LMFDB - Embedded newform 513.2.y.a.28.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(28,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.y (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,0,9,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	513.28
Dual form			513.2.y.a.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.152704 - 0.866025i) q^{2} +(1.15270 - 0.419550i) q^{4} +(-2.37939 - 0.866025i) q^{5} +(1.32635 - 2.29731i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(-0.386659 + 2.19285i) q^{10} +(0.205737 + 0.356347i) q^{11} +(-1.12449 - 0.943555i) q^{13} +(-2.19207 - 0.797847i) q^{14} +(-0.0320889 + 0.0269258i) q^{16} +(0.414878 + 2.35289i) q^{17} +(-4.29813 - 0.725293i) q^{19} -3.10607 q^{20} +(0.277189 - 0.232589i) q^{22} +(-0.826352 + 0.300767i) q^{23} +(1.08125 + 0.907278i) q^{25} +(-0.645430 + 1.11792i) q^{26} +(0.565055 - 3.20459i) q^{28} +(1.06031 - 6.01330i) q^{29} +(1.01114 - 1.75135i) q^{31} +(-4.31908 - 3.62414i) q^{32} +(1.97431 - 0.718589i) q^{34} +(-5.14543 + 4.31753i) q^{35} -9.69459 q^{37} +(0.0282185 + 3.83305i) q^{38} +(1.24763 + 7.07564i) q^{40} +(6.53596 - 5.48432i) q^{41} +(10.6099 + 3.86170i) q^{43} +(0.386659 + 0.324446i) q^{44} +(0.386659 + 0.669713i) q^{46} +(1.47178 - 8.34689i) q^{47} +(-0.0184183 - 0.0319015i) q^{49} +(0.620615 - 1.07494i) q^{50} +(-1.69207 - 0.615862i) q^{52} +(-1.41875 + 0.516382i) q^{53} +(-0.180922 - 1.02606i) q^{55} -7.52704 q^{56} -5.36959 q^{58} +(0.645430 + 3.66041i) q^{59} +(2.35844 - 0.858402i) q^{61} +(-1.67112 - 0.608239i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(1.85844 + 3.21891i) q^{65} +(-0.847296 + 4.80526i) q^{67} +(1.46538 + 2.53812i) q^{68} +(4.52481 + 3.79677i) q^{70} +(9.46451 + 3.44480i) q^{71} +(-7.85117 + 6.58791i) q^{73} +(1.48040 + 8.39576i) q^{74} +(-5.25877 + 0.967233i) q^{76} +1.09152 q^{77} +(12.4251 - 10.4259i) q^{79} +(0.0996702 - 0.0362770i) q^{80} +(-5.74763 - 4.82283i) q^{82} +(-2.81908 + 4.88279i) q^{83} +(1.05051 - 5.95772i) q^{85} +(1.72416 - 9.77817i) q^{86} +(0.583778 - 1.01113i) q^{88} +(1.22803 + 1.03044i) q^{89} +(-3.65910 + 1.33180i) q^{91} +(-0.826352 + 0.693392i) q^{92} -7.45336 q^{94} +(9.59879 + 5.44804i) q^{95} +(-0.0175410 - 0.0994798i) q^{97} +(-0.0248149 + 0.0208222i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 9 q^{4} - 3 q^{5} + 9 q^{7} - 6 q^{8} - 9 q^{10} - 9 q^{11} + 6 q^{13} - 24 q^{14} + 9 q^{16} + 24 q^{17} - 12 q^{19} + 6 q^{20} - 9 q^{22} - 6 q^{23} + 9 q^{25} + 12 q^{26} + 42 q^{28}+ \cdots + 27 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 9 * q^4 - 3 * q^5 + 9 * q^7 - 6 * q^8 - 9 * q^10 - 9 * q^11 + 6 * q^13 - 24 * q^14 + 9 * q^16 + 24 * q^17 - 12 * q^19 + 6 * q^20 - 9 * q^22 - 6 * q^23 + 9 * q^25 + 12 * q^26 + 42 * q^28 + 12 * q^29 - 9 * q^32 - 18 * q^34 - 15 * q^35 - 54 * q^37 + 15 * q^38 - 9 * q^40 + 6 * q^41 + 15 * q^43 + 9 * q^44 + 9 * q^46 - 6 * q^47 - 12 * q^49 + 15 * q^50 - 21 * q^52 - 6 * q^53 - 18 * q^55 - 66 * q^56 - 18 * q^58 - 12 * q^59 + 6 * q^61 - 24 * q^62 - 12 * q^64 + 3 * q^65 - 3 * q^67 + 33 * q^68 + 24 * q^71 - 21 * q^73 + 3 * q^74 - 9 * q^76 - 54 * q^77 + 33 * q^79 + 15 * q^80 - 18 * q^82 + 9 * q^85 + 12 * q^86 - 9 * q^88 - 15 * q^89 + 15 * q^91 - 6 * q^92 - 18 * q^94 + 15 * q^95 + 45 * q^97 + 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.152704	−	0.866025i	−0.107978	−	0.612372i	−0.989989	−	0.141144i	$-0.954922\pi$
$2$	−0.152704	−	0.866025i	−0.107978	−	0.612372i	0.882011	−	0.471228i	$-0.156189\pi$
$3$		0			0
$3$		0			0
$4$	1.15270	−	0.419550i	0.576352	−	0.209775i
$5$	−2.37939	−	0.866025i	−1.06409	−	0.387298i	−0.250129	−	0.968213i	$-0.580473\pi$
$5$	−2.37939	−	0.866025i	−1.06409	−	0.387298i	−0.813965	+	0.580914i	$0.802695\pi$
$6$		0			0
$7$	1.32635	−	2.29731i	0.501314	−	0.868301i	−0.498685	−	0.866783i	$-0.666184\pi$
$7$	1.32635	−	2.29731i	0.501314	−	0.868301i	0.999999	−	0.00151779i	$-0.000483127\pi$
$8$	−1.41875	−	2.45734i	−0.501603	−	0.868802i
$9$		0			0
$10$	−0.386659	+	2.19285i	−0.122272	+	0.693441i
$11$	0.205737	+	0.356347i	0.0620321	+	0.107443i	0.895374	−	0.445316i	$-0.146909\pi$
$11$	0.205737	+	0.356347i	0.0620321	+	0.107443i	−0.833342	+	0.552758i	$0.813575\pi$
$12$		0			0
$13$	−1.12449	−	0.943555i	−0.311876	−	0.261695i	0.473391	−	0.880852i	$-0.343030\pi$
$13$	−1.12449	−	0.943555i	−0.311876	−	0.261695i	−0.785267	+	0.619157i	$0.787474\pi$
$14$	−2.19207	−	0.797847i	−0.585854	−	0.213234i
$15$		0			0
$16$	−0.0320889	+	0.0269258i	−0.00802222	+	0.00673144i
$17$	0.414878	+	2.35289i	0.100623	+	0.570659i	0.992879	+	0.119130i	$0.0380104\pi$
$17$	0.414878	+	2.35289i	0.100623	+	0.570659i	−0.892256	+	0.451530i	$0.850879\pi$
$18$		0			0
$19$	−4.29813	−	0.725293i	−0.986059	−	0.166394i
$19$	−4.29813	−	0.725293i	−0.986059	−	0.166394i
$20$	−3.10607			−0.694538
$21$		0			0
$22$	0.277189	−	0.232589i	0.0590968	−	0.0495881i
$23$	−0.826352	+	0.300767i	−0.172306	+	0.0627144i	−0.426733	−	0.904378i	$-0.640336\pi$
$23$	−0.826352	+	0.300767i	−0.172306	+	0.0627144i	0.254427	+	0.967092i	$0.418113\pi$
$24$		0			0
$25$	1.08125	+	0.907278i	0.216250	+	0.181456i
$26$	−0.645430	+	1.11792i	−0.126579	+	0.219242i
$27$		0			0
$28$	0.565055	−	3.20459i	0.106785	−	0.605610i
$29$	1.06031	−	6.01330i	0.196894	−	1.11664i	−0.712801	−	0.701366i	$-0.752574\pi$
$29$	1.06031	−	6.01330i	0.196894	−	1.11664i	0.909695	−	0.415276i	$-0.136315\pi$
$30$		0			0
$31$	1.01114	−	1.75135i	0.181607	−	0.314552i	−0.760821	−	0.648962i	$-0.775203\pi$
$31$	1.01114	−	1.75135i	0.181607	−	0.314552i	0.942428	+	0.334409i	$0.108537\pi$
$32$	−4.31908	−	3.62414i	−0.763512	−	0.640663i
$33$		0			0
$34$	1.97431	−	0.718589i	0.338591	−	0.123237i
$35$	−5.14543	+	4.31753i	−0.869736	+	0.729795i
$36$		0			0
$37$	−9.69459			−1.59378			−0.796891	−	0.604124i	$-0.793523\pi$
$37$	−9.69459			−1.59378			−0.796891	+	0.604124i	$0.793523\pi$
$38$	0.0282185	+	3.83305i	0.00457764	+	0.621802i
$39$		0			0
$40$	1.24763	+	7.07564i	0.197267	+	1.11876i
$41$	6.53596	−	5.48432i	1.02075	−	0.856507i	0.0310243	−	0.999519i	$-0.490123\pi$
$41$	6.53596	−	5.48432i	1.02075	−	0.856507i	0.989721	+	0.143012i	$0.0456786\pi$
$42$		0			0
$43$	10.6099	+	3.86170i	1.61800	+	0.588904i	0.983000	−	0.183608i	$-0.0587776\pi$
$43$	10.6099	+	3.86170i	1.61800	+	0.588904i	0.635001	+	0.772512i	$0.281000\pi$
$44$	0.386659	+	0.324446i	0.0582911	+	0.0489120i
$45$		0			0
$46$	0.386659	+	0.669713i	0.0570098	+	0.0987439i
$47$	1.47178	−	8.34689i	0.214681	−	1.21752i	−0.666777	−	0.745257i	$-0.732327\pi$
$47$	1.47178	−	8.34689i	0.214681	−	1.21752i	0.881458	−	0.472261i	$-0.156562\pi$
$48$		0			0
$49$	−0.0184183	−	0.0319015i	−0.00263119	−	0.00455735i
$50$	0.620615	−	1.07494i	0.0877682	−	0.152019i
$51$		0			0
$52$	−1.69207	−	0.615862i	−0.234647	−	0.0854047i
$53$	−1.41875	+	0.516382i	−0.194880	+	0.0709305i	−0.437616	−	0.899162i	$-0.644177\pi$
$53$	−1.41875	+	0.516382i	−0.194880	+	0.0709305i	0.242736	+	0.970092i	$0.421955\pi$
$54$		0			0
$55$	−0.180922	−	1.02606i	−0.0243955	−	0.138354i
$56$	−7.52704			−1.00584
$57$		0			0
$58$	−5.36959			−0.705061
$59$	0.645430	+	3.66041i	0.0840278	+	0.476545i	0.997562	+	0.0697837i	$0.0222309\pi$
$59$	0.645430	+	3.66041i	0.0840278	+	0.476545i	−0.913534	+	0.406762i	$0.866658\pi$
$60$		0			0
$61$	2.35844	−	0.858402i	0.301967	−	0.109907i	−0.186593	−	0.982437i	$-0.559744\pi$
$61$	2.35844	−	0.858402i	0.301967	−	0.109907i	0.488560	+	0.872530i	$0.337522\pi$
$62$	−1.67112	−	0.608239i	−0.212233	−	0.0772464i
$63$		0			0
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	1.85844	+	3.21891i	0.230511	+	0.399257i
$66$		0			0
$67$	−0.847296	+	4.80526i	−0.103514	+	0.587056i	0.888290	+	0.459283i	$0.151894\pi$
$67$	−0.847296	+	4.80526i	−0.103514	+	0.587056i	−0.991804	+	0.127772i	$0.959217\pi$
$68$	1.46538	+	2.53812i	0.177704	+	0.307792i
$69$		0			0
$70$	4.52481	+	3.79677i	0.540819	+	0.453801i
$71$	9.46451	+	3.44480i	1.12323	+	0.408822i	0.835830	−	0.548988i	$-0.184987\pi$
$71$	9.46451	+	3.44480i	1.12323	+	0.408822i	0.287400	+	0.957811i	$0.407209\pi$
$72$		0			0
$73$	−7.85117	+	6.58791i	−0.918910	+	0.771057i	−0.973793	−	0.227436i	$-0.926966\pi$
$73$	−7.85117	+	6.58791i	−0.918910	+	0.771057i	0.0548834	+	0.998493i	$0.482521\pi$
$74$	1.48040	+	8.39576i	0.172093	+	0.975988i
$75$		0			0
$76$	−5.25877	+	0.967233i	−0.603222	+	0.110949i
$77$	1.09152			0.124390
$78$		0			0
$79$	12.4251	−	10.4259i	1.39794	−	1.17301i	0.435932	−	0.899979i	$-0.356419\pi$
$79$	12.4251	−	10.4259i	1.39794	−	1.17301i	0.962006	−	0.273030i	$-0.0880258\pi$
$80$	0.0996702	−	0.0362770i	0.0111435	−	0.00405589i
$81$		0			0
$82$	−5.74763	−	4.82283i	−0.634719	−	0.532593i
$83$	−2.81908	+	4.88279i	−0.309434	+	0.535955i	−0.978239	−	0.207483i	$-0.933473\pi$
$83$	−2.81908	+	4.88279i	−0.309434	+	0.535955i	0.668805	+	0.743438i	$0.266806\pi$
$84$		0			0
$85$	1.05051	−	5.95772i	0.113944	−	0.646206i
$86$	1.72416	−	9.77817i	0.185920	−	1.05441i
$87$		0			0
$88$	0.583778	−	1.01113i	0.0622310	−	0.107787i
$89$	1.22803	+	1.03044i	0.130170	+	0.109226i	0.705549	−	0.708662i	$-0.250701\pi$
$89$	1.22803	+	1.03044i	0.130170	+	0.109226i	−0.575378	+	0.817888i	$0.695145\pi$
$90$		0			0
$91$	−3.65910	+	1.33180i	−0.383578	+	0.139611i
$92$	−0.826352	+	0.693392i	−0.0861531	+	0.0722911i
$93$		0			0
$94$	−7.45336			−0.768756
$95$	9.59879	+	5.44804i	0.984815	+	0.558958i
$96$		0			0
$97$	−0.0175410	−	0.0994798i	−0.00178102	−	0.0101006i	0.983904	−	0.178696i	$-0.0571879\pi$
$97$	−0.0175410	−	0.0994798i	−0.00178102	−	0.0101006i	−0.985685	+	0.168596i	$0.946077\pi$
$98$	−0.0248149	+	0.0208222i	−0.00250669	+	0.00210336i
$99$		0			0
$100$	1.62701	+	0.592184i	0.162701	+	0.0592184i
$101$	7.99273	+	6.70669i	0.795306	+	0.667341i	0.947053	−	0.321078i	$-0.104045\pi$
$101$	7.99273	+	6.70669i	0.795306	+	0.667341i	−0.151747	+	0.988419i	$0.548490\pi$
$102$		0			0
$103$	−3.58512	−	6.20961i	−0.353253	−	0.611851i	0.633565	−	0.773690i	$-0.281591\pi$
$103$	−3.58512	−	6.20961i	−0.353253	−	0.611851i	−0.986817	+	0.161838i	$0.948258\pi$
$104$	−0.723278	+	4.10191i	−0.0709232	+	0.402226i
$105$		0			0
$106$	0.663848	+	1.14982i	0.0644786	+	0.111680i
$107$	6.43629	−	11.1480i	0.622220	−	1.07772i	−0.366852	−	0.930279i	$-0.619564\pi$
$107$	6.43629	−	11.1480i	0.622220	−	1.07772i	0.989072	−	0.147437i	$-0.0471022\pi$
$108$		0			0
$109$	12.0103	+	4.37138i	1.15037	+	0.418702i	0.845650	−	0.533738i	$-0.179213\pi$
$109$	12.0103	+	4.37138i	1.15037	+	0.418702i	0.304725	+	0.952440i	$0.401435\pi$
$110$	−0.860967	+	0.313366i	−0.0820900	+	0.0298783i
$111$		0			0
$112$	0.0192957	+	0.109431i	0.00182327	+	0.0103403i
$113$	11.0077			1.03552			0.517761	−	0.855526i	$-0.326766\pi$
$113$	11.0077			1.03552			0.517761	+	0.855526i	$0.326766\pi$
$114$		0			0
$115$	2.22668			0.207639
$116$	−1.30066	−	7.37641i	−0.120763	−	0.684882i
$117$		0			0
$118$	3.07145	−	1.11792i	0.282750	−	0.102913i
$119$	5.95558	+	2.16766i	0.545948	+	0.198709i
$120$		0			0
$121$	5.41534	−	9.37965i	0.492304	−	0.852696i
$122$	−1.10354	−	1.91139i	−0.0999099	−	0.173049i
$123$		0			0
$124$	0.430770	−	2.44302i	0.0386843	−	0.219389i
$125$	4.54323	+	7.86911i	0.406359	+	0.703835i
$126$		0			0
$127$	−4.24897	−	3.56531i	−0.377035	−	0.316370i	0.434502	−	0.900671i	$-0.356924\pi$
$127$	−4.24897	−	3.56531i	−0.377035	−	0.316370i	−0.811537	+	0.584301i	$0.801369\pi$
$128$	−6.42989	−	2.34029i	−0.568328	−	0.206854i
$129$		0			0
$130$	2.50387	−	2.10100i	0.219604	−	0.184270i
$131$	3.40167	+	19.2919i	0.297206	+	1.68554i	0.658100	+	0.752930i	$0.271360\pi$
$131$	3.40167	+	19.2919i	0.297206	+	1.68554i	−0.360895	+	0.932607i	$0.617529\pi$
$132$		0			0
$133$	−7.36706	+	8.91215i	−0.638805	+	0.772781i
$134$	4.29086			0.370674
$135$		0			0
$136$	5.19325	−	4.35765i	0.445317	−	0.373666i
$137$	18.1395	−	6.60224i	1.54976	−	0.564067i	0.581400	−	0.813618i	$-0.302505\pi$
$137$	18.1395	−	6.60224i	1.54976	−	0.564067i	0.968362	+	0.249550i	$0.0802828\pi$
$138$		0			0
$139$	2.43448	+	2.04277i	0.206490	+	0.173265i	0.740168	−	0.672422i	$-0.234746\pi$
$139$	2.43448	+	2.04277i	0.206490	+	0.173265i	−0.533678	+	0.845688i	$0.679191\pi$
$140$	−4.11974	+	7.13559i	−0.348181	+	0.603068i
$141$		0			0
$142$	1.53802	−	8.72254i	0.129068	−	0.731979i
$143$	0.104885	−	0.594831i	0.00877091	−	0.0497423i
$144$		0			0
$145$	−7.73055	+	13.3897i	−0.641987	+	1.11195i
$146$	6.90420	+	5.79331i	0.571396	+	0.479458i
$147$		0			0
$148$	−11.1750	+	4.06736i	−0.918579	+	0.334335i
$149$	−8.05097	+	6.75557i	−0.659561	+	0.553438i	−0.909955	−	0.414706i	$-0.863884\pi$
$149$	−8.05097	+	6.75557i	−0.659561	+	0.553438i	0.250394	+	0.968144i	$0.419440\pi$
$150$		0			0
$151$	9.59627			0.780933			0.390467	−	0.920617i	$-0.372314\pi$
$151$	9.59627			0.780933			0.390467	+	0.920617i	$0.372314\pi$
$152$	4.31567	+	11.5910i	0.350047	+	0.940154i
$153$		0			0
$154$	−0.166679	−	0.945283i	−0.0134314	−	0.0761731i
$155$	−3.92262	+	3.29147i	−0.315072	+	0.264377i
$156$		0			0
$157$	14.4547	+	5.26108i	1.15361	+	0.419880i	0.846811	−	0.531894i	$-0.178519\pi$
$157$	14.4547	+	5.26108i	1.15361	+	0.419880i	0.306800	+	0.951774i	$0.400742\pi$
$158$	−10.9265	−	9.16841i	−0.869265	−	0.729400i
$159$		0			0
$160$	7.13816	+	12.3636i	0.564321	+	0.977432i
$161$	−0.405078	+	2.29731i	−0.0319246	+	0.181053i
$162$		0			0
$163$	−9.19846	−	15.9322i	−0.720479	−	1.24791i	−0.960808	−	0.277215i	$-0.910589\pi$
$163$	−9.19846	−	15.9322i	−0.720479	−	1.24791i	0.240329	−	0.970692i	$-0.422745\pi$
$164$	5.23308	−	9.06396i	0.408635	−	0.707776i
$165$		0			0
$166$	4.65910	+	1.69577i	0.361616	+	0.131618i
$167$	−21.5141	+	7.83051i	−1.66481	+	0.605943i	−0.991108	−	0.133057i	$-0.957521\pi$
$167$	−21.5141	+	7.83051i	−1.66481	+	0.605943i	−0.673706	+	0.739000i	$0.735298\pi$
$168$		0			0
$169$	−1.88326	−	10.6805i	−0.144866	−	0.821575i
$170$	−5.31996			−0.408022
$171$		0			0
$172$	13.8503			1.05607
$173$	−1.88026	−	10.6635i	−0.142954	−	0.810731i	−0.968987	−	0.247110i	$-0.920519\pi$
$173$	−1.88026	−	10.6635i	−0.142954	−	0.810731i	0.826034	−	0.563621i	$-0.190592\pi$
$174$		0			0
$175$	3.51842	−	1.28060i	0.265967	−	0.0968042i
$176$	−0.0161968	−	0.00589515i	−0.00122088	−	0.000444364i
$177$		0			0
$178$	0.704860	−	1.22085i	0.0528315	−	0.0915068i
$179$	−3.27719	−	5.67626i	−0.244949	−	0.424263i	0.717169	−	0.696900i	$-0.245438\pi$
$179$	−3.27719	−	5.67626i	−0.244949	−	0.424263i	−0.962117	+	0.272636i	$0.912104\pi$
$180$		0			0
$181$	0.973126	−	5.51887i	0.0723319	−	0.410214i	−0.927046	−	0.374947i	$-0.877661\pi$
$181$	0.973126	−	5.51887i	0.0723319	−	0.410214i	0.999378	−	0.0352669i	$-0.0112281\pi$
$182$	1.71213	+	2.96550i	0.126912	+	0.219818i
$183$		0			0
$184$	1.91147	+	1.60392i	0.140916	+	0.118242i
$185$	23.0672	+	8.39576i	1.69593	+	0.617269i
$186$		0			0
$187$	−0.753089	+	0.631917i	−0.0550713	+	0.0462103i
$188$	−1.80541	−	10.2390i	−0.131673	−	0.746754i
$189$		0			0
$190$	3.25237	−	9.14473i	0.235952	−	0.663429i
$191$	−3.26857			−0.236505			−0.118253	−	0.992984i	$-0.537729\pi$
$191$	−3.26857			−0.236505			−0.118253	+	0.992984i	$0.537729\pi$
$192$		0			0
$193$	−1.22075	+	1.02433i	−0.0878716	+	0.0737331i	−0.685665	−	0.727917i	$-0.740489\pi$
$193$	−1.22075	+	1.02433i	−0.0878716	+	0.0737331i	0.597794	+	0.801650i	$0.296044\pi$
$194$	−0.0834734	+	0.0303818i	−0.00599304	+	0.00218129i
$195$		0			0
$196$	−0.0346151	−	0.0290455i	−0.00247251	−	0.00207468i
$197$	10.6343	−	18.4191i	0.757661	−	1.31231i	−0.186379	−	0.982478i	$-0.559675\pi$
$197$	10.6343	−	18.4191i	0.757661	−	1.31231i	0.944040	−	0.329830i	$-0.106991\pi$
$198$		0			0
$199$	−3.09580	+	17.5572i	−0.219455	+	1.24459i	0.653550	+	0.756883i	$0.273279\pi$
$199$	−3.09580	+	17.5572i	−0.219455	+	1.24459i	−0.873006	+	0.487710i	$0.837832\pi$
$200$	0.695470	−	3.94421i	0.0491772	−	0.278898i
$201$		0			0
$202$	4.58765	−	7.94604i	0.322786	−	0.559081i
$203$	−12.4081	−	10.4116i	−0.870876	−	0.730752i
$204$		0			0
$205$	−20.3011	+	7.38901i	−1.41789	+	0.516071i
$206$	−4.83022	+	4.05304i	−0.336538	+	0.282389i
$207$		0			0
$208$	0.0614894			0.00426352
$209$	−0.625829	−	1.68085i	−0.0432895	−	0.116267i
$210$		0			0
$211$	3.66132	+	20.7644i	0.252056	+	1.42948i	0.803518	+	0.595280i	$0.202959\pi$
$211$	3.66132	+	20.7644i	0.252056	+	1.42948i	−0.551463	+	0.834200i	$0.685930\pi$
$212$	−1.41875	+	1.19047i	−0.0974400	+	0.0817619i
$213$		0			0
$214$	−10.6373	−	3.87165i	−0.727149	−	0.264661i
$215$	−21.9008	−	18.3770i	−1.49362	−	1.25330i
$216$		0			0
$217$	−2.68227	−	4.64582i	−0.182084	−	0.315379i
$218$	1.95171	−	11.0687i	0.132187	−	0.749668i
$219$		0			0
$220$	−0.639033	−	1.10684i	−0.0430836	−	0.0746230i
$221$	1.75356	−	3.03725i	0.117957	−	0.204307i
$222$		0			0
$223$	−18.5351	−	6.74622i	−1.24120	−	0.451760i	−0.363782	−	0.931484i	$-0.618515\pi$
$223$	−18.5351	−	6.74622i	−1.24120	−	0.451760i	−0.877419	+	0.479724i	$0.840737\pi$
$224$	−14.0544	+	5.11538i	−0.939048	+	0.341785i
$225$		0			0
$226$	−1.68092	−	9.53298i	−0.111813	−	0.634125i
$227$	−26.4020			−1.75236			−0.876180	−	0.481983i	$-0.839917\pi$
$227$	−26.4020			−1.75236			−0.876180	+	0.481983i	$0.839917\pi$
$228$		0			0
$229$	−5.87164			−0.388009			−0.194005	−	0.981001i	$-0.562148\pi$
$229$	−5.87164			−0.388009			−0.194005	+	0.981001i	$0.562148\pi$
$230$	−0.340022	−	1.92836i	−0.0224204	−	0.127152i
$231$		0			0
$232$	−16.2811	+	5.92582i	−1.06890	+	0.389049i
$233$	24.4209	+	8.88847i	1.59986	+	0.582303i	0.979400	−	0.201932i	$-0.0647219\pi$
$233$	24.4209	+	8.88847i	1.59986	+	0.582303i	0.620464	+	0.784235i	$0.286944\pi$
$234$		0			0
$235$	−10.7306	+	18.5859i	−0.699984	+	1.21241i
$236$	2.27972	+	3.94858i	0.148397	+	0.257031i
$237$		0			0
$238$	0.967805	−	5.48870i	0.0627335	−	0.355779i
$239$	−4.18479	−	7.24827i	−0.270692	−	0.468852i	0.698347	−	0.715759i	$-0.253919\pi$
$239$	−4.18479	−	7.24827i	−0.270692	−	0.468852i	−0.969039	+	0.246907i	$0.920586\pi$
$240$		0			0
$241$	−8.33409	−	6.99313i	−0.536846	−	0.450467i	0.333612	−	0.942711i	$-0.391733\pi$
$241$	−8.33409	−	6.99313i	−0.536846	−	0.450467i	−0.870458	+	0.492243i	$0.836177\pi$
$242$	−8.94996	−	3.25752i	−0.575325	−	0.209401i
$243$		0			0
$244$	2.35844	−	1.97897i	0.150984	−	0.126690i
$245$	0.0161968	+	0.0918566i	0.00103478	+	0.00586850i
$246$		0			0
$247$	4.14883	+	4.87111i	0.263984	+	0.309941i
$248$	−5.73824			−0.364378
$249$		0			0
$250$	6.12108	−	5.13620i	0.387131	−	0.324842i
$251$	−5.82547	+	2.12030i	−0.367701	+	0.133832i	−0.519261	−	0.854616i	$-0.673793\pi$
$251$	−5.82547	+	2.12030i	−0.367701	+	0.133832i	0.151560	+	0.988448i	$0.451570\pi$
$252$		0			0
$253$	−0.277189	−	0.232589i	−0.0174267	−	0.0146227i
$254$	−2.43882	+	4.22415i	−0.153025	+	0.265047i
$255$		0			0
$256$	−2.79591	+	15.8564i	−0.174744	+	0.991025i
$257$	2.93835	−	16.6642i	0.183289	−	1.03948i	−0.744845	−	0.667238i	$-0.767476\pi$
$257$	2.93835	−	16.6642i	0.183289	−	1.03948i	0.928134	−	0.372247i	$-0.121412\pi$
$258$		0			0
$259$	−12.8584	+	22.2715i	−0.798985	+	1.38388i
$260$	3.49273	+	2.93075i	0.216610	+	0.181757i
$261$		0			0
$262$	16.1878	−	5.89187i	1.00008	−	0.364001i
$263$	−11.1853	+	9.38555i	−0.689713	+	0.578738i	−0.918826	−	0.394662i	$-0.870862\pi$
$263$	−11.1853	+	9.38555i	−0.689713	+	0.578738i	0.229114	+	0.973400i	$0.426417\pi$
$264$		0			0
$265$	3.82295			0.234842
$266$	8.84312	+	5.01914i	0.542207	+	0.307743i
$267$		0			0
$268$	1.03936	+	5.89452i	0.0634892	+	0.360065i
$269$	−13.2194	+	11.0924i	−0.806002	+	0.676316i	−0.949650	−	0.313313i	$-0.898561\pi$
$269$	−13.2194	+	11.0924i	−0.806002	+	0.676316i	0.143648	+	0.989629i	$0.454117\pi$
$270$		0			0
$271$	4.35117	+	1.58370i	0.264315	+	0.0962026i	0.470778	−	0.882252i	$-0.343973\pi$
$271$	4.35117	+	1.58370i	0.264315	+	0.0962026i	−0.206464	+	0.978454i	$0.566195\pi$
$272$	−0.0766663	−	0.0643307i	−0.00464858	−	0.00390062i
$273$		0			0
$274$	−8.48767	−	14.7011i	−0.512759	−	0.888125i
$275$	−0.100852	+	0.571962i	−0.00608162	+	0.0344906i
$276$		0			0
$277$	2.36184	+	4.09083i	0.141909	+	0.245794i	0.928216	−	0.372043i	$-0.121342\pi$
$277$	2.36184	+	4.09083i	0.141909	+	0.245794i	−0.786306	+	0.617837i	$0.788009\pi$
$278$	1.39734	−	2.42026i	0.0838067	−	0.145157i
$279$		0			0
$280$	17.9097	+	6.51860i	1.07031	+	0.389561i
$281$	−30.6819	+	11.1673i	−1.83033	+	0.666184i	−0.837527	+	0.546397i	$0.815999\pi$
$281$	−30.6819	+	11.1673i	−1.83033	+	0.666184i	−0.992800	+	0.119788i	$0.961779\pi$
$282$		0			0
$283$	−1.69846	−	9.63246i	−0.100963	−	0.572590i	−0.992756	−	0.120147i	$-0.961663\pi$
$283$	−1.69846	−	9.63246i	−0.100963	−	0.572590i	0.891793	−	0.452444i	$-0.149448\pi$
$284$	12.3550			0.733137
$285$		0			0
$286$	−0.531155			−0.0314079
$287$	−3.93020	−	22.2893i	−0.231992	−	1.31569i
$288$		0			0
$289$	10.6108	−	3.86202i	0.624166	−	0.227178i
$290$	12.7763	+	4.65020i	0.750251	+	0.273069i
$291$		0			0
$292$	−6.28611	+	10.8879i	−0.367867	+	0.637164i
$293$	2.06758	+	3.58116i	0.120789	+	0.209213i	0.920079	−	0.391732i	$-0.128124\pi$
$293$	2.06758	+	3.58116i	0.120789	+	0.209213i	−0.799290	+	0.600946i	$0.794791\pi$
$294$		0			0
$295$	1.63429	−	9.26849i	0.0951518	−	0.539633i
$296$	13.7542	+	23.8229i	0.799446	+	1.38468i
$297$		0			0
$298$	7.07991	+	5.94075i	0.410128	+	0.344138i
$299$	1.21301	+	0.441500i	0.0701502	+	0.0255326i
$300$		0			0
$301$	22.9440	−	19.2523i	1.32247	−	1.10969i
$302$	−1.46538	−	8.31061i	−0.0843234	−	0.478222i
$303$		0			0
$304$	0.157451	−	0.0924567i	0.00903046	−	0.00530276i
$305$	−6.35504			−0.363888
$306$		0			0
$307$	−4.76991	+	4.00243i	−0.272233	+	0.228431i	−0.768676	−	0.639639i	$-0.779084\pi$
$307$	−4.76991	+	4.00243i	−0.272233	+	0.228431i	0.496442	+	0.868070i	$0.334639\pi$
$308$	1.25820	−	0.457947i	0.0716925	−	0.0260939i
$309$		0			0
$310$	3.44949	+	2.89447i	0.195918	+	0.164395i
$311$	−1.29426	+	2.24173i	−0.0733909	+	0.127117i	−0.900385	−	0.435093i	$-0.856715\pi$
$311$	−1.29426	+	2.24173i	−0.0733909	+	0.127117i	0.826994	+	0.562210i	$0.190049\pi$
$312$		0			0
$313$	−3.58971	+	20.3582i	−0.202902	+	1.15072i	0.697804	+	0.716288i	$0.254160\pi$
$313$	−3.58971	+	20.3582i	−0.202902	+	1.15072i	−0.900707	+	0.434428i	$0.856951\pi$
$314$	2.34895	−	13.3215i	0.132559	−	0.751777i
$315$		0			0
$316$	9.94831	−	17.2310i	0.559636	−	0.969318i
$317$	−6.99866	−	5.87257i	−0.393084	−	0.329836i	0.424729	−	0.905320i	$-0.360369\pi$
$317$	−6.99866	−	5.87257i	−0.393084	−	0.329836i	−0.817813	+	0.575484i	$0.804814\pi$
$318$		0			0
$319$	2.36097	−	0.859322i	0.132189	−	0.0481128i
$320$	9.77972	−	8.20616i	0.546703	−	0.458738i
$321$		0			0
$322$	2.05138			0.114319
$323$	−0.0766663	−	10.4139i	−0.00426583	−	0.579447i
$324$		0			0
$325$	−0.359785	−	2.04044i	−0.0199573	−	0.113183i
$326$	−12.3931	+	10.3990i	−0.686388	+	0.575948i
$327$		0			0
$328$	−22.7497	−	8.28023i	−1.25614	−	0.457199i
$329$	−17.2233	−	14.4520i	−0.949550	−	0.796767i
$330$		0			0
$331$	−8.04710	−	13.9380i	−0.442309	−	0.766101i	0.555552	−	0.831482i	$-0.312507\pi$
$331$	−8.04710	−	13.9380i	−0.442309	−	0.766101i	−0.997860	+	0.0653807i	$0.979174\pi$
$332$	−1.20099	+	6.81115i	−0.0659129	+	0.373810i
$333$		0			0
$334$	10.0667	+	17.4360i	0.550826	+	0.954058i
$335$	6.17752	−	10.6998i	0.337514	−	0.584591i
$336$		0			0
$337$	19.2071	+	6.99081i	1.04628	+	0.380813i	0.807256	−	0.590201i	$-0.200952\pi$
$337$	19.2071	+	6.99081i	1.04628	+	0.380813i	0.239020	+	0.971015i	$0.423174\pi$
$338$	−8.96198	+	3.26189i	−0.487468	+	0.177424i
$339$		0			0
$340$	−1.28864	−	7.30823i	−0.0698862	−	0.396344i
$341$	0.832119			0.0450618
$342$		0			0
$343$	18.4712			0.997352
$344$	−5.56330	−	31.5510i	−0.299953	−	1.70112i
$345$		0			0
$346$	−8.94774	+	3.25671i	−0.481033	+	0.175082i
$347$	−20.7528	−	7.55342i	−1.11407	−	0.405489i	−0.281586	−	0.959536i	$-0.590860\pi$
$347$	−20.7528	−	7.55342i	−1.11407	−	0.405489i	−0.832485	+	0.554047i	$0.813083\pi$
$348$		0			0
$349$	9.26264	−	16.0434i	0.495818	−	0.858782i	−0.504171	−	0.863604i	$-0.668202\pi$
$349$	9.26264	−	16.0434i	0.495818	−	0.858782i	0.999988	+	0.00482248i	$0.00153505\pi$
$350$	−1.64631	−	2.85149i	−0.0879988	−	0.152418i
$351$		0			0
$352$	0.402856	−	2.28471i	0.0214723	−	0.121775i
$353$	15.5544	+	26.9410i	0.827876	+	1.43392i	0.899701	+	0.436506i	$0.143784\pi$
$353$	15.5544	+	26.9410i	0.827876	+	1.43392i	−0.0718253	+	0.997417i	$0.522882\pi$
$354$		0			0
$355$	−19.5364	−	16.3930i	−1.03689	−	0.870051i
$356$	1.84787	+	0.672569i	0.0979369	+	0.0356461i
$357$		0			0
$358$	−4.41534	+	3.70491i	−0.233358	+	0.195811i
$359$	2.95218	+	16.7427i	0.155810	+	0.883643i	0.958041	+	0.286630i	$0.0925350\pi$
$359$	2.95218	+	16.7427i	0.155810	+	0.883643i	−0.802231	+	0.597013i	$0.796354\pi$
$360$		0			0
$361$	17.9479	+	6.23481i	0.944626	+	0.328148i
$362$	−4.92808			−0.259014
$363$		0			0
$364$	−3.65910	+	3.07035i	−0.191789	+	0.160930i
$365$	24.3862	−	8.87587i	1.27643	−	0.464584i
$366$		0			0
$367$	17.6138	+	14.7797i	0.919433	+	0.771496i	0.973890	−	0.227020i	$-0.0728983\pi$
$367$	17.6138	+	14.7797i	0.919433	+	0.771496i	−0.0544568	+	0.998516i	$0.517343\pi$
$368$	0.0184183	−	0.0319015i	0.000960121	−	0.00166298i
$369$		0			0
$370$	3.74850	−	21.2588i	0.194875	−	1.10519i
$371$	−0.695470	+	3.94421i	−0.0361070	+	0.204773i
$372$		0			0
$373$	−1.71348	+	2.96783i	−0.0887205	+	0.153668i	−0.906971	−	0.421194i	$-0.861611\pi$
$373$	−1.71348	+	2.96783i	−0.0887205	+	0.153668i	0.818250	+	0.574863i	$0.194944\pi$
$374$	0.662255	+	0.555698i	0.0342444	+	0.0287345i
$375$		0			0
$376$	−22.5993	+	8.22546i	−1.16547	+	0.424196i
$377$	−6.86618	+	5.76141i	−0.353626	+	0.296728i
$378$		0			0
$379$	−12.1898			−0.626150			−0.313075	−	0.949728i	$-0.601359\pi$
$379$	−12.1898			−0.626150			−0.313075	+	0.949728i	$0.601359\pi$
$380$	13.3503	+	2.25281i	0.684855	+	0.115567i
$381$		0			0
$382$	0.499123	+	2.83067i	0.0255373	+	0.144829i
$383$	7.09492	−	5.95335i	0.362534	−	0.304202i	−0.443266	−	0.896390i	$-0.646180\pi$
$383$	7.09492	−	5.95335i	0.362534	−	0.304202i	0.805800	+	0.592188i	$0.201736\pi$
$384$		0			0
$385$	−2.59714	−	0.945283i	−0.132363	−	0.0481761i
$386$	1.07351	+	0.900783i	0.0546403	+	0.0458486i
$387$		0			0
$388$	−0.0619563	−	0.107311i	−0.00314535	−	0.00544791i
$389$	6.33363	−	35.9198i	0.321128	−	1.82120i	−0.214469	−	0.976731i	$-0.568802\pi$
$389$	6.33363	−	35.9198i	0.321128	−	1.82120i	0.535596	−	0.844474i	$-0.320087\pi$
$390$		0			0
$391$	−1.05051	−	1.81953i	−0.0531264	−	0.0920177i
$392$	−0.0522619	+	0.0905203i	−0.00263962	+	0.00457196i
$393$		0			0
$394$	−17.5753	−	6.39689i	−0.885432	−	0.322271i
$395$	−38.5933	+	14.0468i	−1.94184	+	0.706772i
$396$		0			0
$397$	−2.72075	−	15.4302i	−0.136551	−	0.774417i	−0.973767	−	0.227546i	$-0.926930\pi$
$397$	−2.72075	−	15.4302i	−0.136551	−	0.774417i	0.837217	−	0.546871i	$-0.184181\pi$
$398$	15.6777			0.785851
$399$		0			0
$400$	−0.0591253			−0.00295627
$401$	1.60426	+	9.09819i	0.0801127	+	0.454342i	0.998305	+	0.0582059i	$0.0185380\pi$
$401$	1.60426	+	9.09819i	0.0801127	+	0.454342i	−0.918192	+	0.396136i	$0.870351\pi$
$402$		0			0
$403$	−2.78952	+	1.01530i	−0.138956	+	0.0505757i
$404$	12.0270	+	4.37748i	0.598367	+	0.217788i
$405$		0			0
$406$	−7.12196	+	12.3356i	−0.353457	+	0.612205i
$407$	−1.99454	−	3.45464i	−0.0988655	−	0.171240i
$408$		0			0
$409$	2.77972	−	15.7645i	0.137448	−	0.779507i	−0.835676	−	0.549223i	$-0.814924\pi$
$409$	2.77972	−	15.7645i	0.137448	−	0.779507i	0.973124	−	0.230283i	$-0.0739653\pi$
$410$	9.49912	+	16.4530i	0.469128	+	0.812554i
$411$		0			0
$412$	−6.73783	−	5.65371i	−0.331949	−	0.278538i
$413$	9.26517	+	3.37225i	0.455909	+	0.165937i
$414$		0			0
$415$	10.9363	−	9.17664i	0.536841	−	0.450463i
$416$	1.43717	+	8.15058i	0.0704629	+	0.399615i
$417$		0			0
$418$	−1.36009	+	0.798656i	−0.0665242	+	0.0390635i
$419$	−20.9828			−1.02508			−0.512538	−	0.858665i	$-0.671294\pi$
$419$	−20.9828			−1.02508			−0.512538	+	0.858665i	$0.671294\pi$
$420$		0			0
$421$	−15.2365	+	12.7849i	−0.742581	+	0.623099i	−0.933529	−	0.358501i	$-0.883288\pi$
$421$	−15.2365	+	12.7849i	−0.742581	+	0.623099i	0.190949	+	0.981600i	$0.438844\pi$
$422$	17.4234	−	6.34160i	0.848157	−	0.308704i
$423$		0			0
$424$	3.28177	+	2.75374i	0.159377	+	0.133733i
$425$	−1.68614	+	2.92047i	−0.0817896	+	0.141664i
$426$		0			0
$427$	1.15611	−	6.55661i	0.0559479	−	0.317297i
$428$	2.74200	−	15.5507i	0.132540	−	0.751670i
$429$		0			0
$430$	−12.5706	+	21.7729i	−0.606207	+	1.04998i
$431$	29.0292	+	24.3584i	1.39829	+	1.17330i	0.961854	+	0.273563i	$0.0882021\pi$
$431$	29.0292	+	24.3584i	1.39829	+	1.17330i	0.436431	+	0.899738i	$0.356242\pi$
$432$		0			0
$433$	−1.89780	+	0.690744i	−0.0912026	+	0.0331950i	−0.387218	−	0.921988i	$-0.626564\pi$
$433$	−1.89780	+	0.690744i	−0.0912026	+	0.0331950i	0.296016	+	0.955183i	$0.404342\pi$
$434$	−3.61381	+	3.03234i	−0.173468	+	0.145557i
$435$		0			0
$436$	15.6783			0.750854
$437$	3.76991	−	0.693392i	0.180339	−	0.0331694i
$438$		0			0
$439$	−5.44356	−	30.8720i	−0.259807	−	1.47344i	−0.783425	−	0.621486i	$-0.786529\pi$
$439$	−5.44356	−	30.8720i	−0.259807	−	1.47344i	0.523618	−	0.851953i	$-0.324582\pi$
$440$	−2.26470	+	1.90031i	−0.107965	+	0.0905937i
$441$		0			0
$442$	−2.89811	−	1.05483i	−0.137849	−	0.0501729i
$443$	−13.5196	−	11.3443i	−0.642336	−	0.538984i	0.262399	−	0.964959i	$-0.415486\pi$
$443$	−13.5196	−	11.3443i	−0.642336	−	0.538984i	−0.904734	+	0.425976i	$0.859931\pi$
$444$		0			0
$445$	−2.02956	−	3.51531i	−0.0962105	−	0.166641i
$446$	−3.01202	+	17.0820i	−0.142623	+	0.808857i
$447$		0			0
$448$	6.68732	+	11.5828i	0.315946	+	0.547235i
$449$	−6.13429	+	10.6249i	−0.289495	+	0.501420i	−0.973689	−	0.227880i	$-0.926821\pi$
$449$	−6.13429	+	10.6249i	−0.289495	+	0.501420i	0.684194	+	0.729300i	$0.260154\pi$
$450$		0			0
$451$	3.29901	+	1.20074i	0.155344	+	0.0565407i
$452$	12.6887	−	4.61830i	0.596825	−	0.217226i
$453$		0			0
$454$	4.03168	+	22.8648i	0.189216	+	1.07310i
$455$	9.85978			0.462234
$456$		0			0
$457$	19.1875			0.897552			0.448776	−	0.893644i	$-0.351860\pi$
$457$	19.1875			0.897552			0.448776	+	0.893644i	$0.351860\pi$
$458$	0.896622	+	5.08499i	0.0418964	+	0.237606i
$459$		0			0
$460$	2.56670	−	0.934204i	0.119673	−	0.0435575i
$461$	37.0933	+	13.5009i	1.72761	+	0.628798i	0.998456	−	0.0555528i	$-0.0176921\pi$
$461$	37.0933	+	13.5009i	1.72761	+	0.628798i	0.729153	+	0.684351i	$0.239914\pi$
$462$		0			0
$463$	−7.09286	+	12.2852i	−0.329633	+	0.570942i	−0.982439	−	0.186584i	$-0.940258\pi$
$463$	−7.09286	+	12.2852i	−0.329633	+	0.570942i	0.652806	+	0.757525i	$0.273592\pi$
$464$	0.127889	+	0.221510i	0.00593708	+	0.0102833i
$465$		0			0
$466$	3.96848	−	22.5064i	0.183836	−	1.04259i
$467$	14.8935	+	25.7963i	0.689190	+	1.19371i	0.972100	+	0.234566i	$0.0753668\pi$
$467$	14.8935	+	25.7963i	0.689190	+	1.19371i	−0.282910	+	0.959146i	$0.591300\pi$
$468$		0			0
$469$	9.91534	+	8.31996i	0.457848	+	0.384180i
$470$	17.7344	+	6.45480i	0.818028	+	0.297738i
$471$		0			0
$472$	8.07919	−	6.77925i	0.371875	−	0.312040i
$473$	0.806751	+	4.57531i	0.0370945	+	0.210373i
$474$		0			0
$475$	−3.98932	−	4.68383i	−0.183043	−	0.214909i
$476$	7.77446			0.356342
$477$		0			0
$478$	−5.63816	+	4.73097i	−0.257883	+	0.216390i
$479$	−0.368241	+	0.134029i	−0.0168254	+	0.00612393i	−0.350419	−	0.936593i	$-0.613961\pi$
$479$	−0.368241	+	0.134029i	−0.0168254	+	0.00612393i	0.333594	+	0.942717i	$0.391739\pi$
$480$		0			0
$481$	10.9014	+	9.14738i	0.497062	+	0.417085i
$482$	−4.78359	+	8.28541i	−0.217886	+	0.377390i
$483$		0			0
$484$	2.30706	−	13.0840i	0.104866	−	0.594726i
$485$	−0.0444153	+	0.251892i	−0.00201679	+	0.0114378i
$486$		0			0
$487$	12.1163	−	20.9861i	0.549043	−	0.950971i	−0.449297	−	0.893383i	$-0.648325\pi$
$487$	12.1163	−	20.9861i	0.549043	−	0.950971i	0.998340	−	0.0575887i	$-0.0183412\pi$
$488$	−5.45542	−	4.57764i	−0.246955	−	0.207220i
$489$		0			0
$490$	0.0770768	−	0.0280537i	0.00348198	−	0.00126734i
$491$	−26.1052	+	21.9049i	−1.17811	+	0.988552i	−0.178121	+	0.984009i	$0.557002\pi$
$491$	−26.1052	+	21.9049i	−1.17811	+	0.988552i	−0.999990	+	0.00454368i	$0.998554\pi$
$492$		0			0
$493$	14.5885			0.657034
$494$	3.58496	−	4.33683i	0.161295	−	0.195123i
$495$		0			0
$496$	0.0147100	+	0.0834248i	0.000660501	+	0.00374589i
$497$	20.4670	−	17.1739i	0.918072	−	0.770354i
$498$		0			0
$499$	27.7215	+	10.0898i	1.24099	+	0.451682i	0.877346	−	0.479858i	$-0.159312\pi$
$499$	27.7215	+	10.0898i	1.24099	+	0.451682i	0.363640	+	0.931540i	$0.381534\pi$
$500$	8.53849	+	7.16464i	0.381853	+	0.320412i
$501$		0			0
$502$	2.72580	+	4.72123i	0.121659	+	0.210719i
$503$	4.04870	−	22.9613i	0.180522	−	1.02379i	−0.751052	−	0.660243i	$-0.770453\pi$
$503$	4.04870	−	22.9613i	0.180522	−	1.02379i	0.931574	−	0.363551i	$-0.118436\pi$
$504$		0			0
$505$	−13.2096	−	22.8797i	−0.587820	−	1.01813i
$506$	−0.159100	+	0.275570i	−0.00707287	+	0.0122506i
$507$		0			0
$508$	−6.39363	−	2.32709i	−0.283671	−	0.103248i
$509$	6.16132	−	2.24254i	0.273096	−	0.0993987i	−0.201842	−	0.979418i	$-0.564693\pi$
$509$	6.16132	−	2.24254i	0.273096	−	0.0993987i	0.474938	+	0.880019i	$0.342471\pi$
$510$		0			0
$511$	4.72106	+	26.7744i	0.208847	+	1.18443i
$512$	0.473897			0.0209435
$513$		0			0
$514$	−14.8803			−0.656343
$515$	3.15270	+	17.8799i	0.138925	+	0.787881i
$516$		0			0
$517$	3.27719	−	1.19280i	0.144131	−	0.0524592i
$518$	21.2512	+	7.73480i	0.933724	+	0.339848i
$519$		0			0
$520$	5.27332	−	9.13366i	0.231250	−	0.400537i
$521$	6.23055	+	10.7916i	0.272965	+	0.472790i	0.969620	−	0.244617i	$-0.0786622\pi$
$521$	6.23055	+	10.7916i	0.272965	+	0.472790i	−0.696654	+	0.717407i	$0.745329\pi$
$522$		0			0
$523$	−4.67483	+	26.5123i	−0.204416	+	1.15930i	0.693940	+	0.720033i	$0.255873\pi$
$523$	−4.67483	+	26.5123i	−0.204416	+	1.15930i	−0.898356	+	0.439268i	$0.855238\pi$
$524$	12.0150	+	20.8106i	0.524878	+	0.909116i
$525$		0			0
$526$	9.83615	+	8.25351i	0.428877	+	0.359870i
$527$	4.54024	+	1.65251i	0.197776	+	0.0719846i
$528$		0			0
$529$	−17.0266	+	14.2870i	−0.740288	+	0.621175i
$530$	−0.583778	−	3.31077i	−0.0253577	−	0.143811i
$531$		0			0
$532$	−4.75295	+	13.3639i	−0.206066	+	0.579399i
$533$	−12.5243			−0.542490
$534$		0			0
$535$	−24.9688	+	20.9513i	−1.07950	+	0.905806i
$536$	13.0103	−	4.73535i	0.561958	−	0.204536i
$537$		0			0
$538$	11.6250	+	9.75449i	0.501187	+	0.420546i
$539$	0.00757866	−	0.0131266i	0.000326436	−	0.000565404i
$540$		0			0
$541$	−4.69506	+	26.6270i	−0.201856	+	1.14478i	0.700454	+	0.713698i	$0.252981\pi$
$541$	−4.69506	+	26.6270i	−0.201856	+	1.14478i	−0.902310	+	0.431087i	$0.858130\pi$
$542$	0.707081	−	4.01006i	0.0303717	−	0.172247i
$543$		0			0
$544$	6.73530	−	11.6659i	0.288774	−	0.500171i
$545$	−24.7913	−	20.8024i	−1.06194	−	0.891077i
$546$		0			0
$547$	0.416527	−	0.151603i	0.0178094	−	0.00648209i	−0.333100	−	0.942891i	$-0.608095\pi$
$547$	0.416527	−	0.151603i	0.0178094	−	0.00648209i	0.350909	+	0.936409i	$0.385872\pi$
$548$	18.1395	−	15.2208i	0.774881	−	0.650202i
$549$		0			0
$550$	0.510734			0.0217778
$551$	−8.91875	+	25.0769i	−0.379951	+	1.06831i
$552$		0			0
$553$	−7.47148	−	42.3729i	−0.317720	−	1.80188i
$554$	3.18210	−	2.67010i	0.135195	−	0.113442i
$555$		0			0
$556$	3.66328	+	1.33332i	0.155357	+	0.0565455i
$557$	−21.8248	−	18.3131i	−0.924745	−	0.775953i	0.0501217	−	0.998743i	$-0.484039\pi$
$557$	−21.8248	−	18.3131i	−0.924745	−	0.775953i	−0.974866	+	0.222790i	$0.928484\pi$
$558$		0			0
$559$	−8.28699	−	14.3535i	−0.350502	−	0.607088i
$560$	0.0488583	−	0.277089i	0.00206464	−	0.0117092i
$561$		0			0
$562$	14.3564	+	24.8660i	0.605587	+	1.04891i
$563$	0.992259	−	1.71864i	0.0418187	−	0.0724322i	−0.844358	−	0.535779i	$-0.820018\pi$
$563$	0.992259	−	1.71864i	0.0418187	−	0.0724322i	0.886177	+	0.463347i	$0.153351\pi$
$564$		0			0
$565$	−26.1917	−	9.53298i	−1.10189	−	0.401056i
$566$	−8.08260	+	2.94182i	−0.339737	+	0.123654i
$567$		0			0
$568$	−4.96270	−	28.1449i	−0.208230	−	1.18093i
$569$	11.7638			0.493165			0.246583	−	0.969122i	$-0.420692\pi$
$569$	11.7638			0.493165			0.246583	+	0.969122i	$0.420692\pi$
$570$		0			0
$571$	3.64227			0.152424			0.0762122	−	0.997092i	$-0.475717\pi$
$571$	3.64227			0.152424			0.0762122	+	0.997092i	$0.475717\pi$
$572$	−0.128660	−	0.729669i	−0.00537956	−	0.0305090i
$573$		0			0
$574$	−18.7029	+	6.80730i	−0.780644	+	0.284131i
$575$	−1.16637	−	0.424525i	−0.0486412	−	0.0177039i
$576$		0			0
$577$	−14.6591	+	25.3903i	−0.610266	+	1.05701i	0.380929	+	0.924604i	$0.375604\pi$
$577$	−14.6591	+	25.3903i	−0.610266	+	1.05701i	−0.991195	+	0.132408i	$0.957729\pi$
$578$	−4.96492	−	8.59949i	−0.206513	−	0.357692i
$579$		0			0
$580$	−3.29339	+	18.6777i	−0.136750	+	0.775550i
$581$	7.47818	+	12.9526i	0.310247	+	0.537364i
$582$		0			0
$583$	−0.475900	−	0.399328i	−0.0197098	−	0.0165385i
$584$	27.3276	+	9.94643i	1.13082	+	0.411586i
$585$		0			0
$586$	2.78564	−	2.33743i	0.115074	−	0.0965585i
$587$	−1.18701	−	6.73189i	−0.0489933	−	0.277855i	0.950463	−	0.310839i	$-0.100610\pi$
$587$	−1.18701	−	6.73189i	−0.0489933	−	0.277855i	−0.999456	+	0.0329842i	$0.989499\pi$
$588$		0			0
$589$	−5.61628	+	6.79417i	−0.231415	+	0.279949i
$590$	−8.27631			−0.340730
$591$		0			0
$592$	0.311089	−	0.261034i	0.0127857	−	0.0107284i
$593$	11.3880	−	4.14489i	0.467649	−	0.170210i	−0.0974379	−	0.995242i	$-0.531065\pi$
$593$	11.3880	−	4.14489i	0.467649	−	0.170210i	0.565087	+	0.825031i	$0.308843\pi$
$594$		0			0
$595$	−12.2934	−	10.3154i	−0.503980	−	0.422889i
$596$	−6.44609	+	11.1650i	−0.264042	+	0.457334i
$597$		0			0
$598$	0.197119	−	1.11792i	0.00806079	−	0.0457150i
$599$	5.09358	−	28.8871i	0.208118	−	1.18030i	−0.684339	−	0.729164i	$-0.739909\pi$
$599$	5.09358	−	28.8871i	0.208118	−	1.18030i	0.892457	−	0.451132i	$-0.148980\pi$
$600$		0			0
$601$	0.410130	−	0.710366i	0.0167295	−	0.0289764i	−0.857539	−	0.514418i	$-0.828008\pi$
$601$	0.410130	−	0.710366i	0.0167295	−	0.0289764i	0.874269	+	0.485442i	$0.161341\pi$
$602$	−20.1766	−	16.9302i	−0.822339	−	0.690024i
$603$		0			0
$604$	11.0617	−	4.02611i	0.450092	−	0.163820i
$605$	−21.0082	+	17.6280i	−0.854105	+	0.716679i
$606$		0			0
$607$	−32.5654			−1.32179			−0.660895	−	0.750479i	$-0.729823\pi$
$607$	−32.5654			−1.32179			−0.660895	+	0.750479i	$0.729823\pi$
$608$	15.9354	+	18.7096i	0.646266	+	0.758775i
$609$		0			0
$610$	0.970437	+	5.50362i	0.0392919	+	0.222835i
$611$	−9.53074	+	7.99724i	−0.385573	+	0.323534i
$612$		0			0
$613$	−7.50134	−	2.73027i	−0.302976	−	0.110274i	0.186058	−	0.982539i	$-0.440429\pi$
$613$	−7.50134	−	2.73027i	−0.302976	−	0.110274i	−0.489035	+	0.872264i	$0.662651\pi$
$614$	4.19459	+	3.51968i	0.169280	+	0.142043i
$615$		0			0
$616$	−1.54859	−	2.68224i	−0.0623945	−	0.108070i
$617$	7.03390	−	39.8912i	0.283174	−	1.60596i	−0.428561	−	0.903513i	$-0.640979\pi$
$617$	7.03390	−	39.8912i	0.283174	−	1.60596i	0.711735	−	0.702448i	$-0.247910\pi$
$618$		0			0
$619$	5.70368	+	9.87906i	0.229250	+	0.397073i	0.957586	−	0.288147i	$-0.0930393\pi$
$619$	5.70368	+	9.87906i	0.229250	+	0.397073i	−0.728336	+	0.685220i	$0.759706\pi$
$620$	−3.14068	+	5.43982i	−0.126133	+	0.218468i
$621$		0			0
$622$	2.13903	+	0.778544i	0.0857674	+	0.0312168i
$623$	3.99602	−	1.45443i	0.160097	−	0.0582707i
$624$		0			0
$625$	−5.22075	−	29.6084i	−0.208830	−	1.18433i
$626$	18.1789			0.726576
$627$		0			0
$628$	18.8693			0.752966
$629$	−4.02207	−	22.8103i	−0.160370	−	0.909506i
$630$		0			0
$631$	−1.01202	+	0.368346i	−0.0402879	+	0.0146636i	−0.362086	−	0.932145i	$-0.617935\pi$
$631$	−1.01202	+	0.368346i	−0.0402879	+	0.0146636i	0.321798	+	0.946808i	$0.395713\pi$
$632$	−43.2483	−	15.7411i	−1.72032	−	0.626146i
$633$		0			0
$634$	−4.01707	+	6.95778i	−0.159538	+	0.276329i
$635$	7.02229	+	12.1630i	0.278671	+	0.482672i
$636$		0			0
$637$	−0.00938966	+	0.0532514i	−0.000372032	+	0.00210990i
$638$	−1.10472	−	1.91344i	−0.0437364	−	0.0757536i
$639$		0			0
$640$	13.2724	+	11.1369i	0.524639	+	0.440225i
$641$	4.39393	+	1.59926i	0.173550	+	0.0631670i	0.427334	−	0.904094i	$-0.359453\pi$
$641$	4.39393	+	1.59926i	0.173550	+	0.0631670i	−0.253784	+	0.967261i	$0.581675\pi$
$642$		0			0
$643$	−17.3255	+	14.5378i	−0.683250	+	0.573315i	−0.916954	−	0.398993i	$-0.869360\pi$
$643$	−17.3255	+	14.5378i	−0.683250	+	0.573315i	0.233704	+	0.972308i	$0.424915\pi$
$644$	0.496901	+	2.81807i	0.0195806	+	0.111047i
$645$		0			0
$646$	−9.00703	+	1.65664i	−0.354377	+	0.0651797i
$647$	−22.0479			−0.866791			−0.433396	−	0.901204i	$-0.642685\pi$
$647$	−22.0479			−0.866791			−0.433396	+	0.901204i	$0.642685\pi$
$648$		0			0
$649$	−1.17159	+	0.983080i	−0.0459889	+	0.0385893i
$650$	−1.71213	+	0.623166i	−0.0671554	+	0.0244426i
$651$		0			0
$652$	−17.2875	−	14.5059i	−0.677029	−	0.568095i
$653$	−19.4898	+	33.7573i	−0.762694	+	1.32103i	0.178763	+	0.983892i	$0.442791\pi$
$653$	−19.4898	+	33.7573i	−0.762694	+	1.32103i	−0.941457	+	0.337133i	$0.890543\pi$
$654$		0			0
$655$	8.61334	−	48.8487i	0.336551	−	1.90868i
$656$	−0.0620621	+	0.351972i	−0.00242312	+	0.0137422i
$657$		0			0
$658$	−9.88578	+	17.1227i	−0.385388	+	0.667511i
$659$	−12.0981	−	10.1515i	−0.471274	−	0.395446i	0.375985	−	0.926626i	$-0.377304\pi$
$659$	−12.0981	−	10.1515i	−0.471274	−	0.395446i	−0.847259	+	0.531180i	$0.821749\pi$
$660$		0			0
$661$	38.5419	−	14.0281i	1.49911	−	0.545631i	0.543278	−	0.839553i	$-0.317183\pi$
$661$	38.5419	−	14.0281i	1.49911	−	0.545631i	0.955829	+	0.293922i	$0.0949606\pi$
$662$	−10.8418	+	9.09738i	−0.421380	+	0.353580i
$663$		0			0
$664$	15.9982			0.620852
$665$	25.2472	−	14.8254i	0.979045	−	0.574903i
$666$		0			0
$667$	0.932419	+	5.28801i	0.0361034	+	0.204753i
$668$	−21.5141	+	18.0525i	−0.832407	+	0.698472i
$669$		0			0
$670$	−10.2096	−	3.71599i	−0.394432	−	0.143561i
$671$	0.791108	+	0.663818i	0.0305404	+	0.0256264i
$672$		0			0
$673$	15.1446	+	26.2311i	0.583780	+	1.01114i	0.995026	+	0.0996119i	$0.0317601\pi$
$673$	15.1446	+	26.2311i	0.583780	+	1.01114i	−0.411247	+	0.911524i	$0.634907\pi$
$674$	3.12122	−	17.7013i	0.120225	−	0.681830i
$675$		0			0
$676$	−6.65183	−	11.5213i	−0.255839	−	0.443127i
$677$	1.35710	−	2.35056i	0.0521575	−	0.0903394i	−0.838768	−	0.544489i	$-0.816724\pi$
$677$	1.35710	−	2.35056i	0.0521575	−	0.0903394i	0.890925	+	0.454150i	$0.150057\pi$
$678$		0			0
$679$	−0.251801	−	0.0916481i	−0.00966324	−	0.00351713i
$680$	−16.1306	+	5.87105i	−0.618579	+	0.225144i
$681$		0			0
$682$	−0.127068	−	0.720637i	−0.00486567	−	0.0275946i
$683$	−32.8803			−1.25813			−0.629065	−	0.777353i	$-0.716562\pi$
$683$	−32.8803			−1.25813			−0.629065	+	0.777353i	$0.716562\pi$
$684$		0			0
$685$	−48.8786			−1.86755
$686$	−2.82062	−	15.9965i	−0.107692	−	0.610751i
$687$		0			0
$688$	−0.444440	+	0.161763i	−0.0169441	+	0.00616716i
$689$	2.08260	+	0.758003i	0.0793406	+	0.0288776i
$690$		0			0
$691$	22.7010	−	39.3193i	0.863586	−	1.49578i	−0.00485771	−	0.999988i	$-0.501546\pi$
$691$	22.7010	−	39.3193i	0.863586	−	1.49578i	0.868444	−	0.495787i	$-0.165120\pi$
$692$	−6.64125	−	11.5030i	−0.252463	−	0.437278i
$693$		0			0
$694$	−3.37242	+	19.1259i	−0.128015	+	0.726010i
$695$	−4.02347	−	6.96886i	−0.152619	−	0.264344i
$696$		0			0
$697$	15.6156	+	13.1031i	0.591484	+	0.496314i
$698$	−15.3084	−	5.57180i	−0.579431	−	0.210896i
$699$		0			0
$700$	3.51842	−	2.95230i	0.132984	−	0.111587i
$701$	−0.281364	−	1.59569i	−0.0106270	−	0.0602685i	0.979033	−	0.203701i	$-0.0652971\pi$
$701$	−0.281364	−	1.59569i	−0.0106270	−	0.0602685i	−0.989660	+	0.143433i	$0.954186\pi$
$702$		0			0
$703$	41.6687	+	7.03142i	1.57156	+	0.265195i
$704$	−2.07461			−0.0781897
$705$		0			0
$706$	20.9564	−	17.5845i	0.788703	−	0.661800i
$707$	26.0085	−	9.46632i	0.978151	−	0.356018i
$708$		0			0
$709$	27.7652	+	23.2977i	1.04274	+	0.874965i	0.992312	−	0.123763i	$-0.0394961\pi$
$709$	27.7652	+	23.2977i	1.04274	+	0.874965i	0.0504309	+	0.998728i	$0.483941\pi$
$710$	−11.2135	+	19.4223i	−0.420834	+	0.728906i
$711$		0			0
$712$	0.789876	−	4.47961i	0.0296019	−	0.167881i
$713$	−0.308811	+	1.75135i	−0.0115651	+	0.0655887i
$714$		0			0
$715$	−0.764700	+	1.32450i	−0.0285982	+	0.0495335i
$716$	−6.15910	−	5.16810i	−0.230176	−	0.193141i
$717$		0			0
$718$	14.0488	−	5.11333i	0.524295	−	0.190828i
$719$	−4.76676	+	3.99979i	−0.177770	+	0.149167i	−0.727331	−	0.686287i	$-0.759239\pi$
$719$	−4.76676	+	3.99979i	−0.177770	+	0.149167i	0.549561	+	0.835454i	$0.314795\pi$
$720$		0			0
$721$	−19.0205			−0.708362
$722$	2.65880	−	16.4954i	0.0989501	−	0.613896i
$723$		0			0
$724$	−1.19372	−	6.76990i	−0.0443641	−	0.251601i
$725$	6.60220	−	5.53990i	0.245199	−	0.205747i
$726$		0			0
$727$	−15.2255	−	5.54163i	−0.564683	−	0.205528i	0.0438755	−	0.999037i	$-0.486030\pi$
$727$	−15.2255	−	5.54163i	−0.564683	−	0.205528i	−0.608558	+	0.793509i	$0.708252\pi$
$728$	8.46404	+	7.10217i	0.313698	+	0.263224i
$729$		0			0
$730$	−11.4106	−	19.7637i	−0.422325	−	0.731489i
$731$	−4.68433	+	26.5661i	−0.173256	+	0.982584i
$732$		0			0
$733$	−9.85251	−	17.0650i	−0.363911	−	0.630312i	0.624690	−	0.780873i	$-0.285225\pi$
$733$	−9.85251	−	17.0650i	−0.363911	−	0.630312i	−0.988601	+	0.150561i	$0.951892\pi$
$734$	10.1099	−	17.5109i	0.373165	−	0.646340i
$735$		0			0
$736$	4.65910	+	1.69577i	0.171737	+	0.0625071i
$737$	−1.88666	+	0.686688i	−0.0694960	+	0.0252945i
$738$		0			0
$739$	3.34049	+	18.9449i	0.122882	+	0.696898i	0.982543	+	0.186034i	$0.0595634\pi$
$739$	3.34049	+	18.9449i	0.122882	+	0.696898i	−0.859661	+	0.510864i	$0.829326\pi$
$740$	30.1121			1.10694
$741$		0			0
$742$	3.52198			0.129296
$743$	−2.61293	−	14.8187i	−0.0958591	−	0.543644i	−0.994481	−	0.104920i	$-0.966542\pi$
$743$	−2.61293	−	14.8187i	−0.0958591	−	0.543644i	0.898622	−	0.438725i	$-0.144570\pi$
$744$		0			0
$745$	25.0069	−	9.10175i	0.916181	−	0.333462i
$746$	2.83187	+	1.03072i	0.103682	+	0.0377372i
$747$		0			0
$748$	−0.602968	+	1.04437i	−0.0220467	+	0.0381860i
$749$	−17.0736	−	29.5723i	−0.623855	−	1.08055i
$750$		0			0
$751$	−4.74469	+	26.9085i	−0.173136	+	0.981904i	0.767137	+	0.641483i	$0.221681\pi$
$751$	−4.74469	+	26.9085i	−0.173136	+	0.981904i	−0.940273	+	0.340421i	$0.889430\pi$
$752$	0.177519	+	0.307471i	0.00647344	+	0.0112123i
$753$		0			0
$754$	6.03802	+	5.06650i	0.219892	+	0.184511i
$755$	−22.8332	−	8.31061i	−0.830986	−	0.302454i
$756$		0			0
$757$	−5.61128	+	4.70842i	−0.203945	+	0.171131i	−0.739040	−	0.673662i	$-0.764720\pi$
$757$	−5.61128	+	4.70842i	−0.203945	+	0.171131i	0.535094	+	0.844792i	$0.320276\pi$
$758$	1.86143	+	10.5567i	0.0676103	+	0.383437i
$759$		0			0
$760$	−0.230552	−	31.3169i	−0.00836300	−	1.13598i
$761$	−23.1830			−0.840384			−0.420192	−	0.907435i	$-0.638037\pi$
$761$	−23.1830			−0.840384			−0.420192	+	0.907435i	$0.638037\pi$
$762$		0			0
$763$	25.9722	−	21.7933i	0.940259	−	0.788971i
$764$	−3.76769	+	1.37133i	−0.136310	+	0.0496129i
$765$		0			0
$766$	−6.23917	−	5.23529i	−0.225430	−	0.189159i
$767$	2.72803	−	4.72508i	0.0985033	−	0.170613i
$768$		0			0
$769$	−0.775845	+	4.40003i	−0.0279777	+	0.158669i	−0.995596	−	0.0937492i	$-0.970115\pi$
$769$	−0.775845	+	4.40003i	−0.0279777	+	0.158669i	0.967618	+	0.252418i	$0.0812259\pi$
$770$	−0.422046	+	2.39354i	−0.0152095	+	0.0862572i
$771$		0			0
$772$	−0.977407	+	1.69292i	−0.0351776	+	0.0609294i
$773$	3.04782	+	2.55742i	0.109622	+	0.0919841i	0.695951	−	0.718089i	$-0.254983\pi$
$773$	3.04782	+	2.55742i	0.109622	+	0.0919841i	−0.586329	+	0.810073i	$0.699427\pi$
$774$		0			0
$775$	2.68227	−	0.976265i	0.0963499	−	0.0350685i
$776$	−0.219570	+	0.184241i	−0.00788210	+	0.00661386i
$777$		0			0
$778$	−32.0746			−1.14993
$779$	−32.0702	+	18.8319i	−1.14903	+	0.674721i
$780$		0			0
$781$	0.719656	+	4.08137i	0.0257513	+	0.146043i
$782$	−1.41534	+	1.18762i	−0.0506126	+	0.0424690i
$783$		0			0
$784$	0.00144999		0.000527755i	5.17855e−5		1.88484e-5i
$785$	−29.8371	−	25.0363i	−1.06493	−	0.893583i
$786$		0			0
$787$	16.6866	+	28.9020i	0.594813	+	1.03025i	0.993573	+	0.113191i	$0.0361073\pi$
$787$	16.6866	+	28.9020i	0.594813	+	1.03025i	−0.398760	+	0.917055i	$0.630559\pi$
$788$	4.53044	−	25.6934i	0.161390	−	0.915290i
$789$		0			0
$790$	18.0582	+	31.2778i	0.642484	+	1.11281i
$791$	14.6001	−	25.2882i	0.519121	−	0.899144i
$792$		0			0
$793$	−3.46198	−	1.26006i	−0.122939	−	0.0447460i
$794$	−12.9474	+	4.71248i	−0.459487	+	0.167240i
$795$		0			0
$796$	3.79756	+	21.5370i	0.134601	+	0.763360i
$797$	−3.56036			−0.126115			−0.0630573	−	0.998010i	$-0.520085\pi$
$797$	−3.56036			−0.126115			−0.0630573	+	0.998010i	$0.520085\pi$
$798$		0			0
$799$	20.2499			0.716390
$800$	−1.38191	−	7.83721i	−0.0488579	−	0.277087i
$801$		0			0
$802$	7.63429	−	2.77865i	0.269576	−	0.0981176i
$803$	−3.96286	−	1.44236i	−0.139846	−	0.0508999i
$804$		0			0
$805$	2.95336	−	5.11538i	0.104092	−	0.180293i
$806$	1.30525	+	2.26075i	0.0459753	+	0.0796316i
$807$		0			0
$808$	5.14099	−	29.1560i	0.180859	−	1.02570i
$809$	−19.2476	−	33.3379i	−0.676710	−	1.17210i	−0.975966	−	0.217924i	$-0.930072\pi$
$809$	−19.2476	−	33.3379i	−0.676710	−	1.17210i	0.299255	−	0.954173i	$-0.403262\pi$
$810$		0			0
$811$	−9.88713	−	8.29628i	−0.347184	−	0.291322i	0.452474	−	0.891778i	$-0.350541\pi$
$811$	−9.88713	−	8.29628i	−0.347184	−	0.291322i	−0.799658	+	0.600456i	$0.794986\pi$
$812$	−18.6710	−	6.79569i	−0.655224	−	0.238482i
$813$		0			0
$814$	−2.68723	+	2.25486i	−0.0941874	+	0.0790327i
$815$	8.08899	+	45.8750i	0.283345	+	1.60693i
$816$		0			0
$817$	−42.8021	−	24.2934i	−1.49745	−	0.849919i
$818$	−14.0770			−0.492190
$819$		0			0
$820$	−20.3011	+	17.0347i	−0.708946	+	0.594876i
$821$	40.7301	−	14.8246i	1.42149	−	0.517381i	0.487011	−	0.873396i	$-0.338087\pi$
$821$	40.7301	−	14.8246i	1.42149	−	0.517381i	0.934480	+	0.356015i	$0.115865\pi$
$822$		0			0
$823$	−10.3452	−	8.68068i	−0.360612	−	0.302590i	0.444422	−	0.895817i	$-0.353409\pi$
$823$	−10.3452	−	8.68068i	−0.360612	−	0.302590i	−0.805035	+	0.593228i	$0.797853\pi$
$824$	−10.1728	+	17.6198i	−0.354385	+	0.613813i
$825$		0			0
$826$	1.50563	−	8.53882i	0.0523874	−	0.297104i
$827$	2.89012	−	16.3907i	0.100499	−	0.569960i	−0.892424	−	0.451199i	$-0.850997\pi$
$827$	2.89012	−	16.3907i	0.100499	−	0.569960i	0.992923	−	0.118761i	$-0.0378923\pi$
$828$		0			0
$829$	24.4334	−	42.3198i	0.848605	−	1.46983i	−0.0338476	−	0.999427i	$-0.510776\pi$
$829$	24.4334	−	42.3198i	0.848605	−	1.46983i	0.882453	−	0.470401i	$-0.155891\pi$
$830$	−9.61721	−	8.06980i	−0.333818	−	0.280107i
$831$		0			0
$832$	6.95471	−	2.53131i	0.241111	−	0.0877573i
$833$	0.0674192	−	0.0565714i	0.00233594	−	0.00196008i
$834$		0			0
$835$	57.9718			2.00620
$836$	−1.42659	−	1.67495i	−0.0493398	−	0.0579294i
$837$		0			0
$838$	3.20414	+	18.1716i	0.110685	+	0.627728i
$839$	27.7401	−	23.2767i	0.957695	−	0.803601i	−0.0228818	−	0.999738i	$-0.507284\pi$
$839$	27.7401	−	23.2767i	0.957695	−	0.803601i	0.980577	+	0.196137i	$0.0628397\pi$
$840$		0			0
$841$	−7.78446	−	2.83331i	−0.268430	−	0.0977004i
$842$	13.3987	+	11.2429i	0.461751	+	0.387455i
$843$		0			0
$844$	12.9321	+	22.3991i	0.445142	+	0.771008i
$845$	−4.76857	+	27.0439i	−0.164044	+	0.930339i
$846$		0			0
$847$	−14.3653	−	24.8814i	−0.493598	−	0.854936i
$848$	0.0316221	−	0.0547710i	0.00108591	−	0.00188084i
$849$		0			0
$850$	2.78668	+	1.01427i	0.0955825	+	0.0347892i
$851$	8.01114	−	2.91582i	0.274618	−	0.0999530i
$852$		0			0
$853$	8.79369	+	49.8715i	0.301090	+	1.70757i	0.641360	+	0.767240i	$0.278370\pi$
$853$	8.79369	+	49.8715i	0.301090	+	1.70757i	−0.340270	+	0.940328i	$0.610519\pi$
$854$	−5.85473			−0.200345
$855$		0			0
$856$	−36.5259			−1.24843
$857$	7.66849	+	43.4902i	0.261951	+	1.48560i	0.777580	+	0.628784i	$0.216447\pi$
$857$	7.66849	+	43.4902i	0.261951	+	1.48560i	−0.515629	+	0.856812i	$0.672442\pi$
$858$		0			0
$859$	4.35457	−	1.58493i	0.148576	−	0.0540772i	−0.266662	−	0.963790i	$-0.585921\pi$
$859$	4.35457	−	1.58493i	0.148576	−	0.0540772i	0.415238	+	0.909713i	$0.363698\pi$
$860$	−32.9552	−	11.9947i	−1.12376	−	0.409016i
$861$		0			0
$862$	16.6621	−	28.8596i	0.567513	−	0.982962i
$863$	23.1202	+	40.0454i	0.787021	+	1.36316i	0.927784	+	0.373117i	$0.121711\pi$
$863$	23.1202	+	40.0454i	0.787021	+	1.36316i	−0.140763	+	0.990043i	$0.544956\pi$
$864$		0			0
$865$	−4.76099	+	27.0009i	−0.161879	+	0.918059i
$866$	0.888003	+	1.53807i	0.0301756	+	0.0522656i
$867$		0			0
$868$	−5.04101	−	4.22991i	−0.171103	−	0.143573i
$869$	6.27156	+	2.28266i	0.212748	+	0.0774340i
$870$		0			0
$871$	5.48680	−	4.60397i	0.185913	−	0.156000i
$872$	−6.29756	−	35.7152i	−0.213262	−	1.20947i
$873$		0			0
$874$	−1.17617	−	3.15896i	−0.0397847	−	0.106853i
$875$	24.1037			0.814854
$876$		0			0
$877$	−16.0646	+	13.4798i	−0.542465	+	0.455182i	−0.872380	−	0.488829i	$-0.837424\pi$
$877$	−16.0646	+	13.4798i	−0.542465	+	0.455182i	0.329915	+	0.944011i	$0.392980\pi$
$878$	−25.9047	+	9.42853i	−0.874240	+	0.318197i
$879$		0			0
$880$	0.0334331	+	0.0280537i	0.00112703	+	0.000945689i
$881$	8.69800	−	15.0654i	0.293043	−	0.507565i	−0.681485	−	0.731832i	$-0.738665\pi$
$881$	8.69800	−	15.0654i	0.293043	−	0.507565i	0.974528	+	0.224267i	$0.0719988\pi$
$882$		0			0
$883$	2.73190	−	15.4934i	0.0919356	−	0.521393i	−0.903708	−	0.428150i	$-0.859166\pi$
$883$	2.73190	−	15.4934i	0.0919356	−	0.521393i	0.995643	−	0.0932430i	$-0.0297233\pi$
$884$	0.747053	−	4.23675i	0.0251261	−	0.142497i
$885$		0			0
$886$	−7.75995	+	13.4406i	−0.260701	+	0.451547i
$887$	−17.7044	−	14.8557i	−0.594455	−	0.498807i	0.295203	−	0.955435i	$-0.404613\pi$
$887$	−17.7044	−	14.8557i	−0.594455	−	0.498807i	−0.889658	+	0.456627i	$0.849057\pi$
$888$		0			0
$889$	−13.8262	+	5.03234i	−0.463717	+	0.168779i
$890$	−2.73442	+	2.29445i	−0.0916580	+	0.0769102i
$891$		0			0
$892$	−24.1958			−0.810136
$893$	−12.3799	+	34.8086i	−0.414276	+	1.16482i
$894$		0			0
$895$	2.88191	+	16.3441i	0.0963317	+	0.546324i
$896$	−13.9047	+	11.6674i	−0.464522	+	0.389781i
$897$		0			0
$898$	10.1382	+	3.68999i	0.338315	+	0.123136i
$899$	−9.45929	−	7.93729i	−0.315485	−	0.264723i
$900$		0			0
$901$	−1.80360	−	3.12392i	−0.0600865	−	0.104073i
$902$	0.536102	−	3.04038i	0.0178502	−	0.101234i
$903$		0			0
$904$	−15.6172	−	27.0498i	−0.519421	−	0.899663i
$905$	−7.09492	+	12.2888i	−0.235843	+	0.408492i
$906$		0			0
$907$	−17.4662	−	6.35716i	−0.579954	−	0.211086i	0.0353511	−	0.999375i	$-0.488745\pi$
$907$	−17.4662	−	6.35716i	−0.579954	−	0.211086i	−0.615305	+	0.788289i	$0.710967\pi$
$908$	−30.4337	+	11.0769i	−1.00998	+	0.367601i
$909$		0			0
$910$	−1.50563	−	8.53882i	−0.0499110	−	0.283059i
$911$	4.35410			0.144258			0.0721289	−	0.997395i	$-0.477021\pi$
$911$	4.35410			0.144258			0.0721289	+	0.997395i	$0.477021\pi$
$912$		0			0
$913$	−2.31996			−0.0767793
$914$	−2.93000	−	16.6168i	−0.0969157	−	0.549636i
$915$		0			0
$916$	−6.76827	+	2.46345i	−0.223630	+	0.0813946i
$917$	48.8312	+	17.7731i	1.61255	+	0.586919i
$918$		0			0
$919$	3.91488	−	6.78077i	0.129140	−	0.223677i	−0.794204	−	0.607652i	$-0.792112\pi$
$919$	3.91488	−	6.78077i	0.129140	−	0.223677i	0.923344	+	0.383975i	$0.125445\pi$
$920$	−3.15910	−	5.47172i	−0.104152	−	0.180397i
$921$		0			0
$922$	6.02781	−	34.1854i	0.198515	−	1.12584i
$923$	−7.39234	−	12.8039i	−0.243322	−	0.421446i
$924$		0			0
$925$	−10.4823	−	8.79569i	−0.344656	−	0.289201i
$926$	11.7224	+	4.26660i	0.385222	+	0.140209i
$927$		0			0
$928$	−26.3726	+	22.1292i	−0.865722	+	0.726427i
$929$	0.423496	+	2.40176i	0.0138944	+	0.0787993i	0.990967	−	0.134109i	$-0.0428174\pi$
$929$	0.423496	+	2.40176i	0.0138944	+	0.0787993i	−0.977072	+	0.212909i	$0.931706\pi$
$930$		0			0
$931$	0.0560265	+	0.150475i	0.00183619	+	0.00493163i
$932$	31.8792			1.04424
$933$		0			0
$934$	20.0660	−	16.8374i	0.656579	−	0.550935i
$935$	2.33915	−	0.851379i	0.0764982	−	0.0278431i
$936$		0			0
$937$	−34.5522	−	28.9927i	−1.12877	−	0.947150i	−0.129756	−	0.991546i	$-0.541419\pi$
$937$	−34.5522	−	28.9927i	−1.12877	−	0.947150i	−0.999014	+	0.0443957i	$0.985864\pi$
$938$	5.69119	−	9.85743i	0.185824	−	0.321856i
$939$		0			0
$940$	−4.57145	+	25.9260i	−0.149104	+	0.845613i
$941$	−9.45290	+	53.6100i	−0.308156	+	1.74764i	0.300111	+	0.953904i	$0.402976\pi$
$941$	−9.45290	+	53.6100i	−0.308156	+	1.74764i	−0.608266	+	0.793733i	$0.708135\pi$
$942$		0			0
$943$	−3.75150	+	6.49778i	−0.122166	+	0.211597i
$944$	−0.119271	−	0.100080i	−0.00388193	−	0.00325732i
$945$		0			0
$946$	3.83915	−	1.39733i	0.124821	−	0.0454313i
$947$	−8.22487	+	6.90149i	−0.267272	+	0.224268i	−0.766567	−	0.642164i	$-0.778037\pi$
$947$	−8.22487	+	6.90149i	−0.267272	+	0.224268i	0.499295	+	0.866432i	$0.333592\pi$
$948$		0			0
$949$	15.0446			0.488368
$950$	−3.44713	+	4.17009i	−0.111840	+	0.135296i
$951$		0			0
$952$	−3.12280	−	17.7103i	−0.101211	−	0.573993i
$953$	7.21760	−	6.05628i	0.233801	−	0.196182i	−0.518359	−	0.855163i	$-0.673457\pi$
$953$	7.21760	−	6.05628i	0.233801	−	0.196182i	0.752159	+	0.658981i	$0.229012\pi$
$954$		0			0
$955$	7.77719	+	2.83067i	0.251664	+	0.0915982i
$956$	−7.86484	−	6.59938i	−0.254367	−	0.213439i
$957$		0			0
$958$	0.172304	+	0.298439i	0.00556689	+	0.00964214i
$959$	8.89198	−	50.4289i	0.287137	−	1.62843i
$960$		0			0
$961$	13.4552	+	23.3050i	0.434038	+	0.751776i
$962$	6.25718	−	10.8378i	0.201740	−	0.349423i
$963$		0			0
$964$	−12.5407	−	4.56444i	−0.403909	−	0.147011i
$965$	3.79174	−	1.38008i	0.122060	−	0.0444263i
$966$		0			0
$967$	4.75847	+	26.9866i	0.153022	+	0.867831i	0.960572	+	0.278031i	$0.0896820\pi$
$967$	4.75847	+	26.9866i	0.153022	+	0.867831i	−0.807550	+	0.589799i	$0.799207\pi$
$968$	−30.7320			−0.987765
$969$		0			0
$970$	0.224927			0.00722197
$971$	3.48932	+	19.7889i	0.111978	+	0.635057i	0.988202	+	0.153154i	$0.0489431\pi$
$971$	3.48932	+	19.7889i	0.111978	+	0.635057i	−0.876225	+	0.481903i	$0.839946\pi$
$972$		0			0
$973$	7.92185	−	2.88332i	0.253963	−	0.0924349i
$974$	−20.0247	−	7.28840i	−0.641633	−	0.233535i
$975$		0			0
$976$	−0.0525666	+	0.0910480i	−0.00168262	+	0.00291438i
$977$	−7.06371	−	12.2347i	−0.225988	−	0.391423i	0.730627	−	0.682776i	$-0.239228\pi$
$977$	−7.06371	−	12.2347i	−0.225988	−	0.391423i	−0.956615	+	0.291354i	$0.905894\pi$
$978$		0			0
$979$	−0.114542	+	0.649602i	−0.00366079	+	0.0207614i
$980$	0.0572085	+	0.0990880i	0.00182746	+	0.00316525i
$981$		0			0
$982$	22.9565	+	19.2628i	0.732572	+	0.614701i
$983$	31.2494	+	11.3739i	0.996702	+	0.362770i	0.788312	−	0.615276i	$-0.210955\pi$
$983$	31.2494	+	11.3739i	0.996702	+	0.362770i	0.208390	+	0.978046i	$0.433178\pi$
$984$		0			0
$985$	−41.2545	+	34.6166i	−1.31448	+	1.10298i
$986$	−2.22772	−	12.6340i	−0.0709451	−	0.402350i
$987$		0			0
$988$	6.82605	+	3.87430i	0.217165	+	0.123258i
$989$	−9.92902			−0.315724
$990$		0			0
$991$	−20.7324	+	17.3965i	−0.658585	+	0.552619i	−0.909662	−	0.415348i	$-0.863660\pi$
$991$	−20.7324	+	17.3965i	−0.658585	+	0.552619i	0.251077	+	0.967967i	$0.419215\pi$
$992$	−10.7144	+	3.89971i	−0.340181	+	0.123816i
$993$		0			0
$994$	−17.9984	−	15.1025i	−0.570875	−	0.479021i
$995$	22.5710	−	39.0942i	0.715550	−	1.23937i
$996$		0			0
$997$	−9.46467	+	53.6768i	−0.299749	+	1.69996i	0.347497	+	0.937681i	$0.387032\pi$
$997$	−9.46467	+	53.6768i	−0.299749	+	1.69996i	−0.647247	+	0.762281i	$0.724080\pi$
$998$	4.50485	−	25.5483i	0.142599	−	0.808717i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.y.a.28.1	✓	6
3.2	odd	2		513.2.y.c.28.1	yes	6
19.6	even	9		9747.2.a.bd.1.1		3
19.13	odd	18		9747.2.a.v.1.3		3
19.17	even	9	inner	513.2.y.a.55.1	yes	6
57.17	odd	18		513.2.y.c.55.1	yes	6
57.32	even	18		9747.2.a.bb.1.1		3
57.44	odd	18		9747.2.a.u.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
513.2.y.a.28.1	✓	6	1.1	even	1	trivial
513.2.y.a.55.1	yes	6	19.17	even	9	inner
513.2.y.c.28.1	yes	6	3.2	odd	2
513.2.y.c.55.1	yes	6	57.17	odd	18
9747.2.a.u.1.3		3	57.44	odd	18
9747.2.a.v.1.3		3	19.13	odd	18
9747.2.a.bb.1.1		3	57.32	even	18
9747.2.a.bd.1.1		3	19.6	even	9

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.152704 - 0.866025i) q^{2} +(1.15270 - 0.419550i) q^{4} +(-2.37939 - 0.866025i) q^{5} +(1.32635 - 2.29731i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(-0.386659 + 2.19285i) q^{10} +(0.205737 + 0.356347i) q^{11} +(-1.12449 - 0.943555i) q^{13} +(-2.19207 - 0.797847i) q^{14} +(-0.0320889 + 0.0269258i) q^{16} +(0.414878 + 2.35289i) q^{17} +(-4.29813 - 0.725293i) q^{19} -3.10607 q^{20} +(0.277189 - 0.232589i) q^{22} +(-0.826352 + 0.300767i) q^{23} +(1.08125 + 0.907278i) q^{25} +(-0.645430 + 1.11792i) q^{26} +(0.565055 - 3.20459i) q^{28} +(1.06031 - 6.01330i) q^{29} +(1.01114 - 1.75135i) q^{31} +(-4.31908 - 3.62414i) q^{32} +(1.97431 - 0.718589i) q^{34} +(-5.14543 + 4.31753i) q^{35} -9.69459 q^{37} +(0.0282185 + 3.83305i) q^{38} +(1.24763 + 7.07564i) q^{40} +(6.53596 - 5.48432i) q^{41} +(10.6099 + 3.86170i) q^{43} +(0.386659 + 0.324446i) q^{44} +(0.386659 + 0.669713i) q^{46} +(1.47178 - 8.34689i) q^{47} +(-0.0184183 - 0.0319015i) q^{49} +(0.620615 - 1.07494i) q^{50} +(-1.69207 - 0.615862i) q^{52} +(-1.41875 + 0.516382i) q^{53} +(-0.180922 - 1.02606i) q^{55} -7.52704 q^{56} -5.36959 q^{58} +(0.645430 + 3.66041i) q^{59} +(2.35844 - 0.858402i) q^{61} +(-1.67112 - 0.608239i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(1.85844 + 3.21891i) q^{65} +(-0.847296 + 4.80526i) q^{67} +(1.46538 + 2.53812i) q^{68} +(4.52481 + 3.79677i) q^{70} +(9.46451 + 3.44480i) q^{71} +(-7.85117 + 6.58791i) q^{73} +(1.48040 + 8.39576i) q^{74} +(-5.25877 + 0.967233i) q^{76} +1.09152 q^{77} +(12.4251 - 10.4259i) q^{79} +(0.0996702 - 0.0362770i) q^{80} +(-5.74763 - 4.82283i) q^{82} +(-2.81908 + 4.88279i) q^{83} +(1.05051 - 5.95772i) q^{85} +(1.72416 - 9.77817i) q^{86} +(0.583778 - 1.01113i) q^{88} +(1.22803 + 1.03044i) q^{89} +(-3.65910 + 1.33180i) q^{91} +(-0.826352 + 0.693392i) q^{92} -7.45336 q^{94} +(9.59879 + 5.44804i) q^{95} +(-0.0175410 - 0.0994798i) q^{97} +(-0.0248149 + 0.0208222i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 9 q^{4} - 3 q^{5} + 9 q^{7} - 6 q^{8} - 9 q^{10} - 9 q^{11} + 6 q^{13} - 24 q^{14} + 9 q^{16} + 24 q^{17} - 12 q^{19} + 6 q^{20} - 9 q^{22} - 6 q^{23} + 9 q^{25} + 12 q^{26} + 42 q^{28}+ \cdots + 27 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^4 - 3 * q^5 + 9 * q^7 - 6 * q^8 - 9 * q^10 - 9 * q^11 + 6 * q^13 - 24 * q^14 + 9 * q^16 + 24 * q^17 - 12 * q^19 + 6 * q^20 - 9 * q^22 - 6 * q^23 + 9 * q^25 + 12 * q^26 + 42 * q^28 + 12 * q^29 - 9 * q^32 - 18 * q^34 - 15 * q^35 - 54 * q^37 + 15 * q^38 - 9 * q^40 + 6 * q^41 + 15 * q^43 + 9 * q^44 + 9 * q^46 - 6 * q^47 - 12 * q^49 + 15 * q^50 - 21 * q^52 - 6 * q^53 - 18 * q^55 - 66 * q^56 - 18 * q^58 - 12 * q^59 + 6 * q^61 - 24 * q^62 - 12 * q^64 + 3 * q^65 - 3 * q^67 + 33 * q^68 + 24 * q^71 - 21 * q^73 + 3 * q^74 - 9 * q^76 - 54 * q^77 + 33 * q^79 + 15 * q^80 - 18 * q^82 + 9 * q^85 + 12 * q^86 - 9 * q^88 - 15 * q^89 + 15 * q^91 - 6 * q^92 - 18 * q^94 + 15 * q^95 + 45 * q^97 + 27 * q^98

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