LMFDB - Embedded newform 567.2.ba.a.341.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] 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("567.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			341.15
Character	$\chi$	$=$	567.341
Dual form			567.2.ba.a.143.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.582560 + 0.694268i) q^{2} +(0.204665 - 1.16071i) q^{4} +(0.931176 + 0.781349i) q^{5} +(-2.06750 + 1.65089i) q^{7} +(2.49483 - 1.44039i) q^{8} +1.10167i q^{10} +(2.30628 + 2.74851i) q^{11} +(0.206055 + 0.566132i) q^{13} +(-2.35060 - 0.473658i) q^{14} +(0.238336 + 0.0867472i) q^{16} +7.94939 q^{17} +1.41477i q^{19} +(1.09750 - 0.920911i) q^{20} +(-0.564660 + 3.20235i) q^{22} +(0.349041 + 0.958983i) q^{23} +(-0.611659 - 3.46889i) q^{25} +(-0.273008 + 0.472864i) q^{26} +(1.49306 + 2.73765i) q^{28} +(0.413325 - 1.13560i) q^{29} +(8.17053 + 1.44069i) q^{31} +(-1.89196 - 5.19810i) q^{32} +(4.63100 + 5.51901i) q^{34} +(-3.21513 - 0.0781722i) q^{35} +(-4.22521 - 7.31828i) q^{37} +(-0.982231 + 0.824190i) q^{38} +(3.44858 + 0.608078i) q^{40} +(-6.73814 + 2.45248i) q^{41} +(1.41438 + 8.02135i) q^{43} +(3.66224 - 2.11440i) q^{44} +(-0.462454 + 0.800993i) q^{46} +(0.0548081 + 0.310832i) q^{47} +(1.54913 - 6.82643i) q^{49} +(2.05201 - 2.44549i) q^{50} +(0.699288 - 0.123303i) q^{52} +(-5.74259 + 3.31549i) q^{53} +4.36136i q^{55} +(-2.78014 + 7.09671i) q^{56} +(1.02920 - 0.374598i) q^{58} +(0.936973 - 0.341030i) q^{59} +(-12.0683 + 2.12796i) q^{61} +(3.75960 + 6.51182i) q^{62} +(2.76033 - 4.78103i) q^{64} +(-0.250473 + 0.688170i) q^{65} +(-7.90859 - 6.63609i) q^{67} +(1.62696 - 9.22694i) q^{68} +(-1.81873 - 2.27770i) q^{70} +(0.952881 + 0.550146i) q^{71} +(-0.808112 - 0.466563i) q^{73} +(2.61941 - 7.19676i) q^{74} +(1.64214 + 0.289554i) q^{76} +(-9.30573 - 1.87515i) q^{77} +(-10.3048 + 8.64674i) q^{79} +(0.154153 + 0.267000i) q^{80} +(-5.62805 - 3.24936i) q^{82} +(5.66119 + 2.06050i) q^{83} +(7.40228 + 6.21125i) q^{85} +(-4.74500 + 5.65488i) q^{86} +(9.71272 + 3.53514i) q^{88} +5.92334 q^{89} +(-1.36064 - 0.830305i) q^{91} +(1.18454 - 0.208866i) q^{92} +(-0.183872 + 0.219130i) q^{94} +(-1.10543 + 1.31740i) q^{95} +(-8.29293 + 1.46227i) q^{97} +(5.64183 - 2.90130i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.582560	+	0.694268i	0.411932	+	0.490922i	0.931620	−	0.363435i	$-0.118396\pi$
$2$	0.582560	+	0.694268i	0.411932	+	0.490922i	−0.519688	+	0.854356i	$0.673952\pi$
$3$		0			0
$3$		0			0
$4$	0.204665	−	1.16071i	0.102332	−	0.580355i
$5$	0.931176	+	0.781349i	0.416434	+	0.349430i	0.826805	−	0.562489i	$-0.190156\pi$
$5$	0.931176	+	0.781349i	0.416434	+	0.349430i	−0.410370	+	0.911919i	$0.634601\pi$
$6$		0			0
$7$	−2.06750	+	1.65089i	−0.781442	+	0.623978i
$7$	−2.06750	+	1.65089i	−0.781442	+	0.623978i
$8$	2.49483	−	1.44039i	0.882057	−	0.509256i
$9$		0			0
$10$			1.10167i			0.348378i
$11$	2.30628	+	2.74851i	0.695369	+	0.828708i	0.991994	−	0.126286i	$-0.0403056\pi$
$11$	2.30628	+	2.74851i	0.695369	+	0.828708i	−0.296625	+	0.954994i	$0.595861\pi$
$12$		0			0
$13$	0.206055	+	0.566132i	0.0571495	+	0.157017i	0.964982	−	0.262316i	$-0.0844863\pi$
$13$	0.206055	+	0.566132i	0.0571495	+	0.157017i	−0.907833	+	0.419333i	$0.862264\pi$
$14$	−2.35060	−	0.473658i	−0.628225	−	0.126590i
$15$		0			0
$16$	0.238336	+	0.0867472i	0.0595840	+	0.0216868i
$17$	7.94939			1.92801			0.964005	−	0.265883i	$-0.0856635\pi$
$17$	7.94939			1.92801			0.964005	+	0.265883i	$0.0856635\pi$
$18$		0			0
$19$			1.41477i			0.324571i	0.986744	+	0.162286i	$0.0518866\pi$
$19$			1.41477i			0.324571i	−0.986744	+	0.162286i	$0.948113\pi$
$20$	1.09750	−	0.920911i	0.245408	−	0.205922i
$21$		0			0
$22$	−0.564660	+	3.20235i	−0.120386	+	0.682743i
$23$	0.349041	+	0.958983i	0.0727802	+	0.199962i	0.970749	−	0.240098i	$-0.0771795\pi$
$23$	0.349041	+	0.958983i	0.0727802	+	0.199962i	−0.897969	+	0.440060i	$0.854957\pi$
$24$		0			0
$25$	−0.611659	−	3.46889i	−0.122332	−	0.693778i
$26$	−0.273008	+	0.472864i	−0.0535413	+	0.0927362i
$27$		0			0
$28$	1.49306	+	2.73765i	0.282162	+	0.517367i
$29$	0.413325	−	1.13560i	0.0767526	−	0.210876i	−0.895382	−	0.445298i	$-0.853098\pi$
$29$	0.413325	−	1.13560i	0.0767526	−	0.210876i	0.972135	+	0.234422i	$0.0753199\pi$
$30$		0			0
$31$	8.17053	+	1.44069i	1.46747	+	0.258755i	0.849560	−	0.527493i	$-0.176868\pi$
$31$	8.17053	+	1.44069i	1.46747	+	0.258755i	0.617912	+	0.786247i	$0.287979\pi$
$32$	−1.89196	−	5.19810i	−0.334454	−	0.918904i
$33$		0			0
$34$	4.63100	+	5.51901i	0.794209	+	0.946502i
$35$	−3.21513	−	0.0781722i	−0.543456	−	0.0132135i
$36$		0			0
$37$	−4.22521	−	7.31828i	−0.694620	−	1.20312i	−0.970309	−	0.241870i	$-0.922239\pi$
$37$	−4.22521	−	7.31828i	−0.694620	−	1.20312i	0.275689	−	0.961247i	$-0.411094\pi$
$38$	−0.982231	+	0.824190i	−0.159339	+	0.133701i
$39$		0			0
$40$	3.44858	+	0.608078i	0.545268	+	0.0961455i
$41$	−6.73814	+	2.45248i	−1.05232	+	0.383013i	−0.809538	−	0.587067i	$-0.800282\pi$
$41$	−6.73814	+	2.45248i	−1.05232	+	0.383013i	−0.242782	+	0.970081i	$0.578060\pi$
$42$		0			0
$43$	1.41438	+	8.02135i	0.215691	+	1.22324i	0.879703	+	0.475523i	$0.157741\pi$
$43$	1.41438	+	8.02135i	0.215691	+	1.22324i	−0.664012	+	0.747722i	$0.731148\pi$
$44$	3.66224	−	2.11440i	0.552104	−	0.318757i
$45$		0			0
$46$	−0.462454	+	0.800993i	−0.0681851	+	0.118100i
$47$	0.0548081	+	0.310832i	0.00799458	+	0.0453395i	0.988544	−	0.150932i	$-0.0482276\pi$
$47$	0.0548081	+	0.310832i	0.00799458	+	0.0453395i	−0.980550	+	0.196272i	$0.937116\pi$
$48$		0			0
$49$	1.54913	−	6.82643i	0.221304	−	0.975205i
$50$	2.05201	−	2.44549i	0.290198	−	0.345845i
$51$		0			0
$52$	0.699288	−	0.123303i	0.0969738	−	0.0170991i
$53$	−5.74259	+	3.31549i	−0.788806	+	0.455417i	−0.839542	−	0.543295i	$-0.817177\pi$
$53$	−5.74259	+	3.31549i	−0.788806	+	0.455417i	0.0507361	+	0.998712i	$0.483843\pi$
$54$		0			0
$55$			4.36136i			0.588085i
$56$	−2.78014	+	7.09671i	−0.371512	+	0.948338i
$57$		0			0
$58$	1.02920	−	0.374598i	0.135140	−	0.0491871i
$59$	0.936973	−	0.341030i	0.121983	−	0.0443983i	−0.280307	−	0.959910i	$-0.590436\pi$
$59$	0.936973	−	0.341030i	0.121983	−	0.0443983i	0.402291	+	0.915512i	$0.368214\pi$
$60$		0			0
$61$	−12.0683	+	2.12796i	−1.54518	+	0.272458i	−0.880274	−	0.474465i	$-0.842641\pi$
$61$	−12.0683	+	2.12796i	−1.54518	+	0.272458i	−0.664911	+	0.746923i	$0.731530\pi$
$62$	3.75960	+	6.51182i	0.477470	+	0.827003i
$63$		0			0
$64$	2.76033	−	4.78103i	0.345041	−	0.597629i
$65$	−0.250473	+	0.688170i	−0.0310674	+	0.0853570i
$66$		0			0
$67$	−7.90859	−	6.63609i	−0.966188	−	0.810728i	0.0157609	−	0.999876i	$-0.494983\pi$
$67$	−7.90859	−	6.63609i	−0.966188	−	0.810728i	−0.981949	+	0.189148i	$0.939427\pi$
$68$	1.62696	−	9.22694i	0.197298	−	1.11893i
$69$		0			0
$70$	−1.81873	−	2.27770i	−0.217380	−	0.272237i
$71$	0.952881	+	0.550146i	0.113086	+	0.0652904i	0.555476	−	0.831532i	$-0.312536\pi$
$71$	0.952881	+	0.550146i	0.113086	+	0.0652904i	−0.442390	+	0.896823i	$0.645869\pi$
$72$		0			0
$73$	−0.808112	−	0.466563i	−0.0945823	−	0.0546071i	0.451963	−	0.892037i	$-0.350724\pi$
$73$	−0.808112	−	0.466563i	−0.0945823	−	0.0546071i	−0.546545	+	0.837430i	$0.684057\pi$
$74$	2.61941	−	7.19676i	0.304500	−	0.836606i
$75$		0			0
$76$	1.64214	+	0.289554i	0.188366	+	0.0332141i
$77$	−9.30573	−	1.87515i	−1.06049	−	0.213693i
$78$		0			0
$79$	−10.3048	+	8.64674i	−1.15938	+	0.972834i	−0.999897	−	0.0143668i	$-0.995427\pi$
$79$	−10.3048	+	8.64674i	−1.15938	+	0.972834i	−0.159482	+	0.987201i	$0.550982\pi$
$80$	0.154153	+	0.267000i	0.0172348	+	0.0298516i
$81$		0			0
$82$	−5.62805	−	3.24936i	−0.621514	−	0.358831i
$83$	5.66119	+	2.06050i	0.621396	+	0.226170i	0.633482	−	0.773757i	$-0.281625\pi$
$83$	5.66119	+	2.06050i	0.621396	+	0.226170i	−0.0120862	+	0.999927i	$0.503847\pi$
$84$		0			0
$85$	7.40228	+	6.21125i	0.802890	+	0.673705i
$86$	−4.74500	+	5.65488i	−0.511667	+	0.609781i
$87$		0			0
$88$	9.71272	+	3.53514i	1.03538	+	0.376847i
$89$	5.92334			0.627873			0.313937	−	0.949444i	$-0.398352\pi$
$89$	5.92334			0.627873			0.313937	+	0.949444i	$0.398352\pi$
$90$		0			0
$91$	−1.36064	−	0.830305i	−0.142634	−	0.0870396i
$92$	1.18454	−	0.208866i	0.123497	−	0.0217758i
$93$		0			0
$94$	−0.183872	+	0.219130i	−0.0189649	+	0.0226015i
$95$	−1.10543	+	1.31740i	−0.113415	+	0.135163i
$96$		0			0
$97$	−8.29293	+	1.46227i	−0.842019	+	0.148471i	−0.577990	−	0.816044i	$-0.696163\pi$
$97$	−8.29293	+	1.46227i	−0.842019	+	0.148471i	−0.264029	+	0.964515i	$0.585052\pi$
$98$	5.64183	−	2.90130i	0.569911	−	0.293075i
$99$		0			0
$100$	−4.15156			−0.415156
$101$	−2.32994	−	0.848029i	−0.231838	−	0.0843821i	0.223489	−	0.974706i	$-0.428255\pi$
$101$	−2.32994	−	0.848029i	−0.231838	−	0.0843821i	−0.455327	+	0.890324i	$0.650478\pi$
$102$		0			0
$103$	6.14176	−	7.31947i	0.605166	−	0.721208i	−0.373279	−	0.927719i	$-0.621766\pi$
$103$	6.14176	−	7.31947i	0.605166	−	0.721208i	0.978444	+	0.206511i	$0.0662109\pi$
$104$	1.32953	+	1.11561i	0.130371	+	0.109394i
$105$		0			0
$106$	−5.64724	−	2.05543i	−0.548509	−	0.199641i
$107$	−10.6429	−	6.14467i	−1.02889	−	0.594028i	−0.112221	−	0.993683i	$-0.535797\pi$
$107$	−10.6429	−	6.14467i	−1.02889	−	0.594028i	−0.916666	+	0.399655i	$0.869130\pi$
$108$		0			0
$109$	−4.67103	−	8.09046i	−0.447404	−	0.774926i	0.550813	−	0.834629i	$-0.314318\pi$
$109$	−4.67103	−	8.09046i	−0.447404	−	0.774926i	−0.998216	+	0.0597033i	$0.980985\pi$
$110$	−3.02795	+	2.54075i	−0.288704	+	0.242251i
$111$		0			0
$112$	−0.635970	+	0.214116i	−0.0600935	+	0.0202321i
$113$	−3.90833	−	0.689145i	−0.367665	−	0.0648293i	−0.0132365	−	0.999912i	$-0.504213\pi$
$113$	−3.90833	−	0.689145i	−0.367665	−	0.0648293i	−0.354428	+	0.935083i	$0.615325\pi$
$114$		0			0
$115$	−0.424282	+	1.16571i	−0.0395645	+	0.108703i
$116$	−1.23351	−	0.712168i	−0.114529	−	0.0661232i
$117$		0			0
$118$	0.782609	+	0.451839i	0.0720450	+	0.0415952i
$119$	−16.4354	+	13.1236i	−1.50663	+	1.20304i
$120$		0			0
$121$	−0.325286	+	1.84479i	−0.0295714	+	0.167708i
$122$	−8.50787	−	7.13895i	−0.770267	−	0.646330i
$123$		0			0
$124$	3.34444	−	9.18877i	0.300339	−	0.825176i
$125$	5.17976	−	8.97161i	0.463292	−	0.802445i
$126$		0			0
$127$	−7.34765	−	12.7265i	−0.651998	−	1.12929i	−0.982637	−	0.185537i	$-0.940598\pi$
$127$	−7.34765	−	12.7265i	−0.651998	−	1.12929i	0.330639	−	0.943757i	$-0.392736\pi$
$128$	−5.96796	+	1.05231i	−0.527498	+	0.0930121i
$129$		0			0
$130$	−0.623690	+	0.227005i	−0.0547012	+	0.0199096i
$131$	16.6664	−	6.06609i	1.45615	−	0.529996i	0.511850	−	0.859075i	$-0.328960\pi$
$131$	16.6664	−	6.06609i	1.45615	−	0.529996i	0.944303	+	0.329078i	$0.106738\pi$
$132$		0			0
$133$	−2.33563	−	2.92504i	−0.202525	−	0.253634i
$134$		−	9.35660i		−	0.808287i
$135$		0			0
$136$	19.8324	−	11.4503i	1.70062	−	0.981851i
$137$	−3.29168	+	0.580412i	−0.281227	+	0.0495879i	−0.312483	−	0.949923i	$-0.601161\pi$
$137$	−3.29168	+	0.580412i	−0.281227	+	0.0495879i	0.0312554	+	0.999511i	$0.490049\pi$
$138$		0			0
$139$	2.56143	−	3.05259i	0.217257	−	0.258917i	−0.646397	−	0.763001i	$-0.723725\pi$
$139$	2.56143	−	3.05259i	0.217257	−	0.258917i	0.863655	+	0.504084i	$0.168170\pi$
$140$	−0.748758	+	3.71583i	−0.0632816	+	0.314045i
$141$		0			0
$142$	0.173162	+	0.982048i	0.0145314	+	0.0824117i
$143$	−1.08080	+	1.87200i	−0.0903812	+	0.156545i
$144$		0			0
$145$	1.27218	−	0.734493i	0.105649	−	0.0609964i
$146$	−0.146853	−	0.832847i	−0.0121537	−	0.0689269i
$147$		0			0
$148$	−9.35915	+	3.40645i	−0.769317	+	0.280009i
$149$	13.8612	+	2.44410i	1.13555	+	0.200228i	0.709659	−	0.704546i	$-0.248849\pi$
$149$	13.8612	+	2.44410i	1.13555	+	0.200228i	0.425892	+	0.904774i	$0.359960\pi$
$150$		0			0
$151$	10.1132	−	8.48596i	0.822998	−	0.690577i	−0.130674	−	0.991425i	$-0.541714\pi$
$151$	10.1132	−	8.48596i	0.822998	−	0.690577i	0.953672	+	0.300848i	$0.0972697\pi$
$152$	2.03783	+	3.52962i	0.165290	+	0.286290i
$153$		0			0
$154$	−4.11929	−	7.55305i	−0.331942	−	0.608642i
$155$	6.48252	+	7.72557i	0.520689	+	0.620533i
$156$		0			0
$157$	−1.70932	−	4.69633i	−0.136419	−	0.374808i	0.852606	−	0.522554i	$-0.175021\pi$
$157$	−1.70932	−	4.69633i	−0.136419	−	0.374808i	−0.989025	+	0.147746i	$0.952798\pi$
$158$	−12.0063	−	2.11704i	−0.955170	−	0.168422i
$159$		0			0
$160$	2.29979	−	6.31863i	0.181815	−	0.499531i
$161$	−2.30482	−	1.40647i	−0.181645	−	0.110845i
$162$		0			0
$163$	−1.07224	+	1.85718i	−0.0839847	+	0.145466i	−0.904958	−	0.425501i	$-0.860098\pi$
$163$	−1.07224	+	1.85718i	−0.0839847	+	0.145466i	0.820973	+	0.570966i	$0.193431\pi$
$164$	1.46756	+	8.32296i	0.114597	+	0.649914i
$165$		0			0
$166$	1.86744	+	5.13075i	0.144941	+	0.398223i
$167$	−2.40447	+	13.6365i	−0.186064	+	1.05522i	0.738517	+	0.674235i	$0.235526\pi$
$167$	−2.40447	+	13.6365i	−0.186064	+	1.05522i	−0.924581	+	0.380986i	$0.875585\pi$
$168$		0			0
$169$	9.68053	−	8.12293i	0.744656	−	0.624841i
$170$			8.75759i			0.671677i
$171$		0			0
$172$	9.59994			0.731988
$173$	3.40013	+	1.23754i	0.258507	+	0.0940888i	0.468023	−	0.883716i	$-0.344967\pi$
$173$	3.40013	+	1.23754i	0.258507	+	0.0940888i	−0.209516	+	0.977805i	$0.567189\pi$
$174$		0			0
$175$	6.99136	+	6.16216i	0.528498	+	0.465815i
$176$	0.311243	+	0.855133i	0.0234608	+	0.0644581i
$177$		0			0
$178$	3.45070	+	4.11239i	0.258641	+	0.308236i
$179$		−	24.4587i		−	1.82813i	−0.405573	−	0.914063i	$-0.632928\pi$
$179$		−	24.4587i		−	1.82813i	0.405573	−	0.914063i	$-0.367072\pi$
$180$		0			0
$181$	−13.8640	+	8.00438i	−1.03050	+	0.594961i	−0.917129	−	0.398591i	$-0.869499\pi$
$181$	−13.8640	+	8.00438i	−1.03050	+	0.594961i	−0.113374	+	0.993552i	$0.536166\pi$
$182$	−0.216201	−	1.42835i	−0.0160259	−	0.105877i
$183$		0			0
$184$	2.25211	+	1.88975i	0.166028	+	0.139314i
$185$	1.78372	−	10.1160i	0.131142	−	0.743740i
$186$		0			0
$187$	18.3335	+	21.8490i	1.34068	+	1.59776i
$188$	0.372003			0.0271311
$189$		0			0
$190$	−1.55861			−0.113073
$191$	−4.13129	−	4.92349i	−0.298930	−	0.356251i	0.595582	−	0.803294i	$-0.296921\pi$
$191$	−4.13129	−	4.92349i	−0.298930	−	0.356251i	−0.894512	+	0.447043i	$0.852477\pi$
$192$		0			0
$193$	−0.237958	+	1.34953i	−0.0171286	+	0.0971411i	−0.992174	−	0.124866i	$-0.960150\pi$
$193$	−0.237958	+	1.34953i	−0.0171286	+	0.0971411i	0.975045	+	0.222007i	$0.0712609\pi$
$194$	−5.84633	−	4.90566i	−0.419742	−	0.352206i
$195$		0			0
$196$	−7.60646	−	3.19522i	−0.543319	−	0.228230i
$197$	−19.2475	+	11.1125i	−1.37132	+	0.791734i	−0.991095	−	0.133158i	$-0.957488\pi$
$197$	−19.2475	+	11.1125i	−1.37132	+	0.791734i	−0.380229	+	0.924892i	$0.624155\pi$
$198$		0			0
$199$			13.3056i			0.943207i	0.881811	+	0.471603i	$0.156325\pi$
$199$			13.3056i			0.943207i	−0.881811	+	0.471603i	$0.843675\pi$
$200$	−6.52256	−	7.77328i	−0.461215	−	0.549654i
$201$		0			0
$202$	−0.768571	−	2.11163i	−0.0540765	−	0.148574i
$203$	1.02020	+	3.03021i	0.0716042	+	0.212679i
$204$		0			0
$205$	−8.19064	−	2.98115i	−0.572059	−	0.208212i
$206$	8.65961			0.603344
$207$		0			0
$208$			0.152804i			0.0105951i
$209$	−3.88852	+	3.26286i	−0.268975	+	0.225697i
$210$		0			0
$211$	−2.63818	+	14.9619i	−0.181620	+	1.03002i	0.748602	+	0.663019i	$0.230725\pi$
$211$	−2.63818	+	14.9619i	−0.181620	+	1.03002i	−0.930222	+	0.366997i	$0.880386\pi$
$212$	2.67302	+	7.34405i	0.183583	+	0.504391i
$213$		0			0
$214$	−1.93407	−	10.9687i	−0.132210	−	0.749802i
$215$	−4.95044	+	8.57441i	−0.337617	+	0.584770i
$216$		0			0
$217$	−19.2710	+	10.5100i	−1.30820	+	0.713467i
$218$	2.89579	−	7.95612i	0.196128	−	0.538857i
$219$		0			0
$220$	5.06227	+	0.892615i	0.341298	+	0.0601801i
$221$	1.63801	+	4.50041i	0.110185	+	0.302730i
$222$		0			0
$223$	−4.53645	−	5.40633i	−0.303783	−	0.362035i	0.592458	−	0.805601i	$-0.298158\pi$
$223$	−4.53645	−	5.40633i	−0.303783	−	0.362035i	−0.896242	+	0.443566i	$0.853713\pi$
$224$	12.4931	+	7.62368i	0.834732	+	0.509379i
$225$		0			0
$226$	−1.79839	−	3.11490i	−0.119627	−	0.207200i
$227$	13.1451	−	11.0301i	0.872471	−	0.732090i	−0.0921457	−	0.995746i	$-0.529373\pi$
$227$	13.1451	−	11.0301i	0.872471	−	0.732090i	0.964617	+	0.263655i	$0.0849281\pi$
$228$		0			0
$229$	8.79697	+	1.55114i	0.581320	+	0.102502i	0.456573	−	0.889686i	$-0.349077\pi$
$229$	8.79697	+	1.55114i	0.581320	+	0.102502i	0.124748	+	0.992189i	$0.460188\pi$
$230$	−1.05648	+	0.384528i	−0.0696623	+	0.0253550i
$231$		0			0
$232$	−0.604535	−	3.42849i	−0.0396897	−	0.225091i
$233$	−7.40115	+	4.27306i	−0.484866	+	0.279937i	−0.722442	−	0.691432i	$-0.756980\pi$
$233$	−7.40115	+	4.27306i	−0.484866	+	0.279937i	0.237576	+	0.971369i	$0.423647\pi$
$234$		0			0
$235$	−0.191832	+	0.332264i	−0.0125138	+	0.0216745i
$236$	−0.204072	−	1.15735i	−0.0132840	−	0.0753371i
$237$		0			0
$238$	−18.6859	−	3.76529i	−1.21122	−	0.244068i
$239$	−8.54791	+	10.1870i	−0.552919	+	0.658943i	−0.968032	−	0.250827i	$-0.919297\pi$
$239$	−8.54791	+	10.1870i	−0.552919	+	0.658943i	0.415113	+	0.909770i	$0.363742\pi$
$240$		0			0
$241$	13.7623	−	2.42667i	0.886510	−	0.156316i	0.288191	−	0.957573i	$-0.406946\pi$
$241$	13.7623	−	2.42667i	0.886510	−	0.156316i	0.598320	+	0.801257i	$0.295835\pi$
$242$	−1.47027	+	0.848864i	−0.0945128	+	0.0545670i
$243$		0			0
$244$			14.4433i			0.924637i
$245$	6.77634	−	5.14620i	0.432924	−	0.328779i
$246$		0			0
$247$	−0.800948	+	0.291521i	−0.0509631	+	0.0185491i
$248$	22.4593	−	8.17451i	1.42617	−	0.519082i
$249$		0			0
$250$	9.24622	−	1.63036i	0.584783	−	0.103113i
$251$	12.8062	+	22.1810i	0.808322	+	1.40005i	0.914025	+	0.405657i	$0.132957\pi$
$251$	12.8062	+	22.1810i	0.808322	+	1.40005i	−0.105704	+	0.994398i	$0.533709\pi$
$252$		0			0
$253$	−1.83079	+	3.17103i	−0.115101	+	0.199361i
$254$	4.55515	−	12.5152i	0.285816	−	0.785272i
$255$		0			0
$256$	−12.6654	−	10.6276i	−0.791589	−	0.664222i
$257$	−2.07412	+	11.7629i	−0.129380	+	0.733751i	0.849229	+	0.528024i	$0.177067\pi$
$257$	−2.07412	+	11.7629i	−0.129380	+	0.733751i	−0.978609	+	0.205727i	$0.934044\pi$
$258$		0			0
$259$	20.8173	+	8.15519i	1.29352	+	0.506739i
$260$	0.747503	+	0.431571i	0.0463582	+	0.0267649i
$261$		0			0
$262$	13.9207	+	8.03711i	0.860023	+	0.496534i
$263$	−4.86540	+	13.3676i	−0.300013	+	0.824280i	0.694483	+	0.719509i	$0.255633\pi$
$263$	−4.86540	+	13.3676i	−0.300013	+	0.824280i	−0.994496	+	0.104771i	$0.966589\pi$
$264$		0			0
$265$	−7.93792	−	1.39967i	−0.487622	−	0.0859810i
$266$	0.670118	−	3.32557i	0.0410876	−	0.203904i
$267$		0			0
$268$	−9.32119	+	7.82141i	−0.569382	+	0.477768i
$269$	−15.2108	−	26.3459i	−0.927421	−	1.60634i	−0.787620	−	0.616161i	$-0.788687\pi$
$269$	−15.2108	−	26.3459i	−0.927421	−	1.60634i	−0.139801	−	0.990180i	$-0.544646\pi$
$270$		0			0
$271$	−11.2849	−	6.51534i	−0.685509	−	0.395779i	0.116418	−	0.993200i	$-0.462859\pi$
$271$	−11.2849	−	6.51534i	−0.685509	−	0.395779i	−0.801927	+	0.597421i	$0.796192\pi$
$272$	1.89463	+	0.689587i	0.114879	+	0.0418124i
$273$		0			0
$274$	−2.32056	−	1.94718i	−0.140190	−	0.117634i
$275$	8.12364	−	9.68138i	0.489874	−	0.583809i
$276$		0			0
$277$	−16.8545	−	6.13455i	−1.01269	−	0.368589i	−0.218225	−	0.975899i	$-0.570027\pi$
$277$	−16.8545	−	6.13455i	−1.01269	−	0.368589i	−0.794465	+	0.607309i	$0.792249\pi$
$278$	3.61150			0.216603
$279$		0			0
$280$	−8.13381	+	4.43602i	−0.486088	+	0.265103i
$281$	9.46609	−	1.66913i	0.564700	−	0.0995718i	0.115992	−	0.993250i	$-0.462995\pi$
$281$	9.46609	−	1.66913i	0.564700	−	0.0995718i	0.448708	+	0.893678i	$0.351884\pi$
$282$		0			0
$283$	−8.57485	+	10.2191i	−0.509722	+	0.607463i	−0.958119	−	0.286372i	$-0.907551\pi$
$283$	−8.57485	+	10.2191i	−0.509722	+	0.607463i	0.448397	+	0.893835i	$0.351995\pi$
$284$	0.833582	−	0.993424i	0.0494640	−	0.0589489i
$285$		0			0
$286$	−1.92930	+	0.340188i	−0.114082	+	0.0201158i
$287$	9.88233	−	16.1944i	0.583336	−	0.955927i
$288$		0			0
$289$	46.1928			2.71722
$290$	1.25106	+	0.455347i	0.0734645	+	0.0267389i
$291$		0			0
$292$	−0.706937	+	0.842495i	−0.0413704	+	0.0493033i
$293$	−1.25235	−	1.05085i	−0.0731631	−	0.0613911i	0.605473	−	0.795866i	$-0.292984\pi$
$293$	−1.25235	−	1.05085i	−0.0731631	−	0.0613911i	−0.678636	+	0.734475i	$0.737429\pi$
$294$		0			0
$295$	1.13895	+	0.414544i	0.0663122	+	0.0241357i
$296$	−21.0824	−	12.1719i	−1.22539	−	0.707479i
$297$		0			0
$298$	6.37810	+	11.0472i	0.369473	+	0.639947i
$299$	−0.470990	+	0.395207i	−0.0272380	+	0.0228554i
$300$		0			0
$301$	−16.1666	−	14.2492i	−0.931827	−	0.821308i
$302$	11.7831	+	2.07767i	0.678039	+	0.119556i
$303$		0			0
$304$	−0.122728	+	0.337191i	−0.00703891	+	0.0193392i
$305$	−12.9004	−	7.44803i	−0.738673	−	0.426473i
$306$		0			0
$307$	−9.99990	−	5.77344i	−0.570724	−	0.329508i	0.186714	−	0.982414i	$-0.440216\pi$
$307$	−9.99990	−	5.77344i	−0.570724	−	0.329508i	−0.757439	+	0.652906i	$0.773549\pi$
$308$	−4.08106	+	10.4175i	−0.232540	+	0.593591i
$309$		0			0
$310$	−1.58716	+	9.00122i	−0.0901445	+	0.511235i
$311$	18.4307	+	15.4652i	1.04511	+	0.876953i	0.992571	−	0.121666i	$-0.0388237\pi$
$311$	18.4307	+	15.4652i	1.04511	+	0.876953i	0.0525406	+	0.998619i	$0.483268\pi$
$312$		0			0
$313$	−11.1193	+	30.5501i	−0.628501	+	1.72679i	0.0566510	+	0.998394i	$0.481958\pi$
$313$	−11.1193	+	30.5501i	−0.628501	+	1.72679i	−0.685153	+	0.728400i	$0.740264\pi$
$314$	2.26473	−	3.92262i	0.127806	−	0.221366i
$315$		0			0
$316$	7.92734	+	13.7305i	0.445947	+	0.772404i
$317$	4.97342	−	0.876947i	0.279335	−	0.0492543i	−0.0322255	−	0.999481i	$-0.510259\pi$
$317$	4.97342	−	0.876947i	0.279335	−	0.0492543i	0.311560	+	0.950226i	$0.399148\pi$
$318$		0			0
$319$	4.07446	−	1.48298i	0.228126	−	0.0830311i
$320$	6.30601	−	2.29520i	0.352517	−	0.128306i
$321$		0			0
$322$	−0.366228	−	2.41952i	−0.0204091	−	0.134834i
$323$			11.2466i			0.625776i
$324$		0			0
$325$	1.83782	−	1.06106i	0.101944	−	0.0588572i
$326$	−1.91403	+	0.337495i	−0.106008	+	0.0186921i
$327$		0			0
$328$	−13.2780	+	15.8241i	−0.733155	+	0.873740i
$329$	−0.626465	−	0.552164i	−0.0345381	−	0.0304418i
$330$		0			0
$331$	2.12634	+	12.0591i	0.116874	+	0.662828i	0.985805	+	0.167894i	$0.0536966\pi$
$331$	2.12634	+	12.0591i	0.116874	+	0.662828i	−0.868931	+	0.494934i	$0.835192\pi$
$332$	3.55029	−	6.14928i	0.194848	−	0.337486i
$333$		0			0
$334$	−10.8681	+	6.27470i	−0.594676	+	0.343336i
$335$	−2.17918	−	12.3587i	−0.119061	−	0.675230i
$336$		0			0
$337$	16.9278	−	6.16122i	0.922116	−	0.335623i	0.163036	−	0.986620i	$-0.447871\pi$
$337$	16.9278	−	6.16122i	0.922116	−	0.335623i	0.759080	+	0.650997i	$0.225649\pi$
$338$	11.2790	+	1.98879i	0.613496	+	0.108176i
$339$		0			0
$340$	8.72445	−	7.32068i	0.473150	−	0.397020i
$341$	14.8838	+	25.7795i	0.806001	+	1.39604i
$342$		0			0
$343$	8.06687	+	16.6711i	0.435570	+	0.900155i
$344$	15.0825	+	17.9747i	0.813196	+	0.969130i
$345$		0			0
$346$	1.12159	+	3.08154i	0.0602970	+	0.165665i
$347$	11.2670	+	1.98668i	0.604846	+	0.106651i	0.467681	−	0.883898i	$-0.345090\pi$
$347$	11.2670	+	1.98668i	0.604846	+	0.106651i	0.137165	+	0.990548i	$0.456201\pi$
$348$		0			0
$349$	2.98735	−	8.20768i	0.159909	−	0.439347i	−0.833701	−	0.552217i	$-0.813782\pi$
$349$	2.98735	−	8.20768i	0.159909	−	0.439347i	0.993610	+	0.112870i	$0.0360043\pi$
$350$	−0.205299	+	8.44371i	−0.0109737	+	0.451335i
$351$		0			0
$352$	9.92369	−	17.1883i	0.528934	−	0.916141i
$353$	−3.86470	−	21.9178i	−0.205697	−	1.16657i	−0.896339	−	0.443370i	$-0.853783\pi$
$353$	−3.86470	−	21.9178i	−0.205697	−	1.16657i	0.690642	−	0.723197i	$-0.257328\pi$
$354$		0			0
$355$	0.457444	+	1.25682i	0.0242786	+	0.0667049i
$356$	1.21230	−	6.87529i	0.0642517	−	0.364389i
$357$		0			0
$358$	16.9809	−	14.2486i	0.897466	−	0.753063i
$359$			26.2189i			1.38378i	0.722002	+	0.691891i	$0.243222\pi$
$359$			26.2189i			1.38378i	−0.722002	+	0.691891i	$0.756778\pi$
$360$		0			0
$361$	16.9984			0.894654
$362$	−13.6338	−	4.96229i	−0.716576	−	0.260812i
$363$		0			0
$364$	−1.24222	+	1.40938i	−0.0651099	+	0.0738714i
$365$	−0.387945	−	1.06587i	−0.0203060	−	0.0557902i
$366$		0			0
$367$	−11.4902	−	13.6935i	−0.599785	−	0.714796i	0.377670	−	0.925940i	$-0.376725\pi$
$367$	−11.4902	−	13.6935i	−0.599785	−	0.714796i	−0.977455	+	0.211144i	$0.932281\pi$
$368$			0.258839i			0.0134929i
$369$		0			0
$370$	8.06231	−	4.65478i	0.419140	−	0.241990i
$371$	6.39932	−	16.3352i	0.332236	−	0.848080i
$372$		0			0
$373$	8.20499	+	6.88480i	0.424838	+	0.356482i	0.830000	−	0.557763i	$-0.188340\pi$
$373$	8.20499	+	6.88480i	0.424838	+	0.356482i	−0.405162	+	0.914245i	$0.632785\pi$
$374$	−4.48871	+	25.4567i	−0.232105	+	1.31634i
$375$		0			0
$376$	0.584458	+	0.696529i	0.0301411	+	0.0359208i
$377$	0.728069			0.0374974
$378$		0			0
$379$	13.1823			0.677127			0.338564	−	0.940944i	$-0.390059\pi$
$379$	13.1823			0.677127			0.338564	+	0.940944i	$0.390059\pi$
$380$	1.30288	+	1.55271i	0.0668363	+	0.0796524i
$381$		0			0
$382$	1.01149	−	5.73645i	0.0517524	−	0.293502i
$383$	−12.1923	−	10.2305i	−0.622997	−	0.522757i	0.275747	−	0.961230i	$-0.411075\pi$
$383$	−12.1923	−	10.2305i	−0.622997	−	0.522757i	−0.898744	+	0.438474i	$0.855519\pi$
$384$		0			0
$385$	−7.20012	−	9.01711i	−0.366952	−	0.459555i
$386$	−1.07556	+	0.620974i	−0.0547445	+	0.0316067i
$387$		0			0
$388$			9.92496i			0.503864i
$389$	16.0481	+	19.1254i	0.813671	+	0.969696i	0.999918	−	0.0128074i	$-0.00407683\pi$
$389$	16.0481	+	19.1254i	0.813671	+	0.969696i	−0.186247	+	0.982503i	$0.559632\pi$
$390$		0			0
$391$	2.77467	+	7.62333i	0.140321	+	0.385529i
$392$	−5.96794	−	19.2622i	−0.301426	−	0.972887i
$393$		0			0
$394$	−18.9279	−	6.88918i	−0.953572	−	0.347072i
$395$	−16.3517			−0.822743
$396$		0			0
$397$		−	21.5681i		−	1.08247i	−0.840871	−	0.541235i	$-0.817957\pi$
$397$		−	21.5681i		−	1.08247i	0.840871	−	0.541235i	$-0.182043\pi$
$398$	−9.23763	+	7.75129i	−0.463041	+	0.388537i
$399$		0			0
$400$	0.155136	−	0.879821i	0.00775681	−	0.0439911i
$401$	3.23776	+	8.89569i	0.161686	+	0.444229i	0.993908	−	0.110214i	$-0.0351535\pi$
$401$	3.23776	+	8.89569i	0.161686	+	0.444229i	−0.832222	+	0.554443i	$0.812931\pi$
$402$		0			0
$403$	0.867963	+	4.92246i	0.0432363	+	0.245205i
$404$	−1.46117	+	2.53083i	−0.0726961	+	0.125913i
$405$		0			0
$406$	−1.50945	+	2.47357i	−0.0749128	+	0.122761i
$407$	10.3699	−	28.4910i	0.514016	−	1.41225i
$408$		0			0
$409$	−12.8196	−	2.26043i	−0.633886	−	0.111771i	−0.152534	−	0.988298i	$-0.548743\pi$
$409$	−12.8196	−	2.26043i	−0.633886	−	0.111771i	−0.481353	+	0.876527i	$0.659854\pi$
$410$	−2.70182	−	7.42319i	−0.133433	−	0.366605i
$411$		0			0
$412$	−7.23878	−	8.62684i	−0.356629	−	0.425014i
$413$	−1.37419	+	2.25192i	−0.0676194	+	0.110810i
$414$		0			0
$415$	3.66159	+	6.34205i	0.179740	+	0.311319i
$416$	2.55297	−	2.14219i	0.125170	−	0.105030i
$417$		0			0
$418$	−4.53059	−	0.798866i	−0.221599	−	0.0390738i
$419$	−11.0177	+	4.01012i	−0.538251	+	0.195907i	−0.596819	−	0.802376i	$-0.703569\pi$
$419$	−11.0177	+	4.01012i	−0.538251	+	0.195907i	0.0585680	+	0.998283i	$0.481347\pi$
$420$		0			0
$421$	−2.93922	−	16.6692i	−0.143249	−	0.812405i	−0.968756	−	0.248014i	$-0.920222\pi$
$421$	−2.93922	−	16.6692i	−0.143249	−	0.812405i	0.825508	−	0.564391i	$-0.190889\pi$
$422$	−11.9244	+	6.88457i	−0.580472	+	0.335136i
$423$		0			0
$424$	−9.55121	+	16.5432i	−0.463848	+	0.803408i
$425$	−4.86232	−	27.5756i	−0.235857	−	1.33761i
$426$		0			0
$427$	21.4382	−	24.3230i	1.03747	−	1.17707i
$428$	−9.31041	+	11.0957i	−0.450036	+	0.536332i
$429$		0			0
$430$	−8.83687	+	1.55818i	−0.426152	+	0.0751420i
$431$	−1.64280	+	0.948469i	−0.0791307	+	0.0456861i	−0.539043	−	0.842278i	$-0.681214\pi$
$431$	−1.64280	+	0.948469i	−0.0791307	+	0.0456861i	0.459913	+	0.887964i	$0.347881\pi$
$432$		0			0
$433$			8.59518i			0.413058i	0.978440	+	0.206529i	$0.0662168\pi$
$433$			8.59518i			0.413058i	−0.978440	+	0.206529i	$0.933783\pi$
$434$	−18.5233	−	7.25652i	−0.889146	−	0.348324i
$435$		0			0
$436$	−10.3467	+	3.76588i	−0.495516	+	0.180353i
$437$	−1.35674	+	0.493814i	−0.0649018	+	0.0236223i
$438$		0			0
$439$	17.1328	−	3.02098i	0.817706	−	0.144184i	0.250877	−	0.968019i	$-0.419281\pi$
$439$	17.1328	−	3.02098i	0.817706	−	0.144184i	0.566829	+	0.823835i	$0.308170\pi$
$440$	6.28207	+	10.8809i	0.299486	+	0.518725i
$441$		0			0
$442$	−2.17025	+	3.75898i	−0.103228	+	0.178796i
$443$	10.4701	−	28.7664i	0.497451	−	1.36673i	−0.396280	−	0.918130i	$-0.629699\pi$
$443$	10.4701	−	28.7664i	0.497451	−	1.36673i	0.893730	−	0.448604i	$-0.148079\pi$
$444$		0			0
$445$	5.51567	+	4.62820i	0.261468	+	0.219398i
$446$	1.11069	−	6.29903i	0.0525926	−	0.298268i
$447$		0			0
$448$	2.18597	+	14.4418i	0.103277	+	0.682311i
$449$	−23.7529	−	13.7137i	−1.12097	−	0.647191i	−0.179320	−	0.983791i	$-0.557390\pi$
$449$	−23.7529	−	13.7137i	−1.12097	−	0.647191i	−0.941648	+	0.336600i	$0.890723\pi$
$450$		0			0
$451$	−22.2807	−	12.8638i	−1.04916	−	0.605731i
$452$	−1.59979	+	4.39540i	−0.0752480	+	0.206742i
$453$		0			0
$454$	15.3156	+	2.70056i	0.718798	+	0.126743i
$455$	−0.618239	−	1.83630i	−0.0289835	−	0.0860869i
$456$		0			0
$457$	17.5654	−	14.7391i	0.821675	−	0.689467i	−0.131689	−	0.991291i	$-0.542040\pi$
$457$	17.5654	−	14.7391i	0.821675	−	0.689467i	0.953364	+	0.301824i	$0.0975955\pi$
$458$	4.04785	+	7.01109i	0.189144	+	0.327607i
$459$		0			0
$460$	1.26621	+	0.731047i	0.0590374	+	0.0340852i
$461$	28.3324	+	10.3121i	1.31957	+	0.480284i	0.903321	−	0.428966i	$-0.141122\pi$
$461$	28.3324	+	10.3121i	1.31957	+	0.480284i	0.416250	+	0.909250i	$0.363344\pi$
$462$		0			0
$463$	−22.9581	−	19.2641i	−1.06695	−	0.895279i	−0.0721787	−	0.997392i	$-0.522995\pi$
$463$	−22.9581	−	19.2641i	−1.06695	−	0.895279i	−0.994773	+	0.102113i	$0.967440\pi$
$464$	0.197020	−	0.234800i	0.00914645	−	0.0109003i
$465$		0			0
$466$	−7.27826	−	2.64907i	−0.337159	−	0.122716i
$467$	2.35105			0.108793			0.0543967	−	0.998519i	$-0.482676\pi$
$467$	2.35105			0.108793			0.0543967	+	0.998519i	$0.482676\pi$
$468$		0			0
$469$	27.3065	+	0.663926i	1.26090	+	0.0306572i
$470$	−0.342434	+	0.0603803i	−0.0157953	+	0.00278514i
$471$		0			0
$472$	1.84637	−	2.20042i	0.0849863	−	0.101283i
$473$	−18.7848	+	22.3869i	−0.863728	+	1.02935i
$474$		0			0
$475$	4.90769	−	0.865359i	0.225180	−	0.0397054i
$476$	11.8689	+	21.7626i	0.544011	+	0.997489i
$477$		0			0
$478$	−12.0522			−0.551254
$479$	−17.6002	−	6.40596i	−0.804175	−	0.292696i	−0.0929597	−	0.995670i	$-0.529633\pi$
$479$	−17.6002	−	6.40596i	−0.804175	−	0.292696i	−0.711216	+	0.702974i	$0.751855\pi$
$480$		0			0
$481$	3.27249	−	3.90000i	0.149213	−	0.177825i
$482$	9.70215	+	8.14107i	0.441921	+	0.370816i
$483$		0			0
$484$	2.07469	+	0.755125i	0.0943040	+	0.0343239i
$485$	−8.86472	−	5.11805i	−0.402526	−	0.232398i
$486$		0			0
$487$	0.370050	+	0.640946i	0.0167686	+	0.0290440i	0.874288	−	0.485408i	$-0.161329\pi$
$487$	0.370050	+	0.640946i	0.0167686	+	0.0290440i	−0.857519	+	0.514452i	$0.827995\pi$
$488$	−27.0433	+	22.6920i	−1.22419	+	1.02722i
$489$		0			0
$490$	7.52047	+	1.70662i	0.339740	+	0.0770973i
$491$	−13.6257	−	2.40259i	−0.614921	−	0.108427i	−0.142492	−	0.989796i	$-0.545512\pi$
$491$	−13.6257	−	2.40259i	−0.614921	−	0.108427i	−0.472429	+	0.881369i	$0.656623\pi$
$492$		0			0
$493$	3.28568	−	9.02734i	0.147980	−	0.406571i
$494$	−0.668994	−	0.386244i	−0.0300995	−	0.0173779i
$495$		0			0
$496$	1.82236	+	1.05214i	0.0818262	+	0.0472424i
$497$	−2.87832	+	0.435674i	−0.129110	+	0.0195426i
$498$		0			0
$499$	0.415762	−	2.35790i	0.0186121	−	0.105554i	−0.974087	−	0.226176i	$-0.927378\pi$
$499$	0.415762	−	2.35790i	0.0186121	−	0.105554i	0.992699	+	0.120622i	$0.0384887\pi$
$500$	−9.35333	−	7.84837i	−0.418294	−	0.350990i
$501$		0			0
$502$	−7.93919	+	21.8127i	−0.354343	+	0.973550i
$503$	−0.926534	+	1.60480i	−0.0413121	+	0.0715547i	−0.885942	−	0.463796i	$-0.846487\pi$
$503$	−0.926534	+	1.60480i	−0.0413121	+	0.0715547i	0.844630	+	0.535350i	$0.179820\pi$
$504$		0			0
$505$	−1.50698	−	2.61016i	−0.0670596	−	0.116151i
$506$	−3.26809	+	0.576252i	−0.145284	+	0.0256175i
$507$		0			0
$508$	−16.2756	+	5.92383i	−0.722112	+	0.262827i
$509$	4.99958	−	1.81970i	0.221602	−	0.0806567i	−0.228833	−	0.973466i	$-0.573491\pi$
$509$	4.99958	−	1.81970i	0.221602	−	0.0806567i	0.450435	+	0.892809i	$0.351269\pi$
$510$		0			0
$511$	2.44102	−	0.369483i	0.107984	−	0.0163449i
$512$		−	2.86433i		−	0.126587i
$513$		0			0
$514$	−9.37492	+	5.41261i	−0.413510	+	0.238740i
$515$	11.4381	−	2.01685i	0.504024	−	0.0888730i
$516$		0			0
$517$	−0.727924	+	0.867506i	−0.0320140	+	0.0381529i
$518$	6.46543	+	19.2037i	0.284075	+	0.843761i
$519$		0			0
$520$	0.366346	+	2.07765i	0.0160653	+	0.0911110i
$521$	−12.2120	+	21.1518i	−0.535018	+	0.926679i	0.464144	+	0.885760i	$0.346362\pi$
$521$	−12.2120	+	21.1518i	−0.535018	+	0.926679i	−0.999162	+	0.0409190i	$0.986971\pi$
$522$		0			0
$523$	−26.6209	+	15.3696i	−1.16405	+	0.672065i	−0.952272	−	0.305252i	$-0.901259\pi$
$523$	−26.6209	+	15.3696i	−1.16405	+	0.672065i	−0.211780	+	0.977317i	$0.567926\pi$
$524$	−3.62994	−	20.5864i	−0.158575	−	0.899322i
$525$		0			0
$526$	−12.1151	+	4.40952i	−0.528242	+	0.192264i
$527$	64.9508	+	11.4526i	2.82930	+	0.498882i
$528$		0			0
$529$	16.8212	−	14.1147i	0.731357	−	0.613681i
$530$	−3.65257	−	6.32643i	−0.158657	−	0.274803i
$531$		0			0
$532$	−3.87315	+	2.11234i	−0.167922	+	0.0915816i
$533$	−2.77686	−	3.30933i	−0.120279	−	0.143343i
$534$		0			0
$535$	−5.10926	−	14.0376i	−0.220893	−	0.606898i
$536$	−29.2892	−	5.16448i	−1.26510	−	0.223071i
$537$		0			0
$538$	9.42992	−	25.9085i	0.406553	−	1.11699i
$539$	22.3353	−	11.4859i	0.962048	−	0.494731i
$540$		0			0
$541$	14.3316	−	24.8231i	0.616166	−	1.06723i	−0.374013	−	0.927423i	$-0.622019\pi$
$541$	14.3316	−	24.8231i	0.616166	−	1.06723i	0.990179	−	0.139807i	$-0.0446481\pi$
$542$	−2.05074	−	11.6303i	−0.0880868	−	0.499565i
$543$		0			0
$544$	−15.0399	−	41.3218i	−0.644830	−	1.77166i
$545$	1.97193	−	11.1833i	0.0844680	−	0.479042i
$546$		0			0
$547$	−28.4534	+	23.8752i	−1.21658	+	1.02083i	−0.217582	+	0.976042i	$0.569817\pi$
$547$	−28.4534	+	23.8752i	−1.21658	+	1.02083i	−0.998996	+	0.0447884i	$0.985739\pi$
$548$			3.93948i			0.168286i
$549$		0			0
$550$	11.4540			0.488399
$551$	1.60662	+	0.584761i	0.0684442	+	0.0249117i
$552$		0			0
$553$	7.03034	−	34.8892i	0.298960	−	1.48364i
$554$	−5.55975	−	15.2753i	−0.236211	−	0.648985i
$555$		0			0
$556$	−3.01894	−	3.59783i	−0.128032	−	0.152582i
$557$		−	24.0793i		−	1.02027i	−0.860094	−	0.510136i	$-0.829595\pi$
$557$		−	24.0793i		−	1.02027i	0.860094	−	0.510136i	$-0.170405\pi$
$558$		0			0
$559$	−4.24971	+	2.45357i	−0.179743	+	0.103775i
$560$	−0.759499	−	0.297535i	−0.0320947	−	0.0125731i
$561$		0			0
$562$	6.67339	+	5.59964i	0.281500	+	0.236206i
$563$	−1.01488	+	5.75568i	−0.0427721	+	0.242573i	−0.998697	−	0.0510398i	$-0.983746\pi$
$563$	−1.01488	+	5.75568i	−0.0427721	+	0.242573i	0.955924	+	0.293613i	$0.0948576\pi$
$564$		0			0
$565$	−3.10088	−	3.69549i	−0.130455	−	0.155470i
$566$	−12.0902			−0.508187
$567$		0			0
$568$	3.16971			0.132998
$569$	−9.33442	−	11.1243i	−0.391319	−	0.466356i	0.534033	−	0.845463i	$-0.320676\pi$
$569$	−9.33442	−	11.1243i	−0.391319	−	0.466356i	−0.925353	+	0.379107i	$0.876231\pi$
$570$		0			0
$571$	−6.94818	+	39.4051i	−0.290772	+	1.64905i	0.393133	+	0.919482i	$0.371391\pi$
$571$	−6.94818	+	39.4051i	−0.290772	+	1.64905i	−0.683906	+	0.729571i	$0.739720\pi$
$572$	1.95165	+	1.63763i	0.0816027	+	0.0684728i
$573$		0			0
$574$	17.0003	−	2.57324i	0.709580	−	0.107405i
$575$	3.11312	−	1.79736i	0.129826	−	0.0749550i
$576$		0			0
$577$		−	12.0256i		−	0.500634i	−0.968164	−	0.250317i	$-0.919465\pi$
$577$		−	12.0256i		−	0.500634i	0.968164	−	0.250317i	$-0.0805348\pi$
$578$	26.9101	+	32.0702i	1.11931	+	1.33394i
$579$		0			0
$580$	−0.592164	−	1.62696i	−0.0245883	−	0.0675557i
$581$	−15.1062	+	5.08590i	−0.626710	+	0.210999i
$582$		0			0
$583$	−22.3567	−	8.13717i	−0.925919	−	0.337007i
$584$	−2.68814			−0.111236
$585$		0			0
$586$		−	1.48165i		−	0.0612063i
$587$	−13.0785	+	10.9742i	−0.539807	+	0.452952i	−0.871472	−	0.490445i	$-0.836834\pi$
$587$	−13.0785	+	10.9742i	−0.539807	+	0.452952i	0.331665	+	0.943397i	$0.392390\pi$
$588$		0			0
$589$	−2.03824	+	11.5594i	−0.0839843	+	0.476299i
$590$	0.375702	+	1.03223i	0.0154674	+	0.0424963i
$591$		0			0
$592$	−0.372179	−	2.11073i	−0.0152965	−	0.0867506i
$593$	−8.82192	+	15.2800i	−0.362273	+	0.627475i	−0.988335	−	0.152299i	$-0.951332\pi$
$593$	−8.82192	+	15.2800i	−0.362273	+	0.627475i	0.626062	+	0.779774i	$0.284666\pi$
$594$		0			0
$595$	−25.5583	−	0.621421i	−1.04779	−	0.0254758i
$596$	5.67378	−	15.5886i	0.232407	−	0.638533i
$597$		0			0
$598$	−0.548759	−	0.0967611i	−0.0224404	−	0.00395685i
$599$	−5.13784	−	14.1161i	−0.209927	−	0.576768i	0.789384	−	0.613900i	$-0.210400\pi$
$599$	−5.13784	−	14.1161i	−0.209927	−	0.576768i	−0.999310	+	0.0371316i	$0.988178\pi$
$600$		0			0
$601$	4.19281	+	4.99680i	0.171028	+	0.203824i	0.844749	−	0.535162i	$-0.179749\pi$
$601$	4.19281	+	4.99680i	0.171028	+	0.203824i	−0.673721	+	0.738986i	$0.735305\pi$
$602$	0.474727	−	19.5249i	0.0193484	−	0.795777i
$603$		0			0
$604$	−7.77993	−	13.4752i	−0.316561	−	0.548299i
$605$	−1.74432	+	1.46366i	−0.0709167	+	0.0595062i
$606$		0			0
$607$	31.9011	+	5.62502i	1.29482	+	0.228312i	0.778263	−	0.627938i	$-0.216101\pi$
$607$	31.9011	+	5.62502i	1.29482	+	0.228312i	0.516561	+	0.856251i	$0.327212\pi$
$608$	7.35413	−	2.67669i	0.298250	−	0.108554i
$609$		0			0
$610$	−2.34431	−	13.2952i	−0.0949183	−	0.538308i
$611$	−0.164679	+	0.0950772i	−0.00666218	+	0.00384641i
$612$		0			0
$613$	−1.92702	+	3.33770i	−0.0778317	+	0.134809i	−0.902314	−	0.431079i	$-0.858133\pi$
$613$	−1.92702	+	3.33770i	−0.0778317	+	0.134809i	0.824482	+	0.565888i	$0.191466\pi$
$614$	−1.81722	−	10.3060i	−0.0733372	−	0.415916i
$615$		0			0
$616$	−25.9172	+	8.72572i	−1.04423	+	0.351569i
$617$	20.8477	−	24.8453i	0.839295	−	1.00023i	−0.160617	−	0.987017i	$-0.551348\pi$
$617$	20.8477	−	24.8453i	0.839295	−	1.00023i	0.999913	−	0.0132165i	$-0.00420707\pi$
$618$		0			0
$619$	−18.5003	+	3.26210i	−0.743589	+	0.131115i	−0.532592	−	0.846372i	$-0.678782\pi$
$619$	−18.5003	+	3.26210i	−0.743589	+	0.131115i	−0.210997	+	0.977487i	$0.567671\pi$
$620$	10.2939	−	5.94318i	0.413413	−	0.238684i
$621$		0			0
$622$			21.8053i			0.874313i
$623$	−12.2465	+	9.77879i	−0.490647	+	0.391779i
$624$		0			0
$625$	−4.71666	+	1.71672i	−0.188666	+	0.0686689i
$626$	−27.6876	+	10.0775i	−1.10662	+	0.402777i
$627$		0			0
$628$	−5.80092	+	1.02286i	−0.231482	+	0.0408165i
$629$	−33.5878	−	58.1758i	−1.33923	−	2.31962i
$630$		0			0
$631$	3.17557	−	5.50025i	0.126417	−	0.218961i	−0.795869	−	0.605469i	$-0.792985\pi$
$631$	3.17557	−	5.50025i	0.126417	−	0.218961i	0.922286	+	0.386508i	$0.126319\pi$
$632$	−13.2540	+	36.4151i	−0.527217	+	1.44852i
$633$		0			0
$634$	3.50615	+	2.94201i	0.139247	+	0.116842i
$635$	3.10189	−	17.5917i	0.123095	−	0.698105i
$636$		0			0
$637$	4.18387	−	0.529613i	0.165771	−	0.0209840i
$638$	3.40320	+	1.96484i	0.134734	+	0.0777888i
$639$		0			0
$640$	−6.37944	−	3.68317i	−0.252170	−	0.145590i
$641$	10.3834	−	28.5283i	0.410122	−	1.12680i	−0.547005	−	0.837129i	$-0.684232\pi$
$641$	10.3834	−	28.5283i	0.410122	−	1.12680i	0.957126	−	0.289670i	$-0.0935457\pi$
$642$		0			0
$643$	−3.55310	−	0.626507i	−0.140121	−	0.0247070i	0.103148	−	0.994666i	$-0.467108\pi$
$643$	−3.55310	−	0.626507i	−0.140121	−	0.0247070i	−0.243268	+	0.969959i	$0.578220\pi$
$644$	−2.10422	+	2.38737i	−0.0829179	+	0.0940757i
$645$		0			0
$646$	−7.80814	+	6.55181i	−0.307207	+	0.257777i
$647$	4.12557	+	7.14569i	0.162193	+	0.280926i	0.935655	−	0.352917i	$-0.114810\pi$
$647$	4.12557	+	7.14569i	0.162193	+	0.280926i	−0.773462	+	0.633843i	$0.781477\pi$
$648$		0			0
$649$	3.09824	+	1.78877i	0.121617	+	0.0702155i
$650$	1.80730	+	0.657804i	0.0708882	+	0.0258012i
$651$		0			0
$652$	1.93620	+	1.62466i	0.0758274	+	0.0636268i
$653$	−25.5407	+	30.4382i	−0.999483	+	1.19114i	−0.0179514	+	0.999839i	$0.505714\pi$
$653$	−25.5407	+	30.4382i	−0.999483	+	1.19114i	−0.981532	+	0.191299i	$0.938730\pi$
$654$		0			0
$655$	20.2591	+	7.37371i	0.791589	+	0.288115i
$656$	−1.81869			−0.0710078
$657$		0			0
$658$	0.0183959	−	0.756603i	0.000717148	−	0.0294955i
$659$	−28.1991	+	4.97227i	−1.09848	+	0.193692i	−0.693375	−	0.720577i	$-0.743877\pi$
$659$	−28.1991	+	4.97227i	−1.09848	+	0.193692i	−0.405107	+	0.914269i	$0.632766\pi$
$660$		0			0
$661$	−0.182595	+	0.217608i	−0.00710211	+	0.00846396i	−0.769584	−	0.638546i	$-0.779536\pi$
$661$	−0.182595	+	0.217608i	−0.00710211	+	0.00846396i	0.762482	+	0.647010i	$0.223981\pi$
$662$	−7.13352	+	8.50139i	−0.277252	+	0.330416i
$663$		0			0
$664$	17.0917	−	3.01372i	0.663285	−	0.116955i
$665$	0.110596	−	4.54868i	0.00428872	−	0.176390i
$666$		0			0
$667$	1.23329			0.0477532
$668$	15.3359	+	5.58180i	0.593362	+	0.215966i
$669$		0			0
$670$	7.31077	−	8.71264i	0.282440	−	0.336599i
$671$	−33.6815	−	28.2622i	−1.30026	−	1.09105i
$672$		0			0
$673$	−4.12151	−	1.50011i	−0.158873	−	0.0578249i	0.261360	−	0.965241i	$-0.415829\pi$
$673$	−4.12151	−	1.50011i	−0.158873	−	0.0578249i	−0.420232	+	0.907417i	$0.638051\pi$
$674$	14.1390	+	8.16315i	0.544614	+	0.314433i
$675$		0			0
$676$	−7.44711	−	12.8988i	−0.286427	−	0.496106i
$677$	−38.8843	+	32.6278i	−1.49445	+	1.25399i	−0.605610	+	0.795762i	$0.707071\pi$
$677$	−38.8843	+	32.6278i	−1.49445	+	1.25399i	−0.888835	+	0.458227i	$0.848485\pi$
$678$		0			0
$679$	14.7316	−	16.7140i	0.565347	−	0.641423i
$680$	27.4141	+	4.83385i	1.05128	+	0.185370i
$681$		0			0
$682$	−9.22715	+	25.3514i	−0.353326	+	0.970755i
$683$	35.1328	+	20.2839i	1.34432	+	0.776143i	0.987438	−	0.158007i	$-0.0505070\pi$
$683$	35.1328	+	20.2839i	1.34432	+	0.776143i	0.356880	+	0.934150i	$0.383840\pi$
$684$		0			0
$685$	−3.51864	−	2.03149i	−0.134440	−	0.0776191i
$686$	−6.87477	+	15.3125i	−0.262480	+	0.584633i
$687$		0			0
$688$	−0.358732	+	2.03447i	−0.0136765	+	0.0775634i
$689$	−3.06030	−	2.56789i	−0.116588	−	0.0978290i
$690$		0			0
$691$	−1.10466	+	3.03503i	−0.0420233	+	0.115458i	−0.958929	−	0.283645i	$-0.908456\pi$
$691$	−1.10466	+	3.03503i	−0.0420233	+	0.115458i	0.916906	+	0.399103i	$0.130678\pi$
$692$	2.13232	−	3.69328i	0.0810585	−	0.140397i
$693$		0			0
$694$	5.18443	+	8.97970i	0.196798	+	0.340865i
$695$	4.77028	−	0.841129i	0.180947	−	0.0319058i
$696$		0			0
$697$	−53.5641	+	19.4957i	−2.02888	+	0.738454i
$698$	7.43864	−	2.70744i	0.281557	−	0.102478i
$699$		0			0
$700$	8.58336	−	6.85377i	0.324421	−	0.259048i
$701$		−	6.55534i		−	0.247592i	−0.992308	−	0.123796i	$-0.960493\pi$
$701$		−	6.55534i		−	0.247592i	0.992308	−	0.123796i	$-0.0395068\pi$
$702$		0			0
$703$	10.3537	−	5.97771i	0.390497	−	0.225454i
$704$	19.5068	−	3.43958i	0.735191	−	0.129634i
$705$		0			0
$706$	12.9654	−	15.4516i	0.487959	−	0.581527i
$707$	6.21716	−	2.09317i	0.233820	−	0.0787219i
$708$		0			0
$709$	−1.70465	−	9.66753i	−0.0640194	−	0.363072i	−0.999941	−	0.0108635i	$-0.996542\pi$
$709$	−1.70465	−	9.66753i	−0.0640194	−	0.363072i	0.935922	−	0.352208i	$-0.114569\pi$
$710$	−0.606079	+	1.04976i	−0.0227457	+	0.0393968i
$711$		0			0
$712$	14.7778	−	8.53195i	0.553820	−	0.319748i
$713$	1.47026	+	8.33826i	0.0550617	+	0.312270i
$714$		0			0
$715$	−2.46911	+	0.898681i	−0.0923393	+	0.0336088i
$716$	−28.3894	−	5.00582i	−1.06096	−	0.187076i
$717$		0			0
$718$	−18.2030	+	15.2741i	−0.679329	+	0.570025i
$719$	5.92304	+	10.2590i	0.220892	+	0.382596i	0.955079	−	0.296351i	$-0.0957698\pi$
$719$	5.92304	+	10.2590i	0.220892	+	0.382596i	−0.734187	+	0.678947i	$0.762437\pi$
$720$		0			0
$721$	−0.614469	+	25.2724i	−0.0228840	+	0.941192i
$722$	9.90260	+	11.8015i	0.368537	+	0.439205i
$723$		0			0
$724$	6.45330	+	17.7303i	0.239835	+	0.658941i
$725$	−4.19209	−	0.739179i	−0.155690	−	0.0274524i
$726$		0			0
$727$	−15.4099	+	42.3383i	−0.571521	+	1.57024i	0.230580	+	0.973053i	$0.425938\pi$
$727$	−15.4099	+	42.3383i	−0.571521	+	1.57024i	−0.802101	+	0.597188i	$0.796284\pi$
$728$	−4.59054	−	0.111614i	−0.170137	−	0.00413668i
$729$		0			0
$730$	0.513998	−	0.890271i	0.0190239	−	0.0329504i
$731$	11.2435	+	63.7649i	0.415855	+	2.35843i
$732$		0			0
$733$	1.46593	+	4.02762i	0.0541454	+	0.148763i	0.963817	−	0.266565i	$-0.0858888\pi$
$733$	1.46593	+	4.02762i	0.0541454	+	0.148763i	−0.909671	+	0.415329i	$0.863667\pi$
$734$	2.81322	−	15.9546i	0.103838	−	0.588895i
$735$		0			0
$736$	4.32452	−	3.62871i	0.159404	−	0.133756i
$737$		−	37.0415i		−	1.36444i
$738$		0			0
$739$	12.5282			0.460857			0.230429	−	0.973089i	$-0.425987\pi$
$739$	12.5282			0.460857			0.230429	+	0.973089i	$0.425987\pi$
$740$	−11.3766	−	4.14076i	−0.418214	−	0.152217i
$741$		0			0
$742$	15.0690	−	5.07337i	0.553199	−	0.186249i
$743$	5.70379	+	15.6710i	0.209252	+	0.574914i	0.999271	−	0.0381673i	$-0.0121520\pi$
$743$	5.70379	+	15.6710i	0.209252	+	0.574914i	−0.790020	+	0.613081i	$0.789930\pi$
$744$		0			0
$745$	10.9975	+	13.1063i	0.402917	+	0.480177i
$746$			9.70727i			0.355408i
$747$		0			0
$748$	29.1126	−	16.8082i	1.06446	−	0.614567i
$749$	32.1484	−	4.86611i	1.17468	−	0.177804i
$750$		0			0
$751$	38.5102	+	32.3139i	1.40526	+	1.17915i	0.958709	+	0.284390i	$0.0917911\pi$
$751$	38.5102	+	32.3139i	1.40526	+	1.17915i	0.446548	+	0.894760i	$0.352653\pi$
$752$	−0.0139011	+	0.0788369i	−0.000506920	+	0.00287489i
$753$		0			0
$754$	0.424144	+	0.505475i	0.0154464	+	0.0184083i
$755$	16.0476			0.584033
$756$		0			0
$757$	8.96036			0.325670			0.162835	−	0.986653i	$-0.447936\pi$
$757$	8.96036			0.325670			0.162835	+	0.986653i	$0.447936\pi$
$758$	7.67946	+	9.15202i	0.278930	+	0.332416i
$759$		0			0
$760$	−0.860292	+	4.87896i	−0.0312061	+	0.176978i
$761$	21.8623	+	18.3447i	0.792509	+	0.664994i	0.946365	−	0.323099i	$-0.104725\pi$
$761$	21.8623	+	18.3447i	0.792509	+	0.664994i	−0.153856	+	0.988093i	$0.549169\pi$
$762$		0			0
$763$	23.0138	+	9.01569i	0.833156	+	0.326390i
$764$	−6.56027	+	3.78757i	−0.237342	+	0.137030i
$765$		0			0
$766$		−	14.4246i		−	0.521183i
$767$	0.386136	+	0.460179i	0.0139426	+	0.0166161i
$768$		0			0
$769$	−0.460020	−	1.26389i	−0.0165887	−	0.0455772i	0.931122	−	0.364708i	$-0.118831\pi$
$769$	−0.460020	−	1.26389i	−0.0165887	−	0.0455772i	−0.947711	+	0.319131i	$0.896609\pi$
$770$	2.06579	−	10.2518i	0.0744459	−	0.369450i
$771$		0			0
$772$	1.51771	+	0.552401i	0.0546235	+	0.0198813i
$773$	−16.7109			−0.601048			−0.300524	−	0.953774i	$-0.597162\pi$
$773$	−16.7109			−0.601048			−0.300524	+	0.953774i	$0.597162\pi$
$774$		0			0
$775$		−	29.2239i		−	1.04975i
$776$	−18.5832	+	15.5932i	−0.667100	+	0.559763i
$777$		0			0
$778$	−3.92916	+	22.2834i	−0.140867	+	0.798897i
$779$	−3.46970	−	9.53293i	−0.124315	−	0.341553i
$780$		0			0
$781$	0.685524	+	3.88780i	0.0245300	+	0.139116i
$782$	−3.67623	+	6.36741i	−0.131462	+	0.227698i
$783$		0			0
$784$	0.961386	−	1.49260i	0.0343352	−	0.0533072i
$785$	2.07779	−	5.70869i	0.0741596	−	0.203752i
$786$		0			0
$787$	12.8919	+	2.27319i	0.459547	+	0.0810305i	0.398629	−	0.917112i	$-0.369486\pi$
$787$	12.8919	+	2.27319i	0.459547	+	0.0810305i	0.0609179	+	0.998143i	$0.480597\pi$
$788$	8.95915	+	24.6151i	0.319156	+	0.876875i
$789$		0			0
$790$	−9.52584	−	11.3524i	−0.338914	−	0.403902i
$791$	9.21819	−	5.02742i	0.327761	−	0.178754i
$792$		0			0
$793$	−3.69144	−	6.39377i	−0.131087	−	0.227049i
$794$	14.9740	−	12.5647i	0.531408	−	0.445904i
$795$		0			0
$796$	15.4439	+	2.72318i	0.547395	+	0.0965205i
$797$	−28.9247	+	10.5277i	−1.02457	+	0.372912i	−0.799010	−	0.601318i	$-0.794642\pi$
$797$	−28.9247	+	10.5277i	−1.02457	+	0.372912i	−0.225557	+	0.974230i	$0.572420\pi$
$798$		0			0
$799$	0.435691	+	2.47093i	0.0154136	+	0.0874151i
$800$	−16.8744	+	9.74246i	−0.596601	+	0.344448i
$801$		0			0
$802$	−4.28980	+	7.43015i	−0.151478	+	0.262368i
$803$	−0.581373	−	3.29713i	−0.0205162	−	0.116353i
$804$		0			0
$805$	−1.04725	−	3.11054i	−0.0369106	−	0.109632i
$806$	−2.91187	+	3.47023i	−0.102566	+	0.122234i
$807$		0			0
$808$	−7.03431	+	1.24034i	−0.247466	+	0.0436350i
$809$	48.9190	−	28.2434i	1.71990	−	0.992985i	0.800832	−	0.598889i	$-0.204391\pi$
$809$	48.9190	−	28.2434i	1.71990	−	0.992985i	0.919069	−	0.394097i	$-0.128942\pi$
$810$		0			0
$811$		−	0.658409i		−	0.0231199i	−0.999933	−	0.0115599i	$-0.996320\pi$
$811$		−	0.658409i		−	0.0231199i	0.999933	−	0.0115599i	$-0.00367972\pi$
$812$	3.72600	−	0.563983i	0.130757	−	0.0197919i
$813$		0			0
$814$	25.8215	−	9.39825i	0.905042	−	0.329408i
$815$	−2.44956	+	0.891565i	−0.0858042	+	0.0312302i
$816$		0			0
$817$	−11.3484	+	2.00103i	−0.397030	+	0.0700071i
$818$	−5.89881	−	10.2170i	−0.206247	−	0.357231i
$819$		0			0
$820$	−5.13658	+	8.89682i	−0.179377	+	0.310690i
$821$	14.2202	−	39.0697i	0.496289	−	1.36354i	−0.398548	−	0.917148i	$-0.630486\pi$
$821$	14.2202	−	39.0697i	0.496289	−	1.36354i	0.894836	−	0.446394i	$-0.147292\pi$
$822$		0			0
$823$	−23.3533	−	19.5958i	−0.814045	−	0.683065i	0.137524	−	0.990498i	$-0.456085\pi$
$823$	−23.3533	−	19.5958i	−0.814045	−	0.683065i	−0.951570	+	0.307433i	$0.900530\pi$
$824$	4.77977	−	27.1074i	0.166511	−	0.944331i
$825$		0			0
$826$	−2.36398	+	0.357822i	−0.0822535	+	0.0124502i
$827$	36.1773	+	20.8870i	1.25801	+	0.726311i	0.972687	−	0.232121i	$-0.0745666\pi$
$827$	36.1773	+	20.8870i	1.25801	+	0.726311i	0.285321	+	0.958432i	$0.407900\pi$
$828$		0			0
$829$	−37.7752	−	21.8095i	−1.31199	−	0.757475i	−0.329561	−	0.944134i	$-0.606901\pi$
$829$	−37.7752	−	21.8095i	−1.31199	−	0.757475i	−0.982425	+	0.186659i	$0.940234\pi$
$830$	−2.26999	+	6.23675i	−0.0787925	+	0.216481i
$831$		0			0
$832$	3.27548	+	0.577555i	0.113557	+	0.0200231i
$833$	12.3146	−	54.2660i	0.426676	−	1.88021i
$834$		0			0
$835$	−12.8938	+	10.8192i	−0.446209	+	0.374414i
$836$	2.99139	+	5.18124i	0.103459	+	0.179197i
$837$		0			0
$838$	−9.20258	−	5.31311i	−0.317898	−	0.183538i
$839$	8.50951	+	3.09721i	0.293781	+	0.106928i	0.484706	−	0.874677i	$-0.338927\pi$
$839$	8.50951	+	3.09721i	0.293781	+	0.106928i	−0.190925	+	0.981605i	$0.561149\pi$
$840$		0			0
$841$	21.0965	+	17.7021i	0.727467	+	0.610417i
$842$	9.86059	−	11.7514i	0.339818	−	0.404980i
$843$		0			0
$844$	16.8264	+	6.12432i	0.579190	+	0.210808i
$845$	15.3611			0.528439
$846$		0			0
$847$	−2.37301	−	4.35111i	−0.0815376	−	0.149506i
$848$	−1.65628	+	0.292046i	−0.0568767	+	0.0100289i
$849$		0			0
$850$	16.3122	−	19.4402i	0.559505	−	0.666793i
$851$	5.54333	−	6.60628i	0.190023	−	0.226461i
$852$		0			0
$853$	49.6962	−	8.76279i	1.70157	−	0.300032i	0.763325	−	0.646014i	$-0.223565\pi$
$853$	49.6962	−	8.76279i	1.70157	−	0.300032i	0.938241	+	0.345982i	$0.112454\pi$
$854$	29.3757	+	0.714236i	1.00521	+	0.0244406i
$855$		0			0
$856$	−35.4030			−1.21005
$857$	−14.4978	−	5.27677i	−0.495235	−	0.180251i	0.0823144	−	0.996606i	$-0.473769\pi$
$857$	−14.4978	−	5.27677i	−0.495235	−	0.180251i	−0.577550	+	0.816355i	$0.695991\pi$
$858$		0			0
$859$	2.96510	−	3.53366i	0.101168	−	0.120567i	−0.713085	−	0.701078i	$-0.752703\pi$
$859$	2.96510	−	3.53366i	0.101168	−	0.120567i	0.814253	+	0.580511i	$0.197147\pi$
$860$	8.93923	+	7.50090i	0.304825	+	0.255779i
$861$		0			0
$862$	−1.61552	−	0.588001i	−0.0550248	−	0.0200274i
$863$	27.5293	+	15.8941i	0.937108	+	0.541040i	0.889053	−	0.457805i	$-0.151364\pi$
$863$	27.5293	+	15.8941i	0.937108	+	0.541040i	0.0480557	+	0.998845i	$0.484698\pi$
$864$		0			0
$865$	2.19916	+	3.80906i	0.0747737	+	0.129512i
$866$	−5.96736	+	5.00721i	−0.202779	+	0.170152i
$867$		0			0
$868$	8.25501	+	24.5191i	0.280193	+	0.832232i
$869$	−47.5314	−	8.38106i	−1.61239	−	0.284308i
$870$		0			0
$871$	2.12730	−	5.84471i	0.0720808	−	0.198040i
$872$	−23.3069	−	13.4562i	−0.789271	−	0.455686i
$873$		0			0
$874$	−1.13322	−	0.654267i	−0.0383319	−	0.0221309i
$875$	4.10198	+	27.1000i	0.138672	+	0.916149i
$876$		0			0
$877$	−3.35762	+	19.0420i	−0.113379	+	0.643003i	0.874161	+	0.485636i	$0.161412\pi$
$877$	−3.35762	+	19.0420i	−0.113379	+	0.643003i	−0.987540	+	0.157367i	$0.949699\pi$
$878$	12.0783	+	10.1349i	0.407622	+	0.342035i
$879$		0			0
$880$	−0.378335	+	1.03947i	−0.0127537	+	0.0350405i
$881$	−0.310834	+	0.538380i	−0.0104723	+	0.0181385i	−0.871214	−	0.490903i	$-0.836667\pi$
$881$	−0.310834	+	0.538380i	−0.0104723	+	0.0181385i	0.860742	+	0.509042i	$0.170000\pi$
$882$		0			0
$883$	−1.97025	−	3.41257i	−0.0663041	−	0.114842i	0.830968	−	0.556321i	$-0.187787\pi$
$883$	−1.97025	−	3.41257i	−0.0663041	−	0.114842i	−0.897272	+	0.441479i	$0.854454\pi$
$884$	5.55891	−	0.980186i	0.186966	−	0.0329672i
$885$		0			0
$886$	26.0711	−	9.48910i	0.875875	−	0.318792i
$887$	47.0455	−	17.1232i	1.57963	−	0.574940i	0.604510	−	0.796597i	$-0.293369\pi$
$887$	47.0455	−	17.1232i	1.57963	−	0.574940i	0.975125	+	0.221657i	$0.0711466\pi$
$888$		0			0
$889$	36.2013	+	14.1819i	1.21415	+	0.475646i
$890$			6.52556i			0.218737i
$891$		0			0
$892$	−7.20364	+	4.15902i	−0.241196	+	0.139254i
$893$	−0.439757	+	0.0775410i	−0.0147159	+	0.00259481i
$894$		0			0
$895$	19.1107	−	22.7753i	0.638802	−	0.761294i
$896$	10.6015	−	12.0281i	0.354172	−	0.401831i
$897$		0			0
$898$	−4.31647	−	24.4799i	−0.144043	−	0.816906i
$899$	5.01313	−	8.68300i	0.167197	−	0.289594i
$900$		0			0
$901$	−45.6501	+	26.3561i	−1.52083	+	0.878049i
$902$	−4.04894	−	22.9627i	−0.134815	−	0.764574i
$903$		0			0
$904$	−10.7433	+	3.91024i	−0.357316	+	0.130053i
$905$	−19.1640	−	3.37914i	−0.637034	−	0.112326i
$906$		0			0
$907$	−17.1617	+	14.4003i	−0.569843	+	0.478155i	−0.881594	−	0.472009i	$-0.843529\pi$
$907$	−17.1617	+	14.4003i	−0.569843	+	0.478155i	0.311751	+	0.950164i	$0.399085\pi$
$908$	−10.1124	−	17.5151i	−0.335590	−	0.581260i
$909$		0			0
$910$	0.914720	−	1.49898i	0.0303227	−	0.0496906i
$911$	24.0775	+	28.6944i	0.797723	+	0.950689i	0.999587	−	0.0287243i	$-0.00914450\pi$
$911$	24.0775	+	28.6944i	0.797723	+	0.950689i	−0.201864	+	0.979413i	$0.564700\pi$
$912$		0			0
$913$	7.39294	+	20.3119i	0.244671	+	0.672227i
$914$	20.4658	+	3.60867i	0.676948	+	0.119364i
$915$		0			0
$916$	3.60086	−	9.89327i	0.118976	−	0.326883i
$917$	−24.4434	+	40.0561i	−0.807193	+	1.32277i
$918$		0			0
$919$	6.76771	−	11.7220i	0.223246	−	0.386674i	−0.732546	−	0.680718i	$-0.761668\pi$
$919$	6.76771	−	11.7220i	0.223246	−	0.386674i	0.955792	+	0.294044i	$0.0950012\pi$
$920$	0.620561	+	3.51937i	0.0204593	+	0.116030i
$921$		0			0
$922$	9.34592	+	25.6777i	0.307791	+	0.845650i
$923$	−0.115109	+	0.652818i	−0.00378887	+	0.0214878i
$924$		0			0
$925$	−22.8019	+	19.1331i	−0.749722	+	0.629092i
$926$		−	27.1615i		−	0.892583i
$927$		0			0
$928$	−6.68497			−0.219445
$929$	34.9579	+	12.7236i	1.14693	+	0.417449i	0.844412	−	0.535695i	$-0.179950\pi$
$929$	34.9579	+	12.7236i	1.14693	+	0.417449i	0.302519	+	0.953143i	$0.402172\pi$
$930$		0			0
$931$	9.65785	+	2.19166i	0.316523	+	0.0718288i
$932$	3.44503	+	9.46514i	0.112846	+	0.310041i
$933$		0			0
$934$	1.36962	+	1.63226i	0.0448155	+	0.0534090i
$935$			34.6701i			1.13383i
$936$		0			0
$937$	42.3336	−	24.4413i	1.38298	−	0.798463i	0.390468	−	0.920617i	$-0.372313\pi$
$937$	42.3336	−	24.4413i	1.38298	−	0.798463i	0.992511	+	0.122153i	$0.0389800\pi$
$938$	15.4467	+	19.3448i	0.504353	+	0.631630i
$939$		0			0
$940$	0.346400	+	0.290664i	0.0112983	+	0.00948043i
$941$	−5.55445	+	31.5009i	−0.181070	+	1.02690i	0.749831	+	0.661629i	$0.230135\pi$
$941$	−5.55445	+	31.5009i	−0.181070	+	1.02690i	−0.930901	+	0.365270i	$0.880977\pi$
$942$		0			0
$943$	−4.70378	−	5.60574i	−0.153176	−	0.182548i
$944$	0.252898			0.00823112
$945$		0			0
$946$	−26.4858			−0.861128
$947$	−22.2598	−	26.5282i	−0.723347	−	0.862052i	0.271604	−	0.962409i	$-0.412446\pi$
$947$	−22.2598	−	26.5282i	−0.723347	−	0.862052i	−0.994951	+	0.100357i	$0.968001\pi$
$948$		0			0
$949$	0.0976210	−	0.553636i	0.00316891	−	0.0179718i
$950$	3.45982	+	2.90313i	0.112251	+	0.0941900i
$951$		0			0
$952$	−22.1005	+	56.4145i	−0.716280	+	1.82841i
$953$	43.1385	−	24.9060i	1.39739	−	0.806786i	0.403275	−	0.915079i	$-0.367872\pi$
$953$	43.1385	−	24.9060i	1.39739	−	0.806786i	0.994119	+	0.108293i	$0.0345386\pi$
$954$		0			0
$955$		−	7.81261i		−	0.252810i
$956$	10.0747	+	12.0066i	0.325839	+	0.388320i
$957$		0			0
$958$	−5.80574	−	15.9511i	−0.187575	−	0.515358i
$959$	5.84736	−	6.63420i	0.188821	−	0.214230i
$960$		0			0
$961$	35.5516	+	12.9397i	1.14683	+	0.417410i
$962$	4.61406			0.148763
$963$		0			0
$964$		−	16.4707i		−	0.530487i
$965$	−1.27603	+	1.07072i	−0.0410770	+	0.0344677i
$966$		0			0
$967$	−0.0919287	+	0.521354i	−0.00295623	+	0.0167656i	−0.986250	−	0.165259i	$-0.947154\pi$
$967$	−0.0919287	+	0.521354i	−0.00295623	+	0.0167656i	0.983294	+	0.182025i	$0.0582651\pi$
$968$	1.84569	+	5.07098i	0.0593226	+	0.162987i
$969$		0			0
$970$	−1.61093	−	9.13605i	−0.0517239	−	0.293341i
$971$	9.94776	−	17.2300i	0.319239	−	0.552938i	−0.661091	−	0.750306i	$-0.729906\pi$
$971$	9.94776	−	17.2300i	0.319239	−	0.552938i	0.980329	+	0.197368i	$0.0632395\pi$
$972$		0			0
$973$	−0.256265	+	10.5399i	−0.00821547	+	0.337893i
$974$	−0.229412	+	0.630304i	−0.00735083	+	0.0201962i
$975$		0			0
$976$	−3.06090	−	0.539719i	−0.0979770	−	0.0172760i
$977$	16.8301	+	46.2403i	0.538442	+	1.47936i	0.848788	+	0.528734i	$0.177333\pi$
$977$	16.8301	+	46.2403i	0.538442	+	1.47936i	−0.310345	+	0.950624i	$0.600445\pi$
$978$		0			0
$979$	13.6609	+	16.2804i	0.436603	+	0.520324i
$980$	−4.58637	−	8.91861i	−0.146506	−	0.284895i
$981$		0			0
$982$	−6.26977	−	10.8596i	−0.200076	−	0.346543i
$983$	−20.9420	+	17.5724i	−0.667945	+	0.560473i	−0.912456	−	0.409174i	$-0.865817\pi$
$983$	−20.9420	+	17.5724i	−0.667945	+	0.560473i	0.244511	+	0.969646i	$0.421372\pi$
$984$		0			0
$985$	−26.6055	−	4.69127i	−0.847722	−	0.149476i
$986$	8.18150	−	2.97782i	0.260552	−	0.0948332i
$987$		0			0
$988$	0.174446	+	0.989333i	0.00554987	+	0.0314749i
$989$	−7.19866	+	4.15615i	−0.228904	+	0.132158i
$990$		0			0
$991$	−22.1860	+	38.4273i	−0.704761	+	1.22068i	0.262017	+	0.965063i	$0.415612\pi$
$991$	−22.1860	+	38.4273i	−0.704761	+	1.22068i	−0.966778	+	0.255619i	$0.917721\pi$
$992$	−7.96945	−	45.1970i	−0.253030	−	1.43501i
$993$		0			0
$994$	−1.97927	−	1.74452i	−0.0627785	−	0.0553327i
$995$	−10.3963	+	12.3898i	−0.329585	+	0.392784i
$996$		0			0
$997$	−25.9214	+	4.57064i	−0.820939	+	0.144754i	−0.568315	−	0.822811i	$-0.692405\pi$
$997$	−25.9214	+	4.57064i	−0.820939	+	0.144754i	−0.252624	+	0.967565i	$0.581293\pi$
$998$	1.87922	−	1.08497i	0.0594857	−	0.0343441i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.341.15		132
3.2	odd	2		189.2.ba.a.131.8	yes	132
7.3	odd	6		567.2.bd.a.17.8		132
21.17	even	6		189.2.bd.a.185.15	yes	132
27.7	even	9		189.2.bd.a.47.15	yes	132
27.20	odd	18		567.2.bd.a.467.8		132
189.101	even	18	inner	567.2.ba.a.143.15		132
189.115	odd	18		189.2.ba.a.101.8	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.8	✓	132	189.115	odd	18
189.2.ba.a.131.8	yes	132	3.2	odd	2
189.2.bd.a.47.15	yes	132	27.7	even	9
189.2.bd.a.185.15	yes	132	21.17	even	6
567.2.ba.a.143.15		132	189.101	even	18	inner
567.2.ba.a.341.15		132	1.1	even	1	trivial
567.2.bd.a.17.8		132	7.3	odd	6
567.2.bd.a.467.8		132	27.20	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.582560 + 0.694268i) q^{2} +(0.204665 - 1.16071i) q^{4} +(0.931176 + 0.781349i) q^{5} +(-2.06750 + 1.65089i) q^{7} +(2.49483 - 1.44039i) q^{8} +1.10167i q^{10} +(2.30628 + 2.74851i) q^{11} +(0.206055 + 0.566132i) q^{13} +(-2.35060 - 0.473658i) q^{14} +(0.238336 + 0.0867472i) q^{16} +7.94939 q^{17} +1.41477i q^{19} +(1.09750 - 0.920911i) q^{20} +(-0.564660 + 3.20235i) q^{22} +(0.349041 + 0.958983i) q^{23} +(-0.611659 - 3.46889i) q^{25} +(-0.273008 + 0.472864i) q^{26} +(1.49306 + 2.73765i) q^{28} +(0.413325 - 1.13560i) q^{29} +(8.17053 + 1.44069i) q^{31} +(-1.89196 - 5.19810i) q^{32} +(4.63100 + 5.51901i) q^{34} +(-3.21513 - 0.0781722i) q^{35} +(-4.22521 - 7.31828i) q^{37} +(-0.982231 + 0.824190i) q^{38} +(3.44858 + 0.608078i) q^{40} +(-6.73814 + 2.45248i) q^{41} +(1.41438 + 8.02135i) q^{43} +(3.66224 - 2.11440i) q^{44} +(-0.462454 + 0.800993i) q^{46} +(0.0548081 + 0.310832i) q^{47} +(1.54913 - 6.82643i) q^{49} +(2.05201 - 2.44549i) q^{50} +(0.699288 - 0.123303i) q^{52} +(-5.74259 + 3.31549i) q^{53} +4.36136i q^{55} +(-2.78014 + 7.09671i) q^{56} +(1.02920 - 0.374598i) q^{58} +(0.936973 - 0.341030i) q^{59} +(-12.0683 + 2.12796i) q^{61} +(3.75960 + 6.51182i) q^{62} +(2.76033 - 4.78103i) q^{64} +(-0.250473 + 0.688170i) q^{65} +(-7.90859 - 6.63609i) q^{67} +(1.62696 - 9.22694i) q^{68} +(-1.81873 - 2.27770i) q^{70} +(0.952881 + 0.550146i) q^{71} +(-0.808112 - 0.466563i) q^{73} +(2.61941 - 7.19676i) q^{74} +(1.64214 + 0.289554i) q^{76} +(-9.30573 - 1.87515i) q^{77} +(-10.3048 + 8.64674i) q^{79} +(0.154153 + 0.267000i) q^{80} +(-5.62805 - 3.24936i) q^{82} +(5.66119 + 2.06050i) q^{83} +(7.40228 + 6.21125i) q^{85} +(-4.74500 + 5.65488i) q^{86} +(9.71272 + 3.53514i) q^{88} +5.92334 q^{89} +(-1.36064 - 0.830305i) q^{91} +(1.18454 - 0.208866i) q^{92} +(-0.183872 + 0.219130i) q^{94} +(-1.10543 + 1.31740i) q^{95} +(-8.29293 + 1.46227i) q^{97} +(5.64183 - 2.90130i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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