LMFDB - Embedded newform 77.2.n.a.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,2,Mod(17,77)] 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("77.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (of order $30$, degree $8$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	77.19
Dual form			77.2.n.a.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.06490 + 0.217030i) q^{2} +(-0.138863 - 0.125032i) q^{3} +(2.26043 - 0.480470i) q^{4} +(-1.04356 - 2.34387i) q^{5} +(0.313874 + 0.228043i) q^{6} +(2.62996 - 0.288618i) q^{7} +(-0.613987 + 0.199497i) q^{8} +(-0.309936 - 2.94884i) q^{9} +(2.66354 + 4.61339i) q^{10} +(0.754864 - 3.22958i) q^{11} +(-0.373964 - 0.215908i) q^{12} +(-0.672688 + 0.488736i) q^{13} +(-5.36798 + 1.16675i) q^{14} +(-0.148149 + 0.455954i) q^{15} +(-2.99776 + 1.33469i) q^{16} +(-0.606752 + 5.77286i) q^{17} +(1.27998 + 6.02181i) q^{18} +(-0.316355 - 0.0672434i) q^{19} +(-3.48505 - 4.79677i) q^{20} +(-0.401290 - 0.288752i) q^{21} +(-0.857806 + 6.83260i) q^{22} +(0.269195 - 0.466260i) q^{23} +(0.110203 + 0.0490657i) q^{24} +(-1.05906 + 1.17621i) q^{25} +(1.28297 - 1.15519i) q^{26} +(-0.655159 + 0.901749i) q^{27} +(5.80618 - 1.91602i) q^{28} +(-0.640236 - 0.208025i) q^{29} +(0.206957 - 0.973655i) q^{30} +(1.94919 - 4.37794i) q^{31} +(7.01860 - 4.05219i) q^{32} +(-0.508624 + 0.354085i) q^{33} -12.0521i q^{34} +(-3.42100 - 5.86310i) q^{35} +(-2.11742 - 6.51675i) q^{36} +(5.39814 + 5.99524i) q^{37} +(0.667837 + 0.0701925i) q^{38} +(0.154519 + 0.0162406i) q^{39} +(1.10833 + 1.23092i) q^{40} +(3.11220 + 9.57836i) q^{41} +(0.891293 + 0.509154i) q^{42} -5.21894i q^{43} +(0.154604 - 7.66294i) q^{44} +(-6.58827 + 3.80374i) q^{45} +(-0.454670 + 1.02121i) q^{46} +(-2.31375 + 10.8853i) q^{47} +(0.583155 + 0.189479i) q^{48} +(6.83340 - 1.51811i) q^{49} +(1.93159 - 2.65861i) q^{50} +(0.806050 - 0.725770i) q^{51} +(-1.28574 + 1.42796i) q^{52} +(2.09401 + 0.932313i) q^{53} +(1.15713 - 2.00422i) q^{54} +(-8.35746 + 1.60095i) q^{55} +(-1.55719 + 0.701876i) q^{56} +(0.0355223 + 0.0488923i) q^{57} +(1.36717 + 0.290602i) q^{58} +(-2.64470 - 12.4423i) q^{59} +(-0.115808 + 1.10184i) q^{60} +(-6.78197 + 3.01953i) q^{61} +(-3.07474 + 9.46306i) q^{62} +(-1.66621 - 7.66589i) q^{63} +(-8.30379 + 6.03306i) q^{64} +(1.84752 + 1.06667i) q^{65} +(0.973414 - 0.841539i) q^{66} +(2.07425 + 3.59270i) q^{67} +(1.40216 + 13.3407i) q^{68} +(-0.0956787 + 0.0310879i) q^{69} +(8.33652 + 11.3643i) q^{70} +(10.1169 + 7.35035i) q^{71} +(0.778580 + 1.74872i) q^{72} +(-12.0858 + 2.56892i) q^{73} +(-12.4478 - 11.2080i) q^{74} +(0.294128 - 0.0309141i) q^{75} -0.747409 q^{76} +(1.05315 - 8.71154i) q^{77} -0.322592 q^{78} +(6.28349 - 0.660421i) q^{79} +(6.25667 + 5.63353i) q^{80} +(-8.49714 + 1.80612i) q^{81} +(-8.50519 - 19.1030i) q^{82} +(2.52659 + 1.83568i) q^{83} +(-1.04583 - 0.459897i) q^{84} +(14.1640 - 4.60217i) q^{85} +(1.13267 + 10.7766i) q^{86} +(0.0628949 + 0.108937i) q^{87} +(0.180813 + 2.13351i) q^{88} +(5.37059 + 3.10071i) q^{89} +(12.7786 - 9.28421i) q^{90} +(-1.62808 + 1.47951i) q^{91} +(0.384474 - 1.18329i) q^{92} +(-0.818053 + 0.364221i) q^{93} +(2.41522 - 22.9793i) q^{94} +(0.172525 + 0.811668i) q^{95} +(-1.48128 - 0.314855i) q^{96} +(0.779173 + 1.07244i) q^{97} +(-13.7808 + 4.61781i) q^{98} +(-9.75747 - 1.22501i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26}+ \cdots - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−2.06490	+	0.217030i	−1.46011	+	0.153464i	−0.801036	−	0.598616i	$-0.795717\pi$
$2$	−2.06490	+	0.217030i	−1.46011	+	0.153464i	−0.659072	+	0.752080i	$0.729051\pi$
$3$	−0.138863	−	0.125032i	−0.0801723	−	0.0721875i	0.628070	−	0.778157i	$-0.283845\pi$
$3$	−0.138863	−	0.125032i	−0.0801723	−	0.0721875i	−0.708243	+	0.705969i	$0.750512\pi$
$4$	2.26043	−	0.480470i	1.13022	−	0.240235i
$5$	−1.04356	−	2.34387i	−0.466694	−	1.04821i	−0.981597	−	0.190963i	$-0.938839\pi$
$5$	−1.04356	−	2.34387i	−0.466694	−	1.04821i	0.514904	−	0.857248i	$-0.327828\pi$
$6$	0.313874	+	0.228043i	0.128138	+	0.0930980i
$7$	2.62996	−	0.288618i	0.994032	−	0.109087i
$7$	2.62996	−	0.288618i	0.994032	−	0.109087i
$8$	−0.613987	+	0.199497i	−0.217077	+	0.0705327i
$9$	−0.309936	−	2.94884i	−0.103312	−	0.982947i
$10$	2.66354	+	4.61339i	0.842285	+	1.45888i
$11$	0.754864	−	3.22958i	0.227600	−	0.973755i
$11$	0.754864	−	3.22958i	0.227600	−	0.973755i
$12$	−0.373964	−	0.215908i	−0.107954	−	0.0623273i
$13$	−0.672688	+	0.488736i	−0.186570	+	0.135551i	−0.677150	−	0.735845i	$-0.736785\pi$
$13$	−0.672688	+	0.488736i	−0.186570	+	0.135551i	0.490580	+	0.871396i	$0.336785\pi$
$14$	−5.36798	+	1.16675i	−1.43465	+	0.311827i
$15$	−0.148149	+	0.455954i	−0.0382518	+	0.117727i
$16$	−2.99776	+	1.33469i	−0.749439	+	0.333672i
$17$	−0.606752	+	5.77286i	−0.147159	+	1.40012i	0.632810	+	0.774307i	$0.281901\pi$
$17$	−0.606752	+	5.77286i	−0.147159	+	1.40012i	−0.779969	+	0.625818i	$0.784765\pi$
$18$	1.27998	+	6.02181i	0.301693	+	1.41935i
$19$	−0.316355	−	0.0672434i	−0.0725769	−	0.0154267i	0.171480	−	0.985188i	$-0.445145\pi$
$19$	−0.316355	−	0.0672434i	−0.0725769	−	0.0154267i	−0.244057	+	0.969761i	$0.578478\pi$
$20$	−3.48505	−	4.79677i	−0.779282	−	1.07259i
$21$	−0.401290	−	0.288752i	−0.0875686	−	0.0630109i
$22$	−0.857806	+	6.83260i	−0.182885	+	1.45672i
$23$	0.269195	−	0.466260i	0.0561311	−	0.0972219i	−0.836594	−	0.547823i	$-0.815457\pi$
$23$	0.269195	−	0.466260i	0.0561311	−	0.0972219i	0.892726	+	0.450601i	$0.148790\pi$
$24$	0.110203	+	0.0490657i	0.0224952	+	0.0100155i
$25$	−1.05906	+	1.17621i	−0.211813	+	0.235242i
$26$	1.28297	−	1.15519i	0.251610	−	0.226551i
$27$	−0.655159	+	0.901749i	−0.126085	+	0.173542i
$28$	5.80618	−	1.91602i	1.09727	−	0.362094i
$29$	−0.640236	−	0.208025i	−0.118889	−	0.0386293i	0.248968	−	0.968512i	$-0.419908\pi$
$29$	−0.640236	−	0.208025i	−0.118889	−	0.0386293i	−0.367857	+	0.929882i	$0.619908\pi$
$30$	0.206957	−	0.973655i	0.0377850	−	0.177764i
$31$	1.94919	−	4.37794i	0.350084	−	0.786302i	−0.649578	−	0.760295i	$-0.725054\pi$
$31$	1.94919	−	4.37794i	0.350084	−	0.786302i	0.999662	−	0.0260064i	$-0.00827903\pi$
$32$	7.01860	−	4.05219i	1.24072	−	0.716333i
$33$	−0.508624	+	0.354085i	−0.0885401	+	0.0616383i
$34$		−	12.0521i		−	2.06692i
$35$	−3.42100	−	5.86310i	−0.578255	−	0.991045i
$36$	−2.11742	−	6.51675i	−0.352903	−	1.08612i
$37$	5.39814	+	5.99524i	0.887448	+	0.985611i	0.999968	−	0.00803850i	$-0.00255876\pi$
$37$	5.39814	+	5.99524i	0.887448	+	0.985611i	−0.112520	+	0.993650i	$0.535892\pi$
$38$	0.667837	+	0.0701925i	0.108338	+	0.0113867i
$39$	0.154519	+	0.0162406i	0.0247428	+	0.00260058i
$40$	1.10833	+	1.23092i	0.175242	+	0.194626i
$41$	3.11220	+	9.57836i	0.486044	+	1.49589i	0.830464	+	0.557073i	$0.188076\pi$
$41$	3.11220	+	9.57836i	0.486044	+	1.49589i	−0.344420	+	0.938816i	$0.611924\pi$
$42$	0.891293	+	0.509154i	0.137530	+	0.0785641i
$43$		−	5.21894i		−	0.795880i	−0.917411	−	0.397940i	$-0.869725\pi$
$43$		−	5.21894i		−	0.795880i	0.917411	−	0.397940i	$-0.130275\pi$
$44$	0.154604	−	7.66294i	0.0233074	−	1.15523i
$45$	−6.58827	+	3.80374i	−0.982121	+	0.567028i
$46$	−0.454670	+	1.02121i	−0.0670374	+	0.150569i
$47$	−2.31375	+	10.8853i	−0.337495	+	1.58779i	0.402658	+	0.915351i	$0.368086\pi$
$47$	−2.31375	+	10.8853i	−0.337495	+	1.58779i	−0.740153	+	0.672439i	$0.765247\pi$
$48$	0.583155	+	0.189479i	0.0841712	+	0.0273489i
$49$	6.83340	−	1.51811i	0.976200	−	0.216873i
$50$	1.93159	−	2.65861i	0.273168	−	0.375984i
$51$	0.806050	−	0.725770i	0.112870	−	0.101628i
$52$	−1.28574	+	1.42796i	−0.178300	+	0.198023i
$53$	2.09401	+	0.932313i	0.287634	+	0.128063i	0.545482	−	0.838122i	$-0.316347\pi$
$53$	2.09401	+	0.932313i	0.287634	+	0.128063i	−0.257848	+	0.966186i	$0.583013\pi$
$54$	1.15713	−	2.00422i	0.157466	−	0.272739i
$55$	−8.35746	+	1.60095i	−1.12692	+	0.215872i
$56$	−1.55719	+	0.701876i	−0.208088	+	0.0937922i
$57$	0.0355223	+	0.0488923i	0.00470504	+	0.00647594i
$58$	1.36717	+	0.290602i	0.179519	+	0.0381579i
$59$	−2.64470	−	12.4423i	−0.344310	−	1.61985i	−0.720600	−	0.693351i	$-0.756134\pi$
$59$	−2.64470	−	12.4423i	−0.344310	−	1.61985i	0.376290	−	0.926502i	$-0.377200\pi$
$60$	−0.115808	+	1.10184i	−0.0149507	+	0.142246i
$61$	−6.78197	+	3.01953i	−0.868342	+	0.386611i	−0.792036	−	0.610474i	$-0.790979\pi$
$61$	−6.78197	+	3.01953i	−0.868342	+	0.386611i	−0.0763054	+	0.997084i	$0.524312\pi$
$62$	−3.07474	+	9.46306i	−0.390492	+	1.20181i
$63$	−1.66621	−	7.66589i	−0.209923	−	0.965811i
$64$	−8.30379	+	6.03306i	−1.03797	+	0.754132i
$65$	1.84752	+	1.06667i	0.229157	+	0.132304i
$66$	0.973414	−	0.841539i	0.119819	−	0.103586i
$67$	2.07425	+	3.59270i	0.253409	+	0.438918i	0.964462	−	0.264221i	$-0.0851147\pi$
$67$	2.07425	+	3.59270i	0.253409	+	0.438918i	−0.711053	+	0.703139i	$0.751781\pi$
$68$	1.40216	+	13.3407i	0.170037	+	1.61780i
$69$	−0.0956787	+	0.0310879i	−0.0115184	+	0.00374254i
$70$	8.33652	+	11.3643i	0.996404	+	1.35829i
$71$	10.1169	+	7.35035i	1.20065	+	0.872326i	0.994349	−	0.106162i	$-0.0338563\pi$
$71$	10.1169	+	7.35035i	1.20065	+	0.872326i	0.206304	+	0.978488i	$0.433856\pi$
$72$	0.778580	+	1.74872i	0.0917566	+	0.206089i
$73$	−12.0858	+	2.56892i	−1.41454	+	0.300670i	−0.850890	−	0.525343i	$-0.823937\pi$
$73$	−12.0858	+	2.56892i	−1.41454	+	0.300670i	−0.563651	+	0.826013i	$0.690604\pi$
$74$	−12.4478	−	11.2080i	−1.44703	−	1.30291i
$75$	0.294128	−	0.0309141i	0.0339630	−	0.00356966i
$76$	−0.747409			−0.0857337
$77$	1.05315	−	8.71154i	0.120017	−	0.992772i
$78$	−0.322592			−0.0365263
$79$	6.28349	−	0.660421i	0.706948	−	0.0743032i	0.255770	−	0.966738i	$-0.417671\pi$
$79$	6.28349	−	0.660421i	0.706948	−	0.0743032i	0.451177	+	0.892434i	$0.351004\pi$
$80$	6.25667	+	5.63353i	0.699517	+	0.629848i
$81$	−8.49714	+	1.80612i	−0.944127	+	0.200680i
$82$	−8.50519	−	19.1030i	−0.939241	−	2.10957i
$83$	2.52659	+	1.83568i	0.277329	+	0.201492i	0.717752	−	0.696299i	$-0.245171\pi$
$83$	2.52659	+	1.83568i	0.277329	+	0.201492i	−0.440422	+	0.897791i	$0.645171\pi$
$84$	−1.04583	−	0.459897i	−0.114109	−	0.0501789i
$85$	14.1640	−	4.60217i	1.53630	−	0.499175i
$86$	1.13267	+	10.7766i	0.122139	+	1.16207i
$87$	0.0628949	+	0.108937i	0.00674304	+	0.0116793i
$88$	0.180813	+	2.13351i	0.0192747	+	0.227433i
$89$	5.37059	+	3.10071i	0.569281	+	0.328675i	0.756862	−	0.653574i	$-0.226731\pi$
$89$	5.37059	+	3.10071i	0.569281	+	0.328675i	−0.187581	+	0.982249i	$0.560065\pi$
$90$	12.7786	−	9.28421i	1.34698	−	0.978641i
$91$	−1.62808	+	1.47951i	−0.170670	+	0.155095i
$92$	0.384474	−	1.18329i	0.0400842	−	0.123366i
$93$	−0.818053	+	0.364221i	−0.0848282	+	0.0377679i
$94$	2.41522	−	22.9793i	0.249111	−	2.37014i
$95$	0.172525	+	0.811668i	0.0177007	+	0.0832754i
$96$	−1.48128	−	0.314855i	−0.151182	−	0.0321347i
$97$	0.779173	+	1.07244i	0.0791131	+	0.108890i	0.846739	−	0.532008i	$-0.178562\pi$
$97$	0.779173	+	1.07244i	0.0791131	+	0.108890i	−0.767626	+	0.640898i	$0.778562\pi$
$98$	−13.7808	+	4.61781i	−1.39208	+	0.466469i
$99$	−9.75747	−	1.22501i	−0.980663	−	0.123118i
$100$	−1.82881	+	3.16759i	−0.182881	+	0.316759i
$101$	7.80825	+	3.47646i	0.776950	+	0.345921i	0.756605	−	0.653872i	$-0.226857\pi$
$101$	7.80825	+	3.47646i	0.776950	+	0.345921i	0.0203455	+	0.999793i	$0.493523\pi$
$102$	−1.50690	+	1.67358i	−0.149206	+	0.165710i
$103$	7.76504	−	6.99167i	0.765112	−	0.688910i	−0.191104	−	0.981570i	$-0.561207\pi$
$103$	7.76504	−	6.99167i	0.765112	−	0.688910i	0.956217	+	0.292660i	$0.0945403\pi$
$104$	0.315521	−	0.434277i	0.0309393	−	0.0425843i
$105$	−0.258028	+	1.24190i	−0.0251810	+	0.121197i
$106$	−4.52627	−	1.47067i	−0.439630	−	0.142845i
$107$	0.662553	−	3.11707i	0.0640514	−	0.301338i	−0.934448	−	0.356099i	$-0.884106\pi$
$107$	0.662553	−	3.11707i	0.0640514	−	0.301338i	0.998499	+	0.0547612i	$0.0174398\pi$
$108$	−1.04768	+	2.35313i	−0.100813	+	0.226430i
$109$	−7.92022	+	4.57274i	−0.758620	+	0.437989i	−0.828800	−	0.559545i	$-0.810976\pi$
$109$	−7.92022	+	4.57274i	−0.758620	+	0.437989i	0.0701803	+	0.997534i	$0.477643\pi$
$110$	16.9099	−	5.11963i	1.61230	−	0.488138i
$111$		−	1.50746i		−	0.143081i
$112$	−7.49877	+	4.37538i	−0.708567	+	0.413435i
$113$	−2.62819	−	8.08875i	−0.247240	−	0.760926i	−0.995260	−	0.0972498i	$-0.968995\pi$
$113$	−2.62819	−	8.08875i	−0.247240	−	0.760926i	0.748020	−	0.663676i	$-0.231005\pi$
$114$	−0.0839613	−	0.0932484i	−0.00786369	−	0.00873352i
$115$	−1.37377	−	0.144389i	−0.128105	−	0.0134644i
$116$	−1.54716	−	0.162613i	−0.143650	−	0.0150983i
$117$	1.64970	+	1.83217i	0.152514	+	0.169384i
$118$	8.16141	+	25.1182i	0.751318	+	2.31232i
$119$	0.0704185	+	15.3575i	0.00645525	+	1.40782i
$120$		−	0.309505i		−	0.0282539i
$121$	−9.86036	−	4.87579i	−0.896396	−	0.443253i
$122$	13.3488	−	7.70693i	1.20854	−	0.697752i
$123$	0.765438	−	1.71920i	0.0690172	−	0.155015i
$124$	2.30253	−	10.8326i	0.206774	−	0.972794i
$125$	−8.33849	−	2.70934i	−0.745817	−	0.242331i
$126$	5.10429	+	15.4677i	0.454726	+	1.37797i
$127$	−5.83289	+	8.02828i	−0.517585	+	0.712394i	−0.985175	−	0.171551i	$-0.945122\pi$
$127$	−5.83289	+	8.02828i	−0.517585	+	0.712394i	0.467590	+	0.883945i	$0.345122\pi$
$128$	3.79172	−	3.41408i	0.335144	−	0.301765i
$129$	−0.652536	+	0.724715i	−0.0574526	+	0.0638076i
$130$	−4.04646	−	1.80160i	−0.354898	−	0.158011i
$131$	1.91787	−	3.32186i	0.167565	−	0.290232i	−0.769998	−	0.638046i	$-0.779743\pi$
$131$	1.91787	−	3.32186i	0.167565	−	0.290232i	0.937563	+	0.347815i	$0.113076\pi$
$132$	−0.979584	+	1.04476i	−0.0852619	+	0.0909351i
$133$	−0.851410	−	0.0855416i	−0.0738266	−	0.00741740i
$134$	−5.06284	−	6.96841i	−0.437363	−	0.601979i
$135$	2.79728	+	0.594580i	0.240752	+	0.0511733i
$136$	−0.779128	−	3.66551i	−0.0668097	−	0.314315i
$137$	1.83336	−	17.4433i	0.156635	−	1.49028i	−0.580348	−	0.814369i	$-0.697083\pi$
$137$	1.83336	−	17.4433i	0.156635	−	1.49028i	0.736982	−	0.675912i	$-0.236250\pi$
$138$	0.190820	−	0.0849587i	0.0162437	−	0.00723217i
$139$	5.83201	−	17.9491i	0.494664	−	1.52242i	−0.322815	−	0.946462i	$-0.604629\pi$
$139$	5.83201	−	17.9491i	0.494664	−	1.52242i	0.817479	−	0.575958i	$-0.195371\pi$
$140$	−10.5500	−	11.6095i	−0.891637	−	0.981179i
$141$	1.68231	−	1.22227i	0.141676	−	0.102934i
$142$	−22.4856	−	12.9821i	−1.88695	−	1.08943i
$143$	1.07062	+	2.54143i	0.0895301	+	0.212525i
$144$	4.86489	+	8.42624i	0.405408	+	0.702187i
$145$	0.180539	+	1.71772i	0.0149930	+	0.142649i
$146$	24.3986	−	7.92758i	2.01924	−	0.656091i
$147$	−1.13872	−	0.643588i	−0.0939197	−	0.0530822i
$148$	15.0827	+	10.9582i	1.23979	+	0.900758i
$149$	4.87212	+	10.9430i	0.399140	+	0.896482i	0.995588	+	0.0938308i	$0.0299113\pi$
$149$	4.87212	+	10.9430i	0.399140	+	0.896482i	−0.596449	+	0.802651i	$0.703422\pi$
$150$	−0.600638	+	0.127669i	−0.0490419	+	0.0104242i
$151$	7.89100	+	7.10509i	0.642160	+	0.578204i	0.924533	−	0.381101i	$-0.124455\pi$
$151$	7.89100	+	7.10509i	0.642160	+	0.578204i	−0.282373	+	0.959305i	$0.591122\pi$
$152$	0.207653	−	0.0218252i	0.0168429	−	0.00177026i
$153$	17.2113			1.39145
$154$	−0.283983	+	18.2171i	−0.0228840	+	1.46797i
$155$	−12.2954			−0.987592
$156$	0.357083	−	0.0375309i	0.0285895	−	0.00300488i
$157$	0.350091	+	0.315224i	0.0279403	+	0.0251576i	0.682983	−	0.730435i	$-0.260682\pi$
$157$	0.350091	+	0.315224i	0.0279403	+	0.0251576i	−0.655042	+	0.755592i	$0.727349\pi$
$158$	−12.8315	+	2.72741i	−1.02082	+	0.216981i
$159$	−0.174210	−	0.391283i	−0.0138158	−	0.0310307i
$160$	−16.8221	−	12.2220i	−1.32991	−	0.966233i
$161$	0.573402	−	1.30394i	0.0451904	−	0.102765i
$162$	17.1538	−	5.57361i	1.34773	−	0.437904i
$163$	−0.0618019	−	0.588006i	−0.00484070	−	0.0460562i	0.991835	−	0.127529i	$-0.0407044\pi$
$163$	−0.0618019	−	0.588006i	−0.00484070	−	0.0460562i	−0.996676	+	0.0814723i	$0.974038\pi$
$164$	11.6370	+	20.1559i	0.908700	+	1.57391i
$165$	1.36071	+	0.822641i	0.105931	+	0.0640425i
$166$	−5.61557	−	3.24215i	−0.435853	−	0.251640i
$167$	−1.38668	+	1.00748i	−0.107305	+	0.0779615i	−0.640144	−	0.768255i	$-0.721125\pi$
$167$	−1.38668	+	1.00748i	−0.107305	+	0.0779615i	0.532839	+	0.846217i	$0.321125\pi$
$168$	0.303992	+	0.0972342i	0.0234535	+	0.00750178i
$169$	−3.80358	+	11.7062i	−0.292583	+	0.900477i
$170$	−28.2485	+	12.5771i	−2.16656	+	0.964617i
$171$	−0.100240	+	0.953723i	−0.00766557	+	0.0729330i
$172$	−2.50754	−	11.7971i	−0.191198	−	0.899517i
$173$	−16.4616	−	3.49902i	−1.25155	−	0.266026i	−0.465979	−	0.884796i	$-0.654298\pi$
$173$	−16.4616	−	3.49902i	−1.25155	−	0.266026i	−0.785572	+	0.618770i	$0.787631\pi$
$174$	−0.153515	−	0.211295i	−0.0116379	−	0.0160182i
$175$	−2.44582	+	3.39905i	−0.184887	+	0.256944i
$176$	2.04758	+	10.6890i	0.154342	+	0.805714i
$177$	−1.18844	+	2.05845i	−0.0893289	+	0.154722i
$178$	−11.7627	−	5.23709i	−0.881652	−	0.392537i
$179$	−2.87568	+	3.19377i	−0.214939	+	0.238713i	−0.840967	−	0.541087i	$-0.818013\pi$
$179$	−2.87568	+	3.19377i	−0.214939	+	0.238713i	0.626028	+	0.779801i	$0.284680\pi$
$180$	−13.0648	+	11.7636i	−0.973790	+	0.876804i
$181$	−9.58833	+	13.1972i	−0.712695	+	0.980941i	0.287040	+	0.957919i	$0.407329\pi$
$181$	−9.58833	+	13.1972i	−0.712695	+	0.980941i	−0.999735	+	0.0230220i	$0.992671\pi$
$182$	3.04074	−	3.40839i	0.225395	−	0.252646i
$183$	1.31930	+	0.428667i	0.0975255	+	0.0316879i
$184$	−0.0722652	+	0.339981i	−0.00532746	+	0.0250637i
$185$	8.41879	−	18.9089i	0.618962	−	1.39021i
$186$	1.61016	−	0.929624i	0.118062	−	0.0681633i
$187$	18.1859	+	6.31728i	1.32988	+	0.461965i
$188$			25.7173i			1.87562i
$189$	−1.46278	+	2.56066i	−0.106402	+	0.186260i
$190$	−0.532405	−	1.63857i	−0.0386247	−	0.118875i
$191$	−4.45476	−	4.94751i	−0.322335	−	0.357989i	0.560099	−	0.828426i	$-0.310763\pi$
$191$	−4.45476	−	4.94751i	−0.322335	−	0.357989i	−0.882434	+	0.470436i	$0.844096\pi$
$192$	1.90741	+	0.200477i	0.137656	+	0.0144682i
$193$	1.39933	+	0.147075i	0.100726	+	0.0105867i	0.154757	−	0.987953i	$-0.450540\pi$
$193$	1.39933	+	0.147075i	0.100726	+	0.0105867i	−0.0540315	+	0.998539i	$0.517207\pi$
$194$	−1.84167	−	2.04538i	−0.132224	−	0.146850i
$195$	−0.123184	−	0.379120i	−0.00882137	−	0.0271494i
$196$	14.7170	−	6.71483i	1.05122	−	0.479631i
$197$		−	7.35131i		−	0.523759i	−0.965101	−	0.261879i	$-0.915658\pi$
$197$		−	7.35131i		−	0.523759i	0.965101	−	0.261879i	$-0.0843423\pi$
$198$	20.4141	+	0.411866i	1.45077	+	0.0292701i
$199$	−2.93228	+	1.69295i	−0.207864	+	0.120010i	−0.600318	−	0.799761i	$-0.704959\pi$
$199$	−2.93228	+	1.69295i	−0.207864	+	0.120010i	0.392454	+	0.919771i	$0.371626\pi$
$200$	0.415602	−	0.933457i	0.0293875	−	0.0660053i
$201$	0.161169	−	0.758239i	0.0113680	−	0.0534821i
$202$	−16.8778	−	5.48393i	−1.18752	−	0.385848i
$203$	−1.74384	−	0.362315i	−0.122393	−	0.0254295i
$204$	1.47331	−	2.02784i	0.103152	−	0.141977i
$205$	19.2027	−	17.2902i	1.34117	−	1.20760i
$206$	−14.5167	+	16.1224i	−1.01142	+	1.12330i
$207$	−1.45836	−	0.649303i	−0.101363	−	0.0451297i
$208$	1.36424	−	2.36294i	0.0945933	−	0.163840i
$209$	−0.455973	+	0.970935i	−0.0315403	+	0.0671610i
$210$	0.263274	−	2.62041i	0.0181676	−	0.180825i
$211$	−8.18718	−	11.2687i	−0.563629	−	0.775768i	0.428154	−	0.903706i	$-0.359164\pi$
$211$	−8.18718	−	11.2687i	−0.563629	−	0.775768i	−0.991782	+	0.127938i	$0.959164\pi$
$212$	5.18132	+	1.10132i	0.355855	+	0.0756392i
$213$	−0.485825	−	2.28563i	−0.0332882	−	0.156609i
$214$	−0.691611	+	6.58024i	−0.0472776	+	0.449816i
$215$	−12.2325	+	5.44626i	−0.834250	+	0.371432i
$216$	0.222364	−	0.684365i	0.0151299	−	0.0465651i
$217$	3.86273	−	12.0764i	0.262219	−	0.819799i
$218$	15.3621	−	11.1612i	1.04045	−	0.755932i
$219$	1.99947	+	1.15439i	0.135112	+	0.0780067i
$220$	−18.1223	+	7.63435i	−1.22180	+	0.514708i
$221$	−2.41325	−	4.17987i	−0.162333	−	0.281169i
$222$	0.327163	+	3.11275i	0.0219578	+	0.208914i
$223$	1.37807	−	0.447763i	0.0922825	−	0.0299844i	−0.262512	−	0.964929i	$-0.584551\pi$
$223$	1.37807	−	0.447763i	0.0922825	−	0.0299844i	0.354794	+	0.934944i	$0.384551\pi$
$224$	17.2891	−	12.6828i	1.15518	−	0.847405i
$225$	3.79669	+	2.75846i	0.253113	+	0.183897i
$226$	7.18248	+	16.1321i	0.477771	+	1.07309i
$227$	9.86136	−	2.09610i	0.654522	−	0.139123i	0.131331	−	0.991339i	$-0.458075\pi$
$227$	9.86136	−	2.09610i	0.654522	−	0.139123i	0.523191	+	0.852216i	$0.324742\pi$
$228$	0.103787	+	0.0934503i	0.00687347	+	0.00618890i
$229$	17.0949	−	1.79674i	1.12966	−	0.118732i	0.478797	−	0.877926i	$-0.341073\pi$
$229$	17.0949	−	1.79674i	1.12966	−	0.118732i	0.650865	+	0.759194i	$0.274406\pi$
$230$	2.86805			0.189114
$231$	−1.23547	+	1.07803i	−0.0812878	+	0.0709291i
$232$	0.434597			0.0285327
$233$	6.31855	−	0.664106i	0.413942	−	0.0435070i	0.104731	−	0.994501i	$-0.466602\pi$
$233$	6.31855	−	0.664106i	0.413942	−	0.0435070i	0.309211	+	0.950994i	$0.399935\pi$
$234$	−3.80410	−	3.42523i	−0.248682	−	0.223914i
$235$	27.9283	−	5.93635i	1.82184	−	0.387245i
$236$	−11.9563	−	26.8544i	−0.778291	−	1.74807i
$237$	−0.955115	−	0.693932i	−0.0620414	−	0.0450757i
$238$	−3.47845	−	31.6965i	−0.225475	−	2.05458i
$239$	−20.0385	+	6.51091i	−1.29618	+	0.421156i	−0.874253	−	0.485471i	$-0.838648\pi$
$239$	−20.0385	+	6.51091i	−1.29618	+	0.421156i	−0.421932	+	0.906627i	$0.638648\pi$
$240$	−0.164443	−	1.56457i	−0.0106148	−	0.100993i
$241$	−2.99486	−	5.18725i	−0.192916	−	0.334140i	0.753299	−	0.657678i	$-0.228461\pi$
$241$	−2.99486	−	5.18725i	−0.192916	−	0.334140i	−0.946215	+	0.323537i	$0.895128\pi$
$242$	21.4189	+	7.92804i	1.37686	+	0.509633i
$243$	4.30164	+	2.48355i	0.275950	+	0.159320i
$244$	−13.8794	+	10.0840i	−0.888537	+	0.645560i
$245$	−10.6893	−	14.4324i	−0.682915	−	0.922050i
$246$	−1.20744	+	3.71611i	−0.0769834	+	0.236930i
$247$	0.245673	−	0.109380i	0.0156318	−	0.00695971i
$248$	−0.323391	+	3.07686i	−0.0205353	+	0.195381i
$249$	−0.121330	−	0.570813i	−0.00768897	−	0.0361738i
$250$	17.8062	+	3.78482i	1.12616	+	0.239373i
$251$	−13.2787	−	18.2766i	−0.838145	−	1.15361i	−0.986352	−	0.164651i	$-0.947350\pi$
$251$	−13.2787	−	18.2766i	−0.838145	−	1.15361i	0.148207	−	0.988956i	$-0.452650\pi$
$252$	−7.44958	−	16.5277i	−0.469280	−	1.04115i
$253$	−1.30262	−	1.22135i	−0.0818948	−	0.0767856i
$254$	10.3020	−	17.8435i	0.646403	−	1.11960i
$255$	−2.54227	−	1.13189i	−0.159203	−	0.0708819i
$256$	6.64740	−	7.38268i	0.415462	−	0.461418i
$257$	−15.9611	+	14.3714i	−0.995625	+	0.896465i	−0.994626	−	0.103535i	$-0.966985\pi$
$257$	−15.9611	+	14.3714i	−0.995625	+	0.896465i	−0.000999023		1.00000i	$0.500318\pi$
$258$	1.19014	−	1.63809i	0.0740949	−	0.101983i
$259$	15.9272	+	14.2092i	0.989670	+	0.882920i
$260$	4.68871	+	1.52345i	0.290781	+	0.0944805i
$261$	−0.415001	+	1.95243i	−0.0256879	+	0.120852i
$262$	−3.23928	+	7.27555i	−0.200124	+	0.449485i
$263$	−21.2791	+	12.2855i	−1.31213	+	0.757557i	−0.982448	−	0.186536i	$-0.940274\pi$
$263$	−21.2791	+	12.2855i	−1.31213	+	0.757557i	−0.329679	+	0.944093i	$0.606941\pi$
$264$	0.241650	−	0.318873i	0.0148725	−	0.0196253i
$265$		−	5.88101i		−	0.361268i
$266$	1.77665	−	0.00814641i	0.108933	−	0.000499489i
$267$	−0.358084	−	1.10207i	−0.0219144	−	0.0674456i
$268$	6.41488	+	7.12445i	0.391851	+	0.435195i
$269$	11.5575	+	1.21474i	0.704670	+	0.0740639i	0.450084	−	0.892986i	$-0.351394\pi$
$269$	11.5575	+	1.21474i	0.704670	+	0.0740639i	0.254586	+	0.967050i	$0.418061\pi$
$270$	−5.90516	−	0.620657i	−0.359377	−	0.0377720i
$271$	14.2595	+	15.8367i	0.866201	+	0.962013i	0.999578	−	0.0290520i	$-0.00924884\pi$
$271$	14.2595	+	15.8367i	0.866201	+	0.962013i	−0.133377	+	0.991065i	$0.542582\pi$
$272$	−5.88607	−	18.1155i	−0.356895	−	1.09841i
$273$	0.411066	−	0.00188485i	0.0248789	−	0.000114076i
$274$			36.4166i			2.20001i
$275$	2.99921	+	4.30820i	0.180859	+	0.259794i
$276$	−0.201339	+	0.116243i	−0.0121192	+	0.00699700i
$277$	−7.77692	+	17.4672i	−0.467270	+	1.04951i	0.514162	+	0.857693i	$0.328103\pi$
$277$	−7.77692	+	17.4672i	−0.467270	+	1.04951i	−0.981432	+	0.191812i	$0.938564\pi$
$278$	−8.14705	+	38.3288i	−0.488627	+	2.29881i
$279$	−13.5140	−	4.39096i	−0.809061	−	0.262880i
$280$	3.27012	+	2.91739i	0.195427	+	0.174347i
$281$	17.5966	−	24.2197i	1.04973	−	1.44482i	0.160679	−	0.987007i	$-0.448632\pi$
$281$	17.5966	−	24.2197i	1.04973	−	1.44482i	0.889047	−	0.457817i	$-0.151368\pi$
$282$	−3.20854	+	2.88899i	−0.191066	+	0.172037i
$283$	−16.1034	+	17.8847i	−0.957250	+	1.06313i	0.0407019	+	0.999171i	$0.487041\pi$
$283$	−16.1034	+	17.8847i	−0.957250	+	1.06313i	−0.997952	+	0.0639629i	$0.979626\pi$
$284$	26.4002	+	11.7541i	1.56656	+	0.697478i
$285$	0.0775275	−	0.134282i	0.00459233	−	0.00795416i
$286$	−2.76230	−	5.01545i	−0.163338	−	0.296570i
$287$	10.9495	+	24.2925i	0.646326	+	1.43394i
$288$	−14.1246	−	19.4408i	−0.832299	−	1.14556i
$289$	−16.3293	−	3.47089i	−0.960545	−	0.204170i
$290$	−0.745593	−	3.50774i	−0.0437827	−	0.205981i
$291$	0.0258918	−	0.246344i	0.00151780	−	0.0144409i
$292$	−26.0850	+	11.6138i	−1.52651	+	0.679645i
$293$	−3.74186	+	11.5163i	−0.218602	+	0.672787i	0.780276	+	0.625435i	$0.215078\pi$
$293$	−3.74186	+	11.5163i	−0.218602	+	0.672787i	−0.998878	+	0.0473525i	$0.984922\pi$
$294$	2.49102	+	1.08181i	0.145279	+	0.0630925i
$295$	−26.4033	+	19.1831i	−1.53726	+	1.11688i
$296$	−4.51042	−	2.60409i	−0.262163	−	0.151360i
$297$	2.41771	+	2.79659i	0.140290	+	0.162274i
$298$	−12.4354	−	21.5388i	−0.720364	−	1.24771i
$299$	0.0467937	+	0.445213i	0.00270615	+	0.0257473i
$300$	0.650004	−	0.211199i	0.0375280	−	0.0121936i
$301$	−1.50628	−	13.7256i	−0.0868206	−	0.791130i
$302$	−17.8362	−	12.9587i	−1.02636	−	0.745692i
$303$	−0.649604	−	1.45903i	−0.0373188	−	0.0838194i
$304$	1.03811	−	0.220656i	0.0595394	−	0.0126555i
$305$	14.1548	+	12.7450i	0.810499	+	0.729777i
$306$	−35.5397	+	3.73537i	−2.03167	+	0.213537i
$307$	14.6934			0.838595			0.419298	−	0.907849i	$-0.362276\pi$
$307$	14.6934			0.838595			0.419298	+	0.907849i	$0.362276\pi$
$308$	−1.80506	−	20.1979i	−0.102853	−	1.15088i
$309$	−1.95246			−0.111072
$310$	25.3889	−	2.66848i	1.44199	−	0.151559i
$311$	5.86586	+	5.28164i	0.332622	+	0.299495i	0.818470	−	0.574549i	$-0.194822\pi$
$311$	5.86586	+	5.28164i	0.332622	+	0.299495i	−0.485848	+	0.874043i	$0.661489\pi$
$312$	−0.0981126	+	0.0208545i	−0.00555453	+	0.00118065i
$313$	0.358405	+	0.804991i	0.0202582	+	0.0455008i	0.923391	−	0.383860i	$-0.125406\pi$
$313$	0.358405	+	0.804991i	0.0202582	+	0.0455008i	−0.903133	+	0.429361i	$0.858739\pi$
$314$	−0.791318	−	0.574926i	−0.0446567	−	0.0324450i
$315$	−16.2291	+	11.9052i	−0.914404	+	0.670781i
$316$	13.8861	−	4.51187i	0.781154	−	0.253812i
$317$	0.724770	+	6.89572i	0.0407071	+	0.387302i	0.995840	+	0.0911234i	$0.0290458\pi$
$317$	0.724770	+	6.89572i	0.0407071	+	0.387302i	−0.955132	+	0.296179i	$0.904288\pi$
$318$	0.444648	+	0.770152i	0.0249346	+	0.0431880i
$319$	−1.15512	+	1.91066i	−0.0646746	+	0.106977i
$320$	22.8062	+	13.1672i	1.27490	+	0.736067i
$321$	−0.481738	+	0.350003i	−0.0268880	+	0.0195353i
$322$	−0.901026	+	2.81696i	−0.0502122	+	0.156983i
$323$	0.580136	−	1.78548i	0.0322796	−	0.0993465i
$324$	−18.3394	+	8.16525i	−1.01886	+	0.453625i
$325$	0.137563	−	1.30882i	0.00763061	−	0.0726004i
$326$	0.255230	+	1.20076i	0.0141359	+	0.0665042i
$327$	1.67156	+	0.355302i	0.0924376	+	0.0196482i
$328$	−3.82170	−	5.26012i	−0.211018	−	0.290442i
$329$	−2.94337	+	29.2958i	−0.162273	+	1.61513i
$330$	−2.98827	−	1.40336i	−0.164499	−	0.0772525i
$331$	−0.930306	+	1.61134i	−0.0511343	+	0.0885671i	−0.890460	−	0.455062i	$-0.849617\pi$
$331$	−0.930306	+	1.61134i	−0.0511343	+	0.0885671i	0.839325	+	0.543629i	$0.182950\pi$
$332$	6.59318	+	2.93547i	0.361848	+	0.161105i
$333$	16.0059	−	17.7764i	0.877119	−	0.974140i
$334$	2.64472	−	2.38131i	0.144712	−	0.130300i
$335$	6.25622	−	8.61095i	0.341814	−	0.470467i
$336$	1.58836	+	0.330012i	0.0866523	+	0.0180036i
$337$	−1.09780	−	0.356698i	−0.0598012	−	0.0194306i	0.278964	−	0.960302i	$-0.410009\pi$
$337$	−1.09780	−	0.356698i	−0.0598012	−	0.0194306i	−0.338765	+	0.940871i	$0.610009\pi$
$338$	5.31342	−	24.9977i	0.289012	−	1.35969i
$339$	−0.646398	+	1.45183i	−0.0351075	+	0.0788528i
$340$	29.8056	−	17.2083i	1.61644	−	0.933250i
$341$	−12.6675	−	9.59980i	−0.685986	−	0.519858i
$342$		−	1.99110i		−	0.107666i
$343$	17.5334	−	5.96482i	0.946716	−	0.322070i
$344$	1.04116	+	3.20436i	0.0561356	+	0.172768i
$345$	0.172712	+	0.191817i	0.00929852	+	0.0103271i
$346$	34.7510	+	3.65248i	1.86823	+	0.196358i
$347$	−11.2514	−	1.18257i	−0.604008	−	0.0634838i	−0.202411	−	0.979301i	$-0.564878\pi$
$347$	−11.2514	−	1.18257i	−0.604008	−	0.0634838i	−0.401596	+	0.915817i	$0.631544\pi$
$348$	0.194511	+	0.216026i	0.0104269	+	0.0115802i
$349$	−4.51300	−	13.8896i	−0.241576	−	0.743493i	−0.996181	−	0.0873141i	$-0.972172\pi$
$349$	−4.51300	−	13.8896i	−0.241576	−	0.743493i	0.754605	−	0.656179i	$-0.227828\pi$
$350$	4.31269	−	7.54953i	0.230523	−	0.403539i
$351$		−	0.926796i		−	0.0494687i
$352$	−7.78878	−	25.7260i	−0.415143	−	1.37120i
$353$	−11.1032	+	6.41046i	−0.590966	+	0.341194i	−0.765479	−	0.643460i	$-0.777498\pi$
$353$	−11.1032	+	6.41046i	−0.590966	+	0.341194i	0.174513	+	0.984655i	$0.444165\pi$
$354$	2.00728	−	4.50842i	0.106686	−	0.239620i
$355$	6.67070	−	31.3832i	0.354044	−	1.66565i
$356$	13.6297	+	4.42855i	0.722371	+	0.234712i
$357$	1.91041	−	2.14139i	0.101110	−	0.113334i
$358$	5.24486	−	7.21894i	0.277200	−	0.381533i
$359$	−13.6691	+	12.3077i	−0.721426	+	0.649575i	−0.945734	−	0.324943i	$-0.894655\pi$
$359$	−13.6691	+	12.3077i	−0.721426	+	0.649575i	0.224307	+	0.974519i	$0.427988\pi$
$360$	3.28628	−	3.64978i	0.173202	−	0.192360i
$361$	−17.2618	−	7.68545i	−0.908516	−	0.404497i
$362$	16.9348	−	29.3319i	0.890073	−	1.54165i
$363$	0.759604	+	1.90993i	0.0398689	+	0.100245i
$364$	−2.96932	+	4.12657i	−0.155635	+	0.216291i
$365$	18.6335	+	25.6468i	0.975323	+	1.34242i
$366$	−2.81726	−	0.598828i	−0.147261	−	0.0313012i
$367$	3.92553	+	18.4682i	0.204911	+	0.964031i	0.953592	+	0.301101i	$0.0973541\pi$
$367$	3.92553	+	18.4682i	0.204911	+	0.964031i	−0.748681	+	0.662930i	$0.769313\pi$
$368$	−0.184671	+	1.75703i	−0.00962663	+	0.0915913i
$369$	27.2805	−	12.1461i	1.42017	−	0.632298i
$370$	−13.2802	+	40.8722i	−0.690404	+	2.12485i
$371$	5.77625	+	1.84758i	0.299888	+	0.0959215i
$372$	−1.67416	+	1.21635i	−0.0868011	+	0.0630647i
$373$	−20.4036	−	11.7800i	−1.05646	−	0.609947i	−0.132008	−	0.991249i	$-0.542142\pi$
$373$	−20.4036	−	11.7800i	−1.05646	−	0.609947i	−0.924451	+	0.381302i	$0.875476\pi$
$374$	−38.9232	−	9.09769i	−2.01267	−	0.470430i
$375$	0.819148	+	1.41881i	0.0423006	+	0.0732669i
$376$	−0.750974	−	7.14504i	−0.0387285	−	0.368477i
$377$	0.532348	−	0.172970i	0.0274173	−	0.00890843i
$378$	2.46477	−	5.60498i	0.126774	−	0.288289i
$379$	10.5001	+	7.62877i	0.539354	+	0.391863i	0.823845	−	0.566815i	$-0.191825\pi$
$379$	10.5001	+	7.62877i	0.539354	+	0.391863i	−0.284491	+	0.958679i	$0.591825\pi$
$380$	0.779965	+	1.75183i	0.0400113	+	0.0898670i
$381$	1.81376	−	0.385527i	0.0929220	−	0.0197512i
$382$	10.2724	+	9.24932i	0.525582	+	0.473236i
$383$	2.89824	−	0.304617i	0.148093	−	0.0155652i	−0.0301918	−	0.999544i	$-0.509612\pi$
$383$	2.89824	−	0.304617i	0.148093	−	0.0155652i	0.178285	+	0.983979i	$0.442945\pi$
$384$	−0.953398			−0.0486529
$385$	−21.5177	+	6.62256i	−1.09665	+	0.337517i
$386$	−2.92140			−0.148695
$387$	−15.3898	+	1.61753i	−0.782308	+	0.0822239i
$388$	2.27655	+	2.04981i	0.115574	+	0.104063i
$389$	19.6936	−	4.18600i	0.998505	−	0.212239i	0.320462	−	0.947261i	$-0.396162\pi$
$389$	19.6936	−	4.18600i	0.998505	−	0.212239i	0.678043	+	0.735023i	$0.262829\pi$
$390$	0.336643	+	0.756113i	0.0170466	+	0.0382873i
$391$	2.52832	+	1.83693i	0.127863	+	0.0928976i
$392$	−3.89276	+	2.29534i	−0.196614	+	0.115932i
$393$	−0.681660	+	0.221485i	−0.0343852	+	0.0111724i
$394$	1.59546	+	15.1797i	0.0803779	+	0.764745i
$395$	−8.10513	−	14.0385i	−0.407813	−	0.706353i
$396$	−22.6447	+	1.91912i	−1.13794	+	0.0964392i
$397$	−33.6624	−	19.4350i	−1.68947	−	0.975413i	−0.954924	−	0.296849i	$-0.904064\pi$
$397$	−33.6624	−	19.4350i	−1.68947	−	0.975413i	−0.734541	−	0.678564i	$-0.762602\pi$
$398$	5.68745	−	4.13218i	0.285086	−	0.207127i
$399$	0.107533	+	0.118332i	0.00538341	+	0.00592403i
$400$	1.60494	−	4.93950i	0.0802471	−	0.246975i
$401$	−17.9506	+	7.99212i	−0.896410	+	0.399108i	−0.802624	−	0.596485i	$-0.796564\pi$
$401$	−17.9506	+	7.99212i	−0.896410	+	0.399108i	−0.0937860	+	0.995592i	$0.529897\pi$
$402$	−0.168237	+	1.60067i	−0.00839091	+	0.0798342i
$403$	0.828466	+	3.89762i	0.0412688	+	0.194154i
$404$	19.3204	+	4.10667i	0.961225	+	0.204315i
$405$	13.1006	+	18.0314i	0.650973	+	0.895988i
$406$	3.67949	+	0.369680i	0.182610	+	0.0183469i
$407$	23.4370	−	12.9081i	1.16173	−	0.639832i
$408$	−0.350116	+	0.606418i	−0.0173333	+	0.0300222i
$409$	−2.47018	−	1.09980i	−0.122143	−	0.0543814i	0.344755	−	0.938693i	$-0.387962\pi$
$409$	−2.47018	−	1.09980i	−0.122143	−	0.0543814i	−0.466898	+	0.884311i	$0.654629\pi$
$410$	−35.8992	+	39.8701i	−1.77294	+	1.96904i
$411$	−2.43556	+	2.19299i	−0.120137	+	0.108172i
$412$	14.1931	−	19.5351i	0.699242	−	0.962425i
$413$	−10.5465	−	31.9595i	−0.518961	−	1.57263i
$414$	3.15229	+	1.02424i	0.154927	+	0.0503387i
$415$	1.66594	−	7.83764i	0.0817779	−	0.384735i
$416$	−2.74087	+	6.15610i	−0.134382	+	0.301828i
$417$	−3.05406	+	1.76326i	−0.149558	+	0.0863474i
$418$	0.730819	−	2.10385i	0.0357455	−	0.102903i
$419$		−	9.95127i		−	0.486151i	−0.970007	−	0.243076i	$-0.921844\pi$
$419$		−	9.95127i		−	0.486151i	0.970007	−	0.243076i	$-0.0781563\pi$
$420$	0.0134404	+	2.93121i	0.000655825	+	0.143028i
$421$	7.92595	+	24.3936i	0.386287	+	1.18887i	0.935542	+	0.353215i	$0.114911\pi$
$421$	7.92595	+	24.3936i	0.386287	+	1.18887i	−0.549255	+	0.835655i	$0.685089\pi$
$422$	19.3514	+	21.4919i	0.942011	+	1.04621i
$423$	32.8162	+	3.44912i	1.59558	+	0.167702i
$424$	−1.47169	−	0.154681i	−0.0714716	−	0.00751196i
$425$	−6.14750	−	6.82749i	−0.298197	−	0.331182i
$426$	1.49923	+	4.61416i	0.0726380	+	0.223557i
$427$	−16.9648	+	9.89864i	−0.820985	+	0.479029i
$428$		−	7.36426i		−	0.355965i
$429$	0.169091	−	0.486772i	0.00816379	−	0.0235016i
$430$	24.0770	−	13.9008i	1.16109	−	0.670358i
$431$	5.91945	−	13.2953i	0.285130	−	0.640412i	−0.713024	−	0.701139i	$-0.752675\pi$
$431$	5.91945	−	13.2953i	0.285130	−	0.640412i	0.998154	+	0.0607267i	$0.0193418\pi$
$432$	0.760455	−	3.57766i	0.0365874	−	0.172130i
$433$	10.0205	+	3.25585i	0.481553	+	0.156466i	0.539726	−	0.841840i	$-0.318528\pi$
$433$	10.0205	+	3.25585i	0.481553	+	0.156466i	−0.0581736	+	0.998306i	$0.518528\pi$
$434$	−5.35522	+	25.7749i	−0.257059	+	1.23724i
$435$	0.189700	−	0.261100i	0.00909542	−	0.0125188i
$436$	−15.7061	+	14.1418i	−0.752184	+	0.677270i
$437$	−0.116514	+	0.129402i	−0.00557363	+	0.00619015i
$438$	−4.37925	−	1.94977i	−0.209249	−	0.0931636i
$439$	8.41649	−	14.5778i	0.401697	−	0.695760i	−0.592234	−	0.805766i	$-0.701754\pi$
$439$	8.41649	−	14.5778i	0.401697	−	0.695760i	0.993931	+	0.110006i	$0.0350871\pi$
$440$	4.81199	−	2.65025i	0.229403	−	0.126346i
$441$	−6.59458	−	19.6801i	−0.314028	−	0.937147i
$442$	5.89029	+	8.10729i	0.280173	+	0.385625i
$443$	2.35142	+	0.499809i	0.111719	+	0.0237466i	0.263432	−	0.964678i	$-0.415146\pi$
$443$	2.35142	+	0.499809i	0.111719	+	0.0237466i	−0.151713	+	0.988425i	$0.548479\pi$
$444$	−0.724287	−	3.40750i	−0.0343732	−	0.161713i
$445$	1.66314	−	15.8237i	0.0788405	−	0.750117i
$446$	−2.74841	+	1.22367i	−0.130141	+	0.0579425i
$447$	0.691669	−	2.12874i	0.0327148	−	0.100686i
$448$	−20.0974	+	18.2633i	−0.949513	+	0.862861i
$449$	7.96535	−	5.78717i	0.375908	−	0.273113i	−0.383748	−	0.923438i	$-0.625367\pi$
$449$	7.96535	−	5.78717i	0.375908	−	0.273113i	0.759657	+	0.650324i	$0.225367\pi$
$450$	−8.43848	−	4.87196i	−0.397794	−	0.229666i
$451$	33.2834	−	2.82073i	1.56725	−	0.132823i
$452$	−9.82726	−	17.0213i	−0.462236	−	0.800616i
$453$	−0.207398	−	1.97326i	−0.00974441	−	0.0927119i
$454$	−19.9079	+	6.46846i	−0.934322	+	0.303580i
$455$	5.16678	+	2.27207i	0.242222	+	0.106516i
$456$	−0.0315641	−	0.0229327i	−0.00147812	−	0.00107392i
$457$	7.15629	+	16.0733i	0.334757	+	0.751876i	0.999986	+	0.00523726i	$0.00166708\pi$
$457$	7.15629	+	16.0733i	0.334757	+	0.751876i	−0.665229	+	0.746639i	$0.731666\pi$
$458$	−34.9093	+	7.42021i	−1.63121	+	0.346724i
$459$	−4.80815	−	4.32928i	−0.224425	−	0.202074i
$460$	−3.17470	+	0.333674i	−0.148021	+	0.0155576i
$461$	9.99896			0.465698			0.232849	−	0.972513i	$-0.425195\pi$
$461$	9.99896			0.465698			0.232849	+	0.972513i	$0.425195\pi$
$462$	2.31716	−	2.49416i	0.107804	−	0.116039i
$463$	12.2956			0.571426			0.285713	−	0.958315i	$-0.407770\pi$
$463$	12.2956			0.571426			0.285713	+	0.958315i	$0.407770\pi$
$464$	2.19692	−	0.230906i	0.101989	−	0.0107195i
$465$	1.70737	+	1.53733i	0.0791775	+	0.0712918i
$466$	−12.9031	+	2.74263i	−0.597723	+	0.127050i
$467$	−9.44958	−	21.2241i	−0.437275	−	0.982135i	−0.988974	−	0.148092i	$-0.952687\pi$
$467$	−9.44958	−	21.2241i	−0.437275	−	0.982135i	0.551699	−	0.834043i	$-0.313980\pi$
$468$	4.60933	+	3.34887i	0.213066	+	0.154802i
$469$	6.49211	+	8.85000i	0.299778	+	0.408655i
$470$	−56.3810	+	18.3193i	−2.60066	+	0.845006i
$471$	−0.00920140	−	0.0875455i	−0.000423978	−	0.00403388i
$472$	4.10601	+	7.11182i	0.188995	+	0.327348i
$473$	−16.8550	−	3.93959i	−0.774992	−	0.181142i
$474$	2.12283	+	1.22561i	0.0975046	+	0.0562943i
$475$	0.414132	−	0.300885i	0.0190017	−	0.0138055i
$476$	7.53801	+	34.6808i	0.345504	+	1.58959i
$477$	2.10024	−	6.46386i	0.0961632	−	0.295960i
$478$	39.9646	−	17.7934i	1.82794	−	0.813850i
$479$	2.30039	−	21.8868i	0.105108	−	1.00003i	−0.807131	−	0.590373i	$-0.798981\pi$
$479$	2.30039	−	21.8868i	0.105108	−	1.00003i	0.912238	−	0.409660i	$-0.134353\pi$
$480$	0.807819	+	3.80049i	0.0368717	+	0.173468i
$481$	−6.56135	−	1.39466i	−0.299172	−	0.0635909i
$482$	7.30989	+	10.0612i	0.332957	+	0.458275i
$483$	−0.242659	+	0.109375i	−0.0110414	+	0.00497672i
$484$	−24.6314	−	6.28378i	−1.11961	−	0.285627i
$485$	1.70055	−	2.94544i	0.0772179	−	0.133745i
$486$	−9.42147	−	4.19471i	−0.427367	−	0.190276i
$487$	0.721440	−	0.801241i	0.0326916	−	0.0363077i	−0.726577	−	0.687085i	$-0.758890\pi$
$487$	0.721440	−	0.801241i	0.0326916	−	0.0363077i	0.759269	+	0.650777i	$0.225557\pi$
$488$	3.56166	−	3.20693i	0.161229	−	0.145171i
$489$	−0.0649379	+	0.0893793i	−0.00293659	+	0.00404187i
$490$	25.2047	+	27.4816i	1.13863	+	1.24149i
$491$	−9.23502	−	3.00064i	−0.416771	−	0.135417i	0.0931227	−	0.995655i	$-0.470315\pi$
$491$	−9.23502	−	3.00064i	−0.416771	−	0.135417i	−0.509893	+	0.860238i	$0.670315\pi$
$492$	0.904197	−	4.25391i	0.0407643	−	0.191781i
$493$	1.58937	−	3.56977i	0.0715814	−	0.160774i
$494$	−0.483552	+	0.279179i	−0.0217560	+	0.0125608i
$495$	7.31123	+	24.1486i	0.328615	+	1.08540i
$496$			15.7256i			0.706098i
$497$	28.7285	+	16.4112i	1.28865	+	0.736143i
$498$	0.374418	+	1.15234i	0.0167781	+	0.0516376i
$499$	−13.8078	−	15.3351i	−0.618121	−	0.686493i	0.350065	−	0.936725i	$-0.386160\pi$
$499$	−13.8078	−	15.3351i	−0.618121	−	0.686493i	−0.968186	+	0.250233i	$0.919493\pi$
$500$	−20.1504	−	2.11789i	−0.901151	−	0.0947148i
$501$	0.318527	+	0.0334785i	0.0142307	+	0.00149571i
$502$	31.3858	+	34.8575i	1.40082	+	1.55577i
$503$	−8.19339	−	25.2167i	−0.365325	−	1.12436i	−0.949777	−	0.312927i	$-0.898690\pi$
$503$	−8.19339	−	25.2167i	−0.365325	−	1.12436i	0.584452	−	0.811428i	$-0.301310\pi$
$504$	2.55235	+	4.37435i	0.113691	+	0.194849i
$505$		−	21.9294i		−	0.975847i
$506$	2.95485	+	2.23926i	0.131359	+	0.0995474i
$507$	1.99183	−	1.14998i	0.0884602	−	0.0510725i
$508$	−9.32751	+	20.9499i	−0.413841	+	0.929502i
$509$	0.287767	−	1.35384i	0.0127550	−	0.0600077i	−0.971310	−	0.237818i	$-0.923568\pi$
$509$	0.287767	−	1.35384i	0.0127550	−	0.0600077i	0.984065	+	0.177810i	$0.0569012\pi$
$510$	5.49520	+	1.78550i	0.243332	+	0.0790633i
$511$	−31.0439	+	10.2444i	−1.37330	+	0.453184i
$512$	−18.1220	+	24.9429i	−0.800889	+	1.10233i
$513$	0.267900	−	0.241218i	0.0118281	−	0.0106500i
$514$	29.8391	−	33.1397i	1.31615	−	1.46173i
$515$	−24.4909	−	10.9040i	−1.07920	−	0.480489i
$516$	−1.12681	+	1.95169i	−0.0496051	+	0.0859185i
$517$	33.4085	+	15.6894i	1.46930	+	0.690018i
$518$	−35.9720	−	25.8840i	−1.58052	−	1.13728i
$519$	1.84841	+	2.54411i	0.0811361	+	0.111674i
$520$	−1.34715	−	0.286346i	−0.0590765	−	0.0125571i
$521$	0.440920	+	2.07436i	0.0193170	+	0.0908795i	0.986750	−	0.162247i	$-0.0518743\pi$
$521$	0.440920	+	2.07436i	0.0193170	+	0.0908795i	−0.967433	+	0.253127i	$0.918541\pi$
$522$	0.433202	−	4.12165i	0.0189608	−	0.180400i
$523$	−16.0909	+	7.16414i	−0.703607	+	0.313266i	−0.727171	−	0.686456i	$-0.759165\pi$
$523$	−16.0909	+	7.16414i	−0.703607	+	0.313266i	0.0235639	+	0.999722i	$0.492499\pi$
$524$	2.73918	−	8.43032i	0.119661	−	0.368280i
$525$	0.764624	−	0.166194i	0.0333709	−	0.00725329i
$526$	41.2730	−	29.9866i	1.79959	−	1.30748i
$527$	24.0906	+	13.9087i	1.04940	+	0.605873i
$528$	1.05214	−	1.74032i	0.0457885	−	0.0757375i
$529$	11.3551	+	19.6676i	0.493699	+	0.855111i
$530$	1.27636	+	12.1437i	0.0554414	+	0.527490i
$531$	−35.8707	+	11.6551i	−1.55666	+	0.505789i
$532$	−1.96566	+	0.215716i	−0.0852220	+	0.00935247i
$533$	−6.77483	−	4.92220i	−0.293450	−	0.213204i
$534$	0.978593	+	2.19795i	0.0423478	+	0.0951148i
$535$	−7.99742	+	1.69990i	−0.345758	+	0.0734932i
$536$	−1.99029	−	1.79207i	−0.0859675	−	0.0774055i
$537$	0.798649	−	0.0839414i	0.0344643	−	0.00362234i
$538$	−24.1287			−1.04026
$539$	0.255429	−	23.2150i	0.0110021	−	0.999939i
$540$	6.60875			0.284395
$541$	−8.74887	+	0.919543i	−0.376143	+	0.0395343i	−0.290714	−	0.956810i	$-0.593893\pi$
$541$	−8.74887	+	0.919543i	−0.376143	+	0.0395343i	−0.0854293	+	0.996344i	$0.527226\pi$
$542$	−32.8815	−	29.6066i	−1.41238	−	1.27171i
$543$	2.98154	−	0.633746i	0.127950	−	0.0271966i
$544$	19.1342	+	42.9761i	0.820371	+	1.84258i
$545$	18.9831	+	13.7921i	0.813148	+	0.590787i
$546$	−0.848404	+	0.0931059i	−0.0363083	+	0.00398456i
$547$	−11.9461	+	3.88154i	−0.510780	+	0.165963i	−0.553057	−	0.833143i	$-0.686539\pi$
$547$	−11.9461	+	3.88154i	−0.510780	+	0.165963i	0.0422769	+	0.999106i	$0.486539\pi$
$548$	−4.23678	−	40.3103i	−0.180986	−	1.72197i
$549$	11.0061	+	19.0631i	0.469728	+	0.813593i
$550$	−7.12809	−	8.24511i	−0.303943	−	0.351573i
$551$	0.188554	+	0.108862i	0.00803266	+	0.00463766i
$552$	0.0525436	−	0.0381752i	0.00223640	−	0.00162484i
$553$	16.3347	−	3.55041i	0.694623	−	0.150979i
$554$	12.2677	−	37.7560i	0.521204	−	1.60410i
$555$	−3.53328	+	1.57312i	−0.149979	+	0.0667752i
$556$	4.55888	−	43.3748i	0.193339	−	1.83950i
$557$	3.91292	+	18.4089i	0.165796	+	0.780008i	0.979932	+	0.199334i	$0.0638778\pi$
$557$	3.91292	+	18.4089i	0.165796	+	0.780008i	−0.814136	+	0.580675i	$0.802789\pi$
$558$	28.8580	+	6.13397i	1.22166	+	0.259672i
$559$	2.55068	+	3.51071i	0.107882	+	0.148487i
$560$	18.0807	+	13.0102i	0.764051	+	0.549780i
$561$	−1.73548	−	3.15106i	−0.0732718	−	0.133038i
$562$	−31.0789	+	53.8303i	−1.31099	+	2.27069i
$563$	−27.2247	−	12.1212i	−1.14739	−	0.510849i	−0.257160	−	0.966369i	$-0.582787\pi$
$563$	−27.2247	−	12.1212i	−1.14739	−	0.510849i	−0.890226	+	0.455519i	$0.849454\pi$
$564$	3.21549	−	3.57116i	0.135397	−	0.150373i
$565$	−16.2163	+	14.6012i	−0.682225	+	0.614279i
$566$	29.3706	−	40.4251i	1.23454	−	1.69919i
$567$	−21.8259	+	7.20247i	−0.916601	+	0.302475i
$568$	−7.67801	−	2.49474i	−0.322162	−	0.104677i
$569$	−1.78100	+	8.37896i	−0.0746635	+	0.351264i	−0.999582	−	0.0289006i	$-0.990799\pi$
$569$	−1.78100	+	8.37896i	−0.0746635	+	0.351264i	0.924919	+	0.380165i	$0.124133\pi$
$570$	−0.130944	+	0.294105i	−0.00548463	+	0.0123187i
$571$	0.896656	−	0.517684i	0.0375239	−	0.0216644i	−0.481121	−	0.876654i	$-0.659770\pi$
$571$	0.896656	−	0.517684i	0.0375239	−	0.0216644i	0.518645	+	0.854990i	$0.326437\pi$
$572$	3.64116	+	5.23032i	0.152244	+	0.218691i
$573$			1.24401i			0.0519694i
$574$	−27.8818	−	47.7853i	−1.16376	−	1.99452i
$575$	0.263324	+	0.810428i	0.0109814	+	0.0337972i
$576$	20.3642	+	22.6167i	0.848507	+	0.942362i
$577$	−41.6486	−	4.37744i	−1.73385	−	0.182235i	−0.815703	−	0.578471i	$-0.803650\pi$
$577$	−41.6486	−	4.37744i	−1.73385	−	0.182235i	−0.918149	+	0.396235i	$0.870316\pi$
$578$	34.4717	+	3.62312i	1.43383	+	0.150702i
$579$	−0.175925	−	0.195384i	−0.00731119	−	0.00811990i
$580$	1.23341	+	3.79604i	0.0512145	+	0.157622i
$581$	7.17465	+	4.09854i	0.297655	+	0.170036i
$582$			0.514296i			0.0213182i
$583$	4.59167	−	6.05900i	0.190168	−	0.250938i
$584$	6.90806	−	3.98837i	0.285858	−	0.165040i
$585$	2.57282	−	5.77865i	0.106373	−	0.238918i
$586$	5.22721	−	24.5921i	0.215934	−	1.01589i
$587$	24.5030	+	7.96152i	1.01135	+	0.328607i	0.767391	−	0.641179i	$-0.221554\pi$
$587$	24.5030	+	7.96152i	1.01135	+	0.328607i	0.243957	+	0.969786i	$0.421554\pi$
$588$	−2.88322	−	0.907668i	−0.118902	−	0.0374316i
$589$	−0.911023	+	1.25392i	−0.0375380	+	0.0516667i
$590$	50.3570	−	45.3416i	2.07316	−	1.86669i
$591$	−0.919152	+	1.02082i	−0.0378088	+	0.0419910i
$592$	−24.1841	−	10.7674i	−0.993959	−	0.442539i
$593$	−1.87769	+	3.25226i	−0.0771076	+	0.133554i	−0.902001	−	0.431734i	$-0.857902\pi$
$593$	−1.87769	+	3.25226i	−0.0771076	+	0.133554i	0.824893	+	0.565289i	$0.191235\pi$
$594$	−5.59929	−	5.24997i	−0.229742	−	0.215409i
$595$	35.9226	−	16.1915i	1.47268	−	0.663788i
$596$	16.2709	+	22.3949i	0.666481	+	0.917332i
$597$	0.618857	+	0.131542i	0.0253281	+	0.00538366i
$598$	−0.193249	−	0.909166i	−0.00790255	−	0.0371786i
$599$	−0.866023	+	8.23966i	−0.0353848	+	0.336663i	0.962480	+	0.271352i	$0.0874707\pi$
$599$	−0.866023	+	8.23966i	−0.0353848	+	0.336663i	−0.997865	+	0.0653114i	$0.979196\pi$
$600$	−0.174424	+	0.0776585i	−0.00712082	+	0.00317039i
$601$	7.61479	−	23.4359i	0.310614	−	0.955971i	−0.666909	−	0.745139i	$-0.732383\pi$
$601$	7.61479	−	23.4359i	0.310614	−	0.955971i	0.977522	−	0.210831i	$-0.0676171\pi$
$602$	6.08920	+	28.0151i	0.248177	+	1.14181i
$603$	9.95141	−	7.23013i	0.405253	−	0.294433i
$604$	21.2509	+	12.2692i	0.864685	+	0.499226i
$605$	−1.13835	+	28.1996i	−0.0462804	+	1.14648i
$606$	1.65803	+	2.87178i	0.0673527	+	0.116658i
$607$	−2.85584	−	27.1715i	−0.115915	−	1.10286i	−0.885605	−	0.464439i	$-0.846256\pi$
$607$	−2.85584	−	27.1715i	−0.115915	−	1.10286i	0.769690	−	0.638417i	$-0.220411\pi$
$608$	−2.49285	+	0.809978i	−0.101099	+	0.0328489i
$609$	0.196852	+	0.268348i	0.00797686	+	0.0108740i
$610$	−31.9943	−	23.2452i	−1.29541	−	0.941171i
$611$	−3.76363	−	8.45324i	−0.152260	−	0.341982i
$612$	38.9050	−	8.26952i	1.57264	−	0.334275i
$613$	−10.0651	−	9.06263i	−0.406524	−	0.366036i	0.440353	−	0.897825i	$-0.354853\pi$
$613$	−10.0651	−	9.06263i	−0.406524	−	0.366036i	−0.846877	+	0.531789i	$0.821520\pi$
$614$	−30.3404	+	3.18891i	−1.22444	+	0.128694i
$615$	−4.82836			−0.194698
$616$	1.09130	+	5.55887i	0.0439698	+	0.223973i
$617$	16.0890			0.647717			0.323858	−	0.946106i	$-0.395020\pi$
$617$	16.0890			0.647717			0.323858	+	0.946106i	$0.395020\pi$
$618$	4.03164	−	0.423743i	0.162176	−	0.0170454i
$619$	0.773147	+	0.696145i	0.0310754	+	0.0279804i	0.684522	−	0.728992i	$-0.260011\pi$
$619$	0.773147	+	0.696145i	0.0310754	+	0.0279804i	−0.653447	+	0.756973i	$0.726678\pi$
$620$	−27.7930	+	5.90758i	−1.11619	+	0.237254i
$621$	0.244084	+	0.548221i	0.00979474	+	0.0219994i
$622$	−13.2587	−	9.63302i	−0.531626	−	0.386249i
$623$	15.0194	+	6.60470i	0.601738	+	0.264612i
$624$	−0.484886	+	0.157549i	−0.0194110	+	0.00630701i
$625$	3.17857	+	30.2421i	0.127143	+	1.20968i
$626$	−0.914779	−	1.58444i	−0.0365619	−	0.0633271i
$627$	0.184716	−	0.0778151i	0.00737684	−	0.00310763i
$628$	0.942814	+	0.544334i	0.0376224	+	0.0217213i
$629$	−37.8850	+	27.5251i	−1.51057	+	1.09750i
$630$	30.9277	−	28.1053i	1.23219	−	1.11974i
$631$	6.05136	−	18.6242i	0.240901	−	0.741416i	−0.755383	−	0.655284i	$-0.772549\pi$
$631$	6.05136	−	18.6242i	0.240901	−	0.741416i	0.996284	−	0.0861327i	$-0.0274509\pi$
$632$	−3.72623	+	1.65902i	−0.148222	+	0.0659925i
$633$	−0.272058	+	2.58846i	−0.0108133	+	0.102882i
$634$	−2.99316	−	14.0817i	−0.118874	−	0.559256i
$635$	24.9042	+	5.29355i	0.988293	+	0.210068i
$636$	−0.581790	−	0.800766i	−0.0230695	−	0.0317524i
$637$	−3.85479	+	4.36094i	−0.152732	+	0.172787i
$638$	1.97055	−	4.19603i	0.0780149	−	0.166122i
$639$	18.5394	−	32.1112i	0.733408	−	1.27030i
$640$	−11.9590	−	5.32451i	−0.472723	−	0.210470i
$641$	16.1772	−	17.9666i	0.638959	−	0.709636i	−0.333489	−	0.942754i	$-0.608226\pi$
$641$	16.1772	−	17.9666i	0.638959	−	0.709636i	0.972449	+	0.233118i	$0.0748928\pi$
$642$	0.918782	−	0.827275i	0.0362614	−	0.0326499i
$643$	−20.4298	+	28.1193i	−0.805674	+	1.10892i	0.186302	+	0.982492i	$0.440350\pi$
$643$	−20.4298	+	28.1193i	−0.805674	+	1.10892i	−0.991976	+	0.126423i	$0.959650\pi$
$644$	0.669633	−	3.22297i	0.0263872	−	0.127003i
$645$	2.37960	+	0.773178i	0.0936965	+	0.0304438i
$646$	−0.810424	+	3.81274i	−0.0318857	+	0.150010i
$647$	7.16071	−	16.0832i	0.281517	−	0.632297i	−0.716339	−	0.697753i	$-0.754183\pi$
$647$	7.16071	−	16.0832i	0.281517	−	0.632297i	0.997855	+	0.0654559i	$0.0208502\pi$
$648$	4.85682	−	2.80409i	0.190794	−	0.110155i
$649$	−42.1798	−	0.851002i	−1.65570	−	0.0334047i
$650$			2.73245i			0.107176i
$651$	−2.04633	+	1.19399i	−0.0802019	+	0.0467962i
$652$	−0.422219	−	1.29946i	−0.0165354	−	0.0508906i
$653$	18.7170	+	20.7874i	0.732454	+	0.813472i	0.988183	−	0.153276i	$-0.0489823\pi$
$653$	18.7170	+	20.7874i	0.732454	+	0.813472i	−0.255730	+	0.966748i	$0.582316\pi$
$654$	−3.52873	−	0.370884i	−0.137984	−	0.0145027i
$655$	−9.78741	−	1.02870i	−0.382426	−	0.0401946i
$656$	−22.1137	−	24.5598i	−0.863396	−	0.958898i
$657$	11.3212	+	34.8430i	0.441682	+	1.35936i
$658$	−0.280306	−	61.1318i	−0.0109275	−	2.38317i
$659$			36.8950i			1.43722i	0.695412	+	0.718612i	$0.255222\pi$
$659$			36.8950i			1.43722i	−0.695412	+	0.718612i	$0.744778\pi$
$660$	3.47105	+	1.20575i	0.135110	+	0.0469336i
$661$	−19.8125	+	11.4388i	−0.770618	+	0.444916i	−0.833095	−	0.553130i	$-0.813433\pi$
$661$	−19.8125	+	11.4388i	−0.770618	+	0.444916i	0.0624773	+	0.998046i	$0.480100\pi$
$662$	1.57129	−	3.52916i	0.0610697	−	0.137165i
$663$	−0.187509	+	0.882162i	−0.00728226	+	0.0342603i
$664$	−1.91751	−	0.623036i	−0.0744137	−	0.0241785i
$665$	0.687998	+	2.08486i	0.0266794	+	0.0808475i
$666$	−29.1927	+	40.1803i	−1.13119	+	1.55696i
$667$	−0.269342	+	0.242517i	−0.0104290	+	0.00939029i
$668$	−2.65044	+	2.94361i	−0.102549	+	0.113892i
$669$	−0.247347	−	0.110126i	−0.00956300	−	0.00425772i
$670$	−11.0497	+	19.1386i	−0.426886	+	0.739388i
$671$	4.63234	+	24.1822i	0.178829	+	0.933545i
$672$	−3.98657	−	0.400533i	−0.153785	−	0.0154509i
$673$	7.72609	+	10.6340i	0.297819	+	0.409912i	0.931534	−	0.363654i	$-0.118471\pi$
$673$	7.72609	+	10.6340i	0.297819	+	0.409912i	−0.633715	+	0.773566i	$0.718471\pi$
$674$	2.34427	+	0.498291i	0.0902981	+	0.0191935i
$675$	−0.366790	−	1.72561i	−0.0141178	−	0.0664189i
$676$	−2.97325	+	28.2886i	−0.114356	+	1.08802i
$677$	4.01197	−	1.78624i	0.154192	−	0.0686509i	−0.328189	−	0.944612i	$-0.606438\pi$
$677$	4.01197	−	1.78624i	0.154192	−	0.0686509i	0.482382	+	0.875961i	$0.339772\pi$
$678$	1.01966	−	3.13819i	0.0391598	−	0.120521i
$679$	2.35872	+	2.59559i	0.0905195	+	0.0996097i
$680$	−7.77841	+	5.65135i	−0.298289	+	0.216719i
$681$	−1.63145	−	0.941921i	−0.0625175	−	0.0360945i
$682$	28.2407	+	17.0734i	1.08139	+	0.653775i
$683$	19.3618	+	33.5356i	0.740858	+	1.28320i	0.952105	+	0.305771i	$0.0989142\pi$
$683$	19.3618	+	33.5356i	0.740858	+	1.28320i	−0.211247	+	0.977433i	$0.567753\pi$
$684$	0.231649	+	2.20399i	0.00885731	+	0.0842717i
$685$	−42.7980	+	13.9059i	−1.63523	+	0.531318i
$686$	−34.9103	+	16.1221i	−1.33288	+	0.615543i
$687$	−2.59849	−	1.88791i	−0.0991386	−	0.0720284i
$688$	6.96565	+	15.6451i	0.265563	+	0.596464i
$689$	−1.86427	+	0.396263i	−0.0710230	+	0.0150964i
$690$	−0.398265	−	0.358599i	−0.0151617	−	0.0136516i
$691$	6.02059	−	0.632790i	0.229034	−	0.0240725i	0.0106839	−	0.999943i	$-0.496599\pi$
$691$	6.02059	−	0.632790i	0.229034	−	0.0240725i	0.218350	+	0.975870i	$0.429932\pi$
$692$	−38.8915			−1.47843
$693$	−26.0153	−	0.405549i	−0.988241	−	0.0154055i
$694$	23.4898			0.891659
$695$	−48.1564	+	5.06144i	−1.82667	+	0.191991i
$696$	−0.0603493	−	0.0543387i	−0.00228753	−	0.00205970i
$697$	−57.1829	+	12.1546i	−2.16596	+	0.460388i
$698$	12.3334	+	27.7012i	0.466825	+	1.04851i
$699$	−0.960444	−	0.697803i	−0.0363273	−	0.0263934i
$700$	−3.89547	+	8.85847i	−0.147235	+	0.334819i
$701$	−0.444114	+	0.144301i	−0.0167740	+	0.00545019i	−0.317392	−	0.948294i	$-0.602807\pi$
$701$	−0.444114	+	0.144301i	−0.0167740	+	0.00545019i	0.300618	+	0.953745i	$0.402807\pi$
$702$	0.201143	+	1.91374i	0.00759164	+	0.0722296i
$703$	−1.30459	−	2.25961i	−0.0492035	−	0.0852230i
$704$	13.2160	+	31.3719i	0.498097	+	1.18237i
$705$	−4.62044	−	2.66761i	−0.174016	−	0.100468i
$706$	21.5359	−	15.6467i	0.810514	−	0.588873i
$707$	21.5388	+	6.88935i	0.810049	+	0.259101i
$708$	−1.69738	+	5.22399i	−0.0637914	+	0.196330i
$709$	−6.92306	+	3.08235i	−0.260001	+	0.115760i	−0.532598	−	0.846368i	$-0.678784\pi$
$709$	−6.92306	+	3.08235i	−0.260001	+	0.115760i	0.272597	+	0.962128i	$0.412118\pi$
$710$	−6.96326	+	66.2510i	−0.261327	+	2.48636i
$711$	−3.89495	−	18.3243i	−0.146072	−	0.687216i
$712$	−3.91606	−	0.832383i	−0.146760	−	0.0311949i
$713$	−1.51655	−	2.08735i	−0.0567951	−	0.0781718i
$714$	−3.48007	+	4.83638i	−0.130238	+	0.180997i
$715$	4.83952	−	5.16153i	0.180988	−	0.193030i
$716$	−4.96578	+	8.60098i	−0.185580	+	0.321434i
$717$	3.59668	+	1.60134i	0.134320	+	0.0598033i
$718$	25.5542	−	28.3808i	0.953675	−	1.05916i
$719$	12.4337	−	11.1954i	0.463700	−	0.417517i	−0.403882	−	0.914811i	$-0.632340\pi$
$719$	12.4337	−	11.1954i	0.463700	−	0.417517i	0.867582	+	0.497294i	$0.165673\pi$
$720$	14.6732	−	20.1960i	0.546839	−	0.752659i
$721$	18.4038	−	20.6290i	0.685395	−	0.768263i
$722$	37.3120	+	12.1234i	1.38861	+	0.451186i
$723$	−0.232701	+	1.09477i	−0.00865423	+	0.0407149i
$724$	−15.3329	+	34.4383i	−0.569844	+	1.27989i
$725$	0.922731	−	0.532739i	0.0342694	−	0.0197854i
$726$	−1.98302	−	3.77896i	−0.0735968	−	0.140250i
$727$		−	36.9759i		−	1.37136i	−0.727904	−	0.685679i	$-0.759505\pi$
$727$		−	36.9759i		−	1.37136i	0.727904	−	0.685679i	$-0.240495\pi$
$728$	0.704467	−	1.23320i	0.0261093	−	0.0457053i
$729$	7.76646	+	23.9027i	0.287647	+	0.885285i
$730$	−44.0426	−	48.9142i	−1.63009	−	1.81040i
$731$	30.1282	+	3.16660i	1.11433	+	0.117121i
$732$	3.18815	+	0.335088i	0.117837	+	0.0123852i
$733$	4.60107	+	5.11001i	0.169944	+	0.188742i	0.822101	−	0.569342i	$-0.192802\pi$
$733$	4.60107	+	5.11001i	0.169944	+	0.188742i	−0.652156	+	0.758085i	$0.726135\pi$
$734$	−12.1140	−	37.2831i	−0.447136	−	1.37614i
$735$	−0.320169	+	3.34062i	−0.0118096	+	0.123221i
$736$		−	4.36332i		−	0.160834i
$737$	13.1687	−	3.98694i	0.485074	−	0.146861i
$738$	−53.6955	+	31.0011i	−1.97656	+	1.14117i
$739$	15.0159	−	33.7262i	0.552367	−	1.24064i	−0.394466	−	0.918911i	$-0.629070\pi$
$739$	15.0159	−	33.7262i	0.552367	−	1.24064i	0.946833	−	0.321726i	$-0.104263\pi$
$740$	9.94495	−	46.7873i	0.365584	−	1.71994i
$741$	−0.0477908	−	0.0155282i	−0.00175564	−	0.000570442i
$742$	−12.3284	−	2.56145i	−0.452589	−	0.0940339i
$743$	4.07652	−	5.61085i	0.149553	−	0.205842i	−0.727667	−	0.685930i	$-0.759395\pi$
$743$	4.07652	−	5.61085i	0.149553	−	0.205842i	0.877220	+	0.480088i	$0.159395\pi$
$744$	0.429614	−	0.386826i	0.0157504	−	0.0141817i
$745$	20.5645	−	22.8392i	0.753426	−	0.836765i
$746$	44.6881	+	19.8964i	1.63615	+	0.728460i
$747$	4.63004	−	8.01946i	0.169404	−	0.293417i
$748$	44.1433	+	5.54201i	1.61404	+	0.202636i
$749$	0.842847	−	8.38899i	0.0307969	−	0.306527i
$750$	−1.99939	−	2.75192i	−0.0730073	−	0.100486i
$751$	−10.5595	−	2.24450i	−0.385323	−	0.0819030i	0.0111771	−	0.999938i	$-0.496442\pi$
$751$	−10.5595	−	2.24450i	−0.385323	−	0.0819030i	−0.396500	+	0.918035i	$0.629775\pi$
$752$	−7.59246	−	35.7197i	−0.276869	−	1.30256i
$753$	−0.441249	+	4.19820i	−0.0160800	+	0.152991i
$754$	−1.06171	+	0.472703i	−0.0386651	+	0.0172148i
$755$	8.41869	−	25.9100i	0.306387	−	0.942963i
$756$	−2.07620	+	6.49102i	−0.0755108	+	0.236076i
$757$	8.71020	−	6.32833i	0.316577	−	0.230007i	−0.418136	−	0.908384i	$-0.637317\pi$
$757$	8.71020	−	6.32833i	0.316577	−	0.230007i	0.734714	+	0.678377i	$0.237317\pi$
$758$	−23.3374	−	13.4738i	−0.847651	−	0.489392i
$759$	0.0281764	+	0.332469i	0.00102274	+	0.0120679i
$760$	−0.267854	−	0.463936i	−0.00971607	−	0.0168287i
$761$	−2.35522	−	22.4084i	−0.0853766	−	0.812304i	−0.950496	−	0.310738i	$-0.899424\pi$
$761$	−2.35522	−	22.4084i	−0.0853766	−	0.812304i	0.865119	−	0.501567i	$-0.167243\pi$
$762$	−3.66158	+	1.18972i	−0.132645	+	0.0430990i
$763$	−19.5101	+	14.3121i	−0.706313	+	0.518131i
$764$	−12.4468	−	9.04314i	−0.450310	−	0.327169i
$765$	−17.9610	−	40.3411i	−0.649381	−	1.45853i
$766$	−5.91847	+	1.25801i	−0.213843	+	0.0454537i
$767$	7.86007	+	7.07724i	0.283811	+	0.255544i
$768$	−1.84615	+	0.194038i	−0.0666172	+	0.00700174i
$769$	17.0653			0.615392			0.307696	−	0.951485i	$-0.400442\pi$
$769$	17.0653			0.615392			0.307696	+	0.951485i	$0.400442\pi$
$770$	42.9948	−	18.3449i	1.54942	−	0.661106i
$771$	4.01329			0.144535
$772$	3.23375	−	0.339881i	0.116385	−	0.0122326i
$773$	28.1298	+	25.3282i	1.01176	+	0.910991i	0.996042	−	0.0888859i	$-0.0283307\pi$
$773$	28.1298	+	25.3282i	1.01176	+	0.910991i	0.0157157	+	0.999877i	$0.494997\pi$
$774$	31.4274	−	6.68011i	1.12964	−	0.240112i
$775$	3.08506	+	6.92916i	0.110819	+	0.248903i
$776$	−0.692351	−	0.503022i	−0.0248539	−	0.0180574i
$777$	−0.435079	−	3.96455i	−0.0156084	−	0.142227i
$778$	−39.7569	+	12.9178i	−1.42535	+	0.463125i
$779$	−0.340479	−	3.23944i	−0.0121989	−	0.116065i
$780$	−0.460605	−	0.797791i	−0.0164923	−	0.0285655i
$781$	31.3754	−	27.1248i	1.12270	−	0.970600i
$782$	−5.61941	−	3.24437i	−0.200950	−	0.116018i
$783$	0.607043	−	0.441043i	0.0216940	−	0.0157616i
$784$	−18.4587	+	13.6714i	−0.659238	+	0.488263i
$785$	0.373503	−	1.14952i	0.0133309	−	0.0410282i
$786$	1.35949	−	0.605286i	0.0484916	−	0.0215898i
$787$	−0.484565	+	4.61033i	−0.0172729	+	0.164340i	−0.999758	−	0.0220009i	$-0.992996\pi$
$787$	−0.484565	+	4.61033i	−0.0172729	+	0.164340i	0.982485	+	0.186341i	$0.0596630\pi$
$788$	−3.53208	−	16.6171i	−0.125825	−	0.591961i
$789$	4.49096	+	0.954583i	0.159882	+	0.0339841i
$790$	19.7831	+	27.2291i	0.703851	+	0.968768i
$791$	−9.24661	−	20.5146i	−0.328772	−	0.729414i
$792$	6.23535	−	1.19444i	0.221564	−	0.0424426i
$793$	3.08639	−	5.34579i	0.109601	−	0.189835i
$794$	73.7275	+	32.8256i	2.61649	+	1.16494i
$795$	−0.735317	+	0.816652i	−0.0260790	+	0.0289637i
$796$	−5.81481	+	5.23568i	−0.206100	+	0.185574i
$797$	8.13875	−	11.2020i	0.288289	−	0.396796i	−0.640168	−	0.768235i	$-0.721135\pi$
$797$	8.13875	−	11.2020i	0.288289	−	0.396796i	0.928457	+	0.371439i	$0.121135\pi$
$798$	−0.247728	−	0.221007i	−0.00876948	−	0.00782357i
$799$	−61.4356	−	19.9617i	−2.17344	−	0.706192i
$800$	−2.66692	+	12.5469i	−0.0942898	+	0.443598i
$801$	7.47897	−	16.7980i	0.264256	−	0.593529i
$802$	35.3318	−	20.3988i	1.24761	−	0.720307i
$803$	−0.826620	+	40.9714i	−0.0291708	+	1.44585i
$804$		−	1.79139i		−	0.0631773i
$805$	−3.65465	+	0.0167576i	−0.128809	+	0.000590626i
$806$	−2.55660	−	7.86842i	−0.0900526	−	0.277153i
$807$	−1.45302	−	1.61374i	−0.0511486	−	0.0568063i
$808$	−5.48771	−	0.576782i	−0.193057	−	0.0202911i
$809$	−14.9603	−	1.57239i	−0.525975	−	0.0552822i	−0.162180	−	0.986761i	$-0.551853\pi$
$809$	−14.9603	−	1.57239i	−0.525975	−	0.0552822i	−0.363795	+	0.931479i	$0.618519\pi$
$810$	−30.9648	−	34.3899i	−1.08799	−	1.20834i
$811$	−10.4061	−	32.0267i	−0.365408	−	1.12461i	−0.949725	−	0.313084i	$-0.898638\pi$
$811$	−10.4061	−	32.0267i	−0.365408	−	1.12461i	0.584318	−	0.811525i	$-0.301362\pi$
$812$	−4.11591	+	0.0188726i	−0.144440	+	0.000662297i
$813$		−	3.98202i		−	0.139656i
$814$	−45.5936	+	31.7406i	−1.59806	+	1.11251i
$815$	−1.31372	+	0.758475i	−0.0460175	+	0.0265682i
$816$	−1.44766	+	3.25151i	−0.0506784	+	0.113826i
$817$	−0.350939	+	1.65104i	−0.0122778	+	0.0577625i
$818$	5.33938	+	1.73487i	0.186687	+	0.0606583i
$819$	4.86743	+	4.34241i	0.170082	+	0.151736i
$820$	35.0990	−	48.3096i	1.22571	−	1.68704i
$821$	−19.4580	+	17.5201i	−0.679089	+	0.611454i	−0.934747	−	0.355313i	$-0.884374\pi$
$821$	−19.4580	+	17.5201i	−0.679089	+	0.611454i	0.255659	+	0.966767i	$0.417708\pi$
$822$	4.55326	−	5.05690i	0.158813	−	0.176380i
$823$	42.5690	+	18.9529i	1.48386	+	0.660658i	0.979244	−	0.202685i	$-0.0649668\pi$
$823$	42.5690	+	18.9529i	1.48386	+	0.660658i	0.504618	+	0.863343i	$0.331633\pi$
$824$	−3.37282	+	5.84190i	−0.117498	+	0.203512i
$825$	0.122187	−	0.973247i	0.00425401	−	0.0338841i
$826$	28.7138	+	63.7045i	0.999080	+	2.21656i
$827$	5.02104	+	6.91086i	0.174599	+	0.240314i	0.887343	−	0.461109i	$-0.152548\pi$
$827$	5.02104	+	6.91086i	0.174599	+	0.240314i	−0.712745	+	0.701423i	$0.752548\pi$
$828$	−3.60850	−	0.767010i	−0.125404	−	0.0266554i
$829$	9.04896	+	42.5720i	0.314283	+	1.47859i	0.797624	+	0.603155i	$0.206090\pi$
$829$	9.04896	+	42.5720i	0.314283	+	1.47859i	−0.483341	+	0.875432i	$0.660577\pi$
$830$	−1.73901	+	16.5455i	−0.0603618	+	0.574304i
$831$	3.26389	−	1.45318i	0.113223	−	0.0504102i
$832$	2.63728	−	8.11672i	0.0914313	−	0.281397i
$833$	4.61766	+	40.3694i	0.159992	+	1.39872i
$834$	5.92367	−	4.30380i	0.205120	−	0.149028i
$835$	3.80850	+	2.19884i	0.131799	+	0.0760939i
$836$	−0.564192	+	2.41382i	−0.0195130	+	0.0834836i
$837$	2.67078	+	4.62593i	0.0923157	+	0.159895i
$838$	2.15973	+	20.5484i	0.0746065	+	0.709833i
$839$	23.2772	−	7.56323i	0.803619	−	0.261112i	0.121726	−	0.992564i	$-0.461157\pi$
$839$	23.2772	−	7.56323i	0.803619	−	0.261112i	0.681893	+	0.731452i	$0.261157\pi$
$840$	−0.0893289	−	0.813988i	−0.00308214	−	0.0280852i
$841$	−23.0949	−	16.7794i	−0.796375	−	0.578600i
$842$	−21.6605	−	48.6502i	−0.746469	−	1.67660i
$843$	−5.47175	+	1.16306i	−0.188457	+	0.0400578i
$844$	−23.9208	−	21.5384i	−0.823389	−	0.741383i
$845$	31.4071	−	3.30102i	1.08044	−	0.113558i
$846$	−68.5110			−2.35546
$847$	−27.3396	−	9.97725i	−0.939400	−	0.342822i
$848$	−7.52168			−0.258296
$849$	4.47233	−	0.470061i	0.153490	−	0.0161324i
$850$	14.1758	+	12.7639i	0.486225	+	0.437799i
$851$	4.24849	−	0.903045i	0.145636	−	0.0309560i
$852$	−2.19635	−	4.93308i	−0.0752457	−	0.169005i
$853$	−22.0941	−	16.0523i	−0.756486	−	0.549620i	0.141344	−	0.989961i	$-0.454858\pi$
$853$	−22.0941	−	16.0523i	−0.756486	−	0.549620i	−0.897831	+	0.440341i	$0.854858\pi$
$854$	32.8824	−	24.1216i	1.12521	−	0.825425i
$855$	2.34001	−	0.760315i	0.0800266	−	0.0260022i
$856$	0.215045	+	2.04602i	0.00735009	+	0.0699314i
$857$	−27.0976	−	46.9344i	−0.925635	−	1.60325i	−0.790536	−	0.612415i	$-0.790198\pi$
$857$	−27.0976	−	46.9344i	−0.925635	−	1.60325i	−0.135099	−	0.990832i	$-0.543135\pi$
$858$	−0.243513	+	1.04184i	−0.00831339	+	0.0355677i
$859$	−2.40664	−	1.38947i	−0.0821135	−	0.0474082i	0.458381	−	0.888756i	$-0.348430\pi$
$859$	−2.40664	−	1.38947i	−0.0821135	−	0.0474082i	−0.540495	+	0.841348i	$0.681763\pi$
$860$	−25.0340	+	18.1883i	−0.853653	+	0.620215i
$861$	1.51688	−	4.74235i	0.0516951	−	0.161619i
$862$	−9.33762	+	28.7382i	−0.318041	+	0.978829i
$863$	17.9801	−	8.00524i	0.612049	−	0.272502i	−0.0772124	−	0.997015i	$-0.524602\pi$
$863$	17.9801	−	8.00524i	0.612049	−	0.272502i	0.689261	+	0.724513i	$0.257935\pi$
$864$	−0.944241	+	8.98385i	−0.0321237	+	0.305637i
$865$	8.97738	+	42.2353i	0.305240	+	1.43604i
$866$	−21.3979	−	4.54827i	−0.727131	−	0.154556i
$867$	1.83355	+	2.52366i	0.0622706	+	0.0857081i
$868$	2.92910	−	29.1538i	0.0994201	−	0.989545i
$869$	2.61030	−	20.7916i	0.0885482	−	0.705305i
$870$	−0.335046	+	0.580317i	−0.0113591	+	0.0196746i
$871$	−3.15120	−	1.40300i	−0.106774	−	0.0475390i
$872$	3.95067	−	4.38766i	0.133787	−	0.148585i
$873$	2.92096	−	2.63005i	0.0988596	−	0.0890136i
$874$	0.212507	−	0.292490i	0.00718814	−	0.00989363i
$875$	−22.7119	−	4.71882i	−0.767801	−	0.159525i
$876$	5.07432	+	1.64875i	0.171445	+	0.0557060i
$877$	6.93090	−	32.6073i	0.234040	−	1.10107i	−0.691487	−	0.722389i	$-0.743044\pi$
$877$	6.93090	−	32.6073i	0.234040	−	1.10107i	0.925527	−	0.378682i	$-0.123623\pi$
$878$	−14.2154	+	31.9284i	−0.479748	+	1.07753i
$879$	1.95951	−	1.13132i	0.0660926	−	0.0381586i
$880$	22.9169	−	15.9539i	0.772527	−	0.537804i
$881$			2.27521i			0.0766537i	0.999265	+	0.0383268i	$0.0122028\pi$
$881$			2.27521i			0.0766537i	−0.999265	+	0.0383268i	$0.987797\pi$
$882$	17.8884	+	39.2063i	0.602332	+	1.32014i
$883$	17.5467	+	54.0033i	0.590495	+	1.81736i	0.575982	+	0.817462i	$0.304620\pi$
$883$	17.5467	+	54.0033i	0.590495	+	1.81736i	0.0145132	+	0.999895i	$0.495380\pi$
$884$	−7.46330	−	8.28883i	−0.251018	−	0.278784i
$885$	6.06494	+	0.637451i	0.203871	+	0.0214277i
$886$	−4.96393	−	0.521730i	−0.166766	−	0.0175278i
$887$	−13.8742	−	15.4088i	−0.465849	−	0.517377i	0.463742	−	0.885970i	$-0.346506\pi$
$887$	−13.8742	−	15.4088i	−0.465849	−	0.517377i	−0.929591	+	0.368593i	$0.879840\pi$
$888$	0.300732	+	0.925559i	0.0100919	+	0.0310597i
$889$	−13.0232	+	22.7975i	−0.436783	+	0.764605i
$890$			33.0355i			1.10735i
$891$	−0.581169	+	28.8056i	−0.0194699	+	0.965023i
$892$	2.89990	−	1.67426i	0.0970959	−	0.0560584i
$893$	1.46393	−	3.28805i	0.0489887	−	0.110030i
$894$	−0.966231	+	4.54576i	−0.0323156	+	0.152033i
$895$	10.4867	+	3.40734i	0.350532	+	0.113895i
$896$	8.98671	−	10.0733i	0.300225	−	0.336524i
$897$	0.0491681	−	0.0676741i	0.00164168	−	0.00225957i
$898$	−15.1917	+	13.6787i	−0.506954	+	0.456463i
$899$	−2.15866	+	2.39744i	−0.0719954	+	0.0799590i
$900$	9.90753	+	4.41112i	0.330251	+	0.147037i
$901$	−6.65266	+	11.5227i	−0.221632	+	0.383878i
$902$	−68.1148	+	13.0480i	−2.26797	+	0.434452i
$903$	−1.50698	+	2.09431i	−0.0501491	+	0.0696941i
$904$	3.22736	+	4.44208i	0.107340	+	0.147741i
$905$	40.9385	+	8.70175i	1.36084	+	0.289256i
$906$	0.856514	+	4.02958i	0.0284558	+	0.133874i
$907$	−4.51570	+	42.9640i	−0.149941	+	1.42660i	0.618051	+	0.786138i	$0.287922\pi$
$907$	−4.51570	+	42.9640i	−0.149941	+	1.42660i	−0.767992	+	0.640459i	$0.778744\pi$
$908$	21.2839	−	9.47618i	0.706329	−	0.314478i
$909$	7.83147	−	24.1028i	0.259753	−	0.799439i
$910$	−11.1620	−	3.57026i	−0.370017	−	0.118353i
$911$	−42.7171	+	31.0358i	−1.41528	+	1.02826i	−0.422752	+	0.906245i	$0.638936\pi$
$911$	−42.7171	+	31.0358i	−1.41528	+	1.02826i	−0.992528	+	0.122016i	$0.961064\pi$
$912$	−0.171743	−	0.0991559i	−0.00568698	−	0.00328338i
$913$	7.83570	−	6.77414i	0.259324	−	0.224191i
$914$	−18.2654	−	31.6367i	−0.604167	−	1.04645i
$915$	−0.372028	−	3.53961i	−0.0122989	−	0.117016i
$916$	37.7786	−	12.2750i	1.24824	−	0.405577i
$917$	4.08519	−	9.28989i	0.134905	−	0.306779i
$918$	10.8680	+	7.89604i	0.358696	+	0.260608i
$919$	6.71635	+	15.0852i	0.221552	+	0.497614i	0.989787	−	0.142554i	$-0.0455315\pi$
$919$	6.71635	+	15.0852i	0.221552	+	0.497614i	−0.768235	+	0.640168i	$0.778865\pi$
$920$	0.872285	−	0.185410i	0.0287584	−	0.00611278i
$921$	−2.04036	−	1.83715i	−0.0672321	−	0.0605361i
$922$	−20.6469	+	2.17008i	−0.679970	+	0.0714677i
$923$	−10.3979			−0.342250
$924$	−2.27473	+	3.03042i	−0.0748332	+	0.0996934i
$925$	−12.7686			−0.419829
$926$	−25.3893	+	2.66852i	−0.834344	+	0.0876931i
$927$	−23.0240	−	20.7309i	−0.756207	−	0.680892i
$928$	−5.33652	+	1.13431i	−0.175180	+	0.0372356i
$929$	4.26613	+	9.58189i	0.139967	+	0.314372i	0.969905	−	0.243485i	$-0.0782906\pi$
$929$	4.26613	+	9.58189i	0.139967	+	0.314372i	−0.829937	+	0.557857i	$0.811624\pi$
$930$	−3.85921	−	2.80388i	−0.126548	−	0.0919428i
$931$	−2.26387	+	0.0207613i	−0.0741952	+	0.000680425i
$932$	13.9636	−	4.53704i	0.457392	−	0.148616i
$933$	−0.154172	−	1.46685i	−0.00504735	−	0.0480224i
$934$	24.1188	+	41.7749i	0.789190	+	1.36692i
$935$	−4.17116	−	49.2178i	−0.136412	−	1.60960i
$936$	−1.37840	−	0.795822i	−0.0450545	−	0.0260123i
$937$	17.8605	−	12.9764i	0.583476	−	0.423920i	−0.256499	−	0.966544i	$-0.582569\pi$
$937$	17.8605	−	12.9764i	0.583476	−	0.423920i	0.839976	+	0.542624i	$0.182569\pi$
$938$	−15.3263	−	16.8654i	−0.500421	−	0.550675i
$939$	0.0508809	−	0.156595i	0.00166043	−	0.00511029i
$940$	60.2779	−	26.8375i	1.96605	−	0.875342i
$941$	−3.79926	+	36.1475i	−0.123852	+	1.17838i	0.739280	+	0.673398i	$0.235166\pi$
$941$	−3.79926	+	36.1475i	−0.123852	+	1.17838i	−0.863132	+	0.504978i	$0.831501\pi$
$942$	0.0380000	+	0.178776i	0.00123811	+	0.00582484i
$943$	5.30379	+	1.12736i	0.172715	+	0.0367118i
$944$	24.5348	+	33.7692i	0.798539	+	1.09909i
$945$	7.52835	+	0.756377i	0.244897	+	0.0246050i
$946$	35.6589	+	4.47683i	1.15937	+	0.145554i
$947$	−2.52168	+	4.36768i	−0.0819436	+	0.141931i	−0.904085	−	0.427353i	$-0.859446\pi$
$947$	−2.52168	+	4.36768i	−0.0819436	+	0.141931i	0.822141	+	0.569284i	$0.192779\pi$
$948$	−2.49239	−	1.10968i	−0.0809490	−	0.0360408i
$949$	6.87447	−	7.63487i	0.223155	−	0.247838i
$950$	−0.789843	+	0.711178i	−0.0256259	+	0.0230737i
$951$	0.761545	−	1.04818i	0.0246948	−	0.0339895i
$952$	−3.10701	−	9.41528i	−0.100699	−	0.305151i
$953$	−31.5498	−	10.2512i	−1.02200	−	0.332067i	−0.250376	−	0.968149i	$-0.580554\pi$
$953$	−31.5498	−	10.2512i	−1.02200	−	0.332067i	−0.771622	+	0.636081i	$0.780554\pi$
$954$	−2.93393	+	13.8031i	−0.0949896	+	0.446891i
$955$	−6.94752	+	15.6044i	−0.224817	+	0.504946i
$956$	−42.1675	+	24.3454i	−1.36379	+	0.787387i
$957$	0.399298	−	0.120891i	0.0129075	−	0.00390786i
$958$			45.6934i			1.47629i
$959$	−0.212777	−	46.4043i	−0.00687092	−	1.49847i
$960$	−1.52060	−	4.67994i	−0.0490773	−	0.151044i
$961$	5.37600	+	5.97065i	0.173419	+	0.192602i
$962$	13.8512	+	1.45582i	0.446582	+	0.0469377i
$963$	−9.39708	−	0.987673i	−0.302817	−	0.0318273i
$964$	−9.26201	−	10.2865i	−0.298309	−	0.331306i
$965$	−1.11555	−	3.43332i	−0.0359110	−	0.110523i
$966$	0.477330	−	0.278512i	0.0153578	−	0.00896099i
$967$		−	42.6572i		−	1.37176i	−0.727713	−	0.685882i	$-0.759417\pi$
$967$		−	42.6572i		−	1.37176i	0.727713	−	0.685882i	$-0.240583\pi$
$968$	7.02684	+	1.02656i	0.225851	+	0.0329950i
$969$	−0.303801	+	0.175400i	−0.00975951	+	0.00563465i
$970$	−2.87222	+	6.45111i	−0.0922215	+	0.207133i
$971$	−7.14014	+	33.5917i	−0.229138	+	1.07801i	0.701670	+	0.712502i	$0.252438\pi$
$971$	−7.14014	+	33.5917i	−0.229138	+	1.07801i	−0.930808	+	0.365508i	$0.880895\pi$
$972$	10.9168	+	3.54710i	0.350158	+	0.113773i
$973$	10.1575	−	48.8886i	0.325635	−	1.56730i
$974$	−1.31581	+	1.81106i	−0.0421613	+	0.0580301i
$975$	−0.182748	+	0.164547i	−0.00585261	+	0.00526971i
$976$	16.3006	−	18.1036i	0.521768	−	0.579482i
$977$	−30.4714	−	13.5667i	−0.974866	−	0.434038i	−0.143431	−	0.989660i	$-0.545813\pi$
$977$	−30.4714	−	13.5667i	−0.974866	−	0.434038i	−0.831435	+	0.555622i	$0.812480\pi$
$978$	0.114692	−	0.198653i	0.00366746	−	0.00635223i
$979$	14.0681	−	15.0041i	0.449617	−	0.479534i
$980$	−31.0968	−	27.4875i	−0.993351	−	0.878057i
$981$	15.9390	+	21.9382i	0.508895	+	0.700433i
$982$	19.7207	+	4.19176i	0.629312	+	0.133764i
$983$	−4.37789	−	20.5964i	−0.139633	−	0.656922i	−0.991167	−	0.132622i	$-0.957660\pi$
$983$	−4.37789	−	20.5964i	−0.139633	−	0.656922i	0.851534	−	0.524300i	$-0.175673\pi$
$984$	−0.126994	+	1.20827i	−0.00404843	+	0.0385182i
$985$	−17.2305	+	7.67152i	−0.549010	+	0.244435i
$986$	−2.50714	+	7.71618i	−0.0798436	+	0.245733i
$987$	4.07165	−	3.70007i	0.129602	−	0.117775i
$988$	0.502773	−	0.365286i	0.0159953	−	0.0116213i
$989$	−2.43338	−	1.40491i	−0.0773770	−	0.0446736i
$990$	−20.3380	−	48.2779i	−0.646383	−	1.53437i
$991$	9.95937	+	17.2501i	0.316370	+	0.547968i	0.979728	−	0.200334i	$-0.0642027\pi$
$991$	9.95937	+	17.2501i	0.316370	+	0.547968i	−0.663358	+	0.748302i	$0.730869\pi$
$992$	−4.05970	−	38.6255i	−0.128896	−	1.22636i
$993$	0.330654	−	0.107436i	0.0104930	−	0.00340938i
$994$	−62.8833	−	27.6526i	−1.99454	−	0.877089i
$995$	7.02806	+	5.10619i	0.222805	+	0.161877i
$996$	−0.548517	−	1.23199i	−0.0173804	−	0.0390371i
$997$	−17.5336	+	3.72688i	−0.555295	+	0.118032i	−0.477008	−	0.878899i	$-0.658279\pi$
$997$	−17.5336	+	3.72688i	−0.555295	+	0.118032i	−0.0782875	+	0.996931i	$0.524945\pi$
$998$	31.8399	+	28.6688i	1.00787	+	0.907495i
$999$	−8.94284	+	0.939931i	−0.282939	+	0.0297381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.19.1	✓	48
3.2	odd	2		693.2.cg.a.19.6		48
7.2	even	3		539.2.m.a.195.12		48
7.3	odd	6	inner	77.2.n.a.52.6	yes	48
7.4	even	3		539.2.s.d.129.6		48
7.5	odd	6		539.2.m.a.195.11		48
7.6	odd	2		539.2.s.d.19.1		48
11.2	odd	10		847.2.i.b.362.3		48
11.3	even	5		847.2.r.d.215.1		48
11.4	even	5		847.2.r.c.40.1		48
11.5	even	5		847.2.r.a.838.6		48
11.6	odd	10		847.2.r.d.838.1		48
11.7	odd	10	inner	77.2.n.a.40.6	yes	48
11.8	odd	10		847.2.r.a.215.6		48
11.9	even	5		847.2.i.b.362.22		48
11.10	odd	2		847.2.r.c.481.6		48
21.17	even	6		693.2.cg.a.514.1		48
33.29	even	10		693.2.cg.a.271.1		48
77.3	odd	30		847.2.r.d.94.1		48
77.10	even	6		847.2.r.c.360.1		48
77.17	even	30		847.2.r.d.717.1		48
77.18	odd	30		539.2.s.d.227.1		48
77.24	even	30		847.2.i.b.241.22		48
77.31	odd	30		847.2.i.b.241.3		48
77.38	odd	30		847.2.r.a.717.6		48
77.40	even	30		539.2.m.a.293.12		48
77.51	odd	30		539.2.m.a.293.11		48
77.52	even	30		847.2.r.a.94.6		48
77.59	odd	30		847.2.r.c.766.6		48
77.62	even	10		539.2.s.d.117.6		48
77.73	even	30	inner	77.2.n.a.73.1	yes	48
231.227	odd	30		693.2.cg.a.73.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.19.1	✓	48	1.1	even	1	trivial
77.2.n.a.40.6	yes	48	11.7	odd	10	inner
77.2.n.a.52.6	yes	48	7.3	odd	6	inner
77.2.n.a.73.1	yes	48	77.73	even	30	inner
539.2.m.a.195.11		48	7.5	odd	6
539.2.m.a.195.12		48	7.2	even	3
539.2.m.a.293.11		48	77.51	odd	30
539.2.m.a.293.12		48	77.40	even	30
539.2.s.d.19.1		48	7.6	odd	2
539.2.s.d.117.6		48	77.62	even	10
539.2.s.d.129.6		48	7.4	even	3
539.2.s.d.227.1		48	77.18	odd	30
693.2.cg.a.19.6		48	3.2	odd	2
693.2.cg.a.73.6		48	231.227	odd	30
693.2.cg.a.271.1		48	33.29	even	10
693.2.cg.a.514.1		48	21.17	even	6
847.2.i.b.241.3		48	77.31	odd	30
847.2.i.b.241.22		48	77.24	even	30
847.2.i.b.362.3		48	11.2	odd	10
847.2.i.b.362.22		48	11.9	even	5
847.2.r.a.94.6		48	77.52	even	30
847.2.r.a.215.6		48	11.8	odd	10
847.2.r.a.717.6		48	77.38	odd	30
847.2.r.a.838.6		48	11.5	even	5
847.2.r.c.40.1		48	11.4	even	5
847.2.r.c.360.1		48	77.10	even	6
847.2.r.c.481.6		48	11.10	odd	2
847.2.r.c.766.6		48	77.59	odd	30
847.2.r.d.94.1		48	77.3	odd	30
847.2.r.d.215.1		48	11.3	even	5
847.2.r.d.717.1		48	77.17	even	30
847.2.r.d.838.1		48	11.6	odd	10

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06490 + 0.217030i) q^{2} +(-0.138863 - 0.125032i) q^{3} +(2.26043 - 0.480470i) q^{4} +(-1.04356 - 2.34387i) q^{5} +(0.313874 + 0.228043i) q^{6} +(2.62996 - 0.288618i) q^{7} +(-0.613987 + 0.199497i) q^{8} +(-0.309936 - 2.94884i) q^{9} +(2.66354 + 4.61339i) q^{10} +(0.754864 - 3.22958i) q^{11} +(-0.373964 - 0.215908i) q^{12} +(-0.672688 + 0.488736i) q^{13} +(-5.36798 + 1.16675i) q^{14} +(-0.148149 + 0.455954i) q^{15} +(-2.99776 + 1.33469i) q^{16} +(-0.606752 + 5.77286i) q^{17} +(1.27998 + 6.02181i) q^{18} +(-0.316355 - 0.0672434i) q^{19} +(-3.48505 - 4.79677i) q^{20} +(-0.401290 - 0.288752i) q^{21} +(-0.857806 + 6.83260i) q^{22} +(0.269195 - 0.466260i) q^{23} +(0.110203 + 0.0490657i) q^{24} +(-1.05906 + 1.17621i) q^{25} +(1.28297 - 1.15519i) q^{26} +(-0.655159 + 0.901749i) q^{27} +(5.80618 - 1.91602i) q^{28} +(-0.640236 - 0.208025i) q^{29} +(0.206957 - 0.973655i) q^{30} +(1.94919 - 4.37794i) q^{31} +(7.01860 - 4.05219i) q^{32} +(-0.508624 + 0.354085i) q^{33} -12.0521i q^{34} +(-3.42100 - 5.86310i) q^{35} +(-2.11742 - 6.51675i) q^{36} +(5.39814 + 5.99524i) q^{37} +(0.667837 + 0.0701925i) q^{38} +(0.154519 + 0.0162406i) q^{39} +(1.10833 + 1.23092i) q^{40} +(3.11220 + 9.57836i) q^{41} +(0.891293 + 0.509154i) q^{42} -5.21894i q^{43} +(0.154604 - 7.66294i) q^{44} +(-6.58827 + 3.80374i) q^{45} +(-0.454670 + 1.02121i) q^{46} +(-2.31375 + 10.8853i) q^{47} +(0.583155 + 0.189479i) q^{48} +(6.83340 - 1.51811i) q^{49} +(1.93159 - 2.65861i) q^{50} +(0.806050 - 0.725770i) q^{51} +(-1.28574 + 1.42796i) q^{52} +(2.09401 + 0.932313i) q^{53} +(1.15713 - 2.00422i) q^{54} +(-8.35746 + 1.60095i) q^{55} +(-1.55719 + 0.701876i) q^{56} +(0.0355223 + 0.0488923i) q^{57} +(1.36717 + 0.290602i) q^{58} +(-2.64470 - 12.4423i) q^{59} +(-0.115808 + 1.10184i) q^{60} +(-6.78197 + 3.01953i) q^{61} +(-3.07474 + 9.46306i) q^{62} +(-1.66621 - 7.66589i) q^{63} +(-8.30379 + 6.03306i) q^{64} +(1.84752 + 1.06667i) q^{65} +(0.973414 - 0.841539i) q^{66} +(2.07425 + 3.59270i) q^{67} +(1.40216 + 13.3407i) q^{68} +(-0.0956787 + 0.0310879i) q^{69} +(8.33652 + 11.3643i) q^{70} +(10.1169 + 7.35035i) q^{71} +(0.778580 + 1.74872i) q^{72} +(-12.0858 + 2.56892i) q^{73} +(-12.4478 - 11.2080i) q^{74} +(0.294128 - 0.0309141i) q^{75} -0.747409 q^{76} +(1.05315 - 8.71154i) q^{77} -0.322592 q^{78} +(6.28349 - 0.660421i) q^{79} +(6.25667 + 5.63353i) q^{80} +(-8.49714 + 1.80612i) q^{81} +(-8.50519 - 19.1030i) q^{82} +(2.52659 + 1.83568i) q^{83} +(-1.04583 - 0.459897i) q^{84} +(14.1640 - 4.60217i) q^{85} +(1.13267 + 10.7766i) q^{86} +(0.0628949 + 0.108937i) q^{87} +(0.180813 + 2.13351i) q^{88} +(5.37059 + 3.10071i) q^{89} +(12.7786 - 9.28421i) q^{90} +(-1.62808 + 1.47951i) q^{91} +(0.384474 - 1.18329i) q^{92} +(-0.818053 + 0.364221i) q^{93} +(2.41522 - 22.9793i) q^{94} +(0.172525 + 0.811668i) q^{95} +(-1.48128 - 0.314855i) q^{96} +(0.779173 + 1.07244i) q^{97} +(-13.7808 + 4.61781i) q^{98} +(-9.75747 - 1.22501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26}+ \cdots - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more