LMFDB - Embedded newform 729.2.g.d.217.5

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			217.5
Character	$\chi$	$=$	729.217
Dual form			729.2.g.d.514.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0454430 - 0.780226i) q^{2} +(1.37979 + 0.161274i) q^{4} +(-1.44081 + 0.341479i) q^{5} +(-2.26996 - 3.04908i) q^{7} +(0.459961 - 2.60857i) q^{8} +(0.200956 + 1.13968i) q^{10} +(-3.46856 + 3.67646i) q^{11} +(-4.01443 - 2.01612i) q^{13} +(-2.48212 + 1.63252i) q^{14} +(0.689105 + 0.163321i) q^{16} +(-4.30582 - 1.56719i) q^{17} +(4.19524 - 1.52694i) q^{19} +(-2.04309 + 0.238803i) q^{20} +(2.71085 + 2.87333i) q^{22} +(-2.06314 + 2.77128i) q^{23} +(-2.50883 + 1.25998i) q^{25} +(-1.75546 + 3.04054i) q^{26} +(-2.64032 - 4.57318i) q^{28} +(-0.545523 - 0.358796i) q^{29} +(0.260680 + 0.604325i) q^{31} +(1.67812 - 5.60530i) q^{32} +(-1.41843 + 3.28829i) q^{34} +(4.31178 + 3.61801i) q^{35} +(0.766165 - 0.642889i) q^{37} +(-1.00072 - 3.34263i) q^{38} +(0.228053 + 3.91553i) q^{40} +(0.0397020 + 0.681658i) q^{41} +(-2.40716 - 8.04048i) q^{43} +(-5.37881 + 4.51336i) q^{44} +(2.06847 + 1.73565i) q^{46} +(3.14280 - 7.28584i) q^{47} +(-2.13657 + 7.13664i) q^{49} +(0.869061 + 2.01471i) q^{50} +(-5.21392 - 3.42925i) q^{52} +(-2.07469 - 3.59347i) q^{53} +(3.74212 - 6.48154i) q^{55} +(-8.99782 + 4.51888i) q^{56} +(-0.304732 + 0.409326i) q^{58} +(-3.61647 - 3.83324i) q^{59} +(6.74505 - 0.788383i) q^{61} +(0.483356 - 0.175927i) q^{62} +(-2.96617 - 1.07960i) q^{64} +(6.47250 + 1.53401i) q^{65} +(-4.42909 + 2.91306i) q^{67} +(-5.68837 - 2.85681i) q^{68} +(3.01881 - 3.19975i) q^{70} +(-1.06500 - 6.03991i) q^{71} +(-0.764322 + 4.33469i) q^{73} +(-0.466781 - 0.626996i) q^{74} +(6.03481 - 1.43028i) q^{76} +(19.0833 + 2.23052i) q^{77} +(-0.653695 + 11.2235i) q^{79} -1.04864 q^{80} +0.533651 q^{82} +(-0.0942903 + 1.61890i) q^{83} +(6.73904 + 0.787681i) q^{85} +(-6.38278 + 1.51275i) q^{86} +(7.99490 + 10.7390i) q^{88} +(-0.181087 + 1.02699i) q^{89} +(2.96526 + 16.8168i) q^{91} +(-3.29364 + 3.49105i) q^{92} +(-5.54178 - 2.78318i) q^{94} +(-5.52314 + 3.63263i) q^{95} +(4.85369 + 1.15034i) q^{97} +(5.47110 + 1.99132i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{14}{27}\right)$

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 $

$2$	0.0454430	−	0.780226i	0.0321330	−	0.551703i	−0.943374	−	0.331732i	$-0.892367\pi$
$2$	0.0454430	−	0.780226i	0.0321330	−	0.551703i	0.975507	−	0.219970i	$-0.0705961\pi$
$3$		0			0
$3$		0			0
$4$	1.37979	+	0.161274i	0.689895	+	0.0806371i
$5$	−1.44081	+	0.341479i	−0.644351	+	0.152714i	−0.539784	−	0.841804i	$-0.681494\pi$
$5$	−1.44081	+	0.341479i	−0.644351	+	0.152714i	−0.104568	+	0.994518i	$0.533346\pi$
$6$		0			0
$7$	−2.26996	−	3.04908i	−0.857963	−	1.15244i	−0.986987	−	0.160803i	$-0.948592\pi$
$7$	−2.26996	−	3.04908i	−0.857963	−	1.15244i	0.129024	−	0.991642i	$-0.458816\pi$
$8$	0.459961	−	2.60857i	0.162621	−	0.922268i
$9$		0			0
$10$	0.200956	+	1.13968i	0.0635478	+	0.360398i
$11$	−3.46856	+	3.67646i	−1.04581	+	1.10850i	−0.0518624	+	0.998654i	$0.516516\pi$
$11$	−3.46856	+	3.67646i	−1.04581	+	1.10850i	−0.993949	+	0.109841i	$0.964966\pi$
$12$		0			0
$13$	−4.01443	−	2.01612i	−1.11340	−	0.559171i	−0.205627	−	0.978630i	$-0.565924\pi$
$13$	−4.01443	−	2.01612i	−1.11340	−	0.559171i	−0.907774	+	0.419459i	$0.862220\pi$
$14$	−2.48212	+	1.63252i	−0.663376	+	0.436309i
$15$		0			0
$16$	0.689105	+	0.163321i	0.172276	+	0.0408303i
$17$	−4.30582	−	1.56719i	−1.04431	−	0.380099i	−0.237800	−	0.971314i	$-0.576426\pi$
$17$	−4.30582	−	1.56719i	−1.04431	−	0.380099i	−0.806514	+	0.591215i	$0.798648\pi$
$18$		0			0
$19$	4.19524	−	1.52694i	0.962455	−	0.350305i	0.187460	−	0.982272i	$-0.439975\pi$
$19$	4.19524	−	1.52694i	0.962455	−	0.350305i	0.774995	+	0.631967i	$0.217752\pi$
$20$	−2.04309	+	0.238803i	−0.456849	+	0.0533980i
$21$		0			0
$22$	2.71085	+	2.87333i	0.577955	+	0.612597i
$23$	−2.06314	+	2.77128i	−0.430195	+	0.577852i	−0.963378	−	0.268148i	$-0.913588\pi$
$23$	−2.06314	+	2.77128i	−0.430195	+	0.577852i	0.533183	+	0.846000i	$0.320996\pi$
$24$		0			0
$25$	−2.50883	+	1.25998i	−0.501766	+	0.251996i
$26$	−1.75546	+	3.04054i	−0.344273	+	0.596299i
$27$		0			0
$28$	−2.64032	−	4.57318i	−0.498974	−	0.864249i
$29$	−0.545523	−	0.358796i	−0.101301	−	0.0666267i	0.497848	−	0.867264i	$-0.334124\pi$
$29$	−0.545523	−	0.358796i	−0.101301	−	0.0666267i	−0.599149	+	0.800638i	$0.704494\pi$
$30$		0			0
$31$	0.260680	+	0.604325i	0.0468196	+	0.108540i	0.940021	−	0.341117i	$-0.110805\pi$
$31$	0.260680	+	0.604325i	0.0468196	+	0.108540i	−0.893201	+	0.449657i	$0.851546\pi$
$32$	1.67812	−	5.60530i	0.296652	−	0.990886i
$33$		0			0
$34$	−1.41843	+	3.28829i	−0.243259	+	0.563937i
$35$	4.31178	+	3.61801i	0.728824	+	0.611556i
$36$		0			0
$37$	0.766165	−	0.642889i	0.125957	−	0.105690i	−0.577633	−	0.816296i	$-0.696024\pi$
$37$	0.766165	−	0.642889i	0.125957	−	0.105690i	0.703590	+	0.710606i	$0.251579\pi$
$38$	−1.00072	−	3.34263i	−0.162338	−	0.542245i
$39$		0			0
$40$	0.228053	+	3.91553i	0.0360584	+	0.619099i
$41$	0.0397020	+	0.681658i	0.00620042	+	0.106457i	0.999988	−	0.00483359i	$-0.00153858\pi$
$41$	0.0397020	+	0.681658i	0.00620042	+	0.106457i	−0.993788	+	0.111291i	$0.964502\pi$
$42$		0			0
$43$	−2.40716	−	8.04048i	−0.367089	−	1.22616i	−0.919666	−	0.392700i	$-0.871541\pi$
$43$	−2.40716	−	8.04048i	−0.367089	−	1.22616i	0.552578	−	0.833461i	$-0.313644\pi$
$44$	−5.37881	+	4.51336i	−0.810886	+	0.680414i
$45$		0			0
$46$	2.06847	+	1.73565i	0.304979	+	0.255908i
$47$	3.14280	−	7.28584i	0.458425	−	1.06275i	−0.519628	−	0.854392i	$-0.673930\pi$
$47$	3.14280	−	7.28584i	0.458425	−	1.06275i	0.978053	−	0.208356i	$-0.0668112\pi$
$48$		0			0
$49$	−2.13657	+	7.13664i	−0.305224	+	1.01952i
$50$	0.869061	+	2.01471i	0.122904	+	0.284923i
$51$		0			0
$52$	−5.21392	−	3.42925i	−0.723040	−	0.475551i
$53$	−2.07469	−	3.59347i	−0.284981	−	0.493601i	0.687624	−	0.726067i	$-0.258654\pi$
$53$	−2.07469	−	3.59347i	−0.284981	−	0.493601i	−0.972605	+	0.232466i	$0.925321\pi$
$54$		0			0
$55$	3.74212	−	6.48154i	0.504587	−	0.873971i
$56$	−8.99782	+	4.51888i	−1.20238	+	0.603860i
$57$		0			0
$58$	−0.304732	+	0.409326i	−0.0400133	+	0.0537471i
$59$	−3.61647	−	3.83324i	−0.470825	−	0.499045i	0.447823	−	0.894122i	$-0.352199\pi$
$59$	−3.61647	−	3.83324i	−0.470825	−	0.499045i	−0.918648	+	0.395077i	$0.870718\pi$
$60$		0			0
$61$	6.74505	−	0.788383i	0.863615	−	0.100942i	0.327260	−	0.944934i	$-0.393875\pi$
$61$	6.74505	−	0.788383i	0.863615	−	0.100942i	0.536355	+	0.843992i	$0.319801\pi$
$62$	0.483356	−	0.175927i	0.0613862	−	0.0223428i
$63$		0			0
$64$	−2.96617	−	1.07960i	−0.370771	−	0.134950i
$65$	6.47250	+	1.53401i	0.802815	+	0.190271i
$66$		0			0
$67$	−4.42909	+	2.91306i	−0.541099	+	0.355886i	−0.790450	−	0.612527i	$-0.790153\pi$
$67$	−4.42909	+	2.91306i	−0.541099	+	0.355886i	0.249351	+	0.968413i	$0.419783\pi$
$68$	−5.68837	−	2.85681i	−0.689817	−	0.346439i
$69$		0			0
$70$	3.01881	−	3.19975i	0.360816	−	0.382443i
$71$	−1.06500	−	6.03991i	−0.126392	−	0.716805i	−0.980471	−	0.196662i	$-0.936990\pi$
$71$	−1.06500	−	6.03991i	−0.126392	−	0.716805i	0.854079	−	0.520143i	$-0.174121\pi$
$72$		0			0
$73$	−0.764322	+	4.33469i	−0.0894571	+	0.507337i	0.906848	+	0.421457i	$0.138481\pi$
$73$	−0.764322	+	4.33469i	−0.0894571	+	0.507337i	−0.996306	+	0.0858796i	$0.972630\pi$
$74$	−0.466781	−	0.626996i	−0.0542622	−	0.0728868i
$75$		0			0
$76$	6.03481	−	1.43028i	0.692240	−	0.164064i
$77$	19.0833	+	2.23052i	2.17475	+	0.254191i
$78$		0			0
$79$	−0.653695	+	11.2235i	−0.0735465	+	1.26274i	0.736524	+	0.676412i	$0.236466\pi$
$79$	−0.653695	+	11.2235i	−0.0735465	+	1.26274i	−0.810070	+	0.586333i	$0.800571\pi$
$80$	−1.04864			−0.117242
$81$		0			0
$82$	0.533651			0.0589319
$83$	−0.0942903	+	1.61890i	−0.0103497	+	0.177698i	0.989172	+	0.146763i	$0.0468854\pi$
$83$	−0.0942903	+	1.61890i	−0.0103497	+	0.177698i	−0.999521	+	0.0309347i	$0.990152\pi$
$84$		0			0
$85$	6.73904	+	0.787681i	0.730952	+	0.0854360i
$86$	−6.38278	+	1.51275i	−0.688273	+	0.163124i
$87$		0			0
$88$	7.99490	+	10.7390i	0.852259	+	1.14478i
$89$	−0.181087	+	1.02699i	−0.0191952	+	0.108861i	−0.992900	−	0.118952i	$-0.962046\pi$
$89$	−0.181087	+	1.02699i	−0.0191952	+	0.108861i	0.973705	+	0.227813i	$0.0731576\pi$
$90$		0			0
$91$	2.96526	+	16.8168i	0.310844	+	1.76288i
$92$	−3.29364	+	3.49105i	−0.343385	+	0.363967i
$93$		0			0
$94$	−5.54178	−	2.78318i	−0.571591	−	0.287064i
$95$	−5.52314	+	3.63263i	−0.566662	+	0.372700i
$96$		0			0
$97$	4.85369	+	1.15034i	0.492817	+	0.116800i	0.469508	−	0.882928i	$-0.344431\pi$
$97$	4.85369	+	1.15034i	0.492817	+	0.116800i	0.0233097	+	0.999728i	$0.492580\pi$
$98$	5.47110	+	1.99132i	0.552664	+	0.201153i
$99$		0			0
$100$	−3.66486	+	1.33390i	−0.366486	+	0.133390i
$101$	9.50577	−	1.11107i	0.945859	−	0.110555i	0.370842	−	0.928696i	$-0.379069\pi$
$101$	9.50577	−	1.11107i	0.945859	−	0.110555i	0.575018	+	0.818141i	$0.304995\pi$
$102$		0			0
$103$	−2.23381	−	2.36770i	−0.220104	−	0.233297i	0.607907	−	0.794008i	$-0.292009\pi$
$103$	−2.23381	−	2.36770i	−0.220104	−	0.233297i	−0.828011	+	0.560711i	$0.810528\pi$
$104$	−7.10567	+	9.54457i	−0.696768	+	0.935922i
$105$		0			0
$106$	−2.89800	+	1.45543i	−0.281479	+	0.141364i
$107$	−8.40680	+	14.5610i	−0.812716	+	1.40767i	0.0982402	+	0.995163i	$0.468679\pi$
$107$	−8.40680	+	14.5610i	−0.812716	+	1.40767i	−0.910956	+	0.412503i	$0.864655\pi$
$108$		0			0
$109$	−3.81772	−	6.61249i	−0.365671	−	0.633361i	0.623212	−	0.782053i	$-0.285827\pi$
$109$	−3.81772	−	6.61249i	−0.365671	−	0.633361i	−0.988884	+	0.148691i	$0.952494\pi$
$110$	−4.88701	−	3.21424i	−0.465958	−	0.306465i
$111$		0			0
$112$	−1.06626	−	2.47187i	−0.100752	−	0.233570i
$113$	2.87359	−	9.59845i	0.270324	−	0.902947i	−0.709773	−	0.704430i	$-0.751203\pi$
$113$	2.87359	−	9.59845i	0.270324	−	0.902947i	0.980098	−	0.198516i	$-0.0636123\pi$
$114$		0			0
$115$	2.02627	−	4.69742i	0.188950	−	0.438036i
$116$	−0.694842	−	0.583042i	−0.0645144	−	0.0541340i
$117$		0			0
$118$	−3.15514	+	2.64747i	−0.290454	+	0.243720i
$119$	4.99553	+	16.6862i	0.457940	+	1.52962i
$120$		0			0
$121$	−0.845852	−	14.5227i	−0.0768956	−	1.32025i
$122$	−0.308602	−	5.29849i	−0.0279395	−	0.479703i
$123$		0			0
$124$	0.262222	+	0.875882i	0.0235482	+	0.0786565i
$125$	8.85601	−	7.43107i	0.792105	−	0.664655i
$126$		0			0
$127$	2.97665	+	2.49770i	0.264135	+	0.221635i	0.765230	−	0.643757i	$-0.222625\pi$
$127$	2.97665	+	2.49770i	0.264135	+	0.221635i	−0.501096	+	0.865392i	$0.667070\pi$
$128$	3.65789	−	8.47994i	0.323315	−	0.749528i
$129$		0			0
$130$	1.49100	−	4.98030i	0.130770	−	0.436801i
$131$	−6.59441	−	15.2876i	−0.576157	−	1.33568i	−0.918245	−	0.396013i	$-0.870393\pi$
$131$	−6.59441	−	15.2876i	−0.576157	−	1.33568i	0.342088	−	0.939668i	$-0.388866\pi$
$132$		0			0
$133$	−14.1788	−	9.32554i	−1.22946	−	0.808627i
$134$	2.07157	+	3.58807i	0.178956	+	0.309962i
$135$		0			0
$136$	−6.06863	+	10.5112i	−0.520380	+	0.901325i
$137$	8.28923	−	4.16301i	0.708197	−	0.355670i	−0.0579639	−	0.998319i	$-0.518461\pi$
$137$	8.28923	−	4.16301i	0.708197	−	0.355670i	0.766161	+	0.642649i	$0.222165\pi$
$138$		0			0
$139$	9.50746	−	12.7707i	0.806412	−	1.08320i	−0.188462	−	0.982080i	$-0.560350\pi$
$139$	9.50746	−	12.7707i	0.806412	−	1.08320i	0.994874	−	0.101119i	$-0.0322422\pi$
$140$	5.36586	+	5.68748i	0.453498	+	0.480680i
$141$		0			0
$142$	−4.76089	+	0.556468i	−0.399525	+	0.0466978i
$143$	21.3365	−	7.76585i	1.78425	−	0.649413i
$144$		0			0
$145$	0.908517	+	0.330673i	0.0754483	+	0.0274609i
$146$	3.34730	+	0.793325i	0.277025	+	0.0656560i
$147$		0			0
$148$	1.16083	−	0.763489i	0.0954195	−	0.0627584i
$149$	20.8590	+	10.4758i	1.70883	+	0.858208i	0.985909	+	0.167281i	$0.0534986\pi$
$149$	20.8590	+	10.4758i	1.70883	+	0.858208i	0.722924	+	0.690928i	$0.242798\pi$
$150$		0			0
$151$	1.60038	−	1.69630i	0.130237	−	0.138043i	−0.658973	−	0.752167i	$-0.729009\pi$
$151$	1.60038	−	1.69630i	0.130237	−	0.138043i	0.789210	+	0.614123i	$0.210490\pi$
$152$	−2.05349	−	11.6459i	−0.166560	−	0.944608i
$153$		0			0
$154$	2.60751	−	14.7879i	0.210119	−	1.19165i
$155$	−0.581956	−	0.781702i	−0.0467438	−	0.0627878i
$156$		0			0
$157$	−19.1527	+	4.53927i	−1.52855	+	0.362273i	−0.907010	−	0.421109i	$-0.861641\pi$
$157$	−19.1527	+	4.53927i	−1.52855	+	0.362273i	−0.621541	+	0.783382i	$0.713493\pi$
$158$	8.72717	+	1.02006i	0.694296	+	0.0811516i
$159$		0			0
$160$	−0.503760	+	8.64923i	−0.0398257	+	0.683782i
$161$	13.1331			1.03503
$162$		0			0
$163$	−17.6622			−1.38341			−0.691707	−	0.722179i	$-0.743141\pi$
$163$	−17.6622			−1.38341			−0.691707	+	0.722179i	$0.743141\pi$
$164$	−0.0551534	+	0.946947i	−0.00430676	+	0.0739442i
$165$		0			0
$166$	1.25882	+	0.147135i	0.0977037	+	0.0114199i
$167$	3.29876	−	0.781820i	0.255266	−	0.0604991i	−0.100991	−	0.994887i	$-0.532201\pi$
$167$	3.29876	−	0.781820i	0.255266	−	0.0604991i	0.356256	+	0.934388i	$0.384053\pi$
$168$		0			0
$169$	4.28782	+	5.75954i	0.329832	+	0.443042i
$170$	0.920811	−	5.22218i	0.0706230	−	0.400523i
$171$		0			0
$172$	−2.02465	−	11.4824i	−0.154378	−	0.875524i
$173$	12.8183	−	13.5866i	0.974557	−	1.03297i	−0.0248887	−	0.999690i	$-0.507923\pi$
$173$	12.8183	−	13.5866i	0.974557	−	1.03297i	0.999446	−	0.0332802i	$-0.0105954\pi$
$174$		0			0
$175$	9.53672	+	4.78952i	0.720908	+	0.362054i
$176$	−2.99065	+	1.96698i	−0.225429	+	0.148267i
$177$		0			0
$178$	0.793058	+	0.187958i	0.0594422	+	0.0140881i
$179$	−11.1678	−	4.06476i	−0.834723	−	0.303814i	−0.110927	−	0.993829i	$-0.535382\pi$
$179$	−11.1678	−	4.06476i	−0.834723	−	0.303814i	−0.723796	+	0.690014i	$0.757604\pi$
$180$		0			0
$181$	14.8329	−	5.39873i	1.10252	−	0.401284i	0.274275	−	0.961651i	$-0.411562\pi$
$181$	14.8329	−	5.39873i	1.10252	−	0.401284i	0.828244	+	0.560367i	$0.189340\pi$
$182$	13.2557	−	1.54937i	0.982575	−	0.114847i
$183$		0			0
$184$	6.28011	+	6.65652i	0.462976	+	0.490725i
$185$	−0.884368	+	1.18791i	−0.0650200	+	0.0873370i
$186$		0			0
$187$	20.6967	−	10.3943i	1.51349	−	0.760105i
$188$	5.51142	−	9.54607i	0.401962	−	0.696219i
$189$		0			0
$190$	2.58328	+	4.47437i	0.187411	+	0.324605i
$191$	−4.81793	−	3.16881i	−0.348614	−	0.229287i	0.363110	−	0.931746i	$-0.381715\pi$
$191$	−4.81793	−	3.16881i	−0.348614	−	0.229287i	−0.711724	+	0.702459i	$0.752085\pi$
$192$		0			0
$193$	0.0696139	+	0.161383i	0.00501092	+	0.0116166i	0.920703	−	0.390264i	$-0.127616\pi$
$193$	0.0696139	+	0.161383i	0.00501092	+	0.0116166i	−0.915692	+	0.401880i	$0.868357\pi$
$194$	1.11809	−	3.73470i	0.0802745	−	0.268136i
$195$		0			0
$196$	−4.09897	+	9.50249i	−0.292784	+	0.678749i
$197$	8.59155	+	7.20917i	0.612123	+	0.513632i	0.895316	−	0.445431i	$-0.146950\pi$
$197$	8.59155	+	7.20917i	0.612123	+	0.513632i	−0.283194	+	0.959063i	$0.591394\pi$
$198$		0			0
$199$	−15.6873	+	13.1632i	−1.11204	+	0.933114i	−0.998175	−	0.0603824i	$-0.980768\pi$
$199$	−15.6873	+	13.1632i	−1.11204	+	0.933114i	−0.113866	+	0.993496i	$0.536324\pi$
$200$	2.13278	+	7.12399i	0.150811	+	0.503742i
$201$		0			0
$202$	−0.434911	−	7.46714i	−0.0306002	−	0.525386i
$203$	0.144315	+	2.47779i	0.0101289	+	0.173907i
$204$		0			0
$205$	−0.289975	−	0.968584i	−0.0202527	−	0.0676489i
$206$	−1.94885	+	1.63528i	−0.135783	+	0.113935i
$207$		0			0
$208$	−2.43709	−	2.04496i	−0.168982	−	0.141792i
$209$	−8.93772	+	20.7200i	−0.618235	+	1.43323i
$210$		0			0
$211$	−0.341693	+	1.14134i	−0.0235231	+	0.0785728i	−0.968945	−	0.247276i	$-0.920465\pi$
$211$	−0.341693	+	1.14134i	−0.0235231	+	0.0785728i	0.945422	+	0.325848i	$0.105650\pi$
$212$	−2.28310	−	5.29283i	−0.156804	−	0.363513i
$213$		0			0
$214$	10.9788	+	7.22090i	0.750498	+	0.493610i
$215$	6.21393	+	10.7628i	0.423786	+	0.734019i
$216$		0			0
$217$	1.25090	−	2.16663i	0.0849168	−	0.147080i
$218$	−5.33272	+	2.67819i	−0.361177	+	0.181390i
$219$		0			0
$220$	6.20864	−	8.33965i	0.418587	−	0.562259i
$221$	14.1257	+	14.9724i	0.950200	+	1.00715i
$222$		0			0
$223$	14.7991	−	1.72977i	0.991024	−	0.115834i	0.394898	−	0.918725i	$-0.370780\pi$
$223$	14.7991	−	1.72977i	0.991024	−	0.115834i	0.596126	+	0.802891i	$0.296706\pi$
$224$	−20.9003	+	7.60707i	−1.39646	+	0.508269i
$225$		0			0
$226$	−7.35838	−	2.67823i	−0.489472	−	0.178153i
$227$	−23.9357	−	5.67287i	−1.58867	−	0.376522i	−0.661138	−	0.750265i	$-0.729926\pi$
$227$	−23.9357	−	5.67287i	−1.58867	−	0.376522i	−0.927532	+	0.373743i	$0.878074\pi$
$228$		0			0
$229$	−1.27577	+	0.839089i	−0.0843054	+	0.0554486i	−0.590962	−	0.806699i	$-0.701252\pi$
$229$	−1.27577	+	0.839089i	−0.0843054	+	0.0554486i	0.506656	+	0.862148i	$0.330881\pi$
$230$	−3.57297	−	1.79441i	−0.235594	−	0.118320i
$231$		0			0
$232$	−1.18686	+	1.25800i	−0.0779213	+	0.0825918i
$233$	2.44148	+	13.8463i	0.159946	+	0.907101i	0.954123	+	0.299414i	$0.0967912\pi$
$233$	2.44148	+	13.8463i	0.159946	+	0.907101i	−0.794177	+	0.607687i	$0.792098\pi$
$234$		0			0
$235$	−2.04023	+	11.5707i	−0.133090	+	0.754791i
$236$	−4.37177	−	5.87231i	−0.284578	−	0.382255i
$237$		0			0
$238$	13.2460	−	3.13937i	0.858613	−	0.203495i
$239$	22.7624	+	2.66054i	1.47238	+	0.172096i	0.814120	−	0.580696i	$-0.197220\pi$
$239$	22.7624	+	2.66054i	1.47238	+	0.172096i	0.658258	+	0.752793i	$0.271294\pi$
$240$		0			0
$241$	0.411011	−	7.05678i	0.0264755	−	0.454567i	−0.958853	−	0.283902i	$-0.908371\pi$
$241$	0.411011	−	7.05678i	0.0264755	−	0.454567i	0.985329	−	0.170666i	$-0.0545918\pi$
$242$	−11.3694			−0.730855
$243$		0			0
$244$	9.43390			0.603943
$245$	0.641385	−	11.0122i	0.0409766	−	0.703541i
$246$		0			0
$247$	−19.9200	−	2.32831i	−1.26748	−	0.148147i
$248$	1.69632	−	0.402036i	0.107717	−	0.0255293i
$249$		0			0
$250$	−5.39547	−	7.24737i	−0.341239	−	0.458364i
$251$	0.0115419	−	0.0654574i	0.000728518	−	0.00413163i	−0.984441	−	0.175714i	$-0.943777\pi$
$251$	0.0115419	−	0.0654574i	0.000728518	−	0.00413163i	0.985170	+	0.171582i	$0.0548878\pi$
$252$		0			0
$253$	−3.03237	−	17.1974i	−0.190644	−	1.08119i
$254$	2.08404	−	2.20895i	0.130764	−	0.138602i
$255$		0			0
$256$	−12.0916	−	6.07263i	−0.755725	−	0.379539i
$257$	−16.1614	+	10.6295i	−1.00812	+	0.663052i	−0.942297	−	0.334779i	$-0.891338\pi$
$257$	−16.1614	+	10.6295i	−1.00812	+	0.663052i	−0.0658251	+	0.997831i	$0.520968\pi$
$258$		0			0
$259$	−3.69938	−	0.876770i	−0.229868	−	0.0544798i
$260$	8.68330	+	3.16046i	0.538515	+	0.196003i
$261$		0			0
$262$	−12.2274	+	4.45042i	−0.755413	+	0.274948i
$263$	−14.9583	+	1.74837i	−0.922367	+	0.107809i	−0.564003	−	0.825773i	$-0.690739\pi$
$263$	−14.9583	+	1.74837i	−0.922367	+	0.107809i	−0.358364	+	0.933582i	$0.616665\pi$
$264$		0			0
$265$	4.21634	+	4.46906i	0.259008	+	0.274532i
$266$	−7.92035	+	10.6389i	−0.485628	+	0.652312i
$267$		0			0
$268$	−6.58101	+	3.30511i	−0.401999	+	0.201892i
$269$	5.86823	−	10.1641i	0.357792	−	0.619715i	−0.629799	−	0.776758i	$-0.716863\pi$
$269$	5.86823	−	10.1641i	0.357792	−	0.619715i	0.987592	+	0.157043i	$0.0501962\pi$
$270$		0			0
$271$	1.44013	+	2.49438i	0.0874817	+	0.151523i	0.906446	−	0.422322i	$-0.138785\pi$
$271$	1.44013	+	2.49438i	0.0874817	+	0.151523i	−0.818964	+	0.573844i	$0.805451\pi$
$272$	−2.71121	−	1.78319i	−0.164391	−	0.108122i
$273$		0			0
$274$	−2.87140	−	6.65665i	−0.173468	−	0.402143i
$275$	4.06976	−	13.5939i	0.245416	−	0.819746i
$276$		0			0
$277$	−0.911389	+	2.11284i	−0.0547601	+	0.126948i	−0.943400	−	0.331658i	$-0.892392\pi$
$277$	−0.911389	+	2.11284i	−0.0547601	+	0.126948i	0.888640	+	0.458606i	$0.151651\pi$
$278$	−9.53200	−	7.99830i	−0.571692	−	0.479706i
$279$		0			0
$280$	11.4211	−	9.58343i	0.682540	−	0.572719i
$281$	−1.81991	−	6.07893i	−0.108567	−	0.362639i	0.886390	−	0.462939i	$-0.153205\pi$
$281$	−1.81991	−	6.07893i	−0.108567	−	0.362639i	−0.994957	+	0.100300i	$0.968020\pi$
$282$		0			0
$283$	0.853670	+	14.6569i	0.0507454	+	0.871265i	0.923617	+	0.383316i	$0.125218\pi$
$283$	0.853670	+	14.6569i	0.0507454	+	0.871265i	−0.872872	+	0.487949i	$0.837745\pi$
$284$	−0.495393	−	8.50556i	−0.0293961	−	0.504712i
$285$		0			0
$286$	−5.08952	−	17.0002i	−0.300950	−	1.00524i
$287$	1.98831	−	1.66839i	0.117366	−	0.0984819i
$288$		0			0
$289$	3.06122	+	2.56867i	0.180072	+	0.151098i
$290$	0.299285	−	0.693822i	0.0175746	−	0.0407426i
$291$		0			0
$292$	−1.75368	+	5.85769i	−0.102626	+	0.342795i
$293$	−10.0427	−	23.2816i	−0.586701	−	1.36013i	−0.910307	−	0.413934i	$-0.864155\pi$
$293$	−10.0427	−	23.2816i	−0.586701	−	1.36013i	0.323606	−	0.946192i	$-0.395105\pi$
$294$		0			0
$295$	6.51964	+	4.28803i	0.379588	+	0.249659i
$296$	−1.32461	−	2.29430i	−0.0769916	−	0.133353i
$297$		0			0
$298$	9.12136	−	15.7987i	0.528386	−	0.915191i
$299$	13.8696	−	6.96556i	0.802098	−	0.402829i
$300$		0			0
$301$	−19.0519	+	25.5912i	−1.09813	+	1.47505i
$302$	−1.25077	−	1.32574i	−0.0719739	−	0.0762879i
$303$		0			0
$304$	3.14035	−	0.367054i	0.180111	−	0.0210520i
$305$	−9.44914	+	3.43921i	−0.541056	+	0.196928i
$306$		0			0
$307$	11.4486	+	4.16694i	0.653405	+	0.237820i	0.647386	−	0.762162i	$-0.275862\pi$
$307$	11.4486	+	4.16694i	0.653405	+	0.237820i	0.00601852	+	0.999982i	$0.498084\pi$
$308$	25.9713	+	6.15530i	1.47985	+	0.350731i
$309$		0			0
$310$	−0.636350	+	0.418534i	−0.0361422	+	0.0237711i
$311$	−22.4620	−	11.2809i	−1.27370	−	0.639679i	−0.322014	−	0.946735i	$-0.604360\pi$
$311$	−22.4620	−	11.2809i	−1.27370	−	0.639679i	−0.951691	+	0.307056i	$0.900656\pi$
$312$		0			0
$313$	−20.2873	+	21.5033i	−1.14671	+	1.21544i	−0.173664	+	0.984805i	$0.555561\pi$
$313$	−20.2873	+	21.5033i	−1.14671	+	1.21544i	−0.973041	+	0.230632i	$0.925921\pi$
$314$	2.67130	+	15.1497i	0.150750	+	0.854947i
$315$		0			0
$316$	−2.71203	+	15.3807i	−0.152563	+	0.865230i
$317$	2.56069	+	3.43961i	0.143823	+	0.193188i	0.868197	−	0.496219i	$-0.165279\pi$
$317$	2.56069	+	3.43961i	0.143823	+	0.193188i	−0.724374	+	0.689407i	$0.757871\pi$
$318$		0			0
$319$	3.21128	−	0.761087i	0.179797	−	0.0426127i
$320$	4.64235	+	0.542613i	0.259515	+	0.0303330i
$321$		0			0
$322$	0.596807	−	10.2468i	0.0332588	−	0.571031i
$323$	−20.4570			−1.13826
$324$		0			0
$325$	12.6118			0.699576
$326$	−0.802624	+	13.7805i	−0.0444533	+	0.763233i
$327$		0			0
$328$	1.79641	+	0.209970i	0.0991902	+	0.0115937i
$329$	−29.3491	+	6.95587i	−1.61807	+	0.383490i
$330$		0			0
$331$	−16.6197	−	22.3242i	−0.913503	−	1.22705i	−0.973463	−	0.228846i	$-0.926505\pi$
$331$	−16.6197	−	22.3242i	−0.913503	−	1.22705i	0.0599599	−	0.998201i	$-0.480903\pi$
$332$	−0.391188	+	2.21854i	−0.0214692	+	0.121758i
$333$		0			0
$334$	−0.460091	−	2.60930i	−0.0251750	−	0.142775i
$335$	5.38674	−	5.70961i	0.294309	−	0.311949i
$336$		0			0
$337$	24.0402	+	12.0735i	1.30956	+	0.657683i	0.960202	−	0.279307i	$-0.0901049\pi$
$337$	24.0402	+	12.0735i	1.30956	+	0.657683i	0.349354	+	0.936991i	$0.386401\pi$
$338$	4.68859	−	3.08374i	0.255026	−	0.167733i
$339$		0			0
$340$	9.17143	+	2.17367i	0.497390	+	0.117884i
$341$	−3.12596	−	1.13776i	−0.169280	−	0.0616130i
$342$		0			0
$343$	1.60598	−	0.584529i	0.0867148	−	0.0315616i
$344$	−22.0813	+	2.58094i	−1.19055	+	0.139155i
$345$		0			0
$346$	−10.0181	−	10.6186i	−0.538577	−	0.570859i
$347$	−18.2126	+	24.4638i	−0.977703	+	1.31328i	−0.0281743	+	0.999603i	$0.508969\pi$
$347$	−18.2126	+	24.4638i	−0.977703	+	1.31328i	−0.949529	+	0.313680i	$0.898438\pi$
$348$		0			0
$349$	−7.12702	+	3.57932i	−0.381500	+	0.191597i	−0.629206	−	0.777239i	$-0.716620\pi$
$349$	−7.12702	+	3.57932i	−0.381500	+	0.191597i	0.247705	+	0.968835i	$0.420323\pi$
$350$	4.17028	−	7.22314i	0.222911	−	0.386093i
$351$		0			0
$352$	14.7870	+	25.6119i	0.788151	+	1.36512i
$353$	18.2389	+	11.9959i	0.970756	+	0.638476i	0.932644	−	0.360797i	$-0.117495\pi$
$353$	18.2389	+	11.9959i	0.970756	+	0.638476i	0.0381118	+	0.999273i	$0.487866\pi$
$354$		0			0
$355$	3.59697	+	8.33871i	0.190907	+	0.442573i
$356$	−0.415490	+	1.38783i	−0.0220209	+	0.0735549i
$357$		0			0
$358$	−3.67893	+	8.52871i	−0.194437	+	0.450757i
$359$	−13.2606	−	11.1269i	−0.699866	−	0.587258i	0.221869	−	0.975076i	$-0.428784\pi$
$359$	−13.2606	−	11.1269i	−0.699866	−	0.587258i	−0.921736	+	0.387819i	$0.873229\pi$
$360$		0			0
$361$	0.713665	−	0.598836i	0.0375613	−	0.0315177i
$362$	−3.53818	−	11.8183i	−0.185962	−	0.621158i
$363$		0			0
$364$	1.37931	+	23.6819i	0.0722957	+	1.24127i
$365$	−0.378959	−	6.50647i	−0.0198356	−	0.340564i
$366$		0			0
$367$	6.85653	+	22.9024i	0.357908	+	1.19550i	0.927580	+	0.373624i	$0.121885\pi$
$367$	6.85653	+	22.9024i	0.357908	+	1.19550i	−0.569672	+	0.821872i	$0.692930\pi$
$368$	−1.87433	+	1.57275i	−0.0977062	+	0.0819853i
$369$		0			0
$370$	0.886651	+	0.743989i	0.0460948	+	0.0386781i
$371$	−6.24733	+	14.4829i	−0.324345	+	0.751916i
$372$		0			0
$373$	3.30709	−	11.0464i	0.171235	−	0.571963i	−0.828690	−	0.559707i	$-0.810914\pi$
$373$	3.30709	−	11.0464i	0.171235	−	0.571963i	0.999925	−	0.0122560i	$-0.00390131\pi$
$374$	−7.16937	−	16.6205i	−0.370719	−	0.859423i
$375$		0			0
$376$	−17.5600	−	11.5494i	−0.905589	−	0.595615i
$377$	1.46658	+	2.54020i	0.0755329	+	0.130827i
$378$		0			0
$379$	−10.3656	+	17.9537i	−0.532443	+	0.922218i	0.466839	+	0.884342i	$0.345393\pi$
$379$	−10.3656	+	17.9537i	−0.532443	+	0.922218i	−0.999282	+	0.0378763i	$0.987941\pi$
$380$	−8.20663	+	4.12152i	−0.420991	+	0.211430i
$381$		0			0
$382$	−2.69132	+	3.61508i	−0.137700	+	0.184963i
$383$	10.8805	+	11.5326i	0.555967	+	0.589290i	0.943007	−	0.332772i	$-0.107984\pi$
$383$	10.8805	+	11.5326i	0.555967	+	0.589290i	−0.387040	+	0.922063i	$0.626503\pi$
$384$		0			0
$385$	−28.2572	+	3.30279i	−1.44012	+	0.168326i
$386$	0.129079	−	0.0469808i	0.00656994	−	0.00239126i
$387$		0			0
$388$	6.51155	+	2.37001i	0.330574	+	0.120319i
$389$	−27.7406	−	6.57464i	−1.40650	−	0.333347i	−0.543866	−	0.839172i	$-0.683040\pi$
$389$	−27.7406	−	6.57464i	−1.40650	−	0.333347i	−0.862636	+	0.505825i	$0.831188\pi$
$390$		0			0
$391$	13.2266	−	8.69929i	0.668899	−	0.439942i
$392$	17.6337	+	8.85596i	0.890635	+	0.447293i
$393$		0			0
$394$	6.01520	−	6.37574i	0.303041	−	0.321205i
$395$	−2.89074	−	16.3942i	−0.145449	−	0.824882i
$396$		0			0
$397$	5.49087	−	31.1403i	0.275579	−	1.56289i	−0.461538	−	0.887120i	$-0.652702\pi$
$397$	5.49087	−	31.1403i	0.275579	−	1.56289i	0.737117	−	0.675765i	$-0.236187\pi$
$398$	9.55738	+	12.8378i	0.479068	+	0.643500i
$399$		0			0
$400$	−1.93463	+	0.458515i	−0.0967314	+	0.0229258i
$401$	−16.9325	−	1.97912i	−0.845568	−	0.0988328i	−0.317734	−	0.948180i	$-0.602922\pi$
$401$	−16.9325	−	1.97912i	−0.845568	−	0.0988328i	−0.527835	+	0.849347i	$0.676996\pi$
$402$		0			0
$403$	0.171910	−	2.95158i	0.00856345	−	0.147029i
$404$	13.2952			0.661458
$405$		0			0
$406$	1.93980			0.0962705
$407$	−0.293936	+	5.04668i	−0.0145698	+	0.250155i
$408$		0			0
$409$	23.6758	+	2.76730i	1.17069	+	0.136834i	0.679136	−	0.734012i	$-0.262354\pi$
$409$	23.6758	+	2.76730i	1.17069	+	0.136834i	0.491555	+	0.870846i	$0.336429\pi$
$410$	−0.768892	+	0.182231i	−0.0379728	+	0.00899973i
$411$		0			0
$412$	−2.70034	−	3.62719i	−0.133036	−	0.178699i
$413$	−3.47862	+	19.7282i	−0.171172	+	0.970762i
$414$		0			0
$415$	−0.416966	−	2.36473i	−0.0204681	−	0.116080i
$416$	−18.0376	+	19.1188i	−0.884368	+	0.937375i
$417$		0			0
$418$	15.7601	+	7.91501i	0.770851	+	0.387136i
$419$	13.1474	−	8.64720i	0.642294	−	0.422443i	−0.186146	−	0.982522i	$-0.559600\pi$
$419$	13.1474	−	8.64720i	0.642294	−	0.422443i	0.828439	+	0.560079i	$0.189229\pi$
$420$		0			0
$421$	−22.9228	−	5.43281i	−1.11719	−	0.264779i	−0.369766	−	0.929125i	$-0.620562\pi$
$421$	−22.9228	−	5.43281i	−1.11719	−	0.264779i	−0.747425	+	0.664346i	$0.768710\pi$
$422$	0.874971	+	0.318464i	0.0425929	+	0.0155026i
$423$		0			0
$424$	−10.3281	+	3.75912i	−0.501577	+	0.182559i
$425$	12.7772	−	1.49344i	0.619784	−	0.0724424i
$426$		0			0
$427$	−17.7148	−	18.7766i	−0.857280	−	0.908664i
$428$	−13.9479	+	18.7353i	−0.674199	+	0.905606i
$429$		0			0
$430$	8.67982	−	4.35917i	0.418578	−	0.210218i
$431$	0.705848	−	1.22256i	0.0339995	−	0.0588888i	−0.848525	−	0.529155i	$-0.822509\pi$
$431$	0.705848	−	1.22256i	0.0339995	−	0.0588888i	0.882524	+	0.470267i	$0.155842\pi$
$432$		0			0
$433$	−6.50524	−	11.2674i	−0.312622	−	0.541477i	0.666307	−	0.745677i	$-0.267874\pi$
$433$	−6.50524	−	11.2674i	−0.312622	−	0.541477i	−0.978929	+	0.204200i	$0.934541\pi$
$434$	−1.63361	−	1.07444i	−0.0784159	−	0.0515750i
$435$		0			0
$436$	−4.20123	−	9.73954i	−0.201202	−	0.466440i
$437$	−4.42379	+	14.7765i	−0.211619	+	0.706856i
$438$		0			0
$439$	8.21406	−	19.0423i	0.392036	−	0.908840i	−0.601869	−	0.798595i	$-0.705577\pi$
$439$	8.21406	−	19.0423i	0.392036	−	0.908840i	0.993904	−	0.110246i	$-0.0351637\pi$
$440$	−15.1863	−	12.7428i	−0.723979	−	0.607490i
$441$		0			0
$442$	12.3238	−	10.3409i	0.586182	−	0.491865i
$443$	−9.74198	−	32.5405i	−0.462855	−	1.54604i	−0.797273	−	0.603619i	$-0.793725\pi$
$443$	−9.74198	−	32.5405i	−0.462855	−	1.54604i	0.334417	−	0.942425i	$-0.391461\pi$
$444$		0			0
$445$	−0.0897847	−	1.54154i	−0.00425621	−	0.0730762i
$446$	−0.677095	−	11.6253i	−0.0320614	−	0.550473i
$447$		0			0
$448$	3.44129	+	11.4947i	0.162586	+	0.543075i
$449$	0.919709	−	0.771727i	0.0434038	−	0.0364201i	−0.620828	−	0.783947i	$-0.713203\pi$
$449$	0.919709	−	0.771727i	0.0434038	−	0.0364201i	0.664231	+	0.747527i	$0.268759\pi$
$450$		0			0
$451$	−2.64380	−	2.21841i	−0.124492	−	0.104461i
$452$	5.51293	−	12.7804i	0.259306	−	0.601140i
$453$		0			0
$454$	−5.51383	+	18.4175i	−0.258777	+	0.864375i
$455$	−10.0150	−	23.2173i	−0.469509	−	1.08844i
$456$		0			0
$457$	26.7801	+	17.6135i	1.25272	+	0.823926i	0.990017	−	0.140951i	$-0.0450161\pi$
$457$	26.7801	+	17.6135i	1.25272	+	0.823926i	0.262702	+	0.964877i	$0.415386\pi$
$458$	0.596704	+	1.03352i	0.0278821	+	0.0482933i
$459$		0			0
$460$	3.55340	−	6.15466i	0.165678	−	0.286963i
$461$	0.300873	−	0.151104i	0.0140130	−	0.00703761i	−0.441779	−	0.897124i	$-0.645652\pi$
$461$	0.300873	−	0.151104i	0.0140130	−	0.00703761i	0.455792	+	0.890086i	$0.349356\pi$
$462$		0			0
$463$	−1.76325	+	2.36845i	−0.0819451	+	0.110071i	−0.841205	−	0.540716i	$-0.818153\pi$
$463$	−1.76325	+	2.36845i	−0.0819451	+	0.110071i	0.759260	+	0.650787i	$0.225561\pi$
$464$	−0.317324	−	0.336343i	−0.0147314	−	0.0156144i
$465$		0			0
$466$	10.9142	−	1.27568i	0.505590	−	0.0590950i
$467$	−3.55605	+	1.29430i	−0.164554	+	0.0598929i	−0.422984	−	0.906137i	$-0.639017\pi$
$467$	−3.55605	+	1.29430i	−0.164554	+	0.0598929i	0.258429	+	0.966030i	$0.416795\pi$
$468$		0			0
$469$	18.9360	+	6.89213i	0.874382	+	0.318249i
$470$	8.93506	+	2.11765i	0.412144	+	0.0976799i
$471$		0			0
$472$	−11.6627	+	7.67068i	−0.536819	+	0.353072i
$473$	37.9099	+	19.0391i	1.74310	+	0.875418i
$474$		0			0
$475$	−8.60123	+	9.11677i	−0.394651	+	0.418306i
$476$	4.20172	+	23.8292i	0.192586	+	1.09221i
$477$		0			0
$478$	3.11022	−	17.6389i	0.142258	−	0.806785i
$479$	−1.89106	−	2.54013i	−0.0864047	−	0.116062i	0.756819	−	0.653625i	$-0.226752\pi$
$479$	−1.89106	−	2.54013i	−0.0864047	−	0.116062i	−0.843224	+	0.537563i	$0.819345\pi$
$480$		0			0
$481$	−4.37186	+	1.03615i	−0.199339	+	0.0472443i
$482$	−5.48721	−	0.641362i	−0.249935	−	0.0292133i
$483$		0			0
$484$	1.17504	−	20.1747i	0.0534110	−	0.917032i
$485$	−7.38607			−0.335384
$486$		0			0
$487$	1.22501			0.0555106			0.0277553	−	0.999615i	$-0.491164\pi$
$487$	1.22501			0.0555106			0.0277553	+	0.999615i	$0.491164\pi$
$488$	1.04591	−	17.9575i	0.0473460	−	0.812900i
$489$		0			0
$490$	−8.56282	−	1.00085i	−0.386829	−	0.0452138i
$491$	−39.4547	+	9.35094i	−1.78057	+	0.422002i	−0.983354	−	0.181698i	$-0.941841\pi$
$491$	−39.4547	+	9.35094i	−1.78057	+	0.422002i	−0.797212	+	0.603700i	$0.793693\pi$
$492$		0			0
$493$	1.78662	+	2.39985i	0.0804653	+	0.108084i
$494$	−2.72183	+	15.4363i	−0.122461	+	0.694512i
$495$		0			0
$496$	0.0809373	+	0.459018i	0.00363419	+	0.0206105i
$497$	−15.9987	+	16.9576i	−0.717639	+	0.760652i
$498$		0			0
$499$	−36.7745	−	18.4688i	−1.64625	−	0.826778i	−0.997854	−	0.0654753i	$-0.979144\pi$
$499$	−36.7745	−	18.4688i	−1.64625	−	0.826778i	−0.648396	−	0.761303i	$-0.724560\pi$
$500$	13.4179	−	8.82507i	0.600065	−	0.394669i
$501$		0			0
$502$	−0.0505470	−	0.0119799i	−0.00225602	−	0.000534687i
$503$	9.54144	+	3.47280i	0.425432	+	0.154845i	0.545858	−	0.837878i	$-0.316204\pi$
$503$	9.54144	+	3.47280i	0.425432	+	0.154845i	−0.120426	+	0.992722i	$0.538426\pi$
$504$		0			0
$505$	−13.3166	+	4.84686i	−0.592582	+	0.215682i
$506$	−13.5557	+	1.58443i	−0.602623	+	0.0704366i
$507$		0			0
$508$	3.70433	+	3.92636i	0.164353	+	0.174204i
$509$	14.4794	−	19.4492i	0.641789	−	0.862073i	−0.355574	−	0.934648i	$-0.615714\pi$
$509$	14.4794	−	19.4492i	0.641789	−	0.862073i	0.997363	+	0.0725757i	$0.0231219\pi$
$510$		0			0
$511$	14.9518	−	7.50907i	0.661428	−	0.332182i
$512$	3.94773	−	6.83768i	0.174467	−	0.302186i
$513$		0			0
$514$	7.55901	+	13.0926i	0.333414	+	0.577490i
$515$	4.02703	+	2.64862i	0.177452	+	0.116712i
$516$		0			0
$517$	15.8851	+	36.8258i	0.698626	+	1.61960i
$518$	−0.852189	+	2.84651i	−0.0374430	+	0.125068i
$519$		0			0
$520$	6.97867	−	16.1784i	0.306035	−	0.709469i
$521$	−4.86477	−	4.08202i	−0.213129	−	0.178837i	0.529973	−	0.848014i	$-0.322202\pi$
$521$	−4.86477	−	4.08202i	−0.213129	−	0.178837i	−0.743102	+	0.669178i	$0.766646\pi$
$522$		0			0
$523$	21.5335	−	18.0688i	0.941595	−	0.790092i	−0.0362674	−	0.999342i	$-0.511547\pi$
$523$	21.5335	−	18.0688i	0.941595	−	0.790092i	0.977862	+	0.209250i	$0.0671024\pi$
$524$	−6.63341	−	22.1571i	−0.289782	−	0.967939i
$525$		0			0
$526$	0.684376	+	11.7503i	0.0298402	+	0.512337i
$527$	−0.175350	−	3.01065i	−0.00763838	−	0.131146i
$528$		0			0
$529$	3.17303	+	10.5987i	0.137958	+	0.460812i
$530$	3.67848	−	3.08661i	0.159783	−	0.134074i
$531$		0			0
$532$	−18.0598	−	15.1540i	−0.782991	−	0.657008i
$533$	1.21492	−	2.81651i	0.0526242	−	0.121997i
$534$		0			0
$535$	7.14035	−	23.8504i	0.308704	−	1.03114i
$536$	5.56170	+	12.8935i	0.240229	+	0.556913i
$537$		0			0
$538$	−7.66360	−	5.04043i	−0.330401	−	0.217308i
$539$	−18.8268	−	32.6089i	−0.810926	−	1.40457i
$540$		0			0
$541$	−1.34390	+	2.32771i	−0.0577788	+	0.100076i	−0.893468	−	0.449127i	$-0.851735\pi$
$541$	−1.34390	+	2.32771i	−0.0577788	+	0.100076i	0.835689	+	0.549203i	$0.185068\pi$
$542$	2.01162	−	1.01028i	0.0864066	−	0.0433950i
$543$		0			0
$544$	−16.0102	+	21.5055i	−0.686433	+	0.922039i
$545$	7.75865	+	8.22369i	0.332344	+	0.352264i
$546$		0			0
$547$	−32.5857	+	3.80872i	−1.39326	+	0.162849i	−0.779381	−	0.626550i	$-0.784466\pi$
$547$	−32.5857	+	3.80872i	−1.39326	+	0.162849i	−0.613881	+	0.789399i	$0.710392\pi$
$548$	12.1088	−	4.40724i	0.517262	−	0.188268i
$549$		0			0
$550$	−10.4214	−	3.79308i	−0.444370	−	0.161737i
$551$	−2.83646	−	0.672254i	−0.120837	−	0.0286390i
$552$		0			0
$553$	35.7053	−	23.4837i	1.51834	−	0.998630i
$554$	1.60707	+	0.807103i	0.0682780	+	0.0342905i
$555$		0			0
$556$	15.1779	−	16.0876i	0.643686	−	0.682267i
$557$	1.71906	+	9.74928i	0.0728390	+	0.413090i	0.999324	+	0.0367591i	$0.0117034\pi$
$557$	1.71906	+	9.74928i	0.0728390	+	0.413090i	−0.926485	+	0.376331i	$0.877185\pi$
$558$		0			0
$559$	−6.54721	+	37.1311i	−0.276917	+	1.57048i
$560$	2.38037	+	3.19740i	0.100589	+	0.135115i
$561$		0			0
$562$	−4.82564	+	1.14370i	−0.203557	+	0.0482440i
$563$	6.98793	+	0.816772i	0.294506	+	0.0344228i	0.262063	−	0.965051i	$-0.415597\pi$
$563$	6.98793	+	0.816772i	0.294506	+	0.0344228i	0.0324431	+	0.999474i	$0.489671\pi$
$564$		0			0
$565$	−0.862634	+	14.8108i	−0.0362913	+	0.623097i
$566$	11.4745			0.482310
$567$		0			0
$568$	−16.2454			−0.681640
$569$	−0.228981	+	3.93146i	−0.00959940	+	0.164815i	0.990101	+	0.140354i	$0.0448241\pi$
$569$	−0.228981	+	3.93146i	−0.00959940	+	0.164815i	−0.999701	+	0.0244612i	$0.992213\pi$
$570$		0			0
$571$	−25.3946	−	2.96820i	−1.06273	−	0.124215i	−0.433282	−	0.901258i	$-0.642645\pi$
$571$	−25.3946	−	2.96820i	−1.06273	−	0.124215i	−0.629448	+	0.777043i	$0.716719\pi$
$572$	30.6923	−	7.27421i	1.28331	−	0.304150i
$573$		0			0
$574$	−1.21136	−	1.62715i	−0.0505614	−	0.0679157i
$575$	1.68431	−	9.55219i	0.0702405	−	0.398354i
$576$		0			0
$577$	0.816045	+	4.62802i	0.0339724	+	0.192667i	0.997071	−	0.0764818i	$-0.0243687\pi$
$577$	0.816045	+	4.62802i	0.0339724	+	0.192667i	−0.963099	+	0.269149i	$0.913258\pi$
$578$	2.14325	−	2.27172i	0.0891476	−	0.0944909i
$579$		0			0
$580$	1.20023	+	0.602780i	0.0498370	+	0.0250291i
$581$	5.15020	−	3.38734i	0.213666	−	0.140530i
$582$		0			0
$583$	20.4075	+	4.83666i	0.845191	+	0.200314i
$584$	10.9558	+	3.98757i	0.453353	+	0.165007i
$585$		0			0
$586$	−18.6213	+	6.77759i	−0.769238	+	0.279980i
$587$	−27.5853	+	3.22426i	−1.13857	+	0.133079i	−0.664415	−	0.747363i	$-0.731319\pi$
$587$	−27.5853	+	3.22426i	−1.13857	+	0.133079i	−0.474152	+	0.880443i	$0.657245\pi$
$588$		0			0
$589$	2.01639	+	2.13725i	0.0830838	+	0.0880637i
$590$	3.64190	−	4.89193i	0.149935	−	0.201397i
$591$		0			0
$592$	0.632966	−	0.317887i	0.0260147	−	0.0130651i
$593$	7.16631	−	12.4124i	0.294285	−	0.509717i	−0.680533	−	0.732717i	$-0.738252\pi$
$593$	7.16631	−	12.4124i	0.294285	−	0.509717i	0.974818	+	0.223000i	$0.0715851\pi$
$594$		0			0
$595$	−12.8956	−	22.3359i	−0.528669	−	0.915682i
$596$	27.0915	+	17.8184i	1.10971	+	0.729869i
$597$		0			0
$598$	−4.80443	−	11.1379i	−0.196468	−	0.455464i
$599$	−7.88798	+	26.3477i	−0.322294	+	1.07654i	0.631324	+	0.775519i	$0.282512\pi$
$599$	−7.88798	+	26.3477i	−0.322294	+	1.07654i	−0.953618	+	0.301018i	$0.902674\pi$
$600$		0			0
$601$	7.42657	−	17.2167i	0.302936	−	0.702285i	−0.696954	−	0.717116i	$-0.745462\pi$
$601$	7.42657	−	17.2167i	0.302936	−	0.702285i	0.999890	+	0.0148309i	$0.00472101\pi$
$602$	19.1011	+	16.0277i	0.778503	+	0.653242i
$603$		0			0
$604$	2.48176	−	2.08244i	0.100981	−	0.0847333i
$605$	6.17792	+	20.6357i	0.251168	+	0.838960i
$606$		0			0
$607$	−1.53553	−	26.3640i	−0.0623252	−	1.07008i	−0.873985	−	0.485952i	$-0.838473\pi$
$607$	−1.53553	−	26.3640i	−0.0623252	−	1.07008i	0.811660	−	0.584130i	$-0.198564\pi$
$608$	−1.51887	−	26.0780i	−0.0615983	−	1.05760i
$609$		0			0
$610$	2.25396	+	7.52875i	0.0912602	+	0.304830i
$611$	−27.3057	+	22.9122i	−1.10467	+	0.926928i
$612$		0			0
$613$	−26.7821	−	22.4728i	−1.08172	−	0.907670i	−0.0856560	−	0.996325i	$-0.527299\pi$
$613$	−26.7821	−	22.4728i	−1.08172	−	0.907670i	−0.996062	+	0.0886553i	$0.971743\pi$
$614$	3.77141	−	8.74312i	0.152202	−	0.352843i
$615$		0			0
$616$	14.5960	−	48.7542i	0.588092	−	1.96436i
$617$	−2.83253	−	6.56654i	−0.114033	−	0.264359i	0.851636	−	0.524134i	$-0.175611\pi$
$617$	−2.83253	−	6.56654i	−0.114033	−	0.264359i	−0.965669	+	0.259775i	$0.916352\pi$
$618$		0			0
$619$	15.7252	+	10.3426i	0.632050	+	0.415706i	0.824707	−	0.565560i	$-0.191340\pi$
$619$	15.7252	+	10.3426i	0.632050	+	0.415706i	−0.192657	+	0.981266i	$0.561710\pi$
$620$	−0.676908	−	1.17244i	−0.0271853	−	0.0470863i
$621$		0			0
$622$	−9.82235	+	17.0128i	−0.393841	+	0.682152i
$623$	3.54245	−	1.77908i	0.141925	−	0.0712775i
$624$		0			0
$625$	−1.83983	+	2.47133i	−0.0735934	+	0.0988530i
$626$	15.8555	+	16.8058i	0.633713	+	0.671696i
$627$		0			0
$628$	−27.1587	+	3.17440i	−1.08375	+	0.126672i
$629$	−4.30649	+	1.56744i	−0.171711	+	0.0624978i
$630$		0			0
$631$	−22.0642	−	8.03070i	−0.878361	−	0.319697i	−0.136813	−	0.990597i	$-0.543686\pi$
$631$	−22.0642	−	8.03070i	−0.878361	−	0.319697i	−0.741548	+	0.670900i	$0.765908\pi$
$632$	28.9766	+	6.86759i	1.15263	+	0.273178i
$633$		0			0
$634$	2.80004	−	1.84161i	0.111204	−	0.0731398i
$635$	−5.14171	−	2.58226i	−0.204042	−	0.102474i
$636$		0			0
$637$	22.9654	−	24.3419i	0.909923	−	0.964463i
$638$	−0.447890	−	2.54011i	−0.0177321	−	0.100564i
$639$		0			0
$640$	−2.37461	+	13.4671i	−0.0938648	+	0.532334i
$641$	−2.60302	−	3.49646i	−0.102813	−	0.138102i	0.747739	−	0.663993i	$-0.231139\pi$
$641$	−2.60302	−	3.49646i	−0.102813	−	0.138102i	−0.850552	+	0.525891i	$0.823732\pi$
$642$		0			0
$643$	18.4995	−	4.38447i	0.729550	−	0.172906i	0.150977	−	0.988537i	$-0.451758\pi$
$643$	18.4995	−	4.38447i	0.729550	−	0.172906i	0.578573	+	0.815631i	$0.303610\pi$
$644$	18.1209	+	2.11803i	0.714064	+	0.0834621i
$645$		0			0
$646$	−0.929625	+	15.9610i	−0.0365756	+	0.627979i
$647$	−20.6268			−0.810924			−0.405462	−	0.914112i	$-0.632889\pi$
$647$	−20.6268			−0.810924			−0.405462	+	0.914112i	$0.632889\pi$
$648$		0			0
$649$	26.6367			1.04558
$650$	0.573117	−	9.84004i	0.0224795	−	0.385958i
$651$		0			0
$652$	−24.3702	−	2.84846i	−0.954410	−	0.111554i
$653$	5.82928	−	1.38157i	0.228117	−	0.0540648i	−0.114967	−	0.993369i	$-0.536676\pi$
$653$	5.82928	−	1.38157i	0.228117	−	0.0540648i	0.343085	+	0.939304i	$0.388528\pi$
$654$		0			0
$655$	14.7217	+	19.7747i	0.575225	+	0.772661i
$656$	−0.0839701	+	0.476218i	−0.00327848	+	0.0185932i
$657$		0			0
$658$	4.09344	+	23.2150i	0.159579	+	0.905016i
$659$	26.6529	−	28.2504i	1.03825	−	1.10048i	0.0434061	−	0.999058i	$-0.486179\pi$
$659$	26.6529	−	28.2504i	1.03825	−	1.10048i	0.994843	−	0.101423i	$-0.0323394\pi$
$660$		0			0
$661$	27.6987	+	13.9108i	1.07736	+	0.541068i	0.896773	−	0.442491i	$-0.145905\pi$
$661$	27.6987	+	13.9108i	1.07736	+	0.541068i	0.180583	+	0.983560i	$0.442202\pi$
$662$	−18.1731	+	11.9527i	−0.706319	+	0.464553i
$663$		0			0
$664$	4.17964	+	0.990594i	0.162202	+	0.0384425i
$665$	23.6135	+	8.59460i	0.915691	+	0.333284i
$666$		0			0
$667$	2.11981	−	0.771549i	0.0820795	−	0.0298745i
$668$	4.67768	−	0.546743i	0.180985	−	0.0211541i
$669$		0			0
$670$	−4.21000	−	4.46233i	−0.162646	−	0.172395i
$671$	−20.4972	+	27.5325i	−0.791285	+	1.06288i
$672$		0			0
$673$	−34.4849	+	17.3190i	−1.32930	+	0.667598i	−0.964646	−	0.263547i	$-0.915108\pi$
$673$	−34.4849	+	17.3190i	−1.32930	+	0.667598i	−0.364650	+	0.931145i	$0.618811\pi$
$674$	10.5125	−	18.2082i	0.404926	−	0.701352i
$675$		0			0
$676$	4.98742	+	8.63847i	0.191824	+	0.332249i
$677$	−3.33250	−	2.19182i	−0.128078	−	0.0842386i	0.483853	−	0.875149i	$-0.339237\pi$
$677$	−3.33250	−	2.19182i	−0.128078	−	0.0842386i	−0.611932	+	0.790911i	$0.709607\pi$
$678$		0			0
$679$	−7.51016	−	17.4105i	−0.288214	−	0.668154i
$680$	5.15441	−	17.2169i	0.197663	−	0.660239i
$681$		0			0
$682$	−1.02976	+	2.38725i	−0.0394316	+	0.0914127i
$683$	32.2624	+	27.0713i	1.23449	+	1.03586i	0.997935	+	0.0642370i	$0.0204614\pi$
$683$	32.2624	+	27.0713i	1.23449	+	1.03586i	0.236551	+	0.971619i	$0.423983\pi$
$684$		0			0
$685$	−10.5217	+	8.82872i	−0.402012	+	0.337328i
$686$	−0.383084	−	1.27959i	−0.0146262	−	0.0488550i
$687$		0			0
$688$	−0.345609	−	5.93388i	−0.0131762	−	0.226227i
$689$	1.08383	+	18.6086i	0.0412905	+	0.708930i
$690$		0			0
$691$	2.45234	+	8.19140i	0.0932916	+	0.311616i	0.991880	−	0.127177i	$-0.0405916\pi$
$691$	2.45234	+	8.19140i	0.0932916	+	0.311616i	−0.898589	+	0.438792i	$0.855406\pi$
$692$	19.8777	−	16.6794i	0.755638	−	0.634056i
$693$		0			0
$694$	18.2596	+	15.3216i	0.693125	+	0.581601i
$695$	−9.33753	+	21.6468i	−0.354193	+	0.821111i
$696$		0			0
$697$	0.897337	−	2.99731i	0.0339891	−	0.113531i
$698$	2.46881	+	5.72333i	0.0934457	+	0.216631i
$699$		0			0
$700$	12.3862	+	8.14656i	0.468156	+	0.307911i
$701$	−0.440975	−	0.763791i	−0.0166554	−	0.0288480i	0.857578	−	0.514355i	$-0.171968\pi$
$701$	−0.440975	−	0.763791i	−0.0166554	−	0.0288480i	−0.874233	+	0.485507i	$0.838635\pi$
$702$		0			0
$703$	2.23259	−	3.86697i	0.0842039	−	0.145845i
$704$	14.2574	−	7.16036i	0.537348	−	0.269866i
$705$		0			0
$706$	10.1883	−	13.6853i	0.383443	−	0.515053i
$707$	−24.9654	−	26.4618i	−0.938921	−	0.995198i
$708$		0			0
$709$	39.9617	−	4.67085i	1.50079	−	0.175417i	0.674338	−	0.738423i	$-0.264429\pi$
$709$	39.9617	−	4.67085i	1.50079	−	0.175417i	0.826453	+	0.563005i	$0.190355\pi$
$710$	6.66953	−	2.42751i	0.250303	−	0.0911028i
$711$		0			0
$712$	2.59569	+	0.944754i	0.0972777	+	0.0354062i
$713$	−2.21257	−	0.524390i	−0.0828615	−	0.0196385i
$714$		0			0
$715$	−28.0900	+	18.4751i	−1.05051	+	0.690930i
$716$	−14.7537	−	7.40960i	−0.551372	−	0.276910i
$717$		0			0
$718$	−9.28413	+	9.84060i	−0.346481	+	0.367248i
$719$	−2.39151	−	13.5629i	−0.0891883	−	0.505812i	−0.996374	−	0.0850815i	$-0.972885\pi$
$719$	−2.39151	−	13.5629i	−0.0891883	−	0.505812i	0.907186	−	0.420730i	$-0.138226\pi$
$720$		0			0
$721$	−2.14866	+	12.1857i	−0.0800203	+	0.453817i
$722$	−0.434796	−	0.584032i	−0.0161814	−	0.0217354i
$723$		0			0
$724$	21.3369	−	5.05695i	0.792981	−	0.187940i
$725$	1.82070	+	0.212809i	0.0676190	+	0.00790353i
$726$		0			0
$727$	0.725932	−	12.4638i	0.0269233	−	0.462256i	−0.957723	−	0.287693i	$-0.907112\pi$
$727$	0.725932	−	12.4638i	0.0269233	−	0.462256i	0.984646	−	0.174563i	$-0.0558512\pi$
$728$	45.2317			1.67640
$729$		0			0
$730$	−5.09374			−0.188528
$731$	−2.23616	+	38.3933i	−0.0827072	+	1.42003i
$732$		0			0
$733$	26.6912	+	3.11976i	0.985864	+	0.115231i	0.593719	−	0.804673i	$-0.297659\pi$
$733$	26.6912	+	3.11976i	0.985864	+	0.115231i	0.392145	+	0.919903i	$0.371733\pi$
$734$	18.1806	−	4.30889i	0.671059	−	0.159044i
$735$		0			0
$736$	12.0717	+	16.2151i	0.444967	+	0.597695i
$737$	4.65283	−	26.3875i	0.171389	−	0.971996i
$738$		0			0
$739$	−4.23374	−	24.0107i	−0.155740	−	0.883248i	−0.958106	−	0.286415i	$-0.907536\pi$
$739$	−4.23374	−	24.0107i	−0.155740	−	0.883248i	0.802365	−	0.596833i	$-0.203575\pi$
$740$	−1.41182	+	1.49644i	−0.0518996	+	0.0550103i
$741$		0			0
$742$	11.0161	+	5.53247i	0.404412	+	0.203103i
$743$	30.1360	−	19.8208i	1.10558	−	0.727154i	0.140758	−	0.990044i	$-0.455046\pi$
$743$	30.1360	−	19.8208i	1.10558	−	0.727154i	0.964826	+	0.262890i	$0.0846757\pi$
$744$		0			0
$745$	−33.6311	−	7.97072i	−1.23215	−	0.292025i
$746$	−8.46844	−	3.08226i	−0.310052	−	0.112850i
$747$		0			0
$748$	30.2335	−	11.0041i	1.10544	−	0.402349i
$749$	63.4808	−	7.41984i	2.31954	−	0.271115i
$750$		0			0
$751$	1.60334	+	1.69945i	0.0585069	+	0.0620137i	0.755966	−	0.654611i	$-0.227168\pi$
$751$	1.60334	+	1.69945i	0.0585069	+	0.0620137i	−0.697459	+	0.716625i	$0.745686\pi$
$752$	3.35565	−	4.50742i	0.122368	−	0.164369i
$753$		0			0
$754$	2.04857	−	1.02883i	0.0746047	−	0.0374679i
$755$	−1.72660	+	2.99055i	−0.0628372	+	0.108837i
$756$		0			0
$757$	8.08646	+	14.0062i	0.293907	+	0.509063i	0.974730	−	0.223386i	$-0.0717109\pi$
$757$	8.08646	+	14.0062i	0.293907	+	0.509063i	−0.680823	+	0.732448i	$0.738378\pi$
$758$	13.5369	+	8.90334i	0.491681	+	0.323384i
$759$		0			0
$760$	6.93553	+	16.0784i	0.251578	+	0.583223i
$761$	13.0085	−	43.4514i	0.471557	−	1.57511i	−0.309657	−	0.950848i	$-0.600214\pi$
$761$	13.0085	−	43.4514i	0.471557	−	1.57511i	0.781215	−	0.624262i	$-0.214600\pi$
$762$		0			0
$763$	−11.4959	+	26.6506i	−0.416181	+	0.964817i
$764$	−6.13669	−	5.14929i	−0.222018	−	0.186295i
$765$		0			0
$766$	9.49250	−	7.96515i	0.342978	−	0.287793i
$767$	6.78980	+	22.6795i	0.245165	+	0.818910i
$768$		0			0
$769$	−1.06788	−	18.3348i	−0.0385087	−	0.661168i	−0.961238	−	0.275720i	$-0.911084\pi$
$769$	−1.06788	−	18.3348i	−0.0385087	−	0.661168i	0.922729	−	0.385448i	$-0.125953\pi$
$770$	1.29283	+	22.1971i	0.0465904	+	0.799927i
$771$		0			0
$772$	0.0700256	+	0.233902i	0.00252028	+	0.00841831i
$773$	22.5821	−	18.9486i	0.812222	−	0.681536i	−0.138915	−	0.990304i	$-0.544361\pi$
$773$	22.5821	−	18.9486i	0.812222	−	0.681536i	0.951137	+	0.308769i	$0.0999169\pi$
$774$		0			0
$775$	−1.41544	−	1.18769i	−0.0508441	−	0.0426633i
$776$	5.23326	−	12.1321i	0.187863	−	0.435515i
$777$		0			0
$778$	−6.39031	+	21.3451i	−0.229104	+	0.765260i
$779$	1.20741	+	2.79910i	0.0432601	+	0.100288i
$780$		0			0
$781$	25.8995	+	17.0344i	0.926758	+	0.609538i
$782$	−6.18635	−	10.7151i	−0.221224	−	0.383170i
$783$		0			0
$784$	−2.63788	+	4.56895i	−0.0942102	+	0.163177i
$785$	26.0454	−	13.0805i	0.929599	−	0.466862i
$786$		0			0
$787$	19.1430	−	25.7135i	0.682375	−	0.916588i	−0.317120	−	0.948386i	$-0.602716\pi$
$787$	19.1430	−	25.7135i	0.682375	−	0.916588i	0.999494	+	0.0317973i	$0.0101231\pi$
$788$	10.6919	+	11.3327i	0.380882	+	0.403712i
$789$		0			0
$790$	−12.9225	+	1.51043i	−0.459764	+	0.0537387i
$791$	−35.7894	+	13.0263i	−1.27252	+	0.463161i
$792$		0			0
$793$	−28.6670	−	10.4339i	−1.01799	−	0.370520i
$794$	−24.0469	−	5.69922i	−0.853393	−	0.202258i
$795$		0			0
$796$	−23.7680	+	15.6325i	−0.842435	+	0.554079i
$797$	10.5327	+	5.28974i	0.373088	+	0.187372i	0.625456	−	0.780259i	$-0.284913\pi$
$797$	10.5327	+	5.28974i	0.373088	+	0.187372i	−0.252368	+	0.967631i	$0.581209\pi$
$798$		0			0
$799$	−24.9506	+	26.4461i	−0.882689	+	0.935596i
$800$	2.85246	+	16.1771i	0.100850	+	0.571948i
$801$		0			0
$802$	−2.31363	+	13.1212i	−0.0816970	+	0.463327i
$803$	−13.2852	−	17.8451i	−0.468825	−	0.629741i
$804$		0			0
$805$	−18.9223	+	4.48468i	−0.666925	+	0.158064i
$806$	−2.29509	−	0.268257i	−0.0808410	−	0.00944895i
$807$		0			0
$808$	1.47399	−	25.3075i	0.0518549	−	0.890314i
$809$	21.4155			0.752929			0.376464	−	0.926431i	$-0.377140\pi$
$809$	21.4155			0.752929			0.376464	+	0.926431i	$0.377140\pi$
$810$		0			0
$811$	1.73790			0.0610258			0.0305129	−	0.999534i	$-0.490286\pi$
$811$	1.73790			0.0610258			0.0305129	+	0.999534i	$0.490286\pi$
$812$	−0.200480	+	3.44211i	−0.00703547	+	0.120794i
$813$		0			0
$814$	3.92419	+	0.458672i	0.137543	+	0.0160765i
$815$	25.4480	−	6.03128i	0.891404	−	0.211267i
$816$		0			0
$817$	−22.3760	−	30.0562i	−0.782837	−	1.05153i
$818$	3.23502	−	18.3467i	0.113110	−	0.641477i
$819$		0			0
$820$	−0.243897	−	1.38321i	−0.00851725	−	0.0483037i
$821$	6.12045	−	6.48730i	0.213605	−	0.226408i	−0.611708	−	0.791084i	$-0.709517\pi$
$821$	6.12045	−	6.48730i	0.213605	−	0.226408i	0.825313	+	0.564675i	$0.190999\pi$
$822$		0			0
$823$	1.65516	+	0.831255i	0.0576954	+	0.0289757i	0.477413	−	0.878679i	$-0.341575\pi$
$823$	1.65516	+	0.831255i	0.0576954	+	0.0289757i	−0.419718	+	0.907655i	$0.637871\pi$
$824$	−7.20378	+	4.73800i	−0.250955	+	0.165056i
$825$		0			0
$826$	15.2344	+	3.61061i	0.530072	+	0.125629i
$827$	−19.7686	−	7.19517i	−0.687420	−	0.250200i	−0.0253900	−	0.999678i	$-0.508083\pi$
$827$	−19.7686	−	7.19517i	−0.687420	−	0.250200i	−0.662030	+	0.749477i	$0.730305\pi$
$828$		0			0
$829$	−5.33030	+	1.94007i	−0.185129	+	0.0673814i	−0.432921	−	0.901432i	$-0.642517\pi$
$829$	−5.33030	+	1.94007i	−0.185129	+	0.0673814i	0.247792	+	0.968813i	$0.420295\pi$
$830$	−1.86397	+	0.217867i	−0.0646995	+	0.00756228i
$831$		0			0
$832$	9.73087	+	10.3141i	0.337357	+	0.357578i
$833$	20.3841	−	27.3807i	0.706269	−	0.948683i
$834$		0			0
$835$	−4.48592	+	2.25291i	−0.155242	+	0.0779653i
$836$	−15.6738	+	27.1478i	−0.542089	+	0.938925i
$837$		0			0
$838$	−6.14931	−	10.6509i	−0.212424	−	0.367930i
$839$	−19.9919	−	13.1489i	−0.690196	−	0.453949i	0.155345	−	0.987860i	$-0.450351\pi$
$839$	−19.9919	−	13.1489i	−0.690196	−	0.453949i	−0.845540	+	0.533911i	$0.820722\pi$
$840$		0			0
$841$	−11.3175	−	26.2368i	−0.390257	−	0.904717i
$842$	−5.28050	+	17.6381i	−0.181978	+	0.607849i
$843$		0			0
$844$	−0.655533	+	1.51970i	−0.0225644	+	0.0523101i
$845$	−8.14471	−	6.83422i	−0.280186	−	0.235104i
$846$		0			0
$847$	−42.3609	+	35.5450i	−1.45554	+	1.22134i
$848$	−0.842792	−	2.81512i	−0.0289416	−	0.0966717i
$849$		0			0
$850$	−0.584586	−	10.0370i	−0.0200511	−	0.344265i
$851$	0.200918	+	3.44963i	0.00688738	+	0.118252i
$852$		0			0
$853$	−1.93688	−	6.46964i	−0.0663176	−	0.221516i	0.918406	−	0.395638i	$-0.129477\pi$
$853$	−1.93688	−	6.46964i	−0.0663176	−	0.221516i	−0.984724	+	0.174122i	$0.944291\pi$
$854$	−15.4550	+	12.9683i	−0.528860	+	0.443766i
$855$		0			0
$856$	34.1166	+	28.6272i	1.16608	+	0.978457i
$857$	−7.46865	+	17.3143i	−0.255124	+	0.591444i	−0.996854	−	0.0792539i	$-0.974746\pi$
$857$	−7.46865	+	17.3143i	−0.255124	+	0.591444i	0.741730	+	0.670698i	$0.234005\pi$
$858$		0			0
$859$	−9.29717	+	31.0547i	−0.317215	+	1.05957i	0.639559	+	0.768742i	$0.279117\pi$
$859$	−9.29717	+	31.0547i	−0.317215	+	1.05957i	−0.956774	+	0.290831i	$0.906068\pi$
$860$	6.83814	+	15.8526i	0.233179	+	0.540569i
$861$		0			0
$862$	−0.921800	−	0.606277i	−0.0313966	−	0.0206499i
$863$	23.6121	+	40.8973i	0.803765	+	1.39216i	0.917122	+	0.398607i	$0.130506\pi$
$863$	23.6121	+	40.8973i	0.803765	+	1.39216i	−0.113357	+	0.993554i	$0.536160\pi$
$864$		0			0
$865$	−13.8292	+	23.9529i	−0.470208	+	0.814424i
$866$	−9.08673	+	4.56353i	−0.308780	+	0.155075i
$867$		0			0
$868$	2.07540	−	2.78775i	0.0704438	−	0.0946224i
$869$	−38.9955	−	41.3328i	−1.32283	−	1.40212i
$870$		0			0
$871$	23.6533	−	2.76468i	0.801462	−	0.0936775i
$872$	−19.0051	+	6.91730i	−0.643595	+	0.234249i
$873$		0			0
$874$	11.3280	+	4.12304i	0.383174	+	0.139464i
$875$	−42.7607	−	10.1345i	−1.44558	−	0.342608i
$876$		0			0
$877$	−4.70518	+	3.09464i	−0.158883	+	0.104499i	−0.626461	−	0.779453i	$-0.715497\pi$
$877$	−4.70518	+	3.09464i	−0.158883	+	0.104499i	0.467578	+	0.883952i	$0.345127\pi$
$878$	−14.4840	−	7.27416i	−0.488813	−	0.245491i
$879$		0			0
$880$	3.63729	−	3.85530i	0.122613	−	0.129962i
$881$	−0.984686	−	5.58443i	−0.0331749	−	0.188144i	0.963717	−	0.266926i	$-0.0860080\pi$
$881$	−0.984686	−	5.58443i	−0.0331749	−	0.188144i	−0.996892	+	0.0787820i	$0.974897\pi$
$882$		0			0
$883$	5.95650	−	33.7810i	0.200452	−	1.13682i	−0.703985	−	0.710215i	$-0.748598\pi$
$883$	5.95650	−	33.7810i	0.200452	−	1.13682i	0.904437	−	0.426606i	$-0.140291\pi$
$884$	17.0759	+	22.9369i	0.574324	+	0.771452i
$885$		0			0
$886$	−25.8316	+	6.12221i	−0.867830	+	0.205680i
$887$	−26.7020	−	3.12102i	−0.896567	−	0.104794i	−0.344687	−	0.938718i	$-0.612015\pi$
$887$	−26.7020	−	3.12102i	−0.896567	−	0.104794i	−0.551879	+	0.833924i	$0.686089\pi$
$888$		0			0
$889$	0.858840	−	14.7457i	0.0288046	−	0.494556i
$890$	−1.20683			−0.0404531
$891$		0			0
$892$	20.6987			0.693043
$893$	2.05976	−	35.3647i	0.0689273	−	1.18344i
$894$		0			0
$895$	17.4788	+	2.04298i	0.584252	+	0.0682892i
$896$	−34.1593	+	8.09590i	−1.14118	+	0.270465i
$897$		0			0
$898$	−0.560327	−	0.752650i	−0.0186984	−	0.0251163i
$899$	0.0746222	−	0.423204i	0.00248879	−	0.0141146i
$900$		0			0
$901$	3.30159	+	18.7243i	0.109992	+	0.623796i
$902$	−1.85100	+	1.96195i	−0.0616317	+	0.0653258i
$903$		0			0
$904$	−23.7165	−	11.9109i	−0.788798	−	0.396149i
$905$	−19.5279	+	12.8437i	−0.649128	+	0.426938i
$906$		0			0
$907$	29.6181	+	7.01961i	0.983452	+	0.233082i	0.690728	−	0.723115i	$-0.257290\pi$
$907$	29.6181	+	7.01961i	0.983452	+	0.233082i	0.292724	+	0.956197i	$0.405438\pi$
$908$	−32.1114	−	11.6876i	−1.06565	−	0.387866i
$909$		0			0
$910$	−18.5699	+	6.75888i	−0.615585	+	0.224055i
$911$	−13.9708	+	1.63296i	−0.462875	+	0.0541023i	−0.344335	−	0.938847i	$-0.611895\pi$
$911$	−13.9708	+	1.63296i	−0.462875	+	0.0541023i	−0.118540	+	0.992949i	$0.537821\pi$
$912$		0			0
$913$	−5.62478	−	5.96192i	−0.186153	−	0.197311i
$914$	14.9595	−	20.0941i	0.494816	−	0.664653i
$915$		0			0
$916$	−1.89562	+	0.952017i	−0.0626331	+	0.0314555i
$917$	−31.6440	+	54.8090i	−1.04498	+	1.80995i
$918$		0			0
$919$	−14.5007	−	25.1160i	−0.478335	−	0.828501i	0.521356	−	0.853339i	$-0.325426\pi$
$919$	−14.5007	−	25.1160i	−0.478335	−	0.828501i	−0.999691	+	0.0248384i	$0.992093\pi$
$920$	−11.3215	−	7.44628i	−0.373260	−	0.245497i
$921$		0			0
$922$	−0.104223	−	0.241615i	−0.00343239	−	0.00795717i
$923$	−7.90183	+	26.3939i	−0.260092	+	0.868767i
$924$		0			0
$925$	−1.11215	+	2.57825i	−0.0365672	+	0.0847724i
$926$	1.76780	+	1.48336i	0.0580935	+	0.0487462i
$927$		0			0
$928$	−2.92661	+	2.45572i	−0.0960706	+	0.0806128i
$929$	12.7796	+	42.6869i	0.419286	+	1.40051i	0.863390	+	0.504537i	$0.168337\pi$
$929$	12.7796	+	42.6869i	0.419286	+	1.40051i	−0.444104	+	0.895975i	$0.646478\pi$
$930$		0			0
$931$	1.93382	+	33.2024i	0.0633783	+	1.08816i
$932$	1.13567	+	19.4987i	0.0372002	+	0.638702i
$933$		0			0
$934$	0.848246	+	2.83334i	0.0277555	+	0.0927097i
$935$	−26.2707	+	22.0437i	−0.859143	+	0.720907i
$936$		0			0
$937$	−15.7744	−	13.2363i	−0.515326	−	0.432409i	0.347673	−	0.937616i	$-0.386972\pi$
$937$	−15.7744	−	13.2363i	−0.515326	−	0.432409i	−0.862999	+	0.505206i	$0.831416\pi$
$938$	6.23793	−	14.4611i	0.203676	−	0.472173i
$939$		0			0
$940$	−4.68115	+	15.6361i	−0.152682	+	0.509995i
$941$	22.4902	+	52.1381i	0.733160	+	1.69966i	0.714307	+	0.699833i	$0.246742\pi$
$941$	22.4902	+	52.1381i	0.733160	+	1.69966i	0.0188529	+	0.999822i	$0.493999\pi$
$942$		0			0
$943$	−1.97098	−	1.29633i	−0.0641838	−	0.0422144i
$944$	−1.86608	−	3.23215i	−0.0607359	−	0.105198i
$945$		0			0
$946$	16.5775	−	28.7131i	0.538982	−	0.933544i
$947$	−14.0976	+	7.08007i	−0.458110	+	0.230071i	−0.662861	−	0.748743i	$-0.730658\pi$
$947$	−14.0976	+	7.08007i	−0.458110	+	0.230071i	0.204751	+	0.978814i	$0.434362\pi$
$948$		0			0
$949$	11.8076	−	15.8603i	0.383290	−	0.514848i
$950$	6.72227	+	7.12519i	0.218099	+	0.231172i
$951$		0			0
$952$	45.8249	−	5.35617i	1.48519	−	0.173594i
$953$	47.3933	−	17.2497i	1.53522	−	0.558774i	0.570326	−	0.821418i	$-0.306817\pi$
$953$	47.3933	−	17.2497i	1.53522	−	0.558774i	0.964893	+	0.262645i	$0.0845947\pi$
$954$		0			0
$955$	8.02382	+	2.92043i	0.259645	+	0.0945030i
$956$	30.9783	+	7.34198i	1.00191	+	0.237457i
$957$		0			0
$958$	−2.06781	+	1.36002i	−0.0668080	+	0.0439403i
$959$	−31.5096	−	15.8247i	−1.01750	−	0.511006i
$960$		0			0
$961$	20.9762	−	22.2335i	0.676653	−	0.717210i
$962$	0.609760	+	3.45812i	0.0196594	+	0.111494i
$963$		0			0
$964$	1.70519	−	9.67059i	0.0549203	−	0.311469i
$965$	−0.155410	−	0.208751i	−0.00500281	−	0.00671994i
$966$		0			0
$967$	21.3040	−	5.04915i	0.685092	−	0.162370i	0.126692	−	0.991942i	$-0.459564\pi$
$967$	21.3040	−	5.04915i	0.685092	−	0.162370i	0.558399	+	0.829572i	$0.311416\pi$
$968$	−38.2725	−	4.47342i	−1.23013	−	0.143781i
$969$		0			0
$970$	−0.335645	+	5.76280i	−0.0107769	+	0.185032i
$971$	−21.3313			−0.684555			−0.342277	−	0.939599i	$-0.611198\pi$
$971$	−21.3313			−0.684555			−0.342277	+	0.939599i	$0.611198\pi$
$972$		0			0
$973$	−60.5205			−1.94020
$974$	0.0556682	−	0.955786i	0.00178372	−	0.0306254i
$975$		0			0
$976$	4.77681	+	0.558329i	0.152902	+	0.0178717i
$977$	6.97799	−	1.65381i	0.223246	−	0.0529102i	−0.117471	−	0.993076i	$-0.537479\pi$
$977$	6.97799	−	1.65381i	0.223246	−	0.0529102i	0.340716	+	0.940166i	$0.389330\pi$
$978$		0			0
$979$	−3.14760	−	4.22796i	−0.100598	−	0.135126i
$980$	2.66095	−	15.0910i	0.0850011	−	0.482065i
$981$		0			0
$982$	5.50290	+	31.2085i	0.175605	+	0.995904i
$983$	28.4197	−	30.1231i	0.906447	−	0.960777i	−0.0929443	−	0.995671i	$-0.529628\pi$
$983$	28.4197	−	30.1231i	0.906447	−	0.960777i	0.999391	+	0.0348939i	$0.0111093\pi$
$984$		0			0
$985$	−14.8406	−	7.45323i	−0.472861	−	0.237480i
$986$	1.95361	−	1.28491i	0.0622156	−	0.0409199i
$987$		0			0
$988$	−27.1099	−	6.42517i	−0.862481	−	0.204412i
$989$	27.2487	+	9.91773i	0.866460	+	0.315365i
$990$		0			0
$991$	51.2878	−	18.6672i	1.62921	−	0.592984i	0.644105	−	0.764937i	$-0.277230\pi$
$991$	51.2878	−	18.6672i	1.62921	−	0.592984i	0.985105	+	0.171953i	$0.0550079\pi$
$992$	3.82487	−	0.447063i	0.121440	−	0.0141943i
$993$		0			0
$994$	12.5037	+	13.2532i	0.396594	+	0.420365i
$995$	18.1075	−	24.3226i	0.574046	−	0.771077i
$996$		0			0
$997$	−23.6921	+	11.8986i	−0.750338	+	0.376834i	−0.782501	−	0.622649i	$-0.786056\pi$
$997$	−23.6921	+	11.8986i	−0.750338	+	0.376834i	0.0321637	+	0.999483i	$0.489760\pi$
$998$	−16.0810	+	27.8531i	−0.509035	+	0.881674i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.217.5		144
3.2	odd	2		729.2.g.a.217.4		144
9.2	odd	6		243.2.g.a.73.5		144
9.4	even	3		729.2.g.c.703.5		144
9.5	odd	6		729.2.g.b.703.4		144
9.7	even	3		81.2.g.a.25.4	yes	144
81.11	odd	54		6561.2.a.d.1.43		72
81.13	even	27		729.2.g.c.28.5		144
81.14	odd	54		243.2.g.a.10.5		144
81.40	even	27	inner	729.2.g.d.514.5		144
81.41	odd	54		729.2.g.a.514.4		144
81.67	even	27		81.2.g.a.13.4	✓	144
81.68	odd	54		729.2.g.b.28.4		144
81.70	even	27		6561.2.a.c.1.30		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.4	✓	144	81.67	even	27
81.2.g.a.25.4	yes	144	9.7	even	3
243.2.g.a.10.5		144	81.14	odd	54
243.2.g.a.73.5		144	9.2	odd	6
729.2.g.a.217.4		144	3.2	odd	2
729.2.g.a.514.4		144	81.41	odd	54
729.2.g.b.28.4		144	81.68	odd	54
729.2.g.b.703.4		144	9.5	odd	6
729.2.g.c.28.5		144	81.13	even	27
729.2.g.c.703.5		144	9.4	even	3
729.2.g.d.217.5		144	1.1	even	1	trivial
729.2.g.d.514.5		144	81.40	even	27	inner
6561.2.a.c.1.30		72	81.70	even	27
6561.2.a.d.1.43		72	81.11	odd	54

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)

\(f(q)\)	\(=\)	\(q+(0.0454430 - 0.780226i) q^{2} +(1.37979 + 0.161274i) q^{4} +(-1.44081 + 0.341479i) q^{5} +(-2.26996 - 3.04908i) q^{7} +(0.459961 - 2.60857i) q^{8} +(0.200956 + 1.13968i) q^{10} +(-3.46856 + 3.67646i) q^{11} +(-4.01443 - 2.01612i) q^{13} +(-2.48212 + 1.63252i) q^{14} +(0.689105 + 0.163321i) q^{16} +(-4.30582 - 1.56719i) q^{17} +(4.19524 - 1.52694i) q^{19} +(-2.04309 + 0.238803i) q^{20} +(2.71085 + 2.87333i) q^{22} +(-2.06314 + 2.77128i) q^{23} +(-2.50883 + 1.25998i) q^{25} +(-1.75546 + 3.04054i) q^{26} +(-2.64032 - 4.57318i) q^{28} +(-0.545523 - 0.358796i) q^{29} +(0.260680 + 0.604325i) q^{31} +(1.67812 - 5.60530i) q^{32} +(-1.41843 + 3.28829i) q^{34} +(4.31178 + 3.61801i) q^{35} +(0.766165 - 0.642889i) q^{37} +(-1.00072 - 3.34263i) q^{38} +(0.228053 + 3.91553i) q^{40} +(0.0397020 + 0.681658i) q^{41} +(-2.40716 - 8.04048i) q^{43} +(-5.37881 + 4.51336i) q^{44} +(2.06847 + 1.73565i) q^{46} +(3.14280 - 7.28584i) q^{47} +(-2.13657 + 7.13664i) q^{49} +(0.869061 + 2.01471i) q^{50} +(-5.21392 - 3.42925i) q^{52} +(-2.07469 - 3.59347i) q^{53} +(3.74212 - 6.48154i) q^{55} +(-8.99782 + 4.51888i) q^{56} +(-0.304732 + 0.409326i) q^{58} +(-3.61647 - 3.83324i) q^{59} +(6.74505 - 0.788383i) q^{61} +(0.483356 - 0.175927i) q^{62} +(-2.96617 - 1.07960i) q^{64} +(6.47250 + 1.53401i) q^{65} +(-4.42909 + 2.91306i) q^{67} +(-5.68837 - 2.85681i) q^{68} +(3.01881 - 3.19975i) q^{70} +(-1.06500 - 6.03991i) q^{71} +(-0.764322 + 4.33469i) q^{73} +(-0.466781 - 0.626996i) q^{74} +(6.03481 - 1.43028i) q^{76} +(19.0833 + 2.23052i) q^{77} +(-0.653695 + 11.2235i) q^{79} -1.04864 q^{80} +0.533651 q^{82} +(-0.0942903 + 1.61890i) q^{83} +(6.73904 + 0.787681i) q^{85} +(-6.38278 + 1.51275i) q^{86} +(7.99490 + 10.7390i) q^{88} +(-0.181087 + 1.02699i) q^{89} +(2.96526 + 16.8168i) q^{91} +(-3.29364 + 3.49105i) q^{92} +(-5.54178 - 2.78318i) q^{94} +(-5.52314 + 3.63263i) q^{95} +(4.85369 + 1.15034i) q^{97} +(5.47110 + 1.99132i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 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

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