LMFDB - Embedded newform 567.2.be.a.62.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(62,567)] 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("567.62"); 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, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.be (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			62.11
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0448460 + 0.123213i) q^{2} +(1.51892 - 1.27452i) q^{4} +(-0.231324 - 1.31190i) q^{5} +(-0.772696 - 2.53040i) q^{7} +(0.452264 + 0.261115i) q^{8} +(0.151270 - 0.0873359i) q^{10} +(4.31014 + 0.759994i) q^{11} +(-1.38870 + 3.81541i) q^{13} +(0.277127 - 0.208685i) q^{14} +(0.676731 - 3.83793i) q^{16} +(-1.85685 - 3.21617i) q^{17} +(-4.31784 - 2.49291i) q^{19} +(-2.02342 - 1.69785i) q^{20} +(0.0996512 + 0.565150i) q^{22} +(-0.242663 - 0.289194i) q^{23} +(3.03088 - 1.10315i) q^{25} -0.532388 q^{26} +(-4.39872 - 2.85866i) q^{28} +(-1.57190 - 4.31876i) q^{29} +(-0.693448 - 0.826419i) q^{31} +(1.53182 - 0.270102i) q^{32} +(0.313002 - 0.373021i) q^{34} +(-3.14090 + 1.59905i) q^{35} +(-0.172576 - 0.298911i) q^{37} +(0.113522 - 0.643813i) q^{38} +(0.237938 - 0.653729i) q^{40} +(5.09719 + 1.85523i) q^{41} +(-0.390810 + 2.21639i) q^{43} +(7.51538 - 4.33901i) q^{44} +(0.0247502 - 0.0428686i) q^{46} +(9.77186 + 8.19957i) q^{47} +(-5.80588 + 3.91046i) q^{49} +(0.271846 + 0.323973i) q^{50} +(2.75352 + 7.56523i) q^{52} +9.19872i q^{53} -5.83030i q^{55} +(0.311263 - 1.34617i) q^{56} +(0.461636 - 0.387359i) q^{58} +(-2.24314 - 12.7215i) q^{59} +(1.14717 - 1.36715i) q^{61} +(0.0707275 - 0.122504i) q^{62} +(-3.79516 - 6.57342i) q^{64} +(5.32670 + 0.939241i) q^{65} +(5.40821 + 1.96843i) q^{67} +(-6.91949 - 2.51849i) q^{68} +(-0.337881 - 0.315291i) q^{70} +(-2.30444 + 1.33047i) q^{71} +(4.63485 + 2.67593i) q^{73} +(0.0290904 - 0.0346686i) q^{74} +(-9.73572 + 1.71667i) q^{76} +(-1.40733 - 11.4936i) q^{77} +(5.48206 - 1.99531i) q^{79} -5.19155 q^{80} +0.711242i q^{82} +(-4.03800 + 1.46971i) q^{83} +(-3.78977 + 3.17999i) q^{85} +(-0.290615 + 0.0512433i) q^{86} +(1.75088 + 1.46916i) q^{88} +(-5.59352 + 9.68826i) q^{89} +(10.7276 + 0.565811i) q^{91} +(-0.737171 - 0.129983i) q^{92} +(-0.572067 + 1.57174i) q^{94} +(-2.27163 + 6.24126i) q^{95} +(14.5132 + 2.55906i) q^{97} +(-0.742192 - 0.539994i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.0448460	+	0.123213i	0.0317109	+	0.0871250i	0.954538	−	0.298090i	$-0.0963495\pi$
$2$	0.0448460	+	0.123213i	0.0317109	+	0.0871250i	−0.922827	+	0.385215i	$0.874127\pi$
$3$		0			0
$3$		0			0
$4$	1.51892	−	1.27452i	0.759459	−	0.637262i
$5$	−0.231324	−	1.31190i	−0.103451	−	0.586701i	−0.991828	−	0.127585i	$-0.959277\pi$
$5$	−0.231324	−	1.31190i	−0.103451	−	0.586701i	0.888376	−	0.459116i	$-0.151834\pi$
$6$		0			0
$7$	−0.772696	−	2.53040i	−0.292051	−	0.956403i
$7$	−0.772696	−	2.53040i	−0.292051	−	0.956403i
$8$	0.452264	+	0.261115i	0.159899	+	0.0923180i
$9$		0			0
$10$	0.151270	−	0.0873359i	0.0478358	−	0.0276180i
$11$	4.31014	+	0.759994i	1.29956	+	0.229147i	0.780264	−	0.625450i	$-0.215085\pi$
$11$	4.31014	+	0.759994i	1.29956	+	0.229147i	0.519292	+	0.854597i	$0.326196\pi$
$12$		0			0
$13$	−1.38870	+	3.81541i	−0.385155	+	1.05821i	0.584000	+	0.811754i	$0.301487\pi$
$13$	−1.38870	+	3.81541i	−0.385155	+	1.05821i	−0.969155	+	0.246452i	$0.920735\pi$
$14$	0.277127	−	0.208685i	0.0740654	−	0.0557734i
$15$		0			0
$16$	0.676731	−	3.83793i	0.169183	−	0.959483i
$17$	−1.85685	−	3.21617i	−0.450353	−	0.780035i	0.548055	−	0.836443i	$-0.315369\pi$
$17$	−1.85685	−	3.21617i	−0.450353	−	0.780035i	−0.998408	+	0.0564079i	$0.982035\pi$
$18$		0			0
$19$	−4.31784	−	2.49291i	−0.990581	−	0.571912i	−0.0851328	−	0.996370i	$-0.527131\pi$
$19$	−4.31784	−	2.49291i	−0.990581	−	0.571912i	−0.905448	+	0.424458i	$0.860465\pi$
$20$	−2.02342	−	1.69785i	−0.452450	−	0.379650i
$21$		0			0
$22$	0.0996512	+	0.565150i	0.0212457	+	0.120490i
$23$	−0.242663	−	0.289194i	−0.0505987	−	0.0603012i	0.740152	−	0.672440i	$-0.234754\pi$
$23$	−0.242663	−	0.289194i	−0.0505987	−	0.0603012i	−0.790750	+	0.612139i	$0.790309\pi$
$24$		0			0
$25$	3.03088	−	1.10315i	0.606176	−	0.220630i
$26$	−0.532388			−0.104410
$27$		0			0
$28$	−4.39872	−	2.85866i	−0.831280	−	0.540236i
$29$	−1.57190	−	4.31876i	−0.291895	−	0.801974i	−0.995789	−	0.0916699i	$-0.970780\pi$
$29$	−1.57190	−	4.31876i	−0.291895	−	0.801974i	0.703895	−	0.710304i	$-0.251443\pi$
$30$		0			0
$31$	−0.693448	−	0.826419i	−0.124547	−	0.148429i	0.700168	−	0.713979i	$-0.253109\pi$
$31$	−0.693448	−	0.826419i	−0.124547	−	0.148429i	−0.824714	+	0.565549i	$0.808664\pi$
$32$	1.53182	−	0.270102i	0.270791	−	0.0477477i
$33$		0			0
$34$	0.313002	−	0.373021i	0.0536794	−	0.0639727i
$35$	−3.14090	+	1.59905i	−0.530910	+	0.270288i
$36$		0			0
$37$	−0.172576	−	0.298911i	−0.0283713	−	0.0491406i	0.851491	−	0.524369i	$-0.175699\pi$
$37$	−0.172576	−	0.298911i	−0.0283713	−	0.0491406i	−0.879862	+	0.475228i	$0.842365\pi$
$38$	0.113522	−	0.643813i	0.0184156	−	0.104440i
$39$		0			0
$40$	0.237938	−	0.653729i	0.0376213	−	0.103364i
$41$	5.09719	+	1.85523i	0.796047	+	0.289738i	0.707848	−	0.706365i	$-0.249666\pi$
$41$	5.09719	+	1.85523i	0.796047	+	0.289738i	0.0881999	+	0.996103i	$0.471889\pi$
$42$		0			0
$43$	−0.390810	+	2.21639i	−0.0595979	+	0.337997i	−0.999998	−	0.00207394i	$-0.999340\pi$
$43$	−0.390810	+	2.21639i	−0.0595979	+	0.337997i	0.940400	+	0.340071i	$0.110451\pi$
$44$	7.51538	−	4.33901i	1.13299	−	0.654130i
$45$		0			0
$46$	0.0247502	−	0.0428686i	0.00364921	−	0.00632062i
$47$	9.77186	+	8.19957i	1.42537	+	1.19603i	0.948386	+	0.317119i	$0.102716\pi$
$47$	9.77186	+	8.19957i	1.42537	+	1.19603i	0.476987	+	0.878910i	$0.341729\pi$
$48$		0			0
$49$	−5.80588	+	3.91046i	−0.829412	+	0.558638i
$50$	0.271846	+	0.323973i	0.0384448	+	0.0458167i
$51$		0			0
$52$	2.75352	+	7.56523i	0.381844	+	1.04911i
$53$			9.19872i			1.26354i	0.775155	+	0.631771i	$0.217672\pi$
$53$			9.19872i			1.26354i	−0.775155	+	0.631771i	$0.782328\pi$
$54$		0			0
$55$		−	5.83030i		−	0.786157i
$56$	0.311263	−	1.34617i	0.0415943	−	0.179890i
$57$		0			0
$58$	0.461636	−	0.387359i	0.0606158	−	0.0508627i
$59$	−2.24314	−	12.7215i	−0.292032	−	1.65620i	−0.679026	−	0.734115i	$-0.737597\pi$
$59$	−2.24314	−	12.7215i	−0.292032	−	1.65620i	0.386993	−	0.922082i	$-0.373514\pi$
$60$		0			0
$61$	1.14717	−	1.36715i	0.146880	−	0.175045i	−0.687588	−	0.726101i	$-0.741330\pi$
$61$	1.14717	−	1.36715i	0.146880	−	0.175045i	0.834468	+	0.551056i	$0.185775\pi$
$62$	0.0707275	−	0.122504i	0.00898240	−	0.0155580i
$63$		0			0
$64$	−3.79516	−	6.57342i	−0.474395	−	0.821677i
$65$	5.32670	+	0.939241i	0.660696	+	0.116498i
$66$		0			0
$67$	5.40821	+	1.96843i	0.660718	+	0.240482i	0.650546	−	0.759467i	$-0.274540\pi$
$67$	5.40821	+	1.96843i	0.660718	+	0.240482i	0.0101714	+	0.999948i	$0.496762\pi$
$68$	−6.91949	−	2.51849i	−0.839111	−	0.305412i
$69$		0			0
$70$	−0.337881	−	0.315291i	−0.0403845	−	0.0376844i
$71$	−2.30444	+	1.33047i	−0.273487	+	0.157898i	−0.630471	−	0.776213i	$-0.717138\pi$
$71$	−2.30444	+	1.33047i	−0.273487	+	0.157898i	0.356984	+	0.934110i	$0.383805\pi$
$72$		0			0
$73$	4.63485	+	2.67593i	0.542469	+	0.313194i	0.746079	−	0.665858i	$-0.231934\pi$
$73$	4.63485	+	2.67593i	0.542469	+	0.313194i	−0.203610	+	0.979052i	$0.565268\pi$
$74$	0.0290904	−	0.0346686i	0.00338169	−	0.00403015i
$75$		0			0
$76$	−9.73572	+	1.71667i	−1.11676	+	0.196916i
$77$	−1.40733	−	11.4936i	−0.160381	−	1.30982i
$78$		0			0
$79$	5.48206	−	1.99531i	0.616780	−	0.224489i	−0.0146875	−	0.999892i	$-0.504675\pi$
$79$	5.48206	−	1.99531i	0.616780	−	0.224489i	0.631467	+	0.775403i	$0.282453\pi$
$80$	−5.19155			−0.580432
$81$		0			0
$82$			0.711242i			0.0785435i
$83$	−4.03800	+	1.46971i	−0.443228	+	0.161322i	−0.553987	−	0.832526i	$-0.686894\pi$
$83$	−4.03800	+	1.46971i	−0.443228	+	0.161322i	0.110759	+	0.993847i	$0.464672\pi$
$84$		0			0
$85$	−3.78977	+	3.17999i	−0.411058	+	0.344918i
$86$	−0.290615	+	0.0512433i	−0.0313379	+	0.00552571i
$87$		0			0
$88$	1.75088	+	1.46916i	0.186644	+	0.156613i
$89$	−5.59352	+	9.68826i	−0.592912	+	1.02695i	0.400926	+	0.916110i	$0.368688\pi$
$89$	−5.59352	+	9.68826i	−0.592912	+	1.02695i	−0.993838	+	0.110843i	$0.964645\pi$
$90$		0			0
$91$	10.7276	+	0.565811i	1.12456	+	0.0593131i
$92$	−0.737171	−	0.129983i	−0.0768554	−	0.0135517i
$93$		0			0
$94$	−0.572067	+	1.57174i	−0.0590042	+	0.162113i
$95$	−2.27163	+	6.24126i	−0.233065	+	0.640340i
$96$		0			0
$97$	14.5132	+	2.55906i	1.47359	+	0.259833i	0.852013	−	0.523521i	$-0.175382\pi$
$97$	14.5132	+	2.55906i	1.47359	+	0.259833i	0.621575	+	0.783354i	$0.286493\pi$
$98$	−0.742192	−	0.539994i	−0.0749727	−	0.0545476i
$99$		0			0
$100$	3.19767	−	5.53853i	0.319767	−	0.553853i
$101$	9.33893	+	7.83629i	0.929258	+	0.779740i	0.975684	−	0.219182i	$-0.0703388\pi$
$101$	9.33893	+	7.83629i	0.929258	+	0.779740i	−0.0464262	+	0.998922i	$0.514783\pi$
$102$		0			0
$103$	8.85590	−	1.56153i	0.872597	−	0.153862i	0.280622	−	0.959818i	$-0.409459\pi$
$103$	8.85590	−	1.56153i	0.872597	−	0.153862i	0.591976	+	0.805956i	$0.298348\pi$
$104$	−1.62432	+	1.36297i	−0.159278	+	0.133650i
$105$		0			0
$106$	−1.13341	+	0.412526i	−0.110086	+	0.0400680i
$107$			18.2346i			1.76280i	0.472370	+	0.881401i	$0.343399\pi$
$107$			18.2346i			1.76280i	−0.472370	+	0.881401i	$0.656601\pi$
$108$		0			0
$109$	−10.0889			−0.966342			−0.483171	−	0.875526i	$-0.660515\pi$
$109$	−10.0889			−0.966342			−0.483171	+	0.875526i	$0.660515\pi$
$110$	0.718371	−	0.261466i	0.0684940	−	0.0249298i
$111$		0			0
$112$	−10.2344	+	1.25315i	−0.967062	+	0.118412i
$113$	−16.1779	+	2.85260i	−1.52189	+	0.268350i	−0.871175	−	0.490973i	$-0.836641\pi$
$113$	−16.1779	+	2.85260i	−1.52189	+	0.268350i	−0.650714	+	0.759323i	$0.725530\pi$
$114$		0			0
$115$	−0.323262	+	0.385248i	−0.0301443	+	0.0359246i
$116$	−7.89196	−	4.55642i	−0.732750	−	0.423053i
$117$		0			0
$118$	1.46686	−	0.846893i	0.135036	−	0.0779628i
$119$	−6.70341	+	7.18371i	−0.614501	+	0.658529i
$120$		0			0
$121$	7.66310	+	2.78914i	0.696646	+	0.253558i
$122$	0.219897	+	0.0800359i	0.0199085	+	0.00724611i
$123$		0			0
$124$	−2.10658	−	0.371447i	−0.189177	−	0.0333569i
$125$	−5.47870	−	9.48939i	−0.490030	−	0.848757i
$126$		0			0
$127$	−10.9612	+	18.9854i	−0.972652	+	1.68468i	−0.285175	+	0.958475i	$0.592052\pi$
$127$	−10.9612	+	18.9854i	−0.972652	+	1.68468i	−0.687476	+	0.726207i	$0.741281\pi$
$128$	2.63939	−	3.14550i	0.233291	−	0.278026i
$129$		0			0
$130$	0.123154	+	0.698442i	0.0108013	+	0.0612574i
$131$	8.67264	−	7.27721i	0.757732	−	0.635813i	−0.179803	−	0.983703i	$-0.557546\pi$
$131$	8.67264	−	7.27721i	0.757732	−	0.635813i	0.937535	+	0.347890i	$0.113102\pi$
$132$		0			0
$133$	−2.97168	+	12.8521i	−0.257678	+	1.11442i
$134$			0.754639i			0.0651909i
$135$		0			0
$136$		−	1.93941i		−	0.166303i
$137$	−3.91826	−	10.7653i	−0.334760	−	0.919745i	−0.986855	−	0.161608i	$-0.948332\pi$
$137$	−3.91826	−	10.7653i	−0.334760	−	0.919745i	0.652095	−	0.758137i	$-0.273890\pi$
$138$		0			0
$139$	9.59685	+	11.4371i	0.813994	+	0.970081i	0.999922	−	0.0124827i	$-0.00397348\pi$
$139$	9.59685	+	11.4371i	0.813994	+	0.970081i	−0.185928	+	0.982563i	$0.559529\pi$
$140$	−2.73275	+	6.43198i	−0.230960	+	0.543601i
$141$		0			0
$142$	−0.267277	−	0.224272i	−0.0224294	−	0.0188205i
$143$	−8.88517	+	15.3896i	−0.743016	+	1.28694i
$144$		0			0
$145$	−5.30219	+	3.06122i	−0.440322	+	0.254220i
$146$	−0.121856	+	0.691081i	−0.0100849	+	0.0571943i
$147$		0			0
$148$	−0.643098	−	0.234068i	−0.0528623	−	0.0192403i
$149$	1.04227	−	2.86360i	0.0853857	−	0.234595i	−0.889650	−	0.456643i	$-0.849052\pi$
$149$	1.04227	−	2.86360i	0.0853857	−	0.234595i	0.975036	+	0.222047i	$0.0712740\pi$
$150$		0			0
$151$	−0.106414	+	0.603503i	−0.00865984	+	0.0491124i	−0.988831	−	0.149038i	$-0.952382\pi$
$151$	−0.106414	+	0.603503i	−0.00865984	+	0.0491124i	0.980172	+	0.198150i	$0.0634934\pi$
$152$	−1.30187	−	2.25490i	−0.105596	−	0.182897i
$153$		0			0
$154$	1.35306	−	0.688846i	0.109032	−	0.0555088i
$155$	−0.923771	+	1.10091i	−0.0741991	+	0.0884270i
$156$		0			0
$157$	−1.89383	+	0.333933i	−0.151144	+	0.0266507i	−0.248708	−	0.968579i	$-0.580006\pi$
$157$	−1.89383	+	0.333933i	−0.151144	+	0.0266507i	0.0975643	+	0.995229i	$0.468895\pi$
$158$	0.491697	+	0.585981i	0.0391173	+	0.0466182i
$159$		0			0
$160$	−0.708696	−	1.94713i	−0.0560273	−	0.153934i
$161$	−0.544274	+	0.837495i	−0.0428948	+	0.0660038i
$162$		0			0
$163$	14.3745			1.12590			0.562949	−	0.826492i	$-0.309667\pi$
$163$	14.3745			1.12590			0.562949	+	0.826492i	$0.309667\pi$
$164$	10.1067	−	3.67856i	0.789204	−	0.287247i
$165$		0			0
$166$	−0.362176	−	0.431625i	−0.0281103	−	0.0335006i
$167$	2.72667	+	15.4637i	0.210996	+	1.19662i	0.887720	+	0.460383i	$0.152288\pi$
$167$	2.72667	+	15.4637i	0.210996	+	1.19662i	−0.676724	+	0.736237i	$0.736601\pi$
$168$		0			0
$169$	−2.67033	−	2.24067i	−0.205410	−	0.172359i
$170$	−0.561773	−	0.324340i	−0.0430861	−	0.0248757i
$171$		0			0
$172$	2.23124	+	3.86462i	0.170130	+	0.294674i
$173$	0.759414	−	4.30685i	0.0577372	−	0.327444i	−0.942235	−	0.334954i	$-0.891279\pi$
$173$	0.759414	−	4.30685i	0.0577372	−	0.327444i	0.999972	+	0.00750984i	$0.00239048\pi$
$174$		0			0
$175$	−5.13336	−	6.81695i	−0.388046	−	0.515313i
$176$	5.83361	−	16.0277i	0.439725	−	1.20813i
$177$		0			0
$178$	−1.44457	−	0.254717i	−0.108275	−	0.0190918i
$179$	12.1181	−	6.99637i	0.905747	−	0.522933i	0.0266868	−	0.999644i	$-0.491504\pi$
$179$	12.1181	−	6.99637i	0.905747	−	0.522933i	0.879060	+	0.476710i	$0.158171\pi$
$180$		0			0
$181$	−18.7936	−	10.8505i	−1.39691	−	0.806509i	−0.402846	−	0.915268i	$-0.631979\pi$
$181$	−18.7936	−	10.8505i	−1.39691	−	0.806509i	−0.994068	+	0.108759i	$0.965312\pi$
$182$	0.411374	+	1.34716i	0.0304930	+	0.0998578i
$183$		0			0
$184$	−0.0342348	−	0.194155i	−0.00252382	−	0.0143133i
$185$	−0.352221	+	0.295548i	−0.0258958	+	0.0217292i
$186$		0			0
$187$	−5.55904	−	15.2733i	−0.406517	−	1.11690i
$188$	25.2932			1.84470
$189$		0			0
$190$	−0.870881			−0.0631803
$191$	7.16981	+	19.6989i	0.518789	+	1.42536i	0.871855	+	0.489763i	$0.162917\pi$
$191$	7.16981	+	19.6989i	0.518789	+	1.42536i	−0.353066	+	0.935598i	$0.614861\pi$
$192$		0			0
$193$	1.16810	−	0.980152i	0.0840817	−	0.0705529i	−0.599778	−	0.800166i	$-0.704744\pi$
$193$	1.16810	−	0.980152i	0.0840817	−	0.0705529i	0.683860	+	0.729614i	$0.260300\pi$
$194$	0.335547	+	1.90298i	0.0240908	+	0.136626i
$195$		0			0
$196$	−3.83468	+	13.3394i	−0.273906	+	0.952815i
$197$	−21.6293	−	12.4877i	−1.54102	−	0.889709i	−0.998775	−	0.0494899i	$-0.984240\pi$
$197$	−21.6293	−	12.4877i	−1.54102	−	0.889709i	−0.542247	−	0.840219i	$-0.682426\pi$
$198$		0			0
$199$	0.716693	−	0.413783i	0.0508050	−	0.0293323i	−0.474382	−	0.880319i	$-0.657329\pi$
$199$	0.716693	−	0.413783i	0.0508050	−	0.0293323i	0.525187	+	0.850987i	$0.323995\pi$
$200$	1.65881	+	0.292492i	0.117295	+	0.0206823i
$201$		0			0
$202$	−0.546722	+	1.50211i	−0.0384672	+	0.105688i
$203$	−9.71361	+	7.31463i	−0.681762	+	0.513387i
$204$		0			0
$205$	1.25478	−	7.11618i	0.0876373	−	0.497016i
$206$	0.589553	+	1.02114i	0.0410761	+	0.0711460i
$207$		0			0
$208$	13.7035	+	7.91174i	0.950169	+	0.548580i
$209$	−16.7159	−	14.0263i	−1.15626	−	0.970220i
$210$		0			0
$211$	1.02986	+	5.84064i	0.0708987	+	0.402086i	0.999518	+	0.0310519i	$0.00988572\pi$
$211$	1.02986	+	5.84064i	0.0708987	+	0.402086i	−0.928619	+	0.371034i	$0.879003\pi$
$212$	11.7240	+	13.9721i	0.805207	+	0.959608i
$213$		0			0
$214$	−2.24674	+	0.817747i	−0.153584	+	0.0559000i
$215$	2.99810			0.204469
$216$		0			0
$217$	−1.55535	+	2.39327i	−0.105584	+	0.162466i
$218$	−0.452447	−	1.24309i	−0.0306436	−	0.0841926i
$219$		0			0
$220$	−7.43085	−	8.85575i	−0.500988	−	0.597054i
$221$	14.8496	−	2.61839i	0.998893	−	0.176132i
$222$		0			0
$223$	9.34376	−	11.1355i	0.625705	−	0.745686i	−0.356336	−	0.934358i	$-0.615974\pi$
$223$	9.34376	−	11.1355i	0.625705	−	0.745686i	0.982040	+	0.188672i	$0.0604184\pi$
$224$	−1.86710	−	3.66743i	−0.124751	−	0.245040i
$225$		0			0
$226$	−1.07699	−	1.86541i	−0.0716405	−	0.124085i
$227$	−1.15766	+	6.56541i	−0.0768366	+	0.435762i	0.921985	+	0.387226i	$0.126567\pi$
$227$	−1.15766	+	6.56541i	−0.0768366	+	0.435762i	−0.998821	+	0.0485359i	$0.984544\pi$
$228$		0			0
$229$	−6.09035	+	16.7331i	−0.402462	+	1.10575i	0.558604	+	0.829434i	$0.311337\pi$
$229$	−6.09035	+	16.7331i	−0.402462	+	1.10575i	−0.961066	+	0.276320i	$0.910885\pi$
$230$	−0.0619647	−	0.0225533i	−0.00408583	−	0.00148712i
$231$		0			0
$232$	0.416778	−	2.36367i	0.0273628	−	0.155182i
$233$	13.8987	−	8.02444i	0.910537	−	0.525699i	0.0299330	−	0.999552i	$-0.490471\pi$
$233$	13.8987	−	8.02444i	0.910537	−	0.525699i	0.880604	+	0.473853i	$0.157137\pi$
$234$		0			0
$235$	8.49658	−	14.7165i	0.554256	−	0.959999i
$236$	−19.6210	−	16.4640i	−1.27722	−	1.07171i
$237$		0			0
$238$	−1.18575	−	0.503790i	−0.0768608	−	0.0326558i
$239$	1.31201	+	1.56359i	0.0848668	+	0.101140i	0.806807	−	0.590815i	$-0.201194\pi$
$239$	1.31201	+	1.56359i	0.0848668	+	0.101140i	−0.721940	+	0.691956i	$0.756749\pi$
$240$		0			0
$241$	−3.55423	−	9.76517i	−0.228948	−	0.629030i	0.771021	−	0.636809i	$-0.219746\pi$
$241$	−3.55423	−	9.76517i	−0.228948	−	0.629030i	−0.999970	+	0.00777897i	$0.997524\pi$
$242$			1.06928i			0.0687359i
$243$		0			0
$244$		−	3.53868i		−	0.226541i
$245$	6.47319	+	6.71218i	0.413557	+	0.428825i
$246$		0			0
$247$	15.5076	−	13.0125i	0.986728	−	0.827963i
$248$	−0.0978313	−	0.554829i	−0.00621230	−	0.0352317i
$249$		0			0
$250$	0.923522	−	1.10061i	0.0584086	−	0.0696087i
$251$	11.7343	−	20.3243i	0.740660	−	1.28286i	−0.211535	−	0.977370i	$-0.567846\pi$
$251$	11.7343	−	20.3243i	0.740660	−	1.28286i	0.952195	−	0.305490i	$-0.0988203\pi$
$252$		0			0
$253$	−0.826126	−	1.43089i	−0.0519381	−	0.0899594i
$254$	−2.83082	−	0.499151i	−0.177622	−	0.0313195i
$255$		0			0
$256$	−13.7592	−	5.00794i	−0.859951	−	0.312996i
$257$	4.71223	+	1.71511i	0.293941	+	0.106986i	0.484781	−	0.874635i	$-0.338899\pi$
$257$	4.71223	+	1.71511i	0.293941	+	0.106986i	−0.190841	+	0.981621i	$0.561121\pi$
$258$		0			0
$259$	−0.623015	+	0.667654i	−0.0387123	+	0.0414860i
$260$	9.28790	−	5.36237i	0.576011	−	0.332560i
$261$		0			0
$262$	1.28558	+	0.742232i	0.0794236	+	0.0458552i
$263$	−3.92830	+	4.68156i	−0.242229	+	0.288678i	−0.873438	−	0.486935i	$-0.838115\pi$
$263$	−3.92830	+	4.68156i	−0.242229	+	0.288678i	0.631209	+	0.775613i	$0.282559\pi$
$264$		0			0
$265$	12.0678	−	2.12789i	0.741321	−	0.130715i
$266$	−1.71682	+	0.210216i	−0.105265	+	0.0128892i
$267$		0			0
$268$	10.7234	−	3.90301i	0.655038	−	0.238414i
$269$	4.75791			0.290095			0.145048	−	0.989425i	$-0.453666\pi$
$269$	4.75791			0.290095			0.145048	+	0.989425i	$0.453666\pi$
$270$		0			0
$271$			11.7607i			0.714413i	0.934025	+	0.357206i	$0.116271\pi$
$271$			11.7607i			0.714413i	−0.934025	+	0.357206i	$0.883729\pi$
$272$	−13.6000	+	4.95000i	−0.824622	+	0.300138i
$273$		0			0
$274$	1.15072	−	0.965565i	0.0695173	−	0.0583319i
$275$	13.9019	−	2.45128i	0.838317	−	0.147818i
$276$		0			0
$277$	−3.40027	−	2.85316i	−0.204302	−	0.171430i	0.534896	−	0.844918i	$-0.320351\pi$
$277$	−3.40027	−	2.85316i	−0.204302	−	0.171430i	−0.739198	+	0.673488i	$0.764795\pi$
$278$	−0.978821	+	1.69537i	−0.0587058	+	0.101681i
$279$		0			0
$280$	−1.83805	−	0.0969454i	−0.109845	−	0.00579360i
$281$	−8.77039	−	1.54646i	−0.523198	−	0.0922539i	−0.0941892	−	0.995554i	$-0.530026\pi$
$281$	−8.77039	−	1.54646i	−0.523198	−	0.0922539i	−0.429009	+	0.903300i	$0.641137\pi$
$282$		0			0
$283$	8.13265	−	22.3443i	0.483436	−	1.32823i	−0.423093	−	0.906086i	$-0.639056\pi$
$283$	8.13265	−	22.3443i	0.483436	−	1.32823i	0.906529	−	0.422143i	$-0.138722\pi$
$284$	−1.80454	+	4.95794i	−0.107080	+	0.294200i
$285$		0			0
$286$	−2.29467	−	0.404612i	−0.135686	−	0.0239252i
$287$	0.755893	−	14.3315i	0.0446190	−	0.845960i
$288$		0			0
$289$	1.60419	−	2.77853i	0.0943639	−	0.163443i
$290$	−0.614965	−	0.516017i	−0.0361120	−	0.0303016i
$291$		0			0
$292$	10.4505	−	1.84271i	0.611570	−	0.107836i
$293$	−20.3420	+	17.0689i	−1.18839	+	0.997178i	−0.188505	+	0.982072i	$0.560364\pi$
$293$	−20.3420	+	17.0689i	−1.18839	+	0.997178i	−0.999886	+	0.0151056i	$0.995192\pi$
$294$		0			0
$295$	−16.1705	+	5.88558i	−0.941482	+	0.342671i
$296$		−	0.180249i		−	0.0104767i
$297$		0			0
$298$	0.399576			0.0231468
$299$	1.44038	−	0.524256i	0.0832995	−	0.0303185i
$300$		0			0
$301$	5.91034	−	0.723690i	0.340666	−	0.0417128i
$302$	−0.0791319	+	0.0139531i	−0.00455353	+	0.000802910i
$303$		0			0
$304$	−12.4896	+	14.8846i	−0.716329	+	0.853688i
$305$	−2.05893	−	1.18873i	−0.117894	−	0.0680662i
$306$		0			0
$307$	−27.6153	+	15.9437i	−1.57609	+	0.909956i	−0.580693	+	0.814123i	$0.697218\pi$
$307$	−27.6153	+	15.9437i	−1.57609	+	0.909956i	−0.995397	+	0.0958335i	$0.969448\pi$
$308$	−16.7865	−	15.6642i	−0.956502	−	0.892552i
$309$		0			0
$310$	−0.177074	−	0.0644497i	−0.0100571	−	0.00366050i
$311$	5.67000	+	2.06371i	0.321516	+	0.117022i	0.497736	−	0.867328i	$-0.334165\pi$
$311$	5.67000	+	2.06371i	0.321516	+	0.117022i	−0.176220	+	0.984351i	$0.556387\pi$
$312$		0			0
$313$	−4.63763	−	0.817739i	−0.262134	−	0.0462213i	0.0410364	−	0.999158i	$-0.486934\pi$
$313$	−4.63763	−	0.817739i	−0.262134	−	0.0462213i	−0.303170	+	0.952936i	$0.598045\pi$
$314$	−0.126076	−	0.218369i	−0.00711485	−	0.0123233i
$315$		0			0
$316$	5.78373	−	10.0177i	0.325360	−	0.563541i
$317$	9.57584	−	11.4120i	0.537833	−	0.640964i	−0.426867	−	0.904314i	$-0.640383\pi$
$317$	9.57584	−	11.4120i	0.537833	−	0.640964i	0.964700	+	0.263350i	$0.0848273\pi$
$318$		0			0
$319$	−3.49288	−	19.8091i	−0.195564	−	1.10910i
$320$	−7.74578	+	6.49948i	−0.433002	+	0.363332i
$321$		0			0
$322$	−0.127599	−	0.0295036i	−0.00711082	−	0.00164417i
$323$			18.5159i			1.03025i
$324$		0			0
$325$			13.0960i			0.726436i
$326$	0.644639	+	1.77113i	0.0357032	+	0.0980938i
$327$		0			0
$328$	1.82085	+	2.17000i	0.100540	+	0.119818i
$329$	13.1975	−	31.0625i	0.727604	−	1.71253i
$330$		0			0
$331$	8.22997	+	6.90576i	0.452360	+	0.379575i	0.840311	−	0.542105i	$-0.182373\pi$
$331$	8.22997	+	6.90576i	0.452360	+	0.379575i	−0.387951	+	0.921680i	$0.626817\pi$
$332$	−4.26021	+	7.37890i	−0.233809	+	0.404970i
$333$		0			0
$334$	−1.78306	+	1.02945i	−0.0975646	+	0.0563290i
$335$	1.33134	−	7.55039i	0.0727388	−	0.412522i
$336$		0			0
$337$	−8.99836	−	3.27514i	−0.490172	−	0.178408i	0.0850964	−	0.996373i	$-0.472880\pi$
$337$	−8.99836	−	3.27514i	−0.490172	−	0.178408i	−0.575268	+	0.817965i	$0.695102\pi$
$338$	0.156327	−	0.429506i	0.00850308	−	0.0233620i
$339$		0			0
$340$	−1.70337	+	9.66030i	−0.0923782	+	0.523903i
$341$	−2.36078	−	4.08900i	−0.127844	−	0.221432i
$342$		0			0
$343$	14.3812	+	11.6696i	0.776513	+	0.630101i
$344$	−0.755482	+	0.900348i	−0.0407328	+	0.0485435i
$345$		0			0
$346$	0.564718	−	0.0995751i	0.0303594	−	0.00535319i
$347$	−14.4006	−	17.1620i	−0.773065	−	0.921303i	0.225533	−	0.974235i	$-0.427588\pi$
$347$	−14.4006	−	17.1620i	−0.773065	−	0.921303i	−0.998598	+	0.0529329i	$0.983143\pi$
$348$		0			0
$349$	−4.98766	−	13.7035i	−0.266983	−	0.733531i	−0.998654	−	0.0518722i	$-0.983481\pi$
$349$	−4.98766	−	13.7035i	−0.266983	−	0.733531i	0.731670	−	0.681659i	$-0.238741\pi$
$350$	0.609729	−	0.938212i	0.0325914	−	0.0501496i
$351$		0			0
$352$	6.80766			0.362849
$353$	7.53944	−	2.74413i	0.401284	−	0.146055i	−0.133491	−	0.991050i	$-0.542619\pi$
$353$	7.53944	−	2.74413i	0.401284	−	0.146055i	0.534775	+	0.844995i	$0.320396\pi$
$354$		0			0
$355$	2.27852	+	2.71544i	0.120931	+	0.144120i
$356$	3.85182	+	21.8447i	0.204146	+	1.15777i
$357$		0			0
$358$	1.40549	+	1.17935i	0.0742827	+	0.0623305i
$359$	1.26586	+	0.730844i	0.0668095	+	0.0385725i	0.533033	−	0.846095i	$-0.321052\pi$
$359$	1.26586	+	0.730844i	0.0668095	+	0.0385725i	−0.466223	+	0.884667i	$0.654386\pi$
$360$		0			0
$361$	2.92916	+	5.07346i	0.154167	+	0.267024i
$362$	0.494107	−	2.80222i	0.0259697	−	0.147281i
$363$		0			0
$364$	17.0155	−	12.8131i	0.891852	−	0.671591i
$365$	2.43842	−	6.69949i	0.127633	−	0.350668i
$366$		0			0
$367$	−25.7879	−	4.54711i	−1.34612	−	0.237357i	−0.546296	−	0.837592i	$-0.683963\pi$
$367$	−25.7879	−	4.54711i	−1.34612	−	0.237357i	−0.799824	+	0.600235i	$0.795074\pi$
$368$	−1.27413	+	0.735617i	−0.0664184	+	0.0383467i
$369$		0			0
$370$	−0.0522112	−	0.0301442i	−0.00271433	−	0.00156712i
$371$	23.2765	−	7.10781i	1.20845	−	0.369019i
$372$		0			0
$373$	−2.15588	−	12.2266i	−0.111627	−	0.633069i	−0.988365	−	0.152101i	$-0.951396\pi$
$373$	−2.15588	−	12.2266i	−0.111627	−	0.633069i	0.876738	−	0.480969i	$-0.159715\pi$
$374$	1.63258	−	1.36990i	0.0844186	−	0.0708356i
$375$		0			0
$376$	2.27843	+	6.25995i	0.117501	+	0.322832i
$377$	18.6608			0.961078
$378$		0			0
$379$	7.53240			0.386913			0.193457	−	0.981109i	$-0.438030\pi$
$379$	7.53240			0.386913			0.193457	+	0.981109i	$0.438030\pi$
$380$	4.50421	+	12.3752i	0.231061	+	0.634835i
$381$		0			0
$382$	−2.10563	+	1.76683i	−0.107733	+	0.0903991i
$383$	−0.508365	−	2.88308i	−0.0259762	−	0.147319i	0.969061	−	0.246821i	$-0.0793860\pi$
$383$	−0.508365	−	2.88308i	−0.0259762	−	0.147319i	−0.995037	+	0.0995025i	$0.968275\pi$
$384$		0			0
$385$	−14.7530	+	4.50504i	−0.751883	+	0.229598i
$386$	0.173152	+	0.0999696i	0.00881323	+	0.00508832i
$387$		0			0
$388$	25.3059	−	14.6104i	1.28471	−	0.741729i
$389$	24.4465	+	4.31058i	1.23949	+	0.218555i	0.754696	−	0.656075i	$-0.227784\pi$
$389$	24.4465	+	4.31058i	1.23949	+	0.218555i	0.484791	+	0.874630i	$0.338896\pi$
$390$		0			0
$391$	−0.479508	+	1.31744i	−0.0242497	+	0.0666256i
$392$	−3.64687	+	0.252560i	−0.184195	+	0.0127562i
$393$		0			0
$394$	0.568661	−	3.22504i	0.0286487	−	0.162475i
$395$	−3.88578	−	6.73037i	−0.195515	−	0.338642i
$396$		0			0
$397$	−18.3498	−	10.5942i	−0.920948	−	0.531710i	−0.0370106	−	0.999315i	$-0.511784\pi$
$397$	−18.3498	−	10.5942i	−0.920948	−	0.531710i	−0.883937	+	0.467605i	$0.845117\pi$
$398$	0.0831244	+	0.0697497i	0.00416665	+	0.00349624i
$399$		0			0
$400$	−2.18273	−	12.3789i	−0.109136	−	0.618943i
$401$	0.873706	+	1.04124i	0.0436308	+	0.0519972i	0.787419	−	0.616419i	$-0.211417\pi$
$401$	0.873706	+	1.04124i	0.0436308	+	0.0519972i	−0.743788	+	0.668416i	$0.766973\pi$
$402$		0			0
$403$	4.11612	−	1.49815i	0.205039	−	0.0746279i
$404$	24.1726			1.20263
$405$		0			0
$406$	−1.33688	−	0.868815i	−0.0663481	−	0.0431186i
$407$	−0.516657	−	1.41950i	−0.0256097	−	0.0703622i
$408$		0			0
$409$	−17.0261	−	20.2910i	−0.841889	−	1.00332i	−0.999874	−	0.0158823i	$-0.994944\pi$
$409$	−17.0261	−	20.2910i	−0.841889	−	1.00332i	0.157985	−	0.987441i	$-0.449500\pi$
$410$	0.933081	−	0.164527i	0.0460816	−	0.00812543i
$411$		0			0
$412$	11.4612	−	13.6589i	0.564651	−	0.672925i
$413$	−30.4572	+	15.5059i	−1.49870	+	0.762995i
$414$		0			0
$415$	2.86221	+	4.95749i	0.140500	+	0.243354i
$416$	−1.09669	+	6.21964i	−0.0537696	+	0.304943i
$417$		0			0
$418$	0.978588	−	2.68865i	0.0478643	−	0.131506i
$419$	16.0247	+	5.83250i	0.782856	+	0.284936i	0.702363	−	0.711819i	$-0.252128\pi$
$419$	16.0247	+	5.83250i	0.782856	+	0.284936i	0.0804931	+	0.996755i	$0.474351\pi$
$420$		0			0
$421$	−3.15843	+	17.9124i	−0.153933	+	0.872995i	0.805823	+	0.592157i	$0.201724\pi$
$421$	−3.15843	+	17.9124i	−0.153933	+	0.872995i	−0.959755	+	0.280838i	$0.909388\pi$
$422$	−0.673460	+	0.388822i	−0.0327835	+	0.0189276i
$423$		0			0
$424$	−2.40192	+	4.16025i	−0.116648	+	0.202040i
$425$	−9.17582	−	7.69943i	−0.445093	−	0.373477i
$426$		0			0
$427$	−4.34584	−	1.84642i	−0.210310	−	0.0893545i
$428$	23.2404	+	27.6968i	1.12337	+	1.33878i
$429$		0			0
$430$	0.134453	+	0.369406i	0.00648389	+	0.0178143i
$431$		−	3.52787i		−	0.169932i	−0.996384	−	0.0849658i	$-0.972922\pi$
$431$		−	3.52787i		−	0.169932i	0.996384	−	0.0849658i	$-0.0270781\pi$
$432$		0			0
$433$			19.5602i			0.940001i	0.882666	+	0.470001i	$0.155746\pi$
$433$			19.5602i			0.940001i	−0.882666	+	0.470001i	$0.844254\pi$
$434$	−0.364635	−	0.0843111i	−0.0175030	−	0.00404706i
$435$		0			0
$436$	−15.3242	+	12.8586i	−0.733897	+	0.615813i
$437$	0.326845	+	1.85363i	0.0156351	+	0.0886712i
$438$		0			0
$439$	5.11723	−	6.09848i	0.244232	−	0.291064i	−0.629977	−	0.776613i	$-0.716936\pi$
$439$	5.11723	−	6.09848i	0.244232	−	0.291064i	0.874209	+	0.485549i	$0.161380\pi$
$440$	1.52238	−	2.63683i	0.0725765	−	0.125706i
$441$		0			0
$442$	0.988566	+	1.71225i	0.0470213	+	0.0814433i
$443$	−27.4654	−	4.84288i	−1.30492	−	0.230092i	−0.522390	−	0.852707i	$-0.674959\pi$
$443$	−27.4654	−	4.84288i	−1.30492	−	0.230092i	−0.782529	+	0.622614i	$0.786071\pi$
$444$		0			0
$445$	14.0040	+	5.09703i	0.663852	+	0.241622i
$446$	1.79107	+	0.651896i	0.0848095	+	0.0308681i
$447$		0			0
$448$	−13.7009	+	14.6825i	−0.647306	+	0.693685i
$449$	15.1431	−	8.74287i	0.714647	−	0.412602i	−0.0981322	−	0.995173i	$-0.531287\pi$
$449$	15.1431	−	8.74287i	0.714647	−	0.412602i	0.812779	+	0.582572i	$0.197953\pi$
$450$		0			0
$451$	20.5596	+	11.8701i	0.968116	+	0.558942i
$452$	−20.9372	+	24.9520i	−0.984803	+	1.17364i
$453$		0			0
$454$	−0.860863	+	0.151793i	−0.0404023	+	0.00712402i
$455$	−1.73926	−	14.2044i	−0.0815377	−	0.665915i
$456$		0			0
$457$	−25.2787	+	9.20069i	−1.18249	+	0.430390i	−0.857080	−	0.515184i	$-0.827724\pi$
$457$	−25.2787	+	9.20069i	−1.18249	+	0.430390i	−0.325407	+	0.945574i	$0.605501\pi$
$458$	−2.33487			−0.109101
$459$		0			0
$460$			0.997166i			0.0464931i
$461$	−17.3925	+	6.33036i	−0.810050	+	0.294834i	−0.713645	−	0.700508i	$-0.752957\pi$
$461$	−17.3925	+	6.33036i	−0.810050	+	0.294834i	−0.0964058	+	0.995342i	$0.530735\pi$
$462$		0			0
$463$	−11.6402	+	9.76728i	−0.540966	+	0.453924i	−0.871868	−	0.489741i	$-0.837091\pi$
$463$	−11.6402	+	9.76728i	−0.540966	+	0.453924i	0.330902	+	0.943665i	$0.392647\pi$
$464$	−17.6389	+	3.11021i	−0.818864	+	0.144388i
$465$		0			0
$466$	1.61202	+	1.35265i	0.0746755	+	0.0626602i
$467$	12.8706	−	22.2926i	0.595581	−	1.03158i	−0.397884	−	0.917436i	$-0.630255\pi$
$467$	12.8706	−	22.2926i	0.595581	−	1.03158i	0.993465	−	0.114140i	$-0.0364114\pi$
$468$		0			0
$469$	0.802015	−	15.2059i	0.0370336	−	0.702145i
$470$	2.19431	+	0.386916i	0.101216	+	0.0178471i
$471$		0			0
$472$	2.30728	−	6.33919i	0.106201	−	0.291785i
$473$	−3.36889	+	9.25595i	−0.154902	+	0.425589i
$474$		0			0
$475$	−15.8369	−	2.79247i	−0.726647	−	0.128128i
$476$	−1.02613	+	19.4551i	−0.0470327	+	0.891724i
$477$		0			0
$478$	−0.133817	+	0.231778i	−0.00612065	+	0.0106013i
$479$	1.75513	+	1.47273i	0.0801939	+	0.0672907i	0.682003	−	0.731349i	$-0.261109\pi$
$479$	1.75513	+	1.47273i	0.0801939	+	0.0672907i	−0.601810	+	0.798640i	$0.705553\pi$
$480$		0			0
$481$	1.38012	−	0.243353i	0.0629282	−	0.0110959i
$482$	1.04381	−	0.875858i	0.0475441	−	0.0398942i
$483$		0			0
$484$	15.1945	−	5.53033i	0.690657	−	0.251379i
$485$		−	19.6319i		−	0.891436i
$486$		0			0
$487$	35.0917			1.59016			0.795078	−	0.606507i	$-0.207430\pi$
$487$	35.0917			1.59016			0.795078	+	0.606507i	$0.207430\pi$
$488$	0.875806	−	0.318767i	0.0396459	−	0.0144299i
$489$		0			0
$490$	−0.536733	+	1.09860i	−0.0242471	+	0.0496296i
$491$	−22.3682	+	3.94412i	−1.00946	+	0.177996i	−0.653840	−	0.756633i	$-0.726843\pi$
$491$	−22.3682	+	3.94412i	−1.00946	+	0.177996i	−0.355624	+	0.934629i	$0.615732\pi$
$492$		0			0
$493$	−10.9711	+	13.0748i	−0.494112	+	0.588860i
$494$	2.29877	+	1.32719i	0.103426	+	0.0597132i
$495$		0			0
$496$	−3.64102	+	2.10214i	−0.163487	+	0.0943890i
$497$	5.14726	+	4.80312i	0.230886	+	0.215449i
$498$		0			0
$499$	−18.3536	−	6.68017i	−0.821621	−	0.299046i	−0.103206	−	0.994660i	$-0.532910\pi$
$499$	−18.3536	−	6.68017i	−0.821621	−	0.299046i	−0.718415	+	0.695615i	$0.755132\pi$
$500$	−20.4161	−	7.43087i	−0.913038	−	0.332319i
$501$		0			0
$502$	3.03046	+	0.534353i	0.135256	+	0.0238493i
$503$	6.03294	+	10.4494i	0.268995	+	0.465914i	0.968603	−	0.248614i	$-0.0799750\pi$
$503$	6.03294	+	10.4494i	0.268995	+	0.465914i	−0.699607	+	0.714528i	$0.746642\pi$
$504$		0			0
$505$	8.12014	−	14.0645i	0.361342	−	0.625862i
$506$	0.139257	−	0.165960i	0.00619071	−	0.00737780i
$507$		0			0
$508$	7.54814	+	42.8076i	0.334895	+	1.89928i
$509$	−25.0698	+	21.0360i	−1.11120	+	0.932406i	−0.998127	−	0.0611805i	$-0.980513\pi$
$509$	−25.0698	+	21.0360i	−1.11120	+	0.932406i	−0.113072	+	0.993587i	$0.536069\pi$
$510$		0			0
$511$	3.18986	−	13.7957i	0.141111	−	0.610287i
$512$		−	10.1322i		−	0.447786i
$513$		0			0
$514$			0.657525i			0.0290022i
$515$	−4.09716	−	11.2569i	−0.180543	−	0.496037i
$516$		0			0
$517$	35.8865	+	42.7678i	1.57829	+	1.88093i
$518$	−0.110204	−	0.0468222i	−0.00484207	−	0.00205725i
$519$		0			0
$520$	2.16382	+	1.81566i	0.0948900	+	0.0796221i
$521$	0.373097	−	0.646223i	0.0163457	−	0.0283115i	−0.857737	−	0.514089i	$-0.828130\pi$
$521$	0.373097	−	0.646223i	0.0163457	−	0.0283115i	0.874083	+	0.485777i	$0.161463\pi$
$522$		0			0
$523$	0.0341810	−	0.0197344i	0.00149463	−	0.000862925i	−0.499252	−	0.866457i	$-0.666392\pi$
$523$	0.0341810	−	0.0197344i	0.00149463	−	0.000862925i	0.500747	+	0.865594i	$0.333059\pi$
$524$	3.89806	−	22.1070i	0.170287	−	0.965748i
$525$		0			0
$526$	−0.753000	−	0.274070i	−0.0328324	−	0.0119500i
$527$	−1.37027	+	3.76478i	−0.0596898	+	0.163996i
$528$		0			0
$529$	3.96916	−	22.5102i	0.172572	−	0.978705i
$530$	0.803378	+	1.39149i	0.0348965	+	0.0604426i
$531$		0			0
$532$	11.8666	+	23.3088i	0.514483	+	1.01057i
$533$	−14.1569	+	16.8715i	−0.613204	+	0.730788i
$534$		0			0
$535$	23.9220	−	4.21809i	1.03424	−	0.182364i
$536$	1.93195	+	2.30241i	0.0834476	+	0.0994490i
$537$		0			0
$538$	0.213373	+	0.586239i	0.00919918	+	0.0252745i
$539$	−27.9961	+	12.4422i	−1.20588	+	0.535924i
$540$		0			0
$541$	−44.3075			−1.90493			−0.952465	−	0.304648i	$-0.901461\pi$
$541$	−44.3075			−1.90493			−0.952465	+	0.304648i	$0.901461\pi$
$542$	−1.44908	+	0.527421i	−0.0622432	+	0.0226547i
$543$		0			0
$544$	−3.71307	−	4.42506i	−0.159196	−	0.189723i
$545$	2.33381	+	13.2357i	0.0999693	+	0.566954i
$546$		0			0
$547$	1.85944	+	1.56025i	0.0795038	+	0.0667116i	0.681673	−	0.731657i	$-0.261252\pi$
$547$	1.85944	+	1.56025i	0.0795038	+	0.0667116i	−0.602170	+	0.798368i	$0.705697\pi$
$548$	−19.6722	−	11.3578i	−0.840355	−	0.485179i
$549$		0			0
$550$	0.925476	+	1.60297i	0.0394624	+	0.0683509i
$551$	−3.97905	+	22.5663i	−0.169513	+	0.961358i
$552$		0			0
$553$	−9.28489	−	12.3301i	−0.394834	−	0.524327i
$554$	0.199059	−	0.546911i	0.00845722	−	0.0232360i
$555$		0			0
$556$	29.1537	+	5.14058i	1.23639	+	0.218009i
$557$	0.292925	−	0.169120i	0.0124116	−	0.00716586i	−0.493781	−	0.869586i	$-0.664386\pi$
$557$	0.292925	−	0.169120i	0.0124116	−	0.00716586i	0.506193	+	0.862420i	$0.331052\pi$
$558$		0			0
$559$	−7.91374	−	4.56900i	−0.334715	−	0.193248i
$560$	4.01148	+	13.1367i	0.169516	+	0.555127i
$561$		0			0
$562$	−0.202773	−	1.14998i	−0.00855346	−	0.0485091i
$563$	12.3087	−	10.3282i	0.518748	−	0.435282i	−0.345447	−	0.938438i	$-0.612273\pi$
$563$	12.3087	−	10.3282i	0.518748	−	0.435282i	0.864195	+	0.503157i	$0.167828\pi$
$564$		0			0
$565$	7.48467	+	20.5640i	0.314883	+	0.865133i
$566$	3.11783			0.131052
$567$		0			0
$568$	−1.38962			−0.0583072
$569$	−8.08739	−	22.2199i	−0.339041	−	0.931507i	−0.985667	−	0.168700i	$-0.946043\pi$
$569$	−8.08739	−	22.2199i	−0.339041	−	0.931507i	0.646627	−	0.762807i	$-0.276179\pi$
$570$		0			0
$571$	−0.278581	+	0.233758i	−0.0116583	+	0.00978245i	−0.648598	−	0.761131i	$-0.724644\pi$
$571$	−0.278581	+	0.233758i	−0.0116583	+	0.00978245i	0.636940	+	0.770913i	$0.280200\pi$
$572$	6.11852	+	34.6999i	0.255828	+	1.45087i
$573$		0			0
$574$	1.79973	−	0.549573i	0.0751192	−	0.0229387i
$575$	−1.05451	−	0.608820i	−0.0439760	−	0.0253896i
$576$		0			0
$577$	−7.66829	+	4.42729i	−0.319235	+	0.184310i	−0.651052	−	0.759034i	$-0.725672\pi$
$577$	−7.66829	+	4.42729i	−0.319235	+	0.184310i	0.331817	+	0.943344i	$0.392339\pi$
$578$	0.414294	+	0.0730512i	0.0172324	+	0.00303853i
$579$		0			0
$580$	−4.15199	+	11.4075i	−0.172402	+	0.473671i
$581$	6.83911	+	9.08213i	0.283734	+	0.376790i
$582$		0			0
$583$	−6.99097	+	39.6478i	−0.289536	+	1.64204i
$584$	1.39745	+	2.42046i	0.0578270	+	0.100159i
$585$		0			0
$586$	−3.01538	−	1.74093i	−0.124564	−	0.0719171i
$587$	−22.0136	−	18.4716i	−0.908598	−	0.762405i	0.0632534	−	0.997997i	$-0.479852\pi$
$587$	−22.0136	−	18.4716i	−0.908598	−	0.762405i	−0.971852	+	0.235593i	$0.924297\pi$
$588$		0			0
$589$	0.934012	+	5.29705i	0.0384853	+	0.218261i
$590$	−1.45036	−	1.72848i	−0.0597105	−	0.0711602i
$591$		0			0
$592$	−1.26399	+	0.460053i	−0.0519495	+	0.0189081i
$593$	7.83158			0.321605			0.160802	−	0.986987i	$-0.448592\pi$
$593$	7.83158			0.321605			0.160802	+	0.986987i	$0.448592\pi$
$594$		0			0
$595$	10.9750	+	7.13247i	0.449931	+	0.292403i
$596$	−2.06661	−	5.67797i	−0.0846517	−	0.232579i
$597$		0			0
$598$	0.129191	+	0.153964i	0.00528300	+	0.00629604i
$599$	25.0073	−	4.40946i	1.02177	−	0.180166i	0.362430	−	0.932011i	$-0.381947\pi$
$599$	25.0073	−	4.40946i	1.02177	−	0.180166i	0.659339	+	0.751845i	$0.270836\pi$
$600$		0			0
$601$	28.8206	−	34.3470i	1.17562	−	1.40104i	0.277819	−	0.960633i	$-0.410388\pi$
$601$	28.8206	−	34.3470i	1.17562	−	1.40104i	0.897796	−	0.440411i	$-0.145167\pi$
$602$	0.354224	+	0.695779i	0.0144371	+	0.0283578i
$603$		0			0
$604$	0.607545	+	1.05230i	0.0247207	+	0.0428174i
$605$	1.88643	−	10.6985i	0.0766941	−	0.434954i
$606$		0			0
$607$	−3.35939	+	9.22986i	−0.136354	+	0.374628i	−0.989011	−	0.147842i	$-0.952767\pi$
$607$	−3.35939	+	9.22986i	−0.136354	+	0.374628i	0.852657	+	0.522470i	$0.174990\pi$
$608$	−7.28751	−	2.65244i	−0.295548	−	0.107571i
$609$		0			0
$610$	0.0541320	−	0.306998i	0.00219174	−	0.0124300i
$611$	−44.8549	+	25.8970i	−1.81464	+	1.04768i
$612$		0			0
$613$	−16.3106	+	28.2507i	−0.658778	+	1.14104i	0.322154	+	0.946687i	$0.395593\pi$
$613$	−16.3106	+	28.2507i	−0.658778	+	1.14104i	−0.980932	+	0.194350i	$0.937740\pi$
$614$	−3.20292	−	2.68757i	−0.129259	−	0.108461i
$615$		0			0
$616$	2.36467	−	5.56564i	0.0952753	−	0.224246i
$617$	−0.764441	−	0.911025i	−0.0307752	−	0.0366765i	0.750437	−	0.660942i	$-0.229843\pi$
$617$	−0.764441	−	0.911025i	−0.0307752	−	0.0366765i	−0.781213	+	0.624265i	$0.785398\pi$
$618$		0			0
$619$	12.4466	+	34.1968i	0.500271	+	1.37448i	0.891011	+	0.453982i	$0.149997\pi$
$619$	12.4466	+	34.1968i	0.500271	+	1.37448i	−0.390740	+	0.920501i	$0.627781\pi$
$620$			2.84956i			0.114441i
$621$		0			0
$622$			0.791169i			0.0317230i
$623$	28.8373	+	6.66778i	1.15534	+	0.267139i
$624$		0			0
$625$	1.17217	−	0.983570i	0.0468869	−	0.0393428i
$626$	−0.107223	−	0.608090i	−0.00428548	−	0.0243042i
$627$		0			0
$628$	−2.45096	+	2.92094i	−0.0978040	+	0.116558i
$629$	−0.640897	+	1.11007i	−0.0255542	+	0.0442612i
$630$		0			0
$631$	17.0123	+	29.4661i	0.677248	+	1.17303i	0.975806	+	0.218637i	$0.0701610\pi$
$631$	17.0123	+	29.4661i	0.677248	+	1.17303i	−0.298558	+	0.954391i	$0.596506\pi$
$632$	3.00034	+	0.529041i	0.119347	+	0.0210441i
$633$		0			0
$634$	1.83556	+	0.668088i	0.0728992	+	0.0265331i
$635$	27.4426	+	9.98830i	1.08903	+	0.396374i
$636$		0			0
$637$	−6.85742	−	27.5823i	−0.271701	−	1.09285i
$638$	2.28411	−	1.31873i	0.0904286	−	0.0522090i
$639$		0			0
$640$	−4.73715	−	2.73500i	−0.187252	−	0.108110i
$641$	−25.3403	+	30.1994i	−1.00088	+	1.19280i	−0.0196832	+	0.999806i	$0.506266\pi$
$641$	−25.3403	+	30.1994i	−1.00088	+	1.19280i	−0.981199	+	0.192999i	$0.938179\pi$
$642$		0			0
$643$	1.58947	−	0.280266i	0.0626824	−	0.0110526i	−0.142219	−	0.989835i	$-0.545424\pi$
$643$	1.58947	−	0.280266i	0.0626824	−	0.0110526i	0.204901	+	0.978783i	$0.434313\pi$
$644$	0.240699	+	1.96578i	0.00948486	+	0.0774624i
$645$		0			0
$646$	−2.28140	+	0.830362i	−0.0897605	+	0.0326702i
$647$	−20.9883			−0.825137			−0.412568	−	0.910927i	$-0.635368\pi$
$647$	−20.9883			−0.825137			−0.412568	+	0.910927i	$0.635368\pi$
$648$		0			0
$649$		−	56.5362i		−	2.21924i
$650$	−1.61360	+	0.587304i	−0.0632908	+	0.0230360i
$651$		0			0
$652$	21.8337	−	18.3206i	0.855073	−	0.717492i
$653$	−7.06142	+	1.24512i	−0.276335	+	0.0487253i	−0.310098	−	0.950705i	$-0.600362\pi$
$653$	−7.06142	+	1.24512i	−0.276335	+	0.0487253i	0.0337633	+	0.999430i	$0.489251\pi$
$654$		0			0
$655$	−11.5532	−	9.69428i	−0.451421	−	0.378787i
$656$	10.5697	−	18.3072i	0.412676	−	0.714776i
$657$		0			0
$658$	4.41918	+	0.233083i	0.172277	+	0.00908652i
$659$	29.4274	+	5.18885i	1.14633	+	0.202129i	0.714372	−	0.699766i	$-0.246712\pi$
$659$	29.4274	+	5.18885i	1.14633	+	0.202129i	0.431957	+	0.901894i	$0.357823\pi$
$660$		0			0
$661$	−8.06882	+	22.1689i	−0.313841	+	0.862270i	0.678032	+	0.735033i	$0.262833\pi$
$661$	−8.06882	+	22.1689i	−0.313841	+	0.862270i	−0.991872	+	0.127238i	$0.959389\pi$
$662$	−0.481801	+	1.32374i	−0.0187257	+	0.0514485i
$663$		0			0
$664$	−2.21001	−	0.389684i	−0.0857649	−	0.0151227i
$665$	17.5482	+	0.925554i	0.680490	+	0.0358915i
$666$		0			0
$667$	−0.867520	+	1.50259i	−0.0335905	+	0.0581805i
$668$	23.8505	+	20.0129i	0.922803	+	0.774324i
$669$		0			0
$670$	0.990015	−	0.174566i	0.0382476	−	0.00674409i
$671$	5.98349	−	5.02075i	0.230990	−	0.193824i
$672$		0			0
$673$	14.5070	−	5.28011i	0.559203	−	0.203533i	−0.0469277	−	0.998898i	$-0.514943\pi$
$673$	14.5070	−	5.28011i	0.559203	−	0.203533i	0.606131	+	0.795365i	$0.292721\pi$
$674$		−	1.25560i		−	0.0483637i
$675$		0			0
$676$	−6.91181			−0.265839
$677$	−35.5524	+	12.9400i	−1.36639	+	0.497325i	−0.918024	−	0.396525i	$-0.870216\pi$
$677$	−35.5524	+	12.9400i	−1.36639	+	0.497325i	−0.448366	+	0.893850i	$0.647994\pi$
$678$		0			0
$679$	−4.73880	−	38.7015i	−0.181858	−	1.48523i
$680$	−2.54432	+	0.448632i	−0.0975701	+	0.0172042i
$681$		0			0
$682$	0.397948	−	0.474256i	0.0152382	−	0.0181602i
$683$	13.2112	+	7.62750i	0.505513	+	0.291858i	0.730987	−	0.682391i	$-0.239060\pi$
$683$	13.2112	+	7.62750i	0.505513	+	0.291858i	−0.225474	+	0.974249i	$0.572393\pi$
$684$		0			0
$685$	−13.2167	+	7.63067i	−0.504985	+	0.291553i
$686$	−0.792914	+	2.29530i	−0.0302736	+	0.0876348i
$687$		0			0
$688$	8.24189	+	2.99980i	0.314219	+	0.114366i
$689$	−35.0969	−	12.7742i	−1.33709	−	0.486660i
$690$		0			0
$691$	32.7662	+	5.77757i	1.24649	+	0.219789i	0.757693	−	0.652611i	$-0.226326\pi$
$691$	32.7662	+	5.77757i	1.24649	+	0.219789i	0.488792	+	0.872400i	$0.337438\pi$
$692$	−4.33570	−	7.50964i	−0.164818	−	0.285474i
$693$		0			0
$694$	1.46877	−	2.54399i	0.0557539	−	0.0965686i
$695$	12.7844	−	15.2358i	0.484939	−	0.577928i
$696$		0			0
$697$	−3.49803	−	19.8383i	−0.132497	−	0.751429i
$698$	1.46478	−	1.22909i	0.0554426	−	0.0465219i
$699$		0			0
$700$	−16.4855	−	3.81180i	−0.623095	−	0.144072i
$701$		−	1.67746i		−	0.0633567i	−0.999498	−	0.0316783i	$-0.989915\pi$
$701$		−	1.67746i		−	0.0633567i	0.999498	−	0.0316783i	$-0.0100852\pi$
$702$		0			0
$703$			1.72086i			0.0649036i
$704$	−11.3619	−	31.2166i	−0.428219	−	1.17652i
$705$		0			0
$706$	0.676227	+	0.805896i	0.0254501	+	0.0303303i
$707$	12.6128	−	29.6863i	0.474354	−	1.11647i
$708$		0			0
$709$	−21.9319	−	18.4031i	−0.823671	−	0.691142i	0.130158	−	0.991493i	$-0.458452\pi$
$709$	−21.9319	−	18.4031i	−0.823671	−	0.691142i	−0.953829	+	0.300351i	$0.902896\pi$
$710$	−0.232395	+	0.402521i	−0.00872165	+	0.0151063i
$711$		0			0
$712$	−5.05949	+	2.92110i	−0.189613	+	0.109473i
$713$	−0.0707217	+	0.401083i	−0.00264855	+	0.0150207i
$714$		0			0
$715$	22.2450	+	8.09652i	0.831916	+	0.302793i
$716$	9.48932	−	26.0717i	0.354633	−	0.974345i
$717$		0			0
$718$	−0.0332810	+	0.188746i	−0.00124204	+	0.00704395i
$719$	−6.37063	−	11.0343i	−0.237584	−	0.411508i	0.722436	−	0.691438i	$-0.243022\pi$
$719$	−6.37063	−	11.0343i	−0.237584	−	0.411508i	−0.960021	+	0.279929i	$0.909689\pi$
$720$		0			0
$721$	−10.7942	−	21.2024i	−0.401998	−	0.789619i
$722$	−0.493757	+	0.588437i	−0.0183757	+	0.0218994i
$723$		0			0
$724$	−42.3750	+	7.47186i	−1.57486	+	0.277690i
$725$	−9.52849	−	11.3556i	−0.353879	−	0.421737i
$726$		0			0
$727$	−15.1297	−	41.5685i	−0.561129	−	1.54169i	−0.817985	−	0.575240i	$-0.804909\pi$
$727$	−15.1297	−	41.5685i	−0.561129	−	1.54169i	0.256856	−	0.966450i	$-0.417313\pi$
$728$	4.70396	+	3.05702i	0.174340	+	0.113301i
$729$		0			0
$730$	0.934821			0.0345993
$731$	7.85396	−	2.85861i	0.290489	−	0.105729i
$732$		0			0
$733$	−13.1054	−	15.6184i	−0.484060	−	0.576880i	0.467637	−	0.883921i	$-0.345106\pi$
$733$	−13.1054	−	15.6184i	−0.484060	−	0.576880i	−0.951696	+	0.307041i	$0.900661\pi$
$734$	−0.596221	−	3.38134i	−0.0220069	−	0.124807i
$735$		0			0
$736$	−0.449829	−	0.377452i	−0.0165809	−	0.0139130i
$737$	21.8141	+	12.5944i	0.803534	+	0.463921i
$738$		0			0
$739$	−20.0545	−	34.7355i	−0.737718	−	1.27777i	−0.953520	−	0.301328i	$-0.902570\pi$
$739$	−20.0545	−	34.7355i	−0.737718	−	1.27777i	0.215802	−	0.976437i	$-0.430763\pi$
$740$	−0.158311	+	0.897828i	−0.00581964	+	0.0330048i
$741$		0			0
$742$	1.91963	+	2.54922i	0.0704720	+	0.0935847i
$743$	3.63149	−	9.97743i	0.133226	−	0.366037i	−0.855084	−	0.518489i	$-0.826495\pi$
$743$	3.63149	−	9.97743i	0.133226	−	0.366037i	0.988311	+	0.152452i	$0.0487170\pi$
$744$		0			0
$745$	−3.99787	−	0.704933i	−0.146471	−	0.0258267i
$746$	1.40980	−	0.813947i	0.0516164	−	0.0298007i
$747$		0			0
$748$	−27.9099	−	16.1138i	−1.02049	−	0.589179i
$749$	46.1408	−	14.0898i	1.68595	−	0.514829i
$750$		0			0
$751$	7.18177	+	40.7298i	0.262066	+	1.48625i	0.777260	+	0.629179i	$0.216609\pi$
$751$	7.18177	+	40.7298i	0.262066	+	1.48625i	−0.515194	+	0.857074i	$0.672280\pi$
$752$	38.0823	−	31.9549i	1.38872	−	1.16527i
$753$		0			0
$754$	0.836861	+	2.29926i	0.0304767	+	0.0837340i
$755$	0.816354			0.0297102
$756$		0			0
$757$	−23.7006			−0.861412			−0.430706	−	0.902492i	$-0.641735\pi$
$757$	−23.7006			−0.861412			−0.430706	+	0.902492i	$0.641735\pi$
$758$	0.337798	+	0.928092i	0.0122694	+	0.0337098i
$759$		0			0
$760$	−2.65706	+	2.22954i	−0.0963818	+	0.0808740i
$761$	−2.04815	−	11.6156i	−0.0742454	−	0.421066i	−0.999163	−	0.0408995i	$-0.986978\pi$
$761$	−2.04815	−	11.6156i	−0.0742454	−	0.421066i	0.924918	−	0.380167i	$-0.124133\pi$
$762$		0			0
$763$	7.79565	+	25.5290i	0.282222	+	0.924212i
$764$	35.9971	+	20.7829i	1.30233	+	0.751899i
$765$		0			0
$766$	0.332436	−	0.191932i	0.0120114	−	0.00693479i
$767$	51.6528	+	9.10778i	1.86507	+	0.328863i
$768$		0			0
$769$	−8.33433	+	22.8984i	−0.300544	+	0.825737i	0.693862	+	0.720108i	$0.255908\pi$
$769$	−8.33433	+	22.8984i	−0.300544	+	0.825737i	−0.994406	+	0.105629i	$0.966314\pi$
$770$	−1.21670	−	1.61573i	−0.0438467	−	0.0582270i
$771$		0			0
$772$	0.525021	−	2.97754i	0.0188959	−	0.107164i
$773$	1.44939	+	2.51041i	0.0521309	+	0.0902933i	0.890913	−	0.454173i	$-0.150065\pi$
$773$	1.44939	+	2.51041i	0.0521309	+	0.0902933i	−0.838782	+	0.544467i	$0.816732\pi$
$774$		0			0
$775$	−3.01342	−	1.73980i	−0.108245	−	0.0624955i
$776$	5.89557	+	4.94697i	0.211639	+	0.177586i
$777$		0			0
$778$	0.565207	+	3.20545i	0.0202637	+	0.114921i
$779$	−17.3840	−	20.7174i	−0.622845	−	0.742277i
$780$		0			0
$781$	−10.9436	+	3.98315i	−0.391593	+	0.142528i
$782$	−0.183830			−0.00657374
$783$		0			0
$784$	11.0791	+	24.9289i	0.395681	+	0.890319i
$785$	0.876175	+	2.40727i	0.0312720	+	0.0859192i
$786$		0			0
$787$	5.60311	+	6.67753i	0.199729	+	0.238028i	0.856608	−	0.515969i	$-0.172568\pi$
$787$	5.60311	+	6.67753i	0.199729	+	0.238028i	−0.656878	+	0.753997i	$0.728123\pi$
$788$	−48.7689	+	8.59928i	−1.73732	+	0.306337i
$789$		0			0
$790$	0.655010	−	0.780611i	0.0233042	−	0.0277729i
$791$	19.7188	+	38.7324i	0.701120	+	1.37717i
$792$		0			0
$793$	3.62315	+	6.27549i	0.128662	+	0.222849i
$794$	0.482439	−	2.73605i	0.0171211	−	0.0970986i
$795$		0			0
$796$	0.561222	−	1.54195i	0.0198920	−	0.0546528i
$797$	−11.0381	−	4.01755i	−0.390990	−	0.142309i	0.139042	−	0.990287i	$-0.455598\pi$
$797$	−11.0381	−	4.01755i	−0.390990	−	0.142309i	−0.530032	+	0.847978i	$0.677820\pi$
$798$		0			0
$799$	8.22624	−	46.6533i	0.291023	−	1.65048i
$800$	4.34482	−	2.50848i	0.153612	−	0.0886882i
$801$		0			0
$802$	−0.0891128	+	0.154348i	−0.00314668	+	0.00545021i
$803$	17.9432	+	15.0561i	0.633201	+	0.531319i
$804$		0			0
$805$	1.22462	+	0.520303i	0.0431621	+	0.0183383i
$806$	0.369183	+	0.439975i	0.0130039	+	0.0154975i
$807$		0			0
$808$	2.17749	+	5.98260i	0.0766038	+	0.210467i
$809$		−	13.3913i		−	0.470814i	−0.971897	−	0.235407i	$-0.924358\pi$
$809$		−	13.3913i		−	0.470814i	0.971897	−	0.235407i	$-0.0756423\pi$
$810$		0			0
$811$		−	14.2545i		−	0.500543i	−0.968176	−	0.250272i	$-0.919480\pi$
$811$		−	14.2545i		−	0.500543i	0.968176	−	0.250272i	$-0.0805200\pi$
$812$	−5.43151	+	23.4906i	−0.190609	+	0.824357i
$813$		0			0
$814$	0.151732	−	0.127318i	0.00531820	−	0.00446250i
$815$	−3.32517	−	18.8580i	−0.116476	−	0.660566i
$816$		0			0
$817$	7.21271	−	8.59577i	0.252341	−	0.300728i
$818$	1.73656	−	3.00782i	0.0607176	−	0.105166i
$819$		0			0
$820$	−7.16385	−	12.4081i	−0.250172	−	0.433311i
$821$	−53.2811	−	9.39490i	−1.85952	−	0.327884i	−0.872520	−	0.488579i	$-0.837515\pi$
$821$	−53.2811	−	9.39490i	−1.85952	−	0.327884i	−0.987004	+	0.160695i	$0.948626\pi$
$822$		0			0
$823$	−24.0026	−	8.73623i	−0.836678	−	0.304526i	−0.112081	−	0.993699i	$-0.535752\pi$
$823$	−24.0026	−	8.73623i	−0.836678	−	0.304526i	−0.724597	+	0.689173i	$0.757974\pi$
$824$	4.41294	+	1.60618i	0.153732	+	0.0559539i
$825$		0			0
$826$	−3.27642	−	3.05736i	−0.114001	−	0.106379i
$827$	−35.7068	+	20.6154i	−1.24165	+	0.716866i	−0.969430	−	0.245369i	$-0.921091\pi$
$827$	−35.7068	+	20.6154i	−1.24165	+	0.716866i	−0.272219	+	0.962235i	$0.587757\pi$
$828$		0			0
$829$	19.7340	+	11.3934i	0.685389	+	0.395710i	0.801883	−	0.597482i	$-0.203832\pi$
$829$	19.7340	+	11.3934i	0.685389	+	0.395710i	−0.116493	+	0.993191i	$0.537165\pi$
$830$	−0.482471	+	0.574986i	−0.0167468	+	0.0199581i
$831$		0			0
$832$	30.3506	−	5.35164i	1.05222	−	0.185535i
$833$	23.3574	+	11.4115i	0.809285	+	0.395386i
$834$		0			0
$835$	19.6562	−	7.15427i	0.680231	−	0.247584i
$836$	−43.2670			−1.49642
$837$		0			0
$838$			2.23602i			0.0772420i
$839$	17.3731	−	6.32330i	0.599786	−	0.218304i	−0.0242419	−	0.999706i	$-0.507717\pi$
$839$	17.3731	−	6.32330i	0.599786	−	0.218304i	0.624028	+	0.781402i	$0.285495\pi$
$840$		0			0
$841$	6.03445	−	5.06350i	0.208084	−	0.174604i
$842$	−2.34869	+	0.414137i	−0.0809411	+	0.0142721i
$843$		0			0
$844$	9.00832	+	7.55887i	0.310079	+	0.260187i
$845$	−2.32184	+	4.02154i	−0.0798736	+	0.138345i
$846$		0			0
$847$	1.13641	−	21.5459i	0.0390474	−	0.740326i
$848$	35.3041	+	6.22506i	1.21235	+	0.213769i
$849$		0			0
$850$	0.537174	−	1.47587i	0.0184249	−	0.0506220i
$851$	−0.0445655	+	0.122443i	−0.00152768	+	0.00419728i
$852$		0			0
$853$	52.2825	+	9.21881i	1.79012	+	0.315646i	0.967485	−	0.252927i	$-0.0813932\pi$
$853$	52.2825	+	9.21881i	1.79012	+	0.315646i	0.822633	+	0.568573i	$0.192504\pi$
$854$	0.0326098	−	0.618271i	0.00111588	−	0.0211568i
$855$		0			0
$856$	−4.76131	+	8.24683i	−0.162738	+	0.281871i
$857$	5.81262	+	4.87737i	0.198555	+	0.166608i	0.736644	−	0.676280i	$-0.236409\pi$
$857$	5.81262	+	4.87737i	0.198555	+	0.166608i	−0.538089	+	0.842888i	$0.680854\pi$
$858$		0			0
$859$	−53.9268	+	9.50876i	−1.83996	+	0.324435i	−0.981942	−	0.189184i	$-0.939416\pi$
$859$	−53.9268	+	9.50876i	−1.83996	+	0.324435i	−0.858018	+	0.513619i	$0.828305\pi$
$860$	4.55387	−	3.82115i	0.155286	−	0.130300i
$861$		0			0
$862$	0.434681	−	0.158211i	0.0148053	−	0.00538869i
$863$		−	17.9590i		−	0.611331i	−0.952139	−	0.305666i	$-0.901121\pi$
$863$		−	17.9590i		−	0.611331i	0.952139	−	0.305666i	$-0.0988789\pi$
$864$		0			0
$865$	−5.82585			−0.198085
$866$	−2.41007	+	0.877195i	−0.0818976	+	0.0298083i
$867$		0			0
$868$	0.687835	+	5.61752i	0.0233466	+	0.190671i
$869$	25.1449	−	4.43372i	0.852981	−	0.150404i
$870$		0			0
$871$	−15.0207	+	17.9010i	−0.508958	+	0.606552i
$872$	−4.56285	−	2.63436i	−0.154518	−	0.0892108i
$873$		0			0
$874$	−0.213735	+	0.123400i	−0.00722968	+	0.00417406i
$875$	−19.7786	+	21.1957i	−0.668639	+	0.716546i
$876$		0			0
$877$	4.40950	+	1.60493i	0.148898	+	0.0541946i	0.415394	−	0.909642i	$-0.363644\pi$
$877$	4.40950	+	1.60493i	0.148898	+	0.0541946i	−0.266496	+	0.963836i	$0.585866\pi$
$878$	0.980901	+	0.357019i	0.0331038	+	0.0120488i
$879$		0			0
$880$	−22.3763	−	3.94554i	−0.754305	−	0.133004i
$881$	2.44317	+	4.23170i	0.0823125	+	0.142569i	0.904243	−	0.427019i	$-0.140436\pi$
$881$	2.44317	+	4.23170i	0.0823125	+	0.142569i	−0.821930	+	0.569588i	$0.807103\pi$
$882$		0			0
$883$	11.8954	−	20.6034i	0.400312	−	0.693361i	−0.593451	−	0.804870i	$-0.702235\pi$
$883$	11.8954	−	20.6034i	0.400312	−	0.693361i	0.993763	+	0.111509i	$0.0355684\pi$
$884$	19.2182	−	22.9033i	0.646376	−	0.770321i
$885$		0			0
$886$	−0.635004	−	3.60128i	−0.0213334	−	0.120988i
$887$	17.0442	−	14.3018i	0.572290	−	0.480208i	−0.310115	−	0.950699i	$-0.600368\pi$
$887$	17.0442	−	14.3018i	0.572290	−	0.480208i	0.882405	+	0.470491i	$0.155923\pi$
$888$		0			0
$889$	56.5104	+	13.0664i	1.89530	+	0.438233i
$890$			1.95406i			0.0655002i
$891$		0			0
$892$		−	28.8227i		−	0.965056i
$893$	−21.7526	−	59.7648i	−0.727923	−	1.99995i
$894$		0			0
$895$	−11.9818	−	14.2793i	−0.400506	−	0.477305i
$896$	−9.99884	−	4.24821i	−0.334038	−	0.141923i
$897$		0			0
$898$	1.75635	+	1.47375i	0.0586100	+	0.0491797i
$899$	−2.47908	+	4.29389i	−0.0826818	+	0.143209i
$900$		0			0
$901$	29.5846	−	17.0807i	0.985606	−	0.569040i
$902$	−0.540539	+	3.06555i	−0.0179980	+	0.102072i
$903$		0			0
$904$	−8.06153	−	2.93416i	−0.268123	−	0.0975887i
$905$	−9.88737	+	27.1653i	−0.328667	+	0.903006i
$906$		0			0
$907$	−3.61323	+	20.4917i	−0.119975	+	0.680414i	0.864191	+	0.503165i	$0.167831\pi$
$907$	−3.61323	+	20.4917i	−0.119975	+	0.680414i	−0.984166	+	0.177249i	$0.943280\pi$
$908$	6.60939	+	11.4478i	0.219340	+	0.379908i
$909$		0			0
$910$	1.67218	−	0.851312i	0.0554322	−	0.0282207i
$911$	9.26438	−	11.0409i	0.306942	−	0.365800i	−0.590418	−	0.807097i	$-0.701037\pi$
$911$	9.26438	−	11.0409i	0.306942	−	0.365800i	0.897361	+	0.441298i	$0.145482\pi$
$912$		0			0
$913$	−18.5213	+	3.26581i	−0.612966	+	0.108082i
$914$	−2.26730	−	2.70206i	−0.0749955	−	0.0893761i
$915$		0			0
$916$	12.0760	+	33.1785i	0.399002	+	1.09625i
$917$	−25.1156	−	16.3222i	−0.829390	−	0.539007i
$918$		0			0
$919$	−23.8940			−0.788192			−0.394096	−	0.919069i	$-0.628942\pi$
$919$	−23.8940			−0.788192			−0.394096	+	0.919069i	$0.628942\pi$
$920$	−0.246794	+	0.0898255i	−0.00813655	+	0.00296146i
$921$		0			0
$922$	−1.55997	−	1.85910i	−0.0513749	−	0.0612262i
$923$	−1.87612	−	10.6400i	−0.0617533	−	0.350220i
$924$		0			0
$925$	−0.852801	−	0.715585i	−0.0280399	−	0.0235283i
$926$	−1.72548	−	0.996204i	−0.0567027	−	0.0327373i
$927$		0			0
$928$	−3.57438	−	6.19101i	−0.117335	−	0.203230i
$929$	8.22973	−	46.6731i	0.270009	−	1.53129i	−0.484375	−	0.874861i	$-0.660953\pi$
$929$	8.22973	−	46.6731i	0.270009	−	1.53129i	0.754383	−	0.656434i	$-0.227936\pi$
$930$		0			0
$931$	34.8173	−	2.41123i	1.14109	−	0.0790249i
$932$	10.8837	−	29.9028i	0.356508	−	0.979497i
$933$		0			0
$934$	3.32394	+	0.586100i	0.108763	+	0.0191778i
$935$	−18.7512	+	10.8260i	−0.613230	+	0.354048i
$936$		0			0
$937$	−3.48018	−	2.00928i	−0.113693	−	0.0656404i	0.442075	−	0.896978i	$-0.354242\pi$
$937$	−3.48018	−	2.00928i	−0.113693	−	0.0656404i	−0.555768	+	0.831337i	$0.687576\pi$
$938$	1.90954	−	0.583107i	0.0623488	−	0.0190391i
$939$		0			0
$940$	−5.85093	−	33.1823i	−0.190836	−	1.08229i
$941$	−17.4001	+	14.6004i	−0.567227	+	0.475960i	−0.880725	−	0.473629i	$-0.842944\pi$
$941$	−17.4001	+	14.6004i	−0.567227	+	0.475960i	0.313497	+	0.949589i	$0.398499\pi$
$942$		0			0
$943$	−0.700379	−	1.92427i	−0.0228075	−	0.0626630i
$944$	−50.3422			−1.63850
$945$		0			0
$946$	−1.29154			−0.0419915
$947$	16.2795	+	44.7277i	0.529014	+	1.45345i	0.860234	+	0.509900i	$0.170318\pi$
$947$	16.2795	+	44.7277i	0.529014	+	1.45345i	−0.331220	+	0.943554i	$0.607460\pi$
$948$		0			0
$949$	−16.6462	+	13.9678i	−0.540359	+	0.453415i
$950$	−0.366152	−	2.07655i	−0.0118795	−	0.0673722i
$951$		0			0
$952$	−4.90748	+	1.49857i	−0.159052	+	0.0485690i
$953$	33.3461	+	19.2524i	1.08019	+	0.623646i	0.930947	−	0.365155i	$-0.118984\pi$
$953$	33.3461	+	19.2524i	1.08019	+	0.623646i	0.149240	+	0.988801i	$0.452317\pi$
$954$		0			0
$955$	24.1845	−	13.9629i	0.782592	−	0.451830i
$956$	3.98567	+	0.702781i	0.128906	+	0.0227296i
$957$		0			0
$958$	−0.102749	+	0.282301i	−0.00331968	+	0.00912074i
$959$	−24.2130	+	18.2331i	−0.781880	+	0.588778i
$960$		0			0
$961$	5.18100	−	29.3829i	0.167129	−	0.947835i
$962$	0.0918774	+	0.159136i	0.00296225	+	0.00513076i
$963$		0			0
$964$	−17.8445	−	10.3025i	−0.574734	−	0.331823i
$965$	−1.55608	−	1.30570i	−0.0500918	−	0.0420320i
$966$		0			0
$967$	0.214600	+	1.21706i	0.00690107	+	0.0391379i	0.988064	−	0.154045i	$-0.0492301\pi$
$967$	0.214600	+	1.21706i	0.00690107	+	0.0391379i	−0.981163	+	0.193183i	$0.938119\pi$
$968$	2.73746	+	3.26238i	0.0879853	+	0.104857i
$969$		0			0
$970$	2.41891	−	0.880410i	0.0776664	−	0.0282683i
$971$	−55.5761			−1.78352			−0.891761	−	0.452507i	$-0.850530\pi$
$971$	−55.5761			−1.78352			−0.891761	+	0.452507i	$0.850530\pi$
$972$		0			0
$973$	21.5250	−	33.1213i	0.690059	−	1.06182i
$974$	1.57372	+	4.32376i	0.0504253	+	0.138542i
$975$		0			0
$976$	−4.47069	−	5.32796i	−0.143103	−	0.170544i
$977$	13.4072	−	2.36405i	0.428933	−	0.0756325i	0.0449862	−	0.998988i	$-0.485676\pi$
$977$	13.4072	−	2.36405i	0.428933	−	0.0756325i	0.383947	+	0.923355i	$0.374564\pi$
$978$		0			0
$979$	−31.4719	+	37.5067i	−1.00585	+	1.19872i
$980$	18.3871	+	1.94501i	0.587354	+	0.0621311i
$981$		0			0
$982$	−1.48909	−	2.57919i	−0.0475189	−	0.0823052i
$983$	−1.53261	+	8.69187i	−0.0488827	+	0.277228i	−0.999445	−	0.0333057i	$-0.989397\pi$
$983$	−1.53261	+	8.69187i	−0.0488827	+	0.277228i	0.950563	+	0.310533i	$0.100508\pi$
$984$		0			0
$985$	−11.3792	+	31.2642i	−0.362573	+	0.996161i
$986$	−2.10300	−	0.765429i	−0.0669732	−	0.0243762i
$987$		0			0
$988$	6.97016	−	39.5297i	0.221750	−	1.25761i
$989$	0.735803	−	0.424816i	0.0233972	−	0.0135084i
$990$		0			0
$991$	7.38836	−	12.7970i	0.234699	−	0.406511i	−0.724486	−	0.689289i	$-0.757923\pi$
$991$	7.38836	−	12.7970i	0.234699	−	0.406511i	0.959185	+	0.282779i	$0.0912562\pi$
$992$	−1.28546	−	1.07863i	−0.0408133	−	0.0342465i
$993$		0			0
$994$	−0.360974	+	0.849611i	−0.0114494	+	0.0269480i
$995$	−0.708632	−	0.844515i	−0.0224651	−	0.0267729i
$996$		0			0
$997$	−0.491617	−	1.35071i	−0.0155697	−	0.0427773i	0.931664	−	0.363320i	$-0.118357\pi$
$997$	−0.491617	−	1.35071i	−0.0155697	−	0.0427773i	−0.947234	+	0.320543i	$0.896135\pi$
$998$		−	2.56099i		−	0.0810667i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.62.11		132
3.2	odd	2		189.2.be.a.20.12	yes	132
7.6	odd	2	inner	567.2.be.a.62.12		132
21.20	even	2		189.2.be.a.20.11	✓	132
27.4	even	9		189.2.be.a.104.11	yes	132
27.23	odd	18	inner	567.2.be.a.503.12		132
189.104	even	18	inner	567.2.be.a.503.11		132
189.139	odd	18		189.2.be.a.104.12	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.11	✓	132	21.20	even	2
189.2.be.a.20.12	yes	132	3.2	odd	2
189.2.be.a.104.11	yes	132	27.4	even	9
189.2.be.a.104.12	yes	132	189.139	odd	18
567.2.be.a.62.11		132	1.1	even	1	trivial
567.2.be.a.62.12		132	7.6	odd	2	inner
567.2.be.a.503.11		132	189.104	even	18	inner
567.2.be.a.503.12		132	27.23	odd	18	inner

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.be (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0448460 + 0.123213i) q^{2} +(1.51892 - 1.27452i) q^{4} +(-0.231324 - 1.31190i) q^{5} +(-0.772696 - 2.53040i) q^{7} +(0.452264 + 0.261115i) q^{8} +(0.151270 - 0.0873359i) q^{10} +(4.31014 + 0.759994i) q^{11} +(-1.38870 + 3.81541i) q^{13} +(0.277127 - 0.208685i) q^{14} +(0.676731 - 3.83793i) q^{16} +(-1.85685 - 3.21617i) q^{17} +(-4.31784 - 2.49291i) q^{19} +(-2.02342 - 1.69785i) q^{20} +(0.0996512 + 0.565150i) q^{22} +(-0.242663 - 0.289194i) q^{23} +(3.03088 - 1.10315i) q^{25} -0.532388 q^{26} +(-4.39872 - 2.85866i) q^{28} +(-1.57190 - 4.31876i) q^{29} +(-0.693448 - 0.826419i) q^{31} +(1.53182 - 0.270102i) q^{32} +(0.313002 - 0.373021i) q^{34} +(-3.14090 + 1.59905i) q^{35} +(-0.172576 - 0.298911i) q^{37} +(0.113522 - 0.643813i) q^{38} +(0.237938 - 0.653729i) q^{40} +(5.09719 + 1.85523i) q^{41} +(-0.390810 + 2.21639i) q^{43} +(7.51538 - 4.33901i) q^{44} +(0.0247502 - 0.0428686i) q^{46} +(9.77186 + 8.19957i) q^{47} +(-5.80588 + 3.91046i) q^{49} +(0.271846 + 0.323973i) q^{50} +(2.75352 + 7.56523i) q^{52} +9.19872i q^{53} -5.83030i q^{55} +(0.311263 - 1.34617i) q^{56} +(0.461636 - 0.387359i) q^{58} +(-2.24314 - 12.7215i) q^{59} +(1.14717 - 1.36715i) q^{61} +(0.0707275 - 0.122504i) q^{62} +(-3.79516 - 6.57342i) q^{64} +(5.32670 + 0.939241i) q^{65} +(5.40821 + 1.96843i) q^{67} +(-6.91949 - 2.51849i) q^{68} +(-0.337881 - 0.315291i) q^{70} +(-2.30444 + 1.33047i) q^{71} +(4.63485 + 2.67593i) q^{73} +(0.0290904 - 0.0346686i) q^{74} +(-9.73572 + 1.71667i) q^{76} +(-1.40733 - 11.4936i) q^{77} +(5.48206 - 1.99531i) q^{79} -5.19155 q^{80} +0.711242i q^{82} +(-4.03800 + 1.46971i) q^{83} +(-3.78977 + 3.17999i) q^{85} +(-0.290615 + 0.0512433i) q^{86} +(1.75088 + 1.46916i) q^{88} +(-5.59352 + 9.68826i) q^{89} +(10.7276 + 0.565811i) q^{91} +(-0.737171 - 0.129983i) q^{92} +(-0.572067 + 1.57174i) q^{94} +(-2.27163 + 6.24126i) q^{95} +(14.5132 + 2.55906i) q^{97} +(-0.742192 - 0.539994i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Introduction

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