LMFDB - Embedded newform 162.2.g.a.43.2

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:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	162.43
Dual form			162.2.g.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.286803 + 0.957990i) q^{2} +(-0.671790 + 1.59646i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.417669 + 0.968265i) q^{5} +(-1.72207 - 0.185697i) q^{6} +(-0.0919975 + 1.57954i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.09740 - 2.14498i) q^{9} +O(q^{10})$	\(q+(0.286803 + 0.957990i) q^{2} +(-0.671790 + 1.59646i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.417669 + 0.968265i) q^{5} +(-1.72207 - 0.185697i) q^{6} +(-0.0919975 + 1.57954i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.09740 - 2.14498i) q^{9} +(-0.807799 + 0.677824i) q^{10} +(-2.80349 - 3.76574i) q^{11} +(-0.315999 - 1.70298i) q^{12} +(4.35285 + 4.61375i) q^{13} +(-1.53956 + 0.364884i) q^{14} +(-1.82639 + 0.0163222i) q^{15} +(0.396080 - 0.918216i) q^{16} +(1.15308 + 6.53944i) q^{17} +(1.45333 - 2.62447i) q^{18} +(0.419952 - 2.38166i) q^{19} +(-0.881028 - 0.579461i) q^{20} +(-2.45987 - 1.20799i) q^{21} +(2.80349 - 3.76574i) q^{22} +(-0.129765 - 2.22799i) q^{23} +(1.54081 - 0.791144i) q^{24} +(2.66812 - 2.82804i) q^{25} +(-3.17151 + 5.49322i) q^{26} +(4.83339 - 1.90744i) q^{27} +(-0.791107 - 1.37024i) q^{28} +(1.01575 + 0.240736i) q^{29} +(-0.539450 - 1.74498i) q^{30} +(6.89550 + 3.46305i) q^{31} +(0.993238 + 0.116093i) q^{32} +(7.89524 - 1.94589i) q^{33} +(-5.93401 + 2.98017i) q^{34} +(-1.56784 + 0.570645i) q^{35} +(2.93103 + 0.639565i) q^{36} +(1.93811 + 0.705415i) q^{37} +(2.40205 - 0.280760i) q^{38} +(-10.2899 + 3.84969i) q^{39} +(0.302436 - 1.01021i) q^{40} +(1.76253 - 5.88725i) q^{41} +(0.451741 - 2.70299i) q^{42} +(-0.444497 + 0.0519543i) q^{43} +(4.41160 + 1.60569i) q^{44} +(1.20089 - 2.92673i) q^{45} +(2.09717 - 0.763307i) q^{46} +(-5.08277 + 2.55266i) q^{47} +(1.19982 + 1.24918i) q^{48} +(4.46620 + 0.522023i) q^{49} +(3.47446 + 1.74494i) q^{50} +(-11.2146 - 2.55228i) q^{51} +(-6.17205 - 1.46280i) q^{52} +(-2.55834 - 4.43118i) q^{53} +(3.21354 + 4.08328i) q^{54} +(2.47531 - 4.28736i) q^{55} +(1.08578 - 1.15086i) q^{56} +(3.52012 + 2.27042i) q^{57} +(0.0606964 + 1.04212i) q^{58} +(-2.57397 + 3.45744i) q^{59} +(1.51695 - 1.01725i) q^{60} +(-7.07255 - 4.65169i) q^{61} +(-1.33991 + 7.59904i) q^{62} +(3.58103 - 3.11558i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-2.64928 + 6.14173i) q^{65} +(4.12852 + 7.00547i) q^{66} +(-8.93095 + 2.11667i) q^{67} +(-4.55686 - 4.82999i) q^{68} +(3.64407 + 1.28957i) q^{69} +(-0.996332 - 1.33831i) q^{70} +(6.70480 - 5.62599i) q^{71} +(0.227933 + 2.99133i) q^{72} +(-9.89062 - 8.29921i) q^{73} +(-0.119923 + 2.05901i) q^{74} +(2.72245 + 6.15940i) q^{75} +(0.957882 + 2.22062i) q^{76} +(6.20605 - 4.08178i) q^{77} +(-6.63914 - 8.75350i) q^{78} +(0.686776 + 2.29399i) q^{79} +1.05451 q^{80} +(-0.201863 + 8.99774i) q^{81} +6.14542 q^{82} +(-4.37599 - 14.6168i) q^{83} +(2.71899 - 0.342462i) q^{84} +(-5.85031 + 3.84781i) q^{85} +(-0.177255 - 0.410923i) q^{86} +(-1.06669 + 1.45988i) q^{87} +(-0.272974 + 4.68678i) q^{88} +(3.18943 + 2.67625i) q^{89} +(3.14819 + 0.311047i) q^{90} +(-7.68804 + 6.45103i) q^{91} +(1.33272 + 1.79015i) q^{92} +(-10.1610 + 8.68198i) q^{93} +(-3.90318 - 4.13712i) q^{94} +(2.48148 - 0.588123i) q^{95} +(-0.852586 + 1.50768i) q^{96} +(-3.13875 + 7.27643i) q^{97} +(0.780826 + 4.42829i) q^{98} +(-2.19741 + 13.9117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{27}\right)$

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 $

$2$	0.286803	+	0.957990i	0.202801	+	0.677401i
$2$	0.286803	+	0.957990i	0.202801	+	0.677401i
$3$	−0.671790	+	1.59646i	−0.387858	+	0.921719i
$3$	−0.671790	+	1.59646i	−0.387858	+	0.921719i
$4$	−0.835488	+	0.549509i	−0.417744	+	0.274754i
$5$	0.417669	+	0.968265i	0.186787	+	0.433021i	0.985719	−	0.168401i	$-0.0538603\pi$
$5$	0.417669	+	0.968265i	0.186787	+	0.433021i	−0.798931	+	0.601422i	$0.794601\pi$
$6$	−1.72207	−	0.185697i	−0.703031	−	0.0758105i
$7$	−0.0919975	+	1.57954i	−0.0347718	+	0.597009i	0.935250	+	0.353989i	$0.115175\pi$
$7$	−0.0919975	+	1.57954i	−0.0347718	+	0.597009i	−0.970021	+	0.243020i	$0.921862\pi$
$8$	−0.766044	−	0.642788i	−0.270838	−	0.227260i
$9$	−2.09740	−	2.14498i	−0.699132	−	0.714993i
$10$	−0.807799	+	0.677824i	−0.255449	+	0.214347i
$11$	−2.80349	−	3.76574i	−0.845285	−	1.13541i	−0.989308	−	0.145841i	$-0.953411\pi$
$11$	−2.80349	−	3.76574i	−0.845285	−	1.13541i	0.144023	−	0.989574i	$-0.453996\pi$
$12$	−0.315999	−	1.70298i	−0.0912210	−	0.491608i
$13$	4.35285	+	4.61375i	1.20726	+	1.27962i	0.949627	+	0.313382i	$0.101462\pi$
$13$	4.35285	+	4.61375i	1.20726	+	1.27962i	0.257636	+	0.966242i	$0.417057\pi$
$14$	−1.53956	+	0.364884i	−0.411466	+	0.0975192i
$15$	−1.82639	+	0.0163222i	−0.471571	+	0.00421437i
$16$	0.396080	−	0.918216i	0.0990199	−	0.229554i
$17$	1.15308	+	6.53944i	0.279663	+	1.58605i	0.723749	+	0.690063i	$0.242417\pi$
$17$	1.15308	+	6.53944i	0.279663	+	1.58605i	−0.444086	+	0.895984i	$0.646472\pi$
$18$	1.45333	−	2.62447i	0.342552	−	0.618593i
$19$	0.419952	−	2.38166i	0.0963435	−	0.546391i	−0.897984	−	0.440028i	$-0.854968\pi$
$19$	0.419952	−	2.38166i	0.0963435	−	0.546391i	0.994327	−	0.106363i	$-0.0339205\pi$
$20$	−0.881028	−	0.579461i	−0.197004	−	0.129571i
$21$	−2.45987	−	1.20799i	−0.536788	−	0.263605i
$22$	2.80349	−	3.76574i	0.597707	−	0.802860i
$23$	−0.129765	−	2.22799i	−0.0270579	−	0.464567i	−0.984438	−	0.175735i	$-0.943770\pi$
$23$	−0.129765	−	2.22799i	−0.0270579	−	0.464567i	0.957380	−	0.288832i	$-0.0932671\pi$
$24$	1.54081	−	0.791144i	0.314516	−	0.161492i
$25$	2.66812	−	2.82804i	0.533624	−	0.565608i
$26$	−3.17151	+	5.49322i	−0.621985	+	1.07731i
$27$	4.83339	−	1.90744i	0.930186	−	0.367087i
$28$	−0.791107	−	1.37024i	−0.149505	−	0.258950i
$29$	1.01575	+	0.240736i	0.188619	+	0.0447036i	0.323840	−	0.946112i	$-0.395026\pi$
$29$	1.01575	+	0.240736i	0.188619	+	0.0447036i	−0.135220	+	0.990816i	$0.543174\pi$
$30$	−0.539450	−	1.74498i	−0.0984897	−	0.318588i
$31$	6.89550	+	3.46305i	1.23847	+	0.621983i	0.942816	−	0.333313i	$-0.108167\pi$
$31$	6.89550	+	3.46305i	1.23847	+	0.621983i	0.295653	+	0.955295i	$0.404463\pi$
$32$	0.993238	+	0.116093i	0.175581	+	0.0205225i
$33$	7.89524	−	1.94589i	1.37438	−	0.338735i
$34$	−5.93401	+	2.98017i	−1.01767	+	0.511095i
$35$	−1.56784	+	0.570645i	−0.265013	+	0.0964567i
$36$	2.93103	+	0.639565i	0.488506	+	0.106594i
$37$	1.93811	+	0.705415i	0.318623	+	0.115969i	0.496381	−	0.868105i	$-0.334662\pi$
$37$	1.93811	+	0.705415i	0.318623	+	0.115969i	−0.177757	+	0.984074i	$0.556884\pi$
$38$	2.40205	−	0.280760i	0.389664	−	0.0455452i
$39$	−10.2899	+	3.84969i	−1.64770	+	0.616444i
$40$	0.302436	−	1.01021i	0.0478193	−	0.159728i
$41$	1.76253	−	5.88725i	0.275260	−	0.919434i	−0.702848	−	0.711340i	$-0.748089\pi$
$41$	1.76253	−	5.88725i	0.275260	−	0.919434i	0.978109	−	0.208094i	$-0.0667261\pi$
$42$	0.451741	−	2.70299i	0.0697052	−	0.417080i
$43$	−0.444497	+	0.0519543i	−0.0677852	+	0.00792295i	−0.149918	−	0.988698i	$-0.547901\pi$
$43$	−0.444497	+	0.0519543i	−0.0677852	+	0.00792295i	0.0821327	+	0.996621i	$0.473827\pi$
$44$	4.41160	+	1.60569i	0.665073	+	0.242067i
$45$	1.20089	−	2.92673i	0.179018	−	0.436291i
$46$	2.09717	−	0.763307i	0.309211	−	0.112544i
$47$	−5.08277	+	2.55266i	−0.741398	+	0.372344i	−0.779062	−	0.626947i	$-0.784304\pi$
$47$	−5.08277	+	2.55266i	−0.741398	+	0.372344i	0.0376647	+	0.999290i	$0.488008\pi$
$48$	1.19982	+	1.24918i	0.173179	+	0.180303i
$49$	4.46620	+	0.522023i	0.638028	+	0.0745748i
$50$	3.47446	+	1.74494i	0.491362	+	0.246771i
$51$	−11.2146	−	2.55228i	−1.57036	−	0.357391i
$52$	−6.17205	−	1.46280i	−0.855909	−	0.202854i
$53$	−2.55834	−	4.43118i	−0.351415	−	0.608669i	0.635082	−	0.772444i	$-0.280966\pi$
$53$	−2.55834	−	4.43118i	−0.351415	−	0.608669i	−0.986498	+	0.163775i	$0.947633\pi$
$54$	3.21354	+	4.08328i	0.437308	+	0.555664i
$55$	2.47531	−	4.28736i	0.333771	−	0.578107i
$56$	1.08578	−	1.15086i	0.145094	−	0.153790i
$57$	3.52012	+	2.27042i	0.466252	+	0.300724i
$58$	0.0606964	+	1.04212i	0.00796983	+	0.136837i
$59$	−2.57397	+	3.45744i	−0.335102	+	0.450120i	−0.937453	−	0.348111i	$-0.886823\pi$
$59$	−2.57397	+	3.45744i	−0.335102	+	0.450120i	0.602351	+	0.798231i	$0.294231\pi$
$60$	1.51695	−	1.01725i	0.195838	−	0.131327i
$61$	−7.07255	−	4.65169i	−0.905547	−	0.595588i	0.00904793	−	0.999959i	$-0.497120\pi$
$61$	−7.07255	−	4.65169i	−0.905547	−	0.595588i	−0.914595	+	0.404372i	$0.867490\pi$
$62$	−1.33991	+	7.59904i	−0.170169	+	0.965078i
$63$	3.58103	−	3.11558i	0.451167	−	0.392526i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−2.64928	+	6.14173i	−0.328603	+	0.761788i
$66$	4.12852	+	7.00547i	0.508185	+	0.862313i
$67$	−8.93095	+	2.11667i	−1.09109	+	0.258593i	−0.736506	−	0.676432i	$-0.763525\pi$
$67$	−8.93095	+	2.11667i	−1.09109	+	0.258593i	−0.354583	+	0.935024i	$0.615377\pi$
$68$	−4.55686	−	4.82999i	−0.552601	−	0.585723i
$69$	3.64407	+	1.28957i	0.438695	+	0.155246i
$70$	−0.996332	−	1.33831i	−0.119085	−	0.159958i
$71$	6.70480	−	5.62599i	0.795713	−	0.667682i	−0.151439	−	0.988467i	$-0.548391\pi$
$71$	6.70480	−	5.62599i	0.795713	−	0.667682i	0.947152	+	0.320784i	$0.103946\pi$
$72$	0.227933	+	2.99133i	0.0268622	+	0.352531i
$73$	−9.89062	−	8.29921i	−1.15761	−	0.971350i	−0.157740	−	0.987481i	$-0.550421\pi$
$73$	−9.89062	−	8.29921i	−1.15761	−	0.971350i	−0.999870	+	0.0161311i	$0.994865\pi$
$74$	−0.119923	+	2.05901i	−0.0139408	+	0.239355i
$75$	2.72245	+	6.15940i	0.314361	+	0.711227i
$76$	0.957882	+	2.22062i	0.109877	+	0.254722i
$77$	6.20605	−	4.08178i	0.707245	−	0.465162i
$78$	−6.63914	−	8.75350i	−0.751735	−	0.991139i
$79$	0.686776	+	2.29399i	0.0772683	+	0.258094i	0.987892	−	0.155142i	$-0.0495836\pi$
$79$	0.686776	+	2.29399i	0.0772683	+	0.258094i	−0.910624	+	0.413236i	$0.864398\pi$
$80$	1.05451			0.117897
$81$	−0.201863	+	8.99774i	−0.0224292	+	0.999748i
$82$	6.14542			0.678648
$83$	−4.37599	−	14.6168i	−0.480327	−	1.60440i	−0.763820	−	0.645429i	$-0.776679\pi$
$83$	−4.37599	−	14.6168i	−0.480327	−	1.60440i	0.283493	−	0.958974i	$-0.408507\pi$
$84$	2.71899	−	0.342462i	0.296666	−	0.0373656i
$85$	−5.85031	+	3.84781i	−0.634555	+	0.417353i
$86$	−0.177255	−	0.410923i	−0.0191139	−	0.0443110i
$87$	−1.06669	+	1.45988i	−0.114362	+	0.156515i
$88$	−0.272974	+	4.68678i	−0.0290991	+	0.499612i
$89$	3.18943	+	2.67625i	0.338079	+	0.283682i	0.795982	−	0.605320i	$-0.206955\pi$
$89$	3.18943	+	2.67625i	0.338079	+	0.283682i	−0.457903	+	0.889002i	$0.651399\pi$
$90$	3.14819	+	0.311047i	0.331849	+	0.0327872i
$91$	−7.68804	+	6.45103i	−0.805925	+	0.676252i
$92$	1.33272	+	1.79015i	0.138945	+	0.186636i
$93$	−10.1610	+	8.68198i	−1.05364	+	0.900279i
$94$	−3.90318	−	4.13712i	−0.402582	−	0.426712i
$95$	2.48148	−	0.588123i	0.254595	−	0.0603401i
$96$	−0.852586	+	1.50768i	−0.0870167	+	0.153877i
$97$	−3.13875	+	7.27643i	−0.318692	+	0.738810i	0.681285	+	0.732018i	$0.261421\pi$
$97$	−3.13875	+	7.27643i	−0.318692	+	0.738810i	−0.999977	+	0.00679211i	$0.997838\pi$
$98$	0.780826	+	4.42829i	0.0788754	+	0.447325i
$99$	−2.19741	+	13.9117i	−0.220848	+	1.39818i
$100$	−0.675147	+	3.82895i	−0.0675147	+	0.382895i
$101$	−7.37545	−	4.85091i	−0.733885	−	0.482684i	0.126732	−	0.991937i	$-0.459551\pi$
$101$	−7.37545	−	4.85091i	−0.733885	−	0.482684i	−0.860617	+	0.509253i	$0.829922\pi$
$102$	−0.771327	−	11.4755i	−0.0763728	−	1.13624i
$103$	7.79287	−	10.4676i	0.767854	−	1.03141i	−0.230444	−	0.973086i	$-0.574018\pi$
$103$	7.79287	−	10.4676i	0.767854	−	1.03141i	0.998298	−	0.0583211i	$-0.0185747\pi$
$104$	−0.368814	−	6.33229i	−0.0361652	−	0.620933i
$105$	0.142242	−	2.88635i	0.0138814	−	0.281679i
$106$	3.51128	−	3.72174i	0.341046	−	0.361487i
$107$	−5.66494	+	9.81197i	−0.547651	+	0.948559i	0.450784	+	0.892633i	$0.351144\pi$
$107$	−5.66494	+	9.81197i	−0.547651	+	0.948559i	−0.998435	+	0.0559257i	$0.982189\pi$
$108$	−2.99008	+	4.24964i	−0.287721	+	0.408921i
$109$	−2.14134	−	3.70890i	−0.205103	−	0.355248i	0.745063	−	0.666994i	$-0.232420\pi$
$109$	−2.14134	−	3.70890i	−0.205103	−	0.355248i	−0.950165	+	0.311746i	$0.899086\pi$
$110$	4.81717	+	1.14169i	0.459299	+	0.108856i
$111$	−2.42817	+	2.62023i	−0.230472	+	0.248702i
$112$	1.41392	+	0.710096i	0.133603	+	0.0670978i
$113$	16.8071	+	1.96447i	1.58108	+	0.184802i	0.860824	−	0.508903i	$-0.169949\pi$
$113$	16.8071	+	1.96447i	1.58108	+	0.184802i	0.720259	+	0.693705i	$0.244023\pi$
$114$	−1.16545	+	4.02340i	−0.109155	+	0.376826i
$115$	2.10308	−	1.05621i	0.196113	−	0.0984918i
$116$	−0.980930	+	0.357029i	−0.0910771	+	0.0331493i
$117$	0.766747	−	19.0136i	0.0708858	−	1.75781i
$118$	−4.05041	−	1.47423i	−0.372870	−	0.135714i
$119$	−10.4354	+	1.21972i	−0.956608	+	0.111811i
$120$	1.40959	+	1.16148i	0.128677	+	0.106028i
$121$	−3.16643	+	10.5766i	−0.287857	+	0.961509i
$122$	2.42784	−	8.10955i	0.219806	−	0.734204i
$123$	8.21474	+	6.76881i	0.740698	+	0.610323i
$124$	−7.66409	+	0.895803i	−0.688255	+	0.0804455i
$125$	8.80724	+	3.20557i	0.787744	+	0.286715i
$126$	4.01174	+	2.53703i	0.357395	+	0.226016i
$127$	10.9042	−	3.96881i	0.967594	−	0.352175i	0.190589	−	0.981670i	$-0.438960\pi$
$127$	10.9042	−	3.96881i	0.967594	−	0.352175i	0.777005	+	0.629495i	$0.216738\pi$
$128$	−0.893633	+	0.448799i	−0.0789867	+	0.0396686i
$129$	0.215666	−	0.744526i	0.0189883	−	0.0655519i
$130$	−6.64354	−	0.776518i	−0.582677	−	0.0681052i
$131$	1.07771	+	0.541246i	0.0941599	+	0.0472889i	0.495256	−	0.868747i	$-0.335074\pi$
$131$	1.07771	+	0.541246i	0.0941599	+	0.0472889i	−0.401096	+	0.916036i	$0.631371\pi$
$132$	−5.52709	+	5.96427i	−0.481072	+	0.519123i
$133$	3.72329	+	0.882436i	0.322850	+	0.0765169i
$134$	−4.58918	−	7.94869i	−0.396444	−	0.686662i
$135$	3.86567	+	3.88333i	0.332704	+	0.334223i
$136$	3.32016	−	5.75069i	0.284701	−	0.493117i
$137$	9.10283	−	9.64843i	0.777707	−	0.824321i	−0.210476	−	0.977599i	$-0.567501\pi$
$137$	9.10283	−	9.64843i	0.777707	−	0.824321i	0.988183	+	0.153278i	$0.0489829\pi$
$138$	−0.190265	+	3.86084i	−0.0161965	+	0.328656i
$139$	0.969001	+	16.6371i	0.0821896	+	1.41114i	0.747346	+	0.664436i	$0.231328\pi$
$139$	0.969001	+	16.6371i	0.0821896	+	1.41114i	−0.665156	+	0.746704i	$0.731635\pi$
$140$	0.996332	−	1.33831i	0.0842055	−	0.113108i
$141$	−0.660679	−	9.82931i	−0.0556392	−	0.827777i
$142$	7.31260	+	4.80957i	0.613660	+	0.403610i
$143$	5.17102	−	29.3263i	0.432423	−	2.45239i
$144$	−2.80029	+	1.07628i	−0.233357	+	0.0896900i
$145$	0.191149	+	1.08406i	0.0158741	+	0.0900262i
$146$	5.11390	−	11.8554i	0.423229	−	0.981156i
$147$	−3.83374	+	6.77943i	−0.316201	+	0.559158i
$148$	−2.00690	+	0.475644i	−0.164966	+	0.0390977i
$149$	−1.06641	−	1.13033i	−0.0873641	−	0.0926005i	0.682216	−	0.731150i	$-0.261016\pi$
$149$	−1.06641	−	1.13033i	−0.0873641	−	0.0926005i	−0.769581	+	0.638550i	$0.779535\pi$
$150$	−5.11984	+	4.37461i	−0.418033	+	0.357186i
$151$	−9.36439	−	12.5786i	−0.762063	−	1.02363i	−0.998646	−	0.0520171i	$-0.983435\pi$
$151$	−9.36439	−	12.5786i	−0.762063	−	1.02363i	0.236583	−	0.971611i	$-0.423972\pi$
$152$	−1.85261	+	1.55452i	−0.150266	+	0.126088i
$153$	11.6085	−	16.1891i	0.938491	−	1.30881i
$154$	5.69022	+	4.77466i	0.458531	+	0.384753i
$155$	−0.473116	+	8.12309i	−0.0380016	+	0.652462i
$156$	6.48163	−	8.87076i	0.518946	−	0.710229i
$157$	−3.83495	−	8.89042i	−0.306063	−	0.709533i	0.693882	−	0.720089i	$-0.255899\pi$
$157$	−3.83495	−	8.89042i	−0.306063	−	0.709533i	−0.999944	+	0.0105562i	$0.996640\pi$
$158$	−2.00065	+	1.31585i	−0.159163	+	0.104683i
$159$	8.79289	−	1.10748i	0.697321	−	0.0878288i
$160$	0.302436	+	1.01021i	0.0239097	+	0.0798639i
$161$	3.53112			0.278291
$162$	−8.67763	+	2.38720i	−0.681779	+	0.187556i
$163$	−3.83113			−0.300077			−0.150039	−	0.988680i	$-0.547940\pi$
$163$	−3.83113			−0.300077			−0.150039	+	0.988680i	$0.547940\pi$
$164$	1.76253	+	5.88725i	0.137630	+	0.459717i
$165$	5.18173	+	6.83195i	0.403397	+	0.531866i
$166$	12.7477	−	8.38430i	0.989414	−	0.650748i
$167$	7.59982	+	17.6184i	0.588092	+	1.36335i	0.909220	+	0.416315i	$0.136679\pi$
$167$	7.59982	+	17.6184i	0.588092	+	1.36335i	−0.321128	+	0.947036i	$0.604062\pi$
$168$	1.10789	+	2.50655i	0.0854756	+	0.193384i
$169$	−1.58351	+	27.1879i	−0.121809	+	2.09138i
$170$	−5.36405	−	4.50097i	−0.411404	−	0.345209i
$171$	−5.98942	+	4.09451i	−0.458023	+	0.313115i
$172$	0.342823	−	0.287662i	0.0261400	−	0.0219340i
$173$	11.1007	+	14.9108i	0.843969	+	1.13365i	0.989534	+	0.144299i	$0.0460926\pi$
$173$	11.1007	+	14.9108i	0.843969	+	1.13365i	−0.145565	+	0.989349i	$0.546500\pi$
$174$	−1.70448	−	0.603185i	−0.129216	−	0.0457273i
$175$	4.22153	+	4.47456i	0.319118	+	0.338245i
$176$	−4.56817	+	1.08268i	−0.344339	+	0.0816099i
$177$	−3.79051	−	6.43192i	−0.284912	−	0.483452i
$178$	−1.64908	+	3.82300i	−0.123604	+	0.286546i
$179$	−1.05456	−	5.98072i	−0.0788217	−	0.447020i	−0.998520	−	0.0543933i	$-0.982678\pi$
$179$	−1.05456	−	5.98072i	−0.0788217	−	0.447020i	0.919698	−	0.392627i	$-0.128434\pi$
$180$	0.604932	+	3.10514i	0.0450890	+	0.231444i
$181$	4.45034	−	25.2391i	0.330791	−	1.87601i	−0.134594	−	0.990901i	$-0.542973\pi$
$181$	4.45034	−	25.2391i	0.330791	−	1.87601i	0.465385	−	0.885108i	$-0.345916\pi$
$182$	−8.38497	−	5.51488i	−0.621536	−	0.408790i
$183$	12.1775	−	8.16611i	0.900188	−	0.603656i
$184$	−1.33272	+	1.79015i	−0.0982491	+	0.131971i
$185$	0.126460	+	2.17124i	0.00929753	+	0.159632i
$186$	−11.2314	−	7.24408i	−0.823530	−	0.531162i
$187$	21.3932	−	22.6755i	1.56443	−	1.65820i
$188$	2.84388	−	4.92574i	0.207411	−	0.359247i
$189$	2.56821	+	7.81000i	0.186810	+	0.568094i
$190$	1.27511	+	2.20856i	0.0925064	+	0.160226i
$191$	−4.38982	−	1.04041i	−0.317636	−	0.0752812i	0.0687052	−	0.997637i	$-0.478113\pi$
$191$	−4.38982	−	1.04041i	−0.317636	−	0.0752812i	−0.386341	+	0.922356i	$0.626261\pi$
$192$	−1.68887	−	0.384361i	−0.121883	−	0.0277389i
$193$	−22.4713	−	11.2855i	−1.61752	−	0.812348i	−0.999660	−	0.0260590i	$-0.991704\pi$
$193$	−22.4713	−	11.2855i	−1.61752	−	0.812348i	−0.617858	−	0.786289i	$-0.711999\pi$
$194$	−7.87095	−	0.919982i	−0.565101	−	0.0660509i
$195$	−8.02529	−	8.35544i	−0.574703	−	0.598346i
$196$	−4.01831	+	2.01807i	−0.287022	+	0.144148i
$197$	−5.44011	+	1.98004i	−0.387592	+	0.141072i	−0.528464	−	0.848956i	$-0.677232\pi$
$197$	−5.44011	+	1.98004i	−0.387592	+	0.141072i	0.140872	+	0.990028i	$0.455009\pi$
$198$	−13.9575	+	1.88483i	−0.991915	+	0.133949i
$199$	−4.77431	−	1.73771i	−0.338442	−	0.123183i	0.167208	−	0.985922i	$-0.446525\pi$
$199$	−4.77431	−	1.73771i	−0.338442	−	0.123183i	−0.505650	+	0.862739i	$0.668747\pi$
$200$	−3.86173	+	0.451371i	−0.273065	+	0.0319167i
$201$	2.62053	−	15.6799i	0.184838	−	1.10597i
$202$	2.53182	−	8.45686i	0.178138	−	0.595023i
$203$	−0.473698	+	1.58226i	−0.0332471	+	0.111053i
$204$	10.7722	−	4.03013i	0.754203	−	0.282165i
$205$	6.43657	−	0.752328i	0.449550	−	0.0525448i
$206$	12.2629	+	4.46333i	0.854397	+	0.310975i
$207$	−4.50681	+	4.95131i	−0.313245	+	0.344140i
$208$	5.96049	−	2.16944i	0.413286	−	0.150424i
$209$	−10.1461	+	5.09555i	−0.701819	+	0.352467i
$210$	2.80589	−	0.691548i	0.193624	−	0.0477213i
$211$	6.48834	+	0.758378i	0.446676	+	0.0522089i	0.336458	−	0.941699i	$-0.390771\pi$
$211$	6.48834	+	0.758378i	0.446676	+	0.0522089i	0.110218	+	0.993907i	$0.464845\pi$
$212$	4.57244	+	2.29636i	0.314036	+	0.157715i
$213$	4.47748	+	14.4835i	0.306792	+	0.992390i
$214$	−11.0245	−	2.61285i	−0.753618	−	0.178611i
$215$	−0.235958	−	0.408691i	−0.0160922	−	0.0278725i
$216$	−4.92867	−	1.64566i	−0.335354	−	0.111973i
$217$	−6.10439	+	10.5731i	−0.414393	+	0.717749i
$218$	2.93895	−	3.11510i	0.199051	−	0.210981i
$219$	19.8938	−	10.2147i	1.34430	−	0.690245i
$220$	0.287853	+	4.94224i	0.0194070	+	0.333206i
$221$	−25.1522	+	33.7852i	−1.69192	+	2.27264i
$222$	−3.20656	−	1.57467i	−0.215211	−	0.105685i
$223$	6.25945	+	4.11691i	0.419164	+	0.275689i	0.741521	−	0.670930i	$-0.234105\pi$
$223$	6.25945	+	4.11691i	0.419164	+	0.275689i	−0.322357	+	0.946618i	$0.604475\pi$
$224$	−0.274749	+	1.55818i	−0.0183574	+	0.104110i
$225$	−11.6622	+	0.208464i	−0.777479	+	0.0138976i
$226$	2.93840	+	16.6645i	0.195459	+	1.10851i
$227$	−8.33078	+	19.3129i	−0.552933	+	1.28184i	0.381059	+	0.924551i	$0.375559\pi$
$227$	−8.33078	+	19.3129i	−0.552933	+	1.28184i	−0.933993	+	0.357293i	$0.883700\pi$
$228$	−4.18863	+	0.0374333i	−0.277399	+	0.00247908i
$229$	−14.7791	+	3.50272i	−0.976633	+	0.231466i	−0.687790	−	0.725910i	$-0.741419\pi$
$229$	−14.7791	+	3.50272i	−0.976633	+	0.231466i	−0.288843	+	0.957376i	$0.593271\pi$
$230$	1.61501	+	1.71181i	0.106490	+	0.112873i
$231$	2.34726	+	12.6498i	0.154438	+	0.832298i
$232$	−0.623364	−	0.837323i	−0.0409259	−	0.0549730i
$233$	−15.4210	+	12.9397i	−1.01026	+	0.847709i	−0.988373	−	0.152051i	$-0.951412\pi$
$233$	−15.4210	+	12.9397i	−1.01026	+	0.847709i	−0.0218880	+	0.999760i	$0.506968\pi$
$234$	18.4348	−	4.71863i	1.20512	−	0.308467i
$235$	−4.59457	−	3.85530i	−0.299716	−	0.251492i
$236$	0.250625	−	4.30306i	0.0163143	−	0.280106i
$237$	−4.12364	−	0.444668i	−0.267859	−	0.0288843i
$238$	−4.16137	−	9.64715i	−0.269742	−	0.625332i
$239$	5.08152	−	3.34217i	0.328696	−	0.216187i	−0.374425	−	0.927257i	$-0.622160\pi$
$239$	5.08152	−	3.34217i	0.328696	−	0.216187i	0.703121	+	0.711071i	$0.251789\pi$
$240$	−0.708408	+	1.68348i	−0.0457275	+	0.108668i
$241$	4.17044	+	13.9302i	0.268641	+	0.897325i	0.980752	+	0.195257i	$0.0625542\pi$
$241$	4.17044	+	13.9302i	0.268641	+	0.897325i	−0.712111	+	0.702067i	$0.752261\pi$
$242$	−11.0404			−0.709704
$243$	−14.2290	−	6.36686i	−0.912788	−	0.408434i
$244$	8.46517			0.541927
$245$	1.35993	+	4.54250i	0.0868830	+	0.290209i
$246$	−4.12844	+	9.81095i	−0.263219	+	0.625523i
$247$	12.8164	−	8.42947i	0.815487	−	0.536354i
$248$	−3.05626	−	7.08520i	−0.194072	−	0.449910i
$249$	26.2750	+	2.83333i	1.66511	+	0.179555i
$250$	−0.544961	+	9.35662i	−0.0344664	+	0.591764i
$251$	−6.32422	−	5.30665i	−0.399181	−	0.334953i	0.420996	−	0.907062i	$-0.361681\pi$
$251$	−6.32422	−	5.30665i	−0.399181	−	0.334953i	−0.820177	+	0.572110i	$0.806125\pi$
$252$	−1.27986	+	4.57084i	−0.0806239	+	0.287936i
$253$	−8.02623	+	6.73480i	−0.504605	+	0.423414i
$254$	6.92945	+	9.30787i	0.434792	+	0.584028i
$255$	−2.21271	−	11.9247i	−0.138565	−	0.746755i
$256$	−0.686242	−	0.727374i	−0.0428901	−	0.0454609i
$257$	3.32038	−	0.786945i	0.207120	−	0.0490883i	−0.125746	−	0.992062i	$-0.540132\pi$
$257$	3.32038	−	0.786945i	0.207120	−	0.0490883i	0.332866	+	0.942974i	$0.391984\pi$
$258$	0.775102	−	0.00692699i	0.0482557	−	0.000431256i
$259$	−1.29253	+	2.99642i	−0.0803139	+	0.186189i
$260$	−1.16149	−	6.58715i	−0.0720327	−	0.408518i
$261$	−1.61405	−	2.68367i	−0.0999070	−	0.166115i
$262$	−0.209417	+	1.18766i	−0.0129378	+	0.0733742i
$263$	6.49215	+	4.26995i	0.400323	+	0.263297i	0.733668	−	0.679508i	$-0.237807\pi$
$263$	6.49215	+	4.26995i	0.400323	+	0.263297i	−0.333345	+	0.942805i	$0.608177\pi$
$264$	−7.29889	−	3.58433i	−0.449216	−	0.220600i
$265$	3.22202	−	4.32792i	0.197927	−	0.265862i
$266$	0.222487	+	3.81996i	0.0136416	+	0.234217i
$267$	−6.41516	+	3.29393i	−0.392602	+	0.201585i
$268$	6.29857	−	6.67609i	0.384746	−	0.407807i
$269$	−10.2711	+	17.7901i	−0.626242	+	1.08468i	0.362057	+	0.932156i	$0.382074\pi$
$269$	−10.2711	+	17.7901i	−0.626242	+	1.08468i	−0.988299	+	0.152527i	$0.951259\pi$
$270$	−2.61150	+	4.81702i	−0.158931	+	0.293154i
$271$	12.6240	+	21.8655i	0.766856	+	1.32823i	0.939260	+	0.343207i	$0.111513\pi$
$271$	12.6240	+	21.8655i	0.766856	+	1.32823i	−0.172404	+	0.985026i	$0.555153\pi$
$272$	6.46133	+	1.53136i	0.391776	+	0.0928525i
$273$	−5.13409	−	16.6074i	−0.310729	−	1.00513i
$274$	11.8538	+	5.95321i	0.716115	+	0.359647i
$275$	−18.1297	−	2.11906i	−1.09326	−	0.127784i
$276$	−3.75321	+	0.925029i	−0.225917	+	0.0556802i
$277$	16.5556	−	8.31454i	0.994730	−	0.499572i	0.124501	−	0.992219i	$-0.460267\pi$
$277$	16.5556	−	8.31454i	0.994730	−	0.499572i	0.870229	+	0.492647i	$0.163971\pi$
$278$	−15.6603	+	5.69987i	−0.939239	+	0.341855i
$279$	−7.03443	−	22.0541i	−0.421140	−	1.32034i
$280$	1.56784	+	0.570645i	0.0936961	+	0.0341026i
$281$	20.0884	−	2.34800i	1.19838	−	0.140070i	0.506599	−	0.862182i	$-0.330902\pi$
$281$	20.0884	−	2.34800i	1.19838	−	0.140070i	0.691777	+	0.722111i	$0.256828\pi$
$282$	9.22689	−	3.45200i	0.549453	−	0.205564i
$283$	−0.752477	+	2.51345i	−0.0447301	+	0.149409i	−0.977437	−	0.211225i	$-0.932255\pi$
$283$	−0.752477	+	2.51345i	−0.0447301	+	0.149409i	0.932707	+	0.360634i	$0.117440\pi$
$284$	−2.51024	+	8.38479i	−0.148955	+	0.497546i
$285$	−0.728120	+	4.35670i	−0.0431301	+	0.258068i
$286$	29.5774	−	3.45710i	1.74895	−	0.204423i
$287$	9.13698	+	3.32559i	0.539339	+	0.196303i
$288$	−1.83420	−	2.37397i	−0.108081	−	0.139887i
$289$	−25.4599	+	9.26664i	−1.49764	+	0.545097i
$290$	−0.983695	+	0.494030i	−0.0577646	+	0.0290105i
$291$	−9.50799	−	9.89914i	−0.557368	−	0.580298i
$292$	12.8240	+	1.49891i	0.750467	+	0.0877170i
$293$	−12.2030	−	6.12859i	−0.712908	−	0.358036i	0.0550958	−	0.998481i	$-0.482454\pi$
$293$	−12.2030	−	6.12859i	−0.712908	−	0.358036i	−0.768004	+	0.640445i	$0.778750\pi$
$294$	−7.59415	−	1.72832i	−0.442900	−	0.100798i
$295$	−4.42278	−	1.04822i	−0.257504	−	0.0610296i
$296$	−1.03125	−	1.78617i	−0.0599400	−	0.103819i
$297$	−20.7333	−	12.8538i	−1.20307	−	0.745854i
$298$	0.776997	−	1.34580i	0.0450102	−	0.0779600i
$299$	9.71452	−	10.2968i	0.561805	−	0.595478i
$300$	−5.65922	−	3.65010i	−0.326735	−	0.210738i
$301$	−0.0411710	−	0.706879i	−0.00237306	−	0.0407438i
$302$	9.36439	−	12.5786i	0.538860	−	0.723815i
$303$	12.6991	−	8.51585i	0.729542	−	0.489223i
$304$	−2.02055	−	1.32894i	−0.115886	−	0.0762197i
$305$	1.55008	−	8.79097i	0.0887576	−	0.503369i
$306$	18.8384	+	6.47772i	1.07692	+	0.370307i
$307$	1.71355	+	9.71803i	0.0977975	+	0.554637i	0.993854	+	0.110697i	$0.0353084\pi$
$307$	1.71355	+	9.71803i	0.0977975	+	0.554637i	−0.896057	+	0.443940i	$0.853580\pi$
$308$	−2.94210	+	6.82056i	−0.167642	+	0.388637i
$309$	11.4760	+	19.4731i	0.652849	+	1.10779i
$310$	−7.91752	+	1.87649i	−0.449685	+	0.106577i
$311$	−12.7805	−	13.5465i	−0.724713	−	0.768151i	0.255347	−	0.966849i	$-0.417810\pi$
$311$	−12.7805	−	13.5465i	−0.724713	−	0.768151i	−0.980061	+	0.198698i	$0.936329\pi$
$312$	10.3570	+	3.66518i	0.586352	+	0.207500i
$313$	−15.4632	−	20.7706i	−0.874030	−	1.17403i	−0.983657	−	0.180053i	$-0.942373\pi$
$313$	−15.4632	−	20.7706i	−0.874030	−	1.17403i	0.109627	−	0.993973i	$-0.465034\pi$
$314$	7.41705	−	6.22365i	0.418569	−	0.351221i
$315$	4.51239	+	2.16610i	0.254245	+	0.122046i
$316$	−1.83436	−	1.53921i	−0.103191	−	0.0865874i
$317$	−0.146010	+	2.50689i	−0.00820071	+	0.140801i	0.991722	+	0.128400i	$0.0409843\pi$
$317$	−0.146010	+	2.50689i	−0.00820071	+	0.140801i	−0.999923	+	0.0124003i	$0.996053\pi$
$318$	3.58278	+	8.10586i	0.200912	+	0.454554i
$319$	−1.94109	−	4.49994i	−0.108680	−	0.251948i
$320$	−0.881028	+	0.579461i	−0.0492510	+	0.0323929i
$321$	−11.8588	−	15.6355i	−0.661894	−	0.872686i
$322$	1.01274	+	3.38278i	0.0564376	+	0.188515i
$323$	16.0590			0.893546
$324$	−4.77568	−	7.62842i	−0.265316	−	0.423801i
$325$	24.6618			1.36799
$326$	−1.09878	−	3.67018i	−0.0608558	−	0.203272i
$327$	7.35966	−	0.926962i	0.406990	−	0.0512611i
$328$	−5.13443	+	3.37697i	−0.283501	+	0.186462i
$329$	−3.56442	−	8.26325i	−0.196513	−	0.455568i
$330$	−5.05880	+	6.92347i	−0.278478	+	0.381124i
$331$	2.00713	−	34.4611i	0.110322	−	1.89415i	−0.260537	−	0.965464i	$-0.583900\pi$
$331$	2.00713	−	34.4611i	0.110322	−	1.89415i	0.370859	−	0.928689i	$-0.379063\pi$
$332$	11.6882	+	9.80752i	0.641471	+	0.538258i
$333$	−2.55189	−	5.63674i	−0.139843	−	0.308891i
$334$	−14.6986	+	12.3336i	−0.804269	+	0.674862i
$335$	−5.77968	−	7.76346i	−0.315778	−	0.424163i
$336$	−2.08350	+	1.78023i	−0.113664	+	0.0971197i
$337$	−15.7439	−	16.6875i	−0.857623	−	0.909027i	0.139071	−	0.990282i	$-0.455588\pi$
$337$	−15.7439	−	16.6875i	−0.857623	−	0.909027i	−0.996693	+	0.0812556i	$0.974107\pi$
$338$	−26.4999	+	6.28059i	−1.44140	+	0.341619i
$339$	−14.4271	+	25.5123i	−0.783572	+	1.38564i
$340$	2.77346	−	6.42959i	0.150412	−	0.348694i
$341$	−6.29053	−	35.6754i	−0.340651	−	1.93193i
$342$	−5.64028	−	4.56349i	−0.304991	−	0.246765i
$343$	−3.15867	+	17.9137i	−0.170552	+	0.967250i
$344$	0.373900	+	0.245918i	0.0201593	+	0.0132590i
$345$	0.273367	+	4.06704i	0.0147176	+	0.218962i
$346$	−11.1007	+	14.9108i	−0.596776	+	0.801610i
$347$	1.50607	+	25.8582i	0.0808501	+	1.38814i	0.757979	+	0.652278i	$0.226187\pi$
$347$	1.50607	+	25.8582i	0.0808501	+	1.38814i	−0.677129	+	0.735864i	$0.736776\pi$
$348$	0.0889947	−	1.80587i	0.00477062	−	0.0968047i
$349$	16.2624	−	17.2371i	0.870504	−	0.922681i	−0.127098	−	0.991890i	$-0.540566\pi$
$349$	16.2624	−	17.2371i	0.870504	−	0.922681i	0.997602	+	0.0692094i	$0.0220477\pi$
$350$	−3.07583	+	5.32750i	−0.164410	+	0.284767i
$351$	29.8395	+	13.9973i	1.59271	+	0.747118i
$352$	−2.34736	−	4.06575i	−0.125115	−	0.216705i
$353$	9.12099	+	2.16171i	0.485461	+	0.115056i	0.466056	−	0.884755i	$-0.345675\pi$
$353$	9.12099	+	2.16171i	0.485461	+	0.115056i	0.0194054	+	0.999812i	$0.493823\pi$
$354$	5.07458	−	5.47596i	0.269711	−	0.291044i
$355$	8.24784	+	4.14222i	0.437750	+	0.219846i
$356$	−4.13535	−	0.483353i	−0.219173	−	0.0256177i
$357$	5.06314	−	17.4791i	0.267970	−	0.925091i
$358$	5.42702	−	2.72555i	0.286827	−	0.144050i
$359$	18.0989	−	6.58746i	0.955224	−	0.347673i	0.183064	−	0.983101i	$-0.441399\pi$
$359$	18.0989	−	6.58746i	0.955224	−	0.347673i	0.772160	+	0.635428i	$0.219176\pi$
$360$	−2.80120	+	1.47008i	−0.147636	+	0.0774803i
$361$	12.3582	+	4.49801i	0.650431	+	0.236738i
$362$	25.4552	−	2.97528i	1.33789	−	0.156377i
$363$	−14.7580	−	12.1603i	−0.774593	−	0.638252i
$364$	2.87836	−	9.61440i	0.150867	−	0.503932i
$365$	3.90484	−	13.0431i	0.204389	−	0.682705i
$366$	11.3156	+	9.32387i	0.591476	+	0.487367i
$367$	−18.5153	+	2.16413i	−0.966492	+	0.112967i	−0.584672	−	0.811270i	$-0.698777\pi$
$367$	−18.5153	+	2.16413i	−0.966492	+	0.112967i	−0.381820	+	0.924237i	$0.624703\pi$
$368$	−2.09717	−	0.763307i	−0.109323	−	0.0397901i
$369$	−16.3247	+	8.56731i	−0.849832	+	0.445996i
$370$	−2.04375	+	0.743865i	−0.106250	+	0.0386717i
$371$	7.23457	−	3.63334i	0.375600	−	0.188633i
$372$	3.71854	−	12.8372i	0.192797	−	0.665580i
$373$	−12.5306	−	1.46462i	−0.648809	−	0.0758349i	−0.214678	−	0.976685i	$-0.568870\pi$
$373$	−12.5306	−	1.46462i	−0.648809	−	0.0758349i	−0.434131	+	0.900850i	$0.642944\pi$
$374$	27.8585	+	13.9911i	1.44053	+	0.723461i
$375$	−11.0342	+	11.9070i	−0.569804	+	0.614874i
$376$	5.53444	+	1.31169i	0.285417	+	0.0676451i
$377$	3.31069	+	5.73428i	0.170509	+	0.295331i
$378$	−6.74532	+	4.70025i	−0.346942	+	0.241755i
$379$	−1.44162	+	2.49696i	−0.0740512	+	0.128260i	−0.900673	−	0.434497i	$-0.856926\pi$
$379$	−1.44162	+	2.49696i	−0.0740512	+	0.128260i	0.826622	+	0.562757i	$0.190259\pi$
$380$	−1.75007	+	1.85497i	−0.0897768	+	0.0951578i
$381$	−0.989284	+	20.0744i	−0.0506826	+	1.02844i
$382$	−0.262316	−	4.50379i	−0.0134213	−	0.230434i
$383$	7.84220	−	10.5339i	0.400718	−	0.538257i	−0.555268	−	0.831672i	$-0.687384\pi$
$383$	7.84220	−	10.5339i	0.400718	−	0.538257i	0.955985	+	0.293414i	$0.0947916\pi$
$384$	−0.116158	−	1.72815i	−0.00592767	−	0.0881894i
$385$	6.54432	+	4.30427i	0.333529	+	0.219366i
$386$	4.36656	−	24.7640i	0.222252	−	1.26045i
$387$	1.04373	+	0.844468i	0.0530556	+	0.0429267i
$388$	−1.37608	−	7.80414i	−0.0698599	−	0.396195i
$389$	2.75819	−	6.39421i	0.139846	−	0.324199i	−0.833872	−	0.551958i	$-0.813881\pi$
$389$	2.75819	−	6.39421i	0.139846	−	0.324199i	0.973717	+	0.227759i	$0.0731400\pi$
$390$	5.70275	−	10.0845i	0.288770	−	0.510649i
$391$	14.4201	−	3.41764i	0.729258	−	0.172837i
$392$	−3.08575	−	3.27071i	−0.155854	−	0.165196i
$393$	−1.58807	+	1.35692i	−0.0801077	+	0.0684476i
$394$	−3.45710	−	4.64369i	−0.174166	−	0.233946i
$395$	−1.93435	+	1.62311i	−0.0973275	+	0.0816675i
$396$	−5.80869	−	12.8305i	−0.291898	−	0.644759i
$397$	0.535831	+	0.449616i	0.0268926	+	0.0225656i	0.656135	−	0.754644i	$-0.272190\pi$
$397$	0.535831	+	0.449616i	0.0268926	+	0.0225656i	−0.629242	+	0.777209i	$0.716635\pi$
$398$	0.295417	−	5.07212i	0.0148079	−	0.254242i
$399$	−3.91005	+	5.35129i	−0.195747	+	0.267900i
$400$	−1.53996	−	3.57004i	−0.0769982	−	0.178502i
$401$	4.11044	−	2.70348i	0.205265	−	0.135005i	−0.442714	−	0.896663i	$-0.645984\pi$
$401$	4.11044	−	2.70348i	0.205265	−	0.135005i	0.647980	+	0.761657i	$0.275614\pi$
$402$	15.7728	−	1.98661i	0.786674	−	0.0990829i
$403$	14.0374	+	46.8883i	0.699254	+	2.33567i
$404$	8.82772			0.439195
$405$	−8.79651	+	3.56262i	−0.437102	+	0.177028i
$406$	−1.65165			−0.0819699
$407$	−2.77707	−	9.27606i	−0.137654	−	0.459797i
$408$	6.95031	+	9.16377i	0.344092	+	0.453674i
$409$	−10.2739	+	6.75726i	−0.508012	+	0.334125i	−0.777504	−	0.628878i	$-0.783515\pi$
$409$	−10.2739	+	6.75726i	−0.508012	+	0.334125i	0.269492	+	0.963003i	$0.413144\pi$
$410$	2.56675	+	5.95040i	0.126763	+	0.293869i
$411$	9.28819	+	21.0141i	0.458152	+	1.03655i
$412$	−0.758785	+	13.0278i	−0.0373826	+	0.641835i
$413$	−5.22435	−	4.38375i	−0.257073	−	0.215710i
$414$	−6.03587	−	2.89742i	−0.296647	−	0.142401i
$415$	12.3252	−	10.3421i	0.605022	−	0.507674i
$416$	3.78779	+	5.08789i	0.185712	+	0.249454i
$417$	−27.2115	−	9.62966i	−1.33255	−	0.471567i
$418$	−7.79141	−	8.25841i	−0.381090	−	0.403932i
$419$	−0.554772	+	0.131483i	−0.0271024	+	0.00642338i	−0.244145	−	0.969739i	$-0.578507\pi$
$419$	−0.554772	+	0.131483i	−0.0271024	+	0.00642338i	0.217042	+	0.976162i	$0.430359\pi$
$420$	1.46723	+	2.48967i	0.0715936	+	0.121483i
$421$	−8.88256	+	20.5921i	−0.432909	+	1.00360i	0.552518	+	0.833501i	$0.313667\pi$
$421$	−8.88256	+	20.5921i	−0.432909	+	1.00360i	−0.985428	+	0.170096i	$0.945592\pi$
$422$	1.13436	+	6.43326i	0.0552197	+	0.313166i
$423$	16.1360	+	5.54848i	0.784558	+	0.269776i
$424$	−0.888503	+	5.03895i	−0.0431495	+	0.244713i
$425$	21.5703	+	14.1870i	1.04632	+	0.688172i
$426$	−12.5908	+	8.44328i	−0.610028	+	0.409078i
$427$	7.99817	−	10.7434i	0.387058	−	0.519910i
$428$	−0.658774	−	11.3107i	−0.0318430	−	0.546724i
$429$	43.3446	+	27.9565i	2.09270	+	1.34975i
$430$	0.323849	−	0.343259i	0.0156174	−	0.0165534i
$431$	−3.40486	+	5.89739i	−0.164006	+	0.284067i	−0.936302	−	0.351196i	$-0.885775\pi$
$431$	−3.40486	+	5.89739i	−0.164006	+	0.284067i	0.772296	+	0.635263i	$0.219108\pi$
$432$	0.162965	−	5.19360i	0.00784064	−	0.249877i
$433$	9.44955	+	16.3671i	0.454116	+	0.786552i	0.998637	−	0.0521950i	$-0.0166217\pi$
$433$	9.44955	+	16.3671i	0.454116	+	0.786552i	−0.544521	+	0.838747i	$0.683288\pi$
$434$	−11.8797	−	2.81554i	−0.570243	−	0.135150i
$435$	−1.85907	−	0.423098i	−0.0891358	−	0.0202860i
$436$	3.82714	+	1.92206i	0.183287	+	0.0920500i
$437$	−5.36081	−	0.626589i	−0.256442	−	0.0299738i
$438$	15.4912	+	16.1285i	0.740197	+	0.770648i
$439$	5.21737	−	2.62026i	0.249012	−	0.125058i	−0.319916	−	0.947446i	$-0.603655\pi$
$439$	5.21737	−	2.62026i	0.249012	−	0.125058i	0.568928	+	0.822388i	$0.307358\pi$
$440$	−4.65206	+	1.69321i	−0.221778	+	0.0807207i
$441$	−8.24765	−	10.6748i	−0.392745	−	0.508323i
$442$	−39.5796	−	14.4058i	−1.88261	−	0.685214i
$443$	−4.72943	+	0.552792i	−0.224702	+	0.0262639i	−0.227699	−	0.973732i	$-0.573120\pi$
$443$	−4.72943	+	0.552792i	−0.224702	+	0.0262639i	0.00299670	+	0.999996i	$0.499046\pi$
$444$	0.588867	−	3.52348i	0.0279464	−	0.167217i
$445$	−1.25919	+	4.20600i	−0.0596915	+	0.199384i
$446$	−2.14872	+	7.17723i	−0.101745	+	0.339852i
$447$	2.52094	−	0.943146i	0.119237	−	0.0446093i
$448$	−1.57152	+	0.183684i	−0.0742471	+	0.00867824i
$449$	−8.45465	−	3.07724i	−0.399000	−	0.145224i	0.134724	−	0.990883i	$-0.456985\pi$
$449$	−8.45465	−	3.07724i	−0.399000	−	0.145224i	−0.533723	+	0.845659i	$0.679208\pi$
$450$	−3.54446	−	11.1125i	−0.167087	−	0.523846i
$451$	−27.1111	+	9.86764i	−1.27661	+	0.464649i
$452$	−15.1217	+	7.59438i	−0.711263	+	0.357210i
$453$	26.3721	−	6.49976i	1.23907	−	0.305385i
$454$	−20.8909	−	2.44179i	−0.980457	−	0.114599i
$455$	−9.45736	−	4.74967i	−0.443368	−	0.222668i
$456$	−1.23717	−	4.00193i	−0.0579360	−	0.187408i
$457$	−25.3650	−	6.01162i	−1.18653	−	0.281212i	−0.410469	−	0.911875i	$-0.634635\pi$
$457$	−25.3650	−	6.01162i	−1.18653	−	0.281212i	−0.776057	+	0.630663i	$0.782783\pi$
$458$	−7.59427	−	13.1537i	−0.354857	−	0.614631i
$459$	18.0469	+	29.4082i	0.842356	+	1.37266i
$460$	−1.17670	+	2.03811i	−0.0548641	+	0.0950274i
$461$	−12.1096	+	12.8355i	−0.564002	+	0.597807i	−0.945122	−	0.326719i	$-0.894057\pi$
$461$	−12.1096	+	12.8355i	−0.564002	+	0.597807i	0.381120	+	0.924526i	$0.375539\pi$
$462$	−11.4452	+	5.87666i	−0.532479	+	0.273407i
$463$	−1.37852	−	23.6683i	−0.0640653	−	1.09996i	−0.865184	−	0.501454i	$-0.832799\pi$
$463$	−1.37852	−	23.6683i	−0.0640653	−	1.09996i	0.801119	−	0.598505i	$-0.204238\pi$
$464$	0.623364	−	0.837323i	0.0289390	−	0.0388718i
$465$	−12.6504	−	6.21232i	−0.586647	−	0.288090i
$466$	−16.8189	−	11.0620i	−0.779120	−	0.512436i
$467$	−0.180505	+	1.02369i	−0.00835277	+	0.0473709i	−0.988699	−	0.149912i	$-0.952101\pi$
$467$	−0.180505	+	1.02369i	−0.00835277	+	0.0473709i	0.980346	+	0.197283i	$0.0632119\pi$
$468$	9.80755	+	16.3070i	0.453354	+	0.753791i
$469$	−2.52174	−	14.3015i	−0.116443	−	0.660381i
$470$	2.37560	−	5.50726i	0.109578	−	0.254031i
$471$	16.7695	−	0.149867i	0.772699	−	0.00690552i
$472$	4.19417	−	0.994036i	0.193052	−	0.0457542i
$473$	1.44179	+	1.52821i	0.0662936	+	0.0702671i
$474$	−0.756687	−	4.07794i	−0.0347558	−	0.187306i
$475$	−5.61496	−	7.54220i	−0.257632	−	0.346060i
$476$	8.04837	−	6.75339i	0.368897	−	0.309541i
$477$	−4.13893	+	14.7815i	−0.189508	+	0.676799i
$478$	4.65916	+	3.90950i	0.213105	+	0.178816i
$479$	2.51899	−	43.2494i	0.115096	−	1.97612i	−0.0851410	−	0.996369i	$-0.527134\pi$
$479$	2.51899	−	43.2494i	0.115096	−	1.97612i	0.200237	−	0.979748i	$-0.435829\pi$
$480$	−1.81593	−	0.195819i	−0.0828856	−	0.00893786i
$481$	5.18170	+	12.0125i	0.236265	+	0.547724i
$482$	−12.1489	+	7.99047i	−0.553368	+	0.363956i
$483$	−2.37217	+	5.63731i	−0.107938	+	0.256506i
$484$	−3.16643	−	10.5766i	−0.143928	−	0.480754i
$485$	−8.35648			−0.379448
$486$	2.01847	−	15.4572i	0.0915598	−	0.701154i
$487$	−40.7327			−1.84578			−0.922888	−	0.385070i	$-0.874177\pi$
$487$	−40.7327			−1.84578			−0.922888	+	0.385070i	$0.874177\pi$
$488$	2.42784	+	8.10955i	0.109903	+	0.367102i
$489$	2.57371	−	6.11626i	0.116387	−	0.276587i
$490$	−3.96163	+	2.60560i	−0.178968	+	0.117709i
$491$	−3.06712	−	7.11039i	−0.138417	−	0.320888i	0.834881	−	0.550430i	$-0.185536\pi$
$491$	−3.06712	−	7.11039i	−0.138417	−	0.320888i	−0.973299	+	0.229543i	$0.926277\pi$
$492$	−10.5828	−	1.14119i	−0.477111	−	0.0514486i
$493$	−0.403044	+	6.92000i	−0.0181522	+	0.311661i
$494$	11.7511	+	9.86037i	0.528708	+	0.443639i
$495$	−14.3880	+	3.68281i	−0.646692	+	0.165530i
$496$	5.91100	−	4.95992i	0.265412	−	0.222707i
$497$	8.26964	+	11.1080i	0.370944	+	0.498264i
$498$	4.82145	+	25.9837i	0.216054	+	1.16436i
$499$	11.0986	+	11.7638i	0.496840	+	0.526620i	0.926462	−	0.376389i	$-0.122834\pi$
$499$	11.0986	+	11.7638i	0.496840	+	0.526620i	−0.429621	+	0.903009i	$0.641353\pi$
$500$	−9.11984	+	2.16144i	−0.407852	+	0.0966626i
$501$	−33.2326	+	0.296996i	−1.48472	+	0.0132688i
$502$	3.26991	−	7.58050i	0.145943	−	0.338334i
$503$	5.70203	+	32.3378i	0.254241	+	1.44187i	0.798014	+	0.602639i	$0.205884\pi$
$503$	5.70203	+	32.3378i	0.254241	+	1.44187i	−0.543773	+	0.839232i	$0.683005\pi$
$504$	−4.74588	+	0.0848335i	−0.211398	+	0.00377879i
$505$	1.61647	−	9.16747i	0.0719320	−	0.407947i
$506$	−8.75382	−	5.75748i	−0.389155	−	0.255951i
$507$	−42.3407	−	20.7926i	−1.88042	−	0.923431i
$508$	−6.92945	+	9.30787i	−0.307445	+	0.412970i
$509$	−2.54789	−	43.7456i	−0.112933	−	1.93899i	−0.294583	−	0.955626i	$-0.595181\pi$
$509$	−2.54789	−	43.7456i	−0.112933	−	1.93899i	0.181649	−	0.983363i	$-0.441856\pi$
$510$	10.7891	−	5.53980i	0.477752	−	0.245306i
$511$	14.0188	−	14.8591i	0.620156	−	0.657327i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	−2.51310	−	12.3125i	−0.110956	−	0.543612i
$514$	1.70618	+	2.95519i	0.0752565	+	0.130348i
$515$	13.3903	+	3.17356i	0.590046	+	0.139844i
$516$	0.228938	+	0.740553i	0.0100784	+	0.0326010i
$517$	23.8622	+	11.9840i	1.04946	+	0.527057i
$518$	−3.24124	−	0.378847i	−0.142412	−	0.0166456i
$519$	−31.2619	+	7.70491i	−1.37224	+	0.338208i
$520$	5.97730	−	3.00191i	0.262122	−	0.131643i
$521$	13.9268	−	5.06895i	0.610146	−	0.222075i	−0.0184214	−	0.999830i	$-0.505864\pi$
$521$	13.9268	−	5.06895i	0.610146	−	0.222075i	0.628567	+	0.777755i	$0.283642\pi$
$522$	2.10802	−	2.31593i	0.0922653	−	0.101365i
$523$	15.8322	+	5.76244i	0.692293	+	0.251974i	0.664117	−	0.747629i	$-0.268808\pi$
$523$	15.8322	+	5.76244i	0.692293	+	0.251974i	0.0281762	+	0.999603i	$0.491030\pi$
$524$	−1.19783	+	0.140006i	−0.0523275	+	0.00611621i
$525$	−9.97946	+	3.73356i	−0.435539	+	0.162946i
$526$	−2.22860	+	7.44404i	−0.0971716	+	0.324576i
$527$	−14.6954	+	49.0859i	−0.640140	+	2.13822i
$528$	1.34040	−	8.02026i	0.0583334	−	0.349037i
$529$	17.8974	−	2.09191i	0.778148	−	0.0909525i
$530$	5.07019	+	1.84540i	0.220235	+	0.0801589i
$531$	12.8148	−	1.73051i	0.556113	−	0.0750978i
$532$	−3.59567	+	1.30872i	−0.155892	+	0.0567401i
$533$	34.8343	−	17.4944i	1.50884	−	0.757769i
$534$	−4.99544	−	5.20095i	−0.216174	−	0.225067i
$535$	−11.8667	−	1.38701i	−0.513040	−	0.0599658i
$536$	8.20208	+	4.11924i	0.354276	+	0.177924i
$537$	10.2565	+	2.33422i	0.442599	+	0.100729i
$538$	−19.9885	−	4.73737i	−0.861767	−	0.204243i
$539$	−10.5551	−	18.2820i	−0.454642	−	0.787463i
$540$	−5.36364	−	1.12025i	−0.230814	−	0.0482080i
$541$	−1.09219	+	1.89173i	−0.0469569	+	0.0813317i	−0.888549	−	0.458783i	$-0.848286\pi$
$541$	−1.09219	+	1.89173i	−0.0469569	+	0.0813317i	0.841592	+	0.540114i	$0.181619\pi$
$542$	−17.3263	+	18.3648i	−0.744228	+	0.788835i
$543$	37.3037	+	24.0602i	1.60085	+	1.03252i
$544$	0.386100	+	6.62909i	0.0165539	+	0.284220i
$545$	2.69683	−	3.62248i	0.115520	−	0.155170i
$546$	14.4373	−	9.68146i	0.617858	−	0.414328i
$547$	−26.6570	−	17.5326i	−1.13977	−	0.749640i	−0.168052	−	0.985778i	$-0.553748\pi$
$547$	−26.6570	−	17.5326i	−1.13977	−	0.749640i	−0.971719	+	0.236139i	$0.924118\pi$
$548$	−2.30340	+	13.0632i	−0.0983964	+	0.558034i
$549$	4.85616	+	24.9269i	0.207256	+	1.06385i
$550$	−3.16963	−	17.9758i	−0.135153	−	0.766492i
$551$	0.999917	−	2.31807i	0.0425979	−	0.0987530i
$552$	−1.96260	−	3.33024i	−0.0835338	−	0.141744i
$553$	−3.68662	+	0.873746i	−0.156771	+	0.0371554i
$554$	12.7134	+	13.4755i	0.540143	+	0.572518i
$555$	−3.55125	−	1.25673i	−0.150742	−	0.0533450i
$556$	−9.95182	−	13.3676i	−0.422051	−	0.566913i
$557$	−2.80197	+	2.35114i	−0.118723	+	0.0996208i	−0.700217	−	0.713931i	$-0.746913\pi$
$557$	−2.80197	+	2.35114i	−0.118723	+	0.0996208i	0.581493	+	0.813551i	$0.302469\pi$
$558$	19.1101	−	13.0641i	0.808995	−	0.553047i
$559$	−2.17453	−	1.82465i	−0.0919729	−	0.0771744i
$560$	−0.0970121	+	1.66563i	−0.00409951	+	0.0703858i
$561$	21.8288	+	49.3867i	0.921614	+	2.08511i
$562$	8.01079	+	18.5711i	0.337915	+	0.783375i
$563$	28.5632	−	18.7863i	1.20380	−	0.791750i	0.220791	−	0.975321i	$-0.429136\pi$
$563$	28.5632	−	18.7863i	1.20380	−	0.791750i	0.983006	+	0.183571i	$0.0587658\pi$
$564$	5.95328	+	7.84922i	0.250678	+	0.330512i
$565$	5.11769	+	17.0943i	0.215303	+	0.719162i
$566$	−2.62367			−0.110281
$567$	−14.1937	−	1.14662i	−0.596079	−	0.0481535i
$568$	−8.75249			−0.367246
$569$	−0.0855012	−	0.285594i	−0.00358440	−	0.0119727i	0.956179	−	0.292784i	$-0.0945817\pi$
$569$	−0.0855012	−	0.285594i	−0.00358440	−	0.0119727i	−0.959763	+	0.280811i	$0.909397\pi$
$570$	−4.38250	+	0.551983i	−0.183563	+	0.0231200i
$571$	−19.5598	+	12.8647i	−0.818552	+	0.538370i	−0.888337	−	0.459192i	$-0.848139\pi$
$571$	−19.5598	+	12.8647i	−0.818552	+	0.538370i	0.0697850	+	0.997562i	$0.477769\pi$
$572$	11.7948	+	27.3433i	0.493164	+	1.14328i
$573$	4.61001	−	6.30926i	0.192586	−	0.263573i
$574$	−0.565364	+	9.70692i	−0.0235978	+	0.405159i
$575$	−6.64706	−	5.57754i	−0.277202	−	0.232600i
$576$	1.74818	−	2.43800i	0.0728409	−	0.101583i
$577$	29.0389	−	24.3665i	1.20890	−	1.01439i	0.209575	−	0.977793i	$-0.432792\pi$
$577$	29.0389	−	24.3665i	1.20890	−	1.01439i	0.999330	−	0.0365987i	$-0.0116523\pi$
$578$	−16.1793	−	21.7326i	−0.672971	−	0.903957i
$579$	33.1129	−	28.2931i	1.37613	−	1.17582i
$580$	−0.755403	−	0.800680i	−0.0313664	−	0.0332464i
$581$	23.4904	−	5.56732i	0.974545	−	0.230971i
$582$	6.75635	−	11.9477i	0.280060	−	0.495246i
$583$	−9.51439	+	22.0568i	−0.394046	+	0.913501i
$584$	2.24202	+	12.7151i	0.0927755	+	0.526156i
$585$	18.7305	−	7.19898i	0.774410	−	0.297641i
$586$	2.37126	−	13.4481i	0.0979557	−	0.555534i
$587$	−6.00142	−	3.94720i	−0.247705	−	0.162918i	0.419585	−	0.907716i	$-0.362176\pi$
$587$	−6.00142	−	3.94720i	−0.247705	−	0.162918i	−0.667290	+	0.744798i	$0.732546\pi$
$588$	−0.522317	−	7.77081i	−0.0215400	−	0.320463i
$589$	11.1436	−	14.9685i	0.459164	−	0.616765i
$590$	−0.264286	−	4.53761i	−0.0108805	−	0.186810i
$591$	0.493553	−	10.0151i	0.0203021	−	0.411967i
$592$	1.41537	−	1.50020i	0.0581713	−	0.0616580i
$593$	−13.4989	+	23.3808i	−0.554333	+	0.960133i	0.443622	+	0.896214i	$0.353693\pi$
$593$	−13.4989	+	23.3808i	−0.554333	+	0.960133i	−0.997955	+	0.0639188i	$0.979640\pi$
$594$	6.36744	−	23.5488i	0.261259	−	0.966220i
$595$	−5.53954	−	9.59476i	−0.227099	−	0.393347i
$596$	1.51211	+	0.358376i	0.0619382	+	0.0146796i
$597$	5.98152	−	6.45464i	0.244807	−	0.264171i
$598$	12.6504	+	6.35325i	0.517312	+	0.259804i
$599$	7.64098	+	0.893103i	0.312202	+	0.0364912i	0.270751	−	0.962649i	$-0.412728\pi$
$599$	7.64098	+	0.893103i	0.312202	+	0.0364912i	0.0414509	+	0.999141i	$0.486802\pi$
$600$	1.87367	−	6.46833i	0.0764923	−	0.264069i
$601$	−8.16690	+	4.10157i	−0.333135	+	0.167307i	−0.607501	−	0.794319i	$-0.707828\pi$
$601$	−8.16690	+	4.10157i	−0.333135	+	0.167307i	0.274367	+	0.961625i	$0.411532\pi$
$602$	0.665375	−	0.242177i	0.0271187	−	0.00987038i
$603$	23.2720	+	14.7172i	0.947707	+	0.599330i
$604$	14.7359	+	5.36341i	0.599594	+	0.218234i
$605$	−11.5635	+	1.35158i	−0.470122	+	0.0549494i
$606$	11.8002	+	9.72319i	0.479351	+	0.394978i
$607$	7.55388	−	25.2317i	0.306603	−	1.02412i	−0.656351	−	0.754456i	$-0.727901\pi$
$607$	7.55388	−	25.2317i	0.306603	−	1.02412i	0.962953	−	0.269668i	$-0.0869140\pi$
$608$	0.693607	−	2.31681i	0.0281295	−	0.0939589i
$609$	−2.20780	−	1.81919i	−0.0894644	−	0.0737172i
$610$	8.86622	−	1.03631i	0.358983	−	0.0419591i
$611$	−33.9018	−	12.3393i	−1.37152	−	0.499193i
$612$	−0.802684	+	19.9048i	−0.0324466	+	0.804603i
$613$	37.8081	−	13.7610i	1.52706	−	0.555803i	0.564157	−	0.825667i	$-0.309201\pi$
$613$	37.8081	−	13.7610i	1.52706	−	0.555803i	0.962898	+	0.269865i	$0.0869789\pi$
$614$	−8.81831	+	4.42872i	−0.355878	+	0.178729i
$615$	−3.12296	+	10.7812i	−0.125930	+	0.434739i
$616$	−7.37783	−	0.862344i	−0.297261	−	0.0347448i
$617$	−28.6495	−	14.3883i	−1.15339	−	0.579253i	−0.233856	−	0.972271i	$-0.575135\pi$
$617$	−28.6495	−	14.3883i	−1.15339	−	0.579253i	−0.919531	+	0.393018i	$0.871431\pi$
$618$	−15.3636	+	16.5789i	−0.618017	+	0.666900i
$619$	−29.0938	−	6.89537i	−1.16938	−	0.277148i	−0.400351	−	0.916362i	$-0.631112\pi$
$619$	−29.0938	−	6.89537i	−1.16938	−	0.277148i	−0.769029	+	0.639214i	$0.779260\pi$
$620$	−4.06843	−	7.04672i	−0.163392	−	0.283003i
$621$	−4.87696	−	10.5212i	−0.195706	−	0.422201i
$622$	9.31193	−	16.1287i	0.373374	−	0.646703i
$623$	−4.52065	+	4.79161i	−0.181116	+	0.191972i
$624$	−0.540765	+	10.9731i	−0.0216479	+	0.439277i
$625$	−0.555675	−	9.54057i	−0.0222270	−	0.381623i
$626$	15.4632	−	20.7706i	0.618033	−	0.830162i
$627$	−1.31883	−	19.6210i	−0.0526690	−	0.783587i
$628$	8.08942	+	5.32050i	0.322803	+	0.212311i
$629$	−2.37822	+	13.4876i	−0.0948259	+	0.537784i
$630$	−0.780935	+	4.94407i	−0.0311132	+	0.196976i
$631$	5.16294	+	29.2805i	0.205534	+	1.16564i	0.896598	+	0.442845i	$0.146031\pi$
$631$	5.16294	+	29.2805i	0.205534	+	1.16564i	−0.691064	+	0.722793i	$0.742858\pi$
$632$	0.948448	−	2.19875i	0.0377272	−	0.0874615i
$633$	−5.56952	+	9.84893i	−0.221369	+	0.391460i
$634$	−2.44345	+	0.579108i	−0.0970417	+	0.0229993i
$635$	8.39722	+	8.90054i	0.333234	+	0.353207i
$636$	−6.73778	+	5.75706i	−0.267170	+	0.228282i
$637$	17.0322	+	22.8782i	0.674840	+	0.906467i
$638$	3.75419	−	3.15014i	0.148630	−	0.124715i
$639$	−26.1302	−	2.58171i	−1.03370	−	0.102131i
$640$	−0.807799	−	0.677824i	−0.0319311	−	0.0267933i
$641$	−1.19632	+	20.5400i	−0.0472517	+	0.811280i	0.888556	+	0.458768i	$0.151709\pi$
$641$	−1.19632	+	20.5400i	−0.0472517	+	0.811280i	−0.935808	+	0.352511i	$0.885328\pi$
$642$	11.5775	−	15.8449i	0.456926	−	0.625349i
$643$	−2.91227	−	6.75139i	−0.114849	−	0.266249i	0.851090	−	0.525019i	$-0.175942\pi$
$643$	−2.91227	−	6.75139i	−0.114849	−	0.266249i	−0.965939	+	0.258771i	$0.916683\pi$
$644$	−2.95021	+	1.94038i	−0.116255	+	0.0764618i
$645$	0.810976	−	0.102144i	0.0319321	−	0.00402191i
$646$	4.60577	+	15.3843i	0.181212	+	0.605289i
$647$	42.3711			1.66578			0.832890	−	0.553438i	$-0.186684\pi$
$647$	42.3711			1.66578			0.832890	+	0.553438i	$0.186684\pi$
$648$	5.93827	−	6.76291i	0.233277	−	0.265672i
$649$	20.2359			0.794329
$650$	7.07308	+	23.6257i	0.277429	+	0.926677i
$651$	−12.7787	−	16.8483i	−0.500838	−	0.660339i
$652$	3.20086	−	2.10524i	0.125355	−	0.0824475i
$653$	−7.59872	−	17.6158i	−0.297361	−	0.689360i	0.702388	−	0.711795i	$-0.252117\pi$
$653$	−7.59872	−	17.6158i	−0.297361	−	0.689360i	−0.999748	+	0.0224350i	$0.992858\pi$
$654$	2.99879	+	6.78462i	0.117262	+	0.265300i
$655$	−0.0739440	+	1.26957i	−0.00288923	+	0.0496062i
$656$	−4.70767	−	3.95020i	−0.183804	−	0.154229i
$657$	2.94291	+	38.6219i	0.114814	+	1.50678i
$658$	6.89382	−	5.78460i	0.268749	−	0.225507i
$659$	−3.41705	−	4.58989i	−0.133109	−	0.178797i	0.730571	−	0.682837i	$-0.239254\pi$
$659$	−3.41705	−	4.58989i	−0.133109	−	0.178797i	−0.863680	+	0.504040i	$0.831846\pi$
$660$	−8.08349	−	2.86060i	−0.314649	−	0.111349i
$661$	−8.62392	−	9.14082i	−0.335432	−	0.355537i	0.537600	−	0.843200i	$-0.319331\pi$
$661$	−8.62392	−	9.14082i	−0.335432	−	0.355537i	−0.873032	+	0.487663i	$0.837849\pi$
$662$	33.5890	−	7.96074i	1.30547	−	0.309403i
$663$	−37.0399	−	62.8511i	−1.43851	−	2.44093i
$664$	−6.04330	+	14.0100i	−0.234526	+	0.543692i
$665$	0.700671	+	3.97370i	0.0271708	+	0.154094i
$666$	4.66805	−	4.06132i	0.180883	−	0.157373i
$667$	0.404548	−	2.29431i	0.0156642	−	0.0888359i
$668$	−16.0310	−	10.5438i	−0.620259	−	0.407950i
$669$	−10.7775	+	7.22730i	−0.416684	+	0.279423i
$670$	5.77968	−	7.76346i	0.223289	−	0.299929i
$671$	2.31077	+	39.6744i	0.0892063	+	1.53161i
$672$	−2.30300	−	1.48539i	−0.0888401	−	0.0573003i
$673$	−8.75501	+	9.27977i	−0.337481	+	0.357709i	−0.873782	−	0.486318i	$-0.838340\pi$
$673$	−8.75501	+	9.27977i	−0.337481	+	0.357709i	0.536301	+	0.844027i	$0.319821\pi$
$674$	11.4711	−	19.8685i	0.441849	−	0.765305i
$675$	7.50174	−	18.7583i	0.288742	−	0.722007i
$676$	−13.6170	−	23.5853i	−0.523730	−	0.907127i
$677$	−50.2950	−	11.9201i	−1.93299	−	0.458128i	−0.993206	−	0.116369i	$-0.962874\pi$
$677$	−50.2950	−	11.9201i	−1.93299	−	0.458128i	−0.939788	−	0.341759i	$-0.888977\pi$
$678$	−28.5782	−	6.50399i	−1.09754	−	0.249784i
$679$	−11.2046	−	5.62718i	−0.429995	−	0.215951i
$680$	6.95492	+	0.812913i	0.266709	+	0.0311738i
$681$	−25.2358	−	26.2740i	−0.967040	−	1.00682i
$682$	32.3725	−	16.2581i	1.23961	−	0.622554i
$683$	−3.12516	+	1.13747i	−0.119581	+	0.0435239i	−0.401118	−	0.916027i	$-0.631378\pi$
$683$	−3.12516	+	1.13747i	−0.119581	+	0.0435239i	0.281537	+	0.959550i	$0.409156\pi$
$684$	2.75412	−	6.71215i	0.105307	−	0.256646i
$685$	13.1442	+	4.78410i	0.502214	+	0.182791i
$686$	−18.0671	+	2.11174i	−0.689804	+	0.0806266i
$687$	4.33651	−	25.9475i	0.165448	−	0.989957i
$688$	−0.128351	+	0.428722i	−0.00489334	+	0.0163449i
$689$	9.30827	−	31.0918i	0.354617	−	1.18450i
$690$	−3.81778	+	1.42832i	−0.145341	+	0.0543754i
$691$	−3.55385	+	0.415386i	−0.135195	+	0.0158020i	−0.183421	−	0.983034i	$-0.558717\pi$
$691$	−3.55385	+	0.415386i	−0.135195	+	0.0158020i	0.0482263	+	0.998836i	$0.484643\pi$
$692$	−17.4681	−	6.35787i	−0.664038	−	0.241690i
$693$	−21.7719	−	4.75072i	−0.827045	−	0.180465i
$694$	−24.3400	+	8.85902i	−0.923932	+	0.336284i
$695$	−15.7044	+	7.88705i	−0.595702	+	0.299173i
$696$	1.75553	−	0.432673i	0.0665431	−	0.0164004i
$697$	40.5317	+	4.73747i	1.53525	+	0.179444i
$698$	21.1771	+	10.6355i	0.801564	+	0.402560i
$699$	−10.2982	−	33.3118i	−0.389512	−	1.25997i
$700$	−5.98585	−	1.41867i	−0.226244	−	0.0536208i
$701$	11.2160	+	19.4268i	0.423624	+	0.733739i	0.996291	−	0.0860497i	$-0.0274244\pi$
$701$	11.2160	+	19.4268i	0.423624	+	0.733739i	−0.572667	+	0.819788i	$0.694091\pi$
$702$	−4.85116	+	32.6004i	−0.183095	+	1.23042i
$703$	2.49397	−	4.31969i	0.0940620	−	0.162920i
$704$	3.22171	−	3.41482i	0.121423	−	0.128701i
$705$	9.24143	−	4.74511i	0.348052	−	0.178711i
$706$	0.545030	+	9.35780i	0.0205125	+	0.352185i
$707$	8.34071	−	11.2035i	0.313685	−	0.421352i
$708$	6.70132	+	3.29087i	0.251851	+	0.123678i
$709$	3.21899	+	2.11717i	0.120892	+	0.0795118i	0.608515	−	0.793542i	$-0.291766\pi$
$709$	3.21899	+	2.11717i	0.120892	+	0.0795118i	−0.487623	+	0.873054i	$0.662136\pi$
$710$	−1.60270	+	9.08934i	−0.0601481	+	0.341117i
$711$	3.48012	−	6.28452i	0.130515	−	0.235688i
$712$	−0.722985	−	4.10025i	−0.0270950	−	0.153663i
$713$	6.82083	−	15.8125i	0.255442	−	0.592181i
$714$	18.1969	−	0.162624i	0.681002	−	0.00608603i
$715$	30.5554	−	7.24177i	1.14271	−	0.270827i
$716$	4.16753	+	4.41733i	0.155748	+	0.165083i
$717$	1.92194	+	10.3577i	0.0717760	+	0.386815i
$718$	11.5015	+	15.4493i	0.429234	+	0.576561i
$719$	−23.0402	+	19.3330i	−0.859254	+	0.721000i	−0.961807	−	0.273728i	$-0.911743\pi$
$719$	−23.0402	+	19.3330i	−0.859254	+	0.721000i	0.102553	+	0.994728i	$0.467299\pi$
$720$	−2.21172	−	2.26189i	−0.0824259	−	0.0842958i
$721$	15.8171	+	13.2721i	0.589059	+	0.494279i
$722$	−0.764681	+	13.1291i	−0.0284585	+	0.488613i
$723$	−25.0408	−	2.70024i	−0.931276	−	0.100423i
$724$	10.1509	+	23.5325i	0.377256	+	0.874578i
$725$	3.39094	−	2.23026i	0.125936	−	0.0828297i
$726$	7.41684	−	17.6256i	0.275265	−	0.654148i
$727$	11.9823	+	40.0236i	0.444398	+	1.48439i	0.827913	+	0.560857i	$0.189528\pi$
$727$	11.9823	+	40.0236i	0.444398	+	1.48439i	−0.383515	+	0.923535i	$0.625286\pi$
$728$	10.0360			0.371960
$729$	19.7233	−	18.4388i	0.730494	−	0.682919i
$730$	13.6150			0.503915
$731$	−0.852292	−	2.84685i	−0.0315232	−	0.105295i
$732$	−5.68682	+	13.5143i	−0.210191	+	0.499504i
$733$	9.62195	−	6.32846i	0.355395	−	0.233747i	−0.359239	−	0.933246i	$-0.616964\pi$
$733$	9.62195	−	6.32846i	0.355395	−	0.233747i	0.714634	+	0.699499i	$0.246593\pi$
$734$	−7.38347	−	17.1168i	−0.272529	−	0.631793i
$735$	−8.16552	−	0.880519i	−0.301190	−	0.0324784i
$736$	0.129765	−	2.22799i	0.00478321	−	0.0821246i
$737$	33.0087	+	27.6976i	1.21589	+	1.02025i
$738$	−12.8894	−	13.1818i	−0.474465	−	0.485229i
$739$	−3.45136	+	2.89603i	−0.126960	+	0.106532i	−0.704057	−	0.710144i	$-0.748630\pi$
$739$	−3.45136	+	2.89603i	−0.126960	+	0.106532i	0.577097	+	0.816676i	$0.304186\pi$
$740$	−1.29877	−	1.74455i	−0.0477437	−	0.0641309i
$741$	4.84742	+	26.1237i	0.178075	+	0.959680i
$742$	5.55560	+	5.88859i	0.203952	+	0.216177i
$743$	−2.70726	+	0.641632i	−0.0993197	+	0.0235392i	−0.279975	−	0.960007i	$-0.590326\pi$
$743$	−2.70726	+	0.641632i	−0.0993197	+	0.0235392i	0.180656	+	0.983546i	$0.442178\pi$
$744$	13.3644	−	0.119436i	0.489964	−	0.00437875i
$745$	0.649055	−	1.50468i	0.0237795	−	0.0551271i
$746$	−2.19073	−	12.4242i	−0.0802082	−	0.454883i
$747$	−22.1746	+	40.0436i	−0.811325	+	1.46512i
$748$	−5.41339	+	30.7008i	−0.197933	+	1.12253i
$749$	−14.9772	−	9.85066i	−0.547255	−	0.359935i
$750$	−14.5714	−	7.15570i	−0.532072	−	0.261289i
$751$	−23.0357	+	30.9423i	−0.840585	+	1.12910i	0.149518	+	0.988759i	$0.452228\pi$
$751$	−23.0357	+	30.9423i	−0.840585	+	1.12910i	−0.990103	+	0.140342i	$0.955180\pi$
$752$	0.330714	+	5.67813i	0.0120599	+	0.207060i
$753$	12.7204	−	6.53143i	0.463558	−	0.238019i
$754$	−4.54387	+	4.81622i	−0.165478	+	0.175396i
$755$	8.26817	−	14.3209i	0.300909	−	0.521190i
$756$	−6.43738	−	5.11390i	−0.234125	−	0.185991i
$757$	−13.3498	−	23.1225i	−0.485205	−	0.840400i	0.514650	−	0.857400i	$-0.327922\pi$
$757$	−13.3498	−	23.1225i	−0.485205	−	0.840400i	−0.999855	+	0.0170001i	$0.994588\pi$
$758$	−2.80553	−	0.664922i	−0.101901	−	0.0241511i
$759$	−5.35993	−	17.3380i	−0.194553	−	0.629328i
$760$	−2.27896	−	1.14454i	−0.0826667	−	0.0415168i
$761$	−1.22820	−	0.143556i	−0.0445222	−	0.00520390i	0.0938027	−	0.995591i	$-0.470098\pi$
$761$	−1.22820	−	0.143556i	−0.0445222	−	0.00520390i	−0.138325	+	0.990387i	$0.544172\pi$
$762$	−19.5148	+	4.80968i	−0.706947	+	0.174236i
$763$	6.05535	−	3.04111i	0.219218	−	0.110096i
$764$	4.23935	−	1.54300i	0.153374	−	0.0558237i
$765$	20.5239	+	4.47841i	0.742042	+	0.161917i
$766$	12.3405	+	4.49159i	0.445882	+	0.162288i
$767$	−27.1558

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)

\(f(q)\)	\(=\)	\(q+(0.286803 + 0.957990i) q^{2} +(-0.671790 + 1.59646i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.417669 + 0.968265i) q^{5} +(-1.72207 - 0.185697i) q^{6} +(-0.0919975 + 1.57954i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.09740 - 2.14498i) q^{9} +O(q^{10})\)	\(q+(0.286803 + 0.957990i) q^{2} +(-0.671790 + 1.59646i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.417669 + 0.968265i) q^{5} +(-1.72207 - 0.185697i) q^{6} +(-0.0919975 + 1.57954i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.09740 - 2.14498i) q^{9} +(-0.807799 + 0.677824i) q^{10} +(-2.80349 - 3.76574i) q^{11} +(-0.315999 - 1.70298i) q^{12} +(4.35285 + 4.61375i) q^{13} +(-1.53956 + 0.364884i) q^{14} +(-1.82639 + 0.0163222i) q^{15} +(0.396080 - 0.918216i) q^{16} +(1.15308 + 6.53944i) q^{17} +(1.45333 - 2.62447i) q^{18} +(0.419952 - 2.38166i) q^{19} +(-0.881028 - 0.579461i) q^{20} +(-2.45987 - 1.20799i) q^{21} +(2.80349 - 3.76574i) q^{22} +(-0.129765 - 2.22799i) q^{23} +(1.54081 - 0.791144i) q^{24} +(2.66812 - 2.82804i) q^{25} +(-3.17151 + 5.49322i) q^{26} +(4.83339 - 1.90744i) q^{27} +(-0.791107 - 1.37024i) q^{28} +(1.01575 + 0.240736i) q^{29} +(-0.539450 - 1.74498i) q^{30} +(6.89550 + 3.46305i) q^{31} +(0.993238 + 0.116093i) q^{32} +(7.89524 - 1.94589i) q^{33} +(-5.93401 + 2.98017i) q^{34} +(-1.56784 + 0.570645i) q^{35} +(2.93103 + 0.639565i) q^{36} +(1.93811 + 0.705415i) q^{37} +(2.40205 - 0.280760i) q^{38} +(-10.2899 + 3.84969i) q^{39} +(0.302436 - 1.01021i) q^{40} +(1.76253 - 5.88725i) q^{41} +(0.451741 - 2.70299i) q^{42} +(-0.444497 + 0.0519543i) q^{43} +(4.41160 + 1.60569i) q^{44} +(1.20089 - 2.92673i) q^{45} +(2.09717 - 0.763307i) q^{46} +(-5.08277 + 2.55266i) q^{47} +(1.19982 + 1.24918i) q^{48} +(4.46620 + 0.522023i) q^{49} +(3.47446 + 1.74494i) q^{50} +(-11.2146 - 2.55228i) q^{51} +(-6.17205 - 1.46280i) q^{52} +(-2.55834 - 4.43118i) q^{53} +(3.21354 + 4.08328i) q^{54} +(2.47531 - 4.28736i) q^{55} +(1.08578 - 1.15086i) q^{56} +(3.52012 + 2.27042i) q^{57} +(0.0606964 + 1.04212i) q^{58} +(-2.57397 + 3.45744i) q^{59} +(1.51695 - 1.01725i) q^{60} +(-7.07255 - 4.65169i) q^{61} +(-1.33991 + 7.59904i) q^{62} +(3.58103 - 3.11558i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-2.64928 + 6.14173i) q^{65} +(4.12852 + 7.00547i) q^{66} +(-8.93095 + 2.11667i) q^{67} +(-4.55686 - 4.82999i) q^{68} +(3.64407 + 1.28957i) q^{69} +(-0.996332 - 1.33831i) q^{70} +(6.70480 - 5.62599i) q^{71} +(0.227933 + 2.99133i) q^{72} +(-9.89062 - 8.29921i) q^{73} +(-0.119923 + 2.05901i) q^{74} +(2.72245 + 6.15940i) q^{75} +(0.957882 + 2.22062i) q^{76} +(6.20605 - 4.08178i) q^{77} +(-6.63914 - 8.75350i) q^{78} +(0.686776 + 2.29399i) q^{79} +1.05451 q^{80} +(-0.201863 + 8.99774i) q^{81} +6.14542 q^{82} +(-4.37599 - 14.6168i) q^{83} +(2.71899 - 0.342462i) q^{84} +(-5.85031 + 3.84781i) q^{85} +(-0.177255 - 0.410923i) q^{86} +(-1.06669 + 1.45988i) q^{87} +(-0.272974 + 4.68678i) q^{88} +(3.18943 + 2.67625i) q^{89} +(3.14819 + 0.311047i) q^{90} +(-7.68804 + 6.45103i) q^{91} +(1.33272 + 1.79015i) q^{92} +(-10.1610 + 8.68198i) q^{93} +(-3.90318 - 4.13712i) q^{94} +(2.48148 - 0.588123i) q^{95} +(-0.852586 + 1.50768i) q^{96} +(-3.13875 + 7.27643i) q^{97} +(0.780826 + 4.42829i) q^{98} +(-2.19741 + 13.9117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

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