.61727 - 4.39783i) q^{89} +(-3.86428 - 2.23104i) q^{91} +(-7.18377 - 8.97842i) q^{93} +(2.81146 - 1.02329i) q^{95} +(0.737508 + 4.18262i) q^{97} +(-2.28469 + 10.1608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^5 - 12 * q^9	\( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) \) 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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