LMFDB - Embedded newform 162.2.e.a.91.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,2,Mod(19,162)] 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("162.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			91.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	162.91
Dual form			162.2.e.a.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(0.673648 + 0.565258i) q^{5} +(3.31908 + 1.20805i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.439693 + 0.761570i) q^{10} +(-2.73783 + 2.29731i) q^{11} +(-0.641559 + 3.63846i) q^{13} +(-0.613341 + 3.47843i) q^{14} +(0.766044 - 0.642788i) q^{16} +(3.12449 - 5.41177i) q^{17} +(-2.08512 - 3.61154i) q^{19} +(-0.826352 - 0.300767i) q^{20} +(-2.73783 - 2.29731i) q^{22} +(1.93969 - 0.705990i) q^{23} +(-0.733956 - 4.16247i) q^{25} -3.69459 q^{26} -3.53209 q^{28} +(-0.0282185 - 0.160035i) q^{29} +(-1.53936 + 0.560282i) q^{31} +(0.766044 + 0.642788i) q^{32} +(5.87211 + 2.13727i) q^{34} +(1.55303 + 2.68993i) q^{35} +(3.85844 - 6.68302i) q^{37} +(3.19459 - 2.68058i) q^{38} +(0.152704 - 0.866025i) q^{40} +(1.33750 - 7.58532i) q^{41} +(-8.29086 + 6.95686i) q^{43} +(1.78699 - 3.09516i) q^{44} +(1.03209 + 1.78763i) q^{46} +(-6.02481 - 2.19285i) q^{47} +(4.19459 + 3.51968i) q^{49} +(3.97178 - 1.44561i) q^{50} +(-0.641559 - 3.63846i) q^{52} -0.716881 q^{53} -3.14290 q^{55} +(-0.613341 - 3.47843i) q^{56} +(0.152704 - 0.0555796i) q^{58} +(5.35117 + 4.49016i) q^{59} +(1.19207 + 0.433877i) q^{61} +(-0.819078 - 1.41868i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-2.48886 + 2.08840i) q^{65} +(0.624485 - 3.54163i) q^{67} +(-1.08512 + 6.15403i) q^{68} +(-2.37939 + 1.99654i) q^{70} +(-6.76991 + 11.7258i) q^{71} +(1.16385 + 2.01584i) q^{73} +(7.25150 + 2.63933i) q^{74} +(3.19459 + 2.68058i) q^{76} +(-11.8623 + 4.31753i) q^{77} +(-1.14930 - 6.51800i) q^{79} +0.879385 q^{80} +7.70233 q^{82} +(0.773318 + 4.38571i) q^{83} +(5.16385 - 1.87949i) q^{85} +(-8.29086 - 6.95686i) q^{86} +(3.35844 + 1.22237i) q^{88} +(4.62449 + 8.00984i) q^{89} +(-6.52481 + 11.3013i) q^{91} +(-1.58125 + 1.32683i) q^{92} +(1.11334 - 6.31407i) q^{94} +(0.636812 - 3.61154i) q^{95} +(-8.64930 + 7.25762i) q^{97} +(-2.73783 + 4.74205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{11} - 12 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} - 6 q^{20} + 3 q^{22} + 6 q^{23} - 9 q^{25} - 18 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} + 6 q^{34}+ \cdots + 3 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 3 * q^11 - 12 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 - 6 * q^20 + 3 * q^22 + 6 * q^23 - 9 * q^25 - 18 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 + 6 * q^34 - 3 * q^35 + 15 * q^37 + 15 * q^38 + 3 * q^40 + 3 * q^41 - 18 * q^43 + 3 * q^44 - 3 * q^46 - 9 * q^47 + 21 * q^49 + 9 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 3 * q^58 + 6 * q^59 + 18 * q^61 + 12 * q^62 - 3 * q^64 - 21 * q^65 - 9 * q^67 + 15 * q^68 - 3 * q^70 - 12 * q^71 + 3 * q^73 + 3 * q^74 + 15 * q^76 - 39 * q^77 + 33 * q^79 - 6 * q^80 - 6 * q^82 + 18 * q^83 + 27 * q^85 - 18 * q^86 + 12 * q^88 + 15 * q^89 - 12 * q^91 - 12 * q^92 - 21 * q^95 - 12 * q^97 + 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.673648	+	0.565258i	0.301265	+	0.252791i	0.780870	−	0.624693i	$-0.214776\pi$
$5$	0.673648	+	0.565258i	0.301265	+	0.252791i	−0.479606	+	0.877484i	$0.659220\pi$
$6$		0			0
$7$	3.31908	+	1.20805i	1.25449	+	0.456598i	0.881918	−	0.471403i	$-0.156252\pi$
$7$	3.31908	+	1.20805i	1.25449	+	0.456598i	0.372576	+	0.928002i	$0.378475\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	−0.439693	+	0.761570i	−0.139043	+	0.240830i
$11$	−2.73783	+	2.29731i	−0.825486	+	0.692665i	−0.954250	−	0.299011i	$-0.903343\pi$
$11$	−2.73783	+	2.29731i	−0.825486	+	0.692665i	0.128764	+	0.991675i	$0.458899\pi$
$12$		0			0
$13$	−0.641559	+	3.63846i	−0.177937	+	1.00913i	0.756763	+	0.653689i	$0.226780\pi$
$13$	−0.641559	+	3.63846i	−0.177937	+	1.00913i	−0.934700	+	0.355439i	$0.884331\pi$
$14$	−0.613341	+	3.47843i	−0.163922	+	0.929649i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	3.12449	−	5.41177i	0.757799	−	1.31255i	−0.186172	−	0.982517i	$-0.559608\pi$
$17$	3.12449	−	5.41177i	0.757799	−	1.31255i	0.943971	−	0.330029i	$-0.107059\pi$
$18$		0			0
$19$	−2.08512	−	3.61154i	−0.478360	−	0.828544i	0.521332	−	0.853354i	$-0.325435\pi$
$19$	−2.08512	−	3.61154i	−0.478360	−	0.828544i	−0.999692	+	0.0248102i	$0.992102\pi$
$20$	−0.826352	−	0.300767i	−0.184778	−	0.0672537i
$21$		0			0
$22$	−2.73783	−	2.29731i	−0.583706	−	0.489788i
$23$	1.93969	−	0.705990i	0.404454	−	0.147209i	−0.131779	−	0.991279i	$-0.542069\pi$
$23$	1.93969	−	0.705990i	0.404454	−	0.147209i	0.536233	+	0.844070i	$0.319847\pi$
$24$		0			0
$25$	−0.733956	−	4.16247i	−0.146791	−	0.832494i
$26$	−3.69459			−0.724569
$27$		0			0
$28$	−3.53209			−0.667502
$29$	−0.0282185	−	0.160035i	−0.00524004	−	0.0297178i	0.982076	−	0.188487i	$-0.0603584\pi$
$29$	−0.0282185	−	0.160035i	−0.00524004	−	0.0297178i	−0.987316	+	0.158770i	$0.949247\pi$
$30$		0			0
$31$	−1.53936	+	0.560282i	−0.276478	+	0.100630i	−0.476538	−	0.879154i	$-0.658108\pi$
$31$	−1.53936	+	0.560282i	−0.276478	+	0.100630i	0.200060	+	0.979784i	$0.435886\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$		0			0
$34$	5.87211	+	2.13727i	1.00706	+	0.366539i
$35$	1.55303	+	2.68993i	0.262511	+	0.454682i
$36$		0			0
$37$	3.85844	−	6.68302i	0.634324	−	1.09868i	−0.352334	−	0.935874i	$-0.614612\pi$
$37$	3.85844	−	6.68302i	0.634324	−	1.09868i	0.986658	−	0.162807i	$-0.0520547\pi$
$38$	3.19459	−	2.68058i	0.518231	−	0.434848i
$39$		0			0
$40$	0.152704	−	0.866025i	0.0241446	−	0.136931i
$41$	1.33750	−	7.58532i	0.208882	−	1.18463i	−0.682331	−	0.731043i	$-0.739034\pi$
$41$	1.33750	−	7.58532i	0.208882	−	1.18463i	0.891213	−	0.453585i	$-0.149855\pi$
$42$		0			0
$43$	−8.29086	+	6.95686i	−1.26434	+	1.06091i	−0.269139	+	0.963101i	$0.586739\pi$
$43$	−8.29086	+	6.95686i	−1.26434	+	1.06091i	−0.995205	+	0.0978094i	$0.968816\pi$
$44$	1.78699	−	3.09516i	0.269399	−	0.466612i
$45$		0			0
$46$	1.03209	+	1.78763i	0.152173	+	0.263572i
$47$	−6.02481	−	2.19285i	−0.878810	−	0.319861i	−0.137080	−	0.990560i	$-0.543772\pi$
$47$	−6.02481	−	2.19285i	−0.878810	−	0.319861i	−0.741729	+	0.670699i	$0.765994\pi$
$48$		0			0
$49$	4.19459	+	3.51968i	0.599228	+	0.502812i
$50$	3.97178	−	1.44561i	0.561695	−	0.204440i
$51$		0			0
$52$	−0.641559	−	3.63846i	−0.0889683	−	0.504564i
$53$	−0.716881			−0.0984712			−0.0492356	−	0.998787i	$-0.515679\pi$
$53$	−0.716881			−0.0984712			−0.0492356	+	0.998787i	$0.515679\pi$
$54$		0			0
$55$	−3.14290			−0.423789
$56$	−0.613341	−	3.47843i	−0.0819611	−	0.464825i
$57$		0			0
$58$	0.152704	−	0.0555796i	0.0200510	−	0.00729796i
$59$	5.35117	+	4.49016i	0.696663	+	0.584569i	0.920822	−	0.389983i	$-0.127519\pi$
$59$	5.35117	+	4.49016i	0.696663	+	0.584569i	−0.224159	+	0.974552i	$0.571964\pi$
$60$		0			0
$61$	1.19207	+	0.433877i	0.152628	+	0.0555522i	0.417205	−	0.908813i	$-0.363010\pi$
$61$	1.19207	+	0.433877i	0.152628	+	0.0555522i	−0.264576	+	0.964365i	$0.585232\pi$
$62$	−0.819078	−	1.41868i	−0.104023	−	0.180173i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.48886	+	2.08840i	−0.308705	+	0.259034i
$66$		0			0
$67$	0.624485	−	3.54163i	0.0762930	−	0.432679i	−0.922605	−	0.385746i	$-0.873944\pi$
$67$	0.624485	−	3.54163i	0.0762930	−	0.432679i	0.998898	−	0.0469331i	$-0.0149448\pi$
$68$	−1.08512	+	6.15403i	−0.131590	+	0.746286i
$69$		0			0
$70$	−2.37939	+	1.99654i	−0.284391	+	0.238632i
$71$	−6.76991	+	11.7258i	−0.803441	+	1.39160i	0.113897	+	0.993493i	$0.463666\pi$
$71$	−6.76991	+	11.7258i	−0.803441	+	1.39160i	−0.917338	+	0.398108i	$0.869667\pi$
$72$		0			0
$73$	1.16385	+	2.01584i	0.136218	+	0.235937i	0.926062	−	0.377371i	$-0.123172\pi$
$73$	1.16385	+	2.01584i	0.136218	+	0.235937i	−0.789844	+	0.613308i	$0.789839\pi$
$74$	7.25150	+	2.63933i	0.842969	+	0.306816i
$75$		0			0
$76$	3.19459	+	2.68058i	0.366445	+	0.307484i
$77$	−11.8623	+	4.31753i	−1.35184	+	0.492028i
$78$		0			0
$79$	−1.14930	−	6.51800i	−0.129306	−	0.733333i	−0.978656	−	0.205503i	$-0.934117\pi$
$79$	−1.14930	−	6.51800i	−0.129306	−	0.733333i	0.849350	−	0.527830i	$-0.176994\pi$
$80$	0.879385			0.0983183
$81$		0			0
$82$	7.70233			0.850580
$83$	0.773318	+	4.38571i	0.0848827	+	0.481394i	0.997382	+	0.0723151i	$0.0230387\pi$
$83$	0.773318	+	4.38571i	0.0848827	+	0.481394i	−0.912499	+	0.409079i	$0.865850\pi$
$84$		0			0
$85$	5.16385	−	1.87949i	0.560098	−	0.203859i
$86$	−8.29086	−	6.95686i	−0.894026	−	0.750177i
$87$		0			0
$88$	3.35844	+	1.22237i	0.358011	+	0.130305i
$89$	4.62449	+	8.00984i	0.490194	+	0.849042i	0.999936	−	0.0112857i	$-0.00359243\pi$
$89$	4.62449	+	8.00984i	0.490194	+	0.849042i	−0.509742	+	0.860327i	$0.670259\pi$
$90$		0			0
$91$	−6.52481	+	11.3013i	−0.683986	+	1.18470i
$92$	−1.58125	+	1.32683i	−0.164857	+	0.138331i
$93$		0			0
$94$	1.11334	−	6.31407i	0.114832	−	0.651247i
$95$	0.636812	−	3.61154i	0.0653355	−	0.370536i
$96$		0			0
$97$	−8.64930	+	7.25762i	−0.878203	+	0.736900i	−0.965809	−	0.259255i	$-0.916523\pi$
$97$	−8.64930	+	7.25762i	−0.878203	+	0.736900i	0.0876055	+	0.996155i	$0.472079\pi$
$98$	−2.73783	+	4.74205i	−0.276562	+	0.479020i
$99$		0			0
$100$	2.11334	+	3.66041i	0.211334	+	0.366041i
$101$	8.80928	+	3.20631i	0.876556	+	0.319040i	0.740819	−	0.671705i	$-0.234438\pi$
$101$	8.80928	+	3.20631i	0.876556	+	0.319040i	0.135737	+	0.990745i	$0.456660\pi$
$102$		0			0
$103$	−2.47178	−	2.07407i	−0.243552	−	0.204364i	0.512838	−	0.858485i	$-0.328594\pi$
$103$	−2.47178	−	2.07407i	−0.243552	−	0.204364i	−0.756390	+	0.654121i	$0.773039\pi$
$104$	3.47178	−	1.26363i	0.340436	−	0.123909i
$105$		0			0
$106$	−0.124485	−	0.705990i	−0.0120911	−	0.0685718i
$107$	2.28312			0.220717			0.110359	−	0.993892i	$-0.464800\pi$
$107$	2.28312			0.220717			0.110359	+	0.993892i	$0.464800\pi$
$108$		0			0
$109$	10.4192			0.997980			0.498990	−	0.866608i	$-0.333704\pi$
$109$	10.4192			0.997980			0.498990	+	0.866608i	$0.333704\pi$
$110$	−0.545759	−	3.09516i	−0.0520361	−	0.295112i
$111$		0			0
$112$	3.31908	−	1.20805i	0.313623	−	0.114150i
$113$	−8.52869	−	7.15642i	−0.802311	−	0.673219i	0.146448	−	0.989218i	$-0.453216\pi$
$113$	−8.52869	−	7.15642i	−0.802311	−	0.673219i	−0.948759	+	0.315999i	$0.897660\pi$
$114$		0			0
$115$	1.70574	+	0.620838i	0.159061	+	0.0578934i
$116$	0.0812519	+	0.140732i	0.00754405	+	0.0130667i
$117$		0			0
$118$	−3.49273	+	6.04958i	−0.321531	+	0.556909i
$119$	16.9081	−	14.1876i	1.54996	−	1.30057i
$120$		0			0
$121$	0.307934	−	1.74638i	0.0279940	−	0.158762i
$122$	−0.220285	+	1.24930i	−0.0199437	+	0.113106i
$123$		0			0
$124$	1.25490	−	1.05299i	0.112693	−	0.0945610i
$125$	4.05690	−	7.02676i	0.362861	−	0.628493i
$126$		0			0
$127$	4.95336	+	8.57948i	0.439540	+	0.761305i	0.997654	−	0.0684588i	$-0.0218082\pi$
$127$	4.95336	+	8.57948i	0.439540	+	0.761305i	−0.558114	+	0.829764i	$0.688475\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$		0			0
$130$	−2.48886	−	2.08840i	−0.218287	−	0.183165i
$131$	−8.48545	+	3.08845i	−0.741377	+	0.269839i	−0.684973	−	0.728569i	$-0.740186\pi$
$131$	−8.48545	+	3.08845i	−0.741377	+	0.269839i	−0.0564046	+	0.998408i	$0.517964\pi$
$132$		0			0
$133$	−2.55778	−	14.5059i	−0.221788	−	1.25782i
$134$	3.59627			0.310670
$135$		0			0
$136$	−6.24897			−0.535845
$137$	−0.352044	−	1.99654i	−0.0300772	−	0.170576i	0.966069	−	0.258284i	$-0.0831570\pi$
$137$	−0.352044	−	1.99654i	−0.0300772	−	0.170576i	−0.996146	+	0.0877077i	$0.972046\pi$
$138$		0			0
$139$	−0.155230	+	0.0564991i	−0.0131664	+	0.00479219i	−0.348595	−	0.937273i	$-0.613341\pi$
$139$	−0.155230	+	0.0564991i	−0.0131664	+	0.00479219i	0.335429	+	0.942066i	$0.391119\pi$
$140$	−2.37939	−	1.99654i	−0.201095	−	0.168739i
$141$		0			0
$142$	−12.7233	−	4.63089i	−1.06771	−	0.388616i
$143$	−6.60220	−	11.4353i	−0.552103	−	0.956271i
$144$		0			0
$145$	0.0714517	−	0.123758i	0.00593374	−	0.0102775i
$146$	−1.78312	+	1.49621i	−0.147572	+	0.123828i
$147$		0			0
$148$	−1.34002	+	7.59964i	−0.110149	+	0.624687i
$149$	1.00727	−	5.71253i	0.0825191	−	0.467989i	−0.915345	−	0.402670i	$-0.868082\pi$
$149$	1.00727	−	5.71253i	0.0825191	−	0.467989i	0.997864	−	0.0653193i	$-0.0208066\pi$
$150$		0			0
$151$	10.7626	−	9.03093i	0.875851	−	0.734926i	−0.0894705	−	0.995989i	$-0.528517\pi$
$151$	10.7626	−	9.03093i	0.875851	−	0.734926i	0.965322	+	0.261063i	$0.0840730\pi$
$152$	−2.08512	+	3.61154i	−0.169126	+	0.292934i
$153$		0			0
$154$	−6.31180	−	10.9324i	−0.508620	−	0.880955i
$155$	−1.35369	−	0.492704i	−0.108731	−	0.0395749i
$156$		0			0
$157$	−3.65657	−	3.06823i	−0.291826	−	0.244871i	0.485106	−	0.874455i	$-0.338781\pi$
$157$	−3.65657	−	3.06823i	−0.291826	−	0.244871i	−0.776933	+	0.629584i	$0.783225\pi$
$158$	6.21941	−	2.26368i	0.494790	−	0.180089i
$159$		0			0
$160$	0.152704	+	0.866025i	0.0120723	+	0.0684653i
$161$	7.29086			0.574600
$162$		0			0
$163$	−10.7169			−0.839411			−0.419705	−	0.907660i	$-0.637867\pi$
$163$	−10.7169			−0.839411			−0.419705	+	0.907660i	$0.637867\pi$
$164$	1.33750	+	7.58532i	0.104441	+	0.592314i
$165$		0			0
$166$	−4.18479	+	1.52314i	−0.324803	+	0.118219i
$167$	9.88120	+	8.29131i	0.764630	+	0.641601i	0.939328	−	0.343021i	$-0.111450\pi$
$167$	9.88120	+	8.29131i	0.764630	+	0.641601i	−0.174698	+	0.984622i	$0.555895\pi$
$168$		0			0
$169$	−0.610815	−	0.222318i	−0.0469857	−	0.0171014i
$170$	2.74763	+	4.75903i	0.210733	+	0.365001i
$171$		0			0
$172$	5.41147	−	9.37295i	0.412621	−	0.714681i
$173$	−9.86097	+	8.27433i	−0.749715	+	0.629086i	−0.935428	−	0.353518i	$-0.884985\pi$
$173$	−9.86097	+	8.27433i	−0.749715	+	0.629086i	0.185712	+	0.982604i	$0.440541\pi$
$174$		0			0
$175$	2.59240	−	14.7022i	0.195967	−	1.11138i
$176$	−0.620615	+	3.51968i	−0.0467806	+	0.265306i
$177$		0			0
$178$	−7.08512	+	5.94512i	−0.531052	+	0.445606i
$179$	−4.48158	+	7.76233i	−0.334969	+	0.580184i	−0.983479	−	0.181023i	$-0.942059\pi$
$179$	−4.48158	+	7.76233i	−0.334969	+	0.580184i	0.648510	+	0.761206i	$0.275393\pi$
$180$		0			0
$181$	0.992726	+	1.71945i	0.0737887	+	0.127806i	0.900559	−	0.434734i	$-0.143158\pi$
$181$	0.992726	+	1.71945i	0.0737887	+	0.127806i	−0.826770	+	0.562540i	$0.809824\pi$
$182$	−12.2626	−	4.46324i	−0.908967	−	0.330837i
$183$		0			0
$184$	−1.58125	−	1.32683i	−0.116571	−	0.0978151i
$185$	6.37686	−	2.32099i	0.468836	−	0.170642i
$186$		0			0
$187$	3.87820	+	21.9944i	0.283602	+	1.60839i
$188$	6.41147			0.467605
$189$		0			0
$190$	3.66725			0.266050
$191$	−2.27853	−	12.9222i	−0.164869	−	0.935018i	−0.949200	−	0.314675i	$-0.898105\pi$
$191$	−2.27853	−	12.9222i	−0.164869	−	0.935018i	0.784331	−	0.620343i	$-0.213007\pi$
$192$		0			0
$193$	−5.40895	+	1.96870i	−0.389345	+	0.141710i	−0.529273	−	0.848452i	$-0.677535\pi$
$193$	−5.40895	+	1.96870i	−0.389345	+	0.141710i	0.139928	+	0.990162i	$0.455313\pi$
$194$	−8.64930	−	7.25762i	−0.620984	−	0.521067i
$195$		0			0
$196$	−5.14543	−	1.87278i	−0.367531	−	0.133770i
$197$	−13.3405	−	23.1064i	−0.950471	−	1.64626i	−0.744409	−	0.667724i	$-0.767269\pi$
$197$	−13.3405	−	23.1064i	−0.950471	−	1.64626i	−0.206062	−	0.978539i	$-0.566065\pi$
$198$		0			0
$199$	5.32160	−	9.21729i	0.377239	−	0.653396i	−0.613421	−	0.789756i	$-0.710207\pi$
$199$	5.32160	−	9.21729i	0.377239	−	0.653396i	0.990659	+	0.136360i	$0.0435404\pi$
$200$	−3.23783	+	2.71686i	−0.228949	+	0.192111i
$201$		0			0
$202$	−1.62789	+	9.23222i	−0.114538	+	0.649576i
$203$	0.0996702	−	0.565258i	0.00699548	−	0.0396733i
$204$		0			0
$205$	5.18866	−	4.35381i	0.362392	−	0.304083i
$206$	1.61334	−	2.79439i	0.112407	−	0.194694i
$207$		0			0
$208$	1.84730	+	3.19961i	0.128087	+	0.221853i
$209$	14.0055	+	5.09759i	0.968782	+	0.352608i
$210$		0			0
$211$	−4.09105	−	3.43280i	−0.281640	−	0.236324i	0.491014	−	0.871152i	$-0.336626\pi$
$211$	−4.09105	−	3.43280i	−0.281640	−	0.236324i	−0.772653	+	0.634828i	$0.781071\pi$
$212$	0.673648	−	0.245188i	0.0462663	−	0.0168396i
$213$		0			0
$214$	0.396459	+	2.24843i	0.0271014	+	0.153700i
$215$	−9.51754			−0.649091
$216$		0			0
$217$	−5.78611			−0.392787
$218$	1.80928	+	10.2609i	0.122540	+	0.694957i
$219$		0			0
$220$	2.95336	−	1.07494i	0.199116	−	0.0724722i
$221$	17.6860	+	14.8403i	1.18969	+	0.998266i
$222$		0			0
$223$	17.9008	+	6.51536i	1.19873	+	0.436301i	0.862779	−	0.505580i	$-0.168722\pi$
$223$	17.9008	+	6.51536i	1.19873	+	0.436301i	0.335947	+	0.941881i	$0.390944\pi$
$224$	1.76604	+	3.05888i	0.117999	+	0.204380i
$225$		0			0
$226$	5.56670	−	9.64181i	0.370292	−	0.641364i
$227$	2.65136	−	2.22475i	0.175977	−	0.147662i	−0.550545	−	0.834806i	$-0.685580\pi$
$227$	2.65136	−	2.22475i	0.175977	−	0.147662i	0.726522	+	0.687143i	$0.241136\pi$
$228$		0			0
$229$	−5.02528	+	28.4998i	−0.332080	+	1.88332i	0.122272	+	0.992497i	$0.460982\pi$
$229$	−5.02528	+	28.4998i	−0.332080	+	1.88332i	−0.454352	+	0.890822i	$0.650129\pi$
$230$	−0.315207	+	1.78763i	−0.0207842	+	0.117873i
$231$		0			0
$232$	−0.124485	+	0.104455i	−0.00817285	+	0.00685784i
$233$	−3.33022	+	5.76811i	−0.218170	+	0.377882i	−0.954249	−	0.299015i	$-0.903342\pi$
$233$	−3.33022	+	5.76811i	−0.218170	+	0.377882i	0.736078	+	0.676896i	$0.236675\pi$
$234$		0			0
$235$	−2.81908	−	4.88279i	−0.183896	−	0.318518i
$236$	−6.56418	−	2.38917i	−0.427292	−	0.155521i
$237$		0			0
$238$	16.9081	+	14.1876i	1.09599	+	0.919643i
$239$	7.31908	−	2.66393i	0.473432	−	0.172315i	−0.0942745	−	0.995546i	$-0.530053\pi$
$239$	7.31908	−	2.66393i	0.473432	−	0.172315i	0.567706	+	0.823231i	$0.307831\pi$
$240$		0			0
$241$	3.80200	+	21.5622i	0.244909	+	1.38895i	0.820705	+	0.571352i	$0.193581\pi$
$241$	3.80200	+	21.5622i	0.244909	+	1.38895i	−0.575796	+	0.817593i	$0.695308\pi$
$242$	1.77332			0.113993
$243$		0			0
$244$	−1.26857			−0.0812119
$245$	0.836152	+	4.74205i	0.0534198	+	0.302959i
$246$		0			0
$247$	14.4782	−	5.26963i	0.921224	−	0.335298i
$248$	1.25490	+	1.05299i	0.0796862	+	0.0668647i
$249$		0			0
$250$	7.62449	+	2.77509i	0.482215	+	0.175512i
$251$	8.04236	+	13.9298i	0.507629	+	0.879239i	0.999961	+	0.00883173i	$0.00281126\pi$
$251$	8.04236	+	13.9298i	0.507629	+	0.879239i	−0.492332	+	0.870407i	$0.663855\pi$
$252$		0			0
$253$	−3.68866	+	6.38895i	−0.231904	+	0.401670i
$254$	−7.58899	+	6.36792i	−0.476176	+	0.399559i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−4.49138	+	25.4719i	−0.280165	+	1.58889i	0.441898	+	0.897065i	$0.354305\pi$
$257$	−4.49138	+	25.4719i	−0.280165	+	1.58889i	−0.722063	+	0.691828i	$0.756806\pi$
$258$		0			0
$259$	20.8799	−	17.5203i	1.29741	−	1.08866i
$260$	1.62449	−	2.81369i	0.100746	−	0.174498i
$261$		0			0
$262$	−4.51501	−	7.82023i	−0.278939	−	0.483136i
$263$	−29.5967	−	10.7723i	−1.82501	−	0.664250i	−0.994180	−	0.107727i	$-0.965643\pi$
$263$	−29.5967	−	10.7723i	−1.82501	−	0.664250i	−0.830832	−	0.556523i	$-0.812135\pi$
$264$		0			0
$265$	−0.482926	−	0.405223i	−0.0296659	−	0.0248926i
$266$	13.8414	−	5.03785i	0.848669	−	0.308890i
$267$		0			0
$268$	0.624485	+	3.54163i	0.0381465	+	0.216340i
$269$	4.60906			0.281019			0.140510	−	0.990079i	$-0.455126\pi$
$269$	4.60906			0.281019			0.140510	+	0.990079i	$0.455126\pi$
$270$		0			0
$271$	−1.31820			−0.0800750			−0.0400375	−	0.999198i	$-0.512748\pi$
$271$	−1.31820			−0.0800750			−0.0400375	+	0.999198i	$0.512748\pi$
$272$	−1.08512	−	6.15403i	−0.0657952	−	0.373143i
$273$		0			0
$274$	1.90508	−	0.693392i	0.115090	−	0.0418893i
$275$	11.5719	+	9.70999i	0.697813	+	0.585535i
$276$		0			0
$277$	−28.9624	−	10.5415i	−1.74018	−	0.633375i	−0.740916	−	0.671598i	$-0.765608\pi$
$277$	−28.9624	−	10.5415i	−1.74018	−	0.633375i	−0.999269	+	0.0382227i	$0.987830\pi$
$278$	−0.0825961	−	0.143061i	−0.00495378	−	0.00858021i
$279$		0			0
$280$	1.55303	−	2.68993i	0.0928115	−	0.160754i
$281$	−16.4172	+	13.7756i	−0.979365	+	0.821785i	−0.983994	−	0.178204i	$-0.942971\pi$
$281$	−16.4172	+	13.7756i	−0.979365	+	0.821785i	0.00462815	+	0.999989i	$0.498527\pi$
$282$		0			0
$283$	−0.307934	+	1.74638i	−0.0183047	+	0.103811i	−0.992591	−	0.121501i	$-0.961229\pi$
$283$	−0.307934	+	1.74638i	−0.0183047	+	0.103811i	0.974287	+	0.225313i	$0.0723403\pi$
$284$	2.35117	−	13.3341i	0.139516	−	0.791235i
$285$		0			0
$286$	10.1152	−	8.48762i	0.598121	−	0.501884i
$287$	13.6027	−	23.5605i	0.802940	−	1.39073i
$288$		0			0
$289$	−11.0248	−	19.0955i	−0.648519	−	1.12327i
$290$	0.134285	+	0.0488759i	0.00788551	+	0.00287009i
$291$		0			0
$292$	−1.78312	−	1.49621i	−0.104349	−	0.0875593i
$293$	−29.0920	+	10.5886i	−1.69957	+	0.618594i	−0.995777	−	0.0918092i	$-0.970735\pi$
$293$	−29.0920	+	10.5886i	−1.69957	+	0.618594i	−0.703795	+	0.710403i	$0.748513\pi$
$294$		0			0
$295$	1.06670	+	6.04958i	0.0621059	+	0.352220i
$296$	−7.71688			−0.448535
$297$		0			0
$298$	5.80066			0.336023
$299$	1.32429	+	7.51044i	0.0765858	+	0.434340i
$300$		0			0
$301$	−35.9222	+	13.0746i	−2.07052	+	0.753608i
$302$	10.7626	+	9.03093i	0.619320	+	0.519672i
$303$		0			0
$304$	−3.91875	−	1.42631i	−0.224756	−	0.0818044i
$305$	0.557781	+	0.966105i	0.0319385	+	0.0553190i
$306$		0			0
$307$	−4.26857	+	7.39338i	−0.243620	+	0.421963i	−0.961743	−	0.273954i	$-0.911668\pi$
$307$	−4.26857	+	7.39338i	−0.243620	+	0.421963i	0.718123	+	0.695917i	$0.245002\pi$
$308$	9.67024	−	8.11430i	0.551013	−	0.462355i
$309$		0			0
$310$	0.250152	−	1.41868i	0.0142077	−	0.0805759i
$311$	3.12789	−	17.7391i	0.177366	−	1.00589i	−0.758011	−	0.652242i	$-0.773829\pi$
$311$	3.12789	−	17.7391i	0.177366	−	1.00589i	0.935377	−	0.353652i	$-0.115060\pi$
$312$		0			0
$313$	13.1800	−	11.0594i	0.744980	−	0.625113i	−0.189190	−	0.981941i	$-0.560586\pi$
$313$	13.1800	−	11.0594i	0.744980	−	0.625113i	0.934170	+	0.356828i	$0.116142\pi$
$314$	2.38666	−	4.13381i	0.134687	−	0.233285i
$315$		0			0
$316$	3.30928	+	5.73184i	0.186161	+	0.322441i
$317$	23.4094	+	8.52033i	1.31480	+	0.478549i	0.901790	−	0.432175i	$-0.142254\pi$
$317$	23.4094	+	8.52033i	1.31480	+	0.478549i	0.413014	+	0.910725i	$0.364476\pi$
$318$		0			0
$319$	0.444907	+	0.373321i	0.0249100	+	0.0209020i
$320$	−0.826352	+	0.300767i	−0.0461945	+	0.0168134i
$321$		0			0
$322$	1.26604	+	7.18009i	0.0705539	+	0.400131i
$323$	−26.0597			−1.45000
$324$		0			0
$325$	15.6159			0.866212
$326$	−1.86097	−	10.5541i	−0.103069	−	0.584536i
$327$		0			0
$328$	−7.23783	+	2.63435i	−0.399642	+	0.145458i
$329$	−17.3478	−	14.5565i	−0.956413	−	0.802526i
$330$		0			0
$331$	−8.32547	−	3.03022i	−0.457609	−	0.166556i	0.102922	−	0.994689i	$-0.467181\pi$
$331$	−8.32547	−	3.03022i	−0.457609	−	0.166556i	−0.560531	+	0.828133i	$0.689403\pi$
$332$	−2.22668	−	3.85673i	−0.122205	−	0.211665i
$333$		0			0
$334$	−6.44949	+	11.1708i	−0.352901	+	0.611242i
$335$	2.42262	−	2.03282i	0.132362	−	0.111065i
$336$		0			0
$337$	3.65910	−	20.7518i	0.199324	−	1.13042i	−0.706801	−	0.707412i	$-0.749862\pi$
$337$	3.65910	−	20.7518i	0.199324	−	1.13042i	0.906125	−	0.423010i	$-0.139026\pi$
$338$	0.112874	−	0.640140i	0.00613953	−	0.0348190i
$339$		0			0
$340$	−4.20961	+	3.53228i	−0.228298	+	0.191565i
$341$	2.92737	−	5.07035i	0.158526	−	0.274575i
$342$		0			0
$343$	−2.69207	−	4.66280i	−0.145358	−	0.251767i
$344$	10.1702	+	3.70167i	0.548343	+	0.199580i
$345$		0			0
$346$	−9.86097	−	8.27433i	−0.530129	−	0.444831i
$347$	20.7754	−	7.56164i	1.11528	−	0.405930i	0.282355	−	0.959310i	$-0.408884\pi$
$347$	20.7754	−	7.56164i	1.11528	−	0.405930i	0.832929	+	0.553380i	$0.186662\pi$
$348$		0			0
$349$	0.381911	+	2.16593i	0.0204433	+	0.115939i	0.993322	−	0.115377i	$-0.0368077\pi$
$349$	0.381911	+	2.16593i	0.0204433	+	0.115939i	−0.972878	+	0.231317i	$0.925697\pi$
$350$	14.9290			0.797989
$351$		0			0
$352$	−3.57398			−0.190494
$353$	−0.826352	−	4.68647i	−0.0439823	−	0.249436i	0.954887	−	0.296968i	$-0.0959755\pi$
$353$	−0.826352	−	4.68647i	−0.0439823	−	0.249436i	−0.998870	+	0.0475321i	$0.984864\pi$
$354$		0			0
$355$	−11.1887	+	4.07234i	−0.593833	+	0.216137i
$356$	−7.08512	−	5.94512i	−0.375511	−	0.315091i
$357$		0			0
$358$	−8.42262	−	3.06558i	−0.445149	−	0.162021i
$359$	−1.30288	−	2.25666i	−0.0687634	−	0.119102i	0.829594	−	0.558367i	$-0.188572\pi$
$359$	−1.30288	−	2.25666i	−0.0687634	−	0.119102i	−0.898357	+	0.439266i	$0.855239\pi$
$360$		0			0
$361$	0.804530	−	1.39349i	0.0423437	−	0.0733414i
$362$	−1.52094	+	1.27622i	−0.0799391	+	0.0670768i
$363$		0			0
$364$	2.26604	−	12.8514i	0.118773	−	0.673595i
$365$	−0.355448	+	2.01584i	−0.0186050	+	0.105514i
$366$		0			0
$367$	−10.9042	+	9.14971i	−0.569195	+	0.477611i	−0.881379	−	0.472411i	$-0.843384\pi$
$367$	−10.9042	+	9.14971i	−0.569195	+	0.477611i	0.312184	+	0.950022i	$0.398939\pi$
$368$	1.03209	−	1.78763i	0.0538014	−	0.0931867i
$369$		0			0
$370$	3.39306	+	5.87695i	0.176397	+	0.305528i
$371$	−2.37939	−	0.866025i	−0.123532	−	0.0449618i
$372$		0			0
$373$	−1.76810	−	1.48362i	−0.0915489	−	0.0768187i	0.595865	−	0.803085i	$-0.296810\pi$
$373$	−1.76810	−	1.48362i	−0.0915489	−	0.0768187i	−0.687413	+	0.726266i	$0.741254\pi$
$374$	−20.9868	+	7.63857i	−1.08520	+	0.394981i
$375$		0			0
$376$	1.11334	+	6.31407i	0.0574162	+	0.325623i
$377$	0.600385			0.0309214
$378$		0			0
$379$	−6.02734			−0.309604			−0.154802	−	0.987946i	$-0.549474\pi$
$379$	−6.02734			−0.309604			−0.154802	+	0.987946i	$0.549474\pi$
$380$	0.636812	+	3.61154i	0.0326677	+	0.185268i
$381$		0			0
$382$	12.3302	−	4.48783i	0.630869	−	0.229618i
$383$	−16.3007	−	13.6779i	−0.832925	−	0.698907i	0.123036	−	0.992402i	$-0.460737\pi$
$383$	−16.3007	−	13.6779i	−0.832925	−	0.698907i	−0.955960	+	0.293495i	$0.905181\pi$
$384$		0			0
$385$	−10.4315	−	3.79677i	−0.531641	−	0.193501i
$386$	−2.87804	−	4.98491i	−0.146488	−	0.253725i
$387$		0			0
$388$	5.64543	−	9.77817i	0.286603	−	0.496411i
$389$	15.8248	−	13.2785i	0.802347	−	0.673249i	−0.146421	−	0.989222i	$-0.546775\pi$
$389$	15.8248	−	13.2785i	0.802347	−	0.673249i	0.948768	+	0.315973i	$0.102331\pi$
$390$		0			0
$391$	2.23989	−	12.7030i	0.113276	−	0.642419i
$392$	0.950837	−	5.39246i	0.0480245	−	0.272361i
$393$		0			0
$394$	20.4388	−	17.1502i	1.02969	−	0.864015i
$395$	2.91013	−	5.04049i	0.146425	−	0.253615i
$396$		0			0
$397$	12.2638	+	21.2416i	0.615504	+	1.06608i	0.990296	+	0.138975i	$0.0443807\pi$
$397$	12.2638	+	21.2416i	0.615504	+	1.06608i	−0.374792	+	0.927109i	$0.622286\pi$
$398$	10.0013	+	3.64019i	0.501322	+	0.182466i
$399$		0			0
$400$	−3.23783	−	2.71686i	−0.161891	−	0.135843i
$401$	13.7433	−	5.00217i	0.686310	−	0.249796i	0.0247555	−	0.999694i	$-0.492119\pi$
$401$	13.7433	−	5.00217i	0.686310	−	0.249796i	0.661554	+	0.749897i	$0.269897\pi$
$402$		0			0
$403$	−1.05097	−	5.96037i	−0.0523527	−	0.296907i
$404$	−9.37464			−0.466406
$405$		0			0
$406$	0.573978			0.0284860
$407$	4.78921	+	27.1610i	0.237392	+	1.34632i
$408$		0			0
$409$	33.9479	−	12.3560i	1.67862	−	0.610966i	0.685497	−	0.728076i	$-0.259585\pi$
$409$	33.9479	−	12.3560i	1.67862	−	0.610966i	0.993119	+	0.117110i	$0.0373629\pi$
$410$	5.18866	+	4.35381i	0.256250	+	0.215019i
$411$		0			0
$412$	3.03209	+	1.10359i	0.149380	+	0.0543700i
$413$	12.3366	+	21.3677i	0.607045	+	1.05143i
$414$		0			0
$415$	−1.95811	+	3.39155i	−0.0961199	+	0.166485i
$416$	−2.83022	+	2.37484i	−0.138763	+	0.116436i
$417$		0			0
$418$	−2.58812	+	14.6779i	−0.126589	+	0.717921i
$419$	−3.42309	+	19.4133i	−0.167229	+	0.948401i	0.779508	+	0.626392i	$0.215469\pi$
$419$	−3.42309	+	19.4133i	−0.167229	+	0.948401i	−0.946737	+	0.322009i	$0.895642\pi$
$420$		0			0
$421$	2.63041	−	2.20718i	0.128199	−	0.107571i	−0.576434	−	0.817144i	$-0.695556\pi$
$421$	2.63041	−	2.20718i	0.128199	−	0.107571i	0.704633	+	0.709572i	$0.251112\pi$
$422$	2.67024	−	4.62500i	0.129985	−	0.225141i
$423$		0			0
$424$	0.358441	+	0.620838i	0.0174074	+	0.0301505i
$425$	−24.8195	−	9.03358i	−1.20392	−	0.438193i
$426$		0			0
$427$	3.43242	+	2.88014i	0.166106	+	0.139380i
$428$	−2.14543	+	0.780873i	−0.103703	+	0.0377449i
$429$		0			0
$430$	−1.65270	−	9.37295i	−0.0797004	−	0.452004i
$431$	28.7151			1.38316			0.691579	−	0.722300i	$-0.256915\pi$
$431$	28.7151			1.38316			0.691579	+	0.722300i	$0.256915\pi$
$432$		0			0
$433$	−14.1179			−0.678464			−0.339232	−	0.940703i	$-0.610167\pi$
$433$	−14.1179			−0.678464			−0.339232	+	0.940703i	$0.610167\pi$
$434$	−1.00475	−	5.69821i	−0.0482294	−	0.273523i
$435$		0			0
$436$	−9.79086	+	3.56358i	−0.468897	+	0.170665i
$437$	−6.59421	−	5.53320i	−0.315444	−	0.264689i
$438$		0			0
$439$	−14.5842	−	5.30823i	−0.696068	−	0.253348i	−0.0303369	−	0.999540i	$-0.509658\pi$
$439$	−14.5842	−	5.30823i	−0.696068	−	0.253348i	−0.665731	+	0.746192i	$0.731880\pi$
$440$	1.57145	+	2.72183i	0.0749160	+	0.129758i
$441$		0			0
$442$	−11.5437	+	19.9943i	−0.549078	+	0.951031i
$443$	27.3897	−	22.9826i	1.30132	−	1.09194i	0.311407	−	0.950277i	$-0.399200\pi$
$443$	27.3897	−	22.9826i	1.30132	−	1.09194i	0.989915	−	0.141662i	$-0.0452445\pi$
$444$		0			0
$445$	−1.41235	+	8.00984i	−0.0669519	+	0.379703i
$446$	−3.30793	+	18.7602i	−0.156635	+	0.888322i
$447$		0			0
$448$	−2.70574	+	2.27038i	−0.127834	+	0.107266i
$449$	−12.8564	+	22.2679i	−0.606730	+	1.05089i	0.385045	+	0.922898i	$0.374186\pi$
$449$	−12.8564	+	22.2679i	−0.606730	+	1.05089i	−0.991775	+	0.127990i	$0.959148\pi$
$450$		0			0
$451$	13.7640	+	23.8399i	0.648121	+	1.12258i
$452$	10.4620	+	3.80785i	0.492090	+	0.179106i
$453$		0			0
$454$	2.65136	+	2.22475i	0.124434	+	0.104413i
$455$	−10.7836	+	3.92490i	−0.505542	+	0.184002i
$456$		0			0
$457$	0.352921	+	2.00152i	0.0165090	+	0.0936270i	0.991949	−	0.126638i	$-0.0404188\pi$
$457$	0.352921	+	2.00152i	0.0165090	+	0.0936270i	−0.975440	+	0.220265i	$0.929308\pi$
$458$	−28.9394			−1.35225
$459$		0			0
$460$	−1.81521			−0.0846345
$461$	−3.74628	−	21.2462i	−0.174482	−	0.989535i	−0.938740	−	0.344625i	$-0.888006\pi$
$461$	−3.74628	−	21.2462i	−0.174482	−	0.989535i	0.764259	−	0.644910i	$-0.223105\pi$
$462$		0			0
$463$	20.2986	−	7.38809i	0.943356	−	0.343353i	0.175866	−	0.984414i	$-0.443728\pi$
$463$	20.2986	−	7.38809i	0.943356	−	0.343353i	0.767490	+	0.641061i	$0.221505\pi$
$464$	−0.124485	−	0.104455i	−0.00577908	−	0.00484922i
$465$		0			0
$466$	−6.25877	−	2.27801i	−0.289932	−	0.105527i
$467$	12.2622	+	21.2387i	0.567426	+	0.982810i	0.996819	+	0.0796928i	$0.0253939\pi$
$467$	12.2622	+	21.2387i	0.567426	+	0.982810i	−0.429394	+	0.903117i	$0.641273\pi$
$468$		0			0
$469$	6.35117	−	11.0005i	0.293270	−	0.507958i
$470$	4.31908	−	3.62414i	0.199224	−	0.167169i
$471$		0			0
$472$	1.21301	−	6.87933i	0.0558334	−	0.316647i
$473$	6.71688	−	38.0933i	0.308843	−	1.75153i
$474$		0			0
$475$	−13.5025	+	11.3300i	−0.619538	+	0.519854i
$476$	−11.0360	+	19.1148i	−0.505832	+	0.876127i
$477$		0			0
$478$	3.89440	+	6.74530i	0.178126	+	0.308523i
$479$	13.4620	+	4.89976i	0.615094	+	0.223876i	0.630730	−	0.776002i	$-0.282755\pi$
$479$	13.4620	+	4.89976i	0.615094	+	0.223876i	−0.0156369	+	0.999878i	$0.504978\pi$
$480$		0			0
$481$	21.8405	+	18.3263i	0.995841	+	0.835609i
$482$	−20.5744	+	7.48849i	−0.937140	+	0.341091i
$483$		0			0
$484$	0.307934	+	1.74638i	0.0139970	+	0.0793808i
$485$	−9.92902			−0.450853
$486$		0			0
$487$	32.3114			1.46417			0.732084	−	0.681214i	$-0.238548\pi$
$487$	32.3114			1.46417			0.732084	+	0.681214i	$0.238548\pi$
$488$	−0.220285	−	1.24930i	−0.00997183	−	0.0565531i
$489$		0			0
$490$	−4.52481	+	1.64690i	−0.204410	+	0.0743993i
$491$	−24.8576	−	20.8580i	−1.12181	−	0.941307i	−0.123112	−	0.992393i	$-0.539287\pi$
$491$	−24.8576	−	20.8580i	−1.12181	−	0.941307i	−0.998694	+	0.0510857i	$0.983732\pi$
$492$		0			0
$493$	−0.954241	−	0.347315i	−0.0429768	−	0.0156423i
$494$	7.70368	+	13.3432i	0.346605	+	0.600337i
$495$		0			0
$496$	−0.819078	+	1.41868i	−0.0367777	+	0.0637008i
$497$	−36.6352	+	30.7406i	−1.64331	+	1.37890i
$498$		0			0
$499$	−4.31180	+	24.4535i	−0.193023	+	1.09469i	0.722184	+	0.691702i	$0.243139\pi$
$499$	−4.31180	+	24.4535i	−0.193023	+	1.09469i	−0.915206	+	0.402985i	$0.867973\pi$
$500$	−1.40895	+	7.99054i	−0.0630101	+	0.357348i
$501$		0			0
$502$	−12.3216	+	10.3391i	−0.549940	+	0.461455i
$503$	−7.46198	+	12.9245i	−0.332713	+	0.576276i	−0.983043	−	0.183376i	$-0.941297\pi$
$503$	−7.46198	+	12.9245i	−0.332713	+	0.576276i	0.650330	+	0.759652i	$0.274631\pi$
$504$		0			0
$505$	4.12196	+	7.13944i	0.183425	+	0.317701i
$506$	−6.93242	−	2.52319i	−0.308184	−	0.112170i
$507$		0			0
$508$	−7.58899	−	6.36792i	−0.336707	−	0.282531i
$509$	14.4595	−	5.26281i	0.640904	−	0.233270i	−0.00106632	−	0.999999i	$-0.500339\pi$
$509$	14.4595	−	5.26281i	0.640904	−	0.233270i	0.641970	+	0.766729i	$0.278117\pi$
$510$		0			0
$511$	1.42767	+	8.09672i	0.0631564	+	0.358178i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−25.8648			−1.14085
$515$	−0.492726	−	2.79439i	−0.0217121	−	0.123135i
$516$		0			0
$517$	21.5326	−	7.83721i	0.947001	−	0.344680i
$518$	20.8799	+	17.5203i	0.917408	+	0.769797i
$519$		0			0
$520$	3.05303	+	1.11121i	0.133884	+	0.0487299i
$521$	6.69207	+	11.5910i	0.293185	+	0.507811i	0.974561	−	0.224122i	$-0.0719516\pi$
$521$	6.69207	+	11.5910i	0.293185	+	0.507811i	−0.681376	+	0.731933i	$0.738618\pi$
$522$		0			0
$523$	12.4402	−	21.5470i	0.543970	−	0.942184i	−0.454701	−	0.890644i	$-0.650254\pi$
$523$	12.4402	−	21.5470i	0.543970	−	0.942184i	0.998671	−	0.0515397i	$-0.0164129\pi$
$524$	6.91740	−	5.80439i	0.302188	−	0.253566i
$525$		0			0
$526$	5.46926	−	31.0177i	0.238471	−	1.35244i
$527$	−1.77760	+	10.0813i	−0.0774334	+	0.439147i
$528$		0			0
$529$	−14.3550	+	12.0453i	−0.624132	+	0.523709i
$530$	0.315207	−	0.545955i	0.0136917	−	0.0237148i
$531$		0			0
$532$	7.36484	+	12.7563i	0.319306	+	0.553055i
$533$	26.7408	+	9.73286i	1.15827	+	0.421577i
$534$		0			0
$535$	1.53802	+	1.29055i	0.0664943	+	0.0557954i
$536$	−3.37939	+	1.23000i	−0.145967	+	0.0531277i
$537$		0			0
$538$	0.800355	+	4.53904i	0.0345057	+	0.195692i
$539$	−19.5699			−0.842934
$540$		0			0
$541$	−9.09421			−0.390991			−0.195495	−	0.980705i	$-0.562631\pi$
$541$	−9.09421			−0.390991			−0.195495	+	0.980705i	$0.562631\pi$
$542$	−0.228903	−	1.29817i	−0.00983223	−	0.0557614i
$543$		0			0
$544$	5.87211	−	2.13727i	0.251765	−	0.0916349i
$545$	7.01889	+	5.88954i	0.300656	+	0.252280i
$546$		0			0
$547$	−20.8701	−	7.59608i	−0.892339	−	0.324785i	−0.145160	−	0.989408i	$-0.546370\pi$
$547$	−20.8701	−	7.59608i	−0.892339	−	0.324785i	−0.747179	+	0.664623i	$0.768592\pi$
$548$	1.01367	+	1.75573i	0.0433019	+	0.0750010i
$549$		0			0
$550$	−7.55303	+	13.0822i	−0.322062	+	0.557828i
$551$	−0.519134	+	0.435605i	−0.0221158	+	0.0185574i
$552$		0			0
$553$	4.05943	−	23.0222i	0.172625	−	0.979002i
$554$	5.35204	−	30.3530i	0.227387	−	1.28957i
$555$		0			0
$556$	0.126545	−	0.106183i	0.00536668	−	0.00450318i
$557$	−1.35369	+	2.34466i	−0.0573578	+	0.0993466i	−0.893279	−	0.449504i	$-0.851601\pi$
$557$	−1.35369	+	2.34466i	−0.0573578	+	0.0993466i	0.835921	+	0.548850i	$0.184934\pi$
$558$		0			0
$559$	−19.9932	−	34.6292i	−0.845622	−	1.46466i
$560$	2.91875	+	1.06234i	0.123340	+	0.0448919i
$561$		0			0
$562$	−16.4172	−	13.7756i	−0.692516	−	0.581090i
$563$	6.60859	−	2.40533i	0.278519	−	0.101373i	−0.198984	−	0.980003i	$-0.563764\pi$
$563$	6.60859	−	2.40533i	0.278519	−	0.101373i	0.477503	+	0.878630i	$0.341542\pi$
$564$		0			0
$565$	−1.70011	−	9.64181i	−0.0715242	−	0.405634i
$566$	−1.77332			−0.0745381
$567$		0			0
$568$	13.5398			0.568119
$569$	−4.34507	−	24.6421i	−0.182155	−	1.03305i	−0.929556	−	0.368680i	$-0.879810\pi$
$569$	−4.34507	−	24.6421i	−0.182155	−	1.03305i	0.747401	−	0.664373i	$-0.231301\pi$
$570$		0			0
$571$	−6.43242	+	2.34121i	−0.269188	+	0.0979765i	−0.473088	−	0.881015i	$-0.656861\pi$
$571$	−6.43242	+	2.34121i	−0.269188	+	0.0979765i	0.203899	+	0.978992i	$0.434638\pi$
$572$	10.1152	+	8.48762i	0.422936	+	0.354885i
$573$		0			0
$574$	25.5646	+	9.30477i	1.06705	+	0.388374i
$575$	−4.36231	−	7.55574i	−0.181921	−	0.315096i
$576$		0			0
$577$	−2.10014	+	3.63754i	−0.0874298	+	0.151433i	−0.906424	−	0.422369i	$-0.861199\pi$
$577$	−2.10014	+	3.63754i	−0.0874298	+	0.151433i	0.818994	+	0.573802i	$0.194532\pi$
$578$	16.8910	−	14.1732i	0.702573	−	0.589529i
$579$		0			0
$580$	−0.0248149	+	0.140732i	−0.00103038	+	0.00584360i
$581$	−2.73143	+	15.4907i	−0.113319	+	0.642663i
$582$		0			0
$583$	1.96270	−	1.64690i	0.0812866	−	0.0682075i
$584$	1.16385	−	2.01584i	0.0481604	−	0.0834162i
$585$		0			0
$586$	−15.4795	−	26.8113i	−0.639453	−	1.10757i
$587$	−34.3491	−	12.5021i	−1.41774	−	0.516015i	−0.484348	−	0.874875i	$-0.660943\pi$
$587$	−34.3491	−	12.5021i	−1.41774	−	0.516015i	−0.933391	+	0.358860i	$0.883165\pi$
$588$		0			0
$589$	5.23324	+	4.39121i	0.215632	+	0.180937i
$590$	−5.77244	+	2.10100i	−0.237648	+	0.0864967i
$591$		0			0
$592$	−1.34002	−	7.59964i	−0.0550746	−	0.312343i
$593$	45.0660			1.85064			0.925320	−	0.379186i	$-0.123796\pi$
$593$	45.0660			1.85064			0.925320	+	0.379186i	$0.123796\pi$
$594$		0			0
$595$	19.4097			0.795721
$596$	1.00727	+	5.71253i	0.0412595	+	0.233995i
$597$		0			0
$598$	−7.16637	+	2.60835i	−0.293055	+	0.106663i
$599$	−12.4531	−	10.4494i	−0.508820	−	0.426951i	0.351893	−	0.936040i	$-0.385538\pi$
$599$	−12.4531	−	10.4494i	−0.508820	−	0.426951i	−0.860714	+	0.509089i	$0.829982\pi$
$600$		0			0
$601$	39.0057	+	14.1969i	1.59107	+	0.579104i	0.977574	−	0.210590i	$-0.0675386\pi$
$601$	39.0057	+	14.1969i	1.59107	+	0.579104i	0.613501	+	0.789694i	$0.289761\pi$
$602$	−19.1138	−	33.1061i	−0.779021	−	1.34930i
$603$		0			0
$604$	−7.02481	+	12.1673i	−0.285836	+	0.495082i
$605$	1.19459	−	1.00238i	0.0485671	−	0.0407526i
$606$		0			0
$607$	−7.34565	+	41.6592i	−0.298151	+	1.69090i	0.355963	+	0.934500i	$0.384153\pi$
$607$	−7.34565	+	41.6592i	−0.298151	+	1.69090i	−0.654114	+	0.756396i	$0.726958\pi$
$608$	0.724155	−	4.10689i	0.0293684	−	0.166556i
$609$		0			0
$610$	−0.854570	+	0.717070i	−0.0346005	+	0.0290333i
$611$	11.8439	−	20.5142i	0.479153	−	0.829917i
$612$		0			0
$613$	−9.50686	−	16.4664i	−0.383979	−	0.665070i	0.607648	−	0.794206i	$-0.292113\pi$
$613$	−9.50686	−	16.4664i	−0.383979	−	0.665070i	−0.991627	+	0.129136i	$0.958780\pi$
$614$	−8.02229	−	2.91987i	−0.323753	−	0.117837i
$615$		0			0
$616$	9.67024	+	8.11430i	0.389625	+	0.326934i
$617$	34.7550	−	12.6498i	1.39918	−	0.509261i	0.471246	−	0.882002i	$-0.343804\pi$
$617$	34.7550	−	12.6498i	1.39918	−	0.509261i	0.927935	+	0.372741i	$0.121582\pi$
$618$		0			0
$619$	−5.29648	−	30.0379i	−0.212884	−	1.20732i	−0.884541	−	0.466462i	$-0.845529\pi$
$619$	−5.29648	−	30.0379i	−0.212884	−	1.20732i	0.671658	−	0.740862i	$-0.265583\pi$
$620$	1.44057			0.0578547
$621$		0			0
$622$	18.0128			0.722247
$623$	5.67277	+	32.1719i	0.227275	+	1.28894i
$624$		0			0
$625$	−13.1540	+	4.78768i	−0.526162	+	0.191507i
$626$	13.1800	+	11.0594i	0.526781	+	0.442021i
$627$		0			0
$628$	4.48545	+	1.63257i	0.178989	+	0.0651467i
$629$	−24.1113	−	41.7620i	−0.961380	−	1.66516i
$630$		0			0
$631$	−6.86349	+	11.8879i	−0.273231	+	0.473251i	−0.969687	−	0.244349i	$-0.921426\pi$
$631$	−6.86349	+	11.8879i	−0.273231	+	0.473251i	0.696456	+	0.717599i	$0.254759\pi$
$632$	−5.07011	+	4.25433i	−0.201678	+	0.169228i
$633$		0			0
$634$	−4.32588	+	24.5333i	−0.171803	+	0.974342i
$635$	−1.51279	+	8.57948i	−0.0600334	+	0.340466i
$636$		0			0
$637$	−15.4973	+	13.0038i	−0.614026	+	0.515229i
$638$	−0.290393	+	0.502975i	−0.0114968	+	0.0199130i
$639$		0			0
$640$	−0.439693	−	0.761570i	−0.0173804	−	0.0301037i
$641$	4.01367	+	1.46086i	0.158530	+	0.0577004i	0.420066	−	0.907493i	$-0.362007\pi$
$641$	4.01367	+	1.46086i	0.158530	+	0.0577004i	−0.261536	+	0.965194i	$0.584229\pi$
$642$		0			0
$643$	−16.1511	−	13.5524i	−0.636938	−	0.534454i	0.266138	−	0.963935i	$-0.414252\pi$
$643$	−16.1511	−	13.5524i	−0.636938	−	0.534454i	−0.903076	+	0.429481i	$0.858697\pi$
$644$	−6.85117	+	2.49362i	−0.269974	+	0.0982624i
$645$		0			0
$646$	−4.52523	−	25.6638i	−0.178043	−	1.00973i
$647$	27.4023			1.07730			0.538648	−	0.842531i	$-0.318935\pi$
$647$	27.4023			1.07730			0.538648	+	0.842531i	$0.318935\pi$
$648$		0			0
$649$	−24.9659			−0.979995
$650$	2.71167	+	15.3786i	0.106360	+	0.603199i
$651$		0			0
$652$	10.0706	−	3.66539i	0.394394	−	0.143548i
$653$	−3.61540	−	3.03368i	−0.141482	−	0.118717i	0.569300	−	0.822130i	$-0.307214\pi$
$653$	−3.61540	−	3.03368i	−0.141482	−	0.118717i	−0.710782	+	0.703413i	$0.751659\pi$
$654$		0			0
$655$	−7.46198	−	2.71594i	−0.291564	−	0.106121i
$656$	−3.85117	−	6.67042i	−0.150363	−	0.260436i
$657$		0			0
$658$	11.3229	−	19.6119i	0.441414	−	0.764552i
$659$	−16.1099	+	13.5178i	−0.627554	+	0.526580i	−0.900168	−	0.435543i	$-0.856556\pi$
$659$	−16.1099	+	13.5178i	−0.627554	+	0.526580i	0.272614	+	0.962124i	$0.412112\pi$
$660$		0			0
$661$	4.40184	−	24.9641i	0.171212	−	0.970989i	−0.771215	−	0.636575i	$-0.780351\pi$
$661$	4.40184	−	24.9641i	0.171212	−	0.970989i	0.942426	−	0.334414i	$-0.108538\pi$
$662$	1.53849	−	8.72518i	0.0597949	−	0.339114i
$663$		0			0
$664$	3.41147	−	2.86257i	0.132391	−	0.111089i
$665$	6.47653	−	11.2177i	0.251149	−	0.435003i
$666$		0			0
$667$	−0.167718	−	0.290497i	−0.00649408	−	0.0112481i
$668$	−12.1211	−	4.41171i	−0.468979	−	0.170694i
$669$		0			0
$670$	2.42262	+	2.03282i	0.0935939	+	0.0785346i
$671$	−4.26042	+	1.55067i	−0.164472	+	0.0598628i
$672$		0			0
$673$	2.47090	+	14.0132i	0.0952464	+	0.540169i	0.994672	+	0.103094i	$0.0328743\pi$
$673$	2.47090	+	14.0132i	0.0952464	+	0.540169i	−0.899425	+	0.437075i	$0.856015\pi$
$674$	21.0719			0.811660
$675$		0			0
$676$	0.650015			0.0250006
$677$	−8.07878	−	45.8170i	−0.310493	−	1.76089i	−0.596450	−	0.802650i	$-0.703423\pi$
$677$	−8.07878	−	45.8170i	−0.310493	−	1.76089i	0.285958	−	0.958242i	$-0.407688\pi$
$678$		0			0
$679$	−37.4752	+	13.6399i	−1.43817	+	0.523450i
$680$	−4.20961	−	3.53228i	−0.161431	−	0.135457i
$681$		0			0
$682$	5.50165	+	2.00244i	0.210669	+	0.0766773i
$683$	−5.10101	−	8.83522i	−0.195185	−	0.338070i	0.751776	−	0.659418i	$-0.229197\pi$
$683$	−5.10101	−	8.83522i	−0.195185	−	0.338070i	−0.946961	+	0.321348i	$0.895864\pi$
$684$		0			0
$685$	0.891407	−	1.54396i	0.0340589	−	0.0589918i
$686$	4.12449	−	3.46085i	0.157474	−	0.132136i
$687$		0			0
$688$	−1.87939	+	10.6585i	−0.0716509	+	0.406352i
$689$	0.459922	−	2.60835i	0.0175216	−	0.0993701i
$690$		0			0
$691$	−0.269915	+	0.226485i	−0.0102680	+	0.00861591i	−0.647907	−	0.761719i	$-0.724356\pi$
$691$	−0.269915	+	0.226485i	−0.0102680	+	0.00861591i	0.637639	+	0.770335i	$0.279911\pi$
$692$	6.43629	−	11.1480i	0.244671	−	0.423783i
$693$		0			0
$694$	11.0544	+	19.1467i	0.419618	+	0.726800i
$695$	−0.136507	−	0.0496844i	−0.00517800	−	0.00188464i
$696$		0			0
$697$	−36.8710	−	30.9384i	−1.39659	−	1.17188i
$698$	−2.06670	+	0.752219i	−0.0782259	+	0.0284719i
$699$		0			0
$700$	2.59240	+	14.7022i	0.0979834	+	0.555691i
$701$	−39.9358			−1.50836			−0.754178	−	0.656671i	$-0.771964\pi$
$701$	−39.9358			−1.50836			−0.754178	+	0.656671i	$0.771964\pi$
$702$		0			0
$703$	−32.1813			−1.21374
$704$	−0.620615	−	3.51968i	−0.0233903	−	0.132653i
$705$		0			0
$706$	4.47178	−	1.62760i	0.168298	−	0.0612554i
$707$	25.3653	+	21.2840i	0.953960	+	0.800468i
$708$		0			0
$709$	46.2789	+	16.8441i	1.73804	+	0.632595i	0.999150	−	0.0412304i	$-0.0131278\pi$
$709$	46.2789	+	16.8441i	1.73804	+	0.632595i	0.738891	+	0.673825i	$0.235350\pi$
$710$	−5.95336	−	10.3115i	−0.223426	−	0.386985i
$711$		0			0
$712$	4.62449	−	8.00984i	0.173310	−	0.300182i
$713$	−2.59034	+	2.17355i	−0.0970089	+	0.0814001i
$714$		0			0
$715$	2.01636	−	11.4353i	0.0754075	−	0.427657i
$716$	1.55644	−	8.82699i	0.0581668	−	0.329880i
$717$		0			0
$718$	1.99613	−	1.67495i	0.0744949	−	0.0625086i
$719$	−25.8050	+	44.6956i	−0.962364	+	1.66686i	−0.245828	+	0.969314i	$0.579060\pi$
$719$	−25.8050	+	44.6956i	−0.962364	+	1.66686i	−0.716536	+	0.697550i	$0.754274\pi$
$720$		0			0
$721$	−5.69846	−	9.87003i	−0.212222	−	0.367579i
$722$	1.51202	+	0.550331i	0.0562716	+	0.0204812i
$723$		0			0
$724$	−1.52094	−	1.27622i	−0.0565255	−	0.0474305i
$725$	−0.645430	+	0.234917i	−0.0239707	+	0.00872461i
$726$		0			0
$727$	−4.79932	−	27.2183i	−0.177997	−	1.00947i	−0.934628	−	0.355628i	$-0.884267\pi$
$727$	−4.79932	−	27.2183i	−0.177997	−	1.00947i	0.756631	−	0.653842i	$-0.226844\pi$
$728$	13.0496			0.483651
$729$		0			0
$730$	−2.04694			−0.0757607
$731$	11.7442	+	66.6048i	0.434376	+	2.46347i
$732$		0			0
$733$	−25.9072	+	9.42945i	−0.956904	+	0.348285i	−0.772820	−	0.634626i	$-0.781154\pi$
$733$	−25.9072	+	9.42945i	−0.956904	+	0.348285i	−0.184084	+	0.982910i	$0.558932\pi$
$734$	−10.9042	−	9.14971i	−0.402481	−	0.337722i
$735$		0			0
$736$	1.93969	+	0.705990i	0.0714980	+	0.0260232i
$737$	6.42649	+	11.1310i	0.236723	+	0.410016i
$738$		0			0
$739$	2.01320	−	3.48697i	0.0740569	−	0.128270i	−0.826619	−	0.562762i	$-0.809739\pi$
$739$	2.01320	−	3.48697i	0.0740569	−	0.128270i	0.900676	+	0.434492i	$0.143072\pi$
$740$	−5.19846	+	4.36203i	−0.191099	+	0.160351i
$741$		0			0
$742$	0.439693	−	2.49362i	0.0161416	−	0.0915437i
$743$	−5.04979	+	28.6388i	−0.185259	+	1.05066i	0.740363	+	0.672207i	$0.234653\pi$
$743$	−5.04979	+	28.6388i	−0.185259	+	1.05066i	−0.925622	+	0.378449i	$0.876458\pi$
$744$		0			0
$745$	3.90760	−	3.27887i	0.143164	−	0.120128i
$746$	1.15405	−	1.99887i	0.0422527	−	0.0731838i
$747$		0			0
$748$	−11.1668	−	19.3415i	−0.408300	−	0.707197i
$749$	7.57785	+	2.75811i	0.276889	+	0.100779i
$750$		0			0
$751$	31.1962	+	26.1768i	1.13837	+	0.955203i	0.999384	−	0.0350914i	$-0.0111722\pi$
$751$	31.1962	+	26.1768i	1.13837	+	0.955203i	0.138983	+	0.990295i	$0.455617\pi$
$752$	−6.02481	+	2.19285i	−0.219702	+	0.0799651i
$753$		0			0
$754$	0.104256	+	0.591264i	0.00379677	+	0.0215326i
$755$	12.3550			0.449646
$756$		0			0
$757$	32.9486			1.19754			0.598769	−	0.800922i	$-0.295657\pi$
$757$	32.9486			1.19754			0.598769	+	0.800922i	$0.295657\pi$
$758$	−1.04664	−	5.93577i	−0.0380156	−	0.215597i
$759$		0			0
$760$	−3.44609	+	1.25427i	−0.125003	+	0.0454973i
$761$	0.773318	+	0.648891i	0.0280328	+	0.0235223i	0.656696	−	0.754155i	$-0.271953\pi$
$761$	0.773318	+	0.648891i	0.0280328	+	0.0235223i	−0.628664	+	0.777677i	$0.716398\pi$
$762$		0			0
$763$	34.5822	+	12.5869i	1.25196	+	0.455676i
$764$	6.56077	+	11.3636i	0.237360	+	0.411120i
$765$		0			0
$766$	10.6395	−	18.4282i	0.384421	−	0.665836i
$767$	−19.7704	+	16.5893i	−0.713867	+	0.599006i
$768$		0			0
$769$	−5.38831	+	30.5586i	−0.194307	+	1.10197i	0.719094	+	0.694912i	$0.244557\pi$
$769$	−5.38831	+	30.5586i	−0.194307	+	1.10197i	−0.913402	+	0.407059i	$0.866554\pi$
$770$	1.92767	−	10.9324i	0.0694684	−	0.393975i
$771$		0			0
$772$	4.40941	−	3.69994i	0.158698	−	0.133164i
$773$	8.32295	−	14.4158i	0.299356	−	0.518499i	−0.676633	−	0.736320i	$-0.736562\pi$
$773$	8.32295	−	14.4158i	0.299356	−	0.518499i	0.975989	+	0.217821i	$0.0698950\pi$
$774$		0			0
$775$	3.46198	+	5.99633i	0.124358	+	0.215394i
$776$	10.6099	+	3.86170i	0.380875	+	0.138627i
$777$		0			0
$778$	15.8248	+	13.2785i	0.567345	+	0.476059i
$779$	−30.1835	+	10.9859i	−1.08144	+	0.393611i
$780$		0			0
$781$	−8.40302	−	47.6559i	−0.300684	−	1.70526i
$782$	12.8990			0.461267
$783$		0			0
$784$	5.47565			0.195559
$785$	−0.728903	−	4.13381i	−0.0260157	−	0.147542i
$786$		0			0
$787$	1.93494	−	0.704262i	0.0689733	−	0.0251042i	−0.307303	−	0.951612i	$-0.599427\pi$
$787$	1.93494	−	0.704262i	0.0689733	−	0.0251042i	0.376276	+	0.926507i	$0.377204\pi$
$788$	20.4388	+	17.1502i	0.728103	+	0.610951i
$789$		0			0
$790$	5.46926	+	1.99065i	0.194587	+	0.0708240i
$791$	−19.6621	−	34.0557i	−0.699104	−	1.21088i
$792$		0			0
$793$	−2.34343	+	4.05893i	−0.0832175	+	0.144137i
$794$	−18.7893	+	15.7661i	−0.666806	+	0.559517i
$795$		0			0
$796$	−1.84817	+	10.4815i	−0.0655068	+	0.371507i
$797$	−8.95336	+	50.7770i	−0.317144	+	1.79862i	0.242791	+	0.970079i	$0.421937\pi$
$797$	−8.95336	+	50.7770i	−0.317144	+	1.79862i	−0.559935	+	0.828537i	$0.689174\pi$
$798$		0			0
$799$	−30.6917	+	25.7534i	−1.08579	+	0.911088i
$800$	2.11334	−	3.66041i	0.0747179	−	0.129415i
$801$		0			0
$802$	7.31268	+	12.6659i	0.258220	+	0.447250i
$803$	−7.81743	−	2.84531i	−0.275871	−	0.100409i
$804$		0			0
$805$	4.91147	+	4.12122i	0.173107	+	0.145254i
$806$	5.68732	−	2.07001i	0.200327	−	0.0729132i
$807$		0			0
$808$	−1.62789	−	9.23222i	−0.0572689	−	0.324788i
$809$	−25.9709			−0.913088			−0.456544	−	0.889701i	$-0.650913\pi$
$809$	−25.9709			−0.913088			−0.456544	+	0.889701i	$0.650913\pi$
$810$		0			0
$811$	−14.4442			−0.507204			−0.253602	−	0.967309i	$-0.581615\pi$
$811$	−14.4442			−0.507204			−0.253602	+	0.967309i	$0.581615\pi$
$812$	0.0996702	+	0.565258i	0.00349774	+	0.0198367i
$813$		0			0
$814$	−25.9167	+	9.43290i	−0.908379	+	0.330623i
$815$	−7.21941	−	6.05780i	−0.252885	−	0.212196i
$816$		0			0
$817$	42.4124	+	15.4369i	1.48382	+	0.540067i
$818$	18.0633	+	31.2866i	0.631568	+	1.09391i
$819$		0			0
$820$	−3.38666	+	5.86587i	−0.118267	+	0.204845i
$821$	5.12061	−	4.29671i	0.178711	−	0.149956i	−0.549044	−	0.835793i	$-0.685008\pi$
$821$	5.12061	−	4.29671i	0.178711	−	0.149956i	0.727755	+	0.685837i	$0.240564\pi$
$822$		0			0
$823$	−1.34343	+	7.61895i	−0.0468289	+	0.265580i	−0.999229	−	0.0392725i	$-0.987496\pi$
$823$	−1.34343	+	7.61895i	−0.0468289	+	0.265580i	0.952400	+	0.304852i	$0.0986071\pi$
$824$	−0.560307	+	3.17766i	−0.0195192	+	0.110699i
$825$		0			0
$826$	−18.9008	+	15.8597i	−0.657643	+	0.551828i
$827$	23.4038	−	40.5366i	0.813830	−	1.40959i	−0.0963358	−	0.995349i	$-0.530712\pi$
$827$	23.4038	−	40.5366i	0.813830	−	1.40959i	0.910165	−	0.414245i	$-0.135954\pi$
$828$		0			0
$829$	22.6648	+	39.2566i	0.787180	+	1.36344i	0.927688	+	0.373357i	$0.121793\pi$
$829$	22.6648	+	39.2566i	0.787180	+	1.36344i	−0.140507	+	0.990080i	$0.544873\pi$
$830$	−3.68004	−	1.33943i	−0.127736	−	0.0464922i
$831$		0			0
$832$	−2.83022	−	2.37484i	−0.0981203	−	0.0823327i
$833$	32.1536	−	11.7030i	1.11406	−	0.405484i
$834$		0			0
$835$	1.96972	+	11.1708i	0.0681650	+	0.386583i
$836$	−14.9044			−0.515478
$837$		0			0
$838$	−19.7128			−0.680966
$839$	−1.81924	−	10.3174i	−0.0628071	−	0.356197i	−0.999973	−	0.00731353i	$-0.997672\pi$
$839$	−1.81924	−	10.3174i	−0.0628071	−	0.356197i	0.937166	−	0.348883i	$-0.113439\pi$
$840$		0			0
$841$	27.2263	−	9.90955i	0.938837	−	0.341709i
$842$	2.63041	+	2.20718i	0.0906501	+	0.0760645i
$843$		0			0
$844$	5.01842	+	1.82655i	0.172741	+	0.0628726i
$845$	−0.285807	−	0.495032i	−0.00983206	−	0.0170296i
$846$		0			0
$847$	3.13176	−	5.42437i	0.107609	−	0.186383i
$848$	−0.549163	+	0.460802i	−0.0188583	+	0.0158240i
$849$		0			0
$850$	4.58647	−	26.0111i	0.157315	−	0.892175i
$851$	2.76604	−	15.6870i	0.0948188	−	0.537744i
$852$		0			0
$853$	27.4932	−	23.0695i	0.941349	−	0.789886i	−0.0364705	−	0.999335i	$-0.511612\pi$
$853$	27.4932	−	23.0695i	0.941349	−	0.789886i	0.977820	+	0.209449i	$0.0671671\pi$
$854$	−2.24035	+	3.88040i	−0.0766633	+	0.132785i
$855$		0			0
$856$	−1.14156	−	1.97724i	−0.0390177	−	0.0675806i
$857$	−15.5488	−	5.65928i	−0.531135	−	0.193317i	0.0625099	−	0.998044i	$-0.480089\pi$
$857$	−15.5488	−	5.65928i	−0.531135	−	0.193317i	−0.593645	+	0.804727i	$0.702312\pi$
$858$		0			0
$859$	10.8369	+	9.09321i	0.369749	+	0.310256i	0.808662	−	0.588273i	$-0.200192\pi$
$859$	10.8369	+	9.09321i	0.369749	+	0.310256i	−0.438913	+	0.898529i	$0.644636\pi$
$860$	8.94356	−	3.25519i	0.304973	−	0.111001i
$861$		0			0
$862$	4.98633	+	28.2789i	0.169835	+	0.963182i
$863$	32.8939			1.11972			0.559861	−	0.828586i	$-0.310854\pi$
$863$	32.8939			1.11972			0.559861	+	0.828586i	$0.310854\pi$
$864$		0			0
$865$	−11.3200			−0.384890
$866$	−2.45155	−	13.9034i	−0.0833071	−	0.472458i
$867$		0			0
$868$	5.43717	−	1.97897i	0.184549	−	0.0671705i
$869$	18.1205	+	15.2049i	0.614694	+	0.515790i
$870$		0			0
$871$	12.4855	+	4.54433i	0.423053	+	0.153979i
$872$	−5.20961	−	9.02330i	−0.176420	−	0.305568i
$873$		0			0
$874$	4.30406	−	7.45486i	0.145587	−	0.252164i
$875$	21.9538	−	18.4215i	0.742175	−	0.622759i
$876$		0			0
$877$	4.15627	−	23.5714i	0.140347	−	0.795949i	−0.830639	−	0.556812i	$-0.812024\pi$
$877$	4.15627	−	23.5714i	0.140347	−	0.795949i	0.970986	−	0.239137i	$-0.0768645\pi$
$878$	2.69506	−	15.2844i	0.0909539	−	0.515825i
$879$		0			0
$880$	−2.40760	+	2.02022i	−0.0811603	+	0.0681016i
$881$	−9.34183	+	16.1805i	−0.314734	+	0.545136i	−0.979381	−	0.202022i	$-0.935249\pi$
$881$	−9.34183	+	16.1805i	−0.314734	+	0.545136i	0.664647	+	0.747158i	$0.268582\pi$
$882$		0			0
$883$	2.99407	+	5.18588i	0.100758	+	0.174519i	0.911997	−	0.410196i	$-0.134540\pi$
$883$	2.99407	+	5.18588i	0.100758	+	0.174519i	−0.811239	+	0.584715i	$0.801206\pi$
$884$	−21.6951	−	7.89636i	−0.729684	−	0.265583i
$885$		0			0
$886$	27.3897	+	22.9826i	0.920173	+	0.772117i
$887$	7.36231	−	2.67966i	0.247202	−	0.0899742i	−0.215447	−	0.976515i	$-0.569121\pi$
$887$	7.36231	−	2.67966i	0.247202	−	0.0899742i	0.462650	+	0.886541i	$0.346899\pi$
$888$		0			0
$889$	6.07620	+	34.4598i	0.203789	+	1.15575i
$890$	−8.13341			−0.272632
$891$		0			0
$892$	−19.0496			−0.637829
$893$	4.64290	+	26.3312i	0.155369	+	0.881140i
$894$		0			0
$895$	−7.40673	+	2.69583i	−0.247580	+	0.0901116i
$896$	−2.70574	−	2.27038i	−0.0903923	−	0.0758482i
$897$		0			0
$898$	−24.1621	−	8.79428i	−0.806299	−	0.293469i
$899$	0.133103	+	0.230542i	0.00443924	+	0.00768899i
$900$		0			0
$901$	−2.23989	+	3.87960i	−0.0746214	+	0.129248i
$902$	−21.0876	+	17.6946i	−0.702142	+	0.589167i
$903$		0			0
$904$	−1.93330	+	10.9643i	−0.0643005	+	0.364666i
$905$	−0.303186	+	1.71945i	−0.0100782	+	0.0571565i
$906$		0			0
$907$	−8.30928	+	6.97231i	−0.275905	+	0.231512i	−0.770231	−	0.637765i	$-0.779859\pi$
$907$	−8.30928	+	6.97231i	−0.275905	+	0.231512i	0.494326	+	0.869276i	$0.335415\pi$
$908$	−1.73055	+	2.99740i	−0.0574304	+	0.0994723i
$909$		0			0
$910$	−5.73783	−	9.93821i	−0.190207	−	0.329448i
$911$	28.4402	+	10.3514i	0.942265	+	0.342956i	0.767060	−	0.641576i	$-0.221719\pi$
$911$	28.4402	+	10.3514i	0.942265	+	0.342956i	0.175205	+	0.984532i	$0.443941\pi$
$912$		0			0
$913$	−12.1925	−	10.2308i	−0.403514	−	0.338588i
$914$	−1.90983	+	0.695120i	−0.0631714	+	0.0229925i
$915$		0			0
$916$	−5.02528	−	28.4998i	−0.166040	−	0.941660i
$917$	−31.8949			−1.05326
$918$		0			0
$919$	16.3492			0.539309			0.269655	−	0.962957i	$-0.413090\pi$
$919$	16.3492			0.539309			0.269655	+	0.962957i	$0.413090\pi$
$920$	−0.315207	−	1.78763i	−0.0103921	−	0.0589364i
$921$		0			0
$922$	20.2729	−	7.37874i	0.667653	−	0.243006i
$923$	−38.3207	−	32.1549i	−1.26134	−	1.05839i
$924$		0			0
$925$	−30.6498	−	11.1556i	−1.00776	−	0.366794i
$926$	10.8007	+	18.7073i	0.354932	+	0.614760i
$927$		0			0
$928$	0.0812519	−	0.140732i	0.00266722	−	0.00461977i
$929$	30.5107	−	25.6015i	1.00102	−	0.839959i	0.0138986	−	0.999903i	$-0.495576\pi$
$929$	30.5107	−	25.6015i	1.00102	−	0.839959i	0.987126	+	0.159944i	$0.0511313\pi$
$930$		0			0
$931$	3.96522	−	22.4879i	0.129955	−	0.737011i
$932$	1.15657	−	6.55926i	0.0378848	−	0.214856i
$933$		0			0
$934$	−18.7867	+	15.7639i	−0.614721	+	0.515812i
$935$	−9.81996	+	17.0087i	−0.321147	+	0.556243i
$936$		0			0
$937$	−24.4124	−	42.2835i	−0.797519	−	1.38134i	−0.921228	−	0.389024i	$-0.872812\pi$
$937$	−24.4124	−	42.2835i	−0.797519	−	1.38134i	0.123709	−	0.992319i	$-0.460521\pi$
$938$	11.9363	+	4.34445i	0.389734	+	0.141851i
$939$		0			0
$940$	4.31908	+	3.62414i	0.140873	+	0.118206i
$941$	11.8751	−	4.32218i	0.387117	−	0.140899i	−0.141127	−	0.989991i	$-0.545073\pi$
$941$	11.8751	−	4.32218i	0.387117	−	0.140899i	0.528245	+	0.849092i	$0.322850\pi$
$942$		0			0
$943$	−2.76083	−	15.6574i	−0.0899050	−	0.509877i
$944$	6.98545			0.227357
$945$		0			0
$946$	38.6810			1.25763
$947$	−6.60261	−	37.4452i	−0.214556	−	1.21681i	−0.881675	−	0.471856i	$-0.843584\pi$
$947$	−6.60261	−	37.4452i	−0.214556	−	1.21681i	0.667120	−	0.744951i	$-0.267527\pi$
$948$		0			0
$949$	−8.08125	+	2.94134i	−0.262329	+	0.0954798i
$950$	−13.5025	−	11.3300i	−0.438080	−	0.367593i
$951$		0			0
$952$	−20.7408	−	7.54904i	−0.672214	−	0.244666i
$953$	7.95353	+	13.7759i	0.257640	+	0.446245i	0.965609	−	0.259998i	$-0.0837218\pi$
$953$	7.95353	+	13.7759i	0.257640	+	0.446245i	−0.707969	+	0.706243i	$0.750388\pi$
$954$		0			0
$955$	5.76945	−	9.99298i	0.186695	−	0.323365i
$956$	−5.96657	+	5.00654i	−0.192973	+	0.161923i
$957$		0			0
$958$	−2.48767	+	14.1083i	−0.0803731	+	0.455818i
$959$	1.24345	−	7.05196i	0.0401531	−	0.227720i
$960$		0			0
$961$	−21.6917	+	18.2015i	−0.699731	+	0.587144i
$962$	−14.2554	+	24.6910i	−0.459611	+	0.796070i
$963$		0			0
$964$	−10.9474	−	18.9615i	−0.352593	−	0.610709i
$965$	−4.75655	−	1.73124i	−0.153119	−	0.0557307i
$966$		0			0
$967$	−45.3023	−	38.0132i	−1.45682	−	1.22242i	−0.927404	−	0.374060i	$-0.877965\pi$
$967$	−45.3023	−	38.0132i	−1.45682	−	1.22242i	−0.529420	−	0.848360i	$-0.677590\pi$
$968$	−1.66637	+	0.606511i	−0.0535593	+	0.0194940i
$969$		0			0
$970$	−1.72416	−	9.77817i	−0.0553593	−	0.313958i
$971$	9.68004			0.310647			0.155324	−	0.987864i	$-0.450358\pi$
$971$	9.68004			0.310647			0.155324	+	0.987864i	$0.450358\pi$
$972$		0			0
$973$	−0.583473			−0.0187053
$974$	5.61081	+	31.8205i	0.179782	+	1.01959i
$975$		0			0
$976$	1.19207	−	0.433877i	0.0381571	−	0.0138881i
$977$	−2.64955	−	2.22324i	−0.0847666	−	0.0711276i	0.599420	−	0.800435i	$-0.295398\pi$
$977$	−2.64955	−	2.22324i	−0.0847666	−	0.0711276i	−0.684186	+	0.729307i	$0.739842\pi$
$978$		0			0
$979$	−31.0621	−	11.3057i	−0.992750	−	0.361331i
$980$	−2.40760	−	4.17009i	−0.0769081	−	0.133209i
$981$		0			0
$982$	16.2246	−	28.1019i	0.517748	−	0.896767i
$983$	32.2649	−	27.0735i	1.02909	−	0.863510i	0.0383486	−	0.999264i	$-0.487790\pi$
$983$	32.2649	−	27.0735i	1.02909	−	0.863510i	0.990743	+	0.135754i	$0.0433458\pi$
$984$		0			0
$985$	4.07428	−	23.1064i	0.129817	−	0.736231i
$986$	0.176337	−	1.00005i	0.00561570	−	0.0318482i
$987$		0			0
$988$	−11.8027	+	9.90366i	−0.375495	+	0.315077i
$989$	−11.1702	+	19.3474i	−0.355193	+	0.615213i
$990$		0			0
$991$	9.26786	+	16.0524i	0.294403	+	0.509921i	0.974846	−	0.222880i	$-0.0715458\pi$
$991$	9.26786	+	16.0524i	0.294403	+	0.509921i	−0.680443	+	0.732801i	$0.738213\pi$
$992$	−1.53936	−	0.560282i	−0.0488748	−	0.0177890i
$993$		0			0
$994$	−36.6352	−	30.7406i	−1.16200	−	0.975033i
$995$	8.79503	−	3.20113i	0.278821	−	0.101483i
$996$		0			0
$997$	−1.90879	−	10.8253i	−0.0604519	−	0.342839i	−1.00000		0.000422427i	$-0.999866\pi$
$997$	−1.90879	−	10.8253i	−0.0604519	−	0.342839i	0.939548	−	0.342417i	$-0.111246\pi$
$998$	−24.8307			−0.786002
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.e.a.91.1		6
3.2	odd	2		54.2.e.a.13.1	✓	6
9.2	odd	6		486.2.e.d.109.1		6
9.4	even	3		486.2.e.c.433.1		6
9.5	odd	6		486.2.e.b.433.1		6
9.7	even	3		486.2.e.a.109.1		6
12.11	even	2		432.2.u.a.337.1		6
27.2	odd	18		54.2.e.a.25.1	yes	6
27.4	even	9		1458.2.c.a.487.1		6
27.5	odd	18		1458.2.a.a.1.1		3
27.7	even	9		486.2.e.a.379.1		6
27.11	odd	18		486.2.e.b.55.1		6
27.13	even	9		1458.2.c.a.973.1		6
27.14	odd	18		1458.2.c.d.973.3		6
27.16	even	9		486.2.e.c.55.1		6
27.20	odd	18		486.2.e.d.379.1		6
27.22	even	9		1458.2.a.d.1.3		3
27.23	odd	18		1458.2.c.d.487.3		6
27.25	even	9	inner	162.2.e.a.73.1		6
108.83	even	18		432.2.u.a.241.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.a.13.1	✓	6	3.2	odd	2
54.2.e.a.25.1	yes	6	27.2	odd	18
162.2.e.a.73.1		6	27.25	even	9	inner
162.2.e.a.91.1		6	1.1	even	1	trivial
432.2.u.a.241.1		6	108.83	even	18
432.2.u.a.337.1		6	12.11	even	2
486.2.e.a.109.1		6	9.7	even	3
486.2.e.a.379.1		6	27.7	even	9
486.2.e.b.55.1		6	27.11	odd	18
486.2.e.b.433.1		6	9.5	odd	6
486.2.e.c.55.1		6	27.16	even	9
486.2.e.c.433.1		6	9.4	even	3
486.2.e.d.109.1		6	9.2	odd	6
486.2.e.d.379.1		6	27.20	odd	18
1458.2.a.a.1.1		3	27.5	odd	18
1458.2.a.d.1.3		3	27.22	even	9
1458.2.c.a.487.1		6	27.4	even	9
1458.2.c.a.973.1		6	27.13	even	9
1458.2.c.d.487.3		6	27.23	odd	18
1458.2.c.d.973.3		6	27.14	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(0.673648 + 0.565258i) q^{5} +(3.31908 + 1.20805i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.439693 + 0.761570i) q^{10} +(-2.73783 + 2.29731i) q^{11} +(-0.641559 + 3.63846i) q^{13} +(-0.613341 + 3.47843i) q^{14} +(0.766044 - 0.642788i) q^{16} +(3.12449 - 5.41177i) q^{17} +(-2.08512 - 3.61154i) q^{19} +(-0.826352 - 0.300767i) q^{20} +(-2.73783 - 2.29731i) q^{22} +(1.93969 - 0.705990i) q^{23} +(-0.733956 - 4.16247i) q^{25} -3.69459 q^{26} -3.53209 q^{28} +(-0.0282185 - 0.160035i) q^{29} +(-1.53936 + 0.560282i) q^{31} +(0.766044 + 0.642788i) q^{32} +(5.87211 + 2.13727i) q^{34} +(1.55303 + 2.68993i) q^{35} +(3.85844 - 6.68302i) q^{37} +(3.19459 - 2.68058i) q^{38} +(0.152704 - 0.866025i) q^{40} +(1.33750 - 7.58532i) q^{41} +(-8.29086 + 6.95686i) q^{43} +(1.78699 - 3.09516i) q^{44} +(1.03209 + 1.78763i) q^{46} +(-6.02481 - 2.19285i) q^{47} +(4.19459 + 3.51968i) q^{49} +(3.97178 - 1.44561i) q^{50} +(-0.641559 - 3.63846i) q^{52} -0.716881 q^{53} -3.14290 q^{55} +(-0.613341 - 3.47843i) q^{56} +(0.152704 - 0.0555796i) q^{58} +(5.35117 + 4.49016i) q^{59} +(1.19207 + 0.433877i) q^{61} +(-0.819078 - 1.41868i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-2.48886 + 2.08840i) q^{65} +(0.624485 - 3.54163i) q^{67} +(-1.08512 + 6.15403i) q^{68} +(-2.37939 + 1.99654i) q^{70} +(-6.76991 + 11.7258i) q^{71} +(1.16385 + 2.01584i) q^{73} +(7.25150 + 2.63933i) q^{74} +(3.19459 + 2.68058i) q^{76} +(-11.8623 + 4.31753i) q^{77} +(-1.14930 - 6.51800i) q^{79} +0.879385 q^{80} +7.70233 q^{82} +(0.773318 + 4.38571i) q^{83} +(5.16385 - 1.87949i) q^{85} +(-8.29086 - 6.95686i) q^{86} +(3.35844 + 1.22237i) q^{88} +(4.62449 + 8.00984i) q^{89} +(-6.52481 + 11.3013i) q^{91} +(-1.58125 + 1.32683i) q^{92} +(1.11334 - 6.31407i) q^{94} +(0.636812 - 3.61154i) q^{95} +(-8.64930 + 7.25762i) q^{97} +(-2.73783 + 4.74205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{11} - 12 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} - 6 q^{20} + 3 q^{22} + 6 q^{23} - 9 q^{25} - 18 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} + 6 q^{34}+ \cdots + 3 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 3 * q^11 - 12 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 - 6 * q^20 + 3 * q^22 + 6 * q^23 - 9 * q^25 - 18 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 + 6 * q^34 - 3 * q^35 + 15 * q^37 + 15 * q^38 + 3 * q^40 + 3 * q^41 - 18 * q^43 + 3 * q^44 - 3 * q^46 - 9 * q^47 + 21 * q^49 + 9 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 3 * q^58 + 6 * q^59 + 18 * q^61 + 12 * q^62 - 3 * q^64 - 21 * q^65 - 9 * q^67 + 15 * q^68 - 3 * q^70 - 12 * q^71 + 3 * q^73 + 3 * q^74 + 15 * q^76 - 39 * q^77 + 33 * q^79 - 6 * q^80 - 6 * q^82 + 18 * q^83 + 27 * q^85 - 18 * q^86 + 12 * q^88 + 15 * q^89 - 12 * q^91 - 12 * q^92 - 21 * q^95 - 12 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more