LMFDB - Embedded newform 117.2.r.b.49.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(43,117)] 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("117.43"); 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([4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.r (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			49.11
Character	$\chi$	$=$	117.49
Dual form			117.2.r.b.43.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.29626 + 1.32574i) q^{2} +(-0.208561 - 1.71945i) q^{3} +(2.51519 + 4.35644i) q^{4} +(-2.43120 - 1.40366i) q^{5} +(1.80064 - 4.22479i) q^{6} +0.261179i q^{7} +8.03502i q^{8} +(-2.91300 + 0.717221i) q^{9} +(-3.72178 - 6.44631i) q^{10} +(-1.34990 - 0.779366i) q^{11} +(6.96610 - 5.23333i) q^{12} +(-1.29932 + 3.36330i) q^{13} +(-0.346256 + 0.599733i) q^{14} +(-1.90646 + 4.47308i) q^{15} +(-5.62200 + 9.73759i) q^{16} +(3.65449 - 6.32976i) q^{17} +(-7.63985 - 2.21497i) q^{18} +(0.447398 + 0.258305i) q^{19} -14.1219i q^{20} +(0.449083 - 0.0544718i) q^{21} +(-2.06648 - 3.57925i) q^{22} +2.74949 q^{23} +(13.8158 - 1.67580i) 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} +(-1.78313 + 3.08847i) q^{29} +(-10.3079 + 7.74385i) q^{30} +(3.17297 + 1.83191i) q^{31} +(-11.9020 + 6.87163i) q^{32} +(-1.05854 + 2.48363i) q^{33} +(16.7833 - 9.68983i) q^{34} +(0.366605 - 0.634978i) q^{35} +(-10.4513 - 10.8864i) q^{36} +(1.90801 - 1.10159i) q^{37} +(0.684893 + 1.18627i) q^{38} +(6.05401 + 1.53265i) q^{39} +(11.2784 - 19.5348i) q^{40} -7.42443i q^{41} +(1.10342 + 0.470288i) q^{42} -3.49719 q^{43} -7.84102i q^{44} +(8.08884 + 2.34515i) q^{45} +(6.31353 + 3.64512i) q^{46} +(-7.10819 + 4.10392i) q^{47} +(17.9158 + 7.63585i) q^{48} +6.93179 q^{49} +7.63895i q^{50} +(-11.6459 - 4.96356i) q^{51} +(-17.9200 + 2.79895i) q^{52} +4.68042 q^{53} +(-2.21515 + 13.5983i) q^{54} +(2.18792 + 3.78960i) q^{55} -2.09858 q^{56} +(0.350832 - 0.823150i) q^{57} +(-8.18905 + 4.72795i) q^{58} +(-9.64903 + 5.57087i) q^{59} +(-24.2818 + 2.94528i) q^{60} -3.61462 q^{61} +(4.85729 + 8.41308i) q^{62} +(-0.187323 - 0.760814i) q^{63} -13.9521 q^{64} +(7.87982 - 6.35307i) q^{65} +(-5.72334 + 4.29970i) q^{66} +8.21327i q^{67} +36.7670 q^{68} +(-0.573438 - 4.72761i) q^{69} +(1.68364 - 0.972048i) q^{70} +(-5.40445 - 3.12026i) q^{71} +(-5.76289 - 23.4061i) q^{72} +3.76021i q^{73} +5.84171 q^{74} +(3.98963 - 2.99724i) q^{75} +2.59875i q^{76} +(0.203554 - 0.352565i) q^{77} +(11.8696 + 11.5454i) q^{78} +(-1.36567 - 2.36542i) q^{79} +(27.3365 - 15.7827i) q^{80} +(7.97119 - 4.17854i) q^{81} +(9.84289 - 17.0484i) q^{82} +(-7.18029 + 4.14554i) q^{83} +(1.36683 + 1.81940i) q^{84} +(-17.7696 + 10.2593i) q^{85} +(-8.03044 - 4.63638i) q^{86} +(5.68236 + 2.42187i) q^{87} +(6.26222 - 10.8465i) 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} +(2.48812 - 5.83782i) q^{93} -21.7630 q^{94} +(-0.725143 - 1.25599i) q^{95} +(14.2977 + 19.0317i) q^{96} -13.5427i q^{97} +(15.9171 + 9.18977i) q^{98} +(4.49125 + 1.30212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 10 * q^4 + 3 * q^5 - 6 * q^6 - 2 * q^9 - 7 * q^10 + 3 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 - 12 * q^16 + 9 * q^17 - 30 * q^18 - 6 * q^19 + 12 * q^21 - 13 * q^22 - 12 * q^23 + 45 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 - 24 * q^29 - 39 * q^30 + 27 * q^31 - 18 * q^33 - 15 * q^34 - 27 * q^35 + 2 * q^36 + 6 * q^37 + 21 * q^38 + 13 * q^39 + 13 * q^40 + 27 * q^42 + 8 * q^43 + 27 * q^45 - 15 * q^46 + 6 * q^47 + 11 * q^48 - 14 * q^49 + 12 * q^51 - 7 * q^52 - 24 * q^53 - 33 * q^54 - 13 * q^55 + 18 * q^56 + 42 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 - 6 * q^61 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 30 * q^66 + 138 * q^68 - 3 * q^69 + 24 * q^70 + 9 * q^71 - 6 * q^72 + 12 * q^74 + 22 * q^75 + 42 * q^77 - 42 * q^78 - 6 * q^79 + 105 * q^80 + 10 * q^81 - 16 * q^82 - 42 * q^83 - 18 * q^84 - 51 * q^85 - 45 * q^86 + 27 * q^87 - 11 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 6 * q^93 - 88 * q^94 - 3 * q^95 + 9 * q^96 + 117 * q^98 - 18 * q^99

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.29626	+	1.32574i	1.62370	+	0.937442i	0.985919	+	0.167222i	$0.0534798\pi$
$2$	2.29626	+	1.32574i	1.62370	+	0.937442i	0.637778	+	0.770220i	$0.279854\pi$
$3$	−0.208561	−	1.71945i	−0.120413	−	0.992724i
$3$	−0.208561	−	1.71945i	−0.120413	−	0.992724i
$4$	2.51519	+	4.35644i	1.25760	+	2.17822i
$5$	−2.43120	−	1.40366i	−1.08727	−	0.627734i	−0.154420	−	0.988005i	$-0.549351\pi$
$5$	−2.43120	−	1.40366i	−1.08727	−	0.627734i	−0.932848	+	0.360271i	$0.882684\pi$
$6$	1.80064	−	4.22479i	0.735107	−	1.72476i
$7$			0.261179i			0.0987162i	0.998781	+	0.0493581i	$0.0157176\pi$
$7$			0.261179i			0.0987162i	−0.998781	+	0.0493581i	$0.984282\pi$
$8$			8.03502i			2.84081i
$9$	−2.91300	+	0.717221i	−0.971001	+	0.239074i
$10$	−3.72178	−	6.44631i	−1.17693	−	2.03850i
$11$	−1.34990	−	0.779366i	−0.407011	−	0.234988i	0.282494	−	0.959269i	$-0.408838\pi$
$11$	−1.34990	−	0.779366i	−0.407011	−	0.234988i	−0.689504	+	0.724281i	$0.742172\pi$
$12$	6.96610	−	5.23333i	2.01094	−	1.51073i
$13$	−1.29932	+	3.36330i	−0.360365	+	0.932811i
$13$	−1.29932	+	3.36330i	−0.360365	+	0.932811i
$14$	−0.346256	+	0.599733i	−0.0925407	+	0.160285i
$15$	−1.90646	+	4.47308i	−0.492246	+	1.15494i
$16$	−5.62200	+	9.73759i	−1.40550	+	2.43440i
$17$	3.65449	−	6.32976i	0.886344	−	1.53519i	0.0421777	−	0.999110i	$-0.486570\pi$
$17$	3.65449	−	6.32976i	0.886344	−	1.53519i	0.844166	−	0.536082i	$-0.180096\pi$
$18$	−7.63985	−	2.21497i	−1.80073	−	0.522074i
$19$	0.447398	+	0.258305i	0.102640	+	0.0592593i	0.550441	−	0.834874i	$-0.314459\pi$
$19$	0.447398	+	0.258305i	0.102640	+	0.0592593i	−0.447801	+	0.894133i	$0.647793\pi$
$20$		−	14.1219i		−	3.15774i
$21$	0.449083	−	0.0544718i	0.0979979	−	0.0118867i
$22$	−2.06648	−	3.57925i	−0.440575	−	0.763098i
$23$	2.74949			0.573308			0.286654	−	0.958034i	$-0.407457\pi$
$23$	2.74949			0.573308			0.286654	+	0.958034i	$0.407457\pi$
$24$	13.8158	−	1.67580i	2.82014	−	0.342071i
$25$	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
$29$	−1.78313	+	3.08847i	−0.331119	+	0.573515i	−0.982732	−	0.185037i	$-0.940760\pi$
$29$	−1.78313	+	3.08847i	−0.331119	+	0.573515i	0.651612	+	0.758552i	$0.274093\pi$
$30$	−10.3079	+	7.74385i	−1.88195	+	1.41383i
$31$	3.17297	+	1.83191i	0.569882	+	0.329021i	0.757102	−	0.653297i	$-0.226615\pi$
$31$	3.17297	+	1.83191i	0.569882	+	0.329021i	−0.187221	+	0.982318i	$0.559948\pi$
$32$	−11.9020	+	6.87163i	−2.10400	+	1.21474i
$33$	−1.05854	+	2.48363i	−0.184269	+	0.432345i
$34$	16.7833	−	9.68983i	2.87831	−	1.66179i
$35$	0.366605	−	0.634978i	0.0619675	−	0.107331i
$36$	−10.4513	−	10.8864i	−1.74188	−	1.81440i
$37$	1.90801	−	1.10159i	0.313675	−	0.181100i	−0.334895	−	0.942256i	$-0.608701\pi$
$37$	1.90801	−	1.10159i	0.313675	−	0.181100i	0.648570	+	0.761155i	$0.275367\pi$
$38$	0.684893	+	1.18627i	0.111104	+	0.192438i
$39$	6.05401	+	1.53265i	0.969417	+	0.245421i
$40$	11.2784	−	19.5348i	1.78327	−	3.08872i
$41$		−	7.42443i		−	1.15950i	−0.814794	−	0.579751i	$-0.803150\pi$
$41$		−	7.42443i		−	1.15950i	0.814794	−	0.579751i	$-0.196850\pi$
$42$	1.10342	+	0.470288i	0.170262	+	0.0725670i
$43$	−3.49719			−0.533316			−0.266658	−	0.963791i	$-0.585919\pi$
$43$	−3.49719			−0.533316			−0.266658	+	0.963791i	$0.585919\pi$
$44$		−	7.84102i		−	1.18208i
$45$	8.08884	+	2.34515i	1.20581	+	0.349594i
$46$	6.31353	+	3.64512i	0.930880	+	0.537444i
$47$	−7.10819	+	4.10392i	−1.03684	+	0.598618i	−0.918936	−	0.394407i	$-0.870950\pi$
$47$	−7.10819	+	4.10392i	−1.03684	+	0.598618i	−0.117901	+	0.993025i	$0.537617\pi$
$48$	17.9158	+	7.63585i	2.58592	+	1.10214i
$49$	6.93179			0.990255
$50$			7.63895i			1.08031i
$51$	−11.6459	−	4.96356i	−1.63075	−	0.695037i
$52$	−17.9200	+	2.79895i	−2.48506	+	0.388144i
$53$	4.68042			0.642905			0.321452	−	0.946926i	$-0.395829\pi$
$53$	4.68042			0.642905			0.321452	+	0.946926i	$0.395829\pi$
$54$	−2.21515	+	13.5983i	−0.301444	+	1.85049i
$55$	2.18792	+	3.78960i	0.295020	+	0.510989i
$56$	−2.09858			−0.280434
$57$	0.350832	−	0.823150i	0.0464689	−	0.109029i
$58$	−8.18905	+	4.72795i	−1.07527	+	0.620810i
$59$	−9.64903	+	5.57087i	−1.25620	+	0.725265i	−0.972333	−	0.233599i	$-0.924950\pi$
$59$	−9.64903	+	5.57087i	−1.25620	+	0.725265i	−0.283864	+	0.958865i	$0.591616\pi$
$60$	−24.2818	+	2.94528i	−3.13477	+	0.380234i
$61$	−3.61462			−0.462805			−0.231403	−	0.972858i	$-0.574331\pi$
$61$	−3.61462			−0.462805			−0.231403	+	0.972858i	$0.574331\pi$
$62$	4.85729	+	8.41308i	0.616877	+	1.06846i
$63$	−0.187323	−	0.760814i	−0.0236005	−	0.0958536i
$64$	−13.9521			−1.74401
$65$	7.87982	−	6.35307i	0.977371	−	0.788002i
$66$	−5.72334	+	4.29970i	−0.704495	+	0.529256i
$67$			8.21327i			1.00341i	0.865038	+	0.501706i	$0.167294\pi$
$67$			8.21327i			1.00341i	−0.865038	+	0.501706i	$0.832706\pi$
$68$	36.7670			4.45865
$69$	−0.573438	−	4.72761i	−0.0690338	−	0.569137i
$70$	1.68364	−	0.972048i	0.201233	−	0.116182i
$71$	−5.40445	−	3.12026i	−0.641390	−	0.370307i	0.143760	−	0.989613i	$-0.454081\pi$
$71$	−5.40445	−	3.12026i	−0.641390	−	0.370307i	−0.785150	+	0.619306i	$0.787414\pi$
$72$	−5.76289	−	23.4061i	−0.679163	−	2.75843i
$73$			3.76021i			0.440099i	0.975489	+	0.220050i	$0.0706220\pi$
$73$			3.76021i			0.440099i	−0.975489	+	0.220050i	$0.929378\pi$
$74$	5.84171			0.679085
$75$	3.98963	−	2.99724i	0.460683	−	0.346091i
$76$			2.59875i			0.298097i
$77$	0.203554	−	0.352565i	0.0231971	−	0.0401785i
$78$	11.8696	+	11.5454i	1.34397	+	1.30726i
$79$	−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
$81$	7.97119	−	4.17854i	0.885687	−	0.464282i
$82$	9.84289	−	17.0484i	1.08697	−	1.88268i
$83$	−7.18029	+	4.14554i	−0.788139	+	0.455032i	−0.839307	−	0.543658i	$-0.817039\pi$
$83$	−7.18029	+	4.14554i	−0.788139	+	0.455032i	0.0511680	+	0.998690i	$0.483706\pi$
$84$	1.36683	+	1.81940i	0.149134	+	0.198512i
$85$	−17.7696	+	10.2593i	−1.92739	+	1.11278i
$86$	−8.03044	−	4.63638i	−0.865944	−	0.499953i
$87$	5.68236	+	2.42187i	0.609213	+	0.259651i
$88$	6.26222	−	10.8465i	0.667555	−	1.15624i
$89$	−1.18531	+	0.684339i	−0.125643	+	0.0725398i	−0.561504	−	0.827474i	$-0.689777\pi$
$89$	−1.18531	+	0.684339i	−0.125643	+	0.0725398i	0.435861	+	0.900014i	$0.356444\pi$
$90$	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
$93$	2.48812	−	5.83782i	0.258006	−	0.605353i
$94$	−21.7630			−2.24468
$95$	−0.725143	−	1.25599i	−0.0743981	−	0.128861i
$96$	14.2977	+	19.0317i	1.45925	+	1.94242i
$97$		−	13.5427i		−	1.37506i	−0.726158	−	0.687528i	$-0.758696\pi$
$97$		−	13.5427i		−	1.37506i	0.726158	−	0.687528i	$-0.241304\pi$
$98$	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
$101$	7.70477	−	13.3451i	0.766653	−	1.32788i	−0.172715	−	0.984972i	$-0.555254\pi$
$101$	7.70477	−	13.3451i	0.766653	−	1.32788i	0.939368	−	0.342911i	$-0.111413\pi$
$102$	−20.1615	−	26.8370i	−1.99629	−	2.65726i
$103$	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	$-0.0154807\pi$
$104$	−27.0242	−	10.4400i	−2.64994	−	1.02373i
$105$	−1.16827	−	0.497926i	−0.114012	−	0.0485926i
$106$	10.7474	+	6.20503i	1.04388	+	0.602686i
$107$	−0.595733	−	1.03184i	−0.0575917	−	0.0997518i	0.835792	−	0.549046i	$-0.185009\pi$
$107$	−0.595733	−	1.03184i	−0.0575917	−	0.0997518i	−0.893384	+	0.449294i	$0.851675\pi$
$108$	−16.5388	+	20.2409i	−1.59145	+	1.94769i
$109$			1.56215i			0.149627i	0.997198	+	0.0748135i	$0.0238362\pi$
$109$			1.56215i			0.149627i	−0.997198	+	0.0748135i	$0.976164\pi$
$110$			11.6025i			1.10626i
$111$	−2.29207	−	3.05098i	−0.217553	−	0.289586i
$112$	−2.54325	−	1.46835i	−0.240314	−	0.138746i
$113$	2.29605	+	3.97687i	0.215994	+	0.374112i	0.953580	−	0.301141i	$-0.0973676\pi$
$113$	2.29605	+	3.97687i	0.215994	+	0.374112i	−0.737586	+	0.675254i	$0.764034\pi$
$114$	1.89689	−	1.42505i	0.177660	−	0.133468i
$115$	−6.68457	−	3.85934i	−0.623340	−	0.359885i
$116$	−17.9397			−1.66566
$117$	1.37268	−	10.7292i	0.126905	−	0.991915i
$118$	−29.5422			−2.71958
$119$	1.65320	+	0.954474i	0.151548	+	0.0874965i
$120$	−35.9413	−	15.3184i	−3.28098	−	1.39838i
$121$	−4.28518	−	7.42214i	−0.389562	−	0.674740i
$122$	−8.30010	−	4.79207i	−0.751456	−	0.433853i
$123$	−12.7659	+	1.54845i	−1.15106	+	0.139619i
$124$			18.4304i			1.65510i
$125$			5.94868i			0.532066i
$126$	0.578503	−	1.99537i	0.0515372	−	0.177761i
$127$	5.62331	+	9.73987i	0.498988	+	0.864273i	0.999999	−	0.00116769i	$-0.000371687\pi$
$127$	5.62331	+	9.73987i	0.498988	+	0.864273i	−0.501011	+	0.865441i	$0.667038\pi$
$128$	−8.23353	−	4.75363i	−0.727749	−	0.420166i
$129$	0.729379	+	6.01323i	0.0642182	+	0.529436i
$130$	26.5166	−	4.14166i	2.32566	−	0.363247i
$131$	−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	$0.220604\pi$
$132$	−13.4822	+	1.63533i	−1.17348	+	0.142338i
$133$	−0.0674638	+	0.116851i	−0.00584985	+	0.0101322i
$134$	−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
$137$		−	2.23092i		−	0.190600i	−0.995449	−	0.0953002i	$-0.969619\pi$
$137$		−	2.23092i		−	0.190600i	0.995449	−	0.0953002i	$-0.0303811\pi$
$138$	4.95083	−	11.6160i	0.421443	−	0.988822i
$139$	−8.12287	−	14.0692i	−0.688973	−	1.19334i	−0.972170	−	0.234275i	$-0.924729\pi$
$139$	−8.12287	−	14.0692i	−0.688973	−	1.19334i	0.283197	−	0.959062i	$-0.408605\pi$
$140$	3.68833			0.311721
$141$	8.53897	+	11.3663i	0.719111	+	0.957211i
$142$	−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
$146$	−4.98508	+	8.63440i	−0.412568	+	0.714588i
$147$	−1.44570	−	11.9188i	−0.119240	−	0.983050i
$148$	9.59803	+	5.54143i	0.788953	+	0.455502i
$149$	6.61334	−	3.81821i	0.541786	−	0.312800i	−0.204017	−	0.978967i	$-0.565400\pi$
$149$	6.61334	−	3.81821i	0.541786	−	0.312800i	0.745802	+	0.666167i	$0.232066\pi$
$150$	13.1348	−	1.59319i	1.07245	−	0.130083i
$151$	10.8516	−	6.26520i	0.883095	−	0.509855i	0.0114171	−	0.999935i	$-0.496366\pi$
$151$	10.8516	−	6.26520i	0.883095	−	0.509855i	0.871677	+	0.490080i	$0.163032\pi$
$152$	−2.07549	+	3.59485i	−0.168344	+	0.291581i
$153$	−6.10570	+	21.0597i	−0.493617	+	1.70258i
$154$	0.934822	−	0.539720i	0.0753301	−	0.0434919i
$155$	−5.14275	−	8.90751i	−0.413076	−	0.715468i
$156$	8.55008	+	30.2288i	0.684554	+	2.42024i
$157$	−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	$0.298497\pi$
$158$		−	7.24214i		−	0.576153i
$159$	−0.976155	−	8.04773i	−0.0774141	−	0.638227i
$160$	38.5816			3.05015
$161$			0.718108i			0.0565948i
$162$	23.8435	+	0.972761i	1.87333	+	0.0764273i
$163$	−10.8176	−	6.24553i	−0.847297	−	0.489187i	0.0124407	−	0.999923i	$-0.496040\pi$
$163$	−10.8176	−	6.24553i	−0.847297	−	0.489187i	−0.859738	+	0.510735i	$0.829373\pi$
$164$	32.3441	−	18.6739i	2.52565	−	1.45818i
$165$	6.05970	−	4.55239i	0.471747	−	0.354403i
$166$	−21.9837			−1.70627
$167$			24.3257i			1.88238i	0.337882	+	0.941189i	$0.390290\pi$
$167$			24.3257i			1.88238i	−0.337882	+	0.941189i	$0.609710\pi$
$168$	0.437682	+	3.60839i	0.0337679	+	0.278394i
$169$	−9.62356	−	8.73998i	−0.740274	−	0.672306i
$170$	−54.4048			−4.17265
$171$	−1.48853	−	0.431561i	−0.113831	−	0.0330023i
$172$	−8.79610	−	15.2353i	−0.670696	−	1.16168i
$173$	−10.5463			−0.801822			−0.400911	−	0.916117i	$-0.631306\pi$
$173$	−10.5463			−0.801822			−0.400911	+	0.916117i	$0.631306\pi$
$174$	9.83738	+	13.0946i	0.745770	+	0.992697i
$175$	−0.651647	+	0.376228i	−0.0492599	+	0.0284402i
$176$	15.1783	−	8.76319i	1.14411	−	0.660550i
$177$	11.5912	+	15.4291i	0.871251	+	1.15972i
$178$	−3.62903			−0.272007
$179$	3.54457	+	6.13938i	0.264934	+	0.458879i	0.967546	−	0.252694i	$-0.0813165\pi$
$179$	3.54457	+	6.13938i	0.264934	+	0.458879i	−0.702612	+	0.711573i	$0.747983\pi$
$180$	10.1285	+	41.1370i	0.754934	+	3.06617i
$181$	15.7315			1.16931			0.584656	−	0.811281i	$-0.301230\pi$
$181$	15.7315			1.16931			0.584656	+	0.811281i	$0.301230\pi$
$182$	−1.56718	−	1.94380i	−0.116167	−	0.144084i
$183$	0.753871	+	6.21516i	0.0557278	+	0.459438i
$184$			22.0922i			1.62866i
$185$	−6.18502			−0.454732
$186$	13.4528	−	10.1065i	0.986408	−	0.741045i
$187$	−9.86640	+	5.69637i	−0.721502	+	0.416560i
$188$	−35.7569	−	20.6443i	−2.60784	−	1.50564i
$189$	−1.26911	+	0.480768i	−0.0923143	+	0.0349708i
$190$		−	3.84542i		−	0.278976i
$191$	8.12183			0.587675			0.293837	−	0.955855i	$-0.405068\pi$
$191$	8.12183			0.587675			0.293837	+	0.955855i	$0.405068\pi$
$192$	2.90987	+	23.9899i	0.210002	+	1.73132i
$193$			7.70792i			0.554828i	0.960750	+	0.277414i	$0.0894774\pi$
$193$			7.70792i			0.554828i	−0.960750	+	0.277414i	$0.910523\pi$
$194$	17.9542	−	31.0976i	1.28904	−	2.23268i
$195$	−12.5672	−	12.2239i	−0.899956	−	0.875374i
$196$	17.4348	+	30.1979i	1.24534	+	2.15699i
$197$	−3.46949	+	2.00311i	−0.247191	+	0.142716i	−0.618477	−	0.785803i	$-0.712250\pi$
$197$	−3.46949	+	2.00311i	−0.247191	+	0.142716i	0.371287	+	0.928518i	$0.378917\pi$
$198$	8.58677	+	8.94424i	0.610235	+	0.635639i
$199$	−6.44292	+	11.1595i	−0.456726	+	0.791073i	−0.998786	−	0.0492670i	$-0.984311\pi$
$199$	−6.44292	+	11.1595i	−0.456726	+	0.791073i	0.542059	+	0.840340i	$0.317645\pi$
$200$	−20.0476	+	11.5745i	−1.41758	+	0.818439i
$201$	14.1223	−	1.71297i	0.996110	−	0.120824i
$202$	35.3842	−	20.4291i	2.48963	−	1.43739i
$203$	−0.806643	−	0.465716i	−0.0566152	−	0.0326868i
$204$	−7.66817	−	63.2189i	−0.536879	−	4.42621i
$205$	−10.4214	+	18.0503i	−0.727859	+	1.26069i
$206$	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
$210$	−2.02253	−	2.69219i	−0.139568	−	0.185779i
$211$	17.2151			1.18513			0.592567	−	0.805521i	$-0.298114\pi$
$211$	17.2151			1.18513			0.592567	+	0.805521i	$0.298114\pi$
$212$	11.7721	+	20.3900i	0.808514	+	1.40039i
$213$	−4.23796	+	9.94343i	−0.290380	+	0.681313i
$214$		−	3.15916i		−	0.215956i
$215$	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
$218$	−2.07101	+	3.58710i	−0.140267	+	0.242949i
$219$	6.46549	−	0.784235i	0.436897	−	0.0529937i
$220$	−11.0061	+	19.0631i	−0.742031	+	1.28524i
$221$	16.5405	+	20.5155i	1.11264	+	1.38002i
$222$	−1.21836	−	10.0445i	−0.0817707	−	0.674144i
$223$	8.17028	+	4.71711i	0.547122	+	0.315881i	0.747961	−	0.663743i	$-0.231033\pi$
$223$	8.17028	+	4.71711i	0.547122	+	0.315881i	−0.200838	+	0.979624i	$0.564367\pi$
$224$	−1.79472	−	3.10855i	−0.119915	−	0.207699i
$225$	−5.98568	−	6.23486i	−0.399045	−	0.415657i
$226$			12.1759i			0.809927i
$227$			18.3577i			1.21844i	0.793001	+	0.609220i	$0.208518\pi$
$227$			18.3577i			1.21844i	−0.793001	+	0.609220i	$0.791482\pi$
$228$	4.46841	−	0.541999i	0.295928	−	0.0358947i
$229$	−11.3476	−	6.55153i	−0.749870	−	0.432937i	0.0757771	−	0.997125i	$-0.475856\pi$
$229$	−11.3476	−	6.55153i	−0.749870	−	0.432937i	−0.825647	+	0.564187i	$0.809190\pi$
$230$	−10.2330	−	17.7241i	−0.674743	−	1.16869i
$231$	−0.648671	−	0.276468i	−0.0426794	−	0.0181903i
$232$	−24.8160	−	14.3275i	−1.62925	−	0.940647i
$233$	4.84195			0.317207			0.158603	−	0.987342i	$-0.449301\pi$
$233$	4.84195			0.317207			0.158603	+	0.987342i	$0.449301\pi$
$234$	17.3762	−	22.8172i	1.13592	−	1.49160i
$235$	23.0420			1.50309
$236$	−48.5383	−	28.0236i	−3.15958	−	1.82418i
$237$	−3.78239	+	2.84154i	−0.245692	+	0.184578i
$238$	2.53078	+	4.38343i	0.164046	+	0.284136i
$239$	13.6653	+	7.88968i	0.883936	+	0.510341i	0.871954	−	0.489587i	$-0.162853\pi$
$239$	13.6653	+	7.88968i	0.883936	+	0.510341i	0.0119822	+	0.999928i	$0.496186\pi$
$240$	−32.8389	−	43.7119i	−2.11974	−	2.82159i
$241$		−	16.2866i		−	1.04911i	−0.851375	−	0.524557i	$-0.824231\pi$
$241$		−	16.2866i		−	1.04911i	0.851375	−	0.524557i	$-0.175769\pi$
$242$		−	22.7242i		−	1.46077i
$243$	−8.84726	−	12.8346i	−0.567552	−	0.823337i
$244$	−9.09147	−	15.7469i	−0.582022	−	1.00809i
$245$	−16.8526	−	9.72985i	−1.07667	−	0.621617i
$246$	−31.3667	−	13.3687i	−1.99987	−	0.852358i
$247$	−1.45007	+	1.16911i	−0.0922656	+	0.0743888i
$248$	−14.7195	+	25.4949i	−0.934687	+	1.61893i
$249$	8.62557	+	11.4815i	0.546624	+	0.727613i
$250$	−7.88642	+	13.6597i	−0.498781	+	0.863914i
$251$	13.7361	−	23.7917i	0.867017	−	1.50172i	0.00198652	−	0.999998i	$-0.499368\pi$
$251$	13.7361	−	23.7917i	0.867017	−	1.50172i	0.865030	−	0.501719i	$-0.167299\pi$
$252$	2.84329	−	2.72965i	0.179110	−	0.171952i
$253$	−3.71154	−	2.14286i	−0.233343	−	0.134720i
$254$			29.8203i			1.87109i
$255$	21.3464	+	28.4142i	1.33676	+	1.77937i
$256$	1.34789	+	2.33462i	0.0842434	+	0.145914i
$257$	−9.79971			−0.611289			−0.305644	−	0.952146i	$-0.598872\pi$
$257$	−9.79971			−0.611289			−0.305644	+	0.952146i	$0.598872\pi$
$258$	−6.29717	+	14.7749i	−0.392045	+	0.919845i
$259$	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
$263$	−11.5486	+	20.0028i	−0.712119	+	1.23343i	0.251941	+	0.967743i	$0.418931\pi$
$263$	−11.5486	+	20.0028i	−0.712119	+	1.23343i	−0.964060	+	0.265684i	$0.914402\pi$
$264$	−19.9560	−	8.50541i	−1.22821	−	0.523472i
$265$	−11.3790	−	6.56970i	−0.699009	−	0.403573i
$266$	−0.309828	+	0.178879i	−0.0189968	+	0.0109678i
$267$	1.42390	+	1.89535i	0.0871410	+	0.115994i
$268$	−35.7806	+	20.6580i	−2.18565	+	1.26189i
$269$	−10.8197	+	18.7403i	−0.659688	+	1.14261i	0.321008	+	0.947076i	$0.395978\pi$
$269$	−10.8197	+	18.7403i	−0.659688	+	1.14261i	−0.980696	+	0.195537i	$0.937355\pi$
$270$	24.4728	−	29.9509i	1.48937	−	1.82275i
$271$	−23.0990	+	13.3362i	−1.40316	+	0.810116i	−0.994716	−	0.102666i	$-0.967263\pi$
$271$	−23.0990	+	13.3362i	−1.40316	+	0.810116i	−0.408447	+	0.912782i	$0.633929\pi$
$272$	41.0911	+	71.1718i	2.49151	+	4.31542i
$273$	−0.400296	+	1.58118i	−0.0242270	+	0.0956971i
$274$	2.95763	−	5.12276i	0.178677	−	0.309478i
$275$		−	4.49072i		−	0.270800i
$276$	19.1532	−	14.3890i	1.15289	−	0.866115i
$277$	6.44278			0.387109			0.193554	−	0.981090i	$-0.437998\pi$
$277$	6.44278			0.387109			0.193554	+	0.981090i	$0.437998\pi$
$278$		−	43.0754i		−	2.58349i
$279$	−10.5567	−	3.06065i	−0.632016	−	0.183236i
$280$	5.10207	+	2.94568i	0.304907	+	0.176038i
$281$	−1.22438	+	0.706894i	−0.0730402	+	0.0421698i	−0.536075	−	0.844170i	$-0.680094\pi$
$281$	−1.22438	+	0.706894i	−0.0730402	+	0.0421698i	0.463035	+	0.886340i	$0.346760\pi$
$282$	4.53892	+	37.4203i	0.270289	+	2.22835i
$283$	19.9798			1.18767			0.593837	−	0.804585i	$-0.297612\pi$
$283$	19.9798			1.18767			0.593837	+	0.804585i	$0.297612\pi$
$284$		−	31.3922i		−	1.86278i
$285$	−2.00836	+	1.50880i	−0.118965	+	0.0893734i
$286$	14.7231	−	2.29961i	0.870594	−	0.135979i
$287$	1.93910			0.114462
$288$	29.7421	−	28.5535i	1.75257	−	1.68253i
$289$	−18.2106	−	31.5416i	−1.07121	−	1.85539i
$290$	26.5457			1.55882
$291$	−23.2860	+	2.82449i	−1.36505	+	0.165575i
$292$	−16.3811	+	9.45765i	−0.958634	+	0.553467i
$293$	−2.92034	+	1.68606i	−0.170608	+	0.0985005i	−0.582872	−	0.812564i	$-0.698071\pi$
$293$	−2.92034	+	1.68606i	−0.170608	+	0.0985005i	0.412265	+	0.911064i	$0.364738\pi$
$294$	12.4816	−	29.2853i	0.727943	−	1.70796i
$295$	31.2783			1.82110
$296$	8.85131	+	15.3309i	0.514472	+	0.891092i
$297$	1.30222	−	7.99404i	0.0755627	−	0.463861i
$298$	20.2479			1.17293
$299$	−3.57246	+	9.24736i	−0.206601	+	0.534789i
$300$	23.0920	+	9.84197i	1.33322	+	0.568226i
$301$		−	0.913391i		−	0.0526470i
$302$	33.2242			1.91184
$303$	−24.5530	−	10.4647i	−1.41054	−	0.601181i
$304$	−5.03054	+	2.90438i	−0.288521	+	0.166578i
$305$	8.78789	+	5.07369i	0.503193	+	0.290519i
$306$	−41.9400	+	40.2638i	−2.39755	+	2.30173i
$307$		−	20.7017i		−	1.18151i	−0.806851	−	0.590756i	$-0.798830\pi$
$307$		−	20.7017i		−	1.18151i	0.806851	−	0.590756i	$-0.201170\pi$
$308$	2.04791			0.116690
$309$	−17.5134	−	7.46435i	−0.996304	−	0.424632i
$310$		−	27.2719i		−	1.54894i
$311$	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	$0.0912585\pi$
$312$	−12.3149	+	48.6441i	−0.697194	+	2.75393i
$313$	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
$315$	−0.612502	+	2.11263i	−0.0345106	+	0.119033i
$316$	6.86987	−	11.8990i	0.386460	−	0.669369i
$317$	28.4498	−	16.4255i	1.59790	−	0.922547i	0.606006	−	0.795460i	$-0.292771\pi$
$317$	28.4498	−	16.4255i	1.59790	−	0.922547i	0.991892	−	0.127087i	$-0.0405628\pi$
$318$	8.42773	−	19.7738i	0.472604	−	1.10886i
$319$	4.81410	−	2.77942i	0.269538	−	0.155618i
$320$	33.9204	+	19.5839i	1.89621	+	1.09478i
$321$	−1.64995	+	1.23953i	−0.0920912	+	0.0691841i
$322$	−0.952027	+	1.64896i	−0.0530544	+	0.0918929i
$323$	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
$327$	2.68604	−	0.325805i	0.148538	−	0.0180171i
$328$	59.6555			3.29392
$329$	−1.07186	−	1.85651i	−0.0590933	−	0.102353i
$330$	19.9499	−	2.41984i	1.09821	−	0.133208i
$331$			13.8802i			0.762922i	0.924385	+	0.381461i	$0.124579\pi$
$331$			13.8802i			0.762922i	−0.924385	+	0.381461i	$0.875421\pi$
$332$	−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
$335$	11.5286	−	19.9681i	0.629876	−	1.09098i
$336$	−1.99432	+	4.67922i	−0.108799	+	0.255273i
$337$	−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	$0.930889\pi$
$338$	−10.5112	−	32.8276i	−0.571733	−	1.78559i
$339$	6.35915	−	4.77735i	0.345382	−	0.259470i
$340$	−89.3880	−	51.6082i	−4.84774	−	2.79885i
$341$	−2.85546	−	4.94580i	−0.154632	−	0.267830i
$342$	−2.84591	−	2.96439i	−0.153889	−	0.160296i
$343$			3.63868i			0.196470i
$344$		−	28.1000i		−	1.51505i
$345$	−5.24179	+	12.2987i	−0.282209	+	0.662139i
$346$	−24.2170	−	13.9817i	−1.30192	−	0.751662i
$347$	−9.52830	−	16.5035i	−0.511506	−	0.885955i	−0.999911	−	0.0133374i	$-0.995754\pi$
$347$	−9.52830	−	16.5035i	−0.511506	−	0.885955i	0.488405	−	0.872617i	$-0.337579\pi$
$348$	3.74152	+	30.8463i	0.200567	+	1.65354i
$349$	20.5588	+	11.8696i	1.10049	+	0.635367i	0.936349	−	0.351070i	$-0.114182\pi$
$349$	20.5588	+	11.8696i	1.10049	+	0.635367i	0.164139	+	0.986437i	$0.447516\pi$
$350$	−1.99513			−0.106644
$351$	−18.7346	−	0.122560i	−0.999979	−	0.00654176i
$352$	21.4221			1.14180
$353$	−1.89779	−	1.09569i	−0.101009	−	0.0583176i	0.448644	−	0.893710i	$-0.351907\pi$
$353$	−1.89779	−	1.09569i	−0.101009	−	0.0583176i	−0.549654	+	0.835393i	$0.685240\pi$
$354$	6.16136	+	50.7962i	0.327473	+	2.69979i
$355$	8.75954	+	15.1720i	0.464908	+	0.805245i
$356$	−5.96256	−	3.44249i	−0.316015	−	0.182452i
$357$	1.29638	−	3.04165i	0.0686114	−	0.160981i
$358$			18.7968i			0.993441i
$359$			5.58420i			0.294723i	0.989083	+	0.147361i	$0.0470780\pi$
$359$			5.58420i			0.294723i	−0.989083	+	0.147361i	$0.952922\pi$
$360$	−18.8433	+	64.9940i	−0.993129	+	3.42549i
$361$	−9.36656	−	16.2234i	−0.492977	−	0.853861i
$362$	36.1235	+	20.8559i	1.89861	+	1.09616i
$363$	−11.8683	+	8.91611i	−0.622923	+	0.467975i
$364$	−0.731025	−	4.68033i	−0.0383161	−	0.245316i
$365$	5.27805	−	9.14184i	0.276266	−	0.478506i
$366$	−6.50863	+	15.2710i	−0.340211	+	0.798230i
$367$	6.68867	−	11.5851i	0.349146	−	0.604738i	−0.636952	−	0.770903i	$-0.719805\pi$
$367$	6.68867	−	11.5851i	0.349146	−	0.604738i	0.986098	+	0.166165i	$0.0531384\pi$
$368$	−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
$371$			1.22242i			0.0634651i
$372$	31.6902	−	3.84388i	1.64306	−	0.199296i
$373$	−3.90999	−	6.77230i	−0.202451	−	0.350656i	0.746866	−	0.664974i	$-0.231558\pi$
$373$	−3.90999	−	6.77230i	−0.202451	−	0.350656i	−0.949318	+	0.314318i	$0.898224\pi$
$374$	−30.2077			−1.56200
$375$	10.2284	−	1.24067i	0.528195	−	0.0640677i
$376$	−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	0.744561	−	0.667554i	$-0.232659\pi$
$379$	32.9974	−	19.0510i	1.69496	−	0.978586i	0.950399	−	0.311032i	$-0.100675\pi$
$380$	3.64775	−	6.31809i	0.187126	−	0.324111i
$381$	15.5744	−	11.7004i	0.797900	−	0.599427i
$382$	18.6498	+	10.7675i	0.954206	+	0.550911i
$383$	−15.4126	+	8.89848i	−0.787548	+	0.454691i	−0.839099	−	0.543979i	$-0.816917\pi$
$383$	−15.4126	+	8.89848i	−0.787548	+	0.454691i	0.0515506	+	0.998670i	$0.483584\pi$
$384$	−6.45643	+	15.1486i	−0.329478	+	0.773047i
$385$	−0.989761	+	0.571439i	−0.0504429	+	0.0291232i
$386$	−10.2187	+	17.6994i	−0.520120	+	0.900873i
$387$	10.1873	−	2.50826i	0.517851	−	0.127502i
$388$	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	$-0.505879\pi$
$390$	−12.6517	−	44.7302i	−0.640644	−	2.26500i
$391$	10.0480	−	17.4036i	0.508148	−	0.880139i
$392$			55.6971i			2.81313i
$393$	6.15096	+	2.62159i	0.310275	+	0.132241i
$394$	−10.6224			−0.535151
$395$			7.66775i			0.385806i
$396$	5.62375	+	22.8409i	0.282604	+	1.14780i
$397$	−7.59209	−	4.38329i	−0.381036	−	0.219991i	0.297233	−	0.954805i	$-0.403936\pi$
$397$	−7.59209	−	4.38329i	−0.381036	−	0.219991i	−0.678269	+	0.734814i	$0.737270\pi$
$398$	−29.5892	+	17.0833i	−1.48317	+	0.856309i
$399$	0.214989	+	0.0916299i	0.0107629	+	0.00458723i
$400$	−32.3940			−1.61970
$401$		−	21.4944i		−	1.07338i	−0.843780	−	0.536690i	$-0.819675\pi$
$401$		−	21.4944i		−	1.07338i	0.843780	−	0.536690i	$-0.180325\pi$
$402$	34.6994	+	14.7891i	1.73065	+	0.737614i
$403$	−10.2840	+	8.29140i	−0.512280	+	0.413024i
$404$	77.5159			3.85656
$405$	−25.2448	−	1.02993i	−1.25443	−	0.0511776i
$406$	−1.23484	−	2.13880i	−0.0612840	−	0.106147i
$407$	−3.43417			−0.170225
$408$	39.8823	−	93.5749i	1.97447	−	4.63265i
$409$	30.7301	−	17.7420i	1.51951	−	0.877287i	0.519770	−	0.854306i	$-0.326018\pi$
$409$	30.7301	−	17.7420i	1.51951	−	0.877287i	0.999736	−	0.0229809i	$-0.00731570\pi$
$410$	−47.8602	+	27.6321i	−2.36365	+	1.36465i
$411$	−3.83595	+	0.465284i	−0.189214	+	0.0229508i
$412$	55.2913			2.72401
$413$	−1.45499	−	2.52012i	−0.0715954	−	0.124007i
$414$	−21.0057	−	6.09005i	−1.03237	−	0.299310i
$415$	23.2757			1.14256
$416$	−7.64687	−	48.9585i	−0.374919	−	2.40039i
$417$	−22.4972	+	16.9012i	−1.10169	+	0.827653i
$418$		−	2.13513i		−	0.104433i
$419$	−20.0287			−0.978464			−0.489232	−	0.872154i	$-0.662723\pi$
$419$	−20.0287			−0.978464			−0.489232	+	0.872154i	$0.662723\pi$
$420$	−0.769243	−	6.34189i	−0.0375352	−	0.309452i
$421$	15.3946	−	8.88807i	0.750286	−	0.433178i	−0.0755111	−	0.997145i	$-0.524059\pi$
$421$	15.3946	−	8.88807i	0.750286	−	0.433178i	0.825797	+	0.563967i	$0.190725\pi$
$422$	39.5302	+	22.8228i	1.92430	+	1.11100i
$423$	17.7628	−	17.0529i	0.863656	−	0.829139i
$424$			37.6073i			1.82637i
$425$	21.0572			1.02142
$426$	−22.9139	+	17.2142i	−1.11018	+	0.834031i
$427$		−	0.944062i		−	0.0456864i
$428$	2.99677	−	5.19055i	0.144854	−	0.250895i
$429$	−6.97781	−	6.78721i	−0.336892	−	0.327690i
$430$	13.0158	+	22.5440i	0.627676	+	1.08717i
$431$	−1.72978	+	0.998690i	−0.0833206	+	0.0481052i	−0.541081	−	0.840970i	$-0.681985\pi$
$431$	−1.72978	+	0.998690i	−0.0833206	+	0.0481052i	0.457761	+	0.889075i	$0.348652\pi$
$432$	−57.6654	−	9.39366i	−2.77443	−	0.451953i
$433$	−12.2465	+	21.2116i	−0.588532	+	1.01937i	0.405893	+	0.913920i	$0.366960\pi$
$433$	−12.2465	+	21.2116i	−0.588532	+	1.01937i	−0.994425	+	0.105446i	$0.966373\pi$
$434$	−2.19732	+	1.26862i	−0.105475	+	0.0608957i
$435$	−10.4155	−	13.8641i	−0.499386	−	0.664734i
$436$	−6.80543	+	3.92911i	−0.325921	+	0.188170i
$437$	1.23012	+	0.710208i	0.0588444	+	0.0339738i
$438$	15.8861	+	6.77078i	0.759068	+	0.323520i
$439$	−7.66518	+	13.2765i	−0.365839	+	0.633652i	−0.988910	−	0.148513i	$-0.952551\pi$
$439$	−7.66518	+	13.2765i	−0.365839	+	0.633652i	0.623071	+	0.782165i	$0.285885\pi$
$440$	−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	$0.761143\pi$
$444$	7.52641	−	17.6590i	0.357188	−	0.838061i
$445$	3.84231			0.182143
$446$	12.5074	+	21.6634i	0.592241	+	1.02579i
$447$	−7.94451	−	10.5750i	−0.375762	−	0.500178i
$448$		−	3.64399i		−	0.172162i
$449$	−14.1283	−	8.15697i	−0.666755	−	0.384951i	0.128091	−	0.991762i	$-0.459115\pi$
$449$	−14.1283	−	8.15697i	−0.666755	−	0.384951i	−0.794846	+	0.606811i	$0.792448\pi$
$450$	−5.47882	−	22.2523i	−0.258274	−	1.04898i
$451$	−5.78635	+	10.0223i	−0.272469	+	0.471929i
$452$	−11.5500	+	20.0052i	−0.543266	+	0.940964i
$453$	−13.0359	−	17.3522i	−0.612481	−	0.815276i
$454$	−24.3376	+	42.1539i	−1.14222	+	1.97838i
$455$	1.65929	+	2.05804i	0.0777885	+	0.0964824i
$456$	6.61403	+	2.81895i	0.309730	+	0.132009i
$457$	−1.87187	−	1.08073i	−0.0875626	−	0.0505543i	0.455579	−	0.890195i	$-0.349432\pi$
$457$	−1.87187	−	1.08073i	−0.0875626	−	0.0505543i	−0.543142	+	0.839641i	$0.682765\pi$
$458$	−17.3713	−	30.0880i	−0.811708	−	1.40592i
$459$	37.4845	+	6.10620i	1.74962	+	0.285013i
$460$		−	38.8279i		−	1.81036i
$461$			3.06596i			0.142796i	0.997448	+	0.0713980i	$0.0227460\pi$
$461$			3.06596i			0.142796i	−0.997448	+	0.0713980i	$0.977254\pi$
$462$	−1.12299	−	1.49481i	−0.0522461	−	0.0695450i
$463$	13.8184	+	7.97807i	0.642197	+	0.370772i	0.785460	−	0.618912i	$-0.212426\pi$
$463$	13.8184	+	7.97807i	0.642197	+	0.370772i	−0.143264	+	0.989685i	$0.545760\pi$
$464$	−20.0495	−	34.7268i	−0.930776	−	1.61215i
$465$	−14.2434	+	10.7005i	−0.660523	+	0.496222i
$466$	11.1184	+	6.41919i	0.515048	+	0.297363i
$467$	3.15406			0.145952			0.0729762	−	0.997334i	$-0.476750\pi$
$467$	3.15406			0.145952			0.0729762	+	0.997334i	$0.476750\pi$
$468$	50.1937	−	21.0060i	2.32020	−	0.971002i
$469$	−2.14513			−0.0990529
$470$	52.9102	+	30.5477i	2.44057	+	1.40906i
$471$	16.0684	+	6.84848i	0.740394	+	0.315561i
$472$	−44.7621	−	77.5302i	−2.06034	−	3.56862i
$473$	4.72086	+	2.72559i	0.217065	+	0.125323i
$474$	−12.4525	+	1.51043i	−0.571961	+	0.0693764i
$475$			1.48836i			0.0682905i
$476$			9.60274i			0.440141i
$477$	−13.6341	+	3.35689i	−0.624261	+	0.153702i
$478$	20.9194	+	36.2334i	0.956830	+	1.65728i
$479$	−8.60548	−	4.96837i	−0.393194	−	0.227011i	0.290349	−	0.956921i	$-0.406229\pi$
$479$	−8.60548	−	4.96837i	−0.393194	−	0.227011i	−0.683543	+	0.729910i	$0.739562\pi$
$480$	−8.04664	−	66.3391i	−0.367277	−	3.02795i
$481$	1.22587	+	7.84853i	0.0558948	+	0.357862i
$482$	21.5919	−	37.3983i	0.983484	−	1.70344i
$483$	1.23475	−	0.149770i	0.0561830	−	0.00681476i
$484$	21.5561	−	37.3362i	0.979822	−	1.69710i
$485$	−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	−0.0278074	−	0.999613i	$-0.508853\pi$
$487$	−20.0246	−	11.5612i	−0.907402	−	0.523889i	−0.879594	+	0.475725i	$0.842186\pi$
$488$		−	29.0436i		−	1.31474i
$489$	−8.48273	+	19.9028i	−0.383602	+	0.900037i
$490$	−25.7986	−	44.6844i	−1.16546	−	2.01864i
$491$	29.7055			1.34059			0.670295	−	0.742095i	$-0.266168\pi$
$491$	29.7055			1.34059			0.670295	+	0.742095i	$0.266168\pi$
$492$	−38.8545	−	51.7193i	−1.75170	−	2.33169i
$493$	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
$497$	0.814945	−	1.41153i	0.0365553	−	0.0633156i
$498$	4.58495	+	37.7998i	0.205457	+	1.69385i
$499$	−32.4943	−	18.7606i	−1.45465	−	0.839841i	−0.455907	−	0.890027i	$-0.650685\pi$
$499$	−32.4943	−	18.7606i	−1.45465	−	0.839841i	−0.998740	+	0.0501867i	$0.984018\pi$
$500$	−25.9151	+	14.9621i	−1.15896	+	0.669124i
$501$	41.8267	−	5.07340i	1.86868	−	0.226663i
$502$	63.0833	−	36.4212i	2.81555	−	1.62556i
$503$	14.5097	−	25.1315i	0.646956	−	1.12056i	−0.336891	−	0.941544i	$-0.609375\pi$
$503$	14.5097	−	25.1315i	0.646956	−	1.12056i	0.983846	−	0.179016i	$-0.0572914\pi$
$504$	6.11316	−	1.50514i	0.272302	−	0.0670444i
$505$	−37.4637	+	21.6297i	−1.66711	+	0.962509i
$506$	−5.68176	−	9.84110i	−0.252585	−	0.437490i
$507$	−13.0208	+	18.3700i	−0.578275	+	0.815842i
$508$	−28.2874	+	48.9953i	−1.25505	+	2.17381i
$509$		−	8.24121i		−	0.365285i	−0.983179	−	0.182643i	$-0.941535\pi$
$509$		−	8.24121i		−	0.365285i	0.983179	−	0.182643i	$-0.0584651\pi$
$510$	11.3467	+	93.5462i	0.502442	+	4.14229i
$511$	−0.982086			−0.0434449
$512$			26.1624i			1.15622i
$513$	−0.431596	+	2.64946i	−0.0190554	+	0.116977i
$514$	−22.5026	−	12.9919i	−0.992548	−	0.573048i
$515$	−26.7225	+	15.4282i	−1.17753	+	0.679849i
$516$	−24.3618	+	18.3019i	−1.07247	+	0.805698i
$517$	12.7938			0.562671
$518$			1.52573i			0.0670367i
$519$	2.19956	+	18.1338i	0.0965498	+	0.795988i
$520$	51.0471	+	63.3145i	2.23856	+	2.77653i
$521$	37.2716			1.63290			0.816449	−	0.577418i	$-0.195940\pi$
$521$	37.2716			1.63290			0.816449	+	0.577418i	$0.195940\pi$
$522$	20.4637	−	19.6459i	0.895674	−	0.859878i
$523$	−1.53435	−	2.65756i	−0.0670922	−	0.116207i	0.830528	−	0.556977i	$-0.188039\pi$
$523$	−1.53435	−	2.65756i	−0.0670922	−	0.116207i	−0.897620	+	0.440770i	$0.854706\pi$
$524$	−19.4191			−0.848326
$525$	0.782814	+	1.04201i	0.0341648	+	0.0454769i
$526$	−53.0372	+	30.6210i	−2.31253	+	1.33514i
$527$	23.1911	−	13.3894i	1.01022	−	0.583252i
$528$	−18.2335	−	24.2706i	−0.793509	−	1.05624i
$529$	−15.4403			−0.671317
$530$	−17.4195	−	30.1714i	−0.756653	−	1.31056i
$531$	24.1121	−	23.1485i	1.04638	−	1.00456i
$532$	−0.678737			−0.0294270
$533$	24.9706	+	9.64668i	1.08160	+	0.417844i
$534$	0.756876	+	6.23993i	0.0327532	+	0.270028i
$535$			3.34482i			0.144609i
$536$	−65.9939			−2.85050
$537$	9.81709	−	7.37515i	0.423639	−	0.318261i
$538$	−49.6896	+	28.6883i	−2.14227	+	1.23684i
$539$	−9.35723	−	5.40240i	−0.403044	−	0.232698i
$540$	68.6206	−	25.9950i	2.95296	−	1.11865i
$541$		−	7.25981i		−	0.312124i	−0.987747	−	0.156062i	$-0.950120\pi$
$541$		−	7.25981i		−	0.312124i	0.987747	−	0.156062i	$-0.0498799\pi$
$542$	−70.7215			−3.03775
$543$	−3.28098	−	27.0495i	−0.140800	−	1.16080i
$544$			100.449i			4.30672i
$545$	2.19273	−	3.79791i	0.0939261	−	0.162685i
$546$	−3.01542	+	3.10009i	−0.129048	+	0.132672i
$547$	−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
$549$	10.5294	−	2.59249i	0.449385	−	0.110645i
$550$	5.95354	−	10.3118i	0.253860	−	0.439698i
$551$	−1.59554	+	0.921184i	−0.0679722	+	0.0392438i
$552$	37.9864	−	4.60759i	1.61681	−	0.196112i
$553$	0.617796	−	0.356685i	0.0262714	−	0.0151678i
$554$	14.7943	+	8.54147i	0.628548	+	0.362892i
$555$	1.28996	+	10.6348i	0.0547556	+	0.451423i
$556$	40.8612	−	70.7736i	1.73290	−	3.00147i
$557$	−7.49468	+	4.32706i	−0.317560	+	0.183343i	−0.650304	−	0.759674i	$-0.725359\pi$
$557$	−7.49468	+	4.32706i	−0.317560	+	0.183343i	0.332744	+	0.943017i	$0.392025\pi$
$558$	−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
$561$	11.8524	+	15.7767i	0.500407	+	0.666094i
$562$	−3.74864			−0.158127
$563$	23.0556	+	39.9334i	0.971677	+	1.68299i	0.690493	+	0.723339i	$0.257394\pi$
$563$	23.0556	+	39.9334i	0.971677	+	1.68299i	0.281184	+	0.959654i	$0.409273\pi$
$564$	−28.0393	+	65.7878i	−1.18067	+	2.77017i
$565$		−	12.8914i		−	0.542347i
$566$	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
$569$	−8.61575	+	14.9229i	−0.361191	+	0.625601i	−0.988157	−	0.153445i	$-0.950963\pi$
$569$	−8.61575	+	14.9229i	−0.361191	+	0.625601i	0.626966	+	0.779047i	$0.284296\pi$
$570$	−6.61199	+	0.802006i	−0.276946	+	0.0335923i
$571$	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	$0.0178266\pi$
$572$	26.3717	+	10.1880i	1.10266	+	0.425980i
$573$	−1.69390	−	13.9651i	−0.0707637	−	0.583399i
$574$	4.45267	+	2.57075i	0.185851	+	0.107301i
$575$	3.96065	+	6.86005i	0.165171	+	0.286084i
$576$	40.6425	−	10.0067i	1.69344	−	0.416947i
$577$			19.9386i			0.830056i	0.909809	+	0.415028i	$0.136228\pi$
$577$			19.9386i			0.830056i	−0.909809	+	0.415028i	$0.863772\pi$
$578$		−	96.5702i		−	4.01679i
$579$	13.2534	−	1.60758i	0.550791	−	0.0668086i
$580$	43.6150	+	25.1811i	1.81101	+	1.04559i
$581$	−1.08273	−	1.87534i	−0.0449191	−	0.0778021i
$582$	−57.2152	−	24.3855i	−2.37165	−	1.01081i
$583$	−6.31810	−	3.64776i	−0.261669	−	0.151075i
$584$	−30.2134			−1.25024
$585$	−18.3974	+	24.1581i	−0.760638	+	0.998815i
$586$	−8.94111			−0.369354
$587$	−14.3659	−	8.29416i	−0.592945	−	0.342337i	0.173316	−	0.984866i	$-0.444552\pi$
$587$	−14.3659	−	8.29416i	−0.592945	−	0.342337i	−0.766261	+	0.642529i	$0.777885\pi$
$588$	48.2875	−	36.2763i	1.99134	−	1.49601i
$589$	0.946385	+	1.63919i	0.0389951	+	0.0675415i
$590$	71.8231	+	41.4671i	2.95691	+	1.70717i
$591$	4.16784	+	5.54783i	0.171442	+	0.228207i
$592$			24.7726i			1.01815i
$593$			15.4909i			0.636137i	0.948068	+	0.318068i	$0.103034\pi$
$593$			15.4909i			0.636137i	−0.948068	+	0.318068i	$0.896966\pi$
$594$	13.5883	−	16.6299i	0.557534	−	0.682335i
$595$	−2.67951	−	4.64104i	−0.109849	−	0.190264i
$596$	33.2676	+	19.2071i	1.36270	+	0.786752i
$597$	20.5319	+	8.75083i	0.840313	+	0.358148i
$598$	−20.4629	+	16.4981i	−0.836790	+	0.674659i
$599$	−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	$0.913407\pi$
$600$	24.0829	+	32.0568i	0.983179	+	1.30871i
$601$	−14.3337	+	24.8266i	−0.584682	+	1.01270i	0.410233	+	0.911981i	$0.365447\pi$
$601$	−14.3337	+	24.8266i	−0.584682	+	1.01270i	−0.994915	+	0.100718i	$0.967886\pi$
$602$	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
$605$			24.0597i			0.978165i
$606$	−42.5066	−	56.5806i	−1.72671	−	2.29843i
$607$	−8.13672	−	14.0932i	−0.330259	−	0.572026i	0.652303	−	0.757958i	$-0.273803\pi$
$607$	−8.13672	−	14.0932i	−0.330259	−	0.572026i	−0.982563	+	0.185932i	$0.940470\pi$
$608$	−7.09991			−0.287939
$609$	−0.632539	+	1.48411i	−0.0256318	+	0.0601392i
$610$	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	−0.818179	−	0.574964i	$-0.805016\pi$
$613$	−18.0575	+	10.4255i	−0.729336	+	0.421082i	0.0888435	+	0.996046i	$0.471683\pi$
$614$	27.4452	−	47.5365i	1.10760	−	1.91842i
$615$	33.2101	+	14.1544i	1.33916	+	0.570759i
$616$	2.83287	+	1.63556i	0.114140	+	0.0658985i
$617$	−15.5643	+	8.98605i	−0.626595	+	0.361765i	−0.779432	−	0.626487i	$-0.784492\pi$
$617$	−15.5643	+	8.98605i	−0.626595	+	0.361765i	0.152837	+	0.988251i	$0.451159\pi$
$618$	−30.3195	−	40.3584i	−1.21963	−	1.62345i
$619$	−6.56515	+	3.79039i	−0.263876	+	0.152349i	−0.626101	−	0.779742i	$-0.715350\pi$
$619$	−6.56515	+	3.79039i	−0.263876	+	0.152349i	0.362226	+	0.932090i	$0.382017\pi$
$620$	25.8700	−	44.8082i	1.03897	−	1.79954i
$621$	5.06117	+	13.3603i	0.203098	+	0.536129i
$622$	19.0077	−	10.9741i	0.762138	−	0.440021i
$623$	−0.178735	−	0.309578i	−0.00716085	−	0.0124030i
$624$	−48.9599	+	50.3348i	−1.95997	+	2.01501i
$625$	15.5524	−	26.9376i	0.622097	−	1.07750i
$626$			32.8276i			1.31205i
$627$	−1.11512	+	0.837744i	−0.0445338	+	0.0334563i
$628$	−50.7293			−2.02432
$629$		−	16.1030i		−	0.642069i
$630$	−4.20727	+	4.03912i	−0.167622	+	0.160922i
$631$	11.9576	+	6.90373i	0.476025	+	0.274833i	0.718758	−	0.695260i	$-0.244711\pi$
$631$	11.9576	+	6.90373i	0.476025	+	0.274833i	−0.242734	+	0.970093i	$0.578044\pi$
$632$	19.0062	−	10.9732i	0.756026	−	0.436492i
$633$	−3.59040	−	29.6004i	−0.142706	−	1.17651i
$634$	87.1039			3.45934
$635$		−	31.5728i		−	1.25293i
$636$	32.6043	−	24.4942i	1.29284	−	0.971257i
$637$	−9.00658	+	23.3137i	−0.356854	+	0.923721i
$638$	14.7392			0.583531
$639$	17.9811	+	5.21314i	0.711321	+	0.206229i
$640$	13.3449	+	23.1141i	0.527505	+	0.913665i
$641$	34.5348			1.36404			0.682022	−	0.731332i	$-0.261101\pi$
$641$	34.5348			1.36404			0.682022	+	0.731332i	$0.261101\pi$
$642$	−5.43201	+	0.658879i	−0.214384	+	0.0260039i
$643$	−7.80782	+	4.50785i	−0.307910	+	0.177772i	−0.645991	−	0.763345i	$-0.723556\pi$
$643$	−7.80782	+	4.50785i	−0.307910	+	0.177772i	0.338081	+	0.941117i	$0.390222\pi$
$644$	−3.12839	+	1.80618i	−0.123276	+	0.0711734i
$645$	6.66725	−	15.6432i	0.262523	−	0.615950i
$646$	10.0117			0.393906
$647$	2.14777	+	3.72004i	0.0844374	+	0.146250i	0.905151	−	0.425089i	$-0.139757\pi$
$647$	2.14777	+	3.72004i	0.0844374	+	0.146250i	−0.820714	+	0.571339i	$0.806424\pi$
$648$	33.5747	+	64.0487i	1.31894	+	2.51607i
$649$	17.3670			0.681714
$650$	−25.6921	−	9.92541i	−1.00773	−	0.389307i
$651$	1.52471	+	0.649844i	0.0597582	+	0.0254694i
$652$		−	62.8348i		−	2.46080i
$653$	−37.1624			−1.45428			−0.727138	−	0.686491i	$-0.759150\pi$
$653$	−37.1624			−1.45428			−0.727138	+	0.686491i	$0.759150\pi$
$654$	6.59977	+	2.81287i	0.258071	+	0.109992i
$655$	9.38531	−	5.41861i	0.366715	−	0.211723i
$656$	72.2960	+	41.7401i	2.82269	+	1.62968i
$657$	−2.69690	−	10.9535i	−0.105216	−	0.427337i
$658$		−	5.68402i		−	0.221586i
$659$	1.31776			0.0513325			0.0256663	−	0.999671i	$-0.491829\pi$
$659$	1.31776			0.0513325			0.0256663	+	0.999671i	$0.491829\pi$
$660$	35.0735	+	14.9486i	1.36523	+	0.581873i
$661$			33.5146i			1.30357i	0.758405	+	0.651783i	$0.225979\pi$
$661$			33.5146i			1.30357i	−0.758405	+	0.651783i	$0.774021\pi$
$662$	−18.4015	+	31.8724i	−0.715196	+	1.23875i
$663$	31.8256	−	32.7193i	1.23600	−	1.27071i
$664$	−33.3095	−	57.6938i	−1.29266	−	2.23895i
$665$	0.328036	−	0.189392i	0.0127207	−	0.00734430i
$666$	−17.0169	+	4.18980i	−0.659392	+	0.162351i
$667$	−4.90270	+	8.49173i	−0.189833	+	0.328801i
$668$	−105.973	+	61.1837i	−4.10023	+	2.36727i
$669$	6.40682	−	15.0322i	0.247702	−	0.581178i
$670$	52.9453	−	30.5680i	2.04545	−	1.18094i
$671$	4.87939	+	2.81712i	0.188367	+	0.108754i
$672$	−4.97068	+	3.73426i	−0.191748	+	0.144052i
$673$	−11.5750	+	20.0485i	−0.446184	+	0.772813i	−0.998134	−	0.0610643i	$-0.980551\pi$
$673$	−11.5750	+	20.0485i	−0.446184	+	0.772813i	0.551950	+	0.833877i	$0.313884\pi$
$674$	−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	$0.938567\pi$
$678$	20.9358	−	2.53942i	0.804034	−	0.0975258i
$679$	3.53707			0.135740
$680$	−82.4337	−	142.779i	−3.16119	−	5.47534i
$681$	31.5650	−	3.82870i	1.20958	−	0.146716i
$682$		−	15.1424i		−	0.579834i
$683$	−19.4097	−	11.2062i	−0.742692	−	0.428793i	0.0803552	−	0.996766i	$-0.474395\pi$
$683$	−19.4097	−	11.2062i	−0.742692	−	0.428793i	−0.823047	+	0.567973i	$0.807728\pi$
$684$	−1.86388	−	7.57016i	−0.0712671	−	0.289452i
$685$	−3.13145	+	5.42383i	−0.119646	+	0.207234i
$686$	−4.82396	+	8.35535i	−0.184180	+	0.319009i
$687$	−8.89835	+	20.8780i	−0.339493	+	0.796545i
$688$	19.6612	−	34.0542i	0.749576	−	1.29830i
$689$	−6.08134	+	15.7416i	−0.231681	+	0.599709i
$690$	−28.3414	+	21.2917i	−1.07894	+	0.810559i
$691$	−22.7060	−	13.1093i	−0.863777	−	0.498702i	0.00149829	−	0.999999i	$-0.499523\pi$
$691$	−22.7060	−	13.1093i	−0.863777	−	0.498702i	−0.865275	+	0.501297i	$0.832856\pi$
$692$	−26.5260	−	45.9444i	−1.00837	−	1.74654i
$693$	−0.340085	+	1.17302i	−0.0129188	+	0.0445592i
$694$		−	50.5283i		−	1.91803i
$695$			45.6069i			1.72997i
$696$	−19.4597	+	45.6579i	−0.737620	+	1.73066i
$697$	−46.9949	−	27.1325i	−1.78006	−	1.02772i
$698$	31.4722	+	54.5114i	1.19124	+	2.06329i
$699$	−1.00985	−	8.32549i	−0.0381959	−	0.314899i
$700$	−3.27803	−	1.89257i	−0.123898	−	0.0715326i
$701$	−49.5379			−1.87102			−0.935510	−	0.353300i	$-0.885059\pi$
$701$	−49.5379			−1.87102			−0.935510	+	0.353300i	$0.885059\pi$
$702$	−42.8569	−	25.1187i	−1.61753	−	0.948044i
$703$	1.13819			0.0429275
$704$	18.8339	+	10.8738i	0.709831	+	0.409821i
$705$	−4.80567	−	39.6195i	−0.180992	−	1.49216i
$706$	−2.90520	−	5.03196i	−0.109339	−	0.189380i
$707$	3.48544	+	2.01232i	0.131084	+	0.0756811i
$708$	−38.0619	+	89.3038i	−1.43045	+	3.35624i
$709$		−	28.9190i		−	1.08608i	−0.839708	−	0.543038i	$-0.817274\pi$
$709$		−	28.9190i		−	1.08608i	0.839708	−	0.543038i	$-0.182726\pi$
$710$			46.4516i			1.74330i
$711$	5.67474	+	5.91098i	0.212820	+	0.221679i
$712$	−5.49868	−	9.52399i	−0.206072	−	0.356927i
$713$	8.72404	+	5.03683i	0.326718	+	0.188631i
$714$	7.00926	−	5.26575i	0.262315	−	0.197066i
$715$	−15.5883	+	2.43476i	−0.582971	+	0.0910549i
$716$	−17.8306	+	30.8835i	−0.666360	+	1.15417i
$717$	10.7158	−	25.1423i	0.400190	−	0.938957i
$718$	−7.40322	+	12.8227i	−0.276286	+	0.478541i
$719$	−5.28737	+	9.15800i	−0.197186	+	0.341536i	−0.947615	−	0.319415i	$-0.896514\pi$
$719$	−5.28737	+	9.15800i	−0.197186	+	0.341536i	0.750429	+	0.660951i	$0.229847\pi$
$720$	−68.3115	+	65.5814i	−2.54582	+	2.44407i
$721$	2.48613	+	1.43537i	0.0925883	+	0.0534559i
$722$		−	49.6706i		−	1.84855i
$723$	−28.0040	+	3.39676i	−1.04148	+	0.126327i
$724$	39.5677	+	68.5333i	1.47052	+	2.54702i
$725$	−10.2744			−0.381583
$726$	−39.0731	+	4.73939i	−1.45014	+	0.175895i
$727$	−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
$731$	−12.7804	+	22.1364i	−0.472701	+	0.818743i
$732$	−25.1798	+	18.9165i	−0.930674	+	0.699175i
$733$	42.6470	+	24.6222i	1.57520	+	0.909443i	0.995515	+	0.0946033i	$0.0301583\pi$
$733$	42.6470	+	24.6222i	1.57520	+	0.909443i	0.579686	+	0.814840i	$0.303175\pi$
$734$	30.7178	−	17.7349i	1.13381	−	0.654608i
$735$	−13.2152	+	31.0064i	−0.487449	+	1.14369i
$736$	−32.7245	+	18.8935i	−1.20624	+	0.696423i
$737$	6.40115	−	11.0871i	0.235789	−	0.408399i
$738$	−16.4449	+	56.7216i	−0.605346	+	2.08795i
$739$	7.35764	−	4.24793i	0.270655	−	0.156263i	−0.358530	−	0.933518i	$-0.616722\pi$
$739$	7.35764	−	4.24793i	0.270655	−	0.156263i	0.629185	+	0.777255i	$0.283389\pi$
$740$	−15.5565	−	26.9447i	−0.571869	−	0.990506i
$741$	2.31266	+	2.24949i	0.0849575	+	0.0826369i
$742$	−1.62062	+	2.80700i	−0.0594949	+	0.103048i
$743$		−	27.3401i		−	1.00301i	−0.865154	−	0.501506i	$-0.832780\pi$
$743$		−	27.3401i		−	1.00301i	0.865154	−	0.501506i	$-0.167220\pi$
$744$	46.9070	+	19.9921i	1.71969	+	0.732946i
$745$	−21.4378			−0.785421
$746$		−	20.7346i		−	0.759146i
$747$	17.9429	−	17.2258i	0.656498	−	0.630260i
$748$	−49.6318	−	28.6549i	−1.81472	−	1.04773i
$749$	0.269494	−	0.155593i	0.00984711	−	0.00568523i
$750$	25.1319	+	10.7114i	0.917688	+	0.391125i
$751$	−32.4964			−1.18581			−0.592906	−	0.805272i	$-0.702019\pi$
$751$	−32.4964			−1.18581			−0.592906	+	0.805272i	$0.702019\pi$
$752$		−	92.2889i		−	3.36543i
$753$	−43.7734	−	18.6565i	−1.59519	−	0.679882i
$754$	−5.26134	−	33.6853i	−0.191607	−	1.22675i
$755$	−35.1768			−1.28021
$756$	−5.28650	−	4.31959i	−0.192268	−	0.157102i
$757$	18.7348	+	32.4496i	0.680928	+	1.17940i	0.974698	+	0.223525i	$0.0717566\pi$
$757$	18.7348	+	32.4496i	0.680928	+	1.17940i	−0.293770	+	0.955876i	$0.594910\pi$
$758$	101.027			3.66947
$759$	−2.91045	+	6.82872i	−0.105643	+	0.247867i
$760$	10.0919	−	5.82654i	0.366071	−	0.211351i
$761$	16.1849	−	9.34435i	0.586702	−	0.338732i	−0.177091	−	0.984195i	$-0.556669\pi$
$761$	16.1849	−	9.34435i	0.586702	−	0.338732i	0.763792	+	0.645462i	$0.223335\pi$
$762$	51.2744	−	6.21936i	1.85748	−	0.225304i
$763$	−0.408001			−0.0147706
$764$	20.4280	+	35.3823i	0.739058	+	1.28009i
$765$	44.4048	−	42.6301i	1.60546	−	1.54129i
$766$	−47.1884			−1.70499
$767$	−6.19936	−	39.6909i	−0.223846	−	1.43315i
$768$	3.73314	−	2.80455i	0.134708	−	0.101200i
$769$		−	44.9114i		−	1.61955i	−0.586744	−	0.809773i	$-0.699590\pi$
$769$		−	44.9114i		−	1.61955i	0.586744	−	0.809773i	$-0.300410\pi$
$770$	−3.03033			−0.109205
$771$	2.04384	+	16.8501i	0.0736071	+	0.606841i
$772$	−33.5791	+	19.3869i	−1.20854	+	0.697750i
$773$	2.77119	+	1.59995i	0.0996728	+	0.0575461i	0.549008	−	0.835817i	$-0.315006\pi$
$773$	2.77119	+	1.59995i	0.0996728	+	0.0575461i	−0.449335	+	0.893363i	$0.648339\pi$
$774$	26.7180	+	7.74618i	0.960359	+	0.278431i
$775$			10.5555i			0.379165i
$776$	108.816			3.90627
$777$	0.796850	−	0.598638i	0.0285868	−	0.0214760i
$778$		−	91.5288i		−	3.28147i
$779$	1.91777	−	3.32167i	0.0687112	−	0.119011i
$780$	21.6439	−	85.4938i	0.774976	−	3.06117i
$781$	4.86365	+	8.42408i	0.174035	+	0.301437i
$782$	46.1455	−	26.6421i	1.65016	−	0.952719i
$783$	−18.2898	−	2.97939i	−0.653623	−	0.106475i
$784$	−38.9705	+	67.4989i	−1.39180	+	2.41067i
$785$	24.5176	−	14.1553i	0.875072	−	0.505223i
$786$	10.6486	+	14.1744i	0.379824	+	0.505585i
$787$	−26.1957	+	15.1241i	−0.933775	+	0.539115i	−0.888003	−	0.459837i	$-0.847908\pi$
$787$	−26.1957	+	15.1241i	−0.933775	+	0.539115i	−0.0457713	+	0.998952i	$0.514575\pi$
$788$	−17.4528	−	10.0764i	−0.621732	−	0.358957i
$789$	36.8024	+	15.6855i	1.31020	+	0.558417i
$790$	−10.1655	+	17.6071i	−0.361671	+	0.626433i
$791$	−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
$795$	−8.92302	+	20.9359i	−0.316467	+	0.742519i
$796$	−64.8207			−2.29751
$797$	−16.4758	−	28.5369i	−0.583602	−	1.01083i	−0.995048	−	0.0993945i	$-0.968309\pi$
$797$	−16.4758	−	28.5369i	−0.583602	−	1.01083i	0.411446	−	0.911434i	$-0.365024\pi$
$798$	0.372192	+	0.495426i	0.0131754	+	0.0175379i
$799$			59.9909i			2.12232i
$800$	−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
$803$	2.93058	−	5.07591i	0.103418	−	0.179125i
$804$	42.9828	+	57.2145i	1.51588	+	2.01780i
$805$	1.00798	−	1.74587i	0.0355265	−	0.0615337i
$806$	−34.6069	+	5.40528i	−1.21897	+	0.190393i
$807$	34.4795	+	14.6954i	1.21373	+	0.517303i
$808$	107.228	+	61.9080i	3.77226	+	2.17792i
$809$	25.6465	+	44.4211i	0.901684	+	1.56176i	0.825308	+	0.564683i	$0.191002\pi$
$809$	25.6465	+	44.4211i	0.901684	+	1.56176i	0.0763761	+	0.997079i	$0.475665\pi$
$810$	−56.6031	−	35.8331i	−1.98883	−	1.25905i
$811$			51.3422i			1.80287i	0.432915	+	0.901435i	$0.357485\pi$
$811$			51.3422i			1.80287i	−0.432915	+	0.901435i	$0.642515\pi$
$812$		−	4.68546i		−	0.164427i
$813$	27.7485	+	36.9361i	0.973181	+	1.29540i
$814$	−7.88573	−	4.55283i	−0.276395	−	0.159577i
$815$	17.5331	+	30.3683i	0.614159	+	1.06376i
$816$	113.806	−	85.4976i	3.98401	−	2.99302i
$817$	−1.56463	−	0.903342i	−0.0547396	−	0.0316039i
$818$	94.0856			3.28962
$819$	2.80224	+	0.358515i	0.0979181	+	0.0125275i
$820$	−104.847			−3.66141
$821$	−3.33889	−	1.92771i	−0.116528	−	0.0672774i	0.440603	−	0.897702i	$-0.354765\pi$
$821$	−3.33889	−	1.92771i	−0.116528	−	0.0672774i	−0.557131	+	0.830425i	$0.688098\pi$
$822$	−9.42518	−	4.01708i	−0.328741	−	0.140112i
$823$	20.9364	+	36.2628i	0.729796	+	1.26404i	0.956969	+	0.290189i	$0.0937181\pi$
$823$	20.9364	+	36.2628i	0.729796	+	1.26404i	−0.227174	+	0.973854i	$0.572949\pi$
$824$	76.4845	+	44.1583i	2.66446	+	1.53833i
$825$	−7.72155	+	0.936590i	−0.268830	+	0.0326079i
$826$		−	7.71578i		−	0.268466i
$827$		−	33.2317i		−	1.15558i	−0.816185	−	0.577790i	$-0.803915\pi$
$827$		−	33.2317i		−	1.15558i	0.816185	−	0.577790i	$-0.196085\pi$
$828$	−28.7357	−	29.9320i	−0.998636	−	1.04021i
$829$	−23.8687	−	41.3417i	−0.828993	−	1.43586i	−0.898829	−	0.438299i	$-0.855581\pi$
$829$	−23.8687	−	41.3417i	−0.828993	−	1.43586i	0.0698363	−	0.997558i	$-0.477752\pi$
$830$	53.4469	+	30.8576i	1.85517	+	1.07108i
$831$	−1.34372	−	11.0780i	−0.0466130	−	0.384292i
$832$	18.1282	−	46.9251i	0.628481	−	1.62683i
$833$	25.3321	−	43.8765i	0.877706	−	1.52023i
$834$	−74.0659	+	8.98387i	−2.56469	+	0.311086i
$835$	34.1449	−	59.1407i	1.18163	−	2.04665i
$836$	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
$839$		−	15.8799i		−	0.548234i	−0.961696	−	0.274117i	$-0.911615\pi$
$839$		−	15.8799i		−	0.548234i	0.961696	−	0.274117i	$-0.0883855\pi$
$840$	4.00085	−	9.38709i	0.138042	−	0.323886i
$841$	8.14089	+	14.1004i	0.280720	+	0.486222i
$842$	47.1332			1.62432
$843$	1.47083	+	1.95782i	0.0506579	+	0.0674309i
$844$	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
$848$	−26.3133	+	45.5760i	−0.903602	+	1.56509i
$849$	−4.16701	−	34.3542i	−0.143011	−	1.17903i
$850$	48.3527	+	27.9165i	1.65848	+	0.957527i
$851$	5.24606	−	3.02881i	0.179833	−	0.103826i
$852$	−53.9773	+	6.54720i	−1.84923	+	0.224304i
$853$	35.9630	−	20.7633i	1.23135	−	0.710921i	0.264040	−	0.964512i	$-0.414945\pi$
$853$	35.9630	−	20.7633i	1.23135	−	0.710921i	0.967312	+	0.253591i	$0.0816117\pi$
$854$	1.25158	−	2.16781i	0.0428283	−	0.0741809i
$855$	3.01317	+	3.13860i	0.103048	+	0.107338i
$856$	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	$0.586636\pi$
$858$	−7.02473	−	24.8360i	−0.239820	−	0.847886i
$859$	−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	$0.327925\pi$
$860$			49.3868i			1.68408i
$861$	−0.404422	−	3.33419i	−0.0137827	−	0.113629i
$862$	−5.29603			−0.180383
$863$			24.5762i			0.836584i	0.908313	+	0.418292i	$0.137371\pi$
$863$			24.5762i			0.836584i	−0.908313	+	0.418292i	$0.862629\pi$
$864$	−55.2993	−	45.1849i	−1.88132	−	1.53722i
$865$	25.6403	+	14.8034i	0.871795	+	0.503331i
$866$	−56.2424	+	32.4716i	−1.91119	+	1.10343i
$867$	−50.4362	+	37.8905i	−1.71290	+	1.28683i
$868$	−4.81364			−0.163386
$869$			4.25744i			0.144424i
$870$	−5.53640	−	45.6439i	−0.187702	−	1.54747i
$871$	−27.6237	−	10.6716i	−0.935993	−	0.361595i
$872$	−12.5519			−0.425062
$873$	9.71314	+	39.4500i	0.328740	+	1.33518i
$874$	1.88311	+	3.26164i	0.0636970	+	0.110326i
$875$	−1.55367			−0.0525235
$876$	19.6784	+	26.1940i	0.664872	+	0.885014i
$877$	12.6543	−	7.30596i	0.427305	−	0.246705i	−0.270893	−	0.962610i	$-0.587319\pi$
$877$	12.6543	−	7.30596i	0.427305	−	0.246705i	0.698198	+	0.715905i	$0.253986\pi$
$878$	−35.2024	+	20.3241i	−1.18802	+	0.685906i
$879$	3.50816	+	4.66972i	0.118327	+	0.157506i
$880$	−49.2020			−1.65860
$881$	1.19861	+	2.07605i	0.0403820	+	0.0699438i	0.885510	−	0.464620i	$-0.153809\pi$
$881$	1.19861	+	2.07605i	0.0403820	+	0.0699438i	−0.845128	+	0.534564i	$0.820476\pi$
$882$	−52.9578	−	15.3537i	−1.78318	−	0.516987i
$883$	−5.90861			−0.198840			−0.0994202	−	0.995046i	$-0.531699\pi$
$883$	−5.90861			−0.198840			−0.0994202	+	0.995046i	$0.531699\pi$
$884$	−47.7719	+	123.658i	−1.60674	+	4.15908i
$885$	−6.52346	−	53.7815i	−0.219284	−	1.80785i
$886$			25.0971i			0.843153i
$887$	−27.2603			−0.915312			−0.457656	−	0.889129i	$-0.651311\pi$
$887$	−27.2603			−0.915312			−0.457656	+	0.889129i	$0.651311\pi$
$888$	24.5147	−	18.4168i	0.822659	−	0.618028i
$889$	−2.54384	+	1.46869i	−0.0853178	+	0.0492582i
$890$	8.82292	+	5.09391i	0.295745	+	0.170748i
$891$	−14.0169	−	0.571858i	−0.469585	−	0.0191580i
$892$			47.4578i			1.58900i
$893$	−4.24025			−0.141895
$894$	−4.22293	−	34.8152i	−0.141236	−	1.16439i
$895$		−	19.9015i		−	0.665233i
$896$	1.24155	−	2.15042i	0.0414772	−	0.0718406i
$897$	16.6454	+	4.21401i	0.555775	+	0.140702i
$898$	−21.6281	−	37.4610i	−0.721739	−	1.25009i
$899$	−11.3156	+	6.53308i	−0.377397	+	0.217890i
$900$	12.1067	−	41.7581i	0.403555	−	1.39194i
$901$	17.1045	−	29.6259i	0.569834	−	0.986982i
$902$	−26.5739	+	15.3424i	−0.884813	+	0.510847i
$903$	−1.57053	+	0.190498i	−0.0522639	+	0.00633938i
$904$	−31.9542	+	18.4488i	−1.06278	+	0.613597i
$905$	−38.2464	−	22.0816i	−1.27135	−	0.734017i
$906$	−6.92929	−	57.1273i	−0.230210	−	1.89793i
$907$	−22.1251	+	38.3217i	−0.734651	+	1.27245i	0.220226	+	0.975449i	$0.429321\pi$
$907$	−22.1251	+	38.3217i	−0.734651	+	1.27245i	−0.954876	+	0.297004i	$0.904013\pi$
$908$	−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	$0.903704\pi$
$912$	6.04311	+	8.04401i	0.200107	+	0.266364i
$913$	12.9236			0.427708
$914$	−2.86553	−	4.96325i	−0.0947834	−	0.164170i
$915$	6.89113	−	16.1685i	0.227814	−	0.534514i
$916$		−	65.9135i		−	2.17784i
$917$	−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	0.255767	+	0.966739i	$0.417672\pi$
$919$	−21.5036	+	37.2452i	−0.709337	+	1.22861i	−0.965103	+	0.261869i	$0.915661\pi$
$920$	31.0099	−	53.7107i	1.02237	−	1.77079i
$921$	−35.5956	+	4.31759i	−1.17291	+	0.142269i
$922$	−4.06468	+	7.04023i	−0.133863	+	0.231858i
$923$	17.5164	−	14.1226i	0.576561	−	0.464850i
$924$	−0.427114	−	3.52127i	−0.0140510	−	0.115841i
$925$	5.49699	+	3.17369i	0.180740	+	0.104350i
$926$	21.1538	+	36.6394i	0.695156	+	1.20404i
$927$	−9.18194	+	31.6702i	−0.301574	+	1.04019i
$928$		−	49.0121i		−	1.60890i
$929$			6.38535i			0.209497i	0.994499	+	0.104748i	$0.0334037\pi$
$929$			6.38535i			0.209497i	−0.994499	+	0.104748i	$0.966596\pi$
$930$	−46.8926	+	5.68786i	−1.53767	+	0.186512i
$931$	3.10126	+	1.79052i	0.101640	+	0.0586818i
$932$	12.1784	+	21.0937i	0.398918	+	0.690947i
$933$	−13.1894	−	5.62141i	−0.431801	−	0.184037i
$934$	7.24252	+	4.18147i	0.236983	+	0.136822i
$935$	31.9830			1.04596
$936$	86.2094	+	11.0295i	2.81784	+	0.360512i
$937$	58.7846			1.92041			0.960204	−	0.279298i	$-0.0901018\pi$
$937$	58.7846			1.92041			0.960204	+	0.279298i	$0.0901018\pi$
$938$	−4.92577	−	2.84389i	−0.160832	−	0.0928564i
$939$	17.1450	−	12.8803i	0.559506	−	0.420333i
$940$	57.9550	+	100.381i	1.89028	+	3.27407i
$941$	−46.2325	−	26.6923i	−1.50714	−	0.870145i	−0.999966	−	0.00829925i	$-0.997358\pi$
$941$	−46.2325	−	26.6923i	−1.50714	−	0.870145i	−0.507170	−	0.861846i	$-0.669308\pi$
$942$	27.8179	+	37.0285i	0.906355	+	1.20645i
$943$		−	20.4134i		−	0.664752i
$944$		−	125.278i		−	4.07744i
$945$	3.76030	+	0.612551i	0.122323	+	0.0199263i
$946$	7.22687	+	12.5173i	0.234966	+	0.406973i
$947$	3.24038	+	1.87083i	0.105298	+	0.0607940i	0.551724	−	0.834027i	$-0.313970\pi$
$947$	3.24038	+	1.87083i	0.105298	+	0.0607940i	−0.446426	+	0.894821i	$0.647303\pi$
$948$	−21.8924	−	9.33072i	−0.711033	−	0.303048i
$949$	−12.6467	−	4.88570i	−0.410530	−	0.158597i
$950$	−1.97318	+	3.41765i	−0.0640184	+	0.110883i
$951$	−34.1763	−	45.4922i	−1.10824	−	1.47518i
$952$	−7.66922	+	13.2835i	−0.248561	+	0.430520i
$953$	11.2711	−	19.5221i	0.365107	−	0.632384i	−0.623686	−	0.781675i	$-0.714366\pi$
$953$	11.2711	−	19.5221i	0.365107	−	0.632384i	0.988793	+	0.149291i	$0.0476990\pi$
$954$	−35.7577	−	10.3670i	−1.15770	−	0.335644i
$955$	−19.7458	−	11.4003i	−0.638960	−	0.368904i
$956$			79.3762i			2.56721i
$957$	−5.78311	−	7.69792i	−0.186941	−	0.248838i
$958$	−13.1736	−	22.8173i	−0.425619	−	0.737194i
$959$	0.582669			0.0188154
$960$	26.5991	−	62.4088i	0.858482	−	2.01424i
$961$	−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
$965$	10.8193	−	18.7395i	0.348285	−	0.603247i
$966$	3.03386	+	1.29305i	0.0976127	+	0.0416033i
$967$	1.37859	+	0.795929i	0.0443325	+	0.0255954i	0.522002	−	0.852944i	$-0.325185\pi$
$967$	1.37859	+	0.795929i	0.0443325	+	0.0255954i	−0.477670	+	0.878539i	$0.658519\pi$
$968$	59.6371	−	34.4315i	1.91681	−	1.10667i
$969$	−3.92823	−	5.22887i	−0.126193	−	0.167976i
$970$	−87.3006	+	50.4030i	−2.80305	+	1.61834i
$971$	−2.45081	+	4.24492i	−0.0786501	+	0.136226i	−0.902668	−	0.430338i	$-0.858394\pi$
$971$	−2.45081	+	4.24492i	−0.0786501	+	0.136226i	0.824018	+	0.566564i	$0.191728\pi$
$972$	33.6604	−	70.8240i	1.07966	−	2.27168i
$973$	3.67458	−	2.12152i	0.117802	−	0.0680128i
$974$	−30.6544	−	53.0950i	−0.982231	−	1.70127i
$975$	4.89681	+	17.3127i	0.156823	+	0.554450i
$976$	20.3214	−	35.1977i	0.650473	−	1.12665i
$977$			3.86735i			0.123727i	0.998085	+	0.0618637i	$0.0197044\pi$
$977$			3.86735i			0.123727i	−0.998085	+	0.0618637i	$0.980296\pi$
$978$	−45.8646	+	34.4560i	−1.46659	+	1.10178i
$979$	2.13340			0.0681838
$980$		−	97.8897i		−	3.12697i
$981$	−1.12041	−	4.55056i	−0.0357719	−	0.145288i
$982$	68.2114	+	39.3819i	2.17671	+	1.25673i
$983$	45.0382	−	26.0028i	1.43650	−	0.829361i	0.438891	−	0.898540i	$-0.355371\pi$
$983$	45.0382	−	26.0028i	1.43650	−	0.829361i	0.997604	+	0.0691791i	$0.0220380\pi$
$984$	−12.4418	−	102.575i	−0.396631	−	3.26996i
$985$	11.2467			0.358350
$986$			69.1129i			2.20100i
$987$	−2.96862	+	2.23020i	−0.0944923	+	0.0709879i
$988$	−8.74037	−	3.37660i	−0.278068	−	0.107424i
$989$	−9.61549			−0.305755
$990$	−8.32157	−	33.7981i	−0.264477	−	1.07418i
$991$	4.08818	+	7.08094i	0.129865	+	0.224933i	0.923624	−	0.383299i	$-0.125212\pi$
$991$	4.08818	+	7.08094i	0.129865	+	0.224933i	−0.793759	+	0.608233i	$0.791879\pi$
$992$	−50.3529			−1.59871
$993$	23.8662	−	2.89487i	0.757371	−	0.0918658i
$994$	3.74264	−	2.16081i	0.118709	−	0.0685369i
$995$	31.3281	−	18.0873i	0.993167	−	0.573406i
$996$	−28.3236	+	66.4551i	−0.897469	+	2.10571i
$997$	30.4678			0.964926			0.482463	−	0.875916i	$-0.339742\pi$
$997$	30.4678			0.964926			0.482463	+	0.875916i	$0.339742\pi$
$998$	−49.7435	−	86.1583i	−1.57460	−	2.72729i
$999$	8.86502	+	7.24359i	0.280477	+	0.229177i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.11	✓	22	13.4	even	6
117.2.l.b.88.1	yes	22	9.7	even	3
117.2.r.b.43.11	yes	22	117.43	even	6	inner
117.2.r.b.49.11	yes	22	1.1	even	1	trivial
351.2.l.b.127.11		22	9.2	odd	6
351.2.l.b.199.1		22	39.17	odd	6
351.2.r.b.10.1		22	3.2	odd	2
351.2.r.b.316.1		22	117.56	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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29626 + 1.32574i) q^{2} +(-0.208561 - 1.71945i) q^{3} +(2.51519 + 4.35644i) q^{4} +(-2.43120 - 1.40366i) q^{5} +(1.80064 - 4.22479i) q^{6} +0.261179i q^{7} +8.03502i q^{8} +(-2.91300 + 0.717221i) q^{9} +(-3.72178 - 6.44631i) q^{10} +(-1.34990 - 0.779366i) q^{11} +(6.96610 - 5.23333i) q^{12} +(-1.29932 + 3.36330i) q^{13} +(-0.346256 + 0.599733i) q^{14} +(-1.90646 + 4.47308i) q^{15} +(-5.62200 + 9.73759i) q^{16} +(3.65449 - 6.32976i) q^{17} +(-7.63985 - 2.21497i) q^{18} +(0.447398 + 0.258305i) q^{19} -14.1219i q^{20} +(0.449083 - 0.0544718i) q^{21} +(-2.06648 - 3.57925i) q^{22} +2.74949 q^{23} +(13.8158 - 1.67580i) 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} +(-1.78313 + 3.08847i) q^{29} +(-10.3079 + 7.74385i) q^{30} +(3.17297 + 1.83191i) q^{31} +(-11.9020 + 6.87163i) q^{32} +(-1.05854 + 2.48363i) q^{33} +(16.7833 - 9.68983i) q^{34} +(0.366605 - 0.634978i) q^{35} +(-10.4513 - 10.8864i) q^{36} +(1.90801 - 1.10159i) q^{37} +(0.684893 + 1.18627i) q^{38} +(6.05401 + 1.53265i) q^{39} +(11.2784 - 19.5348i) q^{40} -7.42443i q^{41} +(1.10342 + 0.470288i) q^{42} -3.49719 q^{43} -7.84102i q^{44} +(8.08884 + 2.34515i) q^{45} +(6.31353 + 3.64512i) q^{46} +(-7.10819 + 4.10392i) q^{47} +(17.9158 + 7.63585i) q^{48} +6.93179 q^{49} +7.63895i q^{50} +(-11.6459 - 4.96356i) q^{51} +(-17.9200 + 2.79895i) q^{52} +4.68042 q^{53} +(-2.21515 + 13.5983i) q^{54} +(2.18792 + 3.78960i) q^{55} -2.09858 q^{56} +(0.350832 - 0.823150i) q^{57} +(-8.18905 + 4.72795i) q^{58} +(-9.64903 + 5.57087i) q^{59} +(-24.2818 + 2.94528i) q^{60} -3.61462 q^{61} +(4.85729 + 8.41308i) q^{62} +(-0.187323 - 0.760814i) q^{63} -13.9521 q^{64} +(7.87982 - 6.35307i) q^{65} +(-5.72334 + 4.29970i) q^{66} +8.21327i q^{67} +36.7670 q^{68} +(-0.573438 - 4.72761i) q^{69} +(1.68364 - 0.972048i) q^{70} +(-5.40445 - 3.12026i) q^{71} +(-5.76289 - 23.4061i) q^{72} +3.76021i q^{73} +5.84171 q^{74} +(3.98963 - 2.99724i) q^{75} +2.59875i q^{76} +(0.203554 - 0.352565i) q^{77} +(11.8696 + 11.5454i) q^{78} +(-1.36567 - 2.36542i) q^{79} +(27.3365 - 15.7827i) q^{80} +(7.97119 - 4.17854i) q^{81} +(9.84289 - 17.0484i) q^{82} +(-7.18029 + 4.14554i) q^{83} +(1.36683 + 1.81940i) q^{84} +(-17.7696 + 10.2593i) q^{85} +(-8.03044 - 4.63638i) q^{86} +(5.68236 + 2.42187i) q^{87} +(6.26222 - 10.8465i) 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} +(2.48812 - 5.83782i) q^{93} -21.7630 q^{94} +(-0.725143 - 1.25599i) q^{95} +(14.2977 + 19.0317i) q^{96} -13.5427i q^{97} +(15.9171 + 9.18977i) q^{98} +(4.49125 + 1.30212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 10 q^{4} + 3 q^{5} - 6 q^{6} - 2 q^{9} - 7 q^{10} + 3 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} - 12 q^{16} + 9 q^{17} - 30 q^{18} - 6 q^{19} + 12 q^{21} - 13 q^{22} - 12 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 10 * q^4 + 3 * q^5 - 6 * q^6 - 2 * q^9 - 7 * q^10 + 3 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 - 12 * q^16 + 9 * q^17 - 30 * q^18 - 6 * q^19 + 12 * q^21 - 13 * q^22 - 12 * q^23 + 45 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 - 24 * q^29 - 39 * q^30 + 27 * q^31 - 18 * q^33 - 15 * q^34 - 27 * q^35 + 2 * q^36 + 6 * q^37 + 21 * q^38 + 13 * q^39 + 13 * q^40 + 27 * q^42 + 8 * q^43 + 27 * q^45 - 15 * q^46 + 6 * q^47 + 11 * q^48 - 14 * q^49 + 12 * q^51 - 7 * q^52 - 24 * q^53 - 33 * q^54 - 13 * q^55 + 18 * q^56 + 42 * q^57 + 15 * q^58 - 33 * q^59 - 6 * q^60 - 6 * q^61 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 30 * q^66 + 138 * q^68 - 3 * q^69 + 24 * q^70 + 9 * q^71 - 6 * q^72 + 12 * q^74 + 22 * q^75 + 42 * q^77 - 42 * q^78 - 6 * q^79 + 105 * q^80 + 10 * q^81 - 16 * q^82 - 42 * q^83 - 18 * q^84 - 51 * q^85 - 45 * q^86 + 27 * q^87 - 11 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 6 * q^93 - 88 * q^94 - 3 * q^95 + 9 * q^96 + 117 * q^98 - 18 * q^99

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