LMFDB - Embedded newform 243.2.i.a.4.11

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			4.11
Character	$\chi$	$=$	243.4
Dual form			243.2.i.a.61.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.815384 - 0.0316406i) q^{2} +(1.60488 - 0.651417i) q^{3} +(-1.33014 - 0.103386i) q^{4} +(0.303466 + 0.376239i) q^{5} +(-1.32921 + 0.480376i) q^{6} +(0.274968 - 0.124988i) q^{7} +(2.70226 + 0.315849i) q^{8} +(2.15131 - 2.09090i) q^{9} +(-0.235537 - 0.316381i) q^{10} +(-0.0593675 - 3.06097i) q^{11} +(-2.20206 + 0.700550i) q^{12} +(5.95686 + 1.90999i) q^{13} +(-0.228159 + 0.0932133i) q^{14} +(0.732116 + 0.406137i) q^{15} +(0.442862 + 0.0692624i) q^{16} +(-1.83044 - 6.11409i) q^{17} +(-1.82030 + 1.63682i) q^{18} +(0.551404 - 0.130685i) q^{19} +(-0.364753 - 0.531823i) q^{20} +(0.359873 - 0.379711i) q^{21} +(-0.0484437 + 2.49775i) q^{22} +(-6.72634 + 4.80770i) q^{23} +(4.54257 - 1.25340i) q^{24} +(1.00906 - 4.65832i) q^{25} +(-4.79670 - 1.74585i) q^{26} +(2.09056 - 4.75705i) q^{27} +(-0.378667 + 0.137824i) q^{28} +(0.744169 + 5.44828i) q^{29} +(-0.584105 - 0.354322i) q^{30} +(6.00244 + 5.88715i) q^{31} +(-5.69823 - 1.11910i) q^{32} +(-2.08925 - 4.87384i) q^{33} +(1.29906 + 5.04325i) q^{34} +(0.130469 + 0.0655239i) q^{35} +(-3.07771 + 2.55876i) q^{36} +(-2.18459 - 1.43683i) q^{37} +(-0.453741 + 0.0891119i) q^{38} +(10.8043 - 0.815086i) q^{39} +(0.701209 + 1.11254i) q^{40} +(1.15243 - 2.18783i) q^{41} +(-0.305449 + 0.298224i) q^{42} +(-2.81393 + 8.22403i) q^{43} +(-0.237496 + 4.07765i) q^{44} +(1.43953 + 0.174890i) q^{45} +(5.63667 - 3.70730i) q^{46} +(5.21053 - 5.11046i) q^{47} +(0.755861 - 0.177330i) q^{48} +(-4.54266 + 5.20532i) q^{49} +(-0.970160 + 3.76639i) q^{50} +(-6.92047 - 8.62004i) q^{51} +(-7.72597 - 3.15640i) q^{52} +(0.954300 + 0.800753i) q^{53} +(-1.85513 + 3.81268i) q^{54} +(1.13364 - 0.951237i) q^{55} +(0.782513 - 0.250903i) q^{56} +(0.799810 - 0.568929i) q^{57} +(-0.434396 - 4.46599i) q^{58} +(-9.95051 + 5.49046i) q^{59} +(-0.931825 - 0.615908i) q^{60} +(-9.36243 + 0.727706i) q^{61} +(-4.70802 - 4.99021i) q^{62} +(0.330204 - 0.843819i) q^{63} +(3.73851 + 0.886043i) q^{64} +(1.08909 + 2.82082i) q^{65} +(1.54933 + 4.04015i) q^{66} +(-1.21871 + 8.92253i) q^{67} +(1.80262 + 8.32182i) q^{68} +(-7.66319 + 12.0975i) q^{69} +(-0.104309 - 0.0575553i) q^{70} +(-2.42021 + 5.61068i) q^{71} +(6.47381 - 4.97067i) q^{72} +(-5.56016 + 7.46859i) q^{73} +(1.73582 + 1.24069i) q^{74} +(-1.41509 - 8.13338i) q^{75} +(-0.746954 + 0.116821i) q^{76} +(-0.398910 - 0.834250i) q^{77} +(-8.83542 + 0.322754i) q^{78} +(4.08174 - 6.47612i) q^{79} +(0.108334 + 0.187641i) q^{80} +(0.256282 - 8.99635i) q^{81} +(-1.00889 + 1.74746i) q^{82} +(-1.91457 - 3.63472i) q^{83} +(-0.517936 + 0.467861i) q^{84} +(1.74488 - 2.54410i) q^{85} +(2.55465 - 6.61670i) q^{86} +(4.74341 + 8.25910i) q^{87} +(0.806379 - 8.29030i) q^{88} +(-1.77629 - 4.11789i) q^{89} +(-1.16823 - 0.188150i) q^{90} +(1.87667 - 0.219352i) q^{91} +(9.44400 - 5.69948i) q^{92} +(13.4682 + 5.53811i) q^{93} +(-4.41028 + 4.00212i) q^{94} +(0.216501 + 0.167801i) q^{95} +(-9.87400 + 1.91590i) q^{96} +(5.85167 - 7.25493i) q^{97} +(3.86872 - 4.10060i) q^{98} +(-6.52790 - 6.46097i) 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 $

$2$	−0.815384	−	0.0316406i	−0.576564	−	0.0223733i	−0.251155	−	0.967947i	$-0.580810\pi$
$2$	−0.815384	−	0.0316406i	−0.576564	−	0.0223733i	−0.325408	+	0.945574i	$0.605502\pi$
$3$	1.60488	−	0.651417i	0.926581	−	0.376096i
$3$	1.60488	−	0.651417i	0.926581	−	0.376096i
$4$	−1.33014	−	0.103386i	−0.665068	−	0.0516932i
$5$	0.303466	+	0.376239i	0.135714	+	0.168259i	0.841662	−	0.540005i	$-0.181578\pi$
$5$	0.303466	+	0.376239i	0.135714	+	0.168259i	−0.705948	+	0.708264i	$0.749479\pi$
$6$	−1.32921	+	0.480376i	−0.542647	+	0.196113i
$7$	0.274968	−	0.124988i	0.103928	−	0.0472411i	−0.361172	−	0.932499i	$-0.617623\pi$
$7$	0.274968	−	0.124988i	0.103928	−	0.0472411i	0.465100	+	0.885258i	$0.346018\pi$
$8$	2.70226	+	0.315849i	0.955393	+	0.111669i
$9$	2.15131	−	2.09090i	0.717104	−	0.696966i
$10$	−0.235537	−	0.316381i	−0.0744833	−	0.100048i
$11$	−0.0593675	−	3.06097i	−0.0179000	−	0.922918i	−0.895900	−	0.444257i	$-0.853468\pi$
$11$	−0.0593675	−	3.06097i	−0.0179000	−	0.922918i	0.878000	−	0.478661i	$-0.158878\pi$
$12$	−2.20206	+	0.700550i	−0.635681	+	0.202231i
$13$	5.95686	+	1.90999i	1.65214	+	0.529736i	0.977952	−	0.208828i	$-0.0669649\pi$
$13$	5.95686	+	1.90999i	1.65214	+	0.529736i	0.674183	+	0.738564i	$0.264496\pi$
$14$	−0.228159	+	0.0932133i	−0.0609781	+	0.0249123i
$15$	0.732116	+	0.406137i	0.189032	+	0.104864i
$16$	0.442862	+	0.0692624i	0.110716	+	0.0173156i
$17$	−1.83044	−	6.11409i	−0.443947	−	1.48289i	−0.828609	−	0.559828i	$-0.810867\pi$
$17$	−1.83044	−	6.11409i	−0.443947	−	1.48289i	0.384662	−	0.923058i	$-0.374318\pi$
$18$	−1.82030	+	1.63682i	−0.429049	+	0.385801i
$19$	0.551404	−	0.130685i	0.126501	−	0.0299812i	−0.166878	−	0.985978i	$-0.553369\pi$
$19$	0.551404	−	0.130685i	0.126501	−	0.0299812i	0.293379	+	0.955996i	$0.405220\pi$
$20$	−0.364753	−	0.531823i	−0.0815612	−	0.118919i
$21$	0.359873	−	0.379711i	0.0785306	−	0.0828597i
$22$	−0.0484437	+	2.49775i	−0.0103282	+	0.532521i
$23$	−6.72634	+	4.80770i	−1.40254	+	1.00247i	−0.406492	+	0.913654i	$0.633248\pi$
$23$	−6.72634	+	4.80770i	−1.40254	+	1.00247i	−0.996048	+	0.0888204i	$0.971690\pi$
$24$	4.54257	−	1.25340i	0.927248	−	0.255849i
$25$	1.00906	−	4.65832i	0.201811	−	0.931664i
$26$	−4.79670	−	1.74585i	−0.940709	−	0.342390i
$27$	2.09056	−	4.75705i	0.402328	−	0.915495i
$28$	−0.378667	+	0.137824i	−0.0715613	+	0.0260462i
$29$	0.744169	+	5.44828i	0.138189	+	1.01172i	0.921028	+	0.389496i	$0.127351\pi$
$29$	0.744169	+	5.44828i	0.138189	+	1.01172i	−0.782839	+	0.622224i	$0.786229\pi$
$30$	−0.584105	−	0.354322i	−0.106643	−	0.0646901i
$31$	6.00244	+	5.88715i	1.07807	+	1.05736i	0.998164	+	0.0605613i	$0.0192891\pi$
$31$	6.00244	+	5.88715i	1.07807	+	1.05736i	0.0799057	+	0.996802i	$0.474538\pi$
$32$	−5.69823	−	1.11910i	−1.00731	−	0.197830i
$33$	−2.08925	−	4.87384i	−0.363691	−	0.848426i
$34$	1.29906	+	5.04325i	0.222787	+	0.864911i
$35$	0.130469	+	0.0655239i	0.0220533	+	0.0110756i
$36$	−3.07771	+	2.55876i	−0.512951	+	0.426461i
$37$	−2.18459	−	1.43683i	−0.359144	−	0.236213i	0.357095	−	0.934068i	$-0.383767\pi$
$37$	−2.18459	−	1.43683i	−0.359144	−	0.236213i	−0.716239	+	0.697856i	$0.754138\pi$
$38$	−0.453741	+	0.0891119i	−0.0736065	+	0.0144559i
$39$	10.8043	−	0.815086i	1.73007	−	0.130518i
$40$	0.701209	+	1.11254i	0.110871	+	0.175909i
$41$	1.15243	−	2.18783i	0.179979	−	0.341681i	−0.778122	−	0.628114i	$-0.783827\pi$
$41$	1.15243	−	2.18783i	0.179979	−	0.341681i	0.958101	+	0.286432i	$0.0924693\pi$
$42$	−0.305449	+	0.298224i	−0.0471318	+	0.0460169i
$43$	−2.81393	+	8.22403i	−0.429121	+	1.25415i	0.493940	+	0.869496i	$0.335556\pi$
$43$	−2.81393	+	8.22403i	−0.429121	+	1.25415i	−0.923060	+	0.384656i	$0.874320\pi$
$44$	−0.237496	+	4.07765i	−0.0358039	+	0.614728i
$45$	1.43953	+	0.174890i	0.214592	+	0.0260711i
$46$	5.63667	−	3.70730i	0.831082	−	0.546611i
$47$	5.21053	−	5.11046i	0.760035	−	0.745437i	−0.212760	−	0.977104i	$-0.568245\pi$
$47$	5.21053	−	5.11046i	0.760035	−	0.745437i	0.972795	+	0.231668i	$0.0744182\pi$
$48$	0.755861	−	0.177330i	0.109099	−	0.0255954i
$49$	−4.54266	+	5.20532i	−0.648952	+	0.743617i
$50$	−0.970160	+	3.76639i	−0.137201	+	0.532648i
$51$	−6.92047	−	8.62004i	−0.969060	−	1.20705i
$52$	−7.72597	−	3.15640i	−1.07140	−	0.437715i
$53$	0.954300	+	0.800753i	0.131083	+	0.109992i	0.705972	−	0.708240i	$-0.250510\pi$
$53$	0.954300	+	0.800753i	0.131083	+	0.109992i	−0.574889	+	0.818231i	$0.694955\pi$
$54$	−1.85513	+	3.81268i	−0.252451	+	0.518840i
$55$	1.13364	−	0.951237i	0.152860	−	0.128265i
$56$	0.782513	−	0.250903i	0.104568	−	0.0335283i
$57$	0.799810	−	0.568929i	0.105937	−	0.0753565i
$58$	−0.434396	−	4.46599i	−0.0570391	−	0.586413i
$59$	−9.95051	+	5.49046i	−1.29545	+	0.714797i	−0.972783	−	0.231717i	$-0.925566\pi$
$59$	−9.95051	+	5.49046i	−1.29545	+	0.714797i	−0.322663	+	0.946514i	$0.604578\pi$
$60$	−0.931825	−	0.615908i	−0.120298	−	0.0795134i
$61$	−9.36243	+	0.727706i	−1.19874	+	0.0931732i	−0.661294	−	0.750127i	$-0.729992\pi$
$61$	−9.36243	+	0.727706i	−1.19874	+	0.0931732i	−0.537443	+	0.843300i	$0.680610\pi$
$62$	−4.70802	−	4.99021i	−0.597919	−	0.633757i
$63$	0.330204	−	0.843819i	0.0416018	−	0.106311i
$64$	3.73851	+	0.886043i	0.467314	+	0.110755i
$65$	1.08909	+	2.82082i	0.135085	+	0.349879i
$66$	1.54933	+	4.04015i	0.190709	+	0.497309i
$67$	−1.21871	+	8.92253i	−0.148889	+	1.09006i	0.752978	+	0.658046i	$0.228617\pi$
$67$	−1.21871	+	8.92253i	−0.148889	+	1.09006i	−0.901867	+	0.432014i	$0.857803\pi$
$68$	1.80262	+	8.32182i	0.218600	+	1.00917i
$69$	−7.66319	+	12.0975i	−0.922539	+	1.45636i
$70$	−0.104309	−	0.0575553i	−0.0124673	−	0.00687917i
$71$	−2.42021	+	5.61068i	−0.287226	+	0.665865i	−0.999345	−	0.0361940i	$-0.988477\pi$
$71$	−2.42021	+	5.61068i	−0.287226	+	0.665865i	0.712119	+	0.702059i	$0.247736\pi$
$72$	6.47381	−	4.97067i	0.762946	−	0.585799i
$73$	−5.56016	+	7.46859i	−0.650768	+	0.874133i	−0.997972	−	0.0636570i	$-0.979724\pi$
$73$	−5.56016	+	7.46859i	−0.650768	+	0.874133i	0.347204	+	0.937790i	$0.387131\pi$
$74$	1.73582	+	1.24069i	0.201784	+	0.144227i
$75$	−1.41509	−	8.13338i	−0.163401	−	0.939162i
$76$	−0.746954	+	0.116821i	−0.0856815	+	0.0134003i
$77$	−0.398910	−	0.834250i	−0.0454600	−	0.0950716i
$78$	−8.83542	+	0.322754i	−1.00041	+	0.0365447i
$79$	4.08174	−	6.47612i	0.459232	−	0.728621i	−0.533909	−	0.845542i	$-0.679278\pi$
$79$	4.08174	−	6.47612i	0.459232	−	0.728621i	0.993141	+	0.116921i	$0.0373024\pi$
$80$	0.108334	+	0.187641i	0.0121121	+	0.0209789i
$81$	0.256282	−	8.99635i	0.0284758	−	0.999594i
$82$	−1.00889	+	1.74746i	−0.111414	+	0.192974i
$83$	−1.91457	−	3.63472i	−0.210151	−	0.398963i	0.756905	−	0.653525i	$-0.226711\pi$
$83$	−1.91457	−	3.63472i	−0.210151	−	0.398963i	−0.967056	+	0.254562i	$0.918069\pi$
$84$	−0.517936	+	0.467861i	−0.0565115	+	0.0510478i
$85$	1.74488	−	2.54410i	0.189259	−	0.275947i
$86$	2.55465	−	6.61670i	0.275475	−	0.713498i
$87$	4.74341	+	8.25910i	0.508547	+	0.885468i
$88$	0.806379	−	8.29030i	0.0859603	−	0.883749i
$89$	−1.77629	−	4.11789i	−0.188286	−	0.436496i	0.797759	−	0.602977i	$-0.206019\pi$
$89$	−1.77629	−	4.11789i	−0.188286	−	0.436496i	−0.986045	+	0.166481i	$0.946760\pi$
$90$	−1.16823	−	0.188150i	−0.123143	−	0.0198328i
$91$	1.87667	−	0.219352i	0.196729	−	0.0229943i
$92$	9.44400	−	5.69948i	0.984605	−	0.594212i
$93$	13.4682	+	5.53811i	1.39659	+	0.574275i
$94$	−4.41028	+	4.00212i	−0.454886	+	0.412787i
$95$	0.216501	+	0.167801i	0.0222126	+	0.0172160i
$96$	−9.87400	+	1.91590i	−1.00776	+	0.195541i
$97$	5.85167	−	7.25493i	0.594147	−	0.736627i	−0.388636	−	0.921391i	$-0.627054\pi$
$97$	5.85167	−	7.25493i	0.594147	−	0.736627i	0.982783	+	0.184765i	$0.0591524\pi$
$98$	3.86872	−	4.10060i	0.390799	−	0.414223i
$99$	−6.52790	−	6.46097i	−0.656079	−	0.649352i
$100$	−1.82379	+	6.09187i	−0.182379	+	0.609187i
$101$	−0.531305	+	1.11113i	−0.0528668	+	0.110562i	−0.926906	−	0.375295i	$-0.877542\pi$
$101$	−0.531305	+	1.11113i	−0.0528668	+	0.110562i	0.874039	+	0.485856i	$0.161492\pi$
$102$	5.37010	+	7.24761i	0.531719	+	0.717620i
$103$	−5.36833	−	3.23981i	−0.528958	−	0.319228i	0.226949	−	0.973907i	$-0.427125\pi$
$103$	−5.36833	−	3.23981i	−0.528958	−	0.319228i	−0.755907	+	0.654679i	$0.772804\pi$
$104$	15.4937	+	7.04276i	1.51928	+	0.690599i
$105$	0.252071	+	0.0201687i	0.0245996	+	0.00196826i
$106$	−0.752785	−	0.683116i	−0.0731169	−	0.0663501i
$107$	1.90327	+	10.7940i	0.183996	+	1.04349i	0.927238	+	0.374472i	$0.122176\pi$
$107$	1.90327	+	10.7940i	0.183996	+	1.04349i	−0.743242	+	0.669022i	$0.766713\pi$
$108$	−3.27254	+	6.11139i	−0.314901	+	0.588069i
$109$	3.15462	−	17.8908i	0.302158	−	1.71362i	−0.334430	−	0.942421i	$-0.608544\pi$
$109$	3.15462	−	17.8908i	0.302158	−	1.71362i	0.636588	−	0.771204i	$-0.280345\pi$
$110$	−0.954450	+	0.739754i	−0.0910032	+	0.0705328i
$111$	−4.44198	−	0.882862i	−0.421614	−	0.0837976i
$112$	0.130430	−	0.0363077i	0.0123245	−	0.00343075i
$113$	1.05488	+	3.08301i	0.0992350	+	0.290025i	0.984587	−	0.174896i	$-0.0559590\pi$
$113$	1.05488	+	3.08301i	0.0992350	+	0.290025i	−0.885352	+	0.464922i	$0.846082\pi$
$114$	−0.670153	+	0.438589i	−0.0627656	+	0.0410776i
$115$	−3.85006	−	1.07174i	−0.359020	−	0.0999400i
$116$	−0.426568	−	7.32389i	−0.0396058	−	0.680006i
$117$	16.8087	−	8.34621i	1.55396	−	0.771607i
$118$	8.28721	−	4.16199i	0.762899	−	0.383142i
$119$	−1.26750	−	1.45240i	−0.116192	−	0.133141i
$120$	1.85009	+	1.32873i	0.168889	+	0.121296i
$121$	1.62570	−	0.0630845i	0.147791	−	0.00573495i
$122$	7.65700	−	0.297127i	0.693233	−	0.0269006i
$123$	0.424324	−	4.26192i	0.0382600	−	0.384285i
$124$	−7.37541	−	8.45128i	−0.662331	−	0.758948i
$125$	4.21863	−	2.11868i	0.377326	−	0.189500i
$126$	−0.295942	+	0.677589i	−0.0263646	+	0.0603644i
$127$	0.0190269	+	0.326679i	0.00168836	+	0.0289881i	0.999047	−	0.0436447i	$-0.0138969\pi$
$127$	0.0190269	+	0.326679i	0.00168836	+	0.0289881i	−0.997359	+	0.0726327i	$0.976860\pi$
$128$	8.16846	+	2.27385i	0.721997	+	0.200981i
$129$	0.841235	+	15.0317i	0.0740666	+	1.32346i
$130$	−0.798775	−	2.33451i	−0.0700572	−	0.204750i
$131$	10.8481	−	3.01976i	0.947800	−	0.263838i	0.240418	−	0.970670i	$-0.422716\pi$
$131$	10.8481	−	3.01976i	0.947800	−	0.263838i	0.707382	+	0.706832i	$0.249876\pi$
$132$	2.27510	+	6.69886i	0.198022	+	0.583061i
$133$	0.135284	−	0.104853i	0.0117306	−	0.00909194i
$134$	1.27603	−	7.23673i	0.110232	−	0.625158i
$135$	2.42420	−	0.657054i	0.208642	−	0.0565502i
$136$	−3.01520	−	17.1000i	−0.258551	−	1.46631i
$137$	1.72930	+	1.56925i	0.147744	+	0.134070i	0.742528	−	0.669815i	$-0.233627\pi$
$137$	1.72930	+	1.56925i	0.147744	+	0.134070i	−0.594784	+	0.803885i	$0.702762\pi$
$138$	6.63121	−	9.62161i	0.564486	−	0.819046i
$139$	9.54460	+	4.33855i	0.809562	+	0.367991i	0.775436	−	0.631426i	$-0.217530\pi$
$139$	9.54460	+	4.33855i	0.809562	+	0.367991i	0.0341264	+	0.999418i	$0.489135\pi$
$140$	−0.166767	−	0.100644i	−0.0140944	−	0.00850601i
$141$	5.03327	−	11.5959i	0.423878	−	0.976553i
$142$	2.15093	−	4.49828i	0.180502	−	0.377487i
$143$	5.49278	−	18.3472i	0.459330	−	1.53427i
$144$	1.09755	−	0.776975i	0.0914629	−	0.0647479i
$145$	−1.82402	+	1.93335i	−0.151477	+	0.160556i
$146$	4.76998	−	5.91384i	0.394766	−	0.489433i
$147$	−3.89962	+	11.3131i	−0.321635	+	0.933089i
$148$	2.75725	+	2.13703i	0.226644	+	0.175663i
$149$	−3.62035	+	3.28530i	−0.296591	+	0.269142i	−0.806691	−	0.590973i	$-0.798744\pi$
$149$	−3.62035	+	3.28530i	−0.296591	+	0.269142i	0.510100	+	0.860115i	$0.329608\pi$
$150$	0.896497	+	6.67660i	0.0731987	+	0.545142i
$151$	−13.1014	+	7.90671i	−1.06617	+	0.643439i	−0.937407	−	0.348236i	$-0.886781\pi$
$151$	−13.1014	+	7.90671i	−1.06617	+	0.643439i	−0.128767	+	0.991675i	$0.541102\pi$
$152$	1.53131	−	0.178985i	0.124206	−	0.0145176i
$153$	−16.7218	−	9.32606i	−1.35188	−	0.753967i
$154$	0.298869	+	0.692856i	0.0240835	+	0.0558319i
$155$	−0.393438	+	4.04490i	−0.0316017	+	0.324894i
$156$	−14.4554	−	0.0328395i	−1.15736	−	0.00262926i
$157$	1.25828	−	3.25902i	0.100421	−	0.260098i	−0.873564	−	0.486710i	$-0.838197\pi$
$157$	1.25828	−	3.25902i	0.100421	−	0.260098i	0.973985	+	0.226612i	$0.0727649\pi$
$158$	−3.53310	+	5.15138i	−0.281078	+	0.409822i
$159$	2.05317	+	0.663469i	0.162827	+	0.0526165i
$160$	−1.30817	−	2.48350i	−0.103420	−	0.196338i
$161$	−1.24862	+	2.16268i	−0.0984053	+	0.170443i
$162$	−0.493618	+	7.32737i	−0.0387823	+	0.575693i
$163$	8.03417	+	13.9156i	0.629284	+	1.08995i	0.987696	+	0.156389i	$0.0499853\pi$
$163$	8.03417	+	13.9156i	0.629284	+	1.08995i	−0.358411	+	0.933564i	$0.616681\pi$
$164$	−1.75908	+	2.79096i	−0.137361	+	0.217938i
$165$	1.19971	−	2.26510i	0.0933973	−	0.176338i
$166$	1.44611	+	3.02427i	0.112240	+	0.234729i
$167$	−19.6001	+	3.06540i	−1.51670	+	0.237208i	−0.857391	−	0.514665i	$-0.827916\pi$
$167$	−19.6001	+	3.06540i	−1.51670	+	0.237208i	−0.659309	+	0.751872i	$0.729151\pi$
$168$	1.09240	−	0.912412i	0.0842806	−	0.0703941i
$169$	21.2599	+	15.1957i	1.63538	+	1.16890i
$170$	−1.50325	+	2.01921i	−0.115294	+	0.154866i
$171$	0.912993	−	1.43408i	0.0698183	−	0.109666i
$172$	4.59316	−	10.6481i	0.350225	−	0.811914i
$173$	6.10078	+	3.36627i	0.463833	+	0.255932i	0.697773	−	0.716319i	$-0.254174\pi$
$173$	6.10078	+	3.36627i	0.463833	+	0.255932i	−0.233940	+	0.972251i	$0.575162\pi$
$174$	−3.60638	−	6.88442i	−0.273399	−	0.521907i
$175$	−0.304777	−	1.40701i	−0.0230390	−	0.106360i
$176$	0.185719	−	1.35970i	0.0139991	−	0.102491i
$177$	−12.3928	+	15.2935i	−0.931503	+	1.14953i
$178$	1.31806	+	3.41387i	0.0987930	+	0.255880i
$179$	−8.02700	−	1.90243i	−0.599966	−	0.142195i	−0.0806000	−	0.996747i	$-0.525684\pi$
$179$	−8.02700	−	1.90243i	−0.599966	−	0.142195i	−0.519366	+	0.854552i	$0.673832\pi$
$180$	−1.89668	−	0.381455i	−0.141371	−	0.0284320i
$181$	−9.43705	−	10.0027i	−0.701450	−	0.743494i	0.274476	−	0.961594i	$-0.411496\pi$
$181$	−9.43705	−	10.0027i	−0.701450	−	0.743494i	−0.975926	+	0.218100i	$0.930014\pi$
$182$	−1.53715	+	0.119477i	−0.113941	+	0.00885620i
$183$	−14.5516	+	7.26673i	−1.07568	+	0.537172i
$184$	−19.6948	+	10.8672i	−1.45192	+	0.801137i
$185$	−0.122358	−	1.25795i	−0.00899596	−	0.0924866i
$186$	−10.8065	−	4.94183i	−0.792374	−	0.362352i
$187$	−18.6064	+	5.96591i	−1.36064	+	0.436270i
$188$	−7.45907	+	6.25890i	−0.544009	+	0.456477i
$189$	−0.0197389	−	1.56933i	−0.00143579	−	0.114152i
$190$	−0.171222	−	0.143673i	−0.0124218	−	0.0104231i
$191$	1.23337	+	0.503888i	0.0892437	+	0.0364600i	0.422382	−	0.906418i	$-0.361194\pi$
$191$	1.23337	+	0.503888i	0.0892437	+	0.0364600i	−0.333138	+	0.942878i	$0.608108\pi$
$192$	6.57706	−	1.01333i	0.474659	−	0.0731309i
$193$	3.66632	−	14.2335i	0.263907	−	1.02455i	−0.689845	−	0.723957i	$-0.742321\pi$
$193$	3.66632	−	14.2335i	0.263907	−	1.02455i	0.953752	−	0.300594i	$-0.0971850\pi$
$194$	−5.00091	+	5.73040i	−0.359044	+	0.411419i
$195$	3.58540	+	3.81763i	0.256755	+	0.273387i
$196$	6.58052	−	6.45413i	0.470037	−	0.461009i
$197$	−3.78594	+	2.49005i	−0.269737	+	0.177409i	−0.677171	−	0.735826i	$-0.736794\pi$
$197$	−3.78594	+	2.49005i	−0.269737	+	0.177409i	0.407434	+	0.913235i	$0.366424\pi$
$198$	5.11832	+	5.47472i	0.363743	+	0.389072i
$199$	0.0639868	−	1.09861i	0.00453591	−	0.0778785i	−0.995280	−	0.0970398i	$-0.969063\pi$
$199$	0.0639868	−	1.09861i	0.00453591	−	0.0778785i	0.999816	+	0.0191613i	$0.00609961\pi$
$200$	4.19806	−	12.2693i	0.296847	−	0.867569i
$201$	3.85640	+	15.1135i	0.272009	+	1.06603i
$202$	0.468374	−	0.889187i	0.0329547	−	0.0625630i
$203$	0.885594	+	1.40509i	0.0621565	+	0.0986180i
$204$	8.31397	+	12.1813i	0.582095	+	0.852862i
$205$	1.17287	−	0.230344i	0.0819166	−	0.0160879i
$206$	4.27474	+	2.81154i	0.297835	+	0.195889i
$207$	−4.41804	+	24.4070i	−0.307075	+	1.69640i
$208$	2.50578	+	1.25845i	0.173744	+	0.0872577i
$209$	−0.432759	−	1.68007i	−0.0299346	−	0.116213i
$210$	−0.204896	−	0.0244209i	−0.0141392	−	0.00168520i
$211$	−17.6136	−	3.45920i	−1.21257	−	0.238141i	−0.454759	−	0.890615i	$-0.650274\pi$
$211$	−17.6136	−	3.45920i	−1.21257	−	0.238141i	−0.757811	+	0.652474i	$0.773731\pi$
$212$	−1.18656	−	1.16377i	−0.0814934	−	0.0799282i
$213$	−0.229267	+	10.5811i	−0.0157091	+	0.725003i
$214$	−1.21037	−	8.86147i	−0.0827391	−	0.605757i
$215$	−3.94813	+	1.43700i	−0.269260	+	0.0980027i
$216$	7.15175	−	12.1945i	0.486615	−	0.829731i
$217$	2.38630	+	0.868544i	0.161993	+	0.0589606i
$218$	−3.13831	+	14.4880i	−0.212553	+	0.981253i
$219$	−4.05825	+	15.6082i	−0.274231	+	1.05471i
$220$	−1.60624	+	1.14807i	−0.108293	+	0.0774030i
$221$	0.774188	−	39.9169i	0.0520775	−	2.68510i
$222$	3.59399	+	0.860419i	0.241213	+	0.0577475i
$223$	−3.15708	−	4.60313i	−0.211413	−	0.308248i	0.704438	−	0.709765i	$-0.251199\pi$
$223$	−3.15708	−	4.60313i	−0.211413	−	0.308248i	−0.915852	+	0.401517i	$0.868483\pi$
$224$	−1.70671	+	0.404497i	−0.114034	+	0.0270266i
$225$	−7.56928	−	12.1313i	−0.504619	−	0.808755i
$226$	−0.762586	−	2.54722i	−0.0507265	−	0.169438i
$227$	3.02269	+	0.472740i	0.200623	+	0.0313769i	0.254032	−	0.967196i	$-0.418243\pi$
$227$	3.02269	+	0.472740i	0.200623	+	0.0313769i	−0.0534087	+	0.998573i	$0.517009\pi$
$228$	−1.12268	+	0.674063i	−0.0743510	+	0.0446409i
$229$	23.8589	−	9.74742i	1.57664	−	0.644127i	0.590051	−	0.807366i	$-0.299108\pi$
$229$	23.8589	−	9.74742i	1.57664	−	0.644127i	0.986587	+	0.163238i	$0.0521939\pi$
$230$	3.10537	+	0.995695i	0.204762	+	0.0656542i
$231$	−1.18365	−	1.07902i	−0.0778784	−	0.0709942i
$232$	0.290105	+	14.9577i	0.0190463	+	0.982022i
$233$	7.77812	+	10.4478i	0.509562	+	0.684460i	0.980233	−	0.197849i	$-0.0633955\pi$
$233$	7.77812	+	10.4478i	0.509562	+	0.684460i	−0.470671	+	0.882309i	$0.655988\pi$
$234$	−13.9696	+	6.27353i	−0.913221	+	0.410113i
$235$	3.50397	+	0.409555i	0.228574	+	0.0267164i
$236$	13.8032	−	6.27431i	0.898510	−	0.408423i
$237$	2.33207	−	13.0524i	0.151484	−	0.847841i
$238$	0.987547	+	1.22437i	0.0640132	+	0.0793639i
$239$	−3.70146	−	0.287700i	−0.239428	−	0.0186098i	−0.0427821	−	0.999084i	$-0.513622\pi$
$239$	−3.70146	−	0.287700i	−0.239428	−	0.0186098i	−0.196646	+	0.980475i	$0.563005\pi$
$240$	0.296096	+	0.230571i	0.0191129	+	0.0148833i
$241$	−14.3782	−	0.557939i	−0.926181	−	0.0359400i	−0.428730	−	0.903432i	$-0.641039\pi$
$241$	−14.3782	−	0.557939i	−0.926181	−	0.0359400i	−0.497450	+	0.867492i	$0.665730\pi$
$242$	−1.32756			−0.0853390
$243$	−5.44907	−	14.6051i	−0.349558	−	0.936915i
$244$	12.5285			0.802058
$245$	−3.33698	−	0.129490i	−0.213192	−	0.00827282i
$246$	−0.480836	+	3.46168i	−0.0306570	+	0.220709i
$247$	3.53425	+	0.274703i	0.224879	+	0.0174789i
$248$	14.3607	+	17.8045i	0.911906	+	1.13059i
$249$	−5.44039	−	4.58613i	−0.344771	−	0.290634i
$250$	−3.50684	+	1.59405i	−0.221792	+	0.100817i
$251$	−10.1161	−	1.18241i	−0.638525	−	0.0746329i	−0.209331	−	0.977845i	$-0.567128\pi$
$251$	−10.1161	−	1.18241i	−0.638525	−	0.0746329i	−0.429195	+	0.903212i	$0.641203\pi$
$252$	−0.526456	+	1.08826i	−0.0331636	+	0.0685537i
$253$	15.1156	+	20.3037i	0.950308	+	1.27648i
$254$	−0.00517789	−	0.266971i	−0.000324890	−	0.0167512i
$255$	1.14306	−	5.21964i	0.0715815	−	0.326866i
$256$	−13.9057	−	4.45868i	−0.869106	−	0.278668i
$257$	23.2426	−	9.49566i	1.44984	−	0.592323i	0.489709	−	0.871886i	$-0.337103\pi$
$257$	23.2426	−	9.49566i	1.44984	−	0.592323i	0.960127	+	0.279563i	$0.0901895\pi$
$258$	−0.210318	−	12.2832i	−0.0130938	−	0.764718i
$259$	−0.780278	−	0.122033i	−0.0484841	−	0.00758278i
$260$	−1.15701	−	3.86467i	−0.0717544	−	0.239677i
$261$	12.9927	+	10.1650i	0.804231	+	0.629196i
$262$	−8.94088	+	2.11903i	−0.552370	+	0.130914i
$263$	10.1311	+	14.7714i	0.624708	+	0.910846i	0.999870	−	0.0161129i	$-0.00512913\pi$
$263$	10.1311	+	14.7714i	0.624708	+	0.910846i	−0.375162	+	0.926959i	$0.622413\pi$
$264$	−4.10630	−	13.8303i	−0.252725	−	0.851194i
$265$	−0.0116767	+	0.602046i	−0.000717292	+	0.0369834i
$266$	−0.113626	+	0.0812153i	−0.00696688	+	0.00497963i
$267$	−5.53320	−	5.45164i	−0.338626	−	0.333635i
$268$	2.54352	−	11.7422i	0.155370	−	0.717268i
$269$	17.5199	+	6.37670i	1.06820	+	0.388795i	0.815505	−	0.578750i	$-0.196459\pi$
$269$	17.5199	+	6.37670i	1.06820	+	0.388795i	0.252699	+	0.967545i	$0.418682\pi$
$270$	−1.99744	+	0.459048i	−0.121561	+	0.0279368i
$271$	−9.55816	+	3.47889i	−0.580617	+	0.211327i	−0.615598	−	0.788061i	$-0.711085\pi$
$271$	−9.55816	+	3.47889i	−0.580617	+	0.211327i	0.0349806	+	0.999388i	$0.488863\pi$
$272$	−0.387156	−	2.83448i	−0.0234748	−	0.171866i
$273$	2.86895	−	1.57453i	0.173637	−	0.0952949i
$274$	−1.36039	−	1.33426i	−0.0821841	−	0.0806056i
$275$	−14.3189	−	2.81214i	−0.863462	−	0.169578i
$276$	11.4438	−	15.2990i	0.688835	−	0.920891i
$277$	2.63098	+	10.2141i	0.158080	+	0.613705i	0.997528	+	0.0702654i	$0.0223846\pi$
$277$	2.63098	+	10.2141i	0.158080	+	0.613705i	−0.839448	+	0.543440i	$0.817122\pi$
$278$	−7.64524	−	3.83958i	−0.458531	−	0.230283i
$279$	25.2226	+	0.114601i	1.51004	+	0.00686096i
$280$	0.331865	+	0.218271i	0.0198327	+	0.0130442i
$281$	−14.2452	+	2.79767i	−0.849798	+	0.166895i	−0.598607	−	0.801043i	$-0.704279\pi$
$281$	−14.2452	+	2.79767i	−0.849798	+	0.166895i	−0.251191	+	0.967938i	$0.580822\pi$
$282$	−4.47095	+	9.29588i	−0.266241	+	0.553561i
$283$	−0.328137	−	0.520625i	−0.0195057	−	0.0309480i	0.836092	−	0.548589i	$-0.184835\pi$
$283$	−0.328137	−	0.520625i	−0.0195057	−	0.0309480i	−0.855598	+	0.517641i	$0.826810\pi$
$284$	3.79928	−	7.21275i	0.225446	−	0.427998i
$285$	0.456768	+	0.128269i	0.0270566	+	0.00759799i
$286$	−5.05924	+	14.7862i	−0.299159	+	0.874326i
$287$	0.0434276	−	0.745623i	0.00256345	−	0.0440127i
$288$	−14.5986	+	9.50690i	−0.860230	+	0.560199i
$289$	−19.8284	+	13.0413i	−1.16637	+	0.767136i
$290$	1.54845	−	1.51871i	0.0909282	−	0.0891818i
$291$	4.66527	−	15.4552i	0.273483	−	0.906000i
$292$	8.16792	−	9.35940i	0.477991	−	0.547717i
$293$	−7.97794	+	30.9723i	−0.466076	+	1.80942i	0.112330	+	0.993671i	$0.464169\pi$
$293$	−7.97794	+	30.9723i	−0.466076	+	1.80942i	−0.578406	+	0.815749i	$0.696325\pi$
$294$	3.53764	−	9.10114i	0.206320	−	0.530789i
$295$	−5.08536	−	2.07760i	−0.296081	−	0.120962i
$296$	−5.44950	−	4.57268i	−0.316746	−	0.265781i
$297$	−14.6853	−	6.11673i	−0.852129	−	0.354929i
$298$	3.05593	−	2.56423i	0.177025	−	0.148542i
$299$	−49.2505	+	15.7916i	−2.84823	+	0.913249i
$300$	1.04138	+	10.9648i	0.0601242	+	0.633053i
$301$	0.254166	+	2.61305i	0.0146499	+	0.150614i
$302$	10.9328	−	6.03247i	0.629113	−	0.347130i
$303$	−0.128874	+	2.12934i	−0.00740363	+	0.122327i
$304$	0.253248	−	0.0196840i	0.0145247	−	0.00112895i
$305$	−3.11497	−	3.30168i	−0.178363	−	0.189053i
$306$	13.3396	+	8.13341i	0.762575	+	0.464956i
$307$	−5.98211	−	1.41779i	−0.341417	−	0.0809174i	0.0563305	−	0.998412i	$-0.482060\pi$
$307$	−5.98211	−	1.41779i	−0.341417	−	0.0809174i	−0.397748	+	0.917495i	$0.630208\pi$
$308$	0.444355	+	1.15091i	0.0253195	+	0.0655790i
$309$	−10.7260	−	1.70249i	−0.610182	−	0.0968513i
$310$	0.448786	−	3.28570i	0.0254894	−	0.186615i
$311$	−1.46342	−	6.75592i	−0.0829831	−	0.383093i	0.916888	−	0.399145i	$-0.130693\pi$
$311$	−1.46342	−	6.75592i	−0.0829831	−	0.383093i	−0.999871	+	0.0160517i	$0.994890\pi$
$312$	29.4534	+	1.20994i	1.66747	+	0.0684996i
$313$	10.1170	+	5.58235i	0.571849	+	0.315533i	0.742551	−	0.669790i	$-0.233616\pi$
$313$	10.1170	+	5.58235i	0.571849	+	0.315533i	−0.170702	+	0.985323i	$0.554603\pi$
$314$	−1.12910	+	2.61754i	−0.0637185	+	0.147716i
$315$	0.417683	−	0.131835i	0.0235338	−	0.00742805i
$316$	−6.09881	+	8.19213i	−0.343085	+	0.460843i
$317$	9.56597	+	6.83734i	0.537278	+	0.384023i	0.817515	−	0.575908i	$-0.195351\pi$
$317$	9.56597	+	6.83734i	0.537278	+	0.384023i	−0.280237	+	0.959931i	$0.590413\pi$
$318$	−1.65313	−	0.605945i	−0.0927027	−	0.0339797i
$319$	16.6329	−	2.60133i	0.931261	−	0.145647i
$320$	0.801147	+	1.67546i	0.0447855	+	0.0936608i
$321$	10.0859	+	16.0833i	0.562941	+	0.897681i
$322$	1.08654	−	1.72391i	0.0605503	−	0.0960695i
$323$	−1.80833	−	3.13213i	−0.100618	−	0.174276i
$324$	−1.27099	+	11.9399i	−0.0706105	+	0.663326i
$325$	14.9081	−	25.8217i	0.826955	−	1.43233i
$326$	−6.11063	−	11.6008i	−0.338437	−	0.642506i
$327$	−6.59154	−	30.7676i	−0.364513	−	1.70145i
$328$	3.80518	−	5.54809i	0.210106	−	0.306342i
$329$	0.793983	−	2.05647i	0.0437737	−	0.113377i
$330$	−1.04989	+	1.80897i	−0.0577947	+	0.0995803i
$331$	0.973721	−	10.0107i	0.0535206	−	0.550239i	−0.929763	−	0.368159i	$-0.879988\pi$
$331$	0.973721	−	10.0107i	0.0535206	−	0.550239i	0.983284	−	0.182081i	$-0.0582833\pi$
$332$	2.17086	+	5.03262i	0.119141	+	0.276201i
$333$	−7.70398	+	1.47669i	−0.422176	+	0.0809222i
$334$	16.0786	−	1.87932i	0.879781	−	0.102832i
$335$	−3.72684	+	2.24916i	−0.203619	+	0.122885i
$336$	0.185674	−	0.143234i	0.0101293	−	0.00781405i
$337$	−14.0200	+	12.7225i	−0.763718	+	0.693038i	−0.957636	−	0.287980i	$-0.907016\pi$
$337$	−14.0200	+	12.7225i	−0.763718	+	0.693038i	0.193918	+	0.981018i	$0.437880\pi$
$338$	−16.8542	−	13.0630i	−0.916748	−	0.710534i
$339$	3.70129	+	4.26071i	0.201027	+	0.231410i
$340$	−2.58396	+	3.20360i	−0.140135	+	0.173740i
$341$	17.6641	−	18.7228i	0.956563	−	1.01390i
$342$	−0.789815	+	1.14043i	−0.0427083	+	0.0616676i
$343$	−1.20487	+	4.02455i	−0.0650569	+	0.217305i
$344$	−10.2015	+	21.3347i	−0.550029	+	1.15029i
$345$	−6.87705	+	0.787979i	−0.370248	+	0.0424234i
$346$	−4.86797	−	2.93783i	−0.261703	−	0.157939i
$347$	−12.4414	−	5.65533i	−0.667891	−	0.303594i	0.0510181	−	0.998698i	$-0.483753\pi$
$347$	−12.4414	−	5.65533i	−0.667891	−	0.303594i	−0.718909	+	0.695104i	$0.755358\pi$
$348$	−5.45550	−	11.4761i	−0.292445	−	0.615185i
$349$	−4.51570	−	4.09778i	−0.241720	−	0.219349i	0.542138	−	0.840290i	$-0.317615\pi$
$349$	−4.51570	−	4.09778i	−0.241720	−	0.219349i	−0.783858	+	0.620940i	$0.786751\pi$
$350$	0.203992	+	1.15690i	0.0109038	+	0.0618387i
$351$	21.5391	−	24.3442i	1.14967	−	1.29939i
$352$	−3.08723	+	17.5086i	−0.164550	+	0.933210i
$353$	19.9161	−	15.4361i	1.06002	−	0.821581i	0.0755561	−	0.997142i	$-0.475927\pi$
$353$	19.9161	−	15.4361i	1.06002	−	0.821581i	0.984469	+	0.175560i	$0.0561737\pi$
$354$	10.5888	−	12.0779i	0.562789	−	0.641936i
$355$	−2.84541	+	0.792073i	−0.151018	+	0.0420389i
$356$	1.93697	+	5.66100i	0.102659	+	0.300033i
$357$	−2.98031	−	1.50526i	−0.157735	−	0.0796667i
$358$	6.48489	+	1.80519i	0.342737	+	0.0954074i
$359$	−0.762632	−	13.0939i	−0.0402502	−	0.691069i	−0.956728	−	0.290983i	$-0.906018\pi$
$359$	−0.762632	−	13.0939i	−0.0402502	−	0.691069i	0.916478	−	0.400085i	$-0.131019\pi$
$360$	3.83474	+	0.927271i	0.202108	+	0.0488715i
$361$	−16.6921	+	8.38306i	−0.878529	+	0.441214i
$362$	7.37833	+	8.45463i	0.387796	+	0.444365i
$363$	2.56796	−	1.16025i	0.134783	−	0.0608974i
$364$	−2.51891	+	0.0977451i	−0.132027	+	0.00512323i
$365$	−4.49729	+	0.174515i	−0.235399	+	0.00913455i
$366$	12.0951	−	5.46476i	0.632219	−	0.285647i
$367$	24.4299	+	27.9935i	1.27523	+	1.46125i	0.821605	+	0.570058i	$0.193079\pi$
$367$	24.4299	+	27.9935i	1.27523	+	1.46125i	0.453625	+	0.891193i	$0.350131\pi$
$368$	−3.31184	+	1.66327i	−0.172641	+	0.0867037i
$369$	−2.09530	−	7.11631i	−0.109077	−	0.370460i
$370$	0.0599666	+	1.02959i	0.00311751	+	0.0535257i
$371$	0.362487	+	0.100905i	0.0188194	+	0.00523873i
$372$	−17.3420	−	8.75887i	−0.899141	−	0.454126i
$373$	−3.12793	−	9.14172i	−0.161958	−	0.473340i	0.835091	−	0.550112i	$-0.185415\pi$
$373$	−3.12793	−	9.14172i	−0.161958	−	0.473340i	−0.997049	+	0.0767722i	$0.975539\pi$
$374$	15.3601	−	4.27579i	0.794254	−	0.221096i
$375$	5.39028	−	6.14832i	0.278353	−	0.317498i
$376$	15.6944	−	12.1640i	0.809375	−	0.627313i
$377$	−5.97325	+	33.8760i	−0.307638	+	1.74470i
$378$	−0.0335599	+	1.28023i	−0.00172613	+	0.0658481i
$379$	−4.84403	−	27.4718i	−0.248821	−	1.41113i	−0.811449	−	0.584424i	$-0.801321\pi$
$379$	−4.84403	−	27.4718i	−0.248821	−	1.41113i	0.562628	−	0.826710i	$-0.309790\pi$
$380$	−0.270628	−	0.245581i	−0.0138829	−	0.0125981i
$381$	0.243340	+	0.511888i	0.0124667	+	0.0262248i
$382$	−0.989729	−	0.449887i	−0.0506389	−	0.0230182i
$383$	−12.5529	−	7.57569i	−0.641421	−	0.387100i	0.158368	−	0.987380i	$-0.449377\pi$
$383$	−12.5529	−	7.57569i	−0.641421	−	0.387100i	−0.799790	+	0.600280i	$0.795056\pi$
$384$	14.5907	−	1.67181i	0.744576	−	0.0853143i
$385$	0.192821	−	0.403252i	0.00982709	−	0.0205516i
$386$	−3.43982	+	11.4898i	−0.175082	+	0.584815i
$387$	11.1420	+	23.5761i	0.566378	+	1.19844i
$388$	−8.53357	+	9.04506i	−0.433227	+	0.459193i
$389$	23.3986	−	29.0097i	1.18635	−	1.47085i	0.338221	−	0.941067i	$-0.390175\pi$
$389$	23.3986	−	29.0097i	1.18635	−	1.47085i	0.848134	−	0.529782i	$-0.177726\pi$
$390$	−2.80268	−	3.22628i	−0.141919	−	0.163369i
$391$	41.7069	+	32.3253i	2.10921	+	1.63476i
$392$	−13.9196	+	12.6313i	−0.703044	+	0.637978i
$393$	15.4428	−	11.9130i	0.778984	−	0.600931i
$394$	3.16578	−	1.91056i	0.159490	−	0.0962526i
$395$	3.67524	−	0.429574i	0.184921	−	0.0216142i
$396$	8.01502	+	9.26887i	0.402770	+	0.465778i
$397$	4.95006	+	11.4755i	0.248437	+	0.575941i	0.996109	−	0.0881267i	$-0.0280880\pi$
$397$	4.95006	+	11.4755i	0.248437	+	0.575941i	−0.747673	+	0.664067i	$0.768829\pi$
$398$	−0.0869346	+	0.893766i	−0.00435764	+	0.0448004i
$399$	0.148813	−	0.256404i	0.00744995	−	0.0128363i
$400$	0.769519	−	1.99310i	0.0384759	−	0.0996552i
$401$	7.69786	−	11.2238i	0.384413	−	0.560487i	−0.583392	−	0.812191i	$-0.698275\pi$
$401$	7.69786	−	11.2238i	0.384413	−	0.560487i	0.967804	+	0.251704i	$0.0809908\pi$
$402$	−2.66625	−	12.4453i	−0.132980	−	0.620717i
$403$	24.5113	+	46.5335i	1.22099	+	2.31800i
$404$	0.821583	−	1.42302i	0.0408753	−	0.0707981i
$405$	3.46255	−	2.63366i	0.172055	−	0.130868i
$406$	−0.677641	−	1.17371i	−0.0336308	−	0.0582502i
$407$	−4.26839	+	6.77226i	−0.211576	+	0.335689i
$408$	−15.9783	−	25.4794i	−0.791043	−	1.26142i
$409$	−14.9282	−	31.2196i	−0.738151	−	1.54371i	−0.836135	−	0.548523i	$-0.815190\pi$
$409$	−14.9282	−	31.2196i	−0.738151	−	1.54371i	0.0979847	−	0.995188i	$-0.468760\pi$
$410$	−0.963626	+	0.150708i	−0.0475901	+	0.00744295i
$411$	3.79756	+	1.39198i	0.187320	+	0.0686612i
$412$	6.80566	+	4.86439i	0.335291	+	0.239651i
$413$	−2.04983	+	2.75340i	−0.100865	+	0.135486i
$414$	4.37465	−	19.7613i	0.215002	−	0.971213i
$415$	0.786516	−	1.82335i	0.0386086	−	0.0895047i
$416$	−31.8061	−	17.5499i	−1.55942	−	0.860453i
$417$	18.1442	+	0.745362i	0.888525	+	0.0365006i
$418$	0.299706	+	1.38360i	0.0146591	+	0.0676740i
$419$	1.74073	−	12.7444i	0.0850404	−	0.622606i	−0.898105	−	0.439781i	$-0.855056\pi$
$419$	1.74073	−	12.7444i	0.0850404	−	0.622606i	0.983145	−	0.182825i	$-0.0585241\pi$
$420$	−0.333203	−	0.0528878i	−0.0162587	−	0.00258066i
$421$	0.159860	+	0.414048i	0.00779110	+	0.0201794i	0.936725	−	0.350067i	$-0.113841\pi$
$421$	0.159860	+	0.414048i	0.00779110	+	0.0201794i	−0.928934	+	0.370246i	$0.879273\pi$
$422$	14.2524	+	3.37788i	0.693796	+	0.164433i
$423$	0.524034	−	21.8889i	0.0254794	−	1.06427i
$424$	2.32585	+	2.46526i	0.112953	+	0.119724i
$425$	−30.3284	+	2.35731i	−1.47114	+	0.114346i
$426$	0.521732	−	8.62038i	0.0252780	−	0.417659i
$427$	−2.48342	+	1.37029i	−0.120181	+	0.0663130i
$428$	−1.41566	−	14.5542i	−0.0684284	−	0.703506i
$429$	−3.13638	−	33.0232i	−0.151426	−	1.59438i
$430$	3.26471	−	1.04679i	0.157438	−	0.0504805i
$431$	−18.1728	+	15.2488i	−0.875351	+	0.734507i	−0.965218	−	0.261447i	$-0.915800\pi$
$431$	−18.1728	+	15.2488i	−0.875351	+	0.734507i	0.0898670	+	0.995954i	$0.471356\pi$
$432$	1.25531	−	1.96192i	0.0603964	−	0.0943930i
$433$	−14.2990	−	11.9983i	−0.687164	−	0.576599i	0.230926	−	0.972971i	$-0.425825\pi$
$433$	−14.2990	−	11.9983i	−0.687164	−	0.576599i	−0.918090	+	0.396372i	$0.870269\pi$
$434$	−1.91827	−	0.783701i	−0.0920801	−	0.0376189i
$435$	−1.66793	+	4.29101i	−0.0799711	+	0.205738i
$436$	−6.04574	+	23.4710i	−0.289538	+	1.12406i
$437$	−3.08064	+	3.53002i	−0.147367	+	0.168864i
$438$	3.80289	−	12.5983i	0.181709	−	0.601969i
$439$	0.279485	−	0.274117i	0.0133391	−	0.0130829i	−0.693517	−	0.720440i	$-0.743940\pi$
$439$	0.279485	−	0.274117i	0.0133391	−	0.0130829i	0.706856	+	0.707357i	$0.250113\pi$
$440$	3.36384	−	2.21243i	0.160365	−	0.105474i
$441$	1.11110	+	20.6965i	0.0529097	+	0.985548i
$442$	−1.89426	+	32.5231i	−0.0901006	+	1.54697i
$443$	−2.94011	+	8.59279i	−0.139689	+	0.408256i	−0.993710	−	0.111982i	$-0.964280\pi$
$443$	−2.94011	+	8.59279i	−0.139689	+	0.408256i	0.854022	+	0.520238i	$0.174157\pi$
$444$	5.81716	+	1.63357i	0.276070	+	0.0775257i
$445$	1.01027	−	1.91795i	0.0478913	−	0.0909194i
$446$	2.42858	+	3.85321i	0.114997	+	0.182455i
$447$	−3.67015	+	7.63088i	−0.173592	+	0.360928i
$448$	1.13872	−	0.223637i	0.0537993	−	0.0105658i
$449$	27.1994	+	17.8893i	1.28362	+	0.844248i	0.993620	−	0.112779i	$-0.0359752\pi$
$449$	27.1994	+	17.8893i	1.28362	+	0.844248i	0.289997	+	0.957027i	$0.406346\pi$
$450$	5.78803	+	10.1312i	0.272850	+	0.477589i
$451$	−6.76530	−	3.39766i	−0.318565	−	0.159990i
$452$	−1.08440	−	4.20988i	−0.0510057	−	0.198016i
$453$	−15.8756	+	21.2238i	−0.745901	+	0.997182i
$454$	−2.44970	−	0.481105i	−0.114970	−	0.0225794i
$455$	0.652035	+	0.639511i	0.0305679	+	0.0299807i
$456$	2.34099	−	1.28478i	0.109627	−	0.0601651i
$457$	−2.21077	−	16.1857i	−0.103415	−	0.757135i	−0.967334	−	0.253504i	$-0.918417\pi$
$457$	−2.21077	−	16.1857i	−0.103415	−	0.757135i	0.863919	−	0.503631i	$-0.168003\pi$
$458$	−19.7625	+	7.19298i	−0.923443	+	0.336106i
$459$	−32.9117	−	4.07438i	−1.53619	−	0.190176i
$460$	5.01030	+	1.82360i	0.233606	+	0.0850257i
$461$	−0.389227	+	1.79687i	−0.0181281	+	0.0836886i	−0.985502	−	0.169665i	$-0.945731\pi$
$461$	−0.389227	+	1.79687i	−0.0181281	+	0.0836886i	0.967374	+	0.253354i	$0.0815338\pi$
$462$	0.930988	+	0.917265i	0.0433135	+	0.0426750i
$463$	17.2121	−	12.3025i	0.799915	−	0.571745i	−0.106412	−	0.994322i	$-0.533936\pi$
$463$	17.2121	−	12.3025i	0.799915	−	0.571745i	0.906327	+	0.422577i	$0.138874\pi$
$464$	−0.0477966	+	2.46438i	−0.00221890	+	0.114406i
$465$	2.00349	+	6.74789i	0.0929098	+	0.312926i
$466$	−6.01158	−	8.76510i	−0.278481	−	0.406035i
$467$	20.3319	−	4.81875i	0.940849	−	0.222985i	0.268551	−	0.963266i	$-0.413455\pi$
$467$	20.3319	−	4.81875i	0.940849	−	0.222985i	0.672299	+	0.740280i	$0.265307\pi$
$468$	−23.2207	+	9.36381i	−1.07338	+	0.432842i
$469$	0.780106	+	2.60574i	0.0360219	+	0.120322i
$470$	−2.84412	−	0.444813i	−0.131190	−	0.0205177i
$471$	−0.103591	−	6.05001i	−0.00477322	−	0.278770i
$472$	−28.6230	+	11.6938i	−1.31748	+	0.538250i
$473$	25.3406	+	8.12513i	1.16516	+	0.373594i
$474$	−2.31452	+	10.5689i	−0.106309	+	0.485445i
$475$	−0.0523758	−	2.70048i	−0.00240317	−	0.123907i
$476$	1.53579	+	2.06293i	0.0703930	+	0.0945542i
$477$	3.72729	−	0.272676i	0.170661	−	0.0124850i
$478$	3.00901	+	0.351703i	0.137629	+	0.0160865i
$479$	−26.1018	+	11.8647i	−1.19262	+	0.542113i	−0.908989	−	0.416820i	$-0.863144\pi$
$479$	−26.1018	+	11.8647i	−1.19262	+	0.542113i	−0.283632	+	0.958933i	$0.591539\pi$
$480$	−3.71726	−	3.13357i	−0.169669	−	0.143027i
$481$	−10.2690	−	12.7315i	−0.468224	−	0.580507i
$482$	11.7061	+	0.909870i	0.533198	+	0.0414434i
$483$	−0.595091	+	4.28422i	−0.0270776	+	0.194939i
$484$	−2.16892	−	0.0841640i	−0.0985873	−	0.00382564i
$485$	4.50537			0.204578
$486$	3.98097	+	12.0811i	0.180581	+	0.548012i
$487$	−12.6522			−0.573327			−0.286664	−	0.958031i	$-0.592546\pi$
$487$	−12.6522			−0.573327			−0.286664	+	0.958031i	$0.592546\pi$
$488$	−25.5296	−	0.990664i	−1.15567	−	0.0448453i
$489$	21.9588	+	17.0993i	0.993009	+	0.773258i
$490$	2.71683	+	0.211168i	0.122734	+	0.00953962i
$491$	6.92580	+	8.58665i	0.312557	+	0.387510i	0.910143	−	0.414295i	$-0.135972\pi$
$491$	6.92580	+	8.58665i	0.312557	+	0.387510i	−0.597585	+	0.801805i	$0.703873\pi$
$492$	−1.00503	+	5.62507i	−0.0453104	+	0.253598i
$493$	31.9491	−	14.5227i	1.43892	−	0.654068i
$494$	−2.87308	−	0.335814i	−0.129266	−	0.0151090i
$495$	0.449872	−	4.41673i	0.0202203	−	0.198517i
$496$	2.25050	+	3.02294i	0.101050	+	0.135734i
$497$	0.0357887	+	1.84526i	0.00160534	+	0.0827711i
$498$	4.29090	+	3.91159i	0.192280	+	0.175283i
$499$	−18.4316	−	5.90986i	−0.825113	−	0.264562i	−0.137373	−	0.990519i	$-0.543866\pi$
$499$	−18.4316	−	5.90986i	−0.825113	−	0.264562i	−0.687739	+	0.725958i	$0.741397\pi$
$500$	−5.83039	+	2.38198i	−0.260743	+	0.106525i
$501$	−29.4590	+	17.6874i	−1.31613	+	0.790217i
$502$	8.21113	+	1.28420i	0.366481	+	0.0573165i
$503$	−1.80945	−	6.04398i	−0.0806793	−	0.269488i	0.908127	−	0.418696i	$-0.137513\pi$
$503$	−1.80945	−	6.04398i	−0.0806793	−	0.269488i	−0.988806	+	0.149208i	$0.952327\pi$
$504$	1.15882	−	2.17593i	0.0516178	−	0.0969234i
$505$	−0.579283	+	0.137293i	−0.0257778	+	0.00610944i
$506$	−11.6826	−	17.0336i	−0.519354	−	0.757236i
$507$	44.0185	+	10.5382i	1.95493	+	0.468020i
$508$	0.00846580	−	0.436494i	0.000375609	−	0.0193663i
$509$	8.06808	−	5.76672i	0.357611	−	0.255605i	−0.388468	−	0.921462i	$-0.626996\pi$
$509$	8.06808	−	5.76672i	0.357611	−	0.255605i	0.746079	+	0.665857i	$0.231934\pi$
$510$	−1.09719	+	4.21984i	−0.0485844	+	0.186858i
$511$	−0.595380	+	2.74858i	−0.0263381	+	0.121590i
$512$	−4.73797	−	1.72448i	−0.209391	−	0.0762120i
$513$	0.531067	−	2.89626i	0.0234472	−	0.127873i
$514$	−19.2521	+	7.00720i	−0.849175	+	0.309074i
$515$	−0.410166	−	3.00294i	−0.0180741	−	0.132326i
$516$	0.435112	−	20.0811i	0.0191547	−	0.884022i
$517$	−15.9523	−	15.6459i	−0.701582	−	0.688106i
$518$	0.632365	+	0.124192i	0.0277845	+	0.00545670i
$519$	11.9839	+	1.42832i	0.526034	+	0.0626963i
$520$	2.05206	+	7.96657i	0.0899886	+	0.349357i
$521$	−21.9253	−	11.0113i	−0.960564	−	0.482413i	−0.101811	−	0.994804i	$-0.532464\pi$
$521$	−21.9253	−	11.0113i	−0.960564	−	0.482413i	−0.858753	+	0.512391i	$0.828760\pi$
$522$	−10.2724	−	8.69945i	−0.449613	−	0.380765i
$523$	10.7985	+	7.10232i	0.472188	+	0.310563i	0.763207	−	0.646155i	$-0.223624\pi$
$523$	10.7985	+	7.10232i	0.472188	+	0.310563i	−0.291019	+	0.956717i	$0.593994\pi$
$524$	−14.7416	+	2.89516i	−0.643990	+	0.126475i
$525$	−1.40568	−	2.05955i	−0.0613490	−	0.0898861i
$526$	−7.79332	−	12.3650i	−0.339805	−	0.539137i
$527$	25.0075	−	47.4756i	1.08934	−	2.06807i
$528$	−0.587675	−	2.30314i	−0.0255753	−	0.100231i
$529$	14.6838	−	42.9151i	0.638427	−	1.86587i
$530$	0.0285701	−	0.490529i	0.00124100	−	0.0213072i
$531$	−9.92665	+	32.6172i	−0.430780	+	1.41547i
$532$	−0.190787	+	0.125483i	−0.00827167	+	0.00544036i
$533$	11.0436	−	10.8315i	0.478350	−	0.469163i
$534$	4.33919	+	4.62026i	0.187775	+	0.199938i
$535$	−3.48354	+	3.99169i	−0.150606	+	0.172576i
$536$	−6.11144	+	23.7261i	−0.263974	+	1.02481i
$537$	−14.1217	+	2.17574i	−0.609396	+	0.0938900i
$538$	−14.0836	−	5.75380i	−0.607189	−	0.248064i
$539$	16.2030	+	13.5959i	0.697913	+	0.585619i
$540$	−3.29245	+	0.623342i	−0.141684	+	0.0268244i
$541$	−17.1314	+	14.3749i	−0.736535	+	0.618026i	−0.931905	−	0.362703i	$-0.881854\pi$
$541$	−17.1314	+	14.3749i	−0.736535	+	0.618026i	0.195370	+	0.980730i	$0.437409\pi$
$542$	7.90365	−	2.53420i	0.339491	−	0.108853i
$543$	−21.6613	−	9.90571i	−0.929575	−	0.425095i
$544$	3.58801	+	36.8880i	0.153835	+	1.58156i
$545$	7.68852	−	4.24234i	0.329340	−	0.181722i
$546$	−2.38912	+	1.19307i	−0.102245	+	0.0510588i
$547$	29.7461	−	2.31205i	1.27185	−	0.0988562i	0.576244	−	0.817278i	$-0.304518\pi$
$547$	29.7461	−	2.31205i	1.27185	−	0.0988562i	0.695608	+	0.718421i	$0.255135\pi$
$548$	−2.13796	−	2.26611i	−0.0913291	−	0.0968032i
$549$	−18.6200	+	21.1414i	−0.794680	+	0.902294i
$550$	11.5864	+	2.74603i	0.494046	+	0.117091i
$551$	1.12235	+	2.90695i	0.0478136	+	0.123840i
$552$	−24.5289	+	30.2701i	−1.04402	+	1.28838i
$553$	0.312909	−	2.29090i	0.0133062	−	0.0974189i
$554$	−1.82208	−	8.41165i	−0.0774127	−	0.357377i
$555$	−1.01582	−	1.93916i	−0.0431193	−	0.0823129i
$556$	−12.2471	−	6.75765i	−0.519391	−	0.286588i
$557$	−1.51310	+	3.50775i	−0.0641119	+	0.148628i	−0.947260	−	0.320466i	$-0.896160\pi$
$557$	−1.51310	+	3.50775i	−0.0641119	+	0.148628i	0.883148	+	0.469094i	$0.155420\pi$
$558$	−20.5624	−	0.891501i	−0.870478	−	0.0377402i
$559$	−32.4700	+	43.6148i	−1.37333	+	1.84471i
$560$	0.0532414	+	0.0380546i	0.00224986	+	0.00160810i
$561$	−25.9749	+	21.6951i	−1.09666	+	0.915969i
$562$	11.7038	−	1.83045i	0.493696	−	0.0772127i
$563$	−13.0574	−	27.3072i	−0.550302	−	1.15086i	−0.969980	−	0.243186i	$-0.921807\pi$
$563$	−13.0574	−	27.3072i	−0.550302	−	1.15086i	0.419677	−	0.907673i	$-0.362143\pi$
$564$	−7.89379	+	14.9038i	−0.332389	+	0.627563i
$565$	−0.839827	+	1.33248i	−0.0353318	+	0.0560577i
$566$	0.251085	+	0.434892i	0.0105539	+	0.0182799i
$567$	−1.05397	−	2.50574i	−0.0442626	−	0.105231i
$568$	−8.31217	+	14.3971i	−0.348771	+	0.604089i
$569$	−8.84765	−	16.7969i	−0.370913	−	0.704161i	0.626235	−	0.779634i	$-0.284595\pi$
$569$	−8.84765	−	16.7969i	−0.370913	−	0.704161i	−0.997148	+	0.0754738i	$0.975953\pi$
$570$	−0.368383	−	0.119041i	−0.0154299	−	0.00498607i
$571$	18.1076	−	26.4016i	0.757782	−	1.10487i	−0.233402	−	0.972380i	$-0.574986\pi$
$571$	18.1076	−	26.4016i	0.757782	−	1.10487i	0.991184	−	0.132492i	$-0.0422980\pi$
$572$	−9.20300	+	23.8364i	−0.384797	+	0.996648i
$573$	2.30766	+	0.00524249i	0.0964039	+	0.000219008i
$574$	−0.0590021	+	0.606595i	−0.00246270	+	0.0253188i
$575$	15.6085	+	36.1847i	0.650921	+	1.50901i
$576$	9.89533	−	5.91069i	0.412305	−	0.246279i
$577$	8.77501	−	1.02565i	0.365308	−	0.0426984i	0.0685412	−	0.997648i	$-0.478166\pi$
$577$	8.77501	−	1.02565i	0.365308	−	0.0426984i	0.296767	+	0.954950i	$0.404091\pi$
$578$	16.5804	−	10.0063i	0.689652	−	0.416207i
$579$	−3.38794	−	25.2315i	−0.140798	−	1.04858i
$580$	2.62608	−	2.38304i	0.109042	−	0.0989504i
$581$	−0.980744	−	0.760134i	−0.0406881	−	0.0315357i
$582$	−4.29300	+	12.4543i	−0.177950	+	0.516248i
$583$	2.39443	−	2.96863i	0.0991671	−	0.122948i
$584$	−17.3840	+	18.4259i	−0.719353	+	0.762470i
$585$	8.24102	+	3.79128i	0.340724	+	0.156750i
$586$	7.48507	−	25.0019i	0.309205	−	1.03282i
$587$	2.76542	−	5.78338i	0.114141	−	0.238706i	−0.837167	−	0.546947i	$-0.815790\pi$
$587$	2.76542	−	5.78338i	0.114141	−	0.238706i	0.951308	+	0.308241i	$0.0997405\pi$
$588$	6.35665	−	14.6448i	0.262144	−	0.603941i
$589$	4.07913	+	2.46177i	0.168078	+	0.101435i
$590$	4.08079	+	1.85494i	0.168003	+	0.0763669i
$591$	−4.45394	+	6.46248i	−0.183211	+	0.265831i
$592$	−0.867953	−	0.787625i	−0.0356726	−	0.0323712i
$593$	5.88077	+	33.3515i	0.241494	+	1.36958i	0.828496	+	0.559995i	$0.189197\pi$
$593$	5.88077	+	33.3515i	0.241494	+	1.36958i	−0.587002	+	0.809586i	$0.699692\pi$
$594$	11.7806	+	5.45214i	0.483366	+	0.223704i
$595$	0.161804	−	0.917637i	0.00663332	−	0.0376194i
$596$	5.15522	−	3.99560i	0.211166	−	0.163666i
$597$	−0.612963	−	1.80483i	−0.0250869	−	0.0738667i
$598$	40.6578	−	11.3179i	1.66262	−	0.462822i
$599$	−5.10260	−	14.9129i	−0.208487	−	0.609326i	0.791512	−	0.611154i	$-0.209294\pi$
$599$	−5.10260	−	14.9129i	−0.208487	−	0.609326i	−0.999998	+	0.00182864i	$0.999418\pi$
$600$	−1.25502	−	22.4255i	−0.0512361	−	0.915516i
$601$	−15.0189	−	4.18080i	−0.612634	−	0.170538i	−0.0520617	−	0.998644i	$-0.516579\pi$
$601$	−15.0189	−	4.18080i	−0.612634	−	0.170538i	−0.560572	+	0.828106i	$0.689419\pi$
$602$	−0.124564	−	2.13868i	−0.00507686	−	0.0871662i
$603$	16.0343	+	21.7433i	0.652967	+	0.885457i
$604$	18.2440	−	9.16250i	0.742339	−	0.372817i
$605$	0.517078	+	0.592506i	0.0210222	+	0.0240888i
$606$	0.172455	−	1.73215i	0.00700552	−	0.0703638i
$607$	13.6136	−	0.528270i	0.552560	−	0.0214418i	0.239016	−	0.971016i	$-0.423175\pi$
$607$	13.6136	−	0.528270i	0.552560	−	0.0214418i	0.313544	+	0.949574i	$0.398484\pi$
$608$	−3.28828	+	0.127600i	−0.133357	+	0.00517487i
$609$	2.33658	+	1.67812i	0.0946829	+	0.0680008i
$610$	2.43543	+	2.79069i	0.0986077	+	0.112992i
$611$	40.7993	−	20.4902i	1.65056	−	0.828945i
$612$	21.2781	+	14.1337i	0.860115	+	0.571322i
$613$	−2.03528	−	34.9443i	−0.0822040	−	1.41139i	−0.747229	−	0.664567i	$-0.768616\pi$
$613$	−2.03528	−	34.9443i	−0.0822040	−	1.41139i	0.665025	−	0.746821i	$-0.268421\pi$
$614$	4.83286	+	1.34532i	0.195038	+	0.0542926i
$615$	1.73227	−	1.13370i	0.0698518	−	0.0457152i
$616$	−0.814462	−	2.38036i	−0.0328156	−	0.0959072i
$617$	−41.6039	+	11.5812i	−1.67491	+	0.466243i	−0.970010	−	0.243065i	$-0.921847\pi$
$617$	−41.6039	+	11.5812i	−1.67491	+	0.466243i	−0.704899	+	0.709307i	$0.749008\pi$
$618$	8.69196	+	1.72756i	0.349642	+	0.0694927i
$619$	−15.2178	+	11.7947i	−0.611654	+	0.474067i	−0.870711	−	0.491795i	$-0.836341\pi$
$619$	−15.2178	+	11.7947i	−0.611654	+	0.474067i	0.259058	+	0.965862i	$0.416588\pi$
$620$	0.941514	−	5.33959i	0.0378121	−	0.214443i
$621$	8.80867	+	42.0484i	0.353480	+	1.68734i
$622$	0.979491	+	5.55497i	0.0392740	+	0.222734i
$623$	−1.00311	−	0.910274i	−0.0401888	−	0.0364694i
$624$	4.84126	+	0.387359i	0.193805	+	0.0155068i
$625$	−19.6182	−	8.91757i	−0.784729	−	0.356703i
$626$	−8.07265	−	4.87187i	−0.322648	−	0.194719i
$627$	−1.78896	−	2.41442i	−0.0714441	−	0.0964227i
$628$	−2.01062	+	4.20485i	−0.0802323	+	0.167792i
$629$	−4.78613	+	15.9868i	−0.190836	+	0.637435i
$630$	−0.344743	+	0.0942803i	−0.0137349	+	0.00375622i
$631$	−8.58309	+	9.09754i	−0.341687	+	0.362168i	−0.875316	−	0.483551i	$-0.839347\pi$
$631$	−8.58309	+	9.09754i	−0.341687	+	0.362168i	0.533628	+	0.845719i	$0.320828\pi$
$632$	13.0754	−	16.2110i	0.520112	−	0.644837i
$633$	−30.5212	+	5.92218i	−1.21311	+	0.235386i
$634$	−7.58360	−	5.87773i	−0.301183	−	0.233435i
$635$	−0.117135	+	0.106295i	−0.00464837	+	0.00421817i
$636$	−2.66240	−	1.09477i	−0.105571	−	0.0434106i
$637$	−37.0021	+	22.3309i	−1.46608	+	0.884782i
$638$	−13.6445	+	1.59481i	−0.540190	+	0.0631391i
$639$	6.52474	+	17.1307i	0.258115	+	0.677682i
$640$	1.62334	+	3.76332i	0.0641681	+	0.148758i
$641$	−1.27494	+	13.1075i	−0.0503571	+	0.517716i	0.935873	+	0.352337i	$0.114613\pi$
$641$	−1.27494	+	13.1075i	−0.0503571	+	0.517716i	−0.986230	+	0.165379i	$0.947115\pi$
$642$	−7.71501	−	13.4332i	−0.304487	−	0.530165i
$643$	8.84670	−	22.9135i	0.348880	−	0.903621i	−0.641734	−	0.766928i	$-0.721784\pi$
$643$	8.84670	−	22.9135i	0.348880	−	0.903621i	0.990613	−	0.136694i	$-0.0436476\pi$
$644$	1.88443	−	2.74757i	0.0742569	−	0.108269i
$645$	−5.40020	+	4.87810i	−0.212633	+	0.192075i
$646$	1.37538	+	2.61110i	0.0541138	+	0.102732i
$647$	24.0936	−	41.7313i	0.947217	−	1.64063i	0.195965	−	0.980611i	$-0.437216\pi$
$647$	24.0936	−	41.7313i	0.947217	−	1.64063i	0.751251	−	0.660016i	$-0.229451\pi$
$648$	3.53403	−	24.2295i	0.138830	−	0.951826i
$649$	17.3969	+	30.1323i	0.682887	+	1.18280i
$650$	−12.9729	+	20.5829i	−0.508838	+	0.807327i
$651$	4.39553	−	0.160567i	0.172274	−	0.00629311i
$652$	−9.24785	−	19.3402i	−0.362174	−	0.757422i
$653$	35.0831	−	5.48690i	1.37291	−	0.214719i	0.575324	−	0.817926i	$-0.304876\pi$
$653$	35.0831	−	5.48690i	1.37291	−	0.214719i	0.797585	+	0.603206i	$0.206111\pi$
$654$	4.40113	+	25.2960i	0.172098	+	0.989151i
$655$	4.42817	+	3.16506i	0.173023	+	0.123669i
$656$	0.661900	−	0.889086i	0.0258429	−	0.0347130i
$657$	3.65443	+	27.6930i	0.142573	+	1.08041i
$658$	−0.712469	+	1.65169i	−0.0277749	+	0.0643896i
$659$	36.6052	+	20.1979i	1.42594	+	0.786799i	0.993387	−	0.114811i	$-0.0366263\pi$
$659$	36.6052	+	20.1979i	1.42594	+	0.786799i	0.432550	+	0.901610i	$0.357614\pi$
$660$	−1.82996	+	2.88886i	−0.0712310	+	0.112449i
$661$	−2.04697	−	9.44985i	−0.0796177	−	0.367556i	0.920091	−	0.391706i	$-0.128115\pi$
$661$	−2.04697	−	9.44985i	−0.0796177	−	0.367556i	−0.999708	+	0.0241491i	$0.992312\pi$
$662$	−1.11070	+	8.13178i	−0.0431687	+	0.316051i
$663$	−24.7601	−	64.5664i	−0.961602	−	2.50755i
$664$	−4.02565	−	10.4267i	−0.156225	−	0.404634i
$665$	0.0805041	+	0.0190798i	0.00312181	+	0.000739884i
$666$	6.32843	−	0.960312i	0.245222	−	0.0372113i
$667$	−31.1992	−	33.0693i	−1.20804	−	1.28045i
$668$	26.3877	−	2.05101i	1.02097	−	0.0793561i
$669$	−8.06530	−	5.33092i	−0.311823	−	0.206105i
$670$	3.10997	−	1.71601i	0.120149	−	0.0662952i
$671$	2.78331	+	28.6150i	0.107449	+	1.10467i
$672$	−2.47557	+	1.76095i	−0.0954972	+	0.0679300i
$673$	7.38884	−	2.36914i	0.284819	−	0.0913235i	−0.159483	−	0.987201i	$-0.550983\pi$
$673$	7.38884	−	2.36914i	0.284819	−	0.0913235i	0.444302	+	0.895877i	$0.353452\pi$
$674$	11.8342	−	9.93010i	0.455838	−	0.382493i
$675$	−20.0504	−	14.5386i	−0.771739	−	0.559592i
$676$	−26.7076	−	22.4103i	−1.02721	−	0.861935i
$677$	−0.762811	−	0.311643i	−0.0293172	−	0.0119774i	0.363494	−	0.931597i	$-0.381584\pi$
$677$	−0.762811	−	0.311643i	−0.0293172	−	0.0119774i	−0.392811	+	0.919619i	$0.628497\pi$
$678$	−2.88316	−	3.59123i	−0.110727	−	0.137920i
$679$	0.702240	−	2.72626i	0.0269495	−	0.104624i
$680$	5.51868	−	6.32371i	0.211632	−	0.242503i
$681$	5.15903	−	1.21034i	0.197694	−	0.0463803i
$682$	−14.9954	+	14.7074i	−0.574203	+	0.563175i
$683$	14.2976	−	9.40370i	0.547084	−	0.359823i	−0.245681	−	0.969351i	$-0.579011\pi$
$683$	14.2976	−	9.40370i	0.547084	−	0.359823i	0.792764	+	0.609528i	$0.208641\pi$
$684$	−1.36267	+	1.81312i	−0.0521029	+	0.0693265i
$685$	−0.0656311	+	1.12684i	−0.00250764	+	0.0430545i
$686$	1.10977	−	3.24343i	0.0423713	−	0.123835i
$687$	31.9411	−	31.1856i	1.21863	−	1.18980i
$688$	−1.81580	+	3.44721i	−0.0692267	+	0.131424i
$689$	4.15520	+	6.59268i	0.158301	+	0.251161i
$690$	5.63237	−	0.424912i	0.214421	−	0.0161761i
$691$	9.77866	−	1.92047i	0.371998	−	0.0730580i	−0.00321970	−	0.999995i	$-0.501025\pi$
$691$	9.77866	−	1.92047i	0.371998	−	0.0730580i	0.375217	+	0.926937i	$0.377568\pi$
$692$	−7.76684	−	5.10833i	−0.295251	−	0.194190i
$693$	−2.60251	−	0.960650i	−0.0988612	−	0.0364921i
$694$	9.96561	+	5.00492i	0.378289	+	0.189984i
$695$	1.26413	+	4.90765i	0.0479511	+	0.186158i
$696$	10.2093	+	23.8164i	0.386982	+	0.902760i
$697$	−15.4860	−	3.04136i	−0.586575	−	0.115200i
$698$	3.55237	+	3.48414i	0.134459	+	0.131877i
$699$	19.2889	+	11.7008i	0.729572	+	0.442563i
$700$	0.259930	+	1.90302i	0.00982442	+	0.0719275i
$701$	19.0770	−	6.94348i	0.720530	−	0.262252i	0.0443793	−	0.999015i	$-0.485869\pi$
$701$	19.0770	−	6.94348i	0.720530	−	0.262252i	0.676151	+	0.736763i	$0.263647\pi$
$702$	−18.3329	+	19.1683i	−0.691931	+	0.723462i
$703$	−1.39236	−	0.506778i	−0.0525139	−	0.0191135i
$704$	2.49021	−	11.4961i	0.0938533	−	0.433275i
$705$	5.89026	−	1.62526i	0.221840	−	0.0612107i
$706$	−16.7276	+	11.9562i	−0.629553	+	0.449978i
$707$	−0.00721362	+	0.371932i	−0.000271296	+	0.0139879i
$708$	18.0653	−	19.0612i	0.678936	−	0.716362i
$709$	−20.0862	−	29.2864i	−0.754354	−	1.09988i	−0.991715	−	0.128454i	$-0.958998\pi$
$709$	−20.0862	−	29.2864i	−0.754354	−	1.09988i	0.237361	−	0.971422i	$-0.423718\pi$
$710$	2.34516	−	0.555813i	0.0880123	−	0.0208593i
$711$	−4.75982	−	22.4667i	−0.178507	−	0.842566i
$712$	−3.49936	−	11.6887i	−0.131144	−	0.438051i
$713$	−68.6781	−	10.7411i	−2.57202	−	0.402256i
$714$	2.38247	+	1.32166i	0.0891618	+	0.0494620i
$715$	8.56979	−	3.50114i	0.320492	−	0.130935i
$716$	10.4803	+	3.36038i	0.391668	+	0.125583i
$717$	−6.12783	+	1.94947i	−0.228848	+	0.0728043i
$718$	0.207539	+	10.7007i	0.00774530	+	0.399346i
$719$	−2.60356	−	3.49719i	−0.0970964	−	0.130423i	0.750920	−	0.660393i	$-0.229610\pi$
$719$	−2.60356	−	3.49719i	−0.0970964	−	0.130423i	−0.848016	+	0.529970i	$0.822203\pi$
$720$	0.625398	+	0.177157i	0.0233072	+	0.00660226i
$721$	−1.88106	−	0.219864i	−0.0700543	−	0.00818817i
$722$	13.8757	−	6.30727i	0.516399	−	0.234732i
$723$	−23.4388	+	8.47077i	−0.871698	+	0.315031i
$724$	11.5184	+	14.2806i	0.428079	+	0.530734i
$725$	26.1307	+	2.03104i	0.970471	+	0.0754310i
$726$	−2.13059	+	0.864798i	−0.0790735	+	0.0320957i
$727$	24.3064	+	0.943199i	0.901474	+	0.0349813i	0.485344	−	0.874324i	$-0.338695\pi$
$727$	24.3064	+	0.943199i	0.901474	+	0.0349813i	0.416131	+	0.909305i	$0.363386\pi$
$728$	5.14054			0.190521
$729$	−18.2591	−	19.8898i	−0.676264	−	0.736660i
$730$	3.67254			0.135927
$731$	55.4332	+	2.15106i	2.05027	+	0.0795599i
$732$	20.1069	−	8.16131i	0.743171	−	0.301651i
$733$	−10.9265	−	0.849274i	−0.403579	−	0.0313687i	−0.125901	−	0.992043i	$-0.540182\pi$
$733$	−10.9265	−	0.849274i	−0.403579	−	0.0313687i	−0.277678	+	0.960674i	$0.589565\pi$
$734$	−19.0340	−	23.5985i	−0.702558	−	0.871035i
$735$	−5.43983	+	1.96595i	−0.200651	+	0.0725152i
$736$	43.7085	−	19.8680i	1.61112	−	0.732343i
$737$	27.3840	+	3.20073i	1.00870	+	0.117900i
$738$	1.48331	+	5.86882i	0.0546014	+	0.216034i
$739$	−20.7301	−	27.8454i	−0.762570	−	1.02431i	−0.998617	−	0.0525677i	$-0.983259\pi$
$739$	−20.7301	−	27.8454i	−0.762570	−	1.02431i	0.236047	−	0.971742i	$-0.424148\pi$
$740$	0.0326980	+	1.68590i	0.00120200	+	0.0619749i
$741$	5.85100	−	1.86140i	0.214942	−	0.0683803i
$742$	−0.292373	−	0.0937457i	−0.0107334	−	0.00344151i
$743$	−17.3265	+	7.07864i	−0.635646	+	0.259690i	−0.673035	−	0.739611i	$-0.735010\pi$
$743$	−17.3265	+	7.07864i	−0.635646	+	0.259690i	0.0373886	+	0.999301i	$0.488096\pi$
$744$	34.6454	+	19.2193i	1.27016	+	0.704615i
$745$	−2.33471	−	0.365142i	−0.0855371	−	0.0133778i
$746$	2.26121	+	7.55298i	0.0827889	+	0.276534i
$747$	−11.7187	−	3.81625i	−0.428764	−	0.139629i
$748$	25.3658	−	6.01182i	0.927467	−	0.219814i
$749$	1.87246	+	2.73012i	0.0684182	+	0.0997562i
$750$	−4.58968	+	4.84269i	−0.167591	+	0.176830i
$751$	−0.541581	+	27.9238i	−0.0197626	+	1.01895i	0.850385	+	0.526162i	$0.176369\pi$
$751$	−0.541581	+	27.9238i	−0.0197626	+	1.01895i	−0.870147	+	0.492792i	$0.835976\pi$
$752$	2.66151	−	1.90233i	0.0970553	−	0.0693710i
$753$	−17.0055	+	4.69220i	−0.619714	+	0.170993i
$754$	5.94235	−	27.4329i	0.216408	−	0.999049i
$755$	−6.95063	−	2.52982i	−0.252959	−	0.0920696i
$756$	−0.135992	+	2.08947i	−0.00494599	+	0.0759932i
$757$	23.2558	−	8.46443i	0.845247	−	0.307645i	0.117146	−	0.993115i	$-0.462625\pi$
$757$	23.2558	−	8.46443i	0.845247	−	0.307645i	0.728101	+	0.685470i	$0.240403\pi$
$758$	3.08052	+	22.5534i	0.111889	+	0.819175i
$759$	37.4849	+	22.7386i	1.36062	+	0.825359i
$760$	0.532043	+	0.521824i	0.0192992	+	0.0189285i
$761$	15.6466	+	3.07289i	0.567188	+	0.111392i	0.468082	−	0.883685i	$-0.344945\pi$
$761$	15.6466	+	3.07289i	0.567188	+	0.111392i	0.0991056	+	0.995077i	$0.468402\pi$
$762$	−0.182219	−	0.425084i	−0.00660111	−	0.0153992i
$763$	−1.36872	−	5.31368i	−0.0495508	−	0.192368i
$764$	−1.58846	−	0.797753i	−0.0574684	−	0.0288617i
$765$	−1.56567	−	9.12153i	−0.0566070	−	0.329790i
$766$	9.99570	+	6.57428i	0.361159	+	0.237538i
$767$	−69.7605	+	13.7005i	−2.51891	+	0.494697i
$768$	−25.2215	+	1.90274i	−0.910103	+	0.0686591i
$769$	8.74454	+	13.8742i	0.315336	+	0.500315i	0.965823	−	0.259203i	$-0.0834598\pi$
$769$	8.74454	+	13.8742i	0.315336	+	0.500315i	−0.650487	+	0.759518i	$0.725435\pi$
$770$	−0.169983	+	0.322704i	−0.00612575	+	0.0116294i
$771$	31.1161	−	30.3801i	1.12062	−	1.09411i
$772$	−6.34826	+	18.5535i	−0.228479	+	0.667754i
$773$	−1.28464	+	22.0565i	−0.0462054	+	0.793317i	0.893020	+	0.450016i	$0.148582\pi$
$773$	−1.28464	+	22.0565i	−0.0462054	+	0.793317i	−0.939226	+	0.343300i	$0.888455\pi$
$774$	−8.33902	−	19.5761i	−0.299740	−	0.703649i
$775$	33.4810	−	22.0208i	1.20267	−	0.791011i
$776$	18.1042	−	17.7565i	0.649903	−	0.637420i
$777$	−1.33175	+	0.312437i	−0.0477763	+	0.0112086i
$778$	−19.9967	+	22.9137i	−0.716917	+	0.821495i
$779$	0.349536	−	1.35698i	0.0125234	−	0.0486189i
$780$	−4.37437	−	5.44865i	−0.156628	−	0.195093i
$781$	17.3178	+	7.07511i	0.619680	+	0.253167i
$782$	−32.9844	−	27.6772i	−1.17952	−	0.989733i
$783$	27.4735	+	7.84990i	0.981822	+	0.280533i
$784$	−2.37231	+	1.99060i	−0.0847252	+	0.0710929i
$785$	1.60801	−	0.515588i	0.0573924	−	0.0184021i
$786$	−12.9687	+	9.22504i	−0.462579	+	0.329046i
$787$	−1.04816	−	10.7761i	−0.0373630	−	0.384126i	−0.995277	−	0.0970715i	$-0.969052\pi$
$787$	−1.04816	−	10.7761i	−0.0373630	−	0.384126i	0.957914	−	0.287054i	$-0.0926759\pi$
$788$	5.29326	−	2.92069i	0.188564	−	0.104045i
$789$	25.8816	+	17.1069i	0.921408	+	0.609023i
$790$	−3.01032	+	0.233981i	−0.107102	+	0.00832466i
$791$	0.675399	+	0.715882i	0.0240144	+	0.0254538i
$792$	−15.5994	−	19.5211i	−0.554301	−	0.693651i
$793$	−57.1606	−	13.5473i	−2.02983	−	0.481079i
$794$	−3.67311	−	9.51359i	−0.130354	−	0.337625i
$795$	0.373443	+	0.973820i	0.0132447	+	0.0345379i
$796$	−0.198693	+	1.45469i	−0.00704247	+	0.0515600i
$797$	7.32287	+	33.8061i	0.259389	+	1.19747i	0.902155	+	0.431412i	$0.141984\pi$
$797$	7.32287	+	33.8061i	0.259389	+	1.19747i	−0.642766	+	0.766063i	$0.722213\pi$
$798$	−0.129452	+	0.204359i	−0.00458256	+	0.00723424i
$799$	−40.7834	−	22.5033i	−1.44281	−	0.796110i
$800$	−10.9629	+	25.4149i	−0.387598	+	0.898554i
$801$	−12.4314	−	5.14484i	−0.439244	−	0.181784i
$802$	−6.63184	+	8.90810i	−0.234178	+	0.314556i
$803$	23.1912	+	16.5761i	0.818401	+	0.584958i
$804$	−3.56700	−	20.5017i	−0.125799	−	0.723040i
$805$	−1.19260	+	0.186519i	−0.0420335	+	0.00657393i
$806$	−18.5138	−	38.7183i	−0.652120	−	1.36379i
$807$	32.2712	−	1.17885i	1.13600	−	0.0414976i
$808$	−1.78667	+	2.83475i	−0.0628550	+	0.0997262i
$809$	−15.3799	−	26.6387i	−0.540728	−	0.936568i	−0.998862	−	0.0476849i	$-0.984816\pi$
$809$	−15.3799	−	26.6387i	−0.540728	−	0.936568i	0.458135	−	0.888883i	$-0.348518\pi$
$810$	−2.90664	+	2.03789i	−0.102129	+	0.0716041i
$811$	0.679054	−	1.17616i	0.0238448	−	0.0413005i	−0.853857	−	0.520508i	$-0.825743\pi$
$811$	0.679054	−	1.17616i	0.0238448	−	0.0413005i	0.877702	+	0.479208i	$0.159076\pi$
$812$	−1.03269	−	1.96052i	−0.0362404	−	0.0688008i
$813$	−13.0735	+	11.8096i	−0.458509	+	0.414179i
$814$	3.69466	−	5.38694i	0.129498	−	0.188812i
$815$	−2.79748	+	7.24567i	−0.0979916	+	0.253805i
$816$	−2.46777	−	4.29682i	−0.0863892	−	0.150419i
$817$	−0.476855	+	4.90250i	−0.0166831	+	0.171517i
$818$	11.1844	+	25.9283i	0.391053	+	0.906562i
$819$	3.57867	−	4.39583i	0.125049	−	0.153603i
$820$	−1.58389	+	0.185130i	−0.0553118	+	0.00646502i
$821$	16.0732	−	9.70022i	0.560958	−	0.338540i	−0.207707	−	0.978191i	$-0.566600\pi$
$821$	16.0732	−	9.70022i	0.560958	−	0.338540i	0.768665	+	0.639651i	$0.220921\pi$
$822$	−3.05243	−	1.25515i	−0.106466	−	0.0437785i
$823$	−6.35075	+	5.76300i	−0.221373	+	0.200886i	−0.775146	−	0.631782i	$-0.782324\pi$
$823$	−6.35075	+	5.76300i	−0.221373	+	0.200886i	0.553772	+	0.832668i	$0.313188\pi$
$824$	−13.4833	−	10.4504i	−0.469715	−	0.364056i
$825$	−24.8120	+	4.81441i	−0.863845	+	0.167616i
$826$	1.75852	−	2.18022i	0.0611866	−	0.0758595i
$827$	23.5130	−	24.9223i	0.817627	−	0.866634i	−0.175403	−	0.984497i	$-0.556123\pi$
$827$	23.5130	−	24.9223i	0.817627	−	0.866634i	0.993030	+	0.117863i	$0.0376044\pi$
$828$	8.39994	−	32.0078i	0.291918	−	1.11235i
$829$	−0.688670	+	2.30032i	−0.0239185	+	0.0798933i	−0.969116	−	0.246607i	$-0.920684\pi$
$829$	−0.688670	+	2.30032i	−0.0239185	+	0.0798933i	0.945197	+	0.326500i	$0.105869\pi$
$830$	−0.699005	+	1.46184i	−0.0242628	+	0.0507414i
$831$	10.8761	+	14.6786i	0.377286	+	0.509194i
$832$	20.5774	+	12.4186i	0.713395	+	0.430536i
$833$	40.1409	+	18.2463i	1.39080	+	0.632196i
$834$	−14.7709	−	1.18185i	−0.511474	−	0.0409241i
$835$	−7.10128	−	6.44407i	−0.245750	−	0.223006i
$836$	0.401932	+	2.27947i	0.0139011	+	0.0788371i
$837$	40.5540	−	16.2465i	1.40175	−	0.561561i
$838$	−1.82261	+	10.3365i	−0.0629609	+	0.357069i
$839$	35.7532	−	27.7109i	1.23434	−	0.956685i	0.234458	−	0.972126i	$-0.424668\pi$
$839$	35.7532	−	27.7109i	1.23434	−	0.956685i	0.999881	+	0.0154413i	$0.00491532\pi$
$840$	0.674791	+	0.134117i	0.0232825	+	0.00462749i
$841$	−1.19221	+	0.331874i	−0.0411107	+	0.0114439i
$842$	−0.117247	−	0.342666i	−0.00404058	−	0.0118090i
$843$	−21.0395	+	13.7695i	−0.724638	+	0.474247i
$844$	23.0708	+	6.42221i	0.794131	+	0.221061i
$845$	0.734460	+	12.6102i	0.0252662	+	0.433803i
$846$	−1.11987	+	17.8313i	−0.0385018	+	0.613052i
$847$	0.439130	−	0.220539i	0.0150887	−	0.00757782i
$848$	0.367161	+	0.420720i	0.0126084	+	0.0144476i
$849$	−0.865767	−	0.621790i	−0.0297131	−	0.0213398i
$850$	24.8039	−	0.962504i	0.850766	−	0.0330136i
$851$	21.6021	−	0.838260i	0.740511	−	0.0287352i
$852$	1.39889	−	14.0506i	0.0479253	−	0.481364i
$853$	−0.0697956	−	0.0799769i	−0.00238976	−	0.00273836i	0.752240	−	0.658889i	$-0.228974\pi$
$853$	−0.0697956	−	0.0799769i	−0.00238976	−	0.00273836i	−0.754630	+	0.656151i	$0.772183\pi$
$854$	2.06829	−	1.03874i	0.0707756	−	0.0355448i
$855$	0.816617	−	0.0916897i	0.0279277	−	0.00313572i
$856$	1.73387	+	29.7693i	0.0592623	+	1.01749i
$857$	21.2206	+	5.90716i	0.724883	+	0.201785i	0.610911	−	0.791699i	$-0.290803\pi$
$857$	21.2206	+	5.90716i	0.724883	+	0.201785i	0.113971	+	0.993484i	$0.463643\pi$
$858$	1.51248	+	27.0258i	0.0516352	+	0.922647i
$859$	1.94101	+	5.67282i	0.0662265	+	0.193554i	0.974299	−	0.225259i	$-0.0723228\pi$
$859$	1.94101	+	5.67282i	0.0662265	+	0.193554i	−0.908072	+	0.418813i	$0.862446\pi$
$860$	5.40011	−	1.50322i	0.184142	−	0.0512595i
$861$	−0.416015	−	1.22493i	−0.0141778	−	0.0417454i
$862$	15.3003	−	11.8586i	0.521129	−	0.403905i
$863$	4.47413	−	25.3740i	0.152301	−	0.863742i	−0.808911	−	0.587931i	$-0.799943\pi$
$863$	4.47413	−	25.3740i	0.152301	−	0.863742i	0.961212	−	0.275811i	$-0.0889463\pi$
$864$	−17.2361	+	24.7672i	−0.586384	+	0.842599i
$865$	0.584858	+	3.31689i	0.0198858	+	0.112778i
$866$	11.2795	+	10.2356i	0.383293	+	0.347820i
$867$	−23.3269	+	33.8463i	−0.792223	+	1.14948i
$868$	−3.08431	−	1.40199i	−0.104688	−	0.0475867i
$869$	−20.0656	−	12.1096i	−0.680678	−	0.410791i
$870$	1.49577	−	3.44604i	0.0507115	−	0.116832i
$871$	−24.3016	+	50.8225i	−0.823429	+	1.72206i
$872$	14.1754	−	47.3491i	0.480040	−	1.60344i
$873$	−2.58057	−	27.8429i	−0.0873389	−	0.942338i
$874$	2.62360	−	2.78085i	0.0887444	−	0.0940636i
$875$	0.895179	−	1.10985i	0.0302626	−	0.0375197i
$876$	7.01170	−	20.3415i	0.236903	−	0.687275i
$877$	−19.4416	−	15.0683i	−0.656495	−	0.508822i	0.229027	−	0.973420i	$-0.426446\pi$
$877$	−19.4416	−	15.0683i	−0.656495	−	0.508822i	−0.885522	+	0.464598i	$0.846199\pi$
$878$	−0.236561	+	0.214667i	−0.00798353	+	0.00724467i
$879$	7.37219	+	54.9039i	0.248658	+	1.85186i
$880$	0.567931	−	0.342748i	0.0191450	−	0.0115540i
$881$	−24.7139	+	2.88863i	−0.832631	+	0.0973206i	−0.521718	−	0.853118i	$-0.674709\pi$
$881$	−24.7139	+	2.88863i	−0.832631	+	0.0973206i	−0.310913	+	0.950438i	$0.600635\pi$
$882$	−0.251126	−	16.9108i	−0.00845586	−	0.569415i
$883$	−17.6928	−	41.0165i	−0.595410	−	1.38032i	−0.903348	−	0.428909i	$-0.858898\pi$
$883$	−17.6928	−	41.0165i	−0.595410	−	1.38032i	0.307937	−	0.951407i	$-0.400361\pi$
$884$	−5.15664	+	53.0149i	−0.173437	+	1.78308i
$885$	−9.51480	−	0.0216155i	−0.319837	−	0.000726597i
$886$	2.66920	−	6.91339i	0.0896734	−	0.232260i
$887$	−31.8936	+	46.5020i	−1.07088	+	1.56139i	−0.269720	+	0.962939i	$0.586931\pi$
$887$	−31.8936	+	46.5020i	−1.07088	+	1.56139i	−0.801163	+	0.598446i	$0.795785\pi$
$888$	−11.7245	−	3.78872i	−0.393450	−	0.127141i
$889$	0.0460628	+	0.0874481i	0.00154490	+	0.00293292i
$890$	−0.884442	+	1.53190i	−0.0296466	+	0.0513494i
$891$	−27.5528	−	0.250382i	−0.923053	−	0.00838810i
$892$	3.72344	+	6.44919i	0.124670	+	0.215935i
$893$	2.20525	−	3.49887i	0.0737959	−	0.117085i
$894$	3.23403	−	6.10597i	0.108162	−	0.204214i
$895$	−1.72015	−	3.59739i	−0.0574983	−	0.120247i
$896$	2.53027	−	0.395727i	0.0845304	−	0.0132203i
$897$	−68.7546	+	57.4263i	−2.29565	+	1.91741i
$898$	−21.6119	−	15.4473i	−0.721198	−	0.515482i
$899$	−27.6080	+	37.0840i	−0.920779	+	1.23682i
$900$	8.81396	+	16.9189i	0.293799	+	0.563962i
$901$	3.14909	−	7.30041i	0.104911	−	0.243212i
$902$	5.40881	+	2.98446i	0.180094	+	0.0993715i
$903$	2.11009	+	4.02808i	0.0702195	+	0.134046i
$904$	1.87680	+	8.66428i	0.0624215	+	0.288170i
$905$	0.899575	−	6.58606i	0.0299029	−	0.218928i
$906$	13.6163	−	16.8032i	0.452370	−	0.558250i
$907$	−18.8507	−	48.8246i	−0.625928	−	1.62120i	−0.774704	−	0.632324i	$-0.782101\pi$
$907$	−18.8507	−	48.8246i	−0.625928	−	1.62120i	0.148775	−	0.988871i	$-0.452467\pi$
$908$	−3.97172	−	0.941314i	−0.131806	−	0.0312386i
$909$	1.18026	+	3.50129i	0.0391467	+	0.116131i
$910$	−0.511424	−	0.542078i	−0.0169535	−	0.0179697i
$911$	−35.9722	+	2.79598i	−1.19181	+	0.0926349i	−0.658033	−	0.752989i	$-0.728611\pi$
$911$	−35.9722	+	2.79598i	−1.19181	+	0.0926349i	−0.533778	+	0.845624i	$0.679228\pi$
$912$	0.393611	−	0.196560i	0.0130338	−	0.00650876i
$913$	−11.0121	+	6.07623i	−0.364448	+	0.201094i
$914$	1.29050	+	13.2675i	0.0426860	+	0.438850i
$915$	−7.14994	−	3.26966i	−0.236370	−	0.108092i
$916$	−32.7433	+	10.4987i	−1.08187	+	0.346887i
$917$	2.60544	−	2.18622i	0.0860391	−	0.0721953i
$918$	26.7068	+	4.36353i	0.881455	+	0.144018i
$919$	11.2076	+	9.40428i	0.369704	+	0.310219i	0.808645	−	0.588298i	$-0.200202\pi$
$919$	11.2076	+	9.40428i	0.369704	+	0.310219i	−0.438940	+	0.898516i	$0.644646\pi$
$920$	−10.0654	−	4.11215i	−0.331845	−	0.135574i
$921$	−10.5242	+	1.62147i	−0.346783	+	0.0534291i
$922$	0.374223	−	1.45282i	0.0123244	−	0.0478462i
$923$	−25.1332	+	28.7995i	−0.827270	+	0.947946i
$924$	1.46286	+	1.55761i	0.0481245	+	0.0512417i
$925$	−8.89756	+	8.72666i	−0.292550	+	0.286931i
$926$	−14.4238	+	9.48665i	−0.473994	+	0.311751i
$927$	−18.3231	+	4.25481i	−0.601808	+	0.139746i
$928$	1.85670	−	31.8783i	0.0609492	−	1.04646i
$929$	−6.48900	+	18.9648i	−0.212897	+	0.622216i	0.787088	+	0.616840i	$0.211588\pi$
$929$	−6.48900	+	18.9648i	−0.212897	+	0.622216i	−0.999986	+	0.00537528i	$0.998289\pi$
$930$	−1.42011	−	5.56551i	−0.0465672	−	0.182500i
$931$	−1.82459	+	3.46389i	−0.0597984	+	0.113524i
$932$	−9.26579	−	14.7012i	−0.303511	−	0.481553i
$933$	−6.74955	−	9.88917i	−0.220970	−	0.323757i
$934$	−16.7308	+	3.28582i	−0.547448	+	0.107515i
$935$	−7.89101	−	5.19000i	−0.258064	−	0.169731i
$936$	48.0575	−	17.2446i	1.57081	−	0.563659i
$937$	37.2436	+	18.7044i	1.21670	+	0.611047i	0.937097	−	0.349070i	$-0.113502\pi$
$937$	37.2436	+	18.7044i	1.21670	+	0.611047i	0.279599	+	0.960117i	$0.409799\pi$
$938$	−0.553639	−	2.14936i	−0.0180769	−	0.0701790i
$939$	19.8731	+	2.36861i	0.648535	+	0.0772967i
$940$	−4.61841	−	0.907027i	−0.150636	−	0.0295840i
$941$	−5.36806	−	5.26496i	−0.174994	−	0.171633i	0.607442	−	0.794364i	$-0.292196\pi$
$941$	−5.36806	−	5.26496i	−0.174994	−	0.171633i	−0.782436	+	0.622731i	$0.786023\pi$
$942$	−0.106960	+	4.93636i	−0.00348493	+	0.160835i
$943$	2.76681	+	20.2566i	0.0900996	+	0.659646i
$944$	−4.78698	+	1.74232i	−0.155803	+	0.0567077i
$945$	0.584454	−	0.483666i	0.0190123	−	0.0157336i
$946$	−20.4052	−	7.42689i	−0.663431	−	0.241469i
$947$	3.69857	−	17.0745i	0.120187	−	0.554846i	−0.877039	−	0.480419i	$-0.840485\pi$
$947$	3.69857	−	17.0745i	0.120187	−	0.554846i	0.997226	−	0.0744272i	$-0.0237128\pi$
$948$	−4.45140	+	17.1203i	−0.144575	+	0.556041i
$949$	−47.3860	+	33.8695i	−1.53822	+	1.09945i
$950$	−0.0427386	+	2.20359i	−0.00138662	+	0.0714939i
$951$	19.8062	+	4.74171i	0.642261	+	0.153761i
$952$	−2.96639	−	4.32510i	−0.0961411	−	0.140177i
$953$	−38.9394	+	9.22881i	−1.26137	+	0.298951i	−0.806301	−	0.591505i	$-0.798534\pi$
$953$	−38.9394	+	9.22881i	−1.26137	+	0.298951i	−0.455070	+	0.890455i	$0.650386\pi$
$954$	−3.04780	+	0.104402i	−0.0986762	+	0.00338015i
$955$	0.184704	+	0.616955i	0.00597689	+	0.0199642i
$956$	4.89370	+	0.765361i	0.158274	+	0.0247536i
$957$	24.9993	−	15.0098i	0.808112	−	0.485197i
$958$	21.6584	−	8.84842i	0.699751	−	0.285880i
$959$	0.671640	+	0.215353i	0.0216884	+	0.00695410i
$960$	2.37717	+	2.16703i	0.0767228	+	0.0699407i
$961$	0.769600	+	39.6804i	0.0248258	+	1.28001i
$962$	7.97031	+	10.7060i	0.256973	+	0.345175i
$963$	26.6637	+	19.2417i	0.859225	+	0.620054i
$964$	19.0673	+	2.22864i	0.614115	+	0.0717798i
$965$	6.46781	−	2.93998i	0.208206	−	0.0946413i
$966$	0.620783	−	3.47446i	0.0199734	−	0.111789i
$967$	−12.4418	−	15.4254i	−0.400100	−	0.496046i	0.537742	−	0.843110i	$-0.319278\pi$
$967$	−12.4418	−	15.4254i	−0.400100	−	0.496046i	−0.937842	+	0.347064i	$0.887179\pi$
$968$	4.41298	+	0.343004i	0.141839	+	0.0110246i
$969$	−4.94249	−	3.84872i	−0.158776	−	0.123639i
$970$	−3.67360	−	0.142553i	−0.117952	−	0.00457709i
$971$	−11.7764			−0.377922			−0.188961	−	0.981985i	$-0.560512\pi$
$971$	−11.7764			−0.377922			−0.188961	+	0.981985i	$0.560512\pi$
$972$	5.73804	+	19.9901i	0.184048	+	0.641182i
$973$	3.16673			0.101521
$974$	10.3164	+	0.400324i	0.330560	+	0.0128272i
$975$	7.10518	−	51.1522i	0.227548	−	1.63818i
$976$	−4.19667	−	0.326191i	−0.134332	−	0.0104411i
$977$	4.62568	+	5.73495i	0.147989	+	0.183477i	0.846934	−	0.531698i	$-0.178446\pi$
$977$	4.62568	+	5.73495i	0.147989	+	0.183477i	−0.698945	+	0.715175i	$0.746347\pi$
$978$	−17.3638	−	14.6373i	−0.555233	−	0.468049i
$979$	−12.4993	+	5.68163i	−0.399480	+	0.181586i
$980$	4.42525	+	0.517238i	0.141360	+	0.0165226i
$981$	−30.6212	−	45.0846i	−0.977660	−	1.43944i
$982$	−5.37550	−	7.22055i	−0.171539	−	0.230417i
$983$	0.708005	+	36.5045i	0.0225818	+	1.16431i	0.824136	+	0.566392i	$0.191661\pi$
$983$	0.708005	+	36.5045i	0.0225818	+	1.16431i	−0.801554	+	0.597922i	$0.795993\pi$
$984$	2.49276	−	11.3828i	0.0794662	−	0.362871i
$985$	−2.08576	−	0.668772i	−0.0664578	−	0.0213088i
$986$	−26.5103	+	10.8307i	−0.844261	+	0.344918i
$987$	−0.0653668	−	3.81761i	−0.00208065	−	0.121516i
$988$	−4.67263	−	0.730785i	−0.148656	−	0.0232494i
$989$	−20.6112	−	68.8462i	−0.655398	−	2.18918i
$990$	−0.506567	+	3.58710i	−0.0160998	+	0.114006i
$991$	29.7649	−	7.05442i	0.945515	−	0.224091i	0.271190	−	0.962526i	$-0.412583\pi$
$991$	29.7649	−	7.05442i	0.945515	−	0.224091i	0.674325	+	0.738435i	$0.264435\pi$
$992$	−27.6150	−	40.2637i	−0.876777	−	1.27837i
$993$	−4.95845	−	16.7004i	−0.157352	−	0.529970i
$994$	0.0292035	−	1.50572i	0.000926279	−	0.0477587i
$995$	0.432758	−	0.309317i	0.0137193	−	0.00980600i
$996$	6.76231	+	6.66264i	0.214272	+	0.211114i
$997$	−9.37588	+	43.2839i	−0.296937	+	1.37081i	0.548237	+	0.836323i	$0.315299\pi$
$997$	−9.37588	+	43.2839i	−0.296937	+	1.37081i	−0.845174	+	0.534491i	$0.820503\pi$
$998$	14.8419	+	5.40199i	0.469811	+	0.170997i
$999$	−11.4021	+	7.38843i	−0.360745	+	0.233759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.4.11	✓	1404
3.2	odd	2		729.2.i.a.64.16		1404
243.61	even	81	inner	243.2.i.a.61.11	yes	1404
243.182	odd	162		729.2.i.a.262.16		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.11	✓	1404	1.1	even	1	trivial
243.2.i.a.61.11	yes	1404	243.61	even	81	inner
729.2.i.a.64.16		1404	3.2	odd	2
729.2.i.a.262.16		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+(-0.815384 - 0.0316406i) q^{2} +(1.60488 - 0.651417i) q^{3} +(-1.33014 - 0.103386i) q^{4} +(0.303466 + 0.376239i) q^{5} +(-1.32921 + 0.480376i) q^{6} +(0.274968 - 0.124988i) q^{7} +(2.70226 + 0.315849i) q^{8} +(2.15131 - 2.09090i) q^{9} +(-0.235537 - 0.316381i) q^{10} +(-0.0593675 - 3.06097i) q^{11} +(-2.20206 + 0.700550i) q^{12} +(5.95686 + 1.90999i) q^{13} +(-0.228159 + 0.0932133i) q^{14} +(0.732116 + 0.406137i) q^{15} +(0.442862 + 0.0692624i) q^{16} +(-1.83044 - 6.11409i) q^{17} +(-1.82030 + 1.63682i) q^{18} +(0.551404 - 0.130685i) q^{19} +(-0.364753 - 0.531823i) q^{20} +(0.359873 - 0.379711i) q^{21} +(-0.0484437 + 2.49775i) q^{22} +(-6.72634 + 4.80770i) q^{23} +(4.54257 - 1.25340i) q^{24} +(1.00906 - 4.65832i) q^{25} +(-4.79670 - 1.74585i) q^{26} +(2.09056 - 4.75705i) q^{27} +(-0.378667 + 0.137824i) q^{28} +(0.744169 + 5.44828i) q^{29} +(-0.584105 - 0.354322i) q^{30} +(6.00244 + 5.88715i) q^{31} +(-5.69823 - 1.11910i) q^{32} +(-2.08925 - 4.87384i) q^{33} +(1.29906 + 5.04325i) q^{34} +(0.130469 + 0.0655239i) q^{35} +(-3.07771 + 2.55876i) q^{36} +(-2.18459 - 1.43683i) q^{37} +(-0.453741 + 0.0891119i) q^{38} +(10.8043 - 0.815086i) q^{39} +(0.701209 + 1.11254i) q^{40} +(1.15243 - 2.18783i) q^{41} +(-0.305449 + 0.298224i) q^{42} +(-2.81393 + 8.22403i) q^{43} +(-0.237496 + 4.07765i) q^{44} +(1.43953 + 0.174890i) q^{45} +(5.63667 - 3.70730i) q^{46} +(5.21053 - 5.11046i) q^{47} +(0.755861 - 0.177330i) q^{48} +(-4.54266 + 5.20532i) q^{49} +(-0.970160 + 3.76639i) q^{50} +(-6.92047 - 8.62004i) q^{51} +(-7.72597 - 3.15640i) q^{52} +(0.954300 + 0.800753i) q^{53} +(-1.85513 + 3.81268i) q^{54} +(1.13364 - 0.951237i) q^{55} +(0.782513 - 0.250903i) q^{56} +(0.799810 - 0.568929i) q^{57} +(-0.434396 - 4.46599i) q^{58} +(-9.95051 + 5.49046i) q^{59} +(-0.931825 - 0.615908i) q^{60} +(-9.36243 + 0.727706i) q^{61} +(-4.70802 - 4.99021i) q^{62} +(0.330204 - 0.843819i) q^{63} +(3.73851 + 0.886043i) q^{64} +(1.08909 + 2.82082i) q^{65} +(1.54933 + 4.04015i) q^{66} +(-1.21871 + 8.92253i) q^{67} +(1.80262 + 8.32182i) q^{68} +(-7.66319 + 12.0975i) q^{69} +(-0.104309 - 0.0575553i) q^{70} +(-2.42021 + 5.61068i) q^{71} +(6.47381 - 4.97067i) q^{72} +(-5.56016 + 7.46859i) q^{73} +(1.73582 + 1.24069i) q^{74} +(-1.41509 - 8.13338i) q^{75} +(-0.746954 + 0.116821i) q^{76} +(-0.398910 - 0.834250i) q^{77} +(-8.83542 + 0.322754i) q^{78} +(4.08174 - 6.47612i) q^{79} +(0.108334 + 0.187641i) q^{80} +(0.256282 - 8.99635i) q^{81} +(-1.00889 + 1.74746i) q^{82} +(-1.91457 - 3.63472i) q^{83} +(-0.517936 + 0.467861i) q^{84} +(1.74488 - 2.54410i) q^{85} +(2.55465 - 6.61670i) q^{86} +(4.74341 + 8.25910i) q^{87} +(0.806379 - 8.29030i) q^{88} +(-1.77629 - 4.11789i) q^{89} +(-1.16823 - 0.188150i) q^{90} +(1.87667 - 0.219352i) q^{91} +(9.44400 - 5.69948i) q^{92} +(13.4682 + 5.53811i) q^{93} +(-4.41028 + 4.00212i) q^{94} +(0.216501 + 0.167801i) q^{95} +(-9.87400 + 1.91590i) q^{96} +(5.85167 - 7.25493i) q^{97} +(3.86872 - 4.10060i) q^{98} +(-6.52790 - 6.46097i) 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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