LMFDB - Embedded newform 729.2.k.a.4.20

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			4.20
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63282 - 0.0211109i) q^{2} +(0.989331 - 1.42170i) q^{3} +(0.666340 + 0.0172332i) q^{4} +(-1.81802 - 0.557111i) q^{5} +(-1.64542 + 2.30050i) q^{6} +(-0.319539 + 0.796813i) q^{7} +(2.17581 + 0.0844315i) q^{8} +(-1.04245 - 2.81306i) q^{9} +O(q^{10})$	\(q+(-1.63282 - 0.0211109i) q^{2} +(0.989331 - 1.42170i) q^{3} +(0.666340 + 0.0172332i) q^{4} +(-1.81802 - 0.557111i) q^{5} +(-1.64542 + 2.30050i) q^{6} +(-0.319539 + 0.796813i) q^{7} +(2.17581 + 0.0844315i) q^{8} +(-1.04245 - 2.81306i) q^{9} +(2.95675 + 0.948044i) q^{10} +(3.32432 + 1.89075i) q^{11} +(0.683731 - 0.930285i) q^{12} +(-2.56163 - 5.73356i) q^{13} +(0.538573 - 1.29431i) q^{14} +(-2.59067 + 2.03351i) q^{15} +(-4.88228 - 0.252705i) q^{16} +(4.27192 + 1.94182i) q^{17} +(1.64275 + 4.61524i) q^{18} +(-0.598085 - 0.872029i) q^{19} +(-1.20182 - 0.402555i) q^{20} +(0.816698 + 1.24260i) q^{21} +(-5.38812 - 3.15745i) q^{22} +(1.80262 - 5.49948i) q^{23} +(2.27264 - 3.00982i) q^{24} +(-1.14674 - 0.775642i) q^{25} +(4.06166 + 9.41598i) q^{26} +(-5.03065 - 1.30100i) q^{27} +(-0.226653 + 0.525442i) q^{28} +(-4.75276 + 3.03865i) q^{29} +(4.27304 - 3.26568i) q^{30} +(-0.863028 - 3.17972i) q^{31} +(3.62077 + 0.234380i) q^{32} +(5.97693 - 2.85560i) q^{33} +(-6.93430 - 3.26084i) q^{34} +(1.02484 - 1.27061i) q^{35} +(-0.646147 - 1.89242i) q^{36} +(-9.86702 - 1.93782i) q^{37} +(0.958158 + 1.43650i) q^{38} +(-10.6857 - 2.03052i) q^{39} +(-3.90864 - 1.36567i) q^{40} +(-7.78969 + 2.94981i) q^{41} +(-1.30729 - 2.04619i) q^{42} +(3.86390 - 1.69643i) q^{43} +(2.18254 + 1.31717i) q^{44} +(0.328011 + 5.69496i) q^{45} +(-3.05947 + 8.94164i) q^{46} +(-0.341120 + 1.25682i) q^{47} +(-5.18946 + 6.69112i) q^{48} +(4.52765 + 4.32728i) q^{49} +(1.85604 + 1.29070i) q^{50} +(6.98702 - 4.15227i) q^{51} +(-1.60811 - 3.86465i) q^{52} +(-2.97902 + 3.15758i) q^{53} +(8.18670 + 2.23050i) q^{54} +(-4.99033 - 5.28945i) q^{55} +(-0.762534 + 1.70674i) q^{56} +(-1.83146 - 0.0124293i) q^{57} +(7.82458 - 4.86126i) q^{58} +(7.33969 - 1.24532i) q^{59} +(-1.76131 + 1.31036i) q^{60} +(-2.57204 + 4.73346i) q^{61} +(1.34205 + 5.21014i) q^{62} +(2.57459 + 0.0682457i) q^{63} +(3.84110 + 0.298554i) q^{64} +(1.46288 + 11.8509i) q^{65} +(-9.81957 + 4.53652i) q^{66} +(-1.93951 + 1.00566i) q^{67} +(2.81308 + 1.36753i) q^{68} +(-6.03521 - 8.00359i) q^{69} +(-1.70021 + 2.05304i) q^{70} +(-11.3409 - 8.78987i) q^{71} +(-2.03066 - 6.20871i) q^{72} +(-7.66548 + 2.45784i) q^{73} +(16.0702 + 3.37242i) q^{74} +(-2.23723 + 0.862945i) q^{75} +(-0.383500 - 0.591374i) q^{76} +(-2.56883 + 2.04469i) q^{77} +(17.4050 + 3.54107i) q^{78} +(-0.586006 + 3.08931i) q^{79} +(8.73532 + 3.17940i) q^{80} +(-6.82660 + 5.86494i) q^{81} +(12.7815 - 4.65207i) q^{82} +(-0.888150 - 5.44789i) q^{83} +(0.522784 + 0.842068i) q^{84} +(-6.68463 - 5.91021i) q^{85} +(-6.34489 + 2.68841i) q^{86} +(-0.382009 + 9.76323i) q^{87} +(7.07347 + 4.39460i) q^{88} +(-11.9092 - 4.86543i) q^{89} +(-0.415359 - 9.30580i) q^{90} +(5.38712 - 0.209045i) q^{91} +(1.29593 - 3.63346i) q^{92} +(-5.37442 - 1.91883i) q^{93} +(0.583523 - 2.04496i) q^{94} +(0.601515 + 1.91857i) q^{95} +(3.91536 - 4.91576i) q^{96} +(2.66636 - 11.5834i) q^{97} +(-7.30151 - 7.16127i) q^{98} +(1.85336 - 11.3225i) 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 $

$2$	−1.63282	−	0.0211109i	−1.15458	−	0.0149277i	−0.566735	−	0.823900i	$-0.691794\pi$
$2$	−1.63282	−	0.0211109i	−1.15458	−	0.0149277i	−0.587847	+	0.808972i	$0.700024\pi$
$3$	0.989331	−	1.42170i	0.571190	−	0.820818i
$3$	0.989331	−	1.42170i	0.571190	−	0.820818i
$4$	0.666340	+	0.0172332i	0.333170	+	0.00861661i
$5$	−1.81802	−	0.557111i	−0.813044	−	0.249147i	−0.141335	−	0.989962i	$-0.545139\pi$
$5$	−1.81802	−	0.557111i	−0.813044	−	0.249147i	−0.671710	+	0.740814i	$0.734440\pi$
$6$	−1.64542	+	2.30050i	−0.671739	+	0.939174i
$7$	−0.319539	+	0.796813i	−0.120775	+	0.301167i	−0.976240	−	0.216693i	$-0.930473\pi$
$7$	−0.319539	+	0.796813i	−0.120775	+	0.301167i	0.855465	+	0.517860i	$0.173271\pi$
$8$	2.17581	+	0.0844315i	0.769266	+	0.0298510i
$9$	−1.04245	−	2.81306i	−0.347483	−	0.937686i
$10$	2.95675	+	0.948044i	0.935007	+	0.299798i
$11$	3.32432	+	1.89075i	1.00232	+	0.570083i	0.905109	−	0.425180i	$-0.139789\pi$
$11$	3.32432	+	1.89075i	1.00232	+	0.570083i	0.0972122	+	0.995264i	$0.469007\pi$
$12$	0.683731	−	0.930285i	0.197376	−	0.268550i
$13$	−2.56163	−	5.73356i	−0.710469	−	1.59020i	−0.804029	−	0.594590i	$-0.797314\pi$
$13$	−2.56163	−	5.73356i	−0.710469	−	1.59020i	0.0935594	−	0.995614i	$-0.470175\pi$
$14$	0.538573	−	1.29431i	0.143940	−	0.345919i
$15$	−2.59067	+	2.03351i	−0.668908	+	0.525051i
$16$	−4.88228	−	0.252705i	−1.22057	−	0.0631763i
$17$	4.27192	+	1.94182i	1.03609	+	0.470961i	0.858322	−	0.513111i	$-0.171507\pi$
$17$	4.27192	+	1.94182i	1.03609	+	0.470961i	0.177769	+	0.984072i	$0.443112\pi$
$18$	1.64275	+	4.61524i	0.387200	+	1.08782i
$19$	−0.598085	−	0.872029i	−0.137210	−	0.200057i	0.749981	−	0.661459i	$-0.230063\pi$
$19$	−0.598085	−	0.872029i	−0.137210	−	0.200057i	−0.887191	+	0.461402i	$0.847347\pi$
$20$	−1.20182	−	0.402555i	−0.268735	−	0.0900141i
$21$	0.816698	+	1.24260i	0.178218	+	0.271158i
$22$	−5.38812	−	3.15745i	−1.14875	−	0.673170i
$23$	1.80262	−	5.49948i	0.375873	−	1.14672i	−0.569850	−	0.821749i	$-0.692999\pi$
$23$	1.80262	−	5.49948i	0.375873	−	1.14672i	0.945723	−	0.324973i	$-0.105355\pi$
$24$	2.27264	−	3.00982i	0.463900	−	0.614377i
$25$	−1.14674	−	0.775642i	−0.229347	−	0.155128i
$26$	4.06166	+	9.41598i	0.796557	+	1.84663i
$27$	−5.03065	−	1.30100i	−0.968148	−	0.250377i
$28$	−0.226653	+	0.525442i	−0.0428335	+	0.0992992i
$29$	−4.75276	+	3.03865i	−0.882566	+	0.564264i	−0.900149	−	0.435581i	$-0.856543\pi$
$29$	−4.75276	+	3.03865i	−0.882566	+	0.564264i	0.0175830	+	0.999845i	$0.494403\pi$
$30$	4.27304	−	3.26568i	0.780146	−	0.596228i
$31$	−0.863028	−	3.17972i	−0.155004	−	0.571094i	−0.999375	−	0.0353357i	$-0.988750\pi$
$31$	−0.863028	−	3.17972i	−0.155004	−	0.571094i	0.844371	−	0.535759i	$-0.179974\pi$
$32$	3.62077	+	0.234380i	0.640068	+	0.0414329i
$33$	5.97693	−	2.85560i	1.04045	−	0.497096i
$34$	−6.93430	−	3.26084i	−1.18922	−	0.559230i
$35$	1.02484	−	1.27061i	0.173230	−	0.214772i
$36$	−0.646147	−	1.89242i	−0.107691	−	0.315403i
$37$	−9.86702	−	1.93782i	−1.62213	−	0.318576i	−0.702596	−	0.711589i	$-0.747976\pi$
$37$	−9.86702	−	1.93782i	−1.62213	−	0.318576i	−0.919533	+	0.393013i	$0.871433\pi$
$38$	0.958158	+	1.43650i	0.155434	+	0.233030i
$39$	−10.6857	−	2.03052i	−1.71108	−	0.325144i
$40$	−3.90864	−	1.36567i	−0.618010	−	0.215931i
$41$	−7.78969	+	2.94981i	−1.21654	+	0.460683i	−0.877267	−	0.480003i	$-0.840635\pi$
$41$	−7.78969	+	2.94981i	−1.21654	+	0.460683i	−0.339278	+	0.940686i	$0.610183\pi$
$42$	−1.30729	−	2.04619i	−0.201719	−	0.315734i
$43$	3.86390	−	1.69643i	0.589240	−	0.258704i	−0.0860081	−	0.996294i	$-0.527411\pi$
$43$	3.86390	−	1.69643i	0.589240	−	0.258704i	0.675248	+	0.737591i	$0.264037\pi$
$44$	2.18254	+	1.31717i	0.329031	+	0.198571i
$45$	0.328011	+	5.69496i	0.0488970	+	0.848955i
$46$	−3.05947	+	8.94164i	−0.451094	+	1.31837i
$47$	−0.341120	+	1.25682i	−0.0497575	+	0.183325i	−0.985600	−	0.169093i	$-0.945916\pi$
$47$	−0.341120	+	1.25682i	−0.0497575	+	0.183325i	0.935843	+	0.352418i	$0.114641\pi$
$48$	−5.18946	+	6.69112i	−0.749035	+	0.965780i
$49$	4.52765	+	4.32728i	0.646807	+	0.618183i
$50$	1.85604	+	1.29070i	0.262484	+	0.182532i
$51$	6.98702	−	4.15227i	0.978379	−	0.581434i
$52$	−1.60811	−	3.86465i	−0.223005	−	0.535930i
$53$	−2.97902	+	3.15758i	−0.409200	+	0.433727i	−0.898893	−	0.438168i	$-0.855627\pi$
$53$	−2.97902	+	3.15758i	−0.409200	+	0.433727i	0.489693	+	0.871895i	$0.337109\pi$
$54$	8.18670	+	2.23050i	1.11407	+	0.303533i
$55$	−4.99033	−	5.28945i	−0.672897	−	0.713229i
$56$	−0.762534	+	1.70674i	−0.101898	+	0.228072i
$57$	−1.83146	−	0.0124293i	−0.242583	−	0.00164630i
$58$	7.82458	−	4.86126i	1.02742	−	0.638314i
$59$	7.33969	−	1.24532i	0.955546	−	0.162127i	0.331449	−	0.943473i	$-0.392463\pi$
$59$	7.33969	−	1.24532i	0.955546	−	0.162127i	0.624098	+	0.781346i	$0.285467\pi$
$60$	−1.76131	+	1.31036i	−0.227384	+	0.169167i
$61$	−2.57204	+	4.73346i	−0.329316	+	0.606058i	−0.989414	−	0.145122i	$-0.953643\pi$
$61$	−2.57204	+	4.73346i	−0.329316	+	0.606058i	0.660097	+	0.751180i	$0.270515\pi$
$62$	1.34205	+	5.21014i	0.170440	+	0.661689i
$63$	2.57459	+	0.0682457i	0.324367	+	0.00859815i
$64$	3.84110	+	0.298554i	0.480137	+	0.0373192i
$65$	1.46288	+	11.8509i	0.181448	+	1.46992i
$66$	−9.81957	+	4.53652i	−1.20871	+	0.558407i
$67$	−1.93951	+	1.00566i	−0.236948	+	0.122861i	−0.574671	−	0.818384i	$-0.694870\pi$
$67$	−1.93951	+	1.00566i	−0.236948	+	0.122861i	0.337723	+	0.941246i	$0.390343\pi$
$68$	2.81308	+	1.36753i	0.341137	+	0.165838i
$69$	−6.03521	−	8.00359i	−0.726554	−	0.963519i
$70$	−1.70021	+	2.05304i	−0.203214	+	0.245385i
$71$	−11.3409	−	8.78987i	−1.34592	−	1.04317i	−0.994255	−	0.107039i	$-0.965863\pi$
$71$	−11.3409	−	8.78987i	−1.34592	−	1.04317i	−0.351664	−	0.936126i	$-0.614384\pi$
$72$	−2.03066	−	6.20871i	−0.239316	−	0.731703i
$73$	−7.66548	+	2.45784i	−0.897176	+	0.287668i	−0.717913	−	0.696133i	$-0.754902\pi$
$73$	−7.66548	+	2.45784i	−0.897176	+	0.287668i	−0.179263	+	0.983801i	$0.557371\pi$
$74$	16.0702	+	3.37242i	1.86812	+	0.392036i
$75$	−2.23723	+	0.862945i	−0.258333	+	0.0996444i
$76$	−0.383500	−	0.591374i	−0.0439904	−	0.0678353i
$77$	−2.56883	+	2.04469i	−0.292745	+	0.233015i
$78$	17.4050	+	3.54107i	1.97073	+	0.400947i
$79$	−0.586006	+	3.08931i	−0.0659308	+	0.347574i	−0.999954	−	0.00963939i	$-0.996932\pi$
$79$	−0.586006	+	3.08931i	−0.0659308	+	0.347574i	0.934023	+	0.357214i	$0.116273\pi$
$80$	8.73532	+	3.17940i	0.976638	+	0.355467i
$81$	−6.82660	+	5.86494i	−0.758511	+	0.651660i
$82$	12.7815	−	4.65207i	1.41148	−	0.513736i
$83$	−0.888150	−	5.44789i	−0.0974871	−	0.597984i	−0.989336	−	0.145651i	$-0.953472\pi$
$83$	−0.888150	−	5.44789i	−0.0974871	−	0.597984i	0.891849	−	0.452333i	$-0.149408\pi$
$84$	0.522784	+	0.842068i	0.0570404	+	0.0918772i
$85$	−6.68463	−	5.91021i	−0.725050	−	0.641052i
$86$	−6.34489	+	2.68841i	−0.684187	+	0.289898i
$87$	−0.382009	+	9.76323i	−0.0409556	+	1.04673i
$88$	7.07347	+	4.39460i	0.754034	+	0.468466i
$89$	−11.9092	−	4.86543i	−1.26237	−	0.515735i	−0.354527	−	0.935046i	$-0.615358\pi$
$89$	−11.9092	−	4.86543i	−1.26237	−	0.515735i	−0.907843	+	0.419311i	$0.862272\pi$
$90$	−0.415359	−	9.30580i	−0.0437826	−	0.980918i
$91$	5.38712	−	0.209045i	0.564724	−	0.0219139i
$92$	1.29593	−	3.63346i	0.135110	−	0.378814i
$93$	−5.37442	−	1.91883i	−0.557301	−	0.198973i
$94$	0.583523	−	2.04496i	0.0601858	−	0.210921i
$95$	0.601515	+	1.91857i	0.0617141	+	0.196841i
$96$	3.91536	−	4.91576i	0.399610	−	0.501713i
$97$	2.66636	−	11.5834i	0.270728	−	1.17612i	−0.641724	−	0.766936i	$-0.721781\pi$
$97$	2.66636	−	11.5834i	0.270728	−	1.17612i	0.912452	−	0.409184i	$-0.134186\pi$
$98$	−7.30151	−	7.16127i	−0.737564	−	0.723397i
$99$	1.85336	−	11.3225i	0.186270	−	1.13796i
$100$	−0.750749	−	0.536603i	−0.0750749	−	0.0536603i
$101$	1.47421	−	9.84242i	0.146690	−	0.979358i	−0.785883	−	0.618375i	$-0.787791\pi$
$101$	1.47421	−	9.84242i	0.146690	−	0.979358i	0.932573	−	0.360982i	$-0.117559\pi$
$102$	−11.4962	+	6.63242i	−1.13830	+	0.656708i
$103$	−3.74269	−	10.4935i	−0.368778	−	1.03396i	−0.971713	−	0.236167i	$-0.924109\pi$
$103$	−3.74269	−	10.4935i	−0.368778	−	1.03396i	0.602934	−	0.797791i	$-0.293998\pi$
$104$	−5.08954	−	12.6914i	−0.499071	−	1.24450i
$105$	−0.792509	−	2.71407i	−0.0773409	−	0.264866i
$106$	4.93088	−	5.09288i	0.478930	−	0.494665i
$107$	0.762212	+	13.0867i	0.0736858	+	1.26514i	0.809162	+	0.587586i	$0.199922\pi$
$107$	0.762212	+	13.0867i	0.0736858	+	1.26514i	−0.735476	+	0.677551i	$0.763041\pi$
$108$	−3.32970	−	0.953601i	−0.320401	−	0.0917603i
$109$	0.700161	−	12.0213i	0.0670633	−	1.15143i	−0.782048	−	0.623218i	$-0.785825\pi$
$109$	0.700161	−	12.0213i	0.0670633	−	1.15143i	0.849111	−	0.528214i	$-0.177138\pi$
$110$	8.03668	+	8.74209i	0.766267	+	0.833525i
$111$	−12.5167	+	12.1108i	−1.18804	+	1.14950i
$112$	1.76144	−	3.80952i	0.166440	−	0.359966i
$113$	3.48002	−	2.55598i	0.327373	−	0.240447i	−0.415938	−	0.909393i	$-0.636547\pi$
$113$	3.48002	−	2.55598i	0.327373	−	0.240447i	0.743311	+	0.668946i	$0.233254\pi$
$114$	2.99020	+	0.0589588i	0.280058	+	0.00552200i
$115$	−6.34103	+	8.99392i	−0.591304	+	0.838687i
$116$	−3.21932	+	1.94287i	−0.298907	+	0.180391i
$117$	−13.4585	+	13.1830i	−1.24424	+	1.21877i
$118$	−12.0107	+	1.87844i	−1.10568	+	0.172925i
$119$	−2.91232	+	2.78343i	−0.266972	+	0.255157i
$120$	−5.80851	+	4.20581i	−0.530242	+	0.383936i
$121$	1.85348	+	3.11656i	0.168498	+	0.283324i
$122$	4.29962	−	7.67462i	0.389270	−	0.694827i
$123$	−3.51284	+	13.9929i	−0.316742	+	1.26170i
$124$	−0.520273	−	2.13365i	−0.0467219	−	0.191607i
$125$	7.62149	+	9.44917i	0.681687	+	0.845160i
$126$	−4.20241	−	0.165785i	−0.374380	−	0.0147693i
$127$	−0.0678820	−	3.49998i	−0.00602355	−	0.310573i	−0.990691	−	0.136130i	$-0.956533\pi$
$127$	−0.0678820	−	3.49998i	−0.00602355	−	0.310573i	0.984667	−	0.174442i	$-0.0558123\pi$
$128$	−13.4925	−	1.22440i	−1.19258	−	0.108223i
$129$	1.41086	−	7.17164i	0.124220	−	0.631428i
$130$	−2.13844	−	19.3813i	−0.187554	−	1.69985i
$131$	18.6735	−	1.69455i	1.63151	−	0.148054i	0.763912	−	0.645320i	$-0.223276\pi$
$131$	18.6735	−	1.69455i	1.63151	−	0.148054i	0.867598	+	0.497267i	$0.165663\pi$
$132$	4.03188	−	1.79980i	0.350930	−	0.156652i
$133$	0.885955	−	0.197914i	0.0768221	−	0.0171613i
$134$	3.18810	−	1.60113i	0.275410	−	0.138316i
$135$	8.42103	+	5.16787i	0.724767	+	0.444779i
$136$	9.13094	+	4.58573i	0.782972	+	0.393223i
$137$	−1.66449	−	0.417291i	−0.142207	−	0.0356516i	0.171418	−	0.985198i	$-0.445165\pi$
$137$	−1.66449	−	0.417291i	−0.142207	−	0.0356516i	−0.313625	+	0.949547i	$0.601544\pi$
$138$	9.68548	+	13.1959i	0.824482	+	1.12331i
$139$	−17.4637	−	2.50043i	−1.48125	−	0.212083i	−0.646586	−	0.762841i	$-0.723804\pi$
$139$	−17.4637	−	2.50043i	−1.48125	−	0.212083i	−0.834665	+	0.550758i	$0.814339\pi$
$140$	0.704790	−	0.828994i	0.0595656	−	0.0700628i
$141$	1.44933	+	1.72838i	0.122056	+	0.145556i
$142$	18.3322	+	14.5917i	1.53840	+	1.22451i
$143$	2.32505	−	23.9036i	0.194431	−	1.99892i
$144$	4.37866	+	13.9976i	0.364888	+	1.16647i
$145$	10.3335	−	2.87653i	0.858150	−	0.238883i
$146$	12.5683	−	3.85139i	1.04016	−	0.318743i
$147$	10.6314	−	2.15584i	0.876865	−	0.177811i
$148$	−6.54140	−	1.46129i	−0.537700	−	0.120117i
$149$	14.5965	−	3.65936i	1.19579	−	0.299787i	0.406410	−	0.913691i	$-0.366780\pi$
$149$	14.5965	−	3.65936i	1.19579	−	0.299787i	0.789381	+	0.613904i	$0.210402\pi$
$150$	3.67122	−	1.36181i	0.299754	−	0.111191i
$151$	6.92680	+	8.14749i	0.563695	+	0.663034i	0.967812	−	0.251673i	$-0.0809809\pi$
$151$	6.92680	+	8.14749i	0.563695	+	0.663034i	−0.404117	+	0.914707i	$0.632421\pi$
$152$	−1.22769	−	1.94787i	−0.0995791	−	0.157993i
$153$	1.00921	−	14.0414i	0.0815898	−	1.13518i
$154$	4.23761	−	3.28440i	0.341477	−	0.264664i
$155$	−0.202451	+	6.26160i	−0.0162613	+	0.502944i
$156$	−7.08531	−	1.53717i	−0.567279	−	0.123072i
$157$	0.388982	−	3.15117i	0.0310442	−	0.251490i	−0.968947	−	0.247269i	$-0.920467\pi$
$157$	0.388982	−	3.15117i	0.0310442	−	0.251490i	0.999991	−	0.00422162i	$-0.00134379\pi$
$158$	1.02206	−	5.03193i	0.0813110	−	0.400319i
$159$	1.54188	+	7.35916i	0.122279	+	0.583619i
$160$	−6.45207	−	2.44328i	−0.510081	−	0.193158i
$161$	3.80605	+	3.19366i	0.299959	+	0.251695i
$162$	11.2705	−	9.43231i	0.885491	−	0.741072i
$163$	8.31929	−	6.98071i	0.651617	−	0.546771i	−0.255944	−	0.966692i	$-0.582386\pi$
$163$	8.31929	−	6.98071i	0.651617	−	0.546771i	0.907561	+	0.419920i	$0.137942\pi$
$164$	−5.24141	+	1.83133i	−0.409286	+	0.143003i
$165$	−12.4571	+	1.86174i	−0.969783	+	0.144936i
$166$	1.33518	+	8.91421i	0.103630	+	0.691877i
$167$	2.58378	−	5.06285i	0.199939	−	0.391775i	−0.768937	−	0.639325i	$-0.779214\pi$
$167$	2.58378	−	5.06285i	0.199939	−	0.391775i	0.968875	+	0.247550i	$0.0796254\pi$
$168$	1.67207	+	2.77262i	0.129003	+	0.213912i
$169$	−17.6381	+	19.6912i	−1.35678	+	1.51471i
$170$	10.7901	+	9.79145i	0.827560	+	0.750970i
$171$	−1.82960	+	2.59149i	−0.139913	+	0.198176i
$172$	2.60391	−	1.06381i	0.198546	−	0.0811150i
$173$	21.4079	+	3.63226i	1.62761	+	0.276156i	0.908234	−	0.418464i	$-0.137431\pi$
$173$	21.4079	+	3.63226i	1.62761	+	0.276156i	0.719378	+	0.694619i	$0.244427\pi$
$174$	0.829864	−	15.9336i	0.0629119	−	1.20792i
$175$	0.984469	−	0.665886i	0.0744189	−	0.0503363i
$176$	−15.7525	−	10.0713i	−1.18739	−	0.759150i
$177$	5.49091	−	11.6669i	0.412722	−	0.876934i
$178$	19.3429	+	8.19581i	1.44981	+	0.614302i
$179$	−3.89898	−	8.15403i	−0.291424	−	0.609461i	0.703432	−	0.710762i	$-0.251650\pi$
$179$	−3.89898	−	8.15403i	−0.291424	−	0.609461i	−0.994856	+	0.101302i	$0.967699\pi$
$180$	0.120424	+	3.80043i	0.00897590	+	0.283268i
$181$	8.98053	+	2.49990i	0.667518	+	0.185816i	0.585323	−	0.810800i	$-0.300968\pi$
$181$	8.98053	+	2.49990i	0.667518	+	0.185816i	0.0821944	+	0.996616i	$0.473807\pi$
$182$	−8.80064	+	0.227606i	−0.652347	+	0.0168713i
$183$	4.18495	+	8.33963i	0.309361	+	0.616483i
$184$	4.38650	−	11.8137i	0.323377	−	0.870914i
$185$	16.8589	+	9.02002i	1.23949	+	0.663165i
$186$	8.73498	+	3.24657i	0.640480	+	0.238050i
$187$	10.5297	+	14.5324i	0.770009	+	1.06271i
$188$	−0.248961	+	0.831588i	−0.0181574	+	0.0606498i
$189$	2.64414	−	3.59277i	0.192333	−	0.261335i
$190$	−0.941666	−	3.14538i	−0.0683156	−	0.228190i
$191$	−4.49516	+	5.87785i	−0.325258	+	0.425306i	−0.927971	−	0.372652i	$-0.878449\pi$
$191$	−4.49516	+	5.87785i	−0.325258	+	0.425306i	0.602713	+	0.797958i	$0.294086\pi$
$192$	4.22457	−	5.16551i	0.304882	−	0.372789i
$193$	6.45517	−	3.03553i	0.464653	−	0.218502i	−0.178956	−	0.983857i	$-0.557272\pi$
$193$	6.45517	−	3.03553i	0.464653	−	0.218502i	0.643609	+	0.765355i	$0.277436\pi$
$194$	−4.59824	+	18.8574i	−0.330134	+	1.35388i
$195$	18.2956	+	9.64465i	1.31018	+	0.690668i
$196$	2.94238	+	2.96146i	0.210170	+	0.211533i
$197$	5.80372	−	1.13981i	0.413498	−	0.0812084i	0.0183630	−	0.999831i	$-0.494155\pi$
$197$	5.80372	−	1.13981i	0.413498	−	0.0812084i	0.395135	+	0.918623i	$0.370698\pi$
$198$	−3.26524	+	18.4486i	−0.232051	+	1.31108i
$199$	−15.0720	+	8.31637i	−1.06843	+	0.589532i	−0.916980	−	0.398934i	$-0.869380\pi$
$199$	−15.0720	+	8.31637i	−1.06843	+	0.589532i	−0.151445	+	0.988466i	$0.548393\pi$
$200$	−2.42960	−	1.78447i	−0.171798	−	0.126181i
$201$	−0.489065	+	3.75232i	−0.0344960	+	0.264668i
$202$	−2.61491	+	16.0398i	−0.183985	+	1.12856i
$203$	−0.902545	−	4.75804i	−0.0633462	−	0.333949i
$204$	4.72729	−	2.64641i	0.330976	−	0.185286i
$205$	15.8052	−	1.02310i	1.10388	−	0.0714565i
$206$	5.88963	+	17.2131i	0.410350	+	1.19929i
$207$	−17.3495	+	0.662041i	−1.20587	+	0.0460150i
$208$	11.0577	+	28.6402i	0.766715	+	1.98584i
$209$	−0.339436	−	4.02973i	−0.0234792	−	0.278743i
$210$	1.23673	+	4.44833i	0.0853426	+	0.306964i
$211$	−10.2690	+	15.3956i	−0.706947	+	1.05987i	0.287818	+	0.957685i	$0.407070\pi$
$211$	−10.2690	+	15.3956i	−0.706947	+	1.05987i	−0.994765	+	0.102189i	$0.967415\pi$
$212$	−2.03946	+	2.05268i	−0.140070	+	0.140979i
$213$	−23.7165	+	7.42726i	−1.62502	+	0.508907i
$214$	−0.968287	−	21.3843i	−0.0661907	−	1.46180i
$215$	−7.96977	+	0.931532i	−0.543534	+	0.0635300i
$216$	−10.8359	−	3.25548i	−0.737290	−	0.221507i
$217$	2.80941	+	0.328373i	0.190715	+	0.0222914i
$218$	−1.39702	+	19.6139i	−0.0946183	+	1.32842i
$219$	−4.08939	+	13.3296i	−0.276335	+	0.900731i
$220$	−3.23410	−	3.61057i	−0.218043	−	0.243424i
$221$	0.190486	−	29.4675i	0.0128135	−	1.98220i
$222$	20.6933	−	19.5105i	1.38884	−	1.30946i
$223$	19.2252	−	16.9980i	1.28742	−	1.13827i	0.304842	−	0.952403i	$-0.401396\pi$
$223$	19.2252	−	16.9980i	1.28742	−	1.13827i	0.982575	−	0.185866i	$-0.0595090\pi$
$224$	−1.34374	+	2.81019i	−0.0897821	+	0.187763i
$225$	−0.986513	+	4.03440i	−0.0657675	+	0.268960i
$226$	−5.73622	+	4.10000i	−0.381568	+	0.272728i
$227$	0.161153	+	0.315775i	0.0106961	+	0.0209587i	0.895999	−	0.444056i	$-0.146461\pi$
$227$	0.161153	+	0.315775i	0.0106961	+	0.0209587i	−0.885303	+	0.465014i	$0.846049\pi$
$228$	−1.22016	−	0.0398442i	−0.0808073	−	0.00263874i
$229$	−5.47787	−	7.16284i	−0.361988	−	0.473334i	0.577266	−	0.816556i	$-0.304119\pi$
$229$	−5.47787	−	7.16284i	−0.361988	−	0.473334i	−0.939254	+	0.343222i	$0.888482\pi$
$230$	10.5437	−	14.5516i	0.695229	−	0.959506i
$231$	0.365516	+	5.67498i	0.0240492	+	0.373386i
$232$	−10.5977	+	6.21026i	−0.695772	+	0.407724i
$233$	3.83946	+	17.7249i	0.251532	+	1.16120i	0.911950	+	0.410301i	$0.134576\pi$
$233$	3.83946	+	17.7249i	0.251532	+	1.16120i	−0.660418	+	0.750898i	$0.729621\pi$
$234$	22.2536	−	21.2414i	1.45477	−	1.38859i
$235$	1.32035	−	2.09488i	0.0861302	−	0.136655i
$236$	4.91219	−	0.703320i	0.319756	−	0.0457822i
$237$	3.81231	+	3.88947i	0.247636	+	0.252648i
$238$	4.81406	−	4.48337i	0.312049	−	0.290614i
$239$	1.42316	+	2.61912i	0.0920566	+	0.169417i	0.920598	−	0.390511i	$-0.127702\pi$
$239$	1.42316	+	2.61912i	0.0920566	+	0.169417i	−0.828542	+	0.559927i	$0.810829\pi$
$240$	13.1623	−	9.27351i	0.849620	−	0.598602i
$241$	7.14668	−	12.0169i	0.460358	−	0.774077i	−0.537234	−	0.843433i	$-0.680531\pi$
$241$	7.14668	−	12.0169i	0.460358	−	0.774077i	0.997592	+	0.0693563i	$0.0220945\pi$
$242$	−2.96061	−	5.12793i	−0.190315	−	0.329636i
$243$	1.58441	+	15.5077i	0.101640	+	0.994821i
$244$	−1.79543	+	3.10977i	−0.114940	+	0.199083i
$245$	−5.82060	−	10.3895i	−0.371864	−	0.663760i
$246$	6.03126	−	22.7738i	0.384539	−	1.45201i
$247$	−3.46776	+	5.66297i	−0.220648	+	0.360326i
$248$	−1.60932	−	6.99134i	−0.102192	−	0.443951i
$249$	−8.62393	−	4.12709i	−0.546520	−	0.261544i
$250$	−12.2451	−	15.5897i	−0.774447	−	0.985982i
$251$	−9.27446	−	17.6071i	−0.585399	−	1.11135i	−0.981196	−	0.193014i	$-0.938174\pi$
$251$	−9.27446	−	17.6071i	−0.585399	−	1.11135i	0.395797	−	0.918338i	$-0.370468\pi$
$252$	1.71437	+	0.0898432i	0.107995	+	0.00565959i
$253$	16.3907	−	14.8737i	1.03047	−	0.935104i
$254$	0.0369516	+	5.71628i	0.00231855	+	0.358671i
$255$	−15.0158	+	3.65637i	−0.940328	+	0.228971i
$256$	14.3409	+	1.48855i	0.896307	+	0.0930343i
$257$	12.1789	−	1.58337i	0.759700	−	0.0987676i	0.260759	−	0.965404i	$-0.416027\pi$
$257$	12.1789	−	1.58337i	0.759700	−	0.0987676i	0.498940	+	0.866636i	$0.333723\pi$
$258$	−2.45509	+	11.6802i	−0.152847	+	0.727180i
$259$	4.69698	−	7.24297i	0.291856	−	0.450056i
$260$	0.770546	+	7.92191i	0.0477873	+	0.491296i
$261$	13.5024	+	10.2022i	0.835779	+	0.631498i
$262$	−30.5263	+	2.37269i	−1.88592	+	0.146585i
$263$	5.91149	+	29.1040i	0.364518	+	1.79463i	0.576217	+	0.817296i	$0.304528\pi$
$263$	5.91149	+	29.1040i	0.364518	+	1.79463i	−0.211700	+	0.977335i	$0.567900\pi$
$264$	13.2458	−	5.70862i	0.815222	−	0.351341i
$265$	7.17505	−	4.08091i	0.440760	−	0.250688i
$266$	−1.45079	+	0.304456i	−0.0889535	+	0.0186674i
$267$	−18.6993	+	12.1177i	−1.14438	+	0.741592i
$268$	−1.30970	+	0.636689i	−0.0800027	+	0.0388920i
$269$	3.58345	−	4.81341i	0.218487	−	0.293479i	−0.679343	−	0.733820i	$-0.737735\pi$
$269$	3.58345	−	4.81341i	0.218487	−	0.293479i	0.897830	+	0.440342i	$0.145143\pi$
$270$	−13.6410	−	8.61600i	−0.830163	−	0.524353i
$271$	8.34832	+	11.2137i	0.507125	+	0.681187i	0.979784	−	0.200059i	$-0.0641133\pi$
$271$	8.34832	+	11.2137i	0.507125	+	0.681187i	−0.472659	+	0.881245i	$0.656706\pi$
$272$	−20.3660	−	10.5601i	−1.23487	−	0.640298i
$273$	5.03245	−	7.86567i	0.304578	−	0.476052i
$274$	2.70901	+	0.716502i	0.163657	+	0.0432854i
$275$	−2.34557	−	4.74668i	−0.141443	−	0.286235i
$276$	−3.88357	−	5.43712i	−0.233764	−	0.327276i
$277$	21.8574	−	15.1997i	1.31328	−	0.913260i	0.313939	−	0.949443i	$-0.398351\pi$
$277$	21.8574	−	15.1997i	1.31328	−	0.913260i	0.999345	+	0.0361830i	$0.0115199\pi$
$278$	28.4624	+	4.45143i	1.70706	+	0.266979i
$279$	−8.04507	+	5.74244i	−0.481646	+	0.343791i
$280$	2.33715	−	2.67807i	0.139671	−	0.160045i
$281$	−2.55738	+	5.17531i	−0.152561	+	0.308733i	−0.959406	−	0.282030i	$-0.908992\pi$
$281$	−2.55738	+	5.17531i	−0.152561	+	0.308733i	0.806845	+	0.590763i	$0.201173\pi$
$282$	−2.33002	−	2.85273i	−0.138751	−	0.169878i
$283$	8.24109	−	7.09866i	0.489882	−	0.421971i	−0.372652	−	0.927971i	$-0.621551\pi$
$283$	8.24109	−	7.09866i	0.489882	−	0.421971i	0.862533	+	0.506000i	$0.168876\pi$
$284$	−7.40542	−	6.05248i	−0.439431	−	0.359149i
$285$	3.32272	+	1.04293i	0.196821	+	0.0617775i
$286$	−4.30103	+	38.9813i	−0.254325	+	2.30502i
$287$	0.138664	−	7.14950i	0.00818511	−	0.422022i
$288$	−3.11515	−	10.4298i	−0.183562	−	0.614580i
$289$	3.30072	+	3.78220i	0.194160	+	0.222483i
$290$	−16.9335	+	4.47871i	−0.994371	+	0.262999i
$291$	−13.8302	−	15.2506i	−0.810742	−	0.894006i
$292$	−5.15017	+	1.50565i	−0.301391	+	0.0881117i
$293$	−0.517974	+	6.14932i	−0.0302603	+	0.359247i	0.965018	+	0.262184i	$0.0844427\pi$
$293$	−0.517974	+	6.14932i	−0.0302603	+	0.359247i	−0.995278	+	0.0970629i	$0.969055\pi$
$294$	−17.4048	+	3.29567i	−1.01507	+	0.192208i
$295$	−14.0375	−	1.82500i	−0.817295	−	0.106256i
$296$	−21.3052	−	5.04942i	−1.23834	−	0.293492i
$297$	−14.2636	−	13.8366i	−0.827659	−	0.802884i
$298$	−23.9108	+	5.66695i	−1.38511	+	0.328278i
$299$	−36.1493	+	3.75220i	−2.09057	+	0.216995i
$300$	−1.50563	+	0.536460i	−0.0869274	+	0.0309725i
$301$	0.117071	+	3.62089i	0.00674787	+	0.208704i
$302$	−11.1382	−	13.4497i	−0.640934	−	0.773941i
$303$	−12.5345	−	11.8333i	−0.720086	−	0.679805i
$304$	2.69965	+	4.40863i	0.154836	+	0.252852i
$305$	7.31309	−	7.17263i	0.418747	−	0.410704i
$306$	−1.94429	+	22.9058i	−0.111148	+	1.30944i
$307$	1.98996	−	2.90143i	0.113573	−	0.165593i	−0.763722	−	0.645546i	$-0.776630\pi$
$307$	1.98996	−	2.90143i	0.113573	−	0.165593i	0.877295	+	0.479952i	$0.159346\pi$
$308$	−1.74695	+	1.31819i	−0.0995417	+	0.0751110i
$309$	−18.6214	−	5.06059i	−1.05933	−	0.287887i
$310$	0.462756	−	10.2198i	0.0262828	−	0.580447i
$311$	1.61810	+	22.7178i	0.0917540	+	1.28821i	0.807509	+	0.589856i	$0.200815\pi$
$311$	1.61810	+	22.7178i	0.0917540	+	1.28821i	−0.715755	+	0.698352i	$0.753917\pi$
$312$	−23.0786	−	5.32025i	−1.30657	−	0.301200i
$313$	6.64870	+	17.9061i	0.375807	+	1.01212i	0.977043	+	0.213044i	$0.0683377\pi$
$313$	6.64870	+	17.9061i	0.375807	+	1.01212i	−0.601236	+	0.799071i	$0.705325\pi$
$314$	−0.701664	+	5.13709i	−0.0395972	+	0.289903i
$315$	−4.64263	−	1.55840i	−0.261583	−	0.0878060i
$316$	−0.443718	+	2.04843i	−0.0249611	+	0.115233i
$317$	−7.39265	−	22.5536i	−0.415213	−	1.26674i	−0.916003	−	0.401171i	$-0.868603\pi$
$317$	−7.39265	−	22.5536i	−0.415213	−	1.26674i	0.500791	−	0.865568i	$-0.333043\pi$
$318$	−2.36227	−	12.0488i	−0.132469	−	0.675661i
$319$	−21.5451	+	1.11516i	−1.20629	+	0.0624372i
$320$	−6.81688	−	2.68269i	−0.381075	−	0.149967i
$321$	19.3594	+	11.8634i	1.08054	+	0.662151i
$322$	−6.14719	−	5.29503i	−0.342570	−	0.295080i
$323$	−0.861641	−	4.88661i	−0.0479430	−	0.271898i
$324$	−4.64991	+	3.79040i	−0.258328	+	0.210578i
$325$	−1.50968	+	8.56179i	−0.0837417	+	0.474923i
$326$	−13.7313	+	11.2226i	−0.760507	+	0.621565i
$327$	−16.3980	−	12.8885i	−0.906810	−	0.712734i
$328$	−17.1980	+	5.76054i	−0.949599	+	0.318073i
$329$	−0.892446	−	0.673412i	−0.0492022	−	0.0371264i
$330$	20.3795	−	2.77691i	1.12186	−	0.152864i
$331$	11.6618	−	6.23943i	0.640992	−	0.342950i	−0.118989	−	0.992896i	$-0.537965\pi$
$331$	11.6618	−	6.23943i	0.640992	−	0.342950i	0.759981	+	0.649945i	$0.225208\pi$
$332$	−0.497925	−	3.64546i	−0.0273272	−	0.200070i
$333$	4.83467	+	29.7766i	0.264938	+	1.63175i
$334$	−4.32573	+	8.21220i	−0.236694	+	0.449352i
$335$	4.08633	−	0.747798i	0.223260	−	0.0408565i
$336$	−3.67334	−	6.27311i	−0.200397	−	0.342226i
$337$	−7.31632	−	7.55669i	−0.398545	−	0.411639i	0.489056	−	0.872253i	$-0.337341\pi$
$337$	−7.31632	−	7.55669i	−0.398545	−	0.411639i	−0.887601	+	0.460613i	$0.847630\pi$
$338$	29.2156	−	31.7800i	1.58912	−	1.72860i
$339$	−0.190943	−	7.47625i	−0.0103706	−	0.406054i
$340$	−4.35238	−	4.05341i	−0.236041	−	0.219827i
$341$	3.14308	−	12.2022i	0.170207	−	0.660785i
$342$	3.04212	−	4.19283i	0.164499	−	0.226722i
$343$	−10.3656	+	4.71174i	−0.559690	+	0.254410i
$344$	8.55037	−	3.36489i	0.461005	−	0.181423i
$345$	6.51326	+	17.9130i	0.350662	+	0.964403i
$346$	−34.8786	−	6.38279i	−1.87509	−	0.343141i
$347$	5.64697	−	7.18940i	0.303145	−	0.385947i	−0.610800	−	0.791785i	$-0.709152\pi$
$347$	5.64697	−	7.18940i	0.303145	−	0.385947i	0.913945	+	0.405838i	$0.133020\pi$
$348$	−0.422800	+	6.49905i	−0.0226644	+	0.348385i
$349$	−9.22437	−	32.3269i	−0.493769	−	1.73042i	−0.666552	−	0.745458i	$-0.732231\pi$
$349$	−9.22437	−	32.3269i	−0.493769	−	1.73042i	0.172783	−	0.984960i	$-0.444724\pi$
$350$	−1.62152	+	1.06649i	−0.0866741	+	0.0570064i
$351$	5.42732	+	32.1762i	0.289689	+	1.71744i
$352$	11.5935	+	7.62514i	0.617933	+	0.406421i
$353$	−7.09801	+	22.6395i	−0.377789	+	1.20498i	0.551043	+	0.834477i	$0.314230\pi$
$353$	−7.09801	+	22.6395i	−0.377789	+	1.20498i	−0.928832	+	0.370502i	$0.879186\pi$
$354$	−9.21200	+	18.9340i	−0.489612	+	1.00633i
$355$	15.7211	+	22.2983i	0.834390	+	1.18347i
$356$	−7.85171	−	3.44726i	−0.416140	−	0.182705i
$357$	1.07595	+	6.89417i	0.0569454	+	0.364878i
$358$	6.19421	+	13.3964i	0.327374	+	0.708022i
$359$	−20.2660	−	11.1823i	−1.06960	−	0.590179i	−0.152280	−	0.988337i	$-0.548662\pi$
$359$	−20.2660	−	11.1823i	−1.06960	−	0.590179i	−0.917317	+	0.398159i	$0.869649\pi$
$360$	0.232857	+	12.4189i	0.0122726	+	0.654532i
$361$	6.44065	−	16.6817i	0.338981	−	0.877984i
$362$	−14.6109	−	4.27149i	−0.767930	−	0.224504i
$363$	6.26451	+	0.448226i	0.328802	+	0.0235257i
$364$	3.59326	−	0.0464575i	0.188338	−	0.00243504i
$365$	15.3053	−	0.197883i	0.801116	−	0.0103577i
$366$	−6.65724	−	13.7055i	−0.347980	−	0.716398i
$367$	33.4085	+	9.76698i	1.74391	+	0.509832i	0.989244	−	0.146278i	$-0.0467294\pi$
$367$	33.4085	+	9.76698i	1.74391	+	0.509832i	0.754665	+	0.656110i	$0.227799\pi$
$368$	−10.1907	+	26.3945i	−0.531225	+	1.37591i
$369$	16.4183	+	18.8378i	0.854704	+	0.980658i
$370$	−27.3372	−	15.0840i	−1.42119	−	0.784181i
$371$	−1.56409	−	3.38270i	−0.0812033	−	0.175621i
$372$	−3.54812	−	1.37121i	−0.183962	−	0.0710940i
$373$	−32.2351	−	14.1527i	−1.66907	−	0.732799i	−0.669123	−	0.743152i	$-0.733330\pi$
$373$	−32.2351	−	14.1527i	−1.66907	−	0.732799i	−0.999946	+	0.0103529i	$0.996705\pi$
$374$	−16.8864	−	23.9511i	−0.873174	−	1.23848i
$375$	20.9740	−	1.48711i	1.08310	−	0.0767938i
$376$	−0.848330	+	2.70580i	−0.0437493	+	0.139541i
$377$	29.5972	+	19.4664i	1.52433	+	1.00257i
$378$	−4.39327	+	5.81054i	−0.225965	+	0.298862i
$379$	23.2844	−	15.3144i	1.19604	−	0.786649i	0.214281	−	0.976772i	$-0.431259\pi$
$379$	23.2844	−	15.3144i	1.19604	−	0.786649i	0.981760	+	0.190123i	$0.0608887\pi$
$380$	0.367750	+	1.28878i	0.0188652	+	0.0661132i
$381$	−5.04307	−	3.36613i	−0.258364	−	0.172452i
$382$	7.46390	−	9.50261i	0.381886	−	0.486196i
$383$	−33.4967	−	6.12989i	−1.71160	−	0.313223i	−0.767050	−	0.641587i	$-0.778276\pi$
$383$	−33.4967	−	6.12989i	−1.71160	−	0.313223i	−0.944551	+	0.328364i	$0.893503\pi$
$384$	−15.0893	+	17.9710i	−0.770023	+	0.917078i
$385$	5.80931	−	2.28618i	0.296070	−	0.116514i
$386$	−10.6042	+	4.82022i	−0.539742	+	0.245343i
$387$	−8.80009	−	9.10095i	−0.447334	−	0.462627i
$388$	1.97632	−	7.67255i	0.100333	−	0.389515i
$389$	−14.1012	−	13.1326i	−0.714959	−	0.665847i	0.237196	−	0.971462i	$-0.423772\pi$
$389$	−14.1012	−	13.1326i	−0.714959	−	0.665847i	−0.952155	+	0.305615i	$0.901138\pi$
$390$	−29.6699	−	16.1343i	−1.50239	−	0.816990i
$391$	18.3797	−	19.9929i	0.929501	−	1.01109i
$392$	9.48597	+	9.79763i	0.479114	+	0.494855i
$393$	16.0651	−	28.2245i	0.810378	−	1.42374i
$394$	−9.50053	+	1.73859i	−0.478630	+	0.0875891i
$395$	2.78646	−	5.28996i	0.140202	−	0.266167i
$396$	1.43009	−	7.51271i	0.0718648	−	0.377528i
$397$	3.62554	+	26.5436i	0.181961	+	1.33219i	0.824469	+	0.565908i	$0.191474\pi$
$397$	3.62554	+	26.5436i	0.181961	+	1.33219i	−0.642508	+	0.766279i	$0.722106\pi$
$398$	24.7855	−	13.2610i	1.24238	−	0.664714i
$399$	0.595129	−	1.45536i	0.0297937	−	0.0728593i
$400$	5.40268	+	4.07669i	0.270134	+	0.203835i
$401$	7.61509	−	2.55071i	0.380279	−	0.127376i	−0.121020	−	0.992650i	$-0.538617\pi$
$401$	7.61509	−	2.55071i	0.380279	−	0.127376i	0.501300	+	0.865274i	$0.332855\pi$
$402$	0.877772	−	6.11656i	0.0437793	−	0.305066i
$403$	−16.0204	+	13.0935i	−0.798031	+	0.652234i
$404$	1.15194	−	6.53299i	0.0573113	−	0.325029i
$405$	15.6783	−	6.85942i	0.779063	−	0.340847i
$406$	1.37325	+	7.78809i	0.0681533	+	0.386517i
$407$	−29.1372	−	25.0980i	−1.44428	−	1.24406i
$408$	15.5530	−	8.44463i	0.769991	−	0.418072i
$409$	−24.5385	−	9.65680i	−1.21335	−	0.477498i	−0.329002	−	0.944329i	$-0.606712\pi$
$409$	−24.5385	−	9.65680i	−1.21335	−	0.477498i	−0.884346	+	0.466831i	$0.845396\pi$
$410$	−25.8287	+	1.33688i	−1.27559	+	0.0660240i
$411$	−2.23999	+	1.95357i	−0.110491	+	0.0963623i
$412$	−2.31307	−	7.05675i	−0.113957	−	0.347661i
$413$	−1.35303	+	6.24629i	−0.0665783	+	0.307360i
$414$	28.3427	−	0.714733i	1.39297	−	0.0351272i
$415$	−1.42040	+	10.3992i	−0.0697249	+	0.510476i
$416$	−7.93126	−	21.3603i	−0.388862	−	1.04728i
$417$	−20.8322	+	22.3543i	−1.02016	+	1.09470i
$418$	0.469167	+	6.58702i	0.0229477	+	0.322181i
$419$	0.104280	−	2.30300i	0.00509442	−	0.112509i	−0.994844	−	0.101416i	$-0.967663\pi$
$419$	0.104280	−	2.30300i	0.00509442	−	0.112509i	0.999938	−	0.0110924i	$-0.00353088\pi$
$420$	−0.481308	−	1.82215i	−0.0234854	−	0.0889117i
$421$	−9.33961	+	7.04737i	−0.455185	+	0.343468i	−0.804923	−	0.593380i	$-0.797793\pi$
$421$	−9.33961	+	7.04737i	−0.455185	+	0.343468i	0.349738	+	0.936848i	$0.386271\pi$
$422$	17.0925	−	24.9215i	0.832049	−	1.21316i
$423$	3.89110	−	0.350575i	0.189192	−	0.0170455i
$424$	−6.74840	+	6.61878i	−0.327731	+	0.321436i
$425$	−3.39260	−	5.54024i	−0.164565	−	0.268741i
$426$	38.8816	−	11.6267i	1.88382	−	0.563317i
$427$	−2.94982	−	3.56197i	−0.142752	−	0.172376i
$428$	0.282367	+	8.73331i	0.0136487	+	0.422140i
$429$	−31.6835	−	26.9541i	−1.52969	−	1.30136i
$430$	13.0329	−	1.35278i	0.628502	−	0.0652368i
$431$	−17.2506	+	4.08847i	−0.830932	+	0.196934i	−0.624003	−	0.781422i	$-0.714495\pi$
$431$	−17.2506	+	4.08847i	−0.830932	+	0.196934i	−0.206928	+	0.978356i	$0.566347\pi$
$432$	24.2323	+	7.62311i	1.16588	+	0.366767i
$433$	25.6084	+	6.06931i	1.23066	+	0.291673i	0.793981	−	0.607943i	$-0.208005\pi$
$433$	25.6084	+	6.06931i	1.23066	+	0.291673i	0.436683	+	0.899616i	$0.356153\pi$
$434$	−4.58035	−	0.595485i	−0.219864	−	0.0285842i
$435$	6.13370	−	17.5369i	0.294088	−	0.840832i
$436$	0.673711	−	7.99821i	0.0322649	−	0.383045i
$437$	−5.87383	+	1.71722i	−0.280983	+	0.0821455i
$438$	6.95866	−	21.6786i	0.332498	−	1.03584i
$439$	28.0850	−	7.42814i	1.34042	−	0.354526i	0.485934	−	0.873996i	$-0.338480\pi$
$439$	28.0850	−	7.42814i	1.34042	−	0.354526i	0.854489	+	0.519470i	$0.173871\pi$
$440$	−10.4114	−	11.9302i	−0.496346	−	0.568750i
$441$	7.45304	−	17.2475i	0.354907	−	0.821310i
$442$	−0.933118	+	48.1113i	−0.0443839	+	2.28842i
$443$	−0.239548	+	2.17109i	−0.0113813	+	0.103151i	−0.998320	−	0.0579466i	$-0.981545\pi$
$443$	−0.239548	+	2.17109i	−0.0113813	+	0.103151i	0.986938	+	0.161098i	$0.0515035\pi$
$444$	−8.54912	+	7.85419i	−0.405723	+	0.372743i
$445$	18.9406	+	15.4802i	0.897868	+	0.733831i
$446$	−31.7503	+	27.3489i	−1.50342	+	1.29501i
$447$	9.23824	−	24.3721i	0.436954	−	1.15276i
$448$	−1.46527	+	2.96524i	−0.0692277	+	0.140094i
$449$	−26.2094	+	30.0326i	−1.23690	+	1.41733i	−0.362594	+	0.931947i	$0.618109\pi$
$449$	−26.2094	+	30.0326i	−1.23690	+	1.41733i	−0.874303	+	0.485380i	$0.838681\pi$
$450$	1.69597	−	6.56665i	0.0799489	−	0.309555i
$451$	−31.4728	−	4.92225i	−1.48200	−	0.231780i
$452$	2.36292	−	1.64318i	0.111143	−	0.0772887i
$453$	18.4362	−	1.78725i	0.866207	−	0.0839722i
$454$	−0.256468	−	0.519007i	−0.0120366	−	0.0243582i
$455$	−9.91037	−	2.62117i	−0.464605	−	0.122883i
$456$	−3.98388	−	0.181677i	−0.186562	−	0.00850781i
$457$	1.10920	+	0.575139i	0.0518864	+	0.0269039i	0.486061	−	0.873925i	$-0.338433\pi$
$457$	1.10920	+	0.575139i	0.0518864	+	0.0269039i	−0.434175	+	0.900829i	$0.642960\pi$
$458$	8.79319	+	11.8113i	0.410879	+	0.551906i
$459$	−18.9642	−	15.3264i	−0.885172	−	0.715374i
$460$	−4.38028	+	5.88373i	−0.204231	+	0.274330i
$461$	24.9499	−	12.1290i	1.16203	−	0.564904i	0.247292	−	0.968941i	$-0.420459\pi$
$461$	24.9499	−	12.1290i	1.16203	−	0.564904i	0.914742	+	0.404037i	$0.132393\pi$
$462$	−0.477020	−	9.27396i	−0.0221930	−	0.431464i
$463$	5.82148	−	1.22167i	0.270547	−	0.0567758i	−0.0681370	−	0.997676i	$-0.521705\pi$
$463$	5.82148	−	1.22167i	0.270547	−	0.0567758i	0.338684	+	0.940900i	$0.390018\pi$
$464$	23.9722	−	13.6345i	1.11288	−	0.632967i
$465$	8.70181	+	6.48262i	0.403537	+	0.300624i
$466$	−5.89498	−	29.0228i	−0.273080	−	1.34445i
$467$	8.81797	−	0.685386i	0.408047	−	0.0317159i	0.128171	−	0.991752i	$-0.459089\pi$
$467$	8.81797	−	0.685386i	0.408047	−	0.0317159i	0.279876	+	0.960036i	$0.409707\pi$
$468$	−9.19510	+	8.55241i	−0.425044	+	0.395335i
$469$	−0.181577	−	1.86677i	−0.00838443	−	0.0861995i
$470$	−2.20013	+	3.39270i	−0.101484	+	0.156493i
$471$	−4.09517	−	3.67056i	−0.188696	−	0.169131i
$472$	16.0749	−	2.08988i	0.739909	−	0.0961947i
$473$	16.0524	+	1.66620i	0.738090	+	0.0766118i
$474$	−6.14272	−	6.43131i	−0.282145	−	0.295400i
$475$	0.00946296	+	1.46389i	0.000434190	+	0.0671677i
$476$	−1.98856	+	1.80452i	−0.0911455	+	0.0827101i
$477$	11.9879	+	5.08855i	0.548890	+	0.232989i
$478$	−2.26848	−	4.30660i	−0.103758	−	0.196979i
$479$	−18.3072	−	23.3076i	−0.836476	−	1.06495i	−0.996960	−	0.0779148i	$-0.975174\pi$
$479$	−18.3072	−	23.3076i	−0.836476	−	1.06495i	0.160484	−	0.987038i	$-0.448695\pi$
$480$	−9.85683	+	6.75568i	−0.449901	+	0.308353i
$481$	14.1651	+	61.5372i	0.645872	+	2.80585i
$482$	−11.9230	+	19.4706i	−0.543076	+	0.886863i
$483$	8.30586	−	2.25147i	0.377930	−	0.102446i
$484$	1.18134	+	2.10863i	0.0536972	+	0.0958469i
$485$	−11.3008	+	19.5735i	−0.513141	+	0.888786i
$486$	−2.25968	−	25.3549i	−0.102501	−	1.15012i
$487$	10.5114	+	18.2063i	0.476318	+	0.825007i	0.999632	−	0.0271329i	$-0.00863773\pi$
$487$	10.5114	+	18.2063i	0.476318	+	0.825007i	−0.523314	+	0.852140i	$0.675304\pi$
$488$	−5.99594	+	10.0820i	−0.271423	+	0.456390i
$489$	−1.69393	−	18.7337i	−0.0766023	−	0.847169i
$490$	9.28469	+	17.0871i	0.419439	+	0.771916i
$491$	20.8987	−	19.4631i	0.943144	−	0.878357i	−0.0495799	−	0.998770i	$-0.515788\pi$
$491$	20.8987	−	19.4631i	0.943144	−	0.878357i	0.992724	+	0.120413i	$0.0384220\pi$
$492$	−2.58189	+	9.26350i	−0.116401	+	0.417631i
$493$	−26.2039	+	3.75184i	−1.18017	+	0.168974i
$494$	5.78179	−	9.17344i	0.260135	−	0.412732i
$495$	−9.67735	+	19.5521i	−0.434965	+	0.878801i
$496$	3.41001	+	15.7424i	0.153114	+	0.706854i
$497$	10.6278	−	6.22788i	0.476720	−	0.279359i
$498$	13.9942	+	6.92087i	0.627097	+	0.310132i
$499$	−15.1115	+	20.8558i	−0.676484	+	0.933636i	−0.999920	−	0.0126141i	$-0.995985\pi$
$499$	−15.1115	+	20.8558i	−0.676484	+	0.933636i	0.323437	+	0.946250i	$0.395162\pi$
$500$	4.91567	+	6.42770i	0.219835	+	0.287456i
$501$	−4.64164	−	8.68218i	−0.207373	−	0.387891i
$502$	14.7719	+	28.9451i	0.659301	+	1.29189i
$503$	−6.93653	+	4.95793i	−0.309285	+	0.221063i	−0.725533	−	0.688188i	$-0.758407\pi$
$503$	−6.93653	+	4.95793i	−0.309285	+	0.221063i	0.416248	+	0.909251i	$0.363345\pi$
$504$	5.59606	+	0.365866i	0.249268	+	0.0162970i
$505$	−8.16347	+	17.0724i	−0.363270	+	0.759714i
$506$	−27.0771	+	23.9402i	−1.20372	+	1.06427i
$507$	10.5451	+	44.5572i	0.468323	+	1.97885i
$508$	0.0150834	−	2.33334i	0.000669216	−	0.103525i
$509$	3.35201	+	3.74220i	0.148575	+	0.165870i	0.814529	−	0.580123i	$-0.196996\pi$
$509$	3.35201	+	3.74220i	0.148575	+	0.165870i	−0.665953	+	0.745993i	$0.731975\pi$
$510$	24.5954	−	5.65321i	1.08910	−	0.250328i
$511$	0.490985	−	6.89333i	0.0217199	−	0.304943i
$512$	3.52797	+	0.412360i	0.155916	+	0.0182239i
$513$	1.87424	+	5.16497i	0.0827499	+	0.228039i
$514$	−19.9195	+	2.32825i	−0.878609	+	0.102695i
$515$	0.958244	+	21.1626i	0.0422253	+	0.932533i
$516$	1.06371	−	4.75444i	0.0468270	−	0.209302i
$517$	−3.51032	+	3.53309i	−0.154384	+	0.155385i
$518$	−7.82226	+	11.7273i	−0.343690	+	0.515270i
$519$	26.3435	−	26.8420i	1.15635	−	1.17823i
$520$	2.18237	+	25.9088i	0.0957031	+	1.13618i
$521$	6.06648	+	15.7126i	0.265777	+	0.688380i	0.999956	+	0.00942346i	$0.00299962\pi$
$521$	6.06648	+	15.7126i	0.265777	+	0.688380i	−0.734178	+	0.678957i	$0.762432\pi$
$522$	−21.8317	−	16.9434i	−0.955549	−	0.741592i
$523$	−0.375001	−	1.09598i	−0.0163976	−	0.0479239i	0.937646	−	0.347592i	$-0.113001\pi$
$523$	−0.375001	−	1.09598i	−0.0163976	−	0.0479239i	−0.954044	+	0.299668i	$0.903124\pi$
$524$	12.4721	−	0.807343i	0.544846	−	0.0352690i
$525$	0.0272767	−	2.05840i	0.00119045	−	0.0898359i
$526$	−9.03801	−	47.6466i	−0.394076	−	2.07749i
$527$	2.48767	−	15.2593i	0.108365	−	0.664707i
$528$	−29.9027	+	12.4315i	−1.30135	+	0.541010i
$529$	−8.45761	−	6.21189i	−0.367722	−	0.270082i
$530$	−11.8018	+	6.51193i	−0.512635	+	0.282860i
$531$	−11.1544	−	19.3488i	−0.484060	−	0.839666i
$532$	0.593758	−	0.116610i	0.0257427	−	0.00505570i
$533$	36.8672	+	37.1063i	1.59690	+	1.60725i
$534$	30.7885	−	19.3914i	1.33235	−	0.839146i
$535$	5.90501	−	24.2165i	0.255296	−	1.04697i
$536$	−4.30491	+	2.02438i	−0.185944	+	0.0874398i
$537$	−15.4499	−	2.52386i	−0.666714	−	0.108912i
$538$	−5.95276	+	7.78380i	−0.256642	+	0.335583i
$539$	6.86956	+	22.9459i	0.295893	+	0.988351i
$540$	5.52221	+	3.58868i	0.237638	+	0.154432i
$541$	4.95577	−	16.5534i	0.213065	−	0.711688i	−0.782916	−	0.622127i	$-0.786269\pi$
$541$	4.95577	−	16.5534i	0.213065	−	0.711688i	0.995981	−	0.0895604i	$-0.0285462\pi$
$542$	−13.3946	−	18.4863i	−0.575348	−	0.794056i
$543$	12.4388	−	10.2944i	0.533801	−	0.441774i
$544$	15.0125	+	8.03215i	0.643656	+	0.344376i
$545$	−7.97011	+	21.4649i	−0.341402	+	0.919457i
$546$	−8.38316	+	12.7370i	−0.358766	+	0.545094i
$547$	15.1881	−	0.392803i	0.649398	−	0.0167951i	0.300247	−	0.953861i	$-0.402931\pi$
$547$	15.1881	−	0.392803i	0.649398	−	0.0167951i	0.349151	+	0.937066i	$0.386470\pi$
$548$	−1.10193	−	0.306742i	−0.0470719	−	0.0131034i
$549$	15.9967	+	2.30091i	0.682724	+	0.0982005i
$550$	3.72970	+	7.80001i	0.159035	+	0.332594i
$551$	5.49235	+	2.32717i	0.233982	+	0.0991410i
$552$	−12.4557	−	17.9239i	−0.530151	−	0.762892i
$553$	−2.27435	−	1.45409i	−0.0967152	−	0.0618343i
$554$	−36.0102	+	24.3570i	−1.52993	+	1.03483i
$555$	29.5028	−	15.0445i	1.25232	−	0.638602i
$556$	−11.5937	−	1.96709i	−0.491681	−	0.0834232i
$557$	34.6259	−	14.1462i	1.46715	−	0.599395i	0.502886	−	0.864353i	$-0.332272\pi$
$557$	34.6259	−	14.1462i	1.46715	−	0.599395i	0.964260	+	0.264958i	$0.0853581\pi$
$558$	13.2574	−	9.20656i	0.561232	−	0.389745i
$559$	−19.6245	−	17.8083i	−0.830029	−	0.753211i
$560$	−5.32466	+	5.94447i	−0.225008	+	0.251200i
$561$	31.0780	−	0.592739i	1.31212	−	0.0250254i
$562$	4.28501	−	8.39638i	0.180752	−	0.354180i
$563$	1.08471	+	7.24193i	0.0457149	+	0.305211i	0.999980	+	0.00625056i	$0.00198963\pi$
$563$	1.08471	+	7.24193i	0.0457149	+	0.305211i	−0.954266	+	0.298960i	$0.903360\pi$
$564$	0.935962	+	1.17666i	0.0394111	+	0.0495465i
$565$	−7.75072	+	2.70808i	−0.326075	+	0.113930i
$566$	−13.6061	+	11.4169i	−0.571908	+	0.479887i
$567$	−2.49190	−	7.31360i	−0.104650	−	0.307143i
$568$	−23.9336	−	20.0827i	−1.00423	−	0.842649i
$569$	15.2482	+	5.77423i	0.639240	+	0.242068i	0.652435	−	0.757845i	$-0.273748\pi$
$569$	15.2482	+	5.77423i	0.639240	+	0.242068i	−0.0131952	+	0.999913i	$0.504200\pi$
$570$	−5.40340	−	1.77306i	−0.226324	−	0.0742653i
$571$	2.08375	−	10.2589i	0.0872020	−	0.429322i	−0.912589	−	0.408878i	$-0.865920\pi$
$571$	2.08375	−	10.2589i	0.0872020	−	0.429322i	0.999791	−	0.0204437i	$-0.00650788\pi$
$572$	1.96121	−	15.8879i	0.0820024	−	0.664305i
$573$	3.90933	+	12.2059i	0.163314	+	0.509909i
$574$	−0.377348	+	11.6710i	−0.0157502	+	0.487137i
$575$	−6.33276	+	4.90826i	−0.264095	+	0.204689i
$576$	−3.16430	−	11.1165i	−0.131846	−	0.463186i
$577$	−11.8478	−	18.7979i	−0.493232	−	0.782566i	0.503445	−	0.864028i	$-0.332066\pi$
$577$	−11.8478	−	18.7979i	−0.493232	−	0.782566i	−0.996676	+	0.0814618i	$0.974041\pi$
$578$	−5.30965	−	6.24536i	−0.220852	−	0.259773i
$579$	2.07069	−	12.1804i	0.0860548	−	0.506202i
$580$	6.93520	−	1.73866i	0.287968	−	0.0721941i
$581$	4.62475	+	1.03313i	0.191867	+	0.0428613i
$582$	22.2604	+	25.1935i	0.922722	+	1.04431i
$583$	−15.8734	+	4.86422i	−0.657410	+	0.201455i
$584$	−16.8862	+	4.70059i	−0.698755	+	0.194512i
$585$	31.8122	−	16.4691i	1.31527	−	0.680913i
$586$	0.975578	−	10.0298i	0.0403008	−	0.414328i
$587$	26.1451	+	20.8105i	1.07912	+	0.858943i	0.990554	−	0.137127i	$-0.0437868\pi$
$587$	26.1451	+	20.8105i	1.07912	+	0.858943i	0.0885700	+	0.996070i	$0.471770\pi$
$588$	7.12130	−	1.25331i	0.293677	−	0.0516856i
$589$	−2.25664	+	2.65433i	−0.0929833	+	0.109370i
$590$	22.8823	+	3.27625i	0.942047	+	0.134881i
$591$	4.12133	−	9.37879i	0.169529	−	0.385792i
$592$	47.6839	+	11.9544i	1.95980	+	0.491324i
$593$	22.8026	+	11.4519i	0.936390	+	0.470273i	0.850467	−	0.526029i	$-0.176320\pi$
$593$	22.8026	+	11.4519i	0.936390	+	0.470273i	0.0859233	+	0.996302i	$0.472616\pi$
$594$	22.9979	+	22.8939i	0.943615	+	0.939350i
$595$	6.84533	−	3.43786i	0.280631	−	0.140938i
$596$	9.78928	−	2.18683i	0.400985	−	0.0895762i
$597$	−3.08782	+	29.6555i	−0.126376	+	1.21372i
$598$	59.1047	−	5.36354i	2.41697	−	0.219331i
$599$	−0.322805	−	2.92566i	−0.0131894	−	0.119539i	0.985575	−	0.169241i	$-0.0541317\pi$
$599$	−0.322805	−	2.92566i	−0.0131894	−	0.119539i	−0.998764	+	0.0497020i	$0.984173\pi$
$600$	−4.94066	+	1.68872i	−0.201701	+	0.0689415i
$601$	−12.8589	−	1.16690i	−0.524524	−	0.0475987i	−0.175077	−	0.984555i	$-0.556017\pi$
$601$	−12.8589	−	1.16690i	−0.524524	−	0.0475987i	−0.349447	+	0.936956i	$0.613631\pi$
$602$	−0.114716	−	5.91475i	−0.00467549	−	0.241067i
$603$	4.85082	+	4.40759i	0.197541	+	0.179491i
$604$	4.47520	+	5.54837i	0.182093	+	0.225760i
$605$	−1.63339	−	6.69857i	−0.0664069	−	0.272336i
$606$	20.2168	+	19.5863i	0.821250	+	0.795640i
$607$	2.67354	−	4.77215i	0.108516	−	0.193695i	−0.812767	−	0.582589i	$-0.802040\pi$
$607$	2.67354	−	4.77215i	0.108516	−	0.193695i	0.921283	+	0.388894i	$0.127143\pi$
$608$	−1.96114	−	3.29760i	−0.0795348	−	0.133735i
$609$	−7.65740	−	3.42413i	−0.310294	−	0.138753i
$610$	−12.0924	+	11.5573i	−0.489608	+	0.467940i
$611$	8.07986	−	1.26367i	0.326876	−	0.0511225i
$612$	0.914456	−	9.33895i	0.0369647	−	0.377505i
$613$	−39.5961	+	23.8964i	−1.59927	+	0.965166i	−0.614997	+	0.788529i	$0.710843\pi$
$613$	−39.5961	+	23.8964i	−1.59927	+	0.965166i	−0.984276	+	0.176637i	$0.943478\pi$
$614$	−3.31050	+	4.69551i	−0.133601	+	0.189495i
$615$	14.1820	−	23.4824i	0.571874	−	0.946902i
$616$	−5.76193	+	4.23198i	−0.232155	+	0.170512i
$617$	−6.30514	+	13.6363i	−0.253835	+	0.548977i	−0.992088	−	0.125548i	$-0.959931\pi$
$617$	−6.30514	+	13.6363i	−0.253835	+	0.548977i	0.738252	+	0.674525i	$0.235651\pi$
$618$	30.2986	+	8.65617i	1.21879	+	0.348202i
$619$	−3.79942	−	4.13291i	−0.152712	−	0.166116i	0.655128	−	0.755518i	$-0.272615\pi$
$619$	−3.79942	−	4.13291i	−0.152712	−	0.166116i	−0.807840	+	0.589402i	$0.799363\pi$
$620$	−0.242809	+	4.16887i	−0.00975144	+	0.167426i
$621$	−16.2232	+	25.3207i	−0.651014	+	1.01609i
$622$	−2.16248	−	37.1283i	−0.0867075	−	1.48871i
$623$	7.68229	−	7.93469i	0.307784	−	0.317897i
$624$	51.6575	+	12.6139i	2.06795	+	0.504961i
$625$	−6.01535	−	15.0001i	−0.240614	−	0.600003i
$626$	−10.4781	−	29.3780i	−0.418791	−	1.17418i
$627$	−6.06488	−	3.50417i	−0.242208	−	0.139943i
$628$	0.313499	−	2.09304i	0.0125100	−	0.0835216i
$629$	−38.3882	−	27.4382i	−1.53064	−	1.09403i
$630$	7.54771	+	2.64261i	0.300708	+	0.105284i
$631$	−20.2857	−	19.8961i	−0.807562	−	0.792051i	0.173686	−	0.984801i	$-0.444432\pi$
$631$	−20.2857	−	19.8961i	−0.807562	−	0.792051i	−0.981248	+	0.192750i	$0.938259\pi$
$632$	−1.53588	+	6.67228i	−0.0610938	+	0.265409i
$633$	11.7284	+	29.8307i	0.466162	+	1.18566i
$634$	11.5948	+	36.9822i	0.460487	+	1.46875i
$635$	−1.82646	+	6.40085i	−0.0724810	+	0.254010i
$636$	0.900597	+	4.93027i	0.0357110	+	0.195498i
$637$	13.2125	−	37.0445i	0.523500	−	1.46776i
$638$	35.2029	−	1.36603i	1.39369	−	0.0540817i
$639$	−12.9041	+	41.0656i	−0.510478	+	1.62453i
$640$	23.8476	+	9.74282i	0.942660	+	0.385119i
$641$	−31.1000	−	19.3218i	−1.22838	−	0.763165i	−0.249649	−	0.968336i	$-0.580315\pi$
$641$	−31.1000	−	19.3218i	−1.22838	−	0.763165i	−0.978726	+	0.205171i	$0.934225\pi$
$642$	−31.3600	−	19.7796i	−1.23768	−	0.780638i
$643$	−19.2473	+	8.15533i	−0.759041	+	0.321615i	−0.734974	−	0.678096i	$-0.762806\pi$
$643$	−19.2473	+	8.15533i	−0.759041	+	0.321615i	−0.0240670	+	0.999710i	$0.507662\pi$
$644$	2.48109	+	2.19365i	0.0977685	+	0.0864419i
$645$	−6.56038	+	12.2522i	−0.258315	+	0.482430i
$646$	1.30375	+	7.99716i	0.0512953	+	0.314644i
$647$	15.7194	−	5.72139i	0.617993	−	0.224931i	−0.0140041	−	0.999902i	$-0.504458\pi$
$647$	15.7194	−	5.72139i	0.617993	−	0.224931i	0.631997	+	0.774971i	$0.282236\pi$
$648$	−15.3486	+	12.1846i	−0.602950	+	0.478658i
$649$	26.7541	+	9.73769i	1.05019	+	0.382238i
$650$	2.64578	−	13.9480i	0.103776	−	0.547087i
$651$	3.24629	−	3.66927i	0.127232	−	0.143810i
$652$	5.66377	−	4.50816i	0.221810	−	0.176553i
$653$	−3.68573	−	5.68356i	−0.144234	−	0.222415i	0.759503	−	0.650504i	$-0.225442\pi$
$653$	−3.68573	−	5.68356i	−0.144234	−	0.222415i	−0.903737	+	0.428089i	$0.859187\pi$
$654$	26.5029	+	21.3908i	1.03635	+	0.836446i
$655$	−34.8929	−	7.32246i	−1.36338	−	0.286112i
$656$	38.7769	−	12.4333i	1.51398	−	0.485439i
$657$	14.9049	+	19.0013i	0.581496	+	0.741310i
$658$	1.44299	+	1.11840i	0.0562537	+	0.0435999i
$659$	1.22563	−	1.47997i	0.0477436	−	0.0576514i	−0.745772	−	0.666201i	$-0.767919\pi$
$659$	1.22563	−	1.47997i	0.0477436	−	0.0576514i	0.793516	+	0.608550i	$0.208248\pi$
$660$	−8.33274	+	1.02587i	−0.324351	+	0.0399321i
$661$	20.4188	+	9.92624i	0.794198	+	0.386086i	0.789382	−	0.613902i	$-0.210401\pi$
$661$	20.4188	+	9.92624i	0.794198	+	0.386086i	0.00481624	+	0.999988i	$0.498467\pi$
$662$	−19.1734	+	9.94171i	−0.745197	+	0.386395i
$663$	−41.7055	−	29.4240i	−1.61971	−	1.14273i
$664$	−1.47247	−	11.9286i	−0.0571431	−	0.462919i
$665$	−1.72095	−	0.133763i	−0.0667355	−	0.00518709i
$666$	−7.26555	−	48.7220i	−0.281534	−	1.88794i
$667$	8.14357	+	31.6153i	0.315320	+	1.22415i
$668$	1.80892	−	3.32905i	0.0699893	−	0.128805i
$669$	−5.14587	−	44.1491i	−0.198951	−	1.70690i
$670$	−6.68805	+	1.13476i	−0.258382	+	0.0438395i
$671$	−17.5001	+	10.8725i	−0.675584	+	0.419727i
$672$	2.66584	+	4.69059i	0.102837	+	0.180943i
$673$	11.7919	−	26.3932i	0.454544	−	1.01738i	−0.530908	−	0.847430i	$-0.678149\pi$
$673$	11.7919	−	26.3932i	0.454544	−	1.01738i	0.985452	−	0.169952i	$-0.0543613\pi$
$674$	11.7867	+	12.4932i	0.454008	+	0.481220i
$675$	4.75971	+	5.39388i	0.183201	+	0.207611i
$676$	−12.0923	+	12.8171i	−0.465089	+	0.492965i
$677$	−7.88631	−	18.9525i	−0.303095	−	0.728405i	−0.999937	−	0.0111808i	$-0.996441\pi$
$677$	−7.88631	−	18.9525i	−0.303095	−	0.728405i	0.696842	−	0.717225i	$-0.254588\pi$
$678$	0.153947	+	12.2114i	0.00591229	+	0.468977i
$679$	8.37782	+	5.82595i	0.321511	+	0.223580i
$680$	−14.0455	−	13.4239i	−0.538620	−	0.514783i
$681$	0.608370	+	0.0832956i	0.0233128	+	0.00319190i
$682$	−5.38970	+	19.8577i	−0.206382	+	0.760390i
$683$	8.06181	−	23.5615i	0.308476	−	0.901556i	−0.677624	−	0.735408i	$-0.736990\pi$
$683$	8.06181	−	23.5615i	0.308476	−	0.901556i	0.986101	−	0.166148i	$-0.0531330\pi$
$684$	−1.26379	+	1.69528i	−0.0483223	+	0.0648208i
$685$	2.79361	+	1.68595i	0.106738	+	0.0644168i
$686$	17.0247	−	7.47462i	0.650005	−	0.285382i
$687$	−15.6028	+	0.701460i	−0.595284	+	0.0267624i
$688$	−19.2934	+	7.30604i	−0.735553	+	0.278540i
$689$	25.7353	+	8.99185i	0.980438	+	0.342562i
$690$	−10.2569	−	29.3863i	−0.390472	−	1.11872i
$691$	−4.34479	−	6.51382i	−0.165283	−	0.247797i	0.739999	−	0.672608i	$-0.234826\pi$
$691$	−4.34479	−	6.51382i	−0.165283	−	0.247797i	−0.905282	+	0.424811i	$0.860341\pi$
$692$	14.2023	+	2.78925i	0.539892	+	0.106031i
$693$	8.42972	+	5.09478i	0.320219	+	0.193535i
$694$	−9.37229	+	11.6198i	−0.355767	+	0.441082i
$695$	30.3564	+	14.2750i	1.15148	+	0.541483i
$696$	−1.65550	+	21.2107i	−0.0627517	+	0.803990i
$697$	−39.0049	−	2.52486i	−1.47742	−	0.0956361i
$698$	14.3793	+	52.9789i	0.544266	+	2.00528i
$699$	28.9980	+	12.0773i	1.09681	+	0.456804i
$700$	0.667467	−	0.426741i	0.0252279	−	0.0161293i
$701$	−6.48703	+	15.0386i	−0.245012	+	0.568001i	−0.995698	−	0.0926578i	$-0.970464\pi$
$701$	−6.48703	+	15.0386i	−0.245012	+	0.568001i	0.750686	+	0.660659i	$0.229723\pi$
$702$	−8.18259	−	52.6527i	−0.308832	−	1.98725i
$703$	4.21148	+	9.76331i	0.158839	+	0.368230i
$704$	12.2046	+	8.25505i	0.459977	+	0.311124i
$705$	−1.67202	−	3.94967i	−0.0629719	−	0.148753i
$706$	12.0677	−	36.8165i	0.454175	−	1.38561i
$707$	7.37150	+	4.31971i	0.277234	+	0.162460i
$708$	3.85987	−	7.67946i	0.145063	−	0.288612i
$709$	−10.4355	−	3.49543i	−0.391915	−	0.131274i	0.114797	−	0.993389i	$-0.463378\pi$
$709$	−10.4355	−	3.49543i	−0.391915	−	0.131274i	−0.506712	+	0.862115i	$0.669139\pi$
$710$	−25.1991	−	36.7411i	−0.945704	−	1.37887i
$711$	9.30129	−	1.57198i	0.348825	−	0.0589537i
$712$	−25.5013	−	11.5918i	−0.955703	−	0.434420i
$713$	−19.0425	−	0.985633i	−0.713148	−	0.0369123i
$714$	−1.61130	−	11.2797i	−0.0603013	−	0.422131i
$715$	−17.5440	+	42.1620i	−0.656107	+	1.57677i
$716$	−2.45753	−	5.50055i	−0.0918421	−	0.205565i
$717$	5.13157	+	0.567869i	0.191642	+	0.0212074i
$718$	32.8547	+	18.6866i	1.22613	+	0.697376i
$719$	27.6114	+	8.85323i	1.02973	+	0.330170i	0.771713	−	0.635970i	$-0.219400\pi$
$719$	27.6114	+	8.85323i	1.02973	+	0.330170i	0.258017	+	0.966140i	$0.416931\pi$
$720$	−0.162297	−	27.8873i	−0.00604843	−	1.03930i
$721$	9.55731	+	0.370867i	0.355933	+	0.0138118i
$722$	−10.8686	+	27.1023i	−0.404488	+	1.00864i
$723$	−10.0140	−	22.0491i	−0.372424	−	0.820015i
$724$	5.94100	+	1.82055i	0.220796	+	0.0676601i
$725$	7.80708	+	0.201910i	0.289948	+	0.00749877i
$726$	−10.2194	−	0.864124i	−0.379277	−	0.0320706i
$727$	7.39866	+	0.0956579i	0.274401	+	0.00354776i	0.150006	−	0.988685i	$-0.452071\pi$
$727$	7.39866	+	0.0956579i	0.274401	+	0.00354776i	0.124395	+	0.992233i	$0.460301\pi$
$728$	11.7390			0.435077
$729$	23.6148	+	13.0897i	0.874622	+	0.484805i
$730$	−24.9950			−0.925108
$731$	19.8004	+	0.256002i	0.732346	+	0.00946856i
$732$	2.64488	+	5.62915i	0.0977577	+	0.208059i
$733$	8.08084	+	0.208991i	0.298473	+	0.00771925i	0.174801	−	0.984604i	$-0.444072\pi$
$733$	8.08084	+	0.208991i	0.298473	+	0.00771925i	0.123672	+	0.992323i	$0.460533\pi$
$734$	−54.3440	−	16.6531i	−2.00587	−	0.614675i
$735$	−20.5292	−	2.00351i	−0.757231	−	0.0739006i
$736$	7.81586	−	19.4899i	0.288096	−	0.718406i
$737$	−8.34900	−	0.323979i	−0.307539	−	0.0119339i
$738$	−26.4106	−	31.1055i	−0.972187	−	1.14501i
$739$	−11.5018	−	3.68791i	−0.423101	−	0.135662i	0.0861453	−	0.996283i	$-0.472545\pi$
$739$	−11.5018	−	3.68791i	−0.423101	−	0.135662i	−0.509247	+	0.860621i	$0.670076\pi$
$740$	11.0783	+	6.30094i	0.407247	+	0.231627i
$741$	4.62028	+	10.5327i	0.169730	+	0.386927i
$742$	2.48247	+	5.55637i	0.0911342	+	0.203981i
$743$	−13.4015	+	32.2068i	−0.491653	+	1.18155i	0.463675	+	0.886005i	$0.346531\pi$
$743$	−13.4015	+	32.2068i	−0.491653	+	1.18155i	−0.955328	+	0.295546i	$0.904498\pi$
$744$	−11.5317	−	4.62879i	−0.422774	−	0.169700i
$745$	−28.5754	−	1.47905i	−1.04692	−	0.0541883i
$746$	52.3355	+	23.7894i	1.91614	+	0.870991i
$747$	−14.3994	+	8.17757i	−0.526846	+	0.299202i
$748$	6.76593	+	9.86497i	0.247387	+	0.360699i
$749$	−10.6712	−	3.57437i	−0.389917	−	0.130605i
$750$	−34.2783	+	1.98540i	−1.25167	+	0.0724966i
$751$	−16.8515	−	9.87500i	−0.614920	−	0.360344i	0.164935	−	0.986304i	$-0.447259\pi$
$751$	−16.8515	−	9.87500i	−0.614920	−	0.360344i	−0.779855	+	0.625960i	$0.784707\pi$
$752$	1.98305	−	6.04993i	0.0723144	−	0.220618i
$753$	−34.2075	−	4.23380i	−1.24659	−	0.154288i
$754$	−47.9160	−	32.4100i	−1.74500	−	1.18030i
$755$	−8.05402	−	18.6713i	−0.293116	−	0.679519i
$756$	1.82381	−	2.34844i	0.0663314	−	0.0854118i
$757$	18.9887	−	44.0207i	0.690155	−	1.59996i	−0.105649	−	0.994404i	$-0.533692\pi$
$757$	18.9887	−	44.0207i	0.690155	−	1.59996i	0.795803	−	0.605555i	$-0.207049\pi$
$758$	−38.3427	+	24.5142i	−1.39267	+	0.890396i
$759$	−4.93017	−	38.0176i	−0.178954	−	1.37995i
$760$	1.14680	+	4.22523i	0.0415987	+	0.153265i
$761$	15.3259	+	0.992074i	0.555562	+	0.0359627i	0.339825	−	0.940489i	$-0.389632\pi$
$761$	15.3259	+	0.992074i	0.555562	+	0.0359627i	0.215737	+	0.976451i	$0.430784\pi$
$762$	8.16338	+	5.60276i	0.295728	+	0.202967i
$763$	9.35501	+	4.39918i	0.338674	+	0.159261i
$764$	−3.09660	+	3.83918i	−0.112031	+	0.138897i
$765$	−9.65738	+	24.9653i	−0.349163	+	0.902624i
$766$	54.5648	+	10.7162i	1.97151	+	0.387192i
$767$	−25.9417	−	38.8925i	−0.936701	−	1.40433i

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)

\(f(q)\)	\(=\)	\(q+(-1.63282 - 0.0211109i) q^{2} +(0.989331 - 1.42170i) q^{3} +(0.666340 + 0.0172332i) q^{4} +(-1.81802 - 0.557111i) q^{5} +(-1.64542 + 2.30050i) q^{6} +(-0.319539 + 0.796813i) q^{7} +(2.17581 + 0.0844315i) q^{8} +(-1.04245 - 2.81306i) q^{9} +O(q^{10})\)	\(q+(-1.63282 - 0.0211109i) q^{2} +(0.989331 - 1.42170i) q^{3} +(0.666340 + 0.0172332i) q^{4} +(-1.81802 - 0.557111i) q^{5} +(-1.64542 + 2.30050i) q^{6} +(-0.319539 + 0.796813i) q^{7} +(2.17581 + 0.0844315i) q^{8} +(-1.04245 - 2.81306i) q^{9} +(2.95675 + 0.948044i) q^{10} +(3.32432 + 1.89075i) q^{11} +(0.683731 - 0.930285i) q^{12} +(-2.56163 - 5.73356i) q^{13} +(0.538573 - 1.29431i) q^{14} +(-2.59067 + 2.03351i) q^{15} +(-4.88228 - 0.252705i) q^{16} +(4.27192 + 1.94182i) q^{17} +(1.64275 + 4.61524i) q^{18} +(-0.598085 - 0.872029i) q^{19} +(-1.20182 - 0.402555i) q^{20} +(0.816698 + 1.24260i) q^{21} +(-5.38812 - 3.15745i) q^{22} +(1.80262 - 5.49948i) q^{23} +(2.27264 - 3.00982i) q^{24} +(-1.14674 - 0.775642i) q^{25} +(4.06166 + 9.41598i) q^{26} +(-5.03065 - 1.30100i) q^{27} +(-0.226653 + 0.525442i) q^{28} +(-4.75276 + 3.03865i) q^{29} +(4.27304 - 3.26568i) q^{30} +(-0.863028 - 3.17972i) q^{31} +(3.62077 + 0.234380i) q^{32} +(5.97693 - 2.85560i) q^{33} +(-6.93430 - 3.26084i) q^{34} +(1.02484 - 1.27061i) q^{35} +(-0.646147 - 1.89242i) q^{36} +(-9.86702 - 1.93782i) q^{37} +(0.958158 + 1.43650i) q^{38} +(-10.6857 - 2.03052i) q^{39} +(-3.90864 - 1.36567i) q^{40} +(-7.78969 + 2.94981i) q^{41} +(-1.30729 - 2.04619i) q^{42} +(3.86390 - 1.69643i) q^{43} +(2.18254 + 1.31717i) q^{44} +(0.328011 + 5.69496i) q^{45} +(-3.05947 + 8.94164i) q^{46} +(-0.341120 + 1.25682i) q^{47} +(-5.18946 + 6.69112i) q^{48} +(4.52765 + 4.32728i) q^{49} +(1.85604 + 1.29070i) q^{50} +(6.98702 - 4.15227i) q^{51} +(-1.60811 - 3.86465i) q^{52} +(-2.97902 + 3.15758i) q^{53} +(8.18670 + 2.23050i) q^{54} +(-4.99033 - 5.28945i) q^{55} +(-0.762534 + 1.70674i) q^{56} +(-1.83146 - 0.0124293i) q^{57} +(7.82458 - 4.86126i) q^{58} +(7.33969 - 1.24532i) q^{59} +(-1.76131 + 1.31036i) q^{60} +(-2.57204 + 4.73346i) q^{61} +(1.34205 + 5.21014i) q^{62} +(2.57459 + 0.0682457i) q^{63} +(3.84110 + 0.298554i) q^{64} +(1.46288 + 11.8509i) q^{65} +(-9.81957 + 4.53652i) q^{66} +(-1.93951 + 1.00566i) q^{67} +(2.81308 + 1.36753i) q^{68} +(-6.03521 - 8.00359i) q^{69} +(-1.70021 + 2.05304i) q^{70} +(-11.3409 - 8.78987i) q^{71} +(-2.03066 - 6.20871i) q^{72} +(-7.66548 + 2.45784i) q^{73} +(16.0702 + 3.37242i) q^{74} +(-2.23723 + 0.862945i) q^{75} +(-0.383500 - 0.591374i) q^{76} +(-2.56883 + 2.04469i) q^{77} +(17.4050 + 3.54107i) q^{78} +(-0.586006 + 3.08931i) q^{79} +(8.73532 + 3.17940i) q^{80} +(-6.82660 + 5.86494i) q^{81} +(12.7815 - 4.65207i) q^{82} +(-0.888150 - 5.44789i) q^{83} +(0.522784 + 0.842068i) q^{84} +(-6.68463 - 5.91021i) q^{85} +(-6.34489 + 2.68841i) q^{86} +(-0.382009 + 9.76323i) q^{87} +(7.07347 + 4.39460i) q^{88} +(-11.9092 - 4.86543i) q^{89} +(-0.415359 - 9.30580i) q^{90} +(5.38712 - 0.209045i) q^{91} +(1.29593 - 3.63346i) q^{92} +(-5.37442 - 1.91883i) q^{93} +(0.583523 - 2.04496i) q^{94} +(0.601515 + 1.91857i) q^{95} +(3.91536 - 4.91576i) q^{96} +(2.66636 - 11.5834i) q^{97} +(-7.30151 - 7.16127i) q^{98} +(1.85336 - 11.3225i) 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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