LMFDB - Embedded newform 162.2.g.b.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	162.97
Dual form			162.2.g.b.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.973045 + 0.230616i) q^{2} +(0.538938 - 1.64607i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-0.200298 + 0.269047i) q^{5} +(0.904020 - 1.47741i) q^{6} +(1.19293 + 0.784601i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.41909 - 1.77426i) q^{9} +(-0.256945 + 0.215603i) q^{10} +(-1.81727 + 0.212408i) q^{11} +(1.22037 - 1.22911i) q^{12} +(0.451373 - 1.50769i) q^{13} +(0.979830 + 1.03856i) q^{14} +(0.334922 + 0.474704i) q^{15} +(0.597159 + 0.802123i) q^{16} +(-0.187292 - 1.06218i) q^{17} +(-1.94471 - 2.28431i) q^{18} +(-0.689063 + 3.90787i) q^{19} +(-0.299741 + 0.150535i) q^{20} +(1.93442 - 1.54079i) q^{21} +(-1.81727 - 0.212408i) q^{22} +(-7.14744 + 4.70095i) q^{23} +(1.47092 - 0.914540i) q^{24} +(1.40175 + 4.68217i) q^{25} +(0.786903 - 1.36296i) q^{26} +(-4.22429 + 3.02578i) q^{27} +(0.713911 + 1.23653i) q^{28} +(0.506714 - 0.537085i) q^{29} +(0.216420 + 0.539146i) q^{30} +(-0.386815 - 6.64136i) q^{31} +(0.396080 + 0.918216i) q^{32} +(-0.629755 + 3.10583i) q^{33} +(0.0627133 - 1.07675i) q^{34} +(-0.450035 + 0.163799i) q^{35} +(-1.36549 - 2.67122i) q^{36} +(8.37507 + 3.04828i) q^{37} +(-1.57171 + 3.64362i) q^{38} +(-2.23850 - 1.55554i) q^{39} +(-0.326377 + 0.0773528i) q^{40} +(-3.61087 + 0.855793i) q^{41} +(2.23761 - 1.05315i) q^{42} +(0.214504 - 0.497277i) q^{43} +(-1.71930 - 0.625774i) q^{44} +(0.961897 - 0.295469i) q^{45} +(-8.03889 + 2.92592i) q^{46} +(0.159487 - 2.73829i) q^{47} +(1.64218 - 0.550671i) q^{48} +(-1.96508 - 4.55557i) q^{49} +(0.284183 + 4.87923i) q^{50} +(-1.84937 - 0.264156i) q^{51} +(1.08001 - 1.14475i) q^{52} +(-4.39541 - 7.61307i) q^{53} +(-4.80822 + 1.97003i) q^{54} +(0.306847 - 0.531475i) q^{55} +(0.409504 + 1.36784i) q^{56} +(6.06126 + 3.24034i) q^{57} +(0.616915 - 0.405752i) q^{58} +(-3.28837 - 0.384355i) q^{59} +(0.0862503 + 0.574523i) q^{60} +(12.4356 - 6.24538i) q^{61} +(1.15522 - 6.55155i) q^{62} +(-1.49372 - 4.01458i) q^{63} +(0.173648 + 0.984808i) q^{64} +(0.315230 + 0.423427i) q^{65} +(-1.32903 + 2.87688i) q^{66} +(-2.32028 - 2.45936i) q^{67} +(0.309337 - 1.03326i) q^{68} +(3.88606 + 14.2987i) q^{69} +(-0.475679 + 0.0555989i) q^{70} +(4.50488 - 3.78005i) q^{71} +(-0.712662 - 2.91412i) q^{72} +(-0.351599 - 0.295026i) q^{73} +(7.44634 + 4.89753i) q^{74} +(8.46263 + 0.216019i) q^{75} +(-2.36962 + 3.18295i) q^{76} +(-2.33453 - 1.17244i) q^{77} +(-1.81943 - 2.02985i) q^{78} +(-5.46707 - 1.29572i) q^{79} -0.335418 q^{80} +(2.70402 + 8.58419i) q^{81} -3.71090 q^{82} +(11.1749 + 2.64851i) q^{83} +(2.42017 - 0.508735i) q^{84} +(0.323291 + 0.162363i) q^{85} +(0.323402 - 0.434404i) q^{86} +(-0.610993 - 1.12354i) q^{87} +(-1.52864 - 1.00540i) q^{88} +(11.7468 + 9.85671i) q^{89} +(1.00411 - 0.0656757i) q^{90} +(1.72139 - 1.44442i) q^{91} +(-8.49697 + 0.993153i) q^{92} +(-11.1406 - 2.94255i) q^{93} +(0.786682 - 2.62770i) q^{94} +(-0.913382 - 0.968128i) q^{95} +(1.72491 - 0.157114i) q^{96} +(5.90711 + 7.93463i) q^{97} +(-0.861525 - 4.88595i) q^{98} +(4.77301 + 2.71047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38}+ \cdots - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{27}\right)$

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 $

$2$	0.973045	+	0.230616i	0.688047	+	0.163070i
$2$	0.973045	+	0.230616i	0.688047	+	0.163070i
$3$	0.538938	−	1.64607i	0.311156	−	0.950359i
$3$	0.538938	−	1.64607i	0.311156	−	0.950359i
$4$	0.893633	+	0.448799i	0.446816	+	0.224400i
$5$	−0.200298	+	0.269047i	−0.0895759	+	0.120321i	−0.844652	−	0.535316i	$-0.820193\pi$
$5$	−0.200298	+	0.269047i	−0.0895759	+	0.120321i	0.755076	+	0.655637i	$0.227600\pi$
$6$	0.904020	−	1.47741i	0.369065	−	0.603151i
$7$	1.19293	+	0.784601i	0.450884	+	0.296551i	0.754568	−	0.656222i	$-0.227846\pi$
$7$	1.19293	+	0.784601i	0.450884	+	0.296551i	−0.303684	+	0.952773i	$0.598217\pi$
$8$	0.766044	+	0.642788i	0.270838	+	0.227260i
$9$	−2.41909	−	1.77426i	−0.806364	−	0.591419i
$10$	−0.256945	+	0.215603i	−0.0812532	+	0.0681796i
$11$	−1.81727	+	0.212408i	−0.547927	+	0.0640435i	−0.385553	−	0.922686i	$-0.625989\pi$
$11$	−1.81727	+	0.212408i	−0.547927	+	0.0640435i	−0.162374	+	0.986729i	$0.551915\pi$
$12$	1.22037	−	1.22911i	0.352290	−	0.354813i
$13$	0.451373	−	1.50769i	0.125188	−	0.418158i	−0.872302	−	0.488968i	$-0.837373\pi$
$13$	0.451373	−	1.50769i	0.125188	−	0.418158i	0.997490	+	0.0708104i	$0.0225585\pi$
$14$	0.979830	+	1.03856i	0.261871	+	0.277567i
$15$	0.334922	+	0.474704i	0.0864764	+	0.122568i
$16$	0.597159	+	0.802123i	0.149290	+	0.200531i
$17$	−0.187292	−	1.06218i	−0.0454249	−	0.257618i	0.953635	−	0.300965i	$-0.0973088\pi$
$17$	−0.187292	−	1.06218i	−0.0454249	−	0.257618i	−0.999060	+	0.0433477i	$0.986198\pi$
$18$	−1.94471	−	2.28431i	−0.458373	−	0.538418i
$19$	−0.689063	+	3.90787i	−0.158082	+	0.896527i	0.797832	+	0.602880i	$0.205980\pi$
$19$	−0.689063	+	3.90787i	−0.158082	+	0.896527i	−0.955914	+	0.293647i	$0.905131\pi$
$20$	−0.299741	+	0.150535i	−0.0670241	+	0.0336607i
$21$	1.93442	−	1.54079i	0.422125	−	0.336228i
$22$	−1.81727	−	0.212408i	−0.387443	−	0.0452856i
$23$	−7.14744	+	4.70095i	−1.49034	+	0.980215i	−0.496667	+	0.867941i	$0.665443\pi$
$23$	−7.14744	+	4.70095i	−1.49034	+	0.980215i	−0.993677	+	0.112274i	$0.964187\pi$
$24$	1.47092	−	0.914540i	0.300251	−	0.186680i
$25$	1.40175	+	4.68217i	0.280350	+	0.936434i
$26$	0.786903	−	1.36296i	0.154324	−	0.267298i
$27$	−4.22429	+	3.02578i	−0.812965	+	0.582312i
$28$	0.713911	+	1.23653i	0.134916	+	0.233682i
$29$	0.506714	−	0.537085i	0.0940944	−	0.0997342i	−0.678615	−	0.734494i	$-0.737420\pi$
$29$	0.506714	−	0.537085i	0.0940944	−	0.0997342i	0.772709	+	0.634760i	$0.218901\pi$
$30$	0.216420	+	0.539146i	0.0395126	+	0.0984342i
$31$	−0.386815	−	6.64136i	−0.0694741	−	1.19282i	−0.835307	−	0.549784i	$-0.814710\pi$
$31$	−0.386815	−	6.64136i	−0.0694741	−	1.19282i	0.765833	−	0.643040i	$-0.222327\pi$
$32$	0.396080	+	0.918216i	0.0700177	+	0.162319i
$33$	−0.629755	+	3.10583i	−0.109626	+	0.540655i
$34$	0.0627133	−	1.07675i	0.0107552	−	0.184660i
$35$	−0.450035	+	0.163799i	−0.0760698	+	0.0276871i
$36$	−1.36549	−	2.67122i	−0.227582	−	0.445204i
$37$	8.37507	+	3.04828i	1.37685	+	0.501133i	0.921223	−	0.389036i	$-0.127192\pi$
$37$	8.37507	+	3.04828i	1.37685	+	0.501133i	0.455630	+	0.890169i	$0.349414\pi$
$38$	−1.57171	+	3.64362i	−0.254964	+	0.591074i
$39$	−2.23850	−	1.55554i	−0.358447	−	0.249086i
$40$	−0.326377	+	0.0773528i	−0.0516047	+	0.0122305i
$41$	−3.61087	+	0.855793i	−0.563924	+	0.133652i	−0.502683	−	0.864471i	$-0.667654\pi$
$41$	−3.61087	+	0.855793i	−0.563924	+	0.133652i	−0.0612405	+	0.998123i	$0.519506\pi$
$42$	2.23761	−	1.05315i	0.345271	−	0.162505i
$43$	0.214504	−	0.497277i	0.0327116	−	0.0758340i	−0.901077	−	0.433659i	$-0.857222\pi$
$43$	0.214504	−	0.497277i	0.0327116	−	0.0758340i	0.933789	+	0.357825i	$0.116482\pi$
$44$	−1.71930	−	0.625774i	−0.259194	−	0.0943389i
$45$	0.961897	−	0.295469i	0.143391	−	0.0440459i
$46$	−8.03889	+	2.92592i	−1.18527	+	0.431403i
$47$	0.159487	−	2.73829i	0.0232636	−	0.399421i	−0.966496	−	0.256680i	$-0.917371\pi$
$47$	0.159487	−	2.73829i	0.0232636	−	0.399421i	0.989760	−	0.142741i	$-0.0455916\pi$
$48$	1.64218	−	0.550671i	0.237029	−	0.0794824i
$49$	−1.96508	−	4.55557i	−0.280726	−	0.650796i
$50$	0.284183	+	4.87923i	0.0401895	+	0.690027i
$51$	−1.84937	−	0.264156i	−0.258963	−	0.0369892i
$52$	1.08001	−	1.14475i	0.149771	−	0.158748i
$53$	−4.39541	−	7.61307i	−0.603756	−	1.04574i	−0.992247	−	0.124283i	$-0.960337\pi$
$53$	−4.39541	−	7.61307i	−0.603756	−	1.04574i	0.388491	−	0.921453i	$-0.372997\pi$
$54$	−4.80822	+	1.97003i	−0.654316	+	0.268087i
$55$	0.306847	−	0.531475i	0.0413753	−	0.0716641i
$56$	0.409504	+	1.36784i	0.0547222	+	0.182785i
$57$	6.06126	+	3.24034i	0.802834	+	0.429194i
$58$	0.616915	−	0.405752i	0.0810050	−	0.0532778i
$59$	−3.28837	−	0.384355i	−0.428109	−	0.0500388i	−0.100690	−	0.994918i	$-0.532105\pi$
$59$	−3.28837	−	0.384355i	−0.428109	−	0.0500388i	−0.327419	+	0.944879i	$0.606179\pi$
$60$	0.0862503	+	0.574523i	0.0111349	+	0.0741706i
$61$	12.4356	−	6.24538i	1.59221	−	0.799638i	0.592230	−	0.805769i	$-0.298248\pi$
$61$	12.4356	−	6.24538i	1.59221	−	0.799638i	0.999981	+	0.00613091i	$0.00195154\pi$
$62$	1.15522	−	6.55155i	0.146712	−	0.832048i
$63$	−1.49372	−	4.01458i	−0.188191	−	0.505790i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	0.315230	+	0.423427i	0.0390995	+	0.0525197i
$66$	−1.32903	+	2.87688i	−0.163593	+	0.354119i
$67$	−2.32028	−	2.45936i	−0.283468	−	0.300458i	0.569957	−	0.821675i	$-0.306960\pi$
$67$	−2.32028	−	2.45936i	−0.283468	−	0.300458i	−0.853425	+	0.521216i	$0.825478\pi$
$68$	0.309337	−	1.03326i	0.0375127	−	0.125301i
$69$	3.88606	+	14.2987i	0.467827	+	1.72136i
$70$	−0.475679	+	0.0555989i	−0.0568545	+	0.00664534i
$71$	4.50488	−	3.78005i	0.534631	−	0.448609i	−0.335066	−	0.942195i	$-0.608759\pi$
$71$	4.50488	−	3.78005i	0.534631	−	0.448609i	0.869697	+	0.493586i	$0.164314\pi$
$72$	−0.712662	−	2.91412i	−0.0839880	−	0.343433i
$73$	−0.351599	−	0.295026i	−0.0411515	−	0.0345302i	0.621980	−	0.783033i	$-0.286329\pi$
$73$	−0.351599	−	0.295026i	−0.0411515	−	0.0345302i	−0.663131	+	0.748503i	$0.730773\pi$
$74$	7.44634	+	4.89753i	0.865619	+	0.569327i
$75$	8.46263	+	0.216019i	0.977181	+	0.0249437i
$76$	−2.36962	+	3.18295i	−0.271814	+	0.365109i
$77$	−2.33453	−	1.17244i	−0.266044	−	0.133612i
$78$	−1.81943	−	2.02985i	−0.206010	−	0.229835i
$79$	−5.46707	−	1.29572i	−0.615093	−	0.145780i	−0.0887528	−	0.996054i	$-0.528288\pi$
$79$	−5.46707	−	1.29572i	−0.615093	−	0.145780i	−0.526340	+	0.850274i	$0.676436\pi$
$80$	−0.335418			−0.0375009
$81$	2.70402	+	8.58419i	0.300447	+	0.953799i
$82$	−3.71090			−0.409801
$83$	11.1749	+	2.64851i	1.22661	+	0.290712i	0.792345	−	0.610074i	$-0.208860\pi$
$83$	11.1749	+	2.64851i	1.22661	+	0.290712i	0.434264	+	0.900785i	$0.357008\pi$
$84$	2.42017	−	0.508735i	0.264062	−	0.0555075i
$85$	0.323291	+	0.162363i	0.0350659	+	0.0176107i
$86$	0.323402	−	0.434404i	0.0348734	−	0.0468430i
$87$	−0.610993	−	1.12354i	−0.0655053	−	0.120456i
$88$	−1.52864	−	1.00540i	−0.162954	−	0.107176i
$89$	11.7468	+	9.85671i	1.24516	+	1.04481i	0.997103	+	0.0760626i	$0.0242349\pi$
$89$	11.7468	+	9.85671i	1.24516	+	1.04481i	0.248052	+	0.968747i	$0.420210\pi$
$90$	1.00411	−	0.0656757i	0.105842	−	0.00692283i
$91$	1.72139	−	1.44442i	0.180451	−	0.151416i
$92$	−8.49697	+	0.993153i	−0.885870	+	0.103543i
$93$	−11.1406	−	2.94255i	−1.15523	−	0.305129i
$94$	0.786682	−	2.62770i	0.0811401	−	0.271027i
$95$	−0.913382	−	0.968128i	−0.0937110	−	0.0993278i
$96$	1.72491	−	0.157114i	0.176048	−	0.0160354i
$97$	5.90711	+	7.93463i	0.599776	+	0.805639i	0.993529	−	0.113577i	$-0.0362308\pi$
$97$	5.90711	+	7.93463i	0.599776	+	0.805639i	−0.393753	+	0.919216i	$0.628823\pi$
$98$	−0.861525	−	4.88595i	−0.0870272	−	0.493556i
$99$	4.77301	+	2.71047i	0.479705	+	0.272412i
$100$	−0.848705	+	4.81324i	−0.0848705	+	0.481324i
$101$	14.2258	−	7.14445i	1.41552	−	0.710899i	0.433758	−	0.901030i	$-0.357187\pi$
$101$	14.2258	−	7.14445i	1.41552	−	0.710899i	0.981759	+	0.190131i	$0.0608912\pi$
$102$	−1.73860	−	0.683529i	−0.172147	−	0.0676794i
$103$	−14.4996	−	1.69476i	−1.42869	−	0.166989i	−0.633682	−	0.773594i	$-0.718457\pi$
$103$	−14.4996	−	1.69476i	−1.42869	−	0.166989i	−0.795004	+	0.606604i	$0.792531\pi$
$104$	1.31490	−	0.864821i	0.128936	−	0.0848026i
$105$	0.0270844	+	0.829067i	0.00264317	+	0.0809086i
$106$	−2.52124	−	8.42151i	−0.244884	−	0.817970i
$107$	4.77487	−	8.27032i	0.461604	−	0.799522i	−0.537437	−	0.843304i	$-0.680607\pi$
$107$	4.77487	−	8.27032i	0.461604	−	0.799522i	0.999041	+	0.0437819i	$0.0139407\pi$
$108$	−5.13293	+	0.808078i	−0.493917	+	0.0777574i
$109$	−1.24198	−	2.15116i	−0.118960	−	0.206044i	0.800396	−	0.599472i	$-0.204623\pi$
$109$	−1.24198	−	2.15116i	−0.118960	−	0.206044i	−0.919356	+	0.393427i	$0.871289\pi$
$110$	0.421143	−	0.446385i	0.0401544	−	0.0425612i
$111$	9.53131	−	12.1431i	0.904672	−	1.15257i
$112$	0.0830204	+	1.42541i	0.00784469	+	0.134688i
$113$	−6.44359	−	14.9379i	−0.606162	−	1.40524i	−0.894220	−	0.447628i	$-0.852269\pi$
$113$	−6.44359	−	14.9379i	−0.606162	−	1.40524i	0.288059	−	0.957613i	$-0.406990\pi$
$114$	5.15061	+	4.55082i	0.482399	+	0.426224i
$115$	0.166843	−	2.86459i	0.0155582	−	0.267124i
$116$	0.693859	−	0.252544i	0.0644232	−	0.0234481i
$117$	−3.76694	+	2.84639i	−0.348254	+	0.263149i
$118$	−3.11109	−	1.13235i	−0.286399	−	0.104241i
$119$	0.609965	−	1.41406i	0.0559154	−	0.129626i
$120$	−0.0485687	+	0.578928i	−0.00443370	+	0.0528486i
$121$	−7.44615	+	1.76477i	−0.676922	+	0.160434i
$122$	13.5406	−	3.20919i	1.22591	−	0.290547i
$123$	−0.537341	+	6.40497i	−0.0484504	+	0.577517i
$124$	2.63497	−	6.10854i	0.236627	−	0.548563i
$125$	−3.11644	−	1.13429i	−0.278743	−	0.101454i
$126$	−0.527628	−	4.25084i	−0.0470049	−	0.378695i
$127$	−11.5398	+	4.20016i	−1.02400	+	0.372704i	−0.798792	−	0.601608i	$-0.794527\pi$
$127$	−11.5398	+	4.20016i	−1.02400	+	0.372704i	−0.225204	+	0.974312i	$0.572305\pi$
$128$	−0.0581448	+	0.998308i	−0.00513933	+	0.0882388i
$129$	−0.702948	−	0.621090i	−0.0618911	−	0.0546839i
$130$	0.209084	+	0.484711i	0.0183379	+	0.0425120i
$131$	1.13800	+	19.5386i	0.0994272	+	1.70710i	0.567471	+	0.823393i	$0.307922\pi$
$131$	1.13800	+	19.5386i	0.0994272	+	1.70710i	−0.468044	+	0.883705i	$0.655041\pi$
$132$	−1.95666	+	2.49283i	−0.170306	+	0.216973i
$133$	−3.88812	+	4.12116i	−0.337143	+	0.357350i
$134$	−1.69057	−	2.92816i	−0.146043	−	0.252954i
$135$	0.0320401	−	1.74259i	0.00275757	−	0.149978i
$136$	0.539285	−	0.934069i	0.0462433	−	0.0800958i
$137$	2.31992	+	7.74907i	0.198204	+	0.662048i	0.998083	+	0.0618867i	$0.0197117\pi$
$137$	2.31992	+	7.74907i	0.198204	+	0.662048i	−0.799879	+	0.600161i	$0.795103\pi$
$138$	0.483804	+	14.8095i	0.0411841	+	1.26067i
$139$	6.69415	−	4.40281i	0.567790	−	0.373441i	−0.232918	−	0.972496i	$-0.574827\pi$
$139$	6.69415	−	4.40281i	0.567790	−	0.373441i	0.800708	+	0.599055i	$0.204457\pi$
$140$	−0.475679	−	0.0555989i	−0.0402022	−	0.00469897i
$141$	−4.42147	−	1.73830i	−0.372355	−	0.146391i
$142$	5.25519	−	2.63926i	0.441006	−	0.221481i
$143$	−0.500020	+	2.83575i	−0.0418138	+	0.237138i
$144$	−0.0214086	−	2.99992i	−0.00178405	−	0.249994i
$145$	0.0430073	+	0.243907i	0.00357156	+	0.0202553i
$146$	−0.274084	−	0.368158i	−0.0226833	−	0.0304690i
$147$	−8.55784	+	0.779493i	−0.705839	+	0.0642915i
$148$	6.11617	+	6.48276i	0.502746	+	0.532880i
$149$	3.37979	−	11.2893i	0.276883	−	0.924854i	−0.700549	−	0.713604i	$-0.747062\pi$
$149$	3.37979	−	11.2893i	0.276883	−	0.924854i	0.977432	−	0.211249i	$-0.0677532\pi$
$150$	8.18470	+	2.16181i	0.668278	+	0.176511i
$151$	−24.2301	+	2.83210i	−1.97182	+	0.230473i	−0.999987	−	0.00519443i	$-0.998347\pi$
$151$	−24.2301	+	2.83210i	−1.97182	+	0.230473i	−0.971834	+	0.235667i	$0.924272\pi$
$152$	−3.03978	+	2.55068i	−0.246559	+	0.206888i
$153$	−1.43151	+	2.90183i	−0.115731	+	0.234599i
$154$	−2.00121	−	1.67922i	−0.161262	−	0.135315i
$155$	1.86432	+	1.22618i	0.149745	+	0.0984891i
$156$	−1.30227	−	2.39472i	−0.104265	−	0.191731i
$157$	−4.29248	+	5.76580i	−0.342577	+	0.460161i	−0.939706	−	0.341985i	$-0.888901\pi$
$157$	−4.29248	+	5.76580i	−0.342577	+	0.460161i	0.597128	+	0.802146i	$0.296308\pi$
$158$	−5.02089	−	2.52159i	−0.399441	−	0.200607i
$159$	−14.9005	+	3.13218i	−1.18169	+	0.248398i
$160$	−0.326377	−	0.0773528i	−0.0258024	−	0.00611527i
$161$	−12.2147			−0.962657
$162$	0.651481	+	8.97639i	0.0511852	+	0.705252i
$163$	−10.2780			−0.805036			−0.402518	−	0.915412i	$-0.631865\pi$
$163$	−10.2780			−0.805036			−0.402518	+	0.915412i	$0.631865\pi$
$164$	−3.61087	−	0.855793i	−0.281962	−	0.0668262i
$165$	−0.709474	−	0.791524i	−0.0552325	−	0.0616201i
$166$	10.2629	+	5.15424i	0.796558	+	0.400046i
$167$	1.91777	−	2.57601i	0.148401	−	0.199338i	−0.721706	−	0.692200i	$-0.756642\pi$
$167$	1.91777	−	2.57601i	0.148401	−	0.199338i	0.870108	+	0.492862i	$0.164049\pi$
$168$	2.47225	+	0.0631073i	0.190739	+	0.00486883i
$169$	8.79195	+	5.78256i	0.676304	+	0.444812i
$170$	0.277134	+	0.232543i	0.0212552	+	0.0178352i
$171$	8.60047	−	8.23092i	0.657695	−	0.629434i
$172$	0.414865	−	0.348113i	0.0316332	−	0.0265434i
$173$	−1.38923	+	0.162378i	−0.105621	+	0.0123454i	−0.168739	−	0.985661i	$-0.553970\pi$
$173$	−1.38923	+	0.162378i	−0.105621	+	0.0123454i	0.0631180	+	0.998006i	$0.479896\pi$
$174$	−0.335417	−	1.23416i	−0.0254279	−	0.0935615i
$175$	−2.00145	+	6.68530i	−0.151295	+	0.505361i
$176$	−1.25558	−	1.33083i	−0.0946425	−	0.100315i
$177$	−2.40490	+	5.20574i	−0.180763	+	0.391288i
$178$	9.15702	+	12.3000i	0.686348	+	0.921925i
$179$	4.05626	+	23.0042i	0.303179	+	1.71941i	0.631955	+	0.775005i	$0.282253\pi$
$179$	4.05626	+	23.0042i	0.303179	+	1.71941i	−0.328776	+	0.944408i	$0.606636\pi$
$180$	0.992189	+	0.167658i	0.0739534	+	0.0124965i
$181$	0.464571	−	2.63471i	0.0345313	−	0.195837i	−0.962662	−	0.270706i	$-0.912743\pi$
$181$	0.464571	−	2.63471i	0.0345313	−	0.195837i	0.997193	+	0.0748693i	$0.0238540\pi$
$182$	2.00809	−	1.00850i	0.148850	−	0.0747552i
$183$	−3.57833	−	23.8357i	−0.264518	−	1.76198i
$184$	−8.49697	−	0.993153i	−0.626405	−	0.0732162i
$185$	−2.49764	+	1.64272i	−0.183630	+	0.120775i
$186$	−10.1617	−	5.43244i	−0.745094	−	0.398326i
$187$	0.565976	+	1.89049i	0.0413883	+	0.138246i
$188$	1.37147	−	2.37545i	0.100024	−	0.173248i
$189$	−7.41330	+	0.295155i	−0.539239	+	0.0214694i
$190$	−0.665496	−	1.15267i	−0.0482801	−	0.0836236i
$191$	−5.81306	+	6.16149i	−0.420618	+	0.445829i	−0.902683	−	0.430306i	$-0.858406\pi$
$191$	−5.81306	+	6.16149i	−0.420618	+	0.445829i	0.482065	+	0.876136i	$0.339887\pi$
$192$	1.71465	+	0.244913i	0.123744	+	0.0176751i
$193$	−1.35732	−	23.3043i	−0.0977023	−	1.67748i	−0.590268	−	0.807208i	$-0.700978\pi$
$193$	−1.35732	−	23.3043i	−0.0977023	−	1.67748i	0.492565	−	0.870275i	$-0.336059\pi$
$194$	3.91803	+	9.08302i	0.281298	+	0.652123i
$195$	0.866881	−	0.290690i	0.0620786	−	0.0208167i
$196$	0.288475	−	4.95293i	0.0206054	−	0.353781i
$197$	−13.5359	+	4.92667i	−0.964394	+	0.351011i	−0.775754	−	0.631036i	$-0.782630\pi$
$197$	−13.5359	+	4.92667i	−0.964394	+	0.351011i	−0.188640	+	0.982046i	$0.560408\pi$
$198$	4.01927	+	3.73814i	0.285637	+	0.265658i
$199$	11.2410	+	4.09139i	0.796854	+	0.290031i	0.708182	−	0.706030i	$-0.249515\pi$
$199$	11.2410	+	4.09139i	0.796854	+	0.290031i	0.0886720	+	0.996061i	$0.471738\pi$
$200$	−1.93584	+	4.48778i	−0.136884	+	0.317334i
$201$	−5.29876	+	2.49391i	−0.373746	+	0.175907i
$202$	15.4899	−	3.67118i	1.08987	−	0.258303i
$203$	1.02587	−	0.243136i	0.0720019	−	0.0170648i
$204$	−1.53410	−	1.06605i	−0.107409	−	0.0746386i
$205$	0.493002	−	1.14291i	0.0344328	−	0.0798241i
$206$	−13.7179	−	4.99291i	−0.955771	−	0.347872i
$207$	25.6310	+	1.30938i	1.78148	+	0.0910081i
$208$	1.47889	−	0.538273i	0.102543	−	0.0373226i
$209$	0.422149	−	7.24801i	0.0292006	−	0.501355i
$210$	−0.164842	+	0.812965i	−0.0113752	+	0.0560999i
$211$	7.16250	+	16.6046i	0.493087	+	1.14310i	0.965187	+	0.261560i	$0.0842368\pi$
$211$	7.16250	+	16.6046i	0.493087	+	1.14310i	−0.472100	+	0.881545i	$0.656504\pi$
$212$	−0.511141	−	8.77595i	−0.0351053	−	0.602735i
$213$	−3.79437	−	9.45256i	−0.259986	−	0.647679i
$214$	6.55343	−	6.94623i	0.447983	−	0.474835i
$215$	0.0908259	+	0.157315i	0.00619428	+	0.0107288i
$216$	−5.18093	−	0.397440i	−0.352518	−	0.0270423i
$217$	4.74938	−	8.22616i	0.322409	−	0.558428i
$218$	−0.712405	−	2.37960i	−0.0482502	−	0.161167i
$219$	−0.675124	+	0.419755i	−0.0456206	+	0.0283644i
$220$	0.512734	−	0.337231i	0.0345685	−	0.0227361i
$221$	−1.68598	−	0.197063i	−0.113411	−	0.0132559i
$222$	12.0748	−	9.61773i	0.810407	−	0.645500i
$223$	17.9240	−	9.00179i	1.20028	−	0.602804i	0.267609	−	0.963528i	$-0.413766\pi$
$223$	17.9240	−	9.00179i	1.20028	−	0.602804i	0.932673	+	0.360723i	$0.117470\pi$
$224$	−0.247939	+	1.40613i	−0.0165661	+	0.0939510i
$225$	4.91641	−	13.8137i	0.327761	−	0.920911i
$226$	−2.82498	−	16.0213i	−0.187915	−	1.06572i
$227$	−13.4405	−	18.0537i	−0.892074	−	1.19826i	−0.979369	−	0.202081i	$-0.935229\pi$
$227$	−13.4405	−	18.0537i	−0.892074	−	1.19826i	0.0872944	−	0.996183i	$-0.472178\pi$
$228$	3.96228	+	5.61597i	0.262408	+	0.371926i
$229$	13.0088	+	13.7885i	0.859643	+	0.911168i	0.996845	−	0.0793751i	$-0.0252925\pi$
$229$	13.0088	+	13.7885i	0.859643	+	0.911168i	−0.137202	+	0.990543i	$0.543811\pi$
$230$	0.822965	−	2.74889i	0.0542647	−	0.181257i
$231$	−3.18809	+	3.21092i	−0.209761	+	0.211263i
$232$	0.733397	−	0.0857218i	0.0481499	−	0.00562791i
$233$	−8.74261	+	7.33592i	−0.572748	+	0.480592i	−0.882556	−	0.470207i	$-0.844179\pi$
$233$	−8.74261	+	7.33592i	−0.572748	+	0.480592i	0.309809	+	0.950799i	$0.399735\pi$
$234$	−4.32183	+	1.90095i	−0.282527	+	0.124269i
$235$	0.704784	+	0.591384i	0.0459750	+	0.0385776i
$236$	−2.76610	−	1.81929i	−0.180058	−	0.118426i
$237$	−5.07925	+	8.30087i	−0.329933	+	0.539199i
$238$	0.919627	−	1.23527i	0.0596106	−	0.0800709i
$239$	16.6715	+	8.37276i	1.07839	+	0.541589i	0.897094	−	0.441840i	$-0.145674\pi$
$239$	16.6715	+	8.37276i	1.07839	+	0.541589i	0.181298	+	0.983428i	$0.441970\pi$
$240$	−0.180769	+	0.552122i	−0.0116686	+	0.0356393i
$241$	−20.6101	−	4.88468i	−1.32761	−	0.314650i	−0.495187	−	0.868787i	$-0.664900\pi$
$241$	−20.6101	−	4.88468i	−1.32761	−	0.314650i	−0.832426	+	0.554137i	$0.813048\pi$
$242$	−7.65242			−0.491916
$243$	15.5875	+	0.175337i	0.999937	+	0.0112479i
$244$	13.9157			0.890864
$245$	1.61926	+	0.383772i	0.103451	+	0.0245183i
$246$	−1.99994	+	6.10840i	−0.127512	+	0.389458i
$247$	5.58083	+	2.80280i	0.355100	+	0.178338i
$248$	3.97267	−	5.33622i	0.252265	−	0.338850i
$249$	10.3822	−	16.9674i	0.657947	−	1.07526i
$250$	−2.77085	−	1.82242i	−0.175244	−	0.115260i
$251$	22.5239	+	18.8998i	1.42170	+	1.19294i	0.950424	+	0.310956i	$0.100649\pi$
$251$	22.5239	+	18.8998i	1.42170	+	1.19294i	0.471272	+	0.881988i	$0.343795\pi$
$252$	0.466906	−	4.25794i	0.0294123	−	0.268225i
$253$	11.9903	−	10.0611i	0.753824	−	0.632533i
$254$	−12.1974	+	1.42567i	−0.765333	+	0.0894546i
$255$	0.441495	−	0.444657i	0.0276475	−	0.0278455i
$256$	−0.286803	+	0.957990i	−0.0179252	+	0.0598743i
$257$	4.10527	+	4.35133i	0.256080	+	0.271429i	0.842640	−	0.538477i	$-0.181000\pi$
$257$	4.10527	+	4.35133i	0.256080	+	0.271429i	−0.586561	+	0.809905i	$0.699518\pi$
$258$	−0.540767	−	0.766459i	−0.0336667	−	0.0477177i
$259$	7.59917	+	10.2075i	0.472189	+	0.634260i
$260$	0.0916660	+	0.519864i	0.00568488	+	0.0322406i
$261$	−2.17871	+	0.400218i	−0.134859	+	0.0247729i
$262$	−3.39860	+	19.2744i	−0.209966	+	1.19078i
$263$	−8.90149	+	4.47050i	−0.548890	+	0.275663i	−0.701555	−	0.712615i	$-0.747511\pi$
$263$	−8.90149	+	4.47050i	−0.548890	+	0.275663i	0.152666	+	0.988278i	$0.451214\pi$
$264$	−2.47881	+	1.97440i	−0.152560	+	0.121516i
$265$	2.92866	+	0.342312i	0.179906	+	0.0210280i
$266$	−4.73372	+	3.11342i	−0.290243	+	0.190896i
$267$	22.5556	−	14.0239i	1.38038	−	0.858246i
$268$	−0.969724	−	3.23910i	−0.0592353	−	0.197860i
$269$	6.86285	−	11.8868i	0.418435	−	0.724751i	−0.577347	−	0.816499i	$-0.695912\pi$
$269$	6.86285	−	11.8868i	0.418435	−	0.724751i	0.995782	+	0.0917479i	$0.0292454\pi$
$270$	0.433045	−	1.68823i	0.0263543	−	0.102742i
$271$	−8.39148	−	14.5345i	−0.509746	−	0.882907i	−0.999936	−	0.0112909i	$-0.996406\pi$
$271$	−8.39148	−	14.5345i	−0.509746	−	0.882907i	0.490190	−	0.871616i	$-0.336927\pi$
$272$	0.740160	−	0.784523i	0.0448788	−	0.0475687i
$273$	−1.44989	−	3.61198i	−0.0877514	−	0.218607i
$274$	0.470327	+	8.07521i	0.0284135	+	0.487841i
$275$	−3.54189	−	8.21101i	−0.213584	−	0.495143i
$276$	−2.94454	+	14.5219i	−0.177240	+	0.874113i
$277$	−1.27196	+	21.8387i	−0.0764246	+	1.31216i	0.714236	+	0.699905i	$0.246774\pi$
$277$	−1.27196	+	21.8387i	−0.0764246	+	1.31216i	−0.790661	+	0.612255i	$0.790263\pi$
$278$	7.52906	−	2.74035i	0.451563	−	0.164356i
$279$	−10.8477	+	16.7524i	−0.649438	+	1.00294i
$280$	−0.450035	−	0.163799i	−0.0268947	−	0.00978888i
$281$	0.0406471	−	0.0942307i	0.00242481	−	0.00562133i	−0.916999	−	0.398889i	$-0.869396\pi$
$281$	0.0406471	−	0.0942307i	0.00242481	−	0.00562133i	0.919424	+	0.393267i	$0.128655\pi$
$282$	−3.90141	−	2.71110i	−0.232325	−	0.161444i
$283$	6.64219	−	1.57423i	0.394837	−	0.0935781i	−0.0284010	−	0.999597i	$-0.509042\pi$
$283$	6.64219	−	1.57423i	0.394837	−	0.0935781i	0.423238	+	0.906018i	$0.360893\pi$
$284$	5.72219	−	1.35618i	0.339550	−	0.0804747i
$285$	−2.08586	+	0.981730i	−0.123556	+	0.0581526i
$286$	−1.14051	+	2.64400i	−0.0674398	+	0.156343i
$287$	−4.97897	−	1.81220i	−0.293899	−	0.106971i
$288$	0.670998	−	2.92400i	0.0395390	−	0.172298i
$289$	14.8816	−	5.41647i	0.875389	−	0.318616i
$290$	−0.0144007	+	0.247250i	−0.000845638	+	0.0145190i
$291$	16.2445	−	5.44725i	0.952270	−	0.319323i
$292$	−0.181792	−	0.421442i	−0.0106386	−	0.0246630i
$293$	−0.377499	−	6.48141i	−0.0220537	−	0.378648i	−0.991218	−	0.132234i	$-0.957785\pi$
$293$	−0.377499	−	6.48141i	−0.0220537	−	0.378648i	0.969165	−	0.246414i	$-0.0792522\pi$
$294$	−8.50693	−	1.21509i	−0.496134	−	0.0708656i
$295$	0.762063	−	0.807740i	0.0443690	−	0.0470284i
$296$	4.45628	+	7.71850i	0.259016	+	0.448629i
$297$	7.03397	−	6.39593i	0.408153	−	0.371130i
$298$	5.89217	−	10.2055i	0.341324	−	0.591191i
$299$	3.86141	+	12.8980i	0.223311	+	0.745911i
$300$	7.46554	+	3.99106i	0.431023	+	0.230424i
$301$	0.646052	−	0.424915i	0.0372378	−	0.0244917i
$302$	−24.2301	−	2.83210i	−1.39429	−	0.162969i
$303$	−4.09346	−	27.2670i	−0.235163	−	1.56645i
$304$	−3.54607	+	1.78090i	−0.203381	+	0.102142i
$305$	−0.810519	+	4.59668i	−0.0464102	+	0.263205i
$306$	−2.06213	+	2.49348i	−0.117884	+	0.142543i
$307$	4.36809	+	24.7727i	0.249300	+	1.41385i	0.810290	+	0.586029i	$0.199309\pi$
$307$	4.36809	+	24.7727i	0.249300	+	1.41385i	−0.560990	+	0.827822i	$0.689579\pi$
$308$	−1.56002	−	2.09547i	−0.0888902	−	0.119400i
$309$	−10.6041	+	22.9540i	−0.603244	+	1.30580i
$310$	1.53129	+	1.62307i	0.0869712	+	0.0921841i
$311$	−1.65961	+	5.54348i	−0.0941077	+	0.314342i	−0.992062	−	0.125746i	$-0.959868\pi$
$311$	−1.65961	+	5.54348i	−0.0941077	+	0.314342i	0.897955	+	0.440088i	$0.145053\pi$
$312$	−0.714909	−	2.63050i	−0.0404737	−	0.148922i
$313$	−23.6311	+	2.76208i	−1.33571	+	0.156122i	−0.753785	−	0.657121i	$-0.771774\pi$
$313$	−23.6311	+	2.76208i	−1.33571	+	0.156122i	−0.581924	+	0.813243i	$0.697700\pi$
$314$	−5.50646	+	4.62047i	−0.310748	+	0.260748i
$315$	1.37930	+	0.402232i	0.0777147	+	0.0226632i
$316$	−4.30403	−	3.61151i	−0.242121	−	0.203163i
$317$	−19.3335	−	12.7158i	−1.08588	−	0.714192i	−0.125274	−	0.992122i	$-0.539981\pi$
$317$	−19.3335	−	12.7158i	−1.08588	−	0.714192i	−0.960601	+	0.277930i	$0.910352\pi$
$318$	−15.2212	−	0.388540i	−0.853562	−	0.0217882i
$319$	−0.806754	+	1.08366i	−0.0451695	+	0.0606732i
$320$	−0.299741	−	0.150535i	−0.0167560	−	0.00841519i
$321$	−11.0402	−	12.3170i	−0.616202	−	0.687466i
$322$	−11.8855	−	2.81691i	−0.662353	−	0.156980i
$323$	4.27993			0.238142
$324$	−1.43618	+	8.88467i	−0.0797876	+	0.493593i
$325$	7.69197			0.426674
$326$	−10.0010	−	2.37027i	−0.553902	−	0.131277i
$327$	−4.21031	+	0.885035i	−0.232831	+	0.0489426i
$328$	−3.31618	−	1.66545i	−0.183106	−	0.0919591i
$329$	2.33872	−	3.14145i	0.128938	−	0.173194i
$330$	−0.507812	−	0.933804i	−0.0279541	−	0.0514042i
$331$	−26.4043	−	17.3664i	−1.45131	−	0.954544i	−0.998001	−	0.0631923i	$-0.979872\pi$
$331$	−26.4043	−	17.3664i	−1.45131	−	0.954544i	−0.453312	−	0.891352i	$-0.649758\pi$
$332$	8.79764	+	7.38210i	0.482833	+	0.405145i
$333$	−14.8516	−	22.2336i	−0.813865	−	1.21839i
$334$	2.46014	−	2.06431i	0.134613	−	0.112954i
$335$	1.12643	−	0.131661i	0.0615434	−	0.00719340i
$336$	2.39106	+	0.631547i	0.130443	+	0.0344537i
$337$	−6.45689	+	21.5675i	−0.351729	+	1.17486i	0.580886	+	0.813985i	$0.302706\pi$
$337$	−6.45689	+	21.5675i	−0.351729	+	1.17486i	−0.932615	+	0.360873i	$0.882479\pi$
$338$	7.22141	+	7.65425i	0.392793	+	0.416336i
$339$	−28.0615	+	2.55599i	−1.52409	+	0.138822i
$340$	0.216035	+	0.290186i	0.0117162	+	0.0157375i
$341$	2.11363	+	11.9870i	0.114459	+	0.649131i
$342$	10.2668	−	6.02565i	0.555167	−	0.325830i
$343$	2.96567	−	16.8192i	0.160131	−	0.908150i
$344$	0.483963	−	0.243055i	0.0260935	−	0.0131047i
$345$	−4.62539	−	1.81847i	−0.249023	−	0.0979030i
$346$	−1.38923	−	0.162378i	−0.0746856	−	0.00872950i
$347$	−1.09689	+	0.721434i	−0.0588840	+	0.0387286i	−0.578610	−	0.815605i	$-0.696405\pi$
$347$	−1.09689	+	0.721434i	−0.0588840	+	0.0387286i	0.519726	+	0.854333i	$0.326034\pi$
$348$	−0.0417585	−	1.27825i	−0.00223849	−	0.0685212i
$349$	1.71648	+	5.73344i	0.0918811	+	0.306904i	0.991560	−	0.129648i	$-0.0413847\pi$
$349$	1.71648	+	5.73344i	0.0918811	+	0.306904i	−0.899679	+	0.436552i	$0.856199\pi$
$350$	−3.48923	+	6.04353i	−0.186507	+	0.323040i
$351$	2.65521	+	7.73468i	0.141725	+	0.412847i
$352$	−0.914820	−	1.58451i	−0.0487601	−	0.0844549i
$353$	−6.49188	+	6.88099i	−0.345528	+	0.366238i	−0.876710	−	0.481020i	$-0.840267\pi$
$353$	−6.49188	+	6.88099i	−0.345528	+	0.366238i	0.531182	+	0.847258i	$0.321748\pi$
$354$	−3.54060	+	4.51081i	−0.188181	+	0.239747i
$355$	0.114690	+	1.96916i	0.00608714	+	0.104512i
$356$	6.07361	+	14.0802i	0.321901	+	0.746250i
$357$	−1.99890	−	1.76613i	−0.105793	−	0.0934737i
$358$	−1.35821	+	23.3195i	−0.0717836	+	1.23248i
$359$	3.16686	−	1.15264i	0.167140	−	0.0608341i	−0.257095	−	0.966386i	$-0.582765\pi$
$359$	3.16686	−	1.15264i	0.167140	−	0.0608341i	0.424235	+	0.905552i	$0.360543\pi$
$360$	0.926780	+	0.391953i	0.0488456	+	0.0206578i
$361$	3.05753	+	1.11285i	0.160922	+	0.0585710i
$362$	1.05966	−	2.45656i	0.0556943	−	0.129114i
$363$	−1.10807	+	13.2080i	−0.0581588	+	0.693239i
$364$	2.18654	−	0.518220i	0.114606	−	0.0271621i
$365$	0.149800	−	0.0355033i	0.00784091	−	0.00185833i
$366$	2.01501	−	24.0184i	0.105326	−	1.25546i
$367$	6.15843	−	14.2768i	0.321467	−	0.745245i	−0.678476	−	0.734622i	$-0.737359\pi$
$367$	6.15843	−	14.2768i	0.321467	−	0.745245i	0.999944	−	0.0106228i	$-0.00338139\pi$
$368$	−8.03889	−	2.92592i	−0.419056	−	0.152524i
$369$	10.2534	+	4.33638i	0.533773	+	0.225743i
$370$	−2.80915	+	1.02245i	−0.146041	+	0.0531545i
$371$	0.729818	−	12.5305i	0.0378902	−	0.650550i
$372$	−8.63500	−	7.62946i	−0.447704	−	0.395569i
$373$	−2.86116	−	6.63290i	−0.148145	−	0.343439i	0.827944	−	0.560811i	$-0.189511\pi$
$373$	−2.86116	−	6.63290i	−0.148145	−	0.343439i	−0.976089	+	0.217372i	$0.930251\pi$
$374$	0.114743	+	1.97006i	0.00593320	+	0.101869i
$375$	−3.54669	+	4.51857i	−0.183150	+	0.233338i
$376$	1.88232	−	1.99514i	0.0970730	−	0.102891i
$377$	−0.581041	−	1.00639i	−0.0299251	−	0.0518319i
$378$	−7.28154	−	1.42243i	−0.374522	−	0.0731617i
$379$	−3.45923	+	5.99155i	−0.177688	+	0.307765i	−0.941088	−	0.338161i	$-0.890195\pi$
$379$	−3.45923	+	5.99155i	−0.177688	+	0.307765i	0.763400	+	0.645926i	$0.223529\pi$
$380$	−0.381733	−	1.27508i	−0.0195825	−	0.0654100i
$381$	0.694501	+	21.2590i	0.0355804	+	1.08913i
$382$	−7.07731	+	4.65482i	−0.362106	+	0.238161i
$383$	25.4120	+	2.97024i	1.29849	+	0.151772i	0.737103	−	0.675780i	$-0.236193\pi$
$383$	25.4120	+	2.97024i	1.29849	+	0.151772i	0.561389	+	0.827552i	$0.310267\pi$
$384$	1.61195	+	0.633736i	0.0822594	+	0.0323402i
$385$	0.783042	−	0.393259i	0.0399075	−	0.0200423i
$386$	4.05361	−	22.9892i	0.206324	−	1.17012i
$387$	−1.40120	+	0.822373i	−0.0712271	+	0.0418036i
$388$	1.71773	+	9.74175i	0.0872047	+	0.494562i
$389$	3.53517	+	4.74856i	0.179240	+	0.240761i	0.882659	−	0.470015i	$-0.155751\pi$
$389$	3.53517	+	4.74856i	0.179240	+	0.240761i	−0.703418	+	0.710776i	$0.748344\pi$
$390$	0.910551	−	0.0829378i	0.0461076	−	0.00419972i
$391$	6.33193	+	6.71145i	0.320219	+	0.339413i
$392$	1.42292	−	4.75290i	0.0718685	−	0.240058i
$393$	32.7753	+	8.65688i	1.65329	+	0.436682i
$394$	−14.3072	+	1.67227i	−0.720787	+	0.0842480i
$395$	1.44365	−	1.21137i	0.0726380	−	0.0609505i
$396$	3.04886	+	4.56428i	0.153211	+	0.229364i
$397$	−0.431437	−	0.362019i	−0.0216532	−	0.0181692i	0.631897	−	0.775053i	$-0.282277\pi$
$397$	−0.431437	−	0.362019i	−0.0216532	−	0.0181692i	−0.653550	+	0.756883i	$0.726721\pi$
$398$	9.99447	+	6.57347i	0.500978	+	0.329498i
$399$	4.68827	+	8.62117i	0.234707	+	0.431598i
$400$	−2.91861	+	3.92037i	−0.145930	+	0.196019i
$401$	11.1435	+	5.59649i	0.556481	+	0.279475i	0.704731	−	0.709475i	$-0.251068\pi$
$401$	11.1435	+	5.59649i	0.556481	+	0.279475i	−0.148250	+	0.988950i	$0.547364\pi$
$402$	−5.73107	+	1.20471i	−0.285840	+	0.0600853i
$403$	−10.1877	−	2.41453i	−0.507486	−	0.120276i
$404$	15.9190			0.792001
$405$	−2.85116	−	0.991887i	−0.141675	−	0.0492873i
$406$	1.05429			0.0523235
$407$	−15.8672	−	3.76060i	−0.786509	−	0.186406i
$408$	−1.24690	−	1.39111i	−0.0617309	−	0.0688700i
$409$	−28.2451	−	14.1852i	−1.39663	−	0.701413i	−0.418269	−	0.908323i	$-0.637363\pi$
$409$	−28.2451	−	14.1852i	−1.39663	−	0.701413i	−0.978360	+	0.206910i	$0.933659\pi$
$410$	0.743286	−	0.998406i	0.0367083	−	0.0493078i
$411$	14.0058	+	0.357515i	0.690856	+	0.0176349i
$412$	−12.1967	−	8.02189i	−0.600888	−	0.395210i
$413$	−3.62122	−	3.03856i	−0.178189	−	0.149518i
$414$	24.6382	+	7.18500i	1.21090	+	0.353124i
$415$	−2.95089	+	2.47609i	−0.144853	+	0.121547i
$416$	1.56316	−	0.182708i	0.0766405	−	0.00895799i
$417$	−3.63960	−	13.3919i	−0.178232	−	0.655803i
$418$	2.08228	−	6.95529i	0.101847	−	0.340194i
$419$	5.02234	+	5.32337i	0.245357	+	0.260064i	0.838335	−	0.545155i	$-0.183529\pi$
$419$	5.02234	+	5.32337i	0.245357	+	0.260064i	−0.592978	+	0.805219i	$0.702048\pi$
$420$	−0.347881	+	0.753037i	−0.0169749	+	0.0367444i
$421$	14.7516	+	19.8148i	0.718948	+	0.965715i	0.999982	+	0.00601689i	$0.00191525\pi$
$421$	14.7516	+	19.8148i	0.718948	+	0.965715i	−0.281034	+	0.959698i	$0.590677\pi$
$422$	3.14017	+	17.8088i	0.152861	+	0.866917i
$423$	−5.24425	+	6.34121i	−0.254984	+	0.308320i
$424$	1.52651	−	8.65727i	0.0741339	−	0.420434i
$425$	4.71079	−	2.36585i	0.228507	−	0.114760i
$426$	−1.51218	−	10.0728i	−0.0732654	−	0.488029i
$427$	19.7348	+	2.30667i	0.955036	+	0.111628i
$428$	7.97870	−	5.24767i	0.385665	−	0.253656i
$429$	4.39837	+	2.35136i	0.212355	+	0.113525i
$430$	0.0520983	+	0.174021i	0.00251241	+	0.00839202i
$431$	6.31861	−	10.9442i	0.304357	−	0.527162i	−0.672761	−	0.739860i	$-0.734892\pi$
$431$	6.31861	−	10.9442i	0.304357	−	0.527162i	0.977118	+	0.212698i	$0.0682251\pi$
$432$	−4.94962	−	1.58153i	−0.238139	−	0.0760915i
$433$	−10.2345	−	17.7267i	−0.491840	−	0.851892i	0.508116	−	0.861289i	$-0.330342\pi$
$433$	−10.2345	−	17.7267i	−0.491840	−	0.851892i	−0.999956	+	0.00939678i	$0.997009\pi$
$434$	6.51844	−	6.90914i	0.312895	−	0.331649i
$435$	0.424666	+	0.0606574i	0.0203612	+	0.00290830i
$436$	−0.144429	−	2.47975i	−0.00691689	−	0.118758i
$437$	−13.4456	−	31.1705i	−0.643192	−	1.49109i
$438$	−0.753728	+	0.252746i	−0.0360145	+	0.0120767i
$439$	0.481679	−	8.27010i	0.0229893	−	0.394711i	−0.967112	−	0.254353i	$-0.918138\pi$
$439$	0.481679	−	8.27010i	0.0229893	−	0.394711i	0.990101	−	0.140358i	$-0.0448253\pi$
$440$	0.576684	−	0.209896i	0.0274923	−	0.0100064i
$441$	−3.32904	+	14.5069i	−0.158526	+	0.690805i
$442$	−1.59509	−	0.580566i	−0.0758707	−	0.0276147i
$443$	6.30068	−	14.6066i	0.299354	−	0.693982i	−0.700451	−	0.713700i	$-0.747018\pi$
$443$	6.30068	−	14.6066i	0.299354	−	0.693982i	0.999806	+	0.0197187i	$0.00627708\pi$
$444$	13.9673	−	6.57384i	0.662859	−	0.311981i
$445$	−5.00477	+	1.18615i	−0.237249	+	0.0562290i
$446$	19.5168	−	4.62558i	0.924149	−	0.219027i
$447$	−16.7614	−	11.6476i	−0.792789	−	0.550912i
$448$	−0.565531	+	1.31105i	−0.0267188	+	0.0619412i
$449$	9.09322	+	3.30966i	0.429135	+	0.156192i	0.547552	−	0.836771i	$-0.315560\pi$
$449$	9.09322	+	3.30966i	0.429135	+	0.156192i	−0.118417	+	0.992964i	$0.537782\pi$
$450$	7.96954	−	12.3075i	0.375688	−	0.580182i
$451$	6.38015	−	2.32218i	0.300430	−	0.109347i
$452$	0.945924	−	16.2409i	0.0444925	−	0.763907i
$453$	−8.39670	+	41.4108i	−0.394511	+	1.94565i
$454$	−8.91470	−	20.6666i	−0.418388	−	0.969932i
$455$	0.0438251	+	0.752448i	0.00205455	+	0.0352753i
$456$	2.56035	+	6.37835i	0.119899	+	0.298694i
$457$	1.72634	−	1.82981i	0.0807546	−	0.0855949i	−0.685736	−	0.727850i	$-0.740520\pi$
$457$	1.72634	−	1.82981i	0.0807546	−	0.0855949i	0.766491	+	0.642255i	$0.222001\pi$
$458$	9.47826	+	16.4168i	0.442890	+	0.767108i
$459$	4.00511	+	3.92027i	0.186943	+	0.182983i
$460$	1.43472	−	2.48501i	0.0668942	−	0.115864i
$461$	1.07568	+	3.59300i	0.0500992	+	0.167343i	0.979378	−	0.202036i	$-0.0647557\pi$
$461$	1.07568	+	3.59300i	0.0500992	+	0.167343i	−0.929279	+	0.369379i	$0.879571\pi$
$462$	−3.84264	+	2.38914i	−0.178776	+	0.111153i
$463$	12.8284	−	8.43736i	0.596185	−	0.392117i	−0.215250	−	0.976559i	$-0.569057\pi$
$463$	12.8284	−	8.43736i	0.596185	−	0.392117i	0.811436	+	0.584442i	$0.198686\pi$
$464$	0.733397	+	0.0857218i	0.0340471	+	0.00397953i
$465$	3.02313	−	2.40796i	0.140194	−	0.111666i
$466$	−10.1987	+	5.12200i	−0.472447	+	0.237272i
$467$	3.64148	−	20.6518i	0.168507	−	0.955653i	−0.776867	−	0.629665i	$-0.783192\pi$
$467$	3.64148	−	20.6518i	0.168507	−	0.955653i	0.945374	−	0.325988i	$-0.105697\pi$
$468$	−4.64372	+	0.853026i	−0.214656	+	0.0394311i
$469$	−0.838317	−	4.75433i	−0.0387099	−	0.219535i
$470$	0.549404	+	0.737977i	0.0253421	+	0.0340404i
$471$	7.17753	+	10.1731i	0.330723	+	0.468753i
$472$	−2.27198	−	2.40816i	−0.104576	−	0.110844i
$473$	−0.284186	+	0.949248i	−0.0130669	+	0.0436465i
$474$	−6.85665	+	6.90576i	−0.314936	+	0.317192i
$475$	−19.2632	+	2.25154i	−0.883856	+	0.103308i
$476$	1.17971	−	0.989896i	0.0540720	−	0.0453718i
$477$	−2.87465	+	26.2153i	−0.131621	+	1.20032i
$478$	14.2913	+	11.9918i	0.653667	+	0.548492i
$479$	−19.8082	−	13.0281i	−0.905060	−	0.595268i	0.00939434	−	0.999956i	$-0.497010\pi$
$479$	−19.8082	−	13.0281i	−0.905060	−	0.595268i	−0.914455	+	0.404688i	$0.867380\pi$
$480$	−0.303225	+	0.495551i	−0.0138403	+	0.0226187i
$481$	8.37613	−	11.2511i	0.381919	−	0.513006i
$482$	−18.9281	−	9.50602i	−0.862149	−	0.432988i
$483$	−6.58298	+	20.1063i	−0.299536	+	0.914869i
$484$	−7.44615	−	1.76477i	−0.338461	−	0.0802168i
$485$	−3.31797			−0.150661
$486$	15.1269	+	3.76533i	0.686169	+	0.170799i
$487$	−25.3432			−1.14841			−0.574205	−	0.818712i	$-0.694689\pi$
$487$	−25.3432			−1.14841			−0.574205	+	0.818712i	$0.694689\pi$
$488$	13.5406	+	3.20919i	0.612956	+	0.145273i
$489$	−5.53921	+	16.9183i	−0.250492	+	0.765073i
$490$	1.48711	+	0.746855i	0.0671808	+	0.0337395i
$491$	−13.5834	+	18.2457i	−0.613012	+	0.823418i	−0.994908	−	0.100787i	$-0.967864\pi$
$491$	−13.5834	+	18.2457i	−0.613012	+	0.823418i	0.381896	+	0.924205i	$0.375271\pi$
$492$	−3.35473	+	5.48253i	−0.151243	+	0.247172i
$493$	−0.665387	−	0.437632i	−0.0299675	−	0.0197099i
$494$	4.78403	+	4.01428i	0.215244	+	0.180611i
$495$	−1.68527	+	0.741261i	−0.0757471	+	0.0333172i
$496$	5.09620	−	4.27622i	0.228826	−	0.192008i
$497$	8.33982	−	0.974786i	0.374092	−	0.0437251i
$498$	14.0153	−	14.1157i	0.628041	−	0.632539i
$499$	2.25683	−	7.53835i	0.101030	−	0.337463i	−0.892498	−	0.451051i	$-0.851049\pi$
$499$	2.25683	−	7.53835i	0.101030	−	0.337463i	0.993528	+	0.113588i	$0.0362344\pi$
$500$	−2.27588	−	2.41230i	−0.101781	−	0.107881i
$501$	−3.20674	−	4.54509i	−0.143266	−	0.203060i
$502$	17.5582	+	23.5847i	0.783659	+	1.05264i
$503$	−3.90756	−	22.1609i	−0.174229	−	0.988104i	−0.939029	−	0.343837i	$-0.888273\pi$
$503$	−3.90756	−	22.1609i	−0.174229	−	0.988104i	0.764800	−	0.644268i	$-0.222838\pi$
$504$	1.43627	−	4.03549i	0.0639765	−	0.179755i
$505$	−0.927200	+	5.25841i	−0.0412599	+	0.233996i
$506$	13.9873	−	7.02471i	0.621813	−	0.312286i
$507$	14.2568	−	11.3557i	0.633167	−	0.504326i
$508$	−12.1974	−	1.42567i	−0.541172	−	0.0632540i
$509$	21.4995	−	14.1404i	0.952949	−	0.626764i	0.0250855	−	0.999685i	$-0.492014\pi$
$509$	21.4995	−	14.1404i	0.952949	−	0.626764i	0.927863	+	0.372921i	$0.121644\pi$
$510$	0.532139	−	0.330855i	0.0235635	−	0.0146505i
$511$	−0.187954	−	0.627810i	−0.00831459	−	0.0277727i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−8.91356	−	18.5929i	−0.393543	−	0.820898i
$514$	2.99113	+	5.18078i	0.131933	+	0.228514i
$515$	3.36020	−	3.56161i	0.148068	−	0.156943i
$516$	−0.349432	−	0.870509i	−0.0153829	−	0.0383220i
$517$	0.291805	+	5.01009i	0.0128335	+	0.220344i
$518$	5.04033	+	11.6848i	0.221459	+	0.513401i
$519$	−0.481424	+	2.37429i	−0.0211322	+	0.104220i
$520$	−0.0306937	+	0.526990i	−0.00134601	+	0.0231101i
$521$	−33.5273	+	12.2030i	−1.46886	+	0.534621i	−0.947790	−	0.318894i	$-0.896689\pi$
$521$	−33.5273	+	12.2030i	−1.46886	+	0.534621i	−0.521069	+	0.853515i	$0.674466\pi$
$522$	−2.21228	−	0.113016i	−0.0968290	−	0.00494658i
$523$	−8.63456	−	3.14272i	−0.377563	−	0.137422i	0.146266	−	0.989245i	$-0.453275\pi$
$523$	−8.63456	−	3.14272i	−0.377563	−	0.137422i	−0.523829	+	0.851824i	$0.675497\pi$
$524$	−7.75197	+	17.9711i	−0.338647	+	0.785071i
$525$	9.92582	+	6.89748i	0.433198	+	0.301031i
$526$	−9.69252	+	2.29717i	−0.422614	+	0.100161i
$527$	−6.98190	+	1.65474i	−0.304137	+	0.0720817i
$528$	−2.86732	+	1.34953i	−0.124784	+	0.0587307i
$529$	19.8772	−	46.0805i	0.864225	−	2.00350i
$530$	2.77078	+	1.00848i	0.120355	+	0.0438056i
$531$	7.27293	+	6.76421i	0.315618	+	0.293542i
$532$	−5.32412	+	1.93782i	−0.230830	+	0.0840153i
$533$	−0.339580	+	5.83036i	−0.0147088	+	0.252541i
$534$	25.1817	−	8.44416i	1.08972	−	0.365414i
$535$	1.26871	+	2.94119i	0.0548510	+	0.127159i
$536$	−0.196596	−	3.37543i	−0.00849166	−	0.145796i
$537$	40.0526	+	5.72093i	1.72840	+	0.246876i
$538$	9.41914	−	9.98371i	0.406088	−	0.430428i
$539$	4.53872	+	7.86129i	0.195497	+	0.338610i
$540$	0.810705	−	1.54286i	0.0348872	−	0.0663939i
$541$	0.244094	−	0.422783i	0.0104944	−	0.0181769i	−0.860731	−	0.509061i	$-0.829993\pi$
$541$	0.244094	−	0.422783i	0.0104944	−	0.0181769i	0.871225	+	0.490884i	$0.163326\pi$
$542$	−4.81341	−	16.0779i	−0.206754	−	0.690605i
$543$	−4.08655	−	2.18466i	−0.175371	−	0.0937529i
$544$	0.901132	−	0.592684i	0.0386357	−	0.0254111i
$545$	0.827529	+	0.0967243i	0.0354474	+	0.00414321i
$546$	−0.577829	−	3.84898i	−0.0247288	−	0.164721i
$547$	7.93984	−	3.98754i	0.339483	−	0.170495i	−0.270887	−	0.962611i	$-0.587317\pi$
$547$	7.93984	−	3.98754i	0.339483	−	0.170495i	0.610370	+	0.792116i	$0.291021\pi$
$548$	−1.40462	+	7.96600i	−0.0600024	+	0.340291i
$549$	−41.1637	−	6.95576i	−1.75682	−	0.296864i
$550$	−1.55282	−	8.80650i	−0.0662126	−	0.375510i
$551$	1.74970	+	2.35026i	0.0745398	+	0.100124i
$552$	−6.21413	+	13.4514i	−0.264491	+	0.572528i
$553$	−5.50519	−	5.83516i	−0.234105	−	0.248136i
$554$	−6.27402	+	20.9567i	−0.266558	+	0.890365i
$555$	1.35796	+	4.99661i	0.0576424	+	0.212094i
$556$	7.95808	−	0.930167i	0.337498	−	0.0394479i
$557$	15.8660	−	13.3132i	0.672266	−	0.564098i	−0.241469	−	0.970409i	$-0.577629\pi$
$557$	15.8660	−	13.3132i	0.672266	−	0.564098i	0.913735	+	0.406310i	$0.133185\pi$
$558$	−14.4187	+	13.7992i	−0.610393	+	0.584165i
$559$	−0.652918	−	0.547863i	−0.0276155	−	0.0231721i
$560$	−0.400130	−	0.263169i	−0.0169086	−	0.0111209i
$561$	3.41691	+	0.0872208i	0.144262	+	0.00368246i
$562$	0.0612826	−	0.0823168i	0.00258505	−	0.00347232i
$563$	−1.34368	−	0.674820i	−0.0566292	−	0.0284403i	0.420259	−	0.907404i	$-0.361939\pi$
$563$	−1.34368	−	0.674820i	−0.0566292	−	0.0284403i	−0.476888	+	0.878964i	$0.658235\pi$
$564$	−3.17102	−	3.53775i	−0.133524	−	0.148966i
$565$	5.30963	+	1.25841i	0.223378	+	0.0529415i
$566$	6.82619			0.286926
$567$	−3.50946	+	12.3619i	−0.147384	+	0.519150i
$568$	5.88071			0.246749
$569$	7.68165	+	1.82058i	0.322031	+	0.0763228i	0.388452	−	0.921469i	$-0.373010\pi$
$569$	7.68165	+	1.82058i	0.322031	+	0.0763228i	−0.0664209	+	0.997792i	$0.521158\pi$
$570$	−2.25604	+	0.474234i	−0.0944951	+	0.0198635i
$571$	19.8206	+	9.95427i	0.829466	+	0.416573i	0.812272	−	0.583279i	$-0.198230\pi$
$571$	19.8206	+	9.95427i	0.829466	+	0.416573i	0.0171938	+	0.999852i	$0.494527\pi$
$572$	−1.71952	+	2.30971i	−0.0718966	+	0.0965740i
$573$	7.00936	+	12.8894i	0.292820	+	0.538461i
$574$	−4.42684	−	2.91158i	−0.184773	−	0.121527i
$575$	−32.0295	−	26.8760i	−1.33572	−	1.12081i
$576$	1.32723	−	2.69044i	0.0553013	−	0.112102i
$577$	−10.3120	+	8.65284i	−0.429296	+	0.360222i	−0.831686	−	0.555246i	$-0.812624\pi$
$577$	−10.3120	+	8.65284i	−0.429296	+	0.360222i	0.402390	+	0.915468i	$0.368180\pi$
$578$	15.7296	−	1.83853i	0.654265	−	0.0764726i
$579$	−39.0921	−	10.3253i	−1.62461	−	0.429106i
$580$	−0.0710324	+	0.237265i	−0.00294946	+	0.00985188i
$581$	11.2529	+	11.9273i	0.466848	+	0.494830i
$582$	17.0629	−	1.55418i	0.707279	−	0.0644226i
$583$	9.60472	+	12.9014i	0.397787	+	0.534320i
$584$	−0.0797010	−	0.452007i	−0.00329805	−	0.0187042i
$585$	−0.0113013	−	1.58361i	−0.000467250	−	0.0654742i
$586$	1.12739	−	6.39376i	0.0465722	−	0.264124i
$587$	−34.3886	+	17.2706i	−1.41937	+	0.712834i	−0.982426	−	0.186655i	$-0.940235\pi$
$587$	−34.3886	+	17.2706i	−1.41937	+	0.712834i	−0.436944	+	0.899489i	$0.643939\pi$
$588$	−7.99740	−	3.14417i	−0.329807	−	0.129663i
$589$	26.2201	+	3.06469i	1.08038	+	0.126278i
$590$	0.927799	−	0.610223i	0.0381969	−	0.0251225i
$591$	0.814631	+	24.9362i	0.0335094	+	1.02574i
$592$	2.55615	+	8.53814i	0.105057	+	0.350915i
$593$	−10.8094	+	18.7224i	−0.443889	+	0.768839i	−0.997974	−	0.0636215i	$-0.979735\pi$
$593$	−10.8094	+	18.7224i	−0.443889	+	0.768839i	0.554085	+	0.832460i	$0.313068\pi$
$594$	8.31937	−	4.60138i	0.341348	−	0.188797i
$595$	0.258273	+	0.447342i	0.0105882	+	0.0183392i
$596$	8.08691	−	8.57162i	0.331253	−	0.351107i
$597$	12.7929	−	16.2985i	0.523580	−	0.667053i
$598$	0.782840	+	13.4408i	0.0320127	+	0.549637i
$599$	−5.99771	−	13.9043i	−0.245060	−	0.568113i	0.750644	−	0.660707i	$-0.229743\pi$
$599$	−5.99771	−	13.9043i	−0.245060	−	0.568113i	−0.995704	+	0.0925942i	$0.970484\pi$
$600$	6.34390	+	5.60516i	0.258989	+	0.228830i
$601$	−0.474864	+	8.15310i	−0.0193701	+	0.332572i	0.974677	+	0.223618i	$0.0717870\pi$
$601$	−0.474864	+	8.15310i	−0.0193701	+	0.332572i	−0.994047	+	0.108953i	$0.965250\pi$
$602$	0.726629	−	0.264471i	0.0296152	−	0.0107791i
$603$	1.24945	+	10.0662i	0.0508815	+	0.409927i
$604$	−22.9239	−	8.34361i	−0.932759	−	0.339497i
$605$	1.01664	−	2.35684i	0.0413324	−	0.0958192i
$606$	2.30508	−	27.4760i	0.0936376	−	1.11614i
$607$	−10.7643	+	2.55119i	−0.436910	+	0.103550i	−0.443184	−	0.896431i	$-0.646151\pi$
$607$	−10.7643	+	2.55119i	−0.436910	+	0.103550i	0.00627358	+	0.999980i	$0.498003\pi$
$608$	−3.86119	+	0.915119i	−0.156592	+	0.0371130i
$609$	0.152662	−	1.81969i	0.00618616	−	0.0737375i
$610$	−1.84874	+	4.28586i	−0.0748533	+	0.173529i
$611$	−4.05651	−	1.47645i	−0.164109	−	0.0597307i
$612$	−2.58158	+	1.95070i	−0.104354	+	0.0788526i
$613$	0.219698	−	0.0799637i	0.00887354	−	0.00322970i	−0.337580	−	0.941297i	$-0.609608\pi$
$613$	0.219698	−	0.0799637i	0.00887354	−	0.00322970i	0.346453	+	0.938067i	$0.387386\pi$
$614$	−1.46262	+	25.1123i	−0.0590267	+	1.01345i
$615$	−1.61561	−	1.42747i	−0.0651476	−	0.0575612i
$616$	−1.03472	−	2.39875i	−0.0416900	−	0.0966483i
$617$	−0.766033	−	13.1523i	−0.0308393	−	0.529490i	−0.977983	−	0.208682i	$-0.933083\pi$
$617$	−0.766033	−	13.1523i	−0.0308393	−	0.529490i	0.947144	−	0.320808i	$-0.103954\pi$
$618$	−15.6118	+	19.8898i	−0.627997	+	0.800083i
$619$	17.6742	−	18.7336i	0.710387	−	0.752966i	−0.267168	−	0.963650i	$-0.586088\pi$
$619$	17.6742	−	18.7336i	0.710387	−	0.752966i	0.977554	+	0.210684i	$0.0675692\pi$
$620$	1.11570	+	1.93246i	0.0448078	+	0.0776094i
$621$	15.9688	−	41.4848i	0.640808	−	1.66473i
$622$	−2.89329	+	5.01132i	−0.116010	+	0.200936i
$623$	6.27946	+	20.9749i	0.251581	+	0.840340i
$624$	−0.0890042	−	2.72446i	−0.00356302	−	0.109066i
$625$	−19.4878	+	12.8173i	−0.779513	+	0.512694i
$626$	−23.6311	−	2.76208i	−0.944489	−	0.110395i
$627$	−11.7032	−	4.60111i	−0.467382	−	0.183751i
$628$	−6.42359	+	3.22605i	−0.256329	+	0.128733i
$629$	1.66925	−	9.46678i	0.0665573	−	0.377465i
$630$	1.24936	+	0.709478i	0.0497756	+	0.0282663i
$631$	3.27051	+	18.5480i	0.130197	+	0.738384i	0.978085	+	0.208208i	$0.0667631\pi$
$631$	3.27051	+	18.5480i	0.130197	+	0.738384i	−0.847888	+	0.530176i	$0.822126\pi$
$632$	−3.35515	−	4.50674i	−0.133461	−	0.179269i
$633$	31.1924	−	2.84117i	1.23979	−	0.112926i
$634$	−15.8799	−	16.8317i	−0.630670	−	0.668471i
$635$	1.18137	−	3.94604i	0.0468811	−	0.156594i
$636$	−14.7213	−	3.88831i	−0.583737	−	0.154182i
$637$	−7.75537	+	0.906473i	−0.307279	+	0.0359158i
$638$	−1.03492	+	0.868398i	−0.0409727	+	0.0343802i
$639$	−17.6045	+	1.15146i	−0.696423	+	0.0455509i
$640$	−0.256945	−	0.215603i	−0.0101567	−	0.00852244i
$641$	24.2963	+	15.9799i	0.959647	+	0.631170i	0.929675	−	0.368381i	$-0.120088\pi$
$641$	24.2963	+	15.9799i	0.959647	+	0.631170i	0.0299718	+	0.999551i	$0.490458\pi$
$642$	−7.90209	−	14.5310i	−0.311871	−	0.573493i
$643$	6.67538	−	8.96660i	0.263251	−	0.353608i	−0.650769	−	0.759276i	$-0.725553\pi$
$643$	6.67538	−	8.96660i	0.263251	−	0.353608i	0.914021	+	0.405667i	$0.132961\pi$
$644$	−10.9155	−	5.48197i	−0.430131	−	0.216020i
$645$	0.307901	−	0.0647228i	0.0121236	−	0.00254846i
$646$	4.16457	+	0.987020i	0.163853	+	0.0388338i
$647$	3.31266			0.130234			0.0651171	−	0.997878i	$-0.479258\pi$
$647$	3.31266			0.130234			0.0651171	+	0.997878i	$0.479258\pi$
$648$	−3.44641	+	8.31398i	−0.135388	+	0.326604i
$649$	6.05749			0.237777
$650$	7.48463	+	1.77389i	0.293571	+	0.0695777i
$651$	−10.9812	−	12.2512i	−0.430388	−	0.480162i
$652$	−9.18477	−	4.61276i	−0.359703	−	0.180650i
$653$	−8.08803	+	10.8641i	−0.316509	+	0.425145i	−0.931698	−	0.363234i	$-0.881672\pi$
$653$	−8.08803	+	10.8641i	−0.316509	+	0.425145i	0.615189	+	0.788380i	$0.289080\pi$
$654$	−4.30093	−	0.109786i	−0.168180	−	0.00429299i
$655$	−5.48474	−	3.60737i	−0.214307	−	0.140952i
$656$	−2.84272	−	2.38532i	−0.110989	−	0.0931312i
$657$	0.327097	+	1.33752i	0.0127613	+	0.0521817i
$658$	3.00015	−	2.51743i	0.116958	−	0.0981395i
$659$	0.691079	−	0.0807755i	0.0269206	−	0.00314657i	−0.102622	−	0.994720i	$-0.532723\pi$
$659$	0.691079	−	0.0807755i	0.0269206	−	0.00314657i	0.129543	+	0.991574i	$0.458649\pi$
$660$	−0.278774	−	1.02574i	−0.0108512	−	0.0399270i
$661$	−2.95037	+	9.85494i	−0.114756	+	0.383313i	−0.996000	−	0.0893488i	$-0.971521\pi$
$661$	−2.95037	+	9.85494i	−0.114756	+	0.383313i	0.881244	+	0.472661i	$0.156707\pi$
$662$	−21.6876	−	22.9876i	−0.842914	−	0.893437i
$663$	−1.23302	+	2.66904i	−0.0478865	+	0.103657i
$664$	6.85807	+	9.21199i	0.266145	+	0.357495i
$665$	−0.330004	−	1.87155i	−0.0127970	−	0.0725755i
$666$	−9.32389	−	25.0593i	−0.361293	−	0.971028i
$667$	−1.09690	+	6.22082i	−0.0424721	+	0.240871i
$668$	2.86989	−	1.44131i	0.111039	−	0.0557661i
$669$	−5.15764	−	34.3556i	−0.199406	−	1.32826i
$670$	1.12643	+	0.131661i	0.0435178	+	0.00508650i
$671$	−21.2722	+	13.9909i	−0.821204	+	0.540114i
$672$	2.18096	+	1.16594i	0.0841325	+	0.0449771i
$673$	6.88644	+	23.0023i	0.265453	+	0.886674i	0.981959	+	0.189093i	$0.0605549\pi$
$673$	6.88644	+	23.0023i	0.265453	+	0.886674i	−0.716506	+	0.697581i	$0.754260\pi$
$674$	−11.2567	+	19.4971i	−0.433590	+	0.751001i
$675$	−20.0886	−	15.5375i	−0.773211	−	0.598037i
$676$	5.26157	+	9.11330i	0.202368	+	0.350512i
$677$	−25.9626	+	27.5188i	−0.997824	+	1.05763i	0.000513791		1.00000i	$0.499836\pi$
$677$	−25.9626	+	27.5188i	−0.997824	+	1.05763i	−0.998338	+	0.0576319i	$0.981645\pi$
$678$	−27.8946	−	3.98434i	−1.07129	−	0.153018i
$679$	0.821241	+	14.1002i	0.0315163	+	0.541114i
$680$	0.143291	+	0.332185i	0.00549494	+	0.0127387i
$681$	−36.9612	+	12.3941i	−1.41635	+	0.474944i
$682$	−0.707733	+	12.1513i	−0.0271005	+	0.465297i
$683$	0.451102	−	0.164188i	0.0172610	−	0.00628247i	−0.333375	−	0.942794i	$-0.608188\pi$
$683$	0.451102	−	0.164188i	0.0172610	−	0.00628247i	0.350636	+	0.936512i	$0.385965\pi$
$684$	11.3797	−	3.49554i	0.435114	−	0.133655i
$685$	−2.54954	−	0.927956i	−0.0974128	−	0.0354554i
$686$	6.76450	−	15.6819i	0.258270	−	0.598737i
$687$	29.7077	−	13.9822i	1.13342	−	0.533454i
$688$	0.526970	−	0.124894i	0.0200906	−	0.00476155i
$689$	−13.4621	+	3.19058i	−0.512866	+	0.121551i
$690$	−4.08134	−	2.83614i	−0.155374	−	0.107970i
$691$	16.1573	−	37.4568i	0.614651	−	1.42492i	−0.271915	−	0.962321i	$-0.587657\pi$
$691$	16.1573	−	37.4568i	0.614651	−	1.42492i	0.886567	−	0.462601i	$-0.153084\pi$
$692$	−1.31434	−	0.478380i	−0.0499637	−	0.0181853i
$693$	3.56722	+	6.97830i	0.135507	+	0.265084i
$694$	−1.23369	+	0.449028i	−0.0468304	+	0.0170449i
$695$	−0.156262	+	2.68291i	−0.00592735	+	0.101769i
$696$	0.254151	−	1.25342i	0.00963357	−	0.0475108i
$697$	1.58530	+	3.67513i	0.0600474	+	0.139205i
$698$	0.347989	+	5.97474i	0.0131716	+	0.226147i
$699$	7.36372	+	18.3446i	0.278521	+	0.693855i
$700$	−4.78892	+	5.07595i	−0.181004	+	0.191853i
$701$	−19.2164	−	33.2838i	−0.725794	−	1.25711i	−0.958646	−	0.284600i	$-0.908139\pi$
$701$	−19.2164	−	33.2838i	−0.725794	−	1.25711i	0.232852	−	0.972512i	$-0.425194\pi$
$702$	0.799899	+	8.13852i	0.0301902	+	0.307169i
$703$	−17.6832	+	30.6282i	−0.666935	+	1.15517i
$704$	−0.524747	−	1.75278i	−0.0197771	−	0.0660602i
$705$	1.35329	−	0.841405i	0.0509680	−	0.0316891i
$706$	−7.90375	+	5.19838i	−0.297462	+	0.195644i
$707$	22.5758	+	2.63874i	0.849052	+	0.0992399i
$708$	−4.48543	+	3.57270i	−0.168573	+	0.134270i
$709$	34.9401	−	17.5476i	1.31220	−	0.659013i	0.351395	−	0.936227i	$-0.385708\pi$
$709$	34.9401	−	17.5476i	1.31220	−	0.659013i	0.960808	+	0.277214i	$0.0894112\pi$
$710$	−0.342520	+	1.94253i	−0.0128546	+	0.0729018i
$711$	10.9264	+	12.8345i	0.409772	+	0.481330i
$712$	2.66278	+	15.1014i	0.0997918	+	0.565947i
$713$	33.9854	+	45.6504i	1.27276	+	1.70962i
$714$	−1.53773	−	2.17951i	−0.0575479	−	0.0815660i
$715$	−0.662797	−	0.702524i	−0.0247872	−	0.0262729i
$716$	−6.69945	+	22.3777i	−0.250370	+	0.836295i
$717$	22.7671	−	22.9301i	0.850251	−	0.856341i
$718$	3.34731	−	0.391245i	0.124921	−	0.0146011i
$719$	3.81176	−	3.19844i	0.142155	−	0.119282i	−0.568937	−	0.822381i	$-0.692645\pi$
$719$	3.81176	−	3.19844i	0.142155	−	0.119282i	0.711092	+	0.703099i	$0.248201\pi$
$720$	0.811408	+	0.595118i	0.0302394	+	0.0221788i
$721$	−15.9672	−	13.3981i	−0.594651	−	0.498971i
$722$	2.71847	+	1.78797i	0.101171	+	0.0665412i
$723$	−19.1481	+	31.2931i	−0.712124	+	1.16380i
$724$	1.59761	−	2.14597i	0.0593748	−	0.0797543i
$725$	3.22501	+	1.61966i	0.119774	+	0.0601527i
$726$	−4.12418	+	12.5964i	−0.153062	+	0.467497i
$727$	47.7675	+	11.3211i	1.77160	+	0.419877i	0.981244	−	0.192772i	$-0.0617477\pi$
$727$	47.7675	+	11.3211i	1.77160	+	0.419877i	0.790356	+	0.612648i	$0.209896\pi$
$728$	2.24711			0.0832836
$729$	8.68929	−	25.5636i	0.321826	−	0.946799i
$730$	0.153950			0.00569795
$731$	−0.568374	−	0.134707i	−0.0210221	−	0.00498233i
$732$	7.49972	−	22.9063i	0.277198	−	0.846641i
$733$	−14.4424	−	7.25327i	−0.533444	−	0.267906i	0.161621	−	0.986853i	$-0.448328\pi$
$733$	−14.4424	−	7.25327i	−0.533444	−	0.267906i	−0.695065	+	0.718947i	$0.744624\pi$
$734$	9.28489	−	12.4718i	0.342712	−	0.460342i
$735$	1.50440	−	2.45859i	0.0554905	−	0.0906865i
$736$	−7.14744	−	4.70095i	−0.263458	−	0.173279i
$737$	4.73897	+	3.97647i	0.174562	+	0.146475i
$738$	8.97701	+	6.58410i	0.330448	+	0.242364i
$739$	−37.5031	+	31.4688i	−1.37957	+	1.15760i	−0.410203	+	0.911994i	$0.634542\pi$
$739$	−37.5031	+	31.4688i	−1.37957	+	1.15760i	−0.969370	+	0.245605i	$0.921013\pi$
$740$	−2.96922	+	0.347052i	−0.109151	+	0.0127579i
$741$	7.62132	−	7.67590i	0.279976	−	0.281981i
$742$	3.59987	−	12.0244i	0.132156	−	0.441430i
$743$	−5.73432	−	6.07802i	−0.210372	−	0.222981i	0.613592	−	0.789623i	$-0.289724\pi$
$743$	−5.73432	−	6.07802i	−0.210372	−	0.222981i	−0.823964	+	0.566642i	$0.808242\pi$
$744$	−6.64277	−	9.41518i	−0.243536	−	0.345177i
$745$	2.36038	+	3.17054i	0.0864776	+	0.116160i
$746$	−1.25438	−	7.11394i	−0.0459261	−	0.260460i
$747$	−22.3341	−	26.2342i	−0.817161	−	0.959860i
$748$	−0.342676	+	1.94341i	−0.0125295	+	0.0710583i
$749$	12.1850	−	6.11952i	0.445229	−	0.223603i
$750$	−4.49314	+	3.57884i	−0.164066	+	0.130681i
$751$	20.4496	+	2.39022i	0.746218	+	0.0872203i	0.480699	−	0.876885i	$-0.340383\pi$
$751$	20.4496	+	2.39022i	0.746218	+	0.0872203i	0.265518	+	0.964106i	$0.414457\pi$
$752$	2.29169	−	1.50727i	0.0835692	−	0.0549644i
$753$	43.2494	−	26.8901i	1.57609	−	0.979930i
$754$	−0.333289	−	1.11326i	−0.0121377	−	0.0405426i
$755$	4.09128	−	7.08630i	0.148897	−	0.257897i
$756$	−6.75724	−	3.06332i	−0.245758	−	0.111412i
$757$	17.5794	+	30.4484i	0.638934	+	1.10667i	0.985667	+	0.168702i	$0.0539576\pi$
$757$	17.5794	+	30.4484i	0.638934	+	1.10667i	−0.346733	+	0.937964i	$0.612709\pi$
$758$	−4.74773	+	5.03230i	−0.172445	+	0.182781i
$759$	−10.0992	−	25.1592i	−0.366577	−	0.913219i
$760$	−0.0773903	−	1.32874i	−0.00280724	−	0.0481985i
$761$	16.7463	+	38.8223i	0.607053	+	1.40731i	0.893436	+	0.449191i	$0.148288\pi$
$761$	16.7463	+	38.8223i	0.607053	+	1.40731i	−0.286383	+	0.958115i	$0.592453\pi$
$762$	−4.22688	+	20.8461i	−0.153124	+	0.755176i
$763$	0.206219	−	3.54064i	0.00746562	−	0.128180i
$764$	−7.96001	+	2.89721i	−0.287983	+	0.104817i
$765$	−0.493998	−	0.966373i	−0.0178605	−	0.0349393i
$766$	24.0420	+	8.75058i	0.868674	+	0.316171i
$767$	−2.06377	+	4.78435i	−0.0745184	+	0.172753i
$768$	1.42235	+	0.988395i	0.0513246	+	0.0356656i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.973045 + 0.230616i) q^{2} +(0.538938 - 1.64607i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-0.200298 + 0.269047i) q^{5} +(0.904020 - 1.47741i) q^{6} +(1.19293 + 0.784601i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.41909 - 1.77426i) q^{9} +(-0.256945 + 0.215603i) q^{10} +(-1.81727 + 0.212408i) q^{11} +(1.22037 - 1.22911i) q^{12} +(0.451373 - 1.50769i) q^{13} +(0.979830 + 1.03856i) q^{14} +(0.334922 + 0.474704i) q^{15} +(0.597159 + 0.802123i) q^{16} +(-0.187292 - 1.06218i) q^{17} +(-1.94471 - 2.28431i) q^{18} +(-0.689063 + 3.90787i) q^{19} +(-0.299741 + 0.150535i) q^{20} +(1.93442 - 1.54079i) q^{21} +(-1.81727 - 0.212408i) q^{22} +(-7.14744 + 4.70095i) q^{23} +(1.47092 - 0.914540i) q^{24} +(1.40175 + 4.68217i) q^{25} +(0.786903 - 1.36296i) q^{26} +(-4.22429 + 3.02578i) q^{27} +(0.713911 + 1.23653i) q^{28} +(0.506714 - 0.537085i) q^{29} +(0.216420 + 0.539146i) q^{30} +(-0.386815 - 6.64136i) q^{31} +(0.396080 + 0.918216i) q^{32} +(-0.629755 + 3.10583i) q^{33} +(0.0627133 - 1.07675i) q^{34} +(-0.450035 + 0.163799i) q^{35} +(-1.36549 - 2.67122i) q^{36} +(8.37507 + 3.04828i) q^{37} +(-1.57171 + 3.64362i) q^{38} +(-2.23850 - 1.55554i) q^{39} +(-0.326377 + 0.0773528i) q^{40} +(-3.61087 + 0.855793i) q^{41} +(2.23761 - 1.05315i) q^{42} +(0.214504 - 0.497277i) q^{43} +(-1.71930 - 0.625774i) q^{44} +(0.961897 - 0.295469i) q^{45} +(-8.03889 + 2.92592i) q^{46} +(0.159487 - 2.73829i) q^{47} +(1.64218 - 0.550671i) q^{48} +(-1.96508 - 4.55557i) q^{49} +(0.284183 + 4.87923i) q^{50} +(-1.84937 - 0.264156i) q^{51} +(1.08001 - 1.14475i) q^{52} +(-4.39541 - 7.61307i) q^{53} +(-4.80822 + 1.97003i) q^{54} +(0.306847 - 0.531475i) q^{55} +(0.409504 + 1.36784i) q^{56} +(6.06126 + 3.24034i) q^{57} +(0.616915 - 0.405752i) q^{58} +(-3.28837 - 0.384355i) q^{59} +(0.0862503 + 0.574523i) q^{60} +(12.4356 - 6.24538i) q^{61} +(1.15522 - 6.55155i) q^{62} +(-1.49372 - 4.01458i) q^{63} +(0.173648 + 0.984808i) q^{64} +(0.315230 + 0.423427i) q^{65} +(-1.32903 + 2.87688i) q^{66} +(-2.32028 - 2.45936i) q^{67} +(0.309337 - 1.03326i) q^{68} +(3.88606 + 14.2987i) q^{69} +(-0.475679 + 0.0555989i) q^{70} +(4.50488 - 3.78005i) q^{71} +(-0.712662 - 2.91412i) q^{72} +(-0.351599 - 0.295026i) q^{73} +(7.44634 + 4.89753i) q^{74} +(8.46263 + 0.216019i) q^{75} +(-2.36962 + 3.18295i) q^{76} +(-2.33453 - 1.17244i) q^{77} +(-1.81943 - 2.02985i) q^{78} +(-5.46707 - 1.29572i) q^{79} -0.335418 q^{80} +(2.70402 + 8.58419i) q^{81} -3.71090 q^{82} +(11.1749 + 2.64851i) q^{83} +(2.42017 - 0.508735i) q^{84} +(0.323291 + 0.162363i) q^{85} +(0.323402 - 0.434404i) q^{86} +(-0.610993 - 1.12354i) q^{87} +(-1.52864 - 1.00540i) q^{88} +(11.7468 + 9.85671i) q^{89} +(1.00411 - 0.0656757i) q^{90} +(1.72139 - 1.44442i) q^{91} +(-8.49697 + 0.993153i) q^{92} +(-11.1406 - 2.94255i) q^{93} +(0.786682 - 2.62770i) q^{94} +(-0.913382 - 0.968128i) q^{95} +(1.72491 - 0.157114i) q^{96} +(5.90711 + 7.93463i) q^{97} +(-0.861525 - 4.88595i) q^{98} +(4.77301 + 2.71047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38}+ \cdots - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more