LMFDB - Embedded newform 729.2.k.a.4.7

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			4.7
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46704 - 0.0318966i) q^{2} +(-0.976238 + 1.43072i) q^{3} +(4.08596 + 0.105673i) q^{4} +(-4.03733 - 1.23719i) q^{5} +(2.45406 - 3.49851i) q^{6} +(-1.39476 + 3.47801i) q^{7} +(-5.14609 - 0.199692i) q^{8} +(-1.09392 - 2.79345i) q^{9} +O(q^{10})$	\(q+(-2.46704 - 0.0318966i) q^{2} +(-0.976238 + 1.43072i) q^{3} +(4.08596 + 0.105673i) q^{4} +(-4.03733 - 1.23719i) q^{5} +(2.45406 - 3.49851i) q^{6} +(-1.39476 + 3.47801i) q^{7} +(-5.14609 - 0.199692i) q^{8} +(-1.09392 - 2.79345i) q^{9} +(9.92081 + 3.18098i) q^{10} +(4.56767 + 2.59792i) q^{11} +(-4.14006 + 5.74270i) q^{12} +(1.64311 + 3.67767i) q^{13} +(3.55187 - 8.53592i) q^{14} +(5.71147 - 4.56849i) q^{15} +(4.52553 + 0.234240i) q^{16} +(3.12478 + 1.42039i) q^{17} +(2.60964 + 6.92645i) q^{18} +(0.984999 + 1.43616i) q^{19} +(-16.3656 - 5.48175i) q^{20} +(-3.61444 - 5.39087i) q^{21} +(-11.1858 - 6.55488i) q^{22} +(-1.40619 + 4.29005i) q^{23} +(5.30951 - 7.16766i) q^{24} +(10.6278 + 7.18857i) q^{25} +(-3.93631 - 9.12539i) q^{26} +(5.06456 + 1.16198i) q^{27} +(-6.06646 + 14.0636i) q^{28} +(-6.71348 + 4.29222i) q^{29} +(-14.2362 + 11.0885i) q^{30} +(0.0138532 + 0.0510402i) q^{31} +(-0.878810 - 0.0568871i) q^{32} +(-8.17603 + 3.99886i) q^{33} +(-7.66366 - 3.60383i) q^{34} +(9.93406 - 12.3163i) q^{35} +(-4.17451 - 11.5295i) q^{36} +(-0.975883 - 0.191657i) q^{37} +(-2.38423 - 3.57450i) q^{38} +(-6.86578 - 1.23946i) q^{39} +(20.5294 + 7.17291i) q^{40} +(2.62786 - 0.995123i) q^{41} +(8.74504 + 13.4148i) q^{42} +(5.88012 - 2.58165i) q^{43} +(18.3888 + 11.0977i) q^{44} +(0.960480 + 12.6314i) q^{45} +(3.60598 - 10.5389i) q^{46} +(-1.70016 + 6.26403i) q^{47} +(-4.75313 + 6.24609i) q^{48} +(-5.09075 - 4.86546i) q^{49} +(-25.9900 - 18.0735i) q^{50} +(-5.08270 + 3.08405i) q^{51} +(6.32504 + 15.2005i) q^{52} +(-0.0957473 + 0.101486i) q^{53} +(-12.4574 - 3.02820i) q^{54} +(-15.2271 - 16.1397i) q^{55} +(7.87207 - 17.6196i) q^{56} +(-3.01634 + 0.00721927i) q^{57} +(16.6994 - 10.3750i) q^{58} +(1.05775 - 0.179468i) q^{59} +(23.8196 - 18.0631i) q^{60} +(-0.977958 + 1.79979i) q^{61} +(-0.0325483 - 0.126360i) q^{62} +(11.2414 + 0.0915249i) q^{63} +(-6.86968 - 0.533954i) q^{64} +(-2.08378 - 16.8808i) q^{65} +(20.2982 - 9.60458i) q^{66} +(1.85920 - 0.964024i) q^{67} +(12.6176 + 6.13385i) q^{68} +(-4.76507 - 6.19998i) q^{69} +(-24.9006 + 30.0680i) q^{70} +(-6.86485 - 5.32066i) q^{71} +(5.07157 + 14.5938i) q^{72} +(-10.9916 + 3.52432i) q^{73} +(2.40143 + 0.503954i) q^{74} +(-20.6601 + 8.18768i) q^{75} +(3.87290 + 5.97219i) q^{76} +(-15.4064 + 12.2629i) q^{77} +(16.8987 + 3.27680i) q^{78} +(1.95154 - 10.2881i) q^{79} +(-17.9813 - 6.54465i) q^{80} +(-6.60669 + 6.11160i) q^{81} +(-6.51480 + 2.37119i) q^{82} +(2.22786 + 13.6657i) q^{83} +(-14.1988 - 22.4089i) q^{84} +(-10.8585 - 9.60051i) q^{85} +(-14.5889 + 6.18148i) q^{86} +(0.412984 - 13.7953i) q^{87} +(-22.9868 - 14.2813i) q^{88} +(3.74951 + 1.53185i) q^{89} +(-1.96665 - 31.1930i) q^{90} +(-15.0827 + 0.585278i) q^{91} +(-6.19900 + 17.3804i) q^{92} +(-0.0865482 - 0.0300075i) q^{93} +(4.39418 - 15.3994i) q^{94} +(-2.19996 - 7.01689i) q^{95} +(0.939317 - 1.20180i) q^{96} +(-2.71696 + 11.8032i) q^{97} +(12.4039 + 12.1657i) q^{98} +(2.26051 - 15.6014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.46704	−	0.0318966i	−1.74446	−	0.0225543i	−0.865911	−	0.500199i	$-0.833260\pi$
$2$	−2.46704	−	0.0318966i	−1.74446	−	0.0225543i	−0.878553	+	0.477644i	$0.841491\pi$
$3$	−0.976238	+	1.43072i	−0.563631	+	0.826026i
$3$	−0.976238	+	1.43072i	−0.563631	+	0.826026i
$4$	4.08596	+	0.105673i	2.04298	+	0.0528366i
$5$	−4.03733	−	1.23719i	−1.80555	−	0.553288i	−0.806280	−	0.591534i	$-0.798523\pi$
$5$	−4.03733	−	1.23719i	−1.80555	−	0.553288i	−0.999268	+	0.0382454i	$0.987823\pi$
$6$	2.45406	−	3.49851i	1.00187	−	1.42826i
$7$	−1.39476	+	3.47801i	−0.527169	+	1.31456i	0.391733	+	0.920079i	$0.371876\pi$
$7$	−1.39476	+	3.47801i	−0.527169	+	1.31456i	−0.918902	+	0.394486i	$0.870923\pi$
$8$	−5.14609	−	0.199692i	−1.81942	−	0.0706017i
$9$	−1.09392	−	2.79345i	−0.364639	−	0.931149i
$10$	9.92081	+	3.18098i	3.13724	+	1.00591i
$11$	4.56767	+	2.59792i	1.37720	+	0.783303i	0.990317	−	0.138824i	$-0.0443324\pi$
$11$	4.56767	+	2.59792i	1.37720	+	0.783303i	0.386887	+	0.922127i	$0.373550\pi$
$12$	−4.14006	+	5.74270i	−1.19513	+	1.65778i
$13$	1.64311	+	3.67767i	0.455716	+	1.02000i	0.985157	+	0.171656i	$0.0549119\pi$
$13$	1.64311	+	3.67767i	0.455716	+	1.02000i	−0.529441	+	0.848347i	$0.677598\pi$
$14$	3.55187	−	8.53592i	0.949276	−	2.28132i
$15$	5.71147	−	4.56849i	1.47469	−	1.17958i
$16$	4.52553	+	0.234240i	1.13138	+	0.0585599i
$17$	3.12478	+	1.42039i	0.757870	+	0.344494i	0.755193	−	0.655502i	$-0.227543\pi$
$17$	3.12478	+	1.42039i	0.757870	+	0.344494i	0.00267684	+	0.999996i	$0.499148\pi$
$18$	2.60964	+	6.92645i	0.615098	+	1.63258i
$19$	0.984999	+	1.43616i	0.225974	+	0.329478i	0.921040	−	0.389468i	$-0.127341\pi$
$19$	0.984999	+	1.43616i	0.225974	+	0.329478i	−0.695066	+	0.718946i	$0.744625\pi$
$20$	−16.3656	−	5.48175i	−3.65947	−	1.22576i
$21$	−3.61444	−	5.39087i	−0.788736	−	1.17639i
$22$	−11.1858	−	6.55488i	−2.38482	−	1.39751i
$23$	−1.40619	+	4.29005i	−0.293212	+	0.894537i	0.691806	+	0.722084i	$0.256815\pi$
$23$	−1.40619	+	4.29005i	−0.293212	+	0.894537i	−0.985018	+	0.172453i	$0.944831\pi$
$24$	5.30951	−	7.16766i	1.08380	−	1.46309i
$25$	10.6278	+	7.18857i	2.12556	+	1.43771i
$26$	−3.93631	−	9.12539i	−0.771974	−	1.78964i
$27$	5.06456	+	1.16198i	0.974676	+	0.223623i
$28$	−6.06646	+	14.0636i	−1.14645	+	2.65778i
$29$	−6.71348	+	4.29222i	−1.24666	+	0.797046i	−0.985734	−	0.168312i	$-0.946168\pi$
$29$	−6.71348	+	4.29222i	−1.24666	+	0.797046i	−0.260927	+	0.965358i	$0.584028\pi$
$30$	−14.2362	+	11.0885i	−2.59916	+	2.02447i
$31$	0.0138532	+	0.0510402i	0.00248810	+	0.00916710i	0.966317	−	0.257353i	$-0.0828504\pi$
$31$	0.0138532	+	0.0510402i	0.00248810	+	0.00916710i	−0.963829	+	0.266520i	$0.914126\pi$
$32$	−0.878810	−	0.0568871i	−0.155353	−	0.0100563i
$33$	−8.17603	+	3.99886i	−1.42326	+	0.696112i
$34$	−7.66366	−	3.60383i	−1.31431	−	0.618051i
$35$	9.93406	−	12.3163i	1.67916	−	2.08183i
$36$	−4.17451	−	11.5295i	−0.695752	−	1.92159i
$37$	−0.975883	−	0.191657i	−0.160434	−	0.0315083i	0.111850	−	0.993725i	$-0.464322\pi$
$37$	−0.975883	−	0.191657i	−0.160434	−	0.0315083i	−0.272284	+	0.962217i	$0.587779\pi$
$38$	−2.38423	−	3.57450i	−0.386773	−	0.579860i
$39$	−6.86578	−	1.23946i	−1.09941	−	0.198473i
$40$	20.5294	+	7.17291i	3.24598	+	1.13414i
$41$	2.62786	−	0.995123i	0.410403	−	0.155412i	−0.140308	−	0.990108i	$-0.544809\pi$
$41$	2.62786	−	0.995123i	0.410403	−	0.155412i	0.550711	+	0.834696i	$0.314357\pi$
$42$	8.74504	+	13.4148i	1.34939	+	2.06995i
$43$	5.88012	−	2.58165i	0.896710	−	0.393697i	0.0978410	−	0.995202i	$-0.468806\pi$
$43$	5.88012	−	2.58165i	0.896710	−	0.393697i	0.798869	+	0.601505i	$0.205432\pi$
$44$	18.3888	+	11.0977i	2.77221	+	1.67304i
$45$	0.960480	+	12.6314i	0.143180	+	1.88299i
$46$	3.60598	−	10.5389i	0.531673	−	1.55387i
$47$	−1.70016	+	6.26403i	−0.247994	+	0.913703i	0.726105	+	0.687583i	$0.241328\pi$
$47$	−1.70016	+	6.26403i	−0.247994	+	0.913703i	−0.974099	+	0.226120i	$0.927396\pi$
$48$	−4.75313	+	6.24609i	−0.686055	+	0.901546i
$49$	−5.09075	−	4.86546i	−0.727251	−	0.695066i
$50$	−25.9900	−	18.0735i	−3.67554	−	2.55598i
$51$	−5.08270	+	3.08405i	−0.711721	+	0.431853i
$52$	6.32504	+	15.2005i	0.877125	+	2.10792i
$53$	−0.0957473	+	0.101486i	−0.0131519	+	0.0139402i	−0.733916	−	0.679240i	$-0.762310\pi$
$53$	−0.0957473	+	0.101486i	−0.0131519	+	0.0139402i	0.720764	+	0.693180i	$0.243791\pi$
$54$	−12.4574	−	3.02820i	−1.69524	−	0.412086i
$55$	−15.2271	−	16.1397i	−2.05322	−	2.17628i
$56$	7.87207	−	17.6196i	1.05195	−	2.35452i
$57$	−3.01634	+	0.00721927i	−0.399524	+	0.000956216i
$58$	16.6994	−	10.3750i	2.19273	−	1.36230i
$59$	1.05775	−	0.179468i	0.137707	−	0.0233647i	−0.0980166	−	0.995185i	$-0.531250\pi$
$59$	1.05775	−	0.179468i	0.137707	−	0.0233647i	0.235724	+	0.971820i	$0.424254\pi$
$60$	23.8196	−	18.0631i	3.07510	−	2.33194i
$61$	−0.977958	+	1.79979i	−0.125215	+	0.230439i	−0.933683	−	0.358101i	$-0.883424\pi$
$61$	−0.977958	+	1.79979i	−0.125215	+	0.230439i	0.808468	+	0.588540i	$0.200297\pi$
$62$	−0.0325483	−	0.126360i	−0.00413364	−	0.0160478i
$63$	11.2414	+	0.0915249i	1.41628	+	0.0115311i
$64$	−6.86968	−	0.533954i	−0.858710	−	0.0667442i
$65$	−2.08378	−	16.8808i	−0.258461	−	2.09381i
$66$	20.2982	−	9.60458i	2.49853	−	1.18224i
$67$	1.85920	−	0.964024i	0.227138	−	0.117774i	−0.342963	−	0.939349i	$-0.611431\pi$
$67$	1.85920	−	0.964024i	0.227138	−	0.117774i	0.570101	+	0.821574i	$0.306904\pi$
$68$	12.6176	+	6.13385i	1.53011	+	0.743838i
$69$	−4.76507	−	6.19998i	−0.573647	−	0.746390i
$70$	−24.9006	+	30.0680i	−2.97619	+	3.59381i
$71$	−6.86485	−	5.32066i	−0.814707	−	0.631446i	0.117621	−	0.993059i	$-0.462473\pi$
$71$	−6.86485	−	5.32066i	−0.814707	−	0.631446i	−0.932328	+	0.361613i	$0.882226\pi$
$72$	5.07157	+	14.5938i	0.597690	+	1.71989i
$73$	−10.9916	+	3.52432i	−1.28647	+	0.412490i	−0.868373	−	0.495912i	$-0.834834\pi$
$73$	−10.9916	+	3.52432i	−1.28647	+	0.412490i	−0.418097	+	0.908402i	$0.637303\pi$
$74$	2.40143	+	0.503954i	0.279161	+	0.0585835i
$75$	−20.6601	+	8.18768i	−2.38562	+	0.945432i
$76$	3.87290	+	5.97219i	0.444252	+	0.685058i
$77$	−15.4064	+	12.2629i	−1.75572	+	1.39749i
$78$	16.8987	+	3.27680i	1.91340	+	0.371025i
$79$	1.95154	−	10.2881i	0.219565	−	1.15750i	−0.684141	−	0.729350i	$-0.739823\pi$
$79$	1.95154	−	10.2881i	0.219565	−	1.15750i	0.903706	−	0.428154i	$-0.140836\pi$
$80$	−17.9813	−	6.54465i	−2.01037	−	0.731714i
$81$	−6.60669	+	6.11160i	−0.734077	+	0.679067i
$82$	−6.51480	+	2.37119i	−0.719439	+	0.261854i
$83$	2.22786	+	13.6657i	0.244540	+	1.50000i	0.763837	+	0.645409i	$0.223313\pi$
$83$	2.22786	+	13.6657i	0.244540	+	1.50000i	−0.519297	+	0.854594i	$0.673806\pi$
$84$	−14.1988	−	22.4089i	−1.54922	−	2.44501i
$85$	−10.8585	−	9.60051i	−1.17777	−	1.04132i
$86$	−14.5889	+	6.18148i	−1.57316	+	0.666566i
$87$	0.412984	−	13.7953i	0.0442765	−	1.47902i
$88$	−22.9868	−	14.2813i	−2.45040	−	1.52239i
$89$	3.74951	+	1.53185i	0.397448	+	0.162375i	0.568107	−	0.822955i	$-0.307676\pi$
$89$	3.74951	+	1.53185i	0.397448	+	0.162375i	−0.170659	+	0.985330i	$0.554590\pi$
$90$	−1.96665	−	31.1930i	−0.207303	−	3.28803i
$91$	−15.0827	+	0.585278i	−1.58110	+	0.0613538i
$92$	−6.19900	+	17.3804i	−0.646290	+	1.81203i
$93$	−0.0865482	−	0.0300075i	−0.00897463	−	0.00311163i
$94$	4.39418	−	15.3994i	0.453225	−	1.58833i
$95$	−2.19996	−	7.01689i	−0.225711	−	0.719918i
$96$	0.939317	−	1.20180i	0.0958687	−	0.122658i
$97$	−2.71696	+	11.8032i	−0.275865	+	1.19844i	0.630583	+	0.776122i	$0.282816\pi$
$97$	−2.71696	+	11.8032i	−0.275865	+	1.19844i	−0.906448	+	0.422316i	$0.861217\pi$
$98$	12.4039	+	12.1657i	1.25299	+	1.22892i
$99$	2.26051	−	15.6014i	0.227189	−	1.56800i
$100$	42.6652	+	30.4953i	4.26652	+	3.04953i
$101$	−1.11760	+	7.46155i	−0.111205	+	0.742452i	0.861048	+	0.508523i	$0.169808\pi$
$101$	−1.11760	+	7.46155i	−0.111205	+	0.742452i	−0.972254	+	0.233929i	$0.924842\pi$
$102$	12.6376	−	7.44636i	1.25131	−	0.737299i
$103$	−6.40652	−	17.9622i	−0.631253	−	1.76987i	−0.638174	−	0.769892i	$-0.720310\pi$
$103$	−6.40652	−	17.9622i	−0.631253	−	1.76987i	0.00692137	−	0.999976i	$-0.497797\pi$
$104$	−7.72117	−	19.2537i	−0.757123	−	1.88798i
$105$	7.92316	+	26.2365i	0.773221	+	2.56042i
$106$	0.239450	−	0.247317i	0.0232574	−	0.0240215i
$107$	−0.302257	−	5.18954i	−0.0292202	−	0.501692i	−0.980889	−	0.194567i	$-0.937670\pi$
$107$	−0.302257	−	5.18954i	−0.0292202	−	0.501692i	0.951669	−	0.307125i	$-0.0993671\pi$
$108$	20.5708	+	5.28300i	1.97943	+	0.508357i
$109$	0.0364586	−	0.625971i	0.00349211	−	0.0599571i	−0.996112	−	0.0880972i	$-0.971921\pi$
$109$	0.0364586	−	0.625971i	0.00349211	−	0.0599571i	0.999604	+	0.0281400i	$0.00895844\pi$
$110$	37.0510	+	40.3031i	3.53268	+	3.84275i
$111$	1.22690	−	1.20911i	0.116452	−	0.114764i
$112$	−7.12671	+	15.4131i	−0.673411	+	1.45641i
$113$	−0.654516	+	0.480725i	−0.0615717	+	0.0452228i	−0.622315	−	0.782767i	$-0.713808\pi$
$113$	−0.654516	+	0.480725i	−0.0615717	+	0.0452228i	0.560743	+	0.827990i	$0.310515\pi$
$114$	7.44168	+	0.0784008i	0.696977	+	0.00734291i
$115$	10.9849	−	15.5806i	1.02434	−	1.45290i
$116$	−27.8846	+	16.8284i	−2.58902	+	1.56248i
$117$	8.47596	−	8.61300i	0.783603	−	0.796272i
$118$	−2.61524	+	0.409016i	−0.240752	+	0.0376530i
$119$	−9.29843	+	8.88692i	−0.852385	+	0.814663i
$120$	−30.3040	+	22.3693i	−2.76636	+	2.04203i
$121$	8.49169	+	14.2785i	0.771972	+	1.29805i
$122$	2.47007	−	4.40896i	0.223630	−	0.399169i
$123$	−1.14168	+	4.73121i	−0.102942	+	0.426599i
$124$	0.0512099	+	0.210012i	0.00459878	+	0.0188597i
$125$	−20.7593	−	25.7375i	−1.85677	−	2.30203i
$126$	−27.7301	−	0.584358i	−2.47039	−	0.0520588i
$127$	−0.231230	−	11.9221i	−0.0205183	−	1.05792i	−0.858685	−	0.512504i	$-0.828718\pi$
$127$	−0.231230	−	11.9221i	−0.0205183	−	1.05792i	0.838167	−	0.545414i	$-0.183628\pi$
$128$	18.6849	+	1.69558i	1.65152	+	0.149870i
$129$	−2.04679	+	10.9331i	−0.180210	+	0.962607i
$130$	4.60234	+	41.7122i	0.403652	+	3.65840i
$131$	19.1651	−	1.73916i	1.67446	−	0.151952i	0.788289	−	0.615305i	$-0.210967\pi$
$131$	19.1651	−	1.73916i	1.67446	−	0.151952i	0.886174	+	0.463353i	$0.153354\pi$
$132$	−33.8295	+	15.4752i	−2.94448	+	1.34694i
$133$	−6.36882	+	1.42274i	−0.552247	+	0.123367i
$134$	−4.61749	+	2.31899i	−0.398890	+	0.200330i
$135$	−19.0097	−	10.9571i	−1.63610	−	0.943039i
$136$	−15.7967	−	7.93342i	−1.35456	−	0.680285i
$137$	−16.3681	−	4.10352i	−1.39842	−	0.350587i	−0.530669	−	0.847579i	$-0.678059\pi$
$137$	−16.3681	−	4.10352i	−1.39842	−	0.350587i	−0.867755	+	0.496992i	$0.834438\pi$
$138$	11.5579	+	15.4476i	0.983873	+	1.31499i
$139$	−4.72626	−	0.676700i	−0.400876	−	0.0573969i	−0.0616410	−	0.998098i	$-0.519633\pi$
$139$	−4.72626	−	0.676700i	−0.400876	−	0.0573969i	−0.339235	+	0.940701i	$0.610168\pi$
$140$	41.8917	−	49.2742i	3.54049	−	4.16443i
$141$	−7.30231	−	8.54765i	−0.614966	−	0.719842i
$142$	16.7662	+	13.3453i	1.40699	+	1.11991i
$143$	−2.04914	+	21.0671i	−0.171358	+	1.76172i
$144$	−4.29622	−	12.8981i	−0.358018	−	1.07484i
$145$	32.4148	−	9.02328i	2.69190	−	0.749343i
$146$	27.2292	−	8.34405i	2.25350	−	0.690559i
$147$	11.9309	−	2.53359i	0.984044	−	0.208967i
$148$	−3.96717	−	0.886229i	−0.326099	−	0.0728476i
$149$	0.807927	−	0.202549i	0.0661880	−	0.0165934i	−0.209941	−	0.977714i	$-0.567327\pi$
$149$	0.807927	−	0.202549i	0.0661880	−	0.0165934i	0.276129	+	0.961121i	$0.410948\pi$
$150$	51.2306	−	19.5404i	4.18296	−	1.59547i
$151$	14.3610	+	16.8918i	1.16868	+	1.37464i	0.913043	+	0.407864i	$0.133726\pi$
$151$	14.3610	+	16.8918i	1.16868	+	1.37464i	0.255639	+	0.966772i	$0.417714\pi$
$152$	−4.78210	−	7.58732i	−0.387879	−	0.615413i
$153$	0.549524	−	10.2827i	0.0444264	−	0.831306i
$154$	38.3994	−	29.7618i	3.09431	−	2.39827i
$155$	0.00721671	−	0.223205i	0.000579660	−	0.0179283i
$156$	−27.9223	−	5.78992i	−2.23558	−	0.463565i
$157$	−0.660075	+	5.34730i	−0.0526797	+	0.426761i	0.942917	+	0.333027i	$0.108070\pi$
$157$	−0.660075	+	5.34730i	−0.0526797	+	0.426761i	−0.995597	+	0.0937348i	$0.970119\pi$
$158$	−5.14269	+	25.3190i	−0.409130	+	2.01427i
$159$	−0.0517261	−	0.236062i	−0.00410215	−	0.0187209i
$160$	3.47767	+	1.31693i	0.274934	+	0.104112i
$161$	−12.9595	−	10.8743i	−1.02135	−	0.857018i
$162$	16.4939	−	14.8669i	1.29589	−	1.16805i
$163$	−12.9090	+	10.8320i	−1.01111	+	0.848425i	−0.988485	−	0.151319i	$-0.951648\pi$
$163$	−12.9090	+	10.8320i	−1.01111	+	0.848425i	−0.0226288	+	0.999744i	$0.507204\pi$
$164$	10.8425	−	3.78834i	0.846658	−	0.295820i
$165$	37.9567	−	6.02942i	2.95492	−	0.469390i
$166$	−5.06035	−	33.7849i	−0.392759	−	2.62222i
$167$	−0.952130	+	1.86568i	−0.0736780	+	0.144370i	−0.924622	−	0.380886i	$-0.875619\pi$
$167$	−0.952130	+	1.86568i	−0.0736780	+	0.144370i	0.850944	+	0.525256i	$0.176031\pi$
$168$	17.5237	+	28.4637i	1.35198	+	2.19602i
$169$	−2.15180	+	2.40227i	−0.165523	+	0.184790i
$170$	26.4821	+	24.0312i	2.03109	+	1.84311i
$171$	2.93434	−	4.32258i	0.224394	−	0.330556i
$172$	24.2988	−	9.92714i	1.85276	−	0.756937i
$173$	0.633880	+	0.107550i	0.0481930	+	0.00817687i	0.191325	−	0.981527i	$-0.438722\pi$
$173$	0.633880	+	0.107550i	0.0481930	+	0.00817687i	−0.143132	+	0.989704i	$0.545717\pi$
$174$	−1.45887	+	34.0205i	−0.110597	+	2.57909i
$175$	−39.8252	+	26.9374i	−3.01050	+	2.03627i
$176$	20.0626	+	12.8269i	1.51227	+	0.966864i
$177$	−0.775847	+	1.68855i	−0.0583163	+	0.126919i
$178$	−9.20136	−	3.89873i	−0.689671	−	0.292222i
$179$	−2.42601	−	5.07356i	−0.181328	−	0.379216i	0.791353	−	0.611359i	$-0.209377\pi$
$179$	−2.42601	−	5.07356i	−0.181328	−	0.379216i	−0.972682	+	0.232143i	$0.925426\pi$
$180$	2.58968	+	51.7131i	0.193023	+	3.85447i
$181$	23.4496	+	6.52764i	1.74299	+	0.485195i	0.985790	−	0.167983i	$-0.0537254\pi$
$181$	23.4496	+	6.52764i	1.74299	+	0.485195i	0.757204	+	0.653179i	$0.226565\pi$
$182$	37.2284	−	0.962820i	2.75955	−	0.0713690i
$183$	−1.62027	−	3.15620i	−0.119774	−	0.233313i
$184$	8.09309	−	21.7962i	0.596630	−	1.60683i
$185$	3.70285	+	1.98114i	0.272239	+	0.145656i
$186$	0.212561	+	0.0767903i	0.0155857	+	0.00563054i
$187$	10.5829	+	14.6058i	0.773898	+	1.06808i
$188$	−7.60873	+	25.4149i	−0.554924	+	1.85357i
$189$	−11.1052	+	15.9939i	−0.807786	+	1.16339i
$190$	5.20358	+	17.3812i	0.377507	+	1.26096i
$191$	−2.39335	+	3.12954i	−0.173177	+	0.226445i	−0.872814	−	0.488053i	$-0.837707\pi$
$191$	−2.39335	+	3.12954i	−0.173177	+	0.226445i	0.699637	+	0.714498i	$0.253345\pi$
$192$	7.47038	−	9.30732i	0.539128	−	0.671698i
$193$	8.45243	−	3.97474i	0.608419	−	0.286108i	−0.0965701	−	0.995326i	$-0.530787\pi$
$193$	8.45243	−	3.97474i	0.608419	−	0.286108i	0.704989	+	0.709218i	$0.250952\pi$
$194$	7.07934	−	29.0325i	0.508267	−	2.08441i
$195$	26.1860	+	13.4984i	1.87522	+	0.966640i
$196$	−20.2865	−	20.4180i	−1.44903	−	1.45843i
$197$	3.89618	−	0.765184i	0.277591	−	0.0545171i	−0.0519791	−	0.998648i	$-0.516553\pi$
$197$	3.89618	−	0.765184i	0.277591	−	0.0545171i	0.329570	+	0.944131i	$0.393096\pi$
$198$	−6.07440	+	38.4174i	−0.431689	+	2.73020i
$199$	3.21404	−	1.77343i	0.227837	−	0.125715i	−0.365087	−	0.930973i	$-0.618961\pi$
$199$	3.21404	−	1.77343i	0.227837	−	0.125715i	0.592925	+	0.805258i	$0.297973\pi$
$200$	−53.2562	−	39.1153i	−3.76578	−	2.76587i
$201$	−0.435777	+	3.60112i	−0.0307373	+	0.254003i
$202$	2.99517	−	18.3723i	0.210739	−	1.29267i
$203$	−5.56473	−	29.3362i	−0.390568	−	2.05899i
$204$	−21.0936	+	12.0642i	−1.47685	+	0.844662i
$205$	−11.8407	+	0.766473i	−0.826991	+	0.0535328i
$206$	15.2322	+	44.5179i	1.06128	+	3.10171i
$207$	13.5223	−	0.764826i	0.939863	−	0.0531591i
$208$	6.57447	+	17.0283i	0.455858	+	1.18070i
$209$	0.768107	+	9.11886i	0.0531311	+	0.630765i
$210$	−18.7099	−	64.9793i	−1.29111	−	4.48400i
$211$	3.99638	−	5.99149i	0.275122	−	0.412471i	−0.668388	−	0.743812i	$-0.733016\pi$
$211$	3.99638	−	5.99149i	0.275122	−	0.412471i	0.943511	+	0.331341i	$0.107501\pi$
$212$	−0.401944	+	0.404551i	−0.0276056	+	0.0277847i
$213$	14.3141	−	4.62744i	0.980786	−	0.317067i
$214$	0.580151	+	12.8125i	0.0396583	+	0.875843i
$215$	−26.9340	+	3.14813i	−1.83688	+	0.214701i
$216$	−25.8306	−	6.99101i	−1.75755	−	0.475678i
$217$	−0.196840	−	0.0230073i	−0.0133624	−	0.00156184i
$218$	−0.109911	+	1.54314i	−0.00744414	+	0.104514i
$219$	5.68812	−	19.1665i	0.384367	−	1.29515i
$220$	−60.5116	−	67.5554i	−4.07969	−	4.55459i
$221$	−0.0893735	+	13.8258i	−0.00601191	+	0.930021i
$222$	−3.06539	+	2.94380i	−0.205736	+	0.197575i
$223$	−10.2215	+	9.03737i	−0.684485	+	0.605187i	−0.931464	−	0.363834i	$-0.881468\pi$
$223$	−10.2215	+	9.03737i	−0.684485	+	0.605187i	0.246979	+	0.969021i	$0.420562\pi$
$224$	1.42358	−	2.97717i	0.0951170	−	0.198920i
$225$	8.45492	−	37.5520i	0.563661	−	2.50346i
$226$	1.63005	−	1.16509i	0.108430	−	0.0775008i
$227$	0.713522	+	1.39813i	0.0473581	+	0.0927972i	0.913183	−	0.407551i	$-0.133617\pi$
$227$	0.713522	+	1.39813i	0.0473581	+	0.0927972i	−0.865824	+	0.500348i	$0.833205\pi$
$228$	−12.3254	−	0.289248i	−0.816270	−	0.0191559i
$229$	−10.6656	−	13.9463i	−0.704804	−	0.921599i	0.294617	−	0.955615i	$-0.404808\pi$
$229$	−10.6656	−	13.9463i	−0.704804	−	0.921599i	−0.999421	+	0.0340168i	$0.989170\pi$
$230$	−27.5971	+	38.0877i	−1.81970	+	2.51143i
$231$	−2.50450	−	34.0138i	−0.164784	−	2.23794i
$232$	35.4053	−	20.7475i	2.32447	−	1.36214i
$233$	−1.86328	−	8.60184i	−0.122067	−	0.563525i	−0.996871	−	0.0790475i	$-0.974812\pi$
$233$	−1.86328	−	8.60184i	−0.122067	−	0.563525i	0.874804	−	0.484478i	$-0.160990\pi$
$234$	−21.1853	+	20.9783i	−1.38493	+	1.37139i
$235$	14.6139	−	23.1866i	0.953307	−	1.51252i
$236$	4.34089	−	0.621522i	0.282568	−	0.0404576i
$237$	12.8142	+	12.8358i	0.832375	+	0.833772i
$238$	23.2231	−	21.6278i	1.50533	−	1.40192i
$239$	2.89910	+	5.33537i	0.187528	+	0.345117i	0.955316	−	0.295587i	$-0.0955152\pi$
$239$	2.89910	+	5.33537i	0.187528	+	0.345117i	−0.767788	+	0.640704i	$0.778643\pi$
$240$	26.9176	−	19.3370i	1.73752	−	1.24820i
$241$	−13.4000	+	22.5316i	−0.863169	+	1.45139i	0.0289455	+	0.999581i	$0.490785\pi$
$241$	−13.4000	+	22.5316i	−0.863169	+	1.45139i	−0.892114	+	0.451809i	$0.850779\pi$
$242$	−20.4940	−	35.4966i	−1.31740	−	2.28181i
$243$	−2.29428	−	15.4187i	−0.147178	−	0.989110i
$244$	−4.18609	+	7.25051i	−0.267987	+	0.464167i
$245$	14.5336	+	25.9417i	0.928515	+	1.65735i
$246$	2.96748	−	11.6357i	0.189200	−	0.741865i
$247$	−3.66328	+	5.98227i	−0.233089	+	0.380643i
$248$	−0.0610972	−	0.265424i	−0.00387968	−	0.0168544i
$249$	−21.7267	−	10.1535i	−1.37687	−	0.643452i
$250$	50.3932	+	64.1577i	3.18714	+	4.05769i
$251$	8.55585	+	16.2429i	0.540041	+	1.02524i	0.991147	+	0.132771i	$0.0423876\pi$
$251$	8.55585	+	16.2429i	0.540041	+	1.02524i	−0.451106	+	0.892470i	$0.648970\pi$
$252$	45.9222	+	1.56188i	2.89283	+	0.0983892i
$253$	−17.5682	+	15.9423i	−1.10451	+	1.00229i
$254$	0.190178	+	29.4198i	0.0119328	+	1.84596i
$255$	24.3361	−	6.16304i	1.52399	−	0.385945i
$256$	−32.3352	−	3.35630i	−2.02095	−	0.209769i
$257$	13.0817	−	1.70073i	0.816011	−	0.106089i	0.290500	−	0.956875i	$-0.406178\pi$
$257$	13.0817	−	1.70073i	0.816011	−	0.106089i	0.525512	+	0.850786i	$0.323874\pi$
$258$	5.39825	−	26.9072i	0.336080	−	1.67517i
$259$	2.02771	−	3.12682i	0.125996	−	0.194291i
$260$	−6.73040	−	69.1946i	−0.417402	−	4.29126i
$261$	19.3341	+	14.0584i	1.19675	+	0.870193i
$262$	−47.3366	+	3.67929i	−2.92447	+	0.227308i
$263$	−1.73709	−	8.55222i	−0.107114	−	0.527352i	−0.997407	−	0.0719652i	$-0.977073\pi$
$263$	−1.73709	−	8.55222i	−0.107114	−	0.527352i	0.890294	−	0.455387i	$-0.150499\pi$
$264$	42.8731	−	18.9458i	2.63866	−	1.16603i
$265$	0.512121	−	0.291276i	0.0314593	−	0.0178929i
$266$	15.7576	−	3.30681i	0.966158	−	0.202754i
$267$	−5.85206	+	3.86906i	−0.358140	+	0.236783i
$268$	7.69850	−	3.74250i	0.470261	−	0.228609i
$269$	−7.31967	+	9.83203i	−0.446288	+	0.599469i	−0.967161	−	0.254165i	$-0.918199\pi$
$269$	−7.31967	+	9.83203i	−0.446288	+	0.599469i	0.520872	+	0.853635i	$0.325607\pi$
$270$	46.5483	+	27.6381i	2.83284	+	1.68200i
$271$	−7.72727	−	10.3795i	−0.469398	−	0.630511i	0.502875	−	0.864359i	$-0.332276\pi$
$271$	−7.72727	−	10.3795i	−0.469398	−	0.630511i	−0.972273	+	0.233848i	$0.924868\pi$
$272$	13.8086	+	7.15995i	0.837268	+	0.434136i
$273$	13.8870	−	22.1505i	0.840477	−	1.34061i
$274$	40.2500	+	10.6456i	2.43159	+	0.643127i
$275$	29.8690	+	60.4452i	1.80117	+	3.64498i
$276$	−18.8147	−	25.8364i	−1.13251	−	1.55517i
$277$	13.3833	−	9.30674i	0.804122	−	0.559188i	−0.0957174	−	0.995409i	$-0.530515\pi$
$277$	13.3833	−	9.30674i	0.804122	−	0.559188i	0.899840	+	0.436221i	$0.143683\pi$
$278$	11.6383	+	1.82020i	0.698020	+	0.109168i
$279$	0.127424	−	0.0945318i	0.00762867	−	0.00565947i
$280$	−53.5810	+	61.3970i	−3.20208	+	3.66917i
$281$	5.85189	−	11.8423i	0.349094	−	0.706454i	−0.649449	−	0.760405i	$-0.725001\pi$
$281$	5.85189	−	11.8423i	0.349094	−	0.706454i	0.998544	+	0.0539513i	$0.0171816\pi$
$282$	17.7425	+	21.3203i	1.05655	+	1.26961i
$283$	0.758883	−	0.653682i	0.0451109	−	0.0388573i	−0.629793	−	0.776763i	$-0.716860\pi$
$283$	0.758883	−	0.653682i	0.0451109	−	0.0388573i	0.674904	+	0.737906i	$0.264185\pi$
$284$	−27.4872	−	22.4654i	−1.63107	−	1.33308i
$285$	12.1869	+	3.70264i	0.721889	+	0.219325i
$286$	5.72730	−	51.9080i	0.338662	−	3.06938i
$287$	−0.204184	+	10.5277i	−0.0120526	+	0.621430i
$288$	0.802434	+	2.51714i	0.0472839	+	0.148324i
$289$	−3.43112	−	3.93163i	−0.201831	−	0.231272i
$290$	−80.2566	+	21.2269i	−4.71283	+	1.24649i
$291$	−14.2347	−	15.4100i	−0.834455	−	0.903350i
$292$	−45.2837	+	13.2387i	−2.65003	+	0.774737i
$293$	0.559827	−	6.64620i	0.0327055	−	0.388275i	−0.961024	−	0.276465i	$-0.910837\pi$
$293$	0.559827	−	6.64620i	0.0327055	−	0.388275i	0.993730	−	0.111810i	$-0.0356649\pi$
$294$	−29.5149	+	5.86993i	−1.72134	+	0.342341i
$295$	−4.49252	−	0.584067i	−0.261564	−	0.0340057i
$296$	4.98371	+	1.18116i	0.289672	+	0.0686536i
$297$	20.1145	+	18.4649i	1.16716	+	1.07144i
$298$	−1.99965	+	0.473927i	−0.115837	+	0.0274538i
$299$	−18.0879	+	1.87748i	−1.04605	+	0.108577i
$300$	−85.2816	+	31.2713i	−4.92374	+	1.80545i
$301$	0.777650	+	24.0519i	0.0448230	+	1.38633i
$302$	−34.8904	−	42.1309i	−2.00772	−	2.42436i
$303$	−9.58434	−	8.88322i	−0.550606	−	0.510328i
$304$	4.12124	+	6.73013i	0.236369	+	0.385999i
$305$	6.17502	−	6.05641i	0.353580	−	0.346789i
$306$	−1.68368	+	25.3503i	−0.0962498	+	1.44918i
$307$	−15.2054	+	22.1700i	−0.867816	+	1.26531i	0.0950891	+	0.995469i	$0.469686\pi$
$307$	−15.2054	+	22.1700i	−0.867816	+	1.26531i	−0.962906	+	0.269839i	$0.913030\pi$
$308$	−64.2458	+	48.4778i	−3.66074	+	2.76228i
$309$	31.9532	+	8.36945i	1.81775	+	0.476122i
$310$	−0.0249234	+	0.550427i	−0.00141556	+	0.0312622i
$311$	−0.787772	−	11.0602i	−0.0446704	−	0.627164i	−0.969235	−	0.246138i	$-0.920838\pi$
$311$	−0.787772	−	11.0602i	−0.0446704	−	0.627164i	0.924564	−	0.381026i	$-0.124429\pi$
$312$	35.0844	+	7.74942i	1.98626	+	0.438724i
$313$	−2.56842	−	6.91722i	−0.145176	−	0.390984i	0.844264	−	0.535927i	$-0.180038\pi$
$313$	−2.56842	−	6.91722i	−0.145176	−	0.390984i	−0.989440	+	0.144943i	$0.953700\pi$
$314$	1.79900	−	13.1710i	0.101523	−	0.743282i
$315$	−45.2720	−	14.2772i	−2.55079	−	0.804432i
$316$	9.06108	−	41.8306i	0.509726	−	2.35316i
$317$	0.453617	+	1.38390i	0.0254777	+	0.0777278i	0.962198	−	0.272351i	$-0.0878010\pi$
$317$	0.453617	+	1.38390i	0.0254777	+	0.0777278i	−0.936720	+	0.350078i	$0.886155\pi$
$318$	0.120081	+	0.584026i	0.00673381	+	0.0327505i
$319$	−41.8158	+	2.16437i	−2.34123	+	0.121181i
$320$	27.0746	+	10.6548i	1.51351	+	0.595624i
$321$	7.71986	+	4.63379i	0.430880	+	0.258633i
$322$	31.6249	+	27.2408i	1.76239	+	1.51807i
$323$	1.03800	+	5.88677i	0.0577557	+	0.327549i
$324$	−27.6405	+	24.2736i	−1.53558	+	1.34853i
$325$	−8.97456	+	50.8972i	−0.497819	+	2.82327i
$326$	32.1927	−	26.3112i	1.78299	−	1.45724i
$327$	0.859996	+	0.663259i	0.0475579	+	0.0366783i
$328$	−13.7219	+	4.59623i	−0.757667	+	0.253784i
$329$	−19.4151	−	14.6500i	−1.07039	−	0.807680i
$330$	−93.8331	+	13.6642i	−5.16534	+	0.752187i
$331$	−9.69274	+	5.18592i	−0.532761	+	0.285044i	−0.716090	−	0.698008i	$-0.754070\pi$
$331$	−9.69274	+	5.18592i	−0.532761	+	0.285044i	0.183329	+	0.983052i	$0.441313\pi$
$332$	7.65887	+	56.0728i	0.420335	+	3.07740i
$333$	0.532151	+	2.93574i	0.0291617	+	0.160877i
$334$	2.40846	−	4.57234i	0.131785	−	0.250187i
$335$	−8.69890	+	1.59190i	−0.475272	+	0.0869746i
$336$	−15.0945	−	25.2432i	−0.823474	−	1.37713i
$337$	−11.1993	−	11.5673i	−0.610067	−	0.630110i	0.340643	−	0.940193i	$-0.389355\pi$
$337$	−11.1993	−	11.5673i	−0.610067	−	0.630110i	−0.950710	+	0.310082i	$0.899643\pi$
$338$	5.38520	−	5.85788i	0.292916	−	0.318627i
$339$	−0.0488186	−	1.40573i	−0.00265146	−	0.0763488i
$340$	−43.3528	−	40.3748i	−2.35113	−	2.18963i
$341$	−0.0693219	+	0.269124i	−0.00375399	+	0.0145739i
$342$	−7.37702	+	10.5704i	−0.398904	+	0.571583i
$343$	0.142969	−	0.0649872i	0.00771958	−	0.00350898i
$344$	−30.7752	+	12.1112i	−1.65929	+	0.652990i
$345$	11.5676	+	30.9267i	0.622780	+	1.66504i
$346$	−1.56038	−	0.285549i	−0.0838865	−	0.0153512i
$347$	2.77658	−	3.53498i	0.149055	−	0.189768i	−0.706144	−	0.708068i	$-0.749567\pi$
$347$	2.77658	−	3.53498i	0.149055	−	0.189768i	0.855199	+	0.518301i	$0.173435\pi$
$348$	3.14523	−	56.3236i	0.168602	−	3.01926i
$349$	−4.33495	−	15.1919i	−0.232045	−	0.813202i	−0.987448	−	0.157943i	$-0.949514\pi$
$349$	−4.33495	−	15.1919i	−0.232045	−	0.813202i	0.755404	−	0.655260i	$-0.227441\pi$
$350$	99.1096	−	65.1854i	5.29763	−	3.48431i
$351$	4.04823	+	20.5351i	0.216078	+	1.09608i
$352$	−3.86632	−	2.54292i	−0.206076	−	0.135538i
$353$	7.11299	−	22.6873i	0.378586	−	1.20752i	−0.549607	−	0.835424i	$-0.685222\pi$
$353$	7.11299	−	22.6873i	0.378586	−	1.20752i	0.928193	−	0.372099i	$-0.121362\pi$
$354$	1.96791	−	4.14097i	0.104593	−	0.220090i
$355$	21.1330	+	29.9744i	1.12162	+	1.59087i
$356$	15.1585	+	6.65528i	0.803399	+	0.352729i
$357$	−3.63721	−	21.9792i	−0.192502	−	1.16326i
$358$	5.82324	+	12.5941i	0.307768	+	0.665618i
$359$	−7.01030	−	3.86812i	−0.369990	−	0.204152i	0.287211	−	0.957867i	$-0.407272\pi$
$359$	−7.01030	−	3.86812i	−0.369990	−	0.204152i	−0.657201	+	0.753716i	$0.728260\pi$
$360$	−2.42032	−	65.1943i	−0.127562	−	3.43604i
$361$	5.75103	−	14.8956i	0.302686	−	0.783977i
$362$	−57.6430	−	16.8519i	−3.02965	−	0.885718i
$363$	−28.7185	−	1.78999i	−1.50733	−	0.0939502i
$364$	−61.6893	+	0.797586i	−3.23340	+	0.0418049i
$365$	48.7370	−	0.630125i	2.55101	−	0.0329822i
$366$	3.89661	+	7.83818i	0.203679	+	0.409708i
$367$	−23.6441	−	6.91235i	−1.23421	−	0.360822i	−0.402184	−	0.915559i	$-0.631749\pi$
$367$	−23.6441	−	6.91235i	−1.23421	−	0.360822i	−0.832026	+	0.554737i	$0.812819\pi$
$368$	−7.36868	+	19.0854i	−0.384119	+	0.994893i
$369$	−5.65449	−	6.25222i	−0.294361	−	0.325477i
$370$	−9.07190	−	5.00566i	−0.471625	−	0.260232i
$371$	−0.219426	−	0.474559i	−0.0113920	−	0.0246379i
$372$	−0.350462	−	0.131755i	−0.0181706	−	0.00683118i
$373$	26.4623	+	11.6182i	1.37017	+	0.601567i	0.951802	−	0.306713i	$-0.0992291\pi$
$373$	26.4623	+	11.6182i	1.37017	+	0.601567i	0.418364	+	0.908279i	$0.362604\pi$
$374$	−25.6426	−	36.3707i	−1.32595	−	1.88068i
$375$	57.0891	−	4.57481i	2.94807	−	0.236242i
$376$	10.0001	−	31.8958i	0.515713	−	1.64490i
$377$	−26.8164	−	17.6374i	−1.38111	−	0.908372i
$378$	27.9072	−	39.1035i	1.43539	−	2.01127i
$379$	−15.2615	+	10.0376i	−0.783930	+	0.515599i	−0.877248	−	0.480038i	$-0.840623\pi$
$379$	−15.2615	+	10.0376i	−0.783930	+	0.515599i	0.0933182	+	0.995636i	$0.470253\pi$
$380$	−8.24744	−	28.9032i	−0.423085	−	1.48270i
$381$	17.2830	+	11.3080i	0.885433	+	0.579327i
$382$	6.00433	−	7.64437i	0.307208	−	0.391120i
$383$	9.59148	+	1.75524i	0.490102	+	0.0896885i	0.419386	−	0.907808i	$-0.362245\pi$
$383$	9.59148	+	1.75524i	0.490102	+	0.0896885i	0.0707156	+	0.997497i	$0.477472\pi$
$384$	−20.6668	+	25.0775i	−1.05465	+	1.27973i
$385$	77.3722	−	30.4489i	3.94325	−	1.55182i
$386$	−20.9793	+	9.53626i	−1.06782	+	0.485383i
$387$	−13.6441	−	13.6017i	−0.693567	−	0.691413i
$388$	−12.3487	+	47.9405i	−0.626909	+	2.43381i
$389$	−23.0447	−	21.4617i	−1.16841	−	1.08815i	−0.994643	−	0.103366i	$-0.967039\pi$
$389$	−23.0447	−	21.4617i	−1.16841	−	1.08815i	−0.173770	−	0.984786i	$-0.555595\pi$
$390$	−64.1714	−	34.1364i	−3.24945	−	1.72856i
$391$	−10.4876	+	11.4081i	−0.530379	+	0.576933i
$392$	25.2259	+	26.0547i	1.27410	+	1.31596i
$393$	−16.2215	+	29.1177i	−0.818264	+	1.46880i
$394$	−9.63645	+	1.76347i	−0.485477	+	0.0888423i
$395$	−20.6074	+	39.1221i	−1.03687	+	1.96845i
$396$	10.8850	−	63.5080i	0.546991	−	3.19140i
$397$	0.208361	+	1.52547i	0.0104574	+	0.0765614i	0.995289	−	0.0969496i	$-0.0309086\pi$
$397$	0.208361	+	1.52547i	0.0104574	+	0.0765614i	−0.984832	+	0.173511i	$0.944489\pi$
$398$	−7.98575	+	4.27262i	−0.400289	+	0.214167i
$399$	4.18195	−	10.5009i	0.209360	−	0.525704i
$400$	46.4127	+	35.0215i	2.32064	+	1.75108i
$401$	−11.5324	+	3.86285i	−0.575903	+	0.192901i	−0.590563	−	0.806991i	$-0.701094\pi$
$401$	−11.5324	+	3.86285i	−0.575903	+	0.192901i	0.0146608	+	0.999893i	$0.495333\pi$
$402$	1.18994	−	8.87022i	0.0593491	−	0.442406i
$403$	−0.164947	+	0.134812i	−0.00821660	+	0.00671546i
$404$	−5.35496	+	30.3695i	−0.266419	+	1.51094i
$405$	34.2346	−	16.5008i	1.70113	−	0.819932i
$406$	12.7927	+	72.5511i	0.634892	+	3.60065i
$407$	−3.95960	−	3.41070i	−0.196270	−	0.169062i
$408$	26.7719	−	14.8558i	1.32541	−	0.735472i
$409$	15.0921	+	5.93930i	0.746256	+	0.293680i	0.708599	−	0.705611i	$-0.249327\pi$
$409$	15.0921	+	5.93930i	0.746256	+	0.293680i	0.0376569	+	0.999291i	$0.488011\pi$
$410$	29.2360	−	1.51324i	1.44386	−	0.0747338i
$411$	21.8502	−	19.4122i	1.07779	−	0.957533i
$412$	−24.2787	−	74.0698i	−1.19612	−	3.64916i
$413$	−0.851113	+	3.92918i	−0.0418806	+	0.193342i
$414$	−33.3845	+	1.45554i	−1.64076	+	0.0715361i
$415$	7.91241	−	57.9291i	0.388405	−	2.84363i
$416$	−1.23477	−	3.32545i	−0.0605394	−	0.163043i
$417$	5.58213	−	6.10134i	0.273358	−	0.298784i
$418$	−1.60409	−	22.5211i	−0.0784588	−	1.10155i
$419$	−0.279243	+	6.16700i	−0.0136419	+	0.301278i	0.980733	+	0.195355i	$0.0625860\pi$
$419$	−0.279243	+	6.16700i	−0.0136419	+	0.301278i	−0.994374	+	0.105922i	$0.966221\pi$
$420$	29.6012	+	108.039i	1.44439	+	5.27174i
$421$	20.0339	−	15.1169i	0.976393	−	0.736755i	0.0116454	−	0.999932i	$-0.496293\pi$
$421$	20.0339	−	15.1169i	0.976393	−	0.736755i	0.964747	+	0.263177i	$0.0847704\pi$
$422$	−10.0504	+	14.6538i	−0.489244	+	0.713336i
$423$	19.3581	−	2.10302i	0.941222	−	0.102253i
$424$	0.512990	−	0.503137i	0.0249130	−	0.0244345i
$425$	22.9991	+	37.5583i	1.11562	+	1.82184i
$426$	−35.4611	+	10.9595i	−1.71810	+	0.530991i
$427$	−4.89566	−	5.91161i	−0.236918	−	0.286083i
$428$	−0.686613	−	21.2362i	−0.0331887	−	1.02649i
$429$	−28.1406	−	23.4982i	−1.35864	−	1.13450i
$430$	66.5478	−	6.90748i	3.20922	−	0.333108i
$431$	33.2748	−	7.88628i	1.60279	−	0.379869i	0.670596	−	0.741823i	$-0.266038\pi$
$431$	33.2748	−	7.88628i	1.60279	−	0.379869i	0.932196	+	0.361954i	$0.117890\pi$
$432$	22.6477	+	6.44490i	1.08964	+	0.310081i
$433$	−18.4189	−	4.36535i	−0.885154	−	0.209785i	−0.237197	−	0.971462i	$-0.576229\pi$
$433$	−18.4189	−	4.36535i	−0.885154	−	0.209785i	−0.647958	+	0.761676i	$0.724377\pi$
$434$	0.484880	+	0.0630386i	0.0232750	+	0.00302595i
$435$	−18.7348	+	55.1854i	−0.898265	+	2.64594i
$436$	0.215117	−	2.55384i	0.0103022	−	0.122307i
$437$	−7.54631	+	2.20617i	−0.360989	+	0.105535i
$438$	−14.6442	+	47.1031i	−0.699726	+	2.25067i
$439$	4.02263	−	1.06394i	0.191990	−	0.0507790i	−0.158437	−	0.987369i	$-0.550646\pi$
$439$	4.02263	−	1.06394i	0.191990	−	0.0507790i	0.350427	+	0.936590i	$0.386036\pi$
$440$	75.1368	+	86.0972i	3.58201	+	4.10452i
$441$	−8.02254	+	19.5432i	−0.382026	+	0.930627i
$442$	0.661484	−	34.1059i	0.0314636	−	1.62225i
$443$	−0.155553	+	1.40982i	−0.00739054	+	0.0669824i	−0.997099	−	0.0761166i	$-0.975748\pi$
$443$	−0.155553	+	1.40982i	−0.00739054	+	0.0669824i	0.989708	+	0.143099i	$0.0457067\pi$
$444$	5.14085	−	4.81074i	0.243974	−	0.228307i
$445$	−13.2428	−	10.8234i	−0.627771	−	0.513080i
$446$	25.5053	−	21.9696i	1.20771	−	1.04029i
$447$	−0.498939	+	1.35365i	−0.0235990	+	0.0640256i
$448$	11.4386	−	23.1481i	0.540425	−	1.09364i
$449$	7.87699	−	9.02602i	0.371738	−	0.425964i	−0.536837	−	0.843686i	$-0.680381\pi$
$449$	7.87699	−	9.02602i	0.371738	−	0.425964i	0.908575	+	0.417721i	$0.137171\pi$
$450$	−22.0564	+	92.3727i	−1.03975	+	4.35449i
$451$	14.5885	+	2.28159i	0.686944	+	0.107436i
$452$	−2.72513	+	1.89506i	−0.128179	+	0.0891360i
$453$	−38.1872	+	4.05613i	−1.79419	+	0.190574i
$454$	−1.71570	−	3.47201i	−0.0805216	−	0.162950i
$455$	61.6180	+	16.2972i	2.88870	+	0.764026i
$456$	15.5238	+	0.565187i	0.726968	+	0.0264673i
$457$	−21.9576	−	11.3854i	−1.02713	−	0.532585i	−0.138097	−	0.990419i	$-0.544099\pi$
$457$	−21.9576	−	11.3854i	−1.02713	−	0.532585i	−0.889038	+	0.457834i	$0.848625\pi$
$458$	25.8677	+	34.7464i	1.20872	+	1.62359i
$459$	14.1752	+	10.8246i	0.661641	+	0.505248i
$460$	46.5302	−	62.5009i	2.16948	−	2.91412i
$461$	28.8088	−	14.0049i	1.34176	−	0.652274i	0.379699	−	0.925110i	$-0.376028\pi$
$461$	28.8088	−	14.0049i	1.34176	−	0.652274i	0.962060	+	0.272836i	$0.0879618\pi$
$462$	5.09379	+	83.9934i	0.236985	+	3.90772i
$463$	15.8515	−	3.32653i	0.736684	−	0.154597i	0.178061	−	0.984019i	$-0.443017\pi$
$463$	15.8515	−	3.32653i	0.736684	−	0.154597i	0.558622	+	0.829422i	$0.311330\pi$
$464$	−31.3875	+	17.8520i	−1.45713	+	0.828760i
$465$	0.312299	+	0.228227i	0.0144825	+	0.0105838i
$466$	4.32242	+	21.2806i	0.200232	+	0.985803i
$467$	4.30750	−	0.334805i	0.199327	−	0.0154930i	0.0225594	−	0.999746i	$-0.492818\pi$
$467$	4.30750	−	0.334805i	0.199327	−	0.0154930i	0.176768	+	0.984253i	$0.443436\pi$
$468$	35.5426	−	34.2967i	1.64296	−	1.58537i
$469$	0.759750	+	7.81091i	0.0350820	+	0.360674i
$470$	−36.7927	+	56.7361i	−1.69712	+	2.61704i
$471$	−7.00610	−	6.16463i	−0.322824	−	0.284051i
$472$	−5.47911	+	0.712332i	−0.252196	+	0.0327877i
$473$	33.5654	+	3.48399i	1.54334	+	0.160194i
$474$	−31.2039	−	32.0751i	−1.43324	−	1.47326i
$475$	0.144438	+	22.3440i	0.00662726	+	1.02521i
$476$	−38.9321	+	35.3290i	−1.78445	+	1.61930i
$477$	0.388236	+	0.156447i	0.0177761	+	0.00716324i
$478$	−6.98204	−	13.2551i	−0.319351	−	0.606273i
$479$	−22.9420	−	29.2084i	−1.04825	−	1.33457i	−0.940276	−	0.340412i	$-0.889434\pi$
$479$	−22.9420	−	29.2084i	−1.04825	−	1.33457i	−0.107969	−	0.994154i	$-0.534435\pi$
$480$	−5.27918	+	3.68993i	−0.240961	+	0.168421i
$481$	−0.898627	−	3.90389i	−0.0409739	−	0.178002i
$482$	33.7770	−	55.1591i	1.53850	−	2.51243i
$483$	28.2097	−	7.92551i	1.28359	−	0.360623i
$484$	33.1879	+	59.2388i	1.50854	+	2.69267i
$485$	25.5721	−	44.2922i	1.16117	−	2.01121i
$486$	5.16829	+	38.1118i	0.234438	+	1.72879i
$487$	−12.1081	−	20.9718i	−0.548669	−	0.950323i	−0.998366	−	0.0571416i	$-0.981801\pi$
$487$	−12.1081	−	20.9718i	−0.548669	−	0.950323i	0.449697	−	0.893181i	$-0.351532\pi$
$488$	5.39206	−	9.06657i	0.244087	−	0.410424i
$489$	−2.89521	−	29.0438i	−0.130926	−	1.31341i
$490$	−35.0275	−	64.4629i	−1.58238	−	2.91214i
$491$	19.5758	−	18.2311i	0.883445	−	0.822758i	−0.101641	−	0.994821i	$-0.532409\pi$
$491$	19.5758	−	18.2311i	0.883445	−	0.822758i	0.985086	+	0.172063i	$0.0550432\pi$
$492$	−5.16482	+	19.2109i	−0.232848	+	0.866095i
$493$	−27.0747	+	3.87652i	−1.21939	+	0.174590i
$494$	9.22829	−	14.6417i	0.415201	−	0.658761i
$495$	−28.4284	+	60.1915i	−1.27776	+	2.70541i
$496$	0.0507372	+	0.234229i	0.00227817	+	0.0105172i
$497$	28.0801	−	16.4550i	1.25956	−	0.738107i
$498$	53.2768	+	25.7422i	2.38739	+	1.15353i
$499$	−3.43861	+	4.74573i	−0.153933	+	0.212448i	−0.879746	−	0.475445i	$-0.842287\pi$
$499$	−3.43861	+	4.74573i	−0.153933	+	0.212448i	0.725812	+	0.687893i	$0.241464\pi$
$500$	−82.1019	−	107.356i	−3.67171	−	4.80111i
$501$	−1.73976	−	3.18358i	−0.0777266	−	0.142232i
$502$	−20.5896	−	40.3448i	−0.918958	−	1.80068i
$503$	−14.2354	+	10.1749i	−0.634727	+	0.453676i	−0.852786	−	0.522260i	$-0.825089\pi$
$503$	−14.2354	+	10.1749i	−0.634727	+	0.453676i	0.218059	+	0.975936i	$0.430027\pi$
$504$	−57.8309	−	2.71581i	−2.57599	−	0.120972i
$505$	13.7435	−	28.7420i	0.611577	−	1.27900i
$506$	43.8501	−	38.7701i	1.94938	−	1.72354i
$507$	−1.33631	−	5.42381i	−0.0593478	−	0.240880i
$508$	0.315054	−	48.7378i	0.0139783	−	2.16239i
$509$	16.1197	+	17.9961i	0.714492	+	0.797662i	0.986348	−	0.164676i	$-0.0526579\pi$
$509$	16.1197	+	17.9961i	0.714492	+	0.797662i	−0.271856	+	0.962338i	$0.587637\pi$
$510$	−60.2348	+	14.4283i	−2.66724	+	0.638894i
$511$	3.07301	−	43.1445i	0.135942	−	1.90860i
$512$	42.3957	+	4.95534i	1.87364	+	0.218997i
$513$	3.31979	+	8.41809i	0.146572	+	0.371668i
$514$	−32.3273	+	3.77852i	−1.42590	+	0.166663i
$515$	3.64258	+	80.4454i	0.160511	+	3.54485i
$516$	−9.51844	+	44.4560i	−0.419026	+	1.95707i
$517$	−24.0392	+	24.1951i	−1.05724	+	1.06410i
$518$	−5.10218	+	7.64932i	−0.224177	+	0.336092i
$519$	−0.772692	+	0.801910i	−0.0339174	+	0.0351999i
$520$	7.35236	+	87.2863i	0.322422	+	3.82776i
$521$	8.17696	+	21.1788i	0.358239	+	0.927862i	0.988465	+	0.151450i	$0.0483944\pi$
$521$	8.17696	+	21.1788i	0.358239	+	0.927862i	−0.630226	+	0.776412i	$0.717038\pi$
$522$	−47.2496	−	35.2994i	−2.06806	−	1.54501i
$523$	−5.40857	−	15.8071i	−0.236500	−	0.691198i	−0.999021	−	0.0442343i	$-0.985915\pi$
$523$	−5.40857	−	15.8071i	−0.236500	−	0.691198i	0.762521	−	0.646963i	$-0.223961\pi$
$524$	78.4916	−	5.08092i	3.42892	−	0.221961i
$525$	0.339001	−	83.2759i	0.0147952	−	3.63446i
$526$	4.01269	+	21.1541i	0.174962	+	0.922363i
$527$	−0.0292088	+	0.179166i	−0.00127236	+	0.00780460i
$528$	−37.9376	+	16.1818i	−1.65102	+	0.704223i
$529$	2.11011	+	1.54982i	0.0917439	+	0.0673835i
$530$	−1.27272	+	0.702255i	−0.0552833	+	0.0305040i
$531$	−1.65842	−	2.75844i	−0.0719694	−	0.119706i
$532$	−26.1731	+	5.14023i	−1.13475	+	0.222857i
$533$	7.97760	+	8.02933i	0.345548	+	0.347789i
$534$	14.5607	−	9.35848i	0.630103	−	0.404981i
$535$	−5.20014	+	21.3259i	−0.224822	+	0.921997i
$536$	−9.76013	+	4.58969i	−0.421573	+	0.198244i
$537$	9.62721	+	1.48207i	0.415445	+	0.0639561i
$538$	18.3716	−	24.0226i	0.792055	−	1.03569i
$539$	−10.6128	−	35.4492i	−0.457125	−	1.52690i
$540$	−76.5151	−	46.7792i	−3.29269	−	2.01306i
$541$	−8.16036	+	27.2575i	−0.350841	+	1.17189i	0.582479	+	0.812846i	$0.302083\pi$
$541$	−8.16036	+	27.2575i	−0.350841	+	1.17189i	−0.933320	+	0.359046i	$0.883102\pi$
$542$	18.7325	+	25.8532i	0.804628	+	1.11049i
$543$	−32.2316	+	27.1772i	−1.38319	+	1.16629i
$544$	−2.66528	−	1.42601i	−0.114273	−	0.0611396i
$545$	−0.921640	+	2.48214i	−0.0394787	+	0.106323i
$546$	−34.9663	+	54.2034i	−1.49642	+	2.31969i
$547$	−20.5342	+	0.531066i	−0.877980	+	0.0227067i	−0.462218	−	0.886767i	$-0.652946\pi$
$547$	−20.5342	+	0.531066i	−0.877980	+	0.0227067i	−0.415762	+	0.909473i	$0.636485\pi$
$548$	−66.4459	−	18.4965i	−2.83843	−	0.790131i
$549$	6.09741	+	0.763055i	0.260231	+	0.0325664i
$550$	−71.7602	−	150.074i	−3.05987	−	6.39917i
$551$	−12.7771	−	5.41381i	−0.544323	−	0.230636i
$552$	23.2834	+	32.8572i	0.991007	+	1.39849i
$553$	33.0603	+	21.1369i	1.40587	+	0.898832i
$554$	−33.3140	+	22.5333i	−1.41537	+	0.957347i
$555$	−6.44931	+	3.36367i	−0.273758	+	0.142780i
$556$	−19.2398	−	3.26441i	−0.815950	−	0.138442i
$557$	14.7545	−	6.02789i	0.625169	−	0.255410i	−0.0434022	−	0.999058i	$-0.513820\pi$
$557$	14.7545	−	6.02789i	0.625169	−	0.255410i	0.668571	+	0.743648i	$0.266906\pi$
$558$	−0.317376	+	0.229150i	−0.0134356	+	0.00970069i
$559$	19.1561	+	17.3833i	0.810218	+	0.735233i
$560$	47.8419	−	53.4108i	2.02169	−	2.25702i
$561$	−31.2282	+	0.882435i	−1.31846	+	0.0372564i
$562$	−14.8146	+	29.0289i	−0.624916	+	1.22451i
$563$	−0.834298	−	5.57010i	−0.0351615	−	0.234752i	0.964397	−	0.264458i	$-0.0851930\pi$
$563$	−0.834298	−	5.57010i	−0.0351615	−	0.234752i	−0.999559	+	0.0297062i	$0.990543\pi$
$564$	−28.9337	−	35.6970i	−1.21833	−	1.50311i
$565$	3.23724	−	1.13108i	0.136192	−	0.0475850i
$566$	−1.89305	+	1.58846i	−0.0795707	+	0.0667678i
$567$	−12.0415	−	31.5023i	−0.505695	−	1.32297i
$568$	34.2646	+	28.7514i	1.43771	+	1.20638i
$569$	−35.3790	−	13.3974i	−1.48316	−	0.561647i	−0.525820	−	0.850596i	$-0.676241\pi$
$569$	−35.3790	−	13.3974i	−1.48316	−	0.561647i	−0.957344	+	0.288949i	$0.906694\pi$
$570$	−29.9475	−	9.52330i	−1.25436	−	0.398887i
$571$	6.87037	−	33.8249i	0.287516	−	1.41553i	−0.534068	−	0.845441i	$-0.679338\pi$
$571$	6.87037	−	33.8249i	0.287516	−	1.41553i	0.821584	−	0.570087i	$-0.193090\pi$
$572$	−10.5989	+	85.8626i	−0.443164	+	3.59010i
$573$	−2.14101	−	6.47939i	−0.0894418	−	0.270680i
$574$	0.839530	−	25.9658i	0.0350413	−	1.08379i
$575$	−45.7841	+	35.4853i	−1.90933	+	1.47984i
$576$	6.02329	+	19.7742i	0.250970	+	0.823924i
$577$	13.6033	+	21.5831i	0.566313	+	0.898516i	0.999997	−	0.00254887i	$-0.000811331\pi$
$577$	13.6033	+	21.5831i	0.566313	+	0.898516i	−0.433684	+	0.901065i	$0.642787\pi$
$578$	8.33932	+	9.80894i	0.346870	+	0.407998i
$579$	−2.56484	+	15.9734i	−0.106591	+	0.663830i
$580$	133.399	−	33.4434i	5.53910	−	1.38866i
$581$	−50.6367	−	11.3118i	−2.10076	−	0.469291i
$582$	34.6262	+	38.4712i	1.43530	+	1.59468i
$583$	−0.700995	+	0.214811i	−0.0290322	+	0.00889657i
$584$	57.2675	−	15.9415i	2.36975	−	0.659664i
$585$	−44.8762	+	24.2871i	−1.85540	+	1.00415i
$586$	−1.59311	+	16.3786i	−0.0658108	+	0.676594i
$587$	−28.4956	−	22.6814i	−1.17614	−	0.936163i	−0.177290	−	0.984159i	$-0.556733\pi$
$587$	−28.4956	−	22.6814i	−1.17614	−	0.936163i	−0.998848	+	0.0479961i	$0.984717\pi$
$588$	49.0169	−	9.09139i	2.02142	−	0.374923i
$589$	−0.0596567	+	0.0701699i	−0.00245811	+	0.00289130i
$590$	11.0646	+	1.58422i	0.455523	+	0.0652211i
$591$	−2.70883	+	6.32134i	−0.111427	+	0.260025i
$592$	−4.37150	−	1.09594i	−0.179667	−	0.0450429i
$593$	−16.0519	−	8.06158i	−0.659174	−	0.331050i	0.0875728	−	0.996158i	$-0.472089\pi$
$593$	−16.0519	−	8.06158i	−0.659174	−	0.331050i	−0.746747	+	0.665109i	$0.768385\pi$
$594$	−49.0344	−	46.1953i	−2.01191	−	1.89542i
$595$	48.5356	−	24.3755i	1.98977	−	0.999298i
$596$	3.32256	−	0.742230i	0.136098	−	0.0304029i
$597$	−0.600385	+	6.32968i	−0.0245721	+	0.259057i
$598$	44.6836	−	4.05488i	1.82725	−	0.165816i
$599$	1.20772	+	10.9459i	0.0493462	+	0.447237i	0.993160	+	0.116760i	$0.0372508\pi$
$599$	1.20772	+	10.9459i	0.0493462	+	0.447237i	−0.943814	+	0.330477i	$0.892790\pi$
$600$	107.954	−	38.0089i	4.40719	−	1.55171i
$601$	−13.8486	−	1.25671i	−0.564896	−	0.0512623i	−0.195784	−	0.980647i	$-0.562725\pi$
$601$	−13.8486	−	1.25671i	−0.564896	−	0.0512623i	−0.369112	+	0.929385i	$0.620338\pi$
$602$	−1.15132	−	59.3619i	−0.0469244	−	2.41941i
$603$	−4.72677	−	4.13902i	−0.192489	−	0.168554i
$604$	56.8935	+	70.5368i	2.31496	+	2.87010i
$605$	−16.6185	−	68.1529i	−0.675640	−	2.77081i
$606$	23.3616	+	22.2210i	0.949002	+	0.902667i
$607$	−18.6805	+	33.3439i	−0.758220	+	1.35339i	0.171524	+	0.985180i	$0.445131\pi$
$607$	−18.6805	+	33.3439i	−0.758220	+	1.35339i	−0.929744	+	0.368206i	$0.879972\pi$
$608$	−0.783927	−	1.31815i	−0.0317924	−	0.0534580i
$609$	47.4043	+	20.6775i	1.92092	+	0.837895i
$610$	−15.4272	+	14.7445i	−0.624630	+	0.596986i
$611$	−25.8306	+	4.03984i	−1.04499	+	0.163434i
$612$	3.33194	−	41.9566i	0.134686	−	1.69599i
$613$	−34.5423	+	20.8464i	−1.39515	+	0.841978i	−0.997153	−	0.0754089i	$-0.975974\pi$
$613$	−34.5423	+	20.8464i	−1.39515	+	0.841978i	−0.397998	+	0.917386i	$0.630295\pi$
$614$	38.2195	−	54.2093i	1.54241	−	2.18771i
$615$	10.4627	−	17.6890i	0.421899	−	0.713289i
$616$	81.7314	−	60.0296i	3.29305	−	2.41866i
$617$	−18.3276	+	39.6376i	−0.737841	+	1.59575i	0.0638119	+	0.997962i	$0.479674\pi$
$617$	−18.3276	+	39.6376i	−0.737841	+	1.59575i	−0.801653	+	0.597789i	$0.796046\pi$
$618$	−78.5629	−	21.6670i	−3.16026	−	0.871575i
$619$	32.4241	+	35.2700i	1.30323	+	1.41762i	0.850499	+	0.525977i	$0.176300\pi$
$619$	32.4241	+	35.2700i	1.30323	+	1.41762i	0.452734	+	0.891646i	$0.350449\pi$
$620$	0.0530740	−	0.911245i	0.00213150	−	0.0365965i
$621$	−12.1067	+	20.0932i	−0.485826	+	0.806314i
$622$	1.59069	+	27.3110i	0.0637807	+	1.09507i
$623$	−10.5574	+	10.9043i	−0.422975	+	0.436872i
$624$	−30.7810	−	7.21746i	−1.23223	−	0.288930i
$625$	28.0916	+	70.0500i	1.12366	+	2.80200i
$626$	6.11577	+	17.1470i	0.244435	+	0.685332i
$627$	−13.7964	−	7.80324i	−0.550975	−	0.311631i
$628$	−3.26211	+	21.7791i	−0.130172	+	0.869082i
$629$	−2.77719	−	1.98502i	−0.110734	−	0.0791478i
$630$	111.233	+	36.6666i	4.43161	+	1.46083i
$631$	29.5595	+	28.9918i	1.17675	+	1.15414i	0.984974	+	0.172704i	$0.0552505\pi$
$631$	29.5595	+	28.9918i	1.17675	+	1.15414i	0.191772	+	0.981440i	$0.438577\pi$
$632$	−12.0972	+	52.5538i	−0.481202	+	2.09048i
$633$	4.67071	+	11.5668i	0.185644	+	0.459740i
$634$	−1.07495	−	3.42862i	−0.0426918	−	0.136168i
$635$	−13.8164	+	48.4197i	−0.548287	+	1.92148i
$636$	−0.186405	−	0.970007i	−0.00739146	−	0.0384633i
$637$	9.52892	−	26.7166i	0.377550	−	1.05855i
$638$	103.230	−	4.00581i	4.08693	−	0.158592i
$639$	−7.35340	+	24.9969i	−0.290896	+	0.988864i
$640$	−73.3392	−	29.9624i	−2.89899	−	1.18437i
$641$	−31.0349	−	19.2814i	−1.22580	−	0.761568i	−0.247530	−	0.968880i	$-0.579619\pi$
$641$	−31.0349	−	19.2814i	−1.22580	−	0.761568i	−0.978275	+	0.207313i	$0.933528\pi$
$642$	−18.8974	−	11.6780i	−0.745822	−	0.460894i
$643$	7.00308	−	2.96729i	0.276174	−	0.117018i	−0.247637	−	0.968853i	$-0.579654\pi$
$643$	7.00308	−	2.96729i	0.276174	−	0.117018i	0.523811	+	0.851835i	$0.324510\pi$
$644$	−51.8030	−	45.8016i	−2.04132	−	1.80484i
$645$	21.7899	−	41.6083i	0.857976	−	1.63833i
$646$	−2.37302	−	14.5560i	−0.0933650	−	0.572699i
$647$	28.2021	−	10.2647i	1.10874	−	0.403548i	0.278208	−	0.960521i	$-0.410260\pi$
$647$	28.2021	−	10.2647i	1.10874	−	0.403548i	0.830530	+	0.556973i	$0.188037\pi$
$648$	35.2190	−	30.1315i	1.38353	−	1.18368i
$649$	5.29769	+	1.92820i	0.207952	+	0.0756885i
$650$	23.7641	−	125.280i	0.932104	−	4.91387i
$651$	0.225080	−	0.259163i	0.00882158	−	0.0101574i
$652$	−53.8905	+	42.8949i	−2.11051	+	1.67989i
$653$	17.4792	+	26.9537i	0.684013	+	1.05478i	0.994554	+	0.104220i	$0.0332345\pi$
$653$	17.4792	+	26.9537i	0.684013	+	1.05478i	−0.310542	+	0.950560i	$0.600510\pi$
$654$	−2.10049	−	1.66372i	−0.0821358	−	0.0650566i
$655$	−79.5275	−	16.6893i	−3.10740	−	0.652105i
$656$	12.1256	−	3.88791i	0.473424	−	0.151797i
$657$	21.8689	+	26.8492i	0.853187	+	1.04749i
$658$	47.4306	+	36.7615i	1.84904	+	1.43311i
$659$	1.46508	−	1.76912i	0.0570715	−	0.0689150i	−0.740877	−	0.671641i	$-0.765590\pi$
$659$	1.46508	−	1.76912i	0.0570715	−	0.0689150i	0.797948	+	0.602726i	$0.205919\pi$
$660$	155.727	−	20.6250i	6.06165	−	0.802826i
$661$	−5.22143	−	2.53831i	−0.203090	−	0.0987289i	0.332868	−	0.942973i	$-0.391984\pi$
$661$	−5.22143	−	2.53831i	−0.203090	−	0.0987289i	−0.535958	+	0.844245i	$0.680050\pi$
$662$	24.0778	−	12.4847i	0.935812	−	0.485232i
$663$	−19.6935	−	13.6251i	−0.764834	−	0.529155i
$664$	−8.73586	−	70.7696i	−0.339017	−	2.74639i
$665$	27.4732	+	2.13539i	1.06537	+	0.0828068i
$666$	−1.21920	−	7.25957i	−0.0472431	−	0.281302i
$667$	−8.97339	−	34.8368i	−0.347451	−	1.34889i
$668$	−4.08752	+	7.52247i	−0.158151	+	0.291053i
$669$	−2.95128	−	23.4468i	−0.114103	−	0.906505i
$670$	21.5113	−	3.64982i	0.831056	−	0.141005i
$671$	−9.14269	+	5.68017i	−0.352950	+	0.219280i
$672$	2.86974	+	4.94317i	0.110702	+	0.190687i
$673$	−11.5931	+	25.9481i	−0.446880	+	1.00023i	0.540425	+	0.841392i	$0.318263\pi$
$673$	−11.5931	+	25.9481i	−0.446880	+	1.00023i	−0.987305	+	0.158835i	$0.949226\pi$
$674$	27.2603	+	28.8942i	1.05003	+	1.11296i
$675$	45.4723	+	48.7563i	1.75023	+	1.87663i
$676$	−9.04601	+	9.58821i	−0.347923	+	0.368777i
$677$	2.87351	+	6.90568i	0.110438	+	0.265407i	0.968892	−	0.247483i	$-0.0796036\pi$
$677$	2.87351	+	6.90568i	0.110438	+	0.265407i	−0.858454	+	0.512890i	$0.828575\pi$
$678$	0.0755995	+	3.46956i	0.00290338	+	0.133248i
$679$	−37.2623	−	25.9123i	−1.43000	−	0.994422i
$680$	53.9615	+	51.5734i	2.06933	+	1.97775i
$681$	−2.69690	−	0.344059i	−0.103345	−	0.0131844i
$682$	0.179604	−	0.661730i	0.00687741	−	0.0253390i
$683$	4.67496	−	13.6631i	0.178882	−	0.522803i	−0.819880	−	0.572535i	$-0.805960\pi$
$683$	4.67496	−	13.6631i	0.178882	−	0.522803i	0.998763	+	0.0497317i	$0.0158366\pi$
$684$	12.4464	−	17.3518i	0.475899	−	0.663464i
$685$	61.0067	+	36.8177i	2.33095	+	1.40673i
$686$	−0.354783	+	0.155766i	−0.0135457	+	0.00594718i
$687$	30.3655	−	1.64458i	1.15851	−	0.0627448i
$688$	27.2154	−	10.3060i	1.03758	−	0.392911i
$689$	−0.530556	−	0.185375i	−0.0202126	−	0.00706221i
$690$	−27.5514	−	76.6664i	−1.04886	−	2.91864i
$691$	16.3420	+	24.5003i	0.621677	+	0.932035i	0.999980	+	0.00635325i	$0.00202232\pi$
$691$	16.3420	+	24.5003i	0.621677	+	0.932035i	−0.378303	+	0.925682i	$0.623492\pi$
$692$	2.57864	+	0.506429i	0.0980253	+	0.0192515i
$693$	51.1091	+	29.6223i	1.94148	+	1.12526i
$694$	−6.96270	+	8.63240i	−0.264301	+	0.327681i
$695$	18.2443	+	8.57935i	0.692045	+	0.325433i
$696$	−4.88006	+	70.9095i	−0.184978	+	2.68782i
$697$	9.62495	+	0.623043i	0.364571	+	0.0235994i
$698$	10.2099	+	37.6173i	0.386452	+	1.42384i
$699$	14.1258	+	5.73162i	0.534288	+	0.216790i
$700$	−165.571	+	105.857i	−6.25798	+	4.00100i
$701$	−17.7588	+	41.1696i	−0.670742	+	1.55495i	0.153147	+	0.988203i	$0.451059\pi$
$701$	−17.7588	+	41.1696i	−0.670742	+	1.55495i	−0.823889	+	0.566752i	$0.808200\pi$
$702$	−9.33216	−	50.7901i	−0.352220	−	1.91695i
$703$	−0.685993	−	1.59031i	−0.0258727	−	0.0599797i
$704$	−29.9912	−	20.2858i	−1.13034	−	0.764550i
$705$	18.9068	+	43.5440i	0.712071	+	1.63996i
$706$	−18.2717	+	55.7437i	−0.687665	+	2.09794i
$707$	−24.3926	−	14.2941i	−0.917377	−	0.537584i
$708$	−3.34852	+	6.81734i	−0.125845	+	0.256212i
$709$	10.3602	+	3.47019i	0.389084	+	0.130326i	0.505397	−	0.862887i	$-0.331346\pi$
$709$	10.3602	+	3.47019i	0.389084	+	0.130326i	−0.116313	+	0.993213i	$0.537107\pi$
$710$	−51.1799	−	74.6222i	−1.92075	−	2.80052i
$711$	−30.8741	+	5.80283i	−1.15787	+	0.217623i
$712$	−18.9894	−	8.63176i	−0.711659	−	0.323489i
$713$	−0.238445	−	0.0123418i	−0.00892984	−	0.000462205i
$714$	8.27210	+	54.3397i	0.309575	+	2.03361i
$715$	34.3370	−	82.5195i	1.28413	−	3.08605i
$716$	−9.37643	−	20.9867i	−0.350414	−	0.784311i
$717$	−10.4636	−	1.06079i	−0.390772	−	0.0396160i
$718$	17.1713	+	9.76643i	0.640829	+	0.364480i
$719$	−26.4257	−	8.47307i	−0.985513	−	0.315992i	−0.231488	−	0.972838i	$-0.574359\pi$
$719$	−26.4257	−	8.47307i	−0.985513	−	0.315992i	−0.754025	+	0.656846i	$0.771890\pi$
$720$	1.38790	+	57.3890i	0.0517239	+	2.13876i
$721$	71.4083	+	2.77097i	2.65938	+	0.103196i
$722$	−14.6632	+	36.5646i	−0.545707	+	1.36079i
$723$	−19.1549	−	41.1679i	−0.712377	−	1.53105i
$724$	95.1243	+	29.1497i	3.53527	+	1.08334i
$725$	−102.205	−	2.64327i	−3.79578	−	0.0981684i
$726$	70.7926	+	5.33201i	2.62736	+	0.197890i
$727$	10.8924	+	0.140829i	0.403978	+	0.00522307i	0.214651	−	0.976691i	$-0.431139\pi$
$727$	10.8924	+	0.140829i	0.403978	+	0.00522307i	0.189328	+	0.981914i	$0.439369\pi$
$728$	77.7339			2.88101
$729$	24.2996	+	11.7699i	0.899985	+	0.435921i
$730$	−120.256			−4.45089
$731$	22.0410	+	0.284970i	0.815217	+	0.0105400i
$732$	−6.28683	−	13.0673i	−0.232368	−	0.482983i
$733$	−21.9807	−	0.568475i	−0.811875	−	0.0209971i	−0.382311	−	0.924034i	$-0.624872\pi$
$733$	−21.9807	−	0.568475i	−0.811875	−	0.0209971i	−0.429564	+	0.903036i	$0.641333\pi$
$734$	58.1105	+	17.8072i	2.14490	+	0.657277i
$735$	−51.3035	−	4.53184i	−1.89236	−	0.167159i
$736$	1.47983	−	3.69014i	0.0545471	−	0.136020i
$737$	10.9967	+	0.426721i	0.405068	+	0.0157185i
$738$	13.7505	+	15.6049i	0.506161	+	0.574423i
$739$	27.6742	+	8.87338i	1.01801	+	0.326412i	0.767052	−	0.641585i	$-0.221723\pi$
$739$	27.6742	+	8.87338i	1.01801	+	0.326412i	0.250960	+	0.967997i	$0.419254\pi$
$740$	14.9203	+	8.48614i	0.548482	+	0.311957i
$741$	−4.98272	−	11.0813i	−0.183045	−	0.407080i
$742$	0.526196	+	1.17776i	0.0193173	+	0.0432368i
$743$	13.5578	−	32.5823i	0.497386	−	1.19533i	−0.455016	−	0.890483i	$-0.650367\pi$
$743$	13.5578	−	32.5823i	0.497386	−	1.19533i	0.952402	−	0.304845i	$-0.0986046\pi$
$744$	0.439393	+	0.171704i	0.0161089	+	0.00629497i
$745$	−3.51246	−	0.181804i	−0.128687	−	0.00666077i
$746$	−64.9131	−	29.5066i	−2.37664	−	1.08031i
$747$	35.7372	−	21.1725i	1.30756	−	0.774662i
$748$	41.6979	+	60.7970i	1.52463	+	2.22296i
$749$	18.4709	+	6.18691i	0.674911	+	0.226065i
$750$	−140.987	+	9.46530i	−5.14813	+	0.345624i
$751$	14.2088	+	8.32635i	0.518485	+	0.303833i	0.741467	−	0.670990i	$-0.234131\pi$
$751$	14.2088	+	8.32635i	0.518485	+	0.303833i	−0.222982	+	0.974823i	$0.571579\pi$
$752$	−9.16142	+	27.9498i	−0.334083	+	1.01923i
$753$	−31.5916	−	3.61590i	−1.15126	−	0.131771i
$754$	65.5946	+	44.3676i	2.38881	+	1.61577i
$755$	−37.0817	−	85.9651i	−1.34954	−	3.12859i
$756$	−47.0656	+	64.1770i	−1.71176	+	2.33410i
$757$	19.2034	−	44.5184i	0.697959	−	1.61805i	−0.0853012	−	0.996355i	$-0.527185\pi$
$757$	19.2034	−	44.5184i	0.697959	−	1.61805i	0.783260	−	0.621695i	$-0.213555\pi$
$758$	37.9709	−	24.2765i	1.37917	−	0.881762i
$759$	−5.65821	−	40.6987i	−0.205380	−	1.47727i
$760$	9.91996	+	36.5489i	0.359835	+	1.32577i
$761$	−14.5882	−	0.944324i	−0.528822	−	0.0342317i	−0.202123	−	0.979360i	$-0.564784\pi$
$761$	−14.5882	−	0.944324i	−0.528822	−	0.0342317i	−0.326699	+	0.945128i	$0.605936\pi$
$762$	−42.2772	−	28.4487i	−1.53154	−	1.03059i
$763$	2.12628	+	0.999881i	0.0769766	+	0.0361981i
$764$	−10.1099	+	12.5343i	−0.365762	+	0.453473i
$765$	−14.9402	+	40.8347i	−0.540166	+	1.47638i
$766$	−23.6066	−	4.63619i	−0.852942	−	0.167512i
$767$	2.39802	+	3.59517i	0.0865874	+	0.129814i
$768$	36.3687

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)

\(f(q)\)	\(=\)	\(q+(-2.46704 - 0.0318966i) q^{2} +(-0.976238 + 1.43072i) q^{3} +(4.08596 + 0.105673i) q^{4} +(-4.03733 - 1.23719i) q^{5} +(2.45406 - 3.49851i) q^{6} +(-1.39476 + 3.47801i) q^{7} +(-5.14609 - 0.199692i) q^{8} +(-1.09392 - 2.79345i) q^{9} +O(q^{10})\)	\(q+(-2.46704 - 0.0318966i) q^{2} +(-0.976238 + 1.43072i) q^{3} +(4.08596 + 0.105673i) q^{4} +(-4.03733 - 1.23719i) q^{5} +(2.45406 - 3.49851i) q^{6} +(-1.39476 + 3.47801i) q^{7} +(-5.14609 - 0.199692i) q^{8} +(-1.09392 - 2.79345i) q^{9} +(9.92081 + 3.18098i) q^{10} +(4.56767 + 2.59792i) q^{11} +(-4.14006 + 5.74270i) q^{12} +(1.64311 + 3.67767i) q^{13} +(3.55187 - 8.53592i) q^{14} +(5.71147 - 4.56849i) q^{15} +(4.52553 + 0.234240i) q^{16} +(3.12478 + 1.42039i) q^{17} +(2.60964 + 6.92645i) q^{18} +(0.984999 + 1.43616i) q^{19} +(-16.3656 - 5.48175i) q^{20} +(-3.61444 - 5.39087i) q^{21} +(-11.1858 - 6.55488i) q^{22} +(-1.40619 + 4.29005i) q^{23} +(5.30951 - 7.16766i) q^{24} +(10.6278 + 7.18857i) q^{25} +(-3.93631 - 9.12539i) q^{26} +(5.06456 + 1.16198i) q^{27} +(-6.06646 + 14.0636i) q^{28} +(-6.71348 + 4.29222i) q^{29} +(-14.2362 + 11.0885i) q^{30} +(0.0138532 + 0.0510402i) q^{31} +(-0.878810 - 0.0568871i) q^{32} +(-8.17603 + 3.99886i) q^{33} +(-7.66366 - 3.60383i) q^{34} +(9.93406 - 12.3163i) q^{35} +(-4.17451 - 11.5295i) q^{36} +(-0.975883 - 0.191657i) q^{37} +(-2.38423 - 3.57450i) q^{38} +(-6.86578 - 1.23946i) q^{39} +(20.5294 + 7.17291i) q^{40} +(2.62786 - 0.995123i) q^{41} +(8.74504 + 13.4148i) q^{42} +(5.88012 - 2.58165i) q^{43} +(18.3888 + 11.0977i) q^{44} +(0.960480 + 12.6314i) q^{45} +(3.60598 - 10.5389i) q^{46} +(-1.70016 + 6.26403i) q^{47} +(-4.75313 + 6.24609i) q^{48} +(-5.09075 - 4.86546i) q^{49} +(-25.9900 - 18.0735i) q^{50} +(-5.08270 + 3.08405i) q^{51} +(6.32504 + 15.2005i) q^{52} +(-0.0957473 + 0.101486i) q^{53} +(-12.4574 - 3.02820i) q^{54} +(-15.2271 - 16.1397i) q^{55} +(7.87207 - 17.6196i) q^{56} +(-3.01634 + 0.00721927i) q^{57} +(16.6994 - 10.3750i) q^{58} +(1.05775 - 0.179468i) q^{59} +(23.8196 - 18.0631i) q^{60} +(-0.977958 + 1.79979i) q^{61} +(-0.0325483 - 0.126360i) q^{62} +(11.2414 + 0.0915249i) q^{63} +(-6.86968 - 0.533954i) q^{64} +(-2.08378 - 16.8808i) q^{65} +(20.2982 - 9.60458i) q^{66} +(1.85920 - 0.964024i) q^{67} +(12.6176 + 6.13385i) q^{68} +(-4.76507 - 6.19998i) q^{69} +(-24.9006 + 30.0680i) q^{70} +(-6.86485 - 5.32066i) q^{71} +(5.07157 + 14.5938i) q^{72} +(-10.9916 + 3.52432i) q^{73} +(2.40143 + 0.503954i) q^{74} +(-20.6601 + 8.18768i) q^{75} +(3.87290 + 5.97219i) q^{76} +(-15.4064 + 12.2629i) q^{77} +(16.8987 + 3.27680i) q^{78} +(1.95154 - 10.2881i) q^{79} +(-17.9813 - 6.54465i) q^{80} +(-6.60669 + 6.11160i) q^{81} +(-6.51480 + 2.37119i) q^{82} +(2.22786 + 13.6657i) q^{83} +(-14.1988 - 22.4089i) q^{84} +(-10.8585 - 9.60051i) q^{85} +(-14.5889 + 6.18148i) q^{86} +(0.412984 - 13.7953i) q^{87} +(-22.9868 - 14.2813i) q^{88} +(3.74951 + 1.53185i) q^{89} +(-1.96665 - 31.1930i) q^{90} +(-15.0827 + 0.585278i) q^{91} +(-6.19900 + 17.3804i) q^{92} +(-0.0865482 - 0.0300075i) q^{93} +(4.39418 - 15.3994i) q^{94} +(-2.19996 - 7.01689i) q^{95} +(0.939317 - 1.20180i) q^{96} +(-2.71696 + 11.8032i) q^{97} +(12.4039 + 12.1657i) q^{98} +(2.26051 - 15.6014i) 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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