LMFDB - Embedded newform 77.2.n.a.19.2

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			19.2
Character	$\chi$	$=$	77.19
Dual form			77.2.n.a.73.2

$q$-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 $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.30277	+	0.136927i	−0.921198	+	0.0968218i	−0.553241	−	0.833021i	$-0.686609\pi$
$2$	−1.30277	+	0.136927i	−0.921198	+	0.0968218i	−0.367957	+	0.929843i	$0.619943\pi$
$3$	2.02980	+	1.82764i	1.17190	+	1.05519i	0.997511	+	0.0705114i	$0.0224631\pi$
$3$	2.02980	+	1.82764i	1.17190	+	1.05519i	0.174393	+	0.984676i	$0.444204\pi$
$4$	−0.277833	+	0.0590552i	−0.138916	+	0.0295276i
$5$	0.166444	+	0.373838i	0.0744359	+	0.167186i	0.946931	−	0.321437i	$-0.104166\pi$
$5$	0.166444	+	0.373838i	0.0744359	+	0.167186i	−0.872495	+	0.488623i	$0.837499\pi$
$6$	−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	−0.461410	−	0.887187i	$-0.652656\pi$
$13$	0.864505	−	0.628100i	0.239771	−	0.174204i	0.701181	+	0.712983i	$0.252656\pi$
$14$	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	−0.669543	−	0.742773i	$-0.733510\pi$
$17$	0.576411	−	5.48418i	0.139800	−	1.33011i	0.809343	−	0.587336i	$-0.199823\pi$
$18$	−1.21479	−	5.71513i	−0.286328	−	1.34707i
$19$	−4.47427	−	0.951036i	−1.02647	−	0.218183i	−0.336242	−	0.941776i	$-0.609156\pi$
$19$	−4.47427	−	0.951036i	−1.02647	−	0.218183i	−0.690227	+	0.723593i	$0.742489\pi$
$20$	−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	−0.685925	−	0.727672i	$-0.740602\pi$
$23$	1.37746	−	2.38583i	0.287220	−	0.497480i	0.973145	+	0.230192i	$0.0739354\pi$
$24$	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	0.405947	−	0.913897i	$-0.366942\pi$
$29$	1.06190	+	0.345031i	0.197189	+	0.0640706i	−0.208757	+	0.977967i	$0.566942\pi$
$30$	0.304415	−	1.43216i	0.0555783	−	0.261475i
$31$	−2.75943	+	6.19778i	−0.495608	+	1.11315i	0.476618	+	0.879110i	$0.341862\pi$
$31$	−2.75943	+	6.19778i	−0.495608	+	1.11315i	−0.972226	+	0.234043i	$0.924804\pi$
$32$	−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	0.250491	−	0.968119i	$-0.419408\pi$
$37$	−4.49217	−	4.98906i	−0.738507	−	0.820196i	−0.988999	+	0.147923i	$0.952741\pi$
$38$	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	0.908627	+	0.417608i	$0.137131\pi$
$41$	2.68289	+	8.25707i	0.418996	+	1.28954i	−0.489631	+	0.871930i	$0.662869\pi$
$42$	9.03722	+	2.81783i	1.39447	+	0.434800i
$43$			4.85761i			0.740779i	0.928877	+	0.370390i	$0.120776\pi$
$43$			4.85761i			0.740779i	−0.928877	+	0.370390i	$0.879224\pi$
$44$	−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	−0.999846	−	0.0175761i	$-0.994405\pi$
$47$	−0.543601	+	2.55744i	−0.0792924	+	0.373041i	0.920553	+	0.390617i	$0.127738\pi$
$48$	−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	−0.999684	−	0.0251218i	$-0.992003\pi$
$53$	−12.2835	−	5.46898i	−1.68727	−	0.751222i	−0.687589	−	0.726101i	$-0.741331\pi$
$54$	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	0.940700	−	0.339239i	$-0.110169\pi$
$59$	−0.435159	−	2.04726i	−0.0566529	−	0.266531i	−0.997353	+	0.0727075i	$0.976836\pi$
$60$	0.0331854	−	0.315738i	0.00428421	−	0.0407616i
$61$	−6.52725	+	2.90612i	−0.835728	+	0.372090i	−0.779557	−	0.626331i	$-0.784556\pi$
$61$	−6.52725	+	2.90612i	−0.835728	+	0.372090i	−0.0561710	+	0.998421i	$0.517889\pi$
$62$	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	0.999989	+	0.00476980i	$0.00151828\pi$
$67$	4.12644	+	7.14721i	0.504125	+	0.873170i	−0.495864	+	0.868400i	$0.665148\pi$
$68$	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	0.704543	−	0.709662i	$-0.251152\pi$
$71$	2.08404	+	1.51414i	0.247330	+	0.179696i	−0.457213	+	0.889357i	$0.651152\pi$
$72$	5.42799	+	12.1915i	0.639694	+	1.43678i
$73$	−9.49087	+	2.01735i	−1.11082	+	0.236113i	−0.726554	−	0.687109i	$-0.758879\pi$
$73$	−9.49087	+	2.01735i	−1.11082	+	0.236113i	−0.384268	+	0.923222i	$0.625546\pi$
$74$	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	0.0123253	−	0.999924i	$-0.496077\pi$
$79$	2.06452	−	0.216990i	0.232277	−	0.0244133i	0.219952	+	0.975511i	$0.429410\pi$
$80$	−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	0.737684	−	0.675146i	$-0.235919\pi$
$83$	2.94758	+	2.14154i	0.323539	+	0.235065i	−0.414145	+	0.910211i	$0.635919\pi$
$84$	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	0.635394	−	0.772188i	$-0.280838\pi$
$89$	2.68261	+	1.54881i	0.284357	+	0.164173i	−0.351037	+	0.936361i	$0.614171\pi$
$90$	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	−0.993615	−	0.112821i	$-0.964011\pi$
$97$	−7.81872	−	10.7615i	−0.793870	−	1.09267i	0.199745	−	0.979848i	$-0.435989\pi$
$98$	−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	0.250151	−	0.968207i	$-0.419520\pi$
$101$	−3.03490	−	1.35123i	−0.301984	−	0.134452i	−0.552135	+	0.833755i	$0.686187\pi$
$102$	−13.2020	+	14.6624i	−1.30720	+	1.45179i
$103$	−2.33864	+	2.10572i	−0.230433	+	0.207483i	−0.776256	−	0.630417i	$-0.782884\pi$
$103$	−2.33864	+	2.10572i	−0.230433	+	0.207483i	0.545823	+	0.837901i	$0.316217\pi$
$104$	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	−0.967713	−	0.252053i	$-0.918894\pi$
$107$	0.195050	−	0.917637i	0.0188562	−	0.0887113i	0.986569	+	0.163342i	$0.0522274\pi$
$108$	0.460814	−	1.03501i	0.0443419	−	0.0995935i
$109$	1.48929	−	0.859845i	0.142649	−	0.0823582i	−0.426977	−	0.904262i	$-0.640422\pi$
$109$	1.48929	−	0.859845i	0.142649	−	0.0823582i	0.569626	+	0.821904i	$0.307088\pi$
$110$	−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	−0.538669	−	0.842518i	$-0.681073\pi$
$113$	−6.35785	−	19.5674i	−0.598096	−	1.84075i	−0.0594272	−	0.998233i	$-0.518927\pi$
$114$	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	−0.364823	−	0.931077i	$-0.618870\pi$
$127$	7.13829	−	9.82501i	0.633421	−	0.871829i	0.998243	+	0.0592484i	$0.0188704\pi$
$128$	−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	−0.748289	−	0.663373i	$-0.769124\pi$
$131$	2.29315	−	3.97185i	0.200353	−	0.347022i	0.948642	+	0.316351i	$0.102458\pi$
$132$	−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	0.931224	+	0.364448i	$0.118742\pi$
$137$	−0.648715	+	6.17211i	−0.0554235	+	0.527319i	−0.986647	+	0.162871i	$0.947924\pi$
$138$	−9.00477	+	4.00918i	−0.766537	+	0.341284i
$139$	−6.52005	+	20.0667i	−0.553023	+	1.70203i	0.148083	+	0.988975i	$0.452690\pi$
$139$	−6.52005	+	20.0667i	−0.553023	+	1.70203i	−0.701107	+	0.713056i	$0.747310\pi$
$140$	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	0.817814	−	0.575482i	$-0.195186\pi$
$149$	−1.91737	−	4.30649i	−0.157077	−	0.352801i	−0.974891	+	0.222681i	$0.928519\pi$
$150$	−16.9127	+	3.59491i	−1.38092	+	0.293523i
$151$	−8.74582	−	7.87478i	−0.711725	−	0.640840i	0.231561	−	0.972820i	$-0.425617\pi$
$151$	−8.74582	−	7.87478i	−0.711725	−	0.640840i	−0.943286	+	0.331980i	$0.892283\pi$
$152$	−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	0.998109	+	0.0614611i	$0.0195760\pi$
$157$	14.5794	+	13.1274i	1.16356	+	1.04768i	0.165455	+	0.986217i	$0.447091\pi$
$158$	−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	−0.985962	−	0.166972i	$-0.946601\pi$
$163$	−0.718293	−	6.83411i	−0.0562611	−	0.535288i	0.929701	−	0.368316i	$-0.120066\pi$
$164$	−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	−0.740639	−	0.671903i	$-0.765477\pi$
$167$	−4.27089	+	3.10299i	−0.330492	+	0.240116i	0.410147	+	0.912019i	$0.365477\pi$
$168$	−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	0.939730	−	0.341917i	$-0.111076\pi$
$173$	21.8227	+	4.63855i	1.65915	+	0.352662i	0.719416	+	0.694580i	$0.244410\pi$
$174$	−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	−0.738014	−	0.674785i	$-0.764236\pi$
$179$	0.136709	−	0.151830i	0.0102181	−	0.0113483i	0.748232	+	0.663437i	$0.230903\pi$
$180$	0.385278	−	0.346906i	0.0287169	−	0.0258568i
$181$	−4.21629	+	5.80323i	−0.313394	+	0.431350i	−0.936436	−	0.350838i	$-0.885897\pi$
$181$	−4.21629	+	5.80323i	−0.313394	+	0.431350i	0.623042	+	0.782189i	$0.285897\pi$
$182$	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	0.997860	+	0.0653872i	$0.0208282\pi$
$191$	13.2479	+	14.7133i	0.958584	+	1.06462i	−0.0392758	+	0.999228i	$0.512505\pi$
$192$	23.8786	+	2.50974i	1.72329	+	0.181125i
$193$	0.579189	+	0.0608752i	0.0416909	+	0.00438189i	0.125351	−	0.992112i	$-0.459994\pi$
$193$	0.579189	+	0.0608752i	0.0416909	+	0.00438189i	−0.0836600	+	0.996494i	$0.526661\pi$
$194$	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	$-0.930489\pi$
$197$		−	6.08149i		−	0.433289i	0.976251	−	0.216644i	$-0.0695112\pi$
$198$	−7.33688	−	17.9358i	−0.521410	−	1.27464i
$199$	−8.92066	+	5.15035i	−0.632369	+	0.365098i	−0.781669	−	0.623694i	$-0.785631\pi$
$199$	−8.92066	+	5.15035i	−0.632369	+	0.365098i	0.149300	+	0.988792i	$0.452298\pi$
$200$	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	0.999656	+	0.0262235i	$0.00834816\pi$
$211$	10.3959	+	14.3088i	0.715685	+	0.985056i	−0.283971	+	0.958833i	$0.591652\pi$
$212$	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	−0.860002	−	0.510290i	$-0.829538\pi$
$223$	−18.7534	+	6.09334i	−1.25582	+	0.408040i	−0.395816	+	0.918330i	$0.629538\pi$
$224$	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	−0.429142	−	0.903237i	$-0.641184\pi$
$227$	−6.83724	+	1.45330i	−0.453804	+	0.0964590i	−0.0246615	+	0.999696i	$0.507851\pi$
$228$	2.63724	+	2.37458i	0.174656	+	0.157261i
$229$	−0.241522	+	0.0253850i	−0.0159602	+	0.00167749i	−0.112505	−	0.993651i	$-0.535888\pi$
$229$	−0.241522	+	0.0253850i	−0.0159602	+	0.00167749i	0.0965450	+	0.995329i	$0.469221\pi$
$230$	−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	0.537374	−	0.843344i	$-0.319416\pi$
$233$	18.9025	−	1.98674i	1.23835	−	0.130155i	0.700972	+	0.713189i	$0.252750\pi$
$234$	−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	−0.179834	−	0.983697i	$-0.557556\pi$
$239$	3.90942	−	1.27025i	0.252879	−	0.0821655i	0.432714	+	0.901531i	$0.357556\pi$
$240$	−0.391538	−	3.72523i	−0.0252737	−	0.240463i
$241$	3.94226	+	6.82819i	0.253943	+	0.439843i	0.964608	−	0.263688i	$-0.0849390\pi$
$241$	3.94226	+	6.82819i	0.253943	+	0.439843i	−0.710665	+	0.703531i	$0.751606\pi$
$242$	−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	0.686572	−	0.727062i	$-0.259115\pi$
$251$	−3.43900	−	4.73338i	−0.217068	−	0.298768i	−0.903639	+	0.428294i	$0.859115\pi$
$252$	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	−0.828166	−	0.560483i	$-0.810616\pi$
$257$	−5.72828	+	5.15777i	−0.357320	+	0.321733i	0.470846	+	0.882216i	$0.343949\pi$
$258$	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	−0.475289	−	0.879830i	$-0.657656\pi$
$263$	0.794994	−	0.458990i	0.0490215	−	0.0283026i	0.524310	+	0.851527i	$0.324323\pi$
$264$	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	0.545096	−	0.838373i	$-0.316493\pi$
$269$	14.8263	+	1.55830i	0.903973	+	0.0950114i	0.358877	+	0.933385i	$0.383160\pi$
$270$	2.12645	+	0.223499i	0.129412	+	0.0136017i
$271$	4.51235	+	5.01147i	0.274106	+	0.304425i	0.864442	−	0.502732i	$-0.167672\pi$
$271$	4.51235	+	5.01147i	0.274106	+	0.304425i	−0.590337	+	0.807157i	$0.701005\pi$
$272$	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	−0.507924	−	0.861402i	$-0.669587\pi$
$277$	7.85714	−	17.6474i	0.472090	−	1.06033i	0.980014	−	0.198930i	$-0.0637465\pi$
$278$	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	−0.705711	−	0.708500i	$-0.749372\pi$
$281$	3.12109	−	4.29582i	0.186189	−	0.256267i	0.891900	+	0.452233i	$0.149372\pi$
$282$	6.95197	−	6.25958i	0.413984	−	0.372753i
$283$	−8.03602	+	8.92491i	−0.477692	+	0.530531i	−0.933035	−	0.359785i	$-0.882850\pi$
$283$	−8.03602	+	8.92491i	−0.477692	+	0.530531i	0.455343	+	0.890316i	$0.349517\pi$
$284$	−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	−0.644853	−	0.764307i	$-0.723081\pi$
$293$	5.58180	−	17.1790i	0.326092	−	1.00361i	0.970945	−	0.239302i	$-0.0769186\pi$
$294$	−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	0.177006	−	0.984210i	$-0.443359\pi$
$311$	−13.8138	−	12.4380i	−0.783310	−	0.705296i	−0.960316	+	0.278914i	$0.910026\pi$
$312$	8.54183	−	1.81562i	0.483586	−	0.102789i
$313$	−1.38286	−	3.10595i	−0.0781638	−	0.175559i	0.870237	−	0.492634i	$-0.163966\pi$
$313$	−1.38286	−	3.10595i	−0.0781638	−	0.175559i	−0.948400	+	0.317075i	$0.897299\pi$
$314$	−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	0.791856	+	0.610708i	$0.209115\pi$
$317$	2.56878	+	24.4403i	0.144277	+	1.37271i	−0.647579	+	0.761998i	$0.724218\pi$
$318$	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	0.407691	+	0.913120i	$0.366334\pi$
$331$	−10.6784	+	18.4956i	−0.586940	+	1.01661i	−0.994631	+	0.103489i	$0.966999\pi$
$332$	−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	−0.100583	−	0.994929i	$-0.532071\pi$
$337$	−14.0759	−	4.57352i	−0.766761	−	0.249136i	−0.666178	+	0.745793i	$0.732071\pi$
$338$	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	0.105470	−	0.994423i	$-0.466365\pi$
$347$	0.0350743	+	0.00368645i	0.00188289	+	0.000197899i	−0.103587	+	0.994620i	$0.533032\pi$
$348$	−0.579622	−	0.643735i	−0.0310710	−	0.0345078i
$349$	2.04800	+	6.30311i	0.109627	+	0.337398i	0.990789	−	0.135418i	$-0.0432377\pi$
$349$	2.04800	+	6.30311i	0.109627	+	0.337398i	−0.881161	+	0.472816i	$0.843238\pi$
$350$	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	−0.0614973	−	0.998107i	$-0.519588\pi$
$353$	14.5072	−	8.37574i	0.772140	−	0.445795i	0.833638	+	0.552312i	$0.186254\pi$
$354$	−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	−0.415019	−	0.909813i	$-0.636225\pi$
$359$	8.45862	−	7.61618i	0.446429	−	0.401966i	0.861448	+	0.507846i	$0.169558\pi$
$360$	−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	−0.994495	−	0.104780i	$-0.966586\pi$
$367$	−2.46356	−	11.5901i	−0.128597	−	0.605000i	0.865899	−	0.500219i	$-0.166747\pi$
$368$	−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	0.760433	−	0.649416i	$-0.224987\pi$
$373$	11.1676	+	6.44764i	0.578239	+	0.333846i	−0.182194	+	0.983263i	$0.558320\pi$
$374$	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	0.528921	−	0.848671i	$-0.322597\pi$
$379$	−2.23429	−	1.62331i	−0.114768	−	0.0833838i	−0.643689	+	0.765287i	$0.722597\pi$
$380$	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	0.0784474	−	0.996918i	$-0.475004\pi$
$383$	7.09331	−	0.745537i	0.362451	−	0.0380952i	0.284004	+	0.958823i	$0.408337\pi$
$384$	−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	−0.285415	−	0.958404i	$-0.592132\pi$
$389$	−3.08345	+	0.655408i	−0.156337	+	0.0332305i	0.129078	+	0.991634i	$0.458798\pi$
$390$	−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	−0.0248080	−	0.999692i	$-0.507897\pi$
$397$	−17.9916	−	10.3874i	−0.902971	−	0.521330i	−0.878163	+	0.478362i	$0.841231\pi$
$398$	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	−0.893794	−	0.448478i	$-0.851966\pi$
$401$	−23.2005	+	10.3295i	−1.15858	+	0.515831i	−0.264781	+	0.964309i	$0.585300\pi$
$402$	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	−0.400038	−	0.916499i	$-0.631003\pi$
$409$	−27.2779	−	12.1449i	−1.34881	−	0.600527i	−0.948769	+	0.315971i	$0.897670\pi$
$410$	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	$-0.976358\pi$
$419$		−	3.03794i		−	0.148413i	0.997243	−	0.0742066i	$-0.0236424\pi$
$420$	0.184411	+	0.819471i	0.00899835	+	0.0399861i
$421$	6.95131	+	21.3939i	0.338786	+	1.04268i	0.964827	+	0.262886i	$0.0846744\pi$
$421$	6.95131	+	21.3939i	0.338786	+	1.04268i	−0.626041	+	0.779791i	$0.715326\pi$
$422$	−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	−0.540180	−	0.841550i	$-0.681644\pi$
$431$	9.27299	−	20.8275i	0.446664	−	1.00322i	0.986844	−	0.161675i	$-0.0516896\pi$
$432$	2.77919	−	13.0751i	0.133714	−	0.629075i
$433$	31.3066	+	10.1721i	1.50450	+	0.488841i	0.941326	−	0.337499i	$-0.109581\pi$
$433$	31.3066	+	10.1721i	1.50450	+	0.488841i	0.563171	+	0.826340i	$0.309581\pi$
$434$	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	−0.119851	−	0.992792i	$-0.538242\pi$
$439$	16.7589	−	29.0272i	0.799858	−	1.38539i	0.919708	−	0.392602i	$-0.128425\pi$
$440$	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	0.197003	−	0.980403i	$-0.436879\pi$
$443$	−0.458647	−	0.0974883i	−0.0217910	−	0.00463181i	−0.218794	+	0.975771i	$0.570212\pi$
$444$	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	−0.825153	−	0.564910i	$-0.808911\pi$
$449$	−11.5034	+	8.35769i	−0.542878	+	0.394424i	0.282275	+	0.959334i	$0.408911\pi$
$450$	−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	0.999071	−	0.0430889i	$-0.0137199\pi$
$457$	6.38207	+	14.3344i	0.298541	+	0.670534i	−0.700530	+	0.713623i	$0.747053\pi$
$458$	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	0.999999	−	0.00149824i	$-0.000476906\pi$
$467$	7.12608	+	16.0054i	0.329756	+	0.740643i	−0.670243	+	0.742141i	$0.733810\pi$
$468$	−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	0.830128	+	0.557573i	$0.188267\pi$
$479$	−2.14014	+	20.3621i	−0.0977856	+	0.930368i	−0.927914	+	0.372795i	$0.878399\pi$
$480$	−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	−0.221487	−	0.975163i	$-0.571091\pi$
$487$	17.0252	−	18.9084i	0.771486	−	0.856822i	0.992973	+	0.118342i	$0.0377578\pi$
$488$	−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	0.353991	−	0.935249i	$-0.384824\pi$
$491$	2.00866	+	0.652654i	0.0906497	+	0.0294539i	−0.263341	+	0.964703i	$0.584824\pi$
$492$	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	0.586824	−	0.809715i	$-0.300378\pi$
$499$	−6.25015	−	6.94149i	−0.279795	−	0.310744i	−0.866619	+	0.498971i	$0.833711\pi$
$500$	−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	−0.831741	−	0.555164i	$-0.812656\pi$
$503$	−10.8811	−	33.4887i	−0.485166	−	1.49319i	0.346575	−	0.938022i	$-0.387344\pi$
$504$	−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	−0.999903	−	0.0138968i	$-0.995576\pi$
$509$	−1.82279	+	8.57557i	−0.0807939	+	0.380105i	0.919110	+	0.394002i	$0.128910\pi$
$510$	−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	−0.969198	−	0.246282i	$-0.920791\pi$
$521$	−4.19904	−	19.7549i	−0.183963	−	0.865480i	0.785235	−	0.619198i	$-0.212542\pi$
$522$	0.681917	−	6.48801i	0.0298467	−	0.283973i
$523$	−15.3533	+	6.83574i	−0.671353	+	0.298906i	−0.713960	−	0.700186i	$-0.753100\pi$
$523$	−15.3533	+	6.83574i	−0.671353	+	0.298906i	0.0426069	+	0.999092i	$0.486434\pi$
$524$	−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	0.761462	−	0.648209i	$-0.224482\pi$
$541$	38.1700	−	4.01183i	1.64106	−	0.172482i	0.879593	+	0.475727i	$0.157815\pi$
$542$	−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	−0.972909	−	0.231188i	$-0.925739\pi$
$547$	−37.9850	+	12.3421i	−1.62412	+	0.527709i	−0.651211	+	0.758897i	$0.725739\pi$
$548$	−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	0.721184	+	0.692743i	$0.243598\pi$
$557$	8.12138	+	38.2081i	0.344114	+	1.61893i	−0.377071	+	0.926185i	$0.623069\pi$
$558$	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	0.311181	−	0.950351i	$-0.399276\pi$
$563$	−4.43344	−	1.97390i	−0.186847	−	0.0831898i	−0.498028	+	0.867161i	$0.665942\pi$
$564$	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	−0.860033	−	0.510238i	$-0.829557\pi$
$569$	3.17680	−	14.9457i	0.133179	−	0.626556i	0.993212	−	0.116318i	$-0.0371092\pi$
$570$	−2.72407	+	6.11836i	−0.114099	+	0.256270i
$571$	−8.90511	+	5.14137i	−0.372667	+	0.215160i	−0.674623	−	0.738162i	$-0.735694\pi$
$571$	−8.90511	+	5.14137i	−0.372667	+	0.215160i	0.301956	+	0.953322i	$0.402361\pi$
$572$	−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	0.599271	−	0.800546i	$-0.295457\pi$
$577$	24.4773	+	2.57267i	1.01900	+	0.107102i	0.419732	+	0.907648i	$0.362124\pi$
$578$	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	0.277047	−	0.960856i	$-0.410644\pi$
$587$	−1.54078	−	0.500630i	−0.0635949	−	0.0206632i	−0.340642	+	0.940193i	$0.610644\pi$
$588$	−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	−0.618515	−	0.785773i	$-0.712265\pi$
$593$	9.04033	−	15.6583i	0.371242	−	0.643010i	0.989757	+	0.142763i	$0.0455988\pi$
$594$	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	0.946827	+	0.321742i	$0.104269\pi$
$599$	−1.13081	+	10.7589i	−0.0462036	+	0.439598i	−0.993031	+	0.117855i	$0.962398\pi$
$600$	36.0780	−	16.0630i	1.47288	−	0.655767i
$601$	7.45445	−	22.9424i	0.304073	−	0.935841i	−0.675948	−	0.736949i	$-0.736266\pi$
$601$	7.45445	−	22.9424i	0.304073	−	0.935841i	0.980021	−	0.198892i	$-0.0637343\pi$
$602$	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	0.997299	+	0.0734448i	$0.0233993\pi$
$607$	0.913145	+	8.68800i	0.0370634	+	0.352635i	−0.960236	+	0.279190i	$0.909934\pi$
$608$	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	0.728663	−	0.684872i	$-0.240142\pi$
$613$	3.06290	+	2.75784i	0.123709	+	0.111388i	−0.604954	+	0.796260i	$0.706809\pi$
$614$	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	0.559575	−	0.828780i	$-0.310964\pi$
$619$	−5.12954	−	4.61866i	−0.206174	−	0.185640i	−0.765748	+	0.643140i	$0.777631\pi$
$620$	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	−0.614767	−	0.788709i	$-0.710750\pi$
$631$	8.69598	−	26.7635i	0.346182	−	1.06544i	0.960948	−	0.276728i	$-0.0892502\pi$
$632$	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	−0.995874	−	0.0907440i	$-0.971076\pi$
$641$	−20.2931	+	22.5378i	−0.801530	+	0.890189i	0.194344	+	0.980933i	$0.437742\pi$
$642$	−2.49444	+	2.24600i	−0.0984477	+	0.0886427i
$643$	13.2785	−	18.2763i	0.523654	−	0.720747i	−0.462493	−	0.886623i	$-0.653045\pi$
$643$	13.2785	−	18.2763i	0.523654	−	0.720747i	0.986147	+	0.165876i	$0.0530450\pi$
$644$	−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	−0.992250	−	0.124256i	$-0.960346\pi$
$647$	−6.00206	+	13.4808i	−0.235965	+	0.529987i	0.756285	+	0.654242i	$0.227012\pi$
$648$	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	0.380235	−	0.924890i	$-0.375843\pi$
$653$	−14.8042	−	16.4418i	−0.579334	−	0.643416i	−0.959569	+	0.281474i	$0.909177\pi$
$654$	−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	$-0.721005\pi$
$659$		−	39.4562i		−	1.53699i	0.639853	−	0.768497i	$-0.278995\pi$
$660$	−0.0779902	−	1.05006i	−0.00303577	−	0.0408735i
$661$	31.1770	−	18.0000i	1.21264	−	0.700121i	0.249310	−	0.968424i	$-0.419796\pi$
$661$	31.1770	−	18.0000i	1.21264	−	0.700121i	0.963335	+	0.268303i	$0.0864629\pi$
$662$	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	−0.999926	−	0.0121550i	$-0.996131\pi$
$673$	−18.2242	−	25.0835i	−0.702492	−	0.966897i	0.297434	−	0.954742i	$-0.403869\pi$
$674$	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	−0.953046	−	0.302825i	$-0.902070\pi$
$677$	−35.5348	+	15.8211i	−1.36572	+	0.608056i	−0.412669	+	0.910881i	$0.635403\pi$
$678$	−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	−0.972400	−	0.233320i	$-0.925041\pi$
$683$	−17.9872	−	31.1548i	−0.688261	−	1.19210i	0.284138	−	0.958783i	$-0.408292\pi$
$684$	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	0.364903	−	0.931046i	$-0.381102\pi$
$691$	24.0632	−	2.52914i	0.915407	−	0.0962131i	0.550504	+	0.834832i	$0.314436\pi$
$692$	−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	−0.656620	−	0.754221i	$-0.728015\pi$
$701$	−19.7121	+	6.40486i	−0.744517	+	0.241908i	−0.0878970	+	0.996130i	$0.528015\pi$
$702$	−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	0.537814	−	0.843064i	$-0.319250\pi$
$709$	40.5850	−	18.0696i	1.52420	−	0.678618i	0.986386	+	0.164446i	$0.0525836\pi$
$710$	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	−0.984410	−	0.175890i	$-0.943720\pi$
$719$	−24.4648	+	22.0282i	−0.912382	+	0.821513i	0.0720277	+	0.997403i	$0.477053\pi$
$720$	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	$-0.573720\pi$
$727$		−	52.4861i		−	1.94660i	0.229534	−	0.973301i	$-0.426280\pi$
$728$	−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	0.945571	−	0.325414i	$-0.105504\pi$
$733$	14.1624	+	15.7289i	0.523101	+	0.580962i	−0.422471	+	0.906376i	$0.638837\pi$
$734$	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	−0.939269	−	0.343182i	$-0.888495\pi$
$739$	−1.51530	+	3.40342i	−0.0557412	+	0.125197i	0.883528	+	0.468379i	$0.155162\pi$
$740$	−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	−0.856302	−	0.516475i	$-0.827244\pi$
$743$	−2.73925	+	3.77026i	−0.100493	+	0.138317i	0.755809	+	0.654792i	$0.227244\pi$
$744$	−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	−0.364832	−	0.931074i	$-0.618873\pi$
$751$	−29.5097	−	6.27248i	−1.07682	−	0.228886i	−0.711992	+	0.702188i	$0.752207\pi$
$752$	−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	−0.551179	−	0.834387i	$-0.685822\pi$
$757$	1.98226	−	1.44020i	0.0720466	−	0.0523449i	0.623226	+	0.782042i	$0.285822\pi$
$758$	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	−0.953226	−	0.302257i	$-0.902260\pi$
$761$	−2.30822	−	21.9613i	−0.0836731	−	0.796096i	0.869553	−	0.493839i	$-0.164407\pi$
$762$	−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	0.478172	−	0.878266i	$-0.341299\pi$
$773$	−9.60033	−	8.64417i	−0.345300	−	0.310909i	−0.823472	+	0.567357i	$0.807966\pi$
$774$	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	−0.776861	−	0.629673i	$-0.783189\pi$
$787$	3.19642	−	30.4119i	0.113940	−	1.08407i	0.890801	−	0.454394i	$-0.150144\pi$
$788$	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	−0.992055	−	0.125806i	$-0.959848\pi$
$797$	−15.9745	+	21.9870i	−0.565845	+	0.778818i	0.426210	+	0.904624i	$0.359848\pi$
$798$	−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	0.759047	−	0.651036i	$-0.225665\pi$
$809$	38.8573	+	4.08407i	1.36615	+	0.143588i	0.607102	+	0.794624i	$0.292332\pi$
$810$	−0.891837	−	0.990486i	−0.0313360	−	0.0348021i
$811$	9.46176	+	29.1203i	0.332247	+	1.02255i	0.968062	+	0.250711i	$0.0806642\pi$
$811$	9.46176	+	29.1203i	0.332247	+	1.02255i	−0.635815	+	0.771842i	$0.719336\pi$
$812$	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	−0.974260	−	0.225428i	$-0.927622\pi$
$821$	−24.4097	+	21.9786i	−0.851904	+	0.767058i	0.122355	+	0.992486i	$0.460955\pi$
$822$	14.8581	−	16.5016i	0.518236	−	0.575559i
$823$	−3.08491	−	1.37349i	−0.107533	−	0.0478769i	0.352265	−	0.935900i	$-0.385412\pi$
$823$	−3.08491	−	1.37349i	−0.107533	−	0.0478769i	−0.459798	+	0.888023i	$0.652078\pi$
$824$	−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	0.956189	+	0.292749i	$0.0945701\pi$
$827$	27.0072	+	37.1722i	0.939132	+	1.29260i	−0.0170577	+	0.999855i	$0.505430\pi$
$828$	−3.41398	−	0.725663i	−0.118644	−	0.0252185i
$829$	8.20724	+	38.6120i	0.285049	+	1.34105i	0.854682	+	0.519152i	$0.173752\pi$
$829$	8.20724	+	38.6120i	0.285049	+	1.34105i	−0.569632	+	0.821900i	$0.692914\pi$
$830$	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	−0.755376	−	0.655292i	$-0.772546\pi$
$839$	−28.4243	+	9.23563i	−0.981317	+	0.318849i	−0.225941	+	0.974141i	$0.572546\pi$
$840$	−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	−0.0479334	−	0.998851i	$-0.515264\pi$
$853$	−29.5773	−	21.4892i	−1.01271	−	0.735776i	−0.964776	+	0.263074i	$0.915264\pi$
$854$	−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	−0.998576	−	0.0533506i	$-0.983010\pi$
$857$	−15.9690	−	27.6591i	−0.545491	−	0.944818i	0.453085	−	0.891467i	$-0.350323\pi$
$858$	−12.4783	+	2.25592i	−0.426002	+	0.0770160i
$859$	−26.7408	−	15.4388i	−0.912384	−	0.526765i	−0.0311863	−	0.999514i	$-0.509929\pi$
$859$	−26.7408	−	15.4388i	−0.912384	−	0.526765i	−0.881197	+	0.472749i	$0.843262\pi$
$860$	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	−0.819080	−	0.573680i	$-0.805515\pi$
$863$	−27.6384	+	12.3054i	−0.940823	+	0.418882i	−0.121744	+	0.992562i	$0.538849\pi$
$864$	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	0.683907	+	0.729569i	$0.260279\pi$
$877$	−7.03679	+	33.1055i	−0.237615	+	1.11789i	−0.921523	+	0.388324i	$0.873054\pi$
$878$	−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	$0.110562\pi$
$881$			20.2072i			0.680798i	−0.940281	+	0.340399i	$0.889438\pi$
$882$	−31.0376	−	26.6355i	−1.04509	−	0.896865i
$883$	−2.10312	−	6.47273i	−0.0707755	−	0.217825i	0.909412	−	0.415896i	$-0.136532\pi$
$883$	−2.10312	−	6.47273i	−0.0707755	−	0.217825i	−0.980188	+	0.198072i	$0.936532\pi$
$884$	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	0.984923	+	0.172995i	$0.0553443\pi$
$887$	31.3913	+	34.8636i	1.05402	+	1.17060i	0.0690944	+	0.997610i	$0.477989\pi$
$888$	−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	0.852174	+	0.523258i	$0.175284\pi$
$907$	−2.71558	+	25.8371i	−0.0901695	+	0.857905i	−0.942344	+	0.334647i	$0.891383\pi$
$908$	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	0.152410	−	0.988317i	$-0.451297\pi$
$911$	34.3918	−	24.9871i	1.13945	−	0.827861i	0.987043	+	0.160457i	$0.0512967\pi$
$912$	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	0.990331	−	0.138728i	$-0.0443013\pi$
$919$	6.80800	+	15.2910i	0.224575	+	0.504404i	−0.765755	+	0.643132i	$0.777635\pi$
$920$	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	−0.991804	−	0.127770i	$-0.959218\pi$
$929$	−12.8962	−	28.9653i	−0.423109	−	0.950319i	0.568694	−	0.822549i	$-0.307449\pi$
$930$	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	−0.647259	−	0.762270i	$-0.724085\pi$
$937$	−3.74400	+	2.72017i	−0.122311	+	0.0888641i	0.524948	+	0.851134i	$0.324085\pi$
$938$	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	0.892453	+	0.451141i	$0.148983\pi$
$941$	−2.27906	+	21.6838i	−0.0742952	+	0.706872i	−0.966748	+	0.255731i	$0.917684\pi$
$942$	−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	−0.846906	−	0.531743i	$-0.821537\pi$
$947$	1.14016	−	1.97482i	0.0370502	−	0.0641729i	0.883956	+	0.467570i	$0.154871\pi$
$948$	−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	0.949560	−	0.313585i	$-0.101530\pi$
$953$	47.3386	+	15.3813i	1.53345	+	0.498248i	0.583889	+	0.811833i	$0.301530\pi$
$954$	−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	$-0.953926\pi$
$967$		−	8.97086i		−	0.288483i	0.989542	−	0.144242i	$-0.0460743\pi$
$968$	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	−0.393658	−	0.919257i	$-0.628791\pi$
$971$	10.5904	−	49.8239i	0.339862	−	1.59892i	0.733520	−	0.679668i	$-0.237876\pi$
$972$	−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	0.832219	−	0.554447i	$-0.187070\pi$
$977$	30.5396	+	13.5971i	0.977049	+	0.435010i	0.144829	+	0.989457i	$0.453737\pi$
$978$	−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	−0.943393	−	0.331677i	$-0.892386\pi$
$983$	−6.78682	−	31.9295i	−0.216466	−	1.01839i	0.726927	−	0.686715i	$-0.240948\pi$
$984$	−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	0.987565	−	0.157214i	$-0.0502514\pi$
$991$	11.2583	+	19.4999i	0.357631	+	0.619434i	−0.629934	+	0.776649i	$0.716918\pi$
$992$	−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	−0.632182	−	0.774820i	$-0.717841\pi$
$997$	−28.2461	+	6.00389i	−0.894562	+	0.190145i	−0.262380	+	0.964965i	$0.584507\pi$
$998$	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.19.2	✓	48
3.2	odd	2		693.2.cg.a.19.5		48
7.2	even	3		539.2.m.a.195.9		48
7.3	odd	6	inner	77.2.n.a.52.5	yes	48
7.4	even	3		539.2.s.d.129.5		48
7.5	odd	6		539.2.m.a.195.10		48
7.6	odd	2		539.2.s.d.19.2		48
11.2	odd	10		847.2.i.b.362.8		48
11.3	even	5		847.2.r.d.215.2		48
11.4	even	5		847.2.r.c.40.2		48
11.5	even	5		847.2.r.a.838.5		48
11.6	odd	10		847.2.r.d.838.2		48
11.7	odd	10	inner	77.2.n.a.40.5	yes	48
11.8	odd	10		847.2.r.a.215.5		48
11.9	even	5		847.2.i.b.362.17		48
11.10	odd	2		847.2.r.c.481.5		48
21.17	even	6		693.2.cg.a.514.2		48
33.29	even	10		693.2.cg.a.271.2		48
77.3	odd	30		847.2.r.d.94.2		48
77.10	even	6		847.2.r.c.360.2		48
77.17	even	30		847.2.r.d.717.2		48
77.18	odd	30		539.2.s.d.227.2		48
77.24	even	30		847.2.i.b.241.17		48
77.31	odd	30		847.2.i.b.241.8		48
77.38	odd	30		847.2.r.a.717.5		48
77.40	even	30		539.2.m.a.293.9		48
77.51	odd	30		539.2.m.a.293.10		48
77.52	even	30		847.2.r.a.94.5		48
77.59	odd	30		847.2.r.c.766.5		48
77.62	even	10		539.2.s.d.117.5		48
77.73	even	30	inner	77.2.n.a.73.2	yes	48
231.227	odd	30		693.2.cg.a.73.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.19.2	✓	48	1.1	even	1	trivial
77.2.n.a.40.5	yes	48	11.7	odd	10	inner
77.2.n.a.52.5	yes	48	7.3	odd	6	inner
77.2.n.a.73.2	yes	48	77.73	even	30	inner
539.2.m.a.195.9		48	7.2	even	3
539.2.m.a.195.10		48	7.5	odd	6
539.2.m.a.293.9		48	77.40	even	30
539.2.m.a.293.10		48	77.51	odd	30
539.2.s.d.19.2		48	7.6	odd	2
539.2.s.d.117.5		48	77.62	even	10
539.2.s.d.129.5		48	7.4	even	3
539.2.s.d.227.2		48	77.18	odd	30
693.2.cg.a.19.5		48	3.2	odd	2
693.2.cg.a.73.5		48	231.227	odd	30
693.2.cg.a.271.2		48	33.29	even	10
693.2.cg.a.514.2		48	21.17	even	6
847.2.i.b.241.8		48	77.31	odd	30
847.2.i.b.241.17		48	77.24	even	30
847.2.i.b.362.8		48	11.2	odd	10
847.2.i.b.362.17		48	11.9	even	5
847.2.r.a.94.5		48	77.52	even	30
847.2.r.a.215.5		48	11.8	odd	10
847.2.r.a.717.5		48	77.38	odd	30
847.2.r.a.838.5		48	11.5	even	5
847.2.r.c.40.2		48	11.4	even	5
847.2.r.c.360.2		48	77.10	even	6
847.2.r.c.481.5		48	11.10	odd	2
847.2.r.c.766.5		48	77.59	odd	30
847.2.r.d.94.2		48	77.3	odd	30
847.2.r.d.215.2		48	11.3	even	5
847.2.r.d.717.2		48	77.17	even	30
847.2.r.d.838.2		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 $\F_{q}$

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more