LMFDB - Embedded newform 117.2.l.b.4.2

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			4.2
Character	$\chi$	$=$	117.4
Dual form			117.2.l.b.88.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.31664i q^{2} +(-0.644502 - 1.60767i) q^{3} -3.36682 q^{4} +(-1.09505 - 0.632228i) q^{5} +(-3.72440 + 1.49308i) q^{6} +(3.61589 + 2.08764i) q^{7} +3.16642i q^{8} +(-2.16923 + 2.07230i) q^{9} +(-1.46464 + 2.53684i) q^{10} -2.71354i q^{11} +(2.16992 + 5.41274i) q^{12} +(1.54000 - 3.26012i) q^{13} +(4.83630 - 8.37672i) q^{14} +(-0.310655 + 2.16796i) q^{15} +0.601814 q^{16} +(1.05102 + 1.82043i) q^{17} +(4.80077 + 5.02533i) q^{18} +(-2.74246 + 1.58336i) q^{19} +(3.68684 + 2.12860i) q^{20} +(1.02579 - 7.15866i) q^{21} -6.28629 q^{22} +(-0.226187 - 0.391767i) q^{23} +(5.09057 - 2.04076i) q^{24} +(-1.70057 - 2.94548i) q^{25} +(-7.55253 - 3.56763i) q^{26} +(4.72966 + 2.15182i) q^{27} +(-12.1740 - 7.02869i) q^{28} +8.58419 q^{29} +(5.02238 + 0.719675i) q^{30} +(3.34195 + 1.92947i) q^{31} +4.93865i q^{32} +(-4.36249 + 1.74888i) q^{33} +(4.21727 - 2.43484i) q^{34} +(-2.63973 - 4.57214i) q^{35} +(7.30341 - 6.97704i) q^{36} +(7.55106 + 4.35961i) q^{37} +(3.66807 + 6.35328i) q^{38} +(-6.23375 - 0.374666i) q^{39} +(2.00190 - 3.46739i) q^{40} +(2.17473 - 1.25558i) q^{41} +(-16.5840 - 2.37639i) q^{42} +(2.49307 - 4.31812i) q^{43} +9.13598i q^{44} +(3.68559 - 0.897822i) q^{45} +(-0.907582 + 0.523993i) q^{46} +(-10.8108 + 6.24161i) q^{47} +(-0.387870 - 0.967520i) q^{48} +(5.21645 + 9.03516i) q^{49} +(-6.82362 + 3.93962i) q^{50} +(2.24927 - 2.86297i) q^{51} +(-5.18490 + 10.9762i) q^{52} -1.14568 q^{53} +(4.98500 - 10.9569i) q^{54} +(-1.71558 + 2.97147i) q^{55} +(-6.61033 + 11.4494i) q^{56} +(4.31304 + 3.38850i) q^{57} -19.8865i q^{58} +6.32407i q^{59} +(1.04592 - 7.29912i) q^{60} +(2.54823 - 4.41366i) q^{61} +(4.46989 - 7.74208i) q^{62} +(-12.1699 + 2.96463i) q^{63} +12.6447 q^{64} +(-3.74752 + 2.59637i) q^{65} +(4.05152 + 10.1063i) q^{66} +(-12.2823 + 7.09120i) q^{67} +(-3.53860 - 6.12904i) q^{68} +(-0.484056 + 0.616129i) q^{69} +(-10.5920 + 6.11529i) q^{70} +(-6.49685 + 3.75096i) q^{71} +(-6.56176 - 6.86870i) q^{72} +7.95754i q^{73} +(10.0996 - 17.4931i) q^{74} +(-3.63935 + 4.63234i) q^{75} +(9.23335 - 5.33087i) q^{76} +(5.66488 - 9.81187i) q^{77} +(-0.867965 + 14.4413i) q^{78} +(-1.82489 - 3.16081i) q^{79} +(-0.659017 - 0.380484i) q^{80} +(0.411161 - 8.99060i) q^{81} +(-2.90873 - 5.03807i) q^{82} +(1.96005 - 1.13164i) q^{83} +(-3.45365 + 24.1019i) q^{84} -2.65795i q^{85} +(-10.0035 - 5.77554i) q^{86} +(-5.53253 - 13.8006i) q^{87} +8.59219 q^{88} +(1.31792 + 0.760899i) q^{89} +(-2.07993 - 8.53818i) q^{90} +(12.3744 - 8.57329i) q^{91} +(0.761528 + 1.31901i) q^{92} +(0.948075 - 6.61631i) q^{93} +(14.4596 + 25.0447i) q^{94} +4.00418 q^{95} +(7.93974 - 3.18297i) q^{96} +(-2.06617 - 1.19290i) q^{97} +(20.9312 - 12.0846i) q^{98} +(5.62326 + 5.88630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	2.31664i		−	1.63811i	−0.573714	−	0.819055i	$-0.694498\pi$
$2$		−	2.31664i		−	1.63811i	0.573714	−	0.819055i	$-0.305502\pi$
$3$	−0.644502	−	1.60767i	−0.372103	−	0.928191i
$3$	−0.644502	−	1.60767i	−0.372103	−	0.928191i
$4$	−3.36682			−1.68341
$5$	−1.09505	−	0.632228i	−0.489722	−	0.282741i	0.234737	−	0.972059i	$-0.424577\pi$
$5$	−1.09505	−	0.632228i	−0.489722	−	0.282741i	−0.724459	+	0.689318i	$0.757910\pi$
$6$	−3.72440	+	1.49308i	−1.52048	+	0.609546i
$7$	3.61589	+	2.08764i	1.36668	+	0.789053i	0.990502	−	0.137495i	$-0.0439052\pi$
$7$	3.61589	+	2.08764i	1.36668	+	0.789053i	0.376177	+	0.926548i	$0.377239\pi$
$8$			3.16642i			1.11950i
$9$	−2.16923	+	2.07230i	−0.723078	+	0.690766i
$10$	−1.46464	+	2.53684i	−0.463161	+	0.802219i
$11$		−	2.71354i		−	0.818163i	−0.912498	−	0.409081i	$-0.865849\pi$
$11$		−	2.71354i		−	0.818163i	0.912498	−	0.409081i	$-0.134151\pi$
$12$	2.16992	+	5.41274i	0.626401	+	1.56252i
$13$	1.54000	−	3.26012i	0.427119	−	0.904195i
$13$	1.54000	−	3.26012i	0.427119	−	0.904195i
$14$	4.83630	−	8.37672i	1.29256	−	2.23877i
$15$	−0.310655	+	2.16796i	−0.0802107	+	0.559765i
$16$	0.601814			0.150453
$17$	1.05102	+	1.82043i	0.254911	+	0.441518i	0.964871	−	0.262723i	$-0.0846206\pi$
$17$	1.05102	+	1.82043i	0.254911	+	0.441518i	−0.709961	+	0.704241i	$0.751287\pi$
$18$	4.80077	+	5.02533i	1.13155	+	1.18448i
$19$	−2.74246	+	1.58336i	−0.629163	+	0.363247i	−0.780428	−	0.625246i	$-0.784999\pi$
$19$	−2.74246	+	1.58336i	−0.629163	+	0.363247i	0.151265	+	0.988493i	$0.451665\pi$
$20$	3.68684	+	2.12860i	0.824402	+	0.475969i
$21$	1.02579	−	7.15866i	0.223846	−	1.56215i
$22$	−6.28629			−1.34024
$23$	−0.226187	−	0.391767i	−0.0471632	−	0.0816890i	0.841480	−	0.540288i	$-0.181685\pi$
$23$	−0.226187	−	0.391767i	−0.0471632	−	0.0816890i	−0.888643	+	0.458599i	$0.848351\pi$
$24$	5.09057	−	2.04076i	1.03911	−	0.416569i
$25$	−1.70057	−	2.94548i	−0.340115	−	0.589096i
$26$	−7.55253	−	3.56763i	−1.48117	−	0.699669i
$27$	4.72966	+	2.15182i	0.910223	+	0.414119i
$28$	−12.1740	−	7.02869i	−2.30068	−	1.32830i
$29$	8.58419			1.59404			0.797022	−	0.603950i	$-0.206407\pi$
$29$	8.58419			1.59404			0.797022	+	0.603950i	$0.206407\pi$
$30$	5.02238	+	0.719675i	0.916957	+	0.131394i
$31$	3.34195	+	1.92947i	0.600231	+	0.346544i	0.769133	−	0.639089i	$-0.220689\pi$
$31$	3.34195	+	1.92947i	0.600231	+	0.346544i	−0.168901	+	0.985633i	$0.554022\pi$
$32$			4.93865i			0.873038i
$33$	−4.36249	+	1.74888i	−0.759412	+	0.304441i
$34$	4.21727	−	2.43484i	0.723256	−	0.417572i
$35$	−2.63973	−	4.57214i	−0.446195	−	0.772833i
$36$	7.30341	−	6.97704i	1.21724	−	1.16284i
$37$	7.55106	+	4.35961i	1.24139	+	0.716715i	0.969377	−	0.245579i	$-0.0789782\pi$
$37$	7.55106	+	4.35961i	1.24139	+	0.716715i	0.272010	+	0.962294i	$0.412311\pi$
$38$	3.66807	+	6.35328i	0.595039	+	1.03064i
$39$	−6.23375	−	0.374666i	−0.998199	−	0.0599946i
$40$	2.00190	−	3.46739i	0.316528	−	0.548243i
$41$	2.17473	−	1.25558i	0.339636	−	0.196089i	−0.320475	−	0.947257i	$-0.603842\pi$
$41$	2.17473	−	1.25558i	0.339636	−	0.196089i	0.660111	+	0.751168i	$0.270509\pi$
$42$	−16.5840	−	2.37639i	−2.55897	−	0.366685i
$43$	2.49307	−	4.31812i	0.380189	−	0.658507i	−0.610900	−	0.791708i	$-0.709192\pi$
$43$	2.49307	−	4.31812i	0.380189	−	0.658507i	0.991089	+	0.133201i	$0.0425255\pi$
$44$			9.13598i			1.37730i
$45$	3.68559	−	0.897822i	0.549415	−	0.133839i
$46$	−0.907582	+	0.523993i	−0.133816	+	0.0772585i
$47$	−10.8108	+	6.24161i	−1.57692	+	0.910432i	−0.581629	+	0.813454i	$0.697584\pi$
$47$	−10.8108	+	6.24161i	−1.57692	+	0.910432i	−0.995287	+	0.0969780i	$0.969082\pi$
$48$	−0.387870	−	0.967520i	−0.0559842	−	0.139650i
$49$	5.21645	+	9.03516i	0.745208	+	1.29074i
$50$	−6.82362	+	3.93962i	−0.965005	+	0.557146i
$51$	2.24927	−	2.86297i	0.314960	−	0.400896i
$52$	−5.18490	+	10.9762i	−0.719016	+	1.52213i
$53$	−1.14568			−0.157371			−0.0786857	−	0.996899i	$-0.525072\pi$
$53$	−1.14568			−0.157371			−0.0786857	+	0.996899i	$0.525072\pi$
$54$	4.98500	−	10.9569i	0.678372	−	1.49105i
$55$	−1.71558	+	2.97147i	−0.231328	+	0.400672i
$56$	−6.61033	+	11.4494i	−0.883342	+	1.52999i
$57$	4.31304	+	3.38850i	0.571277	+	0.448818i
$58$		−	19.8865i		−	2.61122i
$59$			6.32407i			0.823323i	0.911337	+	0.411662i	$0.135051\pi$
$59$			6.32407i			0.823323i	−0.911337	+	0.411662i	$0.864949\pi$
$60$	1.04592	−	7.29912i	0.135027	−	0.942312i
$61$	2.54823	−	4.41366i	0.326267	−	0.565111i	−0.655501	−	0.755195i	$-0.727542\pi$
$61$	2.54823	−	4.41366i	0.326267	−	0.565111i	0.981768	+	0.190083i	$0.0608757\pi$
$62$	4.46989	−	7.74208i	0.567677	−	0.983245i
$63$	−12.1699	+	2.96463i	−1.53327	+	0.373509i
$64$	12.6447			1.58059
$65$	−3.74752	+	2.59637i	−0.464823	+	0.322040i
$66$	4.05152	+	10.1063i	0.498708	+	1.24400i
$67$	−12.2823	+	7.09120i	−1.50052	+	0.866328i	−0.500524	+	0.865723i	$0.666859\pi$
$67$	−12.2823	+	7.09120i	−1.50052	+	0.866328i	−1.00000		0.000605174i	$0.999807\pi$
$68$	−3.53860	−	6.12904i	−0.429118	−	0.743255i
$69$	−0.484056	+	0.616129i	−0.0582734	+	0.0741732i
$70$	−10.5920	+	6.11529i	−1.26599	+	0.730917i
$71$	−6.49685	+	3.75096i	−0.771034	+	0.445157i	−0.833243	−	0.552906i	$-0.813519\pi$
$71$	−6.49685	+	3.75096i	−0.771034	+	0.445157i	0.0622094	+	0.998063i	$0.480185\pi$
$72$	−6.56176	−	6.86870i	−0.773311	−	0.809484i
$73$			7.95754i			0.931360i	0.884953	+	0.465680i	$0.154190\pi$
$73$			7.95754i			0.931360i	−0.884953	+	0.465680i	$0.845810\pi$
$74$	10.0996	−	17.4931i	1.17406	−	2.03353i
$75$	−3.63935	+	4.63234i	−0.420236	+	0.534896i
$76$	9.23335	−	5.33087i	1.05914	−	0.611493i
$77$	5.66488	−	9.81187i	0.645573	−	1.11817i
$78$	−0.867965	+	14.4413i	−0.0982777	+	1.63516i
$79$	−1.82489	−	3.16081i	−0.205317	−	0.355619i	0.744917	−	0.667157i	$-0.232489\pi$
$79$	−1.82489	−	3.16081i	−0.205317	−	0.355619i	−0.950234	+	0.311538i	$0.899156\pi$
$80$	−0.659017	−	0.380484i	−0.0736804	−	0.0425394i
$81$	0.411161	−	8.99060i	0.0456845	−	0.998956i
$82$	−2.90873	−	5.03807i	−0.321216	−	0.556362i
$83$	1.96005	−	1.13164i	0.215144	−	0.124213i	−0.388556	−	0.921425i	$-0.627026\pi$
$83$	1.96005	−	1.13164i	0.215144	−	0.124213i	0.603700	+	0.797212i	$0.293693\pi$
$84$	−3.45365	+	24.1019i	−0.376824	+	2.62973i
$85$		−	2.65795i		−	0.288295i
$86$	−10.0035	−	5.77554i	−1.07871	−	0.622792i
$87$	−5.53253	−	13.8006i	−0.593149	−	1.47958i
$88$	8.59219			0.915931
$89$	1.31792	+	0.760899i	0.139699	+	0.0806552i	0.568220	−	0.822876i	$-0.307632\pi$
$89$	1.31792	+	0.760899i	0.139699	+	0.0806552i	−0.428522	+	0.903532i	$0.640965\pi$
$90$	−2.07993	−	8.53818i	−0.219244	−	0.900003i
$91$	12.3744	−	8.57329i	1.29719	−	0.898725i
$92$	0.761528	+	1.31901i	0.0793948	+	0.137516i
$93$	0.948075	−	6.61631i	0.0983108	−	0.686079i
$94$	14.4596	+	25.0447i	1.49139	+	2.58316i
$95$	4.00418			0.410820
$96$	7.93974	−	3.18297i	0.810346	−	0.324860i
$97$	−2.06617	−	1.19290i	−0.209787	−	0.121121i	0.391425	−	0.920210i	$-0.371982\pi$
$97$	−2.06617	−	1.19290i	−0.209787	−	0.121121i	−0.601213	+	0.799089i	$0.705316\pi$
$98$	20.9312	−	12.0846i	2.11437	−	1.22073i
$99$	5.62326	+	5.88630i	0.565159	+	0.591596i
$100$	5.72552	+	9.91689i	0.572552	+	0.991689i
$101$	−11.1980			−1.11424			−0.557119	−	0.830433i	$-0.688093\pi$
$101$	−11.1980			−1.11424			−0.557119	+	0.830433i	$0.688093\pi$
$102$	−6.63247	−	5.21074i	−0.656712	−	0.515940i
$103$	−1.45757	+	2.52458i	−0.143618	+	0.248754i	−0.928857	−	0.370440i	$-0.879207\pi$
$103$	−1.45757	+	2.52458i	−0.143618	+	0.248754i	0.785238	+	0.619194i	$0.212540\pi$
$104$	10.3229	+	4.87628i	1.01224	+	0.478159i
$105$	−5.64921	+	7.19057i	−0.551306	+	0.701728i
$106$			2.65413i			0.257792i
$107$	−1.33105	+	2.30545i	−0.128678	+	0.222876i	−0.923164	−	0.384405i	$-0.874407\pi$
$107$	−1.33105	+	2.30545i	−0.128678	+	0.222876i	0.794487	+	0.607281i	$0.207740\pi$
$108$	−15.9239	−	7.24479i	−1.53228	−	0.697131i
$109$		−	8.32143i		−	0.797049i	−0.917158	−	0.398524i	$-0.869522\pi$
$109$		−	8.32143i		−	0.797049i	0.917158	−	0.398524i	$-0.130478\pi$
$110$	6.88381	+	3.97437i	0.656346	+	0.378941i
$111$	2.14216	−	14.9494i	0.203325	−	1.41894i
$112$	2.17609	+	1.25637i	0.205622	+	0.118716i
$113$	3.51606			0.330763			0.165382	−	0.986230i	$-0.447114\pi$
$113$	3.51606			0.330763			0.165382	+	0.986230i	$0.447114\pi$
$114$	7.84993	−	9.99176i	0.735214	−	0.935814i
$115$			0.572006i			0.0533399i
$116$	−28.9014			−2.68343
$117$	3.41532	+	10.2633i	0.315747	+	0.948844i
$118$	14.6506			1.34870
$119$			8.77662i			0.804552i
$120$	−6.86466	−	0.983663i	−0.626655	−	0.0897957i
$121$	3.63671			0.330610
$122$	−10.2249	−	5.90333i	−0.925715	−	0.534462i
$123$	−3.42019	−	2.68704i	−0.308388	−	0.242282i
$124$	−11.2517	−	6.49618i	−1.01043	−	0.583374i
$125$			10.6229i			0.950140i
$126$	6.86798	+	28.1933i	0.611849	+	2.51166i
$127$	7.86992	−	13.6311i	0.698342	−	1.20956i	−0.270699	−	0.962664i	$-0.587255\pi$
$127$	7.86992	−	13.6311i	0.698342	−	1.20956i	0.969041	−	0.246900i	$-0.0794119\pi$
$128$		−	19.4159i		−	1.71614i
$129$	−8.54892	−	1.22501i	−0.752690	−	0.107856i
$130$	6.01485	+	8.68166i	0.527537	+	0.761432i
$131$	−6.82094	+	11.8142i	−0.595949	+	1.03221i	0.397464	+	0.917618i	$0.369890\pi$
$131$	−6.82094	+	11.8142i	−0.595949	+	1.03221i	−0.993412	+	0.114595i	$0.963443\pi$
$132$	14.6877	−	5.88816i	1.27840	−	0.512498i
$133$	−13.2219			−1.14648
$134$	16.4277	+	28.4537i	1.41914	+	2.45802i
$135$	−3.81877	−	5.34658i	−0.328668	−	0.460161i
$136$	−5.76423	+	3.32798i	−0.494278	+	0.285372i
$137$	9.91933	+	5.72693i	0.847466	+	0.489285i	0.859795	−	0.510639i	$-0.170591\pi$
$137$	9.91933	+	5.72693i	0.847466	+	0.489285i	−0.0123293	+	0.999924i	$0.503925\pi$
$138$	1.42735	+	1.12138i	0.121504	+	0.0954584i
$139$	4.84634			0.411062			0.205531	−	0.978651i	$-0.434108\pi$
$139$	4.84634			0.411062			0.205531	+	0.978651i	$0.434108\pi$
$140$	8.88747	+	15.3936i	0.751128	+	1.30099i
$141$	17.0020	+	13.3575i	1.43183	+	1.12490i
$142$	8.68961	+	15.0508i	0.729216	+	1.26304i
$143$	−8.84647	−	4.17885i	−0.739779	−	0.349453i
$144$	−1.30548	+	1.24714i	−0.108790	+	0.103928i
$145$	−9.40013	−	5.42717i	−0.780639	−	0.450702i
$146$	18.4348			1.52567
$147$	11.1636	−	14.2095i	0.920757	−	1.17198i
$148$	−25.4230	−	14.6780i	−2.08976	−	1.20652i
$149$		−	21.7031i		−	1.77799i	−0.457918	−	0.888994i	$-0.651405\pi$
$149$		−	21.7031i		−	1.77799i	0.457918	−	0.888994i	$-0.348595\pi$
$150$	10.7315	+	8.43106i	0.876219	+	0.688393i
$151$	2.34152	−	1.35188i	0.190550	−	0.110014i	−0.401690	−	0.915776i	$-0.631577\pi$
$151$	2.34152	−	1.35188i	0.190550	−	0.110014i	0.592240	+	0.805762i	$0.298244\pi$
$152$	−5.01357	−	8.68376i	−0.406654	−	0.704346i
$153$	−6.05238	−	1.77090i	−0.489306	−	0.143169i
$154$	−22.7305	−	13.1235i	−1.83168	−	1.05752i
$155$	−2.43974	−	4.22575i	−0.195964	−	0.339420i
$156$	20.9879	+	1.26143i	1.68038	+	0.100995i
$157$	−7.83378	+	13.5685i	−0.625204	+	1.08288i	0.363298	+	0.931673i	$0.381651\pi$
$157$	−7.83378	+	13.5685i	−0.625204	+	1.08288i	−0.988501	+	0.151212i	$0.951682\pi$
$158$	−7.32245	+	4.22762i	−0.582543	+	0.336331i
$159$	0.738394	+	1.84188i	0.0585584	+	0.146071i
$160$	3.12235	−	5.40808i	0.246844	−	0.427546i
$161$		−	1.88878i		−	0.148857i
$162$	−20.8280	−	0.952511i	−1.63640	−	0.0748364i
$163$	−5.73759	+	3.31260i	−0.449403	+	0.259463i	−0.707578	−	0.706635i	$-0.750212\pi$
$163$	−5.73759	+	3.31260i	−0.449403	+	0.259463i	0.258175	+	0.966098i	$0.416879\pi$
$164$	−7.32193	+	4.22732i	−0.571746	+	0.330098i
$165$	5.88284	+	0.842974i	0.457979	+	0.0656254i
$166$	−2.62159	−	4.54074i	−0.203475	−	0.352429i
$167$	−9.34793	+	5.39703i	−0.723365	+	0.417635i	−0.815990	−	0.578066i	$-0.803808\pi$
$167$	−9.34793	+	5.39703i	−0.723365	+	0.417635i	0.0926250	+	0.995701i	$0.470474\pi$
$168$	22.6673	+	3.24808i	1.74882	+	0.250595i
$169$	−8.25679	−	10.0412i	−0.635138	−	0.772399i
$170$	−6.15751			−0.472259
$171$	2.66784	−	9.11787i	0.204015	−	0.697261i
$172$	−8.39370	+	14.5383i	−0.640013	+	1.10854i
$173$	−2.43830	+	4.22326i	−0.185380	+	0.321088i	−0.943705	−	0.330789i	$-0.892685\pi$
$173$	−2.43830	+	4.22326i	−0.185380	+	0.321088i	0.758324	+	0.651878i	$0.226018\pi$
$174$	−31.9710	+	12.8169i	−2.42371	+	0.971644i
$175$		−	14.2007i		−	1.07347i
$176$		−	1.63304i		−	0.123095i
$177$	10.1670	−	4.07587i	0.764202	−	0.306361i
$178$	1.76273	−	3.05314i	0.132122	−	0.228842i
$179$	6.61646	−	11.4601i	0.494538	−	0.856564i	−0.505442	−	0.862860i	$-0.668671\pi$
$179$	6.61646	−	11.4601i	0.494538	−	0.856564i	0.999980	+	0.00629588i	$0.00200406\pi$
$180$	−12.4087	+	3.02280i	−0.924890	+	0.225306i
$181$	−18.2227			−1.35448			−0.677242	−	0.735760i	$-0.736825\pi$
$181$	−18.2227			−1.35448			−0.677242	+	0.735760i	$0.736825\pi$
$182$	−19.8612	−	28.6671i	−1.47221	−	2.12495i
$183$	−8.73807	−	1.25211i	−0.645937	−	0.0925586i
$184$	1.24050	−	0.716201i	0.0914506	−	0.0527990i
$185$	−5.51254	−	9.54799i	−0.405290	−	0.701982i
$186$	−15.3276	−	2.19635i	−1.12387	−	0.161044i
$187$	4.93980	−	2.85199i	0.361234	−	0.208558i
$188$	36.3979	−	21.0143i	2.65459	−	1.53263i
$189$	12.6097	+	17.6546i	0.917221	+	1.28418i
$190$		−	9.27623i		−	0.672969i
$191$	−7.68539	+	13.3115i	−0.556096	+	0.963186i	0.441722	+	0.897152i	$0.354368\pi$
$191$	−7.68539	+	13.3115i	−0.556096	+	0.963186i	−0.997817	+	0.0660338i	$0.978965\pi$
$192$	−8.14953	−	20.3286i	−0.588141	−	1.46709i
$193$	−4.89620	+	2.82682i	−0.352436	+	0.203479i	−0.665758	−	0.746168i	$-0.731892\pi$
$193$	−4.89620	+	2.82682i	−0.352436	+	0.203479i	0.313322	+	0.949647i	$0.398558\pi$
$194$	−2.76352	+	4.78656i	−0.198409	+	0.343655i
$195$	6.58940	+	4.35143i	0.471877	+	0.311613i
$196$	−17.5628	−	30.4197i	−1.25449	−	2.17284i
$197$	5.46126	+	3.15306i	0.389098	+	0.224646i	0.681769	−	0.731567i	$-0.261211\pi$
$197$	5.46126	+	3.15306i	0.389098	+	0.224646i	−0.292671	+	0.956213i	$0.594544\pi$
$198$	13.6364	−	13.0271i	0.969099	−	0.925793i
$199$	−0.849701	−	1.47173i	−0.0602337	−	0.104328i	0.834336	−	0.551256i	$-0.185851\pi$
$199$	−0.849701	−	1.47173i	−0.0602337	−	0.104328i	−0.894570	+	0.446928i	$0.852518\pi$
$200$	9.32662	−	5.38473i	0.659492	−	0.380758i
$201$	19.3163	+	15.1757i	1.36247	+	1.07041i
$202$			25.9416i			1.82525i
$203$	31.0395	+	17.9207i	2.17855	+	1.25778i
$204$	−7.57286	+	9.63910i	−0.530206	+	0.674872i
$205$	−3.17526			−0.221770
$206$	5.84854	+	3.37665i	0.407487	+	0.235263i
$207$	1.30251	+	0.381108i	0.0905306	+	0.0264888i
$208$	0.926794	−	1.96199i	0.0642616	−	0.136039i
$209$	4.29650	+	7.44176i	0.297195	+	0.514758i
$210$	16.6580	+	13.0872i	1.14951	+	0.903100i
$211$	−2.28196	−	3.95246i	−0.157096	−	0.272099i	0.776724	−	0.629841i	$-0.216880\pi$
$211$	−2.28196	−	3.95246i	−0.157096	−	0.272099i	−0.933820	+	0.357742i	$0.883547\pi$
$212$	3.85730			0.264920
$213$	10.2175	+	8.02732i	0.700095	+	0.550023i
$214$	5.34089	+	3.08357i	0.365096	+	0.210788i
$215$	−5.46008	+	3.15238i	−0.372374	+	0.214990i
$216$	−6.81357	+	14.9761i	−0.463605	+	1.01899i
$217$	8.05608	+	13.9535i	0.546882	+	0.947228i
$218$	−19.2778			−1.30565
$219$	12.7931	−	5.12865i	0.864480	−	0.346562i
$220$	5.77603	−	10.0044i	0.389420	−	0.674495i
$221$	7.55339	−	0.623007i	0.508096	−	0.0419080i
$222$	−34.6324	−	4.96261i	−2.32438	−	0.333068i
$223$			22.2795i			1.49195i	0.665975	+	0.745974i	$0.268016\pi$
$223$			22.2795i			1.49195i	−0.665975	+	0.745974i	$0.731984\pi$
$224$	−10.3101	+	17.8576i	−0.688873	+	1.19316i
$225$	9.79286	+	2.86534i	0.652857	+	0.191023i
$226$		−	8.14545i		−	0.541827i
$227$	3.63895	+	2.10095i	0.241525	+	0.139445i	0.615878	−	0.787842i	$-0.288802\pi$
$227$	3.63895	+	2.10095i	0.241525	+	0.139445i	−0.374352	+	0.927287i	$0.622135\pi$
$228$	−14.5212	−	11.4085i	−0.961691	−	0.755544i
$229$	−19.7986	−	11.4307i	−1.30833	−	0.755365i	−0.326513	−	0.945193i	$-0.605874\pi$
$229$	−19.7986	−	11.4307i	−1.30833	−	0.755365i	−0.981817	+	0.189827i	$0.939207\pi$
$230$	1.32513			0.0873766
$231$	−19.4253	−	2.78352i	−1.27809	−	0.183142i
$232$			27.1811i			1.78453i
$233$	17.2872			1.13252			0.566260	−	0.824226i	$-0.308390\pi$
$233$	17.2872			1.13252			0.566260	+	0.824226i	$0.308390\pi$
$234$	23.7764	−	7.91207i	1.55431	−	0.517228i
$235$	15.7845			1.02967
$236$		−	21.2920i		−	1.38599i
$237$	−3.90540	+	4.97098i	−0.253683	+	0.322900i
$238$	20.3323			1.31794
$239$	5.61354	+	3.24098i	0.363110	+	0.209642i	0.670444	−	0.741960i	$-0.266104\pi$
$239$	5.61354	+	3.24098i	0.363110	+	0.209642i	−0.307334	+	0.951602i	$0.599437\pi$
$240$	−0.186956	+	1.30471i	−0.0120680	+	0.0842185i
$241$	−0.159319	−	0.0919831i	−0.0102627	−	0.00592515i	0.494860	−	0.868973i	$-0.335219\pi$
$241$	−0.159319	−	0.0919831i	−0.0102627	−	0.00592515i	−0.505123	+	0.863048i	$0.668553\pi$
$242$		−	8.42494i		−	0.541575i
$243$	−14.7190	+	5.13345i	−0.944222	+	0.329311i
$244$	−8.57941	+	14.8600i	−0.549241	+	0.951313i
$245$		−	13.1920i		−	0.842804i
$246$	−6.22490	+	7.92334i	−0.396885	+	0.505174i
$247$	0.938555	+	11.3791i	0.0597188	+	0.724036i
$248$	−6.10952	+	10.5820i	−0.387955	+	0.671957i
$249$	−3.08256	−	2.42179i	−0.195349	−	0.153474i
$250$	24.6094			1.55644
$251$	−11.8003	−	20.4387i	−0.744827	−	1.29008i	−0.950276	−	0.311410i	$-0.899199\pi$
$251$	−11.8003	−	20.4387i	−0.744827	−	1.29008i	0.205449	−	0.978668i	$-0.434135\pi$
$252$	40.9739	−	9.98137i	2.58111	−	0.628767i
$253$	−1.06307	+	0.613766i	−0.0668349	+	0.0385871i
$254$	−31.5783	−	18.2318i	−1.98140	−	1.14396i
$255$	−4.27312	+	1.71305i	−0.267593	+	0.107275i
$256$	−19.6902			−1.23064
$257$	2.92492	+	5.06610i	0.182451	+	0.316015i	0.942715	−	0.333600i	$-0.108264\pi$
$257$	2.92492	+	5.06610i	0.182451	+	0.316015i	−0.760263	+	0.649615i	$0.774930\pi$
$258$	−2.83790	+	19.8048i	−0.176680	+	1.23299i
$259$	18.2026	+	31.5277i	1.13105	+	1.95904i
$260$	12.6172	−	8.74150i	0.782487	−	0.542125i
$261$	−18.6211	+	17.7890i	−1.15262	+	1.10111i
$262$	27.3693	+	15.8017i	1.69088	+	0.976230i
$263$	−9.69814			−0.598013			−0.299007	−	0.954251i	$-0.596655\pi$
$263$	−9.69814			−0.598013			−0.299007	+	0.954251i	$0.596655\pi$
$264$	−5.53768	−	13.8135i	−0.340821	−	0.850159i
$265$	1.25458	+	0.724332i	0.0770683	+	0.0444954i
$266$			30.6304i			1.87807i
$267$	0.373879	−	2.60918i	0.0228810	−	0.159679i
$268$	41.3523	−	23.8748i	2.52599	−	1.45838i
$269$	−10.4720	−	18.1380i	−0.638487	−	1.10589i	−0.985765	−	0.168130i	$-0.946227\pi$
$269$	−10.4720	−	18.1380i	−0.638487	−	1.10589i	0.347278	−	0.937762i	$-0.387106\pi$
$270$	−12.3861	+	8.84672i	−0.753794	+	0.538394i
$271$	4.98580	+	2.87855i	0.302866	+	0.174860i	0.643730	−	0.765253i	$-0.277386\pi$
$271$	4.98580	+	2.87855i	0.302866	+	0.174860i	−0.340864	+	0.940113i	$0.610720\pi$
$272$	0.632520	+	1.09556i	0.0383522	+	0.0664279i
$273$	−21.7584	−	14.3686i	−1.31688	−	0.869624i
$274$	13.2672	−	22.9795i	0.801502	−	1.38824i
$275$	−7.99268	+	4.61457i	−0.481977	+	0.278269i
$276$	1.62973	−	2.07439i	0.0980979	−	0.124864i
$277$	7.99986	−	13.8562i	0.480665	−	0.832536i	−0.519089	−	0.854720i	$-0.673729\pi$
$277$	7.99986	−	13.8562i	0.480665	−	0.832536i	0.999754	+	0.0221842i	$0.00706203\pi$
$278$		−	11.2272i		−	0.673364i
$279$	−11.2479	+	2.74003i	−0.673395	+	0.164041i
$280$	14.4773	−	8.35848i	0.865184	−	0.499514i
$281$	16.2457	−	9.37948i	0.969139	−	0.559533i	0.0701653	−	0.997535i	$-0.477647\pi$
$281$	16.2457	−	9.37948i	0.969139	−	0.559533i	0.898974	+	0.438003i	$0.144314\pi$
$282$	30.9445	−	39.3876i	1.84272	−	2.34550i
$283$	2.26166	+	3.91730i	0.134442	+	0.232860i	0.925384	−	0.379031i	$-0.123743\pi$
$283$	2.26166	+	3.91730i	0.134442	+	0.232860i	−0.790942	+	0.611891i	$0.790409\pi$
$284$	21.8737	−	12.6288i	1.29796	−	0.749380i
$285$	−2.58070	−	6.43741i	−0.152867	−	0.381319i
$286$	−9.68089	+	20.4941i	−0.572443	+	1.21184i
$287$	10.4848			0.618899
$288$	−10.2344	−	10.7131i	−0.603065	−	0.631275i
$289$	6.29070	−	10.8958i	0.370041	−	0.640930i
$290$	−12.5728	+	21.7767i	−0.738300	+	1.27877i
$291$	−0.586150	+	4.09055i	−0.0343607	+	0.239792i
$292$		−	26.7916i		−	1.56786i
$293$		−	0.316723i		−	0.0185032i	−0.999957	−	0.00925159i	$-0.997055\pi$
$293$		−	0.316723i		−	0.0185032i	0.999957	−	0.00925159i	$-0.00294491\pi$
$294$	−32.9184	−	25.8620i	−1.91984	−	1.50830i
$295$	3.99826	−	6.92518i	0.232787	−	0.403200i
$296$	−13.8043	+	23.9098i	−0.802361	+	1.38973i
$297$	5.83906	−	12.8341i	0.338817	−	0.744710i
$298$	−50.2783			−2.91254
$299$	−1.62553	+	0.134075i	−0.0940071	+	0.00775375i
$300$	12.2530	−	15.5962i	0.707429	−	0.900448i
$301$	18.0293	−	10.4092i	1.03919	−	0.599979i
$302$	−3.13181	−	5.42445i	−0.180215	−	0.312142i
$303$	7.21710	+	18.0027i	0.414612	+	1.03423i
$304$	−1.65045	+	0.952887i	−0.0946597	+	0.0546518i
$305$	−5.58089	+	3.22213i	−0.319561	+	0.184498i
$306$	−4.10253	+	14.0212i	−0.234526	+	0.801538i
$307$			11.2849i			0.644066i	0.946728	+	0.322033i	$0.104366\pi$
$307$			11.2849i			0.644066i	−0.946728	+	0.322033i	$0.895634\pi$
$308$	−19.0726	+	33.0347i	−1.08676	+	1.88233i
$309$	4.99811	+	0.716197i	0.284332	+	0.0407430i
$310$	−9.78953	+	5.65199i	−0.556008	+	0.321011i
$311$	15.9070	−	27.5517i	0.902004	−	1.56232i	0.0771139	−	0.997022i	$-0.475429\pi$
$311$	15.9070	−	27.5517i	0.902004	−	1.56232i	0.824890	−	0.565294i	$-0.191237\pi$
$312$	1.18635	−	19.7386i	0.0671637	−	1.11748i
$313$	−0.0740804	−	0.128311i	−0.00418727	−	0.00725257i	0.863924	−	0.503622i	$-0.168000\pi$
$313$	−0.0740804	−	0.128311i	−0.00418727	−	0.00725257i	−0.868111	+	0.496369i	$0.834666\pi$
$314$	31.4333	+	18.1480i	1.77389	+	1.02415i
$315$	15.2010	+	4.44775i	0.856481	+	0.250602i
$316$	6.14408	+	10.6419i	0.345631	+	0.598651i
$317$	17.0960	−	9.87036i	0.960205	−	0.554375i	0.0639691	−	0.997952i	$-0.479624\pi$
$317$	17.0960	−	9.87036i	0.960205	−	0.554375i	0.896236	+	0.443577i	$0.146291\pi$
$318$	4.26698	−	1.71059i	0.239280	−	0.0959252i
$319$		−	23.2935i		−	1.30419i
$320$	−13.8466	−	7.99433i	−0.774048	−	0.446897i
$321$	4.56428	+	0.654032i	0.254753	+	0.0365045i
$322$	−4.37562			−0.243844
$323$	−5.76477	−	3.32829i	−0.320761	−	0.185191i
$324$	−1.38430	+	30.2697i	−0.0769057	+	1.68165i
$325$	−12.2215	+	1.00804i	−0.677928	+	0.0559158i
$326$	7.67410	+	13.2919i	0.425029	+	0.736172i
$327$	−13.3782	+	5.36318i	−0.739814	+	0.296584i
$328$	3.97570	+	6.88611i	0.219521	+	0.380222i
$329$	−52.1209			−2.87352
$330$	1.95287	−	13.6284i	0.107502	−	0.750220i
$331$	−14.7464	−	8.51384i	−0.810536	−	0.467963i	0.0366063	−	0.999330i	$-0.488345\pi$
$331$	−14.7464	−	8.51384i	−0.810536	−	0.467963i	−0.847142	+	0.531367i	$0.821679\pi$
$332$	−6.59914	+	3.81001i	−0.362175	+	0.209102i
$333$	−25.4144	+	6.19104i	−1.39270	+	0.339267i
$334$	12.5030	+	21.6558i	0.684132	+	1.18495i
$335$	17.9330			0.979786
$336$	0.617335	−	4.30818i	0.0336784	−	0.235031i
$337$	6.54226	−	11.3315i	0.356379	−	0.617267i	−0.630974	−	0.775804i	$-0.717344\pi$
$337$	6.54226	−	11.3315i	0.356379	−	0.617267i	0.987353	+	0.158537i	$0.0506777\pi$
$338$	−23.2618	+	19.1280i	−1.26527	+	1.04043i
$339$	−2.26611	−	5.65269i	−0.123078	−	0.307012i
$340$			8.94882i			0.485318i
$341$	5.23570	−	9.06850i	0.283529	−	0.491087i
$342$	−21.1228	−	6.18043i	−1.14219	−	0.334199i
$343$			14.3333i			0.773927i
$344$	13.6730	+	7.89409i	0.737197	+	0.425621i
$345$	0.919600	−	0.368659i	0.0495096	−	0.0198479i
$346$	9.78377	+	5.64866i	0.525978	+	0.303674i
$347$	14.9921			0.804816			0.402408	−	0.915460i	$-0.368173\pi$
$347$	14.9921			0.804816			0.402408	+	0.915460i	$0.368173\pi$
$348$	18.6270	+	46.4640i	0.998511	+	2.49073i
$349$			2.08492i			0.111603i	0.998442	+	0.0558015i	$0.0177714\pi$
$349$			2.08492i			0.111603i	−0.998442	+	0.0558015i	$0.982229\pi$
$350$	−32.8980			−1.75847
$351$	14.2989	−	12.1054i	0.763218	−	0.646141i
$352$	13.4012			0.714287
$353$		−	4.13470i		−	0.220068i	−0.993928	−	0.110034i	$-0.964904\pi$
$353$		−	4.13470i		−	0.220068i	0.993928	−	0.110034i	$-0.0350960\pi$
$354$	−9.44232	−	23.5534i	−0.501854	−	1.25185i
$355$	9.48585			0.503456
$356$	−4.43718	−	2.56181i	−0.235170	−	0.135776i
$357$	14.1100	−	5.65655i	0.746778	−	0.299376i
$358$	−26.5488	−	15.3280i	−1.40315	−	0.810108i
$359$			20.5783i			1.08608i	0.839706	+	0.543042i	$0.182727\pi$
$359$			20.5783i			1.08608i	−0.839706	+	0.543042i	$0.817273\pi$
$360$	2.84288	+	11.6701i	0.149833	+	0.615069i
$361$	−4.48595	+	7.76990i	−0.236103	+	0.408942i
$362$			42.2155i			2.21880i
$363$	−2.34386	−	5.84664i	−0.123021	−	0.306869i
$364$	−41.6624	+	28.8647i	−2.18370	+	1.51292i
$365$	5.03099	−	8.71392i	0.263334	−	0.456108i
$366$	−2.90069	+	20.2430i	−0.151621	+	1.05812i
$367$	−14.6764			−0.766101			−0.383050	−	0.923727i	$-0.625126\pi$
$367$	−14.6764			−0.766101			−0.383050	+	0.923727i	$0.625126\pi$
$368$	−0.136122	−	0.235770i	−0.00709586	−	0.0122904i
$369$	−2.11557	+	7.23035i	−0.110132	+	0.376397i
$370$	−22.1192	+	12.7706i	−1.14993	+	0.663910i
$371$	−4.14266	−	2.39177i	−0.215076	−	0.124174i
$372$	−3.19199	+	22.2759i	−0.165497	+	1.15495i
$373$	−29.7917			−1.54256			−0.771279	−	0.636497i	$-0.780383\pi$
$373$	−29.7917			−1.54256			−0.771279	+	0.636497i	$0.780383\pi$
$374$	−6.60704	−	11.4437i	−0.341642	−	0.591741i
$375$	17.0782	−	6.84647i	0.881912	−	0.353550i
$376$	−19.7635	−	34.2315i	−1.01923	−	1.76535i
$377$	13.2197	−	27.9855i	0.680847	−	1.44133i
$378$	40.8993	−	29.2121i	2.10363	−	1.50251i
$379$	−11.5590	−	6.67356i	−0.593743	−	0.342798i	0.172833	−	0.984951i	$-0.444708\pi$
$379$	−11.5590	−	6.67356i	−0.593743	−	0.342798i	−0.766576	+	0.642153i	$0.778041\pi$
$380$	−13.4813			−0.691577
$381$	−26.9865	−	3.86700i	−1.38256	−	0.198112i
$382$	30.8379	+	17.8043i	1.57781	+	0.910946i
$383$			2.94940i			0.150707i	0.997157	+	0.0753536i	$0.0240085\pi$
$383$			2.94940i			0.150707i	−0.997157	+	0.0753536i	$0.975991\pi$
$384$	−31.2144	+	12.5136i	−1.59290	+	0.638581i
$385$	−12.4067	+	7.16300i	−0.632303	+	0.365060i
$386$	6.54872	+	11.3427i	0.333321	+	0.577329i
$387$	3.54038	+	14.5334i	0.179968	+	0.738774i
$388$	6.95640	+	4.01628i	0.353158	+	0.203896i
$389$	8.31532	+	14.4026i	0.421603	+	0.730238i	0.996096	−	0.0882711i	$-0.0281342\pi$
$389$	8.31532	+	14.4026i	0.421603	+	0.730238i	−0.574493	+	0.818509i	$0.694801\pi$
$390$	10.0807	−	15.2653i	0.510456	−	0.772987i
$391$	0.475455	−	0.823512i	0.0240448	−	0.0416468i
$392$	−28.6091	+	16.5175i	−1.44498	+	0.834258i
$393$	23.3895	+	3.35157i	1.17985	+	0.169064i
$394$	7.30449	−	12.6518i	0.367995	−	0.637386i
$395$			4.61500i			0.232206i
$396$	−18.9325	−	19.8181i	−0.951393	−	0.995897i
$397$	5.23157	−	3.02045i	0.262565	−	0.151592i	−0.362939	−	0.931813i	$-0.618227\pi$
$397$	5.23157	−	3.02045i	0.262565	−	0.151592i	0.625504	+	0.780221i	$0.284893\pi$
$398$	−3.40946	+	1.96845i	−0.170901	+	0.0986695i
$399$	8.52154	+	21.2565i	0.426611	+	1.06416i
$400$	−1.02343	−	1.77263i	−0.0511714	−	0.0886315i
$401$	−12.4216	+	7.17161i	−0.620305	+	0.358133i	−0.776988	−	0.629516i	$-0.783253\pi$
$401$	−12.4216	+	7.17161i	−0.620305	+	0.358133i	0.156683	+	0.987649i	$0.449920\pi$
$402$	35.1566	−	44.7489i	1.75345	−	2.23187i
$403$	11.4369	−	7.92376i	0.569713	−	0.394711i
$404$	37.7015			1.87572
$405$	−6.13436	+	9.58523i	−0.304819	+	0.476294i
$406$	41.5157	−	71.9073i	2.06039	−	3.56870i
$407$	11.8300	−	20.4901i	0.586390	−	1.01566i
$408$	9.06536	+	7.12211i	0.448802	+	0.352597i
$409$			6.16181i			0.304682i	0.988328	+	0.152341i	$0.0486812\pi$
$409$			6.16181i			0.304682i	−0.988328	+	0.152341i	$0.951319\pi$
$410$			7.35593i			0.363284i
$411$	2.81401	−	19.6381i	0.138805	−	0.968675i
$412$	4.90736	−	8.49979i	0.241768	−	0.418755i
$413$	−13.2024	+	22.8672i	−0.649645	+	1.12522i
$414$	0.882889	−	3.01744i	0.0433916	−	0.148299i
$415$	−2.86181			−0.140481
$416$	16.1006	+	7.60552i	0.789397	+	0.372891i
$417$	−3.12348	−	7.79134i	−0.152957	−	0.381544i
$418$	17.2399	−	9.95345i	0.843230	−	0.486839i
$419$	6.94229	+	12.0244i	0.339153	+	0.587430i	0.984274	−	0.176651i	$-0.0565262\pi$
$419$	6.94229	+	12.0244i	0.339153	+	0.587430i	−0.645121	+	0.764081i	$0.723193\pi$
$420$	19.0198	−	24.2093i	0.928073	−	1.18129i
$421$	−4.55207	+	2.62814i	−0.221854	+	0.128088i	−0.606808	−	0.794848i	$-0.707551\pi$
$421$	−4.55207	+	2.62814i	−0.221854	+	0.128088i	0.384954	+	0.922936i	$0.374217\pi$
$422$	−9.15643	+	5.28647i	−0.445728	+	0.257341i
$423$	10.5167	−	35.9427i	0.511337	−	1.74759i
$424$		−	3.62770i		−	0.176177i
$425$	3.57469	−	6.19154i	0.173398	−	0.300334i
$426$	18.5964	−	23.6704i	0.900998	−	1.14683i
$427$	18.4282	−	10.6396i	0.891805	−	0.514884i
$428$	4.48141	−	7.76202i	0.216617	−	0.375191i
$429$	−1.01667	+	16.9155i	−0.0490853	+	0.816689i
$430$	7.30292	+	12.6490i	0.352178	+	0.609990i
$431$	−29.8506	−	17.2343i	−1.43785	−	0.830145i	−0.440152	−	0.897923i	$-0.645076\pi$
$431$	−29.8506	−	17.2343i	−1.43785	−	0.830145i	−0.997700	+	0.0677785i	$0.978409\pi$
$432$	2.84637	+	1.29500i	0.136946	+	0.0623056i
$433$	7.36538	+	12.7572i	0.353957	+	0.613072i	0.986939	−	0.161095i	$-0.0515024\pi$
$433$	7.36538	+	12.7572i	0.353957	+	0.613072i	−0.632982	+	0.774167i	$0.718169\pi$
$434$	32.3253	−	18.6630i	1.55166	−	0.895854i
$435$	−2.66672	+	18.6102i	−0.127859	+	0.892290i
$436$			28.0167i			1.34176i
$437$	1.24061	+	0.716269i	0.0593466	+	0.0342638i
$438$	−11.8812	−	29.6371i	−0.567707	−	1.41611i
$439$	−2.54507			−0.121470			−0.0607349	−	0.998154i	$-0.519344\pi$
$439$	−2.54507			−0.121470			−0.0607349	+	0.998154i	$0.519344\pi$
$440$	−9.40890	−	5.43223i	−0.448552	−	0.258971i
$441$	−30.0393	−	8.78935i	−1.43044	−	0.418540i
$442$	−1.44328	−	17.4985i	−0.0686500	−	0.832317i
$443$	−15.7844	−	27.3394i	−0.749941	−	1.29894i	−0.947850	−	0.318716i	$-0.896748\pi$
$443$	−15.7844	−	27.3394i	−0.749941	−	1.29894i	0.197909	−	0.980220i	$-0.436585\pi$
$444$	−7.21225	+	50.3319i	−0.342278	+	2.38865i
$445$	−0.962124	−	1.66645i	−0.0456091	−	0.0789972i
$446$	51.6136			2.44398
$447$	−34.8915	+	13.9877i	−1.65031	+	0.661595i
$448$	45.7219	+	26.3975i	2.16015	+	1.24717i
$449$	−22.0161	+	12.7110i	−1.03900	+	0.599869i	−0.919551	−	0.392971i	$-0.871447\pi$
$449$	−22.0161	+	12.7110i	−1.03900	+	0.599869i	−0.119453	+	0.992840i	$0.538114\pi$
$450$	6.63797	−	22.6865i	0.312917	−	1.06945i
$451$	−3.40707	−	5.90122i	−0.160433	−	0.277878i
$452$	−11.8379			−0.556810
$453$	−3.68249	−	2.89311i	−0.173018	−	0.135930i
$454$	4.86713	−	8.43012i	0.228426	−	0.395645i
$455$	−18.9709	+	1.56473i	−0.889370	+	0.0733557i
$456$	−10.7294	+	13.6569i	−0.502451	+	0.639543i
$457$			22.7357i			1.06353i	0.846892	+	0.531765i	$0.178471\pi$
$457$			22.7357i			1.06353i	−0.846892	+	0.531765i	$0.821529\pi$
$458$	−26.4809	+	45.8663i	−1.23737	+	2.14319i
$459$	1.05374	+	10.8716i	0.0491845	+	0.507443i
$460$		−	1.92584i		−	0.0897927i
$461$	17.6899	+	10.2133i	0.823901	+	0.475679i	0.851760	−	0.523933i	$-0.175536\pi$
$461$	17.6899	+	10.2133i	0.823901	+	0.475679i	−0.0278591	+	0.999612i	$0.508869\pi$
$462$	−6.44842	+	45.0014i	−0.300008	+	2.09366i
$463$	4.68063	+	2.70237i	0.217528	+	0.125590i	0.604805	−	0.796374i	$-0.293251\pi$
$463$	4.68063	+	2.70237i	0.217528	+	0.125590i	−0.387277	+	0.921963i	$0.626584\pi$
$464$	5.16608			0.239829
$465$	−5.22121	+	6.64580i	−0.242128	+	0.308192i
$466$		−	40.0482i		−	1.85519i
$467$	10.0719			0.466072			0.233036	−	0.972468i	$-0.425134\pi$
$467$	10.0719			0.466072			0.233036	+	0.972468i	$0.425134\pi$
$468$	−11.4988	−	34.5547i	−0.531530	−	1.59729i
$469$	−59.2154			−2.73431
$470$		−	36.5670i		−	1.68671i
$471$	26.8626	+	3.84924i	1.23776	+	0.177364i
$472$	−20.0246			−0.921709
$473$	−11.7174	−	6.76504i	−0.538766	−	0.311057i
$474$	11.5160	+	9.04741i	0.528946	+	0.415561i
$475$	9.32750	+	5.38524i	0.427975	+	0.247092i
$476$		−	29.5493i		−	1.35439i
$477$	2.48525	−	2.37419i	0.113792	−	0.108707i
$478$	7.50818	−	13.0046i	0.343416	−	0.594814i
$479$			22.3975i			1.02337i	0.859173	+	0.511685i	$0.170978\pi$
$479$			22.3975i			1.02337i	−0.859173	+	0.511685i	$0.829022\pi$
$480$	−10.7068	−	1.53421i	−0.488696	−	0.0700270i
$481$	25.8415	−	17.9036i	1.17827	−	0.816333i
$482$	−0.213092	+	0.369085i	−0.00970605	+	0.0168114i
$483$	−3.03655	+	1.21732i	−0.138168	+	0.0553901i
$484$	−12.2441			−0.556551
$485$	1.50837	+	2.61258i	0.0684917	+	0.118631i
$486$	11.8923	+	34.0985i	0.539448	+	1.54674i
$487$	−1.75362	+	1.01245i	−0.0794641	+	0.0458786i	−0.539206	−	0.842174i	$-0.681275\pi$
$487$	−1.75362	+	1.01245i	−0.0794641	+	0.0458786i	0.459741	+	0.888053i	$0.347942\pi$
$488$	13.9755	+	8.06875i	0.632641	+	0.365255i
$489$	9.02347	+	7.08920i	0.408055	+	0.320585i
$490$	−30.5610			−1.38061
$491$	−1.52809	−	2.64673i	−0.0689618	−	0.119445i	0.829483	−	0.558532i	$-0.188635\pi$
$491$	−1.52809	−	2.64673i	−0.0689618	−	0.119445i	−0.898445	+	0.439087i	$0.855302\pi$
$492$	11.5151	+	9.04676i	0.519143	+	0.407860i
$493$	9.02218	+	15.6269i	0.406339	+	0.703799i
$494$	26.3613	−	2.17429i	1.18605	−	0.0978261i
$495$	−2.43627	−	10.0010i	−0.109502	−	0.449511i
$496$	2.01123	+	1.16118i	0.0903068	+	0.0521387i
$497$	−31.3225			−1.40501
$498$	−5.61040	+	7.14118i	−0.251408	+	0.320004i
$499$	17.6833	+	10.2094i	0.791613	+	0.457038i	0.840530	−	0.541765i	$-0.182244\pi$
$499$	17.6833	+	10.2094i	0.791613	+	0.457038i	−0.0489173	+	0.998803i	$0.515577\pi$
$500$		−	35.7653i		−	1.59947i
$501$	14.7014	+	11.5500i	0.656812	+	0.516018i
$502$	−47.3490	+	27.3370i	−2.11329	+	1.22011i
$503$	1.22893	+	2.12856i	0.0547951	+	0.0949080i	0.892122	−	0.451795i	$-0.149216\pi$
$503$	1.22893	+	2.12856i	0.0547951	+	0.0949080i	−0.837327	+	0.546703i	$0.815883\pi$
$504$	−9.38726	−	38.5351i	−0.418142	−	1.71649i
$505$	12.2623	+	7.07967i	0.545667	+	0.315041i
$506$	1.42187	+	2.46276i	0.0632100	+	0.109483i
$507$	−10.8214	+	19.7458i	−0.480597	+	0.876942i
$508$	−26.4966	+	45.8934i	−1.17559	+	2.03619i
$509$	34.2026	−	19.7469i	1.51600	−	0.875265i	0.516181	−	0.856480i	$-0.327353\pi$
$509$	34.2026	−	19.7469i	1.51600	−	0.875265i	0.999824	−	0.0187855i	$-0.00597997\pi$
$510$	3.96852	+	9.89926i	0.175729	+	0.438347i
$511$	−16.6125	+	28.7736i	−0.734892	+	1.27287i
$512$			6.78333i			0.299784i
$513$	−16.3780	+	1.58746i	−0.723106	+	0.0700879i
$514$	11.7363	−	6.77597i	0.517667	−	0.298875i
$515$	3.19222	−	1.84303i	0.140666	−	0.0812136i
$516$	28.7826	+	4.12437i	1.26708	+	0.181565i
$517$	16.9369	+	29.3355i	0.744882	+	1.29017i
$518$	73.0384	−	42.1687i	3.20912	−	1.85279i
$519$	8.36111	+	1.19809i	0.367012	+	0.0525905i
$520$	−8.22119	−	11.8662i	−0.360523	−	0.520368i
$521$	33.5976			1.47194			0.735970	−	0.677015i	$-0.236727\pi$
$521$	33.5976			1.47194			0.735970	+	0.677015i	$0.236727\pi$
$522$	41.2107	+	43.1384i	1.80374	+	1.88812i
$523$	3.09661	−	5.36349i	0.135405	−	0.234529i	−0.790347	−	0.612660i	$-0.790100\pi$
$523$	3.09661	−	5.36349i	0.135405	−	0.234529i	0.925752	+	0.378131i	$0.123433\pi$
$524$	22.9649	−	39.7763i	1.00322	−	1.73764i
$525$	−22.8301	+	9.15239i	−0.996389	+	0.399443i
$526$			22.4671i			0.979612i
$527$			8.11169i			0.353351i
$528$	−2.62540	+	1.05250i	−0.114256	+	0.0458042i
$529$	11.3977	−	19.7414i	0.495551	−	0.858320i
$530$	1.67802	−	2.90641i	0.0728884	−	0.126246i
$531$	−13.1054	−	13.7184i	−0.568724	−	0.595327i
$532$	44.5157			1.93000
$533$	−0.744262	−	9.02350i	−0.0322376	−	0.390851i
$534$	−6.04453	−	0.866143i	−0.261572	−	0.0374817i
$535$	2.91514	−	1.68306i	0.126033	−	0.0727649i
$536$	−22.4537	−	38.8909i	−0.969852	−	1.67983i
$537$	−22.6884	−	3.25110i	−0.979075	−	0.140295i
$538$	−42.0192	+	24.2598i	−1.81157	+	1.04591i
$539$	24.5173	−	14.1551i	1.05603	−	0.609701i
$540$	12.8571	+	18.0010i	0.553282	+	0.774638i
$541$		−	13.3436i		−	0.573685i	−0.957978	−	0.286843i	$-0.907394\pi$
$541$		−	13.3436i		−	0.573685i	0.957978	−	0.286843i	$-0.0926057\pi$
$542$	6.66857	−	11.5503i	0.286439	−	0.496128i
$543$	11.7446	+	29.2962i	0.504008	+	1.25722i
$544$	−8.99045	+	5.19064i	−0.385462	+	0.222547i
$545$	−5.26105	+	9.11240i	−0.225358	+	0.390332i
$546$	−33.2868	+	50.4064i	−1.42454	+	2.15719i
$547$	−2.28845	−	3.96371i	−0.0978471	−	0.169476i	0.812946	−	0.582339i	$-0.197862\pi$
$547$	−2.28845	−	3.96371i	−0.0978471	−	0.169476i	−0.910793	+	0.412863i	$0.864529\pi$
$548$	−33.3966	−	19.2815i	−1.42663	−	0.823665i
$549$	3.61872	+	14.8550i	0.154443	+	0.633994i
$550$	10.6903	+	18.5161i	0.455836	+	0.789531i
$551$	−23.5418	+	13.5918i	−1.00291	+	0.579032i
$552$	−1.95092	−	1.53272i	−0.0830367	−	0.0652370i
$553$		−	15.2389i		−	0.648022i
$554$	−32.0997	−	18.5328i	−1.36379	−	0.787382i
$555$	−11.7972	+	15.0161i	−0.500764	+	0.637396i
$556$	−16.3167			−0.691984
$557$	−31.3528	−	18.1016i	−1.32846	−	0.766988i	−0.343400	−	0.939189i	$-0.611579\pi$
$557$	−31.3528	−	18.1016i	−1.32846	−	0.766988i	−0.985062	+	0.172201i	$0.944912\pi$
$558$	6.34765	+	26.0573i	0.268718	+	1.10310i
$559$	−10.2383	−	14.7776i	−0.433033	−	0.625026i
$560$	−1.58862	−	2.75158i	−0.0671316	−	0.116275i
$561$	−7.76878	−	6.10347i	−0.327998	−	0.257689i
$562$	−21.7289	−	37.6355i	−0.916576	−	1.58756i
$563$	40.6641			1.71379			0.856894	−	0.515493i	$-0.172391\pi$
$563$	40.6641			1.71379			0.856894	+	0.515493i	$0.172391\pi$
$564$	−57.2428	−	44.9722i	−2.41035	−	1.89367i
$565$	−3.85027	−	2.22296i	−0.161982	−	0.0935204i
$566$	9.07498	−	5.23944i	0.381450	−	0.220230i
$567$	20.2558	−	31.6507i	0.850665	−	1.32920i
$568$	−11.8771	−	20.5717i	−0.498352	−	0.863171i
$569$	−17.0153			−0.713318			−0.356659	−	0.934235i	$-0.616084\pi$
$569$	−17.0153			−0.713318			−0.356659	+	0.934235i	$0.616084\pi$
$570$	−14.9132	+	5.97855i	−0.624644	+	0.250414i
$571$	−11.0113	+	19.0721i	−0.460809	+	0.798144i	−0.999001	−	0.0446778i	$-0.985774\pi$
$571$	−11.0113	+	19.0721i	−0.460809	+	0.798144i	0.538193	+	0.842822i	$0.319107\pi$
$572$	29.7844	+	14.0694i	1.24535	+	0.588272i
$573$	26.3538	+	3.77633i	1.10095	+	0.157759i
$574$		−	24.2895i		−	1.01382i
$575$	−0.769294	+	1.33246i	−0.0320818	+	0.0555673i
$576$	−27.4293	+	26.2036i	−1.14289	+	1.09182i
$577$		−	8.16526i		−	0.339924i	−0.985451	−	0.169962i	$-0.945635\pi$
$577$		−	8.16526i		−	0.339924i	0.985451	−	0.169962i	$-0.0543645\pi$
$578$	−25.2417	−	14.5733i	−1.04991	−	0.606168i
$579$	7.70022	+	6.04960i	0.320010	+	0.251413i
$580$	31.6485	+	18.2723i	1.31413	+	0.758715i
$581$	9.44979			0.392043
$582$	9.47633	+	1.35790i	0.392807	+	0.0562867i
$583$			3.10885i			0.128755i
$584$	−25.1969			−1.04266
$585$	2.74880	−	13.3981i	0.113649	−	0.553944i
$586$	−0.733734			−0.0303103
$587$			10.6730i			0.440524i	0.975441	+	0.220262i	$0.0706912\pi$
$587$			10.6730i			0.440524i	−0.975441	+	0.220262i	$0.929309\pi$
$588$	−37.5857	+	47.8409i	−1.55001	+	1.97293i
$589$	−12.2202			−0.503524
$590$	−16.0431	−	9.26251i	−0.660486	−	0.381332i
$591$	1.54930	−	10.8121i	0.0637297	−	0.444749i
$592$	4.54433	+	2.62367i	0.186771	+	0.107832i
$593$			9.84678i			0.404359i	0.979348	+	0.202179i	$0.0648024\pi$
$593$			9.84678i			0.404359i	−0.979348	+	0.202179i	$0.935198\pi$
$594$	−29.7320	−	13.5270i	−1.21992	−	0.555019i
$595$	5.54883	−	9.61085i	0.227480	−	0.394007i
$596$			73.0704i			2.99308i
$597$	−1.81842	+	2.31457i	−0.0744230	+	0.0947291i
$598$	0.310603	+	3.76578i	0.0127015	+	0.153994i
$599$	6.98478	−	12.0980i	0.285391	−	0.494311i	−0.687313	−	0.726361i	$-0.741210\pi$
$599$	6.98478	−	12.0980i	0.285391	−	0.494311i	0.972704	+	0.232050i	$0.0745434\pi$
$600$	−14.6679	−	11.5237i	−0.598815	−	0.470453i
$601$	−40.7185			−1.66094			−0.830471	−	0.557062i	$-0.811928\pi$
$601$	−40.7185			−1.66094			−0.830471	+	0.557062i	$0.811928\pi$
$602$	−24.1144	−	41.7674i	−0.982831	−	1.70231i
$603$	11.9482	−	40.8351i	0.486566	−	1.66293i
$604$	−7.88345	+	4.55151i	−0.320773	+	0.185198i
$605$	−3.98238	−	2.29923i	−0.161907	−	0.0934770i
$606$	41.7057	−	16.7194i	1.69418	−	0.679180i
$607$	−44.3369			−1.79958			−0.899789	−	0.436325i	$-0.856280\pi$
$607$	−44.3369			−1.79958			−0.899789	+	0.436325i	$0.856280\pi$
$608$	−7.81965	−	13.5440i	−0.317129	−	0.549283i
$609$	8.80559	−	61.4513i	0.356820	−	2.49013i
$610$	7.46450	+	12.9289i	0.302229	+	0.523476i
$611$	3.69979	+	44.8566i	0.149678	+	1.81470i
$612$	20.3773	+	5.96229i	0.823702	+	0.241011i
$613$	7.43045	+	4.28997i	0.300113	+	0.173270i	0.642494	−	0.766291i	$-0.277900\pi$
$613$	7.43045	+	4.28997i	0.300113	+	0.173270i	−0.342381	+	0.939561i	$0.611233\pi$
$614$	26.1432			1.05505
$615$	2.04646	+	5.10479i	0.0825213	+	0.205845i
$616$	31.0685	+	17.9374i	1.25178	+	0.722718i
$617$			43.1003i			1.73515i	0.497306	+	0.867575i	$0.334323\pi$
$617$			43.1003i			1.73515i	−0.497306	+	0.867575i	$0.665677\pi$
$618$	1.65917	−	11.5788i	0.0667416	−	0.465768i
$619$	40.7267	−	23.5136i	1.63694	−	0.945090i	0.655067	−	0.755570i	$-0.272640\pi$
$619$	40.7267	−	23.5136i	1.63694	−	0.945090i	0.981877	−	0.189520i	$-0.0606932\pi$
$620$	8.21414	+	14.2273i	0.329888	+	0.571382i
$621$	−0.226772	−	2.33964i	−0.00910004	−	0.0938863i
$622$	−63.8274	−	36.8508i	−2.55925	−	1.47758i
$623$	3.17696	+	5.50266i	0.127282	+	0.220459i
$624$	−3.75156	−	0.225479i	−0.150182	−	0.00902639i
$625$	−1.78678	+	3.09479i	−0.0714711	+	0.123792i
$626$	−0.297250	+	0.171617i	−0.0118805	+	0.00685921i
$627$	9.19483	−	11.7036i	0.367206	−	0.467397i
$628$	26.3749	−	45.6827i	1.05247	−	1.82294i
$629$			18.3282i			0.730793i
$630$	10.3038	−	35.2153i	0.410514	−	1.40301i
$631$	24.6130	−	14.2103i	0.979828	−	0.565704i	0.0776098	−	0.996984i	$-0.475271\pi$
$631$	24.6130	−	14.2103i	0.979828	−	0.565704i	0.902218	+	0.431280i	$0.141938\pi$
$632$	10.0084	−	5.77837i	0.398114	−	0.229851i
$633$	−4.88355	+	6.21601i	−0.194104	+	0.247064i
$634$	−22.8661	−	39.6052i	−0.908127	−	1.57292i
$635$	−17.2359	+	9.95117i	−0.683987	+	0.394900i
$636$	−2.48603	−	6.20128i	−0.0985777	−	0.245897i
$637$	37.4891	−	3.09212i	1.48537	−	0.122514i
$638$	−53.9627			−2.13640
$639$	6.32009	−	21.6001i	0.250019	−	0.854487i
$640$	−12.2753	+	21.2614i	−0.485223	+	0.840431i
$641$	−8.35316	+	14.4681i	−0.329930	+	0.571455i	−0.982498	−	0.186275i	$-0.940358\pi$
$641$	−8.35316	+	14.4681i	−0.329930	+	0.571455i	0.652568	+	0.757730i	$0.273692\pi$
$642$	1.51516	−	10.5738i	0.0597984	−	0.417314i
$643$		−	19.8842i		−	0.784154i	−0.919932	−	0.392077i	$-0.871757\pi$
$643$		−	19.8842i		−	0.784154i	0.919932	−	0.392077i	$-0.128243\pi$
$644$			6.35918i			0.250587i
$645$	8.58702	+	6.74631i	0.338114	+	0.265636i
$646$	−7.71045	+	13.3549i	−0.303364	+	0.525441i
$647$	4.08938	−	7.08301i	0.160770	−	0.278462i	−0.774375	−	0.632727i	$-0.781936\pi$
$647$	4.08938	−	7.08301i	0.160770	−	0.278462i	0.935145	+	0.354265i	$0.115269\pi$
$648$	28.4680	+	1.30191i	1.11833	+	0.0511437i
$649$	17.1606			0.673613
$650$	2.33526	+	28.3128i	0.0915963	+	1.11052i
$651$	17.2406	−	21.9446i	0.675712	−	0.860078i
$652$	19.3174	−	11.1529i	0.756528	−	0.436782i
$653$	10.8786	+	18.8423i	0.425713	+	0.737356i	0.996487	−	0.0837510i	$-0.0266901\pi$
$653$	10.8786	+	18.8423i	0.425713	+	0.737356i	−0.570774	+	0.821107i	$0.693357\pi$
$654$	12.4245	+	30.9924i	0.485838	+	1.21190i
$655$	14.9386	−	8.62479i	0.583698	−	0.336998i
$656$	1.30878	−	0.755627i	0.0510994	−	0.0295023i
$657$	−16.4904	−	17.2618i	−0.643352	−	0.673446i
$658$			120.745i			4.70714i
$659$	−18.7070	+	32.4015i	−0.728723	+	1.26219i	0.228700	+	0.973497i	$0.426552\pi$
$659$	−18.7070	+	32.4015i	−0.728723	+	1.26219i	−0.957423	+	0.288688i	$0.906781\pi$
$660$	−19.8064	−	2.83814i	−0.770965	−	0.110474i
$661$	−7.28421	+	4.20554i	−0.283323	+	0.163576i	−0.634927	−	0.772572i	$-0.718970\pi$
$661$	−7.28421	+	4.20554i	−0.283323	+	0.163576i	0.351604	+	0.936149i	$0.385636\pi$
$662$	−19.7235	+	34.1621i	−0.766575	+	1.32775i
$663$	−5.86977	−	11.7419i	−0.227963	−	0.456016i
$664$	3.58324	+	6.20635i	0.139057	+	0.240853i
$665$	14.4787	+	8.35927i	0.561459	+	0.324158i
$666$	14.3424	+	58.8761i	0.555757	+	2.28140i
$667$	−1.94163	−	3.36300i	−0.0751801	−	0.130216i
$668$	31.4728	−	18.1708i	1.21772	−	0.703050i
$669$	35.8182	−	14.3592i	1.38481	−	0.555159i
$670$		−	41.5444i		−	1.60500i
$671$	−11.9766	−	6.91472i	−0.462353	−	0.266940i
$672$	35.3541	+	5.06602i	1.36382	+	0.195426i
$673$	32.9364			1.26961			0.634803	−	0.772674i	$-0.281081\pi$
$673$	32.9364			1.26961			0.634803	+	0.772674i	$0.281081\pi$
$674$	−26.2510	−	15.1560i	−1.01115	−	0.583789i
$675$	−1.70498	−	17.5905i	−0.0656245	−	0.677057i
$676$	27.7991	+	33.8068i	1.06920	+	1.30026i
$677$	−0.651673	−	1.12873i	−0.0250458	−	0.0433806i	0.853231	−	0.521533i	$-0.174640\pi$
$677$	−0.651673	−	1.12873i	−0.0250458	−	0.0433806i	−0.878277	+	0.478153i	$0.841306\pi$
$678$	−13.0952	+	5.24976i	−0.502919	+	0.201616i
$679$	−4.98069	−	8.62681i	−0.191141	−	0.331067i
$680$	8.41617			0.322745
$681$	1.03233	−	7.20430i	0.0395590	−	0.276070i
$682$	−21.0084	−	12.1292i	−0.804455	−	0.464452i
$683$	−0.152548	+	0.0880738i	−0.00583710	+	0.00337005i	−0.502916	−	0.864335i	$-0.667739\pi$
$683$	−0.152548	+	0.0880738i	−0.00583710	+	0.00337005i	0.497079	+	0.867706i	$0.334406\pi$
$684$	−8.98214	+	30.6982i	−0.343441	+	1.17377i
$685$	−7.24145	−	12.5426i	−0.276682	−	0.479227i
$686$	33.2052			1.26778
$687$	−5.61667	+	39.1969i	−0.214289	+	1.49546i
$688$	1.50036	−	2.59870i	0.0572008	−	0.0990746i
$689$	−1.76435	+	3.73506i	−0.0672164	+	0.142294i
$690$	−0.854050	−	2.13038i	−0.0325131	−	0.0811022i
$691$			2.82413i			0.107435i	0.998556	+	0.0537175i	$0.0171070\pi$
$691$			2.82413i			0.107435i	−0.998556	+	0.0537175i	$0.982893\pi$
$692$	8.20930	−	14.2189i	0.312071	−	0.540523i
$693$	8.04465	+	33.0236i	0.305591	+	1.25446i
$694$		−	34.7312i		−	1.31838i
$695$	−5.30700	−	3.06400i	−0.201306	−	0.116224i
$696$	43.6984	−	17.5183i	1.65638	−	0.664029i
$697$	4.57139	+	2.63929i	0.173154	+	0.0999704i
$698$	4.83000			0.182818
$699$	−11.1416	−	27.7922i	−0.421415	−	1.05120i
$700$			47.8112i			1.80709i
$701$	30.2245			1.14156			0.570782	−	0.821102i	$-0.306640\pi$
$701$	30.2245			1.14156			0.570782	+	0.821102i	$0.306640\pi$
$702$	−28.0439	−	33.1254i	−1.05845	−	1.25024i
$703$	−27.6113			−1.04138
$704$		−	34.3119i		−	1.29318i
$705$	−10.1731	−	25.3763i	−0.383142	−	0.955728i
$706$	−9.57861			−0.360496
$707$	−40.4906	−	23.3773i	−1.52281	−	0.879193i
$708$	−34.2306	+	13.7227i	−1.28646	+	0.515731i
$709$	−8.86277	−	5.11692i	−0.332848	−	0.192170i	0.324257	−	0.945969i	$-0.394886\pi$
$709$	−8.86277	−	5.11692i	−0.332848	−	0.192170i	−0.657105	+	0.753799i	$0.728219\pi$
$710$		−	21.9753i		−	0.824718i
$711$	10.5088	+	3.07481i	0.394109	+	0.115314i
$712$	−2.40932	+	4.17307i	−0.0902932	+	0.156392i
$713$		−	1.74568i		−	0.0653764i
$714$	−13.1042	−	32.6877i	−0.490412	−	1.22330i
$715$	7.04535	+	10.1690i	0.263481	+	0.380301i
$716$	−22.2764	+	38.5839i	−0.832508	+	1.44195i
$717$	1.59250	−	11.1136i	0.0594731	−	0.415044i
$718$	47.6726			1.77912
$719$	−15.5196	−	26.8808i	−0.578785	−	1.00248i	−0.995619	−	0.0935023i	$-0.970194\pi$
$719$	−15.5196	−	26.8808i	−0.578785	−	1.00248i	0.416834	−	0.908983i	$-0.363140\pi$
$720$	2.21804	−	0.540321i	0.0826614	−	0.0201366i
$721$	−10.5408	+	6.08574i	−0.392560	+	0.226645i
$722$	18.0000	+	10.3923i	0.669892	+	0.386763i
$723$	−0.0451972	+	0.315417i	−0.00168090	+	0.0117305i
$724$	61.3525			2.28015
$725$	−14.5981	−	25.2846i	−0.542158	−	0.939045i
$726$	−13.5446	+	5.42989i	−0.502686	+	0.201522i
$727$	−12.3666	−	21.4195i	−0.458650	−	0.794406i	0.540240	−	0.841511i	$-0.318334\pi$
$727$	−12.3666	−	21.4195i	−0.458650	−	0.794406i	−0.998890	+	0.0471055i	$0.985000\pi$
$728$	27.1466	+	39.1826i	1.00612	+	1.45220i
$729$	17.7393	+	20.3548i	0.657011	+	0.753881i
$730$	−20.1870	−	11.6550i	−0.747155	−	0.431370i
$731$	10.4811			0.387657
$732$	29.4195	+	4.21562i	1.08737	+	0.155814i
$733$	−32.6554	−	18.8536i	−1.20616	−	0.696375i	−0.244239	−	0.969715i	$-0.578538\pi$
$733$	−32.6554	−	18.8536i	−1.20616	−	0.696375i	−0.961917	+	0.273341i	$0.911871\pi$
$734$			33.9999i			1.25496i
$735$	−21.2084	+	8.50224i	−0.782283	+	0.313610i
$736$	1.93480	−	1.11706i	0.0713176	−	0.0411752i
$737$	19.2422	+	33.3285i	0.708797	+	1.22767i
$738$	16.7501	+	4.90100i	0.616580	+	0.180408i
$739$	23.9351	+	13.8189i	0.880468	+	0.508338i	0.870813	−	0.491615i	$-0.163593\pi$
$739$	23.9351	+	13.8189i	0.880468	+	0.508338i	0.00965499	+	0.999953i	$0.496927\pi$
$740$	18.5597	+	32.1463i	0.682268	+	1.18172i
$741$	17.6890	−	8.84275i	0.649822	−	0.324847i
$742$	−5.54086	+	9.59705i	−0.203411	+	0.352319i
$743$	−8.42399	+	4.86359i	−0.309046	+	0.178428i	−0.646500	−	0.762914i	$-0.723768\pi$
$743$	−8.42399	+	4.86359i	−0.309046	+	0.178428i	0.337453	+	0.941342i	$0.390434\pi$
$744$	20.9500	+	3.00200i	0.768064	+	0.110059i
$745$	−13.7213	+	23.7660i	−0.502711	+	0.870720i
$746$			69.0167i			2.52688i
$747$	−1.90673	+	6.51660i	−0.0697635	+	0.238430i
$748$	−16.6314	+	9.60213i	−0.608104	+	0.351089i
$749$	−9.62588	+	5.55751i	−0.351722	+	0.203067i
$750$	−15.8608	−	39.5639i	−0.579155	−	1.44467i
$751$	13.6290	+	23.6061i	0.497329	+	0.861399i	0.999995	−	0.00308143i	$-0.000980852\pi$
$751$	13.6290	+	23.6061i	0.497329	+	0.861399i	−0.502666	+	0.864481i	$0.667648\pi$
$752$	−6.50608	+	3.75629i	−0.237252	+	0.136978i
$753$	−25.2534	+	32.1438i	−0.920287	+	1.17138i
$754$	−64.8323	−	30.6252i	−2.36105	−	1.11530i
$755$	−3.41878			−0.124422
$756$	−42.4545	−	59.4397i	−1.54406	−	2.16180i
$757$	−16.3688	+	28.3517i	−0.594936	+	1.03046i	0.398620	+	0.917116i	$0.369489\pi$
$757$	−16.3688	+	28.3517i	−0.594936	+	1.03046i	−0.993556	+	0.113343i	$0.963844\pi$
$758$	−15.4602	+	26.7779i	−0.561541	+	0.972618i
$759$	1.67189	+	1.31350i	0.0606857	+	0.0476772i
$760$			12.6789i			0.459912i
$761$		−	46.5350i		−	1.68689i	−0.537213	−	0.843447i	$-0.680523\pi$
$761$		−	46.5350i		−	1.68689i	0.537213	−	0.843447i	$-0.319477\pi$
$762$	−8.95844	+	62.5181i	−0.324530	+	2.26479i
$763$	17.3721	−	30.0894i	0.628913	−	1.08931i
$764$	25.8753	−	44.8173i	0.936136	−	1.62143i
$765$	5.50806	+	5.76571i	0.199144	+	0.208460i
$766$	6.83269			0.246875
$767$	20.6172	+	9.73907i	0.744445	+	0.351657i
$768$	12.6904	+	31.6555i	0.457924	+	1.14227i
$769$	14.3504	−	8.28520i	0.517488	−	0.298772i	−0.218418	−	0.975855i	$-0.570090\pi$
$769$	14.3504	−	8.28520i	0.517488	−	0.298772i	0.735906	+	0.677083i	$0.236756\pi$
$770$	16.5941	+	28.7418i	0.598009	+	1.03578i
$771$	6.25953	−	7.96742i	0.225431	−	0.286940i
$772$	16.4846	−	9.51738i	0.593293	−	0.342538i
$773$	2.28752	−	1.32070i	0.0822764	−	0.0475023i	−0.458297	−	0.888799i	$-0.651541\pi$
$773$	2.28752	−	1.32070i	0.0822764	−	0.0475023i	0.540574	+	0.841297i	$0.318207\pi$
$774$	33.6686	−	8.20179i	1.21019	−	0.294807i
$775$		−	13.1249i		−	0.471459i
$776$	3.77722	−	6.54235i	0.135594	−	0.234857i
$777$	38.9548	−	49.5835i	1.39749	−	1.77880i
$778$	33.3655	−	19.2636i	1.19621	−	0.690633i
$779$	−3.97608	+	6.88677i	−0.142458	+	0.246744i
$780$	−22.1853	−	14.6505i	−0.794361	−	0.524571i
$781$	10.1784	+	17.6294i	0.364211	+	0.630831i
$782$	−1.90778	−	1.10146i	−0.0682220	−	0.0393880i
$783$	40.6003	+	18.4717i	1.45094	+	0.660124i
$784$	3.13933	+	5.43748i	0.112119	+	0.194196i
$785$	17.1568	−	9.90548i	0.612352	−	0.353542i
$786$	7.76438	−	54.1851i	0.276946	−	1.93272i
$787$		−	7.13493i		−	0.254333i	−0.991881	−	0.127166i	$-0.959412\pi$
$787$		−	7.13493i		−	0.254333i	0.991881	−	0.127166i	$-0.0405882\pi$
$788$	−18.3870	−	10.6158i	−0.655011	−	0.378171i
$789$	6.25047	+	15.5915i	0.222523	+	0.555071i
$790$	10.6913			0.380379
$791$	12.7137	+	7.34026i	0.452047	+	0.260990i
$792$	−18.6385	+	17.8056i	−0.662290	+	0.632694i
$793$	−10.4648	−	15.1046i	−0.371616	−	0.536379i
$794$	−6.99729	−	12.1197i	−0.248324	−	0.430111i
$795$	0.355911	−	2.48379i	0.0126229	−	0.0880910i
$796$	2.86079	+	4.95503i	0.101398	+	0.175626i
$797$	−28.8171			−1.02075			−0.510376	−	0.859951i	$-0.670494\pi$
$797$	−28.8171			−1.02075			−0.510376	+	0.859951i	$0.670494\pi$
$798$	49.2437	−	19.7413i	1.74321	−	0.698836i
$799$	−22.7248	−	13.1202i	−0.803945	−	0.464158i
$800$	14.5467	−	8.39854i	0.514303	−	0.296933i
$801$	−4.43568	+	1.08055i	−0.156727	+	0.0381792i
$802$	16.6140	+	28.7763i	0.586662	+	1.01613i
$803$	21.5931			0.762004
$804$	−65.0345	−	51.0937i	−2.29359	−	1.80194i
$805$	−1.19414	+	2.06831i	−0.0420880	+	0.0728985i
$806$	−18.3565	−	26.4952i	−0.646580	−	0.933254i
$807$	−22.4108	+	28.5255i	−0.788897	+	1.00414i
$808$		−	35.4574i		−	1.24739i
$809$	−3.89514	+	6.74657i	−0.136946	+	0.237197i	−0.926339	−	0.376691i	$-0.877062\pi$
$809$	−3.89514	+	6.74657i	−0.136946	+	0.237197i	0.789393	+	0.613888i	$0.210395\pi$
$810$	22.2055	+	14.2111i	0.780222	+	0.499327i
$811$			43.2768i			1.51965i	0.650125	+	0.759827i	$0.274717\pi$
$811$			43.2768i			1.51965i	−0.650125	+	0.759827i	$0.725283\pi$
$812$	−104.504	−	60.3356i	−3.66738	−	2.11736i
$813$	1.41442	−	9.87077i	0.0496058	−	0.346183i
$814$	−47.4682	−	27.4058i	−1.66376	−	0.960571i
$815$	8.37728			0.293443
$816$	1.35364	−	1.72298i	0.0473868	−	0.0603162i
$817$			15.7897i			0.552411i
$818$	14.2747			0.499103
$819$	−9.07663	+	44.2410i	−0.317163	+	1.54591i
$820$	10.6905			0.373329
$821$		−	45.7795i		−	1.59772i	−0.601520	−	0.798858i	$-0.705438\pi$
$821$		−	45.7795i		−	1.59772i	0.601520	−	0.798858i	$-0.294562\pi$
$822$	−45.4943	−	6.51905i	−1.58680	−	0.227378i
$823$	19.2340			0.670453			0.335227	−	0.942137i	$-0.391187\pi$
$823$	19.2340			0.670453			0.335227	+	0.942137i	$0.391187\pi$
$824$	−7.99387	−	4.61526i	−0.278480	−	0.160780i
$825$	12.5700	+	9.87552i	0.437632	+	0.343822i
$826$	52.9749	+	30.5851i	1.84323	+	1.06419i
$827$			34.1215i			1.18652i	0.805010	+	0.593261i	$0.202160\pi$
$827$			34.1215i			1.18652i	−0.805010	+	0.593261i	$0.797840\pi$
$828$	−4.38531	−	1.28312i	−0.152400	−	0.0445915i
$829$	21.0159	−	36.4006i	0.729913	−	1.26425i	−0.227007	−	0.973893i	$-0.572894\pi$
$829$	21.0159	−	36.4006i	0.729913	−	1.26425i	0.956920	−	0.290353i	$-0.0937727\pi$
$830$			6.62979i			0.230123i
$831$	−27.4321	−	3.93085i	−0.951610	−	0.136360i
$832$	19.4728	−	41.2232i	0.675099	−	1.42916i
$833$	−10.9652	+	18.9923i	−0.379923	+	0.658046i
$834$	−18.0497	+	7.23597i	−0.625011	+	0.250561i
$835$	13.6486			0.472330
$836$	−14.4655	−	25.0550i	−0.500301	−	0.866547i
$837$	11.6544	+	16.3170i	0.402834	+	0.563999i
$838$	27.8562	−	16.0828i	0.962276	−	0.555570i
$839$	−20.8519	−	12.0388i	−0.719887	−	0.415627i	0.0948242	−	0.995494i	$-0.469771\pi$
$839$	−20.8519	−	12.0388i	−0.719887	−	0.415627i	−0.814711	+	0.579867i	$0.803104\pi$
$840$	−22.7684	−	17.8877i	−0.785583	−	0.617186i
$841$	44.6883			1.54098
$842$	6.08844	+	10.5455i	0.209822	+	0.363422i
$843$	−25.5495	−	20.0728i	−0.879973	−	0.691342i
$844$	7.68292	+	13.3072i	0.264457	+	0.458053i
$845$	2.69330	+	16.2158i	0.0926522	+	0.557840i
$846$	−83.2662	−	24.3633i	−2.86275	−	0.837627i
$847$	13.1499	+	7.59212i	0.451837	+	0.260868i
$848$	−0.689487			−0.0236771
$849$	4.84011	−	6.16072i	0.166112	−	0.211435i
$850$	−14.3436	−	8.28126i	−0.491980	−	0.284045i
$851$		−	3.94434i		−	0.135210i
$852$	−34.4006	−	27.0265i	−1.17854	−	0.925913i
$853$	−27.8602	+	16.0851i	−0.953914	+	0.550742i	−0.894295	−	0.447479i	$-0.852322\pi$
$853$	−27.8602	+	16.0851i	−0.953914	+	0.550742i	−0.0596193	+	0.998221i	$0.518989\pi$
$854$	−24.6480	−	42.6916i	−0.843437	−	1.46088i
$855$	−8.68600	+	8.29785i	−0.297055	+	0.283780i
$856$	−7.30001	−	4.21466i	−0.249509	−	0.144054i
$857$	7.08968	+	12.2797i	0.242179	+	0.419466i	0.961335	−	0.275383i	$-0.0888046\pi$
$857$	7.08968	+	12.2797i	0.242179	+	0.419466i	−0.719156	+	0.694849i	$0.755471\pi$
$858$	39.1871	+	2.35526i	1.33783	+	0.0804072i
$859$	4.77386	−	8.26856i	0.162882	−	0.282120i	−0.773019	−	0.634383i	$-0.781254\pi$
$859$	4.77386	−	8.26856i	0.162882	−	0.282120i	0.935901	+	0.352263i	$0.114588\pi$
$860$	18.3831	−	10.6135i	0.626857	−	0.361916i
$861$	−6.75748	−	16.8562i	−0.230294	−	0.574456i
$862$	−39.9255	+	69.1531i	−1.35987	+	2.35536i
$863$		−	27.1037i		−	0.922622i	−0.887238	−	0.461311i	$-0.847379\pi$
$863$		−	27.1037i		−	0.922622i	0.887238	−	0.461311i	$-0.152621\pi$
$864$	−10.6271	+	23.3581i	−0.361541	+	0.794659i
$865$	5.34013	−	3.08313i	0.181570	−	0.104829i
$866$	29.5538	−	17.0629i	1.00428	−	0.579822i
$867$	−21.5713	−	3.09103i	−0.732599	−	0.104977i
$868$	−27.1233	−	46.9790i	−0.920626	−	1.59457i
$869$	−8.57698	+	4.95192i	−0.290954	+	0.167982i
$870$	43.1130	+	6.17783i	1.46167	+	0.209448i
$871$	4.20340	+	50.9623i	0.142427	+	1.72679i
$872$	26.3491			0.892294
$873$	6.95405	−	1.69403i	0.235359	−	0.0573342i
$874$	1.65934	−	2.87405i	0.0561279	−	0.0972163i
$875$	−22.1767	+	38.4112i	−0.749711	+	1.29854i
$876$	−43.0721	+	17.2672i	−1.45527	+	0.583405i
$877$			39.6472i			1.33879i	0.742907	+	0.669395i	$0.233447\pi$
$877$			39.6472i			1.33879i	−0.742907	+	0.669395i	$0.766553\pi$
$878$			5.89601i			0.198981i
$879$	−0.509188	+	0.204129i	−0.0171745	+	0.00688509i
$880$	−1.03246	+	1.78827i	−0.0348041	+	0.0602825i
$881$	−4.91250	+	8.50870i	−0.165506	+	0.286665i	−0.936835	−	0.349772i	$-0.886259\pi$
$881$	−4.91250	+	8.50870i	−0.165506	+	0.286665i	0.771329	+	0.636437i	$0.219592\pi$
$882$	−20.3617	+	69.5901i	−0.685615	+	2.34322i
$883$	−31.5744			−1.06256			−0.531282	−	0.847195i	$-0.678290\pi$
$883$	−31.5744			−1.06256			−0.531282	+	0.847195i	$0.678290\pi$
$884$	−25.4309	+	2.09755i	−0.855332	+	0.0705482i
$885$	−13.7103	−	1.96460i	−0.460867	−	0.0660394i
$886$	−63.3356	+	36.5668i	−2.12780	+	1.22849i
$887$	−7.56956	−	13.1109i	−0.254161	−	0.440220i	0.710506	−	0.703691i	$-0.248466\pi$
$887$	−7.56956	−	13.1109i	−0.254161	−	0.440220i	−0.964667	+	0.263471i	$0.915133\pi$
$888$	47.3361	+	6.78296i	1.58850	+	0.227621i
$889$	56.9135	−	32.8591i	1.90882	−	1.10206i
$890$	−3.86056	+	2.22889i	−0.129406	+	0.0747127i
$891$	−24.3964	−	1.11570i	−0.817309	−	0.0373774i
$892$		−	75.0111i		−	2.51156i
$893$	19.7654	−	34.2347i	0.661424	−	1.14562i
$894$	32.4044	+	80.8311i	1.08377	+	2.70340i
$895$	−14.4907	+	8.36623i	−0.484372	+	0.279652i
$896$	40.5333	−	70.2058i	1.35412	−	2.34541i
$897$	1.26321	+	2.52692i	0.0421773	+	0.0843714i
$898$	29.4468	+	51.0033i	0.982652	+	1.70200i
$899$	28.6879	+	16.5630i	0.956795	+	0.552406i
$900$	−32.9708	−	9.64708i	−1.09903	−	0.321569i
$901$	−1.20414	−	2.08563i	−0.0401156	−	0.0694823i
$902$	−13.6710	+	7.89296i	−0.455195	+	0.262807i
$903$	−28.3546	−	22.2765i	−0.943582	−	0.741316i
$904$			11.1333i			0.370289i
$905$	19.9548	+	11.5209i	0.663321	+	0.382968i
$906$	−6.70229	+	8.53099i	−0.222669	+	0.283423i
$907$	−55.5704			−1.84519			−0.922593	−	0.385775i	$-0.873934\pi$
$907$	−55.5704			−1.84519			−0.922593	+	0.385775i	$0.873934\pi$
$908$	−12.2517	−	7.07350i	−0.406586	−	0.234742i
$909$	24.2910	−	23.2055i	0.805682	−	0.769678i
$910$	3.62492	+	43.9488i	0.120165	+	1.45689i
$911$	−17.3371	−	30.0288i	−0.574405	−	0.994899i	−0.996106	−	0.0881637i	$-0.971900\pi$
$911$	−17.3371	−	30.0288i	−0.574405	−	0.994899i	0.421701	−	0.906735i	$-0.361433\pi$
$912$	2.59565	+	2.03925i	0.0859505	+	0.0675262i
$913$	−3.07074	−	5.31868i	−0.101627	−	0.176023i
$914$	52.6703			1.74218
$915$	8.77702	+	6.89558i	0.290159	+	0.227961i
$916$	66.6583	+	38.4852i	2.20245	+	1.27159i
$917$	−49.3276	+	28.4793i	−1.62894	+	0.940469i
$918$	25.1856	−	2.44114i	0.831248	−	0.0805697i
$919$	6.58230	+	11.4009i	0.217130	+	0.376080i	0.953929	−	0.300031i	$-0.0969971\pi$
$919$	6.58230	+	11.4009i	0.217130	+	0.376080i	−0.736799	+	0.676111i	$0.763664\pi$
$920$	−1.81121			−0.0597138
$921$	18.1425	−	7.27317i	0.597817	−	0.239659i
$922$	23.6604	−	40.9811i	0.779215	−	1.34964i
$923$	2.22343	+	26.9570i	0.0731850	+	0.887300i
$924$	65.4014	+	9.37161i	2.15155	+	0.308303i
$925$		−	29.6553i		−	0.975062i
$926$	6.26040	−	10.8433i	0.205730	−	0.356334i
$927$	−2.06988	−	8.49692i	−0.0679837	−	0.279075i
$928$			42.3943i			1.39166i
$929$	−15.8448	−	9.14798i	−0.519850	−	0.300135i	0.217023	−	0.976166i	$-0.430365\pi$
$929$	−15.8448	−	9.14798i	−0.519850	−	0.300135i	−0.736873	+	0.676031i	$0.763699\pi$
$930$	15.3959	+	12.0957i	0.504852	+	0.396632i
$931$	−28.6118	−	16.5190i	−0.937714	−	0.541389i
$932$	−58.2027			−1.90649
$933$	−54.5463	−	7.81614i	−1.78577	−	0.255889i
$934$		−	23.3330i		−	0.763477i
$935$	−7.21244			−0.235872
$936$	−32.4979	+	10.8143i	−1.06223	+	0.353477i
$937$	50.7326			1.65736			0.828681	−	0.559722i	$-0.189092\pi$
$937$	50.7326			1.65736			0.828681	+	0.559722i	$0.189092\pi$
$938$			137.181i			4.47911i
$939$	−0.158537	+	0.201794i	−0.00517367	+	0.00658529i
$940$	−53.1435			−1.73335
$941$	24.2843	+	14.0206i	0.791646	+	0.457057i	0.840542	−	0.541747i	$-0.182237\pi$
$941$	24.2843	+	14.0206i	0.791646	+	0.457057i	−0.0488955	+	0.998804i	$0.515570\pi$
$942$	8.91731	−	62.2310i	0.290542	−	2.02760i
$943$	−0.983791	−	0.567992i	−0.0320366	−	0.0184964i
$944$			3.80591i			0.123872i
$945$	−2.64656	−	27.3049i	−0.0860925	−	0.888228i
$946$	−15.6721	+	27.1450i	−0.509545	+	0.882558i
$947$		−	44.2612i		−	1.43830i	−0.694857	−	0.719148i	$-0.744532\pi$
$947$		−	44.2612i		−	1.43830i	0.694857	−	0.719148i	$-0.255468\pi$
$948$	13.1488	−	16.7364i	0.427052	−	0.543572i
$949$	25.9426	+	12.2546i	0.842131	+	0.397802i
$950$	12.4756	−	21.6085i	0.404764	−	0.701071i
$951$	−26.8867	−	21.1233i	−0.871861	−	0.684970i
$952$	−27.7904			−0.900693
$953$	5.98910	+	10.3734i	0.194006	+	0.336028i	0.946574	−	0.322486i	$-0.104519\pi$
$953$	5.98910	+	10.3734i	0.194006	+	0.336028i	−0.752568	+	0.658514i	$0.771185\pi$
$954$	−5.50015	−	5.75743i	−0.178074	−	0.186404i
$955$	16.8318	−	9.71785i	0.544665	−	0.314462i
$956$	−18.8998	−	10.9118i	−0.611262	−	0.352912i
$957$	−37.4484	+	15.0127i	−1.21054	+	0.485292i
$958$	51.8870			1.67639
$959$	23.9115	+	41.4159i	0.772142	+	1.33739i
$960$	−3.92813	+	27.4132i	−0.126780	+	0.884757i
$961$	−8.05427	−	13.9504i	−0.259815	−	0.450013i
$962$	−41.4761	−	59.8654i	−1.33724	−	1.93014i
$963$	−1.89021	−	7.75940i	−0.0609113	−	0.250043i
$964$	0.536399	+	0.309690i	0.0172762	+	0.00997444i
$965$	7.14879			0.230128
$966$	2.82010	+	7.03458i	0.0907351	+	0.226334i
$967$	7.75706	+	4.47854i	0.249450	+	0.144020i	0.619513	−	0.784987i	$-0.287330\pi$
$967$	7.75706	+	4.47854i	0.249450	+	0.144020i	−0.370062	+	0.929007i	$0.620664\pi$
$968$			11.5153i			0.370117i
$969$	−1.63541	+	11.4130i	−0.0525368	+	0.366637i
$970$	6.05240	−	3.49436i	0.194331	−	0.112197i
$971$	−8.19718	−	14.1979i	−0.263060	−	0.455633i	0.703994	−	0.710206i	$-0.251398\pi$
$971$	−8.19718	−	14.1979i	−0.263060	−	0.455633i	−0.967054	+	0.254573i	$0.918065\pi$
$972$	49.5560	−	17.2834i	1.58951	−	0.554364i
$973$	17.5239	+	10.1174i	0.561789	+	0.324349i
$974$	2.34549	+	4.06250i	0.0751542	+	0.130171i
$975$	9.49738	+	18.9985i	0.304160	+	0.608440i
$976$	1.53356	−	2.65620i	0.0490880	−	0.0850229i
$977$	−32.3176	+	18.6586i	−1.03393	+	0.596941i	−0.918108	−	0.396329i	$-0.870284\pi$
$977$	−32.3176	+	18.6586i	−1.03393	+	0.596941i	−0.115823	+	0.993270i	$0.536951\pi$
$978$	16.4231	−	20.9041i	0.525154	−	0.668440i
$979$	2.06473	−	3.57622i	0.0659891	−	0.114296i
$980$			44.4149i			1.41878i
$981$	17.2445	+	18.0511i	0.550574	+	0.576329i
$982$	−6.13152	+	3.54003i	−0.195665	+	0.112967i
$983$	44.4140	−	25.6424i	1.41659	−	0.817866i	0.420589	−	0.907251i	$-0.361824\pi$
$983$	44.4140	−	25.6424i	1.41659	−	0.817866i	0.995997	+	0.0893852i	$0.0284902\pi$
$984$	8.50828	−	10.8297i	0.271234	−	0.345240i
$985$	−3.98690	−	6.90552i	−0.127033	−	0.220028i
$986$	36.2018	−	20.9011i	1.15290	−	0.665628i
$987$	33.5920	+	83.7934i	1.06924	+	2.66717i
$988$	−3.15994	−	38.3114i	−0.100531	−	1.21885i
$989$	−2.25559			−0.0717237
$990$	−23.1687	+	5.64397i	−0.736349	+	0.179377i
$991$	−28.1237	+	48.7116i	−0.893378	+	1.54738i	−0.0575787	+	0.998341i	$0.518338\pi$
$991$	−28.1237	+	48.7116i	−0.893378	+	1.54738i	−0.835799	+	0.549035i	$0.814995\pi$
$992$	−9.52899	+	16.5047i	−0.302546	+	0.524025i
$993$	−4.18340	+	29.1946i	−0.132756	+	0.926463i
$994$			72.5630i			2.30156i
$995$			2.14882i			0.0681222i
$996$	10.3784	+	8.15370i	0.328853	+	0.258360i
$997$	2.67652	−	4.63586i	0.0847661	−	0.146819i	−0.820525	−	0.571610i	$-0.806319\pi$
$997$	2.67652	−	4.63586i	0.0847661	−	0.146819i	0.905292	+	0.424791i	$0.139652\pi$
$998$	23.6516	−	40.9658i	0.748679	−	1.29675i
$999$	26.3328	+	36.8680i	0.833134	+	1.16645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.4.2	✓	22
3.2	odd	2		351.2.l.b.199.10		22
9.2	odd	6		351.2.r.b.316.10		22
9.7	even	3		117.2.r.b.43.2	yes	22
13.10	even	6		117.2.r.b.49.2	yes	22
39.23	odd	6		351.2.r.b.10.10		22
117.88	even	6	inner	117.2.l.b.88.10	yes	22
117.101	odd	6		351.2.l.b.127.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.2	✓	22	1.1	even	1	trivial
117.2.l.b.88.10	yes	22	117.88	even	6	inner
117.2.r.b.43.2	yes	22	9.7	even	3
117.2.r.b.49.2	yes	22	13.10	even	6
351.2.l.b.127.2		22	117.101	odd	6
351.2.l.b.199.10		22	3.2	odd	2
351.2.r.b.10.10		22	39.23	odd	6
351.2.r.b.316.10		22	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.31664i q^{2} +(-0.644502 - 1.60767i) q^{3} -3.36682 q^{4} +(-1.09505 - 0.632228i) q^{5} +(-3.72440 + 1.49308i) q^{6} +(3.61589 + 2.08764i) q^{7} +3.16642i q^{8} +(-2.16923 + 2.07230i) q^{9} +(-1.46464 + 2.53684i) q^{10} -2.71354i q^{11} +(2.16992 + 5.41274i) q^{12} +(1.54000 - 3.26012i) q^{13} +(4.83630 - 8.37672i) q^{14} +(-0.310655 + 2.16796i) q^{15} +0.601814 q^{16} +(1.05102 + 1.82043i) q^{17} +(4.80077 + 5.02533i) q^{18} +(-2.74246 + 1.58336i) q^{19} +(3.68684 + 2.12860i) q^{20} +(1.02579 - 7.15866i) q^{21} -6.28629 q^{22} +(-0.226187 - 0.391767i) q^{23} +(5.09057 - 2.04076i) q^{24} +(-1.70057 - 2.94548i) q^{25} +(-7.55253 - 3.56763i) q^{26} +(4.72966 + 2.15182i) q^{27} +(-12.1740 - 7.02869i) q^{28} +8.58419 q^{29} +(5.02238 + 0.719675i) q^{30} +(3.34195 + 1.92947i) q^{31} +4.93865i q^{32} +(-4.36249 + 1.74888i) q^{33} +(4.21727 - 2.43484i) q^{34} +(-2.63973 - 4.57214i) q^{35} +(7.30341 - 6.97704i) q^{36} +(7.55106 + 4.35961i) q^{37} +(3.66807 + 6.35328i) q^{38} +(-6.23375 - 0.374666i) q^{39} +(2.00190 - 3.46739i) q^{40} +(2.17473 - 1.25558i) q^{41} +(-16.5840 - 2.37639i) q^{42} +(2.49307 - 4.31812i) q^{43} +9.13598i q^{44} +(3.68559 - 0.897822i) q^{45} +(-0.907582 + 0.523993i) q^{46} +(-10.8108 + 6.24161i) q^{47} +(-0.387870 - 0.967520i) q^{48} +(5.21645 + 9.03516i) q^{49} +(-6.82362 + 3.93962i) q^{50} +(2.24927 - 2.86297i) q^{51} +(-5.18490 + 10.9762i) q^{52} -1.14568 q^{53} +(4.98500 - 10.9569i) q^{54} +(-1.71558 + 2.97147i) q^{55} +(-6.61033 + 11.4494i) q^{56} +(4.31304 + 3.38850i) q^{57} -19.8865i q^{58} +6.32407i q^{59} +(1.04592 - 7.29912i) q^{60} +(2.54823 - 4.41366i) q^{61} +(4.46989 - 7.74208i) q^{62} +(-12.1699 + 2.96463i) q^{63} +12.6447 q^{64} +(-3.74752 + 2.59637i) q^{65} +(4.05152 + 10.1063i) q^{66} +(-12.2823 + 7.09120i) q^{67} +(-3.53860 - 6.12904i) q^{68} +(-0.484056 + 0.616129i) q^{69} +(-10.5920 + 6.11529i) q^{70} +(-6.49685 + 3.75096i) q^{71} +(-6.56176 - 6.86870i) q^{72} +7.95754i q^{73} +(10.0996 - 17.4931i) q^{74} +(-3.63935 + 4.63234i) q^{75} +(9.23335 - 5.33087i) q^{76} +(5.66488 - 9.81187i) q^{77} +(-0.867965 + 14.4413i) q^{78} +(-1.82489 - 3.16081i) q^{79} +(-0.659017 - 0.380484i) q^{80} +(0.411161 - 8.99060i) q^{81} +(-2.90873 - 5.03807i) q^{82} +(1.96005 - 1.13164i) q^{83} +(-3.45365 + 24.1019i) q^{84} -2.65795i q^{85} +(-10.0035 - 5.77554i) q^{86} +(-5.53253 - 13.8006i) q^{87} +8.59219 q^{88} +(1.31792 + 0.760899i) q^{89} +(-2.07993 - 8.53818i) q^{90} +(12.3744 - 8.57329i) q^{91} +(0.761528 + 1.31901i) q^{92} +(0.948075 - 6.61631i) q^{93} +(14.4596 + 25.0447i) q^{94} +4.00418 q^{95} +(7.93974 - 3.18297i) q^{96} +(-2.06617 - 1.19290i) q^{97} +(20.9312 - 12.0846i) q^{98} +(5.62326 + 5.88630i) 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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