LMFDB - Embedded newform 162.2.g.a.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	162.31
Dual form			162.2.g.a.115.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.396080 - 0.918216i) q^{2} +(1.72259 - 0.180780i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.201959 - 3.46750i) q^{5} +(-0.848278 - 1.51011i) q^{6} +(-2.51951 + 0.597135i) q^{7} +(0.939693 + 0.342020i) q^{8} +(2.93464 - 0.622818i) q^{9} +O(q^{10})$	\(q+(-0.396080 - 0.918216i) q^{2} +(1.72259 - 0.180780i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.201959 - 3.46750i) q^{5} +(-0.848278 - 1.51011i) q^{6} +(-2.51951 + 0.597135i) q^{7} +(0.939693 + 0.342020i) q^{8} +(2.93464 - 0.622818i) q^{9} +(-3.26390 + 1.18796i) q^{10} +(0.00472430 - 0.00310722i) q^{11} +(-1.05062 + 1.37703i) q^{12} +(0.753337 - 0.0880524i) q^{13} +(1.54623 + 2.07694i) q^{14} +(-0.278960 - 6.00959i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(5.86304 + 4.91968i) q^{17} +(-1.73423 - 2.44795i) q^{18} +(-1.23604 + 1.03716i) q^{19} +(2.38357 + 2.52644i) q^{20} +(-4.23214 + 1.48410i) q^{21} +(-0.00472430 - 0.00310722i) q^{22} +(-5.90723 - 1.40004i) q^{23} +(1.68054 + 0.419283i) q^{24} +(-7.01655 - 0.820117i) q^{25} +(-0.379233 - 0.656850i) q^{26} +(4.94259 - 1.60338i) q^{27} +(1.29465 - 2.24240i) q^{28} +(3.40377 - 4.57206i) q^{29} +(-5.40761 + 2.63642i) q^{30} +(1.61612 + 5.39823i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(0.00757632 - 0.00620653i) q^{33} +(2.19509 - 7.33213i) q^{34} +(1.56173 + 8.85699i) q^{35} +(-1.56085 + 2.56198i) q^{36} +(-1.90884 + 10.8256i) q^{37} +(1.44191 + 0.724153i) q^{38} +(1.28177 - 0.287866i) q^{39} +(1.37573 - 3.18931i) q^{40} +(-1.60914 + 3.73041i) q^{41} +(3.03898 + 3.29820i) q^{42} +(6.27486 + 3.15135i) q^{43} +(-0.000981901 + 0.00556864i) q^{44} +(-1.56695 - 10.3016i) q^{45} +(1.05420 + 5.97864i) q^{46} +(-1.29272 + 4.31797i) q^{47} +(-0.280633 - 1.70916i) q^{48} +(-0.264065 + 0.132618i) q^{49} +(2.02607 + 6.76754i) q^{50} +(10.9890 + 7.41467i) q^{51} +(-0.452924 + 0.608383i) q^{52} +(6.25091 - 10.8269i) q^{53} +(-3.42991 - 3.90329i) q^{54} +(-0.00982017 - 0.0170090i) q^{55} +(-2.57180 - 0.300600i) q^{56} +(-1.94169 + 2.01005i) q^{57} +(-5.54631 - 1.31450i) q^{58} +(-9.40314 - 6.18454i) q^{59} +(4.56265 + 3.92112i) q^{60} +(-3.73496 - 3.95883i) q^{61} +(4.31663 - 3.62208i) q^{62} +(-7.02194 + 3.32157i) q^{63} +(0.766044 + 0.642788i) q^{64} +(-0.153179 - 2.62998i) q^{65} +(-0.00869976 - 0.00449841i) q^{66} +(-2.51055 - 3.37226i) q^{67} +(-7.60191 + 0.888536i) q^{68} +(-10.4288 - 1.34379i) q^{69} +(7.51406 - 4.94208i) q^{70} +(-8.54902 + 3.11159i) q^{71} +(2.97067 + 0.418447i) q^{72} +(2.27020 + 0.826284i) q^{73} +(10.6963 - 2.53506i) q^{74} +(-12.2349 - 0.144277i) q^{75} +(0.0938186 - 1.61080i) q^{76} +(-0.0100475 + 0.0106497i) q^{77} +(-0.772008 - 1.06293i) q^{78} +(-0.353932 - 0.820506i) q^{79} -3.47337 q^{80} +(8.22419 - 3.65549i) q^{81} +4.06267 q^{82} +(0.0349465 + 0.0810150i) q^{83} +(1.82478 - 4.09679i) q^{84} +(18.2431 - 19.3365i) q^{85} +(0.408278 - 7.00987i) q^{86} +(5.03677 - 8.49112i) q^{87} +(0.00550212 - 0.00130403i) q^{88} +(-11.4053 - 4.15118i) q^{89} +(-8.83849 + 5.51906i) q^{90} +(-1.84546 + 0.671693i) q^{91} +(5.07214 - 3.33600i) q^{92} +(3.75981 + 9.00678i) q^{93} +(4.47685 - 0.523269i) q^{94} +(3.34672 + 4.49542i) q^{95} +(-1.45823 + 0.934648i) q^{96} +(-0.789886 - 13.5618i) q^{97} +(0.226363 + 0.189941i) q^{98} +(0.0119289 - 0.0120610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	−0.396080	−	0.918216i	−0.280071	−	0.649277i
$2$	−0.396080	−	0.918216i	−0.280071	−	0.649277i
$3$	1.72259	−	0.180780i	0.994538	−	0.104373i
$3$	1.72259	−	0.180780i	0.994538	−	0.104373i
$4$	−0.686242	+	0.727374i	−0.343121	+	0.363687i
$5$	0.201959	−	3.46750i	0.0903187	−	1.55071i	−0.583683	−	0.811982i	$-0.698389\pi$
$5$	0.201959	−	3.46750i	0.0903187	−	1.55071i	0.674002	−	0.738730i	$-0.264574\pi$
$6$	−0.848278	−	1.51011i	−0.346308	−	0.616499i
$7$	−2.51951	+	0.597135i	−0.952286	+	0.225696i	−0.677262	−	0.735742i	$-0.736834\pi$
$7$	−2.51951	+	0.597135i	−0.952286	+	0.225696i	−0.275023	+	0.961438i	$0.588686\pi$
$8$	0.939693	+	0.342020i	0.332232	+	0.120922i
$9$	2.93464	−	0.622818i	0.978212	−	0.207606i
$10$	−3.26390	+	1.18796i	−1.03214	+	0.375667i
$11$	0.00472430	−	0.00310722i	0.00142443	−	0.000936863i	−0.548797	−	0.835956i	$-0.684914\pi$
$11$	0.00472430	−	0.00310722i	0.00142443	−	0.000936863i	0.550221	+	0.835019i	$0.314543\pi$
$12$	−1.05062	+	1.37703i	−0.303288	+	0.397513i
$13$	0.753337	−	0.0880524i	0.208938	−	0.0244214i	−0.0109800	−	0.999940i	$-0.503495\pi$
$13$	0.753337	−	0.0880524i	0.208938	−	0.0244214i	0.219918	+	0.975518i	$0.429421\pi$
$14$	1.54623	+	2.07694i	0.413246	+	0.555086i
$15$	−0.278960	−	6.00959i	−0.0720273	−	1.55167i
$16$	−0.0581448	−	0.998308i	−0.0145362	−	0.249577i
$17$	5.86304	+	4.91968i	1.42200	+	1.19320i	0.950260	+	0.311458i	$0.100817\pi$
$17$	5.86304	+	4.91968i	1.42200	+	1.19320i	0.471737	+	0.881739i	$0.343627\pi$
$18$	−1.73423	−	2.44795i	−0.408763	−	0.576986i
$19$	−1.23604	+	1.03716i	−0.283567	+	0.237941i	−0.773465	−	0.633839i	$-0.781478\pi$
$19$	−1.23604	+	1.03716i	−0.283567	+	0.237941i	0.489899	+	0.871779i	$0.337034\pi$
$20$	2.38357	+	2.52644i	0.532983	+	0.564929i
$21$	−4.23214	+	1.48410i	−0.923528	+	0.323856i
$22$	−0.00472430	−	0.00310722i	−0.00100722	−	0.000662462i
$23$	−5.90723	−	1.40004i	−1.23174	−	0.291928i	−0.437327	−	0.899302i	$-0.644075\pi$
$23$	−5.90723	−	1.40004i	−1.23174	−	0.291928i	−0.794416	+	0.607374i	$0.792223\pi$
$24$	1.68054	+	0.419283i	0.343038	+	0.0855859i
$25$	−7.01655	−	0.820117i	−1.40331	−	0.164023i
$26$	−0.379233	−	0.656850i	−0.0743736	−	0.128819i
$27$	4.94259	−	1.60338i	0.951201	−	0.308571i
$28$	1.29465	−	2.24240i	0.244666	−	0.423775i
$29$	3.40377	−	4.57206i	0.632065	−	0.849011i	−0.364553	−	0.931183i	$-0.618778\pi$
$29$	3.40377	−	4.57206i	0.632065	−	0.849011i	0.996618	+	0.0821719i	$0.0261857\pi$
$30$	−5.40761	+	2.63642i	−0.987290	+	0.481343i
$31$	1.61612	+	5.39823i	0.290265	+	0.969551i	0.971411	+	0.237404i	$0.0762965\pi$
$31$	1.61612	+	5.39823i	0.290265	+	0.969551i	−0.681146	+	0.732147i	$0.738518\pi$
$32$	−0.893633	+	0.448799i	−0.157973	+	0.0793372i
$33$	0.00757632	−	0.00620653i	0.00131887	−	0.00108042i
$34$	2.19509	−	7.33213i	0.376456	−	1.25745i
$35$	1.56173	+	8.85699i	0.263980	+	1.49710i
$36$	−1.56085	+	2.56198i	−0.260141	+	0.426997i
$37$	−1.90884	+	10.8256i	−0.313812	+	1.77971i	0.264996	+	0.964250i	$0.414629\pi$
$37$	−1.90884	+	10.8256i	−0.313812	+	1.77971i	−0.578807	+	0.815464i	$0.696482\pi$
$38$	1.44191	+	0.724153i	0.233908	+	0.117473i
$39$	1.28177	−	0.287866i	0.205248	−	0.0460955i
$40$	1.37573	−	3.18931i	0.217522	−	0.504274i
$41$	−1.60914	+	3.73041i	−0.251306	+	0.582592i	−0.996438	−	0.0843240i	$-0.973127\pi$
$41$	−1.60914	+	3.73041i	−0.251306	+	0.582592i	0.745133	+	0.666916i	$0.232386\pi$
$42$	3.03898	+	3.29820i	0.468925	+	0.508923i
$43$	6.27486	+	3.15135i	0.956907	+	0.480577i	0.857508	−	0.514471i	$-0.172012\pi$
$43$	6.27486	+	3.15135i	0.956907	+	0.480577i	0.0993994	+	0.995048i	$0.468308\pi$
$44$	−0.000981901		0.00556864i	−0.000148027		0.000839504i
$45$	−1.56695	−	10.3016i	−0.233586	−	1.53568i
$46$	1.05420	+	5.97864i	0.155433	+	0.881503i
$47$	−1.29272	+	4.31797i	−0.188562	+	0.629841i	0.810467	+	0.585784i	$0.199213\pi$
$47$	−1.29272	+	4.31797i	−0.188562	+	0.629841i	−0.999029	+	0.0440569i	$0.985972\pi$
$48$	−0.280633	−	1.70916i	−0.0405060	−	0.246697i
$49$	−0.264065	+	0.132618i	−0.0377235	+	0.0189455i
$50$	2.02607	+	6.76754i	0.286530	+	0.957075i
$51$	10.9890	+	7.41467i	1.53877	+	1.03826i
$52$	−0.452924	+	0.608383i	−0.0628093	+	0.0843675i
$53$	6.25091	−	10.8269i	0.858628	−	1.48719i	−0.0146102	−	0.999893i	$-0.504651\pi$
$53$	6.25091	−	10.8269i	0.858628	−	1.48719i	0.873238	−	0.487294i	$-0.162016\pi$
$54$	−3.42991	−	3.90329i	−0.466752	−	0.531171i
$55$	−0.00982017	−	0.0170090i	−0.00132415	−	0.00229350i
$56$	−2.57180	−	0.300600i	−0.343671	−	0.0401694i
$57$	−1.94169	+	2.01005i	−0.257183	+	0.266238i
$58$	−5.54631	−	1.31450i	−0.728266	−	0.172602i
$59$	−9.40314	−	6.18454i	−1.22418	−	0.805159i	−0.238073	−	0.971247i	$-0.576516\pi$
$59$	−9.40314	−	6.18454i	−1.22418	−	0.805159i	−0.986111	+	0.166088i	$0.946886\pi$
$60$	4.56265	+	3.92112i	0.589036	+	0.506214i
$61$	−3.73496	−	3.95883i	−0.478213	−	0.506876i	0.442687	−	0.896676i	$-0.354025\pi$
$61$	−3.73496	−	3.95883i	−0.478213	−	0.506876i	−0.920899	+	0.389801i	$0.872544\pi$
$62$	4.31663	−	3.62208i	0.548213	−	0.460005i
$63$	−7.02194	+	3.32157i	−0.884682	+	0.418479i
$64$	0.766044	+	0.642788i	0.0957556	+	0.0803485i
$65$	−0.153179	−	2.62998i	−0.0189995	−	0.326208i
$66$	−0.00869976	−	0.00449841i	−0.00107087	−	0.000553717i
$67$	−2.51055	−	3.37226i	−0.306713	−	0.411987i	0.621865	−	0.783124i	$-0.286375\pi$
$67$	−2.51055	−	3.37226i	−0.306713	−	0.411987i	−0.928578	+	0.371138i	$0.878968\pi$
$68$	−7.60191	+	0.888536i	−0.921867	+	0.107751i
$69$	−10.4288	−	1.34379i	−1.25549	−	0.161773i
$70$	7.51406	−	4.94208i	0.898102	−	0.590691i
$71$	−8.54902	+	3.11159i	−1.01458	+	0.369277i	−0.795191	−	0.606360i	$-0.792629\pi$
$71$	−8.54902	+	3.11159i	−1.01458	+	0.369277i	−0.219391	+	0.975637i	$0.570407\pi$
$72$	2.97067	+	0.418447i	0.350097	+	0.0493145i
$73$	2.27020	+	0.826284i	0.265707	+	0.0967093i	0.471438	−	0.881899i	$-0.343735\pi$
$73$	2.27020	+	0.826284i	0.265707	+	0.0967093i	−0.205731	+	0.978608i	$0.565957\pi$
$74$	10.6963	−	2.53506i	1.24342	−	0.294695i
$75$	−12.2349	−	0.144277i	−1.41277	−	0.0166597i
$76$	0.0938186	−	1.61080i	0.0107617	−	0.184772i
$77$	−0.0100475	+	0.0106497i	−0.00114502	+	0.00121365i
$78$	−0.772008	−	1.06293i	−0.0874127	−	0.120353i
$79$	−0.353932	−	0.820506i	−0.0398204	−	0.0923141i	0.897145	−	0.441736i	$-0.145637\pi$
$79$	−0.353932	−	0.820506i	−0.0398204	−	0.0923141i	−0.936965	+	0.349422i	$0.886378\pi$
$80$	−3.47337			−0.388335
$81$	8.22419	−	3.65549i	0.913799	−	0.406166i
$82$	4.06267			0.448647
$83$	0.0349465	+	0.0810150i	0.00383587	+	0.00889255i	0.920123	−	0.391629i	$-0.128088\pi$
$83$	0.0349465	+	0.0810150i	0.00383587	+	0.00889255i	−0.916287	+	0.400521i	$0.868829\pi$
$84$	1.82478	−	4.09679i	0.199099	−	0.446997i
$85$	18.2431	−	19.3365i	1.97874	−	2.09734i
$86$	0.408278	−	7.00987i	0.0440258	−	0.755893i
$87$	5.03677	−	8.49112i	0.539999	−	0.910344i
$88$	0.00550212	−	0.00130403i	0.000586528	−	0.000139010i
$89$	−11.4053	−	4.15118i	−1.20896	−	0.440024i	−0.342614	−	0.939476i	$-0.611312\pi$
$89$	−11.4053	−	4.15118i	−1.20896	−	0.440024i	−0.866341	+	0.499452i	$0.833535\pi$
$90$	−8.83849	+	5.51906i	−0.931658	+	0.581760i
$91$	−1.84546	+	0.671693i	−0.193457	+	0.0704125i
$92$	5.07214	−	3.33600i	0.528807	−	0.347802i
$93$	3.75981	+	9.00678i	0.389874	+	0.933960i
$94$	4.47685	−	0.523269i	0.461752	−	0.0539711i
$95$	3.34672	+	4.49542i	0.343366	+	0.461221i
$96$	−1.45823	+	0.934648i	−0.148830	+	0.0953921i
$97$	−0.789886	−	13.5618i	−0.0802007	−	1.37699i	−0.763005	−	0.646392i	$-0.776277\pi$
$97$	−0.789886	−	13.5618i	−0.0802007	−	1.37699i	0.682804	−	0.730601i	$-0.260760\pi$
$98$	0.226363	+	0.189941i	0.0228661	+	0.0191870i
$99$	0.0119289	−	0.0120610i	0.00119890	−	0.00121217i
$100$	5.41158	−	4.54086i	0.541158	−	0.454086i
$101$	−5.45383	−	5.78073i	−0.542677	−	0.575204i	0.396762	−	0.917922i	$-0.370134\pi$
$101$	−5.45383	−	5.78073i	−0.542677	−	0.575204i	−0.939438	+	0.342718i	$0.888653\pi$
$102$	2.45575	−	13.0271i	0.243156	−	1.28987i
$103$	2.89086	+	1.90135i	0.284845	+	0.187345i	0.683888	−	0.729587i	$-0.260287\pi$
$103$	2.89086	+	1.90135i	0.284845	+	0.187345i	−0.399044	+	0.916932i	$0.630658\pi$
$104$	0.738021	+	0.174914i	0.0723689	+	0.0171517i
$105$	4.29138	+	14.9746i	0.418796	+	1.46138i
$106$	−12.4173	−	1.45137i	−1.20607	−	0.140970i
$107$	4.92638	+	8.53274i	0.476251	+	0.824891i	0.999630	−	0.0272089i	$-0.00866194\pi$
$107$	4.92638	+	8.53274i	0.476251	+	0.824891i	−0.523379	+	0.852100i	$0.675329\pi$
$108$	−2.22555	+	4.69542i	−0.214154	+	0.451817i
$109$	2.48802	−	4.30938i	0.238309	−	0.412763i	−0.721920	−	0.691976i	$-0.756740\pi$
$109$	2.48802	−	4.30938i	0.238309	−	0.412763i	0.960229	+	0.279213i	$0.0900735\pi$
$110$	−0.0117284	+	0.0157540i	−0.00111826	+	0.00150208i
$111$	−1.33111	+	18.9931i	−0.126343	+	1.80275i
$112$	0.742621	+	2.48053i	0.0701711	+	0.234388i
$113$	6.05781	−	3.04235i	0.569871	−	0.286200i	−0.140439	−	0.990089i	$-0.544851\pi$
$113$	6.05781	−	3.04235i	0.569871	−	0.286200i	0.710309	+	0.703890i	$0.248555\pi$
$114$	2.61473	+	0.986751i	0.244892	+	0.0924177i
$115$	−6.04765	+	20.2006i	−0.563946	+	1.88371i
$116$	0.989786	+	5.61336i	0.0918993	+	0.521187i
$117$	2.15593	−	0.727594i	0.199316	−	0.0672661i
$118$	−1.95435	+	11.0837i	−0.179913	+	1.02034i
$119$	−17.7097	−	8.89415i	−1.62345	−	0.815326i
$120$	1.79326	−	5.74258i	0.163702	−	0.524223i
$121$	−4.35686	+	10.1003i	−0.396079	+	0.918213i
$122$	−2.15572	+	4.99751i	−0.195169	+	0.452454i
$123$	−2.09751	+	6.71687i	−0.189126	+	0.605640i
$124$	−5.03558	−	2.52897i	−0.452209	−	0.227108i
$125$	−1.24508	+	7.06122i	−0.111364	+	0.631575i
$126$	5.83117	+	5.13205i	0.519482	+	0.457200i
$127$	−0.699485	−	3.96698i	−0.0620692	−	0.352012i	−0.999987	−	0.00515370i	$-0.998360\pi$
$127$	−0.699485	−	3.96698i	−0.0620692	−	0.352012i	0.937917	−	0.346858i	$-0.112752\pi$
$128$	0.286803	−	0.957990i	0.0253501	−	0.0846751i
$129$	11.3787	+	4.29413i	1.00184	+	0.378077i
$130$	−2.35422	+	1.18233i	−0.206478	+	0.103697i
$131$	−5.36804	−	17.9305i	−0.469008	−	1.56659i	−0.786038	−	0.618179i	$-0.787871\pi$
$131$	−5.36804	−	17.9305i	−0.469008	−	1.56659i	0.317030	−	0.948416i	$-0.397314\pi$
$132$	−0.000684718		0.00976999i	−5.95970e−5		0.000850369i
$133$	2.49489	−	3.35122i	0.216334	−	0.290587i
$134$	−2.10208	+	3.64091i	−0.181592	+	0.314527i
$135$	−4.56153	−	17.4622i	−0.392594	−	1.50291i
$136$	3.82683	+	6.62826i	0.328148	+	0.568369i
$137$	−2.32743	−	0.272038i	−0.198846	−	0.0232418i	0.0160868	−	0.999871i	$-0.494879\pi$
$137$	−2.32743	−	0.272038i	−0.198846	−	0.0232418i	−0.214933	+	0.976629i	$0.568953\pi$
$138$	2.89677	+	10.1082i	0.246589	+	0.860465i
$139$	21.8152	+	5.17029i	1.85034	+	0.438538i	0.996617	−	0.0821911i	$-0.0261918\pi$
$139$	21.8152	+	5.17029i	1.85034	+	0.438538i	0.853722	+	0.520729i	$0.174340\pi$
$140$	−7.51406	−	4.94208i	−0.635054	−	0.417682i
$141$	−1.44622	+	7.67180i	−0.121794	+	0.646082i
$142$	6.24320	+	6.61741i	0.523918	+	0.555320i
$143$	0.00328539	−	0.00275677i	0.000274738	−	0.000230533i
$144$	−0.792399	−	2.89346i	−0.0660332	−	0.241122i
$145$	−15.1662	−	12.7259i	−1.25948	−	1.05683i
$146$	−0.140472	−	2.41181i	−0.0116255	−	0.199603i
$147$	−0.430901	+	0.276185i	−0.0355401	+	0.0227793i
$148$	−6.56431	−	8.81740i	−0.539583	−	0.724786i
$149$	0.0807515	−	0.00943849i	0.00661542	−	0.000773232i	−0.112785	−	0.993619i	$-0.535977\pi$
$149$	0.0807515	−	0.00943849i	0.00661542	−	0.000773232i	0.119400	+	0.992846i	$0.461903\pi$
$150$	4.71352	+	11.2914i	0.384858	+	0.921942i
$151$	−0.383163	+	0.252010i	−0.0311814	+	0.0205083i	−0.565004	−	0.825088i	$-0.691125\pi$
$151$	−0.383163	+	0.252010i	−0.0311814	+	0.0205083i	0.533823	+	0.845596i	$0.320755\pi$
$152$	−1.51623	+	0.551861i	−0.122982	+	0.0447618i
$153$	20.2700	+	10.7859i	1.63873	+	0.871985i
$154$	0.0137584	+	0.00500763i	0.00110868	+	0.000403527i
$155$	19.0447	−	4.51369i	1.52971	−	0.362548i
$156$	−0.670220	+	1.12987i	−0.0536605	+	0.0904623i
$157$	−0.977719	+	16.7868i	−0.0780305	+	1.33973i	0.701187	+	0.712978i	$0.252654\pi$
$157$	−0.977719	+	16.7868i	−0.0780305	+	1.33973i	−0.779217	+	0.626754i	$0.784383\pi$
$158$	−0.613217	+	0.649972i	−0.0487849	+	0.0517090i
$159$	8.81047	−	19.7803i	0.698716	−	1.56868i
$160$	1.37573	+	3.18931i	0.108761	+	0.252137i
$161$	15.7193			1.23886
$162$	−6.61397	−	6.10372i	−0.519643	−	0.479554i
$163$	−8.85509			−0.693584			−0.346792	−	0.937942i	$-0.612729\pi$
$163$	−8.85509			−0.693584			−0.346792	+	0.937942i	$0.612729\pi$
$164$	−1.60914	−	3.73041i	−0.125653	−	0.291296i
$165$	−0.0199910	−	0.0275243i	−0.00155630	−	0.00214276i
$166$	0.0605477	−	0.0641768i	0.00469941	−	0.00498108i
$167$	−0.284923	+	4.89193i	−0.0220480	+	0.378549i	0.969177	+	0.246365i	$0.0792361\pi$
$167$	−0.284923	+	4.89193i	−0.0220480	+	0.378549i	−0.991225	+	0.132184i	$0.957801\pi$
$168$	−4.48450	−	0.0528823i	−0.345986	−	0.00407996i
$169$	−12.0898	+	2.86534i	−0.929986	+	0.220411i
$170$	−24.9808	−	9.09227i	−1.91594	−	0.697345i
$171$	−2.98136	+	3.81351i	−0.227991	+	0.291627i
$172$	−6.59828	+	2.40158i	−0.503114	+	0.183119i
$173$	−15.3700	+	10.1090i	−1.16856	+	0.768572i	−0.977069	−	0.212923i	$-0.931702\pi$
$173$	−15.3700	+	10.1090i	−1.16856	+	0.768572i	−0.191488	+	0.981495i	$0.561331\pi$
$174$	−9.79165	−	1.26168i	−0.742303	−	0.0956481i
$175$	18.1680	−	2.12353i	1.37337	−	0.160524i
$176$	−0.00337666	−	0.00453564i	−0.000254525	−	0.000341887i
$177$	−17.3158	−	8.95354i	−1.30153	−	0.672989i
$178$	0.705717	+	12.1167i	0.0528957	+	0.908185i
$179$	4.00404	+	3.35979i	0.299276	+	0.251123i	0.780043	−	0.625726i	$-0.215197\pi$
$179$	4.00404	+	3.35979i	0.299276	+	0.251123i	−0.480767	+	0.876849i	$0.659642\pi$
$180$	8.56844	+	5.92965i	0.638654	+	0.441970i
$181$	4.54343	−	3.81239i	0.337711	−	0.283373i	−0.458122	−	0.888889i	$-0.651478\pi$
$181$	4.54343	−	3.81239i	0.337711	−	0.283373i	0.795833	+	0.605516i	$0.207033\pi$
$182$	1.34771	+	1.42849i	0.0998988	+	0.105887i
$183$	−7.14948	−	6.14423i	−0.528505	−	0.454195i
$184$	−5.07214	−	3.33600i	−0.373923	−	0.245933i
$185$	37.1521	+	8.80522i	2.73148	+	0.647373i
$186$	6.78099	−	7.01972i	0.497206	−	0.514711i
$187$	0.0429853	+	0.00502426i	0.00314340	+	0.000367410i
$188$	−2.25366	−	3.90346i	−0.164365	−	0.284689i
$189$	−11.4955	+	6.99113i	−0.836172	+	0.508530i
$190$	2.80220	−	4.85356i	0.203293	−	0.352114i
$191$	2.33909	−	3.14194i	0.169250	−	0.227343i	−0.709403	−	0.704803i	$-0.751035\pi$
$191$	2.33909	−	3.14194i	0.169250	−	0.227343i	0.878653	+	0.477461i	$0.158443\pi$
$192$	1.43578	+	0.968775i	0.103619	+	0.0699153i
$193$	−1.45783	−	4.86948i	−0.104937	−	0.350513i	0.889354	−	0.457220i	$-0.151155\pi$
$193$	−1.45783	−	4.86948i	−0.104937	−	0.350513i	−0.994291	+	0.106707i	$0.965969\pi$
$194$	−12.1398	+	6.09685i	−0.871588	+	0.437728i
$195$	−0.739310	−	4.50268i	−0.0529431	−	0.322444i
$196$	0.0847492	−	0.283082i	0.00605351	−	0.0202201i
$197$	3.09748	+	17.5667i	0.220686	+	1.25157i	0.870762	+	0.491705i	$0.163626\pi$
$197$	3.09748	+	17.5667i	0.220686	+	1.25157i	−0.650075	+	0.759870i	$0.725263\pi$
$198$	−0.0157993	−	0.00617619i	−0.00112281	−	0.000438923i
$199$	4.67750	−	26.5274i	0.331579	−	1.88048i	−0.127118	−	0.991888i	$-0.540573\pi$
$199$	4.67750	−	26.5274i	0.331579	−	1.88048i	0.458698	−	0.888592i	$-0.348316\pi$
$200$	−6.31291	−	3.17046i	−0.446390	−	0.224185i
$201$	−4.93429	−	5.35516i	−0.348038	−	0.377724i
$202$	−3.14780	+	7.29743i	−0.221479	+	0.513445i
$203$	−5.84571	+	13.5519i	−0.410288	+	0.951155i
$204$	−12.9343	+	2.90485i	−0.905585	+	0.203380i
$205$	12.6102	+	6.33308i	0.880735	+	0.442322i
$206$	0.600837	−	3.40752i	0.0418623	−	0.237413i
$207$	−18.2076	−	0.429476i	−1.26551	−	0.0298506i
$208$	−0.131706	−	0.746942i	−0.00913218	−	0.0517911i
$209$	−0.00261673	+	0.00874050i	−0.000181003	+	0.000604593i
$210$	12.0502	−	9.87157i	0.831545	−	0.681203i
$211$	−15.8769	+	7.97367i	−1.09301	+	0.548930i	−0.901596	−	0.432579i	$-0.857604\pi$
$211$	−15.8769	+	7.97367i	−1.09301	+	0.548930i	−0.191414	+	0.981509i	$0.561307\pi$
$212$	3.58556	+	11.9766i	0.246257	+	0.822556i
$213$	−14.1639	+	6.90548i	−0.970497	+	0.473156i
$214$	5.88366	−	7.90313i	0.402199	−	0.540247i
$215$	12.1946	−	21.1216i	0.831663	−	1.44048i
$216$	5.19290	+	0.183776i	0.353332	+	0.0125044i
$217$	−7.29532	−	12.6359i	−0.495238	−	0.857778i
$218$	−4.94239	−	0.577683i	−0.334741	−	0.0391256i
$219$	4.06000	+	1.01294i	0.274349	+	0.0684484i
$220$	0.0191109	+	0.00452937i	0.00128846	+	0.000305370i
$221$	4.85004	+	3.18992i	0.326249	+	0.214577i
$222$	17.9670	−	6.30054i	1.20587	−	0.422865i
$223$	11.7254	+	12.4282i	0.785193	+	0.832256i	0.989178	−	0.146718i	$-0.0468711\pi$
$223$	11.7254	+	12.4282i	0.785193	+	0.832256i	−0.203986	+	0.978974i	$0.565390\pi$
$224$	1.98352	−	1.66437i	0.132530	−	0.111206i
$225$	−21.1018	+	1.96329i	−1.40679	+	0.130886i
$226$	−5.19291	−	4.35737i	−0.345427	−	0.289848i
$227$	1.38922	+	23.8521i	0.0922061	+	1.58312i	0.654424	+	0.756128i	$0.272911\pi$
$227$	1.38922	+	23.8521i	0.0922061	+	1.58312i	−0.562218	+	0.826989i	$0.690052\pi$
$228$	−0.129589	−	2.79172i	−0.00858226	−	0.184886i
$229$	−9.61359	−	12.9133i	−0.635284	−	0.853334i	0.361591	−	0.932337i	$-0.382234\pi$
$229$	−9.61359	−	12.9133i	−0.635284	−	0.853334i	−0.996874	+	0.0790027i	$0.974826\pi$
$230$	20.9438	−	2.44798i	1.38100	−	0.161415i
$231$	−0.0153825	+	0.0201615i	−0.00101209	+	0.00132653i
$232$	4.76224	−	3.13217i	0.312656	−	0.205637i
$233$	−7.50766	+	2.73257i	−0.491843	+	0.179016i	−0.576022	−	0.817434i	$-0.695396\pi$
$233$	−7.50766	+	2.73257i	−0.491843	+	0.179016i	0.0841783	+	0.996451i	$0.473173\pi$
$234$	−1.52201	−	1.69142i	−0.0994968	−	0.110572i
$235$	14.7115	+	5.35454i	0.959671	+	0.349292i
$236$	10.9513	−	2.59551i	0.712869	−	0.168953i
$237$	−0.758010	−	1.34941i	−0.0492381	−	0.0876537i
$238$	−1.15229	+	19.7841i	−0.0746922	+	1.28242i
$239$	10.8354	−	11.4849i	0.700886	−	0.742895i	−0.274936	−	0.961462i	$-0.588657\pi$
$239$	10.8354	−	11.4849i	0.700886	−	0.742895i	0.975822	+	0.218567i	$0.0701383\pi$
$240$	−5.98320	+	0.627915i	−0.386214	+	0.0405317i
$241$	−1.64488	−	3.81325i	−0.105956	−	0.245633i	0.856987	−	0.515337i	$-0.172333\pi$
$241$	−1.64488	−	3.81325i	−0.105956	−	0.245633i	−0.962943	+	0.269704i	$0.913074\pi$
$242$	11.0000			0.707105
$243$	13.5061	−	7.78368i	0.866416	−	0.499324i
$244$	5.44263			0.348429
$245$	0.406523	+	0.942427i	0.0259718	+	0.0602095i
$246$	6.99832	−	0.734448i	0.446197	−	0.0468267i
$247$	−0.839829	+	0.890167i	−0.0534370	+	0.0566399i
$248$	−0.327644	+	5.62543i	−0.0208054	+	0.357215i
$249$	0.0748443	+	0.133238i	0.00474306	+	0.00844362i
$250$	6.97688	−	1.65355i	0.441257	−	0.104580i
$251$	−2.74822	−	1.00027i	−0.173466	−	0.0631364i	0.253827	−	0.967250i	$-0.418311\pi$
$251$	−2.74822	−	1.00027i	−0.173466	−	0.0631364i	−0.427293	+	0.904113i	$0.640533\pi$
$252$	2.40273	−	7.38698i	0.151357	−	0.465336i
$253$	−0.0322578	+	0.0117409i	−0.00202803	+	0.000738142i
$254$	−3.36549	+	2.21352i	−0.211170	+	0.138888i
$255$	27.9297	−	36.6069i	1.74902	−	2.29241i
$256$	−0.993238	+	0.116093i	−0.0620774	+	0.00725581i
$257$	−2.38405	−	3.20233i	−0.148713	−	0.199756i	0.721524	−	0.692389i	$-0.243442\pi$
$257$	−2.38405	−	3.20233i	−0.148713	−	0.199756i	−0.870237	+	0.492633i	$0.836034\pi$
$258$	−0.563945	−	12.1489i	−0.0351097	−	0.756360i
$259$	−1.65498	−	28.4150i	−0.102836	−	1.76562i
$260$	2.01809	+	1.69338i	0.125157	+	0.105019i
$261$	7.14128	−	15.5373i	0.442034	−	0.961733i
$262$	−14.3379	+	12.0309i	−0.885798	+	0.743273i
$263$	10.0650	+	10.6683i	0.620636	+	0.657836i	0.959075	−	0.283152i	$-0.0913802\pi$
$263$	10.0650	+	10.6683i	0.620636	+	0.657836i	−0.338439	+	0.940989i	$0.609899\pi$
$264$	0.00924217	−	0.00324098i	0.000568816	−	0.000199468i
$265$	−36.2798	−	23.8616i	−2.22865	−	1.46580i
$266$	−4.06532	−	0.963497i	−0.249260	−	0.0590758i
$267$	−20.3971	−	5.08894i	−1.24828	−	0.311438i
$268$	4.17573	+	0.488073i	0.255074	+	0.0298138i
$269$	−2.28612	−	3.95967i	−0.139387	−	0.241425i	0.787878	−	0.615832i	$-0.211180\pi$
$269$	−2.28612	−	3.95967i	−0.139387	−	0.241425i	−0.927265	+	0.374406i	$0.877847\pi$
$270$	−14.2274	+	11.1049i	−0.865850	+	0.675823i
$271$	3.39467	−	5.87974i	0.206212	−	0.357169i	−0.744307	−	0.667838i	$-0.767220\pi$
$271$	3.39467	−	5.87974i	0.206212	−	0.357169i	0.950518	+	0.310669i	$0.100553\pi$
$272$	4.57045	−	6.13918i	0.277124	−	0.372242i
$273$	−3.05755	+	1.49067i	−0.185051	+	0.0902197i
$274$	0.672060	+	2.24484i	0.0406006	+	0.135615i
$275$	−0.0356966	+	0.0179275i	−0.00215259	+	0.00108107i
$276$	8.13414	−	6.66350i	0.489618	−	0.401096i
$277$	−2.04196	+	6.82063i	−0.122690	+	0.409812i	−0.997164	−	0.0752597i	$-0.976021\pi$
$277$	−2.04196	+	6.82063i	−0.122690	+	0.409812i	0.874474	+	0.485072i	$0.161207\pi$
$278$	−3.89310	−	22.0789i	−0.233493	−	1.32420i
$279$	8.10486	+	14.8353i	0.485225	+	0.888166i
$280$	−1.56173	+	8.85699i	−0.0933310	+	0.529306i
$281$	11.0614	+	5.55525i	0.659869	+	0.331399i	0.747025	−	0.664796i	$-0.231482\pi$
$281$	11.0614	+	5.55525i	0.659869	+	0.331399i	−0.0871559	+	0.996195i	$0.527778\pi$
$282$	7.61719	−	1.71070i	0.453597	−	0.101871i
$283$	−4.06854	+	9.43193i	−0.241850	+	0.560670i	−0.995301	−	0.0968338i	$-0.969128\pi$
$283$	−4.06854	+	9.43193i	−0.241850	+	0.560670i	0.753451	+	0.657504i	$0.228388\pi$
$284$	3.60340	−	8.35363i	0.213823	−	0.495697i
$285$	6.57771	+	7.13875i	0.389630	+	0.422863i
$286$	−0.00383259	−	0.00192480i	−0.000226626	−	0.000113816i
$287$	1.82669	−	10.3597i	0.107826	−	0.611513i
$288$	−2.34297	+	1.87363i	−0.138061	+	0.110405i
$289$	7.22003	+	40.9468i	0.424708	+	2.40864i
$290$	−5.67815	+	18.9663i	−0.333432	+	1.11374i
$291$	−3.81235	−	23.2187i	−0.223484	−	1.36110i
$292$	−2.15892	+	1.08425i	−0.126341	+	0.0634510i
$293$	1.67993	+	5.61137i	0.0981427	+	0.327819i	0.992934	−	0.118664i	$-0.0378612\pi$
$293$	1.67993	+	5.61137i	0.0981427	+	0.327819i	−0.894792	+	0.446484i	$0.852676\pi$
$294$	0.424268	+	0.286269i	0.0247438	+	0.0166955i
$295$	−23.3439	+	31.3563i	−1.35914	+	1.82564i
$296$	−5.49629	+	9.51985i	−0.319465	+	0.553330i
$297$	0.0183682	−	0.0229326i	0.00106583	−	0.00133068i
$298$	−0.0406506	−	0.0704089i	−0.00235483	−	0.00407868i
$299$	−4.57341	−	0.534555i	−0.264487	−	0.0309141i
$300$	8.50105	−	8.80034i	0.490808	−	0.508088i
$301$	−17.6914	−	4.19293i	−1.01971	−	0.241676i
$302$	0.383163	+	0.252010i	0.0220486	+	0.0145016i
$303$	−10.4398	−	8.97188i	−0.599749	−	0.515421i
$304$	1.10727	+	1.17364i	0.0635065	+	0.0673130i
$305$	−14.4815	+	12.1514i	−0.829210	+	0.695790i
$306$	1.87522	−	22.8843i	0.107199	−	1.30821i
$307$	−2.50920	−	2.10547i	−0.143208	−	0.120165i	0.568370	−	0.822773i	$-0.307574\pi$
$307$	−2.50920	−	2.10547i	−0.143208	−	0.120165i	−0.711577	+	0.702608i	$0.752019\pi$
$308$	−0.000851318	−	0.0146166i	−4.85084e−5	−	0.000832856i
$309$	5.32349	+	2.75263i	0.302843	+	0.156592i
$310$	−11.6878	−	15.6994i	−0.663821	−	0.891667i
$311$	−20.7938	+	2.43044i	−1.17911	+	0.137818i	−0.682983	−	0.730434i	$-0.739318\pi$
$311$	−20.7938	+	2.43044i	−1.17911	+	0.137818i	−0.496124	+	0.868252i	$0.665244\pi$
$312$	1.30293	+	0.167886i	0.0737638	+	0.00950469i
$313$	−1.62928	+	1.07159i	−0.0920922	+	0.0605700i	−0.594720	−	0.803933i	$-0.702737\pi$
$313$	−1.62928	+	1.07159i	−0.0920922	+	0.0605700i	0.502628	+	0.864503i	$0.332367\pi$
$314$	15.8012	−	5.75115i	0.891711	−	0.324556i
$315$	10.0994	+	25.0194i	0.569037	+	1.40968i
$316$	0.839697	+	0.305625i	0.0472366	+	0.0171927i
$317$	5.42484	−	1.28571i	0.304689	−	0.0722127i	−0.0754273	−	0.997151i	$-0.524032\pi$
$317$	5.42484	−	1.28571i	0.304689	−	0.0722127i	0.380116	+	0.924939i	$0.375884\pi$
$318$	−21.6523	−	0.255329i	−1.21420	−	0.0143181i
$319$	0.00187404	−	0.0321761i	0.000104926	−	0.00180151i
$320$	2.38357	−	2.52644i	0.133246	−	0.141232i
$321$	10.0287	+	13.8078i	0.559747	+	0.770678i
$322$	−6.22612	−	14.4338i	−0.346968	−	0.804362i
$323$	−12.3494			−0.687141
$324$	−2.98488	+	8.49061i	−0.165826	+	0.471701i
$325$	−5.35804			−0.297211
$326$	3.50732	+	8.13088i	0.194253	+	0.450328i
$327$	3.50679	−	7.87308i	0.193926	−	0.435382i
$328$	−2.78797	+	2.95508i	−0.153940	+	0.163167i
$329$	0.678600	−	11.6511i	0.0374124	−	0.642346i
$330$	−0.0173552	+	0.0292579i	−0.000955374	+	0.00161059i
$331$	15.2363	−	3.61108i	0.837465	−	0.198483i	0.210563	−	0.977580i	$-0.432470\pi$
$331$	15.2363	−	3.61108i	0.837465	−	0.198483i	0.626903	+	0.779097i	$0.284322\pi$
$332$	−0.0829099	−	0.0301767i	−0.00455027	−	0.00165616i
$333$	1.14061	+	32.9580i	0.0625052	+	1.80609i
$334$	4.60470	−	1.67597i	0.251958	−	0.0917052i
$335$	−12.2003	+	8.02427i	−0.666574	+	0.438413i
$336$	1.72766	+	4.13868i	0.0942516	+	0.225784i
$337$	3.44984	−	0.403229i	0.187925	−	0.0219653i	−0.0216098	−	0.999766i	$-0.506879\pi$
$337$	3.44984	−	0.403229i	0.187925	−	0.0219653i	0.209535	+	0.977801i	$0.432805\pi$
$338$	7.41953	+	9.96616i	0.403569	+	0.542088i
$339$	9.88513	−	6.33584i	0.536887	−	0.344116i
$340$	1.54572	+	26.5390i	0.0838286	+	1.43928i
$341$	0.0244086	+	0.0204812i	0.00132180	+	0.00110912i
$342$	4.68249	+	1.22708i	0.253200	+	0.0663529i
$343$	14.4708	−	12.1424i	0.781349	−	0.655630i
$344$	4.81861	+	5.10743i	0.259802	+	0.275374i
$345$	−6.76578	+	35.8906i	−0.364257	+	1.93228i
$346$	15.3700	+	10.1090i	0.826294	+	0.543462i
$347$	−12.3983	−	2.93845i	−0.665575	−	0.157744i	−0.116078	−	0.993240i	$-0.537032\pi$
$347$	−12.3983	−	2.93845i	−0.665575	−	0.157744i	−0.549497	+	0.835496i	$0.685180\pi$
$348$	2.71978	+	9.49058i	0.145795	+	0.508748i
$349$	32.8569	+	3.84042i	1.75879	+	0.205573i	0.933363	−	0.358935i	$-0.116860\pi$
$349$	32.8569	+	3.84042i	1.75879	+	0.205573i	0.825428	+	0.564508i	$0.190934\pi$
$350$	−9.14584	−	15.8411i	−0.488866	−	0.846740i
$351$	3.58225	−	1.64309i	0.191206	−	0.0877019i
$352$	−0.00282727	+	0.00489698i	−0.000150694	+	0.000261010i
$353$	14.3495	−	19.2747i	0.763745	−	1.02589i	−0.234804	−	0.972043i	$-0.575445\pi$
$353$	14.3495	−	19.2747i	0.763745	−	1.02589i	0.998549	−	0.0538453i	$-0.0171478\pi$
$354$	−1.36285	+	19.4460i	−0.0724344	+	1.03354i
$355$	9.06287	+	30.2721i	0.481007	+	1.60668i
$356$	10.8462	−	5.44718i	0.574849	−	0.288700i
$357$	−32.1145	−	12.1194i	−1.69968	−	0.641428i
$358$	1.49909	−	5.00732i	0.0792296	−	0.264645i
$359$	−6.32467	−	35.8690i	−0.333804	−	1.89309i	−0.438739	−	0.898615i	$-0.644575\pi$
$359$	−6.32467	−	35.8690i	−0.333804	−	1.89309i	0.104935	−	0.994479i	$-0.466537\pi$
$360$	2.05092	−	10.2163i	0.108093	−	0.538446i
$361$	−2.84722	+	16.1474i	−0.149854	+	0.849864i
$362$	−5.30016	−	2.66184i	−0.278570	−	0.139903i
$363$	−5.67916	+	18.1864i	−0.298078	+	0.954538i
$364$	0.777860	−	1.80328i	0.0407710	−	0.0945177i
$365$	3.32362	−	7.70503i	0.173966	−	0.403300i
$366$	−2.80997	+	8.99838i	−0.146879	+	0.470353i
$367$	−16.7736	−	8.42401i	−0.875573	−	0.439730i	−0.0465321	−	0.998917i	$-0.514817\pi$
$367$	−16.7736	−	8.42401i	−0.875573	−	0.439730i	−0.829041	+	0.559187i	$0.811113\pi$
$368$	−1.05420	+	5.97864i	−0.0549538	+	0.311658i
$369$	−2.39888	+	11.9496i	−0.124881	+	0.622072i
$370$	−6.63012	−	37.6013i	−0.344683	−	1.95480i
$371$	−9.28411	+	31.0111i	−0.482007	+	1.61002i
$372$	−9.13144	−	3.44604i	−0.473443	−	0.178669i
$373$	15.1585	−	7.61288i	0.784877	−	0.394180i	−0.0107690	−	0.999942i	$-0.503428\pi$
$373$	15.1585	−	7.61288i	0.784877	−	0.394180i	0.795646	+	0.605762i	$0.207132\pi$
$374$	−0.0124123	−	0.0414598i	−0.000641822	−	0.00214384i
$375$	−0.868245	+	12.3887i	−0.0448360	+	0.639749i
$376$	−2.69159	+	3.61543i	−0.138808	+	0.186452i
$377$	2.16161	−	3.74401i	0.111328	−	0.192826i
$378$	10.9725	+	7.78627i	0.564364	+	0.400483i
$379$	−3.10948	−	5.38577i	−0.159723	−	0.276649i	0.775046	−	0.631905i	$-0.217727\pi$
$379$	−3.10948	−	5.38577i	−0.159723	−	0.276649i	−0.934769	+	0.355257i	$0.884393\pi$
$380$	−5.56651	−	0.650632i	−0.285556	−	0.0333767i
$381$	−1.92207	−	6.70702i	−0.0984709	−	0.343611i
$382$	−3.81144	−	0.903328i	−0.195010	−	0.0462183i
$383$	19.5371	+	12.8497i	0.998298	+	0.656591i	0.939810	−	0.341697i	$-0.111002\pi$
$383$	19.5371	+	12.8497i	0.998298	+	0.656591i	0.0584877	+	0.998288i	$0.481372\pi$
$384$	0.320860	−	1.70207i	0.0163738	−	0.0868585i
$385$	0.0348987	+	0.0369905i	0.00177860	+	0.00188521i
$386$	−3.89382	+	3.26730i	−0.198190	+	0.166301i
$387$	20.3772	+	5.33998i	1.03583	+	0.271447i
$388$	10.4066	+	8.73214i	0.528313	+	0.443307i
$389$	1.28401	+	22.0456i	0.0651019	+	1.11776i	0.859760	+	0.510699i	$0.170613\pi$
$389$	1.28401	+	22.0456i	0.0651019	+	1.11776i	−0.794658	+	0.607058i	$0.792350\pi$
$390$	−3.84161	+	2.46227i	−0.194527	+	0.124682i
$391$	−27.7466	−	37.2702i	−1.40321	−	1.88483i
$392$	−0.293498	+	0.0343050i	−0.0148239	+	0.00173266i
$393$	−12.4884	−	29.9165i	−0.629956	−	1.50909i
$394$	14.9032	−	9.80197i	0.750811	−	0.493816i
$395$	−2.91658	+	1.06155i	−0.146749	+	0.0534123i
$396$	0.000586727		0.0169535i	2.94841e−5		0.000851944i
$397$	2.48118	+	0.903077i	0.124527	+	0.0453242i	0.403532	−	0.914965i	$-0.367782\pi$
$397$	2.48118	+	0.903077i	0.124527	+	0.0453242i	−0.279005	+	0.960290i	$0.590005\pi$
$398$	−26.2106	+	6.21202i	−1.31382	+	0.311381i
$399$	3.69184	−	6.22380i	0.184823	−	0.311580i
$400$	−0.410754	+	7.05237i	−0.0205377	+	0.352618i
$401$	6.00091	−	6.36059i	0.299671	−	0.317633i	−0.559988	−	0.828501i	$-0.689194\pi$
$401$	6.00091	−	6.36059i	0.299671	−	0.317633i	0.859659	+	0.510868i	$0.170676\pi$
$402$	−2.96282	+	6.65181i	−0.147772	+	0.331762i
$403$	1.69281	+	3.92438i	0.0843251	+	0.195487i
$404$	7.94740			0.395398
$405$	−11.0145	−	29.2556i	−0.547313	−	1.45372i
$406$	14.7589			0.732473
$407$	0.0246195	+	0.0570745i	0.00122034	+	0.00282908i
$408$	7.79032	+	10.7260i	0.385678	+	0.531015i
$409$	−7.22255	+	7.65546i	−0.357132	+	0.378538i	−0.880883	−	0.473333i	$-0.843051\pi$
$409$	−7.22255	+	7.65546i	−0.357132	+	0.378538i	0.523751	+	0.851871i	$0.324532\pi$
$410$	0.820492	−	14.0873i	0.0405212	−	0.695722i
$411$	−4.05839	−	0.0478576i	−0.200186	−	0.00236064i
$412$	−3.36682	+	0.797950i	−0.165871	+	0.0393122i
$413$	27.3843	+	9.96707i	1.34749	+	0.490448i
$414$	6.81729	+	16.8886i	0.335052	+	0.830028i
$415$	0.287977	−	0.104815i	0.0141362	−	0.00514517i
$416$	−0.633688	+	0.416783i	−0.0310691	+	0.0204345i
$417$	38.5133	+	4.96256i	1.88600	+	0.243017i
$418$	0.00906210	−	0.00105921i	0.000443242	−	5.18076e-5i
$419$	−1.57575	−	2.11660i	−0.0769805	−	0.103403i	0.761965	−	0.647618i	$-0.224235\pi$
$419$	−1.57575	−	2.11660i	−0.0769805	−	0.103403i	−0.838945	+	0.544215i	$0.816827\pi$
$420$	−13.8371	−	7.15479i	−0.675181	−	0.349118i
$421$	1.01316	+	17.3953i	0.0493784	+	0.847795i	0.928531	+	0.371255i	$0.121072\pi$
$421$	1.01316	+	17.3953i	0.0493784	+	0.847795i	−0.879153	+	0.476540i	$0.841891\pi$
$422$	13.6101	+	11.4202i	0.662528	+	0.555927i
$423$	−1.10434	+	13.4768i	−0.0536949	+	0.655265i
$424$	9.57694	−	8.03601i	0.465097	−	0.390263i
$425$	−37.1036	−	39.3276i	−1.79979	−	1.90767i
$426$	11.9508	+	10.2704i	0.579017	+	0.497604i
$427$	11.7742	+	7.74403i	0.569795	+	0.374760i
$428$	−9.58718	−	2.27220i	−0.463414	−	0.109831i
$429$	0.00516102	−	0.00534272i	0.000249176	−	0.000257949i
$430$	−24.2242	−	2.83141i	−1.16820	−	0.136543i
$431$	−4.21448	−	7.29969i	−0.203004	−	0.351614i	0.746491	−	0.665396i	$-0.231737\pi$
$431$	−4.21448	−	7.29969i	−0.203004	−	0.351614i	−0.949495	+	0.313782i	$0.898404\pi$
$432$	−1.88806	−	4.84100i	−0.0908392	−	0.232913i
$433$	18.1907	−	31.5072i	0.874189	−	1.51414i	0.0165640	−	0.999863i	$-0.494727\pi$
$433$	18.1907	−	31.5072i	0.874189	−	1.51414i	0.857625	−	0.514276i	$-0.171939\pi$
$434$	−8.71292	+	11.7035i	−0.418234	+	0.561785i
$435$	−28.4257	−	19.1799i	−1.36291	−	0.919604i
$436$	1.42714	+	4.76699i	0.0683478	+	0.228298i
$437$	8.75363	−	4.39624i	0.418743	−	0.210301i
$438$	−0.677981	−	4.12916i	−0.0323952	−	0.197299i
$439$	−1.30175	+	4.34816i	−0.0621293	+	0.207526i	−0.983418	−	0.181353i	$-0.941952\pi$
$439$	−1.30175	+	4.34816i	−0.0621293	+	0.207526i	0.921289	+	0.388879i	$0.127138\pi$
$440$	−0.00341051	−	0.0193420i	−0.000162590	−	0.000922092i
$441$	−0.692337	+	0.553651i	−0.0329684	+	0.0263643i
$442$	1.00803	−	5.71684i	0.0479473	−	0.271923i
$443$	−8.56408	−	4.30104i	−0.406892	−	0.204349i	0.233568	−	0.972340i	$-0.424960\pi$
$443$	−8.56408	−	4.30104i	−0.406892	−	0.204349i	−0.640460	+	0.767992i	$0.721256\pi$
$444$	−12.9016	−	14.0021i	−0.612284	−	0.664509i
$445$	−16.6976	+	38.7094i	−0.791541	+	1.83500i
$446$	6.76759	−	15.6890i	0.320455	−	0.742898i
$447$	0.137395	−	0.0308569i	0.00649858	−	0.00145948i
$448$	−2.31389	−	1.16208i	−0.109321	−	0.0549030i
$449$	−1.64283	+	9.31693i	−0.0775298	+	0.439693i	0.921190	+	0.389113i	$0.127218\pi$
$449$	−1.64283	+	9.31693i	−0.0775298	+	0.439693i	−0.998720	+	0.0505806i	$0.983893\pi$
$450$	10.1607	+	18.5984i	0.478981	+	0.876738i
$451$	0.00398914	+	0.0226235i	0.000187841	+	0.00106530i
$452$	−1.94420	+	6.49407i	−0.0914474	+	0.305456i
$453$	−0.614475	+	0.503379i	−0.0288705	+	0.0236508i
$454$	21.3511	−	10.7229i	1.00206	−	0.503252i
$455$	1.95639	+	6.53478i	0.0917168	+	0.306355i
$456$	−2.51207	+	1.22473i	−0.117639	+	0.0573534i
$457$	13.9699	−	18.7648i	0.653483	−	0.877780i	−0.344658	−	0.938728i	$-0.612005\pi$
$457$	13.9699	−	18.7648i	0.653483	−	0.877780i	0.998141	+	0.0609487i	$0.0194126\pi$
$458$	−8.04944	+	13.9420i	−0.376126	+	0.651469i
$459$	36.8667	+	14.9152i	1.72079	+	0.696183i
$460$	−10.5432	−	18.2614i	−0.491579	−	0.851441i
$461$	−12.6693	−	1.48083i	−0.590069	−	0.0689691i	−0.184181	−	0.982892i	$-0.558963\pi$
$461$	−12.6693	−	1.48083i	−0.590069	−	0.0689691i	−0.405887	+	0.913923i	$0.633037\pi$
$462$	0.0246053	+	0.00613887i	0.00114474	+	0.000285606i
$463$	−20.2443	−	4.79798i	−0.940831	−	0.222981i	−0.268540	−	0.963268i	$-0.586541\pi$
$463$	−20.2443	−	4.79798i	−0.940831	−	0.222981i	−0.672290	+	0.740287i	$0.734689\pi$
$464$	−4.76224	−	3.13217i	−0.221081	−	0.145408i
$465$	31.9903	−	11.2181i	1.48352	−	0.520229i
$466$	5.48272	+	5.81134i	0.253982	+	0.269205i
$467$	19.1840	−	16.0973i	0.887728	−	0.744892i	−0.0800254	−	0.996793i	$-0.525500\pi$
$467$	19.1840	−	16.0973i	0.887728	−	0.744892i	0.967753	+	0.251901i	$0.0810557\pi$
$468$	−0.950256	+	2.06747i	−0.0439256	+	0.0955689i
$469$	8.33905	+	6.99729i	0.385062	+	0.323105i
$470$	−0.910294	−	15.6291i	−0.0419887	−	0.720919i
$471$	1.35050	+	29.0935i	0.0622277	+	1.34056i
$472$	−6.72082	−	9.02763i	−0.309351	−	0.415530i
$473$	0.0394363	−	0.00460944i	0.00181328	−	0.000211942i
$474$	−0.938820	+	1.23049i	−0.0431214	+	0.0565184i
$475$	9.52332	−	6.26359i	0.436960	−	0.287393i
$476$	18.6225	−	6.77804i	0.853562	−	0.310671i
$477$	11.6010	−	35.6662i	0.531171	−	1.63304i
$478$	−14.8373	−	5.40033i	−0.678642	−	0.247006i
$479$	−7.16409	+	1.69792i	−0.327336	+	0.0775800i	−0.390998	−	0.920392i	$-0.627870\pi$
$479$	−7.16409	+	1.69792i	−0.327336	+	0.0775800i	0.0636624	+	0.997971i	$0.479722\pi$
$480$	2.94639	+	5.24517i	0.134484	+	0.239408i
$481$	−0.484782	+	8.32338i	−0.0221042	+	0.379514i
$482$	−2.84989	+	3.02070i	−0.129809	+	0.137589i
$483$	27.0780	−	2.84174i	1.23209	−	0.129304i
$484$	−4.35686	−	10.1003i	−0.198039	−	0.459107i
$485$	−47.1851			−2.14256
$486$	−12.4966	−	9.31854i	−0.566857	−	0.422698i
$487$	−3.36873			−0.152652			−0.0763258	−	0.997083i	$-0.524319\pi$
$487$	−3.36873			−0.152652			−0.0763258	+	0.997083i	$0.524319\pi$
$488$	−2.15572	−	4.99751i	−0.0975847	−	0.226227i
$489$	−15.2537	+	1.60082i	−0.689796	+	0.0723915i
$490$	0.704336	−	0.746553i	0.0318187	−	0.0337258i
$491$	0.529704	−	9.09467i	0.0239052	−	0.410437i	−0.965035	−	0.262121i	$-0.915578\pi$
$491$	0.529704	−	9.09467i	0.0239052	−	0.410437i	0.988940	−	0.148315i	$-0.0473851\pi$
$492$	−3.44628	−	6.13507i	−0.155370	−	0.276590i
$493$	42.4495	−	10.0607i	1.91183	−	0.453112i
$494$	1.15000	+	0.418567i	0.0517411	+	0.0188322i
$495$	−0.0394122	−	0.0437992i	−0.00177145	−	0.00196863i
$496$	5.29513	−	1.92727i	0.237758	−	0.0865370i
$497$	19.6813	−	12.9446i	0.882827	−	0.580644i
$498$	0.0926970	−	0.121496i	0.00415385	−	0.00544437i
$499$	33.6920	−	3.93803i	1.50826	−	0.176290i	0.678579	−	0.734528i	$-0.262596\pi$
$499$	33.6920	−	3.93803i	1.50826	−	0.176290i	0.829681	+	0.558238i	$0.188522\pi$
$500$	−4.28172	−	5.75135i	−0.191484	−	0.257208i
$501$	0.393556	+	8.47830i	0.0175828	+	0.378783i
$502$	0.170050	+	2.91964i	0.00758969	+	0.130310i
$503$	−25.3053	−	21.2337i	−1.12831	−	0.946762i	−0.129313	−	0.991604i	$-0.541277\pi$
$503$	−25.3053	−	21.2337i	−1.12831	−	0.946762i	−0.998994	+	0.0448417i	$0.985722\pi$
$504$	−7.73451	+	0.719611i	−0.344523	+	0.0320540i
$505$	−21.1461	+	17.7437i	−0.940989	+	0.789584i
$506$	0.0235573	+	0.0249693i	0.00104725	+	0.00111002i
$507$	−20.3078	+	7.12140i	−0.901902	+	0.316273i
$508$	3.36549	+	2.21352i	0.149319	+	0.0982089i
$509$	−16.6694	−	3.95071i	−0.738856	−	0.175112i	−0.156079	−	0.987744i	$-0.549886\pi$
$509$	−16.6694	−	3.95071i	−0.738856	−	0.175112i	−0.582777	+	0.812632i	$0.698034\pi$
$510$	−44.6754	−	11.1462i	−1.97826	−	0.493564i
$511$	−6.21319	−	0.726218i	−0.274855	−	0.0321260i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	−4.44626	+	7.10809i	−0.196307	+	0.313830i
$514$	−1.99616	+	3.45745i	−0.0880468	+	0.152501i
$515$	7.17675	−	9.64005i	0.316245	−	0.424791i
$516$	−10.9320	+	5.32977i	−0.481254	+	0.234630i
$517$	0.00730972	+	0.0244162i	0.000321481	+	0.00107382i
$518$	−25.4356	+	12.7742i	−1.11758	+	0.561268i
$519$	−24.6487	+	20.1922i	−1.08196	+	0.886340i
$520$	0.755564	−	2.52376i	0.0331337	−	0.110674i
$521$	−5.63546	−	31.9603i	−0.246894	−	1.40020i	−0.816053	−	0.577977i	$-0.803842\pi$
$521$	−5.63546	−	31.9603i	−0.246894	−	1.40020i	0.569159	−	0.822227i	$-0.307269\pi$
$522$	−17.0951	−	0.403235i	−0.748232	−	0.0176491i
$523$	3.63101	−	20.5925i	0.158773	−	0.900446i	−0.796482	−	0.604662i	$-0.793308\pi$
$523$	3.63101	−	20.5925i	0.158773	−	0.900446i	0.955255	−	0.295784i	$-0.0955808\pi$
$524$	16.7259	+	8.40008i	0.730676	+	0.366959i
$525$	30.9121	−	6.94239i	1.34912	−	0.302991i
$526$	5.80926	−	13.4674i	0.253296	−	0.587206i
$527$	−17.0822	+	39.6009i	−0.744110	+	1.72504i
$528$	−0.00663655	−	0.00720262i	−0.000288819	−	0.000313454i
$529$	12.3817	+	6.21834i	0.538336	+	0.270363i
$530$	−7.54040	+	42.7638i	−0.327534	+	1.85754i
$531$	−31.4466	−	12.2929i	−1.36467	−	0.533468i
$532$	0.725490	+	4.11446i	0.0314540	+	0.178384i
$533$	−0.883754	+	2.95194i	−0.0382796	+	0.127863i
$534$	3.40611	+	20.7445i	0.147397	+	0.897704i
$535$	30.5822	−	15.3589i	1.32218	−	0.664025i
$536$	−1.20577	−	4.02754i	−0.0520812	−	0.173963i
$537$	7.50471	+	5.06369i	0.323852	+	0.218515i
$538$	−2.73035	+	3.66750i	−0.117714	+	0.158117i
$539$	−0.000835447		0.00144704i	−3.59853e−5		6.23283e-5i
$540$	15.8319	+	8.66536i	0.681295	+	0.372898i
$541$	1.48708	+	2.57570i	0.0639347	+	0.110738i	0.896221	−	0.443608i	$-0.146302\pi$
$541$	1.48708	+	2.57570i	0.0639347	+	0.110738i	−0.832286	+	0.554346i	$0.812968\pi$
$542$	−6.74343	−	0.788194i	−0.289655	−	0.0338558i
$543$	7.13727	−	7.38855i	0.306290	−	0.317073i
$544$	−7.44735	−	1.76506i	−0.319303	−	0.0756761i
$545$	−14.4403	−	9.49752i	−0.618553	−	0.406829i
$546$	2.57979	+	2.21706i	0.110405	+	0.0948815i
$547$	−16.3477	−	17.3276i	−0.698978	−	0.740873i	0.276490	−	0.961017i	$-0.410829\pi$
$547$	−16.3477	−	17.3276i	−0.698978	−	0.740873i	−0.975467	+	0.220144i	$0.929347\pi$
$548$	1.79506	−	1.50623i	0.0766810	−	0.0643430i
$549$	−13.4264	−	9.29152i	−0.573024	−	0.396552i
$550$	0.0306000	+	0.0256765i	0.00130479	+	0.00109485i
$551$	0.534762	+	9.18150i	0.0227816	+	0.391145i
$552$	−9.34030	−	4.82962i	−0.397550	−	0.205562i
$553$	1.38169	+	1.85593i	0.0587553	+	0.0789221i
$554$	7.07160	−	0.826551i	0.300443	−	0.0351168i
$555$	65.5897	+	8.45144i	2.78413	+	0.358744i
$556$	−18.7312	+	12.3197i	−0.794380	+	0.522472i
$557$	8.09397	−	2.94596i	0.342953	−	0.124825i	−0.164801	−	0.986327i	$-0.552698\pi$
$557$	8.09397	−	2.94596i	0.342953	−	0.124825i	0.507754	+	0.861502i	$0.330476\pi$
$558$	10.4118	−	13.3180i	0.440768	−	0.563795i
$559$	5.00457	+	1.82151i	0.211671	+	0.0770418i
$560$	8.75120	−	2.07407i	0.369806	−	0.0876456i
$561$	0.0749544		0.000883881i	0.00316458		3.73175e-5i
$562$	0.719719	−	12.3571i	0.0303595	−	0.521253i
$563$	9.02702	−	9.56809i	0.380444	−	0.403247i	−0.508649	−	0.860974i	$-0.669855\pi$
$563$	9.02702	−	9.56809i	0.380444	−	0.403247i	0.889093	+	0.457727i	$0.151336\pi$
$564$	−4.58781	−	6.31665i	−0.193182	−	0.265979i
$565$	−9.32590	−	21.6199i	−0.392343	−	0.909554i
$566$	10.2720			0.431765
$567$	−18.5381	+	14.1210i	−0.778528	+	0.593027i
$568$	−9.09767			−0.381730
$569$	−8.60869	−	19.9572i	−0.360895	−	0.836649i	−0.997837	−	0.0657372i	$-0.979060\pi$
$569$	−8.60869	−	19.9572i	−0.360895	−	0.836649i	0.636942	−	0.770912i	$-0.280199\pi$
$570$	3.94962	−	8.86727i	0.165432	−	0.371409i
$571$	13.4312	−	14.2362i	0.562078	−	0.595768i	−0.382540	−	0.923939i	$-0.624951\pi$
$571$	13.4312	−	14.2362i	0.562078	−	0.595768i	0.944618	+	0.328171i	$0.106432\pi$
$572$	−0.000249370		0.00428152i	−1.04267e−5		0.000179019i
$573$	3.46129	−	5.83513i	0.144597	−	0.243766i
$574$	−10.2359	+	2.42596i	−0.427240	+	0.101258i
$575$	40.3002	+	14.6681i	1.68064	+	0.611701i
$576$	2.64840	+	1.40924i	0.110350	+	0.0587184i
$577$	14.6056	−	5.31600i	0.608039	−	0.221308i	−0.0196061	−	0.999808i	$-0.506241\pi$
$577$	14.6056	−	5.31600i	0.608039	−	0.221308i	0.627645	+	0.778500i	$0.284019\pi$
$578$	34.7383	−	22.8478i	1.44492	−	0.950342i
$579$	−3.39154	−	8.12458i	−0.140948	−	0.337646i
$580$	19.6642	−	2.29841i	0.816511	−	0.0954364i
$581$	−0.136425	−	0.183250i	−0.00565986	−	0.00760251i
$582$	−19.8098	+	12.6970i	−0.821141	+	0.526308i
$583$	−0.00411038	−	0.0705724i	−0.000170234	−	0.00292281i
$584$	1.85068	+	1.55291i	0.0765818	+	0.0642597i
$585$	−2.08752	−	7.62262i	−0.0863084	−	0.315157i
$586$	4.48706	−	3.76509i	0.185359	−	0.155534i
$587$	6.11661	+	6.48323i	0.252459	+	0.267591i	0.841192	−	0.540736i	$-0.181854\pi$
$587$	6.11661	+	6.48323i	0.252459	+	0.267591i	−0.588733	+	0.808328i	$0.700373\pi$
$588$	0.0948127	−	0.502955i	0.00391001	−	0.0207415i
$589$	−7.59642	−	4.99624i	−0.313005	−	0.205867i
$590$	38.0379	+	9.01516i	1.56600	+	0.371148i
$591$	8.51139	+	29.7003i	0.350112	+	1.22171i
$592$	10.9183	+	1.27616i	0.448737	+	0.0524499i
$593$	12.2312	+	21.1851i	0.502275	+	0.869966i	0.999997	+	0.00262913i	$0.000836880\pi$
$593$	12.2312	+	21.1851i	0.502275	+	0.869966i	−0.497721	+	0.867337i	$0.665830\pi$
$594$	−0.0283323	−	0.00778284i	−0.00116249	−	0.000319334i
$595$	−34.4171	+	59.6121i	−1.41096	+	2.44386i
$596$	−0.0485497	+	0.0652136i	−0.00198867	+	0.00267125i
$597$	3.26180	−	46.5415i	0.133497	−	1.90482i
$598$	1.32060	+	4.41111i	0.0540033	+	0.180384i
$599$	−23.5028	+	11.8036i	−0.960299	+	0.482280i	−0.858662	−	0.512541i	$-0.828704\pi$
$599$	−23.5028	+	11.8036i	−0.960299	+	0.482280i	−0.101636	+	0.994822i	$0.532408\pi$
$600$	−11.4477	−	4.32016i	−0.467351	−	0.176370i
$601$	−0.196924	+	0.657772i	−0.00803269	+	0.0268311i	−0.961912	−	0.273360i	$-0.911865\pi$
$601$	−0.196924	+	0.657772i	−0.00803269	+	0.0268311i	0.953879	+	0.300191i	$0.0970503\pi$
$602$	3.15718	+	17.9052i	0.128677	+	0.729763i
$603$	−9.46786	−	8.33273i	−0.385561	−	0.339335i
$604$	0.0796368	−	0.451643i	0.00324037	−	0.0183771i
$605$	34.1430	+	17.1473i	1.38811	+	0.697136i
$606$	−4.10315	+	13.1395i	−0.166679	+	0.533757i
$607$	−12.2353	+	28.3646i	−0.496615	+	1.15128i	0.467065	+	0.884223i	$0.345312\pi$
$607$	−12.2353	+	28.3646i	−0.496615	+	1.15128i	−0.963680	+	0.267060i	$0.913948\pi$
$608$	0.639088	−	1.48157i	0.0259184	−	0.0600857i
$609$	−7.61986	+	24.4011i	−0.308772	+	0.988783i
$610$	16.8935	+	8.48423i	0.683998	+	0.343516i
$611$	−0.593643	+	3.36672i	−0.0240162	+	0.136203i
$612$	−21.7554	+	7.34214i	−0.879412	+	0.296788i
$613$	1.12584	+	6.38497i	0.0454724	+	0.257887i	0.999066	−	0.0432100i	$-0.0137585\pi$
$613$	1.12584	+	6.38497i	0.0454724	+	0.257887i	−0.953594	+	0.301097i	$0.902647\pi$
$614$	−0.939431	+	3.13792i	−0.0379124	+	0.126636i
$615$	22.8671	+	8.62964i	0.922091	+	0.347981i
$616$	−0.0130840	+	0.00657102i	−0.000527169	+	0.000264754i
$617$	−0.405546	−	1.35462i	−0.0163266	−	0.0545348i	0.949438	−	0.313954i	$-0.101654\pi$
$617$	−0.405546	−	1.35462i	−0.0163266	−	0.0545348i	−0.965765	+	0.259420i	$0.916469\pi$
$618$	0.418987	−	5.97838i	0.0168541	−	0.240486i
$619$	19.8883	−	26.7146i	0.799378	−	1.07375i	−0.196270	−	0.980550i	$-0.562883\pi$
$619$	19.8883	−	26.7146i	0.799378	−	1.07375i	0.995647	−	0.0932008i	$-0.0297098\pi$
$620$	−9.78616	+	16.9501i	−0.393022	+	0.680733i
$621$	−31.4418	+	2.55174i	−1.26172	+	0.102398i
$622$	10.4677	+	18.1305i	0.419715	+	0.726968i
$623$	31.2145	+	3.64845i	1.25058	+	0.146172i
$624$	−0.361908	−	1.26287i	−0.0144879	−	0.0505551i
$625$	−10.1362	−	2.40232i	−0.405448	−	0.0960929i
$626$	1.62928	+	1.07159i	0.0651190	+	0.0428294i
$627$	−0.00292746	+	0.0155294i	−0.000116911	+	0.000620183i
$628$	−11.5393	−	12.2310i	−0.460469	−	0.488068i
$629$	−64.4500	+	54.0799i	−2.56979	+	2.15631i
$630$	18.9730	−	19.1831i	0.755904	−	0.764273i
$631$	31.6008	+	26.5162i	1.25801	+	1.05559i	0.995891	+	0.0905561i	$0.0288644\pi$
$631$	31.6008	+	26.5162i	1.25801	+	1.05559i	0.262115	+	0.965037i	$0.415580\pi$
$632$	−0.0519575	−	0.892075i	−0.00206676	−	0.0354848i
$633$	−25.9079	+	16.6056i	−1.02975	+	0.660013i
$634$	−3.32923	−	4.47193i	−0.132220	−	0.177603i
$635$	−13.8967	+	1.62430i	−0.551475	+	0.0644582i
$636$	8.34158	+	19.9826i	0.330765	+	0.792361i
$637$	−0.187252	+	0.123158i	−0.00741921	+	0.00487969i
$638$	−0.0302869	+	0.0110235i	−0.00119907	+	0.000436425i
$639$	−23.1503	+	14.4559i	−0.915812	+	0.571865i
$640$	−3.26390	−	1.18796i	−0.129017	−	0.0469584i
$641$	−7.46425	+	1.76906i	−0.294820	+	0.0698736i	−0.375364	−	0.926877i	$-0.622482\pi$
$641$	−7.46425	+	1.76906i	−0.294820	+	0.0698736i	0.0805441	+	0.996751i	$0.474334\pi$
$642$	8.70642	−	14.6775i	0.343615	−	0.579275i
$643$	0.642757	−	11.0357i	0.0253478	−	0.435206i	−0.961630	−	0.274350i	$-0.911537\pi$
$643$	0.642757	−	11.0357i	0.0253478	−	0.435206i	0.986978	−	0.160856i	$-0.0514255\pi$
$644$	−10.7873	+	11.4338i	−0.425078	+	0.450556i
$645$	17.1879	−	38.5884i	0.676773	−	1.51942i
$646$	4.89136	+	11.3395i	0.192448	+	0.446145i
$647$	14.9803			0.588938			0.294469	−	0.955661i	$-0.404857\pi$
$647$	14.9803			0.588938			0.294469	+	0.955661i	$0.404857\pi$
$648$	8.97847	−	0.622200i	0.352707	−	0.0244423i
$649$	−0.0636400			−0.00249809
$650$	2.12221	+	4.91984i	0.0832400	+	0.192972i
$651$	−14.8512	−	20.4476i	−0.582062	−	0.801403i
$652$	6.07673	−	6.44096i	0.237983	−	0.252247i
$653$	−2.46175	+	42.2667i	−0.0963359	+	1.65402i	0.511002	+	0.859580i	$0.329275\pi$
$653$	−2.46175	+	42.2667i	−0.0963359	+	1.65402i	−0.607338	+	0.794444i	$0.707762\pi$
$654$	−8.61815	−	0.101627i	−0.336997	−	0.00397395i
$655$	−63.2580	+	14.9924i	−2.47170	+	0.585803i
$656$	3.81766	+	1.38952i	0.149055	+	0.0542515i
$657$	7.17683	+	1.01092i	0.279995	+	0.0394399i
$658$	−10.9670	+	3.99167i	−0.427539	+	0.155611i
$659$	11.5760	−	7.61364i	0.450936	−	0.296585i	−0.303653	−	0.952783i	$-0.598206\pi$
$659$	11.5760	−	7.61364i	0.450936	−	0.296585i	0.754589	+	0.656197i	$0.227836\pi$
$660$	0.0337391	+	0.00434739i	0.00131329	+	0.000169222i
$661$	−9.52822	+	1.11369i	−0.370605	+	0.0433175i	−0.299357	−	0.954141i	$-0.596772\pi$
$661$	−9.52822	+	1.11369i	−0.370605	+	0.0433175i	−0.0712478	+	0.997459i	$0.522698\pi$
$662$	−9.35056	−	12.5600i	−0.363420	−	0.488158i
$663$	8.93130	+	4.61814i	0.346863	+	0.179354i
$664$	0.00513017	+	0.0880816i	0.000199089	+	0.00341823i
$665$	−11.1165	−	9.32782i	−0.431078	−	0.361717i
$666$	29.8108	−	14.1013i	1.15514	−	0.546415i
$667$	−26.5080	+	22.2428i	−1.02639	+	0.861245i
$668$	−3.36274	−	3.56429i	−0.130108	−	0.137907i
$669$	22.4449	+	19.2890i	0.867769	+	0.745757i
$670$	12.2003	+	8.02427i	0.471339	+	0.310005i
$671$	−0.0299460	−	0.00709734i	−0.00115605	−	0.000273990i
$672$	3.11591	−	3.22562i	0.120199	−	0.124431i
$673$	6.31539	+	0.738163i	0.243440	+	0.0284541i	0.236938	−	0.971525i	$-0.423856\pi$
$673$	6.31539	+	0.738163i	0.243440	+	0.0284541i	0.00650232	+	0.999979i	$0.497930\pi$
$674$	−1.73667	−	3.00799i	−0.0668938	−	0.115864i
$675$	−35.9949	+	7.19673i	−1.38544	+	0.277002i
$676$	6.21237	−	10.7601i	0.238937	−	0.413851i
$677$	−8.40427	+	11.2889i	−0.323003	+	0.433868i	−0.933733	−	0.357971i	$-0.883469\pi$
$677$	−8.40427	+	11.2889i	−0.323003	+	0.433868i	0.610730	+	0.791839i	$0.290876\pi$
$678$	−9.73297	−	6.56719i	−0.373793	−	0.252211i
$679$	10.0884	+	33.6975i	0.387156	+	1.29319i
$680$	23.7563	−	11.9309i	0.911014	−	0.457529i
$681$	6.70503	+	40.8362i	0.256937	+	1.56485i
$682$	0.00913845	−	0.0305245i	0.000349929	−	0.00116884i
$683$	−3.23767	−	18.3618i	−0.123886	−	0.702593i	−0.981963	−	0.189072i	$-0.939452\pi$
$683$	−3.23767	−	18.3618i	−0.123886	−	0.702593i	0.858077	−	0.513521i	$-0.171659\pi$
$684$	−0.727915	−	4.78556i	−0.0278325	−	0.182980i
$685$	−1.41334	+	8.01543i	−0.0540008	+	0.306254i
$686$	−16.8810	−	8.47794i	−0.644518	−	0.323689i
$687$	−18.8947	−	20.5064i	−0.720879	−	0.782367i
$688$	2.78117	−	6.44748i	0.106031	−	0.245808i
$689$	3.75570	−	8.70670i	0.143081	−	0.331699i
$690$	35.6351	−	8.00309i	1.35661	−	0.304672i
$691$	−32.4240	−	16.2839i	−1.23347	−	0.619470i	−0.291948	−	0.956434i	$-0.594304\pi$
$691$	−32.4240	−	16.2839i	−1.23347	−	0.619470i	−0.941517	+	0.336964i	$0.890600\pi$
$692$	3.19450	−	18.1169i	0.121437	−	0.688702i
$693$	−0.0228529	+	0.0375108i	−0.000868110	+	0.00142492i
$694$	2.21258	+	12.5482i	0.0839884	+	0.476322i
$695$	22.3337	−	74.5998i	0.847166	−	2.82973i
$696$	7.63716	−	6.25637i	0.289486	−	0.237147i
$697$	−27.7869	+	13.9551i	−1.05250	+	0.528587i
$698$	−9.48762	−	31.6909i	−0.359112	−	1.19952i
$699$	−12.4386	+	6.06433i	−0.470473	+	0.229374i
$700$	−10.9230	+	14.6722i	−0.412852	+	0.554556i
$701$	2.90137	−	5.02533i	0.109583	−	0.189804i	−0.806018	−	0.591891i	$-0.798382\pi$
$701$	2.90137	−	5.02533i	0.109583	−	0.189804i	0.915602	+	0.402087i	$0.131715\pi$
$702$	−2.92757	−	2.63848i	−0.110494	−	0.0995831i
$703$	−8.86845	−	15.3606i	−0.334480	−	0.579336i
$704$	0.00561631		0.000656452i	0.000211673		2.47410e-5i
$705$	26.3099	+	6.56415i	0.990887	+	0.247220i
$706$	−23.3819	−	5.54160i	−0.879988	−	0.208561i
$707$	17.1929	+	11.3079i	0.646604	+	0.425278i
$708$	18.3954	−	6.45076i	0.691341	−	0.242435i
$709$	5.74553	+	6.08990i	0.215778	+	0.228711i	0.826217	−	0.563352i	$-0.190489\pi$
$709$	5.74553	+	6.08990i	0.215778	+	0.228711i	−0.610439	+	0.792063i	$0.709007\pi$
$710$	24.2067	−	20.3118i	0.908461	−	0.762290i
$711$	−1.54969	−	2.18745i	−0.0581178	−	0.0820359i
$712$	−9.29766	−	7.80166i	−0.348444	−	0.292380i
$713$	−1.98908	−	34.1513i	−0.0744918	−	1.27897i
$714$	1.59164	+	34.2883i	0.0595655	+	1.28321i
$715$	−0.00889558	−	0.0119488i	−0.000332676	−	0.000446861i
$716$	−5.19156	+	0.606807i	−0.194018	+	0.0226774i
$717$	16.5888	−	21.7426i	0.619519	−	0.811991i
$718$	−30.4304	+	20.0144i	−1.13565	+	0.746931i
$719$	22.2781	−	8.10856i	0.830833	−	0.302398i	0.108632	−	0.994082i	$-0.465353\pi$
$719$	22.2781	−	8.10856i	0.830833	−	0.302398i	0.722201	+	0.691684i	$0.243131\pi$
$720$	−10.1931	+	2.16328i	−0.379874	+	0.0806207i
$721$	−8.41891	−	3.06423i	−0.313537	−	0.114118i
$722$	15.9545	−	3.78130i	0.593766	−	0.140725i
$723$	−3.52281	−	6.27131i	−0.131015	−	0.233233i
$724$	−0.344859	+	5.92099i	−0.0128166	+	0.220052i
$725$	−27.6324	+	29.2886i	−1.02624	+	1.08775i
$726$	18.9484	−	1.98857i	0.703243	−	0.0738027i
$727$	7.19330	+	16.6759i	0.266785	+	0.618477i	0.997969	−	0.0637036i	$-0.0202912\pi$
$727$	7.19330	+	16.6759i	0.266785	+	0.618477i	−0.731184	+	0.682180i	$0.761032\pi$
$728$	−1.96390			−0.0727869
$729$	21.8583	−	15.8497i	0.809567	−	0.587027i
$730$	−8.39130			−0.310576
$731$	21.2861	+	49.3468i	0.787296	+	1.82516i
$732$	9.37543	−	0.983917i	0.346526	−	0.0363666i
$733$	29.2769	−	31.0317i	1.08137	−	1.14618i	0.0927557	−	0.995689i	$-0.470432\pi$
$733$	29.2769	−	31.0317i	1.08137	−	1.14618i	0.988611	−	0.150493i	$-0.0480861\pi$
$734$	−1.09138	+	18.7383i	−0.0402837	+	0.691645i
$735$	0.870645	+	1.54993i	0.0321142	+	0.0571699i
$736$	5.90723	−	1.40004i	0.217743	−	0.0516062i
$737$	−0.0223389	−	0.00813071i	−0.000822866	−	0.000299499i
$738$	11.9225	−	2.53031i	0.438872	−	0.0931419i
$739$	−35.1318	+	12.7869i	−1.29234	+	0.470375i	−0.894496	−	0.447076i	$-0.852465\pi$
$739$	−35.1318	+	12.7869i	−1.29234	+	0.470375i	−0.397849	+	0.917451i	$0.630243\pi$
$740$	−31.9000	+	20.9810i	−1.17267	+	0.771276i
$741$	−1.28576	+	1.68522i	−0.0472335	+	0.0619080i
$742$	32.1521	−	3.75804i	1.18034	−	0.137962i
$743$	−1.51077	−	2.02932i	−0.0554248	−	0.0744485i	0.773547	−	0.633739i	$-0.218481\pi$
$743$	−1.51077	−	2.02932i	−0.0554248	−	0.0744485i	−0.828971	+	0.559291i	$0.811073\pi$
$744$	0.452566	+	9.74954i	0.0165919	+	0.357435i
$745$	−0.0164195	−	0.281912i	−0.000601563	−	0.0103284i
$746$	−12.9942	−	10.9035i	−0.475753	−	0.399204i
$747$	0.153013	+	0.215984i	0.00559845	+	0.00790245i
$748$	−0.0331528	+	0.0278185i	−0.00121219	+	0.00101715i
$749$	−17.5073	−	18.5566i	−0.639702	−	0.678044i
$750$	11.7194	−	4.10967i	0.427931	−	0.150064i
$751$	−6.61935	−	4.35361i	−0.241543	−	0.158866i	0.422966	−	0.906146i	$-0.360989\pi$
$751$	−6.61935	−	4.35361i	−0.241543	−	0.158866i	−0.664509	+	0.747280i	$0.731359\pi$
$752$	4.38583	+	1.03946i	0.159935	+	0.0379053i
$753$	−4.91488	−	1.22623i	−0.179108	−	0.0446864i
$754$	−4.29398	−	0.501895i	−0.156378	−	0.0182779i
$755$	0.796462	+	1.37951i	0.0289862	+	0.0502056i
$756$	2.80350	−	13.1591i	0.101962	−	0.478592i
$757$	−22.1532	+	38.3705i	−0.805173	+	1.39460i	0.111001	+	0.993820i	$0.464594\pi$
$757$	−22.1532	+	38.3705i	−0.805173	+	1.39460i	−0.916174	+	0.400781i	$0.868739\pi$
$758$	−3.71370	+	4.98837i	−0.134888	+	0.181186i
$759$	−0.0534444	+	0.0260563i	−0.00193991	+	0.000945783i
$760$	1.60736	+	5.36896i	0.0583051	+	0.194753i
$761$	18.0121	−	9.04603i	0.652939	−	0.327918i	−0.0913082	−	0.995823i	$-0.529105\pi$
$761$	18.0121	−	9.04603i	0.652939	−	0.327918i	0.744247	+	0.667904i	$0.232809\pi$
$762$	−5.39720	+	4.42140i	−0.195520	+	0.160170i
$763$	−3.69531	+	12.3432i	−0.133779	+	0.446854i
$764$	0.680185	+	3.85752i	0.0246082	+	0.139560i
$765$	41.4936	−	68.1078i	1.50021	−	2.46244i
$766$	4.06059	−	23.0288i	0.146715	−	0.832063i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.396080 - 0.918216i) q^{2} +(1.72259 - 0.180780i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.201959 - 3.46750i) q^{5} +(-0.848278 - 1.51011i) q^{6} +(-2.51951 + 0.597135i) q^{7} +(0.939693 + 0.342020i) q^{8} +(2.93464 - 0.622818i) q^{9} +O(q^{10})\)	\(q+(-0.396080 - 0.918216i) q^{2} +(1.72259 - 0.180780i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.201959 - 3.46750i) q^{5} +(-0.848278 - 1.51011i) q^{6} +(-2.51951 + 0.597135i) q^{7} +(0.939693 + 0.342020i) q^{8} +(2.93464 - 0.622818i) q^{9} +(-3.26390 + 1.18796i) q^{10} +(0.00472430 - 0.00310722i) q^{11} +(-1.05062 + 1.37703i) q^{12} +(0.753337 - 0.0880524i) q^{13} +(1.54623 + 2.07694i) q^{14} +(-0.278960 - 6.00959i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(5.86304 + 4.91968i) q^{17} +(-1.73423 - 2.44795i) q^{18} +(-1.23604 + 1.03716i) q^{19} +(2.38357 + 2.52644i) q^{20} +(-4.23214 + 1.48410i) q^{21} +(-0.00472430 - 0.00310722i) q^{22} +(-5.90723 - 1.40004i) q^{23} +(1.68054 + 0.419283i) q^{24} +(-7.01655 - 0.820117i) q^{25} +(-0.379233 - 0.656850i) q^{26} +(4.94259 - 1.60338i) q^{27} +(1.29465 - 2.24240i) q^{28} +(3.40377 - 4.57206i) q^{29} +(-5.40761 + 2.63642i) q^{30} +(1.61612 + 5.39823i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(0.00757632 - 0.00620653i) q^{33} +(2.19509 - 7.33213i) q^{34} +(1.56173 + 8.85699i) q^{35} +(-1.56085 + 2.56198i) q^{36} +(-1.90884 + 10.8256i) q^{37} +(1.44191 + 0.724153i) q^{38} +(1.28177 - 0.287866i) q^{39} +(1.37573 - 3.18931i) q^{40} +(-1.60914 + 3.73041i) q^{41} +(3.03898 + 3.29820i) q^{42} +(6.27486 + 3.15135i) q^{43} +(-0.000981901 + 0.00556864i) q^{44} +(-1.56695 - 10.3016i) q^{45} +(1.05420 + 5.97864i) q^{46} +(-1.29272 + 4.31797i) q^{47} +(-0.280633 - 1.70916i) q^{48} +(-0.264065 + 0.132618i) q^{49} +(2.02607 + 6.76754i) q^{50} +(10.9890 + 7.41467i) q^{51} +(-0.452924 + 0.608383i) q^{52} +(6.25091 - 10.8269i) q^{53} +(-3.42991 - 3.90329i) q^{54} +(-0.00982017 - 0.0170090i) q^{55} +(-2.57180 - 0.300600i) q^{56} +(-1.94169 + 2.01005i) q^{57} +(-5.54631 - 1.31450i) q^{58} +(-9.40314 - 6.18454i) q^{59} +(4.56265 + 3.92112i) q^{60} +(-3.73496 - 3.95883i) q^{61} +(4.31663 - 3.62208i) q^{62} +(-7.02194 + 3.32157i) q^{63} +(0.766044 + 0.642788i) q^{64} +(-0.153179 - 2.62998i) q^{65} +(-0.00869976 - 0.00449841i) q^{66} +(-2.51055 - 3.37226i) q^{67} +(-7.60191 + 0.888536i) q^{68} +(-10.4288 - 1.34379i) q^{69} +(7.51406 - 4.94208i) q^{70} +(-8.54902 + 3.11159i) q^{71} +(2.97067 + 0.418447i) q^{72} +(2.27020 + 0.826284i) q^{73} +(10.6963 - 2.53506i) q^{74} +(-12.2349 - 0.144277i) q^{75} +(0.0938186 - 1.61080i) q^{76} +(-0.0100475 + 0.0106497i) q^{77} +(-0.772008 - 1.06293i) q^{78} +(-0.353932 - 0.820506i) q^{79} -3.47337 q^{80} +(8.22419 - 3.65549i) q^{81} +4.06267 q^{82} +(0.0349465 + 0.0810150i) q^{83} +(1.82478 - 4.09679i) q^{84} +(18.2431 - 19.3365i) q^{85} +(0.408278 - 7.00987i) q^{86} +(5.03677 - 8.49112i) q^{87} +(0.00550212 - 0.00130403i) q^{88} +(-11.4053 - 4.15118i) q^{89} +(-8.83849 + 5.51906i) q^{90} +(-1.84546 + 0.671693i) q^{91} +(5.07214 - 3.33600i) q^{92} +(3.75981 + 9.00678i) q^{93} +(4.47685 - 0.523269i) q^{94} +(3.34672 + 4.49542i) q^{95} +(-1.45823 + 0.934648i) q^{96} +(-0.789886 - 13.5618i) q^{97} +(0.226363 + 0.189941i) q^{98} +(0.0119289 - 0.0120610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more