LMFDB - Embedded newform 405.2.p.a.199.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(19,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.p (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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.12
Character	$\chi$	$=$	405.199
Dual form			405.2.p.a.289.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.831033 + 0.990387i) q^{2} +(0.0570464 - 0.323526i) q^{4} +(-1.34113 - 1.78923i) q^{5} +(0.765094 - 0.134907i) q^{7} +(2.60712 - 1.50522i) q^{8} +(0.657507 - 2.81516i) q^{10} +(-3.66139 - 1.33264i) q^{11} +(3.28913 - 3.91983i) q^{13} +(0.769429 + 0.645628i) q^{14} +(3.03995 + 1.10645i) q^{16} +(3.38295 + 1.95315i) q^{17} +(-1.51356 - 2.62156i) q^{19} +(-0.655371 + 0.331823i) q^{20} +(-1.72291 - 4.73366i) q^{22} +(3.17893 + 0.560532i) q^{23} +(-1.40272 + 4.79921i) q^{25} +6.61553 q^{26} -0.255224i q^{28} +(0.271790 - 0.228059i) q^{29} +(-0.470061 + 2.66585i) q^{31} +(-0.628781 - 1.72756i) q^{32} +(0.876974 + 4.97357i) q^{34} +(-1.26747 - 1.18800i) q^{35} +(-3.70101 - 2.13678i) q^{37} +(1.33854 - 3.67761i) q^{38} +(-6.18969 - 2.64604i) q^{40} +(9.24182 + 7.75481i) q^{41} +(-0.120519 + 0.331124i) q^{43} +(-0.640012 + 1.10853i) q^{44} +(2.08666 + 3.61420i) q^{46} +(-2.58307 + 0.455464i) q^{47} +(-6.01068 + 2.18771i) q^{49} +(-5.91878 + 2.59907i) q^{50} +(-1.08053 - 1.28773i) q^{52} +9.29215i q^{53} +(2.52602 + 8.33833i) q^{55} +(1.79163 - 1.50335i) q^{56} +(0.451732 + 0.0796526i) q^{58} +(-12.4304 + 4.52430i) q^{59} +(1.14463 + 6.49154i) q^{61} +(-3.03086 + 1.74987i) q^{62} +(4.42346 - 7.66166i) q^{64} +(-11.4247 - 0.628002i) q^{65} +(-2.55913 + 3.04985i) q^{67} +(0.824880 - 0.983053i) q^{68} +(0.123271 - 2.24256i) q^{70} +(6.06946 - 10.5126i) q^{71} +(12.2022 - 7.04497i) q^{73} +(-0.959425 - 5.44117i) q^{74} +(-0.934485 + 0.340125i) q^{76} +(-2.98109 - 0.525647i) q^{77} +(8.85574 - 7.43085i) q^{79} +(-2.09728 - 6.92307i) q^{80} +15.5975i q^{82} +(-3.57428 - 4.25966i) q^{83} +(-1.04235 - 8.67233i) q^{85} +(-0.428097 + 0.155815i) q^{86} +(-11.5516 + 2.03686i) q^{88} +(2.60530 + 4.51251i) q^{89} +(1.98768 - 3.44277i) q^{91} +(0.362693 - 0.996492i) q^{92} +(-2.59770 - 2.17973i) q^{94} +(-2.66070 + 6.22397i) q^{95} +(-2.43160 + 6.68077i) q^{97} +(-7.16175 - 4.13484i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46}+ \cdots - 87 q^{95}+O(q^{100}) $ 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.831033	+	0.990387i	0.587629	+	0.700309i	0.975149	−	0.221552i	$-0.0711123\pi$
$2$	0.831033	+	0.990387i	0.587629	+	0.700309i	−0.387519	+	0.921862i	$0.626668\pi$
$3$		0			0
$3$		0			0
$4$	0.0570464	−	0.323526i	0.0285232	−	0.161763i
$5$	−1.34113	−	1.78923i	−0.599773	−	0.800170i
$5$	−1.34113	−	1.78923i	−0.599773	−	0.800170i
$6$		0			0
$7$	0.765094	−	0.134907i	0.289179	−	0.0509900i	−0.0271771	−	0.999631i	$-0.508652\pi$
$7$	0.765094	−	0.134907i	0.289179	−	0.0509900i	0.316356	+	0.948641i	$0.397541\pi$
$8$	2.60712	−	1.50522i	0.921756	−	0.532176i
$9$		0			0
$10$	0.657507	−	2.81516i	0.207922	−	0.890230i
$11$	−3.66139	−	1.33264i	−1.10395	−	0.401805i	−0.275180	−	0.961393i	$-0.588737\pi$
$11$	−3.66139	−	1.33264i	−1.10395	−	0.401805i	−0.828771	+	0.559587i	$0.810960\pi$
$12$		0			0
$13$	3.28913	−	3.91983i	0.912240	−	1.08717i	−0.0836409	−	0.996496i	$-0.526655\pi$
$13$	3.28913	−	3.91983i	0.912240	−	1.08717i	0.995881	−	0.0906695i	$-0.0289007\pi$
$14$	0.769429	+	0.645628i	0.205639	+	0.172551i
$15$		0			0
$16$	3.03995	+	1.10645i	0.759986	+	0.276612i
$17$	3.38295	+	1.95315i	0.820487	+	0.473708i	0.850584	−	0.525839i	$-0.176248\pi$
$17$	3.38295	+	1.95315i	0.820487	+	0.473708i	−0.0300976	+	0.999547i	$0.509582\pi$
$18$		0			0
$19$	−1.51356	−	2.62156i	−0.347234	−	0.601427i	0.638523	−	0.769603i	$-0.279546\pi$
$19$	−1.51356	−	2.62156i	−0.347234	−	0.601427i	−0.985757	+	0.168176i	$0.946212\pi$
$20$	−0.655371	+	0.331823i	−0.146545	+	0.0741978i
$21$		0			0
$22$	−1.72291	−	4.73366i	−0.367326	−	1.00922i
$23$	3.17893	+	0.560532i	0.662854	+	0.116879i	0.494946	−	0.868924i	$-0.335188\pi$
$23$	3.17893	+	0.560532i	0.662854	+	0.116879i	0.167908	+	0.985803i	$0.446299\pi$
$24$		0			0
$25$	−1.40272	+	4.79921i	−0.280544	+	0.959841i
$26$	6.61553			1.29741
$27$		0			0
$28$		−	0.255224i		−	0.0482328i
$29$	0.271790	−	0.228059i	0.0504701	−	0.0423494i	−0.617204	−	0.786803i	$-0.711735\pi$
$29$	0.271790	−	0.228059i	0.0504701	−	0.0423494i	0.667674	+	0.744454i	$0.267290\pi$
$30$		0			0
$31$	−0.470061	+	2.66585i	−0.0844255	+	0.478801i	0.913054	+	0.407840i	$0.133718\pi$
$31$	−0.470061	+	2.66585i	−0.0844255	+	0.478801i	−0.997479	+	0.0709611i	$0.977393\pi$
$32$	−0.628781	−	1.72756i	−0.111154	−	0.305393i
$33$		0			0
$34$	0.876974	+	4.97357i	0.150400	+	0.852959i
$35$	−1.26747	−	1.18800i	−0.214242	−	0.200809i
$36$		0			0
$37$	−3.70101	−	2.13678i	−0.608443	−	0.351285i	0.163913	−	0.986475i	$-0.447588\pi$
$37$	−3.70101	−	2.13678i	−0.608443	−	0.351285i	−0.772356	+	0.635190i	$0.780922\pi$
$38$	1.33854	−	3.67761i	0.217140	−	0.596587i
$39$		0			0
$40$	−6.18969	−	2.64604i	−0.978676	−	0.418376i
$41$	9.24182	+	7.75481i	1.44333	+	1.21110i	0.937272	+	0.348599i	$0.113342\pi$
$41$	9.24182	+	7.75481i	1.44333	+	1.21110i	0.506059	+	0.862499i	$0.331102\pi$
$42$		0			0
$43$	−0.120519	+	0.331124i	−0.0183790	+	0.0504960i	−0.948543	−	0.316649i	$-0.897442\pi$
$43$	−0.120519	+	0.331124i	−0.0183790	+	0.0504960i	0.930164	+	0.367145i	$0.119665\pi$
$44$	−0.640012	+	1.10853i	−0.0964854	+	0.167118i
$45$		0			0
$46$	2.08666	+	3.61420i	0.307661	+	0.532884i
$47$	−2.58307	+	0.455464i	−0.376779	+	0.0664363i	−0.358831	−	0.933403i	$-0.616824\pi$
$47$	−2.58307	+	0.455464i	−0.376779	+	0.0664363i	−0.0179481	+	0.999839i	$0.505713\pi$
$48$		0			0
$49$	−6.01068	+	2.18771i	−0.858668	+	0.312530i
$50$	−5.91878	+	2.59907i	−0.837042	+	0.367564i
$51$		0			0
$52$	−1.08053	−	1.28773i	−0.149843	−	0.178576i
$53$			9.29215i			1.27637i	0.769881	+	0.638187i	$0.220315\pi$
$53$			9.29215i			1.27637i	−0.769881	+	0.638187i	$0.779685\pi$
$54$		0			0
$55$	2.52602	+	8.33833i	0.340608	+	1.12434i
$56$	1.79163	−	1.50335i	0.239416	−	0.200894i
$57$		0			0
$58$	0.451732	+	0.0796526i	0.0593154	+	0.0104589i
$59$	−12.4304	+	4.52430i	−1.61830	+	0.589014i	−0.983058	−	0.183296i	$-0.941323\pi$
$59$	−12.4304	+	4.52430i	−1.61830	+	0.589014i	−0.635245	+	0.772311i	$0.719101\pi$
$60$		0			0
$61$	1.14463	+	6.49154i	0.146555	+	0.831156i	0.966105	+	0.258148i	$0.0831123\pi$
$61$	1.14463	+	6.49154i	0.146555	+	0.831156i	−0.819550	+	0.573008i	$0.805777\pi$
$62$	−3.03086	+	1.74987i	−0.384920	+	0.222233i
$63$		0			0
$64$	4.42346	−	7.66166i	0.552932	−	0.957707i
$65$	−11.4247	−	0.628002i	−1.41705	−	0.0778940i
$66$		0			0
$67$	−2.55913	+	3.04985i	−0.312647	+	0.372599i	−0.899369	−	0.437190i	$-0.855974\pi$
$67$	−2.55913	+	3.04985i	−0.312647	+	0.372599i	0.586722	+	0.809789i	$0.300418\pi$
$68$	0.824880	−	0.983053i	0.100031	−	0.119213i
$69$		0			0
$70$	0.123271	−	2.24256i	0.0147337	−	0.268037i
$71$	6.06946	−	10.5126i	0.720312	−	1.24762i	−0.240563	−	0.970634i	$-0.577332\pi$
$71$	6.06946	−	10.5126i	0.720312	−	1.24762i	0.960875	−	0.276983i	$-0.0893346\pi$
$72$		0			0
$73$	12.2022	−	7.04497i	1.42816	−	0.824551i	0.431189	−	0.902262i	$-0.358094\pi$
$73$	12.2022	−	7.04497i	1.42816	−	0.824551i	0.996976	+	0.0777105i	$0.0247610\pi$
$74$	−0.959425	−	5.44117i	−0.111531	−	0.632523i
$75$		0			0
$76$	−0.934485	+	0.340125i	−0.107193	+	0.0390150i
$77$	−2.98109	−	0.525647i	−0.339727	−	0.0599030i
$78$		0			0
$79$	8.85574	−	7.43085i	0.996349	−	0.836036i	0.00987418	−	0.999951i	$-0.496857\pi$
$79$	8.85574	−	7.43085i	0.996349	−	0.836036i	0.986474	+	0.163916i	$0.0524125\pi$
$80$	−2.09728	−	6.92307i	−0.234483	−	0.774023i
$81$		0			0
$82$			15.5975i			1.72245i
$83$	−3.57428	−	4.25966i	−0.392328	−	0.467558i	0.533337	−	0.845903i	$-0.320938\pi$
$83$	−3.57428	−	4.25966i	−0.392328	−	0.467558i	−0.925665	+	0.378345i	$0.876493\pi$
$84$		0			0
$85$	−1.04235	−	8.67233i	−0.113059	−	0.940646i
$86$	−0.428097	+	0.155815i	−0.0461629	+	0.0168019i
$87$		0			0
$88$	−11.5516	+	2.03686i	−1.23141	+	0.217130i
$89$	2.60530	+	4.51251i	0.276161	+	0.478325i	0.970427	−	0.241393i	$-0.0776044\pi$
$89$	2.60530	+	4.51251i	0.276161	+	0.478325i	−0.694266	+	0.719718i	$0.744271\pi$
$90$		0			0
$91$	1.98768	−	3.44277i	0.208366	−	0.360900i
$92$	0.362693	−	0.996492i	0.0378134	−	0.103891i
$93$		0			0
$94$	−2.59770	−	2.17973i	−0.267932	−	0.224822i
$95$	−2.66070	+	6.22397i	−0.272982	+	0.638566i
$96$		0			0
$97$	−2.43160	+	6.68077i	−0.246892	+	0.678330i	0.752904	+	0.658130i	$0.228652\pi$
$97$	−2.43160	+	6.68077i	−0.246892	+	0.678330i	−0.999796	+	0.0201995i	$0.993570\pi$
$98$	−7.16175	−	4.13484i	−0.723446	−	0.417682i
$99$		0			0
$100$	1.47265	+	0.727593i	0.147265	+	0.0727593i
$101$	−0.306182	−	1.73645i	−0.0304663	−	0.172783i	0.965778	−	0.259370i	$-0.0835150\pi$
$101$	−0.306182	−	1.73645i	−0.0304663	−	0.172783i	−0.996244	+	0.0865873i	$0.972404\pi$
$102$		0			0
$103$	6.55464	+	18.0087i	0.645848	+	1.77445i	0.632524	+	0.774541i	$0.282019\pi$
$103$	6.55464	+	18.0087i	0.645848	+	1.77445i	0.0133237	+	0.999911i	$0.495759\pi$
$104$	2.67494	−	15.1703i	0.262299	−	1.48757i
$105$		0			0
$106$	−9.20282	+	7.72208i	−0.893857	+	0.750035i
$107$		−	5.51306i		−	0.532968i	−0.963839	−	0.266484i	$-0.914138\pi$
$107$		−	5.51306i		−	0.532968i	0.963839	−	0.266484i	$-0.0858619\pi$
$108$		0			0
$109$	−14.2674			−1.36657			−0.683287	−	0.730150i	$-0.739450\pi$
$109$	−14.2674			−1.36657			−0.683287	+	0.730150i	$0.739450\pi$
$110$	−6.15897	+	9.43117i	−0.587235	+	0.899227i
$111$		0			0
$112$	2.47511	+	0.436429i	0.233876	+	0.0412387i
$113$	2.12228	+	5.83093i	0.199648	+	0.548527i	0.998602	−	0.0528647i	$-0.0168352\pi$
$113$	2.12228	+	5.83093i	0.199648	+	0.548527i	−0.798954	+	0.601392i	$0.794613\pi$
$114$		0			0
$115$	−3.26045	−	6.43961i	−0.304039	−	0.600496i
$116$	−0.0582783	−	0.100941i	−0.00541100	−	0.00937213i
$117$		0			0
$118$	−14.8109	−	8.55108i	−1.36345	−	0.787191i
$119$	2.85177	+	1.03796i	0.261421	+	0.0951496i
$120$		0			0
$121$	3.20338	+	2.68795i	0.291216	+	0.244359i
$122$	−5.47790	+	6.52831i	−0.495946	+	0.591046i
$123$		0			0
$124$	0.835656	+	0.304154i	0.0750442	+	0.0273138i
$125$	10.4681	−	3.92659i	0.936299	−	0.351205i
$126$		0			0
$127$	10.4623	−	6.04043i	0.928382	−	0.536002i	0.0420828	−	0.999114i	$-0.486601\pi$
$127$	10.4623	−	6.04043i	0.928382	−	0.536002i	0.886300	+	0.463112i	$0.153267\pi$
$128$	7.64304	−	1.34767i	0.675556	−	0.119119i
$129$		0			0
$130$	−8.87231	−	11.8367i	−0.778153	−	1.03815i
$131$	−0.140206	+	0.795145i	−0.0122498	+	0.0694722i	−0.990320	−	0.138804i	$-0.955674\pi$
$131$	−0.140206	+	0.795145i	−0.0122498	+	0.0694722i	0.978070	+	0.208276i	$0.0667853\pi$
$132$		0			0
$133$	−1.51168	−	1.80155i	−0.131079	−	0.156214i
$134$	−5.14726			−0.444655
$135$		0			0
$136$	11.7597			1.00838
$137$	0.458752	+	0.546720i	0.0391939	+	0.0467094i	0.785285	−	0.619134i	$-0.212516\pi$
$137$	0.458752	+	0.546720i	0.0391939	+	0.0467094i	−0.746091	+	0.665844i	$0.768072\pi$
$138$		0			0
$139$	−2.29439	+	13.0121i	−0.194607	+	1.10367i	0.718370	+	0.695662i	$0.244889\pi$
$139$	−2.29439	+	13.0121i	−0.194607	+	1.10367i	−0.912977	+	0.408011i	$0.866222\pi$
$140$	−0.456655	+	0.342290i	−0.0385944	+	0.0289287i
$141$		0			0
$142$	15.4555	−	2.72522i	1.29699	−	0.228695i
$143$	−17.2665	+	9.96882i	−1.44390	+	0.833635i
$144$		0			0
$145$	−0.772556	−	0.180438i	−0.0641573	−	0.0149846i
$146$	17.1177	+	6.23034i	1.41667	+	0.515627i
$147$		0			0
$148$	−0.902433	+	1.07548i	−0.0741796	+	0.0884038i
$149$	4.06706	+	3.41267i	0.333187	+	0.279577i	0.793997	−	0.607922i	$-0.207997\pi$
$149$	4.06706	+	3.41267i	0.333187	+	0.279577i	−0.460810	+	0.887499i	$0.652441\pi$
$150$		0			0
$151$	5.48224	+	1.99537i	0.446138	+	0.162381i	0.555313	−	0.831641i	$-0.312598\pi$
$151$	5.48224	+	1.99537i	0.446138	+	0.162381i	−0.109174	+	0.994023i	$0.534821\pi$
$152$	−7.89205	−	4.55648i	−0.640130	−	0.369579i
$153$		0			0
$154$	−1.95679	−	3.38927i	−0.157683	−	0.273115i
$155$	5.40024	−	2.73421i	0.433758	−	0.219617i
$156$		0			0
$157$	0.552860	+	1.51897i	0.0441230	+	0.121227i	0.959797	−	0.280694i	$-0.0905647\pi$
$157$	0.552860	+	1.51897i	0.0441230	+	0.121227i	−0.915674	+	0.401921i	$0.868343\pi$
$158$	14.7188	+	2.59533i	1.17097	+	0.206473i
$159$		0			0
$160$	−2.24773	+	3.44193i	−0.177699	+	0.272108i
$161$	2.50780			0.197643
$162$		0			0
$163$		−	3.19497i		−	0.250249i	−0.992141	−	0.125125i	$-0.960067\pi$
$163$		−	3.19497i		−	0.250249i	0.992141	−	0.125125i	$-0.0399331\pi$
$164$	3.03610	−	2.54759i	0.237079	−	0.198933i
$165$		0			0
$166$	1.24837	−	7.07983i	0.0968920	−	0.549502i
$167$	−1.88938	−	5.19103i	−0.146205	−	0.401694i	0.844875	−	0.534963i	$-0.179675\pi$
$167$	−1.88938	−	5.19103i	−0.146205	−	0.401694i	−0.991080	+	0.133270i	$0.957452\pi$
$168$		0			0
$169$	−2.28928	−	12.9832i	−0.176099	−	0.998704i
$170$	7.72273	−	8.23933i	0.592307	−	0.631928i
$171$		0			0
$172$	0.100252	+	0.0578806i	0.00764415	+	0.00441335i
$173$	3.64550	−	10.0159i	0.277162	−	0.761497i	−0.720519	−	0.693435i	$-0.756096\pi$
$173$	3.64550	−	10.0159i	0.277162	−	0.761497i	0.997681	−	0.0680619i	$-0.0216815\pi$
$174$		0			0
$175$	−0.425766	+	3.86108i	−0.0321849	+	0.291870i
$176$	−9.65594	−	8.10229i	−0.727844	−	0.610733i
$177$		0			0
$178$	−2.30404	+	6.33030i	−0.172695	+	0.474476i
$179$	−7.01872	+	12.1568i	−0.524604	+	0.908640i	0.474986	+	0.879993i	$0.342453\pi$
$179$	−7.01872	+	12.1568i	−0.524604	+	0.908640i	−0.999590	+	0.0286466i	$0.990880\pi$
$180$		0			0
$181$	7.75754	+	13.4365i	0.576613	+	0.998723i	0.995864	+	0.0908531i	$0.0289594\pi$
$181$	7.75754	+	13.4365i	0.576613	+	0.998723i	−0.419251	+	0.907870i	$0.637707\pi$
$182$	5.06150	−	0.892479i	0.375183	−	0.0661550i
$183$		0			0
$184$	9.13159	−	3.32363i	0.673190	−	0.245021i
$185$	1.14035	+	9.48769i	0.0838405	+	0.697549i
$186$		0			0
$187$	−9.78348	−	11.6595i	−0.715439	−	0.852627i
$188$			0.861671i			0.0628438i
$189$		0			0
$190$	−8.37527	+	2.53721i	−0.607606	+	0.184068i
$191$	−3.34632	+	2.80790i	−0.242131	+	0.203172i	−0.755775	−	0.654831i	$-0.772740\pi$
$191$	−3.34632	+	2.80790i	−0.242131	+	0.203172i	0.513644	+	0.858004i	$0.328295\pi$
$192$		0			0
$193$	3.24089	+	0.571456i	0.233284	+	0.0411343i	0.289068	−	0.957309i	$-0.406655\pi$
$193$	3.24089	+	0.571456i	0.233284	+	0.0411343i	−0.0557838	+	0.998443i	$0.517766\pi$
$194$	−8.63729	+	3.14372i	−0.620122	+	0.225706i
$195$		0			0
$196$	0.364893	+	2.06941i	0.0260638	+	0.147815i
$197$	18.5561	−	10.7134i	1.32207	−	0.763297i	0.338011	−	0.941142i	$-0.390246\pi$
$197$	18.5561	−	10.7134i	1.32207	−	0.763297i	0.984059	+	0.177845i	$0.0569125\pi$
$198$		0			0
$199$	−7.03013	+	12.1765i	−0.498353	+	0.863172i	−0.999998	−	0.00190098i	$-0.999395\pi$
$199$	−7.03013	+	12.1765i	−0.498353	+	0.863172i	0.501645	+	0.865073i	$0.332728\pi$
$200$	3.56682	+	14.6235i	0.252212	+	1.03404i
$201$		0			0
$202$	1.46531	−	1.74628i	0.103099	−	0.122868i
$203$	0.177178	−	0.211153i	0.0124355	−	0.0148200i
$204$		0			0
$205$	1.48065	−	26.9360i	0.103413	−	1.88129i
$206$	−12.3885	+	21.4575i	−0.863146	+	1.49501i
$207$		0			0
$208$	14.3359	−	8.27682i	0.994014	−	0.573894i
$209$	2.04814	+	11.6156i	0.141673	+	0.803466i
$210$		0			0
$211$	3.90781	−	1.42233i	0.269025	−	0.0979170i	−0.203986	−	0.978974i	$-0.565390\pi$
$211$	3.90781	−	1.42233i	0.269025	−	0.0979170i	0.473010	+	0.881057i	$0.343167\pi$
$212$	3.00625	+	0.530083i	0.206470	+	0.0364063i
$213$		0			0
$214$	5.46007	−	4.58154i	0.373242	−	0.313188i
$215$	0.754092	−	0.228445i	0.0514286	−	0.0155798i
$216$		0			0
$217$			2.10304i			0.142764i
$218$	−11.8567	−	14.1303i	−0.803039	−	0.957024i
$219$		0			0
$220$	2.84177	−	0.341561i	0.191592	−	0.0230280i
$221$	18.7830	−	6.83645i	1.26348	−	0.459869i
$222$		0			0
$223$	−16.3593	+	2.88459i	−1.09550	+	0.193167i	−0.692061	−	0.721839i	$-0.743297\pi$
$223$	−16.3593	+	2.88459i	−1.09550	+	0.193167i	−0.403441	+	0.915006i	$0.632186\pi$
$224$	−0.714137	−	1.23692i	−0.0477153	−	0.0826453i
$225$		0			0
$226$	−4.01118	+	6.94758i	−0.266820	+	0.462146i
$227$	−1.81156	+	4.97722i	−0.120238	+	0.330350i	−0.985181	−	0.171520i	$-0.945132\pi$
$227$	−1.81156	+	4.97722i	−0.120238	+	0.330350i	0.864943	+	0.501870i	$0.167354\pi$
$228$		0			0
$229$	15.6135	+	13.1012i	1.03177	+	0.865754i	0.991060	−	0.133417i	$-0.0425949\pi$
$229$	15.6135	+	13.1012i	1.03177	+	0.865754i	0.0407059	+	0.999171i	$0.487039\pi$
$230$	3.66816	−	8.58064i	0.241871	−	0.565791i
$231$		0			0
$232$	0.365309	−	1.00368i	0.0239837	−	0.0658948i
$233$	1.06238	+	0.613363i	0.0695985	+	0.0401827i	0.534395	−	0.845235i	$-0.320539\pi$
$233$	1.06238	+	0.613363i	0.0695985	+	0.0401827i	−0.464797	+	0.885417i	$0.653873\pi$
$234$		0			0
$235$	4.27917	+	4.01087i	0.279142	+	0.261640i
$236$	0.754619	+	4.27966i	0.0491215	+	0.278582i
$237$		0			0
$238$	1.34194	+	3.68694i	0.0869848	+	0.238989i
$239$	2.66890	−	15.1361i	0.172637	−	0.979073i	−0.768199	−	0.640211i	$-0.778847\pi$
$239$	2.66890	−	15.1361i	0.172637	−	0.979073i	0.940836	−	0.338862i	$-0.110042\pi$
$240$		0			0
$241$	14.2379	−	11.9470i	0.917146	−	0.769577i	−0.0563190	−	0.998413i	$-0.517936\pi$
$241$	14.2379	−	11.9470i	0.917146	−	0.769577i	0.973465	+	0.228836i	$0.0734920\pi$
$242$			5.40637i			0.347534i
$243$		0			0
$244$	2.16548			0.138630
$245$	11.9754	+	7.82050i	0.765083	+	0.499633i
$246$		0			0
$247$	−15.2543	−	2.68975i	−0.970611	−	0.171145i
$248$	2.78719	+	7.65774i	0.176987	+	0.486267i
$249$		0			0
$250$	12.5882	+	7.10438i	0.796149	+	0.449320i
$251$	−3.10032	−	5.36991i	−0.195691	−	0.338946i	0.751436	−	0.659806i	$-0.229361\pi$
$251$	−3.10032	−	5.36991i	−0.195691	−	0.338946i	−0.947127	+	0.320860i	$0.896028\pi$
$252$		0			0
$253$	−10.8923	−	6.28869i	−0.684795	−	0.395367i
$254$	14.6769	+	5.34196i	0.920912	+	0.335185i
$255$		0			0
$256$	−5.86792	−	4.92377i	−0.366745	−	0.307736i
$257$	12.7173	−	15.1559i	0.793285	−	0.945401i	−0.206166	−	0.978517i	$-0.566099\pi$
$257$	12.7173	−	15.1559i	0.793285	−	0.945401i	0.999452	+	0.0331163i	$0.0105432\pi$
$258$		0			0
$259$	−3.11989	−	1.13555i	−0.193861	−	0.0705595i
$260$	−0.854910	+	3.66035i	−0.0530193	+	0.227005i
$261$		0			0
$262$	−0.904017	+	0.521935i	−0.0558504	+	0.0322452i
$263$	−16.7623	+	2.95564i	−1.03360	+	0.182252i	−0.664619	−	0.747183i	$-0.731406\pi$
$263$	−16.7623	+	2.95564i	−1.03360	+	0.182252i	−0.368986	+	0.929435i	$0.620295\pi$
$264$		0			0
$265$	16.6258	−	12.4620i	1.02132	−	0.765535i
$266$	0.527975	−	2.99430i	0.0323722	−	0.183592i
$267$		0			0
$268$	0.840718	+	1.00193i	0.0513550	+	0.0612025i
$269$	−6.07723			−0.370535			−0.185268	−	0.982688i	$-0.559315\pi$
$269$	−6.07723			−0.370535			−0.185268	+	0.982688i	$0.559315\pi$
$270$		0			0
$271$	−30.8933			−1.87664			−0.938318	−	0.345774i	$-0.887617\pi$
$271$	−30.8933			−1.87664			−0.938318	+	0.345774i	$0.887617\pi$
$272$	8.12293	+	9.68054i	0.492525	+	0.586969i
$273$		0			0
$274$	−0.160226	+	0.908685i	−0.00967958	+	0.0548956i
$275$	11.5315	−	15.7025i	0.695376	−	0.946894i
$276$		0			0
$277$	24.3118	−	4.28682i	1.46075	−	0.257570i	0.613895	−	0.789388i	$-0.289602\pi$
$277$	24.3118	−	4.28682i	1.46075	−	0.257570i	0.846859	+	0.531818i	$0.178491\pi$
$278$	−14.7937	+	8.54117i	−0.887269	+	0.512265i
$279$		0			0
$280$	−5.09267	−	1.18944i	−0.304345	−	0.0710828i
$281$	−16.7164	−	6.08427i	−0.997216	−	0.362957i	−0.208706	−	0.977979i	$-0.566925\pi$
$281$	−16.7164	−	6.08427i	−0.997216	−	0.362957i	−0.788510	+	0.615022i	$0.789147\pi$
$282$		0			0
$283$	−1.86958	+	2.22808i	−0.111135	+	0.132446i	−0.818744	−	0.574158i	$-0.805329\pi$
$283$	−1.86958	+	2.22808i	−0.111135	+	0.132446i	0.707609	+	0.706604i	$0.249774\pi$
$284$	−3.05486	−	2.56333i	−0.181273	−	0.152106i
$285$		0			0
$286$	−24.2220	−	8.81610i	−1.43228	−	0.521307i
$287$	8.11705	+	4.68638i	0.479134	+	0.276628i
$288$		0			0
$289$	−0.870418	−	1.50761i	−0.0512011	−	0.0886828i
$290$	−0.463317	−	0.915080i	−0.0272069	−	0.0537353i
$291$		0			0
$292$	−1.58314	−	4.34963i	−0.0926461	−	0.254543i
$293$	6.09217	+	1.07421i	0.355908	+	0.0627563i	0.348744	−	0.937218i	$-0.386608\pi$
$293$	6.09217	+	1.07421i	0.355908	+	0.0627563i	0.00716458	+	0.999974i	$0.497719\pi$
$294$		0			0
$295$	24.7659	+	16.1732i	1.44193	+	0.941642i
$296$	−12.8653			−0.747781
$297$		0			0
$298$			6.86401i			0.397621i
$299$	12.6531	−	10.6172i	0.731748	−	0.614010i
$300$		0			0
$301$	−0.0475378	+	0.269600i	−0.00274003	+	0.0155395i
$302$	2.57973	+	7.08776i	0.148447	+	0.407855i
$303$		0			0
$304$	−1.70051	−	9.64407i	−0.0975309	−	0.553125i
$305$	10.0798	−	10.7540i	0.577166	−	0.615774i
$306$		0			0
$307$	−24.1159	−	13.9233i	−1.37637	−	0.794645i	−0.384646	−	0.923064i	$-0.625676\pi$
$307$	−24.1159	−	13.9233i	−1.37637	−	0.794645i	−0.991720	+	0.128419i	$0.959010\pi$
$308$	−0.340121	+	0.934475i	−0.0193802	+	0.0532466i
$309$		0			0
$310$	7.19571	+	3.07611i	0.408689	+	0.174711i
$311$	−13.2628	−	11.1288i	−0.752062	−	0.631055i	0.183986	−	0.982929i	$-0.441100\pi$
$311$	−13.2628	−	11.1288i	−0.752062	−	0.631055i	−0.936047	+	0.351874i	$0.885544\pi$
$312$		0			0
$313$	−3.42361	+	9.40628i	−0.193514	+	0.531675i	−0.998063	−	0.0622113i	$-0.980185\pi$
$313$	−3.42361	+	9.40628i	−0.193514	+	0.531675i	0.804549	+	0.593886i	$0.202407\pi$
$314$	−1.04492	+	1.80986i	−0.0589684	+	0.102136i
$315$		0			0
$316$	−1.89888	−	3.28897i	−0.106821	−	0.185019i
$317$	−7.89475	+	1.39206i	−0.443413	+	0.0781857i	−0.390897	−	0.920434i	$-0.627835\pi$
$317$	−7.89475	+	1.39206i	−0.443413	+	0.0781857i	−0.0525162	+	0.998620i	$0.516724\pi$
$318$		0			0
$319$	−1.29905	+	0.472815i	−0.0727327	+	0.0264725i
$320$	−19.6410	+	2.36071i	−1.09796	+	0.131967i
$321$		0			0
$322$	2.08407	+	2.48370i	0.116141	+	0.138411i
$323$		−	11.8248i		−	0.657950i
$324$		0			0
$325$	14.1984	+	21.2836i	0.787583	+	1.18060i
$326$	3.16426	−	2.65513i	0.175252	−	0.147054i
$327$		0			0
$328$	35.7673	+	6.30673i	1.97492	+	0.348231i
$329$	−1.91484	+	0.696946i	−0.105569	+	0.0384239i
$330$		0			0
$331$	−4.48752	−	25.4500i	−0.246656	−	1.39886i	−0.816615	−	0.577183i	$-0.804152\pi$
$331$	−4.48752	−	25.4500i	−0.246656	−	1.39886i	0.569958	−	0.821674i	$-0.306959\pi$
$332$	−1.58201	+	0.913374i	−0.0868240	+	0.0501279i
$333$		0			0
$334$	3.57099	−	6.18513i	0.195396	−	0.338435i
$335$	8.88904	+	0.488621i	0.485660	+	0.0266962i
$336$		0			0
$337$	12.6980	−	15.1328i	0.691702	−	0.824338i	−0.299859	−	0.953984i	$-0.596940\pi$
$337$	12.6980	−	15.1328i	0.691702	−	0.824338i	0.991560	+	0.129646i	$0.0413840\pi$
$338$	10.9559	−	13.0567i	0.595921	−	0.710191i
$339$		0			0
$340$	−2.86519	−	0.157496i	−0.155387	−	0.00854144i
$341$	5.27369	−	9.13430i	0.285586	−	0.494650i
$342$		0			0
$343$	−9.01329	+	5.20383i	−0.486672	+	0.280980i
$344$	0.184207	+	1.04469i	0.00993177	+	0.0563259i
$345$		0			0
$346$	12.9492	−	4.71312i	0.696153	−	0.253379i
$347$	−24.8142	−	4.37541i	−1.33210	−	0.234884i	−0.538138	−	0.842857i	$-0.680872\pi$
$347$	−24.8142	−	4.37541i	−1.33210	−	0.234884i	−0.793958	+	0.607973i	$0.791983\pi$
$348$		0			0
$349$	−22.8639	+	19.1851i	−1.22388	+	1.02695i	−0.225263	+	0.974298i	$0.572324\pi$
$349$	−22.8639	+	19.1851i	−1.22388	+	1.02695i	−0.998613	+	0.0526561i	$0.983231\pi$
$350$	−4.17779	+	2.78702i	−0.223312	+	0.148972i
$351$		0			0
$352$			7.16322i			0.381801i
$353$	−8.34269	−	9.94244i	−0.444037	−	0.529182i	0.496880	−	0.867819i	$-0.334479\pi$
$353$	−8.34269	−	9.94244i	−0.444037	−	0.529182i	−0.940917	+	0.338637i	$0.890034\pi$
$354$		0			0
$355$	−26.9495	+	3.23914i	−1.43033	+	0.171916i
$356$	1.60854	−	0.585459i	0.0852523	−	0.0310293i
$357$		0			0
$358$	−17.8727	+	3.15144i	−0.944602	+	0.166559i
$359$	6.77215	+	11.7297i	0.357421	+	0.619071i	0.987529	−	0.157436i	$-0.0503230\pi$
$359$	6.77215	+	11.7297i	0.357421	+	0.619071i	−0.630109	+	0.776507i	$0.716990\pi$
$360$		0			0
$361$	4.91829	−	8.51873i	0.258857	−	0.448354i
$362$	−6.86051	+	18.8491i	−0.360581	+	0.990687i
$363$		0			0
$364$	−1.00043	−	0.839464i	−0.0524370	−	0.0439999i
$365$	−28.9699	−	12.3844i	−1.51636	−	0.648230i
$366$		0			0
$367$	−8.56238	+	23.5250i	−0.446953	+	1.22799i	0.487882	+	0.872910i	$0.337770\pi$
$367$	−8.56238	+	23.5250i	−0.446953	+	1.22799i	−0.934835	+	0.355083i	$0.884453\pi$
$368$	9.04359	+	5.22132i	0.471430	+	0.272180i
$369$		0			0
$370$	−8.44881	+	9.01398i	−0.439233	+	0.468614i
$371$	1.25357	+	7.10937i	0.0650823	+	0.369100i
$372$		0			0
$373$	0.713033	+	1.95904i	0.0369195	+	0.101435i	0.956783	−	0.290804i	$-0.0939227\pi$
$373$	0.713033	+	1.95904i	0.0369195	+	0.101435i	−0.919863	+	0.392239i	$0.871701\pi$
$374$	3.41702	−	19.3789i	0.176690	−	1.00206i
$375$		0			0
$376$	−6.04879	+	5.07553i	−0.311942	+	0.261751i
$377$		−	1.81548i		−	0.0935021i
$378$		0			0
$379$	−9.13522			−0.469245			−0.234622	−	0.972087i	$-0.575385\pi$
$379$	−9.13522			−0.469245			−0.234622	+	0.972087i	$0.575385\pi$
$380$	1.86183	+	1.21586i	0.0955100	+	0.0623723i
$381$		0			0
$382$	−5.56181	−	0.980698i	−0.284567	−	0.0501769i
$383$	3.49449	+	9.60103i	0.178560	+	0.490590i	0.996392	−	0.0848669i	$-0.0270465\pi$
$383$	3.49449	+	9.60103i	0.178560	+	0.490590i	−0.817832	+	0.575457i	$0.804824\pi$
$384$		0			0
$385$	3.05754	+	6.03884i	0.155827	+	0.307768i
$386$	2.12732	+	3.68463i	0.108278	+	0.187543i
$387$		0			0
$388$	2.02269	+	1.16780i	0.102687	+	0.0592861i
$389$	−16.4031	−	5.97024i	−0.831670	−	0.302703i	−0.109126	−	0.994028i	$-0.534805\pi$
$389$	−16.4031	−	5.97024i	−0.831670	−	0.302703i	−0.722544	+	0.691325i	$0.757027\pi$
$390$		0			0
$391$	9.65938	+	8.10519i	0.488496	+	0.409897i
$392$	−12.3776	+	14.7510i	−0.625162	+	0.745039i
$393$		0			0
$394$	26.0312	+	9.47457i	1.31143	+	0.477322i
$395$	−25.1723	−	5.87923i	−1.26655	−	0.295816i
$396$		0			0
$397$	−11.4657	+	6.61971i	−0.575445	+	0.332233i	−0.759321	−	0.650716i	$-0.774469\pi$
$397$	−11.4657	+	6.61971i	−0.575445	+	0.332233i	0.183876	+	0.982949i	$0.441136\pi$
$398$	−17.9018	+	3.15656i	−0.897334	+	0.158224i
$399$		0			0
$400$	−9.57427	+	13.0373i	−0.478713	+	0.651865i
$401$	−6.80556	+	38.5962i	−0.339853	+	1.92740i	0.0328639	+	0.999460i	$0.489537\pi$
$401$	−6.80556	+	38.5962i	−0.339853	+	1.92740i	−0.372717	+	0.927945i	$0.621574\pi$
$402$		0			0
$403$	8.90359	+	10.6109i	0.443519	+	0.528566i
$404$	−0.579252			−0.0288189
$405$		0			0
$406$	0.356364			0.0176860
$407$	10.7033	+	12.7557i	0.530543	+	0.632277i
$408$		0			0
$409$	3.44309	−	19.5268i	0.170250	−	0.965536i	−0.773235	−	0.634120i	$-0.781363\pi$
$409$	3.44309	−	19.5268i	0.170250	−	0.965536i	0.943485	−	0.331416i	$-0.107526\pi$
$410$	27.9076	−	20.9183i	1.37826	−	1.03308i
$411$		0			0
$412$	6.20021	−	1.09326i	0.305462	−	0.0538612i
$413$	−8.90009	+	5.13847i	−0.437945	+	0.252847i
$414$		0			0
$415$	−2.82794	+	12.1080i	−0.138818	+	0.594358i
$416$	−8.83989	−	3.21746i	−0.433411	−	0.157749i
$417$		0			0
$418$	−9.80184	+	11.6814i	−0.479424	+	0.571355i
$419$	20.8598	+	17.5035i	1.01907	+	0.855101i	0.989510	−	0.144462i	$-0.0461450\pi$
$419$	20.8598	+	17.5035i	1.01907	+	0.855101i	0.0295598	+	0.999563i	$0.490589\pi$
$420$		0			0
$421$	−2.12407	−	0.773098i	−0.103521	−	0.0376785i	0.289740	−	0.957105i	$-0.406431\pi$
$421$	−2.12407	−	0.773098i	−0.103521	−	0.0376785i	−0.393261	+	0.919427i	$0.628653\pi$
$422$	4.65617	+	2.68824i	0.226659	+	0.130862i
$423$		0			0
$424$	13.9867	+	24.2257i	0.679256	+	1.17651i
$425$	−14.1189	+	13.4958i	−0.684867	+	0.654641i
$426$		0			0
$427$	1.75150	+	4.81222i	0.0847612	+	0.232880i
$428$	−1.78362	−	0.314500i	−0.0862145	−	0.0152019i
$429$		0			0
$430$	0.852924	+	0.556997i	0.0411317	+	0.0268608i
$431$	−9.69510			−0.466996			−0.233498	−	0.972357i	$-0.575017\pi$
$431$	−9.69510			−0.466996			−0.233498	+	0.972357i	$0.575017\pi$
$432$		0			0
$433$		−	32.3437i		−	1.55434i	−0.629292	−	0.777169i	$-0.716655\pi$
$433$		−	32.3437i		−	1.55434i	0.629292	−	0.777169i	$-0.283345\pi$
$434$	−2.08282	+	1.74770i	−0.0999788	+	0.0838922i
$435$		0			0
$436$	−0.813906	+	4.61589i	−0.0389790	+	0.221061i
$437$	−3.34203	−	9.18216i	−0.159871	−	0.439242i
$438$		0			0
$439$	1.71544	+	9.72872i	0.0818733	+	0.464327i	0.997988	+	0.0634094i	$0.0201974\pi$
$439$	1.71544	+	9.72872i	0.0818733	+	0.464327i	−0.916114	+	0.400917i	$0.868692\pi$
$440$	19.1367	+	17.9368i	0.912305	+	0.855104i
$441$		0			0
$442$	22.3800	+	12.9211i	1.06451	+	0.614594i
$443$	8.94805	−	24.5846i	0.425135	−	1.16805i	−0.523597	−	0.851966i	$-0.675410\pi$
$443$	8.94805	−	24.5846i	0.425135	−	1.16805i	0.948732	−	0.316082i	$-0.102368\pi$
$444$		0			0
$445$	4.57988	−	10.7134i	0.217107	−	0.507862i
$446$	−16.4520	−	13.8049i	−0.779025	−	0.653680i
$447$		0			0
$448$	2.35075	−	6.45865i	0.111063	−	0.305142i
$449$	8.04462	−	13.9337i	0.379649	−	0.657572i	−0.611362	−	0.791351i	$-0.709378\pi$
$449$	8.04462	−	13.9337i	0.379649	−	0.657572i	0.991011	+	0.133779i	$0.0427113\pi$
$450$		0			0
$451$	−23.5036	−	40.7094i	−1.10674	−	1.91693i
$452$	2.00752	−	0.353981i	0.0944260	−	0.0166499i
$453$		0			0
$454$	−6.43484	+	2.34209i	−0.302002	+	0.109920i
$455$	−8.82566	+	1.06078i	−0.413754	+	0.0497303i
$456$		0			0
$457$	−19.5646	−	23.3162i	−0.915193	−	1.09068i	−0.995580	−	0.0939208i	$-0.970060\pi$
$457$	−19.5646	−	23.3162i	−0.915193	−	1.09068i	0.0803867	−	0.996764i	$-0.474384\pi$
$458$			26.3509i			1.23130i
$459$		0			0
$460$	−2.26938	+	0.687486i	−0.105810	+	0.0320542i
$461$	−12.5270	+	10.5114i	−0.583438	+	0.489563i	−0.886074	−	0.463543i	$-0.846578\pi$
$461$	−12.5270	+	10.5114i	−0.583438	+	0.489563i	0.302636	+	0.953106i	$0.402133\pi$
$462$		0			0
$463$	−7.19625	−	1.26889i	−0.334438	−	0.0589705i	0.00390751	−	0.999992i	$-0.498756\pi$
$463$	−7.19625	−	1.26889i	−0.334438	−	0.0589705i	−0.338346	+	0.941022i	$0.609867\pi$
$464$	1.07856	−	0.392564i	0.0500709	−	0.0182243i
$465$		0			0
$466$	0.275403	+	1.56189i	0.0127578	+	0.0723531i
$467$	−8.71268	+	5.03027i	−0.403175	+	0.232773i	−0.687853	−	0.725850i	$-0.741447\pi$
$467$	−8.71268	+	5.03027i	−0.403175	+	0.232773i	0.284678	+	0.958623i	$0.408113\pi$
$468$		0			0
$469$	−1.54653	+	2.67867i	−0.0714121	+	0.123689i
$470$	−0.416181	+	7.57120i	−0.0191970	+	0.349233i
$471$		0			0
$472$	−25.5975	+	30.5059i	−1.17822	+	1.40415i
$473$	0.882537	−	1.05177i	0.0405791	−	0.0483603i
$474$		0			0
$475$	14.7045	−	3.58657i	0.674688	−	0.164563i
$476$	0.498490	−	0.863411i	0.0228483	−	0.0395744i
$477$		0			0
$478$	17.2085	−	9.93536i	0.787100	−	0.454433i
$479$	1.39286	+	7.89931i	0.0636415	+	0.360929i	0.999952	+	0.00975657i	$0.00310566\pi$
$479$	1.39286	+	7.89931i	0.0636415	+	0.360929i	−0.936311	+	0.351172i	$0.885783\pi$
$480$		0			0
$481$	−20.5489	+	7.47920i	−0.936950	+	0.341022i
$482$	23.6644	+	4.17267i	1.07788	+	0.190060i
$483$		0			0
$484$	1.05236	−	0.883038i	0.0478347	−	0.0401381i
$485$	15.2146	−	4.60911i	0.690858	−	0.209289i
$486$		0			0
$487$			1.30014i			0.0589151i	0.999566	+	0.0294575i	$0.00937799\pi$
$487$			1.30014i			0.0589151i	−0.999566	+	0.0294575i	$0.990622\pi$
$488$	12.7554	+	15.2013i	0.577409	+	0.688130i
$489$		0			0
$490$	2.20668	+	18.3594i	0.0996874	+	0.829394i
$491$	−10.4561	+	3.80573i	−0.471879	+	0.171750i	−0.567003	−	0.823715i	$-0.691897\pi$
$491$	−10.4561	+	3.80573i	−0.471879	+	0.171750i	0.0951242	+	0.995465i	$0.469675\pi$
$492$		0			0
$493$	1.36488	−	0.240666i	0.0614713	−	0.0108390i
$494$	−10.0130	−	17.3430i	−0.450505	−	0.780298i
$495$		0			0
$496$	−4.37859	+	7.58394i	−0.196604	+	0.340529i
$497$	3.22548	−	8.86195i	0.144683	−	0.397513i
$498$		0			0
$499$	−13.6131	−	11.4227i	−0.609404	−	0.511351i	0.285049	−	0.958513i	$-0.407990\pi$
$499$	−13.6131	−	11.4227i	−0.609404	−	0.511351i	−0.894453	+	0.447162i	$0.852435\pi$
$500$	−0.673185	−	3.61071i	−0.0301057	−	0.161476i
$501$		0			0
$502$	2.74182	−	7.53309i	0.122374	−	0.336218i
$503$	−11.2798	−	6.51241i	−0.502942	−	0.290374i	0.226985	−	0.973898i	$-0.427113\pi$
$503$	−11.2798	−	6.51241i	−0.502942	−	0.290374i	−0.729928	+	0.683524i	$0.760446\pi$
$504$		0			0
$505$	−2.69628	+	2.87664i	−0.119983	+	0.128009i
$506$	−2.82366	−	16.0137i	−0.125527	−	0.711898i
$507$		0			0
$508$	−1.35740	−	3.72942i	−0.0602248	−	0.165466i
$509$	−3.60691	+	20.4558i	−0.159873	+	0.906687i	0.794321	+	0.607499i	$0.207827\pi$
$509$	−3.60691	+	20.4558i	−0.159873	+	0.906687i	−0.954194	+	0.299188i	$0.903284\pi$
$510$		0			0
$511$	8.38545	−	7.03623i	0.370951	−	0.311265i
$512$		−	25.4252i		−	1.12365i
$513$		0			0
$514$	25.5788			1.12823
$515$	23.4312	−	35.8799i	1.03250	−	1.58106i
$516$		0			0
$517$	10.0646	+	1.77466i	0.442640	+	0.0780493i
$518$	−1.46810	−	4.03358i	−0.0645047	−	0.177225i
$519$		0			0
$520$	−30.7307	+	15.5594i	−1.34763	+	0.682323i
$521$	−12.5826	−	21.7937i	−0.551255	−	0.954801i	−0.998184	−	0.0602320i	$-0.980816\pi$
$521$	−12.5826	−	21.7937i	−0.551255	−	0.954801i	0.446930	−	0.894569i	$-0.352517\pi$
$522$		0			0
$523$	21.4096	+	12.3608i	0.936177	+	0.540502i	0.888760	−	0.458373i	$-0.151568\pi$
$523$	21.4096	+	12.3608i	0.936177	+	0.540502i	0.0474173	+	0.998875i	$0.484901\pi$
$524$	0.249252	+	0.0907203i	0.0108886	+	0.00396313i
$525$		0			0
$526$	−16.8572	−	14.1449i	−0.735010	−	0.616746i
$527$	−6.79700	+	8.10034i	−0.296082	+	0.352857i
$528$		0			0
$529$	−11.8215	−	4.30268i	−0.513978	−	0.187073i
$530$	26.1588	+	6.10965i	1.13627	+	0.265386i
$531$		0			0
$532$	−0.669084	+	0.386296i	−0.0290085	+	0.0167481i
$533$	60.7951	−	10.7198i	2.63333	−	0.464327i
$534$		0			0
$535$	−9.86416	+	7.39376i	−0.426465	+	0.319660i
$536$	−2.08126	+	11.8034i	−0.0898966	+	0.509829i
$537$		0			0
$538$	−5.05038	−	6.01881i	−0.217737	−	0.259489i
$539$	24.9229			1.07350
$540$		0			0
$541$	16.9208			0.727482			0.363741	−	0.931500i	$-0.381499\pi$
$541$	16.9208			0.727482			0.363741	+	0.931500i	$0.381499\pi$
$542$	−25.6734	−	30.5964i	−1.10277	−	1.31423i
$543$		0			0
$544$	1.24705	−	7.07237i	0.0534668	−	0.303225i
$545$	19.1346	+	25.5278i	0.819635	+	1.09349i
$546$		0			0
$547$	−1.40276	+	0.247344i	−0.0599776	+	0.0105757i	−0.203556	−	0.979063i	$-0.565250\pi$
$547$	−1.40276	+	0.247344i	−0.0599776	+	0.0105757i	0.143579	+	0.989639i	$0.454139\pi$
$548$	0.203048	−	0.117230i	0.00867379	−	0.00500781i
$549$		0			0
$550$	25.1346	−	1.62862i	1.07174	−	0.0694446i
$551$	−1.00924	−	0.367332i	−0.0429950	−	0.0156489i
$552$		0			0
$553$	5.77301	−	6.88000i	0.245493	−	0.292567i
$554$	24.4495	+	20.5156i	1.03876	+	0.871624i
$555$		0			0
$556$	4.07887	+	1.48459i	0.172983	+	0.0629605i
$557$	−8.38178	−	4.83922i	−0.355147	−	0.205044i	0.311803	−	0.950147i	$-0.399067\pi$
$557$	−8.38178	−	4.83922i	−0.355147	−	0.205044i	−0.666950	+	0.745102i	$0.732401\pi$
$558$		0			0
$559$	0.901548	+	1.56153i	0.0381314	+	0.0660455i
$560$	−2.53859	−	5.01387i	−0.107275	−	0.211875i
$561$		0			0
$562$	−7.86609	−	21.6119i	−0.331811	−	0.911644i
$563$	37.5918	+	6.62845i	1.58431	+	0.279356i	0.895322	−	0.445420i	$-0.146945\pi$
$563$	37.5918	+	6.62845i	1.58431	+	0.279356i	0.688985	+	0.724776i	$0.258057\pi$
$564$		0			0
$565$	7.58662	−	11.6173i	0.319172	−	0.488744i
$566$	−3.76035			−0.158059
$567$		0			0
$568$		−	36.5435i		−	1.53333i
$569$	−25.8444	+	21.6860i	−1.08345	+	0.909126i	−0.996203	−	0.0870599i	$-0.972253\pi$
$569$	−25.8444	+	21.6860i	−1.08345	+	0.909126i	−0.0872516	+	0.996186i	$0.527808\pi$
$570$		0			0
$571$	0.954517	−	5.41334i	0.0399453	−	0.226541i	−0.958299	−	0.285766i	$-0.907752\pi$
$571$	0.954517	−	5.41334i	0.0399453	−	0.226541i	0.998245	+	0.0592252i	$0.0188630\pi$
$572$	2.24018	+	6.15485i	0.0936667	+	0.257347i
$573$		0			0
$574$	2.10421	+	11.9336i	0.0878279	+	0.498097i
$575$	−7.14926	+	14.4701i	−0.298145	+	0.603445i
$576$		0			0
$577$	23.6596	+	13.6599i	0.984962	+	0.568668i	0.903765	−	0.428030i	$-0.140792\pi$
$577$	23.6596	+	13.6599i	0.984962	+	0.568668i	0.0811975	+	0.996698i	$0.474126\pi$
$578$	0.769769	−	2.11492i	0.0320182	−	0.0879692i
$579$		0			0
$580$	−0.102448	+	0.239649i	−0.00425392	+	0.00995087i
$581$	−3.30932	−	2.77685i	−0.137294	−	0.115203i
$582$		0			0
$583$	12.3831	−	34.0222i	0.512854	−	1.40906i
$584$	21.2085	−	36.7342i	0.877613	−	1.52007i
$585$		0			0
$586$	3.99891	+	6.92632i	0.165193	+	0.286123i
$587$	11.7130	−	2.06533i	0.483449	−	0.0852451i	0.0733885	−	0.997303i	$-0.476619\pi$
$587$	11.7130	−	2.06533i	0.483449	−	0.0852451i	0.410061	+	0.912058i	$0.365508\pi$
$588$		0			0
$589$	7.70014	−	2.80262i	0.317279	−	0.115480i
$590$	4.56353	+	37.9683i	0.187877	+	1.56313i
$591$		0			0
$592$	−8.88664	−	10.5907i	−0.365239	−	0.435274i
$593$			9.14301i			0.375459i	0.982221	+	0.187729i	$0.0601128\pi$
$593$			9.14301i			0.375459i	−0.982221	+	0.187729i	$0.939887\pi$
$594$		0			0
$595$	−1.96746	−	6.49453i	−0.0806578	−	0.266250i
$596$	1.33610	−	1.12112i	0.0547287	−	0.0459229i
$597$		0			0
$598$	21.0303	+	3.70821i	0.859994	+	0.151640i
$599$	−24.8634	+	9.04955i	−1.01589	+	0.369755i	−0.795693	−	0.605700i	$-0.792893\pi$
$599$	−24.8634	+	9.04955i	−1.01589	+	0.369755i	−0.220200	+	0.975455i	$0.570671\pi$
$600$		0			0
$601$	3.19159	+	18.1004i	0.130188	+	0.738330i	0.978091	+	0.208179i	$0.0667537\pi$
$601$	3.19159	+	18.1004i	0.130188	+	0.738330i	−0.847903	+	0.530151i	$0.822135\pi$
$602$	−0.306514	+	0.176966i	−0.0124926	+	0.00721260i
$603$		0			0
$604$	0.958297	−	1.65982i	0.0389925	−	0.0675371i
$605$	0.513218	−	9.33650i	0.0208653	−	0.379583i
$606$		0			0
$607$	19.6443	−	23.4111i	0.797336	−	0.950228i	−0.202240	−	0.979336i	$-0.564822\pi$
$607$	19.6443	−	23.4111i	0.797336	−	0.950228i	0.999576	+	0.0291076i	$0.00926655\pi$
$608$	−3.57721	+	4.26315i	−0.145075	+	0.172894i
$609$		0			0
$610$	19.0273	+	1.04591i	0.770392	+	0.0423477i
$611$	−6.71069	+	11.6233i	−0.271486	+	0.470227i
$612$		0			0
$613$	−17.3635	+	10.0248i	−0.701304	+	0.404898i	−0.807833	−	0.589411i	$-0.799360\pi$
$613$	−17.3635	+	10.0248i	−0.701304	+	0.404898i	0.106529	+	0.994310i	$0.466026\pi$
$614$	−6.25164	−	35.4548i	−0.252295	−	1.43084i
$615$		0			0
$616$	−8.56328	+	3.11678i	−0.345024	+	0.125579i
$617$	−24.8810	−	4.38720i	−1.00167	−	0.176622i	−0.351321	−	0.936255i	$-0.614267\pi$
$617$	−24.8810	−	4.38720i	−1.00167	−	0.176622i	−0.650352	+	0.759633i	$0.725379\pi$
$618$		0			0
$619$	−13.4670	+	11.3002i	−0.541285	+	0.454192i	−0.871977	−	0.489547i	$-0.837162\pi$
$619$	−13.4670	+	11.3002i	−0.541285	+	0.454192i	0.330692	+	0.943739i	$0.392718\pi$
$620$	−0.576525	−	1.90310i	−0.0231538	−	0.0764302i
$621$		0			0
$622$		−	22.3836i		−	0.897502i
$623$	2.60207	+	3.10102i	0.104250	+	0.124240i
$624$		0			0
$625$	−21.0648	−	13.4639i	−0.842591	−	0.538555i
$626$	−12.1610	+	4.42624i	−0.486051	+	0.176908i
$627$		0			0
$628$	0.522965	−	0.0922128i	0.0208686	−	0.00367969i
$629$	−8.34690	−	14.4573i	−0.332813	−	0.576449i
$630$		0			0
$631$	15.3587	−	26.6020i	0.611420	−	1.05901i	−0.379581	−	0.925158i	$-0.623932\pi$
$631$	15.3587	−	26.6020i	0.611420	−	1.05901i	0.991001	−	0.133852i	$-0.0427347\pi$
$632$	11.9029	−	32.7030i	0.473472	−	1.30085i
$633$		0			0
$634$	−7.93948	−	6.66201i	−0.315317	−	0.264582i
$635$	−24.8392	−	10.6185i	−0.985712	−	0.421384i
$636$		0			0
$637$	−11.1944	+	30.7565i	−0.443540	+	1.21862i
$638$	−1.54782	−	0.893635i	−0.0612788	−	0.0353794i
$639$		0			0
$640$	−12.6617	−	11.8678i	−0.500496	−	0.469115i
$641$	−1.59110	−	9.02357i	−0.0628446	−	0.356409i	−0.999972	−	0.00742320i	$-0.997637\pi$
$641$	−1.59110	−	9.02357i	−0.0628446	−	0.356409i	0.937128	−	0.348986i	$-0.113474\pi$
$642$		0			0
$643$	−4.97910	−	13.6800i	−0.196357	−	0.539486i	0.801967	−	0.597369i	$-0.203787\pi$
$643$	−4.97910	−	13.6800i	−0.196357	−	0.539486i	−0.998323	+	0.0578831i	$0.981565\pi$
$644$	0.143061	−	0.811340i	0.00563740	−	0.0319713i
$645$		0			0
$646$	11.7111	−	9.82681i	0.460769	−	0.386631i
$647$			16.6946i			0.656331i	0.944620	+	0.328165i	$0.106430\pi$
$647$			16.6946i			0.656331i	−0.944620	+	0.328165i	$0.893570\pi$
$648$		0			0
$649$	51.5419			2.02320
$650$	−9.27972	+	31.7493i	−0.363980	+	1.24531i
$651$		0			0
$652$	−1.03366	−	0.182262i	−0.0404811	−	0.00713791i
$653$	6.31264	+	17.3438i	0.247033	+	0.678716i	0.999791	+	0.0204201i	$0.00650038\pi$
$653$	6.31264	+	17.3438i	0.247033	+	0.678716i	−0.752759	+	0.658296i	$0.771277\pi$
$654$		0			0
$655$	1.61074	−	0.815536i	0.0629367	−	0.0318656i
$656$	19.5143	+	33.7998i	0.761907	+	1.31966i
$657$		0			0
$658$	−2.28155	−	1.31725i	−0.0889439	−	0.0513518i
$659$	−8.26055	−	3.00660i	−0.321785	−	0.117120i	0.176077	−	0.984376i	$-0.443659\pi$
$659$	−8.26055	−	3.00660i	−0.321785	−	0.117120i	−0.497862	+	0.867256i	$0.665882\pi$
$660$		0			0
$661$	−13.7931	−	11.5737i	−0.536487	−	0.450166i	0.333847	−	0.942627i	$-0.391653\pi$
$661$	−13.7931	−	11.5737i	−0.536487	−	0.450166i	−0.870335	+	0.492461i	$0.836097\pi$
$662$	21.4760	−	25.5942i	0.834690	−	0.994745i
$663$		0			0
$664$	−15.7303	−	5.72536i	−0.610454	−	0.222187i
$665$	−1.19603	+	5.12087i	−0.0463800	+	0.198579i
$666$		0			0
$667$	0.991835	−	0.572636i	0.0384040	−	0.0221726i
$668$	−1.78721	+	0.315134i	−0.0691494	+	0.0121929i
$669$		0			0
$670$	6.90316	+	9.20965i	0.266692	+	0.355800i
$671$	4.45992	−	25.2934i	0.172173	−	0.976442i
$672$		0			0
$673$	−5.25324	−	6.26057i	−0.202498	−	0.241327i	0.655233	−	0.755427i	$-0.272571\pi$
$673$	−5.25324	−	6.26057i	−0.202498	−	0.241327i	−0.857730	+	0.514100i	$0.828126\pi$
$674$	25.5398			0.983756
$675$		0			0
$676$	−4.33098			−0.166576
$677$	−0.529394	−	0.630907i	−0.0203462	−	0.0242477i	0.755775	−	0.654831i	$-0.227260\pi$
$677$	−0.529394	−	0.630907i	−0.0203462	−	0.0242477i	−0.776122	+	0.630583i	$0.782816\pi$
$678$		0			0
$679$	−0.959124	+	5.43946i	−0.0368078	+	0.208747i
$680$	−15.7713	−	21.0408i	−0.604802	−	0.806879i
$681$		0			0
$682$	13.4291	−	2.36791i	0.514227	−	0.0906721i
$683$	33.6587	−	19.4328i	1.28791	−	0.743577i	0.309631	−	0.950857i	$-0.399794\pi$
$683$	33.6587	−	19.4328i	1.28791	−	0.743577i	0.978282	+	0.207280i	$0.0664611\pi$
$684$		0			0
$685$	0.362961	−	1.55404i	0.0138680	−	0.0593768i
$686$	−12.6441	−	4.60209i	−0.482756	−	0.175709i
$687$		0			0
$688$	−0.732745	+	0.873251i	−0.0279356	+	0.0332924i
$689$	36.4236	+	30.5631i	1.38763	+	1.16436i
$690$		0			0
$691$	33.1809	+	12.0769i	1.26226	+	0.459426i	0.884527	−	0.466488i	$-0.154481\pi$
$691$	33.1809	+	12.0769i	1.26226	+	0.459426i	0.377734	+	0.925914i	$0.376703\pi$
$692$	−3.03245	−	1.75079i	−0.115277	−	0.0665549i
$693$		0			0
$694$	−16.2881	−	28.2118i	−0.618287	−	1.07090i
$695$	26.3588	−	13.3458i	0.999846	−	0.506235i
$696$		0			0
$697$	16.1184	+	44.2848i	0.610526	+	1.67741i
$698$	−38.0013	−	6.70066i	−1.43837	−	0.253624i
$699$		0			0
$700$	1.22487	+	0.358007i	0.0462958	+	0.0135314i
$701$	26.7698			1.01108			0.505541	−	0.862803i	$-0.331293\pi$
$701$	26.7698			1.01108			0.505541	+	0.862803i	$0.331293\pi$
$702$		0			0
$703$			12.9366i			0.487912i
$704$	−26.4062	+	22.1575i	−0.995222	+	0.835091i
$705$		0			0
$706$	2.91380	−	16.5250i	0.109662	−	0.621926i
$707$	−0.468517	−	1.28724i	−0.0176204	−	0.0484116i
$708$		0			0
$709$	5.90817	+	33.5069i	0.221886	+	1.25838i	0.868550	+	0.495602i	$0.165053\pi$
$709$	5.90817	+	33.5069i	0.221886	+	1.25838i	−0.646664	+	0.762775i	$0.723836\pi$
$710$	−25.6039	−	23.9986i	−0.960898	−	0.900650i
$711$		0			0
$712$	13.5846	+	7.84310i	0.509106	+	0.293933i
$713$	−2.98859	+	8.21108i	−0.111923	+	0.307507i
$714$		0			0
$715$	40.9933	+	17.5243i	1.53306	+	0.655371i
$716$	3.53264	+	2.96424i	0.132021	+	0.110779i
$717$		0			0
$718$	−5.98907	+	16.4548i	−0.223510	+	0.614089i
$719$	−3.78251	+	6.55150i	−0.141064	+	0.244330i	−0.927898	−	0.372835i	$-0.878386\pi$
$719$	−3.78251	+	6.55150i	−0.141064	+	0.244330i	0.786834	+	0.617165i	$0.211719\pi$
$720$		0			0
$721$	7.44442	+	12.8941i	0.277245	+	0.480202i
$722$	12.5241	−	2.20834i	0.466099	−	0.0821858i
$723$		0			0
$724$	4.78958	−	1.74326i	0.178003	−	0.0647879i
$725$	0.713256	+	1.62428i	0.0264897	+	0.0603241i
$726$		0			0
$727$	18.7705	+	22.3698i	0.696158	+	0.829649i	0.992086	−	0.125561i	$-0.0400731\pi$
$727$	18.7705	+	22.3698i	0.696158	+	0.829649i	−0.295927	+	0.955210i	$0.595629\pi$
$728$		−	11.9676i		−	0.443549i
$729$		0			0
$730$	−11.8096	−	38.9833i	−0.437094	−	1.44284i
$731$	−1.05445	+	0.884786i	−0.0390001	+	0.0327250i
$732$		0			0
$733$	−21.0725	−	3.71565i	−0.778330	−	0.137241i	−0.229650	−	0.973273i	$-0.573758\pi$
$733$	−21.0725	−	3.71565i	−0.778330	−	0.137241i	−0.548680	+	0.836033i	$0.684869\pi$
$734$	−30.4144	+	11.0699i	−1.12262	+	0.408599i
$735$		0			0
$736$	−1.03050	−	5.84426i	−0.0379847	−	0.215422i
$737$	13.4343	−	7.75631i	0.494860	−	0.285707i
$738$		0			0
$739$	−1.12801	+	1.95377i	−0.0414944	+	0.0718704i	−0.886027	−	0.463634i	$-0.846545\pi$
$739$	−1.12801	+	1.95377i	−0.0414944	+	0.0718704i	0.844532	+	0.535505i	$0.179879\pi$
$740$	3.13457	+	0.172304i	0.115229	+	0.00633402i
$741$		0			0
$742$	−5.99927	+	7.14965i	−0.220240	+	0.262472i
$743$	−2.12019	+	2.52675i	−0.0777823	+	0.0926974i	−0.803532	−	0.595261i	$-0.797049\pi$
$743$	−2.12019	+	2.52675i	−0.0777823	+	0.0926974i	0.725750	+	0.687959i	$0.241493\pi$
$744$		0			0
$745$	0.651590	−	11.8538i	0.0238724	−	0.434289i
$746$	−1.34766	+	2.33421i	−0.0493412	+	0.0854615i
$747$		0			0
$748$	−4.33026	+	2.50008i	−0.158330	+	0.0914119i
$749$	−0.743750	−	4.21801i	−0.0271760	−	0.154123i
$750$		0			0
$751$	−29.9156	+	10.8884i	−1.09164	+	0.397323i	−0.824227	−	0.566260i	$-0.808390\pi$
$751$	−29.9156	+	10.8884i	−1.09164	+	0.397323i	−0.267410	+	0.963583i	$0.586168\pi$
$752$	−8.35633	−	1.47345i	−0.304724	−	0.0537310i
$753$		0			0
$754$	1.79803	−	1.50873i	0.0654804	−	0.0549446i
$755$	−3.78223	−	12.4851i	−0.137650	−	0.454378i
$756$		0			0
$757$		−	18.5287i		−	0.673436i	−0.941605	−	0.336718i	$-0.890683\pi$
$757$		−	18.5287i		−	0.673436i	0.941605	−	0.336718i	$-0.109317\pi$
$758$	−7.59167	−	9.04740i	−0.275742	−	0.328616i
$759$		0			0
$760$	2.43169	+	20.2316i	0.0882068	+	0.733876i
$761$	38.6363	−	14.0625i	1.40057	−	0.509764i	0.472219	−	0.881481i	$-0.343453\pi$
$761$	38.6363	−	14.0625i	1.40057	−	0.509764i	0.928346	+	0.371717i	$0.121231\pi$
$762$		0			0
$763$	−10.9159	+	1.92478i	−0.395184	+	0.0696816i
$764$	0.717533	+	1.24280i	0.0259594	+	0.0449630i
$765$		0			0
$766$	−6.60470	+	11.4397i	−0.238638	+	0.413332i
$767$	−23.1507	+	63.6062i	−0.835925	+	2.29669i
$768$		0			0
$769$	−26.1339	−	21.9289i	−0.942412	−	0.790777i	0.0355917	−	0.999366i	$-0.488668\pi$
$769$	−26.1339	−	21.9289i	−0.942412	−	0.790777i	−0.978003	+	0.208589i	$0.933113\pi$
$770$	−3.43987	+	8.04662i	−0.123964	+	0.289980i
$771$		0			0
$772$	0.369762	−	1.01591i	0.0133080	−	0.0365635i
$773$	−4.57453	−	2.64111i	−0.164534	−	0.0949940i	0.415472	−	0.909606i	$-0.363617\pi$
$773$	−4.57453	−	2.64111i	−0.164534	−	0.0949940i	−0.580006	+	0.814612i	$0.696950\pi$
$774$		0			0
$775$	−12.1346	−	5.99536i	−0.435888	−	0.215360i
$776$	3.71656	+	21.0777i	0.133417	+	0.756645i
$777$		0			0
$778$	−7.71867	−	21.2069i	−0.276728	−	0.760303i
$779$	6.34166	−	35.9653i	0.227213	−	1.28859i
$780$		0			0
$781$	−36.2321	+	30.4024i	−1.29649	+	1.08788i
$782$			16.3022i			0.582966i
$783$		0			0
$784$	−20.6927			−0.739026
$785$	1.97633	−	3.02634i	0.0705384	−	0.108015i
$786$		0			0
$787$	11.5446	+	2.03562i	0.411520	+	0.0725620i	0.375575	−	0.926792i	$-0.377445\pi$
$787$	11.5446	+	2.03562i	0.411520	+	0.0725620i	0.0359440	+	0.999354i	$0.488556\pi$
$788$	−2.40750	−	6.61455i	−0.0857636	−	0.235634i
$789$		0			0
$790$	−15.0963	−	29.8161i	−0.537102	−	1.06081i
$791$	2.41038	+	4.17490i	0.0857032	+	0.148442i
$792$		0			0
$793$	29.2106	+	16.8647i	1.03730	+	0.598884i
$794$	−16.0844	−	5.85425i	−0.570815	−	0.207760i
$795$		0			0
$796$	3.53839	+	2.96906i	0.125415	+	0.105235i
$797$	−15.6442	+	18.6441i	−0.554147	+	0.660406i	−0.968297	−	0.249802i	$-0.919634\pi$
$797$	−15.6442	+	18.6441i	−0.554147	+	0.660406i	0.414150	+	0.910209i	$0.364079\pi$
$798$		0			0
$799$	−9.62798	−	3.50430i	−0.340613	−	0.123973i
$800$	9.17293	−	0.594369i	0.324312	−	0.0210141i
$801$		0			0
$802$	−43.8809	+	25.3346i	−1.54949	+	0.894597i
$803$	−54.0656	+	9.53322i	−1.90793	+	0.336420i
$804$		0			0
$805$	−3.36330	−	4.48705i	−0.118541	−	0.158148i
$806$	−3.10970	+	17.6360i	−0.109535	+	0.621201i
$807$		0			0
$808$	−3.41199	−	4.06625i	−0.120033	−	0.143050i
$809$	−2.84260			−0.0999405			−0.0499703	−	0.998751i	$-0.515913\pi$
$809$	−2.84260			−0.0999405			−0.0499703	+	0.998751i	$0.515913\pi$
$810$		0			0
$811$	25.2940			0.888194			0.444097	−	0.895979i	$-0.353525\pi$
$811$	25.2940			0.888194			0.444097	+	0.895979i	$0.353525\pi$
$812$	−0.0582060	−	0.0693672i	−0.00204263	−	0.00243431i
$813$		0			0
$814$	−3.73828	+	21.2008i	−0.131027	+	0.743089i
$815$	−5.71655	+	4.28489i	−0.200242	+	0.150093i
$816$		0			0
$817$	1.05047	−	0.185227i	0.0367514	−	0.00648027i
$818$	22.2004	−	12.8174i	0.776218	−	0.448149i
$819$		0			0
$820$	−8.63004	−	2.01563i	−0.301374	−	0.0703889i
$821$	39.7487	+	14.4673i	1.38724	+	0.504914i	0.924365	−	0.381510i	$-0.124596\pi$
$821$	39.7487	+	14.4673i	1.38724	+	0.504914i	0.462874	+	0.886424i	$0.346818\pi$
$822$		0			0
$823$	1.42693	−	1.70055i	0.0497397	−	0.0592774i	−0.740601	−	0.671945i	$-0.765459\pi$
$823$	1.42693	−	1.70055i	0.0497397	−	0.0592774i	0.790341	+	0.612668i	$0.209904\pi$
$824$	44.1958	+	37.0847i	1.53964	+	1.29191i
$825$		0			0
$826$	−12.4853	−	4.54429i	−0.434421	−	0.158116i
$827$	15.7822	+	9.11184i	0.548800	+	0.316850i	0.748638	−	0.662979i	$-0.230708\pi$
$827$	15.7822	+	9.11184i	0.548800	+	0.316850i	−0.199838	+	0.979829i	$0.564042\pi$
$828$		0			0
$829$	15.8943	+	27.5298i	0.552033	+	0.956149i	0.998128	+	0.0611633i	$0.0194810\pi$
$829$	15.8943	+	27.5298i	0.552033	+	0.956149i	−0.446095	+	0.894986i	$0.647186\pi$
$830$	−14.3417	+	7.26139i	−0.497808	+	0.252047i
$831$		0			0
$832$	−15.4831	−	42.5394i	−0.536779	−	1.47479i
$833$	−24.6068	−	4.33884i	−0.852574	−	0.150332i
$834$		0			0
$835$	−6.75405	+	10.3424i	−0.233734	+	0.357914i
$836$	3.87478			0.134012
$837$		0			0
$838$			35.2053i			1.21615i
$839$	14.1865	−	11.9039i	0.489772	−	0.410968i	−0.364173	−	0.931331i	$-0.618648\pi$
$839$	14.1865	−	11.9039i	0.489772	−	0.410968i	0.853945	+	0.520364i	$0.174204\pi$
$840$		0			0
$841$	−5.01394	+	28.4355i	−0.172894	+	0.980533i
$842$	−0.999506	−	2.74612i	−0.0344453	−	0.0946376i
$843$		0			0
$844$	−0.237233	−	1.34542i	−0.00816591	−	0.0463112i
$845$	−20.1597	+	21.5082i	−0.693514	+	0.739905i
$846$		0			0
$847$	2.81351	+	1.62438i	0.0966734	+	0.0558144i
$848$	−10.2813	+	28.2476i	−0.353061	+	0.970027i
$849$		0			0
$850$	−25.0993	−	2.76773i	−0.860899	−	0.0949324i
$851$	−10.5675	−	8.86722i	−0.362251	−	0.303964i
$852$		0			0
$853$	−7.92056	+	21.7616i	−0.271195	+	0.745102i	0.727089	+	0.686543i	$0.240873\pi$
$853$	−7.92056	+	21.7616i	−0.271195	+	0.745102i	−0.998284	+	0.0585587i	$0.981350\pi$
$854$	−3.31040	+	5.73378i	−0.113280	+	0.196206i
$855$		0			0
$856$	−8.29838	−	14.3732i	−0.283633	−	0.491266i
$857$	−23.4792	+	4.14002i	−0.802035	+	0.141420i	−0.559617	−	0.828751i	$-0.689052\pi$
$857$	−23.4792	+	4.14002i	−0.802035	+	0.141420i	−0.242418	+	0.970172i	$0.577941\pi$
$858$		0			0
$859$	−7.58350	+	2.76017i	−0.258746	+	0.0941757i	−0.468136	−	0.883656i	$-0.655074\pi$
$859$	−7.58350	+	2.76017i	−0.258746	+	0.0941757i	0.209390	+	0.977832i	$0.432852\pi$
$860$	−0.0308896	−	0.257000i	−0.00105333	−	0.00876363i
$861$		0			0
$862$	−8.05695	−	9.60190i	−0.274421	−	0.327042i
$863$			18.5552i			0.631628i	0.948821	+	0.315814i	$0.102277\pi$
$863$			18.5552i			0.631628i	−0.948821	+	0.315814i	$0.897723\pi$
$864$		0			0
$865$	−22.8100	+	6.91006i	−0.775562	+	0.234949i
$866$	32.0328	−	26.8787i	1.08852	−	0.913375i
$867$		0			0
$868$	0.680388	+	0.119971i	0.0230939	+	0.00407208i
$869$	−42.3270	+	15.4058i	−1.43584	+	0.522604i
$870$		0			0
$871$	3.53760	+	20.0627i	0.119867	+	0.679799i
$872$	−37.1970	+	21.4757i	−1.25965	+	0.727258i
$873$		0			0
$874$	6.31655	−	10.9406i	0.213660	−	0.370071i
$875$	7.47939	−	4.41643i	0.252850	−	0.149303i
$876$		0			0
$877$	6.79778	−	8.10128i	0.229545	−	0.273561i	−0.638962	−	0.769238i	$-0.720636\pi$
$877$	6.79778	−	8.10128i	0.229545	−	0.273561i	0.868507	+	0.495678i	$0.165080\pi$
$878$	−8.20962	+	9.78384i	−0.277061	+	0.330189i
$879$		0			0
$880$	−1.54699	+	28.1430i	−0.0521491	+	0.948700i
$881$	5.52419	−	9.56817i	0.186115	−	0.322360i	−0.757837	−	0.652444i	$-0.773744\pi$
$881$	5.52419	−	9.56817i	0.186115	−	0.322360i	0.943952	+	0.330084i	$0.107077\pi$
$882$		0			0
$883$	−45.6600	+	26.3618i	−1.53658	+	0.887146i	−0.537546	+	0.843234i	$0.680649\pi$
$883$	−45.6600	+	26.3618i	−1.53658	+	0.887146i	−0.999035	+	0.0439118i	$0.986018\pi$
$884$	−1.14027	−	6.46678i	−0.0383513	−	0.217501i
$885$		0			0
$886$	31.7844	−	11.5686i	1.06782	−	0.388654i
$887$	41.4529	+	7.30927i	1.39185	+	0.245421i	0.818792	−	0.574091i	$-0.194644\pi$
$887$	41.4529	+	7.30927i	1.39185	+	0.245421i	0.573062	+	0.819512i	$0.305755\pi$
$888$		0			0
$889$	7.18978	−	6.03294i	0.241138	−	0.202338i
$890$	14.4164	−	4.36731i	0.483239	−	0.146393i
$891$		0			0
$892$			5.45722i			0.182721i
$893$	5.10364	+	6.08228i	0.170787	+	0.203536i
$894$		0			0
$895$	31.1644	−	3.74574i	1.04171	−	0.125206i
$896$	5.66584	−	2.06220i	0.189282	−	0.0688932i
$897$		0			0
$898$	20.4851	−	3.61208i	0.683597	−	0.120537i
$899$	0.480212	+	0.831752i	0.0160160	+	0.0277405i
$900$		0			0
$901$	−18.1489	+	31.4349i	−0.604629	+	1.04725i
$902$	20.7858	−	57.1085i	0.692092	−	1.90151i
$903$		0			0
$904$	14.3099	+	12.0074i	0.475940	+	0.399361i
$905$	13.6371	−	31.9001i	0.453311	−	1.06040i
$906$		0			0
$907$	−0.214958	+	0.590592i	−0.00713756	+	0.0196103i	−0.943210	−	0.332196i	$-0.892210\pi$
$907$	−0.214958	+	0.590592i	−0.00713756	+	0.0196103i	0.936073	+	0.351807i	$0.114433\pi$
$908$	1.50692	+	0.870019i	0.0500088	+	0.0288726i
$909$		0			0
$910$	−8.38501	−	7.85928i	−0.277960	−	0.260533i
$911$	−4.64690	−	26.3539i	−0.153959	−	0.873144i	−0.959731	−	0.280919i	$-0.909361\pi$
$911$	−4.64690	−	26.3539i	−0.153959	−	0.873144i	0.805773	−	0.592225i	$-0.201750\pi$
$912$		0			0
$913$	7.41025	+	20.3595i	0.245243	+	0.673801i
$914$	6.83321	−	38.7530i	0.226022	−	1.28184i
$915$		0			0
$916$	5.12928	−	4.30398i	0.169476	−	0.142207i
$917$			0.627276i			0.0207145i
$918$		0			0
$919$	−8.32555			−0.274634			−0.137317	−	0.990527i	$-0.543848\pi$
$919$	−8.32555			−0.274634			−0.137317	+	0.990527i	$0.543848\pi$
$920$	−18.1934	−	11.8811i	−0.599820	−	0.391709i
$921$		0			0
$922$	−20.8206	−	3.67124i	−0.685691	−	0.120906i
$923$	−21.2444	−	58.3685i	−0.699268	−	1.92122i
$924$		0			0
$925$	15.4463	−	14.7646i	0.507872	−	0.485458i
$926$	−4.72363	−	8.18157i	−0.155228	−	0.268863i
$927$		0			0
$928$	−0.564881	−	0.326134i	−0.0185431	−	0.0107059i
$929$	−20.0134	−	7.28427i	−0.656618	−	0.238989i	−0.00784221	−	0.999969i	$-0.502496\pi$
$929$	−20.0134	−	7.28427i	−0.656618	−	0.238989i	−0.648775	+	0.760980i	$0.724719\pi$
$930$		0			0
$931$	14.8327	+	12.4461i	0.486122	+	0.407905i
$932$	0.259044	−	0.308716i	0.00848525	−	0.0101123i
$933$		0			0
$934$	−12.2224	−	4.44860i	−0.399930	−	0.145563i
$935$	−7.74061	+	33.1419i	−0.253145	+	1.08386i
$936$		0			0
$937$	2.68331	−	1.54921i	0.0876598	−	0.0506104i	−0.455529	−	0.890221i	$-0.650550\pi$
$937$	2.68331	−	1.54921i	0.0876598	−	0.0506104i	0.543189	+	0.839610i	$0.317217\pi$
$938$	−3.93814	+	0.694400i	−0.128585	+	0.0226730i
$939$		0			0
$940$	1.54173	−	1.15562i	0.0502857	−	0.0376921i
$941$	2.52290	−	14.3081i	0.0822442	−	0.466430i	−0.915673	−	0.401924i	$-0.868342\pi$
$941$	2.52290	−	14.3081i	0.0822442	−	0.466430i	0.997917	−	0.0645063i	$-0.0205473\pi$
$942$		0			0
$943$	25.0323	+	29.8324i	0.815165	+	0.971476i
$944$	−42.7937			−1.39282
$945$		0			0
$946$	1.77507			0.0577127
$947$	2.63542	+	3.14077i	0.0856396	+	0.102061i	0.807163	−	0.590329i	$-0.201002\pi$
$947$	2.63542	+	3.14077i	0.0856396	+	0.102061i	−0.721523	+	0.692390i	$0.756558\pi$
$948$		0			0
$949$	12.5197	−	71.0025i	0.406406	−	2.30484i
$950$	15.7720	+	11.5826i	0.511712	+	0.375788i
$951$		0			0
$952$	8.99727	−	1.58646i	0.291603	−	0.0514175i
$953$	−24.8072	+	14.3224i	−0.803584	+	0.463950i	−0.844723	−	0.535204i	$-0.820235\pi$
$953$	−24.8072	+	14.3224i	−0.803584	+	0.463950i	0.0411387	+	0.999153i	$0.486901\pi$
$954$		0			0
$955$	9.51186	+	2.22159i	0.307797	+	0.0718889i
$956$	−4.74467	−	1.72692i	−0.153454	−	0.0558525i
$957$		0			0
$958$	−6.66586	+	7.94406i	−0.215364	+	0.256661i
$959$	0.424745	+	0.356403i	0.0137157	+	0.0115089i
$960$		0			0
$961$	22.2447	+	8.09640i	0.717570	+	0.261174i
$962$	−24.4841	−	14.1359i	−0.789401	−	0.455761i
$963$		0			0
$964$	−3.05296	−	5.28788i	−0.0983291	−	0.170311i
$965$	−3.32400	−	6.56510i	−0.107003	−	0.211338i
$966$		0			0
$967$	7.35273	+	20.2015i	0.236448	+	0.649635i	0.999992	+	0.00388011i	$0.00123508\pi$
$967$	7.35273	+	20.2015i	0.236448	+	0.649635i	−0.763545	+	0.645755i	$0.776543\pi$
$968$	12.3976	+	2.18602i	0.398473	+	0.0702615i
$969$		0			0
$970$	17.2086	+	11.2380i	0.552535	+	0.360830i
$971$	−39.3784			−1.26371			−0.631857	−	0.775085i	$-0.717707\pi$
$971$	−39.3784			−1.26371			−0.631857	+	0.775085i	$0.717707\pi$
$972$		0			0
$973$			10.2650i			0.329081i
$974$	−1.28764	+	1.08046i	−0.0412588	+	0.0346202i
$975$		0			0
$976$	−3.70294	+	21.0004i	−0.118528	+	0.672206i
$977$	−7.02896	−	19.3119i	−0.224876	−	0.617843i	0.775024	−	0.631931i	$-0.217738\pi$
$977$	−7.02896	−	19.3119i	−0.224876	−	0.617843i	−0.999901	+	0.0140884i	$0.995515\pi$
$978$		0			0
$979$	−3.52548	−	19.9940i	−0.112675	−	0.639010i
$980$	3.21329	−	3.42824i	0.102645	−	0.109511i
$981$		0			0
$982$	−12.4585	−	7.19295i	−0.397568	−	0.229536i
$983$	−7.78235	+	21.3818i	−0.248218	+	0.681975i	0.751533	+	0.659695i	$0.229315\pi$
$983$	−7.78235	+	21.3818i	−0.248218	+	0.681975i	−0.999752	+	0.0222795i	$0.992908\pi$
$984$		0			0
$985$	−44.0550	−	18.8332i	−1.40371	−	0.600075i
$986$	1.37262	+	1.15176i	0.0437130	+	0.0366796i
$987$		0			0
$988$	−1.74041	+	4.78174i	−0.0553698	+	0.152127i
$989$	−0.568729	+	0.985067i	−0.0180845	+	0.0313233i
$990$		0			0
$991$	−8.61401	−	14.9199i	−0.273633	−	0.473946i	0.696156	−	0.717890i	$-0.254892\pi$
$991$	−8.61401	−	14.9199i	−0.273633	−	0.473946i	−0.969789	+	0.243944i	$0.921559\pi$
$992$	4.90099	−	0.864176i	0.155606	−	0.0274376i
$993$		0			0
$994$	11.4572	−	4.17010i	0.363402	−	0.132267i
$995$	31.2150	−	3.75183i	0.989583	−	0.118941i
$996$		0			0
$997$	−8.68705	−	10.3528i	−0.275122	−	0.327877i	0.610736	−	0.791834i	$-0.290874\pi$
$997$	−8.68705	−	10.3528i	−0.275122	−	0.327877i	−0.885858	+	0.463957i	$0.846429\pi$
$998$		−	22.9749i		−	0.727256i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.p.a.199.12		96
3.2	odd	2		135.2.p.a.49.5	✓	96
5.4	even	2	inner	405.2.p.a.199.5		96
15.2	even	4		675.2.l.h.76.12		96
15.8	even	4		675.2.l.h.76.5		96
15.14	odd	2		135.2.p.a.49.12	yes	96
27.11	odd	18		135.2.p.a.124.12	yes	96
27.16	even	9	inner	405.2.p.a.289.5		96
135.38	even	36		675.2.l.h.151.5		96
135.92	even	36		675.2.l.h.151.12		96
135.119	odd	18		135.2.p.a.124.5	yes	96
135.124	even	18	inner	405.2.p.a.289.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.5	✓	96	3.2	odd	2
135.2.p.a.49.12	yes	96	15.14	odd	2
135.2.p.a.124.5	yes	96	135.119	odd	18
135.2.p.a.124.12	yes	96	27.11	odd	18
405.2.p.a.199.5		96	5.4	even	2	inner
405.2.p.a.199.12		96	1.1	even	1	trivial
405.2.p.a.289.5		96	27.16	even	9	inner
405.2.p.a.289.12		96	135.124	even	18	inner
675.2.l.h.76.5		96	15.8	even	4
675.2.l.h.76.12		96	15.2	even	4
675.2.l.h.151.5		96	135.38	even	36
675.2.l.h.151.12		96	135.92	even	36

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.p (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.831033 + 0.990387i) q^{2} +(0.0570464 - 0.323526i) q^{4} +(-1.34113 - 1.78923i) q^{5} +(0.765094 - 0.134907i) q^{7} +(2.60712 - 1.50522i) q^{8} +(0.657507 - 2.81516i) q^{10} +(-3.66139 - 1.33264i) q^{11} +(3.28913 - 3.91983i) q^{13} +(0.769429 + 0.645628i) q^{14} +(3.03995 + 1.10645i) q^{16} +(3.38295 + 1.95315i) q^{17} +(-1.51356 - 2.62156i) q^{19} +(-0.655371 + 0.331823i) q^{20} +(-1.72291 - 4.73366i) q^{22} +(3.17893 + 0.560532i) q^{23} +(-1.40272 + 4.79921i) q^{25} +6.61553 q^{26} -0.255224i q^{28} +(0.271790 - 0.228059i) q^{29} +(-0.470061 + 2.66585i) q^{31} +(-0.628781 - 1.72756i) q^{32} +(0.876974 + 4.97357i) q^{34} +(-1.26747 - 1.18800i) q^{35} +(-3.70101 - 2.13678i) q^{37} +(1.33854 - 3.67761i) q^{38} +(-6.18969 - 2.64604i) q^{40} +(9.24182 + 7.75481i) q^{41} +(-0.120519 + 0.331124i) q^{43} +(-0.640012 + 1.10853i) q^{44} +(2.08666 + 3.61420i) q^{46} +(-2.58307 + 0.455464i) q^{47} +(-6.01068 + 2.18771i) q^{49} +(-5.91878 + 2.59907i) q^{50} +(-1.08053 - 1.28773i) q^{52} +9.29215i q^{53} +(2.52602 + 8.33833i) q^{55} +(1.79163 - 1.50335i) q^{56} +(0.451732 + 0.0796526i) q^{58} +(-12.4304 + 4.52430i) q^{59} +(1.14463 + 6.49154i) q^{61} +(-3.03086 + 1.74987i) q^{62} +(4.42346 - 7.66166i) q^{64} +(-11.4247 - 0.628002i) q^{65} +(-2.55913 + 3.04985i) q^{67} +(0.824880 - 0.983053i) q^{68} +(0.123271 - 2.24256i) q^{70} +(6.06946 - 10.5126i) q^{71} +(12.2022 - 7.04497i) q^{73} +(-0.959425 - 5.44117i) q^{74} +(-0.934485 + 0.340125i) q^{76} +(-2.98109 - 0.525647i) q^{77} +(8.85574 - 7.43085i) q^{79} +(-2.09728 - 6.92307i) q^{80} +15.5975i q^{82} +(-3.57428 - 4.25966i) q^{83} +(-1.04235 - 8.67233i) q^{85} +(-0.428097 + 0.155815i) q^{86} +(-11.5516 + 2.03686i) q^{88} +(2.60530 + 4.51251i) q^{89} +(1.98768 - 3.44277i) q^{91} +(0.362693 - 0.996492i) q^{92} +(-2.59770 - 2.17973i) q^{94} +(-2.66070 + 6.22397i) q^{95} +(-2.43160 + 6.68077i) q^{97} +(-7.16175 - 4.13484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46}+ \cdots - 87 q^{95}+O(q^{100}) \) 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Introduction

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