LMFDB - Embedded newform 27.11.f.a.14.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,11,Mod(2,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 11, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.2"); S:= CuspForms(chi, 11); N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$17.1546458222$
Analytic rank:	$0$
Dimension:	$174$
Relative dimension:	$29$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.22
Character	$\chi$	$=$	27.14
Dual form			27.11.f.a.2.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(37.9719 - 6.69548i) q^{2} +(156.123 - 186.211i) q^{3} +(434.793 - 158.252i) q^{4} +(2075.88 - 2473.94i) q^{5} +(4681.53 - 8116.11i) q^{6} +(19948.9 + 7260.82i) q^{7} +(-18743.0 + 10821.3i) q^{8} +(-10300.1 - 58143.7i) q^{9} +(62261.0 - 107839. i) q^{10} +(8592.81 + 10240.5i) q^{11} +(38413.1 - 105670. i) q^{12} +(67693.8 - 383911. i) q^{13} +(806115. + 142140. i) q^{14} +(-136581. - 772791. i) q^{15} +(-1.00221e6 + 840952. i) q^{16} +(-677230. - 390999. i) q^{17} +(-780414. - 2.13887e6i) q^{18} +(-34614.8 - 59954.7i) q^{19} +(511074. - 1.40416e6i) q^{20} +(4.46654e6 - 2.58113e6i) q^{21} +(394851. + 331319. i) q^{22} +(1.60699e6 + 4.41518e6i) q^{23} +(-911176. + 5.17960e6i) q^{24} +(-115308. - 653943. i) q^{25} -1.50311e7i q^{26} +(-1.24351e7 - 7.15960e6i) q^{27} +9.82271e6 q^{28} +(1.72635e7 - 3.04402e6i) q^{29} +(-1.03605e7 - 2.84299e7i) q^{30} +(6.46055e6 - 2.35145e6i) q^{31} +(-1.81798e7 + 2.16658e7i) q^{32} +(3.24843e6 - 1294.03i) q^{33} +(-2.83337e7 - 1.03126e7i) q^{34} +(5.93745e7 - 3.42799e7i) q^{35} +(-1.36798e7 - 2.36505e7i) q^{36} +(-5.78685e6 + 1.00231e7i) q^{37} +(-1.71582e6 - 2.04483e6i) q^{38} +(-6.09198e7 - 7.25427e7i) q^{39} +(-1.21371e7 + 6.88327e7i) q^{40} +(1.97179e8 + 3.47680e7i) q^{41} +(1.52321e8 - 1.27916e8i) q^{42} +(-1.95154e8 + 1.63754e8i) q^{43} +(5.35668e6 + 3.09268e6i) q^{44} +(-1.65226e8 - 9.52177e7i) q^{45} +(9.05825e7 + 1.56893e8i) q^{46} +(-1.27251e8 + 3.49620e8i) q^{47} +(126643. + 3.17914e8i) q^{48} +(1.28852e8 + 1.08120e8i) q^{49} +(-8.75693e6 - 2.40595e7i) q^{50} +(-1.78540e8 + 6.50636e7i) q^{51} +(-3.13218e7 - 1.77635e8i) q^{52} +5.55314e8i q^{53} +(-5.20121e8 - 1.88605e8i) q^{54} +4.31721e7 q^{55} +(-4.52474e8 + 7.97834e7i) q^{56} +(-1.65684e7 - 2.91465e6i) q^{57} +(6.35148e8 - 2.31175e8i) q^{58} +(-3.88578e8 + 4.63090e8i) q^{59} +(-1.81680e8 - 3.14390e8i) q^{60} +(1.41965e9 + 5.16712e8i) q^{61} +(2.29575e8 - 1.32545e8i) q^{62} +(2.16696e8 - 1.23469e9i) q^{63} +(1.24586e8 - 2.15790e8i) q^{64} +(-8.09247e8 - 9.64423e8i) q^{65} +(1.23341e8 - 2.17989e7i) q^{66} +(2.82692e8 - 1.60323e9i) q^{67} +(-3.56331e8 - 6.28308e7i) q^{68} +(1.07304e9 + 3.90072e8i) q^{69} +(2.02504e9 - 1.69921e9i) q^{70} +(-5.15975e8 - 2.97898e8i) q^{71} +(8.22243e8 + 9.78327e8i) q^{72} +(-1.82114e9 - 3.15430e9i) q^{73} +(-1.52628e8 + 4.19343e8i) q^{74} +(-1.39774e8 - 8.06242e7i) q^{75} +(-2.45382e7 - 2.05900e7i) q^{76} +(9.70630e7 + 2.66678e8i) q^{77} +(-2.79895e9 - 2.34670e9i) q^{78} +(6.52406e8 + 3.69998e9i) q^{79} +4.22512e9i q^{80} +(-3.27460e9 + 1.19777e9i) q^{81} +7.72006e9 q^{82} +(-2.99717e9 + 5.28482e8i) q^{83} +(1.53355e9 - 1.82910e9i) q^{84} +(-2.37316e9 + 8.63758e8i) q^{85} +(-6.31398e9 + 7.52471e9i) q^{86} +(2.12840e9 - 3.68990e9i) q^{87} +(-2.71870e8 - 9.89527e7i) q^{88} +(1.68789e9 - 9.74502e8i) q^{89} +(-6.91147e9 - 2.50934e9i) q^{90} +(4.13793e9 - 7.16710e9i) q^{91} +(1.39742e9 + 1.66538e9i) q^{92} +(5.70776e8 - 1.57014e9i) q^{93} +(-2.49111e9 + 1.41278e10i) q^{94} +(-2.20181e8 - 3.88238e7i) q^{95} +(1.19613e9 + 6.76780e9i) q^{96} +(1.09765e10 - 9.21035e9i) q^{97} +(5.61668e9 + 3.24279e9i) q^{98} +(5.06915e8 - 6.05096e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 4965 q^{5} + 18234 q^{6} - 6 q^{7} - 9 q^{8} + 119124 q^{9} - 3 q^{10} - 978 q^{11} - 1015107 q^{12} - 6 q^{13} + 2134569 q^{14} - 2548539 q^{15} - 3078 q^{16} - 9 q^{17}+ \cdots - 72892391589 q^{99}+O(q^{100}) $ 174 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 4965 * q^5 + 18234 * q^6 - 6 * q^7 - 9 * q^8 + 119124 * q^9 - 3 * q^10 - 978 * q^11 - 1015107 * q^12 - 6 * q^13 + 2134569 * q^14 - 2548539 * q^15 - 3078 * q^16 - 9 * q^17 + 6676947 * q^18 - 3 * q^19 + 15925353 * q^20 - 21049824 * q^21 + 10420410 * q^22 + 8437692 * q^23 + 87359400 * q^24 - 14881965 * q^25 - 60562494 * q^27 - 12 * q^28 + 7820868 * q^29 + 216153117 * q^30 - 51711531 * q^31 + 76244832 * q^32 - 198927081 * q^33 + 92236410 * q^34 - 260153622 * q^35 + 199074744 * q^36 - 3 * q^37 + 250645020 * q^38 + 152777949 * q^39 - 26151153 * q^40 - 837714012 * q^41 - 1627952634 * q^42 - 213300456 * q^43 + 2245906431 * q^44 + 1041263847 * q^45 - 3 * q^46 - 1685998563 * q^47 - 1664196711 * q^48 - 183168366 * q^49 + 2548576023 * q^50 + 1007158626 * q^51 - 912655665 * q^52 - 1206704682 * q^54 - 12 * q^55 - 4260806997 * q^56 - 1000586442 * q^57 - 496853331 * q^58 + 1806342150 * q^59 + 1176655374 * q^60 - 1784159286 * q^61 + 2786630112 * q^62 + 2270781765 * q^63 + 8858370045 * q^64 - 2961878001 * q^65 - 5594499243 * q^66 - 915608058 * q^67 + 11412166995 * q^68 - 7767764199 * q^69 + 1945422669 * q^70 - 5512912173 * q^71 - 15991303644 * q^72 + 2110132140 * q^73 + 22008588729 * q^74 + 15296936925 * q^75 + 11875694586 * q^76 - 2702962221 * q^77 - 12511026108 * q^78 + 6660721974 * q^79 + 440880768 * q^81 - 12 * q^82 + 7670489421 * q^83 - 31766160684 * q^84 - 6965484381 * q^85 - 33241766118 * q^86 - 10927113525 * q^87 + 28790289402 * q^88 + 34430237370 * q^89 + 12602186028 * q^90 - 991980102 * q^91 + 40280154009 * q^92 + 57140838285 * q^93 - 62587945905 * q^94 - 12104972679 * q^95 - 78182924274 * q^96 + 48297833958 * q^97 - 103117506282 * q^98 - 72892391589 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	37.9719	−	6.69548i	1.18662	−	0.209234i	0.454715	−	0.890637i	$-0.349741\pi$
$2$	37.9719	−	6.69548i	1.18662	−	0.209234i	0.731908	+	0.681403i	$0.238630\pi$
$3$	156.123	−	186.211i	0.642482	−	0.766300i
$3$	156.123	−	186.211i	0.642482	−	0.766300i
$4$	434.793	−	158.252i	0.424603	−	0.154543i
$5$	2075.88	−	2473.94i	0.664282	−	0.791660i	−0.323712	−	0.946156i	$-0.604931\pi$
$5$	2075.88	−	2473.94i	0.664282	−	0.791660i	0.987994	+	0.154495i	$0.0493752\pi$
$6$	4681.53	−	8116.11i	0.602049	−	1.04374i
$7$	19948.9	+	7260.82i	1.18694	+	0.432012i	0.858649	−	0.512564i	$-0.171304\pi$
$7$	19948.9	+	7260.82i	1.18694	+	0.432012i	0.328294	+	0.944576i	$0.393526\pi$
$8$	−18743.0	+	10821.3i	−0.571991	+	0.330239i
$9$	−10300.1	−	58143.7i	−0.174433	−	0.984669i
$10$	62261.0	−	107839.i	0.622610	−	1.07839i
$11$	8592.81	+	10240.5i	0.0533546	+	0.0635855i	0.792062	−	0.610441i	$-0.209008\pi$
$11$	8592.81	+	10240.5i	0.0533546	+	0.0635855i	−0.738707	+	0.674027i	$0.764563\pi$
$12$	38413.1	−	105670.i	0.154374	−	0.424664i
$13$	67693.8	−	383911.i	0.182319	−	1.03398i	−0.747033	−	0.664787i	$-0.768522\pi$
$13$	67693.8	−	383911.i	0.182319	−	1.03398i	0.929352	−	0.369196i	$-0.120367\pi$
$14$	806115.	+	142140.i	1.49884	+	0.264287i
$15$	−136581.	−	772791.i	−0.179860	−	1.01767i
$16$	−1.00221e6	+	840952.i	−0.955780	+	0.801994i
$17$	−677230.	−	390999.i	−0.476970	−	0.275379i	0.242183	−	0.970231i	$-0.422137\pi$
$17$	−677230.	−	390999.i	−0.476970	−	0.275379i	−0.719153	+	0.694852i	$0.755470\pi$
$18$	−780414.	−	2.13887e6i	−0.413012	−	1.13193i
$19$	−34614.8	−	59954.7i	−0.0139796	−	0.0242134i	0.858951	−	0.512058i	$-0.171117\pi$
$19$	−34614.8	−	59954.7i	−0.0139796	−	0.0242134i	−0.872931	+	0.487844i	$0.837783\pi$
$20$	511074.	−	1.40416e6i	0.159711	−	0.438801i
$21$	4.46654e6	−	2.58113e6i	1.09364	−	0.631995i
$22$	394851.	+	331319.i	0.0766160	+	0.0642885i
$23$	1.60699e6	+	4.41518e6i	0.249675	+	0.685977i	0.999698	+	0.0245652i	$0.00782012\pi$
$23$	1.60699e6	+	4.41518e6i	0.249675	+	0.685977i	−0.750023	+	0.661412i	$0.769958\pi$
$24$	−911176.	+	5.17960e6i	−0.114432	+	0.650489i
$25$	−115308.	−	653943.i	−0.0118075	−	0.0669638i
$26$		−	1.50311e7i		−	1.26510i
$27$	−1.24351e7	−	7.15960e6i	−0.866622	−	0.498965i
$28$	9.82271e6			0.570744
$29$	1.72635e7	−	3.04402e6i	0.841665	−	0.148408i	0.263837	−	0.964567i	$-0.415012\pi$
$29$	1.72635e7	−	3.04402e6i	0.841665	−	0.148408i	0.577827	+	0.816159i	$0.303901\pi$
$30$	−1.03605e7	−	2.84299e7i	−0.426357	−	1.16995i
$31$	6.46055e6	−	2.35145e6i	0.225663	−	0.0821347i	−0.226714	−	0.973961i	$-0.572798\pi$
$31$	6.46055e6	−	2.35145e6i	0.225663	−	0.0821347i	0.452377	+	0.891827i	$0.350576\pi$
$32$	−1.81798e7	+	2.16658e7i	−0.541799	+	0.645691i
$33$	3.24843e6	−	1294.03i	0.0830050	−	3.30656e-5i
$34$	−2.83337e7	−	1.03126e7i	−0.623603	−	0.226973i
$35$	5.93745e7	−	3.42799e7i	1.13047	−	0.652678i
$36$	−1.36798e7	−	2.36505e7i	−0.226238	−	0.391136i
$37$	−5.78685e6	+	1.00231e7i	−0.0834514	+	0.144542i	−0.904730	−	0.425985i	$-0.859928\pi$
$37$	−5.78685e6	+	1.00231e7i	−0.0834514	+	0.144542i	0.821279	+	0.570527i	$0.193261\pi$
$38$	−1.71582e6	−	2.04483e6i	−0.0216548	−	0.0258071i
$39$	−6.09198e7	−	7.25427e7i	−0.675205	−	0.804027i
$40$	−1.21371e7	+	6.88327e7i	−0.118526	+	0.672194i
$41$	1.97179e8	+	3.47680e7i	1.70193	+	0.300096i	0.938367	−	0.345640i	$-0.112338\pi$
$41$	1.97179e8	+	3.47680e7i	1.70193	+	0.300096i	0.763561	+	0.645736i	$0.223449\pi$
$42$	1.52321e8	−	1.27916e8i	1.16550	−	0.978766i
$43$	−1.95154e8	+	1.63754e8i	−1.32750	+	1.11391i	−0.342851	+	0.939390i	$0.611393\pi$
$43$	−1.95154e8	+	1.63754e8i	−1.32750	+	1.11391i	−0.984654	+	0.174519i	$0.944163\pi$
$44$	5.35668e6	+	3.09268e6i	0.0324812	+	0.0187530i
$45$	−1.65226e8	−	9.52177e7i	−0.895396	−	0.516006i
$46$	9.05825e7	+	1.56893e8i	0.439800	+	0.761755i
$47$	−1.27251e8	+	3.49620e8i	−0.554847	+	1.52443i	0.272168	+	0.962250i	$0.412259\pi$
$47$	−1.27251e8	+	3.49620e8i	−0.554847	+	1.52443i	−0.827015	+	0.562180i	$0.809963\pi$
$48$	126643.	+	3.17914e8i	0.000497022	+	1.24768i
$49$	1.28852e8	+	1.08120e8i	0.456154	+	0.382759i
$50$	−8.75693e6	−	2.40595e7i	−0.0280222	−	0.0769903i
$51$	−1.78540e8	+	6.50636e7i	−0.517468	+	0.188576i
$52$	−3.13218e7	−	1.77635e8i	−0.0823814	−	0.467208i
$53$			5.55314e8i			1.32788i	0.747786	+	0.663940i	$0.231117\pi$
$53$			5.55314e8i			1.32788i	−0.747786	+	0.663940i	$0.768883\pi$
$54$	−5.20121e8	−	1.88605e8i	−1.13275	−	0.410756i
$55$	4.31721e7			0.0857806
$56$	−4.52474e8	+	7.97834e7i	−0.821587	+	0.144868i
$57$	−1.65684e7	−	2.91465e6i	−0.0275363	−	0.00484409i
$58$	6.35148e8	−	2.31175e8i	0.967687	−	0.352209i
$59$	−3.88578e8	+	4.63090e8i	−0.543524	+	0.647746i	−0.965974	−	0.258640i	$-0.916726\pi$
$59$	−3.88578e8	+	4.63090e8i	−0.543524	+	0.647746i	0.422450	+	0.906386i	$0.361170\pi$
$60$	−1.81680e8	−	3.14390e8i	−0.233642	−	0.404308i
$61$	1.41965e9	+	5.16712e8i	1.68087	+	0.611786i	0.993428	−	0.114456i	$-0.0365125\pi$
$61$	1.41965e9	+	5.16712e8i	1.68087	+	0.611786i	0.687439	+	0.726242i	$0.258735\pi$
$62$	2.29575e8	−	1.32545e8i	0.250592	−	0.144679i
$63$	2.16696e8	−	1.23469e9i	0.218347	−	1.24410i
$64$	1.24586e8	−	2.15790e8i	0.116030	−	0.200970i
$65$	−8.09247e8	−	9.64423e8i	−0.697452	−	0.831191i
$66$	1.23341e8	−	2.17989e7i	0.0984887	−	0.0174067i
$67$	2.82692e8	−	1.60323e9i	0.209382	−	1.18747i	−0.681011	−	0.732274i	$-0.738459\pi$
$67$	2.82692e8	−	1.60323e9i	0.209382	−	1.18747i	0.890393	−	0.455193i	$-0.150430\pi$
$68$	−3.56331e8	−	6.28308e7i	−0.245081	−	0.0432144i
$69$	1.07304e9	+	3.90072e8i	0.686076	+	0.249402i
$70$	2.02504e9	−	1.69921e9i	1.20488	−	1.01102i
$71$	−5.15975e8	−	2.97898e8i	−0.285981	−	0.165111i	0.350147	−	0.936695i	$-0.386132\pi$
$71$	−5.15975e8	−	2.97898e8i	−0.285981	−	0.165111i	−0.636128	+	0.771584i	$0.719465\pi$
$72$	8.22243e8	+	9.78327e8i	0.424950	+	0.505617i
$73$	−1.82114e9	−	3.15430e9i	−0.878473	−	1.52156i	−0.853017	−	0.521883i	$-0.825230\pi$
$73$	−1.82114e9	−	3.15430e9i	−0.878473	−	1.52156i	−0.0254558	−	0.999676i	$-0.508104\pi$
$74$	−1.52628e8	+	4.19343e8i	−0.0687823	+	0.188978i
$75$	−1.39774e8	−	8.06242e7i	−0.0589005	−	0.0339750i
$76$	−2.45382e7	−	2.05900e7i	−0.00967778	−	0.00812062i
$77$	9.70630e7	+	2.66678e8i	0.0358591	+	0.0985222i
$78$	−2.79895e9	−	2.34670e9i	−0.969443	−	0.812802i
$79$	6.52406e8	+	3.69998e9i	0.212023	+	1.20244i	0.885999	+	0.463688i	$0.153474\pi$
$79$	6.52406e8	+	3.69998e9i	0.212023	+	1.20244i	−0.673976	+	0.738754i	$0.735415\pi$
$80$			4.22512e9i			1.28940i
$81$	−3.27460e9	+	1.19777e9i	−0.939146	+	0.343517i
$82$	7.72006e9			2.08234
$83$	−2.99717e9	+	5.28482e8i	−0.760888	+	0.134165i	−0.540612	−	0.841272i	$-0.681807\pi$
$83$	−2.99717e9	+	5.28482e8i	−0.760888	+	0.134165i	−0.220277	+	0.975437i	$0.570696\pi$
$84$	1.53355e9	−	1.82910e9i	0.366693	−	0.437361i
$85$	−2.37316e9	+	8.63758e8i	−0.534850	+	0.194669i
$86$	−6.31398e9	+	7.52471e9i	−1.34218	+	1.59955i
$87$	2.12840e9	−	3.68990e9i	0.427030	−	0.740318i
$88$	−2.71870e8	−	9.89527e7i	−0.0515168	−	0.0187506i
$89$	1.68789e9	−	9.74502e8i	0.302269	−	0.174515i	−0.341193	−	0.939993i	$-0.610831\pi$
$89$	1.68789e9	−	9.74502e8i	0.302269	−	0.174515i	0.643462	+	0.765478i	$0.277498\pi$
$90$	−6.91147e9	−	2.50934e9i	−1.17046	−	0.424958i
$91$	4.13793e9	−	7.16710e9i	0.663095	−	1.14851i
$92$	1.39742e9	+	1.66538e9i	0.212026	+	0.252682i
$93$	5.70776e8	−	1.57014e9i	0.0820448	−	0.225696i
$94$	−2.49111e9	+	1.41278e10i	−0.339432	+	1.92502i
$95$	−2.20181e8	−	3.88238e7i	−0.0284551	−	0.00501741i
$96$	1.19613e9	+	6.76780e9i	0.146697	+	0.830026i
$97$	1.09765e10	−	9.21035e9i	1.27821	−	1.07255i	0.284727	−	0.958609i	$-0.408097\pi$
$97$	1.09765e10	−	9.21035e9i	1.27821	−	1.07255i	0.993488	−	0.113941i	$-0.0363475\pi$
$98$	5.61668e9	+	3.24279e9i	0.621369	+	0.358748i
$99$	5.06915e8	−	6.05096e8i	0.0533039	−	0.0636280i
$100$	−1.53623e8	−	2.66083e8i	−0.0153623	−	0.0266083i
$101$	4.58793e9	−	1.26052e10i	0.436526	−	1.19935i	−0.505211	−	0.862996i	$-0.668585\pi$
$101$	4.58793e9	−	1.26052e10i	0.436526	−	1.19935i	0.941737	−	0.336350i	$-0.109192\pi$
$102$	−6.34386e9	+	3.66600e9i	−0.574583	+	0.332041i
$103$	−1.42779e9	−	1.19806e9i	−0.123162	−	0.103345i	0.579126	−	0.815238i	$-0.303394\pi$
$103$	−1.42779e9	−	1.19806e9i	−0.123162	−	0.103345i	−0.702288	+	0.711893i	$0.747838\pi$
$104$	2.88562e9	+	7.92817e9i	0.237177	+	0.651638i
$105$	2.88645e9	−	1.64081e10i	0.226161	−	1.28561i
$106$	3.71809e9	+	2.10863e10i	0.277837	+	1.57569i
$107$		−	3.36601e9i		−	0.239992i	−0.992774	−	0.119996i	$-0.961712\pi$
$107$		−	3.36601e9i		−	0.239992i	0.992774	−	0.119996i	$-0.0382881\pi$
$108$	−6.53971e9	−	1.14507e9i	−0.445082	−	0.0779316i
$109$	−1.66086e10			−1.07945			−0.539723	−	0.841843i	$-0.681471\pi$
$109$	−1.66086e10			−1.07945			−0.539723	+	0.841843i	$0.681471\pi$
$110$	1.63933e9	−	2.89058e8i	0.101789	−	0.0179482i
$111$	9.62953e8	+	2.64242e9i	0.0571466	+	0.156815i
$112$	−2.60990e10	+	9.49926e9i	−1.48093	+	0.539013i
$113$	−1.81036e10	+	2.15750e10i	−0.982589	+	1.17100i	0.00268130	+	0.999996i	$0.499147\pi$
$113$	−1.81036e10	+	2.15750e10i	−0.982589	+	1.17100i	−0.985270	+	0.171007i	$0.945298\pi$
$114$	−6.48649e8	+	258393.i	−0.0336888	+	1.34201e-5i
$115$	1.42588e10	+	5.18979e9i	0.708915	+	0.258024i
$116$	7.02434e9	−	4.05550e9i	0.334438	−	0.193088i
$117$	−2.30192e10	+	1.83397e7i	−1.04993	+	0.000836495i
$118$	−1.16545e10	+	2.01861e10i	−0.509427	+	0.882354i
$119$	−1.06710e10	−	1.27173e10i	−0.447170	−	0.532916i
$120$	1.09225e10	+	1.30064e10i	0.438952	+	0.522699i
$121$	4.47295e9	−	2.53674e10i	0.172452	−	0.978023i
$122$	5.73667e10	+	1.01153e10i	2.12256	+	0.374265i
$123$	3.72584e10	−	3.12888e10i	1.32342	−	1.11138i
$124$	2.43688e9	−	2.04479e9i	0.0831239	−	0.0697493i
$125$	2.54556e10	+	1.46968e10i	0.834129	+	0.481584i
$126$	−3.85087e7	−	4.83346e10i	−0.00121257	−	1.52197i
$127$	−6.81854e9	−	1.18101e10i	−0.206383	−	0.357465i	0.744190	−	0.667968i	$-0.232836\pi$
$127$	−6.81854e9	−	1.18101e10i	−0.206383	−	0.357465i	−0.950572	+	0.310503i	$0.899502\pi$
$128$	1.31914e10	−	3.62430e10i	0.383919	−	1.05481i
$129$	2.46605e7	+	6.19057e10i	0.000690325	+	1.73293i
$130$	−3.71860e10	−	3.12027e10i	−1.00153	−	0.840380i
$131$	−8.27557e9	−	2.27369e10i	−0.214507	−	0.589353i	0.785040	−	0.619445i	$-0.212642\pi$
$131$	−8.27557e9	−	2.27369e10i	−0.214507	−	0.589353i	−0.999547	+	0.0300919i	$0.990420\pi$
$132$	1.41219e9	−	5.14633e8i	0.0352391	−	0.0128419i
$133$	−2.55209e8	−	1.44736e9i	−0.00613251	−	0.0347792i
$134$		−	6.27704e10i		−	1.45288i
$135$	−4.35262e10	+	1.59012e10i	−0.970692	+	0.354617i
$136$	1.69244e10			0.363764
$137$	−6.31712e10	+	1.11388e10i	−1.30893	+	0.230799i	−0.784220	−	0.620482i	$-0.786937\pi$
$137$	−6.31712e10	+	1.11388e10i	−1.30893	+	0.230799i	−0.524709	+	0.851282i	$0.675826\pi$
$138$	4.33573e10	+	7.62726e9i	0.866297	+	0.152396i
$139$	−2.49299e10	+	9.07373e9i	−0.480447	+	0.174869i	−0.570879	−	0.821034i	$-0.693398\pi$
$139$	−2.49299e10	+	9.07373e9i	−0.480447	+	0.174869i	0.0904318	+	0.995903i	$0.471175\pi$
$140$	2.03908e10	−	2.43008e10i	0.379135	−	0.451835i
$141$	4.52363e10	+	7.82795e10i	0.811692	+	1.40460i
$142$	−2.15871e10	−	7.85708e9i	−0.373898	−	0.136088i
$143$	4.51312e9	−	2.60565e9i	0.0754739	−	0.0435749i
$144$	5.92189e10	+	4.96102e10i	0.956418	+	0.801233i
$145$	2.83063e10	−	4.90279e10i	0.441614	−	0.764898i
$146$	−9.02716e10	−	1.07582e11i	−1.36078	−	1.62171i
$147$	4.02499e10	−	7.11368e9i	0.586379	−	0.103635i
$148$	−9.29907e8	+	5.27376e9i	−0.0130958	+	0.0742698i
$149$	−6.57638e10	−	1.15959e10i	−0.895479	−	0.157897i	−0.293076	−	0.956089i	$-0.594679\pi$
$149$	−6.57638e10	−	1.15959e10i	−0.895479	−	0.157897i	−0.602403	+	0.798192i	$0.705790\pi$
$150$	−5.84729e9	−	2.12560e9i	−0.0770014	−	0.0279915i
$151$	5.50398e10	−	4.61838e10i	0.701119	−	0.588309i	−0.220973	−	0.975280i	$-0.570923\pi$
$151$	5.50398e10	−	4.61838e10i	0.701119	−	0.588309i	0.922092	+	0.386971i	$0.126479\pi$
$152$	1.29757e9	+	7.49153e8i	0.0159924	+	0.00923321i
$153$	−1.57586e10	+	4.34040e10i	−0.187958	+	0.517693i
$154$	5.47121e9	+	9.47641e9i	0.0631654	+	0.109406i
$155$	7.59399e9	−	2.08643e10i	0.0848812	−	0.233209i
$156$	−3.79676e10	−	2.19004e10i	−0.410951	−	0.237044i
$157$	6.26540e8	+	5.25730e8i	0.00656826	+	0.00551143i	0.646066	−	0.763282i	$-0.276413\pi$
$157$	6.26540e8	+	5.25730e8i	0.00656826	+	0.00551143i	−0.639498	+	0.768793i	$0.720858\pi$
$158$	4.95463e10	+	1.36127e11i	0.503183	+	1.38248i
$159$	1.03406e11	+	8.66974e10i	1.01756	+	0.853140i
$160$	1.58608e10	+	8.99512e10i	0.151261	+	0.857842i
$161$			9.97463e10i			0.922078i
$162$	−1.16323e11	+	6.74067e10i	−1.04254	+	0.604126i
$163$	−1.38686e11			−1.20530			−0.602650	−	0.798006i	$-0.705888\pi$
$163$	−1.38686e11			−1.20530			−0.602650	+	0.798006i	$0.705888\pi$
$164$	9.12342e10	−	1.60871e10i	0.769021	−	0.135599i
$165$	6.74016e9	−	8.03911e9i	0.0551126	−	0.0657337i
$166$	−1.10270e11	+	4.01350e10i	−0.874816	+	0.318407i
$167$	3.58306e10	−	4.27013e10i	0.275849	−	0.328744i	−0.610277	−	0.792188i	$-0.708942\pi$
$167$	3.58306e10	−	4.27013e10i	0.275849	−	0.328744i	0.886126	+	0.463444i	$0.153386\pi$
$168$	−5.57852e10	+	9.67117e10i	−0.416843	+	0.722658i
$169$	−1.32604e10	−	4.82638e9i	−0.0961882	−	0.0350096i
$170$	−8.43301e10	+	4.86880e10i	−0.593933	+	0.342908i
$171$	−3.12945e9	+	2.63017e9i	−0.0214036	+	0.0179889i
$172$	−5.89375e10	+	1.02083e11i	−0.391516	+	0.678125i
$173$	1.25228e11	+	1.49241e11i	0.808109	+	0.963067i	0.999831	−	0.0183827i	$-0.00585171\pi$
$173$	1.25228e11	+	1.49241e11i	0.808109	+	0.963067i	−0.191722	+	0.981449i	$0.561407\pi$
$174$	5.61140e10	−	1.54363e11i	0.351824	−	0.967827i
$175$	2.44790e9	−	1.38827e10i	0.0149143	−	0.0845832i
$176$	−1.72236e10	−	3.03698e9i	−0.101990	−	0.0179837i
$177$	2.55663e10	+	1.44657e11i	0.147164	+	0.832668i
$178$	5.75676e10	−	4.83049e10i	0.322165	−	0.270328i
$179$	−1.69833e11	−	9.80531e10i	−0.924180	−	0.533576i	−0.0392139	−	0.999231i	$-0.512485\pi$
$179$	−1.69833e11	−	9.80531e10i	−0.924180	−	0.533576i	−0.884966	+	0.465655i	$0.845819\pi$
$180$	−8.69075e10	−	1.52527e10i	−0.459933	−	0.0807208i
$181$	6.56345e10	+	1.13682e11i	0.337862	+	0.585194i	0.984030	−	0.178001i	$-0.0569629\pi$
$181$	6.56345e10	+	1.13682e11i	0.337862	+	0.585194i	−0.646168	+	0.763195i	$0.723630\pi$
$182$	1.09138e11	−	2.99854e11i	0.546536	−	1.50160i
$183$	3.17859e11	−	1.83685e11i	1.54874	−	0.894988i
$184$	−7.78978e10	−	6.53640e10i	−0.369348	−	0.309920i
$185$	1.27838e10	+	3.51231e10i	0.0589930	+	0.162082i
$186$	1.11606e10	−	6.34429e10i	0.0501331	−	0.284982i
$187$	−1.81528e9	−	1.02950e10i	−0.00793844	−	0.0450212i
$188$			1.72150e11i			0.733025i
$189$	−1.96082e11	−	2.33115e11i	−0.813072	−	0.966633i
$190$	−8.62062e9			−0.0348153
$191$	5.96032e10	−	1.05096e10i	0.234478	−	0.0413448i	−0.0551742	−	0.998477i	$-0.517571\pi$
$191$	5.96032e10	−	1.05096e10i	0.234478	−	0.0413448i	0.289652	+	0.957132i	$0.406460\pi$
$192$	−2.07316e10	−	5.68891e10i	−0.0794561	−	0.218033i
$193$	3.53185e10	−	1.28549e10i	0.131891	−	0.0480044i	−0.275231	−	0.961378i	$-0.588754\pi$
$193$	3.53185e10	−	1.28549e10i	0.131891	−	0.0480044i	0.407122	+	0.913374i	$0.366532\pi$
$194$	3.55130e11	−	4.23227e11i	1.29235	−	1.54016i
$195$	−3.05929e11	+	1.21869e8i	−1.08504	+	0.000432233i
$196$	7.31343e10	+	2.66187e10i	0.252837	+	0.0920251i
$197$	−2.81058e11	+	1.62269e11i	−0.947250	+	0.546895i	−0.892226	−	0.451590i	$-0.850857\pi$
$197$	−2.81058e11	+	1.62269e11i	−0.947250	+	0.546895i	−0.0550247	+	0.998485i	$0.517524\pi$
$198$	1.51971e10	−	2.63707e10i	0.0499385	−	0.0866554i
$199$	−1.55977e11	+	2.70160e11i	−0.499798	+	0.865676i	−1.00000		0.000232818i	$-0.999926\pi$
$199$	−1.55977e11	+	2.70160e11i	−0.499798	+	0.865676i	0.500202	+	0.865909i	$0.333259\pi$
$200$	9.23771e9	+	1.10091e10i	0.0288679	+	0.0344034i
$201$	−2.54404e11	−	3.02942e11i	−0.775432	−	0.923376i
$202$	8.98146e10	−	5.09364e11i	0.267048	−	1.51451i
$203$	3.66491e11	+	6.46222e10i	1.06312	+	0.187457i
$204$	−6.73314e10	+	5.65435e10i	−0.190575	+	0.160041i
$205$	4.95334e11	−	4.15635e11i	1.36813	−	1.14800i
$206$	−6.22374e10	−	3.59328e10i	−0.167771	−	0.0968623i
$207$	2.40163e11	−	1.38913e11i	0.631909	−	0.365504i
$208$	2.55007e11	+	4.41686e11i	0.654992	+	1.13448i
$209$	3.16528e8	−	8.69653e8i	0.000793744	−	0.00218079i
$210$	−2.55893e8	−	6.42372e11i	−0.000626559	−	1.57286i
$211$	2.11439e11	+	1.77419e11i	0.505560	+	0.424216i	0.859564	−	0.511029i	$-0.170735\pi$
$211$	2.11439e11	+	1.77419e11i	0.505560	+	0.424216i	−0.354003	+	0.935244i	$0.615180\pi$
$212$	8.78794e10	+	2.41447e11i	0.205214	+	0.563822i
$213$	−1.36028e11	+	4.95714e10i	−0.310262	+	0.113066i
$214$	−2.25370e10	−	1.27814e11i	−0.0502143	−	0.284780i
$215$			8.22734e11i			1.79088i
$216$	3.10547e11	−	3.71125e8i	0.660478	−	0.000789316i
$217$	1.45955e11			0.303332
$218$	−6.30661e11	+	1.11203e11i	−1.28090	+	0.225856i
$219$	−8.71687e11	−	1.53344e11i	−1.73037	−	0.304401i
$220$	1.87709e10	−	6.83206e9i	0.0364227	−	0.0132568i
$221$	−1.95953e11	+	2.33528e11i	−0.371698	+	0.442973i
$222$	5.42574e10	+	9.38902e10i	0.100622	+	0.174123i
$223$	2.46609e11	+	8.97583e10i	0.447182	+	0.162761i	0.555788	−	0.831324i	$-0.312417\pi$
$223$	2.46609e11	+	8.97583e10i	0.447182	+	0.162761i	−0.108606	+	0.994085i	$0.534639\pi$
$224$	−5.19978e11	+	3.00210e11i	−0.922030	+	0.532334i
$225$	−3.68350e10	+	1.34401e10i	−0.0638776	+	0.0233072i
$226$	−5.42972e11	+	9.40456e11i	−0.920949	+	1.59513i
$227$	1.25482e11	+	1.49543e11i	0.208185	+	0.248106i	0.860026	−	0.510250i	$-0.170447\pi$
$227$	1.25482e11	+	1.49543e11i	0.208185	+	0.248106i	−0.651840	+	0.758356i	$0.726003\pi$
$228$	−7.66508e9	+	1.35471e9i	−0.0124406	+	0.00219873i
$229$	1.86005e11	−	1.05488e12i	0.295356	−	1.67505i	−0.370395	−	0.928874i	$-0.620778\pi$
$229$	1.86005e11	−	1.05488e12i	0.295356	−	1.67505i	0.665751	−	0.746174i	$-0.268111\pi$
$230$	5.76183e11	+	1.01597e11i	0.895203	+	0.157848i
$231$	6.48122e10	+	2.35605e10i	0.0985365	+	0.0358199i
$232$	−2.90630e11	+	2.43867e11i	−0.432414	+	0.362839i
$233$	−7.91347e11	−	4.56884e11i	−1.15236	−	0.665314i	−0.202897	−	0.979200i	$-0.565036\pi$
$233$	−7.91347e11	−	4.56884e11i	−1.15236	−	0.665314i	−0.949461	+	0.313886i	$0.898369\pi$
$234$	−8.73963e11	+	1.54821e11i	−1.24570	+	0.220674i
$235$	6.00781e11	+	1.04058e12i	0.838256	+	1.45190i
$236$	−9.56665e10	+	2.62842e11i	−0.130677	+	0.359033i
$237$	7.90833e11	+	4.56168e11i	1.05765	+	0.610074i
$238$	−4.90348e11	−	4.11451e11i	−0.642126	−	0.538807i
$239$	1.15889e11	+	3.18404e11i	0.148612	+	0.408309i	0.991554	−	0.129696i	$-0.0414003\pi$
$239$	1.15889e11	+	3.18404e11i	0.148612	+	0.408309i	−0.842942	+	0.538005i	$0.819178\pi$
$240$	7.86763e11	+	6.59639e11i	0.988070	+	0.828419i
$241$	−2.76094e11	−	1.56581e12i	−0.339603	−	1.92598i	−0.375941	−	0.926644i	$-0.622680\pi$
$241$	−2.76094e11	−	1.56581e12i	−0.339603	−	1.92598i	0.0363382	−	0.999340i	$-0.488431\pi$
$242$		−	9.93197e11i		−	1.19663i
$243$	−2.88203e11	+	7.96766e11i	−0.340148	+	0.940372i
$244$	6.99027e11			0.808248
$245$	5.34964e11	−	9.43286e10i	0.606030	−	0.106859i
$246$	1.20528e12	−	1.43756e12i	1.33787	−	1.59570i
$247$	−2.53605e10	+	9.23045e9i	−0.0275849	+	0.0100401i
$248$	−9.56443e10	+	1.13984e11i	−0.101953	+	0.121503i
$249$	−3.69519e11	+	6.40614e11i	−0.386047	+	0.669268i
$250$	1.06500e12	+	3.87628e11i	1.09056	+	0.396931i
$251$	−1.60603e12	+	9.27239e11i	−1.61207	+	0.930729i	−0.623179	+	0.782079i	$0.714159\pi$
$251$	−1.60603e12	+	9.27239e11i	−1.61207	+	0.930729i	−0.988890	+	0.148650i	$0.952507\pi$
$252$	−1.01175e11	−	5.71129e11i	−0.0995564	−	0.561994i
$253$	−3.14051e10	+	5.43953e10i	−0.0302969	+	0.0524757i
$254$	−3.37987e11	−	4.02798e11i	−0.319692	−	0.380994i
$255$	−2.09663e11	+	5.76760e11i	−0.194456	+	0.534927i
$256$	2.13931e11	−	1.21326e12i	0.194569	−	1.10346i
$257$	1.02446e12	+	1.80640e11i	0.913756	+	0.161120i	0.610708	−	0.791856i	$-0.290885\pi$
$257$	1.02446e12	+	1.80640e11i	0.913756	+	0.161120i	0.303048	+	0.952975i	$0.401996\pi$
$258$	4.15425e11	+	2.35051e12i	0.363407	+	2.05620i
$259$	−1.88218e11	+	1.57933e11i	−0.161496	+	0.135511i
$260$	−5.04477e11	−	2.91260e11i	−0.424595	−	0.245140i
$261$	−3.54806e11	−	9.72411e11i	−0.292947	−	0.802874i
$262$	−4.66474e11	−	8.07957e11i	−0.377851	−	0.654458i
$263$	2.99940e11	−	8.24079e11i	0.238372	−	0.654923i	−0.761604	−	0.648043i	$-0.775588\pi$
$263$	2.99940e11	−	8.24079e11i	0.238372	−	0.654923i	0.999976	−	0.00687992i	$-0.00218996\pi$
$264$	−6.08714e10	+	3.51764e10i	−0.0474672	+	0.0274304i
$265$	1.37381e12	+	1.15277e12i	1.05123	+	0.882087i
$266$	−1.93816e10	−	5.32505e10i	−0.0145540	−	0.0399867i
$267$	8.20554e10	−	4.66446e11i	0.0604715	−	0.343752i
$268$	−1.30801e11	−	7.41810e11i	−0.0946101	−	0.536560i
$269$			3.50904e11i			0.249130i	0.992211	+	0.124565i	$0.0397536\pi$
$269$			3.50904e11i			0.249130i	−0.992211	+	0.124565i	$0.960246\pi$
$270$	−1.54631e12	+	8.95226e11i	−1.07765	+	0.623899i
$271$	−7.48160e11			−0.511856			−0.255928	−	0.966696i	$-0.582381\pi$
$271$	−7.48160e11			−0.511856			−0.255928	+	0.966696i	$0.582381\pi$
$272$	1.00754e12	−	1.77656e11i	0.676731	−	0.119326i
$273$	−6.88566e11	−	1.88948e12i	−0.454080	−	1.24603i
$274$	−2.32415e12	+	8.45922e11i	−1.50491	+	0.547744i
$275$	5.70590e9	−	6.80002e9i	0.00362794	−	0.00432361i
$276$	5.28282e11	−	2.10445e8i	0.329853	−	0.000131399i
$277$	1.21731e12	+	4.43063e11i	0.746450	+	0.271685i	0.687111	−	0.726552i	$-0.258879\pi$
$277$	1.21731e12	+	4.43063e11i	0.746450	+	0.271685i	0.0593387	+	0.998238i	$0.481101\pi$
$278$	−8.85882e11	+	5.11464e11i	−0.533522	+	0.308029i
$279$	−2.03266e11	−	3.51420e11i	−0.120239	−	0.207877i
$280$	−7.41903e11	+	1.28501e12i	−0.431079	+	0.746651i
$281$	−1.96874e12	−	2.34625e12i	−1.12371	−	1.33919i	−0.933968	−	0.357358i	$-0.883678\pi$
$281$	−1.96874e12	−	2.34625e12i	−1.12371	−	1.33919i	−0.189747	−	0.981833i	$-0.560767\pi$
$282$	2.24183e12	+	2.66954e12i	1.25706	+	1.49690i
$283$	−1.62257e10	+	9.20205e10i	−0.00893863	+	0.0506935i	−0.988951	−	0.148244i	$-0.952638\pi$
$283$	−1.62257e10	+	9.20205e10i	−0.00893863	+	0.0506935i	0.980012	+	0.198937i	$0.0637490\pi$
$284$	−2.71486e11	−	4.78702e10i	−0.146945	−	0.0259104i
$285$	−4.16047e10	+	3.49387e10i	−0.0221268	+	0.0185816i
$286$	1.53926e11	−	1.29159e11i	0.0804418	−	0.0674987i
$287$	3.68107e12	+	2.12527e12i	1.89045	+	1.09145i
$288$	1.44698e12	+	8.33879e11i	0.730299	+	0.420863i
$289$	−7.02237e11	−	1.21631e12i	−0.348333	−	0.603330i
$290$	7.46579e11	−	2.05121e12i	0.363987	−	1.00005i
$291$	−1.38703e9	−	3.48189e12i	−0.000664693	−	1.66859i
$292$	−1.29099e12	−	1.08327e12i	−0.608148	−	0.510297i
$293$	−4.74390e11	−	1.30337e12i	−0.219683	−	0.603575i	0.780072	−	0.625690i	$-0.215182\pi$
$293$	−4.74390e11	−	1.30337e12i	−0.219683	−	0.603575i	−0.999755	+	0.0221147i	$0.992960\pi$
$294$	1.48074e12	−	5.39613e11i	0.674127	−	0.245666i
$295$	3.39013e11	+	1.92264e12i	0.151742	+	0.860572i
$296$		−	2.50484e11i		−	0.110236i
$297$	−3.35344e10	−	1.88863e11i	−0.0145113	−	0.0817267i
$298$	−2.57482e12			−1.09563
$299$	1.80382e12	−	3.18062e11i	0.754809	−	0.133093i
$300$	−7.35316e10	−	1.29354e10i	−0.0302599	−	0.00532321i
$301$	−5.08211e12	+	1.84974e12i	−2.05689	+	0.748648i
$302$	1.78074e12	−	2.12221e12i	0.708870	−	0.844798i
$303$	−1.63095e12	−	2.82229e12i	−0.638599	−	1.10507i
$304$	8.51103e10	+	3.09776e10i	0.0327804	+	0.0119311i
$305$	4.22535e12	−	2.43951e12i	1.60090	−	0.924278i
$306$	−3.07774e11	+	1.75364e12i	−0.114716	+	0.653634i
$307$	7.12225e11	−	1.23361e12i	0.261171	−	0.452362i	−0.705382	−	0.708827i	$-0.749225\pi$
$307$	7.12225e11	−	1.23361e12i	0.261171	−	0.452362i	0.966553	+	0.256465i	$0.0825579\pi$
$308$	8.44047e10	+	1.00590e11i	0.0304518	+	0.0362910i
$309$	−4.46002e11	+	7.88254e10i	−0.158323	+	0.0279817i
$310$	1.48662e11	−	8.43104e11i	0.0519268	−	0.294491i
$311$	3.48373e12	+	6.14276e11i	1.19741	+	0.211136i	0.736578	−	0.676352i	$-0.236440\pi$
$311$	3.48373e12	+	6.14276e11i	1.19741	+	0.211136i	0.460831	+	0.887488i	$0.347551\pi$
$312$	1.92682e12	+	7.00437e11i	0.651732	+	0.236917i
$313$	4.54573e11	−	3.81432e11i	0.151315	−	0.126968i	−0.563987	−	0.825783i	$-0.690733\pi$
$313$	4.54573e11	−	3.81432e11i	0.151315	−	0.126968i	0.715302	+	0.698815i	$0.246289\pi$
$314$	2.73110e10	+	1.57680e10i	0.00894723	+	0.00516569i
$315$	−2.60472e12	−	3.09917e12i	−0.839863	−	0.999292i
$316$	8.69191e11	+	1.50548e12i	0.275854	+	0.477794i
$317$	−4.44877e11	+	1.22229e12i	−0.138977	+	0.381837i	−0.989582	−	0.143968i	$-0.954014\pi$
$317$	−4.44877e11	+	1.22229e12i	−0.138977	+	0.381837i	0.850605	+	0.525805i	$0.176236\pi$
$318$	4.50699e12	+	2.59972e12i	1.38596	+	0.799449i
$319$	1.79514e11	+	1.50630e11i	0.0543433	+	0.0455994i
$320$	−2.75224e11	−	7.56173e11i	−0.0820233	−	0.225357i
$321$	−6.26787e11	−	5.25512e11i	−0.183906	−	0.154190i
$322$	6.67849e11	+	3.78756e12i	0.192930	+	1.09416i
$323$			5.41375e10i			0.0153987i
$324$	−1.23423e12	+	1.03899e12i	−0.345676	+	0.290997i
$325$	−2.58861e11			−0.0713922
$326$	−5.26618e12	+	9.28570e11i	−1.43024	+	0.252189i
$327$	−2.59299e12	+	3.09271e12i	−0.693525	+	0.827180i
$328$	−4.07196e12	+	1.48207e12i	−1.07259	+	0.390391i
$329$	−5.07706e12	+	6.05061e12i	−1.31714	+	1.56971i
$330$	2.02111e11	−	3.50389e11i	0.0516441	−	0.0895326i
$331$	2.52942e12	+	9.20633e11i	0.636621	+	0.231711i	0.640110	−	0.768283i	$-0.278889\pi$
$331$	2.52942e12	+	9.20633e11i	0.636621	+	0.231711i	−0.00348978	+	0.999994i	$0.501111\pi$
$332$	−1.21952e12	+	7.04088e11i	−0.302341	+	0.174557i
$333$	6.42386e11	+	2.33230e11i	0.156883	+	0.0569591i
$334$	1.07465e12	−	1.86135e12i	0.258545	−	0.447813i
$335$	−3.37945e12	−	4.02748e12i	−0.800981	−	0.954572i
$336$	−2.30579e12	+	6.34297e12i	−0.538423	+	1.48114i
$337$	7.67980e11	−	4.35543e12i	0.176685	−	1.00203i	−0.759495	−	0.650513i	$-0.774554\pi$
$337$	7.67980e11	−	4.35543e12i	0.176685	−	1.00203i	0.936181	−	0.351519i	$-0.114335\pi$
$338$	−5.35836e11	−	9.44824e10i	−0.121464	−	0.0214174i
$339$	1.19111e12	+	6.73944e12i	0.266045	+	1.50531i
$340$	−8.95141e11	+	7.51113e11i	−0.197014	+	0.165314i
$341$	7.95943e10	+	4.59538e10i	0.0172627	+	0.00996665i
$342$	−1.01221e11	+	1.20826e11i	−0.0216342	+	0.0258244i
$343$	−1.21294e12	−	2.10087e12i	−0.255486	−	0.442516i
$344$	1.88575e12	−	5.18106e12i	0.391464	−	1.07554i
$345$	3.19253e12	−	1.84490e12i	0.653190	−	0.377466i
$346$	5.75437e12	+	4.82849e12i	1.16043	+	0.973713i
$347$	2.82037e12	+	7.74891e12i	0.560608	+	1.54026i	0.818750	+	0.574151i	$0.194668\pi$
$347$	2.82037e12	+	7.74891e12i	0.560608	+	1.54026i	−0.258142	+	0.966107i	$0.583110\pi$
$348$	3.41483e11	−	1.94117e12i	0.0669072	−	0.380335i
$349$	3.34145e11	+	1.89503e12i	0.0645368	+	0.366006i	0.999923	+	0.0123795i	$0.00394060\pi$
$349$	3.34145e11	+	1.89503e12i	0.0645368	+	0.366006i	−0.935387	+	0.353627i	$0.884948\pi$
$350$		−	5.43543e11i		−	0.103489i
$351$	−3.59042e12	+	4.28930e12i	−0.673923	+	0.805102i
$352$	−3.78084e11			−0.0699641
$353$	1.92491e12	−	3.39413e11i	0.351185	−	0.0619235i	0.00472706	−	0.999989i	$-0.498495\pi$
$353$	1.92491e12	−	3.39413e11i	0.351185	−	0.0619235i	0.346458	+	0.938065i	$0.387384\pi$
$354$	1.93935e12	+	5.32171e12i	0.348850	+	0.957272i
$355$	−1.80809e12	+	6.58089e11i	−0.320684	+	0.116719i
$356$	5.79665e11	−	6.90818e11i	0.101374	−	0.120813i
$357$	−4.03409e12	+	1.60701e9i	−0.695672	+	0.000277125i
$358$	−7.10540e12	−	2.58615e12i	−1.20830	−	0.439784i
$359$	2.23936e12	−	1.29289e12i	0.375536	−	0.216816i	−0.300338	−	0.953833i	$-0.597100\pi$
$359$	2.23936e12	−	1.29289e12i	0.375536	−	0.216816i	0.675874	+	0.737017i	$0.263766\pi$
$360$	4.12720e12	−	3.28819e9i	0.682564	−	0.000543807i
$361$	3.06314e12	−	5.30551e12i	0.499609	−	0.865348i
$362$	3.25343e12	+	3.87728e12i	0.523357	+	0.623713i
$363$	−4.02535e12	−	4.79335e12i	−0.638662	−	0.760512i
$364$	6.64937e11	−	3.77104e12i	0.104057	−	0.590139i
$365$	−1.15840e13	−	2.04257e12i	−1.78811	−	0.315292i
$366$	1.08398e13	−	9.10307e12i	1.65051	−	1.38606i
$367$	8.87342e12	−	7.44568e12i	1.33279	−	1.11834i	0.349370	−	0.936985i	$-0.386396\pi$
$367$	8.87342e12	−	7.44568e12i	1.33279	−	1.11834i	0.983417	−	0.181356i	$-0.0580487\pi$
$368$	−5.32350e12	−	3.07352e12i	−0.788784	−	0.455405i
$369$	−9.41940e9	−	1.18228e13i	−0.00137686	−	1.72818i
$370$	7.20590e11	+	1.24810e12i	0.103915	+	0.179987i
$371$	−4.03203e12	+	1.10779e13i	−0.573660	+	1.57612i
$372$	−3.07934e8	−	7.73013e11i	−4.32259e−5	−	0.108511i
$373$	8.64410e12	+	7.25326e12i	1.19722	+	1.00459i	0.999705	+	0.0242914i	$0.00773296\pi$
$373$	8.64410e12	+	7.25326e12i	1.19722	+	1.00459i	0.197519	+	0.980299i	$0.436711\pi$
$374$	−1.37859e11	−	3.78765e11i	−0.0188399	−	0.0517621i
$375$	6.71091e12	−	2.44560e12i	0.904951	−	0.329784i
$376$	−1.39826e12	−	7.92995e12i	−0.186059	−	1.05519i
$377$		−	6.83371e12i		−	0.897325i
$378$	−9.00644e12	−	7.53898e12i	−1.16706	−	0.976907i
$379$	8.77745e12			1.12246			0.561232	−	0.827659i	$-0.310328\pi$
$379$	8.77745e12			1.12246			0.561232	+	0.827659i	$0.310328\pi$
$380$	−1.01877e11	+	1.79637e10i	−0.0128575	+	0.00226713i
$381$	−3.26370e12	−	5.74137e11i	−0.406523	−	0.0715140i
$382$	2.19288e12	−	7.98143e11i	0.269586	−	0.0981215i
$383$	−4.00005e12	+	4.76708e12i	−0.485369	+	0.578440i	−0.952033	−	0.305994i	$-0.901011\pi$
$383$	−4.00005e12	+	4.76708e12i	−0.485369	+	0.578440i	0.466664	+	0.884435i	$0.345456\pi$
$384$	−4.68937e12	−	8.11475e12i	−0.561640	−	0.971895i
$385$	8.61237e11	+	3.13465e11i	0.101817	+	0.0370582i
$386$	1.25504e12	−	7.24598e11i	0.146461	−	0.0845592i
$387$	1.15314e13	+	9.66033e12i	1.32839	+	1.11285i
$388$	3.31494e12	−	5.74164e12i	0.376979	−	0.652947i
$389$	2.55404e12	+	3.04379e12i	0.286734	+	0.341717i	0.890114	−	0.455737i	$-0.150624\pi$
$389$	2.55404e12	+	3.04379e12i	0.286734	+	0.341717i	−0.603380	+	0.797454i	$0.706180\pi$
$390$	−1.16159e13	+	2.05297e12i	−1.28745	+	0.227540i
$391$	6.38026e11	−	3.61843e12i	0.0698160	−	0.395946i
$392$	−3.58507e12	−	6.32145e11i	−0.387318	−	0.0682946i
$393$	−5.52588e12	−	2.00876e12i	−0.589438	−	0.214272i
$394$	−9.58585e12	+	8.04348e12i	−1.00960	+	0.847155i
$395$	1.05078e13	+	6.06671e12i	1.09277	+	0.630910i
$396$	1.24646e11	−	3.43312e11i	0.0127997	−	0.0352544i
$397$	−8.96622e11	−	1.55300e12i	−0.0909195	−	0.157477i	0.816979	−	0.576668i	$-0.195647\pi$
$397$	−8.96622e11	−	1.55300e12i	−0.0909195	−	0.157477i	−0.907898	+	0.419191i	$0.862314\pi$
$398$	−4.11389e12	+	1.13028e13i	−0.411944	+	1.13181i
$399$	−3.09359e11	−	1.78444e11i	−0.0305914	−	0.0176457i
$400$	6.65497e11	+	5.58419e11i	0.0649900	+	0.0545331i
$401$	−4.15020e11	−	1.14026e12i	−0.0400265	−	0.109972i	0.918069	−	0.396420i	$-0.129748\pi$
$401$	−4.15020e11	−	1.14026e12i	−0.0400265	−	0.109972i	−0.958096	+	0.286448i	$0.907525\pi$
$402$	−1.16885e13	−	9.79992e12i	−1.11335	−	0.933453i
$403$	−4.65406e11	−	2.63945e12i	−0.0437832	−	0.248307i
$404$		−	6.20673e12i		−	0.576708i
$405$	−3.83447e12	+	1.05876e13i	−0.351909	+	0.971677i
$406$	1.43490e13			1.30075
$407$	−1.52367e11	+	2.68664e10i	−0.0136433	+	0.00240568i
$408$	2.64229e12	−	3.15151e12i	0.233712	−	0.278752i
$409$	1.61863e12	−	5.89133e11i	0.141427	−	0.0514751i	−0.270337	−	0.962766i	$-0.587135\pi$
$409$	1.61863e12	−	5.89133e11i	0.141427	−	0.0514751i	0.411764	+	0.911291i	$0.364913\pi$
$410$	1.60259e13	−	1.90989e13i	1.38326	−	1.64850i
$411$	−7.78832e12	+	1.35022e13i	−0.664102	+	1.15132i
$412$	−8.10388e11	−	2.94957e11i	−0.0682663	−	0.0248469i
$413$	−1.11141e13	+	6.41675e12i	−0.924966	+	0.534029i
$414$	8.18936e12	−	6.88282e12i	0.673362	−	0.565932i
$415$	−4.91434e12	+	8.51188e12i	−0.399231	+	0.691489i
$416$	7.08707e12	+	8.44604e12i	0.568853	+	0.677933i
$417$	−2.20250e12	+	6.05883e12i	−0.174677	+	0.480517i
$418$	6.19643e9	−	3.51417e10i	0.000485579	−	0.00275386i
$419$	−1.44031e13	−	2.53965e12i	−1.11528	−	0.196655i	−0.414514	−	0.910043i	$-0.636048\pi$
$419$	−1.44031e13	−	2.53965e12i	−1.11528	−	0.196655i	−0.700769	+	0.713388i	$0.747160\pi$
$420$	−1.34160e12	−	7.59090e12i	−0.102654	−	0.580827i
$421$	−7.44911e12	+	6.25054e12i	−0.563240	+	0.472615i	−0.879395	−	0.476093i	$-0.842053\pi$
$421$	−7.44911e12	+	6.25054e12i	−0.563240	+	0.472615i	0.316155	+	0.948708i	$0.397608\pi$
$422$	9.21666e12	+	5.32124e12i	0.688670	+	0.397604i
$423$	2.16389e13	+	3.79775e12i	1.59784	+	0.280430i
$424$	−6.00920e12	−	1.04082e13i	−0.438518	−	0.759535i
$425$	−1.77601e11	+	4.87955e11i	−0.0128086	+	0.0351913i
$426$	−4.83333e12	+	2.79309e12i	−0.344507	+	0.199084i
$427$	2.45689e13	+	2.06157e13i	1.73079	+	1.45231i
$428$	−5.32677e11	−	1.46352e12i	−0.0370890	−	0.101901i
$429$	2.19402e11	−	1.24720e12i	0.0150992	−	0.0858318i
$430$	5.50860e12	+	3.12408e13i	0.374713	+	2.12510i
$431$			1.42335e13i			0.957032i	0.878079	+	0.478516i	$0.158825\pi$
$431$			1.42335e13i			0.957032i	−0.878079	+	0.478516i	$0.841175\pi$
$432$	1.84834e13	−	3.28191e12i	1.22847	−	0.218126i
$433$	−2.80838e13			−1.84509			−0.922544	−	0.385892i	$-0.873894\pi$
$433$	−2.80838e13			−1.84509			−0.922544	+	0.385892i	$0.873894\pi$
$434$	5.54218e12	−	9.77235e11i	0.359941	−	0.0634674i
$435$	−4.71027e12	−	1.29253e13i	−0.302412	−	0.829842i
$436$	−7.22131e12	+	2.62834e12i	−0.458336	+	0.166821i
$437$	2.09085e11	−	2.49178e11i	0.0131194	−	0.0156351i
$438$	−3.41264e13	+	1.35944e10i	−2.11699	+	0.000843317i
$439$	−2.18289e13	−	7.94506e12i	−1.33878	−	0.487275i	−0.429350	−	0.903138i	$-0.641257\pi$
$439$	−2.18289e13	−	7.94506e12i	−1.33878	−	0.487275i	−0.909427	+	0.415863i	$0.863480\pi$
$440$	−8.09174e11	+	4.67177e11i	−0.0490657	+	0.0283281i
$441$	4.95930e12	−	8.60559e12i	0.297323	−	0.515927i
$442$	−5.87713e12	+	1.01795e13i	−0.348381	+	0.603413i
$443$	3.08224e12	+	3.67327e12i	0.180654	+	0.215295i	0.848770	−	0.528762i	$-0.177343\pi$
$443$	3.08224e12	+	3.67327e12i	0.180654	+	0.215295i	−0.668116	+	0.744057i	$0.732899\pi$
$444$	8.36853e11	+	9.96516e11i	0.0484992	+	0.0577523i
$445$	1.09299e12	−	6.19868e12i	0.0626351	−	0.355221i
$446$	9.96519e12	+	1.75713e12i	0.564692	+	0.0995704i
$447$	−1.24265e13	+	1.04356e13i	−0.696326	+	0.584760i
$448$	4.05218e12	−	3.40018e12i	0.224542	−	0.188413i
$449$	2.09886e13	+	1.21178e13i	1.15014	+	0.664035i	0.948922	−	0.315511i	$-0.102176\pi$
$449$	2.09886e13	+	1.21178e13i	1.15014	+	0.664035i	0.201220	+	0.979546i	$0.435509\pi$
$450$	−1.30871e12	+	7.56975e11i	−0.0709219	+	0.0410222i
$451$	1.33828e12	+	2.31797e12i	0.0717239	+	0.124230i
$452$	−4.45703e12	+	1.22456e13i	−0.236240	+	0.649063i
$453$	−6.95505e9	−	1.74594e13i	−0.000364594	−	0.915246i
$454$	5.76604e12	+	4.83828e12i	0.298950	+	0.250849i
$455$	−9.14112e12	−	2.51150e13i	−0.468751	−	1.28788i
$456$	3.42082e11	−	1.24662e11i	0.0173502	−	0.00632280i
$457$	−1.52004e12	−	8.62058e12i	−0.0762560	−	0.432470i	−0.998903	−	0.0468242i	$-0.985090\pi$
$457$	−1.52004e12	−	8.62058e12i	−0.0762560	−	0.432470i	0.922647	−	0.385645i	$-0.126021\pi$
$458$		−	4.13014e13i		−	2.04945i
$459$	5.62201e12	+	9.71080e12i	0.275949	+	0.476641i
$460$	7.02093e12			0.340883
$461$	1.45624e13	−	2.56775e12i	0.699406	−	0.123324i	0.187371	−	0.982289i	$-0.440003\pi$
$461$	1.45624e13	−	2.56775e12i	0.699406	−	0.123324i	0.512034	+	0.858965i	$0.328892\pi$
$462$	2.61879e12	+	4.60688e11i	0.124420	+	0.0218876i
$463$	7.57420e12	−	2.75679e12i	0.355985	−	0.129568i	−0.157836	−	0.987465i	$-0.550452\pi$
$463$	7.57420e12	−	2.75679e12i	0.355985	−	0.129568i	0.513821	+	0.857897i	$0.328229\pi$
$464$	−1.47417e13	+	1.75685e13i	−0.685424	+	0.816856i
$465$	−2.69957e12	−	4.67149e12i	−0.124174	−	0.214877i
$466$	−3.31080e13	−	1.20503e13i	−1.50662	−	0.548365i
$467$	−1.53503e13	+	8.86252e12i	−0.691089	+	0.399000i	−0.804020	−	0.594603i	$-0.797309\pi$
$467$	−1.53503e13	+	8.86252e12i	−0.691089	+	0.399000i	0.112931	+	0.993603i	$0.463976\pi$
$468$	−1.00057e13	+	3.65081e12i	−0.445676	+	0.162615i
$469$	1.72802e13	−	2.99301e13i	0.761524	−	1.31900i
$470$	2.97800e13	+	3.54904e13i	1.29848	+	1.54747i
$471$	1.95714e11	−	3.45901e10i	0.00844340	−	0.00149227i
$472$	2.27190e12	−	1.28846e13i	0.0969794	−	0.549998i
$473$	−3.35385e12	−	5.91374e11i	−0.141657	−	0.0249779i
$474$	3.30837e13	+	1.20266e13i	1.38268	+	0.502632i
$475$	−3.52156e10	+	2.95494e10i	−0.00145635	+	0.00122203i
$476$	−6.65223e12	−	3.84067e12i	−0.272228	−	0.157171i
$477$	3.22880e13	−	5.71977e12i	1.30752	−	0.231626i
$478$	6.53241e12	+	1.13145e13i	0.261779	+	0.453414i
$479$	3.01651e12	−	8.28779e12i	0.119626	−	0.328671i	−0.865398	−	0.501085i	$-0.832934\pi$
$479$	3.01651e12	−	8.28779e12i	0.119626	−	0.328671i	0.985025	+	0.172414i	$0.0551567\pi$
$480$	1.92262e13	+	1.10900e13i	0.754547	+	0.435237i
$481$	3.45625e12	+	2.90014e12i	0.134239	+	0.112640i
$482$	−2.09676e13	−	5.76081e13i	−0.805961	−	2.21436i
$483$	1.85739e13	+	1.55727e13i	0.706589	+	0.592419i
$484$	−2.06962e12	−	1.17374e13i	−0.0779229	−	0.441922i
$485$		−	4.62747e13i		−	1.72439i
$486$	−5.60891e12	+	3.21844e13i	−0.206870	+	1.18704i
$487$	1.31743e12			0.0480932			0.0240466	−	0.999711i	$-0.492345\pi$
$487$	1.31743e12			0.0480932			0.0240466	+	0.999711i	$0.492345\pi$
$488$	−3.22001e13	+	5.67774e12i	−1.16348	+	0.205152i
$489$	−2.16521e13	+	2.58249e13i	−0.774384	+	0.923622i
$490$	1.96820e13	−	7.16368e12i	0.696771	−	0.253604i
$491$	1.16177e13	−	1.38455e13i	0.407112	−	0.485178i	−0.523062	−	0.852294i	$-0.675211\pi$
$491$	1.16177e13	−	1.38455e13i	0.407112	−	0.485178i	0.930175	+	0.367117i	$0.119655\pi$
$492$	1.12482e13	−	1.95004e13i	0.390173	−	0.676422i
$493$	−1.28816e13	−	4.68851e12i	−0.442318	−	0.160990i
$494$	−9.01183e11	+	5.20298e11i	−0.0306322	+	0.0176855i
$495$	−4.44676e11	−	2.51018e12i	−0.0149630	−	0.0844655i
$496$	−4.49736e12	+	7.78965e12i	−0.149813	+	0.259483i
$497$	−8.13017e12	−	9.68916e12i	−0.268113	−	0.319525i
$498$	−9.74212e12	+	2.67995e13i	−0.318058	+	0.874943i
$499$	−6.72262e12	+	3.81259e13i	−0.217288	+	1.23230i	0.659604	+	0.751614i	$0.270724\pi$
$499$	−6.72262e12	+	3.81259e13i	−0.217288	+	1.23230i	−0.876892	+	0.480688i	$0.840387\pi$
$500$	1.33937e13	+	2.36167e12i	0.428599	+	0.0755735i
$501$	−2.35745e12	−	1.33387e13i	−0.0746886	−	0.422596i
$502$	−5.47756e13	+	4.59622e13i	−1.71818	+	1.44172i
$503$	−2.65714e13	−	1.53410e13i	−0.825229	−	0.476446i	0.0269875	−	0.999636i	$-0.491409\pi$
$503$	−2.65714e13	−	1.53410e13i	−0.825229	−	0.476446i	−0.852216	+	0.523190i	$0.824742\pi$
$504$	9.29943e12	+	2.54868e13i	0.285959	+	0.783722i
$505$	−2.16606e13	−	3.75173e13i	−0.659498	−	1.14228i
$506$	−8.28311e11	+	2.27577e12i	−0.0249713	+	0.0686080i
$507$	−2.96897e12	+	1.71572e12i	−0.0886271	+	0.0512160i
$508$	−4.83362e12	−	4.05589e12i	−0.142874	−	0.119886i
$509$	5.01499e12	+	1.37786e13i	0.146785	+	0.403288i	0.991195	−	0.132409i	$-0.0422712\pi$
$509$	5.01499e12	+	1.37786e13i	0.146785	+	0.403288i	−0.844410	+	0.535697i	$0.820049\pi$
$510$	−4.09964e12	+	2.33045e13i	−0.118822	+	0.675444i
$511$	−1.34269e13	−	7.61479e13i	−0.385365	−	2.18551i
$512$		−	8.00767e12i		−	0.227592i
$513$	1.18715e9	+	9.93370e11i	3.34131e−5	+	0.0279592i
$514$	4.01103e13			1.11800
$515$	−5.92784e12	+	1.04524e12i	−0.163629	+	0.0288522i
$516$	9.80741e12	+	2.69123e13i	0.268106	+	0.735702i
$517$	−4.67374e12	+	1.70110e12i	−0.126535	+	0.0460551i
$518$	−6.08955e12	+	7.25724e12i	−0.163281	+	0.194591i
$519$	4.73412e13	−	1.88586e10i	1.25719	−	0.000500811i
$520$	2.56040e13	+	9.31909e12i	0.673428	+	0.245108i
$521$	2.18001e13	−	1.25863e13i	0.567896	−	0.327875i	−0.188412	−	0.982090i	$-0.560334\pi$
$521$	2.18001e13	−	1.25863e13i	0.567896	−	0.327875i	0.756309	+	0.654215i	$0.227001\pi$
$522$	−1.99834e13	−	3.45487e13i	−0.515606	−	0.891414i
$523$	−7.23604e12	+	1.25332e13i	−0.184924	+	0.320297i	−0.943551	−	0.331228i	$-0.892537\pi$
$523$	−7.23604e12	+	1.25332e13i	−0.184924	+	0.320297i	0.758627	+	0.651525i	$0.225870\pi$
$524$	−7.19632e12	−	8.57625e12i	−0.182161	−	0.217090i
$525$	−2.20294e12	−	2.62324e12i	−0.0552340	−	0.0657720i
$526$	5.87171e12	−	3.33001e13i	0.145826	−	0.827022i
$527$	−5.29469e12	−	9.33596e11i	−0.130253	−	0.0229671i
$528$	−3.25452e12	+	2.73307e12i	−0.0793080	+	0.0666012i
$529$	1.48231e13	−	1.24381e13i	0.357818	−	0.300245i
$530$	5.98846e13	+	3.45744e13i	1.43198	+	0.826752i
$531$	3.09281e13	+	1.78235e13i	0.732624	+	0.422203i
$532$	−3.40012e11	−	5.88917e11i	−0.00797876	−	0.0138196i
$533$	2.66956e13	−	7.33455e13i	0.620588	−	1.70505i
$534$	−7.27448e9	−	1.82612e13i	−0.000167531	−	0.420556i
$535$	−8.32729e12	−	6.98743e12i	−0.189992	−	0.159422i
$536$	1.20505e13	+	3.31084e13i	0.272383	+	0.748366i
$537$	−4.47734e13	+	1.63164e13i	−1.00265	+	0.365387i
$538$	2.34947e12	+	1.33245e13i	0.0521265	+	0.295624i
$539$			2.24857e12i			0.0494267i
$540$	−1.64085e13	+	1.38018e13i	−0.357355	+	0.300585i
$541$	−6.96540e13			−1.50300			−0.751501	−	0.659731i	$-0.770670\pi$
$541$	−6.96540e13			−1.50300			−0.751501	+	0.659731i	$0.770670\pi$
$542$	−2.84091e13	+	5.00929e12i	−0.607380	+	0.107098i
$543$	3.14160e13	+	5.52658e12i	0.665505	+	0.117073i
$544$	2.07832e13	−	7.56446e12i	0.436232	−	0.158775i
$545$	−3.44775e13	+	4.10887e13i	−0.717056	+	0.854554i
$546$	−3.87972e13	−	6.71369e13i	−0.799534	−	1.38356i
$547$	5.22380e13	+	1.90131e13i	1.06672	+	0.388254i	0.814949	−	0.579533i	$-0.196765\pi$
$547$	5.22380e13	+	1.90131e13i	1.06672	+	0.388254i	0.251770	+	0.967787i	$0.418987\pi$
$548$	−2.57037e13	+	1.48400e13i	−0.520107	+	0.300284i
$549$	1.54210e13	−	8.78662e13i	0.309208	−	1.76181i
$550$	1.71135e11	−	2.96414e11i	0.00340036	−	0.00588959i
$551$	−7.80077e11	−	9.29660e11i	−0.0153596	−	0.0183048i
$552$	−2.43331e13	+	4.30059e12i	−0.474791	+	0.0839136i
$553$	−1.38501e13	+	7.85477e13i	−0.267810	+	1.51883i
$554$	4.91899e13	+	8.67352e12i	0.942600	+	0.166206i
$555$	8.53615e12	+	3.10306e12i	0.162105	+	0.0589284i
$556$	−9.40340e12	+	7.89039e12i	−0.176975	+	0.148499i
$557$	8.02469e12	+	4.63306e12i	0.149676	+	0.0864155i	0.572968	−	0.819578i	$-0.305792\pi$
$557$	8.02469e12	+	4.63306e12i	0.149676	+	0.0864155i	−0.423292	+	0.905994i	$0.639125\pi$
$558$	−1.00713e13	−	1.19831e13i	−0.186173	−	0.221513i
$559$	4.96562e13	+	8.60070e13i	0.909733	+	1.57570i
$560$	−3.06778e13	+	8.42866e13i	−0.557037	+	1.53045i
$561$	−2.20044e12	−	1.26926e12i	−0.0396000	−	0.0228421i
$562$	−9.04660e13	−	7.59100e13i	−1.61363	−	1.35400i
$563$	1.85166e13	+	5.08739e13i	0.327355	+	0.899400i	0.988779	+	0.149387i	$0.0477302\pi$
$563$	1.85166e13	+	5.08739e13i	0.327355	+	0.899400i	−0.661424	+	0.750012i	$0.730048\pi$
$564$	3.20563e13	+	2.68767e13i	0.561717	+	0.470956i
$565$	1.57943e13	+	8.95742e13i	0.274321	+	1.55575i
$566$			3.60284e12i			0.0620244i
$567$	−7.40216e13	+	1.17948e11i	−1.26312	+	0.00201268i
$568$	1.28946e13			0.218105
$569$	6.14207e13	−	1.08301e13i	1.02980	−	0.181582i	0.366878	−	0.930269i	$-0.380427\pi$
$569$	6.14207e13	−	1.08301e13i	1.02980	−	0.181582i	0.662923	+	0.748688i	$0.269316\pi$
$570$	−1.34588e12	+	1.60526e12i	−0.0223682	+	0.0266790i
$571$	−9.94061e13	+	3.61809e13i	−1.63769	+	0.596072i	−0.986634	−	0.162955i	$-0.947898\pi$
$571$	−9.94061e13	+	3.61809e13i	−1.63769	+	0.596072i	−0.651060	+	0.759026i	$0.725675\pi$
$572$	1.54993e12	−	1.84713e12i	0.0253123	−	0.0301660i
$573$	7.34843e12	−	1.27396e13i	0.118966	−	0.206244i
$574$	1.54007e14	+	5.60539e13i	2.47162	+	0.899594i
$575$	2.70198e12	−	1.55999e12i	0.0429876	−	0.0248189i
$576$	−1.38301e13	−	5.02126e12i	−0.218128	−	0.0791955i
$577$	1.37773e13	−	2.38630e13i	0.215420	−	0.373118i	−0.737983	−	0.674820i	$-0.764221\pi$
$577$	1.37773e13	−	2.38630e13i	0.215420	−	0.373118i	0.953402	+	0.301702i	$0.0975547\pi$
$578$	−3.48091e13	−	4.14838e13i	−0.539577	−	0.643042i
$579$	3.12031e12	−	8.58363e12i	0.0479519	−	0.131910i
$580$	4.54862e12	−	2.57965e13i	0.0693011	−	0.393026i
$581$	−6.36276e13	−	1.12193e13i	−0.961092	−	0.169466i
$582$	−2.33656e13	−	1.32205e14i	−0.349914	−	1.97985i
$583$	−5.68670e12	+	4.77171e12i	−0.0844340	+	0.0708485i
$584$	6.82671e13	+	3.94140e13i	1.00496	+	0.580212i
$585$	−4.77399e13	+	5.69863e13i	−0.696790	+	0.831747i
$586$	−2.67402e13	−	4.63154e13i	−0.386969	−	0.670251i
$587$	1.71204e13	−	4.70380e13i	0.245654	−	0.674929i	−0.754179	−	0.656669i	$-0.771965\pi$
$587$	1.71204e13	−	4.70380e13i	0.245654	−	0.674929i	0.999833	−	0.0182603i	$-0.00581276\pi$
$588$	1.63747e13	−	9.46261e12i	0.232962	−	0.134625i
$589$	−3.64611e11	−	3.05945e11i	−0.00514344	−	0.00431585i
$590$	2.57460e13	+	7.07364e13i	0.360121	+	0.989426i
$591$	−1.36634e13	+	7.76700e13i	−0.189506	+	1.07725i
$592$	−2.62934e12	−	1.49117e13i	−0.0361608	−	0.205078i
$593$		−	2.20772e13i		−	0.301073i	−0.988604	−	0.150536i	$-0.951900\pi$
$593$		−	2.20772e13i		−	0.301073i	0.988604	−	0.150536i	$-0.0481001\pi$
$594$	−2.53789e12	−	6.94695e12i	−0.0343195	−	0.0939425i
$595$	−5.36135e13			−0.718935
$596$	−3.04287e13	+	5.36541e12i	−0.404625	+	0.0713463i
$597$	2.59551e13	+	7.12228e13i	0.342256	+	0.939177i
$598$	6.63649e13	−	2.41549e13i	0.867826	−	0.315863i
$599$	2.49976e13	−	2.97910e13i	0.324164	−	0.386323i	−0.579209	−	0.815179i	$-0.696639\pi$
$599$	2.49976e13	−	2.97910e13i	0.324164	−	0.386323i	0.903373	+	0.428855i	$0.141083\pi$
$600$	3.49223e12	−	1.39115e9i	0.0449104	−	1.78903e-5i
$601$	−1.15322e13	−	4.19737e12i	−0.147075	−	0.0535309i	0.267434	−	0.963576i	$-0.413824\pi$
$601$	−1.15322e13	−	4.19737e12i	−0.147075	−	0.0535309i	−0.414509	+	0.910045i	$0.636047\pi$
$602$	−1.80593e14	+	1.04265e14i	−2.28412	+	1.31873i
$603$	−9.61294e13	+	7.65875e10i	−1.20578	+	0.000960664i
$604$	1.66222e13	−	2.87906e13i	0.206778	−	0.358151i
$605$	−5.34720e13	−	6.37255e13i	−0.659705	−	0.786206i
$606$	−8.08270e13	−	9.62480e13i	−0.988993	−	1.17768i
$607$	−1.56047e13	+	8.84986e13i	−0.189370	+	1.07397i	0.730840	+	0.682549i	$0.239128\pi$
$607$	−1.56047e13	+	8.84986e13i	−0.189370	+	1.07397i	−0.920211	+	0.391424i	$0.871983\pi$
$608$	1.92825e12	+	3.40003e11i	0.0232085	+	0.00409228i
$609$	6.92511e13	−	5.81556e13i	0.826686	−	0.694233i
$610$	1.44111e14	−	1.20923e14i	1.70627	−	1.43173i
$611$	1.25609e14	+	7.25203e13i	1.47508	+	0.851635i
$612$	1.70222e10	+	2.13656e13i	0.000198271	+	0.248862i
$613$	3.35219e12	+	5.80616e12i	0.0387281	+	0.0670790i	0.884740	−	0.466085i	$-0.154336\pi$
$613$	3.35219e12	+	5.80616e12i	0.0387281	+	0.0670790i	−0.846012	+	0.533164i	$0.821003\pi$
$614$	1.87850e13	−	5.16113e13i	0.215263	−	0.591429i
$615$	−6.25924e10	−	1.57127e14i	−0.000711453	−	1.78597i
$616$	−4.70505e12	−	3.94800e12i	−0.0530470	−	0.0445117i
$617$	3.25797e12	+	8.95121e12i	0.0364352	+	0.100105i	0.956576	−	0.291482i	$-0.0941484\pi$
$617$	3.25797e12	+	8.95121e12i	0.0364352	+	0.100105i	−0.920141	+	0.391587i	$0.871926\pi$
$618$	−1.64078e13	+	5.97935e12i	−0.182015	+	0.0663303i
$619$	−6.85294e12	−	3.88650e13i	−0.0754091	−	0.427666i	−0.999017	−	0.0443278i	$-0.985885\pi$
$619$	−6.85294e12	−	3.88650e13i	−0.0754091	−	0.427666i	0.923608	−	0.383338i	$-0.125226\pi$
$620$		−	1.02734e13i		−	0.112139i
$621$	1.16278e13	−	6.64086e13i	0.125904	−	0.719062i
$622$	1.36397e14			1.46505
$623$	4.07473e13	−	7.18484e12i	0.434168	−	0.0765556i
$624$	1.22059e14	+	2.14722e13i	1.29017	+	0.226962i
$625$	9.52953e13	−	3.46847e13i	0.999244	−	0.363695i
$626$	1.47071e13	−	1.75273e13i	0.152988	−	0.182324i
$627$	−1.12522e11	−	1.94714e11i	−0.00116118	−	0.00200937i
$628$	3.55613e11	+	1.29433e11i	0.00364066	+	0.00132509i
$629$	7.83805e12	−	4.52530e12i	0.0796077	−	0.0459615i
$630$	−1.19657e14	−	1.00242e14i	−1.20569	−	1.01005i
$631$	6.88143e13	−	1.19190e14i	0.687911	−	1.19150i	−0.284602	−	0.958646i	$-0.591861\pi$
$631$	6.88143e13	−	1.19190e14i	0.687911	−	1.19150i	0.972513	−	0.232850i	$-0.0748053\pi$
$632$	−5.22665e13	−	6.22888e13i	−0.518368	−	0.617767i
$633$	6.60478e13	−	1.16731e13i	0.649890	−	0.114860i
$634$	−8.70903e12	+	4.93914e13i	−0.0850205	+	0.482175i
$635$	−4.33719e13	−	7.64763e12i	−0.420087	−	0.0740727i
$636$	5.86801e13	+	2.13313e13i	0.563904	+	0.204990i
$637$	5.02309e13	−	4.21487e13i	0.478932	−	0.401871i
$638$	7.82505e12	+	4.51780e12i	0.0740259	+	0.0427389i
$639$	−1.20063e13	+	3.30691e13i	−0.112695	+	0.310397i
$640$	−6.22792e13	−	1.07871e14i	−0.580021	−	1.00463i
$641$	−1.87477e12	+	5.15087e12i	−0.0173243	+	0.0475982i	−0.948053	−	0.318111i	$-0.896951\pi$
$641$	−1.87477e12	+	5.15087e12i	−0.0173243	+	0.0475982i	0.930729	+	0.365710i	$0.119174\pi$
$642$	−2.73189e13	−	1.57581e13i	−0.250489	−	0.144487i
$643$	−1.06378e14	−	8.92617e13i	−0.967825	−	0.812101i	0.0143834	−	0.999897i	$-0.495421\pi$
$643$	−1.06378e14	−	8.92617e13i	−0.967825	−	0.812101i	−0.982208	+	0.187795i	$0.939866\pi$
$644$	1.57850e13	+	4.33690e13i	0.142501	+	0.391517i
$645$	1.53202e14	+	1.28448e14i	1.37235	+	1.15061i
$646$	3.62476e11	+	2.05570e12i	0.00322193	+	0.0182725i
$647$		−	8.28198e13i		−	0.730487i	−0.930912	−	0.365244i	$-0.880986\pi$
$647$		−	8.28198e13i		−	0.730487i	0.930912	−	0.365244i	$-0.119014\pi$
$648$	4.84144e13	−	5.78851e13i	0.423740	−	0.506631i
$649$	−8.08125e12			−0.0701868
$650$	−9.82947e12	+	1.73320e12i	−0.0847156	+	0.0149376i
$651$	2.27869e13	−	2.71783e13i	0.194886	−	0.232444i
$652$	−6.02998e13	+	2.19473e13i	−0.511774	+	0.186270i
$653$	−7.55883e13	+	9.00827e13i	−0.636633	+	0.758709i	−0.983834	−	0.179081i	$-0.942687\pi$
$653$	−7.55883e13	+	9.00827e13i	−0.636633	+	0.758709i	0.347202	+	0.937790i	$0.387132\pi$
$654$	−7.77537e13	+	1.34797e14i	−0.649879	+	1.12666i
$655$	−7.34289e13	−	2.67259e13i	−0.609060	−	0.221680i
$656$	−2.26852e14	+	1.30973e14i	−1.86734	+	1.07811i
$657$	−1.64645e14	+	1.38377e14i	−1.34500	+	1.13041i
$658$	−1.52274e14	+	2.63747e14i	−1.23452	+	2.13825i
$659$	3.31053e13	+	3.94533e13i	0.266361	+	0.317436i	0.882602	−	0.470121i	$-0.155790\pi$
$659$	3.31053e13	+	3.94533e13i	0.266361	+	0.317436i	−0.616241	+	0.787557i	$0.711345\pi$
$660$	1.65837e12	−	4.56200e12i	0.0132423	−	0.0364280i
$661$	−2.18198e13	+	1.23746e14i	−0.172920	+	0.980676i	0.767598	+	0.640931i	$0.221452\pi$
$661$	−2.18198e13	+	1.23746e14i	−0.172920	+	0.980676i	−0.940518	+	0.339745i	$0.889659\pi$
$662$	1.02211e14	+	1.80226e13i	0.803910	+	0.141751i
$663$	1.28926e13	+	7.29477e13i	0.100641	+	0.569434i
$664$	5.04571e13	−	4.23385e13i	0.390915	−	0.328016i
$665$	−4.11048e12	−	2.37318e12i	−0.0316070	−	0.0182483i
$666$	2.59542e13	+	4.55512e12i	0.198078	+	0.0347639i
$667$	4.11823e13	+	7.13298e13i	0.311947	+	0.540309i
$668$	8.82136e12	−	2.42365e13i	0.0663213	−	0.182216i
$669$	5.52154e13	−	3.19079e13i	0.412030	−	0.238105i
$670$	−1.55290e14	−	1.30304e14i	−1.15019	−	0.965125i
$671$	6.90743e12	+	1.89780e13i	0.0507813	+	0.139520i
$672$	−2.52784e13	+	1.43695e14i	−0.184460	+	1.04857i
$673$	2.89831e13	+	1.64372e14i	0.209928	+	1.19056i	0.889494	+	0.456946i	$0.151057\pi$
$673$	2.89831e13	+	1.64372e14i	0.209928	+	1.19056i	−0.679567	+	0.733614i	$0.737832\pi$
$674$		−	1.70526e14i		−	1.22600i
$675$	−3.24811e12	+	8.95740e12i	−0.0231799	+	0.0639239i
$676$	−6.52930e12			−0.0462523
$677$	−1.12930e14	+	1.99126e13i	−0.794081	+	0.140018i	−0.555951	−	0.831215i	$-0.687646\pi$
$677$	−1.12930e14	+	1.99126e13i	−0.794081	+	0.140018i	−0.238130	+	0.971233i	$0.576535\pi$
$678$	9.03526e13	+	2.47934e14i	0.630656	+	1.73057i
$679$	2.85844e14	−	1.04039e14i	1.98052	−	0.720851i
$680$	3.51331e13	−	4.18700e13i	0.241642	−	0.287977i
$681$	4.74371e13	−	1.88969e10i	0.323879	−	0.000129019i
$682$	3.33003e12	+	1.21203e12i	0.0225697	+	0.00821471i
$683$	−1.98474e14	+	1.14589e14i	−1.33536	+	0.770972i	−0.986116	−	0.166058i	$-0.946896\pi$
$683$	−1.98474e14	+	1.14589e14i	−1.33536	+	0.770972i	−0.349247	+	0.937031i	$0.613563\pi$
$684$	−9.44435e11	+	1.63882e12i	−0.00630800	+	0.0109459i
$685$	−1.03579e14	+	1.79404e14i	−0.686783	+	1.18954i
$686$	−6.01239e13	−	7.16529e13i	−0.395755	−	0.471643i
$687$	−1.67391e14	−	1.99328e14i	−1.09383	−	1.30252i
$688$	5.78760e13	−	3.28231e14i	0.375454	−	2.12930i
$689$	2.13191e14	+	3.75913e13i	1.37301	+	0.242098i
$690$	1.08874e14	−	9.14301e13i	0.696111	−	0.584579i
$691$	−5.37911e13	+	4.51361e13i	−0.341444	+	0.286506i	−0.797344	−	0.603525i	$-0.793762\pi$
$691$	−5.37911e13	+	4.51361e13i	−0.341444	+	0.286506i	0.455899	+	0.890031i	$0.349318\pi$
$692$	7.80658e13	+	4.50713e13i	0.491960	+	0.284033i
$693$	1.45059e13	−	8.39041e12i	0.0907567	−	0.0524949i
$694$	1.58978e14	+	2.75358e14i	0.987504	+	1.71041i
$695$	−2.93036e13	+	8.05109e13i	−0.180716	+	0.496513i
$696$	3.67252e10	+	9.21918e13i	0.000224863	+	0.564477i
$697$	−1.19941e14	−	1.00643e14i	−0.729129	−	0.611812i
$698$	2.53762e13	+	6.97206e13i	0.153162	+	0.420808i
$699$	−2.08625e14	+	7.60273e13i	−1.25020	+	0.455600i
$700$	−1.13264e12	−	6.42349e12i	−0.00673907	−	0.0382192i
$701$		−	2.02525e14i		−	1.19643i	−0.801335	−	0.598215i	$-0.795877\pi$
$701$		−	2.02525e14i		−	1.19643i	0.801335	−	0.598215i	$-0.204123\pi$
$702$	−1.07616e14	+	1.86913e14i	−0.631238	+	1.09636i
$703$	8.01244e11			0.00466646
$704$	3.28034e12	−	5.78413e11i	0.0189695	−	0.00334484i
$705$	2.87564e14	+	5.05871e13i	1.65116	+	0.290465i
$706$	7.08199e13	−	2.57764e13i	0.403768	−	0.146960i
$707$	1.83049e14	−	2.18149e14i	1.03626	−	1.23497i
$708$	3.40082e13	+	5.88498e13i	0.191169	+	0.330810i
$709$	−8.58123e13	−	3.12331e13i	−0.478981	−	0.174335i	0.0912354	−	0.995829i	$-0.470918\pi$
$709$	−8.58123e13	−	3.12331e13i	−0.478981	−	0.174335i	−0.570216	+	0.821495i	$0.693141\pi$
$710$	−6.42503e13	+	3.70949e13i	−0.356109	+	0.205600i
$711$	2.08411e14	−	7.60434e13i	1.14702	−	0.418518i
$712$	−2.10907e13	+	3.65302e13i	−0.115263	+	0.199642i
$713$	2.07641e13	+	2.47457e13i	0.112685	+	0.134293i
$714$	−1.53172e14	+	2.70712e13i	−0.825443	+	0.145887i
$715$	2.92248e12	−	1.65742e13i	0.0156395	−	0.0886957i
$716$	−8.93593e13	−	1.57565e13i	−0.474870	−	0.0837324i
$717$	7.73833e13	+	2.81303e13i	0.408368	+	0.148450i
$718$	7.63762e13	−	6.40872e13i	0.400254	−	0.335853i
$719$	−8.27381e13	−	4.77689e13i	−0.430587	−	0.248600i	0.269010	−	0.963138i	$-0.413304\pi$
$719$	−8.27381e13	−	4.77689e13i	−0.430587	−	0.248600i	−0.699597	+	0.714538i	$0.746637\pi$
$720$	2.45664e14	−	4.35190e13i	1.26964	−	0.224914i
$721$	−1.97840e13	−	3.42669e13i	−0.101540	−	0.175873i
$722$	8.07903e13	−	2.21970e14i	0.411788	−	1.13138i
$723$	−3.34675e14	−	1.93047e14i	−1.69407	−	0.977173i
$724$	4.65279e13	+	3.90415e13i	0.233895	+	0.196261i
$725$	−3.98124e12	−	1.09384e13i	−0.0198760	−	0.0546087i
$726$	−1.84944e14	−	1.55061e14i	−0.916976	−	0.768812i
$727$	−1.85796e13	−	1.05370e14i	−0.0914882	−	0.518855i	−0.995767	−	0.0919131i	$-0.970702\pi$
$727$	−1.85796e13	−	1.05370e14i	−0.0914882	−	0.518855i	0.904279	−	0.426942i	$-0.140409\pi$
$728$			1.79111e14i			0.875920i
$729$	1.03371e14	+	1.78060e14i	0.502068	+	0.864828i
$730$	−4.53543e14			−2.18778
$731$	1.96192e14	−	3.45939e13i	0.939928	−	0.165735i
$732$	1.09134e14	−	1.30167e14i	0.519285	−	0.619361i
$733$	−2.75485e14	+	1.00269e14i	−1.30190	+	0.473854i	−0.897616	−	0.440778i	$-0.854703\pi$
$733$	−2.75485e14	+	1.00269e14i	−1.30190	+	0.473854i	−0.404287	+	0.914632i	$0.632480\pi$
$734$	2.87089e14	−	3.42139e14i	1.34752	−	1.60591i
$735$	6.59553e13	−	1.14343e14i	0.307477	−	0.533056i
$736$	−1.24873e14	−	4.54501e13i	−0.578203	−	0.210449i
$737$	1.88470e13	−	1.08813e13i	0.0866772	−	0.0500431i
$738$	−7.95172e13	−	4.48873e14i	−0.363228	−	2.05041i
$739$	−7.21661e13	+	1.24995e14i	−0.327425	+	0.567116i	−0.982000	−	0.188881i	$-0.939514\pi$
$739$	−7.21661e13	+	1.24995e14i	−0.327425	+	0.567116i	0.654575	+	0.755997i	$0.272847\pi$
$740$	1.11166e13	+	1.32482e13i	0.0500972	+	0.0597035i
$741$	−2.24054e12	+	6.16348e12i	−0.0100291	+	0.0275889i
$742$	−7.89322e13	+	4.47647e14i	−0.350941	+	1.99029i
$743$	2.25520e14	+	3.97652e13i	0.995957	+	0.175614i	0.647790	−	0.761819i	$-0.275693\pi$
$743$	2.25520e14	+	3.97652e13i	0.995957	+	0.175614i	0.348166	+	0.937433i	$0.386804\pi$
$744$	6.29286e12	+	3.56056e13i	0.0276047	+	0.156190i
$745$	−1.65205e14	+	1.38624e14i	−0.719852	+	0.604027i
$746$	3.76797e14	+	2.17544e14i	1.63085	+	0.941571i
$747$	6.15990e13	+	1.68823e14i	0.264832	+	0.725821i
$748$	−2.41847e12	−	4.18891e12i	−0.0103284	−	0.0178893i
$749$	2.44400e13	−	6.71483e13i	0.103679	−	0.284856i
$750$	2.38452e14	−	1.37797e14i	1.00483	−	0.580675i
$751$	−1.52279e14	−	1.27777e14i	−0.637441	−	0.534876i	0.265790	−	0.964031i	$-0.414367\pi$
$751$	−1.52279e14	−	1.27777e14i	−0.637441	−	0.534876i	−0.903231	+	0.429155i	$0.858812\pi$
$752$	−1.66482e14	−	4.57405e14i	−0.692273	−	1.90200i
$753$	−7.80757e13	+	4.43823e14i	−0.322508	+	1.83331i
$754$	−4.57549e13	−	2.59489e14i	−0.187751	−	1.06479i
$755$		−	2.32037e14i		−	0.945851i
$756$	−1.22146e14	−	7.03266e13i	−0.494619	−	0.284781i
$757$	3.98581e14			1.60338			0.801692	−	0.597738i	$-0.203934\pi$
$757$	3.98581e14			1.60338			0.801692	+	0.597738i	$0.203934\pi$
$758$	3.33297e14	−	5.87692e13i	1.33194	−	0.234857i
$759$	5.22593e12	+	1.43403e13i	0.0207470	+	0.0569313i
$760$	4.54696e12	−	1.65496e12i	0.0179330	−	0.00652709i
$761$	−2.62644e14	+	3.13008e14i	−1.02907	+	1.22640i	−0.0553936	+	0.998465i	$0.517641\pi$
$761$	−2.62644e14	+	3.13008e14i	−1.02907	+	1.22640i	−0.973677	+	0.227934i	$0.926803\pi$
$762$	−1.27773e14	+	5.08992e10i	−0.497353	+	0.000198123i
$763$	−3.31324e14	−	1.20592e14i	−1.28124	−	0.466333i
$764$	2.42519e13	−	1.40018e13i	0.0931706	−	0.0537921i
$765$	7.46658e13	+	1.29087e14i	0.284980	+	0.492693i
$766$	−1.19972e14	+	2.07798e14i	−0.454921	+	0.787946i
$767$	1.51481e14	+	1.80528e14i	0.570664	+	0.680091i
$768$	−1.92523e14	−	2.29255e14i	−0.720572	−	0.858050i
$769$	6.39638e12	−	3.62756e13i	0.0237849	−	0.134891i	−0.970603	−	0.240686i	$-0.922628\pi$
$769$	6.39638e12	−	3.62756e13i	0.0237849	−	0.134891i	0.994388	+	0.105795i	$0.0337387\pi$
$770$	3.48016e13	+	6.13647e12i	0.128572	+	0.0226707i
$771$	1.93580e14	−	1.62564e14i	0.710538	−	0.596695i
$772$	1.33219e13	−	1.11784e13i	0.0485826	−	0.0407656i
$773$	−2.77512e14	−	1.60221e14i	−1.00550	−	0.580528i	−0.0956319	−	0.995417i	$-0.530487\pi$
$773$	−2.77512e14	−	1.60221e14i	−1.00550	−	0.580528i	−0.909872	+	0.414889i	$0.863820\pi$
$774$	5.02549e14	+	2.89613e14i	1.80915	+	1.04259i
$775$	−2.28266e12	−	3.95369e12i	−0.00816457	−	0.0141415i
$776$	−1.06064e14	+	2.91409e14i	−0.376929	+	1.03560i
$777$	2.37840e10	+	5.97052e13i	8.39806e−5	+	0.210818i
$778$	1.17361e14	+	9.84780e13i	0.411744	+	0.345494i
$779$	−4.74082e12	−	1.30253e13i	−0.0165259	−	0.0454046i
$780$	−1.32996e14	+	4.84667e13i	−0.460646	+	0.167869i
$781$	−1.38304e12	−	7.84363e12i	−0.00475971	−	0.0269937i
$782$		−	1.41671e14i		−	0.484446i
$783$	−2.36467e14	−	8.57471e13i	−0.803456	−	0.291347i
$784$	−2.20060e14			−0.742953
$785$	2.60125e12	−	4.58670e11i	0.00872636	−	0.00153869i
$786$	−2.23278e14	−	3.92782e13i	−0.744274	−	0.130930i
$787$	4.07682e14	−	1.48384e14i	1.35035	−	0.491488i	0.437295	−	0.899318i	$-0.355936\pi$
$787$	4.07682e14	−	1.48384e14i	1.35035	−	0.491488i	0.913058	+	0.407829i	$0.133714\pi$
$788$	−9.65228e13	+	1.15031e14i	−0.317687	+	0.378604i
$789$	−1.06625e14	−	1.84510e14i	−0.348717	−	0.603441i
$790$	4.39623e14	+	1.60010e14i	1.42871	+	0.520009i
$791$	−5.17799e14	+	2.98951e14i	−1.67216	+	0.965424i
$792$	−2.95319e12	+	1.68268e13i	−0.00947689	+	0.0539977i
$793$	2.94473e14	−	5.10042e14i	0.939031	−	1.62645i
$794$	−4.44445e13	−	5.29669e13i	−0.140837	−	0.167843i
$795$	4.29142e14	−	7.58455e13i	1.35134	−	0.238833i
$796$	−2.50644e13	+	1.42147e14i	−0.0784318	+	0.444809i
$797$	−2.87741e14	−	5.07365e13i	−0.894767	−	0.157772i	−0.292688	−	0.956208i	$-0.594550\pi$
$797$	−2.87741e14	−	5.07365e13i	−0.894767	−	0.157772i	−0.602079	+	0.798436i	$0.705661\pi$
$798$	−1.29417e13	−	4.70457e12i	−0.0399925	−	0.0145380i
$799$	2.22880e14	−	1.87018e14i	0.684442	−	0.574315i
$800$	1.62645e13	+	9.39030e12i	0.0496352	+	0.0286569i
$801$	−7.40466e13	−	8.81026e13i	−0.224565	−	0.267194i
$802$	−2.33937e13	−	4.05191e13i	−0.0705062	−	0.122120i
$803$	1.66530e13	−	4.57537e13i	0.0498786	−	0.137040i
$804$	−1.58554e14	−	9.14571e13i	−0.471952	−	0.272231i
$805$	2.46766e14	+	2.07062e14i	0.729972	+	0.612520i
$806$	−3.53448e13	−	9.71090e13i	−0.103908	−	0.285485i
$807$	6.53422e13	+	5.47843e13i	0.190909	+	0.160062i
$808$	5.04132e13	+	2.85907e14i	0.146382	+	0.830172i
$809$		−	2.69092e13i		−	0.0776531i	−0.999246	−	0.0388266i	$-0.987638\pi$
$809$		−	2.69092e13i		−	0.0776531i	0.999246	−	0.0388266i	$-0.0123620\pi$
$810$	−7.47134e13	+	4.27705e14i	−0.214276	+	1.22665i
$811$	4.01574e14			1.14462			0.572311	−	0.820037i	$-0.306047\pi$
$811$	4.01574e14			1.14462			0.572311	+	0.820037i	$0.306047\pi$
$812$	1.69574e14	−	2.99005e13i	0.480375	−	0.0847030i
$813$	−1.16805e14	+	1.39316e14i	−0.328859	+	0.392236i
$814$	−5.60579e12	+	2.04034e12i	−0.0156861	+	0.00570927i
$815$	−2.87896e14	+	3.43101e14i	−0.800659	+	0.954188i
$816$	1.24218e14	−	2.15351e14i	0.343348	−	0.595244i
$817$	1.65731e13	+	6.03210e12i	0.0455294	+	0.0165714i
$818$	5.75180e13	−	3.32080e13i	0.157050	−	0.0906727i
$819$	−4.59343e14	−	1.66773e14i	−1.24657	−	0.452591i
$820$	1.49593e14	−	2.59103e14i	0.403499	−	0.698880i
$821$	3.04826e14	+	3.63277e14i	0.817214	+	0.973917i	0.999957	−	0.00924325i	$-0.00294226\pi$
$821$	3.04826e14	+	3.63277e14i	0.817214	+	0.973917i	−0.182744	+	0.983161i	$0.558498\pi$
$822$	−2.05334e14	+	5.64851e14i	−0.547144	+	1.50513i
$823$	9.59675e13	−	5.44259e14i	0.254170	−	1.44147i	−0.544023	−	0.839070i	$-0.683099\pi$
$823$	9.59675e13	−	5.44259e14i	0.254170	−	1.44147i	0.798193	−	0.602402i	$-0.205789\pi$
$824$	3.97255e13	+	7.00468e12i	0.104576	+	0.0184396i
$825$	−3.75416e11	−	2.12414e12i	−0.000982298	−	0.00555794i
$826$	−3.79062e14	+	3.18071e14i	−0.985849	+	0.827225i
$827$	−1.00059e14	−	5.77693e13i	−0.258660	−	0.149338i	0.365063	−	0.930983i	$-0.381047\pi$
$827$	−1.00059e14	−	5.77693e13i	−0.258660	−	0.149338i	−0.623723	+	0.781645i	$0.714381\pi$
$828$	8.24380e13	−	9.84049e13i	0.211824	−	0.252851i
$829$	−2.22677e13	−	3.85688e13i	−0.0568726	−	0.0985063i	0.836187	−	0.548444i	$-0.184780\pi$
$829$	−2.22677e13	−	3.85688e13i	−0.0568726	−	0.0985063i	−0.893060	+	0.449938i	$0.851446\pi$
$830$	−1.29616e14	+	3.56117e14i	−0.329054	+	0.904069i
$831$	2.72553e14	−	1.57503e14i	0.687774	−	0.397452i
$832$	−7.44103e13	−	6.24376e13i	−0.186645	−	0.156614i
$833$	−4.49878e13	−	1.23603e14i	−0.112168	−	0.308180i
$834$	−4.30665e13	+	2.44812e14i	−0.106736	+	0.606741i
$835$	−3.12602e13	−	1.77285e14i	−0.0770122	−	0.436758i
$836$		−	4.28210e11i		−	0.00104864i
$837$	−9.71728e13	−	1.70145e13i	−0.236547	−	0.0414182i
$838$	−5.63917e14			−1.36457
$839$	−5.96521e14	+	1.05183e14i	−1.43488	+	0.253008i	−0.836396	−	0.548126i	$-0.815341\pi$
$839$	−5.96521e14	+	1.05183e14i	−1.43488	+	0.253008i	−0.598485	+	0.801134i	$0.704230\pi$
$840$	1.23455e14	+	3.38771e14i	0.295198	+	0.810047i
$841$	−1.06573e14	+	3.87893e13i	−0.253318	+	0.0922002i
$842$	−2.41007e14	+	2.87221e14i	−0.569467	+	0.678665i
$843$	−7.44263e14	+	2.96482e11i	−1.74819	+	0.000696402i
$844$	1.20009e14	+	4.36798e13i	0.280222	+	0.101992i
$845$	−3.94671e13	+	2.27863e13i	−0.0916118	+	0.0528921i
$846$	8.47100e14	−	6.74895e11i	1.95471	−	0.00155734i
$847$	2.73419e14	−	4.73575e14i	0.627208	−	1.08636i
$848$	−4.66992e14	−	5.56540e14i	−1.06495	−	1.26916i
$849$	1.46020e13	+	1.73879e13i	0.0331035	+	0.0394194i
$850$	−3.47677e12	+	1.97177e13i	−0.00783576	+	0.0444388i
$851$	−5.35533e13	−	9.44290e12i	−0.119988	−	0.0211572i
$852$	−5.12992e13	+	4.30799e13i	−0.114265	+	0.0959571i
$853$	1.19491e14	−	1.00265e14i	0.264601	−	0.222026i	−0.500828	−	0.865547i	$-0.666971\pi$
$853$	1.19491e14	−	1.00265e14i	0.264601	−	0.222026i	0.765429	+	0.643520i	$0.222527\pi$
$854$	1.07096e15	+	6.18319e14i	2.35767	+	1.36120i
$855$	1.05182e10	+	1.32020e13i	2.30203e−5	+	0.0288941i
$856$	3.64245e13	+	6.30890e13i	0.0792546	+	0.137273i
$857$	3.61550e12	−	9.93352e12i	0.00782104	−	0.0214881i	−0.935721	−	0.352742i	$-0.885249\pi$
$857$	3.61550e12	−	9.93352e12i	0.00782104	−	0.0214881i	0.943542	+	0.331254i	$0.107472\pi$
$858$	−1.94507e10	−	4.88274e13i	−4.18311e−5	−	0.105009i
$859$	6.82327e14	+	5.72540e14i	1.45890	+	1.22417i	0.925744	+	0.378150i	$0.123440\pi$
$859$	6.82327e14	+	5.72540e14i	1.45890	+	1.22417i	0.533159	+	0.846015i	$0.321005\pi$
$860$	1.30199e14	+	3.57719e14i	0.276768	+	0.760414i
$861$	9.70448e14	−	3.53652e14i	2.05096	−	0.747413i
$862$	9.53003e13	+	5.40475e14i	0.200243	+	1.13564i
$863$		−	6.03260e14i		−	1.26023i	−0.776501	−	0.630116i	$-0.783007\pi$
$863$		−	6.03260e14i		−	1.26023i	0.776501	−	0.630116i	$-0.216993\pi$
$864$	3.81185e14	−	1.39256e14i	0.791712	−	0.289232i
$865$	6.29170e14			1.29923
$866$	−1.06640e15	+	1.88035e14i	−2.18942	+	0.386055i
$867$	−3.36126e14	−	5.91300e13i	−0.686130	−	0.120701i
$868$	6.34601e13	−	2.30976e13i	0.128796	−	0.0468779i
$869$	−3.22837e13	+	3.84742e13i	−0.0651455	+	0.0776374i
$870$	−2.65399e14	−	4.59262e14i	−0.532480	−	0.921435i
$871$	−5.96360e14	−	2.17057e14i	−1.18965	−	0.432996i
$872$	3.11295e14	−	1.79726e14i	0.617433	−	0.356475i
$873$	−6.48582e14	−	5.43345e14i	−1.27907	−	1.07153i
$874$	6.27100e12	−	1.08617e13i	0.0122964	−	0.0212981i
$875$	4.01101e14	+	4.78014e14i	0.782013	+	0.931966i
$876$	−4.03271e14	+	7.12732e13i	−0.781765	+	0.138167i
$877$	−9.58106e13	+	5.43369e14i	−0.184678	+	1.04736i	0.741690	+	0.670743i	$0.234025\pi$
$877$	−9.58106e13	+	5.43369e14i	−0.184678	+	1.04736i	−0.926368	+	0.376619i	$0.877086\pi$
$878$	−8.82080e14	−	1.55535e14i	−1.69058	−	0.298095i
$879$	−3.16766e14	−	1.15150e14i	−0.603662	−	0.219443i
$880$	−4.32674e13	+	3.63056e13i	−0.0819874	+	0.0687956i
$881$	8.45873e14	+	4.88365e14i	1.59377	+	0.920164i	0.992652	+	0.121003i	$0.0386112\pi$
$881$	8.45873e14	+	4.88365e14i	1.59377	+	0.920164i	0.601118	+	0.799160i	$0.294722\pi$
$882$	1.30696e14	−	3.59976e14i	0.244861	−	0.674420i
$883$	−2.55905e14	−	4.43241e14i	−0.476734	−	0.825727i	0.522911	−	0.852388i	$-0.324846\pi$
$883$	−2.55905e14	−	4.43241e14i	−0.476734	−	0.825727i	−0.999645	+	0.0266601i	$0.991513\pi$
$884$	−4.82429e13	+	1.32546e14i	−0.0893659	+	0.245531i
$885$	4.10944e14	+	2.37041e14i	0.756949	+	0.436623i
$886$	1.41633e14	+	1.18844e14i	0.259416	+	0.217676i
$887$	1.15532e14	+	3.17422e14i	0.210419	+	0.578121i	0.999338	−	0.0363757i	$-0.0115813\pi$
$887$	1.15532e14	+	3.17422e14i	0.210419	+	0.578121i	−0.788919	+	0.614497i	$0.789359\pi$
$888$	−4.66429e13	−	3.91064e13i	−0.0844736	−	0.0708244i
$889$	−5.02720e13	−	2.85107e14i	−0.0905351	−	0.513450i
$890$		−	2.42694e14i		−	0.434619i
$891$	−4.04038e13	−	2.32414e13i	−0.0719505	−	0.0413879i
$892$	1.21428e14			0.215028
$893$	2.53662e13	−	4.47274e12i	0.0446681	−	0.00787619i
$894$	−4.01989e14	+	4.79460e14i	−0.703926	+	0.839585i
$895$	−5.95130e14	+	2.16610e14i	−1.03633	+	0.377192i
$896$	5.26308e14	−	6.27229e14i	0.911381	−	1.08614i
$897$	2.22391e14	−	3.85548e14i	0.382962	−	0.663921i
$898$	8.78112e14	+	3.19606e14i	1.50372	+	0.547311i
$899$	1.04374e14	−	6.02603e13i	0.177743	−	0.102620i
$900$	−1.38887e13	+	1.16729e13i	−0.0235206	+	0.0197681i
$901$	2.17127e14	−	3.76075e14i	0.365670	−	0.633360i
$902$	6.63370e13	+	7.90573e13i	0.111102	+	0.132407i
$903$	−4.48994e14	+	1.23513e15i	−0.747829	+	2.05719i
$904$	1.05846e14	−	6.00283e14i	0.175321	−	0.994292i
$905$	4.17493e14	+	7.36152e13i	0.687711	+	0.121262i
$906$	−1.17163e14	−	6.62920e14i	−0.191933	−	1.08598i
$907$	−5.11631e14	+	4.29309e14i	−0.833529	+	0.699414i	−0.956098	−	0.293046i	$-0.905331\pi$
$907$	−5.11631e14	+	4.29309e14i	−0.833529	+	0.699414i	0.122570	+	0.992460i	$0.460887\pi$
$908$	7.82240e13	+	4.51626e13i	0.126739	+	0.0731729i
$909$	−7.80172e14	−	1.36925e14i	−1.25710	−	0.220629i
$910$	−5.15263e14	−	8.92462e14i	−0.825700	−	1.43015i
$911$	−1.81440e14	+	4.98502e14i	−0.289162	+	0.794465i	0.707023	+	0.707191i	$0.250038\pi$
$911$	−1.81440e14	+	4.98502e14i	−0.289162	+	0.794465i	−0.996184	+	0.0872742i	$0.972184\pi$
$912$	1.90561e13	−	1.10121e13i	0.0302036	−	0.0174541i
$913$	−3.11660e13	−	2.61514e13i	−0.0491279	−	0.0412232i
$914$	−1.15438e14	−	3.17163e14i	−0.180974	−	0.497223i
$915$	2.05412e14	−	1.16767e15i	0.320273	−	1.82060i
$916$	−8.60638e13	−	4.88092e14i	−0.133458	−	0.756876i
$917$		−	5.13665e14i		−	0.792198i
$918$	2.78497e14	+	3.31096e14i	0.427177	+	0.507855i
$919$	3.12038e14			0.476025			0.238012	−	0.971262i	$-0.423504\pi$
$919$	3.12038e14			0.476025			0.238012	+	0.971262i	$0.423504\pi$
$920$	−3.23413e14	+	5.70264e13i	−0.490703	+	0.0865241i
$921$	−1.18517e14	−	3.25219e14i	−0.178847	−	0.490770i
$922$	5.35771e14	−	1.95005e14i	0.804127	−	0.292678i
$923$	−1.49295e14	+	1.77922e14i	−0.222862	+	0.265596i
$924$	3.19084e13	−	1.27109e10i	0.0473746	−	1.88720e-5i
$925$	7.22182e12	+	2.62853e12i	0.0106644	+	0.00388154i
$926$	2.69149e14	−	1.55393e14i	0.395310	−	0.228233i
$927$	−5.49531e13	+	9.53570e13i	−0.0802775	+	0.139301i
$928$	−2.47895e14	+	4.29367e14i	−0.360187	+	0.623863i
$929$	3.01617e13	+	3.59453e13i	0.0435891	+	0.0519474i	0.787399	−	0.616444i	$-0.211427\pi$
$929$	3.01617e13	+	3.59453e13i	0.0435891	+	0.0519474i	−0.743809	+	0.668392i	$0.766983\pi$
$930$	−1.33786e14	−	1.59311e14i	−0.192307	−	0.228997i
$931$	2.02209e12	−	1.14678e13i	0.00289103	−	0.0163958i
$932$	−4.16375e14	−	7.34182e13i	−0.592114	−	0.104406i
$933$	6.58276e14	−	5.52807e14i	0.931108	−	0.781925i
$934$	−5.23543e14	+	4.39305e14i	−0.736577	+	0.618062i
$935$	−2.92374e13	−	1.68802e13i	−0.0409148	−	0.0236222i
$936$	4.31251e14	−	2.49441e14i	0.600276	−	0.347208i
$937$	3.48885e14	+	6.04286e14i	0.483041	+	0.836651i	0.999810	−	0.0194733i	$-0.00619893\pi$
$937$	3.48885e14	+	6.04286e14i	0.483041	+	0.836651i	−0.516770	+	0.856125i	$0.672866\pi$
$938$	4.55765e14	−	1.25220e15i	0.627663	−	1.72449i
$939$	−5.74417e10	−	1.44197e14i	−7.86863e−5	−	0.197528i
$940$	4.25890e14	+	3.57364e14i	0.580307	+	0.486935i
$941$	1.41297e14	+	3.88212e14i	0.191508	+	0.526163i	0.997868	−	0.0652612i	$-0.0207881\pi$
$941$	1.41297e14	+	3.88212e14i	0.191508	+	0.526163i	−0.806360	+	0.591424i	$0.798566\pi$
$942$	7.20005e12	−	2.62385e12i	0.00970691	−	0.00353740i
$943$	1.63359e14	+	9.26453e14i	0.219070	+	1.24241i
$944$		−	7.90888e14i		−	1.05501i
$945$	−9.83756e14	+	1.17566e12i	−1.30535	+	0.00155999i
$946$	−1.31312e14			−0.173320
$947$	1.40006e15	−	2.46869e14i	1.83822	−	0.324128i	0.856749	−	0.515734i	$-0.172481\pi$
$947$	1.40006e15	−	2.46869e14i	1.83822	−	0.324128i	0.981472	+	0.191606i	$0.0613695\pi$
$948$	4.16038e14	+	7.31879e13i	0.543365	+	0.0955867i
$949$	−1.33425e15	+	4.85627e14i	−1.73343	+	0.630917i
$950$	−1.13936e12	+	1.35783e12i	−0.00147245	+	0.00175480i
$951$	1.58148e14	+	2.73669e14i	0.203311	+	0.351822i
$952$	3.37624e14	+	1.22885e14i	0.431766	+	0.157150i
$953$	3.90804e14	−	2.25631e14i	0.497158	−	0.287034i	−0.230381	−	0.973100i	$-0.573997\pi$
$953$	3.90804e14	−	2.25631e14i	0.497158	−	0.287034i	0.727539	+	0.686066i	$0.240664\pi$
$954$	1.18774e15	−	4.33375e14i	1.50307	−	0.548430i
$955$	9.77289e13	−	1.69271e14i	0.123029	−	0.213092i
$956$	1.00776e14	+	1.20100e14i	0.126202	+	0.150402i
$957$	5.60754e13	−	9.91065e12i	0.0698575	−	0.0123465i
$958$	5.90520e13	−	3.34900e14i	0.0731824	−	0.415038i
$959$	−1.34107e15	−	2.36468e14i	−1.65333	−	0.291527i
$960$	−1.83777e14	−	6.68063e13i	−0.225390	−	0.0819335i
$961$	−5.91662e14	+	4.96464e14i	−0.721867	+	0.605718i
$962$	1.50658e14	+	8.69826e13i	0.182859	+	0.105574i
$963$	−1.95712e14	+	3.46701e13i	−0.236312	+	0.0418624i
$964$	−3.67835e14	−	6.37109e14i	−0.441843	−	0.765295i
$965$	4.15148e13	−	1.14061e14i	0.0496096	−	0.136301i
$966$	8.09552e14	+	4.66965e14i	0.962408	+	0.555136i
$967$	1.10827e15	+	9.29948e14i	1.31073	+	1.09983i	0.988183	+	0.153279i	$0.0489832\pi$
$967$	1.10827e15	+	9.29948e14i	1.31073	+	1.09983i	0.322546	+	0.946554i	$0.395461\pi$
$968$	1.90671e14	+	5.23864e14i	0.224340	+	0.616370i
$969$	1.00810e13	+	8.45211e12i	0.0118001	+	0.00989342i
$970$	−3.09831e14	−	1.75714e15i	−0.360800	−	2.04620i
$971$		−	4.21933e13i		−	0.0488818i	−0.999701	−	0.0244409i	$-0.992219\pi$
$971$		−	4.21933e13i		−	0.0488818i	0.999701	−	0.0244409i	$-0.00778055\pi$
$972$	7.80854e11	+	3.92038e14i	0.000899991	+	0.451852i
$973$	−5.63207e14			−0.645809
$974$	5.00255e13	−	8.82085e12i	0.0570685	−	0.0100627i
$975$	−4.04143e13	+	4.82029e13i	−0.0458682	+	0.0547079i
$976$	−1.85732e15	+	6.76009e14i	−2.09719	+	0.763314i
$977$	1.62997e14	−	1.94252e14i	0.183108	−	0.218219i	−0.666680	−	0.745344i	$-0.732285\pi$
$977$	1.62997e14	−	1.94252e14i	0.183108	−	0.218219i	0.849788	+	0.527124i	$0.176730\pi$
$978$	−6.49264e14	+	1.12559e15i	−0.725649	+	1.25802i
$979$	2.44831e13	+	8.91112e12i	0.0272241	+	0.00990875i
$980$	2.17671e14	−	1.25672e14i	0.240808	−	0.139030i
$981$	1.71070e14	+	9.65686e14i	0.188291	+	1.06290i
$982$	3.48446e14	−	6.03526e14i	0.381573	−	0.660905i
$983$	8.34385e14	+	9.94381e14i	0.909073	+	1.08339i	0.996191	+	0.0871933i	$0.0277898\pi$
$983$	8.34385e14	+	9.94381e14i	0.909073	+	1.08339i	−0.0871182	+	0.996198i	$0.527766\pi$
$984$	−3.59749e14	+	9.89629e14i	−0.389964	+	1.07275i
$985$	−1.82000e14	+	1.03217e15i	−0.196286	+	1.11319i
$986$	−5.20530e14	−	9.17835e13i	−0.558549	−	0.0984873i
$987$	3.34042e14	+	1.89005e15i	0.356628	+	2.01784i
$988$	−9.56582e12	+	8.02668e12i	−0.0101610	+	0.00852611i
$989$	−1.03662e15	−	5.98490e14i	−1.09556	−	0.632522i
$990$	−3.36921e13	−	9.23392e13i	−0.0354284	−	0.0970980i
$991$	−2.68298e14	−	4.64705e14i	−0.280704	−	0.486193i	0.690854	−	0.722994i	$-0.257235\pi$
$991$	−2.68298e14	−	4.64705e14i	−0.280704	−	0.486193i	−0.971558	+	0.236800i	$0.923901\pi$
$992$	−6.65052e13	+	1.82722e14i	−0.0692305	+	0.190209i
$993$	5.66333e14	−	3.27273e14i	0.586578	−	0.338972i
$994$	−3.73592e14	−	3.13481e14i	−0.385004	−	0.323057i
$995$	3.44570e14	+	9.46697e14i	0.353315	+	0.970724i
$996$	−5.92859e13	+	3.37012e14i	−0.0604860	+	0.343834i
$997$	1.61876e14	+	9.18045e14i	0.164326	+	0.931941i	0.949756	+	0.312990i	$0.101331\pi$
$997$	1.61876e14	+	9.18045e14i	0.164326	+	0.931941i	−0.785430	+	0.618950i	$0.787558\pi$
$998$			1.49272e15i			1.50774i
$999$	1.43721e14	−	8.32068e13i	0.144442	−	0.0836241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.f.a.14.22	yes	174
3.2	odd	2		81.11.f.a.71.8		174
27.2	odd	18	inner	27.11.f.a.2.22	✓	174
27.25	even	9		81.11.f.a.8.8		174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.f.a.2.22	✓	174	27.2	odd	18	inner
27.11.f.a.14.22	yes	174	1.1	even	1	trivial
81.11.f.a.8.8		174	27.25	even	9
81.11.f.a.71.8		174	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(37.9719 - 6.69548i) q^{2} +(156.123 - 186.211i) q^{3} +(434.793 - 158.252i) q^{4} +(2075.88 - 2473.94i) q^{5} +(4681.53 - 8116.11i) q^{6} +(19948.9 + 7260.82i) q^{7} +(-18743.0 + 10821.3i) q^{8} +(-10300.1 - 58143.7i) q^{9} +(62261.0 - 107839. i) q^{10} +(8592.81 + 10240.5i) q^{11} +(38413.1 - 105670. i) q^{12} +(67693.8 - 383911. i) q^{13} +(806115. + 142140. i) q^{14} +(-136581. - 772791. i) q^{15} +(-1.00221e6 + 840952. i) q^{16} +(-677230. - 390999. i) q^{17} +(-780414. - 2.13887e6i) q^{18} +(-34614.8 - 59954.7i) q^{19} +(511074. - 1.40416e6i) q^{20} +(4.46654e6 - 2.58113e6i) q^{21} +(394851. + 331319. i) q^{22} +(1.60699e6 + 4.41518e6i) q^{23} +(-911176. + 5.17960e6i) q^{24} +(-115308. - 653943. i) q^{25} -1.50311e7i q^{26} +(-1.24351e7 - 7.15960e6i) q^{27} +9.82271e6 q^{28} +(1.72635e7 - 3.04402e6i) q^{29} +(-1.03605e7 - 2.84299e7i) q^{30} +(6.46055e6 - 2.35145e6i) q^{31} +(-1.81798e7 + 2.16658e7i) q^{32} +(3.24843e6 - 1294.03i) q^{33} +(-2.83337e7 - 1.03126e7i) q^{34} +(5.93745e7 - 3.42799e7i) q^{35} +(-1.36798e7 - 2.36505e7i) q^{36} +(-5.78685e6 + 1.00231e7i) q^{37} +(-1.71582e6 - 2.04483e6i) q^{38} +(-6.09198e7 - 7.25427e7i) q^{39} +(-1.21371e7 + 6.88327e7i) q^{40} +(1.97179e8 + 3.47680e7i) q^{41} +(1.52321e8 - 1.27916e8i) q^{42} +(-1.95154e8 + 1.63754e8i) q^{43} +(5.35668e6 + 3.09268e6i) q^{44} +(-1.65226e8 - 9.52177e7i) q^{45} +(9.05825e7 + 1.56893e8i) q^{46} +(-1.27251e8 + 3.49620e8i) q^{47} +(126643. + 3.17914e8i) q^{48} +(1.28852e8 + 1.08120e8i) q^{49} +(-8.75693e6 - 2.40595e7i) q^{50} +(-1.78540e8 + 6.50636e7i) q^{51} +(-3.13218e7 - 1.77635e8i) q^{52} +5.55314e8i q^{53} +(-5.20121e8 - 1.88605e8i) q^{54} +4.31721e7 q^{55} +(-4.52474e8 + 7.97834e7i) q^{56} +(-1.65684e7 - 2.91465e6i) q^{57} +(6.35148e8 - 2.31175e8i) q^{58} +(-3.88578e8 + 4.63090e8i) q^{59} +(-1.81680e8 - 3.14390e8i) q^{60} +(1.41965e9 + 5.16712e8i) q^{61} +(2.29575e8 - 1.32545e8i) q^{62} +(2.16696e8 - 1.23469e9i) q^{63} +(1.24586e8 - 2.15790e8i) q^{64} +(-8.09247e8 - 9.64423e8i) q^{65} +(1.23341e8 - 2.17989e7i) q^{66} +(2.82692e8 - 1.60323e9i) q^{67} +(-3.56331e8 - 6.28308e7i) q^{68} +(1.07304e9 + 3.90072e8i) q^{69} +(2.02504e9 - 1.69921e9i) q^{70} +(-5.15975e8 - 2.97898e8i) q^{71} +(8.22243e8 + 9.78327e8i) q^{72} +(-1.82114e9 - 3.15430e9i) q^{73} +(-1.52628e8 + 4.19343e8i) q^{74} +(-1.39774e8 - 8.06242e7i) q^{75} +(-2.45382e7 - 2.05900e7i) q^{76} +(9.70630e7 + 2.66678e8i) q^{77} +(-2.79895e9 - 2.34670e9i) q^{78} +(6.52406e8 + 3.69998e9i) q^{79} +4.22512e9i q^{80} +(-3.27460e9 + 1.19777e9i) q^{81} +7.72006e9 q^{82} +(-2.99717e9 + 5.28482e8i) q^{83} +(1.53355e9 - 1.82910e9i) q^{84} +(-2.37316e9 + 8.63758e8i) q^{85} +(-6.31398e9 + 7.52471e9i) q^{86} +(2.12840e9 - 3.68990e9i) q^{87} +(-2.71870e8 - 9.89527e7i) q^{88} +(1.68789e9 - 9.74502e8i) q^{89} +(-6.91147e9 - 2.50934e9i) q^{90} +(4.13793e9 - 7.16710e9i) q^{91} +(1.39742e9 + 1.66538e9i) q^{92} +(5.70776e8 - 1.57014e9i) q^{93} +(-2.49111e9 + 1.41278e10i) q^{94} +(-2.20181e8 - 3.88238e7i) q^{95} +(1.19613e9 + 6.76780e9i) q^{96} +(1.09765e10 - 9.21035e9i) q^{97} +(5.61668e9 + 3.24279e9i) q^{98} +(5.06915e8 - 6.05096e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 4965 q^{5} + 18234 q^{6} - 6 q^{7} - 9 q^{8} + 119124 q^{9} - 3 q^{10} - 978 q^{11} - 1015107 q^{12} - 6 q^{13} + 2134569 q^{14} - 2548539 q^{15} - 3078 q^{16} - 9 q^{17}+ \cdots - 72892391589 q^{99}+O(q^{100}) \) 174 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 4965 * q^5 + 18234 * q^6 - 6 * q^7 - 9 * q^8 + 119124 * q^9 - 3 * q^10 - 978 * q^11 - 1015107 * q^12 - 6 * q^13 + 2134569 * q^14 - 2548539 * q^15 - 3078 * q^16 - 9 * q^17 + 6676947 * q^18 - 3 * q^19 + 15925353 * q^20 - 21049824 * q^21 + 10420410 * q^22 + 8437692 * q^23 + 87359400 * q^24 - 14881965 * q^25 - 60562494 * q^27 - 12 * q^28 + 7820868 * q^29 + 216153117 * q^30 - 51711531 * q^31 + 76244832 * q^32 - 198927081 * q^33 + 92236410 * q^34 - 260153622 * q^35 + 199074744 * q^36 - 3 * q^37 + 250645020 * q^38 + 152777949 * q^39 - 26151153 * q^40 - 837714012 * q^41 - 1627952634 * q^42 - 213300456 * q^43 + 2245906431 * q^44 + 1041263847 * q^45 - 3 * q^46 - 1685998563 * q^47 - 1664196711 * q^48 - 183168366 * q^49 + 2548576023 * q^50 + 1007158626 * q^51 - 912655665 * q^52 - 1206704682 * q^54 - 12 * q^55 - 4260806997 * q^56 - 1000586442 * q^57 - 496853331 * q^58 + 1806342150 * q^59 + 1176655374 * q^60 - 1784159286 * q^61 + 2786630112 * q^62 + 2270781765 * q^63 + 8858370045 * q^64 - 2961878001 * q^65 - 5594499243 * q^66 - 915608058 * q^67 + 11412166995 * q^68 - 7767764199 * q^69 + 1945422669 * q^70 - 5512912173 * q^71 - 15991303644 * q^72 + 2110132140 * q^73 + 22008588729 * q^74 + 15296936925 * q^75 + 11875694586 * q^76 - 2702962221 * q^77 - 12511026108 * q^78 + 6660721974 * q^79 + 440880768 * q^81 - 12 * q^82 + 7670489421 * q^83 - 31766160684 * q^84 - 6965484381 * q^85 - 33241766118 * q^86 - 10927113525 * q^87 + 28790289402 * q^88 + 34430237370 * q^89 + 12602186028 * q^90 - 991980102 * q^91 + 40280154009 * q^92 + 57140838285 * q^93 - 62587945905 * q^94 - 12104972679 * q^95 - 78182924274 * q^96 + 48297833958 * q^97 - 103117506282 * q^98 - 72892391589 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more