LMFDB - Embedded newform 729.2.k.a.4.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08274 - 0.0269280i) q^{2} +(-1.71559 - 0.238211i) q^{3} +(2.33777 + 0.0604606i) q^{4} +(-0.511598 - 0.156773i) q^{5} +(3.56673 + 0.542331i) q^{6} +(-1.27737 + 3.18529i) q^{7} +(-0.704645 - 0.0273434i) q^{8} +(2.88651 + 0.817346i) q^{9} +O(q^{10})$	\(q+(-2.08274 - 0.0269280i) q^{2} +(-1.71559 - 0.238211i) q^{3} +(2.33777 + 0.0604606i) q^{4} +(-0.511598 - 0.156773i) q^{5} +(3.56673 + 0.542331i) q^{6} +(-1.27737 + 3.18529i) q^{7} +(-0.704645 - 0.0273434i) q^{8} +(2.88651 + 0.817346i) q^{9} +(1.06131 + 0.340294i) q^{10} +(-3.83775 - 2.18277i) q^{11} +(-3.99626 - 0.660609i) q^{12} +(1.07557 + 2.40739i) q^{13} +(2.74621 - 6.59975i) q^{14} +(0.840348 + 0.390827i) q^{15} +(-3.20399 - 0.165837i) q^{16} +(5.33730 + 2.42610i) q^{17} +(-5.98986 - 1.78005i) q^{18} +(2.15762 + 3.14588i) q^{19} +(-1.18652 - 0.397430i) q^{20} +(2.95022 - 5.16037i) q^{21} +(7.93429 + 4.64950i) q^{22} +(1.02608 - 3.13040i) q^{23} +(1.20237 + 0.214764i) q^{24} +(-3.90441 - 2.64091i) q^{25} +(-2.17531 - 5.04294i) q^{26} +(-4.75737 - 2.08983i) q^{27} +(-3.17878 + 7.36924i) q^{28} +(6.15990 - 3.93830i) q^{29} +(-1.73971 - 0.836621i) q^{30} +(0.648314 + 2.38863i) q^{31} +(8.07604 + 0.522778i) q^{32} +(6.06406 + 4.65895i) q^{33} +(-11.0509 - 5.19667i) q^{34} +(1.15287 - 1.42933i) q^{35} +(6.69858 + 2.08529i) q^{36} +(7.02490 + 1.37965i) q^{37} +(-4.40906 - 6.61018i) q^{38} +(-1.27177 - 4.38631i) q^{39} +(0.356208 + 0.124458i) q^{40} +(-10.3979 + 3.93751i) q^{41} +(-6.28351 + 10.6683i) q^{42} +(-1.62554 + 0.713687i) q^{43} +(-8.83981 - 5.33486i) q^{44} +(-1.34860 - 0.870679i) q^{45} +(-2.22136 + 6.49218i) q^{46} +(-1.25524 + 4.62477i) q^{47} +(5.45724 + 1.04774i) q^{48} +(-3.45394 - 3.30109i) q^{49} +(8.06079 + 5.60548i) q^{50} +(-8.57870 - 5.43360i) q^{51} +(2.36888 + 5.69295i) q^{52} +(0.141905 - 0.150410i) q^{53} +(9.85212 + 4.48069i) q^{54} +(1.62119 + 1.71836i) q^{55} +(0.987189 - 2.20957i) q^{56} +(-2.95221 - 5.91102i) q^{57} +(-12.9356 + 8.03660i) q^{58} +(-14.6620 + 2.48769i) q^{59} +(1.94091 + 0.964471i) q^{60} +(-1.64467 + 3.02677i) q^{61} +(-1.28595 - 4.99237i) q^{62} +(-6.29063 + 8.15032i) q^{63} +(-10.4090 - 0.809050i) q^{64} +(-0.172846 - 1.40024i) q^{65} +(-12.5044 - 9.86669i) q^{66} +(-4.43229 + 2.29821i) q^{67} +(12.3307 + 5.99436i) q^{68} +(-2.50604 + 5.12606i) q^{69} +(-2.43962 + 2.94589i) q^{70} +(-9.02049 - 6.99141i) q^{71} +(-2.01162 - 0.654866i) q^{72} +(-10.7315 + 3.44091i) q^{73} +(-14.5939 - 3.06262i) q^{74} +(6.06929 + 5.46080i) q^{75} +(4.85381 + 7.48480i) q^{76} +(11.8550 - 9.43615i) q^{77} +(2.53066 + 9.16981i) q^{78} +(1.17799 - 6.21011i) q^{79} +(1.61316 + 0.587141i) q^{80} +(7.66389 + 4.71856i) q^{81} +(21.7623 - 7.92083i) q^{82} +(-1.96810 - 12.0723i) q^{83} +(7.20893 - 11.8854i) q^{84} +(-2.35020 - 2.07793i) q^{85} +(3.40480 - 1.44266i) q^{86} +(-11.5060 + 5.28916i) q^{87} +(2.64457 + 1.64302i) q^{88} +(-8.74025 - 3.57079i) q^{89} +(2.78533 + 1.84972i) q^{90} +(-9.04213 + 0.350876i) q^{91} +(2.58801 - 7.25611i) q^{92} +(-0.543243 - 4.25236i) q^{93} +(2.73887 - 9.59840i) q^{94} +(-0.610644 - 1.94768i) q^{95} +(-13.7306 - 2.82068i) q^{96} +(-0.744493 + 3.23429i) q^{97} +(7.10479 + 6.96833i) q^{98} +(-9.29364 - 9.43738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.08274	−	0.0269280i	−1.47272	−	0.0190410i	−0.727615	−	0.685985i	$-0.759371\pi$
$2$	−2.08274	−	0.0269280i	−1.47272	−	0.0190410i	−0.745108	+	0.666944i	$0.767602\pi$
$3$	−1.71559	−	0.238211i	−0.990497	−	0.137531i
$3$	−1.71559	−	0.238211i	−0.990497	−	0.137531i
$4$	2.33777	+	0.0604606i	1.16888	+	0.0302303i
$5$	−0.511598	−	0.156773i	−0.228794	−	0.0701110i	0.176488	−	0.984303i	$-0.443526\pi$
$5$	−0.511598	−	0.156773i	−0.228794	−	0.0701110i	−0.405282	+	0.914192i	$0.632827\pi$
$6$	3.56673	+	0.542331i	1.45611	+	0.221406i
$7$	−1.27737	+	3.18529i	−0.482801	+	1.20393i	0.465071	+	0.885273i	$0.346029\pi$
$7$	−1.27737	+	3.18529i	−0.482801	+	1.20393i	−0.947871	+	0.318653i	$0.896770\pi$
$8$	−0.704645	−	0.0273434i	−0.249130	−	0.00966736i
$9$	2.88651	+	0.817346i	0.962170	+	0.272449i
$10$	1.06131	+	0.340294i	0.335615	+	0.107610i
$11$	−3.83775	−	2.18277i	−1.15713	−	0.658131i	−0.209593	−	0.977789i	$-0.567214\pi$
$11$	−3.83775	−	2.18277i	−1.15713	−	0.658131i	−0.947533	+	0.319658i	$0.896432\pi$
$12$	−3.99626	−	0.660609i	−1.15362	−	0.190701i
$13$	1.07557	+	2.40739i	0.298309	+	0.667690i	0.998949	−	0.0458254i	$-0.0145918\pi$
$13$	1.07557	+	2.40739i	0.298309	+	0.667690i	−0.700640	+	0.713515i	$0.747102\pi$
$14$	2.74621	−	6.59975i	0.733955	−	1.76386i
$15$	0.840348	+	0.390827i	0.216977	+	0.100911i
$16$	−3.20399	−	0.165837i	−0.800998	−	0.0414593i
$17$	5.33730	+	2.42610i	1.29448	+	0.588416i	0.938243	−	0.345978i	$-0.112453\pi$
$17$	5.33730	+	2.42610i	1.29448	+	0.588416i	0.356242	+	0.934394i	$0.384058\pi$
$18$	−5.98986	−	1.78005i	−1.41182	−	0.419562i
$19$	2.15762	+	3.14588i	0.494992	+	0.721715i	0.989028	−	0.147726i	$-0.0471952\pi$
$19$	2.15762	+	3.14588i	0.494992	+	0.721715i	−0.494037	+	0.869441i	$0.664479\pi$
$20$	−1.18652	−	0.397430i	−0.265314	−	0.0888681i
$21$	2.95022	−	5.16037i	0.643790	−	1.12609i
$22$	7.93429	+	4.64950i	1.69160	+	0.991278i
$23$	1.02608	−	3.13040i	0.213953	−	0.652733i	−0.785474	−	0.618894i	$-0.787581\pi$
$23$	1.02608	−	3.13040i	0.213953	−	0.652733i	0.999427	−	0.0338381i	$-0.0107730\pi$
$24$	1.20237	+	0.214764i	0.245433	+	0.0438386i
$25$	−3.90441	−	2.64091i	−0.780883	−	0.528182i
$26$	−2.17531	−	5.04294i	−0.426614	−	0.989002i
$27$	−4.75737	−	2.08983i	−0.915557	−	0.402188i
$28$	−3.17878	+	7.36924i	−0.600733	+	1.39266i
$29$	6.15990	−	3.93830i	1.14387	−	0.731324i	0.176398	−	0.984319i	$-0.443555\pi$
$29$	6.15990	−	3.93830i	1.14387	−	0.731324i	0.967468	+	0.252995i	$0.0814156\pi$
$30$	−1.73971	−	0.836621i	−0.317626	−	0.152745i
$31$	0.648314	+	2.38863i	0.116441	+	0.429011i	0.999164	−	0.0408819i	$-0.0130167\pi$
$31$	0.648314	+	2.38863i	0.116441	+	0.429011i	−0.882723	+	0.469893i	$0.844292\pi$
$32$	8.07604	+	0.522778i	1.42765	+	0.0924150i
$33$	6.06406	+	4.65895i	1.05562	+	0.811018i
$34$	−11.0509	−	5.19667i	−1.89521	−	0.891221i
$35$	1.15287	−	1.42933i	0.194870	−	0.241601i
$36$	6.69858	+	2.08529i	1.11643	+	0.347548i
$37$	7.02490	+	1.37965i	1.15489	+	0.226812i	0.733254	−	0.679955i	$-0.238001\pi$
$37$	7.02490	+	1.37965i	1.15489	+	0.226812i	0.421632	+	0.906767i	$0.361457\pi$
$38$	−4.40906	−	6.61018i	−0.715243	−	1.07231i
$39$	−1.27177	−	4.38631i	−0.203647	−	0.702372i
$40$	0.356208	+	0.124458i	0.0563215	+	0.0196785i
$41$	−10.3979	+	3.93751i	−1.62389	+	0.614935i	−0.987666	−	0.156573i	$-0.949955\pi$
$41$	−10.3979	+	3.93751i	−1.62389	+	0.614935i	−0.636219	+	0.771508i	$0.719503\pi$
$42$	−6.28351	+	10.6683i	−0.969566	+	1.64615i
$43$	−1.62554	+	0.713687i	−0.247892	+	0.108836i	−0.522253	−	0.852791i	$-0.674908\pi$
$43$	−1.62554	+	0.713687i	−0.247892	+	0.108836i	0.274361	+	0.961627i	$0.411534\pi$
$44$	−8.83981	−	5.33486i	−1.33265	−	0.804260i
$45$	−1.34860	−	0.870679i	−0.201037	−	0.129793i
$46$	−2.22136	+	6.49218i	−0.327522	+	0.957220i
$47$	−1.25524	+	4.62477i	−0.183095	+	0.674591i	0.812675	+	0.582717i	$0.198010\pi$
$47$	−1.25524	+	4.62477i	−0.183095	+	0.674591i	−0.995771	+	0.0918747i	$0.970714\pi$
$48$	5.45724	+	1.04774i	0.787684	+	0.151228i
$49$	−3.45394	−	3.30109i	−0.493420	−	0.471584i
$50$	8.06079	+	5.60548i	1.13997	+	0.792735i
$51$	−8.57870	−	5.43360i	−1.20126	−	0.760856i
$52$	2.36888	+	5.69295i	0.328505	+	0.789470i
$53$	0.141905	−	0.150410i	0.0194921	−	0.0206604i	−0.717554	−	0.696503i	$-0.754738\pi$
$53$	0.141905	−	0.150410i	0.0194921	−	0.0206604i	0.737046	+	0.675842i	$0.236220\pi$
$54$	9.85212	+	4.48069i	1.34070	+	0.609745i
$55$	1.62119	+	1.71836i	0.218601	+	0.231703i
$56$	0.987189	−	2.20957i	0.131919	−	0.295266i
$57$	−2.95221	−	5.91102i	−0.391029	−	0.782934i
$58$	−12.9356	+	8.03660i	−1.69852	+	1.05526i
$59$	−14.6620	+	2.48769i	−1.90883	+	0.323870i	−0.996358	−	0.0852679i	$-0.972825\pi$
$59$	−14.6620	+	2.48769i	−1.90883	+	0.323870i	−0.912473	+	0.409138i	$0.865829\pi$
$60$	1.94091	+	0.964471i	0.250571	+	0.124513i
$61$	−1.64467	+	3.02677i	−0.210578	+	0.387538i	−0.962320	−	0.271919i	$-0.912342\pi$
$61$	−1.64467	+	3.02677i	−0.210578	+	0.387538i	0.751742	+	0.659458i	$0.229214\pi$
$62$	−1.28595	−	4.99237i	−0.163316	−	0.634032i
$63$	−6.29063	+	8.15032i	−0.792545	+	1.02684i
$64$	−10.4090	−	0.809050i	−1.30112	−	0.101131i
$65$	−0.172846	−	1.40024i	−0.0214389	−	0.173678i
$66$	−12.5044	−	9.86669i	−1.53919	−	1.21451i
$67$	−4.43229	+	2.29821i	−0.541491	+	0.280771i	−0.709130	−	0.705077i	$-0.750912\pi$
$67$	−4.43229	+	2.29821i	−0.541491	+	0.280771i	0.167640	+	0.985848i	$0.446386\pi$
$68$	12.3307	+	5.99436i	1.49532	+	0.726923i
$69$	−2.50604	+	5.12606i	−0.301691	+	0.617105i
$70$	−2.43962	+	2.94589i	−0.291590	+	0.352101i
$71$	−9.02049	−	6.99141i	−1.07054	−	0.829728i	−0.0845267	−	0.996421i	$-0.526938\pi$
$71$	−9.02049	−	6.99141i	−1.07054	−	0.829728i	−0.986009	+	0.166694i	$0.946691\pi$
$72$	−2.01162	−	0.654866i	−0.237071	−	0.0771767i
$73$	−10.7315	+	3.44091i	−1.25603	+	0.402729i	−0.857526	−	0.514440i	$-0.828000\pi$
$73$	−10.7315	+	3.44091i	−1.25603	+	0.402729i	−0.398500	+	0.917168i	$0.630469\pi$
$74$	−14.5939	−	3.06262i	−1.69651	−	0.356022i
$75$	6.06929	+	5.46080i	0.700821	+	0.630559i
$76$	4.85381	+	7.48480i	0.556771	+	0.858566i
$77$	11.8550	−	9.43615i	1.35100	−	1.07535i
$78$	2.53066	+	9.16981i	0.286541	+	1.03828i
$79$	1.17799	−	6.21011i	0.132534	−	0.698692i	−0.852006	−	0.523532i	$-0.824614\pi$
$79$	1.17799	−	6.21011i	0.132534	−	0.698692i	0.984540	−	0.175160i	$-0.0560443\pi$
$80$	1.61316	+	0.587141i	0.180356	+	0.0656444i
$81$	7.66389	+	4.71856i	0.851543	+	0.524284i
$82$	21.7623	−	7.92083i	2.40324	−	0.874709i
$83$	−1.96810	−	12.0723i	−0.216027	−	1.32510i	−0.839543	−	0.543293i	$-0.817177\pi$
$83$	−1.96810	−	12.0723i	−0.216027	−	1.32510i	0.623517	−	0.781810i	$-0.285703\pi$
$84$	7.20893	−	11.8854i	0.786559	−	1.29680i
$85$	−2.35020	−	2.07793i	−0.254915	−	0.225383i
$86$	3.40480	−	1.44266i	0.367149	−	0.155566i
$87$	−11.5060	+	5.28916i	−1.23358	+	0.567057i
$88$	2.64457	+	1.64302i	0.281912	+	0.175146i
$89$	−8.74025	−	3.57079i	−0.926465	−	0.378502i	−0.135789	−	0.990738i	$-0.543357\pi$
$89$	−8.74025	−	3.57079i	−0.926465	−	0.378502i	−0.790676	+	0.612235i	$0.790271\pi$
$90$	2.78533	+	1.84972i	0.293600	+	0.194977i
$91$	−9.04213	+	0.350876i	−0.947873	+	0.0367818i
$92$	2.58801	−	7.25611i	0.269819	−	0.756501i
$93$	−0.543243	−	4.25236i	−0.0563317	−	0.440949i
$94$	2.73887	−	9.59840i	0.282493	−	0.990000i
$95$	−0.610644	−	1.94768i	−0.0626507	−	0.199828i
$96$	−13.7306	−	2.82068i	−1.40138	−	0.287884i
$97$	−0.744493	+	3.23429i	−0.0755918	+	0.328393i	−0.998379	−	0.0569179i	$-0.981873\pi$
$97$	−0.744493	+	3.23429i	−0.0755918	+	0.328393i	0.922787	+	0.385310i	$0.125906\pi$
$98$	7.10479	+	6.96833i	0.717692	+	0.703907i
$99$	−9.29364	−	9.43738i	−0.934046	−	0.948492i
$100$	−8.96795	−	6.40991i	−0.896795	−	0.640991i
$101$	−1.76556	+	11.7876i	−0.175679	+	1.17291i	0.708484	+	0.705727i	$0.249380\pi$
$101$	−1.76556	+	11.7876i	−0.175679	+	1.17291i	−0.884163	+	0.467178i	$0.845271\pi$
$102$	17.7209	+	11.5478i	1.75463	+	1.14340i
$103$	1.36577	+	3.82925i	0.134573	+	0.377308i	0.990084	−	0.140477i	$-0.0448637\pi$
$103$	1.36577	+	3.82925i	0.134573	+	0.377308i	−0.855511	+	0.517785i	$0.826757\pi$
$104$	−0.692069	−	1.72576i	−0.0678629	−	0.169225i
$105$	−2.31833	+	2.17752i	−0.226246	+	0.212504i
$106$	−0.299601	+	0.309444i	−0.0290998	+	0.0300559i
$107$	0.616540	+	10.5856i	0.0596032	+	1.02335i	0.887012	+	0.461747i	$0.152777\pi$
$107$	0.616540	+	10.5856i	0.0596032	+	1.02335i	−0.827409	+	0.561600i	$0.810186\pi$
$108$	−10.9953	−	5.17318i	−1.05802	−	0.497789i
$109$	0.439796	−	7.55101i	0.0421249	−	0.723256i	−0.909445	−	0.415824i	$-0.863493\pi$
$109$	0.439796	−	7.55101i	0.0421249	−	0.723256i	0.951570	−	0.307432i	$-0.0994697\pi$
$110$	−3.33025	−	3.62256i	−0.317527	−	0.345397i
$111$	−11.7232	−	4.04032i	−1.11272	−	0.383490i
$112$	4.62092	−	9.99381i	0.436636	−	0.944326i
$113$	−3.15477	+	2.31710i	−0.296776	+	0.217974i	−0.730230	−	0.683202i	$-0.760587\pi$
$113$	−3.15477	+	2.31710i	−0.296776	+	0.217974i	0.433454	+	0.901176i	$0.357295\pi$
$114$	5.98952	+	12.3907i	0.560970	+	1.16049i
$115$	−1.01570	+	1.44064i	−0.0947148	+	0.134341i
$116$	14.6385	−	8.83441i	1.35916	−	0.820254i
$117$	1.13697	+	7.82807i	0.105113	+	0.723705i
$118$	30.6042	−	4.78641i	2.81735	−	0.440625i
$119$	−14.5455	+	13.9018i	−1.33339	+	1.27438i
$120$	−0.581460	−	0.298372i	−0.0530798	−	0.0272375i
$121$	4.34116	+	7.29952i	0.394651	+	0.663593i
$122$	3.50693	−	6.25970i	0.317503	−	0.566727i
$123$	18.7766	−	4.27825i	1.69303	−	0.385757i
$124$	1.37119	+	5.62327i	0.123137	+	0.504985i
$125$	3.26312	+	4.04563i	0.291862	+	0.361852i
$126$	13.3212	−	16.8056i	1.18675	−	1.49717i
$127$	0.268006	+	13.8183i	0.0237817	+	1.22618i	0.801666	+	0.597772i	$0.203947\pi$
$127$	0.268006	+	13.8183i	0.0237817	+	1.22618i	−0.777884	+	0.628407i	$0.783707\pi$
$128$	5.53782	+	0.502537i	0.489479	+	0.0444185i
$129$	2.95877	−	0.837174i	0.260505	−	0.0737091i
$130$	0.322289	+	2.92099i	0.0282666	+	0.256188i
$131$	2.74191	−	0.248818i	0.239561	−	0.0217393i	0.0300616	−	0.999548i	$-0.490430\pi$
$131$	2.74191	−	0.248818i	0.239561	−	0.0217393i	0.209500	+	0.977809i	$0.432816\pi$
$132$	13.8947	+	11.2582i	1.20938	+	0.979899i
$133$	−12.7766	+	2.85418i	−1.10787	+	0.247489i
$134$	9.29322	−	4.66723i	0.802812	−	0.403187i
$135$	2.10623	+	1.81498i	0.181276	+	0.156209i
$136$	−3.69456	−	1.85548i	−0.316806	−	0.159106i
$137$	−19.5977	−	4.91318i	−1.67435	−	0.419761i	−0.714353	−	0.699786i	$-0.753279\pi$
$137$	−19.5977	−	4.91318i	−1.67435	−	0.419761i	−0.959993	+	0.280025i	$0.909657\pi$
$138$	5.35747	−	10.6088i	0.456058	−	0.903080i
$139$	6.74967	+	0.966408i	0.572499	+	0.0819696i	0.421928	−	0.906629i	$-0.361354\pi$
$139$	6.74967	+	0.966408i	0.572499	+	0.0819696i	0.150572	+	0.988599i	$0.451889\pi$
$140$	2.78156	−	3.27174i	0.235084	−	0.276513i
$141$	3.25514	−	7.63520i	0.274133	−	0.643000i
$142$	18.5991	+	14.8042i	1.56080	+	1.24234i
$143$	1.12701	−	11.5867i	0.0942455	−	0.968928i
$144$	−9.11281	−	3.09746i	−0.759401	−	0.258122i
$145$	−3.76881	+	1.04912i	−0.312983	+	0.0871248i
$146$	22.4436	−	6.87757i	1.85745	−	0.569192i
$147$	5.13920	+	6.48608i	0.423874	+	0.534963i
$148$	16.3392	+	3.65002i	1.34307	+	0.300030i
$149$	5.99508	−	1.50298i	0.491136	−	0.123129i	0.0103139	−	0.999947i	$-0.496717\pi$
$149$	5.99508	−	1.50298i	0.491136	−	0.123129i	0.480822	+	0.876818i	$0.340338\pi$
$150$	−12.4937	−	11.5369i	−1.02011	−	0.941983i
$151$	−9.53056	−	11.2101i	−0.775586	−	0.912266i	0.222448	−	0.974945i	$-0.428595\pi$
$151$	−9.53056	−	11.2101i	−0.775586	−	0.912266i	−0.998034	+	0.0626786i	$0.980036\pi$
$152$	−1.43434	−	2.27573i	−0.116340	−	0.184586i
$153$	13.4232	+	11.3654i	1.08520	+	0.918837i
$154$	−24.9450	+	19.3339i	−2.01013	+	1.55797i
$155$	0.0427967	−	1.32366i	0.00343752	−	0.106319i
$156$	−2.70791	−	10.3311i	−0.216806	−	0.827148i
$157$	2.12611	−	17.2237i	0.169682	−	1.37460i	−0.631127	−	0.775680i	$-0.717407\pi$
$157$	2.12611	−	17.2237i	0.169682	−	1.37460i	0.800809	−	0.598920i	$-0.204403\pi$
$158$	−2.62067	+	12.9023i	−0.208489	+	1.02646i
$159$	−0.279280	+	0.224239i	−0.0221483	+	0.0177833i
$160$	−4.04973	−	1.53356i	−0.320159	−	0.121238i
$161$	8.66053	+	7.26705i	0.682545	+	0.572723i
$162$	−15.8349	−	10.0339i	−1.24410	−	0.788340i
$163$	15.8456	−	13.2961i	1.24113	−	1.04143i	0.243692	−	0.969853i	$-0.421642\pi$
$163$	15.8456	−	13.2961i	1.24113	−	1.04143i	0.997435	−	0.0715763i	$-0.0228029\pi$
$164$	−24.5461	+	8.57632i	−1.91673	+	0.669698i
$165$	−2.37196	−	3.33419i	−0.184657	−	0.259566i
$166$	3.77396	+	25.1964i	0.292916	+	1.95562i
$167$	−0.984245	+	1.92861i	−0.0761632	+	0.149240i	−0.925663	−	0.378348i	$-0.876492\pi$
$167$	−0.984245	+	1.92861i	−0.0761632	+	0.149240i	0.849500	+	0.527588i	$0.176904\pi$
$168$	−2.21996	+	3.55556i	−0.171273	+	0.274318i
$169$	4.03502	−	4.50471i	0.310386	−	0.346516i
$170$	4.83892	+	4.39109i	0.371128	+	0.336781i
$171$	3.65671	+	10.8442i	0.279636	+	0.829273i
$172$	−3.84329	+	1.57016i	−0.293048	+	0.119723i
$173$	23.4145	+	3.97272i	1.78017	+	0.302041i	0.962024	−	0.272966i	$-0.0880046\pi$
$173$	23.4145	+	3.97272i	1.78017	+	0.302041i	0.818149	+	0.575007i	$0.195001\pi$
$174$	24.1065	−	10.7061i	1.82751	−	0.811630i
$175$	13.3995	−	9.06327i	1.01290	−	0.685119i
$176$	11.9341	+	7.63003i	0.899570	+	0.575135i
$177$	25.7466	−	0.775211i	1.93523	−	0.0582684i
$178$	18.1076	+	7.67239i	1.35722	+	0.575070i
$179$	−3.10087	−	6.48492i	−0.231770	−	0.484706i	0.753121	−	0.657882i	$-0.228548\pi$
$179$	−3.10087	−	6.48492i	−0.231770	−	0.484706i	−0.984891	+	0.173176i	$0.944597\pi$
$180$	−3.10006	−	2.11698i	−0.231065	−	0.157791i
$181$	−13.5635	−	3.77567i	−1.00817	−	0.280643i	−0.275554	−	0.961286i	$-0.588861\pi$
$181$	−13.5635	−	3.77567i	−1.00817	−	0.280643i	−0.732616	+	0.680642i	$0.761701\pi$
$182$	18.8419	−	0.487299i	1.39665	−	0.0361210i
$183$	3.54259	−	4.80093i	0.261876	−	0.354895i
$184$	−0.808620	+	2.17776i	−0.0596122	+	0.160547i
$185$	−3.37763	−	1.80714i	−0.248329	−	0.132863i
$186$	1.01693	+	8.87120i	0.0745649	+	0.650468i
$187$	−15.1876	−	20.9609i	−1.11063	−	1.53281i
$188$	−3.21407	+	10.7357i	−0.234410	+	0.782985i
$189$	12.7336	−	12.4841i	0.926237	−	0.908087i
$190$	1.21937	+	4.07297i	0.0884623	+	0.295485i
$191$	−11.1451	+	14.5732i	−0.806428	+	1.05448i	0.190913	+	0.981607i	$0.438855\pi$
$191$	−11.1451	+	14.5732i	−0.806428	+	1.05448i	−0.997341	+	0.0728744i	$0.976783\pi$
$192$	17.6648	+	3.86753i	1.27485	+	0.279115i
$193$	7.65808	−	3.60120i	0.551240	−	0.259220i	−0.129707	−	0.991552i	$-0.541404\pi$
$193$	7.65808	−	3.60120i	0.551240	−	0.259220i	0.680947	+	0.732332i	$0.261568\pi$
$194$	1.63768	−	6.71616i	0.117579	−	0.482192i
$195$	−0.0370183	+	2.44341i	−0.00265094	+	0.174976i
$196$	−7.87493	−	7.92600i	−0.562495	−	0.566143i
$197$	−16.8732	+	3.31378i	−1.20216	+	0.236097i	−0.753406	−	0.657556i	$-0.771590\pi$
$197$	−16.8732	+	3.31378i	−1.20216	+	0.236097i	−0.448758	+	0.893653i	$0.648133\pi$
$198$	19.1021	+	19.9059i	1.35753	+	1.41465i
$199$	−11.2748	+	6.22116i	−0.799248	+	0.441006i	−0.829480	−	0.558537i	$-0.811363\pi$
$199$	−11.2748	+	6.22116i	−0.799248	+	0.441006i	0.0302321	+	0.999543i	$0.490375\pi$
$200$	2.67901	+	1.96766i	0.189435	+	0.139135i
$201$	8.15147	−	2.88697i	0.574960	−	0.203631i
$202$	3.99462	−	24.5029i	0.281060	−	1.72402i
$203$	4.67615	+	24.6517i	0.328202	+	1.73021i
$204$	−19.7265	−	13.2212i	−1.38113	−	0.925668i
$205$	5.93686	−	0.384305i	0.414648	−	0.0268410i
$206$	−2.74143	−	8.01214i	−0.191005	−	0.558232i
$207$	5.52042	−	8.19725i	0.383696	−	0.569749i
$208$	−3.04688	−	7.89162i	−0.211263	−	0.547186i
$209$	−1.41366	−	16.7827i	−0.0977846	−	1.16089i
$210$	4.88713	−	4.47280i	0.337244	−	0.308652i
$211$	8.05903	−	12.0823i	0.554806	−	0.831781i	−0.443099	−	0.896473i	$-0.646121\pi$
$211$	8.05903	−	12.0823i	0.554806	−	0.831781i	0.997905	+	0.0646922i	$0.0206066\pi$
$212$	0.340834	−	0.343044i	0.0234086	−	0.0235604i
$213$	13.8101	+	14.1432i	0.946249	+	0.969075i
$214$	−0.999047	−	22.0637i	−0.0682935	−	1.50824i
$215$	0.943510	−	0.110280i	0.0643468	−	0.00752107i
$216$	3.29512	+	1.60267i	0.224204	+	0.109048i
$217$	−8.43663	−	0.986100i	−0.572716	−	0.0669409i
$218$	−1.11932	+	15.7150i	−0.0758097	+	1.06435i
$219$	19.2305	−	3.34684i	1.29948	−	0.226159i
$220$	3.68607	+	4.11514i	0.248515	+	0.277443i
$221$	−0.0999273	+	15.4584i	−0.00672184	+	1.03984i
$222$	24.3077	+	8.73064i	1.63142	+	0.585962i
$223$	−14.7655	+	13.0549i	−0.988769	+	0.874219i	−0.992059	−	0.125776i	$-0.959858\pi$
$223$	−14.7655	+	13.0549i	−0.988769	+	0.874219i	0.00329013	+	0.999995i	$0.498953\pi$
$224$	−11.9813	+	25.0567i	−0.800533	+	1.67417i
$225$	−9.11160	−	10.8143i	−0.607440	−	0.720952i
$226$	6.63298	−	4.74097i	0.441219	−	0.315364i
$227$	0.636662	+	1.24753i	0.0422568	+	0.0828012i	0.910879	−	0.412674i	$-0.135405\pi$
$227$	0.636662	+	1.24753i	0.0422568	+	0.0828012i	−0.868622	+	0.495476i	$0.834994\pi$
$228$	−6.54420	−	13.9971i	−0.433400	−	0.926981i
$229$	−15.6320	−	20.4403i	−1.03299	−	1.35073i	−0.934646	−	0.355580i	$-0.884283\pi$
$229$	−15.6320	−	20.4403i	−1.03299	−	1.35073i	−0.0983436	−	0.995153i	$-0.531354\pi$
$230$	2.15424	−	2.97314i	0.142047	−	0.196043i
$231$	−22.5861	+	13.3646i	−1.48606	+	0.879326i
$232$	−4.44823	+	2.60667i	−0.292041	+	0.171136i
$233$	2.55282	+	11.7851i	0.167241	+	0.772070i	0.981484	+	0.191546i	$0.0613500\pi$
$233$	2.55282	+	11.7851i	0.167241	+	0.772070i	−0.814243	+	0.580525i	$0.802847\pi$
$234$	−2.15723	−	16.3345i	−0.141023	−	1.06782i
$235$	1.36721	−	2.16923i	0.0891872	−	0.141505i
$236$	−34.4268	+	4.92918i	−2.24099	+	0.320862i
$237$	−3.50026	+	10.3734i	−0.227366	+	0.673825i
$238$	30.6690	−	28.5623i	1.98798	−	1.85142i
$239$	2.85399	+	5.25235i	0.184610	+	0.339747i	0.954390	−	0.298562i	$-0.0965069\pi$
$239$	2.85399	+	5.25235i	0.184610	+	0.339747i	−0.769781	+	0.638308i	$0.779634\pi$
$240$	−2.62766	−	1.39157i	−0.169614	−	0.0898252i
$241$	−8.88441	+	14.9388i	−0.572295	+	0.962295i	0.426045	+	0.904702i	$0.359907\pi$
$241$	−8.88441	+	14.9388i	−0.572295	+	0.962295i	−0.998340	+	0.0575935i	$0.981657\pi$
$242$	−8.84497	−	15.3199i	−0.568576	−	0.984803i
$243$	−12.0241	−	9.92074i	−0.771346	−	0.636416i
$244$	−4.02786	+	6.97646i	−0.257857	+	0.446622i
$245$	1.24951	+	2.23031i	0.0798282	+	0.142489i
$246$	−39.2220	+	8.40488i	−2.50071	+	0.535876i
$247$	−5.25270	+	8.57785i	−0.334221	+	0.545795i
$248$	−0.391518	−	1.70087i	−0.0248614	−	0.108005i
$249$	0.500701	+	21.1799i	0.0317306	+	1.34222i
$250$	−6.68730	−	8.51388i	−0.422942	−	0.538465i
$251$	−8.97767	−	17.0437i	−0.566666	−	1.07579i	−0.985809	−	0.167868i	$-0.946312\pi$
$251$	−8.97767	−	17.0437i	−0.566666	−	1.07579i	0.419144	−	0.907920i	$-0.362330\pi$
$252$	−15.1988	+	18.6732i	−0.957435	+	1.17630i
$253$	−10.7708	+	9.77398i	−0.677154	+	0.614485i
$254$	−0.186089	−	28.7873i	−0.0116763	−	1.80628i
$255$	3.53701	+	4.12473i	0.221496	+	0.258300i
$256$	9.24883	+	0.960003i	0.578052	+	0.0600002i
$257$	−24.4442	+	3.17796i	−1.52478	+	0.198235i	−0.844836	−	0.535025i	$-0.820302\pi$
$257$	−24.4442	+	3.17796i	−1.52478	+	0.198235i	−0.679948	+	0.733260i	$0.737998\pi$
$258$	−6.18491	+	1.66395i	−0.385056	+	0.103593i
$259$	−13.3680	+	20.6140i	−0.830645	+	1.28089i
$260$	−0.319416	−	3.28388i	−0.0198093	−	0.203658i
$261$	20.9996	−	6.33317i	1.29984	−	0.392014i
$262$	−5.71739	+	0.444391i	−0.353221	+	0.0274545i
$263$	−4.81649	−	23.7131i	−0.296998	−	1.46221i	−0.801082	−	0.598555i	$-0.795742\pi$
$263$	−4.81649	−	23.7131i	−0.296998	−	1.46221i	0.504084	−	0.863655i	$-0.331830\pi$
$264$	−4.14562	−	3.44871i	−0.255145	−	0.212254i
$265$	−0.0961783	+	0.0547027i	−0.00590818	+	0.00336036i
$266$	26.6873	−	5.60048i	1.63630	−	0.343388i
$267$	14.1441	+	8.20804i	0.865605	+	0.502324i
$268$	−10.5006	+	5.10471i	−0.641428	+	0.311820i
$269$	4.27749	−	5.74567i	0.260803	−	0.350320i	−0.652363	−	0.757907i	$-0.726222\pi$
$269$	4.27749	−	5.74567i	0.260803	−	0.350320i	0.913166	+	0.407587i	$0.133630\pi$
$270$	−4.33787	−	3.83686i	−0.263995	−	0.233504i
$271$	−10.7454	−	14.4336i	−0.652739	−	0.876781i	0.345356	−	0.938472i	$-0.387758\pi$
$271$	−10.7454	−	14.4336i	−0.652739	−	0.876781i	−0.998095	+	0.0616911i	$0.980351\pi$
$272$	−16.6983	−	8.65833i	−1.01248	−	0.524988i
$273$	15.5962	+	1.55198i	0.943925	+	0.0939299i
$274$	40.6847	+	10.7606i	2.45785	+	0.650073i
$275$	9.21967	+	18.6576i	0.555967	+	1.12510i
$276$	−6.16846	+	11.8320i	−0.371298	+	0.712204i
$277$	−9.07589	+	6.31139i	−0.545317	+	0.379215i	−0.811180	−	0.584796i	$-0.801174\pi$
$277$	−9.07589	+	6.31139i	−0.545317	+	0.379215i	0.265863	+	0.964011i	$0.414343\pi$
$278$	−14.0318	−	2.19454i	−0.841572	−	0.131620i
$279$	−0.0809749	+	7.42471i	−0.00484784	+	0.444506i
$280$	−0.851445	+	0.975647i	−0.0508835	+	0.0583061i
$281$	−3.23303	+	6.54260i	−0.192866	+	0.390299i	−0.971451	−	0.237241i	$-0.923757\pi$
$281$	−3.23303	+	6.54260i	−0.192866	+	0.390299i	0.778584	+	0.627540i	$0.215938\pi$
$282$	−6.98524	+	15.8145i	−0.415965	+	0.941741i
$283$	18.4083	−	15.8565i	1.09426	−	0.942569i	0.0956599	−	0.995414i	$-0.469504\pi$
$283$	18.4083	−	15.8565i	1.09426	−	0.942569i	0.998603	+	0.0528452i	$0.0168290\pi$
$284$	−20.6651	−	16.8897i	−1.22625	−	1.00222i
$285$	0.583655	+	3.48689i	0.0345728	+	0.206546i
$286$	−2.65928	+	24.1018i	−0.157247	+	1.42517i
$287$	0.739921	−	38.1501i	0.0436761	−	2.25193i
$288$	22.8843	+	8.10992i	1.34847	+	0.477882i
$289$	11.4229	+	13.0892i	0.671937	+	0.769954i
$290$	7.87773	−	2.08356i	0.462596	−	0.122351i
$291$	2.04769	−	5.37138i	0.120038	−	0.314876i
$292$	−25.2958	+	7.39523i	−1.48032	+	0.432773i
$293$	2.05092	−	24.3483i	0.119816	−	1.42244i	−0.638031	−	0.770011i	$-0.720251\pi$
$293$	2.05092	−	24.3483i	0.119816	−	1.42244i	0.757847	−	0.652432i	$-0.226251\pi$
$294$	−10.5290	−	13.6472i	−0.614063	−	0.795923i
$295$	7.89106	+	1.02591i	0.459435	+	0.0597306i
$296$	−4.91234	−	1.16424i	−0.285524	−	0.0676704i
$297$	13.6960	+	18.4045i	0.794723	+	1.06794i
$298$	−12.5267	+	2.96888i	−0.725652	+	0.171983i
$299$	8.63970	−	0.896778i	0.499647	−	0.0518620i
$300$	13.8584	+	13.1331i	0.800117	+	0.758237i
$301$	−0.196885	−	6.08946i	−0.0113483	−	0.350991i
$302$	19.5479	+	23.6044i	1.12485	+	1.35828i
$303$	5.83690	−	19.8021i	0.335321	−	1.13760i
$304$	−6.39129	−	10.4372i	−0.366565	−	0.598615i
$305$	1.31593	−	1.29065i	0.0753497	−	0.0739024i
$306$	−27.6511	−	24.0327i	−1.58071	−	1.37386i
$307$	−13.1518	+	19.1757i	−0.750611	+	1.09442i	0.241664	+	0.970360i	$0.422307\pi$
$307$	−13.1518	+	19.1757i	−0.750611	+	1.09442i	−0.992275	+	0.124057i	$0.960409\pi$
$308$	28.2848	−	21.3428i	1.61167	−	1.21612i
$309$	−1.43093	−	6.89478i	−0.0814027	−	0.392230i
$310$	−0.124778	+	2.75569i	−0.00708692	+	0.156513i
$311$	1.74501	+	24.4996i	0.0989507	+	1.38925i	0.765332	+	0.643636i	$0.222575\pi$
$311$	1.74501	+	24.4996i	0.0989507	+	1.38925i	−0.666381	+	0.745611i	$0.732158\pi$
$312$	0.776211	+	3.12556i	0.0439443	+	0.176950i
$313$	12.2151	+	32.8975i	0.690439	+	1.85948i	0.465309	+	0.885149i	$0.345943\pi$
$313$	12.2151	+	32.8975i	0.690439	+	1.85948i	0.225130	+	0.974329i	$0.427719\pi$
$314$	−4.89193	+	35.8153i	−0.276068	+	2.02117i
$315$	4.49602	−	3.18349i	0.253322	−	0.179369i
$316$	3.12933	−	14.4466i	0.176038	−	0.812684i
$317$	5.52581	+	16.8582i	0.310360	+	0.946853i	0.979104	+	0.203360i	$0.0651862\pi$
$317$	5.52581	+	16.8582i	0.310360	+	0.946853i	−0.668744	+	0.743493i	$0.733168\pi$
$318$	0.587706	−	0.459512i	0.0329569	−	0.0257682i
$319$	−32.2366	+	1.66855i	−1.80490	+	0.0934211i
$320$	5.19838	+	2.04575i	0.290598	+	0.114361i
$321$	1.46387	−	18.3074i	0.0817054	−	1.02182i
$322$	−17.8420	−	15.3686i	−0.994295	−	0.856459i
$323$	3.88362	+	22.0251i	0.216091	+	1.22551i
$324$	17.6311	+	11.4943i	0.979507	+	0.638570i
$325$	2.15823	−	12.2399i	0.119717	−	0.678949i
$326$	−33.3605	+	27.2656i	−1.84767	+	1.51010i
$327$	−2.55325	+	12.8497i	−0.141195	+	0.710590i
$328$	7.43452	−	2.49023i	0.410503	−	0.137500i
$329$	−13.1278	−	9.90583i	−0.723760	−	0.546126i
$330$	4.85041	+	7.00813i	0.267006	+	0.385785i
$331$	9.95220	−	5.32473i	0.547022	−	0.292674i	−0.174971	−	0.984574i	$-0.555983\pi$
$331$	9.95220	−	5.32473i	0.547022	−	0.292674i	0.721993	+	0.691900i	$0.243226\pi$
$332$	−3.87106	−	28.3412i	−0.212452	−	1.55542i
$333$	19.1498	+	9.72414i	1.04940	+	0.532880i
$334$	2.10186	−	3.99029i	0.115009	−	0.218339i
$335$	2.62785	−	0.480896i	0.143575	−	0.0262742i
$336$	−10.3083	+	16.0445i	−0.562361	+	0.875301i
$337$	−8.10077	−	8.36692i	−0.441277	−	0.455775i	0.460702	−	0.887555i	$-0.347598\pi$
$337$	−8.10077	−	8.36692i	−0.441277	−	0.455775i	−0.901979	+	0.431780i	$0.857886\pi$
$338$	−8.52522	+	9.27351i	−0.463711	+	0.504412i
$339$	5.96426	−	3.22369i	0.323934	−	0.175087i
$340$	−5.36860	−	4.99982i	−0.291153	−	0.271153i
$341$	2.72578	−	10.5821i	0.147609	−	0.573053i
$342$	−7.32399	−	22.6841i	−0.396036	−	1.22661i
$343$	−6.94287	+	3.15592i	−0.374880	+	0.170404i
$344$	1.16494	−	0.458448i	0.0628095	−	0.0247179i
$345$	2.08571	−	2.22960i	0.112291	−	0.120038i
$346$	−48.6595	−	8.90468i	−2.61595	−	0.478718i
$347$	−5.96032	+	7.58834i	−0.319967	+	0.407363i	−0.919565	−	0.392938i	$-0.871459\pi$
$347$	−5.96032	+	7.58834i	−0.319967	+	0.407363i	0.599598	+	0.800301i	$0.295327\pi$
$348$	−27.2182	+	11.6692i	−1.45905	+	0.625533i
$349$	4.72788	+	16.5689i	0.253077	+	0.886912i	0.979800	+	0.199981i	$0.0640879\pi$
$349$	4.72788	+	16.5689i	0.253077	+	0.886912i	−0.726722	+	0.686931i	$0.758957\pi$
$350$	−28.1517	+	18.5157i	−1.50477	+	0.989704i
$351$	−0.0858504	−	13.7006i	−0.00458236	−	0.731284i
$352$	−29.8527	−	19.6345i	−1.59116	−	1.04652i
$353$	6.42683	−	20.4988i	0.342066	−	1.09104i	−0.611852	−	0.790972i	$-0.709575\pi$
$353$	6.42683	−	20.4988i	0.342066	−	1.09104i	0.953918	−	0.300067i	$-0.0970090\pi$
$354$	−53.6445	+	0.921263i	−2.85117	+	0.0489646i
$355$	3.51880	+	4.99096i	0.186759	+	0.264893i
$356$	−20.2168	−	8.87611i	−1.07149	−	0.470433i
$357$	28.2658	−	20.3849i	1.49598	−	1.07888i
$358$	6.28370	+	13.5899i	0.332104	+	0.718250i
$359$	4.65617	+	2.56916i	0.245743	+	0.135595i	0.601203	−	0.799096i	$-0.294688\pi$
$359$	4.65617	+	2.56916i	0.245743	+	0.135595i	−0.355460	+	0.934691i	$0.615676\pi$
$360$	0.926473	+	0.650395i	0.0488294	+	0.0342788i
$361$	1.60210	−	4.14955i	0.0843212	−	0.218397i
$362$	28.1477	+	8.22899i	1.47941	+	0.432506i
$363$	−5.70884	−	13.5571i	−0.299636	−	0.711564i
$364$	−21.1596	+	0.273575i	−1.10907	+	0.0143392i
$365$	6.02965	−	0.0779579i	0.315606	−	0.00408050i
$366$	−7.50760	+	9.90371i	−0.392428	+	0.517675i
$367$	1.71340	+	0.500912i	0.0894386	+	0.0261474i	0.325019	−	0.945707i	$-0.394629\pi$
$367$	1.71340	+	0.500912i	0.0894386	+	0.0261474i	−0.235581	+	0.971855i	$0.575699\pi$
$368$	−3.80670	+	9.85960i	−0.198438	+	0.513967i
$369$	−33.2321	+	2.86694i	−1.72999	+	0.149247i
$370$	6.98609	+	3.85476i	0.363189	+	0.200399i
$371$	0.297835	+	0.644136i	0.0154628	+	0.0334419i
$372$	−1.01288	−	9.97387i	−0.0525153	−	0.517121i
$373$	−0.736651	−	0.323424i	−0.0381423	−	0.0167463i	0.382849	−	0.923811i	$-0.374943\pi$
$373$	−0.736651	−	0.323424i	−0.0381423	−	0.0167463i	−0.420991	+	0.907065i	$0.638318\pi$
$374$	31.0675	+	44.0652i	1.60646	+	2.27856i
$375$	−4.63446	−	7.71796i	−0.239322	−	0.398554i
$376$	1.01095	−	3.22449i	0.0521359	−	0.166291i
$377$	16.1064	+	10.5934i	0.829523	+	0.545586i
$378$	−26.8571	+	25.6584i	−1.38138	+	1.31972i
$379$	11.0883	−	7.29288i	0.569567	−	0.374610i	−0.231818	−	0.972759i	$-0.574467\pi$
$379$	11.0883	−	7.29288i	0.569567	−	0.374610i	0.801385	+	0.598149i	$0.204097\pi$
$380$	−1.30979	−	4.59016i	−0.0671906	−	0.235470i
$381$	2.83189	−	23.7705i	0.145082	−	1.21780i
$382$	23.6047	−	30.0522i	1.20772	−	1.53760i
$383$	−3.33882	−	0.611003i	−0.170606	−	0.0312208i	0.0940296	−	0.995569i	$-0.470025\pi$
$383$	−3.33882	−	0.611003i	−0.170606	−	0.0312208i	−0.264635	+	0.964349i	$0.585252\pi$
$384$	−9.38093	−	2.18132i	−0.478719	−	0.111315i
$385$	−7.54433	+	2.96897i	−0.384495	+	0.151313i
$386$	−16.0468	+	7.29416i	−0.816760	+	0.371263i
$387$	−5.27547	+	0.731437i	−0.268167	+	0.0371811i
$388$	−1.93600	+	7.51602i	−0.0982855	+	0.381568i
$389$	−17.4966	−	16.2947i	−0.887112	−	0.826173i	0.0985109	−	0.995136i	$-0.468592\pi$
$389$	−17.4966	−	16.2947i	−0.887112	−	0.826173i	−0.985622	+	0.168963i	$0.945958\pi$
$390$	0.142896	−	5.08800i	0.00723581	−	0.257641i
$391$	13.0712	−	14.2185i	0.661037	−	0.719059i
$392$	2.34354	+	2.42053i	0.118367	+	0.122255i
$393$	−4.76326	−	0.226282i	−0.240275	−	0.0114144i
$394$	35.2317	−	6.44740i	1.77495	−	0.324815i
$395$	−1.57623	+	2.99240i	−0.0793088	+	0.150564i
$396$	−21.1558	−	22.6243i	−1.06312	−	1.13691i
$397$	1.00009	+	7.32196i	0.0501931	+	0.367479i	0.998711	+	0.0507553i	$0.0161629\pi$
$397$	1.00009	+	7.32196i	0.0501931	+	0.367479i	−0.948518	+	0.316723i	$0.897417\pi$
$398$	23.6500	−	12.6535i	1.18547	−	0.634262i
$399$	22.5994	−	1.85307i	1.13138	−	0.0927697i
$400$	12.0717	+	9.10896i	0.603587	+	0.455448i
$401$	1.81415	−	0.607659i	0.0905945	−	0.0303451i	−0.271951	−	0.962311i	$-0.587669\pi$
$401$	1.81415	−	0.607659i	0.0905945	−	0.0303451i	0.362546	+	0.931966i	$0.381908\pi$
$402$	−17.0552	+	5.79332i	−0.850634	+	0.288944i
$403$	−5.05306	+	4.12989i	−0.251711	+	0.205724i
$404$	−4.84015	+	27.4498i	−0.240806	+	1.36568i
$405$	−3.18109	−	3.61550i	−0.158070	−	0.179655i
$406$	−9.07541	−	51.4692i	−0.450405	−	2.55437i
$407$	−23.9484	−	20.6285i	−1.18708	−	1.02252i
$408$	5.89636	+	4.06333i	0.291913	+	0.201165i
$409$	−5.94632	−	2.34010i	−0.294027	−	0.115710i	0.214588	−	0.976705i	$-0.431159\pi$
$409$	−5.94632	−	2.34010i	−0.294027	−	0.115710i	−0.508615	+	0.860994i	$0.669842\pi$
$410$	−12.3753	+	0.640542i	−0.611173	+	0.0316341i
$411$	32.4513	+	13.0974i	1.60070	+	0.646047i
$412$	2.96133	+	9.03449i	0.145894	+	0.445097i
$413$	10.8048	−	49.8804i	0.531669	−	2.45446i
$414$	−11.7184	+	16.9241i	−0.575926	+	0.831776i
$415$	−0.885730	+	6.48469i	−0.0434788	+	0.318321i
$416$	7.42781	+	20.0044i	0.364178	+	0.980799i
$417$	−11.3495	−	3.26581i	−0.555786	−	0.159927i
$418$	2.49236	+	34.9922i	0.121905	+	1.71152i
$419$	−1.00174	+	22.1231i	−0.0489382	+	1.08079i	0.815727	+	0.578437i	$0.196337\pi$
$419$	−1.00174	+	22.1231i	−0.0489382	+	1.08079i	−0.864665	+	0.502349i	$0.832469\pi$
$420$	−5.55138	+	4.95038i	−0.270880	+	0.241554i
$421$	1.97400	−	1.48951i	0.0962067	−	0.0725945i	−0.553133	−	0.833093i	$-0.686568\pi$
$421$	1.97400	−	1.48951i	0.0962067	−	0.0725945i	0.649340	+	0.760498i	$0.275045\pi$
$422$	−17.1103	+	24.9474i	−0.832914	+	1.21442i
$423$	−7.40329	+	12.3235i	−0.359960	+	0.599188i
$424$	−0.104105	+	0.102105i	−0.00505579	+	0.00495868i
$425$	−14.4319	−	23.5678i	−0.700050	−	1.14321i
$426$	−28.3820	−	29.8285i	−1.37511	−	1.44520i
$427$	−7.54029	−	9.10506i	−0.364900	−	0.440625i
$428$	0.801318	+	24.7839i	0.0387332	+	1.19798i
$429$	−4.69357	+	19.6096i	−0.226608	+	0.946759i
$430$	−1.96806	+	0.204279i	−0.0949083	+	0.00985122i
$431$	−2.95331	+	0.699946i	−0.142256	+	0.0337152i	−0.301127	−	0.953584i	$-0.597363\pi$
$431$	−2.95331	+	0.699946i	−0.142256	+	0.0337152i	0.158871	+	0.987299i	$0.449215\pi$
$432$	14.8960	+	7.48475i	0.716685	+	0.360110i
$433$	9.84432	+	2.33315i	0.473088	+	0.112124i	0.460242	−	0.887794i	$-0.347763\pi$
$433$	9.84432	+	2.33315i	0.473088	+	0.112124i	0.0128459	+	0.999917i	$0.495911\pi$
$434$	17.5448	+	2.28098i	0.842177	+	0.109490i
$435$	6.71566	−	0.902090i	0.321991	−	0.0432519i
$436$	1.48468	−	17.6259i	0.0711033	−	0.844129i
$437$	12.0618	−	3.52626i	0.576992	−	0.168684i
$438$	−40.1424	+	6.45278i	−1.91808	+	0.308326i
$439$	−3.93837	+	1.04165i	−0.187968	+	0.0497153i	−0.348469	−	0.937320i	$-0.613298\pi$
$439$	−3.93837	+	1.04165i	−0.187968	+	0.0497153i	0.160501	+	0.987036i	$0.448689\pi$
$440$	−1.09538	−	1.25516i	−0.0522200	−	0.0598375i
$441$	−7.27171	−	12.3517i	−0.346272	−	0.588175i
$442$	0.624386	−	32.1932i	0.0296990	−	1.53127i
$443$	−3.39807	+	30.7976i	−0.161447	+	1.46324i	0.592111	+	0.805856i	$0.298295\pi$
$443$	−3.39807	+	30.7976i	−0.161447	+	1.46324i	−0.753558	+	0.657381i	$0.771664\pi$
$444$	−27.1619	−	10.1541i	−1.28905	−	0.481894i
$445$	3.91169	+	3.19704i	0.185432	+	0.151554i
$446$	31.1042	−	26.7924i	1.47283	−	1.26866i
$447$	−10.6431	+	1.15040i	−0.503403	+	0.0544120i
$448$	15.8732	−	32.1222i	0.749937	−	1.51763i
$449$	17.6047	−	20.1727i	0.830815	−	0.952009i	−0.168618	−	0.985682i	$-0.553930\pi$
$449$	17.6047	−	20.1727i	0.830815	−	0.952009i	0.999433	+	0.0336729i	$0.0107205\pi$
$450$	18.6859	+	22.7687i	0.880863	+	1.07333i
$451$	48.4994	+	7.58517i	2.28375	+	0.357172i
$452$	−7.51522	+	5.22610i	−0.353486	+	0.245815i
$453$	13.6802	+	21.5023i	0.642751	+	1.01026i
$454$	−1.29241	−	2.61542i	−0.0606559	−	0.122748i
$455$	4.68095	+	1.23805i	0.219446	+	0.0580409i
$456$	1.91863	+	4.24589i	0.0898481	+	0.198832i
$457$	19.9810	+	10.3604i	0.934670	+	0.484640i	0.858705	−	0.512471i	$-0.171270\pi$
$457$	19.9810	+	10.3604i	0.934670	+	0.484640i	0.0759647	+	0.997111i	$0.475796\pi$
$458$	32.0070	+	42.9928i	1.49559	+	2.00892i
$459$	−20.3214	−	22.6959i	−0.948521	−	1.05935i
$460$	−2.46158	+	3.30648i	−0.114772	+	0.154165i
$461$	1.45605	−	0.707833i	0.0678149	−	0.0329671i	−0.402991	−	0.915204i	$-0.632029\pi$
$461$	1.45605	−	0.707833i	0.0678149	−	0.0329671i	0.470805	+	0.882237i	$0.343963\pi$
$462$	47.4011	−	27.2268i	2.20530	−	1.26671i
$463$	−24.0063	+	5.03786i	−1.11567	+	0.234129i	−0.726587	−	0.687075i	$-0.758895\pi$
$463$	−24.0063	+	5.03786i	−1.11567	+	0.234129i	−0.389081	+	0.921204i	$0.627207\pi$
$464$	−20.3894	+	11.5967i	−0.946554	+	0.538365i
$465$	−0.388732	+	2.26066i	−0.0180270	+	0.104836i
$466$	−4.99953	−	24.6142i	−0.231599	−	1.14023i
$467$	13.5985	−	1.05696i	0.629266	−	0.0489104i	0.241100	−	0.970500i	$-0.422492\pi$
$467$	13.5985	−	1.05696i	0.629266	−	0.0489104i	0.388165	+	0.921590i	$0.373109\pi$
$468$	2.18469	+	18.3690i	0.100988	+	0.849106i
$469$	−1.65879	−	17.0538i	−0.0765956	−	0.787472i
$470$	−2.90597	+	4.48114i	−0.134042	+	0.206700i
$471$	−7.75040	+	29.0424i	−0.357120	+	1.33820i
$472$	10.3995	−	1.35203i	0.478677	−	0.0622322i
$473$	7.79624	+	0.809229i	0.358472	+	0.0372084i
$474$	7.56948	−	21.5109i	0.347678	−	0.988028i
$475$	−0.116234	−	17.9809i	−0.00533316	−	0.825021i
$476$	−34.8446	+	31.6198i	−1.59710	+	1.44929i
$477$	0.532546	−	0.318175i	0.0243836	−	0.0145682i
$478$	−5.80271	−	11.0162i	−0.265410	−	0.503868i
$479$	15.5031	+	19.7376i	0.708353	+	0.901834i	0.998478	−	0.0551549i	$-0.0175653\pi$
$479$	15.5031	+	19.7376i	0.708353	+	0.901834i	−0.290125	+	0.956989i	$0.593697\pi$
$480$	6.58237	+	3.59565i	0.300443	+	0.164118i
$481$	4.23443	+	18.3956i	0.193073	+	0.838766i
$482$	18.9062	−	30.8746i	0.861155	−	1.40630i
$483$	−13.1268	−	14.5303i	−0.597292	−	0.661152i
$484$	9.70730	+	17.3271i	0.441241	+	0.787594i
$485$	0.887930	−	1.53794i	0.0403188	−	0.0698343i
$486$	24.7760	+	20.9862i	1.12386	+	0.951952i
$487$	5.03872	+	8.72733i	0.228326	+	0.395473i	0.957312	−	0.289056i	$-0.0933413\pi$
$487$	5.03872	+	8.72733i	0.228326	+	0.395473i	−0.728986	+	0.684529i	$0.760008\pi$
$488$	1.24167	−	2.08783i	0.0562078	−	0.0945115i
$489$	−30.3519	+	19.0360i	−1.37256	+	0.860839i
$490$	−2.54235	−	4.67882i	−0.114852	−	0.211368i
$491$	−19.7848	+	18.4258i	−0.892877	+	0.831543i	−0.986449	−	0.164070i	$-0.947538\pi$
$491$	−19.7848	+	18.4258i	−0.892877	+	0.831543i	0.0935718	+	0.995613i	$0.470172\pi$
$492$	44.1540	−	8.86632i	1.99062	−	0.399724i
$493$	42.4320	−	6.07535i	1.91104	−	0.273620i
$494$	11.1710	−	17.7240i	0.502608	−	0.797441i
$495$	3.27508	+	6.28513i	0.147204	+	0.282496i
$496$	−1.68107	−	7.76068i	−0.0754822	−	0.348465i
$497$	33.7922	−	19.8023i	1.51579	−	0.888253i
$498$	−0.472500	−	44.1258i	−0.0211732	−	1.97733i
$499$	−2.68077	+	3.69982i	−0.120008	+	0.165627i	−0.865535	−	0.500849i	$-0.833021\pi$
$499$	−2.68077	+	3.69982i	−0.120008	+	0.165627i	0.745527	+	0.666476i	$0.232198\pi$
$500$	7.38381	+	9.65504i	0.330214	+	0.431786i
$501$	2.14798	−	3.07424i	0.0959646	−	0.137347i
$502$	18.2392	+	35.7394i	0.814057	+	1.59513i
$503$	−26.0192	+	18.5974i	−1.16014	+	0.829217i	−0.987786	−	0.155819i	$-0.950198\pi$
$503$	−26.0192	+	18.5974i	−1.16014	+	0.829217i	−0.172352	+	0.985035i	$0.555137\pi$
$504$	4.65552	−	5.57107i	0.207373	−	0.248155i
$505$	2.75122	−	5.75370i	0.122428	−	0.256036i
$506$	22.6960	−	20.0667i	1.00896	−	0.892072i
$507$	−7.99552	+	6.76706i	−0.355093	+	0.300536i
$508$	−0.208927	+	32.3203i	−0.00926965	+	1.43398i
$509$	−8.48580	−	9.47358i	−0.376126	−	0.419909i	0.526607	−	0.850109i	$-0.323464\pi$
$509$	−8.48580	−	9.47358i	−0.376126	−	0.419909i	−0.902734	+	0.430200i	$0.858443\pi$
$510$	−7.25561	−	8.68600i	−0.321284	−	0.384622i
$511$	2.74778	−	38.5782i	0.121554	−	1.70660i
$512$	−30.2831	−	3.53958i	−1.33833	−	0.156429i
$513$	−3.69023	−	19.4752i	−0.162927	−	0.859851i
$514$	50.9965	−	5.96064i	2.24936	−	0.262912i
$515$	−0.0984008	−	2.17315i	−0.00433606	−	0.0957606i
$516$	6.96754	−	1.77823i	0.306729	−	0.0782823i
$517$	14.9121	−	15.0088i	0.655834	−	0.660087i
$518$	28.3972	−	42.5738i	1.24770	−	1.87058i
$519$	−39.2234	−	12.3932i	−1.72172	−	0.544000i
$520$	0.0835079	+	0.991395i	0.00366206	+	0.0434755i
$521$	−7.90673	−	20.4789i	−0.346400	−	0.897198i	−0.991143	−	0.132799i	$-0.957604\pi$
$521$	−7.90673	−	20.4789i	−0.346400	−	0.897198i	0.644743	−	0.764399i	$-0.276964\pi$
$522$	−43.9073	+	12.6249i	−1.92177	+	0.552577i
$523$	2.16470	+	6.32658i	0.0946558	+	0.276642i	0.983311	−	0.181935i	$-0.0582360\pi$
$523$	2.16470	+	6.32658i	0.0946558	+	0.276642i	−0.888655	+	0.458577i	$0.848359\pi$
$524$	6.42499	−	0.415902i	0.280677	−	0.0181688i
$525$	−25.1470	+	12.3570i	−1.09750	+	0.539303i
$526$	9.39298	+	49.5179i	0.409554	+	2.15908i
$527$	−2.33482	+	14.3217i	−0.101706	+	0.623864i
$528$	−18.6566	−	15.9329i	−0.811923	−	0.693389i
$529$	9.79070	+	7.19101i	0.425683	+	0.312653i
$530$	0.201788	−	0.111342i	0.00876510	−	0.00483638i
$531$	−44.3553	−	4.80319i	−1.92486	−	0.208440i
$532$	−30.0414	+	5.89994i	−1.30246	+	0.255795i
$533$	−20.6628	−	20.7968i	−0.895006	−	0.900811i
$534$	−29.2375	−	17.4761i	−1.26523	−	0.756265i
$535$	1.34411	−	5.51222i	0.0581110	−	0.238314i
$536$	3.18603	−	1.49823i	0.137616	−	0.0647136i
$537$	3.77505	+	11.8641i	0.162905	+	0.511975i
$538$	−9.06365	+	11.8516i	−0.390762	+	0.510958i
$539$	6.04986	+	20.2079i	0.260586	+	0.870417i
$540$	4.81415	+	4.37035i	0.207168	+	0.188070i
$541$	−1.86395	+	6.22603i	−0.0801375	+	0.267678i	−0.988663	−	0.150152i	$-0.952024\pi$
$541$	−1.86395	+	6.22603i	−0.0801375	+	0.267678i	0.908526	+	0.417829i	$0.137209\pi$
$542$	21.9913	+	30.3509i	0.944609	+	1.30368i
$543$	22.3701	+	9.70849i	0.959992	+	0.416631i
$544$	41.8359	+	22.3835i	1.79370	+	0.959684i
$545$	−1.40879	+	3.79414i	−0.0603461	+	0.162523i
$546$	−32.4411	−	3.65235i	−1.38835	−	0.156306i
$547$	−24.1485	+	0.624541i	−1.03252	+	0.0267035i	−0.538398	−	0.842691i	$-0.680970\pi$
$547$	−24.1485	+	0.624541i	−1.03252	+	0.0267035i	−0.494119	+	0.869394i	$0.664509\pi$
$548$	−45.5179	−	12.6708i	−1.94443	−	0.541268i
$549$	−7.22128	+	7.39254i	−0.308197	+	0.315506i
$550$	−18.6998	−	39.1073i	−0.797363	−	1.66754i
$551$	25.6802	+	10.8810i	1.09401	+	0.463546i
$552$	1.90603	−	3.54352i	0.0811260	−	0.150822i
$553$	18.2763	+	11.6848i	0.777186	+	0.496890i
$554$	19.0727	−	12.9006i	0.810322	−	0.548095i
$555$	5.36416	+	3.90490i	0.227696	+	0.165754i
$556$	15.7207	+	2.66733i	0.666708	+	0.113120i
$557$	3.55511	−	1.45242i	0.150635	−	0.0615412i	−0.301629	−	0.953426i	$-0.597530\pi$
$557$	3.55511	−	1.45242i	0.150635	−	0.0615412i	0.452264	+	0.891884i	$0.350617\pi$
$558$	0.368583	−	15.4616i	0.0156033	−	0.654542i
$559$	−3.46650	−	3.14569i	−0.146618	−	0.133048i
$560$	−3.93081	+	4.38838i	−0.166107	+	0.185443i
$561$	21.0626	+	39.5782i	0.889265	+	1.67099i
$562$	6.90976	−	13.5395i	0.291470	−	0.571130i
$563$	3.36070	+	22.4374i	0.141637	+	0.945622i	0.939442	+	0.342708i	$0.111344\pi$
$563$	3.36070	+	22.4374i	0.141637	+	0.945622i	−0.797805	+	0.602915i	$0.794006\pi$
$564$	8.07141	−	17.6525i	0.339868	−	0.743305i
$565$	1.97723	−	0.690839i	0.0831828	−	0.0290638i
$566$	−38.7669	+	32.5293i	−1.62949	+	1.36731i
$567$	−24.8196	+	18.3844i	−1.04233	+	0.772071i
$568$	6.16507	+	5.17311i	0.258681	+	0.217059i
$569$	−4.25526	−	1.61139i	−0.178390	−	0.0675529i	0.263331	−	0.964706i	$-0.415179\pi$
$569$	−4.25526	−	1.61139i	−0.178390	−	0.0675529i	−0.441720	+	0.897153i	$0.645632\pi$
$570$	−1.12171	−	7.27803i	−0.0469833	−	0.304843i
$571$	3.76340	−	18.5284i	0.157494	−	0.775388i	−0.821293	−	0.570506i	$-0.806747\pi$
$571$	3.76340	−	18.5284i	0.157494	−	0.775388i	0.978787	−	0.204882i	$-0.0656810\pi$
$572$	3.33523	−	27.0189i	0.139453	−	1.12972i
$573$	22.5919	−	22.3468i	0.943789	−	0.933552i
$574$	−2.56837	+	79.4370i	−0.107202	+	3.31564i
$575$	−12.2734	+	9.51257i	−0.511834	+	0.396701i
$576$	−29.3844	−	10.8431i	−1.22435	−	0.451795i
$577$	−4.23520	−	6.71959i	−0.176313	−	0.279740i	0.746187	−	0.665736i	$-0.231883\pi$
$577$	−4.23520	−	6.71959i	−0.176313	−	0.279740i	−0.922500	+	0.385996i	$0.873858\pi$
$578$	−23.4386	−	27.5691i	−0.974916	−	1.14672i
$579$	−13.9960	+	4.35395i	−0.581653	+	0.180944i
$580$	−8.87405	+	2.22474i	−0.368475	+	0.0923772i
$581$	40.9677	+	9.15179i	1.69962	+	0.379680i
$582$	−4.40946	+	11.1321i	−0.182778	+	0.461439i
$583$	−0.872906	+	0.267491i	−0.0361521	+	0.0110784i
$584$	7.65598	−	2.13119i	0.316807	−	0.0881891i
$585$	0.645555	−	4.18307i	0.0266904	−	0.172949i
$586$	−4.92720	+	50.6561i	−0.203541	+	2.09258i
$587$	9.26966	+	7.37831i	0.382600	+	0.304535i	0.795166	−	0.606392i	$-0.207384\pi$
$587$	9.26966	+	7.37831i	0.382600	+	0.304535i	−0.412566	+	0.910928i	$0.635367\pi$
$588$	11.6221	+	15.4737i	0.479288	+	0.638124i
$589$	−6.11555	+	7.19328i	−0.251987	+	0.296394i
$590$	−16.4074	−	2.34919i	−0.675483	−	0.0967147i
$591$	29.7369	−	1.66572i	1.22321	−	0.0685186i
$592$	−22.2789	−	5.58536i	−0.915658	−	0.229557i
$593$	18.2215	+	9.15118i	0.748267	+	0.375794i	0.781706	−	0.623647i	$-0.214350\pi$
$593$	18.2215	+	9.15118i	0.748267	+	0.375794i	−0.0334389	+	0.999441i	$0.510646\pi$
$594$	−28.0297	−	38.7008i	−1.15007	−	1.58791i
$595$	9.62090	−	4.83180i	0.394418	−	0.198084i
$596$	14.1060	−	3.15115i	0.577804	−	0.129076i
$597$	20.8249	−	7.98719i	0.852305	−	0.326894i
$598$	−18.0184	+	1.63511i	−0.736829	+	0.0668646i
$599$	−4.21899	−	38.2378i	−0.172383	−	1.56235i	−0.700794	−	0.713364i	$-0.747171\pi$
$599$	−4.21899	−	38.2378i	−0.172383	−	1.56235i	0.528410	−	0.848989i	$-0.322788\pi$
$600$	−4.12737	−	4.01388i	−0.168499	−	0.163866i
$601$	8.21085	+	0.745105i	0.334928	+	0.0303935i	0.256552	−	0.966530i	$-0.417414\pi$
$601$	8.21085	+	0.745105i	0.334928	+	0.0303935i	0.0783756	+	0.996924i	$0.475027\pi$
$602$	0.246085	+	12.6881i	0.0100297	+	0.517128i
$603$	−14.6723	+	3.01109i	−0.597502	+	0.122621i
$604$	−21.6025	−	26.7829i	−0.878993	−	1.08978i
$605$	−1.07656	−	4.41500i	−0.0437685	−	0.179495i
$606$	−12.6900	+	41.0855i	−0.515496	+	1.66898i
$607$	−1.10275	+	1.96835i	−0.0447591	+	0.0798929i	−0.893882	−	0.448303i	$-0.852029\pi$
$607$	−1.10275	+	1.96835i	−0.0447591	+	0.0798929i	0.849122	+	0.528196i	$0.177131\pi$
$608$	15.7804	+	26.5342i	0.639980	+	1.07611i
$609$	−2.15005	−	43.4063i	−0.0871244	−	1.75891i
$610$	−2.77549	+	2.65266i	−0.112376	+	0.107403i
$611$	−12.4837	+	1.95242i	−0.505037	+	0.0789863i
$612$	30.6932	+	27.3812i	1.24070	+	1.10682i
$613$	−31.5498	+	19.0404i	−1.27428	+	0.769034i	−0.982287	−	0.187385i	$-0.939999\pi$
$613$	−31.5498	+	19.0404i	−1.27428	+	0.769034i	−0.291997	+	0.956419i	$0.594320\pi$
$614$	27.9081	−	39.5840i	1.12628	−	1.59748i
$615$	−10.2768	−	0.754916i	−0.414400	−	0.0304412i
$616$	−8.61158	+	6.32498i	−0.346970	+	0.254841i
$617$	−15.4425	+	33.3980i	−0.621692	+	1.34455i	0.298997	+	0.954254i	$0.403348\pi$
$617$	−15.4425	+	33.3980i	−0.621692	+	1.34455i	−0.920689	+	0.390297i	$0.872372\pi$
$618$	2.79460	+	14.3986i	0.112415	+	0.579197i
$619$	4.87833	+	5.30652i	0.196076	+	0.213287i	0.826458	−	0.562999i	$-0.190352\pi$
$619$	4.87833	+	5.30652i	0.196076	+	0.213287i	−0.630381	+	0.776286i	$0.717101\pi$
$620$	0.180078	−	3.09182i	0.00723211	−	0.124170i
$621$	−11.4235	+	12.7481i	−0.458408	+	0.511564i
$622$	−2.97469	−	51.0735i	−0.119274	−	2.04786i
$623$	22.5385	−	23.2790i	0.902987	−	0.932654i
$624$	3.34733	+	14.2646i	0.134001	+	0.571041i
$625$	7.73721	+	19.2937i	0.309488	+	0.771749i
$626$	−24.5551	−	68.8460i	−0.981419	−	2.75164i
$627$	−1.57258	+	29.1291i	−0.0628027	+	1.16330i
$628$	6.01170	−	40.1365i	0.239893	−	1.60162i
$629$	34.1468	+	24.4067i	1.36152	+	0.973158i
$630$	−9.44979	+	6.50932i	−0.376489	+	0.259338i
$631$	16.1071	+	15.7978i	0.641215	+	0.628899i	0.946248	−	0.323443i	$-0.104840\pi$
$631$	16.1071	+	15.7978i	0.641215	+	0.628899i	−0.305033	+	0.952342i	$0.598667\pi$
$632$	−0.999867	+	4.34371i	−0.0397726	+	0.172783i
$633$	−16.7041	+	18.8086i	−0.663930	+	0.747573i
$634$	−11.0549	−	35.2602i	−0.439046	−	1.40036i
$635$	2.02923	−	7.11145i	0.0805275	−	0.282209i
$636$	−0.666449	+	0.507334i	−0.0264264	+	0.0201171i
$637$	4.23204	−	11.8655i	0.167680	−	0.470129i
$638$	67.1856	−	2.60711i	2.65990	−	0.103216i
$639$	−20.3233	−	27.5536i	−0.803979	−	1.09001i
$640$	−2.75435	−	1.12528i	−0.108875	−	0.0444805i
$641$	30.1070	+	18.7049i	1.18916	+	0.738799i	0.971457	−	0.237217i	$-0.0762351\pi$
$641$	30.1070	+	18.7049i	1.18916	+	0.738799i	0.217700	+	0.976016i	$0.430145\pi$
$642$	−3.54186	+	38.0902i	−0.139786	+	1.50330i
$643$	−6.84483	+	2.90024i	−0.269934	+	0.114374i	−0.520889	−	0.853625i	$-0.674399\pi$
$643$	−6.84483	+	2.90024i	−0.269934	+	0.114374i	0.250955	+	0.967999i	$0.419255\pi$
$644$	19.8070	+	17.5123i	0.780503	+	0.690081i
$645$	−1.64495	−	0.0355583i	−0.0647697	−	0.00140011i
$646$	−7.49550	−	45.9773i	−0.294907	−	1.80895i
$647$	−7.49744	+	2.72885i	−0.294755	+	0.107282i	−0.485165	−	0.874423i	$-0.661240\pi$
$647$	−7.49744	+	2.72885i	−0.294755	+	0.107282i	0.190410	+	0.981705i	$0.439018\pi$
$648$	−5.27130	−	3.53446i	−0.207076	−	0.138847i
$649$	61.6993	+	22.4567i	2.42191	+	0.881502i
$650$	−4.82464	+	25.4345i	−0.189238	+	0.997625i
$651$	14.2389	+	3.70144i	0.558067	+	0.145071i
$652$	37.8474	−	30.1251i	1.48222	−	1.17979i
$653$	−5.19772	−	8.01512i	−0.203402	−	0.313656i	0.722534	−	0.691335i	$-0.242977\pi$
$653$	−5.19772	−	8.01512i	−0.203402	−	0.313656i	−0.925936	+	0.377680i	$0.876722\pi$
$654$	5.66378	−	26.6939i	0.221471	−	1.04381i
$655$	−1.44176	−	0.302562i	−0.0563343	−	0.0118221i
$656$	33.9679	−	10.8914i	1.32622	−	0.425237i
$657$	−33.7890	+	1.16089i	−1.31823	+	0.0452907i
$658$	27.0751	+	20.9848i	1.05550	+	0.818074i
$659$	24.7679	−	29.9077i	0.964820	−	1.16504i	−0.0214287	−	0.999770i	$-0.506821\pi$
$659$	24.7679	−	29.9077i	0.964820	−	1.16504i	0.986248	−	0.165269i	$-0.0528493\pi$
$660$	−5.34352	−	7.93797i	−0.207996	−	0.308985i
$661$	12.9350	+	6.28815i	0.503115	+	0.244581i	0.671315	−	0.741172i	$-0.265730\pi$
$661$	12.9350	+	6.28815i	0.503115	+	0.244581i	−0.168200	+	0.985753i	$0.553796\pi$
$662$	−20.8713	+	10.8221i	−0.811185	+	0.420611i
$663$	3.85380	−	26.4965i	0.149669	−	1.02904i
$664$	1.05671	+	8.56047i	0.0410084	+	0.332211i
$665$	6.98396	+	0.542836i	0.270826	+	0.0210503i
$666$	−39.6223	−	20.7686i	−1.53533	−	0.804766i
$667$	−6.00786	−	23.3240i	−0.232625	−	0.903107i
$668$	−2.41754	+	4.44913i	−0.0935375	+	0.172142i
$669$	28.4413	−	18.8795i	1.09961	−	0.729925i
$670$	−5.48609	+	0.930821i	−0.211946	+	0.0359608i
$671$	12.9186	−	8.02606i	0.498717	−	0.309843i
$672$	26.5238	−	40.1331i	1.02318	−	1.54817i
$673$	11.7066	−	26.2022i	0.451255	−	1.01002i	−0.535010	−	0.844846i	$-0.679692\pi$
$673$	11.7066	−	26.2022i	0.451255	−	1.01002i	0.986265	−	0.165173i	$-0.0528183\pi$
$674$	16.6465	+	17.6443i	0.641201	+	0.679633i
$675$	13.0557	+	20.7234i	0.502514	+	0.797643i
$676$	9.70530	−	10.2870i	0.373281	−	0.395655i
$677$	−10.7337	−	25.7954i	−0.412529	−	0.991398i	−0.985168	−	0.171591i	$-0.945109\pi$
$677$	−10.7337	−	25.7954i	−0.412529	−	0.991398i	0.572640	−	0.819807i	$-0.305919\pi$
$678$	−12.5088	+	6.55352i	−0.480399	+	0.251686i
$679$	−9.35116	−	6.50281i	−0.358865	−	0.249555i
$680$	1.59924	+	1.52847i	0.0613281	+	0.0586140i
$681$	−0.795078	−	2.29191i	−0.0304675	−	0.0878260i
$682$	−5.96205	+	21.9664i	−0.228299	+	0.841138i
$683$	8.69225	−	25.4041i	0.332600	−	0.972059i	−0.645471	−	0.763785i	$-0.723339\pi$
$683$	8.69225	−	25.4041i	0.332600	−	0.972059i	0.978070	−	0.208274i	$-0.0667847\pi$
$684$	7.89291	+	25.5722i	0.301793	+	0.977778i
$685$	9.25590	+	5.58596i	0.353650	+	0.213429i
$686$	14.5452	−	6.38602i	0.555339	−	0.243819i
$687$	21.9490	+	38.7909i	0.837406	+	1.47997i
$688$	5.32657	−	2.01707i	0.203074	−	0.0769002i
$689$	0.514724	+	0.179843i	0.0196094	+	0.00685147i
$690$	−4.40404	+	4.58753i	−0.167659	+	0.174644i
$691$	19.3959	+	29.0789i	0.737857	+	1.10621i	0.990346	+	0.138615i	$0.0442650\pi$
$691$	19.3959	+	29.0789i	0.737857	+	1.10621i	−0.252490	+	0.967600i	$0.581249\pi$
$692$	54.4975	+	10.7030i	2.07169	+	0.406866i
$693$	41.9322	−	17.5479i	1.59287	−	0.666590i
$694$	12.6182	−	15.6441i	0.478979	−	0.593841i
$695$	−3.30161	−	1.55258i	−0.125237	−	0.0588926i
$696$	8.25229	−	3.41236i	0.312802	−	0.129345i
$697$	−65.0497	−	4.21080i	−2.46393	−	0.159495i
$698$	−9.40079	−	34.6361i	−0.355825	−	1.31099i
$699$	−1.57225	−	20.8266i	−0.0594679	−	0.787735i
$700$	31.8728	−	20.3777i	1.20468	−	0.770205i
$701$	2.35181	−	5.45211i	0.0888267	−	0.205924i	−0.868012	−	0.496544i	$-0.834602\pi$
$701$	2.35181	−	5.45211i	0.0888267	−	0.205924i	0.956839	+	0.290620i	$0.0938616\pi$
$702$	−0.190125	+	28.5372i	−0.00717582	+	1.07707i
$703$	10.8168	+	25.0763i	0.407965	+	0.945770i
$704$	38.1811	+	25.8254i	1.43901	+	0.973331i
$705$	−2.86232	+	3.39583i	−0.107801	+	0.127894i
$706$	−13.9374	+	42.5206i	−0.524543	+	1.60028i
$707$	−35.2915	−	20.6809i	−1.32727	−	0.777785i
$708$	60.2365	−	0.255611i	2.26383	−	0.00960644i
$709$	26.3990	+	8.84248i	0.991437	+	0.332086i	0.766470	−	0.642280i	$-0.222011\pi$
$709$	26.3990	+	8.84248i	0.991437	+	0.332086i	0.224967	+	0.974366i	$0.427773\pi$
$710$	−7.19437	−	10.4897i	−0.270000	−	0.393670i
$711$	8.47608	−	16.9627i	0.317878	−	0.636152i
$712$	6.06113	+	2.75512i	0.227151	+	0.103253i
$713$	8.14259	+	0.421457i	0.304942	+	0.0157837i
$714$	−59.4193	+	41.6955i	−2.22371	+	1.56041i
$715$	−2.39306	+	5.75105i	−0.0894952	+	0.215077i
$716$	−6.85704	−	15.3477i	−0.256260	−	0.573572i
$717$	−3.64512	−	9.69075i	−0.136129	−	0.361908i
$718$	−9.62843	−	5.47630i	−0.359330	−	0.204374i
$719$	3.51760	+	1.12787i	0.131184	+	0.0420626i	0.370193	−	0.928955i	$-0.379292\pi$
$719$	3.51760	+	1.12787i	0.131184	+	0.0420626i	−0.239009	+	0.971017i	$0.576822\pi$
$720$	4.17650	+	3.01330i	0.155649	+	0.112299i
$721$	−13.9419	−	0.541008i	−0.519223	−	0.0201482i
$722$	−3.44851	+	8.59932i	−0.128340	+	0.320033i
$723$	18.8006	−	23.5126i	0.699203	−	0.874443i
$724$	−31.4801	−	9.64670i	−1.16995	−	0.358517i
$725$	−34.4515	−	0.891002i	−1.27950	−	0.0330910i
$726$	11.5250	+	28.3897i	0.427732	+	1.05364i
$727$	6.88820	+	0.0890581i	0.255469	+	0.00330298i	0.140557	−	0.990073i	$-0.455111\pi$
$727$	6.88820	+	0.0890581i	0.255469	+	0.00330298i	0.114912	+	0.993376i	$0.463341\pi$
$728$	6.38109			0.236499
$729$	18.2652	+	19.8842i	0.676489	+	0.736453i
$730$	−12.5603			−0.464879
$731$	−10.4075	−	0.134559i	−0.384934	−	0.00497684i
$732$	8.57203	−	11.0093i	0.316831	−	0.406914i
$733$	−26.6619	−	0.689544i	−0.984781	−	0.0254689i	−0.469891	−	0.882725i	$-0.655707\pi$
$733$	−26.6619	−	0.689544i	−0.984781	−	0.0254689i	−0.514891	+	0.857256i	$0.672168\pi$
$734$	−3.55508	−	1.08941i	−0.131220	−	0.0402109i
$735$	−1.61236	−	4.12395i	−0.0594729	−	0.152114i
$736$	9.92319	−	24.7448i	0.365774	−	0.912104i
$737$	22.0265	+	0.854730i	0.811358	+	0.0314844i
$738$	69.2912	−	5.07622i	2.55064	−	0.186858i
$739$	−13.8294	−	4.43420i	−0.508721	−	0.163115i	0.0398713	−	0.999205i	$-0.487305\pi$
$739$	−13.8294	−	4.43420i	−0.508721	−	0.163115i	−0.548592	+	0.836090i	$0.684836\pi$
$740$	−7.78687	−	4.42889i	−0.286251	−	0.162809i
$741$	11.0548	−	13.4648i	0.406109	−	0.494643i
$742$	−0.602969	−	1.34959i	−0.0221357	−	0.0495451i
$743$	−0.296447	+	0.712427i	−0.0108756	+	0.0261364i	−0.928605	−	0.371069i	$-0.878991\pi$
$743$	−0.296447	+	0.712427i	−0.0108756	+	0.0261364i	0.917730	+	0.397206i	$0.130020\pi$
$744$	0.266520	+	3.01125i	0.00977108	+	0.110398i
$745$	−3.30270	−	0.170946i	−0.121001	−	0.00626299i
$746$	1.52555	+	0.693446i	0.0558542	+	0.0253889i
$747$	4.18629	−	36.4553i	0.153168	−	1.33383i
$748$	−34.2378	−	49.9200i	−1.25186	−	1.82526i
$749$	−34.5057	−	11.5578i	−1.26081	−	0.422315i
$750$	9.44457	+	16.1993i	0.344867	+	0.591516i
$751$	16.5024	+	9.67042i	0.602180	+	0.352879i	0.774892	−	0.632094i	$-0.217804\pi$
$751$	16.5024	+	9.67042i	0.602180	+	0.352879i	−0.172712	+	0.984972i	$0.555253\pi$
$752$	4.78873	−	14.6095i	0.174627	−	0.532755i
$753$	11.3420	+	31.3786i	0.413326	+	1.14350i
$754$	−33.2603	−	22.4970i	−1.21127	−	0.819292i
$755$	3.11838	+	7.22921i	0.113489	+	0.263098i
$756$	30.5231	−	28.4151i	1.11012	−	1.03345i
$757$	−13.1259	+	30.4294i	−0.477071	+	1.10597i	0.494490	+	0.869183i	$0.335355\pi$
$757$	−13.1259	+	30.4294i	−0.477071	+	1.10597i	−0.971561	+	0.236791i	$0.923904\pi$
$758$	−23.2905	+	14.8906i	−0.845948	+	0.540852i
$759$	20.8066	−	14.2024i	0.755231	−	0.515516i
$760$	0.377031	+	1.38912i	0.0136763	+	0.0503888i
$761$	4.86274	+	0.314775i	0.176274	+	0.0114106i	0.152482	−	0.988306i	$-0.451274\pi$
$761$	4.86274	+	0.314775i	0.176274	+	0.0114106i	0.0237928	+	0.999717i	$0.492426\pi$
$762$	−6.53820	+	49.4316i	−0.236854	+	1.79072i
$763$	23.4904	+	11.0463i	0.850409	+	0.399904i
$764$	−26.9357	+	33.3950i	−0.974499	+	1.20819i
$765$	−5.08550	−	7.91890i	−0.183867	−	0.286309i
$766$	6.93745	+	1.36247i	0.250660	+	0.0492281i
$767$	−21.7589	−	32.6215i	−0.785667	−	1.17789i
$768$	&mi

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08274 - 0.0269280i) q^{2} +(-1.71559 - 0.238211i) q^{3} +(2.33777 + 0.0604606i) q^{4} +(-0.511598 - 0.156773i) q^{5} +(3.56673 + 0.542331i) q^{6} +(-1.27737 + 3.18529i) q^{7} +(-0.704645 - 0.0273434i) q^{8} +(2.88651 + 0.817346i) q^{9} +O(q^{10})\)	\(q+(-2.08274 - 0.0269280i) q^{2} +(-1.71559 - 0.238211i) q^{3} +(2.33777 + 0.0604606i) q^{4} +(-0.511598 - 0.156773i) q^{5} +(3.56673 + 0.542331i) q^{6} +(-1.27737 + 3.18529i) q^{7} +(-0.704645 - 0.0273434i) q^{8} +(2.88651 + 0.817346i) q^{9} +(1.06131 + 0.340294i) q^{10} +(-3.83775 - 2.18277i) q^{11} +(-3.99626 - 0.660609i) q^{12} +(1.07557 + 2.40739i) q^{13} +(2.74621 - 6.59975i) q^{14} +(0.840348 + 0.390827i) q^{15} +(-3.20399 - 0.165837i) q^{16} +(5.33730 + 2.42610i) q^{17} +(-5.98986 - 1.78005i) q^{18} +(2.15762 + 3.14588i) q^{19} +(-1.18652 - 0.397430i) q^{20} +(2.95022 - 5.16037i) q^{21} +(7.93429 + 4.64950i) q^{22} +(1.02608 - 3.13040i) q^{23} +(1.20237 + 0.214764i) q^{24} +(-3.90441 - 2.64091i) q^{25} +(-2.17531 - 5.04294i) q^{26} +(-4.75737 - 2.08983i) q^{27} +(-3.17878 + 7.36924i) q^{28} +(6.15990 - 3.93830i) q^{29} +(-1.73971 - 0.836621i) q^{30} +(0.648314 + 2.38863i) q^{31} +(8.07604 + 0.522778i) q^{32} +(6.06406 + 4.65895i) q^{33} +(-11.0509 - 5.19667i) q^{34} +(1.15287 - 1.42933i) q^{35} +(6.69858 + 2.08529i) q^{36} +(7.02490 + 1.37965i) q^{37} +(-4.40906 - 6.61018i) q^{38} +(-1.27177 - 4.38631i) q^{39} +(0.356208 + 0.124458i) q^{40} +(-10.3979 + 3.93751i) q^{41} +(-6.28351 + 10.6683i) q^{42} +(-1.62554 + 0.713687i) q^{43} +(-8.83981 - 5.33486i) q^{44} +(-1.34860 - 0.870679i) q^{45} +(-2.22136 + 6.49218i) q^{46} +(-1.25524 + 4.62477i) q^{47} +(5.45724 + 1.04774i) q^{48} +(-3.45394 - 3.30109i) q^{49} +(8.06079 + 5.60548i) q^{50} +(-8.57870 - 5.43360i) q^{51} +(2.36888 + 5.69295i) q^{52} +(0.141905 - 0.150410i) q^{53} +(9.85212 + 4.48069i) q^{54} +(1.62119 + 1.71836i) q^{55} +(0.987189 - 2.20957i) q^{56} +(-2.95221 - 5.91102i) q^{57} +(-12.9356 + 8.03660i) q^{58} +(-14.6620 + 2.48769i) q^{59} +(1.94091 + 0.964471i) q^{60} +(-1.64467 + 3.02677i) q^{61} +(-1.28595 - 4.99237i) q^{62} +(-6.29063 + 8.15032i) q^{63} +(-10.4090 - 0.809050i) q^{64} +(-0.172846 - 1.40024i) q^{65} +(-12.5044 - 9.86669i) q^{66} +(-4.43229 + 2.29821i) q^{67} +(12.3307 + 5.99436i) q^{68} +(-2.50604 + 5.12606i) q^{69} +(-2.43962 + 2.94589i) q^{70} +(-9.02049 - 6.99141i) q^{71} +(-2.01162 - 0.654866i) q^{72} +(-10.7315 + 3.44091i) q^{73} +(-14.5939 - 3.06262i) q^{74} +(6.06929 + 5.46080i) q^{75} +(4.85381 + 7.48480i) q^{76} +(11.8550 - 9.43615i) q^{77} +(2.53066 + 9.16981i) q^{78} +(1.17799 - 6.21011i) q^{79} +(1.61316 + 0.587141i) q^{80} +(7.66389 + 4.71856i) q^{81} +(21.7623 - 7.92083i) q^{82} +(-1.96810 - 12.0723i) q^{83} +(7.20893 - 11.8854i) q^{84} +(-2.35020 - 2.07793i) q^{85} +(3.40480 - 1.44266i) q^{86} +(-11.5060 + 5.28916i) q^{87} +(2.64457 + 1.64302i) q^{88} +(-8.74025 - 3.57079i) q^{89} +(2.78533 + 1.84972i) q^{90} +(-9.04213 + 0.350876i) q^{91} +(2.58801 - 7.25611i) q^{92} +(-0.543243 - 4.25236i) q^{93} +(2.73887 - 9.59840i) q^{94} +(-0.610644 - 1.94768i) q^{95} +(-13.7306 - 2.82068i) q^{96} +(-0.744493 + 3.23429i) q^{97} +(7.10479 + 6.96833i) q^{98} +(-9.29364 - 9.43738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

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