LMFDB - Embedded newform 81.2.g.a.16.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			16.8
Character	$\chi$	$=$	81.16
Dual form			81.2.g.a.76.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86856 + 0.442858i) q^{2} +(-1.20815 + 1.24112i) q^{3} +(1.50814 + 0.757419i) q^{4} +(0.470835 - 0.632440i) q^{5} +(-2.80714 + 1.78408i) q^{6} +(-0.995721 - 0.654896i) q^{7} +(-0.459476 - 0.385546i) q^{8} +(-0.0807617 - 2.99891i) q^{9} +O(q^{10})$	\(q+(1.86856 + 0.442858i) q^{2} +(-1.20815 + 1.24112i) q^{3} +(1.50814 + 0.757419i) q^{4} +(0.470835 - 0.632440i) q^{5} +(-2.80714 + 1.78408i) q^{6} +(-0.995721 - 0.654896i) q^{7} +(-0.459476 - 0.385546i) q^{8} +(-0.0807617 - 2.99891i) q^{9} +(1.15987 - 0.973243i) q^{10} +(2.04249 - 0.238733i) q^{11} +(-2.76211 + 0.956716i) q^{12} +(-0.874830 + 2.92214i) q^{13} +(-1.57054 - 1.66468i) q^{14} +(0.216098 + 1.34844i) q^{15} +(-2.70341 - 3.63132i) q^{16} +(-0.788777 - 4.47337i) q^{17} +(1.17718 - 5.63943i) q^{18} +(-0.838570 + 4.75577i) q^{19} +(1.18911 - 0.597193i) q^{20} +(2.01578 - 0.444599i) q^{21} +(3.92225 + 0.458445i) q^{22} +(-5.50938 + 3.62358i) q^{23} +(1.03362 - 0.104469i) q^{24} +(1.25572 + 4.19440i) q^{25} +(-2.92877 + 5.07278i) q^{26} +(3.81958 + 3.52289i) q^{27} +(-1.00566 - 1.74186i) q^{28} +(6.90147 - 7.31513i) q^{29} +(-0.193376 + 2.61535i) q^{30} +(0.517918 + 8.89231i) q^{31} +(-2.96821 - 6.88108i) q^{32} +(-2.17133 + 2.82340i) q^{33} +(0.507189 - 8.70810i) q^{34} +(-0.883002 + 0.321387i) q^{35} +(2.14963 - 4.58396i) q^{36} +(-0.563666 - 0.205158i) q^{37} +(-3.67305 + 8.51509i) q^{38} +(-2.56980 - 4.61614i) q^{39} +(-0.460172 + 0.109063i) q^{40} +(-1.08205 + 0.256451i) q^{41} +(3.96351 + 0.0619425i) q^{42} +(2.96602 - 6.87600i) q^{43} +(3.26119 + 1.18698i) q^{44} +(-1.93466 - 1.36091i) q^{45} +(-11.8994 + 4.33101i) q^{46} +(0.0532653 - 0.914529i) q^{47} +(7.77302 + 1.03190i) q^{48} +(-2.20999 - 5.12333i) q^{49} +(0.488872 + 8.39361i) q^{50} +(6.50496 + 4.42553i) q^{51} +(-3.53265 + 3.74439i) q^{52} +(3.63216 + 6.29109i) q^{53} +(5.57700 + 8.27428i) q^{54} +(0.810691 - 1.40416i) q^{55} +(0.205017 + 0.684805i) q^{56} +(-4.88936 - 6.78643i) q^{57} +(16.1354 - 10.6124i) q^{58} +(5.17832 + 0.605259i) q^{59} +(-0.695430 + 2.19732i) q^{60} +(-0.0194107 + 0.00974841i) q^{61} +(-2.97027 + 16.8452i) q^{62} +(-1.88356 + 3.03897i) q^{63} +(-0.926691 - 5.25553i) q^{64} +(1.43618 + 1.92912i) q^{65} +(-5.30764 + 4.31412i) q^{66} +(-10.3329 - 10.9523i) q^{67} +(2.19863 - 7.34393i) q^{68} +(2.15885 - 11.2156i) q^{69} +(-1.79228 + 0.209487i) q^{70} +(3.88852 - 3.26285i) q^{71} +(-1.11911 + 1.40906i) q^{72} +(-0.586995 - 0.492548i) q^{73} +(-0.962390 - 0.632974i) q^{74} +(-6.72285 - 3.50895i) q^{75} +(-4.86679 + 6.53723i) q^{76} +(-2.19010 - 1.09991i) q^{77} +(-2.75754 - 9.76361i) q^{78} +(7.72089 + 1.82988i) q^{79} -3.56945 q^{80} +(-8.98696 + 0.484394i) q^{81} -2.13546 q^{82} +(-13.0235 - 3.08663i) q^{83} +(3.37684 + 0.856271i) q^{84} +(-3.20053 - 1.60736i) q^{85} +(8.58729 - 11.5347i) q^{86} +(0.740971 + 17.4033i) q^{87} +(-1.03052 - 0.677782i) q^{88} +(-4.47086 - 3.75149i) q^{89} +(-3.01234 - 3.39974i) q^{90} +(2.78478 - 2.33671i) q^{91} +(-11.0535 + 1.29197i) q^{92} +(-11.6621 - 10.1004i) q^{93} +(0.504536 - 1.68527i) q^{94} +(2.61291 + 2.76952i) q^{95} +(12.1263 + 4.62945i) q^{96} +(4.33880 + 5.82802i) q^{97} +(-1.86060 - 10.5520i) q^{98} +(-0.880894 - 6.10597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{27}\right)$

Coefficient data

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

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

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

$2$	1.86856	+	0.442858i	1.32127	+	0.313148i	0.829954	−	0.557831i	$-0.188366\pi$
$2$	1.86856	+	0.442858i	1.32127	+	0.313148i	0.491320	+	0.870979i	$0.336515\pi$
$3$	−1.20815	+	1.24112i	−0.697524	+	0.716561i
$3$	−1.20815	+	1.24112i	−0.697524	+	0.716561i
$4$	1.50814	+	0.757419i	0.754072	+	0.378709i
$5$	0.470835	−	0.632440i	0.210564	−	0.282836i	−0.684277	−	0.729222i	$-0.739882\pi$
$5$	0.470835	−	0.632440i	0.210564	−	0.282836i	0.894840	+	0.446387i	$0.147289\pi$
$6$	−2.80714	+	1.78408i	−1.14601	+	0.728346i
$7$	−0.995721	−	0.654896i	−0.376347	−	0.247527i	0.347217	−	0.937785i	$-0.387127\pi$
$7$	−0.995721	−	0.654896i	−0.376347	−	0.247527i	−0.723564	+	0.690258i	$0.757497\pi$
$8$	−0.459476	−	0.385546i	−0.162449	−	0.136311i
$9$	−0.0807617	−	2.99891i	−0.0269206	−	0.999638i
$10$	1.15987	−	0.973243i	0.366782	−	0.307766i
$11$	2.04249	−	0.238733i	0.615834	−	0.0719807i	0.197544	−	0.980294i	$-0.436703\pi$
$11$	2.04249	−	0.238733i	0.615834	−	0.0719807i	0.418290	+	0.908313i	$0.362629\pi$
$12$	−2.76211	+	0.956716i	−0.797352	+	0.276180i
$13$	−0.874830	+	2.92214i	−0.242634	+	0.810455i	0.746747	+	0.665109i	$0.231615\pi$
$13$	−0.874830	+	2.92214i	−0.242634	+	0.810455i	−0.989381	+	0.145346i	$0.953570\pi$
$14$	−1.57054	−	1.66468i	−0.419745	−	0.444904i
$15$	0.216098	+	1.34844i	0.0557962	+	0.348167i
$16$	−2.70341	−	3.63132i	−0.675854	−	0.907829i
$17$	−0.788777	−	4.47337i	−0.191306	−	1.08495i	−0.917581	−	0.397548i	$-0.869861\pi$
$17$	−0.788777	−	4.47337i	−0.191306	−	1.08495i	0.726275	−	0.687404i	$-0.241250\pi$
$18$	1.17718	−	5.63943i	0.277465	−	1.32923i
$19$	−0.838570	+	4.75577i	−0.192381	+	1.09105i	0.723718	+	0.690096i	$0.242432\pi$
$19$	−0.838570	+	4.75577i	−0.192381	+	1.09105i	−0.916099	+	0.400952i	$0.868679\pi$
$20$	1.18911	−	0.597193i	0.265893	−	0.133536i
$21$	2.01578	−	0.444599i	0.439880	−	0.0970195i
$22$	3.92225	+	0.458445i	0.836227	+	0.0977409i
$23$	−5.50938	+	3.62358i	−1.14879	+	0.755568i	−0.973441	−	0.228939i	$-0.926474\pi$
$23$	−5.50938	+	3.62358i	−1.14879	+	0.755568i	−0.175345	+	0.984507i	$0.556104\pi$
$24$	1.03362	−	0.104469i	0.210987	−	0.0213246i
$25$	1.25572	+	4.19440i	0.251144	+	0.838880i
$26$	−2.92877	+	5.07278i	−0.574379	+	0.994853i
$27$	3.81958	+	3.52289i	0.735079	+	0.677981i
$28$	−1.00566	−	1.74186i	−0.190052	−	0.329180i
$29$	6.90147	−	7.31513i	1.28157	−	1.35839i	0.380460	−	0.924797i	$-0.375766\pi$
$29$	6.90147	−	7.31513i	1.28157	−	1.35839i	0.901111	−	0.433589i	$-0.142753\pi$
$30$	−0.193376	+	2.61535i	−0.0353055	+	0.477496i
$31$	0.517918	+	8.89231i	0.0930208	+	1.59711i	0.645620	+	0.763659i	$0.276599\pi$
$31$	0.517918	+	8.89231i	0.0930208	+	1.59711i	−0.552599	+	0.833447i	$0.686364\pi$
$32$	−2.96821	−	6.88108i	−0.524710	−	1.21641i
$33$	−2.17133	+	2.82340i	−0.377981	+	0.491491i
$34$	0.507189	−	8.70810i	0.0869822	−	1.49343i
$35$	−0.883002	+	0.321387i	−0.149255	+	0.0543242i
$36$	2.14963	−	4.58396i	0.358272	−	0.763994i
$37$	−0.563666	−	0.205158i	−0.0926661	−	0.0337277i	0.295271	−	0.955414i	$-0.404590\pi$
$37$	−0.563666	−	0.205158i	−0.0926661	−	0.0337277i	−0.387937	+	0.921686i	$0.626812\pi$
$38$	−3.67305	+	8.51509i	−0.595847	+	1.38133i
$39$	−2.56980	−	4.61614i	−0.411498	−	0.739174i
$40$	−0.460172	+	0.109063i	−0.0727595	+	0.0172443i
$41$	−1.08205	+	0.256451i	−0.168988	+	0.0400510i	−0.314239	−	0.949344i	$-0.601749\pi$
$41$	−1.08205	+	0.256451i	−0.168988	+	0.0400510i	0.145251	+	0.989395i	$0.453601\pi$
$42$	3.96351	+	0.0619425i	0.611583	+	0.00955794i
$43$	2.96602	−	6.87600i	0.452314	−	1.04858i	−0.527660	−	0.849455i	$-0.676931\pi$
$43$	2.96602	−	6.87600i	0.452314	−	1.04858i	0.979974	−	0.199125i	$-0.0638101\pi$
$44$	3.26119	+	1.18698i	0.491643	+	0.178944i
$45$	−1.93466	−	1.36091i	−0.288402	−	0.202873i
$46$	−11.8994	+	4.33101i	−1.75447	+	0.638573i
$47$	0.0532653	−	0.914529i	0.00776954	−	0.133398i	−0.992193	−	0.124714i	$-0.960199\pi$
$47$	0.0532653	−	0.914529i	0.00776954	−	0.133398i	0.999962	−	0.00868399i	$-0.00276424\pi$
$48$	7.77302	+	1.03190i	1.12194	+	0.148942i
$49$	−2.20999	−	5.12333i	−0.315712	−	0.731904i
$50$	0.488872	+	8.39361i	0.0691369	+	1.18704i
$51$	6.50496	+	4.42553i	0.910876	+	0.619698i
$52$	−3.53265	+	3.74439i	−0.489891	+	0.519254i
$53$	3.63216	+	6.29109i	0.498916	+	0.864147i	0.999999	−	0.00125165i	$-0.000398413\pi$
$53$	3.63216	+	6.29109i	0.498916	+	0.864147i	−0.501084	+	0.865399i	$0.667065\pi$
$54$	5.57700	+	8.27428i	0.758934	+	1.12599i
$55$	0.810691	−	1.40416i	0.109314	−	0.189337i
$56$	0.205017	+	0.684805i	0.0273966	+	0.0915109i
$57$	−4.88936	−	6.78643i	−0.647612	−	0.898885i
$58$	16.1354	−	10.6124i	2.11868	−	1.39348i
$59$	5.17832	+	0.605259i	0.674160	+	0.0787981i	0.446283	−	0.894892i	$-0.352747\pi$
$59$	5.17832	+	0.605259i	0.674160	+	0.0787981i	0.227877	+	0.973690i	$0.426822\pi$
$60$	−0.695430	+	2.19732i	−0.0897796	+	0.283673i
$61$	−0.0194107	+	0.00974841i	−0.00248528	+	0.00124816i	−0.450041	−	0.893008i	$-0.648591\pi$
$61$	−0.0194107	+	0.00974841i	−0.00248528	+	0.00124816i	0.447556	+	0.894256i	$0.352294\pi$
$62$	−2.97027	+	16.8452i	−0.377224	+	2.13934i
$63$	−1.88356	+	3.03897i	−0.237306	+	0.382874i
$64$	−0.926691	−	5.25553i	−0.115836	−	0.656941i
$65$	1.43618	+	1.92912i	0.178136	+	0.239278i
$66$	−5.30764	+	4.31412i	−0.653326	+	0.531031i
$67$	−10.3329	−	10.9523i	−1.26237	−	1.33803i	−0.916649	−	0.399694i	$-0.869116\pi$
$67$	−10.3329	−	10.9523i	−1.26237	−	1.33803i	−0.345719	−	0.938338i	$-0.612365\pi$
$68$	2.19863	−	7.34393i	0.266623	−	0.890582i
$69$	2.15885	−	11.2156i	0.259894	−	1.35020i
$70$	−1.79228	+	0.209487i	−0.214218	+	0.0250385i
$71$	3.88852	−	3.26285i	0.461482	−	0.387229i	−0.382194	−	0.924082i	$-0.624831\pi$
$71$	3.88852	−	3.26285i	0.461482	−	0.387229i	0.843676	+	0.536853i	$0.180387\pi$
$72$	−1.11911	+	1.40906i	−0.131888	+	0.166060i
$73$	−0.586995	−	0.492548i	−0.0687026	−	0.0576483i	0.607790	−	0.794098i	$-0.292056\pi$
$73$	−0.586995	−	0.492548i	−0.0687026	−	0.0576483i	−0.676492	+	0.736450i	$0.736501\pi$
$74$	−0.962390	−	0.632974i	−0.111876	−	0.0735817i
$75$	−6.72285	−	3.50895i	−0.776288	−	0.405178i
$76$	−4.86679	+	6.53723i	−0.558259	+	0.749872i
$77$	−2.19010	−	1.09991i	−0.249585	−	0.125346i
$78$	−2.75754	−	9.76361i	−0.312230	−	1.10551i
$79$	7.72089	+	1.82988i	0.868668	+	0.205878i	0.640701	−	0.767791i	$-0.278644\pi$
$79$	7.72089	+	1.82988i	0.868668	+	0.205878i	0.227967	+	0.973669i	$0.426792\pi$
$80$	−3.56945			−0.399077
$81$	−8.98696	+	0.484394i	−0.998551	+	0.0538216i
$82$	−2.13546			−0.235822
$83$	−13.0235	−	3.08663i	−1.42952	−	0.338802i	−0.558276	−	0.829655i	$-0.688537\pi$
$83$	−13.0235	−	3.08663i	−1.42952	−	0.338802i	−0.871242	+	0.490853i	$0.836685\pi$
$84$	3.37684	+	0.856271i	0.368443	+	0.0934268i
$85$	−3.20053	−	1.60736i	−0.347146	−	0.174343i
$86$	8.58729	−	11.5347i	0.925991	−	1.24382i
$87$	0.740971	+	17.4033i	0.0794404	+	1.86583i
$88$	−1.03052	−	0.677782i	−0.109854	−	0.0722518i
$89$	−4.47086	−	3.75149i	−0.473910	−	0.397658i	0.374309	−	0.927304i	$-0.377880\pi$
$89$	−4.47086	−	3.75149i	−0.473910	−	0.397658i	−0.848218	+	0.529647i	$0.822325\pi$
$90$	−3.01234	−	3.39974i	−0.317529	−	0.358364i
$91$	2.78478	−	2.33671i	0.291925	−	0.244954i
$92$	−11.0535	+	1.29197i	−1.15241	+	0.134697i
$93$	−11.6621	−	10.1004i	−1.20931	−	1.04736i
$94$	0.504536	−	1.68527i	0.0520389	−	0.173822i
$95$	2.61291	+	2.76952i	0.268079	+	0.284147i
$96$	12.1263	+	4.62945i	1.23763	+	0.472491i
$97$	4.33880	+	5.82802i	0.440538	+	0.591745i	0.965830	−	0.259177i	$-0.0834512\pi$
$97$	4.33880	+	5.82802i	0.440538	+	0.591745i	−0.525292	+	0.850922i	$0.676044\pi$
$98$	−1.86060	−	10.5520i	−0.187949	−	1.06591i
$99$	−0.880894	−	6.10597i	−0.0885332	−	0.613673i
$100$	−1.28311	+	7.27686i	−0.128311	+	0.727686i
$101$	6.44925	−	3.23894i	0.641725	−	0.322286i	−0.0980094	−	0.995185i	$-0.531248\pi$
$101$	6.44925	−	3.23894i	0.641725	−	0.322286i	0.739734	+	0.672899i	$0.234951\pi$
$102$	10.1950	+	11.1502i	1.00946	+	1.10403i
$103$	1.49559	+	0.174809i	0.147364	+	0.0172244i	0.189455	−	0.981889i	$-0.439328\pi$
$103$	1.49559	+	0.174809i	0.147364	+	0.0172244i	−0.0420908	+	0.999114i	$0.513402\pi$
$104$	1.52858	−	1.00536i	0.149890	−	0.0985840i
$105$	0.667917	−	1.48419i	0.0651820	−	0.144843i
$106$	4.00087	+	13.3638i	0.388599	+	1.29801i
$107$	−1.73493	+	3.00499i	−0.167722	+	0.290503i	−0.937619	−	0.347666i	$-0.886974\pi$
$107$	−1.73493	+	3.00499i	−0.167722	+	0.290503i	0.769897	+	0.638169i	$0.220308\pi$
$108$	3.09218	+	8.20606i	0.297545	+	0.789628i
$109$	3.95947	+	6.85801i	0.379249	+	0.656878i	0.990953	−	0.134209i	$-0.0428492\pi$
$109$	3.95947	+	6.85801i	0.379249	+	0.656878i	−0.611705	+	0.791086i	$0.709516\pi$
$110$	2.13667	−	2.26474i	0.203724	−	0.215934i
$111$	0.935616	−	0.451717i	0.0888048	−	0.0428751i
$112$	0.313712	+	5.38623i	0.0296430	+	0.508951i
$113$	2.12282	+	4.92125i	0.199698	+	0.462953i	0.988409	−	0.151811i	$-0.0485106\pi$
$113$	2.12282	+	4.92125i	0.199698	+	0.462953i	−0.788711	+	0.614764i	$0.789251\pi$
$114$	−6.13067	−	14.8462i	−0.574190	−	1.39047i
$115$	−0.302310	+	5.19046i	−0.0281905	+	0.484013i
$116$	15.9490	−	5.80497i	1.48083	−	0.538978i
$117$	8.83389	+	2.38754i	0.816693	+	0.220728i
$118$	9.40799	+	3.42423i	0.866076	+	0.315226i
$119$	−2.14419	+	4.97080i	−0.196558	+	0.455672i
$120$	0.420595	−	0.702893i	0.0383949	−	0.0641650i
$121$	−6.58872	+	1.56155i	−0.598974	+	0.141959i
$122$	−0.0405873	+	0.00961936i	−0.00367460	+	0.000870896i
$123$	0.988993	−	1.65279i	0.0891745	−	0.149027i
$124$	−5.95410	+	13.8032i	−0.534694	+	1.23956i
$125$	6.94848	+	2.52904i	0.621491	+	0.226204i
$126$	−4.86538	+	4.84436i	−0.433443	+	0.431570i
$127$	5.22612	−	1.90215i	0.463743	−	0.168789i	−0.0995729	−	0.995030i	$-0.531748\pi$
$127$	5.22612	−	1.90215i	0.463743	−	0.168789i	0.563316	+	0.826242i	$0.309525\pi$
$128$	−0.275601	+	4.73189i	−0.0243599	+	0.418244i
$129$	4.95057	+	11.9884i	0.435873	+	1.05552i
$130$	1.82926	+	4.24071i	0.160437	+	0.371935i
$131$	−0.142119	−	2.44009i	−0.0124170	−	0.213192i	−0.998809	−	0.0487834i	$-0.984466\pi$
$131$	−0.142119	−	2.44009i	−0.0124170	−	0.213192i	0.986392	−	0.164408i	$-0.0525714\pi$
$132$	−5.41318	+	2.61349i	−0.471157	+	0.227475i
$133$	3.94951	−	4.18624i	0.342466	−	0.362993i
$134$	−14.4574	−	25.0410i	−1.24893	−	2.16322i
$135$	4.02641	−	0.756961i	0.346538	−	0.0651488i
$136$	−1.36227	+	2.35952i	−0.116813	+	0.202327i
$137$	−3.15207	−	10.5286i	−0.269299	−	0.899522i	−0.980498	−	0.196531i	$-0.937033\pi$
$137$	−3.15207	−	10.5286i	−0.269299	−	0.899522i	0.711199	−	0.702991i	$-0.248153\pi$
$138$	9.00087	−	20.0011i	0.766205	−	1.70260i
$139$	11.9352	−	7.84992i	1.01233	−	0.665821i	0.0689812	−	0.997618i	$-0.478025\pi$
$139$	11.9352	−	7.84992i	1.01233	−	0.665821i	0.943351	+	0.331797i	$0.107655\pi$
$140$	−1.57512	−	0.184105i	−0.133122	−	0.0155597i
$141$	1.07069	+	1.17099i	0.0901683	+	0.0986155i
$142$	8.71092	−	4.37479i	0.731004	−	0.367124i
$143$	−1.08922	+	6.17729i	−0.0910854	+	0.516571i
$144$	−10.6717	+	8.40057i	−0.889305	+	0.700048i
$145$	−1.37694	−	7.80899i	−0.114348	−	0.648501i
$146$	−0.878710	−	1.18031i	−0.0727226	−	0.0976833i
$147$	9.02866	+	3.44687i	0.744671	+	0.284293i
$148$	−0.694699	−	0.736338i	−0.0571039	−	0.0605266i
$149$	−2.95192	+	9.86009i	−0.241830	+	0.807770i	0.747774	+	0.663953i	$0.231123\pi$
$149$	−2.95192	+	9.86009i	−0.241830	+	0.807770i	−0.989604	+	0.143816i	$0.954063\pi$
$150$	−11.0081	−	9.53396i	−0.898808	−	0.778445i
$151$	−10.1082	+	1.18147i	−0.822591	+	0.0961471i	−0.516967	−	0.856005i	$-0.672939\pi$
$151$	−10.1082	+	1.18147i	−0.822591	+	0.0961471i	−0.305624	+	0.952152i	$0.598865\pi$
$152$	2.21887	−	1.86185i	0.179974	−	0.151016i
$153$	−13.3516	+	2.72675i	−1.07941	+	0.220445i
$154$	−3.60523	−	3.02515i	−0.290518	−	0.243774i
$155$	5.86771	+	3.85925i	0.471306	+	0.309983i
$156$	−0.379280	−	8.90822i	−0.0303667	−	0.713229i
$157$	−12.3065	+	16.5306i	−0.982169	+	1.31928i	−0.0347129	+	0.999397i	$0.511052\pi$
$157$	−12.3065	+	16.5306i	−0.982169	+	1.31928i	−0.947456	+	0.319885i	$0.896356\pi$
$158$	13.6166	+	6.83851i	1.08328	+	0.544043i
$159$	−12.1962	−	3.09261i	−0.967220	−	0.245260i
$160$	−5.74941	−	1.36263i	−0.454530	−	0.107726i
$161$	7.85887			0.619366
$162$	−17.0072	−	3.07482i	−1.33621	−	0.241581i
$163$	18.6813			1.46324			0.731618	−	0.681715i	$-0.238766\pi$
$163$	18.6813			1.46324			0.731618	+	0.681715i	$0.238766\pi$
$164$	−1.82613	−	0.432802i	−0.142597	−	0.0337961i
$165$	0.763296	+	2.70259i	0.0594225	+	0.210397i
$166$	−22.9684	−	11.5351i	−1.78269	−	0.895301i
$167$	−10.0780	+	13.5371i	−0.779860	+	1.04753i	0.217581	+	0.976042i	$0.430183\pi$
$167$	−10.0780	+	13.5371i	−0.779860	+	1.04753i	−0.997441	+	0.0714918i	$0.977224\pi$
$168$	−1.09762	−	0.572894i	−0.0846829	−	0.0441997i
$169$	3.08778	+	2.03087i	0.237522	+	0.156221i
$170$	−5.26856	−	4.42084i	−0.404080	−	0.339063i
$171$	14.3299	+	2.13071i	1.09583	+	0.162940i
$172$	9.68120	−	8.12349i	0.738184	−	0.619410i
$173$	1.24407	−	0.145411i	0.0945846	−	0.0110554i	−0.0686689	−	0.997640i	$-0.521875\pi$
$173$	1.24407	−	0.145411i	0.0945846	−	0.0110554i	0.163254	+	0.986584i	$0.447801\pi$
$174$	−6.32264	+	32.8474i	−0.479318	+	2.49015i
$175$	1.49655	−	4.99882i	0.113128	−	0.377875i
$176$	−6.38862	−	6.77154i	−0.481560	−	0.510424i
$177$	−7.00738	+	5.69568i	−0.526707	+	0.428114i
$178$	−6.69270	−	8.98986i	−0.501639	−	0.673819i
$179$	−1.77871	−	10.0875i	−0.132947	−	0.753978i	−0.976268	−	0.216568i	$-0.930514\pi$
$179$	−1.77871	−	10.0875i	−0.132947	−	0.753978i	0.843321	−	0.537410i	$-0.180597\pi$
$180$	−1.88696	−	3.51780i	−0.140646	−	0.262202i
$181$	3.12183	−	17.7048i	0.232044	−	1.31599i	−0.616707	−	0.787193i	$-0.711534\pi$
$181$	3.12183	−	17.7048i	0.232044	−	1.31599i	0.848751	−	0.528793i	$-0.177355\pi$
$182$	6.23838	−	3.13303i	0.462419	−	0.232236i
$183$	0.0113520	−	0.0358685i	0.000839164	−	0.00265148i
$184$	3.92848	+	0.459174i	0.289612	+	0.0338507i
$185$	−0.395143	+	0.259890i	−0.0290515	+	0.0191075i
$186$	−17.3184	−	24.0380i	−1.26985	−	1.76255i
$187$	−2.67901	−	8.94852i	−0.195909	−	0.654381i
$188$	0.773013	−	1.33890i	0.0563778	−	0.0976492i
$189$	−1.49611	−	6.00925i	−0.108826	−	0.437108i
$190$	3.65589	+	6.33218i	0.265226	+	0.459385i
$191$	−5.71668	+	6.05933i	−0.413645	+	0.438438i	−0.900375	−	0.435115i	$-0.856708\pi$
$191$	−5.71668	+	6.05933i	−0.413645	+	0.438438i	0.486731	+	0.873552i	$0.338189\pi$
$192$	7.64232	+	5.19931i	0.551537	+	0.375228i
$193$	1.30343	+	22.3790i	0.0938226	+	1.61087i	0.636735	+	0.771083i	$0.280285\pi$
$193$	1.30343	+	22.3790i	0.0938226	+	1.61087i	−0.542912	+	0.839790i	$0.682678\pi$
$194$	5.52634	+	12.8115i	0.396768	+	0.919812i
$195$	−4.12939	−	0.548192i	−0.295711	−	0.0392569i
$196$	0.547523	−	9.40060i	0.0391088	−	0.671471i
$197$	19.3055	−	7.02662i	1.37546	−	0.500626i	0.454661	−	0.890665i	$-0.349761\pi$
$197$	19.3055	−	7.02662i	1.37546	−	0.500626i	0.920798	+	0.390039i	$0.127538\pi$
$198$	1.05807	−	11.7995i	0.0751938	−	0.838555i
$199$	−23.4867	−	8.54846i	−1.66493	−	0.605984i	−0.673802	−	0.738912i	$-0.735340\pi$
$199$	−23.4867	−	8.54846i	−1.66493	−	0.605984i	−0.991126	+	0.132928i	$0.957562\pi$
$200$	1.04016	−	2.41136i	0.0735504	−	0.170509i
$201$	26.0768	+	0.407533i	1.83931	+	0.0287451i
$202$	13.4852	−	3.19606i	0.948818	−	0.224874i
$203$	−11.6626	+	2.76408i	−0.818553	+	0.194001i
$204$	6.45844	+	11.6013i	0.452181	+	0.812254i
$205$	−0.347278	+	0.805081i	−0.0242549	+	0.0562293i
$206$	2.71718	+	0.988973i	0.189315	+	0.0689050i
$207$	11.3117	+	16.2295i	0.786220	+	1.12803i
$208$	12.9762	−	4.72296i	0.899740	−	0.327478i
$209$	−0.577413	+	9.91381i	−0.0399405	+	0.685752i
$210$	1.90533	−	2.47752i	0.131481	−	0.170965i
$211$	−3.55001	−	8.22985i	−0.244393	−	0.566566i	0.751229	−	0.660042i	$-0.229462\pi$
$211$	−3.55001	−	8.22985i	−0.244393	−	0.566566i	−0.995622	+	0.0934757i	$0.970202\pi$
$212$	0.712837	+	12.2389i	0.0489578	+	0.840573i
$213$	−0.648305	+	8.76812i	−0.0444211	+	0.600782i
$214$	−4.57261	+	4.84668i	−0.312577	+	0.331312i
$215$	−2.95216	−	5.11329i	−0.201336	−	0.348724i
$216$	−0.396770	−	3.09131i	−0.0269968	−	0.210337i
$217$	5.30783	−	9.19344i	0.360319	−	0.624091i
$218$	4.36141	+	14.5681i	0.295392	+	0.986677i
$219$	1.32049	−	0.133462i	0.0892303	−	0.00901854i
$220$	2.28617	−	1.50364i	0.154134	−	0.101375i
$221$	13.7619	+	1.60853i	0.925723	+	0.108201i
$222$	1.94831	−	0.429717i	0.130762	−	0.0288407i
$223$	−6.71938	+	3.37460i	−0.449963	+	0.225980i	−0.659325	−	0.751858i	$-0.729158\pi$
$223$	−6.71938	+	3.37460i	−0.449963	+	0.225980i	0.209362	+	0.977838i	$0.432861\pi$
$224$	−1.55088	+	8.79550i	−0.103623	+	0.587674i
$225$	12.4772	−	4.10454i	0.831815	−	0.273636i
$226$	1.78721	+	10.1358i	0.118884	+	0.674222i
$227$	−5.77214	−	7.75332i	−0.383110	−	0.514606i	0.568180	−	0.822905i	$-0.307648\pi$
$227$	−5.77214	−	7.75332i	−0.383110	−	0.514606i	−0.951290	+	0.308298i	$0.900240\pi$
$228$	−2.23370	−	13.9382i	−0.147930	−	0.923081i
$229$	−5.48865	−	5.81762i	−0.362700	−	0.384439i	0.520166	−	0.854065i	$-0.325870\pi$
$229$	−5.48865	−	5.81762i	−0.362700	−	0.384439i	−0.882865	+	0.469626i	$0.844389\pi$
$230$	−2.86352	+	9.56483i	−0.188815	+	0.630686i
$231$	4.01108	−	1.38932i	0.263910	−	0.0914108i
$232$	−5.99138	+	0.700292i	−0.393353	+	0.0459764i
$233$	−17.1136	+	14.3600i	−1.12115	+	0.940754i	−0.998662	−	0.0517161i	$-0.983531\pi$
$233$	−17.1136	+	14.3600i	−1.12115	+	0.940754i	−0.122485	+	0.992470i	$0.539086\pi$
$234$	15.4493	+	8.37344i	1.00996	+	0.547389i
$235$	−0.553306	−	0.464279i	−0.0360937	−	0.0302862i
$236$	7.35123	+	4.83498i	0.478524	+	0.314730i
$237$	−11.5991	+	7.37179i	−0.753441	+	0.478849i
$238$	−6.20792	+	8.33868i	−0.402400	+	0.540517i
$239$	−5.78760	−	2.90664i	−0.374369	−	0.188015i	0.251659	−	0.967816i	$-0.419024\pi$
$239$	−5.78760	−	2.90664i	−0.374369	−	0.188015i	−0.626027	+	0.779801i	$0.715320\pi$
$240$	4.31242	−	4.43012i	0.278366	−	0.285963i
$241$	−2.71643	−	0.643805i	−0.174980	−	0.0414711i	0.142192	−	0.989839i	$-0.454585\pi$
$241$	−2.71643	−	0.643805i	−0.174980	−	0.0414711i	−0.317172	+	0.948368i	$0.602733\pi$
$242$	−13.0030			−0.835864
$243$	10.2564	−	11.7391i	0.657947	−	0.753065i
$244$	−0.0366577			−0.00234677
$245$	−4.28074	−	1.01455i	−0.273486	−	0.0648174i
$246$	2.57995	−	2.65036i	0.164491	−	0.168981i
$247$	−13.1634	−	6.61091i	−0.837567	−	0.420642i
$248$	3.19042	−	4.28548i	0.202592	−	0.272128i
$249$	19.5652	−	12.4347i	1.23990	−	0.788015i
$250$	11.8637	+	7.80287i	0.750325	+	0.493497i
$251$	−8.90582	−	7.47287i	−0.562131	−	0.471684i	0.316893	−	0.948461i	$-0.397360\pi$
$251$	−8.90582	−	7.47287i	−0.562131	−	0.471684i	−0.879024	+	0.476778i	$0.841805\pi$
$252$	−5.14245	+	3.15656i	−0.323944	+	0.198845i
$253$	−10.3878	+	8.71640i	−0.653075	+	0.547995i
$254$	10.6077	−	1.23986i	0.665587	−	0.0777960i
$255$	5.86164	−	2.03031i	0.367070	−	0.127143i
$256$	−5.67164	+	18.9446i	−0.354478	+	1.18404i
$257$	−14.3190	−	15.1772i	−0.893192	−	0.946728i	0.105671	−	0.994401i	$-0.466301\pi$
$257$	−14.3190	−	15.1772i	−0.893192	−	0.946728i	−0.998863	+	0.0476731i	$0.984819\pi$
$258$	3.94129	+	24.5935i	0.245374	+	1.53113i
$259$	0.426897	+	0.573422i	0.0265261	+	0.0356307i
$260$	0.704811	+	3.99718i	0.0437105	+	0.247895i
$261$	−22.4948	−	20.1061i	−1.39239	−	1.24454i
$262$	0.815054	−	4.62240i	0.0503542	−	0.285573i
$263$	−18.4714	+	9.27669i	−1.13900	+	0.572025i	−0.915355	−	0.402647i	$-0.868090\pi$
$263$	−18.4714	+	9.27669i	−1.13900	+	0.572025i	−0.223640	+	0.974672i	$0.571794\pi$
$264$	2.08623	−	0.460136i	0.128398	−	0.0283194i
$265$	5.68888	+	0.664935i	0.349465	+	0.0408466i
$266$	9.23383	−	6.07318i	0.566162	−	0.372371i
$267$	10.0575	−	1.01652i	0.615509	−	0.0622098i
$268$	−7.28810	−	24.3439i	−0.445191	−	1.48704i
$269$	−6.13247	+	10.6218i	−0.373903	+	0.647620i	−0.990162	−	0.139924i	$-0.955314\pi$
$269$	−6.13247	+	10.6218i	−0.373903	+	0.647620i	0.616259	+	0.787544i	$0.288648\pi$
$270$	7.85884	+	0.368698i	0.478274	+	0.0224383i
$271$	3.52249	+	6.10113i	0.213976	+	0.370617i	0.952955	−	0.303111i	$-0.0980253\pi$
$271$	3.52249	+	6.10113i	0.213976	+	0.370617i	−0.738979	+	0.673728i	$0.764692\pi$
$272$	−14.1118	+	14.9577i	−0.855656	+	0.906943i
$273$	−0.464287	+	6.27934i	−0.0280999	+	0.380043i
$274$	−1.22715	−	21.0693i	−0.0741348	−	1.27285i
$275$	3.56614	+	8.26724i	0.215046	+	0.498533i
$276$	11.7508	−	15.2796i	0.707313	−	0.919726i
$277$	−1.77844	+	30.5346i	−0.106856	+	1.83465i	0.340445	+	0.940264i	$0.389422\pi$
$277$	−1.77844	+	30.5346i	−0.106856	+	1.83465i	−0.447301	+	0.894383i	$0.647615\pi$
$278$	25.7781	−	9.38247i	1.54607	−	0.562723i
$279$	26.6254	−	2.27135i	1.59402	−	0.135982i
$280$	0.529627	+	0.192769i	0.0316513	+	0.0115201i
$281$	6.65299	−	15.4234i	0.396884	−	0.920080i	−0.596218	−	0.802823i	$-0.703330\pi$
$281$	6.65299	−	15.4234i	0.396884	−	0.920080i	0.993102	−	0.117257i	$-0.0374103\pi$
$282$	1.48207	+	2.66224i	0.0882558	+	0.158534i
$283$	19.8576	−	4.70635i	1.18041	−	0.279763i	0.406858	−	0.913491i	$-0.366624\pi$
$283$	19.8576	−	4.70635i	1.18041	−	0.279763i	0.773556	+	0.633728i	$0.218476\pi$
$284$	8.33579	−	1.97562i	0.494638	−	0.117231i
$285$	−6.59410	−	0.103054i	−0.390600	−	0.00610438i
$286$	−4.77095	+	11.0603i	−0.282112	+	0.654009i
$287$	1.24537	+	0.453278i	0.0735120	+	0.0267562i
$288$	−20.3960	+	9.45712i	−1.20185	+	0.557266i
$289$	−3.41413	+	1.24264i	−0.200831	+	0.0730967i
$290$	0.885380	−	15.2014i	0.0519913	−	0.892656i
$291$	−12.4752	−	1.65613i	−0.731308	−	0.0970840i
$292$	−0.512209	−	1.18743i	−0.0299748	−	0.0694893i
$293$	−1.24777	−	21.4234i	−0.0728954	−	1.25157i	−0.814275	−	0.580480i	$-0.802865\pi$
$293$	−1.24777	−	21.4234i	−0.0728954	−	1.25157i	0.741379	−	0.671086i	$-0.234172\pi$
$294$	15.3442	+	10.4391i	0.894889	+	0.608821i
$295$	2.82092	−	2.99001i	0.164241	−	0.174085i
$296$	0.179893	+	0.311584i	0.0104561	+	0.0181104i
$297$	8.64250	+	6.28362i	0.501489	+	0.364612i
$298$	−9.88246	+	17.1169i	−0.572476	+	0.991557i
$299$	−5.76882	−	19.2692i	−0.333619	−	1.11437i
$300$	−7.48128	−	10.3840i	−0.431932	−	0.599521i
$301$	−7.45639	+	4.90415i	−0.429779	+	0.282670i
$302$	−19.4110	−	2.26882i	−1.11698	−	0.130556i
$303$	−3.77173	+	11.9174i	−0.216681	+	0.684638i
$304$	19.5367	−	9.81169i	1.12051	−	0.562739i
$305$	−0.00297393	+	0.0168660i	−0.000170287	+	0.000965744i
$306$	−26.1558	−	0.817736i	−1.49523	−	0.0467468i
$307$	−1.40936	−	7.99290i	−0.0804366	−	0.456179i	−0.998248	−	0.0591628i	$-0.981157\pi$
$307$	−1.40936	−	7.99290i	−0.0804366	−	0.456179i	0.917812	−	0.397016i	$-0.129954\pi$
$308$	−2.46989	−	3.31764i	−0.140735	−	0.189040i
$309$	−2.02385	+	1.64501i	−0.115133	+	0.0935812i
$310$	9.25509	+	9.80982i	0.525654	+	0.557161i
$311$	6.71061	−	22.4150i	0.380524	−	1.27104i	−0.526579	−	0.850126i	$-0.676525\pi$
$311$	6.71061	−	22.4150i	0.380524	−	1.27104i	0.907102	−	0.420911i	$-0.138289\pi$
$312$	−0.598973	+	3.11178i	−0.0339102	+	0.176170i
$313$	3.52727	−	0.412278i	0.199373	−	0.0233033i	−0.0158203	−	0.999875i	$-0.505036\pi$
$313$	3.52727	−	0.412278i	0.199373	−	0.0233033i	0.215193	+	0.976572i	$0.430962\pi$
$314$	−30.3163	+	25.4384i	−1.71085	+	1.43557i
$315$	1.03512	+	2.62209i	0.0583226	+	0.147738i
$316$	10.2582	+	8.60767i	0.577070	+	0.484220i
$317$	15.6329	+	10.2819i	0.878029	+	0.577489i	0.906547	−	0.422104i	$-0.138708\pi$
$317$	15.6329	+	10.2819i	0.878029	+	0.577489i	−0.0285178	+	0.999593i	$0.509079\pi$
$318$	−21.4198	−	11.1799i	−1.20116	−	0.626938i
$319$	12.3498	−	16.5887i	0.691458	−	0.928789i
$320$	−3.76013	−	1.88841i	−0.210197	−	0.105565i
$321$	−1.63350	−	5.78372i	−0.0911731	−	0.322816i
$322$	14.6848	+	3.48036i	0.818352	+	0.193953i
$323$	21.9358			1.22054
$324$	−13.9205	−	6.07635i	−0.773362	−	0.337575i
$325$	−13.3551			−0.740810
$326$	34.9073	+	8.27318i	1.93334	+	0.458209i
$327$	−13.2952	−	3.37130i	−0.735228	−	0.186433i
$328$	0.596051	+	0.299348i	0.0329114	+	0.0165287i
$329$	−0.651959	+	0.875733i	−0.0359437	+	0.0482807i
$330$	0.229402	+	5.38800i	0.0126282	+	0.296600i
$331$	−6.03271	−	3.96778i	−0.331588	−	0.218089i	0.372787	−	0.927917i	$-0.378402\pi$
$331$	−6.03271	−	3.96778i	−0.331588	−	0.218089i	−0.704375	+	0.709828i	$0.748773\pi$
$332$	−17.3035	−	14.5194i	−0.949652	−	0.796853i
$333$	−0.569727	+	1.70695i	−0.0312208	+	0.0935404i
$334$	−24.8264	+	20.8319i	−1.35844	+	1.13987i
$335$	−11.7918	+	1.37826i	−0.644252	+	0.0753023i
$336$	−7.06397	−	6.11800i	−0.385371	−	0.333765i
$337$	5.89338	−	19.6853i	0.321033	−	1.07232i	−0.633382	−	0.773840i	$-0.718334\pi$
$337$	5.89338	−	19.6853i	0.321033	−	1.07232i	0.954414	−	0.298485i	$-0.0964812\pi$
$338$	4.87034	+	5.16226i	0.264911	+	0.280790i
$339$	−8.67255	−	3.31092i	−0.471028	−	0.179824i
$340$	−3.60941	−	4.84828i	−0.195748	−	0.262935i
$341$	3.18073	+	18.0388i	0.172246	+	0.976857i
$342$	25.8326	+	10.3275i	1.39687	+	0.558445i
$343$	−2.60337	+	14.7645i	−0.140569	+	0.797206i
$344$	−4.01383	+	2.01582i	−0.216411	+	0.108686i
$345$	−6.07675	−	6.64604i	−0.327161	−	0.357811i
$346$	2.38901	+	0.279236i	0.128434	+	0.0150118i
$347$	10.8906	−	7.16286i	0.584638	−	0.384523i	−0.222458	−	0.974942i	$-0.571408\pi$
$347$	10.8906	−	7.16286i	0.584638	−	0.384523i	0.807096	+	0.590420i	$0.201038\pi$
$348$	−12.0641	+	26.8079i	−0.646704	+	1.43706i
$349$	2.26400	+	7.56229i	0.121189	+	0.404800i	0.996959	−	0.0779289i	$-0.0248307\pi$
$349$	2.26400	+	7.56229i	0.121189	+	0.404800i	−0.875770	+	0.482729i	$0.839646\pi$
$350$	5.01016	−	8.67785i	0.267804	−	0.463851i
$351$	−13.6359	+	8.07942i	−0.727829	+	0.431247i
$352$	−7.70528	−	13.3459i	−0.410693	−	0.711341i
$353$	−9.67531	+	10.2552i	−0.514965	+	0.545831i	−0.931715	−	0.363190i	$-0.881687\pi$
$353$	−9.67531	+	10.2552i	−0.514965	+	0.545831i	0.416750	+	0.909021i	$0.363169\pi$
$354$	−15.6161	+	7.53948i	−0.829987	+	0.400719i
$355$	−0.232712	−	3.99552i	−0.0123511	−	0.212060i
$356$	−3.90125	−	9.04410i	−0.206766	−	0.479337i
$357$	−3.57886	−	8.66666i	−0.189413	−	0.458688i
$358$	1.14372	−	19.6369i	0.0604475	−	1.03784i
$359$	−2.55305	+	0.929234i	−0.134745	+	0.0490431i	−0.408512	−	0.912753i	$-0.633952\pi$
$359$	−2.55305	+	0.929234i	−0.134745	+	0.0490431i	0.273768	+	0.961796i	$0.411730\pi$
$360$	0.364234	+	1.37121i	0.0191968	+	0.0722689i
$361$	−4.05995	−	1.47770i	−0.213682	−	0.0777738i
$362$	13.6740	−	31.7000i	0.718691	−	1.66611i
$363$	6.02206	−	10.0640i	0.316076	−	0.528222i
$364$	5.96972	−	1.41485i	0.312898	−	0.0741583i
$365$	−0.587885	+	0.139331i	−0.0307713	+	0.00729293i
$366$	0.0370966	−	0.0619953i	0.00193907	−	0.00324055i
$367$	11.0218	−	25.5513i	0.575331	−	1.33377i	−0.343513	−	0.939148i	$-0.611617\pi$
$367$	11.0218	−	25.5513i	0.575331	−	1.33377i	0.918845	−	0.394620i	$-0.129124\pi$
$368$	28.0525	+	10.2103i	1.46234	+	0.532247i
$369$	0.856464	+	3.22427i	0.0445857	+	0.167849i
$370$	−0.853445	+	0.310628i	−0.0443685	+	0.0161488i
$371$	0.503389	−	8.64285i	0.0261346	−	0.448715i
$372$	−9.93796	−	24.0660i	−0.515259	−	1.24776i
$373$	4.29178	+	9.94946i	0.222220	+	0.515164i	0.992457	−	0.122594i	$-0.0391214\pi$
$373$	4.29178	+	9.94946i	0.222220	+	0.515164i	−0.770237	+	0.637758i	$0.779862\pi$
$374$	−1.04298	−	17.9073i	−0.0539313	−	0.925965i
$375$	−11.5336	+	5.56845i	−0.595594	+	0.287554i
$376$	−0.377067	+	0.399668i	−0.0194457	+	0.0206113i
$377$	15.3382	+	26.5665i	0.789958	+	1.36825i
$378$	−0.134340	−	11.8912i	−0.00690968	−	0.611619i
$379$	2.86635	−	4.96467i	0.147235	−	0.255018i	−0.782970	−	0.622060i	$-0.786296\pi$
$379$	2.86635	−	4.96467i	0.147235	−	0.255018i	0.930204	+	0.367042i	$0.119629\pi$
$380$	1.84296	+	6.15591i	0.0945418	+	0.315792i
$381$	−3.95312	+	8.78432i	−0.202524	+	0.450034i
$382$	−13.3654	+	8.79057i	−0.683834	+	0.449765i
$383$	13.6064	+	1.59036i	0.695256	+	0.0812638i	0.456378	−	0.889786i	$-0.349146\pi$
$383$	13.6064	+	1.59036i	0.695256	+	0.0812638i	0.238878	+	0.971050i	$0.423220\pi$
$384$	−5.53988	−	6.05887i	−0.282706	−	0.309190i
$385$	−1.72680	+	0.867231i	−0.0880058	+	0.0441982i
$386$	−7.47516	+	42.3938i	−0.380476	+	2.15779i
$387$	−20.8601	−	8.33951i	−1.06038	−	0.423921i
$388$	2.12928	+	12.0758i	0.108098	+	0.613055i
$389$	8.46395	+	11.3691i	0.429139	+	0.576434i	0.963123	−	0.269060i	$-0.0867131\pi$
$389$	8.46395	+	11.3691i	0.429139	+	0.576434i	−0.533984	+	0.845495i	$0.679306\pi$
$390$	−7.47325	−	2.85306i	−0.378423	−	0.144470i
$391$	20.5553	+	21.7873i	1.03953	+	1.10183i
$392$	−0.959842	+	3.20609i	−0.0484793	+	0.161932i
$393$	3.20015	+	2.77160i	0.161426	+	0.139809i
$394$	39.1853	−	4.58011i	1.97413	−	0.230743i
$395$	4.79255	−	4.02143i	0.241140	−	0.202340i
$396$	3.29626	−	9.87590i	0.165643	−	0.496282i
$397$	−3.48565	−	2.92481i	−0.174940	−	0.146792i	0.551114	−	0.834430i	$-0.314203\pi$
$397$	−3.48565	−	2.92481i	−0.174940	−	0.146792i	−0.726053	+	0.687638i	$0.758647\pi$
$398$	−40.1007	−	26.3746i	−2.01006	−	1.32204i
$399$	0.424036	+	9.95942i	0.0212284	+	0.498594i
$400$	11.8365	−	15.8991i	0.591823	−	0.794956i
$401$	−9.49809	−	4.77012i	−0.474312	−	0.238208i	0.195550	−	0.980694i	$-0.437351\pi$
$401$	−9.49809	−	4.77012i	−0.474312	−	0.238208i	−0.669862	+	0.742485i	$0.733647\pi$
$402$	48.5457	+	12.3098i	2.42124	+	0.613957i
$403$	−26.4376	−	6.26583i	−1.31695	−	0.312123i
$404$	12.1796			0.605960
$405$	−3.92502	+	5.91178i	−0.195036	+	0.293759i
$406$	−23.0164			−1.14228
$407$	−1.20026	−	0.284467i	−0.0594947	−	0.0141005i
$408$	−1.28263	−	4.54138i	−0.0634994	−	0.224832i
$409$	25.8301	+	12.9724i	1.27722	+	0.641442i	0.952549	−	0.304386i	$-0.0984513\pi$
$409$	25.8301	+	12.9724i	1.27722	+	0.641442i	0.324668	+	0.945828i	$0.394748\pi$
$410$	−1.00545	+	1.35055i	−0.0496555	+	0.0666989i
$411$	16.8755	+	8.80804i	0.832405	+	0.434469i
$412$	2.12316	+	1.39642i	0.104600	+	0.0687967i
$413$	−4.75978	−	3.99393i	−0.234214	−	0.196529i
$414$	13.9493	+	35.3354i	0.685573	+	1.73664i
$415$	−8.08404	+	6.78331i	−0.396830	+	0.332980i
$416$	22.7041	−	2.65373i	1.11316	−	0.130110i
$417$	−4.67680	+	24.2969i	−0.229024	+	1.18982i
$418$	−5.46934	+	18.2689i	−0.267514	+	0.893560i
$419$	27.2167	+	28.8480i	1.32962	+	1.40932i	0.845169	+	0.534499i	$0.179500\pi$
$419$	27.2167	+	28.8480i	1.32962	+	1.40932i	0.484452	+	0.874818i	$0.339019\pi$
$420$	2.13147	−	1.73249i	0.104005	−	0.0845367i
$421$	22.4063	+	30.0968i	1.09201	+	1.46683i	0.870821	+	0.491600i	$0.163588\pi$
$421$	22.4063	+	30.0968i	1.09201	+	1.46683i	0.221193	+	0.975230i	$0.429005\pi$
$422$	−2.98877	−	16.9502i	−0.145491	−	0.825121i
$423$	−2.74690	−	0.0858790i	−0.133559	−	0.00417558i
$424$	0.756613	−	4.29097i	0.0367444	−	0.208388i
$425$	17.7726	−	8.92575i	0.862099	−	0.432962i
$426$	−5.09443	+	16.0967i	−0.246826	+	0.779887i
$427$	0.0257118	+	0.00300528i	0.00124428	+	0.000145436i
$428$	−4.89256	+	3.21788i	−0.236491	+	0.155542i
$429$	−6.35082	−	8.81493i	−0.306621	−	0.425589i
$430$	−3.25184	−	10.8619i	−0.156818	−	0.523807i
$431$	0.730348	−	1.26500i	0.0351796	−	0.0609329i	−0.847900	−	0.530157i	$-0.822133\pi$
$431$	0.730348	−	1.26500i	0.0351796	−	0.0609329i	0.883079	+	0.469224i	$0.155466\pi$
$432$	2.46681	−	23.3940i	0.118685	−	1.12554i
$433$	−3.07185	−	5.32060i	−0.147624	−	0.255692i	0.782725	−	0.622368i	$-0.213829\pi$
$433$	−3.07185	−	5.32060i	−0.147624	−	0.255692i	−0.930349	+	0.366676i	$0.880496\pi$
$434$	13.9894	−	14.8279i	0.671514	−	0.711763i
$435$	11.3554	+	7.72546i	0.544451	+	0.370408i
$436$	0.777074	+	13.3418i	0.0372151	+	0.638958i
$437$	−12.6129	−	29.2400i	−0.603356	−	1.39874i
$438$	2.52652	+	0.335406i	0.120722	+	0.0160263i
$439$	−0.918270	+	15.7661i	−0.0438267	+	0.752475i	0.902784	+	0.430095i	$0.141520\pi$
$439$	−0.918270	+	15.7661i	−0.0438267	+	0.752475i	−0.946610	+	0.322380i	$0.895517\pi$
$440$	−0.913860	+	0.332618i	−0.0435666	+	0.0158569i
$441$	−15.1859	+	7.04133i	−0.723139	+	0.335301i
$442$	25.0026	+	9.10019i	1.18925	+	0.432852i
$443$	−7.53462	+	17.4672i	−0.357981	+	0.829893i	0.640119	+	0.768276i	$0.278885\pi$
$443$	−7.53462	+	17.4672i	−0.357981	+	0.829893i	−0.998100	+	0.0616171i	$0.980374\pi$
$444$	1.75318	+	0.0273991i	0.0832024	+	0.00130030i
$445$	−4.47763	+	1.06122i	−0.212260	+	0.0503065i
$446$	−14.0501	+	3.32993i	−0.665290	+	0.157677i
$447$	−8.67121	−	15.5761i	−0.410134	−	0.736725i
$448$	−2.51910	+	5.83992i	−0.119016	+	0.275910i
$449$	−17.8139	−	6.48373i	−0.840690	−	0.305986i	−0.114452	−	0.993429i	$-0.536511\pi$
$449$	−17.8139	−	6.48373i	−0.840690	−	0.305986i	−0.726239	+	0.687443i	$0.758733\pi$
$450$	25.1322	−	2.14397i	1.18474	−	0.101068i
$451$	−2.14886	+	0.782122i	−0.101186	+	0.0368287i
$452$	−0.525927	+	9.02982i	−0.0247375	+	0.424727i
$453$	10.7458	−	13.9728i	0.504881	−	0.656502i
$454$	−7.35199	−	17.0438i	−0.345046	−	0.799906i
$455$	−0.166658	−	2.86141i	−0.00781306	−	0.134145i
$456$	−0.369936	+	5.00327i	−0.0173239	+	0.234300i
$457$	26.2157	−	27.7870i	1.22632	−	1.29982i	0.286529	−	0.958072i	$-0.407499\pi$
$457$	26.2157	−	27.7870i	1.22632	−	1.29982i	0.939791	−	0.341751i	$-0.111020\pi$
$458$	−7.67951	−	13.3013i	−0.358840	−	0.621529i
$459$	12.7464	−	19.8652i	0.594952	−	0.927228i
$460$	−4.38728	+	7.59899i	−0.204558	+	0.354305i
$461$	2.07357	+	6.92620i	0.0965757	+	0.322585i	0.992602	−	0.121416i	$-0.0387436\pi$
$461$	2.07357	+	6.92620i	0.0965757	+	0.322585i	−0.896026	+	0.444002i	$0.853558\pi$
$462$	8.11023	−	0.819704i	0.377322	−	0.0381361i
$463$	−1.14857	+	0.755429i	−0.0533788	+	0.0351078i	−0.575918	−	0.817508i	$-0.695355\pi$
$463$	−1.14857	+	0.755429i	−0.0533788	+	0.0351078i	0.522539	+	0.852615i	$0.324985\pi$
$464$	−45.2211	−	5.28559i	−2.09934	−	0.245377i
$465$	−11.8789	+	2.61999i	−0.550869	+	0.121499i
$466$	−38.3372	+	19.2537i	−1.77594	+	0.891910i
$467$	1.50717	−	8.54757i	0.0697434	−	0.395534i	−0.929874	−	0.367878i	$-0.880084\pi$
$467$	1.50717	−	8.54757i	0.0697434	−	0.395534i	0.999617	−	0.0276564i	$-0.00880442\pi$
$468$	11.5144	+	10.2917i	0.532254	+	0.475734i
$469$	3.11612	+	17.6724i	0.143889	+	0.816035i
$470$	−0.828279	−	1.11257i	−0.0382056	−	0.0513191i
$471$	−5.64831	−	35.2453i	−0.260260	−	1.62402i
$472$	−2.14596	−	2.27458i	−0.0987758	−	0.104696i
$473$	4.41654	−	14.7523i	0.203073	−	0.678310i
$474$	−24.9383	+	8.63792i	−1.14545	+	0.396753i
$475$	−21.0006	+	2.45462i	−0.963573	+	0.112626i
$476$	−6.99873	+	5.87263i	−0.320786	+	0.269172i
$477$	18.5731	−	11.4006i	0.850403	−	0.521998i
$478$	−9.52727	−	7.99433i	−0.435767	−	0.365652i
$479$	1.77547	+	1.16775i	0.0811235	+	0.0533557i	0.589423	−	0.807825i	$-0.299355\pi$
$479$	1.77547	+	1.16775i	0.0811235	+	0.0533557i	−0.508299	+	0.861180i	$0.669726\pi$
$480$	8.63732	−	5.48945i	0.394238	−	0.250558i
$481$	1.09261	−	1.46763i	0.0498187	−	0.0669182i
$482$	−4.79071	−	2.40598i	−0.218211	−	0.109590i
$483$	−9.49467	+	9.75381i	−0.432023	+	0.443814i
$484$	−11.1195	−	2.63537i	−0.505431	−	0.119789i
$485$	5.72873			0.260128
$486$	24.3634	−	17.3932i	1.10515	−	0.788971i
$487$	−7.22045			−0.327190			−0.163595	−	0.986528i	$-0.552309\pi$
$487$	−7.22045			−0.327190			−0.163595	+	0.986528i	$0.552309\pi$
$488$	0.0126772	+	0.00300455i	0.000573870	+	0.000136010i
$489$	−22.5698	+	23.1858i	−1.02064	+	1.04850i
$490$	−7.54953	−	3.79152i	−0.341053	−	0.171283i
$491$	−12.8840	+	17.3062i	−0.581447	+	0.781019i	−0.991369	−	0.131101i	$-0.958149\pi$
$491$	−12.8840	+	17.3062i	−0.581447	+	0.781019i	0.409922	+	0.912121i	$0.365556\pi$
$492$	2.74340	−	1.74356i	0.123682	−	0.0786060i
$493$	−38.1670	−	25.1029i	−1.71896	−	1.13058i
$494$	−21.6690	−	18.1824i	−0.974933	−	0.818066i
$495$	−4.27642	−	2.31779i	−0.192211	−	0.104177i
$496$	30.8906	−	25.9203i	1.38703	−	1.16386i
$497$	−6.00870	+	0.702317i	−0.269527	+	0.0315032i
$498$	42.0657	−	14.5704i	1.88501	−	0.652914i
$499$	−2.21420	+	7.39596i	−0.0991214	+	0.331088i	−0.993138	−	0.116944i	$-0.962690\pi$
$499$	−2.21420	+	7.39596i	−0.0991214	+	0.331088i	0.894017	+	0.448033i	$0.147875\pi$
$500$	8.56378	+	9.07707i	0.382984	+	0.405939i
$501$	−4.62548	−	28.8629i	−0.206651	−	1.28950i
$502$	−13.3317	−	17.9076i	−0.595022	−	0.799253i
$503$	−1.71945	−	9.75150i	−0.0766666	−	0.434798i	−0.998846	−	0.0480347i	$-0.984704\pi$
$503$	−1.71945	−	9.75150i	−0.0766666	−	0.434798i	0.922179	−	0.386763i	$-0.126407\pi$
$504$	2.03711	−	0.670134i	0.0907402	−	0.0298502i
$505$	0.988096	−	5.60377i	0.0439697	−	0.249365i
$506$	−23.2704	+	11.6868i	−1.03450	+	0.519543i
$507$	−6.25105	+	1.37873i	−0.277619	+	0.0612314i
$508$	9.32246	+	1.08964i	0.413617	+	0.0483449i
$509$	−17.5507	+	11.5433i	−0.777920	+	0.511646i	−0.875288	−	0.483602i	$-0.839328\pi$
$509$	−17.5507	+	11.5433i	−0.777920	+	0.511646i	0.0973676	+	0.995248i	$0.468958\pi$
$510$	11.8520	−	1.19789i	0.524815	−	0.0530433i
$511$	0.261916	+	0.874861i	0.0115865	+	0.0387016i
$512$	−14.2477	+	24.6777i	−0.629665	+	1.09061i
$513$	−19.9570	+	15.2109i	−0.881125	+	0.671576i
$514$	−20.0345	−	34.7008i	−0.883686	−	1.53059i
$515$	0.814729	−	0.863563i	0.0359013	−	0.0380531i
$516$	−1.61408	+	21.8299i	−0.0710558	+	0.961008i
$517$	−0.109534	−	1.88063i	−0.00481732	−	0.0827102i
$518$	0.543740	+	1.26053i	0.0238906	+	0.0553845i
$519$	−1.32254	+	1.71971i	−0.0580532	+	0.0754871i
$520$	0.0838761	−	1.44010i	0.00367821	−	0.0631524i
$521$	−20.5557	+	7.48165i	−0.900560	+	0.327777i	−0.750477	−	0.660896i	$-0.770176\pi$
$521$	−20.5557	+	7.48165i	−0.900560	+	0.327777i	−0.150083	+	0.988673i	$0.547954\pi$
$522$	−33.1289	−	47.5316i	−1.45001	−	2.08040i
$523$	28.4317	+	10.3483i	1.24323	+	0.452499i	0.878109	−	0.478461i	$-0.158805\pi$
$523$	28.4317	+	10.3483i	1.24323	+	0.452499i	0.365121	+	0.930960i	$0.381028\pi$
$524$	1.63383	−	3.78765i	0.0713743	−	0.165464i
$525$	4.39608	+	7.89670i	0.191861	+	0.344640i
$526$	−38.6233	+	9.15388i	−1.68405	+	0.399128i
$527$	39.3701	−	9.33089i	1.71499	−	0.406460i
$528$	16.1227	+	0.251968i	0.701650	+	0.0109655i
$529$	8.11314	−	18.8084i	0.352745	−	0.817755i
$530$	10.3356	+	3.76184i	0.448949	+	0.163404i
$531$	1.39691	−	15.5782i	0.0606207	−	0.676037i
$532$	9.12717	−	3.32202i	0.395713	−	0.144028i
$533$	0.197227	−	3.38626i	0.00854286	−	0.146675i
$534$	19.2433	+	2.55462i	0.832738	+	0.110549i
$535$	1.08361	+	2.51209i	0.0468485	+	0.108607i
$536$	0.525129	+	9.01611i	0.0226821	+	0.389437i
$537$	14.6688	+	9.97964i	0.633005	+	0.430653i
$538$	−16.1628	+	17.1316i	−0.696830	+	0.738596i
$539$	−5.73699	−	9.93675i	−0.247110	−	0.428006i
$540$	6.64575	+	1.90807i	0.285987	+	0.0821104i
$541$	−2.75454	+	4.77101i	−0.118427	+	0.205122i	−0.919144	−	0.393921i	$-0.871119\pi$
$541$	−2.75454	+	4.77101i	−0.118427	+	0.205122i	0.800717	+	0.599042i	$0.204452\pi$
$542$	3.88006	+	12.9603i	0.166663	+	0.556693i
$543$	18.2021	+	25.2645i	0.781128	+	1.08420i
$544$	−28.4404	+	18.7055i	−1.21937	+	0.801993i
$545$	6.20154	+	0.724856i	0.265645	+	0.0310494i
$546$	−3.64841	+	11.5277i	−0.156137	+	0.493342i
$547$	−3.56784	+	1.79184i	−0.152550	+	0.0766133i	−0.523436	−	0.852065i	$-0.675350\pi$
$547$	−3.56784	+	1.79184i	−0.152550	+	0.0766133i	0.370887	+	0.928678i	$0.379054\pi$
$548$	3.22081	−	18.2661i	0.137586	−	0.780290i
$549$	0.0308023	+	0.0574236i	0.00131461	+	0.00245078i
$550$	3.00235	+	17.0272i	0.128021	+	0.726041i
$551$	29.0017	+	38.9560i	1.23551	+	1.65958i
$552$	−5.31607	+	4.32097i	−0.226267	+	0.183913i
$553$	−6.48947	−	6.87843i	−0.275960	−	0.292501i
$554$	−16.8456	+	56.2683i	−0.715702	+	2.39061i
$555$	0.154836	−	0.804405i	0.00657244	−	0.0341451i
$556$	23.9457	−	2.79885i	1.01552	−	0.118698i
$557$	4.09443	−	3.43564i	0.173487	−	0.145573i	−0.551910	−	0.833904i	$-0.686101\pi$
$557$	4.09443	−	3.43564i	0.173487	−	0.145573i	0.725397	+	0.688331i	$0.241656\pi$
$558$	50.7572	+	7.54712i	2.14872	+	0.319495i
$559$	17.4979	+	14.6825i	0.740081	+	0.621002i
$560$	3.55418	+	2.33762i	0.150191	+	0.0987824i
$561$	14.3428	+	7.48615i	0.605555	+	0.316066i
$562$	19.2619	−	25.8732i	0.812514	−	1.09140i
$563$	−10.3517	−	5.19881i	−0.436271	−	0.219104i	0.217088	−	0.976152i	$-0.430344\pi$
$563$	−10.3517	−	5.19881i	−0.436271	−	0.219104i	−0.653359	+	0.757049i	$0.726641\pi$
$564$	0.727821	+	2.57699i	0.0306468	+	0.108511i
$565$	4.11190	+	0.974537i	0.172989	+	0.0409991i
$566$	39.1895			1.64726
$567$	9.26573	+	5.40320i	0.389124	+	0.226913i
$568$	−3.04466			−0.127751
$569$	41.6740	+	9.87691i	1.74706	+	0.414062i	0.975129	−	0.221640i	$-0.0711409\pi$
$569$	41.6740	+	9.87691i	1.74706	+	0.414062i	0.771935	+	0.635701i	$0.219289\pi$
$570$	−12.2759	−	3.11281i	−0.514179	−	0.130381i
$571$	28.3056	+	14.2156i	1.18455	+	0.594905i	0.928346	−	0.371717i	$-0.121231\pi$
$571$	28.3056	+	14.2156i	1.18455	+	0.594905i	0.256207	+	0.966622i	$0.417527\pi$
$572$	−6.32150	+	8.49125i	−0.264315	+	0.355037i
$573$	−0.613767	−	14.4157i	−0.0256405	−	0.602223i
$574$	2.12632	+	1.39850i	0.0887509	+	0.0583724i
$575$	−22.1170	−	18.5583i	−0.922341	−	0.773936i
$576$	−15.6860	+	3.20351i	−0.653584	+	0.133480i
$577$	17.4676	−	14.6571i	0.727188	−	0.610183i	−0.202176	−	0.979349i	$-0.564801\pi$
$577$	17.4676	−	14.6571i	0.727188	−	0.610183i	0.929363	+	0.369166i	$0.120357\pi$
$578$	−6.92984	+	0.809983i	−0.288243	+	0.0336908i
$579$	−29.3497	−	25.4194i	−1.21973	−	1.05639i
$580$	3.83805	−	12.8200i	0.159367	−	0.532321i
$581$	10.9464	+	11.6025i	0.454132	+	0.481352i
$582$	−22.5772	−	8.61931i	−0.935857	−	0.357282i
$583$	8.92055	+	11.9824i	0.369451	+	0.496259i
$584$	0.0798104	+	0.452627i	0.00330258	+	0.0187298i
$585$	5.66928	−	4.46277i	0.234396	−	0.184513i
$586$	7.15597	−	40.5835i	0.295610	−	1.67649i
$587$	2.34530	−	1.17785i	0.0968007	−	0.0486152i	−0.399740	−	0.916629i	$-0.630900\pi$
$587$	2.34530	−	1.17785i	0.0968007	−	0.0486152i	0.496541	+	0.868013i	$0.334603\pi$
$588$	11.0058	+	12.0368i	0.453871	+	0.496391i
$589$	−42.7240	−	4.99373i	−1.76041	−	0.205763i
$590$	6.59523	−	4.33775i	0.271521	−	0.178582i
$591$	−14.6030	+	32.4496i	−0.600686	+	1.33480i
$592$	0.778830	+	2.60147i	0.0320097	+	0.106920i
$593$	5.12692	−	8.88008i	0.210537	−	0.364661i	−0.741346	−	0.671124i	$-0.765812\pi$
$593$	5.12692	−	8.88008i	0.210537	−	0.364661i	0.951883	+	0.306462i	$0.0991454\pi$
$594$	13.3663	+	15.5687i	0.548427	+	0.638793i
$595$	2.13417	+	3.69650i	0.0874926	+	0.151542i
$596$	−11.9201	+	12.6346i	−0.488267	+	0.517533i
$597$	38.9850	−	18.8220i	1.59555	−	0.770334i
$598$	−2.24589	−	38.5605i	−0.0918414	−	1.57686i
$599$	2.85396	+	6.61623i	0.116610	+	0.270332i	0.966518	−	0.256599i	$-0.0826020\pi$
$599$	2.85396	+	6.61623i	0.116610	+	0.270332i	−0.849908	+	0.526931i	$0.823343\pi$
$600$	1.73612	+	4.20424i	0.0708770	+	0.171637i
$601$	0.982495	−	16.8688i	0.0400768	−	0.688092i	−0.917112	−	0.398629i	$-0.869486\pi$
$601$	0.982495	−	16.8688i	0.0400768	−	0.688092i	0.957189	−	0.289463i	$-0.0934768\pi$
$602$	−16.1046	+	5.86159i	−0.656374	+	0.238901i
$603$	−32.0104	+	31.8721i	−1.30356	+	1.29793i
$604$	−16.1394	−	5.87428i	−0.656705	−	0.239021i
$605$	−2.11460	+	4.90220i	−0.0859709	+	0.199303i
$606$	−12.3255	+	20.5981i	−0.500687	+	0.836741i
$607$	−10.6268	+	2.51860i	−0.431329	+	0.102227i	−0.440545	−	0.897731i	$-0.645215\pi$
$607$	−10.6268	+	2.51860i	−0.431329	+	0.102227i	0.00921552	+	0.999958i	$0.497067\pi$
$608$	35.2138	−	8.34583i	1.42811	−	0.338468i
$609$	10.6596	−	17.8141i	0.431947	−	0.721864i
$610$	−0.0130262	+	0.0301982i	−0.000527416	+	0.00122269i
$611$	2.62578	+	0.955706i	0.106228	+	0.0386637i
$612$	−22.2014	−	6.00039i	−0.897437	−	0.242551i
$613$	7.35009	−	2.67521i	0.296867	−	0.108051i	−0.189293	−	0.981921i	$-0.560619\pi$
$613$	7.35009	−	2.67521i	0.296867	−	0.108051i	0.486160	+	0.873870i	$0.338397\pi$
$614$	0.906231	−	15.5594i	0.0365725	−	0.627926i
$615$	−0.579640	−	1.40367i	−0.0233733	−	0.0566014i
$616$	0.582231	+	1.34976i	0.0234588	+	0.0543835i
$617$	−0.139965	−	2.40311i	−0.00563479	−	0.0967456i	0.994318	−	0.106449i	$-0.0339482\pi$
$617$	−0.139965	−	2.40311i	−0.00563479	−	0.0967456i	−0.999953	+	0.00970372i	$0.996911\pi$
$618$	−4.51019	+	2.17753i	−0.181426	+	0.0875929i
$619$	−21.7703	+	23.0752i	−0.875023	+	0.927470i	−0.997888	−	0.0649533i	$-0.979310\pi$
$619$	−21.7703	+	23.0752i	−0.875023	+	0.927470i	0.122865	+	0.992423i	$0.460792\pi$
$620$	5.92628	+	10.2646i	0.238005	+	0.412237i
$621$	−33.8090	−	5.56840i	−1.35671	−	0.223452i
$622$	22.4659	−	38.9120i	0.900799	−	1.56023i
$623$	1.99489	+	6.66339i	0.0799234	+	0.266963i
$624$	−9.81543	+	21.8111i	−0.392932	+	0.873143i
$625$	−13.4192	+	8.82593i	−0.536767	+	0.353037i
$626$	6.77351	+	0.791709i	0.270724	+	0.0316431i
$627$	−11.6066	−	12.6940i	−0.463524	−	0.506949i
$628$	−31.0806	+	15.6093i	−1.24025	+	0.622877i
$629$	−0.473140	+	2.68331i	−0.0188653	+	0.106991i
$630$	0.772980	+	5.35796i	0.0307963	+	0.213466i
$631$	−1.13730	−	6.44997i	−0.0452753	−	0.256769i	0.953766	−	0.300551i	$-0.0971705\pi$
$631$	−1.13730	−	6.44997i	−0.0452753	−	0.256769i	−0.999041	+	0.0437817i	$0.986059\pi$
$632$	−2.84206	−	3.81754i	−0.113051	−	0.151854i
$633$	14.5032	+	5.53688i	0.576449	+	0.220071i
$634$	24.6576	+	26.1355i	0.979279	+	1.03797i
$635$	1.25764	−	4.20081i	0.0499079	−	0.166704i
$636$	−16.0512	−	13.9017i	−0.636472	−	0.551239i
$637$	16.9044	−	1.97584i	0.669778	−	0.0782858i
$638$	30.4229	−	25.5278i	1.20445	−	1.01066i
$639$	−10.0991	−	11.3978i	−0.399512	−	0.450890i
$640$	2.86287	+	2.40224i	0.113165	+	0.0949568i
$641$	−30.9563	−	20.3603i	−1.22270	−	0.804182i	−0.236807	−	0.971557i	$-0.576101\pi$
$641$	−30.9563	−	20.3603i	−1.22270	−	0.804182i	−0.985893	+	0.167374i	$0.946471\pi$
$642$	−0.490934	−	11.5307i	−0.0193756	−	0.455079i
$643$	9.63867	−	12.9470i	0.380112	−	0.510579i	−0.570358	−	0.821396i	$-0.693195\pi$
$643$	9.63867	−	12.9470i	0.380112	−	0.510579i	0.950470	+	0.310818i	$0.100603\pi$
$644$	11.8523	+	5.95246i	0.467047	+	0.234560i
$645$	9.91285	+	2.51362i	0.390318	+	0.0989737i
$646$	40.9884	+	9.71443i	1.61267	+	0.382209i
$647$	−9.95741			−0.391466			−0.195733	−	0.980657i	$-0.562709\pi$
$647$	−9.95741			−0.391466			−0.195733	+	0.980657i	$0.562709\pi$
$648$	4.31604	+	3.24232i	0.169550	+	0.127370i
$649$	10.7212			0.420843
$650$	−24.9550	−	5.91443i	−0.978814	−	0.231983i
$651$	4.99752	+	17.6947i	0.195868	+	0.693510i
$652$	28.1742	+	14.1496i	1.10339	+	0.554141i
$653$	−12.0169	+	16.1415i	−0.470258	+	0.631666i	−0.972456	−	0.233086i	$-0.925117\pi$
$653$	−12.0169	+	16.1415i	−0.470258	+	0.631666i	0.502198	+	0.864753i	$0.332525\pi$
$654$	−23.3500	−	12.1874i	−0.913057	−	0.476564i
$655$	−1.61013	−	1.05900i	−0.0629128	−	0.0413784i
$656$	3.85649	+	3.23598i	0.150571	+	0.126344i
$657$	−1.42970	+	1.80013i	−0.0557779	+	0.0702296i
$658$	−1.60605	+	1.34764i	−0.0626104	+	0.0525364i
$659$	8.92846	−	1.04359i	0.347803	−	0.0406524i	0.0596020	−	0.998222i	$-0.481017\pi$
$659$	8.92846	−	1.04359i	0.347803	−	0.0406524i	0.288201	+	0.957570i	$0.406943\pi$
$660$	−0.895835	+	4.65404i	−0.0348703	+	0.181158i
$661$	0.177460	−	0.592757i	0.00690238	−	0.0230556i	−0.954469	−	0.298310i	$-0.903577\pi$
$661$	0.177460	−	0.592757i	0.00690238	−	0.0230556i	0.961371	+	0.275255i	$0.0887622\pi$
$662$	−9.51535	−	10.0857i	−0.369825	−	0.391991i
$663$	−18.6227	+	15.1368i	−0.723247	+	0.587864i
$664$	4.79396	+	6.43940i	0.186042	+	0.249897i
$665$	−0.787980	−	4.46886i	−0.0305566	−	0.173295i
$666$	−1.82051	+	2.93724i	−0.0705433	+	0.113816i
$667$	−11.5159	+	65.3099i	−0.445897	+	2.52881i
$668$	−25.4524	+	12.7827i	−0.984782	+	0.494576i
$669$	3.92971	−	12.4166i	0.151931	−	0.480053i
$670$	−22.6440	−	2.64671i	−0.874815	−	0.102251i
$671$	−0.0373189	+	0.0245450i	−0.00144068	+	0.000947550i
$672$	−9.04258	−	12.5511i	−0.348825	−	0.484169i
$673$	−3.67538	−	12.2766i	−0.141676	−	0.473229i	0.857471	−	0.514532i	$-0.172034\pi$
$673$	−3.67538	−	12.2766i	−0.141676	−	0.473229i	−0.999147	+	0.0413028i	$0.986849\pi$
$674$	19.7299	−	34.1732i	0.759969	−	1.31630i
$675$	−9.98008	+	20.4446i	−0.384134	+	0.786914i
$676$	3.11861	+	5.40159i	0.119946	+	0.207753i
$677$	20.0295	−	21.2301i	0.769797	−	0.815937i	−0.217292	−	0.976107i	$-0.569723\pi$
$677$	20.0295	−	21.2301i	0.769797	−	0.815937i	0.987090	+	0.160169i	$0.0512040\pi$
$678$	−14.7389	−	10.0274i	−0.566046	−	0.385099i
$679$	−0.503487	−	8.64454i	−0.0193221	−	0.331747i
$680$	0.850851	+	1.97249i	0.0326286	+	0.0756417i
$681$	16.5964	+	2.20324i	0.635975	+	0.0844282i
$682$	−2.04523	+	35.1153i	−0.0783160	+	1.34463i
$683$	39.5288	−	14.3873i	1.51253	−	0.550516i	0.553260	−	0.833009i	$-0.313384\pi$
$683$	39.5288	−	14.3873i	1.51253	−	0.550516i	0.959269	+	0.282493i	$0.0911614\pi$
$684$	19.9976	+	14.0671i	0.764629	+	0.537870i
$685$	−8.14283	−	2.96375i	−0.311122	−	0.113239i
$686$	−11.4031	+	26.4354i	−0.435373	+	1.00931i
$687$	13.8515	+	0.216473i	0.528466	+	0.00825897i
$688$	−32.9873	+	7.81814i	−1.25763	+	0.298064i
$689$	−21.5609	+	5.11004i	−0.821407	+	0.194677i
$690$	−8.41155	−	15.1097i	−0.320222	−	0.575216i
$691$	4.98641	−	11.5598i	0.189692	−	0.439756i	−0.796655	−	0.604434i	$-0.793399\pi$
$691$	4.98641	−	11.5598i	0.189692	−	0.439756i	0.986347	+	0.164678i	$0.0526586\pi$
$692$	1.98637	+	0.722979i	0.0755104	+	0.0274835i
$693$	−3.12165	+	6.65674i	−0.118582	+	0.252869i
$694$	23.5219	−	8.56128i	0.892880	−	0.324982i
$695$	0.654908	−	11.2443i	0.0248421	−	0.426522i
$696$	6.36932	−	8.28208i	0.241428	−	0.313931i
$697$	2.00070	+	4.63815i	0.0757820	+	0.175682i
$698$	0.881412	+	15.1333i	0.0333619	+	0.572802i
$699$	2.85323	−	38.5890i	0.107919	−	1.45957i
$700$	6.04320	−	6.40542i	0.228412	−	0.242102i
$701$	−2.24313	−	3.88521i	−0.0847218	−	0.146742i	0.820551	−	0.571574i	$-0.193667\pi$
$701$	−2.24313	−	3.88521i	−0.0847218	−	0.146742i	−0.905273	+	0.424831i	$0.860333\pi$
$702$	−29.0575	+	9.05816i	−1.09671	+	0.341878i
$703$	1.44835	−	2.50862i	0.0546257	−	0.0946145i
$704$	−3.14743	−	10.5131i	−0.118623	−	0.396229i
$705$	1.24470	−	0.125803i	0.0468782	−	0.00473800i
$706$	−22.6205	+	14.8778i	−0.851335	+	0.559932i
$707$	−8.54282	−	0.998513i	−0.321286	−	0.0375529i
$708$	−14.8822	+	3.28240i	−0.559306	+	0.123360i
$709$	3.02909	−	1.52127i	0.113760	−	0.0571323i	−0.391009	−	0.920387i	$-0.627874\pi$
$709$	3.02909	−	1.52127i	0.113760	−	0.0571323i	0.504769	+	0.863254i	$0.331578\pi$
$710$	1.33461	−	7.56894i	0.0500870	−	0.284057i
$711$	4.86411	−	23.3021i	0.182418	−	0.873895i
$712$	0.607877	+	3.44744i	0.0227811	+	0.129198i
$713$	−35.0754	−	47.1144i	−1.31358	−	1.76445i
$714$	−2.84923	−	17.7791i	−0.106630	−	0.665367i
$715$	3.39393	+	3.59735i	0.126926	+	0.134533i
$716$	4.95794	−	16.5607i	0.185287	−	0.618902i
$717$	10.5998	−	3.67146i	0.395855	−	0.137113i
$718$	−5.18205	+	0.605695i	−0.193393	+	0.0226043i
$719$	−14.7252	+	12.3559i	−0.549159	+	0.460799i	−0.874656	−	0.484744i	$-0.838913\pi$
$719$	−14.7252	+	12.3559i	−0.549159	+	0.460799i	0.325497	+	0.945543i	$0.394468\pi$
$720$	0.288275	+	10.7045i	0.0107434	+	0.398932i
$721$	−1.37470	−	1.15351i	−0.0511966	−	0.0429591i
$722$	−6.93187	−	4.55916i	−0.257977	−	0.169674i
$723$	4.08088	−	2.59360i	0.151770	−	0.0964572i
$724$	18.1181	−	24.3368i	0.673354	−	0.904471i
$725$	39.3489	+	19.7618i	1.46138	+	0.733933i
$726$	15.7095	−	16.1383i	0.583035	−	0.598948i
$727$	−25.6289	−	6.07417i	−0.950524	−	0.225278i	−0.274026	−	0.961722i	$-0.588355\pi$
$727$	−25.6289	−	6.07417i	−0.950524	−	0.225278i	−0.676499	+	0.736444i	$0.736503\pi$
$728$	−2.18045			−0.0808128
$729$	2.17846	+	26.9120i	0.0806836	+	0.996740i
$730$	−1.16020			−0.0429411
$731$	−33.0985	−	7.84448i	−1.22419	−	0.290139i
$732$	0.0442879	−	0.0454967i	0.00163693	−	0.00168161i
$733$	13.7743	+	6.91770i	0.508765	+	0.255511i	0.684614	−	0.728906i	$-0.259971\pi$
$733$	13.7743	+	6.91770i	0.508765	+	0.255511i	−0.175849	+	0.984417i	$0.556267\pi$
$734$	31.9105	−	42.8632i	1.17784	−	1.58211i
$735$	6.43094	−	4.08718i	0.237209	−	0.150758i
$736$	41.2871	+	27.1550i	1.52186	+	1.00094i
$737$	−23.7196	−	19.9031i	−0.873722	−	0.733140i
$738$	0.172463	+	6.40405i	0.00634846	+	0.235736i
$739$	−29.4693	+	24.7277i	−1.08405	+	0.909622i	−0.996250	−	0.0865164i	$-0.972427\pi$
$739$	−29.4693	+	24.7277i	−1.08405	+	0.909622i	−0.0877951	+	0.996139i	$0.527982\pi$
$740$	−0.792778	+	0.0926625i	−0.0291431	+	0.00340634i
$741$	24.1082	−	8.35042i	0.885639	−	0.306760i
$742$	4.76817	−	15.9268i	0.175045	−	0.584691i
$743$	6.81015	+	7.21833i	0.249840	+	0.264815i	0.840141	−	0.542368i	$-0.182472\pi$
$743$	6.81015	+	7.21833i	0.249840	+	0.264815i	−0.590301	+	0.807183i	$0.700991\pi$
$744$	1.46430	+	9.13719i	0.0536838	+	0.334986i
$745$	4.84605	+	6.50938i	0.177546	+	0.238485i
$746$	3.61327	+	20.4919i	0.132291	+	0.750260i
$747$	−8.20474	+	39.3057i	−0.300196	+	1.43812i
$748$	2.73744	−	15.5248i	0.100091	−	0.567643i
$749$	3.69546	−	1.85593i	0.135029	−	0.0678142i
$750$	−24.0174	+	5.29725i	−0.876991	+	0.193428i
$751$	1.67463	+	0.195736i	0.0611081	+	0.00714251i	0.146592	−	0.989197i	$-0.453170\pi$
$751$	1.67463	+	0.195736i	0.0611081	+	0.00714251i	−0.0854839	+	0.996340i	$0.527244\pi$
$752$	−3.46494	+	2.27893i	−0.126353	+	0.0831040i
$753$	20.0343	−	2.02487i	0.730090	−	0.0737905i
$754$	16.8952	+	56.4339i	0.615287	+	2.05520i
$755$	−4.01206	+	6.94909i	−0.146014	+	0.252903i
$756$	2.29516	−	10.1960i	0.0834742	−	0.370825i
$757$	−20.2972	−	35.1558i	−0.737716	−	1.27776i	−0.953522	−	0.301325i	$-0.902571\pi$
$757$	−20.2972	−	35.1558i	−0.737716	−	1.27776i	0.215806	−	0.976436i	$-0.430762\pi$
$758$	7.55461	−	8.00742i	0.274396	−	0.290843i
$759$	1.73188	−	23.4232i	0.0628634	−	0.850208i
$760$	−0.132791	−	2.27993i	−0.00481682	−	0.0827016i
$761$	−14.0822	−	32.6463i	−0.510481	−	1.18343i	−0.957377	−	0.288842i	$-0.906730\pi$
$761$	−14.0822	−	32.6463i	−0.510481	−	1.18343i	0.446896	−	0.894586i	$-0.352530\pi$
$762$	−11.2769	+	14.6634i	−0.408518	+	0.531199i
$763$	0.548752	−	9.42170i	0.0198661	−	0.341088i
$764$	−13.2110	+	4.80842i	−0.477958	+	0.173963i
$765$	−4.56187	+	9.72791i	−0.164935	+	0.351713i
$766$	24.7202	+	8.99741i	0.893177	+	0.325090i
$767$	−6.29881	+	14.6023i	−0.227437	+	0.527258i
$768$	−16.6604	−	29.9271i	−0.601179	−	1.07990i
$769$	7.05125	−	1.67118i	0.254275	−	0.0602642i	−0.101502	−	0.994835i	$-0.532365\pi$
$769$	7.05125	−	1.67118i	0.254275	−	0.0602642i	0.355776	+	0.934571i	$0.384217\pi$
$770$	−3.61070	+	0.855751i	−0.130120	+	0.0308391i
$771$	36.1361	+	0.564743i	1.30141	+	0.0203387i
$772$	−14.9845	+	34.7379i	−0.539303	+	1.25025i
$773$	−27.7323	−	10.0937i	−0.997463	−	0.363047i	−0.208857	−	0.977946i	$-0.566974\pi$
$773$	−27.7323	−	10.0937i	−0.997463	−	0.363047i	−0.788606	+	0.614899i	$0.789197\pi$
$774$	−35.2852	−	24.8210i	−1.26830	−	0.892171i
$775$	−36.6475	+	13.3386i	−1.31642	+	0.479137i
$776$	0.253396	−	4.35064i	0.00909638	−	0.156179i
$777$	−1.22744	−	0.162947i	−0.0440342	−	0.00584571i
$778$	10.7806	+	24.9921i	0.386502	+	0.896012i
$779$	−0.312245	−	5.36105i	−0.0111874	−	0.192079i
$780$	−5.81250	−	3.95443i	−0.208121	−	0.141591i
$781$	7.16331	−	7.59266i	0.256323	−	0.271687i
$782$	28.7602	+	49.8141i	1.02846	+	1.78135i
$783$	52.1312	−	3.62763i	1.86302	−	0.129641i
$784$	−12.6299	+	21.8756i	−0.451068	+	0.781273i
$785$	4.66025	+	15.5663i	0.166331	+	0.555586i
$786$	4.75226	+	6.59612i	0.169507	+	0.235276i
$787$	−30.5406	+	20.0868i	−1.08865	+	0.716018i	−0.961207	−	0.275827i	$-0.911048\pi$
$787$	−30.5406	+	20.0868i	−1.08865	+	0.716018i	−0.127446	+	0.991846i	$0.540678\pi$
$788$	34.4376	+	4.02517i	1.22679	+	0.143391i
$789$	10.8027	−	34.1328i	0.384586	−	1.21516i
$790$	10.7361	−	5.39188i	0.381974	−	0.191835i
$791$	1.10917	−	6.29042i	0.0394376	−	0.223662i
$792$	−1.94938	+	3.14517i	−0.0692683	+	0.111759i
$793$	−0.0115051	−	0.0652489i	−0.000408559	−	0.00231706i
$794$	−5.21789	−	7.00884i	−0.185176	−	0.248734i
$795$	−7.69827	+	6.25725i	−0.273030	+	0.221922i
$796$	−28.9466	−	30.6816i	−1.02598	−	1.08748i
$797$	13.8714	−	46.3336i	0.491349	−	1.64122i	−0.248636	−	0.968597i	$-0.579982\pi$
$797$	13.8714	−	46.3336i	0.491349	−	1.64122i	0.739985	−	0.672623i	$-0.234832\pi$
$798$	−3.61827	+	18.7976i	−0.128085	+	0.665428i
$799$	−4.13305	+	0.483084i	−0.146217	+	0.0170903i
$800$	25.1347	−	21.0906i	0.888647	−	0.745664i
$801$	−10.8893	+	13.7107i	−0.384755	+	0.484443i
$802$	−15.6353	−	13.1196i	−0.552102	−	0.463269i
$803$	−1.31652	−	0.865889i	−0.0464590	−	0.0305566i
$804$	39.0189	+	20.3657i	1.37609	+	0.718241i
$805$	3.70023	−	4.97027i	0.130416	−	0.175179i
$806$	−46.6255	−	23.4162i	−1.64231	−	0.824802i
$807$	−5.77395	−	20.4438i	−0.203253	−	0.719655i
$808$	−4.21203	−	0.998270i	−0.148179	−	0.0351190i
$809$	−12.9603			−0.455661			−0.227831	−	0.973701i	$-0.573163\pi$
$809$	−12.9603			−0.455661			−0.227831	+	0.973701i	$0.573163\pi$
$810$	−9.95223	+	9.30832i	−0.349686	+	0.327061i
$811$	16.4612			0.578029			0.289015	−	0.957325i	$-0.406672\pi$
$811$	16.4612			0.578029			0.289015	+	0.957325i	$0.406672\pi$
$812$	−19.6824	−	4.66482i	−0.690718	−	0.163703i
$813$	−11.8279	−	2.99923i	−0.414823	−	0.105187i
$814$	−2.11678	−	1.06309i	−0.0741933	−	0.0372613i
$815$	8.79582	−	11.8148i	0.308104	−	0.413856i
$816$	−1.51511	−	35.5856i	−0.0530393	−	1.24574i
$817$	30.2135	+	19.8717i	1.05704	+	0.695223i
$818$	42.5203	+	35.6788i	1.48669	+	1.24748i
$819$	−7.23249	−	8.16260i	−0.252724	−	0.285224i
$820$	−1.13353	+	0.951143i	−0.0395845	+	0.0332154i
$821$	8.86047	−	1.03564i	0.309232	−	0.0361441i	0.0399386	−	0.999202i	$-0.487284\pi$
$821$	8.86047	−	1.03564i	0.309232	−	0.0361441i	0.269294	+	0.963058i	$0.413210\pi$
$822$	27.6322	+	23.9318i	0.963783	+	0.834718i
$823$	1.23129	−	4.11279i	0.0429200	−	0.143363i	−0.933844	−	0.357681i	$-0.883568\pi$
$823$	1.23129	−	4.11279i	0.0429200	−	0.143363i	0.976764	+	0.214318i	$0.0687528\pi$
$824$	−0.619788	−	0.656937i	−0.0215913	−	0.0228855i
$825$	−14.5691	−	5.56203i	−0.507230	−	0.193645i
$826$	−7.12522	−	9.57083i	−0.247918	−	0.333012i
$827$	−2.12514	−	12.0523i	−0.0738983	−	0.419098i	−0.999205	−	0.0398773i	$-0.987303\pi$
$827$	−2.12514	−	12.0523i	−0.0738983	−	0.419098i	0.925306	−	0.379221i	$-0.123808\pi$
$828$	4.76720	+	33.0442i	0.165672	+	1.14836i
$829$	−1.20691	+	6.84473i	−0.0419177	+	0.237727i	−0.998567	−	0.0535151i	$-0.982957\pi$
$829$	−1.20691	+	6.84473i	−0.0419177	+	0.237727i	0.956649	+	0.291242i	$0.0940686\pi$
$830$	−18.1096	+	9.09498i	−0.628593	+	0.315691i
$831$	−35.7485	−	39.0976i	−1.24010	−	1.35628i
$832$	16.1681	+	1.88978i	0.560527	+	0.0655162i
$833$	−21.1754	+	13.9273i	−0.733683	+	0.482551i
$834$	−19.4990	+	43.3292i	−0.675195	+	1.50037i
$835$	3.81635	+	12.7475i	0.132070	+	0.441145i
$836$	−8.37972	+	14.5141i	−0.289819	+	0.501981i
$837$	−29.3484	+	35.7895i	−1.01443	+	1.23707i
$838$	38.0805	+	65.9574i	1.31547	+	2.27846i
$839$	−4.52340	+	4.79453i	−0.156165	+	0.165526i	−0.800732	−	0.599022i	$-0.795556\pi$
$839$	−4.52340	+	4.79453i	−0.156165	+	0.165526i	0.644567	+	0.764548i	$0.277038\pi$
$840$	−0.879117	+	0.424439i	−0.0303324	+	0.0146445i
$841$	−4.19465	−	72.0194i	−0.144643	−	2.48343i
$842$	28.5389	+	66.1607i	0.983516	+	2.28005i
$843$	11.1045	+	26.8908i	0.382458	+	0.926170i
$844$	0.879512	−	15.1006i	0.0302741	−	0.519786i
$845$	2.73824	−	0.996637i	0.0941983	−	0.0342854i
$846$	−5.09472	−	1.37695i	−0.175160	−	0.0473407i
$847$	7.58318	+	2.76005i	0.260561	+	0.0948365i
$848$	13.0257	−	30.1969i	0.447304	−	1.03697i
$849$	−18.1498	+	30.3317i	−0.622900	+	1.04098i
$850$	37.1621	−	8.80759i	1.27465	−	0.302098i
$851$	3.84885	−	0.912195i	0.131937	−	0.0312696i
$852$	−7.61888	+	12.7326i	−0.261018	+	0.436210i
$853$	−3.29681	+	7.64286i	−0.112880	+	0.261686i	−0.965286	−	0.261195i	$-0.915884\pi$
$853$	−3.29681	+	7.64286i	−0.112880	+	0.261686i	0.852406	+	0.522881i	$0.175143\pi$
$854$	0.0467133	+	0.0170022i	0.00159850	+	0.000581805i
$855$	8.09454	−	8.05956i	0.276827	−	0.275631i
$856$	1.95572	−	0.711823i	0.0668450	−	0.0243296i
$857$	−3.38555	+	58.1276i	−0.115648	+	1.98560i	0.0468929	+	0.998900i	$0.485068\pi$
$857$	−3.38555	+	58.1276i	−0.115648	+	1.98560i	−0.162541	+	0.986702i	$0.551969\pi$
$858$	−7.96316	−	19.2838i	−0.271858	−	0.658337i
$859$	−10.3586	−	24.0139i	−0.353431	−	0.819345i	−0.998475	−	0.0551996i	$-0.982420\pi$
$859$	−10.3586	−	24.0139i	−0.353431	−	0.819345i	0.645045	−	0.764145i	$-0.276839\pi$
$860$	−0.579382	−	9.94760i	−0.0197568	−	0.339210i
$861$	−2.06717	+	0.998030i	−0.0704488	+	0.0340128i
$862$	1.92492	−	2.04029i	0.0655630	−	0.0694927i
$863$	−16.9220	−	29.3098i	−0.576032	−	0.997716i	−0.995929	−	0.0901446i	$-0.971267\pi$
$863$	−16.9220	−	29.3098i	−0.576032	−	0.997716i	0.419897	−	0.907572i	$-0.362066\pi$
$864$	12.9040	−	36.7395i	0.439002	−	1.24990i
$865$	0.493786	−	0.855262i	0.0167892	−	0.0290798i
$866$	−3.38368	−	11.3023i	−0.114982	−	0.384067i
$867$	2.58251	−	5.73865i	0.0877065	−	0.194895i
$868$	14.9683	−	9.84478i	0.508056	−	0.334154i
$869$	16.2067	+	1.89429i	0.549775	+	0.0642595i
$870$	17.7971	+	19.4644i	0.603378	+	0.659904i
$871$	41.0436	−	20.6129i	1.39071	−	0.698440i
$872$	0.824795	−	4.67764i	0.0279311	−	0.158405i
$873$	17.1273	−	13.4824i	0.579671	−	0.456309i
$874$	−10.6188	−	60.2224i	−0.359188	−	2.03705i
$875$	−5.26249	−	7.06875i	−0.177905	−	0.238967i
$876$	2.09257	+	0.798882i	0.0707015	+	0.0269917i
$877$	1.12574	+	1.19322i	0.0380137	+	0.0402921i	0.746101	−	0.665832i	$-0.231923\pi$
$877$	1.12574	+	1.19322i	0.0380137	+	0.0402921i	−0.708088	+	0.706124i	$0.750442\pi$
$878$	−8.69799	+	29.0533i	−0.293543	+	0.980501i
$879$	28.0965	+	24.3339i	0.947670	+	0.820764i
$880$	−7.29057	+	0.852146i	−0.245765	+	0.0287258i
$881$	−33.5691	+	28.1678i	−1.13097	+	0.948998i	−0.999106	−	0.0422700i	$-0.986541\pi$
$881$	−33.5691	+	28.1678i	−1.13097	+	0.948998i	−0.131865	+	0.991268i	$0.542097\pi$
$882$	−31.4942	+	6.43197i	−1.06046	+	0.216576i
$883$	10.9055	+	9.15077i	0.366998	+	0.307948i	0.807573	−	0.589768i	$-0.200781\pi$
$883$	10.9055	+	9.15077i	0.366998	+	0.307948i	−0.440575	+	0.897716i	$0.645225\pi$
$884$	19.5365	+	12.8494i	0.657085	+	0.432172i
$885$	0.302866	+	7.11347i	0.0101807	+	0.239117i
$886$	−21.8144	+	29.3019i	−0.732870	+	0.984415i
$887$	25.7208	+	12.9175i	0.863621	+	0.433727i	0.824737	−	0.565517i	$-0.191323\pi$
$887$	25.7208	+	12.9175i	0.863621	+	0.433727i	0.0388846	+	0.999244i	$0.487620\pi$
$888$	−0.604050	−	0.153170i	−0.0202706	−	0.00514005i
$889$	−6.44946	−	1.52855i	−0.216308	−	0.0512660i
$890$	−8.83671			−0.296207
$891$	−18.2401	+	3.13485i	−0.611068	+	0.105022i
$892$	−12.6898			−0.424885
$893$	4.30462	+	1.02021i	0.144049	+	0.0341402i
$894$	−9.30471	−	32.9451i	−0.311196	−	1.10185i
$895$	−7.21724	−	3.62464i	−0.241246	−	0.121158i
$896$	3.37332	−	4.53115i	0.112695	−	0.151375i
$897$	30.8850	+	16.1202i	1.03122	+	0.538238i
$898$	−30.4151	−	20.0043i	−1.01496	−	0.667552i
$899$	68.6228	+	57.5814i	2.28870	+	1.92045i
$900$	21.9263	+	3.26024i	0.730877	+	0.108675i
$901$	25.2774	−	21.2103i	0.842113	−	0.706617i
$902$	−4.36166	+	0.509804i	−0.145227	+	0.0169746i
$903$	2.92178	−	15.1792i	0.0972308	−	0.505133i
$904$	0.921984	−	3.07964i	0.0306647	−	0.102427i
$905$	−9.72735	−	10.3104i	−0.323348	−	0.342729i
$906$	26.2672	−	21.3503i	0.872669	−	0.709316i
$907$	−11.7394	−	15.7688i	−0.389802	−	0.523595i	0.563297	−	0.826255i	$-0.309533\pi$
$907$	−11.7394	−	15.7688i	−0.389802	−	0.523595i	−0.953099	+	0.302660i	$0.902125\pi$
$908$	−2.83270	−	16.0651i	−0.0940065	−	0.533137i
$909$	−10.2341	−	19.0792i	−0.339445	−	0.632816i
$910$	0.955787	−	5.42054i	0.0316840	−	0.179689i
$911$	36.6050	−	18.3837i	1.21278	−	0.609079i	0.276727	−	0.960948i	$-0.410750\pi$
$911$	36.6050	−	18.3837i	1.21278	−	0.609079i	0.936049	+	0.351869i	$0.114454\pi$
$912$	−11.4257	+	36.1014i	−0.378343	+	1.19544i
$913$	−27.3373	−	3.19528i	−0.904734	−	0.105748i
$914$	61.2914	−	40.3120i	2.02734	−	1.33340i
$915$	−0.0173398	−	0.0240676i	−0.000573236	−	0.000795650i
$916$	−3.87129	−	12.9310i	−0.127911	−	0.427253i
$917$	−1.45649	+	2.52272i	−0.0480977	+	0.0833076i
$918$	32.6150	−	31.4746i	1.07645	−	1.03882i
$919$	10.0461	+	17.4003i	0.331389	+	0.573983i	0.982784	−	0.184756i	$-0.0591494\pi$
$919$	10.0461	+	17.4003i	0.331389	+	0.573983i	−0.651395	+	0.758738i	$0.725816\pi$
$920$	2.14006	−	2.26834i	0.0705558	−	0.0747848i
$921$	11.6229	+	7.90740i	0.382987	+	0.260558i
$922$	0.807273	+	13.8603i	0.0265861	+	0.456466i
$923$	6.13271	+	14.2172i	0.201861	+	0.467965i
$924$	7.10158	+	0.942763i	0.233625	+	0.0310146i
$925$	0.152706	−	2.62186i	0.00502094	−	0.0862062i
$926$	−2.48073	+	0.902913i	−0.0815220	+	0.0296716i
$927$	0.403451	−	4.49925i	0.0132511	−	0.147775i
$928$	−70.8210	−	25.7767i	−2.32481	−	0.846163i
$929$	−15.4707	+	35.8651i	−0.507577	+	1.17669i	0.451171	+	0.892437i	$0.351006\pi$
$929$	−15.4707	+	35.8651i	−0.507577	+	1.17669i	−0.958748	+	0.284257i	$0.908253\pi$
$930$	−23.3567	−	0.365023i	−0.765896	−	0.0119696i
$931$	26.2186	−	6.21391i	0.859279	−	0.203653i
$932$	−36.6863	+	8.69480i	−1.20170	+	0.284808i
$933$	19.7123	+	35.4093i	0.645352	+	1.15925i
$934$	6.60160	−	15.3042i	0.216011	−	0.500769i
$935$	−6.92078	−	2.51896i	−0.226334	−	0.0823787i
$936$	−3.13845	−	4.50289i	−0.102583	−	0.147181i
$937$	6.55624	−	2.38628i	0.214183	−	0.0779563i	−0.232700	−	0.972548i	$-0.574756\pi$
$937$	6.55624	−	2.38628i	0.214183	−	0.0779563i	0.446883	+	0.894592i	$0.352534\pi$
$938$	−2.00369	+	34.4020i	−0.0654227	+	1.12326i
$939$	−3.74977	+	4.87586i	−0.122369	+	0.159118i
$940$	−0.482812	−	1.11928i	−0.0157476	−	0.0365070i
$941$	2.91062	+	49.9733i	0.0948834	+	1.62908i	0.624625	+	0.780925i	$0.285252\pi$
$941$	2.91062	+	49.9733i	0.0948834	+	1.62908i	−0.529741	+	0.848159i	$0.677711\pi$
$942$	5.05442	−	68.3594i	0.164682	−	2.22727i
$943$	5.03217	−	5.33379i	0.163870	−	0.173692i
$944$	−11.8013	−	20.4404i	−0.384099	−	0.665278i
$945$	−4.50491	−	1.88316i	−0.146545	−	0.0612592i
$946$	14.7857	−	25.6097i	0.480726	−	0.832642i
$947$	16.8155	+	56.1677i	0.546431	+	1.82521i	0.564591	+	0.825371i	$0.309034\pi$
$947$	16.8155	+	56.1677i	0.546431	+	1.82521i	−0.0181599	+	0.999835i	$0.505781\pi$
$948$	−23.0766	+	2.33236i	−0.749493	+	0.0757516i
$949$	1.95281	−	1.28439i	0.0633910	−	0.0416929i
$950$	−40.3280	−	4.71367i	−1.30841	−	0.152932i
$951$	−31.6479	+	6.98023i	−1.02625	+	0.226350i
$952$	2.90168	−	1.45728i	0.0940438	−	0.0472306i
$953$	3.77884	−	21.4309i	0.122409	−	0.694214i	−0.860405	−	0.509612i	$-0.829789\pi$
$953$	3.77884	−	21.4309i	0.122409	−	0.694214i	0.982813	−	0.184603i	$-0.0590998\pi$
$954$	39.7538	−	13.0775i	1.28708	−	0.423401i
$955$	1.14055	+	6.46840i	0.0369075	+	0.209313i
$956$	−6.52699	−	8.76727i	−0.211098	−	0.283554i
$957$	5.66817	+	35.3692i	0.183226	+	1.14332i
$958$	2.80044	+	2.96829i	0.0904781	+	0.0959012i
$959$	−3.75658	+	12.5479i	−0.121306	+	0.405191i
$960$	6.88652	−	2.38530i	0.222262	−	0.0769852i
$961$	−48.0145	+	5.61209i	−1.54886	+	0.181035i
$962$	2.69156	−	2.25849i	0.0867795	−	0.0728167i
$963$	9.15181	+	4.96021i	0.294913	+	0.159841i
$964$	−3.60914	−	3.02842i	−0.116242	−	0.0975390i
$965$	14.7671	+	9.71245i	0.475368	+	0.312655i
$966$	−22.0610	+	14.0208i	−0.709800	+	0.451113i
$967$	−19.8809	+	26.7046i	−0.639326	+	0.858763i	−0.997183	−	0.0750131i	$-0.976100\pi$
$967$	−19.8809	+	26.7046i	−0.639326	+	0.858763i	0.357857	+	0.933776i	$0.383508\pi$
$968$	3.62940	+	1.82276i	0.116653	+	0.0585856i
$969$	−26.5016	+	27.2249i	−0.851355	+	0.874591i
$970$	10.7045	+	2.53701i	0.343701	+	0.0814586i
$971$	−49.4538			−1.58705			−0.793524	−	0.608539i	$-0.791756\pi$
$971$	−49.4538			−1.58705			−0.793524	+	0.608539i	$0.791756\pi$
$972$	24.3595	−	9.93592i	0.781332	−	0.318695i
$973$	−17.0250			−0.545797
$974$	−13.4919	−	3.19763i	−0.432308	−	0.102459i
$975$	16.1350	−	16.5754i	0.516733	−	0.530836i
$976$	0.0878747	+	0.0441323i	0.00281280	+	0.00141264i
$977$	−10.8726	+	14.6045i	−0.347846	+	0.467238i	−0.941272	−	0.337651i	$-0.890368\pi$
$977$	−10.8726	+	14.6045i	−0.347846	+	0.467238i	0.593425	+	0.804889i	$0.297775\pi$
$978$	−52.4412	+	33.3290i	−1.67688	+	1.06574i
$979$	−10.0273	−	6.59505i	−0.320474	−	0.210779i
$980$	−5.68753	−	4.77240i	−0.181681	−	0.152449i
$981$	20.2468	−	12.4280i	0.646430	−	0.396795i
$982$	−31.7388	+	26.6320i	−1.01283	+	0.849862i
$983$	−0.175764	+	0.0205439i	−0.00560600	+	0.000655247i	−0.118895	−	0.992907i	$-0.537935\pi$
$983$	−0.175764	+	0.0205439i	−0.00560600	+	0.000655247i	0.113289	+	0.993562i	$0.463861\pi$
$984$	−1.09164	+	0.378115i	−0.0348003	+	0.0120539i
$985$	4.64577	−	15.5179i	0.148026	−	0.494443i
$986$	−60.2006	−	63.8089i	−1.91718	−	2.03209i
$987$	−0.299228	−	1.86717i	−0.00952453	−	0.0594328i
$988$	−14.8451	−	19.9404i	−0.472285	−	0.634389i
$989$	8.57480	+	48.6301i	0.272663	+	1.54635i
$990$	−6.96432	−	6.22479i	−0.221340	−	0.197837i
$991$	8.80351	−	49.9272i	0.279653	−	1.58599i	−0.444131	−	0.895962i	$-0.646487\pi$
$991$	8.80351	−	49.9272i	0.279653	−	1.58599i	0.723783	−	0.690027i	$-0.242401\pi$
$992$	59.6514	−	29.9580i	1.89393	−	0.951169i
$993$	12.2129	−	2.69367i	0.387565	−	0.0854810i
$994$	−11.5387	−	1.34868i	−0.365985	−	0.0427775i
$995$	−16.4647	+	10.8290i	−0.521967	+	0.343303i
$996$	38.9254	−	3.93421i	1.23340	−	0.124660i
$997$	−13.0377	−	43.5489i	−0.412908	−	1.37921i	−0.871427	−	0.490524i	$-0.836805\pi$
$997$	−13.0377	−	43.5489i	−0.412908	−	1.37921i	0.458519	−	0.888684i	$-0.348380\pi$
$998$	−7.41274	+	12.8392i	−0.234646	+	0.406419i
$999$	−1.43022	−	2.76935i	−0.0452502	−	0.0876184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.16.8	✓	144
3.2	odd	2		243.2.g.a.208.1		144
9.2	odd	6		729.2.g.b.379.8		144
9.4	even	3		729.2.g.d.622.1		144
9.5	odd	6		729.2.g.a.622.8		144
9.7	even	3		729.2.g.c.379.1		144
81.5	odd	54		243.2.g.a.118.1		144
81.20	odd	54		6561.2.a.d.1.13		72
81.22	even	27		729.2.g.c.352.1		144
81.32	odd	54		729.2.g.a.109.8		144
81.49	even	27		729.2.g.d.109.1		144
81.59	odd	54		729.2.g.b.352.8		144
81.61	even	27		6561.2.a.c.1.60		72
81.76	even	27	inner	81.2.g.a.76.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.8	✓	144	1.1	even	1	trivial
81.2.g.a.76.8	yes	144	81.76	even	27	inner
243.2.g.a.118.1		144	81.5	odd	54
243.2.g.a.208.1		144	3.2	odd	2
729.2.g.a.109.8		144	81.32	odd	54
729.2.g.a.622.8		144	9.5	odd	6
729.2.g.b.352.8		144	81.59	odd	54
729.2.g.b.379.8		144	9.2	odd	6
729.2.g.c.352.1		144	81.22	even	27
729.2.g.c.379.1		144	9.7	even	3
729.2.g.d.109.1		144	81.49	even	27
729.2.g.d.622.1		144	9.4	even	3
6561.2.a.c.1.60		72	81.61	even	27
6561.2.a.d.1.13		72	81.20	odd	54

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86856 + 0.442858i) q^{2} +(-1.20815 + 1.24112i) q^{3} +(1.50814 + 0.757419i) q^{4} +(0.470835 - 0.632440i) q^{5} +(-2.80714 + 1.78408i) q^{6} +(-0.995721 - 0.654896i) q^{7} +(-0.459476 - 0.385546i) q^{8} +(-0.0807617 - 2.99891i) q^{9} +O(q^{10})\)	\(q+(1.86856 + 0.442858i) q^{2} +(-1.20815 + 1.24112i) q^{3} +(1.50814 + 0.757419i) q^{4} +(0.470835 - 0.632440i) q^{5} +(-2.80714 + 1.78408i) q^{6} +(-0.995721 - 0.654896i) q^{7} +(-0.459476 - 0.385546i) q^{8} +(-0.0807617 - 2.99891i) q^{9} +(1.15987 - 0.973243i) q^{10} +(2.04249 - 0.238733i) q^{11} +(-2.76211 + 0.956716i) q^{12} +(-0.874830 + 2.92214i) q^{13} +(-1.57054 - 1.66468i) q^{14} +(0.216098 + 1.34844i) q^{15} +(-2.70341 - 3.63132i) q^{16} +(-0.788777 - 4.47337i) q^{17} +(1.17718 - 5.63943i) q^{18} +(-0.838570 + 4.75577i) q^{19} +(1.18911 - 0.597193i) q^{20} +(2.01578 - 0.444599i) q^{21} +(3.92225 + 0.458445i) q^{22} +(-5.50938 + 3.62358i) q^{23} +(1.03362 - 0.104469i) q^{24} +(1.25572 + 4.19440i) q^{25} +(-2.92877 + 5.07278i) q^{26} +(3.81958 + 3.52289i) q^{27} +(-1.00566 - 1.74186i) q^{28} +(6.90147 - 7.31513i) q^{29} +(-0.193376 + 2.61535i) q^{30} +(0.517918 + 8.89231i) q^{31} +(-2.96821 - 6.88108i) q^{32} +(-2.17133 + 2.82340i) q^{33} +(0.507189 - 8.70810i) q^{34} +(-0.883002 + 0.321387i) q^{35} +(2.14963 - 4.58396i) q^{36} +(-0.563666 - 0.205158i) q^{37} +(-3.67305 + 8.51509i) q^{38} +(-2.56980 - 4.61614i) q^{39} +(-0.460172 + 0.109063i) q^{40} +(-1.08205 + 0.256451i) q^{41} +(3.96351 + 0.0619425i) q^{42} +(2.96602 - 6.87600i) q^{43} +(3.26119 + 1.18698i) q^{44} +(-1.93466 - 1.36091i) q^{45} +(-11.8994 + 4.33101i) q^{46} +(0.0532653 - 0.914529i) q^{47} +(7.77302 + 1.03190i) q^{48} +(-2.20999 - 5.12333i) q^{49} +(0.488872 + 8.39361i) q^{50} +(6.50496 + 4.42553i) q^{51} +(-3.53265 + 3.74439i) q^{52} +(3.63216 + 6.29109i) q^{53} +(5.57700 + 8.27428i) q^{54} +(0.810691 - 1.40416i) q^{55} +(0.205017 + 0.684805i) q^{56} +(-4.88936 - 6.78643i) q^{57} +(16.1354 - 10.6124i) q^{58} +(5.17832 + 0.605259i) q^{59} +(-0.695430 + 2.19732i) q^{60} +(-0.0194107 + 0.00974841i) q^{61} +(-2.97027 + 16.8452i) q^{62} +(-1.88356 + 3.03897i) q^{63} +(-0.926691 - 5.25553i) q^{64} +(1.43618 + 1.92912i) q^{65} +(-5.30764 + 4.31412i) q^{66} +(-10.3329 - 10.9523i) q^{67} +(2.19863 - 7.34393i) q^{68} +(2.15885 - 11.2156i) q^{69} +(-1.79228 + 0.209487i) q^{70} +(3.88852 - 3.26285i) q^{71} +(-1.11911 + 1.40906i) q^{72} +(-0.586995 - 0.492548i) q^{73} +(-0.962390 - 0.632974i) q^{74} +(-6.72285 - 3.50895i) q^{75} +(-4.86679 + 6.53723i) q^{76} +(-2.19010 - 1.09991i) q^{77} +(-2.75754 - 9.76361i) q^{78} +(7.72089 + 1.82988i) q^{79} -3.56945 q^{80} +(-8.98696 + 0.484394i) q^{81} -2.13546 q^{82} +(-13.0235 - 3.08663i) q^{83} +(3.37684 + 0.856271i) q^{84} +(-3.20053 - 1.60736i) q^{85} +(8.58729 - 11.5347i) q^{86} +(0.740971 + 17.4033i) q^{87} +(-1.03052 - 0.677782i) q^{88} +(-4.47086 - 3.75149i) q^{89} +(-3.01234 - 3.39974i) q^{90} +(2.78478 - 2.33671i) q^{91} +(-11.0535 + 1.29197i) q^{92} +(-11.6621 - 10.1004i) q^{93} +(0.504536 - 1.68527i) q^{94} +(2.61291 + 2.76952i) q^{95} +(12.1263 + 4.62945i) q^{96} +(4.33880 + 5.82802i) q^{97} +(-1.86060 - 10.5520i) q^{98} +(-0.880894 - 6.10597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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