LMFDB - Embedded newform 162.2.g.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	162.25
Dual form			162.2.g.b.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893633 - 0.448799i) q^{2} +(-0.977769 + 1.42967i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-1.15296 + 3.85116i) q^{5} +(-0.232129 + 1.71643i) q^{6} +(-0.663579 + 1.53835i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-1.08794 - 2.79578i) q^{9} +O(q^{10})$	\(q+(0.893633 - 0.448799i) q^{2} +(-0.977769 + 1.42967i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-1.15296 + 3.85116i) q^{5} +(-0.232129 + 1.71643i) q^{6} +(-0.663579 + 1.53835i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-1.08794 - 2.79578i) q^{9} +(0.698073 + 3.95897i) q^{10} +(0.0131573 + 0.00311835i) q^{11} +(0.562892 + 1.63803i) q^{12} +(3.84080 - 2.52614i) q^{13} +(0.0974140 + 1.67253i) q^{14} +(-4.37857 - 5.41390i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(4.83704 + 1.76054i) q^{17} +(-2.22696 - 2.01014i) q^{18} +(2.66092 - 0.968497i) q^{19} +(2.40060 + 3.22457i) q^{20} +(-1.55051 - 2.45285i) q^{21} +(0.0131573 - 0.00311835i) q^{22} +(-0.253001 - 0.586523i) q^{23} +(1.23817 + 1.21117i) q^{24} +(-9.32465 - 6.13292i) q^{25} +(2.29854 - 3.98119i) q^{26} +(5.06081 + 1.17823i) q^{27} +(0.837684 + 1.45091i) q^{28} +(-0.262835 + 4.51270i) q^{29} +(-6.34259 - 2.87294i) q^{30} +(-9.48738 - 1.10892i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-0.0173231 + 0.0157617i) q^{33} +(5.11267 - 0.597585i) q^{34} +(-5.15935 - 4.32920i) q^{35} +(-2.89223 - 0.796865i) q^{36} +(6.03321 - 5.06246i) q^{37} +(1.94323 - 2.05970i) q^{38} +(-0.143865 + 7.96107i) q^{39} +(3.59244 + 1.80419i) q^{40} +(6.30010 + 3.16403i) q^{41} +(-2.48643 - 1.49608i) q^{42} +(4.34864 - 4.60929i) q^{43} +(0.0103583 - 0.00869166i) q^{44} +(12.0213 - 0.966392i) q^{45} +(-0.489321 - 0.410589i) q^{46} +(-11.3730 + 1.32931i) q^{47} +(1.65004 + 0.526657i) q^{48} +(2.87751 + 3.04998i) q^{49} +(-11.0853 - 1.29568i) q^{50} +(-7.24650 + 5.19399i) q^{51} +(0.267296 - 4.58930i) q^{52} +(-2.96943 - 5.14321i) q^{53} +(5.05129 - 1.21838i) q^{54} +(-0.0271791 + 0.0470757i) q^{55} +(1.39975 + 0.920630i) q^{56} +(-1.21713 + 4.75122i) q^{57} +(1.79042 + 4.15065i) q^{58} +(-2.42002 + 0.573555i) q^{59} +(-6.95732 + 0.279198i) q^{60} +(1.39556 + 1.87456i) q^{61} +(-8.97591 + 3.26697i) q^{62} +(5.02282 + 0.181594i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(5.30025 + 17.7041i) q^{65} +(-0.00840662 + 0.0218597i) q^{66} +(0.232730 + 3.99581i) q^{67} +(4.30065 - 2.82858i) q^{68} +(1.08591 + 0.211774i) q^{69} +(-6.55350 - 1.55321i) q^{70} +(-1.01165 - 5.73737i) q^{71} +(-2.94223 + 0.585927i) q^{72} +(1.45371 - 8.24441i) q^{73} +(3.11944 - 7.23168i) q^{74} +(17.8854 - 7.33464i) q^{75} +(0.812139 - 2.71273i) q^{76} +(-0.0135280 + 0.0181713i) q^{77} +(3.44436 + 7.17884i) q^{78} +(-4.39144 + 2.20546i) q^{79} +4.02004 q^{80} +(-6.63278 + 6.08327i) q^{81} +7.04998 q^{82} +(13.5542 - 6.80719i) q^{83} +(-2.89339 - 0.221040i) q^{84} +(-12.3570 + 16.5984i) q^{85} +(1.81744 - 6.07068i) q^{86} +(-6.19470 - 4.78814i) q^{87} +(0.00535572 - 0.0124160i) q^{88} +(1.34899 - 7.65049i) q^{89} +(10.3089 - 6.25877i) q^{90} +(1.33740 + 7.58479i) q^{91} +(-0.621545 - 0.147309i) q^{92} +(10.8619 - 12.4796i) q^{93} +(-9.56667 + 6.29210i) q^{94} +(0.661893 + 11.3643i) q^{95} +(1.71089 - 0.269899i) q^{96} +(0.923670 + 3.08527i) q^{97} +(3.94027 + 1.43414i) q^{98} +(-0.00559615 - 0.0401776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$3$	−0.977769	+	1.42967i	−0.564515	+	0.825423i
$3$	−0.977769	+	1.42967i	−0.564515	+	0.825423i
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	−1.15296	+	3.85116i	−0.515620	+	1.72229i	0.161920	+	0.986804i	$0.448231\pi$
$5$	−1.15296	+	3.85116i	−0.515620	+	1.72229i	−0.677540	+	0.735486i	$0.736954\pi$
$6$	−0.232129	+	1.71643i	−0.0947664	+	0.700728i
$7$	−0.663579	+	1.53835i	−0.250809	+	0.581441i	−0.996382	−	0.0849824i	$-0.972917\pi$
$7$	−0.663579	+	1.53835i	−0.250809	+	0.581441i	0.745573	+	0.666424i	$0.232176\pi$
$8$	0.173648	−	0.984808i	0.0613939	−	0.348182i
$9$	−1.08794	−	2.79578i	−0.362646	−	0.931927i
$10$	0.698073	+	3.95897i	0.220750	+	1.25194i
$11$	0.0131573	+	0.00311835i	0.00396709	+	0.000940217i	0.232599	−	0.972573i	$-0.425277\pi$
$11$	0.0131573	+	0.00311835i	0.00396709	+	0.000940217i	−0.228632	+	0.973513i	$0.573425\pi$
$12$	0.562892	+	1.63803i	0.162493	+	0.472859i
$13$	3.84080	−	2.52614i	1.06525	−	0.700624i	0.109254	−	0.994014i	$-0.465154\pi$
$13$	3.84080	−	2.52614i	1.06525	−	0.700624i	0.955993	+	0.293390i	$0.0947834\pi$
$14$	0.0974140	+	1.67253i	0.0260350	+	0.447003i
$15$	−4.37857	−	5.41390i	−1.13054	−	1.39786i
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	4.83704	+	1.76054i	1.17315	+	0.426993i	0.853779	−	0.520635i	$-0.174305\pi$
$17$	4.83704	+	1.76054i	1.17315	+	0.426993i	0.319375	+	0.947628i	$0.396527\pi$
$18$	−2.22696	−	2.01014i	−0.524900	−	0.473794i
$19$	2.66092	−	0.968497i	0.610457	−	0.222188i	−0.0182459	−	0.999834i	$-0.505808\pi$
$19$	2.66092	−	0.968497i	0.610457	−	0.222188i	0.628703	+	0.777645i	$0.283586\pi$
$20$	2.40060	+	3.22457i	0.536791	+	0.721035i
$21$	−1.55051	−	2.45285i	−0.338349	−	0.535256i
$22$	0.0131573	−	0.00311835i	0.00280516	−	0.000664834i
$23$	−0.253001	−	0.586523i	−0.0527544	−	0.122298i	0.889801	−	0.456350i	$-0.150843\pi$
$23$	−0.253001	−	0.586523i	−0.0527544	−	0.122298i	−0.942555	+	0.334051i	$0.891584\pi$
$24$	1.23817	+	1.21117i	0.252740	+	0.247230i
$25$	−9.32465	−	6.13292i	−1.86493	−	1.22658i
$26$	2.29854	−	3.98119i	0.450781	−	0.780775i
$27$	5.06081	+	1.17823i	0.973953	+	0.226751i
$28$	0.837684	+	1.45091i	0.158307	+	0.274196i
$29$	−0.262835	+	4.51270i	−0.0488072	+	0.837987i	0.881722	+	0.471769i	$0.156384\pi$
$29$	−0.262835	+	4.51270i	−0.0488072	+	0.837987i	−0.930529	+	0.366218i	$0.880653\pi$
$30$	−6.34259	−	2.87294i	−1.15799	−	0.524524i
$31$	−9.48738	−	1.10892i	−1.70398	−	0.199167i	−0.792321	−	0.610105i	$-0.791127\pi$
$31$	−9.48738	−	1.10892i	−1.70398	−	0.199167i	−0.911663	+	0.410938i	$0.865201\pi$
$32$	−0.686242	−	0.727374i	−0.121312	−	0.128583i
$33$	−0.0173231	+	0.0157617i	−0.00301556	+	0.00274376i
$34$	5.11267	−	0.597585i	0.876815	−	0.102485i
$35$	−5.15935	−	4.32920i	−0.872088	−	0.731769i
$36$	−2.89223	−	0.796865i	−0.482039	−	0.132811i
$37$	6.03321	−	5.06246i	0.991853	−	0.832264i	0.00601844	−	0.999982i	$-0.498084\pi$
$37$	6.03321	−	5.06246i	0.991853	−	0.832264i	0.985835	+	0.167718i	$0.0536398\pi$
$38$	1.94323	−	2.05970i	0.315233	−	0.334127i
$39$	−0.143865	+	7.96107i	−0.0230368	+	1.27479i
$40$	3.59244	+	1.80419i	0.568015	+	0.285268i
$41$	6.30010	+	3.16403i	0.983910	+	0.494138i	0.866625	−	0.498960i	$-0.166285\pi$
$41$	6.30010	+	3.16403i	0.983910	+	0.494138i	0.117285	+	0.993098i	$0.462581\pi$
$42$	−2.48643	−	1.49608i	−0.383664	−	0.230850i
$43$	4.34864	−	4.60929i	0.663162	−	0.702911i	−0.305248	−	0.952273i	$-0.598739\pi$
$43$	4.34864	−	4.60929i	0.663162	−	0.702911i	0.968410	+	0.249362i	$0.0802209\pi$
$44$	0.0103583	−	0.00869166i	0.00156158	−	0.00131032i
$45$	12.0213	−	0.966392i	1.79204	−	0.144061i
$46$	−0.489321	−	0.410589i	−0.0721465	−	0.0605381i
$47$	−11.3730	+	1.32931i	−1.65892	+	0.193900i	−0.893321	−	0.449419i	$-0.851631\pi$
$47$	−11.3730	+	1.32931i	−1.65892	+	0.193900i	−0.765598	+	0.643319i	$0.777557\pi$
$48$	1.65004	+	0.526657i	0.238163	+	0.0760164i
$49$	2.87751	+	3.04998i	0.411073	+	0.435712i
$50$	−11.0853	−	1.29568i	−1.56769	−	0.183237i
$51$	−7.24650	+	5.19399i	−1.01471	+	0.727305i
$52$	0.267296	−	4.58930i	0.0370673	−	0.636421i
$53$	−2.96943	−	5.14321i	−0.407883	−	0.706474i	0.586769	−	0.809754i	$-0.300399\pi$
$53$	−2.96943	−	5.14321i	−0.407883	−	0.706474i	−0.994652	+	0.103280i	$0.967066\pi$
$54$	5.05129	−	1.21838i	0.687394	−	0.165801i
$55$	−0.0271791	+	0.0470757i	−0.00366484	+	0.00634768i
$56$	1.39975	+	0.920630i	0.187049	+	0.123024i
$57$	−1.21713	+	4.75122i	−0.161213	+	0.629314i
$58$	1.79042	+	4.15065i	0.235093	+	0.545007i
$59$	−2.42002	+	0.573555i	−0.315060	+	0.0746705i	−0.385103	−	0.922873i	$-0.625834\pi$
$59$	−2.42002	+	0.573555i	−0.315060	+	0.0746705i	0.0700438	+	0.997544i	$0.477686\pi$
$60$	−6.95732	+	0.279198i	−0.898186	+	0.0360443i
$61$	1.39556	+	1.87456i	0.178683	+	0.240013i	0.882437	−	0.470431i	$-0.155902\pi$
$61$	1.39556	+	1.87456i	0.178683	+	0.240013i	−0.703754	+	0.710444i	$0.748494\pi$
$62$	−8.97591	+	3.26697i	−1.13994	+	0.414905i
$63$	5.02282	+	0.181594i	0.632816	+	0.0228787i
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	5.30025	+	17.7041i	0.657415	+	2.19592i
$66$	−0.00840662	+	0.0218597i	−0.00103478	+	0.00269075i
$67$	0.232730	+	3.99581i	0.0284324	+	0.488166i	0.982226	+	0.187703i	$0.0601042\pi$
$67$	0.232730	+	3.99581i	0.0284324	+	0.488166i	−0.953793	+	0.300463i	$0.902859\pi$
$68$	4.30065	−	2.82858i	0.521530	−	0.343016i
$69$	1.08591	+	0.211774i	0.130729	+	0.0254946i
$70$	−6.55350	−	1.55321i	−0.783293	−	0.185644i
$71$	−1.01165	−	5.73737i	−0.120061	−	0.680901i	−0.984119	−	0.177509i	$-0.943196\pi$
$71$	−1.01165	−	5.73737i	−0.120061	−	0.680901i	0.864058	−	0.503392i	$-0.167915\pi$
$72$	−2.94223	+	0.585927i	−0.346745	+	0.0690521i
$73$	1.45371	−	8.24441i	0.170144	−	0.964935i	−0.773457	−	0.633849i	$-0.781474\pi$
$73$	1.45371	−	8.24441i	0.170144	−	0.964935i	0.943601	−	0.331086i	$-0.107415\pi$
$74$	3.11944	−	7.23168i	0.362628	−	0.840666i
$75$	17.8854	−	7.33464i	2.06523	−	0.846931i
$76$	0.812139	−	2.71273i	0.0931587	−	0.311172i
$77$	−0.0135280	+	0.0181713i	−0.00154166	+	0.00207081i
$78$	3.44436	+	7.17884i	0.389997	+	0.812844i
$79$	−4.39144	+	2.20546i	−0.494076	+	0.248134i	−0.678348	−	0.734741i	$-0.737304\pi$
$79$	−4.39144	+	2.20546i	−0.494076	+	0.248134i	0.184272	+	0.982875i	$0.441007\pi$
$80$	4.02004			0.449454
$81$	−6.63278	+	6.08327i	−0.736976	+	0.675919i
$82$	7.04998			0.778541
$83$	13.5542	−	6.80719i	1.48777	−	0.747186i	0.495191	−	0.868784i	$-0.335098\pi$
$83$	13.5542	−	6.80719i	1.48777	−	0.747186i	0.992579	+	0.121598i	$0.0388018\pi$
$84$	−2.89339	−	0.221040i	−0.315695	−	0.0241174i
$85$	−12.3570	+	16.5984i	−1.34031	+	1.80035i
$86$	1.81744	−	6.07068i	0.195980	−	0.654619i
$87$	−6.19470	−	4.78814i	−0.664141	−	0.513343i
$88$	0.00535572	−	0.0124160i	0.000570922	−	0.00132355i
$89$	1.34899	−	7.65049i	0.142992	−	0.810950i	−0.825965	−	0.563722i	$-0.809369\pi$
$89$	1.34899	−	7.65049i	0.142992	−	0.810950i	0.968957	−	0.247229i	$-0.0795199\pi$
$90$	10.3089	−	6.25877i	1.08666	−	0.659732i
$91$	1.33740	+	7.58479i	0.140198	+	0.795102i
$92$	−0.621545	−	0.147309i	−0.0648006	−	0.0153580i
$93$	10.8619	−	12.4796i	1.12632	−	1.29407i
$94$	−9.56667	+	6.29210i	−0.986726	+	0.648980i
$95$	0.661893	+	11.3643i	0.0679088	+	1.16595i
$96$	1.71089	−	0.269899i	0.174617	−	0.0275464i
$97$	0.923670	+	3.08527i	0.0937845	+	0.313262i	0.991990	−	0.126313i	$-0.0403143\pi$
$97$	0.923670	+	3.08527i	0.0937845	+	0.313262i	−0.898206	+	0.439575i	$0.855129\pi$
$98$	3.94027	+	1.43414i	0.398027	+	0.144870i
$99$	−0.00559615	−	0.0401776i	−0.000562434	−	0.00403800i
$100$	−10.4877	+	3.81719i	−1.04877	+	0.381719i
$101$	2.80596	+	3.76905i	0.279203	+	0.375035i	0.919498	−	0.393094i	$-0.128595\pi$
$101$	2.80596	+	3.76905i	0.279203	+	0.375035i	−0.640295	+	0.768129i	$0.721188\pi$
$102$	−4.14465	+	7.89375i	−0.410382	+	0.781598i
$103$	−0.976984	+	0.231550i	−0.0962651	+	0.0228153i	−0.278466	−	0.960446i	$-0.589826\pi$
$103$	−0.976984	+	0.231550i	−0.0962651	+	0.0228153i	0.182201	+	0.983261i	$0.441678\pi$
$104$	−1.82081	−	4.22111i	−0.178545	−	0.413914i
$105$	11.2340	−	3.14322i	1.09633	−	0.306747i
$106$	−4.96185	−	3.26346i	−0.481937	−	0.316975i
$107$	−2.95229	+	5.11352i	−0.285409	+	0.494343i	−0.972708	−	0.232032i	$-0.925463\pi$
$107$	−2.95229	+	5.11352i	−0.285409	+	0.494343i	0.687299	+	0.726374i	$0.258796\pi$
$108$	3.96719	−	3.35580i	0.381743	−	0.322912i
$109$	4.08609	+	7.07731i	0.391376	+	0.677883i	0.992631	−	0.121174i	$-0.0386659\pi$
$109$	4.08609	+	7.07731i	0.391376	+	0.677883i	−0.601255	+	0.799057i	$0.705333\pi$
$110$	−0.00316065	+	0.0542663i	−0.000301357	+	0.00517409i
$111$	1.33859	+	13.5754i	0.127054	+	1.28852i
$112$	1.66404	+	0.194498i	0.157237	+	0.0183784i
$113$	−14.2211	−	15.0735i	−1.33781	−	1.41800i	−0.831366	−	0.555725i	$-0.812441\pi$
$113$	−14.2211	−	15.0735i	−1.33781	−	1.41800i	−0.506445	−	0.862272i	$-0.669041\pi$
$114$	1.04467	+	4.79209i	0.0978427	+	0.448820i
$115$	2.55049	−	0.298110i	0.237835	−	0.0277989i
$116$	3.46278	+	2.90562i	0.321511	+	0.269780i
$117$	−11.2411	−	7.98977i	−1.03924	−	0.738654i
$118$	−1.90520	+	1.59865i	−0.175388	+	0.147168i
$119$	−5.91808	+	6.27280i	−0.542510	+	0.575027i
$120$	−6.09198	+	3.37194i	−0.556119	+	0.307814i
$121$	−9.82980	−	4.93671i	−0.893618	−	0.448792i
$122$	2.08842	+	1.04884i	0.189077	+	0.0949579i
$123$	−10.6836	+	5.91340i	−0.963305	+	0.533193i
$124$	−6.55496	+	6.94785i	−0.588653	+	0.623935i
$125$	18.9722	−	15.9195i	1.69692	−	1.42389i
$126$	4.57006	−	2.09196i	0.407133	−	0.186367i
$127$	6.11180	+	5.12841i	0.542334	+	0.455072i	0.872335	−	0.488908i	$-0.162605\pi$
$127$	6.11180	+	5.12841i	0.542334	+	0.455072i	−0.330001	+	0.943981i	$0.607049\pi$
$128$	−0.993238	+	0.116093i	−0.0877907	+	0.0102613i
$129$	2.33782	+	10.7240i	0.205834	+	0.944193i
$130$	12.6820	+	13.4422i	1.11229	+	1.17896i
$131$	−8.15164	−	0.952790i	−0.712212	−	0.0832456i	−0.247731	−	0.968829i	$-0.579685\pi$
$131$	−8.15164	−	0.952790i	−0.712212	−	0.0832456i	−0.464481	+	0.885583i	$0.653759\pi$
$132$	0.00229821	+	0.0233075i	0.000200033	+	0.00202865i
$133$	−0.275847	+	4.73610i	−0.0239189	+	0.410672i
$134$	2.00129	+	3.46634i	0.172885	+	0.299446i
$135$	−10.3725	+	18.1315i	−0.892720	+	1.56051i
$136$	2.57374	−	4.45784i	0.220696	−	0.382257i
$137$	−10.6949	−	7.03413i	−0.913725	−	0.600967i	0.00321342	−	0.999995i	$-0.498977\pi$
$137$	−10.6949	−	7.03413i	−0.913725	−	0.600967i	−0.916939	+	0.399028i	$0.869348\pi$
$138$	1.06545	−	0.298109i	0.0906973	−	0.0253767i
$139$	−7.43815	−	17.2436i	−0.630896	−	1.46258i	−0.870727	−	0.491766i	$-0.836352\pi$
$139$	−7.43815	−	17.2436i	−0.630896	−	1.46258i	0.239832	−	0.970814i	$-0.422908\pi$
$140$	−6.55350	+	1.55321i	−0.553872	+	0.131270i
$141$	9.21966	−	17.5594i	0.776435	−	1.47877i
$142$	−3.47898	−	4.67307i	−0.291949	−	0.392156i
$143$	0.0584121	−	0.0212603i	0.00488467	−	0.00177787i
$144$	−2.36631	+	1.84407i	−0.197192	+	0.153673i
$145$	−17.0761	−	6.21518i	−1.41809	−	0.516143i
$146$	−2.40100	−	8.01990i	−0.198708	−	0.663731i
$147$	−7.17402	+	1.13173i	−0.591703	+	0.0933431i
$148$	−0.457937	−	7.86247i	−0.0376422	−	0.646291i
$149$	−1.82353	+	1.19935i	−0.149389	+	0.0982549i	−0.622003	−	0.783015i	$-0.713681\pi$
$149$	−1.82353	+	1.19935i	−0.149389	+	0.0982549i	0.472614	+	0.881270i	$0.343311\pi$
$150$	12.6912	−	14.5814i	1.03623	−	1.19057i
$151$	14.4265	+	3.41914i	1.17401	+	0.278245i	0.770930	−	0.636920i	$-0.219792\pi$
$151$	14.4265	+	3.41914i	1.17401	+	0.278245i	0.403079	+	0.915165i	$0.367940\pi$
$152$	−0.491719	−	2.78867i	−0.0398836	−	0.226191i
$153$	−0.340316	−	15.4387i	−0.0275129	−	1.24814i
$154$	−0.00393383	+	0.0223099i	−0.000316997	+	0.00179778i
$155$	15.2092	−	35.2589i	1.22163	−	2.83206i
$156$	6.29985	+	4.86942i	0.504392	+	0.389866i
$157$	−2.31347	+	7.72751i	−0.184635	+	0.616723i	0.814687	+	0.579901i	$0.196909\pi$
$157$	−2.31347	+	7.72751i	−0.184635	+	0.616723i	−0.999322	+	0.0368220i	$0.988277\pi$
$158$	−2.93452	+	3.94175i	−0.233458	+	0.313589i
$159$	10.2565	+	0.783545i	0.813395	+	0.0621392i
$160$	3.59244	−	1.80419i	0.284007	−	0.142634i
$161$	1.07016			0.0843407
$162$	−3.19711	+	8.41300i	−0.251188	+	0.660987i
$163$	17.6946			1.38595			0.692973	−	0.720964i	$-0.256300\pi$
$163$	17.6946			1.38595			0.692973	+	0.720964i	$0.256300\pi$
$164$	6.30010	−	3.16403i	0.491955	−	0.247069i
$165$	−0.0407280	−	0.0848864i	−0.00317067	−	0.00660840i
$166$	9.05744	−	12.1663i	0.702994	−	0.944285i
$167$	2.41890	−	8.07967i	0.187180	−	0.625224i	−0.811958	−	0.583715i	$-0.801598\pi$
$167$	2.41890	−	8.07967i	0.187180	−	0.625224i	0.999138	−	0.0415086i	$-0.0132164\pi$
$168$	−2.68483	+	1.10102i	−0.207139	+	0.0849458i
$169$	3.22137	−	7.46796i	0.247797	−	0.574459i
$170$	−3.59331	+	20.3787i	−0.275594	+	1.56297i
$171$	−5.60262	−	6.38569i	−0.428443	−	0.488326i
$172$	−1.10039	−	6.24063i	−0.0839040	−	0.475843i
$173$	−7.51741	−	1.78166i	−0.571538	−	0.135457i	−0.0653230	−	0.997864i	$-0.520808\pi$
$173$	−7.51741	−	1.78166i	−0.571538	−	0.135457i	−0.506215	+	0.862407i	$0.668956\pi$
$174$	−7.68470	−	1.49866i	−0.582575	−	0.113613i
$175$	15.6222	−	10.2749i	1.18093	−	0.776709i
$176$	−0.000786224	−	0.0134989i	−5.92639e−5	−	0.00101752i
$177$	1.54622	−	4.02064i	0.116221	−	0.302210i
$178$	−2.22803	−	7.44215i	−0.166998	−	0.557813i
$179$	−16.7997	−	6.11459i	−1.25567	−	0.457026i	−0.373355	−	0.927689i	$-0.621793\pi$
$179$	−16.7997	−	6.11459i	−1.25567	−	0.457026i	−0.882313	+	0.470663i	$0.844015\pi$
$180$	6.40348	−	10.2197i	0.477287	−	0.761730i
$181$	−12.8524	+	4.67788i	−0.955309	+	0.347704i	−0.772193	−	0.635388i	$-0.780840\pi$
$181$	−12.8524	+	4.67788i	−0.955309	+	0.347704i	−0.183115	+	0.983091i	$0.558618\pi$
$182$	4.59919	+	6.17779i	0.340915	+	0.457928i
$183$	−4.04455	+	0.162308i	−0.298982	+	0.0119982i
$184$	−0.621545	+	0.147309i	−0.0458209	+	0.0108598i
$185$	12.5403	+	29.0717i	0.921980	+	2.13739i
$186$	4.10567	−	16.0270i	0.301042	−	1.17515i
$187$	0.0581526	+	0.0382476i	0.00425254	+	0.00279694i
$188$	−5.72520	+	9.91634i	−0.417553	+	0.723223i
$189$	−5.17078	+	7.00344i	−0.376119	+	0.509425i
$190$	5.69176	+	9.85842i	0.412924	+	0.715205i
$191$	−0.157227	+	2.69948i	−0.0113765	+	0.195327i	0.987831	+	0.155530i	$0.0497084\pi$
$191$	−0.157227	+	2.69948i	−0.0113765	+	0.195327i	−0.999208	+	0.0397977i	$0.987329\pi$
$192$	1.40778	−	1.00904i	0.101598	−	0.0728210i
$193$	−9.73944	−	1.13838i	−0.701060	−	0.0819422i	−0.241907	−	0.970299i	$-0.577773\pi$
$193$	−9.73944	−	1.13838i	−0.701060	−	0.0819422i	−0.459153	+	0.888357i	$0.651847\pi$
$194$	2.21009	+	2.34256i	0.158675	+	0.168186i
$195$	−30.4935	−	9.73285i	−2.18368	−	0.696984i
$196$	4.16479	−	0.486794i	0.297485	−	0.0347710i
$197$	−1.84963	−	1.55203i	−0.131781	−	0.110577i	0.574515	−	0.818494i	$-0.305191\pi$
$197$	−1.84963	−	1.55203i	−0.131781	−	0.110577i	−0.706296	+	0.707917i	$0.749635\pi$
$198$	−0.0230326	−	0.0333925i	−0.00163685	−	0.00237310i
$199$	−10.4578	+	8.77512i	−0.741332	+	0.622052i	−0.933195	−	0.359370i	$-0.882992\pi$
$199$	−10.4578	+	8.77512i	−0.741332	+	0.622052i	0.191863	+	0.981422i	$0.438547\pi$
$200$	−7.65896	+	8.11802i	−0.541570	+	0.574031i
$201$	−5.94027	−	3.57425i	−0.418994	−	0.252108i
$202$	4.19904	+	2.10884i	0.295443	+	0.148377i
$203$	−6.76769	−	3.39886i	−0.474999	−	0.238553i
$204$	−0.161089	+	8.91423i	−0.0112785	+	0.624121i
$205$	−19.4489	+	20.6147i	−1.35837	+	1.43979i
$206$	−0.769146	+	0.645390i	−0.0535889	+	0.0449664i
$207$	−1.36454	+	1.34544i	−0.0948421	+	0.0935143i
$208$	−3.52157	−	2.95494i	−0.244177	−	0.204889i
$209$	0.0380308	−	0.00444516i	0.00263064	−	0.000307478i
$210$	8.62839	−	7.85070i	0.595416	−	0.541749i
$211$	4.10053	+	4.34631i	0.282292	+	0.299212i	0.852968	−	0.521963i	$-0.174800\pi$
$211$	4.10053	+	4.34631i	0.282292	+	0.299212i	−0.570676	+	0.821175i	$0.693319\pi$
$212$	−5.89871	−	0.689460i	−0.405125	−	0.0473523i
$213$	9.19174	+	4.16349i	0.629808	+	0.285277i
$214$	−0.343321	+	5.89460i	−0.0234690	+	0.402946i
$215$	12.7373	+	22.0616i	0.868677	+	1.50459i
$216$	2.03913	−	4.77932i	0.138745	−	0.325192i
$217$	8.00153	−	13.8591i	0.543179	−	0.940814i
$218$	6.82775	+	4.49068i	0.462434	+	0.304147i
$219$	10.3654	+	10.1395i	0.700430	+	0.685161i
$220$	0.0215302	+	0.0499127i	0.00145157	+	0.00336511i
$221$	23.0255	−	5.45714i	1.54886	−	0.367087i
$222$	7.28886	+	11.5307i	0.489196	+	0.773890i
$223$	7.99100	+	10.7338i	0.535117	+	0.718787i	0.984662	−	0.174470i	$-0.0558213\pi$
$223$	7.99100	+	10.7338i	0.535117	+	0.718787i	−0.449545	+	0.893258i	$0.648414\pi$
$224$	1.57433	−	0.573009i	0.105189	−	0.0382858i
$225$	−7.00167	+	32.7419i	−0.466778	+	2.18280i
$226$	−19.4734	−	7.08776i	−1.29535	−	0.471470i
$227$	6.69929	+	22.3772i	0.444647	+	1.48523i	0.827526	+	0.561427i	$0.189747\pi$
$227$	6.69929	+	22.3772i	0.444647	+	1.48523i	−0.382879	+	0.923798i	$0.625067\pi$
$228$	3.08424	+	3.81352i	0.204259	+	0.252557i
$229$	0.586644	+	10.0723i	0.0387665	+	0.665596i	0.960587	+	0.277979i	$0.0896646\pi$
$229$	0.586644	+	10.0723i	0.0387665	+	0.665596i	−0.921821	+	0.387617i	$0.873298\pi$
$230$	2.14541	−	1.41106i	0.141464	−	0.0930425i
$231$	−0.0127518	−	0.0371081i	−0.000839005	−	0.00244153i
$232$	4.39850	+	1.04246i	0.288776	+	0.0684411i
$233$	−0.251712	−	1.42753i	−0.0164902	−	0.0935207i	0.975452	−	0.220213i	$-0.0706751\pi$
$233$	−0.251712	−	1.42753i	−0.0164902	−	0.0935207i	−0.991942	+	0.126692i	$0.959564\pi$
$234$	−13.6312	−	2.09493i	−0.891099	−	0.136950i
$235$	7.99321	−	45.3318i	0.521420	−	2.95712i
$236$	−0.985073	+	2.28366i	−0.0641228	+	0.148653i
$237$	1.14072	−	8.43477i	0.0740975	−	0.547897i
$238$	−2.47336	+	8.26161i	−0.160324	+	0.535521i
$239$	12.7023	−	17.0622i	0.821644	−	1.10366i	−0.171317	−	0.985216i	$-0.554802\pi$
$239$	12.7023	−	17.0622i	0.821644	−	1.10366i	0.992961	−	0.118443i	$-0.0377904\pi$
$240$	−3.93067	+	5.74735i	−0.253724	+	0.370990i
$241$	8.20274	−	4.11957i	0.528385	−	0.265365i	−0.164545	−	0.986369i	$-0.552616\pi$
$241$	8.20274	−	4.11957i	0.528385	−	0.265365i	0.692930	+	0.721005i	$0.256319\pi$
$242$	−10.9998			−0.707095
$243$	−2.21177	−	15.4308i	−0.141885	−	0.989883i
$244$	2.33700			0.149611
$245$	−15.0636	+	7.56523i	−0.962379	+	0.483325i
$246$	−6.89325	+	10.0792i	−0.439498	+	0.642625i
$247$	7.77352	−	10.4417i	0.494617	−	0.664387i
$248$	−2.73954	+	9.15069i	−0.173961	+	0.581069i
$249$	−3.52084	+	26.0340i	−0.223124	+	1.64984i
$250$	9.80946	−	22.7409i	0.620405	−	1.43826i
$251$	−1.06851	+	6.05983i	−0.0674439	+	0.382493i	0.932338	+	0.361589i	$0.117766\pi$
$251$	−1.06851	+	6.05983i	−0.0674439	+	0.382493i	−0.999781	+	0.0209042i	$0.993345\pi$
$252$	3.14508	−	3.92048i	0.198122	−	0.246967i
$253$	−0.00149984	−	0.00850603i	−9.42943e−5	−	0.000534769i
$254$	7.76333	+	1.83994i	0.487114	+	0.115448i
$255$	−11.6480	−	33.8959i	−0.729423	−	2.12264i
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	0.554373	+	9.51822i	0.0345808	+	0.593730i	0.970438	+	0.241350i	$0.0775903\pi$
$257$	0.554373	+	9.51822i	0.0345808	+	0.593730i	−0.935857	+	0.352380i	$0.885373\pi$
$258$	6.90206	+	8.53408i	0.429704	+	0.531308i
$259$	3.78433	+	12.6405i	0.235147	+	0.785444i
$260$	17.3659	+	6.32068i	1.07699	+	0.391992i
$261$	12.9025	−	4.17470i	0.798642	−	0.258408i
$262$	−7.71218	+	2.80700i	−0.476460	+	0.173417i
$263$	−9.89545	−	13.2919i	−0.610180	−	0.819613i	0.384446	−	0.923147i	$-0.374392\pi$
$263$	−9.89545	−	13.2919i	−0.610180	−	0.819613i	−0.994626	+	0.103534i	$0.966985\pi$
$264$	0.0125141	+	0.0197969i	0.000770191	+	0.00121841i
$265$	23.2309	−	5.50583i	1.42706	−	0.338221i
$266$	1.87905	+	4.35614i	0.115212	+	0.267092i
$267$	9.61871	+	9.40902i	0.588656	+	0.575823i
$268$	3.34411	+	2.19946i	0.204274	+	0.134353i
$269$	−10.1199	+	17.5282i	−0.617023	+	1.06871i	0.373003	+	0.927830i	$0.378328\pi$
$269$	−10.1199	+	17.5282i	−0.617023	+	1.06871i	−0.990026	+	0.140885i	$0.955005\pi$
$270$	−1.13177	+	20.8581i	−0.0688771	+	1.26938i
$271$	6.66484	+	11.5438i	0.404860	+	0.701239i	0.994305	−	0.106570i	$-0.0339868\pi$
$271$	6.66484	+	11.5438i	0.404860	+	0.701239i	−0.589445	+	0.807809i	$0.700654\pi$
$272$	0.299299	−	5.13876i	0.0181477	−	0.311583i
$273$	−12.1514	−	5.50412i	−0.735439	−	0.333124i
$274$	−12.7142	−	1.48608i	−0.768093	−	0.0897772i
$275$	−0.103563	−	0.109770i	−0.00624509	−	0.00661941i
$276$	0.818331	−	0.744573i	0.0492578	−	0.0448181i
$277$	29.4197	−	3.43867i	1.76766	−	0.206610i	0.830861	−	0.556480i	$-0.187848\pi$
$277$	29.4197	−	3.43867i	1.76766	−	0.206610i	0.936798	+	0.349870i	$0.113774\pi$
$278$	−14.3859	−	12.0712i	−0.862807	−	0.723981i
$279$	7.22139	+	27.7311i	0.432333	+	1.66022i
$280$	−5.15935	+	4.32920i	−0.308330	+	0.258719i
$281$	1.06165	−	1.12528i	0.0633324	−	0.0671285i	−0.694933	−	0.719075i	$-0.744566\pi$
$281$	1.06165	−	1.12528i	0.0633324	−	0.0671285i	0.758265	+	0.651946i	$0.226047\pi$
$282$	0.358338	−	19.8294i	0.0213387	−	1.18083i
$283$	−5.12108	−	2.57190i	−0.304417	−	0.152884i	0.290033	−	0.957017i	$-0.406334\pi$
$283$	−5.12108	−	2.57190i	−0.304417	−	0.152884i	−0.594450	+	0.804133i	$0.702630\pi$
$284$	−5.20620	−	2.61465i	−0.308931	−	0.155151i
$285$	−16.8944	−	10.1653i	−1.00074	−	0.602142i
$286$	0.0426574	−	0.0452142i	0.00252238	−	0.00267357i
$287$	−9.04799	+	7.59217i	−0.534086	+	0.448151i
$288$	−1.28699	+	2.70992i	−0.0758366	+	0.159683i
$289$	7.27472	+	6.10421i	0.427925	+	0.359071i
$290$	−18.0491	+	2.10964i	−1.05988	+	0.123882i
$291$	−5.31407	−	1.69614i	−0.311516	−	0.0994292i
$292$	−5.74493	−	6.08927i	−0.336197	−	0.356348i
$293$	1.24181	+	0.145147i	0.0725476	+	0.00847960i	0.152289	−	0.988336i	$-0.451335\pi$
$293$	1.24181	+	0.145147i	0.0725476	+	0.00847960i	−0.0797417	+	0.996816i	$0.525410\pi$
$294$	−5.90302	+	4.23104i	−0.344271	+	0.246759i
$295$	0.581336	−	9.98116i	0.0338467	−	0.581126i
$296$	−3.93790	−	6.82064i	−0.228886	−	0.396442i
$297$	0.0629127	+	0.0312837i	0.00365056	+	0.00181527i
$298$	−1.09130	+	1.89018i	−0.0632171	+	0.109495i
$299$	−2.45336	−	1.61360i	−0.141882	−	0.0933171i
$300$	4.79715	−	18.7263i	0.276964	−	1.08116i
$301$	4.20504	+	9.74837i	0.242374	+	0.561887i
$302$	14.4265	−	3.41914i	0.830150	−	0.196749i
$303$	−8.13209	+	0.326342i	−0.467176	+	0.0187478i
$304$	−1.69097	−	2.27137i	−0.0969838	−	0.130272i
$305$	−8.82826	+	3.21322i	−0.505505	+	0.183989i
$306$	−7.23298	−	13.6438i	−0.413482	−	0.779962i
$307$	17.2059	+	6.26242i	0.981990	+	0.357415i	0.782614	−	0.622508i	$-0.213886\pi$
$307$	17.2059	+	6.26242i	0.981990	+	0.357415i	0.199376	+	0.979923i	$0.436108\pi$
$308$	0.00649725	+	0.0217023i	0.000370215	+	0.00123660i
$309$	0.624224	−	1.62317i	0.0355109	−	0.0923390i
$310$	−2.23272	−	38.3343i	−0.126810	−	2.17724i
$311$	13.9855	−	9.19840i	0.793044	−	0.521593i	−0.0871569	−	0.996195i	$-0.527778\pi$
$311$	13.9855	−	9.19840i	0.793044	−	0.521593i	0.880201	+	0.474601i	$0.157408\pi$
$312$	7.81514	+	1.52410i	0.442445	+	0.0862854i
$313$	12.0680	+	2.86018i	0.682126	+	0.161667i	0.557048	−	0.830480i	$-0.311934\pi$
$313$	12.0680	+	2.86018i	0.682126	+	0.161667i	0.125078	+	0.992147i	$0.460082\pi$
$314$	1.40071	+	7.94384i	0.0790468	+	0.448297i
$315$	−6.49046	+	19.1343i	−0.365696	+	1.07810i
$316$	−0.853333	+	4.83949i	−0.0480037	+	0.272243i
$317$	−8.84525	+	20.5056i	−0.496799	+	1.15171i	0.466801	+	0.884362i	$0.345406\pi$
$317$	−8.84525	+	20.5056i	−0.496799	+	1.15171i	−0.963600	+	0.267347i	$0.913853\pi$
$318$	9.51722	−	3.90292i	0.533699	−	0.218865i
$319$	−0.0175304	+	0.0585555i	−0.000981512	+	0.00327848i
$320$	2.40060	−	3.22457i	0.134198	−	0.180259i
$321$	−4.42401	−	9.22066i	−0.246924	−	0.514647i
$322$	0.956333	−	0.480288i	0.0532944	−	0.0267654i
$323$	14.5761			0.811034
$324$	0.918707	+	8.95299i	0.0510393	+	0.497388i
$325$	−51.3067			−2.84599
$326$	15.8124	−	7.94131i	0.875771	−	0.439829i
$327$	−14.1135	−	1.07820i	−0.780478	−	0.0596245i
$328$	4.20996	−	5.65496i	0.232456	−	0.312243i
$329$	5.50193	−	18.3777i	0.303331	−	1.01320i
$330$	−0.0744928	−	0.0575786i	−0.00410069	−	0.00316960i
$331$	−7.60331	+	17.6265i	−0.417916	+	0.968838i	0.571080	+	0.820895i	$0.306525\pi$
$331$	−7.60331	+	17.6265i	−0.417916	+	0.968838i	−0.988996	+	0.147944i	$0.952735\pi$
$332$	2.63382	−	14.9371i	0.144550	−	0.819782i
$333$	−20.7173	−	11.3599i	−1.13530	−	0.622518i
$334$	−1.46455	−	8.30586i	−0.0801364	−	0.454476i
$335$	−15.6568	−	3.71074i	−0.855424	−	0.202739i
$336$	−1.90511	+	2.18886i	−0.103933	+	0.119412i
$337$	12.3063	−	8.09396i	0.670365	−	0.440906i	−0.168167	−	0.985759i	$-0.553785\pi$
$337$	12.3063	−	8.09396i	0.670365	−	0.440906i	0.838532	+	0.544853i	$0.183414\pi$
$338$	−0.472899	−	8.11936i	−0.0257223	−	0.441635i
$339$	35.4552	−	5.59317i	1.92566	−	0.303779i
$340$	5.93483	+	19.8237i	0.321862	+	1.07509i
$341$	−0.121371	−	0.0441753i	−0.00657260	−	0.00239223i
$342$	−7.87258	−	3.19201i	−0.425700	−	0.172604i
$343$	−17.6217	+	6.41378i	−0.951483	+	0.346311i
$344$	−3.78413	−	5.08297i	−0.204027	−	0.274056i
$345$	−2.06759	+	3.93786i	−0.111315	+	0.212007i
$346$	−7.51741	+	1.78166i	−0.404139	+	0.0957826i
$347$	−3.89123	−	9.02089i	−0.208892	−	0.484267i	0.781269	−	0.624194i	$-0.214572\pi$
$347$	−3.89123	−	9.02089i	−0.208892	−	0.484267i	−0.990162	+	0.139927i	$0.955313\pi$
$348$	−7.53989	+	2.10963i	−0.404181	+	0.113088i
$349$	−21.6854	−	14.2627i	−1.16079	−	0.763464i	−0.185122	−	0.982716i	$-0.559268\pi$
$349$	−21.6854	−	14.2627i	−1.16079	−	0.763464i	−0.975668	+	0.219252i	$0.929638\pi$
$350$	9.34916	−	16.1932i	0.499734	−	0.865564i
$351$	22.4139	−	8.25893i	1.19637	−	0.440829i
$352$	−0.00676091	−	0.0117102i	−0.000360358	−	0.000624158i
$353$	0.0720294	−	1.23670i	0.00383374	−	0.0658227i	−0.995849	−	0.0910246i	$-0.970986\pi$
$353$	0.0720294	−	1.23670i	0.00383374	−	0.0658227i	0.999682	+	0.0252019i	$0.00802285\pi$
$354$	−0.422707	−	4.28692i	−0.0224666	−	0.227847i
$355$	23.2619	+	2.71893i	1.23461	+	0.144306i
$356$	−5.33108	−	5.65061i	−0.282546	−	0.299482i
$357$	−3.18155	−	14.5943i	−0.168385	−	0.772411i
$358$	−17.7570	+	2.07549i	−0.938485	+	0.109693i
$359$	9.38496	+	7.87492i	0.495319	+	0.415622i	0.855928	−	0.517095i	$-0.172987\pi$
$359$	9.38496	+	7.87492i	0.495319	+	0.415622i	−0.360609	+	0.932717i	$0.617431\pi$
$360$	1.13577	−	12.0065i	0.0598606	−	0.632799i
$361$	−8.41232	+	7.05878i	−0.442754	+	0.371515i
$362$	−9.38586	+	9.94843i	−0.493310	+	0.522878i
$363$	16.6692	−	9.22645i	0.874904	−	0.484263i
$364$	6.88258	+	3.45656i	0.360745	+	0.181173i
$365$	30.0744	+	15.1040i	1.57417	+	0.790577i
$366$	−3.54150	+	1.96023i	−0.185117	+	0.102463i
$367$	6.89289	−	7.30603i	0.359806	−	0.381372i	−0.522031	−	0.852926i	$-0.674825\pi$
$367$	6.89289	−	7.30603i	0.359806	−	0.381372i	0.881837	+	0.471555i	$0.156307\pi$
$368$	−0.489321	+	0.410589i	−0.0255076	+	0.0214034i
$369$	1.99182	−	21.0560i	0.103690	−	1.09613i
$370$	24.2537	+	20.3513i	1.26089	+	1.05801i
$371$	9.88250	−	1.15510i	0.513074	−	0.0599697i
$372$	−3.52393	−	16.1648i	−0.182707	−	0.838108i
$373$	−23.8751	−	25.3061i	−1.23620	−	1.31030i	−0.934094	−	0.357026i	$-0.883791\pi$
$373$	−23.8751	−	25.3061i	−1.23620	−	1.31030i	−0.302110	−	0.953273i	$-0.597691\pi$
$374$	0.0691326	+	0.00808044i	0.00357476	+	0.000417830i
$375$	4.20936	+	42.6896i	0.217371	+	2.20448i
$376$	−0.665781	+	11.4310i	−0.0343351	+	0.589510i
$377$	10.3902	+	17.9963i	0.535122	+	0.926858i
$378$	−1.47764	+	8.57914i	−0.0760014	+	0.441264i
$379$	4.86589	−	8.42796i	0.249944	−	0.432915i	−0.713566	−	0.700588i	$-0.752921\pi$
$379$	4.86589	−	8.42796i	0.249944	−	0.432915i	0.963510	+	0.267672i	$0.0862545\pi$
$380$	9.51080	+	6.25535i	0.487894	+	0.320893i
$381$	−13.3079	+	3.72348i	−0.681783	+	0.190760i
$382$	1.07102	+	2.48290i	0.0547982	+	0.127036i
$383$	10.4713	−	2.48175i	0.535061	−	0.126812i	0.0458021	−	0.998951i	$-0.485416\pi$
$383$	10.4713	−	2.48175i	0.535061	−	0.126812i	0.489258	+	0.872139i	$0.337267\pi$
$384$	0.805182	−	1.53352i	0.0410893	−	0.0782571i
$385$	−0.0543833	−	0.0730495i	−0.00277163	−	0.00372295i
$386$	−9.21438	+	3.35376i	−0.469000	+	0.170702i
$387$	−17.6176	−	7.14324i	−0.895554	−	0.363111i
$388$	3.02635	+	1.10150i	0.153639	+	0.0559202i
$389$	−7.51883	−	25.1147i	−0.381220	−	1.27336i	−0.906417	−	0.422383i	$-0.861194\pi$
$389$	−7.51883	−	25.1147i	−0.381220	−	1.27336i	0.525197	−	0.850980i	$-0.323992\pi$
$390$	−31.6181	+	4.98785i	−1.60104	+	0.252570i
$391$	−0.191181	−	3.28245i	−0.00966845	−	0.166001i
$392$	3.50332	−	2.30417i	0.176944	−	0.116378i
$393$	9.33259	−	10.7226i	0.470767	−	0.540882i
$394$	−2.34944	−	0.556827i	−0.118363	−	0.0280526i
$395$	−3.43043	−	19.4549i	−0.172604	−	0.978885i
$396$	−0.0355692	−	0.0195036i	−0.00178742	−	0.000980093i
$397$	2.93006	−	16.6172i	0.147056	−	0.833995i	−0.818638	−	0.574310i	$-0.805270\pi$
$397$	2.93006	−	16.6172i	0.147056	−	0.833995i	0.965694	−	0.259684i	$-0.0836185\pi$
$398$	−5.40715	+	12.5352i	−0.271036	+	0.628332i
$399$	−6.50137	−	5.02518i	−0.325476	−	0.251574i
$400$	−3.20093	+	10.6919i	−0.160047	+	0.534593i
$401$	−7.78193	+	10.4529i	−0.388611	+	0.521995i	−0.952779	−	0.303665i	$-0.901790\pi$
$401$	−7.78193	+	10.4529i	−0.388611	+	0.521995i	0.564168	+	0.825660i	$0.309197\pi$
$402$	−6.91254	−	0.528082i	−0.344766	−	0.0263383i
$403$	−39.2404	+	19.7073i	−1.95471	+	0.981690i
$404$	4.69884			0.233776
$405$	−15.7803	−	32.5577i	−0.784129	−	1.61780i
$406$	−7.57324			−0.375854
$407$	0.0951675	−	0.0477949i	0.00471728	−	0.00236911i
$408$	3.85674	+	8.03834i	0.190937	+	0.397957i
$409$	−15.4125	+	20.7026i	−0.762101	+	1.02368i	0.236543	+	0.971621i	$0.423985\pi$
$409$	−15.4125	+	20.7026i	−0.762101	+	1.02368i	−0.998644	+	0.0520579i	$0.983422\pi$
$410$	−8.12836	+	27.1506i	−0.401431	+	1.34087i
$411$	20.5136	−	8.41244i	1.01186	−	0.414955i
$412$	−0.397683	+	0.921933i	−0.0195924	+	0.0454204i
$413$	0.723546	−	4.10343i	0.0356034	−	0.201917i
$414$	−0.615567	+	1.81473i	−0.0302535	+	0.0891891i
$415$	10.5881	+	60.0479i	0.519748	+	2.94764i
$416$	−4.47316	−	1.06016i	−0.219315	−	0.0519786i
$417$	31.9255	+	6.22609i	1.56340	+	0.304893i
$418$	0.0319906	−	0.0210405i	0.00156471	−	0.00102913i
$419$	0.0325942	+	0.559620i	0.00159233	+	0.0273392i	0.999011	−	0.0444698i	$-0.0141598\pi$
$419$	0.0325942	+	0.559620i	0.00159233	+	0.0273392i	−0.997418	+	0.0718090i	$0.977123\pi$
$420$	4.18723	−	10.8881i	0.204316	−	0.531283i
$421$	−0.596418	−	1.99217i	−0.0290676	−	0.0970926i	0.942225	−	0.334981i	$-0.108730\pi$
$421$	−0.596418	−	1.99217i	−0.0290676	−	0.0970926i	−0.971292	+	0.237888i	$0.923545\pi$
$422$	5.61499	+	2.04369i	0.273333	+	0.0994852i
$423$	16.0895	+	30.3501i	0.782300	+	1.47567i
$424$	−5.58071	+	2.03121i	−0.271023	+	0.0986443i
$425$	−34.3065	−	46.0816i	−1.66411	−	2.23529i
$426$	10.0826	−	0.404616i	0.488504	−	0.0196037i
$427$	−3.80980	+	0.902938i	−0.184369	+	0.0436962i
$428$	2.33869	+	5.42169i	0.113045	+	0.262067i
$429$	−0.0267183	+	0.104298i	−0.00128997	+	0.00503555i
$430$	21.2837	+	13.9985i	1.02639	+	0.675069i
$431$	4.95301	−	8.57886i	0.238578	−	0.413229i	−0.721729	−	0.692176i	$-0.756652\pi$
$431$	4.95301	−	8.57886i	0.238578	−	0.413229i	0.960306	+	0.278947i	$0.0899854\pi$
$432$	−0.322723	−	5.18612i	−0.0155270	−	0.249517i
$433$	−1.14206	−	1.97810i	−0.0548838	−	0.0950615i	0.837278	−	0.546777i	$-0.184145\pi$
$433$	−1.14206	−	1.97810i	−0.0548838	−	0.0950615i	−0.892162	+	0.451716i	$0.850812\pi$
$434$	0.930495	−	15.9760i	0.0446652	−	0.766872i
$435$	25.5821	−	18.3362i	1.22657	−	0.879154i
$436$	8.11691	+	0.948731i	0.388730	+	0.0454360i
$437$	−1.24126	−	1.31566i	−0.0593776	−	0.0629366i
$438$	13.8135	+	4.40896i	0.660033	+	0.210668i
$439$	−32.2822	+	3.77325i	−1.54074	+	0.180087i	−0.843650	−	0.536893i	$-0.819598\pi$
$439$	−32.2822	+	3.77325i	−1.54074	+	0.180087i	−0.697094	+	0.716980i	$0.745524\pi$
$440$	0.0416409	+	0.0349408i	0.00198515	+	0.00166574i
$441$	5.39653	−	11.3631i	0.256978	−	0.541099i
$442$	18.1272	−	15.2105i	0.862221	−	0.723489i
$443$	13.4623	−	14.2692i	0.639613	−	0.677950i	−0.323753	−	0.946142i	$-0.604945\pi$
$443$	13.4623	−	14.2692i	0.639613	−	0.677950i	0.963366	+	0.268192i	$0.0864260\pi$
$444$	11.6885	+	7.03298i	0.554713	+	0.333770i
$445$	27.9079	+	14.0159i	1.32296	+	0.664416i
$446$	11.9583	+	6.00570i	0.566244	+	0.284378i
$447$	0.0683038	−	3.77974i	0.00323066	−	0.178776i
$448$	1.14971	−	1.21862i	0.0543186	−	0.0575743i
$449$	−7.24842	+	6.08214i	−0.342074	+	0.287034i	−0.797598	−	0.603189i	$-0.793896\pi$
$449$	−7.24842	+	6.08214i	−0.342074	+	0.287034i	0.455524	+	0.890223i	$0.349452\pi$
$450$	8.43763	+	32.4016i	0.397754	+	1.52743i
$451$	0.0730260	+	0.0612761i	0.00343866	+	0.00288538i
$452$	−20.5831	+	2.40582i	−0.968147	+	0.113160i
$453$	−18.9940	+	17.2820i	−0.892416	+	0.811981i
$454$	16.0296	+	16.9903i	0.752304	+	0.797396i
$455$	−30.7522	−	3.59441i	−1.44168	−	0.168509i
$456$	4.46768	+	2.02368i	0.209218	+	0.0947675i
$457$	1.42592	−	24.4821i	0.0667017	−	1.14522i	−0.784411	−	0.620242i	$-0.787035\pi$
$457$	1.42592	−	24.4821i	0.0667017	−	1.14522i	0.851113	−	0.524983i	$-0.175928\pi$
$458$	5.04468	+	8.73764i	0.235722	+	0.408283i
$459$	22.4050	+	14.6089i	1.04578	+	0.681885i
$460$	1.28393	−	2.22383i	0.0598634	−	0.103686i
$461$	18.8285	+	12.3837i	0.876932	+	0.576767i	0.906221	−	0.422804i	$-0.138954\pi$
$461$	18.8285	+	12.3837i	0.876932	+	0.576767i	−0.0292894	+	0.999571i	$0.509324\pi$
$462$	−0.0280495	−	0.0274380i	−0.00130498	−	0.00127653i
$463$	−7.14555	−	16.5652i	−0.332082	−	0.769852i	−0.999679	−	0.0253295i	$-0.991936\pi$
$463$	−7.14555	−	16.5652i	−0.332082	−	0.769852i	0.667597	−	0.744522i	$-0.267323\pi$
$464$	4.39850	−	1.04246i	0.204195	−	0.0483951i
$465$	35.5376	+	56.2192i	1.64802	+	2.60710i
$466$	−0.865613	−	1.16272i	−0.0400988	−	0.0538620i
$467$	5.17094	−	1.88207i	0.239283	−	0.0870918i	−0.219595	−	0.975591i	$-0.570474\pi$
$467$	5.17094	−	1.88207i	0.239283	−	0.0870918i	0.458878	+	0.888499i	$0.348251\pi$
$468$	−13.1215	+	4.24557i	−0.606541	+	0.196251i
$469$	−6.30139	−	2.29352i	−0.290971	−	0.105905i
$470$	−13.2019	−	44.0973i	−0.608956	−	2.03406i
$471$	−8.78579	−	10.8632i	−0.404828	−	0.500551i
$472$	0.144610	+	2.48285i	0.00665620	+	0.114282i
$473$	0.0715900	−	0.0470855i	0.00329171	−	0.00216499i
$474$	−2.76613	−	8.04953i	−0.127053	−	0.369727i
$475$	−30.7519	−	7.28833i	−1.41099	−	0.334412i
$476$	1.49753	+	8.49289i	0.0686390	+	0.389271i
$477$	−11.1487	+	13.8974i	−0.510465	+	0.636317i
$478$	3.69371	−	20.9481i	0.168946	−	0.958143i
$479$	−15.6255	+	36.2239i	−0.713946	+	1.65511i	0.0408608	+	0.999165i	$0.486990\pi$
$479$	−15.6255	+	36.2239i	−0.713946	+	1.65511i	−0.754807	+	0.655947i	$0.772269\pi$
$480$	−0.933169	+	6.90010i	−0.0425931	+	0.314945i
$481$	10.3839	−	34.6846i	0.473465	−	1.58148i
$482$	5.48137	−	7.36276i	0.249670	−	0.335365i
$483$	−1.04637	+	1.52999i	−0.0476116	+	0.0696167i
$484$	−9.82980	+	4.93671i	−0.446809	+	0.224396i
$485$	−12.9468			−0.587885
$486$	−8.90181	−	12.7968i	−0.403795	−	0.580474i
$487$	−6.31620			−0.286214			−0.143107	−	0.989707i	$-0.545709\pi$
$487$	−6.31620			−0.286214			−0.143107	+	0.989707i	$0.545709\pi$
$488$	2.08842	−	1.04884i	0.0945383	−	0.0474789i
$489$	−17.3012	+	25.2975i	−0.782387	+	1.14399i
$490$	−10.0661	+	13.5211i	−0.454739	+	0.610820i
$491$	−0.0319262	+	0.106641i	−0.00144081	+	0.00481264i	−0.958707	−	0.284396i	$-0.908207\pi$
$491$	−0.0319262	+	0.106641i	−0.00144081	+	0.00481264i	0.957266	+	0.289209i	$0.0933921\pi$
$492$	−1.63651	+	12.1008i	−0.0737795	+	0.545545i
$493$	−9.21612	+	21.3654i	−0.415073	+	0.962248i
$494$	2.26047	−	12.8198i	0.101703	−	0.576788i
$495$	0.161182	+	0.0247716i	0.00724461	+	0.00111340i
$496$	1.65868	+	9.40685i	0.0744770	+	0.422380i
$497$	9.49740	+	2.25092i	0.426017	+	0.100968i
$498$	8.53770	+	24.8450i	0.382584	+	1.11333i
$499$	9.41139	−	6.18997i	0.421312	−	0.277101i	−0.321100	−	0.947045i	$-0.604052\pi$
$499$	9.41139	−	6.18997i	0.421312	−	0.277101i	0.742411	+	0.669944i	$0.233682\pi$
$500$	−1.44004	−	24.7245i	−0.0644004	−	1.10571i
$501$	9.18618	+	11.3583i	0.410408	+	0.507451i
$502$	1.76479	+	5.89481i	0.0787664	+	0.263098i
$503$	−4.38661	−	1.59659i	−0.195589	−	0.0711886i	0.242368	−	0.970184i	$-0.422076\pi$
$503$	−4.38661	−	1.59659i	−0.195589	−	0.0711886i	−0.437958	+	0.898996i	$0.644298\pi$
$504$	1.05104	−	4.91498i	0.0468170	−	0.218931i
$505$	−17.7504	+	6.46061i	−0.789881	+	0.287493i
$506$	−0.00515781	−	0.00692814i	−0.000229292	−	0.000307993i
$507$	7.52701	+	11.9074i	0.334286	+	0.528828i
$508$	7.76333	−	1.83994i	0.344442	−	0.0816342i
$509$	5.23832	+	12.1438i	0.232184	+	0.538264i	0.993981	−	0.109553i	$-0.0349418\pi$
$509$	5.23832	+	12.1438i	0.232184	+	0.538264i	−0.761797	+	0.647816i	$0.775683\pi$
$510$	−25.6214	−	25.0629i	−1.13454	−	1.10980i
$511$	11.7181	+	7.70713i	0.518379	+	0.340944i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	14.6075	−	1.76619i	0.644938	−	0.0779793i
$514$	4.76717	+	8.25699i	0.210271	+	0.364200i
$515$	0.234691	−	4.02949i	0.0103417	−	0.177560i
$516$	9.99799	+	4.52869i	0.440137	+	0.199364i
$517$	−0.153783	−	0.0179747i	−0.00676339	−	0.000790526i
$518$	9.05486	+	9.59759i	0.397848	+	0.421694i
$519$	9.89748	−	9.00540i	0.434451	−	0.395293i
$520$	18.3555	−	2.14545i	0.804941	−	0.0940841i
$521$	−23.2776	−	19.5322i	−1.01981	−	0.855722i	−0.0302066	−	0.999544i	$-0.509617\pi$
$521$	−23.2776	−	19.5322i	−1.01981	−	0.855722i	−0.989604	+	0.143821i	$0.954061\pi$
$522$	9.65646	−	9.52126i	0.422652	−	0.416734i
$523$	12.9993	−	10.9077i	0.568418	−	0.476959i	−0.312702	−	0.949851i	$-0.601234\pi$
$523$	12.9993	−	10.9077i	0.568418	−	0.476959i	0.881121	+	0.472892i	$0.156790\pi$
$524$	−5.63207	+	5.96965i	−0.246038	+	0.260785i
$525$	−0.585161	+	32.3812i	−0.0255385	+	1.41323i
$526$	−14.8083	−	7.43700i	−0.645672	−	0.324269i
$527$	−43.9386	−	22.0668i	−1.91399	−	0.961244i
$528$	0.0200678	+	0.0120748i	0.000873341	+	0.000525488i
$529$	15.5036	−	16.4328i	0.674068	−	0.714470i
$530$	18.2889	−	15.3462i	0.794419	−	0.666597i
$531$	4.23636	+	6.14185i	0.183843	+	0.266534i
$532$	3.63421	+	3.04947i	0.157563	+	0.132211i
$533$	32.1902	−	3.76249i	1.39431	−	0.162972i
$534$	12.8184	+	4.09134i	0.554704	+	0.177050i
$535$	−16.2891	−	17.2654i	−0.704239	−	0.746450i
$536$	3.97552	+	0.464672i	0.171716	+	0.0200708i
$537$	25.1681	−	18.0394i	1.08608	−	0.778459i
$538$	−1.17684	+	20.2056i	−0.0507373	+	0.871125i
$539$	0.0283495	+	0.0491027i	0.00122110	+	0.00211500i
$540$	8.34970	+	19.1474i	0.359314	+	0.823972i
$541$	−19.9050	+	34.4764i	−0.855782	+	1.48226i	0.0201362	+	0.999797i	$0.493590\pi$
$541$	−19.9050	+	34.4764i	−0.855782	+	1.48226i	−0.875918	+	0.482460i	$0.839743\pi$
$542$	11.1368	+	7.32478i	0.478366	+	0.314626i
$543$	5.87880	−	22.9486i	0.252283	−	0.984818i
$544$	−2.03881	−	4.72649i	−0.0874132	−	0.202647i
$545$	−31.9669	+	7.57630i	−1.36931	+	0.324533i
$546$	−13.3292	+	0.534901i	−0.570436	+	0.0228916i
$547$	−2.53512	−	3.40526i	−0.108394	−	0.145598i	0.744616	−	0.667493i	$-0.232633\pi$
$547$	−2.53512	−	3.40526i	−0.108394	−	0.145598i	−0.853010	+	0.521895i	$0.825225\pi$
$548$	−12.0288	+	4.37812i	−0.513844	+	0.187024i
$549$	3.72258	−	5.94109i	0.158876	−	0.253559i
$550$	−0.141812	−	0.0516154i	−0.00604690	−	0.00220089i
$551$	3.67115	+	12.2625i	0.156396	+	0.522400i
$552$	0.397124	−	1.03264i	0.0169027	−	0.0439521i
$553$	−0.478707	−	8.21907i	−0.0203567	−	0.349511i
$554$	24.7471	−	16.2765i	1.05141	−	0.691520i
$555$	−53.8245	−	10.4968i	−2.28472	−	0.445565i
$556$	−18.2732	−	4.33083i	−0.774957	−	0.183668i
$557$	3.49887	+	19.8431i	0.148252	+	0.840778i	0.964698	+	0.263357i	$0.0848297\pi$
$557$	3.49887	+	19.8431i	0.148252	+	0.840778i	−0.816447	+	0.577421i	$0.804059\pi$
$558$	18.8990	+	21.5404i	0.800057	+	0.911880i
$559$	5.05858	−	28.6887i	0.213955	−	1.21340i
$560$	−2.66762	+	6.18423i	−0.112727	+	0.261331i
$561$	−0.111541	+	0.0457420i	−0.00470928	+	0.00193123i
$562$	0.443697	−	1.48205i	0.0187162	−	0.0625165i
$563$	−6.16547	+	8.28167i	−0.259844	+	0.349031i	−0.912831	−	0.408339i	$-0.866108\pi$
$563$	−6.16547	+	8.28167i	−0.259844	+	0.349031i	0.652987	+	0.757369i	$0.273516\pi$
$564$	−8.57921	−	17.8811i	−0.361250	−	0.752928i
$565$	74.4469	−	37.3886i	3.13200	−	1.57295i
$566$	−5.73063			−0.240876
$567$	−4.95682	−	14.2403i	−0.208167	−	0.598035i
$568$	−5.82588			−0.244449
$569$	−14.7778	+	7.42168i	−0.619517	+	0.311133i	−0.730733	−	0.682663i	$-0.760822\pi$
$569$	−14.7778	+	7.42168i	−0.619517	+	0.311133i	0.111216	+	0.993796i	$0.464525\pi$
$570$	−19.6596	−	1.50189i	−0.823449	−	0.0629072i
$571$	−11.7740	+	15.8152i	−0.492726	+	0.661846i	−0.977042	−	0.213047i	$-0.931661\pi$
$571$	−11.7740	+	15.8152i	−0.492726	+	0.661846i	0.484316	+	0.874893i	$0.339069\pi$
$572$	0.0178279	−	0.0595495i	0.000745424	−	0.00248989i
$573$	−3.70564	−	2.86425i	−0.154805	−	0.119656i
$574$	−4.67822	+	10.8453i	−0.195265	+	0.452676i
$575$	−1.23795	+	7.02076i	−0.0516260	+	0.292786i
$576$	0.0661132	+	2.99927i	0.00275472	+	0.124970i
$577$	4.46863	+	25.3429i	0.186031	+	1.05504i	0.924623	+	0.380884i	$0.124380\pi$
$577$	4.46863	+	25.3429i	0.186031	+	1.05504i	−0.738591	+	0.674153i	$0.764509\pi$
$578$	9.24049	+	2.19004i	0.384354	+	0.0910935i
$579$	11.1504	−	12.8112i	0.463396	−	0.532413i
$580$	−15.1825	+	9.98566i	−0.630417	+	0.414632i
$581$	1.47753	+	25.3683i	0.0612984	+	1.05245i
$582$	−5.51005	+	0.869229i	−0.228399	+	0.0360307i
$583$	−0.0230315	−	0.0769307i	−0.000953868	−	0.00318614i
$584$	−7.86672	−	2.86325i	−0.325527	−	0.118482i
$585$	43.7304	−	34.0793i	1.80803	−	1.40900i
$586$	1.17487	−	0.427617i	0.0485334	−	0.0176647i
$587$	20.5379	+	27.5872i	0.847690	+	1.13864i	0.988888	+	0.148663i	$0.0474971\pi$
$587$	20.5379	+	27.5872i	0.847690	+	1.13864i	−0.141198	+	0.989981i	$0.545096\pi$
$588$	−3.37624	+	6.43027i	−0.139234	+	0.265180i
$589$	−26.3192	+	6.23776i	−1.08446	+	0.257022i
$590$	−3.96004	−	9.18040i	−0.163032	−	0.377951i
$591$	4.02740	−	1.12685i	0.165665	−	0.0463524i
$592$	−6.58013	−	4.32782i	−0.270442	−	0.177872i
$593$	9.43328	−	16.3389i	0.387378	−	0.670959i	−0.604718	−	0.796440i	$-0.706714\pi$
$593$	9.43328	−	16.3389i	0.387378	−	0.670959i	0.992096	+	0.125481i	$0.0400474\pi$
$594$	0.0702609		0.000278969i	0.00288284		1.14462e-5i
$595$	−17.3342	−	30.0238i	−0.710634	−	1.23085i
$596$	−0.126906	+	2.17890i	−0.00519829	+	0.0892512i
$597$	−2.32027	−	23.5313i	−0.0949625	−	0.963070i
$598$	−2.91659	−	0.340900i	−0.119268	−	0.0139405i
$599$	−5.63271	−	5.97033i	−0.230146	−	0.243941i	0.602001	−	0.798495i	$-0.294370\pi$
$599$	−5.63271	−	5.97033i	−0.230146	−	0.243941i	−0.832148	+	0.554554i	$0.812889\pi$
$600$	−4.11744	−	18.8874i	−0.168094	−	0.771073i
$601$	5.46628	−	0.638917i	0.222974	−	0.0260620i	−0.00387210	−	0.999993i	$-0.501233\pi$
$601$	5.46628	−	0.638917i	0.222974	−	0.0260620i	0.226846	+	0.973931i	$0.427158\pi$
$602$	8.13282	+	6.82424i	0.331469	+	0.278135i
$603$	10.9182	−	4.99786i	0.444624	−	0.203528i
$604$	11.3575	−	9.53004i	0.462129	−	0.387772i
$605$	30.3454	−	32.1643i	1.23372	−	1.30766i
$606$	−7.12064	+	3.94131i	−0.289256	+	0.160105i
$607$	−5.82005	−	2.92294i	−0.236229	−	0.118638i	0.326747	−	0.945112i	$-0.394047\pi$
$607$	−5.82005	−	2.92294i	−0.236229	−	0.118638i	−0.562976	+	0.826473i	$0.690344\pi$
$608$	−2.53049	−	1.27086i	−0.102625	−	0.0515403i
$609$	11.4765	−	6.35230i	0.465051	−	0.257408i
$610$	−6.44713	+	6.83356i	−0.261037	+	0.276683i
$611$	−40.3233	+	33.8353i	−1.63131	+	1.36883i
$612$	−12.5869	−	8.94636i	−0.508797	−	0.361635i
$613$	15.4318	+	12.9488i	0.623283	+	0.522997i	0.898834	−	0.438290i	$-0.144416\pi$
$613$	15.4318	+	12.9488i	0.623283	+	0.522997i	−0.275550	+	0.961287i	$0.588860\pi$
$614$	18.1863	−	2.12567i	0.733939	−	0.0857851i
$615$	−10.4557	−	47.9620i	−0.421615	−	1.93401i
$616$	0.0155461	+	0.0164779i	0.000626372	+	0.000663915i
$617$	9.28251	+	1.08497i	0.373700	+	0.0436792i	0.300870	−	0.953665i	$-0.402723\pi$
$617$	9.28251	+	1.08497i	0.373700	+	0.0436792i	0.0728296	+	0.997344i	$0.476797\pi$
$618$	−0.170651	−	1.73067i	−0.00686458	−	0.0696177i
$619$	0.366677	−	6.29560i	0.0147380	−	0.253041i	−0.982889	−	0.184197i	$-0.941032\pi$
$619$	0.366677	−	6.29560i	0.0147380	−	0.253041i	0.997627	−	0.0688447i	$-0.0219313\pi$
$620$	−19.1997	−	33.2548i	−0.771077	−	1.33554i
$621$	−0.589331	−	3.26637i	−0.0236490	−	0.131075i
$622$	8.36965	−	14.4967i	0.335592	−	0.581263i
$623$	10.8740	+	7.15192i	0.435656	+	0.286536i
$624$	7.66788	−	2.14544i	0.306961	−	0.0858863i
$625$	17.3318	+	40.1795i	0.693270	+	1.60718i
$626$	12.0680	−	2.86018i	0.482336	−	0.114316i
$627$	−0.0308302	+	0.0587180i	−0.00123124	+	0.00234497i
$628$	4.81691	+	6.47023i	0.192216	+	0.258190i
$629$	38.0955	−	13.8656i	1.51897	−	0.552859i
$630$	2.78737	+	20.0120i	0.111051	+	0.797295i
$631$	−34.1219	−	12.4194i	−1.35837	−	0.494407i	−0.442821	−	0.896610i	$-0.646022\pi$
$631$	−34.1219	−	12.4194i	−1.35837	−	0.494407i	−0.915550	+	0.402203i	$0.868244\pi$
$632$	1.40939	+	4.70770i	0.0560626	+	0.187262i
$633$	−10.2232	+	1.61274i	−0.406335	+	0.0641007i
$634$	1.29849	+	22.2942i	0.0515696	+	0.885416i
$635$	−26.7970	+	17.6246i	−1.06340	+	0.699412i
$636$	6.75327	−	7.75910i	0.267785	−	0.307668i
$637$	18.7566	+	4.44540i	0.743164	+	0.176133i
$638$	0.0106140	+	0.0601947i	0.000420210	+	0.00238313i
$639$	−14.9398	+	9.07026i	−0.591010	+	0.358814i
$640$	0.698073	−	3.95897i	0.0275938	−	0.156492i
$641$	−11.6086	+	26.9118i	−0.458513	+	1.06295i	0.519511	+	0.854464i	$0.326114\pi$
$641$	−11.6086	+	26.9118i	−0.458513	+	1.06295i	−0.978025	+	0.208490i	$0.933145\pi$
$642$	−8.09166	−	6.25439i	−0.319353	−	0.246841i
$643$	−10.6916	+	35.7124i	−0.421635	+	1.40836i	0.438701	+	0.898633i	$0.355439\pi$
$643$	−10.6916	+	35.7124i	−0.421635	+	1.40836i	−0.860336	+	0.509727i	$0.829746\pi$
$644$	0.639057	−	0.858403i	0.0251824	−	0.0338258i
$645$	−43.9951	−	3.36100i	−1.73231	−	0.132339i
$646$	13.0257	−	6.54173i	0.512487	−	0.257381i
$647$	7.10308			0.279251			0.139625	−	0.990204i	$-0.455410\pi$
$647$	7.10308			0.279251			0.139625	+	0.990204i	$0.455410\pi$
$648$	4.83908	+	7.58837i	0.190097	+	0.298099i
$649$	−0.0336296			−0.00132008
$650$	−45.8494	+	23.0264i	−1.79836	+	0.903171i
$651$	11.9903	+	24.9905i	0.469937	+	0.979456i
$652$	10.5665	−	14.1932i	0.413815	−	0.555850i
$653$	6.10772	−	20.4012i	0.239014	−	0.798361i	−0.751354	−	0.659899i	$-0.770599\pi$
$653$	6.10772	−	20.4012i	0.239014	−	0.798361i	0.990368	−	0.138462i	$-0.0442158\pi$
$654$	−13.0962	+	5.37061i	−0.512101	+	0.210008i
$655$	13.0679	−	30.2947i	0.510603	−	1.18371i
$656$	1.22422	−	6.94288i	0.0477976	−	0.271074i
$657$	−24.6311	+	4.90514i	−0.960951	+	0.191368i
$658$	−3.33120	−	18.8922i	−0.129864	−	0.736494i
$659$	5.77964	+	1.36980i	0.225143	+	0.0533599i	0.341639	−	0.939831i	$-0.389018\pi$
$659$	5.77964	+	1.36980i	0.225143	+	0.0533599i	−0.116496	+	0.993191i	$0.537166\pi$
$660$	−0.0924104	−	0.0180218i	−0.00359707	−	0.000701499i
$661$	−16.2750	+	10.7042i	−0.633023	+	0.416346i	−0.825062	−	0.565042i	$-0.808860\pi$
$661$	−16.2750	+	10.7042i	−0.633023	+	0.416346i	0.192040	+	0.981387i	$0.438490\pi$
$662$	1.11617	+	19.1639i	0.0433813	+	0.744828i
$663$	−14.7117	+	38.2548i	−0.571354	+	1.48569i
$664$	−4.35011	−	14.5304i	−0.168817	−	0.563888i
$665$	−17.9214	−	6.52287i	−0.694963	−	0.252946i
$666$	−23.6120	−	0.853664i	−0.914945	−	0.0330788i
$667$	2.71330	−	0.987559i	0.105059	−	0.0382384i
$668$	−5.03643	−	6.76510i	−0.194865	−	0.261749i
$669$	−23.1592	+	0.929379i	−0.895385	+	0.0359319i
$670$	−15.6568	+	3.71074i	−0.604876	+	0.143358i
$671$	0.0125163	+	0.0290161i	0.000483187	+	0.00112015i
$672$	−0.720114	+	2.81105i	−0.0277790	+	0.108439i
$673$	0.434211	+	0.285585i	0.0167376	+	0.0110085i	0.557850	−	0.829942i	$-0.311626\pi$
$673$	0.434211	+	0.285585i	0.0167376	+	0.0110085i	−0.541113	+	0.840950i	$0.681997\pi$
$674$	7.36472	−	12.7561i	0.283678	−	0.491345i
$675$	−39.9643	−	42.0241i	−1.53823	−	1.61751i
$676$	−4.06656	−	7.04349i	−0.156406	−	0.270903i
$677$	−1.17987	+	20.2575i	−0.0453460	+	0.778561i	0.896609	+	0.442822i	$0.146023\pi$
$677$	−1.17987	+	20.2575i	−0.0453460	+	0.778561i	−0.941955	+	0.335738i	$0.891014\pi$
$678$	29.1737	−	20.9105i	1.12041	−	0.803063i
$679$	−5.35916	−	0.626395i	−0.205666	−	0.0240389i
$680$	14.2004	+	15.0516i	0.544562	+	0.577202i
$681$	−38.5424	−	12.3019i	−1.47695	−	0.471410i
$682$	−0.128287	+	0.0149946i	−0.00491235	+	0.000574172i
$683$	33.8852	+	28.4331i	1.29658	+	1.08796i	0.990725	+	0.135885i	$0.0433879\pi$
$683$	33.8852	+	28.4331i	1.29658	+	1.08796i	0.305858	+	0.952077i	$0.401057\pi$
$684$	−8.46777	+	0.680721i	−0.323773	+	0.0260280i
$685$	39.4203	−	33.0776i	1.50617	−	1.26383i
$686$	−12.8688	+	13.6402i	−0.491334	+	0.520784i
$687$	−14.9737	−	9.00966i	−0.571282	−	0.343740i
$688$	−5.66286	−	2.84400i	−0.215895	−	0.108426i
$689$	−24.3974	−	12.2529i	−0.929468	−	0.466797i
$690$	−0.0803606	+	4.44693i	−0.00305928	+	0.169292i
$691$	18.3720	−	19.4732i	0.698904	−	0.740795i	−0.276550	−	0.961000i	$-0.589191\pi$
$691$	18.3720	−	19.4732i	0.698904	−	0.740795i	0.975454	+	0.220205i	$0.0706726\pi$
$692$	−5.91820	+	4.96596i	−0.224976	+	0.188777i
$693$	0.0655207	+	0.0180522i	0.00248893	+	0.000685747i
$694$	−7.52590	−	6.31498i	−0.285679	−	0.239713i
$695$	74.9836	−	8.76433i	2.84429	−	0.332450i
$696$	−5.79110	+	5.26913i	−0.219511	+	0.199726i
$697$	24.9034	+	26.3961i	0.943285	+	0.999824i
$698$	−25.7798	−	3.01323i	−0.975781	−	0.114052i
$699$	2.28702	+	1.03593i	0.0865031	+	0.0391824i
$700$	1.08721	−	18.6667i	0.0410927	−	0.705535i
$701$	−18.8061	−	32.5731i	−0.710295	−	1.23027i	−0.964746	−	0.263182i	$-0.915228\pi$
$701$	−18.8061	−	32.5731i	−0.710295	−	1.23027i	0.254451	−	0.967086i	$-0.418105\pi$
$702$	16.3232	−	17.4398i	0.616080	−	0.658223i
$703$	11.1509	−	19.3140i	0.420565	−	0.728440i
$704$	−0.0112973	−	0.00743037i	−0.000425784	−	0.000280042i
$705$	56.9941	+	55.7517i	2.14652	+	2.09973i
$706$	−0.490661	−	1.13748i	−0.0184663	−	0.0428096i
$707$	−7.66009	+	1.81548i	−0.288087	+	0.0682780i
$708$	−2.30171	−	3.64122i	−0.0865036	−	0.136846i
$709$	−14.3162	−	19.2300i	−0.537657	−	0.722198i	0.447418	−	0.894325i	$-0.352344\pi$
$709$	−14.3162	−	19.2300i	−0.537657	−	0.722198i	−0.985075	+	0.172127i	$0.944936\pi$
$710$	22.0079	−	8.01021i	0.825941	−	0.300618i
$711$	10.9436	+	9.87810i	0.410417	+	0.370458i
$712$	−7.30001	−	2.65699i	−0.273580	−	0.0995748i
$713$	1.74991	+	5.84512i	0.0655348	+	0.218902i
$714$	−9.39304	−	11.6141i	−0.351526	−	0.434645i
$715$	0.0145298	+	0.249467i	0.000543383	+	0.00932952i
$716$	−14.9367	+	9.82404i	−0.558212	+	0.367142i
$717$	11.9734	+	34.8430i	0.447155	+	1.30124i
$718$	11.9210	+	2.82532i	0.444887	+	0.105440i
$719$	1.44404	+	8.18958i	0.0538537	+	0.305420i	0.999823	−	0.0188379i	$-0.00599664\pi$
$719$	1.44404	+	8.18958i	0.0538537	+	0.305420i	−0.945969	+	0.324258i	$0.894886\pi$
$720$	−4.37355	−	11.2392i	−0.162993	−	0.418859i
$721$	0.292102	−	1.65659i	0.0108785	−	0.0616948i
$722$	−4.34955	+	10.0834i	−0.161874	+	0.375265i
$723$	−2.13074	+	15.7552i	−0.0792429	+	0.585943i
$724$	−3.92266	+	13.1026i	−0.145785	+	0.486955i
$725$	30.1269	−	40.4674i	1.11888	−	1.50292i
$726$	10.7553	−	15.7262i	0.399166	−	0.583652i
$727$	−42.7215	+	21.4555i	−1.58445	+	0.795742i	−0.999878	−	0.0155984i	$-0.995035\pi$
$727$	−42.7215	+	21.4555i	−1.58445	+	0.795742i	−0.584574	+	0.811340i	$0.698738\pi$
$728$	7.70179			0.285448
$729$	24.2235	+	11.9256i	0.897168	+	0.441689i
$730$	33.6541			1.24560
$731$	29.1494	−	14.6394i	1.07813	−	0.541457i
$732$	−2.28505	+	3.34115i	−0.0844577	+	0.123492i
$733$	12.3666	−	16.6112i	0.456771	−	0.613550i	−0.512756	−	0.858535i	$-0.671375\pi$
$733$	12.3666	−	16.6112i	0.456771	−	0.613550i	0.969527	+	0.244984i	$0.0787828\pi$
$734$	2.88077	−	9.62243i	0.106331	−	0.355170i
$735$	3.91291	−	28.9331i	0.144330	−	1.06721i
$736$	−0.253001	+	0.586523i	−0.00932575	+	0.0216195i
$737$	−0.00939823	+	0.0533000i	−0.000346188	+	0.00196333i
$738$	−7.66994	−	19.7102i	−0.282334	−	0.725543i
$739$	−4.41970	−	25.0654i	−0.162581	−	0.922045i	−0.951523	−	0.307577i	$-0.900482\pi$
$739$	−4.41970	−	25.0654i	−0.162581	−	0.922045i	0.788942	−	0.614468i	$-0.210629\pi$
$740$	30.8076	+	7.30153i	1.13251	+	0.268410i
$741$	7.32746	+	21.3231i	0.269181	+	0.783325i
$742$	8.31292	−	5.46749i	0.305177	−	0.200718i
$743$	−1.36294	−	23.4008i	−0.0500015	−	0.858492i	−0.926315	−	0.376751i	$-0.877041\pi$
$743$	−1.36294	−	23.4008i	−0.0500015	−	0.858492i	0.876313	−	0.481742i	$-0.159996\pi$
$744$	−10.4039	−	12.8639i	−0.381424	−	0.471613i
$745$	−2.51644	−	8.40550i	−0.0921953	−	0.307954i
$746$	−32.6929	−	11.8992i	−1.19697	−	0.435662i
$747$	−33.7776	−	30.4889i	−1.23586	−	1.11553i
$748$	0.0654056	−	0.0238057i	0.00239147	−	0.000870423i
$749$	−5.90730	−	7.93489i	−0.215848	−	0.289934i
$750$	22.9207	+	36.2597i	0.836945	+	1.32402i
$751$	21.6246	−	5.12511i	0.789091	−	0.187018i	0.183738	−	0.982975i	$-0.441180\pi$
$751$	21.6246	−	5.12511i	0.789091	−	0.187018i	0.605353	+	0.795957i	$0.293032\pi$
$752$	4.53527	+	10.5139i	0.165384	+	0.383404i
$753$	−7.61883	−	7.45274i	−0.277646	−	0.271593i
$754$	17.3617	+	11.4190i	0.632278	+	0.415856i
$755$	−29.8008	+	51.6165i	−1.08456	+	1.87852i
$756$	2.52985	+	8.32977i	0.0920097	+	0.302951i
$757$	6.59727	+	11.4268i	0.239782	+	0.415314i	0.960652	−	0.277756i	$-0.0895908\pi$
$757$	6.59727	+	11.4268i	0.239782	+	0.415314i	−0.720870	+	0.693071i	$0.756257\pi$
$758$	0.565852	−	9.71531i	0.0205527	−	0.352876i
$759$	0.0136273	+	0.00617264i	0.000494641	+	0.000224053i
$760$	11.3066	+	1.32155i	0.410132	+	0.0479375i
$761$	1.31639	+	1.39529i	0.0477190	+	0.0505792i	0.750793	−	0.660537i	$-0.229671\pi$
$761$	1.31639	+	1.39529i	0.0477190	+	0.0505792i	−0.703074	+	0.711116i	$0.748190\pi$
$762$	−10.2213	+	9.29999i	−0.370277	+	0.336903i
$763$	−13.5988	+	1.58947i	−0.492310	+	0.0575428i
$764$	2.07142	+	1.73813i	0.0749415	+	0.0628834i
$765$	59.8491	+	16.4896i	2.16385	+	0.596182i
$766$	8.24372	−	6.91731i	0.297858	−	0.249932i
$767$	−7.84594	+

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.893633 - 0.448799i) q^{2} +(-0.977769 + 1.42967i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-1.15296 + 3.85116i) q^{5} +(-0.232129 + 1.71643i) q^{6} +(-0.663579 + 1.53835i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-1.08794 - 2.79578i) q^{9} +O(q^{10})\)	\(q+(0.893633 - 0.448799i) q^{2} +(-0.977769 + 1.42967i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-1.15296 + 3.85116i) q^{5} +(-0.232129 + 1.71643i) q^{6} +(-0.663579 + 1.53835i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-1.08794 - 2.79578i) q^{9} +(0.698073 + 3.95897i) q^{10} +(0.0131573 + 0.00311835i) q^{11} +(0.562892 + 1.63803i) q^{12} +(3.84080 - 2.52614i) q^{13} +(0.0974140 + 1.67253i) q^{14} +(-4.37857 - 5.41390i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(4.83704 + 1.76054i) q^{17} +(-2.22696 - 2.01014i) q^{18} +(2.66092 - 0.968497i) q^{19} +(2.40060 + 3.22457i) q^{20} +(-1.55051 - 2.45285i) q^{21} +(0.0131573 - 0.00311835i) q^{22} +(-0.253001 - 0.586523i) q^{23} +(1.23817 + 1.21117i) q^{24} +(-9.32465 - 6.13292i) q^{25} +(2.29854 - 3.98119i) q^{26} +(5.06081 + 1.17823i) q^{27} +(0.837684 + 1.45091i) q^{28} +(-0.262835 + 4.51270i) q^{29} +(-6.34259 - 2.87294i) q^{30} +(-9.48738 - 1.10892i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-0.0173231 + 0.0157617i) q^{33} +(5.11267 - 0.597585i) q^{34} +(-5.15935 - 4.32920i) q^{35} +(-2.89223 - 0.796865i) q^{36} +(6.03321 - 5.06246i) q^{37} +(1.94323 - 2.05970i) q^{38} +(-0.143865 + 7.96107i) q^{39} +(3.59244 + 1.80419i) q^{40} +(6.30010 + 3.16403i) q^{41} +(-2.48643 - 1.49608i) q^{42} +(4.34864 - 4.60929i) q^{43} +(0.0103583 - 0.00869166i) q^{44} +(12.0213 - 0.966392i) q^{45} +(-0.489321 - 0.410589i) q^{46} +(-11.3730 + 1.32931i) q^{47} +(1.65004 + 0.526657i) q^{48} +(2.87751 + 3.04998i) q^{49} +(-11.0853 - 1.29568i) q^{50} +(-7.24650 + 5.19399i) q^{51} +(0.267296 - 4.58930i) q^{52} +(-2.96943 - 5.14321i) q^{53} +(5.05129 - 1.21838i) q^{54} +(-0.0271791 + 0.0470757i) q^{55} +(1.39975 + 0.920630i) q^{56} +(-1.21713 + 4.75122i) q^{57} +(1.79042 + 4.15065i) q^{58} +(-2.42002 + 0.573555i) q^{59} +(-6.95732 + 0.279198i) q^{60} +(1.39556 + 1.87456i) q^{61} +(-8.97591 + 3.26697i) q^{62} +(5.02282 + 0.181594i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(5.30025 + 17.7041i) q^{65} +(-0.00840662 + 0.0218597i) q^{66} +(0.232730 + 3.99581i) q^{67} +(4.30065 - 2.82858i) q^{68} +(1.08591 + 0.211774i) q^{69} +(-6.55350 - 1.55321i) q^{70} +(-1.01165 - 5.73737i) q^{71} +(-2.94223 + 0.585927i) q^{72} +(1.45371 - 8.24441i) q^{73} +(3.11944 - 7.23168i) q^{74} +(17.8854 - 7.33464i) q^{75} +(0.812139 - 2.71273i) q^{76} +(-0.0135280 + 0.0181713i) q^{77} +(3.44436 + 7.17884i) q^{78} +(-4.39144 + 2.20546i) q^{79} +4.02004 q^{80} +(-6.63278 + 6.08327i) q^{81} +7.04998 q^{82} +(13.5542 - 6.80719i) q^{83} +(-2.89339 - 0.221040i) q^{84} +(-12.3570 + 16.5984i) q^{85} +(1.81744 - 6.07068i) q^{86} +(-6.19470 - 4.78814i) q^{87} +(0.00535572 - 0.0124160i) q^{88} +(1.34899 - 7.65049i) q^{89} +(10.3089 - 6.25877i) q^{90} +(1.33740 + 7.58479i) q^{91} +(-0.621545 - 0.147309i) q^{92} +(10.8619 - 12.4796i) q^{93} +(-9.56667 + 6.29210i) q^{94} +(0.661893 + 11.3643i) q^{95} +(1.71089 - 0.269899i) q^{96} +(0.923670 + 3.08527i) q^{97} +(3.94027 + 1.43414i) q^{98} +(-0.00559615 - 0.0401776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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