LMFDB - Embedded newform 243.2.e.b.55.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(28,243)] 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("243.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-3,0,3,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.2
Root			$0.500000 - 2.22827i$ of defining polynomial
Character	$\chi$	$=$	243.55
Dual form			243.2.e.b.190.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.390411 + 0.142098i) q^{2} +(-1.39986 + 1.17462i) q^{4} +(-0.384663 - 2.18153i) q^{5} +(-1.01089 - 0.848241i) q^{7} +(0.795075 - 1.37711i) q^{8} +(0.460168 + 0.797034i) q^{10} +(0.905608 - 5.13596i) q^{11} +(0.0169695 + 0.00617638i) q^{13} +(0.515197 + 0.187516i) q^{14} +(0.519924 - 2.94863i) q^{16} +(-1.56640 - 2.71308i) q^{17} +(-0.208676 + 0.361438i) q^{19} +(3.10095 + 2.60201i) q^{20} +(0.376249 + 2.13382i) q^{22} +(0.792386 - 0.664891i) q^{23} +(0.0873421 - 0.0317899i) q^{25} -0.00750270 q^{26} +2.41147 q^{28} +(-7.33639 + 2.67023i) q^{29} +(2.85709 - 2.39738i) q^{31} +(0.768264 + 4.35704i) q^{32} +(0.997061 + 0.836633i) q^{34} +(-1.46161 + 2.53159i) q^{35} +(-2.21238 - 3.83195i) q^{37} +(0.0301099 - 0.170762i) q^{38} +(-3.31005 - 1.20476i) q^{40} +(-3.45331 - 1.25690i) q^{41} +(-1.44265 + 8.18166i) q^{43} +(4.76508 + 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(5.43731 + 4.56245i) q^{47} +(-0.913143 - 5.17869i) q^{49} +(-0.0295820 + 0.0248222i) q^{50} +(-0.0310098 + 0.0112866i) q^{52} +1.30057 q^{53} -11.5526 q^{55} +(-1.97186 + 0.717698i) q^{56} +(2.48477 - 2.08497i) q^{58} +(0.642813 + 3.64557i) q^{59} +(5.29661 + 4.44439i) q^{61} +(-0.774775 + 1.34195i) q^{62} +(2.07506 + 3.59410i) q^{64} +(0.00694645 - 0.0393953i) q^{65} +(10.3618 + 3.77139i) q^{67} +(5.37958 + 1.95801i) q^{68} +(0.210896 - 1.19605i) q^{70} +(-3.04214 - 5.26914i) q^{71} +(0.273486 - 0.473692i) q^{73} +(1.40825 + 1.18166i) q^{74} +(-0.132435 - 0.751078i) q^{76} +(-5.27200 + 4.42374i) q^{77} +(-0.459645 + 0.167297i) q^{79} -6.63254 q^{80} +1.52681 q^{82} +(4.33543 - 1.57797i) q^{83} +(-5.31614 + 4.46077i) q^{85} +(-0.599371 - 3.39920i) q^{86} +(-6.35275 - 5.33059i) q^{88} +(-1.68653 + 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(-0.328234 + 1.86151i) q^{92} +(-2.77110 - 1.00860i) q^{94} +(0.868758 + 0.316202i) q^{95} +(1.72630 - 9.79033i) q^{97} +(1.09238 + 1.89206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28}+ \cdots + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.390411	+	0.142098i	−0.276062	+	0.100478i	−0.476341	−	0.879261i	$-0.658037\pi$
$2$	−0.390411	+	0.142098i	−0.276062	+	0.100478i	0.200279	+	0.979739i	$0.435815\pi$
$3$		0			0
$3$		0			0
$4$	−1.39986	+	1.17462i	−0.699930	+	0.587311i
$5$	−0.384663	−	2.18153i	−0.172027	−	0.975611i	−0.941520	−	0.336957i	$-0.890602\pi$
$5$	−0.384663	−	2.18153i	−0.172027	−	0.975611i	0.769494	−	0.638655i	$-0.220509\pi$
$6$		0			0
$7$	−1.01089	−	0.848241i	−0.382082	−	0.320605i	0.431437	−	0.902143i	$-0.358007\pi$
$7$	−1.01089	−	0.848241i	−0.382082	−	0.320605i	−0.813519	+	0.581538i	$0.802451\pi$
$8$	0.795075	−	1.37711i	0.281102	−	0.486882i
$9$		0			0
$10$	0.460168	+	0.797034i	0.145518	+	0.252044i
$11$	0.905608	−	5.13596i	0.273051	−	1.54855i	−0.472034	−	0.881580i	$-0.656480\pi$
$11$	0.905608	−	5.13596i	0.273051	−	1.54855i	0.745085	−	0.666969i	$-0.232409\pi$
$12$		0			0
$13$	0.0169695	+	0.00617638i	0.00470648	+	0.00171302i	0.344372	−	0.938833i	$-0.388092\pi$
$13$	0.0169695	+	0.00617638i	0.00470648	+	0.00171302i	−0.339666	+	0.940546i	$0.610314\pi$
$14$	0.515197	+	0.187516i	0.137692	+	0.0501159i
$15$		0			0
$16$	0.519924	−	2.94863i	0.129981	−	0.737159i
$17$	−1.56640	−	2.71308i	−0.379907	−	0.658019i	0.611141	−	0.791522i	$-0.290711\pi$
$17$	−1.56640	−	2.71308i	−0.379907	−	0.658019i	−0.991048	+	0.133503i	$0.957377\pi$
$18$		0			0
$19$	−0.208676	+	0.361438i	−0.0478736	+	0.0829195i	−0.888969	−	0.457967i	$-0.848578\pi$
$19$	−0.208676	+	0.361438i	−0.0478736	+	0.0829195i	0.841096	+	0.540886i	$0.181911\pi$
$20$	3.10095	+	2.60201i	0.693394	+	0.581827i
$21$		0			0
$22$	0.376249	+	2.13382i	0.0802166	+	0.454931i
$23$	0.792386	−	0.664891i	0.165224	−	0.138639i	−0.556427	−	0.830897i	$-0.687828\pi$
$23$	0.792386	−	0.664891i	0.165224	−	0.138639i	0.721651	+	0.692257i	$0.243384\pi$
$24$		0			0
$25$	0.0873421	−	0.0317899i	0.0174684	−	0.00635798i
$26$	−0.00750270			−0.00147140
$27$		0			0
$28$	2.41147			0.455726
$29$	−7.33639	+	2.67023i	−1.36233	+	0.495849i	−0.916775	−	0.399404i	$-0.869217\pi$
$29$	−7.33639	+	2.67023i	−1.36233	+	0.495849i	−0.445558	+	0.895253i	$0.646995\pi$
$30$		0			0
$31$	2.85709	−	2.39738i	0.513148	−	0.430583i	−0.349087	−	0.937090i	$-0.613508\pi$
$31$	2.85709	−	2.39738i	0.513148	−	0.430583i	0.862235	+	0.506508i	$0.169064\pi$
$32$	0.768264	+	4.35704i	0.135811	+	0.770224i
$33$		0			0
$34$	0.997061	+	0.836633i	0.170995	+	0.143481i
$35$	−1.46161	+	2.53159i	−0.247058	+	0.427916i
$36$		0			0
$37$	−2.21238	−	3.83195i	−0.363713	−	0.629969i	0.624856	−	0.780740i	$-0.285158\pi$
$37$	−2.21238	−	3.83195i	−0.363713	−	0.629969i	−0.988569	+	0.150771i	$0.951824\pi$
$38$	0.0301099	−	0.170762i	0.00488446	−	0.0277012i
$39$		0			0
$40$	−3.31005	−	1.20476i	−0.523365	−	0.190489i
$41$	−3.45331	−	1.25690i	−0.539317	−	0.196295i	0.0579766	−	0.998318i	$-0.481535\pi$
$41$	−3.45331	−	1.25690i	−0.539317	−	0.196295i	−0.597294	+	0.802023i	$0.703757\pi$
$42$		0			0
$43$	−1.44265	+	8.18166i	−0.220002	+	1.24769i	0.652012	+	0.758209i	$0.273925\pi$
$43$	−1.44265	+	8.18166i	−0.220002	+	1.24769i	−0.872013	+	0.489482i	$0.837186\pi$
$44$	4.76508	+	8.25337i	0.718363	+	1.24424i
$45$		0			0
$46$	−0.214876	+	0.372177i	−0.0316818	+	0.0548745i
$47$	5.43731	+	4.56245i	0.793114	+	0.665501i	0.946514	−	0.322663i	$-0.104578\pi$
$47$	5.43731	+	4.56245i	0.793114	+	0.665501i	−0.153400	+	0.988164i	$0.549022\pi$
$48$		0			0
$49$	−0.913143	−	5.17869i	−0.130449	−	0.739813i
$50$	−0.0295820	+	0.0248222i	−0.00418353	+	0.00351039i
$51$		0			0
$52$	−0.0310098	+	0.0112866i	−0.00430028	+	0.00156517i
$53$	1.30057			0.178648			0.0893238	−	0.996003i	$-0.471529\pi$
$53$	1.30057			0.178648			0.0893238	+	0.996003i	$0.471529\pi$
$54$		0			0
$55$	−11.5526			−1.55775
$56$	−1.97186	+	0.717698i	−0.263501	+	0.0959064i
$57$		0			0
$58$	2.48477	−	2.08497i	0.326266	−	0.273770i
$59$	0.642813	+	3.64557i	0.0836871	+	0.474613i	0.997632	+	0.0687752i	$0.0219091\pi$
$59$	0.642813	+	3.64557i	0.0836871	+	0.474613i	−0.913945	+	0.405838i	$0.866980\pi$
$60$		0			0
$61$	5.29661	+	4.44439i	0.678162	+	0.569045i	0.915469	−	0.402389i	$-0.131820\pi$
$61$	5.29661	+	4.44439i	0.678162	+	0.569045i	−0.237307	+	0.971435i	$0.576265\pi$
$62$	−0.774775	+	1.34195i	−0.0983965	+	0.170428i
$63$		0			0
$64$	2.07506	+	3.59410i	0.259382	+	0.449263i
$65$	0.00694645	−	0.0393953i	0.000861601	−	0.00488638i
$66$		0			0
$67$	10.3618	+	3.77139i	1.26590	+	0.460748i	0.885743	−	0.464176i	$-0.153649\pi$
$67$	10.3618	+	3.77139i	1.26590	+	0.460748i	0.380152	+	0.924924i	$0.375872\pi$
$68$	5.37958	+	1.95801i	0.652370	+	0.237443i
$69$		0			0
$70$	0.210896	−	1.19605i	0.0252069	−	0.142955i
$71$	−3.04214	−	5.26914i	−0.361035	−	0.625332i	0.627096	−	0.778942i	$-0.284243\pi$
$71$	−3.04214	−	5.26914i	−0.361035	−	0.625332i	−0.988132	+	0.153610i	$0.950910\pi$
$72$		0			0
$73$	0.273486	−	0.473692i	0.0320092	−	0.0554415i	−0.849577	−	0.527465i	$-0.823143\pi$
$73$	0.273486	−	0.473692i	0.0320092	−	0.0554415i	0.881586	+	0.472023i	$0.156476\pi$
$74$	1.40825	+	1.18166i	0.163705	+	0.137365i
$75$		0			0
$76$	−0.132435	−	0.751078i	−0.0151914	−	0.0861545i
$77$	−5.27200	+	4.42374i	−0.600801	+	0.504132i
$78$		0			0
$79$	−0.459645	+	0.167297i	−0.0517141	+	0.0188224i	−0.367748	−	0.929926i	$-0.619871\pi$
$79$	−0.459645	+	0.167297i	−0.0517141	+	0.0188224i	0.316034	+	0.948748i	$0.397649\pi$
$80$	−6.63254			−0.741540
$81$		0			0
$82$	1.52681			0.168608
$83$	4.33543	−	1.57797i	0.475875	−	0.173205i	−0.0929366	−	0.995672i	$-0.529625\pi$
$83$	4.33543	−	1.57797i	0.475875	−	0.173205i	0.568812	+	0.822468i	$0.307403\pi$
$84$		0			0
$85$	−5.31614	+	4.46077i	−0.576616	+	0.483838i
$86$	−0.599371	−	3.39920i	−0.0646318	−	0.366545i
$87$		0			0
$88$	−6.35275	−	5.33059i	−0.677206	−	0.568243i
$89$	−1.68653	+	2.92116i	−0.178772	+	0.309642i	−0.941460	−	0.337124i	$-0.890546\pi$
$89$	−1.68653	+	2.92116i	−0.178772	+	0.309642i	0.762688	+	0.646766i	$0.223879\pi$
$90$		0			0
$91$	−0.0119153	−	0.0206379i	−0.00124906	−	0.00216344i
$92$	−0.328234	+	1.86151i	−0.0342208	+	0.194076i
$93$		0			0
$94$	−2.77110	−	1.00860i	−0.285817	−	0.104029i
$95$	0.868758	+	0.316202i	0.0891327	+	0.0324417i
$96$		0			0
$97$	1.72630	−	9.79033i	0.175279	−	0.994057i	−0.762542	−	0.646939i	$-0.776049\pi$
$97$	1.72630	−	9.79033i	0.175279	−	0.994057i	0.937821	−	0.347119i	$-0.112840\pi$
$98$	1.09238	+	1.89206i	0.110347	+	0.191127i
$99$		0			0
$100$	−0.0849256	+	0.147095i	−0.00849256	+	0.0147095i
$101$	−10.5710	−	8.87014i	−1.05186	−	0.882612i	−0.0585685	−	0.998283i	$-0.518654\pi$
$101$	−10.5710	−	8.87014i	−1.05186	−	0.882612i	−0.993288	+	0.115671i	$0.963098\pi$
$102$		0			0
$103$	0.792725	+	4.49576i	0.0781095	+	0.442981i	0.998632	+	0.0522911i	$0.0166524\pi$
$103$	0.792725	+	4.49576i	0.0781095	+	0.442981i	−0.920522	+	0.390690i	$0.872237\pi$
$104$	0.0219975	−	0.0184581i	0.00215704	−	0.00180997i
$105$		0			0
$106$	−0.507758	+	0.184809i	−0.0493178	+	0.0179502i
$107$	11.2965			1.09207			0.546035	−	0.837762i	$-0.316136\pi$
$107$	11.2965			1.09207			0.546035	+	0.837762i	$0.316136\pi$
$108$		0			0
$109$	14.5032			1.38915			0.694577	−	0.719419i	$-0.255592\pi$
$109$	14.5032			1.38915			0.694577	+	0.719419i	$0.255592\pi$
$110$	4.51026	−	1.64160i	0.430037	−	0.156521i
$111$		0			0
$112$	−3.02674	+	2.53974i	−0.286000	+	0.239983i
$113$	−2.18075	−	12.3676i	−0.205148	−	1.16345i	−0.897207	−	0.441609i	$-0.854408\pi$
$113$	−2.18075	−	12.3676i	−0.205148	−	1.16345i	0.692060	−	0.721840i	$-0.256703\pi$
$114$		0			0
$115$	−1.75528	−	1.47286i	−0.163681	−	0.137345i
$116$	7.13341	−	12.3554i	0.662321	−	1.14717i
$117$		0			0
$118$	−0.768989	−	1.33193i	−0.0707912	−	0.122614i
$119$	−0.717884	+	4.07132i	−0.0658083	+	0.373217i
$120$		0			0
$121$	−15.2213	−	5.54010i	−1.38375	−	0.503646i
$122$	−2.69939	−	0.982498i	−0.244391	−	0.0889512i
$123$		0			0
$124$	−1.18351	+	6.71200i	−0.106282	+	0.602755i
$125$	−5.64092	−	9.77035i	−0.504539	−	0.873887i
$126$		0			0
$127$	4.19749	−	7.27027i	0.372467	−	0.645132i	−0.617477	−	0.786589i	$-0.711845\pi$
$127$	4.19749	−	7.27027i	0.372467	−	0.645132i	0.989944	+	0.141456i	$0.0451785\pi$
$128$	−8.09919	−	6.79603i	−0.715874	−	0.600690i
$129$		0			0
$130$	0.00288601	+	0.0163674i	0.000253120	+	0.00143552i
$131$	11.9004	−	9.98564i	1.03974	−	0.872449i	0.0477666	−	0.998859i	$-0.484790\pi$
$131$	11.9004	−	9.98564i	1.03974	−	0.872449i	0.991978	+	0.126409i	$0.0403452\pi$
$132$		0			0
$133$	0.517536	−	0.188368i	0.0448761	−	0.0163335i
$134$	−4.58126			−0.395761
$135$		0			0
$136$	−4.98162			−0.427170
$137$	11.2833	−	4.10677i	0.963994	−	0.350865i	0.188396	−	0.982093i	$-0.439671\pi$
$137$	11.2833	−	4.10677i	0.963994	−	0.350865i	0.775597	+	0.631228i	$0.217449\pi$
$138$		0			0
$139$	4.70743	−	3.95001i	0.399279	−	0.335035i	−0.420936	−	0.907090i	$-0.638298\pi$
$139$	4.70743	−	3.95001i	0.399279	−	0.335035i	0.820215	+	0.572055i	$0.193854\pi$
$140$	−0.927605	−	5.26071i	−0.0783970	−	0.444611i
$141$		0			0
$142$	1.93642	+	1.62485i	0.162500	+	0.136354i
$143$	0.0470893	−	0.0815610i	0.00393780	−	0.00682047i
$144$		0			0
$145$	8.64723	+	14.9774i	0.718113	+	1.24381i
$146$	−0.0394613	+	0.223796i	−0.00326584	+	0.0185215i
$147$		0			0
$148$	7.59812	+	2.76549i	0.624561	+	0.227322i
$149$	0.829580	+	0.301942i	0.0679618	+	0.0247361i	0.375777	−	0.926710i	$-0.377376\pi$
$149$	0.829580	+	0.301942i	0.0679618	+	0.0247361i	−0.307816	+	0.951446i	$0.599598\pi$
$150$		0			0
$151$	1.42834	−	8.10051i	0.116237	−	0.659210i	−0.869894	−	0.493239i	$-0.835813\pi$
$151$	1.42834	−	8.10051i	0.116237	−	0.659210i	0.986131	−	0.165971i	$-0.0530760\pi$
$152$	0.331826	+	0.574740i	0.0269147	+	0.0466176i
$153$		0			0
$154$	1.42964	−	2.47621i	0.115204	−	0.199539i
$155$	−6.32899	−	5.31065i	−0.508356	−	0.426562i
$156$		0			0
$157$	2.18099	+	12.3690i	0.174062	+	0.987155i	0.939221	+	0.343313i	$0.111549\pi$
$157$	2.18099	+	12.3690i	0.174062	+	0.987155i	−0.765159	+	0.643841i	$0.777340\pi$
$158$	0.155678	−	0.130629i	0.0123851	−	0.0103923i
$159$		0			0
$160$	9.20951	−	3.35199i	0.728076	−	0.264998i
$161$	−1.36501			−0.107578
$162$		0			0
$163$	3.31466			0.259624			0.129812	−	0.991539i	$-0.458563\pi$
$163$	3.31466			0.259624			0.129812	+	0.991539i	$0.458563\pi$
$164$	6.31054	−	2.29685i	0.492771	−	0.179354i
$165$		0			0
$166$	−1.46837	+	1.23211i	−0.113968	+	0.0956303i
$167$	3.57072	+	20.2506i	0.276311	+	1.56704i	0.734767	+	0.678320i	$0.237292\pi$
$167$	3.57072	+	20.2506i	0.276311	+	1.56704i	−0.458456	+	0.888717i	$0.651597\pi$
$168$		0			0
$169$	−9.95833	−	8.35603i	−0.766025	−	0.642771i
$170$	1.44161	−	2.49694i	0.110567	−	0.191507i
$171$		0			0
$172$	−7.59085	−	13.1477i	−0.578797	−	1.00251i
$173$	−2.43685	+	13.8201i	−0.185270	+	1.05072i	0.740337	+	0.672236i	$0.234666\pi$
$173$	−2.43685	+	13.8201i	−0.185270	+	1.05072i	−0.925608	+	0.378485i	$0.876445\pi$
$174$		0			0
$175$	−0.115259	−	0.0419509i	−0.00871277	−	0.00317119i
$176$	−14.6732	−	5.34061i	−1.10603	−	0.402564i
$177$		0			0
$178$	0.243350	−	1.38010i	0.0182398	−	0.103443i
$179$	5.09500	+	8.82479i	0.380818	+	0.659596i	0.991179	−	0.132527i	$-0.0423091\pi$
$179$	5.09500	+	8.82479i	0.380818	+	0.659596i	−0.610361	+	0.792123i	$0.708976\pi$
$180$		0			0
$181$	−12.0274	+	20.8320i	−0.893987	+	1.54843i	−0.0589331	+	0.998262i	$0.518770\pi$
$181$	−12.0274	+	20.8320i	−0.893987	+	1.54843i	−0.835054	+	0.550169i	$0.814563\pi$
$182$	0.00758444	+	0.00636410i	0.000562196	+	0.000471739i
$183$		0			0
$184$	−0.285622	−	1.61984i	−0.0210563	−	0.119416i
$185$	−7.50851	+	6.30039i	−0.552037	+	0.463214i
$186$		0			0
$187$	−15.3528	+	5.58796i	−1.12271	+	0.408632i
$188$	−12.9706			−0.945981
$189$		0			0
$190$	−0.384104			−0.0278658
$191$	10.2862	−	3.74388i	0.744285	−	0.270898i	0.0580861	−	0.998312i	$-0.481500\pi$
$191$	10.2862	−	3.74388i	0.744285	−	0.270898i	0.686199	+	0.727414i	$0.259278\pi$
$192$		0			0
$193$	−8.27785	+	6.94594i	−0.595853	+	0.499980i	−0.890110	−	0.455747i	$-0.849372\pi$
$193$	−8.27785	+	6.94594i	−0.595853	+	0.499980i	0.294257	+	0.955726i	$0.404928\pi$
$194$	0.717219	+	4.06755i	0.0514933	+	0.292033i
$195$		0			0
$196$	7.36128	+	6.17684i	0.525805	+	0.441203i
$197$	−11.0367	+	19.1161i	−0.786331	+	1.36196i	0.141870	+	0.989885i	$0.454689\pi$
$197$	−11.0367	+	19.1161i	−0.786331	+	1.36196i	−0.928201	+	0.372080i	$0.878645\pi$
$198$		0			0
$199$	−6.44338	−	11.1603i	−0.456759	−	0.791130i	0.542028	−	0.840360i	$-0.317657\pi$
$199$	−6.44338	−	11.1603i	−0.456759	−	0.791130i	−0.998787	+	0.0492301i	$0.984323\pi$
$200$	0.0256653	−	0.145555i	0.00181481	−	0.0102923i
$201$		0			0
$202$	5.38747	+	1.96088i	0.379061	+	0.137967i
$203$	9.68131	+	3.52371i	0.679495	+	0.247316i
$204$		0			0
$205$	−1.41361	+	8.01700i	−0.0987311	+	0.559932i
$206$	−0.948326	−	1.64255i	−0.0660730	−	0.114442i
$207$		0			0
$208$	0.0270347	−	0.0468255i	0.00187452	−	0.00324676i
$209$	1.66735	+	1.39907i	0.115333	+	0.0967759i
$210$		0			0
$211$	−4.16680	−	23.6311i	−0.286854	−	1.62683i	−0.698586	−	0.715526i	$-0.746187\pi$
$211$	−4.16680	−	23.6311i	−0.286854	−	1.62683i	0.411732	−	0.911305i	$-0.364924\pi$
$212$	−1.82062	+	1.52768i	−0.125041	+	0.104922i
$213$		0			0
$214$	−4.41026	+	1.60520i	−0.301479	+	0.109729i
$215$	18.4035			1.25511
$216$		0			0
$217$	−4.92177			−0.334112
$218$	−5.66220	+	2.06087i	−0.383492	+	0.139580i
$219$		0			0
$220$	16.1720	−	13.5700i	1.09032	−	0.914886i
$221$	−0.00982391	−	0.0557142i	−0.000660828	−	0.00374774i
$222$		0			0
$223$	16.5942	+	13.9242i	1.11123	+	0.932432i	0.998128	−	0.0611519i	$-0.0194774\pi$
$223$	16.5942	+	13.9242i	1.11123	+	0.932432i	0.113100	+	0.993584i	$0.463922\pi$
$224$	2.91919	−	5.05618i	0.195047	−	0.337831i
$225$		0			0
$226$	2.60880	+	4.51858i	0.173535	+	0.300571i
$227$	−3.75807	+	21.3131i	−0.249432	+	1.41460i	0.560538	+	0.828128i	$0.310594\pi$
$227$	−3.75807	+	21.3131i	−0.249432	+	1.41460i	−0.809970	+	0.586471i	$0.800517\pi$
$228$		0			0
$229$	10.1537	+	3.69565i	0.670976	+	0.244215i	0.654968	−	0.755656i	$-0.272682\pi$
$229$	10.1537	+	3.69565i	0.670976	+	0.244215i	0.0160082	+	0.999872i	$0.494904\pi$
$230$	0.894571	+	0.325597i	0.0589862	+	0.0214692i
$231$		0			0
$232$	−2.15578	+	12.2261i	−0.141534	+	0.802680i
$233$	3.81950	+	6.61557i	0.250224	+	0.433400i	0.963587	−	0.267394i	$-0.0861625\pi$
$233$	3.81950	+	6.61557i	0.250224	+	0.433400i	−0.713364	+	0.700794i	$0.752829\pi$
$234$		0			0
$235$	7.86160	−	13.6167i	0.512834	−	0.888255i
$236$	−5.18202	−	4.34823i	−0.337321	−	0.283046i
$237$		0			0
$238$	−0.298256	−	1.69150i	−0.0193331	−	0.109643i
$239$	2.47547	−	2.07716i	0.160125	−	0.134360i	−0.559205	−	0.829029i	$-0.688894\pi$
$239$	2.47547	−	2.07716i	0.160125	−	0.134360i	0.719330	+	0.694669i	$0.244449\pi$
$240$		0			0
$241$	24.9441	−	9.07891i	1.60679	−	0.584824i	0.625988	−	0.779832i	$-0.284696\pi$
$241$	24.9441	−	9.07891i	1.60679	−	0.584824i	0.980802	+	0.195009i	$0.0624735\pi$
$242$	6.72979			0.432608
$243$		0			0
$244$	−12.6350			−0.808873
$245$	−10.9462	+	3.98410i	−0.699329	+	0.254535i
$246$		0			0
$247$	−0.00577350	+	0.00484454i	−0.000367359	+	0.000308251i
$248$	−1.02986	−	5.84063i	−0.0653962	−	0.370880i
$249$		0			0
$250$	3.59062	+	3.01289i	0.227091	+	0.190552i
$251$	−2.24965	+	3.89651i	−0.141997	+	0.245945i	−0.928248	−	0.371961i	$-0.878686\pi$
$251$	−2.24965	+	3.89651i	−0.141997	+	0.245945i	0.786252	+	0.617906i	$0.212019\pi$
$252$		0			0
$253$	−2.69726	−	4.67179i	−0.169575	−	0.293713i
$254$	−0.605656	+	3.43485i	−0.0380022	+	0.215521i
$255$		0			0
$256$	−3.67195	−	1.33648i	−0.229497	−	0.0835301i
$257$	12.9071	+	4.69779i	0.805121	+	0.293040i	0.711607	−	0.702578i	$-0.247968\pi$
$257$	12.9071	+	4.69779i	0.805121	+	0.293040i	0.0935139	+	0.995618i	$0.470190\pi$
$258$		0			0
$259$	−1.01394	+	5.75033i	−0.0630031	+	0.357308i
$260$	0.0365505	+	0.0633073i	0.00226677	+	0.00392615i
$261$		0			0
$262$	−3.22711	+	5.58952i	−0.199372	+	0.345322i
$263$	18.5402	+	15.5571i	1.14324	+	0.959292i	0.999540	−	0.0303291i	$-0.00965554\pi$
$263$	18.5402	+	15.5571i	1.14324	+	0.959292i	0.143700	+	0.989621i	$0.454100\pi$
$264$		0			0
$265$	−0.500283	−	2.83725i	−0.0307321	−	0.174291i
$266$	−0.175285	+	0.147081i	−0.0107474	+	0.00901814i
$267$		0			0
$268$	−18.9350	+	6.89179i	−1.15664	+	0.420983i
$269$	−12.0062			−0.732032			−0.366016	−	0.930609i	$-0.619278\pi$
$269$	−12.0062			−0.732032			−0.366016	+	0.930609i	$0.619278\pi$
$270$		0			0
$271$	3.71777			0.225839			0.112919	−	0.993604i	$-0.463980\pi$
$271$	3.71777			0.225839			0.112919	+	0.993604i	$0.463980\pi$
$272$	−8.81429	+	3.20814i	−0.534445	+	0.194522i
$273$		0			0
$274$	−3.82154	+	3.20665i	−0.230868	+	0.193721i
$275$	−0.0841740	−	0.477374i	−0.00507588	−	0.0287868i
$276$		0			0
$277$	−17.9891	−	15.0947i	−1.08086	−	0.906950i	−0.0848689	−	0.996392i	$-0.527047\pi$
$277$	−17.9891	−	15.0947i	−1.08086	−	0.906950i	−0.995992	+	0.0894421i	$0.971492\pi$
$278$	−1.27654	+	2.21104i	−0.0765621	+	0.132609i
$279$		0			0
$280$	2.32418	+	4.02560i	0.138897	+	0.240576i
$281$	3.53751	−	20.0622i	0.211030	−	1.19681i	−0.676633	−	0.736320i	$-0.736562\pi$
$281$	3.53751	−	20.0622i	0.211030	−	1.19681i	0.887663	−	0.460493i	$-0.152327\pi$
$282$		0			0
$283$	−10.9004	−	3.96741i	−0.647960	−	0.235838i	−0.00293048	−	0.999996i	$-0.500933\pi$
$283$	−10.9004	−	3.96741i	−0.647960	−	0.235838i	−0.645030	+	0.764157i	$0.723155\pi$
$284$	10.4478	+	3.80269i	0.619964	+	0.225648i
$285$		0			0
$286$	−0.00679451	+	0.0385336i	−0.000401768	+	0.00227854i
$287$	2.42478	+	4.19984i	0.143130	+	0.247909i
$288$		0			0
$289$	3.59280	−	6.22291i	0.211341	−	0.366053i
$290$	−5.50423	−	4.61860i	−0.323220	−	0.271213i
$291$		0			0
$292$	0.173567	+	0.984347i	0.0101572	+	0.0576045i
$293$	−24.1872	+	20.2955i	−1.41303	+	1.18567i	−0.458081	+	0.888910i	$0.651463\pi$
$293$	−24.1872	+	20.2955i	−1.41303	+	1.18567i	−0.954951	+	0.296764i	$0.904093\pi$
$294$		0			0
$295$	7.70567	−	2.80463i	0.448642	−	0.163292i
$296$	−7.03603			−0.408961
$297$		0			0
$298$	−0.366782			−0.0212471
$299$	0.0175530	−	0.00638876i	0.00101511	−	0.000369472i
$300$		0			0
$301$	8.39838	−	7.04708i	0.484075	−	0.406187i
$302$	0.593426	+	3.36549i	0.0341479	+	0.193662i
$303$		0			0
$304$	0.957252	+	0.803230i	0.0549022	+	0.0460684i
$305$	7.65816	−	13.2643i	0.438505	−	0.759513i
$306$		0			0
$307$	4.06027	+	7.03259i	0.231732	+	0.401371i	0.958318	−	0.285704i	$-0.0922275\pi$
$307$	4.06027	+	7.03259i	0.231732	+	0.401371i	−0.726586	+	0.687075i	$0.758894\pi$
$308$	2.18385	−	12.3852i	0.124436	−	0.705714i
$309$		0			0
$310$	3.22553	+	1.17400i	0.183198	+	0.0666786i
$311$	−22.4103	−	8.15669i	−1.27077	−	0.462523i	−0.383402	−	0.923581i	$-0.625248\pi$
$311$	−22.4103	−	8.15669i	−1.27077	−	0.462523i	−0.887370	+	0.461058i	$0.847470\pi$
$312$		0			0
$313$	4.67295	−	26.5016i	0.264131	−	1.49796i	−0.507367	−	0.861730i	$-0.669381\pi$
$313$	4.67295	−	26.5016i	0.264131	−	1.49796i	0.771498	−	0.636231i	$-0.219508\pi$
$314$	−2.60909	−	4.51908i	−0.147240	−	0.255026i
$315$		0			0
$316$	0.446928	−	0.774102i	0.0251417	−	0.0435466i
$317$	6.38294	+	5.35592i	0.358501	+	0.300818i	0.804193	−	0.594368i	$-0.202598\pi$
$317$	6.38294	+	5.35592i	0.358501	+	0.300818i	−0.445692	+	0.895187i	$0.647042\pi$
$318$		0			0
$319$	7.07028	+	40.0976i	0.395860	+	2.24503i
$320$	7.04246	−	5.90933i	0.393685	−	0.330341i
$321$		0			0
$322$	0.532913	−	0.193964i	0.0296981	−	0.0108092i
$323$	1.30748			0.0727501
$324$		0			0
$325$	0.00167849			9.31061e−5
$326$	−1.29408	+	0.471006i	−0.0716724	+	0.0260866i
$327$		0			0
$328$	−4.47654	+	3.75626i	−0.247176	+	0.207405i
$329$	−1.62649	−	9.22431i	−0.0896715	−	0.508553i
$330$		0			0
$331$	−4.91820	−	4.12686i	−0.270329	−	0.226833i	0.497538	−	0.867442i	$-0.334237\pi$
$331$	−4.91820	−	4.12686i	−0.270329	−	0.226833i	−0.767867	+	0.640609i	$0.778682\pi$
$332$	−4.21548	+	7.30143i	−0.231355	+	0.400718i
$333$		0			0
$334$	−4.27161	−	7.39865i	−0.233732	−	0.404836i
$335$	4.24160	−	24.0553i	0.231743	−	1.31428i
$336$		0			0
$337$	−7.02410	−	2.55656i	−0.382627	−	0.139265i	0.143543	−	0.989644i	$-0.454150\pi$
$337$	−7.02410	−	2.55656i	−0.382627	−	0.139265i	−0.526170	+	0.850379i	$0.676373\pi$
$338$	5.07521	+	1.84723i	0.276055	+	0.100476i
$339$		0			0
$340$	2.20213	−	12.4889i	0.119427	−	0.677306i
$341$	−9.72545	−	16.8450i	−0.526663	−	0.912206i
$342$		0			0
$343$	−8.08839	+	14.0095i	−0.436732	+	0.756442i
$344$	10.1200	+	8.49172i	0.545636	+	0.457843i
$345$		0			0
$346$	−1.01243	−	5.74177i	−0.0544285	−	0.308680i
$347$	24.0955	−	20.2186i	1.29352	−	1.08539i	0.302290	−	0.953216i	$-0.402249\pi$
$347$	24.0955	−	20.2186i	1.29352	−	1.08539i	0.991227	−	0.132173i	$-0.0421955\pi$
$348$		0			0
$349$	−11.1381	+	4.05395i	−0.596210	+	0.217003i	−0.622459	−	0.782653i	$-0.713866\pi$
$349$	−11.1381	+	4.05395i	−0.596210	+	0.217003i	0.0262485	+	0.999655i	$0.491644\pi$
$350$	0.0509595			0.00272390
$351$		0			0
$352$	23.0733			1.22981
$353$	−7.71214	+	2.80699i	−0.410476	+	0.149401i	−0.539001	−	0.842305i	$-0.681198\pi$
$353$	−7.71214	+	2.80699i	−0.410476	+	0.149401i	0.128525	+	0.991706i	$0.458976\pi$
$354$		0			0
$355$	−10.3246	+	8.66337i	−0.547973	+	0.459804i
$356$	−1.07035	−	6.07025i	−0.0567284	−	0.321723i
$357$		0			0
$358$	−3.24312	−	2.72130i	−0.171404	−	0.143825i
$359$	8.86365	−	15.3523i	0.467806	−	0.810263i	−0.531517	−	0.847047i	$-0.678378\pi$
$359$	8.86365	−	15.3523i	0.467806	−	0.810263i	0.999323	+	0.0367840i	$0.0117114\pi$
$360$		0			0
$361$	9.41291	+	16.3036i	0.495416	+	0.858086i
$362$	1.73543	−	9.84210i	0.0912120	−	0.517289i
$363$		0			0
$364$	0.0409214	+	0.0148942i	0.00214486	+	0.000780667i
$365$	−1.13858	−	0.414408i	−0.0595958	−	0.0216911i
$366$		0			0
$367$	−3.52845	+	20.0108i	−0.184184	+	1.04456i	0.742816	+	0.669495i	$0.233490\pi$
$367$	−3.52845	+	20.0108i	−0.184184	+	1.04456i	−0.927000	+	0.375062i	$0.877622\pi$
$368$	−1.54854	−	2.68215i	−0.0807232	−	0.139817i
$369$		0			0
$370$	2.03613	−	3.52668i	0.105853	−	0.183343i
$371$	−1.31474	−	1.10320i	−0.0682581	−	0.0572753i
$372$		0			0
$373$	−1.68116	−	9.53435i	−0.0870474	−	0.493670i	−0.996896	−	0.0787298i	$-0.974914\pi$
$373$	−1.68116	−	9.53435i	−0.0870474	−	0.493670i	0.909849	−	0.414940i	$-0.136198\pi$
$374$	5.19986	−	4.36320i	0.268878	−	0.225616i
$375$		0			0
$376$	10.6061	−	3.86029i	0.546966	−	0.199079i
$377$	−0.140987			−0.00726119
$378$		0			0
$379$	−4.12905			−0.212095			−0.106048	−	0.994361i	$-0.533820\pi$
$379$	−4.12905			−0.212095			−0.106048	+	0.994361i	$0.533820\pi$
$380$	−1.58756	+	0.577824i	−0.0814400	+	0.0296417i
$381$		0			0
$382$	−3.48385	+	2.92330i	−0.178249	+	0.149569i
$383$	−0.824861	−	4.67802i	−0.0421484	−	0.239036i	0.956454	−	0.291882i	$-0.0942816\pi$
$383$	−0.824861	−	4.67802i	−0.0421484	−	0.239036i	−0.998603	+	0.0528469i	$0.983170\pi$
$384$		0			0
$385$	11.6785	+	9.79940i	0.595190	+	0.499424i
$386$	2.24476	−	3.88803i	0.114255	−	0.197896i
$387$		0			0
$388$	9.08336	+	15.7328i	0.461138	+	0.798714i
$389$	3.78784	−	21.4819i	0.192051	−	1.08918i	−0.724505	−	0.689270i	$-0.757931\pi$
$389$	3.78784	−	21.4819i	0.192051	−	1.08918i	0.916556	−	0.399907i	$-0.130957\pi$
$390$		0			0
$391$	−3.04509	−	1.10832i	−0.153997	−	0.0560503i
$392$	−7.85765	−	2.85995i	−0.396871	−	0.144449i
$393$		0			0
$394$	1.59248	−	9.03141i	0.0802281	−	0.454996i
$395$	0.541773	+	0.938378i	0.0272595	+	0.0472149i
$396$		0			0
$397$	17.4245	−	30.1802i	0.874512	−	1.51470i	0.0172294	−	0.999852i	$-0.494515\pi$
$397$	17.4245	−	30.1802i	0.874512	−	1.51470i	0.857282	−	0.514847i	$-0.172151\pi$
$398$	4.10141	+	3.44149i	0.205585	+	0.172507i
$399$		0			0
$400$	−0.0483256	−	0.274068i	−0.00241628	−	0.0137034i
$401$	14.4216	−	12.1012i	0.720181	−	0.604304i	−0.207254	−	0.978287i	$-0.566453\pi$
$401$	14.4216	−	12.1012i	0.720181	−	0.604304i	0.927435	+	0.373983i	$0.122008\pi$
$402$		0			0
$403$	0.0632904	−	0.0230358i	0.00315272	−	0.00114750i
$404$	25.2170			1.25459
$405$		0			0
$406$	−4.28040			−0.212433
$407$	−21.6843	+	7.89243i	−1.07485	+	0.391213i
$408$		0			0
$409$	−4.87201	+	4.08810i	−0.240905	+	0.202144i	−0.755244	−	0.655443i	$-0.772482\pi$
$409$	−4.87201	+	4.08810i	−0.240905	+	0.202144i	0.514339	+	0.857587i	$0.328037\pi$
$410$	−0.587309	−	3.33079i	−0.0290051	−	0.164496i
$411$		0			0
$412$	−6.39053	−	5.36229i	−0.314839	−	0.264181i
$413$	2.44251	−	4.23055i	0.120188	−	0.208172i
$414$		0			0
$415$	−5.11007	−	8.85090i	−0.250843	−	0.434474i
$416$	−0.0138737	+	0.0786817i	−0.000680215	+	0.00385769i
$417$		0			0
$418$	−0.849756	−	0.309286i	−0.0415629	−	0.0151277i
$419$	−22.8514	−	8.31724i	−1.11636	−	0.406324i	−0.283040	−	0.959108i	$-0.591343\pi$
$419$	−22.8514	−	8.31724i	−1.11636	−	0.406324i	−0.833324	+	0.552784i	$0.813565\pi$
$420$		0			0
$421$	−1.38746	+	7.86865i	−0.0676204	+	0.383495i	0.932150	+	0.362072i	$0.117931\pi$
$421$	−1.38746	+	7.86865i	−0.0676204	+	0.383495i	−0.999771	+	0.0214224i	$0.993181\pi$
$422$	4.98469	+	8.63373i	0.242651	+	0.420283i
$423$		0			0
$424$	1.03405	−	1.79103i	0.0502181	−	0.0869803i
$425$	−0.223061	−	0.187170i	−0.0108200	−	0.00907910i
$426$		0			0
$427$	−1.58441	−	8.98561i	−0.0766748	−	0.434844i
$428$	−15.8135	+	13.2691i	−0.764373	+	0.641385i
$429$		0			0
$430$	−7.18492	+	2.61510i	−0.346487	+	0.126111i
$431$	−9.87124			−0.475481			−0.237740	−	0.971329i	$-0.576407\pi$
$431$	−9.87124			−0.475481			−0.237740	+	0.971329i	$0.576407\pi$
$432$		0			0
$433$	−6.10369			−0.293325			−0.146662	−	0.989187i	$-0.546853\pi$
$433$	−6.10369			−0.293325			−0.146662	+	0.989187i	$0.546853\pi$
$434$	1.92151	−	0.699373i	0.0922356	−	0.0335710i
$435$		0			0
$436$	−20.3024	+	17.0358i	−0.972310	+	0.815865i
$437$	0.0749645	+	0.425145i	0.00358604	+	0.0203374i
$438$		0			0
$439$	−11.5933	−	9.72796i	−0.553320	−	0.464290i	0.322744	−	0.946486i	$-0.395395\pi$
$439$	−11.5933	−	9.72796i	−0.553320	−	0.464290i	−0.876063	+	0.482196i	$0.839839\pi$
$440$	−9.18520	+	15.9092i	−0.437887	+	0.758443i
$441$		0			0
$442$	0.0117522	+	0.0203554i	0.000558996	+	0.000968210i
$443$	0.125512	−	0.711813i	0.00596324	−	0.0338192i	−0.981681	−	0.190532i	$-0.938979\pi$
$443$	0.125512	−	0.711813i	0.00596324	−	0.0338192i	0.987644	+	0.156713i	$0.0500898\pi$
$444$		0			0
$445$	7.02135	+	2.55556i	0.332844	+	0.121145i
$446$	−8.45714	−	3.07815i	−0.400457	−	0.145754i
$447$		0			0
$448$	0.951004	−	5.39341i	0.0449307	−	0.254815i
$449$	0.834224	+	1.44492i	0.0393695	+	0.0681899i	0.885039	−	0.465517i	$-0.154132\pi$
$449$	0.834224	+	1.44492i	0.0393695	+	0.0681899i	−0.845669	+	0.533707i	$0.820798\pi$
$450$		0			0
$451$	−9.58275	+	16.5978i	−0.451234	+	0.781560i
$452$	17.5800	+	14.7514i	0.826896	+	0.693848i
$453$		0			0
$454$	−1.56135	−	8.85487i	−0.0732779	−	0.415580i
$455$	−0.0404388	+	0.0339322i	−0.00189580	+	0.00159077i
$456$		0			0
$457$	−10.4150	+	3.79076i	−0.487195	+	0.177324i	−0.573926	−	0.818907i	$-0.694580\pi$
$457$	−10.4150	+	3.79076i	−0.487195	+	0.177324i	0.0867310	+	0.996232i	$0.472358\pi$
$458$	−4.48926			−0.209769
$459$		0			0
$460$	4.18720			0.195229
$461$	−20.5646	+	7.48490i	−0.957789	+	0.348607i	−0.773167	−	0.634203i	$-0.781328\pi$
$461$	−20.5646	+	7.48490i	−0.957789	+	0.348607i	−0.184622	+	0.982810i	$0.559106\pi$
$462$		0			0
$463$	19.0375	−	15.9744i	0.884749	−	0.742393i	−0.0824009	−	0.996599i	$-0.526259\pi$
$463$	19.0375	−	15.9744i	0.884749	−	0.742393i	0.967150	+	0.254207i	$0.0818143\pi$
$464$	4.05916	+	23.0206i	0.188442	+	1.06871i
$465$		0			0
$466$	−2.43123	−	2.04004i	−0.112625	−	0.0945032i
$467$	−5.91777	+	10.2499i	−0.273842	+	0.474308i	−0.969842	−	0.243734i	$-0.921628\pi$
$467$	−5.91777	+	10.2499i	−0.273842	+	0.474308i	0.696001	+	0.718041i	$0.254961\pi$
$468$		0			0
$469$	−7.27564	−	12.6018i	−0.335958	−	0.581896i
$470$	−1.13435	+	6.43321i	−0.0523236	+	0.296742i
$471$		0			0
$472$	5.53144	+	2.01328i	0.254605	+	0.0926687i
$473$	40.7142	+	14.8187i	1.87204	+	0.681367i
$474$		0			0
$475$	−0.00673613	+	0.0382025i	−0.000309075	+	0.00175285i
$476$	−3.77733	−	6.54252i	−0.173134	−	0.299876i
$477$		0			0
$478$	−0.671288	+	1.16270i	−0.0307040	+	0.0531809i
$479$	−2.21184	−	1.85595i	−0.101062	−	0.0848007i	0.590857	−	0.806776i	$-0.298790\pi$
$479$	−2.21184	−	1.85595i	−0.101062	−	0.0848007i	−0.691918	+	0.721976i	$0.743234\pi$
$480$		0			0
$481$	−0.0138753	−	0.0786906i	−0.000632658	−	0.00358798i
$482$	−8.44834	+	7.08900i	−0.384811	+	0.322895i
$483$		0			0
$484$	27.8152	−	10.1239i	1.26433	−	0.460178i
$485$	−22.0220			−0.999966
$486$		0			0
$487$	8.75903			0.396910			0.198455	−	0.980110i	$-0.436408\pi$
$487$	8.75903			0.396910			0.198455	+	0.980110i	$0.436408\pi$
$488$	10.3316	−	3.76040i	0.467690	−	0.170225i
$489$		0			0
$490$	3.70739	−	3.11087i	0.167483	−	0.140535i
$491$	3.91977	+	22.2301i	0.176897	+	1.00323i	0.935932	+	0.352181i	$0.114560\pi$
$491$	3.91977	+	22.2301i	0.176897	+	1.00323i	−0.759035	+	0.651050i	$0.774329\pi$
$492$		0			0
$493$	18.7362	+	15.7216i	0.843838	+	0.708064i
$494$	0.00156564	−	0.00271176i	7.04413e−5	−	0.000122008i
$495$		0			0
$496$	−5.58354	−	9.67097i	−0.250708	−	0.434239i
$497$	−1.39422	+	7.90701i	−0.0625393	+	0.354678i
$498$		0			0
$499$	23.8051	+	8.66433i	1.06566	+	0.387869i	0.814552	−	0.580090i	$-0.196983\pi$
$499$	23.8051	+	8.66433i	1.06566	+	0.387869i	0.251108	+	0.967959i	$0.419205\pi$
$500$	19.3730	+	7.05118i	0.866385	+	0.315338i
$501$		0			0
$502$	0.324602	−	1.84091i	0.0144877	−	0.0821637i
$503$	1.87207	+	3.24252i	0.0834714	+	0.144577i	0.904739	−	0.425967i	$-0.140066\pi$
$503$	1.87207	+	3.24252i	0.0834714	+	0.144577i	−0.821267	+	0.570543i	$0.806733\pi$
$504$		0			0
$505$	−15.2842	+	26.4731i	−0.680139	+	1.17804i
$506$	1.71689	+	1.44064i	0.0763250	+	0.0640443i
$507$		0			0
$508$	2.66392	+	15.1078i	0.118192	+	0.670302i
$509$	−18.6531	+	15.6518i	−0.826784	+	0.693754i	−0.954550	−	0.298050i	$-0.903664\pi$
$509$	−18.6531	+	15.6518i	−0.826784	+	0.693754i	0.127766	+	0.991804i	$0.459219\pi$
$510$		0			0
$511$	−0.678271	+	0.246871i	−0.0300050	+	0.0109209i
$512$	22.7690			1.00626
$513$		0			0
$514$	−5.70660			−0.251707
$515$	9.50273	−	3.45871i	0.418740	−	0.152409i
$516$		0			0
$517$	28.3566	−	23.7940i	1.24712	−	1.04646i
$518$	−0.421257	−	2.38907i	−0.0185090	−	0.104970i
$519$		0			0
$520$	−0.0487287	−	0.0408882i	−0.00213689	−	0.00179307i
$521$	9.81046	−	16.9922i	0.429804	−	0.744443i	−0.567051	−	0.823682i	$-0.691916\pi$
$521$	9.81046	−	16.9922i	0.429804	−	0.744443i	0.996856	+	0.0792397i	$0.0252492\pi$
$522$		0			0
$523$	−10.4077	−	18.0267i	−0.455097	−	0.788251i	0.543597	−	0.839346i	$-0.317062\pi$
$523$	−10.4077	−	18.0267i	−0.455097	−	0.788251i	−0.998694	+	0.0510956i	$0.983729\pi$
$524$	−4.92957	+	27.9570i	−0.215349	+	1.22131i
$525$		0			0
$526$	−9.44893	−	3.43913i	−0.411993	−	0.149953i
$527$	−10.9796	−	3.99626i	−0.478280	−	0.174080i
$528$		0			0
$529$	−3.80811	+	21.5969i	−0.165570	+	0.938995i
$530$	0.598482	+	1.03660i	0.0259964	+	0.0450271i
$531$		0			0
$532$	−0.503217	+	0.871598i	−0.0218172	+	0.0377886i
$533$	−0.0508378	−	0.0426579i	−0.00220203	−	0.00184772i
$534$		0			0
$535$	−4.34534	−	24.6436i	−0.187865	−	1.06544i
$536$	13.4320	−	11.2708i	0.580175	−	0.486825i
$537$		0			0
$538$	4.68735	−	1.70606i	0.202086	−	0.0735533i
$539$	−27.4245			−1.18126
$540$		0			0
$541$	−30.6272			−1.31676			−0.658382	−	0.752684i	$-0.728759\pi$
$541$	−30.6272			−1.31676			−0.658382	+	0.752684i	$0.728759\pi$
$542$	−1.45146	+	0.528288i	−0.0623455	+	0.0226919i
$543$		0			0
$544$	10.6176	−	8.90922i	0.455226	−	0.381980i
$545$	−5.57884	−	31.6392i	−0.238971	−	1.35527i
$546$		0			0
$547$	17.3491	+	14.5576i	0.741795	+	0.622440i	0.933319	−	0.359048i	$-0.116899\pi$
$547$	17.3491	+	14.5576i	0.741795	+	0.622440i	−0.191524	+	0.981488i	$0.561343\pi$
$548$	−10.9711	+	19.0025i	−0.468661	+	0.811745i
$549$		0			0
$550$	0.100696	+	0.174411i	0.00429370	+	0.00743691i
$551$	0.565809	−	3.20886i	0.0241043	−	0.136702i
$552$		0			0
$553$	0.606561	+	0.220770i	0.0257936	+	0.00938810i
$554$	9.16806	+	3.33690i	0.389513	+	0.141771i
$555$		0			0
$556$	−1.94998	+	11.0589i	−0.0826978	+	0.469002i
$557$	18.2259	+	31.5682i	0.772256	+	1.33759i	0.936324	+	0.351138i	$0.114205\pi$
$557$	18.2259	+	31.5682i	0.772256	+	1.33759i	−0.164067	+	0.986449i	$0.552461\pi$
$558$		0			0
$559$	−0.0750139	+	0.129928i	−0.00317275	+	0.00549537i
$560$	6.70480	+	5.62599i	0.283329	+	0.237742i
$561$		0			0
$562$	1.46972	+	8.33519i	0.0619963	+	0.351599i
$563$	−20.3126	+	17.0443i	−0.856075	+	0.718332i	−0.961119	−	0.276136i	$-0.910946\pi$
$563$	−20.3126	+	17.0443i	−0.856075	+	0.718332i	0.105044	+	0.994468i	$0.466502\pi$
$564$		0			0
$565$	−26.1416	+	9.51475i	−1.09978	+	0.400288i
$566$	4.81938			0.202574
$567$		0			0
$568$	−9.67492			−0.405950
$569$	21.5823	−	7.85531i	0.904777	−	0.329312i	0.152612	−	0.988286i	$-0.451232\pi$
$569$	21.5823	−	7.85531i	0.904777	−	0.329312i	0.752165	+	0.658974i	$0.229009\pi$
$570$		0			0
$571$	−3.67549	+	3.08410i	−0.153814	+	0.129066i	−0.716447	−	0.697641i	$-0.754233\pi$
$571$	−3.67549	+	3.08410i	−0.153814	+	0.129066i	0.562633	+	0.826707i	$0.309788\pi$
$572$	0.0298850	+	0.169486i	0.00124955	+	0.00708657i
$573$		0			0
$574$	−1.54345	−	1.29511i	−0.0644223	−	0.0540567i
$575$	0.0480718	−	0.0832628i	0.00200473	−	0.00347230i
$576$		0			0
$577$	2.15666	+	3.73545i	0.0897831	+	0.155509i	0.907419	−	0.420226i	$-0.138049\pi$
$577$	2.15666	+	3.73545i	0.0897831	+	0.155509i	−0.817636	+	0.575735i	$0.804716\pi$
$578$	−0.518404	+	2.94002i	−0.0215628	+	0.122289i
$579$		0			0
$580$	−29.6977	−	10.8091i	−1.23313	−	0.448823i
$581$	−5.72116	−	2.08233i	−0.237354	−	0.0863897i
$582$		0			0
$583$	1.17781	−	6.67969i	0.0487799	−	0.276645i
$584$	−0.434885	−	0.753242i	−0.0179957	−	0.0311694i
$585$		0			0
$586$	6.55900	−	11.3605i	0.270950	−	0.469299i
$587$	−32.0377	−	26.8828i	−1.32234	−	1.10957i	−0.985804	−	0.167900i	$-0.946301\pi$
$587$	−32.0377	−	26.8828i	−1.32234	−	1.10957i	−0.336532	−	0.941672i	$-0.609254\pi$
$588$		0			0
$589$	0.270298	+	1.53294i	0.0111374	+	0.0631635i
$590$	−2.60984	+	2.18992i	−0.107446	+	0.0901575i
$591$		0			0
$592$	−12.4493	+	4.53117i	−0.511663	+	0.186230i
$593$	31.5370			1.29507			0.647536	−	0.762035i	$-0.275800\pi$
$593$	31.5370			1.29507			0.647536	+	0.762035i	$0.275800\pi$
$594$		0			0
$595$	9.15786			0.375436
$596$	−1.51596	+	0.551766i	−0.0620963	+	0.0226012i
$597$		0			0
$598$	−0.00594504	+	0.00498848i	−0.000243111	+	0.000203994i
$599$	2.19323	+	12.4384i	0.0896129	+	0.508220i	0.996266	+	0.0863420i	$0.0275178\pi$
$599$	2.19323	+	12.4384i	0.0896129	+	0.508220i	−0.906653	+	0.421878i	$0.861371\pi$
$600$		0			0
$601$	15.7368	+	13.2048i	0.641919	+	0.538634i	0.904607	−	0.426247i	$-0.140165\pi$
$601$	15.7368	+	13.2048i	0.641919	+	0.538634i	−0.262688	+	0.964881i	$0.584609\pi$
$602$	−2.27744	+	3.94465i	−0.0928216	+	0.160772i
$603$		0			0
$604$	7.51556	+	13.0173i	0.305804	+	0.529668i
$605$	−6.23084	+	35.3369i	−0.253320	+	1.43665i
$606$		0			0
$607$	−12.1338	−	4.41636i	−0.492497	−	0.179254i	0.0838192	−	0.996481i	$-0.473288\pi$
$607$	−12.1338	−	4.41636i	−0.492497	−	0.179254i	−0.576316	+	0.817227i	$0.695510\pi$
$608$	−1.73512	−	0.631531i	−0.0703683	−	0.0256120i
$609$		0			0
$610$	−1.10500	+	6.26674i	−0.0447400	+	0.253733i
$611$	0.0640889	+	0.111005i	0.00259276	+	0.00449079i
$612$		0			0
$613$	15.5799	−	26.9851i	0.629265	−	1.08992i	−0.358434	−	0.933555i	$-0.616689\pi$
$613$	15.5799	−	26.9851i	0.629265	−	1.08992i	0.987699	−	0.156364i	$-0.0499774\pi$
$614$	−2.58449	−	2.16864i	−0.104301	−	0.0875193i
$615$		0			0
$616$	1.90034	+	10.7773i	0.0765667	+	0.434231i
$617$	5.47016	−	4.59001i	0.220220	−	0.184787i	−0.526003	−	0.850483i	$-0.676310\pi$
$617$	5.47016	−	4.59001i	0.220220	−	0.184787i	0.746223	+	0.665696i	$0.231865\pi$
$618$		0			0
$619$	9.42596	−	3.43077i	0.378861	−	0.137894i	−0.145568	−	0.989348i	$-0.546501\pi$
$619$	9.42596	−	3.43077i	0.378861	−	0.137894i	0.524429	+	0.851454i	$0.324279\pi$
$620$	15.0977			0.606338
$621$		0			0
$622$	9.90827			0.397285
$623$	4.18276	−	1.52240i	0.167579	−	0.0609936i
$624$		0			0
$625$	−18.7885	+	15.7654i	−0.751539	+	0.630616i
$626$	1.94145	+	11.0105i	0.0775961	+	0.440070i
$627$		0			0
$628$	−17.5820	−	14.7530i	−0.701598	−	0.588711i
$629$	−6.93093	+	12.0047i	−0.276354	+	0.478660i
$630$		0			0
$631$	3.53780	+	6.12765i	0.140838	+	0.243938i	0.927812	−	0.373047i	$-0.121687\pi$
$631$	3.53780	+	6.12765i	0.140838	+	0.243938i	−0.786975	+	0.616985i	$0.788354\pi$
$632$	−0.135066	+	0.765996i	−0.00537263	+	0.0304697i
$633$		0			0
$634$	−3.25303	−	1.18401i	−0.129194	−	0.0470229i
$635$	−17.4750	−	6.36037i	−0.693473	−	0.252403i
$636$		0			0
$637$	0.0164900	−	0.0935195i	0.000653358	−	0.00370538i
$638$	−8.45809	−	14.6498i	−0.334859	−	0.579993i
$639$		0			0
$640$	−11.7103	+	20.2828i	−0.462890	+	0.801750i
$641$	3.83881	+	3.22114i	0.151624	+	0.127228i	0.715444	−	0.698670i	$-0.246224\pi$
$641$	3.83881	+	3.22114i	0.151624	+	0.127228i	−0.563820	+	0.825898i	$0.690669\pi$
$642$		0			0
$643$	0.284506	+	1.61351i	0.0112198	+	0.0636307i	0.989904	−	0.141742i	$-0.0452704\pi$
$643$	0.284506	+	1.61351i	0.0112198	+	0.0636307i	−0.978684	+	0.205373i	$0.934159\pi$
$644$	1.91082	−	1.60337i	0.0752968	−	0.0631815i
$645$		0			0
$646$	−0.510454	+	0.185790i	−0.0200835	+	0.00730981i
$647$	−34.4927			−1.35605			−0.678024	−	0.735040i	$-0.737164\pi$
$647$	−34.4927			−1.35605			−0.678024	+	0.735040i	$0.737164\pi$
$648$		0			0
$649$	19.3056			0.757813
$650$	−0.000655302	0	0.000238510i	−2.57031e−5	0	9.35515e-6i
$651$		0			0
$652$	−4.64006	+	3.89347i	−0.181719	+	0.152480i
$653$	−6.73071	−	38.1717i	−0.263393	−	1.49378i	−0.773573	−	0.633708i	$-0.781532\pi$
$653$	−6.73071	−	38.1717i	−0.263393	−	1.49378i	0.510180	−	0.860068i	$-0.329579\pi$
$654$		0			0
$655$	−26.3617	−	22.1201i	−1.03004	−	0.864302i
$656$	−5.50161	+	9.52907i	−0.214802	+	0.372048i
$657$		0			0
$658$	1.94575	+	3.37015i	0.0758534	+	0.131382i
$659$	−1.63089	+	9.24924i	−0.0635305	+	0.360299i	0.936425	+	0.350868i	$0.114113\pi$
$659$	−1.63089	+	9.24924i	−0.0635305	+	0.360299i	−0.999956	+	0.00943154i	$0.996998\pi$
$660$		0			0
$661$	22.6912	+	8.25891i	0.882584	+	0.321234i	0.743252	−	0.669012i	$-0.233282\pi$
$661$	22.6912	+	8.25891i	0.882584	+	0.321234i	0.139332	+	0.990246i	$0.455505\pi$
$662$	2.50654	+	0.912305i	0.0974193	+	0.0354577i
$663$		0			0
$664$	1.27396	−	7.22497i	0.0494391	−	0.280383i
$665$	−0.610007	−	1.05656i	−0.0236551	−	0.0409718i
$666$		0			0
$667$	−4.03784	+	6.99375i	−0.156346	+	0.270799i
$668$	−28.7853	−	24.1537i	−1.11374	−	0.934536i
$669$		0			0
$670$	1.76224	+	9.99417i	0.0680814	+	0.386109i
$671$	27.6228	−	23.1783i	1.06637	−	0.894788i
$672$		0			0
$673$	24.8700	−	9.05195i	0.958669	−	0.348927i	0.185157	−	0.982709i	$-0.440721\pi$
$673$	24.8700	−	9.05195i	0.958669	−	0.348927i	0.773512	+	0.633782i	$0.218498\pi$
$674$	3.10557			0.119622
$675$		0			0
$676$	23.7554			0.913671
$677$	29.1933	−	10.6255i	1.12199	−	0.408371i	0.286611	−	0.958047i	$-0.407471\pi$
$677$	29.1933	−	10.6255i	1.12199	−	0.408371i	0.835378	+	0.549676i	$0.185249\pi$
$678$		0			0
$679$	−10.0497	+	8.43267i	−0.385671	+	0.323616i
$680$	1.91624	+	10.8676i	0.0734846	+	0.416752i
$681$		0			0
$682$	6.19055	+	5.19449i	0.237048	+	0.198907i
$683$	19.0681	−	33.0268i	0.729619	−	1.26374i	−0.227425	−	0.973796i	$-0.573031\pi$
$683$	19.0681	−	33.0268i	0.729619	−	1.26374i	0.957044	−	0.289942i	$-0.0936359\pi$
$684$		0			0
$685$	−13.2993	−	23.0351i	−0.508140	−	0.880125i
$686$	1.16707	−	6.61880i	0.0445590	−	0.252707i
$687$		0			0
$688$	23.3747	+	8.50768i	0.891150	+	0.324352i
$689$	0.0220700	+	0.00803284i	0.000840802	+	0.000306027i
$690$		0			0
$691$	5.71815	−	32.4293i	0.217529	−	1.23367i	−0.658935	−	0.752200i	$-0.728993\pi$
$691$	5.71815	−	32.4293i	0.217529	−	1.23367i	0.876464	−	0.481468i	$-0.159896\pi$
$692$	−12.8221	−	22.2085i	−0.487424	−	0.844242i
$693$		0			0
$694$	−6.53414	+	11.3175i	−0.248033	+	0.429605i
$695$	−10.4278	−	8.75000i	−0.395551	−	0.331906i
$696$		0			0
$697$	1.99918	+	11.3379i	0.0757244	+	0.429455i
$698$	3.77238	−	3.16541i	0.142787	−	0.119812i
$699$		0			0
$700$	0.210623	−	0.0766606i	0.00796081	−	0.00289750i
$701$	2.30710			0.0871381			0.0435690	−	0.999050i	$-0.486127\pi$
$701$	2.30710			0.0871381			0.0435690	+	0.999050i	$0.486127\pi$
$702$		0			0
$703$	1.84668			0.0696490
$704$	20.3384	−	7.40255i	0.766530	−	0.278994i
$705$		0			0
$706$	2.61203	−	2.19176i	0.0983051	−	0.0824878i
$707$	3.16217	+	17.9336i	0.118926	+	0.674461i
$708$		0			0
$709$	−8.54298	−	7.16841i	−0.320838	−	0.269215i	0.468116	−	0.883667i	$-0.344933\pi$
$709$	−8.54298	−	7.16841i	−0.320838	−	0.269215i	−0.788954	+	0.614452i	$0.789377\pi$
$710$	2.79979	−	4.84937i	0.105074	−	0.181994i
$711$		0			0
$712$	2.68184	+	4.64508i	0.100506	+	0.174082i
$713$	0.669920	−	3.79930i	0.0250887	−	0.142285i
$714$		0			0
$715$	−0.196042	−	0.0713533i	−0.00733154	−	0.00266846i
$716$	−17.4981	−	6.36878i	−0.653934	−	0.238013i
$717$		0			0
$718$	−1.27894	+	7.25321i	−0.0477295	+	0.270687i
$719$	−16.0850	−	27.8600i	−0.599869	−	1.03900i	−0.992840	−	0.119453i	$-0.961886\pi$
$719$	−16.0850	−	27.8600i	−0.599869	−	1.03900i	0.392971	−	0.919551i	$-0.371447\pi$
$720$		0			0
$721$	3.01213	−	5.21717i	0.112178	−	0.194297i
$722$	−5.99161	−	5.02756i	−0.222985	−	0.187106i
$723$		0			0
$724$	−7.63311	−	43.2895i	−0.283682	−	1.60884i
$725$	−0.555889	+	0.466446i	−0.0206452	+	0.0173234i
$726$		0			0
$727$	5.04193	−	1.83511i	0.186995	−	0.0680605i	−0.246826	−	0.969060i	$-0.579387\pi$
$727$	5.04193	−	1.83511i	0.186995	−	0.0680605i	0.433820	+	0.900999i	$0.357165\pi$
$728$	−0.0378942			−0.00140445
$729$		0			0
$730$	0.503399			0.0186316
$731$	24.4573	−	8.90171i	0.904584	−	0.329242i
$732$		0			0
$733$	−11.1815	+	9.38235i	−0.412996	+	0.346545i	−0.825491	−	0.564415i	$-0.809102\pi$
$733$	−11.1815	+	9.38235i	−0.412996	+	0.346545i	0.412495	+	0.910960i	$0.364657\pi$
$734$	−1.46595	−	8.31382i	−0.0541093	−	0.306869i
$735$		0			0
$736$	3.50572	+	2.94165i	0.129223	+	0.108431i
$737$	28.7534	−	49.8023i	1.05915	−	1.83449i
$738$		0			0
$739$	21.6083	+	37.4266i	0.794873	+	1.37676i	0.922920	+	0.384992i	$0.125796\pi$
$739$	21.6083	+	37.4266i	0.794873	+	1.37676i	−0.128047	+	0.991768i	$0.540871\pi$
$740$	3.11029	−	17.6393i	0.114336	−	0.648434i
$741$		0			0
$742$	0.670052	+	0.243879i	0.0245984	+	0.00895308i
$743$	7.62298	+	2.77454i	0.279660	+	0.101788i	0.478042	−	0.878337i	$-0.341347\pi$
$743$	7.62298	+	2.77454i	0.279660	+	0.101788i	−0.198382	+	0.980125i	$0.563569\pi$
$744$		0			0
$745$	0.339588	−	1.92590i	0.0124416	−	0.0705596i
$746$	2.01116	+	3.48342i	0.0736336	+	0.127537i
$747$		0			0
$748$	14.9280	−	25.8561i	0.545823	−	0.945393i
$749$	−11.4195	−	9.58213i	−0.417261	−	0.350123i
$750$		0			0
$751$	1.52037	+	8.62244i	0.0554790	+	0.314637i	0.999901	−	0.0140996i	$-0.00448819\pi$
$751$	1.52037	+	8.62244i	0.0554790	+	0.314637i	−0.944422	+	0.328737i	$0.893377\pi$
$752$	16.2800	−	13.6605i	0.593670	−	0.498148i
$753$		0			0
$754$	0.0550428	−	0.0200339i	0.00200454	−	0.000729593i
$755$	−18.2210			−0.663129
$756$		0			0
$757$	−32.1511			−1.16855			−0.584276	−	0.811555i	$-0.698622\pi$
$757$	−32.1511			−1.16855			−0.584276	+	0.811555i	$0.698622\pi$
$758$	1.61203	−	0.586730i	0.0585514	−	0.0213110i
$759$		0			0
$760$	1.12617	−	0.944972i	0.0408506	−	0.0342777i
$761$	4.26235	+	24.1730i	0.154510	+	0.876271i	0.959232	+	0.282619i	$0.0912032\pi$
$761$	4.26235	+	24.1730i	0.154510	+	0.876271i	−0.804722	+	0.593652i	$0.797686\pi$
$762$		0			0
$763$	−14.6612	−	12.3022i	−0.530771	−	0.445370i
$764$	−10.0016	+	17.3233i	−0.361846	+	0.626736i
$765$		0			0
$766$	0.986770	+	1.70914i	0.0356535	+	0.0617536i
$767$	−0.0116082	+	0.0658336i	−0.000419150	+	0.00237712i
$768$		0			0
$769$	−29.5199	−	10.7444i	−1.06451	−	0.387451i	−0.250392	−	0.968145i	$-0.580559\pi$
$769$	−29.5199	−	10.7444i	−1.06451	−	0.387451i	−0.814122	+	0.580693i	$0.802782\pi$
$770$	−5.95187	−	2.16630i	−0.214491	−	0.0780682i
$771$		0			0
$772$	3.42898	−	19.4467i	0.123412	−	0.699902i
$773$	14.3573	+	24.8675i	0.516395	+	0.894422i	0.999819	+	0.0190355i	$0.00605954\pi$
$773$	14.3573	+	24.8675i	0.516395	+	0.894422i	−0.483424	+	0.875386i	$0.660607\pi$
$774$		0			0
$775$	0.173332	−	0.300219i	0.00622625	−	0.0107842i
$776$	−12.1098	−	10.1614i	−0.434717	−	0.364771i
$777$		0			0
$778$	1.57372	+	8.92501i	0.0564206	+	0.319977i
$779$	1.17492	−	0.985872i	0.0420958	−	0.0353225i
$780$		0			0
$781$	−29.8171	+	10.8525i	−1.06694	+	0.388334i
$782$	1.34633			0.0481446
$783$		0			0
$784$	−15.7448			−0.562315
$785$	26.1445	−	9.51581i	0.933136	−	0.339634i
$786$		0			0
$787$	−29.7348	+	24.9505i	−1.05993	+	0.889388i	−0.994103	−	0.108443i	$-0.965413\pi$
$787$	−29.7348	+	24.9505i	−1.05993	+	0.889388i	−0.0658285	+	0.997831i	$0.520969\pi$
$788$	−7.00437	−	39.7238i	−0.249521	−	1.41510i
$789$		0			0
$790$	−0.344855	−	0.289368i	−0.0122694	−	0.0102952i
$791$	−8.28623	+	14.3522i	−0.294625	+	0.510305i
$792$		0			0
$793$	0.0624304	+	0.108133i	0.00221697	+	0.00383990i
$794$	−2.51418	+	14.2586i	−0.0892250	+	0.506020i
$795$		0			0
$796$	22.1289	+	8.05427i	0.784339	+	0.285476i
$797$	−3.79081	−	1.37974i	−0.134278	−	0.0488730i	0.274007	−	0.961728i	$-0.411651\pi$
$797$	−3.79081	−	1.37974i	−0.134278	−	0.0488730i	−0.408285	+	0.912855i	$0.633873\pi$
$798$		0			0
$799$	3.86129	−	21.8985i	0.136603	−	0.774712i
$800$	0.205612	+	0.356130i	0.00726948	+	0.0125911i
$801$		0			0
$802$	−3.91080	+	6.77371i	−0.138095	+	0.239188i
$803$	−2.18519	−	1.83359i	−0.0771138	−	0.0647061i
$804$		0			0
$805$	0.525068	+	2.97781i	0.0185062	+	0.104954i
$806$	−0.0214359	+	0.0179869i	−0.000755047	+	0.000633560i
$807$		0			0
$808$	−20.6199	+	7.50504i	−0.725406	+	0.264026i
$809$	29.9454			1.05283			0.526413	−	0.850229i	$-0.323537\pi$
$809$	29.9454			1.05283			0.526413	+	0.850229i	$0.323537\pi$
$810$		0			0
$811$	20.2173			0.709927			0.354963	−	0.934880i	$-0.384493\pi$
$811$	20.2173			0.709927			0.354963	+	0.934880i	$0.384493\pi$
$812$	−17.6915	+	6.43918i	−0.620850	+	0.225971i
$813$		0			0
$814$	7.34428	−	6.16258i	0.257417	−	0.215998i
$815$	−1.27503	−	7.23104i	−0.0446623	−	0.253292i
$816$		0			0
$817$	−2.65611	−	2.22874i	−0.0929256	−	0.0779739i
$818$	1.32117	−	2.28834i	0.0461938	−	0.0800099i
$819$		0			0
$820$	−7.43809	−	12.8831i	−0.259749	−	0.449899i
$821$	−4.66656	+	26.4654i	−0.162864	+	0.923648i	0.788375	+	0.615194i	$0.210922\pi$
$821$	−4.66656	+	26.4654i	−0.162864	+	0.923648i	−0.951239	+	0.308453i	$0.900189\pi$
$822$		0			0
$823$	−21.6640	−	7.88504i	−0.755159	−	0.274855i	−0.0643839	−	0.997925i	$-0.520508\pi$
$823$	−21.6640	−	7.88504i	−0.755159	−	0.274855i	−0.690775	+	0.723070i	$0.742730\pi$
$824$	6.82144	+	2.48280i	0.237636	+	0.0864925i
$825$		0			0
$826$	−0.352429	+	1.99873i	−0.0122626	+	0.0695446i
$827$	−2.55476	−	4.42498i	−0.0888378	−	0.153872i	0.818182	−	0.574959i	$-0.194982\pi$
$827$	−2.55476	−	4.42498i	−0.0888378	−	0.153872i	−0.907020	+	0.421087i	$0.861649\pi$
$828$		0			0
$829$	15.2991	−	26.4988i	0.531360	−	0.920343i	−0.467970	−	0.883744i	$-0.655014\pi$
$829$	15.2991	−	26.4988i	0.531360	−	0.920343i	0.999330	−	0.0365985i	$-0.0116523\pi$
$830$	3.25272	+	2.72936i	0.112904	+	0.0947373i
$831$		0			0
$832$	0.0130140	+	0.0738063i	0.000451181	+	0.00255877i
$833$	−12.6199	+	10.5893i	−0.437252	+	0.366898i
$834$		0			0
$835$	42.8038	−	15.5793i	1.48129	−	0.539144i
$836$	−3.97744			−0.137563
$837$		0			0
$838$	10.1033			0.349013
$839$	−52.9129	+	19.2587i	−1.82676	+	0.664884i	−0.833004	+	0.553267i	$0.813381\pi$
$839$	−52.9129	+	19.2587i	−1.82676	+	0.664884i	−0.993751	+	0.111617i	$0.964397\pi$
$840$		0			0
$841$	24.4772	−	20.5388i	0.844042	−	0.708235i
$842$	−0.576441	−	3.26916i	−0.0198655	−	0.112663i
$843$		0			0
$844$	33.5905	+	28.1858i	1.15623	+	0.970195i
$845$	−14.3984	+	24.9387i	−0.495318	+	0.857917i
$846$		0			0
$847$	10.6878	+	18.5118i	0.367237	+	0.636073i
$848$	0.676200	−	3.83492i	0.0232208	−	0.131692i
$849$		0			0
$850$	0.113682	+	0.0413768i	0.00389926	+	0.00141921i
$851$	−4.30089	−	1.56539i	−0.147433	−	0.0536610i
$852$		0			0
$853$	−7.90880	+	44.8531i	−0.270792	+	1.53574i	0.481226	+	0.876597i	$0.340192\pi$
$853$	−7.90880	+	44.8531i	−0.270792	+	1.53574i	−0.752018	+	0.659143i	$0.770919\pi$
$854$	1.89540	+	3.28294i	0.0648594	+	0.112340i
$855$		0			0
$856$	8.98154	−	15.5565i	0.306983	−	0.531710i
$857$	13.3975	+	11.2418i	0.457649	+	0.384013i	0.842265	−	0.539063i	$-0.181222\pi$
$857$	13.3975	+	11.2418i	0.457649	+	0.384013i	−0.384616	+	0.923077i	$0.625666\pi$
$858$		0			0
$859$	3.18575	+	18.0673i	0.108697	+	0.616448i	0.989679	+	0.143300i	$0.0457714\pi$
$859$	3.18575	+	18.0673i	0.108697	+	0.616448i	−0.880983	+	0.473148i	$0.843117\pi$
$860$	−25.7623	+	21.6171i	−0.878488	+	0.737139i
$861$		0			0
$862$	3.85383	−	1.40268i	0.131262	−	0.0477755i
$863$	−4.65373			−0.158415			−0.0792073	−	0.996858i	$-0.525239\pi$
$863$	−4.65373			−0.158415			−0.0792073	+	0.996858i	$0.525239\pi$
$864$		0			0
$865$	31.0863			1.05697
$866$	2.38294	−	0.867321i	0.0809758	−	0.0294728i
$867$		0			0
$868$	6.88980	−	5.78123i	0.233855	−	0.196228i
$869$	0.442973	+	2.51222i	0.0150268	+	0.0852213i
$870$		0			0
$871$	0.152541	+	0.127997i	0.00516864	+	0.00433700i
$872$	11.5311	−	19.9725i	0.390493	−	0.676354i
$873$		0			0
$874$	−0.0896791	−	0.155329i	−0.00303344	−	0.00525407i
$875$	−2.58524	+	14.6617i	−0.0873972	+	0.495654i
$876$		0			0
$877$	3.44594	+	1.25422i	0.116361	+	0.0423520i	0.399545	−	0.916714i	$-0.369168\pi$
$877$	3.44594	+	1.25422i	0.116361	+	0.0423520i	−0.283183	+	0.959066i	$0.591390\pi$
$878$	5.90848	+	2.15051i	0.199402	+	0.0725763i
$879$		0			0
$880$	−6.00648	+	34.0644i	−0.202478	+	1.14831i
$881$	19.1504	+	33.1694i	0.645193	+	1.11751i	0.984257	+	0.176744i	$0.0565564\pi$
$881$	19.1504	+	33.1694i	0.645193	+	1.11751i	−0.339064	+	0.940763i	$0.610110\pi$
$882$		0			0
$883$	−11.3071	+	19.5844i	−0.380513	+	0.659069i	−0.991136	−	0.132853i	$-0.957586\pi$
$883$	−11.3071	+	19.5844i	−0.380513	+	0.659069i	0.610622	+	0.791922i	$0.290919\pi$
$884$	0.0791952	+	0.0664527i	0.00266362	+	0.00223504i
$885$		0			0
$886$	0.0521459	+	0.295734i	0.00175188	+	0.00993538i
$887$	1.45285	−	1.21908i	0.0487818	−	0.0409328i	−0.618071	−	0.786122i	$-0.712085\pi$
$887$	1.45285	−	1.21908i	0.0487818	−	0.0409328i	0.666853	+	0.745190i	$0.267641\pi$
$888$		0			0
$889$	−10.4102	+	3.78899i	−0.349146	+	0.127079i
$890$	−3.10435			−0.104058
$891$		0			0
$892$	−39.5852			−1.32541
$893$	−2.78368	+	1.01318i	−0.0931522	+	0.0339046i
$894$		0			0
$895$	17.2917	−	14.5095i	0.577998	−	0.484998i
$896$	2.42276	+	13.7401i	0.0809386	+	0.459026i
$897$		0			0
$898$	−0.531009	−	0.445570i	−0.0177200	−	0.0148689i
$899$	−14.5592	+	25.2172i	−0.485575	+	0.841041i
$900$		0			0
$901$	−2.03722	−	3.52856i	−0.0678695	−	0.117553i
$902$	1.38269	−	7.84165i	0.0460387	−	0.261098i
$903$		0			0
$904$	−18.7655	−	6.83007i	−0.624130	−	0.227165i
$905$	50.0722	+	18.2248i	1.66446	+	0.605812i
$906$		0			0
$907$	1.13409	−	6.43172i	0.0376567	−	0.213562i	−0.960173	−	0.279405i	$-0.909863\pi$
$907$	1.13409	−	6.43172i	0.0376567	−	0.213562i	0.997830	+	0.0658435i	$0.0209738\pi$
$908$	−19.7740	−	34.2497i	−0.656225	−	1.13661i
$909$		0			0
$910$	0.0109660	−	0.0189938i	0.000363521	−	0.000629637i
$911$	32.9683	+	27.6637i	1.09229	+	0.916540i	0.996883	−	0.0788981i	$-0.0251402\pi$
$911$	32.9683	+	27.6637i	1.09229	+	0.916540i	0.0954074	+	0.995438i	$0.469585\pi$
$912$		0			0
$913$	−4.17818	−	23.6956i	−0.138277	−	0.784210i
$914$	3.52748	−	2.95991i	0.116679	−	0.0979050i
$915$		0			0
$916$	−18.5548	+	6.75339i	−0.613067	+	0.223138i
$917$	−20.5003			−0.676980
$918$		0			0
$919$	−16.7911			−0.553887			−0.276943	−	0.960886i	$-0.589321\pi$
$919$	−16.7911			−0.553887			−0.276943	+	0.960886i	$0.589321\pi$
$920$	−3.42387	+	1.24619i	−0.112882	+	0.0410856i
$921$		0			0
$922$	6.96505	−	5.84437i	0.229382	−	0.192474i
$923$	−0.0190793	−	0.108204i	−0.000628001	−	0.00356157i
$924$		0			0
$925$	−0.315051	−	0.264359i	−0.0103588	−	0.00869208i
$926$	−5.16253	+	8.94176i	−0.169651	+	0.293844i
$927$		0			0
$928$	−17.2706	−	29.9135i	−0.566935	−	0.981960i
$929$	2.01432	−	11.4238i	0.0660877	−	0.374802i	−0.933769	−	0.357876i	$-0.883501\pi$
$929$	2.01432	−	11.4238i	0.0660877	−	0.374802i	0.999857	−	0.0169258i	$-0.00538789\pi$
$930$		0			0
$931$	2.06232	+	0.750625i	0.0675900	+	0.0246007i
$932$	−13.1176	−	4.77440i	−0.429680	−	0.156391i
$933$		0			0
$934$	0.853874	−	4.84256i	0.0279396	−	0.158453i
$935$	18.0960	+	31.3432i	0.591802	+	1.02503i
$936$		0			0
$937$	−23.8976	+	41.3919i	−0.780702	+	1.35222i	0.150832	+	0.988559i	$0.451805\pi$
$937$	−23.8976	+	41.3919i	−0.780702	+	1.35222i	−0.931533	+	0.363656i	$0.881528\pi$
$938$	4.63117	+	3.88601i	0.151213	+	0.126883i
$939$		0			0
$940$	4.98932	+	28.2959i	0.162734	+	0.922909i
$941$	−8.62593	+	7.23801i	−0.281197	+	0.235953i	−0.772467	−	0.635055i	$-0.780977\pi$
$941$	−8.62593	+	7.23801i	−0.281197	+	0.235953i	0.491270	+	0.871008i	$0.336533\pi$
$942$		0			0
$943$	−3.57206	+	1.30012i	−0.116322	+	0.0423379i
$944$	11.0837			0.360743
$945$		0			0
$946$	−18.0010			−0.585261
$947$	6.88973	−	2.50766i	0.223886	−	0.0814879i	−0.227642	−	0.973745i	$-0.573101\pi$
$947$	6.88973	−	2.50766i	0.223886	−	0.0814879i	0.451528	+	0.892257i	$0.350879\pi$
$948$		0			0
$949$	0.00756662	−	0.00634915i	0.000245623	−	0.000206102i
$950$	−0.00279864	−	0.0158719i	−9.07998e−5	−	0.000514951i
$951$		0			0
$952$	5.03589	+	4.22561i	0.163214	+	0.136953i
$953$	−12.4377	+	21.5427i	−0.402895	+	0.697835i	−0.994074	−	0.108705i	$-0.965329\pi$
$953$	−12.4377	+	21.5427i	−0.402895	+	0.697835i	0.591179	+	0.806541i	$0.298663\pi$
$954$		0			0
$955$	−12.1241	−	20.9996i	−0.392328	−	0.679531i
$956$	−1.02543	+	5.81547i	−0.0331646	+	0.188086i
$957$		0			0
$958$	1.12725	+	0.410286i	0.0364199	+	0.0132558i
$959$	−14.8897	−	5.41941i	−0.480814	−	0.175002i
$960$		0			0
$961$	−2.96758	+	16.8300i	−0.0957283	+	0.542902i
$962$	0.0165988	+	0.0287500i	0.000535168	+	0.000926937i
$963$		0			0
$964$	−24.2540	+	42.0091i	−0.781167	+	1.35302i
$965$	18.3370	+	15.3866i	0.590288	+	0.495311i
$966$		0			0
$967$	−5.90924	−	33.5130i	−0.190028	−	1.07770i	−0.919323	−	0.393505i	$-0.871263\pi$
$967$	−5.90924	−	33.5130i	−0.190028	−	1.07770i	0.729294	−	0.684200i	$-0.239849\pi$
$968$	−19.7314	+	16.5566i	−0.634192	+	0.532150i
$969$		0			0
$970$	8.59761	−	3.12927i	0.276053	−	0.100475i
$971$	34.2476			1.09906			0.549530	−	0.835474i	$-0.314807\pi$
$971$	34.2476			1.09906			0.549530	+	0.835474i	$0.314807\pi$
$972$		0			0
$973$	−8.10928			−0.259971
$974$	−3.41962	+	1.24464i	−0.109572	+	0.0398808i
$975$		0			0
$976$	15.8587	−	13.3070i	0.507625	−	0.425948i
$977$	4.06637	+	23.0615i	0.130095	+	0.737804i	0.978151	+	0.207897i	$0.0666620\pi$
$977$	4.06637	+	23.0615i	0.130095	+	0.737804i	−0.848056	+	0.529907i	$0.822227\pi$
$978$		0			0
$979$	13.4756	+	11.3074i	0.430682	+	0.361386i
$980$	10.6434	−	18.4349i	0.339990	−	0.588880i
$981$		0			0
$982$	−4.68917	−	8.12188i	−0.149637	−	0.259180i
$983$	5.76566	−	32.6987i	0.183896	−	1.04293i	−0.743470	−	0.668770i	$-0.766821\pi$
$983$	5.76566	−	32.6987i	0.183896	−	1.04293i	0.927366	−	0.374157i	$-0.122068\pi$
$984$		0			0
$985$	45.9478	+	16.7236i	1.46402	+	0.532859i
$986$	−9.54883	−	3.47549i	−0.304097	−	0.110682i
$987$		0			0
$988$	0.00239159	−	0.0135634i	7.60865e−5	−	0.000431508i
$989$	4.29678	+	7.44223i	0.136630	+	0.236649i
$990$		0			0
$991$	14.0903	−	24.4051i	0.447594	−	0.775255i	−0.550635	−	0.834746i	$-0.685614\pi$
$991$	14.0903	−	24.4051i	0.447594	−	0.775255i	0.998229	+	0.0594912i	$0.0189478\pi$
$992$	12.6405	+	10.6066i	0.401336	+	0.336761i
$993$		0			0
$994$	−0.579251	−	3.28510i	−0.0183727	−	0.104197i
$995$	−21.8680	+	18.3494i	−0.693261	+	0.581715i
$996$		0			0
$997$	42.2398	−	15.3740i	1.33775	−	0.486901i	0.428646	−	0.903472i	$-0.358991\pi$
$997$	42.2398	−	15.3740i	1.33775	−	0.486901i	0.909103	+	0.416571i	$0.136768\pi$
$998$	−10.5249			−0.333161
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.e.b.55.2		12
3.2	odd	2		243.2.e.c.55.1		12
9.2	odd	6		27.2.e.a.16.2	✓	12
9.4	even	3		243.2.e.a.217.1		12
9.5	odd	6		243.2.e.d.217.2		12
9.7	even	3		81.2.e.a.46.1		12
27.2	odd	18		729.2.a.a.1.4		6
27.4	even	9	inner	243.2.e.b.190.2		12
27.5	odd	18		243.2.e.d.28.2		12
27.7	even	9		729.2.c.b.487.4		12
27.11	odd	18		729.2.c.e.244.3		12
27.13	even	9		81.2.e.a.37.1		12
27.14	odd	18		27.2.e.a.22.2	yes	12
27.16	even	9		729.2.c.b.244.4		12
27.20	odd	18		729.2.c.e.487.3		12
27.22	even	9		243.2.e.a.28.1		12
27.23	odd	18		243.2.e.c.190.1		12
27.25	even	9		729.2.a.d.1.3		6
36.11	even	6		432.2.u.c.97.1		12
45.2	even	12		675.2.u.b.124.3		24
45.29	odd	6		675.2.l.c.151.1		12
45.38	even	12		675.2.u.b.124.2		24
108.95	even	18		432.2.u.c.49.1		12
135.14	odd	18		675.2.l.c.76.1		12
135.68	even	36		675.2.u.b.49.3		24
135.122	even	36		675.2.u.b.49.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.2	✓	12	9.2	odd	6
27.2.e.a.22.2	yes	12	27.14	odd	18
81.2.e.a.37.1		12	27.13	even	9
81.2.e.a.46.1		12	9.7	even	3
243.2.e.a.28.1		12	27.22	even	9
243.2.e.a.217.1		12	9.4	even	3
243.2.e.b.55.2		12	1.1	even	1	trivial
243.2.e.b.190.2		12	27.4	even	9	inner
243.2.e.c.55.1		12	3.2	odd	2
243.2.e.c.190.1		12	27.23	odd	18
243.2.e.d.28.2		12	27.5	odd	18
243.2.e.d.217.2		12	9.5	odd	6
432.2.u.c.49.1		12	108.95	even	18
432.2.u.c.97.1		12	36.11	even	6
675.2.l.c.76.1		12	135.14	odd	18
675.2.l.c.151.1		12	45.29	odd	6
675.2.u.b.49.2		24	135.122	even	36
675.2.u.b.49.3		24	135.68	even	36
675.2.u.b.124.2		24	45.38	even	12
675.2.u.b.124.3		24	45.2	even	12
729.2.a.a.1.4		6	27.2	odd	18
729.2.a.d.1.3		6	27.25	even	9
729.2.c.b.244.4		12	27.16	even	9
729.2.c.b.487.4		12	27.7	even	9
729.2.c.e.244.3		12	27.11	odd	18
729.2.c.e.487.3		12	27.20	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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.390411 + 0.142098i) q^{2} +(-1.39986 + 1.17462i) q^{4} +(-0.384663 - 2.18153i) q^{5} +(-1.01089 - 0.848241i) q^{7} +(0.795075 - 1.37711i) q^{8} +(0.460168 + 0.797034i) q^{10} +(0.905608 - 5.13596i) q^{11} +(0.0169695 + 0.00617638i) q^{13} +(0.515197 + 0.187516i) q^{14} +(0.519924 - 2.94863i) q^{16} +(-1.56640 - 2.71308i) q^{17} +(-0.208676 + 0.361438i) q^{19} +(3.10095 + 2.60201i) q^{20} +(0.376249 + 2.13382i) q^{22} +(0.792386 - 0.664891i) q^{23} +(0.0873421 - 0.0317899i) q^{25} -0.00750270 q^{26} +2.41147 q^{28} +(-7.33639 + 2.67023i) q^{29} +(2.85709 - 2.39738i) q^{31} +(0.768264 + 4.35704i) q^{32} +(0.997061 + 0.836633i) q^{34} +(-1.46161 + 2.53159i) q^{35} +(-2.21238 - 3.83195i) q^{37} +(0.0301099 - 0.170762i) q^{38} +(-3.31005 - 1.20476i) q^{40} +(-3.45331 - 1.25690i) q^{41} +(-1.44265 + 8.18166i) q^{43} +(4.76508 + 8.25337i) q^{44} +(-0.214876 + 0.372177i) q^{46} +(5.43731 + 4.56245i) q^{47} +(-0.913143 - 5.17869i) q^{49} +(-0.0295820 + 0.0248222i) q^{50} +(-0.0310098 + 0.0112866i) q^{52} +1.30057 q^{53} -11.5526 q^{55} +(-1.97186 + 0.717698i) q^{56} +(2.48477 - 2.08497i) q^{58} +(0.642813 + 3.64557i) q^{59} +(5.29661 + 4.44439i) q^{61} +(-0.774775 + 1.34195i) q^{62} +(2.07506 + 3.59410i) q^{64} +(0.00694645 - 0.0393953i) q^{65} +(10.3618 + 3.77139i) q^{67} +(5.37958 + 1.95801i) q^{68} +(0.210896 - 1.19605i) q^{70} +(-3.04214 - 5.26914i) q^{71} +(0.273486 - 0.473692i) q^{73} +(1.40825 + 1.18166i) q^{74} +(-0.132435 - 0.751078i) q^{76} +(-5.27200 + 4.42374i) q^{77} +(-0.459645 + 0.167297i) q^{79} -6.63254 q^{80} +1.52681 q^{82} +(4.33543 - 1.57797i) q^{83} +(-5.31614 + 4.46077i) q^{85} +(-0.599371 - 3.39920i) q^{86} +(-6.35275 - 5.33059i) q^{88} +(-1.68653 + 2.92116i) q^{89} +(-0.0119153 - 0.0206379i) q^{91} +(-0.328234 + 1.86151i) q^{92} +(-2.77110 - 1.00860i) q^{94} +(0.868758 + 0.316202i) q^{95} +(1.72630 - 9.79033i) q^{97} +(1.09238 + 1.89206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28}+ \cdots + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Introduction

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