LMFDB - Embedded newform 162.2.g.a.157.4

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			157.4
Character	$\chi$	$=$	162.157
Dual form			162.2.g.a.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.973045 + 0.230616i) q^{2} +(1.56608 + 0.739857i) q^{3} +(0.893633 - 0.448799i) q^{4} +(0.149985 + 0.201464i) q^{5} +(-1.69449 - 0.358751i) q^{6} +(1.83964 - 1.20995i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(1.90522 + 2.31735i) q^{9} +O(q^{10})$	\(q+(-0.973045 + 0.230616i) q^{2} +(1.56608 + 0.739857i) q^{3} +(0.893633 - 0.448799i) q^{4} +(0.149985 + 0.201464i) q^{5} +(-1.69449 - 0.358751i) q^{6} +(1.83964 - 1.20995i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(1.90522 + 2.31735i) q^{9} +(-0.192403 - 0.161445i) q^{10} +(-1.53567 - 0.179494i) q^{11} +(1.73155 - 0.0416959i) q^{12} +(-0.160681 - 0.536712i) q^{13} +(-1.51101 + 1.60158i) q^{14} +(0.0858335 + 0.426477i) q^{15} +(0.597159 - 0.802123i) q^{16} +(-0.434239 + 2.46269i) q^{17} +(-2.38829 - 1.81551i) q^{18} +(0.461285 + 2.61608i) q^{19} +(0.224448 + 0.112722i) q^{20} +(3.77621 - 0.533809i) q^{21} +(1.53567 - 0.179494i) q^{22} +(0.530931 + 0.349199i) q^{23} +(-1.67526 + 0.439895i) q^{24} +(1.41592 - 4.72951i) q^{25} +(0.280124 + 0.485189i) q^{26} +(1.26923 + 5.03876i) q^{27} +(1.10093 - 1.90688i) q^{28} +(-4.73037 - 5.01390i) q^{29} +(-0.181872 - 0.395187i) q^{30} +(0.0928412 - 1.59402i) q^{31} +(-0.396080 + 0.918216i) q^{32} +(-2.27218 - 1.41728i) q^{33} +(-0.145402 - 2.49645i) q^{34} +(0.519679 + 0.189148i) q^{35} +(2.74260 + 1.21580i) q^{36} +(-9.81113 + 3.57096i) q^{37} +(-1.05216 - 2.43918i) q^{38} +(0.145450 - 0.959416i) q^{39} +(-0.244394 - 0.0579224i) q^{40} +(-7.44978 - 1.76563i) q^{41} +(-3.55131 + 1.39027i) q^{42} +(-3.30017 - 7.65066i) q^{43} +(-1.45288 + 0.528805i) q^{44} +(-0.181110 + 0.731402i) q^{45} +(-0.597151 - 0.217345i) q^{46} +(-0.468659 - 8.04657i) q^{47} +(1.52866 - 0.814379i) q^{48} +(-0.852272 + 1.97579i) q^{49} +(-0.287056 + 4.92856i) q^{50} +(-2.50209 + 3.53550i) q^{51} +(-0.384466 - 0.407510i) q^{52} +(3.36870 - 5.83476i) q^{53} +(-2.39703 - 4.61023i) q^{54} +(-0.194165 - 0.336304i) q^{55} +(-0.631503 + 2.10937i) q^{56} +(-1.21311 + 4.43828i) q^{57} +(5.75915 + 3.78785i) q^{58} +(8.40601 - 0.982521i) q^{59} +(0.268106 + 0.342592i) q^{60} +(0.457807 + 0.229919i) q^{61} +(0.277268 + 1.57246i) q^{62} +(6.30879 + 1.95786i) q^{63} +(0.173648 - 0.984808i) q^{64} +(0.0840287 - 0.112870i) q^{65} +(2.53778 + 0.855072i) q^{66} +(-5.52629 + 5.85752i) q^{67} +(0.717204 + 2.39563i) q^{68} +(0.573125 + 0.939687i) q^{69} +(-0.549291 - 0.0642029i) q^{70} +(12.2320 + 10.2639i) q^{71} +(-2.94905 - 0.550541i) q^{72} +(-10.6126 + 8.90507i) q^{73} +(8.72315 - 5.73731i) q^{74} +(5.71662 - 6.35922i) q^{75} +(1.58631 + 2.13079i) q^{76} +(-3.04225 + 1.52787i) q^{77} +(0.0797266 + 0.967098i) q^{78} +(15.0282 - 3.56174i) q^{79} +0.251164 q^{80} +(-1.74025 + 8.83015i) q^{81} +7.65615 q^{82} +(-7.27842 + 1.72502i) q^{83} +(3.13497 - 2.17179i) q^{84} +(-0.561274 + 0.281882i) q^{85} +(4.97558 + 6.68337i) q^{86} +(-3.69858 - 11.3520i) q^{87} +(1.29177 - 0.849608i) q^{88} +(11.9905 - 10.0612i) q^{89} +(0.00755494 - 0.753454i) q^{90} +(-0.944987 - 0.792939i) q^{91} +(0.631178 + 0.0737741i) q^{92} +(1.32474 - 2.42768i) q^{93} +(2.31169 + 7.72159i) q^{94} +(-0.457861 + 0.485304i) q^{95} +(-1.29964 + 1.14496i) q^{96} +(-9.83490 + 13.2106i) q^{97} +(0.373651 - 2.11908i) q^{98} +(-2.50984 - 3.90066i) 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{25}{27}\right)$

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
$3$	1.56608	+	0.739857i	0.904178	+	0.427157i
$3$	1.56608	+	0.739857i	0.904178	+	0.427157i
$4$	0.893633	−	0.448799i	0.446816	−	0.224400i
$5$	0.149985	+	0.201464i	0.0670752	+	0.0900976i	0.834395	−	0.551167i	$-0.185817\pi$
$5$	0.149985	+	0.201464i	0.0670752	+	0.0900976i	−0.767320	+	0.641265i	$0.778410\pi$
$6$	−1.69449	−	0.358751i	−0.691773	−	0.146459i
$7$	1.83964	−	1.20995i	0.695317	−	0.457317i	−0.152017	−	0.988378i	$-0.548577\pi$
$7$	1.83964	−	1.20995i	0.695317	−	0.457317i	0.847334	+	0.531061i	$0.178206\pi$
$8$	−0.766044	+	0.642788i	−0.270838	+	0.227260i
$9$	1.90522	+	2.31735i	0.635075	+	0.772451i
$10$	−0.192403	−	0.161445i	−0.0608431	−	0.0510534i
$11$	−1.53567	−	0.179494i	−0.463021	−	0.0541194i	−0.118615	−	0.992940i	$-0.537846\pi$
$11$	−1.53567	−	0.179494i	−0.463021	−	0.0541194i	−0.344406	+	0.938821i	$0.611920\pi$
$12$	1.73155	−	0.0416959i	0.499855	−	0.0120366i
$13$	−0.160681	−	0.536712i	−0.0445649	−	0.148857i	0.932811	−	0.360365i	$-0.117348\pi$
$13$	−0.160681	−	0.536712i	−0.0445649	−	0.148857i	−0.977376	+	0.211508i	$0.932163\pi$
$14$	−1.51101	+	1.60158i	−0.403836	+	0.428041i
$15$	0.0858335	+	0.426477i	0.0221621	+	0.110116i
$16$	0.597159	−	0.802123i	0.149290	−	0.200531i
$17$	−0.434239	+	2.46269i	−0.105318	+	0.597290i	0.885774	+	0.464116i	$0.153628\pi$
$17$	−0.434239	+	2.46269i	−0.105318	+	0.597290i	−0.991093	+	0.133174i	$0.957483\pi$
$18$	−2.38829	−	1.81551i	−0.562924	−	0.427921i
$19$	0.461285	+	2.61608i	0.105826	+	0.600170i	0.990887	+	0.134695i	$0.0430053\pi$
$19$	0.461285	+	2.61608i	0.105826	+	0.600170i	−0.885061	+	0.465475i	$0.845884\pi$
$20$	0.224448	+	0.112722i	0.0501882	+	0.0252054i
$21$	3.77621	−	0.533809i	0.824036	−	0.116487i
$22$	1.53567	−	0.179494i	0.327405	−	0.0382682i
$23$	0.530931	+	0.349199i	0.110707	+	0.0728130i	0.603655	−	0.797246i	$-0.293710\pi$
$23$	0.530931	+	0.349199i	0.110707	+	0.0728130i	−0.492948	+	0.870059i	$0.664081\pi$
$24$	−1.67526	+	0.439895i	−0.341961	+	0.0897931i
$25$	1.41592	−	4.72951i	0.283185	−	0.945903i
$26$	0.280124	+	0.485189i	0.0549369	+	0.0951534i
$27$	1.26923	+	5.03876i	0.244263	+	0.969709i
$28$	1.10093	−	1.90688i	0.208057	−	0.360366i
$29$	−4.73037	−	5.01390i	−0.878408	−	0.931059i	0.119683	−	0.992812i	$-0.461812\pi$
$29$	−4.73037	−	5.01390i	−0.878408	−	0.931059i	−0.998091	+	0.0617536i	$0.980331\pi$
$30$	−0.181872	−	0.395187i	−0.0332052	−	0.0721509i
$31$	0.0928412	−	1.59402i	0.0166748	−	0.286295i	−0.979655	−	0.200691i	$-0.935681\pi$
$31$	0.0928412	−	1.59402i	0.0166748	−	0.286295i	0.996329	−	0.0856034i	$-0.0272818\pi$
$32$	−0.396080	+	0.918216i	−0.0700177	+	0.162319i
$33$	−2.27218	−	1.41728i	−0.395536	−	0.246716i
$34$	−0.145402	−	2.49645i	−0.0249362	−	0.428138i
$35$	0.519679	+	0.189148i	0.0878417	+	0.0319718i
$36$	2.74260	+	1.21580i	0.457099	+	0.202633i
$37$	−9.81113	+	3.57096i	−1.61294	+	0.587062i	−0.982019	−	0.188784i	$-0.939545\pi$
$37$	−9.81113	+	3.57096i	−1.61294	+	0.587062i	−0.630922	+	0.775846i	$0.717323\pi$
$38$	−1.05216	−	2.43918i	−0.170683	−	0.395688i
$39$	0.145450	−	0.959416i	0.0232907	−	0.153629i
$40$	−0.244394	−	0.0579224i	−0.0386421	−	0.00915834i
$41$	−7.44978	−	1.76563i	−1.16346	−	0.275745i	−0.396865	−	0.917877i	$-0.629902\pi$
$41$	−7.44978	−	1.76563i	−1.16346	−	0.275745i	−0.766594	+	0.642132i	$0.778050\pi$
$42$	−3.55131	+	1.39027i	−0.547980	+	0.214524i
$43$	−3.30017	−	7.65066i	−0.503272	−	1.16672i	−0.960730	−	0.277484i	$-0.910499\pi$
$43$	−3.30017	−	7.65066i	−0.503272	−	1.16672i	0.457459	−	0.889231i	$-0.348760\pi$
$44$	−1.45288	+	0.528805i	−0.219030	+	0.0797203i
$45$	−0.181110	+	0.731402i	−0.0269982	+	0.109031i
$46$	−0.597151	−	0.217345i	−0.0880451	−	0.0320458i
$47$	−0.468659	−	8.04657i	−0.0683610	−	1.17371i	−0.841781	−	0.539819i	$-0.818493\pi$
$47$	−0.468659	−	8.04657i	−0.0683610	−	1.17371i	0.773420	−	0.633894i	$-0.218544\pi$
$48$	1.52866	−	0.814379i	0.220642	−	0.117545i
$49$	−0.852272	+	1.97579i	−0.121753	+	0.282256i
$50$	−0.287056	+	4.92856i	−0.0405959	+	0.697004i
$51$	−2.50209	+	3.53550i	−0.350363	+	0.495069i
$52$	−0.384466	−	0.407510i	−0.0533158	−	0.0565114i
$53$	3.36870	−	5.83476i	0.462727	−	0.801466i	−0.536369	−	0.843984i	$-0.680204\pi$
$53$	3.36870	−	5.83476i	0.462727	−	0.801466i	0.999096	+	0.0425173i	$0.0135378\pi$
$54$	−2.39703	−	4.61023i	−0.326195	−	0.627373i
$55$	−0.194165	−	0.336304i	−0.0261812	−	0.0453472i
$56$	−0.631503	+	2.10937i	−0.0843882	+	0.281876i
$57$	−1.21311	+	4.43828i	−0.160681	+	0.587864i
$58$	5.75915	+	3.78785i	0.756214	+	0.497370i
$59$	8.40601	−	0.982521i	1.09437	−	0.127913i	0.450297	−	0.892879i	$-0.351318\pi$
$59$	8.40601	−	0.982521i	1.09437	−	0.127913i	0.644072	+	0.764965i	$0.277244\pi$
$60$	0.268106	+	0.342592i	0.0346124	+	0.0442284i
$61$	0.457807	+	0.229919i	0.0586162	+	0.0294381i	0.477866	−	0.878433i	$-0.341411\pi$
$61$	0.457807	+	0.229919i	0.0586162	+	0.0294381i	−0.419250	+	0.907871i	$0.637707\pi$
$62$	0.277268	+	1.57246i	0.0352131	+	0.199703i
$63$	6.30879	+	1.95786i	0.794833	+	0.246668i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	0.0840287	−	0.112870i	0.0104225	−	0.0139998i
$66$	2.53778	+	0.855072i	0.312379	+	0.105252i
$67$	−5.52629	+	5.85752i	−0.675143	+	0.715610i	−0.970855	−	0.239667i	$-0.922962\pi$
$67$	−5.52629	+	5.85752i	−0.675143	+	0.715610i	0.295712	+	0.955277i	$0.404443\pi$
$68$	0.717204	+	2.39563i	0.0869737	+	0.290512i
$69$	0.573125	+	0.939687i	0.0689961	+	0.113125i
$70$	−0.549291	−	0.0642029i	−0.0656528	−	0.00767372i
$71$	12.2320	+	10.2639i	1.45168	+	1.21810i	0.931345	+	0.364138i	$0.118636\pi$
$71$	12.2320	+	10.2639i	1.45168	+	1.21810i	0.520332	+	0.853964i	$0.325808\pi$
$72$	−2.94905	−	0.550541i	−0.347549	−	0.0648819i
$73$	−10.6126	+	8.90507i	−1.24212	+	1.04226i	−0.244761	+	0.969583i	$0.578709\pi$
$73$	−10.6126	+	8.90507i	−1.24212	+	1.04226i	−0.997356	+	0.0726761i	$0.976846\pi$
$74$	8.72315	−	5.73731i	1.01405	−	0.666949i
$75$	5.71662	−	6.35922i	0.660098	−	0.734300i
$76$	1.58631	+	2.13079i	0.181963	+	0.244418i
$77$	−3.04225	+	1.52787i	−0.346696	+	0.174117i
$78$	0.0797266	+	0.967098i	0.00902726	+	0.109502i
$79$	15.0282	−	3.56174i	1.69080	−	0.400727i	0.731216	−	0.682146i	$-0.238953\pi$
$79$	15.0282	−	3.56174i	1.69080	−	0.400727i	0.959585	+	0.281418i	$0.0908048\pi$
$80$	0.251164			0.0280810
$81$	−1.74025	+	8.83015i	−0.193361	+	0.981128i
$82$	7.65615			0.845480
$83$	−7.27842	+	1.72502i	−0.798911	+	0.189345i	−0.609743	−	0.792599i	$-0.708727\pi$
$83$	−7.27842	+	1.72502i	−0.798911	+	0.189345i	−0.189168	+	0.981945i	$0.560579\pi$
$84$	3.13497	−	2.17179i	0.342053	−	0.236962i
$85$	−0.561274	+	0.281882i	−0.0608787	+	0.0305744i
$86$	4.97558	+	6.68337i	0.536531	+	0.720686i
$87$	−3.69858	−	11.3520i	−0.396530	−	1.21706i
$88$	1.29177	−	0.849608i	0.137703	−	0.0905685i
$89$	11.9905	−	10.0612i	1.27099	−	1.06649i	0.276569	−	0.960994i	$-0.410802\pi$
$89$	11.9905	−	10.0612i	1.27099	−	1.06649i	0.994420	−	0.105493i	$-0.0336420\pi$
$90$	0.00755494	−	0.753454i	0.000796360	−	0.0794210i
$91$	−0.944987	−	0.792939i	−0.0990616	−	0.0831226i
$92$	0.631178	+	0.0737741i	0.0658048	+	0.00769148i
$93$	1.32474	−	2.42768i	0.137370	−	0.251739i
$94$	2.31169	+	7.72159i	0.238433	+	0.796421i
$95$	−0.457861	+	0.485304i	−0.0469756	+	0.0497912i
$96$	−1.29964	+	1.14496i	−0.132644	+	0.116857i
$97$	−9.83490	+	13.2106i	−0.998582	+	1.34133i	−0.0592790	+	0.998241i	$0.518880\pi$
$97$	−9.83490	+	13.2106i	−0.998582	+	1.34133i	−0.939303	+	0.343088i	$0.888527\pi$
$98$	0.373651	−	2.11908i	0.0377444	−	0.214059i
$99$	−2.50984	−	3.90066i	−0.252248	−	0.392031i
$100$	−0.857287	−	4.86191i	−0.0857287	−	0.486191i
$101$	−1.76455	−	0.886190i	−0.175579	−	0.0881792i	0.358839	−	0.933400i	$-0.383173\pi$
$101$	−1.76455	−	0.886190i	−0.175579	−	0.0881792i	−0.534418	+	0.845220i	$0.679469\pi$
$102$	1.61931	−	4.01722i	0.160335	−	0.397764i
$103$	11.7330	−	1.37139i	1.15609	−	0.135127i	0.483636	−	0.875269i	$-0.339316\pi$
$103$	11.7330	−	1.37139i	1.15609	−	0.135127i	0.672451	+	0.740142i	$0.265242\pi$
$104$	0.468081	+	0.307861i	0.0458991	+	0.0301883i
$105$	0.673917	+	0.680708i	0.0657676	+	0.0664303i
$106$	−1.93231	+	6.45436i	−0.187682	+	0.626903i
$107$	1.86672	+	3.23326i	0.180463	+	0.312571i	0.942038	−	0.335505i	$-0.108907\pi$
$107$	1.86672	+	3.23326i	0.180463	+	0.312571i	−0.761575	+	0.648076i	$0.775574\pi$
$108$	3.39561	+	3.93317i	0.326743	+	0.378469i
$109$	−0.246494	+	0.426940i	−0.0236098	+	0.0408934i	−0.877589	−	0.479414i	$-0.840849\pi$
$109$	−0.246494	+	0.426940i	−0.0236098	+	0.0408934i	0.853979	+	0.520307i	$0.174183\pi$
$110$	0.266488	+	0.282461i	0.0254087	+	0.0269316i
$111$	−18.0070	−	1.66642i	−1.70915	−	0.158170i
$112$	0.128027	−	2.19814i	0.0120974	−	0.207705i
$113$	−1.75394	+	4.06609i	−0.164997	+	0.382506i	−0.980576	−	0.196140i	$-0.937159\pi$
$113$	−1.75394	+	4.06609i	−0.164997	+	0.382506i	0.815579	+	0.578646i	$0.196419\pi$
$114$	0.156877	−	4.59841i	0.0146928	−	0.430680i
$115$	0.00928040	+	0.159338i	0.000865402	+	0.0148584i
$116$	−6.47745	−	2.35760i	−0.601416	−	0.218898i
$117$	0.937617	−	1.39491i	0.0866828	−	0.128960i
$118$	−7.95284	+	2.89460i	−0.732118	+	0.266469i
$119$	2.18089	+	5.05586i	0.199921	+	0.463470i
$120$	−0.339886	−	0.271528i	−0.0310272	−	0.0247870i
$121$	−8.37744	−	1.98549i	−0.761585	−	0.180499i
$122$	−0.498490	−	0.118144i	−0.0451311	−	0.0106963i
$123$	−10.3606	−	8.27689i	−0.934188	−	0.746302i
$124$	−0.632430	−	1.46614i	−0.0567939	−	0.131663i
$125$	2.34528	−	0.853612i	0.209768	−	0.0763494i
$126$	−6.59025	−	0.450182i	−0.587106	−	0.0401054i
$127$	−1.62043	−	0.589788i	−0.143790	−	0.0523352i	0.269123	−	0.963106i	$-0.413266\pi$
$127$	−1.62043	−	0.589788i	−0.143790	−	0.0523352i	−0.412913	+	0.910771i	$0.635489\pi$
$128$	0.0581448	+	0.998308i	0.00513933	+	0.0882388i
$129$	0.492054	−	14.4232i	0.0433229	−	1.26989i
$130$	−0.0557340	+	0.129206i	−0.00488820	+	0.0113321i
$131$	−0.190399	+	3.26902i	−0.0166352	+	0.285616i	0.979723	+	0.200355i	$0.0642095\pi$
$131$	−0.190399	+	3.26902i	−0.0166352	+	0.285616i	−0.996359	+	0.0852612i	$0.972828\pi$
$132$	−2.66657	−	0.246771i	−0.232095	−	0.0214787i
$133$	4.01391	+	4.25450i	0.348050	+	0.368912i
$134$	4.02649	−	6.97408i	0.347836	−	0.602469i
$135$	−0.824766	+	1.01144i	−0.0709845	+	0.0870509i
$136$	−1.25034	−	2.16565i	−0.107216	−	0.185703i
$137$	−3.76625	+	12.5801i	−0.321772	+	1.07479i	0.632177	+	0.774824i	$0.282162\pi$
$137$	−3.76625	+	12.5801i	−0.321772	+	1.07479i	−0.953949	+	0.299970i	$0.903023\pi$
$138$	−0.774383	−	0.782186i	−0.0659198	−	0.0665841i
$139$	6.29646	+	4.14125i	0.534059	+	0.351256i	0.787716	−	0.616038i	$-0.211263\pi$
$139$	6.29646	+	4.14125i	0.534059	+	0.351256i	−0.253657	+	0.967294i	$0.581634\pi$
$140$	0.549291	−	0.0642029i	0.0464236	−	0.00542614i
$141$	5.21935	−	12.9483i	0.439549	−	1.09045i
$142$	−14.2694	−	7.16634i	−1.19746	−	0.601386i
$143$	0.150416	+	0.853052i	0.0125784	+	0.0713358i
$144$	2.99652	−	0.144397i	0.249710	−	0.0120331i
$145$	0.300639	−	1.70501i	0.0249668	−	0.141593i
$146$	8.27293	−	11.1125i	0.684673	−	0.919675i
$147$	−2.79653	+	2.46369i	−0.230654	+	0.203202i
$148$	−7.16491	+	7.59436i	−0.588952	+	0.624252i
$149$	−5.37822	−	17.9645i	−0.440601	−	1.47171i	−0.833702	−	0.552214i	$-0.813783\pi$
$149$	−5.37822	−	17.9645i	−0.440601	−	1.47171i	0.393101	−	0.919495i	$-0.371402\pi$
$150$	−4.09599	+	7.50615i	−0.334436	+	0.612875i
$151$	−2.46180	−	0.287743i	−0.200338	−	0.0234162i	0.0153319	−	0.999882i	$-0.495120\pi$
$151$	−2.46180	−	0.287743i	−0.200338	−	0.0234162i	−0.215670	+	0.976466i	$0.569194\pi$
$152$	−2.03495	−	1.70752i	−0.165056	−	0.138498i
$153$	−6.53425	+	3.68569i	−0.528262	+	0.297971i
$154$	2.60789	−	2.18828i	0.210150	−	0.176337i
$155$	0.335063	−	0.220375i	0.0269129	−	0.0177009i
$156$	−0.300606	−	0.922643i	−0.0240677	−	0.0738706i
$157$	4.93937	+	6.63473i	0.394205	+	0.529509i	0.954273	−	0.298938i	$-0.0966323\pi$
$157$	4.93937	+	6.63473i	0.394205	+	0.529509i	−0.560068	+	0.828447i	$0.689225\pi$
$158$	−13.8017	+	6.93147i	−1.09800	+	0.551438i
$159$	9.59255	−	6.64536i	0.760739	−	0.527011i
$160$	−0.244394	+	0.0579224i	−0.0193210	+	0.00457917i
$161$	1.39923			0.110275
$162$	−0.343034	−	8.99346i	−0.0269513	−	0.706593i
$163$	9.90658			0.775943			0.387972	−	0.921671i	$-0.373176\pi$
$163$	9.90658			0.775943			0.387972	+	0.921671i	$0.373176\pi$
$164$	−7.44978	+	1.76563i	−0.581730	+	0.137873i
$165$	−0.0552617	−	0.670333i	−0.00430212	−	0.0521854i
$166$	6.68442	−	3.35704i	0.518811	−	0.260557i
$167$	5.52496	+	7.42131i	0.427534	+	0.574278i	0.962735	−	0.270447i	$-0.0871714\pi$
$167$	5.52496	+	7.42131i	0.427534	+	0.574278i	−0.535201	+	0.844725i	$0.679764\pi$
$168$	−2.54962	+	2.83622i	−0.196707	+	0.218819i
$169$	10.5991	−	6.97114i	0.815315	−	0.536241i
$170$	0.481138	−	0.403723i	0.0369016	−	0.0309641i
$171$	−5.18352	+	6.05317i	−0.396394	+	0.462898i
$172$	−6.38275	−	5.35577i	−0.486680	−	0.408373i
$173$	14.5022	+	1.69506i	1.10258	+	0.128873i	0.647859	−	0.761760i	$-0.275664\pi$
$173$	14.5022	+	1.69506i	1.10258	+	0.128873i	0.454722	+	0.890633i	$0.349739\pi$
$174$	6.21683	+	10.1930i	0.471297	+	0.772732i
$175$	−3.11768	−	10.4138i	−0.235674	−	0.787207i
$176$	−1.06101	+	1.12461i	−0.0799769	+	0.0847705i
$177$	13.8914	+	4.68053i	1.04414	+	0.351810i
$178$	−9.34701	+	12.5552i	−0.700588	+	0.941053i
$179$	−2.19130	+	12.4275i	−0.163786	+	0.928874i	0.786522	+	0.617562i	$0.211880\pi$
$179$	−2.19130	+	12.4275i	−0.163786	+	0.928874i	−0.950308	+	0.311312i	$0.899232\pi$
$180$	0.166407	+	0.734887i	0.0124033	+	0.0547752i
$181$	2.00310	+	11.3601i	0.148889	+	0.844393i	0.964162	+	0.265315i	$0.0854760\pi$
$181$	2.00310	+	11.3601i	0.148889	+	0.844393i	−0.815273	+	0.579077i	$0.803413\pi$
$182$	1.10238	+	0.553636i	0.0817138	+	0.0410382i
$183$	0.546856	+	0.698784i	0.0404247	+	0.0516556i
$184$	−0.631178	+	0.0737741i	−0.0465310	+	0.00543870i
$185$	−2.19094	−	1.44101i	−0.161081	−	0.105945i
$186$	−0.729175	+	2.66775i	−0.0534657	+	0.195609i
$187$	1.10888	−	3.70393i	0.0810896	−	0.270858i
$188$	−4.03010	−	6.98034i	−0.293925	−	0.509094i
$189$	8.43154	+	7.73378i	0.613305	+	0.562550i
$190$	0.333600	−	0.577813i	0.0242019	−	0.0419190i
$191$	4.43970	+	4.70580i	0.321245	+	0.340500i	0.867791	−	0.496929i	$-0.165539\pi$
$191$	4.43970	+	4.70580i	0.321245	+	0.340500i	−0.546546	+	0.837429i	$0.684058\pi$
$192$	1.00056	−	1.41381i	0.0722095	−	0.102033i
$193$	1.05094	−	18.0440i	0.0756486	−	1.29884i	−0.720381	−	0.693578i	$-0.756033\pi$
$193$	1.05094	−	18.0440i	0.0756486	−	1.29884i	0.796030	−	0.605257i	$-0.206930\pi$
$194$	6.52323	−	15.1225i	0.468341	−	1.08574i
$195$	0.215103	−	0.114595i	0.0154039	−	0.00820629i
$196$	0.125114	+	2.14813i	0.00893673	+	0.153438i
$197$	−22.5434	−	8.20512i	−1.60615	−	0.584591i	−0.625476	−	0.780243i	$-0.715095\pi$
$197$	−22.5434	−	8.20512i	−1.60615	−	0.584591i	−0.980673	+	0.195653i	$0.937317\pi$
$198$	3.34174	+	3.21671i	0.237487	+	0.228601i
$199$	9.19041	−	3.34504i	0.651491	−	0.237123i	0.00493270	−	0.999988i	$-0.498430\pi$
$199$	9.19041	−	3.34504i	0.651491	−	0.237123i	0.646558	+	0.762864i	$0.276208\pi$
$200$	1.95541	+	4.53316i	0.138269	+	0.320543i
$201$	−12.9883	+	5.08470i	−0.916127	+	0.358647i
$202$	1.92136	+	0.455370i	0.135186	+	0.0320397i
$203$	−14.7687	−	3.50025i	−1.03656	−	0.245670i
$204$	−0.649222	+	4.28238i	−0.0454546	+	0.299826i
$205$	−0.761641	−	1.76568i	−0.0531953	−	0.123321i
$206$	−11.1005	+	4.04024i	−0.773407	+	0.281497i
$207$	0.202326	+	1.89566i	0.0140626	+	0.131757i
$208$	−0.526461	−	0.191616i	−0.0365035	−	0.0132862i
$209$	−0.238811	−	4.10022i	−0.0165189	−	0.283618i
$210$	−0.812734	−	0.506944i	−0.0560839	−	0.0349824i
$211$	0.281254	−	0.652020i	0.0193623	−	0.0448869i	−0.908261	−	0.418405i	$-0.862589\pi$
$211$	0.281254	−	0.652020i	0.0193623	−	0.0448869i	0.927623	+	0.373518i	$0.121849\pi$
$212$	0.391745	−	6.72601i	0.0269052	−	0.461944i
$213$	11.5626	+	25.1241i	0.792254	+	1.72147i
$214$	−2.56205	−	2.71561i	−0.175138	−	0.185635i
$215$	1.04636	−	1.81235i	0.0713612	−	0.123601i
$216$	−4.21113	−	3.04407i	−0.286531	−	0.207123i
$217$	−1.75789	−	3.04475i	−0.119333	−	0.206691i
$218$	0.141390	−	0.472277i	0.00957617	−	0.0319866i
$219$	−23.2088	+	6.09422i	−1.56830	+	0.411810i
$220$	−0.324445	−	0.213391i	−0.0218741	−	0.0143868i
$221$	1.39153	−	0.162646i	0.0936044	−	0.0109408i
$222$	17.9060	−	2.53121i	1.20177	−	0.169884i
$223$	−12.0491	−	6.05129i	−0.806868	−	0.405224i	−0.00297286	−	0.999996i	$-0.500946\pi$
$223$	−12.0491	−	6.05129i	−0.806868	−	0.405224i	−0.803895	+	0.594771i	$0.797243\pi$
$224$	0.382351	+	2.16842i	0.0255469	+	0.144884i
$225$	13.6576	−	5.72959i	0.910507	−	0.381973i
$226$	0.768957	−	4.36097i	0.0511503	−	0.290088i
$227$	−9.89164	+	13.2868i	−0.656531	+	0.881875i	−0.998322	−	0.0579015i	$-0.981559\pi$
$227$	−9.89164	+	13.2868i	−0.656531	+	0.881875i	0.341791	+	0.939776i	$0.388966\pi$
$228$	0.907818	+	4.51063i	0.0601217	+	0.298724i
$229$	1.87718	−	1.98970i	0.124048	−	0.131483i	−0.662373	−	0.749174i	$-0.730450\pi$
$229$	1.87718	−	1.98970i	0.124048	−	0.131483i	0.786421	+	0.617691i	$0.211932\pi$
$230$	−0.0457762	−	0.152903i	−0.00301839	−	0.0100821i
$231$	−5.89481	+	0.141948i	−0.387850	+	0.00933948i
$232$	6.84655	+	0.800247i	0.449498	+	0.0525388i
$233$	11.4780	+	9.63120i	0.751950	+	0.630961i	0.936018	−	0.351953i	$-0.114482\pi$
$233$	11.4780	+	9.63120i	0.751950	+	0.630961i	−0.184068	+	0.982914i	$0.558927\pi$
$234$	−0.590655	+	1.57354i	−0.0386123	+	0.102866i
$235$	1.55081	−	1.30128i	0.101163	−	0.0848862i
$236$	7.07093	−	4.65062i	0.460278	−	0.302730i
$237$	26.1705	+	5.54072i	1.69996	+	0.359908i
$238$	−3.28806	−	4.41663i	−0.213133	−	0.286288i
$239$	9.29814	−	4.66970i	0.601447	−	0.302058i	−0.121900	−	0.992542i	$-0.538899\pi$
$239$	9.29814	−	4.66970i	0.601447	−	0.302058i	0.723347	+	0.690484i	$0.242603\pi$
$240$	0.393343	+	0.185825i	0.0253902	+	0.0119950i
$241$	16.5544	−	3.92346i	1.06636	−	0.252732i	0.340268	−	0.940329i	$-0.389482\pi$
$241$	16.5544	−	3.92346i	1.06636	−	0.252732i	0.726093	+	0.687596i	$0.241334\pi$
$242$	8.60951			0.553440
$243$	−9.25842	+	12.5412i	−0.593928	+	0.804518i
$244$	0.512299			0.0327966
$245$	−0.525879	+	0.124636i	−0.0335972	+	0.00796268i
$246$	11.9902	+	5.66446i	0.764464	+	0.361152i
$247$	1.32996	−	0.667931i	0.0846234	−	0.0424994i
$248$	0.953497	+	1.28077i	0.0605471	+	0.0813289i
$249$	−12.6749	−	2.68347i	−0.803238	−	0.170058i
$250$	−2.08521	+	1.37146i	−0.131880	+	0.0867389i
$251$	−7.47331	+	6.27085i	−0.471711	+	0.395813i	−0.847418	−	0.530926i	$-0.821844\pi$
$251$	−7.47331	+	6.27085i	−0.471711	+	0.395813i	0.375707	+	0.926738i	$0.377400\pi$
$252$	6.51643	−	1.08177i	0.410496	−	0.0681450i
$253$	−0.752655	−	0.631552i	−0.0473190	−	0.0397054i
$254$	1.71277	+	0.200194i	0.107468	+	0.0125613i
$255$	−1.08755	+	0.0261884i	−0.0681052	+	0.00163998i
$256$	−0.286803	−	0.957990i	−0.0179252	−	0.0598743i
$257$	11.3853	−	12.0677i	0.710197	−	0.752764i	−0.267323	−	0.963607i	$-0.586139\pi$
$257$	11.3853	−	12.0677i	0.710197	−	0.752764i	0.977520	+	0.210842i	$0.0676207\pi$
$258$	2.84743	+	14.1479i	0.177273	+	0.880811i
$259$	−13.7282	+	18.4402i	−0.853031	+	1.14582i
$260$	0.0244348	−	0.138576i	0.00151538	−	0.00859414i
$261$	2.60656	−	20.5146i	0.161342	−	1.26982i
$262$	−0.568622	−	3.22482i	−0.0351296	−	0.199230i
$263$	−8.74253	−	4.39067i	−0.539088	−	0.270740i	0.158353	−	0.987383i	$-0.449382\pi$
$263$	−8.74253	−	4.39067i	−0.539088	−	0.270740i	−0.697441	+	0.716643i	$0.745678\pi$
$264$	2.65160	−	0.374833i	0.163195	−	0.0230694i
$265$	1.68075	−	0.196452i	0.103248	−	0.0120679i
$266$	−4.88687	−	3.21415i	−0.299633	−	0.197072i
$267$	26.2219	−	6.88544i	1.60476	−	0.421382i
$268$	−2.30962	+	7.71466i	−0.141082	+	0.471248i
$269$	−5.88050	−	10.1853i	−0.358540	−	0.621010i	0.629177	−	0.777262i	$-0.283392\pi$
$269$	−5.88050	−	10.1853i	−0.358540	−	0.621010i	−0.987717	+	0.156252i	$0.950059\pi$
$270$	0.569280	−	1.17438i	0.0346453	−	0.0714705i
$271$	14.1330	−	24.4791i	0.858520	−	1.48700i	−0.0148203	−	0.999890i	$-0.504718\pi$
$271$	14.1330	−	24.4791i	0.858520	−	1.48700i	0.873340	−	0.487110i	$-0.161949\pi$
$272$	1.71607	+	1.81893i	0.104052	+	0.110289i
$273$	−0.893266	−	1.94096i	−0.0540629	−	0.117472i
$274$	0.763547	−	13.1096i	0.0461276	−	0.791980i
$275$	−3.02331	+	7.00881i	−0.182312	+	0.422647i
$276$	0.933894	+	0.582518i	0.0562138	+	0.0350634i
$277$	0.590081	+	10.1313i	0.0354545	+	0.608730i	0.968506	+	0.248989i	$0.0800982\pi$
$277$	0.590081	+	10.1313i	0.0354545	+	0.608730i	−0.933052	+	0.359742i	$0.882865\pi$
$278$	−7.08178	−	2.57756i	−0.424737	−	0.154592i
$279$	3.87079	−	2.82182i	0.231738	−	0.168938i
$280$	−0.519679	+	0.189148i	−0.0310567	+	0.0113037i
$281$	7.16336	+	16.6065i	0.427330	+	0.990662i	0.986819	+	0.161825i	$0.0517380\pi$
$281$	7.16336	+	16.6065i	0.427330	+	0.990662i	−0.559489	+	0.828837i	$0.689003\pi$
$282$	−2.09257	+	13.8030i	−0.124611	+	0.821955i
$283$	−20.6263	−	4.88853i	−1.22611	−	0.290593i	−0.433965	−	0.900930i	$-0.642886\pi$
$283$	−20.6263	−	4.88853i	−1.22611	−	0.290593i	−0.792142	+	0.610337i	$0.791034\pi$
$284$	15.5374	+	3.68243i	0.921975	+	0.218512i
$285$	−1.07610	+	0.421275i	−0.0637429	+	0.0249542i
$286$	−0.343089	−	0.795370i	−0.0202873	−	0.0470312i
$287$	−15.8412	+	5.76572i	−0.935076	+	0.340340i
$288$	−2.88245	+	0.831550i	−0.169850	+	0.0489996i
$289$	10.0985	+	3.67555i	0.594029	+	0.216209i
$290$	0.100667	+	1.72838i	0.00591137	+	0.101494i
$291$	−25.1762	+	13.4124i	−1.47585	+	0.786249i
$292$	−5.48722	+	12.7208i	−0.321115	+	0.744429i
$293$	−0.506130	+	8.68992i	−0.0295684	+	0.507671i	0.950714	+	0.310069i	$0.100352\pi$
$293$	−0.506130	+	8.68992i	−0.0295684	+	0.507671i	−0.980282	+	0.197601i	$0.936685\pi$
$294$	2.15298	−	3.04220i	0.125565	−	0.177425i
$295$	1.45872	+	1.54615i	0.0849297	+	0.0900202i
$296$	5.22040	−	9.04199i	0.303429	−	0.525555i
$297$	−1.04468	−	7.96567i	−0.0606187	−	0.462215i
$298$	9.37615	+	16.2400i	0.543146	+	0.940756i
$299$	0.102109	−	0.341067i	0.00590510	−	0.0197244i
$300$	2.25454	−	8.24842i	0.130166	−	0.476223i
$301$	−15.3280	−	10.0814i	−0.883492	−	0.581082i
$302$	2.46180	−	0.287743i	0.141660	−	0.0165577i
$303$	−2.10778	−	2.69336i	−0.121089	−	0.154730i
$304$	2.37388	+	1.19221i	0.136151	+	0.0683777i
$305$	0.0223435	+	0.126716i	0.00127938	+	0.00725575i
$306$	5.50814	−	5.09324i	0.314879	−	0.291161i
$307$	2.06704	−	11.7228i	0.117972	−	0.669053i	−0.867264	−	0.497849i	$-0.834123\pi$
$307$	2.06704	−	11.7228i	0.117972	−	0.669053i	0.985236	−	0.171204i	$-0.0547656\pi$
$308$	−2.03294	+	2.73072i	−0.115838	+	0.155597i
$309$	19.3895	+	6.53303i	1.10303	+	0.371651i
$310$	−0.275210	+	0.291705i	−0.0156309	+	0.0165678i
$311$	−1.44175	−	4.81578i	−0.0817542	−	0.273078i	0.907332	−	0.420414i	$-0.138115\pi$
$311$	−1.44175	−	4.81578i	−0.0817542	−	0.273078i	−0.989086	+	0.147336i	$0.952930\pi$
$312$	0.505279	+	0.828449i	0.0286058	+	0.0469017i
$313$	26.5783	+	3.10656i	1.50230	+	0.175593i	0.827104	−	0.562049i	$-0.189987\pi$
$313$	26.5783	+	3.10656i	1.50230	+	0.175593i	0.675192	+	0.737642i	$0.264061\pi$
$314$	−6.33631	−	5.31679i	−0.357578	−	0.300044i
$315$	0.551782	+	1.56465i	0.0310894	+	0.0881579i
$316$	11.8312	−	9.92752i	0.665555	−	0.558467i
$317$	−11.9562	+	7.86374i	−0.671529	+	0.441671i	−0.838946	−	0.544215i	$-0.816828\pi$
$317$	−11.9562	+	7.86374i	−0.671529	+	0.441671i	0.167417	+	0.985886i	$0.446457\pi$
$318$	−7.80146	+	8.67843i	−0.437484	+	0.486662i
$319$	6.36432	+	8.54876i	0.356333	+	0.478639i
$320$	0.224448	−	0.112722i	0.0125470	−	0.00630136i
$321$	0.531292	+	6.44466i	0.0296538	+	0.359706i
$322$	−1.36152	+	0.322685i	−0.0758743	+	0.0179825i
$323$	−6.64290			−0.369621
$324$	2.40782	+	8.67193i	0.133768	+	0.481774i
$325$	−2.76590			−0.153424
$326$	−9.63954	+	2.28461i	−0.533885	+	0.126533i
$327$	−0.701904	+	0.486252i	−0.0388154	+	0.0268898i
$328$	6.84179	−	3.43607i	0.377774	−	0.189725i
$329$	−10.5981	−	14.2357i	−0.584291	−	0.784839i
$330$	0.208362	+	0.639520i	0.0114699	+	0.0352044i
$331$	−0.0386053	+	0.0253911i	−0.00212194	+	0.00139562i	−0.550570	−	0.834789i	$-0.685589\pi$
$331$	−0.0386053	+	0.0253911i	−0.00212194	+	0.00139562i	0.548448	+	0.836185i	$0.315219\pi$
$332$	−5.73005	+	4.80808i	−0.314477	+	0.263878i
$333$	−26.9676	−	15.9324i	−1.47781	−	0.873089i
$334$	−7.08751	−	5.94712i	−0.387811	−	0.325412i
$335$	−2.00894	−	0.234812i	−0.109760	−	0.0128291i
$336$	1.82681	−	3.34775i	0.0996609	−	0.182635i
$337$	−8.01302	−	26.7654i	−0.436497	−	1.45800i	−0.839780	−	0.542927i	$-0.817316\pi$
$337$	−8.01302	−	26.7654i	−0.436497	−	1.45800i	0.403283	−	0.915075i	$-0.367869\pi$
$338$	−8.70575	+	9.22755i	−0.473530	+	0.501913i
$339$	−5.75514	+	5.07016i	−0.312576	+	0.275374i
$340$	−0.375064	+	0.503799i	−0.0203407	+	0.0273223i
$341$	−0.428690	+	2.43122i	−0.0232149	+	0.131658i
$342$	3.64784	−	7.08541i	0.197253	−	0.383135i
$343$	3.49919	+	19.8449i	0.188938	+	1.07152i
$344$	7.44583	+	3.73944i	0.401452	+	0.201617i
$345$	−0.103354	+	0.256403i	−0.00556438	+	0.0138043i
$346$	−14.5022	+	1.69506i	−0.779643	+	0.0911272i
$347$	11.2451	+	7.39600i	0.603667	+	0.397038i	0.814230	−	0.580542i	$-0.197159\pi$
$347$	11.2451	+	7.39600i	0.603667	+	0.397038i	−0.210563	+	0.977580i	$0.567530\pi$
$348$	−8.39993	−	8.48458i	−0.450284	−	0.454821i
$349$	−2.89665	+	9.67548i	−0.155054	+	0.517917i	−0.999853	−	0.0171679i	$-0.994535\pi$
$349$	−2.89665	+	9.67548i	−0.155054	+	0.517917i	0.844799	+	0.535084i	$0.179720\pi$
$350$	5.43522	+	9.41408i	0.290525	+	0.503204i
$351$	2.50042	−	1.49084i	0.133463	−	0.0795752i
$352$	0.773061	−	1.33898i	0.0412043	−	0.0713679i
$353$	−3.14161	−	3.32991i	−0.167211	−	0.177233i	0.638350	−	0.769746i	$-0.279617\pi$
$353$	−3.14161	−	3.32991i	−0.167211	−	0.177233i	−0.805561	+	0.592513i	$0.798136\pi$
$354$	−14.5964	−	1.35079i	−0.775789	−	0.0717936i
$355$	−0.233192	+	4.00375i	−0.0123765	+	0.212497i
$356$	6.19963	−	14.3724i	0.328580	−	0.761733i
$357$	−0.325169	+	9.53143i	−0.0172098	+	0.504457i
$358$	−0.733742	−	12.5979i	−0.0387794	−	0.665817i
$359$	−35.1480	−	12.7928i	−1.85504	−	0.675180i	−0.982392	−	0.186831i	$-0.940178\pi$
$359$	−35.1480	−	12.7928i	−1.85504	−	0.675180i	−0.872648	−	0.488349i	$-0.837599\pi$
$360$	−0.331398	−	0.676702i	−0.0174662	−	0.0356653i
$361$	11.2231	−	4.08487i	0.590688	−	0.214993i
$362$	−4.56893	−	10.5920i	−0.240138	−	0.556702i
$363$	−11.6508	−	9.30754i	−0.611507	−	0.488519i
$364$	−1.20034	−	0.284486i	−0.0629150	−	0.0149111i
$365$	−3.38579	−	0.802447i	−0.177220	−	0.0420020i
$366$	−0.693266	−	0.553835i	−0.0362376	−	0.0289494i
$367$	−10.1408	−	23.5089i	−0.529344	−	1.22716i	−0.947784	−	0.318912i	$-0.896682\pi$
$367$	−10.1408	−	23.5089i	−0.529344	−	1.22716i	0.418440	−	0.908244i	$-0.362577\pi$
$368$	0.597151	−	0.217345i	0.0311286	−	0.0113299i
$369$	−10.1019	−	20.6277i	−0.525884	−	1.07383i
$370$	2.46420	+	0.896897i	0.128108	+	0.0466274i
$371$	−0.862572	−	14.8098i	−0.0447825	−	0.768886i
$372$	0.0942949	−	2.76400i	0.00488896	−	0.143307i
$373$	−5.35273	+	12.4090i	−0.277154	+	0.642515i	−0.998760	−	0.0497893i	$-0.984145\pi$
$373$	−5.35273	+	12.4090i	−0.277154	+	0.642515i	0.721606	+	0.692304i	$0.243404\pi$
$374$	−0.224809	+	3.85982i	−0.0116246	+	0.199586i
$375$	4.30445	+	0.398345i	0.222281	+	0.0205705i
$376$	5.53125	+	5.86278i	0.285252	+	0.302350i
$377$	−1.93094	+	3.34449i	−0.0994485	+	0.172250i
$378$	−9.98780	−	5.58087i	−0.513717	−	0.287049i
$379$	−3.06071	−	5.30130i	−0.157218	−	0.272309i	0.776647	−	0.629937i	$-0.216919\pi$
$379$	−3.06071	−	5.30130i	−0.157218	−	0.272309i	−0.933864	+	0.357627i	$0.883586\pi$
$380$	−0.191355	+	0.639171i	−0.00981632	+	0.0327888i
$381$	−2.10137	−	2.12254i	−0.107656	−	0.108741i
$382$	−5.40526	−	3.55509i	−0.276557	−	0.181894i
$383$	21.2157	−	2.47976i	1.08407	−	0.126710i	0.444754	−	0.895653i	$-0.353291\pi$
$383$	21.2157	−	2.47976i	1.08407	−	0.126710i	0.639317	+	0.768943i	$0.279217\pi$
$384$	−0.647546	+	1.60645i	−0.0330449	+	0.0819789i
$385$	−0.764103	−	0.383747i	−0.0389423	−	0.0195575i
$386$	3.13862	+	17.8000i	0.159751	+	0.905995i
$387$	11.4417	−	22.2239i	0.581615	−	1.12970i
$388$	−2.85990	+	16.2193i	−0.145189	+	0.823409i
$389$	−3.52828	+	4.73931i	−0.178891	+	0.240292i	−0.882520	−	0.470276i	$-0.844155\pi$
$389$	−3.52828	+	4.73931i	−0.178891	+	0.240292i	0.703629	+	0.710568i	$0.251562\pi$
$390$	−0.182878	+	0.161112i	−0.00926039	+	0.00815822i
$391$	−1.09052	+	1.15588i	−0.0551500	+	0.0584556i
$392$	−0.617134	−	2.06137i	−0.0311700	−	0.104115i
$393$	−2.71679	+	4.97869i	−0.137044	+	0.251142i
$394$	23.8280	+	2.78509i	1.20043	+	0.140311i
$395$	2.97156	+	2.49344i	0.149515	+	0.125458i
$396$	−3.99349	−	2.35934i	−0.200680	−	0.118561i
$397$	−6.09144	+	5.11133i	−0.305721	+	0.256530i	−0.782721	−	0.622373i	$-0.786169\pi$
$397$	−6.09144	+	5.11133i	−0.305721	+	0.256530i	0.477000	+	0.878903i	$0.341724\pi$
$398$	−8.17127	+	5.37433i	−0.409589	+	0.269391i
$399$	3.13840	+	9.63262i	0.157116	+	0.482234i
$400$	−2.94812	−	3.96002i	−0.147406	−	0.198001i
$401$	4.91089	−	2.46634i	0.245238	−	0.123163i	−0.321935	−	0.946762i	$-0.604333\pi$
$401$	4.91089	−	2.46634i	0.245238	−	0.123163i	0.567173	+	0.823598i	$0.308037\pi$
$402$	11.4656	−	7.94296i	0.571854	−	0.396159i
$403$	−0.870448	+	0.206300i	−0.0433601	+	0.0102765i
$404$	−1.97458			−0.0982391
$405$	−2.03997	+	0.973790i	−0.101367	+	0.0483880i
$406$	15.1778			0.753264
$407$	15.7076	−	3.72277i	0.778597	−	0.184531i
$408$	−0.355862	−	4.31666i	−0.0176178	−	0.213707i
$409$	−17.5940	+	8.83606i	−0.869969	+	0.436915i	−0.827027	−	0.562162i	$-0.809970\pi$
$409$	−17.5940	+	8.83606i	−0.869969	+	0.436915i	−0.0429426	+	0.999078i	$0.513673\pi$
$410$	1.14831	+	1.54244i	0.0567108	+	0.0761758i
$411$	−15.2058	+	16.9150i	−0.750044	+	0.834357i
$412$	9.86951	−	6.49128i	0.486236	−	0.319802i
$413$	14.2752	−	11.9783i	0.702436	−	0.589414i
$414$	−0.634041	−	1.79790i	−0.0311614	−	0.0883620i
$415$	−1.43918	−	1.20762i	−0.0706467	−	0.0592796i
$416$	0.556460	+	0.0650408i	0.0272827	+	0.00318889i
$417$	6.79684	+	11.1440i	0.332843	+	0.545725i
$418$	1.17795	+	3.93463i	0.0576154	+	0.192449i
$419$	20.2581	−	21.4723i	0.989672	−	1.04899i	−0.00912551	−	0.999958i	$-0.502905\pi$
$419$	20.2581	−	21.4723i	0.989672	−	1.04899i	0.998797	−	0.0490323i	$-0.0156137\pi$
$420$	0.907736	+	0.305850i	0.0442930	+	0.0149239i
$421$	−23.2515	+	31.2321i	−1.13321	+	1.52216i	−0.313310	+	0.949651i	$0.601438\pi$
$421$	−23.2515	+	31.2321i	−1.13321	+	1.52216i	−0.819897	+	0.572511i	$0.805969\pi$
$422$	−0.123307	+	0.699306i	−0.00600247	+	0.0340417i
$423$	17.7538	−	16.4166i	0.863221	−	0.798200i
$424$	1.16994	+	6.63505i	0.0568172	+	0.322226i
$425$	11.0325	+	5.54072i	0.535154	+	0.268764i
$426$	−17.0449	−	21.7804i	−0.825828	−	1.05526i
$427$	1.12039	−	0.130955i	0.0542194	−	0.00633734i
$428$	3.11925	+	2.05156i	0.150775	+	0.0991661i
$429$	−0.395573	+	1.44724i	−0.0190984	+	0.0698732i
$430$	−0.600199	+	2.00481i	−0.0289442	+	0.0966803i
$431$	14.3523	+	24.8589i	0.691325	+	1.19741i	0.971404	+	0.237433i	$0.0763060\pi$
$431$	14.3523	+	24.8589i	0.691325	+	1.19741i	−0.280079	+	0.959977i	$0.590361\pi$
$432$	4.79963	+	1.99086i	0.230922	+	0.0957853i
$433$	−5.02440	+	8.70251i	−0.241457	+	0.418216i	−0.961130	−	0.276098i	$-0.910959\pi$
$433$	−5.02440	+	8.70251i	−0.241457	+	0.418216i	0.719673	+	0.694314i	$0.244292\pi$
$434$	2.41267	+	2.55728i	0.115812	+	0.122753i
$435$	1.73229	−	2.44776i	0.0830570	−	0.117361i
$436$	−0.0286647	+	0.492153i	−0.00137279	+	0.0235699i
$437$	−0.668621	+	1.55004i	−0.0319845	+	0.0741484i
$438$	21.1777	−	11.2823i	1.01191	−	0.539087i
$439$	1.48711	+	25.5326i	0.0709757	+	1.21861i	0.826291	+	0.563244i	$0.190447\pi$
$439$	1.48711	+	25.5326i	0.0709757	+	1.21861i	−0.755315	+	0.655362i	$0.772516\pi$
$440$	0.364911	+	0.132817i	0.0173964	+	0.00633179i
$441$	−6.20237	+	1.78930i	−0.295351	+	0.0852050i
$442$	−1.31651	+	0.479171i	−0.0626201	+	0.0227918i
$443$	4.63197	+	10.7381i	0.220072	+	0.510184i	0.992107	−	0.125396i	$-0.0400203\pi$
$443$	4.63197	+	10.7381i	0.220072	+	0.510184i	−0.772035	+	0.635580i	$0.780761\pi$
$444$	−16.8396	+	6.59238i	−0.799170	+	0.312860i
$445$	3.82537	+	0.906629i	0.181340	+	0.0429783i
$446$	13.1198	+	3.10946i	0.621243	+	0.147237i
$447$	4.86843	−	32.1130i	0.230269	−	1.51889i
$448$	−0.872116	−	2.02179i	−0.0412036	−	0.0955207i
$449$	6.66383	−	2.42544i	0.314486	−	0.114463i	−0.179955	−	0.983675i	$-0.557595\pi$
$449$	6.66383	−	2.42544i	0.314486	−	0.114463i	0.494441	+	0.869211i	$0.335373\pi$
$450$	−11.9681	+	8.72481i	−0.564183	+	0.411291i
$451$	11.1235	+	4.04861i	0.523783	+	0.190642i
$452$	0.257480	+	4.42076i	0.0121108	+	0.207935i
$453$	−3.64249	−	2.27201i	−0.171139	−	0.106748i
$454$	6.56087	−	15.2098i	0.307917	−	0.713831i
$455$	0.0180153	−	0.309310i	0.000844568	−	0.0145007i
$456$	−1.92357	−	4.17969i	−0.0900795	−	0.195732i
$457$	−11.4945	−	12.1835i	−0.537690	−	0.569918i	0.400387	−	0.916346i	$-0.368876\pi$
$457$	−11.4945	−	12.1835i	−0.537690	−	0.569918i	−0.938076	+	0.346428i	$0.887394\pi$
$458$	−1.36773	+	2.36898i	−0.0639098	+	0.110695i
$459$	−12.9600	+	0.937688i	−0.604923	+	0.0437675i
$460$	0.0798042	+	0.138225i	0.00372089	+	0.00644477i
$461$	7.60047	−	25.3873i	0.353989	−	1.18241i	−0.576811	−	0.816877i	$-0.695703\pi$
$461$	7.60047	−	25.3873i	0.353989	−	1.18241i	0.930800	−	0.365528i	$-0.119112\pi$
$462$	5.70318	−	1.49756i	0.265336	−	0.0696728i
$463$	−2.88462	−	1.89725i	−0.134060	−	0.0881726i	0.480708	−	0.876881i	$-0.340380\pi$
$463$	−2.88462	−	1.89725i	−0.134060	−	0.0881726i	−0.614768	+	0.788708i	$0.710750\pi$
$464$	−6.84655	+	0.800247i	−0.317843	+	0.0371505i
$465$	0.687782	−	0.0972257i	0.0318951	−	0.00450874i
$466$	−13.3897	−	6.72458i	−0.620268	−	0.311510i
$467$	2.43750	+	13.8238i	0.112794	+	0.639688i	0.987819	+	0.155609i	$0.0497340\pi$
$467$	2.43750	+	13.8238i	0.112794	+	0.639688i	−0.875024	+	0.484079i	$0.839155\pi$
$468$	0.211851	−	1.66734i	0.00979281	−	0.0770728i
$469$	−3.07906	+	17.4622i	−0.142178	+	0.806330i
$470$	−1.20891	+	1.62384i	−0.0557627	+	0.0749024i
$471$	2.82671	+	14.0450i	0.130248	+	0.647158i
$472$	−5.80782	+	6.15593i	−0.267327	+	0.283350i
$473$	3.69472	+	12.3412i	0.169884	+	0.567450i
$474$	−26.7429	+	0.643971i	−1.22834	+	0.0295786i
$475$	13.0259	+	1.52251i	0.597670	+	0.0698577i
$476$	4.21798	+	3.53930i	0.193331	+	0.162224i
$477$	19.9393	−	3.31006i	0.912959	−	0.151557i
$478$	−7.97060	+	6.68813i	−0.364567	+	0.305908i
$479$	14.6921	−	9.66318i	0.671301	−	0.441522i	−0.167564	−	0.985861i	$-0.553590\pi$
$479$	14.6921	−	9.66318i	0.671301	−	0.441522i	0.838865	+	0.544339i	$0.183220\pi$
$480$	−0.425595	−	0.0901052i	−0.0194257	−	0.00411272i
$481$	3.49304	+	4.69197i	0.159269	+	0.213935i
$482$	−15.2033	+	7.63540i	−0.692493	+	0.347783i
$483$	2.19131	+	1.03523i	0.0997082	+	0.0471047i
$484$	−8.37744	+	1.98549i	−0.380793	+	0.0902495i
$485$	−4.13654			−0.187831
$486$	6.11665	−	14.3383i	0.277457	−	0.650398i
$487$	−26.6256			−1.20652			−0.603261	−	0.797544i	$-0.706132\pi$
$487$	−26.6256			−1.20652			−0.603261	+	0.797544i	$0.706132\pi$
$488$	−0.498490	+	0.118144i	−0.0225656	+	0.00534814i
$489$	15.5145	+	7.32945i	0.701590	+	0.331449i
$490$	0.482961	−	0.242552i	0.0218180	−	0.0109574i
$491$	−1.65145	−	2.21828i	−0.0745289	−	0.100110i	0.763295	−	0.646050i	$-0.223580\pi$
$491$	−1.65145	−	2.21828i	−0.0745289	−	0.100110i	−0.837824	+	0.545940i	$0.816173\pi$
$492$	−12.9733	−	2.74665i	−0.584880	−	0.123828i
$493$	14.4018	−	9.47222i	0.648625	−	0.426607i
$494$	−1.14008	+	0.956637i	−0.0512944	+	0.0430411i
$495$	0.409406	−	1.09068i	0.0184015	−	0.0490225i
$496$	−1.22316	−	1.02635i	−0.0549215	−	0.0460846i
$497$	34.9213	+	4.08171i	1.56643	+	0.183090i
$498$	12.9521	−	0.311887i	0.580396	−	0.0139760i
$499$	10.3345	+	34.5195i	0.462634	+	1.54531i	0.797666	+	0.603100i	$0.206068\pi$
$499$	10.3345	+	34.5195i	0.462634	+	1.54531i	−0.335031	+	0.942207i	$0.608747\pi$
$500$	1.71272	−	1.81538i	0.0765951	−	0.0811861i
$501$	3.16183	+	15.7101i	0.141260	+	0.701874i
$502$	5.82571	−	7.82528i	0.260014	−	0.349259i
$503$	6.73651	−	38.2046i	0.300366	−	1.70346i	−0.344187	−	0.938901i	$-0.611845\pi$
$503$	6.73651	−	38.2046i	0.300366	−	1.70346i	0.644553	−	0.764560i	$-0.277044\pi$
$504$	−6.09131	+	2.55540i	−0.271328	+	0.113827i
$505$	−0.0861197	−	0.488409i	−0.00383228	−	0.0217339i
$506$	0.878013	+	0.440955i	0.0390324	+	0.0196028i
$507$	21.7567	−	3.07555i	0.966249	−	0.136590i
$508$	−1.71277	+	0.200194i	−0.0759917	+	0.00888215i
$509$	−4.29416	−	2.82431i	−0.190335	−	0.125185i	0.450765	−	0.892643i	$-0.351151\pi$
$509$	−4.29416	−	2.82431i	−0.190335	−	0.125185i	−0.641100	+	0.767457i	$0.721522\pi$
$510$	1.05220	−	0.276290i	0.0465921	−	0.0122343i
$511$	−8.74874	+	29.2228i	−0.387021	+	1.29274i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	−12.5963	+	5.64470i	−0.556140	+	0.249220i
$514$	−8.29541	+	14.3681i	−0.365895	+	0.633749i
$515$	2.03606	+	2.15809i	0.0897194	+	0.0950970i
$516$	−6.03341	−	13.1099i	−0.265606	−	0.577131i
$517$	−0.724604	+	12.4410i	−0.0318681	+	0.547153i
$518$	9.10558	−	21.1091i	0.400076	−	0.927481i
$519$	21.4575	+	13.3842i	0.941880	+	0.587499i
$520$	0.00818180	+	0.140476i	0.000358796	+	0.00616028i
$521$	12.3521	+	4.49581i	0.541157	+	0.196965i	0.598113	−	0.801411i	$-0.295917\pi$
$521$	12.3521	+	4.49581i	0.541157	+	0.196965i	−0.0569559	+	0.998377i	$0.518139\pi$
$522$	2.19468	+	20.5627i	0.0960585	+	0.900005i
$523$	25.8403	−	9.40509i	1.12992	−	0.411256i	0.291654	−	0.956524i	$-0.405794\pi$
$523$	25.8403	−	9.40509i	1.12992	−	0.411256i	0.838262	+	0.545268i	$0.183572\pi$
$524$	1.29699	+	3.00676i	0.0566592	+	0.131351i
$525$	2.82216	−	18.6155i	0.123169	−	0.812445i
$526$	9.51943	+	2.25615i	0.415067	+	0.0983727i
$527$	3.88527	+	0.920825i	0.169245	+	0.0401118i
$528$	−2.49368	+	0.976230i	−0.108524	+	0.0424850i
$529$	−8.94989	−	20.7482i	−0.389125	−	0.902094i
$530$	−1.59014	+	0.578764i	−0.0690713	+	0.0251399i
$531$	18.2922	+	17.6078i	0.793813	+	0.764112i
$532$	5.49638	+	2.00052i	0.238298	+	0.0867335i
$533$	0.249403	+	4.28209i	0.0108028	+	0.185478i
$534$	−23.9272	+	12.7470i	−1.03543	+	0.551618i
$535$	−0.371407	+	0.861019i	−0.0160573	+	0.0372251i
$536$	0.468239	−	8.03935i	0.0202248	−	0.347247i
$537$	−12.6263	+	17.8412i	−0.544866	+	0.769905i
$538$	8.07088	+	8.55464i	0.347960	+	0.368817i
$539$	1.66345	−	2.88118i	0.0716498	−	0.124101i
$540$	−0.283104	+	1.27401i	−0.0121829	+	0.0548247i
$541$	0.893814	+	1.54813i	0.0384281	+	0.0665594i	0.884600	−	0.466351i	$-0.154432\pi$
$541$	0.893814	+	1.54813i	0.0384281	+	0.0665594i	−0.846172	+	0.532910i	$0.821098\pi$
$542$	−8.10679	+	27.0786i	−0.348217	+	1.16312i
$543$	−5.26786	+	19.2729i	−0.226066	+	0.827080i
$544$	−2.08929	−	1.37415i	−0.0895775	−	0.0589161i
$545$	−0.122983	+	0.0143747i	−0.00526803	+	0.000615745i
$546$	1.31680	+	1.68264i	0.0563541	+	0.0720104i
$547$	−37.3558	−	18.7608i	−1.59722	−	0.802154i	−1.00000		7.60691e-5i	$-0.999976\pi$
$547$	−37.3558	−	18.7608i	−1.59722	−	0.802154i	−0.597220	−	0.802078i	$-0.703728\pi$
$548$	2.28032	+	12.9323i	0.0974102	+	0.552441i
$549$	0.339420	+	1.49895i	0.0144861	+	0.0639735i
$550$	1.32547	−	7.51711i	0.0565182	−	0.320531i
$551$	10.9347	−	14.6879i	0.465834	−	0.625724i
$552$	−1.04306	−	0.351445i	−0.0443955	−	0.0149585i
$553$	23.3368	−	24.7356i	0.992383	−	1.05186i
$554$	−2.91061	−	9.72212i	−0.123660	−	0.413053i
$555$	−2.36506	−	3.87772i	−0.100391	−	0.164600i
$556$	7.48531	+	0.874908i	0.317448	+	0.0371044i
$557$	−7.29261	−	6.11922i	−0.308998	−	0.259280i	0.475080	−	0.879943i	$-0.342419\pi$
$557$	−7.29261	−	6.11922i	−0.308998	−	0.259280i	−0.784078	+	0.620663i	$0.786864\pi$
$558$	−3.11570	+	3.63842i	−0.131898	+	0.154027i
$559$	−3.57593	+	3.00056i	−0.151246	+	0.126910i
$560$	0.462050	−	0.303895i	0.0195252	−	0.0128419i
$561$	4.47698	−	4.98024i	0.189018	−	0.210266i
$562$	−10.8000	−	14.5069i	−0.455570	−	0.611937i
$563$	14.7031	−	7.38420i	0.619664	−	0.311207i	−0.111129	−	0.993806i	$-0.535447\pi$
$563$	14.7031	−	7.38420i	0.619664	−	0.311207i	0.730793	+	0.682599i	$0.239150\pi$
$564$	−1.14702	−	13.9135i	−0.0482980	−	0.585863i
$565$	−1.08224	+	0.256495i	−0.0455300	+	0.0107908i
$566$	21.1977			0.891006
$567$	7.48260	+	18.3499i	0.314239	+	0.770622i
$568$	−15.9678			−0.669994
$569$	2.81704	−	0.667651i	0.118097	−	0.0279894i	−0.171143	−	0.985246i	$-0.554746\pi$
$569$	2.81704	−	0.667651i	0.118097	−	0.0279894i	0.289239	+	0.957257i	$0.406598\pi$
$570$	0.949944	−	0.658086i	0.0397888	−	0.0275642i
$571$	−6.23285	+	3.13026i	−0.260837	+	0.130997i	−0.574412	−	0.818566i	$-0.694769\pi$
$571$	−6.23285	+	3.13026i	−0.260837	+	0.130997i	0.313576	+	0.949563i	$0.398473\pi$
$572$	0.517266	+	0.694809i	0.0216280	+	0.0290514i
$573$	3.47131	+	10.6544i	0.145016	+	0.445094i
$574$	14.0845	−	9.26354i	0.587877	−	0.386653i
$575$	2.40330	−	2.01661i	0.100225	−	0.0840984i
$576$	2.61299	−	1.47387i	0.108874	−	0.0614115i
$577$	−16.4046	−	13.7651i	−0.682931	−	0.573047i	0.233930	−	0.972253i	$-0.424841\pi$
$577$	−16.4046	−	13.7651i	−0.682931	−	0.573047i	−0.916861	+	0.399206i	$0.869286\pi$
$578$	−10.6739	−	1.24760i	−0.443977	−	0.0518934i
$579$	14.9958	−	27.4808i	0.623206	−	1.14206i
$580$	−0.496546	−	1.65858i	−0.0206180	−	0.0688688i
$581$	−11.3025	+	11.9799i	−0.468905	+	0.497011i
$582$	21.4044	−	18.8569i	0.887242	−	0.781643i
$583$	−6.22051	+	8.35559i	−0.257627	+	0.346053i
$584$	2.40569	−	13.6434i	0.0995482	−	0.564566i
$585$	0.421653	−	0.0203187i	0.0174332	−	0.000840074i
$586$	−1.51155	−	8.57241i	−0.0624414	−	0.354123i
$587$	−34.0988	−	17.1250i	−1.40741	−	0.706826i	−0.427081	−	0.904213i	$-0.640458\pi$
$587$	−34.0988	−	17.1250i	−1.40741	−	0.706826i	−0.980326	+	0.197387i	$0.936754\pi$
$588$	−1.39337	+	3.45671i	−0.0574616	+	0.142552i
$589$	4.21291	−	0.492419i	0.173590	−	0.0202898i
$590$	−1.77596	−	1.16807i	−0.0731152	−	0.0480886i
$591$	−29.2342	−	29.5288i	−1.20253	−	1.21465i
$592$	−2.99445	+	10.0022i	−0.123071	+	0.411087i
$593$	−10.6532	−	18.4518i	−0.437473	−	0.757725i	0.560021	−	0.828478i	$-0.310793\pi$
$593$	−10.6532	−	18.4518i	−0.437473	−	0.757725i	−0.997494	+	0.0707531i	$0.977460\pi$
$594$	2.85353	+	7.51004i	0.117082	+	0.308140i
$595$	−0.691477	+	1.19767i	−0.0283478	+	0.0490998i
$596$	−12.8686	−	13.6399i	−0.527119	−	0.558713i
$597$	16.8678	+	1.56099i	0.690353	+	0.0638871i
$598$	−0.0207009	+	0.355421i	−0.000846524	+	0.0145343i
$599$	−16.9415	+	39.2748i	−0.692210	+	1.60472i	0.100366	+	0.994951i	$0.467999\pi$
$599$	−16.9415	+	39.2748i	−0.692210	+	1.60472i	−0.792576	+	0.609773i	$0.791261\pi$
$600$	−0.291551	+	8.54602i	−0.0119025	+	0.348890i
$601$	0.583496	+	10.0182i	0.0238013	+	0.408653i	0.989075	+	0.147412i	$0.0470945\pi$
$601$	0.583496	+	10.0182i	0.0238013	+	0.408653i	−0.965274	+	0.261240i	$0.915868\pi$
$602$	17.2398	+	6.27476i	0.702641	+	0.255740i
$603$	−24.1028	−	1.64647i	−0.981540	−	0.0670493i
$604$	−2.32908	+	0.847716i	−0.0947690	+	0.0344931i
$605$	−0.856482	−	1.98555i	−0.0348210	−	0.0807240i
$606$	2.67209	+	2.13467i	0.108546	+	0.0867152i
$607$	25.9485	+	6.14992i	1.05322	+	0.249617i	0.720533	−	0.693420i	$-0.243897\pi$
$607$	25.9485	+	6.14992i	1.05322	+	0.249617i	0.332686	+	0.943038i	$0.392045\pi$
$608$	−2.58483	−	0.612616i	−0.104829	−	0.0248449i
$609$	−20.5393	−	16.4084i	−0.832296	−	0.664903i
$610$	−0.0509640	−	0.118148i	−0.00206347	−	0.00478366i
$611$	−4.24338	+	1.54447i	−0.171669	+	0.0624824i
$612$	−4.18508	+	6.22622i	−0.169172	+	0.251680i
$613$	−19.8734	−	7.23333i	−0.802680	−	0.292152i	−0.0920832	−	0.995751i	$-0.529353\pi$
$613$	−19.8734	−	7.23333i	−0.802680	−	0.292152i	−0.710596	+	0.703600i	$0.751575\pi$
$614$	0.692132	+	11.8835i	0.0279322	+	0.479577i
$615$	0.113560	−	3.32871i	0.00457919	−	0.134226i
$616$	1.34840	−	3.12594i	0.0543285	−	0.125948i
$617$	−2.33116	+	40.0244i	−0.0938488	+	1.61132i	0.542592	+	0.839997i	$0.317443\pi$
$617$	−2.33116	+	40.0244i	−0.0938488	+	1.61132i	−0.636441	+	0.771326i	$0.719594\pi$
$618$	−20.3734	−	1.88541i	−0.819540	−	0.0758424i
$619$	−20.5839	−	21.8177i	−0.827338	−	0.876928i	0.166694	−	0.986009i	$-0.446691\pi$
$619$	−20.5839	−	21.8177i	−0.827338	−	0.876928i	−0.994033	+	0.109081i	$0.965209\pi$
$620$	0.200520	−	0.347310i	0.00805306	−	0.0139483i
$621$	−1.08566	+	3.11845i	−0.0435659	+	0.125139i
$622$	2.51349	+	4.35348i	0.100782	+	0.174559i
$623$	9.88459	−	33.0168i	0.396018	−	1.32279i
$624$	−0.682712	−	0.689592i	−0.0273304	−	0.0276058i
$625$	−20.0999	−	13.2199i	−0.803998	−	0.528798i
$626$	−26.5783	+	3.10656i	−1.06228	+	0.124163i
$627$	2.65958	−	6.59797i	0.106213	−	0.263498i
$628$	7.39165	+	3.71223i	0.294959	+	0.148134i
$629$	−4.53380	−	25.7124i	−0.180774	−	1.02522i
$630$	−0.897741	−	1.39522i	−0.0357669	−	0.0555870i
$631$	5.09831	−	28.9139i	0.202960	−	1.15105i	−0.697657	−	0.716432i	$-0.745774\pi$
$631$	5.09831	−	28.9139i	0.202960	−	1.15105i	0.900617	−	0.434614i	$-0.143115\pi$
$632$	−9.22280	+	12.3884i	−0.366863	+	0.492783i
$633$	0.922868	−	0.813029i	0.0366807	−	0.0323150i
$634$	9.82045	−	10.4091i	0.390020	−	0.413397i
$635$	−0.124218	−	0.414918i	−0.00492946	−	0.0164655i
$636$	5.58979	−	10.2436i	0.221649	−	0.406187i
$637$	1.19737	+	0.139953i	0.0474417	+	0.00554513i
$638$	−8.16425	−	6.85062i	−0.323226	−	0.271218i
$639$	−0.480307	+	47.9010i	−0.0190006	+	1.89493i
$640$	−0.192403	+	0.161445i	−0.00760539	+	0.00638168i
$641$	−21.7826	+	14.3267i	−0.860362	+	0.565869i	−0.901252	−	0.433295i	$-0.857351\pi$
$641$	−21.7826	+	14.3267i	−0.860362	+	0.565869i	0.0408904	+	0.999164i	$0.486981\pi$
$642$	−2.00321	−	6.14842i	−0.0790605	−	0.242659i
$643$	11.4253	+	15.3468i	0.450568	+	0.605218i	0.968136	−	0.250424i	$-0.0805700\pi$
$643$	11.4253	+	15.3468i	0.450568	+	0.605218i	−0.517568	+	0.855642i	$0.673163\pi$
$644$	1.25040	−	0.627974i	0.0492727	−	0.0247457i
$645$	2.97957	−	2.06413i	0.117320	−	0.0812751i
$646$	6.46384	−	1.53196i	0.254316	−	0.0602741i
$647$	−33.7736			−1.32778			−0.663889	−	0.747831i	$-0.731095\pi$
$647$	−33.7736			−1.32778			−0.663889	+	0.747831i	$0.731095\pi$
$648$	−4.34280	−	7.88290i	−0.170601	−	0.309669i
$649$	−13.0852			−0.513639
$650$	2.69134	−	0.637860i	0.105563	−	0.0250189i
$651$	−0.500316	−	6.06891i	−0.0196089	−	0.237860i
$652$	8.85284	−	4.44606i	0.346704	−	0.174121i
$653$	−25.1651	−	33.8025i	−0.984785	−	1.32280i	−0.946215	−	0.323540i	$-0.895127\pi$
$653$	−25.1651	−	33.8025i	−0.984785	−	1.32280i	−0.0385701	−	0.999256i	$-0.512280\pi$
$654$	0.570846	−	0.635016i	0.0223219	−	0.0248311i
$655$	−0.687149	+	0.451945i	−0.0268491	+	0.0176590i
$656$	−5.86495	+	4.92128i	−0.228988	+	0.192144i
$657$	−40.8557	−	7.62710i	−1.59393	−	0.297562i
$658$	13.5954	+	11.4079i	0.530004	+	0.444726i
$659$	−40.9098	−	4.78167i	−1.59362	−	0.186268i	−0.727502	−	0.686106i	$-0.759319\pi$
$659$	−40.9098	−	4.78167i	−1.59362	−	0.186268i	−0.866119	+	0.499838i	$0.833393\pi$
$660$	−0.350229	−	0.574230i	−0.0136326	−	0.0223519i
$661$	2.03687	+	6.80360i	0.0792249	+	0.264630i	0.988420	−	0.151740i	$-0.0484875\pi$
$661$	2.03687	+	6.80360i	0.0792249	+	0.264630i	−0.909196	+	0.416369i	$0.863302\pi$
$662$	0.0317091	−	0.0336097i	0.00123241	−	0.00130628i
$663$	2.29958	+	0.774815i	0.0893084	+	0.0300913i
$664$	4.46678	−	5.99992i	0.173345	−	0.232842i
$665$	−0.255105	+	1.44677i	−0.00989254	+	0.0561034i
$666$	29.9149	+	9.28377i	1.15918	+	0.359739i
$667$	−0.760654	−	4.31388i	−0.0294526	−	0.167034i
$668$	8.26796	+	4.15233i	0.319897	+	0.160658i
$669$	−14.3928	−	18.3914i	−0.556458	−	0.711054i
$670$	2.00894	−	0.234812i	0.0776122	−	0.00907156i
$671$	−0.661770	−	0.435253i	−0.0255473	−	0.0168028i
$672$	−1.00553	+	3.67881i	−0.0387890	+	0.141913i
$673$	3.42140	−	11.4283i	0.131885	−	0.440527i	−0.866381	−	0.499383i	$-0.833560\pi$
$673$	3.42140	−	11.4283i	0.131885	−	0.440527i	0.998266	+	0.0588559i	$0.0187453\pi$
$674$	13.9695	+	24.1960i	0.538087	+	0.931994i
$675$	25.6280	+	1.13167i	0.986422	+	0.0435580i
$676$	6.34306	−	10.9865i	0.243964	−	0.422558i
$677$	6.70101	+	7.10265i	0.257541	+	0.272977i	0.843223	−	0.537563i	$-0.180655\pi$
$677$	6.70101	+	7.10265i	0.257541	+	0.272977i	−0.585683	+	0.810540i	$0.699174\pi$
$678$	4.43075	−	6.26072i	0.170162	−	0.240442i
$679$	−2.10854	+	36.2023i	−0.0809185	+	1.38932i
$680$	0.248770	−	0.576714i	0.00953990	−	0.0221160i
$681$	−25.3214	+	13.4898i	−0.970319	+	0.516930i
$682$	−0.143544	−	2.46455i	−0.00549657	−	0.0943725i
$683$	40.0570	+	14.5795i	1.53274	+	0.557871i	0.964290	−	0.264849i	$-0.0853221\pi$
$683$	40.0570	+	14.5795i	1.53274	+	0.557871i	0.568447	+	0.822720i	$0.307544\pi$
$684$	−1.91551	+	7.73568i	−0.0732412	+	0.295781i
$685$	−3.09933	+	1.12806i	−0.118419	+	0.0431011i
$686$	−7.98141	−	18.5030i	−0.304731	−	0.706447i
$687$	4.41192	−	1.72718i	0.168325	−	0.0658962i
$688$	−8.10750	−	1.92151i	−0.309096	−	0.0732570i
$689$	−3.67287	−	0.870487i	−0.139925	−	0.0331629i
$690$	0.0414372	−	0.273327i	0.00157749	−	0.0104054i
$691$	−16.8677	−	39.1037i	−0.641677	−	1.48757i	−0.859264	−	0.511533i	$-0.829078\pi$
$691$	−16.8677	−	39.1037i	−0.641677	−	1.48757i	0.217587	−	0.976041i	$-0.430181\pi$
$692$	13.7204	−	4.99381i	0.521571	−	0.189836i
$693$	−9.33678	−	4.13902i	−0.354675	−	0.157228i
$694$	−12.6476	−	4.60335i	−0.480096	−	0.174741i
$695$	0.110059	+	1.88964i	0.00417477	+	0.0716780i
$696$	10.1302	+	6.31872i	0.383984	+	0.239511i
$697$	7.58318	−	17.5798i	0.287234	−	0.665882i
$698$	0.587250	−	10.0827i	0.0222277	−	0.381635i
$699$	10.8498	+	23.5753i	0.410377	+	0.891701i
$700$	−7.45975	−	7.90688i	−0.281952	−	0.298852i
$701$	−12.4900	+	21.6334i	−0.471742	+	0.817080i	−0.999477	−	0.0323282i	$-0.989708\pi$
$701$	−12.4900	+	21.6334i	−0.471742	+	0.817080i	0.527736	+	0.849409i	$0.323041\pi$
$702$	−2.08921	+	2.02729i	−0.0788521	+	0.0765152i
$703$	−13.8676	−	24.0195i	−0.523028	−	0.905911i
$704$	−0.443433	+	1.48117i	−0.0167125	+	0.0558236i
$705$	3.39145	−	0.890537i	0.127729	−	0.0335396i
$706$	3.82485	+	2.51565i	0.143950	+	0.0946776i
$707$	−4.31837	+	0.504745i	−0.162409	+	0.0189829i
$708$	14.5144	−	2.05178i	0.545486	−	0.0771106i
$709$	28.2852	+	14.2054i	1.06227	+	0.533493i	0.892061	−	0.451914i	$-0.149259\pi$
$709$	28.2852	+	14.2054i	1.06227	+	0.533493i	0.170211	+	0.985408i	$0.445555\pi$
$710$	−0.696423	−	3.94961i	−0.0261363	−	0.148226i
$711$	36.8858	+	28.0397i	1.38333	+	1.05157i
$712$	−2.71802	+	15.4147i	−0.101862	+	0.577689i
$713$	0.605923	−	0.813896i	0.0226920	−	0.0304806i
$714$	−1.88170	−	9.34950i	−0.0704207	−	0.349896i
$715$	−0.149300	+	0.158248i	−0.00558349	+	0.00591815i
$716$	3.61923	+	12.0891i	0.135257	+	0.451790i
$717$	18.0166	−	0.433841i	0.672841	−	0.0162021i
$718$	37.1508	+	4.34231i	1.38646	+	0.162053i
$719$	−18.0831	−	15.1736i	−0.674387	−	0.565878i	0.239973	−	0.970780i	$-0.422861\pi$
$719$	−18.0831	−	15.1736i	−0.674387	−	0.565878i	−0.914360	+	0.404901i	$0.867306\pi$
$720$	0.478523	+	0.582035i	0.0178335	+	0.0216912i
$721$	19.9251	−	16.7192i	0.742051	−	0.622655i
$722$	−9.97852	+	6.56298i	−0.371362	+	0.244249i
$723$	28.8283	+	6.10341i	1.07214	+	0.226988i
$724$	6.88846	+	9.25280i	0.256007	+	0.343878i
$725$	−30.4112	+	15.2731i	−1.12944	+	0.567228i
$726$	13.4832	+	6.36980i	0.500408	+	0.236406i
$727$	7.09810	−	1.68228i	0.263254	−	0.0623923i	−0.0968691	−	0.995297i	$-0.530883\pi$
$727$	7.09810	−	1.68228i	0.263254	−	0.0623923i	0.360123	+	0.932905i	$0.382735\pi$
$728$	1.23359			0.0457200
$729$	−23.7781	+	12.7906i	−0.880671	+	0.473728i
$730$	3.47958			0.128785
$731$	20.2743	−	4.80509i	0.749871	−	0.177723i
$732$	0.802302	+	0.379028i	0.0296539	+	0.0140093i
$733$	21.8143	−	10.9555i	0.805729	−	0.404652i	0.00225878	−	0.999997i	$-0.499281\pi$
$733$	21.8143	−	10.9555i	0.805729	−	0.404652i	0.803470	+	0.595345i	$0.202985\pi$
$734$	15.2890	+	20.5366i	0.564326	+	0.758021i
$735$	−0.915782	−	0.193886i	−0.0337791	−	0.00715158i
$736$	−0.530931	+	0.349199i	−0.0195704	+	0.0128716i
$737$	9.53793	−	8.00327i	0.351334	−	0.294804i
$738$	14.5867	+	17.7420i	0.536943	+	0.653092i
$739$	21.5680	+	18.0977i	0.793393	+	0.665736i	0.946583	−	0.322461i	$-0.104510\pi$
$739$	21.5680	+	18.0977i	0.793393	+	0.665736i	−0.153189	+	0.988197i	$0.548954\pi$
$740$	−2.60462	−	0.304436i	−0.0957477	−	0.0111913i
$741$	2.57700	−	0.0620544i	0.0946685	−	0.00227963i
$742$	4.25469	+	14.2117i	0.156195	+	0.521727i
$743$	−23.1674	+	24.5560i	−0.849930	+	0.900873i	−0.996086	−	0.0883887i	$-0.971828\pi$
$743$	−23.1674	+	24.5560i	−0.849930	+	0.900873i	0.146156	+	0.989261i	$0.453310\pi$
$744$	0.545668	+	2.71124i	0.0200052	+	0.0993988i
$745$	2.81256	−	3.77792i	0.103044	−	0.138412i
$746$	2.34673	−	13.3090i	0.0859198	−	0.487276i
$747$	−17.8645	−	13.5801i	−0.653628	−	0.496871i
$748$	−0.671386	−	3.80762i	−0.0245483	−	0.139220i
$749$	7.34617	+	3.68938i	0.268423	+	0.134807i
$750$	−4.28029	+	0.605067i	−0.156294	+	0.0220939i
$751$	−4.98975	+	0.583218i	−0.182078	+	0.0212819i	−0.206643	−	0.978416i	$-0.566254\pi$
$751$	−4.98975	+	0.583218i	−0.182078	+	0.0212819i	0.0245650	+	0.999698i	$0.492180\pi$
$752$	−6.73420	−	4.42915i	−0.245571	−	0.161515i
$753$	−16.3433	+	4.29148i	−0.595585	+	0.156390i
$754$	1.10760	−	3.69964i	0.0403364	−	0.134733i
$755$	−0.311262	−	0.539122i	−0.0113280	−	0.0196206i
$756$	11.0056	+	3.12709i	0.400270	+	0.113731i
$757$	−4.96049	+	8.59183i	−0.180292	+	0.312275i	−0.941980	−	0.335669i	$-0.891038\pi$
$757$	−4.96049	+	8.59183i	−0.180292	+	0.312275i	0.761688	+	0.647944i	$0.224371\pi$
$758$	4.20077	+	4.45255i	0.152579	+	0.161724i
$759$	−0.711461	−	1.54592i	−0.0258244	−	0.0561133i
$760$	0.0387943	−	0.666072i	0.00140722	−	0.0241610i
$761$	−19.9171	+	46.1731i	−0.721996	+	1.67377i	0.0168119	+	0.999859i	$0.494648\pi$
$761$	−19.9171	+	46.1731i	−0.721996	+	1.67377i	−0.738808	+	0.673916i	$0.764611\pi$
$762$	2.53422	+	1.58072i	0.0918050	+	0.0572635i
$763$	0.0631159	+	1.08366i	0.00228495	+	0.0392311i
$764$	6.07942	+	2.21273i	0.219946	+	0.0800537i
$765$	−1.72257	−	0.763621i	−0.0622798	−	0.0276088i
$766$	−20.0719	+	7.30559i	−0.725229	+	0.263962i
$767$	−1.87802	−	4.35373i	−0.0678112	−	0.157204i
$768$	0.259618	&mi

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)

\(f(q)\)	\(=\)	\(q+(-0.973045 + 0.230616i) q^{2} +(1.56608 + 0.739857i) q^{3} +(0.893633 - 0.448799i) q^{4} +(0.149985 + 0.201464i) q^{5} +(-1.69449 - 0.358751i) q^{6} +(1.83964 - 1.20995i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(1.90522 + 2.31735i) q^{9} +O(q^{10})\)	\(q+(-0.973045 + 0.230616i) q^{2} +(1.56608 + 0.739857i) q^{3} +(0.893633 - 0.448799i) q^{4} +(0.149985 + 0.201464i) q^{5} +(-1.69449 - 0.358751i) q^{6} +(1.83964 - 1.20995i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(1.90522 + 2.31735i) q^{9} +(-0.192403 - 0.161445i) q^{10} +(-1.53567 - 0.179494i) q^{11} +(1.73155 - 0.0416959i) q^{12} +(-0.160681 - 0.536712i) q^{13} +(-1.51101 + 1.60158i) q^{14} +(0.0858335 + 0.426477i) q^{15} +(0.597159 - 0.802123i) q^{16} +(-0.434239 + 2.46269i) q^{17} +(-2.38829 - 1.81551i) q^{18} +(0.461285 + 2.61608i) q^{19} +(0.224448 + 0.112722i) q^{20} +(3.77621 - 0.533809i) q^{21} +(1.53567 - 0.179494i) q^{22} +(0.530931 + 0.349199i) q^{23} +(-1.67526 + 0.439895i) q^{24} +(1.41592 - 4.72951i) q^{25} +(0.280124 + 0.485189i) q^{26} +(1.26923 + 5.03876i) q^{27} +(1.10093 - 1.90688i) q^{28} +(-4.73037 - 5.01390i) q^{29} +(-0.181872 - 0.395187i) q^{30} +(0.0928412 - 1.59402i) q^{31} +(-0.396080 + 0.918216i) q^{32} +(-2.27218 - 1.41728i) q^{33} +(-0.145402 - 2.49645i) q^{34} +(0.519679 + 0.189148i) q^{35} +(2.74260 + 1.21580i) q^{36} +(-9.81113 + 3.57096i) q^{37} +(-1.05216 - 2.43918i) q^{38} +(0.145450 - 0.959416i) q^{39} +(-0.244394 - 0.0579224i) q^{40} +(-7.44978 - 1.76563i) q^{41} +(-3.55131 + 1.39027i) q^{42} +(-3.30017 - 7.65066i) q^{43} +(-1.45288 + 0.528805i) q^{44} +(-0.181110 + 0.731402i) q^{45} +(-0.597151 - 0.217345i) q^{46} +(-0.468659 - 8.04657i) q^{47} +(1.52866 - 0.814379i) q^{48} +(-0.852272 + 1.97579i) q^{49} +(-0.287056 + 4.92856i) q^{50} +(-2.50209 + 3.53550i) q^{51} +(-0.384466 - 0.407510i) q^{52} +(3.36870 - 5.83476i) q^{53} +(-2.39703 - 4.61023i) q^{54} +(-0.194165 - 0.336304i) q^{55} +(-0.631503 + 2.10937i) q^{56} +(-1.21311 + 4.43828i) q^{57} +(5.75915 + 3.78785i) q^{58} +(8.40601 - 0.982521i) q^{59} +(0.268106 + 0.342592i) q^{60} +(0.457807 + 0.229919i) q^{61} +(0.277268 + 1.57246i) q^{62} +(6.30879 + 1.95786i) q^{63} +(0.173648 - 0.984808i) q^{64} +(0.0840287 - 0.112870i) q^{65} +(2.53778 + 0.855072i) q^{66} +(-5.52629 + 5.85752i) q^{67} +(0.717204 + 2.39563i) q^{68} +(0.573125 + 0.939687i) q^{69} +(-0.549291 - 0.0642029i) q^{70} +(12.2320 + 10.2639i) q^{71} +(-2.94905 - 0.550541i) q^{72} +(-10.6126 + 8.90507i) q^{73} +(8.72315 - 5.73731i) q^{74} +(5.71662 - 6.35922i) q^{75} +(1.58631 + 2.13079i) q^{76} +(-3.04225 + 1.52787i) q^{77} +(0.0797266 + 0.967098i) q^{78} +(15.0282 - 3.56174i) q^{79} +0.251164 q^{80} +(-1.74025 + 8.83015i) q^{81} +7.65615 q^{82} +(-7.27842 + 1.72502i) q^{83} +(3.13497 - 2.17179i) q^{84} +(-0.561274 + 0.281882i) q^{85} +(4.97558 + 6.68337i) q^{86} +(-3.69858 - 11.3520i) q^{87} +(1.29177 - 0.849608i) q^{88} +(11.9905 - 10.0612i) q^{89} +(0.00755494 - 0.753454i) q^{90} +(-0.944987 - 0.792939i) q^{91} +(0.631178 + 0.0737741i) q^{92} +(1.32474 - 2.42768i) q^{93} +(2.31169 + 7.72159i) q^{94} +(-0.457861 + 0.485304i) q^{95} +(-1.29964 + 1.14496i) q^{96} +(-9.83490 + 13.2106i) q^{97} +(0.373651 - 2.11908i) q^{98} +(-2.50984 - 3.90066i) 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