LMFDB - Embedded newform 729.2.k.a.547.1

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			547.1
Character	$\chi$	$=$	729.547
Dual form			729.2.k.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72490 + 0.0352304i) q^{2} +(-1.51002 + 0.848437i) q^{3} +(5.42450 - 0.140291i) q^{4} +(0.633611 - 0.194162i) q^{5} +(4.08476 - 2.36510i) q^{6} +(1.09035 + 2.71893i) q^{7} +(-9.33012 + 0.362051i) q^{8} +(1.56031 - 2.56231i) q^{9} +O(q^{10})$	\(q+(-2.72490 + 0.0352304i) q^{2} +(-1.51002 + 0.848437i) q^{3} +(5.42450 - 0.140291i) q^{4} +(0.633611 - 0.194162i) q^{5} +(4.08476 - 2.36510i) q^{6} +(1.09035 + 2.71893i) q^{7} +(-9.33012 + 0.362051i) q^{8} +(1.56031 - 2.56231i) q^{9} +(-1.71968 + 0.551395i) q^{10} +(1.46606 - 0.833840i) q^{11} +(-8.07206 + 4.81419i) q^{12} +(2.23325 - 4.99855i) q^{13} +(-3.06688 - 7.37039i) q^{14} +(-0.792029 + 0.830767i) q^{15} +(14.5728 - 0.754280i) q^{16} +(1.23299 - 0.560463i) q^{17} +(-4.16141 + 7.03701i) q^{18} +(1.81231 - 2.64242i) q^{19} +(3.40978 - 1.14212i) q^{20} +(-3.95329 - 3.18054i) q^{21} +(-3.96548 + 2.32378i) q^{22} +(-0.783008 - 2.38882i) q^{23} +(13.7815 - 8.46272i) q^{24} +(-3.77781 + 2.55527i) q^{25} +(-5.90927 + 13.6992i) q^{26} +(-0.182133 + 5.19296i) q^{27} +(6.29604 + 14.5959i) q^{28} +(-6.01114 - 3.84319i) q^{29} +(2.12893 - 2.29166i) q^{30} +(1.42648 - 5.25570i) q^{31} +(-21.0474 + 1.36244i) q^{32} +(-1.50631 + 2.50297i) q^{33} +(-3.34003 + 1.57064i) q^{34} +(1.21877 + 1.51104i) q^{35} +(8.10442 - 14.1182i) q^{36} +(-9.92713 + 1.94962i) q^{37} +(-4.84528 + 7.26417i) q^{38} +(0.868716 + 9.44268i) q^{39} +(-5.84136 + 2.04095i) q^{40} +(-4.95892 - 1.87785i) q^{41} +(10.8844 + 8.52737i) q^{42} +(5.12901 + 2.25187i) q^{43} +(7.83565 - 4.72884i) q^{44} +(0.491124 - 1.92646i) q^{45} +(2.21778 + 6.48170i) q^{46} +(-2.78011 - 10.2430i) q^{47} +(-21.3652 + 13.5030i) q^{48} +(-1.14325 + 1.09266i) q^{49} +(10.2041 - 7.09596i) q^{50} +(-1.38632 + 1.89243i) q^{51} +(11.4130 - 27.4280i) q^{52} +(2.74430 + 2.90879i) q^{53} +(0.313345 - 14.1567i) q^{54} +(0.767010 - 0.812983i) q^{55} +(-11.1575 - 24.9732i) q^{56} +(-0.494700 + 5.52773i) q^{57} +(16.5152 + 10.2605i) q^{58} +(14.3490 + 2.43458i) q^{59} +(-4.17981 + 4.61761i) q^{60} +(-1.85519 - 3.41421i) q^{61} +(-3.70186 + 14.3715i) q^{62} +(8.66802 + 1.44855i) q^{63} +(28.2073 - 2.19245i) q^{64} +(0.444479 - 3.60075i) q^{65} +(4.01637 - 6.87341i) q^{66} +(-7.07605 - 3.66904i) q^{67} +(6.60974 - 3.21321i) q^{68} +(3.20912 + 2.94282i) q^{69} +(-3.37426 - 4.07449i) q^{70} +(6.79467 - 5.26626i) q^{71} +(-13.6302 + 24.4716i) q^{72} +(2.20463 + 0.706886i) q^{73} +(26.9817 - 5.66227i) q^{74} +(3.53656 - 7.06374i) q^{75} +(9.46019 - 14.5881i) q^{76} +(3.86567 + 3.07693i) q^{77} +(-2.69983 - 25.6997i) q^{78} +(-2.76639 - 14.5839i) q^{79} +(9.08700 - 3.30740i) q^{80} +(-4.13088 - 7.99599i) q^{81} +(13.5787 + 4.94225i) q^{82} +(-0.646758 + 3.96720i) q^{83} +(-21.8908 - 16.6982i) q^{84} +(0.672416 - 0.594516i) q^{85} +(-14.0554 - 5.95543i) q^{86} +(12.3376 + 0.703210i) q^{87} +(-13.3766 + 8.31061i) q^{88} +(2.95081 - 1.20554i) q^{89} +(-1.27039 + 5.26671i) q^{90} +(16.0257 + 0.621871i) q^{91} +(-4.58256 - 12.8483i) q^{92} +(2.30512 + 9.14649i) q^{93} +(7.93639 + 27.8132i) q^{94} +(0.635244 - 2.02615i) q^{95} +(30.6260 - 19.9147i) q^{96} +(-0.516441 - 2.24357i) q^{97} +(3.07675 - 3.01766i) q^{98} +(0.150945 - 5.05754i) 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{242}{243}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.72490	+	0.0352304i	−1.92679	+	0.0249117i	−0.966859	−	0.255310i	$-0.917822\pi$
$2$	−2.72490	+	0.0352304i	−1.92679	+	0.0249117i	−0.959935	+	0.280222i	$0.909592\pi$
$3$	−1.51002	+	0.848437i	−0.871809	+	0.489845i
$3$	−1.51002	+	0.848437i	−0.871809	+	0.489845i
$4$	5.42450	−	0.140291i	2.71225	−	0.0701456i
$5$	0.633611	−	0.194162i	0.283359	−	0.0868319i	−0.148076	−	0.988976i	$-0.547308\pi$
$5$	0.633611	−	0.194162i	0.283359	−	0.0868319i	0.431435	+	0.902144i	$0.358007\pi$
$6$	4.08476	−	2.36510i	1.66759	−	0.965550i
$7$	1.09035	+	2.71893i	0.412113	+	1.02766i	0.979000	+	0.203862i	$0.0653495\pi$
$7$	1.09035	+	2.71893i	0.412113	+	1.02766i	−0.566886	+	0.823796i	$0.691852\pi$
$8$	−9.33012	+	0.362051i	−3.29869	+	0.128004i
$9$	1.56031	−	2.56231i	0.520103	−	0.854104i
$10$	−1.71968	+	0.551395i	−0.543812	+	0.174366i
$11$	1.46606	−	0.833840i	0.442033	−	0.251412i	−0.257127	−	0.966378i	$-0.582776\pi$
$11$	1.46606	−	0.833840i	0.442033	−	0.251412i	0.699160	+	0.714966i	$0.253558\pi$
$12$	−8.07206	+	4.81419i	−2.33020	+	1.38974i
$13$	2.23325	−	4.99855i	0.619391	−	1.38635i	−0.284537	−	0.958665i	$-0.591840\pi$
$13$	2.23325	−	4.99855i	0.619391	−	1.38635i	0.903928	−	0.427684i	$-0.140670\pi$
$14$	−3.06688	−	7.37039i	−0.819658	−	1.96982i
$15$	−0.792029	+	0.830767i	−0.204501	+	0.214503i
$16$	14.5728	−	0.754280i	3.64319	−	0.188570i
$17$	1.23299	−	0.560463i	0.299044	−	0.135932i	−0.258669	−	0.965966i	$-0.583284\pi$
$17$	1.23299	−	0.560463i	0.299044	−	0.135932i	0.557713	+	0.830034i	$0.311679\pi$
$18$	−4.16141	+	7.03701i	−0.980854	+	1.65864i
$19$	1.81231	−	2.64242i	0.415773	−	0.606212i	−0.559065	−	0.829124i	$-0.688840\pi$
$19$	1.81231	−	2.64242i	0.415773	−	0.606212i	0.974839	+	0.222911i	$0.0715560\pi$
$20$	3.40978	−	1.14212i	0.762450	−	0.255386i
$21$	−3.95329	−	3.18054i	−0.862678	−	0.694050i
$22$	−3.96548	+	2.32378i	−0.845444	+	0.495431i
$23$	−0.783008	−	2.38882i	−0.163268	−	0.498103i	0.835403	−	0.549638i	$-0.185234\pi$
$23$	−0.783008	−	2.38882i	−0.163268	−	0.498103i	−0.998671	+	0.0515358i	$0.983588\pi$
$24$	13.7815	−	8.46272i	2.81313	−	1.72745i
$25$	−3.77781	+	2.55527i	−0.755561	+	0.511055i
$26$	−5.90927	+	13.6992i	−1.15890	+	2.68664i
$27$	−0.182133	+	5.19296i	−0.0350516	+	0.999386i
$28$	6.29604	+	14.5959i	1.18984	+	2.75836i
$29$	−6.01114	−	3.84319i	−1.11624	−	0.713663i	−0.154601	−	0.987977i	$-0.549409\pi$
$29$	−6.01114	−	3.84319i	−1.11624	−	0.713663i	−0.961640	+	0.274314i	$0.911549\pi$
$30$	2.12893	−	2.29166i	0.388688	−	0.418398i
$31$	1.42648	−	5.25570i	0.256204	−	0.943952i	−0.713697	−	0.700454i	$-0.752981\pi$
$31$	1.42648	−	5.25570i	0.256204	−	0.943952i	0.969901	−	0.243498i	$-0.0782949\pi$
$32$	−21.0474	+	1.36244i	−3.72069	+	0.240848i
$33$	−1.50631	+	2.50297i	−0.262215	+	0.435711i
$34$	−3.34003	+	1.57064i	−0.572811	+	0.269363i
$35$	1.21877	+	1.51104i	0.206010	+	0.255412i
$36$	8.10442	−	14.1182i	1.35074	−	2.35303i
$37$	−9.92713	+	1.94962i	−1.63201	+	0.320516i	−0.923034	−	0.384717i	$-0.874299\pi$
$37$	−9.92713	+	1.94962i	−1.63201	+	0.320516i	−0.708975	+	0.705234i	$0.750842\pi$
$38$	−4.84528	+	7.26417i	−0.786008	+	1.17840i
$39$	0.868716	+	9.44268i	0.139106	+	1.51204i
$40$	−5.84136	+	2.04095i	−0.923601	+	0.322703i
$41$	−4.95892	−	1.87785i	−0.774454	−	0.293271i	−0.0648713	−	0.997894i	$-0.520664\pi$
$41$	−4.95892	−	1.87785i	−0.774454	−	0.293271i	−0.709582	+	0.704622i	$0.751116\pi$
$42$	10.8844	+	8.52737i	1.67949	+	1.31580i
$43$	5.12901	+	2.25187i	0.782166	+	0.343407i	0.754577	−	0.656212i	$-0.227842\pi$
$43$	5.12901	+	2.25187i	0.782166	+	0.343407i	0.0275897	+	0.999619i	$0.491217\pi$
$44$	7.83565	−	4.72884i	1.18127	−	0.712900i
$45$	0.491124	−	1.92646i	0.0732124	−	0.287180i
$46$	2.21778	+	6.48170i	0.326993	+	0.955674i
$47$	−2.78011	−	10.2430i	−0.405521	−	1.49409i	−0.813751	−	0.581214i	$-0.802578\pi$
$47$	−2.78011	−	10.2430i	−0.405521	−	1.49409i	0.408230	−	0.912879i	$-0.366146\pi$
$48$	−21.3652	+	13.5030i	−3.08379	+	1.94900i
$49$	−1.14325	+	1.09266i	−0.163322	+	0.156094i
$50$	10.2041	−	7.09596i	1.44308	−	1.00352i
$51$	−1.38632	+	1.89243i	−0.194124	+	0.264993i
$52$	11.4130	−	27.4280i	1.58270	−	3.80357i
$53$	2.74430	+	2.90879i	0.376959	+	0.399553i	0.887880	−	0.460074i	$-0.152177\pi$
$53$	2.74430	+	2.90879i	0.376959	+	0.399553i	−0.510922	+	0.859627i	$0.670696\pi$
$54$	0.313345	−	14.1567i	0.0426408	−	1.92648i
$55$	0.767010	−	0.812983i	0.103424	−	0.109623i
$56$	−11.1575	−	24.9732i	−1.49098	−	3.33718i
$57$	−0.494700	+	5.52773i	−0.0655247	+	0.732166i
$58$	16.5152	+	10.2605i	2.16855	+	1.34727i
$59$	14.3490	+	2.43458i	1.86808	+	0.316955i	0.987583	−	0.157101i	$-0.0502148\pi$
$59$	14.3490	+	2.43458i	1.86808	+	0.316955i	0.880494	+	0.474056i	$0.157211\pi$
$60$	−4.17981	+	4.61761i	−0.539611	+	0.596131i
$61$	−1.85519	−	3.41421i	−0.237533	−	0.437145i	0.732277	−	0.681007i	$-0.238458\pi$
$61$	−1.85519	−	3.41421i	−0.237533	−	0.437145i	−0.969810	+	0.243863i	$0.921585\pi$
$62$	−3.70186	+	14.3715i	−0.470137	+	1.82518i
$63$	8.66802	+	1.44855i	1.09207	+	0.182501i
$64$	28.2073	−	2.19245i	3.52592	−	0.274056i
$65$	0.444479	−	3.60075i	0.0551309	−	0.446618i
$66$	4.01637	−	6.87341i	0.494381	−	0.846059i
$67$	−7.07605	−	3.66904i	−0.864477	−	0.448244i	−0.0301705	−	0.999545i	$-0.509605\pi$
$67$	−7.07605	−	3.66904i	−0.864477	−	0.448244i	−0.834307	+	0.551301i	$0.814132\pi$
$68$	6.60974	−	3.21321i	0.801548	−	0.389659i
$69$	3.20912	+	2.94282i	0.386332	+	0.354274i
$70$	−3.37426	−	4.07449i	−0.403301	−	0.486994i
$71$	6.79467	−	5.26626i	0.806378	−	0.624990i	−0.123713	−	0.992318i	$-0.539480\pi$
$71$	6.79467	−	5.26626i	0.806378	−	0.624990i	0.930092	+	0.367328i	$0.119727\pi$
$72$	−13.6302	+	24.4716i	−1.60633	+	2.88400i
$73$	2.20463	+	0.706886i	0.258032	+	0.0827348i	0.431527	−	0.902100i	$-0.357975\pi$
$73$	2.20463	+	0.706886i	0.258032	+	0.0827348i	−0.173494	+	0.984835i	$0.555506\pi$
$74$	26.9817	−	5.66227i	3.13656	−	0.658225i
$75$	3.53656	−	7.06374i	0.408367	−	0.815651i
$76$	9.46019	−	14.5881i	1.08516	−	1.67336i
$77$	3.86567	+	3.07693i	0.440534	+	0.350649i
$78$	−2.69983	−	25.6997i	−0.305696	−	2.90992i
$79$	−2.76639	−	14.5839i	−0.311244	−	1.64081i	−0.696177	−	0.717870i	$-0.745117\pi$
$79$	−2.76639	−	14.5839i	−0.311244	−	1.64081i	0.384933	−	0.922944i	$-0.374225\pi$
$80$	9.08700	−	3.30740i	1.01596	−	0.369778i
$81$	−4.13088	−	7.99599i	−0.458986	−	0.888443i
$82$	13.5787	+	4.94225i	1.49952	+	0.545780i
$83$	−0.646758	+	3.96720i	−0.0709909	+	0.435457i	0.927160	+	0.374666i	$0.122243\pi$
$83$	−0.646758	+	3.96720i	−0.0709909	+	0.435457i	−0.998151	+	0.0607904i	$0.980638\pi$
$84$	−21.8908	−	16.6982i	−2.38848	−	1.82192i
$85$	0.672416	−	0.594516i	0.0729337	−	0.0644843i
$86$	−14.0554	−	5.95543i	−1.51563	−	0.642190i
$87$	12.3376	+	0.703210i	1.32273	+	0.0753921i
$88$	−13.3766	+	8.31061i	−1.42595	+	0.885914i
$89$	2.95081	−	1.20554i	0.312785	−	0.127787i	−0.216371	−	0.976311i	$-0.569422\pi$
$89$	2.95081	−	1.20554i	0.312785	−	0.127787i	0.529156	+	0.848524i	$0.322509\pi$
$90$	−1.27039	+	5.26671i	−0.133911	+	0.555160i
$91$	16.0257	+	0.621871i	1.67995	+	0.0651898i
$92$	−4.58256	−	12.8483i	−0.477764	−	1.33953i
$93$	2.30512	+	9.14649i	0.239030	+	0.948447i
$94$	7.93639	+	27.8132i	0.818576	+	2.86871i
$95$	0.635244	−	2.02615i	0.0651746	−	0.207878i
$96$	30.6260	−	19.9147i	3.12576	−	2.03254i
$97$	−0.516441	−	2.24357i	−0.0524366	−	0.227800i	0.941618	−	0.336684i	$-0.109305\pi$
$97$	−0.516441	−	2.24357i	−0.0524366	−	0.227800i	−0.994054	+	0.108884i	$0.965272\pi$
$98$	3.07675	−	3.01766i	0.310799	−	0.304829i
$99$	0.150945	−	5.05754i	0.0151706	−	0.508302i
$100$	−20.1342	+	14.3911i	−2.01342	+	1.43911i
$101$	−0.471912	−	3.15067i	−0.0469570	−	0.313503i	−0.999945	−	0.0104950i	$-0.996659\pi$
$101$	−0.471912	−	3.15067i	−0.0469570	−	0.313503i	0.952988	−	0.303008i	$-0.0979909\pi$
$102$	3.71091	−	5.20551i	0.367435	−	0.515422i
$103$	1.42865	−	4.00557i	0.140770	−	0.394681i	−0.850594	−	0.525823i	$-0.823757\pi$
$103$	1.42865	−	4.00557i	0.140770	−	0.394681i	0.991364	+	0.131142i	$0.0418644\pi$
$104$	−19.0267	+	47.4456i	−1.86572	+	4.65243i
$105$	−3.12238	−	1.24764i	−0.304713	−	0.121758i
$106$	−7.58042	−	7.82948i	−0.736276	−	0.760466i
$107$	−0.593389	+	10.1881i	−0.0573651	+	0.984921i	0.839708	+	0.543038i	$0.182726\pi$
$107$	−0.593389	+	10.1881i	−0.0573651	+	0.984921i	−0.897073	+	0.441882i	$0.854311\pi$
$108$	−0.259456	+	28.1948i	−0.0249662	+	2.71304i
$109$	−0.245628	−	4.21728i	−0.0235269	−	0.403942i	−0.989427	−	0.145028i	$-0.953673\pi$
$109$	−0.245628	−	4.21728i	−0.0235269	−	0.403942i	0.965901	−	0.258913i	$-0.0833644\pi$
$110$	−2.06138	+	2.24232i	−0.196545	+	0.213797i
$111$	13.3360	−	11.3665i	1.26580	−	1.07886i
$112$	17.9402	+	38.7998i	1.69519	+	3.66624i
$113$	−2.40371	−	1.76546i	−0.226122	−	0.166081i	0.473047	−	0.881037i	$-0.343154\pi$
$113$	−2.40371	−	1.76546i	−0.226122	−	0.166081i	−0.699169	+	0.714957i	$0.746446\pi$
$114$	1.15326	−	15.0799i	0.108013	−	1.41237i
$115$	−0.959940	−	1.36155i	−0.0895148	−	0.126965i
$116$	−33.1466	−	20.0041i	−3.07759	−	1.85733i
$117$	−9.32330	−	13.5216i	−0.861939	−	1.25007i
$118$	−39.1853	−	6.12846i	−3.60730	−	0.564171i
$119$	2.86825	+	2.74131i	0.262932	+	0.251296i
$120$	7.08894	−	8.03791i	0.647129	−	0.733757i
$121$	−4.16866	+	7.00946i	−0.378969	+	0.637224i
$122$	5.17550	+	9.23802i	0.468568	+	0.836371i
$123$	9.08130	−	1.37175i	0.818833	−	0.123686i
$124$	7.00063	−	28.7097i	0.628675	−	2.57821i
$125$	−3.97775	+	4.93164i	−0.355781	+	0.441099i
$126$	−23.6705	−	3.64178i	−2.10874	−	0.324436i
$127$	0.409141	−	21.0952i	0.0363054	−	1.87190i	−0.333451	−	0.942767i	$-0.608213\pi$
$127$	0.409141	−	21.0952i	0.0363054	−	1.87190i	0.369757	−	0.929129i	$-0.379441\pi$
$128$	−34.7745	+	3.15567i	−3.07366	+	0.278924i
$129$	−9.65546	+	0.951273i	−0.850116	+	0.0837550i
$130$	−1.08430	+	9.82733i	−0.0950998	+	0.861914i
$131$	0.476593	+	0.0432491i	0.0416401	+	0.00377869i	0.111175	−	0.993801i	$-0.464538\pi$
$131$	0.476593	+	0.0432491i	0.0416401	+	0.00377869i	−0.0695353	+	0.997579i	$0.522152\pi$
$132$	−7.81985	+	13.7887i	−0.680631	+	1.20015i
$133$	9.16060	+	2.04639i	0.794325	+	0.177445i
$134$	19.4108	+	9.74846i	1.67684	+	0.842139i
$135$	0.892874	+	3.32568i	0.0768464	+	0.286229i
$136$	−11.3010	+	5.67560i	−0.969056	+	0.486678i
$137$	19.1363	−	4.79750i	1.63492	−	0.409878i	0.686562	−	0.727072i	$-0.259119\pi$
$137$	19.1363	−	4.79750i	1.63492	−	0.409878i	0.948361	+	0.317194i	$0.102741\pi$
$138$	−8.84819	−	7.90583i	−0.753208	−	0.672989i
$139$	7.68551	−	1.10040i	0.651876	−	0.0933347i	0.192108	−	0.981374i	$-0.438468\pi$
$139$	7.68551	−	1.10040i	0.651876	−	0.0933347i	0.459768	+	0.888039i	$0.347933\pi$
$140$	6.82320	+	8.02564i	0.576666	+	0.678290i
$141$	12.8886	+	13.1083i	1.08541	+	1.10392i
$142$	−18.3292	+	14.5894i	−1.53816	+	1.22432i
$143$	−0.893924	−	9.19034i	−0.0747537	−	0.768535i
$144$	20.8053	−	38.5168i	1.73377	−	3.20974i
$145$	−4.55493	−	1.26795i	−0.378266	−	0.105298i
$146$	−6.03230	−	1.84852i	−0.499237	−	0.152985i
$147$	0.799280	−	2.61991i	0.0659235	−	0.216086i
$148$	−53.5762	+	11.9684i	−4.40394	+	0.983798i
$149$	15.2118	+	3.81363i	1.24620	+	0.312425i	0.809467	−	0.587166i	$-0.199756\pi$
$149$	15.2118	+	3.81363i	1.24620	+	0.312425i	0.436734	+	0.899590i	$0.356135\pi$
$150$	−9.38792	+	19.3726i	−0.766521	+	1.58176i
$151$	−13.3370	+	15.6873i	−1.08535	+	1.27661i	−0.126723	+	0.991938i	$0.540446\pi$
$151$	−13.3370	+	15.6873i	−1.08535	+	1.27661i	−0.958624	+	0.284677i	$0.908114\pi$
$152$	−15.9524	+	25.3102i	−1.29391	+	2.05293i
$153$	0.487765	−	4.03380i	0.0394335	−	0.326114i
$154$	−10.6419	−	8.24813i	−0.857553	−	0.664654i
$155$	−0.116623	−	3.60704i	−0.00936741	−	0.289724i
$156$	6.03707	+	51.0999i	0.483353	+	4.09127i
$157$	−0.945745	−	7.66153i	−0.0754787	−	0.611457i	−0.981943	−	0.189175i	$-0.939419\pi$
$157$	−0.945745	−	7.66153i	−0.0754787	−	0.611457i	0.906465	−	0.422282i	$-0.138771\pi$
$158$	8.05194	+	39.6421i	0.640578	+	3.15376i
$159$	−6.61187	−	2.06396i	−0.524356	−	0.163682i
$160$	−13.0713	+	4.94987i	−1.03338	+	0.391321i
$161$	5.64127	−	4.73358i	0.444594	−	0.373059i
$162$	11.5379	+	21.6427i	0.906505	+	1.70041i
$163$	11.1180	+	9.32912i	0.870830	+	0.730713i	0.964273	−	0.264911i	$-0.0853427\pi$
$163$	11.1180	+	9.32912i	0.870830	+	0.730713i	−0.0934426	+	0.995625i	$0.529787\pi$
$164$	−27.1631	−	9.49071i	−2.12108	−	0.741100i
$165$	−0.468433	+	1.87838i	−0.0364675	+	0.146232i
$166$	1.62258	−	10.8330i	0.125937	−	0.840804i
$167$	4.97299	+	9.74447i	0.384822	+	0.754050i	0.999394	−	0.0348109i	$-0.0110829\pi$
$167$	4.97299	+	9.74447i	0.384822	+	0.754050i	−0.614572	+	0.788861i	$0.710671\pi$
$168$	38.0361	+	28.2435i	2.93455	+	2.17903i
$169$	−11.3245	−	12.6427i	−0.871112	−	0.972513i
$170$	−1.81132	+	1.64368i	−0.138922	+	0.126065i
$171$	−3.94293	−	8.76670i	−0.301523	−	0.670406i
$172$	28.1382	+	11.4957i	2.14552	+	0.876541i
$173$	0.882334	−	0.149705i	0.0670826	−	0.0113819i	−0.133640	−	0.991030i	$-0.542667\pi$
$173$	0.882334	−	0.149705i	0.0670826	−	0.0113819i	0.200723	+	0.979648i	$0.435671\pi$
$174$	−33.6436	−	1.48152i	−2.55052	−	0.112313i
$175$	−11.0667	−	7.48544i	−0.836567	−	0.565846i
$176$	20.7355	−	13.2572i	1.56300	−	0.999296i
$177$	−23.7328	+	8.49794i	−1.78387	+	0.638745i
$178$	−7.99818	+	3.38892i	−0.599489	+	0.254011i
$179$	−10.2758	+	21.4901i	−0.768052	+	1.60625i	0.0269487	+	0.999637i	$0.491421\pi$
$179$	−10.2758	+	21.4901i	−0.768052	+	1.60625i	−0.795001	+	0.606608i	$0.792530\pi$
$180$	2.39384	−	10.5190i	0.178426	−	0.784039i
$181$	18.1807	−	5.06095i	1.35136	−	0.376178i	0.484530	−	0.874775i	$-0.338991\pi$
$181$	18.1807	−	5.06095i	1.35136	−	0.376178i	0.866834	+	0.498597i	$0.166151\pi$
$182$	−43.6904	−	1.12994i	−3.23855	−	0.0837569i
$183$	5.69812	+	3.58150i	0.421217	+	0.264752i
$184$	8.17043	+	22.0044i	0.602332	+	1.62219i
$185$	−5.91139	+	3.16277i	−0.434614	+	0.232532i
$186$	−6.60345	−	24.8420i	−0.484188	−	1.82151i
$187$	1.34030	−	1.84979i	0.0980125	−	0.135270i
$188$	−16.5177	−	55.1731i	−1.20468	−	4.02391i
$189$	−14.3179	+	5.16693i	−1.04147	+	0.375839i
$190$	−1.65959	+	5.54343i	−0.120400	+	0.402162i
$191$	10.5756	+	13.8287i	0.765226	+	1.00061i	0.999595	+	0.0284584i	$0.00905982\pi$
$191$	10.5756	+	13.8287i	0.765226	+	1.00061i	−0.234369	+	0.972148i	$0.575302\pi$
$192$	−40.7334	+	27.2428i	−2.93968	+	1.96608i
$193$	11.9317	+	5.61084i	0.858859	+	0.403877i	0.804009	−	0.594617i	$-0.202696\pi$
$193$	11.9317	+	5.61084i	0.858859	+	0.403877i	0.0548503	+	0.998495i	$0.482532\pi$
$194$	1.48629	+	6.09530i	0.106709	+	0.437617i
$195$	2.38384	+	5.81431i	0.170710	+	0.416371i
$196$	−6.04828	+	6.08751i	−0.432020	+	0.434822i
$197$	−13.0345	−	2.55989i	−0.928670	−	0.182385i	−0.294565	−	0.955632i	$-0.595175\pi$
$197$	−13.0345	−	2.55989i	−0.928670	−	0.182385i	−0.634105	+	0.773247i	$0.718631\pi$
$198$	−0.233131	+	13.7866i	−0.0165679	+	0.979772i
$199$	8.56591	+	4.72647i	0.607221	+	0.335050i	0.756747	−	0.653707i	$-0.226787\pi$
$199$	8.56591	+	4.72647i	0.607221	+	0.335050i	−0.149526	+	0.988758i	$0.547775\pi$
$200$	34.3222	−	25.2088i	2.42695	−	1.78253i
$201$	13.7979	−	0.463274i	0.973230	−	0.0326768i
$202$	1.39691	+	8.56862i	0.0982863	+	0.602886i
$203$	3.89512	−	20.5343i	0.273384	−	1.44122i
$204$	−7.25461	+	10.4600i	−0.507924	+	0.732343i
$205$	−3.50663	−	0.226991i	−0.244914	−	0.0158538i
$206$	−3.75182	+	10.9651i	−0.261402	+	0.763975i
$207$	−7.34262	−	1.72098i	−0.510348	−	0.119616i
$208$	28.7742	−	74.5272i	1.99514	−	5.16753i
$209$	0.453603	−	5.38512i	0.0313764	−	0.372497i
$210$	8.55214	+	3.28970i	0.590153	+	0.227011i
$211$	−10.8114	−	16.2088i	−0.744291	−	1.11586i	−0.989237	−	0.146324i	$-0.953256\pi$
$211$	−10.8114	−	16.2088i	−0.744291	−	1.11586i	0.244946	−	0.969537i	$-0.421230\pi$
$212$	15.2945	+	15.3937i	1.05043	+	1.05725i
$213$	−5.79197	+	13.7170i	−0.396859	+	0.939873i
$214$	1.25799	−	27.7824i	0.0859947	−	1.89917i
$215$	3.68702	+	0.430951i	0.251453	+	0.0293906i
$216$	−0.180791	−	48.5169i	−0.0123013	−	3.30115i
$217$	15.8452	−	1.85204i	1.07565	−	0.125725i
$218$	0.817889	+	11.4830i	0.0553944	+	0.777727i
$219$	−3.92878	+	0.803080i	−0.265482	+	0.0542671i
$220$	4.04659	−	4.51763i	0.272821	−	0.304579i
$221$	−0.0479315	−	7.41483i	−0.00322422	−	0.498775i
$222$	−35.9388	+	31.4424i	−2.41206	+	2.11028i
$223$	4.57967	+	4.04911i	0.306677	+	0.271148i	0.801694	−	0.597735i	$-0.203933\pi$
$223$	4.57967	+	4.04911i	0.306677	+	0.271148i	−0.495016	+	0.868884i	$0.664838\pi$
$224$	−26.6534	−	55.7409i	−1.78086	−	3.72434i
$225$	0.652866	+	13.6669i	0.0435244	+	0.911129i
$226$	6.61207	+	4.72602i	0.439828	+	0.314370i
$227$	6.15563	−	12.0618i	0.408564	−	0.800571i	−0.591420	−	0.806364i	$-0.701432\pi$
$227$	6.15563	−	12.0618i	0.408564	−	0.800571i	0.999983	+	0.00579262i	$0.00184386\pi$
$228$	−1.90801	+	30.0546i	−0.126361	+	1.99041i
$229$	−14.7968	+	19.3482i	−0.977797	+	1.27856i	−0.0174229	+	0.999848i	$0.505546\pi$
$229$	−14.7968	+	19.3482i	−0.977797	+	1.27856i	−0.960374	+	0.278714i	$0.910092\pi$
$230$	2.66371	+	3.67626i	0.175640	+	0.242406i
$231$	−8.44781	−	1.36644i	−0.555825	−	0.0899054i
$232$	57.4761	+	33.6811i	3.77349	+	2.21127i
$233$	1.76446	−	8.14564i	0.115593	−	0.533639i	−0.882410	−	0.470481i	$-0.844080\pi$
$233$	1.76446	−	8.14564i	0.115593	−	0.533639i	0.998004	−	0.0631578i	$-0.0201171\pi$
$234$	25.8814	+	36.5164i	1.69192	+	2.38715i
$235$	−3.75031	−	5.95027i	−0.244643	−	0.388153i
$236$	78.1776	+	11.1933i	5.08893	+	0.728625i
$237$	16.5508	+	19.6748i	1.07509	+	1.27802i
$238$	−7.91227	−	7.36876i	−0.512876	−	0.477645i
$239$	9.39796	−	17.2956i	0.607903	−	1.11876i	−0.373650	−	0.927570i	$-0.621894\pi$
$239$	9.39796	−	17.2956i	0.607903	−	1.11876i	0.981554	−	0.191187i	$-0.0612335\pi$
$240$	−10.9154	+	12.7040i	−0.704587	+	0.820038i
$241$	1.39343	+	2.34300i	0.0897584	+	0.150926i	0.901049	−	0.433717i	$-0.142798\pi$
$241$	1.39343	+	2.34300i	0.0897584	+	0.150926i	−0.811291	+	0.584643i	$0.801235\pi$
$242$	11.1122	−	19.2469i	0.714321	−	1.23724i
$243$	13.0218	+	8.56930i	0.835348	+	0.549721i
$244$	−10.5425	−	18.2601i	−0.674913	−	1.16898i
$245$	−0.512224	+	0.914295i	−0.0327248	+	0.0584122i
$246$	−24.6973	+	4.05781i	−1.57464	+	0.258716i
$247$	−9.16093	−	14.9601i	−0.582896	−	0.951890i
$248$	−11.4064	+	49.5528i	−0.724309	+	3.14660i
$249$	−2.38931	−	6.53928i	−0.151416	−	0.414410i
$250$	10.6652	−	13.5784i	0.674528	−	0.858770i
$251$	−11.8592	+	22.5142i	−0.748549	+	1.42108i	0.152919	+	0.988239i	$0.451133\pi$
$251$	−11.8592	+	22.5142i	−0.748549	+	1.42108i	−0.901468	+	0.432846i	$0.857509\pi$
$252$	47.2229	+	6.64163i	2.97476	+	0.418383i
$253$	−3.13983	−	2.84924i	−0.197399	−	0.179130i
$254$	−0.371674	+	57.4967i	−0.0233209	+	3.60766i
$255$	−0.510950	+	1.46823i	−0.0319970	+	0.0919443i
$256$	38.3635	−	3.98203i	2.39772	−	0.248877i
$257$	−0.775567	−	0.100831i	−0.0483785	−	0.00628963i	0.104696	−	0.994504i	$-0.466613\pi$
$257$	−0.775567	−	0.100831i	−0.0483785	−	0.00628963i	−0.153075	+	0.988215i	$0.548918\pi$
$258$	26.2766	−	2.93229i	1.63591	−	0.182556i
$259$	−16.1249	−	24.8654i	−1.00195	−	1.54506i
$260$	1.90592	−	19.5946i	0.118200	−	1.21521i
$261$	−19.2267	+	9.40586i	−1.19010	+	0.582208i
$262$	−1.30019	−	0.101059i	−0.0803260	−	0.00624343i
$263$	4.31224	−	21.2304i	0.265904	−	1.30913i	−0.596381	−	0.802702i	$-0.703395\pi$
$263$	4.31224	−	21.2304i	0.265904	−	1.30913i	0.862285	−	0.506424i	$-0.169033\pi$
$264$	13.1479	−	23.8984i	0.809196	−	1.47084i
$265$	2.30360	+	1.31020i	0.141509	+	0.0804850i
$266$	−25.0338	−	5.25348i	−1.53492	−	0.322112i
$267$	−3.43295	+	4.32396i	−0.210093	+	0.264622i
$268$	−38.8988	−	18.9100i	−2.37612	−	1.15511i
$269$	−5.53590	−	7.43601i	−0.337530	−	0.453381i	0.600659	−	0.799505i	$-0.294905\pi$
$269$	−5.53590	−	7.43601i	−0.337530	−	0.453381i	−0.938189	+	0.346124i	$0.887498\pi$
$270$	−2.55016	−	9.03068i	−0.155198	−	0.549590i
$271$	−15.1913	+	20.4055i	−0.922808	+	1.23955i	0.0477949	+	0.998857i	$0.484781\pi$
$271$	−15.1913	+	20.4055i	−0.922808	+	1.23955i	−0.970602	+	0.240688i	$0.922627\pi$
$272$	17.5453	−	9.09751i	1.06384	−	0.551618i
$273$	−24.7268	+	12.6578i	−1.49653	+	0.766084i
$274$	−51.9754	+	13.7469i	−3.13995	+	0.830479i
$275$	−3.40779	+	6.89627i	−0.205498	+	0.415861i
$276$	17.8207	+	15.5131i	1.07268	+	0.933780i
$277$	4.87517	+	3.39020i	0.292920	+	0.203697i	0.708228	−	0.705984i	$-0.249495\pi$
$277$	4.87517	+	3.39020i	0.292920	+	0.203697i	−0.415308	+	0.909681i	$0.636326\pi$
$278$	−20.9035	+	3.26924i	−1.25371	+	0.196076i
$279$	−11.2410	−	11.8556i	−0.672981	−	0.709777i
$280$	−11.9183	−	13.6569i	−0.712257	−	0.816156i
$281$	−1.83581	−	3.71509i	−0.109515	−	0.221624i	0.834883	−	0.550428i	$-0.185535\pi$
$281$	−1.83581	−	3.71509i	−0.109515	−	0.221624i	−0.944398	+	0.328804i	$0.893354\pi$
$282$	−35.5818	−	35.2648i	−2.11887	−	2.09999i
$283$	−18.4876	−	15.9248i	−1.09898	−	0.946628i	−0.100145	−	0.994973i	$-0.531931\pi$
$283$	−18.4876	−	15.9248i	−1.09898	−	0.946628i	−0.998831	+	0.0483446i	$0.984605\pi$
$284$	36.1189	−	29.5201i	2.14326	−	1.75169i
$285$	0.759829	+	3.59848i	0.0450084	+	0.213156i
$286$	2.75963	+	25.0113i	0.163180	+	1.47895i
$287$	−0.301213	−	15.5305i	−0.0177800	−	0.916735i
$288$	−29.3495	+	56.0559i	−1.72943	+	3.30312i
$289$	−9.97171	+	11.4263i	−0.586571	+	0.672136i
$290$	12.4564	+	3.29456i	0.731464	+	0.193464i
$291$	2.68336	+	2.94966i	0.157301	+	0.172912i
$292$	12.0582	+	3.52522i	0.705652	+	0.206298i
$293$	−1.25567	−	14.9072i	−0.0733572	−	0.870887i	−0.932973	−	0.359946i	$-0.882795\pi$
$293$	−1.25567	−	14.9072i	−0.0733572	−	0.870887i	0.859616	−	0.510941i	$-0.170703\pi$
$294$	−2.08566	+	7.16715i	−0.121638	+	0.417996i
$295$	9.56436	−	1.24345i	0.556859	−	0.0723965i
$296$	91.9154	−	21.7843i	5.34247	−	1.26619i
$297$	4.06308	+	7.76505i	0.235764	+	0.450574i
$298$	−41.5850	−	9.85583i	−2.40896	−	0.570933i
$299$	−13.6893	−	1.42091i	−0.791671	−	0.0821733i
$300$	18.1931	−	38.8134i	1.05038	−	2.24089i
$301$	−0.530271	+	16.4007i	−0.0305643	+	0.945322i
$302$	35.7892	−	43.2162i	2.05944	−	2.48681i
$303$	3.38574	+	4.35718i	0.194506	+	0.250313i
$304$	24.4173	−	39.8743i	1.40043	−	2.28695i
$305$	−1.83838	−	1.80307i	−0.105265	−	0.103244i
$306$	−1.18700	+	11.0089i	−0.0678562	+	0.629336i
$307$	5.53320	+	8.06760i	0.315796	+	0.460442i	0.949786	−	0.312899i	$-0.101300\pi$
$307$	5.53320	+	8.06760i	0.315796	+	0.460442i	−0.633990	+	0.773341i	$0.718584\pi$
$308$	21.4010	+	16.1485i	1.21943	+	0.920146i
$309$	1.24118	+	7.26061i	0.0706084	+	0.413042i
$310$	0.444864	+	9.82470i	0.0252666	+	0.558006i
$311$	−2.19652	+	30.8387i	−0.124553	+	1.74870i	0.417790	+	0.908544i	$0.362805\pi$
$311$	−2.19652	+	30.8387i	−0.124553	+	1.74870i	−0.542343	+	0.840157i	$0.682463\pi$
$312$	−11.5240	−	87.7868i	−0.652415	−	4.96995i
$313$	−3.57430	+	9.62624i	−0.202031	+	0.544107i	−0.998134	−	0.0610539i	$-0.980554\pi$
$313$	−3.57430	+	9.62624i	−0.202031	+	0.544107i	0.796103	+	0.605161i	$0.206891\pi$
$314$	2.84698	+	20.8436i	0.160664	+	1.17627i
$315$	5.77340	−	0.765183i	0.325294	−	0.0431132i
$316$	−17.0523	−	78.7222i	−0.959267	−	4.42847i
$317$	−2.33888	+	7.13549i	−0.131364	+	0.400769i	−0.994568	−	0.104086i	$-0.966808\pi$
$317$	−2.33888	+	7.13549i	−0.131364	+	0.400769i	0.863204	+	0.504855i	$0.168454\pi$
$318$	18.0894	+	5.39114i	1.01440	+	0.302320i
$319$	−12.0173	−	0.622010i	−0.672839	−	0.0348259i
$320$	17.4468	−	6.86595i	0.975304	−	0.383818i
$321$	−7.74793	−	15.8877i	−0.432447	−	0.886763i
$322$	−15.2051	+	13.0973i	−0.847348	+	0.729883i
$323$	0.753589	−	4.27382i	0.0419308	−	0.237801i
$324$	−23.5297	−	42.7947i	−1.30721	−	2.37748i
$325$	4.33590	+	24.5901i	0.240513	+	1.36401i
$326$	−30.6241	−	25.0292i	−1.69611	−	1.38624i
$327$	3.94900	+	6.15976i	0.218380	+	0.340636i
$328$	46.9472	+	15.7252i	2.59223	+	0.868279i
$329$	24.8186	−	18.7274i	1.36830	−	1.03247i
$330$	1.21026	−	5.13489i	0.0666225	−	0.282667i
$331$	10.0823	+	5.39436i	0.554175	+	0.296501i	0.724941	−	0.688811i	$-0.241867\pi$
$331$	10.0823	+	5.39436i	0.554175	+	0.296501i	−0.170766	+	0.985312i	$0.554624\pi$
$332$	−2.95178	+	21.6108i	−0.162000	+	1.18605i
$333$	−10.4938	+	28.4784i	−0.575059	+	1.56061i
$334$	−13.8942	−	26.3775i	−0.760257	−	1.44331i
$335$	−5.19585	−	0.950839i	−0.283880	−	0.0519499i
$336$	−60.0093	−	43.3673i	−3.27377	−	2.36588i
$337$	14.4936	−	14.9698i	0.789517	−	0.815456i	−0.196778	−	0.980448i	$-0.563048\pi$
$337$	14.4936	−	14.9698i	0.789517	−	0.815456i	0.986295	+	0.164992i	$0.0527597\pi$
$338$	31.3034	+	34.0510i	1.70268	+	1.85213i
$339$	5.12753	+	0.626481i	0.278489	+	0.0340258i
$340$	3.56411	−	3.31929i	0.193291	−	0.180014i
$341$	−2.29111	−	8.89462i	−0.124070	−	0.481671i
$342$	11.0529	+	23.7495i	0.597675	+	1.28422i
$343$	14.4504	+	6.56850i	0.780247	+	0.354666i
$344$	−48.6695	−	19.1533i	−2.62409	−	1.03268i
$345$	2.60471	+	1.24151i	0.140233	+	0.0668409i
$346$	−2.39900	+	0.439016i	−0.128971	+	0.0236017i
$347$	−13.0772	−	16.6491i	−0.702021	−	0.893773i	0.296093	−	0.955159i	$-0.404316\pi$
$347$	−13.0772	−	16.6491i	−0.702021	−	0.893773i	−0.998114	+	0.0613860i	$0.980448\pi$
$348$	67.0242	+	2.08370i	3.59287	+	0.111698i
$349$	6.28726	−	22.0338i	0.336549	−	1.17944i	−0.591290	−	0.806459i	$-0.701381\pi$
$349$	6.28726	−	22.0338i	0.336549	−	1.17944i	0.927839	−	0.372981i	$-0.121664\pi$
$350$	30.4195	+	20.0072i	1.62599	+	1.06943i
$351$	25.5505	+	12.5076i	1.36379	+	0.667604i
$352$	−29.7207	+	19.5476i	−1.58412	+	1.04189i
$353$	−7.02250	−	22.3987i	−0.373770	−	1.19216i	−0.931995	−	0.362472i	$-0.881933\pi$
$353$	−7.02250	−	22.3987i	−0.373770	−	1.19216i	0.558224	−	0.829690i	$-0.311483\pi$
$354$	64.3701	−	23.9922i	3.42123	−	1.27517i
$355$	3.28266	−	4.65603i	0.174226	−	0.247116i
$356$	15.8375	−	6.95341i	0.839387	−	0.368530i
$357$	−6.65694	−	1.70590i	−0.352323	−	0.0902860i
$358$	27.2435	−	58.9204i	1.43986	−	3.11404i
$359$	19.9361	−	11.0003i	1.05219	−	0.580572i	0.139917	−	0.990163i	$-0.455316\pi$
$359$	19.9361	−	11.0003i	1.05219	−	0.580572i	0.912269	+	0.409591i	$0.134329\pi$
$360$	−3.88477	+	18.1519i	−0.204745	+	0.956690i
$361$	3.14548	+	8.14700i	0.165552	+	0.428790i
$362$	−49.3624	+	14.4311i	−2.59443	+	0.758482i
$363$	0.347660	−	14.1213i	0.0182474	−	0.741174i
$364$	87.0188	+	1.12507i	4.56102	+	0.0589699i
$365$	1.53413	+	0.0198349i	0.0802999	+	0.00103820i
$366$	−15.6530	−	9.55849i	−0.818194	−	0.499630i
$367$	13.3386	−	3.89955i	0.696271	−	0.203555i	0.0866391	−	0.996240i	$-0.472387\pi$
$367$	13.3386	−	3.89955i	0.696271	−	0.203555i	0.609632	+	0.792685i	$0.291317\pi$
$368$	−13.2124	−	34.2210i	−0.688745	−	1.78389i
$369$	−12.5491	+	9.77628i	−0.653280	+	0.508933i
$370$	15.9965	−	8.82650i	0.831619	−	0.458868i
$371$	−4.91654	+	10.6332i	−0.255254	+	0.552046i
$372$	13.7873	+	49.2917i	0.714837	+	2.55566i
$373$	−32.6479	+	14.3340i	−1.69045	+	0.742184i	−0.690625	+	0.723213i	$0.742665\pi$
$373$	−32.6479	+	14.3340i	−1.69045	+	0.742184i	−0.999820	+	0.0189710i	$0.993961\pi$
$374$	−3.58701	+	5.08771i	−0.185480	+	0.263079i
$375$	1.82229	−	10.8217i	0.0941027	−	0.558832i
$376$	29.6473	+	94.5617i	1.52894	+	4.87665i
$377$	−32.6348	+	21.4642i	−1.68078	+	1.10546i
$378$	38.8327	−	14.5838i	1.99734	−	0.750109i
$379$	13.7436	+	9.03931i	0.705961	+	0.464318i	0.851039	−	0.525102i	$-0.175973\pi$
$379$	13.7436	+	9.03931i	0.705961	+	0.464318i	−0.145078	+	0.989420i	$0.546343\pi$
$380$	3.16163	−	11.0800i	0.162188	−	0.568390i
$381$	17.2801	+	32.2013i	0.885288	+	1.64972i
$382$	−29.3047	−	37.3091i	−1.49936	−	1.90890i
$383$	−1.61065	+	0.294748i	−0.0823003	+	0.0150609i	−0.221003	−	0.975273i	$-0.570933\pi$
$383$	−1.61065	+	0.294748i	−0.0823003	+	0.0150609i	0.138703	+	0.990334i	$0.455707\pi$
$384$	49.8328	−	34.2691i	2.54302	−	1.74879i
$385$	3.04675	+	1.19901i	0.155277	+	0.0611072i
$386$	−32.7102	−	14.8686i	−1.66491	−	0.756793i
$387$	13.7728	−	9.62850i	0.700112	−	0.489444i
$388$	−3.11619	−	12.0978i	−0.158200	−	0.614171i
$389$	−7.29745	+	6.79617i	−0.369995	+	0.344579i	−0.844386	−	0.535735i	$-0.820035\pi$
$389$	−7.29745	+	6.79617i	−0.369995	+	0.344579i	0.474391	+	0.880314i	$0.342668\pi$
$390$	−6.70056	−	15.7594i	−0.339296	−	0.798009i
$391$	−2.30429	−	2.50654i	−0.116533	−	0.126761i
$392$	10.2711	−	10.6085i	0.518768	−	0.535812i
$393$	−0.756358	+	0.339052i	−0.0381532	+	0.0171029i
$394$	35.6079	+	6.51624i	1.79390	+	0.328283i
$395$	−4.58445	−	8.70337i	−0.230669	−	0.437914i
$396$	0.109274	−	27.4558i	0.00549121	−	1.37971i
$397$	−1.80475	+	13.2131i	−0.0905777	+	0.663146i	0.888384	+	0.459101i	$0.151829\pi$
$397$	−1.80475	+	13.2131i	−0.0905777	+	0.663146i	−0.978962	+	0.204045i	$0.934591\pi$
$398$	−23.5077	−	12.5774i	−1.17834	−	0.630446i
$399$	−15.5689	+	4.68211i	−0.779420	+	0.234398i
$400$	−53.1256	+	40.0869i	−2.65628	+	2.00435i
$401$	−3.58440	−	1.20061i	−0.178997	−	0.0599557i	0.226695	−	0.973966i	$-0.427208\pi$
$401$	−3.58440	−	1.20061i	−0.178997	−	0.0599557i	−0.405692	+	0.914010i	$0.632969\pi$
$402$	−37.5816	+	1.74848i	−1.87440	+	0.0872063i
$403$	−23.0852	−	18.8676i	−1.14996	−	0.939864i
$404$	−3.00189	−	17.0246i	−0.149350	−	0.847005i
$405$	−4.16988	−	4.26428i	−0.207203	−	0.211894i
$406$	−9.89037	+	56.0911i	−0.490851	+	2.78375i
$407$	−12.9281	+	11.1359i	−0.640821	+	0.551986i
$408$	12.2494	−	18.1585i	0.606435	−	0.898978i
$409$	−3.73574	+	1.47015i	−0.184720	+	0.0726943i	−0.456752	−	0.889594i	$-0.650987\pi$
$409$	−3.73574	+	1.47015i	−0.184720	+	0.0726943i	0.272032	+	0.962288i	$0.412304\pi$
$410$	9.56322	+	0.494988i	0.472294	+	0.0244457i
$411$	−24.8257	+	23.4802i	−1.22456	+	1.15819i
$412$	7.18779	−	21.9287i	0.354117	−	1.08035i
$413$	9.02594	+	41.6684i	0.444137	+	2.05037i
$414$	20.0685	+	4.43081i	0.986315	+	0.217762i
$415$	0.360488	+	2.63924i	0.0176956	+	0.129555i
$416$	−40.1939	+	108.249i	−1.97067	+	5.30736i
$417$	−10.6716	+	8.18229i	−0.522592	+	0.400689i
$418$	−1.04630	+	14.6899i	−0.0511764	+	0.718506i
$419$	−1.08223	−	23.9007i	−0.0528704	−	1.16763i	−0.837062	−	0.547109i	$-0.815728\pi$
$419$	−1.08223	−	23.9007i	−0.0528704	−	1.16763i	0.784191	−	0.620519i	$-0.213078\pi$
$420$	−17.1124	−	6.32980i	−0.835000	−	0.308863i
$421$	3.99670	+	3.01578i	0.194787	+	0.146980i	0.695225	−	0.718792i	$-0.255305\pi$
$421$	3.99670	+	3.01578i	0.194787	+	0.146980i	−0.500437	+	0.865773i	$0.666827\pi$
$422$	30.0311	+	43.7865i	1.46189	+	2.13149i
$423$	−30.5835	−	8.85870i	−1.48702	−	0.430725i
$424$	−26.6578	−	26.1458i	−1.29462	−	1.26975i
$425$	−3.22587	+	5.26795i	−0.156477	+	0.255533i
$426$	15.2993	−	37.5815i	0.741253	−	1.82083i
$427$	7.26018	−	8.76682i	0.351345	−	0.424256i
$428$	−1.78954	+	55.3486i	−0.0865007	+	2.67537i
$429$	9.14727	+	13.1191i	0.441634	+	0.633398i
$430$	−10.0619	−	1.04440i	−0.485230	−	0.0503656i
$431$	34.8272	+	8.25421i	1.67757	+	0.397591i	0.955678	−	0.294415i	$-0.0951249\pi$
$431$	34.8272	+	8.25421i	1.67757	+	0.397591i	0.721891	+	0.692007i	$0.243273\pi$
$432$	1.26276	+	75.8131i	0.0607546	+	3.64756i
$433$	−3.40702	+	0.807479i	−0.163731	+	0.0388049i	−0.311664	−	0.950192i	$-0.600886\pi$
$433$	−3.40702	+	0.807479i	−0.163731	+	0.0388049i	0.147933	+	0.988997i	$0.452738\pi$
$434$	−43.1114	+	5.60487i	−2.06942	+	0.269042i
$435$	7.95380	−	1.94994i	0.381355	−	0.0934926i
$436$	−1.92406	−	22.8422i	−0.0921456	−	1.09394i
$437$	−7.73131	−	2.26025i	−0.369839	−	0.108122i
$438$	10.6772	−	2.32672i	0.510178	−	0.111175i
$439$	37.5599	+	9.93414i	1.79264	+	0.474131i	0.992132	−	0.125196i	$-0.0399560\pi$
$439$	37.5599	+	9.93414i	1.79264	+	0.474131i	0.800504	+	0.599327i	$0.204565\pi$
$440$	−6.86195	+	7.86292i	−0.327131	+	0.374850i
$441$	1.01590	+	4.63425i	0.0483762	+	0.220679i
$442$	0.391836	+	20.2030i	0.0186377	+	0.960957i
$443$	0.190242	+	1.72421i	0.00903867	+	0.0819198i	0.997643	−	0.0686170i	$-0.0218587\pi$
$443$	0.190242	+	1.72421i	0.00903867	+	0.0819198i	−0.988604	+	0.150537i	$0.951900\pi$
$444$	70.7465	−	63.5286i	3.35748	−	3.01493i
$445$	1.63559	−	1.33678i	0.0775345	−	0.0633692i
$446$	−12.6218	−	10.8721i	−0.597659	−	0.514807i
$447$	−26.2058	+	7.14763i	−1.23949	+	0.338071i
$448$	36.7169	+	74.3032i	1.73471	+	3.51049i
$449$	−12.4655	−	14.2838i	−0.588282	−	0.674096i	0.379702	−	0.925109i	$-0.376026\pi$
$449$	−12.4655	−	14.2838i	−0.588282	−	0.674096i	−0.967984	+	0.251013i	$0.919236\pi$
$450$	−2.26049	−	37.2180i	−0.106560	−	1.75447i
$451$	−8.83590	+	1.38191i	−0.416066	+	0.0650716i
$452$	−13.2866	−	9.23953i	−0.624949	−	0.434591i
$453$	6.82936	−	35.0037i	0.320871	−	1.64462i
$454$	−16.3485	+	33.0841i	−0.767274	+	1.55271i
$455$	10.2748	−	2.71757i	0.481691	−	0.127401i
$456$	2.61429	−	51.7535i	0.122425	−	2.42358i
$457$	23.4798	−	12.1746i	1.09834	−	0.569505i	0.187500	−	0.982265i	$-0.439962\pi$
$457$	23.4798	−	12.1746i	1.09834	−	0.569505i	0.910840	+	0.412759i	$0.135435\pi$
$458$	39.6380	−	53.2431i	1.85216	−	2.48789i
$459$	2.68589	+	6.50495i	0.125367	+	0.303625i
$460$	−5.39821	−	7.25105i	−0.251693	−	0.338082i
$461$	3.74194	+	1.81908i	0.174280	+	0.0847231i	0.522292	−	0.852767i	$-0.325077\pi$
$461$	3.74194	+	1.81908i	0.174280	+	0.0847231i	−0.348012	+	0.937490i	$0.613143\pi$
$462$	23.0676	+	3.42580i	1.07320	+	0.159383i
$463$	6.91279	+	1.45069i	0.321265	+	0.0674192i	0.363229	−	0.931700i	$-0.381674\pi$
$463$	6.91279	+	1.45069i	0.321265	+	0.0674192i	−0.0419641	+	0.999119i	$0.513362\pi$
$464$	−90.4978	−	51.4718i	−4.20125	−	2.38952i
$465$	3.23645	+	5.34774i	0.150087	+	0.247996i
$466$	−4.52099	+	22.2582i	−0.209431	+	1.03109i
$467$	18.2859	+	1.42129i	0.846169	+	0.0657694i	0.493253	−	0.869886i	$-0.335808\pi$
$467$	18.2859	+	1.42129i	0.846169	+	0.0657694i	0.352916	+	0.935655i	$0.385190\pi$
$468$	−52.4712	−	72.0397i	−2.42548	−	3.33004i
$469$	2.26048	−	23.2398i	0.104379	−	1.07311i
$470$	10.4288	+	16.0818i	0.481047	+	0.741796i
$471$	7.92842	+	10.7666i	0.365322	+	0.496101i
$472$	−134.759	−	17.5199i	−6.20279	−	0.806417i
$473$	9.39712	−	0.975396i	0.432080	−	0.0448488i
$474$	−45.7924	−	53.0288i	−2.10332	−	2.43569i
$475$	−0.0944657	+	14.6135i	−0.00433438	+	0.670514i
$476$	15.9434	+	14.4679i	0.730765	+	0.663134i
$477$	11.7352	−	2.49315i	0.537317	−	0.114153i
$478$	−24.9992	+	47.4597i	−1.14343	+	2.17076i
$479$	−10.4808	+	13.3436i	−0.478882	+	0.609685i	−0.964370	−	0.264559i	$-0.914774\pi$
$479$	−10.4808	+	13.3436i	−0.478882	+	0.609685i	0.485488	+	0.874243i	$0.338642\pi$
$480$	15.5383	−	18.5646i	0.709223	−	0.847354i
$481$	−12.4244	+	53.9753i	−0.566505	+	2.46106i
$482$	−3.87949	−	6.33535i	−0.176706	−	0.288567i
$483$	−4.50226	+	11.9341i	−0.204860	+	0.543018i
$484$	−21.6295	+	38.6077i	−0.983160	+	1.75489i
$485$	−0.762838	−	1.32127i	−0.0346387	−	0.0599960i
$486$	−35.7850	−	22.8917i	−1.62324	−	1.03839i
$487$	−0.771325	+	1.33597i	−0.0349521	+	0.0605387i	−0.882972	−	0.469425i	$-0.844461\pi$
$487$	−0.771325	+	1.33597i	−0.0349521	+	0.0605387i	0.848020	+	0.529964i	$0.177795\pi$
$488$	18.5453	+	31.1833i	0.839506	+	1.41160i
$489$	−24.7036	−	4.65420i	−1.11713	−	0.210470i
$490$	1.36355	−	2.50941i	0.0615988	−	0.113363i
$491$	−1.18496	−	1.10356i	−0.0534766	−	0.0498031i	0.654332	−	0.756207i	$-0.272950\pi$
$491$	−1.18496	−	1.10356i	−0.0534766	−	0.0498031i	−0.707809	+	0.706404i	$0.750316\pi$
$492$	49.0691	−	8.71506i	2.21221	−	0.392905i
$493$	−9.56566	−	1.36960i	−0.430816	−	0.0616836i
$494$	25.4896	+	40.4421i	1.14683	+	1.81958i
$495$	−0.886343	−	3.23382i	−0.0398382	−	0.145349i
$496$	16.8235	−	77.6660i	0.755398	−	3.48731i
$497$	21.7271	+	12.7321i	0.974596	+	0.571115i
$498$	6.74100	+	17.7347i	0.302071	+	0.794711i
$499$	14.7988	+	20.4243i	0.662485	+	0.914316i	0.999632	−	0.0271358i	$-0.00863866\pi$
$499$	14.7988	+	20.4243i	0.662485	+	0.914316i	−0.337146	+	0.941452i	$0.609462\pi$
$500$	−20.8855	+	27.3097i	−0.934026	+	1.22133i
$501$	−15.7769	−	10.4951i	−0.704859	−	0.468884i
$502$	31.5220	−	61.7668i	1.40690	−	2.75679i
$503$	−21.8407	−	15.6108i	−0.973828	−	0.696050i	−0.0210692	−	0.999778i	$-0.506707\pi$
$503$	−21.8407	−	15.6108i	−0.973828	−	0.696050i	−0.952759	+	0.303728i	$0.901769\pi$
$504$	−81.3981	−	10.3769i	−3.62576	−	0.462224i
$505$	−0.910748	−	1.90467i	−0.0405278	−	0.0847566i
$506$	8.65609	+	7.65327i	0.384810	+	0.340229i
$507$	27.8266	+	9.48257i	1.23582	+	0.421136i
$508$	−0.740083	−	114.488i	−0.0328359	−	5.07960i
$509$	−12.6556	+	14.1288i	−0.560951	+	0.626248i	−0.956337	−	0.292267i	$-0.905590\pi$
$509$	−12.6556	+	14.1288i	−0.560951	+	0.626248i	0.395386	+	0.918515i	$0.370611\pi$
$510$	1.34056	−	4.01878i	0.0593611	−	0.177955i
$511$	0.481843	+	6.76498i	0.0213155	+	0.299265i
$512$	−35.0337	+	4.09486i	−1.54829	+	0.180969i
$513$	13.3919	+	9.89255i	0.591266	+	0.436767i
$514$	2.11689	+	0.247429i	0.0933722	+	0.0109136i
$515$	0.127480	−	2.81536i	0.00561745	−	0.124060i
$516$	−52.2426	+	6.51476i	−2.29985	+	0.286796i
$517$	−12.6168	−	12.6986i	−0.554887	−	0.558486i
$518$	44.8148	+	67.1875i	1.96905	+	2.95205i
$519$	−1.20533	+	0.974663i	−0.0529079	+	0.0427829i
$520$	−2.84339	+	33.7563i	−0.124691	+	1.48031i
$521$	−8.91924	+	23.1014i	−0.390759	+	1.01209i	0.588323	+	0.808626i	$0.299788\pi$
$521$	−8.91924	+	23.1014i	−0.390759	+	1.01209i	−0.979082	+	0.203465i	$0.934780\pi$
$522$	52.0594	−	26.3074i	2.27858	−	1.15144i
$523$	−1.84732	+	5.39900i	−0.0807777	+	0.236082i	−0.979145	−	0.203164i	$-0.934878\pi$
$523$	−1.84732	+	5.39900i	−0.0807777	+	0.236082i	0.898367	+	0.439246i	$0.144754\pi$
$524$	2.59134	+	0.167743i	0.113203	+	0.00732788i
$525$	23.0619	+	1.91372i	1.00650	+	0.0835216i
$526$	−11.0025	+	58.0027i	−0.479730	+	2.52904i
$527$	−1.18679	−	7.27973i	−0.0516972	−	0.317110i
$528$	−20.0632	+	37.6114i	−0.873138	+	1.63682i
$529$	13.4439	−	9.87418i	0.584517	−	0.429312i
$530$	−6.32322	−	3.48901i	−0.274663	−	0.151553i
$531$	28.6270	−	32.9678i	1.24230	−	1.43068i
$532$	49.9788	+	9.81551i	2.16685	+	0.425556i
$533$	−20.4610	+	20.5937i	−0.886266	+	0.892014i
$534$	9.20210	−	11.9033i	0.398214	−	0.515106i
$535$	1.60217	+	6.57050i	0.0692676	+	0.284067i
$536$	67.3488	+	31.6707i	2.90902	+	1.36796i
$537$	−2.71630	−	41.1688i	−0.117217	−	1.77657i
$538$	15.3467	+	20.0673i	0.661645	+	0.865164i
$539$	−0.764973	+	2.55519i	−0.0329497	+	0.110060i
$540$	5.30996	+	17.9149i	0.228504	+	0.770933i
$541$	−5.88032	−	19.6417i	−0.252815	−	0.844461i	−0.986329	−	0.164787i	$-0.947306\pi$
$541$	−5.88032	−	19.6417i	−0.252815	−	0.844461i	0.733514	−	0.679674i	$-0.237879\pi$
$542$	40.6759	−	56.1381i	1.74718	−	2.41134i
$543$	−23.1593	+	23.0673i	−0.993862	+	0.989915i
$544$	−25.1877	+	13.4762i	−1.07991	+	0.577787i
$545$	−0.974468	−	2.62442i	−0.0417416	−	0.112418i
$546$	66.9320	−	35.3623i	2.86442	−	1.51337i
$547$	−33.1434	−	0.857171i	−1.41711	−	0.0366500i	−0.690317	−	0.723507i	$-0.742529\pi$
$547$	−33.1434	−	0.857171i	−1.41711	−	0.0366500i	−0.726793	+	0.686857i	$0.758990\pi$
$548$	103.132	−	28.7087i	4.40557	−	1.22637i
$549$	−11.6429	−	0.573637i	−0.496909	−	0.0244822i
$550$	9.04293	−	18.9117i	0.385592	−	0.806397i
$551$	−21.0494	+	8.91889i	−0.896735	+	0.379957i
$552$	−31.0069	−	26.2950i	−1.31974	−	1.11919i
$553$	36.6362	−	23.4231i	1.55793	−	0.996054i
$554$	−13.4038	−	9.06619i	−0.569472	−	0.385186i
$555$	6.24289	−	9.79129i	0.264996	−	0.415617i
$556$	41.5357	−	7.04733i	1.76150	−	0.298873i
$557$	3.07611	+	1.25673i	0.130339	+	0.0532494i	0.442431	−	0.896803i	$-0.354116\pi$
$557$	3.07611	+	1.25673i	0.130339	+	0.0532494i	−0.312092	+	0.950052i	$0.601030\pi$
$558$	31.0482	+	31.9093i	1.31438	+	1.35083i
$559$	22.7104	−	20.6086i	0.960549	−	0.871652i
$560$	18.9006	+	21.1007i	0.798695	+	0.891666i
$561$	−0.454447	+	3.93038i	−0.0191868	+	0.165941i
$562$	5.13329	+	10.0586i	0.216535	+	0.424295i
$563$	−1.45594	+	9.72041i	−0.0613604	+	0.409666i	0.936843	+	0.349750i	$0.113734\pi$
$563$	−1.45594	+	9.72041i	−0.0613604	+	0.409666i	−0.998203	+	0.0599162i	$0.980917\pi$
$564$	71.7529	+	69.2980i	3.02134	+	2.91797i
$565$	−1.86580	−	0.651906i	−0.0784949	−	0.0274259i
$566$	50.9379	+	42.7420i	2.14108	+	1.79658i
$567$	17.2364	−	19.9500i	0.723862	−	0.837820i
$568$	−61.4884	+	51.5949i	−2.57999	+	2.16487i
$569$	−18.0601	+	6.83902i	−0.757118	+	0.286707i	−0.702388	−	0.711795i	$-0.747883\pi$
$569$	−18.0601	+	6.83902i	−0.757118	+	0.286707i	−0.0547305	+	0.998501i	$0.517430\pi$
$570$	−2.19723	−	9.77873i	−0.0920320	−	0.409586i
$571$	−3.61313	−	17.7885i	−0.151205	−	0.744426i	−0.982154	−	0.188078i	$-0.939774\pi$
$571$	−3.61313	−	17.7885i	−0.151205	−	0.744426i	0.830949	−	0.556348i	$-0.187798\pi$
$572$	−6.13841	−	49.7276i	−0.256660	−	2.07922i
$573$	−27.7021	−	11.9087i	−1.15727	−	0.497495i
$574$	1.36792	+	42.3083i	0.0570959	+	1.76592i
$575$	9.06213	+	7.02368i	0.377917	+	0.292908i
$576$	38.3944	−	75.6968i	1.59977	−	3.15403i
$577$	17.6481	−	28.0007i	0.734702	−	1.16568i	−0.245828	−	0.969313i	$-0.579060\pi$
$577$	17.6481	−	28.0007i	0.734702	−	1.16568i	0.980530	−	0.196370i	$-0.0629154\pi$
$578$	26.7694	−	31.4869i	1.11346	−	1.30968i
$579$	−22.7775	+	1.65079i	−0.946599	+	0.0686044i
$580$	−24.8861	−	6.23898i	−1.03334	−	0.259060i
$581$	−11.4917	+	2.56715i	−0.476757	+	0.106503i
$582$	−7.41580	−	7.94298i	−0.307395	−	0.329247i
$583$	6.44877	+	1.97615i	0.267081	+	0.0818436i
$584$	−20.8254	−	5.79714i	−0.861761	−	0.239888i
$585$	−8.53271	−	6.75717i	−0.352784	−	0.279375i
$586$	3.94677	+	40.5763i	0.163039	+	1.67619i
$587$	1.14141	−	0.908524i	0.0471112	−	0.0374988i	−0.598930	−	0.800802i	$-0.704407\pi$
$587$	1.14141	−	0.908524i	0.0471112	−	0.0374988i	0.646041	+	0.763303i	$0.276424\pi$
$588$	3.96815	−	14.3238i	0.163644	−	0.590705i
$589$	−11.3025	−	13.2944i	−0.465713	−	0.547784i
$590$	−26.0181	+	3.72524i	−1.07115	+	0.153366i
$591$	21.8542	−	7.19347i	0.898963	−	0.295900i
$592$	−143.195	+	35.8992i	−5.88528	+	1.47545i
$593$	−10.5508	+	5.29880i	−0.433268	+	0.217596i	−0.652046	−	0.758179i	$-0.726089\pi$
$593$	−10.5508	+	5.29880i	−0.433268	+	0.217596i	0.218778	+	0.975775i	$0.429793\pi$
$594$	−11.3450	−	21.0158i	−0.465493	−	0.862290i
$595$	2.34961	+	1.18002i	0.0963248	+	0.0483761i
$596$	83.0516	+	18.5530i	3.40192	+	0.759958i
$597$	−16.9448	+	0.130584i	−0.693504	+	0.00534445i
$598$	37.3519	+	3.38956i	1.52743	+	0.138609i
$599$	4.49819	−	40.7683i	0.183791	−	1.66575i	−0.450594	−	0.892729i	$-0.648788\pi$
$599$	4.49819	−	40.7683i	0.183791	−	1.66575i	0.634385	−	0.773017i	$-0.281253\pi$
$600$	−30.4391	+	67.1860i	−1.24267	+	2.74286i
$601$	−31.5993	+	2.86753i	−1.28896	+	0.116969i	−0.713382	−	0.700775i	$-0.752838\pi$
$601$	−31.5993	+	2.86753i	−1.28896	+	0.116969i	−0.575582	+	0.817744i	$0.695224\pi$
$602$	0.867130	−	44.7090i	0.0353416	−	1.82220i
$603$	−20.4420	+	12.4062i	−0.832464	+	0.505220i
$604$	−70.1456	+	86.9669i	−2.85418	+	3.53863i
$605$	−1.28033	+	5.25067i	−0.0520530	+	0.213470i
$606$	−9.37930	−	11.7536i	−0.381008	−	0.477457i
$607$	−4.49394	−	8.02147i	−0.182403	−	0.325581i	0.765893	−	0.642969i	$-0.222297\pi$
$607$	−4.49394	−	8.02147i	−0.182403	−	0.325581i	−0.948296	+	0.317387i	$0.897195\pi$
$608$	−34.5444	+	58.0853i	−1.40096	+	2.35567i
$609$	11.5404	+	34.3119i	0.467639	+	1.39039i
$610$	5.07293	+	4.84842i	0.205397	+	0.196307i
$611$	−57.4088	−	8.97857i	−2.32251	−	0.363234i
$612$	2.07998	−	21.9498i	0.0840781	−	0.887268i
$613$	4.53773	+	2.73853i	0.183277	+	0.110608i	0.605370	−	0.795944i	$-0.293025\pi$
$613$	4.53773	+	2.73853i	0.183277	+	0.110608i	−0.422093	+	0.906553i	$0.638704\pi$
$614$	−15.3616	−	21.7885i	−0.619945	−	0.879310i
$615$	5.48767	−	2.63240i	0.221284	−	0.106149i
$616$	−37.1811	−	27.3086i	−1.49807	−	1.10029i
$617$	−15.8646	−	34.3109i	−0.638687	−	1.38131i	−0.908293	−	0.418336i	$-0.862614\pi$
$617$	−15.8646	−	34.3109i	−0.638687	−	1.38131i	0.269606	−	0.962971i	$-0.413107\pi$
$618$	−3.63789	−	19.7407i	−0.146337	−	0.794087i
$619$	−8.29809	+	9.02645i	−0.333528	+	0.362804i	−0.880249	−	0.474511i	$-0.842625\pi$
$619$	−8.29809	+	9.02645i	−0.333528	+	0.362804i	0.546721	+	0.837315i	$0.315876\pi$
$620$	−1.13866	−	19.5500i	−0.0457296	−	0.785148i
$621$	12.5476	−	3.63104i	0.503519	−	0.145709i
$622$	4.89883	−	84.1096i	0.196425	−	3.37249i
$623$	6.49518	+	6.70857i	0.260224	+	0.268773i
$624$	19.7820	+	136.951i	0.791914	+	5.48241i
$625$	6.92509	−	17.2686i	0.277004	−	0.690745i
$626$	9.40047	−	26.3564i	0.375718	−	1.05342i
$627$	3.88399	+	8.51648i	0.155112	+	0.340115i
$628$	−6.20504	−	41.4273i	−0.247608	−	1.65313i
$629$	−11.1474	+	7.96766i	−0.444475	+	0.317691i
$630$	−15.7050	+	2.28845i	−0.625701	+	0.0911738i
$631$	12.0750	−	11.8431i	0.480698	−	0.471465i	−0.418995	−	0.907989i	$-0.637617\pi$
$631$	12.0750	−	11.8431i	0.480698	−	0.471465i	0.899693	+	0.436523i	$0.143790\pi$
$632$	31.0909	+	135.068i	1.23673	+	5.37271i
$633$	30.0776	+	15.3028i	1.19548	+	0.608230i
$634$	6.12181	−	19.5259i	0.243128	−	0.775472i
$635$	−3.83665	−	13.4456i	−0.152253	−	0.533571i
$636$	−36.1557	−	10.2683i	−1.43366	−	0.407167i
$637$	2.90854	+	8.15478i	0.115241	+	0.323104i
$638$	32.7678	+	1.27154i	1.29729	+	0.0503408i
$639$	−2.89203	−	25.6270i	−0.114407	−	1.01379i
$640$	−21.4208	+	8.75136i	−0.846732	+	0.345928i
$641$	−11.4448	+	7.11045i	−0.452044	+	0.280846i	−0.734721	−	0.678369i	$-0.762687\pi$
$641$	−11.4448	+	7.11045i	−0.452044	+	0.280846i	0.282677	+	0.959215i	$0.408777\pi$
$642$	21.6721	+	43.0193i	0.855328	+	1.69784i
$643$	16.0008	+	6.77974i	0.631011	+	0.267367i	0.682023	−	0.731331i	$-0.261101\pi$
$643$	16.0008	+	6.77974i	0.631011	+	0.267367i	−0.0510118	+	0.998698i	$0.516245\pi$
$644$	29.9370	−	26.4688i	1.17968	−	1.04301i
$645$	−5.93310	+	2.47746i	−0.233616	+	0.0975500i
$646$	−1.90289	+	11.6723i	−0.0748680	+	0.459239i
$647$	10.4424	+	3.80074i	0.410535	+	0.149422i	0.539028	−	0.842288i	$-0.318792\pi$
$647$	10.4424	+	3.80074i	0.410535	+	0.149422i	−0.128493	+	0.991710i	$0.541014\pi$
$648$	41.4365	+	73.1079i	1.62778	+	2.87195i
$649$	23.0665	−	8.39551i	0.905438	−	0.329553i
$650$	−12.6812	−	66.8529i	−0.497398	−	2.62218i
$651$	−22.3553	+	16.2403i	−0.876172	+	0.636508i
$652$	61.6185	+	49.0461i	2.41317	+	1.92079i
$653$	−7.70605	+	11.8831i	−0.301561	+	0.465021i	−0.956943	−	0.290277i	$-0.906253\pi$
$653$	−7.70605	+	11.8831i	−0.301561	+	0.465021i	0.655382	+	0.755298i	$0.272508\pi$
$654$	−10.9776	−	16.6456i	−0.429259	−	0.650895i
$655$	0.310371	−	0.0651332i	0.0121272	−	0.00254496i
$656$	−73.6816	−	23.6250i	−2.87678	−	0.922403i
$657$	5.25117	−	4.54599i	0.204867	−	0.177356i
$658$	−66.9685	+	51.9045i	−2.61071	+	2.02345i
$659$	6.49698	+	7.84523i	0.253086	+	0.305607i	0.881416	−	0.472340i	$-0.156591\pi$
$659$	6.49698	+	7.84523i	0.253086	+	0.305607i	−0.628330	+	0.777947i	$0.716261\pi$
$660$	−2.27750	+	10.2550i	−0.0886515	+	0.399175i
$661$	−3.80333	+	1.84893i	−0.147933	+	0.0719149i	−0.509694	−	0.860356i	$-0.670241\pi$
$661$	−3.80333	+	1.84893i	−0.147933	+	0.0719149i	0.361761	+	0.932271i	$0.382176\pi$
$662$	−27.6634	−	14.3439i	−1.07517	−	0.557491i
$663$	6.36339	+	11.1559i	0.247134	+	0.433258i
$664$	4.59800	−	37.2486i	0.178437	−	1.44553i
$665$	6.20159	−	0.482025i	0.240487	−	0.0186921i
$666$	27.5913	−	77.9705i	1.06914	−	3.02129i
$667$	−4.47391	+	17.3688i	−0.173230	+	0.672521i
$668$	28.3431	+	52.1612i	1.09663	+	2.01818i
$669$	−10.3508	−	2.22867i	−0.400185	−	0.0861652i
$670$	14.1917	+	2.40789i	0.548272	+	0.0930249i
$671$	−5.56673	−	3.45850i	−0.214901	−	0.133514i
$672$	87.5398	+	61.5560i	3.37692	+	2.37457i
$673$	6.12658	+	13.7128i	0.236162	+	0.528589i	0.992010	−	0.126158i	$-0.0402648\pi$
$673$	6.12658	+	13.7128i	0.236162	+	0.528589i	−0.755848	+	0.654747i	$0.772775\pi$
$674$	−38.9662	+	41.3018i	−1.50092	+	1.59089i
$675$	−12.5814	−	20.0834i	−0.484257	−	0.773010i
$676$	−63.2032	−	66.9915i	−2.43089	−	2.57659i
$677$	−4.24359	+	10.1983i	−0.163094	+	0.391952i	−0.983768	−	0.179445i	$-0.942570\pi$
$677$	−4.24359	+	10.1983i	−0.163094	+	0.391952i	0.820673	+	0.571397i	$0.193598\pi$
$678$	−13.9941	−	1.52645i	−0.537439	−	0.0586231i
$679$	5.53700	−	3.85044i	0.212490	−	0.147766i
$680$	−6.05847	+	5.79035i	−0.232332	+	0.222050i
$681$	0.938588	+	23.4362i	0.0359668	+	0.898078i
$682$	6.55640	+	24.1562i	0.251057	+	0.924990i
$683$	7.92939	+	23.1745i	0.303410	+	0.886748i	0.987537	+	0.157386i	$0.0503066\pi$
$683$	7.92939	+	23.1745i	0.303410	+	0.886748i	−0.684128	+	0.729362i	$0.739817\pi$
$684$	−22.6183	−	47.0018i	−0.864833	−	1.79716i
$685$	11.1935	−	6.75528i	0.427680	−	0.258106i
$686$	−39.6072	−	17.3894i	−1.51221	−	0.663931i
$687$	5.92766	−	41.7702i	0.226154	−	1.59363i
$688$	76.4423	+	28.9473i	2.91433	+	1.10360i
$689$	20.6684	−	7.22149i	0.787405	−	0.275117i
$690$	−7.14132	−	3.29123i	−0.271865	−	0.125295i
$691$	−10.4774	+	15.7080i	−0.398579	+	0.597561i	−0.975703	−	0.219096i	$-0.929689\pi$
$691$	−10.4774	+	15.7080i	−0.398579	+	0.597561i	0.577124	+	0.816656i	$0.304175\pi$
$692$	4.76522	−	0.935859i	0.181146	−	0.0355760i
$693$	13.9157	−	5.10408i	0.528613	−	0.193888i
$694$	36.2206	+	44.9065i	1.37492	+	1.70463i
$695$	4.65596	−	2.18946i	0.176611	−	0.0830509i
$696$	−115.366	−	2.09418i	−4.37295	−	0.0793796i
$697$	−7.16678	+	0.463920i	−0.271461	+	0.0175722i
$698$	−16.3559	+	60.2612i	−0.619079	+	2.28092i
$699$	4.24671	+	13.7971i	0.160625	+	0.521854i
$700$	−61.0817	−	39.0522i	−2.30867	−	1.47604i
$701$	−17.2417	−	39.9708i	−0.651211	−	1.50968i	−0.848424	−	0.529317i	$-0.822448\pi$
$701$	−17.2417	−	39.9708i	−0.651211	−	1.50968i	0.197213	−	0.980361i	$-0.436811\pi$
$702$	−70.0633	−	33.1817i	−2.64437	−	1.25236i
$703$	−12.8393	+	29.7650i	−0.484245	+	1.12261i
$704$	39.5254	−	26.7347i	1.48967	−	1.00760i
$705$	10.7115	+	5.80311i	0.403417	+	0.218558i
$706$	19.9247	+	60.7868i	0.749877	+	2.28774i
$707$	8.05189	−	4.71842i	0.302823	−	0.177454i
$708$	−127.546	+	49.4266i	−4.79349	+	1.85757i
$709$	22.3976	−	7.50217i	0.841158	−	0.281750i	0.135919	−	0.990720i	$-0.456601\pi$
$709$	22.3976	−	7.50217i	0.841158	−	0.281750i	0.705239	+	0.708970i	$0.250840\pi$
$710$	−8.78089	+	12.8029i	−0.329541	+	0.480482i
$711$	−41.6849	−	15.6670i	−1.56330	−	0.587558i
$712$	−27.0949	+	12.3161i	−1.01542	+	0.461567i
$713$	−13.6719	+	0.707650i	−0.512015	+	0.0265017i
$714$	18.1996	+	4.41389i	0.681103	+	0.165186i
$715$	−2.35082	−	5.64953i	−0.0879155	−	0.211280i
$716$	−52.7264	+	118.015i	−1.97048	+	4.41041i
$717$	0.483106	+	34.0902i	0.0180419	+	1.27312i
$718$	−53.9363	+	30.6770i	−2.01288	+	1.14485i
$719$	−33.1478	+	10.6284i	−1.23620	+	0.396373i	−0.850365	−	0.526194i	$-0.823619\pi$
$719$	−33.1478	+	10.6284i	−1.23620	+	0.396373i	−0.385839	+	0.922566i	$0.626088\pi$
$720$	5.70394	−	28.4443i	0.212573	−	1.06006i
$721$	12.4486	−	0.483062i	0.463610	−	0.0179902i
$722$	−8.85814	−	22.0889i	−0.329666	−	0.822065i
$723$	−4.09199	−	2.35574i	−0.152183	−	0.0876108i
$724$	97.9114	−	30.0037i	3.63885	−	1.11508i
$725$	32.5294	−	0.841290i	1.20811	−	0.0312447i
$726$	−0.449839	+	38.4913i	−0.0166951	+	1.42854i
$727$	28.5516	−	0.369147i	1.05892	−	0.0136909i	0.518494	−	0.855081i	$-0.326493\pi$
$727$	28.5516	−	0.369147i	1.05892	−	0.0136909i	0.540428	+	0.841390i	$0.318262\pi$
$728$	−149.747			−5.55000
$729$	−26.9337	−	1.89162i	−0.997543	−	0.0700601i
$730$	−4.18104			−0.154747
$731$	7.58611	−	0.0980815i	0.280583	−	0.00362768i
$732$	31.4119	+	18.6285i	1.16102	+	0.688528i
$733$	−48.9054	+	1.26482i	−1.80636	+	0.0467170i	−0.914263	−	0.405122i	$-0.867229\pi$
$733$	−48.9054	+	1.26482i	−1.80636	+	0.0467170i	−0.892100	+	0.451839i	$0.850768\pi$
$734$	−36.2090	+	11.0958i	−1.33650	+	0.409554i
$735$	−0.00225467	−	1.81519i	−8.31648e−5	−	0.0669544i
$736$	19.7349	+	49.2116i	0.727439	+	1.81396i
$737$	−13.4333	+	0.521273i	−0.494822	+	0.0192013i
$738$	33.8506	−	27.0815i	1.24606	−	0.996883i
$739$	−7.46137	+	2.39239i	−0.274471	+	0.0880056i	−0.439374	−	0.898304i	$-0.644800\pi$
$739$	−7.46137	+	2.39239i	−0.274471	+	0.0880056i	0.164903	+	0.986310i	$0.447269\pi$
$740$	−31.6226	+	17.9858i	−1.16247	+	0.661171i
$741$	26.5259	+	14.8176i	0.974453	+	0.544338i
$742$	13.0225	−	29.1475i	0.478070	−	1.07004i
$743$	4.51540	+	10.8515i	0.165654	+	0.398104i	0.984374	−	0.176089i	$-0.0563448\pi$
$743$	4.51540	+	10.8515i	0.165654	+	0.398104i	−0.818720	+	0.574193i	$0.805316\pi$
$744$	−24.8185	−	84.5032i	−0.909891	−	3.09804i
$745$	10.3788	−	0.537204i	0.380251	−	0.0196816i
$746$	88.4573	−	40.2088i	3.23865	−	1.47215i
$747$	9.15606	+	7.84725i	0.335003	+	0.287116i
$748$	7.01095	−	10.2222i	0.256346	−	0.373761i
$749$	−28.3477	+	9.49520i	−1.03580	+	0.346947i
$750$	−4.58430	+	29.5523i	−0.167395	+	1.07910i
$751$	−19.3707	+	11.3513i	−0.706847	+	0.414213i	−0.814645	−	0.579959i	$-0.803068\pi$
$751$	−19.3707	+	11.3513i	−0.706847	+	0.414213i	0.107798	+	0.994173i	$0.465620\pi$
$752$	−48.2400	−	147.171i	−1.75913	−	5.36679i
$753$	−1.19423	−	44.0587i	−0.0435202	−	1.60559i
$754$	88.1703	−	59.6376i	3.21097	−	2.17187i
$755$	−5.40456	+	12.5292i	−0.196692	+	0.455983i
$756$	−76.9424	+	30.0367i	−2.79837	+	1.09242i
$757$	−0.544585	−	1.26249i	−0.0197933	−	0.0458860i	0.908033	−	0.418899i	$-0.137584\pi$
$757$	−0.544585	−	1.26249i	−0.0197933	−	0.0458860i	−0.927826	+	0.373013i	$0.878325\pi$
$758$	−37.7684	−	24.1470i	−1.37181	−	0.877059i
$759$	7.15859	+	1.63846i	0.259840	+	0.0594723i
$760$	−5.19333	+	19.1342i	−0.188382	+	0.694070i
$761$	21.7948	−	1.41082i	0.790061	−	0.0511422i	0.335710	−	0.941965i	$-0.391024\pi$
$761$	21.7948	−	1.41082i	0.790061	−	0.0511422i	0.454350	+	0.890823i	$0.349871\pi$
$762$	−48.2211	−	87.1364i	−1.74687	−	3.15662i
$763$	11.1986	−	5.26615i	0.405418	−	0.190647i
$764$	59.3076	+	73.5299i	2.14567	+	2.66022i
$765$	−0.474159	−	2.65057i	−0.0171432	−	0.0958314i
$766$	4.37847	−	0.859904i	0.158201	−	0.0310696i
$767$	44.2142	−	66.2871i	1.59648	−	2.39349i
$768$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.72490 + 0.0352304i) q^{2} +(-1.51002 + 0.848437i) q^{3} +(5.42450 - 0.140291i) q^{4} +(0.633611 - 0.194162i) q^{5} +(4.08476 - 2.36510i) q^{6} +(1.09035 + 2.71893i) q^{7} +(-9.33012 + 0.362051i) q^{8} +(1.56031 - 2.56231i) q^{9} +O(q^{10})\)	\(q+(-2.72490 + 0.0352304i) q^{2} +(-1.51002 + 0.848437i) q^{3} +(5.42450 - 0.140291i) q^{4} +(0.633611 - 0.194162i) q^{5} +(4.08476 - 2.36510i) q^{6} +(1.09035 + 2.71893i) q^{7} +(-9.33012 + 0.362051i) q^{8} +(1.56031 - 2.56231i) q^{9} +(-1.71968 + 0.551395i) q^{10} +(1.46606 - 0.833840i) q^{11} +(-8.07206 + 4.81419i) q^{12} +(2.23325 - 4.99855i) q^{13} +(-3.06688 - 7.37039i) q^{14} +(-0.792029 + 0.830767i) q^{15} +(14.5728 - 0.754280i) q^{16} +(1.23299 - 0.560463i) q^{17} +(-4.16141 + 7.03701i) q^{18} +(1.81231 - 2.64242i) q^{19} +(3.40978 - 1.14212i) q^{20} +(-3.95329 - 3.18054i) q^{21} +(-3.96548 + 2.32378i) q^{22} +(-0.783008 - 2.38882i) q^{23} +(13.7815 - 8.46272i) q^{24} +(-3.77781 + 2.55527i) q^{25} +(-5.90927 + 13.6992i) q^{26} +(-0.182133 + 5.19296i) q^{27} +(6.29604 + 14.5959i) q^{28} +(-6.01114 - 3.84319i) q^{29} +(2.12893 - 2.29166i) q^{30} +(1.42648 - 5.25570i) q^{31} +(-21.0474 + 1.36244i) q^{32} +(-1.50631 + 2.50297i) q^{33} +(-3.34003 + 1.57064i) q^{34} +(1.21877 + 1.51104i) q^{35} +(8.10442 - 14.1182i) q^{36} +(-9.92713 + 1.94962i) q^{37} +(-4.84528 + 7.26417i) q^{38} +(0.868716 + 9.44268i) q^{39} +(-5.84136 + 2.04095i) q^{40} +(-4.95892 - 1.87785i) q^{41} +(10.8844 + 8.52737i) q^{42} +(5.12901 + 2.25187i) q^{43} +(7.83565 - 4.72884i) q^{44} +(0.491124 - 1.92646i) q^{45} +(2.21778 + 6.48170i) q^{46} +(-2.78011 - 10.2430i) q^{47} +(-21.3652 + 13.5030i) q^{48} +(-1.14325 + 1.09266i) q^{49} +(10.2041 - 7.09596i) q^{50} +(-1.38632 + 1.89243i) q^{51} +(11.4130 - 27.4280i) q^{52} +(2.74430 + 2.90879i) q^{53} +(0.313345 - 14.1567i) q^{54} +(0.767010 - 0.812983i) q^{55} +(-11.1575 - 24.9732i) q^{56} +(-0.494700 + 5.52773i) q^{57} +(16.5152 + 10.2605i) q^{58} +(14.3490 + 2.43458i) q^{59} +(-4.17981 + 4.61761i) q^{60} +(-1.85519 - 3.41421i) q^{61} +(-3.70186 + 14.3715i) q^{62} +(8.66802 + 1.44855i) q^{63} +(28.2073 - 2.19245i) q^{64} +(0.444479 - 3.60075i) q^{65} +(4.01637 - 6.87341i) q^{66} +(-7.07605 - 3.66904i) q^{67} +(6.60974 - 3.21321i) q^{68} +(3.20912 + 2.94282i) q^{69} +(-3.37426 - 4.07449i) q^{70} +(6.79467 - 5.26626i) q^{71} +(-13.6302 + 24.4716i) q^{72} +(2.20463 + 0.706886i) q^{73} +(26.9817 - 5.66227i) q^{74} +(3.53656 - 7.06374i) q^{75} +(9.46019 - 14.5881i) q^{76} +(3.86567 + 3.07693i) q^{77} +(-2.69983 - 25.6997i) q^{78} +(-2.76639 - 14.5839i) q^{79} +(9.08700 - 3.30740i) q^{80} +(-4.13088 - 7.99599i) q^{81} +(13.5787 + 4.94225i) q^{82} +(-0.646758 + 3.96720i) q^{83} +(-21.8908 - 16.6982i) q^{84} +(0.672416 - 0.594516i) q^{85} +(-14.0554 - 5.95543i) q^{86} +(12.3376 + 0.703210i) q^{87} +(-13.3766 + 8.31061i) q^{88} +(2.95081 - 1.20554i) q^{89} +(-1.27039 + 5.26671i) q^{90} +(16.0257 + 0.621871i) q^{91} +(-4.58256 - 12.8483i) q^{92} +(2.30512 + 9.14649i) q^{93} +(7.93639 + 27.8132i) q^{94} +(0.635244 - 2.02615i) q^{95} +(30.6260 - 19.9147i) q^{96} +(-0.516441 - 2.24357i) q^{97} +(3.07675 - 3.01766i) q^{98} +(0.150945 - 5.05754i) 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

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