LMFDB - Embedded newform 216.2.t.a.133.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			133.33
Character	$\chi$	$=$	216.133
Dual form			216.2.t.a.13.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40920 - 0.118992i) q^{2} +(1.30914 - 1.13409i) q^{3} +(1.97168 - 0.335368i) q^{4} +(0.508621 + 0.606151i) q^{5} +(1.70988 - 1.75394i) q^{6} +(-3.72062 + 1.35420i) q^{7} +(2.73858 - 0.707214i) q^{8} +(0.427672 - 2.96936i) q^{9} +(0.788875 + 0.793665i) q^{10} +(-2.92987 + 3.49168i) q^{11} +(2.20086 - 2.67511i) q^{12} +(-3.31770 + 0.585000i) q^{13} +(-5.08196 + 2.35106i) q^{14} +(1.35328 + 0.216711i) q^{15} +(3.77506 - 1.32248i) q^{16} +(-2.50743 - 4.34299i) q^{17} +(0.249344 - 4.23531i) q^{18} +(6.10844 + 3.52671i) q^{19} +(1.20612 + 1.02456i) q^{20} +(-3.33502 + 5.99236i) q^{21} +(-3.71328 + 5.26910i) q^{22} +(-4.33163 - 1.57658i) q^{23} +(2.78313 - 4.03165i) q^{24} +(0.759517 - 4.30744i) q^{25} +(-4.60569 + 1.21916i) q^{26} +(-2.80765 - 4.37231i) q^{27} +(-6.88173 + 3.91782i) q^{28} +(3.32150 + 0.585669i) q^{29} +(1.93283 + 0.144358i) q^{30} +(7.51376 + 2.73478i) q^{31} +(5.16244 - 2.31283i) q^{32} +(0.124291 + 7.89382i) q^{33} +(-4.05025 - 5.82177i) q^{34} +(-2.71323 - 1.56649i) q^{35} +(-0.152594 - 5.99806i) q^{36} +(3.56434 - 2.05787i) q^{37} +(9.02765 + 4.24297i) q^{38} +(-3.67987 + 4.52842i) q^{39} +(1.82158 + 1.30029i) q^{40} +(0.333012 + 1.88860i) q^{41} +(-3.98666 + 8.84126i) q^{42} +(-3.66311 + 4.36553i) q^{43} +(-4.60577 + 7.86706i) q^{44} +(2.01740 - 1.25104i) q^{45} +(-6.29173 - 1.70629i) q^{46} +(-7.37860 + 2.68559i) q^{47} +(3.44225 - 6.01256i) q^{48} +(6.64689 - 5.57740i) q^{49} +(0.557759 - 6.16041i) q^{50} +(-8.20791 - 2.84191i) q^{51} +(-6.34526 + 2.26608i) q^{52} -1.95507i q^{53} +(-4.47680 - 5.82737i) q^{54} -3.60667 q^{55} +(-9.23154 + 6.33986i) q^{56} +(11.9964 - 2.31059i) q^{57} +(4.75034 + 0.430092i) q^{58} +(-3.02793 - 3.60855i) q^{59} +(2.74092 - 0.0265629i) q^{60} +(1.87567 + 5.15337i) q^{61} +(10.9138 + 2.95978i) q^{62} +(2.42989 + 11.6270i) q^{63} +(6.99970 - 3.87353i) q^{64} +(-2.04205 - 1.71348i) q^{65} +(1.11445 + 11.1092i) q^{66} +(5.36107 - 0.945302i) q^{67} +(-6.40035 - 7.72209i) q^{68} +(-7.45868 + 2.84850i) q^{69} +(-4.00989 - 1.88464i) q^{70} +(-5.56518 - 9.63918i) q^{71} +(-0.928758 - 8.43430i) q^{72} +(-1.32161 + 2.28909i) q^{73} +(4.77799 - 3.32408i) q^{74} +(-3.89072 - 6.50038i) q^{75} +(13.2266 + 4.90497i) q^{76} +(6.17251 - 16.9588i) q^{77} +(-4.64683 + 6.81932i) q^{78} +(-0.150274 + 0.852245i) q^{79} +(2.72169 + 1.61561i) q^{80} +(-8.63419 - 2.53982i) q^{81} +(0.694009 + 2.62179i) q^{82} +(0.0489550 + 0.00863210i) q^{83} +(-4.56595 + 12.9335i) q^{84} +(1.35718 - 3.72882i) q^{85} +(-4.64259 + 6.58778i) q^{86} +(5.01249 - 3.00016i) q^{87} +(-5.55432 + 11.6343i) q^{88} +(-2.15515 + 3.73283i) q^{89} +(2.69406 - 2.00303i) q^{90} +(11.5517 - 6.66938i) q^{91} +(-9.06933 - 1.65583i) q^{92} +(12.9380 - 4.94109i) q^{93} +(-10.0783 + 4.66252i) q^{94} +(0.969162 + 5.49639i) q^{95} +(4.13537 - 8.88250i) q^{96} +(5.00174 + 4.19696i) q^{97} +(8.70312 - 8.65059i) q^{98} +(9.11503 + 10.1931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.40920	−	0.118992i	0.996454	−	0.0841403i
$2$	1.40920	−	0.118992i	0.996454	−	0.0841403i
$3$	1.30914	−	1.13409i	0.755830	−	0.654768i
$3$	1.30914	−	1.13409i	0.755830	−	0.654768i
$4$	1.97168	−	0.335368i	0.985841	−	0.167684i
$5$	0.508621	+	0.606151i	0.227462	+	0.271079i	0.867689	−	0.497107i	$-0.165604\pi$
$5$	0.508621	+	0.606151i	0.227462	+	0.271079i	−0.640227	+	0.768186i	$0.721160\pi$
$6$	1.70988	−	1.75394i	0.698057	−	0.716042i
$7$	−3.72062	+	1.35420i	−1.40626	+	0.511838i	−0.930031	−	0.367481i	$-0.880220\pi$
$7$	−3.72062	+	1.35420i	−1.40626	+	0.511838i	−0.476233	+	0.879319i	$0.657998\pi$
$8$	2.73858	−	0.707214i	0.968236	−	0.250038i
$9$	0.427672	−	2.96936i	0.142557	−	0.989787i
$10$	0.788875	+	0.793665i	0.249464	+	0.250979i
$11$	−2.92987	+	3.49168i	−0.883388	+	1.05278i	0.114847	+	0.993383i	$0.463362\pi$
$11$	−2.92987	+	3.49168i	−0.883388	+	1.05278i	−0.998234	+	0.0593973i	$0.981082\pi$
$12$	2.20086	−	2.67511i	0.635334	−	0.772238i
$13$	−3.31770	+	0.585000i	−0.920164	+	0.162250i	−0.613615	−	0.789605i	$-0.710285\pi$
$13$	−3.31770	+	0.585000i	−0.920164	+	0.162250i	−0.306549	+	0.951855i	$0.599174\pi$
$14$	−5.08196	+	2.35106i	−1.35821	+	0.628347i
$15$	1.35328	+	0.216711i	0.349417	+	0.0559545i
$16$	3.77506	−	1.32248i	0.943764	−	0.330619i
$17$	−2.50743	−	4.34299i	−0.608140	−	1.05333i	−0.991547	−	0.129750i	$-0.958582\pi$
$17$	−2.50743	−	4.34299i	−0.608140	−	1.05333i	0.383406	−	0.923580i	$-0.374751\pi$
$18$	0.249344	−	4.23531i	0.0587709	−	0.998271i
$19$	6.10844	+	3.52671i	1.40137	+	0.809082i	0.994533	−	0.104418i	$-0.0332981\pi$
$19$	6.10844	+	3.52671i	1.40137	+	0.809082i	0.406838	+	0.913500i	$0.366631\pi$
$20$	1.20612	+	1.02456i	0.269697	+	0.229099i
$21$	−3.33502	+	5.99236i	−0.727761	+	1.30764i
$22$	−3.71328	+	5.26910i	−0.791674	+	1.12338i
$23$	−4.33163	−	1.57658i	−0.903207	−	0.328740i	−0.151670	−	0.988431i	$-0.548465\pi$
$23$	−4.33163	−	1.57658i	−0.903207	−	0.328740i	−0.751537	+	0.659691i	$0.770687\pi$
$24$	2.78313	−	4.03165i	0.568105	−	0.822956i
$25$	0.759517	−	4.30744i	0.151903	−	0.861487i
$26$	−4.60569	+	1.21916i	−0.903249	+	0.239097i
$27$	−2.80765	−	4.37231i	−0.540332	−	0.841452i
$28$	−6.88173	+	3.91782i	−1.30053	+	0.740399i
$29$	3.32150	+	0.585669i	0.616786	+	0.108756i	0.473307	−	0.880897i	$-0.343060\pi$
$29$	3.32150	+	0.585669i	0.616786	+	0.108756i	0.143479	+	0.989653i	$0.454171\pi$
$30$	1.93283	+	0.144358i	0.352885	+	0.0263561i
$31$	7.51376	+	2.73478i	1.34951	+	0.491182i	0.912795	−	0.408418i	$-0.133919\pi$
$31$	7.51376	+	2.73478i	1.34951	+	0.491182i	0.436716	+	0.899600i	$0.356142\pi$
$32$	5.16244	−	2.31283i	0.912599	−	0.408855i
$33$	0.124291	+	7.89382i	0.0216364	+	1.37414i
$34$	−4.05025	−	5.82177i	−0.694611	−	0.998426i
$35$	−2.71323	−	1.56649i	−0.458620	−	0.264785i
$36$	−0.152594	−	5.99806i	−0.0254323	−	0.999677i
$37$	3.56434	−	2.05787i	0.585973	−	0.338312i	−0.177530	−	0.984115i	$-0.556811\pi$
$37$	3.56434	−	2.05787i	0.585973	−	0.338312i	0.763504	+	0.645803i	$0.223477\pi$
$38$	9.02765	+	4.24297i	1.46448	+	0.688301i
$39$	−3.67987	+	4.52842i	−0.589251	+	0.725127i
$40$	1.82158	+	1.30029i	0.288017	+	0.205594i
$41$	0.333012	+	1.88860i	0.0520077	+	0.294950i	0.999707	−	0.0242149i	$-0.00770860\pi$
$41$	0.333012	+	1.88860i	0.0520077	+	0.294950i	−0.947699	+	0.319165i	$0.896597\pi$
$42$	−3.98666	+	8.84126i	−0.615155	+	1.36424i
$43$	−3.66311	+	4.36553i	−0.558619	+	0.665737i	−0.969254	−	0.246064i	$-0.920863\pi$
$43$	−3.66311	+	4.36553i	−0.558619	+	0.665737i	0.410634	+	0.911800i	$0.365307\pi$
$44$	−4.60577	+	7.86706i	−0.694345	+	1.18600i
$45$	2.01740	−	1.25104i	0.300737	−	0.186495i
$46$	−6.29173	−	1.70629i	−0.927664	−	0.251579i
$47$	−7.37860	+	2.68559i	−1.07628	+	0.391733i	−0.818521	−	0.574476i	$-0.805206\pi$
$47$	−7.37860	+	2.68559i	−1.07628	+	0.391733i	−0.257757	+	0.966210i	$0.582984\pi$
$48$	3.44225	−	6.01256i	0.496846	−	0.867839i
$49$	6.64689	−	5.57740i	0.949555	−	0.796771i
$50$	0.557759	−	6.16041i	0.0788790	−	0.871214i
$51$	−8.20791	−	2.84191i	−1.14934	−	0.397947i
$52$	−6.34526	+	2.26608i	−0.879929	+	0.314249i
$53$		−	1.95507i		−	0.268550i	−0.990944	−	0.134275i	$-0.957129\pi$
$53$		−	1.95507i		−	0.268550i	0.990944	−	0.134275i	$-0.0428705\pi$
$54$	−4.47680	−	5.82737i	−0.609216	−	0.793005i
$55$	−3.60667			−0.486324
$56$	−9.23154	+	6.33986i	−1.23362	+	0.847200i
$57$	11.9964	−	2.31059i	1.58896	−	0.306045i
$58$	4.75034	+	0.430092i	0.623750	+	0.0564738i
$59$	−3.02793	−	3.60855i	−0.394203	−	0.469793i	0.532040	−	0.846719i	$-0.321426\pi$
$59$	−3.02793	−	3.60855i	−0.394203	−	0.469793i	−0.926243	+	0.376926i	$0.876981\pi$
$60$	2.74092	−	0.0265629i	0.353852	−	0.00342926i
$61$	1.87567	+	5.15337i	0.240156	+	0.659822i	0.999953	+	0.00966241i	$0.00307569\pi$
$61$	1.87567	+	5.15337i	0.240156	+	0.659822i	−0.759798	+	0.650159i	$0.774702\pi$
$62$	10.9138	+	2.95978i	1.38605	+	0.375892i
$63$	2.42989	+	11.6270i	0.306137	+	1.46487i
$64$	6.99970	−	3.87353i	0.874962	−	0.484192i
$65$	−2.04205	−	1.71348i	−0.253285	−	0.212531i
$66$	1.11445	+	11.1092i	0.137180	+	1.36744i
$67$	5.36107	−	0.945302i	0.654959	−	0.115487i	0.163713	−	0.986508i	$-0.447653\pi$
$67$	5.36107	−	0.945302i	0.654959	−	0.115487i	0.491246	+	0.871021i	$0.336542\pi$
$68$	−6.40035	−	7.72209i	−0.776156	−	0.936441i
$69$	−7.45868	+	2.84850i	−0.897919	+	0.342919i
$70$	−4.00989	−	1.88464i	−0.479273	−	0.225257i
$71$	−5.56518	−	9.63918i	−0.660465	−	1.14396i	−0.980493	−	0.196552i	$-0.937026\pi$
$71$	−5.56518	−	9.63918i	−0.660465	−	1.14396i	0.320028	−	0.947408i	$-0.396308\pi$
$72$	−0.928758	−	8.43430i	−0.109455	−	0.993992i
$73$	−1.32161	+	2.28909i	−0.154683	+	0.267918i	−0.932943	−	0.360023i	$-0.882769\pi$
$73$	−1.32161	+	2.28909i	−0.154683	+	0.267918i	0.778261	+	0.627941i	$0.216102\pi$
$74$	4.77799	−	3.32408i	0.555430	−	0.386416i
$75$	−3.89072	−	6.50038i	−0.449261	−	0.750599i
$76$	13.2266	+	4.90497i	1.51720	+	0.562639i
$77$	6.17251	−	16.9588i	0.703423	−	1.93264i
$78$	−4.64683	+	6.81932i	−0.526150	+	0.772136i
$79$	−0.150274	+	0.852245i	−0.0169071	+	0.0958850i	−0.992094	−	0.125500i	$-0.959947\pi$
$79$	−0.150274	+	0.852245i	−0.0169071	+	0.0958850i	0.975187	+	0.221385i	$0.0710577\pi$
$80$	2.72169	+	1.61561i	0.304295	+	0.180631i
$81$	−8.63419	−	2.53982i	−0.959355	−	0.282203i
$82$	0.694009	+	2.62179i	0.0766405	+	0.289529i
$83$	0.0489550	+	0.00863210i	0.00537351	+	0.000947496i	0.176334	−	0.984330i	$-0.443576\pi$
$83$	0.0489550	+	0.00863210i	0.00537351	+	0.000947496i	−0.170961	+	0.985278i	$0.554687\pi$
$84$	−4.56595	+	12.9335i	−0.498186	+	1.41116i
$85$	1.35718	−	3.72882i	0.147207	−	0.404447i
$86$	−4.64259	+	6.58778i	−0.500623	+	0.710378i
$87$	5.01249	−	3.00016i	0.537395	−	0.321651i
$88$	−5.55432	+	11.6343i	−0.592093	+	1.24022i
$89$	−2.15515	+	3.73283i	−0.228445	+	0.395679i	−0.957348	−	0.288939i	$-0.906698\pi$
$89$	−2.15515	+	3.73283i	−0.228445	+	0.395679i	0.728902	+	0.684618i	$0.240031\pi$
$90$	2.69406	−	2.00303i	0.283978	−	0.211137i
$91$	11.5517	−	6.66938i	1.21095	−	0.699141i
$92$	−9.06933	−	1.65583i	−0.945543	−	0.172633i
$93$	12.9380	−	4.94109i	1.34161	−	0.512367i
$94$	−10.0783	+	4.66252i	−1.03950	+	0.480903i
$95$	0.969162	+	5.49639i	0.0994339	+	0.563918i
$96$	4.13537	−	8.88250i	0.422064	−	0.906566i
$97$	5.00174	+	4.19696i	0.507850	+	0.426137i	0.860372	−	0.509667i	$-0.170231\pi$
$97$	5.00174	+	4.19696i	0.507850	+	0.426137i	−0.352522	+	0.935804i	$0.614676\pi$
$98$	8.70312	−	8.65059i	0.879147	−	0.873842i
$99$	9.11503	+	10.1931i	0.916095	+	1.02445i
$100$	0.0529517	−	8.74761i	0.00529517	−	0.874761i
$101$	1.65905	+	4.55822i	0.165082	+	0.453559i	0.994458	−	0.105131i	$-0.0335262\pi$
$101$	1.65905	+	4.55822i	0.165082	+	0.453559i	−0.829376	+	0.558690i	$0.811304\pi$
$102$	−11.9047	−	3.02814i	−1.17875	−	0.299831i
$103$	2.89374	−	2.42813i	0.285128	−	0.239251i	−0.488994	−	0.872287i	$-0.662636\pi$
$103$	2.89374	−	2.42813i	0.285128	−	0.239251i	0.774122	+	0.633036i	$0.218192\pi$
$104$	−8.67208	+	3.94840i	−0.850367	+	0.387172i
$105$	−5.32853	+	1.02631i	−0.520011	+	0.100158i
$106$	−0.232639	−	2.75509i	−0.0225959	−	0.267598i
$107$			6.44327i			0.622894i	0.950263	+	0.311447i	$0.100814\pi$
$107$			6.44327i			0.622894i	−0.950263	+	0.311447i	$0.899186\pi$
$108$	−7.00212	−	7.67922i	−0.673779	−	0.738933i
$109$		−	1.86527i		−	0.178660i	−0.996002	−	0.0893301i	$-0.971527\pi$
$109$		−	1.86527i		−	0.178660i	0.996002	−	0.0893301i	$-0.0284726\pi$
$110$	−5.08252	+	0.429166i	−0.484599	+	0.0409194i
$111$	2.33239	−	6.73632i	0.221380	−	0.639383i
$112$	−12.2547	+	10.0326i	−1.15796	+	0.947992i
$113$	4.03671	−	3.38720i	0.379741	−	0.318641i	−0.432859	−	0.901461i	$-0.642495\pi$
$113$	4.03671	−	3.38720i	0.379741	−	0.318641i	0.812601	+	0.582821i	$0.198051\pi$
$114$	16.6303	−	4.68356i	1.55757	−	0.438655i
$115$	−1.24751	−	3.42750i	−0.116331	−	0.319616i
$116$	6.74535	+	0.0408314i	0.626290	+	0.00379110i
$117$	0.318188	+	10.1016i	0.0294165	+	0.933896i
$118$	−4.69635	−	4.72486i	−0.432334	−	0.434959i
$119$	15.2105	+	12.7631i	1.39434	+	1.16999i
$120$	3.85935	−	0.363581i	0.352308	−	0.0331903i
$121$	−1.69757	−	9.62741i	−0.154325	−	0.875219i
$122$	3.25641	+	7.03894i	0.294821	+	0.637275i
$123$	2.57781	+	2.09477i	0.232433	+	0.188879i
$124$	15.7319	+	2.87225i	1.41277	+	0.257936i
$125$	6.42358	−	3.70865i	0.574542	−	0.331712i
$126$	4.80772	+	16.0956i	0.428306	+	1.43391i
$127$	8.80265	−	15.2466i	0.781109	−	1.35292i	−0.150187	−	0.988658i	$-0.547988\pi$
$127$	8.80265	−	15.2466i	0.781109	−	1.35292i	0.931296	−	0.364263i	$-0.118679\pi$
$128$	9.40304	−	6.29149i	0.831119	−	0.556094i
$129$	0.155397	+	9.86937i	0.0136820	+	0.868950i
$130$	−3.08154	−	2.17165i	−0.270269	−	0.190466i
$131$	3.58706	−	9.85536i	0.313403	−	0.861067i	−0.678561	−	0.734544i	$-0.737396\pi$
$131$	3.58706	−	9.85536i	0.313403	−	0.861067i	0.991964	−	0.126523i	$-0.0403817\pi$
$132$	2.89239	+	15.5224i	0.251751	+	1.35105i
$133$	−27.5031	−	4.84953i	−2.38482	−	0.420508i
$134$	7.44233	−	1.97004i	0.642920	−	0.170186i
$135$	1.22225	−	3.92571i	0.105195	−	0.337871i
$136$	−9.93823	−	10.1204i	−0.852196	−	0.867814i
$137$	−1.18700	+	6.73181i	−0.101412	+	0.575137i	0.891181	+	0.453649i	$0.149878\pi$
$137$	−1.18700	+	6.73181i	−0.101412	+	0.575137i	−0.992593	+	0.121489i	$0.961233\pi$
$138$	−10.1718	+	4.90163i	−0.865882	+	0.417254i
$139$	−3.94000	+	10.8251i	−0.334187	+	0.918171i	0.652823	+	0.757510i	$0.273585\pi$
$139$	−3.94000	+	10.8251i	−0.334187	+	0.918171i	−0.987010	+	0.160660i	$0.948638\pi$
$140$	−5.87498	−	2.17868i	−0.496527	−	0.184132i
$141$	−6.61388	+	11.8838i	−0.556989	+	1.00080i
$142$	−8.98943	−	12.9213i	−0.754376	−	1.08433i
$143$	7.67778	−	13.2983i	0.642048	−	1.11206i
$144$	−2.31242	−	11.7751i	−0.192702	−	0.981257i
$145$	1.33438	+	2.31121i	0.110814	+	0.191936i
$146$	−1.59003	+	3.38305i	−0.131591	+	0.279983i
$147$	2.37639	−	14.8398i	0.196002	−	1.22396i
$148$	6.33759	−	5.25283i	0.520947	−	0.431780i
$149$	10.7148	−	1.88931i	0.877789	−	0.154778i	0.283445	−	0.958989i	$-0.408523\pi$
$149$	10.7148	−	1.88931i	0.877789	−	0.154778i	0.594344	+	0.804211i	$0.297412\pi$
$150$	−6.25629	−	8.69736i	−0.510824	−	0.710137i
$151$	−13.6914	−	11.4884i	−1.11419	−	0.934917i	−0.115894	−	0.993262i	$-0.536973\pi$
$151$	−13.6914	−	11.4884i	−1.11419	−	0.934917i	−0.998296	+	0.0583451i	$0.981418\pi$
$152$	19.2226	+	5.33821i	1.55916	+	0.432986i
$153$	−13.9683	+	5.58808i	−1.12927	+	0.451769i
$154$	6.68032	−	24.6329i	0.538316	−	1.98497i
$155$	2.16396	+	5.94544i	0.173814	+	0.477549i
$156$	−5.73686	+	10.1627i	−0.459316	+	0.813668i
$157$	−5.09556	−	6.07265i	−0.406670	−	0.484650i	0.523372	−	0.852104i	$-0.324674\pi$
$157$	−5.09556	−	6.07265i	−0.406670	−	0.484650i	−0.930042	+	0.367454i	$0.880229\pi$
$158$	−0.110355	+	1.21886i	−0.00877937	+	0.0969676i
$159$	−2.21723	−	2.55946i	−0.175838	−	0.202978i
$160$	4.02765	+	1.95286i	0.318414	+	0.154387i
$161$	18.2514			1.43841
$162$	−12.4695	−	2.55171i	−0.979697	−	0.200482i
$163$			16.2608i			1.27365i	0.771009	+	0.636824i	$0.219752\pi$
$163$			16.2608i			1.27365i	−0.771009	+	0.636824i	$0.780248\pi$
$164$	1.28997	+	3.61204i	0.100730	+	0.282053i
$165$	−4.72163	+	4.09030i	−0.367578	+	0.318429i
$166$	0.0700145	+	0.00633906i	0.00543418	+	0.000492007i
$167$	−9.24890	+	7.76075i	−0.715701	+	0.600545i	−0.926193	−	0.377051i	$-0.876938\pi$
$167$	−9.24890	+	7.76075i	−0.715701	+	0.600545i	0.210491	+	0.977596i	$0.432494\pi$
$168$	−4.89535	+	18.7691i	−0.377685	+	1.44807i
$169$	−1.55110	+	0.564555i	−0.119316	+	0.0434273i
$170$	1.46883	−	5.41614i	0.112654	−	0.415399i
$171$	13.0845	−	16.6299i	1.00059	−	1.27172i
$172$	−5.75843	+	9.83592i	−0.439076	+	0.749982i
$173$	−2.11267	+	2.51778i	−0.160623	+	0.191423i	−0.840353	−	0.542039i	$-0.817652\pi$
$173$	−2.11267	+	2.51778i	−0.160623	+	0.191423i	0.679730	+	0.733462i	$0.262097\pi$
$174$	6.70660	−	4.82427i	0.508426	−	0.365727i
$175$	3.00724	+	17.0549i	0.227326	+	1.28923i
$176$	−6.44275	+	17.0560i	−0.485641	+	1.28564i
$177$	−8.05640	−	1.29013i	−0.605556	−	0.0969720i
$178$	−2.59285	+	5.51674i	−0.194343	+	0.413497i
$179$	−7.43771	+	4.29416i	−0.555920	+	0.320961i	−0.751506	−	0.659726i	$-0.770672\pi$
$179$	−7.43771	+	4.29416i	−0.555920	+	0.320961i	0.195586	+	0.980687i	$0.437339\pi$
$180$	3.55812	−	3.14323i	0.265206	−	0.234283i
$181$	−10.0107	−	5.77968i	−0.744089	−	0.429600i	0.0794649	−	0.996838i	$-0.474679\pi$
$181$	−10.0107	−	5.77968i	−0.744089	−	0.429600i	−0.823554	+	0.567237i	$0.808012\pi$
$182$	15.4850	−	10.7730i	1.14783	−	0.798551i
$183$	8.29991	+	4.61928i	0.613547	+	0.341467i
$184$	−12.9775	−	1.25422i	−0.956715	−	0.0924622i
$185$	3.06028	+	1.11385i	0.224996	+	0.0818918i
$186$	17.6443	−	8.50250i	1.29374	−	0.623433i
$187$	22.5108	+	3.96925i	1.64615	+	0.290261i
$188$	−13.6476	+	7.76967i	−0.995352	+	0.566661i
$189$	16.3672	+	12.4656i	1.19054	+	0.906741i
$190$	2.01977	+	7.63018i	0.146530	+	0.553552i
$191$	4.01620	−	22.7770i	0.290602	−	1.64809i	−0.393956	−	0.919129i	$-0.628894\pi$
$191$	4.01620	−	22.7770i	0.290602	−	1.64809i	0.684558	−	0.728958i	$-0.259995\pi$
$192$	4.77061	−	13.0093i	0.344289	−	0.938864i
$193$	2.47922	+	0.902363i	0.178458	+	0.0649535i	0.429704	−	0.902970i	$-0.358618\pi$
$193$	2.47922	+	0.902363i	0.178458	+	0.0649535i	−0.251246	+	0.967923i	$0.580840\pi$
$194$	7.54785	+	5.31918i	0.541904	+	0.381895i
$195$	−4.61657	+	0.0726898i	−0.330599	+	0.00520542i
$196$	11.2351	−	13.2260i	0.802505	−	0.944715i
$197$	−13.8978	−	8.02392i	−0.990180	−	0.571680i	−0.0848516	−	0.996394i	$-0.527042\pi$
$197$	−13.8978	−	8.02392i	−0.990180	−	0.571680i	−0.905328	+	0.424713i	$0.860375\pi$
$198$	14.0578	+	13.2795i	0.999043	+	0.943734i
$199$	9.62310	+	16.6677i	0.682164	+	1.18154i	0.974319	+	0.225171i	$0.0722941\pi$
$199$	9.62310	+	16.6677i	0.682164	+	1.18154i	−0.292156	+	0.956371i	$0.594373\pi$
$200$	−0.966279	−	12.3334i	−0.0683262	−	0.872105i
$201$	5.94631	−	7.31748i	0.419421	−	0.516135i
$202$	2.88033	+	6.22602i	0.202659	+	0.438061i
$203$	−13.1512	+	2.31890i	−0.923030	+	0.162755i
$204$	−17.1365	−	2.85068i	−1.19979	−	0.199587i
$205$	−0.975402	+	1.16244i	−0.0681250	+	0.0811883i
$206$	3.78892	−	3.76605i	0.263987	−	0.262393i
$207$	−6.53396	+	12.1879i	−0.454142	+	0.847118i
$208$	−11.7509	+	6.59599i	−0.814775	+	0.457349i
$209$	−30.2110	+	10.9959i	−2.08974	+	0.760603i
$210$	−7.38684	+	2.08033i	−0.509740	+	0.143557i
$211$	−13.9505	−	16.6256i	−0.960392	−	1.14455i	−0.989436	−	0.144973i	$-0.953690\pi$
$211$	−13.9505	−	16.6256i	−0.960392	−	1.14455i	0.0290432	−	0.999578i	$-0.490754\pi$
$212$	−0.655668	−	3.85478i	−0.0450315	−	0.264748i
$213$	−18.2173	−	6.30756i	−1.24823	−	0.432187i
$214$	0.766699	+	9.07985i	0.0524105	+	0.620685i
$215$	−4.50930			−0.307532
$216$	−10.7811	−	9.98835i	−0.733564	−	0.679621i
$217$	−31.6593			−2.14917
$218$	−0.221952	−	2.62853i	−0.0150325	−	0.178027i
$219$	0.865877	+	4.49556i	0.0585106	+	0.303782i
$220$	−7.11121	+	1.20956i	−0.479438	+	0.0815486i
$221$	10.8595	+	12.9419i	0.730492	+	0.870566i
$222$	2.48523	−	9.77034i	0.166797	−	0.655743i
$223$	−5.73818	+	2.08853i	−0.384257	+	0.139858i	−0.526924	−	0.849913i	$-0.676655\pi$
$223$	−5.73818	+	2.08853i	−0.384257	+	0.139858i	0.142666	+	0.989771i	$0.454432\pi$
$224$	−16.0755	+	15.5961i	−1.07409	+	1.04206i
$225$	−12.4655	−	4.09745i	−0.831034	−	0.273163i
$226$	5.28547	−	5.25357i	0.351584	−	0.349462i
$227$	−18.6090	+	22.1773i	−1.23512	+	1.47196i	−0.405059	+	0.914291i	$0.632749\pi$
$227$	−18.6090	+	22.1773i	−1.23512	+	1.47196i	−0.830063	+	0.557670i	$0.811695\pi$
$228$	22.8781	−	8.57894i	1.51514	−	0.568154i
$229$	−12.6630	+	2.23282i	−0.836791	+	0.147549i	−0.575593	−	0.817736i	$-0.695229\pi$
$229$	−12.6630	+	2.23282i	−0.836791	+	0.147549i	−0.261198	+	0.965285i	$0.584118\pi$
$230$	−2.16583	−	4.68159i	−0.142811	−	0.308695i
$231$	−11.1522	−	29.2016i	−0.733762	−	1.92132i
$232$	9.51039	−	0.745105i	0.624388	−	0.0489185i
$233$	13.9217	+	24.1131i	0.912041	+	1.57970i	0.811176	+	0.584802i	$0.198828\pi$
$233$	13.9217	+	24.1131i	0.912041	+	1.57970i	0.100865	+	0.994900i	$0.467839\pi$
$234$	1.65041	+	14.1973i	0.107890	+	0.928109i
$235$	−5.38078	−	3.10659i	−0.351003	−	0.202652i
$236$	−7.18031	−	6.09944i	−0.467399	−	0.397040i
$237$	0.769795	+	1.28613i	0.0500036	+	0.0835430i
$238$	22.9533	+	16.1758i	1.48784	+	1.04852i
$239$	3.89187	+	1.41652i	0.251744	+	0.0916273i	0.464810	−	0.885411i	$-0.346123\pi$
$239$	3.89187	+	1.41652i	0.251744	+	0.0916273i	−0.213066	+	0.977038i	$0.568345\pi$
$240$	5.39532	−	0.971591i	0.348266	−	0.0627159i
$241$	−3.28233	+	18.6150i	−0.211434	+	1.19910i	0.675555	+	0.737309i	$0.263904\pi$
$241$	−3.28233	+	18.6150i	−0.211434	+	1.19910i	−0.886989	+	0.461791i	$0.847207\pi$
$242$	−3.53780	−	13.3649i	−0.227419	−	0.859131i
$243$	−14.1837	+	6.46699i	−0.909886	+	0.414858i
$244$	5.42651	+	9.53177i	0.347397	+	0.610209i
$245$	6.76149	+	1.19223i	0.431976	+	0.0761690i
$246$	3.88190	+	2.64521i	0.247501	+	0.168653i
$247$	−22.3291	−	8.12712i	−1.42076	−	0.517116i
$248$	22.5111	+	2.17560i	1.42946	+	0.138151i
$249$	0.0738784	−	0.0442189i	0.00468185	−	0.00280226i
$250$	8.61080	−	5.99059i	0.544595	−	0.378878i
$251$	−2.74444	−	1.58450i	−0.173228	−	0.100013i	0.410879	−	0.911690i	$-0.365222\pi$
$251$	−2.74444	−	1.58450i	−0.173228	−	0.100013i	−0.584107	+	0.811677i	$0.698555\pi$
$252$	8.69030	+	22.1099i	0.547437	+	1.39279i
$253$	18.1960	−	10.5055i	1.14397	−	0.660473i
$254$	10.5905	−	22.5330i	0.664504	−	1.41385i
$255$	−2.45209	−	6.42069i	−0.153556	−	0.402079i
$256$	12.5021	−	9.98485i	0.781382	−	0.624053i
$257$	−0.803738	−	4.55822i	−0.0501358	−	0.284334i	0.949424	−	0.313996i	$-0.101668\pi$
$257$	−0.803738	−	4.55822i	−0.0501358	−	0.284334i	−0.999560	+	0.0296622i	$0.990557\pi$
$258$	1.39336	+	13.8894i	0.0867471	+	0.864717i
$259$	−10.4748	+	12.4834i	−0.650872	+	0.775679i
$260$	−4.60092	−	2.69361i	−0.285337	−	0.167050i
$261$	3.15957	−	9.61224i	0.195573	−	0.594983i
$262$	3.88217	−	14.3150i	0.239841	−	0.884383i
$263$	16.1355	−	5.87284i	0.994957	−	0.362135i	0.207319	−	0.978273i	$-0.433526\pi$
$263$	16.1355	−	5.87284i	0.994957	−	0.362135i	0.787638	+	0.616139i	$0.211304\pi$
$264$	5.92300	+	21.5300i	0.364536	+	1.32508i
$265$	1.18507	−	0.994391i	0.0727982	−	0.0610850i
$266$	−39.3343	−	3.56130i	−2.41174	−	0.218357i
$267$	1.41199	+	7.33091i	0.0864121	+	0.448645i
$268$	10.2533	−	3.66176i	0.626320	−	0.223678i
$269$			2.41197i			0.147060i	0.997293	+	0.0735302i	$0.0234265\pi$
$269$			2.41197i			0.147060i	−0.997293	+	0.0735302i	$0.976573\pi$
$270$	1.25527	−	5.67754i	0.0763933	−	0.345524i
$271$	17.5762			1.06768			0.533839	−	0.845586i	$-0.320749\pi$
$271$	17.5762			1.06768			0.533839	+	0.845586i	$0.320749\pi$
$272$	−15.2092	−	13.0790i	−0.922192	−	0.793033i
$273$	7.55906	−	21.8318i	0.457495	−	1.32132i
$274$	−0.871685	+	9.62770i	−0.0526604	+	0.581631i
$275$	12.8149	+	15.2722i	0.772767	+	0.920948i
$276$	−13.7508	+	8.11774i	−0.827704	+	0.488630i
$277$	5.51804	+	15.1607i	0.331547	+	0.910917i	0.987710	+	0.156298i	$0.0499560\pi$
$277$	5.51804	+	15.1607i	0.331547	+	0.910917i	−0.656163	+	0.754619i	$0.727822\pi$
$278$	−4.26415	+	15.7235i	−0.255747	+	0.943033i
$279$	11.3340	−	21.1415i	0.678548	−	1.26571i
$280$	−8.53827	−	2.37112i	−0.510259	−	0.141701i
$281$	−7.03652	−	5.90434i	−0.419764	−	0.352223i	0.408310	−	0.912843i	$-0.366118\pi$
$281$	−7.03652	−	5.90434i	−0.419764	−	0.352223i	−0.828073	+	0.560620i	$0.810563\pi$
$282$	−7.90619	+	17.5336i	−0.470807	+	1.04411i
$283$	−0.0113336	+	0.00199842i	−0.000673713	+	0.000118794i	−0.173985	−	0.984748i	$-0.555664\pi$
$283$	−0.0113336	+	0.00199842i	−0.000673713	+	0.000118794i	0.173311	+	0.984867i	$0.444553\pi$
$284$	−14.2054	−	17.1390i	−0.842937	−	1.01701i
$285$	7.50218	+	6.09640i	0.444390	+	0.361120i
$286$	9.23712	−	19.6536i	0.546203	−	1.16214i
$287$	−3.79655	−	6.57582i	−0.224103	−	0.388159i
$288$	−4.65981	−	16.3183i	−0.274582	−	0.961564i
$289$	−4.07438	+	7.05704i	−0.239670	+	0.415120i
$290$	2.15542	+	3.09817i	0.126571	+	0.181931i
$291$	11.3077	−	0.178044i	0.662869	−	0.0104371i
$292$	−1.83810	+	4.95659i	−0.107567	+	0.290063i
$293$	−5.21237	+	14.3209i	−0.304510	+	0.836634i	0.689192	+	0.724579i	$0.257966\pi$
$293$	−5.21237	+	14.3209i	−0.304510	+	0.836634i	−0.993702	+	0.112055i	$0.964257\pi$
$294$	1.58299	−	21.1949i	0.0923220	−	1.23611i
$295$	0.647256	−	3.67077i	0.0376847	−	0.213720i
$296$	8.30588	−	8.15640i	0.482770	−	0.474081i
$297$	23.4927	+	3.00690i	1.36319	+	0.174478i
$298$	14.8744	−	3.93738i	0.861654	−	0.228087i
$299$	15.2933	+	2.69663i	0.884437	+	0.155950i
$300$	−9.85127	−	11.5119i	−0.568763	−	0.664638i
$301$	7.71728	−	21.2031i	0.444817	−	1.22212i
$302$	−20.6609	−	14.5603i	−1.18890	−	0.837853i
$303$	7.34136	+	4.08580i	0.421750	+	0.234723i
$304$	27.7237	+	5.23526i	1.59006	+	0.300263i
$305$	−2.16971	+	3.75806i	−0.124237	+	0.215186i
$306$	−19.0191	+	9.53683i	−1.08725	+	0.545184i
$307$	13.5691	−	7.83415i	0.774432	−	0.447119i	−0.0600213	−	0.998197i	$-0.519117\pi$
$307$	13.5691	−	7.83415i	0.774432	−	0.447119i	0.834453	+	0.551079i	$0.185784\pi$
$308$	6.48278	−	35.5075i	0.369391	−	2.02323i
$309$	1.03457	−	6.46052i	0.0588545	−	0.367526i
$310$	3.75692	+	8.12081i	0.213378	+	0.461231i
$311$	5.64104	+	31.9919i	0.319874	+	1.81410i	0.543486	+	0.839418i	$0.317104\pi$
$311$	5.64104	+	31.9919i	0.319874	+	1.81410i	−0.223612	+	0.974678i	$0.571785\pi$
$312$	−6.87509	+	15.0039i	−0.389225	+	0.849430i
$313$	9.73885	+	8.17186i	0.550472	+	0.461901i	0.875101	−	0.483941i	$-0.160795\pi$
$313$	9.73885	+	8.17186i	0.550472	+	0.461901i	−0.324629	+	0.945842i	$0.605239\pi$
$314$	−7.90326	−	7.95124i	−0.446006	−	0.448714i
$315$	−5.81184	+	7.38663i	−0.327460	+	0.416189i
$316$	−0.0104767	+	1.73075i	−0.000589361	+	0.0973624i
$317$	−6.57901	−	18.0757i	−0.369514	−	1.01523i	−0.975547	−	0.219792i	$-0.929462\pi$
$317$	−6.57901	−	18.0757i	−0.369514	−	1.01523i	0.606033	−	0.795440i	$-0.292760\pi$
$318$	−3.42908	−	3.34295i	−0.192293	−	0.187463i
$319$	−11.7765	+	9.88166i	−0.659358	+	0.553267i
$320$	5.90814	+	2.27271i	0.330275	+	0.127048i
$321$	7.30726	+	8.43511i	0.407851	+	0.470802i
$322$	25.7198	−	2.17177i	1.43331	−	0.121028i
$323$		−	35.3718i		−	1.96814i
$324$	−17.8757	−	2.11210i	−0.993092	−	0.117339i
$325$			14.7351i			0.817356i
$326$	1.93492	+	22.9148i	0.107165	+	1.26913i
$327$	−2.11538	−	2.44189i	−0.116981	−	0.135037i
$328$	2.24763	+	4.93659i	0.124105	+	0.272578i
$329$	23.8162	−	19.9841i	1.31303	−	1.10176i
$330$	−6.16699	+	6.32588i	−0.339482	+	0.348228i
$331$	−1.10235	−	3.02867i	−0.0605905	−	0.166471i	0.905704	−	0.423911i	$-0.139343\pi$
$331$	−1.10235	−	3.02867i	−0.0605905	−	0.166471i	−0.966294	+	0.257440i	$0.917121\pi$
$332$	0.0994187		0.000601809i	0.00545631		3.30285e-5i
$333$	−4.58619	−	11.4639i	−0.251322	−	0.628217i
$334$	−12.1101	+	12.0370i	−0.662634	+	0.658635i
$335$	3.29975	+	2.76882i	0.180285	+	0.151277i
$336$	−4.66514	+	27.0320i	−0.254504	+	1.47471i
$337$	−5.11170	−	28.9899i	−0.278452	−	1.57918i	−0.727778	−	0.685813i	$-0.759447\pi$
$337$	−5.11170	−	28.9899i	−0.278452	−	1.57918i	0.449326	−	0.893368i	$-0.351664\pi$
$338$	−2.11863	+	0.980140i	−0.115239	+	0.0533126i
$339$	1.44320	−	9.01230i	0.0783840	−	0.489481i
$340$	1.42540	−	7.80719i	0.0773031	−	0.423404i
$341$	−31.5633	+	18.2231i	−1.70925	+	0.986835i
$342$	16.4598	−	24.9917i	0.890044	−	1.35140i
$343$	−3.31975	+	5.74998i	−0.179250	+	0.310470i
$344$	−6.94438	+	14.5460i	−0.374416	+	0.784266i
$345$	−5.52026	−	3.07228i	−0.297201	−	0.165406i
$346$	−2.67757	+	3.79944i	−0.143947	+	0.204259i
$347$	0.677943	−	1.86263i	0.0363939	−	0.0999914i	−0.920165	−	0.391531i	$-0.871945\pi$
$347$	0.677943	−	1.86263i	0.0363939	−	0.0999914i	0.956559	+	0.291540i	$0.0941677\pi$
$348$	8.87688	−	7.59639i	0.475851	−	0.407209i
$349$	31.3630	+	5.53015i	1.67882	+	0.296022i	0.930222	−	0.366997i	$-0.119614\pi$
$349$	31.3630	+	5.53015i	1.67882	+	0.296022i	0.748603	+	0.663019i	$0.230725\pi$
$350$	6.26720	+	23.6759i	0.334996	+	1.26553i
$351$	11.8727	+	12.8635i	0.633719	+	0.686605i
$352$	−7.04959	+	24.8019i	−0.375744	+	1.32194i
$353$	6.25698	−	35.4851i	0.333025	−	1.88868i	−0.112892	−	0.993607i	$-0.536011\pi$
$353$	6.25698	−	35.4851i	0.333025	−	1.88868i	0.445917	−	0.895074i	$-0.352878\pi$
$354$	−11.5066	−	0.859397i	−0.611568	−	0.0456764i
$355$	3.01223	−	8.27603i	0.159872	−	0.439246i
$356$	−2.99740	+	8.08271i	−0.158862	+	0.428383i
$357$	34.3871	−	0.541439i	1.81996	−	0.0286560i
$358$	−9.97023	+	6.93636i	−0.526943	+	0.366598i
$359$	8.08048	−	13.9958i	0.426472	−	0.738670i	−0.570085	−	0.821586i	$-0.693090\pi$
$359$	8.08048	−	13.9958i	0.426472	−	0.738670i	0.996557	+	0.0829153i	$0.0264231\pi$
$360$	4.64007	−	4.85283i	0.244553	−	0.255767i
$361$	15.3753	+	26.6308i	0.809228	+	1.40162i
$362$	−14.7948	−	6.95352i	−0.777597	−	0.365469i
$363$	−13.1407	−	10.6784i	−0.689709	−	0.560470i
$364$	20.5396	−	17.0240i	1.07657	−	0.892298i
$365$	−2.05973	+	0.363187i	−0.107811	+	0.0190101i
$366$	12.2459	+	5.52185i	0.640102	+	0.288632i
$367$	−15.7119	−	13.1839i	−0.820156	−	0.688193i	0.132853	−	0.991136i	$-0.457586\pi$
$367$	−15.7119	−	13.1839i	−0.820156	−	0.688193i	−0.953009	+	0.302943i	$0.902031\pi$
$368$	−18.4371	−	0.223218i	−0.961102	−	0.0116361i
$369$	5.75036	−	0.181129i	0.299352	−	0.00942918i
$370$	4.44508	+	1.20549i	0.231089	+	0.0626702i
$371$	2.64755	+	7.27409i	0.137454	+	0.377652i
$372$	23.8526	−	14.0812i	1.23670	−	0.730079i
$373$	16.8068	+	20.0295i	0.870221	+	1.03709i	0.998968	+	0.0454111i	$0.0144598\pi$
$373$	16.8068	+	20.0295i	0.870221	+	1.03709i	−0.128748	+	0.991677i	$0.541096\pi$
$374$	32.1944	+	2.91486i	1.66473	+	0.150724i
$375$	4.20338	−	12.1401i	0.217062	−	0.626910i
$376$	−18.3076	+	12.5730i	−0.944144	+	0.648401i
$377$	−11.3623			−0.585190
$378$	24.5479	+	15.6190i	1.26261	+	0.803354i
$379$		−	6.99042i		−	0.359074i	−0.983751	−	0.179537i	$-0.942540\pi$
$379$		−	6.99042i		−	0.359074i	0.983751	−	0.179537i	$-0.0574599\pi$
$380$	3.75419	+	10.5121i	0.192586	+	0.539260i
$381$	−5.76722	−	29.9429i	−0.295464	−	1.53402i
$382$	2.94934	−	32.5752i	0.150901	−	1.66669i
$383$	−7.84570	+	6.58332i	−0.400896	+	0.336392i	−0.820840	−	0.571158i	$-0.806494\pi$
$383$	−7.84570	+	6.58332i	−0.400896	+	0.336392i	0.419944	+	0.907550i	$0.362050\pi$
$384$	5.17473	−	18.9003i	0.264072	−	0.964503i
$385$	13.4191	−	4.88415i	0.683900	−	0.248919i
$386$	3.60109	+	0.976601i	0.183291	+	0.0497077i
$387$	11.3962	+	12.7441i	0.579302	+	0.647819i
$388$	11.2694	+	6.59765i	0.572115	+	0.334945i
$389$	−7.20890	+	8.59123i	−0.365506	+	0.435593i	−0.917184	−	0.398464i	$-0.869543\pi$
$389$	−7.20890	+	8.59123i	−0.365506	+	0.435593i	0.551678	+	0.834057i	$0.313988\pi$
$390$	−6.49701	+	0.651770i	−0.328989	+	0.0330037i
$391$	4.01415	+	22.7654i	0.203004	+	1.15130i
$392$	14.2586	−	19.9750i	0.720170	−	1.00889i
$393$	−6.48094	−	16.9701i	−0.326920	−	0.856026i
$394$	−20.5396	−	9.65356i	−1.03477	−	0.486339i
$395$	−0.593021	+	0.342381i	−0.0298381	+	0.0172271i
$396$	21.3904	+	17.0407i	1.07491	+	0.856327i
$397$	−3.99340	−	2.30559i	−0.200423	−	0.115714i	0.396430	−	0.918065i	$-0.370249\pi$
$397$	−3.99340	−	2.30559i	−0.200423	−	0.115714i	−0.596853	+	0.802351i	$0.703582\pi$
$398$	15.5442	+	22.3430i	0.779160	+	1.11995i
$399$	−41.5050	+	24.8423i	−2.07785	+	1.24367i
$400$	−2.82926	−	17.2653i	−0.141463	−	0.863263i
$401$	14.3732	+	5.23142i	0.717764	+	0.261245i	0.674976	−	0.737839i	$-0.264154\pi$
$401$	14.3732	+	5.23142i	0.717764	+	0.261245i	0.0427879	+	0.999084i	$0.486376\pi$
$402$	7.50881	−	11.0193i	0.374506	−	0.549595i
$403$	−26.5282	−	4.67764i	−1.32147	−	0.233010i
$404$	4.79981	+	8.43096i	0.238799	+	0.419456i
$405$	−2.85201	−	6.52543i	−0.141718	−	0.324251i
$406$	−18.2567	+	4.83268i	−0.906062	+	0.239842i
$407$	−3.25761	+	18.4748i	−0.161474	+	0.915762i
$408$	−24.4879	−	1.97806i	−1.21233	−	0.0979287i
$409$	0.943481	+	0.343399i	0.0466521	+	0.0169800i	0.365241	−	0.930913i	$-0.380987\pi$
$409$	0.943481	+	0.343399i	0.0466521	+	0.0169800i	−0.318589	+	0.947893i	$0.603209\pi$
$410$	−1.23621	+	1.75417i	−0.0610523	+	0.0866324i
$411$	6.08055	+	10.1590i	0.299931	+	0.501107i
$412$	4.89121	−	5.75797i	0.240973	−	0.283675i
$413$	16.1525	+	9.32565i	0.794812	+	0.458885i
$414$	−7.75738	+	17.9527i	−0.381254	+	0.882325i
$415$	0.0196672	+	0.0340646i	0.000965425	+	0.00167217i
$416$	−15.7744	+	10.6933i	−0.773404	+	0.524283i
$417$	7.11862	+	18.6398i	0.348601	+	0.912796i
$418$	−41.2649	+	19.0903i	−2.01833	+	0.933737i
$419$	23.6393	−	4.16825i	1.15486	−	0.203633i	0.436762	−	0.899577i	$-0.356125\pi$
$419$	23.6393	−	4.16825i	1.15486	−	0.203633i	0.718096	+	0.695944i	$0.245014\pi$
$420$	−10.1620	+	3.81058i	−0.495854	+	0.185937i
$421$	−4.34097	+	5.17337i	−0.211566	+	0.252135i	−0.861383	−	0.507956i	$-0.830401\pi$
$421$	−4.34097	+	5.17337i	−0.211566	+	0.252135i	0.649817	+	0.760091i	$0.274846\pi$
$422$	−21.6373	−	21.7687i	−1.05329	−	1.05968i
$423$	4.81886	+	23.0583i	0.234301	+	1.12113i
$424$	−1.38266	−	5.35413i	−0.0671477	−	0.260020i
$425$	−20.6116	+	7.50201i	−0.999809	+	0.363901i
$426$	−26.4223	−	6.72089i	−1.28017	−	0.325628i
$427$	−13.9574	−	16.6337i	−0.675444	−	0.804963i
$428$	2.16086	+	12.7041i	0.104449	+	0.614075i
$429$	−5.03024	−	26.1166i	−0.242862	−	1.26092i
$430$	−6.35450	+	0.536572i	−0.306441	+	0.0258758i
$431$	−29.2021			−1.40662			−0.703309	−	0.710884i	$-0.748295\pi$
$431$	−29.2021			−1.40662			−0.703309	+	0.710884i	$0.748295\pi$
$432$	−16.3813	−	12.7927i	−0.788146	−	0.615489i
$433$	−11.3701			−0.546412			−0.273206	−	0.961956i	$-0.588084\pi$
$433$	−11.3701			−0.546412			−0.273206	+	0.961956i	$0.588084\pi$
$434$	−44.6143	+	3.76721i	−2.14155	+	0.180832i
$435$	4.36801	+	1.51238i	0.209430	+	0.0725131i
$436$	−0.625550	−	3.67771i	−0.0299584	−	0.176131i
$437$	−20.8993	−	24.9068i	−0.999750	−	1.19146i
$438$	1.75513	+	6.23211i	0.0838634	+	0.297782i
$439$	−8.53681	+	3.10714i	−0.407440	+	0.148296i	−0.537606	−	0.843196i	$-0.680671\pi$
$439$	−8.53681	+	3.10714i	−0.407440	+	0.148296i	0.130166	+	0.991492i	$0.458449\pi$
$440$	−9.87718	+	2.55069i	−0.470876	+	0.121599i
$441$	−13.7186	−	22.1223i	−0.653268	−	1.05344i
$442$	16.8432	+	16.9455i	0.801151	+	0.806015i
$443$	17.5098	−	20.8674i	0.831917	−	0.991440i	−0.168067	−	0.985776i	$-0.553753\pi$
$443$	17.5098	−	20.8674i	0.831917	−	0.991440i	0.999984	−	0.00566416i	$-0.00180297\pi$
$444$	2.33958	−	14.0641i	0.111032	−	0.667452i
$445$	−3.35881	+	0.592249i	−0.159223	+	0.0280753i
$446$	−7.83772	+	3.62595i	−0.371127	+	0.171694i
$447$	11.8845	−	14.6249i	0.562116	−	0.691734i
$448$	−20.7977	+	23.8909i	−0.982599	+	1.12874i
$449$	3.83919	+	6.64967i	0.181183	+	0.313818i	0.942284	−	0.334816i	$-0.108674\pi$
$449$	3.83919	+	6.64967i	0.181183	+	0.313818i	−0.761101	+	0.648633i	$0.775341\pi$
$450$	−18.0539	−	4.29082i	−0.851071	−	0.202271i
$451$	−7.57008	−	4.37059i	−0.356461	−	0.205803i
$452$	6.82314	−	8.03226i	0.320934	−	0.377806i
$453$	−30.9528	+	0.487366i	−1.45429	+	0.0228984i
$454$	−23.5848	+	33.4666i	−1.10689	+	1.57066i
$455$	9.91809	+	3.60989i	0.464967	+	0.169234i
$456$	31.2190	−	14.8118i	1.46196	−	0.693624i
$457$	2.12889	−	12.0735i	0.0995853	−	0.564776i	−0.893660	−	0.448744i	$-0.851871\pi$
$457$	2.12889	−	12.0735i	0.0995853	−	0.564776i	0.993245	−	0.116032i	$-0.0370175\pi$
$458$	−17.5789	+	4.65328i	−0.821409	+	0.217434i
$459$	−11.9490	+	23.1568i	−0.557729	+	1.08087i
$460$	−3.60916	−	6.33957i	−0.168278	−	0.295584i
$461$	16.2573	+	2.86660i	0.757177	+	0.133511i	0.538893	−	0.842374i	$-0.318843\pi$
$461$	16.2573	+	2.86660i	0.757177	+	0.133511i	0.218285	+	0.975885i	$0.429954\pi$
$462$	−19.1905	−	39.8238i	−0.892821	−	1.85277i
$463$	37.1376	+	13.5170i	1.72593	+	0.628187i	0.998327	−	0.0578141i	$-0.0184131\pi$
$463$	37.1376	+	13.5170i	1.72593	+	0.628187i	0.727601	+	0.686001i	$0.240635\pi$
$464$	13.3134	−	2.18166i	0.618058	−	0.101281i
$465$	9.57559	+	5.32925i	0.444058	+	0.247138i
$466$	22.4877	+	32.3236i	1.04172	+	1.49736i
$467$	4.76538	+	2.75129i	0.220516	+	0.127315i	0.606189	−	0.795321i	$-0.292698\pi$
$467$	4.76538	+	2.75129i	0.220516	+	0.127315i	−0.385673	+	0.922635i	$0.626031\pi$
$468$	4.01512	+	19.8105i	0.185599	+	0.915740i
$469$	−18.6664	+	10.7771i	−0.861935	+	0.497638i
$470$	−7.95225	−	3.73754i	−0.366810	−	0.172400i
$471$	−13.5577	−	2.17109i	−0.624707	−	0.100039i
$472$	−10.8443	−	7.74092i	−0.499148	−	0.356305i
$473$	−4.51059	−	25.5808i	−0.207397	−	1.17621i
$474$	1.23783	+	1.72081i	0.0568556	+	0.0790394i
$475$	19.8305	−	23.6331i	0.909887	−	1.08436i
$476$	34.2705	+	20.0637i	1.57079	+	0.919616i
$477$	−5.80532	−	0.836130i	−0.265807	−	0.0382838i
$478$	5.65297	+	1.53306i	0.258561	+	0.0701206i
$479$	−15.7910	+	5.74745i	−0.721508	+	0.262608i	−0.676566	−	0.736382i	$-0.736533\pi$
$479$	−15.7910	+	5.74745i	−0.721508	+	0.262608i	−0.0449423	+	0.998990i	$0.514310\pi$
$480$	7.48747	−	2.01117i	0.341755	−	0.0917967i
$481$	−10.6215	+	8.91253i	−0.484301	+	0.406377i
$482$	−2.41041	+	26.6229i	−0.109791	+	1.21264i
$483$	23.8935	−	20.6987i	1.08719	−	0.941824i
$484$	−6.57579	−	18.4129i	−0.298900	−	0.836949i
$485$			5.16647i			0.234597i
$486$	−19.2182	+	10.8010i	−0.871754	+	0.489945i
$487$	−6.70956			−0.304039			−0.152020	−	0.988377i	$-0.548578\pi$
$487$	−6.70956			−0.304039			−0.152020	+	0.988377i	$0.548578\pi$
$488$	8.78123	+	12.7864i	0.397508	+	0.578815i
$489$	18.4413	+	21.2876i	0.833944	+	0.962661i
$490$	9.67015	+	0.875528i	0.436853	+	0.0395523i
$491$	−19.8688	−	23.6787i	−0.896667	−	1.06861i	−0.997282	−	0.0736810i	$-0.976525\pi$
$491$	−19.8688	−	23.6787i	−0.896667	−	1.06861i	0.100615	−	0.994925i	$-0.467919\pi$
$492$	5.78513	+	3.26571i	0.260814	+	0.147230i
$493$	−5.78485	−	15.8938i	−0.260537	−	0.715819i
$494$	−32.4332	−	8.79574i	−1.45924	−	0.395739i
$495$	−1.54247	+	10.7095i	−0.0693290	+	0.481357i
$496$	31.9816	+	0.387200i	1.43601	+	0.0173858i
$497$	33.7593	+	28.3274i	1.51431	+	1.27066i
$498$	0.0988476	−	0.0711042i	0.00442947	−	0.00318626i
$499$	13.9388	−	2.45779i	0.623986	−	0.110026i	0.147289	−	0.989093i	$-0.452945\pi$
$499$	13.9388	−	2.45779i	0.623986	−	0.110026i	0.476697	+	0.879068i	$0.341834\pi$
$500$	11.4215	−	9.46655i	0.510785	−	0.423357i
$501$	−3.30666	+	20.6490i	−0.147731	+	0.922528i
$502$	−4.05601	−	1.90631i	−0.181029	−	0.0850830i
$503$	9.87132	+	17.0976i	0.440140	+	0.762346i	0.997699	−	0.0677917i	$-0.0215953\pi$
$503$	9.87132	+	17.0976i	0.440140	+	0.762346i	−0.557559	+	0.830137i	$0.688262\pi$
$504$	14.8773	+	30.1231i	0.662686	+	1.34179i
$505$	−1.91914	+	3.32404i	−0.0854004	+	0.147918i
$506$	24.3917	−	16.9695i	1.08434	−	0.754385i
$507$	−1.39035	+	2.49817i	−0.0617475	+	0.110948i
$508$	12.2428	−	33.0136i	0.543186	−	1.46474i
$509$	−11.0783	+	30.4374i	−0.491037	+	1.34911i	0.408696	+	0.912671i	$0.365984\pi$
$509$	−11.0783	+	30.4374i	−0.491037	+	1.34911i	−0.899733	+	0.436442i	$0.856239\pi$
$510$	−4.21949	−	8.75625i	−0.186842	−	0.387733i
$511$	1.81733	−	10.3066i	0.0803939	−	0.455936i
$512$	16.4298	−	15.5583i	0.726103	−	0.687586i
$513$	−1.73045	−	36.6097i	−0.0764013	−	1.61636i
$514$	−1.67502	−	6.32780i	−0.0738819	−	0.279107i
$515$	2.94363	+	0.519041i	0.129712	+	0.0228717i
$516$	3.61626	+	19.4071i	0.159197	+	0.854352i
$517$	12.2411	−	33.6321i	0.538362	−	1.47914i
$518$	−13.2756	+	18.8380i	−0.583298	+	0.827693i
$519$	0.0896241	+	5.69208i	0.00393406	+	0.249854i
$520$	−6.80413	−	3.24835i	−0.298381	−	0.142450i
$521$	−3.03183	+	5.25129i	−0.132827	+	0.230063i	−0.924765	−	0.380538i	$-0.875739\pi$
$521$	−3.03183	+	5.25129i	−0.132827	+	0.230063i	0.791938	+	0.610601i	$0.209072\pi$
$522$	3.30868	−	13.9215i	0.144817	−	0.609329i
$523$	−36.4139	+	21.0236i	−1.59227	+	0.919298i	−0.599354	+	0.800484i	$0.704576\pi$
$523$	−36.4139	+	21.0236i	−1.59227	+	0.919298i	−0.992917	+	0.118814i	$0.962091\pi$
$524$	3.76737	−	20.6346i	0.164578	−	0.901427i
$525$	23.2787	+	18.9167i	1.01597	+	0.825592i
$526$	22.0393	−	10.1960i	0.960958	−	0.444566i
$527$	−6.96306	−	39.4895i	−0.303316	−	1.72019i
$528$	10.9086	+	29.6352i	0.474736	+	1.28971i
$529$	−1.34164	−	1.12577i	−0.0583322	−	0.0489465i
$530$	1.55167	−	1.54231i	0.0674004	−	0.0669936i
$531$	−12.0100	+	7.44775i	−0.521192	+	0.323205i
$532$	−55.8536	−	0.338097i	−2.42156	−	0.0146584i
$533$	−2.20967	−	6.07101i	−0.0957113	−	0.262965i
$534$	2.86209	+	10.1627i	0.123855	+	0.439783i
$535$	−3.90559	+	3.27718i	−0.168853	+	0.141685i
$536$	14.0132	−	6.38022i	0.605279	−	0.275583i
$537$	−4.86699	+	14.0567i	−0.210026	+	0.606591i
$538$	0.287006	+	3.39895i	0.0123737	+	0.146539i
$539$			39.5498i			1.70353i
$540$	1.09334	−	8.15015i	0.0470499	−	0.350727i
$541$		−	10.0195i		−	0.430773i	−0.976529	−	0.215387i	$-0.930899\pi$
$541$		−	10.0195i		−	0.430773i	0.976529	−	0.215387i	$-0.0691012\pi$
$542$	24.7683	−	2.09143i	1.06389	−	0.0898346i
$543$	−19.6600	+	3.78667i	−0.843693	+	0.162501i
$544$	−22.9891	−	16.6212i	−0.985648	−	0.712627i
$545$	1.13063	−	0.948714i	0.0484310	−	0.0406384i
$546$	8.05440	−	31.6648i	0.344697	−	1.35513i
$547$	3.01183	+	8.27494i	0.128777	+	0.353811i	0.987279	−	0.158999i	$-0.0508267\pi$
$547$	3.01183	+	8.27494i	0.128777	+	0.353811i	−0.858502	+	0.512810i	$0.828605\pi$
$548$	−0.0827547	+	13.6711i	−0.00353511	+	0.583999i
$549$	16.1044	−	3.36560i	0.687319	−	0.143640i
$550$	19.8760	+	19.9967i	0.847516	+	0.852662i
$551$	18.2237	+	15.2915i	0.776354	+	0.651438i
$552$	−18.4117	+	13.0757i	−0.783655	+	0.556541i
$553$	−0.594995	−	3.37438i	−0.0253017	−	0.143493i
$554$	9.58001	+	20.7078i	0.407016	+	0.879790i
$555$	5.26952	−	2.01245i	0.223679	−	0.0854239i
$556$	−4.13806	+	22.6649i	−0.175493	+	0.961208i
$557$	3.90866	−	2.25666i	0.165615	−	0.0956179i	−0.414901	−	0.909866i	$-0.636184\pi$
$557$	3.90866	−	2.25666i	0.165615	−	0.0956179i	0.580517	+	0.814248i	$0.302851\pi$
$558$	13.4562	−	31.1412i	0.569645	−	1.31831i
$559$	9.59927	−	16.6264i	0.406006	−	0.703223i
$560$	−12.3143	−	2.32539i	−0.520372	−	0.0982656i
$561$	33.9711	−	20.3330i	1.43426	−	0.858459i
$562$	−10.6184	−	7.48310i	−0.447911	−	0.315655i
$563$	−5.14318	+	14.1308i	−0.216759	+	0.595541i	−0.999646	−	0.0266239i	$-0.991524\pi$
$563$	−5.14318	+	14.1308i	−0.216759	+	0.595541i	0.782886	+	0.622165i	$0.213747\pi$
$564$	−9.05502	+	25.6492i	−0.381285	+	1.08002i
$565$	4.10631	+	0.724053i	0.172754	+	0.0304611i
$566$	−0.0157335	+	0.00416479i	−0.000661329	+	0.000175059i
$567$	35.5640	−	2.24266i	1.49355	−	0.0941829i
$568$	−22.0577	−	22.4619i	−0.925520	−	0.942482i
$569$	4.81063	−	27.2824i	0.201672	−	1.14374i	−0.700919	−	0.713241i	$-0.747227\pi$
$569$	4.81063	−	27.2824i	0.201672	−	1.14374i	0.902591	−	0.430499i	$-0.141662\pi$
$570$	11.2975	+	7.69834i	0.473199	+	0.322448i
$571$	−13.0209	+	35.7745i	−0.544906	+	1.49712i	0.295598	+	0.955312i	$0.404481\pi$
$571$	−13.0209	+	35.7745i	−0.544906	+	1.49712i	−0.840504	+	0.541805i	$0.817741\pi$
$572$	10.6783	−	28.7949i	0.446483	−	1.20398i
$573$	−20.5735	−	34.3730i	−0.859469	−	1.43595i
$574$	−6.13257	−	8.81488i	−0.255968	−	0.367926i
$575$	−10.0810	+	17.4608i	−0.420406	+	0.728164i
$576$	−8.50834	−	22.4412i	−0.354514	−	0.935051i
$577$	−5.45660	−	9.45110i	−0.227161	−	0.393454i	0.729805	−	0.683656i	$-0.239611\pi$
$577$	−5.45660	−	9.45110i	−0.227161	−	0.393454i	−0.956966	+	0.290201i	$0.906278\pi$
$578$	−4.90188	+	10.4296i	−0.203891	+	0.433814i
$579$	4.26900	−	1.63035i	0.177414	−	0.0677550i
$580$	3.40607	+	4.10947i	0.141430	+	0.170636i
$581$	−0.193833	+	0.0341780i	−0.00804154	+	0.00141794i
$582$	15.9136	−	1.59643i	0.659640	−	0.0661741i
$583$	6.82649	+	5.72810i	0.282724	+	0.237234i
$584$	−2.00046	+	7.20354i	−0.0827796	+	0.298085i
$585$	−5.96127	+	5.33077i	−0.246468	+	0.220400i
$586$	−5.64119	+	20.8012i	−0.233035	+	0.859289i
$587$	−15.6970	−	43.1271i	−0.647883	−	1.78004i	−0.625409	−	0.780297i	$-0.715068\pi$
$587$	−15.6970	−	43.1271i	−0.647883	−	1.78004i	−0.0224745	−	0.999747i	$-0.507154\pi$
$588$	−0.291282	−	30.0562i	−0.0120122	−	1.23950i
$589$	36.2525	+	43.2041i	1.49376	+	1.78019i
$590$	0.475318	−	5.24986i	0.0195686	−	0.216133i
$591$	−27.2940	+	5.25702i	−1.12273	+	0.216245i
$592$	10.7341	−	12.4823i	0.441168	−	0.513021i
$593$	−15.2625			−0.626755			−0.313378	−	0.949629i	$-0.601461\pi$
$593$	−15.2625			−0.626755			−0.313378	+	0.949629i	$0.601461\pi$
$594$	33.4637	+	1.44186i	1.37303	+	0.0591604i
$595$			15.7114i			0.644105i
$596$	20.4925	−	7.31850i	0.839407	−	0.299777i
$597$	31.5006	+	10.9068i	1.28924	+	0.446386i
$598$	21.8722	+	1.98030i	0.894422	+	0.0809803i
$599$	−0.191609	+	0.160779i	−0.00782893	+	0.00656925i	−0.646694	−	0.762750i	$-0.723849\pi$
$599$	−0.191609	+	0.160779i	−0.00782893	+	0.00656925i	0.638865	+	0.769319i	$0.279404\pi$
$600$	−15.2522	−	15.0503i	−0.622669	−	0.614425i
$601$	40.8905	−	14.8829i	1.66796	−	0.607087i	0.676374	−	0.736559i	$-0.263550\pi$
$601$	40.8905	−	14.8829i	1.66796	−	0.607087i	0.991583	+	0.129472i	$0.0413282\pi$
$602$	8.35218	−	30.7976i	0.340410	−	1.25522i
$603$	−0.514160	−	16.3232i	−0.0209382	−	0.664734i
$604$	−30.8479	−	18.0599i	−1.25518	−	0.734847i
$605$	4.97224	−	5.92569i	0.202150	−	0.240913i
$606$	10.8316	+	4.88414i	0.440004	+	0.198405i
$607$	−4.64267	−	26.3299i	−0.188440	−	1.06870i	−0.921455	−	0.388485i	$-0.872999\pi$
$607$	−4.64267	−	26.3299i	−0.188440	−	1.06870i	0.733015	−	0.680213i	$-0.238113\pi$
$608$	39.6911	+	4.07862i	1.60969	+	0.165410i
$609$	−14.5868	+	17.9504i	−0.591087	+	0.727386i
$610$	−2.61038	+	5.55403i	−0.105691	+	0.224876i
$611$	22.9089	−	13.2265i	0.926794	−	0.535085i
$612$	−25.6669	+	15.7024i	−1.03752	+	0.634732i
$613$	20.7249	+	11.9655i	0.837070	+	0.483283i	0.856267	−	0.516533i	$-0.172778\pi$
$613$	20.7249	+	11.9655i	0.837070	+	0.483283i	−0.0191971	+	0.999816i	$0.506111\pi$
$614$	18.1894	−	12.6545i	0.734065	−	0.510694i
$615$	0.0413787	+	2.62799i	0.00166855	+	0.105971i
$616$	4.91041	−	50.8085i	0.197846	−	2.04713i
$617$	7.04370	+	2.56370i	0.283569	+	0.103210i	0.479889	−	0.877329i	$-0.340677\pi$
$617$	7.04370	+	2.56370i	0.283569	+	0.103210i	−0.196320	+	0.980540i	$0.562899\pi$
$618$	0.689159	−	9.22726i	0.0277221	−	0.371175i
$619$	−14.0173	−	2.47163i	−0.563402	−	0.0993430i	−0.115309	−	0.993330i	$-0.536786\pi$
$619$	−14.0173	−	2.47163i	−0.563402	−	0.0993430i	−0.448094	+	0.893987i	$0.647897\pi$
$620$	6.26055	+	10.9968i	0.251430	+	0.441642i
$621$	5.26836	+	23.3657i	0.211412	+	0.937634i
$622$	11.7561	+	44.4118i	0.471378	+	1.78075i
$623$	2.96352	−	16.8069i	0.118731	−	0.673356i
$624$	−7.90301	+	21.9616i	−0.316374	+	0.879167i
$625$	−15.0354	−	5.47243i	−0.601415	−	0.218897i
$626$	14.6964	+	10.3569i	0.587385	+	0.413946i
$627$	−27.0800	+	48.6572i	−1.08147	+	1.94318i
$628$	−12.0834	−	10.2645i	−0.482180	−	0.409596i
$629$	−17.8746	−	10.3199i	−0.712708	−	0.411482i
$630$	−7.31108	+	11.1008i	−0.291280	+	0.442266i
$631$	−22.2070	−	38.4637i	−0.884048	−	1.53122i	−0.846801	−	0.531910i	$-0.821474\pi$
$631$	−22.2070	−	38.4637i	−0.884048	−	1.53122i	−0.0372471	−	0.999306i	$-0.511859\pi$
$632$	0.191182	+	2.44022i	0.00760483	+	0.0970668i
$633$	−37.1180	−	5.94397i	−1.47531	−	0.236251i
$634$	−11.4220	−	24.6894i	−0.453626	−	0.980541i
$635$	13.7190	−	2.41903i	0.544421	−	0.0959961i
$636$	−5.23004	−	4.30284i	−0.207384	−	0.170619i
$637$	−18.7896	+	22.3926i	−0.744471	+	0.887226i
$638$	−15.4196	+	15.3265i	−0.610468	+	0.606783i
$639$	−31.0023	+	12.4026i	−1.22643	+	0.490640i
$640$	8.59617	+	2.49968i	0.339794	+	0.0988084i
$641$	−34.2487	+	12.4655i	−1.35274	+	0.492359i	−0.913803	−	0.406157i	$-0.866868\pi$
$641$	−34.2487	+	12.4655i	−1.35274	+	0.492359i	−0.438941	+	0.898516i	$0.644646\pi$
$642$	11.3011	+	11.0172i	0.446018	+	0.434816i
$643$	−12.8834	−	15.3538i	−0.508072	−	0.605496i	0.449646	−	0.893207i	$-0.351550\pi$
$643$	−12.8834	−	15.3538i	−0.508072	−	0.605496i	−0.957717	+	0.287711i	$0.907106\pi$
$644$	35.9859	−	6.12092i	1.41804	−	0.241198i
$645$	−5.90329	+	5.11396i	−0.232442	+	0.201362i
$646$	−4.20898	−	49.8460i	−0.165600	−	1.96116i
$647$	24.2273			0.952475			0.476238	−	0.879317i	$-0.342000\pi$
$647$	24.2273			0.952475			0.476238	+	0.879317i	$0.342000\pi$
$648$	−25.4417	−	0.849299i	−0.999443	−	0.0333636i
$649$	21.4713			0.842824
$650$	1.75336	+	20.7647i	0.0687726	+	0.814458i
$651$	−41.4463	+	35.9046i	−1.62441	+	1.40721i
$652$	5.45336	+	32.0612i	0.213570	+	1.25561i
$653$	18.5592	+	22.1180i	0.726277	+	0.865543i	0.995225	−	0.0976117i	$-0.0311203\pi$
$653$	18.5592	+	22.1180i	0.726277	+	0.865543i	−0.268948	+	0.963155i	$0.586676\pi$
$654$	−3.27156	−	3.18939i	−0.127928	−	0.124715i
$655$	7.79829	−	2.83834i	0.304704	−	0.110903i
$656$	3.75477	+	6.68919i	0.146599	+	0.261169i
$657$	6.23193	+	4.90331i	0.243131	+	0.191297i
$658$	31.1837	−	30.9956i	1.21567	−	1.20833i
$659$	12.4603	−	14.8496i	0.485384	−	0.578458i	−0.466653	−	0.884440i	$-0.654540\pi$
$659$	12.4603	−	14.8496i	0.485384	−	0.578458i	0.952037	+	0.305982i	$0.0989848\pi$
$660$	−7.93779	+	9.64825i	−0.308978	+	0.375558i
$661$	−0.820430	+	0.144664i	−0.0319110	+	0.00562677i	−0.189581	−	0.981865i	$-0.560713\pi$
$661$	−0.820430	+	0.144664i	−0.0319110	+	0.00562677i	0.157670	+	0.987492i	$0.449602\pi$
$662$	−1.91381	−	4.13683i	−0.0743825	−	0.160783i
$663$	28.8939	+	4.62698i	1.12215	+	0.179697i
$664$	0.140172	−	0.0109820i	0.00543974	−	0.000426184i
$665$	−11.0491	−	19.1376i	−0.428465	−	0.742123i
$666$	−7.82697	−	15.6092i	−0.303289	−	0.604843i
$667$	−13.4641	−	7.77352i	−0.521333	−	0.300992i
$668$	−15.6332	+	18.4035i	−0.604866	+	0.712053i
$669$	−5.14348	+	9.24179i	−0.198858	+	0.357308i
$670$	4.97947	+	3.50917i	0.192374	+	0.135571i
$671$	−23.4894	−	8.54944i	−0.906798	−	0.330047i
$672$	−3.35751	+	38.6485i	−0.129519	+	1.49090i
$673$	4.69264	−	26.6133i	0.180888	−	1.02587i	−0.750238	−	0.661168i	$-0.770061\pi$
$673$	4.69264	−	26.6133i	0.180888	−	1.02587i	0.931126	−	0.364698i	$-0.118828\pi$
$674$	−10.6530	−	40.2443i	−0.410337	−	1.55015i
$675$	−20.9659	+	8.77291i	−0.806979	+	0.337669i
$676$	−2.86895	+	1.63331i	−0.110344	+	0.0628197i
$677$	−3.65534	−	0.644536i	−0.140486	−	0.0247715i	0.102963	−	0.994685i	$-0.467168\pi$
$677$	−3.65534	−	0.644536i	−0.140486	−	0.0247715i	−0.243449	+	0.969914i	$0.578279\pi$
$678$	0.961364	−	12.8718i	0.0369210	−	0.494340i
$679$	−24.2931	−	8.84197i	−0.932284	−	0.339324i
$680$	1.07967	−	11.1715i	0.0414036	−	0.428407i
$681$	0.789435	+	50.1374i	0.0302512	+	1.92127i
$682$	−42.3105	+	29.4357i	−1.62015	+	1.12715i
$683$	9.79814	+	5.65696i	0.374916	+	0.216458i	0.675604	−	0.737265i	$-0.263883\pi$
$683$	9.79814	+	5.65696i	0.374916	+	0.216458i	−0.300688	+	0.953722i	$0.597216\pi$
$684$	20.2213	−	37.1769i	0.773180	−	1.42149i
$685$	−4.68423	+	2.70444i	−0.178975	+	0.103331i
$686$	−3.99399	+	8.49789i	−0.152491	+	0.324451i
$687$	−14.0453	+	17.2840i	−0.535862	+	0.659426i
$688$	−8.05515	+	21.3245i	−0.307100	+	0.812989i
$689$	1.14372	+	6.48634i	0.0435722	+	0.247110i
$690$	−8.14472	−	3.67258i	−0.310064	−	0.139813i
$691$	19.6465	−	23.4138i	0.747388	−	0.890703i	−0.249592	−	0.968351i	$-0.580297\pi$
$691$	19.6465	−	23.4138i	0.747388	−	0.890703i	0.996981	+	0.0776481i	$0.0247411\pi$
$692$	−3.32113	+	5.67278i	−0.126250	+	0.215647i
$693$	−47.7171	−	25.5812i	−1.81262	−	0.971750i
$694$	0.733717	−	2.70549i	0.0278515	−	0.102699i
$695$	−8.56559	+	3.11762i	−0.324912	+	0.118258i
$696$	11.6054	−	11.7611i	0.439901	−	0.445803i
$697$	7.36719	−	6.18180i	0.279052	−	0.234153i
$698$	44.8548	+	4.06112i	1.69778	+	0.153716i
$699$	45.5719	+	15.7788i	1.72369	+	0.596810i
$700$	11.6490	+	32.6183i	0.440290	+	1.23286i
$701$		−	17.0117i		−	0.642524i	−0.946990	−	0.321262i	$-0.895893\pi$
$701$		−	17.0117i		−	0.642524i	0.946990	−	0.321262i	$-0.104107\pi$
$702$	18.2617	+	16.7145i	0.689243	+	0.630849i
$703$	29.0300			1.09489
$704$	−6.98303	+	35.7896i	−0.263183	+	1.34887i
$705$	−10.5673	+	2.03534i	−0.397989	+	0.0766555i
$706$	4.59488	−	50.7501i	0.172930	−	1.91000i
$707$	−12.3454	−	14.7127i	−0.464298	−	0.553329i
$708$	−16.3173	+	0.158135i	−0.613243	+	0.00594307i
$709$	−0.200362	−	0.550490i	−0.00752475	−	0.0206741i	0.935873	−	0.352336i	$-0.114613\pi$
$709$	−0.200362	−	0.550490i	−0.00752475	−	0.0206741i	−0.943398	+	0.331662i	$0.892391\pi$
$710$	3.26004	−	12.0210i	0.122347	−	0.451140i
$711$	2.46635	+	0.810698i	0.0924955	+	0.0304036i
$712$	−3.26215	+	11.7468i	−0.122254	+	0.440231i
$713$	−28.2352	−	23.6921i	−1.05742	−	0.887277i
$714$	48.3938	−	4.85479i	1.81109	−	0.181686i
$715$	11.9659	−	2.10990i	0.447498	−	0.0789059i
$716$	−13.2247	+	10.9611i	−0.494229	+	0.409635i
$717$	6.70145	−	2.55931i	0.250270	−	0.0955792i
$718$	9.72161	−	20.6844i	0.362807	−	0.771934i
$719$	−20.6296	−	35.7316i	−0.769356	−	1.33256i	−0.937913	−	0.346872i	$-0.887244\pi$
$719$	−20.6296	−	35.7316i	−0.769356	−	1.33256i	0.168557	−	0.985692i	$-0.446089\pi$
$720$	5.96133	−	7.39073i	0.222166	−	0.275436i
$721$	−7.47833	+	12.9529i	−0.278508	+	0.482390i
$722$	24.8358	+	35.6986i	0.924291	+	1.32856i
$723$	16.8141	+	28.0921i	0.625324	+	1.04476i
$724$	−21.6762	−	8.03842i	−0.805591	−	0.298746i
$725$	5.04547	−	13.8623i	0.187384	−	0.514833i
$726$	−19.7885	−	13.4843i	−0.734421	−	0.500450i
$727$	1.56785	−	8.89170i	0.0581482	−	0.329775i	−0.941832	−	0.336084i	$-0.890897\pi$
$727$	1.56785	−	8.89170i	0.0581482	−	0.329775i	0.999980	+	0.00630954i	$0.00200840\pi$
$728$	26.9186	−	26.4342i	0.997671	−	0.979717i
$729$	−11.2343	+	24.5518i	−0.416084	+	0.909326i
$730$	−2.85936	+	0.756895i	−0.105830	+	0.0280139i
$731$	28.1444	+	4.96262i	1.04096	+	0.183549i
$732$	17.9139	+	6.32422i	0.662118	+	0.233750i
$733$	−4.19617	+	11.5289i	−0.154989	+	0.425829i	−0.992748	−	0.120211i	$-0.961643\pi$
$733$	−4.19617	+	11.5289i	−0.154989	+	0.425829i	0.837759	+	0.546040i	$0.183865\pi$
$734$	−23.7100	−	16.7091i	−0.875152	−	0.616744i
$735$	10.2038	−	6.10736i	0.376373	−	0.225273i
$736$	−26.0081	+	1.87932i	−0.958673	+	0.0692726i
$737$	−12.4065	+	21.4888i	−0.457001	+	0.791548i
$738$	8.08185	−	0.939495i	0.297497	−	0.0345833i
$739$	0.280828	−	0.162136i	0.0103304	−	0.00596427i	−0.494826	−	0.868992i	$-0.664768\pi$
$739$	0.280828	−	0.162136i	0.0103304	−	0.00596427i	0.505156	+	0.863028i	$0.331435\pi$
$740$	6.40744	+	1.16984i	0.235542	+	0.0430041i
$741$	−38.4487	+	14.6837i	−1.41245	+	0.539420i
$742$	4.59649	+	9.93560i	0.168742	+	0.364748i
$743$	2.52359	+	14.3120i	0.0925816	+	0.525056i	0.995462	+	0.0951637i	$0.0303374\pi$
$743$	2.52359	+	14.3120i	0.0925816	+	0.525056i	−0.902880	+	0.429893i	$0.858551\pi$
$744$	31.9375	−	22.6815i	1.17088	−	0.831546i
$745$	6.59497	+	5.53383i	0.241621	+	0.202744i
$746$	26.0674	+	26.2257i	0.954396	+	0.960190i
$747$	0.0465685	−	0.141673i	0.00170385	−	0.00518356i
$748$	45.7152	+	0.276727i	1.67151	+	0.0101181i
$749$	−8.72545	−	23.9730i	−0.318821	−	0.875954i
$750$	4.47882	−	17.6079i	0.163544	−	0.642950i
$751$	29.4541	−	24.7149i	1.07480	−	0.901861i	0.0793178	−	0.996849i	$-0.474726\pi$
$751$	29.4541	−	24.7149i	1.07480	−	0.901861i	0.995478	+	0.0949883i	$0.0302814\pi$
$752$	−24.3030	+	19.8963i	−0.886239	+	0.725542i
$753$	−5.38982	+	1.03812i	−0.196416	+	0.0378311i
$754$	−16.0118	+	1.35203i	−0.583115	+	0.0492381i
$755$		−	14.1423i		−	0.514692i
$756$	36.4514	+	19.0892i	1.32572	+	0.694269i
$757$			18.0723i			0.656850i	0.944530	+	0.328425i	$0.106518\pi$
$757$			18.0723i			0.656850i	−0.944530	+	0.328425i	$0.893482\pi$
$758$	−0.831806	−	9.85089i	−0.0302125	−	0.357800i
$759$	11.9069	−	34.3890i	0.432192	−	1.24824i
$760$	6.54126	+	14.3669i	0.237276	+	0.521143i
$761$	−28.4100	+	23.8388i	−1.02986	+	0.864157i	−0.990835	−	0.135081i	$-0.956870\pi$
$761$	−28.4100	+	23.8388i	−1.02986	+	0.864157i	−0.0390275	+	0.999238i	$0.512426\pi$
$762$	−11.6901	−	41.5093i	−0.423489	−	1.50372i
$763$	2.52594	+	6.93996i	0.0914451	+	0.251243i
$764$	0.280000	−	46.2559i	0.0101300	−	1.67348i
$765$	−10.4918	−	5.62466i	−0.379331	−	0.203360i
$766$	−10.2728	+	10.2108i	−0.371171	+	0.368931i
$767$	12.1568	+	10.2007i	0.438956	+	0.368328i
$768$	5.04323	−	27.2501i	0.181982	−	0.983302i
$769$	3.69811	+	20.9730i	0.133357	+	0.756307i	0.975989	+	0.217818i	$0.0698938\pi$
$769$	3.69811	+	20.9730i	0.133357	+	0.756307i	−0.842632	+	0.538490i	$0.818995\pi$
$770$	18.3290	−	8.47950i	0.660530	−	0.305580i
$771$	−6.22164	−	5.05582i	−0.224067	−	0.182081i
$772$	5.19086	+	0.947722i	0.186823	+	0.0341093i
$773$	21.7593	−	12.5627i	0.782627	−	0.451850i	−0.0547332	−	0.998501i	$-0.517431\pi$
$773$	21.7593	−	12.5627i	0.782627	−	0.451850i	0.837361	+	0.546651i	$0.184097\pi$
$774$	17.5760	+	16.6029i	0.631755	+	0.596780i
$775$	17.4867	−	30.2879i	0.628142	−	1.08797i
$776$	16.6658	+	7.95643i	0.598269	+	0.285619i
$777$	0.444364	+	28.2218i	0.0159415	+	1.01245i
$778$	−9.13648	+	12.9646i	−0.327559	+	0.464802i
$779$	−4.62637	+	12.7109i	−0.165757	+	0.455414i
$780$	−9.07802	+	1.69157i	−0.325045	+	0.0605678i
$781$	49.9621	+	8.80967i	1.78779	+	0.315235i
$782$	8.36564	+	31.6033i	0.299155	+	1.13013i
$783$	−6.76485	−	16.1670i	−0.241756	−	0.577761i
$784$	17.7164	−	29.8454i	0.632728	−	1.06591i
$785$	1.08923	−	6.17736i	0.0388764	−	0.220479i
$786$	−11.1522	−	23.1430i	−0.397787	−	0.825483i
$787$	−15.0107	+	41.2415i	−0.535074	+	1.47010i	0.317888	+	0.948128i	$0.397026\pi$
$787$	−15.0107	+	41.2415i	−0.535074	+	1.47010i	−0.852961	+	0.521974i	$0.825196\pi$
$788$	−30.0931	−	11.1597i	−1.07202	−	0.397549i
$789$	14.4632	−	25.9875i	0.514904	−	0.925178i
$790$	−0.794944	+	0.553048i	−0.0282828	+	0.0196766i
$791$	−10.4321	+	18.0690i	−0.370924	+	0.642459i
$792$	32.1710	+	21.4684i	1.14315	+	0.762848i
$793$	−9.23765	−	16.0001i	−0.328038	−	0.568179i
$794$	−5.90184	−	2.77385i	−0.209448	−	0.0984402i
$795$	0.423686	−	2.64577i	0.0150266	−	0.0938358i
$796$	24.5635	+	29.6361i	0.870630	+	1.05042i
$797$	−45.5449	+	8.03080i	−1.61328	+	0.284466i	−0.906259	−	0.422723i	$-0.861074\pi$
$797$	−45.5449	+	8.03080i	−1.61328	+	0.284466i	−0.707025	+	0.707188i	$0.749963\pi$
$798$	−55.5328	+	39.9465i	−1.96584	+	1.41409i
$799$	30.1648	+	25.3113i	1.06715	+	0.895448i
$800$	−6.04143	−	23.9935i	−0.213597	−	0.848299i
$801$	10.1624	+	7.99584i	0.359071	+	0.282519i
$802$	20.8772	+	5.66181i	0.737200	+	0.199926i
$803$	−4.12064	−	11.3214i	−0.145414	−	0.399523i
$804$	9.27019	−	16.4219i	0.326934	−	0.579157i
$805$	9.28303	+	11.0631i	0.327184	+	0.389922i
$806$	−37.9402	−	3.43507i	−1.33639	−	0.120995i
$807$	2.73540	+	3.15760i	0.0962905	+	0.111153i
$808$	7.76710	+	11.3098i	0.273246	+	0.397876i
$809$	16.8816			0.593524			0.296762	−	0.954951i	$-0.404093\pi$
$809$	16.8816			0.593524			0.296762	+	0.954951i	$0.404093\pi$
$810$	−4.79553	−	8.85626i	−0.168498	−	0.311177i
$811$		−	30.5802i		−	1.07382i	−0.843640	−	0.536909i	$-0.819592\pi$
$811$		−	30.5802i		−	1.07382i	0.843640	−	0.536909i	$-0.180408\pi$
$812$	−25.1522	+	8.98261i	−0.882669	+	0.315228i
$813$	23.0096	−	19.9330i	0.806982	−	0.699081i
$814$	−2.39225	+	26.4223i	−0.0838485	+	0.926101i
$815$	−9.85652	+	8.27060i	−0.345259	+	0.289707i
$816$	−34.7437	+	0.126388i	−1.21627	+	0.00442448i
$817$	−37.7718	+	13.7478i	−1.32147	+	0.480975i
$818$	1.37041	+	0.371650i	0.0479154	+	0.0129945i
$819$	−14.8634	−	37.1535i	−0.519371	−	1.29825i
$820$	−1.53334	+	2.61908i	−0.0535465	+	0.0914622i
$821$	−24.4506	+	29.1391i	−0.853332	+	1.01696i	0.146284	+	0.989243i	$0.453269\pi$
$821$	−24.4506	+	29.1391i	−0.853332	+	1.01696i	−0.999616	+	0.0277185i	$0.991176\pi$
$822$	9.77754	+	13.5925i	0.341031	+	0.474094i
$823$	4.64180	+	26.3249i	0.161803	+	0.917629i	0.952300	+	0.305164i	$0.0987112\pi$
$823$	4.64180	+	26.3249i	0.161803	+	0.917629i	−0.790497	+	0.612466i	$0.790178\pi$
$824$	6.20753	−	8.69614i	0.216250	−	0.302944i
$825$	34.0965	+	5.46011i	1.18709	+	0.190097i
$826$	23.8717	+	11.2197i	0.830604	+	0.390382i
$827$	42.2208	−	24.3762i	1.46816	−	0.847643i	0.468797	−	0.883306i	$-0.344687\pi$
$827$	42.2208	−	24.3762i	1.46816	−	0.847643i	0.999364	+	0.0356625i	$0.0113541\pi$
$828$	−8.79546	+	26.2219i	−0.305663	+	0.911275i
$829$	−10.2346	−	5.90895i	−0.355462	−	0.205226i	0.311626	−	0.950205i	$-0.399126\pi$
$829$	−10.2346	−	5.90895i	−0.355462	−	0.205226i	−0.667088	+	0.744979i	$0.732460\pi$
$830$	0.0317684	+	0.0456636i	0.00110270	+	0.00158501i
$831$	24.4175	+	13.5894i	0.847032	+	0.471412i
$832$	−20.9569	+	16.9460i	−0.726549	+	0.587498i
$833$	−40.8892	−	14.8824i	−1.41673	−	0.515646i
$834$	12.2496	+	25.4201i	0.424167	+	0.880227i
$835$	−9.40837	−	1.65895i	−0.325590	−	0.0574103i
$836$	−55.8788	+	31.8122i	−1.93261	+	1.10025i
$837$	−9.13863	−	40.5308i	−0.315877	−	1.40095i
$838$	32.8165	−	8.68680i	1.13363	−	0.300080i
$839$	6.08118	−	34.4881i	0.209946	−	1.19066i	−0.679520	−	0.733657i	$-0.737812\pi$
$839$	6.08118	−	34.4881i	0.209946	−	1.19066i	0.889465	−	0.457003i	$-0.151077\pi$
$840$	−13.8668	+	6.57906i	−0.478451	+	0.226999i
$841$	−16.5618	−	6.02799i	−0.571095	−	0.207862i
$842$	−5.50170	+	7.80685i	−0.189601	+	0.269042i
$843$	−15.9078	+	0.250475i	−0.547894	+	0.00862683i
$844$	−33.0816	−	28.1018i	−1.13872	−	0.967303i
$845$	−1.13113	−	0.653058i	−0.0389120	−	0.0224659i
$846$	9.53449	+	31.9203i	0.327802	+	1.09744i
$847$	19.3534	+	33.5211i	0.664992	+	1.15180i
$848$	−2.58554	−	7.38051i	−0.0887877	−	0.253448i
$849$	−0.0125708	+	0.0154696i	−0.000431430	+	0.000530914i
$850$	−28.1532	+	13.0244i	−0.965645	+	0.446735i
$851$	−18.6838	+	3.29446i	−0.640472	+	0.112932i
$852$	−38.0340	−	6.32702i	−1.30302	−	0.216760i
$853$	37.0236	−	44.1231i	1.26767	−	1.51074i	0.506410	−	0.862293i	$-0.330972\pi$
$853$	37.0236	−	44.1231i	1.26767	−	1.51074i	0.761255	−	0.648452i	$-0.224583\pi$
$854$	−21.6480	−	21.7794i	−0.740779	−	0.745276i
$855$	16.7352	−	0.527138i	0.572333	−	0.0180277i
$856$	4.55677	+	17.6454i	0.155747	+	0.603109i
$857$	40.8515	−	14.8687i	1.39546	−	0.507906i	0.468634	−	0.883393i	$-0.344746\pi$
$857$	40.8515	−	14.8687i	1.39546	−	0.507906i	0.926828	+	0.375486i	$0.122524\pi$
$858$	−10.1963	−	36.2049i	−0.348095	−	1.23602i
$859$	−2.97958	−	3.55093i	−0.101662	−	0.121156i	0.712814	−	0.701353i	$-0.247420\pi$
$859$	−2.97958	−	3.55093i	−0.101662	−	0.121156i	−0.814476	+	0.580197i	$0.802976\pi$
$860$	−8.89091	+	1.51227i	−0.303177	+	0.0515681i
$861$	−12.4278	−	4.30300i	−0.423538	−	0.146646i
$862$	−41.1516	+	3.47483i	−1.40163	+	0.118353i
$863$	24.4317			0.831665			0.415832	−	0.909441i	$-0.363490\pi$
$863$	24.4317			0.831665			0.415832	+	0.909441i	$0.363490\pi$
$864$	−24.6067	−	16.0782i	−0.837138	−	0.546991i
$865$	−2.60070			−0.0884265
$866$	−16.0227	+	1.35295i	−0.544474	+	0.0459752i
$867$	2.66941	+	13.8593i	0.0906579	+	0.470688i
$868$	−62.4221	+	10.6175i	−2.11874	+	0.360382i
$869$	−2.53548	−	3.02167i	−0.0860103	−	0.102503i
$870$	6.33535	+	1.61149i	0.214789	+	0.0546345i
$871$	−17.2334	+	6.27245i	−0.583932	+	0.212534i
$872$	−1.31914	−	5.10819i	−0.0446719	−	0.172985i
$873$	14.6014	−	13.0570i	0.494182	−	0.441914i
$874$	−32.4150	−	32.6118i	−1.09645	−	1.10311i
$875$	−18.8775	+	22.4973i	−0.638175	+	0.760547i
$876$	3.21490	+	8.57343i	0.108621	+	0.289669i
$877$	−54.5573	+	9.61992i	−1.84227	+	0.324842i	−0.982560	−	0.185944i	$-0.940466\pi$
$877$	−54.5573	+	9.61992i	−1.84227	+	0.324842i	−0.859708	+	0.510785i	$0.829355\pi$
$878$	−11.6603	+	5.39440i	−0.393517	+	0.182052i
$879$	9.41748	+	24.6593i	0.317644	+	0.831736i
$880$	−13.6154	+	4.76974i	−0.458975	+	0.160788i
$881$	8.83907	+	15.3097i	0.297796	+	0.515798i	0.975631	−	0.219416i	$-0.0704152\pi$
$881$	8.83907	+	15.3097i	0.297796	+	0.515798i	−0.677835	+	0.735214i	$0.737082\pi$
$882$	−21.9646	−	29.5423i	−0.739588	−	0.994741i
$883$	1.51759	+	0.876179i	0.0510708	+	0.0294858i	0.525318	−	0.850906i	$-0.323946\pi$
$883$	1.51759	+	0.876179i	0.0510708	+	0.0294858i	−0.474247	+	0.880392i	$0.657280\pi$
$884$	25.7518	+	21.8754i	0.866128	+	0.735748i
$885$	−3.31564	−	5.53958i	−0.111454	−	0.186211i
$886$	22.1918	−	31.4898i	0.745547	−	1.05792i
$887$	−6.07325	−	2.21048i	−0.203920	−	0.0742207i	0.238041	−	0.971255i	$-0.423495\pi$
$887$	−6.07325	−	2.21048i	−0.203920	−	0.0742207i	−0.441961	+	0.897034i	$0.645717\pi$
$888$	1.62342	−	20.0975i	0.0544783	−	0.674427i
$889$	−12.1044	+	68.6475i	−0.405969	+	2.30236i
$890$	−4.66276	+	1.23427i	−0.156296	+	0.0413728i
$891$	34.1653	−	22.7065i	1.14458	−	0.760696i
$892$	−10.6134	+	6.04231i	−0.355364	+	0.202312i
$893$	−54.5430	−	9.61740i	−1.82521	−	0.321834i
$894$	15.0073	−	22.0236i	0.501920	−	0.736578i
$895$	−6.38588	−	2.32427i	−0.213457	−	0.0776918i
$896$	−26.4653	+	36.1418i	−0.884143	+	1.20741i
$897$	23.0793	−	13.8138i	0.770595	−	0.461229i
$898$	6.20144	+	8.91388i	0.206945	+	0.297460i
$899$	23.3552	+	13.4842i	0.778941	+	0.449722i
$900$	−25.9522	−	3.89834i	−0.865072	−	0.129945i
$901$	−8.49087	+	4.90220i	−0.282872	+	0.163316i
$902$	−11.1878	−	5.25824i	−0.372513	−	0.175080i
$903$	−13.9432	−	36.5098i	−0.464002	−	1.21497i
$904$	8.65939	−	12.1309i	0.288007	−	0.403469i
$905$	−1.58829	−	9.00766i	−0.0527967	−	0.299425i
$906$	−43.5607	+	4.36995i	−1.44721	+	0.145182i
$907$	2.37017	−	2.82465i	0.0787001	−	0.0937911i	−0.725258	−	0.688478i	$-0.758279\pi$
$907$	2.37017	−	2.82465i	0.0787001	−	0.0937911i	0.803958	+	0.594686i	$0.202724\pi$
$908$	−29.2534	+	49.9675i	−0.970809	+	1.65823i
$909$	14.2445	−	2.97691i	0.472461	−	0.0987378i
$910$	14.4061	+	3.90688i	0.477558	+	0.129512i
$911$	21.2057	−	7.71823i	0.702575	−	0.255716i	0.0340652	−	0.999420i	$-0.489155\pi$
$911$	21.2057	−	7.71823i	0.702575	−	0.255716i	0.668510	+	0.743703i	$0.266932\pi$
$912$	42.2313	−	24.5875i	1.39842	−	0.814175i
$913$	−0.173572	+	0.145644i	−0.00574440	+	0.00482013i
$914$	1.56337	−	17.2673i	0.0517117	−	0.571153i
$915$	1.42153	+	7.38046i	0.0469943	+	0.243990i
$916$	−24.2185	+	8.64915i	−0.800201	+	0.285776i
$917$			41.5257i			1.37130i
$918$	−14.0830	+	34.0544i	−0.464807	+	1.12396i
$919$	−18.6829			−0.616291			−0.308145	−	0.951339i	$-0.599708\pi$
$919$	−18.6829			−0.616291			−0.308145	+	0.951339i	$0.599708\pi$
$920$	−5.84039	−	8.50425i	−0.192552	−	0.280377i
$921$	8.87921	−	25.6446i	0.292580	−	0.845019i
$922$	23.2509	+	2.10511i	0.765726	+	0.0693283i
$923$	24.1025	+	28.7243i	0.793344	+	0.945470i
$924$	−31.7819	−	53.8362i	−1.04555	−	1.77108i
$925$	−6.15697	−	16.9161i	−0.202440	−	0.556199i
$926$	53.9426	+	14.6290i	1.77266	+	0.480739i
$927$	−5.97243	−	9.63099i	−0.196160	−	0.316323i
$928$	18.5016	−	4.65859i	0.607344	−	0.152926i
$929$	28.8670	+	24.2223i	0.947094	+	0.794706i	0.978806	−	0.204791i	$-0.0656514\pi$
$929$	28.8670	+	24.2223i	0.947094	+	0.794706i	−0.0317116	+	0.999497i	$0.510096\pi$
$930$	14.1281	+	6.37056i	0.463277	+	0.208899i
$931$	60.2719	−	10.6276i	1.97533	−	0.348304i
$932$	35.5359	+	42.8745i	1.16402	+	1.40440i
$933$	43.6667	+	35.4843i	1.42958	+	1.16170i
$934$	7.04275	+	3.31008i	0.230446	+	0.108309i
$935$	9.04347	+	15.6638i	0.295753	+	0.512260i
$936$	8.01540	+	27.4391i	0.261992	+	0.896876i
$937$	9.22218	−	15.9733i	0.301275	−	0.521824i	−0.675150	−	0.737681i	$-0.735921\pi$
$937$	9.22218	−	15.9733i	0.301275	−	0.521824i	0.976425	+	0.215856i	$0.0692543\pi$
$938$	−25.0223	+	17.4082i	−0.817007	+	0.568397i
$939$	22.0171	−	0.346669i	0.718501	−	0.0113131i
$940$	−11.6510	−	4.32068i	−0.380015	−	0.140925i
$941$	−2.21353	+	6.08164i	−0.0721592	+	0.198256i	−0.970529	−	0.240984i	$-0.922530\pi$
$941$	−2.21353	+	6.08164i	−0.0721592	+	0.198256i	0.898370	+	0.439240i	$0.144752\pi$
$942$	−19.3639	−	1.44624i	−0.630909	−	0.0471209i
$943$	1.53506	−	8.70575i	0.0499884	−	0.283498i
$944$	−16.2028	−	9.61812i	−0.527358	−	0.313043i
$945$	0.768629	+	16.2613i	0.0250035	+	0.528979i
$946$	−9.40023	−	35.5117i	−0.305628	−	1.15459i
$947$	−25.1285	−	4.43083i	−0.816566	−	0.143983i	−0.250261	−	0.968178i	$-0.580516\pi$
$947$	−25.1285	−	4.43083i	−0.816566	−	0.143983i	−0.566305	+	0.824196i	$0.691627\pi$
$948$	1.94912	+	2.27767i	0.0633044	+	0.0739753i
$949$	3.04558	−	8.36767i	0.0988638	−	0.271626i
$950$	25.1330	−	35.6634i	0.815422	−	1.15707i
$951$	−29.1123	−	16.2023i	−0.944031	−	0.525396i
$952$	50.6814	+	24.1957i	1.64259	+	0.784189i
$953$	5.24734	−	9.08865i	0.169978	−	0.294410i	−0.768434	−	0.639929i	$-0.778964\pi$
$953$	5.24734	−	9.08865i	0.169978	−	0.294410i	0.938412	+	0.345519i	$0.112297\pi$
$954$	−8.28034	−	0.487486i	−0.268086	−	0.0157829i
$955$	15.8490	−	9.15044i	0.512863	−	0.296101i
$956$	8.14858	+	1.48773i	0.263544	+	0.0481165i
$957$	−4.21033	+	26.2921i	−0.136101	+	0.849902i
$958$	−21.5687	+	9.97830i	−0.696854	+	0.322384i
$959$	−4.69981	−	26.6540i	−0.151765	−	0.860702i
$960$	10.3120	−	3.72508i	0.332819	−	0.120227i
$961$	25.2301	+	21.1706i	0.813876	+	0.682923i
$962$	−13.9073	+	13.8234i	−0.448391	+	0.445685i
$963$	19.1324	+	2.75561i	0.616532	+	0.0887982i
$964$	−0.228836	+	37.8037i	−0.00737032	+	1.21758i
$965$	0.714016	+	1.96174i	0.0229850	+	0.0631508i
$966$	31.2077	−	32.0118i	1.00409	−	1.02996i
$967$	−26.6055	+	22.3246i	−0.855574	+	0.717912i	−0.961010	−	0.276514i	$-0.910821\pi$
$967$	−26.6055	+	22.3246i	−0.855574	+	0.717912i	0.105436	+	0.994426i	$0.466376\pi$
$968$	−11.4576	−	25.1649i	−0.368261	−	0.808832i
$969$	−40.1149	−	46.3065i	−1.28868	−	1.48758i
$970$	0.614770	+	7.28058i	0.0197391	+	0.233765i
$971$		−	13.9739i		−	0.448445i	−0.974538	−	0.224223i	$-0.928016\pi$
$971$		−	13.9739i		−	0.448445i	0.974538	−	0.224223i	$-0.0719843\pi$
$972$	−25.7970	+	17.5076i	−0.827438	+	0.561557i
$973$		−	45.6116i		−	1.46224i
$974$	−9.45510	+	0.798386i	−0.302961	+	0.0255819i
$975$	16.7109	+	19.2902i	0.535179	+	0.617782i
$976$	13.8960	+	16.9737i	0.444800	+	0.543316i
$977$	−11.1693	+	9.37218i	−0.357339	+	0.299843i	−0.803729	−	0.594996i	$-0.797154\pi$
$977$	−11.1693	+	9.37218i	−0.357339	+	0.299843i	0.446390	+	0.894838i	$0.352709\pi$
$978$	28.5205	+	27.8042i	0.911985	+	0.889079i
$979$	−6.71953	−	18.4618i	−0.214757	−	0.590041i
$980$	13.7313	+	0.0831196i	0.438632	+	0.00265516i
$981$	−5.53865	−	0.797723i	−0.176835	−	0.0254693i
$982$	−30.8167	−	31.0038i	−0.983401	−	0.989371i
$983$	8.62000	+	7.23304i	0.274935	+	0.230698i	0.769821	−	0.638260i	$-0.220346\pi$
$983$	8.62000	+	7.23304i	0.274935	+	0.230698i	−0.494885	+	0.868958i	$0.664790\pi$
$984$	8.54100	+	3.91365i	0.272277	+	0.124763i
$985$	−2.20502	−	12.5053i	−0.0702579	−	0.398452i
$986$	−10.0432	−	21.7091i	−0.319842	−	0.691359i
$987$	8.51475	−	53.1717i	0.271027	−	1.69247i
$988$	−46.7514	−	8.53564i	−1.48736	−	0.271555i
$989$	22.7499	−	13.1346i	0.723403	−	0.417657i
$990$	−0.899303	+	15.2754i	−0.0285817	+	0.485483i
$991$	−9.44162	+	16.3534i	−0.299923	+	0.519482i	−0.976118	−	0.217241i	$-0.930294\pi$
$991$	−9.44162	+	16.3534i	−0.299923	+	0.519482i	0.676195	+	0.736723i	$0.263628\pi$
$992$	45.1144	−	3.25992i	1.43238	−	0.103502i
$993$	−4.87792	−	2.71478i	−0.154796	−	0.0861510i
$994$	50.9443	+	35.9018i	1.61585	+	1.13874i
$995$	−5.20863	+	14.3106i	−0.165125	+	0.453676i
$996$	0.130835	−	0.111962i	0.00414567	−	0.00354765i
$997$	−29.3371	−	5.17293i	−0.929117	−	0.163828i	−0.311445	−	0.950264i	$-0.600813\pi$
$997$	−29.3371	−	5.17293i	−0.929117	−	0.163828i	−0.617672	+	0.786436i	$0.711924\pi$
$998$	19.3501	−	5.12212i	0.612516	−	0.162138i
$999$	−19.0051	−	9.80663i	−0.601293	−	0.310268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.133.33	yes	204
3.2	odd	2		648.2.t.a.397.2		204
4.3	odd	2		864.2.bf.a.241.9		204
8.3	odd	2		864.2.bf.a.241.26		204
8.5	even	2	inner	216.2.t.a.133.6	yes	204
24.5	odd	2		648.2.t.a.397.29		204
27.13	even	9	inner	216.2.t.a.13.6	✓	204
27.14	odd	18		648.2.t.a.253.29		204
108.67	odd	18		864.2.bf.a.337.26		204
216.13	even	18	inner	216.2.t.a.13.33	yes	204
216.67	odd	18		864.2.bf.a.337.9		204
216.149	odd	18		648.2.t.a.253.2		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.6	✓	204	27.13	even	9	inner
216.2.t.a.13.33	yes	204	216.13	even	18	inner
216.2.t.a.133.6	yes	204	8.5	even	2	inner
216.2.t.a.133.33	yes	204	1.1	even	1	trivial
648.2.t.a.253.2		204	216.149	odd	18
648.2.t.a.253.29		204	27.14	odd	18
648.2.t.a.397.2		204	3.2	odd	2
648.2.t.a.397.29		204	24.5	odd	2
864.2.bf.a.241.9		204	4.3	odd	2
864.2.bf.a.241.26		204	8.3	odd	2
864.2.bf.a.337.9		204	216.67	odd	18
864.2.bf.a.337.26		204	108.67	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40920 - 0.118992i) q^{2} +(1.30914 - 1.13409i) q^{3} +(1.97168 - 0.335368i) q^{4} +(0.508621 + 0.606151i) q^{5} +(1.70988 - 1.75394i) q^{6} +(-3.72062 + 1.35420i) q^{7} +(2.73858 - 0.707214i) q^{8} +(0.427672 - 2.96936i) q^{9} +(0.788875 + 0.793665i) q^{10} +(-2.92987 + 3.49168i) q^{11} +(2.20086 - 2.67511i) q^{12} +(-3.31770 + 0.585000i) q^{13} +(-5.08196 + 2.35106i) q^{14} +(1.35328 + 0.216711i) q^{15} +(3.77506 - 1.32248i) q^{16} +(-2.50743 - 4.34299i) q^{17} +(0.249344 - 4.23531i) q^{18} +(6.10844 + 3.52671i) q^{19} +(1.20612 + 1.02456i) q^{20} +(-3.33502 + 5.99236i) q^{21} +(-3.71328 + 5.26910i) q^{22} +(-4.33163 - 1.57658i) q^{23} +(2.78313 - 4.03165i) q^{24} +(0.759517 - 4.30744i) q^{25} +(-4.60569 + 1.21916i) q^{26} +(-2.80765 - 4.37231i) q^{27} +(-6.88173 + 3.91782i) q^{28} +(3.32150 + 0.585669i) q^{29} +(1.93283 + 0.144358i) q^{30} +(7.51376 + 2.73478i) q^{31} +(5.16244 - 2.31283i) q^{32} +(0.124291 + 7.89382i) q^{33} +(-4.05025 - 5.82177i) q^{34} +(-2.71323 - 1.56649i) q^{35} +(-0.152594 - 5.99806i) q^{36} +(3.56434 - 2.05787i) q^{37} +(9.02765 + 4.24297i) q^{38} +(-3.67987 + 4.52842i) q^{39} +(1.82158 + 1.30029i) q^{40} +(0.333012 + 1.88860i) q^{41} +(-3.98666 + 8.84126i) q^{42} +(-3.66311 + 4.36553i) q^{43} +(-4.60577 + 7.86706i) q^{44} +(2.01740 - 1.25104i) q^{45} +(-6.29173 - 1.70629i) q^{46} +(-7.37860 + 2.68559i) q^{47} +(3.44225 - 6.01256i) q^{48} +(6.64689 - 5.57740i) q^{49} +(0.557759 - 6.16041i) q^{50} +(-8.20791 - 2.84191i) q^{51} +(-6.34526 + 2.26608i) q^{52} -1.95507i q^{53} +(-4.47680 - 5.82737i) q^{54} -3.60667 q^{55} +(-9.23154 + 6.33986i) q^{56} +(11.9964 - 2.31059i) q^{57} +(4.75034 + 0.430092i) q^{58} +(-3.02793 - 3.60855i) q^{59} +(2.74092 - 0.0265629i) q^{60} +(1.87567 + 5.15337i) q^{61} +(10.9138 + 2.95978i) q^{62} +(2.42989 + 11.6270i) q^{63} +(6.99970 - 3.87353i) q^{64} +(-2.04205 - 1.71348i) q^{65} +(1.11445 + 11.1092i) q^{66} +(5.36107 - 0.945302i) q^{67} +(-6.40035 - 7.72209i) q^{68} +(-7.45868 + 2.84850i) q^{69} +(-4.00989 - 1.88464i) q^{70} +(-5.56518 - 9.63918i) q^{71} +(-0.928758 - 8.43430i) q^{72} +(-1.32161 + 2.28909i) q^{73} +(4.77799 - 3.32408i) q^{74} +(-3.89072 - 6.50038i) q^{75} +(13.2266 + 4.90497i) q^{76} +(6.17251 - 16.9588i) q^{77} +(-4.64683 + 6.81932i) q^{78} +(-0.150274 + 0.852245i) q^{79} +(2.72169 + 1.61561i) q^{80} +(-8.63419 - 2.53982i) q^{81} +(0.694009 + 2.62179i) q^{82} +(0.0489550 + 0.00863210i) q^{83} +(-4.56595 + 12.9335i) q^{84} +(1.35718 - 3.72882i) q^{85} +(-4.64259 + 6.58778i) q^{86} +(5.01249 - 3.00016i) q^{87} +(-5.55432 + 11.6343i) q^{88} +(-2.15515 + 3.73283i) q^{89} +(2.69406 - 2.00303i) q^{90} +(11.5517 - 6.66938i) q^{91} +(-9.06933 - 1.65583i) q^{92} +(12.9380 - 4.94109i) q^{93} +(-10.0783 + 4.66252i) q^{94} +(0.969162 + 5.49639i) q^{95} +(4.13537 - 8.88250i) q^{96} +(5.00174 + 4.19696i) q^{97} +(8.70312 - 8.65059i) q^{98} +(9.11503 + 10.1931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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