LMFDB - Embedded newform 162.2.g.a.103.1

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			103.1
Character	$\chi$	$=$	162.103
Dual form			162.2.g.a.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.686242 + 0.727374i) q^{2} +(-1.68798 + 0.388253i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.71787 + 0.434557i) q^{5} +(-1.44076 - 0.961353i) q^{6} +(-3.25050 - 1.63246i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(2.69852 - 1.31072i) q^{9} +O(q^{10})$	\(q+(0.686242 + 0.727374i) q^{2} +(-1.68798 + 0.388253i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.71787 + 0.434557i) q^{5} +(-1.44076 - 0.961353i) q^{6} +(-3.25050 - 1.63246i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(2.69852 - 1.31072i) q^{9} +(-2.86744 - 2.40607i) q^{10} +(2.08512 + 4.83385i) q^{11} +(-0.289449 - 1.70769i) q^{12} +(-0.202747 - 0.0480518i) q^{13} +(-1.04322 - 3.48460i) q^{14} +(6.10696 - 2.17700i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.290217 + 1.64590i) q^{17} +(2.80522 + 1.06336i) q^{18} +(0.286765 + 1.62633i) q^{19} +(-0.217647 - 3.73685i) q^{20} +(6.12058 + 1.49354i) q^{21} +(-2.08512 + 4.83385i) q^{22} +(-7.81600 + 3.92534i) q^{23} +(1.04350 - 1.38243i) q^{24} +(8.76851 - 2.07818i) q^{25} +(-0.104182 - 0.180448i) q^{26} +(-4.04614 + 3.26017i) q^{27} +(1.81870 - 3.15009i) q^{28} +(0.216107 - 0.721848i) q^{29} +(5.77434 + 2.94810i) q^{30} +(-4.77184 - 3.13849i) q^{31} +(-0.597159 - 0.802123i) q^{32} +(-5.39638 - 7.34986i) q^{33} +(-1.39634 + 0.918389i) q^{34} +(12.7944 + 4.65677i) q^{35} +(1.15160 + 2.77017i) q^{36} +(5.15467 - 1.87615i) q^{37} +(-0.986157 + 1.32464i) q^{38} +(0.360888 + 0.00239336i) q^{39} +(2.56873 - 2.72269i) q^{40} +(3.43214 - 3.63786i) q^{41} +(3.11383 + 5.47688i) q^{42} +(-0.625285 + 0.839904i) q^{43} +(-4.94691 + 1.80053i) q^{44} +(-9.46317 + 6.04576i) q^{45} +(-8.21885 - 2.99142i) q^{46} +(4.54436 - 2.98887i) q^{47} +(1.72163 - 0.189666i) q^{48} +(3.72073 + 4.99781i) q^{49} +(7.52893 + 4.95185i) q^{50} +(-0.149147 - 2.89092i) q^{51} +(0.0597592 - 0.199610i) q^{52} +(-2.43382 + 4.21549i) q^{53} +(-5.14800 - 0.705790i) q^{54} +(-9.85278 - 17.0655i) q^{55} +(3.53936 - 0.838844i) q^{56} +(-1.11548 - 2.63386i) q^{57} +(0.673355 - 0.338172i) q^{58} +(-4.73861 + 10.9853i) q^{59} +(1.81822 + 6.22321i) q^{60} +(0.123728 + 2.12434i) q^{61} +(-0.991781 - 5.62467i) q^{62} +(-10.9113 - 0.144730i) q^{63} +(0.173648 - 0.984808i) q^{64} +(0.774668 + 0.0905456i) q^{65} +(1.64287 - 8.96896i) q^{66} +(1.79201 + 5.98575i) q^{67} +(-1.62624 - 0.385426i) q^{68} +(11.6692 - 9.66046i) q^{69} +(5.39281 + 12.5019i) q^{70} +(-1.97644 - 1.65843i) q^{71} +(-1.22467 + 2.73865i) q^{72} +(-4.28632 + 3.59665i) q^{73} +(4.90201 + 2.46188i) q^{74} +(-13.9942 + 6.91231i) q^{75} +(-1.64025 + 0.191718i) q^{76} +(1.11340 - 19.1163i) q^{77} +(0.245915 + 0.264143i) q^{78} +(2.96988 + 3.14789i) q^{79} +3.74318 q^{80} +(5.56402 - 7.07402i) q^{81} +5.00136 q^{82} +(-9.81132 - 10.3994i) q^{83} +(-1.84690 + 6.02338i) q^{84} +(0.363751 - 6.24536i) q^{85} +(-1.04002 + 0.121561i) q^{86} +(-0.0845240 + 1.30237i) q^{87} +(-4.70443 - 2.36265i) q^{88} +(0.396952 - 0.333082i) q^{89} +(-10.8915 - 2.73441i) q^{90} +(0.580586 + 0.487170i) q^{91} +(-3.46424 - 8.03101i) q^{92} +(9.27327 + 3.44501i) q^{93} +(5.29255 + 1.25436i) q^{94} +(-1.77289 - 5.92186i) q^{95} +(1.31942 + 1.12212i) q^{96} +(1.84818 + 0.216021i) q^{97} +(-1.08195 + 6.13606i) q^{98} +(11.9626 + 10.3112i) 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	0.686242	+	0.727374i	0.485246	+	0.514331i
$2$	0.686242	+	0.727374i	0.485246	+	0.514331i
$3$	−1.68798	+	0.388253i	−0.974553	+	0.224158i
$3$	−1.68798	+	0.388253i	−0.974553	+	0.224158i
$4$	−0.0581448	+	0.998308i	−0.0290724	+	0.499154i
$5$	−3.71787	+	0.434557i	−1.66268	+	0.194340i	−0.894868	−	0.446331i	$-0.852730\pi$
$5$	−3.71787	+	0.434557i	−1.66268	+	0.194340i	−0.767815	+	0.640671i	$0.778656\pi$
$6$	−1.44076	−	0.961353i	−0.588189	−	0.392471i
$7$	−3.25050	−	1.63246i	−1.22858	−	0.617014i	−0.288336	−	0.957529i	$-0.593102\pi$
$7$	−3.25050	−	1.63246i	−1.22858	−	0.617014i	−0.940239	+	0.340515i	$0.889398\pi$
$8$	−0.766044	+	0.642788i	−0.270838	+	0.227260i
$9$	2.69852	−	1.31072i	0.899507	−	0.436907i
$10$	−2.86744	−	2.40607i	−0.906765	−	0.760867i
$11$	2.08512	+	4.83385i	0.628687	+	1.45746i	0.872979	+	0.487758i	$0.162185\pi$
$11$	2.08512	+	4.83385i	0.628687	+	1.45746i	−0.244292	+	0.969702i	$0.578556\pi$
$12$	−0.289449	−	1.70769i	−0.0835567	−	0.492969i
$13$	−0.202747	−	0.0480518i	−0.0562318	−	0.0133272i	0.202404	−	0.979302i	$-0.435125\pi$
$13$	−0.202747	−	0.0480518i	−0.0562318	−	0.0133272i	−0.258635	+	0.965975i	$0.583273\pi$
$14$	−1.04322	−	3.48460i	−0.278812	−	0.931298i
$15$	6.10696	−	2.17700i	1.57681	−	0.562098i
$16$	−0.993238	−	0.116093i	−0.248310	−	0.0290232i
$17$	−0.290217	+	1.64590i	−0.0703879	+	0.399189i	0.929175	+	0.369639i	$0.120519\pi$
$17$	−0.290217	+	1.64590i	−0.0703879	+	0.399189i	−0.999563	+	0.0295503i	$0.990592\pi$
$18$	2.80522	+	1.06336i	0.661197	+	0.250636i
$19$	0.286765	+	1.62633i	0.0657885	+	0.373105i	0.999871	+	0.0160484i	$0.00510858\pi$
$19$	0.286765	+	1.62633i	0.0657885	+	0.373105i	−0.934083	+	0.357057i	$0.883780\pi$
$20$	−0.217647	−	3.73685i	−0.0486673	−	0.835585i
$21$	6.12058	+	1.49354i	1.33562	+	0.325918i
$22$	−2.08512	+	4.83385i	−0.444549	+	1.03058i
$23$	−7.81600	+	3.92534i	−1.62975	+	0.818490i	−0.630648	+	0.776069i	$0.717211\pi$
$23$	−7.81600	+	3.92534i	−1.62975	+	0.818490i	−0.999100	+	0.0424209i	$0.986493\pi$
$24$	1.04350	−	1.38243i	0.213004	−	0.282187i
$25$	8.76851	−	2.07818i	1.75370	−	0.415635i
$26$	−0.104182	−	0.180448i	−0.0204317	−	0.0353887i
$27$	−4.04614	+	3.26017i	−0.778680	+	0.627421i
$28$	1.81870	−	3.15009i	0.343703	−	0.595310i
$29$	0.216107	−	0.721848i	0.0401301	−	0.134044i	−0.935577	−	0.353122i	$-0.885120\pi$
$29$	0.216107	−	0.721848i	0.0401301	−	0.134044i	0.975707	+	0.219079i	$0.0703051\pi$
$30$	5.77434	+	2.94810i	1.05425	+	0.538246i
$31$	−4.77184	−	3.13849i	−0.857047	−	0.563689i	0.0432006	−	0.999066i	$-0.486245\pi$
$31$	−4.77184	−	3.13849i	−0.857047	−	0.563689i	−0.900248	+	0.435377i	$0.856615\pi$
$32$	−0.597159	−	0.802123i	−0.105564	−	0.141797i
$33$	−5.39638	−	7.34986i	−0.939389	−	1.27945i
$34$	−1.39634	+	0.918389i	−0.239471	+	0.157502i
$35$	12.7944	+	4.65677i	2.16264	+	0.787137i
$36$	1.15160	+	2.77017i	0.191933	+	0.461694i
$37$	5.15467	−	1.87615i	0.847423	−	0.308437i	0.118434	−	0.992962i	$-0.462213\pi$
$37$	5.15467	−	1.87615i	0.847423	−	0.308437i	0.728989	+	0.684525i	$0.239990\pi$
$38$	−0.986157	+	1.32464i	−0.159976	+	0.214885i
$39$	0.360888	+	0.00239336i	0.0577883	+	0.000383244i
$40$	2.56873	−	2.72269i	0.406152	−	0.430495i
$41$	3.43214	−	3.63786i	0.536010	−	0.568138i	−0.401605	−	0.915813i	$-0.631547\pi$
$41$	3.43214	−	3.63786i	0.536010	−	0.568138i	0.937615	+	0.347675i	$0.113029\pi$
$42$	3.11383	+	5.47688i	0.480475	+	0.845101i
$43$	−0.625285	+	0.839904i	−0.0953551	+	0.128084i	−0.847240	−	0.531210i	$-0.821737\pi$
$43$	−0.625285	+	0.839904i	−0.0953551	+	0.128084i	0.751885	+	0.659294i	$0.229145\pi$
$44$	−4.94691	+	1.80053i	−0.745774	+	0.271440i
$45$	−9.46317	+	6.04576i	−1.41069	+	0.901248i
$46$	−8.21885	−	2.99142i	−1.21180	−	0.441060i
$47$	4.54436	−	2.98887i	0.662863	−	0.435972i	−0.172991	−	0.984923i	$-0.555343\pi$
$47$	4.54436	−	2.98887i	0.662863	−	0.435972i	0.835854	+	0.548952i	$0.184973\pi$
$48$	1.72163	−	0.189666i	0.248497	−	0.0273759i
$49$	3.72073	+	4.99781i	0.531533	+	0.713972i
$50$	7.52893	+	4.95185i	1.06475	+	0.700298i
$51$	−0.149147	−	2.89092i	−0.0208847	−	0.404809i
$52$	0.0597592	−	0.199610i	0.00828711	−	0.0276809i
$53$	−2.43382	+	4.21549i	−0.334310	+	0.579042i	−0.983352	−	0.181710i	$-0.941837\pi$
$53$	−2.43382	+	4.21549i	−0.334310	+	0.579042i	0.649042	+	0.760753i	$0.275170\pi$
$54$	−5.14800	−	0.705790i	−0.700553	−	0.0960459i
$55$	−9.85278	−	17.0655i	−1.32855	−	2.30111i
$56$	3.53936	−	0.838844i	0.472967	−	0.112095i
$57$	−1.11548	−	2.63386i	−0.147749	−	0.348864i
$58$	0.673355	−	0.338172i	0.0884159	−	0.0444041i
$59$	−4.73861	+	10.9853i	−0.616914	+	1.43017i	0.267542	+	0.963546i	$0.413789\pi$
$59$	−4.73861	+	10.9853i	−0.616914	+	1.43017i	−0.884457	+	0.466622i	$0.845471\pi$
$60$	1.81822	+	6.22321i	0.234732	+	0.803413i
$61$	0.123728	+	2.12434i	0.0158418	+	0.271993i	0.996922	+	0.0783938i	$0.0249792\pi$
$61$	0.123728	+	2.12434i	0.0158418	+	0.271993i	−0.981081	+	0.193599i	$0.937984\pi$
$62$	−0.991781	−	5.62467i	−0.125956	−	0.714334i
$63$	−10.9113	−	0.144730i	−1.37469	−	0.0182343i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	0.774668	+	0.0905456i	0.0960857	+	0.0112308i
$66$	1.64287	−	8.96896i	0.202224	−	1.10400i
$67$	1.79201	+	5.98575i	0.218929	+	0.731275i	0.994932	+	0.100546i	$0.0320590\pi$
$67$	1.79201	+	5.98575i	0.218929	+	0.731275i	−0.776003	+	0.630729i	$0.782756\pi$
$68$	−1.62624	−	0.385426i	−0.197211	−	0.0467398i
$69$	11.6692	−	9.66046i	1.40480	−	1.16298i
$70$	5.39281	+	12.5019i	0.644565	+	1.49427i
$71$	−1.97644	−	1.65843i	−0.234560	−	0.196820i	0.517930	−	0.855423i	$-0.326703\pi$
$71$	−1.97644	−	1.65843i	−0.234560	−	0.196820i	−0.752490	+	0.658604i	$0.771147\pi$
$72$	−1.22467	+	2.73865i	−0.144329	+	0.322753i
$73$	−4.28632	+	3.59665i	−0.501676	+	0.420956i	−0.858189	−	0.513334i	$-0.828410\pi$
$73$	−4.28632	+	3.59665i	−0.501676	+	0.420956i	0.356513	+	0.934291i	$0.383966\pi$
$74$	4.90201	+	2.46188i	0.569847	+	0.286188i
$75$	−13.9942	+	6.91231i	−1.61591	+	0.798164i
$76$	−1.64025	+	0.191718i	−0.188150	+	0.0219915i
$77$	1.11340	−	19.1163i	0.126884	−	2.17851i
$78$	0.245915	+	0.264143i	0.0278444	+	0.0299083i
$79$	2.96988	+	3.14789i	0.334138	+	0.354166i	0.872558	−	0.488511i	$-0.162460\pi$
$79$	2.96988	+	3.14789i	0.334138	+	0.354166i	−0.538420	+	0.842677i	$0.680978\pi$
$80$	3.74318			0.418501
$81$	5.56402	−	7.07402i	0.618224	−	0.786002i
$82$	5.00136			0.552308
$83$	−9.81132	−	10.3994i	−1.07693	−	1.14148i	−0.989385	−	0.145321i	$-0.953579\pi$
$83$	−9.81132	−	10.3994i	−1.07693	−	1.14148i	−0.0875474	−	0.996160i	$-0.527903\pi$
$84$	−1.84690	+	6.02338i	−0.201513	+	0.657205i
$85$	0.363751	−	6.24536i	0.0394543	−	0.677405i
$86$	−1.04002	+	0.121561i	−0.112148	+	0.0131083i
$87$	−0.0845240	+	1.30237i	−0.00906192	+	0.139628i
$88$	−4.70443	−	2.36265i	−0.501494	−	0.251860i
$89$	0.396952	−	0.333082i	0.0420768	−	0.0353067i	−0.621507	−	0.783409i	$-0.713479\pi$
$89$	0.396952	−	0.333082i	0.0420768	−	0.0353067i	0.663584	+	0.748102i	$0.269035\pi$
$90$	−10.8915	−	2.73441i	−1.14807	−	0.288232i
$91$	0.580586	+	0.487170i	0.0608620	+	0.0510692i
$92$	−3.46424	−	8.03101i	−0.361172	−	0.837291i
$93$	9.27327	+	3.44501i	0.961593	+	0.357231i
$94$	5.29255	+	1.25436i	0.545885	+	0.129377i
$95$	−1.77289	−	5.92186i	−0.181895	−	0.607570i
$96$	1.31942	+	1.12212i	0.134662	+	0.114525i
$97$	1.84818	+	0.216021i	0.187654	+	0.0219337i	0.209401	−	0.977830i	$-0.432849\pi$
$97$	1.84818	+	0.216021i	0.187654	+	0.0219337i	−0.0217465	+	0.999764i	$0.506923\pi$
$98$	−1.08195	+	6.13606i	−0.109294	+	0.619836i
$99$	11.9626	+	10.3112i	1.20228	+	1.03632i
$100$	1.56482	+	8.87451i	0.156482	+	0.887451i
$101$	0.668800	+	11.4829i	0.0665481	+	1.14259i	0.851958	+	0.523610i	$0.175415\pi$
$101$	0.668800	+	11.4829i	0.0665481	+	1.14259i	−0.785410	+	0.618976i	$0.787548\pi$
$102$	2.00042	−	2.09235i	0.198072	−	0.207174i
$103$	−5.88743	+	13.6486i	−0.580105	+	1.34484i	0.335228	+	0.942137i	$0.391187\pi$
$103$	−5.88743	+	13.6486i	−0.580105	+	1.34484i	−0.915333	+	0.402698i	$0.868073\pi$
$104$	0.186200	−	0.0935132i	0.0182584	−	0.00916972i
$105$	−23.4046	−	2.89306i	−2.28405	−	0.282334i
$106$	−4.73642	+	1.12255i	−0.460042	+	0.109032i
$107$	1.27937	+	2.21593i	0.123681	+	0.214222i	0.921217	−	0.389050i	$-0.127197\pi$
$107$	1.27937	+	2.21593i	0.123681	+	0.214222i	−0.797535	+	0.603272i	$0.793863\pi$
$108$	−3.01940	−	4.22886i	−0.290541	−	0.406922i
$109$	−5.38593	+	9.32871i	−0.515879	+	0.893528i	0.483951	+	0.875095i	$0.339201\pi$
$109$	−5.38593	+	9.32871i	−0.515879	+	0.893528i	−0.999830	+	0.0184331i	$0.994132\pi$
$110$	5.65162	−	18.8777i	0.538861	−	1.79992i
$111$	−7.97254	+	5.16821i	−0.756720	+	0.490544i
$112$	3.03901	+	1.99879i	0.287159	+	0.188868i
$113$	−7.36982	−	9.89939i	−0.693295	−	0.931256i	0.306493	−	0.951873i	$-0.400844\pi$
$113$	−7.36982	−	9.89939i	−0.693295	−	0.931256i	−0.999787	+	0.0206167i	$0.993437\pi$
$114$	1.15031	−	2.61884i	0.107737	−	0.245276i
$115$	27.3531	−	17.9904i	2.55069	−	1.67761i
$116$	0.708062	+	0.257713i	0.0657419	+	0.0239281i
$117$	−0.610098	+	0.136076i	−0.0564036	+	0.0125802i
$118$	−11.2423	+	4.09185i	−1.03494	+	0.376686i
$119$	3.63022	−	4.87624i	0.332782	−	0.447004i
$120$	−3.27886	+	5.59315i	−0.299317	+	0.510583i
$121$	−11.4697	+	12.1572i	−1.04270	+	1.10520i
$122$	−1.46028	+	1.54780i	−0.132207	+	0.140132i
$123$	−4.38096	+	7.47315i	−0.395018	+	0.673831i
$124$	3.41064	−	4.58128i	0.306284	−	0.411411i
$125$	−14.1099	+	5.13559i	−1.26203	+	0.459341i
$126$	−7.38249	−	8.03588i	−0.657684	−	0.715893i
$127$	17.2415	+	6.27538i	1.52993	+	0.556850i	0.963605	−	0.267331i	$-0.0861417\pi$
$127$	17.2415	+	6.27538i	1.52993	+	0.556850i	0.566327	+	0.824181i	$0.308364\pi$
$128$	0.835488	−	0.549509i	0.0738474	−	0.0485702i
$129$	0.729371	−	1.66051i	0.0642175	−	0.146199i
$130$	0.465749	+	0.625609i	0.0408489	+	0.0548695i
$131$	−0.165733	−	0.109005i	−0.0144802	−	0.00952378i	0.542248	−	0.840218i	$-0.317573\pi$
$131$	−0.165733	−	0.109005i	−0.0144802	−	0.00952378i	−0.556728	+	0.830695i	$0.687944\pi$
$132$	7.65120	−	4.95989i	0.665951	−	0.431703i
$133$	1.72279	−	5.75452i	0.149385	−	0.498980i
$134$	−3.12412	+	5.41113i	−0.269883	+	0.467451i
$135$	13.6263	−	13.8792i	1.17277	−	1.19453i
$136$	−0.835645	−	1.44738i	−0.0716560	−	0.124112i
$137$	−4.29953	+	1.01901i	−0.367333	+	0.0870596i	−0.410137	−	0.912024i	$-0.634519\pi$
$137$	−4.29953	+	1.01901i	−0.367333	+	0.0870596i	0.0428037	+	0.999084i	$0.486371\pi$
$138$	15.0346	+	1.85845i	1.27983	+	0.158201i
$139$	−1.10445	+	0.554676i	−0.0936783	+	0.0470470i	−0.495021	−	0.868881i	$-0.664840\pi$
$139$	−1.10445	+	0.554676i	−0.0936783	+	0.0470470i	0.401343	+	0.915928i	$0.368543\pi$
$140$	−5.39281	+	12.5019i	−0.455776	+	1.05661i
$141$	−6.51032	+	6.80950i	−0.548268	+	0.573463i
$142$	−0.150017	−	2.57570i	−0.0125892	−	0.216148i
$143$	−0.190475	−	1.08024i	−0.0159284	−	0.0903342i
$144$	−2.83244	+	0.988580i	−0.236037	+	0.0823817i
$145$	−0.489775	+	2.77765i	−0.0406736	+	0.230671i
$146$	−5.55756	−	0.649586i	−0.459947	−	0.0537601i
$147$	−8.22091	−	6.99159i	−0.678049	−	0.576657i
$148$	1.57326	+	5.25504i	0.129321	+	0.431962i
$149$	7.84141	+	1.85845i	0.642394	+	0.152250i	0.538886	−	0.842379i	$-0.318845\pi$
$149$	7.84141	+	1.85845i	0.642394	+	0.152250i	0.103507	+	0.994629i	$0.466993\pi$
$150$	−14.6312	−	5.43548i	−1.19463	−	0.443805i
$151$	2.94676	+	6.83136i	0.239804	+	0.555928i	0.995034	−	0.0995312i	$-0.0317343\pi$
$151$	2.94676	+	6.83136i	0.239804	+	0.555928i	−0.755230	+	0.655459i	$0.772475\pi$
$152$	−1.26506	−	1.06151i	−0.102610	−	0.0860998i
$153$	1.37416	+	4.82189i	0.111094	+	0.389826i
$154$	14.6688	−	12.3086i	1.18204	−	0.991852i
$155$	19.1049	+	9.59486i	1.53455	+	0.770678i
$156$	−0.0233731	+	0.360138i	−0.00187134	+	0.0288341i
$157$	19.5842	−	2.28906i	1.56299	−	0.182687i	0.709843	−	0.704360i	$-0.248766\pi$
$157$	19.5842	−	2.28906i	1.56299	−	0.182687i	0.853145	+	0.521673i	$0.174692\pi$
$158$	−0.251636	+	4.32043i	−0.0200191	+	0.343715i
$159$	2.47154	−	8.06058i	0.196006	−	0.639246i
$160$	2.56873	+	2.72269i	0.203076	+	0.215248i
$161$	31.8139			2.50729
$162$	8.96371	−	0.807367i	0.704256	−	0.0634328i
$163$	7.25041			0.567896			0.283948	−	0.958840i	$-0.408356\pi$
$163$	7.25041			0.567896			0.283948	+	0.958840i	$0.408356\pi$
$164$	3.43214	+	3.63786i	0.268005	+	0.284069i
$165$	23.2570	+	24.9808i	1.81055	+	1.94475i
$166$	0.831307	−	14.2730i	0.0645219	−	1.10780i
$167$	18.7077	−	2.18662i	1.44764	−	0.169205i	0.644324	−	0.764753i	$-0.277139\pi$
$167$	18.7077	−	2.18662i	1.44764	−	0.169205i	0.803320	+	0.595547i	$0.203065\pi$
$168$	−5.64867	+	2.79011i	−0.435804	+	0.215262i
$169$	−11.5784	−	5.81490i	−0.890648	−	0.447300i
$170$	4.79233	−	4.02124i	0.367555	−	0.308415i
$171$	2.90550	+	4.01281i	0.222189	+	0.306867i
$172$	−0.802126	−	0.673063i	−0.0611615	−	0.0513206i
$173$	1.82769	+	4.23707i	0.138957	+	0.322138i	0.973457	−	0.228869i	$-0.0735028\pi$
$173$	1.82769	+	4.23707i	0.138957	+	0.322138i	−0.834500	+	0.551007i	$0.814244\pi$
$174$	−1.00531	+	0.832258i	−0.0762124	+	0.0630933i
$175$	−31.8946	−	7.55917i	−2.41101	−	0.571419i
$176$	−1.50984	−	5.04323i	−0.113809	−	0.380148i
$177$	3.73357	−	20.3827i	0.280632	−	1.53206i
$178$	0.514681	+	0.0601575i	0.0385769	+	0.00450900i
$179$	4.34713	−	24.6538i	0.324920	−	1.84271i	−0.185320	−	0.982678i	$-0.559332\pi$
$179$	4.34713	−	24.6538i	0.324920	−	1.84271i	0.510240	−	0.860032i	$-0.329557\pi$
$180$	−5.48529	−	9.79869i	−0.408850	−	0.730351i
$181$	2.73733	+	15.5241i	0.203464	+	1.15390i	0.899839	+	0.436223i	$0.143684\pi$
$181$	2.73733	+	15.5241i	0.203464	+	1.15390i	−0.696375	+	0.717678i	$0.745205\pi$
$182$	0.0440680	+	0.756619i	0.00326654	+	0.0560843i
$183$	−1.03363	−	3.53779i	−0.0764081	−	0.261521i
$184$	3.46424	−	8.03101i	0.255387	−	0.592054i
$185$	−18.3491	+	9.21528i	−1.34905	+	0.677521i
$186$	3.85790	+	9.10924i	0.282875	+	0.667922i
$187$	−8.56116	+	2.02903i	−0.626054	+	0.148378i
$188$	2.71958	+	4.71046i	0.198346	+	0.343545i
$189$	18.4741	−	3.99203i	1.34379	−	0.290377i
$190$	3.09078	−	5.35338i	0.224228	−	0.388375i
$191$	−0.382243	+	1.27678i	−0.0276581	+	0.0923845i	−0.970704	−	0.240277i	$-0.922762\pi$
$191$	−0.382243	+	1.27678i	−0.0276581	+	0.0923845i	0.943046	+	0.332662i	$0.107947\pi$
$192$	0.0892405	+	1.72975i	0.00644038	+	0.124834i
$193$	−11.1785	−	7.35219i	−0.804644	−	0.529222i	0.0792808	−	0.996852i	$-0.474738\pi$
$193$	−11.1785	−	7.35219i	−0.804644	−	0.529222i	−0.883924	+	0.467630i	$0.845108\pi$
$194$	1.11117	+	1.49256i	0.0797774	+	0.107160i
$195$	−1.34277	+	0.147928i	−0.0961580	+	0.0105933i
$196$	−5.20569	+	3.42384i	−0.371835	+	0.244560i
$197$	−24.7068	−	8.99252i	−1.76028	−	0.640691i	−0.760323	−	0.649545i	$-0.774959\pi$
$197$	−24.7068	−	8.99252i	−1.76028	−	0.640691i	−0.999961	+	0.00885463i	$0.997181\pi$
$198$	0.709097	+	15.7772i	0.0503934	+	1.12124i
$199$	−2.18009	+	0.793488i	−0.154542	+	0.0562489i	−0.418133	−	0.908386i	$-0.637315\pi$
$199$	−2.18009	+	0.793488i	−0.154542	+	0.0562489i	0.263591	+	0.964635i	$0.415093\pi$
$200$	−5.38124	+	7.22827i	−0.380511	+	0.511116i
$201$	−5.34886	−	9.40804i	−0.377279	−	0.663592i
$202$	−7.89336	+	8.36648i	−0.555375	+	0.588663i
$203$	−1.88085	+	1.99358i	−0.132010	+	0.139922i
$204$	2.89470	+	0.0191972i	0.202669	+	0.00134408i
$205$	−11.1794	+	15.0166i	−0.780804	+	1.04880i
$206$	−13.9678	+	5.08387i	−0.973184	+	0.354210i
$207$	−15.9466	+	20.8372i	−1.10836	+	1.44829i
$208$	0.195797	+	0.0712644i	0.0135761	+	0.00494130i
$209$	−7.26347	+	4.77726i	−0.502425	+	0.330450i
$210$	−13.9569	−	19.0092i	−0.963114	−	1.31176i
$211$	−5.83455	−	7.83716i	−0.401667	−	0.539532i	0.554566	−	0.832140i	$-0.312884\pi$
$211$	−5.83455	−	7.83716i	−0.401667	−	0.539532i	−0.956233	+	0.292608i	$0.905477\pi$
$212$	−4.06685	−	2.67481i	−0.279312	−	0.183706i
$213$	3.98007	+	2.03203i	0.272710	+	0.139232i
$214$	−0.733854	+	2.45124i	−0.0501653	+	0.167564i
$215$	1.95974	−	3.39438i	0.133653	−	0.231495i
$216$	1.00393	−	5.09825i	0.0683085	−	0.346892i
$217$	10.3874	+	17.9915i	0.705144	+	1.22134i
$218$	−10.4815	+	2.48416i	−0.709897	+	0.168249i
$219$	5.83880	−	7.73524i	0.394549	−	0.522699i
$220$	17.6095	−	8.84384i	1.18723	−	0.596252i
$221$	0.137929	−	0.319755i	0.00927811	−	0.0215091i
$222$	−9.23031	−	2.25238i	−0.619498	−	0.151170i
$223$	−0.340442	−	5.84516i	−0.0227977	−	0.391421i	−0.990335	−	0.138694i	$-0.955710\pi$
$223$	−0.340442	−	5.84516i	−0.0227977	−	0.391421i	0.967538	−	0.252727i	$-0.0813274\pi$
$224$	0.631629	+	3.58215i	0.0422025	+	0.239342i
$225$	20.9381	−	17.1011i	1.39587	−	1.14007i
$226$	2.14308	−	12.1540i	0.142555	−	0.808471i
$227$	−7.48001	−	0.874287i	−0.496465	−	0.0580285i	−0.135824	−	0.990733i	$-0.543368\pi$
$227$	−7.48001	−	0.874287i	−0.496465	−	0.0580285i	−0.360642	+	0.932705i	$0.617442\pi$
$228$	2.69427	−	0.960446i	0.178432	−	0.0636071i
$229$	−3.23898	−	10.8190i	−0.214038	−	0.714937i	−0.995816	−	0.0913799i	$-0.970872\pi$
$229$	−3.23898	−	10.8190i	−0.214038	−	0.714937i	0.781778	−	0.623557i	$-0.214313\pi$
$230$	31.8566	+	7.55015i	2.10056	+	0.497842i
$231$	5.54257	+	32.7002i	0.364675	+	2.15151i
$232$	0.298448	+	0.691879i	0.0195940	+	0.0454241i
$233$	5.82577	+	4.88840i	0.381659	+	0.320250i	0.813353	−	0.581770i	$-0.197640\pi$
$233$	5.82577	+	4.88840i	0.381659	+	0.320250i	−0.431694	+	0.902020i	$0.642084\pi$
$234$	−0.517653	−	0.350389i	−0.0338400	−	0.0229056i
$235$	−15.5965	+	13.0870i	−1.01740	+	0.853703i
$236$	−10.6912	−	5.36933i	−0.695939	−	0.349514i
$237$	−6.23527	−	4.16050i	−0.405024	−	0.270253i
$238$	6.03806	−	0.705748i	0.391389	−	0.0457468i
$239$	1.11084	−	19.0723i	0.0718541	−	1.23369i	−0.749008	−	0.662561i	$-0.769470\pi$
$239$	1.11084	−	19.0723i	0.0718541	−	1.23369i	0.820862	−	0.571126i	$-0.193493\pi$
$240$	−6.31840	+	1.45330i	−0.407851	+	0.0938102i
$241$	4.44457	+	4.71097i	0.286300	+	0.303460i	0.854522	−	0.519415i	$-0.173850\pi$
$241$	4.44457	+	4.71097i	0.286300	+	0.303460i	−0.568222	+	0.822875i	$0.692369\pi$
$242$	−16.7138			−1.07440
$243$	−6.64541	+	14.1010i	−0.426303	+	0.904580i
$244$	−2.12794			−0.136227
$245$	−16.0050	−	16.9643i	−1.02252	−	1.08381i
$246$	−8.44217	+	1.94179i	−0.538253	+	0.123804i
$247$	0.0200073	−	0.343512i	0.00127303	−	0.0218571i
$248$	5.67282	−	0.663058i	0.360224	−	0.0421042i
$249$	20.5989	+	13.7446i	1.30540	+	0.871031i
$250$	−13.4183	−	6.73893i	−0.848648	−	0.426207i
$251$	−6.01053	+	5.04343i	−0.379381	+	0.318339i	−0.812459	−	0.583018i	$-0.801872\pi$
$251$	−6.01053	+	5.04343i	−0.379381	+	0.318339i	0.433078	+	0.901356i	$0.357427\pi$
$252$	0.778919	−	10.8844i	0.0490673	−	0.685652i
$253$	−35.2718	−	29.5965i	−2.21752	−	1.86072i
$254$	7.26726	+	16.8474i	0.455989	+	1.05710i
$255$	1.81078	+	10.6832i	0.113395	+	0.669011i
$256$	0.973045	+	0.230616i	0.0608153	+	0.0144135i
$257$	3.31564	+	11.0750i	0.206824	+	0.690839i	0.996960	+	0.0779088i	$0.0248243\pi$
$257$	3.31564	+	11.0750i	0.206824	+	0.690839i	−0.790137	+	0.612931i	$0.789991\pi$
$258$	1.70833	−	0.608983i	0.106356	−	0.0379136i
$259$	−19.8180	−	2.31640i	−1.23143	−	0.143934i
$260$	−0.135435	+	0.768092i	−0.00839935	+	0.0476351i
$261$	−0.362973	−	2.23118i	−0.0224675	−	0.138106i
$262$	−0.0344461	−	0.195354i	−0.00212809	−	0.0120690i
$263$	0.419053	+	7.19487i	0.0258399	+	0.443655i	0.986271	+	0.165136i	$0.0528063\pi$
$263$	0.419053	+	7.19487i	0.0258399	+	0.443655i	−0.960431	+	0.278519i	$0.910157\pi$
$264$	8.85827	+	2.16159i	0.545189	+	0.133037i
$265$	7.21674	−	16.7303i	0.443321	−	1.02773i
$266$	5.36793	−	2.69588i	0.329129	−	0.165295i
$267$	−0.540725	+	0.716353i	−0.0330918	+	0.0438401i
$268$	−6.07982	+	1.44094i	−0.371384	+	0.0880196i
$269$	10.8367	+	18.7696i	0.660723	+	1.14441i	0.980426	+	0.196888i	$0.0630834\pi$
$269$	10.8367	+	18.7696i	0.660723	+	1.14441i	−0.319703	+	0.947518i	$0.603583\pi$
$270$	19.4463	+	0.386941i	1.18346	+	0.0235485i
$271$	10.7244	−	18.5753i	0.651463	−	1.12837i	−0.331305	−	0.943524i	$-0.607489\pi$
$271$	10.7244	−	18.5753i	0.651463	−	1.12837i	0.982768	−	0.184844i	$-0.0591779\pi$
$272$	0.479332	−	1.60108i	0.0290637	−	0.0970797i
$273$	−1.16916	−	0.596916i	−0.0707608	−	0.0361270i
$274$	−3.69171	−	2.42808i	−0.223024	−	0.146686i
$275$	28.3290	+	38.0524i	1.70830	+	2.29465i
$276$	8.96561	+	12.2111i	0.539666	+	0.735024i
$277$	−10.0441	+	6.60609i	−0.603490	+	0.396922i	−0.814164	−	0.580635i	$-0.802804\pi$
$277$	−10.0441	+	6.60609i	−0.603490	+	0.396922i	0.210674	+	0.977556i	$0.432434\pi$
$278$	−1.16138	−	0.422707i	−0.0696548	−	0.0253523i
$279$	−16.9906	−	2.21472i	−1.01720	−	0.132592i
$280$	−12.7944	+	4.65677i	−0.764609	+	0.278295i
$281$	−5.53844	+	7.43941i	−0.330395	+	0.443798i	−0.936017	−	0.351955i	$-0.885517\pi$
$281$	−5.53844	+	7.43941i	−0.330395	+	0.443798i	0.605622	+	0.795753i	$0.292925\pi$
$282$	−9.42070	−	0.0624768i	−0.560995	−	0.00372044i
$283$	16.3804	−	17.3622i	0.973714	−	1.03208i	−0.0257605	−	0.999668i	$-0.508201\pi$
$283$	16.3804	−	17.3622i	0.973714	−	1.03208i	0.999475	−	0.0324087i	$-0.0103178\pi$
$284$	1.77054	−	1.87667i	0.105063	−	0.111360i
$285$	5.29177	+	9.30762i	0.313457	+	0.551336i
$286$	0.655026	−	0.879852i	0.0387325	−	0.0520268i
$287$	−17.0949	+	6.22202i	−1.00908	+	0.367274i
$288$	−2.66280	−	1.38184i	−0.156907	−	0.0814255i
$289$	13.3500	+	4.85901i	0.785295	+	0.285824i
$290$	−2.35649	+	1.54989i	−0.138378	+	0.0910127i
$291$	−3.20356	+	0.352923i	−0.187796	+	0.0206887i
$292$	−3.34134	−	4.48820i	−0.195537	−	0.262652i
$293$	−11.4171	−	7.50914i	−0.666994	−	0.438689i	0.170337	−	0.985386i	$-0.445515\pi$
$293$	−11.4171	−	7.50914i	−0.666994	−	0.438689i	−0.837330	+	0.546697i	$0.815885\pi$
$294$	−0.556033	−	10.7776i	−0.0324285	−	0.628562i
$295$	12.8438	−	42.9013i	0.747795	−	2.49781i
$296$	−2.74274	+	4.75057i	−0.159419	+	0.276121i
$297$	−24.1959	−	12.7606i	−1.40399	−	0.740444i
$298$	4.02932	+	6.97898i	0.233412	+	0.404282i
$299$	1.77329	−	0.420277i	0.102552	−	0.0243052i
$300$	−6.08692	−	14.3724i	−0.351429	−	0.829792i
$301$	3.40361	−	1.70935i	0.196181	−	0.0985256i
$302$	−2.94676	+	6.83136i	−0.169567	+	0.393101i
$303$	−5.58717	−	19.1231i	−0.320974	−	1.09859i
$304$	−0.0960213	−	1.64862i	−0.00550720	−	0.0945549i
$305$	−1.38315	−	7.84424i	−0.0791990	−	0.449160i
$306$	−2.56431	+	4.30851i	−0.146592	+	0.246301i
$307$	−2.34246	+	13.2847i	−0.133691	+	0.758201i	0.842071	+	0.539367i	$0.181336\pi$
$307$	−2.34246	+	13.2847i	−0.133691	+	0.758201i	−0.975762	+	0.218834i	$0.929775\pi$
$308$	19.0192	+	2.22303i	1.08372	+	0.126669i
$309$	4.63873	−	25.3243i	0.263888	−	1.44065i
$310$	6.13156	+	20.4808i	0.348249	+	1.16323i
$311$	−5.74747	−	1.36218i	−0.325909	−	0.0772419i	0.0644043	−	0.997924i	$-0.479485\pi$
$311$	−5.74747	−	1.36218i	−0.325909	−	0.0772419i	−0.390314	+	0.920682i	$0.627633\pi$
$312$	−0.277994	+	0.230141i	−0.0157383	+	0.0130291i
$313$	3.49181	+	8.09493i	0.197369	+	0.457552i	0.987944	−	0.154813i	$-0.0494775\pi$
$313$	3.49181	+	8.09493i	0.197369	+	0.457552i	−0.790575	+	0.612365i	$0.790218\pi$
$314$	15.1045	+	12.6742i	0.852395	+	0.715245i
$315$	40.6296	−	4.20347i	2.28922	−	0.236839i
$316$	−3.31525	+	2.78182i	−0.186497	+	0.156490i
$317$	−6.52805	−	3.27851i	−0.366652	−	0.184139i	0.255928	−	0.966696i	$-0.417619\pi$
$317$	−6.52805	−	3.27851i	−0.366652	−	0.184139i	−0.622580	+	0.782556i	$0.713915\pi$
$318$	7.55913	−	3.73377i	0.423895	−	0.209379i
$319$	3.93991	−	0.460510i	0.220593	−	0.0257836i
$320$	−0.217647	+	3.73685i	−0.0121668	+	0.208896i
$321$	−3.01989	−	3.24372i	−0.168554	−	0.181047i
$322$	21.8320	+	23.1406i	1.21665	+	1.28958i
$323$	−2.76000			−0.153570
$324$	6.73853	+	5.96592i	0.374363	+	0.331440i
$325$	−1.87765			−0.104153
$326$	4.97554	+	5.27376i	0.275569	+	0.292087i
$327$	5.46942	−	17.8377i	0.302460	−	0.986428i
$328$	−0.290803	+	4.99290i	−0.0160569	+	0.275687i
$329$	−19.6507	+	2.29683i	−1.08338	+	0.126629i
$330$	−2.21046	+	34.0594i	−0.121682	+	1.87491i
$331$	−28.6172	−	14.3721i	−1.57294	−	0.789962i	−0.573374	−	0.819294i	$-0.694366\pi$
$331$	−28.6172	−	14.3721i	−1.57294	−	0.789962i	−0.999570	+	0.0293318i	$0.990662\pi$
$332$	10.9523	−	9.19005i	0.601084	−	0.504369i
$333$	11.4509	−	11.8192i	0.627504	−	0.647686i
$334$	14.4285	+	12.1069i	0.789491	+	0.662462i
$335$	−9.26363	−	21.4755i	−0.506126	−	1.17333i
$336$	−5.90581	−	2.19400i	−0.322188	−	0.119692i
$337$	25.2820	+	5.99194i	1.37720	+	0.326402i	0.851538	−	0.524293i	$-0.175670\pi$
$337$	25.2820	+	5.99194i	1.37720	+	0.326402i	0.525660	+	0.850695i	$0.323819\pi$
$338$	−3.71599	−	12.4123i	−0.202123	−	0.675139i
$339$	16.2835	+	13.8486i	0.884401	+	0.752151i
$340$	6.21365	+	0.726271i	0.336982	+	0.0393876i
$341$	5.22112	−	29.6104i	0.282740	−	1.60350i
$342$	−0.924931	+	4.86714i	−0.0500145	+	0.263185i
$343$	0.485898	+	2.75566i	0.0262360	+	0.148792i
$344$	−0.0608835	−	1.04533i	−0.00328262	−	0.0563604i
$345$	−39.1865	+	40.9873i	−2.10973	+	2.20668i
$346$	−1.82769	+	4.23707i	−0.0982573	+	0.227786i
$347$	11.6904	−	5.87112i	0.627571	−	0.315178i	−0.106436	−	0.994320i	$-0.533944\pi$
$347$	11.6904	−	5.87112i	0.627571	−	0.315178i	0.734007	+	0.679142i	$0.237648\pi$
$348$	−1.29525	−	0.160107i	−0.0694326	−	0.00858263i
$349$	−19.4854	+	4.61812i	−1.04303	+	0.247202i	−0.716210	−	0.697885i	$-0.754125\pi$
$349$	−19.4854	+	4.61812i	−1.04303	+	0.247202i	−0.326819	+	0.945087i	$0.605977\pi$
$350$	−16.3891	−	28.3867i	−0.876034	−	1.51733i
$351$	0.976999	−	0.466565i	0.0521484	−	0.0249034i
$352$	2.63219	−	4.55909i	0.140296	−	0.243001i
$353$	−8.35199	+	27.8976i	−0.444532	+	1.48484i	0.383173	+	0.923676i	$0.374831\pi$
$353$	−8.35199	+	27.8976i	−0.444532	+	1.48484i	−0.827705	+	0.561163i	$0.810354\pi$
$354$	17.3880	−	11.2718i	0.924162	−	0.599089i
$355$	8.06884	+	5.30696i	0.428249	+	0.281664i
$356$	0.309438	+	0.415648i	0.0164002	+	0.0220293i
$357$	−4.23451	+	9.64041i	−0.224114	+	0.510225i
$358$	20.9157	−	13.7565i	1.10543	−	0.727052i
$359$	14.6096	+	5.31744i	0.771063	+	0.280644i	0.697441	−	0.716642i	$-0.254322\pi$
$359$	14.6096	+	5.31744i	0.771063	+	0.280644i	0.0736220	+	0.997286i	$0.476544\pi$
$360$	3.36307	−	10.7141i	0.177249	−	0.564684i
$361$	15.2915	−	5.56563i	0.804813	−	0.292928i
$362$	−9.41339	+	12.6444i	−0.494757	+	0.664574i
$363$	14.6405	−	24.9741i	0.768427	−	1.31080i
$364$	−0.520103	+	0.551277i	−0.0272608	+	0.0288948i
$365$	14.3731	−	15.2345i	0.752320	−	0.797413i
$366$	1.86397	−	3.17961i	0.0974314	−	0.166201i
$367$	−5.51820	+	7.41223i	−0.288048	+	0.386915i	−0.922468	−	0.386073i	$-0.873831\pi$
$367$	−5.51820	+	7.41223i	−0.288048	+	0.386915i	0.634421	+	0.772988i	$0.281239\pi$
$368$	8.21885	−	2.99142i	0.428437	−	0.155938i
$369$	4.49348	−	14.3154i	0.233921	−	0.745231i
$370$	−19.2949	−	7.02276i	−1.00309	−	0.365096i
$371$	14.7928	−	9.72936i	0.768002	−	0.505123i
$372$	−3.97837	+	9.05727i	−0.206269	+	0.469598i
$373$	20.1084	+	27.0103i	1.04117	+	1.39854i	0.913555	+	0.406716i	$0.133326\pi$
$373$	20.1084	+	27.0103i	1.04117	+	1.39854i	0.127619	+	0.991823i	$0.459266\pi$
$374$	−7.35089	−	4.83476i	−0.380106	−	0.249999i
$375$	21.8233	−	14.1470i	1.12695	−	0.730546i
$376$	−1.55997	+	5.21066i	−0.0804493	+	0.268719i
$377$	−0.0785012	+	0.135968i	−0.00404302	+	0.00700271i
$378$	15.5814	+	10.6981i	0.801421	+	0.550251i
$379$	0.117576	+	0.203648i	0.00603950	+	0.0104607i	0.869029	−	0.494761i	$-0.164744\pi$
$379$	0.117576	+	0.203648i	0.00603950	+	0.0104607i	−0.862990	+	0.505221i	$0.831411\pi$
$380$	6.01493	−	1.42556i	0.308559	−	0.0731299i
$381$	−31.5396	−	3.89864i	−1.61582	−	0.199733i
$382$	−1.19101	+	0.598146i	−0.0609372	+	0.0306038i
$383$	5.82441	−	13.5025i	0.297614	−	0.689946i	−0.702142	−	0.712037i	$-0.747773\pi$
$383$	5.82441	−	13.5025i	0.297614	−	0.689946i	0.999756	+	0.0220908i	$0.00703228\pi$
$384$	−1.19693	+	1.25194i	−0.0610808	+	0.0638877i
$385$	4.16766	+	71.5559i	0.212403	+	3.64683i
$386$	−2.32334	−	13.1763i	−0.118255	−	0.670656i
$387$	−0.586464	+	3.08607i	−0.0298116	+	0.156874i
$388$	−0.323118	+	1.83249i	−0.0164038	+	0.0930308i
$389$	−21.2249	−	2.48083i	−1.07614	−	0.125783i	−0.440490	−	0.897757i	$-0.645195\pi$
$389$	−21.2249	−	2.48083i	−1.07614	−	0.125783i	−0.635654	+	0.771974i	$0.719269\pi$
$390$	−1.02907	−	0.875184i	−0.0521088	−	0.0443167i
$391$	−4.19239	−	14.0035i	−0.212018	−	0.708190i
$392$	−6.06277	−	1.43690i	−0.306216	−	0.0725746i
$393$	0.322075	+	0.119651i	0.0162465	+	0.00603557i
$394$	−10.4139	−	24.1421i	−0.524644	−	1.21626i
$395$	−12.4096	−	10.4129i	−0.624394	−	0.523929i
$396$	−10.9893	+	11.3428i	−0.552235	+	0.569996i
$397$	−17.7928	+	14.9299i	−0.892995	+	0.749311i	−0.968809	−	0.247811i	$-0.920289\pi$
$397$	−17.7928	+	14.9299i	−0.892995	+	0.749311i	0.0758139	+	0.997122i	$0.475845\pi$
$398$	−2.07323	−	1.04122i	−0.103922	−	0.0521914i
$399$	−0.673818	+	10.3824i	−0.0337331	+	0.519768i
$400$	−8.95048	+	1.04616i	−0.447524	+	0.0523081i
$401$	−0.933075	+	16.0203i	−0.0465955	+	0.800014i	0.891368	+	0.453280i	$0.149746\pi$
$401$	−0.933075	+	16.0203i	−0.0465955	+	0.800014i	−0.937964	+	0.346734i	$0.887291\pi$
$402$	3.17255	−	10.3468i	0.158232	−	0.516052i
$403$	0.816664	+	0.865613i	0.0406809	+	0.0431193i
$404$	−11.5023			−0.572261
$405$	−17.6122	+	28.7182i	−0.875159	+	1.42702i
$406$	−2.74080			−0.136024
$407$	19.8171	+	21.0049i	0.982298	+	1.04117i
$408$	1.97250	+	2.11870i	0.0976532	+	0.104891i
$409$	−0.205707	+	3.53186i	−0.0101716	+	0.174639i	0.989396	+	0.145242i	$0.0463959\pi$
$409$	−0.205707	+	3.53186i	−0.0101716	+	0.174639i	−0.999568	+	0.0293976i	$0.990641\pi$
$410$	−18.5944	+	2.17338i	−0.918313	+	0.107335i
$411$	6.86186	−	3.38936i	0.338471	−	0.167185i
$412$	−13.2832	−	6.67106i	−0.654415	−	0.328659i
$413$	33.3360	−	27.9723i	1.64036	−	1.37642i
$414$	−26.0996	+	2.70023i	−1.28273	+	0.132709i
$415$	40.9964	+	34.4000i	2.01243	+	1.68863i
$416$	0.0825284	+	0.191322i	0.00404629	+	0.00938035i
$417$	1.64893	−	1.36509i	0.0807485	−	0.0668485i
$418$	−8.45935	−	2.00490i	−0.413761	−	0.0980630i
$419$	8.97055	+	29.9637i	0.438240	+	1.46382i	0.837221	+	0.546865i	$0.184179\pi$
$419$	8.97055	+	29.9637i	0.438240	+	1.46382i	−0.398981	+	0.916959i	$0.630636\pi$
$420$	4.24902	−	23.1968i	0.207331	−	1.13189i
$421$	−17.7199	−	2.07115i	−0.863613	−	0.100942i	−0.327259	−	0.944935i	$-0.606125\pi$
$421$	−17.7199	−	2.07115i	−0.863613	−	0.100942i	−0.536354	+	0.843993i	$0.680199\pi$
$422$	1.69663	−	9.62208i	0.0825907	−	0.468395i
$423$	8.34546	−	14.0219i	0.405770	−	0.681769i
$424$	−0.845255	−	4.79368i	−0.0410492	−	0.232802i
$425$	0.875701	+	15.0352i	0.0424778	+	0.729315i
$426$	1.25325	+	4.28947i	0.0607200	+	0.207825i
$427$	3.06572	−	7.10714i	0.148361	−	0.343939i
$428$	−2.28657	+	1.14836i	−0.110526	+	0.0555081i
$429$	0.740924	+	1.74947i	0.0357721	+	0.0844650i
$430$	3.81384	−	0.903896i	0.183920	−	0.0435898i
$431$	−9.13617	−	15.8243i	−0.440074	−	0.762230i	0.557621	−	0.830096i	$-0.311714\pi$
$431$	−9.13617	−	15.8243i	−0.440074	−	0.762230i	−0.997694	+	0.0678655i	$0.978381\pi$
$432$	4.39727	−	2.76840i	0.211564	−	0.133195i
$433$	14.1667	−	24.5374i	0.680806	−	1.17919i	−0.293929	−	0.955827i	$-0.594963\pi$
$433$	14.1667	−	24.5374i	0.680806	−	1.17919i	0.974735	−	0.223363i	$-0.0717037\pi$
$434$	−5.95829	+	19.9021i	−0.286007	+	0.955330i
$435$	−0.251703	−	4.87876i	−0.0120682	−	0.233919i
$436$	−8.99976	−	5.91923i	−0.431010	−	0.283480i
$437$	−8.62524	−	11.5857i	−0.412601	−	0.554220i
$438$	9.63323	−	1.06125i	0.460294	−	0.0507087i
$439$	−2.64602	+	1.74031i	−0.126287	+	0.0830605i	−0.611081	−	0.791568i	$-0.709265\pi$
$439$	−2.64602	+	1.74031i	−0.126287	+	0.0830605i	0.484794	+	0.874629i	$0.338895\pi$
$440$	18.5172	+	6.73970i	0.882772	+	0.321303i
$441$	16.5912	+	8.60984i	0.790057	+	0.409992i
$442$	0.327234	−	0.119103i	0.0155649	−	0.00566518i
$443$	−19.0944	+	25.6482i	−0.907200	+	1.21858i	0.0680955	+	0.997679i	$0.478308\pi$
$443$	−19.0944	+	25.6482i	−0.907200	+	1.21858i	−0.975296	+	0.220903i	$0.929100\pi$
$444$	−4.69590	−	8.25956i	−0.222858	−	0.391981i
$445$	−1.33107	+	1.41086i	−0.0630990	+	0.0668810i
$446$	4.01799	−	4.25882i	0.190257	−	0.201661i
$447$	−13.9577	−	0.0925653i	−0.660175	−	0.00437819i
$448$	−2.17211	+	2.91765i	−0.102622	+	0.137846i
$449$	−2.30646	+	0.839483i	−0.108849	+	0.0396177i	−0.395870	−	0.918306i	$-0.629557\pi$
$449$	−2.30646	+	0.839483i	−0.108849	+	0.0396177i	0.287022	+	0.957924i	$0.407335\pi$
$450$	26.8075	+	3.49434i	1.26372	+	0.164725i
$451$	24.7413	+	9.00508i	1.16502	+	0.424033i
$452$	10.3112	−	6.78176i	0.484996	−	0.318987i
$453$	−7.62635	−	10.3871i	−0.358317	−	0.488027i
$454$	−4.49716	−	6.04073i	−0.211062	−	0.283506i
$455$	−2.37025	−	1.55894i	−0.111119	−	0.0730841i
$456$	2.54752	+	1.30064i	0.119299	+	0.0609080i
$457$	6.35184	−	21.2166i	0.297126	−	0.992471i	−0.670884	−	0.741562i	$-0.734085\pi$
$457$	6.35184	−	21.2166i	0.297126	−	0.992471i	0.968011	−	0.250909i	$-0.0807295\pi$
$458$	5.64670	−	9.78037i	0.263853	−	0.457007i
$459$	−4.19166	−	7.60570i	−0.195650	−	0.355004i
$460$	16.3695	+	28.3529i	0.763233	+	1.32196i
$461$	8.12571	−	1.92583i	0.378452	−	0.0896948i	−0.0369870	−	0.999316i	$-0.511776\pi$
$461$	8.12571	−	1.92583i	0.378452	−	0.0896948i	0.415439	+	0.909621i	$0.363628\pi$
$462$	−19.9817	+	26.4717i	−0.929632	+	1.23158i
$463$	−21.8558	+	10.9764i	−1.01572	+	0.510116i	−0.877140	−	0.480235i	$-0.840552\pi$
$463$	−21.8558	+	10.9764i	−1.01572	+	0.510116i	−0.138585	+	0.990351i	$0.544255\pi$
$464$	−0.298448	+	0.691879i	−0.0138551	+	0.0321197i
$465$	−35.9739	−	8.77834i	−1.66825	−	0.407086i
$466$	0.442192	+	7.59214i	0.0204841	+	0.351699i
$467$	−4.93682	−	27.9981i	−0.228449	−	1.29560i	−0.855982	−	0.517006i	$-0.827046\pi$
$467$	−4.93682	−	27.9981i	−0.228449	−	1.29560i	0.627533	−	0.778590i	$-0.284065\pi$
$468$	−0.100371	−	0.616978i	−0.00463967	−	0.0285198i
$469$	3.94657	−	22.3821i	0.182236	−	1.03351i
$470$	−20.2221	−	2.36363i	−0.932777	−	0.109026i
$471$	−32.1689	+	11.4675i	−1.48226	+	0.528394i
$472$	−3.43125	−	11.4612i	−0.157936	−	0.527543i
$473$	−5.36376	−	1.27123i	−0.246626	−	0.0584514i
$474$	−1.25266	−	7.39047i	−0.0575367	−	0.339456i
$475$	5.89430	+	13.6645i	0.270449	+	0.626971i
$476$	4.65691	+	3.90761i	0.213449	+	0.179105i
$477$	−1.04236	+	14.5656i	−0.0477264	+	0.666915i
$478$	14.6350	−	12.2802i	0.669390	−	0.561685i
$479$	14.1368	+	7.09975i	0.645926	+	0.324396i	0.741427	−	0.671033i	$-0.234149\pi$
$479$	14.1368	+	7.09975i	0.645926	+	0.324396i	−0.0955017	+	0.995429i	$0.530446\pi$
$480$	−5.39304	−	3.59852i	−0.246158	−	0.164249i
$481$	−1.13525	+	0.132691i	−0.0517627	+	0.00605020i
$482$	−0.376586	+	6.46573i	−0.0171530	+	0.294506i
$483$	−53.7011	+	12.3518i	−2.44348	+	0.562028i
$484$	−11.4697	−	12.1572i	−0.521350	−	0.552598i
$485$	−6.96518			−0.316272
$486$	−14.8171	+	4.84300i	−0.672116	+	0.219683i
$487$	9.74171			0.441439			0.220720	−	0.975337i	$-0.429159\pi$
$487$	9.74171			0.441439			0.220720	+	0.975337i	$0.429159\pi$
$488$	−1.46028	−	1.54780i	−0.0661037	−	0.0700658i
$489$	−12.2385	+	2.81499i	−0.553445	+	0.127298i
$490$	1.35610	−	23.2833i	0.0612622	−	1.05183i
$491$	5.97315	−	0.698161i	0.269565	−	0.0315076i	0.0197632	−	0.999805i	$-0.493709\pi$
$491$	5.97315	−	0.698161i	0.269565	−	0.0315076i	0.249801	+	0.968297i	$0.419635\pi$
$492$	−7.20578	−	4.80807i	−0.324862	−	0.216765i
$493$	1.12537	+	0.565183i	0.0506842	+	0.0254546i
$494$	0.263591	−	0.221179i	0.0118595	−	0.00995133i
$495$	−48.9561	−	33.1374i	−2.20041	−	1.48941i
$496$	4.37522	+	3.67124i	0.196453	+	0.164844i
$497$	3.71710	+	8.61721i	0.166735	+	0.386535i
$498$	4.13830	+	24.4152i	0.185442	+	1.09407i
$499$	9.43087	+	2.23516i	0.422184	+	0.100059i	0.436216	−	0.899842i	$-0.356318\pi$
$499$	9.43087	+	2.23516i	0.422184	+	0.100059i	−0.0140319	+	0.999902i	$0.504467\pi$
$500$	−4.30648	−	14.3847i	−0.192592	−	0.643301i
$501$	−30.7292	+	10.9543i	−1.37288	+	0.489400i
$502$	−7.79314	−	0.910887i	−0.347825	−	0.0406549i
$503$	−6.11251	+	34.6658i	−0.272543	+	1.54567i	0.474116	+	0.880463i	$0.342768\pi$
$503$	−6.11251	+	34.6658i	−0.272543	+	1.54567i	−0.746659	+	0.665207i	$0.768343\pi$
$504$	8.45154	−	6.90275i	0.376461	−	0.307473i
$505$	−7.47647	−	42.4011i	−0.332698	−	1.88683i
$506$	−2.67722	−	45.9661i	−0.119017	−	2.04344i
$507$	21.8017	+	5.32006i	0.968250	+	0.236272i
$508$	−7.26726	+	16.8474i	−0.322433	+	0.747483i
$509$	16.0863	−	8.07886i	0.713014	−	0.358089i	−0.0550313	−	0.998485i	$-0.517526\pi$
$509$	16.0863	−	8.07886i	0.713014	−	0.358089i	0.768045	+	0.640396i	$0.221230\pi$
$510$	−6.52808	+	8.64840i	−0.289068	+	0.382957i
$511$	19.8041	−	4.69366i	0.876083	−	0.207635i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	−6.46240	−	5.64545i	−0.285322	−	0.249253i
$514$	−5.78033	+	10.0118i	−0.254960	+	0.441603i
$515$	15.9576	−	53.3021i	0.703176	−	2.34877i
$516$	1.61529	+	0.824687i	0.0711090	+	0.0363048i
$517$	23.9233	+	15.7346i	1.05214	+	0.692006i
$518$	−11.9151	−	16.0047i	−0.523518	−	0.703207i
$519$	−4.73015	−	6.44245i	−0.207631	−	0.282792i
$520$	−0.651631	+	0.428585i	−0.0285759	+	0.0187947i
$521$	−4.14562	−	1.50888i	−0.181623	−	0.0661054i	0.249608	−	0.968347i	$-0.419698\pi$
$521$	−4.14562	−	1.50888i	−0.181623	−	0.0661054i	−0.431231	+	0.902242i	$0.641921\pi$
$522$	1.37381	−	1.79514i	0.0601302	−	0.0785714i
$523$	−33.2656	+	12.1077i	−1.45460	+	0.529432i	−0.943873	−	0.330309i	$-0.892847\pi$
$523$	−33.2656	+	12.1077i	−1.45460	+	0.529432i	−0.510730	+	0.859741i	$0.670625\pi$
$524$	0.118457	−	0.159115i	0.00517481	−	0.00695097i
$525$	56.7722	+	0.376506i	2.47774	+	0.0164321i
$526$	−4.94579	+	5.24223i	−0.215646	+	0.228572i
$527$	6.55050	−	6.94313i	0.285344	−	0.302447i
$528$	4.50663	+	7.92664i	0.196126	+	0.344963i
$529$	31.9468	−	42.9120i	1.38899	−	1.86574i
$530$	17.1216	−	6.23175i	0.743715	−	0.270690i
$531$	1.61149	+	35.8551i	0.0699325	+	1.55598i
$532$	5.64461	+	2.05447i	0.244725	+	0.0890726i
$533$	−0.870661	+	0.572643i	−0.0377125	+	0.0248039i
$534$	−0.892124	+	0.0982817i	−0.0386060	+	0.00425307i
$535$	−5.71948	−	7.68260i	−0.247275	−	0.332148i
$536$	−5.22033	−	3.43346i	−0.225484	−	0.148303i
$537$	2.23406	+	43.3028i	0.0964067	+	1.86865i
$538$	−6.21598	+	20.7628i	−0.267990	+	0.895148i
$539$	−16.4005	+	28.4064i	−0.706418	+	1.22355i
$540$	13.0634	+	14.4103i	0.562160	+	0.620119i
$541$	−12.5590	−	21.7529i	−0.539955	−	0.935229i	−0.998906	−	0.0467676i	$-0.985108\pi$
$541$	−12.5590	−	21.7529i	−0.539955	−	0.935229i	0.458951	−	0.888462i	$-0.348225\pi$
$542$	20.8707	−	4.94645i	0.896474	−	0.212468i
$543$	−10.6478	−	25.1416i	−0.456942	−	1.07893i
$544$	1.49352	−	0.750074i	0.0640341	−	0.0321591i
$545$	15.9704	−	37.0234i	0.684095	−	1.58591i
$546$	−0.368145	−	1.26004i	−0.0157552	−	0.0539249i
$547$	−0.00653029	−	0.112121i	−0.000279215	−	0.00479394i	0.998166	−	0.0605416i	$-0.0192828\pi$
$547$	−0.00653029	−	0.112121i	−0.000279215	−	0.00479394i	−0.998445	+	0.0557477i	$0.982246\pi$
$548$	−0.767287	−	4.35150i	−0.0327769	−	0.185887i
$549$	3.11830	+	5.57039i	0.133086	+	0.237738i
$550$	−8.23780	+	46.7189i	−0.351261	+	1.99210i
$551$	1.23593	+	0.144460i	0.0526526	+	0.00615420i
$552$	−2.72949	+	14.9011i	−0.116175	+	0.634235i
$553$	−4.51480	−	15.0805i	−0.191989	−	0.641287i
$554$	−11.6978	−	2.77242i	−0.496990	−	0.117789i
$555$	27.3950	−	22.6793i	1.16285	−	0.962681i
$556$	−0.489520	−	1.13483i	−0.0207603	−	0.0481277i
$557$	25.6731	+	21.5423i	1.08780	+	0.912775i	0.996545	−	0.0830527i	$-0.0264670\pi$
$557$	25.6731	+	21.5423i	1.08780	+	0.912775i	0.0912573	+	0.995827i	$0.470911\pi$
$558$	−10.0487	−	13.8783i	−0.425396	−	0.587517i
$559$	0.167133	−	0.140242i	0.00706899	−	0.00593159i
$560$	−12.1672	−	6.11061i	−0.514159	−	0.258221i
$561$	13.6633	−	6.74885i	0.576863	−	0.284937i
$562$	−9.21194	+	1.07672i	−0.388582	+	0.0454187i
$563$	−2.65296	+	45.5495i	−0.111809	+	1.91968i	0.218549	+	0.975826i	$0.429868\pi$
$563$	−2.65296	+	45.5495i	−0.111809	+	1.91968i	−0.330357	+	0.943856i	$0.607169\pi$
$564$	−6.41944	−	6.89525i	−0.270307	−	0.290342i
$565$	31.7019	+	33.6021i	1.33371	+	1.41365i
$566$	23.8697			1.00332
$567$	−29.6339	+	13.9111i	−1.24451	+	0.584210i
$568$	2.58006			0.108257
$569$	3.01473	+	3.19543i	0.126384	+	0.133959i	0.787475	−	0.616346i	$-0.211388\pi$
$569$	3.01473	+	3.19543i	0.126384	+	0.133959i	−0.661091	+	0.750306i	$0.729906\pi$
$570$	−3.13869	+	10.2364i	−0.131465	+	0.428755i
$571$	−2.32506	+	39.9197i	−0.0973006	+	1.67059i	0.498071	+	0.867136i	$0.334042\pi$
$571$	−2.32506	+	39.9197i	−0.0973006	+	1.67059i	−0.595371	+	0.803451i	$0.702995\pi$
$572$	1.08949	−	0.127343i	0.0455538	−	0.00532447i
$573$	0.149503	−	2.30358i	0.00624558	−	0.0962334i
$574$	−16.2569	−	8.16455i	−0.678552	−	0.340782i
$575$	−60.3771	+	50.6624i	−2.51790	+	2.11277i
$576$	−0.822216	−	2.88513i	−0.0342590	−	0.120214i
$577$	−3.85975	−	3.23872i	−0.160684	−	0.134830i	0.558901	−	0.829234i	$-0.311223\pi$
$577$	−3.85975	−	3.23872i	−0.160684	−	0.134830i	−0.719584	+	0.694405i	$0.755668\pi$
$578$	5.62702	+	13.0449i	0.234053	+	0.542596i
$579$	21.7235	+	8.07025i	0.902797	+	0.335388i
$580$	−2.74447	−	0.650452i	−0.113958	−	0.0270086i
$581$	14.9151	+	49.8199i	0.618783	+	2.06688i
$582$	−2.45512	−	2.08799i	−0.101768	−	0.0865500i
$583$	−25.4518	−	2.97489i	−1.05411	−	0.123207i
$584$	0.971631	−	5.51039i	0.0402064	−	0.228022i
$585$	2.20914	−	0.771035i	0.0913365	−	0.0318784i
$586$	−2.37293	−	13.4576i	−0.0980250	−	0.555927i
$587$	−1.27552	−	21.8998i	−0.0526463	−	0.903902i	−0.916469	−	0.400106i	$-0.868973\pi$
$587$	−1.27552	−	21.8998i	−0.0526463	−	0.903902i	0.863823	−	0.503796i	$-0.168064\pi$
$588$	7.45776	−	7.80048i	0.307553	−	0.321686i
$589$	3.73581	−	8.66058i	0.153931	−	0.356853i
$590$	40.0192	−	20.0984i	1.64756	−	0.827438i
$591$	45.1958	+	5.58669i	1.85911	+	0.229806i
$592$	−5.33763	+	1.26504i	−0.219375	+	0.0519929i
$593$	4.13250	+	7.15770i	0.169701	+	0.293931i	0.938315	−	0.345782i	$-0.112386\pi$
$593$	4.13250	+	7.15770i	0.169701	+	0.293931i	−0.768614	+	0.639713i	$0.779053\pi$
$594$	−7.32249	−	26.3563i	−0.300446	−	1.08141i
$595$	−11.3777	+	19.7068i	−0.466441	+	0.807899i
$596$	−2.31124	+	7.72009i	−0.0946722	+	0.316227i
$597$	3.37186	−	2.18581i	0.138001	−	0.0894594i
$598$	1.52260	+	1.00143i	0.0622638	+	0.0409515i
$599$	−8.18252	−	10.9910i	−0.334329	−	0.449081i	0.602890	−	0.797825i	$-0.294016\pi$
$599$	−8.18252	−	10.9910i	−0.334329	−	0.449081i	−0.937218	+	0.348743i	$0.886609\pi$
$600$	6.27701	−	14.2904i	0.256258	−	0.583404i
$601$	26.4263	−	17.3809i	1.07795	−	0.708980i	0.119098	−	0.992882i	$-0.462000\pi$
$601$	26.4263	−	17.3809i	1.07795	−	0.708980i	0.958853	+	0.283902i	$0.0916292\pi$
$602$	3.57904	+	1.30266i	0.145871	+	0.0530926i
$603$	12.6814	+	13.8038i	0.516428	+	0.562135i
$604$	−6.99114	+	2.54457i	−0.284465	+	0.103537i
$605$	37.3599	−	50.1830i	1.51889	−	2.04023i
$606$	10.0755	−	17.1870i	0.409289	−	0.698175i
$607$	−0.851718	+	0.902768i	−0.0345702	+	0.0366422i	−0.744428	−	0.667703i	$-0.767278\pi$
$607$	−0.851718	+	0.902768i	−0.0345702	+	0.0366422i	0.709858	+	0.704345i	$0.248759\pi$
$608$	1.13327	−	1.20120i	0.0459602	−	0.0487149i
$609$	2.40081	−	4.09537i	0.0972859	−	0.165953i
$610$	4.75652	−	6.38911i	0.192586	−	0.258688i
$611$	−1.06497	+	0.387619i	−0.0430842	+	0.0156814i
$612$	−4.89363	+	1.09147i	−0.197813	+	0.0441200i
$613$	−30.1068	−	10.9580i	−1.21600	−	0.442589i	−0.347221	−	0.937783i	$-0.612875\pi$
$613$	−30.1068	−	10.9580i	−1.21600	−	0.442589i	−0.868782	+	0.495195i	$0.835097\pi$
$614$	−11.2705	+	7.41270i	−0.454839	+	0.299152i
$615$	13.0403	−	29.6880i	0.525837	−	1.19714i
$616$	11.4348	+	15.3596i	0.460722	+	0.618857i
$617$	−6.97735	−	4.58907i	−0.280897	−	0.184749i	0.401240	−	0.915973i	$-0.368579\pi$
$617$	−6.97735	−	4.58907i	−0.280897	−	0.184749i	−0.682138	+	0.731224i	$0.738950\pi$
$618$	21.6035	−	14.0045i	0.869020	−	0.563343i
$619$	−7.76825	+	25.9478i	−0.312232	+	1.04293i	0.647512	+	0.762055i	$0.275809\pi$
$619$	−7.76825	+	25.9478i	−0.312232	+	1.04293i	−0.959745	+	0.280874i	$0.909376\pi$
$620$	−10.6895	+	18.5147i	−0.429300	+	0.743569i
$621$	18.8273	−	41.3640i	0.755515	−	1.65988i
$622$	−2.95334	−	5.11534i	−0.118418	−	0.205107i
$623$	−1.83404	+	0.434676i	−0.0734793	+	0.0174149i
$624$	−0.358170	−	0.0442737i	−0.0143383	−	0.00177237i
$625$	9.96269	−	5.00345i	0.398508	−	0.200138i
$626$	−3.49181	+	8.09493i	−0.139561	+	0.323538i
$627$	10.4058	−	10.8840i	0.415567	−	0.434664i
$628$	1.14647	+	19.6841i	0.0457492	+	0.785483i
$629$	1.59198	+	9.02857i	0.0634764	+	0.359992i
$630$	30.9392	+	26.6683i	1.23265	+	1.06249i
$631$	3.72186	−	21.1077i	0.148165	−	0.840284i	−0.816607	−	0.577194i	$-0.804147\pi$
$631$	3.72186	−	21.1077i	0.148165	−	0.840284i	0.964771	−	0.263089i	$-0.0847414\pi$
$632$	−4.29849	−	0.502421i	−0.170985	−	0.0199852i
$633$	12.8914	+	10.9636i	0.512386	+	0.435766i
$634$	−2.09512	−	6.99818i	−0.0832078	−	0.277933i
$635$	−66.8285	−	15.8387i	−2.65201	−	0.628538i
$636$	7.90324	+	2.93604i	0.313384	+	0.116422i
$637$	−0.514212	−	1.19208i	−0.0203738	−	0.0472318i
$638$	3.03870	+	2.54977i	0.120303	+	0.100946i
$639$	−7.50721	−	1.88474i	−0.296981	−	0.0745593i
$640$	−2.86744	+	2.40607i	−0.113346	+	0.0951083i
$641$	−14.0757	−	7.06906i	−0.555955	−	0.279211i	0.148556	−	0.988904i	$-0.452537\pi$
$641$	−14.0757	−	7.06906i	−0.555955	−	0.279211i	−0.704511	+	0.709693i	$0.748834\pi$
$642$	0.287026	−	4.42256i	0.0113280	−	0.174545i
$643$	44.1265	−	5.15764i	1.74018	−	0.203398i	0.814099	−	0.580726i	$-0.197231\pi$
$643$	44.1265	−	5.15764i	1.74018	−	0.203398i	0.926079	+	0.377329i	$0.123157\pi$
$644$	−1.84981	+	31.7601i	−0.0728929	+	1.25152i
$645$	−1.99012	+	6.49050i	−0.0783610	+	0.255563i
$646$	−1.89402	−	2.00755i	−0.0745194	−	0.0789859i
$647$	18.9018			0.743108			0.371554	−	0.928411i	$-0.378825\pi$
$647$	18.9018			0.743108			0.371554	+	0.928411i	$0.378825\pi$
$648$	0.284808	+	8.99549i	0.0111883	+	0.353376i
$649$	−62.9820			−2.47226
$650$	−1.28852	−	1.36575i	−0.0505399	−	0.0535691i
$651$	−24.5190	−	26.3363i	−0.960974	−	1.03220i
$652$	−0.421574	+	7.23815i	−0.0165101	+	0.283468i
$653$	19.0339	−	2.22475i	0.744856	−	0.0870611i	0.264805	−	0.964302i	$-0.414692\pi$
$653$	19.0339	−	2.22475i	0.744856	−	0.0870611i	0.480051	+	0.877241i	$0.340618\pi$
$654$	16.7280	−	8.26268i	0.654118	−	0.323096i
$655$	0.663544	+	0.333245i	0.0259268	+	0.0130209i
$656$	−3.83126	+	3.21481i	−0.149586	+	0.125517i
$657$	−6.85252	+	15.3238i	−0.267342	+	0.597839i
$658$	−15.1558	−	12.7172i	−0.590833	−	0.495768i
$659$	0.654481	+	1.51726i	0.0254950	+	0.0591040i	0.930488	−	0.366323i	$-0.119383\pi$
$659$	0.654481	+	1.51726i	0.0254950	+	0.0591040i	−0.904993	+	0.425427i	$0.860124\pi$
$660$	−26.2908	+	21.7651i	−1.02337	+	0.847207i
$661$	−41.3076	−	9.79007i	−1.60668	−	0.380790i	−0.673211	−	0.739451i	$-0.735085\pi$
$661$	−41.3076	−	9.79007i	−1.60668	−	0.380790i	−0.933468	+	0.358661i	$0.883233\pi$
$662$	−9.18443	−	30.6781i	−0.356963	−	1.19234i
$663$	−0.108675	+	0.593290i	−0.00422058	+	0.0230415i
$664$	14.2005	+	1.65980i	0.551086	+	0.0644128i
$665$	−3.90445	+	22.1432i	−0.151408	+	0.858677i
$666$	16.4550	+	0.218265i	0.637619	+	0.00845758i
$667$	1.14441	+	6.49026i	0.0443116	+	0.251304i
$668$	1.09516	+	18.8032i	0.0423730	+	0.727517i
$669$	2.84406	+	9.73430i	0.109958	+	0.376350i
$670$	9.26363	−	21.4755i	0.357885	−	0.829671i
$671$	−10.0107	+	5.02757i	−0.386460	+	0.194087i
$672$	−2.45695	−	5.80134i	−0.0947790	−	0.223792i
$673$	12.3539	−	2.92794i	0.476209	−	0.112864i	0.0144998	−	0.999895i	$-0.495384\pi$
$673$	12.3539	−	2.92794i	0.476209	−	0.112864i	0.461710	+	0.887031i	$0.347236\pi$
$674$	12.9912	+	22.5014i	0.500401	+	0.866720i
$675$	−28.7034	+	36.9955i	−1.10480	+	1.42396i
$676$	6.47829	−	11.2207i	0.249165	−	0.431567i
$677$	−3.18713	+	10.6457i	−0.122491	+	0.409149i	−0.997137	−	0.0756130i	$-0.975909\pi$
$677$	−3.18713	+	10.6457i	−0.122491	+	0.409149i	0.874646	+	0.484762i	$0.161094\pi$
$678$	1.10136	+	21.3477i	0.0422975	+	0.819853i
$679$	−5.65488	−	3.71927i	−0.217014	−	0.142733i
$680$	3.73579	+	5.01804i	0.143261	+	0.192433i
$681$	12.9655	−	1.42836i	0.496839	−	0.0547348i
$682$	25.1208	−	16.5222i	0.961925	−	0.632668i
$683$	−19.0189	−	6.92231i	−0.727737	−	0.264875i	−0.0485305	−	0.998822i	$-0.515454\pi$
$683$	−19.0189	−	6.92231i	−0.727737	−	0.264875i	−0.679207	+	0.733947i	$0.737676\pi$
$684$	−4.17496	+	2.66726i	−0.159633	+	0.101985i
$685$	15.5423	−	5.65692i	0.593840	−	0.216140i
$686$	−1.67095	+	2.24448i	−0.0637973	+	0.0856947i
$687$	9.66781	+	17.0046i	0.368850	+	0.648765i
$688$	0.718564	−	0.761633i	0.0273950	−	0.0290370i
$689$	0.696010	−	0.737728i	0.0265159	−	0.0281052i
$690$	−56.7045	−	0.376056i	−2.15870	−	0.0143162i
$691$	15.8395	−	21.2762i	0.602564	−	0.809384i	−0.391269	−	0.920277i	$-0.627964\pi$
$691$	15.8395	−	21.2762i	0.602564	−	0.809384i	0.993832	+	0.110893i	$0.0353711\pi$
$692$	−4.33617	+	1.57824i	−0.164836	+	0.0599955i
$693$	−22.0517	−	53.0451i	−0.837673	−	2.01502i
$694$	12.2929	+	4.47425i	0.466632	+	0.169840i
$695$	3.86517	−	2.54216i	0.146614	−	0.0964297i
$696$	−0.772396	−	1.05200i	−0.0292776	−	0.0398760i
$697$	4.99149	+	6.70473i	0.189066	+	0.253960i
$698$	−16.7308	−	11.0040i	−0.633269	−	0.416508i
$699$	−11.7317	−	5.98963i	−0.443733	−	0.226549i
$700$	9.40089	−	31.4011i	0.355320	−	1.18685i
$701$	−5.03336	+	8.71804i	−0.190107	+	0.329276i	−0.945286	−	0.326244i	$-0.894217\pi$
$701$	−5.03336	+	8.71804i	−0.190107	+	0.329276i	0.755178	+	0.655520i	$0.227550\pi$
$702$	1.00982	+	0.390467i	0.0381134	+	0.0147372i
$703$	4.52941	+	7.84517i	0.170830	+	0.295886i
$704$	5.12249	−	1.21405i	0.193061	−	0.0457563i
$705$	21.2454	−	28.1460i	0.800149	−	1.06004i
$706$	−26.0235	+	13.0695i	−0.979406	+	0.491876i
$707$	16.5714	−	38.4169i	0.623232	−	1.44481i
$708$	20.1312	+	4.91240i	0.756576	+	0.184619i
$709$	2.70801	+	46.4947i	0.101701	+	1.74614i	0.534962	+	0.844876i	$0.320326\pi$
$709$	2.70801	+	46.4947i	0.101701	+	1.74614i	−0.433261	+	0.901269i	$0.642637\pi$
$710$	1.67703	+	9.51092i	0.0629379	+	0.356938i
$711$	12.1403	+	4.60196i	0.455297	+	0.172587i
$712$	−0.0899818	+	0.510312i	−0.00337221	+	0.0191247i
$713$	49.6163	+	5.79931i	1.85814	+	0.217186i
$714$	−9.91808	+	3.53558i	−0.371175	+	0.132316i
$715$	1.17759	+	3.93342i	0.0440393	+	0.147102i
$716$	24.3593	+	5.77326i	0.910350	+	0.215757i
$717$	5.52982	+	32.6249i	0.206515	+	1.21840i
$718$	6.15792	+	14.2757i	0.229811	+	0.532763i
$719$	−27.0503	−	22.6979i	−1.00881	−	0.846490i	−0.0206270	−	0.999787i	$-0.506566\pi$
$719$	−27.0503	−	22.6979i	−1.00881	−	0.846490i	−0.988180	+	0.153298i	$0.951011\pi$
$720$	10.1011	−	4.90627i	0.376444	−	0.182846i
$721$	41.4179	−	34.7538i	1.54248	−	1.29430i
$722$	14.5419	+	7.30323i	0.541195	+	0.271798i
$723$	−9.33137	−	6.22638i	−0.347037	−	0.231562i
$724$	−15.6570	+	1.83005i	−0.581889	+	0.0680131i
$725$	0.394811	−	6.77865i	0.0146629	−	0.251753i
$726$	28.2124	−	6.48917i	1.04706	−	0.240836i
$727$	−4.09655	−	4.34209i	−0.151933	−	0.161039i	0.646937	−	0.762544i	$-0.276050\pi$
$727$	−4.09655	−	4.34209i	−0.151933	−	0.161039i	−0.798870	+	0.601504i	$0.794568\pi$
$728$	−0.757901			−0.0280897
$729$	5.74254	−	26.3823i	0.212686	−	0.977120i
$730$	20.9446			0.775194
$731$	−1.20093	−	1.27291i	−0.0444180	−	0.0470803i
$732$	3.59190	−	0.826177i	0.132760	−	0.0305364i
$733$	2.73945	−	47.0345i	0.101184	−	1.73726i	−0.441447	−	0.897287i	$-0.645535\pi$
$733$	2.73945	−	47.0345i	0.101184	−	1.73726i	0.542631	−	0.839971i	$-0.317428\pi$
$734$	−9.17828	+	1.07279i	−0.338776	+	0.0395973i
$735$	33.6025	+	22.4214i	1.23945	+	0.827025i
$736$	7.81600	+	3.92534i	0.288101	+	0.144690i
$737$	−25.1976	+	21.1433i	−0.928166	+	0.778824i
$738$	13.4963	−	6.55539i	0.496805	−	0.241307i
$739$	−9.19760	−	7.71770i	−0.338339	−	0.283900i	0.457748	−	0.889082i	$-0.348656\pi$
$739$	−9.19760	−	7.71770i	−0.338339	−	0.283900i	−0.796088	+	0.605182i	$0.793101\pi$
$740$	−8.13278	−	18.8539i	−0.298967	−	0.693083i
$741$	0.0995977	+	0.587608i	0.00365881	+	0.0215863i
$742$	17.2283	+	4.08318i	0.632471	+	0.149898i
$743$	9.51664	+	31.7878i	0.349132	+	1.16618i	0.934664	+	0.355532i	$0.115700\pi$
$743$	9.51664	+	31.7878i	0.349132	+	1.16618i	−0.585533	+	0.810649i	$0.699115\pi$
$744$	−9.31815	+	3.32171i	−0.341620	+	0.121780i
$745$	−29.9610	−	3.50194i	−1.09769	−	0.128301i
$746$	−5.84734	+	33.1619i	−0.214086	+	1.21414i
$747$	−40.1067	−	15.2030i	−1.46743	−	0.556250i
$748$	−1.52781	−	8.66466i	−0.0558624	−	0.316811i
$749$	−0.541164	−	9.29142i	−0.0197737	−	0.339501i
$750$	25.2662	+	6.16545i	0.922590	+	0.225130i
$751$	−14.2808	+	33.1067i	−0.521115	+	1.20808i	0.431003	+	0.902351i	$0.358160\pi$
$751$	−14.2808	+	33.1067i	−0.521115	+	1.20808i	−0.952118	+	0.305731i	$0.901099\pi$
$752$	−4.86062	+	2.44109i	−0.177248	+	0.0890175i
$753$	8.18750	−	10.8468i	0.298369	−	0.395279i
$754$	−0.152770	+	0.0362072i	−0.00556357	+	0.00131859i
$755$	−13.9243	−	24.1176i	−0.506757	−	0.877729i
$756$	2.91110	+	18.6750i	0.105876	+	0.679203i
$757$	−14.8811	+	25.7749i	−0.540864	+	0.936804i	0.457990	+	0.888957i	$0.348569\pi$
$757$	−14.8811	+	25.7749i	−0.540864	+	0.936804i	−0.998855	+	0.0478471i	$0.984764\pi$
$758$	−0.0674426	+	0.225274i	−0.00244963	+	0.00818232i
$759$	71.0288	+	36.2638i	2.57818	+	1.31629i
$760$	5.16461	+	3.39682i	0.187340	+	0.123216i
$761$	32.1802	+	43.2255i	1.16653	+	1.56692i	0.755281	+	0.655401i	$0.227500\pi$
$761$	32.1802	+	43.2255i	1.16653	+	1.56692i	0.411250	+	0.911522i	$0.365092\pi$
$762$	−18.8080	−	25.6165i	−0.681342	−	0.927987i
$763$	32.7358	−	21.5307i	1.18511	−	0.779462i
$764$	−1.25239	−	0.455834i	−0.0453100	−	0.0164915i
$765$	−7.20434	−	17.3300i	−0.260474	−	0.626568i
$766$	13.8183	−	5.02946i	0.499276	−	0.181722i
$767$	1.48860	−	1.99954i	0.0537503	−	0.0721992i
$768$	−1.73201	−	0.0114865i	−0.0624986	−	0.000414482i
$769$	−5.85019	+	6.20084i	−0.210963	+	0.223608i	−0.824211	−	0.566283i	$-0.808381\pi$
$769$	−5.85019	+	6.20084i	−0.210963	+	0.223608i	0.613248	+	0.789890i	$0.289863\pi$
$770$	−49.1878	+	52.1361i	−1.77261	+	1.87885i
$771$	−9.89661	−	17.4070i	−0.356418	−	0.626898i
$772$	7.98972	−	10.7321i	0.287556	−	0.386255i
$773$	36.4284	−	13.2589i	1.31024	−	0.476888i	0.409921	−	0.912121i	$-0.365556\pi$
$773$	36.4284	−	13.2589i	1.31024	−	0.476888i	0.900318	+	0.435234i	$0.143334\pi$
$774$	−2.64718	+	1.69121i	−0.0951510	+	0.0607894i
$775$	−48.3642	−	17.6031i	−1.73730	−	0.632324i
$776$	−1.55465	+	1.02251i	−0.0558085	+	0.0367058i
$777$	34.3517	−	3.78439i	1.23236	−	0.135764i
$778$	−12.7609	−	17.1409i	−0.457501	−	0.614530i
$779$	6.90057	+	4.53857i	0.247238	+	0.162611i
$780$	−0.0696024	−	1.34910i	−0.00249216	−	0.0483057i
$781$	3.89549	−	13.0118i	0.139392	−	0.465600i
$782$	7.30882	−	12.6592i	0.261363	−	0.452694i
$783$	1.47895	+	3.62525i	0.0528534	+	0.129556i
$784$	−3.11536	−	5.39596i	−0.111263	−	0.192713i
$785$	−71.8168	+	17.0209i	−2.56325	+	0.607502i
$786$	0.133991	+	0.316378i	0.00477929	+	0.0112848i
$787$	6.04121	−	3.03401i	0.215346	−	0.108151i	−0.337857	−	0.941198i	$-0.609702\pi$
$787$	6.04121	−	3.03401i	0.215346	−	0.108151i	0.553202	+	0.833047i	$0.313406\pi$
$788$	10.4139	−	24.1421i	0.370979	−	0.860026i
$789$	−3.50078	−	11.9821i	−0.124631	−	0.426573i
$790$	−0.941921	−	16.1722i	−0.0335120	−	0.575379i
$791$	7.79524	+	44.2090i	0.277167	+	1.57189i
$792$	−15.7918	−	0.209467i	−0.561136	−	0.00744309i
$793$	0.0769927	−	0.436647i	0.00273409	−	0.0155058i
$794$	−23.0698	−	2.69647i	−0.818716	−	0.0956942i
$795$	−5.68610	+	31.0422i	−0.201665	+	1.10095i
$796$	−0.665384	−	2.22254i	−0.0235839	−	0.0787758i
$797$	1.49748	+	0.354909i	0.0530434	+	0.0125715i	0.257052	−	0.966398i	$-0.417249\pi$
$797$	1.49748	+	0.354909i	0.0530434	+	0.0125715i	−0.204008	+	0.978969i	$0.565397\pi$
$798$	−8.01426	+	6.63469i	−0.283702	+	0.234866i
$799$	3.60053	+	8.34698i	0.127378	+	0.295295i
$800$	−6.90314	−	5.79243i	−0.244063	−	0.204793i
$801$	0.634605	−	1.41912i	0.0224227	−	0.0501423i
$802$	−12.2930	+	10.3151i	−0.434082	+	0.364238i
$803$	−26.3232	−	13.2200i	−0.928924	−	0.466523i
$804$	9.70313	−	4.79278i	0.342203	−	0.169028i
$805$	−118.280	+	13.8250i	−4.16882	+	0.487266i
$806$	−0.0691955	+	1.18804i	−0.00243731	+	0.0418469i
$807$	−25.5794	−	27.4753i	−0.900437	−	0.967177i
$808$	−7.89336	−	8.36648i	−0.277688	−	0.294332i
$809$	−35.4763			−1.24728			−0.623639	−	0.781712i	$-0.714347\pi$
$809$	−35.4763			−1.24728			−0.623639	+	0.781712i	$0.714347\pi$
$810$	−32.9751	+	6.89693i	−1.15863	+	0.242333i
$811$	2.83568			0.0995740			0.0497870	−	0.998760i	$-0.484146\pi$
$811$	2.83568			0.0995740			0.0497870	+	0.998760i	$0.484146\pi$
$812$	−1.88085	−	1.99358i	−0.0660049	−	0.0699611i
$813$	−10.8907	+	35.5184i	−0.381953	+	1.24568i
$814$	−1.67909	+	28.8289i	−0.0588521	+	1.01045i
$815$	−26.9561	+	3.15072i	−0.944232	+	0.110365i
$816$	−0.187476	+	2.88868i	−0.00656299	+	0.101124i
$817$	−1.54527	−	0.776063i	−0.0540621	−	0.0271510i
$818$	−2.71014	+	2.27408i	−0.0947580	+	0.0795114i
$819$	2.20527	+	0.553650i	0.0770583	+	0.0193461i
$820$	−14.3411	−	12.0336i	−0.500814	−	0.420233i
$821$	−21.4821	−	49.8012i	−0.749731	−	1.73807i	−0.671340	−	0.741150i	$-0.734281\pi$
$821$	−21.4821	−	49.8012i	−0.749731	−	1.73807i	−0.0783916	−	0.996923i	$-0.524978\pi$
$822$	7.17423	+	2.66522i	0.250230	+	0.0929601i
$823$	7.83046	+	1.85585i	0.272953	+	0.0646910i	0.364813	−	0.931081i	$-0.381133\pi$
$823$	7.83046	+	1.85585i	0.272953	+	0.0646910i	−0.0918599	+	0.995772i	$0.529281\pi$
$824$	−4.26311	−	14.2398i	−0.148513	−	0.496066i
$825$	−62.5925	−	53.2327i	−2.17919	−	1.85332i
$826$	43.2229	+	5.05203i	1.50392	+	0.175783i
$827$	8.15370	−	46.2420i	0.283532	−	1.60799i	−0.426950	−	0.904275i	$-0.640412\pi$
$827$	8.15370	−	46.2420i	0.283532	−	1.60799i	0.710482	−	0.703715i	$-0.248477\pi$
$828$	−19.8747	−	17.1312i	−0.690695	−	0.595350i
$829$	4.57598	+	25.9517i	0.158930	+	0.901339i	0.955104	+	0.296271i	$0.0957430\pi$
$829$	4.57598	+	25.9517i	0.158930	+	0.901339i	−0.796174	+	0.605068i	$0.793146\pi$
$830$	3.11173	+	53.4264i	0.108010	+	1.85446i
$831$	14.3893	−	15.0506i	0.499160	−	0.522098i
$832$	−0.0825284	+	0.191322i	−0.00286116	+	0.00663291i
$833$	−9.30571	+	4.67350i	−0.322424	+	0.161927i
$834$	2.12449	+	0.262610i	0.0735652	+	0.00909346i
$835$	−68.6026	+	16.2591i	−2.37409	+	0.562670i
$836$	−4.34685	−	7.52896i	−0.150339	−	0.260395i
$837$	29.5396	−	2.85825i	1.02104	−	0.0987957i
$838$	−15.6389	+	27.0873i	−0.540235	+	0.935715i
$839$	−1.55115	+	5.18120i	−0.0535516	+	0.178875i	−0.980581	−	0.196113i	$-0.937168\pi$
$839$	−1.55115	+	5.18120i	−0.0535516	+	0.178875i	0.927030	+	0.374988i	$0.122353\pi$
$840$	19.7886	−	12.8280i	0.682770	−	0.442606i
$841$	23.7548	+	15.6238i	0.819130	+	0.538751i
$842$	−10.6536	−	14.3103i	−0.367147	−	0.493165i
$843$	6.46037	−	14.7079i	0.222507	−	0.506565i
$844$	8.16315	−	5.36899i	0.280987	−	0.184808i
$845$	45.5740	+	16.5876i	1.56779	+	0.570630i
$846$	15.9262	−	3.55216i	0.547553	−	0.122126i
$847$	57.1284	−	20.7930i	1.96296	−	0.714458i
$848$	2.90675	−	3.90444i	0.0998181	−	0.134079i
$849$	−20.9088	+	35.6667i	−0.717588	+	1.22408i
$850$	−10.3353	+	10.9548i	−0.354497	+	0.375745i
$851$	−32.9244	+	34.8978i	−1.12863	+	1.19628i
$852$	−2.26001	+	3.85519i	−0.0774268	+	0.132077i
$853$	−12.8338	+	17.2388i	−0.439421	+	0.590244i	−0.965569	−	0.260149i	$-0.916228\pi$
$853$	−12.8338	+	17.2388i	−0.439421	+	0.590244i	0.526148	+	0.850393i	$0.323636\pi$
$854$	7.27338	−	2.64729i	0.248890	−	0.0905885i
$855$	−12.5461	−	13.6565i	−0.429067	−	0.467042i
$856$	−2.40443	−	0.875140i	−0.0821816	−	0.0299117i
$857$	−12.5216	+	8.23558i	−0.427729	+	0.281322i	−0.745066	−	0.666991i	$-0.767582\pi$
$857$	−12.5216	+	8.23558i	−0.427729	+	0.281322i	0.317336	+	0.948313i	$0.397212\pi$
$858$	−0.764062	+	1.73948i	−0.0260847	+	0.0593850i
$859$	−30.0492	−	40.3630i	−1.02526	−	1.37717i	−0.924036	−	0.382306i	$-0.875130\pi$
$859$	−30.0492	−	40.3630i	−1.02526	−	1.37717i	−0.101229	−	0.994863i	$-0.532277\pi$
$860$	3.27469	+	2.15379i	0.111666	+	0.0734438i
$861$	26.4400	−	17.1397i	0.901073	−	0.584121i
$862$	5.24057	−	17.5047i	0.178494	−	0.596213i
$863$	12.2875	−	21.2826i	0.418272	−	0.724468i	−0.577494	−	0.816395i	$-0.695969\pi$
$863$	12.2875	−	21.2826i	0.418272	−	0.724468i	0.995766	+	0.0919267i	$0.0293025\pi$
$864$	5.03125	+	1.29866i	0.171167	+	0.0441814i
$865$	−8.63637	−	14.9586i	−0.293645	−	0.508609i
$866$	27.5696	−	6.53411i	0.936853	−	0.222038i
$867$	−24.4210	−	3.01870i	−0.829381	−	0.102521i
$868$	−18.5651	+	9.32372i	−0.630139	+	0.316468i
$869$	−9.02387	+	20.9197i	−0.306114	+	0.709652i
$870$	3.37595	−	3.53109i	0.114456	−	0.119715i
$871$	−0.0756989	−	1.29970i	−0.00256496	−	0.0440386i
$872$	−1.87051	−	10.6082i	−0.0633436	−	0.359239i
$873$	5.27050	−	1.83951i	0.178379	−	0.0622581i
$874$	2.50814	−	14.2244i	0.0848391	−	0.481147i
$875$	54.2480	+	6.34068i	1.83392	+	0.214354i
$876$	7.38265	+	6.27868i	0.249437	+	0.212137i
$877$	11.9131	+	39.7924i	0.402275	+	1.34369i	0.884048	+	0.467397i	$0.154808\pi$
$877$	11.9131	+	39.7924i	0.402275	+	1.34369i	−0.481772	+	0.876296i	$0.660007\pi$
$878$	−3.08166	−	0.730367i	−0.104001	−	0.0246487i
$879$	22.1872	+	8.24252i	0.748356	+	0.278013i
$880$	7.80498	+	18.0940i	0.263106	+	0.609948i
$881$	39.4074	+	33.0667i	1.32767	+	1.11405i	0.984616	+	0.174731i	$0.0559054\pi$
$881$	39.4074	+	33.0667i	1.32767	+	1.11405i	0.343053	+	0.939316i	$0.388539\pi$
$882$	5.12300	+	17.9764i	0.172500	+	0.605298i
$883$	11.6864	−	9.80605i	0.393279	−	0.330000i	−0.424610	−	0.905376i	$-0.639589\pi$
$883$	11.6864	−	9.80605i	0.393279	−	0.330000i	0.817889	+	0.575376i	$0.195144\pi$
$884$	0.311194	+	0.156288i	0.0104666	+	0.00525653i
$885$	−5.02347	+	77.4029i	−0.168862	+	2.60187i
$886$	−31.7592	+	3.71211i	−1.06697	+	0.124711i
$887$	2.91698	−	50.0825i	0.0979424	−	1.68161i	−0.489238	−	0.872150i	$-0.662725\pi$
$887$	2.91698	−	50.0825i	0.0979424	−	1.68161i	0.587180	−	0.809456i	$-0.300238\pi$
$888$	2.78526	−	9.08373i	0.0934672	−	0.304830i
$889$	−45.7991	−	48.5442i	−1.53605	−	1.62812i
$890$	−1.93966			−0.0650175
$891$	45.7963	+	12.1454i	1.53424	+	0.406887i
$892$	5.85506			0.196042
$893$	6.16404	+	6.53351i	0.206272	+	0.218635i
$894$	−9.51100	−	10.2160i	−0.318095	−	0.341673i
$895$	−5.44859	+	93.5487i	−0.182126	+	3.12699i
$896$	−3.61281	+	0.422277i	−0.120696	+	0.0141073i
$897$	−2.83009	+	1.39790i	−0.0944940	+	0.0466745i
$898$	−2.19341	−	1.10157i	−0.0731950	−	0.0367599i
$899$	−3.29674	+	2.76629i	−0.109952	+	0.0922611i
$900$	15.8547	+	21.8970i	0.528490	+	0.729900i
$901$	−6.23194	−	5.22922i	−0.207616	−	0.174211i
$902$	10.4284	+	24.1758i	0.347229	+	0.804966i
$903$	−5.08154	+	4.20681i	−0.169103	+	0.139994i
$904$	12.0088	+	2.84614i	0.399407	+	0.0946613i
$905$	−16.9232	−	56.5273i	−0.562545	−	1.87903i
$906$	2.32176	−	12.6753i	0.0771355	−	0.421107i
$907$	54.9677	+	6.42481i	1.82517	+	0.213332i	0.958411	−	0.285390i	$-0.0921232\pi$
$907$	54.9677	+	6.42481i	1.82517	+	0.213332i	0.866762	+	0.498722i	$0.166197\pi$
$908$	1.30773	−	7.41652i	0.0433986	−	0.246126i
$909$	16.8556	+	30.1101i	0.559065	+	0.998689i
$910$	−0.492633	−	2.79386i	−0.0163306	−	0.0926157i
$911$	−2.36181	−	40.5508i	−0.0782503	−	1.34351i	−0.777615	−	0.628741i	$-0.783571\pi$
$911$	−2.36181	−	40.5508i	−0.0782503	−	1.34351i	0.699364	−	0.714765i	$-0.253466\pi$
$912$	0.802164	+	2.74555i	0.0265623	+	0.0909143i
$913$	29.8113	−	69.1103i	0.986610	−	2.28722i
$914$	19.7913	−	9.93956i	0.654638	−	0.328771i
$915$	5.38027	+	12.7039i	0.177866	+	0.419977i
$916$	10.9890	−	2.60444i	0.363086	−	0.0860530i
$917$	0.360771	+	0.624874i	0.0119137	+	0.0206352i
$918$	2.65569	−	8.26825i	0.0876510	−	0.272893i
$919$	−16.3221	+	28.2707i	−0.538417	+	0.932565i	0.460573	+	0.887622i	$0.347644\pi$
$919$	−16.3221	+	28.2707i	−0.538417	+	0.932565i	−0.998990	+	0.0449430i	$0.985689\pi$
$920$	−9.38967	+	31.3637i	−0.309568	+	1.03403i
$921$	−1.20383	−	23.3338i	−0.0396674	−	0.768874i
$922$	6.97700	+	4.58885i	0.229775	+	0.151126i
$923$	0.321026	+	0.431213i	0.0105667	+	0.0141935i
$924$	−32.9671	+	3.63185i	−1.08454	+	0.119479i
$925$	41.2999	−	27.1633i	1.35793	−	0.893125i
$926$	−22.9823	−	8.36487i	−0.755245	−	0.274887i
$927$	2.00217	+	44.5478i	0.0657599	+	1.46314i
$928$	−0.708062	+	0.257713i	−0.0232433	+	0.00845986i
$929$	28.9953	−	38.9475i	0.951306	−	1.27783i	−0.00931285	−	0.999957i	$-0.502964\pi$
$929$	28.9953	−	38.9475i	0.951306	−	1.27783i	0.960619	−	0.277869i	$-0.0896282\pi$
$930$	−18.3016	−	32.1905i	−0.600135	−	1.05557i
$931$	−7.06109	+	7.48432i	−0.231418	+	0.245289i
$932$	−5.21887	+	5.53168i	−0.170950	+	0.181196i
$933$	10.2305	+	0.0678470i	0.334930	+	0.00222121i
$934$	16.9772	−	22.8044i	0.555511	−	0.746181i
$935$	30.9476	−	11.2640i	1.01209	−	0.368372i
$936$	0.379895	−	0.496404i	0.0124172	−	0.0162255i
$937$	4.72115	+	1.71836i	0.154233	+	0.0561363i	0.417983	−	0.908455i	$-0.362737\pi$
$937$	4.72115	+	1.71836i	0.154233	+	0.0561363i	−0.263750	+	0.964591i	$0.584959\pi$
$938$	18.9884	−	12.4889i	0.619995	−	0.407777i
$939$	−9.03697	−	12.3083i	−0.294910	−	0.401667i
$940$	−12.1580	−	16.3311i	−0.396551	−	0.532660i
$941$	−19.7386	−	12.9823i	−0.643459	−	0.423210i	0.185403	−	0.982663i	$-0.440641\pi$
$941$	−19.7386	−	12.9823i	−0.643459	−	0.423210i	−0.828862	+	0.559453i	$0.811011\pi$
$942$	−30.4168	−	15.5293i	−0.991032	−	0.505973i
$943$	−12.5458	+	41.9058i	−0.408547	+	1.36464i
$944$	5.98189	−	10.3609i	0.194694	−	0.337220i
$945$	−66.9497	+	22.8699i	−2.17787	+	0.743958i
$946$	−2.75617	−	4.77383i	−0.0896109	−	0.155211i
$947$	17.0613	−	4.04359i	0.554416	−	0.131399i	0.0561488	−	0.998422i	$-0.482118\pi$
$947$	17.0613	−	4.04359i	0.554416	−	0.131399i	0.498268	+	0.867023i	$0.333970\pi$
$948$	4.51601	−	5.98281i	0.146673	−	0.194312i
$949$	1.04186	−	0.523244i	0.0338203	−	0.0169852i
$950$	−5.89430	+	13.6645i	−0.191236	+	0.443336i
$951$	12.2921	+	2.99951i	0.398598	+	0.0972658i
$952$	0.353472	+	6.06888i	0.0114561	+	0.196693i
$953$	8.32666	+	47.2228i	0.269727	+	1.52970i	0.755229	+	0.655462i	$0.227526\pi$
$953$	8.32666	+	47.2228i	0.269727	+	1.52970i	−0.485502	+	0.874236i	$0.661363\pi$
$954$	−11.3100	+	9.23736i	−0.366174	+	0.299071i
$955$	0.866296	−	4.91301i	0.0280327	−	0.158981i
$956$	18.9755	+	2.21792i	0.613711	+	0.0717325i
$957$	−6.47168	+	2.30701i	−0.209200	+	0.0745751i
$958$	4.53707	+	15.1549i	0.146586	+	0.489631i
$959$	15.6391	+	3.70654i	0.505014	+	0.119690i
$960$	−1.08346	−	6.39221i	−0.0349685	−	0.206308i
$961$	0.641865	+	1.48801i	0.0207053	+	0.0480003i
$962$	−0.875569	−	0.734689i	−0.0282295	−	0.0236873i
$963$	6.35687	+	4.30284i	0.204847	+	0.138657i
$964$	−4.96143	+	4.16313i	−0.159797	+	0.134085i
$965$	44.7551	+	22.4768i	1.44072	+	0.723555i
$966$	−45.8363	−	30.5844i	−1.47476	−	0.984037i
$967$	41.5836	−	4.86042i	1.33724	−	0.156301i	0.582770	−	0.812637i	$-0.301969\pi$
$967$	41.5836	−	4.86042i	1.33724	−	0.156301i	0.754468	+	0.656337i	$0.227895\pi$
$968$	0.971820	−	16.6855i	0.0312355	−	0.536292i
$969$	4.65880	−	1.07158i	0.149662	−	0.0344240i
$970$	−4.77979	−	5.06629i	−0.153470	−	0.162669i
$971$	2.57508			0.0826384			0.0413192	−	0.999146i	$-0.486844\pi$
$971$	2.57508			0.0826384			0.0413192	+	0.999146i	$0.486844\pi$
$972$	−13.6908	−	7.45407i	−0.439131	−	0.239089i
$973$	4.49551			0.144120
$974$	6.68517	+	7.08586i	0.214207	+	0.227046i
$975$	3.16942	−	0.729002i	0.101503	−	0.0233467i
$976$	0.123728	−	2.12434i	0.00396045	−	0.0679983i
$977$	−9.91440	+	1.15883i	−0.317190	+	0.0370741i	−0.273198	−	0.961958i	$-0.588081\pi$
$977$	−9.91440	+	1.15883i	−0.317190	+	0.0370741i	−0.0439914	+	0.999032i	$0.514007\pi$
$978$	−10.4461	−	6.97021i	−0.334030	−	0.222883i
$979$	2.43776	+	1.22429i	0.0779112	+	0.0391285i
$980$	17.8662	−	14.9916i	0.570716	−	0.478888i
$981$	−2.30670	+	32.2332i	−0.0736473	+	1.02913i
$982$	4.60685	+	3.86561i	0.147010	+	0.123356i
$983$	2.72214	+	6.31062i	0.0868227	+	0.201278i	0.956096	−	0.293055i	$-0.0946718\pi$
$983$	2.72214	+	6.31062i	0.0868227	+	0.201278i	−0.869273	+	0.494332i	$0.835413\pi$
$984$	−1.44764	−	8.54079i	−0.0461490	−	0.272271i
$985$	95.7643	+	22.6966i	3.05131	+	0.723173i
$986$	0.361178	+	1.20642i	0.0115023	+	0.0384202i
$987$	32.2781	−	11.5064i	1.02742	−	0.366254i
$988$	0.341768	+	0.0399469i	0.0108731	+	0.00127088i
$989$	1.59032	−	9.01914i	0.0505692	−	0.286792i
$990$	−9.49244	−	58.3496i	−0.301690	−	1.85447i
$991$	−4.53010	−	25.6915i	−0.143903	−	0.816117i	−0.968241	−	0.250019i	$-0.919563\pi$
$991$	−4.53010	−	25.6915i	−0.143903	−	0.816117i	0.824338	−	0.566099i	$-0.191548\pi$
$992$	0.332091	+	5.70178i	0.0105439	+	0.181032i
$993$	53.8851	+	13.1490i	1.70999	+	0.417272i
$994$	−3.71710	+	8.61721i	−0.117899	+	0.273321i
$995$	7.76048	−	3.89746i	0.246024	−	0.123558i
$996$	−14.9191	+	19.7648i	−0.472730	+	0.626272i
$997$	−50.0674	+	11.8662i	−1.58565	+	0.375806i	−0.926527	−	0.376228i	$-0.877221\pi$
$997$	−50.0674	+	11.8662i	−1.58565	+	0.375806i	−0.659124	+	0.752035i	$0.729073\pi$
$998$	4.84606	+	8.39362i	0.153399	+	0.265696i
$999$	−14.7400	+	24.3963i	−0.466352	+	0.771865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.103.1	✓	72
3.2	odd	2		486.2.g.a.199.4		72
81.11	odd	54		486.2.g.a.127.4		72
81.70	even	27	inner	162.2.g.a.151.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.103.1	✓	72	1.1	even	1	trivial
162.2.g.a.151.1	yes	72	81.70	even	27	inner
486.2.g.a.127.4		72	81.11	odd	54
486.2.g.a.199.4		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)

\(f(q)\)	\(=\)	\(q+(0.686242 + 0.727374i) q^{2} +(-1.68798 + 0.388253i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.71787 + 0.434557i) q^{5} +(-1.44076 - 0.961353i) q^{6} +(-3.25050 - 1.63246i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(2.69852 - 1.31072i) q^{9} +O(q^{10})\)	\(q+(0.686242 + 0.727374i) q^{2} +(-1.68798 + 0.388253i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.71787 + 0.434557i) q^{5} +(-1.44076 - 0.961353i) q^{6} +(-3.25050 - 1.63246i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(2.69852 - 1.31072i) q^{9} +(-2.86744 - 2.40607i) q^{10} +(2.08512 + 4.83385i) q^{11} +(-0.289449 - 1.70769i) q^{12} +(-0.202747 - 0.0480518i) q^{13} +(-1.04322 - 3.48460i) q^{14} +(6.10696 - 2.17700i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.290217 + 1.64590i) q^{17} +(2.80522 + 1.06336i) q^{18} +(0.286765 + 1.62633i) q^{19} +(-0.217647 - 3.73685i) q^{20} +(6.12058 + 1.49354i) q^{21} +(-2.08512 + 4.83385i) q^{22} +(-7.81600 + 3.92534i) q^{23} +(1.04350 - 1.38243i) q^{24} +(8.76851 - 2.07818i) q^{25} +(-0.104182 - 0.180448i) q^{26} +(-4.04614 + 3.26017i) q^{27} +(1.81870 - 3.15009i) q^{28} +(0.216107 - 0.721848i) q^{29} +(5.77434 + 2.94810i) q^{30} +(-4.77184 - 3.13849i) q^{31} +(-0.597159 - 0.802123i) q^{32} +(-5.39638 - 7.34986i) q^{33} +(-1.39634 + 0.918389i) q^{34} +(12.7944 + 4.65677i) q^{35} +(1.15160 + 2.77017i) q^{36} +(5.15467 - 1.87615i) q^{37} +(-0.986157 + 1.32464i) q^{38} +(0.360888 + 0.00239336i) q^{39} +(2.56873 - 2.72269i) q^{40} +(3.43214 - 3.63786i) q^{41} +(3.11383 + 5.47688i) q^{42} +(-0.625285 + 0.839904i) q^{43} +(-4.94691 + 1.80053i) q^{44} +(-9.46317 + 6.04576i) q^{45} +(-8.21885 - 2.99142i) q^{46} +(4.54436 - 2.98887i) q^{47} +(1.72163 - 0.189666i) q^{48} +(3.72073 + 4.99781i) q^{49} +(7.52893 + 4.95185i) q^{50} +(-0.149147 - 2.89092i) q^{51} +(0.0597592 - 0.199610i) q^{52} +(-2.43382 + 4.21549i) q^{53} +(-5.14800 - 0.705790i) q^{54} +(-9.85278 - 17.0655i) q^{55} +(3.53936 - 0.838844i) q^{56} +(-1.11548 - 2.63386i) q^{57} +(0.673355 - 0.338172i) q^{58} +(-4.73861 + 10.9853i) q^{59} +(1.81822 + 6.22321i) q^{60} +(0.123728 + 2.12434i) q^{61} +(-0.991781 - 5.62467i) q^{62} +(-10.9113 - 0.144730i) q^{63} +(0.173648 - 0.984808i) q^{64} +(0.774668 + 0.0905456i) q^{65} +(1.64287 - 8.96896i) q^{66} +(1.79201 + 5.98575i) q^{67} +(-1.62624 - 0.385426i) q^{68} +(11.6692 - 9.66046i) q^{69} +(5.39281 + 12.5019i) q^{70} +(-1.97644 - 1.65843i) q^{71} +(-1.22467 + 2.73865i) q^{72} +(-4.28632 + 3.59665i) q^{73} +(4.90201 + 2.46188i) q^{74} +(-13.9942 + 6.91231i) q^{75} +(-1.64025 + 0.191718i) q^{76} +(1.11340 - 19.1163i) q^{77} +(0.245915 + 0.264143i) q^{78} +(2.96988 + 3.14789i) q^{79} +3.74318 q^{80} +(5.56402 - 7.07402i) q^{81} +5.00136 q^{82} +(-9.81132 - 10.3994i) q^{83} +(-1.84690 + 6.02338i) q^{84} +(0.363751 - 6.24536i) q^{85} +(-1.04002 + 0.121561i) q^{86} +(-0.0845240 + 1.30237i) q^{87} +(-4.70443 - 2.36265i) q^{88} +(0.396952 - 0.333082i) q^{89} +(-10.8915 - 2.73441i) q^{90} +(0.580586 + 0.487170i) q^{91} +(-3.46424 - 8.03101i) q^{92} +(9.27327 + 3.44501i) q^{93} +(5.29255 + 1.25436i) q^{94} +(-1.77289 - 5.92186i) q^{95} +(1.31942 + 1.12212i) q^{96} +(1.84818 + 0.216021i) q^{97} +(-1.08195 + 6.13606i) q^{98} +(11.9626 + 10.3112i) 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

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