LMFDB - Embedded newform 117.2.l.b.88.4

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			88.4
Character	$\chi$	$=$	117.88
Dual form			117.2.l.b.4.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.782672i q^{2} +(-1.67281 + 0.449109i) q^{3} +1.38742 q^{4} +(0.0536139 - 0.0309540i) q^{5} +(0.351505 + 1.30926i) q^{6} +(3.25250 - 1.87783i) q^{7} -2.65124i q^{8} +(2.59660 - 1.50255i) q^{9} +(-0.0242268 - 0.0419621i) q^{10} +1.28253i q^{11} +(-2.32090 + 0.623105i) q^{12} +(-3.60145 - 0.171963i) q^{13} +(-1.46973 - 2.54564i) q^{14} +(-0.0757843 + 0.0758587i) q^{15} +0.699796 q^{16} +(-2.74383 + 4.75245i) q^{17} +(-1.17600 - 2.03229i) q^{18} +(2.72231 + 1.57173i) q^{19} +(0.0743853 - 0.0429463i) q^{20} +(-4.59748 + 4.60199i) q^{21} +1.00380 q^{22} +(2.82990 - 4.90152i) q^{23} +(1.19070 + 4.43503i) q^{24} +(-2.49808 + 4.32681i) q^{25} +(-0.134590 + 2.81875i) q^{26} +(-3.66882 + 3.67964i) q^{27} +(4.51260 - 2.60535i) q^{28} -7.13444 q^{29} +(0.0593725 + 0.0593142i) q^{30} +(-3.62246 + 2.09143i) q^{31} -5.85020i q^{32} +(-0.575997 - 2.14544i) q^{33} +(3.71961 + 2.14752i) q^{34} +(0.116253 - 0.201356i) q^{35} +(3.60259 - 2.08468i) q^{36} +(-4.03923 + 2.33205i) q^{37} +(1.23015 - 2.13067i) q^{38} +(6.10178 - 1.32978i) q^{39} +(-0.0820666 - 0.142143i) q^{40} +(8.56482 + 4.94490i) q^{41} +(3.60185 + 3.59832i) q^{42} +(-2.11380 - 3.66122i) q^{43} +1.77942i q^{44} +(0.0927041 - 0.160933i) q^{45} +(-3.83628 - 2.21488i) q^{46} +(-2.73495 - 1.57902i) q^{47} +(-1.17063 + 0.314285i) q^{48} +(3.55252 - 6.15314i) q^{49} +(3.38647 + 1.95518i) q^{50} +(2.45554 - 9.18223i) q^{51} +(-4.99674 - 0.238585i) q^{52} -0.752963 q^{53} +(2.87995 + 2.87148i) q^{54} +(0.0396996 + 0.0687616i) q^{55} +(-4.97859 - 8.62317i) q^{56} +(-5.25979 - 1.40659i) q^{57} +5.58392i q^{58} -0.359005i q^{59} +(-0.105145 + 0.105248i) q^{60} +(-0.825473 - 1.42976i) q^{61} +(1.63690 + 2.83520i) q^{62} +(5.62392 - 9.76304i) q^{63} -3.17919 q^{64} +(-0.198411 + 0.102260i) q^{65} +(-1.67917 + 0.450817i) q^{66} +(1.43574 + 0.828926i) q^{67} +(-3.80685 + 6.59366i) q^{68} +(-2.53257 + 9.47026i) q^{69} +(-0.157596 - 0.0909879i) q^{70} +(11.3838 + 6.57246i) q^{71} +(-3.98362 - 6.88422i) q^{72} -6.09030i q^{73} +(1.82523 + 3.16139i) q^{74} +(2.23562 - 8.35985i) q^{75} +(3.77700 + 2.18065i) q^{76} +(2.40838 + 4.17145i) q^{77} +(-1.04078 - 4.77569i) q^{78} +(-0.616191 + 1.06727i) q^{79} +(0.0375188 - 0.0216615i) q^{80} +(4.48469 - 7.80305i) q^{81} +(3.87024 - 6.70345i) q^{82} +(11.0538 + 6.38193i) q^{83} +(-6.37865 + 6.38492i) q^{84} +0.339730i q^{85} +(-2.86553 + 1.65442i) q^{86} +(11.9346 - 3.20414i) q^{87} +3.40031 q^{88} +(1.30142 - 0.751374i) q^{89} +(-0.125958 - 0.0725569i) q^{90} +(-12.0366 + 6.20361i) q^{91} +(3.92627 - 6.80049i) q^{92} +(5.12042 - 5.12545i) q^{93} +(-1.23586 + 2.14057i) q^{94} +0.194605 q^{95} +(2.62738 + 9.78628i) q^{96} +(-8.68058 + 5.01173i) q^{97} +(-4.81589 - 2.78046i) q^{98} +(1.92707 + 3.33023i) 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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	0.782672i		−	0.553433i	−0.960952	−	0.276716i	$-0.910754\pi$
$2$		−	0.782672i		−	0.553433i	0.960952	−	0.276716i	$-0.0892462\pi$
$3$	−1.67281	+	0.449109i	−0.965799	+	0.259293i
$3$	−1.67281	+	0.449109i	−0.965799	+	0.259293i
$4$	1.38742			0.693712
$5$	0.0536139	−	0.0309540i	0.0239769	−	0.0138431i	−0.487964	−	0.872864i	$-0.662260\pi$
$5$	0.0536139	−	0.0309540i	0.0239769	−	0.0138431i	0.511941	+	0.859021i	$0.328927\pi$
$6$	0.351505	+	1.30926i	0.143501	+	0.534504i
$7$	3.25250	−	1.87783i	1.22933	−	0.709754i	0.262441	−	0.964948i	$-0.415473\pi$
$7$	3.25250	−	1.87783i	1.22933	−	0.709754i	0.966890	+	0.255194i	$0.0821392\pi$
$8$		−	2.65124i		−	0.937356i
$9$	2.59660	−	1.50255i	0.865534	−	0.500850i
$10$	−0.0242268	−	0.0419621i	−0.00766120	−	0.0132696i
$11$			1.28253i			0.386698i	0.981130	+	0.193349i	$0.0619350\pi$
$11$			1.28253i			0.386698i	−0.981130	+	0.193349i	$0.938065\pi$
$12$	−2.32090	+	0.623105i	−0.669986	+	0.179875i
$13$	−3.60145	−	0.171963i	−0.998862	−	0.0476938i
$13$	−3.60145	−	0.171963i	−0.998862	−	0.0476938i
$14$	−1.46973	−	2.54564i	−0.392801	−	0.680352i
$15$	−0.0757843	+	0.0758587i	−0.0195674	+	0.0195866i
$16$	0.699796			0.174949
$17$	−2.74383	+	4.75245i	−0.665476	+	1.15264i	0.313681	+	0.949529i	$0.398438\pi$
$17$	−2.74383	+	4.75245i	−0.665476	+	1.15264i	−0.979156	+	0.203109i	$0.934895\pi$
$18$	−1.17600	−	2.03229i	−0.277187	−	0.479015i
$19$	2.72231	+	1.57173i	0.624540	+	0.360579i	0.778635	−	0.627478i	$-0.215913\pi$
$19$	2.72231	+	1.57173i	0.624540	+	0.360579i	−0.154094	+	0.988056i	$0.549246\pi$
$20$	0.0743853	−	0.0429463i	0.0166330	−	0.00960310i
$21$	−4.59748	+	4.60199i	−1.00325	+	1.00424i
$22$	1.00380			0.214012
$23$	2.82990	−	4.90152i	0.590074	−	1.02204i	−0.404148	−	0.914694i	$-0.632432\pi$
$23$	2.82990	−	4.90152i	0.590074	−	1.02204i	0.994222	−	0.107344i	$-0.0342347\pi$
$24$	1.19070	+	4.43503i	0.243050	+	0.905297i
$25$	−2.49808	+	4.32681i	−0.499617	+	0.865362i
$26$	−0.134590	+	2.81875i	−0.0263953	+	0.552803i
$27$	−3.66882	+	3.67964i	−0.706065	+	0.708147i
$28$	4.51260	−	2.60535i	0.852802	−	0.492365i
$29$	−7.13444			−1.32483			−0.662416	−	0.749136i	$-0.730469\pi$
$29$	−7.13444			−1.32483			−0.662416	+	0.749136i	$0.730469\pi$
$30$	0.0593725	+	0.0593142i	0.0108399	+	0.0108292i
$31$	−3.62246	+	2.09143i	−0.650613	+	0.375632i	−0.788691	−	0.614790i	$-0.789241\pi$
$31$	−3.62246	+	2.09143i	−0.650613	+	0.375632i	0.138078	+	0.990421i	$0.455908\pi$
$32$		−	5.85020i		−	1.03418i
$33$	−0.575997	−	2.14544i	−0.100268	−	0.373473i
$34$	3.71961	+	2.14752i	0.637907	+	0.368296i
$35$	0.116253	−	0.201356i	0.0196503	−	0.0340354i
$36$	3.60259	−	2.08468i	0.600432	−	0.347446i
$37$	−4.03923	+	2.33205i	−0.664045	+	0.383386i	−0.793816	−	0.608158i	$-0.791909\pi$
$37$	−4.03923	+	2.33205i	−0.664045	+	0.383386i	0.129772	+	0.991544i	$0.458576\pi$
$38$	1.23015	−	2.13067i	0.199556	−	0.345641i
$39$	6.10178	−	1.32978i	0.977066	−	0.212935i
$40$	−0.0820666	−	0.142143i	−0.0129759	−	0.0224749i
$41$	8.56482	+	4.94490i	1.33760	+	0.772264i	0.986451	−	0.164055i	$-0.0524576\pi$
$41$	8.56482	+	4.94490i	1.33760	+	0.772264i	0.351150	+	0.936319i	$0.385791\pi$
$42$	3.60185	+	3.59832i	0.555778	+	0.555232i
$43$	−2.11380	−	3.66122i	−0.322352	−	0.558330i	0.658621	−	0.752475i	$-0.271140\pi$
$43$	−2.11380	−	3.66122i	−0.322352	−	0.558330i	−0.980973	+	0.194145i	$0.937807\pi$
$44$			1.77942i			0.268257i
$45$	0.0927041	−	0.160933i	0.0138195	−	0.0239904i
$46$	−3.83628	−	2.21488i	−0.565629	−	0.326566i
$47$	−2.73495	−	1.57902i	−0.398933	−	0.230324i	0.287090	−	0.957904i	$-0.407312\pi$
$47$	−2.73495	−	1.57902i	−0.398933	−	0.230324i	−0.686024	+	0.727579i	$0.740645\pi$
$48$	−1.17063	+	0.314285i	−0.168966	+	0.0453631i
$49$	3.55252	−	6.15314i	0.507503	−	0.879021i
$50$	3.38647	+	1.95518i	0.478919	+	0.276504i
$51$	2.45554	−	9.18223i	0.343844	−	1.28577i
$52$	−4.99674	−	0.238585i	−0.692923	−	0.0330858i
$53$	−0.752963			−0.103427			−0.0517137	−	0.998662i	$-0.516468\pi$
$53$	−0.752963			−0.103427			−0.0517137	+	0.998662i	$0.516468\pi$
$54$	2.87995	+	2.87148i	0.391912	+	0.390759i
$55$	0.0396996	+	0.0687616i	0.00535309	+	0.00927182i
$56$	−4.97859	−	8.62317i	−0.665292	−	1.15232i
$57$	−5.25979	−	1.40659i	−0.696676	−	0.186307i
$58$			5.58392i			0.733205i
$59$		−	0.359005i		−	0.0467385i	−0.999727	−	0.0233692i	$-0.992561\pi$
$59$		−	0.359005i		−	0.0467385i	0.999727	−	0.0233692i	$-0.00743934\pi$
$60$	−0.105145	+	0.105248i	−0.0135742	+	0.0135875i
$61$	−0.825473	−	1.42976i	−0.105691	−	0.183062i	0.808329	−	0.588731i	$-0.200372\pi$
$61$	−0.825473	−	1.42976i	−0.105691	−	0.183062i	−0.914020	+	0.405668i	$0.867039\pi$
$62$	1.63690	+	2.83520i	0.207887	+	0.360071i
$63$	5.62392	−	9.76304i	0.708547	−	1.23003i
$64$	−3.17919			−0.397399
$65$	−0.198411	+	0.102260i	−0.0246098	+	0.0126838i
$66$	−1.67917	+	0.450817i	−0.206692	+	0.0554917i
$67$	1.43574	+	0.828926i	0.175404	+	0.101269i	0.585131	−	0.810938i	$-0.301043\pi$
$67$	1.43574	+	0.828926i	0.175404	+	0.101269i	−0.409728	+	0.912208i	$0.634376\pi$
$68$	−3.80685	+	6.59366i	−0.461649	+	0.799599i
$69$	−2.53257	+	9.47026i	−0.304885	+	1.14009i
$70$	−0.157596	−	0.0909879i	−0.0188363	−	0.0108751i
$71$	11.3838	+	6.57246i	1.35101	+	0.780008i	0.988391	−	0.151929i	$-0.0485484\pi$
$71$	11.3838	+	6.57246i	1.35101	+	0.780008i	0.362622	+	0.931936i	$0.381882\pi$
$72$	−3.98362	−	6.88422i	−0.469475	−	0.811313i
$73$		−	6.09030i		−	0.712816i	−0.934330	−	0.356408i	$-0.884001\pi$
$73$		−	6.09030i		−	0.712816i	0.934330	−	0.356408i	$-0.115999\pi$
$74$	1.82523	+	3.16139i	0.212178	+	0.367504i
$75$	2.23562	−	8.35985i	0.258147	−	0.965312i
$76$	3.77700	+	2.18065i	0.433251	+	0.250138i
$77$	2.40838	+	4.17145i	0.274461	+	0.475380i
$78$	−1.04078	−	4.77569i	−0.117845	−	0.540740i
$79$	−0.616191	+	1.06727i	−0.0693269	+	0.120078i	−0.898605	−	0.438758i	$-0.855418\pi$
$79$	−0.616191	+	1.06727i	−0.0693269	+	0.120078i	0.829278	+	0.558836i	$0.188752\pi$
$80$	0.0375188	−	0.0216615i	0.00419473	−	0.00242183i
$81$	4.48469	−	7.80305i	0.498298	−	0.867006i
$82$	3.87024	−	6.70345i	0.427396	−	0.740272i
$83$	11.0538	+	6.38193i	1.21332	+	0.700508i	0.963480	−	0.267781i	$-0.0862903\pi$
$83$	11.0538	+	6.38193i	1.21332	+	0.700508i	0.249835	+	0.968288i	$0.419624\pi$
$84$	−6.37865	+	6.38492i	−0.695968	+	0.696652i
$85$			0.339730i			0.0368489i
$86$	−2.86553	+	1.65442i	−0.308998	+	0.178400i
$87$	11.9346	−	3.20414i	1.27952	−	0.343520i
$88$	3.40031			0.362474
$89$	1.30142	−	0.751374i	0.137950	−	0.0796455i	−0.429437	−	0.903097i	$-0.641288\pi$
$89$	1.30142	−	0.751374i	0.137950	−	0.0796455i	0.567387	+	0.823452i	$0.307955\pi$
$90$	−0.125958	−	0.0725569i	−0.0132771	−	0.00764816i
$91$	−12.0366	+	6.20361i	−1.26178	+	0.650315i
$92$	3.92627	−	6.80049i	0.409342	−	0.709000i
$93$	5.12042	−	5.12545i	0.530963	−	0.531484i
$94$	−1.23586	+	2.14057i	−0.127469	+	0.220783i
$95$	0.194605			0.0199660
$96$	2.62738	+	9.78628i	0.268155	+	0.998808i
$97$	−8.68058	+	5.01173i	−0.881379	+	0.508865i	−0.871113	−	0.491083i	$-0.836601\pi$
$97$	−8.68058	+	5.01173i	−0.881379	+	0.508865i	−0.0102663	+	0.999947i	$0.503268\pi$
$98$	−4.81589	−	2.78046i	−0.486479	−	0.280869i
$99$	1.92707	+	3.33023i	0.193678	+	0.334701i
$100$	−3.46590	+	6.00312i	−0.346590	+	0.600312i
$101$	−17.2005			−1.71152			−0.855758	−	0.517376i	$-0.826909\pi$
$101$	−17.2005			−1.71152			−0.855758	+	0.517376i	$0.826909\pi$
$102$	−7.18667	−	1.92188i	−0.711587	−	0.190295i
$103$	−8.82611	−	15.2873i	−0.869662	−	1.50630i	−0.862342	−	0.506326i	$-0.831003\pi$
$103$	−8.82611	−	15.2873i	−0.869662	−	1.50630i	−0.00732055	−	0.999973i	$-0.502330\pi$
$104$	−0.455914	+	9.54831i	−0.0447061	+	0.936289i
$105$	−0.104039	+	0.389041i	−0.0101531	+	0.0379665i
$106$			0.589323i			0.0572401i
$107$	5.14019	+	8.90307i	0.496921	+	0.860692i	0.999994	−	0.00355197i	$-0.00113063\pi$
$107$	5.14019	+	8.90307i	0.496921	+	0.860692i	−0.503073	+	0.864244i	$0.667797\pi$
$108$	−5.09021	+	5.10523i	−0.489806	+	0.491251i
$109$			7.16152i			0.685949i	0.939345	+	0.342975i	$0.111434\pi$
$109$			7.16152i			0.685949i	−0.939345	+	0.342975i	$0.888566\pi$
$110$	0.0538178	−	0.0310717i	0.00513133	−	0.00296257i
$111$	5.70952	−	5.71513i	0.541924	−	0.542456i
$112$	2.27609	−	1.31410i	0.215070	−	0.124171i
$113$	3.30432			0.310844			0.155422	−	0.987848i	$-0.450326\pi$
$113$	3.30432			0.310844			0.155422	+	0.987848i	$0.450326\pi$
$114$	−1.10090	+	4.11669i	−0.103108	+	0.385563i
$115$		−	0.350386i		−	0.0326737i
$116$	−9.89849			−0.919052
$117$	−9.60991	+	4.96484i	−0.888437	+	0.458999i
$118$	−0.280983			−0.0258666
$119$			20.6098i			1.88930i
$120$	0.201120	+	0.200923i	0.0183596	+	0.0183416i
$121$	9.35511			0.850464
$122$	−1.11903	+	0.646075i	−0.101313	+	0.0584929i
$123$	−16.5481	−	4.42536i	−1.49210	−	0.399021i
$124$	−5.02589	+	2.90170i	−0.451338	+	0.260580i
$125$			0.618843i			0.0553510i
$126$	−7.64125	−	4.40168i	−0.680737	−	0.392133i
$127$	−3.56802	−	6.18000i	−0.316611	−	0.548386i	0.663168	−	0.748471i	$-0.269212\pi$
$127$	−3.56802	−	6.18000i	−0.316611	−	0.548386i	−0.979779	+	0.200085i	$0.935878\pi$
$128$		−	9.21213i		−	0.814245i
$129$	5.18028	+	5.17520i	0.456099	+	0.455651i
$130$	0.0800358	+	0.155290i	0.00701960	+	0.0136199i
$131$	−9.76000	−	16.9048i	−0.852735	−	1.47698i	−0.878730	−	0.477319i	$-0.841609\pi$
$131$	−9.76000	−	16.9048i	−0.852735	−	1.47698i	0.0259946	−	0.999662i	$-0.491725\pi$
$132$	−0.799153	−	2.97663i	−0.0695573	−	0.259083i
$133$	11.8058			1.02369
$134$	0.648777	−	1.12372i	0.0560458	−	0.0970742i
$135$	−0.0828001	+	0.310845i	−0.00712630	+	0.0267532i
$136$	12.5999	+	7.27455i	1.08043	+	0.623787i
$137$	7.20855	−	4.16186i	0.615868	−	0.355571i	−0.159391	−	0.987216i	$-0.550953\pi$
$137$	7.20855	−	4.16186i	0.615868	−	0.355571i	0.775258	+	0.631644i	$0.217620\pi$
$138$	7.41211	+	1.98217i	0.630960	+	0.168733i
$139$	3.82478			0.324414			0.162207	−	0.986757i	$-0.448139\pi$
$139$	3.82478			0.324414			0.162207	+	0.986757i	$0.448139\pi$
$140$	0.161292	−	0.279366i	0.0136317	−	0.0236108i
$141$	5.28421	+	1.41312i	0.445011	+	0.119006i
$142$	5.14408	−	8.90981i	0.431682	−	0.747695i
$143$	0.220548	−	4.61898i	0.0184431	−	0.386258i
$144$	1.81709	−	1.05148i	0.151424	−	0.0876233i
$145$	−0.382505	+	0.220839i	−0.0317653	+	0.0183397i
$146$	−4.76671			−0.394495
$147$	−3.17927	+	11.8885i	−0.262221	+	0.980549i
$148$	−5.60412	+	3.23554i	−0.460656	+	0.265960i
$149$		−	20.0582i		−	1.64323i	−0.570044	−	0.821614i	$-0.693074\pi$
$149$		−	20.0582i		−	1.64323i	0.570044	−	0.821614i	$-0.306926\pi$
$150$	−6.54302	−	1.74975i	−0.534235	−	0.142867i
$151$	−12.0273	−	6.94396i	−0.978767	−	0.565092i	−0.0768696	−	0.997041i	$-0.524493\pi$
$151$	−12.0273	−	6.94396i	−0.978767	−	0.565092i	−0.901898	+	0.431950i	$0.857826\pi$
$152$	4.16702	−	7.21750i	0.337990	−	0.585416i
$153$	0.0161637	+	16.4629i	0.00130676	+	1.33095i
$154$	3.26487	−	1.88498i	0.263091	−	0.151896i
$155$	−0.129476	+	0.224259i	−0.0103998	+	0.0180129i
$156$	8.46576	−	1.84497i	0.677803	−	0.147716i
$157$	7.95334	+	13.7756i	0.634746	+	1.09941i	0.986569	+	0.163346i	$0.0522286\pi$
$157$	7.95334	+	13.7756i	0.634746	+	1.09941i	−0.351823	+	0.936067i	$0.614438\pi$
$158$	0.835325	+	0.482275i	0.0664549	+	0.0383678i
$159$	1.25957	−	0.338162i	0.0998901	−	0.0268180i
$160$	−0.181087	−	0.313652i	−0.0143162	−	0.0247964i
$161$		−	21.2563i		−	1.67523i
$162$	−6.10723	−	3.51004i	−0.479829	−	0.275775i
$163$	11.4205	+	6.59365i	0.894525	+	0.516454i	0.875420	−	0.483363i	$-0.160585\pi$
$163$	11.4205	+	6.59365i	0.894525	+	0.516454i	0.0191051	+	0.999817i	$0.493918\pi$
$164$	11.8830	+	6.86068i	0.927910	+	0.535729i
$165$	−0.0972914	−	0.0971959i	−0.00757412	−	0.00756669i
$166$	4.99496	−	8.65152i	0.387684	−	0.671488i
$167$	−1.16879	−	0.674802i	−0.0904438	−	0.0522177i	0.454096	−	0.890953i	$-0.349962\pi$
$167$	−1.16879	−	0.674802i	−0.0904438	−	0.0522177i	−0.544540	+	0.838735i	$0.683296\pi$
$168$	12.2010	+	12.1890i	0.941327	+	0.940403i
$169$	12.9409	+	1.23863i	0.995451	+	0.0952791i
$170$	0.265897			0.0203934
$171$	9.43035	−	0.00925895i	0.721157	−	0.000708049i
$172$	−2.93274	−	5.07966i	−0.223620	−	0.387321i
$173$	−7.35718	−	12.7430i	−0.559356	−	0.968834i	−0.997550	−	0.0699531i	$-0.977715\pi$
$173$	−7.35718	−	12.7430i	−0.559356	−	0.968834i	0.438194	−	0.898880i	$-0.355618\pi$
$174$	−2.50779	−	9.34085i	−0.190115	−	0.708128i
$175$			18.7639i			1.41842i
$176$			0.897512i			0.0676525i
$177$	0.161232	+	0.600548i	0.0121190	+	0.0451400i
$178$	−0.588079	−	1.01858i	−0.0440784	−	0.0763461i
$179$	−2.60130	−	4.50559i	−0.194431	−	0.336764i	0.752283	−	0.658840i	$-0.228953\pi$
$179$	−2.60130	−	4.50559i	−0.194431	−	0.336764i	−0.946714	+	0.322076i	$0.895619\pi$
$180$	0.128620	−	0.223282i	0.00958676	−	0.0166425i
$181$	10.0948			0.750340			0.375170	−	0.926956i	$-0.377584\pi$
$181$	10.0948			0.750340			0.375170	+	0.926956i	$0.377584\pi$
$182$	4.85539	+	9.42074i	0.359906	+	0.698312i
$183$	2.02298	+	2.02100i	0.149543	+	0.149396i
$184$	−12.9951	−	7.50274i	−0.958013	−	0.553109i
$185$	−0.144372	+	0.250060i	−0.0106145	+	0.0183848i
$186$	−4.01154	−	4.00761i	−0.294141	−	0.293852i
$187$	−6.09517	−	3.51905i	−0.445723	−	0.257338i
$188$	−3.79454	−	2.19078i	−0.276745	−	0.159779i
$189$	−5.02309	+	18.8575i	−0.365376	+	1.37168i
$190$		−	0.152312i		−	0.0110499i
$191$	1.35894	+	2.35376i	0.0983297	+	0.170312i	0.910993	−	0.412421i	$-0.135317\pi$
$191$	1.35894	+	2.35376i	0.0983297	+	0.170312i	−0.812664	+	0.582733i	$0.801983\pi$
$192$	5.31819	−	1.42780i	0.383807	−	0.103043i
$193$	−16.5292	−	9.54314i	−1.18980	−	0.686930i	−0.231537	−	0.972826i	$-0.574376\pi$
$193$	−16.5292	−	9.54314i	−1.18980	−	0.686930i	−0.958261	+	0.285896i	$0.907709\pi$
$194$	3.92254	+	6.79405i	0.281622	+	0.487784i
$195$	0.285978	−	0.260169i	0.0204793	−	0.0186311i
$196$	4.92885	−	8.53702i	0.352061	−	0.609787i
$197$	1.87976	−	1.08528i	0.133927	−	0.0773230i	−0.431539	−	0.902094i	$-0.642029\pi$
$197$	1.87976	−	1.08528i	0.133927	−	0.0773230i	0.565467	+	0.824771i	$0.308696\pi$
$198$	2.60648	−	1.50826i	0.185234	−	0.107188i
$199$	5.21774	−	9.03739i	0.369876	−	0.640644i	−0.619670	−	0.784862i	$-0.712734\pi$
$199$	5.21774	−	9.03739i	0.369876	−	0.640644i	0.989546	+	0.144219i	$0.0460669\pi$
$200$	11.4714	+	6.62302i	0.811152	+	0.468319i
$201$	−2.77401	−	0.741833i	−0.195663	−	0.0523249i
$202$			13.4624i			0.947209i
$203$	−23.2048	+	13.3973i	−1.62866	+	0.940305i
$204$	3.40688	−	12.7396i	0.238529	−	0.891954i
$205$	0.612258			0.0427620
$206$	−11.9649	+	6.90795i	−0.833635	+	0.481300i
$207$	−0.0166708	−	16.9794i	−0.00115870	−	1.18015i
$208$	−2.52028	−	0.120339i	−0.174750	−	0.00834399i
$209$	−2.01579	+	3.49145i	−0.139435	+	0.241509i
$210$	0.304492	+	0.0814281i	0.0210119	+	0.00561907i
$211$	−0.193251	+	0.334720i	−0.0133039	+	0.0230431i	−0.872601	−	0.488434i	$-0.837568\pi$
$211$	−0.193251	+	0.334720i	−0.0133039	+	0.0230431i	0.859297	+	0.511477i	$0.170902\pi$
$212$	−1.04468			−0.0717489
$213$	−21.9948	−	5.88191i	−1.50706	−	0.403022i
$214$	6.96818	−	4.02308i	0.476335	−	0.275012i
$215$	−0.226659	−	0.130861i	−0.0154580	−	0.00892467i
$216$	9.75562	+	9.72693i	0.663786	+	0.661834i
$217$	−7.85471	+	13.6048i	−0.533213	+	0.923551i
$218$	5.60512			0.379627
$219$	2.73521	+	10.1879i	0.184828	+	0.688436i
$220$	0.0550801	+	0.0954016i	0.00371350	+	0.00643197i
$221$	10.6990	−	16.6439i	0.719692	−	1.11959i
$222$	−4.47307	−	4.46868i	−0.300213	−	0.299918i
$223$		−	2.03212i		−	0.136081i	−0.997683	−	0.0680405i	$-0.978325\pi$
$223$		−	2.03212i		−	0.136081i	0.997683	−	0.0680405i	$-0.0216747\pi$
$224$	−10.9857	−	19.0278i	−0.734013	−	1.27135i
$225$	0.0147161	+	14.9885i	0.000981072	+	0.999233i
$226$		−	2.58620i		−	0.172031i
$227$	22.7802	−	13.1522i	1.51198	−	0.872941i	0.512076	−	0.858940i	$-0.328877\pi$
$227$	22.7802	−	13.1522i	1.51198	−	0.872941i	0.999902	−	0.0140007i	$-0.00445672\pi$
$228$	−7.29756	−	1.95154i	−0.483293	−	0.129244i
$229$	23.2482	−	13.4224i	1.53629	−	0.886976i	0.537236	−	0.843432i	$-0.319469\pi$
$229$	23.2482	−	13.4224i	1.53629	−	0.886976i	0.999052	−	0.0435436i	$-0.0138648\pi$
$230$	−0.274238			−0.0180827
$231$	−5.90221	−	5.89642i	−0.388337	−	0.387956i
$232$			18.9151i			1.24184i
$233$	−8.15619			−0.534330			−0.267165	−	0.963651i	$-0.586087\pi$
$233$	−8.15619			−0.534330			−0.267165	+	0.963651i	$0.586087\pi$
$234$	3.88584	+	7.52141i	0.254025	+	0.491690i
$235$	−0.195508			−0.0127536
$236$		−	0.498093i		−	0.0324231i
$237$	0.551449	−	2.06209i	0.0358205	−	0.133947i
$238$	16.1307			1.04560
$239$	−11.8525	+	6.84307i	−0.766677	+	0.442641i	−0.831688	−	0.555243i	$-0.812625\pi$
$239$	−11.8525	+	6.84307i	−0.766677	+	0.442641i	0.0650107	+	0.997885i	$0.479292\pi$
$240$	−0.0530336	+	0.0530857i	−0.00342330	+	0.00342667i
$241$	11.4993	−	6.63911i	0.740733	−	0.427663i	−0.0816026	−	0.996665i	$-0.526004\pi$
$241$	11.4993	−	6.63911i	0.740733	−	0.427663i	0.822336	+	0.569002i	$0.192671\pi$
$242$		−	7.32198i		−	0.470675i
$243$	−3.99762	+	15.0672i	−0.256447	+	0.966558i
$244$	−1.14528	−	1.98369i	−0.0733192	−	0.126993i
$245$		−	0.439859i		−	0.0281015i
$246$	−3.46360	+	12.9518i	−0.220831	+	0.825774i
$247$	−9.53397	−	6.12862i	−0.606632	−	0.389955i
$248$	5.54488	+	9.60402i	0.352101	+	0.609856i
$249$	−21.3572	−	5.71140i	−1.35345	−	0.361945i
$250$	0.484351			0.0306330
$251$	−2.59137	+	4.48838i	−0.163566	+	0.283304i	−0.936145	−	0.351614i	$-0.885633\pi$
$251$	−2.59137	+	4.48838i	−0.163566	+	0.283304i	0.772579	+	0.634918i	$0.218966\pi$
$252$	7.80276	−	13.5455i	0.491528	−	0.853285i
$253$	6.28637	+	3.62944i	0.395220	+	0.228181i
$254$	−4.83691	+	2.79259i	−0.303495	+	0.175223i
$255$	−0.152576	−	0.568304i	−0.00955466	−	0.0355886i
$256$	−13.5685			−0.848028
$257$	−14.6011	+	25.2898i	−0.910789	+	1.57753i	−0.0978359	+	0.995203i	$0.531192\pi$
$257$	−14.6011	+	25.2898i	−0.910789	+	1.57753i	−0.812953	+	0.582330i	$0.802141\pi$
$258$	4.05048	−	4.05446i	0.252172	−	0.252420i
$259$	−8.75840	+	15.1700i	−0.544220	+	0.942617i
$260$	−0.275280	+	0.141878i	−0.0170721	+	0.00879887i
$261$	−18.5253	+	10.7198i	−1.14669	+	0.663542i
$262$	−13.2309	+	7.63888i	−0.817410	+	0.471932i
$263$	5.42799			0.334704			0.167352	−	0.985897i	$-0.446478\pi$
$263$	5.42799			0.334704			0.167352	+	0.985897i	$0.446478\pi$
$264$	−5.68808	+	1.52711i	−0.350077	+	0.0939870i
$265$	−0.0403693	+	0.0233072i	−0.00247987	+	0.00143175i
$266$		−	9.24003i		−	0.566543i
$267$	−1.83958	+	1.84139i	−0.112580	+	0.112691i
$268$	1.99198	+	1.15007i	0.121680	+	0.0702519i
$269$	−6.85146	+	11.8671i	−0.417741	+	0.723549i	−0.995712	−	0.0925087i	$-0.970511\pi$
$269$	−6.85146	+	11.8671i	−0.417741	+	0.723549i	0.577971	+	0.816057i	$0.303845\pi$
$270$	0.243289	+	0.0648053i	0.0148061	+	0.00394393i
$271$	10.5946	−	6.11677i	0.643573	−	0.371567i	−0.142416	−	0.989807i	$-0.545487\pi$
$271$	10.5946	−	6.11677i	0.643573	−	0.371567i	0.785990	+	0.618240i	$0.212154\pi$
$272$	−1.92012	+	3.32575i	−0.116424	+	0.201653i
$273$	17.3489	−	15.7832i	1.05001	−	0.955245i
$274$	−3.25737	−	5.64193i	−0.196785	−	0.340841i
$275$	−5.54928	−	3.20388i	−0.334634	−	0.193201i
$276$	−3.51374	+	13.1393i	−0.211503	+	0.790891i
$277$	7.02000	+	12.1590i	0.421791	+	0.730563i	0.996115	−	0.0880651i	$-0.0280683\pi$
$277$	7.02000	+	12.1590i	0.421791	+	0.730563i	−0.574324	+	0.818628i	$0.694735\pi$
$278$		−	2.99355i		−	0.179541i
$279$	−6.26361	+	10.8735i	−0.374993	+	0.650982i
$280$	−0.533844	−	0.308215i	−0.0319033	−	0.0184194i
$281$	−18.6400	−	10.7618i	−1.11197	−	0.641997i	−0.172632	−	0.984986i	$-0.555227\pi$
$281$	−18.6400	−	10.7618i	−1.11197	−	0.641997i	−0.939339	+	0.342990i	$0.888560\pi$
$282$	1.10601	−	4.13580i	0.0658619	−	0.246284i
$283$	−11.5554	+	20.0145i	−0.686897	+	1.18974i	0.285940	+	0.958248i	$0.407694\pi$
$283$	−11.5554	+	20.0145i	−0.686897	+	1.18974i	−0.972837	+	0.231493i	$0.925639\pi$
$284$	15.7942	+	9.11880i	0.937215	+	0.541101i
$285$	−0.325537	+	0.0873988i	−0.0192832	+	0.00517706i
$286$	−3.61514	−	0.172617i	−0.213768	−	0.0102070i
$287$	37.1428			2.19247
$288$	−8.79021	−	15.1906i	−0.517968	−	0.895116i
$289$	−6.55717	−	11.3573i	−0.385716	−	0.668079i
$290$	0.172845	+	0.299376i	0.0101498	+	0.0175800i
$291$	12.2702	−	12.2822i	0.719290	−	0.719996i
$292$		−	8.44983i		−	0.494489i
$293$			0.299960i			0.0175239i	0.999962	+	0.00876193i	$0.00278905\pi$
$293$			0.299960i			0.0175239i	−0.999962	+	0.00876193i	$0.997211\pi$
$294$	9.30481	+	2.48832i	0.542668	+	0.145122i
$295$	−0.0111126	−	0.0192477i	−0.000647003	−	0.00112064i
$296$	6.18282	+	10.7090i	0.359369	+	0.622446i
$297$	−4.71926	−	4.70538i	−0.273839	−	0.273034i
$298$	−15.6990			−0.909416
$299$	−11.0346	+	17.1659i	−0.638147	+	0.992732i
$300$	3.10175	−	11.5987i	0.179080	−	0.669649i
$301$	−13.7503	−	7.93875i	−0.792555	−	0.457582i
$302$	−5.43484	+	9.41343i	−0.312740	+	0.541682i
$303$	28.7732	−	7.72491i	1.65298	−	0.443784i
$304$	1.90506	+	1.09989i	0.109263	+	0.0630829i
$305$	−0.0885137	−	0.0511034i	−0.00506828	−	0.00292617i
$306$	12.8851	−	0.0126509i	0.736591	−	0.000723204i
$307$		−	13.4090i		−	0.765291i	−0.923895	−	0.382646i	$-0.875013\pi$
$307$		−	13.4090i		−	0.765291i	0.923895	−	0.382646i	$-0.124987\pi$
$308$	3.34145	+	5.78757i	0.190397	+	0.329777i
$309$	21.6301	+	21.6089i	1.23049	+	1.22928i
$310$	0.175522	+	0.101337i	0.00996895	+	0.00575558i
$311$	6.66305	+	11.5407i	0.377827	+	0.654415i	0.990746	−	0.135731i	$-0.0433382\pi$
$311$	6.66305	+	11.5407i	0.377827	+	0.654415i	−0.612919	+	0.790146i	$0.710005\pi$
$312$	−3.52557	−	16.1773i	−0.199596	−	0.915859i
$313$	−7.54812	+	13.0737i	−0.426645	+	0.738971i	−0.996572	−	0.0827243i	$-0.973638\pi$
$313$	−7.54812	+	13.0737i	−0.426645	+	0.738971i	0.569928	+	0.821695i	$0.306971\pi$
$314$	10.7818	−	6.22486i	0.608451	−	0.351289i
$315$	−0.000684840	−	0.697517i	−3.85864e−5	−	0.0393007i
$316$	−0.854918	+	1.48076i	−0.0480929	+	0.0832994i
$317$	16.1108	+	9.30158i	0.904873	+	0.522429i	0.878778	−	0.477231i	$-0.158359\pi$
$317$	16.1108	+	9.30158i	0.904873	+	0.522429i	0.0260952	+	0.999659i	$0.491693\pi$
$318$	−0.264670	−	0.985827i	−0.0148420	−	0.0552824i
$319$		−	9.15015i		−	0.512310i
$320$	−0.170449	+	0.0984087i	−0.00952838	+	0.00550121i
$321$	−12.5970	−	12.5847i	−0.703097	−	0.702407i
$322$	−16.6367			−0.927127
$323$	−14.9391	+	8.62508i	−0.831233	+	0.479912i
$324$	6.22216	−	10.8261i	0.345676	−	0.601452i
$325$	9.74077	−	15.1532i	0.540321	−	0.840548i
$326$	5.16066	−	8.93853i	0.285823	−	0.495059i
$327$	−3.21630	−	11.9799i	−0.177862	−	0.662489i
$328$	13.1101	−	22.7074i	0.723886	−	1.25381i
$329$	−11.8606			−0.653895
$330$	−0.0760725	+	0.0761472i	−0.00418765	+	0.00419177i
$331$	−4.93467	+	2.84903i	−0.271234	+	0.156597i	−0.629448	−	0.777042i	$-0.716719\pi$
$331$	−4.93467	+	2.84903i	−0.271234	+	0.156597i	0.358214	+	0.933639i	$0.383386\pi$
$332$	15.3364	+	8.85445i	0.841692	+	0.485951i
$333$	−6.98424	+	12.1245i	−0.382734	+	0.664421i
$334$	−0.528149	+	0.914780i	−0.0288990	+	0.0500545i
$335$	0.102634			0.00560751
$336$	−3.21730	+	3.22046i	−0.175518	+	0.175690i
$337$	16.0839	+	27.8581i	0.876146	+	1.51753i	0.855537	+	0.517741i	$0.173227\pi$
$337$	16.0839	+	27.8581i	0.876146	+	1.51753i	0.0206081	+	0.999788i	$0.493440\pi$
$338$	0.969440	−	10.1284i	0.0527306	−	0.550915i
$339$	−5.52750	+	1.48400i	−0.300213	+	0.0805997i
$340$			0.471349i			0.0255625i
$341$	−2.68233	−	4.64593i	−0.145256	−	0.251591i
$342$	−0.00724672	−	7.38087i	−0.000391858	−	0.399112i
$343$		−	0.394490i		−	0.0213005i
$344$	−9.70677	+	5.60421i	−0.523354	+	0.302159i
$345$	0.157362	+	0.586131i	0.00847207	+	0.0315562i
$346$	−9.97360	+	5.75826i	−0.536184	+	0.309566i
$347$	16.0489			0.861553			0.430776	−	0.902459i	$-0.358240\pi$
$347$	16.0489			0.861553			0.430776	+	0.902459i	$0.358240\pi$
$348$	16.5583	−	4.44550i	0.887619	−	0.238304i
$349$		−	27.2101i		−	1.45652i	−0.685298	−	0.728262i	$-0.740328\pi$
$349$		−	27.2101i		−	1.45652i	0.685298	−	0.728262i	$-0.259672\pi$
$350$	14.6860			0.785000
$351$	13.8458	−	12.6211i	0.739035	−	0.673667i
$352$	7.50307			0.399915
$353$		−	4.63249i		−	0.246562i	−0.992372	−	0.123281i	$-0.960658\pi$
$353$		−	4.63249i		−	0.246562i	0.992372	−	0.123281i	$-0.0393417\pi$
$354$	0.470032	−	0.126192i	0.0249819	−	0.00670703i
$355$	0.813776			0.0431908
$356$	1.80562	−	1.04248i	0.0956977	−	0.0552511i
$357$	−9.25605	−	34.4763i	−0.489882	−	1.82468i
$358$	−3.52640	+	2.03597i	−0.186376	+	0.107604i
$359$		−	16.1406i		−	0.851870i	−0.904754	−	0.425935i	$-0.859945\pi$
$359$		−	16.1406i		−	0.851870i	0.904754	−	0.425935i	$-0.140055\pi$
$360$	−0.426672	−	0.245781i	−0.0224876	−	0.0129538i
$361$	−4.55936	−	7.89704i	−0.239966	−	0.415634i
$362$		−	7.90091i		−	0.415263i
$363$	−15.6493	+	4.20146i	−0.821377	+	0.220520i
$364$	−16.6999	+	8.60704i	−0.875314	+	0.451132i
$365$	−0.188519	−	0.326525i	−0.00986754	−	0.0170911i
$366$	1.58178	−	1.58333i	0.0826808	−	0.0827620i
$367$	−20.7667			−1.08401			−0.542005	−	0.840375i	$-0.682335\pi$
$367$	−20.7667			−1.08401			−0.542005	+	0.840375i	$0.682335\pi$
$368$	1.98035	−	3.43007i	0.103233	−	0.178805i
$369$	29.6694	−	0.0291302i	1.54453	−	0.00151646i
$370$	0.195715	+	0.112996i	0.0101748	+	0.00587440i
$371$	−2.44901	+	1.41394i	−0.127146	+	0.0734081i
$372$	7.10419	−	7.11117i	0.368335	−	0.368697i
$373$	6.07906			0.314762			0.157381	−	0.987538i	$-0.449695\pi$
$373$	6.07906			0.314762			0.157381	+	0.987538i	$0.449695\pi$
$374$	−2.75426	+	4.77052i	−0.142419	+	0.246678i
$375$	−0.277928	−	1.03521i	−0.0143521	−	0.0534579i
$376$	−4.18638	+	7.25101i	−0.215896	+	0.373943i
$377$	25.6943	+	1.22686i	1.32332	+	0.0631863i
$378$	14.7592	+	3.93143i	0.759132	+	0.202211i
$379$	−13.7130	+	7.91718i	−0.704388	+	0.406678i	−0.808979	−	0.587837i	$-0.799980\pi$
$379$	−13.7130	+	7.91718i	−0.704388	+	0.406678i	0.104592	+	0.994515i	$0.466646\pi$
$380$	0.269999			0.0138507
$381$	8.74413	+	8.73555i	0.447975	+	0.447536i
$382$	1.84222	−	1.06361i	0.0942563	−	0.0544189i
$383$		−	14.9997i		−	0.766450i	−0.923655	−	0.383225i	$-0.874813\pi$
$383$		−	14.9997i		−	0.766450i	0.923655	−	0.383225i	$-0.125187\pi$
$384$	4.13725	+	15.4102i	0.211128	+	0.786396i
$385$	0.258246	+	0.149098i	0.0131614	+	0.00759875i
$386$	−7.46915	+	12.9369i	−0.380170	+	0.658473i
$387$	−10.9899	−	6.33063i	−0.558647	−	0.321804i
$388$	−12.0436	+	6.95340i	−0.611424	+	0.353006i
$389$	8.69825	−	15.0658i	0.441019	−	0.763867i	−0.556747	−	0.830682i	$-0.687951\pi$
$389$	8.69825	−	15.0658i	0.441019	−	0.763867i	0.997765	+	0.0668155i	$0.0212839\pi$
$390$	−0.203627	−	0.223827i	−0.0103111	−	0.0113339i
$391$	15.5295	+	26.8979i	0.785360	+	1.36028i
$392$	−16.3135	−	9.41859i	−0.823955	−	0.475711i
$393$	23.9188	+	23.8953i	1.20654	+	1.20536i
$394$	−0.849418	−	1.47123i	−0.0427930	−	0.0741197i
$395$			0.0762943i			0.00383878i
$396$	2.67367	+	4.62044i	0.134357	+	0.232186i
$397$	−9.89799	−	5.71461i	−0.496766	−	0.286808i	0.230611	−	0.973046i	$-0.425928\pi$
$397$	−9.89799	−	5.71461i	−0.496766	−	0.286808i	−0.727377	+	0.686238i	$0.759261\pi$
$398$	−7.07331	−	4.08378i	−0.354553	−	0.204701i
$399$	−19.7488	+	5.30207i	−0.988677	+	0.265436i
$400$	−1.74815	+	3.02788i	−0.0874075	+	0.151394i
$401$	11.0669	+	6.38948i	0.552655	+	0.319075i	0.750192	−	0.661220i	$-0.229961\pi$
$401$	11.0669	+	6.38948i	0.552655	+	0.319075i	−0.197537	+	0.980295i	$0.563294\pi$
$402$	−0.580612	+	2.17114i	−0.0289583	+	0.108286i
$403$	13.4058	−	6.90925i	0.667788	−	0.344174i
$404$	−23.8644			−1.18730
$405$	−0.00109409	−	0.557171i	−5.43658e−5	−	0.0276861i
$406$	10.4857	+	18.1617i	0.520395	+	0.901351i
$407$	−2.99093	−	5.18044i	−0.148255	−	0.256785i
$408$	−24.3443	−	6.51023i	−1.20522	−	0.322304i
$409$		−	19.7767i		−	0.977897i	−0.872313	−	0.488949i	$-0.837381\pi$
$409$		−	19.7767i		−	0.977897i	0.872313	−	0.488949i	$-0.162619\pi$
$410$		−	0.479197i		−	0.0236659i
$411$	−10.1894	+	10.1994i	−0.502607	+	0.503101i
$412$	−12.2456	−	21.2099i	−0.603296	−	1.04494i
$413$	−0.674152	−	1.16767i	−0.0331728	−	0.0574571i
$414$	−13.2893	+	0.0130477i	−0.653132	+	0.000641261i
$415$	0.790185			0.0387887
$416$	−1.00601	+	21.0692i	−0.0493239	+	1.03300i
$417$	−6.39814	+	1.71774i	−0.313318	+	0.0841183i
$418$	2.73266	+	1.57770i	0.133659	+	0.0771680i
$419$	−0.513836	+	0.889990i	−0.0251025	+	0.0434789i	−0.878304	−	0.478103i	$-0.841325\pi$
$419$	−0.513836	+	0.889990i	−0.0251025	+	0.0434789i	0.853201	+	0.521582i	$0.174658\pi$
$420$	−0.144346	+	0.539765i	−0.00704335	+	0.0263378i
$421$	19.3455	+	11.1691i	0.942843	+	0.544351i	0.890850	−	0.454297i	$-0.150109\pi$
$421$	19.3455	+	11.1691i	0.942843	+	0.544351i	0.0519927	+	0.998647i	$0.483443\pi$
$422$	0.261976	+	0.151252i	0.0127528	+	0.00736283i
$423$	−9.47414	+	0.00930194i	−0.460648	+	0.000452276i
$424$			1.99629i			0.0969483i
$425$	−13.7086	−	23.7440i	−0.664966	−	1.15175i
$426$	−4.60361	+	17.2147i	−0.223046	+	0.834055i
$427$	−5.36971	−	3.10020i	−0.259859	−	0.150029i
$428$	7.13162	+	12.3523i	0.344720	+	0.597073i
$429$	1.70549	+	7.82573i	0.0823418	+	0.377830i
$430$	−0.102422	+	0.177399i	−0.00493921	+	0.00855496i
$431$	−6.38655	+	3.68727i	−0.307629	+	0.177610i	−0.645865	−	0.763452i	$-0.723503\pi$
$431$	−6.38655	+	3.68727i	−0.307629	+	0.177610i	0.338236	+	0.941061i	$0.390170\pi$
$432$	−2.56743	+	2.57500i	−0.123525	+	0.123890i
$433$	2.96921	−	5.14283i	0.142691	−	0.247148i	−0.785818	−	0.618458i	$-0.787758\pi$
$433$	2.96921	−	5.14283i	0.142691	−	0.247148i	0.928509	+	0.371309i	$0.121091\pi$
$434$	10.6481	+	6.14766i	0.511123	+	0.295097i
$435$	0.540678	−	0.541209i	0.0259235	−	0.0259490i
$436$			9.93607i			0.475851i
$437$	15.4077	−	8.89564i	0.737050	−	0.425536i
$438$	7.97381	−	2.14077i	0.381003	−	0.102290i
$439$	23.6921			1.13076			0.565382	−	0.824829i	$-0.308729\pi$
$439$	23.6921			1.13076			0.565382	+	0.824829i	$0.308729\pi$
$440$	0.182304	−	0.105253i	0.00869099	−	0.00501775i
$441$	−0.0209277	−	21.3151i	−0.000996557	−	1.01501i
$442$	−13.0267	−	8.37380i	−0.619616	−	0.398301i
$443$	−19.8468	+	34.3756i	−0.942948	+	1.63323i	−0.183138	+	0.983087i	$0.558626\pi$
$443$	−19.8468	+	34.3756i	−0.942948	+	1.63323i	−0.759809	+	0.650146i	$0.774708\pi$
$444$	7.92153	−	7.92931i	0.375939	−	0.376309i
$445$	0.0465161	−	0.0805682i	0.00220507	−	0.00381930i
$446$	−1.59049			−0.0753117
$447$	9.00830	+	33.5535i	0.426078	+	1.58703i
$448$	−10.3403	+	5.96999i	−0.488535	+	0.282056i
$449$	−7.64958	−	4.41649i	−0.361006	−	0.208427i	0.308516	−	0.951219i	$-0.400168\pi$
$449$	−7.64958	−	4.41649i	−0.361006	−	0.208427i	−0.669522	+	0.742792i	$0.733501\pi$
$450$	11.7311	−	0.0115179i	0.553008	−	0.000542957i
$451$	−6.34200	+	10.9847i	−0.298633	+	0.517248i
$452$	4.58449			0.215636
$453$	23.2380	+	6.21438i	1.09182	+	0.291977i
$454$	−10.2938	−	17.8295i	−0.483114	−	0.836778i
$455$	−0.453305	+	0.705182i	−0.0212513	+	0.0330594i
$456$	−3.72921	+	13.9450i	−0.174636	+	0.653033i
$457$			20.7736i			0.971749i	0.874029	+	0.485874i	$0.161499\pi$
$457$			20.7736i			0.971749i	−0.874029	+	0.485874i	$0.838501\pi$
$458$	−10.5053	−	18.1957i	−0.490881	−	0.850231i
$459$	−7.42070	−	27.5322i	−0.346369	−	1.28509i
$460$		−	0.486135i		−	0.0226661i
$461$	−9.07688	+	5.24054i	−0.422752	+	0.244076i	−0.696254	−	0.717795i	$-0.745151\pi$
$461$	−9.07688	+	5.24054i	−0.422752	+	0.244076i	0.273502	+	0.961871i	$0.411818\pi$
$462$	−4.61496	+	4.61949i	−0.214707	+	0.214918i
$463$	17.5850	−	10.1527i	0.817243	−	0.471835i	−0.0322220	−	0.999481i	$-0.510258\pi$
$463$	17.5850	−	10.1527i	0.817243	−	0.471835i	0.849465	+	0.527645i	$0.176925\pi$
$464$	−4.99265			−0.231778
$465$	0.115873	−	0.433293i	0.00537346	−	0.0200935i
$466$			6.38362i			0.295716i
$467$	−14.0228			−0.648897			−0.324448	−	0.945903i	$-0.605179\pi$
$467$	−14.0228			−0.648897			−0.324448	+	0.945903i	$0.605179\pi$
$468$	−13.3330	+	6.88834i	−0.616319	+	0.318414i
$469$	6.22634			0.287506
$470$			0.153019i			0.00705824i
$471$	−19.4912	−	19.4721i	−0.898107	−	0.897226i
$472$	−0.951809			−0.0438106
$473$	4.69563	−	2.71103i	0.215905	−	0.124653i
$474$	−1.61394	−	0.431604i	−0.0741306	−	0.0198242i
$475$	−13.6011	+	7.85260i	−0.624062	+	0.360302i
$476$			28.5945i			1.31063i
$477$	−1.95515	+	1.13136i	−0.0895199	+	0.0518016i
$478$	5.35588	+	9.27665i	0.244972	+	0.424304i
$479$		−	9.89301i		−	0.452023i	−0.974125	−	0.226012i	$-0.927431\pi$
$479$		−	9.89301i		−	0.452023i	0.974125	−	0.226012i	$-0.0725687\pi$
$480$	0.443788	+	0.443353i	0.0202561	+	0.0202362i
$481$	14.9481	−	7.70415i	0.681574	−	0.351279i
$482$	−5.19624	−	9.00016i	−0.236682	−	0.409946i
$483$	9.54639	+	35.5578i	0.434376	+	1.61794i
$484$	12.9795			0.589978
$485$	−0.310267	+	0.537397i	−0.0140885	+	0.0244020i
$486$	11.7926	+	3.12882i	0.534925	+	0.141926i
$487$	35.6312	+	20.5717i	1.61460	+	0.932192i	0.988284	+	0.152626i	$0.0487731\pi$
$487$	35.6312	+	20.5717i	1.61460	+	0.932192i	0.626320	+	0.779566i	$0.284560\pi$
$488$	−3.79065	+	2.18853i	−0.171594	+	0.0990701i
$489$	−22.0657	−	5.90087i	−0.997844	−	0.266847i
$490$	−0.344265			−0.0155523
$491$	8.85594	−	15.3389i	0.399663	−	0.692236i	−0.594021	−	0.804449i	$-0.702461\pi$
$491$	8.85594	−	15.3389i	0.399663	−	0.692236i	0.993684	+	0.112213i	$0.0357939\pi$
$492$	−22.9593	−	6.13985i	−1.03509	−	0.276806i
$493$	19.5757	−	33.9060i	0.881643	−	1.52705i
$494$	−4.79670	+	7.46197i	−0.215814	+	0.335730i
$495$	0.206402	+	0.118896i	0.00927707	+	0.00534398i
$496$	−2.53499	+	1.46357i	−0.113824	+	0.0657164i
$497$	49.3680			2.21446
$498$	−4.47015	+	16.7156i	−0.200312	+	0.749046i
$499$	−16.2710	+	9.39408i	−0.728391	+	0.420537i	−0.817833	−	0.575455i	$-0.804825\pi$
$499$	−16.2710	+	9.39408i	−0.728391	+	0.420537i	0.0894423	+	0.995992i	$0.471492\pi$
$500$			0.858598i			0.0383977i
$501$	2.25823	+	0.603902i	0.100890	+	0.0269804i
$502$	3.51293	+	2.02819i	0.156790	+	0.0905226i
$503$	−7.83131	+	13.5642i	−0.349181	+	0.604799i	−0.986104	−	0.166128i	$-0.946873\pi$
$503$	−7.83131	+	13.5642i	−0.349181	+	0.604799i	0.636923	+	0.770927i	$0.280207\pi$
$504$	−25.8842	−	14.9104i	−1.15297	−	0.664161i
$505$	−0.922187	+	0.532425i	−0.0410368	+	0.0236926i
$506$	2.84066	−	4.92016i	0.126283	−	0.218728i
$507$	−22.2039	+	3.73986i	−0.986110	+	0.166093i
$508$	−4.95036	−	8.57428i	−0.219637	−	0.380422i
$509$	−32.5897	−	18.8157i	−1.44451	−	0.833989i	−0.446365	−	0.894851i	$-0.647282\pi$
$509$	−32.5897	−	18.8157i	−1.44451	−	0.833989i	−0.998146	+	0.0608617i	$0.980615\pi$
$510$	−0.444796	+	0.119417i	−0.0196959	+	0.00528786i
$511$	−11.4366	−	19.8087i	−0.505924	−	0.876286i
$512$		−	7.80461i		−	0.344918i
$513$	−15.7710	+	4.25074i	−0.696309	+	0.187675i
$514$	19.7936	+	11.4278i	0.873058	+	0.504060i
$515$	−0.946405	−	0.546407i	−0.0417036	−	0.0240776i
$516$	7.18725	+	7.18020i	0.316401	+	0.316091i
$517$	2.02515	−	3.50767i	0.0890661	−	0.154267i
$518$	11.8731	+	6.85495i	0.521675	+	0.301189i
$519$	18.0302	+	18.0125i	0.791438	+	0.790661i
$520$	0.271115	+	0.526035i	0.0118892	+	0.0230681i
$521$	3.84164			0.168305			0.0841526	−	0.996453i	$-0.473182\pi$
$521$	3.84164			0.168305			0.0841526	+	0.996453i	$0.473182\pi$
$522$	8.39012	+	14.4992i	0.367226	+	0.634614i
$523$	−19.6605	−	34.0529i	−0.859692	−	1.48903i	−0.872222	−	0.489109i	$-0.837322\pi$
$523$	−19.6605	−	34.0529i	−0.859692	−	1.48903i	0.0125300	−	0.999921i	$-0.496011\pi$
$524$	−13.5413	−	23.4542i	−0.591553	−	1.02460i
$525$	−8.42706	−	31.3886i	−0.367787	−	1.36991i
$526$		−	4.24833i		−	0.185236i
$527$		−	22.9541i		−	0.999895i
$528$	−0.403081	−	1.50137i	−0.0175418	−	0.0653387i
$529$	−4.51661	−	7.82300i	−0.196374	−	0.340131i
$530$	0.0182419	+	0.0315959i	0.000792378	+	0.00137244i
$531$	−0.539423	−	0.932193i	−0.0234090	−	0.0404537i
$532$	16.3796			0.710146
$533$	−29.9954	−	19.2816i	−1.29925	−	0.835181i
$534$	1.44120	+	1.43979i	0.0623669	+	0.0623057i
$535$	0.551171	+	0.318219i	0.0238292	+	0.0137578i
$536$	2.19768	−	3.80650i	0.0949255	−	0.164416i
$537$	6.37500	+	6.36874i	0.275101	+	0.274831i
$538$	9.28803	+	5.36245i	0.400436	+	0.231192i
$539$	7.89161	+	4.55623i	0.339916	+	0.196251i
$540$	−0.114879	+	0.431274i	−0.00494360	+	0.0185591i
$541$			45.4115i			1.95239i	0.216885	+	0.976197i	$0.430410\pi$
$541$			45.4115i			1.95239i	−0.216885	+	0.976197i	$0.569590\pi$
$542$	−4.78742	−	8.29206i	−0.205637	−	0.356174i
$543$	−16.8867	+	4.53366i	−0.724678	+	0.194558i
$544$	27.8027	+	16.0519i	1.19203	+	0.688220i
$545$	0.221678	+	0.383957i	0.00949563	+	0.0164469i
$546$	−12.3531	−	13.5785i	−0.528664	−	0.581107i
$547$	7.70865	−	13.3518i	0.329598	−	0.570881i	−0.652834	−	0.757501i	$-0.726420\pi$
$547$	7.70865	−	13.3518i	0.329598	−	0.570881i	0.982432	+	0.186620i	$0.0597534\pi$
$548$	10.0013	−	5.77426i	0.427235	−	0.246664i
$549$	−4.29172	−	2.47221i	−0.183166	−	0.105511i
$550$	−2.50758	+	4.34326i	−0.106924	+	0.185197i
$551$	−19.4221	−	11.2134i	−0.827411	−	0.477706i
$552$	25.1079	+	6.71445i	1.06867	+	0.285786i
$553$			4.62842i			0.196820i
$554$	9.51650	−	5.49436i	0.404317	−	0.233433i
$555$	0.129204	−	0.483143i	0.00548439	−	0.0205083i
$556$	5.30660			0.225050
$557$	−24.1319	+	13.9325i	−1.02250	+	0.590341i	−0.914827	−	0.403846i	$-0.867673\pi$
$557$	−24.1319	+	13.9325i	−1.02250	+	0.590341i	−0.107673	+	0.994186i	$0.534340\pi$
$558$	8.51041	+	4.90236i	0.360275	+	0.207533i
$559$	6.98316	+	13.5492i	0.295356	+	0.573069i
$560$	0.0813534	−	0.140908i	0.00343781	−	0.00595446i
$561$	11.7765	+	3.14931i	0.497205	+	0.132964i
$562$	−8.42298	+	14.5890i	−0.355302	+	0.615401i
$563$	26.6983			1.12520			0.562599	−	0.826730i	$-0.309801\pi$
$563$	26.6983			1.12520			0.562599	+	0.826730i	$0.309801\pi$
$564$	7.33145	+	1.96060i	0.308710	+	0.0825561i
$565$	0.177157	−	0.102282i	0.00745306	−	0.00430303i
$566$	15.6648	+	9.04408i	0.658441	+	0.380151i
$567$	−0.0663733	−	33.8009i	−0.00278742	−	1.41951i
$568$	17.4252	−	30.1813i	0.731145	−	1.26638i
$569$	−15.8534			−0.664609			−0.332305	−	0.943172i	$-0.607826\pi$
$569$	−15.8534			−0.664609			−0.332305	+	0.943172i	$0.607826\pi$
$570$	0.0684046	+	0.254789i	0.00286515	+	0.0106719i
$571$	−5.89230	−	10.2058i	−0.246585	−	0.427098i	0.715991	−	0.698109i	$-0.245975\pi$
$571$	−5.89230	−	10.2058i	−0.246585	−	0.427098i	−0.962576	+	0.271012i	$0.912642\pi$
$572$	0.305993	−	6.40848i	0.0127942	−	0.267952i
$573$	−3.33035	−	3.32709i	−0.139128	−	0.138991i
$574$		−	29.0706i		−	1.21339i
$575$	14.1386	+	24.4888i	0.589622	+	1.02125i
$576$	−8.25509	+	4.77689i	−0.343962	+	0.199037i
$577$			3.85716i			0.160576i	0.996772	+	0.0802879i	$0.0255840\pi$
$577$			3.85716i			0.160576i	−0.996772	+	0.0802879i	$0.974416\pi$
$578$	−8.88907	+	5.13211i	−0.369737	+	0.213468i
$579$	31.9362	+	8.54047i	1.32722	+	0.354930i
$580$	−0.530697	+	0.306398i	−0.0220360	+	0.0127225i
$581$	47.9368			1.98875
$582$	−9.61295	−	9.60351i	−0.398469	−	0.398078i
$583$		−	0.965700i		−	0.0399952i
$584$	−16.1469			−0.668162
$585$	−0.361543	+	0.563650i	−0.0149480	+	0.0233040i
$586$	0.234771			0.00969828
$587$			25.6213i			1.05751i	0.848776	+	0.528753i	$0.177340\pi$
$587$			25.6213i			1.05751i	−0.848776	+	0.528753i	$0.822660\pi$
$588$	−4.41099	+	16.4944i	−0.181906	+	0.680219i
$589$	−13.1486			−0.541779
$590$	−0.0150646	+	0.00869756i	−0.000620200	+	0.000358073i
$591$	−2.65708	+	2.65969i	−0.109297	+	0.109405i
$592$	−2.82664	+	1.63196i	−0.116174	+	0.0670731i
$593$			10.1922i			0.418543i	0.977858	+	0.209272i	$0.0671093\pi$
$593$			10.1922i			0.418543i	−0.977858	+	0.209272i	$0.932891\pi$
$594$	−3.68277	+	3.69364i	−0.151106	+	0.151552i
$595$	0.637956	+	1.10497i	0.0261536	+	0.0452994i
$596$		−	27.8292i		−	1.13993i
$597$	−4.66953	+	17.4612i	−0.191111	+	0.714639i
$598$	13.4353	+	8.63647i	0.549410	+	0.353172i
$599$	−6.90176	−	11.9542i	−0.281998	−	0.488435i	0.689878	−	0.723925i	$-0.257664\pi$
$599$	−6.90176	−	11.9542i	−0.281998	−	0.488435i	−0.971877	+	0.235490i	$0.924331\pi$
$600$	−22.1640	−	5.92716i	−0.904841	−	0.241975i
$601$	−11.3285			−0.462097			−0.231049	−	0.972942i	$-0.574216\pi$
$601$	−11.3285			−0.462097			−0.231049	+	0.972942i	$0.574216\pi$
$602$	−6.21343	+	10.7620i	−0.253241	+	0.438626i
$603$	4.97356	−	0.00488316i	0.202539	−	0.000198858i
$604$	−16.6870	−	9.63422i	−0.678983	−	0.392011i
$605$	0.501564	−	0.289578i	0.0203915	−	0.0117730i
$606$	−6.04607	−	22.5200i	−0.245605	−	0.914813i
$607$	10.8930			0.442135			0.221067	−	0.975259i	$-0.429046\pi$
$607$	10.8930			0.442135			0.221067	+	0.975259i	$0.429046\pi$
$608$	9.19490	−	15.9260i	0.372902	−	0.645886i
$609$	32.8004	−	32.8326i	1.32914	−	1.33044i
$610$	−0.0399972	+	0.0692772i	−0.00161944	+	0.00280495i
$611$	9.57825	+	6.15708i	0.387494	+	0.249089i
$612$	0.0224260	+	22.8411i	0.000906516	+	0.923297i
$613$	27.0132	−	15.5961i	1.09105	−	0.629920i	0.157197	−	0.987567i	$-0.449754\pi$
$613$	27.0132	−	15.5961i	1.09105	−	0.629920i	0.933857	+	0.357647i	$0.116421\pi$
$614$	−10.4948			−0.423537
$615$	−1.02419	+	0.274971i	−0.0412995	+	0.0110879i
$616$	11.0595	−	6.38521i	0.445600	−	0.257268i
$617$			34.0530i			1.37092i	0.728110	+	0.685460i	$0.240399\pi$
$617$			34.0530i			1.37092i	−0.728110	+	0.685460i	$0.759601\pi$
$618$	16.9126	−	16.9293i	0.680326	−	0.680994i
$619$	7.48048	+	4.31886i	0.300666	+	0.173589i	0.642742	−	0.766083i	$-0.277797\pi$
$619$	7.48048	+	4.31886i	0.300666	+	0.173589i	−0.342076	+	0.939672i	$0.611130\pi$
$620$	−0.179638	+	0.311143i	−0.00721446	+	0.0124958i
$621$	7.65347	+	28.3958i	0.307123	+	1.13948i
$622$	9.03261	−	5.21498i	0.362175	−	0.209102i
$623$	2.82191	−	4.88769i	0.113057	−	0.195821i
$624$	4.27000	−	0.930577i	0.170937	−	0.0372529i
$625$	−12.4713	−	21.6009i	−0.498851	−	0.864034i
$626$	10.2324	+	5.90770i	0.408970	+	0.236119i
$627$	1.80400	−	6.74585i	0.0720447	−	0.269403i
$628$	11.0347	+	19.1126i	0.440331	+	0.762676i
$629$		−	25.5949i		−	1.02054i
$630$	−0.545927		0.000536005i	−0.0217503		2.13549e-5i
$631$	−34.8576	−	20.1250i	−1.38766	−	0.801165i	−0.394608	−	0.918850i	$-0.629120\pi$
$631$	−34.8576	−	20.1250i	−1.38766	−	0.801165i	−0.993051	+	0.117684i	$0.962453\pi$
$632$	2.82960	+	1.63367i	0.112555	+	0.0649839i
$633$	0.172946	−	0.646715i	0.00687400	−	0.0257046i
$634$	7.28009	−	12.6095i	0.289129	−	0.500786i
$635$	−0.382591	−	0.220889i	−0.0151827	−	0.00876572i
$636$	1.74755	−	0.469175i	0.0692950	−	0.0186040i
$637$	−13.8523	+	21.5493i	−0.548849	+	0.853816i
$638$	−7.16157			−0.283529
$639$	39.4348	−	0.0387180i	1.56001	−	0.00153166i
$640$	−0.285152	−	0.493898i	−0.0112716	−	0.0195230i
$641$	12.8832	+	22.3143i	0.508855	+	0.881362i	0.999947	+	0.0102547i	$0.00326424\pi$
$641$	12.8832	+	22.3143i	0.508855	+	0.881362i	−0.491093	+	0.871107i	$0.663402\pi$
$642$	−9.84966	+	9.85933i	−0.388735	+	0.389117i
$643$			4.45687i			0.175762i	0.996131	+	0.0878809i	$0.0280095\pi$
$643$			4.45687i			0.175762i	−0.996131	+	0.0878809i	$0.971991\pi$
$644$		−	29.4915i		−	1.16213i
$645$	0.437928	+	0.117112i	0.0172434	+	0.00461129i
$646$	6.75061	+	11.6924i	0.265599	+	0.460031i
$647$	−4.35879	−	7.54964i	−0.171362	−	0.296807i	0.767535	−	0.641008i	$-0.221483\pi$
$647$	−4.35879	−	7.54964i	−0.171362	−	0.296807i	−0.938896	+	0.344201i	$0.888150\pi$
$648$	−20.6878	−	11.8900i	−0.812693	−	0.467083i
$649$	0.460436			0.0180737
$650$	−11.8600	−	7.62383i	−0.465187	−	0.299031i
$651$	7.02944	−	26.2858i	0.275505	−	1.03022i
$652$	15.8451	+	9.14819i	0.620543	+	0.358271i
$653$	−5.49249	+	9.51327i	−0.214938	+	0.372283i	−0.953253	−	0.302172i	$-0.902288\pi$
$653$	−5.49249	+	9.51327i	−0.214938	+	0.372283i	0.738316	+	0.674455i	$0.235621\pi$
$654$	−9.37632	+	2.51731i	−0.366643	+	0.0984346i
$655$	−1.04654	−	0.604222i	−0.0408919	−	0.0236089i
$656$	5.99363	+	3.46043i	0.234012	+	0.135107i
$657$	−9.15098	−	15.8141i	−0.357014	−	0.616966i
$658$			9.28294i			0.361887i
$659$	−9.10116	−	15.7637i	−0.354531	−	0.614065i	0.632507	−	0.774555i	$-0.282026\pi$
$659$	−9.10116	−	15.7637i	−0.354531	−	0.614065i	−0.987038	+	0.160489i	$0.948693\pi$
$660$	−0.134984	−	0.134852i	−0.00525426	−	0.00524911i
$661$	−9.05968	−	5.23061i	−0.352381	−	0.203447i	0.313353	−	0.949637i	$-0.398548\pi$
$661$	−9.05968	−	5.23061i	−0.352381	−	0.203447i	−0.665733	+	0.746190i	$0.731881\pi$
$662$	2.22986	+	3.86223i	0.0866659	+	0.150110i
$663$	−10.4225	+	32.6471i	−0.404776	+	1.26791i
$664$	16.9200	−	29.3064i	0.656625	−	1.13731i
$665$	0.632953	−	0.365435i	0.0245449	−	0.0141710i
$666$	9.48954	+	5.46637i	0.367712	+	0.211818i
$667$	−20.1897	+	34.9696i	−0.781749	+	1.35403i
$668$	−1.62161	−	0.936237i	−0.0627420	−	0.0362241i
$669$	0.912644	+	3.39936i	0.0352849	+	0.131427i
$670$		−	0.0803290i		−	0.00310338i
$671$	1.83372	−	1.05870i	0.0707899	−	0.0408706i
$672$	26.9226	+	26.8961i	1.03856	+	1.03754i
$673$	−14.6282			−0.563874			−0.281937	−	0.959433i	$-0.590977\pi$
$673$	−14.6282			−0.563874			−0.281937	+	0.959433i	$0.590977\pi$
$674$	21.8038	−	12.5884i	0.839850	−	0.484888i
$675$	−6.75609	−	25.0663i	−0.260042	−	0.964803i
$676$	17.9545	+	1.71850i	0.690556	+	0.0660963i
$677$	5.21183	−	9.02716i	0.200307	−	0.346942i	−0.748320	−	0.663338i	$-0.769139\pi$
$677$	5.21183	−	9.02716i	0.200307	−	0.346942i	0.948627	+	0.316396i	$0.102473\pi$
$678$	1.16148	+	4.32622i	0.0446065	+	0.166147i
$679$	−18.8224	+	32.6014i	−0.722338	+	1.25113i
$680$	0.900706			0.0345405
$681$	−32.2003	+	32.2319i	−1.23392	+	1.23513i
$682$	−3.63624	+	2.09938i	−0.139239	+	0.0803895i
$683$	5.83030	+	3.36612i	0.223090	+	0.128801i	0.607380	−	0.794411i	$-0.292220\pi$
$683$	5.83030	+	3.36612i	0.223090	+	0.128801i	−0.384290	+	0.923212i	$0.625554\pi$
$684$	13.0839	−	0.0128461i	0.500275	−	0.000491183i
$685$	0.257652	−	0.446267i	0.00984439	−	0.0170510i
$686$	−0.308757			−0.0117884
$687$	−32.8618	+	32.8941i	−1.25376	+	1.25499i
$688$	−1.47923	−	2.56211i	−0.0563952	−	0.0976794i
$689$	2.71176	+	0.129481i	0.103310	+	0.00493285i
$690$	0.458748	−	0.123163i	0.0174642	−	0.00468872i
$691$			7.39456i			0.281303i	0.990059	+	0.140651i	$0.0449196\pi$
$691$			7.39456i			0.281303i	−0.990059	+	0.140651i	$0.955080\pi$
$692$	−10.2075	−	17.6800i	−0.388032	−	0.672092i
$693$	12.5214	+	7.21286i	0.475650	+	0.273994i
$694$		−	12.5611i		−	0.476811i
$695$	0.205062	−	0.118392i	0.00777843	−	0.00449088i
$696$	−8.49495	−	31.6414i	−0.322000	−	1.19937i
$697$	−47.0008	+	27.1359i	−1.78028	+	1.02785i
$698$	−21.2966			−0.806088
$699$	13.6438	−	3.66302i	0.516055	−	0.138548i
$700$			26.0336i			0.983976i
$701$	−30.2665			−1.14315			−0.571576	−	0.820549i	$-0.693668\pi$
$701$	−30.2665			−1.14315			−0.571576	+	0.820549i	$0.693668\pi$
$702$	−9.87821	−	10.8367i	−0.372829	−	0.409006i
$703$	−14.6614			−0.552963
$704$		−	4.07742i		−	0.153674i
$705$	0.327049	−	0.0878046i	0.0123174	−	0.00330691i
$706$	−3.62572			−0.136456
$707$	−55.9448	+	32.2997i	−2.10402	+	1.21476i
$708$	0.223698	+	0.833215i	0.00840708	+	0.0313141i
$709$	0.0571976	−	0.0330231i	0.00214810	−	0.00124021i	−0.498926	−	0.866645i	$-0.666272\pi$
$709$	0.0571976	−	0.0330231i	0.00214810	−	0.00124021i	0.501074	+	0.865405i	$0.332939\pi$
$710$		−	0.636920i		−	0.0239032i
$711$	0.00362995	+	3.69714i	0.000136134	+	0.138654i
$712$	−1.99207	−	3.45037i	−0.0746562	−	0.129308i
$713$			23.6741i			0.886602i
$714$	−26.9837	+	7.24445i	−1.00984	+	0.271117i
$715$	−0.131151	−	0.254468i	−0.00490479	−	0.00951658i
$716$	−3.60911	−	6.25117i	−0.134879	−	0.233617i
$717$	16.7538	−	16.7703i	0.625682	−	0.626297i
$718$	−12.6328			−0.471453
$719$	1.90007	−	3.29102i	0.0708607	−	0.122734i	−0.828418	−	0.560110i	$-0.810759\pi$
$719$	1.90007	−	3.29102i	0.0708607	−	0.122734i	0.899279	+	0.437376i	$0.144092\pi$
$720$	0.0648740	−	0.112620i	0.00241771	−	0.00419711i
$721$	−57.4139	−	33.1479i	−2.13821	−	1.23449i
$722$	−6.18079	+	3.56848i	−0.230025	+	0.132805i
$723$	−16.2544	+	16.2704i	−0.604509	+	0.605103i
$724$	14.0058			0.520520
$725$	17.8224	−	30.8693i	0.661908	−	1.14646i
$726$	3.28837	+	12.2483i	0.122043	+	0.454577i
$727$	−18.0132	+	31.1997i	−0.668071	+	1.15713i	0.310372	+	0.950615i	$0.399546\pi$
$727$	−18.0132	+	31.1997i	−0.668071	+	1.15713i	−0.978443	+	0.206518i	$0.933787\pi$
$728$	16.4473	+	31.9120i	0.609577	+	1.18274i
$729$	−0.0795277	−	26.9999i	−0.00294547	−	0.999996i
$730$	−0.255562	+	0.147549i	−0.00945877	+	0.00546102i
$731$	23.1996			0.858070
$732$	2.80673	+	2.80398i	0.103740	+	0.103638i
$733$	6.90293	−	3.98541i	0.254966	−	0.147204i	−0.367070	−	0.930193i	$-0.619639\pi$
$733$	6.90293	−	3.98541i	0.254966	−	0.147204i	0.622036	+	0.782989i	$0.286306\pi$
$734$			16.2535i			0.599927i
$735$	0.197545	+	0.735801i	0.00728654	+	0.0271404i
$736$	−28.6749	−	16.5554i	−1.05697	−	0.610242i
$737$	−1.06313	+	1.84139i	−0.0391607	+	0.0678284i
$738$	−0.0227994	−	23.2214i	−0.000839256	−	0.854792i
$739$	−8.98365	+	5.18671i	−0.330469	+	0.190796i	−0.656049	−	0.754718i	$-0.727774\pi$
$739$	−8.98365	+	5.18671i	−0.330469	+	0.190796i	0.325580	+	0.945514i	$0.394440\pi$
$740$	−0.200306	+	0.346940i	−0.00736339	+	0.0127538i
$741$	18.7010	+	5.97024i	0.686997	+	0.219322i
$742$	1.10665	+	1.91677i	0.0406264	+	0.0703670i
$743$	1.14467	+	0.660876i	0.0419939	+	0.0242452i	0.520850	−	0.853648i	$-0.325615\pi$
$743$	1.14467	+	0.660876i	0.0419939	+	0.0242452i	−0.478856	+	0.877893i	$0.658948\pi$
$744$	−13.5888	−	13.5755i	−0.498190	−	0.497701i
$745$	−0.620880	−	1.07540i	−0.0227473	−	0.0393995i
$746$		−	4.75791i		−	0.174199i
$747$	38.2916	−	0.0375956i	1.40101	−	0.00137555i
$748$	−8.45659	−	4.88242i	−0.309204	−	0.178519i
$749$	33.4370	+	19.3048i	1.22176	+	0.705383i
$750$	−0.810228	+	0.217526i	−0.0295854	+	0.00794294i
$751$	6.94474	−	12.0286i	0.253417	−	0.438931i	−0.711047	−	0.703144i	$-0.751779\pi$
$751$	6.94474	−	12.0286i	0.253417	−	0.438931i	0.964464	+	0.264213i	$0.0851122\pi$
$752$	−1.91391	−	1.10500i	−0.0697930	−	0.0402950i
$753$	2.31910	−	8.67202i	0.0845127	−	0.316026i
$754$	0.960225	−	20.1102i	0.0349693	−	0.732371i
$755$	−0.859774			−0.0312904
$756$	−6.96916	+	26.1633i	−0.253466	+	0.951551i
$757$	15.7299	+	27.2450i	0.571712	+	0.990235i	0.996390	+	0.0848903i	$0.0270540\pi$
$757$	15.7299	+	27.2450i	0.571712	+	0.990235i	−0.424678	+	0.905344i	$0.639613\pi$
$758$	6.19656	+	10.7328i	0.225069	+	0.389831i
$759$	−12.1459	−	3.24810i	−0.440869	−	0.117899i
$760$		−	0.515944i		−	0.0187153i
$761$			48.4944i			1.75792i	0.476896	+	0.878960i	$0.341762\pi$
$761$			48.4944i			1.75792i	−0.476896	+	0.878960i	$0.658238\pi$
$762$	6.83707	−	6.84378i	0.247681	−	0.247924i
$763$	13.4481	+	23.2929i	0.486856	+	0.843259i
$764$	1.88543	+	3.26567i	0.0682126	+	0.118148i
$765$	0.510461	+	0.882143i	0.0184558	+	0.0318939i
$766$	−11.7399			−0.424178
$767$	−0.0617354	+	1.29294i	−0.00222914	+	0.0466853i
$768$	22.6975	−	6.09372i	0.819025	−	0.219888i
$769$	9.81686	+	5.66777i	0.354005	+	0.204385i	0.666448	−	0.745552i	$-0.267814\pi$
$769$	9.81686	+	5.66777i	0.354005	+	0.204385i	−0.312443	+	0.949937i	$0.601147\pi$
$770$	0.116695	−	0.202122i	0.00420540	−	0.00728396i
$771$	13.0670	−	48.8625i	0.470595	−	1.75974i
$772$	−22.9330	−	13.2404i	−0.825378	−	0.476532i
$773$	6.57982	+	3.79886i	0.236660	+	0.136635i	0.613640	−	0.789586i	$-0.289704\pi$
$773$	6.57982	+	3.79886i	0.236660	+	0.136635i	−0.376981	+	0.926221i	$0.623038\pi$
$774$	−4.95480	+	8.60146i	−0.178097	+	0.309173i
$775$		−	20.8983i		−	0.750688i
$776$	13.2873	+	23.0143i	0.476987	+	0.826166i
$777$	7.83818	−	29.3100i	0.281193	−	1.05149i
$778$	−11.7916	−	6.80788i	−0.422749	−	0.244074i
$779$	15.5441	+	26.9231i	0.556924	+	0.964620i
$780$	0.396773	−	0.360965i	0.0142068	−	0.0129246i
$781$	−8.42940	+	14.6002i	−0.301628	+	0.522435i
$782$	21.0522	−	12.1545i	0.752825	−	0.434644i
$783$	26.1750	−	26.2522i	0.935417	−	0.938176i
$784$	2.48604	−	4.30595i	0.0887872	−	0.153784i
$785$	0.852820	+	0.492376i	0.0304384	+	0.0175736i
$786$	18.7022	−	18.7205i	0.667084	−	0.667740i
$787$		−	37.1798i		−	1.32532i	−0.748922	−	0.662658i	$-0.769428\pi$
$787$		−	37.1798i		−	1.32532i	0.748922	−	0.662658i	$-0.230572\pi$
$788$	2.60802	−	1.50574i	0.0929070	−	0.0536399i
$789$	−9.08000	+	2.43776i	−0.323257	+	0.0867865i
$790$	0.0597134			0.00212451
$791$	10.7473	−	6.20496i	0.382130	−	0.220623i
$792$	8.82925	−	5.10913i	0.313734	−	0.181545i
$793$	2.72703	+	5.29116i	0.0968398	+	0.187895i
$794$	−4.47266	+	7.74688i	−0.158729	+	0.274927i
$795$	0.0570628	−	0.0571188i	0.00202381	−	0.00202580i
$796$	7.23922	−	12.5387i	0.256587	−	0.444422i
$797$	−6.80862			−0.241174			−0.120587	−	0.992703i	$-0.538478\pi$
$797$	−6.80862			−0.241174			−0.120587	+	0.992703i	$0.538478\pi$
$798$	4.14978	+	15.4568i	0.146901	+	0.547166i
$799$	15.0085	−	8.66514i	0.530961	−	0.306550i
$800$	25.3127	+	14.6143i	0.894938	+	0.516693i
$801$	2.25029	−	3.90647i	0.0795100	−	0.138028i
$802$	5.00086	−	8.66175i	0.176587	−	0.305857i
$803$	7.81101			0.275645
$804$	−3.84872	−	1.02924i	−0.135734	−	0.0362984i
$805$	−0.657967	−	1.13963i	−0.0231903	−	0.0401668i
$806$	−5.40767	−	10.4923i	−0.190477	−	0.369576i
$807$	6.13160	−	22.9285i	0.215843	−	0.807120i
$808$			45.6028i			1.60430i
$809$	8.57387	+	14.8504i	0.301441	+	0.522112i	0.976463	−	0.215687i	$-0.0691989\pi$
$809$	8.57387	+	14.8504i	0.301441	+	0.522112i	−0.675021	+	0.737798i	$0.735866\pi$
$810$	−0.436082		0.000856313i	−0.0153224		3.00878e-5i
$811$		−	21.7276i		−	0.762959i	−0.924377	−	0.381480i	$-0.875415\pi$
$811$		−	21.7276i		−	0.762959i	0.924377	−	0.381480i	$-0.124585\pi$
$812$	−32.1949	+	18.5877i	−1.12982	+	0.652301i
$813$	−14.9756	+	14.9903i	−0.525217	+	0.525733i
$814$	−4.05459	+	2.34092i	−0.142113	+	0.0820491i
$815$	0.816399			0.0285972
$816$	1.71838	−	6.42569i	0.0601553	−	0.224944i
$817$		−	13.2893i		−	0.464933i
$818$	−15.4787			−0.541200
$819$	−21.9331	+	34.1940i	−0.766405	+	1.19483i
$820$	0.849462			0.0296645
$821$		−	13.5508i		−	0.472928i	−0.971640	−	0.236464i	$-0.924011\pi$
$821$		−	13.5508i		−	0.472928i	0.971640	−	0.236464i	$-0.0759885\pi$
$822$	7.98280	+	7.97497i	0.278432	+	0.278159i
$823$	−36.7740			−1.28186			−0.640931	−	0.767599i	$-0.721451\pi$
$823$	−36.7740			−1.28186			−0.640931	+	0.767599i	$0.721451\pi$
$824$	−40.5303	+	23.4002i	−1.41194	+	0.815183i
$825$	10.7218	+	2.86725i	0.373285	+	0.0998250i
$826$	−0.913899	+	0.527640i	−0.0317986	+	0.0183589i
$827$		−	46.7697i		−	1.62634i	−0.582026	−	0.813170i	$-0.697740\pi$
$827$		−	46.7697i		−	1.62634i	0.582026	−	0.813170i	$-0.302260\pi$
$828$	−0.0231294	−	23.5576i	−0.000803803	−	0.818683i
$829$	9.45842	+	16.3825i	0.328505	+	0.568987i	0.982215	−	0.187758i	$-0.0601220\pi$
$829$	9.45842	+	16.3825i	0.328505	+	0.568987i	−0.653711	+	0.756744i	$0.726789\pi$
$830$		−	0.618456i		−	0.0214669i
$831$	−17.2039	−	17.1870i	−0.596795	−	0.596209i
$832$	11.4497	+	0.546702i	0.396947	+	0.0189535i
$833$	19.4950	+	33.7663i	0.675461	+	1.16993i
$834$	1.34443	+	5.00765i	0.0465538	+	0.173401i
$835$	−0.0835513			−0.00289141
$836$	−2.79676	+	4.84413i	−0.0967279	+	0.167538i
$837$	5.59445	−	21.0024i	0.193372	−	0.725950i
$838$	0.696571	+	0.402165i	0.0240626	+	0.0138926i
$839$	−10.2713	+	5.93016i	−0.354606	+	0.204732i	−0.666712	−	0.745315i	$-0.732299\pi$
$839$	−10.2713	+	5.93016i	−0.354606	+	0.204732i	0.312106	+	0.950047i	$0.398966\pi$
$840$	1.03144	+	0.275831i	0.0355881	+	0.00951709i
$841$	21.9002			0.755178
$842$	8.74178	−	15.1412i	0.301261	−	0.521800i
$843$	36.0145	+	9.63111i	1.24041	+	0.331713i
$844$	−0.268121	+	0.464399i	−0.00922910	+	0.0159853i
$845$	0.732150	−	0.334164i	0.0251867	−	0.0114956i
$846$	0.00728037	+	7.41514i	0.000250304	+	0.254938i
$847$	30.4275	−	17.5673i	1.04550	−	0.603621i
$848$	−0.526921			−0.0180945
$849$	10.3413	−	38.6702i	0.354912	−	1.32716i
$850$	−18.5838	+	10.7293i	−0.637418	+	0.368014i
$851$			26.3978i			0.904905i
$852$	−30.5161	−	8.16071i	−1.04546	−	0.279581i
$853$	28.3691	+	16.3789i	0.971340	+	0.560804i	0.899645	−	0.436623i	$-0.143826\pi$
$853$	28.3691	+	16.3789i	0.971340	+	0.560804i	0.0716956	+	0.997427i	$0.477159\pi$
$854$	−2.42644	+	4.20272i	−0.0830312	+	0.143814i
$855$	0.505311	−	0.292403i	0.0172813	−	0.00999999i
$856$	23.6042	−	13.6279i	0.806775	−	0.465791i
$857$	27.4207	−	47.4941i	0.936674	−	1.62237i	0.165052	−	0.986285i	$-0.447221\pi$
$857$	27.4207	−	47.4941i	0.936674	−	1.62237i	0.771622	−	0.636081i	$-0.219446\pi$
$858$	6.12498	−	1.33484i	0.209103	−	0.0455707i
$859$	−17.3224	−	30.0032i	−0.591031	−	1.02370i	−0.994094	−	0.108524i	$-0.965388\pi$
$859$	−17.3224	−	30.0032i	−0.591031	−	1.02370i	0.403063	−	0.915172i	$-0.367946\pi$
$860$	−0.314472	−	0.181560i	−0.0107234	−	0.00619116i
$861$	−62.1330	+	16.6812i	−2.11749	+	0.568493i
$862$	2.88593	+	4.99857i	0.0982950	+	0.170252i
$863$		−	8.43673i		−	0.287190i	−0.989637	−	0.143595i	$-0.954134\pi$
$863$		−	8.43673i		−	0.287190i	0.989637	−	0.143595i	$-0.0458662\pi$
$864$	21.5266	+	21.4633i	0.732351	+	0.730197i
$865$	−0.788895	−	0.455469i	−0.0268232	−	0.0154864i
$866$	−4.02515	−	2.32392i	−0.136780	−	0.0789700i
$867$	16.0696	+	16.0538i	0.545752	+	0.545216i
$868$	−10.8978	+	18.8756i	−0.369896	+	0.640679i
$869$	−1.36881	−	0.790285i	−0.0464339	−	0.0268086i
$870$	−0.423589	−	0.423174i	−0.0143610	−	0.0143469i
$871$	−5.02821	−	3.23223i	−0.170374	−	0.109520i
$872$	18.9869			0.642978
$873$	−15.0096	+	26.0565i	−0.507999	+	0.881878i
$874$	−6.96236	−	12.0592i	−0.235505	−	0.407907i
$875$	1.16208	+	2.01279i	0.0392856	+	0.0680447i
$876$	3.79490	+	14.1350i	0.128218	+	0.477577i
$877$			9.79437i			0.330732i	0.986232	+	0.165366i	$0.0528806\pi$
$877$			9.79437i			0.330732i	−0.986232	+	0.165366i	$0.947119\pi$
$878$		−	18.5432i		−	0.625801i
$879$	−0.134715	−	0.501777i	−0.00454382	−	0.0169245i
$880$	0.0277816	+	0.0481192i	0.000936518	+	0.00162210i
$881$	13.3270	+	23.0831i	0.448999	+	0.777689i	0.998321	−	0.0579215i	$-0.0184473\pi$
$881$	13.3270	+	23.0831i	0.448999	+	0.777689i	−0.549322	+	0.835611i	$0.685114\pi$
$882$	−16.6827	+	0.0163795i	−0.561737	+	0.000551527i
$883$	13.3367			0.448816			0.224408	−	0.974495i	$-0.427955\pi$
$883$	13.3367			0.448816			0.224408	+	0.974495i	$0.427955\pi$
$884$	14.8440	−	23.0921i	0.499259	−	0.776671i
$885$	0.0272337	+	0.0272069i	0.000915450	+	0.000914551i
$886$	26.9048	+	15.5335i	0.903884	+	0.521858i
$887$	−11.2780	+	19.5340i	−0.378678	+	0.655889i	−0.990870	−	0.134820i	$-0.956954\pi$
$887$	−11.2780	+	19.5340i	−0.378678	+	0.655889i	0.612192	+	0.790709i	$0.290288\pi$
$888$	−15.1522	−	15.1373i	−0.508474	−	0.507975i
$889$	−23.2100	−	13.4003i	−0.778439	−	0.449432i
$890$	−0.0630585	−	0.0364068i	−0.00211372	−	0.00122036i
$891$	10.0077	+	5.75176i	0.335270	+	0.192691i
$892$		−	2.81942i		−	0.0944011i
$893$	−4.96358	−	8.59718i	−0.166100	−	0.287694i
$894$	26.2614	−	7.05054i	0.878313	−	0.235805i
$895$	−0.278932	−	0.161042i	−0.00932367	−	0.00538303i
$896$	−17.2988	−	29.9625i	−0.577914	−	1.00098i
$897$	10.7494	−	33.6711i	0.358913	−	1.12425i
$898$	−3.45666	+	5.98711i	−0.115350	+	0.199793i
$899$	25.8442	−	14.9212i	0.861953	−	0.497649i
$900$	0.0204174	+	20.7954i	0.000680582	+	0.693180i
$901$	2.06600	−	3.57842i	0.0688284	−	0.119214i
$902$	8.59740	+	4.96371i	0.286262	+	0.165273i
$903$	26.5671	+	7.10464i	0.884096	+	0.236428i
$904$		−	8.76054i		−	0.291371i
$905$	0.541222	−	0.312474i	0.0179908	−	0.0103870i
$906$	4.86382	−	18.1877i	0.161590	−	0.604247i
$907$	−3.02872			−0.100567			−0.0502835	−	0.998735i	$-0.516012\pi$
$907$	−3.02872			−0.100567			−0.0502835	+	0.998735i	$0.516012\pi$
$908$	31.6059	−	18.2477i	1.04888	−	0.605570i
$909$	−44.6629	+	25.8447i	−1.48138	+	0.857213i
$910$	0.551926	+	0.354789i	0.0182962	+	0.0117611i
$911$	8.08483	−	14.0033i	0.267862	−	0.463951i	−0.700447	−	0.713704i	$-0.747016\pi$
$911$	8.08483	−	14.0033i	0.267862	−	0.463951i	0.968310	+	0.249753i	$0.0803494\pi$
$912$	−3.68078	−	0.984326i	−0.121883	−	0.0325943i
$913$	−8.18504	+	14.1769i	−0.270885	+	0.469187i
$914$	16.2589			0.537797
$915$	0.171018	+	0.0457341i	0.00565368	+	0.00151192i
$916$	32.2552	−	18.6225i	1.06574	−	0.615306i
$917$	−63.4889	−	36.6553i	−2.09659	−	1.21047i
$918$	−21.5487	+	5.80797i	−0.711212	+	0.191692i
$919$	−1.41858	+	2.45706i	−0.0467947	+	0.0810509i	−0.888474	−	0.458927i	$-0.848234\pi$
$919$	−1.41858	+	2.45706i	−0.0467947	+	0.0810509i	0.841679	+	0.539978i	$0.181567\pi$
$920$	−0.928959			−0.0306269
$921$	6.02210	+	22.4307i	0.198435	+	0.739117i
$922$	4.10162	+	7.10422i	0.135080	+	0.233965i
$923$	−39.8681	−	25.6280i	−1.31227	−	0.843555i
$924$	−8.18887	−	8.18083i	−0.269394	−	0.269130i
$925$		−	23.3026i		−	0.766185i
$926$	−7.94622	−	13.7633i	−0.261129	−	0.452289i
$927$	−45.8878	−	26.4333i	−1.50715	−	0.868183i
$928$			41.7378i			1.37011i
$929$	−32.8194	+	18.9483i	−1.07677	+	0.621674i	−0.930023	−	0.367500i	$-0.880214\pi$
$929$	−32.8194	+	18.9483i	−1.07677	+	0.621674i	−0.146747	+	0.989174i	$0.546880\pi$
$930$	−0.339126	−	0.0906902i	−0.0111204	−	0.00297385i
$931$	19.3421	−	11.1672i	0.633912	−	0.365989i
$932$	−11.3161			−0.370671
$933$	−16.3291	−	16.3131i	−0.534590	−	0.534065i
$934$			10.9752i			0.359121i
$935$	−0.435715			−0.0142494
$936$	13.1630	+	25.4782i	0.430246	+	0.832781i
$937$	−41.8330			−1.36662			−0.683312	−	0.730126i	$-0.739461\pi$
$937$	−41.8330			−1.36662			−0.683312	+	0.730126i	$0.739461\pi$
$938$		−	4.87318i		−	0.159115i
$939$	6.75506	−	25.2598i	0.220443	−	0.824323i
$940$	−0.271253			−0.00884731
$941$	1.89154	−	1.09208i	0.0616623	−	0.0356008i	−0.468852	−	0.883277i	$-0.655332\pi$
$941$	1.89154	−	1.09208i	0.0616623	−	0.0356008i	0.530514	+	0.847676i	$0.321999\pi$
$942$	−15.2402	+	15.2552i	−0.496554	+	0.497042i
$943$	48.4751	−	27.9871i	1.57857	−	0.911386i
$944$		−	0.251230i		−	0.00817686i
$945$	0.314407	+	1.16651i	0.0102277	+	0.0379465i
$946$	−2.12184	−	3.67514i	−0.0689871	−	0.119489i
$947$			41.2618i			1.34083i	0.741987	+	0.670414i	$0.233884\pi$
$947$			41.2618i			1.34083i	−0.741987	+	0.670414i	$0.766116\pi$
$948$	0.765094	−	2.86099i	0.0248491	−	0.0929206i
$949$	−1.04730	+	21.9339i	−0.0339969	+	0.712004i
$950$	6.14601	+	10.6452i	0.199403	+	0.345376i
$951$	−31.1278	−	8.32429i	−1.00939	−	0.269934i
$952$	54.6416			1.77094
$953$	−24.5159	+	42.4627i	−0.794146	+	1.37550i	0.129233	+	0.991614i	$0.458748\pi$
$953$	−24.5159	+	42.4627i	−0.794146	+	1.37550i	−0.923380	+	0.383888i	$0.874585\pi$
$954$	0.885487	+	1.53024i	0.0286687	+	0.0495433i
$955$	0.145717	+	0.0841295i	0.00471528	+	0.00272237i
$956$	−16.4445	+	9.49424i	−0.531854	+	0.307066i
$957$	4.10942	+	15.3065i	0.132839	+	0.494789i
$958$	−7.74298			−0.250164
$959$	15.6305	−	27.0729i	0.504737	−	0.874230i
$960$	0.240933	−	0.241169i	0.00777607	−	0.00778371i
$961$	−6.75185	+	11.6945i	−0.217802	+	0.377243i
$962$	−6.02983	−	11.6994i	−0.194409	−	0.377205i
$963$	26.7243	+	15.3943i	0.861179	+	0.496075i
$964$	15.9544	−	9.21126i	0.513856	−	0.296675i
$965$	−1.18159			−0.0380368
$966$	27.8301	−	7.47169i	0.895418	−	0.240398i
$967$	48.5763	−	28.0455i	1.56211	−	0.901884i	0.565064	−	0.825047i	$-0.308851\pi$
$967$	48.5763	−	28.0455i	1.56211	−	0.901884i	0.997044	−	0.0768368i	$-0.0244821\pi$
$968$		−	24.8027i		−	0.797188i
$969$	21.1167	−	21.1374i	0.678365	−	0.679032i
$970$	0.420606	+	0.242837i	0.0135048	+	0.00779702i
$971$	16.5122	−	28.6000i	0.529903	−	0.917819i	−0.469488	−	0.882939i	$-0.655562\pi$
$971$	16.5122	−	28.6000i	0.529903	−	0.917819i	0.999391	−	0.0348805i	$-0.0111051\pi$
$972$	−5.54639	+	20.9045i	−0.177901	+	0.670513i
$973$	12.4401	−	7.18231i	0.398812	−	0.230254i
$974$	16.1009	−	27.8875i	0.515906	−	0.893575i
$975$	−9.48904	+	29.7231i	−0.303892	+	0.951902i
$976$	−0.577663	−	1.00054i	−0.0184906	−	0.0320266i
$977$	28.9443	+	16.7110i	0.926011	+	0.534633i	0.885548	−	0.464548i	$-0.153783\pi$
$977$	28.9443	+	16.7110i	0.926011	+	0.534633i	0.0404634	+	0.999181i	$0.487117\pi$
$978$	−4.61845	+	17.2702i	−0.147682	+	0.552240i
$979$	0.963663	+	1.66911i	0.0307988	+	0.0533451i
$980$		−	0.610271i		−	0.0194944i
$981$	10.7605	+	18.5956i	0.343558	+	0.593712i
$982$	−12.0054	−	6.93129i	−0.383106	−	0.221186i
$983$	31.4108	+	18.1350i	1.00185	+	0.578418i	0.908795	−	0.417243i	$-0.137004\pi$
$983$	31.4108	+	18.1350i	1.00185	+	0.578418i	0.0930545	+	0.995661i	$0.470337\pi$
$984$	−11.7327	+	43.8731i	−0.374024	+	1.39862i
$985$	0.0671875	−	0.116372i	0.00214077	−	0.00370793i
$986$	−26.5373	−	15.3213i	−0.845120	−	0.487930i
$987$	19.8405	−	5.32669i	0.631531	−	0.169550i
$988$	−13.2277	−	8.50300i	−0.420828	−	0.270517i
$989$	−23.9274			−0.760846
$990$	0.0930566	−	0.161545i	0.00295753	−	0.00513423i
$991$	20.1550	+	34.9095i	0.640244	+	1.10894i	0.985378	+	0.170382i	$0.0545003\pi$
$991$	20.1550	+	34.9095i	0.640244	+	1.10894i	−0.345134	+	0.938554i	$0.612166\pi$
$992$	12.2353	+	21.1921i	0.388470	+	0.672850i
$993$	6.97525	−	6.98210i	0.221353	−	0.221570i
$994$		−	38.6389i		−	1.22555i
$995$		−	0.646040i		−	0.0204808i
$996$	−29.6314	−	7.92413i	−0.938908	−	0.251086i
$997$	−16.3601	−	28.3365i	−0.518129	−	0.897426i	−0.999778	−	0.0210615i	$-0.993295\pi$
$997$	−16.3601	−	28.3365i	−0.518129	−	0.897426i	0.481649	−	0.876364i	$-0.340038\pi$
$998$	7.35248	+	12.7349i	0.232739	+	0.403115i
$999$	6.23809	−	23.4188i	0.197364	−	0.740937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.88.4	yes	22
3.2	odd	2		351.2.l.b.127.8		22
9.4	even	3		117.2.r.b.49.8	yes	22
9.5	odd	6		351.2.r.b.10.4		22
13.4	even	6		117.2.r.b.43.8	yes	22
39.17	odd	6		351.2.r.b.316.4		22
117.4	even	6	inner	117.2.l.b.4.8	✓	22
117.95	odd	6		351.2.l.b.199.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.8	✓	22	117.4	even	6	inner
117.2.l.b.88.4	yes	22	1.1	even	1	trivial
117.2.r.b.43.8	yes	22	13.4	even	6
117.2.r.b.49.8	yes	22	9.4	even	3
351.2.l.b.127.8		22	3.2	odd	2
351.2.l.b.199.4		22	117.95	odd	6
351.2.r.b.10.4		22	9.5	odd	6
351.2.r.b.316.4		22	39.17	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-0.782672i q^{2} +(-1.67281 + 0.449109i) q^{3} +1.38742 q^{4} +(0.0536139 - 0.0309540i) q^{5} +(0.351505 + 1.30926i) q^{6} +(3.25250 - 1.87783i) q^{7} -2.65124i q^{8} +(2.59660 - 1.50255i) q^{9} +(-0.0242268 - 0.0419621i) q^{10} +1.28253i q^{11} +(-2.32090 + 0.623105i) q^{12} +(-3.60145 - 0.171963i) q^{13} +(-1.46973 - 2.54564i) q^{14} +(-0.0757843 + 0.0758587i) q^{15} +0.699796 q^{16} +(-2.74383 + 4.75245i) q^{17} +(-1.17600 - 2.03229i) q^{18} +(2.72231 + 1.57173i) q^{19} +(0.0743853 - 0.0429463i) q^{20} +(-4.59748 + 4.60199i) q^{21} +1.00380 q^{22} +(2.82990 - 4.90152i) q^{23} +(1.19070 + 4.43503i) q^{24} +(-2.49808 + 4.32681i) q^{25} +(-0.134590 + 2.81875i) q^{26} +(-3.66882 + 3.67964i) q^{27} +(4.51260 - 2.60535i) q^{28} -7.13444 q^{29} +(0.0593725 + 0.0593142i) q^{30} +(-3.62246 + 2.09143i) q^{31} -5.85020i q^{32} +(-0.575997 - 2.14544i) q^{33} +(3.71961 + 2.14752i) q^{34} +(0.116253 - 0.201356i) q^{35} +(3.60259 - 2.08468i) q^{36} +(-4.03923 + 2.33205i) q^{37} +(1.23015 - 2.13067i) q^{38} +(6.10178 - 1.32978i) q^{39} +(-0.0820666 - 0.142143i) q^{40} +(8.56482 + 4.94490i) q^{41} +(3.60185 + 3.59832i) q^{42} +(-2.11380 - 3.66122i) q^{43} +1.77942i q^{44} +(0.0927041 - 0.160933i) q^{45} +(-3.83628 - 2.21488i) q^{46} +(-2.73495 - 1.57902i) q^{47} +(-1.17063 + 0.314285i) q^{48} +(3.55252 - 6.15314i) q^{49} +(3.38647 + 1.95518i) q^{50} +(2.45554 - 9.18223i) q^{51} +(-4.99674 - 0.238585i) q^{52} -0.752963 q^{53} +(2.87995 + 2.87148i) q^{54} +(0.0396996 + 0.0687616i) q^{55} +(-4.97859 - 8.62317i) q^{56} +(-5.25979 - 1.40659i) q^{57} +5.58392i q^{58} -0.359005i q^{59} +(-0.105145 + 0.105248i) q^{60} +(-0.825473 - 1.42976i) q^{61} +(1.63690 + 2.83520i) q^{62} +(5.62392 - 9.76304i) q^{63} -3.17919 q^{64} +(-0.198411 + 0.102260i) q^{65} +(-1.67917 + 0.450817i) q^{66} +(1.43574 + 0.828926i) q^{67} +(-3.80685 + 6.59366i) q^{68} +(-2.53257 + 9.47026i) q^{69} +(-0.157596 - 0.0909879i) q^{70} +(11.3838 + 6.57246i) q^{71} +(-3.98362 - 6.88422i) q^{72} -6.09030i q^{73} +(1.82523 + 3.16139i) q^{74} +(2.23562 - 8.35985i) q^{75} +(3.77700 + 2.18065i) q^{76} +(2.40838 + 4.17145i) q^{77} +(-1.04078 - 4.77569i) q^{78} +(-0.616191 + 1.06727i) q^{79} +(0.0375188 - 0.0216615i) q^{80} +(4.48469 - 7.80305i) q^{81} +(3.87024 - 6.70345i) q^{82} +(11.0538 + 6.38193i) q^{83} +(-6.37865 + 6.38492i) q^{84} +0.339730i q^{85} +(-2.86553 + 1.65442i) q^{86} +(11.9346 - 3.20414i) q^{87} +3.40031 q^{88} +(1.30142 - 0.751374i) q^{89} +(-0.125958 - 0.0725569i) q^{90} +(-12.0366 + 6.20361i) q^{91} +(3.92627 - 6.80049i) q^{92} +(5.12042 - 5.12545i) q^{93} +(-1.23586 + 2.14057i) q^{94} +0.194605 q^{95} +(2.62738 + 9.78628i) q^{96} +(-8.68058 + 5.01173i) q^{97} +(-4.81589 - 2.78046i) q^{98} +(1.92707 + 3.33023i) 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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