LMFDB - Embedded newform 162.2.g.a.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.973045 - 0.230616i) q^{2} +(1.56608 - 0.739857i) q^{3} +(0.893633 + 0.448799i) q^{4} +(0.149985 - 0.201464i) q^{5} +(-1.69449 + 0.358751i) q^{6} +(1.83964 + 1.20995i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(1.90522 - 2.31735i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.973045	−	0.230616i	−0.688047	−	0.163070i
$2$	−0.973045	−	0.230616i	−0.688047	−	0.163070i
$3$	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	−0.767320	−	0.641265i	$-0.778410\pi$
$5$	0.149985	−	0.201464i	0.0670752	−	0.0900976i	0.834395	+	0.551167i	$0.185817\pi$
$6$	−1.69449	+	0.358751i	−0.691773	+	0.146459i
$7$	1.83964	+	1.20995i	0.695317	+	0.457317i	0.847334	−	0.531061i	$-0.178206\pi$
$7$	1.83964	+	1.20995i	0.695317	+	0.457317i	−0.152017	+	0.988378i	$0.548577\pi$
$8$	−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	−0.344406	−	0.938821i	$-0.611920\pi$
$11$	−1.53567	+	0.179494i	−0.463021	+	0.0541194i	−0.118615	+	0.992940i	$0.537846\pi$
$12$	1.73155	+	0.0416959i	0.499855	+	0.0120366i
$13$	−0.160681	+	0.536712i	−0.0445649	+	0.148857i	−0.977376	−	0.211508i	$-0.932163\pi$
$13$	−0.160681	+	0.536712i	−0.0445649	+	0.148857i	0.932811	+	0.360365i	$0.117348\pi$
$14$	−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	−0.991093	−	0.133174i	$-0.957483\pi$
$17$	−0.434239	−	2.46269i	−0.105318	−	0.597290i	0.885774	−	0.464116i	$-0.153628\pi$
$18$	−2.38829	+	1.81551i	−0.562924	+	0.427921i
$19$	0.461285	−	2.61608i	0.105826	−	0.600170i	−0.885061	−	0.465475i	$-0.845884\pi$
$19$	0.461285	−	2.61608i	0.105826	−	0.600170i	0.990887	−	0.134695i	$-0.0430053\pi$
$20$	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	−0.492948	−	0.870059i	$-0.664081\pi$
$23$	0.530931	−	0.349199i	0.110707	−	0.0728130i	0.603655	+	0.797246i	$0.293710\pi$
$24$	−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	−0.998091	−	0.0617536i	$-0.980331\pi$
$29$	−4.73037	+	5.01390i	−0.878408	+	0.931059i	0.119683	+	0.992812i	$0.461812\pi$
$30$	−0.181872	+	0.395187i	−0.0332052	+	0.0721509i
$31$	0.0928412	+	1.59402i	0.0166748	+	0.286295i	0.996329	+	0.0856034i	$0.0272818\pi$
$31$	0.0928412	+	1.59402i	0.0166748	+	0.286295i	−0.979655	+	0.200691i	$0.935681\pi$
$32$	−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	−0.630922	−	0.775846i	$-0.717323\pi$
$37$	−9.81113	−	3.57096i	−1.61294	−	0.587062i	−0.982019	+	0.188784i	$0.939545\pi$
$38$	−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	−0.766594	−	0.642132i	$-0.778050\pi$
$41$	−7.44978	+	1.76563i	−1.16346	+	0.275745i	−0.396865	+	0.917877i	$0.629902\pi$
$42$	−3.55131	−	1.39027i	−0.547980	−	0.214524i
$43$	−3.30017	+	7.65066i	−0.503272	+	1.16672i	0.457459	+	0.889231i	$0.348760\pi$
$43$	−3.30017	+	7.65066i	−0.503272	+	1.16672i	−0.960730	+	0.277484i	$0.910499\pi$
$44$	−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	0.773420	+	0.633894i	$0.218544\pi$
$47$	−0.468659	+	8.04657i	−0.0683610	+	1.17371i	−0.841781	+	0.539819i	$0.818493\pi$
$48$	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	0.999096	−	0.0425173i	$-0.0135378\pi$
$53$	3.36870	+	5.83476i	0.462727	+	0.801466i	−0.536369	+	0.843984i	$0.680204\pi$
$54$	−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	0.644072	−	0.764965i	$-0.277244\pi$
$59$	8.40601	+	0.982521i	1.09437	+	0.127913i	0.450297	+	0.892879i	$0.351318\pi$
$60$	0.268106	−	0.342592i	0.0346124	−	0.0442284i
$61$	0.457807	−	0.229919i	0.0586162	−	0.0294381i	−0.419250	−	0.907871i	$-0.637707\pi$
$61$	0.457807	−	0.229919i	0.0586162	−	0.0294381i	0.477866	+	0.878433i	$0.341411\pi$
$62$	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	0.295712	−	0.955277i	$-0.404443\pi$
$67$	−5.52629	−	5.85752i	−0.675143	−	0.715610i	−0.970855	+	0.239667i	$0.922962\pi$
$68$	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	0.520332	−	0.853964i	$-0.325808\pi$
$71$	12.2320	−	10.2639i	1.45168	−	1.21810i	0.931345	−	0.364138i	$-0.118636\pi$
$72$	−2.94905	+	0.550541i	−0.347549	+	0.0648819i
$73$	−10.6126	−	8.90507i	−1.24212	−	1.04226i	−0.997356	−	0.0726761i	$-0.976846\pi$
$73$	−10.6126	−	8.90507i	−1.24212	−	1.04226i	−0.244761	−	0.969583i	$-0.578709\pi$
$74$	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	0.959585	−	0.281418i	$-0.0908048\pi$
$79$	15.0282	+	3.56174i	1.69080	+	0.400727i	0.731216	+	0.682146i	$0.238953\pi$
$80$	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	−0.189168	−	0.981945i	$-0.560579\pi$
$83$	−7.27842	−	1.72502i	−0.798911	−	0.189345i	−0.609743	+	0.792599i	$0.708727\pi$
$84$	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	0.994420	+	0.105493i	$0.0336420\pi$
$89$	11.9905	+	10.0612i	1.27099	+	1.06649i	0.276569	+	0.960994i	$0.410802\pi$
$90$	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	−0.939303	−	0.343088i	$-0.888527\pi$
$97$	−9.83490	−	13.2106i	−0.998582	−	1.34133i	−0.0592790	−	0.998241i	$-0.518880\pi$
$98$	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	−0.534418	−	0.845220i	$-0.679469\pi$
$101$	−1.76455	+	0.886190i	−0.175579	+	0.0881792i	0.358839	+	0.933400i	$0.383173\pi$
$102$	1.61931	+	4.01722i	0.160335	+	0.397764i
$103$	11.7330	+	1.37139i	1.15609	+	0.135127i	0.672451	−	0.740142i	$-0.265242\pi$
$103$	11.7330	+	1.37139i	1.15609	+	0.135127i	0.483636	+	0.875269i	$0.339316\pi$
$104$	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	−0.761575	−	0.648076i	$-0.775574\pi$
$107$	1.86672	−	3.23326i	0.180463	−	0.312571i	0.942038	+	0.335505i	$0.108907\pi$
$108$	3.39561	−	3.93317i	0.326743	−	0.378469i
$109$	−0.246494	−	0.426940i	−0.0236098	−	0.0408934i	0.853979	−	0.520307i	$-0.174183\pi$
$109$	−0.246494	−	0.426940i	−0.0236098	−	0.0408934i	−0.877589	+	0.479414i	$0.840849\pi$
$110$	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	0.815579	−	0.578646i	$-0.196419\pi$
$113$	−1.75394	−	4.06609i	−0.164997	−	0.382506i	−0.980576	+	0.196140i	$0.937159\pi$
$114$	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	−0.412913	−	0.910771i	$-0.635489\pi$
$127$	−1.62043	+	0.589788i	−0.143790	+	0.0523352i	0.269123	+	0.963106i	$0.413266\pi$
$128$	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	−0.996359	−	0.0852612i	$-0.972828\pi$
$131$	−0.190399	−	3.26902i	−0.0166352	−	0.285616i	0.979723	−	0.200355i	$-0.0642095\pi$
$132$	−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	−0.953949	−	0.299970i	$-0.903023\pi$
$137$	−3.76625	−	12.5801i	−0.321772	−	1.07479i	0.632177	−	0.774824i	$-0.282162\pi$
$138$	−0.774383	+	0.782186i	−0.0659198	+	0.0665841i
$139$	6.29646	−	4.14125i	0.534059	−	0.351256i	−0.253657	−	0.967294i	$-0.581634\pi$
$139$	6.29646	−	4.14125i	0.534059	−	0.351256i	0.787716	+	0.616038i	$0.211263\pi$
$140$	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	0.393101	+	0.919495i	$0.371402\pi$
$149$	−5.37822	+	17.9645i	−0.440601	+	1.47171i	−0.833702	+	0.552214i	$0.813783\pi$
$150$	−4.09599	−	7.50615i	−0.334436	−	0.612875i
$151$	−2.46180	+	0.287743i	−0.200338	+	0.0234162i	−0.215670	−	0.976466i	$-0.569194\pi$
$151$	−2.46180	+	0.287743i	−0.200338	+	0.0234162i	0.0153319	+	0.999882i	$0.495120\pi$
$152$	−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	−0.560068	−	0.828447i	$-0.689225\pi$
$157$	4.93937	−	6.63473i	0.394205	−	0.529509i	0.954273	+	0.298938i	$0.0966323\pi$
$158$	−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	−0.535201	−	0.844725i	$-0.679764\pi$
$167$	5.52496	−	7.42131i	0.427534	−	0.574278i	0.962735	+	0.270447i	$0.0871714\pi$
$168$	−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	0.454722	−	0.890633i	$-0.349739\pi$
$173$	14.5022	−	1.69506i	1.10258	−	0.128873i	0.647859	+	0.761760i	$0.275664\pi$
$174$	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	−0.950308	−	0.311312i	$-0.899232\pi$
$179$	−2.19130	−	12.4275i	−0.163786	−	0.928874i	0.786522	−	0.617562i	$-0.211880\pi$
$180$	0.166407	−	0.734887i	0.0124033	−	0.0547752i
$181$	2.00310	−	11.3601i	0.148889	−	0.844393i	−0.815273	−	0.579077i	$-0.803413\pi$
$181$	2.00310	−	11.3601i	0.148889	−	0.844393i	0.964162	−	0.265315i	$-0.0854760\pi$
$182$	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	−0.546546	−	0.837429i	$-0.684058\pi$
$191$	4.43970	−	4.70580i	0.321245	−	0.340500i	0.867791	+	0.496929i	$0.165539\pi$
$192$	1.00056	+	1.41381i	0.0722095	+	0.102033i
$193$	1.05094	+	18.0440i	0.0756486	+	1.29884i	0.796030	+	0.605257i	$0.206930\pi$
$193$	1.05094	+	18.0440i	0.0756486	+	1.29884i	−0.720381	+	0.693578i	$0.756033\pi$
$194$	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	−0.980673	−	0.195653i	$-0.937317\pi$
$197$	−22.5434	+	8.20512i	−1.60615	+	0.584591i	−0.625476	+	0.780243i	$0.715095\pi$
$198$	3.34174	−	3.21671i	0.237487	−	0.228601i
$199$	9.19041	+	3.34504i	0.651491	+	0.237123i	0.646558	−	0.762864i	$-0.276208\pi$
$199$	9.19041	+	3.34504i	0.651491	+	0.237123i	0.00493270	+	0.999988i	$0.498430\pi$
$200$	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	0.927623	−	0.373518i	$-0.121849\pi$
$211$	0.281254	+	0.652020i	0.0193623	+	0.0448869i	−0.908261	+	0.418405i	$0.862589\pi$
$212$	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	−0.803895	−	0.594771i	$-0.797243\pi$
$223$	−12.0491	+	6.05129i	−0.806868	+	0.405224i	−0.00297286	+	0.999996i	$0.500946\pi$
$224$	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	0.341791	−	0.939776i	$-0.388966\pi$
$227$	−9.89164	−	13.2868i	−0.656531	−	0.881875i	−0.998322	+	0.0579015i	$0.981559\pi$
$228$	0.907818	−	4.51063i	0.0601217	−	0.298724i
$229$	1.87718	+	1.98970i	0.124048	+	0.131483i	0.786421	−	0.617691i	$-0.211932\pi$
$229$	1.87718	+	1.98970i	0.124048	+	0.131483i	−0.662373	+	0.749174i	$0.730450\pi$
$230$	−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	−0.184068	−	0.982914i	$-0.558927\pi$
$233$	11.4780	−	9.63120i	0.751950	−	0.630961i	0.936018	+	0.351953i	$0.114482\pi$
$234$	−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	0.723347	−	0.690484i	$-0.242603\pi$
$239$	9.29814	+	4.66970i	0.601447	+	0.302058i	−0.121900	+	0.992542i	$0.538899\pi$
$240$	0.393343	−	0.185825i	0.0253902	−	0.0119950i
$241$	16.5544	+	3.92346i	1.06636	+	0.252732i	0.726093	−	0.687596i	$-0.241334\pi$
$241$	16.5544	+	3.92346i	1.06636	+	0.252732i	0.340268	+	0.940329i	$0.389482\pi$
$242$	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	0.375707	−	0.926738i	$-0.377400\pi$
$251$	−7.47331	−	6.27085i	−0.471711	−	0.395813i	−0.847418	+	0.530926i	$0.821844\pi$
$252$	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	0.977520	−	0.210842i	$-0.0676207\pi$
$257$	11.3853	+	12.0677i	0.710197	+	0.752764i	−0.267323	+	0.963607i	$0.586139\pi$
$258$	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	−0.697441	−	0.716643i	$-0.745678\pi$
$263$	−8.74253	+	4.39067i	−0.539088	+	0.270740i	0.158353	+	0.987383i	$0.449382\pi$
$264$	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	−0.987717	−	0.156252i	$-0.950059\pi$
$269$	−5.88050	+	10.1853i	−0.358540	+	0.621010i	0.629177	+	0.777262i	$0.283392\pi$
$270$	0.569280	+	1.17438i	0.0346453	+	0.0714705i
$271$	14.1330	+	24.4791i	0.858520	+	1.48700i	0.873340	+	0.487110i	$0.161949\pi$
$271$	14.1330	+	24.4791i	0.858520	+	1.48700i	−0.0148203	+	0.999890i	$0.504718\pi$
$272$	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	−0.933052	−	0.359742i	$-0.882865\pi$
$277$	0.590081	−	10.1313i	0.0354545	−	0.608730i	0.968506	−	0.248989i	$-0.0800982\pi$
$278$	−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	−0.559489	−	0.828837i	$-0.689003\pi$
$281$	7.16336	−	16.6065i	0.427330	−	0.990662i	0.986819	−	0.161825i	$-0.0517380\pi$
$282$	−2.09257	−	13.8030i	−0.124611	−	0.821955i
$283$	−20.6263	+	4.88853i	−1.22611	+	0.290593i	−0.792142	−	0.610337i	$-0.791034\pi$
$283$	−20.6263	+	4.88853i	−1.22611	+	0.290593i	−0.433965	+	0.900930i	$0.642886\pi$
$284$	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	−0.980282	−	0.197601i	$-0.936685\pi$
$293$	−0.506130	−	8.68992i	−0.0295684	−	0.507671i	0.950714	−	0.310069i	$-0.100352\pi$
$294$	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	0.985236	+	0.171204i	$0.0547656\pi$
$307$	2.06704	+	11.7228i	0.117972	+	0.669053i	−0.867264	+	0.497849i	$0.834123\pi$
$308$	−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	−0.989086	−	0.147336i	$-0.952930\pi$
$311$	−1.44175	+	4.81578i	−0.0817542	+	0.273078i	0.907332	+	0.420414i	$0.138115\pi$
$312$	0.505279	−	0.828449i	0.0286058	−	0.0469017i
$313$	26.5783	−	3.10656i	1.50230	−	0.175593i	0.675192	−	0.737642i	$-0.264061\pi$
$313$	26.5783	−	3.10656i	1.50230	−	0.175593i	0.827104	+	0.562049i	$0.189987\pi$
$314$	−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	0.167417	−	0.985886i	$-0.446457\pi$
$317$	−11.9562	−	7.86374i	−0.671529	−	0.441671i	−0.838946	+	0.544215i	$0.816828\pi$
$318$	−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	0.548448	−	0.836185i	$-0.315219\pi$
$331$	−0.0386053	−	0.0253911i	−0.00212194	−	0.00139562i	−0.550570	+	0.834789i	$0.685589\pi$
$332$	−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	0.403283	+	0.915075i	$0.367869\pi$
$337$	−8.01302	+	26.7654i	−0.436497	+	1.45800i	−0.839780	+	0.542927i	$0.817316\pi$
$338$	−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	−0.210563	−	0.977580i	$-0.567530\pi$
$347$	11.2451	−	7.39600i	0.603667	−	0.397038i	0.814230	+	0.580542i	$0.197159\pi$
$348$	−8.39993	+	8.48458i	−0.450284	+	0.454821i
$349$	−2.89665	−	9.67548i	−0.155054	−	0.517917i	0.844799	−	0.535084i	$-0.179720\pi$
$349$	−2.89665	−	9.67548i	−0.155054	−	0.517917i	−0.999853	+	0.0171679i	$0.994535\pi$
$350$	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	−0.805561	−	0.592513i	$-0.798136\pi$
$353$	−3.14161	+	3.32991i	−0.167211	+	0.177233i	0.638350	+	0.769746i	$0.279617\pi$
$354$	−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	−0.872648	+	0.488349i	$0.837599\pi$
$359$	−35.1480	+	12.7928i	−1.85504	+	0.675180i	−0.982392	+	0.186831i	$0.940178\pi$
$360$	−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	0.418440	+	0.908244i	$0.362577\pi$
$367$	−10.1408	+	23.5089i	−0.529344	+	1.22716i	−0.947784	+	0.318912i	$0.896682\pi$
$368$	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	0.721606	−	0.692304i	$-0.243404\pi$
$373$	−5.35273	−	12.4090i	−0.277154	−	0.642515i	−0.998760	+	0.0497893i	$0.984145\pi$
$374$	−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	−0.933864	−	0.357627i	$-0.883586\pi$
$379$	−3.06071	+	5.30130i	−0.157218	+	0.272309i	0.776647	+	0.629937i	$0.216919\pi$
$380$	−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	0.639317	−	0.768943i	$-0.279217\pi$
$383$	21.2157	+	2.47976i	1.08407	+	0.126710i	0.444754	+	0.895653i	$0.353291\pi$
$384$	−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	0.703629	−	0.710568i	$-0.251562\pi$
$389$	−3.52828	−	4.73931i	−0.178891	−	0.240292i	−0.882520	+	0.470276i	$0.844155\pi$
$390$	−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	0.477000	−	0.878903i	$-0.341724\pi$
$397$	−6.09144	−	5.11133i	−0.305721	−	0.256530i	−0.782721	+	0.622373i	$0.786169\pi$
$398$	−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	0.567173	−	0.823598i	$-0.308037\pi$
$401$	4.91089	+	2.46634i	0.245238	+	0.123163i	−0.321935	+	0.946762i	$0.604333\pi$
$402$	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	−0.0429426	−	0.999078i	$-0.513673\pi$
$409$	−17.5940	−	8.83606i	−0.869969	−	0.436915i	−0.827027	+	0.562162i	$0.809970\pi$
$410$	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	0.998797	+	0.0490323i	$0.0156137\pi$
$419$	20.2581	+	21.4723i	0.989672	+	1.04899i	−0.00912551	+	0.999958i	$0.502905\pi$
$420$	0.907736	−	0.305850i	0.0442930	−	0.0149239i
$421$	−23.2515	−	31.2321i	−1.13321	−	1.52216i	−0.819897	−	0.572511i	$-0.805969\pi$
$421$	−23.2515	−	31.2321i	−1.13321	−	1.52216i	−0.313310	−	0.949651i	$-0.601438\pi$
$422$	−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	−0.280079	−	0.959977i	$-0.590361\pi$
$431$	14.3523	−	24.8589i	0.691325	−	1.19741i	0.971404	−	0.237433i	$-0.0763060\pi$
$432$	4.79963	−	1.99086i	0.230922	−	0.0957853i
$433$	−5.02440	−	8.70251i	−0.241457	−	0.418216i	0.719673	−	0.694314i	$-0.244292\pi$
$433$	−5.02440	−	8.70251i	−0.241457	−	0.418216i	−0.961130	+	0.276098i	$0.910959\pi$
$434$	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	−0.755315	−	0.655362i	$-0.772516\pi$
$439$	1.48711	−	25.5326i	0.0709757	−	1.21861i	0.826291	−	0.563244i	$-0.190447\pi$
$440$	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	−0.772035	−	0.635580i	$-0.780761\pi$
$443$	4.63197	−	10.7381i	0.220072	−	0.510184i	0.992107	+	0.125396i	$0.0400203\pi$
$444$	−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	0.494441	−	0.869211i	$-0.335373\pi$
$449$	6.66383	+	2.42544i	0.314486	+	0.114463i	−0.179955	+	0.983675i	$0.557595\pi$
$450$	−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	−0.938076	−	0.346428i	$-0.887394\pi$
$457$	−11.4945	+	12.1835i	−0.537690	+	0.569918i	0.400387	+	0.916346i	$0.368876\pi$
$458$	−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	0.930800	+	0.365528i	$0.119112\pi$
$461$	7.60047	+	25.3873i	0.353989	+	1.18241i	−0.576811	+	0.816877i	$0.695703\pi$
$462$	5.70318	+	1.49756i	0.265336	+	0.0696728i
$463$	−2.88462	+	1.89725i	−0.134060	+	0.0881726i	−0.614768	−	0.788708i	$-0.710750\pi$
$463$	−2.88462	+	1.89725i	−0.134060	+	0.0881726i	0.480708	+	0.876881i	$0.340380\pi$
$464$	−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	−0.875024	−	0.484079i	$-0.839155\pi$
$467$	2.43750	−	13.8238i	0.112794	−	0.639688i	0.987819	−	0.155609i	$-0.0497340\pi$
$468$	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	0.838865	−	0.544339i	$-0.183220\pi$
$479$	14.6921	+	9.66318i	0.671301	+	0.441522i	−0.167564	+	0.985861i	$0.553590\pi$
$480$	−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	−0.837824	−	0.545940i	$-0.816173\pi$
$491$	−1.65145	+	2.21828i	−0.0745289	+	0.100110i	0.763295	+	0.646050i	$0.223580\pi$
$492$	−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	−0.335031	−	0.942207i	$-0.608747\pi$
$499$	10.3345	−	34.5195i	0.462634	−	1.54531i	0.797666	−	0.603100i	$-0.206068\pi$
$500$	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	0.644553	+	0.764560i	$0.277044\pi$
$503$	6.73651	+	38.2046i	0.300366	+	1.70346i	−0.344187	+	0.938901i	$0.611845\pi$
$504$	−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	−0.641100	−	0.767457i	$-0.721522\pi$
$509$	−4.29416	+	2.82431i	−0.190335	+	0.125185i	0.450765	+	0.892643i	$0.351151\pi$
$510$	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	−0.0569559	−	0.998377i	$-0.518139\pi$
$521$	12.3521	−	4.49581i	0.541157	−	0.196965i	0.598113	+	0.801411i	$0.295917\pi$
$522$	2.19468	−	20.5627i	0.0960585	−	0.900005i
$523$	25.8403	+	9.40509i	1.12992	+	0.411256i	0.838262	−	0.545268i	$-0.183572\pi$
$523$	25.8403	+	9.40509i	1.12992	+	0.411256i	0.291654	+	0.956524i	$0.405794\pi$
$524$	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	−0.846172	−	0.532910i	$-0.821098\pi$
$541$	0.893814	−	1.54813i	0.0384281	−	0.0665594i	0.884600	+	0.466351i	$0.154432\pi$
$542$	−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	−0.597220	+	0.802078i	$0.703728\pi$
$547$	−37.3558	+	18.7608i	−1.59722	+	0.802154i	−1.00000		7.60691e-5i	$0.999976\pi$
$548$	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	−0.784078	−	0.620663i	$-0.786864\pi$
$557$	−7.29261	+	6.11922i	−0.308998	+	0.259280i	0.475080	+	0.879943i	$0.342419\pi$
$558$	−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	0.730793	−	0.682599i	$-0.239150\pi$
$563$	14.7031	+	7.38420i	0.619664	+	0.311207i	−0.111129	+	0.993806i	$0.535447\pi$
$564$	−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	0.289239	−	0.957257i	$-0.406598\pi$
$569$	2.81704	+	0.667651i	0.118097	+	0.0279894i	−0.171143	+	0.985246i	$0.554746\pi$
$570$	0.949944	+	0.658086i	0.0397888	+	0.0275642i
$571$	−6.23285	−	3.13026i	−0.260837	−	0.130997i	0.313576	−	0.949563i	$-0.398473\pi$
$571$	−6.23285	−	3.13026i	−0.260837	−	0.130997i	−0.574412	+	0.818566i	$0.694769\pi$
$572$	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	−0.916861	−	0.399206i	$-0.869286\pi$
$577$	−16.4046	+	13.7651i	−0.682931	+	0.573047i	0.233930	+	0.972253i	$0.424841\pi$
$578$	−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	−0.980326	−	0.197387i	$-0.936754\pi$
$587$	−34.0988	+	17.1250i	−1.40741	+	0.706826i	−0.427081	+	0.904213i	$0.640458\pi$
$588$	−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	−0.997494	−	0.0707531i	$-0.977460\pi$
$593$	−10.6532	+	18.4518i	−0.437473	+	0.757725i	0.560021	+	0.828478i	$0.310793\pi$
$594$	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	−0.792576	−	0.609773i	$-0.791261\pi$
$599$	−16.9415	−	39.2748i	−0.692210	−	1.60472i	0.100366	−	0.994951i	$-0.467999\pi$
$600$	−0.291551	−	8.54602i	−0.0119025	−	0.348890i
$601$	0.583496	−	10.0182i	0.0238013	−	0.408653i	−0.965274	−	0.261240i	$-0.915868\pi$
$601$	0.583496	−	10.0182i	0.0238013	−	0.408653i	0.989075	−	0.147412i	$-0.0470945\pi$
$602$	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	0.332686	−	0.943038i	$-0.392045\pi$
$607$	25.9485	−	6.14992i	1.05322	−	0.249617i	0.720533	+	0.693420i	$0.243897\pi$
$608$	−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	−0.710596	−	0.703600i	$-0.751575\pi$
$613$	−19.8734	+	7.23333i	−0.802680	+	0.292152i	−0.0920832	+	0.995751i	$0.529353\pi$
$614$	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	−0.636441	−	0.771326i	$-0.719594\pi$
$617$	−2.33116	−	40.0244i	−0.0938488	−	1.61132i	0.542592	−	0.839997i	$-0.317443\pi$
$618$	−20.3734	+	1.88541i	−0.819540	+	0.0758424i
$619$	−20.5839	+	21.8177i	−0.827338	+	0.876928i	−0.994033	−	0.109081i	$-0.965209\pi$
$619$	−20.5839	+	21.8177i	−0.827338	+	0.876928i	0.166694	+	0.986009i	$0.446691\pi$
$620$	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	0.900617	+	0.434614i	$0.143115\pi$
$631$	5.09831	+	28.9139i	0.202960	+	1.15105i	−0.697657	+	0.716432i	$0.745774\pi$
$632$	−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	0.0408904	−	0.999164i	$-0.486981\pi$
$641$	−21.7826	−	14.3267i	−0.860362	−	0.565869i	−0.901252	+	0.433295i	$0.857351\pi$
$642$	−2.00321	+	6.14842i	−0.0790605	+	0.242659i
$643$	11.4253	−	15.3468i	0.450568	−	0.605218i	−0.517568	−	0.855642i	$-0.673163\pi$
$643$	11.4253	−	15.3468i	0.450568	−	0.605218i	0.968136	+	0.250424i	$0.0805700\pi$
$644$	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	−0.0385701	+	0.999256i	$0.512280\pi$
$653$	−25.1651	+	33.8025i	−0.984785	+	1.32280i	−0.946215	+	0.323540i	$0.895127\pi$
$654$	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	−0.866119	−	0.499838i	$-0.833393\pi$
$659$	−40.9098	+	4.78167i	−1.59362	+	0.186268i	−0.727502	+	0.686106i	$0.759319\pi$
$660$	−0.350229	+	0.574230i	−0.0136326	+	0.0223519i
$661$	2.03687	−	6.80360i	0.0792249	−	0.264630i	−0.909196	−	0.416369i	$-0.863302\pi$
$661$	2.03687	−	6.80360i	0.0792249	−	0.264630i	0.988420	+	0.151740i	$0.0484875\pi$
$662$	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	0.998266	−	0.0588559i	$-0.0187453\pi$
$673$	3.42140	+	11.4283i	0.131885	+	0.440527i	−0.866381	+	0.499383i	$0.833560\pi$
$674$	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	−0.585683	−	0.810540i	$-0.699174\pi$
$677$	6.70101	−	7.10265i	0.257541	−	0.272977i	0.843223	+	0.537563i	$0.180655\pi$
$678$	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	0.568447	−	0.822720i	$-0.307544\pi$
$683$	40.0570	−	14.5795i	1.53274	−	0.557871i	0.964290	+	0.264849i	$0.0853221\pi$
$684$	−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	0.217587	+	0.976041i	$0.430181\pi$
$691$	−16.8677	+	39.1037i	−0.641677	+	1.48757i	−0.859264	+	0.511533i	$0.829078\pi$
$692$	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	0.527736	−	0.849409i	$-0.323041\pi$
$701$	−12.4900	−	21.6334i	−0.471742	−	0.817080i	−0.999477	+	0.0323282i	$0.989708\pi$
$702$	−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	0.170211	−	0.985408i	$-0.445555\pi$
$709$	28.2852	−	14.2054i	1.06227	−	0.533493i	0.892061	+	0.451914i	$0.149259\pi$
$710$	−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	−0.914360	−	0.404901i	$-0.867306\pi$
$719$	−18.0831	+	15.1736i	−0.674387	+	0.565878i	0.239973	+	0.970780i	$0.422861\pi$
$720$	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	0.360123	−	0.932905i	$-0.382735\pi$
$727$	7.09810	+	1.68228i	0.263254	+	0.0623923i	−0.0968691	+	0.995297i	$0.530883\pi$
$728$	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	0.803470	−	0.595345i	$-0.202985\pi$
$733$	21.8143	+	10.9555i	0.805729	+	0.404652i	0.00225878	+	0.999997i	$0.499281\pi$
$734$	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	−0.153189	−	0.988197i	$-0.548954\pi$
$739$	21.5680	−	18.0977i	0.793393	−	0.665736i	0.946583	+	0.322461i	$0.104510\pi$
$740$	−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	0.146156	−	0.989261i	$-0.453310\pi$
$743$	−23.1674	−	24.5560i	−0.849930	−	0.900873i	−0.996086	+	0.0883887i	$0.971828\pi$
$744$	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	0.0245650	−	0.999698i	$-0.492180\pi$
$751$	−4.98975	−	0.583218i	−0.182078	−	0.0212819i	−0.206643	+	0.978416i	$0.566254\pi$
$752$	−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	0.761688	−	0.647944i	$-0.224371\pi$
$757$	−4.96049	−	8.59183i	−0.180292	−	0.312275i	−0.941980	+	0.335669i	$0.891038\pi$
$758$	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	−0.738808	−	0.673916i	$-0.764611\pi$
$761$	−19.9171	−	46.1731i	−0.721996	−	1.67377i	0.0168119	−	0.999859i	$-0.494648\pi$
$762$	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	+	1.71248i	0.00936815	+	0.0617939i
$769$	48.8041	−	11.5668i	1.75992	−	0.417109i	0.781528	−	0.623870i	$-0.214440\pi$
$769$	48.8041	−	11.5668i	1.75992	−	0.417109i	0.978391	+	0.206761i	$0.0662922\pi$
$770$	0.832004	−	0.197189i	0.0299834	−	0.00710618i
$771$	26.7587	+	10.4755i	0.963692	+	0.377268i
$772$	−7.15897	+	16.5964i	−0.257657	+	0.597316i
$773$	24.0958	+	8.77014i	0.866665	+	0.315440i	0.736816	−	0.676094i	$-0.236329\pi$
$773$	24.0958	+	8.77014i	0.866665	+	0.315440i	0.129849	+	0.991534i	$0.458551\pi$
$774$	−6.00812	−	24.2635i	−0.215957	−	0.872133i
$775$	−7.40749	+	2.69611i	−0.266085	+	0.0968470i
$776$	−0.957616	+	16.4416i	−0.0343764	+	0.590220i
$777$	−35.1427	−	18.7220i	−1.26074	−	0.671647i
$778$	2.34022	+	5.42524i	0.0839009	+	0.194504i
$779$	1.18255	+	20.3037i	0.0423694	+	0.727454i
$780$	0.140794	+	0.198944i	0.00504122	+	0.00712333i
$781$	−16.9421	+	17.9575i	−0.606234	+	0.642571i
$782$	0.794560	+	1.37622i	0.0284134	+	0.0492135i
$783$	19.2599	+	30.1990i	0.688294	+	1.07922i
$784$	1.07588	−	1.86349i	0.0384244	−	0.0665531i
$785$	−0.595832	−	1.99022i	−0.0212661	−	0.0710339i
$786$	1.49539	+	5.47102i	0.0533389	+	0.195145i
$787$	36.2459	−	23.8393i	1.29203	−	0.849779i	0.297546	−	0.954707i	$-0.403832\pi$
$787$	36.2459	−	23.8393i	1.29203	−	0.849779i	0.994480	+	0.104929i	$0.0334614\pi$
$788$	−23.8280	−	2.78509i	−0.848836	−	0.0992147i
$789$	−10.4431	+	13.3444i	−0.371783	+	0.475072i
$790$	−3.46649	+	1.74094i	−0.123332	+	0.0619397i
$791$	1.69314	−	9.60230i	0.0602013	−	0.341418i
$792$	4.42994	−	1.37478i	0.157411	−	0.0488508i
$793$	0.0498395	+	0.282654i	0.00176985	+	0.0100373i
$794$	4.74850	+	6.37834i	0.168518	+	0.226359i
$795$	2.77754	−	0.935856i	0.0985092	−	0.0331914i
$796$	6.71160	+	7.11388i	0.237886	+	0.252145i
$797$	14.0437	−	46.9092i	0.497453	−	1.66161i	−0.228250	−	0.973603i	$-0.573300\pi$
$797$	14.0437	−	46.9092i	0.497453	−	1.66161i	0.725704	−	0.688008i	$-0.241514\pi$
$798$	−5.27523	+	8.64920i	−0.186741	+	0.306178i
$799$	20.0197	−	2.33997i	0.708247	−	0.0827822i
$800$	3.78190	−	3.17339i	0.133710	−	0.112196i
$801$	46.1599	−	8.61733i	1.63098	−	0.304478i
$802$	−4.20974	−	3.53239i	−0.148651	−	0.124733i
$803$	17.8959	+	11.7703i	0.631533	+	0.415366i
$804$	−9.32480	−	10.3730i	−0.328860	−	0.365828i
$805$	0.209864	−	0.281896i	0.00739672	−	0.00993551i
$806$	0.799409	+	0.401478i	0.0281580	+	0.0141415i
$807$	−1.67366	+	20.3018i	−0.0589156	+	0.714656i
$808$	1.92136	+	0.455370i	0.0675931	+	0.0160198i
$809$	0.394821			0.0138812			0.00694058	−	0.999976i	$-0.497791\pi$
$809$	0.394821			0.0138812			0.00694058	+	0.999976i	$0.497791\pi$
$810$	1.76041	+	1.41799i	0.0618546	+	0.0498231i
$811$	−4.73714			−0.166343			−0.0831717	−	0.996535i	$-0.526505\pi$
$811$	−4.73714			−0.166343			−0.0831717	+	0.996535i	$0.526505\pi$
$812$	−14.7687	−	3.50025i	−0.518281	−	0.122835i
$813$	40.2445	+	27.8799i	1.41144	+	0.977790i
$814$	−14.4257	−	7.24485i	−0.505620	−	0.253932i
$815$	1.48584	−	1.99582i	0.0520465	−	0.0699106i
$816$	1.34176	−	4.11824i	0.0469710	−	0.144167i
$817$	18.4924	+	12.1626i	0.646968	+	0.425517i
$818$	15.0821	+	12.6553i	0.527332	+	0.442484i
$819$	0.0371061	+	3.70059i	0.00129659	+	0.129309i
$820$	−1.47306	+	1.23605i	−0.0514416	+	0.0431647i
$821$	−26.7319	+	3.12451i	−0.932950	+	0.109046i	−0.568968	−	0.822360i	$-0.692657\pi$
$821$	−26.7319	+	3.12451i	−0.932950	+	0.109046i	−0.363982	+	0.931406i	$0.618583\pi$
$822$	10.8950	+	19.9658i	0.380007	+	0.696387i
$823$	−2.39343	+	7.99462i	−0.0834298	+	0.278675i	−0.989517	−	0.144416i	$-0.953870\pi$
$823$	−2.39343	+	7.99462i	−0.0834298	+	0.278675i	0.906087	+	0.423091i	$0.139055\pi$
$824$	−8.10649	−	8.59237i	−0.282403	−	0.299330i
$825$	−9.92026	−	8.73956i	−0.345379	−	0.304272i
$826$	−11.1280	−	14.9475i	−0.387193	−	0.520091i
$827$	−0.754093	−	4.27667i	−0.0262224	−	0.148715i	0.968885	−	0.247510i	$-0.0796122\pi$
$827$	−0.754093	−	4.27667i	−0.0262224	−	0.148715i	−0.995108	+	0.0987952i	$0.968501\pi$
$828$	1.03157	−	1.60322i	0.0358497	−	0.0557157i
$829$	−8.16704	+	46.3176i	−0.283653	+	1.60868i	0.426405	+	0.904533i	$0.359780\pi$
$829$	−8.16704	+	46.3176i	−0.283653	+	1.60868i	−0.710058	+	0.704144i	$0.751331\pi$
$830$	1.67888	−	0.843168i	0.0582749	−	0.0292668i
$831$	−6.57159	−	16.3030i	−0.227966	−	0.565545i
$832$	−0.556460	−	0.0650408i	−0.0192918	−	0.00225489i
$833$	−4.49567	+	2.95685i	−0.155766	+	0.102449i
$834$	−9.18362	+	9.27617i	−0.318003	+	0.321207i
$835$	−0.666470	−	2.22617i	−0.0230642	−	0.0770396i
$836$	−2.05359	+	3.55692i	−0.0710248	+	0.123019i
$837$	8.14972	+	1.55537i	0.281696	+	0.0537614i
$838$	−14.7602	−	25.5653i	−0.509881	−	0.883140i
$839$	−10.1072	+	10.7130i	−0.348940	+	0.369855i	−0.877943	−	0.478765i	$-0.841085\pi$
$839$	−10.1072	+	10.7130i	−0.348940	+	0.369855i	0.529003	+	0.848620i	$0.322566\pi$
$840$	−0.953801	+	0.0882673i	−0.0329093	+	0.00304551i
$841$	−1.07659	−	18.4844i	−0.0371238	−	0.637391i
$842$	15.4221	+	35.7524i	0.531481	+	1.23211i
$843$	−1.06805	−	31.3070i	−0.0367857	−	1.07827i
$844$	−0.0412883	+	0.708893i	−0.00142120	+	0.0244011i
$845$	2.99414	−	1.08978i	0.103002	−	0.0374895i
$846$	−13.4894	−	20.0684i	−0.463774	−	0.689965i
$847$	−17.8138	−	6.48368i	−0.612088	−	0.222782i
$848$	−2.66855	+	6.18639i	−0.0916384	+	0.212442i
$849$	−28.6857	+	22.9164i	−0.984490	+	0.786487i
$850$	−12.0129	+	2.84710i	−0.412038	+	0.0976549i
$851$	−6.45602	+	1.53010i	−0.221309	+	0.0524513i
$852$	21.6084	−	17.2624i	0.740290	−	0.591401i
$853$	−6.13163	+	14.2147i	−0.209943	+	0.486702i	−0.990353	−	0.138565i	$-0.955751\pi$
$853$	−6.13163	+	14.2147i	−0.209943	+	0.486702i	0.780410	+	0.625268i	$0.215010\pi$
$854$	−1.05999	−	0.385804i	−0.0362720	−	0.0132019i
$855$	−1.99695	+	0.136412i	−0.0682942	+	0.00466520i
$856$	−3.50829	+	1.27691i	−0.119911	+	0.0436440i
$857$	2.91341	−	50.0214i	0.0995203	−	1.70870i	−0.466678	−	0.884427i	$-0.654549\pi$
$857$	2.91341	−	50.0214i	0.0995203	−	1.70870i	0.566198	−	0.824269i	$-0.308414\pi$
$858$	0.0511544	+	1.49945i	0.00174638	+	0.0511904i
$859$	−1.68987	−	3.91757i	−0.0576577	−	0.133666i	0.886952	−	0.461862i	$-0.152818\pi$
$859$	−1.68987	−	3.91757i	−0.0576577	−	0.133666i	−0.944610	+	0.328196i	$0.893559\pi$
$860$	0.121681	+	2.08918i	0.00414929	+	0.0712405i
$861$	−29.0744	+	2.69062i	−0.990853	+	0.0916962i
$862$	−19.6983	+	20.8789i	−0.670925	+	0.711139i
$863$	5.56996	+	9.64745i	0.189604	+	0.328403i	0.945118	−	0.326729i	$-0.105946\pi$
$863$	5.56996	+	9.64745i	0.189604	+	0.328403i	−0.755514	+	0.655132i	$0.772613\pi$
$864$	−5.12938	+	0.830325i	−0.174505	+	0.0282482i
$865$	1.83361	−	3.17591i	0.0623447	−	0.107984i
$866$	2.88203	+	9.62664i	0.0979352	+	0.327126i
$867$	13.0957	−	13.2276i	0.444753	−	0.449235i
$868$	−2.93739	+	1.93195i	−0.0997014	+	0.0655747i
$869$	−23.7176	−	2.77219i	−0.804564	−	0.0940400i
$870$	−1.12110	−	2.78127i	−0.0380090	−	0.0942939i
$871$	4.03177	−	2.02483i	0.136611	−	0.0686088i
$872$	−0.0856064	+	0.485498i	−0.00289900	+	0.0164410i
$873$	−49.3512	−	2.37814i	−1.67029	−	0.0804880i
$874$	0.293135	+	1.66245i	0.00991544	+	0.0562333i
$875$	3.28164	+	4.40800i	0.110940	+	0.149018i
$876$	−18.0050	−	15.8621i	−0.608333	−	0.535930i
$877$	7.27104	+	7.70685i	0.245526	+	0.260242i	0.838403	−	0.545051i	$-0.183490\pi$
$877$	7.27104	+	7.70685i	0.245526	+	0.260242i	−0.592877	+	0.805293i	$0.702008\pi$
$878$	−7.33525	+	24.5014i	−0.247553	+	0.826884i
$879$	−7.22194	−	13.2347i	−0.243590	−	0.446394i
$880$	−0.385704	+	0.0450824i	−0.0130021	+	0.00151973i
$881$	24.5788	−	20.6241i	0.828080	−	0.694842i	−0.126769	−	0.991932i	$-0.540461\pi$
$881$	24.5788	−	20.6241i	0.828080	−	0.694842i	0.954849	+	0.297090i	$0.0960162\pi$
$882$	5.62254	+	3.17144i	0.189321	+	0.106788i
$883$	3.71066	+	3.11361i	0.124874	+	0.104781i	0.703086	−	0.711105i	$-0.251805\pi$
$883$	3.71066	+	3.11361i	0.124874	+	0.104781i	−0.578212	+	0.815886i	$0.696249\pi$
$884$	1.17052	+	0.769863i	0.0393689	+	0.0258933i
$885$	1.14054	−	3.50064i	0.0383388	−	0.117673i
$886$	−6.98350	+	9.38047i	−0.234615	+	0.315143i
$887$	37.6172	+	18.8921i	1.26306	+	0.634334i	0.949062	−	0.315089i	$-0.102034\pi$
$887$	37.6172	+	18.8921i	1.26306	+	0.634334i	0.314000	+	0.949423i	$0.398331\pi$
$888$	14.8653	+	10.2981i	0.498848	+	0.345583i
$889$	−3.69461	−	0.875639i	−0.123913	−	0.0293680i
$890$	−3.93134			−0.131779
$891$	4.25740	+	13.2478i	0.142628	+	0.443818i
$892$	−13.4833			−0.451454
$893$	20.8343	+	4.93781i	0.697192	+	0.165238i
$894$	2.66856	−	32.3701i	0.0892501	−	1.08262i
$895$	−2.83236	−	1.42246i	−0.0946753	−	0.0475477i
$896$	1.31487	−	1.76617i	0.0439266	−	0.0590036i
$897$	0.412251	+	0.458593i	0.0137647	+	0.0153120i
$898$	−5.92486	−	3.89684i	−0.197715	−	0.130039i
$899$	−8.43144	−	7.07482i	−0.281204	−	0.235959i
$900$	9.63345	+	11.2497i	0.321115	+	0.374989i
$901$	12.9064	−	10.8298i	0.429974	−	0.360791i
$902$	−11.7573	+	1.37423i	−0.391475	+	0.0457569i
$903$	−16.5461	+	27.1288i	−0.550621	+	0.902791i
$904$	−1.27004	+	4.24222i	−0.0422408	+	0.141094i
$905$	−1.98823	−	2.10740i	−0.0660910	−	0.0700524i
$906$	4.06826	−	1.37075i	0.135159	−	0.0455401i
$907$	16.1173	+	21.6493i	0.535167	+	0.718854i	0.984670	−	0.174425i	$-0.0558066\pi$
$907$	16.1173	+	21.6493i	0.535167	+	0.718854i	−0.449504	+	0.893278i	$0.648399\pi$
$908$	−2.87640	−	16.3129i	−0.0954566	−	0.541361i
$909$	−1.30825	+	5.77747i	−0.0433918	+	0.191627i
$910$	0.0538022	−	0.305127i	0.00178352	−	0.0101149i
$911$	−29.2864	+	14.7082i	−0.970303	+	0.487304i	−0.862052	−	0.506819i	$-0.830821\pi$
$911$	−29.2864	+	14.7082i	−0.970303	+	0.487304i	−0.108251	+	0.994124i	$0.534525\pi$
$912$	2.83562	−	3.62342i	0.0938969	−	0.119983i
$913$	11.4869	+	1.34262i	0.380160	+	0.0444343i
$914$	13.9944	−	9.20423i	0.462892	−	0.304449i
$915$	−0.0587601	−	0.214979i	−0.00194255	−	0.00710698i
$916$	0.784538	+	2.62054i	0.0259219	+	0.0865850i
$917$	3.60508	−	6.24419i	0.119050	−	0.206201i
$918$	12.3945	+	3.90121i	0.409078	+	0.128759i
$919$	−21.9404	−	38.0019i	−0.723746	−	1.25357i	−0.959488	−	0.281750i	$-0.909085\pi$
$919$	−21.9404	−	38.0019i	−0.723746	−	1.25357i	0.235742	−	0.971816i	$-0.424248\pi$
$920$	−0.109530	+	0.116095i	−0.00361109	+	0.00382754i
$921$	11.9103	+	16.8295i	0.392458	+	0.554550i
$922$	−1.54087	−	26.4558i	−0.0507460	−	0.871275i
$923$	3.54330	+	8.21430i	0.116629	+	0.270377i
$924$	−5.20409	−	2.77244i	−0.171202	−	0.0912065i
$925$	2.99709	−	51.4581i	0.0985438	−	1.69193i
$926$	3.24440	−	1.18087i	0.106618	−	0.0388057i
$927$	25.5320	−	24.5767i	0.838580	−	0.807205i
$928$	6.47745	+	2.35760i	0.212633	+	0.0773920i
$929$	−12.1375	+	28.1379i	−0.398219	+	0.923175i	0.594652	+	0.803983i	$0.297290\pi$
$929$	−12.1375	+	28.1379i	−0.398219	+	0.923175i	−0.992871	+	0.119192i	$0.961970\pi$
$930$	−0.646821	−	0.253219i	−0.0212101	−	0.00830336i
$931$	−5.56196	+	1.31821i	−0.182286	+	0.0432025i
$932$	14.5796	−	3.45543i	0.477571	−	0.113186i
$933$	1.30509	+	8.60860i	0.0427268	+	0.281833i
$934$	−5.55978	+	12.8890i	−0.181922	+	0.421742i
$935$	0.912526	+	0.332132i	0.0298428	+	0.0108619i
$936$	0.178375	−	1.67125i	0.00583036	−	0.0546266i
$937$	−9.69881	+	3.53008i	−0.316846	+	0.115323i	−0.495548	−	0.868581i	$-0.665033\pi$
$937$	−9.69881	+	3.53008i	−0.316846	+	0.115323i	0.178701	+	0.983903i	$0.442810\pi$
$938$	−1.03100	+	17.7016i	−0.0336634	+	0.577978i
$939$	39.3254	−	24.5293i	1.28334	−	0.800483i
$940$	0.801837	+	1.85887i	0.0261530	+	0.0606296i
$941$	2.13316	+	36.6250i	0.0695391	+	1.19394i	0.834923	+	0.550367i	$0.185512\pi$
$941$	2.13316	+	36.6250i	0.0695391	+	1.19394i	−0.765384	+	0.643574i	$0.777451\pi$
$942$	−5.98951	+	13.0145i	−0.195149	+	0.424035i
$943$	−3.33876	+	3.53888i	−0.108725	+	0.115242i
$944$	4.23162	+	7.32937i	0.137727	+	0.238551i
$945$	−0.293479	−	2.85860i	−0.00954686	−	0.0929904i
$946$	−6.44121	+	11.1565i	−0.209422	+	0.362729i
$947$	1.33915	+	4.47308i	0.0435166	+	0.145356i	0.976987	−	0.213299i	$-0.0684208\pi$
$947$	1.33915	+	4.47308i	0.0435166	+	0.145356i	−0.933470	+	0.358655i	$0.883236\pi$
$948$	25.8735	+	6.79394i	0.840332	+	0.220657i
$949$	6.48471	−	4.26506i	0.210502	−	0.138450i
$950$	−13.0259	−	1.52251i	−0.422617	−	0.0493968i
$951$	−24.5425	−	3.46935i	−0.795844	−	0.112502i
$952$	−4.92050	+	2.47117i	−0.159474	+	0.0800910i
$953$	1.00860	−	5.72004i	0.0326717	−	0.185290i	−0.964104	−	0.265523i	$-0.914455\pi$
$953$	1.00860	−	5.72004i	0.0326717	−	0.185290i	0.996776	+	0.0802330i	$0.0255664\pi$
$954$	−18.6385	−	7.81916i	−0.603444	−	0.253155i
$955$	−0.282165	−	1.60024i	−0.00913066	−	0.0517825i
$956$	6.21337	+	8.34600i	0.200955	+	0.269929i
$957$	3.64218	−	18.0967i	0.117735	−	0.584985i
$958$	−12.0676	−	12.7909i	−0.389888	−	0.413257i
$959$	8.29278	−	27.6998i	0.267788	−	0.894474i
$960$	0.434903	+	0.0104725i	0.0140364	+	0.000337999i
$961$	28.2581	−	3.30290i	0.911552	−	0.106545i
$962$	−4.48093	+	3.75994i	−0.144471	+	0.121225i
$963$	−3.93608	−	10.4859i	−0.126838	−	0.337905i
$964$	13.0327	+	10.9357i	0.419754	+	0.352216i
$965$	3.79285	+	2.49460i	0.122096	+	0.0803039i
$966$	−2.37099	+	0.501976i	−0.0762852	+	0.0161508i
$967$	−29.3454	+	39.4177i	−0.943685	+	1.26759i	0.0197942	+	0.999804i	$0.493699\pi$
$967$	−29.3454	+	39.4177i	−0.943685	+	1.26759i	−0.963479	+	0.267784i	$0.913709\pi$
$968$	7.69374	+	3.86394i	0.247286	+	0.124192i
$969$	−10.4033	+	4.91480i	−0.334203	+	0.157886i
$970$	4.02504	+	0.953952i	0.129236	+	0.0306296i
$971$	27.7876			0.891747			0.445873	−	0.895096i	$-0.352893\pi$
$971$	27.7876			0.891747			0.445873	+	0.895096i	$0.352893\pi$
$972$	−2.64514	−	15.3624i	−0.0848430	−	0.492749i
$973$	16.5939			0.531976
$974$	25.9079	+	6.14029i	0.830144	+	0.196748i
$975$	−4.33162	+	2.04637i	−0.138723	+	0.0655363i
$976$	0.457807	+	0.229919i	0.0146540	+	0.00735954i
$977$	5.96461	−	8.01187i	0.190825	−	0.256322i	−0.696406	−	0.717648i	$-0.745219\pi$
$977$	5.96461	−	8.01187i	0.190825	−	0.256322i	0.887231	+	0.461326i	$0.152626\pi$
$978$	−16.7866	+	3.55399i	−0.536776	+	0.113644i
$979$	−20.2193	−	13.2985i	−0.646213	−	0.425021i
$980$	−0.414006	−	0.347393i	−0.0132249	−	0.0110970i
$981$	−1.45900	−	0.242203i	−0.0465821	−	0.00773293i
$982$	2.11851	−	1.77764i	0.0676042	−	0.0567267i
$983$	−2.22308	+	0.259840i	−0.0709051	+	0.00828762i	−0.151472	−	0.988462i	$-0.548401\pi$
$983$	−2.22308	+	0.259840i	−0.0709051	+	0.00828762i	0.0805664	+	0.996749i	$0.474327\pi$
$984$	13.2570	+	0.319230i	0.422618	+	0.0101767i
$985$	−1.72812	+	5.77233i	−0.0550626	+	0.183922i
$986$	−11.8292	−	12.5382i	−0.376717	−	0.399297i
$987$	−6.06509	+	30.1353i	−0.193054	+	0.959218i
$988$	0.888729	+	1.19377i	0.0282742	+	0.0379789i
$989$	0.919438	+	5.21439i	0.0292364	+	0.165808i
$990$	−0.146842	−	1.15570i	−0.00466695	−	0.0367305i
$991$	0.834598	−	4.73324i	0.0265119	−	0.150356i	−0.968678	−	0.248320i	$-0.920122\pi$
$991$	0.834598	−	4.73324i	0.0265119	−	0.150356i	0.995190	+	0.0979633i	$0.0312328\pi$
$992$	1.42688	−	0.716608i	0.0453036	−	0.0227523i
$993$	−0.0792449	−	0.0112022i	−0.00251476	−	0.000355490i
$994$	−34.9213	−	4.08171i	−1.10764	−	0.129464i
$995$	2.05233	−	1.34984i	0.0650632	−	0.0427927i
$996$	−12.5310	−	3.29043i	−0.397061	−	0.104261i
$997$	10.7554	+	35.9255i	0.340627	+	1.13777i	0.941100	+	0.338128i	$0.109794\pi$
$997$	10.7554	+	35.9255i	0.340627	+	1.13777i	−0.600473	+	0.799645i	$0.705021\pi$
$998$	−18.0167	+	31.2058i	−0.570307	+	0.987801i
$999$	−30.4458	+	44.9036i	−0.963261	+	1.42069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.97.4	✓	72
3.2	odd	2		486.2.g.a.451.2		72
81.5	odd	54		486.2.g.a.361.2		72
81.76	even	27	inner	162.2.g.a.157.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.97.4	✓	72	1.1	even	1	trivial
162.2.g.a.157.4	yes	72	81.76	even	27	inner
486.2.g.a.361.2		72	81.5	odd	54
486.2.g.a.451.2		72	3.2	odd	2

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