LMFDB - Embedded newform 162.2.g.a.43.4

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:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			43.4
Character	$\chi$	$=$	162.43
Dual form			162.2.g.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.286803 + 0.957990i) q^{2} +(1.38972 + 1.03377i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.266390 + 0.617563i) q^{5} +(-0.591767 + 1.62782i) q^{6} +(0.0791338 - 1.35867i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(0.862631 + 2.87330i) q^{9} +O(q^{10})$	\(q+(0.286803 + 0.957990i) q^{2} +(1.38972 + 1.03377i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.266390 + 0.617563i) q^{5} +(-0.591767 + 1.62782i) q^{6} +(0.0791338 - 1.35867i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(0.862631 + 2.87330i) q^{9} +(-0.515217 + 0.432318i) q^{10} +(0.692281 + 0.929895i) q^{11} +(-1.72916 - 0.100042i) q^{12} +(-3.16403 - 3.35368i) q^{13} +(1.32429 - 0.313863i) q^{14} +(-0.268211 + 1.13362i) q^{15} +(0.396080 - 0.918216i) q^{16} +(-0.129844 - 0.736381i) q^{17} +(-2.50519 + 1.65046i) q^{18} +(0.362214 - 2.05422i) q^{19} +(-0.561922 - 0.369582i) q^{20} +(1.51453 - 1.80637i) q^{21} +(-0.692281 + 0.929895i) q^{22} +(0.116279 + 1.99643i) q^{23} +(-0.400090 - 1.68521i) q^{24} +(3.12079 - 3.30784i) q^{25} +(2.30533 - 3.99296i) q^{26} +(-1.77153 + 4.88484i) q^{27} +(0.680488 + 1.17864i) q^{28} +(6.48811 + 1.53771i) q^{29} +(-1.16292 + 0.0681835i) q^{30} +(-8.39222 - 4.21473i) q^{31} +(0.993238 + 0.116093i) q^{32} +(0.000775914 + 2.00795i) q^{33} +(0.668205 - 0.335585i) q^{34} +(0.860147 - 0.313068i) q^{35} +(-2.29962 - 1.92659i) q^{36} +(-1.25876 - 0.458152i) q^{37} +(2.07180 - 0.242159i) q^{38} +(-0.930173 - 7.93155i) q^{39} +(0.192895 - 0.644313i) q^{40} +(0.361029 - 1.20592i) q^{41} +(2.16485 + 0.932835i) q^{42} +(2.55885 - 0.299087i) q^{43} +(-1.08938 - 0.396501i) q^{44} +(-1.54465 + 1.29815i) q^{45} +(-1.87921 + 0.683975i) q^{46} +(2.53181 - 1.27152i) q^{47} +(1.49967 - 0.866605i) q^{48} +(5.11293 + 0.597616i) q^{49} +(4.06393 + 2.04098i) q^{50} +(0.580804 - 1.15759i) q^{51} +(4.48639 + 1.06329i) q^{52} +(-5.67138 - 9.82312i) q^{53} +(-5.18771 - 0.296116i) q^{54} +(-0.389851 + 0.675242i) q^{55} +(-0.933959 + 0.989939i) q^{56} +(2.62697 - 2.48034i) q^{57} +(0.387700 + 6.65656i) q^{58} +(-8.55645 + 11.4933i) q^{59} +(-0.398850 - 1.09451i) q^{60} +(-4.68953 - 3.08435i) q^{61} +(1.63075 - 9.24846i) q^{62} +(3.97215 - 0.944659i) q^{63} +(0.173648 + 0.984808i) q^{64} +(1.22824 - 2.84738i) q^{65} +(-1.92337 + 0.576630i) q^{66} +(-12.5297 + 2.96960i) q^{67} +(0.513131 + 0.543887i) q^{68} +(-1.90226 + 2.89468i) q^{69} +(0.546609 + 0.734223i) q^{70} +(-10.2441 + 8.59582i) q^{71} +(1.18611 - 2.75557i) q^{72} +(8.73007 + 7.32539i) q^{73} +(0.0778877 - 1.33728i) q^{74} +(7.75657 - 1.37078i) q^{75} +(0.826186 + 1.91532i) q^{76} +(1.31821 - 0.866998i) q^{77} +(7.33157 - 3.16589i) q^{78} +(3.95975 + 13.2265i) q^{79} +0.672568 q^{80} +(-7.51174 + 4.95720i) q^{81} +1.25880 q^{82} +(1.89914 + 6.34357i) q^{83} +(-0.272759 + 2.34145i) q^{84} +(0.420172 - 0.276351i) q^{85} +(1.02041 + 2.36558i) q^{86} +(7.42699 + 8.84420i) q^{87} +(0.0674068 - 1.15733i) q^{88} +(0.867446 + 0.727874i) q^{89} +(-1.68662 - 1.10744i) q^{90} +(-4.80694 + 4.03350i) q^{91} +(-1.19420 - 1.60409i) q^{92} +(-7.30574 - 14.5329i) q^{93} +(1.94424 + 2.06077i) q^{94} +(1.36510 - 0.323535i) q^{95} +(1.26031 + 1.18812i) q^{96} +(0.566782 - 1.31395i) q^{97} +(0.893896 + 5.06954i) q^{98} +(-2.07469 + 2.79129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{27}\right)$

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 $

$2$	0.286803	+	0.957990i	0.202801	+	0.677401i
$2$	0.286803	+	0.957990i	0.202801	+	0.677401i
$3$	1.38972	+	1.03377i	0.802354	+	0.596849i
$3$	1.38972	+	1.03377i	0.802354	+	0.596849i
$4$	−0.835488	+	0.549509i	−0.417744	+	0.274754i
$5$	0.266390	+	0.617563i	0.119133	+	0.276182i	0.967340	−	0.253484i	$-0.0815765\pi$
$5$	0.266390	+	0.617563i	0.119133	+	0.276182i	−0.848206	+	0.529666i	$0.822317\pi$
$6$	−0.591767	+	1.62782i	−0.241588	+	0.664556i
$7$	0.0791338	−	1.35867i	0.0299098	−	0.513531i	−0.949768	−	0.312954i	$-0.898681\pi$
$7$	0.0791338	−	1.35867i	0.0299098	−	0.513531i	0.979678	−	0.200577i	$-0.0642816\pi$
$8$	−0.766044	−	0.642788i	−0.270838	−	0.227260i
$9$	0.862631	+	2.87330i	0.287544	+	0.957768i
$10$	−0.515217	+	0.432318i	−0.162926	+	0.136711i
$11$	0.692281	+	0.929895i	0.208731	+	0.280374i	0.894143	−	0.447781i	$-0.147786\pi$
$11$	0.692281	+	0.929895i	0.208731	+	0.280374i	−0.685413	+	0.728155i	$0.740378\pi$
$12$	−1.72916	−	0.100042i	−0.499165	−	0.0288795i
$13$	−3.16403	−	3.35368i	−0.877545	−	0.930143i	0.120496	−	0.992714i	$-0.461552\pi$
$13$	−3.16403	−	3.35368i	−0.877545	−	0.930143i	−0.998041	+	0.0625708i	$0.980070\pi$
$14$	1.32429	−	0.313863i	0.353932	−	0.0838834i
$15$	−0.268211	+	1.13362i	−0.0692519	+	0.292701i
$16$	0.396080	−	0.918216i	0.0990199	−	0.229554i
$17$	−0.129844	−	0.736381i	−0.0314917	−	0.178599i	0.965005	−	0.262232i	$-0.0844586\pi$
$17$	−0.129844	−	0.736381i	−0.0314917	−	0.178599i	−0.996497	+	0.0836335i	$0.973347\pi$
$18$	−2.50519	+	1.65046i	−0.590479	+	0.389018i
$19$	0.362214	−	2.05422i	0.0830977	−	0.471270i	−0.914653	−	0.404239i	$-0.867536\pi$
$19$	0.362214	−	2.05422i	0.0830977	−	0.471270i	0.997751	−	0.0670309i	$-0.0213526\pi$
$20$	−0.561922	−	0.369582i	−0.125650	−	0.0826411i
$21$	1.51453	−	1.80637i	0.330498	−	0.394182i
$22$	−0.692281	+	0.929895i	−0.147595	+	0.198254i
$23$	0.116279	+	1.99643i	0.0242458	+	0.416284i	0.988492	+	0.151275i	$0.0483379\pi$
$23$	0.116279	+	1.99643i	0.0242458	+	0.416284i	−0.964246	+	0.265009i	$0.914625\pi$
$24$	−0.400090	−	1.68521i	−0.0816680	−	0.343992i
$25$	3.12079	−	3.30784i	0.624158	−	0.661569i
$26$	2.30533	−	3.99296i	0.452113	−	0.783083i
$27$	−1.77153	+	4.88484i	−0.340931	+	0.940088i
$28$	0.680488	+	1.17864i	0.128600	+	0.222742i
$29$	6.48811	+	1.53771i	1.20481	+	0.285545i	0.783512	−	0.621376i	$-0.213426\pi$
$29$	6.48811	+	1.53771i	1.20481	+	0.285545i	0.421299	+	0.906922i	$0.361574\pi$
$30$	−1.16292	+	0.0681835i	−0.212320	+	0.0124486i
$31$	−8.39222	−	4.21473i	−1.50729	−	0.756988i	−0.512473	−	0.858703i	$-0.671271\pi$
$31$	−8.39222	−	4.21473i	−1.50729	−	0.756988i	−0.994814	+	0.101715i	$0.967567\pi$
$32$	0.993238	+	0.116093i	0.175581	+	0.0205225i
$33$	0.000775914		2.00795i	0.000135069		0.349539i
$34$	0.668205	−	0.335585i	0.114596	−	0.0575524i
$35$	0.860147	−	0.313068i	0.145391	−	0.0529181i
$36$	−2.29962	−	1.92659i	−0.383270	−	0.321098i
$37$	−1.25876	−	0.458152i	−0.206939	−	0.0753197i	0.236471	−	0.971639i	$-0.424009\pi$
$37$	−1.25876	−	0.458152i	−0.206939	−	0.0753197i	−0.443410	+	0.896319i	$0.646231\pi$
$38$	2.07180	−	0.242159i	0.336091	−	0.0392834i
$39$	−0.930173	−	7.93155i	−0.148947	−	1.27007i
$40$	0.192895	−	0.644313i	0.0304993	−	0.101875i
$41$	0.361029	−	1.20592i	0.0563833	−	0.188333i	−0.925159	−	0.379581i	$-0.876068\pi$
$41$	0.361029	−	1.20592i	0.0563833	−	0.188333i	0.981542	+	0.191248i	$0.0612534\pi$
$42$	2.16485	+	0.932835i	0.334044	+	0.143940i
$43$	2.55885	−	0.299087i	0.390222	−	0.0456104i	0.0812798	−	0.996691i	$-0.474099\pi$
$43$	2.55885	−	0.299087i	0.390222	−	0.0456104i	0.308942	+	0.951081i	$0.400025\pi$
$44$	−1.08938	−	0.396501i	−0.164230	−	0.0597748i
$45$	−1.54465	+	1.29815i	−0.230262	+	0.193517i
$46$	−1.87921	+	0.683975i	−0.277074	+	0.100847i
$47$	2.53181	−	1.27152i	0.369303	−	0.185471i	−0.254462	−	0.967083i	$-0.581899\pi$
$47$	2.53181	−	1.27152i	0.369303	−	0.185471i	0.623765	+	0.781612i	$0.285602\pi$
$48$	1.49967	−	0.866605i	0.216458	−	0.125084i
$49$	5.11293	+	0.597616i	0.730419	+	0.0853738i
$50$	4.06393	+	2.04098i	0.574727	+	0.288639i
$51$	0.580804	−	1.15759i	0.0813288	−	0.162095i
$52$	4.48639	+	1.06329i	0.622150	+	0.147452i
$53$	−5.67138	−	9.82312i	−0.779024	−	1.34931i	−0.932505	−	0.361158i	$-0.882381\pi$
$53$	−5.67138	−	9.82312i	−0.779024	−	1.34931i	0.153480	−	0.988152i	$-0.450952\pi$
$54$	−5.18771	−	0.296116i	−0.705958	−	0.0402962i
$55$	−0.389851	+	0.675242i	−0.0525675	+	0.0910496i
$56$	−0.933959	+	0.989939i	−0.124806	+	0.132286i
$57$	2.62697	−	2.48034i	0.347951	−	0.328529i
$58$	0.387700	+	6.65656i	0.0509075	+	0.874049i
$59$	−8.55645	+	11.4933i	−1.11395	+	1.49630i	−0.267716	+	0.963498i	$0.586269\pi$
$59$	−8.55645	+	11.4933i	−1.11395	+	1.49630i	−0.846239	+	0.532803i	$0.821139\pi$
$60$	−0.398850	−	1.09451i	−0.0514913	−	0.141301i
$61$	−4.68953	−	3.08435i	−0.600432	−	0.394911i	0.212591	−	0.977141i	$-0.431810\pi$
$61$	−4.68953	−	3.08435i	−0.600432	−	0.394911i	−0.813024	+	0.582231i	$0.802180\pi$
$62$	1.63075	−	9.24846i	0.207106	−	1.17456i
$63$	3.97215	−	0.944659i	0.500443	−	0.119016i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	1.22824	−	2.84738i	0.152344	−	0.353173i
$66$	−1.92337	+	0.576630i	−0.236751	+	0.0709783i
$67$	−12.5297	+	2.96960i	−1.53075	+	0.362794i	−0.907778	−	0.419451i	$-0.862223\pi$
$67$	−12.5297	+	2.96960i	−1.53075	+	0.362794i	−0.622971	+	0.782245i	$0.714075\pi$
$68$	0.513131	+	0.543887i	0.0622262	+	0.0659560i
$69$	−1.90226	+	2.89468i	−0.229005	+	0.348478i
$70$	0.546609	+	0.734223i	0.0653322	+	0.0877564i
$71$	−10.2441	+	8.59582i	−1.21575	+	1.02014i	−0.216716	+	0.976235i	$0.569534\pi$
$71$	−10.2441	+	8.59582i	−1.21575	+	1.02014i	−0.999036	+	0.0439019i	$0.986021\pi$
$72$	1.18611	−	2.75557i	0.139784	−	0.324747i
$73$	8.73007	+	7.32539i	1.02178	+	0.857373i	0.989850	−	0.142118i	$-0.0453911\pi$
$73$	8.73007	+	7.32539i	1.02178	+	0.857373i	0.0319271	+	0.999490i	$0.489836\pi$
$74$	0.0778877	−	1.33728i	0.00905426	−	0.155456i
$75$	7.75657	−	1.37078i	0.895652	−	0.158284i
$76$	0.826186	+	1.91532i	0.0947701	+	0.219702i
$77$	1.31821	−	0.866998i	0.150224	−	0.0988036i
$78$	7.33157	−	3.16589i	0.830137	−	0.358467i
$79$	3.95975	+	13.2265i	0.445507	+	1.48810i	0.826191	+	0.563391i	$0.190503\pi$
$79$	3.95975	+	13.2265i	0.445507	+	1.48810i	−0.380684	+	0.924705i	$0.624311\pi$
$80$	0.672568			0.0751954
$81$	−7.51174	+	4.95720i	−0.834637	+	0.550800i
$82$	1.25880			0.139012
$83$	1.89914	+	6.34357i	0.208458	+	0.696297i	0.996718	+	0.0809549i	$0.0257970\pi$
$83$	1.89914	+	6.34357i	0.208458	+	0.696297i	−0.788260	+	0.615342i	$0.789018\pi$
$84$	−0.272759	+	2.34145i	−0.0297604	+	0.255473i
$85$	0.420172	−	0.276351i	0.0455741	−	0.0299745i
$86$	1.02041	+	2.36558i	0.110034	+	0.255087i
$87$	7.42699	+	8.84420i	0.796257	+	0.948198i
$88$	0.0674068	−	1.15733i	0.00718559	−	0.123372i
$89$	0.867446	+	0.727874i	0.0919491	+	0.0771545i	0.687603	−	0.726086i	$-0.258663\pi$
$89$	0.867446	+	0.727874i	0.0919491	+	0.0771545i	−0.595654	+	0.803241i	$0.703107\pi$
$90$	−1.68662	−	1.10744i	−0.177786	−	0.116735i
$91$	−4.80694	+	4.03350i	−0.503904	+	0.422826i
$92$	−1.19420	−	1.60409i	−0.124504	−	0.167238i
$93$	−7.30574	−	14.5329i	−0.757570	−	1.50699i
$94$	1.94424	+	2.06077i	0.200533	+	0.212552i
$95$	1.36510	−	0.323535i	0.140056	−	0.0331939i
$96$	1.26031	+	1.18812i	0.128630	+	0.121262i
$97$	0.566782	−	1.31395i	0.0575480	−	0.133411i	−0.887016	−	0.461739i	$-0.847226\pi$
$97$	0.566782	−	1.31395i	0.0575480	−	0.133411i	0.944564	+	0.328328i	$0.106485\pi$
$98$	0.893896	+	5.06954i	0.0902971	+	0.512100i
$99$	−2.07469	+	2.79129i	−0.208514	+	0.280535i
$100$	−0.789692	+	4.47856i	−0.0789692	+	0.447856i
$101$	−6.18705	−	4.06928i	−0.615634	−	0.404909i	0.203037	−	0.979171i	$-0.434919\pi$
$101$	−6.18705	−	4.06928i	−0.615634	−	0.404909i	−0.818672	+	0.574262i	$0.805289\pi$
$102$	1.27554	+	0.224403i	0.126297	+	0.0222192i
$103$	5.00209	−	6.71897i	0.492871	−	0.662040i	−0.484200	−	0.874958i	$-0.660889\pi$
$103$	5.00209	−	6.71897i	0.492871	−	0.662040i	0.977070	+	0.212918i	$0.0682966\pi$
$104$	0.268086	+	4.60287i	0.0262880	+	0.451348i
$105$	1.51900	+	0.454120i	0.148239	+	0.0443176i
$106$	7.78388	−	8.25043i	0.756037	−	0.801353i
$107$	−4.19144	+	7.25979i	−0.405202	+	0.701831i	−0.994345	−	0.106198i	$-0.966132\pi$
$107$	−4.19144	+	7.25979i	−0.405202	+	0.701831i	0.589143	+	0.808029i	$0.299466\pi$
$108$	−1.20418	−	5.05470i	−0.115872	−	0.486388i
$109$	7.46704	+	12.9333i	0.715212	+	1.23878i	0.962878	+	0.269938i	$0.0870033\pi$
$109$	7.46704	+	12.9333i	0.715212	+	1.23878i	−0.247665	+	0.968846i	$0.579663\pi$
$110$	−0.758685	−	0.179812i	−0.0723378	−	0.0171444i
$111$	−1.27570	−	1.93797i	−0.121084	−	0.183944i
$112$	−1.21621	−	0.610805i	−0.114921	−	0.0577157i
$113$	−18.4465	−	2.15608i	−1.73530	−	0.202827i	−0.811144	−	0.584847i	$-0.801155\pi$
$113$	−18.4465	−	2.15608i	−1.73530	−	0.202827i	−0.924154	+	0.382020i	$0.875229\pi$
$114$	3.12956	+	1.80524i	0.293110	+	0.169076i
$115$	−1.20194	+	0.603638i	−0.112082	+	0.0562896i
$116$	−6.26572	+	2.28054i	−0.581757	+	0.211742i
$117$	6.90674	−	11.9842i	0.638529	−	1.10794i
$118$	−13.4645	−	4.90067i	−1.23951	−	0.451143i
$119$	−1.01078	+	0.118143i	−0.0926578	+	0.0108301i
$120$	0.934142	−	0.696004i	0.0852751	−	0.0635362i
$121$	2.76938	−	9.25039i	0.251762	−	0.840944i
$122$	1.60980	−	5.37712i	0.145745	−	0.486821i
$123$	1.74838	−	1.30267i	0.157646	−	0.117458i
$124$	9.32763	−	1.09024i	0.837646	−	0.0979068i
$125$	6.03418	+	2.19626i	0.539714	+	0.196440i
$126$	2.04420	+	3.53434i	0.182112	+	0.314864i
$127$	12.9867	−	4.72677i	1.15238	−	0.419433i	0.306012	−	0.952028i	$-0.401005\pi$
$127$	12.9867	−	4.72677i	1.15238	−	0.419433i	0.846370	+	0.532595i	$0.178783\pi$
$128$	−0.893633	+	0.448799i	−0.0789867	+	0.0396686i
$129$	3.86527	+	2.22963i	0.340318	+	0.196308i
$130$	3.08002	+	0.360003i	0.270136	+	0.0315743i
$131$	−4.25425	−	2.13657i	−0.371696	−	0.186673i	0.253139	−	0.967430i	$-0.418537\pi$
$131$	−4.25425	−	2.13657i	−0.371696	−	0.186673i	−0.624834	+	0.780757i	$0.714833\pi$
$132$	−1.10404	−	1.67719i	−0.0960940	−	0.145981i
$133$	−2.76235	−	0.654689i	−0.239526	−	0.0567688i
$134$	−6.43841	−	11.1517i	−0.556194	−	0.963356i
$135$	−3.48861	+	0.207247i	−0.300252	+	0.0178370i
$136$	−0.373870	+	0.647562i	−0.0320591	+	0.0555280i
$137$	10.8940	−	11.5470i	0.930739	−	0.986526i	−0.0691992	−	0.997603i	$-0.522044\pi$
$137$	10.8940	−	11.5470i	0.930739	−	0.986526i	0.999939	+	0.0110766i	$0.00352588\pi$
$138$	−3.31864	−	0.992139i	−0.282502	−	0.0844565i
$139$	−0.121917	−	2.09324i	−0.0103409	−	0.177546i	−0.999524	−	0.0308585i	$-0.990176\pi$
$139$	−0.121917	−	2.09324i	−0.0103409	−	0.177546i	0.989183	−	0.146687i	$-0.0468612\pi$
$140$	−0.546609	+	0.734223i	−0.0461969	+	0.0620532i
$141$	4.83297	+	0.850257i	0.407009	+	0.0716046i
$142$	−11.1728	−	7.34843i	−0.937596	−	0.616667i
$143$	0.928168	−	5.26390i	0.0776173	−	0.440190i
$144$	2.97998	+	0.345976i	0.248332	+	0.0288313i
$145$	0.778738	+	4.41644i	0.0646707	+	0.366766i
$146$	−4.51384	+	10.4643i	−0.373568	+	0.866028i
$147$	6.48774	+	6.11613i	0.535099	+	0.504450i
$148$	1.30344	−	0.308921i	0.107142	−	0.0253931i
$149$	4.21893	+	4.47180i	0.345628	+	0.366344i	0.876746	−	0.480954i	$-0.159709\pi$
$149$	4.21893	+	4.47180i	0.345628	+	0.366344i	−0.531118	+	0.847298i	$0.678228\pi$
$150$	3.53781	+	7.03757i	0.288861	+	0.574615i
$151$	−9.00011	−	12.0892i	−0.732419	−	0.983809i	−0.999796	−	0.0202171i	$-0.993564\pi$
$151$	−9.00011	−	12.0892i	−0.732419	−	0.983809i	0.267377	−	0.963592i	$-0.413843\pi$
$152$	−1.59790	+	1.34080i	−0.129607	+	0.108753i
$153$	2.00384	−	1.00831i	0.162001	−	0.0815166i
$154$	1.20864	+	1.01417i	0.0973951	+	0.0817242i
$155$	0.367253	−	6.30548i	0.0294984	−	0.506469i
$156$	5.13561	+	6.11558i	0.411178	+	0.489638i
$157$	4.80942	+	11.1495i	0.383834	+	0.889827i	0.995143	+	0.0984354i	$0.0313838\pi$
$157$	4.80942	+	11.1495i	0.383834	+	0.889827i	−0.611310	+	0.791392i	$0.709357\pi$
$158$	−11.5352	+	7.58680i	−0.917689	+	0.603573i
$159$	2.27325	−	19.5143i	0.180280	−	1.54758i
$160$	0.192895	+	0.644313i	0.0152497	+	0.0509374i
$161$	2.72170			0.214500
$162$	−6.90333	−	5.77443i	−0.542377	−	0.453682i
$163$	0.799475			0.0626197			0.0313099	−	0.999510i	$-0.490032\pi$
$163$	0.799475			0.0626197			0.0313099	+	0.999510i	$0.490032\pi$
$164$	0.361029	+	1.20592i	0.0281917	+	0.0941667i
$165$	−1.23983	+	0.535378i	−0.0965205	+	0.0416791i
$166$	−5.53239	+	3.63871i	−0.429397	+	0.282419i
$167$	−7.38724	−	17.1255i	−0.571641	−	1.32521i	−0.921488	−	0.388407i	$-0.873026\pi$
$167$	−7.38724	−	17.1255i	−0.571641	−	1.32521i	0.349847	−	0.936807i	$-0.386234\pi$
$168$	−2.32131	+	0.410235i	−0.179093	+	0.0316503i
$169$	−0.480175	+	8.24429i	−0.0369365	+	0.634176i
$170$	0.385249	+	0.323262i	0.0295472	+	0.0247931i
$171$	6.21485	−	0.731281i	0.475262	−	0.0559225i
$172$	−1.97354	+	1.65600i	−0.150481	+	0.126269i
$173$	−3.93940	−	5.29153i	−0.299507	−	0.402308i	0.626738	−	0.779230i	$-0.284390\pi$
$173$	−3.93940	−	5.29153i	−0.299507	−	0.402308i	−0.926245	+	0.376922i	$0.876982\pi$
$174$	−6.34257	+	9.65153i	−0.480829	+	0.731681i
$175$	−4.24732	−	4.50190i	−0.321067	−	0.340311i
$176$	1.12804	−	0.267351i	0.0850294	−	0.0201523i
$177$	−23.7725	+	7.12703i	−1.78685	+	0.535701i
$178$	−0.448509	+	1.03976i	−0.0336172	+	0.0779334i
$179$	2.13435	+	12.1045i	0.159529	+	0.904732i	0.954528	+	0.298122i	$0.0963601\pi$
$179$	2.13435	+	12.1045i	0.159529	+	0.904732i	−0.794999	+	0.606610i	$0.792529\pi$
$180$	0.577190	−	1.93339i	0.0430212	−	0.144106i
$181$	1.56131	−	8.85465i	0.116052	−	0.658161i	−0.870173	−	0.492747i	$-0.835993\pi$
$181$	1.56131	−	8.85465i	0.116052	−	0.658161i	0.986224	−	0.165414i	$-0.0528961\pi$
$182$	−5.24270	−	3.44818i	−0.388615	−	0.255596i
$183$	−3.32860	−	9.13428i	−0.246057	−	0.675225i
$184$	1.19420	−	1.60409i	0.0880379	−	0.118255i
$185$	−0.0523847	−	0.899411i	−0.00385140	−	0.0661260i
$186$	11.8271	−	11.1669i	0.867204	−	0.818798i
$187$	0.594868	−	0.630523i	0.0435011	−	0.0461084i
$188$	−1.41658	+	2.45360i	−0.103315	+	0.178947i
$189$	6.49672	+	2.79348i	0.472567	+	0.203196i
$190$	0.701458	+	1.21496i	0.0508891	+	0.0881425i
$191$	24.3252	+	5.76517i	1.76011	+	0.417153i	0.978438	−	0.206540i	$-0.0662204\pi$
$191$	24.3252	+	5.76517i	1.76011	+	0.417153i	0.781669	+	0.623693i	$0.214369\pi$
$192$	−0.776745	+	1.54812i	−0.0560567	+	0.111726i
$193$	7.77770	+	3.90611i	0.559851	+	0.281168i	0.706138	−	0.708074i	$-0.250436\pi$
$193$	7.77770	+	3.90611i	0.559851	+	0.281168i	−0.146287	+	0.989242i	$0.546732\pi$
$194$	1.42130	+	0.166127i	0.102044	+	0.0119272i
$195$	4.65044	−	2.68733i	0.333025	−	0.192444i
$196$	−4.60019	+	2.31030i	−0.328585	+	0.165022i
$197$	15.0611	−	5.48178i	1.07306	−	0.390561i	0.255738	−	0.966746i	$-0.417681\pi$
$197$	15.0611	−	5.48178i	1.07306	−	0.390561i	0.817319	+	0.576185i	$0.195459\pi$
$198$	−3.26905	−	1.18698i	−0.232321	−	0.0843548i
$199$	−9.35208	−	3.40388i	−0.662952	−	0.241295i	−0.0114415	−	0.999935i	$-0.503642\pi$
$199$	−9.35208	−	3.40388i	−0.662952	−	0.241295i	−0.651510	+	0.758640i	$0.725864\pi$
$200$	−4.51690	+	0.527950i	−0.319393	+	0.0373317i
$201$	−20.4827	−	8.82597i	−1.44474	−	0.622536i
$202$	2.12387	−	7.09421i	0.149435	−	0.499147i
$203$	2.60267	−	8.69354i	0.182672	−	0.610167i
$204$	0.150852	+	1.28631i	0.0105617	+	0.0900597i
$205$	0.840907	−	0.0982879i	0.0587315	−	0.00686473i
$206$	7.87132	+	2.86493i	0.548421	+	0.199609i
$207$	−5.63603	+	2.05628i	−0.391731	+	0.142922i
$208$	−4.33261	+	1.57694i	−0.300412	+	0.109341i
$209$	2.16096	−	1.08528i	0.149477	−	0.0750701i
$210$	0.000612643		1.58543i	4.22764e−5		0.109405i
$211$	10.6229	+	1.24164i	0.731311	+	0.0854780i	0.473595	−	0.880743i	$-0.342956\pi$
$211$	10.6229	+	1.24164i	0.731311	+	0.0854780i	0.257716	+	0.966221i	$0.417030\pi$
$212$	10.1363	+	5.09062i	0.696162	+	0.349626i
$213$	−23.1225	+	1.35570i	−1.58433	+	0.0928910i
$214$	−8.15693	−	1.93323i	−0.557596	−	0.132153i
$215$	0.866359	+	1.50058i	0.0590852	+	0.102339i
$216$	4.49699	−	2.60329i	0.305981	−	0.177132i
$217$	−6.39056	+	11.0688i	−0.433819	+	0.751397i
$218$	−10.2484	+	10.8627i	−0.694108	+	0.735711i
$219$	4.55954	+	19.2051i	0.308105	+	1.29776i
$220$	−0.0453356	−	0.778383i	−0.00305653	−	0.0524786i
$221$	−2.05875	+	2.76539i	−0.138487	+	0.186020i
$222$	1.49068	−	1.77792i	0.100048	−	0.119326i
$223$	−5.33090	−	3.50619i	−0.356983	−	0.234792i	0.358331	−	0.933595i	$-0.383346\pi$
$223$	−5.33090	−	3.50619i	−0.356983	−	0.234792i	−0.715314	+	0.698803i	$0.753716\pi$
$224$	0.236331	−	1.34030i	0.0157905	−	0.0895526i
$225$	12.1965	+	6.11352i	0.813101	+	0.407568i
$226$	−3.22500	−	18.2899i	−0.214524	−	1.21663i
$227$	−0.740715	+	1.71717i	−0.0491630	+	0.113973i	−0.941028	−	0.338330i	$-0.890138\pi$
$227$	−0.740715	+	1.71717i	−0.0491630	+	0.113973i	0.891865	+	0.452303i	$0.149397\pi$
$228$	−0.831834	+	3.51584i	−0.0550895	+	0.232842i
$229$	−3.86075	+	0.915014i	−0.255125	+	0.0604658i	−0.356188	−	0.934414i	$-0.615924\pi$
$229$	−3.86075	+	0.915014i	−0.255125	+	0.0604658i	0.101063	+	0.994880i	$0.467776\pi$
$230$	−0.923000	−	0.978323i	−0.0608608	−	0.0645087i
$231$	2.72821	+	0.157843i	0.179503	+	0.0103853i
$232$	−3.98176	−	5.34843i	−0.261415	−	0.351141i
$233$	5.34607	−	4.48589i	0.350233	−	0.293880i	−0.450651	−	0.892700i	$-0.648808\pi$
$233$	5.34607	−	4.48589i	0.350233	−	0.293880i	0.800884	+	0.598820i	$0.204364\pi$
$234$	13.4616	+	3.17948i	0.880014	+	0.207849i
$235$	1.45970	+	1.22483i	0.0952200	+	0.0798991i
$236$	0.833134	−	14.3044i	0.0542324	−	0.931135i
$237$	−8.17024	+	22.4746i	−0.530714	+	1.45988i
$238$	−0.403074	−	0.934430i	−0.0261274	−	0.0605701i
$239$	10.0388	−	6.60259i	0.649353	−	0.427086i	−0.181643	−	0.983365i	$-0.558142\pi$
$239$	10.0388	−	6.60259i	0.649353	−	0.427086i	0.830996	+	0.556278i	$0.187771\pi$
$240$	0.934679	+	0.695282i	0.0603333	+	0.0448802i
$241$	8.68494	+	29.0097i	0.559446	+	1.86868i	0.491272	+	0.871006i	$0.336532\pi$
$241$	8.68494	+	29.0097i	0.559446	+	1.86868i	0.0681739	+	0.997673i	$0.478283\pi$
$242$	9.65604			0.620714
$243$	−15.5638	−	0.876319i	−0.998419	−	0.0562159i
$244$	5.61292			0.359330
$245$	0.992972	+	3.31676i	0.0634386	+	0.211900i
$246$	1.74938	+	1.30132i	0.111537	+	0.0829690i
$247$	−8.03525	+	5.28487i	−0.511271	+	0.336268i
$248$	3.71964	+	8.62309i	0.236197	+	0.547566i
$249$	−3.91854	+	10.7790i	−0.248327	+	0.683094i
$250$	−0.373374	+	6.41058i	−0.0236142	+	0.405441i
$251$	20.7795	+	17.4360i	1.31159	+	1.10055i	0.988016	+	0.154349i	$0.0493279\pi$
$251$	20.7795	+	17.4360i	1.31159	+	1.10055i	0.323571	+	0.946204i	$0.395117\pi$
$252$	−2.79958	+	2.97198i	−0.176357	+	0.187217i
$253$	−1.77597	+	1.49021i	−0.111654	+	0.0936890i
$254$	8.25281	+	11.0855i	0.517828	+	0.695563i
$255$	0.869605	+	0.0503116i	0.0544568	+	0.00315063i
$256$	−0.686242	−	0.727374i	−0.0428901	−	0.0454609i
$257$	24.4246	−	5.78873i	1.52356	−	0.361091i	0.618300	−	0.785942i	$-0.287822\pi$
$257$	24.4246	−	5.78873i	1.52356	−	0.361091i	0.905263	+	0.424851i	$0.139674\pi$
$258$	−1.02738	+	4.34235i	−0.0639622	+	0.270343i
$259$	−0.722090	+	1.67399i	−0.0448685	+	0.104017i
$260$	0.538481	+	3.05388i	0.0333952	+	0.189393i
$261$	1.17853	+	19.9688i	0.0729494	+	1.23604i
$262$	0.826674	−	4.68830i	0.0510721	−	0.289644i
$263$	0.243478	+	0.160138i	0.0150135	+	0.00987455i	0.556994	−	0.830517i	$-0.311955\pi$
$263$	0.243478	+	0.160138i	0.0150135	+	0.00987455i	−0.541980	+	0.840391i	$0.682325\pi$
$264$	1.29009	−	1.53868i	0.0793997	−	0.0946991i
$265$	4.55559	−	6.11922i	0.279848	−	0.375901i
$266$	−0.165066	−	2.83407i	−0.0101208	−	0.173768i
$267$	0.453050	+	1.90828i	0.0277262	+	0.116785i
$268$	8.83661	−	9.36626i	0.539782	−	0.572135i
$269$	−8.14941	+	14.1152i	−0.496878	+	0.860618i	−0.999994	−	0.00360104i	$-0.998854\pi$
$269$	−8.14941	+	14.1152i	−0.496878	+	0.860618i	0.503115	+	0.864219i	$0.332187\pi$
$270$	−1.19909	−	3.28262i	−0.0729741	−	0.199774i
$271$	−8.96220	−	15.5230i	−0.544415	−	0.942954i	−0.998643	−	0.0520688i	$-0.983418\pi$
$271$	−8.96220	−	15.5230i	−0.544415	−	0.942954i	0.454229	−	0.890885i	$-0.349915\pi$
$272$	−0.727585	−	0.172441i	−0.0441163	−	0.0104558i
$273$	−10.8500	+	0.636148i	−0.656672	+	0.0385014i
$274$	14.1863	+	7.12465i	0.857028	+	0.430416i
$275$	5.23641	+	0.612048i	0.315767	+	0.0369079i
$276$	−0.00133847	−	3.46377i	−8.05666e−5	−	0.208495i
$277$	−13.3252	+	6.69215i	−0.800632	+	0.402093i	−0.801566	−	0.597907i	$-0.795999\pi$
$277$	−13.3252	+	6.69215i	−0.800632	+	0.402093i	0.000933299		1.00000i	$0.499703\pi$
$278$	1.97033	−	0.717142i	0.118173	−	0.0430113i
$279$	4.87081	−	27.7491i	0.291608	−	1.66130i
$280$	−0.860147	−	0.313068i	−0.0514036	−	0.0187094i
$281$	−31.4683	+	3.67812i	−1.87724	+	0.219418i	−0.976588	−	0.215119i	$-0.930986\pi$
$281$	−31.4683	+	3.67812i	−1.87724	+	0.219418i	−0.900654	+	0.434537i	$0.856912\pi$
$282$	0.571573	+	4.87379i	0.0340367	+	0.290230i
$283$	0.463887	−	1.54949i	0.0275752	−	0.0921077i	−0.943094	−	0.332525i	$-0.892099\pi$
$283$	0.463887	−	1.54949i	0.0275752	−	0.0921077i	0.970670	+	0.240418i	$0.0772844\pi$
$284$	3.83534	−	12.8109i	0.227586	−	0.760189i
$285$	2.23156	+	0.961580i	0.132186	+	0.0569591i
$286$	5.30897	−	0.620529i	0.313926	−	0.0366927i
$287$	−1.60989	−	0.585950i	−0.0950285	−	0.0345876i
$288$	0.523228	+	2.95402i	0.0308315	+	0.174067i
$289$	15.4494	−	5.62311i	0.908787	−	0.330771i
$290$	−4.00756	+	2.01267i	−0.235332	+	0.118188i
$291$	2.14599	−	1.24009i	0.125800	−	0.0726956i
$292$	−11.3192	−	1.32303i	−0.662408	−	0.0774244i
$293$	8.65650	+	4.34746i	0.505718	+	0.253981i	0.683317	−	0.730122i	$-0.260537\pi$
$293$	8.65650	+	4.34746i	0.505718	+	0.253981i	−0.177599	+	0.984103i	$0.556833\pi$
$294$	−3.99848	+	7.96931i	−0.233196	+	0.464780i
$295$	−9.37719	−	2.22244i	−0.545961	−	0.129395i
$296$	0.669773	+	1.16008i	0.0389298	+	0.0674283i
$297$	−5.76878	+	1.73435i	−0.334739	+	0.100637i
$298$	−3.07394	+	5.32421i	−0.178068	+	0.308423i
$299$	6.32746	−	6.70672i	0.365927	−	0.387860i
$300$	−5.72726	+	5.40758i	−0.330664	+	0.312207i
$301$	−0.203870	−	3.50032i	−0.0117509	−	0.201755i
$302$	9.00011	−	12.0892i	0.517898	−	0.695658i
$303$	−4.39154	−	12.0512i	−0.252287	−	0.692321i
$304$	−1.74275	−	1.14623i	−0.0999537	−	0.0657406i
$305$	0.655534	−	3.71772i	0.0375358	−	0.212876i
$306$	1.54065	+	1.63047i	0.0880733	+	0.0932078i
$307$	−3.39044	−	19.2282i	−0.193503	−	1.09741i	−0.914535	−	0.404507i	$-0.867443\pi$
$307$	−3.39044	−	19.2282i	−0.193503	−	1.09741i	0.721032	−	0.692902i	$-0.243668\pi$
$308$	−0.624922	+	1.44873i	−0.0356083	+	0.0825492i
$309$	13.8974	−	4.16645i	0.790594	−	0.237021i
$310$	6.14592	−	1.45661i	0.349065	−	0.0827298i
$311$	−10.0107	−	10.6108i	−0.567657	−	0.601681i	0.378416	−	0.925636i	$-0.376469\pi$
$311$	−10.0107	−	10.6108i	−0.567657	−	0.601681i	−0.946073	+	0.323955i	$0.894987\pi$
$312$	−4.38575	+	6.67383i	−0.248294	+	0.377831i
$313$	−16.8161	−	22.5880i	−0.950504	−	1.27675i	−0.960927	−	0.276802i	$-0.910725\pi$
$313$	−16.8161	−	22.5880i	−0.950504	−	1.27675i	0.0104234	−	0.999946i	$-0.496682\pi$
$314$	−9.30175	+	7.80509i	−0.524928	+	0.440467i
$315$	1.64153	+	2.20140i	0.0924896	+	0.124035i
$316$	−10.5764	−	8.87465i	−0.594969	−	0.499238i
$317$	−0.0397431	+	0.682363i	−0.00223220	+	0.0383253i	−0.999240	−	0.0389715i	$-0.987592\pi$
$317$	−0.0397431	+	0.682363i	−0.00223220	+	0.0383253i	0.997008	+	0.0772968i	$0.0246289\pi$
$318$	19.3465	−	3.41901i	1.08490	−	0.191729i
$319$	3.06168	+	7.09778i	0.171421	+	0.397399i
$320$	−0.561922	+	0.369582i	−0.0314124	+	0.0206603i
$321$	−13.3299	+	5.75607i	−0.744002	+	0.321272i
$322$	0.780591	+	2.60736i	0.0435006	+	0.145302i
$323$	−1.55972			−0.0867851
$324$	3.55194	−	8.26945i	0.197330	−	0.459414i
$325$	−20.9677			−1.16308
$326$	0.229292	+	0.765889i	0.0126993	+	0.0424187i
$327$	−2.99300	+	25.6928i	−0.165513	+	1.42082i
$328$	−1.05172	+	0.691725i	−0.0580713	+	0.0381941i
$329$	−1.52723	−	3.54053i	−0.0841992	−	0.195196i
$330$	−0.868474	−	1.03419i	−0.0478079	−	0.0569306i
$331$	−1.19226	+	20.4704i	−0.0655327	+	1.12515i	0.791932	+	0.610609i	$0.209075\pi$
$331$	−1.19226	+	20.4704i	−0.0655327	+	1.12515i	−0.857465	+	0.514543i	$0.827962\pi$
$332$	−5.07256	−	4.25638i	−0.278393	−	0.233599i
$333$	0.230562	−	4.01202i	0.0126347	−	0.219857i
$334$	14.2874	−	11.9886i	0.781772	−	0.655984i
$335$	−5.17171	−	6.94681i	−0.282561	−	0.379545i
$336$	−1.05876	−	2.10613i	−0.0577601	−	0.114899i
$337$	4.24993	+	4.50466i	0.231508	+	0.245384i	0.832705	−	0.553716i	$-0.186791\pi$
$337$	4.24993	+	4.50466i	0.231508	+	0.245384i	−0.601197	+	0.799101i	$0.705309\pi$
$338$	−8.03566	+	1.90449i	−0.437082	+	0.103590i
$339$	−23.4065	−	22.0658i	−1.27127	−	1.19845i
$340$	−0.199191	+	0.461777i	−0.0108026	+	0.0250434i
$341$	−1.89052	−	10.7217i	−0.102377	−	0.580610i
$342$	2.48300	+	5.74403i	0.134265	+	0.310602i
$343$	2.87089	−	16.2816i	0.155013	−	0.879125i
$344$	−2.15245	−	1.41569i	−0.116052	−	0.0763287i
$345$	−2.29439	−	0.403648i	−0.123526	−	0.0217317i
$346$	3.93940	−	5.29153i	0.211784	−	0.284475i
$347$	0.619334	+	10.6335i	0.0332476	+	0.570839i	0.973261	+	0.229702i	$0.0737750\pi$
$347$	0.619334	+	10.6335i	0.0332476	+	0.570839i	−0.940014	+	0.341137i	$0.889188\pi$
$348$	−11.0651	−	3.30802i	−0.593153	−	0.177329i
$349$	8.52175	−	9.03253i	0.456159	−	0.483500i	−0.457945	−	0.888981i	$-0.651414\pi$
$349$	8.52175	−	9.03253i	0.456159	−	0.483500i	0.914104	+	0.405480i	$0.132896\pi$
$350$	3.09463	−	5.36005i	0.165415	−	0.286507i
$351$	21.9874	−	9.51467i	1.17360	−	0.507855i
$352$	0.579646	+	1.00398i	0.0308952	+	0.0535121i
$353$	−24.4271	−	5.78933i	−1.30012	−	0.308135i	−0.478461	−	0.878109i	$-0.658805\pi$
$353$	−24.4271	−	5.78933i	−1.30012	−	0.308135i	−0.821663	+	0.569974i	$0.806953\pi$
$354$	−13.6457	−	20.7298i	−0.725258	−	1.10177i
$355$	−8.03739	−	4.03653i	−0.426580	−	0.214237i
$356$	−1.12471	−	0.131460i	−0.0596097	−	0.00696738i
$357$	−1.52683	−	0.880728i	−0.0808083	−	0.0466130i
$358$	−10.9838	+	5.51629i	−0.580514	+	0.291545i
$359$	−3.21545	+	1.17033i	−0.169705	+	0.0617675i	−0.425475	−	0.904970i	$-0.639893\pi$
$359$	−3.21545	+	1.17033i	−0.169705	+	0.0617675i	0.255771	+	0.966738i	$0.417671\pi$
$360$	2.01770	−	0.00155936i	0.106342	−	8.21857e-5i
$361$	13.7655	+	5.01025i	0.724502	+	0.263697i
$362$	8.93045	−	1.04382i	0.469374	−	0.0548620i
$363$	13.4115	−	9.99252i	0.703919	−	0.524471i
$364$	1.79969	−	6.01140i	0.0943296	−	0.315083i
$365$	−2.19828	+	7.34278i	−0.115063	+	0.384338i
$366$	7.79589	−	5.80851i	0.407498	−	0.303616i
$367$	11.4369	−	1.33678i	0.596999	−	0.0697792i	0.187774	−	0.982212i	$-0.439873\pi$
$367$	11.4369	−	1.33678i	0.596999	−	0.0697792i	0.409226	+	0.912433i	$0.365799\pi$
$368$	1.87921	+	0.683975i	0.0979604	+	0.0356547i
$369$	3.77641	−	0.00291857i	0.196592	−	0.000151935i
$370$	0.846602	−	0.308138i	0.0440128	−	0.0160193i
$371$	−13.7952	+	6.92822i	−0.716212	+	0.359695i
$372$	14.0898	+	8.12751i	0.730524	+	0.421392i
$373$	15.6136	+	1.82497i	0.808443	+	0.0944935i	0.510265	−	0.860017i	$-0.329547\pi$
$373$	15.6136	+	1.82497i	0.808443	+	0.0944935i	0.298178	+	0.954510i	$0.403621\pi$
$374$	0.774645	+	0.389041i	0.0400559	+	0.0201168i
$375$	6.11538	+	9.29016i	0.315797	+	0.479742i
$376$	−2.75680	−	0.653373i	−0.142171	−	0.0336952i
$377$	−15.3716	−	26.6244i	−0.791677	−	1.37123i
$378$	−0.812848	+	7.02497i	−0.0418084	+	0.361326i
$379$	6.79731	−	11.7733i	0.349154	−	0.604753i	−0.636945	−	0.770909i	$-0.719802\pi$
$379$	6.79731	−	11.7733i	0.349154	−	0.604753i	0.986099	+	0.166156i	$0.0531356\pi$
$380$	−0.962739	+	1.02044i	−0.0493875	+	0.0523476i
$381$	22.9342	+	6.85640i	1.17496	+	0.351264i
$382$	1.45356	+	24.9567i	0.0743708	+	1.27690i
$383$	3.35185	−	4.50231i	0.171271	−	0.230057i	−0.708197	−	0.706015i	$-0.750491\pi$
$383$	3.35185	−	4.50231i	0.171271	−	0.230057i	0.879468	+	0.475958i	$0.157898\pi$
$384$	−1.70585	−	0.300108i	−0.0870515	−	0.0153148i
$385$	0.886583	+	0.583115i	0.0451845	+	0.0297183i
$386$	−1.51134	+	8.57124i	−0.0769253	+	0.436265i
$387$	3.06671	+	7.09436i	0.155890	+	0.360627i
$388$	0.248487	+	1.40924i	0.0126150	+	0.0715433i
$389$	−10.0594	+	23.3204i	−0.510034	+	1.18239i	0.447555	+	0.894256i	$0.352295\pi$
$389$	−10.0594	+	23.3204i	−0.510034	+	1.18239i	−0.957589	+	0.288136i	$0.906964\pi$
$390$	3.90820	+	3.68434i	0.197899	+	0.186564i
$391$	1.45503	−	0.344849i	0.0735841	−	0.0174398i
$392$	−3.53259	−	3.74433i	−0.178423	−	0.189117i
$393$	−3.70349	−	7.36715i	−0.186816	−	0.371624i
$394$	9.57106	+	12.8562i	0.482183	+	0.647684i
$395$	−7.11334	+	5.96880i	−0.357911	+	0.300323i
$396$	0.199537	−	3.47215i	0.0100271	−	0.174482i
$397$	−17.9656	−	15.0749i	−0.901665	−	0.756587i	0.0688500	−	0.997627i	$-0.478067\pi$
$397$	−17.9656	−	15.0749i	−0.901665	−	0.756587i	−0.970515	+	0.241040i	$0.922511\pi$
$398$	0.578674	−	9.93544i	0.0290063	−	0.498019i
$399$	−3.16209	−	3.76548i	−0.158302	−	0.188510i
$400$	−1.80123	−	4.17573i	−0.0900617	−	0.208786i
$401$	23.2450	−	15.2885i	1.16080	−	0.763471i	0.185131	−	0.982714i	$-0.440729\pi$
$401$	23.2450	−	15.2885i	1.16080	−	0.763471i	0.975670	+	0.219242i	$0.0703585\pi$
$402$	2.58070	−	22.1535i	0.128713	−	1.10492i
$403$	12.4184	+	41.4803i	0.618605	+	2.06628i
$404$	7.40531			0.368428
$405$	−5.06243	−	3.31842i	−0.251554	−	0.164893i
$406$	9.07477			0.450373
$407$	−0.445384	−	1.48768i	−0.0220768	−	0.0737418i
$408$	−1.18901	+	0.513432i	−0.0588646	+	0.0254187i
$409$	12.5606	−	8.26123i	0.621081	−	0.408492i	−0.199600	−	0.979877i	$-0.563964\pi$
$409$	12.5606	−	8.26123i	0.621081	−	0.408492i	0.820682	+	0.571386i	$0.193594\pi$
$410$	0.335334	+	0.777391i	0.0165609	+	0.0383926i
$411$	27.0766	−	4.78512i	1.33559	−	0.236033i
$412$	−0.487049	+	8.36231i	−0.0239952	+	0.411982i
$413$	14.9386	+	12.5349i	0.735078	+	0.616804i
$414$	−3.58633	−	4.80951i	−0.176258	−	0.236375i
$415$	−3.41164	+	2.86270i	−0.167471	+	0.140525i
$416$	−2.75330	−	3.69832i	−0.134992	−	0.181325i
$417$	1.99450	−	3.03504i	0.0976710	−	0.148627i
$418$	1.65945	+	1.75892i	0.0811665	+	0.0860315i
$419$	−11.9398	+	2.82978i	−0.583297	+	0.138244i	−0.511662	−	0.859187i	$-0.670970\pi$
$419$	−11.9398	+	2.82978i	−0.583297	+	0.138244i	−0.0716351	+	0.997431i	$0.522822\pi$
$420$	−1.51865	+	0.455294i	−0.0741026	+	0.0222161i
$421$	−5.36254	+	12.4318i	−0.261354	+	0.605887i	−0.997479	−	0.0709583i	$-0.977394\pi$
$421$	−5.36254	+	12.4318i	−0.261354	+	0.605887i	0.736125	+	0.676846i	$0.236654\pi$
$422$	1.85721	+	10.5327i	0.0904074	+	0.512726i
$423$	5.83749	+	6.17780i	0.283828	+	0.300375i
$424$	−1.96965	+	11.1704i	−0.0956547	+	0.542485i
$425$	−2.84105	−	1.86859i	−0.137811	−	0.0906397i
$426$	−7.93036	−	21.7623i	−0.384227	−	1.05439i
$427$	−4.56173	+	6.12746i	−0.220757	+	0.296529i
$428$	−0.487422	−	8.36871i	−0.0235604	−	0.404517i
$429$	6.73157	−	6.35583i	0.325003	−	0.306862i
$430$	−1.18906	+	1.26033i	−0.0573418	+	0.0607787i
$431$	−19.1715	+	33.2060i	−0.923457	+	1.59948i	−0.129434	+	0.991588i	$0.541316\pi$
$431$	−19.1715	+	33.2060i	−0.923457	+	1.59948i	−0.794023	+	0.607887i	$0.792017\pi$
$432$	3.78368	+	3.56143i	0.182042	+	0.171349i
$433$	0.766207	+	1.32711i	0.0368215	+	0.0637768i	0.883849	−	0.467773i	$-0.154943\pi$
$433$	0.766207	+	1.32711i	0.0368215	+	0.0637768i	−0.847027	+	0.531549i	$0.821610\pi$
$434$	−12.4366	−	2.94753i	−0.596976	−	0.141486i
$435$	−3.48337	+	6.94265i	−0.167015	+	0.332874i
$436$	−13.3456	−	6.70240i	−0.639137	−	0.320987i
$437$	4.14322	+	0.484273i	0.198197	+	0.0231659i
$438$	−17.0906	+	9.87608i	−0.816621	+	0.471897i
$439$	33.6767	−	16.9131i	1.60730	−	0.807217i	0.607383	−	0.794409i	$-0.292219\pi$
$439$	33.6767	−	16.9131i	1.60730	−	0.807217i	0.999918	−	0.0128075i	$-0.00407685\pi$
$440$	0.732680	−	0.266674i	0.0349292	−	0.0127132i
$441$	2.69344	+	15.2065i	0.128259	+	0.724121i
$442$	−3.23967	−	1.17914i	−0.154095	−	0.0560861i
$443$	−5.84898	+	0.683648i	−0.277893	+	0.0324811i	−0.253898	−	0.967231i	$-0.581713\pi$
$443$	−5.84898	+	0.683648i	−0.277893	+	0.0324811i	−0.0239954	+	0.999712i	$0.507639\pi$
$444$	2.13076	+	0.918146i	0.101122	+	0.0435733i
$445$	−0.218428	+	0.729601i	−0.0103545	+	0.0345864i
$446$	1.82997	−	6.11253i	0.0866516	−	0.289437i
$447$	1.24029	+	10.5759i	0.0586639	+	0.500225i
$448$	1.35177	−	0.158000i	0.0638653	−	0.00746479i
$449$	1.43327	+	0.521667i	0.0676401	+	0.0246190i	0.375619	−	0.926774i	$-0.377430\pi$
$449$	1.43327	+	0.521667i	0.0676401	+	0.0246190i	−0.307978	+	0.951393i	$0.599652\pi$
$450$	−2.35869	+	13.4375i	−0.111190	+	0.633451i
$451$	1.37131	−	0.499117i	0.0645726	−	0.0235025i
$452$	16.5966	−	8.33512i	0.780638	−	0.392051i
$453$	−0.0100874	−	26.1047i	−0.000473947	−	1.22651i
$454$	−1.85747	−	0.217107i	−0.0871754	−	0.0101893i
$455$	−3.77146	−	1.89410i	−0.176809	−	0.0887967i
$456$	−3.60671	+	0.211465i	−0.168900	+	0.00990277i
$457$	−40.7731	−	9.66341i	−1.90729	−	0.452035i	−0.999466	−	0.0326743i	$-0.989598\pi$
$457$	−40.7731	−	9.66341i	−1.90729	−	0.452035i	−0.907820	−	0.419361i	$-0.862254\pi$
$458$	−1.98385	−	3.43613i	−0.0926991	−	0.160560i
$459$	3.82713	+	0.670252i	0.178635	+	0.0312847i
$460$	0.672504	−	1.16481i	0.0313557	−	0.0543096i
$461$	−11.8787	+	12.5907i	−0.553247	+	0.586407i	−0.942284	−	0.334815i	$-0.891326\pi$
$461$	−11.8787	+	12.5907i	−0.553247	+	0.586407i	0.389037	+	0.921222i	$0.372808\pi$
$462$	0.631249	+	2.65887i	0.0293684	+	0.123702i
$463$	1.19557	+	20.5272i	0.0555631	+	0.953981i	0.904765	+	0.425912i	$0.140047\pi$
$463$	1.19557	+	20.5272i	0.0555631	+	0.953981i	−0.849202	+	0.528069i	$0.822916\pi$
$464$	3.98176	−	5.34843i	0.184848	−	0.248295i
$465$	7.02881	−	8.38319i	0.325953	−	0.388761i
$466$	5.83070	+	3.83491i	0.270102	+	0.177649i
$467$	3.39754	−	19.2684i	0.157219	−	0.891635i	−0.799509	−	0.600654i	$-0.794907\pi$
$467$	3.39754	−	19.2684i	0.157219	−	0.891635i	0.956729	−	0.290981i	$-0.0939818\pi$
$468$	0.814931	+	13.8080i	0.0376702	+	0.638274i
$469$	3.04319	+	17.2588i	0.140522	+	0.796938i
$470$	−0.754729	+	1.74966i	−0.0348130	+	0.0807057i
$471$	−4.84230	+	20.4665i	−0.223121	+	0.943047i
$472$	13.9424	−	3.30440i	0.641750	−	0.152098i
$473$	2.04957	+	2.17241i	0.0942391	+	0.0998876i
$474$	−23.8736	−	1.38123i	−1.09655	−	0.0634418i
$475$	−5.66464	−	7.60893i	−0.259912	−	0.349122i
$476$	0.779571	−	0.654138i	0.0357316	−	0.0299824i
$477$	23.3325	−	24.7693i	1.06832	−	1.13411i
$478$	9.20436	+	7.72338i	0.420998	+	0.353259i
$479$	−0.971295	+	16.6765i	−0.0443796	+	0.761968i	0.900562	+	0.434728i	$0.143156\pi$
$479$	−0.971295	+	16.6765i	−0.0443796	+	0.761968i	−0.944941	+	0.327240i	$0.893881\pi$
$480$	−0.398004	+	1.09482i	−0.0181663	+	0.0499716i
$481$	2.44627	+	5.67109i	0.111540	+	0.258579i
$482$	−25.3001	+	16.6402i	−1.15239	+	0.757938i
$483$	3.78239	+	2.81361i	0.172105	+	0.128024i
$484$	2.76938	+	9.25039i	0.125881	+	0.420472i
$485$	0.962431			0.0437017
$486$	−3.62425	−	15.1613i	−0.164399	−	0.687730i
$487$	1.00343			0.0454698			0.0227349	−	0.999742i	$-0.492763\pi$
$487$	1.00343			0.0454698			0.0227349	+	0.999742i	$0.492763\pi$
$488$	1.60980	+	5.37712i	0.0728724	+	0.243411i
$489$	1.11105	+	0.826475i	0.0502432	+	0.0373745i
$490$	−2.89263	+	1.90251i	−0.130676	+	0.0859468i
$491$	−6.77775	−	15.7126i	−0.305876	−	0.709100i	0.694066	−	0.719912i	$-0.255818\pi$
$491$	−6.77775	−	15.7126i	−0.305876	−	0.709100i	−0.999942	+	0.0108119i	$0.996558\pi$
$492$	−0.744920	+	2.04911i	−0.0335836	+	0.0923811i
$493$	0.289899	−	4.97738i	0.0130564	−	0.224170i
$494$	−7.36738	−	6.18197i	−0.331474	−	0.278140i
$495$	−2.27647	−	0.537676i	−0.102320	−	0.0241667i
$496$	−7.19402	+	6.03650i	−0.323021	+	0.271047i
$497$	10.8683	+	14.5986i	0.487509	+	0.654838i
$498$	−11.4501	−	0.662451i	−0.513090	−	0.0296851i
$499$	2.40498	+	2.54913i	0.107662	+	0.114115i	0.778963	−	0.627070i	$-0.215746\pi$
$499$	2.40498	+	2.54913i	0.107662	+	0.114115i	−0.671302	+	0.741184i	$0.734264\pi$
$500$	−6.24835	+	1.48089i	−0.279435	+	0.0662273i
$501$	7.43773	−	31.4364i	0.332293	−	1.40447i
$502$	−10.7439	+	24.9072i	−0.479525	+	1.11166i
$503$	−4.44463	−	25.2068i	−0.198176	−	1.12391i	−0.907822	−	0.419356i	$-0.862256\pi$
$503$	−4.44463	−	25.2068i	−0.198176	−	1.12391i	0.709646	−	0.704559i	$-0.248855\pi$
$504$	−3.65006	−	1.82960i	−0.162586	−	0.0814967i
$505$	0.864867	−	4.90491i	0.0384861	−	0.218265i
$506$	−1.93696	−	1.27396i	−0.0861085	−	0.0566345i
$507$	−9.19002	+	10.9608i	−0.408143	+	0.486788i
$508$	−8.25281	+	11.0855i	−0.366159	+	0.491837i
$509$	1.92841	+	33.1095i	0.0854752	+	1.46755i	0.719636	+	0.694351i	$0.244308\pi$
$509$	1.92841	+	33.1095i	0.0854752	+	1.46755i	−0.634161	+	0.773201i	$0.718654\pi$
$510$	0.201208	+	0.847502i	0.00890962	+	0.0375280i
$511$	10.6437	−	11.2816i	0.470848	−	0.499070i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	9.39287	+	5.40847i	0.414705	+	0.238790i
$514$	12.5506	+	21.7383i	0.553583	+	0.958833i
$515$	5.48189	+	1.29923i	0.241561	+	0.0572510i
$516$	−4.45459	+	0.261177i	−0.196102	+	0.0114977i
$517$	2.93511	+	1.47407i	0.129086	+	0.0648293i
$518$	−1.81076	−	0.211648i	−0.0795604	−	0.00929928i
$519$	−0.00441531	−	11.4262i	−0.000193811	−	0.501554i
$520$	−2.77114	+	1.39172i	−0.121523	+	0.0610310i
$521$	−22.7781	+	8.29056i	−0.997928	+	0.363216i	−0.788785	−	0.614669i	$-0.789290\pi$
$521$	−22.7781	+	8.29056i	−0.997928	+	0.363216i	−0.209143	+	0.977885i	$0.567067\pi$
$522$	−18.7919	+	6.85613i	−0.822497	+	0.300085i
$523$	10.4821	+	3.81517i	0.458350	+	0.166826i	0.560868	−	0.827905i	$-0.310468\pi$
$523$	10.4821	+	3.81517i	0.458350	+	0.166826i	−0.102518	+	0.994731i	$0.532690\pi$
$524$	4.72844	−	0.552675i	0.206563	−	0.0241437i
$525$	−1.24864	−	10.6471i	−0.0544952	−	0.464679i
$526$	−0.0835804	+	0.279178i	−0.00364428	+	0.0121727i
$527$	−2.01397	+	6.72713i	−0.0877299	+	0.293038i
$528$	1.84404	+	0.794596i	0.0802516	+	0.0345804i
$529$	18.8723	−	2.20585i	0.820534	−	0.0959067i
$530$	7.16871	+	2.60920i	0.311389	+	0.113336i
$531$	−40.4048	−	14.6708i	−1.75342	−	0.636658i
$532$	2.66767	−	0.970952i	0.115658	−	0.0420961i
$533$	−5.18658	+	2.60480i	−0.224656	+	0.112826i
$534$	−1.69818	+	0.981318i	−0.0734873	+	0.0424658i
$535$	−5.59994	−	0.654539i	−0.242106	−	0.0282982i
$536$	11.5071	+	5.77911i	0.497033	+	0.249619i
$537$	−9.54714	+	19.0283i	−0.411990	+	0.821130i
$538$	−15.8595	−	3.75877i	−0.683751	−	0.162052i
$539$	2.98387	+	5.16821i	0.128524	+	0.222610i
$540$	2.80081	−	2.09018i	0.120528	−	0.0899469i
$541$	−12.5010	+	21.6524i	−0.537461	+	0.930909i	0.461579	+	0.887099i	$0.347283\pi$
$541$	−12.5010	+	21.6524i	−0.537461	+	0.930909i	−0.999040	+	0.0438103i	$0.986050\pi$
$542$	12.3005	−	13.0377i	0.528350	−	0.560019i
$543$	11.3235	−	10.6914i	0.485937	−	0.458813i
$544$	−0.0434773	−	0.746476i	−0.00186407	−	0.0320049i
$545$	−5.99797	+	8.05667i	−0.256925	+	0.345110i
$546$	−3.72124	−	10.2117i	−0.159254	−	0.437022i
$547$	8.96262	+	5.89481i	0.383214	+	0.252044i	0.726470	−	0.687198i	$-0.241159\pi$
$547$	8.96262	+	5.89481i	0.383214	+	0.252044i	−0.343256	+	0.939242i	$0.611530\pi$
$548$	−2.75665	+	15.6337i	−0.117758	+	0.667840i
$549$	4.81694	−	16.1351i	0.205582	−	0.688629i
$550$	0.915483	+	5.19196i	0.0390363	+	0.221386i
$551$	5.50888	−	12.7710i	0.234686	−	0.544063i
$552$	3.31787	−	0.994703i	0.141218	−	0.0423374i
$553$	18.2838	−	4.33335i	0.777508	−	0.184273i
$554$	−10.2327	−	10.8460i	−0.434747	−	0.460804i
$555$	0.856986	−	1.30408i	0.0363770	−	0.0553552i
$556$	1.25211	+	1.68188i	0.0531014	+	0.0713275i
$557$	20.8076	−	17.4597i	0.881646	−	0.739789i	−0.0848705	−	0.996392i	$-0.527048\pi$
$557$	20.8076	−	17.4597i	0.881646	−	0.739789i	0.966517	+	0.256603i	$0.0826032\pi$
$558$	27.9804	−	3.29236i	1.18450	−	0.139377i
$559$	−9.09934	−	7.63525i	−0.384861	−	0.322937i
$560$	0.0532228	−	0.913801i	0.00224907	−	0.0386151i
$561$	1.47852	−	0.261291i	0.0624230	−	0.0110317i
$562$	−12.5488	−	29.0914i	−0.529340	−	1.22715i
$563$	0.606344	−	0.398798i	0.0255543	−	0.0168074i	−0.536668	−	0.843794i	$-0.680317\pi$
$563$	0.606344	−	0.398798i	0.0255543	−	0.0168074i	0.562222	+	0.826986i	$0.309947\pi$
$564$	−4.50511	+	1.94538i	−0.189699	+	0.0819153i
$565$	−3.58245	−	11.9662i	−0.150715	−	0.503422i
$566$	1.61744			0.0679861
$567$	6.14079	+	10.5983i	0.257889	+	0.445086i
$568$	13.3727			0.561107
$569$	−5.81528	−	19.4244i	−0.243789	−	0.814313i	−0.989055	−	0.147546i	$-0.952863\pi$
$569$	−5.81528	−	19.4244i	−0.243789	−	0.814313i	0.745266	−	0.666767i	$-0.232323\pi$
$570$	−0.281164	+	2.41360i	−0.0117767	+	0.101095i
$571$	−15.9488	+	10.4897i	−0.667436	+	0.438980i	−0.837488	−	0.546455i	$-0.815977\pi$
$571$	−15.9488	+	10.4897i	−0.667436	+	0.438980i	0.170052	+	0.985435i	$0.445606\pi$
$572$	2.11709	+	4.90796i	0.0885199	+	0.205212i
$573$	27.8452	+	33.1586i	1.16325	+	1.38522i
$574$	0.0996140	−	1.71031i	0.00415781	−	0.0713868i
$575$	6.96675	+	5.84579i	0.290533	+	0.243786i
$576$	−2.67986	+	1.34847i	−0.111661	+	0.0561862i
$577$	−1.73198	+	1.45330i	−0.0721031	+	0.0605017i	−0.678127	−	0.734945i	$-0.737208\pi$
$577$	−1.73198	+	1.45330i	−0.0721031	+	0.0605017i	0.606024	+	0.795446i	$0.292764\pi$
$578$	9.81782	+	13.1876i	0.408367	+	0.548532i
$579$	6.77079	+	13.4688i	0.281384	+	0.559743i
$580$	−3.07750	−	3.26196i	−0.127786	−	0.135446i
$581$	8.76913	−	2.07832i	0.363805	−	0.0862233i
$582$	1.80347	+	1.70017i	0.0747564	+	0.0704745i
$583$	5.20828	−	12.0741i	0.215705	−	0.500060i
$584$	−1.97895	−	11.2232i	−0.0818893	−	0.464417i
$585$	9.24089	+	1.07287i	0.382064	+	0.0443576i
$586$	−1.68211	+	9.53970i	−0.0694872	+	0.394081i
$587$	26.9439	+	17.7213i	1.11209	+	0.731436i	0.966182	−	0.257862i	$-0.0830178\pi$
$587$	26.9439	+	17.7213i	1.11209	+	0.731436i	0.145912	+	0.989298i	$0.453388\pi$
$588$	−8.78129	−	1.54488i	−0.362134	−	0.0637098i
$589$	−11.6978	+	15.7128i	−0.481998	+	0.647436i
$590$	−0.560339	−	9.62065i	−0.0230688	−	0.396076i
$591$	26.5976	+	7.95159i	1.09408	+	0.327085i
$592$	−0.919252	+	0.974350i	−0.0377810	+	0.0400456i
$593$	16.1452	−	27.9644i	0.663005	−	1.14836i	−0.316817	−	0.948487i	$-0.602614\pi$
$593$	16.1452	−	27.9644i	0.663005	−	1.14836i	0.979822	−	0.199872i	$-0.0640527\pi$
$594$	−3.31599	−	5.02902i	−0.136057	−	0.206343i
$595$	−0.342222	−	0.592746i	−0.0140297	−	0.0243002i
$596$	−5.98216	−	1.41780i	−0.245039	−	0.0580752i
$597$	−9.47792	−	14.3984i	−0.387905	−	0.589285i
$598$	8.23970	+	4.13814i	0.336947	+	0.169221i
$599$	−3.62024	−	0.423145i	−0.147919	−	0.0172892i	0.0418112	−	0.999126i	$-0.486687\pi$
$599$	−3.62024	−	0.423145i	−0.147919	−	0.0172892i	−0.189730	+	0.981836i	$0.560761\pi$
$600$	−6.82300	−	3.93575i	−0.278548	−	0.160676i
$601$	38.1217	−	19.1455i	1.55502	−	0.780959i	0.556271	−	0.831001i	$-0.312232\pi$
$601$	38.1217	−	19.1455i	1.55502	−	0.780959i	0.998747	+	0.0500418i	$0.0159355\pi$
$602$	3.29480	−	1.19921i	0.134286	−	0.0488761i
$603$	−19.3411	−	33.4400i	−0.787630	−	1.36178i
$604$	14.1626	+	5.15478i	0.576269	+	0.209745i
$605$	6.45043	−	0.753947i	0.262247	−	0.0306523i
$606$	10.2854	−	7.66335i	0.417815	−	0.311302i
$607$	−9.28108	+	31.0010i	−0.376708	+	1.25829i	0.534086	+	0.845430i	$0.320656\pi$
$607$	−9.28108	+	31.0010i	−0.376708	+	1.25829i	−0.910794	+	0.412861i	$0.864530\pi$
$608$	0.598245	−	1.99828i	0.0242621	−	0.0810409i
$609$	12.6041	−	9.39099i	0.510745	−	0.380542i
$610$	3.74954	−	0.438259i	0.151815	−	0.0177446i
$611$	−12.2750	−	4.46774i	−0.496594	−	0.180745i
$612$	−1.12011	+	1.94355i	−0.0452777	+	0.0785635i
$613$	−9.02920	+	3.28636i	−0.364686	+	0.132735i	−0.517862	−	0.855464i	$-0.673272\pi$
$613$	−9.02920	+	3.28636i	−0.364686	+	0.132735i	0.153176	+	0.988199i	$0.451050\pi$
$614$	17.4480	−	8.76270i	0.704143	−	0.353634i
$615$	1.27023	+	0.732714i	0.0512206	+	0.0295459i
$616$	−1.56710	−	0.183168i	−0.0631403	−	0.00738004i
$617$	−35.1371	−	17.6465i	−1.41456	−	0.710421i	−0.432972	−	0.901407i	$-0.642535\pi$
$617$	−35.1371	−	17.6465i	−1.41456	−	0.710421i	−0.981593	+	0.190986i	$0.938831\pi$
$618$	7.97723	+	12.1186i	0.320891	+	0.487481i
$619$	−32.2832	−	7.65125i	−1.29757	−	0.307530i	−0.476913	−	0.878951i	$-0.658244\pi$
$619$	−32.2832	−	7.65125i	−1.29757	−	0.307530i	−0.820657	+	0.571421i	$0.806392\pi$
$620$	3.15809	+	5.46996i	0.126832	+	0.219679i
$621$	−9.95822	−	2.96872i	−0.399610	−	0.119131i
$622$	7.29388	−	12.6334i	0.292458	−	0.506552i
$623$	1.05759	−	1.12098i	0.0423714	−	0.0449110i
$624$	−7.65130	−	2.28743i	−0.306297	−	0.0915704i
$625$	−1.07099	−	18.3882i	−0.0428397	−	0.735530i
$626$	16.8161	−	22.5880i	0.672107	−	0.902797i
$627$	4.12505	+	0.725715i	0.164739	+	0.0289823i
$628$	−10.1450	−	6.67245i	−0.404828	−	0.266260i
$629$	−0.173932	+	0.986416i	−0.00693511	+	0.0393310i
$630$	−1.63812	+	2.20394i	−0.0652644	+	0.0878069i
$631$	2.18374	+	12.3846i	0.0869334	+	0.493024i	0.996923	+	0.0783919i	$0.0249785\pi$
$631$	2.18374	+	12.3846i	0.0869334	+	0.493024i	−0.909989	+	0.414632i	$0.863910\pi$
$632$	5.46848	−	12.6774i	0.217524	−	0.504278i
$633$	13.4793	+	12.7072i	0.535753	+	0.505066i
$634$	−0.665095	+	0.157630i	−0.0264143	+	0.00626030i
$635$	6.37860	+	6.76092i	0.253127	+	0.268299i
$636$	8.82400	+	17.5531i	0.349895	+	0.696027i
$637$	−14.1733	−	19.0380i	−0.561566	−	0.754314i
$638$	−5.92150	+	4.96873i	−0.234434	+	0.196714i
$639$	−33.5353	−	22.0194i	−1.32664	−	0.871074i
$640$	−0.515217	−	0.432318i	−0.0203657	−	0.0170889i
$641$	−0.483188	+	8.29601i	−0.0190848	+	0.327673i	0.975230	+	0.221193i	$0.0709950\pi$
$641$	−0.483188	+	8.29601i	−0.0190848	+	0.327673i	−0.994315	+	0.106480i	$0.966042\pi$
$642$	−9.33731	−	11.1190i	−0.368514	−	0.438834i
$643$	−12.7309	−	29.5134i	−0.502056	−	1.16390i	−0.961279	−	0.275576i	$-0.911131\pi$
$643$	−12.7309	−	29.5134i	−0.502056	−	1.16390i	0.459223	−	0.888321i	$-0.348128\pi$
$644$	−2.27394	+	1.49560i	−0.0896059	+	0.0589347i
$645$	−0.347261	+	2.98100i	−0.0136734	+	0.117377i
$646$	−0.447332	−	1.49419i	−0.0176001	−	0.0587883i
$647$	−18.4363			−0.724807			−0.362403	−	0.932021i	$-0.618044\pi$
$647$	−18.4363			−0.724807			−0.362403	+	0.932021i	$0.618044\pi$
$648$	8.94075	+	1.03102i	0.351226	+	0.0405022i
$649$	−16.6110			−0.652040
$650$	−6.01361	−	20.0869i	−0.235873	−	0.787871i
$651$	−20.3236	+	8.77608i	−0.796547	+	0.343962i
$652$	−0.667952	+	0.439319i	−0.0261590	+	0.0172051i
$653$	14.0671	+	32.6113i	0.550490	+	1.27618i	0.935520	+	0.353274i	$0.114932\pi$
$653$	14.0671	+	32.6113i	0.550490	+	1.27618i	−0.385030	+	0.922904i	$0.625809\pi$
$654$	−25.4719	+	4.50153i	−0.996029	+	0.176024i
$655$	0.186171	−	3.19643i	0.00727429	−	0.124895i
$656$	−0.964300	−	0.809144i	−0.0376496	−	0.0315918i
$657$	−13.5173	+	31.4032i	−0.527358	+	1.22516i
$658$	2.95377	−	2.47851i	0.115150	−	0.0966224i
$659$	−22.4233	−	30.1198i	−0.873489	−	1.17330i	−0.983776	−	0.179399i	$-0.942585\pi$
$659$	−22.4233	−	30.1198i	−0.873489	−	1.17330i	0.110288	−	0.993900i	$-0.464823\pi$
$660$	0.741667	−	1.12860i	0.0288693	−	0.0439307i
$661$	−29.5165	−	31.2857i	−1.14806	−	1.21687i	−0.972625	−	0.232380i	$-0.925349\pi$
$661$	−29.5165	−	31.2857i	−1.14806	−	1.21687i	−0.175434	−	0.984491i	$-0.556133\pi$
$662$	−19.9523	+	4.72879i	−0.775469	+	0.183790i
$663$	−5.71987	+	1.71482i	−0.222141	+	0.0665983i
$664$	2.62274	−	6.08020i	0.101782	−	0.235957i
$665$	−0.331553	−	1.88033i	−0.0128571	−	0.0729160i
$666$	3.90960	−	0.929783i	0.151494	−	0.0360284i
$667$	−2.31550	+	13.1318i	−0.0896564	+	0.508467i
$668$	15.5826	+	10.2488i	0.602908	+	0.396539i
$669$	−3.78384	−	10.3835i	−0.146292	−	0.401451i
$670$	5.17171	−	6.94681i	0.199801	−	0.268379i
$671$	−0.378349	−	6.49600i	−0.0146060	−	0.250775i
$672$	1.71400	−	1.61833i	0.0661189	−	0.0624283i
$673$	20.0834	−	21.2872i	0.774160	−	0.820562i	−0.213538	−	0.976935i	$-0.568499\pi$
$673$	20.0834	−	21.2872i	0.774160	−	0.820562i	0.987698	+	0.156373i	$0.0499802\pi$
$674$	−3.09652	+	5.36334i	−0.119274	+	0.206588i
$675$	10.6297	+	21.1045i	0.409139	+	0.812312i
$676$	−4.12913	−	7.15186i	−0.158813	−	0.275072i
$677$	−16.5462	−	3.92152i	−0.635923	−	0.150716i	−0.100005	−	0.994987i	$-0.531886\pi$
$677$	−16.5462	−	3.92152i	−0.635923	−	0.150716i	−0.535917	+	0.844270i	$0.680034\pi$
$678$	14.4257	−	28.7517i	0.554017	−	1.10420i
$679$	−1.74038	−	0.874050i	−0.0667895	−	0.0335430i
$680$	−0.499506	−	0.0583839i	−0.0191552	−	0.00223892i
$681$	−2.80455	+	1.62065i	−0.107471	+	0.0621035i
$682$	9.72903	−	4.88610i	0.372544	−	0.187098i
$683$	24.5064	−	8.91960i	0.937711	−	0.341299i	0.172450	−	0.985018i	$-0.444832\pi$
$683$	24.5064	−	8.91960i	0.937711	−	0.341299i	0.765262	+	0.643719i	$0.222610\pi$
$684$	−4.79059	+	4.02609i	−0.183173	+	0.153942i
$685$	10.0331	+	3.65173i	0.383343	+	0.139526i
$686$	16.4210	−	1.91934i	0.626957	−	0.0732808i
$687$	−6.31126	−	2.71952i	−0.240790	−	0.103756i
$688$	0.738884	−	2.46804i	0.0281697	−	0.0940933i
$689$	−14.9992	+	50.1007i	−0.571422	+	1.90868i
$690$	−0.271347	−	2.31377i	−0.0103300	−	0.0880835i
$691$	16.1021	−	1.88207i	0.612553	−	0.0715972i	0.195841	−	0.980636i	$-0.437256\pi$
$691$	16.1021	−	1.88207i	0.612553	−	0.0715972i	0.416712	+	0.909038i	$0.363182\pi$
$692$	6.19907	+	2.25628i	0.235653	+	0.0857707i
$693$	3.62827	+	3.03971i	0.137827	+	0.115469i
$694$	−10.0092	+	3.64305i	−0.379944	+	0.138288i
$695$	1.26023	−	0.632910i	0.0478031	−	0.0240076i
$696$	−0.00446278	−	11.5490i	−0.000169161	−	0.437765i
$697$	−0.934895	−	0.109274i	−0.0354117	−	0.00413903i
$698$	11.0971	+	5.57319i	0.420033	+	0.210948i
$699$	12.0669	−	0.707497i	0.456413	−	0.0267600i
$700$	6.02242	+	1.42734i	0.227626	+	0.0539484i
$701$	9.94638	+	17.2276i	0.375670	+	0.650679i	0.990427	−	0.138037i	$-0.0440794\pi$
$701$	9.94638	+	17.2276i	0.375670	+	0.650679i	−0.614757	+	0.788716i	$0.710746\pi$
$702$	15.4210	+	18.3348i	0.582028	+	0.692003i
$703$	−1.39709	+	2.41982i	−0.0526921	+	0.0912654i
$704$	−0.795554	+	0.843238i	−0.0299836	+	0.0317807i
$705$	0.762370	+	3.21116i	0.0287125	+	0.120939i
$706$	−1.45966	−	25.0613i	−0.0549349	−	0.943195i
$707$	−6.01844	+	8.08416i	−0.226347	+	0.304036i
$708$	15.9453	−	19.0178i	0.599260	−	0.714731i
$709$	−28.5421	−	18.7724i	−1.07192	−	0.705013i	−0.114416	−	0.993433i	$-0.536500\pi$
$709$	−28.5421	−	18.7724i	−1.07192	−	0.705013i	−0.957504	+	0.288420i	$0.906870\pi$
$710$	1.56180	−	8.85743i	0.0586134	−	0.332413i
$711$	−34.5879	+	22.7871i	−1.29715	+	0.854584i
$712$	−0.196634	−	1.11517i	−0.00736917	−	0.0417927i
$713$	7.43857	−	17.2445i	0.278576	−	0.645813i
$714$	0.405829	−	1.71528i	0.0151878	−	0.0641927i
$715$	3.49804	−	0.829052i	0.130819	−	0.0310048i
$716$	−8.43475	−	8.94031i	−0.315221	−	0.334115i
$717$	20.7766	+	1.20204i	0.775917	+	0.0448912i
$718$	−2.04336	−	2.74471i	−0.0762575	−	0.102432i
$719$	−6.77495	+	5.68486i	−0.252663	+	0.212009i	−0.760318	−	0.649551i	$-0.774957\pi$
$719$	−6.77495	+	5.68486i	−0.252663	+	0.212009i	0.507655	+	0.861560i	$0.330512\pi$
$720$	0.580177	+	1.93249i	0.0216219	+	0.0720197i
$721$	−8.73306	−	7.32791i	−0.325236	−	0.272906i
$722$	−0.851763	+	14.6242i	−0.0316993	+	0.544256i
$723$	−17.9198	+	49.2936i	−0.666445	+	1.83325i
$724$	3.56125	+	8.25591i	0.132353	+	0.306828i
$725$	25.3345	−	16.6628i	0.940900	−	0.618840i
$726$	13.4192	+	9.98215i	0.498032	+	0.370472i
$727$	1.01611	+	3.39405i	0.0376855	+	0.125878i	0.974763	−	0.223244i	$-0.0716648\pi$
$727$	1.01611	+	3.39405i	0.0376855	+	0.125878i	−0.937077	+	0.349123i	$0.886480\pi$
$728$	6.27501			0.232567
$729$	−20.7234	−	17.3073i	−0.767533	−	0.641010i
$730$	−7.66478			−0.283686
$731$	−0.552493	−	1.84546i	−0.0204347	−	0.0682567i
$732$	7.80037	+	5.80248i	0.288310	+	0.214466i
$733$	32.5520	−	21.4098i	1.20233	−	0.790787i	0.219560	−	0.975599i	$-0.429538\pi$
$733$	32.5520	−	21.4098i	1.20233	−	0.790787i	0.982774	+	0.184812i	$0.0591675\pi$
$734$	4.56075	+	10.5730i	0.168340	+	0.390257i
$735$	−2.04882	+	5.63586i	−0.0755719	+	0.207882i
$736$	−0.116279	+	1.99643i	−0.00428609	+	0.0735893i
$737$	−11.4355	−	9.59552i	−0.421232	−	0.353456i
$738$	1.08588	+	3.61693i	0.0399719	+	0.133141i
$739$	8.45465	−	7.09429i	0.311009	−	0.260968i	−0.473900	−	0.880579i	$-0.657154\pi$
$739$	8.45465	−	7.09429i	0.311009	−	0.260968i	0.784909	+	0.619611i	$0.212710\pi$
$740$	0.538001	+	0.722661i	0.0197773	+	0.0265656i
$741$	−16.6301	−	0.962144i	−0.610921	−	0.0353452i
$742$	−10.5937	−	11.2286i	−0.388906	−	0.412217i
$743$	−12.5454	+	2.97332i	−0.460246	+	0.109080i	−0.454197	−	0.890901i	$-0.650074\pi$
$743$	−12.5454	+	2.97332i	−0.460246	+	0.109080i	−0.00604946	+	0.999982i	$0.501926\pi$
$744$	−3.74506	+	15.8289i	−0.137301	+	0.580316i
$745$	−1.63773	+	3.79670i	−0.0600020	+	0.139100i
$746$	2.72974	+	15.4811i	0.0999427	+	0.566803i
$747$	−16.5887	+	10.9290i	−0.606950	+	0.399870i
$748$	−0.150527	+	0.853680i	−0.00550381	+	0.0312136i
$749$	9.53201	+	6.26930i	0.348292	+	0.229075i
$750$	−7.14596	+	8.52291i	−0.260934	+	0.311213i
$751$	−1.35670	+	1.82236i	−0.0495065	+	0.0664988i	−0.826187	−	0.563396i	$-0.809495\pi$
$751$	−1.35670	+	1.82236i	−0.0495065	+	0.0664988i	0.776681	+	0.629895i	$0.216902\pi$
$752$	−0.164734	−	2.82837i	−0.00600723	−	0.103140i
$753$	10.8527	+	45.7124i	0.395494	+	1.66585i
$754$	21.0973	−	22.3618i	0.768317	−	0.814368i
$755$	5.06832	−	8.77859i	0.184455	−	0.319486i
$756$	−6.96298	+	1.23609i	−0.253241	+	0.0449560i
$757$	−10.1664	−	17.6088i	−0.369505	−	0.640001i	0.619983	−	0.784615i	$-0.287139\pi$
$757$	−10.1664	−	17.6088i	−0.369505	−	0.640001i	−0.989488	+	0.144614i	$0.953806\pi$
$758$	13.2282	+	3.13513i	0.480469	+	0.113873i
$759$	−4.00864	+	0.235031i	−0.145504	+	0.00853108i
$760$	−1.25369	−	0.629627i	−0.0454761	−	0.0228390i
$761$	14.9605	+	1.74863i	0.542317	+	0.0633877i	0.382841	−	0.923814i	$-0.374946\pi$
$761$	14.9605	+	1.74863i	0.542317	+	0.0633877i	0.159475	+	0.987202i	$0.449020\pi$
$762$	0.00924982	+	23.9372i	0.000335086	+	0.867153i
$763$	18.1630	−	9.12181i	0.657545	−	0.330232i
$764$	−23.4914	+	8.55017i	−0.849889	+	0.309334i
$765$	1.15649	+	0.968892i	0.0418132	+	0.0350304i
$766$	5.27449	+	1.91976i	0.190575	+	0.0693637i
$767$	65.6177	−	7.66961i

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)

\(f(q)\)	\(=\)	\(q+(0.286803 + 0.957990i) q^{2} +(1.38972 + 1.03377i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.266390 + 0.617563i) q^{5} +(-0.591767 + 1.62782i) q^{6} +(0.0791338 - 1.35867i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(0.862631 + 2.87330i) q^{9} +O(q^{10})\)	\(q+(0.286803 + 0.957990i) q^{2} +(1.38972 + 1.03377i) q^{3} +(-0.835488 + 0.549509i) q^{4} +(0.266390 + 0.617563i) q^{5} +(-0.591767 + 1.62782i) q^{6} +(0.0791338 - 1.35867i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(0.862631 + 2.87330i) q^{9} +(-0.515217 + 0.432318i) q^{10} +(0.692281 + 0.929895i) q^{11} +(-1.72916 - 0.100042i) q^{12} +(-3.16403 - 3.35368i) q^{13} +(1.32429 - 0.313863i) q^{14} +(-0.268211 + 1.13362i) q^{15} +(0.396080 - 0.918216i) q^{16} +(-0.129844 - 0.736381i) q^{17} +(-2.50519 + 1.65046i) q^{18} +(0.362214 - 2.05422i) q^{19} +(-0.561922 - 0.369582i) q^{20} +(1.51453 - 1.80637i) q^{21} +(-0.692281 + 0.929895i) q^{22} +(0.116279 + 1.99643i) q^{23} +(-0.400090 - 1.68521i) q^{24} +(3.12079 - 3.30784i) q^{25} +(2.30533 - 3.99296i) q^{26} +(-1.77153 + 4.88484i) q^{27} +(0.680488 + 1.17864i) q^{28} +(6.48811 + 1.53771i) q^{29} +(-1.16292 + 0.0681835i) q^{30} +(-8.39222 - 4.21473i) q^{31} +(0.993238 + 0.116093i) q^{32} +(0.000775914 + 2.00795i) q^{33} +(0.668205 - 0.335585i) q^{34} +(0.860147 - 0.313068i) q^{35} +(-2.29962 - 1.92659i) q^{36} +(-1.25876 - 0.458152i) q^{37} +(2.07180 - 0.242159i) q^{38} +(-0.930173 - 7.93155i) q^{39} +(0.192895 - 0.644313i) q^{40} +(0.361029 - 1.20592i) q^{41} +(2.16485 + 0.932835i) q^{42} +(2.55885 - 0.299087i) q^{43} +(-1.08938 - 0.396501i) q^{44} +(-1.54465 + 1.29815i) q^{45} +(-1.87921 + 0.683975i) q^{46} +(2.53181 - 1.27152i) q^{47} +(1.49967 - 0.866605i) q^{48} +(5.11293 + 0.597616i) q^{49} +(4.06393 + 2.04098i) q^{50} +(0.580804 - 1.15759i) q^{51} +(4.48639 + 1.06329i) q^{52} +(-5.67138 - 9.82312i) q^{53} +(-5.18771 - 0.296116i) q^{54} +(-0.389851 + 0.675242i) q^{55} +(-0.933959 + 0.989939i) q^{56} +(2.62697 - 2.48034i) q^{57} +(0.387700 + 6.65656i) q^{58} +(-8.55645 + 11.4933i) q^{59} +(-0.398850 - 1.09451i) q^{60} +(-4.68953 - 3.08435i) q^{61} +(1.63075 - 9.24846i) q^{62} +(3.97215 - 0.944659i) q^{63} +(0.173648 + 0.984808i) q^{64} +(1.22824 - 2.84738i) q^{65} +(-1.92337 + 0.576630i) q^{66} +(-12.5297 + 2.96960i) q^{67} +(0.513131 + 0.543887i) q^{68} +(-1.90226 + 2.89468i) q^{69} +(0.546609 + 0.734223i) q^{70} +(-10.2441 + 8.59582i) q^{71} +(1.18611 - 2.75557i) q^{72} +(8.73007 + 7.32539i) q^{73} +(0.0778877 - 1.33728i) q^{74} +(7.75657 - 1.37078i) q^{75} +(0.826186 + 1.91532i) q^{76} +(1.31821 - 0.866998i) q^{77} +(7.33157 - 3.16589i) q^{78} +(3.95975 + 13.2265i) q^{79} +0.672568 q^{80} +(-7.51174 + 4.95720i) q^{81} +1.25880 q^{82} +(1.89914 + 6.34357i) q^{83} +(-0.272759 + 2.34145i) q^{84} +(0.420172 - 0.276351i) q^{85} +(1.02041 + 2.36558i) q^{86} +(7.42699 + 8.84420i) q^{87} +(0.0674068 - 1.15733i) q^{88} +(0.867446 + 0.727874i) q^{89} +(-1.68662 - 1.10744i) q^{90} +(-4.80694 + 4.03350i) q^{91} +(-1.19420 - 1.60409i) q^{92} +(-7.30574 - 14.5329i) q^{93} +(1.94424 + 2.06077i) q^{94} +(1.36510 - 0.323535i) q^{95} +(1.26031 + 1.18812i) q^{96} +(0.566782 - 1.31395i) q^{97} +(0.893896 + 5.06954i) q^{98} +(-2.07469 + 2.79129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more