LMFDB - Embedded newform 117.3.u.a.68.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(68,117)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("117.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.7
Character	$\chi$	$=$	117.68
Dual form			117.3.u.a.74.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.11714 - 1.22233i) q^{2} +(2.89505 - 0.786578i) q^{3} +(0.988182 + 1.71158i) q^{4} +(2.73246 + 1.57759i) q^{5} +(-7.09067 - 1.87341i) q^{6} +7.65083 q^{7} +4.94710i q^{8} +(7.76259 - 4.55436i) q^{9} +(-3.85666 - 6.67994i) q^{10} +(-5.32659 - 3.07531i) q^{11} +(4.20712 + 4.17782i) q^{12} +(7.83575 + 10.3731i) q^{13} +(-16.1979 - 9.35184i) q^{14} +(9.15149 + 2.41789i) q^{15} +(9.99972 - 17.3200i) q^{16} +(-18.6707 - 10.7795i) q^{17} +(-22.0014 + 0.153762i) q^{18} +(15.0726 - 26.1066i) q^{19} +6.23577i q^{20} +(22.1495 - 6.01798i) q^{21} +(7.51808 + 13.0217i) q^{22} +8.21173i q^{23} +(3.89128 + 14.3221i) q^{24} +(-7.52244 - 13.0293i) q^{25} +(-3.91002 - 31.5391i) q^{26} +(18.8907 - 19.2910i) q^{27} +(7.56041 + 13.0950i) q^{28} +(-3.65390 - 2.10958i) q^{29} +(-16.4195 - 16.3052i) q^{30} +(-25.9263 + 44.9057i) q^{31} +(-25.2043 + 14.5517i) q^{32} +(-17.8397 - 4.71338i) q^{33} +(26.3523 + 45.6435i) q^{34} +(20.9056 + 12.0698i) q^{35} +(15.4660 + 8.78576i) q^{36} +(22.3585 + 38.7261i) q^{37} +(-63.8217 + 36.8475i) q^{38} +(30.8441 + 23.8672i) q^{39} +(-7.80448 + 13.5178i) q^{40} +55.3551i q^{41} +(-54.2495 - 14.3331i) q^{42} -51.5014 q^{43} -12.1558i q^{44} +(28.3959 - 0.198451i) q^{45} +(10.0374 - 17.3854i) q^{46} +(24.2699 - 14.0122i) q^{47} +(15.3261 - 58.0078i) q^{48} +9.53523 q^{49} +36.7796i q^{50} +(-62.5314 - 16.5213i) q^{51} +(-10.0112 + 23.6620i) q^{52} +0.382421i q^{53} +(-63.5741 + 17.7510i) q^{54} +(-9.70312 - 16.8063i) q^{55} +37.8495i q^{56} +(23.1011 - 87.4356i) q^{57} +(5.15721 + 8.93255i) q^{58} +(41.5363 - 23.9810i) q^{59} +(4.90492 + 18.0528i) q^{60} -51.3571 q^{61} +(109.779 - 63.3811i) q^{62} +(59.3903 - 34.8446i) q^{63} -8.84980 q^{64} +(5.04643 + 40.7056i) q^{65} +(32.0078 + 31.7848i) q^{66} +25.9108 q^{67} -42.6085i q^{68} +(6.45917 + 23.7733i) q^{69} +(-29.5067 - 51.1071i) q^{70} +(-7.07732 - 4.08609i) q^{71} +(22.5309 + 38.4023i) q^{72} -24.8357 q^{73} -109.318i q^{74} +(-32.0263 - 31.8033i) q^{75} +59.5780 q^{76} +(-40.7528 - 23.5286i) q^{77} +(-36.1277 - 88.2317i) q^{78} +(8.23711 + 14.2671i) q^{79} +(54.6477 - 31.5508i) q^{80} +(39.5156 - 70.7073i) q^{81} +(67.6622 - 117.194i) q^{82} +(-39.7129 + 22.9283i) q^{83} +(32.1880 + 31.9638i) q^{84} +(-34.0113 - 58.9092i) q^{85} +(109.036 + 62.9518i) q^{86} +(-12.2376 - 3.23326i) q^{87} +(15.2139 - 26.3512i) q^{88} +(-70.5240 + 40.7171i) q^{89} +(-60.3605 - 34.2890i) q^{90} +(59.9500 + 79.3628i) q^{91} +(-14.0550 + 8.11468i) q^{92} +(-39.7361 + 150.397i) q^{93} -68.5102 q^{94} +(82.3708 - 47.5568i) q^{95} +(-61.5216 + 61.9530i) q^{96} +46.9466 q^{97} +(-20.1874 - 11.6552i) q^{98} +(-55.3541 + 0.386854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{2} - q^{3} + 49 q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{9} - 6 q^{10} + 33 q^{11} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 28 q^{15} - 83 q^{16} + 34 q^{18} + 5 q^{19} - 91 q^{21} - 15 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - 3 * q^2 - q^3 + 49 * q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^9 - 6 * q^10 + 33 * q^11 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 28 * q^15 - 83 * q^16 + 34 * q^18 + 5 * q^19 - 91 * q^21 - 15 * q^22 + 36 * q^24 + 88 * q^25 + 132 * q^26 - 34 * q^27 - 22 * q^28 - 30 * q^29 + 31 * q^30 + 14 * q^31 - 63 * q^32 - 112 * q^33 - 6 * q^34 - 228 * q^35 + 47 * q^36 - 13 * q^37 - 192 * q^38 + 147 * q^39 + 72 * q^40 - 84 * q^42 + 62 * q^43 - 107 * q^45 + 6 * q^46 - 69 * q^47 - 58 * q^48 + 246 * q^49 + 235 * q^51 + 112 * q^52 + 444 * q^54 - 27 * q^55 + 189 * q^57 - 105 * q^58 - 435 * q^59 + 213 * q^60 - 16 * q^61 - 471 * q^62 - 170 * q^63 - 98 * q^64 - 435 * q^65 - 576 * q^66 + 68 * q^67 + 152 * q^69 - 57 * q^70 - 144 * q^71 + 513 * q^72 - 106 * q^73 + 98 * q^75 + 158 * q^76 + 282 * q^77 - 433 * q^78 - 25 * q^79 + 1050 * q^80 + 9 * q^81 + 81 * q^82 + 219 * q^83 - 172 * q^84 + 54 * q^85 - 24 * q^86 + 325 * q^87 - 15 * q^88 - 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 - 171 * q^93 - 606 * q^94 - 258 * q^95 - 439 * q^96 - 424 * q^97 + 405 * q^98 + 522 * q^99

Character values

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

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

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 $

$2$	−2.11714	−	1.22233i	−1.05857	−	0.611165i	−0.133533	−	0.991044i	$-0.542632\pi$
$2$	−2.11714	−	1.22233i	−1.05857	−	0.611165i	−0.925036	+	0.379879i	$0.875966\pi$
$3$	2.89505	−	0.786578i	0.965016	−	0.262193i
$3$	2.89505	−	0.786578i	0.965016	−	0.262193i
$4$	0.988182	+	1.71158i	0.247045	+	0.427895i
$5$	2.73246	+	1.57759i	0.546492	+	0.315517i	0.747706	−	0.664030i	$-0.231155\pi$
$5$	2.73246	+	1.57759i	0.546492	+	0.315517i	−0.201214	+	0.979547i	$0.564489\pi$
$6$	−7.09067	−	1.87341i	−1.18178	−	0.312235i
$7$	7.65083			1.09298			0.546488	−	0.837467i	$-0.315964\pi$
$7$	7.65083			1.09298			0.546488	+	0.837467i	$0.315964\pi$
$8$			4.94710i			0.618388i
$9$	7.76259	−	4.55436i	0.862510	−	0.506040i
$10$	−3.85666	−	6.67994i	−0.385666	−	0.667994i
$11$	−5.32659	−	3.07531i	−0.484235	−	0.279573i	0.237945	−	0.971279i	$-0.423526\pi$
$11$	−5.32659	−	3.07531i	−0.484235	−	0.279573i	−0.722180	+	0.691705i	$0.756860\pi$
$12$	4.20712	+	4.17782i	0.350594	+	0.348152i
$13$	7.83575	+	10.3731i	0.602750	+	0.797930i
$13$	7.83575	+	10.3731i	0.602750	+	0.797930i
$14$	−16.1979	−	9.35184i	−1.15699	−	0.667989i
$15$	9.15149	+	2.41789i	0.610100	+	0.161193i
$16$	9.99972	−	17.3200i	0.624983	−	1.08250i
$17$	−18.6707	−	10.7795i	−1.09828	−	0.634090i	−0.162508	−	0.986707i	$-0.551958\pi$
$17$	−18.6707	−	10.7795i	−1.09828	−	0.634090i	−0.935768	+	0.352617i	$0.885292\pi$
$18$	−22.0014	+	0.153762i	−1.22230	+	0.00854231i
$19$	15.0726	−	26.1066i	0.793297	−	1.37403i	−0.130618	−	0.991433i	$-0.541696\pi$
$19$	15.0726	−	26.1066i	0.793297	−	1.37403i	0.923915	−	0.382598i	$-0.124971\pi$
$20$			6.23577i			0.311788i
$21$	22.1495	−	6.01798i	1.05474	−	0.286570i
$22$	7.51808	+	13.0217i	0.341731	+	0.591895i
$23$			8.21173i			0.357032i	0.983937	+	0.178516i	$0.0571296\pi$
$23$			8.21173i			0.357032i	−0.983937	+	0.178516i	$0.942870\pi$
$24$	3.89128	+	14.3221i	0.162137	+	0.596754i
$25$	−7.52244	−	13.0293i	−0.300898	−	0.521170i
$26$	−3.91002	−	31.5391i	−0.150386	−	1.21304i
$27$	18.8907	−	19.2910i	0.699656	−	0.714480i
$28$	7.56041	+	13.0950i	0.270015	+	0.467679i
$29$	−3.65390	−	2.10958i	−0.125997	−	0.0727442i	0.435677	−	0.900103i	$-0.356509\pi$
$29$	−3.65390	−	2.10958i	−0.125997	−	0.0727442i	−0.561674	+	0.827359i	$0.689842\pi$
$30$	−16.4195	−	16.3052i	−0.547317	−	0.543505i
$31$	−25.9263	+	44.9057i	−0.836333	+	1.44857i	0.0566070	+	0.998397i	$0.481972\pi$
$31$	−25.9263	+	44.9057i	−0.836333	+	1.44857i	−0.892940	+	0.450175i	$0.851362\pi$
$32$	−25.2043	+	14.5517i	−0.787634	+	0.454741i
$33$	−17.8397	−	4.71338i	−0.540596	−	0.142830i
$34$	26.3523	+	45.6435i	0.775067	+	1.34246i
$35$	20.9056	+	12.0698i	0.597303	+	0.344853i
$36$	15.4660	+	8.78576i	0.429611	+	0.244049i
$37$	22.3585	+	38.7261i	0.604285	+	1.04665i	0.992164	+	0.124942i	$0.0398744\pi$
$37$	22.3585	+	38.7261i	0.604285	+	1.04665i	−0.387879	+	0.921710i	$0.626792\pi$
$38$	−63.8217	+	36.8475i	−1.67952	+	0.969671i
$39$	30.8441	+	23.8672i	0.790875	+	0.611978i
$40$	−7.80448	+	13.5178i	−0.195112	+	0.337944i
$41$			55.3551i			1.35012i	0.737761	+	0.675062i	$0.235883\pi$
$41$			55.3551i			1.35012i	−0.737761	+	0.675062i	$0.764117\pi$
$42$	−54.2495	−	14.3331i	−1.29166	−	0.341265i
$43$	−51.5014			−1.19771			−0.598854	−	0.800858i	$-0.704377\pi$
$43$	−51.5014			−1.19771			−0.598854	+	0.800858i	$0.704377\pi$
$44$		−	12.1558i		−	0.276269i
$45$	28.3959	−	0.198451i	0.631019	−	0.00441001i
$46$	10.0374	−	17.3854i	0.218205	−	0.377943i
$47$	24.2699	−	14.0122i	0.516380	−	0.298132i	−0.219072	−	0.975709i	$-0.570303\pi$
$47$	24.2699	−	14.0122i	0.516380	−	0.298132i	0.735452	+	0.677577i	$0.236970\pi$
$48$	15.3261	−	58.0078i	0.319294	−	1.20850i
$49$	9.53523			0.194596
$50$			36.7796i			0.735593i
$51$	−62.5314	−	16.5213i	−1.22611	−	0.323947i
$52$	−10.0112	+	23.6620i	−0.192524	+	0.455039i
$53$			0.382421i			0.00721549i	0.999993	+	0.00360774i	$0.00114838\pi$
$53$			0.382421i			0.00721549i	−0.999993	+	0.00360774i	$0.998852\pi$
$54$	−63.5741	+	17.7510i	−1.17730	+	0.328722i
$55$	−9.70312	−	16.8063i	−0.176420	−	0.305569i
$56$			37.8495i			0.675883i
$57$	23.1011	−	87.4356i	0.405283	−	1.53396i
$58$	5.15721	+	8.93255i	0.0889175	+	0.154010i
$59$	41.5363	−	23.9810i	0.704005	−	0.406457i	−0.104833	−	0.994490i	$-0.533431\pi$
$59$	41.5363	−	23.9810i	0.704005	−	0.406457i	0.808837	+	0.588033i	$0.200097\pi$
$60$	4.90492	+	18.0528i	0.0817486	+	0.300881i
$61$	−51.3571			−0.841920			−0.420960	−	0.907079i	$-0.638307\pi$
$61$	−51.3571			−0.841920			−0.420960	+	0.907079i	$0.638307\pi$
$62$	109.779	−	63.3811i	1.77063	−	1.02228i
$63$	59.3903	−	34.8446i	0.942703	−	0.553090i
$64$	−8.84980			−0.138278
$65$	5.04643	+	40.7056i	0.0776373	+	0.626240i
$66$	32.0078	+	31.7848i	0.484966	+	0.481589i
$67$	25.9108			0.386728			0.193364	−	0.981127i	$-0.438060\pi$
$67$	25.9108			0.386728			0.193364	+	0.981127i	$0.438060\pi$
$68$		−	42.6085i		−	0.626596i
$69$	6.45917	+	23.7733i	0.0936111	+	0.344541i
$70$	−29.5067	−	51.1071i	−0.421524	−	0.730101i
$71$	−7.07732	−	4.08609i	−0.0996806	−	0.0575506i	0.449331	−	0.893365i	$-0.351662\pi$
$71$	−7.07732	−	4.08609i	−0.0996806	−	0.0575506i	−0.549012	+	0.835815i	$0.684996\pi$
$72$	22.5309	+	38.4023i	0.312929	+	0.533366i
$73$	−24.8357			−0.340215			−0.170107	−	0.985426i	$-0.554411\pi$
$73$	−24.8357			−0.340215			−0.170107	+	0.985426i	$0.554411\pi$
$74$		−	109.318i		−	1.47727i
$75$	−32.0263	−	31.8033i	−0.427018	−	0.424044i
$76$	59.5780			0.783922
$77$	−40.7528	−	23.5286i	−0.529257	−	0.305567i
$78$	−36.1277	−	88.2317i	−0.463176	−	1.13118i
$79$	8.23711	+	14.2671i	0.104267	+	0.180596i	0.913439	−	0.406977i	$-0.133417\pi$
$79$	8.23711	+	14.2671i	0.104267	+	0.180596i	−0.809171	+	0.587573i	$0.800084\pi$
$80$	54.6477	−	31.5508i	0.683096	−	0.394386i
$81$	39.5156	−	70.7073i	0.487847	−	0.872929i
$82$	67.6622	−	117.194i	0.825149	−	1.42920i
$83$	−39.7129	+	22.9283i	−0.478469	+	0.276244i	−0.719778	−	0.694204i	$-0.755757\pi$
$83$	−39.7129	+	22.9283i	−0.478469	+	0.276244i	0.241309	+	0.970448i	$0.422423\pi$
$84$	32.1880	+	31.9638i	0.383190	+	0.380522i
$85$	−34.0113	−	58.9092i	−0.400133	−	0.693050i
$86$	109.036	+	62.9518i	1.26786	+	0.731997i
$87$	−12.2376	−	3.23326i	−0.140662	−	0.0371639i
$88$	15.2139	−	26.3512i	0.172885	−	0.299445i
$89$	−70.5240	+	40.7171i	−0.792405	+	0.457495i	−0.840809	−	0.541333i	$-0.817920\pi$
$89$	−70.5240	+	40.7171i	−0.792405	+	0.457495i	0.0484035	+	0.998828i	$0.484587\pi$
$90$	−60.3605	−	34.2890i	−0.670672	−	0.380989i
$91$	59.9500	+	79.3628i	0.658791	+	0.872118i
$92$	−14.0550	+	8.11468i	−0.152772	+	0.0882030i
$93$	−39.7361	+	150.397i	−0.427270	+	1.61717i
$94$	−68.5102			−0.728832
$95$	82.3708	−	47.5568i	0.867061	−	0.500598i
$96$	−61.5216	+	61.9530i	−0.640850	+	0.645344i
$97$	46.9466			0.483986			0.241993	−	0.970278i	$-0.422199\pi$
$97$	46.9466			0.483986			0.241993	+	0.970278i	$0.422199\pi$
$98$	−20.1874	−	11.6552i	−0.205994	−	0.118931i
$99$	−55.3541	+	0.386854i	−0.559133	+	0.00390762i
$100$	14.8671	−	25.7505i	0.148671	−	0.257505i
$101$	−31.9723	−	18.4592i	−0.316557	−	0.182764i	0.333300	−	0.942821i	$-0.391838\pi$
$101$	−31.9723	−	18.4592i	−0.316557	−	0.182764i	−0.649857	+	0.760057i	$0.725171\pi$
$102$	112.193	+	111.412i	1.09993	+	1.09227i
$103$	−34.9957	+	60.6143i	−0.339764	+	0.588488i	−0.984388	−	0.176011i	$-0.943680\pi$
$103$	−34.9957	+	60.6143i	−0.339764	+	0.588488i	0.644624	+	0.764500i	$0.277014\pi$
$104$	−51.3168	+	38.7643i	−0.493430	+	0.372733i
$105$	70.0165	+	18.4989i	0.666824	+	0.176180i
$106$	0.467445	−	0.809638i	0.00440985	−	0.00763809i
$107$	−97.4131	+	56.2415i	−0.910403	+	0.525621i	−0.880561	−	0.473933i	$-0.842834\pi$
$107$	−97.4131	+	56.2415i	−0.910403	+	0.525621i	−0.0298423	+	0.999555i	$0.509500\pi$
$108$	51.6855	+	13.2700i	0.478569	+	0.122870i
$109$	−206.693			−1.89627			−0.948133	−	0.317875i	$-0.897031\pi$
$109$	−206.693			−1.89627			−0.948133	+	0.317875i	$0.897031\pi$
$110$			47.4417i			0.431288i
$111$	95.1901	+	94.5272i	0.857569	+	0.851596i
$112$	76.5062	−	132.513i	0.683091	−	1.18315i
$113$	150.016	−	86.6115i	1.32757	−	0.766473i	0.342648	−	0.939464i	$-0.388676\pi$
$113$	150.016	−	86.6115i	1.32757	−	0.766473i	0.984923	+	0.172991i	$0.0553430\pi$
$114$	−155.783	+	156.876i	−1.36652	+	1.37611i
$115$	−12.9547	+	22.4382i	−0.112650	+	0.195115i
$116$		−	8.33860i		−	0.0718845i
$117$	108.069	+	44.8352i	0.923663	+	0.383207i
$118$	−117.251			−0.993650
$119$	−142.846	−	82.4723i	−1.20039	−	0.693045i
$120$	−11.9616	+	45.2734i	−0.0996797	+	0.377278i
$121$	−41.5850	−	72.0273i	−0.343678	−	0.595267i
$122$	108.730	+	62.7753i	0.891230	+	0.514552i
$123$	43.5411	+	160.256i	0.353993	+	1.30289i
$124$	−102.480			−0.826449
$125$		−	126.349i		−	1.01079i
$126$	−168.329	+	1.17640i	−1.33594	+	0.00933654i
$127$	82.2784	+	142.510i	0.647862	+	1.12213i	0.983633	+	0.180186i	$0.0576699\pi$
$127$	82.2784	+	142.510i	0.647862	+	1.12213i	−0.335771	+	0.941944i	$0.608997\pi$
$128$	119.553	+	69.0242i	0.934011	+	0.539252i
$129$	−149.099	+	40.5099i	−1.15581	+	0.314030i
$130$	39.0717	−	92.3478i	0.300552	−	0.710368i
$131$	143.908	+	83.0856i	1.09854	+	0.634241i	0.935836	−	0.352435i	$-0.114646\pi$
$131$	143.908	+	83.0856i	1.09854	+	0.634241i	0.162701	+	0.986675i	$0.447979\pi$
$132$	−9.56152	−	35.1917i	−0.0724357	−	0.266604i
$133$	115.318	−	199.737i	0.867055	−	1.50178i
$134$	−54.8567	−	31.6715i	−0.409378	−	0.236355i
$135$	82.0512	−	22.9101i	0.607787	−	0.169704i
$136$	53.3274	−	92.3658i	0.392114	−	0.679161i
$137$		−	189.899i		−	1.38613i	−0.720877	−	0.693063i	$-0.756261\pi$
$137$		−	189.899i		−	1.38613i	0.720877	−	0.693063i	$-0.243739\pi$
$138$	15.3839	−	58.2267i	0.111478	−	0.421932i
$139$	−1.96059	−	3.39584i	−0.0141050	−	0.0244305i	0.858887	−	0.512166i	$-0.171157\pi$
$139$	−1.96059	−	3.39584i	−0.0141050	−	0.0244305i	−0.872992	+	0.487735i	$0.837823\pi$
$140$			47.7088i			0.340777i
$141$	59.2407	−	59.6561i	0.420147	−	0.423093i
$142$	9.98911	+	17.3016i	0.0703459	+	0.121843i
$143$	−9.83737	−	79.3505i	−0.0687928	−	0.554898i
$144$	−1.25790	−	179.991i	−0.00873544	−	1.24993i
$145$	−6.65610	−	11.5287i	−0.0459041	−	0.0795083i
$146$	52.5805	+	30.3574i	0.360141	+	0.207927i
$147$	27.6049	−	7.50020i	0.187789	−	0.0510218i
$148$	−44.1886	+	76.5369i	−0.298572	+	0.517141i
$149$	−238.240	+	137.548i	−1.59893	+	0.923141i	−0.607232	+	0.794524i	$0.707720\pi$
$149$	−238.240	+	137.548i	−1.59893	+	0.923141i	−0.991694	+	0.128616i	$0.958946\pi$
$150$	28.9301	+	106.479i	0.192867	+	0.709858i
$151$	−10.8588	−	18.8080i	−0.0719127	−	0.124556i	0.827827	−	0.560984i	$-0.189577\pi$
$151$	−10.8588	−	18.8080i	−0.0719127	−	0.124556i	−0.899740	+	0.436427i	$0.856244\pi$
$152$	129.152	+	74.5659i	0.849684	+	0.490565i
$153$	−194.027	+	1.35600i	−1.26815	+	0.00886273i
$154$	57.5195	+	99.6268i	0.373503	+	0.646927i
$155$	−141.685	+	81.8021i	−0.914099	+	0.527755i
$156$	−10.3710	+	76.3773i	−0.0664806	+	0.489598i
$157$	31.9519	−	55.3422i	0.203515	−	0.352498i	−0.746144	−	0.665785i	$-0.768097\pi$
$157$	31.9519	−	55.3422i	0.203515	−	0.352498i	0.949659	+	0.313287i	$0.101430\pi$
$158$		−	40.2738i		−	0.254898i
$159$	0.300804	+	1.10713i	0.00189185	+	0.00696306i
$160$	−91.8263			−0.573914
$161$			62.8266i			0.390227i
$162$	−170.088	+	101.396i	−1.04992	+	0.625901i
$163$	−88.7596	+	153.736i	−0.544537	+	0.943166i	0.454098	+	0.890952i	$0.349961\pi$
$163$	−88.7596	+	153.736i	−0.544537	+	0.943166i	−0.998636	+	0.0522150i	$0.983372\pi$
$164$	−94.7447	+	54.7009i	−0.577712	+	0.333542i
$165$	−41.3104	−	41.0227i	−0.250366	−	0.248623i
$166$	112.104			0.675323
$167$		−	63.8495i		−	0.382332i	−0.981558	−	0.191166i	$-0.938773\pi$
$167$		−	63.8495i		−	0.382332i	0.981558	−	0.191166i	$-0.0612269\pi$
$168$	29.7716	+	109.576i	0.177212	+	0.652238i
$169$	−46.2020	+	162.562i	−0.273385	+	0.961905i
$170$			166.292i			0.978188i
$171$	−1.89605	−	271.301i	−0.0110880	−	1.58656i
$172$	−50.8928	−	88.1489i	−0.295888	−	0.512493i
$173$		−	245.835i		−	1.42101i	−0.703693	−	0.710505i	$-0.748467\pi$
$173$		−	245.835i		−	1.42101i	0.703693	−	0.710505i	$-0.251533\pi$
$174$	21.9565	+	21.8036i	0.126187	+	0.125308i
$175$	−57.5529	−	99.6846i	−0.328874	−	0.569626i
$176$	−106.529	+	61.5044i	−0.605277	+	0.349457i
$177$	101.387	−	102.098i	0.572805	−	0.576822i
$178$	199.079			1.11842
$179$	101.540	−	58.6239i	0.567260	−	0.327508i	−0.188794	−	0.982017i	$-0.560458\pi$
$179$	101.540	−	58.6239i	0.567260	−	0.327508i	0.756054	+	0.654509i	$0.227124\pi$
$180$	28.3999	+	48.4057i	0.157777	+	0.268921i
$181$	260.434			1.43886			0.719431	−	0.694564i	$-0.244403\pi$
$181$	260.434			1.43886			0.719431	+	0.694564i	$0.244403\pi$
$182$	−29.9149	−	241.301i	−0.164368	−	1.32583i
$183$	−148.681	+	40.3964i	−0.812466	+	0.220745i
$184$	−40.6243			−0.220784
$185$			141.090i			0.762649i
$186$	267.962	−	269.841i	1.44066	−	1.45076i
$187$	66.3007	+	114.836i	0.354549	+	0.614097i
$188$	47.9661	+	27.6932i	0.255139	+	0.147304i
$189$	144.530	−	147.592i	0.764707	−	0.780910i
$190$	−232.520			−1.22379
$191$			349.637i			1.83056i	0.402818	+	0.915280i	$0.368031\pi$
$191$			349.637i			1.83056i	−0.402818	+	0.915280i	$0.631969\pi$
$192$	−25.6206	+	6.96106i	−0.133440	+	0.0362555i
$193$	−297.412			−1.54100			−0.770499	−	0.637442i	$-0.779993\pi$
$193$	−297.412			−1.54100			−0.770499	+	0.637442i	$0.779993\pi$
$194$	−99.3924	−	57.3843i	−0.512332	−	0.295795i
$195$	46.6278	+	113.875i	0.239117	+	0.583976i
$196$	9.42254	+	16.3203i	0.0480742	+	0.0832669i
$197$	301.201	−	173.899i	1.52894	−	0.882734i	0.529534	−	0.848289i	$-0.322367\pi$
$197$	301.201	−	173.899i	1.52894	−	0.882734i	0.999407	−	0.0344457i	$-0.0109666\pi$
$198$	117.665	+	66.8420i	0.594269	+	0.337586i
$199$	32.5912	−	56.4496i	0.163775	−	0.283666i	−0.772445	−	0.635082i	$-0.780966\pi$
$199$	32.5912	−	56.4496i	0.163775	−	0.283666i	0.936220	+	0.351416i	$0.114300\pi$
$200$	64.4571	−	37.2143i	0.322285	−	0.186072i
$201$	75.0129	−	20.3808i	0.373198	−	0.101397i
$202$	45.1265	+	78.1613i	0.223398	+	0.386937i
$203$	−27.9554	−	16.1401i	−0.137711	−	0.0795077i
$204$	−33.5149	−	123.354i	−0.164289	−	0.604675i
$205$	−87.3274	+	151.256i	−0.425987	+	0.737832i
$206$	148.181	−	85.5525i	0.719327	−	0.415304i
$207$	37.3992	+	63.7443i	0.180672	+	0.307943i
$208$	258.018	−	31.9874i	1.24047	−	0.153786i
$209$	−160.571	+	92.7060i	−0.768284	+	0.443569i
$210$	−125.623	−	124.748i	−0.598204	−	0.594038i
$211$	−93.2505			−0.441945			−0.220973	−	0.975280i	$-0.570923\pi$
$211$	−93.2505			−0.441945			−0.220973	+	0.975280i	$0.570923\pi$
$212$	−0.654544	+	0.377901i	−0.00308747	+	0.00178255i
$213$	−23.7032	−	6.26257i	−0.111283	−	0.0294017i
$214$	274.983			1.28497
$215$	−140.726	−	81.2480i	−0.654538	−	0.377898i
$216$	95.4344	+	93.4543i	0.441826	+	0.432659i
$217$	−198.358	+	343.566i	−0.914092	+	1.58325i
$218$	437.597	+	252.647i	2.00733	+	1.15893i
$219$	−71.9004	+	19.5352i	−0.328312	+	0.0892018i
$220$	19.1769	−	33.2153i	0.0871677	−	0.150979i
$221$	−34.4818	−	278.138i	−0.156026	−	1.25854i
$222$	−85.9872	−	316.481i	−0.387330	−	1.42559i
$223$	123.122	−	213.253i	0.552115	−	0.956291i	−0.446007	−	0.895030i	$-0.647154\pi$
$223$	123.122	−	213.253i	0.552115	−	0.956291i	0.998122	−	0.0612615i	$-0.0195124\pi$
$224$	−192.834	+	111.333i	−0.860865	+	0.497021i
$225$	−117.734	−	66.8808i	−0.523260	−	0.297248i
$226$	−423.471			−1.87377
$227$			189.843i			0.836313i	0.908375	+	0.418156i	$0.137324\pi$
$227$			189.843i			0.836313i	−0.908375	+	0.418156i	$0.862676\pi$
$228$	172.481	−	46.8628i	0.756496	−	0.205539i
$229$	21.0010	−	36.3747i	0.0917072	−	0.158842i	−0.816522	−	0.577314i	$-0.804101\pi$
$229$	21.0010	−	36.3747i	0.0917072	−	0.158842i	0.908230	+	0.418472i	$0.137434\pi$
$230$	54.8538	−	31.6699i	0.238495	−	0.137695i
$231$	−136.488	−	36.0613i	−0.590859	−	0.156109i
$232$	10.4363	−	18.0762i	0.0449842	−	0.0779148i
$233$		−	151.808i		−	0.651536i	−0.945450	−	0.325768i	$-0.894377\pi$
$233$		−	151.808i		−	0.651536i	0.945450	−	0.325768i	$-0.105623\pi$
$234$	−173.993	−	227.018i	−0.743558	−	0.970161i
$235$	88.4219			0.376263
$236$	82.0908	+	47.3951i	0.347842	+	0.200827i
$237$	35.0690	+	34.8247i	0.147970	+	0.146940i
$238$	201.617	+	349.211i	0.847130	+	1.46727i
$239$	171.028	+	98.7429i	0.715597	+	0.413150i	0.813130	−	0.582082i	$-0.197762\pi$
$239$	171.028	+	98.7429i	0.715597	+	0.413150i	−0.0975330	+	0.995232i	$0.531095\pi$
$240$	133.390	−	134.326i	0.555793	−	0.559691i
$241$	−8.10289			−0.0336220			−0.0168110	−	0.999859i	$-0.505351\pi$
$241$	−8.10289			−0.0336220			−0.0168110	+	0.999859i	$0.505351\pi$
$242$			203.322i			0.840175i
$243$	58.7827	−	235.783i	0.241904	−	0.970300i
$244$	−50.7502	−	87.9018i	−0.207992	−	0.360253i
$245$	26.0546	+	15.0426i	0.106345	+	0.0613985i
$246$	103.703	−	392.505i	0.421556	−	1.59555i
$247$	388.911	−	48.2148i	1.57454	−	0.195202i
$248$	−222.153	−	128.260i	−0.895779	−	0.517178i
$249$	−96.9359	+	97.6157i	−0.389301	+	0.392031i
$250$	−154.440	+	267.497i	−0.617758	+	1.06999i
$251$	−95.8522	−	55.3403i	−0.381881	−	0.220479i	0.296755	−	0.954954i	$-0.404095\pi$
$251$	−95.8522	−	55.3403i	−0.381881	−	0.220479i	−0.678636	+	0.734474i	$0.737429\pi$
$252$	118.328	+	67.2184i	0.469555	+	0.266740i
$253$	25.2536	−	43.7405i	0.0998165	−	0.172887i
$254$		−	402.286i		−	1.58380i
$255$	−144.801	−	143.792i	−0.567847	−	0.563892i
$256$	−151.041	−	261.611i	−0.590004	−	1.02192i
$257$		−	502.733i		−	1.95616i	−0.208229	−	0.978080i	$-0.566770\pi$
$257$		−	502.733i		−	1.95616i	0.208229	−	0.978080i	$-0.433230\pi$
$258$	365.180	+	96.4832i	1.41543	+	0.373966i
$259$	171.061	+	296.287i	0.660469	+	1.14397i
$260$	−64.6842	+	48.8619i	−0.248785	+	0.187930i
$261$	−37.9716	+	0.265372i	−0.145485	+	0.00101675i
$262$	−203.116	−	351.807i	−0.775252	−	1.34278i
$263$	174.851	+	100.950i	0.664831	+	0.383840i	0.794115	−	0.607767i	$-0.207935\pi$
$263$	174.851	+	100.950i	0.664831	+	0.383840i	−0.129284	+	0.991608i	$0.541268\pi$
$264$	23.3176	−	88.2548i	0.0883241	−	0.334298i
$265$	−0.603302	+	1.04495i	−0.00227661	+	0.00394321i
$266$	−488.289	+	281.914i	−1.83567	+	1.05983i
$267$	−172.143	+	173.351i	−0.644731	+	0.649253i
$268$	25.6045	+	44.3484i	0.0955393	+	0.165479i
$269$	−241.432	−	139.391i	−0.897515	−	0.518180i	−0.0211218	−	0.999777i	$-0.506724\pi$
$269$	−241.432	−	139.391i	−0.897515	−	0.518180i	−0.876393	+	0.481596i	$0.840057\pi$
$270$	−201.717	−	51.7899i	−0.747102	−	0.191814i
$271$	−58.8505	−	101.932i	−0.217161	−	0.376133i	0.736778	−	0.676135i	$-0.236346\pi$
$271$	−58.8505	−	101.932i	−0.217161	−	0.376133i	−0.953939	+	0.300001i	$0.903013\pi$
$272$	−373.403	+	215.584i	−1.37281	+	0.792590i
$273$	235.983	+	182.604i	0.864407	+	0.668877i
$274$	−232.119	+	402.043i	−0.847151	+	1.46731i
$275$			92.5352i			0.336492i
$276$	−34.3072	+	34.5478i	−0.124301	+	0.125173i
$277$	110.305			0.398211			0.199106	−	0.979978i	$-0.436196\pi$
$277$	110.305			0.398211			0.199106	+	0.979978i	$0.436196\pi$
$278$			9.58595i			0.0344818i
$279$	3.26137	+	466.663i	0.0116895	+	1.67263i
$280$	−59.7108	+	103.422i	−0.213253	+	0.369365i
$281$	−15.0724	+	8.70203i	−0.0536383	+	0.0309681i	−0.526579	−	0.850126i	$-0.676526\pi$
$281$	−15.0724	+	8.70203i	−0.0536383	+	0.0309681i	0.472941	+	0.881094i	$0.343192\pi$
$282$	−198.340	+	53.8886i	−0.703334	+	0.191094i
$283$	492.929			1.74180			0.870900	−	0.491460i	$-0.163537\pi$
$283$	492.929			1.74180			0.870900	+	0.491460i	$0.163537\pi$
$284$		−	16.1512i		−	0.0568705i
$285$	201.060	−	202.470i	0.705474	−	0.710422i
$286$	−76.1654	+	180.020i	−0.266313	+	0.629442i
$287$			423.512i			1.47565i
$288$	−129.377	+	227.748i	−0.449225	+	0.790793i
$289$	87.8963	+	152.241i	0.304140	+	0.526785i
$290$			32.5438i			0.112220i
$291$	135.913	−	36.9272i	0.467054	−	0.126898i
$292$	−24.5422	−	42.5083i	−0.0840485	−	0.145576i
$293$	−299.742	+	173.056i	−1.02301	+	0.590636i	−0.914975	−	0.403511i	$-0.867790\pi$
$293$	−299.742	+	173.056i	−1.02301	+	0.590636i	−0.108036	+	0.994147i	$0.534456\pi$
$294$	−67.6112	−	17.8634i	−0.229970	−	0.0607598i
$295$	151.328			0.512977
$296$	−191.582	+	110.610i	−0.647237	+	0.373682i
$297$	−159.949	+	44.6603i	−0.538547	+	0.150371i
$298$	672.516			2.25677
$299$	−85.1810	+	64.3451i	−0.284886	+	0.215201i
$300$	22.7861	−	86.2431i	0.0759536	−	0.287477i
$301$	−394.029			−1.30907
$302$			53.0923i			0.175802i
$303$	−107.081	−	28.2915i	−0.353402	−	0.0933714i
$304$	−301.444	−	522.117i	−0.991594	−	1.71749i
$305$	−140.331	−	81.0203i	−0.460102	−	0.265640i
$306$	412.439	+	234.294i	1.34784	+	0.765666i
$307$	446.987			1.45598			0.727992	−	0.685586i	$-0.240454\pi$
$307$	446.987			1.45598			0.727992	+	0.685586i	$0.240454\pi$
$308$		−	93.0023i		−	0.301955i
$309$	−53.6362	+	203.008i	−0.173580	+	0.656984i
$310$	399.956			1.29018
$311$	76.2524	+	44.0243i	0.245184	+	0.141557i	0.617557	−	0.786526i	$-0.288122\pi$
$311$	76.2524	+	44.0243i	0.245184	+	0.141557i	−0.372373	+	0.928083i	$0.621456\pi$
$312$	−118.073	+	152.589i	−0.378440	+	0.489067i
$313$	−171.445	−	296.951i	−0.547747	−	0.948726i	−0.998428	−	0.0560413i	$-0.982152\pi$
$313$	−171.445	−	296.951i	−0.547747	−	0.948726i	0.450681	−	0.892685i	$-0.351181\pi$
$314$	−135.293	+	78.1114i	−0.430869	+	0.248763i
$315$	217.252	−	1.51831i	0.689689	−	0.00482004i
$316$	−16.2795	+	28.1969i	−0.0515174	+	0.0892308i
$317$	290.108	−	167.494i	0.915166	−	0.528371i	0.0330763	−	0.999453i	$-0.489470\pi$
$317$	290.108	−	167.494i	0.915166	−	0.528371i	0.882090	+	0.471081i	$0.156136\pi$
$318$	0.716431	−	2.71162i	0.00225293	−	0.00852711i
$319$	12.9752	+	22.4737i	0.0406747	+	0.0704506i
$320$	−24.1817	−	13.9613i	−0.0755678	−	0.0436291i
$321$	−237.777	+	239.445i	−0.740739	+	0.745934i
$322$	76.7948	−	133.012i	0.238493	−	0.413082i
$323$	−562.833	+	324.952i	−1.74252	+	1.00604i
$324$	160.070	−	2.23747i	0.494043	−	0.00690578i
$325$	76.2096	−	180.125i	0.234491	−	0.554231i
$326$	375.833	−	216.987i	1.15286	−	0.665604i
$327$	−598.386	+	162.580i	−1.82993	+	0.497187i
$328$	−273.847			−0.834901
$329$	185.685	−	107.205i	0.564391	−	0.325851i
$330$	37.3166	+	137.346i	0.113081	+	0.416199i
$331$	−54.8197			−0.165618			−0.0828092	−	0.996565i	$-0.526389\pi$
$331$	−54.8197			−0.165618			−0.0828092	+	0.996565i	$0.526389\pi$
$332$	−78.4872	−	45.3146i	−0.236407	−	0.136490i
$333$	349.933	+	198.786i	1.05085	+	0.596955i
$334$	−78.0451	+	135.178i	−0.233668	+	0.404725i
$335$	70.8001	+	40.8765i	0.211344	+	0.122019i
$336$	117.257	−	443.808i	0.348981	−	1.32086i
$337$	−93.3550	+	161.696i	−0.277018	+	0.479809i	−0.970642	−	0.240528i	$-0.922679\pi$
$337$	−93.3550	+	161.696i	−0.277018	+	0.479809i	0.693624	+	0.720337i	$0.256013\pi$
$338$	296.520	−	287.692i	0.877279	−	0.851159i
$339$	366.175	−	368.743i	1.08016	−	1.08774i
$340$	67.2186	−	116.426i	0.197702	−	0.342430i
$341$	276.198	−	159.463i	0.809964	−	0.467633i
$342$	−327.605	+	576.699i	−0.957910	+	1.68625i
$343$	−301.938			−0.880287
$344$		−	254.783i		−	0.740648i
$345$	−19.8551	+	75.1496i	−0.0575510	+	0.217825i
$346$	−300.491	+	520.466i	−0.868471	+	1.50424i
$347$	−135.831	+	78.4220i	−0.391444	+	0.226000i	−0.682785	−	0.730619i	$-0.739232\pi$
$347$	−135.831	+	78.4220i	−0.391444	+	0.226000i	0.291342	+	0.956619i	$0.405898\pi$
$348$	−6.55896	−	24.1406i	−0.0188476	−	0.0693697i
$349$	10.9673	−	18.9959i	0.0314250	−	0.0544296i	−0.849885	−	0.526968i	$-0.823329\pi$
$349$	10.9673	−	18.9959i	0.0314250	−	0.0544296i	0.881310	+	0.472538i	$0.156662\pi$
$350$			281.395i			0.803985i
$351$	348.130	+	44.7957i	0.991823	+	0.127623i
$352$	179.004			0.508534
$353$	463.677	+	267.704i	1.31353	+	0.758368i	0.982679	−	0.185315i	$-0.0593304\pi$
$353$	463.677	+	267.704i	1.31353	+	0.758368i	0.330853	+	0.943682i	$0.392664\pi$
$354$	−339.446	+	92.2268i	−0.958887	+	0.260528i
$355$	−12.8923	−	22.3302i	−0.0363164	−	0.0629019i
$356$	−139.381	−	80.4717i	−0.391520	−	0.226044i
$357$	−478.418	−	126.402i	−1.34011	−	0.354066i
$358$	−286.631			−0.800646
$359$		−	100.858i		−	0.280941i	−0.990085	−	0.140471i	$-0.955138\pi$
$359$		−	100.858i		−	0.280941i	0.990085	−	0.140471i	$-0.0448615\pi$
$360$	0.981756	+	140.477i	0.00272710	+	0.390215i
$361$	−273.869	−	474.355i	−0.758641	−	1.31400i
$362$	−551.375	−	318.336i	−1.52314	−	0.879382i
$363$	−177.046	−	175.813i	−0.487729	−	0.484332i
$364$	−76.5943	+	181.034i	−0.210424	+	0.497346i
$365$	−67.8625	−	39.1804i	−0.185925	−	0.107344i
$366$	364.156	+	96.2128i	0.994963	+	0.262877i
$367$	286.890	−	496.909i	0.781718	−	1.35397i	−0.149223	−	0.988804i	$-0.547677\pi$
$367$	286.890	−	496.909i	0.781718	−	1.35397i	0.930940	−	0.365171i	$-0.118990\pi$
$368$	142.227	+	82.1150i	0.386487	+	0.223139i
$369$	252.107	+	429.699i	0.683217	+	1.16450i
$370$	172.459	−	298.707i	0.466104	−	0.807317i
$371$			2.92584i			0.00788636i
$372$	−296.683	+	80.6083i	−0.797536	+	0.216689i
$373$	146.457	+	253.672i	0.392647	+	0.680085i	0.992798	−	0.119802i	$-0.0382261\pi$
$373$	146.457	+	253.672i	0.392647	+	0.680085i	−0.600151	+	0.799887i	$0.704893\pi$
$374$		−	324.165i		−	0.866752i
$375$	−99.3830	−	365.785i	−0.265021	−	0.975426i
$376$	69.3199	+	120.066i	0.184361	+	0.319323i
$377$	−6.74819	−	54.4324i	−0.0178997	−	0.144383i
$378$	−486.395	+	135.810i	−1.28676	+	0.359285i
$379$	111.262	+	192.712i	0.293568	+	0.508475i	0.974651	−	0.223731i	$-0.0718238\pi$
$379$	111.262	+	192.712i	0.293568	+	0.508475i	−0.681082	+	0.732207i	$0.738491\pi$
$380$	162.795	+	93.9895i	0.428407	+	0.247341i
$381$	350.295	+	347.856i	0.919411	+	0.913008i
$382$	427.372	−	740.230i	1.11877	−	1.93777i
$383$	491.491	−	283.762i	1.28327	−	0.740894i	0.305822	−	0.952089i	$-0.401069\pi$
$383$	491.491	−	283.762i	1.28327	−	0.740894i	0.977444	+	0.211195i	$0.0677355\pi$
$384$	400.406	+	105.790i	1.04272	+	0.275495i
$385$	−74.2369	−	128.582i	−0.192823	−	0.333980i
$386$	629.663	+	363.536i	1.63125	+	0.941804i
$387$	−399.785	+	234.556i	−1.03303	+	0.606088i
$388$	46.3918	+	80.3529i	0.119566	+	0.207095i
$389$	192.834	−	111.333i	0.495718	−	0.286203i	−0.231225	−	0.972900i	$-0.574273\pi$
$389$	192.834	−	111.333i	0.495718	−	0.286203i	0.726944	+	0.686697i	$0.240940\pi$
$390$	40.4757	−	298.084i	0.103784	−	0.764318i
$391$	88.5185	−	153.319i	0.226390	−	0.392119i
$392$			47.1718i			0.120336i
$393$	481.975	+	127.341i	1.22640	+	0.324024i
$394$	−850.246			−2.15799
$395$			51.9790i			0.131592i
$396$	−55.3621	−	94.3608i	−0.139803	−	0.238285i
$397$	54.6826	−	94.7131i	0.137740	−	0.238572i	−0.788901	−	0.614520i	$-0.789350\pi$
$397$	54.6826	−	94.7131i	0.137740	−	0.238572i	0.926641	+	0.375948i	$0.122683\pi$
$398$	−138.000	+	79.6744i	−0.346734	+	0.200187i
$399$	176.743	−	668.955i	0.442965	−	1.67658i
$400$	−300.889			−0.752223
$401$			165.394i			0.412454i	0.978504	+	0.206227i	$0.0661186\pi$
$401$			165.394i			0.412454i	−0.978504	+	0.206227i	$0.933881\pi$
$402$	−183.725	−	48.5415i	−0.457027	−	0.120750i
$403$	−668.963	+	82.9339i	−1.65996	+	0.205791i
$404$		−	72.9641i		−	0.180604i
$405$	219.522	−	130.865i	0.542029	−	0.323125i
$406$	39.4570	+	68.3415i	0.0971846	+	0.168329i
$407$		−	275.037i		−	0.675767i
$408$	81.7325	−	309.350i	0.200325	−	0.758210i
$409$	−22.7676	−	39.4346i	−0.0556665	−	0.0964172i	0.836849	−	0.547433i	$-0.184395\pi$
$409$	−22.7676	−	39.4346i	−0.0556665	−	0.0964172i	−0.892516	+	0.451016i	$0.851062\pi$
$410$	369.768	−	213.486i	0.901874	−	0.520697i
$411$	−149.370	−	549.767i	−0.363432	−	1.33763i
$412$	−138.328			−0.335748
$413$	317.787	−	183.474i	0.769460	−	0.444248i
$414$	−1.26265	−	180.670i	−0.00304988	−	0.436400i
$415$	−144.685			−0.348639
$416$	−348.441	−	147.423i	−0.837598	−	0.354382i
$417$	−8.34709	−	8.28896i	−0.0200170	−	0.0198776i
$418$	453.269			1.08438
$419$		−	391.475i		−	0.934308i	−0.884176	−	0.467154i	$-0.845279\pi$
$419$		−	391.475i		−	0.934308i	0.884176	−	0.467154i	$-0.154721\pi$
$420$	37.5267	+	138.119i	0.0893493	+	0.328855i
$421$	111.844	+	193.719i	0.265662	+	0.460140i	0.967737	−	0.251963i	$-0.0810762\pi$
$421$	111.844	+	193.719i	0.265662	+	0.460140i	−0.702075	+	0.712103i	$0.747743\pi$
$422$	197.424	+	113.983i	0.467830	+	0.270102i
$423$	124.580	−	219.305i	0.294516	−	0.518451i
$424$	−1.89188			−0.00446197
$425$			324.353i			0.763185i
$426$	42.5280	+	42.2319i	0.0998311	+	0.0991358i
$427$	−392.925			−0.920198
$428$	−192.524	−	111.154i	−0.449822	−	0.259705i
$429$	−90.8950	−	221.985i	−0.211876	−	0.517449i
$430$	198.624	+	344.026i	0.461915	+	0.800061i
$431$	210.330	−	121.434i	0.488006	−	0.281750i	−0.235741	−	0.971816i	$-0.575752\pi$
$431$	210.330	−	121.434i	0.488006	−	0.281750i	0.723747	+	0.690066i	$0.242418\pi$
$432$	−145.218	−	520.092i	−0.336154	−	1.20392i
$433$	−31.9975	+	55.4212i	−0.0738972	+	0.127994i	−0.900606	−	0.434636i	$-0.856877\pi$
$433$	−31.9975	+	55.4212i	−0.0738972	+	0.127994i	0.826709	+	0.562630i	$0.190210\pi$
$434$	839.902	−	484.918i	1.93526	−	1.11732i
$435$	−28.3379	−	28.1406i	−0.0651447	−	0.0646910i
$436$	−204.250	−	353.772i	−0.468464	−	0.811403i
$437$	214.380	+	123.772i	0.490573	+	0.283232i
$438$	176.102	+	46.5274i	0.402058	+	0.106227i
$439$	121.693	−	210.779i	0.277205	−	0.480134i	−0.693484	−	0.720472i	$-0.743925\pi$
$439$	121.693	−	210.779i	0.277205	−	0.480134i	0.970689	+	0.240338i	$0.0772584\pi$
$440$	83.1425	−	48.0023i	0.188960	−	0.109096i
$441$	74.0181	−	43.4269i	0.167841	−	0.0984736i
$442$	−266.974	+	631.006i	−0.604014	+	1.42761i
$443$	−8.10700	+	4.68058i	−0.0183002	+	0.0105656i	−0.509122	−	0.860694i	$-0.670030\pi$
$443$	−8.10700	+	4.68058i	−0.0183002	+	0.0105656i	0.490822	+	0.871260i	$0.336697\pi$
$444$	−67.7258	+	256.336i	−0.152536	+	0.577332i
$445$	−256.939			−0.577391
$446$	−521.331	+	300.991i	−1.16890	+	0.674867i
$447$	−581.524	+	585.602i	−1.30095	+	1.31007i
$448$	−67.7083			−0.151135
$449$	351.048	+	202.678i	0.781844	+	0.451398i	0.837083	−	0.547075i	$-0.184259\pi$
$449$	351.048	+	202.678i	0.781844	+	0.451398i	−0.0552392	+	0.998473i	$0.517592\pi$
$450$	167.508	+	285.505i	0.372239	+	0.634456i
$451$	170.234	−	294.854i	0.377459	−	0.653777i
$452$	296.485	+	171.176i	0.655941	+	0.378707i
$453$	−46.2308	−	45.9088i	−0.102055	−	0.101344i
$454$	232.051	−	401.924i	0.511125	−	0.885295i
$455$	38.6094	+	311.432i	0.0848557	+	0.684466i
$456$	432.553	+	114.284i	0.948581	+	0.250622i
$457$	−4.84651	+	8.39440i	−0.0106050	+	0.0183685i	−0.871279	−	0.490788i	$-0.836709\pi$
$457$	−4.84651	+	8.39440i	−0.0106050	+	0.0183685i	0.860674	+	0.509156i	$0.170042\pi$
$458$	−88.9238	+	51.3402i	−0.194157	+	0.112097i
$459$	−560.650	+	156.543i	−1.22146	+	0.341052i
$460$	−51.2064			−0.111318
$461$			340.965i			0.739620i	0.929107	+	0.369810i	$0.120577\pi$
$461$			340.965i			0.739620i	−0.929107	+	0.369810i	$0.879423\pi$
$462$	244.886	+	243.181i	0.530056	+	0.526365i
$463$	235.726	−	408.289i	0.509127	−	0.881834i	−0.490817	−	0.871263i	$-0.663302\pi$
$463$	235.726	−	408.289i	0.509127	−	0.881834i	0.999944	−	0.0105715i	$-0.00336507\pi$
$464$	−73.0760	+	42.1905i	−0.157491	+	0.0909277i
$465$	−345.842	+	348.267i	−0.743746	+	0.748962i
$466$	−185.559	+	321.398i	−0.398196	+	0.689696i
$467$			766.744i			1.64185i	0.571036	+	0.820925i	$0.306542\pi$
$467$			766.744i			1.64185i	−0.571036	+	0.820925i	$0.693458\pi$
$468$	30.0522	+	229.273i	0.0642142	+	0.489900i
$469$	198.239			0.422684
$470$	−187.201	−	108.081i	−0.398301	−	0.229959i
$471$	48.9711	−	185.351i	0.103973	−	0.393527i
$472$	118.636	+	205.484i	0.251348	+	0.435348i
$473$	274.327	+	158.383i	0.579972	+	0.334847i
$474$	−31.6785	−	116.595i	−0.0668323	−	0.245980i
$475$	−453.532			−0.954805
$476$		−	325.991i		−	0.684854i
$477$	1.74168	+	2.96858i	0.00365133	+	0.00622343i
$478$	−241.393	−	418.105i	−0.505006	−	0.874696i
$479$	195.853	+	113.075i	0.408878	+	0.236066i	0.690307	−	0.723516i	$-0.257475\pi$
$479$	195.853	+	113.075i	0.408878	+	0.236066i	−0.281430	+	0.959582i	$0.590809\pi$
$480$	−265.841	+	72.2286i	−0.553836	+	0.150476i
$481$	−226.514	+	535.375i	−0.470922	+	1.11305i
$482$	17.1549	+	9.90441i	0.0355912	+	0.0205486i
$483$	49.4180	+	181.886i	0.102315	+	0.376575i
$484$	82.1871	−	142.352i	0.169808	−	0.294116i
$485$	128.280	+	74.0623i	0.264494	+	0.152706i
$486$	−412.656	+	427.333i	−0.849086	+	0.879286i
$487$	313.254	−	542.572i	0.643232	−	1.11411i	−0.341475	−	0.939891i	$-0.610926\pi$
$487$	313.254	−	542.572i	0.643232	−	1.11411i	0.984707	−	0.174220i	$-0.0557403\pi$
$488$		−	254.069i		−	0.520633i
$489$	−136.038	+	514.890i	−0.278196	+	1.05294i
$490$	−36.7742	−	63.6947i	−0.0750493	−	0.129989i
$491$			388.719i			0.791689i	0.918317	+	0.395845i	$0.129548\pi$
$491$			388.719i			0.791689i	−0.918317	+	0.395845i	$0.870452\pi$
$492$	−231.264	+	232.886i	−0.470048	+	0.473345i
$493$	45.4806	+	78.7747i	0.0922527	+	0.159786i
$494$	−882.314	−	373.301i	−1.78606	−	0.755670i
$495$	−151.863	−	86.2689i	−0.306794	−	0.174281i
$496$	518.512	+	898.089i	1.04539	+	1.81066i
$497$	−54.1474	−	31.2620i	−0.108948	−	0.0629014i
$498$	324.545	−	88.1783i	0.651697	−	0.177065i
$499$	16.1707	−	28.0084i	0.0324062	−	0.0561291i	−0.849367	−	0.527802i	$-0.823016\pi$
$499$	16.1707	−	28.0084i	0.0324062	−	0.0561291i	0.881774	+	0.471673i	$0.156350\pi$
$500$	216.256	−	124.855i	0.432511	−	0.249711i
$501$	−50.2226	−	184.847i	−0.100245	−	0.368956i
$502$	135.288	+	234.326i	0.269498	+	0.466785i
$503$	−431.726	−	249.257i	−0.858302	−	0.495541i	0.00514126	−	0.999987i	$-0.498363\pi$
$503$	−431.726	−	249.257i	−0.858302	−	0.495541i	−0.863443	+	0.504446i	$0.831697\pi$
$504$	172.380	+	293.810i	0.342024	+	0.582956i
$505$	−58.2419	−	100.878i	−0.115331	−	0.199758i
$506$	−106.931	+	61.7364i	−0.211325	+	0.122009i
$507$	−5.88936	+	506.966i	−0.0116161	+	0.999933i
$508$	−162.612	+	281.652i	−0.320102	+	0.554434i
$509$			915.918i			1.79945i	0.436462	+	0.899723i	$0.356231\pi$
$509$			915.918i			1.79945i	−0.436462	+	0.899723i	$0.643769\pi$
$510$	130.802	+	481.423i	0.256474	+	0.943967i
$511$	−190.014			−0.371847
$512$			186.295i			0.363857i
$513$	−218.889	−	783.938i	−0.426683	−	1.52814i
$514$	−614.506	+	1064.36i	−1.19554	+	2.07073i
$515$	−191.249	+	110.417i	−0.371356	+	0.214403i
$516$	−216.673	−	215.164i	−0.419909	−	0.416984i
$517$	−172.367			−0.333399
$518$		−	836.374i		−	1.61462i
$519$	−193.368	−	711.703i	−0.372578	−	1.37130i
$520$	−201.375	+	24.9652i	−0.387260	+	0.0480100i
$521$			62.7872i			0.120513i	0.998183	+	0.0602564i	$0.0191918\pi$
$521$			62.7872i			0.120513i	−0.998183	+	0.0602564i	$0.980808\pi$
$522$	80.7154	+	45.8519i	0.154627	+	0.0878390i
$523$	77.4887	+	134.214i	0.148162	+	0.256624i	0.930548	−	0.366169i	$-0.119331\pi$
$523$	77.4887	+	134.214i	0.148162	+	0.256624i	−0.782386	+	0.622794i	$0.785998\pi$
$524$			328.414i			0.626745i
$525$	−245.028	−	243.322i	−0.466720	−	0.463470i
$526$	−246.789	−	427.450i	−0.469180	−	0.812643i
$527$	968.125	−	558.947i	1.83705	−	1.06062i
$528$	−260.028	+	261.851i	−0.492477	+	0.495930i
$529$	461.568			0.872528
$530$	2.55455	−	1.47487i	0.00481990	−	0.00278277i
$531$	213.211	−	375.326i	0.401527	−	0.706828i
$532$	455.822			0.856807
$533$	−574.203	+	433.749i	−1.07730	+	0.813787i
$534$	576.343	−	156.591i	1.07929	−	0.293242i
$535$	−354.903			−0.663371
$536$			128.183i			0.239148i
$537$	247.850	−	249.588i	0.461545	−	0.464782i
$538$	340.763	+	590.218i	0.633388	+	1.09706i
$539$	−50.7902	−	29.3237i	−0.0942304	−	0.0544040i
$540$	120.294	+	117.798i	0.222767	+	0.218144i
$541$	−849.273			−1.56982			−0.784910	−	0.619609i	$-0.787291\pi$
$541$	−849.273			−1.56982			−0.784910	+	0.619609i	$0.787291\pi$
$542$			287.739i			0.530884i
$543$	753.969	−	204.852i	1.38852	−	0.377259i
$544$	627.442			1.15339
$545$	−564.780	−	326.076i	−1.03629	−	0.598304i
$546$	−276.407	−	675.046i	−0.506240	−	1.23635i
$547$	−167.503	−	290.123i	−0.306221	−	0.530390i	0.671312	−	0.741175i	$-0.265731\pi$
$547$	−167.503	−	290.123i	−0.306221	−	0.530390i	−0.977532	+	0.210785i	$0.932398\pi$
$548$	325.028	−	187.655i	0.593116	−	0.342436i
$549$	−398.664	+	233.899i	−0.726164	+	0.426045i
$550$	113.109	−	195.910i	0.205652	−	0.356200i
$551$	−110.148	+	63.5940i	−0.199906	+	0.115416i
$552$	−117.609	+	31.9542i	−0.213060	+	0.0578880i
$553$	63.0207	+	109.155i	0.113961	+	0.197387i
$554$	−233.530	−	134.829i	−0.421534	−	0.243373i
$555$	110.978	+	408.462i	0.199961	+	0.735968i
$556$	3.87484	−	6.71141i	0.00696913	−	0.0120709i
$557$	−291.748	+	168.441i	−0.523785	+	0.302407i	−0.738482	−	0.674273i	$-0.764457\pi$
$557$	−291.748	+	168.441i	−0.523785	+	0.302407i	0.214697	+	0.976681i	$0.431124\pi$
$558$	563.511	−	991.975i	1.00988	−	1.77773i
$559$	−403.552	−	534.229i	−0.721919	−	0.955687i
$560$	418.100	−	241.390i	0.746607	−	0.431054i
$561$	282.271	+	280.305i	0.503157	+	0.499653i
$562$	42.5470			0.0757064
$563$	−789.550	+	455.847i	−1.40240	+	0.809675i	−0.994638	−	0.103414i	$-0.967023\pi$
$563$	−789.550	+	455.847i	−1.40240	+	0.809675i	−0.407760	+	0.913089i	$0.633690\pi$
$564$	160.647	+	42.4441i	0.284835	+	0.0752555i
$565$	546.548			0.967342
$566$	−1043.60	−	602.522i	−1.84382	−	1.06453i
$567$	302.327	−	540.969i	0.533205	−	0.954091i
$568$	20.2143	−	35.0123i	0.0355886	−	0.0616413i
$569$	368.892	+	212.980i	0.648316	+	0.374306i	0.787811	−	0.615917i	$-0.211214\pi$
$569$	368.892	+	212.980i	0.648316	+	0.374306i	−0.139495	+	0.990223i	$0.544548\pi$
$570$	−673.157	+	182.895i	−1.18098	+	0.320869i
$571$	383.824	−	664.803i	0.672196	−	1.16428i	−0.305084	−	0.952325i	$-0.598685\pi$
$571$	383.824	−	664.803i	0.672196	−	1.16428i	0.977280	−	0.211952i	$-0.0679822\pi$
$572$	126.094	−	95.2501i	0.220443	−	0.166521i
$573$	275.017	+	1012.22i	0.479959	+	1.76652i
$574$	517.672	−	896.634i	0.901868	−	1.56208i
$575$	106.993	−	61.7723i	0.186074	−	0.107430i
$576$	−68.6973	+	40.3052i	−0.119266	+	0.0699742i
$577$	−535.973			−0.928895			−0.464448	−	0.885601i	$-0.653747\pi$
$577$	−535.973			−0.928895			−0.464448	+	0.885601i	$0.653747\pi$
$578$		−	429.753i		−	0.743518i
$579$	−861.023	+	233.938i	−1.48709	+	0.404038i
$580$	13.1549	−	22.7849i	0.0226808	−	0.0392843i
$581$	−303.837	+	175.420i	−0.522955	+	0.301928i
$582$	−332.883	−	87.9502i	−0.571964	−	0.151117i
$583$	1.17606	−	2.03700i	0.00201726	−	0.00349399i
$584$		−	122.865i		−	0.210385i
$585$	224.561	+	292.998i	0.383866	+	0.500851i
$586$	846.127			1.44390
$587$	−14.5571	−	8.40452i	−0.0247991	−	0.0143178i	0.487549	−	0.873096i	$-0.337891\pi$
$587$	−14.5571	−	8.40452i	−0.0247991	−	0.0143178i	−0.512348	+	0.858778i	$0.671224\pi$
$588$	40.1159	+	39.8365i	0.0682243	+	0.0677491i
$589$	781.557	+	1353.70i	1.32692	+	2.29830i
$590$	−320.383	−	184.973i	−0.543022	−	0.313514i
$591$	735.207	−	740.363i	1.24401	−	1.25273i
$592$	894.316			1.51067
$593$		−	363.547i		−	0.613065i	−0.951860	−	0.306532i	$-0.900831\pi$
$593$		−	363.547i		−	0.613065i	0.951860	−	0.306532i	$-0.0991688\pi$
$594$	393.223	+	100.958i	0.661991	+	0.169963i
$595$	−260.214	−	450.705i	−0.437335	−	0.757487i
$596$	−470.849	−	271.845i	−0.790015	−	0.456115i
$597$	49.9510	−	189.060i	0.0836700	−	0.316683i
$598$	258.991	−	32.1081i	0.433095	−	0.0536924i
$599$	−808.916	−	467.028i	−1.35044	−	0.779679i	−0.362132	−	0.932127i	$-0.617951\pi$
$599$	−808.916	−	467.028i	−1.35044	−	0.779679i	−0.988312	+	0.152448i	$0.951284\pi$
$600$	157.334	−	158.438i	0.262224	−	0.264063i
$601$	100.771	−	174.540i	0.167672	−	0.290416i	−0.769929	−	0.638130i	$-0.779708\pi$
$601$	100.771	−	174.540i	0.167672	−	0.290416i	0.937601	+	0.347713i	$0.113042\pi$
$602$	834.213	+	481.633i	1.38574	+	0.800055i
$603$	201.135	−	118.007i	0.333557	−	0.195700i
$604$	21.4610	−	37.1715i	0.0355314	−	0.0615422i
$605$		−	262.416i		−	0.433745i
$606$	192.123	+	190.785i	0.317035	+	0.314827i
$607$	−338.910	−	587.010i	−0.558337	−	0.967068i	−0.997636	−	0.0687265i	$-0.978106\pi$
$607$	−338.910	−	587.010i	−0.558337	−	0.967068i	0.439299	−	0.898341i	$-0.355227\pi$
$608$			877.331i			1.44298i
$609$	−93.6276	−	24.7371i	−0.153740	−	0.0406192i
$610$	198.067	+	343.062i	0.324700	+	0.562397i
$611$	335.522	+	141.957i	0.549137	+	0.232336i
$612$	−194.055	−	330.752i	−0.317083	−	0.540445i
$613$	−314.267	−	544.326i	−0.512671	−	0.887971i	−0.999892	−	0.0146930i	$-0.995323\pi$
$613$	−314.267	−	544.326i	−0.512671	−	0.887971i	0.487222	−	0.873278i	$-0.338010\pi$
$614$	−946.333	−	546.366i	−1.54126	−	0.889846i
$615$	−133.843	+	506.582i	−0.217630	+	0.823710i
$616$	116.399	−	201.608i	0.188959	−	0.327286i
$617$	845.672	−	488.249i	1.37062	−	0.791327i	0.379613	−	0.925145i	$-0.376057\pi$
$617$	845.672	−	488.249i	1.37062	−	0.791327i	0.991006	+	0.133818i	$0.0427239\pi$
$618$	361.698	−	364.235i	0.585272	−	0.589377i
$619$	337.425	+	584.436i	0.545112	+	0.944162i	0.998600	+	0.0528997i	$0.0168464\pi$
$619$	337.425	+	584.436i	0.545112	+	0.944162i	−0.453487	+	0.891263i	$0.649820\pi$
$620$	−280.022	−	161.671i	−0.451648	−	0.260759i
$621$	158.412	+	155.125i	0.255092	+	0.249799i
$622$	−107.625	−	186.411i	−0.173030	−	0.299696i
$623$	−539.568	+	311.520i	−0.866080	+	0.500031i
$624$	721.812	−	295.556i	1.15675	−	0.473647i
$625$	11.2646	−	19.5109i	0.0180234	−	0.0312175i
$626$			838.249i			1.33906i
$627$	−391.941	+	394.690i	−0.625106	+	0.629490i
$628$	126.297			0.201110
$629$		−	964.058i		−	1.53268i
$630$	−461.808	−	262.339i	−0.733029	−	0.416411i
$631$	−425.578	+	737.123i	−0.674451	+	1.16818i	0.302178	+	0.953251i	$0.402286\pi$
$631$	−425.578	+	737.123i	−0.674451	+	1.16818i	−0.976629	+	0.214932i	$0.931047\pi$
$632$	−70.5808	+	40.7498i	−0.111678	+	0.0644776i
$633$	−269.965	+	73.3488i	−0.426484	+	0.115875i
$634$	−818.930			−1.29169
$635$			519.205i			0.817646i
$636$	−1.59769	+	1.60889i	−0.00251209	+	0.00252970i
$637$	74.7157	+	98.9098i	0.117293	+	0.155274i
$638$		−	63.4400i		−	0.0994357i
$639$	−73.5479	+	0.514005i	−0.115098	+	0.000804390i
$640$	217.783	+	377.212i	0.340286	+	0.589393i
$641$		−	198.537i		−	0.309730i	−0.987936	−	0.154865i	$-0.950506\pi$
$641$		−	198.537i		−	0.309730i	0.987936	−	0.154865i	$-0.0494943\pi$
$642$	796.088	−	216.295i	1.24001	−	0.336909i
$643$	600.731	+	1040.50i	0.934263	+	1.61819i	0.775943	+	0.630803i	$0.217274\pi$
$643$	600.731	+	1040.50i	0.934263	+	1.61819i	0.158319	+	0.987388i	$0.449392\pi$
$644$	−107.533	+	62.0840i	−0.166976	+	0.0964038i
$645$	−471.315	−	124.525i	−0.730721	−	0.193062i
$646$	1588.79			2.45943
$647$	−951.412	+	549.298i	−1.47050	+	0.848993i	−0.999452	−	0.0331157i	$-0.989457\pi$
$647$	−951.412	+	549.298i	−1.47050	+	0.848993i	−0.471047	+	0.882108i	$0.656124\pi$
$648$	349.796	+	195.488i	0.539809	+	0.301679i
$649$	−294.995			−0.454538
$650$	−381.518	+	288.196i	−0.586951	+	0.443379i
$651$	−304.014	+	1150.66i	−0.466995	+	1.76753i
$652$	−350.842			−0.538102
$653$			92.5624i			0.141749i	0.997485	+	0.0708747i	$0.0225791\pi$
$653$			92.5624i			0.141749i	−0.997485	+	0.0708747i	$0.977421\pi$
$654$	1465.59	+	387.220i	2.24097	+	0.592080i
$655$	262.149	+	454.056i	0.400228	+	0.693215i
$656$	958.751	+	553.535i	1.46151	+	0.843804i
$657$	−192.789	+	113.111i	−0.293439	+	0.172162i
$658$	−524.160			−0.796595
$659$		−	611.542i		−	0.927986i	−0.885839	−	0.463993i	$-0.846416\pi$
$659$		−	611.542i		−	0.927986i	0.885839	−	0.463993i	$-0.153584\pi$
$660$	29.3915	−	111.244i	0.0445326	−	0.168552i
$661$	−584.830			−0.884765			−0.442383	−	0.896826i	$-0.645867\pi$
$661$	−584.830			−0.884765			−0.442383	+	0.896826i	$0.645867\pi$
$662$	116.061	+	67.0078i	0.175319	+	0.101220i
$663$	−318.604	−	778.101i	−0.480549	−	1.17361i
$664$	−113.429	−	196.464i	−0.170826	−	0.295879i
$665$	630.205	−	363.849i	0.947677	−	0.547141i
$666$	−497.874	−	848.591i	−0.747558	−	1.27416i
$667$	17.3233	−	30.0049i	0.0259720	−	0.0449848i
$668$	109.284	−	63.0949i	0.163598	−	0.0944534i
$669$	188.703	−	714.222i	0.282067	−	1.06760i
$670$	−99.9291	−	173.082i	−0.149148	−	0.258332i
$671$	273.558	+	157.939i	0.407687	+	0.235378i
$672$	−470.691	+	473.992i	−0.700433	+	0.705346i
$673$	144.560	−	250.385i	0.214799	−	0.372043i	−0.738411	−	0.674351i	$-0.764424\pi$
$673$	144.560	−	250.385i	0.214799	−	0.372043i	0.953210	+	0.302308i	$0.0977570\pi$
$674$	395.291	−	228.221i	0.586485	−	0.338607i
$675$	−393.451	−	101.016i	−0.582891	−	0.149654i
$676$	−323.894	+	81.5622i	−0.479133	+	0.120654i
$677$	−963.176	+	556.090i	−1.42271	+	0.821403i	−0.996530	−	0.0832338i	$-0.973475\pi$
$677$	−963.176	+	556.090i	−1.42271	+	0.821403i	−0.426182	+	0.904637i	$0.640142\pi$
$678$	−1225.97	+	333.093i	−1.80821	+	0.491288i
$679$	359.181			0.528985
$680$	291.430	−	168.257i	0.428574	−	0.247437i
$681$	149.326	+	549.604i	0.219275	+	0.807055i
$682$	−779.665			−1.14320
$683$	−943.198	−	544.556i	−1.38096	−	0.797300i	−0.388690	−	0.921369i	$-0.627072\pi$
$683$	−943.198	−	544.556i	−1.38096	−	0.797300i	−0.992274	+	0.124069i	$0.960406\pi$
$684$	462.480	−	271.340i	0.676140	−	0.396696i
$685$	299.582	−	518.892i	0.437346	−	0.757506i
$686$	639.245	+	369.068i	0.931844	+	0.538000i
$687$	32.1872	−	121.825i	0.0468518	−	0.177330i
$688$	−515.000	+	892.006i	−0.748547	+	1.29652i
$689$	−3.96689	+	2.99656i	−0.00575746	+	0.00434914i
$690$	133.894	−	134.833i	0.194049	−	0.195409i
$691$	66.7244	−	115.570i	0.0965621	−	0.167250i	−0.813697	−	0.581289i	$-0.802549\pi$
$691$	66.7244	−	115.570i	0.0965621	−	0.167250i	0.910259	+	0.414038i	$0.135882\pi$
$692$	420.766	−	242.929i	0.608043	−	0.351054i
$693$	−423.505	+	2.95976i	−0.611119	+	0.00427094i
$694$	383.430			0.552493
$695$		−	12.3720i		−	0.0178014i
$696$	15.9953	−	60.5406i	0.0229817	−	0.0869836i
$697$	596.702	−	1033.52i	0.856100	−	1.48281i
$698$	−46.4386	+	26.8114i	−0.0665310	+	0.0384117i
$699$	−119.409	−	439.491i	−0.170828	−	0.628742i
$700$	113.746	−	197.013i	0.162494	−	0.281447i
$701$		−	693.561i		−	0.989388i	−0.869067	−	0.494694i	$-0.835280\pi$
$701$		−	693.561i		−	0.989388i	0.869067	−	0.494694i	$-0.164720\pi$
$702$	−682.284	−	520.368i	−0.971914	−	0.741265i
$703$	1348.01			1.91751
$704$	47.1392	+	27.2158i	0.0669591	+	0.0386588i
$705$	255.985	−	69.5507i	0.363100	−	0.0986535i
$706$	−654.445	−	1133.53i	−0.926976	−	1.60557i
$707$	−244.614	−	141.228i	−0.345989	−	0.199757i
$708$	274.937	+	72.6403i	0.388328	+	0.102599i
$709$	156.542			0.220793			0.110397	−	0.993888i	$-0.464788\pi$
$709$	156.542			0.220793			0.110397	+	0.993888i	$0.464788\pi$
$710$			63.0347i			0.0887813i
$711$	128.919	+	73.2348i	0.181320	+	0.103003i
$712$	−201.432	−	348.890i	−0.282910	−	0.490014i
$713$	−368.754	−	212.900i	−0.517186	−	0.298597i
$714$	858.372	+	852.394i	1.20220	+	1.19383i
$715$	98.3020	−	232.341i	0.137485	−	0.324953i
$716$	200.679	+	115.862i	0.280278	+	0.161819i
$717$	572.802	+	151.339i	0.798887	+	0.211072i
$718$	−123.282	+	213.530i	−0.171701	+	0.297396i
$719$	105.238	+	60.7593i	0.146367	+	0.0845053i	0.571395	−	0.820675i	$-0.306402\pi$
$719$	105.238	+	60.7593i	0.146367	+	0.0845053i	−0.425028	+	0.905180i	$0.639736\pi$
$720$	280.514	−	493.801i	0.389602	−	0.685835i
$721$	−267.746	+	463.750i	−0.371354	+	0.643204i
$722$			1339.03i			1.85462i
$723$	−23.4582	+	6.37356i	−0.0324457	+	0.00881543i
$724$	257.356	+	445.754i	0.355464	+	0.615682i
$725$			63.4769i			0.0875543i
$726$	159.929	+	588.628i	0.220288	+	0.810782i
$727$	343.562	+	595.068i	0.472576	+	0.818525i	0.999507	−	0.0313826i	$-0.00999103\pi$
$727$	343.562	+	595.068i	0.472576	+	0.818525i	−0.526932	+	0.849908i	$0.676658\pi$
$728$	−392.616	+	296.579i	−0.539308	+	0.407389i
$729$	−15.2830	−	728.840i	−0.0209643	−	0.999780i
$730$	95.7828	+	165.901i	0.131209	+	0.227261i
$731$	961.567	+	555.161i	1.31541	+	0.759454i
$732$	−216.066	−	214.561i	−0.295172	−	0.293116i
$733$	−17.5857	+	30.4593i	−0.0239914	+	0.0415542i	−0.877772	−	0.479079i	$-0.840971\pi$
$733$	−17.5857	+	30.4593i	−0.0239914	+	0.0415542i	0.853780	+	0.520633i	$0.174304\pi$
$734$	−1214.77	+	701.350i	−1.65500	+	0.955517i
$735$	87.2616	+	23.0552i	0.118723	+	0.0313676i
$736$	−119.495	−	206.971i	−0.162357	−	0.281210i
$737$	−138.016	−	79.6835i	−0.187267	−	0.108119i
$738$	−8.51149	−	1217.89i	−0.0115332	−	1.65026i
$739$	700.539	+	1213.37i	0.947956	+	1.64191i	0.749722	+	0.661753i	$0.230187\pi$
$739$	700.539	+	1213.37i	0.947956	+	1.64191i	0.198234	+	0.980155i	$0.436479\pi$
$740$	−241.487	+	139.423i	−0.326334	+	0.188409i
$741$	1087.99	−	445.493i	1.46828	−	0.601206i
$742$	3.57634	−	6.19440i	0.00481987	−	0.00834825i
$743$		−	830.282i		−	1.11747i	−0.829346	−	0.558736i	$-0.811287\pi$
$743$		−	830.282i		−	1.11747i	0.829346	−	0.558736i	$-0.188713\pi$
$744$	−744.031	−	196.579i	−1.00004	−	0.264218i
$745$	−867.975			−1.16507
$746$		−	716.077i		−	0.959889i
$747$	−203.852	+	358.850i	−0.272894	+	0.480388i
$748$	−131.034	+	226.958i	−0.175179	+	0.303420i
$749$	−745.291	+	430.294i	−0.995049	+	0.574492i
$750$	−236.702	+	895.896i	−0.315603	+	1.19453i
$751$	725.958			0.966655			0.483327	−	0.875440i	$-0.339428\pi$
$751$	725.958			0.966655			0.483327	+	0.875440i	$0.339428\pi$
$752$		−	560.473i		−	0.745309i
$753$	−321.026	−	84.8175i	−0.426329	−	0.112639i
$754$	−52.2476	+	123.489i	−0.0692938	+	0.163779i
$755$		−	68.5229i		−	0.0907588i
$756$	395.437	+	101.526i	0.523065	+	0.134294i
$757$	455.691	+	789.279i	0.601969	+	1.04264i	0.992523	+	0.122061i	$0.0389503\pi$
$757$	455.691	+	789.279i	0.601969	+	1.04264i	−0.390554	+	0.920580i	$0.627716\pi$
$758$		−	543.998i		−	0.717675i
$759$	38.7050	−	146.495i	0.0509947	−	0.193010i
$760$	235.268	+	407.497i	0.309564	+	0.536180i
$761$	1000.60	−	577.695i	1.31485	−	0.759126i	0.331951	−	0.943297i	$-0.392293\pi$
$761$	1000.60	−	577.695i	1.31485	−	0.759126i	0.982894	+	0.184170i	$0.0589598\pi$
$762$	−316.429	−	1164.64i	−0.415261	−	1.52839i
$763$	−1581.37			−2.07257
$764$	−598.432	+	345.505i	−0.783288	+	0.452231i
$765$	−532.309	−	302.389i	−0.695829	−	0.395279i
$766$	−1387.40			−1.81123
$767$	574.225	+	242.951i	0.748663	+	0.316754i
$768$	−643.049	−	638.570i	−0.837303	−	0.831472i
$769$	−550.108			−0.715356			−0.357678	−	0.933845i	$-0.616431\pi$
$769$	−550.108			−0.715356			−0.357678	+	0.933845i	$0.616431\pi$
$770$			362.968i			0.471387i
$771$	−395.439	−	1455.44i	−0.512891	−	1.88772i
$772$	−293.898	−	509.045i	−0.380696	−	0.659385i
$773$	507.118	+	292.785i	0.656039	+	0.378764i	0.790766	−	0.612118i	$-0.209682\pi$
$773$	507.118	+	292.785i	0.656039	+	0.378764i	−0.134727	+	0.990883i	$0.543016\pi$
$774$	1133.10	−	7.91894i	1.46396	−	0.0102312i
$775$	780.117			1.00660
$776$			232.250i			0.299291i
$777$	728.284	+	723.212i	0.937302	+	0.930774i
$778$	−544.343			−0.699669
$779$	1445.13	+	834.348i	1.85511	+	1.07105i
$780$	−148.830	+	192.337i	−0.190808	+	0.246585i
$781$	25.1320	+	43.5299i	0.0321792	+	0.0557360i
$782$	−374.812	+	216.398i	−0.479299	+	0.276723i
$783$	−109.721	+	30.6359i	−0.140129	+	0.0391263i
$784$	95.3496	−	165.150i	0.121619	−	0.210651i
$785$	174.614	−	100.814i	0.222439	−	0.128425i
$786$	−864.754	−	858.732i	−1.10020	−	1.09253i
$787$	−199.539	−	345.611i	−0.253544	−	0.439150i	0.710955	−	0.703237i	$-0.248263\pi$
$787$	−199.539	−	345.611i	−0.253544	−	0.439150i	−0.964499	+	0.264087i	$0.914929\pi$
$788$	595.283	+	343.687i	0.755436	+	0.436151i
$789$	585.606	+	154.721i	0.742212	+	0.196098i
$790$	63.5355	−	110.047i	0.0804246	−	0.139300i
$791$	1147.74	−	662.650i	1.45100	−	0.837737i
$792$	−1.91381	−	273.843i	−0.00241643	−	0.345761i
$793$	−402.422	−	532.732i	−0.507467	−	0.671793i
$794$	−231.541	+	133.680i	−0.291614	+	0.168363i
$795$	−0.924653	+	3.49972i	−0.00116309	+	0.00440217i
$796$	128.824			0.161839
$797$	−418.101	+	241.391i	−0.524593	+	0.302874i	−0.738812	−	0.673912i	$-0.764613\pi$
$797$	−418.101	+	241.391i	−0.524593	+	0.302874i	0.214219	+	0.976786i	$0.431280\pi$
$798$	−1191.87	+	1200.23i	−1.49358	+	1.50405i
$799$	−604.180			−0.756170
$800$	379.196	+	218.929i	0.473995	+	0.273661i
$801$	−362.009	+	637.262i	−0.451946	+	0.795583i
$802$	202.166	−	350.162i	0.252078	−	0.436611i
$803$	132.289	+	76.3773i	0.164744	+	0.0951149i
$804$	109.010	+	108.251i	0.135584	+	0.134640i
$805$	−99.1143	+	171.671i	−0.123123	+	0.213256i
$806$	1517.66	+	642.112i	1.88295	+	0.796665i
$807$	−808.597	−	213.637i	−1.00198	−	0.264730i
$808$	91.3196	−	158.170i	0.113019	−	0.195755i
$809$	1069.07	−	617.227i	1.32147	−	0.762950i	0.337505	−	0.941324i	$-0.390417\pi$
$809$	1069.07	−	617.227i	1.32147	−	0.762950i	0.983963	+	0.178374i	$0.0570836\pi$
$810$	−624.718	+	8.73239i	−0.771257	+	0.0107807i
$811$	−169.669			−0.209209			−0.104605	−	0.994514i	$-0.533358\pi$
$811$	−169.669			−0.209209			−0.104605	+	0.994514i	$0.533358\pi$
$812$		−	63.7972i		−	0.0785680i
$813$	−250.553	−	248.808i	−0.308183	−	0.306036i
$814$	−336.186	+	582.292i	−0.413005	+	0.715346i
$815$	−485.064	+	280.052i	−0.595171	+	0.343622i
$816$	−911.446	+	917.838i	−1.11697	+	1.12480i
$817$	−776.263	+	1344.53i	−0.950138	+	1.64569i
$818$			111.318i			0.136086i
$819$	826.814	+	343.027i	1.00954	+	0.418836i
$820$	−345.181			−0.420953
$821$	−754.672	−	435.710i	−0.919210	−	0.530706i	−0.0358273	−	0.999358i	$-0.511407\pi$
$821$	−754.672	−	435.710i	−0.919210	−	0.530706i	−0.883383	+	0.468652i	$0.844740\pi$
$822$	−355.759	+	1346.51i	−0.432796	+	1.63809i
$823$	227.405	+	393.878i	0.276313	+	0.478588i	0.970465	−	0.241240i	$-0.0775541\pi$
$823$	227.405	+	393.878i	0.276313	+	0.478588i	−0.694153	+	0.719828i	$0.744221\pi$
$824$	−299.865	−	173.127i	−0.363914	−	0.210106i
$825$	72.7862	+	267.894i	0.0882257	+	0.324720i
$826$	−897.065			−1.08604
$827$		−	58.1961i		−	0.0703702i	−0.999381	−	0.0351851i	$-0.988798\pi$
$827$		−	58.1961i		−	0.0703702i	0.999381	−	0.0351851i	$-0.0112021\pi$
$828$	−72.1463	+	127.003i	−0.0871332	+	0.153385i
$829$	184.684	+	319.882i	0.222779	+	0.385865i	0.955651	−	0.294502i	$-0.0951537\pi$
$829$	184.684	+	319.882i	0.222779	+	0.385865i	−0.732872	+	0.680367i	$0.761820\pi$
$830$	306.319	+	176.853i	0.369059	+	0.213076i
$831$	319.337	−	86.7631i	0.384280	−	0.104408i
$832$	−69.3448	−	91.7997i	−0.0833471	−	0.110336i
$833$	−178.029	−	102.785i	−0.213721	−	0.123392i
$834$	7.54010	+	27.7518i	0.00904089	+	0.0332755i
$835$	100.728	−	174.466i	0.120632	−	0.208941i
$836$	−317.347	−	183.221i	−0.379602	−	0.219163i
$837$	376.508	+	1348.44i	0.449831	+	1.61104i
$838$	−478.512	+	828.806i	−0.571016	+	0.989029i
$839$		−	436.464i		−	0.520219i	−0.965579	−	0.260109i	$-0.916241\pi$
$839$		−	436.464i		−	0.520219i	0.965579	−	0.260109i	$-0.0837586\pi$
$840$	−91.5160	+	346.379i	−0.108948	+	0.412356i
$841$	−411.599	−	712.911i	−0.489417	−	0.847694i
$842$		−	546.840i		−	0.649453i
$843$	−36.7904	+	37.0484i	−0.0436422	+	0.0439483i
$844$	−92.1484	−	159.606i	−0.109181	−	0.189106i
$845$	−382.701	+	371.306i	−0.452900	+	0.439416i
$846$	−531.816	+	312.020i	−0.628625	+	0.368818i
$847$	−318.160	−	551.069i	−0.375631	−	0.650613i
$848$	6.62354	+	3.82410i	0.00781078	+	0.00450955i
$849$	1427.05	−	387.727i	1.68086	−	0.456687i
$850$	396.467	−	686.701i	0.466432	−	0.807883i
$851$	−318.008	+	183.602i	−0.373688	+	0.215749i
$852$	−12.7042	−	46.7585i	−0.0149110	−	0.0548809i
$853$	4.91575	+	8.51433i	0.00576290	+	0.00998163i	0.868892	−	0.495001i	$-0.164832\pi$
$853$	4.91575	+	8.51433i	0.00576290	+	0.00998163i	−0.863130	+	0.504983i	$0.831499\pi$
$854$	831.876	+	480.284i	0.974093	+	0.562393i
$855$	422.820	−	744.310i	0.494526	−	0.870538i
$856$	−278.233	−	481.913i	−0.325038	−	0.562982i
$857$	1224.81	−	707.143i	1.42918	−	0.825138i	0.432125	−	0.901814i	$-0.357764\pi$
$857$	1224.81	−	707.143i	1.42918	−	0.825138i	0.997056	+	0.0766755i	$0.0244305\pi$
$858$	−78.9023	+	581.077i	−0.0919607	+	0.677246i
$859$	97.9732	−	169.694i	0.114055	−	0.197549i	−0.803347	−	0.595512i	$-0.796949\pi$
$859$	97.9732	−	169.694i	0.114055	−	0.197549i	0.917402	+	0.397963i	$0.130283\pi$
$860$		−	321.151i		−	0.373431i
$861$	333.126	+	1226.09i	0.386905	+	1.42403i
$862$	−593.731			−0.688783
$863$			414.684i			0.480514i	0.970709	+	0.240257i	$0.0772318\pi$
$863$			414.684i			0.480514i	−0.970709	+	0.240257i	$0.922768\pi$
$864$	−195.410	+	761.107i	−0.226169	+	0.880911i
$865$	387.825	−	671.733i	0.448353	−	0.776570i
$866$	135.486	−	78.2229i	0.156450	−	0.0903267i
$867$	374.213	+	371.607i	0.431619	+	0.428613i
$868$	−784.055			−0.903289
$869$		−	101.326i		−	0.116601i
$870$	25.5982	+	94.2158i	0.0294233	+	0.108294i
$871$	203.030	+	268.775i	0.233100	+	0.308582i
$872$		−	1022.53i		−	1.17263i
$873$	364.427	−	213.812i	0.417442	−	0.244916i
$874$	−302.582	−	524.087i	−0.346203	−	0.599642i
$875$		−	966.671i		−	1.10477i
$876$	−104.487	−	103.759i	−0.119277	−	0.118446i
$877$	235.547	+	407.980i	0.268583	+	0.465200i	0.968496	−	0.249028i	$-0.0801113\pi$
$877$	235.547	+	407.980i	0.268583	+	0.465200i	−0.699913	+	0.714228i	$0.746778\pi$
$878$	−515.282	+	297.498i	−0.586882	+	0.338836i
$879$	−731.645	+	736.776i	−0.832361	+	0.838198i
$880$	−388.114			−0.441039
$881$	−1476.32	+	852.355i	−1.67574	+	0.967486i	−0.711406	+	0.702781i	$0.751941\pi$
$881$	−1476.32	+	852.355i	−1.67574	+	0.967486i	−0.964329	+	0.264705i	$0.914725\pi$
$882$	−209.788	+	1.46615i	−0.237855	+	0.00166230i
$883$	650.040			0.736172			0.368086	−	0.929792i	$-0.380013\pi$
$883$	650.040			0.736172			0.368086	+	0.929792i	$0.380013\pi$
$884$	441.982	−	333.870i	0.499980	−	0.377681i
$885$	438.102	−	119.031i	0.495031	−	0.134499i
$886$	22.8848			0.0258294
$887$		−	338.912i		−	0.382088i	−0.981581	−	0.191044i	$-0.938813\pi$
$887$		−	338.912i		−	0.382088i	0.981581	−	0.191044i	$-0.0611873\pi$
$888$	−467.636	+	470.915i	−0.526617	+	0.530310i
$889$	629.498	+	1090.32i	0.708097	+	1.22646i
$890$	543.975	+	314.064i	0.611208	+	0.352881i
$891$	−427.930	+	255.106i	−0.480280	+	0.286314i
$892$	486.666			0.545590
$893$		−	844.804i		−	0.946029i
$894$	1946.97	−	528.986i	2.17781	−	0.591707i
$895$	369.937			0.413338
$896$	914.683	+	528.093i	1.02085	+	0.589389i
$897$	−195.991	+	253.283i	−0.218496	+	0.282367i
$898$	−495.478	−	858.193i	−0.551757	−	0.955672i
$899$	189.465	−	109.387i	0.210750	−	0.121677i
$900$	−1.87019	−	267.601i	−0.00207799	−	0.297334i
$901$	4.12232	−	7.14006i	0.00457527	−	0.00792460i
$902$	−720.817	+	416.164i	−0.799132	+	0.461379i
$903$	−1140.73	+	309.934i	−1.26327	+	0.343228i
$904$	428.476	+	742.142i	0.473978	+	0.820954i
$905$	711.626	+	410.857i	0.786327	+	0.453986i
$906$	41.7612	+	153.705i	0.0460940	+	0.169652i
$907$	545.835	−	945.414i	0.601803	−	1.04235i	−0.390745	−	0.920499i	$-0.627783\pi$
$907$	545.835	−	945.414i	0.601803	−	1.04235i	0.992548	−	0.121854i	$-0.0388840\pi$
$908$	−324.932	+	187.599i	−0.357854	+	0.206607i
$909$	−332.257	+	2.32205i	−0.365520	+	0.00255451i
$910$	298.931	−	706.538i	0.328496	−	0.776415i
$911$	−680.446	+	392.856i	−0.746922	+	0.431236i	−0.824581	−	0.565744i	$-0.808589\pi$
$911$	−680.446	+	392.856i	−0.746922	+	0.431236i	0.0776587	+	0.996980i	$0.475256\pi$
$912$	−1283.38	−	1274.44i	−1.40722	−	1.39742i
$913$	282.046			0.308922
$914$	20.5214	−	11.8481i	0.0224524	−	0.0129629i
$915$	−469.994	−	124.176i	−0.513655	−	0.135711i
$916$	83.0110			0.0906234
$917$	1101.02	+	635.674i	1.20068	+	0.693210i
$918$	1378.32	+	353.876i	1.50144	+	0.385486i
$919$	0.983854	−	1.70409i	0.00107057	−	0.00185428i	−0.865490	−	0.500927i	$-0.832993\pi$
$919$	0.983854	−	1.70409i	0.00107057	−	0.00185428i	0.866560	+	0.499073i	$0.166326\pi$
$920$	−111.004	−	64.0883i	−0.120657	−	0.0696612i
$921$	1294.05	−	351.590i	1.40505	−	0.381748i
$922$	416.772	−	721.870i	0.452030	−	0.782939i
$923$	−13.0707	−	105.431i	−0.0141611	−	0.114227i
$924$	−73.1536	−	269.246i	−0.0791705	−	0.291392i
$925$	336.382	−	582.630i	0.363656	−	0.629870i
$926$	−998.128	+	576.270i	−1.07789	+	0.622322i
$927$	4.40224	+	629.907i	0.00474891	+	0.679511i
$928$	122.792			0.132319
$929$		−	545.424i		−	0.587109i	−0.955942	−	0.293555i	$-0.905162\pi$
$929$		−	545.424i		−	0.587109i	0.955942	−	0.293555i	$-0.0948383\pi$
$930$	1157.89	−	314.597i	1.24505	−	0.338276i
$931$	143.721	−	248.932i	0.154373	−	0.267382i
$932$	259.831	−	150.014i	0.278789	−	0.160959i
$933$	255.383	+	67.4740i	0.273722	+	0.0723194i
$934$	937.214	−	1623.30i	1.00344	−	1.73801i
$935$			418.380i			0.447465i
$936$	−221.804	+	534.626i	−0.236971	+	0.571182i
$937$	1697.45			1.81158			0.905790	−	0.423726i	$-0.139278\pi$
$937$	1697.45			1.81158			0.905790	+	0.423726i	$0.139278\pi$
$938$	−419.699	−	242.313i	−0.447440	−	0.258330i
$939$	−729.916	−	724.833i	−0.777334	−	0.771920i
$940$	87.3769	+	151.341i	0.0929541	+	0.161001i
$941$	−886.312	−	511.713i	−0.941884	−	0.543797i	−0.0513333	−	0.998682i	$-0.516347\pi$
$941$	−886.312	−	511.713i	−0.941884	−	0.543797i	−0.890550	+	0.454885i	$0.849680\pi$
$942$	−330.239	+	332.555i	−0.350572	+	0.353031i
$943$	−454.561			−0.482037
$944$		−	959.212i		−	1.01611i
$945$	627.760	−	175.281i	0.664297	−	0.185483i
$946$	−387.192	−	670.636i	−0.409294	−	0.708917i
$947$	370.242	+	213.759i	0.390963	+	0.225723i	0.682577	−	0.730813i	$-0.260859\pi$
$947$	370.242	+	213.759i	0.390963	+	0.225723i	−0.291614	+	0.956536i	$0.594192\pi$
$948$	−24.9508	+	94.4366i	−0.0263195	+	0.0996166i
$949$	−194.606	−	257.623i	−0.205064	−	0.271468i
$950$	960.191	+	554.366i	1.01073	+	0.583543i
$951$	708.128	−	713.094i	0.744614	−	0.749836i
$952$	407.999	−	706.675i	0.428571	−	0.742306i
$953$	−124.120	−	71.6609i	−0.130242	−	0.0751951i	0.433464	−	0.901171i	$-0.357291\pi$
$953$	−124.120	−	71.6609i	−0.130242	−	0.0751951i	−0.563705	+	0.825976i	$0.690625\pi$
$954$	−0.0588016	−	8.41380i	−6.16369e−5	−	0.00881949i
$955$	−551.582	+	955.369i	−0.577573	+	1.00039i
$956$			390.304i			0.408267i
$957$	55.2412	+	54.8565i	0.0577233	+	0.0573213i
$958$	−276.431	−	478.793i	−0.288550	−	0.499784i
$959$		−	1452.89i		−	1.51500i
$960$	−80.9889	−	21.3979i	−0.0843634	−	0.0222894i
$961$	−863.849	−	1496.23i	−0.898907	−	1.55695i
$962$	1133.97	−	856.589i	1.17876	−	0.890425i
$963$	−500.034	+	880.234i	−0.519246	+	0.914054i
$964$	−8.00713	−	13.8687i	−0.00830615	−	0.0143867i
$965$	−812.668	−	469.194i	−0.842143	−	0.486211i
$966$	117.700	−	445.482i	0.121842	−	0.461162i
$967$	208.251	−	360.702i	0.215358	−	0.373011i	−0.738025	−	0.674773i	$-0.764242\pi$
$967$	208.251	−	360.702i	0.215358	−	0.373011i	0.953383	+	0.301762i	$0.0975748\pi$
$968$	356.327	−	205.725i	0.368106	−	0.212526i
$969$	−1373.83	+	1383.46i	−1.41778	+	1.42772i
$970$	−181.057	−	313.600i	−0.186657	−	0.323299i
$971$	−940.061	−	542.744i	−0.968136	−	0.558954i	−0.0694689	−	0.997584i	$-0.522130\pi$
$971$	−940.061	−	542.744i	−0.968136	−	0.558954i	−0.898668	+	0.438630i	$0.855464\pi$
$972$	461.650	−	132.385i	0.474948	−	0.136199i
$973$	−15.0001	−	25.9810i	−0.0154164	−	0.0267020i
$974$	−1326.40	+	765.800i	−1.36181	+	0.786242i
$975$	78.9481	−	581.415i	0.0809724	−	0.596323i
$976$	−513.557	+	889.506i	−0.526185	+	0.911380i
$977$			816.416i			0.835636i	0.908531	+	0.417818i	$0.137205\pi$
$977$			816.416i			0.835636i	−0.908531	+	0.417818i	$0.862795\pi$
$978$	917.376	−	923.809i	0.938012	−	0.944590i
$979$	500.870			0.511614
$980$			59.4595i			0.0606729i
$981$	−1604.47	+	941.354i	−1.63555	+	0.959586i
$982$	475.144	−	822.973i	0.483853	−	0.838058i
$983$	−492.034	+	284.076i	−0.500543	+	0.288989i	−0.728938	−	0.684580i	$-0.759986\pi$
$983$	−492.034	+	284.076i	−0.500543	+	0.288989i	0.228395	+	0.973569i	$0.426652\pi$
$984$	−792.801	+	215.402i	−0.805692	+	0.218905i
$985$	1097.36			1.11407
$986$		−	222.369i		−	0.225527i
$987$	453.240	−	456.419i	0.459210	−	0.462431i
$988$	466.839	+	618.008i	0.472509	+	0.625515i
$989$		−	422.916i		−	0.427620i
$990$	216.066	+	368.270i	0.218249	+	0.371990i
$991$	−110.273	−	190.998i	−0.111274	−	0.192732i	0.805010	−	0.593261i	$-0.202160\pi$
$991$	−110.273	−	190.998i	−0.111274	−	0.192732i	−0.916284	+	0.400529i	$0.868826\pi$
$992$		−	1509.09i		−	1.52126i
$993$	−158.706	+	43.1200i	−0.159824	+	0.0434239i
$994$	76.4250	+	132.372i	0.0768863	+	0.133171i
$995$	178.108	−	102.831i	0.179003	−	0.103348i
$996$	−262.867	−	69.4515i	−0.263923	−	0.0697305i
$997$	−610.251			−0.612088			−0.306044	−	0.952017i	$-0.599005\pi$
$997$	−610.251			−0.612088			−0.306044	+	0.952017i	$0.599005\pi$
$998$	−68.4711	+	39.5318i	−0.0686083	+	0.0396110i
$999$	1169.43	+	300.246i	1.17060	+	0.300546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.u.a.68.7	yes	52
3.2	odd	2		351.3.u.a.341.20		52
9.2	odd	6		117.3.k.a.29.7	✓	52
9.7	even	3		351.3.k.a.224.20		52
13.9	even	3		117.3.k.a.113.20	yes	52
39.35	odd	6		351.3.k.a.152.7		52
117.61	even	3		351.3.u.a.35.20		52
117.74	odd	6	inner	117.3.u.a.74.7	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.k.a.29.7	✓	52	9.2	odd	6
117.3.k.a.113.20	yes	52	13.9	even	3
117.3.u.a.68.7	yes	52	1.1	even	1	trivial
117.3.u.a.74.7	yes	52	117.74	odd	6	inner
351.3.k.a.152.7		52	39.35	odd	6
351.3.k.a.224.20		52	9.7	even	3
351.3.u.a.35.20		52	117.61	even	3
351.3.u.a.341.20		52	3.2	odd	2

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.11714 - 1.22233i) q^{2} +(2.89505 - 0.786578i) q^{3} +(0.988182 + 1.71158i) q^{4} +(2.73246 + 1.57759i) q^{5} +(-7.09067 - 1.87341i) q^{6} +7.65083 q^{7} +4.94710i q^{8} +(7.76259 - 4.55436i) q^{9} +(-3.85666 - 6.67994i) q^{10} +(-5.32659 - 3.07531i) q^{11} +(4.20712 + 4.17782i) q^{12} +(7.83575 + 10.3731i) q^{13} +(-16.1979 - 9.35184i) q^{14} +(9.15149 + 2.41789i) q^{15} +(9.99972 - 17.3200i) q^{16} +(-18.6707 - 10.7795i) q^{17} +(-22.0014 + 0.153762i) q^{18} +(15.0726 - 26.1066i) q^{19} +6.23577i q^{20} +(22.1495 - 6.01798i) q^{21} +(7.51808 + 13.0217i) q^{22} +8.21173i q^{23} +(3.89128 + 14.3221i) q^{24} +(-7.52244 - 13.0293i) q^{25} +(-3.91002 - 31.5391i) q^{26} +(18.8907 - 19.2910i) q^{27} +(7.56041 + 13.0950i) q^{28} +(-3.65390 - 2.10958i) q^{29} +(-16.4195 - 16.3052i) q^{30} +(-25.9263 + 44.9057i) q^{31} +(-25.2043 + 14.5517i) q^{32} +(-17.8397 - 4.71338i) q^{33} +(26.3523 + 45.6435i) q^{34} +(20.9056 + 12.0698i) q^{35} +(15.4660 + 8.78576i) q^{36} +(22.3585 + 38.7261i) q^{37} +(-63.8217 + 36.8475i) q^{38} +(30.8441 + 23.8672i) q^{39} +(-7.80448 + 13.5178i) q^{40} +55.3551i q^{41} +(-54.2495 - 14.3331i) q^{42} -51.5014 q^{43} -12.1558i q^{44} +(28.3959 - 0.198451i) q^{45} +(10.0374 - 17.3854i) q^{46} +(24.2699 - 14.0122i) q^{47} +(15.3261 - 58.0078i) q^{48} +9.53523 q^{49} +36.7796i q^{50} +(-62.5314 - 16.5213i) q^{51} +(-10.0112 + 23.6620i) q^{52} +0.382421i q^{53} +(-63.5741 + 17.7510i) q^{54} +(-9.70312 - 16.8063i) q^{55} +37.8495i q^{56} +(23.1011 - 87.4356i) q^{57} +(5.15721 + 8.93255i) q^{58} +(41.5363 - 23.9810i) q^{59} +(4.90492 + 18.0528i) q^{60} -51.3571 q^{61} +(109.779 - 63.3811i) q^{62} +(59.3903 - 34.8446i) q^{63} -8.84980 q^{64} +(5.04643 + 40.7056i) q^{65} +(32.0078 + 31.7848i) q^{66} +25.9108 q^{67} -42.6085i q^{68} +(6.45917 + 23.7733i) q^{69} +(-29.5067 - 51.1071i) q^{70} +(-7.07732 - 4.08609i) q^{71} +(22.5309 + 38.4023i) q^{72} -24.8357 q^{73} -109.318i q^{74} +(-32.0263 - 31.8033i) q^{75} +59.5780 q^{76} +(-40.7528 - 23.5286i) q^{77} +(-36.1277 - 88.2317i) q^{78} +(8.23711 + 14.2671i) q^{79} +(54.6477 - 31.5508i) q^{80} +(39.5156 - 70.7073i) q^{81} +(67.6622 - 117.194i) q^{82} +(-39.7129 + 22.9283i) q^{83} +(32.1880 + 31.9638i) q^{84} +(-34.0113 - 58.9092i) q^{85} +(109.036 + 62.9518i) q^{86} +(-12.2376 - 3.23326i) q^{87} +(15.2139 - 26.3512i) q^{88} +(-70.5240 + 40.7171i) q^{89} +(-60.3605 - 34.2890i) q^{90} +(59.9500 + 79.3628i) q^{91} +(-14.0550 + 8.11468i) q^{92} +(-39.7361 + 150.397i) q^{93} -68.5102 q^{94} +(82.3708 - 47.5568i) q^{95} +(-61.5216 + 61.9530i) q^{96} +46.9466 q^{97} +(-20.1874 - 11.6552i) q^{98} +(-55.3541 + 0.386854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{2} - q^{3} + 49 q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{9} - 6 q^{10} + 33 q^{11} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 28 q^{15} - 83 q^{16} + 34 q^{18} + 5 q^{19} - 91 q^{21} - 15 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - 3 * q^2 - q^3 + 49 * q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^9 - 6 * q^10 + 33 * q^11 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 28 * q^15 - 83 * q^16 + 34 * q^18 + 5 * q^19 - 91 * q^21 - 15 * q^22 + 36 * q^24 + 88 * q^25 + 132 * q^26 - 34 * q^27 - 22 * q^28 - 30 * q^29 + 31 * q^30 + 14 * q^31 - 63 * q^32 - 112 * q^33 - 6 * q^34 - 228 * q^35 + 47 * q^36 - 13 * q^37 - 192 * q^38 + 147 * q^39 + 72 * q^40 - 84 * q^42 + 62 * q^43 - 107 * q^45 + 6 * q^46 - 69 * q^47 - 58 * q^48 + 246 * q^49 + 235 * q^51 + 112 * q^52 + 444 * q^54 - 27 * q^55 + 189 * q^57 - 105 * q^58 - 435 * q^59 + 213 * q^60 - 16 * q^61 - 471 * q^62 - 170 * q^63 - 98 * q^64 - 435 * q^65 - 576 * q^66 + 68 * q^67 + 152 * q^69 - 57 * q^70 - 144 * q^71 + 513 * q^72 - 106 * q^73 + 98 * q^75 + 158 * q^76 + 282 * q^77 - 433 * q^78 - 25 * q^79 + 1050 * q^80 + 9 * q^81 + 81 * q^82 + 219 * q^83 - 172 * q^84 + 54 * q^85 - 24 * q^86 + 325 * q^87 - 15 * q^88 - 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 - 171 * q^93 - 606 * q^94 - 258 * q^95 - 439 * q^96 - 424 * q^97 + 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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