LMFDB - Embedded newform 567.2.be.a.503.12

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			503.12
Character	$\chi$	$=$	567.503
Dual form			567.2.be.a.62.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0448460 - 0.123213i) q^{2} +(1.51892 + 1.27452i) q^{4} +(0.231324 - 1.31190i) q^{5} +(-2.62614 + 0.321557i) q^{7} +(0.452264 - 0.261115i) q^{8} +(-0.151270 - 0.0873359i) q^{10} +(4.31014 - 0.759994i) q^{11} +(1.38870 + 3.81541i) q^{13} +(-0.0781517 + 0.337996i) q^{14} +(0.676731 + 3.83793i) q^{16} +(1.85685 - 3.21617i) q^{17} +(4.31784 - 2.49291i) q^{19} +(2.02342 - 1.69785i) q^{20} +(0.0996512 - 0.565150i) q^{22} +(-0.242663 + 0.289194i) q^{23} +(3.03088 + 1.10315i) q^{25} +0.532388 q^{26} +(-4.39872 - 2.85866i) q^{28} +(-1.57190 + 4.31876i) q^{29} +(0.693448 - 0.826419i) q^{31} +(1.53182 + 0.270102i) q^{32} +(-0.313002 - 0.373021i) q^{34} +(-0.185638 + 3.51963i) q^{35} +(-0.172576 + 0.298911i) q^{37} +(-0.113522 - 0.643813i) q^{38} +(-0.237938 - 0.653729i) q^{40} +(-5.09719 + 1.85523i) q^{41} +(-0.390810 - 2.21639i) q^{43} +(7.51538 + 4.33901i) q^{44} +(0.0247502 + 0.0428686i) q^{46} +(-9.77186 + 8.19957i) q^{47} +(6.79320 - 1.68890i) q^{49} +(0.271846 - 0.323973i) q^{50} +(-2.75352 + 7.56523i) q^{52} -9.19872i q^{53} -5.83030i q^{55} +(-1.10374 + 0.831152i) q^{56} +(0.461636 + 0.387359i) q^{58} +(2.24314 - 12.7215i) q^{59} +(-1.14717 - 1.36715i) q^{61} +(-0.0707275 - 0.122504i) q^{62} +(-3.79516 + 6.57342i) q^{64} +(5.32670 - 0.939241i) q^{65} +(5.40821 - 1.96843i) q^{67} +(6.91949 - 2.51849i) q^{68} +(0.425340 + 0.180714i) q^{70} +(-2.30444 - 1.33047i) q^{71} +(-4.63485 + 2.67593i) q^{73} +(0.0290904 + 0.0346686i) q^{74} +(9.73572 + 1.71667i) q^{76} +(-11.0746 + 3.38180i) q^{77} +(5.48206 + 1.99531i) q^{79} +5.19155 q^{80} +0.711242i q^{82} +(4.03800 + 1.46971i) q^{83} +(-3.78977 - 3.17999i) q^{85} +(-0.290615 - 0.0512433i) q^{86} +(1.75088 - 1.46916i) q^{88} +(5.59352 + 9.68826i) q^{89} +(-4.87378 - 9.57326i) q^{91} +(-0.737171 + 0.129983i) q^{92} +(0.572067 + 1.57174i) q^{94} +(-2.27163 - 6.24126i) q^{95} +(-14.5132 + 2.55906i) q^{97} +(0.0965524 - 0.912754i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	0.0448460	−	0.123213i	0.0317109	−	0.0871250i	−0.922827	−	0.385215i	$-0.874127\pi$
$2$	0.0448460	−	0.123213i	0.0317109	−	0.0871250i	0.954538	+	0.298090i	$0.0963495\pi$
$3$		0			0
$3$		0			0
$4$	1.51892	+	1.27452i	0.759459	+	0.637262i
$5$	0.231324	−	1.31190i	0.103451	−	0.586701i	−0.888376	−	0.459116i	$-0.848166\pi$
$5$	0.231324	−	1.31190i	0.103451	−	0.586701i	0.991828	−	0.127585i	$-0.0407227\pi$
$6$		0			0
$7$	−2.62614	+	0.321557i	−0.992587	+	0.121537i
$7$	−2.62614	+	0.321557i	−0.992587	+	0.121537i
$8$	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	0.519292	−	0.854597i	$-0.326196\pi$
$11$	4.31014	−	0.759994i	1.29956	−	0.229147i	0.780264	+	0.625450i	$0.215085\pi$
$12$		0			0
$13$	1.38870	+	3.81541i	0.385155	+	1.05821i	0.969155	+	0.246452i	$0.0792647\pi$
$13$	1.38870	+	3.81541i	0.385155	+	1.05821i	−0.584000	+	0.811754i	$0.698513\pi$
$14$	−0.0781517	+	0.337996i	−0.0208869	+	0.0903332i
$15$		0			0
$16$	0.676731	+	3.83793i	0.169183	+	0.959483i
$17$	1.85685	−	3.21617i	0.450353	−	0.780035i	−0.548055	−	0.836443i	$-0.684631\pi$
$17$	1.85685	−	3.21617i	0.450353	−	0.780035i	0.998408	+	0.0564079i	$0.0179647\pi$
$18$		0			0
$19$	4.31784	−	2.49291i	0.990581	−	0.571912i	0.0851328	−	0.996370i	$-0.472869\pi$
$19$	4.31784	−	2.49291i	0.990581	−	0.571912i	0.905448	+	0.424458i	$0.139535\pi$
$20$	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	−0.790750	−	0.612139i	$-0.790309\pi$
$23$	−0.242663	+	0.289194i	−0.0505987	+	0.0603012i	0.740152	+	0.672440i	$0.234754\pi$
$24$		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	0.703895	+	0.710304i	$0.251443\pi$
$29$	−1.57190	+	4.31876i	−0.291895	+	0.801974i	−0.995789	+	0.0916699i	$0.970780\pi$
$30$		0			0
$31$	0.693448	−	0.826419i	0.124547	−	0.148429i	−0.700168	−	0.713979i	$-0.746891\pi$
$31$	0.693448	−	0.826419i	0.124547	−	0.148429i	0.824714	+	0.565549i	$0.191336\pi$
$32$	1.53182	+	0.270102i	0.270791	+	0.0477477i
$33$		0			0
$34$	−0.313002	−	0.373021i	−0.0536794	−	0.0639727i
$35$	−0.185638	+	3.51963i	−0.0313785	+	0.594925i
$36$		0			0
$37$	−0.172576	+	0.298911i	−0.0283713	+	0.0491406i	−0.879862	−	0.475228i	$-0.842365\pi$
$37$	−0.172576	+	0.298911i	−0.0283713	+	0.0491406i	0.851491	+	0.524369i	$0.175699\pi$
$38$	−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	$-0.750334\pi$
$41$	−5.09719	+	1.85523i	−0.796047	+	0.289738i	−0.0881999	+	0.996103i	$0.528111\pi$
$42$		0			0
$43$	−0.390810	−	2.21639i	−0.0595979	−	0.337997i	0.940400	−	0.340071i	$-0.110451\pi$
$43$	−0.390810	−	2.21639i	−0.0595979	−	0.337997i	−0.999998	+	0.00207394i	$0.999340\pi$
$44$	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	−0.476987	+	0.878910i	$0.658271\pi$
$47$	−9.77186	+	8.19957i	−1.42537	+	1.19603i	−0.948386	+	0.317119i	$0.897284\pi$
$48$		0			0
$49$	6.79320	−	1.68890i	0.970458	−	0.241272i
$50$	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	$-0.782328\pi$
$53$		−	9.19872i		−	1.26354i	0.775155	−	0.631771i	$-0.217672\pi$
$54$		0			0
$55$		−	5.83030i		−	0.786157i
$56$	−1.10374	+	0.831152i	−0.147494	+	0.111067i
$57$		0			0
$58$	0.461636	+	0.387359i	0.0606158	+	0.0508627i
$59$	2.24314	−	12.7215i	0.292032	−	1.65620i	−0.386993	−	0.922082i	$-0.626486\pi$
$59$	2.24314	−	12.7215i	0.292032	−	1.65620i	0.679026	−	0.734115i	$-0.262403\pi$
$60$		0			0
$61$	−1.14717	−	1.36715i	−0.146880	−	0.175045i	0.687588	−	0.726101i	$-0.258670\pi$
$61$	−1.14717	−	1.36715i	−0.146880	−	0.175045i	−0.834468	+	0.551056i	$0.814225\pi$
$62$	−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	0.0101714	−	0.999948i	$-0.496762\pi$
$67$	5.40821	−	1.96843i	0.660718	−	0.240482i	0.650546	+	0.759467i	$0.274540\pi$
$68$	6.91949	−	2.51849i	0.839111	−	0.305412i
$69$		0			0
$70$	0.425340	+	0.180714i	0.0508378	+	0.0215995i
$71$	−2.30444	−	1.33047i	−0.273487	−	0.157898i	0.356984	−	0.934110i	$-0.383805\pi$
$71$	−2.30444	−	1.33047i	−0.273487	−	0.157898i	−0.630471	+	0.776213i	$0.717138\pi$
$72$		0			0
$73$	−4.63485	+	2.67593i	−0.542469	+	0.313194i	−0.746079	−	0.665858i	$-0.768066\pi$
$73$	−4.63485	+	2.67593i	−0.542469	+	0.313194i	0.203610	+	0.979052i	$0.434732\pi$
$74$	0.0290904	+	0.0346686i	0.00338169	+	0.00403015i
$75$		0			0
$76$	9.73572	+	1.71667i	1.11676	+	0.196916i
$77$	−11.0746	+	3.38180i	−1.26207	+	0.385392i
$78$		0			0
$79$	5.48206	+	1.99531i	0.616780	+	0.224489i	0.631467	−	0.775403i	$-0.282453\pi$
$79$	5.48206	+	1.99531i	0.616780	+	0.224489i	−0.0146875	+	0.999892i	$0.504675\pi$
$80$	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	$-0.313106\pi$
$83$	4.03800	+	1.46971i	0.443228	+	0.161322i	−0.110759	+	0.993847i	$0.535328\pi$
$84$		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	0.993838	+	0.110843i	$0.0353550\pi$
$89$	5.59352	+	9.68826i	0.592912	+	1.02695i	−0.400926	+	0.916110i	$0.631312\pi$
$90$		0			0
$91$	−4.87378	−	9.57326i	−0.510911	−	1.00355i
$92$	−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	$-0.824618\pi$
$97$	−14.5132	+	2.55906i	−1.47359	+	0.259833i	−0.621575	+	0.783354i	$0.713507\pi$
$98$	0.0965524	−	0.912754i	0.00975327	−	0.0922021i
$99$		0			0
$100$	3.19767	+	5.53853i	0.319767	+	0.553853i
$101$	−9.33893	+	7.83629i	−0.929258	+	0.779740i	−0.975684	−	0.219182i	$-0.929661\pi$
$101$	−9.33893	+	7.83629i	−0.929258	+	0.779740i	0.0464262	+	0.998922i	$0.485217\pi$
$102$		0			0
$103$	−8.85590	−	1.56153i	−0.872597	−	0.153862i	−0.280622	−	0.959818i	$-0.590541\pi$
$103$	−8.85590	−	1.56153i	−0.872597	−	0.153862i	−0.591976	+	0.805956i	$0.701652\pi$
$104$	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	$-0.656601\pi$
$107$		−	18.2346i		−	1.76280i	0.472370	−	0.881401i	$-0.343399\pi$
$108$		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
$112$	−3.01130	−	9.86133i	−0.284541	−	0.931809i
$113$	−16.1779	−	2.85260i	−1.52189	−	0.268350i	−0.650714	−	0.759323i	$-0.725530\pi$
$113$	−16.1779	−	2.85260i	−1.52189	−	0.268350i	−0.871175	+	0.490973i	$0.836641\pi$
$114$		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
$119$	−3.84218	+	9.04318i	−0.352212	+	0.828987i
$120$		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	−0.687476	−	0.726207i	$-0.741281\pi$
$127$	−10.9612	−	18.9854i	−0.972652	−	1.68468i	−0.285175	−	0.958475i	$-0.592052\pi$
$128$	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	$-0.442454\pi$
$131$	−8.67264	−	7.27721i	−0.757732	−	0.635813i	−0.937535	+	0.347890i	$0.886898\pi$
$132$		0			0
$133$	−10.5376	+	7.93515i	−0.913729	+	0.688064i
$134$		−	0.754639i		−	0.0651909i
$135$		0			0
$136$		−	1.93941i		−	0.166303i
$137$	−3.91826	+	10.7653i	−0.334760	+	0.919745i	0.652095	+	0.758137i	$0.273890\pi$
$137$	−3.91826	+	10.7653i	−0.334760	+	0.919745i	−0.986855	+	0.161608i	$0.948332\pi$
$138$		0			0
$139$	−9.59685	+	11.4371i	−0.813994	+	0.970081i	−0.999922	−	0.0124827i	$-0.996027\pi$
$139$	−9.59685	+	11.4371i	−0.813994	+	0.970081i	0.185928	+	0.982563i	$0.440471\pi$
$140$	−4.76782	+	5.10942i	−0.402954	+	0.431825i
$141$		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	0.975036	−	0.222047i	$-0.0712740\pi$
$149$	1.04227	+	2.86360i	0.0853857	+	0.234595i	−0.889650	+	0.456643i	$0.849052\pi$
$150$		0			0
$151$	−0.106414	−	0.603503i	−0.00865984	−	0.0491124i	0.980172	−	0.198150i	$-0.0634934\pi$
$151$	−0.106414	−	0.603503i	−0.00865984	−	0.0491124i	−0.988831	+	0.149038i	$0.952382\pi$
$152$	1.30187	−	2.25490i	0.105596	−	0.182897i
$153$		0			0
$154$	−0.0799700	+	1.51620i	−0.00644417	+	0.122179i
$155$	−0.923771	−	1.10091i	−0.0741991	−	0.0884270i
$156$		0			0
$157$	1.89383	+	0.333933i	0.151144	+	0.0266507i	0.248708	−	0.968579i	$-0.419994\pi$
$157$	1.89383	+	0.333933i	0.151144	+	0.0266507i	−0.0975643	+	0.995229i	$0.531105\pi$
$158$	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	0.676724	+	0.736237i	$0.263399\pi$
$167$	−2.72667	+	15.4637i	−0.210996	+	1.19662i	−0.887720	+	0.460383i	$0.847712\pi$
$168$		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	$-0.108721\pi$
$173$	−0.759414	−	4.30685i	−0.0577372	−	0.327444i	−0.999972	+	0.00750984i	$0.997610\pi$
$174$		0			0
$175$	−8.31424	−	1.92243i	−0.628497	−	0.145322i
$176$	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	0.879060	−	0.476710i	$-0.158171\pi$
$179$	12.1181	+	6.99637i	0.905747	+	0.522933i	0.0266868	+	0.999644i	$0.491504\pi$
$180$		0			0
$181$	18.7936	−	10.8505i	1.39691	−	0.806509i	0.402846	−	0.915268i	$-0.368021\pi$
$181$	18.7936	−	10.8505i	1.39691	−	0.806509i	0.994068	+	0.108759i	$0.0346878\pi$
$182$	−1.39812	+	0.171193i	−0.103636	+	0.0126897i
$183$		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	−0.353066	−	0.935598i	$-0.614861\pi$
$191$	7.16981	−	19.6989i	0.518789	−	1.42536i	0.871855	−	0.489763i	$-0.162917\pi$
$192$		0			0
$193$	1.16810	+	0.980152i	0.0840817	+	0.0705529i	0.683860	−	0.729614i	$-0.260300\pi$
$193$	1.16810	+	0.980152i	0.0840817	+	0.0705529i	−0.599778	+	0.800166i	$0.704744\pi$
$194$	−0.335547	+	1.90298i	−0.0240908	+	0.136626i
$195$		0			0
$196$	12.4709	+	6.09279i	0.890776	+	0.435199i
$197$	−21.6293	+	12.4877i	−1.54102	+	0.889709i	−0.542247	+	0.840219i	$0.682426\pi$
$197$	−21.6293	+	12.4877i	−1.54102	+	0.889709i	−0.998775	+	0.0494899i	$0.984240\pi$
$198$		0			0
$199$	−0.716693	−	0.413783i	−0.0508050	−	0.0293323i	0.474382	−	0.880319i	$-0.342671\pi$
$199$	−0.716693	−	0.413783i	−0.0508050	−	0.0293323i	−0.525187	+	0.850987i	$0.676005\pi$
$200$	1.65881	−	0.292492i	0.117295	−	0.0206823i
$201$		0			0
$202$	0.546722	+	1.50211i	0.0384672	+	0.105688i
$203$	2.73930	−	11.8471i	0.192261	−	0.831505i
$204$		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	−0.928619	−	0.371034i	$-0.879003\pi$
$211$	1.02986	−	5.84064i	0.0708987	−	0.402086i	0.999518	−	0.0310519i	$-0.00988572\pi$
$212$	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	$-0.384026\pi$
$223$	−9.34376	−	11.1355i	−0.625705	−	0.745686i	−0.982040	+	0.188672i	$0.939582\pi$
$224$	−4.10964	−	0.216757i	−0.274587	−	0.0144827i
$225$		0			0
$226$	−1.07699	+	1.86541i	−0.0716405	+	0.124085i
$227$	1.15766	+	6.56541i	0.0768366	+	0.435762i	0.998821	+	0.0485359i	$0.0154555\pi$
$227$	1.15766	+	6.56541i	0.0768366	+	0.435762i	−0.921985	+	0.387226i	$0.873433\pi$
$228$		0			0
$229$	6.09035	+	16.7331i	0.402462	+	1.10575i	0.961066	+	0.276320i	$0.0891149\pi$
$229$	6.09035	+	16.7331i	0.402462	+	1.10575i	−0.558604	+	0.829434i	$0.688663\pi$
$230$	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	0.880604	−	0.473853i	$-0.157137\pi$
$233$	13.8987	+	8.02444i	0.910537	+	0.525699i	0.0299330	+	0.999552i	$0.490471\pi$
$234$		0			0
$235$	8.49658	+	14.7165i	0.554256	+	0.959999i
$236$	19.6210	−	16.4640i	1.27722	−	1.07171i
$237$		0			0
$238$	0.941934	+	0.878958i	0.0610565	+	0.0569744i
$239$	1.31201	−	1.56359i	0.0848668	−	0.101140i	−0.721940	−	0.691956i	$-0.756749\pi$
$239$	1.31201	−	1.56359i	0.0848668	−	0.101140i	0.806807	+	0.590815i	$0.201194\pi$
$240$		0			0
$241$	3.55423	−	9.76517i	0.228948	−	0.629030i	−0.771021	−	0.636809i	$-0.780254\pi$
$241$	3.55423	−	9.76517i	0.228948	−	0.629030i	0.999970	+	0.00777897i	$0.00247615\pi$
$242$		−	1.06928i		−	0.0687359i
$243$		0			0
$244$		−	3.53868i		−	0.226541i
$245$	−0.644249	−	9.30272i	−0.0411596	−	0.594329i
$246$		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	−0.952195	−	0.305490i	$-0.901180\pi$
$251$	−11.7343	−	20.3243i	−0.740660	−	1.28286i	0.211535	−	0.977370i	$-0.432154\pi$
$252$		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	$-0.661101\pi$
$257$	−4.71223	+	1.71511i	−0.293941	+	0.106986i	0.190841	+	0.981621i	$0.438879\pi$
$258$		0			0
$259$	0.357092	−	0.840473i	0.0221886	−	0.0522245i
$260$	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	0.631209	−	0.775613i	$-0.282559\pi$
$263$	−3.92830	−	4.68156i	−0.242229	−	0.288678i	−0.873438	+	0.486935i	$0.838115\pi$
$264$		0			0
$265$	−12.0678	−	2.12789i	−0.741321	−	0.130715i
$266$	0.505146	+	1.65424i	0.0309725	+	0.101428i
$267$		0			0
$268$	10.7234	+	3.90301i	0.655038	+	0.238414i
$269$	−4.75791			−0.290095			−0.145048	−	0.989425i	$-0.546334\pi$
$269$	−4.75791			−0.290095			−0.145048	+	0.989425i	$0.546334\pi$
$270$		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	−0.739198	−	0.673488i	$-0.764795\pi$
$277$	−3.40027	+	2.85316i	−0.204302	+	0.171430i	0.534896	+	0.844918i	$0.320351\pi$
$278$	0.978821	+	1.69537i	0.0587058	+	0.101681i
$279$		0			0
$280$	0.835069	+	1.64027i	0.0499049	+	0.0980250i
$281$	−8.77039	+	1.54646i	−0.523198	+	0.0922539i	−0.429009	−	0.903300i	$-0.641137\pi$
$281$	−8.77039	+	1.54646i	−0.523198	+	0.0922539i	−0.0941892	+	0.995554i	$0.530026\pi$
$282$		0			0
$283$	−8.13265	−	22.3443i	−0.483436	−	1.32823i	−0.906529	−	0.422143i	$-0.861278\pi$
$283$	−8.13265	−	22.3443i	−0.483436	−	1.32823i	0.423093	−	0.906086i	$-0.360944\pi$
$284$	−1.80454	−	4.95794i	−0.107080	−	0.294200i
$285$		0			0
$286$	2.29467	−	0.404612i	0.135686	−	0.0239252i
$287$	12.7894	−	6.51111i	0.754932	−	0.384339i
$288$		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	0.999886	+	0.0151056i	$0.00480846\pi$
$293$	20.3420	+	17.0689i	1.18839	+	0.997178i	0.188505	+	0.982072i	$0.439636\pi$
$294$		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
$301$	1.73902	+	5.69488i	0.100235	+	0.328248i
$302$	−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	0.995397	+	0.0958335i	$0.0305517\pi$
$307$	27.6153	+	15.9437i	1.57609	+	0.909956i	0.580693	+	0.814123i	$0.302782\pi$
$308$	−21.1317	−	8.97821i	−1.20409	−	0.511581i
$309$		0			0
$310$	−0.177074	+	0.0644497i	−0.0100571	+	0.00366050i
$311$	−5.67000	+	2.06371i	−0.321516	+	0.117022i	−0.497736	−	0.867328i	$-0.665835\pi$
$311$	−5.67000	+	2.06371i	−0.321516	+	0.117022i	0.176220	+	0.984351i	$0.443613\pi$
$312$		0			0
$313$	4.63763	−	0.817739i	0.262134	−	0.0462213i	−0.0410364	−	0.999158i	$-0.513066\pi$
$313$	4.63763	−	0.817739i	0.262134	−	0.0462213i	0.303170	+	0.952936i	$0.401955\pi$
$314$	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	0.964700	−	0.263350i	$-0.0848273\pi$
$317$	9.57584	+	11.4120i	0.537833	+	0.640964i	−0.426867	+	0.904314i	$0.640383\pi$
$318$		0			0
$319$	−3.49288	+	19.8091i	−0.195564	+	1.10910i
$320$	7.74578	+	6.49948i	0.433002	+	0.363332i
$321$		0			0
$322$	−0.0787820	−	0.104620i	−0.00439035	−	0.00583025i
$323$		−	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
$329$	23.0256	−	24.6754i	1.26944	−	1.36040i
$330$		0			0
$331$	8.22997	−	6.90576i	0.452360	−	0.379575i	−0.387951	−	0.921680i	$-0.626817\pi$
$331$	8.22997	−	6.90576i	0.452360	−	0.379575i	0.840311	+	0.542105i	$0.182373\pi$
$332$	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	−0.575268	−	0.817965i	$-0.695102\pi$
$337$	−8.99836	+	3.27514i	−0.490172	+	0.178408i	0.0850964	+	0.996373i	$0.472880\pi$
$338$	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
$343$	−17.2968	+	6.61969i	−0.933940	+	0.357430i
$344$	−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	−0.998598	−	0.0529329i	$-0.983143\pi$
$347$	−14.4006	+	17.1620i	−0.773065	+	0.921303i	0.225533	+	0.974235i	$0.427588\pi$
$348$		0			0
$349$	4.98766	−	13.7035i	0.266983	−	0.733531i	−0.731670	−	0.681659i	$-0.761259\pi$
$349$	4.98766	−	13.7035i	0.266983	−	0.733531i	0.998654	−	0.0518722i	$-0.0165189\pi$
$350$	−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	$-0.457381\pi$
$353$	−7.53944	−	2.74413i	−0.401284	−	0.146055i	−0.534775	+	0.844995i	$0.679604\pi$
$354$		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	−0.466223	−	0.884667i	$-0.654386\pi$
$359$	1.26586	−	0.730844i	0.0668095	−	0.0385725i	0.533033	+	0.846095i	$0.321052\pi$
$360$		0			0
$361$	2.92916	−	5.07346i	0.154167	−	0.267024i
$362$	−0.494107	−	2.80222i	−0.0259697	−	0.147281i
$363$		0			0
$364$	4.79847	−	20.7528i	0.251508	−	1.08774i
$365$	2.43842	+	6.69949i	0.127633	+	0.350668i
$366$		0			0
$367$	25.7879	−	4.54711i	1.34612	−	0.237357i	0.546296	−	0.837592i	$-0.316037\pi$
$367$	25.7879	−	4.54711i	1.34612	−	0.237357i	0.799824	+	0.600235i	$0.204926\pi$
$368$	−1.27413	−	0.735617i	−0.0664184	−	0.0383467i
$369$		0			0
$370$	0.0522112	−	0.0301442i	0.00271433	−	0.00156712i
$371$	2.95791	+	24.1571i	0.153567	+	1.25417i
$372$		0			0
$373$	−2.15588	+	12.2266i	−0.111627	+	0.633069i	0.876738	+	0.480969i	$0.159715\pi$
$373$	−2.15588	+	12.2266i	−0.111627	+	0.633069i	−0.988365	+	0.152101i	$0.951396\pi$
$374$	−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	$-0.920614\pi$
$383$	0.508365	−	2.88308i	0.0259762	−	0.147319i	0.995037	+	0.0995025i	$0.0317251\pi$
$384$		0			0
$385$	1.87477	+	15.3112i	0.0955472	+	0.780329i
$386$	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	0.484791	−	0.874630i	$-0.338896\pi$
$389$	24.4465	−	4.31058i	1.23949	−	0.218555i	0.754696	+	0.656075i	$0.227784\pi$
$390$		0			0
$391$	0.479508	+	1.31744i	0.0242497	+	0.0666256i
$392$	2.63132	−	2.53764i	0.132902	−	0.128170i
$393$		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	$-0.488216\pi$
$397$	18.3498	−	10.5942i	0.920948	−	0.531710i	0.883937	+	0.467605i	$0.154883\pi$
$398$	−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	−0.743788	−	0.668416i	$-0.766973\pi$
$401$	0.873706	−	1.04124i	0.0436308	−	0.0519972i	0.787419	+	0.616419i	$0.211417\pi$
$402$		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	−0.157985	−	0.987441i	$-0.550500\pi$
$409$	17.0261	−	20.2910i	0.841889	−	1.00332i	0.999874	−	0.0158823i	$-0.00505571\pi$
$410$	0.933081	+	0.164527i	0.0460816	+	0.00812543i
$411$		0			0
$412$	−11.4612	−	13.6589i	−0.564651	−	0.672925i
$413$	−1.80012	+	34.1297i	−0.0885782	+	1.67941i
$414$		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	$-0.747872\pi$
$419$	−16.0247	+	5.83250i	−0.782856	+	0.284936i	−0.0804931	+	0.996755i	$0.525649\pi$
$420$		0			0
$421$	−3.15843	−	17.9124i	−0.153933	−	0.872995i	−0.959755	−	0.280838i	$-0.909388\pi$
$421$	−3.15843	−	17.9124i	−0.153933	−	0.872995i	0.805823	−	0.592157i	$-0.201724\pi$
$422$	−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
$427$	3.45225	+	3.22143i	0.167066	+	0.155896i
$428$	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	$0.0270781\pi$
$431$			3.52787i			0.169932i	−0.996384	+	0.0849658i	$0.972922\pi$
$432$		0			0
$433$			19.5602i			0.940001i	0.882666	+	0.470001i	$0.155746\pi$
$433$			19.5602i			0.940001i	−0.882666	+	0.470001i	$0.844254\pi$
$434$	0.225132	+	0.298969i	0.0108067	+	0.0143510i
$435$		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	$-0.283064\pi$
$439$	−5.11723	−	6.09848i	−0.244232	−	0.291064i	−0.874209	+	0.485549i	$0.838620\pi$
$440$	−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	−0.782529	−	0.622614i	$-0.786071\pi$
$443$	−27.4654	+	4.84288i	−1.30492	+	0.230092i	−0.522390	+	0.852707i	$0.674959\pi$
$444$		0			0
$445$	14.0040	−	5.09703i	0.663852	−	0.241622i
$446$	−1.79107	+	0.651896i	−0.0848095	+	0.0308681i
$447$		0			0
$448$	7.85290	−	18.4831i	0.371015	−	0.873242i
$449$	15.1431	+	8.74287i	0.714647	+	0.412602i	0.812779	−	0.582572i	$-0.197953\pi$
$449$	15.1431	+	8.74287i	0.714647	+	0.412602i	−0.0981322	+	0.995173i	$0.531287\pi$
$450$		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
$455$	−13.6866	+	4.17941i	−0.641639	+	0.195934i
$456$		0			0
$457$	−25.2787	−	9.20069i	−1.18249	−	0.430390i	−0.325407	−	0.945574i	$-0.605501\pi$
$457$	−25.2787	−	9.20069i	−1.18249	−	0.430390i	−0.857080	+	0.515184i	$0.827724\pi$
$458$	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	$-0.247043\pi$
$461$	17.3925	+	6.33036i	0.810050	+	0.294834i	0.0964058	+	0.995342i	$0.469265\pi$
$462$		0			0
$463$	−11.6402	−	9.76728i	−0.540966	−	0.453924i	0.330902	−	0.943665i	$-0.392647\pi$
$463$	−11.6402	−	9.76728i	−0.540966	−	0.453924i	−0.871868	+	0.489741i	$0.837091\pi$
$464$	−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	−0.993465	−	0.114140i	$-0.963589\pi$
$467$	−12.8706	−	22.2926i	−0.595581	−	1.03158i	0.397884	−	0.917436i	$-0.369745\pi$
$468$		0			0
$469$	−13.5697	+	6.90840i	−0.626592	+	0.319000i
$470$	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
$476$	−17.3617	+	8.83891i	−0.795772	+	0.405131i
$477$		0			0
$478$	−0.133817	−	0.231778i	−0.00612065	−	0.0106013i
$479$	−1.75513	+	1.47273i	−0.0801939	+	0.0672907i	−0.682003	−	0.731349i	$-0.738891\pi$
$479$	−1.75513	+	1.47273i	−0.0801939	+	0.0672907i	0.601810	+	0.798640i	$0.294447\pi$
$480$		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
$490$	−1.17511	−	0.337810i	−0.0530861	−	0.0152607i
$491$	−22.3682	−	3.94412i	−1.00946	−	0.177996i	−0.355624	−	0.934629i	$-0.615732\pi$
$491$	−22.3682	−	3.94412i	−1.00946	−	0.177996i	−0.653840	+	0.756633i	$0.726843\pi$
$492$		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
$497$	6.47960	+	2.75299i	0.290650	+	0.123488i
$498$		0			0
$499$	−18.3536	+	6.68017i	−0.821621	+	0.299046i	−0.718415	−	0.695615i	$-0.755132\pi$
$499$	−18.3536	+	6.68017i	−0.821621	+	0.299046i	−0.103206	+	0.994660i	$0.532910\pi$
$500$	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	$-0.920025\pi$
$503$	−6.03294	+	10.4494i	−0.268995	+	0.465914i	0.699607	+	0.714528i	$0.253358\pi$
$504$		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	$-0.0194865\pi$
$509$	25.0698	+	21.0360i	1.11120	+	0.932406i	0.113072	+	0.993587i	$0.463931\pi$
$510$		0			0
$511$	11.3113	−	8.51774i	0.500383	−	0.376803i
$512$			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
$518$	−0.0875434	−	0.0816904i	−0.00384644	−	0.00358927i
$519$		0			0
$520$	2.16382	−	1.81566i	0.0948900	−	0.0796221i
$521$	−0.373097	−	0.646223i	−0.0163457	−	0.0283115i	0.857737	−	0.514089i	$-0.171870\pi$
$521$	−0.373097	−	0.646223i	−0.0163457	−	0.0283115i	−0.874083	+	0.485777i	$0.838537\pi$
$522$		0			0
$523$	−0.0341810	−	0.0197344i	−0.00149463	−	0.000862925i	0.499252	−	0.866457i	$-0.333608\pi$
$523$	−0.0341810	−	0.0197344i	−0.00149463	−	0.000862925i	−0.500747	+	0.865594i	$0.666941\pi$
$524$	−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
$532$	−26.1193	−	1.37763i	−1.13242	−	0.0597277i
$533$	−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	−0.602170	−	0.798368i	$-0.705697\pi$
$547$	1.85944	−	1.56025i	0.0795038	−	0.0667116i	0.681673	+	0.731657i	$0.261252\pi$
$548$	−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
$553$	−15.0382	−	3.47716i	−0.639491	−	0.147864i
$554$	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	0.506193	−	0.862420i	$-0.331052\pi$
$557$	0.292925	+	0.169120i	0.0124116	+	0.00716586i	−0.493781	+	0.869586i	$0.664386\pi$
$558$		0			0
$559$	7.91374	−	4.56900i	0.334715	−	0.193248i
$560$	−13.6337	+	1.66938i	−0.576130	+	0.0705440i
$561$		0			0
$562$	−0.202773	+	1.14998i	−0.00855346	+	0.0485091i
$563$	−12.3087	−	10.3282i	−0.518748	−	0.435282i	0.345447	−	0.938438i	$-0.387727\pi$
$563$	−12.3087	−	10.3282i	−0.518748	−	0.435282i	−0.864195	+	0.503157i	$0.832172\pi$
$564$		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	0.646627	+	0.762807i	$0.276179\pi$
$569$	−8.08739	+	22.2199i	−0.339041	+	0.931507i	−0.985667	+	0.168700i	$0.946043\pi$
$570$		0			0
$571$	−0.278581	−	0.233758i	−0.0116583	−	0.00978245i	0.636940	−	0.770913i	$-0.280200\pi$
$571$	−0.278581	−	0.233758i	−0.0116583	−	0.00978245i	−0.648598	+	0.761131i	$0.724644\pi$
$572$	−6.11852	+	34.6999i	−0.255828	+	1.45087i
$573$		0			0
$574$	−0.228704	−	1.86782i	−0.00954594	−	0.0779613i
$575$	−1.05451	+	0.608820i	−0.0439760	+	0.0253896i
$576$		0			0
$577$	7.66829	+	4.42729i	0.319235	+	0.184310i	0.651052	−	0.759034i	$-0.274328\pi$
$577$	7.66829	+	4.42729i	0.319235	+	0.184310i	−0.331817	+	0.943344i	$0.607661\pi$
$578$	0.414294	−	0.0730512i	0.0172324	−	0.00303853i
$579$		0			0
$580$	4.15199	+	11.4075i	0.172402	+	0.473671i
$581$	−11.0769	−	2.56122i	−0.459549	−	0.106257i
$582$		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	$-0.520148\pi$
$587$	22.0136	−	18.4716i	0.908598	−	0.762405i	0.971852	+	0.235593i	$0.0757032\pi$
$588$		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	$-0.551408\pi$
$593$	−7.83158			−0.321605			−0.160802	+	0.986987i	$0.551408\pi$
$594$		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	0.659339	−	0.751845i	$-0.270836\pi$
$599$	25.0073	+	4.40946i	1.02177	+	0.180166i	0.362430	+	0.932011i	$0.381947\pi$
$600$		0			0
$601$	−28.8206	−	34.3470i	−1.17562	−	1.40104i	−0.897796	−	0.440411i	$-0.854833\pi$
$601$	−28.8206	−	34.3470i	−1.17562	−	1.40104i	−0.277819	−	0.960633i	$-0.589612\pi$
$602$	0.779674	+	0.0411228i	0.0317771	+	0.00167604i
$603$		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	$-0.0472327\pi$
$607$	3.35939	+	9.22986i	0.136354	+	0.374628i	−0.852657	+	0.522470i	$0.825010\pi$
$608$	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	−0.980932	−	0.194350i	$-0.937740\pi$
$613$	−16.3106	−	28.2507i	−0.658778	−	1.14104i	0.322154	−	0.946687i	$-0.395593\pi$
$614$	3.20292	−	2.68757i	0.129259	−	0.108461i
$615$		0			0
$616$	−4.12562	+	4.42122i	−0.166226	+	0.178136i
$617$	−0.764441	+	0.911025i	−0.0307752	+	0.0366765i	−0.781213	−	0.624265i	$-0.785398\pi$
$617$	−0.764441	+	0.911025i	−0.0307752	+	0.0366765i	0.750437	+	0.660942i	$0.229843\pi$
$618$		0			0
$619$	−12.4466	+	34.1968i	−0.500271	+	1.37448i	0.390740	+	0.920501i	$0.372219\pi$
$619$	−12.4466	+	34.1968i	−0.500271	+	1.37448i	−0.891011	+	0.453982i	$0.850003\pi$
$620$		−	2.84956i		−	0.114441i
$621$		0			0
$622$			0.791169i			0.0317230i
$623$	−17.8047	−	23.6441i	−0.713329	−	0.947279i
$624$		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	−0.298558	−	0.954391i	$-0.596506\pi$
$631$	17.0123	−	29.4661i	0.677248	−	1.17303i	0.975806	−	0.218637i	$-0.0701610\pi$
$632$	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
$637$	15.8776	+	23.5735i	0.629092	+	0.934016i
$638$	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	−0.981199	−	0.192999i	$-0.938179\pi$
$641$	−25.3403	−	30.1994i	−1.00088	−	1.19280i	−0.0196832	−	0.999806i	$-0.506266\pi$
$642$		0			0
$643$	−1.58947	−	0.280266i	−0.0626824	−	0.0110526i	0.142219	−	0.989835i	$-0.454576\pi$
$643$	−1.58947	−	0.280266i	−0.0626824	−	0.0110526i	−0.204901	+	0.978783i	$0.565687\pi$
$644$	1.89411	−	0.578396i	0.0746386	−	0.0227920i
$645$		0			0
$646$	−2.28140	−	0.830362i	−0.0897605	−	0.0326702i
$647$	20.9883			0.825137			0.412568	−	0.910927i	$-0.364632\pi$
$647$	20.9883			0.825137			0.412568	+	0.910927i	$0.364632\pi$
$648$		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	0.0337633	−	0.999430i	$-0.489251\pi$
$653$	−7.06142	−	1.24512i	−0.276335	−	0.0487253i	−0.310098	+	0.950705i	$0.600362\pi$
$654$		0			0
$655$	−11.5532	+	9.69428i	−0.451421	+	0.378787i
$656$	−10.5697	−	18.3072i	−0.412676	−	0.714776i
$657$		0			0
$658$	−2.00773	−	3.94366i	−0.0782695	−	0.153740i
$659$	29.4274	−	5.18885i	1.14633	−	0.202129i	0.431957	−	0.901894i	$-0.357823\pi$
$659$	29.4274	−	5.18885i	1.14633	−	0.202129i	0.714372	+	0.699766i	$0.246712\pi$
$660$		0			0
$661$	8.06882	+	22.1689i	0.313841	+	0.862270i	0.991872	+	0.127238i	$0.0406110\pi$
$661$	8.06882	+	22.1689i	0.313841	+	0.862270i	−0.678032	+	0.735033i	$0.737167\pi$
$662$	−0.481801	−	1.32374i	−0.0187257	−	0.0514485i
$663$		0			0
$664$	2.21001	−	0.389684i	0.0857649	−	0.0151227i
$665$	7.97254	+	15.6600i	0.309162	+	0.607267i
$666$		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	0.606131	−	0.795365i	$-0.292721\pi$
$673$	14.5070	+	5.28011i	0.559203	+	0.203533i	−0.0469277	+	0.998898i	$0.514943\pi$
$674$			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	$-0.129784\pi$
$677$	35.5524	+	12.9400i	1.36639	+	0.497325i	0.448366	+	0.893850i	$0.352006\pi$
$678$		0			0
$679$	37.2907	−	11.3873i	1.43109	−	0.437003i
$680$	−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	−0.225474	−	0.974249i	$-0.572393\pi$
$683$	13.2112	−	7.62750i	0.505513	−	0.291858i	0.730987	+	0.682391i	$0.239060\pi$
$684$		0			0
$685$	13.2167	+	7.63067i	0.504985	+	0.291553i
$686$	0.0399422	+	2.42807i	0.00152500	+	0.0927040i
$687$		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	$-0.773674\pi$
$691$	−32.7662	+	5.77757i	−1.24649	+	0.219789i	−0.488792	+	0.872400i	$0.662562\pi$
$692$	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
$700$	−10.1785	−	13.5167i	−0.384710	−	0.510883i
$701$			1.67746i			0.0633567i	0.999498	+	0.0316783i	$0.0100852\pi$
$701$			1.67746i			0.0633567i	−0.999498	+	0.0316783i	$0.989915\pi$
$702$		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
$707$	22.0055	−	23.5822i	0.827602	−	0.886899i
$708$		0			0
$709$	−21.9319	+	18.4031i	−0.823671	+	0.691142i	−0.953829	−	0.300351i	$-0.902896\pi$
$709$	−21.9319	+	18.4031i	−0.823671	+	0.691142i	0.130158	+	0.991493i	$0.458452\pi$
$710$	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	$-0.756978\pi$
$719$	6.37063	−	11.0343i	0.237584	−	0.411508i	0.960021	+	0.279929i	$0.0903110\pi$
$720$		0			0
$721$	23.7589	+	1.25313i	0.884829	+	0.0466690i
$722$	−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	−0.256856	−	0.966450i	$-0.582687\pi$
$727$	15.1297	−	41.5685i	0.561129	−	1.54169i	0.817985	−	0.575240i	$-0.195091\pi$
$728$	−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	$-0.654894\pi$
$733$	13.1054	−	15.6184i	0.484060	−	0.576880i	0.951696	+	0.307041i	$0.0993388\pi$
$734$	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	0.215802	+	0.976437i	$0.430763\pi$
$739$	−20.0545	+	34.7355i	−0.737718	+	1.27777i	−0.953520	+	0.301328i	$0.902570\pi$
$740$	0.158311	+	0.897828i	0.00581964	+	0.0330048i
$741$		0			0
$742$	3.10913	+	0.718896i	0.114140	+	0.0263915i
$743$	3.63149	+	9.97743i	0.133226	+	0.366037i	0.988311	−	0.152452i	$-0.0487170\pi$
$743$	3.63149	+	9.97743i	0.133226	+	0.366037i	−0.855084	+	0.518489i	$0.826495\pi$
$744$		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
$749$	5.86344	+	47.8865i	0.214246	+	1.74973i
$750$		0			0
$751$	7.18177	−	40.7298i	0.262066	−	1.48625i	−0.515194	−	0.857074i	$-0.672280\pi$
$751$	7.18177	−	40.7298i	0.262066	−	1.48625i	0.777260	−	0.629179i	$-0.216609\pi$
$752$	−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	−0.924918	−	0.380167i	$-0.875867\pi$
$761$	2.04815	−	11.6156i	0.0742454	−	0.421066i	0.999163	−	0.0408995i	$-0.0130223\pi$
$762$		0			0
$763$	26.4949	−	3.24415i	0.959178	−	0.117446i
$764$	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	0.994406	+	0.105629i	$0.0336855\pi$
$769$	8.33433	+	22.8984i	0.300544	+	0.825737i	−0.693862	+	0.720108i	$0.744092\pi$
$770$	1.97062	+	0.455648i	0.0710161	+	0.0164204i
$771$		0			0
$772$	0.525021	+	2.97754i	0.0188959	+	0.107164i
$773$	−1.44939	+	2.51041i	−0.0521309	+	0.0902933i	−0.890913	−	0.454173i	$-0.849935\pi$
$773$	−1.44939	+	2.51041i	−0.0521309	+	0.0902933i	0.838782	+	0.544467i	$0.183268\pi$
$774$		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	$-0.827432\pi$
$787$	−5.60311	+	6.67753i	−0.199729	+	0.238028i	0.656878	+	0.753997i	$0.271877\pi$
$788$	−48.7689	−	8.59928i	−1.73732	−	0.306337i
$789$		0			0
$790$	−0.655010	−	0.780611i	−0.0233042	−	0.0277729i
$791$	43.4027	+	2.28921i	1.54322	+	0.0813950i
$792$		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	$-0.544402\pi$
$797$	11.0381	−	4.01755i	0.390990	−	0.142309i	0.530032	+	0.847978i	$0.322180\pi$
$798$		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
$805$	−0.972809	−	0.907768i	−0.0342870	−	0.0319946i
$806$	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	$0.0756423\pi$
$809$			13.3913i			0.470814i	−0.971897	+	0.235407i	$0.924358\pi$
$810$		0			0
$811$		−	14.2545i		−	0.500543i	−0.968176	−	0.250272i	$-0.919480\pi$
$811$		−	14.2545i		−	0.500543i	0.968176	−	0.250272i	$-0.0805200\pi$
$812$	19.2602	−	14.5035i	0.675901	−	0.508973i
$813$		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	−0.987004	−	0.160695i	$-0.948626\pi$
$821$	−53.2811	+	9.39490i	−1.85952	+	0.327884i	−0.872520	+	0.488579i	$0.837515\pi$
$822$		0			0
$823$	−24.0026	+	8.73623i	−0.836678	+	0.304526i	−0.724597	−	0.689173i	$-0.757974\pi$
$823$	−24.0026	+	8.73623i	−0.836678	+	0.304526i	−0.112081	+	0.993699i	$0.535752\pi$
$824$	−4.41294	+	1.60618i	−0.153732	+	0.0559539i
$825$		0			0
$826$	4.12451	+	1.75238i	0.143510	+	0.0609731i
$827$	−35.7068	−	20.6154i	−1.24165	−	0.716866i	−0.272219	−	0.962235i	$-0.587757\pi$
$827$	−35.7068	−	20.6154i	−1.24165	−	0.716866i	−0.969430	+	0.245369i	$0.921091\pi$
$828$		0			0
$829$	−19.7340	+	11.3934i	−0.685389	+	0.395710i	−0.801883	−	0.597482i	$-0.796168\pi$
$829$	−19.7340	+	11.3934i	−0.685389	+	0.395710i	0.116493	+	0.993191i	$0.462835\pi$
$830$	−0.482471	−	0.574986i	−0.0167468	−	0.0199581i
$831$		0			0
$832$	−30.3506	−	5.35164i	−1.05222	−	0.185535i
$833$	7.18219	−	24.9841i	0.248848	−	0.865648i
$834$		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	$-0.492283\pi$
$839$	−17.3731	−	6.32330i	−0.599786	−	0.218304i	−0.624028	+	0.781402i	$0.714505\pi$
$840$		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
$847$	−19.2275	+	9.78879i	−0.660665	+	0.336347i
$848$	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	$-0.918607\pi$
$853$	−52.2825	+	9.21881i	−1.79012	+	0.315646i	−0.822633	+	0.568573i	$0.807496\pi$
$854$	0.551743	−	0.280894i	0.0188803	−	0.00961201i
$855$		0			0
$856$	−4.76131	−	8.24683i	−0.162738	−	0.281871i
$857$	−5.81262	+	4.87737i	−0.198555	+	0.166608i	−0.736644	−	0.676280i	$-0.763591\pi$
$857$	−5.81262	+	4.87737i	−0.198555	+	0.166608i	0.538089	+	0.842888i	$0.319146\pi$
$858$		0			0
$859$	53.9268	+	9.50876i	1.83996	+	0.324435i	0.981942	−	0.189184i	$-0.0605843\pi$
$859$	53.9268	+	9.50876i	1.83996	+	0.324435i	0.858018	+	0.513619i	$0.171695\pi$
$860$	−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	$0.0988789\pi$
$863$			17.9590i			0.611331i	−0.952139	+	0.305666i	$0.901121\pi$
$864$		0			0
$865$	−5.82585			−0.198085
$866$	2.41007	+	0.877195i	0.0818976	+	0.0298083i
$867$		0			0
$868$	−5.41273	+	1.65286i	−0.183720	+	0.0561016i
$869$	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
$875$	−11.3364	+	26.6822i	−0.383242	+	0.902021i
$876$		0			0
$877$	4.40950	−	1.60493i	0.148898	−	0.0541946i	−0.266496	−	0.963836i	$-0.585866\pi$
$877$	4.40950	−	1.60493i	0.148898	−	0.0541946i	0.415394	+	0.909642i	$0.363644\pi$
$878$	−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	$-0.859564\pi$
$881$	−2.44317	+	4.23170i	−0.0823125	+	0.142569i	0.821930	+	0.569588i	$0.192897\pi$
$882$		0			0
$883$	11.8954	+	20.6034i	0.400312	+	0.693361i	0.993763	−	0.111509i	$-0.0355684\pi$
$883$	11.8954	+	20.6034i	0.400312	+	0.693361i	−0.593451	+	0.804870i	$0.702235\pi$
$884$	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	$-0.399632\pi$
$887$	−17.0442	−	14.3018i	−0.572290	−	0.480208i	−0.882405	+	0.470491i	$0.844077\pi$
$888$		0			0
$889$	34.8906	+	46.3336i	1.17019	+	1.55398i
$890$		−	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
$896$	−7.94286	−	7.41181i	−0.265352	−	0.247611i
$897$		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	−0.984166	−	0.177249i	$-0.943280\pi$
$907$	−3.61323	−	20.4917i	−0.119975	−	0.680414i	0.864191	−	0.503165i	$-0.167831\pi$
$908$	−6.60939	+	11.4478i	−0.219340	+	0.379908i
$909$		0			0
$910$	−0.0988312	+	1.87381i	−0.00327622	+	0.0621160i
$911$	9.26438	+	11.0409i	0.306942	+	0.365800i	0.897361	−	0.441298i	$-0.145482\pi$
$911$	9.26438	+	11.0409i	0.306942	+	0.365800i	−0.590418	+	0.807097i	$0.701037\pi$
$912$		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	−0.754383	−	0.656434i	$-0.772064\pi$
$929$	−8.22973	−	46.6731i	−0.270009	−	1.53129i	0.484375	−	0.874861i	$-0.339047\pi$
$930$		0			0
$931$	25.1217	−	24.2272i	0.823330	−	0.794016i
$932$	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	$-0.645758\pi$
$937$	3.48018	−	2.00928i	0.113693	−	0.0656404i	0.555768	+	0.831337i	$0.312424\pi$
$938$	0.242659	+	1.98179i	0.00792311	+	0.0647077i
$939$		0			0
$940$	−5.85093	+	33.1823i	−0.190836	+	1.08229i
$941$	17.4001	+	14.6004i	0.567227	+	0.475960i	0.880725	−	0.473629i	$-0.157056\pi$
$941$	17.4001	+	14.6004i	0.567227	+	0.475960i	−0.313497	+	0.949589i	$0.601501\pi$
$942$		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	−0.331220	−	0.943554i	$-0.607460\pi$
$947$	16.2795	−	44.7277i	0.529014	−	1.45345i	0.860234	−	0.509900i	$-0.170318\pi$
$948$		0			0
$949$	−16.6462	−	13.9678i	−0.540359	−	0.453415i
$950$	0.366152	−	2.07655i	0.0118795	−	0.0673722i
$951$		0			0
$952$	0.623629	+	5.09315i	0.0202119	+	0.165070i
$953$	33.3461	−	19.2524i	1.08019	−	0.623646i	0.149240	−	0.988801i	$-0.452317\pi$
$953$	33.3461	−	19.2524i	1.08019	−	0.623646i	0.930947	+	0.365155i	$0.118984\pi$
$954$		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
$959$	6.82824	−	29.5312i	0.220495	−	0.953613i
$960$		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	−0.981163	−	0.193183i	$-0.938119\pi$
$967$	0.214600	−	1.21706i	0.00690107	−	0.0391379i	0.988064	+	0.154045i	$0.0492301\pi$
$968$	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	$-0.149470\pi$
$971$	55.5761			1.78352			0.891761	+	0.452507i	$0.149470\pi$
$972$		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	0.383947	−	0.923355i	$-0.374564\pi$
$977$	13.4072	+	2.36405i	0.428933	+	0.0756325i	0.0449862	+	0.998988i	$0.485676\pi$
$978$		0			0
$979$	31.4719	+	37.5067i	1.00585	+	1.19872i
$980$	10.8780	−	14.9512i	0.347484	−	0.477598i
$981$		0			0
$982$	−1.48909	+	2.57919i	−0.0475189	+	0.0823052i
$983$	1.53261	+	8.69187i	0.0488827	+	0.277228i	0.999445	−	0.0333057i	$-0.0106035\pi$
$983$	1.53261	+	8.69187i	0.0488827	+	0.277228i	−0.950563	+	0.310533i	$0.899492\pi$
$984$		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	0.959185	−	0.282779i	$-0.0912562\pi$
$991$	7.38836	+	12.7970i	0.234699	+	0.406511i	−0.724486	+	0.689289i	$0.757923\pi$
$992$	1.28546	−	1.07863i	0.0408133	−	0.0342465i
$993$		0			0
$994$	0.629789	−	0.674913i	0.0199757	−	0.0214069i
$995$	−0.708632	+	0.844515i	−0.0224651	+	0.0267729i
$996$		0			0
$997$	0.491617	−	1.35071i	0.0155697	−	0.0427773i	−0.931664	−	0.363320i	$-0.881643\pi$
$997$	0.491617	−	1.35071i	0.0155697	−	0.0427773i	0.947234	+	0.320543i	$0.103865\pi$
$998$			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.503.12		132
3.2	odd	2		189.2.be.a.104.11	yes	132
7.6	odd	2	inner	567.2.be.a.503.11		132
21.20	even	2		189.2.be.a.104.12	yes	132
27.7	even	9		189.2.be.a.20.12	yes	132
27.20	odd	18	inner	567.2.be.a.62.11		132
189.20	even	18	inner	567.2.be.a.62.12		132
189.34	odd	18		189.2.be.a.20.11	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.11	✓	132	189.34	odd	18
189.2.be.a.20.12	yes	132	27.7	even	9
189.2.be.a.104.11	yes	132	3.2	odd	2
189.2.be.a.104.12	yes	132	21.20	even	2
567.2.be.a.62.11		132	27.20	odd	18	inner
567.2.be.a.62.12		132	189.20	even	18	inner
567.2.be.a.503.11		132	7.6	odd	2	inner
567.2.be.a.503.12		132	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.0448460 - 0.123213i) q^{2} +(1.51892 + 1.27452i) q^{4} +(0.231324 - 1.31190i) q^{5} +(-2.62614 + 0.321557i) q^{7} +(0.452264 - 0.261115i) q^{8} +(-0.151270 - 0.0873359i) q^{10} +(4.31014 - 0.759994i) q^{11} +(1.38870 + 3.81541i) q^{13} +(-0.0781517 + 0.337996i) q^{14} +(0.676731 + 3.83793i) q^{16} +(1.85685 - 3.21617i) q^{17} +(4.31784 - 2.49291i) q^{19} +(2.02342 - 1.69785i) q^{20} +(0.0996512 - 0.565150i) q^{22} +(-0.242663 + 0.289194i) q^{23} +(3.03088 + 1.10315i) q^{25} +0.532388 q^{26} +(-4.39872 - 2.85866i) q^{28} +(-1.57190 + 4.31876i) q^{29} +(0.693448 - 0.826419i) q^{31} +(1.53182 + 0.270102i) q^{32} +(-0.313002 - 0.373021i) q^{34} +(-0.185638 + 3.51963i) q^{35} +(-0.172576 + 0.298911i) q^{37} +(-0.113522 - 0.643813i) q^{38} +(-0.237938 - 0.653729i) q^{40} +(-5.09719 + 1.85523i) q^{41} +(-0.390810 - 2.21639i) q^{43} +(7.51538 + 4.33901i) q^{44} +(0.0247502 + 0.0428686i) q^{46} +(-9.77186 + 8.19957i) q^{47} +(6.79320 - 1.68890i) q^{49} +(0.271846 - 0.323973i) q^{50} +(-2.75352 + 7.56523i) q^{52} -9.19872i q^{53} -5.83030i q^{55} +(-1.10374 + 0.831152i) q^{56} +(0.461636 + 0.387359i) q^{58} +(2.24314 - 12.7215i) q^{59} +(-1.14717 - 1.36715i) q^{61} +(-0.0707275 - 0.122504i) q^{62} +(-3.79516 + 6.57342i) q^{64} +(5.32670 - 0.939241i) q^{65} +(5.40821 - 1.96843i) q^{67} +(6.91949 - 2.51849i) q^{68} +(0.425340 + 0.180714i) q^{70} +(-2.30444 - 1.33047i) q^{71} +(-4.63485 + 2.67593i) q^{73} +(0.0290904 + 0.0346686i) q^{74} +(9.73572 + 1.71667i) q^{76} +(-11.0746 + 3.38180i) q^{77} +(5.48206 + 1.99531i) q^{79} +5.19155 q^{80} +0.711242i q^{82} +(4.03800 + 1.46971i) q^{83} +(-3.78977 - 3.17999i) q^{85} +(-0.290615 - 0.0512433i) q^{86} +(1.75088 - 1.46916i) q^{88} +(5.59352 + 9.68826i) q^{89} +(-4.87378 - 9.57326i) q^{91} +(-0.737171 + 0.129983i) q^{92} +(0.572067 + 1.57174i) q^{94} +(-2.27163 - 6.24126i) q^{95} +(-14.5132 + 2.55906i) q^{97} +(0.0965524 - 0.912754i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 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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