LMFDB - Embedded newform 380.2.bj.a.283.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			283.29
Character	$\chi$	$=$	380.283
Dual form			380.2.bj.a.47.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0775850 - 1.41208i) q^{2} +(1.06054 - 0.0927854i) q^{3} +(-1.98796 - 0.219113i) q^{4} +(0.225970 + 2.22462i) q^{5} +(-0.0487386 - 1.50477i) q^{6} +(-1.02923 + 3.84113i) q^{7} +(-0.463642 + 2.79017i) q^{8} +(-1.83828 + 0.324139i) q^{9} +O(q^{10})$	\(q+(0.0775850 - 1.41208i) q^{2} +(1.06054 - 0.0927854i) q^{3} +(-1.98796 - 0.219113i) q^{4} +(0.225970 + 2.22462i) q^{5} +(-0.0487386 - 1.50477i) q^{6} +(-1.02923 + 3.84113i) q^{7} +(-0.463642 + 2.79017i) q^{8} +(-1.83828 + 0.324139i) q^{9} +(3.15888 - 0.146492i) q^{10} +(1.69839 + 0.980566i) q^{11} +(-2.12865 - 0.0479249i) q^{12} +(6.62433 + 0.579554i) q^{13} +(5.34415 + 1.75137i) q^{14} +(0.446064 + 2.33834i) q^{15} +(3.90398 + 0.871177i) q^{16} +(-0.236628 - 0.337940i) q^{17} +(0.315088 + 2.62096i) q^{18} +(-1.97618 - 3.88519i) q^{19} +(0.0382231 - 4.47197i) q^{20} +(-0.735139 + 4.16918i) q^{21} +(1.51641 - 2.32219i) q^{22} +(-2.82380 + 1.31676i) q^{23} +(-0.232825 + 3.00211i) q^{24} +(-4.89787 + 1.00540i) q^{25} +(1.33233 - 9.30915i) q^{26} +(-5.00446 + 1.34094i) q^{27} +(2.88771 - 7.41051i) q^{28} +(4.25746 - 0.750704i) q^{29} +(3.33654 - 0.448459i) q^{30} +(-5.38558 + 3.10936i) q^{31} +(1.53306 - 5.44515i) q^{32} +(1.89220 + 0.882346i) q^{33} +(-0.495559 + 0.307920i) q^{34} +(-8.77764 - 1.42166i) q^{35} +(3.72546 - 0.241584i) q^{36} +(5.24459 - 5.24459i) q^{37} +(-5.63954 + 2.48910i) q^{38} +7.07916 q^{39} +(-6.31183 - 0.400932i) q^{40} +(7.24645 + 6.08049i) q^{41} +(5.83020 + 1.36154i) q^{42} +(0.830266 - 1.78051i) q^{43} +(-3.16148 - 2.32147i) q^{44} +(-1.13648 - 4.01624i) q^{45} +(1.64029 + 4.08961i) q^{46} +(2.71213 - 3.87332i) q^{47} +(4.22117 + 0.561687i) q^{48} +(-7.63282 - 4.40681i) q^{49} +(1.03970 + 6.99421i) q^{50} +(-0.282310 - 0.336444i) q^{51} +(-13.0419 - 2.60361i) q^{52} +(-1.46784 - 3.14780i) q^{53} +(1.50525 + 7.17075i) q^{54} +(-1.79760 + 3.99985i) q^{55} +(-10.2402 - 4.65263i) q^{56} +(-2.45631 - 3.93705i) q^{57} +(-0.729743 - 6.07013i) q^{58} +(-1.83537 + 10.4089i) q^{59} +(-0.374397 - 4.74626i) q^{60} +(8.52071 + 3.10129i) q^{61} +(3.97284 + 7.84613i) q^{62} +(0.646952 - 7.39470i) q^{63} +(-7.57007 - 2.58728i) q^{64} +(0.207615 + 14.8676i) q^{65} +(1.39275 - 2.60348i) q^{66} +(6.44604 - 9.20589i) q^{67} +(0.396361 + 0.723661i) q^{68} +(-2.87259 + 1.65849i) q^{69} +(-2.68852 + 12.2845i) q^{70} +(-3.55406 - 9.76470i) q^{71} +(-0.0520966 - 5.27940i) q^{72} +(-0.702728 - 8.03222i) q^{73} +(-6.99889 - 7.81270i) q^{74} +(-5.10112 + 1.52072i) q^{75} +(3.07728 + 8.15661i) q^{76} +(-5.51452 + 5.51452i) q^{77} +(0.549237 - 9.99637i) q^{78} +(5.21451 + 4.37550i) q^{79} +(-1.05585 + 8.88173i) q^{80} +(0.0791886 - 0.0288223i) q^{81} +(9.14838 - 9.76084i) q^{82} +(4.33680 + 1.16204i) q^{83} +(2.37495 - 8.12709i) q^{84} +(0.698318 - 0.602773i) q^{85} +(-2.44981 - 1.31055i) q^{86} +(4.44556 - 1.19118i) q^{87} +(-3.52339 + 4.28416i) q^{88} +(1.97027 + 2.34807i) q^{89} +(-5.75943 + 1.29321i) q^{90} +(-9.04410 + 24.8484i) q^{91} +(5.90213 - 1.99894i) q^{92} +(-5.42313 + 3.79732i) q^{93} +(-5.25903 - 4.13026i) q^{94} +(8.19652 - 5.27420i) q^{95} +(1.12065 - 5.91706i) q^{96} +(1.97826 + 2.82524i) q^{97} +(-6.81497 + 10.4363i) q^{98} +(-3.43996 - 1.25204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.0775850	−	1.41208i	0.0548609	−	0.998494i
$2$	0.0775850	−	1.41208i	0.0548609	−	0.998494i
$3$	1.06054	−	0.0927854i	0.612304	−	0.0535697i	0.223214	−	0.974769i	$-0.428345\pi$
$3$	1.06054	−	0.0927854i	0.612304	−	0.0535697i	0.389090	+	0.921200i	$0.372789\pi$
$4$	−1.98796	−	0.219113i	−0.993981	−	0.109557i
$5$	0.225970	+	2.22462i	0.101057	+	0.994881i
$5$	0.225970	+	2.22462i	0.101057	+	0.994881i
$6$	−0.0487386	−	1.50477i	−0.0198975	−	0.614321i
$7$	−1.02923	+	3.84113i	−0.389012	+	1.45181i	0.442733	+	0.896654i	$0.354009\pi$
$7$	−1.02923	+	3.84113i	−0.389012	+	1.45181i	−0.831745	+	0.555158i	$0.812658\pi$
$8$	−0.463642	+	2.79017i	−0.163922	+	0.986473i
$9$	−1.83828	+	0.324139i	−0.612761	+	0.108046i
$10$	3.15888	−	0.146492i	0.998926	−	0.0463248i
$11$	1.69839	+	0.980566i	0.512084	+	0.295652i	0.733690	−	0.679484i	$-0.237796\pi$
$11$	1.69839	+	0.980566i	0.512084	+	0.295652i	−0.221606	+	0.975136i	$0.571130\pi$
$12$	−2.12865	−	0.0479249i	−0.614488	−	0.0138347i
$13$	6.62433	+	0.579554i	1.83726	+	0.160739i	0.952347	−	0.305018i	$-0.0986624\pi$
$13$	6.62433	+	0.579554i	1.83726	+	0.160739i	0.884913	+	0.465757i	$0.154218\pi$
$14$	5.34415	+	1.75137i	1.42828	+	0.468074i
$15$	0.446064	+	2.33834i	0.115173	+	0.603756i
$16$	3.90398	+	0.871177i	0.975995	+	0.217794i
$17$	−0.236628	−	0.337940i	−0.0573908	−	0.0819626i	0.789431	−	0.613839i	$-0.210376\pi$
$17$	−0.236628	−	0.337940i	−0.0573908	−	0.0819626i	−0.846822	+	0.531877i	$0.821487\pi$
$18$	0.315088	+	2.62096i	0.0742669	+	0.617766i
$19$	−1.97618	−	3.88519i	−0.453367	−	0.891324i
$19$	−1.97618	−	3.88519i	−0.453367	−	0.891324i
$20$	0.0382231	−	4.47197i	0.00854695	−	0.999963i
$21$	−0.735139	+	4.16918i	−0.160421	+	0.909790i
$22$	1.51641	−	2.32219i	0.323300	−	0.495093i
$23$	−2.82380	+	1.31676i	−0.588804	+	0.274564i	−0.694102	−	0.719877i	$-0.744198\pi$
$23$	−2.82380	+	1.31676i	−0.588804	+	0.274564i	0.105298	+	0.994441i	$0.466420\pi$
$24$	−0.232825	+	3.00211i	−0.0475252	+	0.612803i
$25$	−4.89787	+	1.00540i	−0.979575	+	0.201079i
$26$	1.33233	−	9.30915i	0.261291	−	1.82567i
$27$	−5.00446	+	1.34094i	−0.963108	+	0.258064i
$28$	2.88771	−	7.41051i	0.545726	−	1.40045i
$29$	4.25746	−	0.750704i	0.790590	−	0.139402i	0.236250	−	0.971692i	$-0.424082\pi$
$29$	4.25746	−	0.750704i	0.790590	−	0.139402i	0.554340	+	0.832290i	$0.312971\pi$
$30$	3.33654	−	0.448459i	0.609165	−	0.0818771i
$31$	−5.38558	+	3.10936i	−0.967278	+	0.558458i	−0.898405	−	0.439167i	$-0.855274\pi$
$31$	−5.38558	+	3.10936i	−0.967278	+	0.558458i	−0.0688728	+	0.997625i	$0.521940\pi$
$32$	1.53306	−	5.44515i	0.271010	−	0.962577i
$33$	1.89220	+	0.882346i	0.329389	+	0.153597i
$34$	−0.495559	+	0.307920i	−0.0849877	+	0.0528079i
$35$	−8.77764	−	1.42166i	−1.48369	−	0.240305i
$36$	3.72546	−	0.241584i	0.620910	−	0.0402639i
$37$	5.24459	−	5.24459i	0.862205	−	0.862205i	−0.129389	−	0.991594i	$-0.541302\pi$
$37$	5.24459	−	5.24459i	0.862205	−	0.862205i	0.991594	+	0.129389i	$0.0413016\pi$
$38$	−5.63954	+	2.48910i	−0.914854	+	0.403786i
$39$	7.07916			1.13357
$40$	−6.31183	−	0.400932i	−0.997989	−	0.0633930i
$41$	7.24645	+	6.08049i	1.13171	+	0.949613i	0.999136	−	0.0415603i	$-0.0132329\pi$
$41$	7.24645	+	6.08049i	1.13171	+	0.949613i	0.132569	+	0.991174i	$0.457677\pi$
$42$	5.83020	+	1.36154i	0.899619	+	0.210091i
$43$	0.830266	−	1.78051i	0.126614	−	0.271525i	−0.832774	−	0.553612i	$-0.813249\pi$
$43$	0.830266	−	1.78051i	0.126614	−	0.271525i	0.959389	+	0.282087i	$0.0910267\pi$
$44$	−3.16148	−	2.32147i	−0.476611	−	0.349974i
$45$	−1.13648	−	4.01624i	−0.169417	−	0.598705i
$46$	1.64029	+	4.08961i	0.241848	+	0.602980i
$47$	2.71213	−	3.87332i	0.395605	−	0.564982i	−0.571099	−	0.820881i	$-0.693483\pi$
$47$	2.71213	−	3.87332i	0.395605	−	0.564982i	0.966703	+	0.255899i	$0.0823716\pi$
$48$	4.22117	+	0.561687i	0.609273	+	0.0810726i
$49$	−7.63282	−	4.40681i	−1.09040	−	0.629544i
$50$	1.03970	+	6.99421i	0.147036	+	0.989131i
$51$	−0.282310	−	0.336444i	−0.0395314	−	0.0471116i
$52$	−13.0419	−	2.60361i	−1.80859	−	0.361056i
$53$	−1.46784	−	3.14780i	−0.201624	−	0.432383i	0.779333	−	0.626610i	$-0.215558\pi$
$53$	−1.46784	−	3.14780i	−0.201624	−	0.432383i	−0.980957	+	0.194227i	$0.937780\pi$
$54$	1.50525	+	7.17075i	0.204838	+	0.975815i
$55$	−1.79760	+	3.99985i	−0.242389	+	0.539340i
$56$	−10.2402	−	4.65263i	−1.36841	−	0.621734i
$57$	−2.45631	−	3.93705i	−0.325347	−	0.521475i
$58$	−0.729743	−	6.07013i	−0.0958199	−	0.797047i
$59$	−1.83537	+	10.4089i	−0.238945	+	1.35512i	0.595199	+	0.803578i	$0.297073\pi$
$59$	−1.83537	+	10.4089i	−0.238945	+	1.35512i	−0.834144	+	0.551546i	$0.814038\pi$
$60$	−0.374397	−	4.74626i	−0.0483344	−	0.612740i
$61$	8.52071	+	3.10129i	1.09097	+	0.397079i	0.823978	−	0.566621i	$-0.191750\pi$
$61$	8.52071	+	3.10129i	1.09097	+	0.397079i	0.266987	+	0.963700i	$0.413972\pi$
$62$	3.97284	+	7.84613i	0.504552	+	0.996459i
$63$	0.646952	−	7.39470i	0.0815083	−	0.931645i
$64$	−7.57007	−	2.58728i	−0.946259	−	0.323410i
$65$	0.207615	+	14.8676i	0.0257515	+	1.84410i
$66$	1.39275	−	2.60348i	0.171436	−	0.320467i
$67$	6.44604	−	9.20589i	0.787509	−	1.12468i	−0.201883	−	0.979410i	$-0.564706\pi$
$67$	6.44604	−	9.20589i	0.787509	−	1.12468i	0.989392	−	0.145269i	$-0.0464049\pi$
$68$	0.396361	+	0.723661i	0.0480658	+	0.0877568i
$69$	−2.87259	+	1.65849i	−0.345819	+	0.199659i
$70$	−2.68852	+	12.2845i	−0.321339	+	1.46827i
$71$	−3.55406	−	9.76470i	−0.421789	−	1.15886i	−0.950682	−	0.310168i	$-0.899615\pi$
$71$	−3.55406	−	9.76470i	−0.421789	−	1.15886i	0.528892	−	0.848689i	$-0.322607\pi$
$72$	−0.0520966	−	5.27940i	−0.00613964	−	0.622183i
$73$	−0.702728	−	8.03222i	−0.0822481	−	0.940100i	−0.919450	−	0.393206i	$-0.871366\pi$
$73$	−0.702728	−	8.03222i	−0.0822481	−	0.940100i	0.837202	−	0.546894i	$-0.184190\pi$
$74$	−6.99889	−	7.81270i	−0.813605	−	0.908208i
$75$	−5.10112	+	1.52072i	−0.589026	+	0.175597i
$76$	3.07728	+	8.15661i	0.352988	+	0.935628i
$77$	−5.51452	+	5.51452i	−0.628438	+	0.628438i
$78$	0.549237	−	9.99637i	0.0621888	−	1.13187i
$79$	5.21451	+	4.37550i	0.586679	+	0.492282i	0.887133	−	0.461514i	$-0.152694\pi$
$79$	5.21451	+	4.37550i	0.586679	+	0.492282i	−0.300454	+	0.953796i	$0.597138\pi$
$80$	−1.05585	+	8.88173i	−0.118048	+	0.993008i
$81$	0.0791886	−	0.0288223i	0.00879873	−	0.00320248i
$82$	9.14838	−	9.76084i	1.01027	−	1.07790i
$83$	4.33680	+	1.16204i	0.476026	+	0.127551i	0.488851	−	0.872367i	$-0.337416\pi$
$83$	4.33680	+	1.16204i	0.476026	+	0.127551i	−0.0128257	+	0.999918i	$0.504083\pi$
$84$	2.37495	−	8.12709i	0.259128	−	0.886739i
$85$	0.698318	−	0.602773i	0.0757432	−	0.0653799i
$86$	−2.44981	−	1.31055i	−0.264170	−	0.141320i
$87$	4.44556	−	1.19118i	0.476614	−	0.127708i
$88$	−3.52339	+	4.28416i	−0.375595	+	0.456693i
$89$	1.97027	+	2.34807i	0.208848	+	0.248895i	0.860292	−	0.509801i	$-0.170281\pi$
$89$	1.97027	+	2.34807i	0.208848	+	0.248895i	−0.651444	+	0.758696i	$0.725837\pi$
$90$	−5.75943	+	1.29321i	−0.607098	+	0.136316i
$91$	−9.04410	+	24.8484i	−0.948079	+	2.60483i
$92$	5.90213	−	1.99894i	0.615340	−	0.208404i
$93$	−5.42313	+	3.79732i	−0.562352	+	0.393763i
$94$	−5.25903	−	4.13026i	−0.542428	−	0.426004i
$95$	8.19652	−	5.27420i	0.840945	−	0.541121i
$96$	1.12065	−	5.91706i	0.114376	−	0.603908i
$97$	1.97826	+	2.82524i	0.200861	+	0.286860i	0.906928	−	0.421286i	$-0.138421\pi$
$97$	1.97826	+	2.82524i	0.200861	+	0.286860i	−0.706067	+	0.708145i	$0.749532\pi$
$98$	−6.81497	+	10.4363i	−0.688416	+	1.05422i
$99$	−3.43996	−	1.25204i	−0.345729	−	0.125835i
$100$	9.95708	−	0.925502i	0.995708	−	0.0925502i
$101$	−5.93748	+	4.98213i	−0.590801	+	0.495741i	−0.888474	−	0.458927i	$-0.848234\pi$
$101$	−5.93748	+	4.98213i	−0.590801	+	0.495741i	0.297673	+	0.954668i	$0.403789\pi$
$102$	−0.496991	+	0.372543i	−0.0492094	+	0.0368872i
$103$	0.681163	+	2.54214i	0.0671170	+	0.250484i	0.991330	−	0.131392i	$-0.0419447\pi$
$103$	0.681163	+	2.54214i	0.0671170	+	0.250484i	−0.924213	+	0.381876i	$0.875278\pi$
$104$	−4.68837	+	18.2143i	−0.459733	+	1.78606i
$105$	−9.44097	−	0.693294i	−0.921344	−	0.0676586i
$106$	−4.55884	+	1.82849i	−0.442793	+	0.177599i
$107$	−0.775283	+	2.89339i	−0.0749494	+	0.279715i	−0.993222	−	0.116234i	$-0.962918\pi$
$107$	−0.775283	+	2.89339i	−0.0749494	+	0.279715i	0.918272	+	0.395949i	$0.129584\pi$
$108$	10.2425	−	1.56919i	0.985583	−	0.150996i
$109$	−4.60635	−	12.6558i	−0.441209	−	1.21221i	−0.938698	−	0.344741i	$-0.887967\pi$
$109$	−4.60635	−	12.6558i	−0.441209	−	1.21221i	0.497489	−	0.867470i	$-0.334255\pi$
$110$	5.50866	+	2.84869i	0.525230	+	0.271612i
$111$	5.07548	−	6.04873i	0.481744	−	0.574120i
$112$	−7.36439	+	14.0991i	−0.695870	+	1.33224i
$113$	−6.62414	−	6.62414i	−0.623147	−	0.623147i	0.323188	−	0.946335i	$-0.395245\pi$
$113$	−6.62414	−	6.62414i	−0.623147	−	0.623147i	−0.946335	+	0.323188i	$0.895245\pi$
$114$	−5.75001	+	3.16307i	−0.538538	+	0.296248i
$115$	−3.56739	−	5.98434i	−0.332661	−	0.558043i
$116$	−8.62815	+	0.559507i	−0.801103	+	0.0519489i
$117$	−12.3652	+	1.08182i	−1.14317	+	0.100014i
$118$	14.5559	+	3.39927i	1.33997	+	0.312928i
$119$	1.54162	−	0.561103i	0.141320	−	0.0514363i
$120$	−6.73117	+	0.160441i	−0.614469	+	0.0146462i
$121$	−3.57698	−	6.19551i	−0.325180	−	0.563228i
$122$	5.04036	−	11.7913i	0.456332	−	1.06754i
$123$	8.24935	+	5.77625i	0.743819	+	0.520827i
$124$	11.3876	−	5.00125i	1.02264	−	0.449125i
$125$	−3.34340	−	10.6687i	−0.299043	−	0.954240i
$126$	−10.3917	−	1.48727i	−0.925770	−	0.132496i
$127$	10.0430	+	0.878647i	0.891170	+	0.0779673i	0.523536	−	0.852003i	$-0.324612\pi$
$127$	10.0430	+	0.878647i	0.891170	+	0.0779673i	0.367634	+	0.929971i	$0.380168\pi$
$128$	−4.24078	+	10.4888i	−0.374835	+	0.927091i
$129$	0.715327	−	1.96534i	0.0629810	−	0.173039i
$130$	21.0104	+	0.860332i	1.84273	+	0.0754561i
$131$	−9.80361	−	1.72864i	−0.856546	−	0.151032i	−0.271905	−	0.962324i	$-0.587654\pi$
$131$	−9.80361	−	1.72864i	−0.856546	−	0.151032i	−0.584641	+	0.811292i	$0.698765\pi$
$132$	−3.56828	−	2.16868i	−0.310579	−	0.188759i
$133$	16.9575	−	3.59203i	1.47040	−	0.311469i
$134$	−12.4994	−	9.81658i	−1.07978	−	0.848024i
$135$	−4.11394	−	10.8300i	−0.354072	−	0.932098i
$136$	1.05262	−	0.503550i	0.0902615	−	0.0431790i
$137$	−11.4101	+	5.32064i	−0.974834	+	0.454573i	−0.843714	−	0.536794i	$-0.819635\pi$
$137$	−11.4101	+	5.32064i	−0.974834	+	0.454573i	−0.131121	+	0.991366i	$0.541858\pi$
$138$	2.11906	+	4.18501i	0.180386	+	0.356252i
$139$	11.4668	−	9.62179i	0.972602	−	0.816110i	−0.0103551	−	0.999946i	$-0.503296\pi$
$139$	11.4668	−	9.62179i	0.972602	−	0.816110i	0.982957	+	0.183837i	$0.0588518\pi$
$140$	17.1381	+	4.74950i	1.44843	+	0.401406i
$141$	2.51694	−	4.35947i	0.211964	−	0.367133i
$142$	−14.0643	+	4.26104i	−1.18025	+	0.357578i
$143$	10.6824	+	7.47991i	0.893308	+	0.625501i
$144$	−7.45900	−	0.336038i	−0.621583	−	0.0280031i
$145$	2.63209	+	9.30159i	0.218583	+	0.772455i
$146$	−11.3967	+	0.369131i	−0.943196	+	0.0305495i
$147$	−8.50381	−	3.96539i	−0.701383	−	0.327060i
$148$	−11.5752	+	9.27688i	−0.951475	+	0.762555i
$149$	−10.9514	+	13.0514i	−0.897176	+	1.06921i	0.100065	+	0.994981i	$0.468095\pi$
$149$	−10.9514	+	13.0514i	−0.897176	+	1.06921i	−0.997241	+	0.0742323i	$0.976349\pi$
$150$	1.75161	+	7.32119i	0.143018	+	0.597773i
$151$		−	13.2947i		−	1.08190i	−0.841054	−	0.540952i	$-0.818064\pi$
$151$		−	13.2947i		−	1.08190i	0.841054	−	0.540952i	$-0.181936\pi$
$152$	11.7566	−	3.71254i	0.953584	−	0.301127i
$153$	0.544529	+	0.544529i	0.0440226	+	0.0440226i
$154$	7.35912	+	8.21481i	0.593015	+	0.661968i
$155$	−8.13414	−	11.2782i	−0.653350	−	0.905890i
$156$	−14.0731	−	1.55114i	−1.12675	−	0.124190i
$157$	5.41031	−	11.6024i	0.431790	−	0.925976i	−0.563230	−	0.826300i	$-0.690442\pi$
$157$	5.41031	−	11.6024i	0.431790	−	0.925976i	0.995020	−	0.0996760i	$-0.0317806\pi$
$158$	6.58314	−	7.02386i	0.523726	−	0.558788i
$159$	−1.84878	−	3.20218i	−0.146618	−	0.253949i
$160$	12.4598	+	2.18004i	0.985036	+	0.172348i
$161$	−2.15152	−	12.2019i	−0.169563	−	0.961641i
$162$	−0.0345556	−	0.114057i	−0.00271495	−	0.00896117i
$163$	0.521364	+	1.94576i	0.0408364	+	0.152403i	0.983334	−	0.181811i	$-0.0581958\pi$
$163$	0.521364	+	1.94576i	0.0408364	+	0.152403i	−0.942497	+	0.334214i	$0.891529\pi$
$164$	−13.0733	−	13.6756i	−1.02086	−	1.06788i
$165$	−1.53531	+	4.40881i	−0.119523	+	0.343225i
$166$	1.97737	−	6.03377i	0.153474	−	0.468311i
$167$	1.46020	+	3.13142i	0.112994	+	0.242316i	0.954670	−	0.297667i	$-0.0962084\pi$
$167$	1.46020	+	3.13142i	0.112994	+	0.242316i	−0.841676	+	0.539983i	$0.818431\pi$
$168$	−11.2919	−	3.98417i	−0.871187	−	0.307385i
$169$	30.7434	+	5.42089i	2.36488	+	0.416992i
$170$	−0.796987	−	1.03285i	−0.0611261	−	0.0792160i
$171$	4.89212	+	6.50152i	0.374110	+	0.497184i
$172$	−2.04067	+	3.35767i	−0.155600	+	0.256020i
$173$	13.3340	−	9.33659i	1.01377	−	0.709848i	0.0563078	−	0.998413i	$-0.482067\pi$
$173$	13.3340	−	9.33659i	1.01377	−	0.709848i	0.957460	+	0.288565i	$0.0931783\pi$
$174$	−1.33714	−	6.36992i	−0.101369	−	0.482902i
$175$	1.17917	−	19.8482i	0.0891368	−	1.50038i
$176$	5.77624	+	5.30771i	0.435400	+	0.400084i
$177$	−0.980694	+	11.2094i	−0.0737135	+	0.842549i
$178$	3.46854	−	2.60000i	0.259978	−	0.194879i
$179$	−3.76736	+	6.52527i	−0.281586	+	0.487721i	−0.971776	−	0.235907i	$-0.924194\pi$
$179$	−3.76736	+	6.52527i	−0.281586	+	0.487721i	0.690190	+	0.723629i	$0.257527\pi$
$180$	1.37927	+	8.23314i	0.102805	+	0.613662i
$181$	3.15286	+	17.8808i	0.234350	+	1.32907i	0.843977	+	0.536379i	$0.180208\pi$
$181$	3.15286	+	17.8808i	0.234350	+	1.32907i	−0.609627	+	0.792688i	$0.708681\pi$
$182$	34.3864	+	14.6989i	2.54889	+	1.08955i
$183$	9.32433	+	2.49845i	0.689274	+	0.184691i
$184$	−2.36475	−	8.48939i	−0.174332	−	0.625846i
$185$	12.8523	+	10.4821i	0.944923	+	0.770659i
$186$	4.94137	+	7.95253i	0.362319	+	0.583108i
$187$	−0.0705145	−	0.805985i	−0.00515653	−	0.0589394i
$188$	−6.24030	+	7.10575i	−0.455121	+	0.518240i
$189$		−	20.6029i		−	1.49864i
$190$	−6.81168	−	11.9834i	−0.494171	−	0.869365i
$191$			9.57394i			0.692746i	0.938097	+	0.346373i	$0.112587\pi$
$191$			9.57394i			0.692746i	−0.938097	+	0.346373i	$0.887413\pi$
$192$	−8.26844	−	2.04153i	−0.596724	−	0.147334i
$193$	−0.821592	−	9.39084i	−0.0591395	−	0.675968i	−0.966677	−	0.255997i	$-0.917596\pi$
$193$	−0.821592	−	9.39084i	−0.0591395	−	0.675968i	0.907538	−	0.419970i	$-0.137959\pi$
$194$	4.14296	−	2.57427i	0.297447	−	0.184822i
$195$	1.59968	+	15.7484i	0.114555	+	1.12777i
$196$	14.2082	+	10.4330i	1.01487	+	0.745215i
$197$	1.75370	+	0.469903i	0.124946	+	0.0334792i	0.320750	−	0.947164i	$-0.396065\pi$
$197$	1.75370	+	0.469903i	0.124946	+	0.0334792i	−0.195804	+	0.980643i	$0.562732\pi$
$198$	−2.03488	+	4.76037i	−0.144613	+	0.338305i
$199$	0.698745	+	3.96278i	0.0495328	+	0.280914i	0.999506	−	0.0314159i	$-0.0100016\pi$
$199$	0.698745	+	3.96278i	0.0495328	+	0.280914i	−0.949974	+	0.312330i	$0.898891\pi$
$200$	−0.534366	−	14.1320i	−0.0377854	−	0.999286i
$201$	5.98212	−	10.3613i	0.421946	−	0.730832i
$202$	6.57453	+	8.77075i	0.462582	+	0.617108i
$203$	−1.49834	+	17.1261i	−0.105163	+	1.20202i
$204$	0.487503	+	0.730696i	0.0341320	+	0.0511590i
$205$	−11.8893	+	17.4946i	−0.830385	+	1.22188i
$206$	3.64256	−	0.764628i	0.253789	−	0.0532741i
$207$	4.76414	−	3.33588i	0.331130	−	0.231860i
$208$	25.3564	+	8.03353i	1.75815	+	0.557025i
$209$	0.453356	−	8.53635i	0.0313593	−	0.590472i
$210$	−1.71147	+	13.2776i	−0.118102	+	0.916245i
$211$	16.7408	+	2.95185i	1.15248	+	0.203214i	0.717059	−	0.697012i	$-0.245488\pi$
$211$	16.7408	+	2.95185i	1.15248	+	0.203214i	0.435423	+	0.900226i	$0.356599\pi$
$212$	2.22829	+	6.57932i	0.153040	+	0.451870i
$213$	−4.67525	−	10.0261i	−0.320343	−	0.686978i
$214$	4.02556	+	1.31925i	0.275182	+	0.0901819i
$215$	4.14858	+	1.44468i	0.282931	+	0.0985266i
$216$	−1.42117	−	14.5850i	−0.0966984	−	0.992383i
$217$	−6.40049	−	23.8870i	−0.434494	−	1.62155i
$218$	−18.2285	+	5.52265i	−1.23459	+	0.374041i
$219$	−1.49055	−	8.45330i	−0.100722	−	0.571221i
$220$	4.44998	−	7.55768i	0.300018	−	0.509539i
$221$	−1.37165	−	2.37577i	−0.0922672	−	0.159811i
$222$	−8.14753	−	7.63630i	−0.546826	−	0.512515i
$223$	10.4251	−	22.3567i	0.698117	−	1.49712i	−0.161877	−	0.986811i	$-0.551755\pi$
$223$	10.4251	−	22.3567i	0.698117	−	1.49712i	0.859994	−	0.510305i	$-0.170467\pi$
$224$	19.3377	+	11.4930i	1.29205	+	0.767909i
$225$	8.67779	−	3.43579i	0.578519	−	0.229053i
$226$	−9.86777	+	8.83990i	−0.656394	+	0.588022i
$227$	−12.3183	−	12.3183i	−0.817596	−	0.817596i	0.168163	−	0.985759i	$-0.446216\pi$
$227$	−12.3183	−	12.3183i	−0.817596	−	0.817596i	−0.985759	+	0.168163i	$0.946216\pi$
$228$	4.02040	+	8.36491i	0.266257	+	0.553980i
$229$		−	11.3009i		−	0.746781i	−0.927674	−	0.373391i	$-0.878195\pi$
$229$		−	11.3009i		−	0.746781i	0.927674	−	0.373391i	$-0.121805\pi$
$230$	−8.72717	+	4.57316i	−0.575453	+	0.301545i
$231$	−5.33671	+	6.36005i	−0.351130	+	0.418460i
$232$	0.120656	+	12.2271i	0.00792143	+	0.802747i
$233$	4.85667	+	2.26470i	0.318171	+	0.148366i	0.575142	−	0.818054i	$-0.304947\pi$
$233$	4.85667	+	2.26470i	0.318171	+	0.148366i	−0.256971	+	0.966419i	$0.582725\pi$
$234$	0.568261	+	17.5447i	0.0371484	+	1.14693i
$235$	9.22953	+	5.15820i	0.602068	+	0.336484i
$236$	5.92937	−	20.2903i	0.385969	−	1.32079i
$237$	5.93620	+	4.15657i	0.385597	+	0.269998i
$238$	−0.672718	−	2.22043i	−0.0436059	−	0.143929i
$239$	−0.820826	+	1.42171i	−0.0530948	+	0.0919629i	−0.891351	−	0.453313i	$-0.850242\pi$
$239$	−0.820826	+	1.42171i	−0.0530948	+	0.0919629i	0.838256	+	0.545276i	$0.183575\pi$
$240$	−0.295682	+	9.51742i	−0.0190862	+	0.614347i
$241$	−10.8504	+	9.10459i	−0.698938	+	0.586478i	−0.921471	−	0.388447i	$-0.873012\pi$
$241$	−10.8504	+	9.10459i	−0.698938	+	0.586478i	0.222534	+	0.974925i	$0.428567\pi$
$242$	−9.02610	+	4.57031i	−0.580220	+	0.293791i
$243$	14.1680	−	6.60666i	0.908880	−	0.423818i
$244$	−16.2593	−	8.03224i	−1.04090	−	0.514211i
$245$	8.07869	−	17.9759i	0.516128	−	1.14844i
$246$	8.79658	−	11.2006i	0.560850	−	0.714125i
$247$	−10.8392	−	26.8821i	−0.689683	−	1.71047i
$248$	−6.17867	−	16.4683i	−0.392346	−	1.04574i
$249$	4.70718	+	0.830003i	0.298305	+	0.0525993i
$250$	−15.3245	+	3.89343i	−0.969208	+	0.246242i
$251$	−6.72165	+	18.4676i	−0.424267	+	1.16566i	0.524975	+	0.851118i	$0.324075\pi$
$251$	−6.72165	+	18.4676i	−0.424267	+	1.16566i	−0.949242	+	0.314547i	$0.898148\pi$
$252$	−2.90639	+	14.5586i	−0.183085	+	0.917107i
$253$	−6.08710	−	0.532552i	−0.382692	−	0.0334813i
$254$	2.01991	−	14.1134i	0.126740	−	0.885551i
$255$	0.684667	−	0.704060i	0.0428755	−	0.0440900i
$256$	14.4821	+	6.80211i	0.905131	+	0.425132i
$257$	−4.49709	−	3.14889i	−0.280521	−	0.196423i	0.424845	−	0.905266i	$-0.360328\pi$
$257$	−4.49709	−	3.14889i	−0.280521	−	0.196423i	−0.705366	+	0.708843i	$0.749217\pi$
$258$	−2.71973	−	1.16258i	−0.169323	−	0.0723792i
$259$	14.7473	+	25.5430i	0.916351	+	1.58717i
$260$	2.84495	−	29.6017i	0.176436	−	1.83582i
$261$	−7.58307	+	2.76001i	−0.469381	+	0.170841i
$262$	−3.20160	+	13.7094i	−0.197796	+	0.846970i
$263$	−10.9653	+	0.959337i	−0.676148	+	0.0591553i	−0.420057	−	0.907498i	$-0.637990\pi$
$263$	−10.9653	+	0.959337i	−0.676148	+	0.0591553i	−0.256090	+	0.966653i	$0.582434\pi$
$264$	−3.33920	+	4.87046i	−0.205513	+	0.299756i
$265$	6.67097	−	3.97670i	0.409794	−	0.244287i
$266$	−3.75661	−	24.2241i	−0.230332	−	1.48527i
$267$	2.30742	+	2.30742i	0.141212	+	0.141212i
$268$	−14.8316	+	16.8885i	−0.905984	+	1.03163i
$269$	−11.1634	+	13.3040i	−0.680644	+	0.811160i	−0.990190	−	0.139724i	$-0.955378\pi$
$269$	−11.1634	+	13.3040i	−0.680644	+	0.811160i	0.309546	+	0.950884i	$0.399823\pi$
$270$	−15.6121	+	4.96898i	−0.950119	+	0.302403i
$271$	1.03094	+	2.83248i	0.0626251	+	0.172061i	0.967059	−	0.254553i	$-0.0819284\pi$
$271$	1.03094	+	2.83248i	0.0626251	+	0.172061i	−0.904434	+	0.426614i	$0.859706\pi$
$272$	−0.629387	−	1.52546i	−0.0381622	−	0.0924944i
$273$	−7.28607	+	27.1920i	−0.440973	+	1.64573i
$274$	6.62793	+	16.5249i	0.400408	+	0.998305i
$275$	−9.30436	−	3.09513i	−0.561074	−	0.186644i
$276$	6.07399	−	2.66759i	0.365611	−	0.160570i
$277$	3.84109	+	14.3351i	0.230789	+	0.861315i	0.980002	+	0.198987i	$0.0637650\pi$
$277$	3.84109	+	14.3351i	0.230789	+	0.861315i	−0.749213	+	0.662329i	$0.769568\pi$
$278$	−12.6971	−	16.9386i	−0.761523	−	1.01591i
$279$	8.89235	−	7.46156i	0.532371	−	0.446712i
$280$	8.03635	−	23.8319i	0.480264	−	1.42423i
$281$	15.3109	+	5.57269i	0.913369	+	0.332439i	0.755597	−	0.655037i	$-0.227347\pi$
$281$	15.3109	+	5.57269i	0.913369	+	0.332439i	0.157772	+	0.987476i	$0.449569\pi$
$282$	−5.96065	−	3.89236i	−0.354952	−	0.231787i
$283$	−17.2135	−	24.5835i	−1.02324	−	1.46134i	−0.881936	−	0.471369i	$-0.843760\pi$
$283$	−17.2135	−	24.5835i	−1.02324	−	1.46134i	−0.141302	−	0.989967i	$-0.545129\pi$
$284$	4.92576	+	20.1906i	0.292290	+	1.19809i
$285$	8.20338	−	6.35402i	0.485926	−	0.376380i
$286$	11.3911	−	14.5041i	0.673567	−	0.857648i
$287$	−30.8142	+	21.5764i	−1.81891	+	1.27361i
$288$	−1.05322	+	10.5067i	−0.0620616	+	0.619111i
$289$	5.75613	−	15.8148i	0.338596	−	0.930285i
$290$	13.3388	−	2.99507i	0.783283	−	0.175877i
$291$	2.36017	+	2.81274i	0.138355	+	0.164885i
$292$	−0.362968	+	16.1217i	−0.0212411	+	0.943452i
$293$	2.48216	−	0.665093i	0.145009	−	0.0388552i	−0.185584	−	0.982628i	$-0.559418\pi$
$293$	2.48216	−	0.665093i	0.145009	−	0.0388552i	0.330594	+	0.943773i	$0.392751\pi$
$294$	−6.25923	+	11.7004i	−0.365046	+	0.682383i
$295$	−23.5706	−	1.73090i	−1.37233	−	0.100777i
$296$	12.2017	+	17.0649i	0.709207	+	0.991876i
$297$	−9.81440	−	2.62976i	−0.569489	−	0.152594i
$298$	17.5800	+	16.4769i	1.01838	+	0.954483i
$299$	−19.4690	+	7.08612i	−1.12592	+	0.409801i
$300$	10.4740	−	1.90541i	0.604719	−	0.110009i
$301$	5.98465	+	5.02172i	0.344949	+	0.289447i
$302$	−18.7732	−	1.03147i	−1.08027	−	0.0593542i
$303$	−5.83467	+	5.83467i	−0.335193	+	0.335193i
$304$	−4.33029	−	16.8893i	−0.248359	−	0.968668i
$305$	−4.97376	+	19.6562i	−0.284796	+	1.12551i
$306$	0.811169	−	0.726674i	0.0463714	−	0.0415412i
$307$	0.700348	+	8.00502i	0.0399710	+	0.456870i	0.989636	+	0.143602i	$0.0458684\pi$
$307$	0.700348	+	8.00502i	0.0399710	+	0.456870i	−0.949665	+	0.313269i	$0.898576\pi$
$308$	12.1710	−	9.75435i	0.693504	−	0.555805i
$309$	0.958275	+	2.63284i	0.0545144	+	0.149777i
$310$	−16.5569	+	10.6111i	−0.940369	+	0.602668i
$311$	6.92712	−	3.99938i	0.392801	−	0.226784i	−0.290572	−	0.956853i	$-0.593846\pi$
$311$	6.92712	−	3.99938i	0.392801	−	0.226784i	0.683373	+	0.730069i	$0.260512\pi$
$312$	−3.28220	+	19.7520i	−0.185818	+	1.11824i
$313$	−8.72292	+	12.4576i	−0.493049	+	0.704146i	−0.986156	−	0.165822i	$-0.946972\pi$
$313$	−8.72292	+	12.4576i	−0.493049	+	0.704146i	0.493107	+	0.869969i	$0.335861\pi$
$314$	−15.9639	−	8.53999i	−0.900893	−	0.481939i
$315$	16.5966	−	0.231760i	0.935112	−	0.0130582i
$316$	−9.40752	−	9.84089i	−0.529215	−	0.553593i
$317$	0.477423	−	5.45697i	0.0268148	−	0.306494i	−0.970930	−	0.239365i	$-0.923061\pi$
$317$	0.477423	−	5.45697i	0.0268148	−	0.306494i	0.997744	−	0.0671287i	$-0.0213838\pi$
$318$	−4.66518	+	2.36219i	−0.261610	+	0.132465i
$319$	7.96694	+	2.89973i	0.446063	+	0.162354i
$320$	4.04510	−	17.4252i	0.226128	−	0.974098i
$321$	−0.553755	+	3.14050i	−0.0309076	+	0.175286i
$322$	−17.3970	+	2.09144i	−0.969495	+	0.116551i
$323$	−0.845342	+	1.58718i	−0.0470361	+	0.0883130i
$324$	−0.163739	+	0.0399463i	−0.00909662	+	0.00221924i
$325$	−33.0278	+	3.82150i	−1.83205	+	0.211979i
$326$	2.78802	−	0.585248i	0.154414	−	0.0324139i
$327$	−6.05951	−	12.9947i	−0.335092	−	0.718606i
$328$	−20.3254	+	17.3996i	−1.12228	+	0.960734i
$329$	12.0865	+	14.4042i	0.666352	+	0.794128i
$330$	6.10649	+	2.51004i	0.336151	+	0.138173i
$331$	−4.20239	−	2.42625i	−0.230984	−	0.133359i	0.380042	−	0.924969i	$-0.375910\pi$
$331$	−4.20239	−	2.42625i	−0.230984	−	0.133359i	−0.611026	+	0.791610i	$0.709243\pi$
$332$	−8.36677	−	3.26034i	−0.459186	−	0.178935i
$333$	−7.94106	+	11.3410i	−0.435167	+	0.621483i
$334$	4.53511	−	1.81898i	0.248150	−	0.0995301i
$335$	21.9362	+	12.2597i	1.19850	+	0.669820i
$336$	−6.50206	+	15.6360i	−0.354717	+	0.853012i
$337$	−3.80261	+	8.15473i	−0.207141	+	0.444216i	−0.982241	−	0.187623i	$-0.939922\pi$
$337$	−3.80261	+	8.15473i	−0.207141	+	0.444216i	0.775100	+	0.631839i	$0.217700\pi$
$338$	10.0400	−	42.9917i	0.546103	−	2.33844i
$339$	−7.63980	−	6.41056i	−0.414937	−	0.348174i
$340$	−1.52030	+	1.04528i	−0.0824501	+	0.0566882i
$341$	−12.1958			−0.660437
$342$	9.56024	−	6.40367i	0.516959	−	0.346271i
$343$	5.09972	−	5.09972i	0.275359	−	0.275359i
$344$	4.58298	+	3.14210i	0.247098	+	0.169411i
$345$	−4.33863	−	6.01565i	−0.233584	−	0.323872i
$346$	−12.1495	−	19.5532i	−0.653163	−	1.05118i
$347$	19.5632	+	9.12247i	1.05021	+	0.489720i	0.869560	−	0.493828i	$-0.164403\pi$
$347$	19.5632	+	9.12247i	1.05021	+	0.489720i	0.180648	+	0.983548i	$0.442181\pi$
$348$	−9.09860	+	1.39395i	−0.487736	+	0.0747234i
$349$	−11.3728	+	6.56607i	−0.608770	+	0.351474i	−0.772484	−	0.635034i	$-0.780986\pi$
$349$	−11.3728	+	6.56607i	−0.608770	+	0.351474i	0.163714	+	0.986508i	$0.447653\pi$
$350$	−27.9358	−	3.20501i	−1.49323	−	0.171315i
$351$	−33.9283	+	5.98248i	−1.81096	+	0.319321i
$352$	7.94308	−	7.74473i	0.423368	−	0.412796i
$353$	−9.39860	+	2.51835i	−0.500237	+	0.134038i	−0.500110	−	0.865962i	$-0.666707\pi$
$353$	−9.39860	+	2.51835i	−0.500237	+	0.134038i	−0.000127107		1.00000i	$0.500040\pi$
$354$	15.7525	+	2.25450i	0.837236	+	0.119825i
$355$	20.9196	−	10.1130i	1.11030	−	0.536741i
$356$	−3.40232	−	5.09958i	−0.180322	−	0.270277i
$357$	1.58289	−	0.738114i	0.0837754	−	0.0390651i
$358$	8.92193	+	5.82610i	0.471539	+	0.307919i
$359$	2.23917	−	12.6990i	0.118179	−	0.670225i	−0.866948	−	0.498398i	$-0.833922\pi$
$359$	2.23917	−	12.6990i	0.118179	−	0.670225i	0.985127	−	0.171827i	$-0.0549671\pi$
$360$	11.7329	−	1.30888i	0.618378	−	0.0689842i
$361$	−11.1894	+	15.3557i	−0.588916	+	0.808194i
$362$	25.4938	−	3.06483i	1.33992	−	0.161084i
$363$	−4.36839	−	6.23871i	−0.229281	−	0.327447i
$364$	23.4239	−	47.4161i	1.22775	−	2.48528i
$365$	17.7098	−	3.37835i	0.926975	−	0.176831i
$366$	4.25144	−	12.9729i	0.222227	−	0.678104i
$367$	31.7214	+	2.77526i	1.65584	+	0.144867i	0.876392	−	0.481598i	$-0.159943\pi$
$367$	31.7214	+	2.77526i	1.65584	+	0.144867i	0.779449	+	0.626465i	$0.215499\pi$
$368$	−12.1712	+	2.68058i	−0.634468	+	0.139735i
$369$	−15.2919	−	8.82881i	−0.796067	−	0.459609i
$370$	15.7987	−	17.3353i	0.821338	−	0.901221i
$371$	13.6019	−	2.39837i	0.706173	−	0.124517i
$372$	11.6130	−	6.36064i	0.602107	−	0.329784i
$373$	−0.604055	+	2.25437i	−0.0312768	+	0.116727i	−0.979799	−	0.199983i	$-0.935911\pi$
$373$	−0.604055	+	2.25437i	−0.0312768	+	0.116727i	0.948523	+	0.316709i	$0.102578\pi$
$374$	−1.14359	+	0.0370401i	−0.0591336	+	0.00191530i
$375$	−4.53572	−	11.0044i	−0.234224	−	0.568265i
$376$	9.54976	+	9.36313i	0.492491	+	0.482866i
$377$	28.6379	−	2.50549i	1.47493	−	0.129039i
$378$	−29.0930	−	1.59848i	−1.49638	−	0.0822168i
$379$	−36.9468			−1.89783			−0.948914	−	0.315536i	$-0.897816\pi$
$379$	−36.9468			−1.89783			−0.948914	+	0.315536i	$0.897816\pi$
$380$	−17.4500	+	8.68893i	−0.895166	+	0.445733i
$381$	10.7325			0.549844
$382$	13.5192	+	0.742794i	0.691703	+	0.0380047i
$383$	14.6667	−	1.28317i	0.749432	−	0.0655668i	0.293961	−	0.955817i	$-0.405026\pi$
$383$	14.6667	−	1.28317i	0.749432	−	0.0655668i	0.455471	+	0.890251i	$0.349471\pi$
$384$	−3.52431	+	11.5173i	−0.179849	+	0.587742i
$385$	−13.5138	−	11.0216i	−0.688729	−	0.561713i
$386$	−13.3244	+	0.431568i	−0.678194	+	0.0219663i
$387$	−0.949131	+	3.54220i	−0.0482470	+	0.180060i
$388$	−3.31365	−	6.04993i	−0.168225	−	0.307139i
$389$	31.0025	−	5.46657i	1.57189	−	0.277166i	0.681309	−	0.731996i	$-0.261411\pi$
$389$	31.0025	−	5.46657i	1.57189	−	0.277166i	0.890578	+	0.454830i	$0.150300\pi$
$390$	22.3622	−	1.03704i	1.13236	−	0.0525125i
$391$	1.11318	+	0.642694i	0.0562959	+	0.0325025i
$392$	15.8346	−	19.2537i	0.799769	−	0.972456i
$393$	−10.5575	−	0.923665i	−0.532557	−	0.0465927i
$394$	0.799604	−	2.43992i	0.0402835	−	0.122921i
$395$	−8.55550	+	12.5891i	−0.430474	+	0.633424i
$396$	6.56417	+	3.24275i	0.329862	+	0.162955i
$397$	10.5072	+	15.0059i	0.527343	+	0.753125i	0.991141	−	0.132817i	$-0.0424022\pi$
$397$	10.5072	+	15.0059i	0.527343	+	0.753125i	−0.463797	+	0.885941i	$0.653513\pi$
$398$	5.64999	−	0.679235i	0.283209	−	0.0340470i
$399$	17.6508	−	5.38291i	0.883647	−	0.269483i
$400$	−19.9971	−	0.341865i	−0.999854	−	0.0170933i
$401$	4.74520	−	26.9114i	0.236964	−	1.34389i	−0.601474	−	0.798892i	$-0.705420\pi$
$401$	4.74520	−	26.9114i	0.236964	−	1.34389i	0.838438	−	0.544997i	$-0.183469\pi$
$402$	−14.1670	−	9.25114i	−0.706583	−	0.461405i
$403$	−37.4779	+	17.4762i	−1.86691	+	0.870553i
$404$	12.8951	−	8.60331i	0.641556	−	0.428031i
$405$	0.0820129	+	0.169652i	0.00407526	+	0.00843006i
$406$	24.0672	+	3.44451i	1.19444	+	0.170948i
$407$	14.0500	−	3.76469i	0.696434	−	0.186609i
$408$	1.06963	−	0.631704i	0.0529544	−	0.0312740i
$409$	−4.03708	+	0.711847i	−0.199621	+	0.0351986i	−0.272565	−	0.962138i	$-0.587872\pi$
$409$	−4.03708	+	0.711847i	−0.199621	+	0.0351986i	0.0729435	+	0.997336i	$0.476761\pi$
$410$	23.7814	+	18.1460i	1.17448	+	0.896168i
$411$	−11.6073	+	6.70146i	−0.572544	+	0.330558i
$412$	−0.797111	−	5.20292i	−0.0392708	−	0.256329i
$413$	−38.0930	−	17.7631i	−1.87443	−	0.874063i
$414$	−4.34092	−	6.98617i	−0.213345	−	0.343352i
$415$	−1.60511	+	9.91032i	−0.0787920	+	0.486479i
$416$	13.3113	−	35.1820i	0.652640	−	1.72494i
$417$	11.2683	−	11.2683i	0.551810	−	0.551810i
$418$	−12.0189	−	1.30247i	−0.587862	−	0.0637059i
$419$	5.22229			0.255126			0.127563	−	0.991830i	$-0.459285\pi$
$419$	5.22229			0.255126			0.127563	+	0.991830i	$0.459285\pi$
$420$	18.6164	+	3.44688i	0.908386	+	0.168191i
$421$	5.46650	+	4.58693i	0.266421	+	0.223554i	0.766205	−	0.642597i	$-0.222143\pi$
$421$	5.46650	+	4.58693i	0.266421	+	0.223554i	−0.499784	+	0.866150i	$0.666587\pi$
$422$	5.46709	−	23.4104i	0.266134	−	1.13960i
$423$	−3.73016	+	7.99936i	−0.181367	+	0.388942i
$424$	9.46344	−	2.63607i	0.459585	−	0.128019i
$425$	1.49874	+	1.41728i	0.0726996	+	0.0687484i
$426$	−14.5204	+	5.82397i	−0.703518	+	0.282172i
$427$	−20.6822	+	29.5373i	−1.00088	+	1.42941i
$428$	2.17521	−	5.58208i	0.105143	−	0.269820i
$429$	12.0232	+	6.94159i	0.580485	+	0.335143i
$430$	2.36188	−	5.74605i	0.113900	−	0.277099i
$431$	−13.1932	−	15.7230i	−0.635493	−	0.757352i	0.348158	−	0.937436i	$-0.386807\pi$
$431$	−13.1932	−	15.7230i	−0.635493	−	0.757352i	−0.983651	+	0.180084i	$0.942363\pi$
$432$	−20.7055	+	0.875236i	−0.996193	+	0.0421098i
$433$	−11.1110	−	23.8276i	−0.533959	−	1.14508i	−0.969541	−	0.244930i	$-0.921235\pi$
$433$	−11.1110	−	23.8276i	−0.533959	−	1.14508i	0.435582	−	0.900149i	$-0.356543\pi$
$434$	−34.2270	+	7.18476i	−1.64295	+	0.344880i
$435$	3.65450	+	9.62051i	0.175220	+	0.461268i
$436$	6.38419	+	26.1686i	0.305747	+	1.25325i
$437$	10.6962	+	8.36886i	0.511670	+	0.400337i
$438$	−12.0524	+	1.44893i	−0.575887	+	0.0692323i
$439$	−1.29353	+	7.33597i	−0.0617368	+	0.350127i	0.938254	+	0.345946i	$0.112442\pi$
$439$	−1.29353	+	7.33597i	−0.0617368	+	0.350127i	−0.999991	+	0.00418090i	$0.998669\pi$
$440$	−10.3268	−	6.87011i	−0.492312	−	0.327520i
$441$	15.4597	+	5.62687i	0.736176	+	0.267946i
$442$	−3.46120	+	1.75256i	−0.164633	+	0.0833608i
$443$	0.771466	−	8.81789i	0.0366534	−	0.418951i	−0.955595	−	0.294682i	$-0.904786\pi$
$443$	0.771466	−	8.81789i	0.0366534	−	0.418951i	0.992249	−	0.124268i	$-0.0396583\pi$
$444$	−11.4152	+	10.9125i	−0.541742	+	0.517886i
$445$	−4.77834	+	4.91369i	−0.226515	+	0.232931i
$446$	−30.7607	−	16.4557i	−1.45656	−	0.779198i
$447$	−10.4035	+	14.8577i	−0.492068	+	0.702745i
$448$	17.7294	−	26.4148i	0.837636	−	1.24798i
$449$	−20.6263	+	11.9086i	−0.973417	+	0.562002i	−0.900276	−	0.435319i	$-0.856635\pi$
$449$	−20.6263	+	11.9086i	−0.973417	+	0.562002i	−0.0731405	+	0.997322i	$0.523302\pi$
$450$	−4.17836	−	12.5203i	−0.196970	−	0.590214i
$451$	6.34498	+	17.4327i	0.298773	+	0.820873i
$452$	11.7171	+	14.6200i	0.551126	+	0.687665i
$453$	−1.23355	−	14.0995i	−0.0579572	−	0.662454i
$454$	−18.3502	+	16.4388i	−0.861219	+	0.771511i
$455$	−57.3221	−	14.5047i	−2.68730	−	0.679989i
$456$	12.1239	−	5.02815i	0.567752	−	0.235465i
$457$	−17.0907	+	17.0907i	−0.799468	+	0.799468i	−0.983012	−	0.183544i	$-0.941243\pi$
$457$	−17.0907	+	17.0907i	−0.799468	+	0.799468i	0.183544	+	0.983012i	$0.441243\pi$
$458$	−15.9577	−	0.876777i	−0.745657	−	0.0409691i
$459$	1.63735	+	1.37390i	0.0764252	+	0.0641283i
$460$	5.78059	+	12.6783i	0.269521	+	0.591129i
$461$	−13.6348	+	4.96267i	−0.635037	+	0.231135i	−0.639422	−	0.768856i	$-0.720826\pi$
$461$	−13.6348	+	4.96267i	−0.635037	+	0.231135i	0.00438505	+	0.999990i	$0.498604\pi$
$462$	8.56687	+	8.02933i	0.398567	+	0.373558i
$463$	−8.48683	−	2.27404i	−0.394416	−	0.105684i	0.0561592	−	0.998422i	$-0.482115\pi$
$463$	−8.48683	−	2.27404i	−0.394416	−	0.105684i	−0.450576	+	0.892738i	$0.648781\pi$
$464$	17.2750	+	0.778262i	0.801972	+	0.0361299i
$465$	−9.67305	−	11.2063i	−0.448577	−	0.519681i
$466$	3.57475	−	6.68232i	0.165597	−	0.309552i
$467$	−37.3140	+	9.99825i	−1.72668	+	0.462664i	−0.979415	−	0.201858i	$-0.935302\pi$
$467$	−37.3140	+	9.99825i	−1.72668	+	0.462664i	−0.747269	+	0.664521i	$0.768635\pi$
$468$	24.8187	+	0.558774i	1.14724	+	0.0258293i
$469$	28.7266	+	34.2351i	1.32647	+	1.58083i
$470$	7.99988	−	12.6327i	0.369007	−	0.582702i
$471$	4.66132	−	12.8069i	0.214782	−	0.590110i
$472$	−28.1916	−	9.94700i	−1.29763	−	0.457848i
$473$	3.15603	−	2.20987i	0.145114	−	0.101610i
$474$	6.32998	−	8.05992i	0.290746	−	0.370204i
$475$	13.5853	+	17.0423i	0.623334	+	0.781956i
$476$	−3.18762	+	0.777663i	−0.146104	+	0.0356441i
$477$	3.71863	+	5.31076i	0.170264	+	0.243163i
$478$	1.94389	+	1.26938i	0.0889116	+	0.0580600i
$479$	38.9504	+	14.1768i	1.77969	+	0.647754i	0.999761	+	0.0218846i	$0.00696664\pi$
$479$	38.9504	+	14.1768i	1.77969	+	0.647754i	0.779928	+	0.625869i	$0.215256\pi$
$480$	13.4165	+	1.15594i	0.612375	+	0.0527611i
$481$	37.7814	−	31.7024i	1.72268	−	1.44550i
$482$	12.0146	+	16.0281i	0.547251	+	0.730060i
$483$	−3.41393	−	12.7410i	−0.155339	−	0.579734i
$484$	5.75338	+	13.1002i	0.261517	+	0.595463i
$485$	−5.83807	+	5.03929i	−0.265093	+	0.228822i
$486$	−8.22993	−	20.5190i	−0.373317	−	0.930762i
$487$	3.73685	−	13.9461i	0.169333	−	0.631959i	−0.828115	−	0.560559i	$-0.810586\pi$
$487$	3.73685	−	13.9461i	0.169333	−	0.631959i	0.997448	−	0.0714005i	$-0.0227468\pi$
$488$	−12.6037	+	22.3363i	−0.570541	+	1.01112i
$489$	0.733466	+	2.01518i	0.0331685	+	0.0911297i
$490$	−24.7567	−	12.8024i	−1.11840	−	0.578355i
$491$	−5.10897	+	6.08863i	−0.230565	+	0.274776i	−0.868906	−	0.494977i	$-0.835176\pi$
$491$	−5.10897	+	6.08863i	−0.230565	+	0.274776i	0.638341	+	0.769753i	$0.279621\pi$
$492$	−15.1337	−	13.2905i	−0.682281	−	0.599182i
$493$	−1.26113	−	1.26113i	−0.0567984	−	0.0567984i
$494$	−38.8007	+	13.2202i	−1.74573	+	0.594806i
$495$	2.00799	−	7.93554i	0.0902526	−	0.356676i
$496$	−23.7340	+	7.44710i	−1.06569	+	0.334385i
$497$	41.1655	−	3.60151i	1.84652	−	0.161550i
$498$	1.53724	−	6.58254i	0.0688854	−	0.294971i
$499$	−19.5135	+	7.10233i	−0.873544	+	0.317944i	−0.739601	−	0.673045i	$-0.764986\pi$
$499$	−19.5135	+	7.10233i	−0.873544	+	0.317944i	−0.133942	+	0.990989i	$0.542764\pi$
$500$	4.30890	+	21.9416i	0.192700	+	0.981258i
$501$	1.83916	+	3.18551i	0.0821675	+	0.142318i
$502$	25.5563	+	10.9243i	1.14063	+	0.487578i
$503$	13.9933	+	9.79824i	0.623932	+	0.436882i	0.842318	−	0.538981i	$-0.181190\pi$
$503$	13.9933	+	9.79824i	0.623932	+	0.436882i	−0.218386	+	0.975862i	$0.570079\pi$
$504$	20.3325	+	5.23360i	0.905682	+	0.233123i
$505$	−12.4251	−	12.0828i	−0.552907	−	0.537678i
$506$	−1.22428	+	8.55417i	−0.0544257	+	0.380279i
$507$	33.1077	+	2.89654i	1.47036	+	0.128640i
$508$	−19.7725	−	3.94726i	−0.877264	−	0.175132i
$509$	−4.47501	+	12.2950i	−0.198351	+	0.544966i	−0.998495	−	0.0548427i	$-0.982534\pi$
$509$	−4.47501	+	12.2950i	−0.198351	+	0.544966i	0.800144	+	0.599808i	$0.204756\pi$
$510$	−0.941072	−	1.02143i	−0.0416714	−	0.0452298i
$511$	31.5761	+	5.56772i	1.39684	+	0.246301i
$512$	10.7287	−	19.9222i	0.474148	−	0.880445i
$513$	15.0995	+	16.7933i	0.666660	+	0.741443i
$514$	−4.79541	+	6.10596i	−0.211516	+	0.269322i
$515$	−5.50136	+	2.08978i	−0.242419	+	0.0920866i
$516$	−1.85267	+	3.75029i	−0.0815594	+	0.165097i
$517$	8.40430	−	3.91899i	0.369621	−	0.172357i
$518$	37.2131	−	18.8426i	1.63505	−	0.827898i
$519$	13.2750	−	11.1391i	0.582708	−	0.488950i
$520$	−41.5793	−	6.31396i	−1.82337	−	0.276885i
$521$	2.76373	−	4.78692i	0.121081	−	0.209719i	−0.799113	−	0.601181i	$-0.794697\pi$
$521$	2.76373	−	4.78692i	0.121081	−	0.209719i	0.920194	+	0.391462i	$0.128031\pi$
$522$	3.30904	+	10.9221i	0.144833	+	0.478046i
$523$	6.58598	+	4.61155i	0.287985	+	0.201649i	0.708638	−	0.705573i	$-0.249310\pi$
$523$	6.58598	+	4.61155i	0.287985	+	0.201649i	−0.420653	+	0.907222i	$0.638199\pi$
$524$	19.1104	+	5.58457i	0.834843	+	0.243963i
$525$	−0.591063	−	21.1592i	−0.0257961	−	0.923465i
$526$	0.503923	+	15.5583i	0.0219721	+	0.678375i
$527$	2.32516	+	1.08424i	0.101286	+	0.0472302i
$528$	6.61842	+	5.09310i	0.288030	+	0.221649i
$529$	−8.54410	+	10.1825i	−0.371483	+	0.442716i
$530$	−5.09787	−	9.72850i	−0.221437	−	0.422579i
$531$		−	19.7294i		−	0.856184i
$532$	−34.4979	+	3.42522i	−1.49567	+	0.148502i
$533$	44.4789	+	44.4789i	1.92660	+	1.92660i
$534$	3.43729	−	3.07924i	0.148746	−	0.133252i
$535$	−6.61190	−	1.07089i	−0.285857	−	0.0462985i
$536$	22.6973	+	22.2538i	0.980376	+	0.961216i
$537$	−3.39000	+	7.26988i	−0.146289	+	0.313718i
$538$	17.9203	+	16.7958i	0.772598	+	0.724120i
$539$	−8.64234	−	14.9690i	−0.372252	−	0.644759i
$540$	5.80536	+	22.4310i	0.249823	+	0.965278i
$541$	−2.73754	−	15.5254i	−0.117696	−	0.667488i	−0.985380	−	0.170371i	$-0.945503\pi$
$541$	−2.73754	−	15.5254i	−0.117696	−	0.667488i	0.867684	−	0.497117i	$-0.165608\pi$
$542$	4.07968	−	1.23601i	0.175237	−	0.0530913i
$543$	5.00282	+	18.6708i	0.214692	+	0.801240i
$544$	−2.20290	+	0.770394i	−0.0944488	+	0.0330304i
$545$	27.1136	−	13.1072i	1.16142	−	0.561452i
$546$	37.8321	+	12.3982i	1.61906	+	0.530596i
$547$	−17.4183	−	37.3536i	−0.744752	−	1.59713i	−0.800968	−	0.598707i	$-0.795681\pi$
$547$	−17.4183	−	37.3536i	−0.744752	−	1.59713i	0.0562162	−	0.998419i	$-0.482096\pi$
$548$	23.8487	−	8.07711i	1.01877	−	0.345037i
$549$	−16.6687	−	2.93915i	−0.711404	−	0.125440i
$550$	−5.09247	+	12.8984i	−0.217144	+	0.549990i
$551$	−11.3301	−	15.0575i	−0.482680	−	0.641471i
$552$	−3.29561	−	8.78395i	−0.140271	−	0.373870i
$553$	−22.1738	+	15.5263i	−0.942926	+	0.660244i
$554$	20.5404	−	4.31175i	0.872679	−	0.183189i
$555$	14.6030	+	9.92420i	0.619864	+	0.421259i
$556$	−24.9038	+	16.6152i	−1.05616	+	0.704642i
$557$	−1.99209	+	22.7697i	−0.0844077	+	0.964785i	0.829405	+	0.558648i	$0.188680\pi$
$557$	−1.99209	+	22.7697i	−0.0844077	+	0.964785i	−0.913812	+	0.406136i	$0.866876\pi$
$558$	−9.84644	−	13.1356i	−0.416833	−	0.556076i
$559$	6.53186	−	11.3135i	0.276268	−	0.478511i
$560$	−33.0292	−	13.1970i	−1.39574	−	0.557675i
$561$	−0.149567	−	0.848238i	−0.00631474	−	0.0358126i
$562$	9.05700	−	21.1878i	0.382047	−	0.893755i
$563$	−30.3394	−	8.12942i	−1.27865	−	0.342614i	−0.445313	−	0.895375i	$-0.646908\pi$
$563$	−30.3394	−	8.12942i	−1.27865	−	0.342614i	−0.833340	+	0.552761i	$0.813574\pi$
$564$	−5.95879	+	8.11495i	−0.250910	+	0.341701i
$565$	13.2393	−	16.2331i	0.556983	−	0.682930i
$566$	−36.0494	+	22.3996i	−1.51527	+	0.941527i
$567$	0.0292071	+	0.333839i	0.00122658	+	0.0140199i
$568$	28.8930	−	5.38910i	1.21232	−	0.226122i
$569$		−	10.0803i		−	0.422589i	−0.977422	−	0.211294i	$-0.932232\pi$
$569$		−	10.0803i		−	0.422589i	0.977422	−	0.211294i	$-0.0677678\pi$
$570$	−8.33596	−	12.0768i	−0.349155	−	0.505843i
$571$		−	11.7246i		−	0.490659i	−0.969440	−	0.245329i	$-0.921104\pi$
$571$		−	11.7246i		−	0.490659i	0.969440	−	0.245329i	$-0.0788961\pi$
$572$	−19.5973	−	17.2104i	−0.819403	−	0.719604i
$573$	0.888322	+	10.1536i	0.0371102	+	0.424171i
$574$	28.0769	+	45.1863i	1.17191	+	1.88604i
$575$	12.5068	−	9.28838i	0.521568	−	0.387352i
$576$	14.7546	+	2.30239i	0.614774	+	0.0959331i
$577$	−34.7822	−	9.31987i	−1.44800	−	0.387991i	−0.552674	−	0.833397i	$-0.686393\pi$
$577$	−34.7822	−	9.31987i	−1.44800	−	0.387991i	−0.895329	+	0.445406i	$0.853059\pi$
$578$	−21.8853	−	9.35513i	−0.910308	−	0.389122i
$579$	−1.74267	−	9.88315i	−0.0724227	−	0.410730i
$580$	−3.19440	−	19.0679i	−0.132640	−	0.791752i
$581$	−8.92712	+	15.4622i	−0.370359	+	0.641481i
$582$	4.15493	−	3.11453i	0.172227	−	0.129101i
$583$	0.593655	−	6.78551i	0.0245867	−	0.281027i
$584$	22.7370	+	1.76334i	0.940866	+	0.0729677i
$585$	−5.20082	−	27.2635i	−0.215027	−	1.12721i
$586$	−0.746589	−	3.55662i	−0.0308413	−	0.146923i
$587$	33.8375	−	23.6933i	1.39662	−	0.977927i	0.398471	−	0.917181i	$-0.369541\pi$
$587$	33.8375	−	23.6933i	1.39662	−	0.977927i	0.998153	−	0.0607462i	$-0.0193480\pi$
$588$	16.0364	+	9.74634i	0.661329	+	0.401932i
$589$	22.7234	+	14.7793i	0.936300	+	0.608971i
$590$	−4.27290	+	33.1494i	−0.175913	+	1.36474i
$591$	1.90348	+	0.335634i	0.0782985	+	0.0138061i
$592$	25.0437	−	15.9058i	1.02929	−	0.653724i
$593$	−7.84754	−	16.8291i	−0.322260	−	0.691088i	0.676720	−	0.736240i	$-0.263401\pi$
$593$	−7.84754	−	16.8291i	−0.322260	−	0.691088i	−0.998980	+	0.0451517i	$0.985623\pi$
$594$	−4.47489	+	13.6547i	−0.183607	+	0.560260i
$595$	1.59660	+	3.30272i	0.0654543	+	0.135399i
$596$	24.6308	−	23.5461i	1.00892	−	0.964486i
$597$	1.10874	+	4.13786i	0.0453776	+	0.169352i
$598$	8.49570	+	28.0416i	0.347415	+	1.14671i
$599$	1.32760	+	7.52918i	0.0542442	+	0.307634i	0.999843	−	0.0177001i	$-0.00563440\pi$
$599$	1.32760	+	7.52918i	0.0542442	+	0.307634i	−0.945599	+	0.325334i	$0.894523\pi$
$600$	−1.87796	−	14.9380i	−0.0766676	−	0.609843i
$601$	−1.08906	−	1.88630i	−0.0444235	−	0.0769438i	0.842959	−	0.537978i	$-0.180812\pi$
$601$	−1.08906	−	1.88630i	−0.0444235	−	0.0769438i	−0.887382	+	0.461034i	$0.847478\pi$
$602$	7.55540	−	8.06121i	0.307935	−	0.328551i
$603$	−8.86565	+	19.0124i	−0.361037	+	0.774247i
$604$	−2.91303	+	26.4292i	−0.118530	+	1.07539i
$605$	12.9744	−	9.35742i	0.527483	−	0.380433i
$606$	7.78637	+	8.69173i	0.316299	+	0.353077i
$607$	16.9227	+	16.9227i	0.686873	+	0.686873i	0.961539	−	0.274667i	$-0.0885676\pi$
$607$	16.9227	+	16.9227i	0.686873	+	0.686873i	−0.274667	+	0.961539i	$0.588568\pi$
$608$	−24.1851	+	4.80437i	−0.980834	+	0.194843i
$609$			18.3020i			0.741634i
$610$	27.3702	+	8.54838i	1.10819	+	0.346114i
$611$	20.2108	−	24.0863i	0.817643	−	0.974429i
$612$	−0.963190	−	1.20182i	−0.0389346	−	0.0485806i
$613$	−11.7700	−	5.48843i	−0.475385	−	0.221676i	0.170133	−	0.985421i	$-0.445580\pi$
$613$	−11.7700	−	5.48843i	−0.475385	−	0.221676i	−0.645517	+	0.763746i	$0.723358\pi$
$614$	11.3581	−	0.367881i	0.458375	−	0.0148465i
$615$	−10.9859	+	19.6569i	−0.442993	+	0.792644i
$616$	−12.8297	−	17.9432i	−0.516922	−	0.722952i
$617$	8.78866	+	6.15388i	0.353818	+	0.247746i	0.736950	−	0.675948i	$-0.236266\pi$
$617$	8.78866	+	6.15388i	0.353818	+	0.247746i	−0.383132	+	0.923694i	$0.625154\pi$
$618$	3.79214	−	1.14890i	0.152542	−	0.0462154i
$619$	−6.00496	+	10.4009i	−0.241360	+	0.418047i	−0.961102	−	0.276194i	$-0.910927\pi$
$619$	−6.00496	+	10.4009i	−0.241360	+	0.418047i	0.719742	+	0.694242i	$0.244260\pi$
$620$	13.6991	+	24.2030i	0.550171	+	0.972016i
$621$	12.3659	−	10.3762i	0.496227	−	0.416384i
$622$	−5.11001	−	10.0920i	−0.204893	−	0.404651i
$623$	−11.0471	+	5.15135i	−0.442593	+	0.206384i
$624$	27.6369	+	6.16720i	1.10636	+	0.246885i
$625$	22.9784	−	9.84862i	0.919134	−	0.393945i
$626$	16.9144	+	13.2840i	0.676037	+	0.530936i
$627$	−0.311246	−	9.09523i	−0.0124300	−	0.363228i
$628$	−13.2977	+	21.8797i	−0.530637	+	0.873097i
$629$	−3.01338	−	0.531339i	−0.120151	−	0.0211859i
$630$	0.960383	−	23.4538i	0.0382626	−	0.934420i
$631$	−3.24089	+	8.90428i	−0.129018	+	0.354474i	−0.987336	−	0.158645i	$-0.949288\pi$
$631$	−3.24089	+	8.90428i	−0.129018	+	0.354474i	0.858318	+	0.513118i	$0.171510\pi$
$632$	−14.6260	+	12.5207i	−0.581793	+	0.498047i
$633$	18.0282	+	1.57726i	0.716556	+	0.0626906i
$634$	−7.66866	−	1.09754i	−0.304561	−	0.0435889i
$635$	0.314760	+	22.5404i	0.0124909	+	0.894487i
$636$	2.97366	+	6.77090i	0.117913	+	0.268484i
$637$	−48.0083	−	33.6158i	−1.90216	−	1.33191i
$638$	4.71278	−	11.0250i	0.186581	−	0.436484i
$639$	9.69848	+	16.7983i	0.383666	+	0.664529i
$640$	−24.2920	−	7.06395i	−0.960225	−	0.279227i
$641$	−15.4772	+	5.63325i	−0.611314	+	0.222500i	−0.629078	−	0.777342i	$-0.716567\pi$
$641$	−15.4772	+	5.63325i	−0.611314	+	0.222500i	0.0177643	+	0.999842i	$0.494345\pi$
$642$	4.39169	+	1.02560i	0.173326	+	0.0404774i
$643$	32.3846	−	2.83328i	1.27712	−	0.111734i	0.571666	−	0.820487i	$-0.306297\pi$
$643$	32.3846	−	2.83328i	1.27712	−	0.111734i	0.705457	+	0.708753i	$0.250742\pi$
$644$	1.60354	+	24.7282i	0.0631885	+	0.974429i
$645$	4.53379	+	1.14722i	0.178518	+	0.0451718i
$646$	2.17564	+	1.31683i	0.0855995	+	0.0518102i
$647$	12.2520	+	12.2520i	0.481676	+	0.481676i	0.905667	−	0.423990i	$-0.139371\pi$
$647$	12.2520	+	12.2520i	0.481676	+	0.481676i	−0.423990	+	0.905667i	$0.639371\pi$
$648$	0.0437039	+	0.234313i	0.00171685	+	0.00920467i
$649$	−13.3238	+	15.8787i	−0.523005	+	0.623293i
$650$	2.83381	+	46.9346i	0.111151	+	1.84092i
$651$	−9.00436	−	24.7393i	−0.352909	−	0.969608i
$652$	−0.610110	−	3.98233i	−0.0238938	−	0.155960i
$653$	0.312887	−	1.16771i	0.0122442	−	0.0456960i	−0.959533	−	0.281595i	$-0.909137\pi$
$653$	0.312887	−	1.16771i	0.0122442	−	0.0456960i	0.971778	+	0.235899i	$0.0758033\pi$
$654$	−18.8197	+	7.54834i	−0.735908	+	0.295164i
$655$	1.63025	−	22.1999i	0.0636989	−	0.867424i
$656$	22.9928	+	30.0511i	0.897718	+	1.17330i
$657$	3.89537	+	14.5377i	0.151973	+	0.567170i
$658$	21.2776	−	15.9497i	0.829489	−	0.621782i
$659$	−27.4922	+	23.0687i	−1.07094	+	0.898629i	−0.995138	−	0.0984931i	$-0.968598\pi$
$659$	−27.4922	+	23.0687i	−1.07094	+	0.898629i	−0.0758071	+	0.997123i	$0.524153\pi$
$660$	4.01815	−	8.42813i	0.156406	−	0.328065i
$661$	5.91708	+	2.15364i	0.230148	+	0.0837670i	0.454520	−	0.890737i	$-0.349811\pi$
$661$	5.91708	+	2.15364i	0.230148	+	0.0837670i	−0.224372	+	0.974504i	$0.572033\pi$
$662$	−3.75212	+	5.74589i	−0.145830	+	0.223320i
$663$	−1.67513	−	2.39233i	−0.0650567	−	0.0929105i
$664$	−5.25302	+	11.5616i	−0.203857	+	0.448678i
$665$	11.8228	+	36.9123i	0.458468	+	1.43140i
$666$	15.3983	+	12.0933i	0.596674	+	0.468607i
$667$	−11.0337	+	7.72590i	−0.427228	+	0.299148i
$668$	−2.21669	−	6.54508i	−0.0857664	−	0.253237i
$669$	8.98189	−	24.6775i	0.347260	−	0.954088i
$670$	19.0137	−	30.0246i	0.734563	−	1.15995i
$671$	11.4305	+	13.6223i	0.441269	+	0.525884i
$672$	21.5748	+	10.3946i	0.832267	+	0.400979i
$673$	1.31139	−	0.351387i	0.0505505	−	0.0135450i	−0.233455	−	0.972368i	$-0.575003\pi$
$673$	1.31139	−	0.351387i	0.0505505	−	0.0135450i	0.284006	+	0.958823i	$0.408337\pi$
$674$	11.2201	+	6.00229i	0.432183	+	0.231200i
$675$	23.1630	−	11.5992i	0.891545	−	0.446454i
$676$	−59.9289	−	17.5128i	−2.30496	−	0.673569i
$677$	−38.0164	−	10.1865i	−1.46109	−	0.391498i	−0.561223	−	0.827665i	$-0.689669\pi$
$677$	−38.0164	−	10.1865i	−1.46109	−	0.391498i	−0.899866	+	0.436167i	$0.856336\pi$
$678$	−9.64498	+	10.2907i	−0.370413	+	0.395211i
$679$	−12.8882	+	4.69092i	−0.494604	+	0.180021i
$680$	1.35807	+	2.22790i	0.0520795	+	0.0854359i
$681$	−14.2071	−	11.9211i	−0.544416	−	0.456819i
$682$	−0.946208	+	17.2214i	−0.0362322	+	0.659442i
$683$	14.9395	−	14.9395i	0.571646	−	0.571646i	−0.360943	−	0.932588i	$-0.617545\pi$
$683$	14.9395	−	14.9395i	0.571646	−	0.571646i	0.932588	+	0.360943i	$0.117545\pi$
$684$	−8.30078	−	13.9967i	−0.317388	−	0.535177i
$685$	−14.4148	−	24.1809i	−0.550760	−	0.923906i
$686$	−6.80556	−	7.59689i	−0.259838	−	0.290050i
$687$	−1.04855	−	11.9850i	−0.0400048	−	0.457257i
$688$	4.79248	−	6.22777i	0.182712	−	0.237432i
$689$	−7.89916	−	21.7028i	−0.300934	−	0.826809i
$690$	−8.83121	+	5.65978i	−0.336199	+	0.215464i
$691$	42.1986	−	24.3634i	1.60531	−	0.926826i	0.614910	−	0.788597i	$-0.289192\pi$
$691$	42.1986	−	24.3634i	1.60531	−	0.926826i	0.990400	−	0.138229i	$-0.0441410\pi$
$692$	−28.5533	+	15.6391i	−1.08543	+	0.594510i
$693$	8.34977	−	11.9247i	0.317182	−	0.452982i
$694$	14.3995	−	26.9171i	0.546598	−	1.02176i
$695$	23.9960	+	23.3351i	0.910220	+	0.885149i
$696$	1.26245	+	12.9561i	0.0478532	+	0.491101i
$697$	0.340128	−	3.88769i	0.0128833	−	0.147257i
$698$	8.38948	+	16.5687i	0.317547	+	0.627135i
$699$	5.36083	+	1.95118i	0.202765	+	0.0738005i
$700$	−6.69314	+	39.1990i	−0.252977	+	1.48158i
$701$	−1.66748	+	9.45672i	−0.0629797	+	0.357175i	0.936990	+	0.349357i	$0.113600\pi$
$701$	−1.66748	+	9.45672i	−0.0629797	+	0.357175i	−0.999969	+	0.00781866i	$0.997511\pi$
$702$	5.81543	+	48.3738i	0.219489	+	1.82575i
$703$	−30.7405	−	10.0120i	−1.15940	−	0.377608i
$704$	−10.3199	−	11.8172i	−0.388948	−	0.445376i
$705$	10.2669	+	4.61412i	0.386674	+	0.173778i
$706$	2.82693	+	13.4670i	0.106393	+	0.506837i
$707$	−13.0260	−	27.9344i	−0.489894	−	1.05058i
$708$	4.40570	−	22.0689i	0.165576	−	0.829401i
$709$	−13.9370	−	16.6094i	−0.523414	−	0.623781i	0.437970	−	0.898989i	$-0.355697\pi$
$709$	−13.9370	−	16.6094i	−0.523414	−	0.623781i	−0.961384	+	0.275209i	$0.911253\pi$
$710$	−12.6573	−	30.3249i	−0.475020	−	1.13807i
$711$	−11.0040	−	6.35317i	−0.412683	−	0.238263i
$712$	−7.46501	+	4.40871i	−0.279763	+	0.165223i
$713$	11.1135	−	15.8718i	0.416205	−	0.594402i
$714$	−0.919470	−	2.29244i	−0.0344103	−	0.0857924i
$715$	−14.2260	+	25.4546i	−0.532024	+	0.951947i
$716$	8.91914	−	12.1465i	0.333324	−	0.453936i
$717$	−0.738606	+	1.58395i	−0.0275838	+	0.0591536i
$718$	−17.7583	−	4.14714i	−0.662732	−	0.154770i
$719$	−35.0808	−	29.4363i	−1.30829	−	1.09779i	−0.988648	−	0.150250i	$-0.951992\pi$
$719$	−35.0808	−	29.4363i	−1.30829	−	1.09779i	−0.319644	−	0.947538i	$-0.603563\pi$
$720$	−0.937957	−	16.6694i	−0.0349556	−	0.621231i
$721$	−10.4658			−0.389765
$722$	20.8154	+	16.9917i	0.774669	+	0.632367i
$723$	−10.6626	+	10.6626i	−0.396545	+	0.396545i
$724$	−2.34986	−	36.2371i	−0.0873317	−	1.34674i
$725$	−20.0977	+	7.95729i	−0.746411	+	0.295526i
$726$	−9.14850	+	5.68450i	−0.339533	+	0.210972i
$727$	13.4707	+	6.28151i	0.499602	+	0.232968i	0.656049	−	0.754718i	$-0.272226\pi$
$727$	13.4707	+	6.28151i	0.499602	+	0.232968i	−0.156447	+	0.987686i	$0.550004\pi$
$728$	−65.1381	−	36.7553i	−2.41418	−	1.36224i
$729$	14.1939	−	8.19483i	0.525698	−	0.303512i
$730$	−3.39649	−	25.2699i	−0.125710	−	0.935280i
$731$	−0.798171	+	0.140739i	−0.0295214	+	0.00520542i
$732$	−17.9890	−	7.00990i	−0.664891	−	0.259093i
$733$	−26.1957	+	7.01911i	−0.967559	+	0.259257i	−0.707797	−	0.706416i	$-0.750311\pi$
$733$	−26.1957	+	7.01911i	−0.967559	+	0.259257i	−0.259762	+	0.965673i	$0.583644\pi$
$734$	6.38000	−	44.5779i	0.235490	−	1.64540i
$735$	6.89988	−	19.8138i	0.254506	−	0.730844i
$736$	2.84090	+	17.3947i	0.104717	+	0.641178i
$737$	19.9749	−	9.31444i	0.735784	−	0.343102i
$738$	−13.6534	+	20.9085i	−0.502590	+	0.769653i
$739$	−1.84013	+	10.4359i	−0.0676904	+	0.383892i	0.932076	+	0.362264i	$0.117996\pi$
$739$	−1.84013	+	10.4359i	−0.0676904	+	0.383892i	−0.999766	+	0.0216278i	$0.993115\pi$
$740$	−23.2532	−	23.6541i	−0.854804	−	0.869542i
$741$	−13.9897	−	27.5039i	−0.513925	−	1.01038i
$742$	−2.33141	−	19.3930i	−0.0855886	−	0.711941i
$743$	9.80523	+	14.0033i	0.359719	+	0.513732i	0.957696	−	0.287781i	$-0.0929176\pi$
$743$	9.80523	+	14.0033i	0.359719	+	0.513732i	−0.597977	+	0.801513i	$0.704029\pi$
$744$	−8.08076	−	16.8920i	−0.296255	−	0.619292i
$745$	−31.5091	−	21.4136i	−1.15441	−	0.784532i
$746$	3.13649	+	1.02788i	0.114835	+	0.0376334i
$747$	−8.34893	−	0.730436i	−0.305471	−	0.0267253i
$748$	−0.0364217	+	1.61772i	−0.00133171	+	0.0591496i
$749$	−10.3160	−	5.95593i	−0.376937	−	0.217625i
$750$	−15.8911	+	5.55104i	−0.580259	+	0.202695i
$751$	−0.735141	+	0.129625i	−0.0268257	+	0.00473009i	−0.187045	−	0.982351i	$-0.559891\pi$
$751$	−0.735141	+	0.129625i	−0.0268257	+	0.00473009i	0.160219	+	0.987081i	$0.448780\pi$
$752$	13.9624	−	12.7586i	0.509158	−	0.465259i
$753$	−5.41508	+	20.2093i	−0.197336	+	0.736469i
$754$	−1.31609	−	40.6335i	−0.0479292	−	1.47978i
$755$	29.5756	−	3.00420i	1.07636	−	0.109334i
$756$	−4.51437	+	40.9578i	−0.164186	+	1.48962i
$757$	2.73005	−	0.238848i	0.0992254	−	0.00868109i	−0.0374349	−	0.999299i	$-0.511919\pi$
$757$	2.73005	−	0.238848i	0.0992254	−	0.00868109i	0.136660	+	0.990618i	$0.456363\pi$
$758$	−2.86651	+	52.1719i	−0.104117	+	1.89497i
$759$	−6.50504			−0.236118
$760$	10.9156	+	25.3150i	0.395952	+	0.918271i
$761$	−37.9086			−1.37418			−0.687092	−	0.726570i	$-0.741113\pi$
$761$	−37.9086			−1.37418			−0.687092	+	0.726570i	$0.741113\pi$
$762$	0.832684	−	15.1552i	0.0301649	−	0.549016i
$763$	53.3538	−	4.66785i	1.93154	−	0.168988i
$764$	2.09778	−	19.0326i	0.0758949	−	0.688576i
$765$	−1.08832	+	1.33442i	−0.0393484	+	0.0482460i
$766$	−0.674026	−	20.8101i	−0.0243536	−	0.751901i
$767$	−18.1906	+	67.8884i	−0.656826	+	2.45131i
$768$	15.9900	+	5.87020i	0.576990	+	0.211823i
$769$	21.8407	−	3.85110i	0.787595	−	0.138874i	0.234637	−	0.972083i	$-0.424610\pi$
$769$	21.8407	−	3.85110i	0.787595	−	0.138874i	0.552959	+	0.833209i	$0.313499\pi$
$770$	−16.6119	+	18.2276i	−0.598651	+	0.656875i
$771$	−5.06152	−	2.92227i	−0.182286	−	0.105243i
$772$	−0.424363	+	18.8486i	−0.0152732	+	0.678378i
$773$	10.6452	+	0.931338i	0.382883	+	0.0334979i	0.276973	−	0.960878i	$-0.410669\pi$
$773$	10.6452	+	0.931338i	0.382883	+	0.0334979i	0.105910	+	0.994376i	$0.466224\pi$
$774$	4.92825	+	1.61507i	0.177142	+	0.0580526i
$775$	23.2517	−	20.6439i	0.835227	−	0.741551i
$776$	−8.80010	+	4.20977i	−0.315905	+	0.151122i
$777$	18.0101	+	25.7211i	0.646110	+	0.922741i
$778$	−5.31393	−	44.2022i	−0.190514	−	1.58473i
$779$	9.30356	−	40.1700i	0.333335	−	1.43924i
$780$	0.270587	−	31.6578i	0.00968858	−	1.13353i
$781$	3.53875	−	20.0693i	0.126627	−	0.718135i
$782$	0.993904	−	1.52204i	0.0355419	−	0.0544280i
$783$	−20.2996	+	9.46586i	−0.725449	+	0.338282i
$784$	−25.9592	−	23.8536i	−0.927116	−	0.851915i
$785$	27.0336	+	9.41408i	0.964871	+	0.336003i
$786$	−2.12340	+	14.8365i	−0.0757391	+	0.529199i
$787$	−14.5078	+	3.88735i	−0.517147	+	0.138569i	−0.507947	−	0.861389i	$-0.669595\pi$
$787$	−14.5078	+	3.88735i	−0.517147	+	0.138569i	−0.00920034	+	0.999958i	$0.502929\pi$
$788$	−3.38333	−	1.31841i	−0.120526	−	0.0469664i
$789$	−11.5401	+	2.03484i	−0.410839	+	0.0724421i
$790$	17.1130	+	13.0578i	0.608854	+	0.464576i
$791$	32.2619	−	18.6264i	1.14710	−	0.662280i
$792$	5.08832	−	9.01757i	0.180806	−	0.320425i
$793$	54.6467	+	25.4822i	1.94056	+	0.904898i
$794$	22.0048	−	13.6729i	0.780921	−	0.485232i
$795$	6.70586	−	4.83643i	0.237832	−	0.171530i
$796$	−0.520781	−	8.03096i	−0.0184586	−	0.284650i
$797$	22.7610	−	22.7610i	0.806236	−	0.806236i	−0.177826	−	0.984062i	$-0.556906\pi$
$797$	22.7610	−	22.7610i	0.806236	−	0.806236i	0.984062	+	0.177826i	$0.0569064\pi$
$798$	−6.23168	−	25.3421i	−0.220599	−	0.897100i
$799$	−1.95072			−0.0690114
$800$	−2.03422	+	28.2110i	−0.0719204	+	0.997410i
$801$	−4.38300	−	3.67778i	−0.154866	−	0.129948i
$802$	−37.6330	−	8.78854i	−1.32887	−	0.310334i
$803$	6.68262	−	14.3309i	0.235824	−	0.505727i
$804$	−14.1625	+	19.2872i	−0.499474	+	0.680206i
$805$	26.6583	−	7.54357i	0.939583	−	0.265876i
$806$	21.7702	+	54.2778i	0.766822	+	1.91185i
$807$	−10.6048	+	15.1453i	−0.373308	+	0.533139i
$808$	−11.1481	−	18.8765i	−0.392190	−	0.664072i
$809$	−36.7382	−	21.2108i	−1.29165	−	0.745732i	−0.312699	−	0.949852i	$-0.601233\pi$
$809$	−36.7382	−	21.2108i	−1.29165	−	0.745732i	−0.978946	+	0.204121i	$0.934567\pi$
$810$	0.245925	−	0.102647i	0.00864093	−	0.00360664i
$811$	−14.0970	−	16.8001i	−0.495012	−	0.589933i	0.459473	−	0.888192i	$-0.348038\pi$
$811$	−14.0970	−	16.8001i	−0.495012	−	0.589933i	−0.954485	+	0.298259i	$0.903594\pi$
$812$	6.73119	−	33.7177i	0.236219	−	1.18326i
$813$	1.35617	+	2.90831i	0.0475628	+	0.101999i
$814$	−4.22599	−	20.1319i	−0.148121	−	0.705623i
$815$	−4.21076	+	1.59952i	−0.147496	+	0.0560287i
$816$	−0.809031	−	1.55941i	−0.0283218	−	0.0545904i
$817$	−8.55838	+	0.292874i	−0.299420	+	0.0102464i
$818$	0.691970	+	5.75593i	0.0241942	+	0.201251i
$819$	8.57126	−	48.6100i	0.299504	−	1.69857i
$820$	27.4688	−	32.1735i	0.959251	−	1.12355i
$821$	−34.7301	−	12.6407i	−1.21209	−	0.441164i	−0.344661	−	0.938727i	$-0.612006\pi$
$821$	−34.7301	−	12.6407i	−1.21209	−	0.441164i	−0.867428	+	0.497563i	$0.834228\pi$
$822$	8.56247	+	16.9104i	0.298650	+	0.589817i
$823$	1.53027	−	17.4911i	0.0533420	−	0.609702i	−0.921733	−	0.387825i	$-0.873226\pi$
$823$	1.53027	−	17.4911i	0.0533420	−	0.609702i	0.975075	−	0.221876i	$-0.0712181\pi$
$824$	−7.40880	+	0.721919i	−0.258098	+	0.0251492i
$825$	−10.1549	−	2.41921i	−0.353547	−	0.0842261i
$826$	−28.0384	+	52.4123i	−0.975579	+	1.82366i
$827$	−18.8035	+	26.8542i	−0.653862	+	0.933812i	−0.999990	−	0.00437521i	$-0.998607\pi$
$827$	−18.8035	+	26.8542i	−0.653862	+	0.933812i	0.346128	+	0.938187i	$0.387496\pi$
$828$	−10.2019	+	5.58772i	−0.354539	+	0.194187i
$829$	−11.9644	+	6.90762i	−0.415539	+	0.239912i	−0.693167	−	0.720777i	$-0.743785\pi$
$829$	−11.9644	+	6.90762i	−0.415539	+	0.239912i	0.277628	+	0.960689i	$0.410452\pi$
$830$	13.8697	+	3.03545i	0.481423	+	0.105362i
$831$	5.40373	+	14.8466i	0.187453	+	0.515024i
$832$	−48.6472	−	21.5263i	−1.68654	−	0.746289i
$833$	0.316903	+	3.62221i	0.0109800	+	0.125502i
$834$	−15.0375	−	16.7860i	−0.520706	−	0.581251i
$835$	−6.63625	+	3.95601i	−0.229657	+	0.136903i
$836$	−2.77168	+	16.8706i	−0.0958606	+	0.583482i
$837$	22.7824	−	22.7824i	0.787475	−	0.787475i
$838$	0.405172	−	7.37432i	0.0139964	−	0.254742i
$839$	−4.61720	−	3.87429i	−0.159404	−	0.133755i	0.559597	−	0.828765i	$-0.310956\pi$
$839$	−4.61720	−	3.87429i	−0.159404	−	0.133755i	−0.719001	+	0.695009i	$0.755400\pi$
$840$	6.31164	−	26.0204i	0.217772	−	0.897791i
$841$	−9.68871	+	3.52640i	−0.334093	+	0.121600i
$842$	6.90125	−	7.36327i	0.237833	−	0.253755i
$843$	16.7549	+	4.48945i	0.577068	+	0.154625i
$844$	−32.6332	−	9.53629i	−1.12328	−	0.328253i
$845$	−5.11233	+	69.6174i	−0.175869	+	2.39491i
$846$	11.0064	+	5.88793i	0.378407	+	0.202431i
$847$	27.4793	−	7.36306i	0.944200	−	0.252998i
$848$	−2.98814	−	13.5677i	−0.102613	−	0.465916i
$849$	−20.5367	−	24.4746i	−0.704816	−	0.839968i
$850$	2.11760	−	2.00639i	0.0726332	−	0.0688185i
$851$	−7.90382	+	21.7156i	−0.270939	+	0.744400i
$852$	7.09737	+	20.9559i	0.243152	+	0.717938i
$853$	28.6763	−	20.0793i	0.981856	−	0.687503i	0.0317714	−	0.999495i	$-0.489885\pi$
$853$	28.6763	−	20.0793i	0.981856	−	0.687503i	0.950085	+	0.311992i	$0.100996\pi$
$854$	40.1045	+	31.4967i	1.37235	+	1.07779i
$855$	−13.3579	+	12.3523i	−0.456832	+	0.422439i
$856$	−7.71360	−	3.50467i	−0.263645	−	0.119787i
$857$	−1.23824	−	1.76840i	−0.0422976	−	0.0604073i	0.797446	−	0.603390i	$-0.206184\pi$
$857$	−1.23824	−	1.76840i	−0.0422976	−	0.0604073i	−0.839744	+	0.542983i	$0.817295\pi$
$858$	10.7349	−	16.4392i	0.366484	−	0.561224i
$859$	−21.6445	−	7.87794i	−0.738499	−	0.268792i	−0.0547412	−	0.998501i	$-0.517433\pi$
$859$	−21.6445	−	7.87794i	−0.738499	−	0.268792i	−0.683758	+	0.729709i	$0.739656\pi$
$860$	−7.93066	−	3.78098i	−0.270433	−	0.128930i
$861$	−30.6778	+	25.7418i	−1.04550	+	0.877277i
$862$	−23.2258	+	17.4100i	−0.791075	+	0.592987i
$863$	13.0892	+	48.8494i	0.445560	+	1.66285i	0.714453	+	0.699683i	$0.246676\pi$
$863$	13.0892	+	48.8494i	0.445560	+	1.66285i	−0.268893	+	0.963170i	$0.586658\pi$
$864$	−0.370529	+	29.3058i	−0.0126056	+	0.997003i
$865$	23.7835	+	27.5534i	0.808662	+	0.936843i
$866$	−34.5085	+	13.8410i	−1.17265	+	0.470335i
$867$	4.63723	−	17.3064i	0.157489	−	0.587756i
$868$	7.48998	+	48.8888i	0.254227	+	1.65939i
$869$	4.56582	+	12.5445i	0.154885	+	0.425542i
$870$	13.8685	−	4.41405i	0.470186	−	0.149650i
$871$	48.0360	−	57.2471i	1.62764	−	1.93974i
$872$	37.4476	−	6.98471i	1.26814	−	0.236532i
$873$	−4.55236	−	4.55236i	−0.154074	−	0.154074i
$874$	12.6474	−	14.4547i	0.427804	−	0.488936i
$875$	44.4211	−	1.86190i	1.50171	−	0.0629436i
$876$	1.11092	+	17.1314i	0.0375344	+	0.578818i
$877$	−43.3607	+	3.79357i	−1.46419	+	0.128100i	−0.791202	−	0.611555i	$-0.790544\pi$
$877$	−43.3607	+	3.79357i	−1.46419	+	0.128100i	−0.672986	+	0.739655i	$0.734989\pi$
$878$	10.2586	+	2.39573i	0.346213	+	0.0808521i
$879$	2.57073	−	0.935668i	0.0867085	−	0.0315593i
$880$	−10.5024	+	14.0493i	−0.354035	+	0.473602i
$881$	1.07609	+	1.86384i	0.0362543	+	0.0627944i	0.883583	−	0.468274i	$-0.155124\pi$
$881$	1.07609	+	1.86384i	0.0362543	+	0.0627944i	−0.847329	+	0.531068i	$0.821791\pi$
$882$	9.14505	−	21.3938i	0.307930	−	0.720367i
$883$	−14.8479	−	10.3966i	−0.499673	−	0.349874i	0.296412	−	0.955060i	$-0.404210\pi$
$883$	−14.8479	−	10.3966i	−0.499673	−	0.349874i	−0.796084	+	0.605186i	$0.793099\pi$
$884$	2.20623	+	5.02348i	0.0742034	+	0.168958i
$885$	−25.1582	+	0.351317i	−0.845685	+	0.0118094i
$886$	−12.3917	−	1.77351i	−0.416309	−	0.0595822i
$887$	−9.19365	−	0.804340i	−0.308693	−	0.0270071i	−0.0682430	−	0.997669i	$-0.521739\pi$
$887$	−9.19365	−	0.804340i	−0.308693	−	0.0270071i	−0.240450	+	0.970662i	$0.577295\pi$
$888$	14.5238	+	16.9659i	0.487385	+	0.569338i
$889$	−13.7115	+	37.6721i	−0.459870	+	1.26348i
$890$	6.56781	+	7.12865i	0.220153	+	0.238953i
$891$	0.162755	+	0.0286982i	0.00545251	+	0.000961425i
$892$	−25.6233	+	42.1600i	−0.857933	+	1.41162i
$893$	−20.4082	−	2.88274i	−0.682936	−	0.0964673i
$894$	20.1732	+	15.8433i	0.674692	+	0.529880i
$895$	−15.3676	−	6.90644i	−0.513681	−	0.230857i
$896$	−35.9243	−	27.0848i	−1.20015	−	0.904840i
$897$	−19.9902	+	9.32156i	−0.667452	+	0.311238i
$898$	15.2157	+	30.0500i	0.507754	+	1.00278i
$899$	−20.5946	+	17.2810i	−0.686870	+	0.576352i
$900$	−18.0039	+	4.92881i	−0.600131	+	0.164294i
$901$	−0.716435	+	1.24090i	−0.0238679	+	0.0413404i
$902$	25.1087	−	7.60712i	0.836028	−	0.253289i
$903$	6.81291	+	4.77045i	0.226720	+	0.158751i
$904$	21.5537	−	15.4112i	0.716865	−	0.512570i
$905$	−39.0655	+	11.0544i	−1.29858	+	0.367462i
$906$	−20.0054	+	0.647963i	−0.664636	+	0.0215271i
$907$	21.5599	+	10.0535i	0.715884	+	0.333822i	0.746204	−	0.665718i	$-0.231875\pi$
$907$	21.5599	+	10.0535i	0.715884	+	0.333822i	−0.0303191	+	0.999540i	$0.509652\pi$
$908$	21.7892	+	27.1875i	0.723102	+	0.902248i
$909$	9.29985	−	11.0831i	0.308457	−	0.367604i
$910$	−24.9291	+	79.8182i	−0.826393	+	2.64595i
$911$			30.9883i			1.02669i	0.858182	+	0.513345i	$0.171594\pi$
$911$			30.9883i			1.02669i	−0.858182	+	0.513345i	$0.828406\pi$
$912$	−6.15954	−	17.5100i	−0.203963	−	0.579815i
$913$	6.22612	+	6.22612i	0.206055	+	0.206055i
$914$	22.8075	+	25.4594i	0.754404	+	0.842123i
$915$	−3.45107	+	21.3077i	−0.114089	+	0.704410i
$916$	−2.47616	+	22.4657i	−0.0818148	+	0.742286i
$917$	16.7301	−	35.8778i	0.552477	−	1.18479i
$918$	2.06710	−	2.20549i	0.0682245	−	0.0727919i
$919$	−7.81422	−	13.5346i	−0.257767	−	0.446466i	0.707876	−	0.706337i	$-0.249654\pi$
$919$	−7.81422	−	13.5346i	−0.257767	−	0.446466i	−0.965644	+	0.259870i	$0.916320\pi$
$920$	18.3513	−	7.17903i	0.605025	−	0.236686i
$921$	1.48550	+	8.42468i	0.0489488	+	0.277603i
$922$	5.94985	+	19.6385i	0.195948	+	0.646761i
$923$	−17.8841	−	66.7444i	−0.588663	−	2.19692i
$924$	12.0027	−	11.4742i	0.394861	−	0.377473i
$925$	−20.4144	+	30.9602i	−0.671223	+	1.01797i
$926$	−3.86958	+	11.8077i	−0.127162	+	0.388025i
$927$	−2.07617	−	4.45237i	−0.0681905	−	0.146235i
$928$	2.43925	−	24.3334i	0.0800724	−	0.798783i
$929$	−21.2671	−	3.74997i	−0.697752	−	0.123033i	−0.186490	−	0.982457i	$-0.559711\pi$
$929$	−21.2671	−	3.74997i	−0.697752	−	0.123033i	−0.511263	+	0.859424i	$0.670822\pi$
$930$	−16.5748	+	12.7897i	−0.543508	+	0.419391i
$931$	−2.03745	+	38.3636i	−0.0667747	+	1.25732i
$932$	−9.15864	−	5.56630i	−0.300001	−	0.182330i
$933$	6.97542	−	4.88424i	0.228365	−	0.159903i
$934$	11.2234	+	53.4661i	0.367239	+	1.74947i
$935$	1.77708	−	0.338997i	0.0581166	−	0.0110864i
$936$	2.71459	−	35.0027i	0.0887292	−	1.14410i
$937$	0.123259	−	1.40886i	0.00402669	−	0.0460253i	−0.993916	−	0.110145i	$-0.964868\pi$
$937$	0.123259	−	1.40886i	0.00402669	−	0.0460253i	0.997942	+	0.0641198i	$0.0204240\pi$
$938$	50.5715	−	37.9083i	1.65122	−	1.23775i
$939$	−8.09514	+	14.0212i	−0.264175	+	0.457564i
$940$	−17.2177	−	12.2766i	−0.561580	−	0.400419i
$941$	−5.79915	−	32.8886i	−0.189047	−	1.07214i	−0.920645	−	0.390401i	$-0.872336\pi$
$941$	−5.79915	−	32.8886i	−0.189047	−	1.07214i	0.731598	−	0.681736i	$-0.238775\pi$
$942$	−17.7227	−	7.57580i	−0.577438	−	0.246833i
$943$	−28.4691	−	7.62828i	−0.927082	−	0.248411i
$944$	−16.2332	+	39.0372i	−0.528347	+	1.27055i
$945$	45.8337	−	4.65565i	1.49097	−	0.151448i
$946$	−2.87567	−	4.62803i	−0.0934960	−	0.150470i
$947$	−2.34371	−	26.7887i	−0.0761604	−	0.870517i	−0.934157	−	0.356862i	$-0.883847\pi$
$947$	−2.34371	−	26.7887i	−0.0761604	−	0.870517i	0.857997	−	0.513655i	$-0.171709\pi$
$948$	−10.8902	−	9.56380i	−0.353696	−	0.310618i
$949$		−	53.6153i		−	1.74043i
$950$	25.1192	−	17.8613i	0.814975	−	0.579497i
$951$		−	5.83165i		−	0.189104i
$952$	0.850813	+	4.56153i	0.0275750	+	0.147840i
$953$	−0.716607	−	8.19085i	−0.0232132	−	0.265328i	−0.998928	−	0.0462844i	$-0.985262\pi$
$953$	−0.716607	−	8.19085i	−0.0232132	−	0.265328i	0.975715	−	0.219043i	$-0.0702936\pi$
$954$	7.78774	−	4.83898i	0.252138	−	0.156668i
$955$	−21.2984	+	2.16343i	−0.689200	+	0.0700069i
$956$	1.94329	−	2.64645i	0.0628503	−	0.0855924i
$957$	8.71833	+	2.33607i	0.281824	+	0.0755144i
$958$	23.0408	−	53.9013i	0.744413	−	1.74147i
$959$	−8.69363	−	49.3040i	−0.280732	−	1.59211i
$960$	2.67320	−	18.8555i	0.0862770	−	0.608558i
$961$	3.83629	−	6.64465i	0.123751	−	0.214344i
$962$	−41.8351	−	55.8101i	−1.34882	−	1.79939i
$963$	0.487327	−	5.57017i	0.0157039	−	0.179496i
$964$	23.5652	−	15.7221i	0.758983	−	0.506375i
$965$	20.7054	−	3.94978i	0.666531	−	0.127148i
$966$	−18.2562	+	3.83225i	−0.587383	+	0.123301i
$967$	29.3678	−	20.5635i	0.944404	−	0.661279i	0.00351496	−	0.999994i	$-0.498881\pi$
$967$	29.3678	−	20.5635i	0.944404	−	0.661279i	0.940889	+	0.338715i	$0.109992\pi$
$968$	18.9449	−	7.10787i	0.608914	−	0.228456i
$969$	−0.749254	+	1.76171i	−0.0240695	+	0.0565941i
$970$	6.66295	+	8.63481i	0.213935	+	0.277247i
$971$	36.2246	+	6.38737i	1.16250	+	0.204980i	0.721427	−	0.692490i	$-0.243486\pi$
$971$	36.2246	+	6.38737i	1.16250	+	0.204980i	0.441074	+	0.897471i	$0.354598\pi$
$972$	−29.6131	+	10.0294i	−0.949841	+	0.321693i
$973$	25.1566	+	53.9485i	0.806484	+	1.72951i
$974$	−19.4032	−	6.35876i	−0.621718	−	0.203748i
$975$	−34.6728	+	7.11736i	−1.11042	+	0.227938i
$976$	30.5629	+	19.5304i	0.978295	+	0.625153i
$977$	10.1566	+	37.9048i	0.324937	+	1.21268i	0.914375	+	0.404868i	$0.132683\pi$
$977$	10.1566	+	37.9048i	0.324937	+	1.21268i	−0.589438	+	0.807814i	$0.700651\pi$
$978$	2.90251	−	0.879368i	0.0928121	−	0.0281191i
$979$	1.04384	+	5.91992i	0.0333613	+	0.189201i
$980$	−19.9989	+	33.9653i	−0.638841	+	1.08498i
$981$	12.5700	+	21.7719i	0.401330	+	0.695124i
$982$	8.20128	+	7.68668i	0.261713	+	0.245292i
$983$	−19.4647	+	41.7422i	−0.620828	+	1.33137i	0.304612	+	0.952476i	$0.401473\pi$
$983$	−19.4647	+	41.7422i	−0.620828	+	1.33137i	−0.925440	+	0.378894i	$0.876305\pi$
$984$	−19.9415	+	20.3389i	−0.635711	+	0.648382i
$985$	−0.649071	+	4.00751i	−0.0206811	+	0.127690i
$986$	−1.87866	+	1.68297i	−0.0598288	+	0.0535968i
$987$	14.1548	+	14.1548i	0.450552	+	0.450552i
$988$	15.6577	+	55.8156i	0.498138	+	1.77573i
$989$			6.12108i			0.194639i
$990$	−11.0499	−	3.45113i	−0.351187	−	0.109684i
$991$	−6.12434	+	7.29870i	−0.194546	+	0.231851i	−0.854495	−	0.519459i	$-0.826133\pi$
$991$	−6.12434	+	7.29870i	−0.194546	+	0.231851i	0.659949	+	0.751310i	$0.270578\pi$
$992$	8.67453	+	34.0922i	0.275417	+	1.08243i
$993$	−4.68194	−	2.18322i	−0.148577	−	0.0692825i
$994$	−1.89181	−	58.4085i	−0.0600046	−	1.85261i
$995$	−8.65779	+	2.44992i	−0.274470	+	0.0776675i
$996$	−9.17583	−	2.68142i	−0.290747	−	0.0849640i
$997$	−50.7358	−	35.5256i	−1.60682	−	1.12511i	−0.915317	−	0.402733i	$-0.868060\pi$
$997$	−50.7358	−	35.5256i	−1.60682	−	1.12511i	−0.691503	−	0.722374i	$-0.743051\pi$
$998$	8.51513	+	28.1057i	0.269542	+	0.889671i
$999$	−19.2136	+	33.2790i	−0.607892	+	1.05290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.283.29	yes	672
4.3	odd	2	inner	380.2.bj.a.283.5	yes	672
5.2	odd	4	inner	380.2.bj.a.207.56	yes	672
19.9	even	9	inner	380.2.bj.a.123.35	yes	672
20.7	even	4	inner	380.2.bj.a.207.35	yes	672
76.47	odd	18	inner	380.2.bj.a.123.56	yes	672
95.47	odd	36	inner	380.2.bj.a.47.5	✓	672
380.47	even	36	inner	380.2.bj.a.47.29	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.47.5	✓	672	95.47	odd	36	inner
380.2.bj.a.47.29	yes	672	380.47	even	36	inner
380.2.bj.a.123.35	yes	672	19.9	even	9	inner
380.2.bj.a.123.56	yes	672	76.47	odd	18	inner
380.2.bj.a.207.35	yes	672	20.7	even	4	inner
380.2.bj.a.207.56	yes	672	5.2	odd	4	inner
380.2.bj.a.283.5	yes	672	4.3	odd	2	inner
380.2.bj.a.283.29	yes	672	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0775850 - 1.41208i) q^{2} +(1.06054 - 0.0927854i) q^{3} +(-1.98796 - 0.219113i) q^{4} +(0.225970 + 2.22462i) q^{5} +(-0.0487386 - 1.50477i) q^{6} +(-1.02923 + 3.84113i) q^{7} +(-0.463642 + 2.79017i) q^{8} +(-1.83828 + 0.324139i) q^{9} +O(q^{10})\)	\(q+(0.0775850 - 1.41208i) q^{2} +(1.06054 - 0.0927854i) q^{3} +(-1.98796 - 0.219113i) q^{4} +(0.225970 + 2.22462i) q^{5} +(-0.0487386 - 1.50477i) q^{6} +(-1.02923 + 3.84113i) q^{7} +(-0.463642 + 2.79017i) q^{8} +(-1.83828 + 0.324139i) q^{9} +(3.15888 - 0.146492i) q^{10} +(1.69839 + 0.980566i) q^{11} +(-2.12865 - 0.0479249i) q^{12} +(6.62433 + 0.579554i) q^{13} +(5.34415 + 1.75137i) q^{14} +(0.446064 + 2.33834i) q^{15} +(3.90398 + 0.871177i) q^{16} +(-0.236628 - 0.337940i) q^{17} +(0.315088 + 2.62096i) q^{18} +(-1.97618 - 3.88519i) q^{19} +(0.0382231 - 4.47197i) q^{20} +(-0.735139 + 4.16918i) q^{21} +(1.51641 - 2.32219i) q^{22} +(-2.82380 + 1.31676i) q^{23} +(-0.232825 + 3.00211i) q^{24} +(-4.89787 + 1.00540i) q^{25} +(1.33233 - 9.30915i) q^{26} +(-5.00446 + 1.34094i) q^{27} +(2.88771 - 7.41051i) q^{28} +(4.25746 - 0.750704i) q^{29} +(3.33654 - 0.448459i) q^{30} +(-5.38558 + 3.10936i) q^{31} +(1.53306 - 5.44515i) q^{32} +(1.89220 + 0.882346i) q^{33} +(-0.495559 + 0.307920i) q^{34} +(-8.77764 - 1.42166i) q^{35} +(3.72546 - 0.241584i) q^{36} +(5.24459 - 5.24459i) q^{37} +(-5.63954 + 2.48910i) q^{38} +7.07916 q^{39} +(-6.31183 - 0.400932i) q^{40} +(7.24645 + 6.08049i) q^{41} +(5.83020 + 1.36154i) q^{42} +(0.830266 - 1.78051i) q^{43} +(-3.16148 - 2.32147i) q^{44} +(-1.13648 - 4.01624i) q^{45} +(1.64029 + 4.08961i) q^{46} +(2.71213 - 3.87332i) q^{47} +(4.22117 + 0.561687i) q^{48} +(-7.63282 - 4.40681i) q^{49} +(1.03970 + 6.99421i) q^{50} +(-0.282310 - 0.336444i) q^{51} +(-13.0419 - 2.60361i) q^{52} +(-1.46784 - 3.14780i) q^{53} +(1.50525 + 7.17075i) q^{54} +(-1.79760 + 3.99985i) q^{55} +(-10.2402 - 4.65263i) q^{56} +(-2.45631 - 3.93705i) q^{57} +(-0.729743 - 6.07013i) q^{58} +(-1.83537 + 10.4089i) q^{59} +(-0.374397 - 4.74626i) q^{60} +(8.52071 + 3.10129i) q^{61} +(3.97284 + 7.84613i) q^{62} +(0.646952 - 7.39470i) q^{63} +(-7.57007 - 2.58728i) q^{64} +(0.207615 + 14.8676i) q^{65} +(1.39275 - 2.60348i) q^{66} +(6.44604 - 9.20589i) q^{67} +(0.396361 + 0.723661i) q^{68} +(-2.87259 + 1.65849i) q^{69} +(-2.68852 + 12.2845i) q^{70} +(-3.55406 - 9.76470i) q^{71} +(-0.0520966 - 5.27940i) q^{72} +(-0.702728 - 8.03222i) q^{73} +(-6.99889 - 7.81270i) q^{74} +(-5.10112 + 1.52072i) q^{75} +(3.07728 + 8.15661i) q^{76} +(-5.51452 + 5.51452i) q^{77} +(0.549237 - 9.99637i) q^{78} +(5.21451 + 4.37550i) q^{79} +(-1.05585 + 8.88173i) q^{80} +(0.0791886 - 0.0288223i) q^{81} +(9.14838 - 9.76084i) q^{82} +(4.33680 + 1.16204i) q^{83} +(2.37495 - 8.12709i) q^{84} +(0.698318 - 0.602773i) q^{85} +(-2.44981 - 1.31055i) q^{86} +(4.44556 - 1.19118i) q^{87} +(-3.52339 + 4.28416i) q^{88} +(1.97027 + 2.34807i) q^{89} +(-5.75943 + 1.29321i) q^{90} +(-9.04410 + 24.8484i) q^{91} +(5.90213 - 1.99894i) q^{92} +(-5.42313 + 3.79732i) q^{93} +(-5.25903 - 4.13026i) q^{94} +(8.19652 - 5.27420i) q^{95} +(1.12065 - 5.91706i) q^{96} +(1.97826 + 2.82524i) q^{97} +(-6.81497 + 10.4363i) q^{98} +(-3.43996 - 1.25204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more