LMFDB - Embedded newform 243.2.i.a.4.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	243.4
Dual form			243.2.i.a.61.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.905616 + 0.0351420i) q^{2} +(-1.29585 + 1.14925i) q^{3} +(-1.17508 - 0.0913345i) q^{4} +(-1.68295 - 2.08654i) q^{5} +(-1.21393 + 0.995240i) q^{6} +(0.467604 - 0.212552i) q^{7} +(-2.86130 - 0.334438i) q^{8} +(0.358453 - 2.97851i) q^{9} +(-1.45079 - 1.94874i) q^{10} +(-0.113535 - 5.85382i) q^{11} +(1.62769 - 1.23210i) q^{12} +(-0.532128 - 0.170620i) q^{13} +(0.430939 - 0.176058i) q^{14} +(4.57881 + 0.769703i) q^{15} +(-0.250550 - 0.0391853i) q^{16} +(1.26092 + 4.21177i) q^{17} +(0.429292 - 2.68479i) q^{18} +(-6.87969 + 1.63052i) q^{19} +(1.78703 + 2.60556i) q^{20} +(-0.361669 + 0.812829i) q^{21} +(0.102896 - 5.30530i) q^{22} +(-5.83346 + 4.16951i) q^{23} +(4.09217 - 2.85497i) q^{24} +(-0.462778 + 2.13642i) q^{25} +(-0.475908 - 0.173216i) q^{26} +(2.95855 + 4.27165i) q^{27} +(-0.568885 + 0.207057i) q^{28} +(-1.25076 - 9.15719i) q^{29} +(4.11959 + 0.857964i) q^{30} +(2.75759 + 2.70463i) q^{31} +(5.42804 + 1.06603i) q^{32} +(6.87462 + 7.45519i) q^{33} +(0.993900 + 3.85856i) q^{34} +(-1.23045 - 0.617957i) q^{35} +(-0.693251 + 3.46725i) q^{36} +(-2.71437 - 1.78527i) q^{37} +(-6.28766 + 1.23486i) q^{38} +(0.885643 - 0.390450i) q^{39} +(4.11762 + 6.53305i) q^{40} +(4.51286 - 8.56746i) q^{41} +(-0.356098 + 0.723401i) q^{42} +(0.245349 - 0.717059i) q^{43} +(-0.401243 + 6.88908i) q^{44} +(-6.81802 + 4.26477i) q^{45} +(-5.42940 + 3.57098i) q^{46} +(5.06358 - 4.96633i) q^{47} +(0.369709 - 0.237166i) q^{48} +(-4.42917 + 5.07527i) q^{49} +(-0.494177 + 1.91851i) q^{50} +(-6.47433 - 4.00870i) q^{51} +(0.609710 + 0.249094i) q^{52} +(0.0666653 + 0.0559388i) q^{53} +(2.52919 + 3.97245i) q^{54} +(-12.0231 + 10.0886i) q^{55} +(-1.40904 + 0.451791i) q^{56} +(7.04117 - 10.0194i) q^{57} +(-0.810907 - 8.33686i) q^{58} +(4.40083 - 2.42828i) q^{59} +(-5.31016 - 1.32267i) q^{60} +(8.82405 - 0.685859i) q^{61} +(2.40227 + 2.54626i) q^{62} +(-0.465474 - 1.46895i) q^{63} +(5.37178 + 1.27313i) q^{64} +(0.539543 + 1.39745i) q^{65} +(5.96378 + 6.99313i) q^{66} +(-1.01498 + 7.43096i) q^{67} +(-1.09700 - 5.06433i) q^{68} +(2.76749 - 12.1072i) q^{69} +(-1.09260 - 0.602872i) q^{70} +(0.0961826 - 0.222976i) q^{71} +(-2.02177 + 8.40253i) q^{72} +(5.74951 - 7.72293i) q^{73} +(-2.39544 - 1.71216i) q^{74} +(-1.85559 - 3.30032i) q^{75} +(8.23311 - 1.28763i) q^{76} +(-1.29733 - 2.71314i) q^{77} +(0.815774 - 0.322475i) q^{78} +(-4.46842 + 7.08963i) q^{79} +(0.339903 + 0.588729i) q^{80} +(-8.74302 - 2.13531i) q^{81} +(4.38800 - 7.60024i) q^{82} +(-2.81318 - 5.34070i) q^{83} +(0.499229 - 0.922106i) q^{84} +(6.66593 - 9.71916i) q^{85} +(0.247391 - 0.640758i) q^{86} +(12.1447 + 10.4289i) q^{87} +(-1.63288 + 16.7875i) q^{88} +(-3.97177 - 9.20760i) q^{89} +(-6.32439 + 3.62264i) q^{90} +(-0.285091 + 0.0333223i) q^{91} +(7.23561 - 4.36671i) q^{92} +(-6.68171 - 0.335630i) q^{93} +(4.76019 - 4.31964i) q^{94} +(14.9803 + 11.6106i) q^{95} +(-8.25906 + 4.85675i) q^{96} +(-1.84316 + 2.28516i) q^{97} +(-4.18949 + 4.44060i) q^{98} +(-17.4763 - 1.76015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{81}\right)$

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 $

$2$	0.905616	+	0.0351420i	0.640367	+	0.0248492i	0.356915	−	0.934137i	$-0.383829\pi$
$2$	0.905616	+	0.0351420i	0.640367	+	0.0248492i	0.283453	+	0.958986i	$0.408520\pi$
$3$	−1.29585	+	1.14925i	−0.748159	+	0.663519i
$3$	−1.29585	+	1.14925i	−0.748159	+	0.663519i
$4$	−1.17508	−	0.0913345i	−0.587540	−	0.0456672i
$5$	−1.68295	−	2.08654i	−0.752640	−	0.933127i	0.246713	−	0.969089i	$-0.420649\pi$
$5$	−1.68295	−	2.08654i	−0.752640	−	0.933127i	−0.999353	+	0.0359614i	$0.988551\pi$
$6$	−1.21393	+	0.995240i	−0.495585	+	0.406305i
$7$	0.467604	−	0.212552i	0.176738	−	0.0803371i	−0.323488	−	0.946232i	$-0.604855\pi$
$7$	0.467604	−	0.212552i	0.176738	−	0.0803371i	0.500225	+	0.865895i	$0.333251\pi$
$8$	−2.86130	−	0.334438i	−1.01162	−	0.118242i
$9$	0.358453	−	2.97851i	0.119484	−	0.992836i
$10$	−1.45079	−	1.94874i	−0.458779	−	0.616247i
$11$	−0.113535	−	5.85382i	−0.0342320	−	1.76499i	−0.487035	−	0.873382i	$-0.661922\pi$
$11$	−0.113535	−	5.85382i	−0.0342320	−	1.76499i	0.452803	−	0.891610i	$-0.350424\pi$
$12$	1.62769	−	1.23210i	0.469875	−	0.355678i
$13$	−0.532128	−	0.170620i	−0.147586	−	0.0473215i	0.230615	−	0.973045i	$-0.425926\pi$
$13$	−0.532128	−	0.170620i	−0.147586	−	0.0473215i	−0.378201	+	0.925724i	$0.623457\pi$
$14$	0.430939	−	0.176058i	0.115173	−	0.0470535i
$15$	4.57881	+	0.769703i	1.18224	+	0.198737i
$16$	−0.250550	−	0.0391853i	−0.0626376	−	0.00979634i
$17$	1.26092	+	4.21177i	0.305818	+	1.02150i	0.963388	+	0.268110i	$0.0863991\pi$
$17$	1.26092	+	4.21177i	0.305818	+	1.02150i	−0.657570	+	0.753393i	$0.728416\pi$
$18$	0.429292	−	2.68479i	0.101185	−	0.632811i
$19$	−6.87969	+	1.63052i	−1.57831	+	0.374066i	−0.924070	−	0.382223i	$-0.875159\pi$
$19$	−6.87969	+	1.63052i	−1.57831	+	0.374066i	−0.654238	+	0.756289i	$0.727011\pi$
$20$	1.78703	+	2.60556i	0.399593	+	0.582621i
$21$	−0.361669	+	0.812829i	−0.0789227	+	0.177374i
$22$	0.102896	−	5.30530i	0.0219375	−	1.13109i
$23$	−5.83346	+	4.16951i	−1.21636	+	0.869403i	−0.994403	−	0.105653i	$-0.966307\pi$
$23$	−5.83346	+	4.16951i	−1.21636	+	0.869403i	−0.221958	+	0.975056i	$0.571245\pi$
$24$	4.09217	−	2.85497i	0.835311	−	0.582768i
$25$	−0.462778	+	2.13642i	−0.0925555	+	0.427284i
$26$	−0.475908	−	0.173216i	−0.0933332	−	0.0339705i
$27$	2.95855	+	4.27165i	0.569373	+	0.822080i
$28$	−0.568885	+	0.207057i	−0.107509	+	0.0391302i
$29$	−1.25076	−	9.15719i	−0.232261	−	1.70045i	−0.624859	−	0.780738i	$-0.714843\pi$
$29$	−1.25076	−	9.15719i	−0.232261	−	1.70045i	0.392598	−	0.919710i	$-0.371576\pi$
$30$	4.11959	+	0.857964i	0.752131	+	0.156642i
$31$	2.75759	+	2.70463i	0.495278	+	0.485765i	0.904383	−	0.426722i	$-0.140332\pi$
$31$	2.75759	+	2.70463i	0.495278	+	0.485765i	−0.409105	+	0.912487i	$0.634159\pi$
$32$	5.42804	+	1.06603i	0.959550	+	0.188450i
$33$	6.87462	+	7.45519i	1.19672	+	1.29778i
$34$	0.993900	+	3.85856i	0.170452	+	0.661737i
$35$	−1.23045	−	0.617957i	−0.207985	−	0.104454i
$36$	−0.693251	+	3.46725i	−0.115542	+	0.577874i
$37$	−2.71437	−	1.78527i	−0.446239	−	0.293496i	0.306432	−	0.951893i	$-0.400865\pi$
$37$	−2.71437	−	1.78527i	−0.446239	−	0.293496i	−0.752671	+	0.658396i	$0.771235\pi$
$38$	−6.28766	+	1.23486i	−1.01999	+	0.200320i
$39$	0.885643	−	0.390450i	0.141816	−	0.0625220i
$40$	4.11762	+	6.53305i	0.651053	+	1.03297i
$41$	4.51286	−	8.56746i	0.704790	−	1.33801i	−0.226599	−	0.973988i	$-0.572761\pi$
$41$	4.51286	−	8.56746i	0.704790	−	1.33801i	0.931390	−	0.364024i	$-0.118597\pi$
$42$	−0.356098	+	0.723401i	−0.0549471	+	0.111623i
$43$	0.245349	−	0.717059i	0.0374153	−	0.109350i	−0.925859	−	0.377868i	$-0.876657\pi$
$43$	0.245349	−	0.717059i	0.0374153	−	0.109350i	0.963275	+	0.268518i	$0.0865338\pi$
$44$	−0.401243	+	6.88908i	−0.0604896	+	1.03857i
$45$	−6.81802	+	4.26477i	−1.01637	+	0.635754i
$46$	−5.42940	+	3.57098i	−0.800522	+	0.526512i
$47$	5.06358	−	4.96633i	0.738600	−	0.724413i	−0.229959	−	0.973200i	$-0.573859\pi$
$47$	5.06358	−	4.96633i	0.738600	−	0.724413i	0.968558	+	0.248787i	$0.0800319\pi$
$48$	0.369709	−	0.237166i	0.0533629	−	0.0342320i
$49$	−4.42917	+	5.07527i	−0.632739	+	0.725039i
$50$	−0.494177	+	1.91851i	−0.0698872	+	0.271319i
$51$	−6.47433	−	4.00870i	−0.906588	−	0.561331i
$52$	0.609710	+	0.249094i	0.0845515	+	0.0345431i
$53$	0.0666653	+	0.0559388i	0.00915718	+	0.00768379i	0.647355	−	0.762189i	$-0.275875\pi$
$53$	0.0666653	+	0.0559388i	0.00915718	+	0.00768379i	−0.638198	+	0.769873i	$0.720320\pi$
$54$	2.52919	+	3.97245i	0.344180	+	0.540581i
$55$	−12.0231	+	10.0886i	−1.62120	+	1.36035i
$56$	−1.40904	+	0.451791i	−0.188291	+	0.0603731i
$57$	7.04117	−	10.0194i	0.932626	−	1.32710i
$58$	−0.810907	−	8.33686i	−0.106477	−	1.09468i
$59$	4.40083	−	2.42828i	0.572940	−	0.316135i	−0.170052	−	0.985435i	$-0.554394\pi$
$59$	4.40083	−	2.42828i	0.572940	−	0.316135i	0.742992	+	0.669300i	$0.233406\pi$
$60$	−5.31016	−	1.32267i	−0.685539	−	0.170755i
$61$	8.82405	−	0.685859i	1.12980	−	0.0878153i	0.501049	−	0.865419i	$-0.332948\pi$
$61$	8.82405	−	0.685859i	1.12980	−	0.0878153i	0.628755	+	0.777604i	$0.283565\pi$
$62$	2.40227	+	2.54626i	0.305089	+	0.323375i
$63$	−0.465474	−	1.46895i	−0.0586442	−	0.185071i
$64$	5.37178	+	1.27313i	0.671472	+	0.159142i
$65$	0.539543	+	1.39745i	0.0669220	+	0.173332i
$66$	5.96378	+	6.99313i	0.734090	+	0.860795i
$67$	−1.01498	+	7.43096i	−0.123999	+	0.907836i	0.818707	+	0.574212i	$0.194691\pi$
$67$	−1.01498	+	7.43096i	−0.123999	+	0.907836i	−0.942706	+	0.333624i	$0.891728\pi$
$68$	−1.09700	−	5.06433i	−0.133031	−	0.614140i
$69$	2.76749	−	12.1072i	0.333166	−	1.45753i
$70$	−1.09260	−	0.602872i	−0.130591	−	0.0720570i
$71$	0.0961826	−	0.222976i	0.0114148	−	0.0264624i	−0.912413	−	0.409270i	$-0.865783\pi$
$71$	0.0961826	−	0.222976i	0.0114148	−	0.0264624i	0.923828	+	0.382807i	$0.125043\pi$
$72$	−2.02177	+	8.40253i	−0.238268	+	0.990248i
$73$	5.74951	−	7.72293i	0.672929	−	0.903900i	−0.326214	−	0.945296i	$-0.605773\pi$
$73$	5.74951	−	7.72293i	0.672929	−	0.903900i	0.999143	+	0.0413956i	$0.0131804\pi$
$74$	−2.39544	−	1.71216i	−0.278464	−	0.199034i
$75$	−1.85559	−	3.30032i	−0.214265	−	0.381089i
$76$	8.23311	−	1.28763i	0.944402	−	0.147702i
$77$	−1.29733	−	2.71314i	−0.147844	−	0.309191i
$78$	0.815774	−	0.322475i	0.0923682	−	0.0365130i
$79$	−4.46842	+	7.08963i	−0.502737	+	0.797646i	−0.997447	−	0.0714120i	$-0.977249\pi$
$79$	−4.46842	+	7.08963i	−0.502737	+	0.797646i	0.494710	+	0.869058i	$0.335274\pi$
$80$	0.339903	+	0.588729i	0.0380023	+	0.0658219i
$81$	−8.74302	−	2.13531i	−0.971447	−	0.237257i
$82$	4.38800	−	7.60024i	0.484573	−	0.839306i
$83$	−2.81318	−	5.34070i	−0.308787	−	0.586218i	0.680406	−	0.732835i	$-0.261803\pi$
$83$	−2.81318	−	5.34070i	−0.308787	−	0.586218i	−0.989193	+	0.146617i	$0.953161\pi$
$84$	0.499229	−	0.922106i	0.0544704	−	0.100610i
$85$	6.66593	−	9.71916i	0.723022	−	1.05419i
$86$	0.247391	−	0.640758i	0.0266768	−	0.0690947i
$87$	12.1447	+	10.4289i	1.30205	+	1.11810i
$88$	−1.63288	+	16.7875i	−0.174066	+	1.78955i
$89$	−3.97177	−	9.20760i	−0.421007	−	0.976004i	−0.988305	−	0.152491i	$-0.951270\pi$
$89$	−3.97177	−	9.20760i	−0.421007	−	0.976004i	0.567298	−	0.823513i	$-0.307989\pi$
$90$	−6.32439	+	3.62264i	−0.666649	+	0.381860i
$91$	−0.285091	+	0.0333223i	−0.0298856	+	0.00349313i
$92$	7.23561	−	4.36671i	0.754364	−	0.455261i
$93$	−6.68171	−	0.335630i	−0.692861	−	0.0348032i
$94$	4.76019	−	4.31964i	0.490976	−	0.445537i
$95$	14.9803	+	11.6106i	1.53695	+	1.19123i
$96$	−8.25906	+	4.85675i	−0.842936	+	0.495690i
$97$	−1.84316	+	2.28516i	−0.187144	+	0.232023i	−0.863243	−	0.504788i	$-0.831570\pi$
$97$	−1.84316	+	2.28516i	−0.187144	+	0.232023i	0.676099	+	0.736811i	$0.263669\pi$
$98$	−4.18949	+	4.44060i	−0.423202	+	0.448568i
$99$	−17.4763	−	1.76015i	−1.75644	−	0.176902i
$100$	0.738929	−	2.46820i	0.0738929	−	0.246820i
$101$	−3.65415	+	7.64200i	−0.363601	+	0.760407i	−0.999939	−	0.0110027i	$-0.996498\pi$
$101$	−3.65415	+	7.64200i	−0.363601	+	0.760407i	0.636338	+	0.771410i	$0.280448\pi$
$102$	−5.72239	−	3.85787i	−0.566601	−	0.381986i
$103$	−6.36265	−	3.83988i	−0.626931	−	0.378355i	0.167357	−	0.985896i	$-0.446477\pi$
$103$	−6.36265	−	3.83988i	−0.626931	−	0.378355i	−0.794288	+	0.607542i	$0.792156\pi$
$104$	1.46552	+	0.666159i	0.143706	+	0.0653223i
$105$	2.30467	−	0.613318i	0.224913	−	0.0598537i
$106$	0.0584074	+	0.0530019i	0.00567302	+	0.00514800i
$107$	−0.751787	−	4.26360i	−0.0726780	−	0.412178i	−0.999341	−	0.0362855i	$-0.988447\pi$
$107$	−0.751787	−	4.26360i	−0.0726780	−	0.412178i	0.926663	−	0.375892i	$-0.122664\pi$
$108$	−3.08638	−	5.28975i	−0.296987	−	0.509006i
$109$	3.55651	−	20.1699i	0.340651	−	1.93193i	−0.0213973	−	0.999771i	$-0.506812\pi$
$109$	3.55651	−	20.1699i	0.340651	−	1.93193i	0.362049	−	0.932159i	$-0.382077\pi$
$110$	−11.2429	+	8.71388i	−1.07197	+	0.830836i
$111$	5.56913	−	0.806046i	0.528599	−	0.0765065i
$112$	−0.125487	+	0.0349317i	−0.0118574	+	0.00330074i
$113$	−0.345803	−	1.01065i	−0.0325304	−	0.0950738i	0.928688	−	0.370862i	$-0.120938\pi$
$113$	−0.345803	−	1.01065i	−0.0325304	−	0.0950738i	−0.961218	+	0.275788i	$0.911061\pi$
$114$	6.72870	−	8.82627i	0.630201	−	0.826656i
$115$	18.5173	+	5.15464i	1.72675	+	0.480672i
$116$	0.633378	+	10.8747i	0.0588076	+	1.00969i
$117$	−0.698936	+	1.52379i	−0.0646167	+	0.140874i
$118$	4.07080	−	2.04443i	0.374747	−	0.188205i
$119$	1.48483	+	1.70143i	0.136114	+	0.155970i
$120$	−12.8439	−	3.73368i	−1.17248	−	0.340837i
$121$	−23.2626	+	0.902694i	−2.11478	+	0.0820631i
$122$	8.01530	−	0.311030i	0.725671	−	0.0281594i
$123$	3.99815	+	16.2885i	0.360501	+	1.46869i
$124$	−2.99336	−	3.43001i	−0.268812	−	0.308024i
$125$	−6.74110	+	3.38551i	−0.602942	+	0.302809i
$126$	−0.369919	−	1.34666i	−0.0329550	−	0.119970i
$127$	−0.198846	−	3.41405i	−0.0176447	−	0.302948i	−0.995572	−	0.0940024i	$-0.970034\pi$
$127$	−0.198846	−	3.41405i	−0.0176447	−	0.302948i	0.977927	−	0.208946i	$-0.0670032\pi$
$128$	−5.83818	−	1.62517i	−0.516027	−	0.143646i
$129$	0.506144	+	1.21117i	0.0445635	+	0.106637i
$130$	0.439509	+	1.28451i	0.0385475	+	0.112659i
$131$	0.624500	−	0.173841i	0.0545628	−	0.0151886i	−0.240784	−	0.970579i	$-0.577404\pi$
$131$	0.624500	−	0.173841i	0.0545628	−	0.0151886i	0.295346	+	0.955390i	$0.404565\pi$
$132$	−7.39731	−	9.38833i	−0.643853	−	0.817150i
$133$	−2.87040	+	2.22473i	−0.248895	+	0.192908i
$134$	−1.18032	+	6.69393i	−0.101964	+	0.578267i
$135$	3.93385	−	13.3621i	0.338572	−	1.15003i
$136$	−2.19930	−	12.4728i	−0.188588	−	1.06954i
$137$	7.69077	+	6.97900i	0.657067	+	0.596257i	0.930791	−	0.365552i	$-0.119120\pi$
$137$	7.69077	+	6.97900i	0.657067	+	0.596257i	−0.273724	+	0.961808i	$0.588255\pi$
$138$	2.93175	−	10.8672i	0.249567	−	0.925076i
$139$	14.6760	+	6.67105i	1.24480	+	0.565831i	0.924390	−	0.381448i	$-0.124574\pi$
$139$	14.6760	+	6.67105i	1.24480	+	0.565831i	0.320410	+	0.947279i	$0.396179\pi$
$140$	1.38944	+	0.838532i	0.117429	+	0.0708689i
$141$	−0.854095	+	12.2549i	−0.0719278	+	1.03205i
$142$	0.0949403	−	0.198551i	0.00796722	−	0.0166620i
$143$	−0.938364	+	3.13435i	−0.0784699	+	0.262108i
$144$	−0.206524	+	0.732220i	−0.0172104	+	0.0610183i
$145$	−17.0018	+	18.0209i	−1.41193	+	1.49655i
$146$	5.47825	−	6.79196i	0.453383	−	0.562107i
$147$	−0.0932061	−	11.6670i	−0.00768751	−	0.962279i
$148$	3.02654	+	2.34575i	0.248780	+	0.192819i
$149$	−1.18455	+	1.07492i	−0.0970420	+	0.0880610i	−0.719085	−	0.694922i	$-0.755439\pi$
$149$	−1.18455	+	1.07492i	−0.0970420	+	0.0880610i	0.622043	+	0.782983i	$0.286303\pi$
$150$	−1.56447	−	3.05404i	−0.127738	−	0.249361i
$151$	1.15403	−	0.696462i	0.0939138	−	0.0566773i	−0.468965	−	0.883217i	$-0.655373\pi$
$151$	1.15403	−	0.696462i	0.0939138	−	0.0566773i	0.562879	+	0.826540i	$0.309694\pi$
$152$	20.2302	−	2.36457i	1.64088	−	0.191792i
$153$	12.9968	−	2.24594i	1.05073	−	0.181574i
$154$	−1.07954	−	2.50265i	−0.0869917	−	0.201669i
$155$	1.00240	−	10.3056i	0.0805147	−	0.827763i
$156$	−1.07636	+	0.377920i	−0.0861780	+	0.0302578i
$157$	3.83123	−	9.92313i	0.305765	−	0.791952i	−0.691792	−	0.722097i	$-0.743178\pi$
$157$	3.83123	−	9.92313i	0.305765	−	0.791952i	0.997557	−	0.0698551i	$-0.0222537\pi$
$158$	−4.29582	+	6.26346i	−0.341757	+	0.498294i
$159$	−0.150676	+	0.00412672i	−0.0119494	+	0.000327270i
$160$	−6.91082	−	13.1199i	−0.546349	−	1.03722i
$161$	−1.84151	+	3.18959i	−0.145131	+	0.251375i
$162$	−7.84278	−	2.24102i	−0.616187	−	0.176071i
$163$	−1.00390	−	1.73881i	−0.0786315	−	0.136194i	0.824028	−	0.566549i	$-0.191722\pi$
$163$	−1.00390	−	1.73881i	−0.0786315	−	0.136194i	−0.902660	+	0.430355i	$0.858388\pi$
$164$	−6.08548	+	9.65527i	−0.475196	+	0.753950i
$165$	3.98585	−	26.8909i	0.310298	−	2.09345i
$166$	−2.35998	−	4.93548i	−0.183170	−	0.383068i
$167$	−12.2106	+	1.90970i	−0.944883	+	0.147777i	−0.608149	−	0.793823i	$-0.708088\pi$
$167$	−12.2106	+	1.90970i	−0.944883	+	0.147777i	−0.336734	+	0.941600i	$0.609322\pi$
$168$	1.30669	−	2.20479i	0.100813	−	0.170103i
$169$	−10.3221	−	7.37781i	−0.794010	−	0.567524i
$170$	6.37833	−	8.56758i	0.489195	−	0.657103i
$171$	2.39046	+	21.0757i	0.182803	+	1.61170i
$172$	−0.353797	+	0.820193i	−0.0269767	+	0.0625391i
$173$	−14.0370	−	7.74528i	−1.06721	−	0.588863i	−0.150582	−	0.988598i	$-0.548115\pi$
$173$	−14.0370	−	7.74528i	−1.06721	−	0.588863i	−0.916631	+	0.399735i	$0.869102\pi$
$174$	10.6319	+	9.87138i	0.806005	+	0.748347i
$175$	0.237704	+	1.09736i	0.0179687	+	0.0829528i
$176$	−0.200938	+	1.47112i	−0.0151463	+	0.110890i
$177$	−2.91212	+	8.20433i	−0.218889	+	0.616676i
$178$	−3.27333	−	8.47813i	−0.245346	−	0.635463i
$179$	5.39244	+	1.27803i	0.403050	+	0.0955246i	0.427141	−	0.904185i	$-0.359521\pi$
$179$	5.39244	+	1.27803i	0.403050	+	0.0955246i	−0.0240907	+	0.999710i	$0.507669\pi$
$180$	8.40125	−	4.38872i	0.626192	−	0.327116i
$181$	2.93195	+	3.10769i	0.217930	+	0.230993i	0.827111	−	0.562039i	$-0.189983\pi$
$181$	2.93195	+	3.10769i	0.217930	+	0.230993i	−0.609180	+	0.793032i	$0.708501\pi$
$182$	−0.259354	+	0.0201586i	−0.0192246	+	0.00149425i
$183$	−10.6464	+	11.0298i	−0.787006	+	0.815346i
$184$	18.0857	−	9.97929i	1.33330	−	0.735683i
$185$	0.843132	+	8.66815i	0.0619883	+	0.637295i
$186$	−6.03927	−	0.538761i	−0.442821	−	0.0395039i
$187$	24.5118	−	7.85938i	1.79248	−	0.574735i
$188$	−6.40371	+	5.37335i	−0.467039	+	0.391892i
$189$	2.29138	+	1.36860i	0.166673	+	0.0995506i
$190$	13.1584	+	11.0412i	0.954611	+	0.801014i
$191$	−17.1087	−	6.98969i	−1.23794	−	0.505756i	−0.337746	−	0.941237i	$-0.609665\pi$
$191$	−17.1087	−	6.98969i	−1.23794	−	0.505756i	−0.900198	+	0.435481i	$0.856578\pi$
$192$	−8.42416	+	4.52372i	−0.607962	+	0.326471i
$193$	3.22534	−	12.5215i	0.232165	−	0.901320i	−0.741055	−	0.671444i	$-0.765674\pi$
$193$	3.22534	−	12.5215i	0.232165	−	0.901320i	0.973220	−	0.229875i	$-0.0738319\pi$
$194$	−1.74950	+	2.00470i	−0.125607	+	0.143929i
$195$	−2.30518	−	1.19082i	−0.165078	−	0.0852762i
$196$	5.66818	−	5.55931i	0.404870	−	0.397094i
$197$	−5.79073	+	3.80862i	−0.412572	+	0.271353i	−0.738782	−	0.673944i	$-0.764599\pi$
$197$	−5.79073	+	3.80862i	−0.412572	+	0.271353i	0.326210	+	0.945297i	$0.394228\pi$
$198$	−15.7650	−	2.20818i	−1.12037	−	0.156928i
$199$	−0.378853	+	6.50465i	−0.0268561	+	0.461102i	0.957893	+	0.287124i	$0.0926992\pi$
$199$	−0.378853	+	6.50465i	−0.0268561	+	0.461102i	−0.984750	+	0.173978i	$0.944338\pi$
$200$	2.03865	−	5.95817i	0.144154	−	0.421306i
$201$	−7.22476	−	10.7959i	−0.509595	−	0.761482i
$202$	−3.57781	+	6.79230i	−0.251734	+	0.477905i
$203$	−2.53124	−	4.01609i	−0.177658	−	0.281874i
$204$	7.24173	+	5.30188i	0.507022	+	0.371206i
$205$	−25.4712	+	5.00239i	−1.77899	+	0.349382i
$206$	−5.62718	−	3.70105i	−0.392064	−	0.257865i
$207$	10.3279	+	18.8696i	0.717838	+	1.31153i
$208$	0.126639	+	0.0636005i	0.00878084	+	0.00440990i
$209$	10.3258	+	40.0873i	0.714252	+	2.77290i
$210$	2.10870	−	0.474440i	0.145514	−	0.0327395i
$211$	0.847297	+	0.166404i	0.0583303	+	0.0114557i	0.221792	−	0.975094i	$-0.428809\pi$
$211$	0.847297	+	0.166404i	0.0583303	+	0.0114557i	−0.163462	+	0.986550i	$0.552266\pi$
$212$	−0.0732279	−	0.0718214i	−0.00502931	−	0.00493272i
$213$	0.131617	+	0.399481i	0.00901826	+	0.0273720i
$214$	−0.530999	−	3.88760i	−0.0362984	−	0.265751i
$215$	−1.90908	+	0.694848i	−0.130198	+	0.0473883i
$216$	−7.03669	−	13.2119i	−0.478786	−	0.898958i
$217$	1.86433	+	0.678562i	0.126559	+	0.0460638i
$218$	3.92964	−	18.1412i	0.266149	−	1.22868i
$219$	1.42507	+	16.6154i	0.0962974	+	1.12276i
$220$	15.0496	−	10.7568i	1.01464	−	0.725223i
$221$	0.0476406	−	2.45634i	0.00320466	−	0.165231i
$222$	5.07182	−	0.534258i	0.340398	−	0.0358570i
$223$	7.17493	+	10.4613i	0.480469	+	0.700541i	0.986826	−	0.161783i	$-0.0517244\pi$
$223$	7.17493	+	10.4613i	0.480469	+	0.700541i	−0.506357	+	0.862324i	$0.669008\pi$
$224$	2.76476	−	0.655260i	0.184728	−	0.0437814i
$225$	6.19746	+	2.14419i	0.413164	+	0.142946i
$226$	−0.277649	−	0.927411i	−0.0184689	−	0.0616905i
$227$	11.7077	+	1.83105i	0.777068	+	0.121531i	0.530603	−	0.847620i	$-0.321966\pi$
$227$	11.7077	+	1.83105i	0.777068	+	0.121531i	0.246465	+	0.969152i	$0.420731\pi$
$228$	−9.18906	+	11.1305i	−0.608560	+	0.737133i
$229$	12.5009	−	5.10718i	0.826083	−	0.337492i	0.0745743	−	0.997215i	$-0.476240\pi$
$229$	12.5009	−	5.10718i	0.826083	−	0.337492i	0.751508	+	0.659724i	$0.229327\pi$
$230$	16.5884	+	5.31886i	1.09381	+	0.350715i
$231$	4.79921	+	2.02486i	0.315765	+	0.133226i
$232$	0.516290	+	26.6198i	0.0338961	+	1.74767i
$233$	16.0540	+	21.5643i	1.05173	+	1.41272i	0.905938	+	0.423409i	$0.139167\pi$
$233$	16.0540	+	21.5643i	1.05173	+	1.41272i	0.145796	+	0.989315i	$0.453426\pi$
$234$	−0.686517	+	1.35541i	−0.0448790	+	0.0886057i
$235$	−18.8842	−	2.20725i	−1.23187	−	0.143985i
$236$	−5.39312	+	2.45147i	−0.351062	+	0.159577i
$237$	−2.35735	−	14.3224i	−0.153126	−	0.930342i
$238$	1.28489	+	1.59302i	0.0832874	+	0.103260i
$239$	5.68791	+	0.442099i	0.367920	+	0.0285970i	0.260122	−	0.965576i	$-0.416237\pi$
$239$	5.68791	+	0.442099i	0.367920	+	0.0285970i	0.107798	+	0.994173i	$0.465620\pi$
$240$	−1.11706	−	0.372271i	−0.0721059	−	0.0240300i
$241$	5.82142	+	0.225898i	0.374991	+	0.0145513i	0.225582	−	0.974224i	$-0.427572\pi$
$241$	5.82142	+	0.225898i	0.374991	+	0.0145513i	0.149409	+	0.988776i	$0.452263\pi$
$242$	−21.0987			−1.35627
$243$	13.7836	−	7.28087i	0.884221	−	0.467068i
$244$	−10.4316			−0.667815
$245$	18.0438	+	0.700183i	1.15278	+	0.0447330i
$246$	3.04838	+	14.8917i	0.194357	+	0.949458i
$247$	3.93907	+	0.306169i	0.250637	+	0.0194811i
$248$	−6.98577	−	8.66099i	−0.443597	−	0.549973i
$249$	9.78326	+	3.68769i	0.619989	+	0.233698i
$250$	−6.22382	+	2.82908i	−0.393629	+	0.178926i
$251$	−4.47940	−	0.523567i	−0.282737	−	0.0330473i	−0.0264578	−	0.999650i	$-0.508423\pi$
$251$	−4.47940	−	0.523567i	−0.282737	−	0.0330473i	−0.256280	+	0.966603i	$0.582497\pi$
$252$	0.412803	+	1.76865i	0.0260042	+	0.111414i
$253$	25.0698	+	33.6746i	1.57613	+	2.11711i
$254$	−0.0601013	−	3.09881i	−0.00377109	−	0.194437i
$255$	2.53170	+	20.2554i	0.158541	+	1.26844i
$256$	−15.7440	−	5.04810i	−0.983998	−	0.315506i
$257$	13.6932	−	5.59430i	0.854161	−	0.348963i	0.0915339	−	0.995802i	$-0.470823\pi$
$257$	13.6932	−	5.59430i	0.854161	−	0.348963i	0.762627	+	0.646839i	$0.223909\pi$
$258$	0.415809	+	1.11464i	0.0258872	+	0.0693944i
$259$	−1.64871	−	0.257854i	−0.102446	−	0.0160223i
$260$	−0.506370	−	1.69140i	−0.0314038	−	0.104896i
$261$	−27.7231	+	0.442980i	−1.71602	+	0.0274198i
$262$	0.571666	−	0.135487i	0.0353177	−	0.00837044i
$263$	2.29649	+	3.34837i	0.141608	+	0.206469i	0.888992	−	0.457923i	$-0.151406\pi$
$263$	2.29649	+	3.34837i	0.141608	+	0.206469i	−0.747384	+	0.664392i	$0.768690\pi$
$264$	−17.1771	−	23.6307i	−1.05717	−	1.45437i
$265$	0.00452372	−	0.233242i	0.000277890	−	0.0143279i
$266$	−2.67766	+	1.91388i	−0.164178	+	0.117347i
$267$	15.7287	+	7.36711i	0.962578	+	0.450860i
$268$	1.87138	−	8.63927i	0.114313	−	0.527727i
$269$	−18.5292	−	6.74408i	−1.12975	−	0.411194i	−0.291546	−	0.956557i	$-0.594170\pi$
$269$	−18.5292	−	6.74408i	−1.12975	−	0.411194i	−0.838200	+	0.545363i	$0.816392\pi$
$270$	4.03213	−	11.9627i	0.245388	−	0.728027i
$271$	−4.68794	+	1.70627i	−0.284772	+	0.103649i	−0.480457	−	0.877018i	$-0.659529\pi$
$271$	−4.68794	+	1.70627i	−0.284772	+	0.103649i	0.195685	+	0.980667i	$0.437307\pi$
$272$	−0.150884	−	1.10467i	−0.00914871	−	0.0669804i
$273$	0.331139	−	0.370821i	0.0200415	−	0.0224431i
$274$	6.71963	+	6.59057i	0.405948	+	0.398151i
$275$	12.5587	+	2.46646i	0.757321	+	0.148733i
$276$	−4.35782	+	13.9741i	−0.262310	+	0.841143i
$277$	−7.13432	−	27.6971i	−0.428660	−	1.66416i	−0.709731	−	0.704473i	$-0.751183\pi$
$277$	−7.13432	−	27.6971i	−0.428660	−	1.66416i	0.281071	−	0.959687i	$-0.409310\pi$
$278$	13.0564	+	6.55716i	0.783069	+	0.393272i
$279$	9.04421	−	7.24402i	0.541463	−	0.433688i
$280$	3.31403	+	2.17967i	0.198051	+	0.130260i
$281$	−0.0527116	+	0.0103522i	−0.00314451	+	0.000617562i	−0.194284	−	0.980945i	$-0.562238\pi$
$281$	−0.0527116	+	0.0103522i	−0.00314451	+	0.000617562i	0.191140	+	0.981563i	$0.438782\pi$
$282$	−1.20415	+	11.0683i	−0.0717058	+	0.659105i
$283$	11.2265	+	17.8120i	0.667345	+	1.05882i	0.993537	+	0.113512i	$0.0362099\pi$
$283$	11.2265	+	17.8120i	0.667345	+	1.05882i	−0.326191	+	0.945304i	$0.605765\pi$
$284$	−0.133388	+	0.253230i	−0.00791510	+	0.0150264i
$285$	−32.7558	+	2.17050i	−1.94028	+	0.128569i
$286$	−0.959945	+	2.80555i	−0.0567627	+	0.165895i
$287$	0.289201	−	4.96539i	0.0170710	−	0.293098i
$288$	5.12088	−	15.7853i	0.301751	−	0.930159i
$289$	−1.94576	+	1.27975i	−0.114457	+	0.0752793i
$290$	−16.0304	+	15.7225i	−0.941339	+	0.923259i
$291$	−0.237759	−	5.07947i	−0.0139377	−	0.297764i
$292$	−7.46150	+	8.54993i	−0.436651	+	0.500347i
$293$	−2.24690	+	8.72298i	−0.131265	+	0.509602i	0.868635	+	0.495453i	$0.164998\pi$
$293$	−2.24690	+	8.72298i	−0.131265	+	0.509602i	−0.999900	+	0.0141493i	$0.995496\pi$
$294$	0.325594	−	10.5691i	0.0189890	−	0.616403i
$295$	−12.4731	−	5.09582i	−0.726211	−	0.296690i
$296$	7.16956	+	6.01598i	0.416722	+	0.349672i
$297$	24.6696	−	17.8038i	1.43147	−	1.03308i
$298$	−1.11052	+	0.931838i	−0.0643308	+	0.0539799i
$299$	3.81555	−	1.22341i	0.220659	−	0.0707515i
$300$	1.87903	+	4.04763i	0.108486	+	0.233690i
$301$	−0.0376863	−	0.387449i	−0.00217220	−	0.0223322i
$302$	1.06959	−	0.590172i	0.0615477	−	0.0339606i
$303$	−4.04734	−	14.1024i	−0.232513	−	0.810162i
$304$	1.78760	−	0.138943i	0.102526	−	0.00796894i
$305$	−16.2815	−	17.2574i	−0.932278	−	0.988157i
$306$	11.8490	−	1.57723i	0.677362	−	0.0901641i
$307$	6.31768	+	1.49732i	0.360569	+	0.0854564i	0.406907	−	0.913469i	$-0.366607\pi$
$307$	6.31768	+	1.49732i	0.360569	+	0.0854564i	−0.0463386	+	0.998926i	$0.514755\pi$
$308$	1.27666	+	3.30664i	0.0727447	+	0.188413i
$309$	12.6580	−	2.33636i	0.720090	−	0.132911i
$310$	1.26995	−	9.29766i	0.0721282	−	0.528072i
$311$	−0.716987	−	3.30998i	−0.0406566	−	0.187692i	0.952489	−	0.304572i	$-0.0985133\pi$
$311$	−0.716987	−	3.30998i	−0.0406566	−	0.187692i	−0.993146	+	0.116880i	$0.962711\pi$
$312$	−2.66467	+	0.821002i	−0.150857	+	0.0464801i
$313$	15.2593	+	8.41975i	0.862509	+	0.475913i	0.851700	−	0.524029i	$-0.175572\pi$
$313$	15.2593	+	8.41975i	0.862509	+	0.475913i	0.0108090	+	0.999942i	$0.496559\pi$
$314$	3.81834	−	8.85191i	0.215482	−	0.499542i
$315$	−2.28165	+	3.44341i	−0.128556	+	0.194014i
$316$	5.89828	−	7.92277i	0.331804	−	0.445690i
$317$	−0.354389	−	0.253302i	−0.0199045	−	0.0142269i	0.571496	−	0.820605i	$-0.306363\pi$
$317$	−0.354389	−	0.253302i	−0.0199045	−	0.0142269i	−0.591401	+	0.806378i	$0.701425\pi$
$318$	−0.136599	−	0.00155783i	−0.00766012	−	8.73587e-5i
$319$	−53.4625	+	8.36139i	−2.99333	+	0.468148i
$320$	−6.38401	−	13.3510i	−0.356877	−	0.746345i
$321$	5.87414	+	4.66099i	0.327863	+	0.260151i
$322$	−1.77979	+	2.82383i	−0.0991839	+	0.157366i
$323$	−15.5421	−	26.9197i	−0.864785	−	1.49785i
$324$	10.0787	+	3.30770i	0.559929	+	0.183761i
$325$	0.610773	−	1.05789i	0.0338796	−	0.0586812i
$326$	−0.848043	−	1.60997i	−0.0469688	−	0.0891680i
$327$	18.5716	+	30.2245i	1.02701	+	1.67142i
$328$	−15.7779	+	23.0048i	−0.871191	+	1.27023i
$329$	1.31215	−	3.39855i	0.0723411	−	0.187368i
$330$	4.55465	−	24.2127i	0.250725	−	1.33287i
$331$	0.628047	−	6.45689i	0.0345206	−	0.354903i	−0.962096	−	0.272711i	$-0.912080\pi$
$331$	0.628047	−	6.45689i	0.0345206	−	0.354903i	0.996617	−	0.0821917i	$-0.0261920\pi$
$332$	2.81793	+	6.53269i	0.154654	+	0.358528i
$333$	−6.29041	+	7.44483i	−0.344712	+	0.407974i
$334$	−11.1252	+	1.30035i	−0.608745	+	0.0711520i
$335$	17.2131	−	10.3882i	0.940453	−	0.567566i
$336$	0.122467	−	0.189482i	0.00668114	−	0.0103371i
$337$	14.0354	−	12.7365i	0.764558	−	0.693800i	−0.193269	−	0.981146i	$-0.561909\pi$
$337$	14.0354	−	12.7365i	0.764558	−	0.693800i	0.957827	+	0.287346i	$0.0927731\pi$
$338$	−9.08861	−	7.04421i	−0.494355	−	0.383154i
$339$	1.60960	+	0.912234i	0.0874212	+	0.0495457i
$340$	−8.72070	+	10.8120i	−0.472946	+	0.586361i
$341$	15.5193	−	16.4495i	0.840417	−	0.890790i
$342$	1.42420	+	19.1705i	0.0770118	+	1.03662i
$343$	−2.02355	+	6.75912i	−0.109261	+	0.364958i
$344$	−0.941829	+	1.96967i	−0.0507800	+	0.106197i
$345$	−29.9196	+	14.6013i	−1.61082	+	0.786109i
$346$	−12.4399	−	7.50754i	−0.668775	−	0.403608i
$347$	−16.3382	−	7.42664i	−0.877083	−	0.398683i	−0.0759090	−	0.997115i	$-0.524186\pi$
$347$	−16.3382	−	7.42664i	−0.877083	−	0.398683i	−0.801174	+	0.598432i	$0.795791\pi$
$348$	−13.3185	−	13.3640i	−0.713945	−	0.716387i
$349$	−9.50893	−	8.62890i	−0.509001	−	0.461894i	0.376576	−	0.926386i	$-0.377101\pi$
$349$	−9.50893	−	8.62890i	−0.509001	−	0.461894i	−0.885578	+	0.464491i	$0.846237\pi$
$350$	0.176705	+	1.00214i	0.00944526	+	0.0535668i
$351$	−0.845497	−	2.77785i	−0.0451293	−	0.148271i
$352$	5.62408	−	31.8958i	0.299765	−	1.70005i
$353$	14.6362	−	11.3439i	0.779004	−	0.603774i	−0.143549	−	0.989643i	$-0.545852\pi$
$353$	14.6362	−	11.3439i	0.779004	−	0.603774i	0.922553	+	0.385869i	$0.126098\pi$
$354$	−2.92558	+	7.32764i	−0.155493	+	0.389460i
$355$	−0.627119	+	0.174570i	−0.0332840	+	0.00926524i
$356$	3.82618	+	11.1824i	0.202787	+	0.592668i
$357$	−3.87948	−	0.498353i	−0.205324	−	0.0263757i
$358$	4.83857	+	1.34691i	0.255726	+	0.0711863i
$359$	−1.71882	−	29.5111i	−0.0907160	−	1.55753i	−0.669971	−	0.742388i	$-0.733693\pi$
$359$	−1.71882	−	29.5111i	−0.0907160	−	1.55753i	0.579255	−	0.815147i	$-0.303344\pi$
$360$	20.9347	−	9.92258i	1.10336	−	0.522966i
$361$	27.6925	−	13.9077i	1.45750	−	0.731984i
$362$	2.54601	+	2.91741i	0.133815	+	0.153336i
$363$	29.1074	−	27.9042i	1.52774	−	1.46459i
$364$	0.338048	−	0.0131178i	0.0177185	−	0.000687560i
$365$	−25.7903	+	1.00078i	−1.34993	+	0.0523833i
$366$	−10.0292	+	9.61463i	−0.524233	+	0.502565i
$367$	−11.2984	−	12.9465i	−0.589770	−	0.675801i	0.378531	−	0.925589i	$-0.376429\pi$
$367$	−11.2984	−	12.9465i	−0.589770	−	0.675801i	−0.968301	+	0.249787i	$0.919639\pi$
$368$	1.62496	−	0.816085i	0.0847069	−	0.0425414i
$369$	−23.9006	−	16.5126i	−1.24421	−	0.859613i
$370$	0.458937	+	7.87965i	0.0238590	+	0.409643i
$371$	0.0430629	+	0.0119874i	0.00223571	+	0.000622353i
$372$	7.82089	+	1.00466i	0.405494	+	0.0520893i
$373$	−1.33945	−	3.91470i	−0.0693542	−	0.202695i	0.906027	−	0.423219i	$-0.139100\pi$
$373$	−1.33945	−	3.91470i	−0.0693542	−	0.202695i	−0.975382	+	0.220524i	$0.929223\pi$
$374$	22.4744	−	6.25619i	1.16213	−	0.323500i
$375$	4.84466	−	12.1343i	0.250177	−	0.626613i
$376$	−16.1494	+	12.5167i	−0.832840	+	0.645500i
$377$	−0.896835	+	5.08621i	−0.0461894	+	0.261953i
$378$	2.02701	+	1.31995i	0.104258	+	0.0678907i
$379$	3.96292	+	22.4749i	0.203562	+	1.15446i	0.899687	+	0.436535i	$0.143795\pi$
$379$	3.96292	+	22.4749i	0.203562	+	1.15446i	−0.696125	+	0.717920i	$0.745094\pi$
$380$	−16.5426	−	15.0116i	−0.848619	−	0.770081i
$381$	4.18127	+	4.19557i	0.214213	+	0.214946i
$382$	−15.2483	−	6.93121i	−0.780171	−	0.354631i
$383$	−29.4476	−	17.7717i	−1.50470	−	0.908093i	−0.998969	−	0.0454042i	$-0.985542\pi$
$383$	−29.4476	−	17.7717i	−1.50470	−	0.908093i	−0.505735	−	0.862689i	$-0.668779\pi$
$384$	9.43313	−	4.60355i	0.481382	−	0.234924i
$385$	−3.47771	+	7.27301i	−0.177240	+	0.370667i
$386$	3.36095	−	11.2264i	0.171068	−	0.571406i
$387$	−2.04782	−	0.987805i	−0.104097	−	0.0502130i
$388$	2.37457	−	2.51690i	0.120551	−	0.127776i
$389$	−4.36508	+	5.41185i	−0.221318	+	0.274392i	−0.876837	−	0.480787i	$-0.840351\pi$
$389$	−4.36508	+	5.41185i	−0.221318	+	0.274392i	0.655519	+	0.755179i	$0.272450\pi$
$390$	−2.04576	−	1.15943i	−0.103591	−	0.0587101i
$391$	−24.9165	−	19.3118i	−1.26008	−	0.976638i
$392$	14.3706	−	13.0406i	0.725823	−	0.658650i
$393$	−0.609471	+	0.942979i	−0.0307437	+	0.0475670i
$394$	−5.37802	+	3.24565i	−0.270941	+	0.163513i
$395$	22.3129	−	2.60801i	1.12268	−	0.131223i
$396$	20.3753	+	3.66451i	1.02390	+	0.184149i
$397$	1.16037	+	2.69004i	0.0582372	+	0.135009i	0.944850	−	0.327503i	$-0.106207\pi$
$397$	1.16037	+	2.69004i	0.0582372	+	0.135009i	−0.886613	+	0.462512i	$0.846948\pi$
$398$	−0.571682	+	5.87740i	−0.0286558	+	0.294607i
$399$	1.16284	−	6.18171i	0.0582148	−	0.309473i
$400$	0.199665	−	0.517146i	0.00998327	−	0.0258573i
$401$	−15.8292	+	23.0795i	−0.790471	+	1.15253i	0.194684	+	0.980866i	$0.437632\pi$
$401$	−15.8292	+	23.0795i	−0.790471	+	1.15253i	−0.985155	+	0.171669i	$0.945084\pi$
$402$	−6.16347	−	10.0308i	−0.307406	−	0.500291i
$403$	−1.00593	−	1.90971i	−0.0501089	−	0.0951293i
$404$	4.99189	−	8.64621i	0.248356	−	0.430165i
$405$	10.2587	+	21.8363i	0.509759	+	1.08505i
$406$	−2.15120	−	3.72599i	−0.106762	−	0.184918i
$407$	−10.1425	+	16.0921i	−0.502743	+	0.797656i
$408$	17.1843	+	13.6354i	0.850752	+	0.675052i
$409$	10.5942	+	22.1558i	0.523847	+	1.09553i	0.978762	+	0.204999i	$0.0657191\pi$
$409$	10.5942	+	22.1558i	0.523847	+	1.09553i	−0.454915	+	0.890535i	$0.650330\pi$
$410$	−23.2430	+	3.63513i	−1.14789	+	0.179526i
$411$	−17.9867	−	0.205127i	−0.887218	−	0.0101182i
$412$	7.12591	+	5.09330i	0.351068	+	0.250929i
$413$	1.54171	−	2.07088i	0.0758626	−	0.101901i
$414$	8.68999	+	17.4516i	0.427090	+	0.857697i
$415$	−6.40910	+	14.8580i	−0.314610	+	0.729348i
$416$	−2.70653	−	1.49340i	−0.132698	−	0.0732198i
$417$	−26.6846	+	8.22168i	−1.30675	+	0.402617i
$418$	7.94249	+	36.6666i	0.388480	+	1.79342i
$419$	−4.58194	+	33.5458i	−0.223843	+	1.63882i	0.445084	+	0.895489i	$0.353174\pi$
$419$	−4.58194	+	33.5458i	−0.223843	+	1.63882i	−0.668927	+	0.743329i	$0.733246\pi$
$420$	−2.76419	+	0.510202i	−0.134879	+	0.0248953i
$421$	6.56907	+	17.0143i	0.320157	+	0.829228i	0.995762	+	0.0919641i	$0.0293145\pi$
$421$	6.56907	+	17.0143i	0.320157	+	0.829228i	−0.675605	+	0.737264i	$0.736118\pi$
$422$	0.761478	+	0.180474i	0.0370682	+	0.00878532i
$423$	−12.9772	−	16.8621i	−0.630973	−	0.819864i
$424$	−0.172041	−	0.182353i	−0.00835507	−	0.00885586i
$425$	−9.58162	+	0.744743i	−0.464777	+	0.0361253i
$426$	0.105156	+	0.366402i	0.00509483	+	0.0177522i
$427$	3.98038	−	2.19628i	0.192624	−	0.106285i
$428$	0.493997	+	5.07873i	0.0238782	+	0.245490i
$429$	−2.38617	−	5.14006i	−0.115206	−	0.248165i
$430$	−1.75331	+	0.562177i	−0.0845522	+	0.0271106i
$431$	−8.71786	+	7.31515i	−0.419925	+	0.352359i	−0.828134	−	0.560530i	$-0.810598\pi$
$431$	−8.71786	+	7.31515i	−0.419925	+	0.352359i	0.408210	+	0.912888i	$0.366153\pi$
$432$	−0.573879	−	1.18619i	−0.0276107	−	0.0570708i
$433$	26.6500	+	22.3620i	1.28072	+	1.07465i	0.993145	+	0.116892i	$0.0372932\pi$
$433$	26.6500	+	22.3620i	1.28072	+	1.07465i	0.287574	+	0.957758i	$0.407151\pi$
$434$	1.66452	+	0.680033i	0.0798997	+	0.0326426i
$435$	1.32133	−	42.8917i	0.0633529	−	2.05650i
$436$	−6.02139	+	23.3765i	−0.288372	+	1.11953i
$437$	33.3340	−	38.1965i	1.59458	−	1.82719i
$438$	0.706670	+	15.0972i	0.0337660	+	0.721373i
$439$	4.22746	−	4.14626i	0.201765	−	0.197890i	−0.592309	−	0.805711i	$-0.701783\pi$
$439$	4.22746	−	4.14626i	0.201765	−	0.197890i	0.794074	+	0.607821i	$0.207956\pi$
$440$	37.7758	−	24.8455i	1.80089	−	1.18446i
$441$	13.5291	+	15.0116i	0.644242	+	0.714837i
$442$	0.129465	−	2.22283i	0.00615801	−	0.105729i
$443$	11.5516	−	33.7608i	0.548832	−	1.60402i	−0.227554	−	0.973765i	$-0.573073\pi$
$443$	11.5516	−	33.7608i	0.548832	−	1.60402i	0.776386	−	0.630257i	$-0.217051\pi$
$444$	−6.61780	+	0.438515i	−0.314067	+	0.0208110i
$445$	−12.5277	+	23.7832i	−0.593869	+	1.12743i
$446$	6.13010	+	9.72607i	0.290269	+	0.460543i
$447$	0.299646	−	2.75428i	0.0141728	−	0.130273i
$448$	2.78247	−	0.546459i	0.131459	−	0.0258178i
$449$	−15.8949	−	10.4543i	−0.750129	−	0.493367i	0.115962	−	0.993254i	$-0.463005\pi$
$449$	−15.8949	−	10.4543i	−0.750129	−	0.493367i	−0.866091	+	0.499886i	$0.833375\pi$
$450$	5.53717	+	2.15961i	0.261025	+	0.101805i
$451$	−50.6647	−	25.4448i	−2.38571	−	1.19815i
$452$	0.314039	+	1.21918i	0.0147712	+	0.0573452i
$453$	−0.695044	+	2.22878i	−0.0326560	+	0.104717i
$454$	10.5383	+	2.06966i	0.494589	+	0.0971341i
$455$	0.549323	+	0.538772i	0.0257527	+	0.0252580i
$456$	−23.4978	+	26.3136i	−1.10038	+	1.23225i
$457$	−3.34948	−	24.5225i	−0.156682	−	1.14712i	−0.886250	−	0.463207i	$-0.846699\pi$
$457$	−3.34948	−	24.5225i	−0.156682	−	1.14712i	0.729568	−	0.683908i	$-0.239721\pi$
$458$	11.5005	−	4.18584i	0.537383	−	0.195591i
$459$	−14.2607	+	17.8469i	−0.665633	+	0.833023i
$460$	−21.2885	−	7.74838i	−0.992581	−	0.361270i
$461$	0.839959	−	3.87768i	0.0391208	−	0.180602i	−0.953593	−	0.301099i	$-0.902646\pi$
$461$	0.839959	−	3.87768i	0.0391208	−	0.180602i	0.992714	+	0.120497i	$0.0384489\pi$
$462$	4.27509	+	2.00240i	0.198895	+	0.0931601i
$463$	1.16379	−	0.831826i	0.0540858	−	0.0386582i	−0.554128	−	0.832432i	$-0.686948\pi$
$463$	1.16379	−	0.831826i	0.0540858	−	0.0386582i	0.608214	+	0.793773i	$0.291886\pi$
$464$	−0.0454492	+	2.34335i	−0.00210993	+	0.108787i
$465$	10.5447	+	14.5065i	0.488999	+	0.672722i
$466$	13.7810	+	20.0931i	0.638391	+	0.930797i
$467$	−22.1925	+	5.25971i	−1.02695	+	0.243390i	−0.709365	−	0.704841i	$-0.751018\pi$
$467$	−22.1925	+	5.25971i	−1.02695	+	0.243390i	−0.317580	+	0.948232i	$0.602870\pi$
$468$	0.960480	−	1.72674i	0.0443982	−	0.0798185i
$469$	1.10486	+	3.69048i	0.0510176	+	0.170410i
$470$	−17.0243	−	2.66255i	−0.785271	−	0.122814i
$471$	6.43945	+	17.2619i	0.296714	+	0.795388i
$472$	−13.4042	+	5.47622i	−0.616979	+	0.252064i
$473$	−4.22539	−	1.35482i	−0.194284	−	0.0622945i
$474$	−1.63154	−	13.0535i	−0.0749390	−	0.599565i
$475$	−0.299700	−	15.4525i	−0.0137512	−	0.709008i
$476$	−1.58940	−	2.13493i	−0.0728498	−	0.0978543i
$477$	0.190511	−	0.178512i	0.00872288	−	0.00817349i
$478$	5.13552	+	0.600257i	0.234893	+	0.0274551i
$479$	17.5336	−	7.96999i	0.801130	−	0.364158i	0.0289648	−	0.999580i	$-0.490779\pi$
$479$	17.5336	−	7.96999i	0.801130	−	0.364158i	0.772165	+	0.635422i	$0.219174\pi$
$480$	24.0334	+	9.05913i	1.09697	+	0.413491i
$481$	1.13979	+	1.41312i	0.0519699	+	0.0644326i
$482$	5.26403	+	0.409153i	0.239770	+	0.0186364i
$483$	−1.27931	−	6.24959i	−0.0582108	−	0.284366i
$484$	27.4178	+	1.06394i	1.24626	+	0.0483608i
$485$	7.87001			0.357359
$486$	12.7386	−	6.10929i	0.577833	−	0.277123i
$487$	40.6290			1.84108			0.920539	−	0.390651i	$-0.127750\pi$
$487$	40.6290			1.84108			0.920539	+	0.390651i	$0.127750\pi$
$488$	−25.4776	−	0.988648i	−1.15332	−	0.0447540i
$489$	3.29922	+	1.09950i	0.149196	+	0.0497211i
$490$	16.3162	+	1.26819i	0.737090	+	0.0572912i
$491$	−16.2128	−	20.1007i	−0.731673	−	0.907133i	0.266721	−	0.963774i	$-0.414060\pi$
$491$	−16.2128	−	20.1007i	−0.731673	−	0.907133i	−0.998395	+	0.0566410i	$0.981961\pi$
$492$	−3.21044	−	19.5055i	−0.144738	−	0.879376i
$493$	36.9908	−	16.8144i	1.66598	−	0.757283i
$494$	3.55653	+	0.415699i	0.160016	+	0.0187032i
$495$	25.7393	+	39.4273i	1.15689	+	1.77212i
$496$	−0.584933	−	0.785702i	−0.0262643	−	0.0352790i
$497$	−0.00241872	−	0.124708i	−0.000108494	−	0.00559393i
$498$	8.73028	+	3.68344i	0.391213	+	0.165059i
$499$	−7.75166	−	2.48547i	−0.347012	−	0.111265i	0.126709	−	0.991940i	$-0.459559\pi$
$499$	−7.75166	−	2.48547i	−0.347012	−	0.111265i	−0.473721	+	0.880675i	$0.657089\pi$
$500$	8.23055	−	3.36255i	0.368081	−	0.150378i
$501$	13.6284	−	16.5077i	0.608870	−	0.737509i
$502$	−4.03822	−	0.631566i	−0.180235	−	0.0281882i
$503$	8.74033	+	29.1947i	0.389712	+	1.30173i	0.897792	+	0.440419i	$0.145170\pi$
$503$	8.74033	+	29.1947i	0.389712	+	1.30173i	−0.508080	+	0.861310i	$0.669645\pi$
$504$	0.840588	+	4.35879i	0.0374428	+	0.194156i
$505$	22.0951	−	5.23663i	0.983218	−	0.233027i
$506$	21.5203	+	31.3773i	0.956692	+	1.39489i
$507$	21.8549	−	2.30216i	0.970609	−	0.102242i
$508$	−0.0781607	+	4.02995i	−0.00346782	+	0.178800i
$509$	−22.1126	+	15.8052i	−0.980126	+	0.700552i	−0.954218	−	0.299113i	$-0.903309\pi$
$509$	−22.1126	+	15.8052i	−0.980126	+	0.700552i	−0.0259078	+	0.999664i	$0.508248\pi$
$510$	1.58093	+	18.4326i	0.0700048	+	0.816208i
$511$	1.04697	−	4.83334i	0.0463151	−	0.213814i
$512$	−2.69122	−	0.979522i	−0.118936	−	0.0432892i
$513$	−27.3189	−	24.5637i	−1.20616	−	1.08451i
$514$	12.5974	−	4.58508i	0.555648	−	0.202239i
$515$	2.69600	+	19.7382i	0.118800	+	0.869771i
$516$	−0.484139	−	1.46945i	−0.0213130	−	0.0646888i
$517$	−29.6469	−	29.0774i	−1.30387	−	1.27882i
$518$	−1.48404	−	0.291456i	−0.0652049	−	0.0128058i
$519$	27.0911	−	6.09527i	1.18917	−	0.267553i
$520$	−1.07643	−	4.17897i	−0.0472047	−	0.183260i
$521$	7.13268	+	3.58217i	0.312488	+	0.156938i	0.598130	−	0.801399i	$-0.295910\pi$
$521$	7.13268	+	3.58217i	0.312488	+	0.156938i	−0.285642	+	0.958336i	$0.592207\pi$
$522$	−25.1221	−	0.573077i	−1.09956	−	0.0250829i
$523$	−5.48191	−	3.60551i	−0.239707	−	0.157658i	0.423972	−	0.905675i	$-0.360636\pi$
$523$	−5.48191	−	3.60551i	−0.239707	−	0.157658i	−0.663679	+	0.748018i	$0.731006\pi$
$524$	−0.749715	+	0.147239i	−0.0327515	+	0.00643218i
$525$	−1.56917	−	1.14884i	−0.0684842	−	0.0501393i
$526$	1.96207	+	3.11304i	0.0855504	+	0.135735i
$527$	−7.91415	+	15.0246i	−0.344746	+	0.654484i
$528$	−1.43030	−	2.13728i	−0.0622460	−	0.0930133i
$529$	9.19861	−	26.8840i	0.399940	−	1.16887i
$530$	0.0122934	−	0.211069i	0.000533989	−	0.00916824i
$531$	−5.65515	−	13.9783i	−0.245413	−	0.606608i
$532$	3.57614	−	2.35207i	0.155045	−	0.101975i
$533$	−3.86320	+	3.78900i	−0.167334	+	0.164120i
$534$	13.9852	+	7.22451i	0.605200	+	0.312635i
$535$	−7.63093	+	8.74407i	−0.329914	+	0.378039i
$536$	5.38935	−	20.9228i	0.232785	−	0.903725i
$537$	−8.45657	+	4.54112i	−0.364928	+	0.195964i
$538$	−16.5433	−	6.75870i	−0.713234	−	0.291388i
$539$	30.2126	+	25.3514i	1.30135	+	1.09196i
$540$	−5.84301	+	15.3422i	−0.251443	+	0.660225i
$541$	8.36672	−	7.02051i	0.359713	−	0.301835i	−0.444963	−	0.895549i	$-0.646783\pi$
$541$	8.36672	−	7.02051i	0.359713	−	0.301835i	0.804676	+	0.593714i	$0.202339\pi$
$542$	−4.30544	+	1.38048i	−0.184934	+	0.0592968i
$543$	−7.37088	−	0.657553i	−0.316315	−	0.0282183i
$544$	2.35444	+	24.2058i	0.100946	+	1.03782i
$545$	−48.0707	+	26.5243i	−2.05912	+	1.13618i
$546$	0.312916	−	0.324185i	0.0133916	−	0.0138738i
$547$	−36.1608	+	2.81064i	−1.54612	+	0.120174i	−0.821997	−	0.569492i	$-0.807140\pi$
$547$	−36.1608	+	2.81064i	−1.54612	+	0.120174i	−0.724127	+	0.689666i	$0.757757\pi$
$548$	−8.39985	−	8.90332i	−0.358824	−	0.380331i
$549$	1.12017	−	26.5283i	0.0478076	−	1.13220i
$550$	11.2867	+	2.67500i	0.481268	+	0.114063i
$551$	23.5358	+	60.9592i	1.00266	+	2.59695i
$552$	−11.9677	+	33.7167i	−0.509380	+	1.43508i
$553$	−0.582535	+	4.26491i	−0.0247719	+	0.181362i
$554$	−5.48763	−	25.3337i	−0.233147	−	1.07633i
$555$	−11.0544	−	10.2637i	−0.469235	−	0.435668i
$556$	−16.6362	−	9.17944i	−0.705530	−	0.389295i
$557$	1.27340	−	2.95207i	0.0539557	−	0.125083i	−0.889106	−	0.457702i	$-0.848673\pi$
$557$	1.27340	−	2.95207i	0.0539557	−	0.125083i	0.943062	+	0.332618i	$0.107932\pi$
$558$	8.44516	−	6.24247i	0.357512	−	0.264265i
$559$	−0.252902	+	0.339706i	−0.0106966	+	0.0143680i
$560$	0.284075	+	0.203045i	0.0120044	+	0.00858022i
$561$	−22.7312	+	38.3547i	−0.959711	+	1.61934i
$562$	−0.0481003	+	0.00752274i	−0.00202899	+	0.000317328i
$563$	16.9591	+	35.4669i	0.714740	+	1.49475i	0.862677	+	0.505756i	$0.168786\pi$
$563$	16.9591	+	35.4669i	0.714740	+	1.49475i	−0.147936	+	0.988997i	$0.547263\pi$
$564$	2.12293	−	14.3225i	0.0893914	−	0.603087i
$565$	−1.52678	+	2.42240i	−0.0642322	+	0.101911i
$566$	9.54094	+	16.5254i	0.401035	+	0.694614i
$567$	−4.54214	+	0.859868i	−0.190752	+	0.0361111i
$568$	−0.349779	+	0.605835i	−0.0146764	+	0.0254203i
$569$	18.4990	+	35.1195i	0.775518	+	1.47228i	0.878573	+	0.477608i	$0.158496\pi$
$569$	18.4990	+	35.1195i	0.775518	+	1.47228i	−0.103055	+	0.994676i	$0.532862\pi$
$570$	−29.7404	+	0.814533i	−1.24569	+	0.0341170i
$571$	12.3643	−	18.0276i	0.517431	−	0.754432i	−0.474631	−	0.880185i	$-0.657418\pi$
$571$	12.3643	−	18.0276i	0.517431	−	0.754432i	0.992062	+	0.125752i	$0.0401345\pi$
$572$	1.38893	−	3.59741i	0.0580740	−	0.150415i
$573$	30.2032	−	10.6046i	1.26176	−	0.443014i
$574$	0.436399	−	4.48658i	0.0182150	−	0.187266i
$575$	−6.20822	−	14.3923i	−0.258901	−	0.600199i
$576$	5.71757	−	15.5435i	0.238232	−	0.647647i
$577$	−19.8713	+	2.32262i	−0.827253	+	0.0966920i	−0.519174	−	0.854669i	$-0.673760\pi$
$577$	−19.8713	+	2.32262i	−0.827253	+	0.0966920i	−0.308079	+	0.951361i	$0.599686\pi$
$578$	−1.80709	+	1.09058i	−0.0751649	+	0.0453623i
$579$	10.2108	+	19.9327i	0.424347	+	0.828376i
$580$	21.6244	−	19.6231i	0.897906	−	0.814807i
$581$	−2.45063	−	1.89938i	−0.101669	−	0.0787997i
$582$	−0.0368159	−	4.60840i	−0.00152607	−	0.191024i
$583$	0.319887	−	0.396597i	0.0132484	−	0.0164254i
$584$	−19.0339	+	20.1748i	−0.787629	+	0.834838i
$585$	4.35572	−	1.10611i	0.180087	−	0.0457321i
$586$	−2.34137	+	7.82071i	−0.0967210	+	0.323071i
$587$	11.8439	−	24.7694i	0.488849	−	1.02234i	−0.498953	−	0.866629i	$-0.666282\pi$
$587$	11.8439	−	24.7694i	0.488849	−	1.02234i	0.987802	−	0.155713i	$-0.0497674\pi$
$588$	−0.956076	+	13.7182i	−0.0394279	+	0.565729i
$589$	−23.3813	−	14.1107i	−0.963409	−	0.581420i
$590$	−11.1168	−	5.05318i	−0.457669	−	0.208036i
$591$	3.12686	−	11.5904i	0.128622	−	0.476765i
$592$	0.610129	+	0.553663i	0.0250762	+	0.0227554i
$593$	0.511405	+	2.90032i	0.0210009	+	0.119102i	0.993506	−	0.113779i	$-0.0362957\pi$
$593$	0.511405	+	2.90032i	0.0210009	+	0.119102i	−0.972505	+	0.232881i	$0.925185\pi$
$594$	22.9668	−	15.2564i	0.942340	−	0.625980i
$595$	1.05119	−	5.96158i	0.0430944	−	0.244401i
$596$	1.49012	−	1.15493i	0.0610376	−	0.0473077i
$597$	−6.98453	−	8.86444i	−0.285858	−	0.362797i
$598$	3.49842	−	0.973852i	0.143061	−	0.0398238i
$599$	−3.10041	−	9.06130i	−0.126679	−	0.370235i	0.864522	−	0.502594i	$-0.167621\pi$
$599$	−3.10041	−	9.06130i	−0.126679	−	0.370235i	−0.991202	+	0.132360i	$0.957745\pi$
$600$	4.20564	+	10.0638i	0.171695	+	0.410853i
$601$	−12.4093	−	3.45437i	−0.506187	−	0.140907i	0.00565899	−	0.999984i	$-0.498199\pi$
$601$	−12.4093	−	3.45437i	−0.506187	−	0.140907i	−0.511846	+	0.859077i	$0.671038\pi$
$602$	−0.0205136	−	0.352204i	−0.000836071	−	0.0143548i
$603$	21.7693	+	5.68677i	0.886516	+	0.231583i
$604$	−1.41969	+	0.712996i	−0.0577664	+	0.0290114i
$605$	41.0333	+	47.0190i	1.66824	+	1.91159i
$606$	−3.16975	−	12.9136i	−0.128762	−	0.524579i
$607$	−24.8356	+	0.963733i	−1.00804	+	0.0391167i	−0.537503	−	0.843262i	$-0.680632\pi$
$607$	−24.8356	+	0.963733i	−1.00804	+	0.0391167i	−0.470541	+	0.882378i	$0.655941\pi$
$608$	−39.0814	+	1.51654i	−1.58496	+	0.0615036i
$609$	7.89559	+	2.29522i	0.319945	+	0.0930069i
$610$	−14.1384	−	16.2008i	−0.572446	−	0.655950i
$611$	−3.54183	+	1.77877i	−0.143287	+	0.0719615i
$612$	−15.4774	+	1.45211i	−0.625636	+	0.0586980i
$613$	−1.01795	−	17.4775i	−0.0411146	−	0.705910i	−0.954389	−	0.298566i	$-0.903492\pi$
$613$	−1.01795	−	17.4775i	−0.0411146	−	0.705910i	0.913275	−	0.407345i	$-0.133545\pi$
$614$	5.66877	+	1.57801i	0.228773	+	0.0636833i
$615$	27.2579	−	35.7551i	1.09914	−	1.44179i
$616$	2.80468	+	8.19698i	0.113004	+	0.330266i
$617$	−3.94167	+	1.09724i	−0.158686	+	0.0441732i	−0.346604	−	0.938011i	$-0.612665\pi$
$617$	−3.94167	+	1.09724i	−0.158686	+	0.0441732i	0.187919	+	0.982185i	$0.439826\pi$
$618$	11.5454	−	1.67102i	0.464425	−	0.0672183i
$619$	0.138731	−	0.107524i	0.00557606	−	0.00432177i	−0.609809	−	0.792549i	$-0.708754\pi$
$619$	0.138731	−	0.107524i	0.00557606	−	0.00432177i	0.615385	+	0.788227i	$0.289001\pi$
$620$	−2.11915	+	12.0183i	−0.0851073	+	0.482667i
$621$	−35.0693	−	12.5828i	−1.40728	−	0.504932i
$622$	−0.532996	−	3.02277i	−0.0213712	−	0.121202i
$623$	−3.81431	−	3.46130i	−0.152817	−	0.138674i
$624$	−0.237198	+	0.0631231i	−0.00949552	+	0.00252695i
$625$	28.3591	+	12.8908i	1.13436	+	0.515631i
$626$	13.5232	+	8.16131i	0.540497	+	0.326192i
$627$	−59.4510	−	40.0802i	−2.37425	−	1.60065i
$628$	−5.40833	+	11.3106i	−0.215816	+	0.451340i
$629$	4.09653	−	13.6834i	0.163339	−	0.545591i
$630$	−2.18731	+	3.03822i	−0.0871444	+	0.121046i
$631$	5.22631	−	5.53956i	0.208056	−	0.220526i	−0.614940	−	0.788574i	$-0.710820\pi$
$631$	5.22631	−	5.53956i	0.208056	−	0.220526i	0.822996	+	0.568048i	$0.192301\pi$
$632$	15.1565	−	18.7912i	0.602895	−	0.747472i
$633$	−1.28921	+	0.758121i	−0.0512415	+	0.0301326i
$634$	−0.312039	−	0.241849i	−0.0123927	−	0.00960504i
$635$	−6.78889	+	6.16059i	−0.269409	+	0.244476i
$636$	0.177433	+	0.00891267i	0.00703568	+	0.000353410i
$637$	3.22283	−	1.94499i	0.127693	−	0.0770633i
$638$	−48.7104	+	5.69343i	−1.92846	+	0.225405i
$639$	−0.629660	−	0.366407i	−0.0249090	−	0.0144948i
$640$	6.43442	+	14.9167i	0.254343	+	0.589633i
$641$	1.35034	−	13.8827i	0.0533352	−	0.548334i	−0.930129	−	0.367232i	$-0.880305\pi$
$641$	1.35034	−	13.8827i	0.0533352	−	0.548334i	0.983464	−	0.181101i	$-0.0579662\pi$
$642$	5.15592	+	4.42750i	0.203488	+	0.174739i
$643$	−1.66450	+	4.31116i	−0.0656414	+	0.170016i	−0.961823	−	0.273671i	$-0.911762\pi$
$643$	−1.66450	+	4.31116i	−0.0656414	+	0.170016i	0.896182	+	0.443687i	$0.146330\pi$
$644$	2.45524	−	3.57983i	0.0967502	−	0.141065i
$645$	1.67533	−	3.09443i	0.0659659	−	0.121843i
$646$	−13.1292	−	24.9251i	−0.516560	−	0.980664i
$647$	−12.2620	+	21.2384i	−0.482069	+	0.834968i	−0.999788	−	0.0205823i	$-0.993448\pi$
$647$	−12.2620	+	21.2384i	−0.482069	+	0.834968i	0.517719	+	0.855551i	$0.326781\pi$
$648$	24.3023	+	9.03377i	0.954684	+	0.354880i
$649$	−14.7143	−	25.4860i	−0.577588	−	1.00041i
$650$	0.590302	−	0.936578i	0.0231536	−	0.0367356i
$651$	−3.19573	+	1.26327i	−0.125251	+	0.0495114i
$652$	1.02085	+	2.13493i	0.0399796	+	0.0836102i
$653$	36.1381	−	5.65189i	1.41419	−	0.221176i	0.599178	−	0.800616i	$-0.295494\pi$
$653$	36.1381	−	5.65189i	1.41419	−	0.221176i	0.815015	+	0.579440i	$0.196729\pi$
$654$	15.7566	+	28.0245i	0.616131	+	1.09584i
$655$	−1.41373	−	1.01047i	−0.0552391	−	0.0394825i
$656$	−1.46642	+	1.96974i	−0.0572540	+	0.0769054i
$657$	−20.9419	−	19.8933i	−0.817020	−	0.776110i
$658$	1.30773	−	3.03167i	0.0509808	−	0.118187i
$659$	8.33057	+	4.59661i	0.324513	+	0.179059i	0.637001	−	0.770863i	$-0.280175\pi$
$659$	8.33057	+	4.59661i	0.324513	+	0.179059i	−0.312488	+	0.949922i	$0.601162\pi$
$660$	−7.13976	+	31.2349i	−0.277915	+	1.21582i
$661$	6.09723	+	28.1479i	0.237155	+	1.09483i	0.928219	+	0.372035i	$0.121340\pi$
$661$	6.09723	+	28.1479i	0.237155	+	1.09483i	−0.691064	+	0.722794i	$0.742858\pi$
$662$	0.795678	−	5.82540i	0.0309249	−	0.226410i
$663$	2.76121	+	3.23780i	0.107236	+	0.125746i
$664$	6.26323	+	16.2222i	0.243061	+	0.629543i
$665$	9.47272	+	2.24508i	0.367336	+	0.0870603i
$666$	−5.95832	+	6.52110i	−0.230880	+	0.252688i
$667$	45.4773	+	48.2031i	1.76089	+	1.86643i
$668$	14.5228	−	1.12880i	0.561905	−	0.0436747i
$669$	−21.3203	−	5.31050i	−0.824290	−	0.205316i
$670$	15.9535	−	8.80279i	0.616339	−	0.340081i
$671$	−5.01673	−	51.5765i	−0.193669	−	1.99109i
$672$	−2.82965	+	4.02651i	−0.109156	+	0.155326i
$673$	43.9892	−	14.1046i	1.69566	−	0.543691i	0.708819	−	0.705391i	$-0.249228\pi$
$673$	43.9892	−	14.1046i	1.69566	−	0.543691i	0.986840	+	0.161700i	$0.0516976\pi$
$674$	13.1583	−	11.0411i	0.506838	−	0.425288i
$675$	−10.4952	+	4.34387i	−0.403960	+	0.167196i
$676$	11.4555	+	9.61229i	0.440595	+	0.369703i
$677$	−32.2741	−	13.1854i	−1.24039	−	0.506756i	−0.339422	−	0.940634i	$-0.610231\pi$
$677$	−32.2741	−	13.1854i	−1.24039	−	0.506756i	−0.900972	+	0.433878i	$0.857145\pi$
$678$	1.42562	+	0.882698i	0.0547505	+	0.0338998i
$679$	−0.376153	+	1.46032i	−0.0144354	+	0.0560418i
$680$	−22.3237	+	25.5801i	−0.856075	+	0.980953i
$681$	−17.2758	+	11.0823i	−0.662009	+	0.424675i
$682$	14.6326	−	14.3516i	0.560311	−	0.549549i
$683$	−18.5187	+	12.1800i	−0.708600	+	0.466053i	−0.851953	−	0.523618i	$-0.824582\pi$
$683$	−18.5187	+	12.1800i	−0.708600	+	0.466053i	0.143353	+	0.989672i	$0.454211\pi$
$684$	−0.884048	−	24.9839i	−0.0338024	−	0.955284i
$685$	1.61872	−	27.7924i	0.0618483	−	1.06189i
$686$	−2.07009	+	6.05005i	−0.0790362	+	0.230992i
$687$	−10.3299	+	20.9848i	−0.394109	+	0.800620i
$688$	−0.0895704	+	0.170045i	−0.00341484	+	0.00648291i
$689$	−0.0259302	−	0.0411411i	−0.000987862	−	0.00156735i
$690$	−27.6088	+	12.1718i	−1.05105	+	0.463371i
$691$	33.1528	−	6.51100i	1.26119	−	0.247690i	0.482947	−	0.875650i	$-0.339567\pi$
$691$	33.1528	−	6.51100i	1.26119	−	0.247690i	0.778246	+	0.627960i	$0.216110\pi$
$692$	15.7872	+	10.3834i	0.600138	+	0.394717i
$693$	−8.54613	+	2.89158i	−0.324641	+	0.109842i
$694$	−14.5352	−	7.29985i	−0.551748	−	0.277098i
$695$	−10.7796	−	41.8490i	−0.408894	−	1.58742i
$696$	−31.2618	−	33.9019i	−1.18498	−	1.28505i
$697$	41.7745	+	8.20424i	1.58232	+	0.310758i
$698$	−8.30821	−	8.14863i	−0.314470	−	0.308430i
$699$	−45.5864	−	9.49402i	−1.72423	−	0.359097i
$700$	−0.179094	−	1.31120i	−0.00676911	−	0.0495587i
$701$	16.5254	−	6.01477i	0.624157	−	0.227175i	−0.0105290	−	0.999945i	$-0.503352\pi$
$701$	16.5254	−	6.01477i	0.624157	−	0.227175i	0.634686	+	0.772770i	$0.281129\pi$
$702$	−0.668076	−	2.54538i	−0.0252149	−	0.0960692i
$703$	21.5849	+	7.85627i	0.814090	+	0.296305i
$704$	6.84281	−	31.5899i	0.257898	−	1.19059i
$705$	27.0078	−	18.8424i	1.01717	−	0.709645i
$706$	13.6534	−	9.75886i	0.513852	−	0.367279i
$707$	−0.0843706	+	4.35012i	−0.00317308	+	0.163603i
$708$	4.17132	−	9.37477i	0.156768	−	0.352326i
$709$	13.8338	+	20.1702i	0.519539	+	0.757506i	0.992323	−	0.123672i	$-0.0394670\pi$
$709$	13.8338	+	20.1702i	0.519539	+	0.757506i	−0.472784	+	0.881178i	$0.656751\pi$
$710$	−0.574064	+	0.136056i	−0.0215442	+	0.00510608i
$711$	19.5148	+	15.8505i	0.731863	+	0.594441i
$712$	8.28506	+	27.6740i	0.310496	+	1.03713i
$713$	−27.3633	−	4.27954i	−1.02476	−	0.160270i
$714$	−3.49581	−	0.587650i	−0.130827	−	0.0219922i
$715$	8.11916	−	3.31704i	0.303639	−	0.124050i
$716$	−6.21982	−	1.99431i	−0.232446	−	0.0745307i
$717$	−7.87875	+	5.96393i	−0.294237	+	0.222727i
$718$	−0.519516	−	26.7861i	−0.0193882	−	0.999648i
$719$	−11.9019	−	15.9870i	−0.443865	−	0.596214i	0.522738	−	0.852494i	$-0.324911\pi$
$719$	−11.9019	−	15.9870i	−0.443865	−	0.596214i	−0.966603	+	0.256279i	$0.917503\pi$
$720$	1.87537	−	0.801372i	0.0698911	−	0.0298654i
$721$	−3.79137	−	0.443148i	−0.141198	−	0.0165037i
$722$	25.5675	−	11.6219i	0.951524	−	0.432521i
$723$	−7.80330	+	6.39753i	−0.290208	+	0.237927i
$724$	−3.16144	−	3.91957i	−0.117494	−	0.145670i
$725$	20.1424	+	1.56559i	0.748071	+	0.0581447i
$726$	27.3407	−	24.2476i	1.01471	−	0.899914i
$727$	−24.9119	−	0.966693i	−0.923929	−	0.0358527i	−0.427582	−	0.903977i	$-0.640634\pi$
$727$	−24.9119	−	0.966693i	−0.923929	−	0.0358527i	−0.496348	+	0.868124i	$0.665326\pi$
$728$	0.826875			0.0306460
$729$	−9.49400	+	25.2758i	−0.351630	+	0.936139i
$730$	−23.3913			−0.865751
$731$	3.32945	+	0.129198i	0.123144	+	0.00477855i
$732$	13.5178	−	11.9885i	0.499632	−	0.443108i
$733$	−1.13586	−	0.0882856i	−0.0419538	−	0.00326090i	0.0564984	−	0.998403i	$-0.482006\pi$
$733$	−1.13586	−	0.0882856i	−0.0419538	−	0.00326090i	−0.0984522	+	0.995142i	$0.531389\pi$
$734$	−9.77702	−	12.1216i	−0.360876	−	0.447417i
$735$	−24.1868	+	19.8295i	−0.892143	+	0.731423i
$736$	−36.1091	+	16.4136i	−1.33100	+	0.605013i
$737$	43.6147	+	5.09783i	1.60657	+	0.187781i
$738$	−21.0645	−	15.7940i	−0.775394	−	0.581386i
$739$	−30.5311	−	41.0103i	−1.12310	−	1.50859i	−0.834391	−	0.551173i	$-0.814180\pi$
$739$	−30.5311	−	41.0103i	−1.12310	−	1.50859i	−0.288712	−	0.957416i	$-0.593227\pi$
$740$	−0.199046	−	10.2628i	−0.00731709	−	0.377267i
$741$	−5.45631	+	4.13023i	−0.200443	+	0.151728i
$742$	0.0385772	+	0.0123693i	0.00141621	+	0.000454090i
$743$	27.6731	−	11.3057i	1.01523	−	0.414766i	0.191342	−	0.981523i	$-0.438716\pi$
$743$	27.6731	−	11.3057i	1.01523	−	0.414766i	0.823885	+	0.566757i	$0.191802\pi$
$744$	19.0061	+	3.19496i	0.696799	+	0.117133i
$745$	4.23640	+	0.662561i	0.155210	+	0.0242744i
$746$	−1.07546	−	3.59228i	−0.0393754	−	0.131523i
$747$	−16.9157	+	6.46470i	−0.618913	+	0.236531i
$748$	−29.5211	+	6.99663i	−1.07940	+	0.255822i
$749$	−1.25778	−	1.83388i	−0.0459581	−	0.0670085i
$750$	4.81383	−	10.8188i	0.175776	−	0.395046i
$751$	0.431703	−	22.2585i	0.0157531	−	0.812225i	−0.905741	−	0.423832i	$-0.860685\pi$
$751$	0.431703	−	22.2585i	0.0157531	−	0.812225i	0.921494	−	0.388393i	$-0.126970\pi$
$752$	−1.46329	+	1.04590i	−0.0533607	+	0.0381399i
$753$	6.40634	−	4.46949i	0.233460	−	0.162877i
$754$	−0.990928	+	4.57463i	−0.0360875	+	0.166598i
$755$	−3.39538	−	1.23582i	−0.123570	−	0.0449759i
$756$	−2.56755	−	1.81749i	−0.0933809	−	0.0661015i
$757$	13.6915	−	4.98332i	0.497628	−	0.181122i	−0.0809989	−	0.996714i	$-0.525811\pi$
$757$	13.6915	−	4.98332i	0.497628	−	0.181122i	0.578627	+	0.815592i	$0.303589\pi$
$758$	2.79907	+	20.4929i	0.101667	+	0.744334i
$759$	−71.1873	−	14.8258i	−2.58394	−	0.538142i
$760$	−38.9802	−	38.2315i	−1.41396	−	1.38680i
$761$	16.6293	+	3.26589i	0.602812	+	0.118388i	0.484802	−	0.874624i	$-0.338892\pi$
$761$	16.6293	+	3.26589i	0.602812	+	0.118388i	0.118010	+	0.993012i	$0.462349\pi$
$762$	3.63919	+	3.94652i	0.131834	+	0.142967i
$763$	−2.62413	−	10.1875i	−0.0949998	−	0.368812i
$764$	19.4657	+	9.77606i	0.704245	+	0.353685i
$765$	−26.5592	−	23.3384i	−0.960250	−	0.843801i
$766$	−26.0437	−	17.1292i	−0.940998	−	0.618904i
$767$	−2.75612	+	0.541284i	−0.0995177	+	0.0195446i
$768$	26.2033	−	11.5522i	0.945532	−	0.416853i
$769$	20.3016	+	32.2107i	0.732095	+	1.16155i	0.981186	+	0.193067i	$0.0618435\pi$
$769$	20.3016	+	32.2107i	0.732095	+	1.16155i	−0.249091	+	0.968480i	$0.580132\pi$
$770$	−3.40506	+	6.46434i	−0.122710	+	0.232959i
$771$	−11.3151	+	22.9863i	−0.407504	+	0.827832i
$772$	−4.93368	+	14.4192i	−0.177567	+	0.518959i
$773$	1.71053	−	29.3687i	0.0615236	−	1.05632i	−0.816390	−	0.577500i	$-0.804028\pi$
$773$	1.71053	−	29.3687i	0.0615236	−	1.05632i	0.877914	−	0.478818i	$-0.158935\pi$
$774$	−1.81983	−	0.966537i	−0.0654123	−	0.0347415i
$775$	−7.05436	+	4.63973i	−0.253400	+	0.166664i
$776$	6.03807	−	5.92210i	0.216754	−	0.212591i
$777$	2.43282	−	1.56064i	0.0872769	−	0.0559877i
$778$	−4.14327	+	4.74766i	−0.148543	+	0.170212i
$779$	−17.0777	+	66.2997i	−0.611872	+	2.37543i
$780$	2.60001	+	1.60985i	0.0930954	+	0.0576418i
$781$	−1.31618	−	0.537720i	−0.0470967	−	0.0192411i
$782$	−21.8862	−	18.3647i	−0.782647	−	0.656719i
$783$	35.4159	−	32.4348i	1.26566	−	1.15913i
$784$	1.30861	−	1.09805i	0.0467360	−	0.0392161i
$785$	−27.1528	+	8.70618i	−0.969123	+	0.310737i
$786$	−0.585085	+	0.832559i	−0.0208693	+	0.0296964i
$787$	0.196511	+	2.02031i	0.00700486	+	0.0720163i	0.998154	−	0.0607393i	$-0.0193458\pi$
$787$	0.196511	+	2.02031i	0.00700486	+	0.0720163i	−0.991149	+	0.132756i	$0.957617\pi$
$788$	7.15242	−	3.94654i	0.254795	−	0.140590i
$789$	−6.82402	−	1.69974i	−0.242941	−	0.0605123i
$790$	20.2986	−	1.57773i	0.722191	−	0.0561332i
$791$	−0.376514	−	0.399082i	−0.0133873	−	0.0141897i
$792$	49.4164	+	10.8811i	1.75594	+	0.386643i
$793$	−4.81255	−	1.14059i	−0.170899	−	0.0405037i
$794$	0.956315	+	2.47692i	0.0339383	+	0.0879025i
$795$	0.262191	+	0.307445i	0.00929896	+	0.0109040i
$796$	1.03928	−	7.60888i	0.0368363	−	0.269690i
$797$	5.89734	+	27.2251i	0.208894	+	0.964364i	0.954554	+	0.298037i	$0.0963320\pi$
$797$	5.89734	+	27.2251i	0.208894	+	0.964364i	−0.745660	+	0.666327i	$0.767866\pi$
$798$	1.27032	−	5.55740i	0.0449690	−	0.196730i
$799$	27.3018	+	15.0645i	0.965868	+	0.532943i
$800$	−4.78946	+	11.1032i	−0.169333	+	0.392558i
$801$	−28.8486	+	8.52946i	−1.01932	+	0.301374i
$802$	−15.1462	+	20.3449i	−0.534831	+	0.718403i
$803$	−45.8614	−	32.7797i	−1.61841	−	1.15677i
$804$	7.50364	+	13.3459i	0.264633	+	0.470673i
$805$	9.75438	−	1.52556i	0.343797	−	0.0537688i
$806$	−0.843874	−	1.76481i	−0.0297242	−	0.0621629i
$807$	31.7617	−	12.5554i	1.11806	−	0.441970i
$808$	13.0114	−	20.6440i	0.457739	−	0.726253i
$809$	17.9857	+	31.1522i	0.632345	+	1.09525i	0.987071	+	0.160284i	$0.0512409\pi$
$809$	17.9857	+	31.1522i	0.632345	+	1.09525i	−0.354726	+	0.934970i	$0.615426\pi$
$810$	8.52308	+	20.1358i	0.299470	+	0.707499i
$811$	−7.25012	+	12.5576i	−0.254586	+	0.440956i	−0.964783	−	0.263047i	$-0.915273\pi$
$811$	−7.25012	+	12.5576i	−0.254586	+	0.440956i	0.710197	+	0.704003i	$0.248606\pi$
$812$	2.60760	+	4.95041i	0.0915089	+	0.173725i
$813$	4.11394	−	7.59868i	0.144282	−	0.266497i
$814$	−9.75068	+	14.2168i	−0.341761	+	0.498300i
$815$	−1.93856	+	5.02100i	−0.0679049	+	0.175878i
$816$	1.46506	+	1.25808i	0.0512875	+	0.0440416i
$817$	−0.518747	+	5.33319i	−0.0181487	+	0.186585i
$818$	8.81564	+	20.4370i	0.308232	+	0.714561i
$819$	−0.00294078	+	0.861090i	−0.000102759	+	0.0300889i
$820$	30.3876	−	3.55181i	1.06118	−	0.124034i
$821$	−13.4955	+	8.14460i	−0.470998	+	0.284249i	−0.732267	−	0.681017i	$-0.761538\pi$
$821$	−13.4955	+	8.14460i	−0.470998	+	0.284249i	0.261270	+	0.965266i	$0.415859\pi$
$822$	−16.2818	−	0.817855i	−0.567894	−	0.0285260i
$823$	18.1568	−	16.4764i	0.632907	−	0.574333i	−0.291107	−	0.956690i	$-0.594024\pi$
$823$	18.1568	−	16.4764i	0.632907	−	0.574333i	0.924014	+	0.382358i	$0.124888\pi$
$824$	16.9213	+	13.1150i	0.589480	+	0.456882i
$825$	−19.1088	+	11.2370i	−0.665284	+	0.391221i
$826$	1.46897	−	1.82124i	0.0511121	−	0.0633691i
$827$	−7.93503	+	8.41064i	−0.275928	+	0.292467i	−0.850486	−	0.525997i	$-0.823692\pi$
$827$	−7.93503	+	8.41064i	−0.275928	+	0.292467i	0.574558	+	0.818464i	$0.305174\pi$
$828$	−10.4127	−	23.1166i	−0.361865	−	0.803357i
$829$	9.94059	−	33.2039i	0.345251	−	1.15322i	−0.592401	−	0.805643i	$-0.701820\pi$
$829$	9.94059	−	33.2039i	0.345251	−	1.15322i	0.937652	−	0.347575i	$-0.112995\pi$
$830$	−6.32632	+	13.2304i	−0.219590	+	0.459233i
$831$	41.0759	+	27.6922i	1.42491	+	0.960633i
$832$	−2.64125	−	1.59400i	−0.0915689	−	0.0552621i
$833$	−26.9607	−	12.2551i	−0.934133	−	0.424615i
$834$	−24.4549	+	6.50793i	−0.846804	+	0.225351i
$835$	24.5345	+	22.2639i	0.849052	+	0.770473i
$836$	−8.47232	−	48.0489i	−0.293021	−	1.66181i
$837$	−3.39475	+	19.7812i	−0.117340	+	0.683739i
$838$	−5.32835	+	30.2186i	−0.184065	+	1.04388i
$839$	32.4462	−	25.1477i	1.12017	−	0.868195i	0.127835	−	0.991796i	$-0.459197\pi$
$839$	32.4462	−	25.1477i	1.12017	−	0.868195i	0.992332	+	0.123601i	$0.0394443\pi$
$840$	−6.79947	+	0.984119i	−0.234604	+	0.0339553i
$841$	−54.3520	+	15.1299i	−1.87421	+	0.521721i
$842$	5.35114	+	15.6393i	0.184413	+	0.538966i
$843$	0.0564090	−	0.0739937i	0.00194283	−	0.00254848i
$844$	−0.980443	−	0.272925i	−0.0337483	−	0.00939447i
$845$	1.97760	+	33.9540i	0.0680314	+	1.16805i
$846$	−11.1598	−	15.7267i	−0.383681	−	0.540693i
$847$	−10.6858	+	5.36661i	−0.367168	+	0.184399i
$848$	−0.0145110	−	0.0166278i	−0.000498311	−	0.000571001i
$849$	−35.0183	−	10.1797i	−1.20182	−	0.349366i
$850$	−8.70344	+	0.337733i	−0.298526	+	0.0115842i
$851$	23.2779	−	0.903287i	0.797955	−	0.0309643i
$852$	−0.118174	−	0.481444i	−0.00404858	−	0.0164940i
$853$	6.87539	+	7.87832i	0.235409	+	0.269749i	0.858970	−	0.512026i	$-0.171105\pi$
$853$	6.87539	+	7.87832i	0.235409	+	0.269749i	−0.623561	+	0.781775i	$0.714315\pi$
$854$	3.68188	−	1.84911i	0.125991	−	0.0632752i
$855$	39.9521	−	40.4572i	1.36633	−	1.38361i
$856$	0.725180	+	12.4509i	0.0247862	+	0.425562i
$857$	3.35102	+	0.932819i	0.114469	+	0.0318645i	0.324933	−	0.945737i	$-0.394658\pi$
$857$	3.35102	+	0.932819i	0.114469	+	0.0318645i	−0.210465	+	0.977601i	$0.567498\pi$
$858$	−1.98033	−	4.73878i	−0.0676072	−	0.161779i
$859$	−9.23310	−	26.9848i	−0.315029	−	0.920708i	−0.984116	−	0.177524i	$-0.943191\pi$
$859$	−9.23310	−	26.9848i	−0.315029	−	0.920708i	0.669087	−	0.743184i	$-0.266685\pi$
$860$	2.30679	−	0.642138i	0.0786607	−	0.0218967i
$861$	5.33171	+	6.76677i	0.181704	+	0.230611i
$862$	−8.15211	+	6.31836i	−0.277662	+	0.215204i
$863$	6.87480	−	38.9889i	0.234021	−	1.32720i	−0.610645	−	0.791905i	$-0.709090\pi$
$863$	6.87480	−	38.9889i	0.234021	−	1.32720i	0.844666	−	0.535294i	$-0.179799\pi$
$864$	11.5054	+	26.3406i	0.391421	+	0.896125i
$865$	7.46280	+	42.3236i	0.253743	+	1.43905i
$866$	23.3489	+	21.1880i	0.793426	+	0.719996i
$867$	1.05067	−	3.89453i	0.0356825	−	0.132265i
$868$	−2.12876	−	0.967642i	−0.0722550	−	0.0328439i
$869$	42.0087	+	25.3524i	1.42505	+	0.860021i
$870$	2.70392	−	38.7970i	0.0916714	−	1.31534i
$871$	1.80797	−	3.78105i	0.0612607	−	0.128116i
$872$	−16.9218	+	56.5229i	−0.573046	+	1.91411i
$873$	6.14567	+	6.30898i	0.208000	+	0.213527i
$874$	31.5301	−	33.4199i	1.06652	−	1.13045i
$875$	−2.43257	+	3.01591i	−0.0822358	+	0.101956i
$876$	−0.157017	−	19.6545i	−0.00530512	−	0.664066i
$877$	22.4718	+	17.4170i	0.758820	+	0.588130i	0.916816	−	0.399310i	$-0.130750\pi$
$877$	22.4718	+	17.4170i	0.758820	+	0.588130i	−0.157996	+	0.987440i	$0.550503\pi$
$878$	3.97416	−	3.60636i	0.134121	−	0.121709i
$879$	−7.11324	−	13.8859i	−0.239924	−	0.468360i
$880$	3.40772	−	2.05657i	0.114874	−	0.0693270i
$881$	55.0252	−	6.43153i	1.85385	−	0.216684i	0.885215	−	0.465182i	$-0.154011\pi$
$881$	55.0252	−	6.43153i	1.85385	−	0.216684i	0.968632	+	0.248498i	$0.0799370\pi$
$882$	11.7246	+	14.0702i	0.394789	+	0.473767i
$883$	16.3814	+	37.9763i	0.551277	+	1.27800i	0.935030	+	0.354568i	$0.115372\pi$
$883$	16.3814	+	37.9763i	0.551277	+	1.27800i	−0.383754	+	0.923435i	$0.625369\pi$
$884$	−0.280330	+	2.88204i	−0.00942851	+	0.0969336i
$885$	22.0196	−	7.73127i	0.740181	−	0.259884i
$886$	11.6477	−	30.1684i	0.391313	−	1.01353i
$887$	−8.62877	+	12.5810i	−0.289726	+	0.422430i	−0.942031	−	0.335526i	$-0.891086\pi$
$887$	−8.62877	+	12.5810i	−0.289726	+	0.422430i	0.652305	+	0.757956i	$0.273802\pi$
$888$	−16.2045	+	0.443811i	−0.543789	+	0.0148933i
$889$	−0.818645	−	1.55416i	−0.0274565	−	0.0521248i
$890$	−12.1811	+	21.0982i	−0.408310	+	0.707214i
$891$	−11.5071	+	51.4225i	−0.385502	+	1.72272i
$892$	−7.47564	−	12.9482i	−0.250303	−	0.433538i
$893$	−26.7382	+	42.4230i	−0.894760	+	1.41963i
$894$	0.368155	−	2.48379i	0.0123129	−	0.0830703i
$895$	−6.40857	−	13.4024i	−0.214215	−	0.447993i
$896$	−3.07539	+	0.480982i	−0.102742	+	0.0160685i
$897$	−3.53838	+	5.97037i	−0.118143	+	0.199345i
$898$	−14.0273	−	10.0261i	−0.468098	−	0.334577i
$899$	21.3177	−	28.6346i	0.710985	−	0.955018i
$900$	−7.08667	−	3.08564i	−0.236222	−	0.102855i
$901$	−0.151542	+	0.351313i	−0.00504858	+	0.0117039i
$902$	−44.9886	−	24.8237i	−1.49796	−	0.826537i
$903$	0.494111	+	0.458765i	0.0164430	+	0.0152667i
$904$	0.651448	+	3.00742i	0.0216668	+	0.100025i
$905$	1.54996	−	11.3477i	0.0515224	−	0.377211i
$906$	−0.707767	+	1.99399i	−0.0235140	+	0.0662460i
$907$	21.2051	+	54.9227i	0.704105	+	1.82368i	0.549086	+	0.835766i	$0.314976\pi$
$907$	21.2051	+	54.9227i	0.704105	+	1.82368i	0.155019	+	0.987912i	$0.450456\pi$
$908$	−13.5903	−	3.22095i	−0.451009	−	0.106891i
$909$	21.4519	+	13.6232i	0.711515	+	0.451853i
$910$	0.478542	+	0.507225i	0.0158635	+	0.0168144i
$911$	49.5930	−	3.85468i	1.64309	−	0.127711i	0.777642	−	0.628708i	$-0.216416\pi$
$911$	49.5930	−	3.85468i	1.64309	−	0.127711i	0.865449	+	0.500997i	$0.167033\pi$
$912$	−2.15678	+	2.23445i	−0.0714181	+	0.0739899i
$913$	−30.9441	+	17.0742i	−1.02410	+	0.565074i
$914$	−2.17157	−	22.3257i	−0.0718292	−	0.738469i
$915$	40.9315	+	3.65148i	1.35315	+	0.120714i
$916$	−15.1560	+	4.85958i	−0.500769	+	0.160565i
$917$	0.255068	−	0.214028i	0.00842310	−	0.00706782i
$918$	−13.5419	+	15.6613i	−0.446949	+	0.516900i
$919$	−37.1917	−	31.2075i	−1.22684	−	1.02944i	−0.998438	−	0.0558744i	$-0.982205\pi$
$919$	−37.1917	−	31.2075i	−1.22684	−	1.02944i	−0.228402	−	0.973567i	$-0.573350\pi$
$920$	−51.2596	−	20.9419i	−1.68998	−	0.690433i
$921$	−9.90755	+	5.32029i	−0.326465	+	0.175309i
$922$	0.896951	−	3.48218i	0.0295395	−	0.114679i
$923$	−0.0892257	+	0.102241i	−0.00293690	+	0.00336531i
$924$	−5.45452	−	2.81771i	−0.179441	−	0.0926958i
$925$	5.07023	−	4.97285i	0.166708	−	0.163506i
$926$	1.08318	−	0.712417i	0.0355954	−	0.0234115i
$927$	−13.7178	+	17.5748i	−0.450552	+	0.577232i
$928$	2.97268	−	51.0389i	0.0975830	−	1.67543i
$929$	6.40248	−	18.7120i	0.210059	−	0.613919i	−0.789941	−	0.613183i	$-0.789889\pi$
$929$	6.40248	−	18.7120i	0.210059	−	0.613919i	1.00000		0.000736715i	$-0.000234504\pi$
$930$	9.03967	+	13.5079i	0.296422	+	0.442940i
$931$	22.1960	−	42.1381i	0.727445	−	1.38102i
$932$	−16.8952	−	26.8061i	−0.553421	−	0.878062i
$933$	4.73310	+	3.46524i	0.154955	+	0.113447i
$934$	−20.2827	+	3.98339i	−0.663670	+	0.130341i
$935$	−57.6510	−	37.9177i	−1.88539	−	1.24004i
$936$	2.50948	−	4.12627i	0.0820249	−	0.134871i
$937$	−0.455941	−	0.228982i	−0.0148949	−	0.00748052i	0.441336	−	0.897342i	$-0.354505\pi$
$937$	−0.455941	−	0.228982i	−0.0148949	−	0.00748052i	−0.456231	+	0.889861i	$0.650801\pi$
$938$	0.870885	+	3.38098i	0.0284354	+	0.110393i
$939$	−29.4502	+	6.62606i	−0.961072	+	0.216233i
$940$	21.9888	+	4.31847i	0.717197	+	0.140853i
$941$	11.9105	+	11.6817i	0.388272	+	0.380814i	0.867968	−	0.496621i	$-0.165426\pi$
$941$	11.9105	+	11.6817i	0.388272	+	0.380814i	−0.479696	+	0.877435i	$0.659253\pi$
$942$	5.22505	+	15.8590i	0.170241	+	0.516713i
$943$	9.39647	+	68.7944i	0.305991	+	2.24025i
$944$	−1.19778	+	0.435957i	−0.0389845	+	0.0141892i
$945$	−1.00066	−	7.08432i	−0.0325514	−	0.230453i
$946$	−3.77897	−	1.37543i	−0.122865	−	0.0447192i
$947$	2.84729	−	13.1446i	0.0925245	−	0.427140i	−0.907451	−	0.420158i	$-0.861975\pi$
$947$	2.84729	−	13.1446i	0.0925245	−	0.427140i	0.999976	−	0.00698289i	$-0.00222274\pi$
$948$	1.46195	+	17.0453i	0.0474818	+	0.553606i
$949$	−4.37716	+	3.12861i	−0.142089	+	0.101559i
$950$	0.271618	−	14.0045i	0.00881244	−	0.454367i
$951$	0.750343	−	0.0790400i	0.0243315	−	0.00256305i
$952$	−3.67953	−	5.36488i	−0.119254	−	0.173877i
$953$	−44.1127	+	10.4549i	−1.42895	+	0.338668i	−0.871031	−	0.491227i	$-0.836548\pi$
$953$	−44.1127	+	10.4549i	−1.42895	+	0.338668i	−0.557920	+	0.829895i	$0.688400\pi$
$954$	0.178803	−	0.154968i	0.00578895	−	0.00501728i
$955$	14.2090	+	47.4613i	0.459792	+	1.53581i
$956$	−6.64337	−	1.03900i	−0.214862	−	0.0336038i
$957$	59.6701	−	72.2769i	1.92886	−	2.33638i
$958$	16.1588	−	6.60159i	0.522066	−	0.213288i
$959$	5.07964	+	1.62872i	0.164030	+	0.0525941i
$960$	23.6164	+	9.96411i	0.762215	+	0.321590i
$961$	−0.311826	−	16.0777i	−0.0100589	−	0.518635i
$962$	0.982552	+	1.31980i	0.0316787	+	0.0425519i
$963$	−12.9686	+	0.710906i	−0.417909	+	0.0229086i
$964$	−6.82000	−	0.797144i	−0.219658	−	0.0256743i
$965$	−31.5547	+	14.3434i	−1.01578	+	0.461730i
$966$	−0.938944	−	5.70469i	−0.0302100	−	0.183545i
$967$	−23.3552	−	28.9559i	−0.751051	−	0.931158i	0.248244	−	0.968698i	$-0.420147\pi$
$967$	−23.3552	−	28.9559i	−0.751051	−	0.931158i	−0.999295	+	0.0375400i	$0.988048\pi$
$968$	66.8631	+	5.19701i	2.14906	+	0.167038i
$969$	51.0776	+	17.0221i	1.64085	+	0.546830i
$970$	7.12721	+	0.276568i	0.228841	+	0.00888007i
$971$	−28.7172			−0.921577			−0.460789	−	0.887510i	$-0.652433\pi$
$971$	−28.7172			−0.921577			−0.460789	+	0.887510i	$0.652433\pi$
$972$	−16.8619	+	7.29668i	−0.540845	+	0.234041i
$973$	8.28049			0.265460
$974$	36.7943	+	1.42779i	1.17897	+	0.0457493i
$975$	0.424309	+	2.07280i	0.0135888	+	0.0663826i
$976$	−2.23774	−	0.173931i	−0.0716284	−	0.00556740i
$977$	3.85311	+	4.77711i	0.123272	+	0.152833i	0.836241	−	0.548363i	$-0.184749\pi$
$977$	3.85311	+	4.77711i	0.123272	+	0.152833i	−0.712969	+	0.701196i	$0.752650\pi$
$978$	2.94919	+	1.11167i	0.0943048	+	0.0355472i
$979$	−53.4487	+	24.2954i	−1.70823	+	0.776485i
$980$	−21.1390	−	2.47079i	−0.675261	−	0.0789266i
$981$	−58.8015	−	17.8231i	−1.87739	−	0.569046i
$982$	−13.9762	−	18.7733i	−0.445998	−	0.599080i
$983$	0.228438	+	11.7782i	0.00728603	+	0.375666i	0.985653	+	0.168787i	$0.0539850\pi$
$983$	0.228438	+	11.7782i	0.00728603	+	0.375666i	−0.978367	+	0.206879i	$0.933669\pi$
$984$	−5.99241	−	47.9435i	−0.191031	−	1.52838i
$985$	17.6923	+	5.67282i	0.563725	+	0.180751i
$986$	34.0904	−	13.9275i	1.08566	−	0.443541i
$987$	2.20543	+	5.91199i	0.0701997	+	0.188181i
$988$	−4.60076	−	0.719546i	−0.146370	−	0.0228918i
$989$	1.55855	+	5.20592i	0.0495590	+	0.165539i
$990$	21.9243	+	36.6105i	0.696801	+	1.16356i
$991$	−35.3466	+	8.37730i	−1.12282	+	0.266114i	−0.749771	−	0.661697i	$-0.769836\pi$
$991$	−35.3466	+	8.37730i	−1.12282	+	0.266114i	−0.373051	+	0.927811i	$0.621688\pi$
$992$	12.0851	+	17.6205i	0.383702	+	0.559451i
$993$	6.60672	+	9.08895i	0.209658	+	0.288429i
$994$	0.00219208	−	0.113023i	6.95285e−5	−	0.00358487i
$995$	14.2098	−	10.1565i	0.450480	−	0.321984i
$996$	−11.1593	−	5.22688i	−0.353596	−	0.165620i
$997$	−5.69852	+	26.3073i	−0.180474	+	0.833161i	0.793868	+	0.608090i	$0.208064\pi$
$997$	−5.69852	+	26.3073i	−0.180474	+	0.833161i	−0.974342	+	0.225071i	$0.927738\pi$
$998$	−6.93268	−	2.52329i	−0.219450	−	0.0798734i
$999$	−0.404544	−	16.8766i	−0.0127992	−	0.533953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.4.17	✓	1404
3.2	odd	2		729.2.i.a.64.10		1404
243.61	even	81	inner	243.2.i.a.61.17	yes	1404
243.182	odd	162		729.2.i.a.262.10		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.17	✓	1404	1.1	even	1	trivial
243.2.i.a.61.17	yes	1404	243.61	even	81	inner
729.2.i.a.64.10		1404	3.2	odd	2
729.2.i.a.262.10		1404	243.182	odd	162

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(0.905616 + 0.0351420i) q^{2} +(-1.29585 + 1.14925i) q^{3} +(-1.17508 - 0.0913345i) q^{4} +(-1.68295 - 2.08654i) q^{5} +(-1.21393 + 0.995240i) q^{6} +(0.467604 - 0.212552i) q^{7} +(-2.86130 - 0.334438i) q^{8} +(0.358453 - 2.97851i) q^{9} +(-1.45079 - 1.94874i) q^{10} +(-0.113535 - 5.85382i) q^{11} +(1.62769 - 1.23210i) q^{12} +(-0.532128 - 0.170620i) q^{13} +(0.430939 - 0.176058i) q^{14} +(4.57881 + 0.769703i) q^{15} +(-0.250550 - 0.0391853i) q^{16} +(1.26092 + 4.21177i) q^{17} +(0.429292 - 2.68479i) q^{18} +(-6.87969 + 1.63052i) q^{19} +(1.78703 + 2.60556i) q^{20} +(-0.361669 + 0.812829i) q^{21} +(0.102896 - 5.30530i) q^{22} +(-5.83346 + 4.16951i) q^{23} +(4.09217 - 2.85497i) q^{24} +(-0.462778 + 2.13642i) q^{25} +(-0.475908 - 0.173216i) q^{26} +(2.95855 + 4.27165i) q^{27} +(-0.568885 + 0.207057i) q^{28} +(-1.25076 - 9.15719i) q^{29} +(4.11959 + 0.857964i) q^{30} +(2.75759 + 2.70463i) q^{31} +(5.42804 + 1.06603i) q^{32} +(6.87462 + 7.45519i) q^{33} +(0.993900 + 3.85856i) q^{34} +(-1.23045 - 0.617957i) q^{35} +(-0.693251 + 3.46725i) q^{36} +(-2.71437 - 1.78527i) q^{37} +(-6.28766 + 1.23486i) q^{38} +(0.885643 - 0.390450i) q^{39} +(4.11762 + 6.53305i) q^{40} +(4.51286 - 8.56746i) q^{41} +(-0.356098 + 0.723401i) q^{42} +(0.245349 - 0.717059i) q^{43} +(-0.401243 + 6.88908i) q^{44} +(-6.81802 + 4.26477i) q^{45} +(-5.42940 + 3.57098i) q^{46} +(5.06358 - 4.96633i) q^{47} +(0.369709 - 0.237166i) q^{48} +(-4.42917 + 5.07527i) q^{49} +(-0.494177 + 1.91851i) q^{50} +(-6.47433 - 4.00870i) q^{51} +(0.609710 + 0.249094i) q^{52} +(0.0666653 + 0.0559388i) q^{53} +(2.52919 + 3.97245i) q^{54} +(-12.0231 + 10.0886i) q^{55} +(-1.40904 + 0.451791i) q^{56} +(7.04117 - 10.0194i) q^{57} +(-0.810907 - 8.33686i) q^{58} +(4.40083 - 2.42828i) q^{59} +(-5.31016 - 1.32267i) q^{60} +(8.82405 - 0.685859i) q^{61} +(2.40227 + 2.54626i) q^{62} +(-0.465474 - 1.46895i) q^{63} +(5.37178 + 1.27313i) q^{64} +(0.539543 + 1.39745i) q^{65} +(5.96378 + 6.99313i) q^{66} +(-1.01498 + 7.43096i) q^{67} +(-1.09700 - 5.06433i) q^{68} +(2.76749 - 12.1072i) q^{69} +(-1.09260 - 0.602872i) q^{70} +(0.0961826 - 0.222976i) q^{71} +(-2.02177 + 8.40253i) q^{72} +(5.74951 - 7.72293i) q^{73} +(-2.39544 - 1.71216i) q^{74} +(-1.85559 - 3.30032i) q^{75} +(8.23311 - 1.28763i) q^{76} +(-1.29733 - 2.71314i) q^{77} +(0.815774 - 0.322475i) q^{78} +(-4.46842 + 7.08963i) q^{79} +(0.339903 + 0.588729i) q^{80} +(-8.74302 - 2.13531i) q^{81} +(4.38800 - 7.60024i) q^{82} +(-2.81318 - 5.34070i) q^{83} +(0.499229 - 0.922106i) q^{84} +(6.66593 - 9.71916i) q^{85} +(0.247391 - 0.640758i) q^{86} +(12.1447 + 10.4289i) q^{87} +(-1.63288 + 16.7875i) q^{88} +(-3.97177 - 9.20760i) q^{89} +(-6.32439 + 3.62264i) q^{90} +(-0.285091 + 0.0333223i) q^{91} +(7.23561 - 4.36671i) q^{92} +(-6.68171 - 0.335630i) q^{93} +(4.76019 - 4.31964i) q^{94} +(14.9803 + 11.6106i) q^{95} +(-8.25906 + 4.85675i) q^{96} +(-1.84316 + 2.28516i) q^{97} +(-4.18949 + 4.44060i) q^{98} +(-17.4763 - 1.76015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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