LMFDB - Embedded newform 972.2.l.b.215.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,-3,0,3,-6,0,0,9,0,-3,0,0,6,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			215.8
Character	$\chi$	$=$	972.215
Dual form			972.2.l.b.755.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.267275 - 1.38873i) q^{2} +(-1.85713 + 0.742344i) q^{4} +(-2.21508 + 2.63983i) q^{5} +(-1.00203 + 2.75305i) q^{7} +(1.52728 + 2.38064i) q^{8} +(4.25804 + 2.37058i) q^{10} +(-2.00243 + 1.68024i) q^{11} +(0.941927 - 5.34193i) q^{13} +(4.09105 + 0.655722i) q^{14} +(2.89785 - 2.75726i) q^{16} +(-1.15583 - 0.667320i) q^{17} +(-0.0790760 + 0.0456546i) q^{19} +(2.15403 - 6.54685i) q^{20} +(2.86860 + 2.33175i) q^{22} +(-0.797738 + 0.290353i) q^{23} +(-1.19388 - 6.77083i) q^{25} +(-7.67024 + 0.119685i) q^{26} +(-0.182815 - 5.85661i) q^{28} +(-0.493578 + 0.0870310i) q^{29} +(-2.27906 - 6.26168i) q^{31} +(-4.60360 - 3.28738i) q^{32} +(-0.617801 + 1.78349i) q^{34} +(-5.04800 - 8.74340i) q^{35} +(2.75869 - 4.77819i) q^{37} +(0.0845368 + 0.0976128i) q^{38} +(-9.66751 - 1.24155i) q^{40} +(-2.81281 - 0.495975i) q^{41} +(3.65343 + 4.35398i) q^{43} +(2.47146 - 4.60692i) q^{44} +(0.616436 + 1.03024i) q^{46} +(-6.20947 - 2.26006i) q^{47} +(-1.21289 - 1.01774i) q^{49} +(-9.08374 + 3.46765i) q^{50} +(2.21627 + 10.6199i) q^{52} -7.37249i q^{53} -9.00795i q^{55} +(-8.08437 + 1.81920i) q^{56} +(0.252783 + 0.662184i) q^{58} +(-2.33273 - 1.95739i) q^{59} +(2.27868 + 0.829371i) q^{61} +(-8.08663 + 4.83859i) q^{62} +(-3.33485 + 7.27178i) q^{64} +(12.0154 + 14.3193i) q^{65} +(4.74821 + 0.837237i) q^{67} +(2.64191 + 0.381274i) q^{68} +(-10.7930 + 9.34719i) q^{70} +(-5.91940 + 10.2527i) q^{71} +(-5.83049 - 10.0987i) q^{73} +(-7.37294 - 2.55398i) q^{74} +(0.112963 - 0.143488i) q^{76} +(-2.61929 - 7.19644i) q^{77} +(-1.66138 + 0.292946i) q^{79} +(0.859714 + 13.7574i) q^{80} +(0.0630204 + 4.03879i) q^{82} +(-0.375017 - 2.12683i) q^{83} +(4.32187 - 1.57303i) q^{85} +(5.07003 - 6.23732i) q^{86} +(-7.05831 - 2.20087i) q^{88} +(12.5801 - 7.26310i) q^{89} +(13.7628 + 7.94593i) q^{91} +(1.26596 - 1.13142i) q^{92} +(-1.47897 + 9.22731i) q^{94} +(0.0546395 - 0.309876i) q^{95} +(5.05588 - 4.24238i) q^{97} +(-1.08919 + 1.95639i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.267275	−	1.38873i	−0.188992	−	0.981979i
$2$	−0.267275	−	1.38873i	−0.188992	−	0.981979i
$3$		0			0
$3$		0			0
$4$	−1.85713	+	0.742344i	−0.928564	+	0.371172i
$5$	−2.21508	+	2.63983i	−0.990614	+	1.18057i	−0.00705588	+	0.999975i	$0.502246\pi$
$5$	−2.21508	+	2.63983i	−0.990614	+	1.18057i	−0.983558	+	0.180593i	$0.942198\pi$
$6$		0			0
$7$	−1.00203	+	2.75305i	−0.378731	+	1.04055i	0.593153	+	0.805090i	$0.297883\pi$
$7$	−1.00203	+	2.75305i	−0.378731	+	1.04055i	−0.971883	+	0.235464i	$0.924339\pi$
$8$	1.52728	+	2.38064i	0.539974	+	0.841682i
$9$		0			0
$10$	4.25804	+	2.37058i	1.34651	+	0.749644i
$11$	−2.00243	+	1.68024i	−0.603757	+	0.506612i	−0.892651	−	0.450749i	$-0.851157\pi$
$11$	−2.00243	+	1.68024i	−0.603757	+	0.506612i	0.288894	+	0.957361i	$0.406712\pi$
$12$		0			0
$13$	0.941927	−	5.34193i	0.261244	−	1.48159i	−0.518279	−	0.855212i	$-0.673427\pi$
$13$	0.941927	−	5.34193i	0.261244	−	1.48159i	0.779522	−	0.626374i	$-0.215462\pi$
$14$	4.09105	+	0.655722i	1.09338	+	0.175249i
$15$		0			0
$16$	2.89785	−	2.75726i	0.724463	−	0.689314i
$17$	−1.15583	−	0.667320i	−0.280330	−	0.161849i	0.353243	−	0.935532i	$-0.385079\pi$
$17$	−1.15583	−	0.667320i	−0.280330	−	0.161849i	−0.633573	+	0.773683i	$0.718412\pi$
$18$		0			0
$19$	−0.0790760	+	0.0456546i	−0.0181413	+	0.0104739i	−0.509043	−	0.860741i	$-0.670001\pi$
$19$	−0.0790760	+	0.0456546i	−0.0181413	+	0.0104739i	0.490902	+	0.871215i	$0.336667\pi$
$20$	2.15403	−	6.54685i	0.481655	−	1.46392i
$21$		0			0
$22$	2.86860	+	2.33175i	0.611587	+	0.497131i
$23$	−0.797738	+	0.290353i	−0.166340	+	0.0605428i	−0.423848	−	0.905733i	$-0.639321\pi$
$23$	−0.797738	+	0.290353i	−0.166340	+	0.0605428i	0.257508	+	0.966276i	$0.417099\pi$
$24$		0			0
$25$	−1.19388	−	6.77083i	−0.238776	−	1.35417i
$26$	−7.67024	+	0.119685i	−1.50426	+	0.0234721i
$27$		0			0
$28$	−0.182815	−	5.85661i	−0.0345487	−	1.10679i
$29$	−0.493578	+	0.0870310i	−0.0916551	+	0.0161613i	−0.219288	−	0.975660i	$-0.570373\pi$
$29$	−0.493578	+	0.0870310i	−0.0916551	+	0.0161613i	0.127633	+	0.991822i	$0.459262\pi$
$30$		0			0
$31$	−2.27906	−	6.26168i	−0.409332	−	1.12463i	−0.957543	−	0.288290i	$-0.906913\pi$
$31$	−2.27906	−	6.26168i	−0.409332	−	1.12463i	0.548211	−	0.836340i	$-0.315309\pi$
$32$	−4.60360	−	3.28738i	−0.813809	−	0.581132i
$33$		0			0
$34$	−0.617801	+	1.78349i	−0.105952	+	0.305867i
$35$	−5.04800	−	8.74340i	−0.853268	−	1.47790i
$36$		0			0
$37$	2.75869	−	4.77819i	0.453526	−	0.785530i	−0.545076	−	0.838387i	$-0.683499\pi$
$37$	2.75869	−	4.77819i	0.453526	−	0.785530i	0.998602	+	0.0528563i	$0.0168325\pi$
$38$	0.0845368	+	0.0976128i	0.0137137	+	0.0158349i
$39$		0			0
$40$	−9.66751	−	1.24155i	−1.52857	−	0.196306i
$41$	−2.81281	−	0.495975i	−0.439288	−	0.0774583i	−0.0503696	−	0.998731i	$-0.516040\pi$
$41$	−2.81281	−	0.495975i	−0.439288	−	0.0774583i	−0.388918	+	0.921272i	$0.627151\pi$
$42$		0			0
$43$	3.65343	+	4.35398i	0.557142	+	0.663976i	0.968939	−	0.247299i	$-0.0795431\pi$
$43$	3.65343	+	4.35398i	0.557142	+	0.663976i	−0.411797	+	0.911276i	$0.635099\pi$
$44$	2.47146	−	4.60692i	0.372587	−	0.694519i
$45$		0			0
$46$	0.616436	+	1.03024i	0.0908886	+	0.151900i
$47$	−6.20947	−	2.26006i	−0.905744	−	0.329664i	−0.153192	−	0.988197i	$-0.548955\pi$
$47$	−6.20947	−	2.26006i	−0.905744	−	0.329664i	−0.752552	+	0.658533i	$0.771177\pi$
$48$		0			0
$49$	−1.21289	−	1.01774i	−0.173271	−	0.145391i
$50$	−9.08374	+	3.46765i	−1.28464	+	0.490399i
$51$		0			0
$52$	2.21627	+	10.6199i	0.307342	+	1.47271i
$53$		−	7.37249i		−	1.01269i	−0.862331	−	0.506345i	$-0.830996\pi$
$53$		−	7.37249i		−	1.01269i	0.862331	−	0.506345i	$-0.169004\pi$
$54$		0			0
$55$		−	9.00795i		−	1.21463i
$56$	−8.08437	+	1.81920i	−1.08032	+	0.243101i
$57$		0			0
$58$	0.252783	+	0.662184i	0.0331921	+	0.0869490i
$59$	−2.33273	−	1.95739i	−0.303696	−	0.254831i	0.478185	−	0.878259i	$-0.341295\pi$
$59$	−2.33273	−	1.95739i	−0.303696	−	0.254831i	−0.781880	+	0.623428i	$0.785739\pi$
$60$		0			0
$61$	2.27868	+	0.829371i	0.291755	+	0.106190i	0.483751	−	0.875206i	$-0.339274\pi$
$61$	2.27868	+	0.829371i	0.291755	+	0.106190i	−0.191996	+	0.981396i	$0.561496\pi$
$62$	−8.08663	+	4.83859i	−1.02700	+	0.614501i
$63$		0			0
$64$	−3.33485	+	7.27178i	−0.416856	+	0.908973i
$65$	12.0154	+	14.3193i	1.49032	+	1.77610i
$66$		0			0
$67$	4.74821	+	0.837237i	0.580086	+	0.102285i	0.455989	−	0.889985i	$-0.349286\pi$
$67$	4.74821	+	0.837237i	0.580086	+	0.102285i	0.124097	+	0.992270i	$0.460397\pi$
$68$	2.64191	+	0.381274i	0.320379	+	0.0462362i
$69$		0			0
$70$	−10.7930	+	9.34719i	−1.29001	+	1.11720i
$71$	−5.91940	+	10.2527i	−0.702504	+	1.21677i	0.265081	+	0.964226i	$0.414601\pi$
$71$	−5.91940	+	10.2527i	−0.702504	+	1.21677i	−0.967585	+	0.252546i	$0.918732\pi$
$72$		0			0
$73$	−5.83049	−	10.0987i	−0.682408	−	1.18197i	−0.974244	−	0.225497i	$-0.927600\pi$
$73$	−5.83049	−	10.0987i	−0.682408	−	1.18197i	0.291836	−	0.956468i	$-0.405734\pi$
$74$	−7.37294	−	2.55398i	−0.857087	−	0.296894i
$75$		0			0
$76$	0.112963	−	0.143488i	0.0129577	−	0.0164592i
$77$	−2.61929	−	7.19644i	−0.298496	−	0.820110i
$78$		0			0
$79$	−1.66138	+	0.292946i	−0.186920	+	0.0329590i	−0.266324	−	0.963884i	$-0.585809\pi$
$79$	−1.66138	+	0.292946i	−0.186920	+	0.0329590i	0.0794047	+	0.996842i	$0.474698\pi$
$80$	0.859714	+	13.7574i	0.0961190	+	1.53812i
$81$		0			0
$82$	0.0630204	+	4.03879i	0.00695944	+	0.446010i
$83$	−0.375017	−	2.12683i	−0.0411635	−	0.233450i	0.957284	−	0.289149i	$-0.0933723\pi$
$83$	−0.375017	−	2.12683i	−0.0411635	−	0.233450i	−0.998448	+	0.0556992i	$0.982261\pi$
$84$		0			0
$85$	4.32187	−	1.57303i	0.468773	−	0.170619i
$86$	5.07003	−	6.23732i	0.546715	−	0.672588i
$87$		0			0
$88$	−7.05831	−	2.20087i	−0.752419	−	0.234614i
$89$	12.5801	−	7.26310i	1.33348	−	0.769887i	0.347652	−	0.937624i	$-0.386979\pi$
$89$	12.5801	−	7.26310i	1.33348	−	0.769887i	0.985832	+	0.167737i	$0.0536458\pi$
$90$		0			0
$91$	13.7628	+	7.94593i	1.44273	+	0.832960i
$92$	1.26596	−	1.13142i	0.131985	−	0.117959i
$93$		0			0
$94$	−1.47897	+	9.22731i	−0.152545	+	0.951725i
$95$	0.0546395	−	0.309876i	0.00560589	−	0.0317926i
$96$		0			0
$97$	5.05588	−	4.24238i	0.513347	−	0.430749i	−0.348958	−	0.937138i	$-0.613465\pi$
$97$	5.05588	−	4.24238i	0.513347	−	0.430749i	0.862305	+	0.506389i	$0.169020\pi$
$98$	−1.08919	+	1.95639i	−0.110024	+	0.197626i
$99$		0			0
$100$	7.24347	+	11.6880i	0.724347	+	1.16880i
$101$	2.82004	−	7.74801i	0.280605	−	0.770956i	−0.716686	−	0.697396i	$-0.754342\pi$
$101$	2.82004	−	7.74801i	0.280605	−	0.770956i	0.997291	−	0.0735595i	$-0.0234359\pi$
$102$		0			0
$103$	−10.3468	+	12.3309i	−1.01950	+	1.21500i	−0.0430954	+	0.999071i	$0.513722\pi$
$103$	−10.3468	+	12.3309i	−1.01950	+	1.21500i	−0.976409	+	0.215928i	$0.930722\pi$
$104$	14.1558	−	5.91623i	1.38809	−	0.580134i
$105$		0			0
$106$	−10.2384	+	1.97048i	−0.994440	+	0.191390i
$107$	9.71808			0.939482			0.469741	−	0.882804i	$-0.344347\pi$
$107$	9.71808			0.939482			0.469741	+	0.882804i	$0.344347\pi$
$108$		0			0
$109$	−4.69860			−0.450044			−0.225022	−	0.974354i	$-0.572245\pi$
$109$	−4.69860			−0.450044			−0.225022	+	0.974354i	$0.572245\pi$
$110$	−12.5096	+	2.40760i	−1.19274	+	0.229556i
$111$		0			0
$112$	4.68713	+	10.7408i	0.442892	+	1.01491i
$113$	0.362829	−	0.432403i	0.0341321	−	0.0406770i	−0.748708	−	0.662900i	$-0.769326\pi$
$113$	0.362829	−	0.432403i	0.0341321	−	0.0406770i	0.782840	+	0.622222i	$0.213770\pi$
$114$		0			0
$115$	1.00057	−	2.74905i	0.0933038	−	0.256350i
$116$	0.852030	−	0.528032i	0.0791090	−	0.0490266i
$117$		0			0
$118$	−2.09480	+	3.76269i	−0.192842	+	0.346383i
$119$	2.99534	−	2.51339i	0.274582	−	0.230402i
$120$		0			0
$121$	−0.723600	+	4.10374i	−0.0657818	+	0.373067i
$122$	0.542737	−	3.38613i	0.0491371	−	0.306566i
$123$		0			0
$124$	8.88083	+	9.93689i	0.797522	+	0.892359i
$125$	5.59652	+	3.23116i	0.500568	+	0.289003i
$126$		0			0
$127$	−9.63141	+	5.56070i	−0.854649	+	0.493432i	−0.862217	−	0.506539i	$-0.830924\pi$
$127$	−9.63141	+	5.56070i	−0.854649	+	0.493432i	0.00756758	+	0.999971i	$0.497591\pi$
$128$	10.9898	+	2.68763i	0.971374	+	0.237555i
$129$		0			0
$130$	16.6743	−	20.5132i	1.46243	−	1.79913i
$131$	−2.91519	+	1.06104i	−0.254701	+	0.0927037i	−0.466215	−	0.884671i	$-0.654383\pi$
$131$	−2.91519	+	1.06104i	−0.254701	+	0.0927037i	0.211514	+	0.977375i	$0.432161\pi$
$132$		0			0
$133$	−0.0464528	−	0.263447i	−0.00402797	−	0.0228438i
$134$	−0.106382	−	6.81774i	−0.00919004	−	0.588963i
$135$		0			0
$136$	−0.176631	−	3.77080i	−0.0151459	−	0.323343i
$137$	−17.0059	+	2.99860i	−1.45291	+	0.256188i	−0.843698	−	0.536818i	$-0.819626\pi$
$137$	−17.0059	+	2.99860i	−1.45291	+	0.256188i	−0.609214	+	0.793006i	$0.708515\pi$
$138$		0			0
$139$	−3.82721	−	10.5152i	−0.324620	−	0.891885i	−0.989448	−	0.144889i	$-0.953718\pi$
$139$	−3.82721	−	10.5152i	−0.324620	−	0.891885i	0.664828	−	0.746996i	$-0.268505\pi$
$140$	15.8654	+	12.4903i	1.34087	+	1.05562i
$141$		0			0
$142$	15.8203	+	5.48014i	1.32761	+	0.459883i
$143$	7.08959	+	12.2795i	0.592862	+	1.02687i
$144$		0			0
$145$	0.863567	−	1.49574i	0.0717153	−	0.124215i
$146$	−12.4660	+	10.7961i	−1.03169	+	0.893492i
$147$		0			0
$148$	−1.57618	+	10.9216i	−0.129561	+	0.897751i
$149$	−17.9746	−	3.16940i	−1.47253	−	0.259647i	−0.620943	−	0.783855i	$-0.713250\pi$
$149$	−17.9746	−	3.16940i	−1.47253	−	0.259647i	−0.851590	+	0.524208i	$0.824361\pi$
$150$		0			0
$151$	−12.3734	−	14.7460i	−1.00693	−	1.20001i	−0.979718	−	0.200383i	$-0.935781\pi$
$151$	−12.3734	−	14.7460i	−1.00693	−	1.20001i	−0.0272126	−	0.999630i	$-0.508663\pi$
$152$	−0.229458	−	0.118524i	−0.0186115	−	0.00961357i
$153$		0			0
$154$	−9.29382	+	5.56091i	−0.748918	+	0.448111i
$155$	21.5781	+	7.85378i	1.73319	+	0.630830i
$156$		0			0
$157$	−12.9003	−	10.8246i	−1.02955	−	0.863897i	−0.0387551	−	0.999249i	$-0.512339\pi$
$157$	−12.9003	−	10.8246i	−1.02955	−	0.863897i	−0.990798	+	0.135351i	$0.956784\pi$
$158$	0.850866	+	2.22890i	0.0676913	+	0.177322i
$159$		0			0
$160$	18.8755	−	4.87091i	1.49224	−	0.385079i
$161$		−	2.48715i		−	0.196015i
$162$		0			0
$163$			8.02606i			0.628650i	0.949315	+	0.314325i	$0.101778\pi$
$163$			8.02606i			0.628650i	−0.949315	+	0.314325i	$0.898222\pi$
$164$	5.59194	−	1.16699i	0.436657	−	0.0911263i
$165$		0			0
$166$	−2.85335	+	1.08924i	−0.221463	+	0.0845418i
$167$	1.00020	+	0.839268i	0.0773979	+	0.0649445i	0.680666	−	0.732594i	$-0.261691\pi$
$167$	1.00020	+	0.839268i	0.0773979	+	0.0649445i	−0.603268	+	0.797539i	$0.706135\pi$
$168$		0			0
$169$	−15.4330	−	5.61716i	−1.18716	−	0.432090i
$170$	−3.33964	−	5.58147i	−0.256139	−	0.428079i
$171$		0			0
$172$	−10.0170	−	5.37381i	−0.763792	−	0.409749i
$173$	7.36046	+	8.77186i	0.559606	+	0.666912i	0.969463	−	0.245238i	$-0.0788660\pi$
$173$	7.36046	+	8.77186i	0.559606	+	0.666912i	−0.409857	+	0.912150i	$0.634422\pi$
$174$		0			0
$175$	19.8367	+	3.49775i	1.49951	+	0.264405i
$176$	−1.16990	+	10.3903i	−0.0881844	+	0.783199i
$177$		0			0
$178$	−13.4488	−	15.5290i	−1.00803	−	1.16395i
$179$	10.7064	−	18.5441i	0.800237	−	1.38605i	−0.119222	−	0.992868i	$-0.538040\pi$
$179$	10.7064	−	18.5441i	0.800237	−	1.38605i	0.919460	−	0.393184i	$-0.128627\pi$
$180$		0			0
$181$	7.31416	+	12.6685i	0.543657	+	0.941641i	0.998690	+	0.0511670i	$0.0162941\pi$
$181$	7.31416	+	12.6685i	0.543657	+	0.941641i	−0.455033	+	0.890474i	$0.650373\pi$
$182$	7.35629	−	21.2365i	0.545285	−	1.57415i
$183$		0			0
$184$	−1.90959	−	1.45567i	−0.140777	−	0.107314i
$185$	6.50290	+	17.8666i	0.478102	+	1.31358i
$186$		0			0
$187$	3.43574	−	0.605813i	0.251246	−	0.0443014i
$188$	13.2095	−	0.412337i	0.963403	−	0.0300728i
$189$		0			0
$190$	−0.444937	+	0.00694269i	−0.0322791	+	0.000503676i
$191$	0.333749	+	1.89278i	0.0241492	+	0.136957i	0.994499	−	0.104749i	$-0.0334040\pi$
$191$	0.333749	+	1.89278i	0.0241492	+	0.136957i	−0.970349	+	0.241706i	$0.922293\pi$
$192$		0			0
$193$	5.88386	−	2.14155i	0.423530	−	0.154152i	−0.121457	−	0.992597i	$-0.538757\pi$
$193$	5.88386	−	2.14155i	0.423530	−	0.154152i	0.544987	+	0.838444i	$0.316535\pi$
$194$	−7.24283	−	5.88735i	−0.520005	−	0.422687i
$195$		0			0
$196$	3.00801	+	0.989687i	0.214858	+	0.0706919i
$197$	−13.1022	+	7.56456i	−0.933494	+	0.538953i	−0.887915	−	0.460008i	$-0.847847\pi$
$197$	−13.1022	+	7.56456i	−0.933494	+	0.538953i	−0.0455788	+	0.998961i	$0.514513\pi$
$198$		0			0
$199$	−22.4427	−	12.9573i	−1.59092	−	0.918517i	−0.993150	−	0.116849i	$-0.962721\pi$
$199$	−22.4427	−	12.9573i	−1.59092	−	0.918517i	−0.597769	−	0.801669i	$-0.703946\pi$
$200$	14.2955	−	13.1831i	1.01084	−	0.932188i
$201$		0			0
$202$	−11.5136	−	1.84543i	−0.810094	−	0.129844i
$203$	0.254977	−	1.44605i	0.0178959	−	0.101493i
$204$		0			0
$205$	7.53990	−	6.32672i	0.526609	−	0.441878i
$206$	19.8897	+	11.0732i	1.38578	+	0.771507i
$207$		0			0
$208$	−11.9995	−	18.0773i	−0.832017	−	1.25343i
$209$	0.0816338	−	0.224287i	0.00564673	−	0.0155143i
$210$		0			0
$211$	−11.2158	+	13.3665i	−0.772127	+	0.920186i	−0.998549	−	0.0538436i	$-0.982853\pi$
$211$	−11.2158	+	13.3665i	−0.772127	+	0.920186i	0.226422	+	0.974029i	$0.427297\pi$
$212$	5.47293	+	13.6917i	0.375882	+	0.940347i
$213$		0			0
$214$	−2.59740	−	13.4958i	−0.177555	−	0.922551i
$215$	−19.5864			−1.33578
$216$		0			0
$217$	19.5224			1.32526
$218$	1.25582	+	6.52508i	0.0850547	+	0.441934i
$219$		0			0
$220$	6.68700	+	16.7289i	0.450837	+	1.12786i
$221$	−4.65349	+	5.54581i	−0.313028	+	0.373052i
$222$		0			0
$223$	6.04555	−	16.6100i	0.404840	−	1.11229i	−0.555027	−	0.831832i	$-0.687292\pi$
$223$	6.04555	−	16.6100i	0.404840	−	1.11229i	0.959867	−	0.280456i	$-0.0904857\pi$
$224$	13.6632	−	9.37988i	0.912914	−	0.626720i
$225$		0			0
$226$	−0.697465	−	0.388300i	−0.0463947	−	0.0258294i
$227$	7.14681	−	5.99689i	0.474351	−	0.398027i	−0.374028	−	0.927417i	$-0.622024\pi$
$227$	7.14681	−	5.99689i	0.474351	−	0.398027i	0.848379	+	0.529390i	$0.177579\pi$
$228$		0			0
$229$	2.92027	−	16.5617i	0.192977	−	1.09442i	−0.722294	−	0.691586i	$-0.756912\pi$
$229$	2.92027	−	16.5617i	0.192977	−	1.09442i	0.915271	−	0.402839i	$-0.131977\pi$
$230$	−4.08511	−	0.654770i	−0.269364	−	0.0431742i
$231$		0			0
$232$	−0.961019	−	1.04211i	−0.0630940	−	0.0684177i
$233$	−15.2659	−	8.81379i	−1.00010	−	0.577410i	−0.0918250	−	0.995775i	$-0.529270\pi$
$233$	−15.2659	−	8.81379i	−1.00010	−	0.577410i	−0.908279	+	0.418365i	$0.862603\pi$
$234$		0			0
$235$	19.7206	−	11.3857i	1.28643	−	0.742722i
$236$	5.78524	+	1.90344i	0.376587	+	0.123903i
$237$		0			0
$238$	−4.29099	−	3.48794i	−0.278143	−	0.226090i
$239$	8.65868	−	3.15150i	0.560084	−	0.203854i	−0.0464374	−	0.998921i	$-0.514787\pi$
$239$	8.65868	−	3.15150i	0.560084	−	0.203854i	0.606521	+	0.795067i	$0.292565\pi$
$240$		0			0
$241$	1.08125	+	6.13209i	0.0696496	+	0.395003i	0.999625	+	0.0273809i	$0.00871671\pi$
$241$	1.08125	+	6.13209i	0.0696496	+	0.395003i	−0.929975	+	0.367622i	$0.880172\pi$
$242$	5.89238	−	0.0919433i	0.378776	−	0.00591034i
$243$		0			0
$244$	−4.84747	+	0.151315i	−0.310328	+	0.00968692i
$245$	5.37331	−	0.947460i	0.343288	−	0.0605310i
$246$		0			0
$247$	0.169400	+	0.465422i	0.0107787	+	0.0296141i
$248$	11.4260	−	14.9889i	0.725552	−	0.951798i
$249$		0			0
$250$	2.99138	−	8.63565i	0.189192	−	0.546167i
$251$	14.1765	+	24.5545i	0.894814	+	1.54986i	0.834034	+	0.551713i	$0.186026\pi$
$251$	14.1765	+	24.5545i	0.894814	+	1.54986i	0.0607805	+	0.998151i	$0.480641\pi$
$252$		0			0
$253$	1.10955	−	1.92181i	0.0697571	−	0.120823i
$254$	10.2965	+	11.8892i	0.646061	+	0.745993i
$255$		0			0
$256$	0.795079	−	15.9802i	0.0496925	−	0.998765i
$257$	16.2474	+	2.86485i	1.01348	+	0.178705i	0.655638	−	0.755076i	$-0.272400\pi$
$257$	16.2474	+	2.86485i	1.01348	+	0.178705i	0.357847	+	0.933780i	$0.383511\pi$
$258$		0			0
$259$	10.3903	+	12.3827i	0.645622	+	0.769423i
$260$	−32.9439	−	17.6733i	−2.04310	−	1.09605i
$261$		0			0
$262$	2.25266	+	3.76481i	0.139170	+	0.232591i
$263$	−22.7564	−	8.28265i	−1.40322	−	0.510730i	−0.474087	−	0.880478i	$-0.657222\pi$
$263$	−22.7564	−	8.28265i	−1.40322	−	0.510730i	−0.929132	+	0.369748i	$0.879444\pi$
$264$		0			0
$265$	19.4621	+	16.3307i	1.19555	+	1.00318i
$266$	−0.353441	+	0.134923i	−0.0216708	+	0.00827267i
$267$		0			0
$268$	−9.43955	+	1.96995i	−0.576612	+	0.120334i
$269$			12.1956i			0.743578i	0.928317	+	0.371789i	$0.121255\pi$
$269$			12.1956i			0.743578i	−0.928317	+	0.371789i	$0.878745\pi$
$270$		0			0
$271$			25.0009i			1.51870i	0.650683	+	0.759349i	$0.274483\pi$
$271$			25.0009i			1.51870i	−0.650683	+	0.759349i	$0.725517\pi$
$272$	−5.18940	+	1.25313i	−0.314654	+	0.0759822i
$273$		0			0
$274$	8.70949	+	22.8151i	0.526159	+	1.37831i
$275$	13.7673	+	11.5521i	0.830199	+	0.696620i
$276$		0			0
$277$	8.21089	+	2.98852i	0.493345	+	0.179563i	0.576698	−	0.816957i	$-0.304341\pi$
$277$	8.21089	+	2.98852i	0.493345	+	0.179563i	−0.0833536	+	0.996520i	$0.526563\pi$
$278$	−13.5798	+	8.12539i	−0.814462	+	0.487329i
$279$		0			0
$280$	13.1051	−	25.3710i	0.783182	−	1.51621i
$281$	−14.0693	−	16.7671i	−0.839303	−	1.00024i	−0.999913	−	0.0132243i	$-0.995790\pi$
$281$	−14.0693	−	16.7671i	−0.839303	−	1.00024i	0.160610	−	0.987018i	$-0.448654\pi$
$282$		0			0
$283$	29.6450	+	5.22722i	1.76221	+	0.310726i	0.958670	−	0.284520i	$-0.0918344\pi$
$283$	29.6450	+	5.22722i	1.76221	+	0.310726i	0.803543	+	0.595246i	$0.202945\pi$
$284$	3.38205	−	23.4348i	0.200688	−	1.39060i
$285$		0			0
$286$	15.1581	−	13.1275i	0.896315	−	0.776247i
$287$	4.18396	−	7.24682i	0.246971	−	0.427766i
$288$		0			0
$289$	−7.60937	−	13.1798i	−0.447610	−	0.775283i
$290$	−2.30799	−	0.799485i	−0.135530	−	0.0469474i
$291$		0			0
$292$	18.3247	+	14.4264i	1.07237	+	0.844240i
$293$	−4.52797	−	12.4405i	−0.264527	−	0.726782i	−0.998848	−	0.0479801i	$-0.984722\pi$
$293$	−4.52797	−	12.4405i	−0.264527	−	0.726782i	0.734321	−	0.678802i	$-0.237501\pi$
$294$		0			0
$295$	10.3344	−	1.82223i	0.601690	−	0.106094i
$296$	15.5884	−	0.730189i	0.906059	−	0.0424413i
$297$		0			0
$298$	0.402716	+	25.8089i	0.0233287	+	1.49507i
$299$	0.799635	+	4.53496i	0.0462441	+	0.262263i
$300$		0			0
$301$	−15.6475	+	5.69524i	−0.901910	+	0.328268i
$302$	−17.1711	+	21.1245i	−0.988085	+	1.21558i
$303$		0			0
$304$	−0.103269	+	0.350333i	−0.00592290	+	0.0200930i
$305$	−7.23685	+	4.17820i	−0.414381	+	0.239243i
$306$		0			0
$307$	−11.4064	−	6.58546i	−0.650995	−	0.375852i	0.137842	−	0.990454i	$-0.455983\pi$
$307$	−11.4064	−	6.58546i	−0.650995	−	0.375852i	−0.788837	+	0.614602i	$0.789317\pi$
$308$	10.2066	+	11.4203i	0.581575	+	0.650732i
$309$		0			0
$310$	5.13948	−	32.0652i	0.291903	−	1.82118i
$311$	−1.07244	+	6.08211i	−0.0608125	+	0.344885i	0.939186	+	0.343408i	$0.111581\pi$
$311$	−1.07244	+	6.08211i	−0.0608125	+	0.344885i	−0.999999	+	0.00147712i	$0.999530\pi$
$312$		0			0
$313$	−16.4217	+	13.7794i	−0.928207	+	0.778858i	−0.975495	−	0.220023i	$-0.929387\pi$
$313$	−16.4217	+	13.7794i	−0.928207	+	0.778858i	0.0472879	+	0.998881i	$0.484942\pi$
$314$	−11.5845	+	20.8081i	−0.653752	+	1.17427i
$315$		0			0
$316$	2.86792	−	1.77735i	0.161333	−	0.0999838i
$317$	5.02856	−	13.8159i	0.282432	−	0.775976i	−0.714639	−	0.699494i	$-0.753409\pi$
$317$	5.02856	−	13.8159i	0.282432	−	0.775976i	0.997071	−	0.0764825i	$-0.0243689\pi$
$318$		0			0
$319$	0.842123	−	1.00360i	0.0471499	−	0.0561910i
$320$	−11.8093	−	24.9110i	−0.660160	−	1.39257i
$321$		0			0
$322$	−3.45398	+	0.664753i	−0.192483	+	0.0370452i
$323$	0.121865			0.00678074
$324$		0			0
$325$	−37.2939			−2.06869
$326$	11.1460	−	2.14516i	0.617321	−	0.118810i
$327$		0			0
$328$	−3.11521	−	7.45377i	−0.172009	−	0.411566i
$329$	12.4441	−	14.8303i	0.686066	−	0.817621i
$330$		0			0
$331$	−9.07166	+	24.9242i	−0.498624	+	1.36996i	0.393982	+	0.919118i	$0.371097\pi$
$331$	−9.07166	+	24.9242i	−0.498624	+	1.36996i	−0.892605	+	0.450839i	$0.851125\pi$
$332$	2.27529	+	3.67140i	0.124873	+	0.201494i
$333$		0			0
$334$	0.898186	−	1.61332i	0.0491466	−	0.0882770i
$335$	−12.7278	+	10.6799i	−0.695395	+	0.583506i
$336$		0			0
$337$	−2.67934	+	15.1953i	−0.145953	+	0.827740i	0.820644	+	0.571439i	$0.193615\pi$
$337$	−2.67934	+	15.1953i	−0.145953	+	0.827740i	−0.966597	+	0.256300i	$0.917496\pi$
$338$	−3.67585	+	22.9336i	−0.199940	+	1.24742i
$339$		0			0
$340$	−6.85854	+	6.12964i	−0.371956	+	0.332426i
$341$	15.0848	+	8.70922i	0.816888	+	0.471631i
$342$		0			0
$343$	−13.7433	+	7.93471i	−0.742069	+	0.428434i
$344$	−4.78545	+	15.3472i	−0.258014	+	0.827466i
$345$		0			0
$346$	10.2145	−	12.5662i	0.549133	−	0.675562i
$347$	20.2264	−	7.36182i	1.08581	−	0.395203i	0.263744	−	0.964593i	$-0.415043\pi$
$347$	20.2264	−	7.36182i	1.08581	−	0.395203i	0.822068	+	0.569390i	$0.192820\pi$
$348$		0			0
$349$	2.19509	+	12.4490i	0.117501	+	0.666379i	0.985482	+	0.169782i	$0.0543063\pi$
$349$	2.19509	+	12.4490i	0.117501	+	0.666379i	−0.867981	+	0.496597i	$0.834583\pi$
$350$	−0.444436	−	28.4826i	−0.0237561	−	1.52246i
$351$		0			0
$352$	14.7420	−	1.15240i	0.785751	−	0.0614231i
$353$	11.0190	−	1.94295i	0.586484	−	0.103413i	0.127471	−	0.991842i	$-0.459314\pi$
$353$	11.0190	−	1.94295i	0.586484	−	0.103413i	0.459013	+	0.888429i	$0.348203\pi$
$354$		0			0
$355$	−13.9534	−	38.3368i	−0.740572	−	2.03470i
$356$	−17.9711	+	22.8272i	−0.952465	+	1.20984i
$357$		0			0
$358$	−28.6143	−	9.91196i	−1.51231	−	0.523864i
$359$	−16.1699	−	28.0070i	−0.853413	−	1.47816i	−0.878109	−	0.478460i	$-0.841195\pi$
$359$	−16.1699	−	28.0070i	−0.853413	−	1.47816i	0.0246959	−	0.999695i	$-0.492138\pi$
$360$		0			0
$361$	−9.49583	+	16.4473i	−0.499781	+	0.865645i
$362$	15.6382	−	13.5433i	0.821925	−	0.711822i
$363$		0			0
$364$	−31.4578	−	4.53991i	−1.64884	−	0.237956i
$365$	39.5739	+	6.97795i	2.07139	+	0.365242i
$366$		0			0
$367$	0.428395	+	0.510541i	0.0223620	+	0.0266500i	0.777110	−	0.629365i	$-0.216685\pi$
$367$	0.428395	+	0.510541i	0.0223620	+	0.0266500i	−0.754748	+	0.656015i	$0.772241\pi$
$368$	−1.51115	+	3.04097i	−0.0787741	+	0.158521i
$369$		0			0
$370$	23.0737	−	13.8060i	1.19955	−	0.717741i
$371$	20.2968	+	7.38744i	1.05376	+	0.383537i
$372$		0			0
$373$	15.9574	+	13.3899i	0.826243	+	0.693300i	0.954425	−	0.298450i	$-0.0964697\pi$
$373$	15.9574	+	13.3899i	0.826243	+	0.693300i	−0.128182	+	0.991751i	$0.540914\pi$
$374$	−1.75960	−	4.60938i	−0.0909865	−	0.238345i
$375$		0			0
$376$	−4.10320	−	18.2342i	−0.211606	−	0.940358i
$377$			2.71864i			0.140017i
$378$		0			0
$379$		−	19.1904i		−	0.985744i	−0.870102	−	0.492872i	$-0.835947\pi$
$379$		−	19.1904i		−	0.985744i	0.870102	−	0.492872i	$-0.164053\pi$
$380$	0.128562	+	0.616040i	0.00659509	+	0.0316022i
$381$		0			0
$382$	2.53936	−	0.969380i	0.129925	−	0.0495978i
$383$	−6.07655	−	5.09883i	−0.310497	−	0.260538i	0.474200	−	0.880417i	$-0.342737\pi$
$383$	−6.07655	−	5.09883i	−0.310497	−	0.260538i	−0.784697	+	0.619879i	$0.787182\pi$
$384$		0			0
$385$	24.7993	+	9.02621i	1.26389	+	0.460018i
$386$	−4.54664	−	7.59870i	−0.231418	−	0.386763i
$387$		0			0
$388$	−6.24010	+	11.6319i	−0.316793	+	0.590518i
$389$	−7.93591	−	9.45764i	−0.402366	−	0.479522i	0.526374	−	0.850253i	$-0.323551\pi$
$389$	−7.93591	−	9.45764i	−0.402366	−	0.479522i	−0.928740	+	0.370732i	$0.879107\pi$
$390$		0			0
$391$	1.11581	+	0.196747i	0.0564289	+	0.00994994i
$392$	0.570440	−	4.44183i	0.0288115	−	0.224346i
$393$		0			0
$394$	14.0070	+	16.1736i	0.705663	+	0.814813i
$395$	2.90676	−	5.03465i	0.146255	−	0.253321i
$396$		0			0
$397$	11.5959	+	20.0847i	0.581982	+	1.00802i	0.995244	+	0.0974099i	$0.0310558\pi$
$397$	11.5959	+	20.0847i	0.581982	+	1.00802i	−0.413263	+	0.910612i	$0.635611\pi$
$398$	−11.9958	+	34.6299i	−0.601294	+	1.73584i
$399$		0			0
$400$	−22.1286	−	16.3290i	−1.10643	−	0.816451i
$401$	−2.32432	−	6.38601i	−0.116071	−	0.318902i	0.868030	−	0.496511i	$-0.165386\pi$
$401$	−2.32432	−	6.38601i	−0.116071	−	0.318902i	−0.984101	+	0.177609i	$0.943164\pi$
$402$		0			0
$403$	−35.5962	+	6.27657i	−1.77317	+	0.312658i
$404$	0.514503	+	16.4825i	0.0255975	+	0.820034i
$405$		0			0
$406$	−2.07632	+	0.0323984i	−0.103046	+	0.00160790i
$407$	2.50442	+	14.2033i	0.124140	+	0.704031i
$408$		0			0
$409$	−17.0717	+	6.21358i	−0.844140	+	0.307242i	−0.727649	−	0.685950i	$-0.759387\pi$
$409$	−17.0717	+	6.21358i	−0.844140	+	0.307242i	−0.116491	+	0.993192i	$0.537165\pi$
$410$	−10.8013	−	8.77989i	−0.533439	−	0.433608i
$411$		0			0
$412$	10.0617	−	30.5810i	0.495702	−	1.50662i
$413$	7.72625	−	4.46075i	0.380184	−	0.219499i
$414$		0			0
$415$	6.44516	+	3.72111i	0.316380	+	0.182662i
$416$	−21.8972	+	21.4957i	−1.07360	+	1.05391i
$417$		0			0
$418$	−0.333292	−	0.0534208i	−0.0163019	−	0.00261290i
$419$	0.854595	−	4.84665i	0.0417497	−	0.236774i	−0.956791	−	0.290776i	$-0.906087\pi$
$419$	0.854595	−	4.84665i	0.0417497	−	0.236774i	0.998541	+	0.0540017i	$0.0171976\pi$
$420$		0			0
$421$	−9.01524	+	7.56468i	−0.439376	+	0.368680i	−0.835476	−	0.549527i	$-0.814808\pi$
$421$	−9.01524	+	7.56468i	−0.439376	+	0.368680i	0.396100	+	0.918207i	$0.370363\pi$
$422$	21.5601	+	12.0032i	1.04953	+	0.584305i
$423$		0			0
$424$	17.5512	−	11.2598i	0.852362	−	0.546826i
$425$	−3.13838	+	8.62264i	−0.152234	+	0.418259i
$426$		0			0
$427$	−4.56659	+	5.44225i	−0.220993	+	0.263369i
$428$	−18.0477	+	7.21416i	−0.872369	+	0.348709i
$429$		0			0
$430$	5.23495	+	27.2002i	0.252452	+	1.31171i
$431$	4.40894			0.212371			0.106186	−	0.994346i	$-0.466136\pi$
$431$	4.40894			0.212371			0.106186	+	0.994346i	$0.466136\pi$
$432$		0			0
$433$	28.5232			1.37074			0.685369	−	0.728196i	$-0.259641\pi$
$433$	28.5232			1.37074			0.685369	+	0.728196i	$0.259641\pi$
$434$	−5.21784	−	27.1113i	−0.250464	−	1.30138i
$435$		0			0
$436$	8.72591	−	3.48798i	0.417895	−	0.167044i
$437$	0.0498260	−	0.0593804i	0.00238350	−	0.00284055i
$438$		0			0
$439$	1.65430	−	4.54515i	0.0789555	−	0.216928i	−0.893934	−	0.448198i	$-0.852066\pi$
$439$	1.65430	−	4.54515i	0.0789555	−	0.216928i	0.972890	+	0.231270i	$0.0742881\pi$
$440$	21.4447	−	13.7576i	1.02233	−	0.655870i
$441$		0			0
$442$	8.94538	+	4.98017i	0.425488	+	0.236883i
$443$	−5.56660	+	4.67093i	−0.264477	+	0.221923i	−0.765376	−	0.643583i	$-0.777447\pi$
$443$	−5.56660	+	4.67093i	−0.264477	+	0.221923i	0.500899	+	0.865506i	$0.333003\pi$
$444$		0			0
$445$	−8.69249	+	49.2976i	−0.412064	+	2.33693i
$446$	−24.6826	−	3.95618i	−1.16875	−	0.187331i
$447$		0			0
$448$	−16.6779	−	16.4675i	−0.787958	−	0.778017i
$449$	5.50442	+	3.17798i	0.259769	+	0.149978i	0.624229	−	0.781241i	$-0.285413\pi$
$449$	5.50442	+	3.17798i	0.259769	+	0.149978i	−0.364460	+	0.931219i	$0.618746\pi$
$450$		0			0
$451$	6.46583	−	3.73305i	0.304464	−	0.175782i
$452$	−0.352828	+	1.07237i	−0.0165957	+	0.0504401i
$453$		0			0
$454$	−10.2382	−	8.32216i	−0.480503	−	0.390578i
$455$	−51.4615	+	18.7305i	−2.41255	+	0.878097i
$456$		0			0
$457$	−0.155269	−	0.880575i	−0.00726318	−	0.0411916i	0.980961	−	0.194206i	$-0.0622130\pi$
$457$	−0.155269	−	0.880575i	−0.00726318	−	0.0411916i	−0.988224	+	0.153014i	$0.951102\pi$
$458$	−23.7801	+	0.371060i	−1.11117	+	0.0173385i
$459$		0			0
$460$	0.182549	+	5.84810i	0.00851140	+	0.272669i
$461$	−12.9026	+	2.27507i	−0.600934	+	0.105961i	−0.465835	−	0.884871i	$-0.654246\pi$
$461$	−12.9026	+	2.27507i	−0.600934	+	0.105961i	−0.135098	+	0.990832i	$0.543135\pi$
$462$		0			0
$463$	0.461244	+	1.26726i	0.0214358	+	0.0588945i	0.949949	−	0.312405i	$-0.101135\pi$
$463$	0.461244	+	1.26726i	0.0214358	+	0.0588945i	−0.928513	+	0.371299i	$0.878912\pi$
$464$	−1.19035	+	1.61312i	−0.0552605	+	0.0748873i
$465$		0			0
$466$	−8.15975	+	23.5559i	−0.377993	+	1.09121i
$467$	−9.81172	−	16.9944i	−0.454032	−	0.786407i	0.544600	−	0.838696i	$-0.316682\pi$
$467$	−9.81172	−	16.9944i	−0.454032	−	0.786407i	−0.998632	+	0.0522890i	$0.983348\pi$
$468$		0			0
$469$	−7.06278	+	12.2331i	−0.326129	+	0.564872i
$470$	−21.0825	−	24.3435i	−0.972463	−	1.12288i
$471$		0			0
$472$	1.09711	−	8.54286i	0.0504987	−	0.393217i
$473$	−14.6315	−	2.57993i	−0.672756	−	0.118625i
$474$		0			0
$475$	0.403527	+	0.480904i	0.0185151	+	0.0220654i
$476$	−3.69693	+	6.89125i	−0.169448	+	0.315860i
$477$		0			0
$478$	−6.69083	−	11.1822i	−0.306031	−	0.511464i
$479$	−17.9117	−	6.51932i	−0.818405	−	0.297875i	−0.101314	−	0.994854i	$-0.532305\pi$
$479$	−17.9117	−	6.51932i	−0.818405	−	0.297875i	−0.717091	+	0.696979i	$0.754527\pi$
$480$		0			0
$481$	−22.9263	−	19.2375i	−1.04535	−	0.877153i
$482$	8.22681	−	3.14052i	0.374721	−	0.143047i
$483$		0			0
$484$	−1.70257	−	8.15833i	−0.0773895	−	0.370833i
$485$			22.7439i			1.03275i
$486$		0			0
$487$		−	12.7440i		−	0.577486i	−0.957407	−	0.288743i	$-0.906763\pi$
$487$		−	12.7440i		−	0.577486i	0.957407	−	0.288743i	$-0.0932373\pi$
$488$	1.50574	+	6.69138i	0.0681618	+	0.302904i
$489$		0			0
$490$	−2.75192	−	7.20884i	−0.124319	−	0.325662i
$491$	−18.9461	−	15.8977i	−0.855027	−	0.717453i	0.105864	−	0.994381i	$-0.466239\pi$
$491$	−18.9461	−	15.8977i	−0.855027	−	0.717453i	−0.960891	+	0.276928i	$0.910684\pi$
$492$		0			0
$493$	0.628570	+	0.228781i	0.0283094	+	0.0103038i
$494$	0.601068	−	0.359646i	0.0270433	−	0.0161812i
$495$		0			0
$496$	−23.8694	−	11.8614i	−1.07177	−	0.532595i
$497$	−22.2948	−	26.5699i	−1.00006	−	1.19182i
$498$		0			0
$499$	−38.9086	−	6.86064i	−1.74179	−	0.307124i	−0.789824	−	0.613334i	$-0.789828\pi$
$499$	−38.9086	−	6.86064i	−1.74179	−	0.307124i	−0.951964	+	0.306209i	$0.900939\pi$
$500$	−12.7921	−	1.84612i	−0.572080	−	0.0825611i
$501$		0			0
$502$	30.3104	−	26.2501i	1.35282	−	1.17160i
$503$	−18.2058	+	31.5334i	−0.811757	+	1.40600i	0.0998757	+	0.995000i	$0.468155\pi$
$503$	−18.2058	+	31.5334i	−0.811757	+	1.40600i	−0.911633	+	0.411005i	$0.865178\pi$
$504$		0			0
$505$	14.2068	+	24.6069i	0.632194	+	1.09499i
$506$	−2.96542	−	1.02722i	−0.131829	−	0.0456655i
$507$		0			0
$508$	13.7588	−	17.4767i	0.610449	−	0.775405i
$509$	1.23919	+	3.40464i	0.0549260	+	0.150908i	0.964121	−	0.265462i	$-0.0855244\pi$
$509$	1.23919	+	3.40464i	0.0549260	+	0.150908i	−0.909195	+	0.416370i	$0.863302\pi$
$510$		0			0
$511$	33.6445	−	5.93244i	1.48835	−	0.262436i
$512$	−22.4047	+	3.16697i	−0.990157	+	0.139961i
$513$		0			0
$514$	−0.364019	−	23.3289i	−0.0160562	−	1.02899i
$515$	−9.63236	−	54.6278i	−0.424452	−	2.40719i
$516$		0			0
$517$	16.2315	−	5.90778i	0.713860	−	0.259824i
$518$	14.4191	−	17.7389i	0.633539	−	0.779402i
$519$		0			0
$520$	−15.7383	+	50.4738i	−0.690172	+	2.21342i
$521$	−18.0443	+	10.4179i	−0.790534	+	0.456415i	−0.840151	−	0.542353i	$-0.817534\pi$
$521$	−18.0443	+	10.4179i	−0.790534	+	0.456415i	0.0496162	+	0.998768i	$0.484200\pi$
$522$		0			0
$523$	19.0780	+	11.0147i	0.834223	+	0.481639i	0.855296	−	0.518139i	$-0.173375\pi$
$523$	19.0780	+	11.0147i	0.834223	+	0.481639i	−0.0210733	+	0.999778i	$0.506708\pi$
$524$	4.62622	−	4.13456i	0.202097	−	0.180619i
$525$		0			0
$526$	−5.42013	+	33.8162i	−0.236329	+	1.47446i
$527$	−1.54433	+	8.75831i	−0.0672719	+	0.381518i
$528$		0			0
$529$	−17.0669	+	14.3209i	−0.742041	+	0.622646i
$530$	17.4771	−	31.3924i	0.759157	−	1.36360i
$531$		0			0
$532$	0.281837	+	0.454771i	0.0122192	+	0.0197168i
$533$	−5.29893	+	14.5587i	−0.229522	+	0.630607i
$534$		0			0
$535$	−21.5263	+	25.6541i	−0.930664	+	1.10912i
$536$	5.25867	+	12.5824i	0.227140	+	0.543479i
$537$		0			0
$538$	16.9363	−	3.25957i	0.730178	−	0.140530i
$539$	4.13879			0.178270
$540$		0			0
$541$	−13.2610			−0.570135			−0.285067	−	0.958507i	$-0.592016\pi$
$541$	−13.2610			−0.570135			−0.285067	+	0.958507i	$0.592016\pi$
$542$	34.7195	−	6.68212i	1.49133	−	0.287022i
$543$		0			0
$544$	3.12725	+	6.87173i	0.134080	+	0.294623i
$545$	10.4078	−	12.4035i	0.445820	−	0.531308i
$546$		0			0
$547$	−4.89178	+	13.4401i	−0.209157	+	0.574655i	−0.999266	−	0.0383119i	$-0.987802\pi$
$547$	−4.89178	+	13.4401i	−0.209157	+	0.574655i	0.790108	+	0.612967i	$0.210024\pi$
$548$	29.3561	−	18.1930i	1.25403	−	0.777167i
$549$		0			0
$550$	12.3631	−	22.2066i	0.527165	−	0.946893i
$551$	0.0350568	−	0.0294161i	0.00149347	−	0.00125317i
$552$		0			0
$553$	0.858252	−	4.86739i	0.0364966	−	0.206982i
$554$	1.95567	−	12.2014i	0.0830887	−	0.518390i
$555$		0			0
$556$	14.9135	+	16.6869i	0.632473	+	0.707683i
$557$	−6.40425	−	3.69750i	−0.271357	−	0.156668i	0.358147	−	0.933665i	$-0.383409\pi$
$557$	−6.40425	−	3.69750i	−0.271357	−	0.156668i	−0.629504	+	0.776997i	$0.716742\pi$
$558$		0			0
$559$	26.6999	−	15.4152i	1.12929	−	0.651994i
$560$	−38.7361	−	11.4184i	−1.63690	−	0.482517i
$561$		0			0
$562$	−19.5246	+	24.0198i	−0.823595	+	1.01322i
$563$	19.9054	−	7.24497i	0.838912	−	0.305339i	0.113401	−	0.993549i	$-0.463826\pi$
$563$	19.9054	−	7.24497i	0.838912	−	0.305339i	0.725511	+	0.688210i	$0.241603\pi$
$564$		0			0
$565$	0.337774	+	1.91561i	0.0142103	+	0.0805905i
$566$	−0.664189	−	42.5660i	−0.0279180	−	1.78918i
$567$		0			0
$568$	−33.4485	+	1.56679i	−1.40347	+	0.0657409i
$569$	−4.38899	+	0.773898i	−0.183996	+	0.0324435i	−0.264887	−	0.964279i	$-0.585335\pi$
$569$	−4.38899	+	0.773898i	−0.183996	+	0.0324435i	0.0808907	+	0.996723i	$0.474224\pi$
$570$		0			0
$571$	−0.735560	−	2.02093i	−0.0307822	−	0.0845734i	0.923350	−	0.383960i	$-0.125440\pi$
$571$	−0.735560	−	2.02093i	−0.0307822	−	0.0845734i	−0.954132	+	0.299387i	$0.903218\pi$
$572$	−22.2819	−	17.5418i	−0.931654	−	0.733458i
$573$		0			0
$574$	−11.1821	−	3.87348i	−0.466733	−	0.161676i
$575$	2.91833	+	5.05470i	0.121703	+	0.210796i
$576$		0			0
$577$	−16.0706	+	27.8351i	−0.669028	+	1.15879i	0.309148	+	0.951014i	$0.399956\pi$
$577$	−16.0706	+	27.8351i	−0.669028	+	1.15879i	−0.978176	+	0.207777i	$0.933377\pi$
$578$	−16.2694	+	14.0900i	−0.676717	+	0.586066i
$579$		0			0
$580$	−0.493400	+	3.41885i	−0.0204873	+	0.141960i
$581$	6.23104	+	1.09870i	0.258507	+	0.0455817i
$582$		0			0
$583$	12.3876	+	14.7629i	0.513041	+	0.611418i
$584$	15.1366	−	29.3038i	0.626356	−	1.21260i
$585$		0			0
$586$	−16.0663	+	9.61316i	−0.663691	+	0.397116i
$587$	−33.8753	−	12.3296i	−1.39818	−	0.508897i	−0.470545	−	0.882376i	$-0.655943\pi$
$587$	−33.8753	−	12.3296i	−1.39818	−	0.508897i	−0.927639	+	0.373478i	$0.878165\pi$
$588$		0			0
$589$	0.466094	+	0.391099i	0.0192051	+	0.0161150i
$590$	−5.29269	−	13.8646i	−0.217897	−	0.570796i
$591$		0			0
$592$	−5.18043	−	21.4529i	−0.212914	−	0.881709i
$593$			4.09387i			0.168115i	0.996461	+	0.0840576i	$0.0267880\pi$
$593$			4.09387i			0.168115i	−0.996461	+	0.0840576i	$0.973212\pi$
$594$		0			0
$595$			13.4745i			0.552402i
$596$	35.7339	−	7.45732i	1.46372	−	0.305464i
$597$		0			0
$598$	6.08410	−	2.32256i	0.248797	−	0.0949763i
$599$	−6.47708	−	5.43491i	−0.264646	−	0.222065i	0.500802	−	0.865562i	$-0.333038\pi$
$599$	−6.47708	−	5.43491i	−0.264646	−	0.222065i	−0.765449	+	0.643497i	$0.777483\pi$
$600$		0			0
$601$	−27.4438	−	9.98874i	−1.11946	−	0.407449i	−0.285003	−	0.958527i	$-0.591995\pi$
$601$	−27.4438	−	9.98874i	−1.11946	−	0.407449i	−0.834454	+	0.551078i	$0.814217\pi$
$602$	12.0913	+	20.2080i	0.492806	+	0.823616i
$603$		0			0
$604$	33.9255	+	18.1999i	1.38041	+	0.740544i
$605$	−9.23034	−	11.0003i	−0.375267	−	0.447225i
$606$		0			0
$607$	38.2139	+	6.73814i	1.55105	+	0.273493i	0.882551	−	0.470217i	$-0.155824\pi$
$607$	38.2139	+	6.73814i	1.55105	+	0.273493i	0.668503	+	0.743710i	$0.266936\pi$
$608$	0.514118	+	0.0497776i	0.0208503	+	0.00201875i
$609$		0			0
$610$	7.73660	+	8.93328i	0.313246	+	0.361698i
$611$	−17.9220	+	31.0417i	−0.725045	+	1.25581i
$612$		0			0
$613$	−0.677216	−	1.17297i	−0.0273525	−	0.0473759i	0.852025	−	0.523501i	$-0.175374\pi$
$613$	−0.677216	−	1.17297i	−0.0273525	−	0.0473759i	−0.879378	+	0.476125i	$0.842041\pi$
$614$	−6.09678	+	17.6004i	−0.246046	+	0.710296i
$615$		0			0
$616$	13.1317	−	17.2265i	0.529092	−	0.694077i
$617$	7.59537	+	20.8681i	0.305778	+	0.840118i	0.993468	+	0.114114i	$0.0364028\pi$
$617$	7.59537	+	20.8681i	0.305778	+	0.840118i	−0.687690	+	0.726005i	$0.741375\pi$
$618$		0			0
$619$	−2.18009	+	0.384409i	−0.0876253	+	0.0154507i	−0.217289	−	0.976107i	$-0.569721\pi$
$619$	−2.18009	+	0.384409i	−0.0876253	+	0.0154507i	0.129664	+	0.991558i	$0.458610\pi$
$620$	−45.9034	+	1.43288i	−1.84353	+	0.0575459i
$621$		0			0
$622$	8.73303	−	0.136268i	0.350163	−	0.00546386i
$623$	7.39009	+	41.9113i	0.296078	+	1.67914i
$624$		0			0
$625$	11.3768	−	4.14082i	0.455072	−	0.165633i
$626$	23.5249	+	19.1223i	0.940245	+	0.764281i
$627$		0			0
$628$	31.9930	+	10.5262i	1.27666	+	0.420043i
$629$	−6.37717	+	3.68186i	−0.254274	+	0.146805i
$630$		0			0
$631$	10.3534	+	5.97752i	0.412161	+	0.237961i	0.691718	−	0.722168i	$-0.256854\pi$
$631$	10.3534	+	5.97752i	0.412161	+	0.237961i	−0.279557	+	0.960129i	$0.590187\pi$
$632$	−3.23478	−	3.50772i	−0.128673	−	0.139530i
$633$		0			0
$634$	−20.5305	−	3.29067i	−0.815370	−	0.130689i
$635$	6.65505	−	37.7427i	0.264098	−	1.49777i
$636$		0			0
$637$	−6.57915	+	5.52056i	−0.260675	+	0.218733i
$638$	−1.61881	−	0.901242i	−0.0640893	−	0.0356805i
$639$		0			0
$640$	−31.4383	+	23.0580i	−1.24271	+	0.911447i
$641$	−4.61107	+	12.6688i	−0.182126	+	0.500388i	−0.996836	−	0.0794805i	$-0.974674\pi$
$641$	−4.61107	+	12.6688i	−0.182126	+	0.500388i	0.814710	+	0.579868i	$0.196896\pi$
$642$		0			0
$643$	17.7513	−	21.1552i	0.700044	−	0.834280i	−0.292487	−	0.956269i	$-0.594483\pi$
$643$	17.7513	−	21.1552i	0.700044	−	0.834280i	0.992531	+	0.121989i	$0.0389273\pi$
$644$	1.84632	+	4.61896i	0.0727553	+	0.182012i
$645$		0			0
$646$	−0.0325714	−	0.169237i	−0.00128150	−	0.00665854i
$647$	−15.2634			−0.600064			−0.300032	−	0.953929i	$-0.596997\pi$
$647$	−15.2634			−0.600064			−0.300032	+	0.953929i	$0.596997\pi$
$648$		0			0
$649$	7.96003			0.312458
$650$	9.96771	+	51.7910i	0.390966	+	2.03141i
$651$		0			0
$652$	−5.95810	−	14.9054i	−0.233337	−	0.583742i
$653$	−19.6661	+	23.4372i	−0.769595	+	0.917167i	−0.998414	−	0.0563018i	$-0.982069\pi$
$653$	−19.6661	+	23.4372i	−0.769595	+	0.917167i	0.228819	+	0.973469i	$0.426514\pi$
$654$		0			0
$655$	3.65641	−	10.0459i	0.142868	−	0.392526i
$656$	−9.51864	+	6.31838i	−0.371641	+	0.246691i
$657$		0			0
$658$	−23.9212	−	13.3177i	−0.932547	−	0.519178i
$659$	32.0036	−	26.8542i	1.24668	−	1.04609i	0.249714	−	0.968320i	$-0.419663\pi$
$659$	32.0036	−	26.8542i	1.24668	−	1.04609i	0.996971	−	0.0777732i	$-0.0247810\pi$
$660$		0			0
$661$	5.68117	−	32.2195i	0.220972	−	1.25319i	−0.649265	−	0.760562i	$-0.724924\pi$
$661$	5.68117	−	32.2195i	0.220972	−	1.25319i	0.870237	−	0.492633i	$-0.163965\pi$
$662$	37.0375	+	5.93646i	1.43950	+	0.230727i
$663$		0			0
$664$	4.49045	−	4.14104i	0.174263	−	0.160703i
$665$	0.798352	+	0.460929i	0.0309588	+	0.0178741i
$666$		0			0
$667$	0.368476	−	0.212740i	0.0142674	−	0.00823731i
$668$	−2.48053	−	0.816136i	−0.0959745	−	0.0315772i
$669$		0			0
$670$	18.2333	+	14.8210i	0.704414	+	0.572585i
$671$	−5.95644	+	2.16797i	−0.229946	+	0.0836935i
$672$		0			0
$673$	4.92417	+	27.9264i	0.189813	+	1.07648i	0.919614	+	0.392823i	$0.128501\pi$
$673$	4.92417	+	27.9264i	0.189813	+	1.07648i	−0.729801	+	0.683659i	$0.760387\pi$
$674$	21.8182	−	0.340446i	0.840407	−	0.0131135i
$675$		0			0
$676$	32.8310	−	1.02482i	1.26273	−	0.0394163i
$677$	39.6598	−	6.99309i	1.52425	−	0.268766i	0.652148	−	0.758092i	$-0.273868\pi$
$677$	39.6598	−	6.99309i	1.52425	−	0.268766i	0.872101	+	0.489326i	$0.162757\pi$
$678$		0			0
$679$	6.61336	+	18.1700i	0.253797	+	0.697302i
$680$	10.3455	+	7.88634i	0.396732	+	0.302427i
$681$		0			0
$682$	8.06294	−	23.2764i	0.308746	−	0.891301i
$683$	−2.35647	−	4.08153i	−0.0901678	−	0.156175i	0.817414	−	0.576051i	$-0.195407\pi$
$683$	−2.35647	−	4.08153i	−0.0901678	−	0.156175i	−0.907582	+	0.419876i	$0.862074\pi$
$684$		0			0
$685$	29.7536	−	51.5348i	1.13683	−	1.96904i
$686$	14.6924	+	16.9650i	0.560958	+	0.647726i
$687$		0			0
$688$	22.5921	+	2.54376i	0.861317	+	0.0969801i
$689$	−39.3834	−	6.94435i	−1.50039	−	0.264559i
$690$		0			0
$691$	−31.2420	−	37.2328i	−1.18850	−	1.41640i	−0.886270	−	0.463169i	$-0.846712\pi$
$691$	−31.2420	−	37.2328i	−1.18850	−	1.41640i	−0.302234	−	0.953234i	$-0.597732\pi$
$692$	−20.1811	−	10.8265i	−0.767169	−	0.411561i
$693$		0			0
$694$	−15.6296	−	26.1214i	−0.593291	−	0.991553i
$695$	36.2358	+	13.1888i	1.37450	+	0.500278i
$696$		0			0
$697$	2.92017	+	2.45031i	0.110609	+	0.0928121i
$698$	16.7016	−	6.37569i	0.632163	−	0.241323i
$699$		0			0
$700$	−39.4358	+	8.22989i	−1.49053	+	0.311061i
$701$		−	5.10945i		−	0.192981i	−0.995334	−	0.0964906i	$-0.969238\pi$
$701$		−	5.10945i		−	0.192981i	0.995334	−	0.0964906i	$-0.0307618\pi$
$702$		0			0
$703$			0.503788i			0.0190007i
$704$	−5.54053	−	20.1646i	−0.208817	−	0.759982i
$705$		0			0
$706$	−5.64335	−	14.7831i	−0.212390	−	0.556371i
$707$	18.5049	+	15.5274i	0.695947	+	0.583969i
$708$		0			0
$709$	8.59158	+	3.12708i	0.322663	+	0.117440i	0.498273	−	0.867020i	$-0.333968\pi$
$709$	8.59158	+	3.12708i	0.322663	+	0.117440i	−0.175610	+	0.984460i	$0.556190\pi$
$710$	−49.5099	+	29.6240i	−1.85807	+	1.11177i
$711$		0			0
$712$	36.5040	+	18.8558i	1.36805	+	0.706650i
$713$	3.63619	+	4.33345i	0.136176	+	0.162289i
$714$		0			0
$715$	−48.1199	−	8.48484i	−1.79958	−	0.317315i
$716$	−6.11714	+	42.3867i	−0.228608	+	1.58406i
$717$		0			0
$718$	−34.5724	+	29.9411i	−1.29023	+	1.11739i
$719$	11.2528	−	19.4904i	0.419658	−	0.726869i	−0.576247	−	0.817276i	$-0.695483\pi$
$719$	11.2528	−	19.4904i	0.419658	−	0.726869i	0.995905	+	0.0904064i	$0.0288166\pi$
$720$		0			0
$721$	−23.5797	−	40.8412i	−0.878153	−	1.52101i
$722$	25.3788	+	8.79118i	0.944500	+	0.327174i
$723$		0			0
$724$	−22.9877	−	18.0974i	−0.854331	−	0.672584i
$725$	1.17854	+	3.23802i	0.0437700	+	0.120257i
$726$		0			0
$727$	−17.2598	+	3.04338i	−0.640132	+	0.112873i	−0.484287	−	0.874909i	$-0.660921\pi$
$727$	−17.2598	+	3.04338i	−0.640132	+	0.112873i	−0.155845	+	0.987782i	$0.549810\pi$
$728$	2.10318	+	44.8997i	0.0779491	+	1.66409i
$729$		0			0
$730$	−0.886643	−	56.8224i	−0.0328161	−	2.10309i
$731$	−1.31725	−	7.47048i	−0.0487201	−	0.276306i
$732$		0			0
$733$	21.1222	−	7.68786i	0.780167	−	0.283958i	0.0789247	−	0.996881i	$-0.474851\pi$
$733$	21.1222	−	7.68786i	0.780167	−	0.283958i	0.701242	+	0.712923i	$0.252629\pi$
$734$	0.594504	−	0.731379i	0.0219435	−	0.0269957i
$735$		0			0
$736$	4.62697	+	1.28580i	0.170552	+	0.0473952i
$737$	−10.9147	+	6.30162i	−0.402049	+	0.232123i
$738$		0			0
$739$	7.76664	+	4.48407i	0.285700	+	0.164949i	0.636001	−	0.771688i	$-0.280587\pi$
$739$	7.76664	+	4.48407i	0.285700	+	0.164949i	−0.350301	+	0.936637i	$0.613921\pi$
$740$	−25.3398	−	28.3531i	−0.931511	−	1.04228i
$741$		0			0
$742$	4.83431	−	30.1612i	0.177473	−	1.10725i
$743$	−8.24486	+	46.7589i	−0.302474	+	1.71542i	0.332686	+	0.943038i	$0.392045\pi$
$743$	−8.24486	+	46.7589i	−0.302474	+	1.71542i	−0.635161	+	0.772380i	$0.719066\pi$
$744$		0			0
$745$	48.1818	−	40.4293i	1.76524	−	1.48122i
$746$	14.3298	−	25.7393i	0.524653	−	0.942381i
$747$		0			0
$748$	−5.93088	+	3.67557i	−0.216854	+	0.134392i
$749$	−9.73778	+	26.7543i	−0.355811	+	0.977582i
$750$		0			0
$751$	8.95708	−	10.6746i	0.326848	−	0.389523i	−0.577448	−	0.816427i	$-0.695951\pi$
$751$	8.95708	−	10.6746i	0.326848	−	0.389523i	0.904297	+	0.426904i	$0.140396\pi$
$752$	−24.2257	+	10.5718i	−0.883419	+	0.385513i
$753$		0			0
$754$	3.77544	−	0.726623i	0.137494	−	0.0264621i
$755$	66.3349			2.41418
$756$		0			0
$757$	12.8098			0.465582			0.232791	−	0.972527i	$-0.425214\pi$
$757$	12.8098			0.465582			0.232791	+	0.972527i	$0.425214\pi$
$758$	−26.6502	+	5.12911i	−0.967980	+	0.186298i
$759$		0			0
$760$	0.821151	−	0.343190i	0.0297863	−	0.0124488i
$761$	19.9205	−	23.7403i	0.722117	−	0.860586i	−0.272718	−	0.962094i	$-0.587922\pi$
$761$	19.9205	−	23.7403i	0.722117	−	0.860586i	0.994835	+	0.101509i	$0.0323669\pi$
$762$		0			0
$763$	4.70813	−	12.9355i	0.170446	−	0.468295i
$764$	−2.02491	−	3.26739i	−0.0732587	−	0.118210i
$765$		0			0
$766$	−5.45678	+	9.80146i	−0.197161	+	0.354141i
$767$	−12.6535	+	10.6176i	−0.456892	+	0.383378i
$768$		0			0
$769$	2.97310	−	16.8613i	0.107213	−	0.608034i	−0.883101	−	0.469184i	$-0.844548\pi$
$769$	2.97310	−	16.8613i	0.107213	−	0.608034i	0.990313	−	0.138850i	$-0.0443406\pi$
$770$	5.90672	−	36.8520i	0.212863	−	1.32805i
$771$		0			0
$772$	−9.33732	+	8.34498i	−0.336057	+	0.300342i
$773$	−37.1476	−	21.4472i	−1.33610	−	0.771401i	−0.349877	−	0.936795i	$-0.613777\pi$
$773$	−37.1476	−	21.4472i	−1.33610	−	0.771401i	−0.986227	+	0.165395i	$0.947110\pi$
$774$		0			0
$775$	−39.6758	+	22.9068i	−1.42520	+	0.822838i
$776$	17.8213	+	5.55690i	0.639747	+	0.199481i
$777$		0			0
$778$	−11.0130	+	13.5486i	−0.394836	+	0.485741i
$779$	0.245070	−	0.0891981i	0.00878053	−	0.00319585i
$780$		0			0
$781$	−5.37381	−	30.4764i	−0.192290	−	1.09053i
$782$	−0.0249994	−	1.60214i	−0.000893978	−	0.0572924i
$783$		0			0
$784$	−6.32095	+	0.395004i	−0.225748	+	0.0141073i
$785$	57.1502	−	10.0771i	2.03978	−	0.359668i
$786$		0			0
$787$	−2.03832	−	5.60024i	−0.0726582	−	0.199627i	0.898047	−	0.439899i	$-0.144986\pi$
$787$	−2.03832	−	5.60024i	−0.0726582	−	0.199627i	−0.970706	+	0.240272i	$0.922763\pi$
$788$	18.7170	−	23.7747i	0.666765	−	0.846939i
$789$		0			0
$790$	−7.76866	−	2.69106i	−0.276397	−	0.0957435i
$791$	0.826860	+	1.43216i	0.0293998	+	0.0509219i
$792$		0			0
$793$	6.57679	−	11.3913i	0.233549	−	0.404518i
$794$	24.7929	−	21.4717i	0.879866	−	0.762002i
$795$		0			0
$796$	51.2977	+	7.40315i	1.81820	+	0.262398i
$797$	40.7435	+	7.18417i	1.44321	+	0.254477i	0.839774	−	0.542936i	$-0.182688\pi$
$797$	40.7435	+	7.18417i	1.44321	+	0.254477i	0.603434	+	0.797413i	$0.293799\pi$
$798$		0			0
$799$	5.66892	+	6.75595i	0.200552	+	0.239008i
$800$	−16.7621	+	35.0949i	−0.592631	+	1.24079i
$801$		0			0
$802$	−8.24720	+	4.93467i	−0.291219	+	0.174249i
$803$	28.6435	+	10.4254i	1.01081	+	0.367903i
$804$		0			0
$805$	6.56566	+	5.50924i	0.231409	+	0.194175i
$806$	18.2304	+	47.7558i	0.642139	+	1.68213i
$807$		0			0
$808$	22.7522	−	5.11986i	0.800419	−	0.180116i
$809$		−	45.8780i		−	1.61298i	−0.591245	−	0.806492i	$-0.701363\pi$
$809$		−	45.8780i		−	1.61298i	0.591245	−	0.806492i	$-0.298637\pi$
$810$		0			0
$811$		−	25.4302i		−	0.892974i	−0.894790	−	0.446487i	$-0.852675\pi$
$811$		−	25.4302i		−	0.892974i	0.894790	−	0.446487i	$-0.147325\pi$
$812$	0.599940	+	2.87478i	0.0210538	+	0.100885i
$813$		0			0
$814$	19.0551	−	7.27414i	0.667882	−	0.254959i
$815$	−21.1874	−	17.7784i	−0.742163	−	0.622749i
$816$		0			0
$817$	−0.487678	−	0.177500i	−0.0170617	−	0.00620994i
$818$	13.1918	+	22.0472i	0.461241	+	0.770861i
$819$		0			0
$820$	−9.30595	+	17.3467i	−0.324978	+	0.605774i
$821$	−5.04053	−	6.00706i	−0.175916	−	0.209648i	0.670881	−	0.741565i	$-0.265916\pi$
$821$	−5.04053	−	6.00706i	−0.175916	−	0.209648i	−0.846796	+	0.531917i	$0.821472\pi$
$822$		0			0
$823$	8.63034	+	1.52176i	0.300835	+	0.0530453i	0.322028	−	0.946730i	$-0.395635\pi$
$823$	8.63034	+	1.52176i	0.300835	+	0.0530453i	−0.0211934	+	0.999775i	$0.506747\pi$
$824$	−45.1578	−	5.79938i	−1.57315	−	0.202031i
$825$		0			0
$826$	−8.25980	−	9.53741i	−0.287395	−	0.331849i
$827$	9.57006	−	16.5758i	0.332784	−	0.576398i	−0.650273	−	0.759701i	$-0.725345\pi$
$827$	9.57006	−	16.5758i	0.332784	−	0.576398i	0.983057	+	0.183303i	$0.0586788\pi$
$828$		0			0
$829$	−0.0258029	−	0.0446919i	−0.000896172	−	0.00155222i	0.865577	−	0.500776i	$-0.166952\pi$
$829$	−0.0258029	−	0.0446919i	−0.000896172	−	0.00155222i	−0.866473	+	0.499224i	$0.833619\pi$
$830$	3.44499	−	9.94513i	0.119577	−	0.345201i
$831$		0			0
$832$	35.7042	+	24.6640i	1.23782	+	0.855071i
$833$	0.722744	+	1.98572i	0.0250416	+	0.0688012i
$834$		0			0
$835$	−4.43105	+	0.781314i	−0.153343	+	0.0270385i
$836$	0.0148937	+	0.477130i	0.000515109	+	0.0165019i
$837$		0			0
$838$	−6.95909	+	0.108588i	−0.240398	+	0.00375111i
$839$	−1.86814	−	10.5948i	−0.0644954	−	0.365771i	−0.999925	−	0.0122581i	$-0.996098\pi$
$839$	−1.86814	−	10.5948i	−0.0644954	−	0.365771i	0.935429	−	0.353513i	$-0.115013\pi$
$840$		0			0
$841$	−27.0150	+	9.83267i	−0.931553	+	0.339058i
$842$	12.9148	+	10.4979i	0.445075	+	0.361780i
$843$		0			0
$844$	10.9067	−	33.1492i	0.375423	−	1.14104i
$845$	49.0137	−	28.2981i	1.68612	−	0.973484i
$846$		0			0
$847$	−10.5727	−	6.10416i	−0.363283	−	0.209741i
$848$	−20.3279	−	21.3644i	−0.698061	−	0.733656i
$849$		0			0
$850$	12.8133	+	2.05375i	0.439493	+	0.0704429i
$851$	−0.813351	+	4.61274i	−0.0278813	+	0.158123i
$852$		0			0
$853$	30.2999	−	25.4247i	1.03745	−	0.870524i	0.0457315	−	0.998954i	$-0.485438\pi$
$853$	30.2999	−	25.4247i	1.03745	−	0.870524i	0.991719	+	0.128430i	$0.0409937\pi$
$854$	8.77834	+	4.88717i	0.300389	+	0.167236i
$855$		0			0
$856$	14.8422	+	23.1352i	0.507296	+	0.790745i
$857$	3.50870	−	9.64007i	0.119855	−	0.329299i	−0.865228	−	0.501378i	$-0.832826\pi$
$857$	3.50870	−	9.64007i	0.119855	−	0.329299i	0.985083	+	0.172080i	$0.0550487\pi$
$858$		0			0
$859$	2.27840	−	2.71529i	0.0777381	−	0.0926446i	−0.725774	−	0.687934i	$-0.758518\pi$
$859$	2.27840	−	2.71529i	0.0777381	−	0.0926446i	0.803512	+	0.595289i	$0.202962\pi$
$860$	36.3745	−	14.5398i	1.24036	−	0.495805i
$861$		0			0
$862$	−1.17840	−	6.12282i	−0.0401365	−	0.208544i
$863$	−6.36151			−0.216548			−0.108274	−	0.994121i	$-0.534532\pi$
$863$	−6.36151			−0.216548			−0.108274	+	0.994121i	$0.534532\pi$
$864$		0			0
$865$	−39.4602			−1.34169
$866$	−7.62354	−	39.6110i	−0.259058	−	1.34604i
$867$		0			0
$868$	−36.2555	+	14.4923i	−1.23059	+	0.491901i
$869$	2.83458	−	3.37812i	0.0961565	−	0.114595i
$870$		0			0
$871$	8.94493	−	24.5760i	0.303087	−	0.832726i
$872$	−7.17607	−	11.1857i	−0.243012	−	0.378794i
$873$		0			0
$874$	−0.0957804	−	0.0533239i	−0.00323982	−	0.00180371i
$875$	−14.5034	+	12.1698i	−0.490304	+	0.411414i
$876$		0			0
$877$	−2.83565	+	16.0818i	−0.0957531	+	0.543043i	0.898761	+	0.438439i	$0.144468\pi$
$877$	−2.83565	+	16.0818i	−0.0957531	+	0.543043i	−0.994514	+	0.104604i	$0.966643\pi$
$878$	−6.75413	−	1.08257i	−0.227941	−	0.0365349i
$879$		0			0
$880$	−24.8372	−	26.1037i	−0.837263	−	0.879956i
$881$	43.1593	+	24.9180i	1.45407	+	0.839509i	0.998709	−	0.0507963i	$-0.0161759\pi$
$881$	43.1593	+	24.9180i	1.45407	+	0.839509i	0.455364	+	0.890306i	$0.349509\pi$
$882$		0			0
$883$	−38.2077	+	22.0592i	−1.28579	+	0.742352i	−0.977901	−	0.209070i	$-0.932956\pi$
$883$	−38.2077	+	22.0592i	−1.28579	+	0.742352i	−0.307890	+	0.951422i	$0.599623\pi$
$884$	4.52523	−	13.7538i	0.152200	−	0.462589i
$885$		0			0
$886$	7.97446	+	6.48207i	0.267907	+	0.217769i
$887$	−2.25857	+	0.822052i	−0.0758353	+	0.0276018i	−0.379659	−	0.925126i	$-0.623959\pi$
$887$	−2.25857	+	0.822052i	−0.0758353	+	0.0276018i	0.303824	+	0.952728i	$0.401737\pi$
$888$		0			0
$889$	−5.65792	−	32.0877i	−0.189761	−	1.07619i
$890$	70.7842	−	1.10450i	2.37269	−	0.0370229i
$891$		0			0
$892$	1.10298	+	35.3348i	0.0369305	+	1.18310i
$893$	0.594202	−	0.104774i	0.0198842	−	0.00350612i
$894$		0			0
$895$	25.2377	+	69.3399i	0.843602	+	2.31778i
$896$	−18.4113	+	27.5625i	−0.615078	+	0.920797i
$897$		0			0
$898$	2.94215	−	8.49353i	0.0981808	−	0.283433i
$899$	1.66986	+	2.89227i	0.0556928	+	0.0964627i
$900$		0			0
$901$	−4.91981	+	8.52136i	−0.163903	+	0.283888i
$902$	−6.91234	−	7.98153i	−0.230156	−	0.265756i
$903$		0			0
$904$	1.58353	+	0.203365i	0.0526676	+	0.00676381i
$905$	−49.6441	−	8.75359i	−1.65023	−	0.290979i
$906$		0			0
$907$	22.5530	+	26.8776i	0.748858	+	0.892455i	0.997089	−	0.0762463i	$-0.0242935\pi$
$907$	22.5530	+	26.8776i	0.748858	+	0.892455i	−0.248231	+	0.968701i	$0.579849\pi$
$908$	−8.82079	+	16.4424i	−0.292728	+	0.545660i
$909$		0			0
$910$	39.7659	+	66.4598i	1.31823	+	2.20312i
$911$	−10.1501	−	3.69433i	−0.336287	−	0.122399i	0.168357	−	0.985726i	$-0.446154\pi$
$911$	−10.1501	−	3.69433i	−0.336287	−	0.122399i	−0.504644	+	0.863328i	$0.668376\pi$
$912$		0			0
$913$	4.32453	+	3.62872i	0.143121	+	0.120093i
$914$	−1.18138	+	0.450982i	−0.0390766	+	0.0149172i
$915$		0			0
$916$	6.87113	+	32.9250i	0.227029	+	1.08787i
$917$		−	9.08884i		−	0.300140i
$918$		0			0
$919$		−	20.9319i		−	0.690481i	−0.938514	−	0.345241i	$-0.887797\pi$
$919$		−	20.9319i		−	0.690481i	0.938514	−	0.345241i	$-0.112203\pi$
$920$	8.07263	−	1.81656i	0.266147	−	0.0598903i
$921$		0			0
$922$	6.60800	+	17.3101i	0.217623	+	0.570078i
$923$	49.1936	+	41.2783i	1.61923	+	1.35869i
$924$		0			0
$925$	−35.6459	−	12.9740i	−1.17203	−	0.426584i
$926$	1.63660	−	0.979249i	0.0537819	−	0.0321801i
$927$		0			0
$928$	2.55834	+	1.22192i	0.0839816	+	0.0401115i
$929$	21.6205	+	25.7663i	0.709345	+	0.845365i	0.993550	−	0.113399i	$-0.0361738\pi$
$929$	21.6205	+	25.7663i	0.709345	+	0.845365i	−0.284204	+	0.958764i	$0.591729\pi$
$930$		0			0
$931$	0.142375	+	0.0251046i	0.00466616	+	0.000822770i
$932$	34.8936	+	5.03576i	1.14298	+	0.164952i
$933$		0			0
$934$	−20.9782	+	18.1680i	−0.686427	+	0.594475i
$935$	−6.01119	+	10.4117i	−0.196587	+	0.340498i
$936$		0			0
$937$	−12.5767	−	21.7834i	−0.410862	−	0.711634i	0.584122	−	0.811666i	$-0.301439\pi$
$937$	−12.5767	−	21.7834i	−0.410862	−	0.711634i	−0.994984	+	0.100032i	$0.968106\pi$
$938$	18.8761	+	6.53868i	0.616328	+	0.213496i
$939$		0			0
$940$	−28.1716	+	35.7842i	−0.918857	+	1.16715i
$941$	−14.1661	−	38.9209i	−0.461801	−	1.26879i	−0.924130	−	0.382078i	$-0.875208\pi$
$941$	−14.1661	−	38.9209i	−0.461801	−	1.26879i	0.462329	−	0.886708i	$-0.347014\pi$
$942$		0			0
$943$	2.38790	−	0.421051i	0.0777606	−	0.0137113i
$944$	−12.1569	+	0.759701i	−0.395675	+	0.0247262i
$945$		0			0
$946$	0.327815	+	21.0087i	0.0106582	+	0.683052i
$947$	9.81759	+	55.6783i	0.319029	+	1.80930i	0.548684	+	0.836030i	$0.315129\pi$
$947$	9.81759	+	55.6783i	0.319029	+	1.80930i	−0.229656	+	0.973272i	$0.573760\pi$
$948$		0			0
$949$	−59.4386	+	21.6339i	−1.92946	+	0.702265i
$950$	0.559992	−	0.688922i	0.0181686	−	0.0223516i
$951$		0			0
$952$	10.5582	+	3.29217i	0.342192	+	0.106700i
$953$	31.8569	−	18.3926i	1.03195	−	0.595795i	0.114405	−	0.993434i	$-0.463504\pi$
$953$	31.8569	−	18.3926i	1.03195	−	0.595795i	0.917542	+	0.397639i	$0.130170\pi$
$954$		0			0
$955$	−5.73591	−	3.31163i	−0.185610	−	0.107162i
$956$	−13.7408	+	12.2805i	−0.444409	+	0.397179i
$957$		0			0
$958$	−4.26621	+	26.6169i	−0.137835	+	0.859953i
$959$	8.78509	−	49.8227i	0.283685	−	1.60886i
$960$		0			0
$961$	−10.2671	+	8.61511i	−0.331196	+	0.277907i
$962$	−20.5880	+	36.9801i	−0.663783	+	1.19229i
$963$		0			0
$964$	−6.56014	−	10.5854i	−0.211288	−	0.340933i
$965$	−7.37989	+	20.2761i	−0.237567	+	0.652711i
$966$		0			0
$967$	28.9550	−	34.5072i	0.931129	−	1.10968i	−0.0626196	−	0.998037i	$-0.519945\pi$
$967$	28.9550	−	34.5072i	0.931129	−	1.10968i	0.993749	−	0.111639i	$-0.0356101\pi$
$968$	−10.8746	+	4.54492i	−0.349524	+	0.146079i
$969$		0			0
$970$	31.5850	−	6.07887i	1.01413	−	0.195181i
$971$	−40.1053			−1.28704			−0.643520	−	0.765429i	$-0.722527\pi$
$971$	−40.1053			−1.28704			−0.643520	+	0.765429i	$0.722527\pi$
$972$		0			0
$973$	32.7837			1.05100
$974$	−17.6980	+	3.40615i	−0.567079	+	0.109140i
$975$		0			0
$976$	8.89005	−	3.87950i	0.284564	−	0.124180i
$977$	−23.6105	+	28.1379i	−0.755368	+	0.900213i	−0.997546	−	0.0700194i	$-0.977694\pi$
$977$	−23.6105	+	28.1379i	−0.755368	+	0.900213i	0.242178	+	0.970232i	$0.422138\pi$
$978$		0			0
$979$	−12.9870	+	35.6814i	−0.415066	+	1.14038i
$980$	−9.27559	+	5.74840i	−0.296298	+	0.183626i
$981$		0			0
$982$	−17.0137	+	30.5601i	−0.542930	+	0.975211i
$983$	−14.5073	+	12.1730i	−0.462710	+	0.388259i	−0.844127	−	0.536144i	$-0.819881\pi$
$983$	−14.5073	+	12.1730i	−0.462710	+	0.388259i	0.381417	+	0.924403i	$0.375436\pi$
$984$		0			0
$985$	9.05328	−	51.3437i	0.288462	−	1.63595i
$986$	0.149713	−	0.934060i	0.00476784	−	0.0297465i
$987$		0			0
$988$	−0.660101	−	0.738596i	−0.0210006	−	0.0234979i
$989$	−4.17867	−	2.41256i	−0.132874	−	0.0767148i
$990$		0			0
$991$	−30.3997	+	17.5513i	−0.965680	+	0.557535i	−0.897916	−	0.440166i	$-0.854920\pi$
$991$	−30.3997	+	17.5513i	−0.965680	+	0.557535i	−0.0677633	+	0.997701i	$0.521586\pi$
$992$	−10.0926	+	36.3184i	−0.320441	+	1.15311i
$993$		0			0
$994$	−30.9395	+	38.0628i	−0.981340	+	1.20728i
$995$	83.9173	−	30.5434i	2.66036	−	0.968291i
$996$		0			0
$997$	4.16898	+	23.6435i	0.132033	+	0.748796i	0.976880	+	0.213788i	$0.0685803\pi$
$997$	4.16898	+	23.6435i	0.132033	+	0.748796i	−0.844847	+	0.535008i	$0.820309\pi$
$998$	0.871737	+	55.8671i	0.0275944	+	1.76844i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.b.215.8		96
3.2	odd	2		972.2.l.c.215.9		96
4.3	odd	2	inner	972.2.l.b.215.10		96
9.2	odd	6		972.2.l.d.863.13		96
9.4	even	3		324.2.l.a.179.15		96
9.5	odd	6		108.2.l.a.23.2	✓	96
9.7	even	3		972.2.l.a.863.4		96
12.11	even	2		972.2.l.c.215.7		96
27.2	odd	18	inner	972.2.l.b.755.10		96
27.7	even	9		972.2.l.d.107.5		96
27.11	odd	18		324.2.l.a.143.2		96
27.16	even	9		108.2.l.a.47.15	yes	96
27.20	odd	18		972.2.l.a.107.12		96
27.25	even	9		972.2.l.c.755.7		96
36.7	odd	6		972.2.l.a.863.12		96
36.11	even	6		972.2.l.d.863.5		96
36.23	even	6		108.2.l.a.23.15	yes	96
36.31	odd	6		324.2.l.a.179.2		96
108.7	odd	18		972.2.l.d.107.13		96
108.11	even	18		324.2.l.a.143.15		96
108.43	odd	18		108.2.l.a.47.2	yes	96
108.47	even	18		972.2.l.a.107.4		96
108.79	odd	18		972.2.l.c.755.9		96
108.83	even	18	inner	972.2.l.b.755.8		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.2	✓	96	9.5	odd	6
108.2.l.a.23.15	yes	96	36.23	even	6
108.2.l.a.47.2	yes	96	108.43	odd	18
108.2.l.a.47.15	yes	96	27.16	even	9
324.2.l.a.143.2		96	27.11	odd	18
324.2.l.a.143.15		96	108.11	even	18
324.2.l.a.179.2		96	36.31	odd	6
324.2.l.a.179.15		96	9.4	even	3
972.2.l.a.107.4		96	108.47	even	18
972.2.l.a.107.12		96	27.20	odd	18
972.2.l.a.863.4		96	9.7	even	3
972.2.l.a.863.12		96	36.7	odd	6
972.2.l.b.215.8		96	1.1	even	1	trivial
972.2.l.b.215.10		96	4.3	odd	2	inner
972.2.l.b.755.8		96	108.83	even	18	inner
972.2.l.b.755.10		96	27.2	odd	18	inner
972.2.l.c.215.7		96	12.11	even	2
972.2.l.c.215.9		96	3.2	odd	2
972.2.l.c.755.7		96	27.25	even	9
972.2.l.c.755.9		96	108.79	odd	18
972.2.l.d.107.5		96	27.7	even	9
972.2.l.d.107.13		96	108.7	odd	18
972.2.l.d.863.5		96	36.11	even	6
972.2.l.d.863.13		96	9.2	odd	6

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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.267275 - 1.38873i) q^{2} +(-1.85713 + 0.742344i) q^{4} +(-2.21508 + 2.63983i) q^{5} +(-1.00203 + 2.75305i) q^{7} +(1.52728 + 2.38064i) q^{8} +(4.25804 + 2.37058i) q^{10} +(-2.00243 + 1.68024i) q^{11} +(0.941927 - 5.34193i) q^{13} +(4.09105 + 0.655722i) q^{14} +(2.89785 - 2.75726i) q^{16} +(-1.15583 - 0.667320i) q^{17} +(-0.0790760 + 0.0456546i) q^{19} +(2.15403 - 6.54685i) q^{20} +(2.86860 + 2.33175i) q^{22} +(-0.797738 + 0.290353i) q^{23} +(-1.19388 - 6.77083i) q^{25} +(-7.67024 + 0.119685i) q^{26} +(-0.182815 - 5.85661i) q^{28} +(-0.493578 + 0.0870310i) q^{29} +(-2.27906 - 6.26168i) q^{31} +(-4.60360 - 3.28738i) q^{32} +(-0.617801 + 1.78349i) q^{34} +(-5.04800 - 8.74340i) q^{35} +(2.75869 - 4.77819i) q^{37} +(0.0845368 + 0.0976128i) q^{38} +(-9.66751 - 1.24155i) q^{40} +(-2.81281 - 0.495975i) q^{41} +(3.65343 + 4.35398i) q^{43} +(2.47146 - 4.60692i) q^{44} +(0.616436 + 1.03024i) q^{46} +(-6.20947 - 2.26006i) q^{47} +(-1.21289 - 1.01774i) q^{49} +(-9.08374 + 3.46765i) q^{50} +(2.21627 + 10.6199i) q^{52} -7.37249i q^{53} -9.00795i q^{55} +(-8.08437 + 1.81920i) q^{56} +(0.252783 + 0.662184i) q^{58} +(-2.33273 - 1.95739i) q^{59} +(2.27868 + 0.829371i) q^{61} +(-8.08663 + 4.83859i) q^{62} +(-3.33485 + 7.27178i) q^{64} +(12.0154 + 14.3193i) q^{65} +(4.74821 + 0.837237i) q^{67} +(2.64191 + 0.381274i) q^{68} +(-10.7930 + 9.34719i) q^{70} +(-5.91940 + 10.2527i) q^{71} +(-5.83049 - 10.0987i) q^{73} +(-7.37294 - 2.55398i) q^{74} +(0.112963 - 0.143488i) q^{76} +(-2.61929 - 7.19644i) q^{77} +(-1.66138 + 0.292946i) q^{79} +(0.859714 + 13.7574i) q^{80} +(0.0630204 + 4.03879i) q^{82} +(-0.375017 - 2.12683i) q^{83} +(4.32187 - 1.57303i) q^{85} +(5.07003 - 6.23732i) q^{86} +(-7.05831 - 2.20087i) q^{88} +(12.5801 - 7.26310i) q^{89} +(13.7628 + 7.94593i) q^{91} +(1.26596 - 1.13142i) q^{92} +(-1.47897 + 9.22731i) q^{94} +(0.0546395 - 0.309876i) q^{95} +(5.05588 - 4.24238i) q^{97} +(-1.08919 + 1.95639i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

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