LMFDB - Embedded newform 27.11.f.a.2.17

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			2.17
Character	$\chi$	$=$	27.2
Dual form			27.11.f.a.14.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(9.99045 + 1.76159i) q^{2} +(58.8240 - 235.773i) q^{3} +(-865.539 - 315.031i) q^{4} +(2619.44 + 3121.73i) q^{5} +(1003.01 - 2251.85i) q^{6} +(-15129.3 + 5506.60i) q^{7} +(-17088.5 - 9866.04i) q^{8} +(-52128.5 - 27738.2i) q^{9} +(20670.2 + 35801.9i) q^{10} +(45611.2 - 54357.3i) q^{11} +(-125190. + 185539. i) q^{12} +(121958. + 691659. i) q^{13} +(-160849. + 28361.9i) q^{14} +(890105. - 433960. i) q^{15} +(569186. + 477604. i) q^{16} +(109192. - 63041.9i) q^{17} +(-471924. - 368946. i) q^{18} +(-1.20002e6 + 2.07849e6i) q^{19} +(-1.28379e6 - 3.52719e6i) q^{20} +(408342. + 3.89099e6i) q^{21} +(551431. - 462706. i) q^{22} +(-2.26289e6 + 6.21725e6i) q^{23} +(-3.33136e6 + 3.44864e6i) q^{24} +(-1.18794e6 + 6.73715e6i) q^{25} +7.12483e6i q^{26} +(-9.60631e6 + 1.06588e7i) q^{27} +1.48297e7 q^{28} +(2.11083e7 + 3.72196e6i) q^{29} +(9.65702e6 - 2.76746e6i) q^{30} +(-4.32758e7 - 1.57511e7i) q^{31} +(1.78330e7 + 2.12526e7i) q^{32} +(-1.01329e7 - 1.39514e7i) q^{33} +(1.20193e6 - 437466. i) q^{34} +(-5.68204e7 - 3.28053e7i) q^{35} +(3.63809e7 + 4.04305e7i) q^{36} +(3.39317e7 + 5.87714e7i) q^{37} +(-1.56501e7 + 1.86511e7i) q^{38} +(1.70248e8 + 1.19318e7i) q^{39} +(-1.39632e7 - 7.91892e7i) q^{40} +(-8.50271e7 + 1.49926e7i) q^{41} +(-2.77479e6 + 3.95921e7i) q^{42} +(-8.62677e7 - 7.23872e7i) q^{43} +(-5.66025e7 + 3.26795e7i) q^{44} +(-4.99564e7 - 2.35390e8i) q^{45} +(-3.35595e7 + 5.81268e7i) q^{46} +(-8.10430e7 - 2.22664e8i) q^{47} +(1.46088e8 - 1.06104e8i) q^{48} +(-1.78166e7 + 1.49499e7i) q^{49} +(-2.37361e7 + 6.52145e7i) q^{50} +(-8.44045e6 - 2.94528e7i) q^{51} +(1.12334e8 - 6.37078e8i) q^{52} -5.12143e8i q^{53} +(-1.14748e8 + 8.95639e7i) q^{54} +2.89165e8 q^{55} +(3.12865e8 + 5.51665e7i) q^{56} +(4.19461e8 + 4.05196e8i) q^{57} +(2.04325e8 + 7.43681e7i) q^{58} +(7.08786e8 + 8.44699e8i) q^{59} +(-9.07132e8 + 9.51995e7i) q^{60} +(-6.03944e8 + 2.19817e8i) q^{61} +(-4.04598e8 - 2.33595e8i) q^{62} +(9.41408e8 + 1.32608e8i) q^{63} +(-2.39704e8 - 4.15180e8i) q^{64} +(-1.83971e9 + 2.19248e9i) q^{65} +(-7.66560e7 - 1.57231e8i) q^{66} +(-3.30698e8 - 1.87548e9i) q^{67} +(-1.14370e8 + 2.01665e7i) q^{68} +(1.33274e9 + 8.99251e8i) q^{69} +(-5.09872e8 - 4.27834e8i) q^{70} +(-1.80207e9 + 1.04043e9i) q^{71} +(6.17130e8 + 9.88305e8i) q^{72} +(-1.61956e7 + 2.80516e7i) q^{73} +(2.35462e8 + 6.46927e8i) q^{74} +(1.51856e9 + 6.76390e8i) q^{75} +(1.69345e9 - 1.42097e9i) q^{76} +(-3.90740e8 + 1.07355e9i) q^{77} +(1.67984e9 + 4.19111e8i) q^{78} +(-5.52812e7 + 3.13515e8i) q^{79} +3.02791e9i q^{80} +(1.94797e9 + 2.89190e9i) q^{81} -8.75870e8 q^{82} +(-5.26514e9 - 9.28386e8i) q^{83} +(8.72344e8 - 3.49644e9i) q^{84} +(4.82822e8 + 1.75733e8i) q^{85} +(-7.34337e8 - 8.75149e8i) q^{86} +(2.11921e9 - 4.75782e9i) q^{87} +(-1.31572e9 + 4.78882e8i) q^{88} +(5.25641e9 + 3.03479e9i) q^{89} +(-8.44280e7 - 2.43965e9i) q^{90} +(-5.65383e9 - 9.79271e9i) q^{91} +(3.91724e9 - 4.66839e9i) q^{92} +(-6.25934e9 + 9.27671e9i) q^{93} +(-4.17415e8 - 2.36728e9i) q^{94} +(-9.63186e9 + 1.69836e9i) q^{95} +(6.05979e9 - 2.95438e9i) q^{96} +(4.82972e9 + 4.05261e9i) q^{97} +(-2.04332e8 + 1.17971e8i) q^{98} +(-3.88541e9 + 1.56839e9i) 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	9.99045	+	1.76159i	0.312202	+	0.0550496i	0.327554	−	0.944833i	$-0.393776\pi$
$2$	9.99045	+	1.76159i	0.312202	+	0.0550496i	−0.0153520	+	0.999882i	$0.504887\pi$
$3$	58.8240	−	235.773i	0.242074	−	0.970258i
$3$	58.8240	−	235.773i	0.242074	−	0.970258i
$4$	−865.539	−	315.031i	−0.845253	−	0.307647i
$5$	2619.44	+	3121.73i	0.838222	+	0.998954i	0.999927	+	0.0121151i	$0.00385646\pi$
$5$	2619.44	+	3121.73i	0.838222	+	0.998954i	−0.161704	+	0.986839i	$0.551699\pi$
$6$	1003.01	−	2251.85i	0.128988	−	0.289590i
$7$	−15129.3	+	5506.60i	−0.900176	+	0.327637i	−0.750323	−	0.661071i	$-0.770102\pi$
$7$	−15129.3	+	5506.60i	−0.900176	+	0.327637i	−0.149853	+	0.988708i	$0.547880\pi$
$8$	−17088.5	−	9866.04i	−0.521499	−	0.301088i
$9$	−52128.5	−	27738.2i	−0.882800	−	0.469749i
$10$	20670.2	+	35801.9i	0.206702	+	0.358019i
$11$	45611.2	−	54357.3i	0.283210	−	0.337516i	−0.605620	−	0.795754i	$-0.707075\pi$
$11$	45611.2	−	54357.3i	0.283210	−	0.337516i	0.888830	+	0.458238i	$0.151519\pi$
$12$	−125190.	+	185539.i	−0.503111	+	0.745640i
$13$	121958.	+	691659.i	0.328469	+	1.86284i	0.484085	+	0.875021i	$0.339153\pi$
$13$	121958.	+	691659.i	0.328469	+	1.86284i	−0.155616	+	0.987818i	$0.549736\pi$
$14$	−160849.	+	28361.9i	−0.299073	+	0.0527346i
$15$	890105.	−	433960.i	1.17216	−	0.571471i
$16$	569186.	+	477604.i	0.542819	+	0.455479i
$17$	109192.	−	63041.9i	0.0769033	−	0.0444002i	−0.461055	−	0.887371i	$-0.652529\pi$
$17$	109192.	−	63041.9i	0.0769033	−	0.0444002i	0.537959	+	0.842971i	$0.319196\pi$
$18$	−471924.	−	368946.i	−0.249752	−	0.195254i
$19$	−1.20002e6	+	2.07849e6i	−0.484640	+	0.839420i	−0.999844	−	0.0176468i	$-0.994383\pi$
$19$	−1.20002e6	+	2.07849e6i	−0.484640	+	0.839420i	0.515205	+	0.857067i	$0.327716\pi$
$20$	−1.28379e6	−	3.52719e6i	−0.401185	−	1.10225i
$21$	408342.	+	3.89099e6i	0.0999833	+	0.952716i
$22$	551431.	−	462706.i	0.106999	−	0.0897825i
$23$	−2.26289e6	+	6.21725e6i	−0.351580	+	0.965959i	0.630282	+	0.776366i	$0.282939\pi$
$23$	−2.26289e6	+	6.21725e6i	−0.351580	+	0.965959i	−0.981863	+	0.189593i	$0.939283\pi$
$24$	−3.33136e6	+	3.44864e6i	−0.418374	+	0.433103i
$25$	−1.18794e6	+	6.73715e6i	−0.121645	+	0.689884i
$26$			7.12483e6i			0.599663i
$27$	−9.60631e6	+	1.06588e7i	−0.669480	+	0.742830i
$28$	1.48297e7			0.861674
$29$	2.11083e7	+	3.72196e6i	1.02911	+	0.181460i	0.662616	−	0.748959i	$-0.269446\pi$
$29$	2.11083e7	+	3.72196e6i	1.02911	+	0.181460i	0.366497	+	0.930419i	$0.380557\pi$
$30$	9.65702e6	−	2.76746e6i	0.397408	−	0.113887i
$31$	−4.32758e7	−	1.57511e7i	−1.51160	−	0.550177i	−0.552566	−	0.833469i	$-0.686351\pi$
$31$	−4.32758e7	−	1.57511e7i	−1.51160	−	0.550177i	−0.959034	+	0.283292i	$0.908574\pi$
$32$	1.78330e7	+	2.12526e7i	0.531466	+	0.633376i
$33$	−1.01329e7	−	1.39514e7i	−0.258920	−	0.356490i
$34$	1.20193e6	−	437466.i	0.0264536	−	0.00962831i
$35$	−5.68204e7	−	3.28053e7i	−1.08184	−	0.624602i
$36$	3.63809e7	+	4.04305e7i	0.601673	+	0.668647i
$37$	3.39317e7	+	5.87714e7i	0.489325	+	0.847535i	0.999925	−	0.0122834i	$-0.00391003\pi$
$37$	3.39317e7	+	5.87714e7i	0.489325	+	0.847535i	−0.510600	+	0.859818i	$0.670577\pi$
$38$	−1.56501e7	+	1.86511e7i	−0.197515	+	0.235389i
$39$	1.70248e8	+	1.19318e7i	1.88695	+	0.132246i
$40$	−1.39632e7	−	7.91892e7i	−0.136359	−	0.773332i
$41$	−8.50271e7	+	1.49926e7i	−0.733902	+	0.129407i	−0.528094	−	0.849186i	$-0.677093\pi$
$41$	−8.50271e7	+	1.49926e7i	−0.733902	+	0.129407i	−0.205808	+	0.978592i	$0.565982\pi$
$42$	−2.77479e6	+	3.95921e7i	−0.0212316	+	0.302943i
$43$	−8.62677e7	−	7.23872e7i	−0.586821	−	0.492402i	0.300358	−	0.953827i	$-0.402894\pi$
$43$	−8.62677e7	−	7.23872e7i	−0.586821	−	0.492402i	−0.887179	+	0.461425i	$0.847338\pi$
$44$	−5.66025e7	+	3.26795e7i	−0.343220	+	0.198158i
$45$	−4.99564e7	−	2.35390e8i	−0.270725	−	1.27563i
$46$	−3.35595e7	+	5.81268e7i	−0.162940	+	0.282220i
$47$	−8.10430e7	−	2.22664e8i	−0.353367	−	0.970868i	−0.981280	−	0.192585i	$-0.938313\pi$
$47$	−8.10430e7	−	2.22664e8i	−0.353367	−	0.970868i	0.627913	−	0.778283i	$-0.283909\pi$
$48$	1.46088e8	−	1.06104e8i	0.573334	−	0.416414i
$49$	−1.78166e7	+	1.49499e7i	−0.0630733	+	0.0529248i
$50$	−2.37361e7	+	6.52145e7i	−0.0759556	+	0.208686i
$51$	−8.44045e6	−	2.94528e7i	−0.0244633	−	0.0853642i
$52$	1.12334e8	−	6.37078e8i	0.295457	−	1.67562i
$53$		−	5.12143e8i		−	1.22465i	−0.790606	−	0.612325i	$-0.790235\pi$
$53$		−	5.12143e8i		−	1.22465i	0.790606	−	0.612325i	$-0.209765\pi$
$54$	−1.14748e8	+	8.95639e7i	−0.249905	+	0.195058i
$55$	2.89165e8			0.574556
$56$	3.12865e8	+	5.51665e7i	0.568089	+	0.100169i
$57$	4.19461e8	+	4.05196e8i	0.697135	+	0.673427i
$58$	2.04325e8	+	7.43681e7i	0.311301	+	0.113304i
$59$	7.08786e8	+	8.44699e8i	0.991415	+	1.18152i	0.983381	+	0.181554i	$0.0581128\pi$
$59$	7.08786e8	+	8.44699e8i	0.991415	+	1.18152i	0.00803363	+	0.999968i	$0.497443\pi$
$60$	−9.07132e8	+	9.51995e7i	−1.16658	+	0.122427i
$61$	−6.03944e8	+	2.19817e8i	−0.715068	+	0.260263i	−0.673830	−	0.738886i	$-0.735352\pi$
$61$	−6.03944e8	+	2.19817e8i	−0.715068	+	0.260263i	−0.0412373	+	0.999149i	$0.513130\pi$
$62$	−4.04598e8	−	2.33595e8i	−0.441637	−	0.254979i
$63$	9.41408e8	+	1.32608e8i	0.948583	+	0.133618i
$64$	−2.39704e8	−	4.15180e8i	−0.223242	−	0.386667i
$65$	−1.83971e9	+	2.19248e9i	−1.58556	+	1.88960i
$66$	−7.66560e7	−	1.57231e8i	−0.0612106	−	0.125550i
$67$	−3.30698e8	−	1.87548e9i	−0.244939	−	1.38912i	−0.820635	−	0.571452i	$-0.806380\pi$
$67$	−3.30698e8	−	1.87548e9i	−0.244939	−	1.38912i	0.575697	−	0.817663i	$-0.304731\pi$
$68$	−1.14370e8	+	2.01665e7i	−0.0786624	+	0.0138703i
$69$	1.33274e9	+	8.99251e8i	0.852121	+	0.574957i
$70$	−5.09872e8	−	4.27834e8i	−0.303369	−	0.254557i
$71$	−1.80207e9	+	1.04043e9i	−0.998805	+	0.576660i	−0.907894	−	0.419199i	$-0.862311\pi$
$71$	−1.80207e9	+	1.04043e9i	−0.998805	+	0.576660i	−0.0909103	+	0.995859i	$0.528978\pi$
$72$	6.17130e8	+	9.88305e8i	0.318944	+	0.510774i
$73$	−1.61956e7	+	2.80516e7i	−0.00781237	+	0.0135314i	−0.869905	−	0.493219i	$-0.835820\pi$
$73$	−1.61956e7	+	2.80516e7i	−0.00781237	+	0.0135314i	0.862093	+	0.506750i	$0.169153\pi$
$74$	2.35462e8	+	6.46927e8i	0.106111	+	0.291539i
$75$	1.51856e9	+	6.76390e8i	0.639918	+	0.285030i
$76$	1.69345e9	−	1.42097e9i	0.667888	−	0.560425i
$77$	−3.90740e8	+	1.07355e9i	−0.144356	+	0.396614i
$78$	1.67984e9	+	4.19111e8i	0.581828	+	0.145163i
$79$	−5.52812e7	+	3.13515e8i	−0.0179656	+	0.101888i	−0.992472	−	0.122472i	$-0.960918\pi$
$79$	−5.52812e7	+	3.13515e8i	−0.0179656	+	0.101888i	0.974506	+	0.224360i	$0.0720291\pi$
$80$			3.02791e9i			0.924043i
$81$	1.94797e9	+	2.89190e9i	0.558672	+	0.829388i
$82$	−8.75870e8			−0.236249
$83$	−5.26514e9	−	9.28386e8i	−1.33665	−	0.235688i	−0.540788	−	0.841159i	$-0.681874\pi$
$83$	−5.26514e9	−	9.28386e8i	−1.33665	−	0.235688i	−0.795867	+	0.605471i	$0.792985\pi$
$84$	8.72344e8	−	3.49644e9i	0.208589	−	0.836045i
$85$	4.82822e8	+	1.75733e8i	0.108816	+	0.0396057i
$86$	−7.34337e8	−	8.75149e8i	−0.156100	−	0.186033i
$87$	2.11921e9	−	4.75782e9i	0.425185	−	0.954578i
$88$	−1.31572e9	+	4.78882e8i	−0.249315	+	0.0907434i
$89$	5.25641e9	+	3.03479e9i	0.941324	+	0.543473i	0.890375	−	0.455228i	$-0.150442\pi$
$89$	5.25641e9	+	3.03479e9i	0.941324	+	0.543473i	0.0509486	+	0.998701i	$0.483776\pi$
$90$	−8.44280e7	−	2.43965e9i	−0.0142980	−	0.413157i
$91$	−5.65383e9	−	9.79271e9i	−0.906015	−	1.56926i
$92$	3.91724e9	−	4.66839e9i	0.594349	−	0.708318i
$93$	−6.25934e9	+	9.27671e9i	−0.899733	+	1.33346i
$94$	−4.17415e8	−	2.36728e9i	−0.0568759	−	0.322559i
$95$	−9.63186e9	+	1.69836e9i	−1.24478	+	0.219488i
$96$	6.05979e9	−	2.95438e9i	0.743192	−	0.362335i
$97$	4.82972e9	+	4.05261e9i	0.562423	+	0.471929i	0.879122	−	0.476597i	$-0.158130\pi$
$97$	4.82972e9	+	4.05261e9i	0.562423	+	0.471929i	−0.316699	+	0.948526i	$0.602574\pi$
$98$	−2.04332e8	+	1.17971e8i	−0.0226051	+	0.0130510i
$99$	−3.88541e9	+	1.56839e9i	−0.408565	+	0.164922i
$100$	3.15062e9	−	5.45703e9i	0.315062	−	0.545703i
$101$	−1.32022e9	−	3.62727e9i	−0.125614	−	0.345122i	0.860906	−	0.508765i	$-0.169898\pi$
$101$	−1.32022e9	−	3.62727e9i	−0.125614	−	0.345122i	−0.986520	+	0.163643i	$0.947676\pi$
$102$	−3.24403e7	−	3.09115e8i	−0.00293822	−	0.0279975i
$103$	4.64727e9	−	3.89952e9i	0.400877	−	0.336376i	−0.419955	−	0.907545i	$-0.637954\pi$
$103$	4.64727e9	−	3.89952e9i	0.400877	−	0.336376i	0.820833	+	0.571169i	$0.193510\pi$
$104$	4.73986e9	−	1.30226e10i	0.389582	−	1.07037i
$105$	−1.10770e10	+	1.14670e10i	−0.867911	+	0.898466i
$106$	9.02184e8	−	5.11654e9i	0.0674164	−	0.382338i
$107$			7.88025e9i			0.561851i	0.959730	+	0.280926i	$0.0906414\pi$
$107$			7.88025e9i			0.561851i	−0.959730	+	0.280926i	$0.909359\pi$
$108$	1.16725e10	−	6.19932e9i	0.794410	−	0.421916i
$109$	4.24804e9			0.276093			0.138047	−	0.990426i	$-0.455918\pi$
$109$	4.24804e9			0.276093			0.138047	+	0.990426i	$0.455918\pi$
$110$	2.88889e9	+	5.09389e8i	0.179377	+	0.0316290i
$111$	1.58527e10	−	4.54299e9i	0.940780	−	0.269605i
$112$	−1.12413e10	−	4.09152e9i	−0.637864	−	0.232164i
$113$	9.97564e9	+	1.18885e10i	0.541438	+	0.645261i	0.965509	−	0.260368i	$-0.0838439\pi$
$113$	9.97564e9	+	1.18885e10i	0.541438	+	0.645261i	−0.424072	+	0.905629i	$0.639399\pi$
$114$	3.47682e9	+	4.78701e9i	0.180575	+	0.248622i
$115$	−2.53361e10	+	9.22159e9i	−1.25965	+	0.458476i
$116$	−1.70975e10	−	9.87126e9i	−0.814035	−	0.469983i
$117$	1.28279e10	−	3.94380e10i	0.585094	−	1.79881i
$118$	5.59309e9	+	9.68751e9i	0.244479	+	0.423450i
$119$	−1.30484e9	+	1.55505e9i	−0.0546794	+	0.0651644i
$120$	−1.94920e10	−	1.36609e9i	−0.783341	−	0.0549000i
$121$	3.62965e9	+	2.05848e10i	0.139939	+	0.793632i
$122$	−6.42090e9	+	1.13218e9i	−0.237573	+	0.0418905i
$123$	−1.46680e9	+	2.09290e10i	−0.0521008	+	0.743400i
$124$	3.24948e10	+	2.72664e10i	1.10842	+	0.930078i
$125$	1.03212e10	−	5.95896e9i	0.338206	−	0.195263i
$126$	9.17150e9	+	2.98318e9i	0.288794	+	0.0939349i
$127$	−1.29148e10	+	2.23692e10i	−0.390904	+	0.677066i	−0.992569	−	0.121683i	$-0.961171\pi$
$127$	−1.29148e10	+	2.23692e10i	−0.390904	+	0.677066i	0.601665	+	0.798749i	$0.294504\pi$
$128$	−1.13799e10	−	3.12659e10i	−0.331198	−	0.909958i
$129$	−2.21415e10	+	1.60815e10i	−0.619811	+	0.450170i
$130$	−2.22418e10	+	1.86631e10i	−0.599036	+	0.502651i
$131$	−9.89610e9	+	2.71893e10i	−0.256512	+	0.704761i	0.742864	+	0.669442i	$0.233467\pi$
$131$	−9.89610e9	+	2.71893e10i	−0.256512	+	0.704761i	−0.999376	+	0.0353185i	$0.988755\pi$
$132$	4.37534e9	+	1.52677e10i	0.109180	+	0.380980i
$133$	6.70995e9	−	3.80540e10i	0.161236	−	0.914412i
$134$		−	1.93194e10i		−	0.447168i
$135$	−5.84371e10	−	2.06821e9i	−1.30323	−	0.0461239i
$136$	−2.48790e9			−0.0534734
$137$	4.59637e10	+	8.10465e9i	0.952385	+	0.167931i	0.628191	−	0.778059i	$-0.283796\pi$
$137$	4.59637e10	+	8.10465e9i	0.952385	+	0.167931i	0.324194	+	0.945991i	$0.394907\pi$
$138$	1.17306e10	+	1.13317e10i	0.234382	+	0.226412i
$139$	2.81258e10	+	1.02369e10i	0.542039	+	0.197286i	0.598506	−	0.801118i	$-0.295761\pi$
$139$	2.81258e10	+	1.02369e10i	0.542039	+	0.197286i	−0.0564669	+	0.998404i	$0.517984\pi$
$140$	3.88456e10	+	4.62944e10i	0.722274	+	0.860773i
$141$	−5.72653e10	+	6.00974e9i	−1.02753	+	0.107835i
$142$	−1.98363e10	+	7.21983e9i	−0.343573	+	0.125050i
$143$	4.31594e10	+	2.49181e10i	0.721763	+	0.416710i
$144$	−1.64229e10	−	4.06850e10i	−0.265240	−	0.657085i
$145$	4.36730e10	+	7.56439e10i	0.681355	+	1.18014i
$146$	−2.11217e8	+	2.51718e8i	−0.00318393	+	0.00379446i
$147$	2.47674e9	+	5.08009e9i	0.0360823	+	0.0740091i
$148$	−1.08544e10	−	6.15585e10i	−0.152862	−	0.866921i
$149$	6.94305e10	−	1.22425e10i	0.945407	−	0.166701i	0.320367	−	0.947293i	$-0.396194\pi$
$149$	6.94305e10	−	1.22425e10i	0.945407	−	0.166701i	0.625040	+	0.780593i	$0.285083\pi$
$150$	1.39795e10	+	9.43251e9i	0.184093	+	0.124214i
$151$	2.46243e10	+	2.06622e10i	0.313674	+	0.263204i	0.786009	−	0.618216i	$-0.212144\pi$
$151$	2.46243e10	+	2.06622e10i	0.313674	+	0.263204i	−0.472335	+	0.881419i	$0.656589\pi$
$152$	4.10129e10	−	2.36788e10i	0.505478	−	0.291838i
$153$	−7.44067e9	+	2.57496e8i	−0.0887472	+	0.00307123i
$154$	−5.79481e9	+	1.00369e10i	−0.0669015	+	0.115877i
$155$	−6.41879e10	−	1.76355e11i	−0.717455	−	1.97119i
$156$	−1.43598e11	−	6.39608e10i	−1.55426	−	0.692295i
$157$	8.44811e10	−	7.08880e10i	0.885648	−	0.743147i	−0.0816845	−	0.996658i	$-0.526030\pi$
$157$	8.44811e10	−	7.08880e10i	0.885648	−	0.743147i	0.967332	+	0.253511i	$0.0815855\pi$
$158$	−1.10457e9	+	3.03478e9i	−0.0112178	+	0.0308206i
$159$	−1.20749e11	−	3.01263e10i	−1.18823	−	0.296456i
$160$	−1.96322e10	+	1.11340e11i	−0.187228	+	1.06182i
$161$		−	1.06523e11i		−	0.984725i
$162$	1.43668e10	+	3.23229e10i	0.128761	+	0.289691i
$163$	1.22297e11			1.06286			0.531430	−	0.847102i	$-0.321655\pi$
$163$	1.22297e11			1.06286			0.531430	+	0.847102i	$0.321655\pi$
$164$	7.83174e10	+	1.38095e10i	0.660145	+	0.116401i
$165$	1.70098e10	−	6.81772e10i	0.139085	−	0.557467i
$166$	−5.09657e10	−	1.85500e10i	−0.404331	−	0.147165i
$167$	−7.41669e10	−	8.83886e10i	−0.570989	−	0.680478i	0.400845	−	0.916146i	$-0.368717\pi$
$167$	−7.41669e10	−	8.83886e10i	−0.570989	−	0.680478i	−0.971834	+	0.235668i	$0.924272\pi$
$168$	3.14107e10	−	7.05198e10i	0.234710	−	0.526944i
$169$	−3.33974e11	+	1.21556e11i	−2.42258	+	0.881748i
$170$	4.51404e9	+	2.60618e9i	0.0317922	+	0.0183552i
$171$	1.20208e11	−	7.50621e10i	0.822156	−	0.513382i
$172$	5.18639e10	+	8.98309e10i	0.344527	+	0.596738i
$173$	−1.95267e11	+	2.32710e11i	−1.26008	+	1.50170i	−0.478234	+	0.878232i	$0.658723\pi$
$173$	−1.95267e11	+	2.32710e11i	−1.26008	+	1.50170i	−0.781845	+	0.623472i	$0.785721\pi$
$174$	2.95532e10	−	4.37996e10i	0.185293	−	0.274615i
$175$	−1.91261e10	−	1.08470e11i	−0.116530	−	0.660873i
$176$	5.19225e10	−	9.15534e9i	0.307463	−	0.0542140i
$177$	2.40851e11	−	1.17424e11i	1.38638	−	0.675912i
$178$	4.71678e10	+	3.95785e10i	0.263965	+	0.221493i
$179$	2.29281e11	−	1.32375e11i	1.24768	−	0.720348i	0.277033	−	0.960860i	$-0.410649\pi$
$179$	2.29281e11	−	1.32375e11i	1.24768	−	0.720348i	0.970646	+	0.240512i	$0.0773154\pi$
$180$	−3.09157e10	+	2.19477e11i	−0.163613	+	1.16152i
$181$	1.37071e11	−	2.37413e11i	0.705588	−	1.22211i	−0.260891	−	0.965368i	$-0.584016\pi$
$181$	1.37071e11	−	2.37413e11i	0.705588	−	1.22211i	0.966479	−	0.256746i	$-0.0826505\pi$
$182$	−3.92336e10	−	1.07793e11i	−0.196472	−	0.539803i
$183$	1.63006e10	+	1.55324e11i	0.0794231	+	0.756803i
$184$	1.00009e11	−	8.39175e10i	0.474187	−	0.397890i
$185$	−9.45865e10	+	2.59874e11i	−0.436486	+	1.19924i
$186$	−7.88754e10	+	8.16522e10i	−0.354304	+	0.366778i
$187$	1.55358e9	−	8.81078e9i	0.00679399	−	0.0385307i
$188$			2.18255e11i			0.929342i
$189$	8.66427e10	−	2.14158e11i	0.359272	−	0.888025i
$190$	−9.92184e10			−0.400705
$191$	−4.42635e11	−	7.80484e10i	−1.74132	−	0.307042i	−0.789512	−	0.613736i	$-0.789666\pi$
$191$	−4.42635e11	−	7.80484e10i	−1.74132	−	0.307042i	−0.951808	+	0.306694i	$0.900777\pi$
$192$	−1.11989e11	+	3.20932e10i	−0.429208	+	0.123000i
$193$	−7.92276e10	−	2.88365e10i	−0.295863	−	0.107685i	0.189824	−	0.981818i	$-0.439208\pi$
$193$	−7.92276e10	−	2.88365e10i	−0.295863	−	0.107685i	−0.485687	+	0.874133i	$0.661430\pi$
$194$	4.11120e10	+	4.89954e10i	0.149610	+	0.178298i
$195$	4.08708e11	+	5.62724e11i	1.44957	+	1.99583i
$196$	2.01307e10	−	7.32697e9i	0.0695951	−	0.0253305i
$197$	3.58667e11	+	2.07077e11i	1.20882	+	0.697911i	0.962501	−	0.271278i	$-0.0874464\pi$
$197$	3.58667e11	+	2.07077e11i	1.20882	+	0.697911i	0.246317	+	0.969189i	$0.420780\pi$
$198$	−4.15799e10	+	8.82444e9i	−0.136634	+	0.0289976i
$199$	−2.60376e9	−	4.50985e9i	−0.00834326	−	0.0144510i	0.861824	−	0.507208i	$-0.169322\pi$
$199$	−2.60376e9	−	4.50985e9i	−0.00834326	−	0.0144510i	−0.870167	+	0.492757i	$0.835989\pi$
$200$	8.67691e10	−	1.03407e11i	0.271153	−	0.323148i
$201$	−4.61640e11	−	3.23538e10i	−1.40709	−	0.0986154i
$202$	−6.79982e9	−	3.85637e10i	−0.0202181	−	0.114663i
$203$	−3.39848e11	+	5.99244e10i	−0.985836	+	0.173830i
$204$	−1.97299e9	+	2.81516e10i	−0.00558436	+	0.0796804i
$205$	−2.69527e11	−	2.26160e11i	−0.744445	−	0.624663i
$206$	5.32977e10	−	3.07714e10i	0.143672	−	0.0829491i
$207$	2.90416e11	−	2.61327e11i	0.764133	−	0.687595i
$208$	−2.60922e11	+	4.51931e11i	−0.670185	+	1.16079i
$209$	5.82468e10	+	1.60032e11i	0.146063	+	0.401305i
$210$	−1.30864e11	+	9.50470e10i	−0.320424	+	0.232725i
$211$	−5.56689e10	+	4.67117e10i	−0.133107	+	0.111690i	−0.706911	−	0.707303i	$-0.749912\pi$
$211$	−5.56689e10	+	4.67117e10i	−0.133107	+	0.111690i	0.573804	+	0.818993i	$0.305467\pi$
$212$	−1.61341e11	+	4.43280e11i	−0.376760	+	1.03514i
$213$	1.39299e11	+	4.86082e11i	0.317724	+	1.10869i
$214$	−1.38818e10	+	7.87273e10i	−0.0309297	+	0.175411i
$215$		−	4.58919e11i		−	0.998950i
$216$	2.69317e11	−	8.73664e10i	0.572790	−	0.185813i
$217$	7.41466e11			1.54097
$218$	4.24399e10	+	7.48329e9i	0.0861969	+	0.0151988i
$219$	5.66111e9	+	5.46859e9i	0.0112378	+	0.0108556i
$220$	−2.50284e11	−	9.10958e10i	−0.485645	−	0.176760i
$221$	5.69203e10	+	6.78350e10i	0.107971	+	0.128674i
$222$	1.66378e11	−	1.74607e10i	0.308555	−	0.0323815i
$223$	2.56481e11	−	9.33515e10i	0.465084	−	0.169277i	−0.0988402	−	0.995103i	$-0.531513\pi$
$223$	2.56481e11	−	9.33515e10i	0.465084	−	0.169277i	0.563924	+	0.825827i	$0.309291\pi$
$224$	−3.86830e11	−	2.23337e11i	−0.685931	−	0.396022i
$225$	2.48802e11	−	3.18246e11i	0.431460	−	0.551887i
$226$	7.87186e10	+	1.36345e11i	0.133517	+	0.231257i
$227$	5.97259e10	−	7.11786e10i	0.0990909	−	0.118092i	−0.714220	−	0.699921i	$-0.753218\pi$
$227$	5.97259e10	−	7.11786e10i	0.0990909	−	0.118092i	0.813311	+	0.581829i	$0.197663\pi$
$228$	−2.35411e11	−	4.82856e11i	−0.382078	−	0.783688i
$229$	−1.86324e11	−	1.05670e12i	−0.295864	−	1.67793i	−0.663671	−	0.748025i	$-0.731002\pi$
$229$	−1.86324e11	−	1.05670e12i	−0.295864	−	1.67793i	0.367807	−	0.929902i	$-0.380109\pi$
$230$	−2.69364e11	+	4.74961e10i	−0.418504	+	0.0737936i
$231$	2.30128e11	+	1.55276e11i	0.349873	+	0.236072i
$232$	−3.23988e11	−	2.71858e11i	−0.482046	−	0.404485i
$233$	−3.90677e11	+	2.25557e11i	−0.568903	+	0.328456i	−0.756711	−	0.653750i	$-0.773195\pi$
$233$	−3.90677e11	+	2.25557e11i	−0.568903	+	0.328456i	0.187808	+	0.982206i	$0.439862\pi$
$234$	1.97630e11	−	3.71406e11i	0.281691	−	0.529383i
$235$	4.82809e11	−	8.36250e11i	0.673653	−	1.16680i
$236$	−3.47377e11	−	9.54409e11i	−0.474505	−	1.30369i
$237$	7.06665e10	+	3.14760e10i	0.0945087	+	0.0420957i
$238$	−1.57753e10	+	1.32371e10i	−0.0206583	+	0.0173344i
$239$	−3.40143e11	+	9.34536e11i	−0.436187	+	1.19841i	0.505767	+	0.862670i	$0.331210\pi$
$239$	−3.40143e11	+	9.34536e11i	−0.436187	+	1.19841i	−0.941954	+	0.335743i	$0.891013\pi$
$240$	7.13897e11	+	1.78114e11i	0.896560	+	0.223687i
$241$	−4.66091e10	+	2.64333e11i	−0.0573305	+	0.325137i	−0.999962	−	0.00869729i	$-0.997232\pi$
$241$	−4.66091e10	+	2.64333e11i	−0.0573305	+	0.325137i	0.942632	+	0.333834i	$0.108343\pi$
$242$			2.12045e11i			0.255477i
$243$	7.96418e11	−	2.89165e11i	0.939961	−	0.341283i
$244$	5.91986e11			0.684483
$245$	−9.33394e10	−	1.64583e10i	−0.105739	−	0.0186446i
$246$	−5.15222e10	+	2.06506e11i	−0.0571898	+	0.229223i
$247$	−1.58396e12	−	5.76513e11i	−1.72289	−	0.627082i
$248$	5.84117e11	+	6.96124e11i	0.622646	+	0.742041i
$249$	−5.28605e11	+	1.18676e12i	−0.552248	+	1.23985i
$250$	1.13611e11	−	4.13510e10i	0.116338	−	0.0423434i
$251$	9.74308e11	+	5.62517e11i	0.977975	+	0.564634i	0.901658	−	0.432449i	$-0.142351\pi$
$251$	9.74308e11	+	5.62517e11i	0.977975	+	0.564634i	0.0763169	+	0.997084i	$0.475684\pi$
$252$	−7.73051e11	−	4.11350e11i	−0.760686	−	0.404770i
$253$	2.34739e11	+	4.06581e11i	0.226456	+	0.392233i
$254$	−1.68430e11	+	2.00728e11i	−0.159313	+	0.189862i
$255$	6.98345e10	−	1.03499e11i	0.0647693	−	0.0959919i
$256$	2.66340e10	+	1.51049e11i	0.0242235	+	0.137378i
$257$	−1.61231e12	+	2.84294e11i	−1.43808	+	0.253572i	−0.837695	−	0.546139i	$-0.816097\pi$
$257$	−1.61231e12	+	2.84294e11i	−1.43808	+	0.253572i	−0.600385	+	0.799711i	$0.704986\pi$
$258$	−2.49533e11	+	1.21657e11i	−0.218288	+	0.106424i
$259$	−8.36992e11	−	7.02320e11i	−0.718162	−	0.602610i
$260$	2.28304e12	−	1.31811e12i	1.92153	−	1.10940i
$261$	−9.97102e11	−	7.79526e11i	−0.823260	−	0.643618i
$262$	−1.46763e11	+	2.54201e11i	−0.118880	+	0.205907i
$263$	−3.83886e11	−	1.05472e12i	−0.305087	−	0.838220i	−0.993596	−	0.112992i	$-0.963957\pi$
$263$	−3.83886e11	−	1.05472e12i	−0.305087	−	0.838220i	0.688509	−	0.725228i	$-0.258266\pi$
$264$	3.55115e10	+	3.38380e11i	0.0276917	+	0.263867i
$265$	1.59877e12	−	1.34153e12i	1.22337	−	1.02653i
$266$	1.34071e11	−	3.68357e11i	0.100676	−	0.276605i
$267$	1.02472e12	−	1.06080e12i	0.755179	−	0.781766i
$268$	−3.04602e11	+	1.72748e12i	−0.220322	+	1.24951i
$269$			4.74835e11i			0.337118i	0.985692	+	0.168559i	$0.0539113\pi$
$269$			4.74835e11i			0.337118i	−0.985692	+	0.168559i	$0.946089\pi$
$270$	−5.80170e11	−	1.23604e11i	−0.404330	−	0.0861420i
$271$	9.85383e11			0.674154			0.337077	−	0.941477i	$-0.390562\pi$
$271$	9.85383e11			0.674154			0.337077	+	0.941477i	$0.390562\pi$
$272$	9.22595e10	+	1.62678e10i	0.0619679	+	0.0109266i
$273$	−2.64144e12	+	7.56971e11i	−1.74191	+	0.499190i
$274$	4.44922e11	+	1.61938e11i	0.288092	+	0.104857i
$275$	3.12030e11	+	3.71862e11i	0.198396	+	0.236439i
$276$	−8.70251e11	−	1.19819e12i	−0.543374	−	0.748137i
$277$	−1.23505e12	+	4.49522e11i	−0.757332	+	0.275646i	−0.691688	−	0.722197i	$-0.743133\pi$
$277$	−1.23505e12	+	4.49522e11i	−0.757332	+	0.275646i	−0.0656445	+	0.997843i	$0.520910\pi$
$278$	2.62956e11	+	1.51818e11i	0.158365	+	0.0914321i
$279$	1.81900e12	+	2.02147e12i	1.07600	+	1.19577i
$280$	6.47316e11	+	1.12118e12i	0.376120	+	0.651459i
$281$	−2.98197e11	+	3.55378e11i	−0.170205	+	0.202842i	−0.844403	−	0.535708i	$-0.820045\pi$
$281$	−2.98197e11	+	3.55378e11i	−0.170205	+	0.202842i	0.674198	+	0.738550i	$0.264489\pi$
$282$	−5.82693e11	−	4.08377e10i	−0.326734	−	0.0228990i
$283$	2.26890e11	+	1.28676e12i	0.124993	+	0.708868i	0.981312	+	0.192422i	$0.0616342\pi$
$283$	2.26890e11	+	1.28676e12i	0.124993	+	0.708868i	−0.856320	+	0.516446i	$0.827255\pi$
$284$	1.88753e12	−	3.32823e11i	1.02165	−	0.180145i
$285$	−1.66159e11	+	2.37083e12i	−0.0883687	+	1.26089i
$286$	3.87286e11	+	3.24972e11i	0.202396	+	0.169830i
$287$	1.20384e12	−	6.95037e11i	0.618243	−	0.356943i
$288$	−3.40101e11	−	1.60252e12i	−0.171650	−	0.808800i
$289$	−1.00005e12	+	1.73213e12i	−0.496057	+	0.859196i
$290$	3.03060e11	+	8.32651e11i	0.147754	+	0.405950i
$291$	1.23960e12	−	9.00324e11i	0.594040	−	0.431453i
$292$	2.28550e10	−	1.91776e10i	0.0107663	−	0.00903402i
$293$	3.98373e11	−	1.09452e12i	0.184481	−	0.506858i	−0.812633	−	0.582776i	$-0.801967\pi$
$293$	3.98373e11	−	1.09452e12i	0.184481	−	0.506858i	0.997114	+	0.0759181i	$0.0241888\pi$
$294$	1.57947e10	+	5.51154e10i	0.00719078	+	0.0250921i
$295$	−7.80297e11	+	4.42528e12i	−0.349261	+	1.98076i
$296$		−	1.33909e12i		−	0.589318i
$297$	1.41228e11	+	1.00833e12i	0.0611137	+	0.436337i
$298$	7.15208e11			0.304334
$299$	−4.57619e12	−	8.06906e11i	−1.91491	−	0.337650i
$300$	−1.10129e12	−	1.06383e12i	−0.453204	−	0.437792i
$301$	1.70377e12	+	6.20123e11i	0.689572	+	0.250984i
$302$	2.09609e11	+	2.49803e11i	0.0834403	+	0.0994403i
$303$	−9.32871e11	+	9.79006e10i	−0.365265	+	0.0383330i
$304$	−1.67573e12	+	6.09915e11i	−0.645410	+	0.234910i
$305$	−2.26821e12	−	1.30955e12i	−0.859377	−	0.496161i
$306$	−7.47892e10	−	1.05349e10i	−0.0278761	−	0.00392665i
$307$	4.75877e11	+	8.24244e11i	0.174503	+	0.302248i	0.939989	−	0.341204i	$-0.110835\pi$
$307$	4.75877e11	+	8.24244e11i	0.174503	+	0.302248i	−0.765486	+	0.643452i	$0.777501\pi$
$308$	6.76401e11	−	8.06103e11i	0.244034	−	0.290829i
$309$	−6.46029e11	−	1.32508e12i	−0.229329	−	0.470382i
$310$	−3.30602e11	−	1.87494e12i	−0.115477	−	0.654904i
$311$	2.37003e12	−	4.17900e11i	0.814614	−	0.143638i	0.249207	−	0.968450i	$-0.419830\pi$
$311$	2.37003e12	−	4.17900e11i	0.814614	−	0.143638i	0.565407	+	0.824812i	$0.308719\pi$
$312$	−2.79157e12	−	1.88357e12i	−0.944224	−	0.637103i
$313$	−1.53320e11	−	1.28651e11i	−0.0510361	−	0.0428243i	0.616913	−	0.787031i	$-0.288383\pi$
$313$	−1.53320e11	−	1.28651e11i	−0.0510361	−	0.0428243i	−0.667949	+	0.744207i	$0.732828\pi$
$314$	9.68880e11	−	5.59383e11i	0.317411	−	0.183257i
$315$	2.05200e12	+	3.28618e12i	0.661645	+	1.05959i
$316$	1.46615e11	−	2.53945e11i	0.0465311	−	0.0805941i
$317$	1.58311e11	+	4.34957e11i	0.0494556	+	0.135878i	0.961961	−	0.273186i	$-0.0880774\pi$
$317$	1.58311e11	+	4.34957e11i	0.0494556	+	0.135878i	−0.912506	+	0.409064i	$0.865855\pi$
$318$	−1.15327e12	−	5.13686e11i	−0.354646	−	0.157965i
$319$	1.16509e12	−	9.77626e11i	0.352700	−	0.295951i
$320$	6.68189e11	−	1.83584e12i	0.199136	−	0.547122i
$321$	1.85795e12	+	4.63548e11i	0.545141	+	0.136010i
$322$	1.87650e11	−	1.06422e12i	0.0542087	−	0.307433i
$323$			3.02605e11i			0.0860723i
$324$	−7.75008e11	−	3.11672e12i	−0.217061	−	0.872917i
$325$	−4.80469e12			−1.32510
$326$	1.22180e12	+	2.15436e11i	0.331827	+	0.0585100i
$327$	2.49887e11	−	1.00157e12i	0.0668351	−	0.267882i
$328$	1.60090e12	+	5.82681e11i	0.421692	+	0.153483i
$329$	2.45224e12	+	2.92247e12i	0.636185	+	0.758176i
$330$	2.90036e11	−	6.51156e11i	0.0741109	−	0.166386i
$331$	2.52288e12	−	9.18253e11i	0.634975	−	0.231112i	−0.00442042	−	0.999990i	$-0.501407\pi$
$331$	2.52288e12	−	9.18253e11i	0.634975	−	0.231112i	0.639395	+	0.768878i	$0.279185\pi$
$332$	4.26471e12	+	2.46223e12i	1.05730	+	0.610434i
$333$	−1.38595e11	−	4.00487e12i	−0.0338474	−	0.978064i
$334$	−5.85257e11	−	1.01369e12i	−0.140804	−	0.243879i
$335$	4.98850e12	−	5.94506e12i	1.18235	−	1.40907i
$336$	−1.62593e12	+	2.40972e12i	−0.379669	+	0.562692i
$337$	−1.82497e11	−	1.03499e12i	−0.0419863	−	0.238116i	0.956591	−	0.291432i	$-0.0941319\pi$
$337$	−1.82497e11	−	1.03499e12i	−0.0419863	−	0.238116i	−0.998578	+	0.0533166i	$0.983021\pi$
$338$	−3.55068e12	+	6.26081e11i	−0.804874	+	0.141921i
$339$	3.38979e12	−	1.65265e12i	0.757137	−	0.369133i
$340$	−3.62540e11	−	3.04207e11i	−0.0797923	−	0.0669537i
$341$	−2.83005e12	+	1.63393e12i	−0.613793	+	0.354374i
$342$	1.33317e12	−	5.38147e11i	0.284940	−	0.115019i
$343$	2.46119e12	−	4.26290e12i	0.518411	−	0.897914i
$344$	7.60009e11	+	2.08811e12i	0.157771	+	0.433472i
$345$	6.83826e11	+	6.51601e12i	0.139911	+	1.33317i
$346$	−2.36074e12	+	1.98090e12i	−0.476067	+	0.399468i
$347$	−1.44397e12	+	3.96727e12i	−0.287019	+	0.788578i	0.709461	+	0.704745i	$0.248938\pi$
$347$	−1.44397e12	+	3.96727e12i	−0.287019	+	0.788578i	−0.996480	+	0.0838331i	$0.973284\pi$
$348$	−3.33312e12	+	3.45046e12i	−0.653062	+	0.676053i
$349$	1.56302e12	−	8.86431e12i	0.301881	−	1.71205i	−0.335951	−	0.941879i	$-0.609058\pi$
$349$	1.56302e12	−	8.86431e12i	0.301881	−	1.71205i	0.637832	−	0.770175i	$-0.279831\pi$
$350$		−	1.11735e12i		−	0.212740i
$351$	−8.54382e12	−	5.34436e12i	−1.60368	−	1.00314i
$352$	1.96862e12			0.364291
$353$	−4.68733e12	−	8.26502e11i	−0.855169	−	0.150789i	−0.271158	−	0.962535i	$-0.587406\pi$
$353$	−4.68733e12	−	8.26502e11i	−0.855169	−	0.150789i	−0.584011	+	0.811746i	$0.698518\pi$
$354$	2.61306e12	−	7.48839e11i	0.470038	−	0.134701i
$355$	−7.96836e12	−	2.90025e12i	−1.41328	−	0.514391i
$356$	−3.59358e12	−	4.28266e12i	−0.628459	−	0.748968i
$357$	2.89883e11	+	3.99121e11i	0.0499898	+	0.0688277i
$358$	2.52381e12	−	9.18593e11i	0.429183	−	0.156210i
$359$	−6.94809e12	−	4.01148e12i	−1.16518	−	0.672718i	−0.212641	−	0.977130i	$-0.568206\pi$
$359$	−6.94809e12	−	4.01148e12i	−1.16518	−	0.672718i	−0.952540	+	0.304413i	$0.901540\pi$
$360$	−1.46869e12	+	4.51533e12i	−0.242894	+	0.746753i
$361$	1.85458e11	+	3.21224e11i	0.0302490	+	0.0523928i
$362$	1.78762e12	−	2.13040e12i	0.287563	−	0.342704i
$363$	5.06684e12	+	3.55107e11i	0.803903	+	0.0563412i
$364$	1.80860e12	+	1.02571e13i	0.283033	+	1.60516i
$365$	−1.29993e11	+	2.29213e10i	−0.0200658	+	0.00353814i
$366$	−1.10767e11	+	1.58047e12i	−0.0168657	+	0.240647i
$367$	6.31275e12	+	5.29702e12i	0.948174	+	0.795613i	0.978989	−	0.203912i	$-0.0653658\pi$
$367$	6.31275e12	+	5.29702e12i	0.948174	+	0.795613i	−0.0308149	+	0.999525i	$0.509810\pi$
$368$	−4.25739e12	+	2.45801e12i	−0.630818	+	0.364203i
$369$	4.84820e12	+	1.57696e12i	0.708678	+	0.230509i
$370$	−1.40275e12	+	2.42964e12i	−0.202289	+	0.350375i
$371$	2.82017e12	+	7.74835e12i	0.401241	+	1.10240i
$372$	8.34015e12	−	6.05747e12i	1.17074	−	0.850309i
$373$	2.38443e12	−	2.00077e12i	0.330248	−	0.277111i	−0.462553	−	0.886592i	$-0.653066\pi$
$373$	2.38443e12	−	2.00077e12i	0.330248	−	0.277111i	0.792801	+	0.609481i	$0.208622\pi$
$374$	3.10419e10	−	8.52869e10i	0.00424219	−	0.0116553i
$375$	−7.97824e11	−	2.78399e12i	−0.107585	−	0.375415i
$376$	−8.11908e11	+	4.60456e12i	−0.108036	+	0.612701i
$377$			1.50537e13i			1.97667i
$378$	1.24286e12	−	1.98691e12i	0.161051	−	0.257465i
$379$	−1.54124e12			−0.197094			−0.0985471	−	0.995132i	$-0.531419\pi$
$379$	−1.54124e12			−0.197094			−0.0985471	+	0.995132i	$0.531419\pi$
$380$	8.87178e12	+	1.56434e12i	1.11968	+	0.197429i
$381$	4.51433e12	+	4.36081e12i	0.562301	+	0.543178i
$382$	−4.28463e12	−	1.55948e12i	−0.526740	−	0.191718i
$383$	−4.62166e12	−	5.50788e12i	−0.560795	−	0.668330i	0.408919	−	0.912571i	$-0.365906\pi$
$383$	−4.62166e12	−	5.50788e12i	−0.560795	−	0.668330i	−0.969715	+	0.244241i	$0.921461\pi$
$384$	−8.04106e12	+	8.43874e11i	−0.963069	+	0.101070i
$385$	−4.37485e12	+	1.59232e12i	−0.517201	+	0.188246i
$386$	−7.40722e11	−	4.27656e11i	−0.0864408	−	0.0499066i
$387$	2.48911e12	+	6.16634e12i	0.286741	+	0.710351i
$388$	−2.90361e12	−	5.02920e12i	−0.330202	−	0.571927i
$389$	−2.57745e12	+	3.07168e12i	−0.289362	+	0.344849i	−0.891068	−	0.453869i	$-0.850043\pi$
$389$	−2.57745e12	+	3.07168e12i	−0.289362	+	0.344849i	0.601706	+	0.798718i	$0.294488\pi$
$390$	3.09189e12	+	6.34185e12i	0.342690	+	0.702899i
$391$	1.44858e11	+	8.21529e11i	0.0158510	+	0.0898957i
$392$	4.51956e11	−	7.96921e10i	0.0488277	−	0.00860964i
$393$	5.82837e12	+	3.93261e12i	0.621705	+	0.419487i
$394$	3.21847e12	+	2.70061e12i	0.338975	+	0.284434i
$395$	−1.12352e12	+	6.48663e11i	−0.116841	+	0.0674580i
$396$	3.85707e12	−	1.33480e11i	0.396079	−	0.0137069i
$397$	3.02106e12	−	5.23262e12i	0.306342	−	0.530600i	−0.671217	−	0.741261i	$-0.734228\pi$
$397$	3.02106e12	−	5.23262e12i	0.306342	−	0.530600i	0.977559	+	0.210661i	$0.0675616\pi$
$398$	−1.80683e10	−	4.96422e10i	−0.00180926	−	0.00497090i
$399$	−8.57739e12	−	3.82051e12i	−0.848185	−	0.377796i
$400$	−3.89385e12	+	3.26733e12i	−0.380259	+	0.319075i
$401$	−1.63980e12	+	4.50531e12i	−0.158150	+	0.434513i	−0.993308	−	0.115497i	$-0.963154\pi$
$401$	−1.63980e12	+	4.50531e12i	−0.158150	+	0.434513i	0.835158	+	0.550010i	$0.185376\pi$
$402$	−4.55500e12	−	1.13645e12i	−0.433868	−	0.108248i
$403$	5.61656e12	−	3.18531e13i	0.528378	−	2.99658i
$404$			3.55545e12i			0.330360i
$405$	−3.92513e12	+	1.36562e13i	−0.360230	+	1.25330i
$406$	−3.50080e12			−0.317349
$407$	4.74232e12	+	8.36199e11i	0.424638	+	0.0748751i
$408$	−1.46348e11	+	5.86578e11i	−0.0129445	+	0.0518830i
$409$	1.15109e13	+	4.18961e12i	1.00575	+	0.366064i	0.791800	−	0.610780i	$-0.209144\pi$
$409$	1.15109e13	+	4.18961e12i	1.00575	+	0.366064i	0.213952	+	0.976844i	$0.431366\pi$
$410$	−2.29429e12	−	2.73423e12i	−0.198029	−	0.236002i
$411$	4.61463e12	−	1.03602e13i	0.393484	−	0.883407i
$412$	−5.25086e12	+	1.91116e12i	−0.442328	+	0.160994i
$413$	−1.53748e13	−	8.87667e12i	−1.27956	−	0.738754i
$414$	3.36174e12	−	2.09918e12i	0.276416	−	0.172603i
$415$	−1.08936e13	−	1.88682e13i	−0.884972	−	1.53282i
$416$	−1.25247e13	+	1.49263e13i	−1.00531	+	1.19808i
$417$	4.06806e12	−	6.02911e12i	0.322632	−	0.478160i
$418$	3.00002e11	+	1.70140e12i	0.0235095	+	0.133329i
$419$	1.37363e13	−	2.42209e12i	1.06366	−	0.187551i	0.385678	−	0.922633i	$-0.373968\pi$
$419$	1.37363e13	−	2.42209e12i	1.06366	−	0.187551i	0.677978	+	0.735082i	$0.262856\pi$
$420$	1.32000e13	−	6.43551e12i	1.01002	−	0.492421i
$421$	−3.46784e12	−	2.90986e12i	−0.262210	−	0.220020i	0.502199	−	0.864752i	$-0.332525\pi$
$421$	−3.46784e12	−	2.90986e12i	−0.262210	−	0.220020i	−0.764409	+	0.644732i	$0.776969\pi$
$422$	−6.38444e11	+	3.68606e11i	−0.0477046	+	0.0275423i
$423$	−1.95164e12	+	1.38551e13i	−0.144111	+	1.02308i
$424$	−5.05282e12	+	8.75175e12i	−0.368727	+	0.638654i
$425$	2.95009e11	+	8.10531e11i	0.0212760	+	0.0584554i
$426$	5.35386e11	+	5.10156e12i	0.0381610	+	0.363626i
$427$	7.92677e12	−	6.65135e12i	0.558415	−	0.468566i
$428$	2.48252e12	−	6.82067e12i	0.172852	−	0.474907i
$429$	8.41380e12	−	8.71001e12i	0.579037	−	0.599422i
$430$	8.08425e11	−	4.58481e12i	0.0549918	−	0.311874i
$431$			3.63360e12i			0.244316i	0.992511	+	0.122158i	$0.0389814\pi$
$431$			3.63360e12i			0.244316i	−0.992511	+	0.122158i	$0.961019\pi$
$432$	−1.05585e13	+	1.47883e12i	−0.701750	+	0.0982876i
$433$	−2.75243e13			−1.80832			−0.904162	−	0.427189i	$-0.859504\pi$
$433$	−2.75243e13			−1.80832			−0.904162	+	0.427189i	$0.859504\pi$
$434$	7.40759e12	+	1.30616e12i	0.481092	+	0.0848295i
$435$	2.04038e13	−	5.84723e12i	1.30998	−	0.375408i
$436$	−3.67685e12	−	1.33826e12i	−0.233369	−	0.0849393i
$437$	−1.02070e13	−	1.21642e13i	−0.640456	−	0.763266i
$438$	4.69237e10	+	6.46062e10i	0.00291086	+	0.00400778i
$439$	2.19176e13	−	7.97734e12i	1.34422	−	0.489255i	0.433079	−	0.901356i	$-0.357427\pi$
$439$	2.19176e13	−	7.97734e12i	1.34422	−	0.489255i	0.911138	+	0.412101i	$0.135205\pi$
$440$	−4.94139e12	−	2.85291e12i	−0.299630	−	0.172992i
$441$	1.34344e12	−	2.85116e11i	0.0805425	−	0.0170934i
$442$	4.49162e11	+	7.77972e11i	0.0266252	+	0.0461161i
$443$	−1.17695e13	+	1.40264e13i	−0.689828	+	0.822105i	−0.991335	−	0.131359i	$-0.958066\pi$
$443$	−1.17695e13	+	1.40264e13i	−0.689828	+	0.822105i	0.301507	+	0.953464i	$0.402510\pi$
$444$	−1.51523e13	−	1.06194e12i	−0.878140	−	0.0615440i
$445$	4.29507e12	+	2.43586e13i	0.246133	+	1.39589i
$446$	2.72681e12	−	4.80810e11i	0.154519	−	0.0272458i
$447$	1.19774e12	−	1.70900e13i	0.0671159	−	0.957642i
$448$	5.91279e12	+	4.96142e12i	0.327644	+	0.274926i
$449$	1.63500e13	−	9.43966e12i	0.895953	−	0.517279i	0.0200679	−	0.999799i	$-0.493612\pi$
$449$	1.63500e13	−	9.43966e12i	0.895953	−	0.517279i	0.875885	+	0.482520i	$0.160278\pi$
$450$	3.04626e12	−	2.74113e12i	0.165084	−	0.148548i
$451$	−3.06323e12	+	5.30567e12i	−0.164171	+	0.284353i
$452$	−4.88907e12	−	1.34326e13i	−0.259140	−	0.711980i
$453$	6.32008e12	−	4.59029e12i	0.331308	−	0.240630i
$454$	7.22076e11	−	6.05894e11i	0.0374372	−	0.0314136i
$455$	1.57604e13	−	4.33012e13i	0.808181	−	2.22046i
$456$	−3.17027e12	−	1.10626e13i	−0.160795	−	0.561091i
$457$	−6.34401e12	+	3.59786e13i	−0.318260	+	1.80494i	0.235066	+	0.971980i	$0.424470\pi$
$457$	−6.34401e12	+	3.59786e13i	−0.318260	+	1.80494i	−0.553326	+	0.832965i	$0.686642\pi$
$458$		−	1.08851e13i		−	0.540139i
$459$	−3.76979e11	+	1.76945e12i	−0.0185035	+	0.0868511i
$460$	2.48345e13			1.20577
$461$	1.35602e13	+	2.39103e12i	0.651270	+	0.114836i	0.489516	−	0.871995i	$-0.337174\pi$
$461$	1.35602e13	+	2.39103e12i	0.651270	+	0.114836i	0.161754	+	0.986831i	$0.448285\pi$
$462$	2.02556e12	+	1.95667e12i	0.0962353	+	0.0929625i
$463$	1.64814e13	+	5.99872e12i	0.774619	+	0.281938i	0.698927	−	0.715193i	$-0.253661\pi$
$463$	1.64814e13	+	5.99872e12i	0.774619	+	0.281938i	0.0756918	+	0.997131i	$0.475883\pi$
$464$	1.02369e13	+	1.21999e13i	0.475970	+	0.567239i
$465$	−4.53554e13	+	4.75985e12i	−2.08624	+	0.218942i
$466$	−4.30038e12	+	1.56521e12i	−0.195694	+	0.0712267i
$467$	−1.20289e13	−	6.94489e12i	−0.541554	−	0.312666i	0.204155	−	0.978939i	$-0.434555\pi$
$467$	−1.20289e13	−	6.94489e12i	−0.541554	−	0.312666i	−0.745708	+	0.666272i	$0.767889\pi$
$468$	−2.35272e13	+	3.00940e13i	−1.04795	+	1.34045i
$469$	1.53307e13	+	2.65536e13i	0.675614	+	1.17020i
$470$	6.29661e12	−	7.50400e12i	0.274547	−	0.327193i
$471$	−1.17439e13	−	2.40882e13i	−0.506652	−	1.03920i
$472$	−3.77825e12	−	2.14275e13i	−0.161280	−	0.914665i
$473$	−7.86954e12	+	1.38761e12i	−0.332387	+	0.0586088i
$474$	6.50542e11	+	4.38945e11i	0.0271884	+	0.0183450i
$475$	−1.25775e13	−	1.05538e13i	−0.520148	−	0.436456i
$476$	1.61928e12	−	9.34893e11i	0.0662656	−	0.0382584i
$477$	−1.42059e13	+	2.66972e13i	−0.575277	+	1.08112i
$478$	−5.04445e12	+	8.73725e12i	−0.202150	+	0.350135i
$479$	1.49020e13	+	4.09429e13i	0.590972	+	1.62368i	0.768706	+	0.639603i	$0.220901\pi$
$479$	1.49020e13	+	4.09429e13i	0.590972	+	1.62368i	−0.177734	+	0.984079i	$0.556877\pi$
$480$	2.50961e13	+	1.11782e13i	0.984916	+	0.438698i
$481$	−3.65115e13	+	3.06368e13i	−1.41809	+	1.18992i
$482$	−9.31292e11	+	2.55870e12i	−0.0357973	+	0.0983523i
$483$	−2.51153e13	−	6.26612e12i	−0.955437	−	0.238376i
$484$	3.34323e12	−	1.89604e13i	0.125875	−	0.713872i
$485$			2.56927e13i			0.957416i
$486$	8.46597e12	−	1.48593e12i	0.312245	−	0.0548046i
$487$	1.25305e13			0.457429			0.228714	−	0.973494i	$-0.426548\pi$
$487$	1.25305e13			0.457429			0.228714	+	0.973494i	$0.426548\pi$
$488$	1.24892e13	+	2.20218e12i	0.451269	+	0.0795710i
$489$	7.19398e12	−	2.88342e13i	0.257291	−	1.03125i
$490$	−9.03511e11	−	3.28851e11i	−0.0319855	−	0.0116418i
$491$	9.59230e12	+	1.14317e13i	0.336136	+	0.400592i	0.907464	−	0.420131i	$-0.138016\pi$
$491$	9.59230e12	+	1.14317e13i	0.336136	+	0.400592i	−0.571327	+	0.820722i	$0.693571\pi$
$492$	7.86284e12	−	1.76528e13i	0.272743	−	0.612333i
$493$	2.53949e12	−	9.24299e11i	0.0871991	−	0.0317379i
$494$	−1.48089e13	−	8.54990e12i	−0.503370	−	0.290621i
$495$	−1.50737e13	−	8.02091e12i	−0.507218	−	0.269897i
$496$	−1.71092e13	−	2.96340e13i	−0.569930	−	0.987148i
$497$	2.15348e13	−	2.56642e13i	0.710165	−	0.846342i
$498$	−7.37159e12	+	1.09251e13i	−0.240666	+	0.356681i
$499$	9.25634e12	+	5.24953e13i	0.299183	+	1.69675i	0.649698	+	0.760192i	$0.274895\pi$
$499$	9.25634e12	+	5.24953e13i	0.299183	+	1.69675i	−0.350515	+	0.936557i	$0.613994\pi$
$500$	−1.08107e13	+	1.90621e12i	−0.345942	+	0.0609988i
$501$	−2.52024e13	+	1.22871e13i	−0.798461	+	0.389280i
$502$	8.74286e12	+	7.33613e12i	0.274243	+	0.230117i
$503$	6.45379e12	−	3.72610e12i	0.200436	−	0.115722i	−0.396423	−	0.918068i	$-0.629749\pi$
$503$	6.45379e12	−	3.72610e12i	0.200436	−	0.115722i	0.596859	+	0.802346i	$0.296415\pi$
$504$	−1.47789e13	−	1.15540e13i	−0.454454	−	0.355288i
$505$	7.86512e12	−	1.36228e13i	0.239469	−	0.414772i
$506$	1.62893e12	+	4.47544e12i	0.0491076	+	0.134922i
$507$	9.01402e12	+	8.58923e13i	0.269078	+	2.56398i
$508$	1.82253e13	−	1.52928e13i	0.538711	−	0.452032i
$509$	3.42725e12	−	9.41630e12i	0.100313	−	0.275608i	−0.879377	−	0.476126i	$-0.842041\pi$
$509$	3.42725e12	−	9.41630e12i	0.100313	−	0.275608i	0.979690	+	0.200519i	$0.0642627\pi$
$510$	8.80000e11	−	9.10981e11i	0.0255054	−	0.0264033i
$511$	9.05585e10	−	5.13583e11i	0.00259911	−	0.0147403i
$512$			3.56270e13i			1.01258i
$513$	−1.06265e13	−	3.27573e13i	−0.299090	−	0.921980i
$514$	−1.66085e13			−0.462930
$515$	2.43465e13	+	4.29295e12i	0.672049	+	0.118500i
$516$	2.42305e13	−	6.94387e12i	0.662390	−	0.189825i
$517$	−1.57999e13	−	5.75068e12i	−0.427760	−	0.155692i
$518$	−7.12474e12	−	8.49093e12i	−0.191038	−	0.227670i
$519$	4.33803e13	+	5.97275e13i	1.15201	+	1.58613i
$520$	5.30690e13	−	1.93155e13i	1.39580	−	0.508031i
$521$	−8.26731e12	−	4.77314e12i	−0.215365	−	0.124341i	0.388437	−	0.921475i	$-0.373015\pi$
$521$	−8.26731e12	−	4.77314e12i	−0.215365	−	0.124341i	−0.603802	+	0.797134i	$0.706348\pi$
$522$	−8.58830e12	−	9.54430e12i	−0.221592	−	0.246259i
$523$	1.87328e13	+	3.24462e13i	0.478734	+	0.829192i	0.999703	−	0.0243840i	$-0.00776244\pi$
$523$	1.87328e13	+	3.24462e13i	0.478734	+	0.829192i	−0.520969	+	0.853576i	$0.674429\pi$
$524$	1.71309e13	−	2.04158e13i	0.433635	−	0.516786i
$525$	−2.66992e13	−	1.87120e12i	−0.669426	−	0.0469164i
$526$	−1.97722e12	−	1.12134e13i	−0.0491050	−	0.278489i
$527$	−5.71834e12	+	1.00830e12i	−0.140675	+	0.0248048i
$528$	8.95713e11	−	1.27805e13i	0.0218273	−	0.311442i
$529$	−1.79891e12	−	1.50947e12i	−0.0434242	−	0.0364372i
$530$	1.83357e13	−	1.05861e13i	0.438448	−	0.253138i
$531$	−1.35175e13	−	6.36933e13i	−0.320203	−	1.50876i
$532$	−1.77959e13	+	3.08234e13i	−0.417601	+	0.723306i
$533$	−2.07395e13	−	5.69813e13i	−0.482128	−	1.32464i
$534$	1.21061e13	−	8.79272e12i	0.278804	−	0.202496i
$535$	−2.46000e13	+	2.06419e13i	−0.561264	+	0.470956i
$536$	−1.28524e13	+	3.53118e13i	−0.290510	+	0.798171i
$537$	−1.77233e13	−	6.18451e13i	−0.396892	−	1.38495i
$538$	−8.36464e11	+	4.74382e12i	−0.0185582	+	0.105249i
$539$			1.65035e12i			0.0362771i
$540$	4.99281e13	+	2.01996e13i	1.08737	+	0.439920i
$541$	−5.58959e13			−1.20613			−0.603064	−	0.797692i	$-0.706054\pi$
$541$	−5.58959e13			−1.20613			−0.603064	+	0.797692i	$0.706054\pi$
$542$	9.84443e12	+	1.73584e12i	0.210472	+	0.0371119i
$543$	−4.79125e13	−	4.62831e13i	−1.01496	−	0.980445i
$544$	3.28702e12	+	1.19638e12i	0.0689935	+	0.0251116i
$545$	1.11275e13	+	1.32612e13i	0.231428	+	0.275805i
$546$	−2.77226e13	+	2.90936e12i	−0.571309	+	0.0599563i
$547$	1.27180e13	−	4.62899e12i	0.259707	−	0.0945255i	−0.208885	−	0.977940i	$-0.566984\pi$
$547$	1.27180e13	−	4.62899e12i	0.259707	−	0.0945255i	0.468592	+	0.883415i	$0.344761\pi$
$548$	−3.72302e13	−	2.14949e13i	−0.753343	−	0.434943i
$549$	3.75800e13	+	5.29355e12i	0.753520	+	0.106142i
$550$	2.46225e12	+	4.26474e12i	0.0489236	+	0.0847382i
$551$	−3.30663e13	+	3.94069e13i	−0.651070	+	0.775915i
$552$	−1.39025e13	−	2.85158e13i	−0.271268	−	0.556403i
$553$	−8.90040e11	−	5.04767e12i	−0.0172101	−	0.0976034i
$554$	−1.31306e13	+	2.31528e12i	−0.251615	+	0.0443665i
$555$	5.57073e13	+	3.75877e13i	1.05791	+	0.713808i
$556$	−2.11190e13	−	1.77210e13i	−0.397466	−	0.333513i
$557$	3.34073e13	−	1.92877e13i	0.623111	−	0.359753i	−0.154968	−	0.987919i	$-0.549528\pi$
$557$	3.34073e13	−	1.92877e13i	0.623111	−	0.359753i	0.778079	+	0.628166i	$0.216194\pi$
$558$	1.46116e13	+	2.33998e13i	0.270101	+	0.432554i
$559$	3.95462e13	−	6.84960e13i	0.724512	−	1.25489i
$560$	−1.66735e13	−	4.58100e13i	−0.302751	−	0.831802i
$561$	−1.98595e12	−	8.84577e11i	−0.0357400	−	0.0159192i
$562$	−3.60515e12	+	3.02508e12i	−0.0643046	+	0.0539580i
$563$	1.41182e13	−	3.87895e13i	0.249596	−	0.685760i	−0.750105	−	0.661319i	$-0.769997\pi$
$563$	1.41182e13	−	3.87895e13i	0.249596	−	0.685760i	0.999701	−	0.0244411i	$-0.00778061\pi$
$564$	5.14586e13	+	1.28386e13i	0.901701	+	0.224970i
$565$	−1.09821e13	+	6.22826e13i	−0.190741	+	1.08174i
$566$			1.32550e13i			0.228191i
$567$	−4.53959e13	−	3.30256e13i	−0.774642	−	0.563554i
$568$	4.10596e13			0.694501
$569$	−2.30034e13	−	4.05612e12i	−0.385684	−	0.0680064i	−0.0225554	−	0.999746i	$-0.507180\pi$
$569$	−2.30034e13	−	4.05612e12i	−0.385684	−	0.0680064i	−0.363128	+	0.931739i	$0.618291\pi$
$570$	−5.83643e12	+	2.33930e13i	−0.0970002	+	0.388787i
$571$	2.48593e13	+	9.04806e12i	0.409552	+	0.149065i	0.538576	−	0.842577i	$-0.318962\pi$
$571$	2.48593e13	+	9.04806e12i	0.409552	+	0.149065i	−0.129024	+	0.991641i	$0.541185\pi$
$572$	−2.95062e13	−	3.51641e13i	−0.481873	−	0.574274i
$573$	−4.44392e13	+	9.97700e13i	−0.719438	+	1.61520i
$574$	1.32513e13	−	4.82307e12i	0.212666	−	0.0774041i
$575$	−3.91983e13	−	2.26312e13i	−0.623632	−	0.360054i
$576$	9.79078e11	+	2.82917e13i	0.0154420	+	0.446217i
$577$	−2.73120e13	−	4.73057e13i	−0.427046	−	0.739665i	0.569563	−	0.821947i	$-0.307112\pi$
$577$	−2.73120e13	−	4.73057e13i	−0.427046	−	0.739665i	−0.996609	+	0.0822828i	$0.973779\pi$
$578$	−1.30422e13	+	1.55431e13i	−0.202168	+	0.240935i
$579$	−1.14593e13	+	1.69834e13i	−0.176103	+	0.260995i
$580$	−1.39706e13	−	7.92311e13i	−0.212850	−	1.20713i
$581$	8.47699e13	−	1.49472e13i	1.28045	−	0.225777i
$582$	1.39701e13	−	6.81098e12i	0.209212	−	0.101999i
$583$	−2.78387e13	−	2.33594e13i	−0.413339	−	0.346832i
$584$	5.53516e11	−	3.19573e11i	0.00814829	−	0.00470442i
$585$	1.56717e14	−	6.32605e13i	2.28737	−	0.923322i
$586$	5.90802e12	−	1.02330e13i	0.0854976	−	0.148086i
$587$	9.49394e12	+	2.60844e13i	0.136225	+	0.374274i	0.988983	−	0.148032i	$-0.0472939\pi$
$587$	9.49394e12	+	2.60844e13i	0.136225	+	0.374274i	−0.852758	+	0.522306i	$0.825072\pi$
$588$	−5.43332e11	−	5.17727e12i	−0.00772998	−	0.0736570i
$589$	8.46701e13	−	7.10467e13i	1.19441	−	1.00223i
$590$	−1.55910e13	+	4.28360e13i	−0.218080	+	0.599169i
$591$	6.99213e13	−	7.23829e13i	0.969777	−	1.00392i
$592$	−8.75601e12	+	4.96578e13i	−0.120420	+	0.682935i
$593$			9.96408e13i			1.35883i	0.733756	+	0.679413i	$0.237765\pi$
$593$			9.96408e13i			1.35883i	−0.733756	+	0.679413i	$0.762235\pi$
$594$	−3.65335e11	+	1.03225e13i	−0.00494036	+	0.139589i
$595$	−8.27243e12			−0.110930
$596$	−6.39516e13	−	1.12764e13i	−0.850393	−	0.149947i
$597$	−1.21646e12	+	3.48608e11i	−0.0160408	+	0.00459691i
$598$	−4.42968e13	−	1.61227e13i	−0.579250	−	0.210830i
$599$	2.81867e13	+	3.35916e13i	0.365520	+	0.435609i	0.917188	−	0.398454i	$-0.130453\pi$
$599$	2.81867e13	+	3.35916e13i	0.365520	+	0.435609i	−0.551669	+	0.834063i	$0.686009\pi$
$600$	−1.92765e13	−	2.65406e13i	−0.247898	−	0.341314i
$601$	−8.80659e13	+	3.20534e13i	−1.12314	+	0.408791i	−0.835798	−	0.549036i	$-0.814995\pi$
$601$	−8.80659e13	+	3.20534e13i	−1.12314	+	0.408791i	−0.287345	+	0.957827i	$0.592773\pi$
$602$	1.59291e13	+	9.19666e12i	0.201469	+	0.116318i
$603$	−3.47836e13	+	1.06939e14i	−0.436303	+	1.34137i
$604$	−1.48040e13	−	2.56413e13i	−0.184160	−	0.318975i
$605$	−5.47525e13	+	6.52515e13i	−0.675503	+	0.805033i
$606$	−9.49226e12	−	6.65260e11i	−0.116147	−	0.00814008i
$607$	−1.38808e13	−	7.87220e13i	−0.168450	−	0.955328i	−0.945435	−	0.325809i	$-0.894363\pi$
$607$	−1.38808e13	−	7.87220e13i	−0.168450	−	0.955328i	0.776985	−	0.629519i	$-0.216748\pi$
$608$	−6.55732e13	+	1.15623e13i	−0.789238	+	0.139164i
$609$	−5.86270e12	+	8.36519e13i	−0.0699860	+	0.998595i
$610$	−2.03535e13	−	1.70786e13i	−0.240985	−	0.202211i
$611$	1.44124e14	−	8.32097e13i	1.69250	−	0.977165i
$612$	6.52131e12	+	2.12116e12i	0.0759587	+	0.0247068i
$613$	−3.09829e13	+	5.36639e13i	−0.357947	+	0.619983i	−0.987618	−	0.156879i	$-0.949857\pi$
$613$	−3.09829e13	+	5.36639e13i	−0.357947	+	0.619983i	0.629670	+	0.776862i	$0.283190\pi$
$614$	3.30225e12	+	9.07287e12i	0.0378415	+	0.103969i
$615$	−6.91769e13	+	5.02434e13i	−0.786295	+	0.571088i
$616$	1.72688e13	−	1.44903e13i	0.194697	−	0.163370i
$617$	−4.20061e13	+	1.15411e14i	−0.469771	+	1.29069i	0.448163	+	0.893952i	$0.352079\pi$
$617$	−4.20061e13	+	1.15411e14i	−0.469771	+	1.29069i	−0.917934	+	0.396734i	$0.870144\pi$
$618$	−4.11988e12	−	1.43762e13i	−0.0457027	−	0.159479i
$619$	−3.00636e11	+	1.70499e12i	−0.00330817	+	0.0187616i	−0.986417	−	0.164260i	$-0.947477\pi$
$619$	−3.00636e11	+	1.70499e12i	−0.00330817	+	0.0187616i	0.983109	+	0.183021i	$0.0585877\pi$
$620$			1.72863e14i			1.88688i
$621$	−4.45303e13	−	8.38445e13i	−0.482167	−	0.907855i
$622$	2.44138e13			0.262231
$623$	−9.62369e13	−	1.69692e13i	−1.02542	−	0.180809i
$624$	9.12044e13	+	8.81027e13i	0.964035	+	0.931250i
$625$	1.08417e14	+	3.94604e13i	1.13683	+	0.413772i
$626$	−1.30511e12	−	1.55537e12i	−0.0135761	−	0.0161793i
$627$	4.11574e13	−	4.31929e12i	0.424728	−	0.0445733i
$628$	−9.54536e13	+	3.47423e13i	−0.977224	+	0.355680i
$629$	7.41012e12	+	4.27824e12i	0.0752614	+	0.0434522i
$630$	1.47115e13	+	3.64452e13i	0.148237	+	0.367230i
$631$	4.82379e13	+	8.35504e13i	0.482215	+	0.835222i	0.999792	−	0.0204154i	$-0.00649889\pi$
$631$	4.82379e13	+	8.35504e13i	0.482215	+	0.835222i	−0.517576	+	0.855637i	$0.673166\pi$
$632$	4.03783e12	−	4.81210e12i	0.0400463	−	0.0477253i
$633$	7.73868e12	+	1.58730e13i	0.0761462	+	0.156185i
$634$	8.15388e11	+	4.62429e12i	0.00796009	+	0.0451439i
$635$	−1.03660e14	+	1.82781e13i	−1.00402	+	0.177036i
$636$	9.50225e13	+	6.41152e13i	0.913148	+	0.616134i
$637$	−1.25131e13	−	1.04998e13i	−0.119308	−	0.100111i
$638$	1.33619e13	−	7.71452e12i	0.126406	−	0.0729803i
$639$	1.22799e14	−	4.24965e12i	1.15263	−	0.0398886i
$640$	6.77949e13	−	1.17424e14i	0.631390	−	1.09360i
$641$	−4.13375e13	−	1.13574e14i	−0.381992	−	1.04952i	−0.970516	−	0.241035i	$-0.922513\pi$
$641$	−4.13375e13	−	1.13574e14i	−0.381992	−	1.04952i	0.588524	−	0.808480i	$-0.299709\pi$
$642$	1.77452e13	+	7.90399e12i	0.162707	+	0.0724722i
$643$	−3.76309e13	+	3.15761e13i	−0.342365	+	0.287279i	−0.797716	−	0.603034i	$-0.793958\pi$
$643$	−3.76309e13	+	3.15761e13i	−0.342365	+	0.287279i	0.455350	+	0.890312i	$0.349514\pi$
$644$	−3.35581e13	+	9.22000e13i	−0.302948	+	0.832342i
$645$	−1.08201e14	−	2.69954e13i	−0.969239	−	0.241820i
$646$	−5.33065e11	+	3.02316e12i	−0.00473824	+	0.0268719i
$647$		−	1.09289e14i		−	0.963953i	−0.876184	−	0.481976i	$-0.839919\pi$
$647$		−	1.09289e14i		−	0.963953i	0.876184	−	0.481976i	$-0.160081\pi$
$648$	−4.75627e12	−	6.86369e13i	−0.0416286	−	0.600735i
$649$	7.82441e13			0.679561
$650$	−4.80010e13	−	8.46387e12i	−0.413698	−	0.0729461i
$651$	4.36160e13	−	1.74817e14i	0.373028	−	1.49513i
$652$	−1.05852e14	−	3.85272e13i	−0.898386	−	0.326986i
$653$	5.36919e13	+	6.39876e13i	0.452213	+	0.538927i	0.943193	−	0.332244i	$-0.107806\pi$
$653$	5.36919e13	+	6.39876e13i	0.452213	+	0.538927i	−0.490980	+	0.871171i	$0.663361\pi$
$654$	4.26084e12	−	9.56596e12i	0.0356128	−	0.0799539i
$655$	−1.10800e14	+	4.03279e13i	−0.919038	+	0.334502i
$656$	−5.55568e13	−	3.20757e13i	−0.457318	−	0.264033i
$657$	1.62235e12	−	1.01305e12i	0.0132531	−	0.00827569i
$658$	1.93508e13	+	3.35166e13i	0.156881	+	0.271726i
$659$	1.10487e14	−	1.31673e14i	0.888965	−	1.05943i	−0.108896	−	0.994053i	$-0.534731\pi$
$659$	1.10487e14	−	1.31673e14i	0.888965	−	1.05943i	0.997861	−	0.0653744i	$-0.0208242\pi$
$660$	−3.62006e13	+	5.36514e13i	−0.289065	+	0.428412i
$661$	−3.34541e13	−	1.89728e14i	−0.265120	−	1.50357i	−0.768694	−	0.639616i	$-0.779093\pi$
$661$	−3.34541e13	−	1.89728e14i	−0.265120	−	1.50357i	0.503575	−	0.863952i	$-0.332018\pi$
$662$	2.68223e13	−	4.72949e12i	0.210963	−	0.0371984i
$663$	1.93419e13	−	9.42992e12i	0.150984	−	0.0736106i
$664$	8.08137e13	+	6.78108e13i	0.626102	+	0.525362i
$665$	1.36371e14	−	7.87337e13i	1.04861	−	0.605414i
$666$	5.67030e12	−	4.02546e13i	0.0432748	−	0.307216i
$667$	−7.09061e13	+	1.22813e14i	−0.537099	+	0.930283i
$668$	3.63492e13	+	9.98687e13i	0.273283	+	0.750839i
$669$	−6.92248e12	−	6.59626e13i	−0.0516572	−	0.492229i
$670$	6.03101e13	−	5.06062e13i	0.446700	−	0.374826i
$671$	−1.55979e13	+	4.28549e13i	−0.114671	+	0.315056i
$672$	−7.54115e13	+	7.80664e13i	−0.550290	+	0.569663i
$673$	2.30414e13	−	1.30674e14i	0.166891	−	0.946485i	−0.780202	−	0.625527i	$-0.784884\pi$
$673$	2.30414e13	−	1.30674e14i	0.166891	−	0.946485i	0.947093	−	0.320958i	$-0.104005\pi$
$674$		−	1.06615e13i		−	0.0766515i
$675$	−6.03981e13	−	7.73811e13i	−0.431027	−	0.552225i
$676$	3.27361e14			2.31896
$677$	−1.21705e14	−	2.14599e13i	−0.855788	−	0.150899i	−0.271494	−	0.962440i	$-0.587518\pi$
$677$	−1.21705e14	−	2.14599e13i	−0.855788	−	0.150899i	−0.584295	+	0.811542i	$0.698629\pi$
$678$	3.67769e13	−	1.05393e13i	0.256700	−	0.0735640i
$679$	−9.53862e13	−	3.47177e13i	−0.660901	−	0.240548i
$680$	−6.51690e12	−	7.76654e12i	−0.0448226	−	0.0534175i
$681$	−1.32686e13	−	1.82687e13i	−0.0905922	−	0.124731i
$682$	−3.11518e13	+	1.13383e13i	−0.211135	+	0.0768470i
$683$	−2.13529e14	−	1.23281e14i	−1.43666	−	0.829453i	−0.439040	−	0.898468i	$-0.644681\pi$
$683$	−2.13529e14	−	1.23281e14i	−1.43666	−	0.829453i	−0.997616	+	0.0690143i	$0.978015\pi$
$684$	−1.27692e14	+	2.70999e13i	−0.852871	+	0.181004i
$685$	9.50989e13	+	1.64716e14i	0.630555	+	1.09215i
$686$	3.20978e13	−	3.82527e13i	0.211278	−	0.251792i
$687$	−2.60101e14	−	1.82290e13i	−1.69964	−	0.119119i
$688$	−1.45300e13	−	8.24036e13i	−0.0942590	−	0.534569i
$689$	3.54228e14	−	6.24600e13i	2.28132	−	0.402259i
$690$	−4.64678e12	+	6.63025e13i	−0.0297103	+	0.423921i
$691$	5.25801e13	+	4.41199e13i	0.333757	+	0.280056i	0.794229	−	0.607619i	$-0.207875\pi$
$691$	5.25801e13	+	4.41199e13i	0.333757	+	0.280056i	−0.460471	+	0.887675i	$0.652320\pi$
$692$	2.42322e14	−	1.39905e14i	1.52708	−	0.881661i
$693$	5.01469e13	−	4.51240e13i	0.313746	−	0.282320i
$694$	−2.14146e13	+	3.70912e13i	−0.133019	+	0.230395i
$695$	4.17169e13	+	1.14616e14i	0.257269	+	0.706842i
$696$	−8.31549e13	+	6.03956e13i	−0.509145	+	0.369794i
$697$	−8.33910e12	+	6.99734e12i	−0.0506938	+	0.0425372i
$698$	3.12305e13	−	8.58051e13i	0.188496	−	0.517888i
$699$	3.01991e13	+	1.05379e14i	0.180970	+	0.631493i
$700$	−1.76168e13	+	9.99100e13i	−0.104818	+	0.594455i
$701$			8.47626e13i			0.500742i	0.968150	+	0.250371i	$0.0805526\pi$
$701$			8.47626e13i			0.500742i	−0.968150	+	0.250371i	$0.919447\pi$
$702$	−7.59421e13	−	6.84433e13i	−0.445448	−	0.401463i
$703$	−1.62874e14			−0.948584
$704$	−3.35013e13	−	5.90718e12i	−0.193731	−	0.0341599i
$705$	−1.68764e14	−	1.63025e14i	−0.969024	−	0.936069i
$706$	−4.53726e13	−	1.65143e13i	−0.258684	−	0.0941534i
$707$	3.99478e13	+	4.76080e13i	0.226150	+	0.269515i
$708$	−2.45458e14	+	2.57597e13i	−1.37978	+	0.144802i
$709$	8.27516e13	−	3.01191e13i	0.461897	−	0.168117i	−0.100581	−	0.994929i	$-0.532070\pi$
$709$	8.27516e13	−	3.01191e13i	0.461897	−	0.168117i	0.562478	+	0.826812i	$0.309848\pi$
$710$	−7.44985e13	−	4.30118e13i	−0.412911	−	0.238394i
$711$	1.15781e13	−	1.48097e13i	0.0637218	−	0.0815075i
$712$	−5.98827e13	−	1.03720e14i	−0.327266	−	0.566842i
$713$	1.95857e14	−	2.33413e14i	1.06290	−	1.26671i
$714$	2.19297e12	+	4.49805e12i	0.0118180	+	0.0242401i
$715$	3.52660e13	+	2.00003e14i	0.188724	+	1.07030i
$716$	−2.40154e14	+	4.23456e13i	−1.27622	+	0.225032i
$717$	2.00329e14	+	1.35170e14i	1.05718	+	0.713318i
$718$	−6.23480e13	−	5.23162e13i	−0.326739	−	0.274166i
$719$	2.12924e14	−	1.22931e14i	1.10810	−	0.639762i	0.169764	−	0.985485i	$-0.445700\pi$
$719$	2.12924e14	−	1.22931e14i	1.10810	−	0.639762i	0.938337	+	0.345723i	$0.112366\pi$
$720$	8.39886e13	−	1.57840e14i	0.434068	−	0.815746i
$721$	−4.88366e13	+	8.45875e13i	−0.250651	+	0.434140i
$722$	1.28695e12	+	3.53587e12i	0.00655958	+	0.0180223i
$723$	5.95808e13	+	2.65383e13i	0.301589	+	0.134333i
$724$	−1.93432e14	+	1.62309e14i	−0.972381	+	0.815924i
$725$	−5.01508e13	+	1.37788e14i	−0.250373	+	0.687894i
$726$	4.99945e13	+	1.24734e13i	0.247878	+	0.0618444i
$727$	3.98357e13	−	2.25919e14i	0.196155	−	1.11245i	−0.714608	−	0.699525i	$-0.753395\pi$
$727$	3.98357e13	−	2.25919e14i	0.196155	−	1.11245i	0.910764	−	0.412928i	$-0.135494\pi$
$728$			2.23124e14i			1.09116i
$729$	−2.13287e13	−	2.04783e14i	−0.103592	−	0.994620i
$730$	−1.33907e12			−0.00645934
$731$	−1.39831e13	−	2.46561e12i	−0.0669912	−	0.0118124i
$732$	3.48230e13	−	1.39574e14i	0.165696	−	0.664124i
$733$	2.87961e14	+	1.04809e14i	1.36086	+	0.495313i	0.916320	−	0.400446i	$-0.131145\pi$
$733$	2.87961e14	+	1.04809e14i	1.36086	+	0.495313i	0.444540	+	0.895759i	$0.353367\pi$
$734$	5.37361e13	+	6.40401e13i	0.252223	+	0.300588i
$735$	−9.37101e12	+	2.10387e13i	−0.0436867	+	0.0980806i
$736$	−1.72487e14	+	6.27800e13i	−0.798669	+	0.290692i
$737$	−1.17030e14	−	6.75670e13i	−0.538218	−	0.310740i
$738$	4.56578e13	+	2.42951e13i	0.208561	+	0.110978i
$739$	1.09594e14	+	1.89823e14i	0.497241	+	0.861246i	0.999995	−	0.00318340i	$-0.00101331\pi$
$739$	1.09594e14	+	1.89823e14i	0.497241	+	0.861246i	−0.502754	+	0.864429i	$0.667680\pi$
$740$	1.63737e14	−	1.95134e14i	0.737882	−	0.879374i
$741$	−2.29101e14	+	3.39541e14i	−1.02550	+	1.51985i
$742$	1.45254e13	+	8.23775e13i	0.0645814	+	0.366259i
$743$	−3.56907e14	+	6.29324e13i	−1.57620	+	0.277927i	−0.892229	−	0.451583i	$-0.850860\pi$
$743$	−3.56907e14	+	6.29324e13i	−1.57620	+	0.277927i	−0.683971	+	0.729509i	$0.739749\pi$
$744$	1.98487e14	−	9.67700e13i	0.870698	−	0.424499i
$745$	2.20087e14	+	1.84675e14i	0.958988	+	0.804686i
$746$	2.73461e13	−	1.57883e13i	0.118359	−	0.0683345i
$747$	2.48712e14	+	1.94441e14i	1.06929	+	0.835958i
$748$	−4.12035e12	+	7.13665e12i	−0.0175965	+	0.0304780i
$749$	−4.33934e13	−	1.19222e14i	−0.184083	−	0.505765i
$750$	−3.06638e12	−	2.92188e13i	−0.0129217	−	0.123128i
$751$	−1.46418e14	+	1.22859e14i	−0.612905	+	0.514289i	−0.895564	−	0.444932i	$-0.853228\pi$
$751$	−1.46418e14	+	1.22859e14i	−0.612905	+	0.514289i	0.282659	+	0.959220i	$0.408783\pi$
$752$	6.02166e13	−	1.65444e14i	0.250396	−	0.687956i
$753$	1.89939e14	−	1.96626e14i	0.784583	−	0.812205i
$754$	−2.65183e13	+	1.50393e14i	−0.108815	+	0.617121i
$755$			1.30994e14i			0.533969i
$756$	−1.42459e14	+	1.58067e14i	−0.576874	+	0.640077i
$757$	−1.12893e14			−0.454139			−0.227070	−	0.973879i	$-0.572914\pi$
$757$	−1.12893e14			−0.454139			−0.227070	+	0.973879i	$0.572914\pi$
$758$	−1.53977e13	−	2.71502e12i	−0.0615331	−	0.0108499i
$759$	1.09669e14	−	3.14284e13i	0.435386	−	0.124771i
$760$	1.81350e14	+	6.60060e13i	0.715236	+	0.260325i
$761$	−1.09973e14	−	1.31061e14i	−0.430886	−	0.513510i	0.506292	−	0.862362i	$-0.331016\pi$
$761$	−1.09973e14	−	1.31061e14i	−0.430886	−	0.513510i	−0.937178	+	0.348852i	$0.886571\pi$
$762$	3.74183e13	+	5.15189e13i	0.145650	+	0.200536i
$763$	−6.42697e13	+	2.33923e13i	−0.248533	+	0.0904585i
$764$	3.58530e14	+	2.06997e14i	1.37740	+	0.795240i
$765$	−2.02942e13	−	2.25533e13i	−0.0774579	−	0.0860800i
$766$	−3.64699e13	−	6.31677e13i	−0.138290	−	0.239525i
$767$	−4.97801e14	+	5.93256e14i	−1.87534	+	2.23494i
$768$	3.71800e13	+	2.60574e12i	0.139156	+	0.00975271i
$769$	−5.45862e12	−	3.09574e13i	−0.0202979	−	0.115115i	0.972975	−	0.230909i	$-0.0741699\pi$
$769$	−5.45862e12	−	3.09574e13i	−0.0202979	−	0.115115i	−0.993273	+	0.115794i	$0.963059\pi$
$770$	−4.65118e13	+	8.20128e12i	−0.171834	+	0.0302990i
$771$	−2.78139e13	+	3.96862e14i	−0.102091	+	1.45669i
$772$	5.94902e13	+	4.99182e13i	0.216950	+	0.182042i
$773$	1.41721e14	−	8.18225e13i	0.513495	−	0.296466i	−0.220774	−	0.975325i	$-0.570858\pi$
$773$	1.41721e14	−	8.18225e13i	0.513495	−	0.296466i	0.734269	+	0.678859i	$0.237525\pi$
$774$	1.40048e13	+	6.59893e13i	0.0504165	+	0.237558i
$775$	1.57527e14	−	2.72844e14i	0.563437	−	0.975902i
$776$	−4.25493e13	−	1.16903e14i	−0.151211	−	0.415449i
$777$	−2.14823e14	+	1.56027e14i	−0.758535	+	0.550926i
$778$	−3.11609e13	+	2.61471e13i	−0.109323	+	0.0917330i
$779$	7.08720e13	−	1.94719e14i	0.247051	−	0.678768i
$780$	−1.76478e14	−	6.15816e14i	−0.611247	−	2.13293i
$781$	−2.56399e13	+	1.45411e14i	−0.0882390	+	0.500428i
$782$			8.46263e12i			0.0289382i
$783$	−2.42444e14	+	1.89235e14i	−0.823765	+	0.642971i
$784$	−1.72811e13			−0.0583435
$785$	4.42587e14	+	7.80400e13i	1.48474	+	0.261800i
$786$	5.13004e13	+	4.95558e13i	0.171005	+	0.165189i
$787$	−3.50294e14	−	1.27496e14i	−1.16027	−	0.422303i	−0.311075	−	0.950385i	$-0.600689\pi$
$787$	−3.50294e14	−	1.27496e14i	−1.16027	−	0.422303i	−0.849193	+	0.528082i	$0.822911\pi$
$788$	−2.45205e14	−	2.92224e14i	−0.807047	−	0.961801i
$789$	−2.71256e14	+	2.84671e13i	−0.887143	+	0.0931017i
$790$	−1.23671e13	+	4.50126e12i	−0.0401914	+	0.0146285i
$791$	−2.16389e14	−	1.24932e14i	−0.698801	−	0.403453i
$792$	8.18696e13	+	1.15322e13i	0.262722	+	0.0370073i
$793$	−2.25695e14	−	3.90914e14i	−0.719706	−	1.24657i
$794$	3.93994e13	−	4.69544e13i	0.124850	−	0.148790i
$795$	−2.22250e14	−	4.55861e14i	−0.699851	−	1.43548i
$796$	8.32918e11	+	4.72371e12i	0.00260638	+	0.0147815i
$797$	4.22217e14	−	7.44482e13i	1.31294	−	0.231506i	0.527028	−	0.849848i	$-0.323306\pi$
$797$	4.22217e14	−	7.44482e13i	1.31294	−	0.231506i	0.785909	+	0.618342i	$0.212195\pi$
$798$	−7.89618e13	−	5.32784e13i	−0.244007	−	0.164641i
$799$	−2.28864e13	−	1.92039e13i	−0.0702818	−	0.0589734i
$800$	−1.64366e14	+	9.48970e13i	−0.501606	+	0.289603i
$801$	−1.89829e14	−	3.04002e14i	−0.575705	−	0.921964i
$802$	−2.43188e13	+	4.21215e13i	−0.0732945	+	0.126950i
$803$	7.86108e11	+	2.15981e12i	0.00235453	+	0.00646902i
$804$	3.89375e14	+	1.73434e14i	1.15901	+	0.516243i
$805$	3.32537e14	−	2.79032e14i	0.983695	−	0.825418i
$806$	1.12224e14	−	3.08333e14i	0.329921	−	0.906451i
$807$	1.11953e14	+	2.79317e13i	0.327091	+	0.0816075i
$808$	−1.32263e13	+	7.50098e13i	−0.0384043	+	0.217802i
$809$			3.70981e14i			1.07055i	0.844676	+	0.535277i	$0.179793\pi$
$809$			3.70981e14i			1.07055i	−0.844676	+	0.535277i	$0.820207\pi$
$810$	−6.32705e13	+	1.29517e14i	−0.181458	+	0.371452i
$811$	4.10883e13			0.117115			0.0585577	−	0.998284i	$-0.481350\pi$
$811$	4.10883e13			0.117115			0.0585577	+	0.998284i	$0.481350\pi$
$812$	3.13030e14	+	5.51956e13i	0.886759	+	0.156360i
$813$	5.79642e13	−	2.32326e14i	0.163195	−	0.654103i
$814$	4.59049e13	+	1.67080e13i	0.128451	+	0.0467523i
$815$	3.20349e14	+	3.81777e14i	0.890913	+	1.06175i
$816$	9.26259e12	−	2.07953e13i	0.0256025	−	0.0574798i
$817$	2.53978e14	−	9.24406e13i	0.697729	−	0.253952i
$818$	1.07618e14	+	6.21335e13i	0.293846	+	0.169652i
$819$	2.30932e13	+	6.67306e14i	0.0626706	+	1.81095i
$820$	1.62039e14	+	2.80659e14i	0.437068	+	0.757025i
$821$	−3.61207e14	+	4.30470e14i	−0.968368	+	1.15406i	0.0196641	+	0.999807i	$0.493740\pi$
$821$	−3.61207e14	+	4.30470e14i	−0.968368	+	1.15406i	−0.988032	+	0.154249i	$0.950704\pi$
$822$	6.43527e13	−	9.53745e13i	0.171478	−	0.254140i
$823$	−1.15181e13	−	6.53224e13i	−0.0305057	−	0.173007i	0.965748	−	0.259480i	$-0.0835513\pi$
$823$	−1.15181e13	−	6.53224e13i	−0.0305057	−	0.173007i	−0.996254	+	0.0864737i	$0.972440\pi$
$824$	−1.17888e14	+	2.07868e13i	−0.310336	+	0.0547206i
$825$	1.06030e14	−	5.16936e13i	0.277433	−	0.135259i
$826$	−1.37965e14	−	1.15766e14i	−0.358812	−	0.301079i
$827$	7.15261e13	−	4.12956e13i	0.184900	−	0.106752i	−0.404693	−	0.914453i	$-0.632622\pi$
$827$	7.15261e13	−	4.12956e13i	0.184900	−	0.106752i	0.589593	+	0.807701i	$0.299288\pi$
$828$	−3.33693e14	+	1.34699e14i	−0.857423	+	0.346108i
$829$	7.85456e13	−	1.36045e14i	0.200608	−	0.347464i	−0.748116	−	0.663568i	$-0.769041\pi$
$829$	7.85456e13	−	1.36045e14i	0.200608	−	0.347464i	0.948725	+	0.316104i	$0.102375\pi$
$830$	−7.55937e13	−	2.07692e14i	−0.191909	−	0.527265i
$831$	3.33343e13	+	3.17634e14i	0.0841175	+	0.801534i
$832$	2.57929e14	−	2.16428e14i	0.646970	−	0.542872i
$833$	−1.00296e12	+	2.75561e12i	−0.00250068	+	0.00687056i
$834$	5.12626e13	−	5.30673e13i	0.127049	−	0.131522i
$835$	8.16497e13	−	4.63058e14i	0.201151	−	1.14078i
$836$		−	1.56863e14i		−	0.384141i
$837$	5.83609e14	−	3.09958e14i	1.42067	−	0.754528i
$838$	1.41499e14			0.342400
$839$	−2.60896e14	−	4.60029e13i	−0.627562	−	0.110656i	−0.149183	−	0.988810i	$-0.547664\pi$
$839$	−2.60896e14	−	4.60029e13i	−0.627562	−	0.110656i	−0.478379	+	0.878153i	$0.658776\pi$
$840$	3.02422e14	−	8.66669e13i	0.723132	−	0.207232i
$841$	3.63712e13	+	1.32380e13i	0.0864526	+	0.0314662i
$842$	−2.95193e13	−	3.51798e13i	−0.0697503	−	0.0831252i
$843$	6.62472e13	+	9.12115e13i	0.155607	+	0.214245i
$844$	6.28992e13	−	2.28934e13i	0.146870	−	0.0534563i
$845$	−1.25429e15	−	7.24166e14i	−2.91149	−	1.68095i
$846$	−4.39048e13	+	1.34981e14i	−0.101312	+	0.311473i
$847$	−1.68266e14	−	2.91445e14i	−0.385993	−	0.668560i
$848$	2.44602e14	−	2.91505e14i	0.557802	−	0.664762i
$849$	3.16729e14	+	2.21978e13i	0.718042	+	0.0503236i
$850$	1.51945e12	+	8.61726e12i	0.00342447	+	0.0194211i
$851$	−4.42180e14	+	7.79683e13i	−0.990721	+	0.174691i
$852$	3.25617e13	−	4.64606e14i	0.0725285	−	1.03487i
$853$	−6.72605e14	−	5.64382e14i	−1.48941	−	1.24976i	−0.895364	−	0.445335i	$-0.853085\pi$
$853$	−6.72605e14	−	5.64382e14i	−1.48941	−	1.24976i	−0.594048	−	0.804430i	$-0.702471\pi$
$854$	9.09090e13	−	5.24863e13i	0.200132	−	0.115547i
$855$	5.49203e14	+	1.78638e14i	1.20199	+	0.390969i
$856$	7.77469e13	−	1.34662e14i	0.169167	−	0.293005i
$857$	2.31946e14	+	6.37267e14i	0.501745	+	1.37853i	0.889569	+	0.456800i	$0.151005\pi$
$857$	2.31946e14	+	6.37267e14i	0.501745	+	1.37853i	−0.387824	+	0.921733i	$0.626773\pi$
$858$	9.94012e13	−	7.21954e13i	0.213774	−	0.155265i
$859$	−7.04258e13	+	5.90943e13i	−0.150580	+	0.126351i	−0.714965	−	0.699160i	$-0.753558\pi$
$859$	−7.04258e13	+	5.90943e13i	−0.150580	+	0.126351i	0.564386	+	0.825511i	$0.309113\pi$
$860$	−1.44573e14	+	3.97212e14i	−0.307324	+	0.844365i
$861$	−9.30560e13	−	3.24717e14i	−0.196666	−	0.686261i
$862$	−6.40091e12	+	3.63014e13i	−0.0134495	+	0.0762758i
$863$			7.91444e14i			1.65336i	0.562675	+	0.826678i	$0.309772\pi$
$863$			7.91444e14i			1.65336i	−0.562675	+	0.826678i	$0.690228\pi$
$864$	−3.97837e14	−	1.40803e13i	−0.826297	−	0.0292444i
$865$	−1.23795e15			−2.55636
$866$	−2.74980e14	−	4.84864e13i	−0.564562	−	0.0995475i
$867$	3.49563e14	+	3.37675e14i	0.713559	+	0.689293i
$868$	−6.41768e14	−	2.33585e14i	−1.30251	−	0.474073i
$869$	1.45204e13	+	1.73047e13i	0.0293008	+	0.0349194i
$870$	2.14143e14	−	2.24734e13i	0.429644	−	0.0450892i
$871$	1.25686e15	−	4.57460e14i	2.50724	−	0.912562i
$872$	−7.25926e13	−	4.19113e13i	−0.143983	−	0.0831283i
$873$	−1.39354e14	−	3.45224e14i	−0.274819	−	0.680816i
$874$	−8.05439e13	−	1.39506e14i	−0.157934	−	0.273550i
$875$	−1.23339e14	+	1.46989e14i	−0.240469	+	0.286580i
$876$	−3.17714e12	−	6.51670e12i	−0.00615908	−	0.0126330i
$877$	1.40488e14	+	7.96747e14i	0.270796	+	1.53576i	0.752008	+	0.659154i	$0.229085\pi$
$877$	1.40488e14	+	7.96747e14i	0.270796	+	1.53576i	−0.481213	+	0.876604i	$0.659803\pi$
$878$	2.33019e14	−	4.10876e13i	0.446600	−	0.0787477i
$879$	−2.34624e14	−	1.58310e14i	−0.447125	−	0.301691i
$880$	1.64589e14	+	1.38106e14i	0.311879	+	0.261698i
$881$	−4.36217e14	+	2.51850e14i	−0.821908	+	0.474529i	−0.851074	−	0.525046i	$-0.824048\pi$
$881$	−4.36217e14	+	2.51850e14i	−0.821908	+	0.474529i	0.0291662	+	0.999575i	$0.490715\pi$
$882$	1.39238e13	−	4.81855e11i	0.0260865	−	0.000902763i
$883$	−3.75469e14	+	6.50331e14i	−0.699472	+	1.21152i	0.269177	+	0.963091i	$0.413248\pi$
$883$	−3.75469e14	+	6.50331e14i	−0.699472	+	1.21152i	−0.968650	+	0.248431i	$0.920085\pi$
$884$	−2.78967e13	−	7.66455e13i	−0.0516763	−	0.141979i
$885$	9.97460e14	+	4.44286e14i	1.83730	+	0.818363i
$886$	−1.42292e14	+	1.19397e14i	−0.260622	+	0.218688i
$887$	4.36674e13	−	1.19975e14i	0.0795315	−	0.218511i	−0.893554	−	0.448956i	$-0.851796\pi$
$887$	4.36674e13	−	1.19975e14i	0.0795315	−	0.218511i	0.973085	+	0.230445i	$0.0740182\pi$
$888$	−3.15720e14	−	7.87704e13i	−0.571791	−	0.142659i
$889$	7.22140e13	−	4.09546e14i	0.130051	−	0.737554i
$890$			2.50919e14i			0.449349i
$891$	2.46045e14	+	2.60165e13i	0.438153	+	0.0463298i
$892$	−2.51403e14			−0.445191
$893$	5.60057e14	+	9.87531e13i	0.986222	+	0.173898i
$894$	4.20714e13	−	1.68627e14i	0.0736715	−	0.295283i
$895$	1.01383e15	+	3.69004e14i	1.76543	+	0.642563i
$896$	3.44338e14	+	4.10366e14i	0.596273	+	0.710610i
$897$	−4.59436e14	+	1.03148e15i	−0.791158	+	1.77622i
$898$	1.79972e14	−	6.55046e13i	0.308194	−	0.112173i
$899$	−8.54853e14	−	4.93550e14i	−1.45577	−	0.840490i
$900$	−3.15605e14	+	1.97074e14i	−0.534480	+	0.333747i
$901$	−3.22865e13	−	5.59218e13i	−0.0543746	−	0.0941796i
$902$	−3.99495e13	+	4.76099e13i	−0.0669080	+	0.0797379i
$903$	2.46431e14	−	3.65225e14i	0.410446	−	0.608306i
$904$	−5.31761e13	−	3.01577e14i	−0.0880794	−	0.499523i
$905$	1.10019e15	−	1.93993e14i	1.81228	−	0.319553i
$906$	7.12267e13	−	3.47257e13i	0.116681	−	0.0568867i
$907$	−3.17141e14	−	2.66113e14i	−0.516673	−	0.433540i	0.346797	−	0.937940i	$-0.387269\pi$
$907$	−3.17141e14	−	2.66113e14i	−0.516673	−	0.433540i	−0.863470	+	0.504400i	$0.831714\pi$
$908$	−7.41186e13	+	4.27924e13i	−0.120087	+	0.0693325i
$909$	−3.17929e13	+	2.25704e14i	−0.0512284	+	0.363681i
$910$	2.33732e14	−	4.04836e14i	0.374551	−	0.648741i
$911$	1.02063e14	+	2.80417e14i	0.162659	+	0.446902i	0.994068	−	0.108759i	$-0.0346876\pi$
$911$	1.02063e14	+	2.80417e14i	0.162659	+	0.446902i	−0.831409	+	0.555661i	$0.812465\pi$
$912$	4.52282e13	+	4.30968e14i	0.0716861	+	0.683079i
$913$	−2.90614e14	+	2.43854e14i	−0.458102	+	0.384393i
$914$	−1.26759e14	+	3.48267e14i	−0.198723	+	0.545987i
$915$	−4.42181e14	+	4.57748e14i	−0.689437	+	0.713709i
$916$	−1.71621e14	+	9.73310e14i	−0.266129	+	1.50929i
$917$		−	4.65848e14i		−	0.718452i
$918$	−6.88324e12	+	1.70136e13i	−0.0105579	+	0.0260965i
$919$	9.70745e14			1.48091			0.740453	−	0.672108i	$-0.234611\pi$
$919$	9.70745e14			1.48091			0.740453	+	0.672108i	$0.234611\pi$
$920$	5.23936e14	+	9.23841e13i	0.794949	+	0.140171i
$921$	2.22327e14	−	6.37135e13i	0.335501	−	0.0961465i
$922$	1.31260e14	+	4.77749e13i	0.197006	+	0.0717043i
$923$	−9.39398e14	−	1.11953e15i	−1.40230	−	1.67120i
$924$	−1.50268e14	−	2.06895e14i	−0.223104	−	0.307178i
$925$	−4.36261e14	+	1.58786e14i	−0.644225	+	0.234479i
$926$	1.54089e14	+	8.89633e13i	0.226317	+	0.130664i
$927$	−3.50421e14	+	7.43693e13i	−0.511907	+	0.108641i
$928$	2.97323e14	+	5.14979e14i	0.432006	+	0.748256i
$929$	−1.90340e14	+	2.26839e14i	−0.275075	+	0.327822i	−0.885841	−	0.463990i	$-0.846417\pi$
$929$	−1.90340e14	+	2.26839e14i	−0.275075	+	0.327822i	0.610765	+	0.791812i	$0.290862\pi$
$930$	−4.61506e14	−	3.23444e13i	−0.663380	−	0.0464927i
$931$	−9.69302e12	−	5.49718e13i	−0.0138583	−	0.0785945i
$932$	4.09203e14	−	7.21536e13i	0.581915	−	0.102607i
$933$	4.08852e13	−	5.83371e14i	0.0578307	−	0.825157i
$934$	−1.07940e14	−	9.05726e13i	−0.151862	−	0.127427i
$935$	3.15744e13	−	1.82295e13i	0.0441852	−	0.0255104i
$936$	−6.08306e14	+	5.47376e14i	−0.846726	+	0.761914i
$937$	−3.20169e14	+	5.54550e14i	−0.443284	+	0.767790i	−0.997931	−	0.0642955i	$-0.979520\pi$
$937$	−3.20169e14	+	5.54550e14i	−0.443284	+	0.767790i	0.554647	+	0.832086i	$0.312853\pi$
$938$	1.06384e14	+	2.92289e14i	0.146509	+	0.402530i
$939$	−3.93512e13	+	2.85809e13i	−0.0539052	+	0.0391515i
$940$	−6.81334e14	+	5.71707e14i	−0.928370	+	0.778995i
$941$	3.05110e14	−	8.38283e14i	0.413531	−	1.13617i	−0.541768	−	0.840528i	$-0.682245\pi$
$941$	3.05110e14	−	8.38283e14i	0.413531	−	1.13617i	0.955299	−	0.295640i	$-0.0955329\pi$
$942$	−7.48938e13	−	2.61340e14i	−0.100970	−	0.352332i
$943$	9.91947e13	−	5.62561e14i	0.133024	−	0.754416i
$944$			8.19310e14i			1.09292i
$945$	8.95499e14	−	2.90499e14i	1.18825	−	0.385466i
$946$	−8.10647e13			−0.106998
$947$	2.93964e14	+	5.18339e13i	0.385962	+	0.0680556i	0.363263	−	0.931687i	$-0.381663\pi$
$947$	2.93964e14	+	5.18339e13i	0.385962	+	0.0680556i	0.0226997	+	0.999742i	$0.492774\pi$
$948$	−5.12487e13	−	4.95058e13i	−0.0669331	−	0.0646569i
$949$	−2.13773e13	−	7.78071e12i	−0.0277730	−	0.0101085i
$950$	−1.07064e14	−	1.27594e14i	−0.138364	−	0.164896i
$951$	1.11863e14	−	1.17396e13i	0.143809	−	0.0150921i
$952$	3.76400e13	−	1.36998e13i	0.0481355	−	0.0175199i
$953$	6.87575e14	+	3.96972e14i	0.874693	+	0.505004i	0.868905	−	0.494979i	$-0.164824\pi$
$953$	6.87575e14	+	3.96972e14i	0.874693	+	0.505004i	0.00578794	+	0.999983i	$0.498158\pi$
$954$	−1.88953e14	+	2.41692e14i	−0.239118	+	0.305859i
$955$	−9.15810e14	−	1.58623e15i	−1.15289	−	1.99687i
$956$	5.88815e14	−	7.01722e14i	0.737376	−	0.878771i
$957$	−1.61962e14	−	3.32204e14i	−0.201769	−	0.413852i
$958$	7.67532e13	+	4.35289e14i	0.0951194	+	0.539449i
$959$	−7.40027e14	+	1.30487e14i	−0.912335	+	0.160869i
$960$	−3.93534e14	−	2.65532e14i	−0.482643	−	0.325657i
$961$	9.96827e14	+	8.36438e14i	1.21619	+	1.02051i
$962$	−4.18736e14	+	2.41757e14i	−0.508236	+	0.293430i
$963$	2.18584e14	−	4.10786e14i	0.263929	−	0.496002i
$964$	1.23615e14	−	2.14108e14i	0.148486	−	0.257186i
$965$	−1.17513e14	−	3.22863e14i	−0.140426	−	0.385817i
$966$	−2.39874e14	−	1.06844e14i	−0.285166	−	0.127018i
$967$	5.72046e14	−	4.80004e14i	0.676548	−	0.567691i	−0.238447	−	0.971155i	$-0.576638\pi$
$967$	5.72046e14	−	4.80004e14i	0.676548	−	0.567691i	0.914995	+	0.403464i	$0.132194\pi$
$968$	1.41065e14	−	3.87573e14i	0.165975	−	0.456012i
$969$	7.13460e13	+	1.78004e13i	0.0835123	+	0.0208359i
$970$	−4.52599e13	+	2.56681e14i	−0.0527053	+	0.298907i
$971$		−	7.09172e14i		−	0.821591i	−0.911728	−	0.410795i	$-0.865251\pi$
$971$		−	7.09172e14i		−	0.821591i	0.911728	−	0.410795i	$-0.134749\pi$
$972$	−7.80427e14	−	6.12316e11i	−0.899499	−	0.000705739i
$973$	−4.81893e14			−0.552569
$974$	1.25185e14	+	2.20736e13i	0.142810	+	0.0251813i
$975$	−2.82631e14	+	1.13281e15i	−0.320772	+	1.28569i
$976$	−4.48742e14	−	1.63329e14i	−0.506696	−	0.184422i
$977$	−4.26967e14	−	5.08839e14i	−0.479646	−	0.571620i	0.470906	−	0.882183i	$-0.343927\pi$
$977$	−4.26967e14	−	5.08839e14i	−0.479646	−	0.571620i	−0.950553	+	0.310563i	$0.899482\pi$
$978$	1.22665e14	−	2.75394e14i	0.137096	−	0.307794i
$979$	4.04714e14	−	1.47304e14i	0.450023	−	0.163795i
$980$	7.56041e13	+	4.36500e13i	0.0836402	+	0.0482897i
$981$	−2.21444e14	−	1.17833e14i	−0.243735	−	0.129695i
$982$	7.56936e13	+	1.31105e14i	0.0828899	+	0.143570i
$983$	7.15276e13	−	8.52433e13i	0.0779303	−	0.0928737i	−0.725671	−	0.688042i	$-0.758470\pi$
$983$	7.15276e13	−	8.52433e13i	0.0779303	−	0.0928737i	0.803601	+	0.595169i	$0.202915\pi$
$984$	2.31552e14	−	3.43173e14i	0.250999	−	0.371996i
$985$	2.93071e14	+	1.66209e15i	0.316076	+	1.79256i
$986$	2.69989e13	−	4.76063e12i	0.0289709	−	0.00510834i
$987$	8.33288e14	−	4.06260e14i	0.889630	−	0.433729i
$988$	1.18936e15	+	9.97989e14i	1.26336	+	1.06009i
$989$	6.45263e14	−	3.72543e14i	0.681955	−	0.393727i
$990$	−1.36464e14	−	1.06686e14i	−0.143497	−	0.112184i
$991$	2.19628e13	−	3.80407e13i	0.0229784	−	0.0397997i	−0.854308	−	0.519768i	$-0.826018\pi$
$991$	2.19628e13	−	3.80407e13i	0.0229784	−	0.0397997i	0.877286	+	0.479968i	$0.159352\pi$
$992$	−4.36987e14	−	1.20061e15i	−0.454894	−	1.24981i
$993$	−6.80930e13	−	6.48841e14i	−0.0705271	−	0.672035i
$994$	2.60352e14	−	2.18461e14i	0.268305	−	0.225135i
$995$	7.25813e12	−	1.99415e13i	0.00744233	−	0.0204476i
$996$	8.31395e14	−	8.60664e14i	0.848224	−	0.878086i
$997$	−7.08333e13	+	4.01715e14i	−0.0719054	+	0.407796i	0.927516	+	0.373783i	$0.121940\pi$
$997$	−7.08333e13	+	4.01715e14i	−0.0719054	+	0.407796i	−0.999421	+	0.0340123i	$0.989171\pi$
$998$			5.40758e14i			0.546198i
$999$	−9.52391e14	−	2.02906e14i	−0.957167	−	0.203923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.f.a.2.17	✓	174
3.2	odd	2		81.11.f.a.8.13		174
27.13	even	9		81.11.f.a.71.13		174
27.14	odd	18	inner	27.11.f.a.14.17	yes	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.f.a.2.17	✓	174	1.1	even	1	trivial
27.11.f.a.14.17	yes	174	27.14	odd	18	inner
81.11.f.a.8.13		174	3.2	odd	2
81.11.f.a.71.13		174	27.13	even	9

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+(9.99045 + 1.76159i) q^{2} +(58.8240 - 235.773i) q^{3} +(-865.539 - 315.031i) q^{4} +(2619.44 + 3121.73i) q^{5} +(1003.01 - 2251.85i) q^{6} +(-15129.3 + 5506.60i) q^{7} +(-17088.5 - 9866.04i) q^{8} +(-52128.5 - 27738.2i) q^{9} +(20670.2 + 35801.9i) q^{10} +(45611.2 - 54357.3i) q^{11} +(-125190. + 185539. i) q^{12} +(121958. + 691659. i) q^{13} +(-160849. + 28361.9i) q^{14} +(890105. - 433960. i) q^{15} +(569186. + 477604. i) q^{16} +(109192. - 63041.9i) q^{17} +(-471924. - 368946. i) q^{18} +(-1.20002e6 + 2.07849e6i) q^{19} +(-1.28379e6 - 3.52719e6i) q^{20} +(408342. + 3.89099e6i) q^{21} +(551431. - 462706. i) q^{22} +(-2.26289e6 + 6.21725e6i) q^{23} +(-3.33136e6 + 3.44864e6i) q^{24} +(-1.18794e6 + 6.73715e6i) q^{25} +7.12483e6i q^{26} +(-9.60631e6 + 1.06588e7i) q^{27} +1.48297e7 q^{28} +(2.11083e7 + 3.72196e6i) q^{29} +(9.65702e6 - 2.76746e6i) q^{30} +(-4.32758e7 - 1.57511e7i) q^{31} +(1.78330e7 + 2.12526e7i) q^{32} +(-1.01329e7 - 1.39514e7i) q^{33} +(1.20193e6 - 437466. i) q^{34} +(-5.68204e7 - 3.28053e7i) q^{35} +(3.63809e7 + 4.04305e7i) q^{36} +(3.39317e7 + 5.87714e7i) q^{37} +(-1.56501e7 + 1.86511e7i) q^{38} +(1.70248e8 + 1.19318e7i) q^{39} +(-1.39632e7 - 7.91892e7i) q^{40} +(-8.50271e7 + 1.49926e7i) q^{41} +(-2.77479e6 + 3.95921e7i) q^{42} +(-8.62677e7 - 7.23872e7i) q^{43} +(-5.66025e7 + 3.26795e7i) q^{44} +(-4.99564e7 - 2.35390e8i) q^{45} +(-3.35595e7 + 5.81268e7i) q^{46} +(-8.10430e7 - 2.22664e8i) q^{47} +(1.46088e8 - 1.06104e8i) q^{48} +(-1.78166e7 + 1.49499e7i) q^{49} +(-2.37361e7 + 6.52145e7i) q^{50} +(-8.44045e6 - 2.94528e7i) q^{51} +(1.12334e8 - 6.37078e8i) q^{52} -5.12143e8i q^{53} +(-1.14748e8 + 8.95639e7i) q^{54} +2.89165e8 q^{55} +(3.12865e8 + 5.51665e7i) q^{56} +(4.19461e8 + 4.05196e8i) q^{57} +(2.04325e8 + 7.43681e7i) q^{58} +(7.08786e8 + 8.44699e8i) q^{59} +(-9.07132e8 + 9.51995e7i) q^{60} +(-6.03944e8 + 2.19817e8i) q^{61} +(-4.04598e8 - 2.33595e8i) q^{62} +(9.41408e8 + 1.32608e8i) q^{63} +(-2.39704e8 - 4.15180e8i) q^{64} +(-1.83971e9 + 2.19248e9i) q^{65} +(-7.66560e7 - 1.57231e8i) q^{66} +(-3.30698e8 - 1.87548e9i) q^{67} +(-1.14370e8 + 2.01665e7i) q^{68} +(1.33274e9 + 8.99251e8i) q^{69} +(-5.09872e8 - 4.27834e8i) q^{70} +(-1.80207e9 + 1.04043e9i) q^{71} +(6.17130e8 + 9.88305e8i) q^{72} +(-1.61956e7 + 2.80516e7i) q^{73} +(2.35462e8 + 6.46927e8i) q^{74} +(1.51856e9 + 6.76390e8i) q^{75} +(1.69345e9 - 1.42097e9i) q^{76} +(-3.90740e8 + 1.07355e9i) q^{77} +(1.67984e9 + 4.19111e8i) q^{78} +(-5.52812e7 + 3.13515e8i) q^{79} +3.02791e9i q^{80} +(1.94797e9 + 2.89190e9i) q^{81} -8.75870e8 q^{82} +(-5.26514e9 - 9.28386e8i) q^{83} +(8.72344e8 - 3.49644e9i) q^{84} +(4.82822e8 + 1.75733e8i) q^{85} +(-7.34337e8 - 8.75149e8i) q^{86} +(2.11921e9 - 4.75782e9i) q^{87} +(-1.31572e9 + 4.78882e8i) q^{88} +(5.25641e9 + 3.03479e9i) q^{89} +(-8.44280e7 - 2.43965e9i) q^{90} +(-5.65383e9 - 9.79271e9i) q^{91} +(3.91724e9 - 4.66839e9i) q^{92} +(-6.25934e9 + 9.27671e9i) q^{93} +(-4.17415e8 - 2.36728e9i) q^{94} +(-9.63186e9 + 1.69836e9i) q^{95} +(6.05979e9 - 2.95438e9i) q^{96} +(4.82972e9 + 4.05261e9i) q^{97} +(-2.04332e8 + 1.17971e8i) q^{98} +(-3.88541e9 + 1.56839e9i) 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

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