LMFDB - Embedded newform 729.2.k.a.4.16

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			4.16
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90902 - 0.0246819i) q^{2} +(0.0146033 - 1.73199i) q^{3} +(1.64441 + 0.0425285i) q^{4} +(-2.27162 - 0.696109i) q^{5} +(-0.0706267 + 3.30604i) q^{6} +(0.132583 - 0.330612i) q^{7} +(0.677327 + 0.0262834i) q^{8} +(-2.99957 - 0.0505857i) q^{9} +O(q^{10})$	\(q+(-1.90902 - 0.0246819i) q^{2} +(0.0146033 - 1.73199i) q^{3} +(1.64441 + 0.0425285i) q^{4} +(-2.27162 - 0.696109i) q^{5} +(-0.0706267 + 3.30604i) q^{6} +(0.132583 - 0.330612i) q^{7} +(0.677327 + 0.0262834i) q^{8} +(-2.99957 - 0.0505857i) q^{9} +(4.31938 + 1.38495i) q^{10} +(-4.51004 - 2.56515i) q^{11} +(0.0976728 - 2.84748i) q^{12} +(1.99430 + 4.46372i) q^{13} +(-0.261263 + 0.627872i) q^{14} +(-1.23883 + 3.92425i) q^{15} +(-4.57790 - 0.236950i) q^{16} +(0.761861 + 0.346308i) q^{17} +(5.72499 + 0.170604i) q^{18} +(-0.376229 - 0.548556i) q^{19} +(-3.70586 - 1.24130i) q^{20} +(-0.570681 - 0.234460i) q^{21} +(8.54644 + 5.00822i) q^{22} +(0.0415526 - 0.126769i) q^{23} +(0.0554138 - 1.17274i) q^{24} +(0.534112 + 0.361268i) q^{25} +(-3.69697 - 8.57055i) q^{26} +(-0.131418 + 5.19449i) q^{27} +(0.232081 - 0.538023i) q^{28} +(-4.04583 + 2.58668i) q^{29} +(2.46180 - 7.46089i) q^{30} +(1.19820 + 4.41462i) q^{31} +(7.38060 + 0.477761i) q^{32} +(-4.50867 + 7.77388i) q^{33} +(-1.44586 - 0.679913i) q^{34} +(-0.531320 + 0.658733i) q^{35} +(-4.93037 - 0.210751i) q^{36} +(-5.74445 - 1.12817i) q^{37} +(0.704689 + 1.05649i) q^{38} +(7.76024 - 3.38891i) q^{39} +(-1.52033 - 0.531200i) q^{40} +(8.11419 - 3.07269i) q^{41} +(1.08365 + 0.461673i) q^{42} +(6.88896 - 3.02457i) q^{43} +(-7.30726 - 4.40995i) q^{44} +(6.77867 + 2.20294i) q^{45} +(-0.0824536 + 0.240980i) q^{46} +(0.700712 - 2.58169i) q^{47} +(-0.477248 + 7.92541i) q^{48} +(4.96873 + 4.74884i) q^{49} +(-1.01071 - 0.702851i) q^{50} +(0.610928 - 1.31448i) q^{51} +(3.08960 + 7.42500i) q^{52} +(-8.09261 + 8.57766i) q^{53} +(0.379088 - 9.91313i) q^{54} +(8.45947 + 8.96651i) q^{55} +(0.0984915 - 0.220448i) q^{56} +(-0.955587 + 0.643615i) q^{57} +(7.78741 - 4.83816i) q^{58} +(2.21717 - 0.376185i) q^{59} +(-2.20403 + 6.40039i) q^{60} +(2.04561 - 3.76464i) q^{61} +(-2.17842 - 8.45716i) q^{62} +(-0.414416 + 0.984989i) q^{63} +(-4.93742 - 0.383767i) q^{64} +(-1.42304 - 11.5281i) q^{65} +(8.79900 - 14.7292i) q^{66} +(6.15186 - 3.18983i) q^{67} +(1.23808 + 0.601873i) q^{68} +(-0.218957 - 0.0738199i) q^{69} +(1.03056 - 1.24442i) q^{70} +(1.24349 + 0.963775i) q^{71} +(-2.03036 - 0.113102i) q^{72} +(8.81650 - 2.82690i) q^{73} +(10.9384 + 2.29549i) q^{74} +(0.633513 - 0.919800i) q^{75} +(-0.595346 - 0.918051i) q^{76} +(-1.44602 + 1.15098i) q^{77} +(-14.8981 + 6.27796i) q^{78} +(-1.29940 + 6.85018i) q^{79} +(10.2343 + 3.72498i) q^{80} +(8.99488 + 0.303471i) q^{81} +(-15.5660 + 5.66555i) q^{82} +(0.886303 + 5.43657i) q^{83} +(-0.928461 - 0.409818i) q^{84} +(-1.48959 - 1.31702i) q^{85} +(-13.2258 + 5.60393i) q^{86} +(4.42102 + 7.04511i) q^{87} +(-2.98735 - 1.85598i) q^{88} +(10.8971 + 4.45194i) q^{89} +(-12.8862 - 4.37277i) q^{90} +(1.74017 - 0.0675266i) q^{91} +(0.0737208 - 0.206694i) q^{92} +(7.66357 - 2.01080i) q^{93} +(-1.40139 + 4.91119i) q^{94} +(0.472795 + 1.50801i) q^{95} +(0.935259 - 12.7761i) q^{96} +(-1.91603 + 8.32379i) q^{97} +(-9.36819 - 9.18825i) q^{98} +(13.3984 + 7.92249i) 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 $

$2$	−1.90902	−	0.0246819i	−1.34988	−	0.0174527i	−0.665401	−	0.746486i	$-0.731740\pi$
$2$	−1.90902	−	0.0246819i	−1.34988	−	0.0174527i	−0.684478	+	0.729033i	$0.739970\pi$
$3$	0.0146033	−	1.73199i	0.00843124	−	0.999964i
$3$	0.0146033	−	1.73199i	0.00843124	−	0.999964i
$4$	1.64441	+	0.0425285i	0.822204	+	0.0212643i
$5$	−2.27162	−	0.696109i	−1.01590	−	0.311310i	−0.259726	−	0.965682i	$-0.583632\pi$
$5$	−2.27162	−	0.696109i	−1.01590	−	0.311310i	−0.756172	+	0.654373i	$0.772933\pi$
$6$	−0.0706267	+	3.30604i	−0.0288332	+	1.34968i
$7$	0.132583	−	0.330612i	0.0501115	−	0.124960i	−0.900988	−	0.433844i	$-0.857157\pi$
$7$	0.132583	−	0.330612i	0.0501115	−	0.124960i	0.951100	+	0.308884i	$0.0999554\pi$
$8$	0.677327	+	0.0262834i	0.239471	+	0.00929258i
$9$	−2.99957	−	0.0505857i	−0.999858	−	0.0168619i
$10$	4.31938	+	1.38495i	1.36591	+	0.437961i
$11$	−4.51004	−	2.56515i	−1.35983	−	0.773420i	−0.371891	−	0.928276i	$-0.621291\pi$
$11$	−4.51004	−	2.56515i	−1.35983	−	0.773420i	−0.987937	+	0.154856i	$0.950509\pi$
$12$	0.0976728	−	2.84748i	0.0281957	−	0.821996i
$13$	1.99430	+	4.46372i	0.553118	+	1.23801i	0.947703	+	0.319154i	$0.103399\pi$
$13$	1.99430	+	4.46372i	0.553118	+	1.23801i	−0.394584	+	0.918860i	$0.629111\pi$
$14$	−0.261263	+	0.627872i	−0.0698254	+	0.167806i
$15$	−1.23883	+	3.92425i	−0.319864	+	1.01324i
$16$	−4.57790	−	0.236950i	−1.14448	−	0.0592376i
$17$	0.761861	+	0.346308i	0.184778	+	0.0839921i	0.504063	−	0.863667i	$-0.331838\pi$
$17$	0.761861	+	0.346308i	0.184778	+	0.0839921i	−0.319285	+	0.947659i	$0.603443\pi$
$18$	5.72499	+	0.170604i	1.34939	+	0.0402117i
$19$	−0.376229	−	0.548556i	−0.0863130	−	0.125847i	0.779114	−	0.626882i	$-0.215669\pi$
$19$	−0.376229	−	0.548556i	−0.0863130	−	0.125847i	−0.865427	+	0.501034i	$0.832953\pi$
$20$	−3.70586	−	1.24130i	−0.828656	−	0.277562i
$21$	−0.570681	−	0.234460i	−0.124533	−	0.0511633i
$22$	8.54644	+	5.00822i	1.82211	+	1.06776i
$23$	0.0415526	−	0.126769i	0.00866432	−	0.0264333i	−0.945830	−	0.324662i	$-0.894750\pi$
$23$	0.0415526	−	0.126769i	0.00866432	−	0.0264333i	0.954495	+	0.298228i	$0.0963957\pi$
$24$	0.0554138	−	1.17274i	0.0113113	−	0.239385i
$25$	0.534112	+	0.361268i	0.106822	+	0.0722537i
$26$	−3.69697	−	8.57055i	−0.725036	−	1.68082i
$27$	−0.131418	+	5.19449i	−0.0252913	+	0.999680i
$28$	0.232081	−	0.538023i	0.0438591	−	0.101677i
$29$	−4.04583	+	2.58668i	−0.751292	+	0.480335i	−0.857804	−	0.513977i	$-0.828172\pi$
$29$	−4.04583	+	2.58668i	−0.751292	+	0.480335i	0.106512	+	0.994311i	$0.466032\pi$
$30$	2.46180	−	7.46089i	0.449461	−	1.36217i
$31$	1.19820	+	4.41462i	0.215203	+	0.792889i	0.987499	+	0.157626i	$0.0503841\pi$
$31$	1.19820	+	4.41462i	0.215203	+	0.792889i	−0.772296	+	0.635263i	$0.780892\pi$
$32$	7.38060	+	0.477761i	1.30472	+	0.0844571i
$33$	−4.50867	+	7.77388i	−0.784858	+	1.35326i
$34$	−1.44586	−	0.679913i	−0.247963	−	0.116604i
$35$	−0.531320	+	0.658733i	−0.0898094	+	0.111346i
$36$	−4.93037	−	0.210751i	−0.821729	−	0.0351251i
$37$	−5.74445	−	1.12817i	−0.944382	−	0.185471i	−0.303259	−	0.952908i	$-0.598075\pi$
$37$	−5.74445	−	1.12817i	−0.944382	−	0.185471i	−0.641124	+	0.767438i	$0.721531\pi$
$38$	0.704689	+	1.05649i	0.114316	+	0.171385i
$39$	7.76024	−	3.38891i	1.24263	−	0.542661i
$40$	−1.52033	−	0.531200i	−0.240386	−	0.0839901i
$41$	8.11419	−	3.07269i	1.26722	−	0.479874i	0.373140	−	0.927775i	$-0.378281\pi$
$41$	8.11419	−	3.07269i	1.26722	−	0.479874i	0.894083	+	0.447901i	$0.147828\pi$
$42$	1.08365	+	0.461673i	0.167211	+	0.0712378i
$43$	6.88896	−	3.02457i	1.05056	−	0.461243i	0.196001	−	0.980604i	$-0.437204\pi$
$43$	6.88896	−	3.02457i	1.05056	−	0.461243i	0.854555	+	0.519361i	$0.173830\pi$
$44$	−7.30726	−	4.40995i	−1.10161	−	0.664825i
$45$	6.77867	+	2.20294i	1.01050	+	0.328395i
$46$	−0.0824536	+	0.240980i	−0.0121571	+	0.0355305i
$47$	0.700712	−	2.58169i	0.102209	−	0.376578i	−0.895434	−	0.445195i	$-0.853134\pi$
$47$	0.700712	−	2.58169i	0.102209	−	0.376578i	0.997643	+	0.0686171i	$0.0218587\pi$
$48$	−0.477248	+	7.92541i	−0.0688848	+	1.14393i
$49$	4.96873	+	4.74884i	0.709819	+	0.678405i
$50$	−1.01071	−	0.702851i	−0.142936	−	0.0993981i
$51$	0.610928	−	1.31448i	0.0855470	−	0.184064i
$52$	3.08960	+	7.42500i	0.428451	+	1.02966i
$53$	−8.09261	+	8.57766i	−1.11161	+	1.17823i	−0.129171	+	0.991622i	$0.541232\pi$
$53$	−8.09261	+	8.57766i	−1.11161	+	1.17823i	−0.982434	+	0.186610i	$0.940250\pi$
$54$	0.379088	−	9.91313i	0.0515874	−	1.34901i
$55$	8.45947	+	8.96651i	1.14067	+	1.20904i
$56$	0.0984915	−	0.220448i	0.0131615	−	0.0294586i
$57$	−0.955587	+	0.643615i	−0.126571	+	0.0852488i
$58$	7.78741	−	4.83816i	1.02254	−	0.635282i
$59$	2.21717	−	0.376185i	0.288650	−	0.0489751i	−0.0211514	−	0.999776i	$-0.506733\pi$
$59$	2.21717	−	0.376185i	0.288650	−	0.0489751i	0.309802	+	0.950801i	$0.399737\pi$
$60$	−2.20403	+	6.40039i	−0.284539	+	0.826287i
$61$	2.04561	−	3.76464i	0.261914	−	0.482013i	−0.714007	−	0.700138i	$-0.753122\pi$
$61$	2.04561	−	3.76464i	0.261914	−	0.482013i	0.975921	+	0.218125i	$0.0699941\pi$
$62$	−2.17842	−	8.45716i	−0.276660	−	1.07406i
$63$	−0.414416	+	0.984989i	−0.0522115	+	0.124097i
$64$	−4.93742	−	0.383767i	−0.617178	−	0.0479708i
$65$	−1.42304	−	11.5281i	−0.176506	−	1.42989i
$66$	8.79900	−	14.7292i	1.08308	−	1.81304i
$67$	6.15186	−	3.18983i	0.751569	−	0.389700i	−0.0412564	−	0.999149i	$-0.513136\pi$
$67$	6.15186	−	3.18983i	0.751569	−	0.389700i	0.792825	+	0.609449i	$0.208609\pi$
$68$	1.23808	+	0.601873i	0.150140	+	0.0729878i
$69$	−0.218957	−	0.0738199i	−0.0263593	−	0.00888687i
$70$	1.03056	−	1.24442i	0.123175	−	0.148737i
$71$	1.24349	+	0.963775i	0.147575	+	0.114379i	0.683713	−	0.729751i	$-0.260364\pi$
$71$	1.24349	+	0.963775i	0.147575	+	0.114379i	−0.536138	+	0.844130i	$0.680117\pi$
$72$	−2.03036	−	0.113102i	−0.239281	−	0.0133292i
$73$	8.81650	−	2.82690i	1.03189	−	0.330863i	0.259322	−	0.965791i	$-0.416501\pi$
$73$	8.81650	−	2.82690i	1.03189	−	0.330863i	0.772571	+	0.634928i	$0.218970\pi$
$74$	10.9384	+	2.29549i	1.27157	+	0.266845i
$75$	0.633513	−	0.919800i	0.0731518	−	0.106209i
$76$	−0.595346	−	0.918051i	−0.0682908	−	0.105308i
$77$	−1.44602	+	1.15098i	−0.164789	+	0.131166i
$78$	−14.8981	+	6.27796i	−1.68688	+	0.710839i
$79$	−1.29940	+	6.85018i	−0.146194	+	0.770705i	0.830657	+	0.556784i	$0.187965\pi$
$79$	−1.29940	+	6.85018i	−0.146194	+	0.770705i	−0.976851	+	0.213921i	$0.931377\pi$
$80$	10.2343	+	3.72498i	1.14423	+	0.416465i
$81$	8.99488	+	0.303471i	0.999431	+	0.0337190i
$82$	−15.5660	+	5.66555i	−1.71897	+	0.625655i
$83$	0.886303	+	5.43657i	0.0972844	+	0.596741i	0.989432	+	0.144997i	$0.0463173\pi$
$83$	0.886303	+	5.43657i	0.0972844	+	0.596741i	−0.892148	+	0.451744i	$0.850802\pi$
$84$	−0.928461	−	0.409818i	−0.101303	−	0.0447148i
$85$	−1.48959	−	1.31702i	−0.161569	−	0.142851i
$86$	−13.2258	+	5.60393i	−1.42617	+	0.604287i
$87$	4.42102	+	7.04511i	0.473983	+	0.755315i
$88$	−2.98735	−	1.85598i	−0.318453	−	0.197848i
$89$	10.8971	+	4.45194i	1.15509	+	0.471904i	0.873113	−	0.487518i	$-0.162098\pi$
$89$	10.8971	+	4.45194i	1.15509	+	0.471904i	0.281973	+	0.959422i	$0.409011\pi$
$90$	−12.8862	−	4.37277i	−1.35833	−	0.460930i
$91$	1.74017	−	0.0675266i	0.182419	−	0.00707871i
$92$	0.0737208	−	0.206694i	0.00768592	−	0.0215493i
$93$	7.66357	−	2.01080i	0.794676	−	0.208510i
$94$	−1.40139	+	4.91119i	−0.144543	+	0.506551i
$95$	0.472795	+	1.50801i	0.0485077	+	0.154718i
$96$	0.935259	−	12.7761i	0.0954545	−	1.30396i
$97$	−1.91603	+	8.32379i	−0.194543	+	0.845152i	0.780857	+	0.624710i	$0.214783\pi$
$97$	−1.91603	+	8.32379i	−0.194543	+	0.845152i	−0.975400	+	0.220442i	$0.929250\pi$
$98$	−9.36819	−	9.18825i	−0.946330	−	0.928154i
$99$	13.3984	+	7.92249i	1.34659	+	0.796240i
$100$	0.862934	+	0.616788i	0.0862934	+	0.0616788i
$101$	−1.28969	+	8.61046i	−0.128329	+	0.856772i	0.827207	+	0.561897i	$0.189928\pi$
$101$	−1.28969	+	8.61046i	−0.128329	+	0.856772i	−0.955536	+	0.294875i	$0.904722\pi$
$102$	−1.19872	+	2.49428i	−0.118691	+	0.246971i
$103$	−0.818579	−	2.29508i	−0.0806570	−	0.226141i	0.894744	−	0.446580i	$-0.147358\pi$
$103$	−0.818579	−	2.29508i	−0.0806570	−	0.226141i	−0.975401	+	0.220439i	$0.929251\pi$
$104$	1.23347	+	3.07582i	0.120952	+	0.301609i
$105$	1.13316	+	0.929859i	0.110585	+	0.0907450i
$106$	15.6606	−	16.1752i	1.52110	−	1.57107i
$107$	0.183354	+	3.14806i	0.0177255	+	0.304335i	0.995506	+	0.0947019i	$0.0301898\pi$
$107$	0.183354	+	3.14806i	0.0177255	+	0.304335i	−0.977780	+	0.209633i	$0.932773\pi$
$108$	−0.437018	+	8.53628i	−0.0420521	+	0.821404i
$109$	−1.06165	+	18.2278i	−0.101687	+	1.74590i	0.433486	+	0.901160i	$0.357283\pi$
$109$	−1.06165	+	18.2278i	−0.101687	+	1.74590i	−0.535173	+	0.844742i	$0.679754\pi$
$110$	−15.9280	−	17.3260i	−1.51867	−	1.65197i
$111$	−2.03787	+	9.93286i	−0.193426	+	0.942785i
$112$	−0.685289	+	1.48209i	−0.0647537	+	0.140045i
$113$	−8.25585	+	6.06370i	−0.776645	+	0.570425i	−0.907044	−	0.421037i	$-0.861666\pi$
$113$	−8.25585	+	6.06370i	−0.776645	+	0.570425i	0.130399	+	0.991462i	$0.458374\pi$
$114$	1.84012	−	1.20509i	0.172343	−	0.112867i
$115$	−0.182637	+	0.259047i	−0.0170310	+	0.0241562i
$116$	−6.76301	+	4.08150i	−0.627930	+	0.378958i
$117$	−5.75624	−	13.4901i	−0.532164	−	1.24716i
$118$	−4.24189	+	0.663420i	−0.390498	+	0.0610728i
$119$	0.215503	−	0.205966i	0.0197552	−	0.0188809i
$120$	−0.942234	+	2.62544i	−0.0860138	+	0.239669i
$121$	8.13780	+	13.6834i	0.739800	+	1.24395i
$122$	−3.99803	+	7.13628i	−0.361964	+	0.646089i
$123$	−5.20337	−	14.0986i	−0.469173	−	1.27122i
$124$	1.78258	+	7.31040i	0.160081	+	0.656493i
$125$	6.49622	+	8.05405i	0.581040	+	0.720376i
$126$	0.815438	−	1.87013i	0.0726450	−	0.166605i
$127$	−0.362296	−	18.6799i	−0.0321486	−	1.65757i	−0.575304	−	0.817939i	$-0.695116\pi$
$127$	−0.362296	−	18.6799i	−0.0321486	−	1.65757i	0.543156	−	0.839632i	$-0.317229\pi$
$128$	−5.31541	−	0.482355i	−0.469820	−	0.0426345i
$129$	−5.13792	−	11.9758i	−0.452369	−	1.05441i
$130$	2.43207	+	22.0425i	0.213307	+	1.93326i
$131$	5.69871	−	0.517137i	0.497898	−	0.0451825i	0.161443	−	0.986882i	$-0.448385\pi$
$131$	5.69871	−	0.517137i	0.497898	−	0.0451825i	0.336455	+	0.941699i	$0.390772\pi$
$132$	−7.74470	+	12.5917i	−0.674090	+	1.09597i
$133$	−0.231241	+	0.0516571i	−0.0200511	+	0.00447924i
$134$	−11.8227	+	5.93760i	−1.02133	+	0.512931i
$135$	3.91446	−	11.7084i	0.336903	−	1.00770i
$136$	0.506927	+	0.254588i	0.0434686	+	0.0218308i
$137$	−2.46745	−	0.618593i	−0.210808	−	0.0528500i	0.136332	−	0.990663i	$-0.456469\pi$
$137$	−2.46745	−	0.618593i	−0.210808	−	0.0528500i	−0.347140	+	0.937813i	$0.612847\pi$
$138$	0.416170	+	0.146328i	0.0354267	+	0.0124562i
$139$	−10.3000	−	1.47474i	−0.873634	−	0.125086i	−0.309629	−	0.950857i	$-0.600205\pi$
$139$	−10.3000	−	1.47474i	−0.873634	−	0.125086i	−0.564004	+	0.825772i	$0.690740\pi$
$140$	−0.901721	+	1.06063i	−0.0762094	+	0.0896396i
$141$	−4.46122	−	1.25133i	−0.375703	−	0.105381i
$142$	−2.35005	−	1.87056i	−0.197212	−	0.156974i
$143$	2.45574	−	25.2472i	0.205359	−	2.11128i
$144$	13.7198	+	0.942326i	1.14331	+	0.0785272i
$145$	10.9912	−	3.05961i	0.912770	−	0.254087i
$146$	−16.9006	+	5.17899i	−1.39871	+	0.428616i
$147$	8.29749	−	8.53644i	0.684366	−	0.704074i
$148$	−9.39825	−	2.09948i	−0.772531	−	0.172576i
$149$	−14.1476	+	3.54682i	−1.15902	+	0.290567i	−0.774514	−	0.632557i	$-0.782005\pi$
$149$	−14.1476	+	3.54682i	−1.15902	+	0.290567i	−0.384502	+	0.923124i	$0.625627\pi$
$150$	−1.23209	+	1.74028i	−0.100600	+	0.142093i
$151$	−11.9507	−	14.0567i	−0.972534	−	1.14392i	−0.989568	−	0.144066i	$-0.953982\pi$
$151$	−11.9507	−	14.0567i	−0.972534	−	1.14392i	0.0170345	−	0.999855i	$-0.494577\pi$
$152$	−0.240413	−	0.381441i	−0.0195000	−	0.0309389i
$153$	−2.26774	−	1.07732i	−0.183336	−	0.0870958i
$154$	2.78889	−	2.16155i	0.224735	−	0.174183i
$155$	0.351205	−	10.8624i	0.0282095	−	0.872490i
$156$	12.9051	−	5.24273i	1.03324	−	0.419754i
$157$	1.08505	−	8.79007i	0.0865966	−	0.701524i	−0.885118	−	0.465366i	$-0.845923\pi$
$157$	1.08505	−	8.79007i	0.0865966	−	0.701524i	0.971715	−	0.236157i	$-0.0758881\pi$
$158$	2.64965	−	13.0450i	0.210795	−	1.03781i
$159$	14.7382	+	14.1416i	1.16882	+	1.12150i
$160$	−16.4333	−	6.22300i	−1.29917	−	0.491971i
$161$	−0.0364024	−	0.0305452i	−0.00286891	−	0.00240730i
$162$	−17.1639	−	0.801342i	−1.34852	−	0.0629593i
$163$	−16.0231	+	13.4449i	−1.25502	+	1.05309i	−0.258829	+	0.965923i	$0.583336\pi$
$163$	−16.0231	+	13.4449i	−1.25502	+	1.05309i	−0.996194	+	0.0871656i	$0.972219\pi$
$164$	13.4737	−	4.70768i	1.05212	−	0.367608i
$165$	15.6534	−	14.5208i	1.21862	−	1.13044i
$166$	−1.55778	−	10.4004i	−0.120908	−	0.807226i
$167$	0.340913	−	0.668012i	0.0263807	−	0.0516923i	−0.877147	−	0.480221i	$-0.840556\pi$
$167$	0.340913	−	0.668012i	0.0263807	−	0.0516923i	0.903528	+	0.428529i	$0.140968\pi$
$168$	−0.380375	−	0.173805i	−0.0293466	−	0.0134094i
$169$	−7.27392	+	8.12063i	−0.559532	+	0.624664i
$170$	2.81114	+	2.55098i	0.215605	+	0.195651i
$171$	1.10078	+	1.66447i	0.0841787	+	0.127285i
$172$	11.4569	−	4.68065i	0.873580	−	0.356897i
$173$	−9.72685	−	1.65035i	−0.739518	−	0.125474i	−0.214691	−	0.976682i	$-0.568874\pi$
$173$	−9.72685	−	1.65035i	−0.739518	−	0.125474i	−0.524828	+	0.851209i	$0.675870\pi$
$174$	−8.26592	−	13.5584i	−0.626638	−	1.02786i
$175$	0.190254	−	0.128686i	0.0143818	−	0.00972775i
$176$	20.0387	+	12.8116i	1.51047	+	0.965713i
$177$	−0.619170	−	3.84560i	−0.0465397	−	0.289053i
$178$	−20.6928	−	8.76779i	−1.55099	−	0.657173i
$179$	4.63738	+	9.69827i	0.346614	+	0.724882i	0.999468	−	0.0326012i	$-0.0103791\pi$
$179$	4.63738	+	9.69827i	0.346614	+	0.724882i	−0.652854	+	0.757484i	$0.726429\pi$
$180$	11.0532	+	3.91082i	0.823858	+	0.291496i
$181$	−11.7942	−	3.28313i	−0.876654	−	0.244033i	−0.199520	−	0.979894i	$-0.563938\pi$
$181$	−11.7942	−	3.28313i	−0.876654	−	0.244033i	−0.677133	+	0.735860i	$0.736778\pi$
$182$	−3.32368	+	0.0859588i	−0.246368	+	0.00637169i
$183$	−6.49045	−	3.59795i	−0.479788	−	0.265968i
$184$	0.0314766	−	0.0847723i	0.00232049	−	0.00624950i
$185$	12.2639	+	6.56155i	0.901658	+	0.482415i
$186$	−14.6795	+	3.64951i	−1.07636	+	0.267595i
$187$	−2.54769	−	3.51615i	−0.186306	−	0.257126i
$188$	1.26205	−	4.21555i	0.0920446	−	0.307450i
$189$	1.69994	+	0.732148i	0.123652	+	0.0532559i
$190$	−0.865353	−	2.89048i	−0.0627793	−	0.209698i
$191$	3.39438	−	4.43847i	0.245609	−	0.321157i	−0.655132	−	0.755515i	$-0.727387\pi$
$191$	3.39438	−	4.43847i	0.245609	−	0.321157i	0.900740	+	0.434358i	$0.143025\pi$
$192$	−0.736783	+	8.54596i	−0.0531727	+	0.616751i
$193$	−9.00909	+	4.23651i	−0.648489	+	0.304951i	−0.721535	−	0.692378i	$-0.756563\pi$
$193$	−9.00909	+	4.23651i	−0.648489	+	0.304951i	0.0730465	+	0.997329i	$0.476728\pi$
$194$	3.86318	−	15.8430i	0.277360	−	1.13746i
$195$	−19.9874	+	2.29634i	−1.43133	+	0.164444i
$196$	7.96866	+	8.02034i	0.569190	+	0.572882i
$197$	7.35081	−	1.44365i	0.523724	−	0.102856i	0.0761384	−	0.997097i	$-0.475741\pi$
$197$	7.35081	−	1.44365i	0.523724	−	0.102856i	0.447585	+	0.894241i	$0.352284\pi$
$198$	−25.3823	−	15.4549i	−1.80384	−	1.09833i
$199$	−20.8565	+	11.5081i	−1.47848	+	0.815789i	−0.998120	−	0.0612849i	$-0.980480\pi$
$199$	−20.8565	+	11.5081i	−1.47848	+	0.815789i	−0.480356	+	0.877074i	$0.659493\pi$
$200$	0.352273	+	0.258735i	0.0249095	+	0.0182953i
$201$	−5.43491	−	10.7015i	−0.383349	−	0.754828i
$202$	2.67456	−	16.4057i	0.188181	−	1.15430i
$203$	0.318781	+	1.68055i	0.0223741	+	0.117952i
$204$	1.06052	−	2.13556i	0.0742511	−	0.149519i
$205$	−20.5713	+	1.33162i	−1.43676	+	0.0930044i
$206$	1.50604	+	4.40155i	0.104930	+	0.306671i
$207$	−0.131053	+	0.378152i	−0.00910880	+	0.0262834i
$208$	−8.07201	−	20.9070i	−0.559693	−	1.44964i
$209$	0.289684	+	3.43909i	0.0200379	+	0.237887i
$210$	−2.14027	−	1.80309i	−0.147693	−	0.124425i
$211$	6.93650	−	10.3994i	0.477528	−	0.715923i	−0.512203	−	0.858864i	$-0.671170\pi$
$211$	6.93650	−	10.3994i	0.477528	−	0.715923i	0.989731	+	0.142942i	$0.0456561\pi$
$212$	−13.6723	+	13.7610i	−0.939021	+	0.945110i
$213$	1.68741	−	2.13963i	0.115619	−	0.146605i
$214$	−0.272326	−	6.01423i	−0.0186158	−	0.411124i
$215$	−17.7545	+	2.07520i	−1.21085	+	0.141528i
$216$	−0.225542	+	3.51492i	−0.0153462	+	0.239160i
$217$	1.61839	+	0.189162i	0.109863	+	0.0128412i
$218$	2.47660	−	34.7709i	0.167736	−	2.35498i
$219$	−4.76740	−	15.3114i	−0.322151	−	1.03465i
$220$	13.5295	+	15.1044i	0.912158	+	1.01834i
$221$	−0.0264478	+	4.09138i	−0.00177907	+	0.275216i
$222$	4.13550	−	18.9117i	0.277556	−	1.26927i
$223$	−10.3609	+	9.16060i	−0.693818	+	0.613439i	−0.933993	−	0.357291i	$-0.883701\pi$
$223$	−10.3609	+	9.16060i	−0.693818	+	0.613439i	0.240175	+	0.970730i	$0.422795\pi$
$224$	1.13649	−	2.37677i	0.0759352	−	0.158805i
$225$	−1.58383	−	1.11067i	−0.105589	−	0.0740447i
$226$	15.9102	−	11.3719i	1.05833	−	0.756450i
$227$	11.9725	+	23.4598i	0.794639	+	1.55708i	0.830039	+	0.557705i	$0.188318\pi$
$227$	11.9725	+	23.4598i	0.794639	+	1.55708i	−0.0353996	+	0.999373i	$0.511270\pi$
$228$	−1.59875	+	1.01773i	−0.105880	+	0.0674005i
$229$	2.77834	+	3.63294i	0.183598	+	0.240071i	0.877013	−	0.480467i	$-0.159533\pi$
$229$	2.77834	+	3.63294i	0.183598	+	0.240071i	−0.693415	+	0.720538i	$0.743895\pi$
$230$	0.355051	−	0.490017i	0.0234114	−	0.0323108i
$231$	1.97237	+	2.52130i	0.129772	+	0.165890i
$232$	−2.80834	+	1.64569i	−0.184377	+	0.108045i
$233$	−2.51604	−	11.6153i	−0.164831	−	0.760946i	−0.982650	−	0.185470i	$-0.940619\pi$
$233$	−2.51604	−	11.6153i	−0.164831	−	0.760946i	0.817819	−	0.575476i	$-0.195183\pi$
$234$	10.6558	+	25.8950i	0.696591	+	1.69281i
$235$	−3.38889	+	5.37683i	−0.221067	+	0.350746i
$236$	3.66192	−	0.524309i	0.238371	−	0.0341296i
$237$	11.8455	+	2.35058i	0.769445	+	0.152687i
$238$	−0.416483	+	0.387874i	−0.0269966	+	0.0251421i
$239$	10.9718	+	20.1920i	0.709706	+	1.30611i	0.942703	+	0.333632i	$0.108274\pi$
$239$	10.9718	+	20.1920i	0.709706	+	1.30611i	−0.232997	+	0.972477i	$0.574853\pi$
$240$	6.60108	−	17.6713i	0.426098	−	1.14068i
$241$	9.65980	−	16.2426i	0.622243	−	1.04628i	−0.370821	−	0.928704i	$-0.620924\pi$
$241$	9.65980	−	16.2426i	0.622243	−	1.04628i	0.993064	−	0.117576i	$-0.0375125\pi$
$242$	−15.1975	−	26.3228i	−0.976930	−	1.69209i
$243$	0.656964	−	15.5746i	0.0421442	−	0.999112i
$244$	3.52392	−	6.10362i	0.225596	−	0.390744i
$245$	−7.98135	−	14.2463i	−0.509910	−	0.910164i
$246$	9.58536	+	27.0428i	0.611140	+	1.72419i
$247$	1.69829	−	2.77337i	0.108060	−	0.176465i
$248$	0.695543	+	3.02164i	0.0441670	+	0.191874i
$249$	9.42902	−	1.45568i	0.597540	−	0.0922497i
$250$	−12.2026	−	15.5357i	−0.771761	−	0.982562i
$251$	8.54285	+	16.2182i	0.539220	+	1.02368i	0.991290	+	0.131701i	$0.0420438\pi$
$251$	8.54285	+	16.2182i	0.539220	+	1.02368i	−0.452070	+	0.891983i	$0.649314\pi$
$252$	−0.723359	+	1.60210i	−0.0455673	+	0.100923i
$253$	−0.512586	+	0.465147i	−0.0322260	+	0.0292435i
$254$	0.230575	+	35.6692i	0.0144676	+	2.23808i
$255$	−2.30281	+	2.56072i	−0.144208	+	0.160358i
$256$	19.9870	+	2.07460i	1.24919	+	0.129662i
$257$	−23.9325	+	3.11144i	−1.49287	+	0.194086i	−0.831312	−	0.555806i	$-0.812410\pi$
$257$	−23.9325	+	3.11144i	−1.49287	+	0.194086i	−0.661559	+	0.749893i	$0.730105\pi$
$258$	9.51280	+	22.9888i	0.592241	+	1.43122i
$259$	−1.13460	+	1.74961i	−0.0705008	+	0.108716i
$260$	−1.84979	−	19.0175i	−0.114719	−	1.17941i
$261$	12.2666	−	7.55428i	0.759285	−	0.467598i
$262$	−10.8917	+	0.846570i	−0.672891	+	0.0523013i
$263$	−3.21515	−	15.8291i	−0.198254	−	0.976066i	−0.948952	−	0.315420i	$-0.897854\pi$
$263$	−3.21515	−	15.8291i	−0.198254	−	0.976066i	0.750698	−	0.660646i	$-0.229718\pi$
$264$	−3.25817	+	5.14696i	−0.200526	+	0.316773i
$265$	24.3543	−	13.8518i	1.49607	−	0.850911i
$266$	0.442718	−	0.0929068i	0.0271448	−	0.00569648i
$267$	7.86984	−	18.8086i	0.481626	−	1.15107i
$268$	10.2518	−	4.98375i	0.626230	−	0.304431i
$269$	−11.2604	+	15.1253i	−0.686558	+	0.922208i	−0.999621	−	0.0275244i	$-0.991238\pi$
$269$	−11.2604	+	15.1253i	−0.686558	+	0.922208i	0.313063	+	0.949732i	$0.398645\pi$
$270$	−7.76177	+	22.2550i	−0.472366	+	1.35439i
$271$	18.1753	+	24.4137i	1.10407	+	1.48302i	0.857913	+	0.513794i	$0.171761\pi$
$271$	18.1753	+	24.4137i	1.10407	+	1.48302i	0.246157	+	0.969230i	$0.420832\pi$
$272$	−3.40566	−	1.76589i	−0.206499	−	0.107073i
$273$	−0.0915430	−	3.01494i	−0.00554043	−	0.182473i
$274$	4.69514	+	1.24181i	0.283643	+	0.0750203i
$275$	−1.48216	−	2.99941i	−0.0893776	−	0.180871i
$276$	−0.356915	−	0.130702i	−0.0214837	−	0.00786734i
$277$	−23.8087	+	16.5566i	−1.43053	+	0.994790i	−0.434987	+	0.900437i	$0.643247\pi$
$277$	−23.8087	+	16.5566i	−1.43053	+	0.994790i	−0.995539	+	0.0943530i	$0.969922\pi$
$278$	19.6265	+	3.06952i	1.17712	+	0.184098i
$279$	−3.37077	−	13.3026i	−0.201803	−	0.796405i
$280$	−0.377191	+	0.432213i	−0.0225415	+	0.0258297i
$281$	5.92227	−	11.9847i	0.353293	−	0.714950i	−0.645516	−	0.763747i	$-0.723358\pi$
$281$	5.92227	−	11.9847i	0.353293	−	0.714950i	0.998809	+	0.0487967i	$0.0155386\pi$
$282$	8.48567	+	2.49892i	0.505314	+	0.148808i
$283$	8.48289	−	7.30694i	0.504256	−	0.434352i	−0.363315	−	0.931666i	$-0.618355\pi$
$283$	8.48289	−	7.30694i	0.504256	−	0.434352i	0.867571	+	0.497314i	$0.165680\pi$
$284$	2.00381	+	1.63772i	0.118904	+	0.0971811i
$285$	2.61876	−	0.796854i	0.155122	−	0.0472015i
$286$	−5.31120	+	48.1368i	−0.314058	+	2.84639i
$287$	0.0599312	−	3.09004i	0.00353763	−	0.182399i
$288$	−22.1145	−	1.80643i	−1.30311	−	0.106445i
$289$	−10.7174	−	12.2807i	−0.630433	−	0.722396i
$290$	−21.0579	+	5.56957i	−1.23656	+	0.327056i
$291$	14.3887	+	3.44010i	0.843482	+	0.201662i
$292$	14.6181	−	4.27362i	0.855462	−	0.250095i
$293$	−2.17956	+	25.8754i	−0.127331	+	1.51166i	0.585701	+	0.810527i	$0.300819\pi$
$293$	−2.17956	+	25.8754i	−0.127331	+	1.51166i	−0.713032	+	0.701131i	$0.752679\pi$
$294$	−16.0508	+	16.0914i	−0.936099	+	0.938471i
$295$	−5.29842	−	0.688841i	−0.308486	−	0.0401059i
$296$	−3.86122	−	0.915127i	−0.224429	−	0.0531907i
$297$	13.9173	−	23.0903i	0.807565	−	1.33983i
$298$	27.0955	−	6.42176i	1.56960	−	0.372003i
$299$	0.648732	−	0.0673366i	0.0375171	−	0.00389418i
$300$	1.08087	−	1.48558i	0.0624042	−	0.0857703i
$301$	−0.0866043	−	2.67858i	−0.00499179	−	0.154391i
$302$	22.4671	+	27.1295i	1.29284	+	1.56113i
$303$	14.8944	+	2.35946i	0.855660	+	0.135548i
$304$	1.59236	+	2.60038i	0.0913281	+	0.149142i
$305$	−7.26745	+	7.12787i	−0.416133	+	0.408140i
$306$	4.30256	+	2.11259i	0.245961	+	0.120769i
$307$	−8.75115	+	12.7595i	−0.499455	+	0.728223i	−0.989668	−	0.143380i	$-0.954203\pi$
$307$	−8.75115	+	12.7595i	−0.499455	+	0.728223i	0.490213	+	0.871603i	$0.336919\pi$
$308$	−2.42680	+	1.83119i	−0.138280	+	0.104342i
$309$	−3.98701	+	1.38425i	−0.226813	+	0.0787475i
$310$	−0.938562	+	20.7279i	−0.0533067	+	1.17726i
$311$	1.97638	+	27.7480i	0.112070	+	1.57344i	0.669242	+	0.743045i	$0.266619\pi$
$311$	1.97638	+	27.7480i	0.112070	+	1.57344i	−0.557172	+	0.830397i	$0.688113\pi$
$312$	5.34530	−	2.09144i	0.302618	−	0.118404i
$313$	11.0990	+	29.8917i	0.627353	+	1.68958i	0.720085	+	0.693885i	$0.244103\pi$
$313$	11.0990	+	29.8917i	0.627353	+	1.68958i	−0.0927319	+	0.995691i	$0.529560\pi$
$314$	−2.28834	+	16.7536i	−0.129139	+	0.945461i
$315$	1.62705	−	1.94904i	0.0916741	−	0.109816i
$316$	−2.42807	+	11.2092i	−0.136590	+	0.630568i
$317$	−0.837802	−	2.55598i	−0.0470556	−	0.143558i	0.924012	−	0.382364i	$-0.124890\pi$
$317$	−0.837802	−	2.55598i	−0.0470556	−	0.143558i	−0.971067	+	0.238806i	$0.923244\pi$
$318$	−27.7865	−	27.3603i	−1.55819	−	1.53429i
$319$	24.8821	−	1.28789i	1.39313	−	0.0721078i
$320$	10.9488	+	4.30876i	0.612056	+	0.240867i
$321$	5.45509	−	0.271594i	0.304473	−	0.0151589i
$322$	0.0687389	+	0.0592099i	0.00383067	+	0.00329964i
$323$	−0.0966650	−	0.548215i	−0.00537859	−	0.0305035i
$324$	14.7784	+	0.881569i	0.821020	+	0.0489761i
$325$	−0.547425	+	3.10460i	−0.0303657	+	0.172212i
$326$	30.9201	−	25.2711i	1.71251	−	1.39964i
$327$	31.5548	+	2.10495i	1.74498	+	0.116404i
$328$	5.57672	−	1.86795i	0.307923	−	0.103140i
$329$	−0.760635	−	0.573951i	−0.0419352	−	0.0316429i
$330$	−30.2411	+	27.3340i	−1.66472	+	1.50469i
$331$	7.31819	−	3.91546i	0.402244	−	0.215213i	−0.258195	−	0.966093i	$-0.583128\pi$
$331$	7.31819	−	3.91546i	0.402244	−	0.215213i	0.660439	+	0.750880i	$0.270370\pi$
$332$	1.22624	+	8.97763i	0.0672984	+	0.492712i
$333$	17.1738	+	3.67463i	0.941121	+	0.201368i
$334$	−0.667297	+	1.26683i	−0.0365129	+	0.0693180i
$335$	−16.1951	+	2.96371i	−0.884835	+	0.161925i
$336$	2.55696	+	1.20856i	0.139494	+	0.0659322i
$337$	−4.99454	−	5.15863i	−0.272070	−	0.281009i	0.568533	−	0.822660i	$-0.307511\pi$
$337$	−4.99454	−	5.15863i	−0.272070	−	0.281009i	−0.840603	+	0.541652i	$0.817799\pi$
$338$	14.0865	−	15.3229i	0.766203	−	0.833456i
$339$	10.3817	+	14.3876i	0.563857	+	0.781426i
$340$	−2.39348	−	2.22907i	−0.129805	−	0.120888i
$341$	5.92021	−	22.9837i	0.320597	−	1.24464i
$342$	−2.06032	−	3.20466i	−0.111410	−	0.173288i
$343$	4.49873	−	2.04492i	0.242908	−	0.110415i
$344$	4.74557	−	1.86756i	0.255864	−	0.100692i
$345$	0.445999	+	0.320108i	0.0240118	+	0.0172341i
$346$	18.5280	+	3.39062i	0.996071	+	0.182281i
$347$	−17.5730	+	22.3730i	−0.943370	+	1.20104i	0.0360781	+	0.999349i	$0.488513\pi$
$347$	−17.5730	+	22.3730i	−0.943370	+	1.20104i	−0.979448	+	0.201696i	$0.935355\pi$
$348$	6.97035	+	11.7731i	0.373650	+	0.631103i
$349$	6.75097	+	23.6588i	0.361371	+	1.26643i	0.904390	+	0.426707i	$0.140326\pi$
$349$	6.75097	+	23.6588i	0.361371	+	1.26643i	−0.543019	+	0.839721i	$0.682719\pi$
$350$	−0.366374	+	0.240968i	−0.0195835	+	0.0128803i
$351$	−23.4489	+	9.77274i	−1.25161	+	0.521630i
$352$	−32.0613	−	21.0870i	−1.70887	−	1.12394i
$353$	6.18176	−	19.7171i	0.329022	−	1.04943i	−0.632467	−	0.774588i	$-0.717957\pi$
$353$	6.18176	−	19.7171i	0.329022	−	1.04943i	0.961488	−	0.274846i	$-0.0886270\pi$
$354$	1.08709	+	7.35660i	0.0577782	+	0.390999i
$355$	−2.15384	−	3.05493i	−0.114314	−	0.162139i
$356$	17.7299	+	7.78424i	0.939682	+	0.412564i
$357$	−0.353584	−	0.376257i	−0.0187136	−	0.0199136i
$358$	−8.61348	−	18.6286i	−0.455236	−	0.984553i
$359$	19.3716	+	10.6888i	1.02239	+	0.564133i	0.903417	−	0.428764i	$-0.141051\pi$
$359$	19.3716	+	10.6888i	1.02239	+	0.564133i	0.118977	+	0.992897i	$0.462038\pi$
$360$	4.53348	+	1.67028i	0.238935	+	0.0880315i
$361$	6.68401	−	17.3120i	0.351790	−	0.911159i
$362$	22.4342	+	6.55866i	1.17912	+	0.344715i
$363$	23.8184	−	13.8948i	1.25014	−	0.729285i
$364$	2.86442	−	0.0370344i	0.150137	−	0.00194113i
$365$	−21.9955	+	0.284382i	−1.15130	+	0.0148852i
$366$	12.3016	+	7.02875i	0.643014	+	0.367399i
$367$	−21.8851	−	6.39812i	−1.14239	−	0.333979i	−0.345689	−	0.938349i	$-0.612355\pi$
$367$	−21.8851	−	6.39812i	−1.14239	−	0.333979i	−0.796704	+	0.604370i	$0.793425\pi$
$368$	−0.220262	+	0.570492i	−0.0114819	+	0.0297390i
$369$	−24.4945	+	8.80630i	−1.27513	+	0.458438i
$370$	−23.2500	−	12.8288i	−1.20871	−	0.666938i
$371$	1.76294	+	3.81276i	0.0915273	+	0.197949i
$372$	12.6876	−	2.98066i	0.657820	−	0.154540i
$373$	−22.5678	−	9.90831i	−1.16852	−	0.513033i	−0.274728	−	0.961522i	$-0.588588\pi$
$373$	−22.5678	−	9.90831i	−1.16852	−	0.513033i	−0.893788	+	0.448490i	$0.851962\pi$
$374$	4.77680	+	6.77527i	0.247003	+	0.350341i
$375$	14.0444	−	11.1338i	0.725250	−	0.574946i
$376$	0.542467	−	1.73023i	0.0279756	−	0.0892298i
$377$	−19.6148	−	12.9009i	−1.01021	−	0.664429i
$378$	−3.22714	−	1.43964i	−0.165986	−	0.0740471i
$379$	18.9792	−	12.4828i	0.974894	−	0.641198i	0.0411552	−	0.999153i	$-0.486896\pi$
$379$	18.9792	−	12.4828i	0.974894	−	0.641198i	0.933739	+	0.357955i	$0.116526\pi$
$380$	0.713335	+	2.49989i	0.0365933	+	0.128241i
$381$	−32.3586	+	0.354704i	−1.65778	+	0.0181720i
$382$	−6.58948	+	8.38935i	−0.337147	+	0.429236i
$383$	14.1590	+	2.59109i	0.723491	+	0.132399i	0.529141	−	0.848534i	$-0.322514\pi$
$383$	14.1590	+	2.59109i	0.723491	+	0.132399i	0.194349	+	0.980932i	$0.437740\pi$
$384$	−0.913056	+	9.19919i	−0.0465942	+	0.469444i
$385$	4.08602	−	1.60800i	0.208243	−	0.0819513i
$386$	17.3031	−	7.86522i	0.880704	−	0.400329i
$387$	−20.8169	+	8.72394i	−1.05818	+	0.443463i
$388$	−3.50474	+	13.6062i	−0.177926	+	0.690751i
$389$	−8.55546	−	7.96776i	−0.433779	−	0.403982i	0.434015	−	0.900906i	$-0.357096\pi$
$389$	−8.55546	−	7.96776i	−0.433779	−	0.403982i	−0.867794	+	0.496924i	$0.834463\pi$
$390$	38.2129	−	3.89043i	1.93499	−	0.197000i
$391$	0.0755586	−	0.0821907i	0.00382116	−	0.00415656i
$392$	3.24064	+	3.34711i	0.163677	+	0.169055i
$393$	−0.812456	−	9.87765i	−0.0409830	−	0.498262i
$394$	−14.0685	+	2.57453i	−0.708759	+	0.129703i
$395$	7.72021	−	14.6565i	0.388446	−	0.737447i
$396$	21.6956	+	13.5976i	1.09024	+	0.683306i
$397$	0.172245	+	1.26106i	0.00864473	+	0.0632906i	0.994617	−	0.103617i	$-0.0330416\pi$
$397$	0.172245	+	1.26106i	0.00864473	+	0.0632906i	−0.985973	+	0.166908i	$0.946622\pi$
$398$	40.0994	−	21.4544i	2.01000	−	1.07541i
$399$	0.0860926	+	0.401261i	0.00431002	+	0.0200882i
$400$	−2.35951	−	1.78041i	−0.117975	−	0.0890205i
$401$	−2.77486	+	0.929451i	−0.138570	+	0.0464146i	−0.386047	−	0.922479i	$-0.626160\pi$
$401$	−2.77486	+	0.929451i	−0.138570	+	0.0464146i	0.247477	+	0.968894i	$0.420398\pi$
$402$	10.1112	+	20.5636i	0.504301	+	1.02562i
$403$	−17.3161	+	14.1525i	−0.862575	+	0.704986i
$404$	−2.48696	+	14.1043i	−0.123731	+	0.701713i
$405$	−20.2217	−	6.95079i	−1.00482	−	0.345388i
$406$	−0.567080	−	3.21607i	−0.0281437	−	0.159611i
$407$	23.0138	+	19.8235i	1.14075	+	0.982613i
$408$	0.448347	−	0.874274i	0.0221965	−	0.0432830i
$409$	−7.15508	−	2.81579i	−0.353796	−	0.139232i	0.182625	−	0.983183i	$-0.441541\pi$
$409$	−7.15508	−	2.81579i	−0.353796	−	0.139232i	−0.536420	+	0.843951i	$0.680224\pi$
$410$	39.3038	−	2.03435i	1.94108	−	0.100469i
$411$	−1.10743	+	4.26456i	−0.0546255	+	0.210355i
$412$	−1.24847	−	3.80886i	−0.0615078	−	0.187649i
$413$	0.169586	−	0.782898i	0.00834480	−	0.0385239i
$414$	0.259516	−	0.718665i	0.0127545	−	0.0353205i
$415$	1.77110	−	12.9668i	0.0869401	−	0.636514i
$416$	12.5865	+	33.8978i	0.617105	+	1.66197i
$417$	−2.70464	+	17.8179i	−0.132447	+	0.872548i
$418$	−0.468129	−	6.57244i	−0.0228969	−	0.321469i
$419$	0.577784	−	12.7602i	0.0282266	−	0.623377i	−0.934994	−	0.354664i	$-0.884595\pi$
$419$	0.577784	−	12.7602i	0.0282266	−	0.623377i	0.963220	−	0.268713i	$-0.0865982\pi$
$420$	1.82383	+	1.57726i	0.0889939	+	0.0769624i
$421$	−0.318709	+	0.240487i	−0.0155329	+	0.0117206i	−0.610069	−	0.792348i	$-0.708858\pi$
$421$	−0.318709	+	0.240487i	−0.0155329	+	0.0117206i	0.594536	+	0.804069i	$0.297336\pi$
$422$	−13.4986	+	19.6814i	−0.657100	+	0.958075i
$423$	−2.23243	+	7.70851i	−0.108545	+	0.374801i
$424$	−5.70679	+	5.59718i	−0.277146	+	0.271823i
$425$	0.281809	+	0.460204i	0.0136697	+	0.0223232i
$426$	−3.27410	+	4.04295i	−0.158631	+	0.195881i
$427$	−0.973425	−	1.17543i	−0.0471073	−	0.0568831i
$428$	0.167626	+	5.18450i	0.00810251	+	0.250602i
$429$	−43.6921	−	4.62201i	−2.10947	−	0.223153i
$430$	33.9449	−	3.52339i	1.63697	−	0.169913i
$431$	−6.96148	+	1.64990i	−0.335323	+	0.0794730i	−0.394828	−	0.918755i	$-0.629196\pi$
$431$	−6.96148	+	1.64990i	−0.335323	+	0.0794730i	0.0595053	+	0.998228i	$0.481048\pi$
$432$	1.83245	−	23.7487i	0.0881639	−	1.14261i
$433$	0.979436	+	0.232131i	0.0470687	+	0.0111555i	0.254083	−	0.967182i	$-0.418226\pi$
$433$	0.979436	+	0.232131i	0.0470687	+	0.0111555i	−0.207014	+	0.978338i	$0.566375\pi$
$434$	−3.08486	−	0.401059i	−0.148078	−	0.0192515i
$435$	−5.13870	−	19.0813i	−0.246382	−	0.914879i
$436$	−2.52098	+	29.9287i	−0.120733	+	1.43333i
$437$	−0.0851735	+	0.0249005i	−0.00407440	+	0.00119115i
$438$	8.72315	+	29.3473i	0.416808	+	1.40227i
$439$	10.3839	−	2.74641i	0.495594	−	0.131079i	0.000643568	−	1.00000i	$-0.499795\pi$
$439$	10.3839	−	2.74641i	0.495594	−	0.131079i	0.494951	+	0.868921i	$0.335186\pi$
$440$	5.49416	+	6.29561i	0.261924	+	0.300131i
$441$	−14.6639	−	14.4958i	−0.698279	−	0.690278i
$442$	0.151472	−	7.80986i	0.00720479	−	0.371477i
$443$	0.429120	−	3.88922i	0.0203881	−	0.184783i	−0.979471	−	0.201587i	$-0.935390\pi$
$443$	0.429120	−	3.88922i	0.0203881	−	0.184783i	0.999859	+	0.0168039i	$0.00534911\pi$
$444$	−3.77353	+	16.2470i	−0.179084	+	0.771049i
$445$	−21.6549	−	17.6986i	−1.02654	−	0.838996i
$446$	20.0053	−	17.2320i	0.947277	−	0.815960i
$447$	5.93646	+	24.5553i	0.280785	+	1.16142i
$448$	−0.781495	+	1.58149i	−0.0369222	+	0.0747185i
$449$	−17.7050	+	20.2877i	−0.835551	+	0.957435i	−0.999579	−	0.0290203i	$-0.990761\pi$
$449$	−17.7050	+	20.2877i	−0.835551	+	0.957435i	0.164028	+	0.986456i	$0.447551\pi$
$450$	2.99615	+	2.15938i	0.141240	+	0.101794i
$451$	−44.4772	−	6.95611i	−2.09435	−	0.327550i
$452$	−13.8339	+	9.62009i	−0.650690	+	0.452491i
$453$	−24.5206	+	20.4932i	−1.15208	+	0.962854i
$454$	−22.2766	−	45.0806i	−1.04549	−	2.11574i
$455$	−4.00001	−	1.05795i	−0.187523	−	0.0495977i
$456$	−0.664162	+	0.410822i	−0.0311022	+	0.0192385i
$457$	−4.08721	−	2.11928i	−0.191191	−	0.0991356i	0.362042	−	0.932162i	$-0.382080\pi$
$457$	−4.08721	−	2.11928i	−0.191191	−	0.0991356i	−0.553234	+	0.833026i	$0.686606\pi$
$458$	−5.21423	−	7.00392i	−0.243645	−	0.327272i
$459$	−1.89902	+	3.91197i	−0.0886385	+	0.182595i
$460$	−0.311347	+	0.418211i	−0.0145166	+	0.0194992i
$461$	21.8838	−	10.6384i	1.01923	−	0.495482i	0.149371	−	0.988781i	$-0.452275\pi$
$461$	21.8838	−	10.6384i	1.01923	−	0.495482i	0.869860	+	0.493300i	$0.164209\pi$
$462$	−3.70306	−	4.86189i	−0.172282	−	0.226196i
$463$	24.2045	−	5.07945i	1.12488	−	0.236062i	0.394361	−	0.918956i	$-0.370966\pi$
$463$	24.2045	−	5.07945i	1.12488	−	0.236062i	0.730518	+	0.682894i	$0.239279\pi$
$464$	19.1343	−	10.8829i	0.888289	−	0.505226i
$465$	−18.8085	−	0.766911i	−0.872221	−	0.0355647i
$466$	4.51648	+	22.2360i	0.209222	+	1.03006i
$467$	38.5628	−	2.99734i	1.78447	−	0.138700i	0.857658	−	0.514220i	$-0.171919\pi$
$467$	38.5628	−	2.99734i	1.78447	−	0.138700i	0.926814	+	0.375520i	$0.122536\pi$
$468$	−8.89189	−	22.4281i	−0.411028	−	1.03674i
$469$	−0.238967	−	2.45680i	−0.0110345	−	0.113444i
$470$	6.60216	−	10.1808i	0.304535	−	0.469607i
$471$	−15.2085	−	2.00766i	−0.700769	−	0.0925083i
$472$	1.51163	−	0.196526i	0.0695786	−	0.00904583i
$473$	−38.8279	−	4.03023i	−1.78531	−	0.185310i
$474$	−22.5552	−	4.77967i	−1.03599	−	0.219538i
$475$	−0.00277259	−	0.428910i	−0.000127215	−	0.0196797i
$476$	0.363135	−	0.329527i	0.0166443	−	0.0151039i
$477$	24.7083	−	25.3200i	1.13131	−	1.15932i
$478$	−20.4470	−	38.8176i	−0.935223	−	1.77548i
$479$	−3.31677	−	4.22272i	−0.151547	−	0.192941i	0.704703	−	0.709502i	$-0.251080\pi$
$479$	−3.31677	−	4.22272i	−0.151547	−	0.192941i	−0.856250	+	0.516561i	$0.827212\pi$
$480$	−11.0181	+	28.3715i	−0.502907	+	1.29498i
$481$	−6.42029	−	27.8916i	−0.292740	−	1.27175i
$482$	−18.8416	+	30.7691i	−0.858213	+	1.40149i
$483$	−0.0534356	+	0.0626025i	−0.00243140	+	0.00284851i
$484$	12.7999	+	22.8473i	0.581815	+	1.03851i
$485$	10.1468	−	17.5747i	0.460741	−	0.798026i
$486$	−1.63857	+	29.7160i	−0.0743268	+	1.34794i
$487$	17.6235	+	30.5247i	0.798595	+	1.38321i	0.920531	+	0.390670i	$0.127757\pi$
$487$	17.6235	+	30.5247i	0.798595	+	1.38321i	−0.121936	+	0.992538i	$0.538910\pi$
$488$	1.48450	−	2.49613i	0.0672000	−	0.112995i
$489$	23.0525	+	27.9481i	1.04247	+	1.26386i
$490$	14.8849	+	27.3935i	0.672432	+	1.23751i
$491$	−6.16971	+	5.74589i	−0.278435	+	0.259309i	−0.808296	−	0.588776i	$-0.799610\pi$
$491$	−6.16971	+	5.74589i	−0.278435	+	0.259309i	0.529862	+	0.848084i	$0.322244\pi$
$492$	−7.95688	−	23.4051i	−0.358724	−	1.05518i
$493$	−3.97815	+	0.569586i	−0.179167	+	0.0256529i
$494$	−3.31052	+	5.25249i	−0.148947	+	0.236321i
$495$	−24.9212	−	27.3236i	−1.12013	−	1.22811i
$496$	−4.43920	−	20.4936i	−0.199326	−	0.920190i
$497$	0.483501	−	0.283332i	0.0216880	−	0.0127092i
$498$	−18.0361	+	2.54619i	−0.808217	+	0.114097i
$499$	−16.1352	+	22.2688i	−0.722313	+	0.996886i	0.277038	+	0.960859i	$0.410647\pi$
$499$	−16.1352	+	22.2688i	−0.722313	+	0.996886i	−0.999351	+	0.0360272i	$0.988530\pi$
$500$	10.3399	+	13.5204i	0.462415	+	0.604652i
$501$	−1.15201	−	0.600213i	−0.0514681	−	0.0268156i
$502$	−15.9082	−	31.1717i	−0.710015	−	1.39126i
$503$	9.34912	−	6.68235i	0.416857	−	0.297951i	−0.353656	−	0.935375i	$-0.615062\pi$
$503$	9.34912	−	6.68235i	0.416857	−	0.297951i	0.770513	+	0.637424i	$0.220000\pi$
$504$	−0.306584	+	0.656268i	−0.0136563	+	0.0292325i
$505$	8.92349	−	18.6619i	0.397090	−	0.830444i
$506$	0.990017	−	0.875323i	0.0440116	−	0.0389128i
$507$	13.9586	+	12.7169i	0.619924	+	0.564779i
$508$	0.198665	−	30.7328i	0.00881433	−	1.36355i
$509$	−25.2911	−	28.2350i	−1.12101	−	1.25150i	−0.964575	−	0.263808i	$-0.915022\pi$
$509$	−25.2911	−	28.2350i	−1.12101	−	1.25150i	−0.156431	−	0.987689i	$-0.549999\pi$
$510$	4.45932	−	4.83162i	0.197462	−	0.213948i
$511$	0.234308	−	3.28964i	0.0103652	−	0.145525i
$512$	−27.5020	−	3.21453i	−1.21543	−	0.142063i
$513$	2.89891	−	1.88223i	0.127990	−	0.0831025i
$514$	45.7645	−	5.34910i	2.01858	−	0.235939i
$515$	0.261872	+	5.78337i	0.0115395	+	0.254846i
$516$	−7.93953	−	19.9116i	−0.349519	−	0.876558i
$517$	−9.78264	+	9.84608i	−0.430240	+	0.433030i
$518$	2.20916	−	3.31203i	0.0970650	−	0.145522i
$519$	−3.00043	+	16.8227i	−0.131704	+	0.738434i
$520$	−0.660866	−	7.84572i	−0.0289809	−	0.344057i
$521$	7.27453	+	18.8415i	0.318703	+	0.825461i	0.995967	+	0.0897212i	$0.0285976\pi$
$521$	7.27453	+	18.8415i	0.318703	+	0.825461i	−0.677264	+	0.735740i	$0.736834\pi$
$522$	−23.6037	+	14.1185i	−1.03310	+	0.617950i
$523$	5.45346	+	15.9383i	0.238463	+	0.696935i	0.998872	+	0.0474899i	$0.0151222\pi$
$523$	5.45346	+	15.9383i	0.238463	+	0.696935i	−0.760409	+	0.649445i	$0.775001\pi$
$524$	9.39300	−	0.608028i	0.410335	−	0.0265618i
$525$	−0.220104	−	0.331397i	−0.00960614	−	0.0144633i
$526$	5.74708	+	30.2975i	0.250585	+	1.32103i
$527$	−0.615958	+	3.77827i	−0.0268315	+	0.164584i
$528$	22.4822	−	34.5197i	0.978414	−	1.50228i
$529$	18.5229	+	13.6046i	0.805343	+	0.591503i
$530$	−46.8347	+	25.8423i	−2.03437	+	1.12252i
$531$	−6.66958	+	1.01624i	−0.289435	+	0.0441010i
$532$	−0.382451	+	0.0751110i	−0.0165814	+	0.00325647i
$533$	29.8977	+	30.0916i	1.29502	+	1.30341i
$534$	−15.4879	+	35.7116i	−0.670227	+	1.54539i
$535$	1.77489	−	7.27883i	0.0767350	−	0.314691i
$536$	4.25066	−	1.99887i	0.183601	−	0.0863379i
$537$	16.8650	−	7.89027i	0.727779	−	0.340490i
$538$	21.8696	−	28.5966i	0.942866	−	1.23289i
$539$	−10.2277	−	34.1630i	−0.440539	−	1.47150i
$540$	6.93492	−	19.0869i	0.298431	−	0.821371i
$541$	1.98490	−	6.63002i	0.0853374	−	0.285047i	−0.904660	−	0.426135i	$-0.859875\pi$
$541$	1.98490	−	6.63002i	0.0853374	−	0.285047i	0.989997	+	0.141088i	$0.0450601\pi$
$542$	−34.0944	−	47.0547i	−1.46448	−	2.02117i
$543$	−5.85858	+	20.3794i	−0.251416	+	0.874565i
$544$	5.45754	+	2.91995i	0.233990	+	0.125192i
$545$	15.1002	−	40.6675i	0.646820	−	1.74200i
$546$	0.100343	+	5.75784i	0.00429427	+	0.246413i
$547$	1.89344	−	0.0489691i	0.0809577	−	0.00209377i	0.0146462	−	0.999893i	$-0.495338\pi$
$547$	1.89344	−	0.0489691i	0.0809577	−	0.00209377i	0.0663115	+	0.997799i	$0.478877\pi$
$548$	−4.03119	−	1.12216i	−0.172204	−	0.0479362i
$549$	−6.32640	+	11.1888i	−0.270004	+	0.477528i
$550$	2.75544	+	5.76251i	0.117492	+	0.245714i
$551$	2.94110	+	1.24618i	0.125295	+	0.0530891i
$552$	−0.146365	−	0.0557552i	−0.00622971	−	0.00237310i
$553$	2.09247	+	1.33781i	0.0889811	+	0.0568896i
$554$	45.8599	−	31.0192i	1.94840	−	1.31788i
$555$	11.5436	−	21.1451i	0.490000	−	0.897559i
$556$	−16.8747	−	2.86311i	−0.715646	−	0.121423i
$557$	12.9584	−	5.29408i	0.549064	−	0.224317i	−0.0866543	−	0.996238i	$-0.527618\pi$
$557$	12.9584	−	5.29408i	0.549064	−	0.224317i	0.635718	+	0.771921i	$0.280704\pi$
$558$	6.10653	+	25.4781i	0.258510	+	1.07857i
$559$	27.2395	+	24.7185i	1.15211	+	1.04548i
$560$	2.58841	−	2.88972i	0.109380	−	0.122113i
$561$	−6.12713	+	4.36123i	−0.258688	+	0.184131i
$562$	−11.6015	+	22.7329i	−0.489381	+	0.958931i
$563$	−6.22463	−	41.5581i	−0.262337	−	1.75147i	−0.590679	−	0.806906i	$-0.701140\pi$
$563$	−6.22463	−	41.5581i	−0.262337	−	1.75147i	0.328342	−	0.944559i	$-0.393510\pi$
$564$	−7.28285	−	2.24742i	−0.306663	−	0.0946335i
$565$	22.9751	−	8.02744i	0.966571	−	0.337717i
$566$	−16.3743	+	13.7397i	−0.688265	+	0.577523i
$567$	1.29290	−	2.93358i	0.0542966	−	0.123199i
$568$	0.816917	+	0.685475i	0.0342771	+	0.0287619i
$569$	18.8348	+	7.13237i	0.789594	+	0.299004i	0.715833	−	0.698271i	$-0.246047\pi$
$569$	18.8348	+	7.13237i	0.789594	+	0.299004i	0.0737609	+	0.997276i	$0.476500\pi$
$570$	−5.01892	+	1.45657i	−0.210219	+	0.0610091i
$571$	2.69498	−	13.2682i	0.112781	−	0.555257i	−0.883450	−	0.468525i	$-0.844786\pi$
$571$	2.69498	−	13.2682i	0.112781	−	0.555257i	0.996232	−	0.0867321i	$-0.0276424\pi$
$572$	5.11197	−	41.4123i	0.213742	−	1.73154i
$573$	−7.63782	−	5.94384i	−0.319074	−	0.248308i
$574$	−0.190678	+	5.89746i	−0.00795873	+	0.246155i
$575$	0.0679916	−	0.0526974i	0.00283544	−	0.00219763i
$576$	14.7907	+	1.40090i	0.616281	+	0.0583708i
$577$	3.84546	+	6.10124i	0.160089	+	0.253998i	0.916444	−	0.400163i	$-0.131047\pi$
$577$	3.84546	+	6.10124i	0.160089	+	0.253998i	−0.756355	+	0.654161i	$0.773022\pi$
$578$	20.1565	+	23.7087i	0.838401	+	0.986150i
$579$	7.20603	+	15.6655i	0.299472	+	0.651037i
$580$	18.2041	−	4.56381i	0.755886	−	0.189502i
$581$	1.91490	+	0.427772i	0.0794436	+	0.0177470i
$582$	−27.3834	−	6.92235i	−1.13508	−	0.286941i
$583$	58.5009	−	17.9269i	2.42286	−	0.742456i
$584$	6.04596	−	1.68301i	0.250183	−	0.0696433i
$585$	3.68536	+	34.6514i	0.152371	+	1.43266i
$586$	4.79947	−	49.3428i	0.198264	−	2.03833i
$587$	13.4372	+	10.6955i	0.554612	+	0.441451i	0.859646	−	0.510891i	$-0.170684\pi$
$587$	13.4372	+	10.6955i	0.554612	+	0.441451i	−0.305034	+	0.952341i	$0.598668\pi$
$588$	14.0075	−	13.6845i	0.577660	−	0.564340i
$589$	1.97087	−	2.31819i	0.0812082	−	0.0955194i
$590$	10.0978	+	1.44578i	0.415719	+	0.0595220i
$591$	−2.39304	−	12.7526i	−0.0984367	−	0.524572i
$592$	26.0302	+	6.52582i	1.06984	+	0.268210i
$593$	−27.9582	−	14.0411i	−1.14810	−	0.576600i	−0.230099	−	0.973167i	$-0.573905\pi$
$593$	−27.9582	−	14.0411i	−1.14810	−	0.576600i	−0.918006	+	0.396567i	$0.870201\pi$
$594$	−27.1383	+	43.7362i	−1.11350	+	1.79452i
$595$	−0.632916	+	0.317862i	−0.0259470	+	0.0130311i
$596$	−23.4153	+	5.23075i	−0.959126	+	0.214260i
$597$	19.6274	+	36.2912i	0.803294	+	1.48530i
$598$	−1.24010	+	0.112535i	−0.0507116	+	0.00460190i
$599$	1.80632	+	16.3712i	0.0738043	+	0.668907i	0.972911	+	0.231178i	$0.0742581\pi$
$599$	1.80632	+	16.3712i	0.0738043	+	0.668907i	−0.899107	+	0.437729i	$0.855783\pi$
$600$	0.453271	−	0.606355i	0.0185047	−	0.0247543i
$601$	−2.69794	−	0.244828i	−0.110051	−	0.00998675i	0.0352115	−	0.999380i	$-0.488790\pi$
$601$	−2.69794	−	0.244828i	−0.110051	−	0.00998675i	−0.145263	+	0.989393i	$0.546403\pi$
$602$	0.0992168	+	5.11559i	0.00404378	+	0.208496i
$603$	−18.6143	+	9.25693i	−0.758033	+	0.376971i
$604$	−19.0540	−	23.6233i	−0.775297	−	0.961217i
$605$	−8.96080	−	36.7483i	−0.364308	−	1.49403i
$606$	−28.3754	−	4.87188i	−1.15267	−	0.197907i
$607$	13.9472	−	24.8951i	0.566099	−	1.01046i	−0.428185	−	0.903691i	$-0.640847\pi$
$607$	13.9472	−	24.8951i	0.566099	−	1.01046i	0.994284	−	0.106768i	$-0.0340502\pi$
$608$	−2.51472	−	4.22842i	−0.101985	−	0.171485i
$609$	2.91535	−	0.527584i	0.118136	−	0.0213788i
$610$	14.0496	−	13.4278i	0.568853	−	0.543678i
$611$	12.9214	−	2.02086i	0.522742	−	0.0817554i
$612$	−3.68327	−	1.86799i	−0.148887	−	0.0755091i
$613$	−6.19807	+	3.74056i	−0.250338	+	0.151080i	−0.636317	−	0.771428i	$-0.719543\pi$
$613$	−6.19807	+	3.74056i	−0.250338	+	0.151080i	0.385979	+	0.922508i	$0.373864\pi$
$614$	17.0210	−	24.1421i	0.686913	−	0.974296i
$615$	2.00594	+	35.6487i	0.0808874	+	1.43749i
$616$	−1.00968	+	0.741585i	−0.0406812	+	0.0298793i
$617$	5.27718	−	11.4131i	0.212451	−	0.459475i	−0.771888	−	0.635759i	$-0.780687\pi$
$617$	5.27718	−	11.4131i	0.212451	−	0.459475i	0.984339	+	0.176284i	$0.0564076\pi$
$618$	7.64544	−	2.54416i	0.307545	−	0.102341i
$619$	−27.1255	−	29.5064i	−1.09026	−	1.18596i	−0.981414	−	0.191903i	$-0.938534\pi$
$619$	−27.1255	−	29.5064i	−1.09026	−	1.18596i	−0.108851	−	0.994058i	$-0.534717\pi$
$620$	1.03949	−	17.8473i	0.0417468	−	0.716765i
$621$	0.653042	+	0.232504i	0.0262057	+	0.00933008i
$622$	−3.08807	−	53.0201i	−0.123820	−	2.12591i
$623$	2.91663	−	3.01245i	0.116852	−	0.120691i
$624$	−36.3286	+	13.6753i	−1.45431	+	0.547451i
$625$	−10.3505	−	25.8103i	−0.414019	−	1.03241i
$626$	−20.4504	−	57.3377i	−0.817364	−	2.29167i
$627$	5.96070	−	0.451508i	0.238048	−	0.0180315i
$628$	2.15810	−	14.4083i	0.0861175	−	0.574954i
$629$	−3.98578	−	2.84886i	−0.158923	−	0.113592i
$630$	−3.15418	+	3.68059i	−0.125666	+	0.146638i
$631$	−12.2659	−	12.0304i	−0.488300	−	0.478921i	0.413849	−	0.910345i	$-0.364184\pi$
$631$	−12.2659	−	12.0304i	−0.488300	−	0.478921i	−0.902149	+	0.431424i	$0.858011\pi$
$632$	−1.06017	+	4.60566i	−0.0421711	+	0.183203i
$633$	−17.9103	−	12.1658i	−0.711871	−	0.483547i
$634$	1.53629	+	4.90010i	0.0610140	+	0.194608i
$635$	−12.1802	+	42.6858i	−0.483358	+	1.69393i
$636$	23.6343	+	23.8813i	0.937160	+	0.946956i
$637$	−11.2884	+	31.6496i	−0.447262	+	1.25400i
$638$	−47.5321	+	1.84446i	−1.88182	+	0.0730230i
$639$	−3.68118	−	2.95382i	−0.145625	−	0.116851i
$640$	11.7388	+	4.79583i	0.464017	+	0.189572i
$641$	−10.6910	−	6.64208i	−0.422268	−	0.262346i	0.300029	−	0.953930i	$-0.403004\pi$
$641$	−10.6910	−	6.64208i	−0.422268	−	0.262346i	−0.722296	+	0.691584i	$0.756913\pi$
$642$	−10.4206	+	0.383837i	−0.411267	+	0.0151488i
$643$	−36.2444	+	15.3572i	−1.42934	+	0.605628i	−0.960656	−	0.277739i	$-0.910415\pi$
$643$	−36.2444	+	15.3572i	−1.42934	+	0.605628i	−0.468681	+	0.883367i	$0.655271\pi$
$644$	−0.0585614	−	0.0517770i	−0.00230764	−	0.00204030i
$645$	3.33496	+	30.7809i	0.131314	+	1.21200i
$646$	0.171004	+	1.04894i	0.00672807	+	0.0412699i
$647$	−0.908653	+	0.330723i	−0.0357228	+	0.0130020i	−0.359820	−	0.933022i	$-0.617162\pi$
$647$	−0.908653	+	0.330723i	−0.0357228	+	0.0130020i	0.324097	+	0.946024i	$0.394940\pi$
$648$	6.08450	+	0.441965i	0.239022	+	0.0173620i
$649$	−10.9645	−	3.99074i	−0.430393	−	0.156650i
$650$	1.12167	−	5.91323i	0.0439956	−	0.231936i
$651$	0.351261	−	2.80027i	0.0137670	−	0.109751i
$652$	−26.9202	+	21.4275i	−1.05428	+	0.839167i
$653$	−18.0973	−	27.9069i	−0.708203	−	1.09208i	−0.991124	−	0.132938i	$-0.957559\pi$
$653$	−18.0973	−	27.9069i	−0.708203	−	1.09208i	0.282922	−	0.959143i	$-0.408696\pi$
$654$	−60.1867	−	4.79721i	−2.35349	−	0.187586i
$655$	−13.3053	−	2.79219i	−0.519880	−	0.109100i
$656$	−37.8740	+	12.1438i	−1.47873	+	0.474136i
$657$	−26.5887	+	8.03349i	−1.03733	+	0.313416i
$658$	1.43790	+	1.11446i	0.0560552	+	0.0434460i
$659$	−4.77085	+	5.76090i	−0.185846	+	0.224413i	−0.854889	−	0.518811i	$-0.826375\pi$
$659$	−4.77085	+	5.76090i	−0.185846	+	0.224413i	0.669043	+	0.743224i	$0.266704\pi$
$660$	26.3582	−	23.2124i	1.02599	−	0.903540i
$661$	−21.9168	−	10.6545i	−0.852466	−	0.414412i	−0.0412429	−	0.999149i	$-0.513132\pi$
$661$	−21.9168	−	10.6545i	−0.852466	−	0.414412i	−0.811223	+	0.584737i	$0.801198\pi$
$662$	−14.0672	+	7.29405i	−0.546737	+	0.283491i
$663$	7.08583	+	0.105555i	0.275191	+	0.00409942i
$664$	0.457426	+	3.70563i	0.0177516	+	0.143806i
$665$	0.561250	+	0.0436238i	0.0217643	+	0.00169166i
$666$	−32.6945	−	7.43881i	−1.26689	−	0.288248i
$667$	0.159797	+	0.620372i	0.00618738	+	0.0240209i
$668$	0.589010	−	1.08399i	0.0227895	−	0.0419407i
$669$	15.7148	+	18.0788i	0.607567	+	0.698966i
$670$	30.9900	−	5.25805i	1.19725	−	0.203136i
$671$	−18.8826	+	11.7314i	−0.728956	+	0.452886i
$672$	−4.09995	−	2.00310i	−0.158159	−	0.0772714i
$673$	−16.4928	+	36.9149i	−0.635750	+	1.42296i	0.254310	+	0.967123i	$0.418152\pi$
$673$	−16.4928	+	36.9149i	−0.635750	+	1.42296i	−0.890061	+	0.455842i	$0.849338\pi$
$674$	9.40734	+	9.97119i	0.362357	+	0.384076i
$675$	−1.94680	+	2.72696i	−0.0749323	+	0.104961i
$676$	−12.3067	+	13.0443i	−0.473333	+	0.501704i
$677$	−7.31618	−	17.5824i	−0.281184	−	0.675747i	0.718623	−	0.695400i	$-0.244773\pi$
$677$	−7.31618	−	17.5824i	−0.281184	−	0.675747i	−0.999807	+	0.0196531i	$0.993744\pi$
$678$	−19.4637	−	27.7224i	−0.747500	−	1.06467i
$679$	2.49791	+	1.73705i	0.0958611	+	0.0666620i
$680$	−0.974323	−	0.931204i	−0.0373636	−	0.0357100i
$681$	40.8069	−	20.3936i	1.56372	−	0.781483i
$682$	−11.8691	+	43.7301i	−0.454490	+	1.67451i
$683$	−2.39564	+	7.00152i	−0.0916666	+	0.267906i	−0.982451	−	0.186520i	$-0.940279\pi$
$683$	−2.39564	+	7.00152i	−0.0916666	+	0.267906i	0.890785	+	0.454426i	$0.150156\pi$
$684$	1.73934	+	2.78388i	0.0665054	+	0.106444i
$685$	5.17449	+	3.12282i	0.197707	+	0.119317i
$686$	−8.63863	+	3.79276i	−0.329824	+	0.144808i
$687$	6.33279	−	4.75900i	0.241611	−	0.181567i
$688$	−32.2536	+	12.2138i	−1.22966	+	0.465649i
$689$	−54.4274	−	19.0168i	−2.07352	−	0.724481i
$690$	−0.843519	−	0.622101i	−0.0321122	−	0.0236830i
$691$	−16.6312	−	24.9340i	−0.632681	−	0.948533i	−0.999831	−	0.0183709i	$-0.994152\pi$
$691$	−16.6312	−	24.9340i	−0.632681	−	0.948533i	0.367150	−	0.930162i	$-0.380334\pi$
$692$	−15.9247	−	3.12751i	−0.605367	−	0.118890i
$693$	4.39567	−	3.37930i	0.166978	−	0.128369i
$694$	34.0995	−	42.2767i	1.29440	−	1.60480i
$695$	22.3711	+	10.5200i	0.848583	+	0.399045i
$696$	2.80931	+	4.88805i	0.106487	+	0.185281i
$697$	7.24598	+	0.469047i	0.274461	+	0.0177664i
$698$	−12.3038	−	45.3317i	−0.465705	−	1.71583i
$699$	−20.1544	+	4.18813i	−0.762309	+	0.158410i
$700$	0.318328	−	0.203521i	0.0120317	−	0.00769238i
$701$	6.47932	−	15.0208i	0.244721	−	0.567326i	−0.750941	−	0.660369i	$-0.770400\pi$
$701$	6.47932	−	15.0208i	0.244721	−	0.567326i	0.995662	+	0.0930425i	$0.0296592\pi$
$702$	45.0055	−	18.0776i	1.69862	−	0.682294i
$703$	1.54237	+	3.57561i	0.0581715	+	0.134857i
$704$	21.2836	+	14.3960i	0.802154	+	0.542570i
$705$	9.26313	+	5.94803i	0.348870	+	0.224016i
$706$	−12.2877	+	37.4877i	−0.462455	+	1.41087i
$707$	2.67573	+	1.56798i	0.100631	+	0.0589701i
$708$	−0.854621	−	6.35007i	−0.0321186	−	0.238650i
$709$	39.9098	+	13.3680i	1.49884	+	0.502045i	0.944010	−	0.329916i	$-0.107020\pi$
$709$	39.9098	+	13.3680i	1.49884	+	0.502045i	0.554834	+	0.831961i	$0.312782\pi$
$710$	4.03631	+	5.88508i	0.151480	+	0.220863i
$711$	4.24417	−	20.4819i	0.159169	−	0.768130i
$712$	7.26386	+	3.30183i	0.272225	+	0.123741i
$713$	0.609428	+	0.0315437i	0.0228232	+	0.00118132i
$714$	0.665711	+	0.727009i	0.0249136	+	0.0272076i
$715$	−23.1533	+	55.6426i	−0.865886	+	2.08092i
$716$	7.21330	+	16.1451i	0.269574	+	0.603372i
$717$	35.1325	−	18.7082i	1.31205	−	0.698669i
$718$	−36.7169	−	20.8832i	−1.37026	−	0.779355i
$719$	48.4956	+	15.5495i	1.80858	+	0.579898i	0.999964	−	0.00844093i	$-0.00268686\pi$
$719$	48.4956	+	15.5495i	1.80858	+	0.579898i	0.808615	+	0.588338i	$0.200218\pi$
$720$	−30.5101	−	11.6911i	−1.13704	−	0.435700i
$721$	−0.867311	−	0.0336556i	−0.0323004	−	0.00125340i
$722$	−13.1872	+	32.8840i	−0.490776	+	1.22382i
$723$	−27.9910	−	16.9679i	−1.04100	−	0.631042i
$724$	−19.2548	−	5.90040i	−0.715599	−	0.219287i
$725$	−3.09541	−	0.0800551i	−0.114961	−	0.00297317i
$726$	−45.8127	+	25.9375i	−1.70027	+	0.962629i
$727$	37.1505	+	0.480322i	1.37784	+	0.0178141i	0.698288	−	0.715817i	$-0.253946\pi$
$727$	37.1505	+	0.480322i	1.37784	+	0.0178141i	0.679548	+	0.733631i	$0.262176\pi$
$728$	1.18044			0.0437500
$729$	−26.9655	−	1.36530i	−0.998721	−	0.0505665i
$730$	41.9969			1.55438
$731$	6.29586	+	0.0813997i	0.232861	+	0.00301068i
$732$	−10.5199	−	6.19253i	−0.388828	−	0.228883i
$733$	−11.7340	−	0.303470i	−0.433405	−	0.0112089i	−0.191463	−	0.981500i	$-0.561323\pi$
$733$	−11.7340	−	0.303470i	−0.433405	−	0.0112089i	−0.241942	+	0.970291i	$0.577784\pi$
$734$	41.6211	+	12.7543i	1.53626	+	0.470769i
$735$	−24.7910	+	13.6156i	−0.914431	+	0.502218i
$736$	0.367249	−	0.915783i	0.0135370	−	0.0337562i
$737$	−35.9275	−	1.39415i	−1.32341	−	0.0513542i
$738$	46.9779	−	16.2068i	1.72928	−	0.596581i
$739$	41.3227	+	13.2496i	1.52008	+	0.487394i	0.943985	−	0.329989i	$-0.107045\pi$
$739$	41.3227	+	13.2496i	1.52008	+	0.487394i	0.576095	+	0.817383i	$0.304576\pi$
$740$	19.8878	+	11.3114i	0.731089	+	0.415817i
$741$	−4.77864	−	2.98192i	−0.175548	−	0.109544i
$742$	−3.27138	−	7.32215i	−0.120096	−	0.268805i
$743$	−2.31169	+	5.55551i	−0.0848079	+	0.203812i	−0.960023	−	0.279923i	$-0.909691\pi$
$743$	−2.31169	+	5.55551i	−0.0848079	+	0.203812i	0.875215	+	0.483735i	$0.160720\pi$
$744$	5.24360	−	1.16055i	0.192240	−	0.0425477i
$745$	34.6069	+	1.79124i	1.26790	+	0.0656259i
$746$	42.8378	+	19.4721i	1.56840	+	0.712926i
$747$	−2.38352	−	16.3522i	−0.0872084	−	0.598296i
$748$	−4.03991	−	5.89033i	−0.147714	−	0.215372i
$749$	1.06510	+	0.356759i	0.0389178	+	0.0130357i
$750$	−27.0858	+	20.9079i	−0.989034	+	0.763450i
$751$	−11.6570	−	6.83103i	−0.425371	−	0.249268i	0.277300	−	0.960784i	$-0.410561\pi$
$751$	−11.6570	−	6.83103i	−0.425371	−	0.249268i	−0.702670	+	0.711516i	$0.748009\pi$
$752$	−3.81952	+	11.6527i	−0.139284	+	0.424929i
$753$	28.2145	−	14.5593i	1.02819	−	0.530570i
$754$	37.1266	+	25.1121i	1.35207	+	0.914530i
$755$	17.3624	+	40.2505i	0.631882	+	1.46487i
$756$	2.76426	+	1.27625i	0.100535	+	0.0464166i
$757$	−9.31937	+	21.6047i	−0.338718	+	0.785237i	0.660684	+	0.750664i	$0.270266\pi$
$757$	−9.31937	+	21.6047i	−0.338718	+	0.785237i	−0.999402	+	0.0345728i	$0.988993\pi$
$758$	−36.5397	+	23.3614i	−1.32718	+	0.848525i
$759$	0.798144	+	0.894586i	0.0289708	+	0.0324714i
$760$	0.280601	+	1.03384i	0.0101785	+	0.0375014i
$761$	−29.2066	−	1.89060i	−1.05874	−	0.0685342i	−0.474610	−	0.880196i	$-0.657411\pi$
$761$	−29.2066	−	1.89060i	−1.05874	−	0.0685342i	−0.584128	+	0.811662i	$0.698563\pi$
$762$	61.7820	+	0.121535i	2.23813	+	0.00440276i
$763$	5.88556	+	2.76768i	0.213072	+	0.100197i
$764$	5.77051	−	7.15431i	0.208770	−	0.258834i
$765$	4.40151	+	4.02585i	0.159137	+	0.145555i
$766$	−26.9658	−	5.29591i	−0.974315	−	0.191349i
$767$	6.10087	+	9.14659i	0.220290	+	0.330264i

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)

\(f(q)\)	\(=\)	\(q+(-1.90902 - 0.0246819i) q^{2} +(0.0146033 - 1.73199i) q^{3} +(1.64441 + 0.0425285i) q^{4} +(-2.27162 - 0.696109i) q^{5} +(-0.0706267 + 3.30604i) q^{6} +(0.132583 - 0.330612i) q^{7} +(0.677327 + 0.0262834i) q^{8} +(-2.99957 - 0.0505857i) q^{9} +O(q^{10})\)	\(q+(-1.90902 - 0.0246819i) q^{2} +(0.0146033 - 1.73199i) q^{3} +(1.64441 + 0.0425285i) q^{4} +(-2.27162 - 0.696109i) q^{5} +(-0.0706267 + 3.30604i) q^{6} +(0.132583 - 0.330612i) q^{7} +(0.677327 + 0.0262834i) q^{8} +(-2.99957 - 0.0505857i) q^{9} +(4.31938 + 1.38495i) q^{10} +(-4.51004 - 2.56515i) q^{11} +(0.0976728 - 2.84748i) q^{12} +(1.99430 + 4.46372i) q^{13} +(-0.261263 + 0.627872i) q^{14} +(-1.23883 + 3.92425i) q^{15} +(-4.57790 - 0.236950i) q^{16} +(0.761861 + 0.346308i) q^{17} +(5.72499 + 0.170604i) q^{18} +(-0.376229 - 0.548556i) q^{19} +(-3.70586 - 1.24130i) q^{20} +(-0.570681 - 0.234460i) q^{21} +(8.54644 + 5.00822i) q^{22} +(0.0415526 - 0.126769i) q^{23} +(0.0554138 - 1.17274i) q^{24} +(0.534112 + 0.361268i) q^{25} +(-3.69697 - 8.57055i) q^{26} +(-0.131418 + 5.19449i) q^{27} +(0.232081 - 0.538023i) q^{28} +(-4.04583 + 2.58668i) q^{29} +(2.46180 - 7.46089i) q^{30} +(1.19820 + 4.41462i) q^{31} +(7.38060 + 0.477761i) q^{32} +(-4.50867 + 7.77388i) q^{33} +(-1.44586 - 0.679913i) q^{34} +(-0.531320 + 0.658733i) q^{35} +(-4.93037 - 0.210751i) q^{36} +(-5.74445 - 1.12817i) q^{37} +(0.704689 + 1.05649i) q^{38} +(7.76024 - 3.38891i) q^{39} +(-1.52033 - 0.531200i) q^{40} +(8.11419 - 3.07269i) q^{41} +(1.08365 + 0.461673i) q^{42} +(6.88896 - 3.02457i) q^{43} +(-7.30726 - 4.40995i) q^{44} +(6.77867 + 2.20294i) q^{45} +(-0.0824536 + 0.240980i) q^{46} +(0.700712 - 2.58169i) q^{47} +(-0.477248 + 7.92541i) q^{48} +(4.96873 + 4.74884i) q^{49} +(-1.01071 - 0.702851i) q^{50} +(0.610928 - 1.31448i) q^{51} +(3.08960 + 7.42500i) q^{52} +(-8.09261 + 8.57766i) q^{53} +(0.379088 - 9.91313i) q^{54} +(8.45947 + 8.96651i) q^{55} +(0.0984915 - 0.220448i) q^{56} +(-0.955587 + 0.643615i) q^{57} +(7.78741 - 4.83816i) q^{58} +(2.21717 - 0.376185i) q^{59} +(-2.20403 + 6.40039i) q^{60} +(2.04561 - 3.76464i) q^{61} +(-2.17842 - 8.45716i) q^{62} +(-0.414416 + 0.984989i) q^{63} +(-4.93742 - 0.383767i) q^{64} +(-1.42304 - 11.5281i) q^{65} +(8.79900 - 14.7292i) q^{66} +(6.15186 - 3.18983i) q^{67} +(1.23808 + 0.601873i) q^{68} +(-0.218957 - 0.0738199i) q^{69} +(1.03056 - 1.24442i) q^{70} +(1.24349 + 0.963775i) q^{71} +(-2.03036 - 0.113102i) q^{72} +(8.81650 - 2.82690i) q^{73} +(10.9384 + 2.29549i) q^{74} +(0.633513 - 0.919800i) q^{75} +(-0.595346 - 0.918051i) q^{76} +(-1.44602 + 1.15098i) q^{77} +(-14.8981 + 6.27796i) q^{78} +(-1.29940 + 6.85018i) q^{79} +(10.2343 + 3.72498i) q^{80} +(8.99488 + 0.303471i) q^{81} +(-15.5660 + 5.66555i) q^{82} +(0.886303 + 5.43657i) q^{83} +(-0.928461 - 0.409818i) q^{84} +(-1.48959 - 1.31702i) q^{85} +(-13.2258 + 5.60393i) q^{86} +(4.42102 + 7.04511i) q^{87} +(-2.98735 - 1.85598i) q^{88} +(10.8971 + 4.45194i) q^{89} +(-12.8862 - 4.37277i) q^{90} +(1.74017 - 0.0675266i) q^{91} +(0.0737208 - 0.206694i) q^{92} +(7.66357 - 2.01080i) q^{93} +(-1.40139 + 4.91119i) q^{94} +(0.472795 + 1.50801i) q^{95} +(0.935259 - 12.7761i) q^{96} +(-1.91603 + 8.32379i) q^{97} +(-9.36819 - 9.18825i) q^{98} +(13.3984 + 7.92249i) 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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