LMFDB - Embedded newform 729.2.g.b.136.4

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,-18,63] 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			136.4
Character	$\chi$	$=$	729.136
Dual form			729.2.g.b.595.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.235229 - 0.0557502i) q^{2} +(-1.73504 - 0.871370i) q^{4} +(2.53668 - 3.40735i) q^{5} +(0.962610 + 0.633118i) q^{7} +(0.729927 + 0.612481i) q^{8} +(-0.786660 + 0.660086i) q^{10} +(1.96124 - 0.229235i) q^{11} +(1.14870 - 3.83692i) q^{13} +(-0.191137 - 0.202593i) q^{14} +(2.18128 + 2.92997i) q^{16} +(0.731666 + 4.14948i) q^{17} +(0.525049 - 2.97770i) q^{19} +(-7.37031 + 3.70151i) q^{20} +(-0.474118 - 0.0554165i) q^{22} +(-1.01926 + 0.670375i) q^{23} +(-3.74129 - 12.4968i) q^{25} +(-0.484116 + 0.838513i) q^{26} +(-1.11849 - 1.93728i) q^{28} +(-0.409584 + 0.434134i) q^{29} +(0.113119 + 1.94217i) q^{31} +(-1.10456 - 2.56067i) q^{32} +(0.0592258 - 1.01687i) q^{34} +(4.59909 - 1.67393i) q^{35} +(-4.95333 - 1.80287i) q^{37} +(-0.289514 + 0.671168i) q^{38} +(3.93853 - 0.933449i) q^{40} +(-5.57409 + 1.32108i) q^{41} +(2.89097 - 6.70201i) q^{43} +(-3.60257 - 1.31123i) q^{44} +(0.277132 - 0.100868i) q^{46} +(-0.0253896 + 0.435922i) q^{47} +(-2.24678 - 5.20862i) q^{49} +(0.183360 + 3.14818i) q^{50} +(-5.33642 + 5.65627i) q^{52} +(2.23695 + 3.87450i) q^{53} +(4.19394 - 7.26412i) q^{55} +(0.314861 + 1.05171i) q^{56} +(0.120549 - 0.0792863i) q^{58} +(8.27664 + 0.967400i) q^{59} +(-9.42504 + 4.73343i) q^{61} +(0.0816677 - 0.463161i) q^{62} +(-1.15153 - 6.53063i) q^{64} +(-10.1599 - 13.6471i) q^{65} +(-5.02725 - 5.32857i) q^{67} +(2.34627 - 7.83708i) q^{68} +(-1.17516 + 0.137356i) q^{70} +(3.66891 - 3.07858i) q^{71} +(5.52198 + 4.63349i) q^{73} +(1.06466 + 0.700235i) q^{74} +(-3.50566 + 4.70892i) q^{76} +(2.03304 + 1.02103i) q^{77} +(12.2632 + 2.90642i) q^{79} +15.5167 q^{80} +1.38483 q^{82} +(11.2643 + 2.66968i) q^{83} +(15.9948 + 8.03287i) q^{85} +(-1.05368 + 1.41533i) q^{86} +(1.57196 + 1.03389i) q^{88} +(-8.43420 - 7.07713i) q^{89} +(3.53497 - 2.96620i) q^{91} +(2.35260 - 0.274979i) q^{92} +(0.0302751 - 0.101126i) q^{94} +(-8.81419 - 9.34250i) q^{95} +(3.75478 + 5.04355i) q^{97} +(0.238125 + 1.35047i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 63 q^{20} + 9 q^{22} - 36 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 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Character values

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

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

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 $

$2$	−0.235229	−	0.0557502i	−0.166332	−	0.0394213i	0.146606	−	0.989195i	$-0.453165\pi$
$2$	−0.235229	−	0.0557502i	−0.166332	−	0.0394213i	−0.312938	+	0.949774i	$0.601313\pi$
$3$		0			0
$3$		0			0
$4$	−1.73504	−	0.871370i	−0.867520	−	0.435685i
$5$	2.53668	−	3.40735i	1.13444	−	1.52381i	0.316422	−	0.948619i	$-0.397518\pi$
$5$	2.53668	−	3.40735i	1.13444	−	1.52381i	0.818016	−	0.575196i	$-0.195074\pi$
$6$		0			0
$7$	0.962610	+	0.633118i	0.363832	+	0.239296i	0.718241	−	0.695794i	$-0.244948\pi$
$7$	0.962610	+	0.633118i	0.363832	+	0.239296i	−0.354409	+	0.935091i	$0.615318\pi$
$8$	0.729927	+	0.612481i	0.258068	+	0.216545i
$9$		0			0
$10$	−0.786660	+	0.660086i	−0.248764	+	0.208738i
$11$	1.96124	−	0.229235i	0.591335	−	0.0691171i	0.184837	−	0.982769i	$-0.440824\pi$
$11$	1.96124	−	0.229235i	0.591335	−	0.0691171i	0.406497	+	0.913652i	$0.366750\pi$
$12$		0			0
$13$	1.14870	−	3.83692i	0.318592	−	1.06417i	−0.637340	−	0.770583i	$-0.719965\pi$
$13$	1.14870	−	3.83692i	0.318592	−	1.06417i	0.955932	−	0.293588i	$-0.0948494\pi$
$14$	−0.191137	−	0.202593i	−0.0510835	−	0.0541453i
$15$		0			0
$16$	2.18128	+	2.92997i	0.545321	+	0.732493i
$17$	0.731666	+	4.14948i	0.177455	+	1.00640i	0.935272	+	0.353930i	$0.115155\pi$
$17$	0.731666	+	4.14948i	0.177455	+	1.00640i	−0.757817	+	0.652467i	$0.773734\pi$
$18$		0			0
$19$	0.525049	−	2.97770i	0.120454	−	0.683131i	−0.863450	−	0.504435i	$-0.831701\pi$
$19$	0.525049	−	2.97770i	0.120454	−	0.683131i	0.983904	−	0.178696i	$-0.0571880\pi$
$20$	−7.37031	+	3.70151i	−1.64805	+	0.827682i
$21$		0			0
$22$	−0.474118	−	0.0554165i	−0.101082	−	0.0118148i
$23$	−1.01926	+	0.670375i	−0.212529	+	0.139783i	−0.651311	−	0.758811i	$-0.725781\pi$
$23$	−1.01926	+	0.670375i	−0.212529	+	0.139783i	0.438781	+	0.898594i	$0.355410\pi$
$24$		0			0
$25$	−3.74129	−	12.4968i	−0.748258	−	2.49936i
$26$	−0.484116	+	0.838513i	−0.0949430	+	0.164446i
$27$		0			0
$28$	−1.11849	−	1.93728i	−0.211374	−	0.366111i
$29$	−0.409584	+	0.434134i	−0.0760579	+	0.0806166i	−0.764285	−	0.644879i	$-0.776908\pi$
$29$	−0.409584	+	0.434134i	−0.0760579	+	0.0806166i	0.688227	+	0.725495i	$0.258389\pi$
$30$		0			0
$31$	0.113119	+	1.94217i	0.0203167	+	0.348824i	0.993113	+	0.117162i	$0.0373796\pi$
$31$	0.113119	+	1.94217i	0.0203167	+	0.348824i	−0.972796	+	0.231663i	$0.925583\pi$
$32$	−1.10456	−	2.56067i	−0.195261	−	0.452666i
$33$		0			0
$34$	0.0592258	−	1.01687i	0.0101571	−	0.174391i
$35$	4.59909	−	1.67393i	0.777388	−	0.282946i
$36$		0			0
$37$	−4.95333	−	1.80287i	−0.814323	−	0.296389i	−0.0989148	−	0.995096i	$-0.531537\pi$
$37$	−4.95333	−	1.80287i	−0.814323	−	0.296389i	−0.715408	+	0.698706i	$0.753759\pi$
$38$	−0.289514	+	0.671168i	−0.0469653	+	0.108878i
$39$		0			0
$40$	3.93853	−	0.933449i	0.622736	−	0.147591i
$41$	−5.57409	+	1.32108i	−0.870526	+	0.206318i	−0.641520	−	0.767106i	$-0.721696\pi$
$41$	−5.57409	+	1.32108i	−0.870526	+	0.206318i	−0.229006	+	0.973425i	$0.573548\pi$
$42$		0			0
$43$	2.89097	−	6.70201i	0.440868	−	1.02205i	−0.542439	−	0.840095i	$-0.682499\pi$
$43$	2.89097	−	6.70201i	0.440868	−	1.02205i	0.983307	−	0.181952i	$-0.0582416\pi$
$44$	−3.60257	−	1.31123i	−0.543108	−	0.197675i
$45$		0			0
$46$	0.277132	−	0.100868i	0.0408608	−	0.0148721i
$47$	−0.0253896	+	0.435922i	−0.00370345	+	0.0635858i	−0.999654	−	0.0263225i	$-0.991620\pi$
$47$	−0.0253896	+	0.435922i	−0.00370345	+	0.0635858i	0.995950	+	0.0899082i	$0.0286574\pi$
$48$		0			0
$49$	−2.24678	−	5.20862i	−0.320969	−	0.744089i
$50$	0.183360	+	3.14818i	0.0259311	+	0.445219i
$51$		0			0
$52$	−5.33642	+	5.65627i	−0.740028	+	0.784384i
$53$	2.23695	+	3.87450i	0.307268	+	0.532204i	0.977764	−	0.209710i	$-0.0672518\pi$
$53$	2.23695	+	3.87450i	0.307268	+	0.532204i	−0.670496	+	0.741913i	$0.733919\pi$
$54$		0			0
$55$	4.19394	−	7.26412i	0.565511	−	0.979493i
$56$	0.314861	+	1.05171i	0.0420751	+	0.140541i
$57$		0			0
$58$	0.120549	−	0.0792863i	0.0158289	−	0.0104108i
$59$	8.27664	+	0.967400i	1.07753	+	0.125945i	0.636293	−	0.771448i	$-0.280467\pi$
$59$	8.27664	+	0.967400i	1.07753	+	0.125945i	0.441234	+	0.897392i	$0.354541\pi$
$60$		0			0
$61$	−9.42504	+	4.73343i	−1.20675	+	0.606054i	−0.934428	−	0.356151i	$-0.884089\pi$
$61$	−9.42504	+	4.73343i	−1.20675	+	0.606054i	−0.272325	+	0.962205i	$0.587792\pi$
$62$	0.0816677	−	0.463161i	0.0103718	−	0.0588215i
$63$		0			0
$64$	−1.15153	−	6.53063i	−0.143941	−	0.816329i
$65$	−10.1599	−	13.6471i	−1.26018	−	1.69271i
$66$		0			0
$67$	−5.02725	−	5.32857i	−0.614176	−	0.650989i	0.343393	−	0.939192i	$-0.388424\pi$
$67$	−5.02725	−	5.32857i	−0.614176	−	0.650989i	−0.957569	+	0.288203i	$0.906942\pi$
$68$	2.34627	−	7.83708i	0.284527	−	0.950385i
$69$		0			0
$70$	−1.17516	+	0.137356i	−0.140458	+	0.0164172i
$71$	3.66891	−	3.07858i	0.435420	−	0.365361i	−0.398572	−	0.917137i	$-0.630494\pi$
$71$	3.66891	−	3.07858i	0.435420	−	0.365361i	0.833992	+	0.551776i	$0.186050\pi$
$72$		0			0
$73$	5.52198	+	4.63349i	0.646298	+	0.542309i	0.905945	−	0.423395i	$-0.139162\pi$
$73$	5.52198	+	4.63349i	0.646298	+	0.542309i	−0.259647	+	0.965704i	$0.583606\pi$
$74$	1.06466	+	0.700235i	0.123764	+	0.0814007i
$75$		0			0
$76$	−3.50566	+	4.70892i	−0.402127	+	0.540150i
$77$	2.03304	+	1.02103i	0.231686	+	0.116357i
$78$		0			0
$79$	12.2632	+	2.90642i	1.37971	+	0.326998i	0.852497	−	0.522732i	$-0.175087\pi$
$79$	12.2632	+	2.90642i	1.37971	+	0.326998i	0.527217	+	0.849731i	$0.323235\pi$
$80$	15.5167			1.73482
$81$		0			0
$82$	1.38483			0.152929
$83$	11.2643	+	2.66968i	1.23641	+	0.293035i	0.796297	−	0.604905i	$-0.206789\pi$
$83$	11.2643	+	2.66968i	1.23641	+	0.293035i	0.440116	+	0.897941i	$0.354937\pi$
$84$		0			0
$85$	15.9948	+	8.03287i	1.73487	+	0.871287i
$86$	−1.05368	+	1.41533i	−0.113621	+	0.152619i
$87$		0			0
$88$	1.57196	+	1.03389i	0.167572	+	0.110214i
$89$	−8.43420	−	7.07713i	−0.894023	−	0.750174i	0.0749899	−	0.997184i	$-0.476108\pi$
$89$	−8.43420	−	7.07713i	−0.894023	−	0.750174i	−0.969013	+	0.247010i	$0.920552\pi$
$90$		0			0
$91$	3.53497	−	2.96620i	0.370566	−	0.310942i
$92$	2.35260	−	0.274979i	0.245275	−	0.0286685i
$93$		0			0
$94$	0.0302751	−	0.101126i	0.00312264	−	0.0104303i
$95$	−8.81419	−	9.34250i	−0.904317	−	0.958520i
$96$		0			0
$97$	3.75478	+	5.04355i	0.381241	+	0.512095i	0.950779	−	0.309870i	$-0.100285\pi$
$97$	3.75478	+	5.04355i	0.381241	+	0.512095i	−0.569538	+	0.821965i	$0.692878\pi$
$98$	0.238125	+	1.35047i	0.0240543	+	0.136419i
$99$		0			0
$100$	−4.39803	+	24.9425i	−0.439803	+	2.49425i
$101$	3.61725	−	1.81665i	0.359930	−	0.180764i	−0.259639	−	0.965706i	$-0.583604\pi$
$101$	3.61725	−	1.81665i	0.359930	−	0.180764i	0.619569	+	0.784942i	$0.287307\pi$
$102$		0			0
$103$	−8.22877	−	0.961806i	−0.810805	−	0.0947695i	−0.299420	−	0.954121i	$-0.596793\pi$
$103$	−8.22877	−	0.961806i	−0.810805	−	0.0947695i	−0.511385	+	0.859352i	$0.670867\pi$
$104$	3.18851	−	2.09712i	0.312659	−	0.205639i
$105$		0			0
$106$	−0.310189	−	1.03610i	−0.0301282	−	0.100635i
$107$	−7.95369	+	13.7762i	−0.768912	+	1.33179i	0.169241	+	0.985575i	$0.445868\pi$
$107$	−7.95369	+	13.7762i	−0.768912	+	1.33179i	−0.938153	+	0.346220i	$0.887465\pi$
$108$		0			0
$109$	1.81056	+	3.13598i	0.173420	+	0.300372i	0.939613	−	0.342238i	$-0.111185\pi$
$109$	1.81056	+	3.13598i	0.173420	+	0.300372i	−0.766193	+	0.642610i	$0.777852\pi$
$110$	−1.39151	+	1.47491i	−0.132675	+	0.140628i
$111$		0			0
$112$	0.244705	+	4.20143i	0.0231225	+	0.396998i
$113$	3.76083	+	8.71858i	0.353789	+	0.820175i	0.998447	+	0.0557040i	$0.0177403\pi$
$113$	3.76083	+	8.71858i	0.353789	+	0.820175i	−0.644659	+	0.764471i	$0.723000\pi$
$114$		0			0
$115$	−0.301321	+	5.17349i	−0.0280984	+	0.482430i
$116$	1.08894	−	0.396341i	0.101105	−	0.0367993i
$117$		0			0
$118$	−1.89297	−	0.688984i	−0.174262	−	0.0634261i
$119$	−1.92281	+	4.45756i	−0.176263	+	0.408624i
$120$		0			0
$121$	−6.90960	+	1.63761i	−0.628145	+	0.148873i
$122$	2.48093	−	0.587991i	0.224613	−	0.0532342i
$123$		0			0
$124$	1.49609	−	3.46832i	0.134352	−	0.311464i
$125$	−32.1127	−	11.6881i	−2.87225	−	1.04541i
$126$		0			0
$127$	−10.4753	+	3.81269i	−0.929532	+	0.338322i	−0.762024	−	0.647549i	$-0.775794\pi$
$127$	−10.4753	+	3.81269i	−0.929532	+	0.338322i	−0.167508	+	0.985871i	$0.553572\pi$
$128$	−0.417514	+	7.16844i	−0.0369034	+	0.633606i
$129$		0			0
$130$	1.62906	+	3.77659i	0.142878	+	0.331229i
$131$	0.705371	+	12.1107i	0.0616285	+	1.05812i	0.877404	+	0.479752i	$0.159273\pi$
$131$	0.705371	+	12.1107i	0.0616285	+	1.05812i	−0.815775	+	0.578369i	$0.803690\pi$
$132$		0			0
$133$	2.39065	−	2.53394i	0.207296	−	0.219721i
$134$	0.885484	+	1.53370i	0.0764941	+	0.132492i
$135$		0			0
$136$	−2.00742	+	3.47695i	−0.172135	+	0.298146i
$137$	−0.0858165	−	0.286647i	−0.00733180	−	0.0244899i	0.954245	−	0.299025i	$-0.0966613\pi$
$137$	−0.0858165	−	0.286647i	−0.00733180	−	0.0244899i	−0.961577	+	0.274535i	$0.911476\pi$
$138$		0			0
$139$	4.68674	−	3.08252i	0.397524	−	0.261456i	−0.334970	−	0.942229i	$-0.608726\pi$
$139$	4.68674	−	3.08252i	0.397524	−	0.261456i	0.732495	+	0.680773i	$0.238356\pi$
$140$	−9.43822	−	1.10317i	−0.797675	−	0.0932349i
$141$		0			0
$142$	−1.03466	+	0.519628i	−0.0868271	+	0.0436062i
$143$	1.37331	−	7.78843i	0.114842	−	0.651301i
$144$		0			0
$145$	0.440263	+	2.49686i	0.0365619	+	0.207353i
$146$	−1.04061	−	1.39778i	−0.0861214	−	0.115681i
$147$		0			0
$148$	7.02327	+	7.44424i	0.577310	+	0.611912i
$149$	−3.90806	+	13.0538i	−0.320161	+	1.06941i	0.634799	+	0.772677i	$0.281083\pi$
$149$	−3.90806	+	13.0538i	−0.320161	+	1.06941i	−0.954960	+	0.296735i	$0.904102\pi$
$150$		0			0
$151$	9.38937	−	1.09746i	0.764096	−	0.0893101i	0.274887	−	0.961476i	$-0.411359\pi$
$151$	9.38937	−	1.09746i	0.764096	−	0.0893101i	0.489209	+	0.872166i	$0.337285\pi$
$152$	2.20703	−	1.85192i	0.179014	−	0.150211i
$153$		0			0
$154$	−0.421306	−	0.353517i	−0.0339498	−	0.0284872i
$155$	6.90461	+	4.54123i	0.554592	+	0.364761i
$156$		0			0
$157$	−5.44744	+	7.31718i	−0.434753	+	0.583975i	−0.964468	−	0.264201i	$-0.914892\pi$
$157$	−5.44744	+	7.31718i	−0.434753	+	0.583975i	0.529714	+	0.848176i	$0.322299\pi$
$158$	−2.72261	−	1.36735i	−0.216600	−	0.108780i
$159$		0			0
$160$	−11.5270	−	2.73195i	−0.911291	−	0.215980i
$161$	−1.40557			−0.110775
$162$		0			0
$163$	7.94158			0.622033			0.311016	−	0.950405i	$-0.399331\pi$
$163$	7.94158			0.622033			0.311016	+	0.950405i	$0.399331\pi$
$164$	10.8224	+	2.56496i	0.845089	+	0.200290i
$165$		0			0
$166$	−2.50084	−	1.25597i	−0.194103	−	0.0974822i
$167$	2.65433	−	3.56538i	0.205398	−	0.275897i	−0.687473	−	0.726210i	$-0.741280\pi$
$167$	2.65433	−	3.56538i	0.205398	−	0.275897i	0.892871	+	0.450312i	$0.148687\pi$
$168$		0			0
$169$	−2.54112	−	1.67132i	−0.195471	−	0.128563i
$170$	−3.31459	−	2.78127i	−0.254217	−	0.213314i
$171$		0			0
$172$	−10.8559	+	9.10916i	−0.827753	+	0.694567i
$173$	3.09739	−	0.362033i	0.235491	−	0.0275249i	0.00247098	−	0.999997i	$-0.499213\pi$
$173$	3.09739	−	0.362033i	0.235491	−	0.0275249i	0.233020	+	0.972472i	$0.425139\pi$
$174$		0			0
$175$	4.31054	−	14.3982i	0.325846	−	1.08840i
$176$	4.94966	+	5.24634i	0.373095	+	0.395458i
$177$		0			0
$178$	1.58941	+	2.13495i	0.119132	+	0.160021i
$179$	2.47200	+	14.0194i	0.184766	+	1.04786i	0.926255	+	0.376897i	$0.123009\pi$
$179$	2.47200	+	14.0194i	0.184766	+	1.04786i	−0.741489	+	0.670965i	$0.765880\pi$
$180$		0			0
$181$	2.75966	−	15.6508i	0.205124	−	1.16332i	−0.692120	−	0.721783i	$-0.743323\pi$
$181$	2.75966	−	15.6508i	0.205124	−	1.16332i	0.897244	−	0.441535i	$-0.145566\pi$
$182$	−0.996893	+	0.500658i	−0.0738946	+	0.0371113i
$183$		0			0
$184$	−1.15457	−	0.134950i	−0.0851163	−	0.00994867i
$185$	−18.7080	+	12.3045i	−1.37544	+	0.904642i
$186$		0			0
$187$	2.38618	+	7.97039i	0.174495	+	0.582853i
$188$	0.423901	−	0.734219i	0.0309162	−	0.0535484i
$189$		0			0
$190$	1.55250	+	2.68901i	0.112630	+	0.195082i
$191$	13.9359	−	14.7712i	1.00836	−	1.06880i	0.0107379	−	0.999942i	$-0.496582\pi$
$191$	13.9359	−	14.7712i	1.00836	−	1.06880i	0.997626	−	0.0688612i	$-0.0219366\pi$
$192$		0			0
$193$	0.155389	+	2.66793i	0.0111852	+	0.192042i	0.999272	+	0.0381456i	$0.0121451\pi$
$193$	0.155389	+	2.66793i	0.0111852	+	0.192042i	−0.988087	+	0.153896i	$0.950818\pi$
$194$	−0.602053	−	1.39572i	−0.0432249	−	0.100207i
$195$		0			0
$196$	−0.640383	+	10.9949i	−0.0457416	+	0.785353i
$197$	15.7132	−	5.71915i	1.11952	−	0.407473i	0.285044	−	0.958514i	$-0.407992\pi$
$197$	15.7132	−	5.71915i	1.11952	−	0.407473i	0.834478	+	0.551042i	$0.185770\pi$
$198$		0			0
$199$	−1.83812	−	0.669021i	−0.130301	−	0.0474257i	0.276047	−	0.961144i	$-0.410976\pi$
$199$	−1.83812	−	0.669021i	−0.130301	−	0.0474257i	−0.406348	+	0.913719i	$0.633198\pi$
$200$	4.92317	−	11.4132i	0.348121	−	0.807035i
$201$		0			0
$202$	−0.952160	+	0.225666i	−0.0669937	+	0.0158778i
$203$	−0.669128	+	0.158586i	−0.0469636	+	0.0111306i
$204$		0			0
$205$	−9.63828	+	22.3440i	−0.673167	+	1.56058i
$206$	1.88202	+	0.685000i	0.131127	+	0.0477262i
$207$		0			0
$208$	13.7477	−	5.00376i	0.953233	−	0.346948i
$209$	0.347150	−	5.96033i	0.0240128	−	0.412285i
$210$		0			0
$211$	4.10509	+	9.51668i	0.282606	+	0.655155i	0.999099	−	0.0424394i	$-0.0135129\pi$
$211$	4.10509	+	9.51668i	0.282606	+	0.655155i	−0.716493	+	0.697595i	$0.754254\pi$
$212$	−0.505065	−	8.67163i	−0.0346880	−	0.595570i
$213$		0			0
$214$	2.63896	−	2.79713i	0.180396	−	0.191208i
$215$	−15.5027	−	26.8514i	−1.05727	−	1.83125i
$216$		0			0
$217$	−1.12074	+	1.94117i	−0.0760805	+	0.131775i
$218$	−0.251063	−	0.838610i	−0.0170042	−	0.0567978i
$219$		0			0
$220$	−13.6064	+	8.94906i	−0.917343	+	0.603346i
$221$	16.7617	+	1.95916i	1.12751	+	0.131788i
$222$		0			0
$223$	6.54862	−	3.28884i	0.438528	−	0.220237i	−0.215816	−	0.976434i	$-0.569241\pi$
$223$	6.54862	−	3.28884i	0.438528	−	0.220237i	0.654344	+	0.756197i	$0.272945\pi$
$224$	0.557941	−	3.16424i	0.0372790	−	0.211420i
$225$		0			0
$226$	−0.398592	−	2.26052i	−0.0265139	−	0.150368i
$227$	13.9005	+	18.6716i	0.922608	+	1.23928i	0.970666	+	0.240434i	$0.0772897\pi$
$227$	13.9005	+	18.6716i	0.922608	+	1.23928i	−0.0480571	+	0.998845i	$0.515303\pi$
$228$		0			0
$229$	0.0342534	+	0.0363064i	0.00226353	+	0.00239920i	0.728504	−	0.685041i	$-0.240216\pi$
$229$	0.0342534	+	0.0363064i	0.00226353	+	0.00239920i	−0.726241	+	0.687440i	$0.758734\pi$
$230$	0.359302	−	1.20015i	0.0236917	−	0.0791358i
$231$		0			0
$232$	−0.564865	+	0.0660233i	−0.0370852	+	0.00433464i
$233$	17.1664	−	14.4043i	1.12461	−	0.943660i	0.125782	−	0.992058i	$-0.459856\pi$
$233$	17.1664	−	14.4043i	1.12461	−	0.943660i	0.998828	+	0.0483977i	$0.0154115\pi$
$234$		0			0
$235$	1.42093	+	1.19231i	0.0926916	+	0.0777775i
$236$	−13.5173	−	8.89050i	−0.879904	−	0.578722i
$237$		0			0
$238$	0.700809	−	0.941349i	0.0454267	−	0.0610186i
$239$	18.3490	+	9.21523i	1.18690	+	0.596084i	0.928997	−	0.370087i	$-0.120672\pi$
$239$	18.3490	+	9.21523i	1.18690	+	0.596084i	0.257903	+	0.966171i	$0.416968\pi$
$240$		0			0
$241$	−28.0110	−	6.63872i	−1.80435	−	0.427638i	−0.815772	−	0.578374i	$-0.803688\pi$
$241$	−28.0110	−	6.63872i	−1.80435	−	0.427638i	−0.988574	+	0.150736i	$0.951836\pi$
$242$	1.71663			0.110349
$243$		0			0
$244$	20.4774			1.31093
$245$	−23.4470	−	5.55703i	−1.49797	−	0.355026i
$246$		0			0
$247$	−10.8221	−	5.43505i	−0.688592	−	0.345824i
$248$	−1.10698	+	1.48693i	−0.0702930	+	0.0944199i
$249$		0			0
$250$	6.90221	+	4.53966i	0.436534	+	0.287113i
$251$	7.80826	+	6.55190i	0.492853	+	0.413553i	0.855047	−	0.518550i	$-0.173528\pi$
$251$	7.80826	+	6.55190i	0.492853	+	0.413553i	−0.362195	+	0.932102i	$0.617972\pi$
$252$		0			0
$253$	−1.84533	+	1.54841i	−0.116015	+	0.0973479i
$254$	2.67665	−	0.312855i	0.167948	−	0.0196303i
$255$		0			0
$256$	−3.30595	+	11.0426i	−0.206622	+	0.690165i
$257$	4.15896	+	4.40824i	0.259429	+	0.274978i	0.843976	−	0.536382i	$-0.180209\pi$
$257$	4.15896	+	4.40824i	0.259429	+	0.274978i	−0.584547	+	0.811360i	$0.698728\pi$
$258$		0			0
$259$	−3.62670	−	4.87150i	−0.225352	−	0.302700i
$260$	5.73613	+	32.5312i	0.355740	+	2.01750i
$261$		0			0
$262$	0.509253	−	2.88812i	0.0314618	−	0.178429i
$263$	−11.9907	+	6.02194i	−0.739376	+	0.371329i	−0.778283	−	0.627914i	$-0.783909\pi$
$263$	−11.9907	+	6.02194i	−0.739376	+	0.371329i	0.0389065	+	0.999243i	$0.487613\pi$
$264$		0			0
$265$	18.8762	+	2.20631i	1.15956	+	0.135533i
$266$	−0.703618	+	0.462777i	−0.0431416	+	0.0283747i
$267$		0			0
$268$	4.07932	+	13.6259i	0.249184	+	0.832333i
$269$	−1.44120	+	2.49623i	−0.0878715	+	0.152198i	−0.906611	−	0.421967i	$-0.861340\pi$
$269$	−1.44120	+	2.49623i	−0.0878715	+	0.152198i	0.818740	+	0.574165i	$0.194673\pi$
$270$		0			0
$271$	−1.60573	−	2.78120i	−0.0975410	−	0.168946i	0.813125	−	0.582089i	$-0.197764\pi$
$271$	−1.60573	−	2.78120i	−0.0975410	−	0.168946i	−0.910666	+	0.413143i	$0.864431\pi$
$272$	−10.5619	+	11.1950i	−0.640409	+	0.678794i
$273$		0			0
$274$	0.00420586	+	0.0722119i	0.000254086	+	0.00436248i
$275$	−10.2023	−	23.6515i	−0.615219	−	1.42624i
$276$		0			0
$277$	0.198058	−	3.40052i	0.0119001	−	0.204317i	−0.987117	−	0.159998i	$-0.948851\pi$
$277$	0.198058	−	3.40052i	0.0119001	−	0.204317i	0.999017	−	0.0443191i	$-0.0141118\pi$
$278$	−1.27431	+	0.463810i	−0.0764278	+	0.0278174i
$279$		0			0
$280$	4.38225	+	1.59501i	0.261889	+	0.0953200i
$281$	4.54892	−	10.5456i	0.271366	−	0.629097i	−0.726976	−	0.686663i	$-0.759075\pi$
$281$	4.54892	−	10.5456i	0.271366	−	0.629097i	0.998342	+	0.0575661i	$0.0183340\pi$
$282$		0			0
$283$	24.6585	−	5.84418i	1.46580	−	0.347401i	0.581202	−	0.813759i	$-0.302582\pi$
$283$	24.6585	−	5.84418i	1.46580	−	0.347401i	0.884596	+	0.466358i	$0.154434\pi$
$284$	−9.04830	+	2.14449i	−0.536918	+	0.127252i
$285$		0			0
$286$	−0.757248	+	1.75550i	−0.0447770	+	0.103805i
$287$	−6.20207	−	2.25737i	−0.366097	−	0.133248i
$288$		0			0
$289$	−0.708104	+	0.257729i	−0.0416532	+	0.0151605i
$290$	0.0356378	−	0.611877i	0.00209272	−	0.0359306i
$291$		0			0
$292$	−5.54337	−	12.8510i	−0.324401	−	0.752047i
$293$	−0.233518	−	4.00934i	−0.0136422	−	0.234228i	−0.998236	−	0.0593708i	$-0.981091\pi$
$293$	−0.233518	−	4.00934i	−0.0136422	−	0.234228i	0.984594	−	0.174858i	$-0.0559465\pi$
$294$		0			0
$295$	24.2915	−	25.7474i	1.41430	−	1.49907i
$296$	−2.51135	−	4.34978i	−0.145969	−	0.252826i
$297$		0			0
$298$	1.64704	−	2.85276i	0.0954106	−	0.165256i
$299$	1.40136	+	4.68086i	0.0810427	+	0.270701i
$300$		0			0
$301$	7.02604	−	4.62110i	0.404974	−	0.266356i
$302$	−2.26983	−	0.265305i	−0.130614	−	0.0152666i
$303$		0			0
$304$	9.86986	−	4.95683i	0.566075	−	0.284294i
$305$	−7.77984	+	44.1216i	−0.445472	+	2.52640i
$306$		0			0
$307$	3.45206	+	19.5776i	0.197020	+	1.11735i	0.909513	+	0.415675i	$0.136455\pi$
$307$	3.45206	+	19.5776i	0.197020	+	1.11735i	−0.712493	+	0.701679i	$0.752434\pi$
$308$	−2.63771	−	3.54306i	−0.150297	−	0.201884i
$309$		0			0
$310$	−1.37099	−	1.45316i	−0.0778668	−	0.0825340i
$311$	0.442878	−	1.47932i	0.0251133	−	0.0838843i	−0.944514	−	0.328470i	$-0.893467\pi$
$311$	0.442878	−	1.47932i	0.0251133	−	0.0838843i	0.969628	+	0.244586i	$0.0786521\pi$
$312$		0			0
$313$	17.3808	−	2.03153i	0.982423	−	0.114829i	0.390310	−	0.920684i	$-0.372368\pi$
$313$	17.3808	−	2.03153i	0.982423	−	0.114829i	0.592113	+	0.805855i	$0.298294\pi$
$314$	1.68933	−	1.41751i	0.0953343	−	0.0799950i
$315$		0			0
$316$	−18.7445	−	15.7285i	−1.05446	−	0.884799i
$317$	1.64131	+	1.07951i	0.0921853	+	0.0606312i	0.594765	−	0.803900i	$-0.297245\pi$
$317$	1.64131	+	1.07951i	0.0921853	+	0.0606312i	−0.502579	+	0.864531i	$0.667616\pi$
$318$		0			0
$319$	−0.703772	+	0.945330i	−0.0394037	+	0.0529283i
$320$	−25.1732	−	12.6425i	−1.40723	−	0.706736i
$321$		0			0
$322$	0.330631	+	0.0783609i	0.0184253	+	0.00436688i
$323$	12.7401			0.708877
$324$		0			0
$325$	−52.2468			−2.89813
$326$	−1.86809	−	0.442745i	−0.103464	−	0.0245214i
$327$		0			0
$328$	−4.87781	−	2.44973i	−0.269332	−	0.135264i
$329$	−0.300430	+	0.403548i	−0.0165633	+	0.0222483i
$330$		0			0
$331$	−28.8095	−	18.9483i	−1.58351	−	1.04149i	−0.967208	−	0.253986i	$-0.918258\pi$
$331$	−28.8095	−	18.9483i	−1.58351	−	1.04149i	−0.616305	−	0.787507i	$-0.711371\pi$
$332$	−17.2177	−	14.4474i	−0.944943	−	0.792901i
$333$		0			0
$334$	−0.823144	+	0.690700i	−0.0450405	+	0.0377934i
$335$	−30.9088	+	3.61273i	−1.68873	+	0.197384i
$336$		0			0
$337$	−4.63935	+	15.4965i	−0.252722	+	0.844149i	0.733637	+	0.679541i	$0.237821\pi$
$337$	−4.63935	+	15.4965i	−0.252722	+	0.844149i	−0.986359	+	0.164608i	$0.947364\pi$
$338$	0.504568	+	0.534811i	0.0274449	+	0.0290899i
$339$		0			0
$340$	−20.7520	−	27.8747i	−1.12543	−	1.51172i
$341$	0.667067	+	3.78313i	0.0361237	+	0.204868i
$342$		0			0
$343$	2.53539	−	14.3789i	0.136898	−	0.776387i
$344$	6.21505	−	3.12132i	0.335093	−	0.168290i
$345$		0			0
$346$	−0.748779	−	0.0875197i	−0.0402546	−	0.00470509i
$347$	26.5809	−	17.4825i	1.42694	−	0.938511i	0.427532	−	0.904000i	$-0.359383\pi$
$347$	26.5809	−	17.4825i	1.42694	−	0.938511i	0.999404	−	0.0345108i	$-0.0109873\pi$
$348$		0			0
$349$	4.97182	+	16.6070i	0.266135	+	0.888954i	0.981704	+	0.190412i	$0.0609824\pi$
$349$	4.97182	+	16.6070i	0.266135	+	0.888954i	−0.715569	+	0.698542i	$0.753832\pi$
$350$	−1.81666	+	3.14655i	−0.0971048	+	0.168190i
$351$		0			0
$352$	−2.75331	−	4.76887i	−0.146752	−	0.254181i
$353$	−2.33309	+	2.47293i	−0.124178	+	0.131621i	−0.786479	−	0.617617i	$-0.788098\pi$
$353$	−2.33309	+	2.47293i	−0.124178	+	0.131621i	0.662301	+	0.749237i	$0.269580\pi$
$354$		0			0
$355$	−1.18296	−	20.3107i	−0.0627851	−	1.07798i
$356$	8.46687	+	19.6284i	0.448743	+	1.04030i
$357$		0			0
$358$	0.200100	−	3.43559i	0.0105756	−	0.181576i
$359$	−9.53489	+	3.47042i	−0.503232	+	0.183162i	−0.581147	−	0.813798i	$-0.697396\pi$
$359$	−9.53489	+	3.47042i	−0.503232	+	0.183162i	0.0779150	+	0.996960i	$0.475174\pi$
$360$		0			0
$361$	9.26314	+	3.37151i	0.487534	+	0.177448i
$362$	−1.52169	+	3.52767i	−0.0799782	+	0.185410i
$363$		0			0
$364$	−8.71798	+	2.06620i	−0.456946	+	0.108298i
$365$	29.7954	−	7.06164i	1.55956	−	0.369623i
$366$		0			0
$367$	5.88732	−	13.6483i	0.307315	−	0.712437i	−0.692646	−	0.721278i	$-0.743555\pi$
$367$	5.88732	−	13.6483i	0.307315	−	0.712437i	0.999961	+	0.00884100i	$0.00281421\pi$
$368$	−4.18747	−	1.52411i	−0.218287	−	0.0794499i
$369$		0			0
$370$	5.08664	−	1.85138i	0.264442	−	0.0962489i
$371$	−0.299714	+	5.14588i	−0.0155604	+	0.267161i
$372$		0			0
$373$	−8.34970	−	19.3568i	−0.432331	−	1.00226i	−0.985575	−	0.169237i	$-0.945870\pi$
$373$	−8.34970	−	19.3568i	−0.432331	−	1.00226i	0.553244	−	0.833019i	$-0.313390\pi$
$374$	−0.116946	−	2.00789i	−0.00604716	−	0.103826i
$375$		0			0
$376$	−0.285527	+	0.302640i	−0.0147249	+	0.0156075i
$377$	1.19525	+	2.07023i	0.0615585	+	0.106622i
$378$		0			0
$379$	−3.47462	+	6.01822i	−0.178479	+	0.309135i	−0.941360	−	0.337404i	$-0.890451\pi$
$379$	−3.47462	+	6.01822i	−0.178479	+	0.309135i	0.762880	+	0.646540i	$0.223784\pi$
$380$	7.15221	+	23.8900i	0.366901	+	1.22553i
$381$		0			0
$382$	−4.10161	+	2.69767i	−0.209857	+	0.138025i
$383$	−35.0934	−	4.10183i	−1.79319	−	0.209594i	−0.846643	−	0.532161i	$-0.821380\pi$
$383$	−35.0934	−	4.10183i	−1.79319	−	0.209594i	−0.946547	+	0.322567i	$0.895454\pi$
$384$		0			0
$385$	8.63617	−	4.33725i	0.440140	−	0.221047i
$386$	0.112186	−	0.636236i	0.00571010	−	0.0323836i
$387$		0			0
$388$	−2.11990	−	12.0226i	−0.107622	−	0.610354i
$389$	15.3611	+	20.6335i	0.778837	+	1.04616i	0.997521	+	0.0703643i	$0.0224162\pi$
$389$	15.3611	+	20.6335i	0.778837	+	1.04616i	−0.218684	+	0.975796i	$0.570176\pi$
$390$		0			0
$391$	−3.52746	−	3.73889i	−0.178392	−	0.189084i
$392$	1.55020	−	5.17802i	0.0782968	−	0.261530i
$393$		0			0
$394$	−4.01505	+	0.469291i	−0.202275	+	0.0236426i
$395$	41.0109	−	34.4123i	2.06348	−	1.73147i
$396$		0			0
$397$	14.2470	+	11.9547i	0.715038	+	0.599988i	0.926008	−	0.377504i	$-0.123218\pi$
$397$	14.2470	+	11.9547i	0.715038	+	0.599988i	−0.210970	+	0.977493i	$0.567662\pi$
$398$	0.395080	+	0.259848i	0.0198036	+	0.0130250i
$399$		0			0
$400$	28.4544	−	38.2209i	1.42272	−	1.91105i
$401$	4.13190	+	2.07512i	0.206337	+	0.103626i	0.548967	−	0.835844i	$-0.315021\pi$
$401$	4.13190	+	2.07512i	0.206337	+	0.103626i	−0.342630	+	0.939471i	$0.611318\pi$
$402$		0			0
$403$	7.58190	+	1.79694i	0.377682	+	0.0895122i
$404$	−7.85906			−0.391003
$405$		0			0
$406$	0.166239			0.00825031
$407$	−10.1279	−	2.40036i	−0.502023	−	0.118982i
$408$		0			0
$409$	−9.77547	−	4.90943i	−0.483366	−	0.242756i	0.190391	−	0.981708i	$-0.439024\pi$
$409$	−9.77547	−	4.90943i	−0.483366	−	0.242756i	−0.673757	+	0.738953i	$0.735321\pi$
$410$	3.51288	−	4.71862i	0.173489	−	0.233036i
$411$		0			0
$412$	13.4392	+	8.83908i	0.662100	+	0.435470i
$413$	7.35469	+	6.17132i	0.361901	+	0.303671i
$414$		0			0
$415$	37.6704	−	31.6092i	1.84917	−	1.55163i
$416$	−11.0939	+	1.29669i	−0.543923	+	0.0635755i
$417$		0			0
$418$	−0.413949	+	1.38269i	−0.0202469	+	0.0676294i
$419$	−23.0174	−	24.3970i	−1.12447	−	1.19187i	−0.979289	−	0.202466i	$-0.935105\pi$
$419$	−23.0174	−	24.3970i	−1.12447	−	1.19187i	−0.145182	−	0.989405i	$-0.546377\pi$
$420$		0			0
$421$	0.990474	+	1.33044i	0.0482727	+	0.0648415i	0.825604	−	0.564250i	$-0.190835\pi$
$421$	0.990474	+	1.33044i	0.0482727	+	0.0648415i	−0.777331	+	0.629091i	$0.783427\pi$
$422$	−0.435079	−	2.46745i	−0.0211793	−	0.120114i
$423$		0			0
$424$	−0.740254	+	4.19819i	−0.0359499	+	0.203882i
$425$	49.1178	−	24.6679i	2.38256	−	1.19657i
$426$		0			0
$427$	−12.0695	−	1.41072i	−0.584082	−	0.0682694i
$428$	25.8041	−	16.9716i	1.24729	−	0.820356i
$429$		0			0
$430$	2.14970	+	7.18049i	0.103668	+	0.346274i
$431$	−7.55425	+	13.0843i	−0.363876	+	0.630251i	−0.988595	−	0.150598i	$-0.951880\pi$
$431$	−7.55425	+	13.0843i	−0.363876	+	0.630251i	0.624720	+	0.780849i	$0.285213\pi$
$432$		0			0
$433$	−2.46655	−	4.27218i	−0.118535	−	0.205308i	0.800653	−	0.599129i	$-0.204486\pi$
$433$	−2.46655	−	4.27218i	−0.118535	−	0.205308i	−0.919187	+	0.393821i	$0.871153\pi$
$434$	0.371850	−	0.394138i	0.0178494	−	0.0189192i
$435$		0			0
$436$	−0.408793	−	7.01871i	−0.0195777	−	0.336135i
$437$	1.46102	+	3.38702i	0.0698899	+	0.162023i
$438$		0			0
$439$	1.17340	−	20.1465i	0.0560033	−	0.961539i	−0.846915	−	0.531728i	$-0.821543\pi$
$439$	1.17340	−	20.1465i	0.0560033	−	0.961539i	0.902919	−	0.429812i	$-0.141420\pi$
$440$	7.51040	−	2.73356i	0.358044	−	0.130318i
$441$		0			0
$442$	−3.83361	−	1.39532i	−0.182346	−	0.0663686i
$443$	−11.1640	+	25.8811i	−0.530419	+	1.22965i	0.416781	+	0.909007i	$0.363158\pi$
$443$	−11.1640	+	25.8811i	−0.530419	+	1.22965i	−0.947200	+	0.320643i	$0.896101\pi$
$444$		0			0
$445$	−45.5091	+	10.7859i	−2.15734	+	0.511299i
$446$	−1.72378	+	0.408542i	−0.0816232	+	0.0193450i
$447$		0			0
$448$	3.02619	−	7.01550i	0.142974	−	0.331451i
$449$	0.407937	+	0.148477i	0.0192517	+	0.00700706i	0.351628	−	0.936140i	$-0.385628\pi$
$449$	0.407937	+	0.148477i	0.0192517	+	0.00700706i	−0.332376	+	0.943147i	$0.607850\pi$
$450$		0			0
$451$	−10.6293	+	3.86873i	−0.500512	+	0.182171i
$452$	1.07192	−	18.4042i	0.0504189	−	0.865659i
$453$		0			0
$454$	−2.22885	−	5.16705i	−0.104605	−	0.242502i
$455$	−1.13978	−	19.5692i	−0.0534335	−	0.917418i
$456$		0			0
$457$	−18.5985	+	19.7132i	−0.870000	+	0.922146i	−0.997569	−	0.0696833i	$-0.977801\pi$
$457$	−18.5985	+	19.7132i	−0.870000	+	0.922146i	0.127569	+	0.991830i	$0.459283\pi$
$458$	−0.00603328	−	0.0104499i	−0.000281917	−	0.000488294i
$459$		0			0
$460$	5.03083	−	8.71365i	0.234564	−	0.406276i
$461$	−12.2540	−	40.9313i	−0.570727	−	1.90636i	−0.381236	−	0.924478i	$-0.624501\pi$
$461$	−12.2540	−	40.9313i	−0.570727	−	1.90636i	−0.189491	−	0.981882i	$-0.560684\pi$
$462$		0			0
$463$	25.3500	−	16.6730i	1.17812	−	0.774859i	0.199368	−	0.979925i	$-0.436111\pi$
$463$	25.3500	−	16.6730i	1.17812	−	0.774859i	0.978748	+	0.205065i	$0.0657407\pi$
$464$	−2.16542	−	0.253101i	−0.100527	−	0.0117499i
$465$		0			0
$466$	−4.84108	+	2.43128i	−0.224259	+	0.112627i
$467$	−2.33662	+	13.2516i	−0.108126	+	0.613212i	0.881800	+	0.471624i	$0.156332\pi$
$467$	−2.33662	+	13.2516i	−0.108126	+	0.613212i	−0.989926	+	0.141588i	$0.954779\pi$
$468$		0			0
$469$	−1.46566	−	8.31218i	−0.0676779	−	0.383821i
$470$	−0.267773	−	0.359682i	−0.0123515	−	0.0165909i
$471$		0			0
$472$	5.44882	+	5.77542i	0.250802	+	0.265835i
$473$	4.13352	−	13.8069i	0.190060	−	0.634843i
$474$		0			0
$475$	−39.1760	+	4.57902i	−1.79752	+	0.210100i
$476$	7.22033	−	6.05858i	0.330943	−	0.277695i
$477$		0			0
$478$	−3.80246	−	3.19065i	−0.173921	−	0.145937i
$479$	−21.7030	−	14.2743i	−0.991636	−	0.652209i	−0.0535333	−	0.998566i	$-0.517048\pi$
$479$	−21.7030	−	14.2743i	−0.991636	−	0.652209i	−0.938103	+	0.346357i	$0.887419\pi$
$480$		0			0
$481$	−12.6074	+	16.9346i	−0.574846	+	0.772152i
$482$	6.21887	+	3.12324i	0.283262	+	0.142259i
$483$		0			0
$484$	13.4154	+	3.17951i	0.609791	+	0.144523i
$485$	26.7098			1.21283
$486$		0			0
$487$	2.70578			0.122611			0.0613053	−	0.998119i	$-0.480474\pi$
$487$	2.70578			0.122611			0.0613053	+	0.998119i	$0.480474\pi$
$488$	−9.77873	−	2.31760i	−0.442662	−	0.104913i
$489$		0			0
$490$	5.20559	+	2.61435i	0.235165	+	0.118104i
$491$	−23.7715	+	31.9306i	−1.07279	+	1.44101i	−0.183868	+	0.982951i	$0.558862\pi$
$491$	−23.7715	+	31.9306i	−1.07279	+	1.44101i	−0.888923	+	0.458057i	$0.848545\pi$
$492$		0			0
$493$	−2.10111	−	1.38192i	−0.0946292	−	0.0622386i
$494$	2.24266	+	1.88181i	0.100902	+	0.0846667i
$495$		0			0
$496$	−5.44377	+	4.56786i	−0.244432	+	0.205103i
$497$	5.48084	−	0.640618i	0.245849	−	0.0287356i
$498$		0			0
$499$	−0.712812	+	2.38096i	−0.0319099	+	0.106586i	−0.972461	−	0.233066i	$-0.925124\pi$
$499$	−0.712812	+	2.38096i	−0.0319099	+	0.106586i	0.940551	+	0.339652i	$0.110309\pi$
$500$	45.5322	+	48.2613i	2.03626	+	2.15831i
$501$		0			0
$502$	−1.47145	−	1.97651i	−0.0656742	−	0.0882158i
$503$	2.56729	+	14.5598i	0.114470	+	0.649191i	0.987011	+	0.160651i	$0.0513594\pi$
$503$	2.56729	+	14.5598i	0.114470	+	0.649191i	−0.872541	+	0.488540i	$0.837530\pi$
$504$		0			0
$505$	2.98584	−	16.9335i	0.132868	−	0.753532i
$506$	0.520398	−	0.261354i	0.0231345	−	0.0116186i
$507$		0			0
$508$	21.4973	+	2.51268i	0.953790	+	0.111482i
$509$	−20.0592	+	13.1931i	−0.889107	+	0.584775i	−0.909817	−	0.415011i	$-0.863778\pi$
$509$	−20.0592	+	13.1931i	−0.889107	+	0.584775i	0.0207096	+	0.999786i	$0.493407\pi$
$510$		0			0
$511$	2.38196	+	7.95630i	0.105372	+	0.351966i
$512$	8.57387	−	14.8504i	0.378915	−	0.656300i
$513$		0			0
$514$	−0.732546	−	1.26881i	−0.0323112	−	0.0559646i
$515$	−24.1510	+	25.5985i	−1.06422	+	1.12801i
$516$		0			0
$517$	0.0501339	+	0.860766i	0.00220489	+	0.0378564i
$518$	0.581516	+	1.34811i	0.0255504	+	0.0592324i
$519$		0			0
$520$	0.942616	−	16.1841i	0.0413364	−	0.709719i
$521$	−18.5919	+	6.76690i	−0.814526	+	0.296463i	−0.715492	−	0.698621i	$-0.753798\pi$
$521$	−18.5919	+	6.76690i	−0.814526	+	0.296463i	−0.0990342	+	0.995084i	$0.531575\pi$
$522$		0			0
$523$	32.2975	+	11.7553i	1.41227	+	0.514025i	0.931796	−	0.362982i	$-0.118241\pi$
$523$	32.2975	+	11.7553i	1.41227	+	0.514025i	0.480477	+	0.877007i	$0.340464\pi$
$524$	9.32910	−	21.6273i	0.407544	−	0.944792i
$525$		0			0
$526$	3.15627	−	0.748050i	0.137620	−	0.0326165i
$527$	−7.97625	+	1.89041i	−0.347451	+	0.0823473i
$528$		0			0
$529$	−8.52036	+	19.7524i	−0.370450	+	0.858800i
$530$	−4.31722	−	1.57134i	−0.187528	−	0.0682547i
$531$		0			0
$532$	−6.35588	+	2.31335i	−0.275563	+	0.100297i
$533$	−1.33406	+	22.9049i	−0.0577844	+	0.992120i
$534$		0			0
$535$	26.7644	+	62.0468i	1.15712	+	2.68252i
$536$	−0.405873	−	6.96856i	−0.0175310	−	0.300996i
$537$		0			0
$538$	0.478177	−	0.506838i	0.0206157	−	0.0218513i
$539$	−5.60046	−	9.70029i	−0.241229	−	0.417821i
$540$		0			0
$541$	−18.0270	+	31.2237i	−0.775042	+	1.34241i	0.159728	+	0.987161i	$0.448938\pi$
$541$	−18.0270	+	31.2237i	−0.775042	+	1.34241i	−0.934771	+	0.355252i	$0.884395\pi$
$542$	0.222661	+	0.743738i	0.00956409	+	0.0319463i
$543$		0			0
$544$	9.81728	−	6.45692i	0.420912	−	0.276838i
$545$	15.2782	+	1.78576i	0.654445	+	0.0764937i
$546$		0			0
$547$	7.72112	−	3.87769i	0.330131	−	0.165798i	−0.276011	−	0.961155i	$-0.589013\pi$
$547$	7.72112	−	3.87769i	0.330131	−	0.165798i	0.606142	+	0.795356i	$0.292716\pi$
$548$	−0.100881	+	0.572123i	−0.00430941	+	0.0244399i
$549$		0			0
$550$	1.08129	+	6.13228i	0.0461062	+	0.261481i
$551$	1.07767	+	1.44756i	0.0459102	+	0.0616681i
$552$		0			0
$553$	9.96453	+	10.5618i	0.423735	+	0.449133i
$554$	−0.236168	+	0.788858i	−0.0100338	+	0.0335153i
$555$		0			0
$556$	−10.8177	+	1.26441i	−0.458773	+	0.0536228i
$557$	−16.3664	+	13.7330i	−0.693466	+	0.581887i	−0.919906	−	0.392138i	$-0.871736\pi$
$557$	−16.3664	+	13.7330i	−0.693466	+	0.581887i	0.226441	+	0.974025i	$0.427291\pi$
$558$		0			0
$559$	−22.3943	−	18.7910i	−0.947176	−	0.794775i
$560$	14.9365	+	9.82389i	0.631182	+	0.415135i
$561$		0			0
$562$	−1.65795	+	2.22702i	−0.0699366	+	0.0939412i
$563$	−24.7195	−	12.4146i	−1.04180	−	0.523213i	−0.156234	−	0.987720i	$-0.549935\pi$
$563$	−24.7195	−	12.4146i	−1.04180	−	0.523213i	−0.885569	+	0.464507i	$0.846232\pi$
$564$		0			0
$565$	39.2473	+	9.30178i	1.65115	+	0.391329i
$566$	−6.12621			−0.257504
$567$		0			0
$568$	4.56361			0.191485
$569$	−21.5106	−	5.09810i	−0.901769	−	0.213723i	−0.246522	−	0.969137i	$-0.579288\pi$
$569$	−21.5106	−	5.09810i	−0.901769	−	0.213723i	−0.655248	+	0.755414i	$0.727436\pi$
$570$		0			0
$571$	1.90182	+	0.955132i	0.0795889	+	0.0399710i	0.488148	−	0.872761i	$-0.337672\pi$
$571$	1.90182	+	0.955132i	0.0795889	+	0.0399710i	−0.408560	+	0.912732i	$0.633969\pi$
$572$	−9.16936	+	12.3166i	−0.383390	+	0.514982i
$573$		0			0
$574$	1.33306	+	0.876764i	0.0556407	+	0.0365954i
$575$	12.1909	+	10.2293i	0.508394	+	0.426593i
$576$		0			0
$577$	−15.8954	+	13.3378i	−0.661733	+	0.555260i	−0.910606	−	0.413276i	$-0.864384\pi$
$577$	−15.8954	+	13.3378i	−0.661733	+	0.555260i	0.248872	+	0.968536i	$0.419940\pi$
$578$	0.180935	−	0.0211482i	0.00752589	−	0.000879651i
$579$		0			0
$580$	1.41181	−	4.71578i	0.0586223	−	0.195812i
$581$	9.15287	+	9.70147i	0.379725	+	0.402485i
$582$		0			0
$583$	5.27535	+	7.08602i	0.218483	+	0.293473i
$584$	1.19271	+	6.76421i	0.0493548	+	0.279905i
$585$		0			0
$586$	−0.168592	+	0.956131i	−0.00696446	+	0.0394974i
$587$	−10.4955	+	5.27105i	−0.433196	+	0.217559i	−0.652015	−	0.758206i	$-0.726076\pi$
$587$	−10.4955	+	5.27105i	−0.433196	+	0.217559i	0.218819	+	0.975766i	$0.429780\pi$
$588$		0			0
$589$	5.84260	+	0.682902i	0.240740	+	0.0281385i
$590$	−7.14947	+	4.70228i	−0.294339	+	0.193590i
$591$		0			0
$592$	−5.52228	−	18.4457i	−0.226964	−	0.758114i
$593$	−10.8840	+	18.8516i	−0.446952	+	0.774144i	−0.998186	−	0.0602070i	$-0.980824\pi$
$593$	−10.8840	+	18.8516i	−0.446952	+	0.774144i	0.551234	+	0.834351i	$0.314157\pi$
$594$		0			0
$595$	10.3109	+	17.8591i	0.422708	+	0.732151i
$596$	18.1554	−	19.2436i	0.743673	−	0.788247i
$597$		0			0
$598$	−0.0686805	−	1.17920i	−0.00280855	−	0.0482210i
$599$	−4.05744	−	9.40621i	−0.165783	−	0.384327i	0.814992	−	0.579473i	$-0.196741\pi$
$599$	−4.05744	−	9.40621i	−0.165783	−	0.384327i	−0.980774	+	0.195145i	$0.937482\pi$
$600$		0			0
$601$	−0.164117	+	2.81778i	−0.00669448	+	0.114940i	−1.00000		0.000578543i	$-0.999816\pi$
$601$	−0.164117	+	2.81778i	−0.00669448	+	0.114940i	0.993305	+	0.115518i	$0.0368529\pi$
$602$	−1.91035	+	0.695311i	−0.0778601	+	0.0283388i
$603$		0			0
$604$	−17.2472	−	6.27748i	−0.701780	−	0.255427i
$605$	−11.9475	+	27.6975i	−0.485737	+	1.12606i
$606$		0			0
$607$	13.2373	−	3.13730i	0.537285	−	0.127339i	0.0469899	−	0.998895i	$-0.485037\pi$
$607$	13.2373	−	3.13730i	0.537285	−	0.127339i	0.490295	+	0.871556i	$0.336889\pi$
$608$	−8.20485	+	1.94458i	−0.332751	+	0.0788633i
$609$		0			0
$610$	4.28983	−	9.94494i	0.173690	−	0.402659i
$611$	1.64343	+	0.598161i	0.0664862	+	0.0241990i
$612$		0			0
$613$	15.3111	−	5.57278i	0.618410	−	0.225083i	−0.0137693	−	0.999905i	$-0.504383\pi$
$613$	15.3111	−	5.57278i	0.618410	−	0.225083i	0.632179	+	0.774823i	$0.282161\pi$
$614$	0.279432	−	4.79767i	0.0112770	−	0.193618i
$615$		0			0
$616$	0.858606	+	1.99047i	0.0345942	+	0.0801985i
$617$	−0.451265	−	7.74792i	−0.0181672	−	0.311919i	−0.995134	−	0.0985288i	$-0.968586\pi$
$617$	−0.451265	−	7.74792i	−0.0181672	−	0.311919i	0.976967	−	0.213391i	$-0.0684507\pi$
$618$		0			0
$619$	−30.0734	+	31.8760i	−1.20875	+	1.28120i	−0.259844	+	0.965651i	$0.583671\pi$
$619$	−30.0734	+	31.8760i	−1.20875	+	1.28120i	−0.948908	+	0.315552i	$0.897810\pi$
$620$	−8.02269	−	13.8957i	−0.322199	−	0.558065i
$621$		0			0
$622$	−0.186650	+	0.323287i	−0.00748397	+	0.0129626i
$623$	−3.63818	−	12.1524i	−0.145760	−	0.486874i
$624$		0			0
$625$	−66.7912	+	43.9292i	−2.67165	+	1.75717i
$626$	−4.20173	−	0.491111i	−0.167935	−	0.0196288i
$627$		0			0
$628$	15.8275	−	7.94888i	0.631586	−	0.317195i
$629$	3.85678	−	21.8729i	0.153780	−	0.872129i
$630$		0			0
$631$	3.55734	+	20.1747i	0.141615	+	0.803141i	0.970023	+	0.243015i	$0.0781363\pi$
$631$	3.55734	+	20.1747i	0.141615	+	0.803141i	−0.828407	+	0.560126i	$0.810753\pi$
$632$	7.17108	+	9.63244i	0.285250	+	0.383158i
$633$		0			0
$634$	−0.325901	−	0.345435i	−0.0129432	−	0.0137190i
$635$	−13.5813	+	45.3646i	−0.538956	+	1.80024i
$636$		0			0
$637$	−22.5660	+	2.63758i	−0.894096	+	0.104505i
$638$	0.218250	−	0.183133i	0.00864058	−	0.00725031i
$639$		0			0
$640$	23.3663	+	19.6066i	0.923634	+	0.775021i
$641$	28.8733	+	18.9903i	1.14043	+	0.750071i	0.971846	−	0.235617i	$-0.0757112\pi$
$641$	28.8733	+	18.9903i	1.14043	+	0.750071i	0.168581	+	0.985688i	$0.446082\pi$
$642$		0			0
$643$	17.7604	−	23.8564i	0.700402	−	0.940803i	−0.299510	−	0.954093i	$-0.596823\pi$
$643$	17.7604	−	23.8564i	0.700402	−	0.940803i	0.999912	+	0.0132902i	$0.00423054\pi$
$644$	2.43872	+	1.22477i	0.0960992	+	0.0482628i
$645$		0			0
$646$	−2.99683	−	0.710262i	−0.117909	−	0.0279449i
$647$	−43.1443			−1.69618			−0.848089	−	0.529853i	$-0.822247\pi$
$647$	−43.1443			−1.69618			−0.848089	+	0.529853i	$0.822247\pi$
$648$		0			0
$649$	16.4542			0.645884
$650$	12.2899	+	2.91277i	0.482051	+	0.114248i
$651$		0			0
$652$	−13.7790	−	6.92006i	−0.539626	−	0.271010i
$653$	18.6252	−	25.0179i	0.728859	−	0.979028i	−0.271006	−	0.962578i	$-0.587356\pi$
$653$	18.6252	−	25.0179i	0.728859	−	0.979028i	0.999865	−	0.0164499i	$-0.00523641\pi$
$654$		0			0
$655$	43.0549	+	28.3176i	1.68229	+	1.10646i
$656$	−16.0294	−	13.4503i	−0.625843	−	0.525145i
$657$		0			0
$658$	0.0931677	−	0.0781770i	0.00363205	−	0.00304766i
$659$	40.3919	−	4.72113i	1.57344	−	0.183909i	0.715856	−	0.698248i	$-0.246037\pi$
$659$	40.3919	−	4.72113i	1.57344	−	0.183909i	0.857587	+	0.514339i	$0.171963\pi$
$660$		0			0
$661$	−4.97967	+	16.6332i	−0.193687	+	0.646958i	0.804880	+	0.593437i	$0.202230\pi$
$661$	−4.97967	+	16.6332i	−0.193687	+	0.646958i	−0.998567	+	0.0535209i	$0.982956\pi$
$662$	5.72044	+	6.06332i	0.222331	+	0.235658i
$663$		0			0
$664$	6.58696	+	8.84782i	0.255624	+	0.343362i
$665$	−2.56972	−	14.5736i	−0.0996494	−	0.565140i
$666$		0			0
$667$	0.126439	−	0.717068i	0.00489572	−	0.0277650i
$668$	−7.71214	+	3.87318i	−0.298391	+	0.149858i
$669$		0			0
$670$	7.47205	+	0.873358i	0.288671	+	0.0337408i
$671$	−17.3997	+	11.4439i	−0.671706	+	0.441788i
$672$		0			0
$673$	−12.6447	−	42.2363i	−0.487418	−	1.62809i	−0.748759	−	0.662843i	$-0.769350\pi$
$673$	−12.6447	−	42.2363i	−0.487418	−	1.62809i	0.261341	−	0.965247i	$-0.415835\pi$
$674$	1.95524	−	3.38658i	0.0753131	−	0.130446i
$675$		0			0
$676$	2.95261	+	5.11407i	0.113562	+	0.196695i
$677$	23.8082	−	25.2352i	0.915022	−	0.969867i	−0.0846257	−	0.996413i	$-0.526969\pi$
$677$	23.8082	−	25.2352i	0.915022	−	0.969867i	0.999648	+	0.0265462i	$0.00845092\pi$
$678$		0			0
$679$	0.421227	+	7.23219i	0.0161652	+	0.277546i
$680$	6.75502	+	15.6599i	0.259043	+	0.600529i
$681$		0			0
$682$	0.0539967	−	0.927088i	0.00206764	−	0.0355000i
$683$	40.1564	−	14.6157i	1.53654	−	0.559256i	0.571329	−	0.820721i	$-0.306428\pi$
$683$	40.1564	−	14.6157i	1.53654	−	0.559256i	0.965213	+	0.261465i	$0.0842057\pi$
$684$		0			0
$685$	−1.19440	−	0.434725i	−0.0456356	−	0.0166100i
$686$	−1.39802	+	3.24098i	−0.0533767	+	0.123741i
$687$		0			0
$688$	25.9427	−	6.14854i	0.989057	−	0.234411i
$689$	17.4357	−	4.13235i	0.664249	−	0.157430i
$690$		0			0
$691$	−6.34997	+	14.7209i	−0.241564	+	0.560009i	−0.995264	−	0.0972100i	$-0.969008\pi$
$691$	−6.34997	+	14.7209i	−0.241564	+	0.560009i	0.753700	+	0.657219i	$0.228267\pi$
$692$	−5.68957	−	2.07083i	−0.216285	−	0.0787213i
$693$		0			0
$694$	−7.22724	+	2.63050i	−0.274342	+	0.0998524i
$695$	1.38554	−	23.7887i	0.0525564	−	0.902358i
$696$		0			0
$697$	−9.56018	−	22.1630i	−0.362118	−	0.839483i
$698$	−0.243669	−	4.18363i	−0.00922299	−	0.158353i
$699$		0			0
$700$	−20.0251	+	21.2254i	−0.756878	+	0.802244i
$701$	−20.8919	−	36.1858i	−0.789075	−	1.36672i	−0.926534	−	0.376211i	$-0.877227\pi$
$701$	−20.8919	−	36.1858i	−0.789075	−	1.36672i	0.137459	−	0.990507i	$-0.456106\pi$
$702$		0			0
$703$	−7.96914	+	13.8029i	−0.300562	+	0.520588i
$704$	−3.75547	−	12.5441i	−0.141540	−	0.472775i
$705$		0			0
$706$	0.686676	−	0.451634i	0.0258434	−	0.0169975i
$707$	4.63216	+	0.541421i	0.174210	+	0.0203623i
$708$		0			0
$709$	−15.0984	+	7.58272i	−0.567034	+	0.284775i	−0.709130	−	0.705078i	$-0.750912\pi$
$709$	−15.0984	+	7.58272i	−0.567034	+	0.284775i	0.142096	+	0.989853i	$0.454616\pi$
$710$	−0.854057	+	4.84360i	−0.0320522	+	0.181777i
$711$		0			0
$712$	−1.82174	−	10.3316i	−0.0682724	−	0.387192i
$713$	−1.41728	−	1.90374i	−0.0530776	−	0.0712955i
$714$		0			0
$715$	−23.0543	−	24.4361i	−0.862181	−	0.913858i
$716$	7.92709	−	26.4783i	0.296249	−	0.989541i
$717$		0			0
$718$	2.43635	−	0.284769i	0.0909239	−	0.0106275i
$719$	12.7933	−	10.7349i	0.477111	−	0.400344i	−0.372269	−	0.928125i	$-0.621420\pi$
$719$	12.7933	−	10.7349i	0.477111	−	0.400344i	0.849381	+	0.527781i	$0.176976\pi$
$720$		0			0
$721$	−7.31216	−	6.13563i	−0.272319	−	0.228503i
$722$	−1.99099	−	1.30950i	−0.0740971	−	0.0487344i
$723$		0			0
$724$	−18.4258	+	24.7502i	−0.684790	+	0.919832i
$725$	6.95765	+	3.49426i	0.258401	+	0.129774i
$726$		0			0
$727$	21.5230	+	5.10104i	0.798244	+	0.189187i	0.609445	−	0.792829i	$-0.291392\pi$
$727$	21.5230	+	5.10104i	0.798244	+	0.189187i	0.188799	+	0.982016i	$0.439541\pi$
$728$	4.39701			0.162964
$729$		0			0
$730$	−7.40242			−0.273976
$731$	29.9251	+	7.09238i	1.10682	+	0.262321i
$732$		0			0
$733$	−11.7394	−	5.89576i	−0.433605	−	0.217765i	0.218588	−	0.975817i	$-0.429855\pi$
$733$	−11.7394	−	5.89576i	−0.433605	−	0.217765i	−0.652194	+	0.758052i	$0.726151\pi$
$734$	−2.14576	+	2.88226i	−0.0792015	+	0.106386i
$735$		0			0
$736$	2.84244	+	1.86950i	0.104774	+	0.0689108i
$737$	−11.0811	−	9.29816i	−0.408178	−	0.342502i
$738$		0			0
$739$	−34.4177	+	28.8799i	−1.26608	+	1.06236i	−0.271070	+	0.962560i	$0.587378\pi$
$739$	−34.4177	+	28.8799i	−1.26608	+	1.06236i	−0.995007	+	0.0998052i	$0.968178\pi$
$740$	43.1809	−	5.04713i	1.58736	−	0.185536i
$741$		0			0
$742$	0.357385	−	1.19375i	0.0131200	−	0.0438239i
$743$	−15.3510	−	16.2712i	−0.563175	−	0.596931i	0.381731	−	0.924274i	$-0.375328\pi$
$743$	−15.3510	−	16.2712i	−0.563175	−	0.596931i	−0.944906	+	0.327343i	$0.893847\pi$
$744$		0			0
$745$	34.5655	+	46.4296i	1.26638	+	1.70105i
$746$	0.884944	+	5.01877i	0.0324001	+	0.183750i
$747$		0			0
$748$	2.80504	−	15.9082i	0.102563	−	0.581661i
$749$	−16.3783	+	8.22547i	−0.598448	+	0.300552i
$750$		0			0
$751$	−11.8057	−	1.37988i	−0.430795	−	0.0503527i	−0.102067	−	0.994777i	$-0.532546\pi$
$751$	−11.8057	−	1.37988i	−0.430795	−	0.0503527i	−0.328728	+	0.944425i	$0.606620\pi$
$752$	−1.33262	+	0.876479i	−0.0485957	+	0.0319619i
$753$		0			0
$754$	−0.165741	−	0.553613i	−0.00603593	−	0.0201614i
$755$	20.0784	−	34.7768i	0.730728	−	1.26566i
$756$		0			0
$757$	−2.60890	−	4.51875i	−0.0948221	−	0.164237i	0.814712	−	0.579865i	$-0.196895\pi$
$757$	−2.60890	−	4.51875i	−0.0948221	−	0.164237i	−0.909534	+	0.415629i	$0.863562\pi$
$758$	1.15285	−	1.22195i	0.0418733	−	0.0443831i
$759$		0			0
$760$	−0.711609	−	12.2179i	−0.0258128	−	0.443188i
$761$	0.276625	+	0.641289i	0.0100276	+	0.0232467i	0.923156	−	0.384425i	$-0.125600\pi$
$761$	0.276625	+	0.641289i	0.0100276	+	0.0232467i	−0.913129	+	0.407671i	$0.866341\pi$
$762$		0			0
$763$	−0.242585	+	4.16502i	−0.00878215	+	0.150784i
$764$	−37.0505	+	13.4853i	−1.34044	+	0.487880i
$765$		0			0
$766$	8.02630	+	2.92133i	0.290002	+	0.105552i
$767$	13.2192	−	30.6456i	0.477318	−	1.10655i
$768$		0			0
$769$	10.8267	−	2.56597i	0.390419	−	0.0925311i	−0.0307176	−	0.999528i	$-0.509779\pi$
$769$	10.8267	−	2.56597i	0.390419	−	0.0925311i	0.421137	+	0.906997i	$0.361631\pi$
$770$	−2.27328	+	0.538776i	−0.0819232	+	0.0194162i
$771$		0			0
$772$	2.05515	−	4.76437i	0.0739664	−	0.171473i
$773$	14.5554	+	5.29774i	0.523522	+	0.190546i	0.590243	−	0.807225i	$-0.299032\pi$
$773$	14.5554	+	5.29774i	0.523522	+	0.190546i	−0.0667217	+	0.997772i	$0.521254\pi$
$774$		0			0
$775$	23.8477	−	8.67985i	0.856634	−	0.311789i
$776$	−0.348363	+	5.98116i	−0.0125055	+	0.214711i
$777$		0			0
$778$	−2.46304	−	5.70997i	−0.0883043	−	0.204712i
$779$	1.00712	+	17.2916i	0.0360838	+	0.619535i
$780$		0			0
$781$	6.48988	−	6.87887i	0.232226	−	0.246145i
$782$	0.621316	+	1.07615i	0.0222182	+	0.0384831i
$783$		0			0
$784$	10.3603	−	17.9445i	0.370009	−	0.640875i
$785$	11.1138	+	37.1227i	0.396669	+	1.32497i
$786$		0			0
$787$	29.4391	−	19.3624i	1.04939	−	0.690195i	0.0970652	−	0.995278i	$-0.469054\pi$
$787$	29.4391	−	19.3624i	1.04939	−	0.690195i	0.952326	+	0.305083i	$0.0986841\pi$
$788$	−32.2466	−	3.76909i	−1.14874	−	0.134268i
$789$		0			0
$790$	−11.5654	+	5.80838i	−0.411480	+	0.206653i
$791$	−1.89968	+	10.7736i	−0.0675449	+	0.383066i
$792$		0			0
$793$	7.33528	+	41.6004i	0.260483	+	1.47728i
$794$	−2.68483	−	3.60636i	−0.0952812	−	0.127985i
$795$		0			0
$796$	2.60625	+	2.76246i	0.0923761	+	0.0979129i
$797$	−7.60395	+	25.3990i	−0.269346	+	0.899678i	0.711134	+	0.703057i	$0.248182\pi$
$797$	−7.60395	+	25.3990i	−0.269346	+	0.899678i	−0.980480	+	0.196621i	$0.937003\pi$
$798$		0			0
$799$	−1.82743	+	0.213596i	−0.0646498	+	0.00755647i
$800$	−27.8676	+	23.3837i	−0.985268	+	0.826738i
$801$		0			0
$802$	−0.856252	−	0.718481i	−0.0302353	−	0.0253704i
$803$	11.8921	+	7.82153i	0.419661	+	0.276016i
$804$		0			0
$805$	−3.56549	+	4.78928i	−0.125667	+	0.168800i
$806$	−1.68330	−	0.845385i	−0.0592917	−	0.0297774i
$807$		0			0
$808$	3.75299	+	0.889476i	0.132030	+	0.0312917i
$809$	4.72350			0.166070			0.0830348	−	0.996547i	$-0.473539\pi$
$809$	4.72350			0.166070			0.0830348	+	0.996547i	$0.473539\pi$
$810$		0			0
$811$	−14.2884			−0.501733			−0.250866	−	0.968022i	$-0.580716\pi$
$811$	−14.2884			−0.501733			−0.250866	+	0.968022i	$0.580716\pi$
$812$	1.29915	+	0.307904i	0.0455913	+	0.0108053i
$813$		0			0
$814$	2.24856	+	1.12927i	0.0788119	+	0.0395808i
$815$	20.1453	−	27.0598i	0.705657	−	0.947862i
$816$		0			0
$817$	−18.4387	−	12.1273i	−0.645088	−	0.424281i
$818$	2.02577	+	1.69982i	0.0708294	+	0.0594329i
$819$		0			0
$820$	36.1927	−	30.3693i	1.26391	−	1.06054i
$821$	−21.7224	+	2.53899i	−0.758118	+	0.0886113i	−0.486365	−	0.873756i	$-0.661677\pi$
$821$	−21.7224	+	2.53899i	−0.758118	+	0.0886113i	−0.271753	+	0.962367i	$0.587603\pi$
$822$		0			0
$823$	−6.74214	+	22.5203i	−0.235016	+	0.785009i	0.756382	+	0.654130i	$0.226965\pi$
$823$	−6.74214	+	22.5203i	−0.235016	+	0.785009i	−0.991398	+	0.130879i	$0.958220\pi$
$824$	−5.41731	−	5.74202i	−0.188721	−	0.200033i
$825$		0			0
$826$	−1.38598	−	1.86170i	−0.0482245	−	0.0647767i
$827$	−3.09330	−	17.5430i	−0.107565	−	0.610030i	−0.990165	−	0.139905i	$-0.955320\pi$
$827$	−3.09330	−	17.5430i	−0.107565	−	0.610030i	0.882600	−	0.470124i	$-0.155791\pi$
$828$		0			0
$829$	−9.35023	+	53.0278i	−0.324747	+	1.84173i	0.186700	+	0.982417i	$0.440221\pi$
$829$	−9.35023	+	53.0278i	−0.324747	+	1.84173i	−0.511447	+	0.859315i	$0.670890\pi$
$830$	−10.6234	+	5.33526i	−0.368743	+	0.185189i
$831$		0			0
$832$	−26.3803	−	3.08341i	−0.914572	−	0.106898i
$833$	19.9692	−	13.1339i	0.691892	−	0.455064i
$834$		0			0
$835$	−5.41533	−	18.0885i	−0.187405	−	0.625977i
$836$	−5.79597	+	10.0389i	−0.200458	+	0.347203i
$837$		0			0
$838$	4.05420	+	7.02209i	0.140050	+	0.242574i
$839$	−35.7416	+	37.8839i	−1.23394	+	1.30790i	−0.298498	+	0.954410i	$0.596486\pi$
$839$	−35.7416	+	37.8839i	−1.23394	+	1.30790i	−0.935440	+	0.353487i	$0.884996\pi$
$840$		0			0
$841$	1.66549	+	28.5953i	0.0574306	+	0.986045i
$842$	−0.158816	−	0.368176i	−0.00547315	−	0.0126882i
$843$		0			0
$844$	1.17004	−	20.0889i	0.0402746	−	0.691488i
$845$	−12.1408	+	4.41889i	−0.417656	+	0.152014i
$846$		0			0
$847$	−7.68804	−	2.79822i	−0.264164	−	0.0961480i
$848$	−6.47278	+	15.0056i	−0.222276	+	0.515294i
$849$		0			0
$850$	−12.9291	+	3.06426i	−0.443466	+	0.105103i
$851$	6.25731	−	1.48301i	0.214498	−	0.0508369i
$852$		0			0
$853$	19.2347	−	44.5911i	0.658585	−	1.52677i	−0.180966	−	0.983489i	$-0.557922\pi$
$853$	19.2347	−	44.5911i	0.658585	−	1.52677i	0.839550	−	0.543282i	$-0.182818\pi$
$854$	2.76043	+	1.00472i	0.0944601	+	0.0343807i
$855$		0			0
$856$	−14.2433	+	5.18412i	−0.486825	+	0.177190i
$857$	2.53509	−	43.5259i	0.0865971	−	1.48682i	−0.623008	−	0.782215i	$-0.714090\pi$
$857$	2.53509	−	43.5259i	0.0865971	−	1.48682i	0.709605	−	0.704600i	$-0.248873\pi$
$858$		0			0
$859$	6.45769	+	14.9706i	0.220333	+	0.510790i	0.992150	−	0.125055i	$-0.0399108\pi$
$859$	6.45769	+	14.9706i	0.220333	+	0.510790i	−0.771816	+	0.635845i	$0.780652\pi$
$860$	3.50024	+	60.0968i	0.119357	+	2.04929i
$861$		0			0
$862$	2.50643	−	2.65666i	0.0853694	−	0.0904862i
$863$	25.0920	+	43.4607i	0.854142	+	1.47942i	0.877439	+	0.479689i	$0.159251\pi$
$863$	25.0920	+	43.4607i	0.854142	+	1.47942i	−0.0232963	+	0.999729i	$0.507416\pi$
$864$		0			0
$865$	6.62352	−	11.4723i	0.225207	−	0.390069i
$866$	0.342027	+	1.14245i	0.0116226	+	0.0388220i
$867$		0			0
$868$	3.63600	−	2.39144i	0.123414	−	0.0811706i
$869$	24.7172	+	2.88903i	0.838474	+	0.0980035i
$870$		0			0
$871$	−26.2201	+	13.1682i	−0.888435	+	0.446189i
$872$	−0.599153	+	3.39796i	−0.0202899	+	0.115070i
$873$		0			0
$874$	−0.154846	−	0.878175i	−0.00523774	−	0.0297047i
$875$	−23.5121	−	31.5822i	−0.794853	−	1.06767i
$876$		0			0
$877$	30.7887	+	32.6341i	1.03966	+	1.10198i	0.994683	+	0.102988i	$0.0328403\pi$
$877$	30.7887	+	32.6341i	1.03966	+	1.10198i	0.0449780	+	0.998988i	$0.485678\pi$
$878$	−1.39919	+	4.67361i	−0.0472203	+	0.157727i
$879$		0			0
$880$	30.4318	−	3.55697i	1.02586	−	0.119905i
$881$	−13.9661	+	11.7190i	−0.470531	+	0.394822i	−0.846988	−	0.531612i	$-0.821587\pi$
$881$	−13.9661	+	11.7190i	−0.470531	+	0.394822i	0.376457	+	0.926434i	$0.377142\pi$
$882$		0			0
$883$	−13.4700	−	11.3026i	−0.453300	−	0.380364i	0.387359	−	0.921929i	$-0.373388\pi$
$883$	−13.4700	−	11.3026i	−0.453300	−	0.380364i	−0.840659	+	0.541565i	$0.817832\pi$
$884$	−27.3751	−	18.0049i	−0.920724	−	0.605570i
$885$		0			0
$886$	4.06898	−	5.46559i	0.136700	−	0.183620i
$887$	29.4603	+	14.7955i	0.989182	+	0.496786i	0.868385	−	0.495891i	$-0.165159\pi$
$887$	29.4603	+	14.7955i	0.989182	+	0.496786i	0.120797	+	0.992677i	$0.461455\pi$
$888$		0			0
$889$	−12.4975	−	2.96196i	−0.419153	−	0.0993410i
$890$	11.3064			0.378990
$891$		0			0
$892$	−14.2279			−0.476386
$893$	1.28471	+	0.304483i	0.0429913	+	0.0101891i
$894$		0			0
$895$	54.0398	+	27.1398i	1.80635	+	0.907184i
$896$	−4.94037	+	6.63607i	−0.165046	+	0.221696i
$897$		0			0
$898$	−0.0876808	−	0.0576686i	−0.00292595	−	0.00192443i
$899$	−0.889494	−	0.746374i	−0.0296663	−	0.0248930i
$900$		0			0
$901$	−14.4405	+	12.1170i	−0.481082	+	0.403676i
$902$	2.71599	−	0.317453i	0.0904325	−	0.0105700i
$903$		0			0
$904$	−2.59484	+	8.66736i	−0.0863030	+	0.288272i
$905$	−46.3275	−	49.1043i	−1.53998	−	1.63228i
$906$		0			0
$907$	−23.4421	−	31.4881i	−0.778381	−	1.04555i	−0.997557	−	0.0698614i	$-0.977744\pi$
$907$	−23.4421	−	31.4881i	−0.778381	−	1.04555i	0.219176	−	0.975685i	$-0.429663\pi$
$908$	−7.84805	−	44.5085i	−0.260447	−	1.47707i
$909$		0			0
$910$	−0.822878	+	4.66678i	−0.0272782	+	0.154702i
$911$	−13.6097	+	6.83505i	−0.450910	+	0.226455i	−0.659736	−	0.751497i	$-0.729332\pi$
$911$	−13.6097	+	6.83505i	−0.450910	+	0.226455i	0.208826	+	0.977953i	$0.433036\pi$
$912$		0			0
$913$	22.7039	+	2.65370i	0.751388	+	0.0878247i
$914$	5.47391	−	3.60025i	0.181061	−	0.119086i
$915$		0			0
$916$	−0.0277946	−	0.0928405i	−0.000918361	−	0.00306754i
$917$	−6.98854	+	12.1045i	−0.230782	+	0.399726i
$918$		0			0
$919$	−7.39953	−	12.8164i	−0.244088	−	0.422773i	0.717787	−	0.696263i	$-0.245155\pi$
$919$	−7.39953	−	12.8164i	−0.244088	−	0.422773i	−0.961875	+	0.273490i	$0.911822\pi$
$920$	−3.38861	+	3.59171i	−0.111719	+	0.118415i
$921$		0			0
$922$	0.600569	+	10.3114i	0.0197787	+	0.339587i
$923$	−7.59781	−	17.6137i	−0.250085	−	0.579762i
$924$		0			0
$925$	−3.99816	+	68.6458i	−0.131459	+	2.25706i
$926$	−6.89258	+	2.50869i	−0.226504	+	0.0824407i
$927$		0			0
$928$	1.56408	+	0.569280i	0.0513436	+	0.0186875i
$929$	−12.1228	+	28.1039i	−0.397737	+	0.922059i	0.595217	+	0.803565i	$0.297066\pi$
$929$	−12.1228	+	28.1039i	−0.397737	+	0.922059i	−0.992955	+	0.118494i	$0.962193\pi$
$930$		0			0
$931$	−16.6894	+	3.95546i	−0.546972	+	0.129635i
$932$	−42.3360	+	10.0338i	−1.38676	+	0.328668i
$933$		0			0
$934$	1.28842	−	2.98689i	0.0421584	−	0.0977341i
$935$	33.2109	+	12.0878i	1.08611	+	0.395313i
$936$		0			0
$937$	3.22880	−	1.17519i	0.105480	−	0.0383917i	−0.288741	−	0.957407i	$-0.593237\pi$
$937$	3.22880	−	1.17519i	0.105480	−	0.0383917i	0.394221	+	0.919016i	$0.371014\pi$
$938$	−0.118640	+	2.03697i	−0.00387374	+	0.0665095i
$939$		0			0
$940$	−1.42644	−	3.30686i	−0.0465253	−	0.107858i
$941$	−1.12635	−	19.3387i	−0.0367180	−	0.630423i	−0.965598	−	0.260041i	$-0.916264\pi$
$941$	−1.12635	−	19.3387i	−0.0367180	−	0.630423i	0.928880	−	0.370382i	$-0.120773\pi$
$942$		0			0
$943$	4.79580	−	5.08325i	0.156173	−	0.165533i
$944$	15.2192	+	26.3605i	0.495344	+	0.857961i
$945$		0			0
$946$	−1.74206	+	3.01734i	−0.0566393	+	0.0981022i
$947$	3.95475	+	13.2098i	0.128512	+	0.429260i	0.997893	−	0.0648825i	$-0.0206672\pi$
$947$	3.95475	+	13.2098i	0.128512	+	0.429260i	−0.869381	+	0.494143i	$0.835482\pi$
$948$		0			0
$949$	24.1214	−	15.8649i	0.783015	−	0.514997i
$950$	9.47060	+	1.10695i	0.307267	+	0.0359143i
$951$		0			0
$952$	−4.13368	+	2.07601i	−0.133973	+	0.0672839i
$953$	6.51937	−	36.9732i	0.211183	−	1.19768i	−0.676225	−	0.736695i	$-0.736385\pi$
$953$	6.51937	−	36.9732i	0.211183	−	1.19768i	0.887408	−	0.460984i	$-0.152503\pi$
$954$		0			0
$955$	−14.9797	−	84.9541i	−0.484732	−	2.74905i
$956$	−23.8064	−	31.9776i	−0.769955	−	1.03423i
$957$		0			0
$958$	4.30937	+	4.56767i	0.139230	+	0.147575i
$959$	0.0988737	−	0.330261i	0.00319280	−	0.0106647i
$960$		0			0
$961$	27.0312	−	3.15949i	0.871973	−	0.101919i
$962$	3.90972	−	3.28064i	0.126054	−	0.105772i
$963$		0			0
$964$	42.8154	+	35.9264i	1.37899	+	1.15711i
$965$	9.48475	+	6.23822i	0.305325	+	0.200815i
$966$		0			0
$967$	14.6794	−	19.7178i	0.472057	−	0.634082i	−0.500780	−	0.865575i	$-0.666953\pi$
$967$	14.6794	−	19.7178i	0.472057	−	0.634082i	0.972837	+	0.231492i	$0.0743608\pi$
$968$	−6.04650	−	3.03667i	−0.194342	−	0.0976022i
$969$		0			0
$970$	−6.28292	−	1.48908i	−0.201732	−	0.0478114i
$971$	−13.0415			−0.418522			−0.209261	−	0.977860i	$-0.567106\pi$
$971$	−13.0415			−0.418522			−0.209261	+	0.977860i	$0.567106\pi$
$972$		0			0
$973$	6.46310			0.207197
$974$	−0.636477	−	0.150848i	−0.0203940	−	0.00483348i
$975$		0			0
$976$	−34.4275	−	17.2902i	−1.10200	−	0.553444i
$977$	−28.9261	+	38.8545i	−0.925427	+	1.24306i	0.0443362	+	0.999017i	$0.485883\pi$
$977$	−28.9261	+	38.8545i	−0.925427	+	1.24306i	−0.969763	+	0.244048i	$0.921525\pi$
$978$		0			0
$979$	−18.1638	−	11.9465i	−0.580517	−	0.381812i
$980$	35.8392	+	30.0727i	1.14484	+	0.960636i
$981$		0			0
$982$	7.37186	−	6.18573i	0.235246	−	0.197394i
$983$	−32.8784	+	3.84293i	−1.04866	+	0.122570i	−0.622927	−	0.782280i	$-0.714057\pi$
$983$	−32.8784	+	3.84293i	−1.04866	+	0.122570i	−0.425730	+	0.904850i	$0.639983\pi$
$984$		0			0
$985$	20.3723	−	68.0482i	0.649115	−	2.16820i
$986$	0.417199	+	0.442205i	0.0132863	+	0.0140827i
$987$		0			0
$988$	14.0408	+	18.8601i	0.446698	+	0.600019i
$989$	1.54623	+	8.76910i	0.0491672	+	0.278841i
$990$		0			0
$991$	−3.02007	+	17.1276i	−0.0959355	+	0.544078i	0.898521	+	0.438930i	$0.144642\pi$
$991$	−3.02007	+	17.1276i	−0.0959355	+	0.544078i	−0.994457	+	0.105147i	$0.966469\pi$
$992$	4.84831	−	2.43491i	0.153934	−	0.0773086i
$993$		0			0
$994$	−1.32496	−	0.154866i	−0.0420253	−	0.00491205i
$995$	−6.94232	+	4.56603i	−0.220086	+	0.144753i
$996$		0			0
$997$	4.95693	+	16.5573i	0.156987	+	0.524375i	0.999907	−	0.0136656i	$-0.00435005\pi$
$997$	4.95693	+	16.5573i	0.156987	+	0.524375i	−0.842919	+	0.538040i	$0.819165\pi$
$998$	0.300413	−	0.520330i	0.00950940	−	0.0164708i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.b.136.4		144
3.2	odd	2		729.2.g.c.136.5		144
9.2	odd	6		729.2.g.d.379.4		144
9.4	even	3		243.2.g.a.127.5		144
9.5	odd	6		81.2.g.a.70.4	yes	144
9.7	even	3		729.2.g.a.379.5		144
81.5	odd	54		729.2.g.c.595.5		144
81.20	odd	54		6561.2.a.c.1.41		72
81.22	even	27		729.2.g.a.352.5		144
81.32	odd	54		81.2.g.a.22.4	✓	144
81.49	even	27		243.2.g.a.199.5		144
81.59	odd	54		729.2.g.d.352.4		144
81.61	even	27		6561.2.a.d.1.32		72
81.76	even	27	inner	729.2.g.b.595.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.4	✓	144	81.32	odd	54
81.2.g.a.70.4	yes	144	9.5	odd	6
243.2.g.a.127.5		144	9.4	even	3
243.2.g.a.199.5		144	81.49	even	27
729.2.g.a.352.5		144	81.22	even	27
729.2.g.a.379.5		144	9.7	even	3
729.2.g.b.136.4		144	1.1	even	1	trivial
729.2.g.b.595.4		144	81.76	even	27	inner
729.2.g.c.136.5		144	3.2	odd	2
729.2.g.c.595.5		144	81.5	odd	54
729.2.g.d.352.4		144	81.59	odd	54
729.2.g.d.379.4		144	9.2	odd	6
6561.2.a.c.1.41		72	81.20	odd	54
6561.2.a.d.1.32		72	81.61	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)

\(f(q)\)	\(=\)	\(q+(-0.235229 - 0.0557502i) q^{2} +(-1.73504 - 0.871370i) q^{4} +(2.53668 - 3.40735i) q^{5} +(0.962610 + 0.633118i) q^{7} +(0.729927 + 0.612481i) q^{8} +(-0.786660 + 0.660086i) q^{10} +(1.96124 - 0.229235i) q^{11} +(1.14870 - 3.83692i) q^{13} +(-0.191137 - 0.202593i) q^{14} +(2.18128 + 2.92997i) q^{16} +(0.731666 + 4.14948i) q^{17} +(0.525049 - 2.97770i) q^{19} +(-7.37031 + 3.70151i) q^{20} +(-0.474118 - 0.0554165i) q^{22} +(-1.01926 + 0.670375i) q^{23} +(-3.74129 - 12.4968i) q^{25} +(-0.484116 + 0.838513i) q^{26} +(-1.11849 - 1.93728i) q^{28} +(-0.409584 + 0.434134i) q^{29} +(0.113119 + 1.94217i) q^{31} +(-1.10456 - 2.56067i) q^{32} +(0.0592258 - 1.01687i) q^{34} +(4.59909 - 1.67393i) q^{35} +(-4.95333 - 1.80287i) q^{37} +(-0.289514 + 0.671168i) q^{38} +(3.93853 - 0.933449i) q^{40} +(-5.57409 + 1.32108i) q^{41} +(2.89097 - 6.70201i) q^{43} +(-3.60257 - 1.31123i) q^{44} +(0.277132 - 0.100868i) q^{46} +(-0.0253896 + 0.435922i) q^{47} +(-2.24678 - 5.20862i) q^{49} +(0.183360 + 3.14818i) q^{50} +(-5.33642 + 5.65627i) q^{52} +(2.23695 + 3.87450i) q^{53} +(4.19394 - 7.26412i) q^{55} +(0.314861 + 1.05171i) q^{56} +(0.120549 - 0.0792863i) q^{58} +(8.27664 + 0.967400i) q^{59} +(-9.42504 + 4.73343i) q^{61} +(0.0816677 - 0.463161i) q^{62} +(-1.15153 - 6.53063i) q^{64} +(-10.1599 - 13.6471i) q^{65} +(-5.02725 - 5.32857i) q^{67} +(2.34627 - 7.83708i) q^{68} +(-1.17516 + 0.137356i) q^{70} +(3.66891 - 3.07858i) q^{71} +(5.52198 + 4.63349i) q^{73} +(1.06466 + 0.700235i) q^{74} +(-3.50566 + 4.70892i) q^{76} +(2.03304 + 1.02103i) q^{77} +(12.2632 + 2.90642i) q^{79} +15.5167 q^{80} +1.38483 q^{82} +(11.2643 + 2.66968i) q^{83} +(15.9948 + 8.03287i) q^{85} +(-1.05368 + 1.41533i) q^{86} +(1.57196 + 1.03389i) q^{88} +(-8.43420 - 7.07713i) q^{89} +(3.53497 - 2.96620i) q^{91} +(2.35260 - 0.274979i) q^{92} +(0.0302751 - 0.101126i) q^{94} +(-8.81419 - 9.34250i) q^{95} +(3.75478 + 5.04355i) q^{97} +(0.238125 + 1.35047i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 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 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

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