LMFDB - Embedded newform 153.2.s.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	153.11
Dual form			153.2.s.a.14.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.135712 + 0.176863i) q^{2} +(-1.63883 + 0.560569i) q^{3} +(0.504775 - 1.88385i) q^{4} +(1.50417 + 0.0985882i) q^{5} +(-0.321553 - 0.213773i) q^{6} +(-0.139720 - 2.13171i) q^{7} +(0.813611 - 0.337009i) q^{8} +(2.37153 - 1.83735i) q^{9} +O(q^{10})$	\(q+(0.135712 + 0.176863i) q^{2} +(-1.63883 + 0.560569i) q^{3} +(0.504775 - 1.88385i) q^{4} +(1.50417 + 0.0985882i) q^{5} +(-0.321553 - 0.213773i) q^{6} +(-0.139720 - 2.13171i) q^{7} +(0.813611 - 0.337009i) q^{8} +(2.37153 - 1.83735i) q^{9} +(0.186697 + 0.279412i) q^{10} +(0.776131 + 0.680648i) q^{11} +(0.228785 + 3.37026i) q^{12} +(3.92991 + 1.05302i) q^{13} +(0.358061 - 0.314011i) q^{14} +(-2.52034 + 0.681619i) q^{15} +(-3.20800 - 1.85214i) q^{16} +(4.07115 - 0.652511i) q^{17} +(0.646805 + 0.170085i) q^{18} +(-6.74095 - 2.79219i) q^{19} +(0.944991 - 2.78385i) q^{20} +(1.42395 + 3.41519i) q^{21} +(-0.0150515 + 0.229641i) q^{22} +(1.48528 + 4.37548i) q^{23} +(-1.14445 + 1.00839i) q^{24} +(-2.70443 - 0.356045i) q^{25} +(0.347096 + 0.837965i) q^{26} +(-2.85656 + 4.34051i) q^{27} +(-4.08635 - 0.812825i) q^{28} +(-7.00719 + 3.45556i) q^{29} +(-0.462594 - 0.353252i) q^{30} +(3.02610 + 3.45061i) q^{31} +(-0.337684 - 2.56496i) q^{32} +(-1.65350 - 0.680392i) q^{33} +(0.667909 + 0.631483i) q^{34} -3.22023i q^{35} +(-2.26420 - 5.39504i) q^{36} +(0.117832 + 0.592384i) q^{37} +(-0.420992 - 1.57116i) q^{38} +(-7.03074 + 0.477270i) q^{39} +(1.25703 - 0.426705i) q^{40} +(-2.90192 + 5.88451i) q^{41} +(-0.410776 + 0.715328i) q^{42} +(0.118602 - 0.900874i) q^{43} +(1.67401 - 1.11854i) q^{44} +(3.74831 - 2.52988i) q^{45} +(-0.572293 + 0.856497i) q^{46} +(8.55178 - 2.29144i) q^{47} +(6.29562 + 1.23704i) q^{48} +(2.41543 - 0.317998i) q^{49} +(-0.304052 - 0.526634i) q^{50} +(-6.30614 + 3.35151i) q^{51} +(3.96744 - 6.87181i) q^{52} +(-1.80626 + 4.36069i) q^{53} +(-1.15535 + 0.0838381i) q^{54} +(1.10033 + 1.10033i) q^{55} +(-0.832084 - 1.68730i) q^{56} +(12.6125 + 0.797164i) q^{57} +(-1.56212 - 0.770354i) q^{58} +(2.26928 + 1.74128i) q^{59} +(0.0118616 + 5.09199i) q^{60} +(3.37778 - 0.221391i) q^{61} +(-0.199608 + 1.00350i) q^{62} +(-4.24806 - 4.79870i) q^{63} +(-4.83082 + 4.83082i) q^{64} +(5.80742 + 1.97135i) q^{65} +(-0.104063 - 0.384780i) q^{66} +(-0.0193978 + 0.0111993i) q^{67} +(0.825783 - 7.99879i) q^{68} +(-4.88687 - 6.33807i) q^{69} +(0.569540 - 0.437024i) q^{70} +(-14.9748 + 2.97867i) q^{71} +(1.31030 - 2.29412i) q^{72} +(8.86525 + 5.92357i) q^{73} +(-0.0887798 + 0.101234i) q^{74} +(4.63169 - 0.932521i) q^{75} +(-8.66273 + 11.2895i) q^{76} +(1.34251 - 1.74959i) q^{77} +(-1.03857 - 1.17871i) q^{78} +(3.66763 - 4.18213i) q^{79} +(-4.64277 - 3.10220i) q^{80} +(2.24827 - 8.71466i) q^{81} +(-1.43458 + 0.285356i) q^{82} +(-11.3511 + 8.71002i) q^{83} +(7.15247 - 0.958596i) q^{84} +(6.18801 - 0.580118i) q^{85} +(0.175427 - 0.101283i) q^{86} +(9.54651 - 9.59109i) q^{87} +(0.860853 + 0.292220i) q^{88} +(7.61763 - 7.61763i) q^{89} +(0.956134 + 0.319604i) q^{90} +(1.69564 - 8.52457i) q^{91} +(8.99247 - 0.589397i) q^{92} +(-6.89357 - 3.95862i) q^{93} +(1.56585 + 1.20152i) q^{94} +(-9.86423 - 4.86450i) q^{95} +(1.99124 + 4.01424i) q^{96} +(0.927015 + 1.87980i) q^{97} +(0.384046 + 0.384046i) q^{98} +(3.09120 + 0.188149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.135712	+	0.176863i	0.0959629	+	0.125061i	0.838867	−	0.544337i	$-0.183219\pi$
$2$	0.135712	+	0.176863i	0.0959629	+	0.125061i	−0.742904	+	0.669398i	$0.766552\pi$
$3$	−1.63883	+	0.560569i	−0.946179	+	0.323644i
$3$	−1.63883	+	0.560569i	−0.946179	+	0.323644i
$4$	0.504775	−	1.88385i	0.252388	−	0.941923i
$5$	1.50417	+	0.0985882i	0.672683	+	0.0440900i	0.397918	−	0.917421i	$-0.369733\pi$
$5$	1.50417	+	0.0985882i	0.672683	+	0.0440900i	0.274766	+	0.961511i	$0.411400\pi$
$6$	−0.321553	−	0.213773i	−0.131274	−	0.0872725i
$7$	−0.139720	−	2.13171i	−0.0528092	−	0.805712i	−0.939328	−	0.343020i	$-0.888550\pi$
$7$	−0.139720	−	2.13171i	−0.0528092	−	0.805712i	0.886519	−	0.462692i	$-0.153116\pi$
$8$	0.813611	−	0.337009i	0.287655	−	0.119151i
$9$	2.37153	−	1.83735i	0.790509	−	0.612451i
$10$	0.186697	+	0.279412i	0.0590387	+	0.0883577i
$11$	0.776131	+	0.680648i	0.234012	+	0.205223i	0.768318	−	0.640068i	$-0.221094\pi$
$11$	0.776131	+	0.680648i	0.234012	+	0.205223i	−0.534306	+	0.845291i	$0.679427\pi$
$12$	0.228785	+	3.37026i	0.0660444	+	0.972912i
$13$	3.92991	+	1.05302i	1.08996	+	0.292054i	0.758670	−	0.651475i	$-0.225849\pi$
$13$	3.92991	+	1.05302i	1.08996	+	0.292054i	0.331291	+	0.943529i	$0.392516\pi$
$14$	0.358061	−	0.314011i	0.0956957	−	0.0839229i
$15$	−2.52034	+	0.681619i	−0.650748	+	0.175993i
$16$	−3.20800	−	1.85214i	−0.802000	−	0.463035i
$17$	4.07115	−	0.652511i	0.987398	−	0.158257i
$17$	4.07115	−	0.652511i	0.987398	−	0.158257i
$18$	0.646805	+	0.170085i	0.152453	+	0.0400895i
$19$	−6.74095	−	2.79219i	−1.54648	−	0.640573i	−0.563805	−	0.825908i	$-0.690663\pi$
$19$	−6.74095	−	2.79219i	−1.54648	−	0.640573i	−0.982675	+	0.185335i	$0.940663\pi$
$20$	0.944991	−	2.78385i	0.211306	−	0.622488i
$21$	1.42395	+	3.41519i	0.310731	+	0.745256i
$22$	−0.0150515	+	0.229641i	−0.00320899	+	0.0489597i
$23$	1.48528	+	4.37548i	0.309701	+	0.912351i	0.984658	+	0.174494i	$0.0558289\pi$
$23$	1.48528	+	4.37548i	0.309701	+	0.912351i	−0.674957	+	0.737857i	$0.735838\pi$
$24$	−1.14445	+	1.00839i	−0.233611	+	0.205836i
$25$	−2.70443	−	0.356045i	−0.540886	−	0.0712090i
$26$	0.347096	+	0.837965i	0.0680712	+	0.164338i
$27$	−2.85656	+	4.34051i	−0.549746	+	0.835332i
$28$	−4.08635	−	0.812825i	−0.772247	−	0.153610i
$29$	−7.00719	+	3.45556i	−1.30120	+	0.641682i	−0.955036	−	0.296491i	$-0.904184\pi$
$29$	−7.00719	+	3.45556i	−1.30120	+	0.641682i	−0.346167	+	0.938173i	$0.612517\pi$
$30$	−0.462594	−	0.353252i	−0.0844577	−	0.0644946i
$31$	3.02610	+	3.45061i	0.543504	+	0.619748i	0.956764	−	0.290865i	$-0.0939432\pi$
$31$	3.02610	+	3.45061i	0.543504	+	0.619748i	−0.413260	+	0.910613i	$0.635610\pi$
$32$	−0.337684	−	2.56496i	−0.0596946	−	0.453425i
$33$	−1.65350	−	0.680392i	−0.287837	−	0.118441i
$34$	0.667909	+	0.631483i	0.114545	+	0.108298i
$35$		−	3.22023i		−	0.544317i
$36$	−2.26420	−	5.39504i	−0.377367	−	0.899173i
$37$	0.117832	+	0.592384i	0.0193715	+	0.0973873i	0.989262	−	0.146156i	$-0.0466902\pi$
$37$	0.117832	+	0.592384i	0.0193715	+	0.0973873i	−0.969890	+	0.243543i	$0.921690\pi$
$38$	−0.420992	−	1.57116i	−0.0682939	−	0.254876i
$39$	−7.03074	+	0.477270i	−1.12582	+	0.0764243i
$40$	1.25703	−	0.426705i	0.198754	−	0.0674679i
$41$	−2.90192	+	5.88451i	−0.453204	+	0.919006i	0.543617	+	0.839333i	$0.317054\pi$
$41$	−2.90192	+	5.88451i	−0.453204	+	0.919006i	−0.996821	+	0.0796729i	$0.974612\pi$
$42$	−0.410776	+	0.715328i	−0.0633841	+	0.110377i
$43$	0.118602	−	0.900874i	0.0180867	−	0.137382i	−0.980019	−	0.198904i	$-0.936262\pi$
$43$	0.118602	−	0.900874i	0.0180867	−	0.137382i	0.998106	+	0.0615216i	$0.0195953\pi$
$44$	1.67401	−	1.11854i	0.252366	−	0.168626i
$45$	3.74831	−	2.52988i	0.558765	−	0.377132i
$46$	−0.572293	+	0.856497i	−0.0843800	+	0.126284i
$47$	8.55178	−	2.29144i	1.24740	−	0.334241i	0.426071	−	0.904690i	$-0.359897\pi$
$47$	8.55178	−	2.29144i	1.24740	−	0.334241i	0.821333	+	0.570448i	$0.193231\pi$
$48$	6.29562	+	1.23704i	0.908694	+	0.178551i
$49$	2.41543	−	0.317998i	0.345062	−	0.0454283i
$50$	−0.304052	−	0.526634i	−0.0429995	−	0.0744773i
$51$	−6.30614	+	3.35151i	−0.883036	+	0.469305i
$52$	3.96744	−	6.87181i	0.550185	−	0.952949i
$53$	−1.80626	+	4.36069i	−0.248108	+	0.598987i	−0.998043	−	0.0625248i	$-0.980085\pi$
$53$	−1.80626	+	4.36069i	−0.248108	+	0.598987i	0.749935	+	0.661512i	$0.230085\pi$
$54$	−1.15535	+	0.0838381i	−0.157223	+	0.0114089i
$55$	1.10033	+	1.10033i	0.148368	+	0.148368i
$56$	−0.832084	−	1.68730i	−0.111192	−	0.225475i
$57$	12.6125	+	0.797164i	1.67056	+	0.105587i
$58$	−1.56212	−	0.770354i	−0.205117	−	0.101152i
$59$	2.26928	+	1.74128i	0.295435	+	0.226695i	0.745833	−	0.666133i	$-0.232051\pi$
$59$	2.26928	+	1.74128i	0.295435	+	0.226695i	−0.450399	+	0.892828i	$0.648718\pi$
$60$	0.0118616	+	5.09199i	0.00153133	+	0.657374i
$61$	3.37778	−	0.221391i	0.432480	−	0.0283463i	0.152391	−	0.988320i	$-0.451303\pi$
$61$	3.37778	−	0.221391i	0.432480	−	0.0283463i	0.280089	+	0.959974i	$0.409636\pi$
$62$	−0.199608	+	1.00350i	−0.0253502	+	0.127444i
$63$	−4.24806	−	4.79870i	−0.535205	−	0.604579i
$64$	−4.83082	+	4.83082i	−0.603853	+	0.603853i
$65$	5.80742	+	1.97135i	0.720322	+	0.244516i
$66$	−0.104063	−	0.384780i	−0.0128093	−	0.0473632i
$67$	−0.0193978	+	0.0111993i	−0.00236982	+	0.00136821i	−0.501184	−	0.865340i	$-0.667102\pi$
$67$	−0.0193978	+	0.0111993i	−0.00236982	+	0.00136821i	0.498815	+	0.866709i	$0.333769\pi$
$68$	0.825783	−	7.99879i	0.100141	−	0.969995i
$69$	−4.88687	−	6.33807i	−0.588310	−	0.763014i
$70$	0.569540	−	0.437024i	0.0680731	−	0.0522343i
$71$	−14.9748	+	2.97867i	−1.77718	+	0.353503i	−0.971168	−	0.238397i	$-0.923378\pi$
$71$	−14.9748	+	2.97867i	−1.77718	+	0.353503i	−0.806011	+	0.591900i	$0.798378\pi$
$72$	1.31030	−	2.29412i	0.154420	−	0.270364i
$73$	8.86525	+	5.92357i	1.03760	+	0.693302i	0.952956	−	0.303110i	$-0.0980248\pi$
$73$	8.86525	+	5.92357i	1.03760	+	0.693302i	0.0846435	+	0.996411i	$0.473025\pi$
$74$	−0.0887798	+	0.101234i	−0.0103204	+	0.0117682i
$75$	4.63169	−	0.932521i	0.534821	−	0.107678i
$76$	−8.66273	+	11.2895i	−0.993683	+	1.29499i
$77$	1.34251	−	1.74959i	0.152993	−	0.199384i
$78$	−1.03857	−	1.17871i	−0.117595	−	0.133463i
$79$	3.66763	−	4.18213i	0.412641	−	0.470526i	−0.507763	−	0.861497i	$-0.669527\pi$
$79$	3.66763	−	4.18213i	0.412641	−	0.470526i	0.920403	+	0.390971i	$0.127861\pi$
$80$	−4.64277	−	3.10220i	−0.519077	−	0.346836i
$81$	2.24827	−	8.71466i	0.249808	−	0.968295i
$82$	−1.43458	+	0.285356i	−0.158423	+	0.0315123i
$83$	−11.3511	+	8.71002i	−1.24595	+	0.956049i	−0.999913	−	0.0132124i	$-0.995794\pi$
$83$	−11.3511	+	8.71002i	−1.24595	+	0.956049i	−0.246034	+	0.969261i	$0.579128\pi$
$84$	7.15247	−	0.958596i	0.780399	−	0.104591i
$85$	6.18801	−	0.580118i	0.671184	−	0.0629226i
$86$	0.175427	−	0.101283i	0.0189168	−	0.0109216i
$87$	9.54651	−	9.59109i	1.02349	−	1.02827i
$88$	0.860853	+	0.292220i	0.0917673	+	0.0311508i
$89$	7.61763	−	7.61763i	0.807467	−	0.807467i	−0.176783	−	0.984250i	$-0.556569\pi$
$89$	7.61763	−	7.61763i	0.807467	−	0.807467i	0.984250	+	0.176783i	$0.0565691\pi$
$90$	0.956134	+	0.319604i	0.100785	+	0.0336892i
$91$	1.69564	−	8.52457i	0.177752	−	0.893618i
$92$	8.99247	−	0.589397i	0.937529	−	0.0614489i
$93$	−6.89357	−	3.95862i	−0.714830	−	0.410490i
$94$	1.56585	+	1.20152i	0.161505	+	0.123927i
$95$	−9.86423	−	4.86450i	−1.01205	−	0.499087i
$96$	1.99124	+	4.01424i	0.203230	+	0.409702i
$97$	0.927015	+	1.87980i	0.0941241	+	0.190865i	0.938843	−	0.344345i	$-0.111899\pi$
$97$	0.927015	+	1.87980i	0.0941241	+	0.190865i	−0.844719	+	0.535210i	$0.820232\pi$
$98$	0.384046	+	0.384046i	0.0387945	+	0.0387945i
$99$	3.09120	+	0.188149i	0.310678	+	0.0189097i
$100$	−2.03586	+	4.91501i	−0.203586	+	0.491501i
$101$	1.36485	−	2.36400i	0.135808	−	0.235226i	−0.790098	−	0.612981i	$-0.789970\pi$
$101$	1.36485	−	2.36400i	0.135808	−	0.235226i	0.925906	+	0.377754i	$0.123304\pi$
$102$	−1.44858	−	0.660485i	−0.143431	−	0.0653977i
$103$	0.278613	+	0.482571i	0.0274525	+	0.0475492i	0.879425	−	0.476037i	$-0.157927\pi$
$103$	0.278613	+	0.482571i	0.0274525	+	0.0475492i	−0.851973	+	0.523586i	$0.824594\pi$
$104$	3.55230	−	0.467669i	0.348331	−	0.0458587i
$105$	1.80516	+	5.27740i	0.176165	+	0.515022i
$106$	−1.01638	+	0.272338i	−0.0987193	+	0.0264518i
$107$	0.557520	−	0.834388i	0.0538975	−	0.0806633i	−0.803542	−	0.595248i	$-0.797054\pi$
$107$	0.557520	−	0.834388i	0.0538975	−	0.0806633i	0.857440	+	0.514585i	$0.172054\pi$
$108$	6.73493	+	7.57231i	0.648069	+	0.728646i
$109$	−4.28808	+	2.86520i	−0.410724	+	0.274437i	−0.743720	−	0.668491i	$-0.766940\pi$
$109$	−4.28808	+	2.86520i	−0.410724	+	0.274437i	0.332996	+	0.942928i	$0.391940\pi$
$110$	−0.0452799	+	0.343935i	−0.00431727	+	0.0327929i
$111$	−0.525179	−	0.904763i	−0.0498478	−	0.0858763i
$112$	−3.50001	+	7.09732i	−0.330720	+	0.670633i
$113$	−6.75914	+	2.29442i	−0.635847	+	0.215841i	−0.620705	−	0.784044i	$-0.713153\pi$
$113$	−6.75914	+	2.29442i	−0.635847	+	0.215841i	−0.0151421	+	0.999885i	$0.504820\pi$
$114$	1.57068	+	2.33887i	0.147107	+	0.219055i
$115$	1.80273	+	6.72788i	0.168105	+	0.627378i
$116$	2.97270	+	14.9448i	0.276008	+	1.38759i
$117$	11.2546	−	4.72338i	1.04049	−	0.436676i
$118$			0.637665i			0.0587018i
$119$	−1.95979	−	8.58735i	−0.179653	−	0.787201i
$120$	−1.82086	+	1.40395i	−0.166221	+	0.128162i
$121$	−1.29669	−	9.84935i	−0.117881	−	0.895395i
$122$	0.497562	+	0.567360i	0.0450471	+	0.0513664i
$123$	1.45708	−	11.2704i	0.131380	−	1.01622i
$124$	8.02792	−	3.95893i	0.720929	−	0.355523i
$125$	−11.4250	−	2.27256i	−1.02188	−	0.203264i
$126$	0.272201	−	1.40257i	0.0242496	−	0.124951i
$127$	5.02705	+	12.1364i	0.446079	+	1.07693i	0.973778	+	0.227499i	$0.0730547\pi$
$127$	5.02705	+	12.1364i	0.446079	+	1.07693i	−0.527699	+	0.849431i	$0.676945\pi$
$128$	−6.63992	−	0.874162i	−0.586891	−	0.0772657i
$129$	0.310633	+	1.54286i	0.0273497	+	0.135842i
$130$	0.439477	+	1.29466i	0.0385447	+	0.113549i
$131$	0.754026	−	11.5042i	0.0658796	−	1.00513i	−0.829123	−	0.559067i	$-0.811160\pi$
$131$	0.754026	−	11.5042i	0.0658796	−	1.00513i	0.895002	−	0.446061i	$-0.147174\pi$
$132$	−2.11640	+	2.77149i	−0.184209	+	0.241227i
$133$	−5.01031	+	14.7599i	−0.434449	+	1.27985i
$134$	−0.00461326	−	0.00191088i	−0.000398525	−	0.000165074i
$135$	−4.72467	+	6.24723i	−0.406635	+	0.537676i
$136$	3.09243	−	1.90290i	0.265174	−	0.163173i
$137$	−15.6155	−	9.01562i	−1.33412	−	0.770256i	−0.348194	−	0.937422i	$-0.613205\pi$
$137$	−15.6155	−	9.01562i	−1.33412	−	0.770256i	−0.985929	+	0.167166i	$0.946538\pi$
$138$	0.457765	−	1.72446i	0.0389676	−	0.146796i
$139$	0.313385	−	0.274831i	0.0265810	−	0.0233109i	−0.645952	−	0.763378i	$-0.723540\pi$
$139$	0.313385	−	0.274831i	0.0265810	−	0.0233109i	0.672533	+	0.740067i	$0.265206\pi$
$140$	−6.06641	−	1.62549i	−0.512705	−	0.137379i
$141$	−12.7304	+	8.54914i	−1.07209	+	0.719968i
$142$	−2.55908	−	2.24425i	−0.214753	−	0.188333i
$143$	2.33339	+	3.49216i	0.195128	+	0.292029i
$144$	−11.0109	+	1.50183i	−0.917574	+	0.125153i
$145$	−10.8807	+	4.50692i	−0.903589	+	0.374279i
$146$	0.155459	+	2.37184i	0.0128658	+	0.196295i
$147$	−3.78022	+	1.87516i	−0.311788	+	0.154661i
$148$	1.17544	+	0.0770424i	0.0966205	+	0.00633284i
$149$	−1.63715	+	6.10992i	−0.134120	+	0.500544i	0.865880	+	0.500253i	$0.166760\pi$
$149$	−1.63715	+	6.10992i	−0.134120	+	0.500544i	−1.00000		0.000291710i	$0.999907\pi$
$150$	0.793505	+	0.692622i	0.0647894	+	0.0565523i
$151$	−12.2518	−	15.9668i	−0.997035	−	1.29936i	−0.953847	−	0.300294i	$-0.902915\pi$
$151$	−12.2518	−	15.9668i	−0.997035	−	1.29936i	−0.0431885	−	0.999067i	$-0.513752\pi$
$152$	−6.42551			−0.521178
$153$	8.45593	−	9.02758i	0.683622	−	0.729836i
$154$	0.491633			0.0396169
$155$	4.21157	+	5.48863i	0.338282	+	0.440857i
$156$	−2.64984	+	13.4858i	−0.212157	+	1.07972i
$157$	2.41164	−	9.00035i	0.192469	−	0.718306i	−0.800438	−	0.599416i	$-0.795400\pi$
$157$	2.41164	−	9.00035i	0.192469	−	0.718306i	0.992907	−	0.118890i	$-0.0379337\pi$
$158$	1.23741	+	0.0811040i	0.0984429	+	0.00645229i
$159$	0.515682	−	8.15896i	0.0408962	−	0.647048i
$160$	−0.255057	−	3.89142i	−0.0201640	−	0.307644i
$161$	9.11975	−	3.77752i	0.718737	−	0.297711i
$162$	1.84642	−	0.785048i	0.145069	−	0.0616792i
$163$	4.60388	+	6.89019i	0.360604	+	0.539681i	0.966767	−	0.255659i	$-0.0822923\pi$
$163$	4.60388	+	6.89019i	0.360604	+	0.539681i	−0.606164	+	0.795340i	$0.707292\pi$
$164$	9.62070	+	8.43712i	0.751250	+	0.658829i
$165$	−2.42005	−	1.18644i	−0.188401	−	0.0923641i
$166$	−3.08097	−	0.825543i	−0.239129	−	0.0640746i
$167$	−0.382113	+	0.335104i	−0.0295688	+	0.0259311i	−0.674003	−	0.738729i	$-0.735426\pi$
$167$	−0.382113	+	0.335104i	−0.0295688	+	0.0259311i	0.644434	+	0.764660i	$0.277093\pi$
$168$	2.30949	+	2.29876i	0.178181	+	0.177353i
$169$	3.07702	+	1.77652i	0.236694	+	0.136655i
$170$	0.942389	+	1.01570i	0.0722780	+	0.0779009i
$171$	−21.1166	+	5.76375i	−1.61483	+	0.440765i
$172$	−1.63724	−	0.678167i	−0.124838	−	0.0517098i
$173$	−2.26714	+	6.67877i	−0.172367	+	0.507778i	−0.998443	−	0.0557814i	$-0.982235\pi$
$173$	−2.26714	+	6.67877i	−0.172367	+	0.507778i	0.826076	+	0.563559i	$0.190568\pi$
$174$	2.99189	+	0.386802i	0.226815	+	0.0293234i
$175$	−0.381123	+	5.81481i	−0.0288102	+	0.439559i
$176$	−1.22917	−	3.62102i	−0.0926523	−	0.272945i
$177$	−4.69506	−	1.58157i	−0.352903	−	0.118878i
$178$	2.38108	+	0.313476i	0.178470	+	0.0234960i
$179$	9.72705	+	23.4832i	0.727034	+	1.75521i	0.652236	+	0.758016i	$0.273831\pi$
$179$	9.72705	+	23.4832i	0.727034	+	1.75521i	0.0747976	+	0.997199i	$0.476169\pi$
$180$	−2.87385	−	8.33826i	−0.214204	−	0.621497i
$181$	−9.38624	−	1.86704i	−0.697674	−	0.138776i	−0.166503	−	0.986041i	$-0.553248\pi$
$181$	−9.38624	−	1.86704i	−0.697674	−	0.138776i	−0.531171	+	0.847265i	$0.678248\pi$
$182$	1.73780	−	0.856990i	0.128815	−	0.0635243i
$183$	−5.41150	+	2.25630i	−0.400030	+	0.166791i
$184$	2.68301	+	3.05939i	0.197794	+	0.225541i
$185$	0.118838	+	0.902661i	0.00873711	+	0.0663649i
$186$	−0.235405	−	1.75645i	−0.0172608	−	0.128789i
$187$	3.60387	+	2.26458i	0.263541	+	0.165603i
$188$		−	17.2669i		−	1.25932i
$189$	9.65185	+	5.48292i	0.702068	+	0.398824i
$190$	−0.478343	−	2.40479i	−0.0347027	−	0.174462i
$191$	3.36927	+	12.5743i	0.243792	+	0.909845i	0.973987	+	0.226605i	$0.0727628\pi$
$191$	3.36927	+	12.5743i	0.243792	+	0.909845i	−0.730194	+	0.683239i	$0.760571\pi$
$192$	5.20889	−	10.6249i	0.375919	−	0.766786i
$193$	22.5822	−	7.66562i	1.62550	−	0.551784i	0.647806	−	0.761806i	$-0.275687\pi$
$193$	22.5822	−	7.66562i	1.62550	−	0.551784i	0.977697	+	0.210022i	$0.0673535\pi$
$194$	−0.206661	+	0.419067i	−0.0148374	+	0.0300872i
$195$	−10.6225	+	0.0247446i	−0.760690	+	0.00177200i
$196$	0.620192	−	4.71082i	0.0442994	−	0.336487i
$197$	17.0086	−	11.3648i	1.21181	−	0.809707i	0.225444	−	0.974256i	$-0.427617\pi$
$197$	17.0086	−	11.3648i	1.21181	−	0.809707i	0.986369	+	0.164549i	$0.0526169\pi$
$198$	0.386237	+	0.572255i	0.0274487	+	0.0406684i
$199$	14.5040	−	21.7068i	1.02816	−	1.53875i	0.198803	−	0.980040i	$-0.436295\pi$
$199$	14.5040	−	21.7068i	1.02816	−	1.53875i	0.829360	−	0.558715i	$-0.188705\pi$
$200$	−2.32034	+	0.621734i	−0.164073	+	0.0439633i
$201$	0.0255117	−	0.0292275i	0.00179945	−	0.00206155i
$202$	0.603332	−	0.0794301i	0.0424503	−	0.00558869i
$203$	8.34532	+	14.4545i	0.585726	+	1.01451i
$204$	3.13055	+	13.5716i	0.219182	+	0.950199i
$205$	−4.94511	+	8.56518i	−0.345382	+	0.598218i
$206$	−0.0475381	+	0.114767i	−0.00331214	+	0.00799621i
$207$	11.5617	+	7.64759i	0.803592	+	0.531544i
$208$	−10.6568	−	10.6568i	−0.738917	−	0.738917i
$209$	−3.33136	−	6.75532i	−0.230435	−	0.467275i
$210$	−0.688398	+	1.03547i	−0.0475040	+	0.0714545i
$211$	−13.8576	−	6.83383i	−0.953999	−	0.470460i	−0.102452	−	0.994738i	$-0.532669\pi$
$211$	−13.8576	−	6.83383i	−0.953999	−	0.470460i	−0.851547	+	0.524278i	$0.824335\pi$
$212$	7.30312	+	5.60388i	0.501580	+	0.384876i
$213$	22.8714	−	13.2759i	1.56712	−	0.909651i
$214$	0.223235	−	0.0146316i	0.0152600	−	0.00100019i
$215$	0.267213	−	1.34337i	0.0182238	−	0.0916171i
$216$	−0.861343	+	4.49418i	−0.0586069	+	0.305790i
$217$	6.93290	−	6.93290i	0.470636	−	0.470636i
$218$	−1.08869	−	0.369562i	−0.0737357	−	0.0250299i
$219$	−17.8492	−	4.73814i	−1.20614	−	0.320174i
$220$	2.62826	−	1.51743i	0.177197	−	0.102305i
$221$	16.6863	+	1.72267i	1.12244	+	0.115880i
$222$	0.0887464	−	0.215672i	0.00595627	−	0.0144750i
$223$	−1.99838	+	1.53341i	−0.133822	+	0.102685i	−0.673503	−	0.739184i	$-0.735211\pi$
$223$	−1.99838	+	1.53341i	−0.133822	+	0.102685i	0.539682	+	0.841869i	$0.318545\pi$
$224$	−5.42058	+	1.07822i	−0.362178	+	0.0720416i
$225$	−7.06780	+	4.12462i	−0.471187	+	0.274975i
$226$	−1.32310	−	0.884065i	−0.0880111	−	0.0588071i
$227$	9.76149	−	11.1308i	0.647893	−	0.738780i	−0.330892	−	0.943668i	$-0.607350\pi$
$227$	9.76149	−	11.1308i	0.647893	−	0.738780i	0.978785	+	0.204888i	$0.0656831\pi$
$228$	7.86820	−	23.3576i	0.521085	−	1.54689i
$229$	−8.37715	+	10.9173i	−0.553578	+	0.721436i	−0.983395	−	0.181480i	$-0.941911\pi$
$229$	−8.37715	+	10.9173i	−0.553578	+	0.721436i	0.429817	+	0.902916i	$0.358578\pi$
$230$	−0.945264	+	1.23189i	−0.0623289	+	0.0812286i
$231$	−1.21937	+	3.61984i	−0.0802290	+	0.238168i
$232$	−4.53657	+	5.17297i	−0.297841	+	0.339622i
$233$	−18.0339	−	12.0498i	−1.18144	−	0.789411i	−0.199738	−	0.979849i	$-0.564009\pi$
$233$	−18.0339	−	12.0498i	−1.18144	−	0.789411i	−0.981699	+	0.190438i	$0.939009\pi$
$234$	2.36278	+	1.34952i	0.154460	+	0.0882206i
$235$	13.0892	−	2.60360i	0.853845	−	0.169840i
$236$	4.42577	−	3.39602i	0.288093	−	0.221062i
$237$	−3.66625	+	8.90976i	−0.238149	+	0.578751i
$238$	1.25282	−	1.51202i	0.0812083	−	0.0980098i
$239$	17.8365	−	10.2979i	1.15375	−	0.666118i	0.203952	−	0.978981i	$-0.434622\pi$
$239$	17.8365	−	10.2979i	1.15375	−	0.666118i	0.949798	+	0.312863i	$0.101288\pi$
$240$	9.34770	+	2.48138i	0.603391	+	0.160173i
$241$	−12.9025	−	4.37979i	−0.831120	−	0.282127i	−0.126727	−	0.991938i	$-0.540447\pi$
$241$	−12.9025	−	4.37979i	−0.831120	−	0.282127i	−0.704393	+	0.709810i	$0.748781\pi$
$242$	1.56601	−	1.56601i	0.100667	−	0.100667i
$243$	1.20064	+	15.5422i	0.0770208	+	0.997029i
$244$	1.28795	−	6.47497i	0.0824527	−	0.414518i
$245$	3.66456	−	0.240188i	0.234120	−	0.0153451i
$246$	2.19107	−	1.27183i	0.139698	−	0.0810889i
$247$	−23.5511	−	18.0714i	−1.49852	−	1.14986i
$248$	3.62496	+	1.78763i	0.230185	+	0.113515i
$249$	13.7200	−	20.6373i	0.869469	−	1.30784i
$250$	−1.14857	−	2.32907i	−0.0726420	−	0.147303i
$251$	14.7939	+	14.7939i	0.933784	+	0.933784i	0.997940	−	0.0641558i	$-0.0204355\pi$
$251$	14.7939	+	14.7939i	0.933784	+	0.933784i	−0.0641558	+	0.997940i	$0.520435\pi$
$252$	−11.1843	+	5.58043i	−0.704546	+	0.351534i
$253$	−1.82540	+	4.40690i	−0.114762	+	0.277059i
$254$	−1.46425	+	2.53616i	−0.0918752	+	0.159133i
$255$	−9.81590	+	4.41952i	−0.614695	+	0.276761i
$256$	6.08530	+	10.5401i	0.380331	+	0.658753i
$257$	−6.23320	+	0.820616i	−0.388816	+	0.0511887i	−0.322400	−	0.946603i	$-0.604490\pi$
$257$	−6.23320	+	0.820616i	−0.388816	+	0.0511887i	−0.0664159	+	0.997792i	$0.521156\pi$
$258$	−0.230719	+	0.264325i	−0.0143640	+	0.0164561i
$259$	1.24633	−	0.333953i	0.0774431	−	0.0207508i
$260$	6.64517	−	9.94520i	0.412116	−	0.616775i
$261$	−10.2686	+	21.0696i	−0.635613	+	1.30418i
$262$	2.13701	−	1.42790i	0.132025	−	0.0882161i
$263$	2.70759	−	20.5662i	0.166957	−	1.26817i	−0.678690	−	0.734425i	$-0.737452\pi$
$263$	2.70759	−	20.5662i	0.166957	−	1.26817i	0.845647	−	0.533742i	$-0.179215\pi$
$264$	−1.57460	+	0.00366798i	−0.0969100	+	0.000225748i
$265$	−3.14682	+	6.38113i	−0.193308	+	0.391989i
$266$	−3.29045	+	1.11696i	−0.201750	+	0.0684850i
$267$	−8.21379	+	16.7542i	−0.502676	+	1.02534i
$268$	0.0113063	+	0.0421956i	0.000690640	+	0.00257750i
$269$	−3.12229	−	15.6968i	−0.190369	−	0.957050i	−0.951312	−	0.308231i	$-0.900263\pi$
$269$	−3.12229	−	15.6968i	−0.190369	−	0.957050i	0.760942	−	0.648819i	$-0.224737\pi$
$270$	−1.74610	+	0.0122026i	−0.106264	+	0.000742627i
$271$		−	1.54867i		−	0.0940751i	−0.998893	−	0.0470376i	$-0.985022\pi$
$271$		−	1.54867i		−	0.0940751i	0.998893	−	0.0470376i	$-0.0149780\pi$
$272$	−14.2688	−	5.44708i	−0.865172	−	0.330277i
$273$	1.99974	+	14.9208i	0.121030	+	0.903050i
$274$	−0.524680	−	3.98534i	−0.0316971	−	0.240763i
$275$	−1.85665	−	2.11710i	−0.111960	−	0.127666i
$276$	−14.4067	+	6.00682i	−0.867183	+	0.361568i
$277$	−17.9171	+	8.83573i	−1.07653	+	0.530887i	−0.892045	−	0.451947i	$-0.850730\pi$
$277$	−17.9171	+	8.83573i	−1.07653	+	0.530887i	−0.184489	+	0.982835i	$0.559063\pi$
$278$	0.0911377	+	0.0181284i	0.00546607	+	0.00108727i
$279$	13.5165	+	2.62319i	0.809210	+	0.157046i
$280$	−1.08524	−	2.62001i	−0.0648558	−	0.156576i
$281$	4.39227	+	0.578253i	0.262021	+	0.0344957i	0.260392	−	0.965503i	$-0.416148\pi$
$281$	4.39227	+	0.578253i	0.262021	+	0.0344957i	0.00162876	+	0.999999i	$0.499482\pi$
$282$	−3.23970	−	1.09132i	−0.192921	−	0.0649872i
$283$	−4.14850	−	12.2211i	−0.246603	−	0.726468i	−0.997794	−	0.0663838i	$-0.978854\pi$
$283$	−4.14850	−	12.2211i	−0.246603	−	0.726468i	0.751191	−	0.660084i	$-0.229479\pi$
$284$	−1.94754	+	29.7137i	−0.115565	+	1.76319i
$285$	18.8927	+	2.44251i	1.11911	+	0.144682i
$286$	−0.300967	+	0.886620i	−0.0177966	+	0.0524270i
$287$	12.9495	+	5.36388i	0.764387	+	0.316620i
$288$	−5.51356	−	5.46243i	−0.324890	−	0.321877i
$289$	16.1485	−	5.31294i	0.949909	−	0.312526i
$290$	−2.27375	−	1.31275i	−0.133519	−	0.0770872i
$291$	−2.57298	−	2.56102i	−0.150831	−	0.150130i
$292$	15.6341	−	13.7107i	0.914914	−	0.802358i
$293$	−5.77063	−	1.54624i	−0.337124	−	0.0903321i	0.0862857	−	0.996270i	$-0.472500\pi$
$293$	−5.77063	−	1.54624i	−0.337124	−	0.0903321i	−0.423410	+	0.905938i	$0.639167\pi$
$294$	−0.844669	−	0.414102i	−0.0492621	−	0.0241509i
$295$	3.24170	+	2.84289i	0.188739	+	0.165520i
$296$	0.295508	+	0.442260i	0.0171761	+	0.0257058i
$297$	−5.17143	+	1.42449i	−0.300077	+	0.0826572i
$298$	−1.30280	+	0.539639i	−0.0754693	+	0.0312604i
$299$	1.22955	+	18.7593i	0.0711066	+	1.08488i
$300$	0.581233	−	9.19610i	0.0335575	−	0.530937i
$301$	−1.93698	−	0.126956i	−0.111645	−	0.00731763i
$302$	1.16123	−	4.33378i	0.0668215	−	0.249381i
$303$	−0.911581	+	4.63928i	−0.0523690	+	0.266520i
$304$	16.4534	+	21.4425i	0.943669	+	1.22981i
$305$	5.10257			0.292172
$306$	2.74422	+	0.270394i	0.156877	+	0.0154574i
$307$	19.9810			1.14038			0.570188	−	0.821514i	$-0.306870\pi$
$307$	19.9810			1.14038			0.570188	+	0.821514i	$0.306870\pi$
$308$	−2.61829	−	3.41222i	−0.149191	−	0.194430i
$309$	−0.727113	−	0.634671i	−0.0413640	−	0.0361051i
$310$	−0.399176	+	1.48975i	−0.0226717	+	0.0846119i
$311$	−5.00598	−	0.328109i	−0.283863	−	0.0186054i	−0.0771933	−	0.997016i	$-0.524596\pi$
$311$	−5.00598	−	0.328109i	−0.283863	−	0.0186054i	−0.206670	+	0.978411i	$0.566263\pi$
$312$	−5.55945	+	2.75773i	−0.314742	+	0.156126i
$313$	2.00917	+	30.6539i	0.113565	+	1.73266i	0.551951	+	0.833877i	$0.313884\pi$
$313$	2.00917	+	30.6539i	0.113565	+	1.73266i	−0.438386	+	0.898787i	$0.644450\pi$
$314$	1.91912	−	0.794926i	0.108302	−	0.0448603i
$315$	−5.91669	−	7.63685i	−0.333368	−	0.430288i
$316$	−6.02716	−	9.02029i	−0.339054	−	0.507431i
$317$	11.5376	+	10.1182i	0.648017	+	0.568296i	0.918985	−	0.394293i	$-0.129010\pi$
$317$	11.5376	+	10.1182i	0.648017	+	0.568296i	−0.270968	+	0.962588i	$0.587344\pi$
$318$	1.51301	−	1.01606i	0.0848452	−	0.0569781i
$319$	−7.79052	−	2.08746i	−0.436185	−	0.116876i
$320$	−7.74262	+	6.79010i	−0.432826	+	0.379578i
$321$	−0.445949	+	1.67995i	−0.0248904	+	0.0937655i
$322$	1.90577	+	1.10029i	0.106204	+	0.0613170i
$323$	−29.2653	−	6.96888i	−1.62837	−	0.387759i
$324$	−15.2822	−	8.63434i	−0.849012	−	0.479685i
$325$	−10.2532	−	4.24703i	−0.568747	−	0.235583i
$326$	−0.593821	+	1.74934i	−0.0328887	+	0.0968870i
$327$	5.42129	−	7.09934i	0.299798	−	0.392595i
$328$	−0.377902	+	5.76568i	−0.0208662	+	0.318356i
$329$	−6.07955	−	17.9098i	−0.335176	−	0.987398i
$330$	−0.118593	−	0.589033i	−0.00652833	−	0.0324252i
$331$	17.6711	+	2.32644i	0.971289	+	0.127873i	0.599439	−	0.800420i	$-0.295390\pi$
$331$	17.6711	+	2.32644i	0.971289	+	0.127873i	0.371850	+	0.928293i	$0.378724\pi$
$332$	10.6786	+	25.7804i	0.586063	+	1.41488i
$333$	1.36786	+	1.18835i	0.0749583	+	0.0651214i
$334$	−0.111125	−	0.0221042i	−0.00608049	−	0.00120949i
$335$	−0.0302816	+	0.0149332i	−0.00165446	+	0.000815889i
$336$	1.75739	−	13.5933i	0.0958733	−	0.741575i
$337$	−20.0711	−	22.8867i	−1.09334	−	1.24672i	−0.967012	−	0.254731i	$-0.918013\pi$
$337$	−20.0711	−	22.8867i	−1.09334	−	1.24672i	−0.126331	−	0.991988i	$-0.540320\pi$
$338$	0.103388	+	0.785307i	0.00562355	+	0.0427151i
$339$	9.79091	−	7.54913i	0.531769	−	0.410012i
$340$	2.03070	−	11.9501i	0.110130	−	0.648085i
$341$			4.73784i			0.256568i
$342$	−3.88517	−	2.95254i	−0.210086	−	0.159655i
$343$	−3.93275	−	19.7713i	−0.212348	−	1.06755i
$344$	−0.207106	−	0.772931i	−0.0111664	−	0.0416736i
$345$	−6.72581	−	10.0153i	−0.362105	−	0.539206i
$346$	−1.48891	+	0.505417i	−0.0800443	+	0.0271714i
$347$	−8.11084	+	16.4471i	−0.435412	+	0.882929i	0.562992	+	0.826462i	$0.309650\pi$
$347$	−8.11084	+	16.4471i	−0.435412	+	0.882929i	−0.998404	+	0.0564668i	$0.982016\pi$
$348$	−13.2493	−	22.8255i	−0.710237	−	1.22358i
$349$	−1.46452	+	11.1241i	−0.0783937	+	0.595459i	0.906488	+	0.422231i	$0.138753\pi$
$349$	−1.46452	+	11.1241i	−0.0783937	+	0.595459i	−0.984882	+	0.173228i	$0.944580\pi$
$350$	−1.08015	+	0.721734i	−0.0577365	+	0.0385783i
$351$	−15.7967	+	14.0498i	−0.843164	+	0.749923i
$352$	1.48375	−	2.22059i	0.0790841	−	0.118358i
$353$	−21.2283	+	5.68810i	−1.12987	+	0.302747i	−0.774870	−	0.632120i	$-0.782185\pi$
$353$	−21.2283	+	5.68810i	−1.12987	+	0.302747i	−0.354997	+	0.934867i	$0.615518\pi$
$354$	−0.357455	−	1.04502i	−0.0189985	−	0.0555424i
$355$	−22.8182	+	3.00407i	−1.21106	+	0.159440i
$356$	−10.5053	−	18.1956i	−0.556777	−	0.964366i
$357$	8.02555	+	12.9746i	0.424757	+	0.686689i
$358$	−2.83324	+	4.90731i	−0.149741	+	0.259359i
$359$	−9.15612	+	22.1048i	−0.483241	+	1.16665i	0.474820	+	0.880083i	$0.342513\pi$
$359$	−9.15612	+	22.1048i	−0.483241	+	1.16665i	−0.958061	+	0.286565i	$0.907487\pi$
$360$	2.19708	−	3.32155i	0.115796	−	0.175061i
$361$	24.2090	+	24.2090i	1.27416	+	1.27416i
$362$	−0.943616	−	1.91346i	−0.0495953	−	0.100569i
$363$	7.64629	+	15.4145i	0.401326	+	0.809053i
$364$	−15.2031	−	7.49732i	−0.796857	−	0.392966i
$365$	12.7508	+	9.78404i	0.667408	+	0.512120i
$366$	−1.13346	−	0.650890i	−0.0592471	−	0.0340225i
$367$	−8.72079	+	0.571591i	−0.455222	+	0.0298368i	−0.291290	−	0.956635i	$-0.594084\pi$
$367$	−8.72079	+	0.571591i	−0.455222	+	0.0298368i	−0.163932	+	0.986472i	$0.552418\pi$
$368$	3.33924	−	16.7875i	0.174070	−	0.875108i
$369$	3.92995	+	19.2871i	0.204585	+	1.00405i
$370$	−0.143520	+	0.143520i	−0.00746125	+	0.00746125i
$371$	9.54811	+	3.24115i	0.495713	+	0.168272i
$372$	−10.9371	+	10.9882i	−0.567064	+	0.569713i
$373$	−7.27693	+	4.20134i	−0.376785	+	0.217537i	−0.676419	−	0.736517i	$-0.736469\pi$
$373$	−7.27693	+	4.20134i	−0.376785	+	0.217537i	0.299633	+	0.954054i	$0.403136\pi$
$374$	0.0885667	+	0.944725i	0.00457968	+	0.0488506i
$375$	19.9975	−	2.68012i	1.03267	−	0.138401i
$376$	6.18559	−	4.74637i	0.318997	−	0.244775i
$377$	−31.1764	+	6.20137i	−1.60567	+	0.319387i
$378$	0.340144	+	2.45116i	0.0174951	+	0.126074i
$379$	−6.14007	−	4.10266i	−0.315394	−	0.210740i	0.387789	−	0.921748i	$-0.373239\pi$
$379$	−6.14007	−	4.10266i	−0.315394	−	0.210740i	−0.703184	+	0.711008i	$0.748239\pi$
$380$	−14.1432	+	16.1272i	−0.725530	+	0.827309i
$381$	−15.0418	−	17.0715i	−0.770613	−	0.874597i
$382$	−1.76668	+	2.30239i	−0.0903914	+	0.117800i
$383$	15.9831	−	20.8296i	0.816697	−	1.06434i	−0.180043	−	0.983659i	$-0.557624\pi$
$383$	15.9831	−	20.8296i	0.816697	−	1.06434i	0.996740	−	0.0806818i	$-0.0257098\pi$
$384$	11.3717	−	2.28953i	0.580311	−	0.116837i
$385$	2.19184	−	2.49932i	0.111707	−	0.127377i
$386$	4.42045	+	2.95365i	0.224995	+	0.150337i
$387$	−1.37395	−	2.35436i	−0.0698420	−	0.119679i
$388$	4.00919	−	0.797477i	0.203536	−	0.0404858i
$389$	24.3581	−	18.6907i	1.23501	−	0.947654i	0.235301	−	0.971922i	$-0.424392\pi$
$389$	24.3581	−	18.6907i	1.23501	−	0.947654i	0.999705	+	0.0242683i	$0.00772561\pi$
$390$	−1.44597	−	1.87537i	−0.0732196	−	0.0949628i
$391$	8.90183	+	16.8441i	0.450185	+	0.851841i
$392$	1.85806	−	1.07275i	0.0938460	−	0.0541820i
$393$	5.21318	+	19.2761i	0.262970	+	0.972352i
$394$	4.31829	+	1.46586i	0.217552	+	0.0738490i
$395$	5.92903	−	5.92903i	0.298322	−	0.298322i
$396$	1.91481	−	5.72838i	0.0962227	−	0.287862i
$397$	−1.33280	+	6.70045i	−0.0668915	+	0.336286i	−0.999711	−	0.0240589i	$-0.992341\pi$
$397$	−1.33280	+	6.70045i	−0.0668915	+	0.336286i	0.932819	+	0.360345i	$0.117341\pi$
$398$	5.80751	−	0.380644i	0.291104	−	0.0190800i
$399$	−0.0628899	−	26.9976i	−0.00314843	−	1.35157i
$400$	8.01636	+	6.15117i	0.400818	+	0.307559i
$401$	−15.5152	−	7.65127i	−0.774794	−	0.382086i	0.0115039	−	0.999934i	$-0.496338\pi$
$401$	−15.5152	−	7.65127i	−0.774794	−	0.382086i	−0.786298	+	0.617848i	$0.788005\pi$
$402$	0.00863153		0.000545550i	0.000430501		2.72096e-5i
$403$	8.25877	+	16.7471i	0.411398	+	0.834234i
$404$	−3.76446	−	3.76446i	−0.187289	−	0.187289i
$405$	4.24093	−	12.8866i	0.210734	−	0.640342i
$406$	−1.42391	+	3.43763i	−0.0706677	+	0.170607i
$407$	−0.311752	+	0.539970i	−0.0154530	+	0.0267653i
$408$	−4.00126	+	4.85205i	−0.198092	+	0.240212i
$409$	14.7420	+	25.5339i	0.728946	+	1.26257i	0.957329	+	0.289000i	$0.0933227\pi$
$409$	14.7420	+	25.5339i	0.728946	+	1.26257i	−0.228383	+	0.973571i	$0.573344\pi$
$410$	−2.18598	+	0.287790i	−0.107958	+	0.0142129i
$411$	30.6450	+	6.02150i	1.51161	+	0.297019i
$412$	1.04973	−	0.281273i	0.0517163	−	0.0138573i
$413$	3.39484	−	5.08074i	0.167049	−	0.250007i
$414$	0.216480	+	3.08271i	0.0106394	+	0.151507i
$415$	−17.9327	+	11.9822i	−0.880280	+	0.588184i
$416$	1.37388	−	10.4357i	0.0673600	−	0.511650i
$417$	−0.359523	+	0.626075i	−0.0176059	+	0.0306590i
$418$	0.742664	−	1.50597i	0.0363249	−	0.0736596i
$419$	−28.2353	+	9.58460i	−1.37939	+	0.468238i	−0.909946	−	0.414726i	$-0.863877\pi$
$419$	−28.2353	+	9.58460i	−1.37939	+	0.468238i	−0.469440	+	0.882964i	$0.655544\pi$
$420$	10.8530	−	0.736738i	0.529573	−	0.0359491i
$421$	−7.31899	−	27.3148i	−0.356706	−	1.33124i	−0.878325	−	0.478065i	$-0.841338\pi$
$421$	−7.31899	−	27.3148i	−0.356706	−	1.33124i	0.521619	−	0.853179i	$-0.325328\pi$
$422$	−0.671994	−	3.37834i	−0.0327122	−	0.164455i
$423$	16.0706	−	21.1468i	0.781378	−	1.02819i
$424$			4.15663i			0.201864i
$425$	−11.2424	+	0.315159i	−0.545339	+	0.0152875i
$426$	5.45194	+	2.24340i	0.264148	+	0.108693i
$427$	−0.943886	−	7.16953i	−0.0456778	−	0.346958i
$428$	−1.29044	−	1.47146i	−0.0623756	−	0.0711257i
$429$	−5.78163	−	4.41504i	−0.279140	−	0.213160i
$430$	0.273857	−	0.135051i	0.0132066	−	0.00651276i
$431$	−14.2559	−	2.83568i	−0.686685	−	0.136590i	−0.160597	−	0.987020i	$-0.551342\pi$
$431$	−14.2559	−	2.83568i	−0.686685	−	0.136590i	−0.526088	+	0.850430i	$0.676342\pi$
$432$	17.2031	−	8.63360i	0.827684	−	0.415384i
$433$	15.6664	+	37.8220i	0.752879	+	1.81761i	0.542653	+	0.839957i	$0.317420\pi$
$433$	15.6664	+	37.8220i	0.752879	+	1.81761i	0.210226	+	0.977653i	$0.432580\pi$
$434$	2.16706	+	0.285298i	0.104022	+	0.0136948i
$435$	15.3051	−	13.4854i	0.733824	−	0.646576i
$436$	3.23309	+	9.52437i	0.154837	+	0.456134i
$437$	2.20502	−	33.6421i	0.105480	−	1.60932i
$438$	−1.58435	−	3.79990i	−0.0757031	−	0.181566i
$439$	11.3630	−	33.4742i	0.542325	−	1.59764i	−0.237331	−	0.971429i	$-0.576273\pi$
$439$	11.3630	−	33.4742i	0.542325	−	1.59764i	0.779656	−	0.626208i	$-0.215394\pi$
$440$	1.26606	+	0.524418i	0.0603569	+	0.0250006i
$441$	5.14399	−	5.19214i	0.244952	−	0.247245i
$442$	1.95986	+	3.18499i	0.0932211	+	0.151495i
$443$	−1.98886	−	1.14827i	−0.0944935	−	0.0545558i	0.452009	−	0.892014i	$-0.350708\pi$
$443$	−1.98886	−	1.14827i	−0.0944935	−	0.0545558i	−0.546502	+	0.837458i	$0.684041\pi$
$444$	−1.96953	+	0.532655i	−0.0934699	+	0.0252787i
$445$	12.2092	−	10.7072i	0.578771	−	0.507568i
$446$	−0.542410	−	0.145338i	−0.0256839	−	0.00688197i
$447$	−0.742022	−	10.9309i	−0.0350965	−	0.517012i
$448$	10.9729	+	9.62297i	0.518420	+	0.454642i
$449$	−0.252106	−	0.377304i	−0.0118976	−	0.0178061i	0.825473	−	0.564441i	$-0.190908\pi$
$449$	−0.252106	−	0.377304i	−0.0118976	−	0.0178061i	−0.837371	+	0.546635i	$0.815908\pi$
$450$	−1.68868	−	0.690275i	−0.0796052	−	0.0325399i
$451$	−6.25755	+	2.59196i	−0.294657	+	0.122051i
$452$	0.910488	+	13.8914i	0.0428257	+	0.653395i
$453$	29.0291	+	19.2989i	1.36390	+	0.906743i
$454$	3.29339	+	0.215860i	0.154567	+	0.0101308i
$455$	3.39095	−	12.6552i	0.158970	−	0.593285i
$456$	10.5303	−	3.60194i	0.493127	−	0.168676i
$457$	−4.47206	−	5.82810i	−0.209194	−	0.272627i	0.676958	−	0.736022i	$-0.263298\pi$
$457$	−4.47206	−	5.82810i	−0.209194	−	0.272627i	−0.886152	+	0.463395i	$0.846631\pi$
$458$	−3.06775			−0.143347
$459$	−8.79726	+	19.5348i	−0.410621	+	0.911806i
$460$	13.5843			0.633370
$461$	−17.1578	−	22.3605i	−0.799117	−	1.04143i	−0.998111	−	0.0614293i	$-0.980434\pi$
$461$	−17.1578	−	22.3605i	−0.799117	−	1.04143i	0.198994	−	0.980001i	$-0.436233\pi$
$462$	−0.805702	+	0.275594i	−0.0374847	+	0.0128218i
$463$	−0.482098	+	1.79921i	−0.0224050	+	0.0836166i	−0.976223	−	0.216768i	$-0.930448\pi$
$463$	−0.482098	+	1.79921i	−0.0224050	+	0.0836166i	0.953818	+	0.300385i	$0.0971151\pi$
$464$	28.8793	+	1.89285i	1.34069	+	0.0878732i
$465$	−9.97880	−	6.63405i	−0.462756	−	0.307647i
$466$	−0.316237	−	4.82484i	−0.0146494	−	0.223506i
$467$	24.9916	−	10.3519i	1.15647	−	0.479027i	0.279774	−	0.960066i	$-0.409741\pi$
$467$	24.9916	−	10.3519i	1.15647	−	0.479027i	0.876699	+	0.481039i	$0.159741\pi$
$468$	−3.21705	−	23.5863i	−0.148708	−	1.09028i
$469$	0.0265840	+	0.0397857i	0.00122753	+	0.00183713i
$470$	2.23685	+	1.96166i	0.103178	+	0.0904847i
$471$	1.09305	+	16.1019i	0.0503652	+	0.741938i
$472$	2.43314	+	0.651957i	0.111994	+	0.0300087i
$473$	0.705229	−	0.618469i	0.0324265	−	0.0284372i
$474$	−2.07336	+	0.560736i	−0.0952328	+	0.0257555i
$475$	17.2363	+	9.95137i	0.790854	+	0.456600i
$476$	−17.1665	−	0.642743i	−0.786825	−	0.0294601i
$477$	3.72854	+	13.6602i	0.170718	+	0.625458i
$478$	4.24196	+	1.75708i	0.194023	+	0.0803669i
$479$	4.00762	−	11.8061i	0.183113	−	0.539432i	−0.816149	−	0.577841i	$-0.803895\pi$
$479$	4.00762	−	11.8061i	0.183113	−	0.539432i	0.999262	+	0.0384084i	$0.0122288\pi$
$480$	2.59940	+	6.23440i	0.118646	+	0.284560i
$481$	−0.160719	+	2.45209i	−0.00732815	+	0.111806i
$482$	−0.976394	−	2.87636i	−0.0444735	−	0.131015i
$483$	−12.8282	+	11.3030i	−0.583701	+	0.514303i
$484$	−19.2092	−	2.52894i	−0.873146	−	0.114952i
$485$	1.20906	+	2.91892i	0.0549005	+	0.132542i
$486$	−2.58590	+	2.32161i	−0.117299	+	0.105310i
$487$	3.28596	+	0.653619i	0.148901	+	0.0296183i	0.268978	−	0.963146i	$-0.413314\pi$
$487$	3.28596	+	0.653619i	0.148901	+	0.0296183i	−0.120077	+	0.992765i	$0.538314\pi$
$488$	2.67359	−	1.31847i	0.121028	−	0.0596843i
$489$	−11.4074	−	8.71106i	−0.515860	−	0.393928i
$490$	0.539806	+	0.615531i	0.0243860	+	0.0278068i
$491$	1.26238	+	9.58874i	0.0569705	+	0.432734i	0.996033	+	0.0889868i	$0.0283629\pi$
$491$	1.26238	+	9.58874i	0.0569705	+	0.432734i	−0.939062	+	0.343747i	$0.888304\pi$
$492$	−20.4963	−	8.43395i	−0.924043	−	0.380232i
$493$	−26.2725	+	18.6404i	−1.18325	+	0.839520i
$494$		−	6.61784i		−	0.297751i
$495$	4.63114	+	0.587764i	0.208154	+	0.0264180i
$496$	−3.31673	−	16.6743i	−0.148926	−	0.748699i
$497$	8.44194	+	31.5058i	0.378673	+	1.41323i
$498$	5.51196	−	0.374170i	0.246997	−	0.0167669i
$499$	−32.7229	+	11.1079i	−1.46488	+	0.497259i	−0.936170	−	0.351546i	$-0.885656\pi$
$499$	−32.7229	+	11.1079i	−1.46488	+	0.497259i	−0.528706	+	0.848805i	$0.677323\pi$
$500$	−10.0482	+	20.3757i	−0.449369	+	0.911230i
$501$	0.438370	−	0.763380i	0.0195849	−	0.0341053i
$502$	−0.608790	+	4.62422i	−0.0271716	+	0.206389i
$503$	16.7073	−	11.1634i	0.744940	−	0.497753i	−0.124238	−	0.992252i	$-0.539649\pi$
$503$	16.7073	−	11.1634i	0.744940	−	0.497753i	0.869178	+	0.494500i	$0.164649\pi$
$504$	−5.07347	−	2.47264i	−0.225990	−	0.110140i
$505$	2.28603	−	3.42128i	0.101727	−	0.152245i
$506$	−1.02715	+	0.275223i	−0.0456623	+	0.0122352i
$507$	−6.03857	−	1.18653i	−0.268182	−	0.0526957i
$508$	25.4006	−	3.34405i	1.12697	−	0.148368i
$509$	−13.8520	−	23.9924i	−0.613979	−	1.06344i	−0.990563	−	0.137060i	$-0.956235\pi$
$509$	−13.8520	−	23.9924i	−0.613979	−	1.06344i	0.376584	−	0.926383i	$-0.377099\pi$
$510$	−2.11379	−	1.13629i	−0.0936001	−	0.0503158i
$511$	11.3887	−	19.7258i	0.503807	−	0.872619i
$512$	−6.16413	+	14.8815i	−0.272419	+	0.657676i
$513$	31.3755	−	21.2831i	1.38526	−	0.939672i
$514$	−0.991058	−	0.991058i	−0.0437137	−	0.0437137i
$515$	0.371504	+	0.753335i	0.0163704	+	0.0331959i
$516$	3.06332	+	0.193615i	0.134855	+	0.00852342i
$517$	8.19696	+	4.04229i	0.360502	+	0.177780i
$518$	0.228206	+	0.175109i	0.0100268	+	0.00769383i
$519$	−0.0284573	−	12.2163i	−0.00124914	−	0.536234i
$520$	5.38935	−	0.353237i	0.236339	−	0.0154904i
$521$	−5.24561	+	26.3714i	−0.229814	+	1.15535i	0.677702	+	0.735337i	$0.262976\pi$
$521$	−5.24561	+	26.3714i	−0.229814	+	1.15535i	−0.907516	+	0.420017i	$0.862024\pi$
$522$	−5.12003	+	1.04326i	−0.224098	+	0.0456622i
$523$	−16.9333	+	16.9333i	−0.740440	+	0.740440i	−0.972663	−	0.232223i	$-0.925400\pi$
$523$	−16.9333	+	16.9333i	−0.740440	+	0.740440i	0.232223	+	0.972663i	$0.425400\pi$
$524$	−21.2916	−	7.22751i	−0.930126	−	0.315735i
$525$	−2.63501	−	9.74314i	−0.115001	−	0.425225i
$526$	4.00486	−	2.31221i	0.174620	−	0.100817i
$527$	14.5713	+	12.0734i	0.634734	+	0.525924i
$528$	4.04423	+	5.24520i	0.176003	+	0.228268i
$529$	1.30833	−	1.00392i	0.0568839	−	0.0436486i
$530$	−1.55565	+	0.309438i	−0.0675731	+	0.0134411i
$531$	8.58099	−	0.0399784i	0.372383	−	0.00173492i
$532$	25.2763	+	16.8891i	1.09587	+	0.732235i
$533$	−17.6008	+	20.0698i	−0.762374	+	0.869321i
$534$	−4.07792	+	0.821028i	−0.176469	+	0.0355293i
$535$	0.920864	−	1.20009i	0.0398124	−	0.0518845i
$536$	−0.0120080	+	0.0156491i	−0.000518666	+	0.000675939i
$537$	−29.1049	−	33.0322i	−1.25597	−	1.42545i
$538$	2.35246	−	2.68246i	0.101422	−	0.115649i
$539$	2.09114	+	1.39725i	0.0900716	+	0.0601839i
$540$	9.38392	+	12.0540i	0.403820	+	0.518722i
$541$	−22.7220	+	4.51970i	−0.976897	+	0.194317i	−0.657624	−	0.753346i	$-0.728439\pi$
$541$	−22.7220	+	4.51970i	−0.976897	+	0.194317i	−0.319273	+	0.947663i	$0.603439\pi$
$542$	0.273903	−	0.210173i	0.0117652	−	0.00902772i
$543$	16.4291	−	2.20187i	0.705038	−	0.0944914i
$544$	−3.04842	−	10.2220i	−0.130700	−	0.438264i
$545$	−6.73246	+	3.88699i	−0.288387	+	0.166500i
$546$	−2.36756	+	2.37862i	−0.101322	+	0.101796i
$547$	−2.40504	−	0.816401i	−0.102832	−	0.0349068i	0.269549	−	0.962987i	$-0.413125\pi$
$547$	−2.40504	−	0.816401i	−0.102832	−	0.0349068i	−0.372381	+	0.928080i	$0.621459\pi$
$548$	−24.8664	+	24.8664i	−1.06224	+	1.06224i
$549$	7.60372	−	6.73121i	0.324519	−	0.287281i
$550$	0.122468	−	0.615690i	0.00522207	−	0.0262531i
$551$	56.8837	−	3.72836i	2.42333	−	0.158833i
$552$	−6.11200	−	3.50981i	−0.260144	−	0.149387i
$553$	−9.42754	−	7.23401i	−0.400900	−	0.307621i
$554$	−3.99428	−	1.96976i	−0.169701	−	0.0836872i
$555$	−0.700758	−	1.41269i	−0.0297455	−	0.0599654i
$556$	−0.359551	−	0.729097i	−0.0152483	−	0.0309206i
$557$	−15.8076	−	15.8076i	−0.669791	−	0.669791i	0.287876	−	0.957668i	$-0.407051\pi$
$557$	−15.8076	−	15.8076i	−0.669791	−	0.669791i	−0.957668	+	0.287876i	$0.907051\pi$
$558$	1.37040	+	2.74657i	0.0580137	+	0.116271i
$559$	1.41473	−	3.41546i	0.0598367	−	0.144459i
$560$	−5.96431	+	10.3305i	−0.252038	+	0.436543i
$561$	−7.17559	−	1.69105i	−0.302954	−	0.0713963i
$562$	0.493812	+	0.855308i	0.0208302	+	0.0360790i
$563$	−9.19314	+	1.21030i	−0.387445	+	0.0510081i	−0.321733	−	0.946831i	$-0.604265\pi$
$563$	−9.19314	+	1.21030i	−0.387445	+	0.0510081i	−0.0657121	+	0.997839i	$0.520932\pi$
$564$	9.67928	+	28.2975i	0.407571	+	1.19154i
$565$	−10.3931	+	2.78482i	−0.437240	+	0.117158i
$566$	1.59846	−	2.39227i	0.0671884	−	0.100554i
$567$	−18.8913	−	3.57505i	−0.793359	−	0.150138i
$568$	−11.1798	+	7.47011i	−0.469094	+	0.313439i
$569$	2.30195	−	17.4850i	0.0965027	−	0.733011i	−0.872963	−	0.487786i	$-0.837805\pi$
$569$	2.30195	−	17.4850i	0.0965027	−	0.733011i	0.969466	−	0.245225i	$-0.0788619\pi$
$570$	2.13197	+	3.67290i	0.0892986	+	0.153841i
$571$	5.90835	−	11.9810i	0.247257	−	0.501387i	−0.737495	−	0.675353i	$-0.763991\pi$
$571$	5.90835	−	11.9810i	0.247257	−	0.501387i	0.984752	+	0.173965i	$0.0556581\pi$
$572$	7.75654	−	2.63299i	0.324317	−	0.110091i
$573$	−12.5704	−	18.7184i	−0.525137	−	0.781974i
$574$	0.808736	+	3.01824i	0.0337560	+	0.125979i
$575$	−2.45896	−	12.3620i	−0.102546	−	0.515531i
$576$	−2.58049	+	20.3323i	−0.107521	+	0.847181i
$577$		−	20.3967i		−	0.849125i	−0.905399	−	0.424563i	$-0.860428\pi$
$577$		−	20.3967i		−	0.849125i	0.905399	−	0.424563i	$-0.139572\pi$
$578$	3.13121	+	2.13504i	0.130241	+	0.0888061i
$579$	−32.7113	+	25.2215i	−1.35943	+	1.04817i
$580$	2.99805	+	22.7725i	0.124487	+	0.945575i
$581$	20.1532	+	22.9804i	0.836097	+	0.953386i
$582$	0.103766	−	0.802627i	0.00430125	−	0.0332699i
$583$	−4.36999	+	2.15504i	−0.180986	+	0.0892526i
$584$	9.20917	+	1.83182i	0.381078	+	0.0758011i
$585$	17.3945	−	5.99517i	0.719175	−	0.247870i
$586$	−0.509672	−	1.23046i	−0.0210544	−	0.0508297i
$587$	−9.03489	−	1.18947i	−0.372910	−	0.0490945i	−0.0582576	−	0.998302i	$-0.518554\pi$
$587$	−9.03489	−	1.18947i	−0.372910	−	0.0490945i	−0.314652	+	0.949207i	$0.601888\pi$
$588$	1.62435	+	8.06790i	0.0669871	+	0.332714i
$589$	−10.7640	−	31.7099i	−0.443525	−	1.30658i
$590$	−0.0628662	+	0.959153i	−0.00258816	+	0.0394877i
$591$	−21.5035	+	28.1594i	−0.884534	+	1.15832i
$592$	0.719171	−	2.11861i	0.0295577	−	0.0870743i
$593$	−8.15390	−	3.37746i	−0.334840	−	0.138695i	0.208927	−	0.977931i	$-0.433003\pi$
$593$	−8.15390	−	3.37746i	−0.334840	−	0.138695i	−0.543768	+	0.839236i	$0.683003\pi$
$594$	−0.953765	−	0.721316i	−0.0391335	−	0.0295960i
$595$	−2.10123	−	13.1100i	−0.0861421	−	0.537458i
$596$	10.6838	+	6.16827i	0.437624	+	0.252662i
$597$	−11.6015	+	43.7042i	−0.474817	+	1.78870i
$598$	−3.15096	+	2.76332i	−0.128853	+	0.113001i
$599$	−8.35805	−	2.23953i	−0.341501	−	0.0915049i	0.0839926	−	0.996466i	$-0.473233\pi$
$599$	−8.35805	−	2.23953i	−0.341501	−	0.0915049i	−0.425493	+	0.904962i	$0.639899\pi$
$600$	3.45412	−	2.31963i	0.141014	−	0.0946985i
$601$	−21.6970	−	19.0278i	−0.885039	−	0.776159i	0.0905202	−	0.995895i	$-0.471147\pi$
$601$	−21.6970	−	19.0278i	−0.885039	−	0.776159i	−0.975559	+	0.219736i	$0.929480\pi$
$602$	−0.240417	−	0.359810i	−0.00979867	−	0.0146647i
$603$	−0.0254252	+	0.0622000i	−0.00103540	+	0.00253298i
$604$	−36.2634	+	15.0208i	−1.47554	+	0.611188i
$605$	−0.979409	−	14.9429i	−0.0398186	−	0.607515i
$606$	−0.944232	+	0.468381i	−0.0383568	+	0.0190267i
$607$	46.0465	+	3.01805i	1.86897	+	0.122499i	0.957421	−	0.288695i	$-0.0932213\pi$
$607$	46.0465	+	3.01805i	1.86897	+	0.122499i	0.911548	+	0.411194i	$0.134888\pi$
$608$	−4.88556	+	18.2332i	−0.198136	+	0.739452i
$609$	−21.7793	−	19.0104i	−0.882542	−	0.770339i
$610$	0.692480	+	0.902458i	0.0280377	+	0.0365394i
$611$	36.0206			1.45724
$612$	−12.7382	−	20.4866i	−0.514912	−	0.828121i
$613$	−7.71246			−0.311503			−0.155752	−	0.987796i	$-0.549780\pi$
$613$	−7.71246			−0.311503			−0.155752	+	0.987796i	$0.549780\pi$
$614$	2.71167	+	3.53391i	0.109434	+	0.142617i
$615$	3.30282	−	16.8090i	0.133183	−	0.677802i
$616$	0.502652	−	1.87592i	0.0202524	−	0.0755830i
$617$	10.8194	+	0.709140i	0.435572	+	0.0285489i	0.281612	−	0.959528i	$-0.409131\pi$
$617$	10.8194	+	0.709140i	0.435572	+	0.0285489i	0.153960	+	0.988077i	$0.450797\pi$
$618$	0.0135720	−	0.214732i	0.000545946	−	0.00863779i
$619$	−0.407444	−	6.21639i	−0.0163765	−	0.249858i	−0.998196	−	0.0600403i	$-0.980877\pi$
$619$	−0.407444	−	6.21639i	−0.0163765	−	0.249858i	0.981819	−	0.189817i	$-0.0607896\pi$
$620$	12.4656	−	5.16343i	0.500632	−	0.207368i
$621$	−23.2346	−	6.05199i	−0.932373	−	0.242858i
$622$	−0.621341	−	0.929903i	−0.0249135	−	0.0372857i
$623$	−17.3029	−	15.1743i	−0.693227	−	0.607944i
$624$	23.4386	+	11.4908i	0.938294	+	0.460001i
$625$	−3.78689	−	1.01469i	−0.151475	−	0.0405877i
$626$	−5.14890	+	4.51546i	−0.205791	+	0.180474i
$627$	9.24635	+	9.20337i	0.369264	+	0.367547i
$628$	−15.7379	−	9.08630i	−0.628012	−	0.362583i
$629$	0.866250	+	2.33479i	0.0345397	+	0.0930943i
$630$	0.547713	−	2.08286i	0.0218214	−	0.0829831i
$631$	10.1637	+	4.20994i	0.404611	+	0.167595i	0.575701	−	0.817660i	$-0.304729\pi$
$631$	10.1637	+	4.20994i	0.404611	+	0.167595i	−0.171091	+	0.985255i	$0.554729\pi$
$632$	1.57461	−	4.63865i	0.0626346	−	0.184516i
$633$	26.5411	+	3.43133i	1.05492	+	0.136383i
$634$	−0.223749	+	3.41375i	−0.00888620	+	0.135577i
$635$	6.36502	+	18.7507i	0.252588	+	0.744101i
$636$	−15.1099	−	5.08991i	−0.599147	−	0.201828i
$637$	9.82729	+	1.29379i	0.389371	+	0.0512617i
$638$	−0.688072	−	1.66115i	−0.0272410	−	0.0657656i
$639$	−30.0402	+	34.5779i	−1.18837	+	1.36788i
$640$	−9.90136	−	1.96950i	−0.391386	−	0.0778514i
$641$	−3.16388	+	1.56025i	−0.124966	+	0.0616263i	−0.503697	−	0.863880i	$-0.668027\pi$
$641$	−3.16388	+	1.56025i	−0.124966	+	0.0616263i	0.378731	+	0.925507i	$0.376360\pi$
$642$	−0.357642	+	0.149117i	−0.0141150	+	0.00588518i
$643$	15.9848	+	18.2272i	0.630379	+	0.718810i	0.975562	−	0.219726i	$-0.0705162\pi$
$643$	15.9848	+	18.2272i	0.630379	+	0.718810i	−0.345182	+	0.938536i	$0.612183\pi$
$644$	−2.51285	−	19.0870i	−0.0990203	−	0.752134i
$645$	0.315135	+	2.35135i	0.0124084	+	0.0925842i
$646$	−2.73912	−	6.12173i	−0.107769	−	0.240856i
$647$			3.35095i			0.131739i	0.997828	+	0.0658697i	$0.0209822\pi$
$647$			3.35095i			0.131739i	−0.997828	+	0.0658697i	$0.979018\pi$
$648$	−1.10770	−	7.84803i	−0.0435146	−	0.308300i
$649$	0.576058	+	2.89604i	0.0226122	+	0.113679i
$650$	−0.640344	−	2.38980i	−0.0251164	−	0.0937356i
$651$	−7.47548	+	15.2482i	−0.292987	+	0.597625i
$652$	15.3040	−	5.19500i	0.599350	−	0.203452i
$653$	−6.06598	+	12.3006i	−0.237380	+	0.481359i	−0.982666	−	0.185386i	$-0.940646\pi$
$653$	−6.06598	+	12.3006i	−0.237380	+	0.481359i	0.745286	+	0.666745i	$0.232313\pi$
$654$	1.99135	−	0.00463877i	0.0778679	−	0.000181390i
$655$	2.26836	−	17.2299i	0.0886322	−	0.673228i
$656$	20.2083	−	13.5027i	0.789001	−	0.527194i
$657$	31.9079	−	2.24069i	1.24484	−	0.0874178i
$658$	2.34252	−	3.50582i	0.0913208	−	0.136671i
$659$	3.35762	−	0.899672i	0.130794	−	0.0350462i	−0.192828	−	0.981233i	$-0.561766\pi$
$659$	3.35762	−	0.899672i	0.130794	−	0.0350462i	0.323622	+	0.946186i	$0.395099\pi$
$660$	−3.45665	+	3.96013i	−0.134550	+	0.154148i
$661$	19.9495	−	2.62641i	0.775947	−	0.102155i	0.267856	−	0.963459i	$-0.413685\pi$
$661$	19.9495	−	2.62641i	0.775947	−	0.102155i	0.508091	+	0.861304i	$0.330351\pi$
$662$	1.98671	+	3.44109i	0.0772159	+	0.133742i
$663$	−28.3118	+	6.53067i	−1.09954	+	0.253630i
$664$	−6.30005	+	10.9120i	−0.244489	+	0.423468i
$665$	−8.99149	+	21.7074i	−0.348675	+	0.841776i
$666$	−0.0245411	+	0.403199i	−0.000950947	+	0.0156236i
$667$	−25.5274	−	25.5274i	−0.988424	−	0.988424i
$668$	0.438404	+	0.888995i	0.0169624	+	0.0343962i
$669$	2.41543	−	3.63324i	0.0933859	−	0.140469i
$670$	−0.00675072	−	0.00332909i	−0.000260803	−	0.000128614i
$671$	2.77229	+	2.12725i	0.107023	+	0.0821216i
$672$	8.27899	−	4.80563i	0.319369	−	0.185381i
$673$	11.4764	−	0.752201i	0.442381	−	0.0289952i	0.157415	−	0.987533i	$-0.449684\pi$
$673$	11.4764	−	0.752201i	0.442381	−	0.0289952i	0.284967	+	0.958537i	$0.408017\pi$
$674$	1.32393	−	6.65585i	0.0509959	−	0.256374i
$675$	9.27079	−	10.7215i	0.356833	−	0.412672i
$676$	4.89989	−	4.89989i	0.188457	−	0.188457i
$677$	−15.6283	−	5.30508i	−0.600643	−	0.203891i	0.00452331	−	0.999990i	$-0.498560\pi$
$677$	−15.6283	−	5.30508i	−0.600643	−	0.203891i	−0.605167	+	0.796099i	$0.706894\pi$
$678$	2.66391	+	0.707146i	0.102307	+	0.0271578i
$679$	3.87767	−	2.23878i	0.148811	−	0.0859163i
$680$	4.83913	−	2.55740i	0.185572	−	0.0980720i
$681$	−9.75782	+	23.7136i	−0.373920	+	0.908705i
$682$	−0.837950	+	0.642982i	−0.0320868	+	0.0246210i
$683$	5.45816	−	1.08569i	0.208851	−	0.0415429i	−0.0895561	−	0.995982i	$-0.528545\pi$
$683$	5.45816	−	1.08569i	0.208851	−	0.0415429i	0.298407	+	0.954439i	$0.403545\pi$
$684$	0.198890	+	42.6898i	0.00760474	+	1.63229i
$685$	−22.5995	−	15.1005i	−0.863482	−	0.576960i
$686$	2.96309	−	3.37876i	0.113131	−	0.129002i
$687$	7.60882	−	22.5876i	0.290294	−	0.861770i
$688$	−2.04902	+	2.67033i	−0.0781181	+	0.101806i
$689$	−11.6903	+	15.2351i	−0.445365	+	0.580411i
$690$	0.858567	−	2.54875i	0.0326851	−	0.0970291i
$691$	3.95316	−	4.50771i	0.150385	−	0.171481i	−0.671742	−	0.740785i	$-0.734454\pi$
$691$	3.95316	−	4.50771i	0.150385	−	0.171481i	0.822127	+	0.569304i	$0.192787\pi$
$692$	11.4374	+	7.64222i	0.434784	+	0.290514i
$693$	−0.0308229	−	6.61585i	−0.00117087	−	0.251315i
$694$	−4.00964	+	0.797567i	−0.152204	+	0.0302752i
$695$	0.498478	−	0.382495i	0.0189083	−	0.0145089i
$696$	4.53487	−	11.0207i	0.171894	−	0.417738i
$697$	−7.97443	+	25.8502i	−0.302053	+	0.979147i
$698$	−2.16620	+	1.25066i	−0.0819919	+	0.0473380i
$699$	36.3092	+	9.63842i	1.37334	+	0.364559i
$700$	10.7618	+	3.65315i	0.406759	+	0.138076i
$701$	34.7346	−	34.7346i	1.31191	−	1.31191i	0.391903	−	0.920007i	$-0.371817\pi$
$701$	34.7346	−	34.7346i	1.31191	−	1.31191i	0.920007	−	0.391903i	$-0.128183\pi$
$702$	−4.62870	−	0.887124i	−0.174699	−	0.0334824i
$703$	0.859747	−	4.32224i	0.0324260	−	0.163016i
$704$	−7.03744	+	0.461258i	−0.265233	+	0.0173843i
$705$	−19.9915	+	11.6043i	−0.752922	+	0.437042i
$706$	−3.88695	−	2.98256i	−0.146287	−	0.112250i
$707$	−5.23006	−	2.57918i	−0.196697	−	0.0970001i
$708$	−5.34939	+	8.04644i	−0.201042	+	0.302404i
$709$	−8.58536	−	17.4094i	−0.322430	−	0.653823i	0.673955	−	0.738772i	$-0.264594\pi$
$709$	−8.58536	−	17.4094i	−0.322430	−	0.653823i	−0.996385	+	0.0849490i	$0.972927\pi$
$710$	−3.62802	−	3.62802i	−0.136157	−	0.136157i
$711$	1.01383	−	16.6568i	0.0380216	−	0.624677i
$712$	3.63058	−	8.76500i	0.136062	−	0.328482i
$713$	−10.6035	+	18.3658i	−0.397103	+	0.687803i
$714$	−1.20557	+	3.18024i	−0.0451173	+	0.119017i
$715$	3.16552	+	5.48284i	0.118384	+	0.205047i
$716$	49.1487	−	6.47054i	1.83677	−	0.241816i
$717$	−23.4584	+	26.8752i	−0.876068	+	1.00367i
$718$	−5.15213	+	1.38051i	−0.192276	+	0.0515201i
$719$	−5.68277	+	8.50486i	−0.211931	+	0.317178i	−0.922171	−	0.386782i	$-0.873587\pi$
$719$	−5.68277	+	8.50486i	−0.211931	+	0.317178i	0.710240	+	0.703960i	$0.248587\pi$
$720$	−16.7103	+	1.17346i	−0.622755	+	0.0437322i
$721$	0.989776	−	0.661347i	0.0368612	−	0.0246299i
$722$	−0.996235	+	7.56715i	−0.0370760	+	0.281620i
$723$	23.6001	−	0.0549756i	0.877698	−	0.00204456i
$724$	−8.25516	+	16.7398i	−0.306801	+	0.622130i
$725$	20.1808	−	6.85045i	0.749495	−	0.254419i
$726$	−1.68857	+	3.44429i	−0.0626688	+	0.127829i
$727$	1.97735	+	7.37957i	0.0733358	+	0.273693i	0.992851	−	0.119362i	$-0.0380849\pi$
$727$	1.97735	+	7.37957i	0.0733358	+	0.273693i	−0.919515	+	0.393055i	$0.871418\pi$
$728$	−1.49326	−	7.50713i	−0.0553440	−	0.278233i
$729$	−10.6801	−	24.7979i	−0.395558	−	0.918441i
$730$			3.58297i			0.132612i
$731$	−0.104983	−	3.74498i	−0.00388293	−	0.138513i
$732$	1.51893	+	11.3334i	0.0561413	+	0.418893i
$733$	−2.46564	−	18.7284i	−0.0910704	−	0.691748i	−0.974693	−	0.223548i	$-0.928236\pi$
$733$	−2.46564	−	18.7284i	−0.0910704	−	0.691748i	0.883622	−	0.468200i	$-0.155097\pi$
$734$	−1.28461	−	1.46482i	−0.0474158	−	0.0540674i
$735$	−5.87095	+	2.44787i	−0.216553	+	0.0902909i
$736$	10.7214	−	5.28720i	0.395196	−	0.194889i
$737$	−0.0226780	−	0.00451093i	−0.000835355	−	0.000166162i
$738$	−2.87784	+	3.31256i	−0.105935	+	0.121937i
$739$	−6.86733	−	16.5792i	−0.252619	−	0.609876i	0.745795	−	0.666176i	$-0.232070\pi$
$739$	−6.86733	−	16.5792i	−0.252619	−	0.609876i	−0.998414	+	0.0562994i	$0.982070\pi$
$740$	1.76046	+	0.231769i	0.0647158	+	0.00852000i
$741$	48.7265	+	16.4139i	1.79001	+	0.602981i
$742$	0.722554	+	2.12857i	0.0265258	+	0.0781424i
$743$	1.51094	−	23.0525i	0.0554311	−	0.845715i	−0.876117	−	0.482098i	$-0.839875\pi$
$743$	1.51094	−	23.0525i	0.0554311	−	0.845715i	0.931548	−	0.363617i	$-0.118458\pi$
$744$	−6.94278	−	0.897586i	−0.254535	−	0.0329071i
$745$	−3.06491	+	9.02893i	−0.112290	+	0.330795i
$746$	−1.73063	−	0.716851i	−0.0633629	−	0.0262458i
$747$	−10.9161	+	41.5120i	−0.399399	+	1.51885i
$748$	6.08528	−	5.64604i	0.222500	−	0.206439i
$749$	−1.85657	−	1.07189i	−0.0678377	−	0.0391661i
$750$	3.18792	+	3.17310i	0.116406	+	0.115865i
$751$	23.0513	−	20.2154i	0.841153	−	0.737671i	−0.125956	−	0.992036i	$-0.540200\pi$
$751$	23.0513	−	20.2154i	0.841153	−	0.737671i	0.967108	+	0.254365i	$0.0818664\pi$
$752$	−31.6782	−	8.48814i	−1.15518	−	0.309531i
$753$	−32.5377	−	15.9517i	−1.18574	−	0.581313i
$754$	−5.32781	−	4.67236i	−0.194027	−	0.170157i
$755$	−16.8546	−	25.2246i	−0.613400	−	0.918018i
$756$	15.2010	−	15.4150i	0.552855	−	0.560636i
$757$	12.6527	−	5.24090i	0.459869	−	0.190484i	−0.140708	−	0.990051i	$-0.544938\pi$
$757$	12.6527	−	5.24090i	0.459869	−	0.190484i	0.600576	+	0.799567i	$0.294938\pi$
$758$	−0.107671	−	1.64273i	−0.00391077	−	0.0596668i
$759$	0.521146	−	8.24541i	0.0189164	−	0.299289i
$760$	−9.66503	−	0.633480i	−0.350588	−	0.0229787i
$761$	−3.59911	+	13.4320i	−0.130468	+	0.486911i	−0.999975	−	0.00700759i	$-0.997769\pi$
$761$	−3.59911	+	13.4320i	−0.130468	+	0.486911i	0.869508	+	0.493919i	$0.164436\pi$
$762$	0.977968	−	4.97714i	0.0354280	−	0.180303i
$763$	6.70692	+	8.74063i	0.242807	+	0.316432i
$764$	25.3888			0.918534
$765$	13.6091	−	12.7453i	0.492040	−	0.460808i
$766$	5.85308			0.211481
$767$	7.08446	+	9.23265i	0.255805	+	0.333372i
$768$	−15.8812	−	13.8621i	−0.573063	−	0.500206i
$769$	−12.2838	+	45.8438i	−0.442965	+	1.65317i	0.278288	+	0.960498i	$0.410233\pi$
$769$	−12.2838	+	45.8438i	−0.442965	+	1.65317i	−0.721253	+	0.692672i	$0.756433\pi$
$770$	0.739497	+	0.0484692i	0.0266496	+	0.00174671i
$771$	9.75514	−	4.83899i	0.351323	−	0.174272i
$772$	−3.04193	−	46.4108i	−0.109481	−	1.67036i
$773$	27.1124	−	11.2303i	0.975165	−	0.403927i	0.162533	−	0.986703i	$-0.448034\pi$
$773$	27.1124	−	11.2303i	0.975165	−	0.403927i	0.812632	+	0.582777i	$0.198034\pi$
$774$	0.229938	−	0.562517i	0.00826494	−	0.0202193i
$775$	−6.95531	−	10.4094i	−0.249842	−	0.373915i
$776$	1.38774	+	1.21701i	0.0498169	+	0.0436883i
$777$	−1.85532	+	1.24594i	−0.0665592	+	0.0446980i
$778$	6.61139	+	1.77152i	0.237030	+	0.0635119i
$779$	35.9924	−	31.5645i	1.28956	−	1.13091i
$780$	−5.31534	+	20.0236i	−0.190320	+	0.716959i
$781$	−13.6498	−	7.88072i	−0.488428	−	0.281994i
$782$	−1.77101	+	3.86035i	−0.0633313	+	0.138046i
$783$	5.01758	−	40.2858i	0.179314	−	1.43970i
$784$	−8.33769	−	3.45358i	−0.297774	−	0.123342i
$785$	4.51483	−	13.3003i	0.161141	−	0.474707i
$786$	−2.70175	+	3.53803i	−0.0963683	+	0.126197i
$787$	−1.06040	+	16.1786i	−0.0377992	+	0.576704i	0.936389	+	0.350965i	$0.114146\pi$
$787$	−1.06040	+	16.1786i	−0.0377992	+	0.576704i	−0.974188	+	0.225739i	$0.927520\pi$
$788$	−12.8240	−	37.7782i	−0.456836	−	1.34579i
$789$	7.09149	+	35.2223i	0.252464	+	1.25395i
$790$	1.85327	+	0.243988i	0.0659364	+	0.00868069i
$791$	5.83543	+	14.0880i	0.207484	+	0.500911i
$792$	2.57845	−	0.888683i	0.0916211	−	0.0315780i
$793$	13.5075	+	2.68681i	0.479665	+	0.0954114i
$794$	−1.36594	+	0.673609i	−0.0484755	+	0.0239055i
$795$	1.58005	−	12.2216i	0.0560385	−	0.433455i
$796$	−33.5710	−	38.2804i	−1.18989	−	1.35681i
$797$	5.97023	+	45.3484i	0.211476	+	1.60632i	0.687025	+	0.726633i	$0.258916\pi$
$797$	5.97023	+	45.3484i	0.211476	+	1.60632i	−0.475549	+	0.879689i	$0.657751\pi$
$798$	4.76635	−	3.67502i	0.168727	−	0.130094i
$799$	33.3203	−	14.9089i	1.17879	−	0.527440i
$800$			7.05698i			0.249502i
$801$	4.06913	−	32.0617i	0.143776	−	1.13284i
$802$	−0.752376	−	3.78245i	−0.0265673	−	0.133563i
$803$	2.84872	+	10.6316i	0.100529	+	0.375180i
$804$	−0.0421826	−	0.0628134i	−0.00148766	−	0.00221526i
$805$	14.0900	−	4.78292i	0.496609	−	0.168576i
$806$	−1.84114	+	3.73346i	−0.0648514	+	0.131506i
$807$	13.9160	+	23.9741i	0.489867	+	0.843929i
$808$	0.313773	−	2.38334i	0.0110385	−	0.0838457i
$809$	−22.8182	+	15.2466i	−0.802244	+	0.536043i	−0.887767	−	0.460294i	$-0.847744\pi$
$809$	−22.8182	+	15.2466i	−0.802244	+	0.536043i	0.0855224	+	0.996336i	$0.472744\pi$
$810$	2.85472	−	0.998807i	0.100305	−	0.0350945i
$811$	−2.51905	+	3.77003i	−0.0884559	+	0.132384i	−0.873059	−	0.487615i	$-0.837867\pi$
$811$	−2.51905	+	3.77003i	−0.0884559	+	0.132384i	0.784603	+	0.619999i	$0.212867\pi$
$812$	31.4426	−	8.42502i	1.10342	−	0.295660i
$813$	0.868137	+	2.53801i	0.0304469	+	0.0890119i
$814$	−0.137809	+	0.0181430i	−0.00483022	+	0.000635910i
$815$	6.24570	+	10.8179i	0.218777	+	0.378934i
$816$	26.4376	+	0.928201i	0.925500	+	0.0324935i
$817$	−3.31490	+	5.74158i	−0.115974	+	0.200873i
$818$	−2.51535	+	6.07259i	−0.0879471	+	0.212323i
$819$	−11.6414	−	23.3317i	−0.406783	−	0.815277i
$820$	13.6393	+	13.6393i	0.476306	+	0.476306i
$821$	0.0272217	+	0.0552002i	0.000950044	+	0.00192650i	0.897347	−	0.441325i	$-0.145491\pi$
$821$	0.0272217	+	0.0552002i	0.000950044	+	0.00192650i	−0.896397	+	0.443252i	$0.853825\pi$
$822$	3.09392	+	6.23718i	0.107913	+	0.217547i
$823$	18.2925	+	9.02087i	0.637637	+	0.314448i	0.732219	−	0.681069i	$-0.238485\pi$
$823$	18.2925	+	9.02087i	0.637637	+	0.314448i	−0.0945819	+	0.995517i	$0.530151\pi$
$824$	0.389313	+	0.298731i	0.0135624	+	0.0104068i
$825$	4.22951	+	2.42879i	0.147253	+	0.0845596i
$826$	1.35932	−	0.0890944i	0.0472967	−	0.00309999i
$827$	−4.88825	+	24.5749i	−0.169981	+	0.854553i	0.797831	+	0.602881i	$0.205981\pi$
$827$	−4.88825	+	24.5749i	−0.169981	+	0.854553i	−0.967812	+	0.251672i	$0.919019\pi$
$828$	20.2429	−	17.9201i	0.703491	−	0.622767i
$829$	−8.40972	+	8.40972i	−0.292082	+	0.292082i	−0.837902	−	0.545820i	$-0.816218\pi$
$829$	−8.40972	+	8.40972i	−0.292082	+	0.292082i	0.545820	+	0.837902i	$0.316218\pi$
$830$	−4.55290	−	1.54550i	−0.158033	−	0.0536451i
$831$	24.4100	−	24.5240i	0.846774	−	0.850728i
$832$	−24.0716	+	13.8978i	−0.834534	+	0.481818i
$833$	9.62608	−	2.87071i	0.333524	−	0.0994643i
$834$	−0.159521	+	0.0213795i	−0.00552377	+	0.000740313i
$835$	−0.607799	+	0.466381i	−0.0210338	+	0.0161398i
$836$	−14.4076	+	2.86585i	−0.498297	+	0.0991173i
$837$	−23.6217	+	3.27795i	−0.816484	+	0.113302i
$838$	−5.52704	−	3.69305i	−0.190928	−	0.127574i
$839$	−25.8883	+	29.5199i	−0.893763	+	1.01914i	0.105931	+	0.994374i	$0.466218\pi$
$839$	−25.8883	+	29.5199i	−0.893763	+	1.01914i	−0.999693	+	0.0247674i	$0.992115\pi$
$840$	3.24723	+	3.68540i	0.112040	+	0.127158i
$841$	19.5057	−	25.4203i	0.672611	−	0.876564i
$842$	3.83772	−	5.00141i	0.132257	−	0.172360i
$843$	−7.52233	+	1.51451i	−0.259083	+	0.0521625i
$844$	−19.8689	+	22.6561i	−0.683915	+	0.779856i
$845$	4.45321	+	2.97554i	0.153195	+	0.102362i
$846$	5.92108	−	0.0275860i	0.203571	−	0.000948427i
$847$	−20.8148	+	4.14032i	−0.715206	+	0.142263i
$848$	13.8711	−	10.6437i	0.476335	−	0.365505i
$849$	13.6494	+	17.7028i	0.468448	+	0.607557i
$850$	−1.58148	−	1.94561i	−0.0542442	−	0.0667338i
$851$	−2.41695	+	1.39543i	−0.0828520	+	0.0478346i
$852$	−13.4649	−	49.7875i	−0.461300	−	1.70569i
$853$	10.5803	+	3.59152i	0.362261	+	0.122971i	0.496635	−	0.867960i	$-0.334569\pi$
$853$	10.5803	+	3.59152i	0.362261	+	0.122971i	−0.134373	+	0.990931i	$0.542902\pi$
$854$	1.13993	−	1.13993i	0.0390076	−	0.0390076i
$855$	−32.3311	+	6.58779i	−1.10570	+	0.225298i
$856$	0.172409	−	0.866757i	0.00589280	−	0.0296251i
$857$	32.6375	−	2.13917i	1.11487	−	0.0730727i	0.503191	−	0.864175i	$-0.332159\pi$
$857$	32.6375	−	2.13917i	1.11487	−	0.0730727i	0.611684	+	0.791103i	$0.290493\pi$
$858$	−0.00377777	−	1.62173i	−0.000128971	−	0.0553650i
$859$	35.2774	+	27.0693i	1.20365	+	0.923592i	0.998479	−	0.0551349i	$-0.0175589\pi$
$859$	35.2774	+	27.0693i	1.20365	+	0.923592i	0.205169	+	0.978727i	$0.434226\pi$
$860$	−2.39582	−	1.18149i	−0.0816968	−	0.0402884i
$861$	−24.2289	−	1.53137i	−0.825719	−	0.0521891i
$862$	−1.43318	−	2.90619i	−0.0488142	−	0.0989853i
$863$	−6.66931	−	6.66931i	−0.227026	−	0.227026i	0.584423	−	0.811449i	$-0.301321\pi$
$863$	−6.66931	−	6.66931i	−0.227026	−	0.227026i	−0.811449	+	0.584423i	$0.801321\pi$
$864$	12.0979	+	5.86126i	0.411577	+	0.199404i
$865$	−4.06860	+	9.82247i	−0.138337	+	0.333974i
$866$	−4.56321	+	7.90372i	−0.155064	+	0.268579i
$867$	−23.4863	+	17.7593i	−0.797637	+	0.603138i
$868$	−9.56097	−	16.5601i	−0.324520	−	0.562086i
$869$	5.69312	−	0.749513i	0.193126	−	0.0254255i
$870$	4.46217	+	0.876779i	0.151282	+	0.0297256i
$871$	−0.0880246	+	0.0235861i	−0.00298260	+	0.000799185i
$872$	−2.52323	+	3.77628i	−0.0854474	+	0.127881i
$873$	5.65230	+	2.75474i	0.191301	+	0.0932339i
$874$	6.24930	−	4.17565i	0.211386	−	0.141243i
$875$	−3.24816	+	24.6723i	−0.109808	+	0.834074i
$876$	−17.9358	+	31.2335i	−0.605994	+	1.05528i
$877$	6.71071	−	13.6080i	0.226604	−	0.459508i	−0.753643	−	0.657284i	$-0.771705\pi$
$877$	6.71071	−	13.6080i	0.226604	−	0.459508i	0.980247	+	0.197776i	$0.0633718\pi$
$878$	7.46246	−	2.53316i	0.251846	−	0.0854901i
$879$	10.3239	−	0.700817i	0.348215	−	0.0236380i
$880$	−1.49189	−	5.56780i	−0.0502915	−	0.187690i
$881$	4.67595	+	23.5076i	0.157537	+	0.791991i	0.976057	+	0.217514i	$0.0697947\pi$
$881$	4.67595	+	23.5076i	0.157537	+	0.791991i	−0.818520	+	0.574477i	$0.805205\pi$
$882$	1.61640	+	0.205147i	0.0544271	+	0.00690765i
$883$			33.2578i			1.11921i	0.828758	+	0.559607i	$0.189048\pi$
$883$			33.2578i			1.11921i	−0.828758	+	0.559607i	$0.810952\pi$
$884$	11.6681	−	30.5649i	0.392441	−	1.02801i
$885$	−6.90623	−	2.84182i	−0.232150	−	0.0955269i
$886$	−0.0668255	−	0.507590i	−0.00224505	−	0.0170528i
$887$	2.46538	+	2.81123i	0.0827795	+	0.0943920i	0.791747	−	0.610849i	$-0.209172\pi$
$887$	2.46538	+	2.81123i	0.0827795	+	0.0943920i	−0.708967	+	0.705241i	$0.750839\pi$
$888$	−0.732205	−	0.559136i	−0.0245712	−	0.0187634i
$889$	25.1689	−	12.4119i	0.844138	−	0.416283i
$890$	3.55064	+	0.706266i	0.119018	+	0.0236741i
$891$	7.67657	−	5.23343i	0.257175	−	0.175327i
$892$	1.87998	+	4.53868i	0.0629465	+	0.151966i
$893$	−64.0453	−	8.43172i	−2.14319	−	0.282157i
$894$	1.83257	−	1.61469i	0.0612902	−	0.0540032i
$895$	12.3159	+	36.2816i	0.411676	+	1.21276i
$896$	−0.935734	+	14.2765i	−0.0312607	+	0.476946i
$897$	−12.5309	−	30.0540i	−0.418394	−	1.00347i
$898$	0.0325174	−	0.0957930i	0.00108512	−	0.00319666i
$899$	−33.1283	−	13.7222i	−1.10489	−	0.457661i
$900$	4.20250	+	15.3967i	0.140083	+	0.513222i
$901$	−4.50814	+	18.9316i	−0.150188	+	0.630703i
$902$	−1.30765	−	0.754971i	−0.0435399	−	0.0251378i
$903$	3.24554	−	0.877748i	0.108005	−	0.0292096i
$904$	−4.72608	+	4.14466i	−0.157187	+	0.137849i
$905$	−13.9344	−	3.73371i	−0.463195	−	0.124113i
$906$	0.526318	+	7.75328i	0.0174858	+	0.257585i
$907$	−1.60823	−	1.41038i	−0.0534004	−	0.0468309i	0.632230	−	0.774781i	$-0.282140\pi$
$907$	−1.60823	−	1.41038i	−0.0534004	−	0.0468309i	−0.685630	+	0.727950i	$0.740473\pi$
$908$	−16.0415	−	24.0077i	−0.532354	−	0.796724i
$909$	−1.10671	−	8.11400i	−0.0367072	−	0.269124i
$910$	2.69843	−	1.11773i	0.0894522	−	0.0370523i
$911$	1.59343	+	24.3111i	0.0527928	+	0.805463i	0.939375	+	0.342892i	$0.111406\pi$
$911$	1.59343	+	24.3111i	0.0527928	+	0.805463i	−0.886582	+	0.462571i	$0.846927\pi$
$912$	−38.9844	−	25.9174i	−1.29090	−	0.858210i
$913$	−14.7384	−	0.966006i	−0.487770	−	0.0319701i
$914$	0.423865	−	1.58189i	0.0140202	−	0.0523242i
$915$	−8.36224	+	2.86034i	−0.276447	+	0.0945599i
$916$	16.3380	+	21.2920i	0.539822	+	0.703509i
$917$	−24.6290			−0.813323
$918$	−4.64889	+	1.09519i	−0.153436	+	0.0361468i
$919$	−24.5758			−0.810682			−0.405341	−	0.914165i	$-0.632847\pi$
$919$	−24.5758			−0.810682			−0.405341	+	0.914165i	$0.632847\pi$
$920$	3.73408	+	4.86635i	0.123109	+	0.160439i
$921$	−32.7455	+	11.2007i	−1.07900	+	0.369077i
$922$	1.62623	−	6.06917i	0.0535570	−	0.199877i
$923$	−61.9861	−	4.06278i	−2.04030	−	0.133728i
$924$	6.20372	+	4.12432i	0.204087	+	0.135680i
$925$	−0.107754	−	1.64401i	−0.00354294	−	0.0540548i
$926$	−0.383642	+	0.158910i	−0.0126073	+	0.00522210i
$927$	1.54739	+	0.632520i	0.0508230	+	0.0207747i
$928$	11.2296	+	16.8063i	0.368630	+	0.551693i
$929$	0.917254	+	0.804410i	0.0300941	+	0.0263918i	0.674261	−	0.738493i	$-0.264462\pi$
$929$	0.917254	+	0.804410i	0.0300941	+	0.0263918i	−0.644167	+	0.764885i	$0.722796\pi$
$930$	−0.180923	−	2.66521i	−0.00593270	−	0.0873956i
$931$	−17.1702	−	4.60075i	−0.562731	−	0.150783i
$932$	−31.8031	+	27.8906i	−1.04175	+	0.913586i
$933$	8.38787	−	2.26848i	0.274607	−	0.0742667i
$934$	5.22253	+	3.01523i	0.170886	+	0.0986612i
$935$	5.19756	+	3.76161i	0.169978	+	0.123018i
$936$	7.56509	−	7.63591i	0.247273	−	0.249587i
$937$	1.69237	+	0.701001i	0.0552872	+	0.0229007i	0.410156	−	0.912016i	$-0.365474\pi$
$937$	1.69237	+	0.701001i	0.0552872	+	0.0229007i	−0.354868	+	0.934916i	$0.615474\pi$
$938$	−0.00342887	+	0.0101011i	−0.000111957	+	0.000329814i
$939$	−20.4763	−	49.1103i	−0.668220	−	1.60265i
$940$	1.70231	−	25.9723i	0.0555233	−	0.847122i
$941$	−5.59918	−	16.4947i	−0.182528	−	0.537711i	0.816697	−	0.577067i	$-0.195803\pi$
$941$	−5.59918	−	16.4947i	−0.182528	−	0.537711i	−0.999225	+	0.0393559i	$0.987469\pi$
$942$	−2.69950	+	2.37855i	−0.0879545	+	0.0774972i
$943$	−30.0577	−	3.95717i	−0.978814	−	0.128863i
$944$	−4.05475	−	9.78903i	−0.131971	−	0.318606i
$945$	13.9774	+	9.19878i	0.454686	+	0.299236i
$946$	0.205093	+	0.0407955i	0.00666814	+	0.00132638i
$947$	−28.1865	+	13.9000i	−0.915938	+	0.451690i	−0.838249	−	0.545287i	$-0.816421\pi$
$947$	−28.1865	+	13.9000i	−0.915938	+	0.451690i	−0.0776883	+	0.996978i	$0.524754\pi$
$948$	14.9340	+	11.4041i	0.485033	+	0.370387i
$949$	28.6020	+	32.6144i	0.928461	+	1.05871i
$950$	0.579138	+	4.39899i	0.0187897	+	0.142722i
$951$	−24.5801	−	10.1144i	−0.797065	−	0.327982i
$952$	−4.48852	−	6.32630i	−0.145474	−	0.205037i
$953$			43.6734i			1.41472i	0.706854	+	0.707360i	$0.250114\pi$
$953$			43.6734i			1.41472i	−0.706854	+	0.707360i	$0.749886\pi$
$954$	−1.90999	+	2.51330i	−0.0618381	+	0.0813711i
$955$	3.82827	+	19.2460i	0.123880	+	0.622786i
$956$	−10.3963	−	38.7994i	−0.336240	−	1.25486i
$957$	13.9375	−	0.946123i	0.450535	−	0.0305838i
$958$	2.63194	−	0.893424i	0.0850342	−	0.0288652i
$959$	−17.0369	+	34.5475i	−0.550151	+	1.11560i
$960$	8.88252	−	15.4681i	0.286682	−	0.499230i
$961$	1.29691	−	9.85099i	0.0418357	−	0.317774i
$962$	−0.455497	+	0.304354i	−0.0146858	+	0.00981276i
$963$	−0.210892	−	3.00313i	−0.00679589	−	0.0967746i
$964$	−14.7637	+	22.0954i	−0.475507	+	0.711646i
$965$	34.7231	−	9.30403i	1.11778	−	0.299507i
$966$	−3.74002	−	0.734883i	−0.120333	−	0.0236445i
$967$	−60.9136	+	8.01943i	−1.95885	+	0.257888i	−0.999688	−	0.0249702i	$-0.992051\pi$
$967$	−60.9136	+	8.01943i	−1.95885	+	0.257888i	−0.959162	+	0.282858i	$0.908718\pi$
$968$	−4.37432	−	7.57655i	−0.140596	−	0.243519i
$969$	51.8674	−	4.98442i	1.66622	−	0.160122i
$970$	−0.352167	+	0.609972i	−0.0113074	+	0.0195850i
$971$	0.0500235	−	0.120767i	0.00160533	−	0.00387561i	−0.923075	−	0.384620i	$-0.874332\pi$
$971$	0.0500235	−	0.120767i	0.00160533	−	0.00387561i	0.924680	+	0.380745i	$0.124332\pi$
$972$	29.8851	+	5.58348i	0.958564	+	0.179090i
$973$	−0.629647	−	0.629647i	−0.0201856	−	0.0201856i
$974$	0.330344	+	0.669871i	0.0105849	+	0.0214641i
$975$	19.1841	+	1.21252i	0.614382	+	0.0388316i
$976$	−11.2460	−	5.54590i	−0.359975	−	0.177520i
$977$	−46.0206	−	35.3128i	−1.47233	−	1.12976i	−0.963106	−	0.269122i	$-0.913266\pi$
$977$	−46.0206	−	35.3128i	−1.47233	−	1.12976i	−0.509222	−	0.860635i	$-0.670067\pi$
$978$	−0.00745370	−	3.19975i	−0.000238343	−	0.102317i
$979$	11.0972	−	0.727349i	0.354668	−	0.0232462i
$980$	1.39730	−	7.02472i	0.0446352	−	0.224396i
$981$	−4.90490	+	14.6736i	−0.156601	+	0.468493i
$982$	−1.52458	+	1.52458i	−0.0486512	+	0.0486512i
$983$	−6.89004	−	2.33885i	−0.219758	−	0.0745978i	0.209389	−	0.977832i	$-0.432852\pi$
$983$	−6.89004	−	2.33885i	−0.219758	−	0.0745978i	−0.429147	+	0.903235i	$0.641186\pi$
$984$	−2.61274	−	9.66080i	−0.0832911	−	0.307975i
$985$	26.7042	−	15.4177i	0.850866	−	0.491248i
$986$	−6.86230	−	2.11692i	−0.218540	−	0.0674165i
$987$	20.0030	+	25.9431i	0.636703	+	0.825777i
$988$	−45.9318	+	35.2447i	−1.46128	+	1.12128i
$989$	4.11791	−	0.819104i	0.130942	−	0.0260460i
$990$	0.524547	+	0.898845i	0.0166712	+	0.0285672i
$991$	40.8851	+	27.3186i	1.29876	+	0.867803i	0.996349	−	0.0853752i	$-0.0272089\pi$
$991$	40.8851	+	27.3186i	1.29876	+	0.867803i	0.302410	+	0.953178i	$0.402209\pi$
$992$	7.82881	−	8.92705i	0.248565	−	0.283434i
$993$	−30.2640	+	6.09320i	−0.960399	+	0.193362i
$994$	−4.42654	+	5.76878i	−0.140401	+	0.182975i
$995$	23.9565	−	31.2207i	0.759472	−	0.989763i
$996$	−31.9520	−	36.2636i	−1.01244	−	1.14905i
$997$	2.81307	−	3.20769i	0.0890908	−	0.101589i	−0.705577	−	0.708634i	$-0.749312\pi$
$997$	2.81307	−	3.20769i	0.0890908	−	0.101589i	0.794667	+	0.607045i	$0.207645\pi$
$998$	−6.40547	−	4.28000i	−0.202762	−	0.135481i
$999$	−2.90785	−	1.18073i	−0.0920001	−	0.0373566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.11.9	✓	256
3.2	odd	2		459.2.y.a.62.8		256
9.4	even	3		459.2.y.a.368.8		256
9.5	odd	6	inner	153.2.s.a.113.9	yes	256
17.14	odd	16	inner	153.2.s.a.65.9	yes	256
51.14	even	16		459.2.y.a.116.8		256
153.14	even	48	inner	153.2.s.a.14.9	yes	256
153.31	odd	48		459.2.y.a.422.8		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.9	✓	256	1.1	even	1	trivial
153.2.s.a.14.9	yes	256	153.14	even	48	inner
153.2.s.a.65.9	yes	256	17.14	odd	16	inner
153.2.s.a.113.9	yes	256	9.5	odd	6	inner
459.2.y.a.62.8		256	3.2	odd	2
459.2.y.a.116.8		256	51.14	even	16
459.2.y.a.368.8		256	9.4	even	3
459.2.y.a.422.8		256	153.31	odd	48

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.135712 + 0.176863i) q^{2} +(-1.63883 + 0.560569i) q^{3} +(0.504775 - 1.88385i) q^{4} +(1.50417 + 0.0985882i) q^{5} +(-0.321553 - 0.213773i) q^{6} +(-0.139720 - 2.13171i) q^{7} +(0.813611 - 0.337009i) q^{8} +(2.37153 - 1.83735i) q^{9} +O(q^{10})\)	\(q+(0.135712 + 0.176863i) q^{2} +(-1.63883 + 0.560569i) q^{3} +(0.504775 - 1.88385i) q^{4} +(1.50417 + 0.0985882i) q^{5} +(-0.321553 - 0.213773i) q^{6} +(-0.139720 - 2.13171i) q^{7} +(0.813611 - 0.337009i) q^{8} +(2.37153 - 1.83735i) q^{9} +(0.186697 + 0.279412i) q^{10} +(0.776131 + 0.680648i) q^{11} +(0.228785 + 3.37026i) q^{12} +(3.92991 + 1.05302i) q^{13} +(0.358061 - 0.314011i) q^{14} +(-2.52034 + 0.681619i) q^{15} +(-3.20800 - 1.85214i) q^{16} +(4.07115 - 0.652511i) q^{17} +(0.646805 + 0.170085i) q^{18} +(-6.74095 - 2.79219i) q^{19} +(0.944991 - 2.78385i) q^{20} +(1.42395 + 3.41519i) q^{21} +(-0.0150515 + 0.229641i) q^{22} +(1.48528 + 4.37548i) q^{23} +(-1.14445 + 1.00839i) q^{24} +(-2.70443 - 0.356045i) q^{25} +(0.347096 + 0.837965i) q^{26} +(-2.85656 + 4.34051i) q^{27} +(-4.08635 - 0.812825i) q^{28} +(-7.00719 + 3.45556i) q^{29} +(-0.462594 - 0.353252i) q^{30} +(3.02610 + 3.45061i) q^{31} +(-0.337684 - 2.56496i) q^{32} +(-1.65350 - 0.680392i) q^{33} +(0.667909 + 0.631483i) q^{34} -3.22023i q^{35} +(-2.26420 - 5.39504i) q^{36} +(0.117832 + 0.592384i) q^{37} +(-0.420992 - 1.57116i) q^{38} +(-7.03074 + 0.477270i) q^{39} +(1.25703 - 0.426705i) q^{40} +(-2.90192 + 5.88451i) q^{41} +(-0.410776 + 0.715328i) q^{42} +(0.118602 - 0.900874i) q^{43} +(1.67401 - 1.11854i) q^{44} +(3.74831 - 2.52988i) q^{45} +(-0.572293 + 0.856497i) q^{46} +(8.55178 - 2.29144i) q^{47} +(6.29562 + 1.23704i) q^{48} +(2.41543 - 0.317998i) q^{49} +(-0.304052 - 0.526634i) q^{50} +(-6.30614 + 3.35151i) q^{51} +(3.96744 - 6.87181i) q^{52} +(-1.80626 + 4.36069i) q^{53} +(-1.15535 + 0.0838381i) q^{54} +(1.10033 + 1.10033i) q^{55} +(-0.832084 - 1.68730i) q^{56} +(12.6125 + 0.797164i) q^{57} +(-1.56212 - 0.770354i) q^{58} +(2.26928 + 1.74128i) q^{59} +(0.0118616 + 5.09199i) q^{60} +(3.37778 - 0.221391i) q^{61} +(-0.199608 + 1.00350i) q^{62} +(-4.24806 - 4.79870i) q^{63} +(-4.83082 + 4.83082i) q^{64} +(5.80742 + 1.97135i) q^{65} +(-0.104063 - 0.384780i) q^{66} +(-0.0193978 + 0.0111993i) q^{67} +(0.825783 - 7.99879i) q^{68} +(-4.88687 - 6.33807i) q^{69} +(0.569540 - 0.437024i) q^{70} +(-14.9748 + 2.97867i) q^{71} +(1.31030 - 2.29412i) q^{72} +(8.86525 + 5.92357i) q^{73} +(-0.0887798 + 0.101234i) q^{74} +(4.63169 - 0.932521i) q^{75} +(-8.66273 + 11.2895i) q^{76} +(1.34251 - 1.74959i) q^{77} +(-1.03857 - 1.17871i) q^{78} +(3.66763 - 4.18213i) q^{79} +(-4.64277 - 3.10220i) q^{80} +(2.24827 - 8.71466i) q^{81} +(-1.43458 + 0.285356i) q^{82} +(-11.3511 + 8.71002i) q^{83} +(7.15247 - 0.958596i) q^{84} +(6.18801 - 0.580118i) q^{85} +(0.175427 - 0.101283i) q^{86} +(9.54651 - 9.59109i) q^{87} +(0.860853 + 0.292220i) q^{88} +(7.61763 - 7.61763i) q^{89} +(0.956134 + 0.319604i) q^{90} +(1.69564 - 8.52457i) q^{91} +(8.99247 - 0.589397i) q^{92} +(-6.89357 - 3.95862i) q^{93} +(1.56585 + 1.20152i) q^{94} +(-9.86423 - 4.86450i) q^{95} +(1.99124 + 4.01424i) q^{96} +(0.927015 + 1.87980i) q^{97} +(0.384046 + 0.384046i) q^{98} +(3.09120 + 0.188149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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