LMFDB - Embedded newform 117.2.l.b.4.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(4,117)] 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("117.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.l (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.11
Character	$\chi$	$=$	117.4
Dual form			117.2.l.b.88.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.65149i q^{2} +(-1.38481 + 1.04034i) q^{3} -5.03038 q^{4} +(2.43120 + 1.40366i) q^{5} +(-2.75846 - 3.67179i) q^{6} +(0.226187 + 0.130589i) q^{7} -8.03502i q^{8} +(0.835370 - 2.88135i) q^{9} +(-3.72178 + 6.44631i) q^{10} -1.55873i q^{11} +(6.96610 - 5.23333i) q^{12} +(-2.26304 + 2.80689i) q^{13} +(-0.346256 + 0.599733i) q^{14} +(-4.82703 + 0.585497i) q^{15} +11.2440 q^{16} +(3.65449 + 6.32976i) q^{17} +(7.63985 + 2.21497i) q^{18} +(0.447398 - 0.258305i) q^{19} +(-12.2299 - 7.06093i) q^{20} +(-0.449083 + 0.0544718i) q^{21} +4.13296 q^{22} +(-1.37475 - 2.38113i) q^{23} +(8.35919 + 11.1269i) q^{24} +(1.44050 + 2.49502i) q^{25} +(-7.44243 - 6.00043i) q^{26} +(1.84077 + 4.85918i) q^{27} +(-1.13781 - 0.656914i) q^{28} +3.56626 q^{29} +(-1.55244 - 12.7988i) q^{30} +(-3.17297 - 1.83191i) q^{31} +13.7433i q^{32} +(1.62162 + 2.15854i) q^{33} +(-16.7833 + 9.68983i) q^{34} +(0.366605 + 0.634978i) q^{35} +(-4.20223 + 14.4943i) q^{36} +(1.90801 + 1.10159i) q^{37} +(0.684893 + 1.18627i) q^{38} +(0.213745 - 6.24134i) q^{39} +(11.2784 - 19.5348i) q^{40} +(6.42975 - 3.71222i) q^{41} +(-0.144431 - 1.19074i) q^{42} +(1.74859 - 3.02865i) q^{43} +7.84102i q^{44} +(6.07538 - 5.83257i) q^{45} +(6.31353 - 3.64512i) q^{46} +(7.10819 - 4.10392i) q^{47} +(-15.5707 + 11.6976i) q^{48} +(-3.46589 - 6.00310i) q^{49} +(-6.61553 + 3.81948i) q^{50} +(-11.6459 - 4.96356i) q^{51} +(11.3840 - 14.1197i) q^{52} +4.68042 q^{53} +(-12.8840 + 4.88077i) q^{54} +(2.18792 - 3.78960i) q^{55} +(1.04929 - 1.81742i) q^{56} +(-0.350832 + 0.823150i) q^{57} +9.45590i q^{58} +11.1417i q^{59} +(24.2818 - 2.94528i) q^{60} +(1.80731 - 3.13036i) q^{61} +(4.85729 - 8.41308i) q^{62} +(0.565223 - 0.542633i) q^{63} -13.9521 q^{64} +(-9.44183 + 3.64759i) q^{65} +(-5.72334 + 4.29970i) q^{66} +(-7.11290 + 4.10664i) q^{67} +(-18.3835 - 31.8411i) q^{68} +(4.38095 + 1.86719i) q^{69} +(-1.68364 + 0.972048i) q^{70} +(-5.40445 + 3.12026i) q^{71} +(-23.1517 - 6.71222i) q^{72} -3.76021i q^{73} +(-2.92085 + 5.05907i) q^{74} +(-4.59050 - 1.95650i) q^{75} +(-2.25058 + 1.29937i) q^{76} +(0.203554 - 0.352565i) q^{77} +(16.5488 + 0.566741i) q^{78} +(-1.36567 - 2.36542i) q^{79} +(27.3365 + 15.7827i) q^{80} +(-7.60431 - 4.81398i) q^{81} +(9.84289 + 17.0484i) q^{82} +(7.18029 - 4.14554i) q^{83} +(2.25906 - 0.274014i) q^{84} +20.5186i q^{85} +(8.03044 + 4.63638i) q^{86} +(-4.93858 + 3.71014i) q^{87} -12.5244 q^{88} +(-1.18531 - 0.684339i) q^{89} +(15.4650 + 16.1088i) q^{90} +(-0.878421 + 0.339353i) q^{91} +(6.91550 + 11.9780i) q^{92} +(6.29976 - 0.764133i) q^{93} +(10.8815 + 18.8473i) q^{94} +1.45029 q^{95} +(-14.2977 - 19.0317i) q^{96} +(-11.7284 - 6.77137i) q^{97} +(15.9171 - 9.18977i) q^{98} +(-4.49125 - 1.30212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			2.65149i			1.87488i	0.348141	+	0.937442i	$0.386813\pi$
$2$			2.65149i			1.87488i	−0.348141	+	0.937442i	$0.613187\pi$
$3$	−1.38481	+	1.04034i	−0.799518	+	0.600643i
$3$	−1.38481	+	1.04034i	−0.799518	+	0.600643i
$4$	−5.03038			−2.51519
$5$	2.43120	+	1.40366i	1.08727	+	0.627734i	0.932848	−	0.360271i	$-0.117316\pi$
$5$	2.43120	+	1.40366i	1.08727	+	0.627734i	0.154420	+	0.988005i	$0.450649\pi$
$6$	−2.75846	−	3.67179i	−1.12614	−	1.49900i
$7$	0.226187	+	0.130589i	0.0854907	+	0.0493581i	0.542136	−	0.840291i	$-0.317616\pi$
$7$	0.226187	+	0.130589i	0.0854907	+	0.0493581i	−0.456645	+	0.889649i	$0.650949\pi$
$8$		−	8.03502i		−	2.84081i
$9$	0.835370	−	2.88135i	0.278457	−	0.960449i
$10$	−3.72178	+	6.44631i	−1.17693	+	2.03850i
$11$		−	1.55873i		−	0.469975i	−0.971998	−	0.234988i	$-0.924495\pi$
$11$		−	1.55873i		−	0.469975i	0.971998	−	0.234988i	$-0.0755050\pi$
$12$	6.96610	−	5.23333i	2.01094	−	1.51073i
$13$	−2.26304	+	2.80689i	−0.627656	+	0.778491i
$13$	−2.26304	+	2.80689i	−0.627656	+	0.778491i
$14$	−0.346256	+	0.599733i	−0.0925407	+	0.160285i
$15$	−4.82703	+	0.585497i	−1.24633	+	0.151175i
$16$	11.2440			2.81100
$17$	3.65449	+	6.32976i	0.886344	+	1.53519i	0.844166	+	0.536082i	$0.180096\pi$
$17$	3.65449	+	6.32976i	0.886344	+	1.53519i	0.0421777	+	0.999110i	$0.486570\pi$
$18$	7.63985	+	2.21497i	1.80073	+	0.522074i
$19$	0.447398	−	0.258305i	0.102640	−	0.0592593i	−0.447801	−	0.894133i	$-0.647793\pi$
$19$	0.447398	−	0.258305i	0.102640	−	0.0592593i	0.550441	+	0.834874i	$0.314459\pi$
$20$	−12.2299	−	7.06093i	−2.73469	−	1.57887i
$21$	−0.449083	+	0.0544718i	−0.0979979	+	0.0118867i
$22$	4.13296			0.881150
$23$	−1.37475	−	2.38113i	−0.286654	−	0.496500i	0.686355	−	0.727267i	$-0.259210\pi$
$23$	−1.37475	−	2.38113i	−0.286654	−	0.496500i	−0.973009	+	0.230767i	$0.925876\pi$
$24$	8.35919	+	11.1269i	1.70631	+	2.27128i
$25$	1.44050	+	2.49502i	0.288101	+	0.499005i
$26$	−7.44243	−	6.00043i	−1.45958	−	1.17678i
$27$	1.84077	+	4.85918i	0.354255	+	0.935149i
$28$	−1.13781	−	0.656914i	−0.215026	−	0.124145i
$29$	3.56626			0.662238			0.331119	−	0.943589i	$-0.392574\pi$
$29$	3.56626			0.662238			0.331119	+	0.943589i	$0.392574\pi$
$30$	−1.55244	−	12.7988i	−0.283435	−	2.33673i
$31$	−3.17297	−	1.83191i	−0.569882	−	0.329021i	0.187221	−	0.982318i	$-0.440052\pi$
$31$	−3.17297	−	1.83191i	−0.569882	−	0.329021i	−0.757102	+	0.653297i	$0.773385\pi$
$32$			13.7433i			2.42949i
$33$	1.62162	+	2.15854i	0.282287	+	0.375754i
$34$	−16.7833	+	9.68983i	−2.87831	+	1.66179i
$35$	0.366605	+	0.634978i	0.0619675	+	0.107331i
$36$	−4.20223	+	14.4943i	−0.700372	+	2.41571i
$37$	1.90801	+	1.10159i	0.313675	+	0.181100i	0.648570	−	0.761155i	$-0.275367\pi$
$37$	1.90801	+	1.10159i	0.313675	+	0.181100i	−0.334895	+	0.942256i	$0.608701\pi$
$38$	0.684893	+	1.18627i	0.111104	+	0.192438i
$39$	0.213745	−	6.24134i	0.0342266	−	0.999414i
$40$	11.2784	−	19.5348i	1.78327	−	3.08872i
$41$	6.42975	−	3.71222i	1.00416	−	0.579751i	0.0946819	−	0.995508i	$-0.469817\pi$
$41$	6.42975	−	3.71222i	1.00416	−	0.579751i	0.909476	+	0.415757i	$0.136483\pi$
$42$	−0.144431	−	1.19074i	−0.0222862	−	0.183735i
$43$	1.74859	−	3.02865i	0.266658	−	0.461865i	−0.701339	−	0.712828i	$-0.747414\pi$
$43$	1.74859	−	3.02865i	0.266658	−	0.461865i	0.967997	+	0.250963i	$0.0807472\pi$
$44$			7.84102i			1.18208i
$45$	6.07538	−	5.83257i	0.905664	−	0.869468i
$46$	6.31353	−	3.64512i	0.930880	−	0.537444i
$47$	7.10819	−	4.10392i	1.03684	−	0.598618i	0.117901	−	0.993025i	$-0.462383\pi$
$47$	7.10819	−	4.10392i	1.03684	−	0.598618i	0.918936	+	0.394407i	$0.129050\pi$
$48$	−15.5707	+	11.6976i	−2.24744	+	1.68841i
$49$	−3.46589	−	6.00310i	−0.495128	−	0.857586i
$50$	−6.61553	+	3.81948i	−0.935577	+	0.540155i
$51$	−11.6459	−	4.96356i	−1.63075	−	0.695037i
$52$	11.3840	−	14.1197i	1.57867	−	1.95805i
$53$	4.68042			0.642905			0.321452	−	0.946926i	$-0.395829\pi$
$53$	4.68042			0.642905			0.321452	+	0.946926i	$0.395829\pi$
$54$	−12.8840	+	4.88077i	−1.75330	+	0.664188i
$55$	2.18792	−	3.78960i	0.295020	−	0.510989i
$56$	1.04929	−	1.81742i	0.140217	−	0.242863i
$57$	−0.350832	+	0.823150i	−0.0464689	+	0.109029i
$58$			9.45590i			1.24162i
$59$			11.1417i			1.45053i	0.688469	+	0.725265i	$0.258283\pi$
$59$			11.1417i			1.45053i	−0.688469	+	0.725265i	$0.741717\pi$
$60$	24.2818	−	2.94528i	3.13477	−	0.380234i
$61$	1.80731	−	3.13036i	0.231403	−	0.400801i	−0.726818	−	0.686830i	$-0.759002\pi$
$61$	1.80731	−	3.13036i	0.231403	−	0.400801i	0.958221	+	0.286028i	$0.0923352\pi$
$62$	4.85729	−	8.41308i	0.616877	−	1.06846i
$63$	0.565223	−	0.542633i	0.0712114	−	0.0683654i
$64$	−13.9521			−1.74401
$65$	−9.44183	+	3.64759i	−1.17112	+	0.452427i
$66$	−5.72334	+	4.29970i	−0.704495	+	0.529256i
$67$	−7.11290	+	4.10664i	−0.868979	+	0.501706i	−0.867009	−	0.498293i	$-0.833961\pi$
$67$	−7.11290	+	4.10664i	−0.868979	+	0.501706i	−0.00197050	+	0.999998i	$0.500627\pi$
$68$	−18.3835	−	31.8411i	−2.22932	−	3.86130i
$69$	4.38095	+	1.86719i	0.527404	+	0.224783i
$70$	−1.68364	+	0.972048i	−0.201233	+	0.116182i
$71$	−5.40445	+	3.12026i	−0.641390	+	0.370307i	−0.785150	−	0.619306i	$-0.787414\pi$
$71$	−5.40445	+	3.12026i	−0.641390	+	0.370307i	0.143760	+	0.989613i	$0.454081\pi$
$72$	−23.1517	−	6.71222i	−2.72845	−	0.791043i
$73$		−	3.76021i		−	0.440099i	−0.975489	−	0.220050i	$-0.929378\pi$
$73$		−	3.76021i		−	0.440099i	0.975489	−	0.220050i	$-0.0706220\pi$
$74$	−2.92085	+	5.05907i	−0.339542	+	0.588105i
$75$	−4.59050	−	1.95650i	−0.530065	−	0.225918i
$76$	−2.25058	+	1.29937i	−0.258159	+	0.149048i
$77$	0.203554	−	0.352565i	0.0231971	−	0.0401785i
$78$	16.5488	+	0.566741i	1.87379	+	0.0641708i
$79$	−1.36567	−	2.36542i	−0.153650	−	0.266130i	0.778916	−	0.627128i	$-0.215770\pi$
$79$	−1.36567	−	2.36542i	−0.153650	−	0.266130i	−0.932567	+	0.360998i	$0.882436\pi$
$80$	27.3365	+	15.7827i	3.05631	+	1.76456i
$81$	−7.60431	−	4.81398i	−0.844924	−	0.534887i
$82$	9.84289	+	17.0484i	1.08697	+	1.88268i
$83$	7.18029	−	4.14554i	0.788139	−	0.455032i	−0.0511680	−	0.998690i	$-0.516294\pi$
$83$	7.18029	−	4.14554i	0.788139	−	0.455032i	0.839307	+	0.543658i	$0.182961\pi$
$84$	2.25906	−	0.274014i	0.246484	−	0.0298974i
$85$			20.5186i			2.22555i
$86$	8.03044	+	4.63638i	0.865944	+	0.499953i
$87$	−4.93858	+	3.71014i	−0.529471	+	0.397769i
$88$	−12.5244			−1.33511
$89$	−1.18531	−	0.684339i	−0.125643	−	0.0725398i	0.435861	−	0.900014i	$-0.356444\pi$
$89$	−1.18531	−	0.684339i	−0.125643	−	0.0725398i	−0.561504	+	0.827474i	$0.689777\pi$
$90$	15.4650	+	16.1088i	1.63015	+	1.69801i
$91$	−0.878421	+	0.339353i	−0.0920836	+	0.0355739i
$92$	6.91550	+	11.9780i	0.720990	+	1.24879i
$93$	6.29976	−	0.764133i	0.653254	−	0.0792369i
$94$	10.8815	+	18.8473i	1.12234	+	1.94395i
$95$	1.45029			0.148796
$96$	−14.2977	−	19.0317i	−1.45925	−	1.94242i
$97$	−11.7284	−	6.77137i	−1.19083	−	0.687528i	−0.232338	−	0.972635i	$-0.574638\pi$
$97$	−11.7284	−	6.77137i	−1.19083	−	0.687528i	−0.958496	+	0.285107i	$0.907971\pi$
$98$	15.9171	−	9.18977i	1.60787	−	0.928307i
$99$	−4.49125	−	1.30212i	−0.451387	−	0.130868i
$100$	−7.24628	−	12.5509i	−0.724628	−	1.25509i
$101$	−15.4095			−1.53331			−0.766653	−	0.642061i	$-0.778079\pi$
$101$	−15.4095			−1.53331			−0.766653	+	0.642061i	$0.778079\pi$
$102$	13.1608	−	30.8789i	1.30311	−	3.05747i
$103$	5.49573	−	9.51889i	0.541510	−	0.937924i	−0.457307	−	0.889309i	$-0.651186\pi$
$103$	5.49573	−	9.51889i	0.541510	−	0.937924i	0.998818	−	0.0486148i	$-0.0154807\pi$
$104$	22.5534	+	18.1836i	2.21155	+	1.78305i
$105$	−1.16827	−	0.497926i	−0.114012	−	0.0485926i
$106$			12.4101i			1.20537i
$107$	−0.595733	+	1.03184i	−0.0575917	+	0.0997518i	−0.893384	−	0.449294i	$-0.851675\pi$
$107$	−0.595733	+	1.03184i	−0.0575917	+	0.0997518i	0.835792	+	0.549046i	$0.185009\pi$
$108$	−9.25976	−	24.4435i	−0.891021	−	2.35208i
$109$		−	1.56215i		−	0.149627i	−0.997198	−	0.0748135i	$-0.976164\pi$
$109$		−	1.56215i		−	0.149627i	0.997198	−	0.0748135i	$-0.0238362\pi$
$110$	10.0481	+	5.80125i	0.958045	+	0.553128i
$111$	−3.78826	+	0.459499i	−0.359565	+	0.0436137i
$112$	2.54325	+	1.46835i	0.240314	+	0.138746i
$113$	−4.59209			−0.431988			−0.215994	−	0.976395i	$-0.569299\pi$
$113$	−4.59209			−0.431988			−0.215994	+	0.976395i	$0.569299\pi$
$114$	−2.18257	−	0.930228i	−0.204416	−	0.0871238i
$115$		−	7.71868i		−	0.719771i
$116$	−17.9397			−1.66566
$117$	6.19714	+	8.86541i	0.572926	+	0.819607i
$118$	−29.5422			−2.71958
$119$			1.90895i			0.174993i
$120$	4.70449	+	38.7853i	0.429459	+	3.54060i
$121$	8.57035			0.779123
$122$	8.30010	+	4.79207i	0.751456	+	0.433853i
$123$	−5.04197	+	11.8298i	−0.454619	+	1.06666i
$124$	15.9612	+	9.21522i	1.43336	+	0.827552i
$125$		−	5.94868i		−	0.532066i
$126$	1.43879	+	1.49868i	0.128177	+	0.133513i
$127$	5.62331	−	9.73987i	0.498988	−	0.864273i	−0.501011	−	0.865441i	$-0.667038\pi$
$127$	5.62331	−	9.73987i	0.498988	−	0.864273i	0.999999	+	0.00116769i	$0.000371687\pi$
$128$		−	9.50727i		−	0.840332i
$129$	0.729379	+	6.01323i	0.0642182	+	0.529436i
$130$	−9.67153	−	25.0349i	−0.848249	−	2.19571i
$131$	−1.93018	+	3.34317i	−0.168640	+	0.292094i	−0.937942	−	0.346792i	$-0.887271\pi$
$131$	−1.93018	+	3.34317i	−0.168640	+	0.292094i	0.769302	+	0.638886i	$0.220604\pi$
$132$	−8.15736	−	10.8583i	−0.710007	−	0.945092i
$133$	0.134928			0.0116997
$134$	−10.8887	−	18.8598i	−0.940640	−	1.62924i
$135$	−2.34534	+	14.3975i	−0.201854	+	1.23914i
$136$	50.8598	−	29.3639i	4.36119	−	2.51793i
$137$	−1.93203	−	1.11546i	−0.165065	−	0.0953002i	0.415192	−	0.909734i	$-0.363714\pi$
$137$	−1.93203	−	1.11546i	−0.165065	−	0.0953002i	−0.580257	+	0.814434i	$0.697048\pi$
$138$	−4.95083	+	11.6160i	−0.421443	+	0.988822i
$139$	16.2457			1.37795			0.688973	−	0.724787i	$-0.258062\pi$
$139$	16.2457			1.37795			0.688973	+	0.724787i	$0.258062\pi$
$140$	−1.84416	−	3.19419i	−0.155860	−	0.269958i
$141$	−5.57398	+	13.0781i	−0.469414	+	1.10137i
$142$	−8.27333	−	14.3298i	−0.694282	−	1.20253i
$143$	4.37519	+	3.52748i	0.365872	+	0.294983i
$144$	9.39290	−	32.3978i	0.782742	−	2.69982i
$145$	8.67031	+	5.00581i	0.720030	+	0.415710i
$146$	9.97015			0.825136
$147$	11.0449	+	4.70741i	0.910966	+	0.388260i
$148$	−9.59803	−	5.54143i	−0.788953	−	0.455502i
$149$		−	7.63642i		−	0.625600i	−0.949819	−	0.312800i	$-0.898733\pi$
$149$		−	7.63642i		−	0.625600i	0.949819	−	0.312800i	$-0.101267\pi$
$150$	5.18765	−	12.1716i	0.423570	−	0.993811i
$151$	−10.8516	+	6.26520i	−0.883095	+	0.509855i	−0.871677	−	0.490080i	$-0.836968\pi$
$151$	−10.8516	+	6.26520i	−0.883095	+	0.509855i	−0.0114171	+	0.999935i	$0.503634\pi$
$152$	−2.07549	−	3.59485i	−0.168344	−	0.291581i
$153$	21.2911	−	5.24215i	1.72128	−	0.423803i
$154$	0.934822	+	0.539720i	0.0753301	+	0.0434919i
$155$	−5.14275	−	8.90751i	−0.413076	−	0.715468i
$156$	−1.07522	+	31.3963i	−0.0860864	+	2.51372i
$157$	−5.04228	+	8.73349i	−0.402418	+	0.697009i	−0.994017	−	0.109224i	$-0.965164\pi$
$157$	−5.04228	+	8.73349i	−0.402418	+	0.697009i	0.591599	+	0.806232i	$0.298497\pi$
$158$	6.27187	−	3.62107i	0.498964	−	0.288077i
$159$	−6.48146	+	4.86924i	−0.514014	+	0.386156i
$160$	−19.2908	+	33.4127i	−1.52507	+	2.64150i
$161$		−	0.718108i		−	0.0565948i
$162$	12.7642	−	20.1627i	1.00285	−	1.58413i
$163$	−10.8176	+	6.24553i	−0.847297	+	0.489187i	−0.859738	−	0.510735i	$-0.829373\pi$
$163$	−10.8176	+	6.24553i	−0.847297	+	0.489187i	0.0124407	+	0.999923i	$0.496040\pi$
$164$	−32.3441	+	18.6739i	−2.52565	+	1.45818i
$165$	0.912633	+	7.52404i	0.0710484	+	0.585746i
$166$	10.9918	+	19.0384i	0.853133	+	1.47767i
$167$	−21.0667	+	12.1628i	−1.63019	+	0.941189i	−0.646152	+	0.763209i	$0.723623\pi$
$167$	−21.0667	+	12.1628i	−1.63019	+	0.941189i	−0.984034	+	0.177980i	$0.943044\pi$
$168$	0.437682	+	3.60839i	0.0337679	+	0.278394i
$169$	−2.75726	−	12.7042i	−0.212097	−	0.977249i
$170$	−54.4048			−4.17265
$171$	−0.370524	−	1.50489i	−0.0283347	−	0.115082i
$172$	−8.79610	+	15.2353i	−0.670696	+	1.16168i
$173$	5.27316	−	9.13338i	0.400911	−	0.694398i	−0.592925	−	0.805258i	$-0.702027\pi$
$173$	5.27316	−	9.13338i	0.400911	−	0.694398i	0.993836	+	0.110860i	$0.0353604\pi$
$174$	−9.83738	−	13.0946i	−0.745770	−	0.992697i
$175$			0.752457i			0.0568804i
$176$		−	17.5264i		−	1.32110i
$177$	−11.5912	−	15.4291i	−0.871251	−	1.15972i
$178$	1.81452	−	3.14283i	0.136004	−	0.235565i
$179$	3.54457	−	6.13938i	0.264934	−	0.458879i	−0.702612	−	0.711573i	$-0.747983\pi$
$179$	3.54457	−	6.13938i	0.264934	−	0.458879i	0.967546	+	0.252694i	$0.0813165\pi$
$180$	−30.5615	+	29.3401i	−2.27792	+	2.18688i
$181$	15.7315			1.16931			0.584656	−	0.811281i	$-0.301230\pi$
$181$	15.7315			1.16931			0.584656	+	0.811281i	$0.301230\pi$
$182$	−0.899791	−	2.32912i	−0.0666970	−	0.172646i
$183$	0.753871	+	6.21516i	0.0557278	+	0.459438i
$184$	−19.1324	+	11.0461i	−1.41046	+	0.814330i
$185$	3.09251	+	5.35639i	0.227366	+	0.393809i
$186$	2.02609	+	16.7037i	0.148560	+	1.22478i
$187$	9.86640	−	5.69637i	0.721502	−	0.416560i
$188$	−35.7569	+	20.6443i	−2.60784	+	1.50564i
$189$	−0.218198	+	1.33947i	−0.0158716	+	0.0974319i
$190$			3.84542i			0.278976i
$191$	−4.06091	+	7.03371i	−0.293837	+	0.508941i	−0.974714	−	0.223457i	$-0.928266\pi$
$191$	−4.06091	+	7.03371i	−0.293837	+	0.508941i	0.680876	+	0.732398i	$0.261599\pi$
$192$	19.3209	−	14.5150i	1.39437	−	1.04753i
$193$	−6.67526	+	3.85396i	−0.480495	+	0.277414i	−0.720623	−	0.693327i	$-0.756144\pi$
$193$	−6.67526	+	3.85396i	−0.480495	+	0.277414i	0.240127	+	0.970741i	$0.422811\pi$
$194$	17.9542	−	31.0976i	1.28904	−	2.23268i
$195$	9.28035	−	14.8739i	0.664580	−	1.06515i
$196$	17.4348	+	30.1979i	1.24534	+	2.15699i
$197$	−3.46949	−	2.00311i	−0.247191	−	0.142716i	0.371287	−	0.928518i	$-0.378917\pi$
$197$	−3.46949	−	2.00311i	−0.247191	−	0.142716i	−0.618477	+	0.785803i	$0.712250\pi$
$198$	3.45255	−	11.9085i	0.245362	−	0.846299i
$199$	−6.44292	−	11.1595i	−0.456726	−	0.791073i	0.542059	−	0.840340i	$-0.317645\pi$
$199$	−6.44292	−	11.1595i	−0.456726	−	0.791073i	−0.998786	+	0.0492670i	$0.984311\pi$
$200$	20.0476	−	11.5745i	1.41758	−	0.818439i
$201$	5.57767	−	13.0868i	0.393419	−	0.923069i
$202$		−	40.8582i		−	2.87477i
$203$	0.806643	+	0.465716i	0.0566152	+	0.0326868i
$204$	58.5832	+	24.9686i	4.10165	+	1.74815i
$205$	20.8427			1.45572
$206$	25.2392	+	14.5719i	1.75850	+	1.01527i
$207$	−8.00928	+	1.97199i	−0.556683	+	0.137063i
$208$	−25.4457	+	31.5607i	−1.76434	+	2.18834i
$209$	−0.402628	−	0.697373i	−0.0278504	−	0.0482383i
$210$	1.32024	−	3.09766i	0.0911055	−	0.213759i
$211$	−8.60754	−	14.9087i	−0.592567	−	1.02636i	−0.993885	−	0.110418i	$-0.964781\pi$
$211$	−8.60754	−	14.9087i	−0.592567	−	1.02636i	0.401318	−	0.915939i	$-0.368552\pi$
$212$	−23.5443			−1.61703
$213$	4.23796	−	9.94343i	0.290380	−	0.681313i
$214$	−2.73591	−	1.57958i	−0.187023	−	0.107978i
$215$	8.50238	−	4.90885i	0.579858	−	0.334781i
$216$	39.0436	−	14.7906i	2.65658	−	1.00637i
$217$	−0.478456	−	0.828711i	−0.0324797	−	0.0562565i
$218$	4.14203			0.280534
$219$	3.91191	+	5.20716i	0.264343	+	0.351867i
$220$	−11.0061	+	19.0631i	−0.742031	+	1.28524i
$221$	−26.0372	−	4.06678i	−1.75145	−	0.273561i
$222$	−1.21836	−	10.0445i	−0.0817707	−	0.674144i
$223$			9.43422i			0.631762i	0.948799	+	0.315881i	$0.102300\pi$
$223$			9.43422i			0.631762i	−0.948799	+	0.315881i	$0.897700\pi$
$224$	−1.79472	+	3.10855i	−0.119915	+	0.207699i
$225$	8.39238	−	2.06632i	0.559492	−	0.137755i
$226$		−	12.1759i		−	0.809927i
$227$	15.8982	+	9.17883i	1.05520	+	0.609220i	0.924101	−	0.382149i	$-0.124816\pi$
$227$	15.8982	+	9.17883i	1.05520	+	0.609220i	0.131100	+	0.991369i	$0.458149\pi$
$228$	1.76482	−	4.14076i	0.116878	−	0.274228i
$229$	11.3476	+	6.55153i	0.749870	+	0.432937i	0.825647	−	0.564187i	$-0.190810\pi$
$229$	11.3476	+	6.55153i	0.749870	+	0.432937i	−0.0757771	+	0.997125i	$0.524144\pi$
$230$	20.4660			1.34949
$231$	0.0849069	+	0.700000i	0.00558646	+	0.0460566i
$232$		−	28.6550i		−	1.88129i
$233$	4.84195			0.317207			0.158603	−	0.987342i	$-0.449301\pi$
$233$	4.84195			0.317207			0.158603	+	0.987342i	$0.449301\pi$
$234$	−23.5065	+	16.4316i	−1.53667	+	1.07417i
$235$	23.0420			1.50309
$236$		−	56.0472i		−	3.64836i
$237$	4.35204	+	1.85487i	0.282695	+	0.120487i
$238$	−5.06155			−0.328092
$239$	−13.6653	−	7.88968i	−0.883936	−	0.510341i	−0.0119822	−	0.999928i	$-0.503814\pi$
$239$	−13.6653	−	7.88968i	−0.883936	−	0.510341i	−0.871954	+	0.489587i	$0.837147\pi$
$240$	−54.2751	+	6.58333i	−3.50344	+	0.424952i
$241$	−14.1046	−	8.14332i	−0.908560	−	0.524557i	−0.0285922	−	0.999591i	$-0.509102\pi$
$241$	−14.1046	−	8.14332i	−0.908560	−	0.524557i	−0.879967	+	0.475034i	$0.842436\pi$
$242$			22.7242i			1.46077i
$243$	15.5387	−	1.24467i	0.996807	−	0.0798458i
$244$	−9.09147	+	15.7469i	−0.582022	+	1.00809i
$245$		−	19.4597i		−	1.24323i
$246$	−31.3667	−	13.3687i	−1.99987	−	0.852358i
$247$	−0.287446	+	1.84035i	−0.0182898	+	0.117099i
$248$	−14.7195	+	25.4949i	−0.934687	+	1.61893i
$249$	−5.63051	+	13.2107i	−0.356819	+	0.837196i
$250$	15.7728			0.997562
$251$	13.7361	+	23.7917i	0.867017	+	1.50172i	0.865030	+	0.501719i	$0.167299\pi$
$251$	13.7361	+	23.7917i	0.867017	+	1.50172i	0.00198652	+	0.999998i	$0.499368\pi$
$252$	−2.84329	+	2.72965i	−0.179110	+	0.171952i
$253$	−3.71154	+	2.14286i	−0.233343	+	0.134720i
$254$	25.8251	+	14.9101i	1.62041	+	0.935546i
$255$	−21.3464	−	28.4142i	−1.33676	−	1.77937i
$256$	−2.69579			−0.168487
$257$	4.89985	+	8.48679i	0.305644	+	0.529392i	0.977405	−	0.211377i	$-0.0677948\pi$
$257$	4.89985	+	8.48679i	0.305644	+	0.529392i	−0.671760	+	0.740769i	$0.734461\pi$
$258$	−15.9440	+	1.93394i	−0.992631	+	0.120402i
$259$	0.287712	+	0.498332i	0.0178775	+	0.0309648i
$260$	47.4960	−	18.3488i	2.94558	−	1.13794i
$261$	2.97915	−	10.2756i	0.184405	−	0.636046i
$262$	−8.86436	−	5.11784i	−0.547642	−	0.316181i
$263$	23.0973			1.42424			0.712119	−	0.702059i	$-0.247736\pi$
$263$	23.0973			1.42424			0.712119	+	0.702059i	$0.247736\pi$
$264$	17.3439	−	13.0297i	1.06744	−	0.801925i
$265$	11.3790	+	6.56970i	0.699009	+	0.403573i
$266$			0.357759i			0.0219356i
$267$	2.35337	−	0.285454i	0.144024	−	0.0174695i
$268$	35.7806	−	20.6580i	2.18565	−	1.26189i
$269$	−10.8197	−	18.7403i	−0.659688	−	1.14261i	−0.980696	−	0.195537i	$-0.937355\pi$
$269$	−10.8197	−	18.7403i	−0.659688	−	1.14261i	0.321008	−	0.947076i	$-0.395978\pi$
$270$	−38.1747	−	6.21863i	−2.32324	−	0.378454i
$271$	−23.0990	−	13.3362i	−1.40316	−	0.810116i	−0.408447	−	0.912782i	$-0.633929\pi$
$271$	−23.0990	−	13.3362i	−1.40316	−	0.810116i	−0.994716	+	0.102666i	$0.967263\pi$
$272$	41.0911	+	71.1718i	2.49151	+	4.31542i
$273$	0.863398	−	1.38380i	0.0522552	−	0.0837513i
$274$	2.95763	−	5.12276i	0.178677	−	0.309478i
$275$	3.88907	−	2.24536i	0.234520	−	0.135400i
$276$	−22.0378	−	9.39269i	−1.32652	−	0.565374i
$277$	−3.22139	+	5.57961i	−0.193554	+	0.335246i	−0.946426	−	0.322922i	$-0.895335\pi$
$277$	−3.22139	+	5.57961i	−0.193554	+	0.335246i	0.752871	+	0.658168i	$0.228668\pi$
$278$			43.0754i			2.58349i
$279$	−7.92898	+	7.61209i	−0.474695	+	0.455724i
$280$	5.10207	−	2.94568i	0.304907	−	0.176038i
$281$	1.22438	−	0.706894i	0.0730402	−	0.0421698i	−0.463035	−	0.886340i	$-0.653240\pi$
$281$	1.22438	−	0.706894i	0.0730402	−	0.0421698i	0.536075	+	0.844170i	$0.319906\pi$
$282$	−34.6764	−	14.7793i	−2.06495	−	0.880096i
$283$	−9.98988	−	17.3030i	−0.593837	−	1.02856i	−0.993710	−	0.111985i	$-0.964279\pi$
$283$	−9.98988	−	17.3030i	−0.593837	−	1.02856i	0.399873	−	0.916571i	$-0.369054\pi$
$284$	27.1864	−	15.6961i	1.61322	−	0.931392i
$285$	−2.00836	+	1.50880i	−0.118965	+	0.0893734i
$286$	−9.35307	+	11.6008i	−0.553058	+	0.685967i
$287$	1.93910			0.114462
$288$	39.5991	+	11.4807i	2.33340	+	0.676507i
$289$	−18.2106	+	31.5416i	−1.07121	+	1.85539i
$290$	−13.2728	+	22.9892i	−0.779408	+	1.34997i
$291$	23.2860	−	2.82449i	1.36505	−	0.165575i
$292$			18.9153i			1.10693i
$293$			3.37211i			0.197001i	0.995137	+	0.0985005i	$0.0314046\pi$
$293$			3.37211i			0.197001i	−0.995137	+	0.0985005i	$0.968595\pi$
$294$	−12.4816	+	29.2853i	−0.727943	+	1.70796i
$295$	−15.6392	+	27.0878i	−0.910548	+	1.57712i
$296$	8.85131	−	15.3309i	0.514472	−	0.891092i
$297$	7.57415	−	2.86926i	0.439497	−	0.166491i
$298$	20.2479			1.17293
$299$	9.79468	+	1.52984i	0.566441	+	0.0884730i
$300$	23.0920	+	9.84197i	1.33322	+	0.568226i
$301$	0.791019	−	0.456695i	0.0455936	−	0.0263235i
$302$	−16.6121	−	28.7730i	−0.955919	−	1.65570i
$303$	21.3392	−	16.0312i	1.22591	−	0.920969i
$304$	5.03054	−	2.90438i	0.288521	−	0.166578i
$305$	8.78789	−	5.07369i	0.503193	−	0.290519i
$306$	13.8995	+	56.4530i	0.794582	+	3.22720i
$307$			20.7017i			1.18151i	0.806851	+	0.590756i	$0.201170\pi$
$307$			20.7017i			1.18151i	−0.806851	+	0.590756i	$0.798830\pi$
$308$	−1.02395	+	1.77354i	−0.0583451	+	0.101057i
$309$	2.29240	+	18.8992i	0.130410	+	1.07514i
$310$	23.6181	−	13.6359i	1.34142	−	0.774469i
$311$	4.13884	−	7.16868i	0.234692	−	0.406499i	−0.724491	−	0.689284i	$-0.757925\pi$
$311$	4.13884	−	7.16868i	0.234692	−	0.406499i	0.959183	+	0.282786i	$0.0912585\pi$
$312$	−50.1493	−	1.71744i	−2.83915	−	0.0972311i
$313$	6.19041	+	10.7221i	0.349902	+	0.606049i	0.986232	−	0.165369i	$-0.0528814\pi$
$313$	6.19041	+	10.7221i	0.349902	+	0.606049i	−0.636329	+	0.771417i	$0.719548\pi$
$314$	−23.1567	−	13.3696i	−1.30681	−	0.754488i
$315$	2.13584	−	0.525874i	0.120341	−	0.0296296i
$316$	6.86987	+	11.8990i	0.386460	+	0.669369i
$317$	−28.4498	+	16.4255i	−1.59790	+	0.922547i	−0.606006	+	0.795460i	$0.707229\pi$
$317$	−28.4498	+	16.4255i	−1.59790	+	0.922547i	−0.991892	+	0.127087i	$0.959437\pi$
$318$	−12.9107	−	17.1855i	−0.723998	−	0.963716i
$319$		−	5.55885i		−	0.311236i
$320$	−33.9204	−	19.5839i	−1.89621	−	1.09478i
$321$	−0.248494	−	2.04866i	−0.0138696	−	0.114345i
$322$	1.90405			0.106109
$323$	3.27002	+	1.88795i	0.181949	+	0.105048i
$324$	38.2526	+	24.2162i	2.12515	+	1.34534i
$325$	−10.2632	−	1.60302i	−0.569299	−	0.0889194i
$326$	−16.5599	−	28.6826i	−0.917170	−	1.58858i
$327$	1.62518	+	2.16328i	0.0898724	+	0.119629i
$328$	−29.8277	−	51.6632i	−1.64696	−	2.85262i
$329$	2.14371			0.118187
$330$	−19.9499	+	2.41984i	−1.09821	+	0.133208i
$331$	12.0206	+	6.94008i	0.660710	+	0.381461i	0.792547	−	0.609810i	$-0.208754\pi$
$331$	12.0206	+	6.94008i	0.660710	+	0.381461i	−0.131837	+	0.991271i	$0.542088\pi$
$332$	−36.1196	+	20.8537i	−1.98232	+	1.14449i
$333$	4.76796	−	4.57741i	0.261283	−	0.250840i
$334$	−32.2496	−	55.8580i	−1.76462	−	3.05641i
$335$	−23.0572			−1.25975
$336$	−5.04949	+	0.612481i	−0.275472	+	0.0334136i
$337$	−12.3880	+	21.4566i	−0.674816	+	1.16882i	0.301706	+	0.953401i	$0.402444\pi$
$337$	−12.3880	+	21.4566i	−0.674816	+	1.16882i	−0.976522	+	0.215415i	$0.930889\pi$
$338$	33.6851	−	7.31085i	1.83223	−	0.397658i
$339$	6.35915	−	4.77735i	0.345382	−	0.259470i
$340$		−	103.216i		−	5.59769i
$341$	−2.85546	+	4.94580i	−0.154632	+	0.267830i
$342$	3.99019	−	0.982439i	0.215765	−	0.0531242i
$343$		−	3.63868i		−	0.196470i
$344$	−24.3353	−	14.0500i	−1.31207	−	0.757525i
$345$	8.03008	+	10.6889i	0.432325	+	0.575469i
$346$	24.2170	+	13.9817i	1.30192	+	0.751662i
$347$	19.0566			1.02301			0.511506	−	0.859280i	$-0.329088\pi$
$347$	19.0566			1.02301			0.511506	+	0.859280i	$0.329088\pi$
$348$	24.8429	−	18.6634i	1.33172	−	1.00046i
$349$			23.7393i			1.27073i	0.772210	+	0.635367i	$0.219151\pi$
$349$			23.7393i			1.27073i	−0.772210	+	0.635367i	$0.780849\pi$
$350$	−1.99513			−0.106644
$351$	−17.8049	−	5.82970i	−0.950355	−	0.311166i
$352$	21.4221			1.14180
$353$		−	2.19138i		−	0.116635i	−0.998298	−	0.0583176i	$-0.981426\pi$
$353$		−	2.19138i		−	0.116635i	0.998298	−	0.0583176i	$-0.0185736\pi$
$354$	40.9102	−	30.7340i	2.17435	−	1.63349i
$355$	−17.5191			−0.929816
$356$	5.96256	+	3.44249i	0.316015	+	0.182452i
$357$	−1.98596	−	2.64352i	−0.105108	−	0.139910i
$358$	16.2785	+	9.39839i	0.860345	+	0.496721i
$359$		−	5.58420i		−	0.294723i	−0.989083	−	0.147361i	$-0.952922\pi$
$359$		−	5.58420i		−	0.294723i	0.989083	−	0.147361i	$-0.0470780\pi$
$360$	−46.8648	−	48.8158i	−2.46999	−	2.57282i
$361$	−9.36656	+	16.2234i	−0.492977	+	0.853861i
$362$			41.7118i			2.19232i
$363$	−11.8683	+	8.91611i	−0.622923	+	0.467975i
$364$	4.41880	−	1.70708i	0.231608	−	0.0894752i
$365$	5.27805	−	9.14184i	0.276266	−	0.478506i
$366$	−16.4794	+	1.99888i	−0.861393	+	0.104483i
$367$	−13.3773			−0.698292			−0.349146	−	0.937068i	$-0.613528\pi$
$367$	−13.3773			−0.698292			−0.349146	+	0.937068i	$0.613528\pi$
$368$	−15.4576	−	26.7734i	−0.805785	−	1.39566i
$369$	−5.32496	−	21.6274i	−0.277206	−	1.12588i
$370$	−14.2024	+	8.19975i	−0.738347	+	0.426285i
$371$	1.05865	+	0.611212i	0.0549624	+	0.0317326i
$372$	−31.6902	+	3.84388i	−1.64306	+	0.199296i
$373$	7.81997			0.404903			0.202451	−	0.979292i	$-0.435109\pi$
$373$	7.81997			0.404903			0.202451	+	0.979292i	$0.435109\pi$
$374$	15.1038	+	26.1606i	0.781001	+	1.35273i
$375$	6.18867	+	8.23776i	0.319582	+	0.425396i
$376$	−32.9751	−	57.1145i	−1.70056	−	2.94546i
$377$	−8.07061	+	10.0101i	−0.415658	+	0.515547i
$378$	−3.55158	−	0.578550i	−0.182674	−	0.0297574i
$379$	32.9974	+	19.0510i	1.69496	+	0.978586i	0.950399	+	0.311032i	$0.100675\pi$
$379$	32.9974	+	19.0510i	1.69496	+	0.978586i	0.744561	+	0.667554i	$0.232659\pi$
$380$	−7.29550			−0.374251
$381$	2.34561	+	19.3380i	0.120169	+	0.990715i
$382$	−18.6498	−	10.7675i	−0.954206	−	0.550911i
$383$			17.7970i			0.909382i	0.890649	+	0.454691i	$0.150250\pi$
$383$			17.7970i			0.909382i	−0.890649	+	0.454691i	$0.849750\pi$
$384$	9.89082	+	13.1657i	0.504739	+	0.671860i
$385$	0.989761	−	0.571439i	0.0504429	−	0.0291232i
$386$	−10.2187	−	17.6994i	−0.520120	−	0.900873i
$387$	−7.26588	−	7.56835i	−0.369345	−	0.384721i
$388$	58.9981	+	34.0626i	2.99518	+	1.72927i
$389$	−17.2599	−	29.8950i	−0.875112	−	1.51574i	−0.856644	−	0.515909i	$-0.827454\pi$
$389$	−17.2599	−	29.8950i	−0.875112	−	1.51574i	−0.0184682	−	0.999829i	$-0.505879\pi$
$390$	39.4381	+	24.6067i	1.99702	+	1.24601i
$391$	10.0480	−	17.4036i	0.508148	−	0.880139i
$392$	−48.2351	+	27.8485i	−2.43624	+	1.40656i
$393$	−0.805122	−	6.63768i	−0.0406130	−	0.334827i
$394$	5.31122	−	9.19930i	0.267575	−	0.463454i
$395$		−	7.66775i		−	0.385806i
$396$	22.5927	+	6.55015i	1.13533	+	0.329158i
$397$	−7.59209	+	4.38329i	−0.381036	+	0.219991i	−0.678269	−	0.734814i	$-0.737270\pi$
$397$	−7.59209	+	4.38329i	−0.381036	+	0.219991i	0.297233	+	0.954805i	$0.403936\pi$
$398$	29.5892	−	17.0833i	1.48317	−	0.856309i
$399$	−0.186848	+	0.140371i	−0.00935412	+	0.00702734i
$400$	16.1970	+	28.0540i	0.809851	+	1.40270i
$401$	18.6147	−	10.7472i	0.929574	−	0.536690i	0.0428973	−	0.999079i	$-0.486341\pi$
$401$	18.6147	−	10.7472i	0.929574	−	0.536690i	0.886677	+	0.462390i	$0.153008\pi$
$402$	34.6994	+	14.7891i	1.73065	+	0.737614i
$403$	12.3225	−	4.76047i	0.613829	−	0.237136i
$404$	77.5159			3.85656
$405$	−11.7305	−	22.3776i	−0.582891	−	1.11195i
$406$	−1.23484	+	2.13880i	−0.0612840	+	0.106147i
$407$	1.71708	−	2.97408i	0.0851127	−	0.147420i
$408$	−39.8823	+	93.5749i	−1.97447	+	4.63265i
$409$		−	35.4841i		−	1.75457i	−0.479966	−	0.877287i	$-0.659351\pi$
$409$		−	35.4841i		−	1.75457i	0.479966	−	0.877287i	$-0.340649\pi$
$410$			55.2642i			2.72930i
$411$	3.83595	−	0.465284i	0.189214	−	0.0229508i
$412$	−27.6456	+	47.8837i	−1.36200	+	2.35906i
$413$	−1.45499	+	2.52012i	−0.0715954	+	0.124007i
$414$	−5.22872	−	21.2365i	−0.256977	−	1.04372i
$415$	23.2757			1.14256
$416$	−38.5758	−	31.1016i	−1.89134	−	1.52488i
$417$	−22.4972	+	16.9012i	−1.10169	+	0.827653i
$418$	1.84908	−	1.06756i	0.0904412	−	0.0522163i
$419$	10.0143	+	17.3453i	0.489232	+	0.847375i	0.999923	−	0.0123892i	$-0.00394372\pi$
$419$	10.0143	+	17.3453i	0.489232	+	0.847375i	−0.510691	+	0.859764i	$0.670610\pi$
$420$	5.87686	+	2.50476i	0.286761	+	0.122220i
$421$	−15.3946	+	8.88807i	−0.750286	+	0.433178i	−0.825797	−	0.563967i	$-0.809275\pi$
$421$	−15.3946	+	8.88807i	−0.750286	+	0.433178i	0.0755111	+	0.997145i	$0.475941\pi$
$422$	39.5302	−	22.8228i	1.92430	−	1.11100i
$423$	−5.88684	−	23.9095i	−0.286228	−	1.16252i
$424$		−	37.6073i		−	1.82637i
$425$	−10.5286	+	18.2361i	−0.510712	+	0.884580i
$426$	26.3649	+	11.2369i	1.27738	+	0.544430i
$427$	0.817582	−	0.472031i	0.0395656	−	0.0228432i
$428$	2.99677	−	5.19055i	0.144854	−	0.250895i
$429$	−9.72857	−	0.333171i	−0.469700	−	0.0160856i
$430$	13.0158	+	22.5440i	0.627676	+	1.08717i
$431$	−1.72978	−	0.998690i	−0.0833206	−	0.0481052i	0.457761	−	0.889075i	$-0.348652\pi$
$431$	−1.72978	−	0.998690i	−0.0833206	−	0.0481052i	−0.541081	+	0.840970i	$0.681985\pi$
$432$	20.6976	+	54.6365i	0.995812	+	2.62870i
$433$	−12.2465	−	21.2116i	−0.588532	−	1.01937i	−0.994425	−	0.105446i	$-0.966373\pi$
$433$	−12.2465	−	21.2116i	−0.588532	−	1.01937i	0.405893	−	0.913920i	$-0.366960\pi$
$434$	2.19732	−	1.26862i	0.105475	−	0.0608957i
$435$	−17.2145	+	2.08804i	−0.825370	+	0.100114i
$436$			7.85823i			0.376341i
$437$	−1.23012	−	0.710208i	−0.0588444	−	0.0339738i
$438$	−13.8067	+	10.3724i	−0.659710	+	0.495612i
$439$	15.3304			0.731678			0.365839	−	0.930678i	$-0.380782\pi$
$439$	15.3304			0.731678			0.365839	+	0.930678i	$0.380782\pi$
$440$	−30.4495	−	17.5800i	−1.45162	−	0.838095i
$441$	−20.1923	+	4.97162i	−0.961539	+	0.236744i
$442$	10.7830	−	69.0373i	0.512895	−	3.28377i
$443$	4.73265	+	8.19718i	0.224855	+	0.389460i	0.956276	−	0.292466i	$-0.0944759\pi$
$443$	4.73265	+	8.19718i	0.224855	+	0.389460i	−0.731421	+	0.681926i	$0.761143\pi$
$444$	19.0564	−	2.31146i	0.904376	−	0.109697i
$445$	−1.92115	−	3.32754i	−0.0910714	−	0.157740i
$446$	−25.0147			−1.18448
$447$	7.94451	+	10.5750i	0.375762	+	0.500178i
$448$	−3.15579	−	1.82199i	−0.149097	−	0.0860811i
$449$	−14.1283	+	8.15697i	−0.666755	+	0.384951i	−0.794846	−	0.606811i	$-0.792448\pi$
$449$	−14.1283	+	8.15697i	−0.666755	+	0.384951i	0.128091	+	0.991762i	$0.459115\pi$
$450$	5.47882	+	22.2523i	0.258274	+	1.04898i
$451$	−5.78635	−	10.0223i	−0.272469	−	0.471929i
$452$	23.1000			1.08653
$453$	8.50945	−	19.9655i	0.399809	−	0.938062i
$454$	−24.3376	+	42.1539i	−1.14222	+	1.97838i
$455$	−2.61196	−	0.407964i	−0.122450	−	0.0191257i
$456$	6.61403	+	2.81895i	0.309730	+	0.132009i
$457$		−	2.16145i		−	0.101109i	−0.998721	−	0.0505543i	$-0.983901\pi$
$457$		−	2.16145i		−	0.101109i	0.998721	−	0.0505543i	$-0.0160988\pi$
$458$	−17.3713	+	30.0880i	−0.811708	+	1.40592i
$459$	−24.0304	+	29.4094i	−1.12164	+	1.37271i
$460$			38.8279i			1.81036i
$461$	2.65520	+	1.53298i	0.123665	+	0.0713980i	0.560556	−	0.828116i	$-0.310587\pi$
$461$	2.65520	+	1.53298i	0.123665	+	0.0713980i	−0.436891	+	0.899514i	$0.643921\pi$
$462$	−1.85604	+	0.225130i	−0.0863508	+	0.0104740i
$463$	−13.8184	−	7.97807i	−0.642197	−	0.370772i	0.143264	−	0.989685i	$-0.454240\pi$
$463$	−13.8184	−	7.97807i	−0.642197	−	0.370772i	−0.785460	+	0.618912i	$0.787574\pi$
$464$	40.0990			1.86155
$465$	16.3886	+	6.98493i	0.760002	+	0.323919i
$466$			12.8384i			0.594726i
$467$	3.15406			0.145952			0.0729762	−	0.997334i	$-0.476750\pi$
$467$	3.15406			0.145952			0.0729762	+	0.997334i	$0.476750\pi$
$468$	−31.1740	−	44.5964i	−1.44102	−	2.06147i
$469$	−2.14513			−0.0990529
$470$			61.0955i			2.81812i
$471$	−2.10325	−	17.3399i	−0.0969128	−	0.798980i
$472$	89.5241			4.12068
$473$	−4.72086	−	2.72559i	−0.217065	−	0.125323i
$474$	−4.91817	+	11.5394i	−0.225899	+	0.530021i
$475$	1.28896	+	0.744179i	0.0591413	+	0.0341453i
$476$		−	9.60274i		−	0.440141i
$477$	3.90988	−	13.4859i	0.179021	−	0.617477i
$478$	20.9194	−	36.2334i	0.956830	−	1.65728i
$479$		−	9.93675i		−	0.454022i	−0.973892	−	0.227011i	$-0.927105\pi$
$479$		−	9.93675i		−	0.454022i	0.973892	−	0.227011i	$-0.0728953\pi$
$480$	−8.04664	−	66.3391i	−0.367277	−	3.02795i
$481$	−7.40996	+	2.86263i	−0.337865	+	0.130525i
$482$	21.5919	−	37.3983i	0.983484	−	1.70344i
$483$	0.747079	+	0.994439i	0.0339933	+	0.0452486i
$484$	−43.1122			−1.95964
$485$	−19.0093	−	32.9251i	−0.863170	−	1.49505i
$486$	3.30023	+	41.2006i	0.149702	+	1.86890i
$487$	−20.0246	+	11.5612i	−0.907402	+	0.523889i	−0.879594	−	0.475725i	$-0.842186\pi$
$487$	−20.0246	+	11.5612i	−0.907402	+	0.523889i	−0.0278074	+	0.999613i	$0.508853\pi$
$488$	−25.1525	−	14.5218i	−1.13860	−	0.657371i
$489$	8.48273	−	19.9028i	0.383602	−	0.900037i
$490$	51.5971			2.33092
$491$	−14.8527	−	25.7257i	−0.670295	−	1.16098i	−0.977820	−	0.209445i	$-0.932834\pi$
$491$	−14.8527	−	25.7257i	−0.670295	−	1.16098i	0.307526	−	0.951540i	$-0.400499\pi$
$492$	25.3630	−	59.5086i	1.14345	−	2.68286i
$493$	13.0329	+	22.5736i	0.586971	+	1.01666i
$494$	−4.87967	−	0.762161i	−0.219547	−	0.0342912i
$495$	−9.09141	−	9.46988i	−0.408629	−	0.425640i
$496$	−35.6768	−	20.5980i	−1.60194	−	0.924878i
$497$	−1.62989			−0.0731105
$498$	−35.0281	−	14.9292i	−1.56965	−	0.668995i
$499$	32.4943	+	18.7606i	1.45465	+	0.839841i	0.998740	−	0.0501867i	$-0.0159817\pi$
$499$	32.4943	+	18.7606i	1.45465	+	0.839841i	0.455907	+	0.890027i	$0.349315\pi$
$500$			29.9241i			1.33825i
$501$	16.5197	−	38.7597i	0.738045	−	1.73166i
$502$	−63.0833	+	36.4212i	−2.81555	+	1.62556i
$503$	14.5097	+	25.1315i	0.646956	+	1.12056i	0.983846	+	0.179016i	$0.0572914\pi$
$503$	14.5097	+	25.1315i	0.646956	+	1.12056i	−0.336891	+	0.941544i	$0.609375\pi$
$504$	−4.36007	−	4.54158i	−0.194213	−	0.202298i
$505$	−37.4637	−	21.6297i	−1.66711	−	0.962509i
$506$	−5.68176	−	9.84110i	−0.252585	−	0.437490i
$507$	17.0350	+	14.7244i	0.756553	+	0.653933i
$508$	−28.2874	+	48.9953i	−1.25505	+	2.17381i
$509$	7.13709	−	4.12060i	0.316346	−	0.182643i	−0.333417	−	0.942780i	$-0.608202\pi$
$509$	7.13709	−	4.12060i	0.316346	−	0.182643i	0.649763	+	0.760137i	$0.274868\pi$
$510$	75.3400	−	56.5996i	3.33611	−	2.50627i
$511$	0.491043	−	0.850512i	0.0217225	−	0.0376244i
$512$		−	26.1624i		−	1.15622i
$513$	2.07870	+	1.69850i	0.0917770	+	0.0749908i
$514$	−22.5026	+	12.9919i	−0.992548	+	0.573048i
$515$	26.7225	−	15.4282i	1.17753	−	0.679849i
$516$	−3.66906	−	30.2489i	−0.161521	−	1.33163i
$517$	−6.39691	−	11.0798i	−0.281336	−	0.487288i
$518$	−1.32132	+	0.762864i	−0.0580555	+	0.0335183i
$519$	2.19956	+	18.1338i	0.0965498	+	0.795988i
$520$	29.3084	+	75.8654i	1.28526	+	3.32692i
$521$	37.2716			1.63290			0.816449	−	0.577418i	$-0.195940\pi$
$521$	37.2716			1.63290			0.816449	+	0.577418i	$0.195940\pi$
$522$	27.2457	+	7.89918i	1.19251	+	0.345738i
$523$	−1.53435	+	2.65756i	−0.0670922	+	0.116207i	−0.897620	−	0.440770i	$-0.854706\pi$
$523$	−1.53435	+	2.65756i	−0.0670922	+	0.116207i	0.830528	+	0.556977i	$0.188039\pi$
$524$	9.70954	−	16.8174i	0.424163	−	0.734672i
$525$	−0.782814	−	1.04201i	−0.0341648	−	0.0454769i
$526$			61.2421i			2.67028i
$527$		−	26.7788i		−	1.16650i
$528$	18.2335	+	24.2706i	0.793509	+	1.05624i
$529$	7.72015	−	13.3717i	0.335659	−	0.581378i
$530$	−17.4195	+	30.1714i	−0.756653	+	1.31056i
$531$	32.1032	+	9.30748i	1.39316	+	0.403910i
$532$	−0.678737			−0.0294270
$533$	−4.13102	+	26.4485i	−0.178934	+	1.14561i
$534$	0.756876	+	6.23993i	0.0327532	+	0.270028i
$535$	−2.89670	+	1.67241i	−0.125235	+	0.0723046i
$536$	32.9969	+	57.1524i	1.42525	+	2.46861i
$537$	1.47852	+	12.1894i	0.0638030	+	0.526013i
$538$	49.6896	−	28.6883i	2.14227	−	1.23684i
$539$	−9.35723	+	5.40240i	−0.403044	+	0.232698i
$540$	11.7979	−	72.4247i	0.507702	−	3.11666i
$541$			7.25981i			0.312124i	0.987747	+	0.156062i	$0.0498799\pi$
$541$			7.25981i			0.312124i	−0.987747	+	0.156062i	$0.950120\pi$
$542$	35.3608	−	61.2466i	1.51887	−	2.63077i
$543$	−21.7850	+	16.3661i	−0.934885	+	0.702338i
$544$	−86.9915	+	50.2246i	−3.72973	+	2.15336i
$545$	2.19273	−	3.79791i	0.0939261	−	0.162685i
$546$	3.66912	+	2.28929i	0.157024	+	0.0979725i
$547$	−12.8226	−	22.2094i	−0.548256	−	0.949607i	−0.998394	−	0.0566482i	$-0.981959\pi$
$547$	−12.8226	−	22.2094i	−0.548256	−	0.949607i	0.450138	−	0.892959i	$-0.351375\pi$
$548$	9.71888	+	5.61120i	0.415170	+	0.239698i
$549$	−7.50987	−	7.82250i	−0.320513	−	0.333856i
$550$	5.95354	+	10.3118i	0.253860	+	0.439698i
$551$	1.59554	−	0.921184i	0.0679722	−	0.0392438i
$552$	15.0029	−	35.2010i	0.638567	−	1.49825i
$553$		−	0.713370i		−	0.0303356i
$554$	−14.7943	−	8.54147i	−0.628548	−	0.362892i
$555$	−9.85501	−	4.20028i	−0.418322	−	0.178292i
$556$	−81.7223			−3.46580
$557$	−7.49468	−	4.32706i	−0.317560	−	0.183343i	0.332744	−	0.943017i	$-0.392025\pi$
$557$	−7.49468	−	4.32706i	−0.317560	−	0.183343i	−0.650304	+	0.759674i	$0.725359\pi$
$558$	−20.1834	−	21.0236i	−0.854430	−	0.889999i
$559$	4.54395	+	11.7621i	0.192189	+	0.497483i
$560$	4.12210	+	7.13969i	0.174191	+	0.301707i
$561$	−7.73686	+	18.1528i	−0.326650	+	0.766412i
$562$	1.87432	+	3.24642i	0.0790634	+	0.136942i
$563$	−46.1111			−1.94335			−0.971677	−	0.236315i	$-0.924060\pi$
$563$	−46.1111			−1.94335			−0.971677	+	0.236315i	$0.924060\pi$
$564$	28.0393	−	65.7878i	1.18067	−	2.77017i
$565$	−11.1643	−	6.44572i	−0.469686	−	0.271173i
$566$	45.8786	−	26.4880i	1.92842	−	1.11338i
$567$	−1.09134	−	2.08190i	−0.0458322	−	0.0874317i
$568$	25.0714	+	43.4249i	1.05197	+	1.82207i
$569$	17.2315			0.722382			0.361191	−	0.932492i	$-0.382370\pi$
$569$	17.2315			0.722382			0.361191	+	0.932492i	$0.382370\pi$
$570$	−4.00055	−	5.32515i	−0.167565	−	0.223046i
$571$	10.7707	−	18.6554i	0.450741	−	0.780706i	−0.547692	−	0.836680i	$-0.684493\pi$
$571$	10.7707	−	18.6554i	0.450741	−	0.780706i	0.998432	+	0.0559746i	$0.0178266\pi$
$572$	−22.0089	−	17.7446i	−0.920238	−	0.741938i
$573$	−1.69390	−	13.9651i	−0.0707637	−	0.583399i
$574$			5.14150i			0.214602i
$575$	3.96065	−	6.86005i	0.165171	−	0.286084i
$576$	−11.6552	+	40.2008i	−0.485632	+	1.67503i
$577$		−	19.9386i		−	0.830056i	−0.909809	−	0.415028i	$-0.863772\pi$
$577$		−	19.9386i		−	0.830056i	0.909809	−	0.415028i	$-0.136228\pi$
$578$	−83.6322	−	48.2851i	−3.47864	−	2.00839i
$579$	5.23448	−	12.2815i	0.217538	−	0.510404i
$580$	−43.6150	−	25.1811i	−1.81101	−	1.04559i
$581$	2.16545			0.0898381
$582$	7.48911	+	61.7426i	0.310433	+	2.55931i
$583$		−	7.29552i		−	0.302149i
$584$	−30.2134			−1.25024
$585$	2.62254	+	30.2523i	0.108428	+	1.25078i
$586$	−8.94111			−0.369354
$587$		−	16.5883i		−	0.684674i	−0.939577	−	0.342337i	$-0.888782\pi$
$587$		−	16.5883i		−	0.684674i	0.939577	−	0.342337i	$-0.111218\pi$
$588$	−55.5600	−	23.6801i	−2.29125	−	0.976549i
$589$	−1.89277			−0.0779902
$590$	−71.8231	−	41.4671i	−2.95691	−	1.70717i
$591$	6.88848	−	0.835543i	0.283354	−	0.0343696i
$592$	21.4537	+	12.3863i	0.881741	+	0.509073i
$593$		−	15.4909i		−	0.636137i	−0.948068	−	0.318068i	$-0.896966\pi$
$593$		−	15.4909i		−	0.636137i	0.948068	−	0.318068i	$-0.103034\pi$
$594$	7.60781	+	20.0828i	0.312152	+	0.824006i
$595$	−2.67951	+	4.64104i	−0.109849	+	0.190264i
$596$			38.4142i			1.57350i
$597$	20.5319	+	8.75083i	0.840313	+	0.358148i
$598$	−4.05635	+	25.9705i	−0.165877	+	1.06201i
$599$	−17.4824	+	30.2804i	−0.714312	+	1.23722i	0.248913	+	0.968526i	$0.419927\pi$
$599$	−17.4824	+	30.2804i	−0.714312	+	1.23722i	−0.963224	+	0.268698i	$0.913407\pi$
$600$	−15.7206	+	36.8848i	−0.641789	+	1.50581i
$601$	28.6673			1.16936			0.584682	−	0.811262i	$-0.301219\pi$
$601$	28.6673			1.16936			0.584682	+	0.811262i	$0.301219\pi$
$602$	1.21092	+	2.09738i	0.0493535	+	0.0854827i
$603$	5.89074	+	23.9253i	0.239889	+	0.974314i
$604$	54.5880	−	31.5164i	2.22115	−	1.28238i
$605$	20.8363	+	12.0298i	0.847115	+	0.489082i
$606$	42.5066	+	56.5806i	1.72671	+	2.29843i
$607$	16.2734			0.660518			0.330259	−	0.943890i	$-0.392864\pi$
$607$	16.2734			0.660518			0.330259	+	0.943890i	$0.392864\pi$
$608$	3.54996	+	6.14870i	0.143970	+	0.249363i
$609$	−1.60155	+	0.194261i	−0.0648980	+	0.00787184i
$610$	13.4528	+	23.3010i	0.544689	+	0.943429i
$611$	−4.56691	+	29.2393i	−0.184757	+	1.18289i
$612$	−107.102	+	26.3700i	−4.32935	+	1.06595i
$613$	−18.0575	−	10.4255i	−0.729336	−	0.421082i	0.0888435	−	0.996046i	$-0.471683\pi$
$613$	−18.0575	−	10.4255i	−0.729336	−	0.421082i	−0.818179	+	0.574964i	$0.805016\pi$
$614$	−54.8904			−2.21520
$615$	−28.8631	+	21.6836i	−1.16387	+	0.874366i
$616$	−2.83287	−	1.63556i	−0.114140	−	0.0658985i
$617$			17.9721i			0.723530i	0.932269	+	0.361765i	$0.117826\pi$
$617$			17.9721i			0.723530i	−0.932269	+	0.361765i	$0.882174\pi$
$618$	−50.1111	+	6.07826i	−2.01576	+	0.244503i
$619$	6.56515	−	3.79039i	0.263876	−	0.152349i	−0.362226	−	0.932090i	$-0.617983\pi$
$619$	6.56515	−	3.79039i	0.263876	−	0.152349i	0.626101	+	0.779742i	$0.284650\pi$
$620$	25.8700	+	44.8082i	1.03897	+	1.79954i
$621$	9.03974	−	11.0632i	0.362752	−	0.443952i
$622$	19.0077	+	10.9741i	0.762138	+	0.440021i
$623$	−0.178735	−	0.309578i	−0.00716085	−	0.0124030i
$624$	2.40335	−	70.1776i	0.0962108	−	2.80935i
$625$	15.5524	−	26.9376i	0.622097	−	1.07750i
$626$	−28.4295	+	16.4138i	−1.13627	+	0.656027i
$627$	1.28307	+	0.546854i	0.0512409	+	0.0218392i
$628$	25.3646	−	43.9328i	1.01216	−	1.75311i
$629$			16.1030i			0.642069i
$630$	1.39435	+	5.66316i	0.0555521	+	0.225626i
$631$	11.9576	−	6.90373i	0.476025	−	0.274833i	−0.242734	−	0.970093i	$-0.578044\pi$
$631$	11.9576	−	6.90373i	0.476025	−	0.274833i	0.718758	+	0.695260i	$0.244711\pi$
$632$	−19.0062	+	10.9732i	−0.756026	+	0.436492i
$633$	27.4299	+	11.6908i	1.09024	+	0.464669i
$634$	−43.5519	−	75.4342i	−1.72967	−	2.99587i
$635$	27.3428	−	15.7864i	1.08507	−	0.626464i
$636$	32.6043	−	24.4942i	1.29284	−	0.971257i
$637$	24.6935	+	3.85691i	0.978393	+	0.152816i
$638$	14.7392			0.583531
$639$	4.47583	+	18.1787i	0.177061	+	0.719136i
$640$	13.3449	−	23.1141i	0.527505	−	0.913665i
$641$	−17.2674	+	29.9080i	−0.682022	+	1.18130i	0.292341	+	0.956314i	$0.405566\pi$
$641$	−17.2674	+	29.9080i	−0.682022	+	1.18130i	−0.974363	+	0.224982i	$0.927768\pi$
$642$	5.43201	−	0.658879i	0.214384	−	0.0260039i
$643$			9.01569i			0.355544i	0.984072	+	0.177772i	$0.0568890\pi$
$643$			9.01569i			0.355544i	−0.984072	+	0.177772i	$0.943111\pi$
$644$			3.61236i			0.142347i
$645$	−6.66725	+	15.6432i	−0.262523	+	0.615950i
$646$	−5.00587	+	8.67041i	−0.196953	+	0.341133i
$647$	2.14777	−	3.72004i	0.0844374	−	0.146250i	−0.820714	−	0.571339i	$-0.806424\pi$
$647$	2.14777	−	3.72004i	0.0844374	−	0.146250i	0.905151	+	0.425089i	$0.139757\pi$
$648$	−38.6805	+	61.1008i	−1.51951	+	2.40027i
$649$	17.3670			0.681714
$650$	4.25038	−	27.2127i	0.166714	−	1.06737i
$651$	1.52471	+	0.649844i	0.0597582	+	0.0254694i
$652$	54.4165	−	31.4174i	2.13112	−	1.23040i
$653$	18.5812	+	32.1836i	0.727138	+	1.25944i	0.958088	+	0.286474i	$0.0924833\pi$
$653$	18.5812	+	32.1836i	0.727138	+	1.25944i	−0.230950	+	0.972966i	$0.574183\pi$
$654$	−5.73590	+	4.30913i	−0.224291	+	0.168500i
$655$	−9.38531	+	5.41861i	−0.366715	+	0.211723i
$656$	72.2960	−	41.7401i	2.82269	−	1.62968i
$657$	−10.8345	−	3.14117i	−0.422693	−	0.122549i
$658$			5.68402i			0.221586i
$659$	−0.658878	+	1.14121i	−0.0256663	+	0.0444553i	−0.878573	−	0.477608i	$-0.841504\pi$
$659$	−0.658878	+	1.14121i	−0.0256663	+	0.0444553i	0.852907	+	0.522063i	$0.174837\pi$
$660$	−4.59090	−	37.8488i	−0.178700	−	1.47326i
$661$	−29.0245	+	16.7573i	−1.12892	+	0.651783i	−0.943664	−	0.330906i	$-0.892646\pi$
$661$	−29.0245	+	16.7573i	−1.12892	+	0.651783i	−0.185258	+	0.982690i	$0.559312\pi$
$662$	−18.4015	+	31.8724i	−0.715196	+	1.23875i
$663$	40.2873	−	21.4559i	1.56463	−	0.833280i
$664$	−33.3095	−	57.6938i	−1.29266	−	2.23895i
$665$	0.328036	+	0.189392i	0.0127207	+	0.00734430i
$666$	12.1369	+	12.6422i	0.470297	+	0.489875i
$667$	−4.90270	−	8.49173i	−0.189833	−	0.328801i
$668$	105.973	−	61.1837i	4.10023	−	2.36727i
$669$	−9.81484	−	13.0646i	−0.379463	−	0.505105i
$670$		−	61.1359i		−	2.36189i
$671$	−4.87939	−	2.81712i	−0.188367	−	0.108754i
$672$	−0.748620	−	6.17186i	−0.0288786	−	0.238085i
$673$	23.1500			0.892367			0.446184	−	0.894941i	$-0.352783\pi$
$673$	23.1500			0.892367			0.446184	+	0.894941i	$0.352783\pi$
$674$	−56.8919	−	32.8466i	−2.19140	−	1.26520i
$675$	−9.47213	+	11.5924i	−0.364583	+	0.446192i
$676$	13.8701	+	63.9072i	0.533465	+	2.45797i
$677$	−8.44612	−	14.6291i	−0.324611	−	0.562243i	0.656823	−	0.754045i	$-0.271900\pi$
$677$	−8.44612	−	14.6291i	−0.324611	−	0.562243i	−0.981434	+	0.191803i	$0.938567\pi$
$678$	12.6671	+	16.8612i	0.486477	+	0.647551i
$679$	−1.76854	−	3.06319i	−0.0678702	−	0.117555i
$680$	164.867			6.32237
$681$	−31.5650	+	3.82870i	−1.20958	+	0.146716i
$682$	−13.1137	−	7.57122i	−0.502151	−	0.289917i
$683$	−19.4097	+	11.2062i	−0.742692	+	0.428793i	−0.823047	−	0.567973i	$-0.807728\pi$
$683$	−19.4097	+	11.2062i	−0.742692	+	0.428793i	0.0803552	+	0.996766i	$0.474395\pi$
$684$	1.86388	+	7.57016i	0.0712671	+	0.289452i
$685$	−3.13145	−	5.42383i	−0.119646	−	0.207234i
$686$	9.64792			0.368359
$687$	−22.5300	+	2.73279i	−0.859575	+	0.104263i
$688$	19.6612	−	34.0542i	0.749576	−	1.29830i
$689$	−10.5920	+	13.1374i	−0.403523	+	0.500496i
$690$	−28.3414	+	21.2917i	−1.07894	+	0.810559i
$691$		−	26.2186i		−	0.997404i	−0.866774	−	0.498702i	$-0.833810\pi$
$691$		−	26.2186i		−	0.997404i	0.866774	−	0.498702i	$-0.166190\pi$
$692$	−26.5260	+	45.9444i	−1.00837	+	1.74654i
$693$	−0.845820	−	0.881031i	−0.0321300	−	0.0334676i
$694$			50.5283i			1.91803i
$695$	39.4967	+	22.8034i	1.49820	+	0.864984i
$696$	29.8111	+	39.6816i	1.12999	+	1.50413i
$697$	46.9949	+	27.1325i	1.78006	+	1.02772i
$698$	−62.9444			−2.38248
$699$	−6.70516	+	5.03730i	−0.253613	+	0.190528i
$700$		−	3.78515i		−	0.143065i
$701$	−49.5379			−1.87102			−0.935510	−	0.353300i	$-0.885059\pi$
$701$	−49.5379			−1.87102			−0.935510	+	0.353300i	$0.885059\pi$
$702$	15.4574	−	47.2095i	0.583401	−	1.78181i
$703$	1.13819			0.0429275
$704$			21.7476i			0.819642i
$705$	−31.9086	+	23.9716i	−1.20175	+	0.902821i
$706$	5.81041			0.218678
$707$	−3.48544	−	2.01232i	−0.131084	−	0.0756811i
$708$	58.3084	+	77.6145i	2.19136	+	2.91693i
$709$	−25.0446	−	14.4595i	−0.940569	−	0.543038i	−0.0504304	−	0.998728i	$-0.516059\pi$
$709$	−25.0446	−	14.4595i	−0.940569	−	0.543038i	−0.890139	+	0.455690i	$0.849393\pi$
$710$		−	46.4516i		−	1.74330i
$711$	−7.95643	+	1.95898i	−0.298389	+	0.0734676i
$712$	−5.49868	+	9.52399i	−0.206072	+	0.356927i
$713$			10.0737i			0.377261i
$714$	7.00926	−	5.26575i	0.262315	−	0.197066i
$715$	5.68561	+	14.7173i	0.212630	+	0.550395i
$716$	−17.8306	+	30.8835i	−0.666360	+	1.15417i
$717$	27.1318	−	3.29097i	1.01326	−	0.122903i
$718$	14.8064			0.552571
$719$	−5.28737	−	9.15800i	−0.197186	−	0.341536i	0.750429	−	0.660951i	$-0.229847\pi$
$719$	−5.28737	−	9.15800i	−0.197186	−	0.341536i	−0.947615	+	0.319415i	$0.896514\pi$
$720$	68.3115	−	65.5814i	2.54582	−	2.44407i
$721$	2.48613	−	1.43537i	0.0925883	−	0.0534559i
$722$	−43.0160	−	24.8353i	−1.60089	−	0.924274i
$723$	28.0040	−	3.39676i	1.04148	−	0.126327i
$724$	−79.1354			−2.94104
$725$	5.13721	+	8.89791i	0.190791	+	0.330460i
$726$	−23.6410	−	31.4686i	−0.877398	−	1.16791i
$727$	−4.91833	−	8.51880i	−0.182411	−	0.315945i	0.760290	−	0.649584i	$-0.225057\pi$
$727$	−4.91833	−	8.51880i	−0.182411	−	0.315945i	−0.942701	+	0.333639i	$0.891723\pi$
$728$	2.72671	+	7.05814i	0.101059	+	0.261592i
$729$	−20.2232	+	17.8892i	−0.749006	+	0.662563i
$730$	24.2395	+	13.9947i	0.897143	+	0.517966i
$731$	25.5609			0.945403
$732$	−3.79226	−	31.2646i	−0.140166	−	1.15557i
$733$	−42.6470	−	24.6222i	−1.57520	−	0.909443i	−0.995515	−	0.0946033i	$-0.969842\pi$
$733$	−42.6470	−	24.6222i	−1.57520	−	0.909443i	−0.579686	−	0.814840i	$-0.696825\pi$
$734$		−	35.4699i		−	1.30922i
$735$	20.2448	+	26.9479i	0.746739	+	0.993988i
$736$	32.7245	−	18.8935i	1.20624	−	0.696423i
$737$	6.40115	+	11.0871i	0.235789	+	0.408399i
$738$	57.3448	−	14.1191i	2.11089	−	0.519730i
$739$	7.35764	+	4.24793i	0.270655	+	0.156263i	0.629185	−	0.777255i	$-0.283389\pi$
$739$	7.35764	+	4.24793i	0.270655	+	0.156263i	−0.358530	+	0.933518i	$0.616722\pi$
$740$	−15.5565	−	26.9447i	−0.571869	−	0.990506i
$741$	−1.51654	−	2.84757i	−0.0557115	−	0.104608i
$742$	−1.62062	+	2.80700i	−0.0594949	+	0.103048i
$743$	23.6772	−	13.6701i	0.868634	−	0.501506i	0.00173965	−	0.999998i	$-0.499446\pi$
$743$	23.6772	−	13.6701i	0.868634	−	0.501506i	0.866894	+	0.498493i	$0.166113\pi$
$744$	−6.13983	−	50.6187i	−0.225097	−	1.85577i
$745$	10.7189	−	18.5657i	0.392711	−	0.680195i
$746$			20.7346i			0.759146i
$747$	−5.94654	−	24.1520i	−0.217573	−	0.883674i
$748$	−49.6318	+	28.6549i	−1.81472	+	1.04773i
$749$	−0.269494	+	0.155593i	−0.00984711	+	0.00568523i
$750$	−21.8423	+	16.4092i	−0.797569	+	0.599179i
$751$	16.2482	+	28.1427i	0.592906	+	1.02694i	0.993839	+	0.110835i	$0.0353526\pi$
$751$	16.2482	+	28.1427i	0.592906	+	1.02694i	−0.400933	+	0.916107i	$0.631314\pi$
$752$	79.9245	−	46.1444i	2.91455	−	1.68271i
$753$	−43.7734	−	18.6565i	−1.59519	−	0.679882i
$754$	−26.5417	−	21.3991i	−0.966591	−	0.779310i
$755$	−35.1768			−1.28021
$756$	1.09762	−	6.73804i	0.0399201	−	0.245060i
$757$	18.7348	−	32.4496i	0.680928	−	1.17940i	−0.293770	−	0.955876i	$-0.594910\pi$
$757$	18.7348	−	32.4496i	0.680928	−	1.17940i	0.974698	−	0.223525i	$-0.0717566\pi$
$758$	−50.5136	+	87.4921i	−1.83474	+	3.17786i
$759$	2.91045	−	6.82872i	0.105643	−	0.247867i
$760$		−	11.6531i		−	0.422702i
$761$		−	18.6887i		−	0.677465i	−0.940883	−	0.338732i	$-0.890002\pi$
$761$		−	18.6887i		−	0.677465i	0.940883	−	0.338732i	$-0.109998\pi$
$762$	−51.2744	+	6.21936i	−1.85748	+	0.225304i
$763$	0.204000	−	0.353339i	0.00738531	−	0.0127917i
$764$	20.4280	−	35.3823i	0.739058	−	1.28009i
$765$	59.1211	+	17.1406i	2.13753	+	0.619720i
$766$	−47.1884			−1.70499
$767$	−31.2736	−	25.2142i	−1.12923	−	0.910434i
$768$	3.73314	−	2.80455i	0.134708	−	0.101200i
$769$	38.8944	−	22.4557i	1.40257	−	0.809773i	0.407912	−	0.913021i	$-0.366257\pi$
$769$	38.8944	−	22.4557i	1.40257	−	0.809773i	0.994656	+	0.103248i	$0.0329237\pi$
$770$	1.51516	+	2.62434i	0.0546027	+	0.0945746i
$771$	−15.6145	−	6.65502i	−0.562343	−	0.239675i
$772$	33.5791	−	19.3869i	1.20854	−	0.697750i
$773$	2.77119	−	1.59995i	0.0996728	−	0.0575461i	−0.449335	−	0.893363i	$-0.648339\pi$
$773$	2.77119	−	1.59995i	0.0996728	−	0.0575461i	0.549008	+	0.835817i	$0.315006\pi$
$774$	20.0674	−	19.2654i	0.721308	−	0.692480i
$775$		−	10.5555i		−	0.379165i
$776$	−54.4081	+	94.2376i	−1.95314	+	3.38293i
$777$	−0.916861	−	0.390773i	−0.0328922	−	0.0140189i
$778$	79.2663	−	45.7644i	2.84183	−	1.64073i
$779$	1.91777	−	3.32167i	0.0687112	−	0.119011i
$780$	−46.6837	+	74.8217i	−1.67155	+	2.67905i
$781$	4.86365	+	8.42408i	0.174035	+	0.301437i
$782$	46.1455	+	26.6421i	1.65016	+	0.952719i
$783$	6.56465	+	17.3291i	0.234602	+	0.619291i
$784$	−38.9705	−	67.4989i	−1.39180	−	2.41067i
$785$	−24.5176	+	14.1553i	−0.875072	+	0.505223i
$786$	17.5997	−	2.13477i	0.627762	−	0.0761447i
$787$			30.2482i			1.07823i	0.842232	+	0.539115i	$0.181241\pi$
$787$			30.2482i			1.07823i	−0.842232	+	0.539115i	$0.818759\pi$
$788$	17.4528	+	10.0764i	0.621732	+	0.358957i
$789$	−31.9852	+	24.0291i	−1.13870	+	0.855458i
$790$	20.3309			0.723343
$791$	−1.03867	−	0.599678i	−0.0369309	−	0.0213221i
$792$	−10.4626	+	36.0873i	−0.371771	+	1.28231i
$793$	4.69654	+	12.1571i	0.166779	+	0.431710i
$794$	−11.6223	−	20.1303i	−0.412458	−	0.714399i
$795$	−22.5925	+	2.74037i	−0.801274	+	0.0971910i
$796$	32.4103	+	56.1364i	1.14875	+	1.98970i
$797$	32.9516			1.16720			0.583602	−	0.812040i	$-0.301643\pi$
$797$	32.9516			1.16720			0.583602	+	0.812040i	$0.301643\pi$
$798$	−0.372192	−	0.495426i	−0.0131754	−	0.0175379i
$799$	51.9536	+	29.9954i	1.83799	+	1.06116i
$800$	−34.2898	+	19.7972i	−1.21233	+	0.699937i
$801$	−2.96199	+	2.84361i	−0.104657	+	0.100474i
$802$	28.4961	+	49.3567i	1.00623	+	1.74284i
$803$	−5.86116			−0.206836
$804$	−28.0578	+	65.8314i	−0.989523	+	2.32169i
$805$	1.00798	−	1.74587i	0.0355265	−	0.0615337i
$806$	12.6223	+	32.6731i	0.444602	+	1.15086i
$807$	34.4795	+	14.6954i	1.21373	+	0.517303i
$808$			123.816i			4.35583i
$809$	25.6465	−	44.4211i	0.901684	−	1.56176i	0.0763761	−	0.997079i	$-0.475665\pi$
$809$	25.6465	−	44.4211i	0.901684	−	1.56176i	0.825308	−	0.564683i	$-0.191002\pi$
$810$	59.3340	−	31.1032i	2.08478	−	1.09285i
$811$		−	51.3422i		−	1.80287i	−0.432915	−	0.901435i	$-0.642515\pi$
$811$		−	51.3422i		−	1.80287i	0.432915	−	0.901435i	$-0.357485\pi$
$812$	−4.05772	−	2.34273i	−0.142398	−	0.0822136i
$813$	45.8618	−	5.56283i	1.60844	−	0.195097i
$814$	7.88573	+	4.55283i	0.276395	+	0.159577i
$815$	−35.0663			−1.22832
$816$	−130.946	−	55.8102i	−4.58403	−	1.95375i
$817$		−	1.80668i		−	0.0632079i
$818$	94.0856			3.28962
$819$	0.243988	+	2.81452i	0.00852562	+	0.0983474i
$820$	−104.847			−3.66141
$821$		−	3.85541i		−	0.134555i	−0.997734	−	0.0672774i	$-0.978569\pi$
$821$		−	3.85541i		−	0.134555i	0.997734	−	0.0672774i	$-0.0214313\pi$
$822$	1.23370	+	10.1710i	0.0430301	+	0.354754i
$823$	−41.8727			−1.45959			−0.729796	−	0.683665i	$-0.760385\pi$
$823$	−41.8727			−1.45959			−0.729796	+	0.683665i	$0.760385\pi$
$824$	−76.4845	−	44.1583i	−2.66446	−	1.53833i
$825$	−3.04967	+	7.15536i	−0.106176	+	0.249118i
$826$	−6.68206	−	3.85789i	−0.232499	−	0.134233i
$827$			33.2317i			1.15558i	0.816185	+	0.577790i	$0.196085\pi$
$827$			33.2317i			1.15558i	−0.816185	+	0.577790i	$0.803915\pi$
$828$	40.2897	−	9.91988i	1.40017	−	0.344740i
$829$	−23.8687	+	41.3417i	−0.828993	+	1.43586i	0.0698363	+	0.997558i	$0.477752\pi$
$829$	−23.8687	+	41.3417i	−0.828993	+	1.43586i	−0.898829	+	0.438299i	$0.855581\pi$
$830$			61.7151i			2.14216i
$831$	−1.34372	−	11.0780i	−0.0466130	−	0.384292i
$832$	31.5742	−	39.1620i	1.09464	−	1.35770i
$833$	25.3321	−	43.8765i	0.877706	−	1.52023i
$834$	−44.8132	−	59.6510i	−1.55175	−	2.06555i
$835$	−68.2898			−2.36327
$836$	2.02538	+	3.50805i	0.0700491	+	0.121329i
$837$	3.06090	−	18.7901i	0.105800	−	0.649482i
$838$	−45.9909	+	26.5529i	−1.58873	+	0.917254i
$839$	−13.7524	−	7.93993i	−0.474784	−	0.274117i	0.243456	−	0.969912i	$-0.421719\pi$
$839$	−13.7524	−	7.93993i	−0.474784	−	0.274117i	−0.718240	+	0.695795i	$0.755052\pi$
$840$	−4.00085	+	9.38709i	−0.138042	+	0.323886i
$841$	−16.2818			−0.561440
$842$	−23.5666	−	40.8185i	−0.812159	−	1.40670i
$843$	−0.960110	+	2.25268i	−0.0330679	+	0.0775865i
$844$	43.2992	+	74.9965i	1.49042	+	2.58148i
$845$	11.1289	−	34.7568i	0.382846	−	1.19567i
$846$	63.3956	−	15.6089i	2.17959	−	0.536644i
$847$	1.93850	+	1.11920i	0.0666078	+	0.0384560i
$848$	52.6266			1.80720
$849$	31.8351	+	13.5683i	1.09258	+	0.465665i
$850$	−48.3527	−	27.9165i	−1.65848	−	0.957527i
$851$		−	6.05763i		−	0.207653i
$852$	−21.3186	+	50.0193i	−0.730363	+	1.71363i
$853$	−35.9630	+	20.7633i	−1.23135	+	0.710921i	−0.967312	−	0.253591i	$-0.918388\pi$
$853$	−35.9630	+	20.7633i	−1.23135	+	0.710921i	−0.264040	+	0.964512i	$0.585055\pi$
$854$	1.25158	+	2.16781i	0.0428283	+	0.0741809i
$855$	1.21153	−	4.17878i	0.0414333	−	0.142911i
$856$	8.29086	+	4.78673i	0.283376	+	0.163607i
$857$	20.4844	+	35.4799i	0.699732	+	1.21197i	0.968559	+	0.248783i	$0.0800307\pi$
$857$	20.4844	+	35.4799i	0.699732	+	1.21197i	−0.268827	+	0.963188i	$0.586636\pi$
$858$	0.883398	−	25.7952i	0.0301587	−	0.880633i
$859$	−14.2210	+	24.6315i	−0.485215	+	0.840417i	−0.999856	−	0.0169889i	$-0.994592\pi$
$859$	−14.2210	+	24.6315i	−0.485215	+	0.840417i	0.514641	+	0.857406i	$0.327925\pi$
$860$	−42.7702	+	24.6934i	−1.45845	+	0.842038i
$861$	−2.68528	+	2.01733i	−0.0915140	+	0.0687505i
$862$	2.64801	−	4.58649i	0.0901917	−	0.156217i
$863$		−	24.5762i		−	0.836584i	−0.908313	−	0.418292i	$-0.862629\pi$
$863$		−	24.5762i		−	0.836584i	0.908313	−	0.418292i	$-0.137371\pi$
$864$	−66.7809	+	25.2981i	−2.27193	+	0.860660i
$865$	25.6403	−	14.8034i	0.871795	−	0.503331i
$866$	56.2424	−	32.4716i	1.91119	−	1.10343i
$867$	−7.59605	−	62.6243i	−0.257975	−	2.12683i
$868$	2.40682	+	4.16873i	0.0816928	+	0.141496i
$869$	−3.68705	+	2.12872i	−0.125075	+	0.0722119i
$870$	−5.53640	−	45.6439i	−0.187702	−	1.54747i
$871$	4.56994	−	29.2586i	0.154846	−	0.991391i
$872$	−12.5519			−0.425062
$873$	−29.3082	+	28.1368i	−0.991931	+	0.952288i
$874$	1.88311	−	3.26164i	0.0636970	−	0.110326i
$875$	0.776834	−	1.34552i	0.0262618	−	0.0454867i
$876$	−19.6784	−	26.1940i	−0.664872	−	0.885014i
$877$		−	14.6119i		−	0.493410i	−0.969091	−	0.246705i	$-0.920652\pi$
$877$		−	14.6119i		−	0.493410i	0.969091	−	0.246705i	$-0.0793478\pi$
$878$			40.6483i			1.37181i
$879$	−3.50816	−	4.66972i	−0.118327	−	0.157506i
$880$	24.6010	−	42.6102i	0.829300	−	1.43639i
$881$	1.19861	−	2.07605i	0.0403820	−	0.0699438i	−0.845128	−	0.534564i	$-0.820476\pi$
$881$	1.19861	−	2.07605i	0.0403820	−	0.0699438i	0.885510	+	0.464620i	$0.153809\pi$
$882$	−13.1822	−	53.5397i	−0.443868	−	1.80277i
$883$	−5.90861			−0.198840			−0.0994202	−	0.995046i	$-0.531699\pi$
$883$	−5.90861			−0.198840			−0.0994202	+	0.995046i	$0.531699\pi$
$884$	130.977	+	20.4575i	4.40524	+	0.688059i
$885$	−6.52346	−	53.7815i	−0.219284	−	1.80785i
$886$	−21.7347	+	12.5485i	−0.730192	+	0.421577i
$887$	13.6302	+	23.6081i	0.457656	+	0.792683i	0.998837	−	0.0482229i	$-0.0153558\pi$
$887$	13.6302	+	23.6081i	0.457656	+	0.792683i	−0.541181	+	0.840906i	$0.682022\pi$
$888$	3.69208	+	30.4387i	0.123898	+	1.02146i
$889$	2.54384	−	1.46869i	0.0853178	−	0.0492582i
$890$	8.82292	−	5.09391i	0.295745	−	0.170748i
$891$	−7.50371	+	11.8531i	−0.251384	+	0.397093i
$892$		−	47.4578i		−	1.58900i
$893$	2.12013	−	3.67217i	0.0709473	−	0.122884i
$894$	−28.0394	+	21.0648i	−0.937777	+	0.704511i
$895$	17.2352	−	9.95073i	0.576108	−	0.332616i
$896$	1.24155	−	2.15042i	0.0414772	−	0.0718406i
$897$	−15.1553	+	8.07130i	−0.506020	+	0.269493i
$898$	−21.6281	−	37.4610i	−0.721739	−	1.25009i
$899$	−11.3156	−	6.53308i	−0.377397	−	0.217890i
$900$	−42.2169	+	10.3944i	−1.40723	+	0.346479i
$901$	17.1045	+	29.6259i	0.569834	+	0.986982i
$902$	26.5739	−	15.3424i	0.884813	−	0.510847i
$903$	−0.620288	+	1.45537i	−0.0206419	+	0.0484315i
$904$			36.8976i			1.22719i
$905$	38.2464	+	22.0816i	1.27135	+	0.734017i
$906$	52.9383	+	22.5627i	1.75876	+	0.749596i
$907$	44.2501			1.46930			0.734651	−	0.678445i	$-0.237346\pi$
$907$	44.2501			1.46930			0.734651	+	0.678445i	$0.237346\pi$
$908$	−79.9741	−	46.1730i	−2.65403	−	1.53231i
$909$	−12.8727	+	44.4002i	−0.426960	+	1.47266i
$910$	1.08171	−	6.92557i	0.0358584	−	0.229580i
$911$	−6.61845	−	11.4635i	−0.219279	−	0.379802i	0.735309	−	0.677732i	$-0.237037\pi$
$911$	−6.61845	−	11.4635i	−0.219279	−	0.379802i	−0.954588	+	0.297930i	$0.903704\pi$
$912$	−3.94476	+	9.25549i	−0.130624	+	0.306480i
$913$	−6.46179	−	11.1921i	−0.213854	−	0.370406i
$914$	5.73107			0.189567
$915$	−6.89113	+	16.1685i	−0.227814	+	0.534514i
$916$	−57.0827	−	32.9567i	−1.88607	−	1.08892i
$917$	−0.873163	+	0.504121i	−0.0288344	+	0.0166475i
$918$	−77.9786	−	63.7162i	−2.57368	−	2.10295i
$919$	−21.5036	−	37.2452i	−0.709337	−	1.22861i	−0.965103	−	0.261869i	$-0.915661\pi$
$919$	−21.5036	−	37.2452i	−0.709337	−	1.22861i	0.255767	−	0.966739i	$-0.417672\pi$
$920$	−62.0198			−2.04473
$921$	−21.5369	−	28.6679i	−0.709666	−	0.944639i
$922$	−4.06468	+	7.04023i	−0.133863	+	0.231858i
$923$	3.47228	−	22.2310i	0.114291	−	0.731741i
$924$	−0.427114	−	3.52127i	−0.0140510	−	0.115841i
$925$			6.34738i			0.208701i
$926$	21.1538	−	36.6394i	0.695156	−	1.20404i
$927$	−22.8362	−	23.7869i	−0.750040	−	0.781264i
$928$			49.0121i			1.60890i
$929$	5.52988	+	3.19267i	0.181429	+	0.104748i	0.587964	−	0.808887i	$-0.299930\pi$
$929$	5.52988	+	3.19267i	0.181429	+	0.104748i	−0.406535	+	0.913635i	$0.633263\pi$
$930$	−18.5205	+	43.4541i	−0.607310	+	1.42492i
$931$	−3.10126	−	1.79052i	−0.101640	−	0.0586818i
$932$	−24.3569			−0.797837
$933$	1.72641	+	14.2330i	0.0565200	+	0.465969i
$934$			8.36295i			0.273644i
$935$	31.9830			1.04596
$936$	71.2338	−	49.7942i	2.32835	−	1.62757i
$937$	58.7846			1.92041			0.960204	−	0.279298i	$-0.0901018\pi$
$937$	58.7846			1.92041			0.960204	+	0.279298i	$0.0901018\pi$
$938$		−	5.68779i		−	0.185713i
$939$	−19.7272	−	8.40787i	−0.643772	−	0.274380i
$940$	−115.910			−3.78057
$941$	46.2325	+	26.6923i	1.50714	+	0.870145i	0.999966	+	0.00829925i	$0.00264176\pi$
$941$	46.2325	+	26.6923i	1.50714	+	0.870145i	0.507170	+	0.861846i	$0.330692\pi$
$942$	45.9765	−	5.57675i	1.49800	−	0.181700i
$943$	−17.6785	−	10.2067i	−0.575692	−	0.332376i
$944$			125.278i			4.07744i
$945$	−2.41064	+	2.95024i	−0.0784180	+	0.0959714i
$946$	7.22687	−	12.5173i	0.234966	−	0.406973i
$947$			3.74167i			0.121588i	0.998150	+	0.0607940i	$0.0193633\pi$
$947$			3.74167i			0.121588i	−0.998150	+	0.0607940i	$0.980637\pi$
$948$	−21.8924	−	9.33072i	−0.711033	−	0.303048i
$949$	10.5545	+	8.50952i	0.342614	+	0.276231i
$950$	−1.97318	+	3.41765i	−0.0640184	+	0.110883i
$951$	22.3092	−	52.3436i	0.723427	−	1.69736i
$952$	15.3384			0.497122
$953$	11.2711	+	19.5221i	0.365107	+	0.632384i	0.988793	−	0.149291i	$-0.0476990\pi$
$953$	11.2711	+	19.5221i	0.365107	+	0.632384i	−0.623686	+	0.781675i	$0.714366\pi$
$954$	35.7577	+	10.3670i	1.15770	+	0.335644i
$955$	−19.7458	+	11.4003i	−0.638960	+	0.368904i
$956$	68.7418	+	39.6881i	2.22327	+	1.28361i
$957$	5.78311	+	7.69792i	0.186941	+	0.248838i
$958$	26.3472			0.851238
$959$	−0.291334	−	0.504606i	−0.00940768	−	0.0162946i
$960$	67.3472	−	8.16891i	2.17362	−	0.263651i
$961$	−8.78819	−	15.2216i	−0.283490	−	0.491019i
$962$	−7.59023	−	19.6474i	−0.244719	−	0.633458i
$963$	2.47543	+	2.57848i	0.0797697	+	0.0830904i
$964$	70.9518	+	40.9640i	2.28520	+	1.31936i
$965$	−21.6385			−0.696570
$966$	−2.63674	+	1.98087i	−0.0848358	+	0.0637335i
$967$	−1.37859	−	0.795929i	−0.0443325	−	0.0255954i	0.477670	−	0.878539i	$-0.341481\pi$
$967$	−1.37859	−	0.795929i	−0.0443325	−	0.0255954i	−0.522002	+	0.852944i	$0.674815\pi$
$968$		−	68.8630i		−	2.21334i
$969$	−6.49245	+	0.787506i	−0.208568	+	0.0252983i
$970$	87.3006	−	50.4030i	2.80305	−	1.61834i
$971$	−2.45081	−	4.24492i	−0.0786501	−	0.136226i	0.824018	−	0.566564i	$-0.191728\pi$
$971$	−2.45081	−	4.24492i	−0.0786501	−	0.136226i	−0.902668	+	0.430338i	$0.858394\pi$
$972$	−78.1656	+	6.26118i	−2.50716	+	0.200828i
$973$	3.67458	+	2.12152i	0.117802	+	0.0680128i
$974$	−30.6544	−	53.0950i	−0.982231	−	1.70127i
$975$	15.8802	−	8.45737i	0.508573	−	0.270853i
$976$	20.3214	−	35.1977i	0.650473	−	1.12665i
$977$	−3.34922	+	1.93367i	−0.107151	+	0.0618637i	−0.552618	−	0.833435i	$-0.686371\pi$
$977$	−3.34922	+	1.93367i	−0.107151	+	0.0618637i	0.445467	+	0.895298i	$0.353038\pi$
$978$	52.7721	+	22.4918i	1.68747	+	0.719210i
$979$	−1.06670	+	1.84758i	−0.0340919	+	0.0590489i
$980$			97.8897i			3.12697i
$981$	−4.50110	−	1.30498i	−0.143709	−	0.0416647i
$982$	68.2114	−	39.3819i	2.17671	−	1.25673i
$983$	−45.0382	+	26.0028i	−1.43650	+	0.829361i	−0.997604	−	0.0691791i	$-0.977962\pi$
$983$	−45.0382	+	26.0028i	−1.43650	+	0.829361i	−0.438891	+	0.898540i	$0.644629\pi$
$984$	95.0531	+	40.5123i	3.03018	+	1.29149i
$985$	−5.62335	−	9.73993i	−0.179175	−	0.310340i
$986$	−59.8536	+	34.5565i	−1.90613	+	1.10050i
$987$	−2.96862	+	2.23020i	−0.0944923	+	0.0709879i
$988$	1.44597	−	9.25768i	0.0460023	−	0.294526i
$989$	−9.61549			−0.305755
$990$	25.1093	−	24.1058i	0.798025	−	0.766131i
$991$	4.08818	−	7.08094i	0.129865	−	0.224933i	−0.793759	−	0.608233i	$-0.791879\pi$
$991$	4.08818	−	7.08094i	0.129865	−	0.224933i	0.923624	+	0.383299i	$0.125212\pi$
$992$	25.1765	−	43.6069i	0.799353	−	1.38452i
$993$	−23.8662	+	2.89487i	−0.757371	+	0.0918658i
$994$		−	4.32163i		−	0.137074i
$995$		−	36.1746i		−	1.14681i
$996$	28.3236	−	66.4551i	0.897469	−	2.10571i
$997$	−15.2339	+	26.3859i	−0.482463	+	0.835650i	−0.999797	−	0.0201329i	$-0.993591\pi$
$997$	−15.2339	+	26.3859i	−0.482463	+	0.835650i	0.517334	+	0.855783i	$0.326924\pi$
$998$	−49.7435	+	86.1583i	−1.57460	+	2.72729i
$999$	−1.84062	+	11.2991i	−0.0582347	+	0.357489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.4.11	✓	22
3.2	odd	2		351.2.l.b.199.1		22
9.2	odd	6		351.2.r.b.316.1		22
9.7	even	3		117.2.r.b.43.11	yes	22
13.10	even	6		117.2.r.b.49.11	yes	22
39.23	odd	6		351.2.r.b.10.1		22
117.88	even	6	inner	117.2.l.b.88.1	yes	22
117.101	odd	6		351.2.l.b.127.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.11	✓	22	1.1	even	1	trivial
117.2.l.b.88.1	yes	22	117.88	even	6	inner
117.2.r.b.43.11	yes	22	9.7	even	3
117.2.r.b.49.11	yes	22	13.10	even	6
351.2.l.b.127.11		22	117.101	odd	6
351.2.l.b.199.1		22	3.2	odd	2
351.2.r.b.10.1		22	39.23	odd	6
351.2.r.b.316.1		22	9.2	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.65149i q^{2} +(-1.38481 + 1.04034i) q^{3} -5.03038 q^{4} +(2.43120 + 1.40366i) q^{5} +(-2.75846 - 3.67179i) q^{6} +(0.226187 + 0.130589i) q^{7} -8.03502i q^{8} +(0.835370 - 2.88135i) q^{9} +(-3.72178 + 6.44631i) q^{10} -1.55873i q^{11} +(6.96610 - 5.23333i) q^{12} +(-2.26304 + 2.80689i) q^{13} +(-0.346256 + 0.599733i) q^{14} +(-4.82703 + 0.585497i) q^{15} +11.2440 q^{16} +(3.65449 + 6.32976i) q^{17} +(7.63985 + 2.21497i) q^{18} +(0.447398 - 0.258305i) q^{19} +(-12.2299 - 7.06093i) q^{20} +(-0.449083 + 0.0544718i) q^{21} +4.13296 q^{22} +(-1.37475 - 2.38113i) q^{23} +(8.35919 + 11.1269i) q^{24} +(1.44050 + 2.49502i) q^{25} +(-7.44243 - 6.00043i) q^{26} +(1.84077 + 4.85918i) q^{27} +(-1.13781 - 0.656914i) q^{28} +3.56626 q^{29} +(-1.55244 - 12.7988i) q^{30} +(-3.17297 - 1.83191i) q^{31} +13.7433i q^{32} +(1.62162 + 2.15854i) q^{33} +(-16.7833 + 9.68983i) q^{34} +(0.366605 + 0.634978i) q^{35} +(-4.20223 + 14.4943i) q^{36} +(1.90801 + 1.10159i) q^{37} +(0.684893 + 1.18627i) q^{38} +(0.213745 - 6.24134i) q^{39} +(11.2784 - 19.5348i) q^{40} +(6.42975 - 3.71222i) q^{41} +(-0.144431 - 1.19074i) q^{42} +(1.74859 - 3.02865i) q^{43} +7.84102i q^{44} +(6.07538 - 5.83257i) q^{45} +(6.31353 - 3.64512i) q^{46} +(7.10819 - 4.10392i) q^{47} +(-15.5707 + 11.6976i) q^{48} +(-3.46589 - 6.00310i) q^{49} +(-6.61553 + 3.81948i) q^{50} +(-11.6459 - 4.96356i) q^{51} +(11.3840 - 14.1197i) q^{52} +4.68042 q^{53} +(-12.8840 + 4.88077i) q^{54} +(2.18792 - 3.78960i) q^{55} +(1.04929 - 1.81742i) q^{56} +(-0.350832 + 0.823150i) q^{57} +9.45590i q^{58} +11.1417i q^{59} +(24.2818 - 2.94528i) q^{60} +(1.80731 - 3.13036i) q^{61} +(4.85729 - 8.41308i) q^{62} +(0.565223 - 0.542633i) q^{63} -13.9521 q^{64} +(-9.44183 + 3.64759i) q^{65} +(-5.72334 + 4.29970i) q^{66} +(-7.11290 + 4.10664i) q^{67} +(-18.3835 - 31.8411i) q^{68} +(4.38095 + 1.86719i) q^{69} +(-1.68364 + 0.972048i) q^{70} +(-5.40445 + 3.12026i) q^{71} +(-23.1517 - 6.71222i) q^{72} -3.76021i q^{73} +(-2.92085 + 5.05907i) q^{74} +(-4.59050 - 1.95650i) q^{75} +(-2.25058 + 1.29937i) q^{76} +(0.203554 - 0.352565i) q^{77} +(16.5488 + 0.566741i) q^{78} +(-1.36567 - 2.36542i) q^{79} +(27.3365 + 15.7827i) q^{80} +(-7.60431 - 4.81398i) q^{81} +(9.84289 + 17.0484i) q^{82} +(7.18029 - 4.14554i) q^{83} +(2.25906 - 0.274014i) q^{84} +20.5186i q^{85} +(8.03044 + 4.63638i) q^{86} +(-4.93858 + 3.71014i) q^{87} -12.5244 q^{88} +(-1.18531 - 0.684339i) q^{89} +(15.4650 + 16.1088i) q^{90} +(-0.878421 + 0.339353i) q^{91} +(6.91550 + 11.9780i) q^{92} +(6.29976 - 0.764133i) q^{93} +(10.8815 + 18.8473i) q^{94} +1.45029 q^{95} +(-14.2977 - 19.0317i) q^{96} +(-11.7284 - 6.77137i) q^{97} +(15.9171 - 9.18977i) q^{98} +(-4.49125 - 1.30212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Introduction

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