LMFDB - Embedded newform 77.2.n.a.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(17,77)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			73.2
Character	$\chi$	$=$	77.73
Dual form			77.2.n.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30277 - 0.136927i) q^{2} +(2.02980 - 1.82764i) q^{3} +(-0.277833 - 0.0590552i) q^{4} +(0.166444 - 0.373838i) q^{5} +(-2.89461 + 2.10306i) q^{6} +(-2.50634 - 0.847492i) q^{7} +(2.84553 + 0.924570i) q^{8} +(0.466233 - 4.43591i) q^{9} +O(q^{10})$	\(q+(-1.30277 - 0.136927i) q^{2} +(2.02980 - 1.82764i) q^{3} +(-0.277833 - 0.0590552i) q^{4} +(0.166444 - 0.373838i) q^{5} +(-2.89461 + 2.10306i) q^{6} +(-2.50634 - 0.847492i) q^{7} +(2.84553 + 0.924570i) q^{8} +(0.466233 - 4.43591i) q^{9} +(-0.268026 + 0.464235i) q^{10} +(3.26372 + 0.590040i) q^{11} +(-0.671876 + 0.387908i) q^{12} +(0.864505 + 0.628100i) q^{13} +(3.14915 + 1.44727i) q^{14} +(-0.345395 - 1.06302i) q^{15} +(-3.06151 - 1.36307i) q^{16} +(0.576411 + 5.48418i) q^{17} +(-1.21479 + 5.71513i) q^{18} +(-4.47427 + 0.951036i) q^{19} +(-0.0683206 + 0.0940352i) q^{20} +(-6.63628 + 2.86045i) q^{21} +(-4.17108 - 1.21558i) q^{22} +(1.37746 + 2.38583i) q^{23} +(7.46564 - 3.32392i) q^{24} +(3.23360 + 3.59128i) q^{25} +(-1.04025 - 0.936644i) q^{26} +(-2.34451 - 3.22694i) q^{27} +(0.646295 + 0.383474i) q^{28} +(1.06190 - 0.345031i) q^{29} +(0.304415 + 1.43216i) q^{30} +(-2.75943 - 6.19778i) q^{31} +(-1.38044 - 0.796996i) q^{32} +(7.70307 - 4.76723i) q^{33} -7.22356i q^{34} +(-0.733990 + 0.795908i) q^{35} +(-0.391498 + 1.20491i) q^{36} +(-4.49217 + 4.98906i) q^{37} +(5.95917 - 0.626334i) q^{38} +(2.90271 - 0.305087i) q^{39} +(0.819261 - 0.909881i) q^{40} +(2.68289 - 8.25707i) q^{41} +(9.03722 - 2.81783i) q^{42} -4.85761i q^{43} +(-0.871922 - 0.356672i) q^{44} +(-1.58071 - 0.912624i) q^{45} +(-1.46783 - 3.29680i) q^{46} +(-0.543601 - 2.55744i) q^{47} +(-8.70546 + 2.82857i) q^{48} +(5.56351 + 4.24821i) q^{49} +(-3.72090 - 5.12138i) q^{50} +(11.1931 + 10.0783i) q^{51} +(-0.203095 - 0.225560i) q^{52} +(-12.2835 + 5.46898i) q^{53} +(2.61251 + 4.52499i) q^{54} +(0.763805 - 1.12189i) q^{55} +(-6.34832 - 4.72886i) q^{56} +(-7.34372 + 10.1078i) q^{57} +(-1.43065 + 0.304094i) q^{58} +(-0.435159 + 2.04726i) q^{59} +(0.0331854 + 0.315738i) q^{60} +(-6.52725 - 2.90612i) q^{61} +(2.74626 + 8.45212i) q^{62} +(-4.92794 + 10.7228i) q^{63} +(7.11169 + 5.16694i) q^{64} +(0.378699 - 0.218642i) q^{65} +(-10.6881 + 5.15586i) q^{66} +(4.12644 - 7.14721i) q^{67} +(0.163723 - 1.55772i) q^{68} +(7.15641 + 2.32526i) q^{69} +(1.06520 - 0.936383i) q^{70} +(2.08404 - 1.51414i) q^{71} +(5.42799 - 12.1915i) q^{72} +(-9.49087 - 2.01735i) q^{73} +(6.53540 - 5.88450i) q^{74} +(13.1271 + 1.37972i) q^{75} +1.29926 q^{76} +(-7.67994 - 4.24482i) q^{77} -3.82334 q^{78} +(2.06452 + 0.216990i) q^{79} +(-1.01914 + 0.917636i) q^{80} +(2.43204 + 0.516947i) q^{81} +(-4.62580 + 10.3897i) q^{82} +(2.94758 - 2.14154i) q^{83} +(2.01270 - 0.402820i) q^{84} +(2.14614 + 0.697322i) q^{85} +(-0.665137 + 6.32836i) q^{86} +(1.52484 - 2.64110i) q^{87} +(8.74148 + 4.69651i) q^{88} +(2.68261 - 1.54881i) q^{89} +(1.93434 + 1.40538i) q^{90} +(-1.63444 - 2.30690i) q^{91} +(-0.241808 - 0.744208i) q^{92} +(-16.9284 - 7.53700i) q^{93} +(0.358005 + 3.40619i) q^{94} +(-0.389180 + 1.83095i) q^{95} +(-4.25863 + 0.905199i) q^{96} +(-7.81872 + 10.7615i) q^{97} +(-6.66629 - 6.29624i) q^{98} +(4.13901 - 14.2025i) 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}+O(q^{10}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.30277	−	0.136927i	−0.921198	−	0.0968218i	−0.367957	−	0.929843i	$-0.619943\pi$
$2$	−1.30277	−	0.136927i	−0.921198	−	0.0968218i	−0.553241	+	0.833021i	$0.686609\pi$
$3$	2.02980	−	1.82764i	1.17190	−	1.05519i	0.174393	−	0.984676i	$-0.444204\pi$
$3$	2.02980	−	1.82764i	1.17190	−	1.05519i	0.997511	−	0.0705114i	$-0.0224631\pi$
$4$	−0.277833	−	0.0590552i	−0.138916	−	0.0295276i
$5$	0.166444	−	0.373838i	0.0744359	−	0.167186i	−0.872495	−	0.488623i	$-0.837499\pi$
$5$	0.166444	−	0.373838i	0.0744359	−	0.167186i	0.946931	+	0.321437i	$0.104166\pi$
$6$	−2.89461	+	2.10306i	−1.18172	+	0.858571i
$7$	−2.50634	−	0.847492i	−0.947309	−	0.320322i
$7$	−2.50634	−	0.847492i	−0.947309	−	0.320322i
$8$	2.84553	+	0.924570i	1.00605	+	0.326885i
$9$	0.466233	−	4.43591i	0.155411	−	1.47864i
$10$	−0.268026	+	0.464235i	−0.0847574	+	0.146804i
$11$	3.26372	+	0.590040i	0.984048	+	0.177904i
$11$	3.26372	+	0.590040i	0.984048	+	0.177904i
$12$	−0.671876	+	0.387908i	−0.193954	+	0.111979i
$13$	0.864505	+	0.628100i	0.239771	+	0.174204i	0.701181	−	0.712983i	$-0.252656\pi$
$13$	0.864505	+	0.628100i	0.239771	+	0.174204i	−0.461410	+	0.887187i	$0.652656\pi$
$14$	3.14915	+	1.44727i	0.841645	+	0.386800i
$15$	−0.345395	−	1.06302i	−0.0891805	−	0.274469i
$16$	−3.06151	−	1.36307i	−0.765378	−	0.340768i
$17$	0.576411	+	5.48418i	0.139800	+	1.33011i	0.809343	+	0.587336i	$0.199823\pi$
$17$	0.576411	+	5.48418i	0.139800	+	1.33011i	−0.669543	+	0.742773i	$0.733510\pi$
$18$	−1.21479	+	5.71513i	−0.286328	+	1.34707i
$19$	−4.47427	+	0.951036i	−1.02647	+	0.218183i	−0.690227	−	0.723593i	$-0.742489\pi$
$19$	−4.47427	+	0.951036i	−1.02647	+	0.218183i	−0.336242	+	0.941776i	$0.609156\pi$
$20$	−0.0683206	+	0.0940352i	−0.0152769	+	0.0210269i
$21$	−6.63628	+	2.86045i	−1.44816	+	0.624201i
$22$	−4.17108	−	1.21558i	−0.889278	−	0.259162i
$23$	1.37746	+	2.38583i	0.287220	+	0.497480i	0.973145	−	0.230192i	$-0.0739354\pi$
$23$	1.37746	+	2.38583i	0.287220	+	0.497480i	−0.685925	+	0.727672i	$0.740602\pi$
$24$	7.46564	−	3.32392i	1.52392	−	0.678491i
$25$	3.23360	+	3.59128i	0.646720	+	0.718256i
$26$	−1.04025	−	0.936644i	−0.204010	−	0.183691i
$27$	−2.34451	−	3.22694i	−0.451202	−	0.621026i
$28$	0.646295	+	0.383474i	0.122138	+	0.0724697i
$29$	1.06190	−	0.345031i	0.197189	−	0.0640706i	−0.208757	−	0.977967i	$-0.566942\pi$
$29$	1.06190	−	0.345031i	0.197189	−	0.0640706i	0.405947	+	0.913897i	$0.366942\pi$
$30$	0.304415	+	1.43216i	0.0555783	+	0.261475i
$31$	−2.75943	−	6.19778i	−0.495608	−	1.11315i	−0.972226	−	0.234043i	$-0.924804\pi$
$31$	−2.75943	−	6.19778i	−0.495608	−	1.11315i	0.476618	−	0.879110i	$-0.341862\pi$
$32$	−1.38044	−	0.796996i	−0.244029	−	0.140890i
$33$	7.70307	−	4.76723i	1.34093	−	0.829869i
$34$		−	7.22356i		−	1.23883i
$35$	−0.733990	+	0.795908i	−0.124067	+	0.134533i
$36$	−0.391498	+	1.20491i	−0.0652496	+	0.200818i
$37$	−4.49217	+	4.98906i	−0.738507	+	0.820196i	−0.988999	−	0.147923i	$-0.952741\pi$
$37$	−4.49217	+	4.98906i	−0.738507	+	0.820196i	0.250491	+	0.968119i	$0.419408\pi$
$38$	5.95917	−	0.626334i	0.966706	−	0.101605i
$39$	2.90271	−	0.305087i	0.464806	−	0.0488530i
$40$	0.819261	−	0.909881i	0.129536	−	0.143865i
$41$	2.68289	−	8.25707i	0.418996	−	1.28954i	−0.489631	−	0.871930i	$-0.662869\pi$
$41$	2.68289	−	8.25707i	0.418996	−	1.28954i	0.908627	−	0.417608i	$-0.137131\pi$
$42$	9.03722	−	2.81783i	1.39447	−	0.434800i
$43$		−	4.85761i		−	0.740779i	−0.928877	−	0.370390i	$-0.879224\pi$
$43$		−	4.85761i		−	0.740779i	0.928877	−	0.370390i	$-0.120776\pi$
$44$	−0.871922	−	0.356672i	−0.131447	−	0.0537703i
$45$	−1.58071	−	0.912624i	−0.235639	−	0.136046i
$46$	−1.46783	−	3.29680i	−0.216420	−	0.486087i
$47$	−0.543601	−	2.55744i	−0.0792924	−	0.373041i	0.920553	−	0.390617i	$-0.127738\pi$
$47$	−0.543601	−	2.55744i	−0.0792924	−	0.373041i	−0.999846	+	0.0175761i	$0.994405\pi$
$48$	−8.70546	+	2.82857i	−1.25652	+	0.408269i
$49$	5.56351	+	4.24821i	0.794788	+	0.606888i
$50$	−3.72090	−	5.12138i	−0.526215	−	0.724272i
$51$	11.1931	+	10.0783i	1.56735	+	1.41125i
$52$	−0.203095	−	0.225560i	−0.0281642	−	0.0312796i
$53$	−12.2835	+	5.46898i	−1.68727	+	0.751222i	−0.687589	+	0.726101i	$0.741331\pi$
$53$	−12.2835	+	5.46898i	−1.68727	+	0.751222i	−0.999684	+	0.0251218i	$0.992003\pi$
$54$	2.61251	+	4.52499i	0.355517	+	0.615774i
$55$	0.763805	−	1.12189i	0.102991	−	0.151276i
$56$	−6.34832	−	4.72886i	−0.848329	−	0.631920i
$57$	−7.34372	+	10.1078i	−0.972700	+	1.33881i
$58$	−1.43065	+	0.304094i	−0.187854	+	0.0399295i
$59$	−0.435159	+	2.04726i	−0.0566529	+	0.266531i	−0.997353	−	0.0727075i	$-0.976836\pi$
$59$	−0.435159	+	2.04726i	−0.0566529	+	0.266531i	0.940700	+	0.339239i	$0.110169\pi$
$60$	0.0331854	+	0.315738i	0.00428421	+	0.0407616i
$61$	−6.52725	−	2.90612i	−0.835728	−	0.372090i	−0.0561710	−	0.998421i	$-0.517889\pi$
$61$	−6.52725	−	2.90612i	−0.835728	−	0.372090i	−0.779557	+	0.626331i	$0.784556\pi$
$62$	2.74626	+	8.45212i	0.348776	+	1.07342i
$63$	−4.92794	+	10.7228i	−0.620862	+	1.35094i
$64$	7.11169	+	5.16694i	0.888961	+	0.645868i
$65$	0.378699	−	0.218642i	0.0469719	−	0.0271192i
$66$	−10.6881	+	5.15586i	−1.31561	+	0.634642i
$67$	4.12644	−	7.14721i	0.504125	−	0.873170i	−0.495864	−	0.868400i	$-0.665148\pi$
$67$	4.12644	−	7.14721i	0.504125	−	0.873170i	0.999989	−	0.00476980i	$-0.00151828\pi$
$68$	0.163723	−	1.55772i	0.0198544	−	0.188902i
$69$	7.15641	+	2.32526i	0.861530	+	0.279928i
$70$	1.06520	−	0.936383i	0.127316	−	0.111919i
$71$	2.08404	−	1.51414i	0.247330	−	0.179696i	−0.457213	−	0.889357i	$-0.651152\pi$
$71$	2.08404	−	1.51414i	0.247330	−	0.179696i	0.704543	+	0.709662i	$0.251152\pi$
$72$	5.42799	−	12.1915i	0.639694	−	1.43678i
$73$	−9.49087	−	2.01735i	−1.11082	−	0.236113i	−0.384268	−	0.923222i	$-0.625546\pi$
$73$	−9.49087	−	2.01735i	−1.11082	−	0.236113i	−0.726554	+	0.687109i	$0.758879\pi$
$74$	6.53540	−	5.88450i	0.759724	−	0.684059i
$75$	13.1271	+	1.37972i	1.51579	+	0.159316i
$76$	1.29926			0.149036
$77$	−7.67994	−	4.24482i	−0.875211	−	0.483742i
$78$	−3.82334			−0.432908
$79$	2.06452	+	0.216990i	0.232277	+	0.0244133i	0.219952	−	0.975511i	$-0.429410\pi$
$79$	2.06452	+	0.216990i	0.232277	+	0.0244133i	0.0123253	+	0.999924i	$0.496077\pi$
$80$	−1.01914	+	0.917636i	−0.113943	+	0.102595i
$81$	2.43204	+	0.516947i	0.270227	+	0.0574386i
$82$	−4.62580	+	10.3897i	−0.510834	+	1.14735i
$83$	2.94758	−	2.14154i	0.323539	−	0.235065i	−0.414145	−	0.910211i	$-0.635919\pi$
$83$	2.94758	−	2.14154i	0.323539	−	0.235065i	0.737684	+	0.675146i	$0.235919\pi$
$84$	2.01270	−	0.402820i	0.219604	−	0.0439513i
$85$	2.14614	+	0.697322i	0.232781	+	0.0756352i
$86$	−0.665137	+	6.32836i	−0.0717236	+	0.682404i
$87$	1.52484	−	2.64110i	0.163480	−	0.283156i
$88$	8.74148	+	4.69651i	0.931845	+	0.500650i
$89$	2.68261	−	1.54881i	0.284357	−	0.164173i	−0.351037	−	0.936361i	$-0.614171\pi$
$89$	2.68261	−	1.54881i	0.284357	−	0.164173i	0.635394	+	0.772188i	$0.280838\pi$
$90$	1.93434	+	1.40538i	0.203898	+	0.148140i
$91$	−1.63444	−	2.30690i	−0.171336	−	0.241828i
$92$	−0.241808	−	0.744208i	−0.0252102	−	0.0775891i
$93$	−16.9284	−	7.53700i	−1.75539	−	0.781550i
$94$	0.358005	+	3.40619i	0.0369254	+	0.351322i
$95$	−0.389180	+	1.83095i	−0.0399291	+	0.187851i
$96$	−4.25863	+	0.905199i	−0.434644	+	0.0923865i
$97$	−7.81872	+	10.7615i	−0.793870	+	1.09267i	0.199745	+	0.979848i	$0.435989\pi$
$97$	−7.81872	+	10.7615i	−0.793870	+	1.09267i	−0.993615	+	0.112821i	$0.964011\pi$
$98$	−6.66629	−	6.29624i	−0.673397	−	0.636016i
$99$	4.13901	−	14.2025i	0.415987	−	1.42740i
$100$	−0.686317	−	1.18874i	−0.0686317	−	0.118874i
$101$	−3.03490	+	1.35123i	−0.301984	+	0.134452i	−0.552135	−	0.833755i	$-0.686187\pi$
$101$	−3.03490	+	1.35123i	−0.301984	+	0.134452i	0.250151	+	0.968207i	$0.419520\pi$
$102$	−13.2020	−	14.6624i	−1.30720	−	1.45179i
$103$	−2.33864	−	2.10572i	−0.230433	−	0.207483i	0.545823	−	0.837901i	$-0.316217\pi$
$103$	−2.33864	−	2.10572i	−0.230433	−	0.207483i	−0.776256	+	0.630417i	$0.782884\pi$
$104$	1.87926	+	2.58657i	0.184276	+	0.253634i
$105$	−0.0352199	+	2.95700i	−0.00343711	+	0.288574i
$106$	16.7515	−	5.44288i	1.62705	−	0.528660i
$107$	0.195050	+	0.917637i	0.0188562	+	0.0887113i	0.986569	−	0.163342i	$-0.0522274\pi$
$107$	0.195050	+	0.917637i	0.0188562	+	0.0887113i	−0.967713	+	0.252053i	$0.918894\pi$
$108$	0.460814	+	1.03501i	0.0443419	+	0.0995935i
$109$	1.48929	+	0.859845i	0.142649	+	0.0823582i	0.569626	−	0.821904i	$-0.307088\pi$
$109$	1.48929	+	0.859845i	0.142649	+	0.0823582i	−0.426977	+	0.904262i	$0.640422\pi$
$110$	−1.14868	+	1.35699i	−0.109522	+	0.129384i
$111$			18.3368i			1.74045i
$112$	6.51801	+	6.01094i	0.615894	+	0.567980i
$113$	−6.35785	+	19.5674i	−0.598096	+	1.84075i	−0.0594272	+	0.998233i	$0.518927\pi$
$113$	−6.35785	+	19.5674i	−0.598096	+	1.84075i	−0.538669	+	0.842518i	$0.681073\pi$
$114$	10.9512	−	12.1625i	1.02567	−	1.13913i
$115$	1.12119	−	0.117841i	0.104551	−	0.0109888i
$116$	−0.315405	+	0.0331504i	−0.0292846	+	0.00307794i
$117$	3.18925	−	3.54202i	0.294847	−	0.327460i
$118$	0.847238	−	2.60753i	0.0779946	−	0.240043i
$119$	3.20312	−	14.2337i	0.293629	−	1.30480i
$120$		−	3.34419i		−	0.305281i
$121$	10.3037	+	3.85145i	0.936700	+	0.350132i
$122$	8.10558	+	4.67976i	0.733845	+	0.423685i
$123$	−9.64522	−	21.6635i	−0.869681	−	1.95333i
$124$	0.400649	+	1.88490i	0.0359793	+	0.169269i
$125$	3.82671	−	1.24337i	0.342272	−	0.111211i
$126$	7.88821	−	13.2946i	0.702737	−	1.18437i
$127$	7.13829	+	9.82501i	0.633421	+	0.871829i	0.998243	−	0.0592484i	$-0.0188704\pi$
$127$	7.13829	+	9.82501i	0.633421	+	0.871829i	−0.364823	+	0.931077i	$0.618870\pi$
$128$	−6.18827	−	5.57194i	−0.546971	−	0.492495i
$129$	−8.87796	−	9.85997i	−0.781661	−	0.868122i
$130$	−0.523296	+	0.232987i	−0.0458961	+	0.0204343i
$131$	2.29315	+	3.97185i	0.200353	+	0.347022i	0.948642	−	0.316351i	$-0.102458\pi$
$131$	2.29315	+	3.97185i	0.200353	+	0.347022i	−0.748289	+	0.663373i	$0.769124\pi$
$132$	−2.42169	+	0.869587i	−0.210781	+	0.0756879i
$133$	12.0201	+	1.40829i	1.04227	+	0.122114i
$134$	−6.35445	+	8.74615i	−0.548941	+	0.755552i
$135$	−1.59658	+	0.339365i	−0.137412	+	0.0292079i
$136$	−3.43031	+	16.1383i	−0.294147	+	1.38385i
$137$	−0.648715	−	6.17211i	−0.0554235	−	0.527319i	−0.986647	−	0.162871i	$-0.947924\pi$
$137$	−0.648715	−	6.17211i	−0.0554235	−	0.527319i	0.931224	−	0.364448i	$-0.118742\pi$
$138$	−9.00477	−	4.00918i	−0.766537	−	0.341284i
$139$	−6.52005	−	20.0667i	−0.553023	−	1.70203i	−0.701107	−	0.713056i	$-0.747310\pi$
$139$	−6.52005	−	20.0667i	−0.553023	−	1.70203i	0.148083	−	0.988975i	$-0.452690\pi$
$140$	0.250929	−	0.177783i	0.0212074	−	0.0150254i
$141$	−5.77748	−	4.19758i	−0.486551	−	0.353500i
$142$	−2.92235	+	1.68722i	−0.245238	+	0.141588i
$143$	2.45090	+	2.56003i	0.204954	+	0.214081i
$144$	−7.47384	+	12.9451i	−0.622820	+	1.07876i
$145$	0.0477600	−	0.454406i	0.00396625	−	0.0377363i
$146$	12.0882	+	3.92769i	1.00043	+	0.325058i
$147$	19.0570	−	1.54507i	1.57180	−	0.127436i
$148$	1.54270	−	1.12084i	0.126809	−	0.0921322i
$149$	−1.91737	+	4.30649i	−0.157077	+	0.352801i	−0.974891	−	0.222681i	$-0.928519\pi$
$149$	−1.91737	+	4.30649i	−0.157077	+	0.352801i	0.817814	+	0.575482i	$0.195186\pi$
$150$	−16.9127	−	3.59491i	−1.38092	−	0.293523i
$151$	−8.74582	+	7.87478i	−0.711725	+	0.640840i	−0.943286	−	0.331980i	$-0.892283\pi$
$151$	−8.74582	+	7.87478i	−0.711725	+	0.640840i	0.231561	+	0.972820i	$0.425617\pi$
$152$	−13.6110	−	1.43057i	−1.10400	−	0.116035i
$153$	24.5961			1.98847
$154$	9.42397	+	6.58161i	0.759406	+	0.530362i
$155$	−2.77626			−0.222994
$156$	−0.824485	−	0.0866568i	−0.0660116	−	0.00693810i
$157$	14.5794	−	13.1274i	1.16356	−	1.04768i	0.165455	−	0.986217i	$-0.447091\pi$
$157$	14.5794	−	13.1274i	1.16356	−	1.04768i	0.998109	−	0.0614611i	$-0.0195760\pi$
$158$	−2.65989	−	0.565377i	−0.211610	−	0.0449790i
$159$	−14.9378	+	33.5508i	−1.18464	+	2.66075i
$160$	−0.527713	+	0.383406i	−0.0417193	+	0.0303109i
$161$	−1.43042	−	7.14710i	−0.112732	−	0.563271i
$162$	−3.09761	−	1.00648i	−0.243371	−	0.0790762i
$163$	−0.718293	+	6.83411i	−0.0562611	+	0.535288i	0.929701	+	0.368316i	$0.120066\pi$
$163$	−0.718293	+	6.83411i	−0.0562611	+	0.535288i	−0.985962	+	0.166972i	$0.946601\pi$
$164$	−1.23302	+	2.13565i	−0.0962824	+	0.166766i
$165$	−0.500049	−	3.67318i	−0.0389288	−	0.285957i
$166$	−4.13326	+	2.38634i	−0.320803	+	0.185216i
$167$	−4.27089	−	3.10299i	−0.330492	−	0.240116i	0.410147	−	0.912019i	$-0.365477\pi$
$167$	−4.27089	−	3.10299i	−0.330492	−	0.240116i	−0.740639	+	0.671903i	$0.765477\pi$
$168$	−21.5284	+	2.00380i	−1.66096	+	0.154597i
$169$	−3.66436	−	11.2777i	−0.281874	−	0.867519i
$170$	−2.70044	−	1.20231i	−0.207115	−	0.0922133i
$171$	2.13266	+	20.2909i	0.163088	+	1.55168i
$172$	−0.286867	+	1.34960i	−0.0218734	+	0.102906i
$173$	21.8227	−	4.63855i	1.65915	−	0.352662i	0.719416	−	0.694580i	$-0.244410\pi$
$173$	21.8227	−	4.63855i	1.65915	−	0.352662i	0.939730	+	0.341917i	$0.111076\pi$
$174$	−2.34816	+	3.23196i	−0.178013	+	0.245014i
$175$	−5.06093	−	11.7414i	−0.382571	−	0.887569i
$176$	−9.18764	−	6.25510i	−0.692545	−	0.471496i
$177$	2.85837	+	4.95084i	0.214848	+	0.372128i
$178$	−3.70690	+	1.65042i	−0.277844	+	0.123704i
$179$	0.136709	+	0.151830i	0.0102181	+	0.0113483i	0.748232	−	0.663437i	$-0.230903\pi$
$179$	0.136709	+	0.151830i	0.0102181	+	0.0113483i	−0.738014	+	0.674785i	$0.764236\pi$
$180$	0.385278	+	0.346906i	0.0287169	+	0.0258568i
$181$	−4.21629	−	5.80323i	−0.313394	−	0.431350i	0.623042	−	0.782189i	$-0.285897\pi$
$181$	−4.21629	−	5.80323i	−0.313394	−	0.431350i	−0.936436	+	0.350838i	$0.885897\pi$
$182$	1.81342	+	3.22915i	0.134420	+	0.239361i
$183$	−18.5603	+	6.03061i	−1.37202	+	0.445796i
$184$	1.71374	+	8.06252i	0.126339	+	0.594377i
$185$	1.11741	+	2.50974i	0.0821535	+	0.184520i
$186$	21.0218	+	12.1369i	1.54139	+	0.889923i
$187$	−1.35464	+	18.2389i	−0.0990614	+	1.33376i
$188$			0.742643i			0.0541628i
$189$	3.14134	+	10.0748i	0.228499	+	0.732833i
$190$	0.757719	−	2.33202i	0.0549707	−	0.169182i
$191$	13.2479	−	14.7133i	0.958584	−	1.06462i	−0.0392758	−	0.999228i	$-0.512505\pi$
$191$	13.2479	−	14.7133i	0.958584	−	1.06462i	0.997860	−	0.0653872i	$-0.0208282\pi$
$192$	23.8786	−	2.50974i	1.72329	−	0.181125i
$193$	0.579189	−	0.0608752i	0.0416909	−	0.00438189i	−0.0836600	−	0.996494i	$-0.526661\pi$
$193$	0.579189	−	0.0608752i	0.0416909	−	0.00438189i	0.125351	+	0.992112i	$0.459994\pi$
$194$	11.6595	−	12.9492i	0.837106	−	0.929700i
$195$	0.369084	−	1.13592i	0.0264307	−	0.0813453i
$196$	−1.29485	−	1.50885i	−0.0924891	−	0.107775i
$197$			6.08149i			0.433289i	0.976251	+	0.216644i	$0.0695112\pi$
$197$			6.08149i			0.433289i	−0.976251	+	0.216644i	$0.930489\pi$
$198$	−7.33688	+	17.9358i	−0.521410	+	1.27464i
$199$	−8.92066	−	5.15035i	−0.632369	−	0.365098i	0.149300	−	0.988792i	$-0.452298\pi$
$199$	−8.92066	−	5.15035i	−0.632369	−	0.365098i	−0.781669	+	0.623694i	$0.785631\pi$
$200$	5.88093	+	13.2088i	0.415845	+	0.934002i
$201$	−4.68667	−	22.0490i	−0.330572	−	1.55522i
$202$	4.13880	−	1.34478i	0.291205	−	0.0946182i
$203$	−2.95389	−	0.0351828i	−0.207322	−	0.00246935i
$204$	−2.51463	−	3.46109i	−0.176059	−	0.242325i
$205$	−2.64026	−	2.37730i	−0.184404	−	0.166038i
$206$	2.75839	+	3.06350i	0.192186	+	0.213444i
$207$	11.2255	−	4.99794i	0.780229	−	0.347381i
$208$	−1.79055	−	3.10132i	−0.124152	−	0.215038i
$209$	−15.1639	+	0.463913i	−1.04891	+	0.0320895i
$210$	0.450776	−	3.84747i	0.0311065	−	0.265501i
$211$	10.3959	−	14.3088i	0.715685	−	0.985056i	−0.283971	−	0.958833i	$-0.591652\pi$
$211$	10.3959	−	14.3088i	0.715685	−	0.985056i	0.999656	−	0.0262235i	$-0.00834816\pi$
$212$	3.73574	−	0.794056i	0.256572	−	0.0545360i
$213$	1.46287	−	6.88227i	0.100234	−	0.471566i
$214$	−0.128456	−	1.22218i	−0.00878108	−	0.0835464i
$215$	−1.81596	−	0.808519i	−0.123848	−	0.0551405i
$216$	−3.68785	−	11.3500i	−0.250926	−	0.772272i
$217$	1.66351	+	17.8724i	0.112926	+	1.21325i
$218$	−1.82247	−	1.32410i	−0.123433	−	0.0896797i
$219$	−22.9515	+	13.2511i	−1.55092	+	0.895424i
$220$	−0.278464	+	0.266592i	−0.0187740	+	0.0179737i
$221$	−2.94630	+	5.10315i	−0.198190	+	0.343275i
$222$	2.51080	−	23.8887i	0.168514	−	1.60330i
$223$	−18.7534	−	6.09334i	−1.25582	−	0.408040i	−0.395816	−	0.918330i	$-0.629538\pi$
$223$	−18.7534	−	6.09334i	−1.25582	−	0.408040i	−0.860002	+	0.510290i	$0.829538\pi$
$224$	2.78440	+	3.16746i	0.186041	+	0.211634i
$225$	17.4382	−	12.6696i	1.16255	−	0.844639i
$226$	10.9621	−	24.6213i	0.729190	−	1.63779i
$227$	−6.83724	−	1.45330i	−0.453804	−	0.0964590i	−0.0246615	−	0.999696i	$-0.507851\pi$
$227$	−6.83724	−	1.45330i	−0.453804	−	0.0964590i	−0.429142	+	0.903237i	$0.641184\pi$
$228$	2.63724	−	2.37458i	0.174656	−	0.157261i
$229$	−0.241522	−	0.0253850i	−0.0159602	−	0.00167749i	0.0965450	−	0.995329i	$-0.469221\pi$
$229$	−0.241522	−	0.0253850i	−0.0159602	−	0.00167749i	−0.112505	+	0.993651i	$0.535888\pi$
$230$	−1.47678			−0.0973762
$231$	−23.3467	+	5.42003i	−1.53610	+	0.356612i
$232$	3.34066			0.219325
$233$	18.9025	+	1.98674i	1.23835	+	0.130155i	0.700972	−	0.713189i	$-0.252750\pi$
$233$	18.9025	+	1.98674i	1.23835	+	0.130155i	0.537374	+	0.843344i	$0.319416\pi$
$234$	−4.63986	+	4.17775i	−0.303317	+	0.273108i
$235$	−1.04655	−	0.222451i	−0.0682693	−	0.0145111i
$236$	0.241803	−	0.543098i	0.0157400	−	0.0353527i
$237$	4.58715	−	3.33276i	0.297967	−	0.216486i
$238$	−6.12191	+	18.1047i	−0.396824	+	1.17355i
$239$	3.90942	+	1.27025i	0.252879	+	0.0821655i	0.432714	−	0.901531i	$-0.357556\pi$
$239$	3.90942	+	1.27025i	0.252879	+	0.0821655i	−0.179834	+	0.983697i	$0.557556\pi$
$240$	−0.391538	+	3.72523i	−0.0252737	+	0.240463i
$241$	3.94226	−	6.82819i	0.253943	−	0.439843i	−0.710665	−	0.703531i	$-0.751606\pi$
$241$	3.94226	−	6.82819i	0.253943	−	0.439843i	0.964608	+	0.263688i	$0.0849390\pi$
$242$	−12.8960	−	6.42841i	−0.828986	−	0.413234i
$243$	16.2444	−	9.37868i	1.04208	−	0.601643i
$244$	1.64186	+	1.19288i	0.105109	+	0.0763664i
$245$	2.51416	−	1.37277i	0.160624	−	0.0877029i
$246$	9.59920	+	29.5433i	0.612023	+	1.88361i
$247$	−4.46538	−	1.98811i	−0.284125	−	0.126501i
$248$	−2.12177	−	20.1873i	−0.134732	−	1.28189i
$249$	2.06903	−	9.73402i	0.131119	−	0.616868i
$250$	−5.15558	+	1.09585i	−0.326068	+	0.0693078i
$251$	−3.43900	+	4.73338i	−0.217068	+	0.298768i	−0.903639	−	0.428294i	$-0.859115\pi$
$251$	−3.43900	+	4.73338i	−0.217068	+	0.298768i	0.686572	+	0.727062i	$0.259115\pi$
$252$	2.00238	−	2.68812i	0.126138	−	0.169336i
$253$	3.08791	+	8.59944i	0.194135	+	0.540642i
$254$	−7.95425	−	13.7772i	−0.499094	−	0.864456i
$255$	5.63068	−	2.50694i	0.352607	−	0.156991i
$256$	−4.46507	−	4.95897i	−0.279067	−	0.309935i
$257$	−5.72828	−	5.15777i	−0.357320	−	0.321733i	0.470846	−	0.882216i	$-0.343949\pi$
$257$	−5.72828	−	5.15777i	−0.357320	−	0.321733i	−0.828166	+	0.560483i	$0.810616\pi$
$258$	10.2159	+	14.0609i	0.636011	+	0.875394i
$259$	15.4871	−	8.69721i	0.962321	−	0.540418i
$260$	−0.118127	+	0.0383818i	−0.00732592	+	0.00238034i
$261$	−1.03543	−	4.87134i	−0.0640918	−	0.301528i
$262$	−2.44360	−	5.48840i	−0.150966	−	0.339075i
$263$	0.794994	+	0.458990i	0.0490215	+	0.0283026i	0.524310	−	0.851527i	$-0.324323\pi$
$263$	0.794994	+	0.458990i	0.0490215	+	0.0283026i	−0.475289	+	0.879830i	$0.657656\pi$
$264$	26.3270	−	6.44330i	1.62031	−	0.396557i
$265$			5.50233i			0.338006i
$266$	−15.4665	−	3.48055i	−0.948315	−	0.213406i
$267$	2.61450	−	8.04662i	0.160005	−	0.492445i
$268$	−1.56854	+	1.74204i	−0.0958138	+	0.106412i
$269$	14.8263	−	1.55830i	0.903973	−	0.0950114i	0.358877	−	0.933385i	$-0.383160\pi$
$269$	14.8263	−	1.55830i	0.903973	−	0.0950114i	0.545096	+	0.838373i	$0.316493\pi$
$270$	2.12645	−	0.223499i	0.129412	−	0.0136017i
$271$	4.51235	−	5.01147i	0.274106	−	0.304425i	−0.590337	−	0.807157i	$-0.701005\pi$
$271$	4.51235	−	5.01147i	0.274106	−	0.304425i	0.864442	+	0.502732i	$0.167672\pi$
$272$	5.71065	−	17.5756i	0.346259	−	1.06568i
$273$	−7.53375	−	1.69537i	−0.455963	−	0.102609i
$274$			8.12967i			0.491132i
$275$	8.43456	+	13.6289i	0.508623	+	0.821852i
$276$	−1.85096	−	1.06865i	−0.111415	−	0.0643255i
$277$	7.85714	+	17.6474i	0.472090	+	1.06033i	0.980014	+	0.198930i	$0.0637465\pi$
$277$	7.85714	+	17.6474i	0.472090	+	1.06033i	−0.507924	+	0.861402i	$0.669587\pi$
$278$	5.74647	+	27.0350i	0.344650	+	1.62145i
$279$	−28.7793	+	9.35096i	−1.72297	+	0.559827i
$280$	−2.82447	+	1.58616i	−0.168794	+	0.0947910i
$281$	3.12109	+	4.29582i	0.186189	+	0.256267i	0.891900	−	0.452233i	$-0.149372\pi$
$281$	3.12109	+	4.29582i	0.186189	+	0.256267i	−0.705711	+	0.708500i	$0.749372\pi$
$282$	6.95197	+	6.25958i	0.413984	+	0.372753i
$283$	−8.03602	−	8.92491i	−0.477692	−	0.530531i	0.455343	−	0.890316i	$-0.349517\pi$
$283$	−8.03602	−	8.92491i	−0.477692	−	0.530531i	−0.933035	+	0.359785i	$0.882850\pi$
$284$	−0.668432	+	0.297605i	−0.0396641	+	0.0176596i
$285$	2.55636	+	4.42774i	0.151425	+	0.262277i
$286$	−2.84242	−	3.67073i	−0.168076	−	0.217055i
$287$	−13.7220	+	18.4213i	−0.809986	+	1.08738i
$288$	−4.17900	+	5.75191i	−0.246250	+	0.338934i
$289$	−13.1155	+	2.78778i	−0.771498	+	0.163987i
$290$	−0.124441	+	0.585447i	−0.00730740	+	0.0343786i
$291$	3.79779	+	36.1335i	0.222630	+	2.11819i
$292$	2.51774	+	1.12097i	0.147339	+	0.0655998i
$293$	5.58180	+	17.1790i	0.326092	+	1.00361i	0.970945	+	0.239302i	$0.0769186\pi$
$293$	5.58180	+	17.1790i	0.326092	+	1.00361i	−0.644853	+	0.764307i	$0.723081\pi$
$294$	−25.0385	−	0.596536i	−1.46027	−	0.0347907i
$295$	0.692916	+	0.503433i	0.0403432	+	0.0293110i
$296$	−17.3953	+	10.0432i	−1.01108	+	0.583749i
$297$	−5.74780	−	11.9152i	−0.333521	−	0.691389i
$298$	3.08757	−	5.34783i	0.178858	−	0.309791i
$299$	−0.307719	+	2.92775i	−0.0177958	+	0.169316i
$300$	−3.56566	−	1.15855i	−0.205864	−	0.0668891i
$301$	−4.11679	+	12.1748i	−0.237288	+	0.701746i
$302$	12.4721	−	9.06149i	0.717687	−	0.521430i
$303$	−3.69069	+	8.28942i	−0.212024	+	0.476215i
$304$	14.9944	+	3.18715i	0.859986	+	0.182796i
$305$	−2.17284	+	1.95643i	−0.124416	+	0.112025i
$306$	−32.0430	−	3.36786i	−1.83178	−	0.192528i
$307$	−3.39611			−0.193826			−0.0969132	−	0.995293i	$-0.530897\pi$
$307$	−3.39611			−0.193826			−0.0969132	+	0.995293i	$0.530897\pi$
$308$	1.88306	+	1.63289i	0.107297	+	0.0930425i
$309$	−8.59548			−0.488980
$310$	3.61683	+	0.380144i	0.205422	+	0.0215907i
$311$	−13.8138	+	12.4380i	−0.783310	+	0.705296i	−0.960316	−	0.278914i	$-0.910026\pi$
$311$	−13.8138	+	12.4380i	−0.783310	+	0.705296i	0.177006	+	0.984210i	$0.443359\pi$
$312$	8.54183	+	1.81562i	0.483586	+	0.102789i
$313$	−1.38286	+	3.10595i	−0.0781638	+	0.175559i	−0.948400	−	0.317075i	$-0.897299\pi$
$313$	−1.38286	+	3.10595i	−0.0781638	+	0.175559i	0.870237	+	0.492634i	$0.163966\pi$
$314$	−20.7911	+	15.1056i	−1.17331	+	0.852461i
$315$	3.18836	+	3.62699i	0.179644	+	0.204358i
$316$	−0.560778	−	0.182208i	−0.0315462	−	0.0102500i
$317$	2.56878	−	24.4403i	0.144277	−	1.37271i	−0.647579	−	0.761998i	$-0.724218\pi$
$317$	2.56878	−	24.4403i	0.144277	−	1.37271i	0.791856	−	0.610708i	$-0.209115\pi$
$318$	24.0545	−	41.6636i	1.34891	−	2.33638i
$319$	3.66931	−	0.499522i	0.205442	−	0.0279679i
$320$	3.11530	−	1.79862i	0.174150	−	0.100546i
$321$	2.07302	+	1.50614i	0.115705	+	0.0840644i
$322$	0.884874	+	9.50690i	0.0493121	+	0.529799i
$323$	−7.79467	−	23.9895i	−0.433707	−	1.33481i
$324$	−0.645173	−	0.287250i	−0.0358430	−	0.0159583i
$325$	0.539784	+	5.13570i	0.0299418	+	0.284878i
$326$	1.87154	−	8.80492i	0.103655	−	0.487659i
$327$	4.59445	−	0.976581i	0.254074	−	0.0540050i
$328$	15.2685	−	21.0153i	0.843060	−	1.16037i
$329$	−0.804962	+	6.87052i	−0.0443790	+	0.378784i
$330$	0.148493	+	4.85378i	0.00817425	+	0.267192i
$331$	−10.6784	−	18.4956i	−0.586940	−	1.01661i	−0.994631	−	0.103489i	$-0.966999\pi$
$331$	−10.6784	−	18.4956i	−0.586940	−	1.01661i	0.407691	−	0.913120i	$-0.366334\pi$
$332$	−0.945404	+	0.420921i	−0.0518858	+	0.0231010i
$333$	20.0366	+	22.2529i	1.09800	+	1.21945i
$334$	5.13911	+	4.62728i	0.281200	+	0.253193i
$335$	−1.98508	−	2.73223i	−0.108457	−	0.149278i
$336$	24.2161	+	0.288430i	1.32109	+	0.0157352i
$337$	−14.0759	+	4.57352i	−0.766761	+	0.249136i	−0.666178	−	0.745793i	$-0.732071\pi$
$337$	−14.0759	+	4.57352i	−0.766761	+	0.249136i	−0.100583	+	0.994929i	$0.532071\pi$
$338$	3.22960	+	15.1941i	0.175667	+	0.826448i
$339$	22.8571	+	51.3378i	1.24143	+	2.78829i
$340$	−0.555087	−	0.320479i	−0.0301038	−	0.0173804i
$341$	−5.34906	−	21.8560i	−0.289668	−	1.18357i
$342$		−	26.7264i		−	1.44520i
$343$	−10.3437	−	15.3625i	−0.558510	−	0.829498i
$344$	4.49120	−	13.8225i	0.242149	−	0.745259i
$345$	2.06041	−	2.28832i	0.110929	−	0.123199i
$346$	−29.0651	+	3.05486i	−1.56255	+	0.164230i
$347$	0.0350743	−	0.00368645i	0.00188289	−	0.000197899i	−0.103587	−	0.994620i	$-0.533032\pi$
$347$	0.0350743	−	0.00368645i	0.00188289	−	0.000197899i	0.105470	+	0.994423i	$0.466365\pi$
$348$	−0.579622	+	0.643735i	−0.0310710	+	0.0345078i
$349$	2.04800	−	6.30311i	0.109627	−	0.337398i	−0.881161	−	0.472816i	$-0.843238\pi$
$349$	2.04800	−	6.30311i	0.109627	−	0.337398i	0.990789	+	0.135418i	$0.0432377\pi$
$350$	4.98552	+	15.9894i	0.266487	+	0.854668i
$351$		−	4.26230i		−	0.227505i
$352$	−4.03510	−	3.41568i	−0.215071	−	0.182056i
$353$	14.5072	+	8.37574i	0.772140	+	0.445795i	0.833638	−	0.552312i	$-0.186254\pi$
$353$	14.5072	+	8.37574i	0.772140	+	0.445795i	−0.0614973	+	0.998107i	$0.519588\pi$
$354$	−3.04590	−	6.84120i	−0.161888	−	0.363606i
$355$	−0.219170	−	1.03111i	−0.0116323	−	0.0547258i
$356$	−0.836783	+	0.271887i	−0.0443494	+	0.0144100i
$357$	−19.5124	−	34.7458i	−1.03271	−	1.83894i
$358$	−0.157310	−	0.216519i	−0.00831411	−	0.0114434i
$359$	8.45862	+	7.61618i	0.446429	+	0.401966i	0.861448	−	0.507846i	$-0.169558\pi$
$359$	8.45862	+	7.61618i	0.446429	+	0.401966i	−0.415019	+	0.909813i	$0.636225\pi$
$360$	−3.65418	−	4.05838i	−0.192592	−	0.213895i
$361$	1.75729	−	0.782394i	0.0924887	−	0.0411786i
$362$	4.69824	+	8.13759i	0.246934	+	0.427702i
$363$	27.9535	−	11.0138i	1.46718	−	0.578074i
$364$	0.317866	+	0.737453i	0.0166607	+	0.0386530i
$365$	−2.33386	+	3.21228i	−0.122160	+	0.168138i
$366$	25.0056	−	5.31510i	1.30706	−	0.277825i
$367$	−2.46356	+	11.5901i	−0.128597	+	0.605000i	0.865899	+	0.500219i	$0.166747\pi$
$367$	−2.46356	+	11.5901i	−0.128597	+	0.605000i	−0.994495	+	0.104780i	$0.966586\pi$
$368$	−0.965050	−	9.18183i	−0.0503067	−	0.478636i
$369$	−35.3768	−	15.7507i	−1.84164	−	0.819951i
$370$	−1.11208	−	3.42262i	−0.0578141	−	0.177934i
$371$	35.4217	−	3.29694i	1.83900	−	0.171169i
$372$	4.25816	+	3.09373i	0.220775	+	0.160403i
$373$	11.1676	−	6.44764i	0.578239	−	0.333846i	−0.182194	−	0.983263i	$-0.558320\pi$
$373$	11.1676	−	6.44764i	0.578239	−	0.333846i	0.760433	+	0.649416i	$0.224987\pi$
$374$	4.26219	−	23.5756i	0.220392	−	1.21907i
$375$	5.49502	−	9.51765i	0.283761	−	0.491489i
$376$	0.817698	−	7.77988i	0.0421696	−	0.401217i
$377$	1.13473	+	0.368696i	0.0584415	+	0.0189888i
$378$	−2.71294	−	13.5553i	−0.139539	−	0.697208i
$379$	−2.23429	+	1.62331i	−0.114768	+	0.0833838i	−0.643689	−	0.765287i	$-0.722597\pi$
$379$	−2.23429	+	1.62331i	−0.114768	+	0.0833838i	0.528921	+	0.848671i	$0.322597\pi$
$380$	0.216254	−	0.485714i	0.0110936	−	0.0249166i
$381$	32.4458	+	6.89658i	1.66225	+	0.353322i
$382$	−19.2736	+	17.3540i	−0.986124	+	0.887910i
$383$	7.09331	+	0.745537i	0.362451	+	0.0380952i	0.284004	−	0.958823i	$-0.408337\pi$
$383$	7.09331	+	0.745537i	0.362451	+	0.0380952i	0.0784474	+	0.996918i	$0.475004\pi$
$384$	−22.7444			−1.16067
$385$	−2.86515	+	2.16454i	−0.146022	+	0.110315i
$386$	−0.762886			−0.0388299
$387$	−21.5479	−	2.26478i	−1.09534	−	0.115125i
$388$	2.80782	−	2.52817i	0.142545	−	0.128348i
$389$	−3.08345	−	0.655408i	−0.156337	−	0.0332305i	0.129078	−	0.991634i	$-0.458798\pi$
$389$	−3.08345	−	0.655408i	−0.156337	−	0.0332305i	−0.285415	+	0.958404i	$0.592132\pi$
$390$	−0.636371	+	1.42931i	−0.0322239	+	0.0723760i
$391$	−12.2903	+	8.92946i	−0.621550	+	0.451582i
$392$	11.9034	+	17.2323i	0.601212	+	0.870362i
$393$	11.9137	+	3.87101i	0.600969	+	0.195267i
$394$	0.832719	−	7.92279i	0.0419518	−	0.399145i
$395$	0.424746	−	0.735682i	0.0213713	−	0.0370162i
$396$	−1.98868	+	3.70148i	−0.0999350	+	0.186006i
$397$	−17.9916	+	10.3874i	−0.902971	+	0.521330i	−0.878163	−	0.478362i	$-0.841231\pi$
$397$	−17.9916	+	10.3874i	−0.902971	+	0.521330i	−0.0248080	+	0.999692i	$0.507897\pi$
$398$	10.9164	+	7.93120i	0.547188	+	0.397555i
$399$	26.9721	−	19.1098i	1.35030	−	0.956686i
$400$	−5.00454	−	15.4024i	−0.250227	−	0.770119i
$401$	−23.2005	−	10.3295i	−1.15858	−	0.515831i	−0.264781	−	0.964309i	$-0.585300\pi$
$401$	−23.2005	−	10.3295i	−1.15858	−	0.515831i	−0.893794	+	0.448478i	$0.851966\pi$
$402$	3.08655	+	29.3666i	0.153943	+	1.46467i
$403$	1.50728	−	7.09121i	0.0750831	−	0.353238i
$404$	0.922992	−	0.196188i	0.0459206	−	0.00976072i
$405$	0.598053	−	0.823149i	0.0297175	−	0.0409026i
$406$	3.84342	+	0.450301i	0.190746	+	0.0223481i
$407$	−17.6049	+	13.6323i	−0.872643	+	0.675729i
$408$	22.5322	+	39.0269i	1.11551	+	1.93212i
$409$	−27.2779	+	12.1449i	−1.34881	+	0.600527i	−0.948769	−	0.315971i	$-0.897670\pi$
$409$	−27.2779	+	12.1449i	−1.34881	+	0.600527i	−0.400038	+	0.916499i	$0.631003\pi$
$410$	3.11414	+	3.45860i	0.153796	+	0.170808i
$411$	−12.5971	−	11.3425i	−0.621372	−	0.559485i
$412$	0.525398	+	0.723148i	0.0258845	+	0.0356269i
$413$	2.82570	−	4.76235i	0.139044	−	0.234340i
$414$	−15.3087	+	4.97409i	−0.752380	+	0.244463i
$415$	−0.309985	−	1.45837i	−0.0152166	−	0.0715884i
$416$	−0.692802	−	1.55606i	−0.0339674	−	0.0762921i
$417$	−49.9090	−	28.8150i	−2.44405	−	1.41107i
$418$	19.8186	+	1.47197i	0.969361	+	0.0719965i
$419$			3.03794i			0.148413i	0.997243	+	0.0742066i	$0.0236424\pi$
$419$			3.03794i			0.148413i	−0.997243	+	0.0742066i	$0.976358\pi$
$420$	0.184411	−	0.819471i	0.00899835	−	0.0399861i
$421$	6.95131	−	21.3939i	0.338786	−	1.04268i	−0.626041	−	0.779791i	$-0.715326\pi$
$421$	6.95131	−	21.3939i	0.338786	−	1.04268i	0.964827	−	0.262886i	$-0.0846744\pi$
$422$	−15.5028	+	17.2176i	−0.754663	+	0.838138i
$423$	−11.5980	+	1.21900i	−0.563915	+	0.0592699i
$424$	−40.0096	+	4.20518i	−1.94304	+	0.204222i
$425$	−17.8313	+	19.8037i	−0.864947	+	0.960621i
$426$	−2.84815	+	8.76572i	−0.137994	+	0.424700i
$427$	13.8966	+	12.8155i	0.672504	+	0.620186i
$428$		−	0.266468i		−	0.0128802i
$429$	9.65364	+	0.716997i	0.466082	+	0.0346169i
$430$	2.25508	+	1.30197i	0.108749	+	0.0627865i
$431$	9.27299	+	20.8275i	0.446664	+	1.00322i	0.986844	+	0.161675i	$0.0516896\pi$
$431$	9.27299	+	20.8275i	0.446664	+	1.00322i	−0.540180	+	0.841550i	$0.681644\pi$
$432$	2.77919	+	13.0751i	0.133714	+	0.629075i
$433$	31.3066	−	10.1721i	1.50450	−	0.488841i	0.563171	−	0.826340i	$-0.309581\pi$
$433$	31.3066	−	10.1721i	1.50450	−	0.488841i	0.941326	+	0.337499i	$0.109581\pi$
$434$	0.280037	−	23.5114i	0.0134422	−	1.12858i
$435$	−0.733546	−	1.00964i	−0.0351708	−	0.0484085i
$436$	−0.362996	−	0.326843i	−0.0173844	−	0.0156530i
$437$	−8.43215	−	9.36485i	−0.403364	−	0.447981i
$438$	31.7150	−	14.1204i	1.51540	−	0.674700i
$439$	16.7589	+	29.0272i	0.799858	+	1.38539i	0.919708	+	0.392602i	$0.128425\pi$
$439$	16.7589	+	29.0272i	0.799858	+	1.38539i	−0.119851	+	0.992792i	$0.538242\pi$
$440$	3.21070	−	2.48620i	0.153064	−	0.118525i
$441$	21.4386	−	22.6986i	1.02088	−	1.08088i
$442$	4.53711	−	6.24480i	0.215808	−	0.297035i
$443$	−0.458647	+	0.0974883i	−0.0217910	+	0.00463181i	−0.218794	−	0.975771i	$-0.570212\pi$
$443$	−0.458647	+	0.0974883i	−0.0217910	+	0.00463181i	0.197003	+	0.980403i	$0.436879\pi$
$444$	1.08288	−	5.09457i	0.0513914	−	0.241778i
$445$	−0.132500	−	1.26065i	−0.00628111	−	0.0597607i
$446$	23.5970	+	10.5061i	1.11735	+	0.497476i
$447$	3.97882	+	12.2456i	0.188192	+	0.579195i
$448$	−13.4454	−	18.9772i	−0.635235	−	0.896590i
$449$	−11.5034	−	8.35769i	−0.542878	−	0.394424i	0.282275	−	0.959334i	$-0.408911\pi$
$449$	−11.5034	−	8.35769i	−0.542878	−	0.394424i	−0.825153	+	0.564910i	$0.808911\pi$
$450$	−24.4528	+	14.1178i	−1.15271	+	0.665520i
$451$	13.6282	−	25.3657i	0.641726	−	1.19443i
$452$	2.92198	−	5.06101i	0.137438	−	0.238050i
$453$	−3.36001	+	31.9684i	−0.157867	+	1.50201i
$454$	8.70837	+	2.82952i	0.408704	+	0.132796i
$455$	−1.13445	+	0.227047i	−0.0531837	+	0.0106441i
$456$	−30.2421	+	21.9722i	−1.41622	+	1.02894i
$457$	6.38207	−	14.3344i	0.298541	−	0.670534i	−0.700530	−	0.713623i	$-0.747053\pi$
$457$	6.38207	−	14.3344i	0.298541	−	0.670534i	0.999071	+	0.0430889i	$0.0137199\pi$
$458$	0.311172	+	0.0661416i	0.0145401	+	0.00309060i
$459$	16.3457	−	14.7178i	0.762954	−	0.686967i
$460$	−0.318461	−	0.0334716i	−0.0148483	−	0.00156062i
$461$	25.8384			1.20342			0.601708	−	0.798717i	$-0.294487\pi$
$461$	25.8384			1.20342			0.601708	+	0.798717i	$0.294487\pi$
$462$	31.1576	−	3.86427i	1.44958	−	0.179782i
$463$	25.2824			1.17497			0.587486	−	0.809234i	$-0.300118\pi$
$463$	25.2824			1.17497			0.587486	+	0.809234i	$0.300118\pi$
$464$	−3.72131	−	0.391125i	−0.172757	−	0.0181575i
$465$	−5.63524	+	5.07399i	−0.261328	+	0.235301i
$466$	−24.3536	−	5.17652i	−1.12816	−	0.239798i
$467$	7.12608	−	16.0054i	0.329756	−	0.740643i	−0.670243	−	0.742141i	$-0.733810\pi$
$467$	7.12608	−	16.0054i	0.329756	−	0.740643i	0.999999	+	0.00149824i	$0.000476906\pi$
$468$	−1.09525	+	0.795748i	−0.0506281	+	0.0367835i
$469$	−16.3995	+	14.4162i	−0.757258	+	0.665679i
$470$	1.33295	+	0.433103i	0.0614846	+	0.0199776i
$471$	5.60120	−	53.2918i	0.258090	−	2.45556i
$472$	−3.13110	+	5.42322i	−0.144120	+	0.249624i
$473$	2.86619	−	15.8539i	0.131787	−	0.728962i
$474$	−6.43235	+	3.71372i	−0.295447	+	0.170577i
$475$	−17.8834	−	12.9931i	−0.820549	−	0.596164i
$476$	−1.73051	+	3.76544i	−0.0793176	+	0.172589i
$477$	18.5329	+	57.0384i	0.848564	+	2.61161i
$478$	−4.91915	−	2.19015i	−0.224997	−	0.100175i
$479$	−2.14014	−	20.3621i	−0.0977856	−	0.930368i	−0.927914	−	0.372795i	$-0.878399\pi$
$479$	−2.14014	−	20.3621i	−0.0977856	−	0.930368i	0.830128	−	0.557573i	$-0.188267\pi$
$480$	−0.370423	+	1.74270i	−0.0169074	+	0.0795432i
$481$	−7.01713	+	1.49154i	−0.319953	+	0.0680082i
$482$	−6.07082	+	8.35577i	−0.276518	+	0.380595i
$483$	−15.9658	−	11.8929i	−0.726468	−	0.541145i
$484$	−2.63526	−	1.67855i	−0.119784	−	0.0762975i
$485$	2.72170	+	4.71413i	0.123586	+	0.214057i
$486$	−22.4469	+	9.99399i	−1.01821	+	0.453336i
$487$	17.0252	+	18.9084i	0.771486	+	0.856822i	0.992973	−	0.118342i	$-0.0377578\pi$
$487$	17.0252	+	18.9084i	0.771486	+	0.856822i	−0.221487	+	0.975163i	$0.571091\pi$
$488$	−15.8866	−	14.3043i	−0.719152	−	0.647527i
$489$	11.0323	+	15.1846i	0.498897	+	0.686673i
$490$	−3.46334	+	1.44415i	−0.156458	+	0.0652399i
$491$	2.00866	−	0.652654i	0.0906497	−	0.0294539i	−0.263341	−	0.964703i	$-0.584824\pi$
$491$	2.00866	−	0.652654i	0.0906497	−	0.0294539i	0.353991	+	0.935249i	$0.384824\pi$
$492$	1.40042	+	6.58844i	0.0631356	+	0.297030i
$493$	2.50430	+	5.62475i	0.112788	+	0.253326i
$494$	5.54514	+	3.20149i	0.249488	+	0.144042i
$495$	−4.62051	−	3.91123i	−0.207677	−	0.175797i
$496$			22.7359i			1.02087i
$497$	−6.50654	+	2.02875i	−0.291858	+	0.0910021i
$498$	−4.02832	+	12.3979i	−0.180513	+	0.555563i
$499$	−6.25015	+	6.94149i	−0.279795	+	0.310744i	−0.866619	−	0.498971i	$-0.833711\pi$
$499$	−6.25015	+	6.94149i	−0.279795	+	0.310744i	0.586824	+	0.809715i	$0.300378\pi$
$500$	−1.13661	+	0.119463i	−0.0508309	+	0.00534254i
$501$	−14.3402	+	1.50721i	−0.640672	+	0.0673374i
$502$	5.12836	−	5.69562i	0.228890	−	0.254208i
$503$	−10.8811	+	33.4887i	−0.485166	+	1.49319i	0.346575	+	0.938022i	$0.387344\pi$
$503$	−10.8811	+	33.4887i	−0.485166	+	1.49319i	−0.831741	+	0.555164i	$0.812656\pi$
$504$	−23.9366	+	25.9558i	−1.06622	+	1.15616i
$505$			1.35947i			0.0604955i
$506$	−2.84534	−	11.6259i	−0.126491	−	0.516835i
$507$	−28.0495	−	16.1944i	−1.24572	−	0.719219i
$508$	−1.40303	−	3.15126i	−0.0622495	−	0.139815i
$509$	−1.82279	−	8.57557i	−0.0807939	−	0.380105i	0.919110	−	0.394002i	$-0.128910\pi$
$509$	−1.82279	−	8.57557i	−0.0807939	−	0.380105i	−0.999903	+	0.0138968i	$0.995576\pi$
$510$	−7.67875	+	2.49498i	−0.340021	+	0.110479i
$511$	22.0777	+	13.0996i	0.976659	+	0.579492i
$512$	14.9271	+	20.5454i	0.659690	+	0.907986i
$513$	13.5589	+	12.2085i	0.598641	+	0.539019i
$514$	6.75640	+	7.50374i	0.298012	+	0.330976i
$515$	−1.17645	+	0.523791i	−0.0518407	+	0.0230810i
$516$	1.88431	+	3.26371i	0.0829519	+	0.143677i
$517$	−0.265167	−	8.66751i	−0.0116620	−	0.381197i
$518$	−21.3670	+	9.20987i	−0.938813	+	0.404659i
$519$	35.8180	−	49.2992i	1.57224	−	2.16400i
$520$	1.27975	−	0.272019i	0.0561208	−	0.0119288i
$521$	−4.19904	+	19.7549i	−0.183963	+	0.865480i	0.785235	+	0.619198i	$0.212542\pi$
$521$	−4.19904	+	19.7549i	−0.183963	+	0.865480i	−0.969198	+	0.246282i	$0.920791\pi$
$522$	0.681917	+	6.48801i	0.0298467	+	0.283973i
$523$	−15.3533	−	6.83574i	−0.671353	−	0.298906i	0.0426069	−	0.999092i	$-0.486434\pi$
$523$	−15.3533	−	6.83574i	−0.671353	−	0.298906i	−0.713960	+	0.700186i	$0.753100\pi$
$524$	−0.402553	−	1.23893i	−0.0175856	−	0.0541230i
$525$	−31.7318	−	14.5832i	−1.38489	−	0.636462i
$526$	−0.972847	−	0.706815i	−0.0424182	−	0.0308186i
$527$	32.3992	−	18.7057i	1.41133	−	0.814832i
$528$	−30.0811	+	4.09510i	−1.30911	+	0.178216i
$529$	7.70520	−	13.3458i	0.335009	−	0.580252i
$530$	0.753417	−	7.16828i	0.0327263	−	0.311370i
$531$	8.87859	+	2.88483i	0.385298	+	0.125191i
$532$	−3.25640	−	1.10112i	−0.141183	−	0.0477394i
$533$	7.50563	−	5.45316i	0.325105	−	0.236203i
$534$	−4.50790	+	10.1249i	−0.195076	+	0.438147i
$535$	0.375513	+	0.0798177i	0.0162348	+	0.00345082i
$536$	18.3500	−	16.5224i	0.792600	−	0.713660i
$537$	0.554982	+	0.0583309i	0.0239492	+	0.00251717i
$538$	−19.5286			−0.841938
$539$	15.6511	+	17.1477i	0.674141	+	0.738602i
$540$	0.463625			0.0199512
$541$	38.1700	+	4.01183i	1.64106	+	0.172482i	0.879593	−	0.475727i	$-0.157815\pi$
$541$	38.1700	+	4.01183i	1.64106	+	0.172482i	0.761462	+	0.648209i	$0.224482\pi$
$542$	−6.56476	+	5.91094i	−0.281981	+	0.253897i
$543$	−19.1644	−	4.07352i	−0.822424	−	0.174812i
$544$	3.57517	−	8.02996i	0.153284	−	0.344282i
$545$	0.569327	−	0.413640i	0.0243873	−	0.0177184i
$546$	9.58260	+	3.24025i	0.410098	+	0.138670i
$547$	−37.9850	−	12.3421i	−1.62412	−	0.527709i	−0.651211	−	0.758897i	$-0.725739\pi$
$547$	−37.9850	−	12.3421i	−1.62412	−	0.527709i	−0.972909	+	0.231188i	$0.925739\pi$
$548$	−0.184261	+	1.75312i	−0.00787123	+	0.0748898i
$549$	−15.9345	+	27.5993i	−0.680067	+	1.17791i
$550$	−9.12215	−	18.9102i	−0.388970	−	0.806334i
$551$	−4.42307	+	2.55366i	−0.188429	+	0.108790i
$552$	18.2139	+	13.2332i	0.775236	+	0.563242i
$553$	−4.99051	−	2.29352i	−0.212218	−	0.0975304i
$554$	−7.81965	−	24.0664i	−0.332225	−	1.02248i
$555$	6.85501	+	3.05205i	0.290979	+	0.129552i
$556$	0.626444	+	5.96021i	0.0265671	+	0.252769i
$557$	8.12138	−	38.2081i	0.344114	−	1.61893i	−0.377071	−	0.926185i	$-0.623069\pi$
$557$	8.12138	−	38.2081i	0.344114	−	1.61893i	0.721184	−	0.692743i	$-0.243598\pi$
$558$	38.7732	−	8.24150i	1.64140	−	0.348891i
$559$	3.05107	−	4.19943i	0.129046	−	0.177617i
$560$	3.33200	−	1.43620i	0.140803	−	0.0606905i
$561$	30.5845	+	39.4971i	1.29128	+	1.66757i
$562$	−3.47786	−	6.02383i	−0.146705	−	0.254100i
$563$	−4.43344	+	1.97390i	−0.186847	+	0.0831898i	−0.498028	−	0.867161i	$-0.665942\pi$
$563$	−4.43344	+	1.97390i	−0.186847	+	0.0831898i	0.311181	+	0.950351i	$0.399276\pi$
$564$	1.35728	+	1.50742i	0.0571519	+	0.0634737i
$565$	6.25684	+	5.63368i	0.263227	+	0.237011i
$566$	9.24704	+	12.7275i	0.388682	+	0.534975i
$567$	−5.65743	−	3.35679i	−0.237590	−	0.140972i
$568$	7.33013	−	2.38170i	0.307565	−	0.0999341i
$569$	3.17680	+	14.9457i	0.133179	+	0.626556i	0.993212	+	0.116318i	$0.0371092\pi$
$569$	3.17680	+	14.9457i	0.133179	+	0.626556i	−0.860033	+	0.510238i	$0.829557\pi$
$570$	−2.72407	−	6.11836i	−0.114099	−	0.256270i
$571$	−8.90511	−	5.14137i	−0.372667	−	0.215160i	0.301956	−	0.953322i	$-0.402361\pi$
$571$	−8.90511	−	5.14137i	−0.372667	−	0.215160i	−0.674623	+	0.738162i	$0.735694\pi$
$572$	−0.529756	−	0.855999i	−0.0221502	−	0.0357911i
$573$		−	54.0773i		−	2.25911i
$574$	20.3990	−	22.1199i	0.851439	−	0.923265i
$575$	−4.11403	+	12.6617i	−0.171567	+	0.528028i
$576$	26.2358	−	29.1378i	1.09316	−	1.21407i
$577$	24.4773	−	2.57267i	1.01900	−	0.107102i	0.419732	−	0.907648i	$-0.362124\pi$
$577$	24.4773	−	2.57267i	1.01900	−	0.107102i	0.599271	+	0.800546i	$0.295457\pi$
$578$	17.4682	−	1.83598i	0.726580	−	0.0763667i
$579$	1.06438	−	1.18211i	0.0442341	−	0.0491269i
$580$	−0.0401043	+	0.123428i	−0.00166524	+	0.00512508i
$581$	−9.20260	+	2.86939i	−0.381788	+	0.119042i
$582$		−	47.5937i		−	1.97282i
$583$	−43.3169	+	10.6014i	−1.79400	+	0.439067i
$584$	−25.1414	−	14.5154i	−1.04036	−	0.600651i
$585$	−0.793314	−	1.78181i	−0.0327995	−	0.0736689i
$586$	−4.91954	−	23.1446i	−0.203224	−	0.956095i
$587$	−1.54078	+	0.500630i	−0.0635949	+	0.0206632i	−0.340642	−	0.940193i	$-0.610644\pi$
$587$	−1.54078	+	0.500630i	−0.0635949	+	0.0206632i	0.277047	+	0.960856i	$0.410644\pi$
$588$	−5.38590	−	0.696142i	−0.222111	−	0.0287084i
$589$	18.2407	+	25.1062i	0.751597	+	1.03448i
$590$	−0.833778	−	0.750737i	−0.0343261	−	0.0309073i
$591$	11.1148	+	12.3442i	0.457201	+	0.507773i
$592$	20.5533	−	9.15090i	0.844734	−	0.376100i
$593$	9.04033	+	15.6583i	0.371242	+	0.643010i	0.989757	−	0.142763i	$-0.0455988\pi$
$593$	9.04033	+	15.6583i	0.371242	+	0.643010i	−0.618515	+	0.785773i	$0.712265\pi$
$594$	5.85656	+	16.3098i	0.240297	+	0.669199i
$595$	−4.78798	−	3.56656i	−0.196288	−	0.146215i
$596$	0.787029	−	1.08325i	0.0322379	−	0.0443717i
$597$	−27.5201	+	5.84958i	−1.12632	+	0.239407i
$598$	0.801774	−	3.77205i	0.0327870	−	0.154251i
$599$	−1.13081	−	10.7589i	−0.0462036	−	0.439598i	−0.993031	−	0.117855i	$-0.962398\pi$
$599$	−1.13081	−	10.7589i	−0.0462036	−	0.439598i	0.946827	−	0.321742i	$-0.104269\pi$
$600$	36.0780	+	16.0630i	1.47288	+	0.655767i
$601$	7.45445	+	22.9424i	0.304073	+	0.935841i	0.980021	+	0.198892i	$0.0637343\pi$
$601$	7.45445	+	22.9424i	0.304073	+	0.935841i	−0.675948	+	0.736949i	$0.736266\pi$
$602$	7.03030	−	15.2973i	0.286533	−	0.623473i
$603$	−29.7805	−	21.6368i	−1.21275	−	0.881118i
$604$	2.89492	−	1.67138i	0.117793	−	0.0680076i
$605$	3.15481	−	3.21087i	0.128261	−	0.130541i
$606$	5.94316	−	10.2939i	0.241424	−	0.418159i
$607$	0.913145	−	8.68800i	0.0370634	−	0.352635i	−0.960236	−	0.279190i	$-0.909934\pi$
$607$	0.913145	−	8.68800i	0.0370634	−	0.352635i	0.997299	−	0.0734448i	$-0.0233993\pi$
$608$	6.93442	+	2.25313i	0.281228	+	0.0913765i
$609$	−6.06009	+	5.32722i	−0.245567	+	0.215870i
$610$	3.09860	−	2.25126i	0.125458	−	0.0911509i
$611$	1.13638	−	2.55236i	0.0459731	−	0.103257i
$612$	−6.83359	−	1.45252i	−0.276231	−	0.0587148i
$613$	3.06290	−	2.75784i	0.123709	−	0.111388i	−0.604954	−	0.796260i	$-0.706809\pi$
$613$	3.06290	−	2.75784i	0.123709	−	0.111388i	0.728663	+	0.684872i	$0.240142\pi$
$614$	4.42436	+	0.465018i	0.178552	+	0.0187666i
$615$	−9.70405			−0.391305
$616$	−17.9289	−	19.1794i	−0.722376	−	0.772761i
$617$	−9.12985			−0.367554			−0.183777	−	0.982968i	$-0.558832\pi$
$617$	−9.12985			−0.367554			−0.183777	+	0.982968i	$0.558832\pi$
$618$	11.1979	+	1.17695i	0.450447	+	0.0473439i
$619$	−5.12954	+	4.61866i	−0.206174	+	0.185640i	−0.765748	−	0.643140i	$-0.777631\pi$
$619$	−5.12954	+	4.61866i	−0.206174	+	0.185640i	0.559575	+	0.828780i	$0.310964\pi$
$620$	0.771335	+	0.163952i	0.0309776	+	0.00658448i
$621$	4.46947	−	10.0386i	0.179354	−	0.402835i
$622$	19.6994	−	14.3124i	0.789872	−	0.573876i
$623$	−8.03616	+	1.60835i	−0.321962	+	0.0644372i
$624$	−9.30254	−	3.02258i	−0.372400	−	0.121000i
$625$	−2.35358	+	22.3928i	−0.0941432	+	0.895713i
$626$	2.22683	−	3.85699i	0.0890022	−	0.154156i
$627$	−29.9318	+	28.6558i	−1.19536	+	1.14440i
$628$	−4.82588	+	2.78622i	−0.192574	+	0.111182i
$629$	−29.9502	−	21.7601i	−1.19419	−	0.867632i
$630$	−3.65707	−	5.16171i	−0.145701	−	0.205647i
$631$	8.69598	+	26.7635i	0.346182	+	1.06544i	0.960948	+	0.276728i	$0.0892502\pi$
$631$	8.69598	+	26.7635i	0.346182	+	1.06544i	−0.614767	+	0.788709i	$0.710750\pi$
$632$	5.67405	+	2.52625i	0.225702	+	0.100489i
$633$	−5.04962	−	48.0439i	−0.200704	−	1.90957i
$634$	−6.69307	+	31.4884i	−0.265816	+	1.25056i
$635$	4.86109	−	1.03326i	0.192906	−	0.0410035i
$636$	6.13155	−	8.43935i	0.243132	−	0.334642i
$637$	2.14138	+	7.16704i	0.0848447	+	0.283969i
$638$	−4.84867	+	0.148336i	−0.191961	+	0.00587269i
$639$	−5.74495	−	9.95055i	−0.227267	−	0.393638i
$640$	−3.11301	+	1.38600i	−0.123052	+	0.0547864i
$641$	−20.2931	−	22.5378i	−0.801530	−	0.890189i	0.194344	−	0.980933i	$-0.437742\pi$
$641$	−20.2931	−	22.5378i	−0.801530	−	0.890189i	−0.995874	+	0.0907440i	$0.971076\pi$
$642$	−2.49444	−	2.24600i	−0.0984477	−	0.0886427i
$643$	13.2785	+	18.2763i	0.523654	+	0.720747i	0.986147	−	0.165876i	$-0.0530450\pi$
$643$	13.2785	+	18.2763i	0.523654	+	0.720747i	−0.462493	+	0.886623i	$0.653045\pi$
$644$	−0.0246572	+	2.07017i	−0.000971629	+	0.0815762i
$645$	−5.16372	+	1.67779i	−0.203321	+	0.0660631i
$646$	6.86986	+	32.3202i	0.270291	+	1.27162i
$647$	−6.00206	−	13.4808i	−0.235965	−	0.529987i	0.756285	−	0.654242i	$-0.227012\pi$
$647$	−6.00206	−	13.4808i	−0.235965	−	0.529987i	−0.992250	+	0.124256i	$0.960346\pi$
$648$	6.44251	+	3.71958i	0.253086	+	0.146119i
$649$	−2.62820	+	6.42493i	−0.103166	+	0.252200i
$650$		−	6.76455i		−	0.265328i
$651$	36.0408	+	33.2370i	1.41255	+	1.30266i
$652$	0.603155	−	1.85632i	0.0236214	−	0.0726991i
$653$	−14.8042	+	16.4418i	−0.579334	+	0.643416i	−0.959569	−	0.281474i	$-0.909177\pi$
$653$	−14.8042	+	16.4418i	−0.579334	+	0.643416i	0.380235	+	0.924890i	$0.375843\pi$
$654$	−6.11924	+	0.643158i	−0.239281	+	0.0251495i
$655$	1.86651	−	0.196178i	0.0729306	−	0.00766532i
$656$	−19.4687	+	21.6222i	−0.760124	+	0.844203i
$657$	−13.3737	+	41.1601i	−0.521758	+	1.60581i
$658$	1.98944	−	8.84050i	0.0775564	−	0.344638i
$659$			39.4562i			1.53699i	0.639853	+	0.768497i	$0.278995\pi$
$659$			39.4562i			1.53699i	−0.639853	+	0.768497i	$0.721005\pi$
$660$	−0.0779902	+	1.05006i	−0.00303577	+	0.0408735i
$661$	31.1770	+	18.0000i	1.21264	+	0.700121i	0.963335	−	0.268303i	$-0.0864629\pi$
$661$	31.1770	+	18.0000i	1.21264	+	0.700121i	0.249310	+	0.968424i	$0.419796\pi$
$662$	11.3790	+	25.5577i	0.442258	+	0.993327i
$663$	3.34631	+	15.7431i	0.129960	+	0.611413i
$664$	10.3675	−	3.36859i	0.402335	−	0.130727i
$665$	2.52714	−	4.25916i	0.0979981	−	0.165163i
$666$	−23.0561	−	31.7340i	−0.893405	−	1.22967i
$667$	2.28591	+	2.05824i	0.0885106	+	0.0796953i
$668$	1.00335	+	1.11433i	0.0388206	+	0.0431147i
$669$	−49.2019	+	21.9061i	−1.90226	+	0.846940i
$670$	2.21199	+	3.83128i	0.0854566	+	0.148015i
$671$	−19.5884	−	13.3361i	−0.756200	−	0.514834i
$672$	11.4407	+	1.34041i	0.441336	+	0.0517076i
$673$	−18.2242	+	25.0835i	−0.702492	+	0.966897i	0.297434	+	0.954742i	$0.403869\pi$
$673$	−18.2242	+	25.0835i	−0.702492	+	0.966897i	−0.999926	+	0.0121550i	$0.996131\pi$
$674$	18.9639	−	4.03089i	0.730461	−	0.155264i
$675$	4.00764	−	18.8544i	0.154254	−	0.725708i
$676$	0.352070	+	3.34972i	0.0135412	+	0.128836i
$677$	−35.5348	−	15.8211i	−1.36572	−	0.608056i	−0.412669	−	0.910881i	$-0.635403\pi$
$677$	−35.5348	−	15.8211i	−1.36572	−	0.608056i	−0.953046	+	0.302825i	$0.902070\pi$
$678$	−22.7480	−	70.0111i	−0.873631	−	2.68876i
$679$	28.7167	−	20.3458i	1.10205	−	0.780800i
$680$	5.46218	+	3.96851i	0.209465	+	0.152185i
$681$	−16.5343	+	9.54610i	−0.633597	+	0.365807i
$682$	3.97593	+	29.2057i	0.152246	+	1.11835i
$683$	−17.9872	+	31.1548i	−0.688261	+	1.19210i	0.284138	+	0.958783i	$0.408292\pi$
$683$	−17.9872	+	31.1548i	−0.688261	+	1.19210i	−0.972400	+	0.233320i	$0.925041\pi$
$684$	0.605759	−	5.76341i	0.0231618	−	0.220369i
$685$	−2.41535	−	0.784794i	−0.0922857	−	0.0299854i
$686$	11.3720	+	21.4302i	0.434185	+	0.818208i
$687$	−0.536636	+	0.389889i	−0.0204739	+	0.0148752i
$688$	−6.62128	+	14.8716i	−0.252434	+	0.566976i
$689$	−14.0542	−	2.98732i	−0.535424	−	0.113808i
$690$	−2.99757	+	2.69903i	−0.114116	+	0.102750i
$691$	24.0632	+	2.52914i	0.915407	+	0.0962131i	0.550504	−	0.834832i	$-0.314436\pi$
$691$	24.0632	+	2.52914i	0.915407	+	0.0962131i	0.364903	+	0.931046i	$0.381102\pi$
$692$	−6.33698			−0.240896
$693$	−22.4103	+	32.0884i	−0.851295	+	1.21894i
$694$	−0.0461985			−0.00175367
$695$	−8.58691	−	0.902520i	−0.325720	−	0.0342346i
$696$	6.78087	−	6.10553i	0.257028	−	0.231429i
$697$	46.8297	+	9.95396i	1.77380	+	0.377033i
$698$	−3.53114	+	7.93108i	−0.133656	+	0.300196i
$699$	41.9993	−	30.5143i	1.58856	−	1.15416i
$700$	0.712701	+	3.56103i	0.0269376	+	0.134594i
$701$	−19.7121	−	6.40486i	−0.744517	−	0.241908i	−0.0878970	−	0.996130i	$-0.528015\pi$
$701$	−19.7121	−	6.40486i	−0.744517	−	0.241908i	−0.656620	+	0.754221i	$0.728015\pi$
$702$	−0.583622	+	5.55280i	−0.0220274	+	0.209577i
$703$	15.3544	−	26.5946i	0.579102	−	1.00303i
$704$	20.1618	+	21.0596i	0.759878	+	0.793714i
$705$	−2.53084	+	1.46118i	−0.0953171	+	0.0550313i
$706$	−17.7527	−	12.8981i	−0.668131	−	0.485426i
$707$	8.75166	−	0.814578i	0.329140	−	0.0306354i
$708$	−0.501776	−	1.54431i	−0.0188579	−	0.0580386i
$709$	40.5850	+	18.0696i	1.52420	+	0.678618i	0.986386	−	0.164446i	$-0.0525836\pi$
$709$	40.5850	+	18.0696i	1.52420	+	0.678618i	0.537814	+	0.843064i	$0.319250\pi$
$710$	0.144341	+	1.37331i	0.00541703	+	0.0515396i
$711$	1.92510	−	9.05687i	0.0721968	−	0.339659i
$712$	9.06545	−	1.92692i	0.339742	−	0.0722144i
$713$	10.9859	−	15.1207i	0.411423	−	0.566276i
$714$	20.6626	+	47.9375i	0.773279	+	1.79402i
$715$	1.36498	−	0.490138i	0.0510472	−	0.0183301i
$716$	−0.0290158	−	0.0502568i	−0.00108437	−	0.00187818i
$717$	10.2569	−	4.56666i	0.383051	−	0.170545i
$718$	−9.97679	−	11.0803i	−0.372330	−	0.413515i
$719$	−24.4648	−	22.0282i	−0.912382	−	0.821513i	0.0720277	−	0.997403i	$-0.477053\pi$
$719$	−24.4648	−	22.0282i	−0.912382	−	0.821513i	−0.984410	+	0.175890i	$0.943720\pi$
$720$	3.59539	+	4.94864i	0.133992	+	0.184425i
$721$	4.07686	+	7.25965i	0.151830	+	0.270364i
$722$	−2.39647	+	0.778660i	−0.0891874	+	0.0289787i
$723$	−4.47748	−	21.0649i	−0.166519	−	0.783411i
$724$	0.828713	+	1.86132i	0.0307989	+	0.0691754i
$725$	4.67285	+	2.69787i	0.173545	+	0.100196i
$726$	−37.9251	+	10.5209i	−1.40753	+	0.390466i
$727$			52.4861i			1.94660i	0.229534	+	0.973301i	$0.426280\pi$
$727$			52.4861i			1.94660i	−0.229534	+	0.973301i	$0.573720\pi$
$728$	−2.51796	−	8.07550i	−0.0933218	−	0.299298i
$729$	13.5269	−	41.6316i	0.500997	−	1.54191i
$730$	3.48033	−	3.86529i	0.128813	−	0.143061i
$731$	26.6400	−	2.79998i	0.985317	−	0.103561i
$732$	5.51280	−	0.579419i	0.203759	−	0.0214159i
$733$	14.1624	−	15.7289i	0.523101	−	0.580962i	−0.422471	−	0.906376i	$-0.638837\pi$
$733$	14.1624	−	15.7289i	0.523101	−	0.580962i	0.945571	+	0.325414i	$0.105504\pi$
$734$	4.79645	−	14.7620i	0.177040	−	0.544874i
$735$	2.59431	−	7.38141i	0.0956925	−	0.272267i
$736$		−	4.39132i		−	0.161866i
$737$	17.6847	−	20.8917i	0.651424	−	0.769556i
$738$	43.9311	+	25.3636i	1.61713	+	0.933648i
$739$	−1.51530	−	3.40342i	−0.0557412	−	0.125197i	0.883528	−	0.468379i	$-0.155162\pi$
$739$	−1.51530	−	3.40342i	−0.0557412	−	0.125197i	−0.939269	+	0.343182i	$0.888495\pi$
$740$	−0.162239	−	0.763277i	−0.00596404	−	0.0280586i
$741$	−12.6974	+	4.12563i	−0.466450	+	0.151559i
$742$	−46.5978	−	0.555012i	−1.71066	−	0.0203751i
$743$	−2.73925	−	3.77026i	−0.100493	−	0.138317i	0.755809	−	0.654792i	$-0.227244\pi$
$743$	−2.73925	−	3.77026i	−0.100493	−	0.138317i	−0.856302	+	0.516475i	$0.827244\pi$
$744$	−41.2018	−	37.0982i	−1.51053	−	1.36009i
$745$	1.29080	+	1.43357i	0.0472911	+	0.0525221i
$746$	−15.4317	+	6.87065i	−0.564996	+	0.251552i
$747$	−8.12543	−	14.0737i	−0.297294	−	0.514928i
$748$	1.45347	−	4.98737i	0.0531440	−	0.182356i
$749$	0.288829	−	2.46522i	0.0105536	−	0.0900771i
$750$	−8.46197	+	11.6469i	−0.308987	+	0.425285i
$751$	−29.5097	+	6.27248i	−1.07682	+	0.228886i	−0.711992	−	0.702188i	$-0.752207\pi$
$751$	−29.5097	+	6.27248i	−1.07682	+	0.228886i	−0.364832	+	0.931074i	$0.618873\pi$
$752$	−1.82174	+	8.57061i	−0.0664320	+	0.312538i
$753$	1.67043	+	15.8931i	0.0608738	+	0.579175i
$754$	−1.42781	−	0.635700i	−0.0519976	−	0.0231508i
$755$	1.48821	+	4.58023i	0.0541614	+	0.166692i
$756$	−0.277799	−	2.98462i	−0.0101035	−	0.108549i
$757$	1.98226	+	1.44020i	0.0720466	+	0.0523449i	0.623226	−	0.782042i	$-0.285822\pi$
$757$	1.98226	+	1.44020i	0.0720466	+	0.0523449i	−0.551179	+	0.834387i	$0.685822\pi$
$758$	3.13305	−	1.80886i	0.113797	−	0.0657009i
$759$	21.9845	+	11.8115i	0.797986	+	0.428732i
$760$	−2.80027	+	4.85020i	−0.101576	+	0.175935i
$761$	−2.30822	+	21.9613i	−0.0836731	+	0.796096i	0.869553	+	0.493839i	$0.164407\pi$
$761$	−2.30822	+	21.9613i	−0.0836731	+	0.796096i	−0.953226	+	0.302257i	$0.902260\pi$
$762$	−41.3252	−	13.4274i	−1.49705	−	0.486422i
$763$	−3.00397	−	3.41723i	−0.108751	−	0.123712i
$764$	−4.54959	+	3.30547i	−0.164599	+	0.119588i
$765$	4.09386	−	9.19495i	0.148014	−	0.332444i
$766$	−9.13888	−	1.94253i	−0.330201	−	0.0701864i
$767$	−1.66208	+	1.49655i	−0.0600143	+	0.0540372i
$768$	−18.1264	−	1.90516i	−0.654080	−	0.0687466i
$769$	−4.09639			−0.147720			−0.0738599	−	0.997269i	$-0.523532\pi$
$769$	−4.09639			−0.147720			−0.0738599	+	0.997269i	$0.523532\pi$
$770$	4.02902	−	2.42758i	0.145196	−	0.0874838i
$771$	−21.0538			−0.758234
$772$	−0.164513	−	0.0172910i	−0.00592094	−	0.000622316i
$773$	−9.60033	+	8.64417i	−0.345300	+	0.310909i	−0.823472	−	0.567357i	$-0.807966\pi$
$773$	−9.60033	+	8.64417i	−0.345300	+	0.310909i	0.478172	+	0.878266i	$0.341299\pi$
$774$	27.7619	+	5.90097i	0.997881	+	0.212106i
$775$	13.3351	−	29.9510i	0.479009	−	1.07587i
$776$	−32.1982	+	23.3934i	−1.15585	+	0.839773i
$777$	15.5403	−	45.9584i	0.557506	−	1.64875i
$778$	3.92729	+	1.27605i	0.140800	+	0.0457487i
$779$	−4.15119	+	39.4959i	−0.148732	+	1.41509i
$780$	−0.169626	+	0.293801i	−0.00607358	+	0.0105198i
$781$	7.69512	−	3.71207i	0.275353	−	0.132828i
$782$	17.2342	−	9.95016i	0.616293	−	0.355817i
$783$	−3.60302	−	2.61775i	−0.128762	−	0.0935507i
$784$	−11.2421	−	20.5894i	−0.401505	−	0.735337i
$785$	−2.48087	−	7.63532i	−0.0885459	−	0.272516i
$786$	−14.9908	−	6.67434i	−0.534705	−	0.238066i
$787$	3.19642	+	30.4119i	0.113940	+	1.08407i	0.890801	+	0.454394i	$0.150144\pi$
$787$	3.19642	+	30.4119i	0.113940	+	1.08407i	−0.776861	+	0.629673i	$0.783189\pi$
$788$	0.359144	−	1.68964i	0.0127940	−	0.0601909i
$789$	2.45255	−	0.521305i	0.0873130	−	0.0185589i
$790$	−0.654082	+	0.900266i	−0.0232712	+	0.0320300i
$791$	32.5182	−	43.6545i	1.15621	−	1.55218i
$792$	24.9089	−	36.5867i	0.885098	−	1.30005i
$793$	−3.81751	−	6.61212i	−0.135564	−	0.234803i
$794$	24.8612	−	11.0689i	0.882291	−	0.392821i
$795$	10.0563	+	11.1686i	0.356659	+	0.396110i
$796$	2.17430	+	1.95775i	0.0770659	+	0.0693905i
$797$	−15.9745	−	21.9870i	−0.565845	−	0.778818i	0.426210	−	0.904624i	$-0.359848\pi$
$797$	−15.9745	−	21.9870i	−0.565845	−	0.778818i	−0.992055	+	0.125806i	$0.959848\pi$
$798$	−37.7551	+	21.2025i	−1.33652	+	0.750559i
$799$	13.7121	−	4.45534i	0.485100	−	0.157619i
$800$	−1.60155	−	7.53470i	−0.0566233	−	0.266392i
$801$	−5.61965	−	12.6219i	−0.198560	−	0.445974i
$802$	28.8105	+	16.6337i	1.01733	+	0.587358i
$803$	−29.7852	−	12.1840i	−1.05110	−	0.429965i
$804$			6.40271i			0.225806i
$805$	−2.90995	−	0.654845i	−0.102562	−	0.0230803i
$806$	−2.93462	+	9.03183i	−0.103368	+	0.318133i
$807$	27.2463	−	30.2601i	0.959116	−	1.06521i
$808$	−9.88522	+	1.03898i	−0.347761	+	0.0365511i
$809$	38.8573	−	4.08407i	1.36615	−	0.143588i	0.607102	−	0.794624i	$-0.292332\pi$
$809$	38.8573	−	4.08407i	1.36615	−	0.143588i	0.759047	+	0.651036i	$0.225665\pi$
$810$	−0.891837	+	0.990486i	−0.0313360	+	0.0348021i
$811$	9.46176	−	29.1203i	0.332247	−	1.02255i	−0.635815	−	0.771842i	$-0.719336\pi$
$811$	9.46176	−	29.1203i	0.332247	−	1.02255i	0.968062	−	0.250711i	$-0.0806642\pi$
$812$	0.818608	+	0.184217i	0.0287275	+	0.00646475i
$813$		−	18.4192i		−	0.645990i
$814$	24.8018	−	15.3492i	0.869302	−	0.537989i
$815$	2.43530	+	1.40602i	0.0853047	+	0.0492507i
$816$	−20.5303	−	46.1119i	−0.718705	−	1.61424i
$817$	4.61977	+	21.7343i	0.161625	+	0.760386i
$818$	37.1999	−	12.0870i	1.30066	−	0.422611i
$819$	−10.9952	+	6.17466i	−0.384203	+	0.215760i
$820$	0.593159	+	0.816413i	0.0207140	+	0.0285104i
$821$	−24.4097	−	21.9786i	−0.851904	−	0.767058i	0.122355	−	0.992486i	$-0.460955\pi$
$821$	−24.4097	−	21.9786i	−0.851904	−	0.767058i	−0.974260	+	0.225428i	$0.927622\pi$
$822$	14.8581	+	16.5016i	0.518236	+	0.575559i
$823$	−3.08491	+	1.37349i	−0.107533	+	0.0478769i	−0.459798	−	0.888023i	$-0.652078\pi$
$823$	−3.08491	+	1.37349i	−0.107533	+	0.0478769i	0.352265	+	0.935900i	$0.385412\pi$
$824$	−4.70780	−	8.15415i	−0.164004	−	0.284063i
$825$	42.0291	+	12.2485i	1.46327	+	0.426439i
$826$	−4.33333	+	5.81734i	−0.150776	+	0.202411i
$827$	27.0072	−	37.1722i	0.939132	−	1.29260i	−0.0170577	−	0.999855i	$-0.505430\pi$
$827$	27.0072	−	37.1722i	0.939132	−	1.29260i	0.956189	−	0.292749i	$-0.0945701\pi$
$828$	−3.41398	+	0.725663i	−0.118644	+	0.0252185i
$829$	8.20724	−	38.6120i	0.285049	−	1.34105i	−0.569632	−	0.821900i	$-0.692914\pi$
$829$	8.20724	−	38.6120i	0.285049	−	1.34105i	0.854682	−	0.519152i	$-0.173752\pi$
$830$	0.204151	+	1.94236i	0.00708617	+	0.0674204i
$831$	48.2015	+	21.4607i	1.67209	+	0.744464i
$832$	2.90273	+	8.93370i	0.100634	+	0.309720i
$833$	−20.0911	+	32.9600i	−0.696115	+	1.14200i
$834$	61.0744	+	44.3732i	2.11483	+	1.53652i
$835$	−1.87088	+	1.08015i	−0.0647444	+	0.0373802i
$836$	4.24043	+	0.766617i	0.146658	+	0.0265140i
$837$	−13.5304	+	23.4353i	−0.467678	+	0.810042i
$838$	0.415975	−	3.95774i	0.0143696	−	0.136718i
$839$	−28.4243	−	9.23563i	−0.981317	−	0.318849i	−0.225941	−	0.974141i	$-0.572546\pi$
$839$	−28.4243	−	9.23563i	−0.981317	−	0.318849i	−0.755376	+	0.655292i	$0.772546\pi$
$840$	−2.83417	+	8.38168i	−0.0977882	+	0.289195i
$841$	−22.4529	+	16.3130i	−0.774239	+	0.562517i
$842$	−11.9854	+	26.9196i	−0.413043	+	0.927710i
$843$	14.1864	+	3.01541i	0.488605	+	0.103856i
$844$	−3.73334	+	3.36151i	−0.128507	+	0.115708i
$845$	−4.82596	−	0.507229i	−0.166018	−	0.0174492i
$846$	15.2765			0.525216
$847$	−22.5605	−	18.3854i	−0.775190	−	0.631729i
$848$	45.0608			1.54739
$849$	−32.6230	−	3.42882i	−1.11962	−	0.117677i
$850$	25.9418	−	23.3581i	0.889796	−	0.801176i
$851$	−18.0908	−	3.84532i	−0.620146	−	0.131816i
$852$	−0.812867	+	1.82573i	−0.0278484	+	0.0625485i
$853$	−29.5773	+	21.4892i	−1.01271	+	0.735776i	−0.964776	−	0.263074i	$-0.915264\pi$
$853$	−29.5773	+	21.4892i	−1.01271	+	0.735776i	−0.0479334	+	0.998851i	$0.515264\pi$
$854$	−16.3493	−	18.5985i	−0.559462	−	0.636428i
$855$	7.94047	+	2.58002i	0.271558	+	0.0882347i
$856$	−0.293399	+	2.79150i	−0.0100282	+	0.0954116i
$857$	−15.9690	+	27.6591i	−0.545491	+	0.944818i	0.453085	+	0.891467i	$0.350323\pi$
$857$	−15.9690	+	27.6591i	−0.545491	+	0.944818i	−0.998576	+	0.0533506i	$0.983010\pi$
$858$	−12.4783	−	2.25592i	−0.426002	−	0.0770160i
$859$	−26.7408	+	15.4388i	−0.912384	+	0.526765i	−0.881197	−	0.472749i	$-0.843262\pi$
$859$	−26.7408	+	15.4388i	−0.912384	+	0.526765i	−0.0311863	+	0.999514i	$0.509929\pi$
$860$	0.456787	+	0.331875i	0.0155763	+	0.0113168i
$861$	5.81457	+	62.4705i	0.198160	+	2.12899i
$862$	−9.22875	−	28.4032i	−0.314332	−	0.967415i
$863$	−27.6384	−	12.3054i	−0.940823	−	0.418882i	−0.121744	−	0.992562i	$-0.538849\pi$
$863$	−27.6384	−	12.3054i	−0.940823	−	0.418882i	−0.819080	+	0.573680i	$0.805515\pi$
$864$	0.664591	+	6.32316i	0.0226098	+	0.215118i
$865$	1.89817	−	8.93021i	0.0645398	−	0.303636i
$866$	−42.1781	+	8.96523i	−1.43327	+	0.304651i
$867$	−21.5267	+	29.6290i	−0.731085	+	1.00625i
$868$	0.593278	−	5.06376i	0.0201372	−	0.171875i
$869$	6.60999	+	1.92635i	0.224229	+	0.0653469i
$870$	0.817396	+	1.41577i	0.0277123	+	0.0479991i
$871$	8.05649	−	3.58698i	0.272984	−	0.121540i
$872$	3.44285	+	3.82367i	0.116590	+	0.129486i
$873$	44.0918	+	39.7005i	1.49228	+	1.34366i
$874$	9.70286	+	13.3548i	0.328204	+	0.451734i
$875$	−10.6448	−	0.126787i	−0.359860	−	0.00428619i
$876$	7.15923	−	2.32617i	0.241888	−	0.0785941i
$877$	−7.03679	−	33.1055i	−0.237615	−	1.11789i	−0.921523	−	0.388324i	$-0.873054\pi$
$877$	−7.03679	−	33.1055i	−0.237615	−	1.11789i	0.683907	−	0.729569i	$-0.260279\pi$
$878$	−17.8584	−	40.1106i	−0.602691	−	1.35367i
$879$	42.7269	+	24.6684i	1.44114	+	0.832045i
$880$	−3.86762	+	2.39357i	−0.130378	+	0.0806873i
$881$		−	20.2072i		−	0.680798i	−0.940281	−	0.340399i	$-0.889438\pi$
$881$		−	20.2072i		−	0.680798i	0.940281	−	0.340399i	$-0.110562\pi$
$882$	−31.0376	+	26.6355i	−1.04509	+	0.896865i
$883$	−2.10312	+	6.47273i	−0.0707755	+	0.217825i	−0.980188	−	0.198072i	$-0.936532\pi$
$883$	−2.10312	+	6.47273i	−0.0707755	+	0.217825i	0.909412	+	0.415896i	$0.136532\pi$
$884$	1.11995	−	1.24383i	0.0376679	−	0.0418344i
$885$	2.32657	−	0.244533i	0.0782069	−	0.00821988i
$886$	0.610860	−	0.0642040i	0.0205222	−	0.00215697i
$887$	31.3913	−	34.8636i	1.05402	−	1.17060i	0.0690944	−	0.997610i	$-0.477989\pi$
$887$	31.3913	−	34.8636i	1.05402	−	1.17060i	0.984923	−	0.172995i	$-0.0553443\pi$
$888$	−16.9537	+	52.1780i	−0.568928	+	1.75098i
$889$	−9.56438	−	30.6745i	−0.320779	−	1.02879i
$890$			1.66049i			0.0556596i
$891$	7.63249	+	3.12217i	0.255698	+	0.104597i
$892$	4.85045	+	2.80041i	0.162405	+	0.0937647i
$893$	4.86444	+	10.9257i	0.162782	+	0.365615i
$894$	−3.50675	−	16.4980i	−0.117283	−	0.551774i
$895$	0.0795143	−	0.0258358i	0.00265787	−	0.000863594i
$896$	10.7878	+	19.2097i	0.360394	+	0.641752i
$897$	4.72626	+	6.50513i	0.157805	+	0.217200i
$898$	13.8419	+	12.4633i	0.461909	+	0.415905i
$899$	−5.06865	−	5.62931i	−0.169049	−	0.187748i
$900$	−5.59310	+	2.49021i	−0.186437	+	0.0830070i
$901$	−37.0732	−	64.2127i	−1.23509	−	2.13924i
$902$	−21.2276	+	31.1797i	−0.706803	+	1.03817i
$903$	13.8950	+	32.2365i	0.462395	+	1.07276i
$904$	−36.1829	+	49.8015i	−1.20343	+	1.65637i
$905$	−2.87124	+	0.610302i	−0.0954434	+	0.0202871i
$906$	8.75466	−	41.1874i	0.290854	−	1.36836i
$907$	−2.71558	−	25.8371i	−0.0901695	−	0.857905i	−0.942344	−	0.334647i	$-0.891383\pi$
$907$	−2.71558	−	25.8371i	−0.0901695	−	0.857905i	0.852174	−	0.523258i	$-0.175284\pi$
$908$	1.81378	+	0.807549i	0.0601926	+	0.0267995i
$909$	4.57894	+	14.0925i	0.151874	+	0.467420i
$910$	1.50901	−	0.140455i	0.0500233	−	0.00465602i
$911$	34.3918	+	24.9871i	1.13945	+	0.827861i	0.987043	−	0.160457i	$-0.0512967\pi$
$911$	34.3918	+	24.9871i	1.13945	+	0.827861i	0.152410	+	0.988317i	$0.451297\pi$
$912$	36.2605	−	20.9350i	1.20071	−	0.693228i
$913$	10.8837	−	5.25020i	0.360197	−	0.173756i
$914$	−10.2771	+	17.8005i	−0.339937	+	0.588789i
$915$	−0.834771	+	7.94232i	−0.0275967	+	0.262565i
$916$	0.0656036	+	0.0213159i	0.00216760	+	0.000704297i
$917$	−2.38131	−	11.8982i	−0.0786376	−	0.392915i
$918$	−23.3100	+	16.9357i	−0.769345	+	0.558962i
$919$	6.80800	−	15.2910i	0.224575	−	0.504404i	−0.765755	−	0.643132i	$-0.777635\pi$
$919$	6.80800	−	15.2910i	0.224575	−	0.504404i	0.990331	+	0.138728i	$0.0443013\pi$
$920$	3.29932	+	0.701293i	0.108775	+	0.0231209i
$921$	−6.89342	+	6.20686i	−0.227146	+	0.204523i
$922$	−33.6615	−	3.53797i	−1.10858	−	0.116517i
$923$	2.75270			0.0906061
$924$	6.80656	−	0.127117i	0.223919	−	0.00418186i
$925$	−32.4430			−1.06672
$926$	−32.9371	−	3.46183i	−1.08238	−	0.113763i
$927$	−10.4312	+	9.39225i	−0.342604	+	0.308482i
$928$	−1.74087	−	0.370033i	−0.0571468	−	0.0121469i
$929$	−12.8962	+	28.9653i	−0.423109	+	0.950319i	0.568694	+	0.822549i	$0.307449\pi$
$929$	−12.8962	+	28.9653i	−0.423109	+	0.950319i	−0.991804	+	0.127770i	$0.959218\pi$
$930$	8.03619	−	5.83864i	0.263517	−	0.191456i
$931$	−28.9329	−	13.7166i	−0.948237	−	0.449542i
$932$	−5.13441	−	1.66827i	−0.168183	−	0.0546461i
$933$	−5.30707	+	50.4934i	−0.173746	+	1.65308i
$934$	−11.4752	+	19.8757i	−0.375481	+	0.650352i
$935$	6.59294	+	3.54217i	0.215612	+	0.115841i
$936$	12.3500	−	7.13026i	0.403671	−	0.233060i
$937$	−3.74400	−	2.72017i	−0.122311	−	0.0888641i	0.524948	−	0.851134i	$-0.324085\pi$
$937$	−3.74400	−	2.72017i	−0.122311	−	0.0888641i	−0.647259	+	0.762270i	$0.724085\pi$
$938$	23.3387	−	16.5355i	0.762037	−	0.539903i
$939$	2.86963	+	8.83182i	0.0936469	+	0.288215i
$940$	0.277629	+	0.123608i	0.00905525	+	0.00403166i
$941$	−2.27906	−	21.6838i	−0.0742952	−	0.706872i	−0.966748	−	0.255731i	$-0.917684\pi$
$941$	−2.27906	−	21.6838i	−0.0742952	−	0.706872i	0.892453	−	0.451141i	$-0.148983\pi$
$942$	−14.5942	+	68.6601i	−0.475503	+	2.23707i
$943$	23.3956	−	4.97288i	0.761864	−	0.161939i
$944$	4.12281	−	5.67457i	0.134186	−	0.184691i
$945$	4.28920	+	0.502529i	0.139528	+	0.0163473i
$946$	−5.90480	+	20.2615i	−0.191982	+	0.658759i
$947$	1.14016	+	1.97482i	0.0370502	+	0.0641729i	0.883956	−	0.467570i	$-0.154871\pi$
$947$	1.14016	+	1.97482i	0.0370502	+	0.0641729i	−0.846906	+	0.531743i	$0.821537\pi$
$948$	−1.47128	+	0.655054i	−0.0477848	+	0.0212752i
$949$	−6.93781	−	7.70522i	−0.225211	−	0.250122i
$950$	21.5189	+	19.3757i	0.698166	+	0.628632i
$951$	−39.4540	−	54.3038i	−1.27938	−	1.76092i
$952$	22.2747	−	37.5411i	0.721926	−	1.21671i
$953$	47.3386	−	15.3813i	1.53345	−	0.498248i	0.583889	−	0.811833i	$-0.301530\pi$
$953$	47.3386	−	15.3813i	1.53345	−	0.498248i	0.949560	+	0.313585i	$0.101530\pi$
$954$	−16.3340	−	76.8456i	−0.528834	−	2.48797i
$955$	−3.29536	−	7.40151i	−0.106635	−	0.239507i
$956$	−1.01115	−	0.583788i	−0.0327029	−	0.0188811i
$957$	6.53501	−	7.72010i	0.211247	−	0.249555i
$958$			26.8202i			0.866521i
$959$	−3.60492	+	16.0192i	−0.116409	+	0.517287i
$960$	3.03620	−	9.34447i	0.0979930	−	0.301591i
$961$	−10.0550	+	11.1672i	−0.324353	+	0.360231i
$962$	9.34594	−	0.982298i	0.301325	−	0.0316705i
$963$	4.16149	−	0.437390i	0.134102	−	0.0140947i
$964$	−1.49853	+	1.66428i	−0.0482643	+	0.0536030i
$965$	0.0736448	−	0.226655i	0.00237071	−	0.00729630i
$966$	19.1713	+	17.6799i	0.616826	+	0.568840i
$967$			8.97086i			0.288483i	0.989542	+	0.144242i	$0.0460743\pi$
$967$			8.97086i			0.288483i	−0.989542	+	0.144242i	$0.953926\pi$
$968$	25.7586	+	20.4859i	0.827913	+	0.658442i
$969$	−59.6658	−	34.4481i	−1.91674	−	1.10663i
$970$	−2.90026	−	6.51410i	−0.0931219	−	0.209155i
$971$	10.5904	+	49.8239i	0.339862	+	1.59892i	0.733520	+	0.679668i	$0.237876\pi$
$971$	10.5904	+	49.8239i	0.339862	+	1.59892i	−0.393658	+	0.919257i	$0.628791\pi$
$972$	−5.06707	+	1.64639i	−0.162526	+	0.0528080i
$973$	−0.664851	+	55.8196i	−0.0213141	+	1.78949i
$974$	−19.5909	−	26.9645i	−0.627732	−	0.863999i
$975$	10.4819	+	9.43791i	0.335688	+	0.302255i
$976$	16.0220	+	17.7942i	0.512852	+	0.569579i
$977$	30.5396	−	13.5971i	0.977049	−	0.435010i	0.144829	−	0.989457i	$-0.453737\pi$
$977$	30.5396	−	13.5971i	0.977049	−	0.435010i	0.832219	+	0.554447i	$0.187070\pi$
$978$	−12.2934	−	21.2927i	−0.393098	−	0.680866i
$979$	9.66916	−	3.47202i	0.309028	−	0.110966i
$980$	−0.779584	+	0.232926i	−0.0249029	+	0.00744054i
$981$	4.50855	−	6.20548i	0.143947	−	0.198126i
$982$	−2.70619	+	0.575219i	−0.0863581	+	0.0183560i
$983$	−6.78682	+	31.9295i	−0.216466	+	1.01839i	0.726927	+	0.686715i	$0.240948\pi$
$983$	−6.78682	+	31.9295i	−0.216466	+	1.01839i	−0.943393	+	0.331677i	$0.892386\pi$
$984$	−7.41636	−	70.5620i	−0.236425	−	2.24943i
$985$	2.27350	+	1.01223i	0.0724396	+	0.0322522i
$986$	−2.49235	−	7.67066i	−0.0793726	−	0.244284i
$987$	10.9229	+	15.4170i	0.347681	+	0.490727i
$988$	1.12322	+	0.816067i	0.0357344	+	0.0259625i
$989$	11.5894	−	6.69117i	0.368523	−	0.212767i
$990$	5.48391	+	5.72811i	0.174290	+	0.182051i
$991$	11.2583	−	19.4999i	0.357631	−	0.619434i	−0.629934	−	0.776649i	$-0.716918\pi$
$991$	11.2583	−	19.4999i	0.357631	−	0.619434i	0.987565	+	0.157214i	$0.0502514\pi$
$992$	−1.13039	+	10.7549i	−0.0358898	+	0.341468i
$993$	−55.4783	−	18.0260i	−1.76055	−	0.572038i
$994$	8.75432	−	1.75208i	0.277670	−	0.0555727i
$995$	−3.41019	+	2.47764i	−0.108110	+	0.0785466i
$996$	−1.14969	+	2.58224i	−0.0364293	+	0.0818214i
$997$	−28.2461	−	6.00389i	−0.894562	−	0.190145i	−0.262380	−	0.964965i	$-0.584507\pi$
$997$	−28.2461	−	6.00389i	−0.894562	−	0.190145i	−0.632182	+	0.774820i	$0.717841\pi$
$998$	9.09298	−	8.18736i	0.287833	−	0.259166i
$999$	26.6313	+	2.79907i	0.842578	+	0.0885585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.73.2	yes	48
3.2	odd	2		693.2.cg.a.73.5		48
7.2	even	3		539.2.s.d.117.5		48
7.3	odd	6		539.2.m.a.293.10		48
7.4	even	3		539.2.m.a.293.9		48
7.5	odd	6	inner	77.2.n.a.40.5	yes	48
7.6	odd	2		539.2.s.d.227.2		48
11.2	odd	10		847.2.r.d.94.2		48
11.3	even	5		847.2.r.c.360.2		48
11.4	even	5		847.2.r.d.717.2		48
11.5	even	5		847.2.i.b.241.17		48
11.6	odd	10		847.2.i.b.241.8		48
11.7	odd	10		847.2.r.a.717.5		48
11.8	odd	10	inner	77.2.n.a.52.5	yes	48
11.9	even	5		847.2.r.a.94.5		48
11.10	odd	2		847.2.r.c.766.5		48
21.5	even	6		693.2.cg.a.271.2		48
33.8	even	10		693.2.cg.a.514.2		48
77.5	odd	30		847.2.i.b.362.8		48
77.19	even	30	inner	77.2.n.a.19.2	✓	48
77.26	odd	30		847.2.r.d.838.2		48
77.30	odd	30		539.2.s.d.19.2		48
77.40	even	30		847.2.r.a.838.5		48
77.41	even	10		539.2.s.d.129.5		48
77.47	odd	30		847.2.r.c.481.5		48
77.52	even	30		539.2.m.a.195.9		48
77.54	even	6		847.2.r.c.40.2		48
77.61	even	30		847.2.i.b.362.17		48
77.68	even	30		847.2.r.d.215.2		48
77.74	odd	30		539.2.m.a.195.10		48
77.75	odd	30		847.2.r.a.215.5		48
231.173	odd	30		693.2.cg.a.19.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.19.2	✓	48	77.19	even	30	inner
77.2.n.a.40.5	yes	48	7.5	odd	6	inner
77.2.n.a.52.5	yes	48	11.8	odd	10	inner
77.2.n.a.73.2	yes	48	1.1	even	1	trivial
539.2.m.a.195.9		48	77.52	even	30
539.2.m.a.195.10		48	77.74	odd	30
539.2.m.a.293.9		48	7.4	even	3
539.2.m.a.293.10		48	7.3	odd	6
539.2.s.d.19.2		48	77.30	odd	30
539.2.s.d.117.5		48	7.2	even	3
539.2.s.d.129.5		48	77.41	even	10
539.2.s.d.227.2		48	7.6	odd	2
693.2.cg.a.19.5		48	231.173	odd	30
693.2.cg.a.73.5		48	3.2	odd	2
693.2.cg.a.271.2		48	21.5	even	6
693.2.cg.a.514.2		48	33.8	even	10
847.2.i.b.241.8		48	11.6	odd	10
847.2.i.b.241.17		48	11.5	even	5
847.2.i.b.362.8		48	77.5	odd	30
847.2.i.b.362.17		48	77.61	even	30
847.2.r.a.94.5		48	11.9	even	5
847.2.r.a.215.5		48	77.75	odd	30
847.2.r.a.717.5		48	11.7	odd	10
847.2.r.a.838.5		48	77.40	even	30
847.2.r.c.40.2		48	77.54	even	6
847.2.r.c.360.2		48	11.3	even	5
847.2.r.c.481.5		48	77.47	odd	30
847.2.r.c.766.5		48	11.10	odd	2
847.2.r.d.94.2		48	11.2	odd	10
847.2.r.d.215.2		48	77.68	even	30
847.2.r.d.717.2		48	11.4	even	5
847.2.r.d.838.2		48	77.26	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.30277 - 0.136927i) q^{2} +(2.02980 - 1.82764i) q^{3} +(-0.277833 - 0.0590552i) q^{4} +(0.166444 - 0.373838i) q^{5} +(-2.89461 + 2.10306i) q^{6} +(-2.50634 - 0.847492i) q^{7} +(2.84553 + 0.924570i) q^{8} +(0.466233 - 4.43591i) q^{9} +O(q^{10})\)	\(q+(-1.30277 - 0.136927i) q^{2} +(2.02980 - 1.82764i) q^{3} +(-0.277833 - 0.0590552i) q^{4} +(0.166444 - 0.373838i) q^{5} +(-2.89461 + 2.10306i) q^{6} +(-2.50634 - 0.847492i) q^{7} +(2.84553 + 0.924570i) q^{8} +(0.466233 - 4.43591i) q^{9} +(-0.268026 + 0.464235i) q^{10} +(3.26372 + 0.590040i) q^{11} +(-0.671876 + 0.387908i) q^{12} +(0.864505 + 0.628100i) q^{13} +(3.14915 + 1.44727i) q^{14} +(-0.345395 - 1.06302i) q^{15} +(-3.06151 - 1.36307i) q^{16} +(0.576411 + 5.48418i) q^{17} +(-1.21479 + 5.71513i) q^{18} +(-4.47427 + 0.951036i) q^{19} +(-0.0683206 + 0.0940352i) q^{20} +(-6.63628 + 2.86045i) q^{21} +(-4.17108 - 1.21558i) q^{22} +(1.37746 + 2.38583i) q^{23} +(7.46564 - 3.32392i) q^{24} +(3.23360 + 3.59128i) q^{25} +(-1.04025 - 0.936644i) q^{26} +(-2.34451 - 3.22694i) q^{27} +(0.646295 + 0.383474i) q^{28} +(1.06190 - 0.345031i) q^{29} +(0.304415 + 1.43216i) q^{30} +(-2.75943 - 6.19778i) q^{31} +(-1.38044 - 0.796996i) q^{32} +(7.70307 - 4.76723i) q^{33} -7.22356i q^{34} +(-0.733990 + 0.795908i) q^{35} +(-0.391498 + 1.20491i) q^{36} +(-4.49217 + 4.98906i) q^{37} +(5.95917 - 0.626334i) q^{38} +(2.90271 - 0.305087i) q^{39} +(0.819261 - 0.909881i) q^{40} +(2.68289 - 8.25707i) q^{41} +(9.03722 - 2.81783i) q^{42} -4.85761i q^{43} +(-0.871922 - 0.356672i) q^{44} +(-1.58071 - 0.912624i) q^{45} +(-1.46783 - 3.29680i) q^{46} +(-0.543601 - 2.55744i) q^{47} +(-8.70546 + 2.82857i) q^{48} +(5.56351 + 4.24821i) q^{49} +(-3.72090 - 5.12138i) q^{50} +(11.1931 + 10.0783i) q^{51} +(-0.203095 - 0.225560i) q^{52} +(-12.2835 + 5.46898i) q^{53} +(2.61251 + 4.52499i) q^{54} +(0.763805 - 1.12189i) q^{55} +(-6.34832 - 4.72886i) q^{56} +(-7.34372 + 10.1078i) q^{57} +(-1.43065 + 0.304094i) q^{58} +(-0.435159 + 2.04726i) q^{59} +(0.0331854 + 0.315738i) q^{60} +(-6.52725 - 2.90612i) q^{61} +(2.74626 + 8.45212i) q^{62} +(-4.92794 + 10.7228i) q^{63} +(7.11169 + 5.16694i) q^{64} +(0.378699 - 0.218642i) q^{65} +(-10.6881 + 5.15586i) q^{66} +(4.12644 - 7.14721i) q^{67} +(0.163723 - 1.55772i) q^{68} +(7.15641 + 2.32526i) q^{69} +(1.06520 - 0.936383i) q^{70} +(2.08404 - 1.51414i) q^{71} +(5.42799 - 12.1915i) q^{72} +(-9.49087 - 2.01735i) q^{73} +(6.53540 - 5.88450i) q^{74} +(13.1271 + 1.37972i) q^{75} +1.29926 q^{76} +(-7.67994 - 4.24482i) q^{77} -3.82334 q^{78} +(2.06452 + 0.216990i) q^{79} +(-1.01914 + 0.917636i) q^{80} +(2.43204 + 0.516947i) q^{81} +(-4.62580 + 10.3897i) q^{82} +(2.94758 - 2.14154i) q^{83} +(2.01270 - 0.402820i) q^{84} +(2.14614 + 0.697322i) q^{85} +(-0.665137 + 6.32836i) q^{86} +(1.52484 - 2.64110i) q^{87} +(8.74148 + 4.69651i) q^{88} +(2.68261 - 1.54881i) q^{89} +(1.93434 + 1.40538i) q^{90} +(-1.63444 - 2.30690i) q^{91} +(-0.241808 - 0.744208i) q^{92} +(-16.9284 - 7.53700i) q^{93} +(0.358005 + 3.40619i) q^{94} +(-0.389180 + 1.83095i) q^{95} +(-4.25863 + 0.905199i) q^{96} +(-7.81872 + 10.7615i) q^{97} +(-6.66629 - 6.29624i) q^{98} +(4.13901 - 14.2025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) \) 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

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