LMFDB - Embedded newform 117.2.l.b.4.5

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			4.5
Character	$\chi$	$=$	117.4
Dual form			117.2.l.b.88.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.968164i q^{2} +(-0.767957 - 1.55250i) q^{3} +1.06266 q^{4} +(3.54737 + 2.04808i) q^{5} +(-1.50307 + 0.743509i) q^{6} +(-3.06763 - 1.77110i) q^{7} -2.96516i q^{8} +(-1.82048 + 2.38450i) q^{9} +(1.98287 - 3.43444i) q^{10} +2.27381i q^{11} +(-0.816076 - 1.64977i) q^{12} +(-3.37269 - 1.27474i) q^{13} +(-1.71472 + 2.96997i) q^{14} +(0.455398 - 7.08011i) q^{15} -0.745441 q^{16} +(1.48152 + 2.56606i) q^{17} +(2.30859 + 1.76253i) q^{18} +(-0.575621 + 0.332335i) q^{19} +(3.76964 + 2.17640i) q^{20} +(-0.393811 + 6.12262i) q^{21} +2.20142 q^{22} +(1.27686 + 2.21159i) q^{23} +(-4.60339 + 2.27711i) q^{24} +(5.88923 + 10.2004i) q^{25} +(-1.23416 + 3.26532i) q^{26} +(5.09998 + 0.995097i) q^{27} +(-3.25985 - 1.88207i) q^{28} -1.93360 q^{29} +(-6.85471 - 0.440900i) q^{30} +(-0.733160 - 0.423290i) q^{31} -5.20860i q^{32} +(3.53007 - 1.74619i) q^{33} +(2.48437 - 1.43435i) q^{34} +(-7.25469 - 12.5655i) q^{35} +(-1.93455 + 2.53391i) q^{36} +(-1.34335 - 0.775584i) q^{37} +(0.321755 + 0.557296i) q^{38} +(0.611054 + 6.21503i) q^{39} +(6.07286 - 10.5185i) q^{40} +(-1.84600 + 1.06579i) q^{41} +(5.92770 + 0.381274i) q^{42} +(1.22191 - 2.11641i) q^{43} +2.41628i q^{44} +(-11.3416 + 4.73022i) q^{45} +(2.14118 - 1.23621i) q^{46} +(-4.45149 + 2.57007i) q^{47} +(0.572467 + 1.15729i) q^{48} +(2.77359 + 4.80400i) q^{49} +(9.87570 - 5.70174i) q^{50} +(2.84606 - 4.27068i) q^{51} +(-3.58402 - 1.35461i) q^{52} +3.82370 q^{53} +(0.963417 - 4.93762i) q^{54} +(-4.65693 + 8.06604i) q^{55} +(-5.25159 + 9.09602i) q^{56} +(0.958001 + 0.638430i) q^{57} +1.87204i q^{58} -0.343666i q^{59} +(0.483932 - 7.52374i) q^{60} +(5.85687 - 10.1444i) q^{61} +(-0.409815 + 0.709820i) q^{62} +(9.80777 - 4.09052i) q^{63} -6.53366 q^{64} +(-9.35342 - 11.4295i) q^{65} +(-1.69060 - 3.41769i) q^{66} +(-9.78152 + 5.64737i) q^{67} +(1.57435 + 2.72685i) q^{68} +(2.45291 - 3.68073i) q^{69} +(-12.1655 + 7.02373i) q^{70} +(7.40141 - 4.27320i) q^{71} +(7.07042 + 5.39802i) q^{72} +0.0644878i q^{73} +(-0.750893 + 1.30058i) q^{74} +(11.3135 - 16.9765i) q^{75} +(-0.611688 + 0.353158i) q^{76} +(4.02714 - 6.97521i) q^{77} +(6.01717 - 0.591601i) q^{78} +(1.74347 + 3.01978i) q^{79} +(-2.64436 - 1.52672i) q^{80} +(-2.37168 - 8.68188i) q^{81} +(1.03186 + 1.78723i) q^{82} +(-5.65071 + 3.26244i) q^{83} +(-0.418487 + 6.50625i) q^{84} +12.1370i q^{85} +(-2.04903 - 1.18301i) q^{86} +(1.48492 + 3.00191i) q^{87} +6.74219 q^{88} +(-13.1316 - 7.58156i) q^{89} +(4.57963 + 10.9805i) q^{90} +(8.08849 + 9.88381i) q^{91} +(1.35687 + 2.35017i) q^{92} +(-0.0941203 + 1.46330i) q^{93} +(2.48825 + 4.30977i) q^{94} -2.72259 q^{95} +(-8.08633 + 3.99998i) q^{96} +(-14.4349 - 8.33399i) q^{97} +(4.65106 - 2.68529i) q^{98} +(-5.42189 - 4.13943i) 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 $

$2$		−	0.968164i		−	0.684595i	−0.939592	−	0.342298i	$-0.888795\pi$
$2$		−	0.968164i		−	0.684595i	0.939592	−	0.342298i	$-0.111205\pi$
$3$	−0.767957	−	1.55250i	−0.443380	−	0.896334i
$3$	−0.767957	−	1.55250i	−0.443380	−	0.896334i
$4$	1.06266			0.531329
$5$	3.54737	+	2.04808i	1.58643	+	0.915927i	0.993888	+	0.110389i	$0.0352098\pi$
$5$	3.54737	+	2.04808i	1.58643	+	0.915927i	0.592544	+	0.805538i	$0.298124\pi$
$6$	−1.50307	+	0.743509i	−0.613626	+	0.303536i
$7$	−3.06763	−	1.77110i	−1.15946	−	0.669413i	−0.208283	−	0.978069i	$-0.566788\pi$
$7$	−3.06763	−	1.77110i	−1.15946	−	0.669413i	−0.951174	+	0.308656i	$0.900121\pi$
$8$		−	2.96516i		−	1.04834i
$9$	−1.82048	+	2.38450i	−0.606828	+	0.794833i
$10$	1.98287	−	3.43444i	0.627040	−	1.08606i
$11$			2.27381i			0.685578i	0.939412	+	0.342789i	$0.111372\pi$
$11$			2.27381i			0.685578i	−0.939412	+	0.342789i	$0.888628\pi$
$12$	−0.816076	−	1.64977i	−0.235581	−	0.476248i
$13$	−3.37269	−	1.27474i	−0.935416	−	0.353549i
$13$	−3.37269	−	1.27474i	−0.935416	−	0.353549i
$14$	−1.71472	+	2.96997i	−0.458277	+	0.793759i
$15$	0.455398	−	7.08011i	0.117583	−	1.82808i
$16$	−0.745441			−0.186360
$17$	1.48152	+	2.56606i	0.359321	+	0.622362i	0.987848	−	0.155426i	$-0.0496751\pi$
$17$	1.48152	+	2.56606i	0.359321	+	0.622362i	−0.628527	+	0.777788i	$0.716342\pi$
$18$	2.30859	+	1.76253i	0.544139	+	0.415431i
$19$	−0.575621	+	0.332335i	−0.132057	+	0.0762429i	−0.564573	−	0.825383i	$-0.690959\pi$
$19$	−0.575621	+	0.332335i	−0.132057	+	0.0762429i	0.432516	+	0.901626i	$0.357626\pi$
$20$	3.76964	+	2.17640i	0.842918	+	0.486659i
$21$	−0.393811	+	6.12262i	−0.0859367	+	1.33606i
$22$	2.20142			0.469344
$23$	1.27686	+	2.21159i	0.266244	+	0.461149i	0.967889	−	0.251378i	$-0.0808838\pi$
$23$	1.27686	+	2.21159i	0.266244	+	0.461149i	−0.701645	+	0.712527i	$0.747551\pi$
$24$	−4.60339	+	2.27711i	−0.939663	+	0.464814i
$25$	5.88923	+	10.2004i	1.17785	+	2.04009i
$26$	−1.23416	+	3.26532i	−0.242038	+	0.640381i
$27$	5.09998	+	0.995097i	0.981491	+	0.191506i
$28$	−3.25985	−	1.88207i	−0.616053	−	0.355678i
$29$	−1.93360			−0.359061			−0.179530	−	0.983752i	$-0.557458\pi$
$29$	−1.93360			−0.359061			−0.179530	+	0.983752i	$0.557458\pi$
$30$	−6.85471	−	0.440900i	−1.25149	−	0.0804970i
$31$	−0.733160	−	0.423290i	−0.131680	−	0.0760252i	0.432713	−	0.901532i	$-0.357556\pi$
$31$	−0.733160	−	0.423290i	−0.131680	−	0.0760252i	−0.564393	+	0.825506i	$0.690890\pi$
$32$		−	5.20860i		−	0.920759i
$33$	3.53007	−	1.74619i	0.614507	−	0.303972i
$34$	2.48437	−	1.43435i	0.426066	−	0.245989i
$35$	−7.25469	−	12.5655i	−1.22627	−	2.12396i
$36$	−1.93455	+	2.53391i	−0.322425	+	0.422318i
$37$	−1.34335	−	0.775584i	−0.220846	−	0.127505i	0.385496	−	0.922709i	$-0.374030\pi$
$37$	−1.34335	−	0.775584i	−0.220846	−	0.127505i	−0.606342	+	0.795204i	$0.707364\pi$
$38$	0.321755	+	0.557296i	0.0521955	+	0.0904053i
$39$	0.611054	+	6.21503i	0.0978470	+	0.995201i
$40$	6.07286	−	10.5185i	0.960204	−	1.66312i
$41$	−1.84600	+	1.06579i	−0.288297	+	0.166449i	−0.637174	−	0.770720i	$-0.719897\pi$
$41$	−1.84600	+	1.06579i	−0.288297	+	0.166449i	0.348876	+	0.937169i	$0.386563\pi$
$42$	5.92770	+	0.381274i	0.914664	+	0.0588319i
$43$	1.22191	−	2.11641i	0.186340	−	0.322750i	−0.757688	−	0.652618i	$-0.773671\pi$
$43$	1.22191	−	2.11641i	0.186340	−	0.322750i	0.944027	+	0.329868i	$0.107004\pi$
$44$			2.41628i			0.364268i
$45$	−11.3416	+	4.73022i	−1.69070	+	0.705140i
$46$	2.14118	−	1.23621i	0.315700	−	0.182270i
$47$	−4.45149	+	2.57007i	−0.649317	+	0.374883i	−0.788194	−	0.615426i	$-0.788984\pi$
$47$	−4.45149	+	2.57007i	−0.649317	+	0.374883i	0.138878	+	0.990310i	$0.455650\pi$
$48$	0.572467	+	1.15729i	0.0826285	+	0.167041i
$49$	2.77359	+	4.80400i	0.396227	+	0.686285i
$50$	9.87570	−	5.70174i	1.39664	−	0.806348i
$51$	2.84606	−	4.27068i	0.398528	−	0.598014i
$52$	−3.58402	−	1.35461i	−0.497014	−	0.187851i
$53$	3.82370			0.525225			0.262612	−	0.964901i	$-0.415416\pi$
$53$	3.82370			0.525225			0.262612	+	0.964901i	$0.415416\pi$
$54$	0.963417	−	4.93762i	0.131104	−	0.671925i
$55$	−4.65693	+	8.06604i	−0.627940	+	1.08762i
$56$	−5.25159	+	9.09602i	−0.701773	+	1.21551i
$57$	0.958001	+	0.638430i	0.126890	+	0.0845621i
$58$			1.87204i			0.245811i
$59$		−	0.343666i		−	0.0447415i	−0.999750	−	0.0223708i	$-0.992879\pi$
$59$		−	0.343666i		−	0.0447415i	0.999750	−	0.0223708i	$-0.00712143\pi$
$60$	0.483932	−	7.52374i	0.0624754	−	0.971310i
$61$	5.85687	−	10.1444i	0.749896	−	1.29886i	−0.197976	−	0.980207i	$-0.563437\pi$
$61$	5.85687	−	10.1444i	0.749896	−	1.29886i	0.947872	−	0.318651i	$-0.103230\pi$
$62$	−0.409815	+	0.709820i	−0.0520465	+	0.0901472i
$63$	9.80777	−	4.09052i	1.23566	−	0.515357i
$64$	−6.53366			−0.816708
$65$	−9.35342	−	11.4295i	−1.16015	−	1.41766i
$66$	−1.69060	−	3.41769i	−0.208098	−	0.420689i
$67$	−9.78152	+	5.64737i	−1.19500	+	0.689936i	−0.959437	−	0.281923i	$-0.909028\pi$
$67$	−9.78152	+	5.64737i	−1.19500	+	0.689936i	−0.235566	+	0.971858i	$0.575694\pi$
$68$	1.57435	+	2.72685i	0.190918	+	0.330679i
$69$	2.45291	−	3.68073i	0.295296	−	0.443108i
$70$	−12.1655	+	7.02373i	−1.45405	+	0.839497i
$71$	7.40141	−	4.27320i	0.878385	−	0.507136i	0.00825973	−	0.999966i	$-0.497371\pi$
$71$	7.40141	−	4.27320i	0.878385	−	0.507136i	0.870126	+	0.492830i	$0.164037\pi$
$72$	7.07042	+	5.39802i	0.833256	+	0.636162i
$73$			0.0644878i			0.00754772i	0.999993	+	0.00377386i	$0.00120126\pi$
$73$			0.0644878i			0.00754772i	−0.999993	+	0.00377386i	$0.998799\pi$
$74$	−0.750893	+	1.30058i	−0.0872895	+	0.151190i
$75$	11.3135	−	16.9765i	1.30637	−	1.96028i
$76$	−0.611688	+	0.353158i	−0.0701655	+	0.0405101i
$77$	4.02714	−	6.97521i	0.458935	−	0.794899i
$78$	6.01717	−	0.591601i	0.681310	−	0.0669856i
$79$	1.74347	+	3.01978i	0.196156	+	0.339752i	0.947279	−	0.320410i	$-0.103821\pi$
$79$	1.74347	+	3.01978i	0.196156	+	0.339752i	−0.751123	+	0.660162i	$0.770487\pi$
$80$	−2.64436	−	1.52672i	−0.295648	−	0.170693i
$81$	−2.37168	−	8.68188i	−0.263520	−	0.964654i
$82$	1.03186	+	1.78723i	0.113950	+	0.197367i
$83$	−5.65071	+	3.26244i	−0.620246	+	0.358099i	−0.776965	−	0.629544i	$-0.783242\pi$
$83$	−5.65071	+	3.26244i	−0.620246	+	0.358099i	0.156719	+	0.987643i	$0.449908\pi$
$84$	−0.418487	+	6.50625i	−0.0456606	+	0.709890i
$85$			12.1370i			1.31645i
$86$	−2.04903	−	1.18301i	−0.220953	−	0.127567i
$87$	1.48492	+	3.00191i	0.159200	+	0.321838i
$88$	6.74219			0.718720
$89$	−13.1316	−	7.58156i	−1.39195	−	0.803643i	−0.398420	−	0.917203i	$-0.630441\pi$
$89$	−13.1316	−	7.58156i	−1.39195	−	0.803643i	−0.993531	+	0.113560i	$0.963775\pi$
$90$	4.57963	+	10.9805i	0.482735	+	1.15745i
$91$	8.08849	+	9.88381i	0.847904	+	1.03610i
$92$	1.35687	+	2.35017i	0.141463	+	0.245022i
$93$	−0.0941203	+	1.46330i	−0.00975983	+	0.151737i
$94$	2.48825	+	4.30977i	0.256643	+	0.444519i
$95$	−2.72259			−0.279332
$96$	−8.08633	+	3.99998i	−0.825308	+	0.408247i
$97$	−14.4349	−	8.33399i	−1.46564	−	0.846189i	−0.466379	−	0.884585i	$-0.654442\pi$
$97$	−14.4349	−	8.33399i	−1.46564	−	0.846189i	−0.999263	+	0.0383962i	$0.987775\pi$
$98$	4.65106	−	2.68529i	0.469828	−	0.271255i
$99$	−5.42189	−	4.13943i	−0.544921	−	0.416028i
$100$	6.25824	+	10.8396i	0.625824	+	1.08396i
$101$	8.94305			0.889866			0.444933	−	0.895564i	$-0.353227\pi$
$101$	8.94305			0.889866			0.444933	+	0.895564i	$0.353227\pi$
$102$	−4.13472	−	2.75545i	−0.409398	−	0.272830i
$103$	4.51888	−	7.82693i	0.445259	−	0.771211i	−0.552812	−	0.833306i	$-0.686445\pi$
$103$	4.51888	−	7.82693i	0.445259	−	0.771211i	0.998070	+	0.0620957i	$0.0197784\pi$
$104$	−3.77980	+	10.0006i	−0.370640	+	0.980635i
$105$	−13.9366	+	20.9126i	−1.36007	+	2.04086i
$106$		−	3.70197i		−	0.359567i
$107$	1.45083	−	2.51291i	0.140257	−	0.242932i	−0.787336	−	0.616524i	$-0.788540\pi$
$107$	1.45083	−	2.51291i	0.140257	−	0.242932i	0.927593	+	0.373592i	$0.121874\pi$
$108$	5.41953	+	1.05745i	0.521495	+	0.101753i
$109$		−	12.9389i		−	1.23932i	−0.784869	−	0.619662i	$-0.787270\pi$
$109$		−	12.9389i		−	1.23932i	0.784869	−	0.619662i	$-0.212730\pi$
$110$	7.80925	+	4.50867i	0.744583	+	0.429885i
$111$	−0.172454	+	2.68116i	−0.0163686	+	0.254485i
$112$	2.28674	+	1.32025i	0.216077	+	0.124752i
$113$	8.78523			0.826445			0.413223	−	0.910630i	$-0.364403\pi$
$113$	8.78523			0.826445			0.413223	+	0.910630i	$0.364403\pi$
$114$	0.618105	−	0.927502i	0.0578908	−	0.0868685i
$115$			10.4605i			0.975442i
$116$	−2.05476			−0.190779
$117$	9.17954	−	5.72154i	0.848649	−	0.528956i
$118$	−0.332725			−0.0306299
$119$		−	10.4957i		−	0.962136i
$120$	−20.9936	−	1.35033i	−1.91645	−	0.123267i
$121$	5.82980			0.529982
$122$	−9.82145	−	5.67042i	−0.889192	−	0.513375i
$123$	3.07229	+	2.04743i	0.277019	+	0.184611i
$124$	−0.779099	−	0.449813i	−0.0699651	−	0.0403944i
$125$			27.7656i			2.48343i
$126$	−3.96029	−	9.49553i	−0.352811	−	0.845929i
$127$	−1.42914	+	2.47534i	−0.126815	+	0.219651i	−0.922441	−	0.386138i	$-0.873809\pi$
$127$	−1.42914	+	2.47534i	−0.126815	+	0.219651i	0.795626	+	0.605789i	$0.207142\pi$
$128$		−	4.09154i		−	0.361645i
$129$	−4.22409	−	0.271697i	−0.371911	−	0.0239216i
$130$	−11.0656	+	9.05565i	−0.970520	+	0.794233i
$131$	−0.619332	+	1.07271i	−0.0541112	+	0.0937234i	−0.891812	−	0.452406i	$-0.850566\pi$
$131$	−0.619332	+	1.07271i	−0.0541112	+	0.0937234i	0.837701	+	0.546129i	$0.183899\pi$
$132$	3.75126	−	1.85560i	0.326505	−	0.161509i
$133$	2.35439			0.204152
$134$	5.46758	+	9.47012i	0.472327	+	0.818094i
$135$	16.0535	+	13.9751i	1.38166	+	1.20279i
$136$	7.60878	−	4.39293i	0.652447	−	0.376691i
$137$	2.54945	+	1.47193i	0.217814	+	0.125755i	0.604938	−	0.796273i	$-0.293198\pi$
$137$	2.54945	+	1.47193i	0.217814	+	0.125755i	−0.387124	+	0.922028i	$0.626531\pi$
$138$	−3.56355	−	2.37482i	−0.303350	−	0.202158i
$139$	−23.0024			−1.95104			−0.975518	−	0.219921i	$-0.929420\pi$
$139$	−23.0024			−1.95104			−0.975518	+	0.219921i	$0.929420\pi$
$140$	−7.70926	−	13.3528i	−0.651551	−	1.12852i
$141$	7.40857	+	4.93721i	0.623915	+	0.415788i
$142$	−4.13716	−	7.16578i	−0.347183	−	0.601339i
$143$	2.89851	−	7.66884i	0.242386	−	0.641301i
$144$	1.35706	−	1.77751i	0.113089	−	0.148125i
$145$	−6.85920	−	3.96016i	−0.569626	−	0.328874i
$146$	0.0624347			0.00516714
$147$	5.32818	−	7.99525i	0.439461	−	0.659437i
$148$	−1.42752	−	0.824181i	−0.117342	−	0.0677472i
$149$			21.9962i			1.80200i	0.433822	+	0.900999i	$0.357165\pi$
$149$			21.9962i			1.80200i	−0.433822	+	0.900999i	$0.642835\pi$
$150$	−16.4360	−	10.9533i	−1.34200	−	0.894332i
$151$	14.4238	−	8.32759i	1.17379	−	0.677690i	0.219223	−	0.975675i	$-0.429648\pi$
$151$	14.4238	−	8.32759i	1.17379	−	0.677690i	0.954571	+	0.297985i	$0.0963146\pi$
$152$	0.985425	+	1.70681i	0.0799285	+	0.138440i
$153$	−8.81586	−	1.13880i	−0.712720	−	0.0920662i
$154$	−6.75315	−	3.89893i	−0.544184	−	0.314185i
$155$	−1.73386	−	3.00314i	−0.139267	−	0.241218i
$156$	0.649342	+	6.60445i	0.0519889	+	0.528779i
$157$	1.19835	−	2.07560i	0.0956387	−	0.165651i	−0.814236	−	0.580534i	$-0.802844\pi$
$157$	1.19835	−	2.07560i	0.0956387	−	0.165651i	0.909875	+	0.414882i	$0.136177\pi$
$158$	2.92364	−	1.68797i	0.232593	−	0.134287i
$159$	−2.93644	−	5.93627i	−0.232874	−	0.470777i
$160$	10.6676	−	18.4768i	0.843349	−	1.46072i
$161$		−	9.04581i		−	0.712910i
$162$	−8.40549	+	2.29618i	−0.660398	+	0.180405i
$163$	18.0064	−	10.3960i	1.41037	−	0.814279i	0.414950	−	0.909844i	$-0.363799\pi$
$163$	18.0064	−	10.3960i	1.41037	−	0.814279i	0.995423	+	0.0955653i	$0.0304659\pi$
$164$	−1.96167	+	1.13257i	−0.153181	+	0.0884390i
$165$	16.0988	+	1.03549i	1.25329	+	0.0806126i
$166$	3.15858	+	5.47082i	0.245153	+	0.424618i
$167$	−6.31324	+	3.64495i	−0.488534	+	0.282055i	−0.723966	−	0.689836i	$-0.757683\pi$
$167$	−6.31324	+	3.64495i	−0.488534	+	0.282055i	0.235432	+	0.971891i	$0.424349\pi$
$168$	18.1545	+	1.16771i	1.40065	+	0.0900909i
$169$	9.75008	+	8.59861i	0.750006	+	0.661431i
$170$	11.7506			0.901233
$171$	0.255455	−	1.97758i	0.0195352	−	0.151229i
$172$	1.29847	−	2.24902i	0.0990076	−	0.171486i
$173$	−7.11419	+	12.3221i	−0.540882	+	0.936835i	0.457972	+	0.888967i	$0.348576\pi$
$173$	−7.11419	+	12.3221i	−0.540882	+	0.936835i	−0.998854	+	0.0478684i	$0.984757\pi$
$174$	2.90634	−	1.43765i	0.220329	−	0.108988i
$175$		−	41.7216i		−	3.15386i
$176$		−	1.69499i		−	0.127765i
$177$	−0.533540	+	0.263921i	−0.0401033	+	0.0198375i
$178$	−7.34019	+	12.7136i	−0.550171	+	0.952923i
$179$	−3.33151	+	5.77035i	−0.249009	+	0.431296i	−0.963251	−	0.268603i	$-0.913438\pi$
$179$	−3.33151	+	5.77035i	−0.249009	+	0.431296i	0.714242	+	0.699899i	$0.246771\pi$
$180$	−12.0522	+	5.02661i	−0.898319	+	0.374661i
$181$	−4.85699			−0.361017			−0.180508	−	0.983573i	$-0.557774\pi$
$181$	−4.85699			−0.361017			−0.180508	+	0.983573i	$0.557774\pi$
$182$	9.56915	−	7.83099i	0.709312	−	0.580471i
$183$	−20.2470	−	1.30230i	−1.49670	−	0.0962688i
$184$	6.55771	−	3.78610i	0.483441	−	0.279115i
$185$	−3.17691	−	5.50257i	−0.233571	−	0.404557i
$186$	1.41671	+	0.0911239i	0.103878	+	0.00668153i
$187$	−5.83473	+	3.36868i	−0.426678	+	0.246343i
$188$	−4.73041	+	2.73110i	−0.345001	+	0.199186i
$189$	−13.8825	−	12.0852i	−1.00980	−	0.879066i
$190$			2.63591i			0.191229i
$191$	6.41858	−	11.1173i	0.464432	−	0.804420i	−0.534744	−	0.845014i	$-0.679592\pi$
$191$	6.41858	−	11.1173i	0.464432	−	0.804420i	0.999176	+	0.0405946i	$0.0129252\pi$
$192$	5.01758	+	10.1435i	0.362112	+	0.732043i
$193$	18.2971	−	10.5638i	1.31705	−	0.760402i	0.333801	−	0.942644i	$-0.391669\pi$
$193$	18.2971	−	10.5638i	1.31705	−	0.760402i	0.983254	+	0.182242i	$0.0583354\pi$
$194$	−8.06867	+	13.9754i	−0.579297	+	1.00337i
$195$	−10.5612	+	23.2985i	−0.756305	+	1.66844i
$196$	2.94738	+	5.10501i	0.210527	+	0.364643i
$197$	8.09478	+	4.67353i	0.576729	+	0.332975i	0.759833	−	0.650119i	$-0.225281\pi$
$197$	8.09478	+	4.67353i	0.576729	+	0.332975i	−0.183103	+	0.983094i	$0.558614\pi$
$198$	−4.00764	+	5.24928i	−0.284811	+	0.373050i
$199$	1.63740	+	2.83606i	0.116072	+	0.201043i	0.918208	−	0.396099i	$-0.129636\pi$
$199$	1.63740	+	2.83606i	0.116072	+	0.201043i	−0.802136	+	0.597142i	$0.796303\pi$
$200$	30.2459	−	17.4625i	2.13871	−	1.23478i
$201$	16.2793	+	10.8488i	1.14825	+	0.765218i
$202$		−	8.65834i		−	0.609198i
$203$	5.93158	+	3.42460i	0.416315	+	0.240360i
$204$	3.02439	−	4.53827i	0.211749	−	0.317742i
$205$	−8.73128			−0.609819
$206$	−7.57776	−	4.37502i	−0.527967	−	0.304822i
$207$	−7.59805	−	0.981485i	−0.528101	−	0.0682179i
$208$	2.51414	+	0.950244i	0.174324	+	0.0658876i
$209$	−0.755665	−	1.30885i	−0.0522705	−	0.0905351i
$210$	20.2469	+	13.4929i	1.39717	+	0.931098i
$211$	9.76451	+	16.9126i	0.672216	+	1.16431i	0.977274	+	0.211979i	$0.0679909\pi$
$211$	9.76451	+	16.9126i	0.672216	+	1.16431i	−0.305058	+	0.952334i	$0.598676\pi$
$212$	4.06328			0.279067
$213$	−12.3181	−	8.20901i	−0.844022	−	0.562472i
$214$	−2.43291	−	1.40464i	−0.166310	−	0.0960193i
$215$	8.66914	−	5.00513i	0.591230	−	0.341347i
$216$	2.95062	−	15.1222i	0.200764	−	1.02894i
$217$	1.49938	+	2.59700i	0.101784	+	0.176296i
$218$	−12.5270			−0.848436
$219$	0.100117	−	0.0495239i	0.00676528	−	0.00334651i
$220$	−4.94872	+	8.57144i	−0.333643	+	0.577886i
$221$	−1.72564	−	10.5431i	−0.116079	−	0.709205i
$222$	2.59580	+	0.166964i	0.174219	+	0.0112059i
$223$			14.3672i			0.962097i	0.876694	+	0.481049i	$0.159744\pi$
$223$			14.3672i			0.962097i	−0.876694	+	0.481049i	$0.840256\pi$
$224$	−9.22495	+	15.9781i	−0.616368	+	1.06758i
$225$	−35.0442	−	4.52687i	−2.33628	−	0.301791i
$226$		−	8.50555i		−	0.565781i
$227$	2.92922	+	1.69118i	0.194419	+	0.112248i	0.594050	−	0.804428i	$-0.297528\pi$
$227$	2.92922	+	1.69118i	0.194419	+	0.112248i	−0.399631	+	0.916676i	$0.630862\pi$
$228$	1.01803	+	0.678433i	0.0674205	+	0.0449303i
$229$	−5.69129	−	3.28587i	−0.376091	−	0.217136i	0.300025	−	0.953931i	$-0.403005\pi$
$229$	−5.69129	−	3.28587i	−0.376091	−	0.217136i	−0.676116	+	0.736795i	$0.736338\pi$
$230$	10.1274			0.667783
$231$	−13.9216	−	0.895451i	−0.915977	−	0.0589163i
$232$			5.73343i			0.376418i
$233$	−15.3667			−1.00670			−0.503352	−	0.864081i	$-0.667900\pi$
$233$	−15.3667			−1.00670			−0.503352	+	0.864081i	$0.667900\pi$
$234$	−5.53939	−	8.88730i	−0.362121	−	0.580981i
$235$	−21.0548			−1.37346
$236$		−	0.365200i		−	0.0237725i
$237$	3.34929	−	5.02580i	0.217559	−	0.326461i
$238$	−10.1615			−0.658674
$239$	−12.2339	−	7.06327i	−0.791348	−	0.456885i	0.0490892	−	0.998794i	$-0.484368\pi$
$239$	−12.2339	−	7.06327i	−0.791348	−	0.456885i	−0.840437	+	0.541910i	$0.817701\pi$
$240$	−0.339473	+	5.27781i	−0.0219129	+	0.340681i
$241$	−10.3647	−	5.98409i	−0.667652	−	0.385469i	0.127534	−	0.991834i	$-0.459294\pi$
$241$	−10.3647	−	5.98409i	−0.667652	−	0.385469i	−0.795186	+	0.606365i	$0.792627\pi$
$242$		−	5.64421i		−	0.362823i
$243$	−11.6572	+	10.3493i	−0.747812	+	0.663911i
$244$	6.22385	−	10.7800i	0.398441	−	0.690121i
$245$			22.7221i			1.45166i
$246$	1.98225	−	2.97448i	0.126384	−	0.189646i
$247$	2.36503	−	0.387096i	0.150483	−	0.0246303i
$248$	−1.25512	+	2.17393i	−0.0797003	+	0.138045i
$249$	9.40443	+	6.26729i	0.595981	+	0.397173i
$250$	26.8816			1.70014
$251$	1.74332	+	3.01951i	0.110037	+	0.190590i	0.915785	−	0.401669i	$-0.131570\pi$
$251$	1.74332	+	3.01951i	0.110037	+	0.190590i	−0.805748	+	0.592259i	$0.798236\pi$
$252$	10.4223	−	4.34682i	0.656543	−	0.273824i
$253$	−5.02873	+	2.90334i	−0.316154	+	0.182531i
$254$	2.39653	+	1.38364i	0.150372	+	0.0868173i
$255$	18.8427	−	9.32073i	1.17998	−	0.583687i
$256$	−17.0286			−1.06429
$257$	5.08393	+	8.80563i	0.317127	+	0.549280i	0.979887	−	0.199552i	$-0.0639486\pi$
$257$	5.08393	+	8.80563i	0.317127	+	0.549280i	−0.662760	+	0.748831i	$0.730615\pi$
$258$	−0.263047	+	4.08962i	−0.0163766	+	0.254608i
$259$	2.74727	+	4.75842i	0.170707	+	0.295674i
$260$	−9.93949	−	12.1457i	−0.616421	−	0.753241i
$261$	3.52009	−	4.61067i	0.217888	−	0.285393i
$262$	1.03856	+	0.599615i	0.0641626	+	0.0370443i
$263$	14.6961			0.906198			0.453099	−	0.891460i	$-0.350318\pi$
$263$	14.6961			0.906198			0.453099	+	0.891460i	$0.350318\pi$
$264$	−5.17772	−	10.4672i	−0.318666	−	0.644213i
$265$	13.5641	+	7.83122i	0.833234	+	0.481068i
$266$		−	2.27944i		−	0.139761i
$267$	−1.68579	+	26.2091i	−0.103169	+	1.60397i
$268$	−10.3944	+	6.00122i	−0.634940	+	0.366583i
$269$	13.5989	+	23.5540i	0.829140	+	1.43611i	0.898714	+	0.438536i	$0.144503\pi$
$269$	13.5989	+	23.5540i	0.829140	+	1.43611i	−0.0695737	+	0.997577i	$0.522164\pi$
$270$	13.5302	−	15.5424i	0.823422	−	0.945881i
$271$	4.71707	+	2.72340i	0.286541	+	0.165435i	0.636381	−	0.771375i	$-0.280431\pi$
$271$	4.71707	+	2.72340i	0.286541	+	0.165435i	−0.349840	+	0.936810i	$0.613764\pi$
$272$	−1.10438	−	1.91285i	−0.0669631	−	0.115984i
$273$	9.13295	−	20.1477i	0.552751	−	1.21939i
$274$	1.42507	−	2.46829i	0.0860914	−	0.149115i
$275$	−23.1938	+	13.3910i	−1.39864	+	0.807506i
$276$	2.60660	−	3.91136i	0.156899	−	0.235436i
$277$	−2.22352	+	3.85124i	−0.133598	+	0.231399i	−0.925061	−	0.379818i	$-0.875986\pi$
$277$	−2.22352	+	3.85124i	−0.133598	+	0.231399i	0.791463	+	0.611217i	$0.209320\pi$
$278$			22.2701i			1.33567i
$279$	2.34404	−	0.977628i	0.140334	−	0.0585291i
$280$	−37.2587	+	21.5113i	−2.22663	+	1.28555i
$281$	−9.43122	+	5.44512i	−0.562620	+	0.324829i	−0.754196	−	0.656649i	$-0.771973\pi$
$281$	−9.43122	+	5.44512i	−0.562620	+	0.324829i	0.191577	+	0.981478i	$0.438640\pi$
$282$	4.78003	−	7.17272i	0.284647	−	0.427129i
$283$	10.4536	+	18.1063i	0.621405	+	1.07630i	0.989224	+	0.146408i	$0.0467711\pi$
$283$	10.4536	+	18.1063i	0.621405	+	1.07630i	−0.367819	+	0.929897i	$0.619896\pi$
$284$	7.86517	−	4.54096i	0.466712	−	0.269456i
$285$	2.09083	+	4.22681i	0.123850	+	0.250374i
$286$	−7.42470	−	2.80624i	−0.439032	−	0.165936i
$287$	7.55049			0.445691
$288$	12.4199	+	9.48217i	0.731850	+	0.558742i
$289$	4.11021	−	7.11910i	0.241777	−	0.418770i
$290$	−3.83409	+	6.64083i	−0.225145	+	0.389963i
$291$	−1.85310	+	28.8103i	−0.108630	+	1.68889i
$292$			0.0685284i			0.00401032i
$293$			7.89443i			0.461197i	0.973049	+	0.230599i	$0.0740685\pi$
$293$			7.89443i			0.461197i	−0.973049	+	0.230599i	$0.925932\pi$
$294$	−7.74071	−	5.15856i	−0.451448	−	0.300853i
$295$	0.703855	−	1.21911i	0.0409800	−	0.0709794i
$296$	−2.29973	+	3.98324i	−0.133669	+	0.231521i
$297$	−2.26266	+	11.5964i	−0.131293	+	0.672889i
$298$	21.2959			1.23364
$299$	−1.48726	−	9.08668i	−0.0860104	−	0.525496i
$300$	12.0223	−	18.0402i	0.694110	−	1.04155i
$301$	−7.49675	+	4.32825i	−0.432105	+	0.249476i
$302$	−8.06248	−	13.9646i	−0.463943	−	0.803573i
$303$	−6.86788	−	13.8840i	−0.394549	−	0.797617i
$304$	0.429092	−	0.247736i	0.0246101	−	0.0142086i
$305$	41.5530	−	23.9906i	2.37932	−	1.37370i
$306$	−1.10254	+	8.53520i	−0.0630281	+	0.487925i
$307$			25.3814i			1.44859i	0.689488	+	0.724297i	$0.257836\pi$
$307$			25.3814i			1.44859i	−0.689488	+	0.724297i	$0.742164\pi$
$308$	4.27947	−	7.41226i	0.243846	−	0.422353i
$309$	−15.6216	−	1.00479i	−0.888681	−	0.0571606i
$310$	−2.90753	+	1.67866i	−0.165137	+	0.0953416i
$311$	12.4112	−	21.4969i	0.703777	−	1.21898i	−0.263354	−	0.964699i	$-0.584829\pi$
$311$	12.4112	−	21.4969i	0.703777	−	1.21898i	0.967131	−	0.254278i	$-0.0818379\pi$
$312$	18.4285	−	1.81187i	1.04331	−	0.102577i
$313$	−13.2866	−	23.0131i	−0.751003	−	1.30078i	−0.947337	−	0.320239i	$-0.896237\pi$
$313$	−13.2866	−	23.0131i	−0.751003	−	1.30078i	0.196333	−	0.980537i	$-0.437097\pi$
$314$	−2.00952	−	1.16020i	−0.113404	−	0.0654738i
$315$	43.1695	+	5.57646i	2.43232	+	0.314198i
$316$	1.85271	+	3.20900i	0.104223	+	0.180520i
$317$	25.3330	−	14.6260i	1.42284	−	0.821479i	0.426302	−	0.904581i	$-0.359816\pi$
$317$	25.3330	−	14.6260i	1.42284	−	0.821479i	0.996541	+	0.0831020i	$0.0264827\pi$
$318$	−5.74728	+	2.84295i	−0.322292	+	0.159425i
$319$		−	4.39664i		−	0.246164i
$320$	−23.1773	−	13.3814i	−1.29565	−	0.748045i
$321$	−5.01545	−	0.322598i	−0.279935	−	0.0180056i
$322$	−8.75783			−0.488055
$323$	−1.70559	−	0.984720i	−0.0949013	−	0.0547913i
$324$	−2.52029	−	9.22588i	−0.140016	−	0.512549i
$325$	−6.85963	−	41.9102i	−0.380504	−	2.32476i
$326$	−10.0651	−	17.4332i	−0.557452	−	0.965535i
$327$	−20.0876	+	9.93655i	−1.11085	+	0.549492i
$328$	3.16024	+	5.47369i	0.174495	+	0.302234i
$329$	18.2074			1.00381
$330$	1.00252	−	15.5863i	0.0551870	−	0.857997i
$331$	0.519141	+	0.299726i	0.0285346	+	0.0164744i	0.514199	−	0.857671i	$-0.328089\pi$
$331$	0.519141	+	0.299726i	0.0285346	+	0.0164744i	−0.485665	+	0.874145i	$0.661422\pi$
$332$	−6.00478	+	3.46686i	−0.329555	+	0.190269i
$333$	4.29493	−	1.79128i	0.235361	−	0.0981617i
$334$	3.52891	+	6.11226i	0.193094	+	0.334448i
$335$	−46.2649			−2.52772
$336$	0.293563	−	4.56405i	0.0160152	−	0.248989i
$337$	−2.33017	+	4.03597i	−0.126932	+	0.219853i	−0.922487	−	0.386029i	$-0.873846\pi$
$337$	−2.33017	+	4.03597i	−0.126932	+	0.219853i	0.795554	+	0.605882i	$0.207180\pi$
$338$	8.32486	−	9.43967i	0.452813	−	0.513451i
$339$	−6.74668	−	13.6390i	−0.366430	−	0.740771i
$340$			12.8975i			0.699466i
$341$	0.962480	−	1.66707i	0.0521212	−	0.0902766i
$342$	−1.91462	−	0.247323i	−0.103531	−	0.0133737i
$343$			5.14618i			0.277868i
$344$	−6.27549	−	3.62315i	−0.338352	−	0.195347i
$345$	16.2398	−	8.03318i	0.874321	−	0.432492i
$346$	11.9299	+	6.88771i	0.641353	+	0.370285i
$347$	−30.3048			−1.62685			−0.813423	−	0.581672i	$-0.802399\pi$
$347$	−30.3048			−1.62685			−0.813423	+	0.581672i	$0.802399\pi$
$348$	1.57797	+	3.19000i	0.0845878	+	0.171002i
$349$		−	12.4086i		−	0.664220i	−0.943241	−	0.332110i	$-0.892240\pi$
$349$		−	12.4086i		−	0.664220i	0.943241	−	0.332110i	$-0.107760\pi$
$350$	−40.3934			−2.15912
$351$	−15.9322	−	9.85730i	−0.850396	−	0.526144i
$352$	11.8434			0.631253
$353$		−	16.9403i		−	0.901641i	−0.892615	−	0.450821i	$-0.851131\pi$
$353$		−	16.9403i		−	0.901641i	0.892615	−	0.450821i	$-0.148869\pi$
$354$	0.255519	+	0.516555i	0.0135807	+	0.0274546i
$355$	35.0074			1.85800
$356$	−13.9544	−	8.05660i	−0.739584	−	0.426999i
$357$	−16.2945	+	8.06022i	−0.862394	+	0.426592i
$358$	5.58664	+	3.22545i	0.295263	+	0.170470i
$359$		−	5.61852i		−	0.296534i	−0.988947	−	0.148267i	$-0.952630\pi$
$359$		−	5.61852i		−	0.296534i	0.988947	−	0.148267i	$-0.0473695\pi$
$360$	14.0258	+	33.6295i	0.739227	+	1.77243i
$361$	−9.27911	+	16.0719i	−0.488374	+	0.845889i
$362$			4.70236i			0.247151i
$363$	−4.47704	−	9.05074i	−0.234984	−	0.475041i
$364$	8.59530	+	10.5031i	0.450516	+	0.550512i
$365$	−0.132076	+	0.228762i	−0.00691316	+	0.0119740i
$366$	−1.26084	+	19.6024i	−0.0659052	+	1.02463i
$367$	−35.1018			−1.83230			−0.916149	−	0.400839i	$-0.868719\pi$
$367$	−35.1018			−1.83230			−0.916149	+	0.400839i	$0.868719\pi$
$368$	−0.951827	−	1.64861i	−0.0496174	−	0.0859399i
$369$	0.819240	−	6.34205i	0.0426479	−	0.330154i
$370$	−5.32739	+	3.07577i	−0.276958	+	0.159902i
$371$	−11.7297	−	6.77215i	−0.608976	−	0.351592i
$372$	−0.100018	+	1.55498i	−0.00518568	+	0.0806222i
$373$	2.41098			0.124836			0.0624178	−	0.998050i	$-0.480119\pi$
$373$	2.41098			0.124836			0.0624178	+	0.998050i	$0.480119\pi$
$374$	3.26144	+	5.64898i	0.168645	+	0.292102i
$375$	43.1059	−	21.3228i	2.22598	−	1.10110i
$376$	7.62066	+	13.1994i	0.393005	+	0.680705i
$377$	6.52144	+	2.46484i	0.335871	+	0.126946i
$378$	−11.7004	+	13.4405i	−0.601805	+	0.691305i
$379$	24.0816	+	13.9035i	1.23699	+	0.714175i	0.968477	−	0.249102i	$-0.0801355\pi$
$379$	24.0816	+	13.9035i	1.23699	+	0.714175i	0.268510	+	0.963277i	$0.413469\pi$
$380$	−2.89318			−0.148417
$381$	4.94047	+	0.317775i	0.253108	+	0.0162801i
$382$	−10.7634	−	6.21424i	−0.550702	−	0.317948i
$383$			0.593328i			0.0303177i	0.999885	+	0.0151588i	$0.00482539\pi$
$383$			0.593328i			0.0303177i	−0.999885	+	0.0151588i	$0.995175\pi$
$384$	−6.35210	+	3.14213i	−0.324154	+	0.160346i
$385$	28.5715	−	16.4958i	1.45614	−	0.840702i
$386$	−10.2275	−	17.7146i	−0.520568	−	0.901650i
$387$	2.82212	+	6.76654i	0.143456	+	0.343962i
$388$	−15.3394	−	8.85618i	−0.778738	−	0.449605i
$389$	8.95789	+	15.5155i	0.454183	+	0.786668i	0.998641	−	0.0521200i	$-0.0165978\pi$
$389$	8.95789	+	15.5155i	0.454183	+	0.786668i	−0.544458	+	0.838788i	$0.683265\pi$
$390$	22.5568	+	10.2250i	1.14221	+	0.517763i
$391$	−3.78339	+	6.55302i	−0.191334	+	0.331401i
$392$	14.2446	−	8.22412i	0.719461	−	0.415381i
$393$	2.14100	+	0.137711i	0.107999	+	0.00694660i
$394$	4.52474	−	7.83708i	0.227953	−	0.394826i
$395$			14.2831i			0.718658i
$396$	−5.76162	−	4.39879i	−0.289532	−	0.221048i
$397$	12.6425	−	7.29914i	0.634508	−	0.366333i	−0.147988	−	0.988989i	$-0.547280\pi$
$397$	12.6425	−	7.29914i	0.634508	−	0.366333i	0.782496	+	0.622656i	$0.213946\pi$
$398$	2.74577	−	1.58527i	0.137633	−	0.0794625i
$399$	−1.80807	−	3.65518i	−0.0905169	−	0.182988i
$400$	−4.39007	−	7.60383i	−0.219504	−	0.380192i
$401$	10.1732	−	5.87352i	0.508027	−	0.293310i	−0.223995	−	0.974590i	$-0.571910\pi$
$401$	10.1732	−	5.87352i	0.508027	−	0.293310i	0.732022	+	0.681281i	$0.238577\pi$
$402$	10.5035	−	15.7610i	0.523865	−	0.786089i
$403$	1.93314	+	2.36222i	0.0962964	+	0.117670i
$404$	9.50340			0.472812
$405$	9.36792	−	35.6553i	0.465495	−	1.77172i
$406$	3.31558	−	5.74275i	0.164549	−	0.285008i
$407$	1.76353	−	3.05452i	0.0874148	−	0.151407i
$408$	−12.6632	−	8.43901i	−0.626923	−	0.417793i
$409$			14.1035i			0.697372i	0.937240	+	0.348686i	$0.113372\pi$
$409$			14.1035i			0.697372i	−0.937240	+	0.348686i	$0.886628\pi$
$410$			8.45331i			0.417479i
$411$	0.327289	−	5.08839i	0.0161440	−	0.250992i
$412$	4.80203	−	8.31735i	0.236579	−	0.409767i
$413$	−0.608667	+	1.05424i	−0.0299506	+	0.0518759i
$414$	−0.950238	+	7.35616i	−0.0467017	+	0.361536i
$415$	−26.7269			−1.31197
$416$	−6.63961	+	17.5670i	−0.325534	+	0.861293i
$417$	17.6648	+	35.7111i	0.865051	+	1.74878i
$418$	−1.26718	+	0.731608i	−0.0619799	+	0.0357841i
$419$	−5.52029	−	9.56143i	−0.269684	−	0.467106i	0.699096	−	0.715028i	$-0.253586\pi$
$419$	−5.52029	−	9.56143i	−0.269684	−	0.467106i	−0.968780	+	0.247921i	$0.920253\pi$
$420$	−14.8098	+	22.2230i	−0.722645	+	1.08437i
$421$	0.220050	−	0.127046i	0.0107246	−	0.00619183i	−0.494628	−	0.869105i	$-0.664696\pi$
$421$	0.220050	−	0.127046i	0.0107246	−	0.00619183i	0.505353	+	0.862913i	$0.331362\pi$
$422$	16.3742	−	9.45365i	0.797083	−	0.460196i
$423$	1.97553	−	15.2933i	0.0960536	−	0.743588i
$424$		−	11.3379i		−	0.550615i
$425$	−17.4500	+	30.2243i	−0.846449	+	1.46609i
$426$	−7.94767	+	11.9259i	−0.385066	+	0.577814i
$427$	−35.9335	+	20.7462i	−1.73894	+	1.00398i
$428$	1.54174	−	2.67036i	0.0745226	−	0.129077i
$429$	−14.1318	+	1.38942i	−0.682289	+	0.0670818i
$430$	−4.84579	−	8.39315i	−0.233685	−	0.404754i
$431$	−1.28731	−	0.743226i	−0.0620073	−	0.0357999i	0.468676	−	0.883370i	$-0.344731\pi$
$431$	−1.28731	−	0.743226i	−0.0620073	−	0.0357999i	−0.530683	+	0.847570i	$0.678065\pi$
$432$	−3.80174	−	0.741786i	−0.182911	−	0.0356892i
$433$	−10.2717	−	17.7911i	−0.493626	−	0.854985i	0.506347	−	0.862330i	$-0.330995\pi$
$433$	−10.2717	−	17.7911i	−0.493626	−	0.854985i	−0.999973	+	0.00734473i	$0.997662\pi$
$434$	2.51432	−	1.45165i	0.120691	−	0.0696812i
$435$	−0.880558	+	13.6901i	−0.0422195	+	0.656391i
$436$		−	13.7497i		−	0.658489i
$437$	−1.46998	−	0.848693i	−0.0703186	−	0.0405985i
$438$	−0.0479472	−	0.0969296i	−0.00229101	−	0.00463148i
$439$	18.4553			0.880822			0.440411	−	0.897796i	$-0.354833\pi$
$439$	18.4553			0.880822			0.440411	+	0.897796i	$0.354833\pi$
$440$	23.9171	+	13.8085i	1.14020	+	0.658295i
$441$	−16.5044	−	2.13197i	−0.785924	−	0.101522i
$442$	−10.2074	+	1.67070i	−0.485518	+	0.0794670i
$443$	17.7387	+	30.7244i	0.842792	+	1.45976i	0.887525	+	0.460760i	$0.152423\pi$
$443$	17.7387	+	30.7244i	0.842792	+	1.45976i	−0.0447323	+	0.998999i	$0.514243\pi$
$444$	−0.183260	+	2.84916i	−0.00869713	+	0.135215i
$445$	−31.0552	−	53.7892i	−1.47216	−	2.54985i
$446$	13.9098			0.658647
$447$	34.1490	−	16.8921i	1.61519	−	0.798970i
$448$	20.0429	+	11.5718i	0.946938	+	0.546715i
$449$	−18.0094	+	10.3977i	−0.849917	+	0.490700i	−0.860623	−	0.509243i	$-0.829926\pi$
$449$	−18.0094	+	10.3977i	−0.849917	+	0.490700i	0.0107058	+	0.999943i	$0.496592\pi$
$450$	−4.38275	+	33.9285i	−0.206605	+	1.59941i
$451$	−2.42340	−	4.19746i	−0.114114	−	0.197650i
$452$	9.33570			0.439114
$453$	−24.0054	−	15.9977i	−1.12787	−	0.751636i
$454$	1.63734	−	2.83596i	0.0768444	−	0.133098i
$455$	8.45009	+	51.6274i	0.396146	+	2.42033i
$456$	1.89304	−	2.84062i	0.0886499	−	0.133024i
$457$			20.4661i			0.957365i	0.877988	+	0.478682i	$0.158885\pi$
$457$			20.4661i			0.957365i	−0.877988	+	0.478682i	$0.841115\pi$
$458$	−3.18126	+	5.51010i	−0.148650	+	0.257470i
$459$	5.00223	+	14.5611i	0.233484	+	0.679655i
$460$			11.1159i			0.518281i
$461$	21.8263	+	12.6014i	1.01655	+	0.586908i	0.913104	−	0.407727i	$-0.133678\pi$
$461$	21.8263	+	12.6014i	1.01655	+	0.586908i	0.103450	+	0.994635i	$0.467012\pi$
$462$	−0.866943	+	13.4784i	−0.0403339	+	0.627074i
$463$	3.32602	+	1.92028i	0.154573	+	0.0892428i	0.575291	−	0.817948i	$-0.304889\pi$
$463$	3.32602	+	1.92028i	0.154573	+	0.0892428i	−0.420718	+	0.907191i	$0.638222\pi$
$464$	1.44139			0.0669147
$465$	−3.33082	+	4.99809i	−0.154463	+	0.231781i
$466$			14.8775i			0.689185i
$467$	33.8330			1.56560			0.782802	−	0.622271i	$-0.213790\pi$
$467$	33.8330			1.56560			0.782802	+	0.622271i	$0.213790\pi$
$468$	9.75472	−	6.08004i	0.450912	−	0.281050i
$469$	40.0082			1.84741
$470$			20.3845i			0.940266i
$471$	−4.14265	−	0.266458i	−0.190883	−	0.0122777i
$472$	−1.01902			−0.0469044
$473$	4.81231	+	2.77839i	0.221270	+	0.127750i
$474$	−4.86580	−	3.24266i	−0.223493	−	0.148940i
$475$	−6.77993	−	3.91439i	−0.311084	−	0.179605i
$476$		−	11.1533i		−	0.511211i
$477$	−6.96097	+	9.11760i	−0.318721	+	0.417466i
$478$	−6.83840	+	11.8445i	−0.312781	+	0.541753i
$479$		−	26.7692i		−	1.22312i	−0.791199	−	0.611559i	$-0.790543\pi$
$479$		−	26.7692i		−	1.22312i	0.791199	−	0.611559i	$-0.209457\pi$
$480$	−36.8775	−	2.37199i	−1.68322	−	0.108266i
$481$	3.54204	+	4.32823i	0.161503	+	0.197350i
$482$	−5.79358	+	10.0348i	−0.263890	+	0.457072i
$483$	−14.0436	+	6.94680i	−0.639005	+	0.316090i
$484$	6.19509			0.281595
$485$	−34.1373	−	59.1275i	−1.55009	−	2.68484i
$486$	10.0199	+	11.2861i	0.454510	+	0.511949i
$487$	−26.3844	+	15.2330i	−1.19559	+	0.690274i	−0.959569	−	0.281474i	$-0.909177\pi$
$487$	−26.3844	+	15.2330i	−1.19559	+	0.690274i	−0.236020	+	0.971748i	$0.575843\pi$
$488$	−30.0797	−	17.3665i	−1.36165	−	0.786147i
$489$	−29.9679	−	19.9712i	−1.35520	−	0.903129i
$490$	21.9987			0.993800
$491$	20.1264	+	34.8600i	0.908293	+	1.57321i	0.816435	+	0.577437i	$0.195947\pi$
$491$	20.1264	+	34.8600i	0.908293	+	1.57321i	0.0918579	+	0.995772i	$0.470719\pi$
$492$	3.26479	+	2.17572i	0.147188	+	0.0980890i
$493$	−2.86466	−	4.96174i	−0.129018	−	0.223466i
$494$	−0.374772	−	2.28974i	−0.0168618	−	0.103020i
$495$	−10.7556	−	25.7885i	−0.483429	−	1.15911i
$496$	0.546528	+	0.315538i	0.0245398	+	0.0141681i
$497$	−30.2731			−1.35793
$498$	6.06776	−	9.10503i	0.271903	−	0.408006i
$499$	−17.1325	−	9.89148i	−0.766958	−	0.442804i	0.0648302	−	0.997896i	$-0.479349\pi$
$499$	−17.1325	−	9.89148i	−0.766958	−	0.442804i	−0.831788	+	0.555093i	$0.812683\pi$
$500$			29.5053i			1.31952i
$501$	10.5071	+	7.00211i	0.469421	+	0.312831i
$502$	2.92338	−	1.68782i	0.130477	−	0.0753309i
$503$	−11.3997	−	19.7448i	−0.508287	−	0.880378i	−0.999954	−	0.00959504i	$-0.996946\pi$
$503$	−11.3997	−	19.7448i	−0.508287	−	0.880378i	0.491667	−	0.870783i	$-0.336388\pi$
$504$	−12.1290	−	29.0816i	−0.540270	−	1.29540i
$505$	31.7243	+	18.3160i	1.41171	+	0.815053i
$506$	2.81091	+	4.86864i	0.124960	+	0.216437i
$507$	5.86165	−	21.7403i	0.260325	−	0.965521i
$508$	−1.51868	+	2.63044i	−0.0673807	+	0.116707i
$509$	19.8971	−	11.4876i	0.881923	−	0.509178i	0.0106308	−	0.999943i	$-0.496616\pi$
$509$	19.8971	−	11.4876i	0.881923	−	0.509178i	0.871292	+	0.490765i	$0.163283\pi$
$510$	−9.02400	−	18.2428i	−0.399589	−	0.807806i
$511$	0.114214	−	0.197825i	0.00505254	−	0.00875126i
$512$			8.30341i			0.366962i
$513$	−3.26636	+	1.12210i	−0.144213	+	0.0495420i
$514$	8.52529	−	4.92208i	0.376034	−	0.217104i
$515$	32.0603	−	18.5100i	1.41275	−	0.815649i
$516$	−4.48877	−	0.288721i	−0.197607	−	0.0127102i
$517$	−5.84384	−	10.1218i	−0.257012	−	0.445157i
$518$	4.60693	−	2.65981i	0.202417	−	0.116865i
$519$	24.5935	+	1.58187i	1.07953	+	0.0694364i
$520$	−33.8903	+	27.7343i	−1.48619	+	1.21623i
$521$	−31.4592			−1.37825			−0.689126	−	0.724641i	$-0.742006\pi$
$521$	−31.4592			−1.37825			−0.689126	+	0.724641i	$0.742006\pi$
$522$	−4.46389	−	3.40802i	−0.195379	−	0.149165i
$523$	8.96088	−	15.5207i	0.391832	−	0.678673i	−0.600859	−	0.799355i	$-0.705175\pi$
$523$	8.96088	−	15.5207i	0.391832	−	0.678673i	0.992691	+	0.120682i	$0.0385082\pi$
$524$	−0.658138	+	1.13993i	−0.0287509	+	0.0497980i
$525$	−64.7727	+	32.0404i	−2.82691	+	1.39836i
$526$		−	14.2282i		−	0.620379i
$527$		−	2.50845i		−	0.109270i
$528$	−2.63146	+	1.30168i	−0.114520	+	0.0566483i
$529$	8.23924	−	14.2708i	0.358228	−	0.620469i
$530$	7.58191	−	13.1322i	0.329337	−	0.570428i
$531$	0.819472	+	0.625639i	0.0355621	+	0.0271504i
$532$	2.50192			0.108472
$533$	7.58460	−	1.24141i	0.328526	−	0.0537713i
$534$	25.3747	+	1.63212i	1.09807	+	0.0706288i
$535$	10.2933	−	5.94281i	0.445016	−	0.256930i
$536$	16.7453	+	29.0037i	0.723288	+	1.25277i
$537$	11.5169	+	0.740775i	0.496991	+	0.0319668i
$538$	22.8041	−	13.1660i	0.983156	−	0.567625i
$539$	−10.9234	+	6.30661i	−0.470502	+	0.271645i
$540$	17.0594	+	14.8508i	0.734118	+	0.639076i
$541$		−	0.881444i		−	0.0378962i	−0.999820	−	0.0189481i	$-0.993968\pi$
$541$		−	0.881444i		−	0.0378962i	0.999820	−	0.0189481i	$-0.00603173\pi$
$542$	2.63670	−	4.56689i	0.113256	−	0.196165i
$543$	3.72996	+	7.54045i	0.160068	+	0.323592i
$544$	13.3656	−	7.71663i	0.573046	−	0.330848i
$545$	26.4999	−	45.8992i	1.13513	−	1.96610i
$546$	−19.5063	−	8.84219i	−0.834791	−	0.378411i
$547$	−19.5489	−	33.8597i	−0.835852	−	1.44774i	−0.893335	−	0.449391i	$-0.851641\pi$
$547$	−19.5489	−	33.8597i	−0.835852	−	1.44774i	0.0574831	−	0.998346i	$-0.481692\pi$
$548$	2.70919	+	1.56415i	0.115731	+	0.0668174i
$549$	13.5270	+	32.4334i	0.577318	+	1.38423i
$550$	12.9647	+	22.4554i	0.552815	+	0.957503i
$551$	1.11302	−	0.642603i	0.0474163	−	0.0273758i
$552$	−10.9139	−	7.27326i	−0.464528	−	0.309570i
$553$		−	12.3515i		−	0.525237i
$554$	3.72864	+	2.15273i	0.158415	+	0.0914607i
$555$	−6.10298	+	9.15788i	−0.259057	+	0.388730i
$556$	−24.4437			−1.03664
$557$	−11.7840	−	6.80348i	−0.499303	−	0.288273i	0.229122	−	0.973398i	$-0.426414\pi$
$557$	−11.7840	−	6.80348i	−0.499303	−	0.288273i	−0.728426	+	0.685125i	$0.759748\pi$
$558$	−0.946505	−	2.26942i	−0.0400687	−	0.0960721i
$559$	−6.81900	+	5.58038i	−0.288413	+	0.236025i
$560$	5.40795	+	9.36684i	0.228528	+	0.395821i
$561$	9.71069	+	6.47139i	0.409986	+	0.273222i
$562$	5.27177	+	9.13097i	0.222376	+	0.385167i
$563$	−26.6859			−1.12468			−0.562339	−	0.826907i	$-0.690098\pi$
$563$	−26.6859			−1.12468			−0.562339	+	0.826907i	$0.690098\pi$
$564$	7.87278	+	5.24657i	0.331504	+	0.220920i
$565$	31.1645	+	17.9928i	1.31110	+	0.756964i
$566$	17.5298	−	10.1208i	0.736833	−	0.425411i
$567$	−8.10103	+	30.8333i	−0.340211	+	1.29488i
$568$	−12.6707	−	21.9463i	−0.531652	−	0.920847i
$569$	2.44217			0.102381			0.0511906	−	0.998689i	$-0.483698\pi$
$569$	2.44217			0.102381			0.0511906	+	0.998689i	$0.483698\pi$
$570$	4.09224	−	2.02427i	0.171405	−	0.0847873i
$571$	−7.72799	+	13.3853i	−0.323406	+	0.560156i	−0.981188	−	0.193052i	$-0.938161\pi$
$571$	−7.72799	+	13.3853i	−0.323406	+	0.560156i	0.657782	+	0.753208i	$0.271495\pi$
$572$	3.08013	−	8.14936i	0.128787	−	0.340742i
$573$	−22.1887	−	1.42720i	−0.926948	−	0.0596220i
$574$		−	7.31011i		−	0.305118i
$575$	−15.0395	+	26.0491i	−0.627190	+	1.08632i
$576$	11.8944	−	15.5795i	0.495601	−	0.649147i
$577$			20.6448i			0.859452i	0.902959	+	0.429726i	$0.141390\pi$
$577$			20.6448i			0.859452i	−0.902959	+	0.429726i	$0.858610\pi$
$578$	−6.89245	−	3.97936i	−0.286688	−	0.165520i
$579$	−30.4517	−	20.2936i	−1.26553	−	0.843373i
$580$	−7.28899	−	4.20830i	−0.302659	−	0.174740i
$581$	23.1124			0.958865
$582$	27.8931	+	1.79410i	1.15620	+	0.0743679i
$583$			8.69434i			0.360083i
$584$	0.191216			0.00791259
$585$	44.2814	−	1.49602i	1.83081	−	0.0618528i
$586$	7.64310			0.315734
$587$		−	15.3075i		−	0.631806i	−0.948791	−	0.315903i	$-0.897693\pi$
$587$		−	15.3075i		−	0.631806i	0.948791	−	0.315903i	$-0.102307\pi$
$588$	5.66204	−	8.49622i	0.233499	−	0.350378i
$589$	0.562697			0.0231855
$590$	−1.18030	−	0.681447i	−0.0485922	−	0.0280547i
$591$	1.03918	−	16.1562i	0.0427460	−	0.664576i
$592$	1.00139	+	0.578152i	0.0411569	+	0.0237619i
$593$			30.2852i			1.24366i	0.783151	+	0.621832i	$0.213611\pi$
$593$			30.2852i			1.24366i	−0.783151	+	0.621832i	$0.786389\pi$
$594$	11.2272	+	2.19062i	0.460657	+	0.0898824i
$595$	21.4959	−	37.2320i	0.881246	−	1.52636i
$596$			23.3744i			0.957453i
$597$	3.14552	−	4.72003i	0.128737	−	0.193178i
$598$	−8.79740	+	1.43991i	−0.359752	+	0.0588823i
$599$	1.68387	−	2.91655i	0.0688012	−	0.119167i	−0.829573	−	0.558399i	$-0.811416\pi$
$599$	1.68387	−	2.91655i	0.0688012	−	0.119167i	0.898374	+	0.439232i	$0.144749\pi$
$600$	−50.3380	−	33.5462i	−2.05504	−	1.36952i
$601$	−1.24264			−0.0506885			−0.0253443	−	0.999679i	$-0.508068\pi$
$601$	−1.24264			−0.0506885			−0.0253443	+	0.999679i	$0.508068\pi$
$602$	4.19046	+	7.25808i	0.170790	+	0.295817i
$603$	4.34095	−	33.6050i	0.176777	−	1.36850i
$604$	15.3276	−	8.84938i	0.623670	−	0.360076i
$605$	20.6805	+	11.9399i	0.840781	+	0.485425i
$606$	−13.4420	+	6.64923i	−0.546045	+	0.270107i
$607$	27.5452			1.11802			0.559012	−	0.829159i	$-0.311180\pi$
$607$	27.5452			1.11802			0.559012	+	0.829159i	$0.311180\pi$
$608$	1.73100	+	2.99818i	0.0702013	+	0.121592i
$609$	0.761474	−	11.8387i	0.0308565	−	0.479728i
$610$	−23.2269	−	40.2301i	−0.940429	−	1.62887i
$611$	18.2897	−	2.99355i	0.739921	−	0.121106i
$612$	−9.36824	−	1.21015i	−0.378689	−	0.0489175i
$613$	−19.6643	−	11.3532i	−0.794233	−	0.458550i	0.0472178	−	0.998885i	$-0.484965\pi$
$613$	−19.6643	−	11.3532i	−0.794233	−	0.458550i	−0.841451	+	0.540334i	$0.818298\pi$
$614$	24.5734			0.991702
$615$	6.70525	+	13.5553i	0.270382	+	0.546601i
$616$	−20.6826	−	11.9411i	−0.833325	−	0.481120i
$617$		−	42.3583i		−	1.70528i	−0.522497	−	0.852641i	$-0.674999\pi$
$617$		−	42.3583i		−	1.70528i	0.522497	−	0.852641i	$-0.325001\pi$
$618$	−0.972803	+	15.1243i	−0.0391319	+	0.608387i
$619$	−34.7623	+	20.0700i	−1.39722	+	0.806683i	−0.994100	−	0.108466i	$-0.965406\pi$
$619$	−34.7623	+	20.0700i	−1.39722	+	0.806683i	−0.403116	+	0.915149i	$0.632073\pi$
$620$	−1.84250	−	3.19131i	−0.0739967	−	0.128166i
$621$	4.31123	+	12.5497i	0.173004	+	0.503601i
$622$	−20.8125	−	12.0161i	−0.834506	−	0.481802i
$623$	26.8554	+	46.5149i	1.07594	+	1.86358i
$624$	−0.455505	−	4.63294i	−0.0182348	−	0.185466i
$625$	−27.4199	+	47.4926i	−1.09680	+	1.89971i
$626$	−22.2804	+	12.8636i	−0.890505	+	0.514134i
$627$	−1.45167	+	2.17831i	−0.0579740	+	0.0869933i
$628$	1.27344	−	2.20566i	0.0508156	−	0.0880153i
$629$		−	4.59616i		−	0.183261i
$630$	5.39892	−	41.7951i	0.215098	−	1.66516i
$631$	24.4895	−	14.1390i	0.974911	−	0.562865i	0.0741809	−	0.997245i	$-0.476366\pi$
$631$	24.4895	−	14.1390i	0.974911	−	0.562865i	0.900730	+	0.434380i	$0.143032\pi$
$632$	8.95412	−	5.16967i	0.356176	−	0.205638i
$633$	18.7580	−	28.1475i	0.745565	−	1.11876i
$634$	−14.1604	−	24.5265i	−0.562381	−	0.974072i
$635$	−10.1394	+	5.85396i	−0.402368	+	0.232308i
$636$	−3.12043	−	6.30822i	−0.123733	−	0.250137i
$637$	−3.23061	−	19.7380i	−0.128001	−	0.782048i
$638$	−4.25666			−0.168523
$639$	−3.28468	+	25.4280i	−0.129940	+	1.00591i
$640$	8.37979	−	14.5142i	0.331240	−	0.573725i
$641$	−20.1403	+	34.8840i	−0.795493	+	1.37783i	0.127032	+	0.991899i	$0.459455\pi$
$641$	−20.1403	+	34.8840i	−0.795493	+	1.37783i	−0.922525	+	0.385936i	$0.873879\pi$
$642$	−0.312328	+	4.85578i	−0.0123266	+	0.191642i
$643$			17.2285i			0.679426i	0.940529	+	0.339713i	$0.110330\pi$
$643$			17.2285i			0.679426i	−0.940529	+	0.339713i	$0.889670\pi$
$644$		−	9.61260i		−	0.378790i
$645$	−14.4280	−	9.61507i	−0.568101	−	0.378593i
$646$	−0.953371	+	1.65129i	−0.0375099	+	0.0649690i
$647$	19.9930	−	34.6289i	0.786005	−	1.36140i	−0.142391	−	0.989810i	$-0.545479\pi$
$647$	19.9930	−	34.6289i	0.786005	−	1.36140i	0.928397	−	0.371591i	$-0.121188\pi$
$648$	−25.7431	+	7.03241i	−1.01129	+	0.276259i
$649$	0.781431			0.0306738
$650$	−40.5759	+	6.64125i	−1.59152	+	0.260491i
$651$	2.88037	−	4.32216i	0.112891	−	0.169399i
$652$	19.1347	−	11.0474i	0.749372	−	0.432650i
$653$	−4.37830	−	7.58345i	−0.171336	−	0.296763i	0.767551	−	0.640988i	$-0.221475\pi$
$653$	−4.37830	−	7.58345i	−0.171336	−	0.296763i	−0.938887	+	0.344225i	$0.888142\pi$
$654$	9.62021	+	19.4481i	0.376180	+	0.760482i
$655$	−4.39400	+	2.53688i	−0.171688	+	0.0991239i
$656$	1.37609	−	0.794485i	0.0537272	−	0.0310194i
$657$	−0.153771	−	0.117399i	−0.00599918	−	0.00458017i
$658$		−	17.6277i		−	0.687201i
$659$	−5.52272	+	9.56563i	−0.215135	+	0.372624i	−0.953314	−	0.301980i	$-0.902352\pi$
$659$	−5.52272	+	9.56563i	−0.215135	+	0.372624i	0.738180	+	0.674604i	$0.235686\pi$
$660$	17.1075	+	1.10037i	0.665910	+	0.0428318i
$661$	−1.26703	+	0.731518i	−0.0492816	+	0.0284527i	−0.524438	−	0.851448i	$-0.675725\pi$
$661$	−1.26703	+	0.731518i	−0.0492816	+	0.0284527i	0.475157	+	0.879901i	$0.342391\pi$
$662$	0.290184	−	0.502614i	0.0112783	−	0.0195346i
$663$	−15.0429	+	10.7757i	−0.584217	+	0.418493i
$664$	9.67364	+	16.7552i	0.375410	+	0.650229i
$665$	8.35191	+	4.82198i	0.323873	+	0.186988i
$666$	−1.73426	−	4.15820i	−0.0672011	−	0.161127i
$667$	−2.46894	−	4.27634i	−0.0955979	−	0.165580i
$668$	−6.70882	+	3.87334i	−0.259572	+	0.149864i
$669$	22.3050	−	11.0334i	0.862360	−	0.426575i
$670$			44.7920i			1.73047i
$671$	23.0664	+	13.3174i	0.890469	+	0.514112i
$672$	31.8903	+	2.05121i	1.23019	+	0.0791270i
$673$	31.7555			1.22408			0.612042	−	0.790825i	$-0.290348\pi$
$673$	31.7555			1.22408			0.612042	+	0.790825i	$0.290348\pi$
$674$	3.90748	+	2.25598i	0.150510	+	0.0868972i
$675$	19.8845	+	57.8824i	0.765355	+	2.22789i
$676$	10.3610	+	9.13738i	0.398500	+	0.351438i
$677$	−21.9025	−	37.9362i	−0.841780	−	1.45801i	−0.888388	−	0.459093i	$-0.848174\pi$
$677$	−21.9025	−	37.9362i	−0.841780	−	1.45801i	0.0466080	−	0.998913i	$-0.485159\pi$
$678$	−13.2048	+	6.53190i	−0.507128	+	0.250856i
$679$	29.5207	+	51.1313i	1.13290	+	1.96224i
$680$	35.9882			1.38009
$681$	0.376042	−	5.84635i	0.0144100	−	0.224033i
$682$	−1.61399	−	0.931839i	−0.0618030	−	0.0356820i
$683$	−36.0323	+	20.8032i	−1.37874	+	0.796014i	−0.992007	−	0.126180i	$-0.959728\pi$
$683$	−36.0323	+	20.8032i	−1.37874	+	0.796014i	−0.386729	+	0.922193i	$0.626395\pi$
$684$	0.271462	−	2.10149i	0.0103796	−	0.0803525i
$685$	6.02923	+	10.4429i	0.230365	+	0.399004i
$686$	4.98235			0.190227
$687$	−0.730626	+	11.3591i	−0.0278751	+	0.433377i
$688$	−0.910863	+	1.57766i	−0.0347263	+	0.0601477i
$689$	−12.8961	−	4.87422i	−0.491304	−	0.185693i
$690$	−7.77744	−	15.7228i	−0.296082	−	0.598556i
$691$		−	33.2002i		−	1.26299i	−0.775378	−	0.631497i	$-0.782441\pi$
$691$		−	33.2002i		−	1.26299i	0.775378	−	0.631497i	$-0.217559\pi$
$692$	−7.55996	+	13.0942i	−0.287386	+	0.497768i
$693$	9.30105	+	22.3010i	0.353318	+	0.847143i
$694$			29.3400i			1.11373i
$695$	−81.5979	−	47.1106i	−3.09519	−	1.78701i
$696$	8.90112	−	4.40303i	0.337396	−	0.166896i
$697$	−5.46977	−	3.15797i	−0.207182	−	0.119617i
$698$	−12.0136			−0.454722
$699$	11.8009	+	23.8567i	0.446353	+	0.902343i
$700$		−	44.3358i		−	1.67574i
$701$	−46.0762			−1.74027			−0.870137	−	0.492809i	$-0.835970\pi$
$701$	−46.0762			−1.74027			−0.870137	+	0.492809i	$0.835970\pi$
$702$	−9.54348	+	15.4249i	−0.360196	+	0.582177i
$703$	1.03101			0.0388855
$704$		−	14.8563i		−	0.559917i
$705$	16.1692	+	32.6875i	0.608966	+	1.23108i
$706$	−16.4010			−0.617260
$707$	−27.4340	−	15.8390i	−1.03176	−	0.595688i
$708$	−0.566971	+	0.280458i	−0.0213081	+	0.0105403i
$709$	32.1117	+	18.5397i	1.20598	+	0.696274i	0.961879	−	0.273476i	$-0.0881734\pi$
$709$	32.1117	+	18.5397i	1.20598	+	0.696274i	0.244102	+	0.969749i	$0.421507\pi$
$710$		−	33.8929i		−	1.27198i
$711$	−10.3746	−	1.34015i	−0.389079	−	0.0502596i
$712$	−22.4805	+	38.9374i	−0.842492	+	1.45924i
$713$		−	2.16194i		−	0.0809651i
$714$	7.80362	+	15.7757i	0.292043	+	0.590391i
$715$	25.9885	−	21.2679i	0.971914	−	0.795373i
$716$	−3.54026	+	6.13191i	−0.132306	+	0.229160i
$717$	−1.57055	+	24.4174i	−0.0586531	+	0.911885i
$718$	−5.43965			−0.203006
$719$	8.89441	+	15.4056i	0.331705	+	0.574531i	0.982846	−	0.184426i	$-0.0590427\pi$
$719$	8.89441	+	15.4056i	0.331705	+	0.574531i	−0.651141	+	0.758957i	$0.725709\pi$
$720$	8.45447	−	3.52610i	0.315080	−	0.131410i
$721$	−27.7246	+	16.0068i	−1.03252	+	0.596124i
$722$	15.5602	+	8.98370i	0.579092	+	0.334339i
$723$	−1.33059	+	20.6867i	−0.0494851	+	0.769348i
$724$	−5.16132			−0.191819
$725$	−11.3874	−	19.7236i	−0.422918	−	0.732516i
$726$	−8.76260	+	4.33451i	−0.325211	+	0.160869i
$727$	19.7326	+	34.1779i	0.731842	+	1.26759i	0.956095	+	0.293056i	$0.0946722\pi$
$727$	19.7326	+	34.1779i	0.731842	+	1.26759i	−0.224254	+	0.974531i	$0.571994\pi$
$728$	29.3070	−	23.9836i	1.08619	−	0.888893i
$729$	25.0196	+	10.1499i	0.926651	+	0.375924i
$730$	0.221479	+	0.127871i	0.00819731	+	0.00473272i
$731$	7.24113			0.267823
$732$	−21.5156	−	1.38390i	−0.795240	−	0.0511504i
$733$	28.5776	+	16.4993i	1.05554	+	0.609415i	0.924194	−	0.381922i	$-0.124738\pi$
$733$	28.5776	+	16.4993i	1.05554	+	0.609415i	0.131343	+	0.991337i	$0.458071\pi$
$734$			33.9843i			1.25438i
$735$	35.2759	−	17.4496i	1.30117	−	0.643638i
$736$	11.5193	−	6.65067i	0.424607	−	0.245147i
$737$	−12.8410	−	22.2413i	−0.473005	−	0.819269i
$738$	−6.14015	−	0.793159i	−0.226022	−	0.0291966i
$739$	−6.07175	−	3.50552i	−0.223353	−	0.128953i	0.384149	−	0.923271i	$-0.374495\pi$
$739$	−6.07175	−	3.50552i	−0.223353	−	0.128953i	−0.607502	+	0.794318i	$0.707828\pi$
$740$	−3.37597	−	5.84735i	−0.124103	−	0.214953i
$741$	−2.41721	−	3.37443i	−0.0887983	−	0.123963i
$742$	−6.55655	+	11.3563i	−0.240699	+	0.416902i
$743$	−29.7212	+	17.1595i	−1.09036	+	0.629522i	−0.933673	−	0.358125i	$-0.883416\pi$
$743$	−29.7212	+	17.1595i	−1.09036	+	0.629522i	−0.156691	+	0.987648i	$0.550083\pi$
$744$	4.33890	+	0.279081i	0.159072	+	0.0102316i
$745$	−45.0498	+	78.0286i	−1.65050	+	2.85875i
$746$		−	2.33422i		−	0.0854619i
$747$	2.50774	−	19.4133i	0.0917533	−	0.710297i
$748$	−6.20033	+	3.57976i	−0.226706	+	0.130889i
$749$	−8.90123	+	5.13913i	−0.325244	+	0.187780i
$750$	−20.6440	−	41.7336i	−0.753811	−	1.52390i
$751$	−19.9920	−	34.6271i	−0.729518	−	1.26356i	−0.957087	−	0.289800i	$-0.906411\pi$
$751$	−19.9920	−	34.6271i	−0.729518	−	1.26356i	0.227569	−	0.973762i	$-0.426922\pi$
$752$	3.31833	−	1.91584i	0.121007	−	0.0698633i
$753$	3.34899	−	5.02535i	0.122044	−	0.183134i
$754$	2.38637	−	6.31382i	0.0869064	−	0.229936i
$755$	68.2222			2.48286
$756$	−14.7523	−	12.8424i	−0.536536	−	0.467074i
$757$	−7.37600	+	12.7756i	−0.268085	+	0.464337i	−0.968367	−	0.249529i	$-0.919724\pi$
$757$	−7.37600	+	12.7756i	−0.268085	+	0.464337i	0.700282	+	0.713866i	$0.253058\pi$
$758$	13.4609	−	23.3149i	0.488921	−	0.846836i
$759$	8.36927	+	5.57744i	0.303785	+	0.202448i
$760$			8.07290i			0.292835i
$761$		−	3.78186i		−	0.137092i	−0.997648	−	0.0685461i	$-0.978164\pi$
$761$		−	3.78186i		−	0.137092i	0.997648	−	0.0685461i	$-0.0218360\pi$
$762$	0.307658	−	4.78319i	0.0111453	−	0.173277i
$763$	−22.9161	+	39.6919i	−0.829620	+	1.43694i
$764$	6.82075	−	11.8139i	0.246766	−	0.427412i
$765$	−28.9408	−	22.0953i	−1.04636	−	0.798856i
$766$	0.574439			0.0207553
$767$	−0.438085	+	1.15908i	−0.0158183	+	0.0418519i
$768$	13.0773	+	26.4368i	0.471885	+	0.953957i
$769$	16.8221	−	9.71222i	0.606619	−	0.350232i	−0.165022	−	0.986290i	$-0.552770\pi$
$769$	16.8221	−	9.71222i	0.606619	−	0.350232i	0.771641	+	0.636058i	$0.219436\pi$
$770$	−15.9706	−	27.6619i	−0.575541	−	0.996866i
$771$	9.76645	−	14.6551i	0.351730	−	0.527791i
$772$	19.4436	−	11.2258i	0.699789	−	0.404024i
$773$	−39.9410	+	23.0600i	−1.43658	+	0.829410i	−0.997610	−	0.0690925i	$-0.977990\pi$
$773$	−39.9410	+	23.0600i	−1.43658	+	0.829410i	−0.438969	+	0.898502i	$0.644656\pi$
$774$	6.55112	−	2.73227i	0.235475	−	0.0982095i
$775$		−	9.97142i		−	0.358184i
$776$	−24.7116	+	42.8017i	−0.887094	+	1.53649i
$777$	5.27763	−	7.91939i	0.189334	−	0.284107i
$778$	15.0216	−	8.67271i	0.538550	−	0.310932i
$779$	0.708399	−	1.22698i	0.0253810	−	0.0439612i
$780$	−11.2230	+	24.7583i	−0.401847	+	0.886491i
$781$	9.71644	+	16.8294i	0.347682	+	0.602202i
$782$	6.34440	+	3.66294i	0.226875	+	0.130987i
$783$	−9.86133	−	1.92412i	−0.352415	−	0.0687624i
$784$	−2.06755	−	3.58110i	−0.0738410	−	0.127896i
$785$	8.50198	−	4.90862i	0.303449	−	0.175196i
$786$	0.133327	−	2.07284i	0.00475561	−	0.0739358i
$787$		−	17.4527i		−	0.622122i	−0.950390	−	0.311061i	$-0.899316\pi$
$787$		−	17.4527i		−	0.622122i	0.950390	−	0.311061i	$-0.100684\pi$
$788$	8.60199	+	4.96636i	0.306433	+	0.176919i
$789$	−11.2860	−	22.8156i	−0.401791	−	0.812256i
$790$	13.8283			0.491990
$791$	−26.9499	−	15.5595i	−0.958228	−	0.553233i
$792$	−12.2740	+	16.0768i	−0.436139	+	0.571263i
$793$	−32.6849	+	26.7479i	−1.16067	+	0.949847i
$794$	−7.06676	−	12.2400i	−0.250790	−	0.434381i
$795$	1.74130	−	27.0722i	0.0617577	−	0.960152i
$796$	1.74000	+	3.01376i	0.0616726	+	0.106820i
$797$	−34.1753			−1.21055			−0.605276	−	0.796016i	$-0.706937\pi$
$797$	−34.1753			−1.21055			−0.605276	+	0.796016i	$0.706937\pi$
$798$	−3.53882	+	1.75051i	−0.125273	+	0.0619675i
$799$	−13.1899	−	7.61520i	−0.466626	−	0.269407i
$800$	53.1301	−	30.6746i	1.87843	−	1.08451i
$801$	41.9841	−	17.5103i	1.48344	−	0.618696i
$802$	−5.68653	−	9.84936i	−0.200798	−	0.347793i
$803$	−0.146633			−0.00517456
$804$	17.2993	+	11.5286i	0.610100	+	0.406582i
$805$	18.5265	−	32.0888i	0.652973	−	1.13098i
$806$	2.28701	−	1.87159i	0.0805566	−	0.0659241i
$807$	26.1241	−	39.2007i	0.919611	−	1.37993i
$808$		−	26.5175i		−	0.932883i
$809$	3.18619	−	5.51863i	0.112020	−	0.194025i	−0.804564	−	0.593865i	$-0.797601\pi$
$809$	3.18619	−	5.51863i	0.112020	−	0.194025i	0.916585	+	0.399841i	$0.130934\pi$
$810$	−34.5201	−	9.06968i	−1.21291	−	0.318676i
$811$		−	27.4423i		−	0.963629i	−0.876273	−	0.481814i	$-0.839978\pi$
$811$		−	27.4423i		−	0.963629i	0.876273	−	0.481814i	$-0.160022\pi$
$812$	6.30324	+	3.63918i	0.221201	+	0.127710i
$813$	0.605559	−	9.41468i	0.0212379	−	0.330187i
$814$	−2.95728	−	1.70738i	−0.103653	−	0.0598438i
$815$	85.1673			2.98328
$816$	−2.12157	+	3.18354i	−0.0742698	+	0.111446i
$817$			1.62433i			0.0568283i
$818$	13.6545			0.477418
$819$	−38.2929	+	1.29370i	−1.33806	+	0.0452056i
$820$	−9.27837			−0.324015
$821$		−	25.4933i		−	0.889723i	−0.895599	−	0.444862i	$-0.853253\pi$
$821$		−	25.4933i		−	0.889723i	0.895599	−	0.444862i	$-0.146747\pi$
$822$	−4.92639	−	0.316869i	−0.171828	−	0.0110521i
$823$	−11.7167			−0.408420			−0.204210	−	0.978927i	$-0.565463\pi$
$823$	−11.7167			−0.408420			−0.204210	+	0.978927i	$0.565463\pi$
$824$	−23.2081	−	13.3992i	−0.808492	−	0.466783i
$825$	38.6013	+	25.7246i	1.34392	+	0.895617i
$826$	1.02068	+	0.589290i	0.0355140	+	0.0205040i
$827$			14.2521i			0.495594i	0.968812	+	0.247797i	$0.0797066\pi$
$827$			14.2521i			0.495594i	−0.968812	+	0.247797i	$0.920293\pi$
$828$	−8.07413	−	1.04298i	−0.280595	−	0.0362462i
$829$	1.94037	−	3.36081i	0.0673917	−	0.116726i	−0.830361	−	0.557226i	$-0.811866\pi$
$829$	1.94037	−	3.36081i	0.0673917	−	0.116726i	0.897752	+	0.440500i	$0.145199\pi$
$830$			25.8760i			0.898170i
$831$	7.68660	+	0.494408i	0.266645	+	0.0171508i
$832$	22.0360	+	8.32872i	0.763962	+	0.288747i
$833$	−8.21824	+	14.2344i	−0.284745	+	0.493193i
$834$	34.5742	−	17.1025i	1.19721	−	0.592210i
$835$	−29.8606			−1.03337
$836$	−0.803014	−	1.39086i	−0.0277728	−	0.0481039i
$837$	−3.31789	−	2.88834i	−0.114683	−	0.0998355i
$838$	−9.25703	+	5.34455i	−0.319779	+	0.184624i
$839$	2.48653	+	1.43560i	0.0858446	+	0.0495624i	0.542308	−	0.840180i	$-0.317551\pi$
$839$	2.48653	+	1.43560i	0.0858446	+	0.0495624i	−0.456463	+	0.889742i	$0.650884\pi$
$840$	62.0092	+	41.3241i	2.13952	+	1.42582i
$841$	−25.2612			−0.871075
$842$	−0.123001	−	0.213044i	−0.00423890	−	0.00734199i
$843$	15.6963	+	10.4603i	0.540609	+	0.360272i
$844$	10.3763	+	17.9723i	0.357168	+	0.618633i
$845$	16.9765	+	50.4713i	0.584011	+	1.73627i
$846$	−14.8065	−	1.91264i	−0.509057	−	0.0657579i
$847$	−17.8837	−	10.3252i	−0.614492	−	0.354777i
$848$	−2.85034			−0.0978811
$849$	20.0819	−	30.1341i	0.689209	−	1.03420i
$850$	29.2621	+	16.8945i	1.00368	+	0.579475i
$851$		−	3.96126i		−	0.135790i
$852$	−13.0899	−	8.72337i	−0.448453	−	0.298858i
$853$	−41.0367	+	23.6925i	−1.40507	+	0.811217i	−0.994907	−	0.100795i	$-0.967861\pi$
$853$	−41.0367	+	23.6925i	−1.40507	+	0.811217i	−0.410163	+	0.912012i	$0.634528\pi$
$854$	20.0857	+	34.7895i	0.687320	+	1.19047i
$855$	4.95643	−	6.49201i	0.169506	−	0.222022i
$856$	−7.45117	−	4.30193i	−0.254676	−	0.147037i
$857$	11.4698	+	19.8663i	0.391802	+	0.678621i	0.992687	−	0.120714i	$-0.0385185\pi$
$857$	11.4698	+	19.8663i	0.391802	+	0.678621i	−0.600885	+	0.799335i	$0.705185\pi$
$858$	1.34519	+	13.6819i	0.0459239	+	0.467092i
$859$	−1.07796	+	1.86708i	−0.0367795	+	0.0637040i	−0.883829	−	0.467810i	$-0.845043\pi$
$859$	−1.07796	+	1.86708i	−0.0367795	+	0.0637040i	0.847050	+	0.531514i	$0.178377\pi$
$860$	9.21233	−	5.31874i	0.314138	−	0.181368i
$861$	−5.79845	−	11.7221i	−0.197611	−	0.399488i
$862$	−0.719565	+	1.24632i	−0.0245085	+	0.0424499i
$863$			43.2790i			1.47323i	0.676310	+	0.736617i	$0.263578\pi$
$863$			43.2790i			1.47323i	−0.676310	+	0.736617i	$0.736422\pi$
$864$	5.18306	−	26.5638i	0.176331	−	0.903717i
$865$	−50.4734	+	29.1408i	−1.71615	+	0.990817i
$866$	−17.2247	+	9.94468i	−0.585319	+	0.337934i
$867$	−14.2088	−	0.913923i	−0.482557	−	0.0310384i
$868$	1.59333	+	2.75972i	0.0540811	+	0.0936711i
$869$	−6.86640	+	3.96432i	−0.232927	+	0.134480i
$870$	13.2543	+	0.852525i	0.449362	+	0.0289033i
$871$	40.1890	−	6.57791i	1.36175	−	0.222884i
$872$	−38.3659			−1.29923
$873$	46.1509	−	19.2481i	1.56197	−	0.651450i
$874$	−0.821674	+	1.42318i	−0.0277935	+	0.0481398i
$875$	49.1756	−	85.1747i	1.66244	−	2.87943i
$876$	0.106390	−	0.0526269i	0.00359459	−	0.00177810i
$877$		−	4.06906i		−	0.137402i	−0.997637	−	0.0687011i	$-0.978115\pi$
$877$		−	4.06906i		−	0.137402i	0.997637	−	0.0687011i	$-0.0218855\pi$
$878$		−	17.8677i		−	0.603006i
$879$	12.2561	−	6.06258i	0.413387	−	0.204486i
$880$	3.47147	−	6.01276i	0.117023	−	0.202690i
$881$	15.1086	−	26.1688i	0.509020	−	0.881649i	−0.490925	−	0.871202i	$-0.663341\pi$
$881$	15.1086	−	26.1688i	0.509020	−	0.881649i	0.999945	−	0.0104469i	$-0.00332541\pi$
$882$	−2.06410	+	15.9790i	−0.0695018	+	0.538040i
$883$	−26.8248			−0.902725			−0.451362	−	0.892341i	$-0.649062\pi$
$883$	−26.8248			−0.902725			−0.451362	+	0.892341i	$0.649062\pi$
$884$	−1.83376	−	11.2037i	−0.0616760	−	0.376821i
$885$	−2.43320	−	0.156505i	−0.0817910	−	0.00526086i
$886$	29.7462	−	17.1740i	0.999345	−	0.576972i
$887$	−21.8925	−	37.9190i	−0.735079	−	1.27319i	−0.954688	−	0.297607i	$-0.903812\pi$
$887$	−21.8925	−	37.9190i	−0.735079	−	1.27319i	0.219609	−	0.975588i	$-0.429522\pi$
$888$	7.95006	+	0.511354i	0.266787	+	0.0171599i
$889$	8.76815	−	5.06229i	0.294074	−	0.169784i
$890$	−52.0768	+	30.0665i	−1.74562	+	1.00783i
$891$	19.7409	−	5.39275i	0.661346	−	0.180664i
$892$			15.2674i			0.511190i
$893$	1.70825	−	2.95877i	0.0571643	−	0.0990115i
$894$	−16.3544	−	33.0618i	−0.546971	−	1.10575i
$895$	−23.6362	+	13.6464i	−0.790072	+	0.456148i
$896$	−7.24653	+	12.5514i	−0.242090	+	0.419312i
$897$	−12.9649	+	9.28715i	−0.432885	+	0.310089i
$898$	10.0667	+	17.4361i	0.335931	+	0.581849i
$899$	1.41764	+	0.818475i	0.0472809	+	0.0272977i
$900$	−37.2400	−	4.81051i	−1.24133	−	0.160350i
$901$	5.66487	+	9.81185i	0.188724	+	0.326880i
$902$	−4.06383	+	2.34625i	−0.135311	+	0.0781216i
$903$	12.4768	+	8.31476i	0.415201	+	0.276698i
$904$		−	26.0496i		−	0.866396i
$905$	−17.2295	−	9.94748i	−0.572729	−	0.330665i
$906$	−15.4884	+	23.2412i	−0.514566	+	0.772137i
$907$	41.1054			1.36488			0.682442	−	0.730940i	$-0.260918\pi$
$907$	41.1054			1.36488			0.682442	+	0.730940i	$0.260918\pi$
$908$	3.11276	+	1.79715i	0.103300	+	0.0596405i
$909$	−16.2807	+	21.3247i	−0.539996	+	0.707296i
$910$	49.9838	−	8.18107i	1.65695	−	0.271200i
$911$	−6.48770	−	11.2370i	−0.214947	−	0.372299i	0.738309	−	0.674462i	$-0.235625\pi$
$911$	−6.48770	−	11.2370i	−0.214947	−	0.372299i	−0.953256	+	0.302163i	$0.902291\pi$
$912$	−0.714134	−	0.475912i	−0.0236473	−	0.0157590i
$913$	−7.41816	−	12.8486i	−0.245505	−	0.425227i
$914$	19.8146			0.655407
$915$	−69.1563	−	46.0871i	−2.28624	−	1.52359i
$916$	−6.04789	−	3.49175i	−0.199828	−	0.115371i
$917$	3.79977	−	2.19380i	0.125479	−	0.0724455i
$918$	14.0976	−	4.84298i	0.465289	−	0.159842i
$919$	−6.20859	−	10.7536i	−0.204802	−	0.354728i	0.745267	−	0.666766i	$-0.232322\pi$
$919$	−6.20859	−	10.7536i	−0.204802	−	0.354728i	−0.950070	+	0.312038i	$0.898988\pi$
$920$	31.0169			1.02260
$921$	39.4046	−	19.4919i	1.29842	−	0.642279i
$922$	12.2003	−	21.1315i	0.401794	−	0.695928i
$923$	−30.4099	+	4.97732i	−1.00095	+	0.163831i
$924$	−14.7940	−	0.951558i	−0.486685	−	0.0313040i
$925$		−	18.2704i		−	0.600726i
$926$	1.85914	−	3.22013i	0.0610952	−	0.105820i
$927$	10.4368	+	25.0241i	0.342789	+	0.821898i
$928$			10.0714i			0.330609i
$929$	12.7323	+	7.35098i	0.417732	+	0.241178i	0.694107	−	0.719872i	$-0.255800\pi$
$929$	12.7323	+	7.35098i	0.417732	+	0.241178i	−0.276374	+	0.961050i	$0.589133\pi$
$930$	4.83897	+	3.22478i	0.158676	+	0.105745i
$931$	−3.19307	−	1.84352i	−0.104649	−	0.0604190i
$932$	−16.3295			−0.534891
$933$	−42.9051	−	2.75969i	−1.40465	−	0.0903482i
$934$		−	32.7559i		−	1.07181i
$935$	−27.5973			−0.902528
$936$	−16.9653	−	27.2188i	−0.554527	−	0.889674i
$937$	−7.97668			−0.260587			−0.130293	−	0.991475i	$-0.541592\pi$
$937$	−7.97668			−0.260587			−0.130293	+	0.991475i	$0.541592\pi$
$938$		−	38.7345i		−	1.26473i
$939$	−25.5241	+	38.3005i	−0.832949	+	1.24989i
$940$	−22.3740			−0.729761
$941$	43.7845	+	25.2790i	1.42733	+	0.824072i	0.996910	−	0.0785545i	$-0.0250305\pi$
$941$	43.7845	+	25.2790i	1.42733	+	0.824072i	0.430425	+	0.902626i	$0.358364\pi$
$942$	−0.257975	+	4.01076i	−0.00840528	+	0.130678i
$943$	−4.71419	−	2.72174i	−0.153515	−	0.0886320i
$944$			0.256183i			0.00833805i
$945$	−24.4949	−	71.3029i	−0.796819	−	2.31948i
$946$	2.68994	−	4.65911i	0.0874574	−	0.151481i
$947$			2.15187i			0.0699264i	0.999389	+	0.0349632i	$0.0111314\pi$
$947$			2.15187i			0.0699264i	−0.999389	+	0.0349632i	$0.988869\pi$
$948$	3.55915	−	5.34070i	0.115596	−	0.173458i
$949$	0.0822051	−	0.217497i	0.00266849	−	0.00706026i
$950$	−3.78978	+	6.56408i	−0.122957	+	0.212967i
$951$	−42.1615	−	28.0972i	−1.36718	−	0.911114i
$952$	−31.1213			−1.00865
$953$	5.29851	+	9.17729i	0.171636	+	0.297281i	0.938992	−	0.343940i	$-0.111762\pi$
$953$	5.29851	+	9.17729i	0.171636	+	0.297281i	−0.767356	+	0.641221i	$0.778428\pi$
$954$	8.82734	+	6.73936i	0.285796	+	0.218195i
$955$	45.5381	−	26.2915i	1.47358	−	0.850772i
$956$	−13.0005	−	7.50584i	−0.420466	−	0.242756i
$957$	−6.82576	+	3.37643i	−0.220645	+	0.109144i
$958$	−25.9170			−0.837341
$959$	−5.21386	−	9.03066i	−0.168364	−	0.291615i
$960$	−2.97542	+	46.2591i	−0.0960312	+	1.49301i
$961$	−15.1417	−	26.2261i	−0.488440	−	0.846003i
$962$	4.19043	−	3.42927i	0.135105	−	0.110564i
$963$	3.35082	+	8.03421i	0.107979	+	0.258899i
$964$	−11.0142	−	6.35904i	−0.354743	−	0.204811i
$965$	86.5422			2.78589
$966$	6.72564	+	13.5965i	0.216394	+	0.437460i
$967$	−9.57792	−	5.52981i	−0.308005	−	0.177827i	0.338028	−	0.941136i	$-0.390240\pi$
$967$	−9.57792	−	5.52981i	−0.308005	−	0.177827i	−0.646033	+	0.763309i	$0.723573\pi$
$968$		−	17.2863i		−	0.555602i
$969$	−0.218957	+	3.40414i	−0.00703390	+	0.109357i
$970$	−57.2452	+	33.0505i	−1.83803	+	1.06119i
$971$	18.7302	+	32.4417i	0.601082	+	1.04110i	0.992658	+	0.120958i	$0.0385966\pi$
$971$	18.7302	+	32.4417i	0.601082	+	1.04110i	−0.391576	+	0.920146i	$0.628070\pi$
$972$	−12.3877	+	10.9978i	−0.397334	+	0.352755i
$973$	70.5629	+	40.7395i	2.26214	+	1.30605i
$974$	14.7481	+	25.5444i	0.472558	+	0.818495i
$975$	−59.7974	+	42.8348i	−1.91505	+	1.37181i
$976$	−4.36596	+	7.56206i	−0.139751	+	0.242056i
$977$	−26.6963	+	15.4131i	−0.854089	+	0.493109i	−0.862028	−	0.506860i	$-0.830806\pi$
$977$	−26.6963	+	15.4131i	−0.854089	+	0.493109i	0.00793932	+	0.999968i	$0.497473\pi$
$978$	−19.3354	+	29.0139i	−0.618278	+	0.927762i
$979$	17.2390	−	29.8588i	0.550961	−	0.954292i
$980$			24.1458i			0.771309i
$981$	30.8529	+	23.5551i	0.985057	+	0.752056i
$982$	33.7502	−	19.4857i	1.07701	−	0.621813i
$983$	34.1531	−	19.7183i	1.08932	−	0.628917i	0.155922	−	0.987769i	$-0.450165\pi$
$983$	34.1531	−	19.7183i	1.08932	−	0.628917i	0.933394	+	0.358853i	$0.116832\pi$
$984$	6.07095	−	9.10981i	0.193535	−	0.290410i
$985$	19.1435	+	33.1575i	0.609962	+	1.05648i
$986$	−4.80378	+	2.77346i	−0.152984	+	0.0883251i
$987$	−13.9825	−	28.2669i	−0.445068	−	0.899745i
$988$	2.51322	−	0.411350i	0.0799562	−	0.0130868i
$989$	6.24085			0.198447
$990$	−24.9675	+	10.4132i	−0.793520	+	0.330953i
$991$	−1.34048	+	2.32178i	−0.0425818	+	0.0737539i	−0.886531	−	0.462670i	$-0.846892\pi$
$991$	−1.34048	+	2.32178i	−0.0425818	+	0.0737539i	0.843949	+	0.536423i	$0.180225\pi$
$992$	−2.20475	+	3.81874i	−0.0700009	+	0.121245i
$993$	0.0666454	−	1.03614i	0.00211493	−	0.0328809i
$994$			29.3093i			0.929635i
$995$			13.4141i			0.425255i
$996$	9.99369	+	6.65999i	0.316662	+	0.211030i
$997$	22.5345	−	39.0309i	0.713675	−	1.23612i	−0.249793	−	0.968299i	$-0.580363\pi$
$997$	22.5345	−	39.0309i	0.713675	−	1.23612i	0.963468	−	0.267823i	$-0.0863041\pi$
$998$	−9.57658	+	16.5871i	−0.303141	+	0.525056i
$999$	−6.07928	−	5.29223i	−0.192340	−	0.167439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.4.5	✓	22
3.2	odd	2		351.2.l.b.199.7		22
9.2	odd	6		351.2.r.b.316.7		22
9.7	even	3		117.2.r.b.43.5	yes	22
13.10	even	6		117.2.r.b.49.5	yes	22
39.23	odd	6		351.2.r.b.10.7		22
117.88	even	6	inner	117.2.l.b.88.7	yes	22
117.101	odd	6		351.2.l.b.127.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.5	✓	22	1.1	even	1	trivial
117.2.l.b.88.7	yes	22	117.88	even	6	inner
117.2.r.b.43.5	yes	22	9.7	even	3
117.2.r.b.49.5	yes	22	13.10	even	6
351.2.l.b.127.5		22	117.101	odd	6
351.2.l.b.199.7		22	3.2	odd	2
351.2.r.b.10.7		22	39.23	odd	6
351.2.r.b.316.7		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-0.968164i q^{2} +(-0.767957 - 1.55250i) q^{3} +1.06266 q^{4} +(3.54737 + 2.04808i) q^{5} +(-1.50307 + 0.743509i) q^{6} +(-3.06763 - 1.77110i) q^{7} -2.96516i q^{8} +(-1.82048 + 2.38450i) q^{9} +(1.98287 - 3.43444i) q^{10} +2.27381i q^{11} +(-0.816076 - 1.64977i) q^{12} +(-3.37269 - 1.27474i) q^{13} +(-1.71472 + 2.96997i) q^{14} +(0.455398 - 7.08011i) q^{15} -0.745441 q^{16} +(1.48152 + 2.56606i) q^{17} +(2.30859 + 1.76253i) q^{18} +(-0.575621 + 0.332335i) q^{19} +(3.76964 + 2.17640i) q^{20} +(-0.393811 + 6.12262i) q^{21} +2.20142 q^{22} +(1.27686 + 2.21159i) q^{23} +(-4.60339 + 2.27711i) q^{24} +(5.88923 + 10.2004i) q^{25} +(-1.23416 + 3.26532i) q^{26} +(5.09998 + 0.995097i) q^{27} +(-3.25985 - 1.88207i) q^{28} -1.93360 q^{29} +(-6.85471 - 0.440900i) q^{30} +(-0.733160 - 0.423290i) q^{31} -5.20860i q^{32} +(3.53007 - 1.74619i) q^{33} +(2.48437 - 1.43435i) q^{34} +(-7.25469 - 12.5655i) q^{35} +(-1.93455 + 2.53391i) q^{36} +(-1.34335 - 0.775584i) q^{37} +(0.321755 + 0.557296i) q^{38} +(0.611054 + 6.21503i) q^{39} +(6.07286 - 10.5185i) q^{40} +(-1.84600 + 1.06579i) q^{41} +(5.92770 + 0.381274i) q^{42} +(1.22191 - 2.11641i) q^{43} +2.41628i q^{44} +(-11.3416 + 4.73022i) q^{45} +(2.14118 - 1.23621i) q^{46} +(-4.45149 + 2.57007i) q^{47} +(0.572467 + 1.15729i) q^{48} +(2.77359 + 4.80400i) q^{49} +(9.87570 - 5.70174i) q^{50} +(2.84606 - 4.27068i) q^{51} +(-3.58402 - 1.35461i) q^{52} +3.82370 q^{53} +(0.963417 - 4.93762i) q^{54} +(-4.65693 + 8.06604i) q^{55} +(-5.25159 + 9.09602i) q^{56} +(0.958001 + 0.638430i) q^{57} +1.87204i q^{58} -0.343666i q^{59} +(0.483932 - 7.52374i) q^{60} +(5.85687 - 10.1444i) q^{61} +(-0.409815 + 0.709820i) q^{62} +(9.80777 - 4.09052i) q^{63} -6.53366 q^{64} +(-9.35342 - 11.4295i) q^{65} +(-1.69060 - 3.41769i) q^{66} +(-9.78152 + 5.64737i) q^{67} +(1.57435 + 2.72685i) q^{68} +(2.45291 - 3.68073i) q^{69} +(-12.1655 + 7.02373i) q^{70} +(7.40141 - 4.27320i) q^{71} +(7.07042 + 5.39802i) q^{72} +0.0644878i q^{73} +(-0.750893 + 1.30058i) q^{74} +(11.3135 - 16.9765i) q^{75} +(-0.611688 + 0.353158i) q^{76} +(4.02714 - 6.97521i) q^{77} +(6.01717 - 0.591601i) q^{78} +(1.74347 + 3.01978i) q^{79} +(-2.64436 - 1.52672i) q^{80} +(-2.37168 - 8.68188i) q^{81} +(1.03186 + 1.78723i) q^{82} +(-5.65071 + 3.26244i) q^{83} +(-0.418487 + 6.50625i) q^{84} +12.1370i q^{85} +(-2.04903 - 1.18301i) q^{86} +(1.48492 + 3.00191i) q^{87} +6.74219 q^{88} +(-13.1316 - 7.58156i) q^{89} +(4.57963 + 10.9805i) q^{90} +(8.08849 + 9.88381i) q^{91} +(1.35687 + 2.35017i) q^{92} +(-0.0941203 + 1.46330i) q^{93} +(2.48825 + 4.30977i) q^{94} -2.72259 q^{95} +(-8.08633 + 3.99998i) q^{96} +(-14.4349 - 8.33399i) q^{97} +(4.65106 - 2.68529i) q^{98} +(-5.42189 - 4.13943i) 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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