LMFDB - Embedded newform 729.2.g.a.622.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] 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("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,-45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			622.2
Character	$\chi$	$=$	729.622
Dual form			729.2.g.a.109.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38579 + 1.46885i) q^{2} +(-0.120822 - 2.07444i) q^{4} +(-2.74943 - 0.321362i) q^{5} +(-0.546257 + 0.274341i) q^{7} +(0.120591 + 0.101188i) q^{8} +(4.28217 - 3.59317i) q^{10} +(1.48325 - 3.43857i) q^{11} +(3.32773 - 0.788687i) q^{13} +(0.354033 - 1.18255i) q^{14} +(3.81206 - 0.445566i) q^{16} +(1.31516 + 7.45862i) q^{17} +(0.132568 - 0.751830i) q^{19} +(-0.334454 + 5.74235i) q^{20} +(2.99528 + 6.94383i) q^{22} +(-1.94270 - 0.975661i) q^{23} +(2.59085 + 0.614044i) q^{25} +(-3.45308 + 5.98091i) q^{26} +(0.635103 + 1.10003i) q^{28} +(-1.30287 - 4.35188i) q^{29} +(-6.83895 + 4.49805i) q^{31} +(-4.81627 + 6.46937i) q^{32} +(-12.7782 - 8.40432i) q^{34} +(1.59006 - 0.578734i) q^{35} +(3.96908 + 1.44463i) q^{37} +(0.920617 + 1.23660i) q^{38} +(-0.299038 - 0.316962i) q^{40} +(6.20503 + 6.57695i) q^{41} +(1.04785 + 1.40751i) q^{43} +(-7.31231 - 2.66146i) q^{44} +(4.12528 - 1.50148i) q^{46} +(9.82847 + 6.46428i) q^{47} +(-3.95698 + 5.31514i) q^{49} +(-4.49233 + 2.95465i) q^{50} +(-2.03815 - 6.80788i) q^{52} +(2.80062 + 4.85082i) q^{53} +(-5.18313 + 8.97744i) q^{55} +(-0.0936337 - 0.0221916i) q^{56} +(8.19779 + 4.11708i) q^{58} +(-0.599347 - 1.38944i) q^{59} +(-0.175804 + 3.01844i) q^{61} +(2.87039 - 16.2788i) q^{62} +(-1.49529 - 8.48019i) q^{64} +(-9.40281 + 1.09903i) q^{65} +(2.19466 - 7.33068i) q^{67} +(15.3135 - 3.62938i) q^{68} +(-1.35341 + 3.13757i) q^{70} +(5.19850 - 4.36206i) q^{71} +(0.438511 + 0.367955i) q^{73} +(-7.62227 + 3.82805i) q^{74} +(-1.57564 - 0.184166i) q^{76} +(0.133101 + 2.28526i) q^{77} +(-6.32380 + 6.70284i) q^{79} -10.6242 q^{80} -18.2595 q^{82} +(-4.24676 + 4.50130i) q^{83} +(-1.21901 - 20.9296i) q^{85} +(-3.51954 - 0.411375i) q^{86} +(0.526809 - 0.264573i) q^{88} +(3.52742 + 2.95986i) q^{89} +(-1.60143 + 1.34376i) q^{91} +(-1.78923 + 4.14790i) q^{92} +(-23.1153 + 5.47843i) q^{94} +(-0.606095 + 2.02450i) q^{95} +(10.4458 - 1.22093i) q^{97} +(-2.32362 - 13.1779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

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 $

$2$	−1.38579	+	1.46885i	−0.979903	+	1.03864i	0.0193427	+	0.999813i	$0.493843\pi$
$2$	−1.38579	+	1.46885i	−0.979903	+	1.03864i	−0.999246	+	0.0388240i	$0.987639\pi$
$3$		0			0
$3$		0			0
$4$	−0.120822	−	2.07444i	−0.0604111	−	1.03722i
$5$	−2.74943	−	0.321362i	−1.22958	−	0.143717i	−0.523610	−	0.851958i	$-0.675415\pi$
$5$	−2.74943	−	0.321362i	−1.22958	−	0.143717i	−0.705971	+	0.708241i	$0.749489\pi$
$6$		0			0
$7$	−0.546257	+	0.274341i	−0.206466	+	0.103691i	−0.549027	−	0.835804i	$-0.685002\pi$
$7$	−0.546257	+	0.274341i	−0.206466	+	0.103691i	0.342562	+	0.939495i	$0.388705\pi$
$8$	0.120591	+	0.101188i	0.0426353	+	0.0357753i
$9$		0			0
$10$	4.28217	−	3.59317i	1.35414	−	1.13626i
$11$	1.48325	−	3.43857i	0.447218	−	1.03677i	−0.534282	−	0.845306i	$-0.679418\pi$
$11$	1.48325	−	3.43857i	0.447218	−	1.03677i	0.981500	−	0.191462i	$-0.0613228\pi$
$12$		0			0
$13$	3.32773	−	0.788687i	0.922947	−	0.218742i	0.258442	−	0.966027i	$-0.416791\pi$
$13$	3.32773	−	0.788687i	0.922947	−	0.218742i	0.664504	+	0.747284i	$0.268643\pi$
$14$	0.354033	−	1.18255i	0.0946193	−	0.316050i
$15$		0			0
$16$	3.81206	−	0.445566i	0.953016	−	0.111392i
$17$	1.31516	+	7.45862i	0.318972	+	1.80898i	0.549030	+	0.835803i	$0.314997\pi$
$17$	1.31516	+	7.45862i	0.318972	+	1.80898i	−0.230058	+	0.973177i	$0.573891\pi$
$18$		0			0
$19$	0.132568	−	0.751830i	0.0304132	−	0.172482i	−0.965818	−	0.259222i	$-0.916534\pi$
$19$	0.132568	−	0.751830i	0.0304132	−	0.172482i	0.996231	+	0.0867403i	$0.0276450\pi$
$20$	−0.334454	+	5.74235i	−0.0747861	+	1.28403i
$21$		0			0
$22$	2.99528	+	6.94383i	0.638595	+	1.48043i
$23$	−1.94270	−	0.975661i	−0.405081	−	0.203439i	0.234579	−	0.972097i	$-0.424629\pi$
$23$	−1.94270	−	0.975661i	−0.405081	−	0.203439i	−0.639660	+	0.768658i	$0.720925\pi$
$24$		0			0
$25$	2.59085	+	0.614044i	0.518171	+	0.122809i
$26$	−3.45308	+	5.98091i	−0.677205	+	1.17295i
$27$		0			0
$28$	0.635103	+	1.10003i	0.120023	+	0.207886i
$29$	−1.30287	−	4.35188i	−0.241937	−	0.808124i	−0.989575	−	0.144018i	$-0.953998\pi$
$29$	−1.30287	−	4.35188i	−0.241937	−	0.808124i	0.747639	−	0.664106i	$-0.231188\pi$
$30$		0			0
$31$	−6.83895	+	4.49805i	−1.22831	+	0.807873i	−0.986708	−	0.162502i	$-0.948044\pi$
$31$	−6.83895	+	4.49805i	−1.22831	+	0.807873i	−0.241603	+	0.970375i	$0.577673\pi$
$32$	−4.81627	+	6.46937i	−0.851404	+	1.14363i
$33$		0			0
$34$	−12.7782	−	8.40432i	−2.19143	−	1.44133i
$35$	1.59006	−	0.578734i	0.268769	−	0.0978239i
$36$		0			0
$37$	3.96908	+	1.44463i	0.652513	+	0.237495i	0.647001	−	0.762489i	$-0.276023\pi$
$37$	3.96908	+	1.44463i	0.652513	+	0.237495i	0.00551256	+	0.999985i	$0.498245\pi$
$38$	0.920617	+	1.23660i	0.149344	+	0.200604i
$39$		0			0
$40$	−0.299038	−	0.316962i	−0.0472821	−	0.0501161i
$41$	6.20503	+	6.57695i	0.969063	+	1.02715i	0.999619	+	0.0276134i	$0.00879075\pi$
$41$	6.20503	+	6.57695i	0.969063	+	1.02715i	−0.0305559	+	0.999533i	$0.509728\pi$
$42$		0			0
$43$	1.04785	+	1.40751i	0.159796	+	0.214644i	0.874809	−	0.484468i	$-0.160987\pi$
$43$	1.04785	+	1.40751i	0.159796	+	0.214644i	−0.715013	+	0.699111i	$0.753579\pi$
$44$	−7.31231	−	2.66146i	−1.10237	−	0.401231i
$45$		0			0
$46$	4.12528	−	1.50148i	0.608240	−	0.221381i
$47$	9.82847	+	6.46428i	1.43363	+	0.942913i	0.999107	+	0.0422515i	$0.0134531\pi$
$47$	9.82847	+	6.46428i	1.43363	+	0.942913i	0.434522	+	0.900661i	$0.356917\pi$
$48$		0			0
$49$	−3.95698	+	5.31514i	−0.565282	+	0.759306i
$50$	−4.49233	+	2.95465i	−0.635311	+	0.417851i
$51$		0			0
$52$	−2.03815	−	6.80788i	−0.282640	−	0.944084i
$53$	2.80062	+	4.85082i	0.384695	+	0.666312i	0.991727	−	0.128366i	$-0.0409732\pi$
$53$	2.80062	+	4.85082i	0.384695	+	0.666312i	−0.607032	+	0.794678i	$0.707640\pi$
$54$		0			0
$55$	−5.18313	+	8.97744i	−0.698893	+	1.21052i
$56$	−0.0936337	−	0.0221916i	−0.0125123	−	0.00296548i
$57$		0			0
$58$	8.19779	+	4.11708i	1.07642	+	0.540599i
$59$	−0.599347	−	1.38944i	−0.0780283	−	0.180890i	0.874737	−	0.484599i	$-0.161034\pi$
$59$	−0.599347	−	1.38944i	−0.0780283	−	0.180890i	−0.952765	+	0.303709i	$0.901775\pi$
$60$		0			0
$61$	−0.175804	+	3.01844i	−0.0225094	+	0.386471i	0.968173	+	0.250281i	$0.0805229\pi$
$61$	−0.175804	+	3.01844i	−0.0225094	+	0.386471i	−0.990683	+	0.136190i	$0.956514\pi$
$62$	2.87039	−	16.2788i	0.364540	−	2.06741i
$63$		0			0
$64$	−1.49529	−	8.48019i	−0.186911	−	1.06002i
$65$	−9.40281	+	1.09903i	−1.16628	+	0.136318i
$66$		0			0
$67$	2.19466	−	7.33068i	0.268121	−	0.895585i	−0.712831	−	0.701335i	$-0.752588\pi$
$67$	2.19466	−	7.33068i	0.268121	−	0.895585i	0.980952	−	0.194250i	$-0.0622272\pi$
$68$	15.3135	−	3.62938i	1.85704	−	0.440126i
$69$		0			0
$70$	−1.35341	+	3.13757i	−0.161764	+	0.375011i
$71$	5.19850	−	4.36206i	0.616948	−	0.517681i	−0.279895	−	0.960031i	$-0.590299\pi$
$71$	5.19850	−	4.36206i	0.616948	−	0.517681i	0.896843	+	0.442350i	$0.145855\pi$
$72$		0			0
$73$	0.438511	+	0.367955i	0.0513238	+	0.0430658i	0.668089	−	0.744082i	$-0.267113\pi$
$73$	0.438511	+	0.367955i	0.0513238	+	0.0430658i	−0.616765	+	0.787147i	$0.711557\pi$
$74$	−7.62227	+	3.82805i	−0.886071	+	0.445002i
$75$		0			0
$76$	−1.57564	−	0.184166i	−0.180739	−	0.0211253i
$77$	0.133101	+	2.28526i	0.0151683	+	0.260430i
$78$		0			0
$79$	−6.32380	+	6.70284i	−0.711483	+	0.754128i	−0.977751	−	0.209771i	$-0.932728\pi$
$79$	−6.32380	+	6.70284i	−0.711483	+	0.754128i	0.266267	+	0.963899i	$0.414210\pi$
$80$	−10.6242			−1.18782
$81$		0			0
$82$	−18.2595			−2.01642
$83$	−4.24676	+	4.50130i	−0.466143	+	0.494082i	−0.917208	−	0.398409i	$-0.869563\pi$
$83$	−4.24676	+	4.50130i	−0.466143	+	0.494082i	0.451065	+	0.892491i	$0.351044\pi$
$84$		0			0
$85$	−1.21901	−	20.9296i	−0.132220	−	2.27013i
$86$	−3.51954	−	0.411375i	−0.379522	−	0.0443597i
$87$		0			0
$88$	0.526809	−	0.264573i	0.0561580	−	0.0282036i
$89$	3.52742	+	2.95986i	0.373906	+	0.313744i	0.810304	−	0.586009i	$-0.199302\pi$
$89$	3.52742	+	2.95986i	0.373906	+	0.313744i	−0.436399	+	0.899753i	$0.643746\pi$
$90$		0			0
$91$	−1.60143	+	1.34376i	−0.167875	+	0.140864i
$92$	−1.78923	+	4.14790i	−0.186540	+	0.432448i
$93$		0			0
$94$	−23.1153	+	5.47843i	−2.38416	+	0.565057i
$95$	−0.606095	+	2.02450i	−0.0621841	+	0.207709i
$96$		0			0
$97$	10.4458	−	1.22093i	1.06061	−	0.123967i	0.432142	−	0.901806i	$-0.357758\pi$
$97$	10.4458	−	1.22093i	1.06061	−	0.123967i	0.628464	+	0.777839i	$0.283684\pi$
$98$	−2.32362	−	13.1779i	−0.234721	−	1.33117i
$99$		0			0
$100$	0.960763	−	5.44876i	0.0960763	−	0.544876i
$101$	0.142370	−	2.44440i	0.0141663	−	0.243227i	−0.983790	−	0.179325i	$-0.942609\pi$
$101$	0.142370	−	2.44440i	0.0141663	−	0.243227i	0.997956	−	0.0639015i	$-0.0203544\pi$
$102$		0			0
$103$	6.75628	+	15.6628i	0.665716	+	1.54330i	0.830527	+	0.556978i	$0.188039\pi$
$103$	6.75628	+	15.6628i	0.665716	+	1.54330i	−0.164811	+	0.986325i	$0.552701\pi$
$104$	0.481100	+	0.241617i	0.0471757	+	0.0236925i
$105$		0			0
$106$	−11.0062	−	2.60853i	−1.06902	−	0.253362i
$107$	−0.402056	+	0.696381i	−0.0388682	+	0.0673217i	−0.884805	−	0.465961i	$-0.845709\pi$
$107$	−0.402056	+	0.696381i	−0.0388682	+	0.0673217i	0.845937	+	0.533283i	$0.179042\pi$
$108$		0			0
$109$	2.11135	+	3.65696i	0.202230	+	0.350273i	0.949247	−	0.314532i	$-0.101848\pi$
$109$	2.11135	+	3.65696i	0.202230	+	0.350273i	−0.747016	+	0.664806i	$0.768514\pi$
$110$	−6.00381	−	20.0541i	−0.572441	−	1.91209i
$111$		0			0
$112$	−1.96013	+	1.28920i	−0.185215	+	0.121818i
$113$	7.37084	−	9.90076i	0.693390	−	0.931385i	−0.306399	−	0.951903i	$-0.599124\pi$
$113$	7.37084	−	9.90076i	0.693390	−	0.931385i	0.999789	+	0.0205182i	$0.00653160\pi$
$114$		0			0
$115$	5.02778	+	3.30682i	0.468842	+	0.308363i
$116$	−8.87030	+	3.22852i	−0.823586	+	0.299761i
$117$		0			0
$118$	2.87146	+	1.04513i	0.264339	+	0.0962116i
$119$	−2.76462	−	3.71352i	−0.253432	−	0.340418i
$120$		0			0
$121$	−2.07506	−	2.19944i	−0.188642	−	0.199949i
$122$	−4.19002	−	4.44116i	−0.379346	−	0.402083i
$123$		0			0
$124$	10.1572	+	13.6435i	0.912145	+	1.22522i
$125$	6.07999	+	2.21294i	0.543811	+	0.197931i
$126$		0			0
$127$	−9.37360	+	3.41171i	−0.831772	+	0.302740i	−0.722586	−	0.691281i	$-0.757047\pi$
$127$	−9.37360	+	3.41171i	−0.831772	+	0.302740i	−0.109186	+	0.994021i	$0.534824\pi$
$128$	1.05138	+	0.691505i	0.0929300	+	0.0611210i
$129$		0			0
$130$	11.4160	−	15.3344i	1.00125	−	1.34491i
$131$	4.58946	−	3.01853i	0.400983	−	0.263731i	−0.332961	−	0.942941i	$-0.608048\pi$
$131$	4.58946	−	3.01853i	0.400983	−	0.263731i	0.733944	+	0.679210i	$0.237677\pi$
$132$		0			0
$133$	0.133841	+	0.447061i	0.0116055	+	0.0387651i
$134$	7.72636	+	13.3824i	0.667456	+	1.15607i
$135$		0			0
$136$	−0.596125	+	1.03252i	−0.0511173	+	0.0885378i
$137$	14.8200	+	3.51241i	1.26616	+	0.300086i	0.808211	−	0.588893i	$-0.200436\pi$
$137$	14.8200	+	3.51241i	1.26616	+	0.300086i	0.457949	+	0.888978i	$0.348584\pi$
$138$		0			0
$139$	14.3127	+	7.18809i	1.21398	+	0.609686i	0.936373	−	0.351008i	$-0.114161\pi$
$139$	14.3127	+	7.18809i	1.21398	+	0.609686i	0.277612	+	0.960693i	$0.410457\pi$
$140$	−1.39266	−	3.22855i	−0.117701	−	0.272863i
$141$		0			0
$142$	−0.796812	+	13.6807i	−0.0668670	+	1.14806i
$143$	2.22392	−	12.6125i	0.185973	−	1.05471i
$144$		0			0
$145$	2.18361	+	12.3839i	0.181339	+	1.02842i
$146$	−1.14816	+	0.134200i	−0.0950222	+	0.0111065i
$147$		0			0
$148$	2.51724	−	8.40816i	0.206916	−	0.691147i
$149$	−8.60207	+	2.03873i	−0.704709	+	0.167019i	−0.567319	−	0.823498i	$-0.692019\pi$
$149$	−8.60207	+	2.03873i	−0.704709	+	0.167019i	−0.137390	+	0.990517i	$0.543871\pi$
$150$		0			0
$151$	0.391266	−	0.907056i	0.0318408	−	0.0738152i	−0.901554	−	0.432667i	$-0.857572\pi$
$151$	0.391266	−	0.907056i	0.0318408	−	0.0738152i	0.933394	+	0.358852i	$0.116832\pi$
$152$	0.0920625	−	0.0772496i	0.00746726	−	0.00626577i
$153$		0			0
$154$	−3.54117	−	2.97139i	−0.285355	−	0.239442i
$155$	20.2487	−	10.1693i	1.62641	−	0.816816i
$156$		0			0
$157$	−18.0755	−	2.11272i	−1.44258	−	0.168613i	−0.641478	−	0.767141i	$-0.721679\pi$
$157$	−18.0755	−	2.11272i	−1.44258	−	0.168613i	−0.801102	+	0.598528i	$0.795753\pi$
$158$	−1.08202	−	18.5775i	−0.0860805	−	1.47795i
$159$		0			0
$160$	15.3210	−	16.2393i	1.21123	−	1.28383i
$161$	1.32888			0.104730
$162$		0			0
$163$	17.1469			1.34305			0.671524	−	0.740983i	$-0.265640\pi$
$163$	17.1469			1.34305			0.671524	+	0.740983i	$0.265640\pi$
$164$	12.8938	−	13.6666i	1.00683	−	1.06718i
$165$		0			0
$166$	−0.726629	−	12.4757i	−0.0563974	−	0.968306i
$167$	5.86126	+	0.685083i	0.453558	+	0.0530133i	0.339805	−	0.940496i	$-0.389639\pi$
$167$	5.86126	+	0.685083i	0.453558	+	0.0530133i	0.113753	+	0.993509i	$0.463713\pi$
$168$		0			0
$169$	−1.16546	+	0.585314i	−0.0896505	+	0.0450242i
$170$	32.4318	+	27.2135i	2.48740	+	2.08718i
$171$		0			0
$172$	2.79319	−	2.34377i	0.212979	−	0.178711i
$173$	−3.56184	+	8.25726i	−0.270801	+	0.627788i	−0.998298	−	0.0583234i	$-0.981425\pi$
$173$	−3.56184	+	8.25726i	−0.270801	+	0.627788i	0.727496	+	0.686111i	$0.240684\pi$
$174$		0			0
$175$	−1.58373	+	0.375351i	−0.119719	+	0.0283739i
$176$	4.12215	−	13.7689i	0.310719	−	1.03787i
$177$		0			0
$178$	−9.23587	+	1.07952i	−0.692258	+	0.0809134i
$179$	−0.223820	−	1.26935i	−0.0167291	−	0.0948754i	0.975300	−	0.220884i	$-0.0708943\pi$
$179$	−0.223820	−	1.26935i	−0.0167291	−	0.0948754i	−0.992029	+	0.126009i	$0.959783\pi$
$180$		0			0
$181$	0.645386	−	3.66017i	0.0479712	−	0.272058i	−0.951382	−	0.308013i	$-0.900336\pi$
$181$	0.645386	−	3.66017i	0.0479712	−	0.272058i	0.999353	+	0.0359546i	$0.0114472\pi$
$182$	0.245463	−	4.21444i	0.0181949	−	0.312395i
$183$		0			0
$184$	−0.135547	−	0.314234i	−0.00999267	−	0.0231656i
$185$	−10.4485	−	5.24741i	−0.768186	−	0.385797i
$186$		0			0
$187$	27.5977	+	6.54077i	2.01814	+	0.478309i
$188$	12.2223	−	21.1696i	0.891400	−	1.54395i
$189$		0			0
$190$	−2.13377	−	3.69580i	−0.154800	−	0.268122i
$191$	2.09081	+	6.98378i	0.151285	+	0.505328i	0.999712	−	0.0239841i	$-0.00763509\pi$
$191$	2.09081	+	6.98378i	0.151285	+	0.505328i	−0.848427	+	0.529313i	$0.822450\pi$
$192$		0			0
$193$	8.04337	−	5.29021i	0.578974	−	0.380797i	−0.225982	−	0.974131i	$-0.572559\pi$
$193$	8.04337	−	5.29021i	0.578974	−	0.380797i	0.804956	+	0.593334i	$0.202189\pi$
$194$	−12.6823	+	17.0352i	−0.910534	+	1.22306i
$195$		0			0
$196$	11.5040	+	7.56632i	0.821716	+	0.540451i
$197$	−4.63898	+	1.68845i	−0.330513	+	0.120297i	−0.501946	−	0.864899i	$-0.667383\pi$
$197$	−4.63898	+	1.68845i	−0.330513	+	0.120297i	0.171433	+	0.985196i	$0.445160\pi$
$198$		0			0
$199$	−2.36550	−	0.860973i	−0.167686	−	0.0610327i	0.256813	−	0.966461i	$-0.417328\pi$
$199$	−2.36550	−	0.860973i	−0.167686	−	0.0610327i	−0.424499	+	0.905428i	$0.639550\pi$
$200$	0.250300	+	0.336211i	0.0176989	+	0.0237737i
$201$		0			0
$202$	3.39317	+	3.59655i	0.238743	+	0.253052i
$203$	1.90560	+	2.01982i	0.133747	+	0.141763i
$204$		0			0
$205$	−14.9467	−	20.0769i	−1.04392	−	1.40223i
$206$	−32.3692	−	11.7814i	−2.25527	−	0.820851i
$207$		0			0
$208$	12.3341	−	4.48925i	0.855217	−	0.311273i
$209$	−2.38859	−	1.57100i	−0.165222	−	0.108668i
$210$		0			0
$211$	4.17283	−	5.60508i	0.287269	−	0.385870i	−0.634939	−	0.772562i	$-0.718975\pi$
$211$	4.17283	−	5.60508i	0.287269	−	0.385870i	0.922209	+	0.386692i	$0.126382\pi$
$212$	9.72436	−	6.39581i	0.667872	−	0.439266i
$213$		0			0
$214$	−0.465716	−	1.55560i	−0.0318357	−	0.106339i
$215$	−2.42868	−	4.20659i	−0.165634	−	0.286887i
$216$		0			0
$217$	2.50183	−	4.33330i	0.169835	−	0.294163i
$218$	−8.29743	−	1.96653i	−0.561973	−	0.133190i
$219$		0			0
$220$	19.2494	+	9.66740i	1.29779	+	0.651776i
$221$	10.2590	+	23.7830i	0.690095	+	1.59982i
$222$		0			0
$223$	1.04650	−	17.9678i	0.0700790	−	1.20321i	−0.761635	−	0.648006i	$-0.775603\pi$
$223$	1.04650	−	17.9678i	0.0700790	−	1.20321i	0.831714	−	0.555204i	$-0.187360\pi$
$224$	0.856110	−	4.85524i	0.0572012	−	0.324404i
$225$		0			0
$226$	4.32831	+	24.5471i	0.287915	+	1.63285i
$227$	−0.609362	+	0.0712243i	−0.0404448	+	0.00472732i	−0.136291	−	0.990669i	$-0.543518\pi$
$227$	−0.609362	+	0.0712243i	−0.0404448	+	0.00472732i	0.0958464	+	0.995396i	$0.469444\pi$
$228$		0			0
$229$	1.43265	−	4.78538i	0.0946720	−	0.316227i	−0.897515	−	0.440983i	$-0.854630\pi$
$229$	1.43265	−	4.78538i	0.0946720	−	0.316227i	0.992187	+	0.124757i	$0.0398150\pi$
$230$	−11.8247	+	2.80250i	−0.779697	+	0.184792i
$231$		0			0
$232$	0.283243	−	0.656632i	0.0185958	−	0.0431100i
$233$	−10.0792	+	8.45747i	−0.660311	+	0.554067i	−0.910180	−	0.414213i	$-0.864057\pi$
$233$	−10.0792	+	8.45747i	−0.660311	+	0.554067i	0.249869	+	0.968280i	$0.419613\pi$
$234$		0			0
$235$	−24.9453	−	20.9316i	−1.62725	−	1.36543i
$236$	−2.80990	+	1.41118i	−0.182909	+	0.0918603i
$237$		0			0
$238$	9.28581	+	1.08536i	0.601910	+	0.0703531i
$239$	−0.529012	−	9.08278i	−0.0342189	−	0.587517i	−0.971219	−	0.238188i	$-0.923447\pi$
$239$	−0.529012	−	9.08278i	−0.0342189	−	0.587517i	0.937000	−	0.349329i	$-0.113590\pi$
$240$		0			0
$241$	9.77902	−	10.3652i	0.629922	−	0.667679i	−0.331277	−	0.943534i	$-0.607479\pi$
$241$	9.77902	−	10.3652i	0.629922	−	0.667679i	0.961199	+	0.275855i	$0.0889609\pi$
$242$	6.10626			0.392526
$243$		0			0
$244$	6.28280			0.402215
$245$	12.5875	−	13.3420i	0.804186	−	0.852387i
$246$		0			0
$247$	−0.151808	−	2.60644i	−0.00965931	−	0.165844i
$248$	−1.27986	−	0.149595i	−0.0812714	−	0.00949926i
$249$		0			0
$250$	−11.6761	+	5.86395i	−0.738461	+	0.370869i
$251$	−6.58379	−	5.52445i	−0.415565	−	0.348700i	0.410908	−	0.911677i	$-0.365212\pi$
$251$	−6.58379	−	5.52445i	−0.415565	−	0.348700i	−0.826473	+	0.562976i	$0.809656\pi$
$252$		0			0
$253$	−6.23640	+	5.23296i	−0.392079	+	0.328993i
$254$	7.97856	−	18.4964i	0.500619	−	1.16057i
$255$		0			0
$256$	14.2851	−	3.38562i	0.892817	−	0.211602i
$257$	−6.36608	+	21.2642i	−0.397105	+	1.32642i	0.492746	+	0.870173i	$0.335993\pi$
$257$	−6.36608	+	21.2642i	−0.397105	+	1.32642i	−0.889851	+	0.456251i	$0.849192\pi$
$258$		0			0
$259$	−2.56446	+	0.299743i	−0.159348	+	0.0186251i
$260$	3.41594	+	19.3728i	0.211848	+	1.20145i
$261$		0			0
$262$	−1.92625	+	10.9243i	−0.119004	+	0.674906i
$263$	0.305988	−	5.25362i	0.0188681	−	0.323952i	−0.975646	−	0.219350i	$-0.929606\pi$
$263$	0.305988	−	5.25362i	0.0188681	−	0.323952i	0.994514	−	0.104602i	$-0.0333568\pi$
$264$		0			0
$265$	−6.14124	−	14.2370i	−0.377254	−	0.874572i
$266$	−0.842145	−	0.422941i	−0.0516352	−	0.0259322i
$267$		0			0
$268$	−15.4722	−	3.66698i	−0.945116	−	0.223997i
$269$	3.11423	−	5.39401i	0.189878	−	0.328878i	−0.755331	−	0.655343i	$-0.772524\pi$
$269$	3.11423	−	5.39401i	0.189878	−	0.328878i	0.945209	+	0.326465i	$0.105857\pi$
$270$		0			0
$271$	−3.65935	−	6.33818i	−0.222290	−	0.385017i	0.733213	−	0.679999i	$-0.238020\pi$
$271$	−3.65935	−	6.33818i	−0.222290	−	0.385017i	−0.955503	+	0.294982i	$0.904686\pi$
$272$	8.33676	+	27.8467i	0.505490	+	1.68846i
$273$		0			0
$274$	−25.6967	+	16.9010i	−1.55239	+	1.02103i
$275$	5.95433	−	7.99805i	0.359060	−	0.482301i
$276$		0			0
$277$	15.5663	+	10.2381i	0.935287	+	0.615148i	0.923010	−	0.384776i	$-0.125721\pi$
$277$	15.5663	+	10.2381i	0.935287	+	0.615148i	0.0122776	+	0.999925i	$0.496092\pi$
$278$	−30.3926	+	11.0620i	−1.82283	+	0.663456i
$279$		0			0
$280$	0.250307	+	0.0911045i	0.0149587	+	0.00544453i
$281$	0.610261	+	0.819722i	0.0364051	+	0.0489005i	0.819953	−	0.572431i	$-0.193999\pi$
$281$	0.610261	+	0.819722i	0.0364051	+	0.0489005i	−0.783548	+	0.621331i	$0.786592\pi$
$282$		0			0
$283$	7.52347	+	7.97442i	0.447224	+	0.474030i	0.911287	−	0.411773i	$-0.135090\pi$
$283$	7.52347	+	7.97442i	0.447224	+	0.474030i	−0.464063	+	0.885802i	$0.653609\pi$
$284$	−9.67691	−	10.2569i	−0.574219	−	0.608637i
$285$		0			0
$286$	15.4440	+	20.7449i	0.913222	+	1.22667i
$287$	−5.19387	−	1.89041i	−0.306584	−	0.111588i
$288$		0			0
$289$	−37.9265	+	13.8041i	−2.23097	+	0.812008i
$290$	−21.2161	−	13.9541i	−1.24585	−	0.819412i
$291$		0			0
$292$	0.710317	−	0.954122i	0.0415682	−	0.0558357i
$293$	20.2853	−	13.3418i	1.18508	−	0.779438i	0.205138	−	0.978733i	$-0.434236\pi$
$293$	20.2853	−	13.3418i	1.18508	−	0.779438i	0.979939	+	0.199295i	$0.0638654\pi$
$294$		0			0
$295$	1.20135	+	4.01278i	0.0699451	+	0.233633i
$296$	0.332457	+	0.575832i	0.0193237	+	0.0334696i
$297$		0			0
$298$	8.92609	−	15.4604i	0.517075	−	0.895599i
$299$	−7.23428	−	1.71456i	−0.418369	−	0.0991553i
$300$		0			0
$301$	−0.958536	−	0.481395i	−0.0552491	−	0.0277471i
$302$	0.790120	+	1.83170i	0.0454663	+	0.105403i
$303$		0			0
$304$	0.170367	−	2.92509i	0.00977123	−	0.167765i
$305$	1.45337	−	8.24247i	0.0832198	−	0.471963i
$306$		0			0
$307$	−4.31169	−	24.4528i	−0.246081	−	1.39560i	−0.817968	−	0.575264i	$-0.804899\pi$
$307$	−4.31169	−	24.4528i	−0.246081	−	1.39560i	0.571887	−	0.820333i	$-0.306212\pi$
$308$	4.72455	−	0.552221i	0.269206	−	0.0314657i
$309$		0			0
$310$	−13.1233	+	43.8349i	−0.745354	+	2.48966i
$311$	−1.80082	+	0.426803i	−0.102115	+	0.0242018i	−0.281356	−	0.959604i	$-0.590784\pi$
$311$	−1.80082	+	0.426803i	−0.102115	+	0.0242018i	0.179241	+	0.983805i	$0.442636\pi$
$312$		0			0
$313$	−2.75336	+	6.38301i	−0.155629	+	0.360789i	−0.978136	−	0.207966i	$-0.933316\pi$
$313$	−2.75336	+	6.38301i	−0.155629	+	0.360789i	0.822507	+	0.568755i	$0.192575\pi$
$314$	28.1521	−	23.6225i	1.58872	−	1.33309i
$315$		0			0
$316$	14.6687	+	12.3085i	0.825178	+	0.692406i
$317$	−23.2678	+	11.6855i	−1.30685	+	0.656324i	−0.959578	−	0.281441i	$-0.909188\pi$
$317$	−23.2678	+	11.6855i	−1.30685	+	0.656324i	−0.347270	+	0.937765i	$0.612891\pi$
$318$		0			0
$319$	−16.8967	−	1.97495i	−0.946036	−	0.110576i
$320$	1.38597	+	23.7962i	0.0774781	+	1.33025i
$321$		0			0
$322$	−1.84155	+	1.95193i	−0.102626	+	0.108777i
$323$	5.78196			0.321717
$324$		0			0
$325$	9.10595			0.505107
$326$	−23.7620	+	25.1863i	−1.31606	+	1.39494i
$327$		0			0
$328$	0.0827635	+	1.42099i	0.00456985	+	0.0784613i
$329$	−7.14229	−	0.834814i	−0.393767	−	0.0460248i
$330$		0			0
$331$	−23.2661	+	11.6847i	−1.27882	+	0.642249i	−0.952939	−	0.303161i	$-0.901958\pi$
$331$	−23.2661	+	11.6847i	−1.27882	+	0.642249i	−0.325884	+	0.945410i	$0.605662\pi$
$332$	9.85078	+	8.26579i	0.540632	+	0.453644i
$333$		0			0
$334$	−9.12878	+	7.65996i	−0.499505	+	0.419134i
$335$	−8.38987	+	19.4499i	−0.458387	+	1.06266i
$336$		0			0
$337$	−14.6259	+	3.46641i	−0.796726	+	0.188828i	−0.608767	−	0.793349i	$-0.708335\pi$
$337$	−14.6259	+	3.46641i	−0.796726	+	0.188828i	−0.187959	+	0.982177i	$0.560187\pi$
$338$	0.755339	−	2.52301i	0.0410850	−	0.137234i
$339$		0			0
$340$	−43.2698	+	5.05752i	−2.34663	+	0.274282i
$341$	5.32295	+	30.1880i	0.288254	+	1.63477i
$342$		0			0
$343$	1.44640	−	8.20293i	0.0780981	−	0.442917i
$344$	−0.0160614	+	0.275763i	−0.000865972	+	0.0148682i
$345$		0			0
$346$	−7.19275	−	16.6747i	−0.386685	−	0.896436i
$347$	22.7180	+	11.4094i	1.21957	+	0.612490i	0.937861	−	0.347011i	$-0.112803\pi$
$347$	22.7180	+	11.4094i	1.21957	+	0.612490i	0.281706	+	0.959501i	$0.409100\pi$
$348$		0			0
$349$	−28.4767	−	6.74910i	−1.52432	−	0.361271i	−0.618793	−	0.785554i	$-0.712378\pi$
$349$	−28.4767	−	6.74910i	−1.52432	−	0.361271i	−0.905530	+	0.424283i	$0.860526\pi$
$350$	1.64339	−	2.84643i	0.0878427	−	0.152148i
$351$		0			0
$352$	15.1016	+	26.1568i	0.804920	+	1.39416i
$353$	8.22886	+	27.4863i	0.437978	+	1.46295i	0.837608	+	0.546272i	$0.183954\pi$
$353$	8.22886	+	27.4863i	0.437978	+	1.46295i	−0.399629	+	0.916677i	$0.630861\pi$
$354$		0			0
$355$	−15.6947	+	10.3226i	−0.832988	+	0.547865i
$356$	5.71385	−	7.67504i	0.302834	−	0.406776i
$357$		0			0
$358$	2.17465	+	1.43029i	0.114934	+	0.0755932i
$359$	−19.5984	+	7.13322i	−1.03436	+	0.376477i	−0.802740	−	0.596329i	$-0.796625\pi$
$359$	−19.5984	+	7.13322i	−1.03436	+	0.376477i	−0.231622	+	0.972806i	$0.574403\pi$
$360$		0			0
$361$	17.3065	+	6.29905i	0.910868	+	0.331529i
$362$	4.48188	+	6.02021i	0.235563	+	0.316415i
$363$		0			0
$364$	2.98103	+	3.15971i	0.156249	+	0.165614i
$365$	−1.08741	−	1.15259i	−0.0569175	−	0.0603291i
$366$		0			0
$367$	−20.6418	−	27.7268i	−1.07750	−	1.44733i	−0.884742	−	0.466080i	$-0.845666\pi$
$367$	−20.6418	−	27.7268i	−1.07750	−	1.44733i	−0.192753	−	0.981247i	$-0.561742\pi$
$368$	−7.84042	−	2.85368i	−0.408710	−	0.148758i
$369$		0			0
$370$	22.1871	−	8.07544i	1.15345	−	0.419822i
$371$	−2.86064	−	1.88147i	−0.148517	−	0.0976812i
$372$		0			0
$373$	−5.59504	+	7.51544i	−0.289700	+	0.389135i	−0.923018	−	0.384757i	$-0.874285\pi$
$373$	−5.59504	+	7.51544i	−0.289700	+	0.389135i	0.633318	+	0.773892i	$0.281693\pi$
$374$	−47.8521	+	31.4728i	−2.47437	+	1.62742i
$375$		0			0
$376$	0.531117	+	1.77406i	0.0273903	+	0.0914899i
$377$	−7.76787	−	13.4543i	−0.400065	−	0.692934i
$378$		0			0
$379$	0.963771	−	1.66930i	0.0495056	−	0.0857462i	−0.840211	−	0.542260i	$-0.817569\pi$
$379$	0.963771	−	1.66930i	0.0495056	−	0.0857462i	0.889716	+	0.456514i	$0.150902\pi$
$380$	4.27293	+	1.01270i	0.219197	+	0.0519506i
$381$		0			0
$382$	−13.1556	−	6.60698i	−0.673098	−	0.338042i
$383$	−7.72041	−	17.8979i	−0.394494	−	0.914541i	−0.993504	−	0.113799i	$-0.963698\pi$
$383$	−7.72041	−	17.8979i	−0.394494	−	0.914541i	0.599010	−	0.800742i	$-0.295561\pi$
$384$		0			0
$385$	0.368444	−	6.32594i	0.0187776	−	0.322400i
$386$	−3.37590	+	19.1457i	−0.171829	+	0.974489i
$387$		0			0
$388$	−3.79483	−	21.5216i	−0.192653	−	1.09259i
$389$	−9.07811	+	1.06108i	−0.460279	+	0.0537989i	−0.343073	−	0.939309i	$-0.611468\pi$
$389$	−9.07811	+	1.06108i	−0.460279	+	0.0537989i	−0.117206	+	0.993108i	$0.537394\pi$
$390$		0			0
$391$	4.72213	−	15.7730i	0.238808	−	0.797675i
$392$	−1.01500	+	0.240560i	−0.0512654	+	0.0121501i
$393$		0			0
$394$	3.94857	−	9.15382i	0.198926	−	0.461163i
$395$	19.5409	−	16.3967i	0.983208	−	0.825009i
$396$		0			0
$397$	25.5466	+	21.4361i	1.28215	+	1.07585i	0.992944	+	0.118581i	$0.0378344\pi$
$397$	25.5466	+	21.4361i	1.28215	+	1.07585i	0.289202	+	0.957268i	$0.406610\pi$
$398$	4.54274	−	2.28145i	0.227707	−	0.114359i
$399$		0			0
$400$	10.1501	+	1.18638i	0.507505	+	0.0593188i
$401$	−0.206340	−	3.54271i	−0.0103041	−	0.176915i	−0.999534	−	0.0305412i	$-0.990277\pi$
$401$	−0.206340	−	3.54271i	−0.0103041	−	0.176915i	0.989229	−	0.146373i	$-0.0467601\pi$
$402$		0			0
$403$	−19.2106	+	20.3621i	−0.956950	+	1.01431i
$404$	−5.08795			−0.253135
$405$		0			0
$406$	−5.60758			−0.278300
$407$	10.8546	−	11.5052i	0.538043	−	0.570293i
$408$		0			0
$409$	1.86266	+	31.9807i	0.0921027	+	1.58134i	0.655525	+	0.755173i	$0.272447\pi$
$409$	1.86266	+	31.9807i	0.0921027	+	1.58134i	−0.563422	+	0.826169i	$0.690516\pi$
$410$	50.2031	+	5.86790i	2.47935	+	0.289795i
$411$		0			0
$412$	31.6752	−	15.9079i	1.56053	−	0.783726i
$413$	0.708579	+	0.594568i	0.0348669	+	0.0292568i
$414$		0			0
$415$	13.1227	−	11.0113i	0.644168	−	0.540522i
$416$	−10.9249	+	25.3268i	−0.535639	+	1.24175i
$417$		0			0
$418$	5.61766	−	1.33141i	0.274769	−	0.0651213i
$419$	−4.25467	+	14.2116i	−0.207854	+	0.694281i	0.788955	+	0.614452i	$0.210623\pi$
$419$	−4.25467	+	14.2116i	−0.207854	+	0.694281i	−0.996809	+	0.0798292i	$0.974563\pi$
$420$		0			0
$421$	15.4744	−	1.80870i	0.754176	−	0.0881505i	0.269687	−	0.962948i	$-0.413080\pi$
$421$	15.4744	−	1.80870i	0.754176	−	0.0881505i	0.484489	+	0.874798i	$0.339006\pi$
$422$	2.45037	+	13.8968i	0.119282	+	0.676484i
$423$		0			0
$424$	−0.153114	+	0.868355i	−0.00743589	+	0.0421710i
$425$	−1.17254	+	20.1317i	−0.0568766	+	0.976533i
$426$		0			0
$427$	−0.732046	−	1.69707i	−0.0354262	−	0.0821271i
$428$	1.49318	+	0.749902i	0.0721754	+	0.0362479i
$429$		0			0
$430$	9.54451	+	2.26209i	0.460277	+	0.109088i
$431$	0.648713	−	1.12360i	0.0312474	−	0.0541221i	−0.849979	−	0.526817i	$-0.823385\pi$
$431$	0.648713	−	1.12360i	0.0312474	−	0.0541221i	0.881226	+	0.472695i	$0.156719\pi$
$432$		0			0
$433$	−8.76506	−	15.1815i	−0.421222	−	0.729577i	0.574838	−	0.818268i	$-0.305065\pi$
$433$	−8.76506	−	15.1815i	−0.421222	−	0.729577i	−0.996059	+	0.0886901i	$0.971732\pi$
$434$	2.89796	+	9.67987i	0.139107	+	0.464649i
$435$		0			0
$436$	7.33105	−	4.82170i	0.351093	−	0.230918i
$437$	−0.991071	+	1.33124i	−0.0474094	+	0.0636818i
$438$		0			0
$439$	−18.1453	−	11.9344i	−0.866028	−	0.569596i	0.0369331	−	0.999318i	$-0.488241\pi$
$439$	−18.1453	−	11.9344i	−0.866028	−	0.569596i	−0.902961	+	0.429722i	$0.858612\pi$
$440$	−1.53345	+	0.558129i	−0.0731042	+	0.0266077i
$441$		0			0
$442$	−49.1506	−	17.8894i	−2.33786	−	0.850910i
$443$	−5.46021	−	7.33434i	−0.259422	−	0.348465i	0.653260	−	0.757133i	$-0.273401\pi$
$443$	−5.46021	−	7.33434i	−0.259422	−	0.348465i	−0.912683	+	0.408668i	$0.865993\pi$
$444$		0			0
$445$	−8.74720	−	9.27149i	−0.414657	−	0.439511i
$446$	24.9418	+	26.4367i	1.18103	+	1.25182i
$447$		0			0
$448$	3.14327	+	4.22215i	0.148506	+	0.199478i
$449$	11.6732	+	4.24870i	0.550893	+	0.200509i	0.602443	−	0.798162i	$-0.294194\pi$
$449$	11.6732	+	4.24870i	0.550893	+	0.200509i	−0.0515501	+	0.998670i	$0.516416\pi$
$450$		0			0
$451$	31.8189	−	11.5811i	1.49829	−	0.545335i
$452$	−21.4291	−	14.0941i	−1.00794	−	0.662932i
$453$		0			0
$454$	0.739832	−	0.993767i	0.0347220	−	0.0466398i
$455$	4.83485	−	3.17993i	0.226661	−	0.149077i
$456$		0			0
$457$	5.36176	+	17.9095i	0.250812	+	0.837772i	0.986962	+	0.160953i	$0.0514567\pi$
$457$	5.36176	+	17.9095i	0.250812	+	0.837772i	−0.736150	+	0.676819i	$0.763358\pi$
$458$	5.04367	+	8.73589i	0.235675	+	0.408201i
$459$		0			0
$460$	6.25233	−	10.8293i	0.291516	−	0.504921i
$461$	−39.9745	−	9.47414i	−1.86180	−	0.441255i	−0.863764	−	0.503897i	$-0.831899\pi$
$461$	−39.9745	−	9.47414i	−1.86180	−	0.441255i	−0.998036	+	0.0626425i	$0.980047\pi$
$462$		0			0
$463$	−3.69053	−	1.85346i	−0.171514	−	0.0861374i	0.360971	−	0.932577i	$-0.382445\pi$
$463$	−3.69053	−	1.85346i	−0.171514	−	0.0861374i	−0.532485	+	0.846440i	$0.678742\pi$
$464$	−6.90567	−	16.0091i	−0.320588	−	0.743205i
$465$		0			0
$466$	1.54492	−	26.5252i	0.0715669	−	1.22876i
$467$	4.38922	−	24.8925i	0.203109	−	1.15189i	−0.697279	−	0.716799i	$-0.745606\pi$
$467$	4.38922	−	24.8925i	0.203109	−	1.15189i	0.900388	−	0.435087i	$-0.143283\pi$
$468$		0			0
$469$	0.812254	+	4.60652i	0.0375064	+	0.212710i
$470$	65.3144	−	7.63416i	3.01273	−	0.352138i
$471$		0			0
$472$	0.0683188	−	0.228201i	0.00314463	−	0.0105038i
$473$	6.39406	−	1.51542i	0.293999	−	0.0696791i
$474$		0			0
$475$	0.805121	−	1.86648i	0.0369415	−	0.0856399i
$476$	−7.36945	+	6.18370i	−0.337778	+	0.283430i
$477$		0			0
$478$	14.0744	+	11.8098i	0.643748	+	0.540168i
$479$	18.5894	−	9.33596i	0.849372	−	0.426571i	0.0298064	−	0.999556i	$-0.490511\pi$
$479$	18.5894	−	9.33596i	0.849372	−	0.426571i	0.819566	+	0.572985i	$0.194215\pi$
$480$		0			0
$481$	14.3474	+	1.67697i	0.654185	+	0.0764633i
$482$	1.67321	+	28.7279i	0.0762127	+	1.30852i
$483$		0			0
$484$	−4.31189	+	4.57033i	−0.195995	+	0.207742i
$485$	−29.1122			−1.32192
$486$		0			0
$487$	−6.60060			−0.299102			−0.149551	−	0.988754i	$-0.547783\pi$
$487$	−6.60060			−0.299102			−0.149551	+	0.988754i	$0.547783\pi$
$488$	−0.326629	+	0.346207i	−0.0147858	+	0.0156721i
$489$		0			0
$490$	2.15375	+	36.9784i	0.0972964	+	1.67051i
$491$	−36.2982	−	4.24265i	−1.63811	−	0.191468i	−0.753387	−	0.657577i	$-0.771581\pi$
$491$	−36.2982	−	4.24265i	−1.63811	−	0.191468i	−0.884727	+	0.466109i	$0.845655\pi$
$492$		0			0
$493$	30.7455	−	15.4410i	1.38471	−	0.695427i
$494$	4.03886	+	3.38900i	0.181717	+	0.152479i
$495$		0			0
$496$	−24.0663	+	20.1941i	−1.08061	+	0.906740i
$497$	−1.64303	+	3.80897i	−0.0736998	+	0.170855i
$498$		0			0
$499$	35.4129	−	8.39301i	1.58530	−	0.375723i	0.658890	−	0.752239i	$-0.271026\pi$
$499$	35.4129	−	8.39301i	1.58530	−	0.375723i	0.926410	+	0.376517i	$0.122878\pi$
$500$	3.85600	−	12.8799i	0.172446	−	0.576008i
$501$		0			0
$502$	17.2384	−	2.01488i	0.769387	−	0.0899284i
$503$	−1.38230	−	7.83939i	−0.0616335	−	0.349541i	−0.999992	−	0.00387871i	$-0.998765\pi$
$503$	−1.38230	−	7.83939i	−0.0616335	−	0.349541i	0.938359	−	0.345662i	$-0.112346\pi$
$504$		0			0
$505$	−1.17697	+	6.67494i	−0.0523746	+	0.297031i
$506$	0.955899	−	16.4122i	0.0424949	−	0.729610i
$507$		0			0
$508$	8.20992	+	19.0327i	0.364256	+	0.844441i
$509$	1.49130	+	0.748960i	0.0661008	+	0.0331971i	0.481543	−	0.876423i	$-0.340077\pi$
$509$	1.49130	+	0.748960i	0.0661008	+	0.0331971i	−0.415442	+	0.909620i	$0.636373\pi$
$510$		0			0
$511$	−0.340485	−	0.0806964i	−0.0150622	−	0.00356980i
$512$	−16.0816	+	27.8541i	−0.710711	+	1.23099i
$513$		0			0
$514$	−22.4119	−	38.8186i	−0.988548	−	1.71221i
$515$	−13.5425	−	45.2350i	−0.596753	−	1.99329i
$516$		0			0
$517$	36.8060	−	24.2077i	1.61873	−	1.06465i
$518$	3.11353	−	4.18220i	0.136801	−	0.183755i
$519$		0			0
$520$	−1.24510	−	0.818917i	−0.0546014	−	0.0359119i
$521$	−32.9725	+	12.0010i	−1.44455	+	0.525773i	−0.941063	−	0.338230i	$-0.890172\pi$
$521$	−32.9725	+	12.0010i	−1.44455	+	0.525773i	−0.503486	+	0.864003i	$0.667950\pi$
$522$		0			0
$523$	11.3086	+	4.11600i	0.494491	+	0.179980i	0.577214	−	0.816593i	$-0.304140\pi$
$523$	11.3086	+	4.11600i	0.494491	+	0.179980i	−0.0827236	+	0.996573i	$0.526362\pi$
$524$	−6.81627	−	9.15584i	−0.297770	−	0.399975i
$525$		0			0
$526$	7.29276	+	7.72988i	0.317980	+	0.337039i
$527$	−42.5435	−	45.0935i	−1.85322	−	1.96430i
$528$		0			0
$529$	−10.9125	−	14.6580i	−0.474455	−	0.637304i
$530$	29.4226	+	10.7089i	1.27803	+	0.465167i
$531$		0			0
$532$	0.911231	−	0.331661i	0.0395069	−	0.0143793i
$533$	25.8358	+	16.9925i	1.11907	+	0.736026i
$534$		0			0
$535$	1.32921	−	1.78544i	0.0574669	−	0.0771915i
$536$	1.00643	−	0.661941i	0.0434712	−	0.0285915i
$537$		0			0
$538$	3.60733	+	12.0493i	0.155523	+	0.519483i
$539$	12.4073	+	21.4900i	0.534420	+	0.925642i
$540$		0			0
$541$	−9.81306	+	16.9967i	−0.421896	+	0.730746i	−0.996125	−	0.0879490i	$-0.971969\pi$
$541$	−9.81306	+	16.9967i	−0.421896	+	0.730746i	0.574229	+	0.818695i	$0.305302\pi$
$542$	14.3810	+	3.40835i	0.617715	+	0.146401i
$543$		0			0
$544$	−54.5867	−	27.4145i	−2.34038	−	1.17539i
$545$	−4.62979	−	10.7331i	−0.198318	−	0.459754i
$546$		0			0
$547$	−0.507250	+	8.70914i	−0.0216884	+	0.372376i	0.969948	+	0.243313i	$0.0782341\pi$
$547$	−0.507250	+	8.70914i	−0.0216884	+	0.372376i	−0.991636	+	0.129063i	$0.958803\pi$
$548$	5.49569	−	31.1676i	0.234764	−	1.33141i
$549$		0			0
$550$	3.49651	+	19.8297i	0.149092	+	0.845540i
$551$	−3.44459	+	0.402615i	−0.146745	+	0.0171520i
$552$		0			0
$553$	1.61556	−	5.39635i	0.0687007	−	0.229476i
$554$	−36.6099	+	8.67671i	−1.55541	+	0.368638i
$555$		0			0
$556$	13.1820	−	30.5592i	0.559040	−	1.29600i
$557$	−15.1698	+	12.7290i	−0.642765	+	0.539344i	−0.904866	−	0.425696i	$-0.860029\pi$
$557$	−15.1698	+	12.7290i	−0.642765	+	0.539344i	0.262101	+	0.965041i	$0.415585\pi$
$558$		0			0
$559$	4.59706	+	3.85739i	0.194435	+	0.163150i
$560$	5.80354	−	2.91465i	0.245244	−	0.123166i
$561$		0			0
$562$	−2.04975	−	0.239581i	−0.0864634	−	0.0101061i
$563$	1.97439	+	33.8990i	0.0832108	+	1.42867i	0.738987	+	0.673719i	$0.235304\pi$
$563$	1.97439	+	33.8990i	0.0832108	+	1.42867i	−0.655777	+	0.754955i	$0.727659\pi$
$564$		0			0
$565$	−23.4473	+	24.8527i	−0.986436	+	1.04556i
$566$	−22.1392			−0.930581
$567$		0			0
$568$	1.06828			0.0448240
$569$	−13.2027	+	13.9941i	−0.553486	+	0.586661i	−0.942348	−	0.334635i	$-0.891387\pi$
$569$	−13.2027	+	13.9941i	−0.553486	+	0.586661i	0.388861	+	0.921296i	$0.372868\pi$
$570$		0			0
$571$	0.144601	+	2.48271i	0.00605138	+	0.103898i	0.999981	−	0.00611695i	$-0.00194710\pi$
$571$	0.144601	+	2.48271i	0.00605138	+	0.103898i	−0.993930	+	0.110015i	$0.964910\pi$
$572$	−26.4325	−	3.08951i	−1.10520	−	0.129179i
$573$		0			0
$574$	9.97437	−	5.00931i	0.416322	−	0.209085i
$575$	−4.43416	−	3.72070i	−0.184917	−	0.155164i
$576$		0			0
$577$	19.5278	−	16.3857i	0.812951	−	0.682147i	−0.138359	−	0.990382i	$-0.544183\pi$
$577$	19.5278	−	16.3857i	0.812951	−	0.682147i	0.951310	+	0.308235i	$0.0997383\pi$
$578$	32.2821	−	74.8382i	1.34276	−	3.11286i
$579$		0			0
$580$	25.4258	−	6.02602i	1.05575	−	0.250217i
$581$	1.08493	−	3.62393i	0.0450106	−	0.150346i
$582$		0			0
$583$	20.8339	−	2.43514i	0.862854	−	0.100853i
$584$	0.0156480	+	0.0887440i	0.000647517	+	0.00367225i
$585$		0			0
$586$	−8.51396	+	48.2851i	−0.351709	+	1.99464i
$587$	0.0520618	−	0.893866i	0.00214882	−	0.0368938i	−0.997063	−	0.0765818i	$-0.975599\pi$
$587$	0.0520618	−	0.893866i	0.00214882	−	0.0368938i	0.999212	+	0.0396880i	$0.0126364\pi$
$588$		0			0
$589$	2.47514	+	5.73802i	0.101986	+	0.236431i
$590$	−7.55901	−	3.79628i	−0.311199	−	0.156290i
$591$		0			0
$592$	15.7741	+	3.73852i	0.648310	+	0.153652i
$593$	16.2145	−	28.0843i	0.665848	−	1.15328i	−0.313207	−	0.949685i	$-0.601403\pi$
$593$	16.2145	−	28.0843i	0.665848	−	1.15328i	0.979055	−	0.203597i	$-0.0652634\pi$
$594$		0			0
$595$	6.40773	+	11.0985i	0.262691	+	0.454994i
$596$	5.26854	+	17.5981i	0.215808	+	0.720848i
$597$		0			0
$598$	12.5436	−	8.25008i	0.512948	−	0.337371i
$599$	25.1367	−	33.7644i	1.02706	−	1.37958i	0.104148	−	0.994562i	$-0.466788\pi$
$599$	25.1367	−	33.7644i	1.02706	−	1.37958i	0.922910	−	0.385016i	$-0.125804\pi$
$600$		0			0
$601$	25.8496	+	17.0016i	1.05443	+	0.693509i	0.953502	−	0.301385i	$-0.0974490\pi$
$601$	25.8496	+	17.0016i	1.05443	+	0.693509i	0.100926	+	0.994894i	$0.467819\pi$
$602$	2.03543	−	0.740836i	0.0829580	−	0.0301942i
$603$		0			0
$604$	−1.92891	−	0.702064i	−0.0784861	−	0.0285666i
$605$	4.99842	+	6.71405i	0.203215	+	0.272965i
$606$		0			0
$607$	10.2760	+	10.8919i	0.417090	+	0.442090i	0.901518	−	0.432742i	$-0.142454\pi$
$607$	10.2760	+	10.8919i	0.417090	+	0.442090i	−0.484428	+	0.874831i	$0.660972\pi$
$608$	4.22538	+	4.47864i	0.171362	+	0.181633i
$609$		0			0
$610$	10.0929	+	13.5572i	0.408651	+	0.548913i
$611$	37.8048	+	13.7598i	1.52942	+	0.556663i
$612$		0			0
$613$	17.2467	−	6.27730i	0.696589	−	0.253538i	0.0306353	−	0.999531i	$-0.490247\pi$
$613$	17.2467	−	6.27730i	0.696589	−	0.253538i	0.665954	+	0.745993i	$0.268025\pi$
$614$	41.8928	+	27.5533i	1.69065	+	1.11196i
$615$		0			0
$616$	−0.215190	+	0.289050i	−0.00867025	+	0.0116462i
$617$	−27.3834	+	18.0103i	−1.10241	+	0.725069i	−0.964158	−	0.265328i	$-0.914520\pi$
$617$	−27.3834	+	18.0103i	−1.10241	+	0.725069i	−0.138255	+	0.990397i	$0.544149\pi$
$618$		0			0
$619$	1.72149	+	5.75017i	0.0691925	+	0.231119i	0.985590	−	0.169150i	$-0.0541021\pi$
$619$	1.72149	+	5.75017i	0.0691925	+	0.231119i	−0.916398	+	0.400268i	$0.868917\pi$
$620$	−23.5420	−	40.7760i	−0.945471	−	1.63760i
$621$		0			0
$622$	1.86865	−	3.23661i	0.0749262	−	0.129776i
$623$	−2.73889	−	0.649129i	−0.109731	−	0.0260068i
$624$		0			0
$625$	−27.9024	−	14.0131i	−1.11610	−	0.560524i
$626$	−5.56013	−	12.8898i	−0.222227	−	0.515181i
$627$		0			0
$628$	−2.19879	+	37.7517i	−0.0877412	+	1.50646i
$629$	−5.55497	+	31.5038i	−0.221491	+	1.25614i
$630$		0			0
$631$	−4.24361	−	24.0667i	−0.168935	−	0.958080i	−0.944914	−	0.327320i	$-0.893854\pi$
$631$	−4.24361	−	24.0667i	−0.168935	−	0.958080i	0.775978	−	0.630760i	$-0.217257\pi$
$632$	−1.44084	+	0.168410i	−0.0573135	+	0.00669899i
$633$		0			0
$634$	15.0800	−	50.3707i	0.598903	−	2.00048i
$635$	26.8684	−	6.36793i	1.06624	−	0.252704i
$636$		0			0
$637$	−8.97577	+	20.8082i	−0.355633	+	0.824450i
$638$	26.3163	−	22.0820i	1.04187	−	0.874234i
$639$		0			0
$640$	−2.66848	−	2.23912i	−0.105481	−	0.0885089i
$641$	−9.21794	+	4.62942i	−0.364087	+	0.182851i	−0.621432	−	0.783468i	$-0.713449\pi$
$641$	−9.21794	+	4.62942i	−0.364087	+	0.182851i	0.257345	+	0.966320i	$0.417152\pi$
$642$		0			0
$643$	43.0139	+	5.02761i	1.69630	+	0.198270i	0.908566	−	0.417741i	$-0.137178\pi$
$643$	43.0139	+	5.02761i	1.69630	+	0.198270i	0.787738	+	0.616010i	$0.211252\pi$
$644$	−0.160558	−	2.75668i	−0.00632688	−	0.108628i
$645$		0			0
$646$	−8.01259	+	8.49285i	−0.315251	+	0.334147i
$647$	−6.50021			−0.255550			−0.127775	−	0.991803i	$-0.540783\pi$
$647$	−6.50021			−0.255550			−0.127775	+	0.991803i	$0.540783\pi$
$648$		0			0
$649$	−5.66668			−0.222437
$650$	−12.6190	+	13.3753i	−0.494956	+	0.524623i
$651$		0			0
$652$	−2.07173	−	35.5702i	−0.0811350	−	1.39303i
$653$	2.95697	+	0.345620i	0.115715	+	0.0135251i	0.173753	−	0.984789i	$-0.444410\pi$
$653$	2.95697	+	0.345620i	0.115715	+	0.0135251i	−0.0580383	+	0.998314i	$0.518485\pi$
$654$		0			0
$655$	−13.5884	+	6.82436i	−0.530944	+	0.266650i
$656$	26.5844	+	22.3070i	1.03795	+	0.870941i
$657$		0			0
$658$	11.1240	−	9.33410i	0.433657	−	0.363881i
$659$	11.1338	−	25.8110i	0.433710	−	1.00545i	−0.551512	−	0.834167i	$-0.685949\pi$
$659$	11.1338	−	25.8110i	0.433710	−	1.00545i	0.985221	−	0.171285i	$-0.0547920\pi$
$660$		0			0
$661$	−3.16302	+	0.749650i	−0.123027	+	0.0291580i	−0.291668	−	0.956520i	$-0.594210\pi$
$661$	−3.16302	+	0.749650i	−0.123027	+	0.0291580i	0.168641	+	0.985678i	$0.446062\pi$
$662$	15.0789	−	50.3671i	0.586059	−	1.95757i
$663$		0			0
$664$	−0.967598	+	0.113096i	−0.0375501	+	0.00438898i
$665$	−0.224319	−	1.27217i	−0.00869871	−	0.0493328i
$666$		0			0
$667$	−1.71488	+	9.72556i	−0.0664004	+	0.376575i
$668$	0.712992	−	12.2416i	0.0275865	−	0.473642i
$669$		0			0
$670$	−16.9424	−	39.2770i	−0.654544	−	1.51740i
$671$	10.1183	+	5.08162i	0.390614	+	0.196174i
$672$		0			0
$673$	13.5198	+	3.20426i	0.521152	+	0.123515i	0.482769	−	0.875748i	$-0.339631\pi$
$673$	13.5198	+	3.20426i	0.521152	+	0.123515i	0.0383830	+	0.999263i	$0.487779\pi$
$674$	15.1769	−	26.2871i	0.584591	−	1.01254i
$675$		0			0
$676$	1.35501	+	2.34695i	0.0521158	+	0.0902672i
$677$	−3.11373	−	10.4006i	−0.119670	−	0.399727i	0.877074	−	0.480356i	$-0.159492\pi$
$677$	−3.11373	−	10.4006i	−0.119670	−	0.399727i	−0.996744	+	0.0806287i	$0.974307\pi$
$678$		0			0
$679$	−5.37112	+	3.53264i	−0.206125	+	0.135570i
$680$	1.97082	−	2.64726i	0.0755773	−	0.101518i
$681$		0			0
$682$	−51.7182	−	34.0156i	−1.98039	−	1.30253i
$683$	31.5858	−	11.4963i	1.20860	−	0.439893i	0.342380	−	0.939562i	$-0.388767\pi$
$683$	31.5858	−	11.4963i	1.20860	−	0.439893i	0.866217	+	0.499668i	$0.166545\pi$
$684$		0			0
$685$	−39.6178	−	14.4197i	−1.51372	−	0.550949i
$686$	10.0445	+	13.4921i	0.383501	+	0.515131i
$687$		0			0
$688$	4.62162	+	4.89864i	0.176198	+	0.186759i
$689$	13.1455	+	13.9334i	0.500804	+	0.530821i
$690$		0			0
$691$	−0.267326	−	0.359082i	−0.0101696	−	0.0136601i	0.797009	−	0.603967i	$-0.206414\pi$
$691$	−0.267326	−	0.359082i	−0.0101696	−	0.0136601i	−0.807179	+	0.590307i	$0.799007\pi$
$692$	17.5595	+	6.39115i	0.667513	+	0.242955i
$693$		0			0
$694$	−48.2412	+	17.5584i	−1.83121	+	0.666507i
$695$	−37.0417	−	24.3627i	−1.40507	−	0.924129i
$696$		0			0
$697$	−40.8943	+	54.9306i	−1.54898	+	2.08065i
$698$	49.3762	−	32.4753i	1.86892	−	1.22921i
$699$		0			0
$700$	0.969993	+	3.24000i	0.0366623	+	0.122461i
$701$	−1.94332	−	3.36593i	−0.0733982	−	0.127129i	0.826990	−	0.562216i	$-0.190051\pi$
$701$	−1.94332	−	3.36593i	−0.0733982	−	0.127129i	−0.900389	+	0.435087i	$0.856718\pi$
$702$		0			0
$703$	1.61229	−	2.79256i	0.0608086	−	0.105324i
$704$	−31.3776	−	7.43663i	−1.18259	−	0.280278i
$705$		0			0
$706$	−51.7769	−	26.0033i	−1.94865	−	0.978648i
$707$	0.592827	+	1.37433i	0.0222956	+	0.0516869i
$708$		0			0
$709$	0.857054	−	14.7150i	0.0321873	−	0.552635i	−0.943212	−	0.332191i	$-0.892212\pi$
$709$	0.857054	−	14.7150i	0.0321873	−	0.552635i	0.975400	−	0.220444i	$-0.0707507\pi$
$710$	6.58725	−	37.3581i	0.247215	−	1.40203i
$711$		0			0
$712$	0.125874	+	0.713864i	0.00471731	+	0.0267532i
$713$	17.6746	−	2.06587i	0.661919	−	0.0773673i
$714$		0			0
$715$	−10.1677	+	33.9624i	−0.380249	+	1.27012i
$716$	−2.60614	+	0.617666i	−0.0973959	+	0.0230833i
$717$		0			0
$718$	16.6816	−	38.6723i	0.622552	−	1.44324i
$719$	−24.7821	+	20.7947i	−0.924218	+	0.775511i	−0.974770	−	0.223210i	$-0.928346\pi$
$719$	−24.7821	+	20.7947i	−0.924218	+	0.775511i	0.0505523	+	0.998721i	$0.483902\pi$
$720$		0			0
$721$	−7.98762	−	6.70241i	−0.297474	−	0.249611i
$722$	−33.2356	+	16.6915i	−1.23690	+	0.621195i
$723$		0			0
$724$	−7.67077	−	0.896585i	−0.285082	−	0.0333213i
$725$	−0.703295	−	12.0751i	−0.0261197	−	0.448458i
$726$		0			0
$727$	6.33415	−	6.71380i	0.234921	−	0.249001i	−0.599179	−	0.800615i	$-0.704506\pi$
$727$	6.33415	−	6.71380i	0.234921	−	0.249001i	0.834100	+	0.551614i	$0.185988\pi$
$728$	−0.329090			−0.0121969
$729$		0			0
$730$	3.19990			0.118434
$731$	−9.12000	+	9.66663i	−0.337315	+	0.357533i
$732$		0			0
$733$	3.08131	+	52.9040i	0.113811	+	1.95405i	0.261936	+	0.965085i	$0.415639\pi$
$733$	3.08131	+	52.9040i	0.113811	+	1.95405i	−0.148126	+	0.988969i	$0.547324\pi$
$734$	69.3320	+	8.10374i	2.55909	+	0.299115i
$735$		0			0
$736$	15.6685	−	7.86901i	0.577548	−	0.290055i
$737$	−21.9518	−	18.4198i	−0.808606	−	0.678501i
$738$		0			0
$739$	2.18316	−	1.83188i	0.0803087	−	0.0673870i	−0.601750	−	0.798685i	$-0.705529\pi$
$739$	2.18316	−	1.83188i	0.0803087	−	0.0673870i	0.682058	+	0.731298i	$0.261085\pi$
$740$	−9.62303	+	22.3087i	−0.353750	+	0.820084i
$741$		0			0
$742$	6.72786	−	1.59453i	0.246988	−	0.0585372i
$743$	−8.43563	+	28.1770i	−0.309473	+	1.03371i	0.651863	+	0.758337i	$0.273988\pi$
$743$	−8.43563	+	28.1770i	−0.309473	+	1.03371i	−0.961336	+	0.275376i	$0.911198\pi$
$744$		0			0
$745$	24.3059	−	2.84096i	0.890501	−	0.104085i
$746$	−3.28553	−	18.6331i	−0.120292	−	0.682208i
$747$		0			0
$748$	10.2340	−	58.0400i	0.374193	−	2.12215i
$749$	0.0285802	−	0.490704i	0.00104430	−	0.0179299i
$750$		0			0
$751$	−10.8644	−	25.1865i	−0.396447	−	0.919067i	−0.993176	−	0.116624i	$-0.962793\pi$
$751$	−10.8644	−	25.1865i	−0.396447	−	0.919067i	0.596729	−	0.802443i	$-0.296467\pi$
$752$	40.3470	+	20.2630i	1.47130	+	0.738917i
$753$		0			0
$754$	30.5271	+	7.23506i	1.11173	+	0.263485i
$755$	−1.36725	+	2.36815i	−0.0497593	+	0.0861857i
$756$		0			0
$757$	14.2323	+	24.6511i	0.517282	+	0.895959i	0.999799	+	0.0200719i	$0.00638952\pi$
$757$	14.2323	+	24.6511i	0.517282	+	0.895959i	−0.482516	+	0.875887i	$0.660277\pi$
$758$	1.11637	+	3.72894i	0.0405485	+	0.135441i
$759$		0			0
$760$	−0.277944	+	0.182807i	−0.0100821	+	0.00663110i
$761$	−16.7039	+	22.4372i	−0.605514	+	0.813347i	−0.994146	−	0.108046i	$-0.965541\pi$
$761$	−16.7039	+	22.4372i	−0.605514	+	0.813347i	0.388631	+	0.921393i	$0.372948\pi$
$762$		0			0
$763$	−2.15659	−	1.41841i	−0.0780739	−	0.0513500i
$764$	14.2348	−	5.18104i	0.514997	−	0.187444i
$765$		0			0
$766$	36.9883	+	13.4626i	1.33644	+	0.486425i
$767$	−3.09030	−	4.15099i	−0.111584	−	0.149884i
$768$		0			0
$769$	−32.2285	−	34.1602i	−1.16219	−	1.23185i	−0.968018	−	0.250879i	$-0.919280\pi$
$769$	−32.2285	−	34.1602i	−1.16219	−	1.23185i	−0.194169	−	0.980968i	$-0.562201\pi$
$770$	8.78129	+	9.30762i	0.316456	+	0.335424i
$771$		0			0
$772$	−11.9460	−	16.0463i	−0.429947	−	0.577519i
$773$	−41.5507	−	15.1232i	−1.49447	−	0.543944i	−0.539851	−	0.841761i	$-0.681519\pi$
$773$	−41.5507	−	15.1232i	−1.49447	−	0.543944i	−0.954623	+	0.297816i	$0.903742\pi$
$774$		0			0
$775$	−20.4807	+	7.45437i	−0.735689	+	0.267769i
$776$	1.38321	+	0.909749i	0.0496542	+	0.0326581i
$777$		0			0
$778$	11.0218	−	14.8049i	0.395151	−	0.530780i
$779$	5.76733	−	3.79323i	0.206636	−	0.135907i
$780$		0			0
$781$	−7.28855	−	24.3454i	−0.260805	−	0.871148i
$782$	16.6244	+	28.7942i	0.594486	+	1.02968i
$783$		0			0
$784$	−12.7160	+	22.0247i	−0.454143	+	0.786598i
$785$	49.0183	+	11.6175i	1.74954	+	0.414648i
$786$		0			0
$787$	32.6021	+	16.3734i	1.16214	+	0.583649i	0.922038	−	0.387099i	$-0.126523\pi$
$787$	32.6021	+	16.3734i	1.16214	+	0.583649i	0.240102	+	0.970748i	$0.422819\pi$
$788$	4.06308	+	9.41927i	0.144741	+	0.335548i
$789$		0			0
$790$	−2.99517	+	51.4252i	−0.106564	+	1.82963i
$791$	−1.31019	+	7.43049i	−0.0465852	+	0.264198i
$792$		0			0
$793$	1.79557	+	10.1832i	0.0637627	+	0.361616i
$794$	−66.8888	+	7.81818i	−2.37380	+	0.277457i
$795$		0			0
$796$	−1.50023	+	5.01112i	−0.0531742	+	0.177614i
$797$	14.7098	−	3.48628i	0.521046	−	0.123490i	0.0383267	−	0.999265i	$-0.487797\pi$
$797$	14.7098	−	3.48628i	0.521046	−	0.123490i	0.482719	+	0.875775i	$0.339649\pi$
$798$		0			0
$799$	−35.2886	+	81.8083i	−1.24842	+	2.89417i
$800$	−16.4507	+	13.8038i	−0.581621	+	0.488038i
$801$		0			0
$802$	5.48967	+	4.60638i	0.193847	+	0.162657i
$803$	1.91566	−	0.962081i	0.0676022	−	0.0339511i
$804$		0			0
$805$	−3.65366	−	0.427051i	−0.128774	−	0.0150516i
$806$	−3.28698	−	56.4353i	−0.115779	−	1.98785i
$807$		0			0
$808$	0.264512	−	0.280366i	0.00930549	−	0.00986325i
$809$	49.6978			1.74728			0.873641	−	0.486571i	$-0.161753\pi$
$809$	49.6978			1.74728			0.873641	+	0.486571i	$0.161753\pi$
$810$		0			0
$811$	−8.76133			−0.307652			−0.153826	−	0.988098i	$-0.549159\pi$
$811$	−8.76133			−0.307652			−0.153826	+	0.988098i	$0.549159\pi$
$812$	3.95975	−	4.19709i	0.138960	−	0.147289i
$813$		0			0
$814$	1.85725	+	31.8877i	0.0650965	+	1.11766i
$815$	−47.1441	−	5.51036i	−1.65139	−	0.193019i
$816$		0			0
$817$	1.19712	−	0.601217i	0.0418820	−	0.0210339i
$818$	−49.5562	−	41.5826i	−1.73269	−	1.45390i
$819$		0			0
$820$	−39.8424	+	33.4317i	−1.39136	+	1.16749i
$821$	14.0466	−	32.5637i	0.490230	−	1.13648i	−0.476150	−	0.879364i	$-0.657968\pi$
$821$	14.0466	−	32.5637i	0.490230	−	1.13648i	0.966380	−	0.257117i	$-0.0827726\pi$
$822$		0			0
$823$	−1.82849	+	0.433361i	−0.0637372	+	0.0151060i	−0.262361	−	0.964970i	$-0.584501\pi$
$823$	−1.82849	+	0.433361i	−0.0637372	+	0.0151060i	0.198624	+	0.980076i	$0.436353\pi$
$824$	−0.770140	+	2.57245i	−0.0268291	+	0.0896155i
$825$		0			0
$826$	−1.85528	+	0.216851i	−0.0645533	+	0.00754520i
$827$	−1.66995	−	9.47075i	−0.0580698	−	0.329330i	0.941909	−	0.335869i	$-0.109030\pi$
$827$	−1.66995	−	9.47075i	−0.0580698	−	0.329330i	−0.999979	+	0.00653851i	$0.997919\pi$
$828$		0			0
$829$	−1.31856	+	7.47791i	−0.0457954	+	0.259719i	−0.999106	−	0.0422726i	$-0.986540\pi$
$829$	−1.31856	+	7.47791i	−0.0457954	+	0.259719i	0.953311	+	0.301991i	$0.0976513\pi$
$830$	−2.01142	+	34.5347i	−0.0698173	+	1.19872i
$831$		0			0
$832$	−11.6641	−	27.0405i	−0.404381	−	0.937460i
$833$	−44.8476	−	22.5233i	−1.55388	−	0.780387i
$834$		0			0
$835$	−15.8950	−	3.76717i	−0.550068	−	0.130368i
$836$	−2.97035	+	5.14479i	−0.102732	+	0.177936i
$837$		0			0
$838$	−14.9786	−	25.9438i	−0.517429	−	0.896213i
$839$	−11.3639	−	37.9580i	−0.392325	−	1.31046i	−0.895033	−	0.446001i	$-0.852848\pi$
$839$	−11.3639	−	37.9580i	−0.392325	−	1.31046i	0.502707	−	0.864457i	$-0.332337\pi$
$840$		0			0
$841$	6.98773	−	4.59591i	0.240956	−	0.158479i
$842$	−18.7876	+	25.2361i	−0.647463	+	0.869694i
$843$		0			0
$844$	−12.1316	−	7.97906i	−0.417586	−	0.274651i
$845$	3.39243	−	1.23475i	0.116703	−	0.0424765i
$846$		0			0
$847$	1.73692	+	0.632185i	0.0596811	+	0.0217221i
$848$	12.8375	+	17.2438i	0.440842	+	0.592154i
$849$		0			0
$850$	−27.9457	−	29.6207i	−0.958530	−	1.01598i
$851$	−6.30127	−	6.67896i	−0.216005	−	0.228952i
$852$		0			0
$853$	2.05643	+	2.76227i	0.0704110	+	0.0945783i	0.835933	−	0.548831i	$-0.184927\pi$
$853$	2.05643	+	2.76227i	0.0704110	+	0.0945783i	−0.765523	+	0.643409i	$0.777519\pi$
$854$	3.50722	+	1.27652i	0.120015	+	0.0436817i
$855$		0			0
$856$	−0.118950	+	0.0432941i	−0.00406561	+	0.00147976i
$857$	−18.5031	−	12.1697i	−0.632053	−	0.415708i	0.192655	−	0.981267i	$-0.438290\pi$
$857$	−18.5031	−	12.1697i	−0.632053	−	0.415708i	−0.824708	+	0.565559i	$0.808661\pi$
$858$		0			0
$859$	21.2724	−	28.5737i	0.725804	−	0.974924i	−0.274109	−	0.961699i	$-0.588383\pi$
$859$	21.2724	−	28.5737i	0.725804	−	0.974924i	0.999913	−	0.0132249i	$-0.00420973\pi$
$860$	−8.43288	+	5.54639i	−0.287559	+	0.189130i
$861$		0			0
$862$	0.751429	+	2.50995i	0.0255938	+	0.0854891i
$863$	−10.4873	−	18.1645i	−0.356992	−	0.618328i	0.630465	−	0.776218i	$-0.282864\pi$
$863$	−10.4873	−	18.1645i	−0.356992	−	0.618328i	−0.987457	+	0.157890i	$0.949531\pi$
$864$		0			0
$865$	12.4466	−	21.5581i	0.423196	−	0.732998i
$866$	34.4460	+	8.16385i	1.17052	+	0.277419i
$867$		0			0
$868$	−9.29143	−	4.66633i	−0.315372	−	0.158386i
$869$	13.6684	+	31.6868i	0.463668	+	1.07490i
$870$		0			0
$871$	1.52163	−	26.1254i	0.0515586	−	0.885227i
$872$	−0.115431	+	0.654639i	−0.00390897	+	0.0221689i
$873$		0			0
$874$	−0.581978	−	3.30056i	−0.0196857	−	0.111643i
$875$	−3.92834	+	0.459157i	−0.132802	+	0.0155223i
$876$		0			0
$877$	−12.1070	+	40.4401i	−0.408823	+	1.36556i	0.467565	+	0.883959i	$0.345131\pi$
$877$	−12.1070	+	40.4401i	−0.408823	+	1.36556i	−0.876388	+	0.481605i	$0.840054\pi$
$878$	42.6755	−	10.1143i	1.44023	−	0.341340i
$879$		0			0
$880$	−15.7584	+	36.5320i	−0.531214	+	1.23149i
$881$	29.2913	−	24.5783i	0.986848	−	0.828064i	0.00173943	−	0.999998i	$-0.499446\pi$
$881$	29.2913	−	24.5783i	0.986848	−	0.828064i	0.985108	+	0.171935i	$0.0550019\pi$
$882$		0			0
$883$	−22.0694	−	18.5184i	−0.742693	−	0.623194i	0.190866	−	0.981616i	$-0.438870\pi$
$883$	−22.0694	−	18.5184i	−0.742693	−	0.623194i	−0.933560	+	0.358422i	$0.883315\pi$
$884$	48.0969	−	24.1552i	1.61767	−	0.812426i
$885$		0			0
$886$	18.3398	+	2.14361i	0.616137	+	0.0720161i
$887$	−0.797647	−	13.6951i	−0.0267824	−	0.459835i	−0.984863	−	0.173336i	$-0.944545\pi$
$887$	−0.797647	−	13.6951i	−0.0267824	−	0.459835i	0.958080	−	0.286500i	$-0.0924917\pi$
$888$		0			0
$889$	4.18443	−	4.43523i	0.140341	−	0.148753i
$890$	25.7403			0.862816
$891$		0			0
$892$	−37.3995			−1.25223
$893$	6.16298	−	6.53238i	0.206236	−	0.218598i
$894$		0			0
$895$	0.207457	+	3.56190i	0.00693453	+	0.119061i
$896$	−0.764034	−	0.0893027i	−0.0255246	−	0.00298340i
$897$		0			0
$898$	−22.4174	+	11.2584i	−0.748078	+	0.375699i
$899$	28.4852	+	23.9019i	0.950035	+	0.797174i
$900$		0			0
$901$	−32.4972	+	27.2684i	−1.08264	+	0.908441i
$902$	−27.0834	+	62.7864i	−0.901779	+	2.09056i
$903$		0			0
$904$	1.89069	−	0.448102i	0.0628835	−	0.0149037i
$905$	−2.95068	+	9.85597i	−0.0980840	+	0.327623i
$906$		0			0
$907$	−56.3534	+	6.58677i	−1.87119	+	0.218710i	−0.974567	−	0.224094i	$-0.928058\pi$
$907$	−56.3534	+	6.58677i	−1.87119	+	0.218710i	−0.896618	+	0.442805i	$0.853984\pi$
$908$	0.221375	+	1.25548i	0.00734659	+	0.0416646i
$909$		0			0
$910$	−2.02924	+	11.5084i	−0.0672687	+	0.381500i
$911$	−0.0414988	+	0.712508i	−0.00137492	+	0.0236064i	−0.998926	−	0.0463376i	$-0.985245\pi$
$911$	−0.0414988	+	0.712508i	−0.00137492	+	0.0236064i	0.997551	+	0.0699440i	$0.0222821\pi$
$912$		0			0
$913$	9.17902	+	21.2794i	0.303781	+	0.704244i
$914$	−33.7367	−	16.9432i	−1.11591	−	0.560432i
$915$		0			0
$916$	−10.1001	−	2.39376i	−0.333716	−	0.0790921i
$917$	−1.67892	+	2.90797i	−0.0554428	+	0.0960297i
$918$		0			0
$919$	28.6606	+	49.6416i	0.945425	+	1.63752i	0.754898	+	0.655842i	$0.227686\pi$
$919$	28.6606	+	49.6416i	0.945425	+	1.63752i	0.190527	+	0.981682i	$0.438980\pi$
$920$	0.271694	+	0.907522i	0.00895750	+	0.0299201i
$921$		0			0
$922$	69.3125	−	45.5876i	2.28269	−	1.50135i
$923$	13.8589	−	18.6157i	0.456171	−	0.612744i
$924$		0			0
$925$	9.39625	+	6.18001i	0.308947	+	0.203198i
$926$	7.83677	−	2.85235i	0.257532	−	0.0937341i
$927$		0			0
$928$	34.4289	+	12.5311i	1.13018	+	0.411353i
$929$	−8.93536	−	12.0023i	−0.293160	−	0.393782i	0.631003	−	0.775780i	$-0.282643\pi$
$929$	−8.93536	−	12.0023i	−0.293160	−	0.393782i	−0.924163	+	0.381998i	$0.875236\pi$
$930$		0			0
$931$	3.47151	+	3.67959i	0.113774	+	0.120594i
$932$	18.7623	+	19.8869i	0.614579	+	0.651416i
$933$		0			0
$934$	30.4809	+	40.9429i	0.997365	+	1.33969i
$935$	−73.7759	−	26.8522i	−2.41273	−	0.878162i
$936$		0			0
$937$	23.1819	−	8.43751i	0.757319	−	0.275641i	0.0656366	−	0.997844i	$-0.479092\pi$
$937$	23.1819	−	8.43751i	0.757319	−	0.275641i	0.691682	+	0.722202i	$0.256870\pi$
$938$	−7.89193	−	5.19060i	−0.257681	−	0.169479i
$939$		0			0
$940$	−40.4073	+	54.2765i	−1.31794	+	1.77030i
$941$	−19.4338	+	12.7818i	−0.633523	+	0.416675i	−0.825245	−	0.564775i	$-0.808963\pi$
$941$	−19.4338	+	12.7818i	−0.633523	+	0.416675i	0.191722	+	0.981449i	$0.438593\pi$
$942$		0			0
$943$	−5.63765	−	18.8310i	−0.183587	−	0.613223i
$944$	−2.90384	−	5.02959i	−0.0945119	−	0.163699i
$945$		0			0
$946$	−6.63491	+	11.4920i	−0.215720	+	0.373637i
$947$	18.6605	+	4.42261i	0.606384	+	0.143716i	0.522327	−	0.852745i	$-0.325064\pi$
$947$	18.6605	+	4.42261i	0.606384	+	0.143716i	0.0840570	+	0.996461i	$0.473212\pi$
$948$		0			0
$949$	1.74945	+	0.878606i	0.0567895	+	0.0285208i
$950$	1.62586	+	3.76916i	0.0527497	+	0.122288i
$951$		0			0
$952$	0.0423757	−	0.727563i	0.00137340	−	0.0235804i
$953$	−5.37991	+	30.5110i	−0.174272	+	0.988348i	0.764708	+	0.644377i	$0.222883\pi$
$953$	−5.37991	+	30.5110i	−0.174272	+	0.988348i	−0.938980	+	0.343971i	$0.888228\pi$
$954$		0			0
$955$	−3.50420	−	19.8733i	−0.113393	−	0.643085i
$956$	−18.7778	+	2.19481i	−0.607316	+	0.0709851i
$957$		0			0
$958$	−12.0479	+	40.2429i	−0.389251	+	1.30019i
$959$	−9.05915	+	2.14706i	−0.292535	+	0.0693321i
$960$		0			0
$961$	14.2603	−	33.0592i	0.460011	−	1.06642i
$962$	−22.3457	+	18.7503i	−0.720456	+	0.604534i
$963$		0			0
$964$	−22.6834	−	19.0336i	−0.730583	−	0.613032i
$965$	−23.8147	+	11.9602i	−0.766623	+	0.385013i
$966$		0			0
$967$	−19.7235	−	2.30534i	−0.634264	−	0.0741348i	−0.207116	−	0.978316i	$-0.566408\pi$
$967$	−19.7235	−	2.30534i	−0.634264	−	0.0741348i	−0.427148	+	0.904182i	$0.640482\pi$
$968$	−0.0276775	−	0.475204i	−0.000889587	−	0.0152736i
$969$		0			0
$970$	40.3435	−	42.7616i	1.29535	−	1.37299i
$971$	3.39436			0.108930			0.0544651	−	0.998516i	$-0.482655\pi$
$971$	3.39436			0.108930			0.0544651	+	0.998516i	$0.482655\pi$
$972$		0			0
$973$	−9.79039			−0.313865
$974$	9.14706	−	9.69532i	0.293091	−	0.310658i
$975$		0			0
$976$	0.674738	+	11.5848i	0.0215978	+	0.370820i
$977$	−53.2053	−	6.21881i	−1.70219	−	0.198957i	−0.791249	−	0.611494i	$-0.790569\pi$
$977$	−53.2053	−	6.21881i	−1.70219	−	0.198957i	−0.910941	+	0.412537i	$0.864643\pi$
$978$		0			0
$979$	15.4097	−	7.73906i	0.492497	−	0.247342i
$980$	−29.1980	−	24.5000i	−0.932694	−	0.782624i
$981$		0			0
$982$	56.5336	−	47.4373i	1.80406	−	1.51379i
$983$	−11.0201	+	25.5474i	−0.351486	+	0.814836i	0.647137	+	0.762374i	$0.275966\pi$
$983$	−11.0201	+	25.5474i	−0.351486	+	0.814836i	−0.998623	+	0.0524620i	$0.983293\pi$
$984$		0			0
$985$	13.2971	−	3.15148i	0.423682	−	0.100414i
$986$	−19.9264	+	66.5587i	−0.634585	+	2.11966i
$987$		0			0
$988$	−5.38856	+	0.629833i	−0.171433	+	0.0200376i
$989$	−0.662412	−	3.75672i	−0.0210635	−	0.119457i
$990$		0			0
$991$	2.53438	−	14.3732i	0.0805071	−	0.456579i	−0.917729	−	0.397207i	$-0.869979\pi$
$991$	2.53438	−	14.3732i	0.0805071	−	0.456579i	0.998236	−	0.0593711i	$-0.0189095\pi$
$992$	3.83867	−	65.9075i	0.121878	−	2.09257i
$993$		0			0
$994$	−3.31792	−	7.69180i	−0.105238	−	0.243969i
$995$	6.22710	+	3.12737i	0.197412	+	0.0991441i
$996$		0			0
$997$	−2.37129	−	0.562006i	−0.0750995	−	0.0177989i	0.192894	−	0.981220i	$-0.438213\pi$
$997$	−2.37129	−	0.562006i	−0.0750995	−	0.0177989i	−0.267994	+	0.963421i	$0.586361\pi$
$998$	−36.7468	+	63.6474i	−1.16320	+	2.01472i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.622.2		144
3.2	odd	2		729.2.g.d.622.7		144
9.2	odd	6		81.2.g.a.16.2	✓	144
9.4	even	3		729.2.g.b.379.2		144
9.5	odd	6		729.2.g.c.379.7		144
9.7	even	3		243.2.g.a.208.7		144
81.5	odd	54		729.2.g.c.352.7		144
81.22	even	27	inner	729.2.g.a.109.2		144
81.32	odd	54		81.2.g.a.76.2	yes	144
81.34	even	27		6561.2.a.d.1.59		72
81.47	odd	54		6561.2.a.c.1.14		72
81.49	even	27		243.2.g.a.118.7		144
81.59	odd	54		729.2.g.d.109.7		144
81.76	even	27		729.2.g.b.352.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.2	✓	144	9.2	odd	6
81.2.g.a.76.2	yes	144	81.32	odd	54
243.2.g.a.118.7		144	81.49	even	27
243.2.g.a.208.7		144	9.7	even	3
729.2.g.a.109.2		144	81.22	even	27	inner
729.2.g.a.622.2		144	1.1	even	1	trivial
729.2.g.b.352.2		144	81.76	even	27
729.2.g.b.379.2		144	9.4	even	3
729.2.g.c.352.7		144	81.5	odd	54
729.2.g.c.379.7		144	9.5	odd	6
729.2.g.d.109.7		144	81.59	odd	54
729.2.g.d.622.7		144	3.2	odd	2
6561.2.a.c.1.14		72	81.47	odd	54
6561.2.a.d.1.59		72	81.34	even	27

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38579 + 1.46885i) q^{2} +(-0.120822 - 2.07444i) q^{4} +(-2.74943 - 0.321362i) q^{5} +(-0.546257 + 0.274341i) q^{7} +(0.120591 + 0.101188i) q^{8} +(4.28217 - 3.59317i) q^{10} +(1.48325 - 3.43857i) q^{11} +(3.32773 - 0.788687i) q^{13} +(0.354033 - 1.18255i) q^{14} +(3.81206 - 0.445566i) q^{16} +(1.31516 + 7.45862i) q^{17} +(0.132568 - 0.751830i) q^{19} +(-0.334454 + 5.74235i) q^{20} +(2.99528 + 6.94383i) q^{22} +(-1.94270 - 0.975661i) q^{23} +(2.59085 + 0.614044i) q^{25} +(-3.45308 + 5.98091i) q^{26} +(0.635103 + 1.10003i) q^{28} +(-1.30287 - 4.35188i) q^{29} +(-6.83895 + 4.49805i) q^{31} +(-4.81627 + 6.46937i) q^{32} +(-12.7782 - 8.40432i) q^{34} +(1.59006 - 0.578734i) q^{35} +(3.96908 + 1.44463i) q^{37} +(0.920617 + 1.23660i) q^{38} +(-0.299038 - 0.316962i) q^{40} +(6.20503 + 6.57695i) q^{41} +(1.04785 + 1.40751i) q^{43} +(-7.31231 - 2.66146i) q^{44} +(4.12528 - 1.50148i) q^{46} +(9.82847 + 6.46428i) q^{47} +(-3.95698 + 5.31514i) q^{49} +(-4.49233 + 2.95465i) q^{50} +(-2.03815 - 6.80788i) q^{52} +(2.80062 + 4.85082i) q^{53} +(-5.18313 + 8.97744i) q^{55} +(-0.0936337 - 0.0221916i) q^{56} +(8.19779 + 4.11708i) q^{58} +(-0.599347 - 1.38944i) q^{59} +(-0.175804 + 3.01844i) q^{61} +(2.87039 - 16.2788i) q^{62} +(-1.49529 - 8.48019i) q^{64} +(-9.40281 + 1.09903i) q^{65} +(2.19466 - 7.33068i) q^{67} +(15.3135 - 3.62938i) q^{68} +(-1.35341 + 3.13757i) q^{70} +(5.19850 - 4.36206i) q^{71} +(0.438511 + 0.367955i) q^{73} +(-7.62227 + 3.82805i) q^{74} +(-1.57564 - 0.184166i) q^{76} +(0.133101 + 2.28526i) q^{77} +(-6.32380 + 6.70284i) q^{79} -10.6242 q^{80} -18.2595 q^{82} +(-4.24676 + 4.50130i) q^{83} +(-1.21901 - 20.9296i) q^{85} +(-3.51954 - 0.411375i) q^{86} +(0.526809 - 0.264573i) q^{88} +(3.52742 + 2.95986i) q^{89} +(-1.60143 + 1.34376i) q^{91} +(-1.78923 + 4.14790i) q^{92} +(-23.1153 + 5.47843i) q^{94} +(-0.606095 + 2.02450i) q^{95} +(10.4458 - 1.22093i) q^{97} +(-2.32362 - 13.1779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

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