LMFDB - Embedded newform 27.12.e.a.4.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,12,Mod(4,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.4"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, 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:	$20.7452658751$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	27.4
Dual form			27.12.e.a.7.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-58.6349 - 21.3414i) q^{2} +(176.782 + 381.962i) q^{3} +(1413.74 + 1186.27i) q^{4} +(-404.877 + 2296.17i) q^{5} +(-2213.98 - 26169.1i) q^{6} +(-56857.8 + 47709.4i) q^{7} +(6317.45 + 10942.1i) q^{8} +(-114643. + 135048. i) q^{9} +(72743.5 - 125995. i) q^{10} +(60239.0 + 341632. i) q^{11} +(-203187. + 749708. i) q^{12} +(1.60328e6 - 583546. i) q^{13} +(4.35204e6 - 1.58401e6i) q^{14} +(-948627. + 251274. i) q^{15} +(-793225. - 4.49860e6i) q^{16} +(-3.38117e6 + 5.85636e6i) q^{17} +(9.60422e6 - 5.47188e6i) q^{18} +(8.10496e6 + 1.40382e7i) q^{19} +(-3.29628e6 + 2.76591e6i) q^{20} +(-2.82746e7 - 1.32834e7i) q^{21} +(3.75879e6 - 2.13172e7i) q^{22} +(-3.18273e7 - 2.67062e7i) q^{23} +(-3.06268e6 + 4.34740e6i) q^{24} +(4.07749e7 + 1.48409e7i) q^{25} -1.06462e8 q^{26} +(-7.18501e7 - 1.99155e7i) q^{27} -1.36979e8 q^{28} +(-6.21097e7 - 2.26061e7i) q^{29} +(6.09852e7 + 5.51159e6i) q^{30} +(-1.68295e8 - 1.41216e8i) q^{31} +(-4.50023e7 + 2.55221e8i) q^{32} +(-1.19842e8 + 8.34034e7i) q^{33} +(3.23237e8 - 2.71228e8i) q^{34} +(-8.65285e7 - 1.49872e8i) q^{35} +(-3.22280e8 + 5.49248e7i) q^{36} +(2.12756e8 - 3.68504e8i) q^{37} +(-1.75639e8 - 9.96101e8i) q^{38} +(5.06323e8 + 5.09232e8i) q^{39} +(-2.76828e7 + 1.00757e7i) q^{40} +(5.56693e7 - 2.02620e7i) q^{41} +(1.37439e9 + 1.38229e9i) q^{42} +(-1.73035e7 - 9.81332e7i) q^{43} +(-3.20106e8 + 5.54441e8i) q^{44} +(-2.63677e8 - 3.17919e8i) q^{45} +(1.29624e9 + 2.24516e9i) q^{46} +(-1.52496e9 + 1.27959e9i) q^{47} +(1.57807e9 - 1.09825e9i) q^{48} +(6.13267e8 - 3.47801e9i) q^{49} +(-2.07411e9 - 1.74039e9i) q^{50} +(-2.83464e9 - 2.56183e8i) q^{51} +(2.95887e9 + 1.07694e9i) q^{52} -1.91462e9 q^{53} +(3.78790e9 + 2.70112e9i) q^{54} -8.08837e8 q^{55} +(-8.81239e8 - 3.20745e8i) q^{56} +(-3.92926e9 + 5.57749e9i) q^{57} +(3.15935e9 + 2.65101e9i) q^{58} +(1.31234e8 - 7.44263e8i) q^{59} +(-1.63919e9 - 7.70093e8i) q^{60} +(4.75406e9 - 3.98913e9i) q^{61} +(6.85421e9 + 1.18718e10i) q^{62} +(7.53272e7 - 1.31481e10i) q^{63} +(3.40783e9 - 5.90254e9i) q^{64} +(6.90791e8 + 3.91767e9i) q^{65} +(8.80685e9 - 2.33277e9i) q^{66} +(-1.06557e9 + 3.87835e8i) q^{67} +(-1.17273e10 + 4.26840e9i) q^{68} +(4.57430e9 - 1.68780e10i) q^{69} +(1.87513e9 + 1.06344e10i) q^{70} +(7.98925e9 - 1.38378e10i) q^{71} +(-2.20197e9 - 4.01287e8i) q^{72} +(1.35392e10 + 2.34506e10i) q^{73} +(-2.03393e10 + 1.70667e10i) q^{74} +(1.53961e9 + 1.81981e10i) q^{75} +(-5.19479e9 + 2.94611e10i) q^{76} +(-1.97241e10 - 1.65505e10i) q^{77} +(-1.88205e10 - 4.06644e10i) q^{78} +(-2.69303e10 - 9.80184e9i) q^{79} +1.06507e10 q^{80} +(-5.09481e9 - 3.09647e10i) q^{81} -3.69659e9 q^{82} +(2.10798e10 + 7.67243e9i) q^{83} +(-2.42153e10 - 5.23207e10i) q^{84} +(-1.20783e10 - 1.01349e10i) q^{85} +(-1.07971e9 + 6.12331e9i) q^{86} +(-2.34518e9 - 2.77199e10i) q^{87} +(-3.35763e9 + 2.81739e9i) q^{88} +(9.43880e9 + 1.63485e10i) q^{89} +(8.67585e9 + 2.42684e10i) q^{90} +(-6.33183e10 + 1.09671e11i) q^{91} +(-1.33147e10 - 7.55116e10i) q^{92} +(2.41878e10 - 8.92467e10i) q^{93} +(1.16724e11 - 4.24841e10i) q^{94} +(-3.55157e10 + 1.29267e10i) q^{95} +(-1.05440e11 + 2.79292e10i) q^{96} +(-2.44983e9 - 1.38937e10i) q^{97} +(-1.10184e11 + 1.90845e11i) q^{98} +(-5.30428e10 - 3.10308e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2931 q^{5} + 4410 q^{6} - 6 q^{7} - 294915 q^{8} + 96228 q^{9} - 3 q^{10} - 1594293 q^{11} + 323823 q^{12} - 6 q^{13} + 5263143 q^{14} + 3836529 q^{15} + 6138 q^{16}+ \cdots - 581308635231 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2931 * q^5 + 4410 * q^6 - 6 * q^7 - 294915 * q^8 + 96228 * q^9 - 3 * q^10 - 1594293 * q^11 + 323823 * q^12 - 6 * q^13 + 5263143 * q^14 + 3836529 * q^15 + 6138 * q^16 - 17038287 * q^17 + 8396685 * q^18 - 3 * q^19 + 33966483 * q^20 + 73765320 * q^21 - 6811494 * q^22 - 154612956 * q^23 - 52250526 * q^24 - 39922647 * q^25 + 72169026 * q^26 + 406211103 * q^27 - 12 * q^28 - 818363742 * q^29 - 845653581 * q^30 - 114913365 * q^31 + 2449907208 * q^32 + 792631584 * q^33 + 250353882 * q^34 - 1986199152 * q^35 - 1271261664 * q^36 - 3 * q^37 - 199328700 * q^38 + 2330844945 * q^39 + 159067281 * q^40 + 2363326233 * q^41 - 3110154678 * q^42 + 2031687507 * q^43 - 6781787259 * q^44 + 9102254625 * q^45 - 3 * q^46 + 1321238505 * q^47 - 6384109047 * q^48 + 5300190696 * q^49 - 19347232641 * q^50 + 1310770386 * q^51 - 7435159623 * q^52 + 7067989026 * q^53 + 22629480894 * q^54 - 12 * q^55 - 8014324821 * q^56 - 32645841267 * q^57 + 16115317383 * q^58 + 21931606932 * q^59 + 50690195514 * q^60 - 16510964208 * q^61 + 11823393570 * q^62 - 30632962095 * q^63 - 80530636803 * q^64 + 4275338385 * q^65 + 38229021261 * q^66 - 38080922415 * q^67 + 82368304983 * q^68 - 30801215529 * q^69 + 60497186367 * q^70 - 50263647093 * q^71 + 3848431572 * q^72 + 1424119740 * q^73 - 72634311813 * q^74 + 108769340739 * q^75 - 116456331270 * q^76 + 62223517041 * q^77 - 72959471478 * q^78 + 90355950390 * q^79 + 24737530830 * q^80 - 144648556128 * q^81 - 12 * q^82 + 113535448779 * q^83 + 273199455402 * q^84 - 164592103131 * q^85 - 28905145338 * q^86 - 308647046223 * q^87 + 67619592186 * q^88 - 100969659531 * q^89 + 650525024790 * q^90 - 61084040502 * q^91 - 29835580269 * q^92 - 323782133601 * q^93 - 264765665733 * q^94 + 349741980687 * q^95 + 620032058802 * q^96 - 109680687051 * q^97 + 282639387726 * q^98 - 581308635231 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−58.6349	−	21.3414i	−1.29566	−	0.471582i	−0.400080	−	0.916480i	$-0.631018\pi$
$2$	−58.6349	−	21.3414i	−1.29566	−	0.471582i	−0.895581	+	0.444898i	$0.853240\pi$
$3$	176.782	+	381.962i	0.420020	+	0.907515i
$3$	176.782	+	381.962i	0.420020	+	0.907515i
$4$	1413.74	+	1186.27i	0.690305	+	0.579234i
$5$	−404.877	+	2296.17i	−0.0579413	+	0.328602i	−0.999976	−	0.00691364i	$-0.997799\pi$
$5$	−404.877	+	2296.17i	−0.0579413	+	0.328602i	0.942035	+	0.335515i	$0.108910\pi$
$6$	−2213.98	−	26169.1i	−0.116236	−	1.37391i
$7$	−56857.8	+	47709.4i	−1.27865	+	1.07291i	−0.285219	+	0.958463i	$0.592066\pi$
$7$	−56857.8	+	47709.4i	−1.27865	+	1.07291i	−0.993429	+	0.114450i	$0.963489\pi$
$8$	6317.45	+	10942.1i	0.0681627	+	0.118061i
$9$	−114643.	+	135048.i	−0.647166	+	0.762349i
$10$	72743.5	−	125995.i	0.230035	−	0.398432i
$11$	60239.0	+	341632.i	0.112776	+	0.639587i	0.987827	+	0.155555i	$0.0497167\pi$
$11$	60239.0	+	341632.i	0.112776	+	0.639587i	−0.875051	+	0.484031i	$0.839172\pi$
$12$	−203187.	+	749708.i	−0.235722	+	0.869752i
$13$	1.60328e6	−	583546.i	1.19762	−	0.435900i	0.335230	−	0.942136i	$-0.391186\pi$
$13$	1.60328e6	−	583546.i	1.19762	−	0.435900i	0.862395	+	0.506237i	$0.168964\pi$
$14$	4.35204e6	−	1.58401e6i	2.16266	−	0.787144i
$15$	−948627.	+	251274.i	−0.322547	+	0.0854368i
$16$	−793225.	−	4.49860e6i	−0.189120	−	1.07255i
$17$	−3.38117e6	+	5.85636e6i	−0.577561	+	1.00037i	0.418197	+	0.908356i	$0.362662\pi$
$17$	−3.38117e6	+	5.85636e6i	−0.577561	+	1.00037i	−0.995758	+	0.0920089i	$0.970671\pi$
$18$	9.60422e6	−	5.47188e6i	1.19802	−	0.682555i
$19$	8.10496e6	+	1.40382e7i	0.750942	+	1.30067i	0.947367	+	0.320150i	$0.103733\pi$
$19$	8.10496e6	+	1.40382e7i	0.750942	+	1.30067i	−0.196425	+	0.980519i	$0.562933\pi$
$20$	−3.29628e6	+	2.76591e6i	−0.230334	+	0.193274i
$21$	−2.82746e7	−	1.32834e7i	−1.51074	−	0.709746i
$22$	3.75879e6	−	2.13172e7i	0.155498	−	0.881871i
$23$	−3.18273e7	−	2.67062e7i	−1.03109	−	0.865186i	−0.0401088	−	0.999195i	$-0.512770\pi$
$23$	−3.18273e7	−	2.67062e7i	−1.03109	−	0.865186i	−0.990980	+	0.134009i	$0.957215\pi$
$24$	−3.06268e6	+	4.34740e6i	−0.0785126	+	0.111447i
$25$	4.07749e7	+	1.48409e7i	0.835071	+	0.303941i
$26$	−1.06462e8			−1.75728
$27$	−7.18501e7	−	1.99155e7i	−0.963666	−	0.267110i
$28$	−1.36979e8			−1.50412
$29$	−6.21097e7	−	2.26061e7i	−0.562303	−	0.204661i	0.0452015	−	0.998978i	$-0.485607\pi$
$29$	−6.21097e7	−	2.26061e7i	−0.562303	−	0.204661i	−0.607504	+	0.794316i	$0.707829\pi$
$30$	6.09852e7	+	5.51159e6i	0.458203	+	0.0414105i
$31$	−1.68295e8	−	1.41216e8i	−1.05580	−	0.885921i	−0.0621082	−	0.998069i	$-0.519782\pi$
$31$	−1.68295e8	−	1.41216e8i	−1.05580	−	0.885921i	−0.993691	+	0.112148i	$0.964227\pi$
$32$	−4.50023e7	+	2.55221e8i	−0.237088	+	1.34459i
$33$	−1.19842e8	+	8.34034e7i	−0.533066	+	0.370986i
$34$	3.23237e8	−	2.71228e8i	1.22008	−	1.02377i
$35$	−8.65285e7	−	1.49872e8i	−0.278474	−	0.482332i
$36$	−3.22280e8	+	5.49248e7i	−0.888320	+	0.151393i
$37$	2.12756e8	−	3.68504e8i	0.504397	−	0.873641i	−0.495590	−	0.868557i	$-0.665048\pi$
$37$	2.12756e8	−	3.68504e8i	0.504397	−	0.873641i	0.999987	−	0.00508479i	$-0.00161855\pi$
$38$	−1.75639e8	−	9.96101e8i	−0.359594	−	2.03936i
$39$	5.06323e8	+	5.09232e8i	0.898612	+	0.903775i
$40$	−2.76828e7	+	1.00757e7i	−0.0427445	+	0.0155577i
$41$	5.56693e7	−	2.02620e7i	0.0750421	−	0.0273131i	−0.304226	−	0.952600i	$-0.598398\pi$
$41$	5.56693e7	−	2.02620e7i	0.0750421	−	0.0273131i	0.379268	+	0.925287i	$0.376176\pi$
$42$	1.37439e9	+	1.38229e9i	1.62271	+	1.63203i
$43$	−1.73035e7	−	9.81332e7i	−0.0179497	−	0.101798i	0.974517	−	0.224315i	$-0.0720145\pi$
$43$	−1.73035e7	−	9.81332e7i	−0.0179497	−	0.101798i	−0.992466	+	0.122517i	$0.960903\pi$
$44$	−3.20106e8	+	5.54441e8i	−0.292620	+	0.506833i
$45$	−2.63677e8	−	3.17919e8i	−0.213012	−	0.256831i
$46$	1.29624e9	+	2.24516e9i	0.927936	+	1.60723i
$47$	−1.52496e9	+	1.27959e9i	−0.969884	+	0.813829i	−0.982533	−	0.186091i	$-0.940418\pi$
$47$	−1.52496e9	+	1.27959e9i	−0.969884	+	0.813829i	0.0126489	+	0.999920i	$0.495974\pi$
$48$	1.57807e9	−	1.09825e9i	0.893921	−	0.622122i
$49$	6.13267e8	−	3.47801e9i	0.310150	−	1.75895i
$50$	−2.07411e9	−	1.74039e9i	−0.938636	−	0.787609i
$51$	−2.83464e9	−	2.56183e8i	−1.15043	−	0.103971i
$52$	2.95887e9	+	1.07694e9i	1.07921	+	0.392802i
$53$	−1.91462e9			−0.628876			−0.314438	−	0.949278i	$-0.601816\pi$
$53$	−1.91462e9			−0.628876			−0.314438	+	0.949278i	$0.601816\pi$
$54$	3.78790e9	+	2.70112e9i	1.12262	+	0.800532i
$55$	−8.08837e8			−0.216704
$56$	−8.81239e8	−	3.20745e8i	−0.213825	−	0.0778261i
$57$	−3.92926e9	+	5.57749e9i	−0.864966	+	1.22780i
$58$	3.15935e9	+	2.65101e9i	0.632039	+	0.530344i
$59$	1.31234e8	−	7.44263e8i	0.0238979	−	0.135531i	−0.970525	−	0.241002i	$-0.922524\pi$
$59$	1.31234e8	−	7.44263e8i	0.0238979	−	0.135531i	0.994422	+	0.105471i	$0.0336350\pi$
$60$	−1.63919e9	−	7.70093e8i	−0.272144	−	0.127853i
$61$	4.75406e9	−	3.98913e9i	0.720693	−	0.604734i	−0.206884	−	0.978366i	$-0.566332\pi$
$61$	4.75406e9	−	3.98913e9i	0.720693	−	0.604734i	0.927577	+	0.373632i	$0.121888\pi$
$62$	6.85421e9	+	1.18718e10i	0.950174	+	1.64575i
$63$	7.53272e7	−	1.31481e10i	0.00956267	−	1.66913i
$64$	3.40783e9	−	5.90254e9i	0.396724	−	0.687146i
$65$	6.90791e8	+	3.91767e9i	0.0738454	+	0.418798i
$66$	8.80685e9	−	2.33277e9i	0.865623	−	0.229287i
$67$	−1.06557e9	+	3.87835e8i	−0.0964206	+	0.0350942i	−0.389780	−	0.920908i	$-0.627449\pi$
$67$	−1.06557e9	+	3.87835e8i	−0.0964206	+	0.0350942i	0.293359	+	0.956002i	$0.405227\pi$
$68$	−1.17273e10	+	4.26840e9i	−0.978139	+	0.356013i
$69$	4.57430e9	−	1.68780e10i	0.352091	−	1.29912i
$70$	1.87513e9	+	1.06344e10i	0.133349	+	0.756262i
$71$	7.98925e9	−	1.38378e10i	0.525515	−	0.910219i	−0.474043	−	0.880502i	$-0.657206\pi$
$71$	7.98925e9	−	1.38378e10i	0.525515	−	0.910219i	0.999558	−	0.0297175i	$-0.00946076\pi$
$72$	−2.20197e9	−	4.01287e8i	−0.134116	−	0.0244414i
$73$	1.35392e10	+	2.34506e10i	0.764394	+	1.32397i	0.940566	+	0.339611i	$0.110295\pi$
$73$	1.35392e10	+	2.34506e10i	0.764394	+	1.32397i	−0.176172	+	0.984359i	$0.556371\pi$
$74$	−2.03393e10	+	1.70667e10i	−1.06552	+	0.894079i
$75$	1.53961e9	+	1.81981e10i	0.0749159	+	0.885500i
$76$	−5.19479e9	+	2.94611e10i	−0.235014	+	1.33283i
$77$	−1.97241e10	−	1.65505e10i	−0.830422	−	0.696807i
$78$	−1.88205e10	−	4.06644e10i	−0.738093	−	1.59476i
$79$	−2.69303e10	−	9.80184e9i	−0.984675	−	0.358392i	−0.201019	−	0.979587i	$-0.564425\pi$
$79$	−2.69303e10	−	9.80184e9i	−0.984675	−	0.358392i	−0.783656	+	0.621195i	$0.786647\pi$
$80$	1.06507e10			0.363400
$81$	−5.09481e9	−	3.09647e10i	−0.162353	−	0.986733i
$82$	−3.69659e9			−0.110109
$83$	2.10798e10	+	7.67243e9i	0.587405	+	0.213798i	0.618588	−	0.785716i	$-0.287705\pi$
$83$	2.10798e10	+	7.67243e9i	0.587405	+	0.213798i	−0.0311826	+	0.999514i	$0.509927\pi$
$84$	−2.42153e10	−	5.23207e10i	−0.631763	−	1.36501i
$85$	−1.20783e10	−	1.01349e10i	−0.295257	−	0.247750i
$86$	−1.07971e9	+	6.12331e9i	−0.0247494	+	0.140361i
$87$	−2.34518e9	−	2.77199e10i	−0.0504453	−	0.596260i
$88$	−3.35763e9	+	2.81739e9i	−0.0678232	+	0.0569105i
$89$	9.43880e9	+	1.63485e10i	0.179173	+	0.310336i	0.941597	−	0.336741i	$-0.109325\pi$
$89$	9.43880e9	+	1.63485e10i	0.179173	+	0.310336i	−0.762425	+	0.647077i	$0.775991\pi$
$90$	8.67585e9	+	2.42684e10i	0.154874	+	0.433219i
$91$	−6.33183e10	+	1.09671e11i	−1.06366	+	1.84231i
$92$	−1.33147e10	−	7.55116e10i	−0.210620	−	1.19448i
$93$	2.41878e10	−	8.92467e10i	0.360529	−	1.33026i
$94$	1.16724e11	−	4.24841e10i	1.64043	−	0.597067i
$95$	−3.55157e10	+	1.29267e10i	−0.470913	+	0.171398i
$96$	−1.05440e11	+	2.79292e10i	−1.31982	+	0.349596i
$97$	−2.44983e9	−	1.38937e10i	−0.0289662	−	0.164276i	0.966893	−	0.255181i	$-0.0821351\pi$
$97$	−2.44983e9	−	1.38937e10i	−0.0289662	−	0.164276i	−0.995860	+	0.0909053i	$0.971024\pi$
$98$	−1.10184e11	+	1.90845e11i	−1.23134	+	2.13274i
$99$	−5.30428e10	−	3.10308e10i	−0.560573	−	0.327944i
$100$	4.00400e10	+	6.93513e10i	0.400400	+	0.693513i
$101$	−3.26434e9	+	2.73910e9i	−0.0309049	+	0.0259323i	−0.658109	−	0.752922i	$-0.728644\pi$
$101$	−3.26434e9	+	2.73910e9i	−0.0309049	+	0.0259323i	0.627204	+	0.778855i	$0.284199\pi$
$102$	1.60742e11	+	7.55163e10i	1.44154	+	0.677236i
$103$	1.34268e10	−	7.61472e10i	0.114122	−	0.647216i	−0.873060	−	0.487613i	$-0.837868\pi$
$103$	1.34268e10	−	7.61472e10i	0.114122	−	0.647216i	0.987181	−	0.159603i	$-0.0510213\pi$
$104$	1.65139e10	+	1.38568e10i	0.133096	+	0.111681i
$105$	4.19487e10	−	5.95452e10i	0.320758	−	0.455309i
$106$	1.12264e11	+	4.08606e10i	0.814810	+	0.296567i
$107$	−2.85235e9			−0.0196604			−0.00983020	−	0.999952i	$-0.503129\pi$
$107$	−2.85235e9			−0.0196604			−0.00983020	+	0.999952i	$0.503129\pi$
$108$	−7.79524e10	−	1.13389e11i	−0.510504	−	0.742576i
$109$	1.92106e11			1.19590			0.597951	−	0.801532i	$-0.295982\pi$
$109$	1.92106e11			1.19590			0.597951	+	0.801532i	$0.295982\pi$
$110$	4.74261e10	+	1.72617e10i	0.280775	+	0.102194i
$111$	1.78366e11	+	1.61200e10i	1.00470	+	0.0908006i
$112$	2.59726e11	+	2.17936e11i	1.39257	+	1.16850i
$113$	−5.41721e10	+	3.07225e11i	−0.276595	+	1.56865i	0.457255	+	0.889336i	$0.348833\pi$
$113$	−5.41721e10	+	3.07225e11i	−0.276595	+	1.56865i	−0.733850	+	0.679312i	$0.762278\pi$
$114$	3.49423e11	−	2.43180e11i	1.69971	−	1.18291i
$115$	7.42083e10	−	6.22682e10i	0.344044	−	0.288687i
$116$	−6.09902e10	−	1.05638e11i	−0.269613	−	0.466984i
$117$	−1.04999e11	+	2.83419e11i	−0.442754	+	1.19511i
$118$	−2.35785e10	+	4.08391e10i	−0.0948778	+	0.164333i
$119$	−8.71572e10	−	4.94293e11i	−0.334807	−	1.89879i
$120$	−8.74237e9	−	8.79260e9i	−0.0320725	−	0.0322567i
$121$	1.55021e11	−	5.64231e10i	0.543340	−	0.197760i
$122$	−3.63888e11	+	1.32444e11i	−1.21896	+	0.443664i
$123$	1.75806e10	+	1.76816e10i	0.0563062	+	0.0566297i
$124$	−7.04051e10	−	3.99287e11i	−0.215667	−	1.22311i
$125$	−1.07510e11	+	1.86212e11i	−0.315096	+	0.545762i
$126$	−2.85015e11	+	7.69330e11i	−0.799521	+	2.15812i
$127$	1.03067e10	+	1.78518e10i	0.0276822	+	0.0479470i	0.879535	−	0.475835i	$-0.157854\pi$
$127$	1.03067e10	+	1.78518e10i	0.0276822	+	0.0479470i	−0.851852	+	0.523782i	$0.824521\pi$
$128$	8.07956e10	−	6.77955e10i	0.207842	−	0.174400i
$129$	3.44242e10	−	2.39574e10i	0.0848439	−	0.0590469i
$130$	4.31040e10	−	2.44455e11i	0.101819	−	0.577445i
$131$	−5.74977e11	−	4.82463e11i	−1.30214	−	1.09263i	−0.989771	−	0.142666i	$-0.954433\pi$
$131$	−5.74977e11	−	4.82463e11i	−1.30214	−	1.09263i	−0.312370	−	0.949960i	$-0.601123\pi$
$132$	−2.68364e11	−	2.42537e10i	−0.582865	−	0.0526770i
$133$	−1.13058e12	−	4.11499e11i	−2.35569	−	0.857403i
$134$	7.07565e10			0.141478
$135$	7.48199e10	−	1.56917e11i	0.143609	−	0.301185i
$136$	−8.54414e10			−0.157472
$137$	9.70887e11	+	3.53374e11i	1.71872	+	0.625564i	0.997728	−	0.0673770i	$-0.0214630\pi$
$137$	9.70887e11	+	3.53374e11i	1.71872	+	0.625564i	0.720995	+	0.692941i	$0.243685\pi$
$138$	−6.28413e11	+	8.92018e11i	−1.06883	+	1.51719i
$139$	7.75415e10	+	6.50650e10i	0.126751	+	0.106357i	0.703960	−	0.710240i	$-0.251414\pi$
$139$	7.75415e10	+	6.50650e10i	0.126751	+	0.106357i	−0.577208	+	0.816597i	$0.695858\pi$
$140$	5.54595e10	−	3.14527e11i	0.0871509	−	0.494258i
$141$	−7.58340e11	−	3.56268e11i	−1.14593	−	0.538359i
$142$	−7.63767e11	+	6.40877e11i	−1.11013	+	0.931512i
$143$	2.95938e11	+	5.12580e11i	0.413859	+	0.716826i
$144$	6.98465e11	+	4.08612e11i	0.940049	+	0.549943i
$145$	7.70543e10	−	1.33462e11i	0.0998327	−	0.172915i
$146$	−2.93403e11	−	1.66397e12i	−0.366036	−	2.07589i
$147$	1.43688e12	−	3.80604e11i	1.72654	−	0.457328i
$148$	7.37929e11	−	2.68584e11i	0.854231	−	0.310915i
$149$	−7.82636e11	+	2.84856e11i	−0.873042	+	0.317761i	−0.739398	−	0.673268i	$-0.764890\pi$
$149$	−7.82636e11	+	2.84856e11i	−0.873042	+	0.317761i	−0.133644	+	0.991029i	$0.542668\pi$
$150$	2.98097e11	−	1.09990e12i	0.320521	−	1.18264i
$151$	−1.63220e11	−	9.25667e11i	−0.169200	−	0.959581i	−0.944628	−	0.328145i	$-0.893577\pi$
$151$	−1.63220e11	−	9.25667e11i	−0.169200	−	0.959581i	0.775427	−	0.631437i	$-0.217534\pi$
$152$	−1.02405e11	+	1.77371e11i	−0.102372	+	0.177314i
$153$	−4.03260e11	−	1.12801e12i	−0.388850	−	1.08771i
$154$	8.03312e11	+	1.39138e12i	0.747344	+	1.29444i
$155$	3.92396e11	−	3.29259e11i	0.352290	−	0.295606i
$156$	1.11723e11	+	1.32056e12i	0.0968185	+	1.14439i
$157$	−8.34167e10	+	4.73079e11i	−0.0697919	+	0.395809i	0.929822	+	0.368010i	$0.119961\pi$
$157$	−8.34167e10	+	4.73079e11i	−0.0697919	+	0.395809i	−0.999614	+	0.0277989i	$0.991150\pi$
$158$	1.36987e12	+	1.14946e12i	1.10679	+	0.928710i
$159$	−3.38469e11	−	7.31312e11i	−0.264141	−	0.570714i
$160$	−5.67810e11	−	2.06666e11i	−0.428098	−	0.155815i
$161$	3.08377e12			2.24667
$162$	−3.62096e11	+	1.92434e12i	−0.254971	+	1.35503i
$163$	−2.76206e12			−1.88019			−0.940095	−	0.340913i	$-0.889264\pi$
$163$	−2.76206e12			−1.88019			−0.940095	+	0.340913i	$0.889264\pi$
$164$	1.02738e11	+	3.73937e10i	0.0676225	+	0.0246126i
$165$	−1.42988e11	−	3.08945e11i	−0.0910199	−	0.196662i
$166$	−1.07227e12	−	8.99745e11i	−0.660255	−	0.554020i
$167$	5.40582e10	−	3.06579e11i	0.0322048	−	0.182643i	−0.964462	−	0.264221i	$-0.914885\pi$
$167$	5.40582e10	−	3.06579e11i	0.0322048	−	0.182643i	0.996667	+	0.0815787i	$0.0259962\pi$
$168$	−3.32745e10	−	3.93302e11i	−0.0191827	−	0.226738i
$169$	8.57104e11	−	7.19196e11i	0.478252	−	0.401301i
$170$	4.91916e11	+	8.52024e11i	0.265719	+	0.460238i
$171$	−2.82501e12	−	5.14831e11i	−1.47755	−	0.269269i
$172$	9.19499e10	−	1.59262e11i	0.0465741	−	0.0806687i
$173$	2.63830e11	+	1.49625e12i	0.129441	+	0.734094i	0.978571	+	0.205910i	$0.0660155\pi$
$173$	2.63830e11	+	1.49625e12i	0.129441	+	0.734094i	−0.849130	+	0.528183i	$0.822873\pi$
$174$	−4.54071e11	+	1.67540e12i	−0.215826	+	0.796340i
$175$	−3.02642e12	+	1.10153e12i	−1.39386	+	0.507325i
$176$	1.48909e12	−	5.41983e11i	0.664660	−	0.241917i
$177$	3.07480e11	−	8.14457e10i	0.133034	−	0.0352383i
$178$	−2.04544e11	−	1.16003e12i	−0.0857981	−	0.486585i
$179$	−5.90846e11	+	1.02338e12i	−0.240316	+	0.416240i	−0.960804	−	0.277228i	$-0.910584\pi$
$179$	−5.90846e11	+	1.02338e12i	−0.240316	+	0.416240i	0.720488	+	0.693467i	$0.243918\pi$
$180$	4.36703e9	−	7.62249e11i	0.00172261	−	0.300675i
$181$	1.93205e12	+	3.34641e12i	0.739241	+	1.28040i	0.952837	+	0.303481i	$0.0981490\pi$
$181$	1.93205e12	+	3.34641e12i	0.739241	+	1.28040i	−0.213596	+	0.976922i	$0.568518\pi$
$182$	6.05319e12	−	5.07923e12i	2.24694	−	1.88541i
$183$	2.36413e12	+	1.11067e12i	0.851511	+	0.400039i
$184$	9.11564e10	−	5.16973e11i	0.0318632	−	0.180705i
$185$	7.60010e11	+	6.37724e11i	0.257855	+	0.216366i
$186$	−3.32290e12	+	4.71678e12i	−1.09445	+	1.55355i
$187$	−2.20440e12	−	8.02336e11i	−0.704956	−	0.256583i
$188$	−3.67384e12			−1.14091
$189$	5.03539e12	−	2.29557e12i	1.51878	−	0.692390i
$190$	2.35833e12			0.690972
$191$	−2.00511e12	−	7.29801e11i	−0.570762	−	0.207740i	0.0404851	−	0.999180i	$-0.487110\pi$
$191$	−2.00511e12	−	7.29801e11i	−0.570762	−	0.207740i	−0.611247	+	0.791440i	$0.709332\pi$
$192$	2.85699e12	+	2.58203e11i	0.790227	+	0.0714175i
$193$	−8.52205e11	−	7.15085e11i	−0.229076	−	0.192217i	0.521024	−	0.853542i	$-0.325550\pi$
$193$	−8.52205e11	−	7.15085e11i	−0.229076	−	0.192217i	−0.750100	+	0.661325i	$0.769995\pi$
$194$	−1.52865e11	+	8.66939e11i	−0.0399391	+	0.226506i
$195$	−1.37428e12	+	9.56429e11i	−0.349049	+	0.242919i
$196$	4.99287e12	−	4.18952e12i	1.23294	−	1.03456i
$197$	−2.57058e12	−	4.45237e12i	−0.617258	−	1.06912i	−0.989984	−	0.141181i	$-0.954910\pi$
$197$	−2.57058e12	−	4.45237e12i	−0.617258	−	1.06912i	0.372726	−	0.927941i	$-0.378423\pi$
$198$	2.44792e12	+	2.95149e12i	0.571661	+	0.689260i
$199$	−3.26232e12	+	5.65051e12i	−0.741028	+	1.28350i	0.210999	+	0.977486i	$0.432328\pi$
$199$	−3.26232e12	+	5.65051e12i	−0.741028	+	1.28350i	−0.952028	+	0.306012i	$0.901005\pi$
$200$	9.52027e10	+	5.39921e11i	0.0210370	+	0.119307i
$201$	−3.36511e11	−	3.38445e11i	−0.0723472	−	0.0727628i
$202$	2.49860e11	−	9.09418e10i	0.0522715	−	0.0190253i
$203$	4.60994e12	−	1.67788e12i	0.938571	−	0.341612i
$204$	−3.70355e12	−	3.72483e12i	−0.733926	−	0.738143i
$205$	2.39858e10	+	1.36030e11i	0.00462708	+	0.0262415i
$206$	−2.41237e12	+	4.17834e12i	−0.453078	+	0.784755i
$207$	7.25541e12	−	1.23651e12i	1.32686	−	0.226131i
$208$	−3.89690e12	−	6.74963e12i	−0.694018	−	1.20208i
$209$	−4.30767e12	+	3.61457e12i	−0.747202	+	0.626977i
$210$	−3.73044e12	+	2.59619e12i	−0.630309	+	0.438662i
$211$	8.21048e10	−	4.65640e11i	0.0135150	−	0.0766472i	−0.977304	−	0.211840i	$-0.932054\pi$
$211$	8.21048e10	−	4.65640e11i	0.0135150	−	0.0766472i	0.990819	+	0.135193i	$0.0431655\pi$
$212$	−2.70678e12	−	2.27126e12i	−0.434116	−	0.364266i
$213$	6.69787e12	+	6.05326e11i	1.04676	+	0.0946022i
$214$	1.67247e11	+	6.08731e10i	0.0254732	+	0.00927149i
$215$	2.32337e11			0.0344910
$216$	−2.35991e11	−	9.12009e11i	−0.0341507	−	0.131979i
$217$	1.63062e13			2.30051
$218$	−1.12641e13	−	4.09981e12i	−1.54949	−	0.563966i
$219$	−6.56376e12	+	9.31710e12i	−0.880461	+	1.24979i
$220$	−1.14349e12	−	9.59500e11i	−0.149591	−	0.125522i
$221$	−2.00351e12	+	1.13624e13i	−0.255643	+	1.44982i
$222$	−1.01145e13	−	4.75178e12i	−1.25893	−	0.591445i
$223$	5.44886e11	−	4.57214e11i	0.0661651	−	0.0555191i	−0.609105	−	0.793089i	$-0.708471\pi$
$223$	5.44886e11	−	4.57214e11i	0.0661651	−	0.0555191i	0.675270	+	0.737570i	$0.264027\pi$
$224$	−9.61768e12	−	1.66583e13i	−1.13948	−	1.97364i
$225$	−6.67881e12	+	3.80516e12i	−0.772138	+	0.439915i
$226$	9.73298e12	−	1.68580e13i	1.09812	−	1.90200i
$227$	9.91570e11	+	5.62347e12i	0.109190	+	0.619245i	0.989464	+	0.144780i	$0.0462474\pi$
$227$	9.91570e11	+	5.62347e12i	0.109190	+	0.619245i	−0.880274	+	0.474465i	$0.842641\pi$
$228$	−1.21714e13	+	3.22397e12i	−1.30827	+	0.346537i
$229$	−1.12416e13	+	4.09160e12i	−1.17959	+	0.429336i	−0.856058	−	0.516880i	$-0.827093\pi$
$229$	−1.12416e13	+	4.09160e12i	−1.17959	+	0.429336i	−0.323534	+	0.946216i	$0.604871\pi$
$230$	−5.68009e12	+	2.06738e12i	−0.581905	+	0.211796i
$231$	2.83481e12	−	1.04597e13i	0.283568	−	1.04629i
$232$	−1.45016e11	−	8.22425e11i	−0.0141655	−	0.0803364i
$233$	−5.97633e12	+	1.03513e13i	−0.570134	+	0.987501i	0.426418	+	0.904526i	$0.359775\pi$
$233$	−5.97633e12	+	1.03513e13i	−0.570134	+	0.987501i	−0.996552	+	0.0829746i	$0.973558\pi$
$234$	1.22052e13	−	1.43775e13i	1.13725	−	1.33966i
$235$	−2.32074e12	−	4.01965e12i	−0.211229	−	0.365860i
$236$	1.06843e12	−	8.96518e11i	0.0950013	−	0.0797155i
$237$	−1.01686e12	−	1.20192e13i	−0.0883372	−	1.04414i
$238$	−5.43844e12	+	3.08429e13i	−0.461637	+	2.61807i
$239$	1.17949e13	+	9.89712e12i	0.978378	+	0.820957i	0.983844	−	0.179028i	$-0.0572954\pi$
$239$	1.17949e13	+	9.89712e12i	0.978378	+	0.820957i	−0.00546583	+	0.999985i	$0.501740\pi$
$240$	1.88285e12	+	4.06818e12i	0.152635	+	0.329790i
$241$	−1.74801e12	−	6.36223e11i	−0.138500	−	0.0504099i	0.271840	−	0.962342i	$-0.412368\pi$
$241$	−1.74801e12	−	6.36223e11i	−0.138500	−	0.0504099i	−0.410340	+	0.911933i	$0.634590\pi$
$242$	−1.02938e13			−0.797245
$243$	1.09267e13	−	7.42002e12i	0.827283	−	0.561786i
$244$	1.14532e13			0.847780
$245$	7.73782e12	+	2.81634e12i	0.560022	+	0.203831i
$246$	−6.53489e11	−	1.41196e12i	−0.0462482	−	0.0999260i
$247$	2.11865e13	+	1.77775e13i	1.46631	+	1.23038i
$248$	4.82013e11	−	2.73363e12i	0.0326268	−	0.185036i
$249$	7.95948e11	+	9.40805e12i	0.0526973	+	0.622878i
$250$	1.02779e13	−	8.62415e12i	0.665630	−	0.558530i
$251$	−8.95063e12	−	1.55029e13i	−0.567085	−	0.982220i	−0.996852	−	0.0792801i	$-0.974738\pi$
$251$	−8.95063e12	−	1.55029e13i	−0.567085	−	0.982220i	0.429768	−	0.902940i	$-0.358595\pi$
$252$	1.57037e13	−	1.84987e13i	0.973418	−	1.14667i
$253$	7.20648e12	−	1.24820e13i	0.437079	−	0.757043i
$254$	−2.23353e11	−	1.26670e12i	−0.0132558	−	0.0751775i
$255$	1.73592e12	−	6.40510e12i	0.100823	−	0.372010i
$256$	−1.93010e13	+	7.02498e12i	−1.09713	+	0.399324i
$257$	9.03328e12	−	3.28785e12i	0.502589	−	0.182928i	−0.0782689	−	0.996932i	$-0.524939\pi$
$257$	9.03328e12	−	3.28785e12i	0.502589	−	0.182928i	0.580858	+	0.814005i	$0.302717\pi$
$258$	−2.52975e12	+	6.70083e11i	−0.137774	+	0.0364939i
$259$	5.48426e12	+	3.11028e13i	0.292395	+	1.65825i
$260$	−3.67082e12	+	6.35805e12i	−0.191606	+	0.331872i
$261$	1.01734e13	−	5.79614e12i	0.519927	−	0.296221i
$262$	2.34173e13	+	4.05600e13i	1.17187	+	2.02974i
$263$	1.44972e13	−	1.21646e13i	0.710442	−	0.596132i	−0.214281	−	0.976772i	$-0.568741\pi$
$263$	1.44972e13	−	1.21646e13i	0.710442	−	0.596132i	0.924723	+	0.380640i	$0.124296\pi$
$264$	−1.66970e12	−	7.84427e11i	−0.0801342	−	0.0376470i
$265$	7.75185e11	−	4.39630e12i	0.0364379	−	0.206650i
$266$	5.75098e13	+	4.82564e13i	2.64785	+	2.22181i
$267$	−4.57590e12	+	6.49538e12i	−0.206378	+	0.292949i
$268$	−1.96652e12	−	7.15754e11i	−0.0868874	−	0.0316244i
$269$	−3.94055e13			−1.70577			−0.852883	−	0.522103i	$-0.825148\pi$
$269$	−3.94055e13			−1.70577			−0.852883	+	0.522103i	$0.825148\pi$
$270$	−7.73588e12	+	7.60406e12i	−0.328102	+	0.322511i
$271$	−1.91718e13			−0.796768			−0.398384	−	0.917219i	$-0.630429\pi$
$271$	−1.91718e13			−0.796768			−0.398384	+	0.917219i	$0.630429\pi$
$272$	2.90274e13	+	1.05651e13i	1.18217	+	0.430275i
$273$	−5.30835e13	−	4.79747e12i	−2.11868	−	0.191478i
$274$	−4.93864e13	−	4.14401e13i	−1.93188	−	1.62104i
$275$	−2.61388e12	+	1.48240e13i	−0.100220	+	0.568377i
$276$	2.64888e13	−	1.84348e13i	0.995547	−	0.692848i
$277$	6.15546e12	−	5.16505e12i	0.226789	−	0.190299i	−0.522312	−	0.852755i	$-0.674930\pi$
$277$	6.15546e12	−	5.16505e12i	0.226789	−	0.190299i	0.749101	+	0.662456i	$0.230486\pi$
$278$	−3.15806e12	−	5.46993e12i	−0.114071	−	0.197576i
$279$	3.83649e13	−	6.53836e12i	1.35866	−	0.231550i
$280$	1.09328e12	−	1.89361e12i	0.0379631	−	0.0657540i
$281$	−5.70365e12	−	3.23470e13i	−0.194208	−	1.10141i	−0.913541	−	0.406746i	$-0.866664\pi$
$281$	−5.70365e12	−	3.23470e13i	−0.194208	−	1.10141i	0.719333	−	0.694665i	$-0.244448\pi$
$282$	3.68620e13	+	3.70738e13i	1.23086	+	1.23793i
$283$	−2.55359e13	+	9.29431e12i	−0.836231	+	0.304363i	−0.724413	−	0.689366i	$-0.757889\pi$
$283$	−2.55359e13	+	9.29431e12i	−0.836231	+	0.304363i	−0.111817	+	0.993729i	$0.535667\pi$
$284$	2.77101e13	−	1.00857e13i	0.889996	−	0.323932i
$285$	−1.12160e13	−	1.12805e13i	−0.353339	−	0.355369i
$286$	−6.41316e12	−	3.63708e13i	−0.198180	−	1.12393i
$287$	−2.19855e12	+	3.80800e12i	−0.0666478	+	0.115437i
$288$	−2.93078e13	−	3.53368e13i	−0.871614	−	1.05092i
$289$	−5.72868e12	−	9.92236e12i	−0.167154	−	0.289519i
$290$	−7.36633e12	+	6.18109e12i	−0.210893	+	0.176960i
$291$	4.87379e12	−	3.39190e12i	0.136916	−	0.0952865i
$292$	−8.67781e12	+	4.92143e13i	−0.239224	+	1.35671i
$293$	−3.70794e13	−	3.11133e13i	−1.00314	−	0.841732i	−0.0157215	−	0.999876i	$-0.505005\pi$
$293$	−3.70794e13	−	3.11133e13i	−1.00314	−	0.841732i	−0.987416	+	0.158144i	$0.949449\pi$
$294$	−9.23742e13	−	8.34840e12i	−2.45268	−	0.221663i
$295$	1.65582e12	+	6.02670e11i	0.0431512	+	0.0157058i
$296$	5.37630e12			0.137524
$297$	2.47560e12	−	2.57460e13i	0.0621613	−	0.646472i
$298$	5.19690e13			1.28102
$299$	−6.66123e13	−	2.42449e13i	−1.61199	−	0.586717i
$300$	−1.94113e13	+	2.75538e13i	−0.461197	+	0.654659i
$301$	5.66571e12	+	4.75410e12i	0.132172	+	0.110905i
$302$	−1.01846e13	+	5.77598e13i	−0.233295	+	1.32308i
$303$	−1.62331e12	−	7.62630e11i	−0.0365146	−	0.0171546i
$304$	5.67232e13	−	4.75964e13i	1.25302	−	1.05140i
$305$	7.23492e12	+	1.25313e13i	0.156959	+	0.271860i
$306$	−4.28236e11	+	7.47471e13i	−0.00912464	+	1.59267i
$307$	−1.21058e13	+	2.09679e13i	−0.253357	+	0.438827i	−0.964448	−	0.264273i	$-0.914868\pi$
$307$	−1.21058e13	+	2.09679e13i	−0.253357	+	0.438827i	0.711091	+	0.703100i	$0.248201\pi$
$308$	−8.25146e12	−	4.67963e13i	−0.169630	−	0.962018i
$309$	3.14590e13	−	8.33289e12i	0.635291	−	0.168277i
$310$	−3.00349e13	+	1.09318e13i	−0.595851	+	0.216872i
$311$	−9.08343e11	+	3.30610e11i	−0.0177038	+	0.00644367i	−0.350857	−	0.936429i	$-0.614110\pi$
$311$	−9.08343e11	+	3.30610e11i	−0.0177038	+	0.00644367i	0.333153	+	0.942873i	$0.391887\pi$
$312$	−2.37342e12	+	8.75730e12i	−0.0454490	+	0.167695i
$313$	−1.10542e11	−	6.26917e11i	−0.00207986	−	0.0117955i	0.983750	−	0.179543i	$-0.0574618\pi$
$313$	−1.10542e11	−	6.26917e11i	−0.00207986	−	0.0117955i	−0.985830	+	0.167747i	$0.946351\pi$
$314$	1.49873e13	−	2.59588e13i	0.277083	−	0.479922i
$315$	3.01598e13	+	5.49633e12i	0.547924	+	0.0998538i
$316$	−2.64450e13	−	4.58040e13i	−0.472132	−	0.817757i
$317$	6.04343e12	−	5.07104e12i	0.106037	−	0.0889756i	−0.588228	−	0.808695i	$-0.700174\pi$
$317$	6.04343e12	−	5.07104e12i	0.106037	−	0.0889756i	0.694265	+	0.719720i	$0.255730\pi$
$318$	4.23893e12	+	5.01038e13i	0.0730983	+	0.864016i
$319$	3.98154e12	−	2.25804e13i	0.0674843	−	0.382722i
$320$	1.21735e13	+	1.02148e13i	0.202811	+	0.170178i
$321$	−5.04244e11	−	1.08949e12i	−0.00825777	−	0.0178421i
$322$	−1.80816e14	−	6.58118e13i	−2.91092	−	1.05949i
$323$	−1.09617e14			−1.73486
$324$	2.95298e13	−	4.98200e13i	0.459476	−	0.775186i
$325$	7.40339e13			1.13259
$326$	1.61953e14	+	5.89462e13i	2.43609	+	0.886664i
$327$	3.39609e13	+	7.33774e13i	0.502303	+	1.08530i
$328$	5.73397e11	+	4.81138e11i	0.00833968	+	0.00699783i
$329$	2.56573e13	−	1.45510e14i	0.366972	−	2.08120i
$330$	1.79075e12	+	2.11665e13i	0.0251889	+	0.297730i
$331$	6.44030e13	−	5.40406e13i	0.890948	−	0.747594i	−0.0774522	−	0.996996i	$-0.524679\pi$
$331$	6.44030e13	−	5.40406e13i	0.890948	−	0.747594i	0.968400	+	0.249402i	$0.0802341\pi$
$332$	2.06999e13	+	3.58533e13i	0.281649	+	0.487831i
$333$	2.53746e13	+	7.09789e13i	0.339591	+	0.949918i
$334$	−9.71252e12	+	1.68226e13i	−0.127857	+	0.221456i
$335$	−4.59112e11	−	2.60376e12i	−0.00594528	−	0.0337174i
$336$	−3.73286e13	+	1.37733e14i	−0.475528	+	1.75457i
$337$	1.09631e14	−	3.99023e13i	1.37394	−	0.500073i	0.453605	−	0.891203i	$-0.350138\pi$
$337$	1.09631e14	−	3.99023e13i	1.37394	−	0.500073i	0.920336	+	0.391130i	$0.127916\pi$
$338$	−6.56049e13	+	2.38782e13i	−0.808899	+	0.294415i
$339$	−1.26925e14	+	3.36201e13i	−1.53975	+	0.407850i
$340$	−5.05286e12	−	2.86562e13i	−0.0603119	−	0.342046i
$341$	3.81061e13	−	6.60017e13i	0.447554	−	0.775186i
$342$	1.54657e14	+	9.04767e13i	1.78742	+	1.04567i
$343$	5.76835e13	+	9.99108e13i	0.656046	+	1.13630i
$344$	9.64473e11	−	8.09289e11i	0.0107949	−	0.00905799i
$345$	3.69028e13	+	1.73369e13i	0.406494	+	0.190971i
$346$	1.64625e13	−	9.33632e13i	0.178474	−	1.01218i
$347$	−1.25162e13	−	1.05023e13i	−0.133555	−	0.112066i	0.573563	−	0.819161i	$-0.305561\pi$
$347$	−1.25162e13	−	1.05023e13i	−0.133555	−	0.112066i	−0.707118	+	0.707095i	$0.750005\pi$
$348$	2.95678e13	−	4.19709e13i	0.310552	−	0.440821i
$349$	−1.62364e14	−	5.90958e13i	−1.67861	−	0.610965i	−0.685495	−	0.728078i	$-0.740414\pi$
$349$	−1.62364e14	−	5.90958e13i	−1.67861	−	0.610965i	−0.993119	+	0.117112i	$0.962636\pi$
$350$	2.00962e14			2.04522
$351$	−1.26817e14	+	9.99772e12i	−1.27054	+	0.100164i
$352$	−8.99025e13			−0.886722
$353$	−1.09171e13	−	3.97351e12i	−0.106010	−	0.0385846i	0.288470	−	0.957489i	$-0.406853\pi$
$353$	−1.09171e13	−	3.97351e12i	−0.106010	−	0.0385846i	−0.394481	+	0.918904i	$0.629076\pi$
$354$	−1.97672e13	−	1.78648e12i	−0.188985	−	0.0170797i
$355$	2.85393e13	+	2.39473e13i	0.268650	+	0.225424i
$356$	−6.04970e12	+	3.43095e13i	−0.0560736	+	0.318009i
$357$	1.73394e14	−	1.20673e14i	1.58255	−	1.10137i
$358$	5.64845e13	−	4.73961e13i	0.507659	−	0.425977i
$359$	5.25324e13	+	9.09887e13i	0.464951	+	0.805319i	0.999199	−	0.0400084i	$-0.0127385\pi$
$359$	5.25324e13	+	9.09887e13i	0.464951	+	0.805319i	−0.534248	+	0.845328i	$0.679405\pi$
$360$	1.81295e12	−	4.89363e12i	0.0158024	−	0.0426547i
$361$	−7.31357e13	+	1.26675e14i	−0.627827	+	1.08743i
$362$	−4.18687e13	−	2.37449e14i	−0.353991	−	2.00758i
$363$	4.89564e13	+	4.92377e13i	0.407684	+	0.410026i
$364$	−2.19615e14	+	7.99333e13i	−1.80138	+	0.655647i
$365$	−5.93284e13	+	2.15938e13i	−0.479349	+	0.174469i
$366$	−1.14917e14	−	1.15578e14i	−0.914618	−	0.919873i
$367$	1.68540e13	+	9.55837e13i	0.132141	+	0.749411i	0.976808	+	0.214118i	$0.0686878\pi$
$367$	1.68540e13	+	9.55837e13i	0.132141	+	0.749411i	−0.844666	+	0.535293i	$0.820201\pi$
$368$	−9.48945e13	+	1.64362e14i	−0.732957	+	1.26952i
$369$	−3.64579e12	+	9.84093e12i	−0.0277425	+	0.0748844i
$370$	−3.09532e13	−	5.36126e13i	−0.232058	−	0.401936i
$371$	1.08861e14	−	9.13452e13i	0.804110	−	0.674729i
$372$	1.40066e14	−	9.74787e13i	1.01941	−	0.709453i
$373$	−1.53181e13	+	8.68730e13i	−0.109851	+	0.622997i	0.879320	+	0.476231i	$0.157998\pi$
$373$	−1.53181e13	+	8.68730e13i	−0.109851	+	0.622997i	−0.989171	+	0.146766i	$0.953114\pi$
$374$	1.12132e14	+	9.40899e13i	0.792384	+	0.664889i
$375$	−9.01319e13	−	8.14575e12i	−0.627634	−	0.0567230i
$376$	−2.36353e13	−	8.60255e12i	−0.162192	−	0.0590329i
$377$	−1.12771e14			−0.762640
$378$	−3.44241e14	+	2.71384e13i	−2.29434	+	0.180875i
$379$	1.30041e14			0.854207			0.427103	−	0.904203i	$-0.359534\pi$
$379$	1.30041e14			0.854207			0.427103	+	0.904203i	$0.359534\pi$
$380$	−6.55446e13	−	2.38563e13i	−0.424353	−	0.154452i
$381$	−4.99667e12	+	7.09265e12i	−0.0318855	+	0.0452607i
$382$	1.01995e14	+	8.55837e13i	0.641548	+	0.538323i
$383$	−4.54181e13	+	2.57579e14i	−0.281602	+	1.59704i	0.435574	+	0.900153i	$0.356545\pi$
$383$	−4.54181e13	+	2.57579e14i	−0.281602	+	1.59704i	−0.717176	+	0.696892i	$0.754566\pi$
$384$	4.01785e13	+	1.88759e13i	0.245568	+	0.115368i
$385$	4.59887e13	−	3.85891e13i	0.277088	−	0.232504i
$386$	3.47081e13	+	6.01162e13i	0.206158	+	0.357076i
$387$	1.52364e13	+	8.91352e12i	0.0892221	+	0.0521962i
$388$	1.30183e13	−	2.25483e13i	0.0751586	−	0.130179i
$389$	4.99321e12	+	2.83179e13i	0.0284221	+	0.161190i	0.995715	−	0.0924707i	$-0.0294765\pi$
$389$	4.99321e12	+	2.83179e13i	0.0284221	+	0.161190i	−0.967293	+	0.253661i	$0.918365\pi$
$390$	1.00993e14	−	2.67510e13i	0.566806	−	0.150136i
$391$	2.64015e14	−	9.60935e13i	1.46102	−	0.531767i
$392$	4.19312e13	−	1.52617e13i	0.228804	−	0.0832778i
$393$	8.26372e13	−	3.04910e14i	0.444648	−	1.64064i
$394$	5.57060e13	+	3.15924e14i	0.295578	+	1.67631i
$395$	3.34102e13	−	5.78682e13i	0.174822	−	0.302800i
$396$	−3.81779e13	−	1.06793e14i	−0.197010	−	0.551084i
$397$	1.27189e14	+	2.20298e14i	0.647294	+	1.12115i	0.983767	+	0.179453i	$0.0574328\pi$
$397$	1.27189e14	+	2.20298e14i	0.647294	+	1.12115i	−0.336472	+	0.941693i	$0.609234\pi$
$398$	3.11876e14	−	2.61695e14i	1.56540	−	1.31352i
$399$	−4.26895e13	−	5.04586e14i	−0.211334	−	2.49795i
$400$	3.44194e13	−	1.95202e14i	0.168064	−	0.953136i
$401$	−1.59606e14	−	1.33926e14i	−0.768699	−	0.645015i	0.171676	−	0.985153i	$-0.445082\pi$
$401$	−1.59606e14	−	1.33926e14i	−0.768699	−	0.645015i	−0.940375	+	0.340138i	$0.889526\pi$
$402$	1.25084e13	+	2.70263e13i	0.0594238	+	0.128394i
$403$	−3.52230e14	−	1.28201e14i	−1.65062	−	0.600778i
$404$	−7.86426e12			−0.0363547
$405$	7.31631e13	+	8.38351e11i	0.333649	+	0.00382317i
$406$	−3.06112e14			−1.37717
$407$	1.38709e14	+	5.04861e13i	0.615653	+	0.224080i
$408$	−1.51045e13	−	3.26354e13i	−0.0661416	−	0.142909i
$409$	−1.83084e14	−	1.53626e14i	−0.790991	−	0.663720i	0.154999	−	0.987915i	$-0.450462\pi$
$409$	−1.83084e14	−	1.53626e14i	−0.790991	−	0.663720i	−0.945991	+	0.324194i	$0.894907\pi$
$410$	1.49666e12	−	8.48800e12i	0.00637989	−	0.0361822i
$411$	3.66595e13	+	4.33312e14i	0.154190	+	1.82252i
$412$	1.09313e14	−	9.17248e13i	0.453668	−	0.380673i
$413$	2.80466e13	+	4.85782e13i	0.114857	+	0.198937i
$414$	−4.51809e14	−	8.23378e13i	−1.82580	−	0.332734i
$415$	−2.61520e13	+	4.52966e13i	−0.104289	+	0.180635i
$416$	7.67817e13	+	4.35451e14i	0.302165	+	1.71366i
$417$	−1.11445e13	+	4.11202e13i	−0.0432824	+	0.159701i
$418$	3.29720e14	−	1.20008e14i	1.26379	−	0.459983i
$419$	−3.09316e14	+	1.12582e14i	−1.17011	+	0.425884i	−0.852698	−	0.522405i	$-0.825035\pi$
$419$	−3.09316e14	+	1.12582e14i	−1.17011	+	0.425884i	−0.317409	+	0.948289i	$0.602813\pi$
$420$	1.29942e14	−	3.44191e13i	0.485151	−	0.128507i
$421$	2.39297e13	+	1.35712e14i	0.0881830	+	0.500111i	0.996624	+	0.0820982i	$0.0261621\pi$
$421$	2.39297e13	+	1.35712e14i	0.0881830	+	0.500111i	−0.908441	+	0.418013i	$0.862727\pi$
$422$	−1.47516e13	+	2.55505e13i	−0.0536563	+	0.0929355i
$423$	2.02032e12	−	3.52639e14i	0.00725350	−	1.26607i
$424$	−1.20955e13	−	2.09500e13i	−0.0428659	−	0.0742458i
$425$	−2.24780e14	+	1.88613e14i	−0.786356	+	0.659831i
$426$	−3.79811e14	−	1.78435e14i	−1.31164	−	0.616208i
$427$	−7.99866e13	+	4.53626e14i	−0.272687	+	1.54648i
$428$	−4.03249e12	−	3.38366e12i	−0.0135717	−	0.0113880i
$429$	−1.43470e14	+	2.03652e14i	−0.476700	+	0.676665i
$430$	−1.36230e13	−	4.95838e12i	−0.0446887	−	0.0162654i
$431$	−5.69837e14			−1.84555			−0.922775	−	0.385339i	$-0.874085\pi$
$431$	−5.69837e14			−1.84555			−0.922775	+	0.385339i	$0.874085\pi$
$432$	−3.25986e13	+	3.39022e14i	−0.104241	+	1.08410i
$433$	−1.71172e14			−0.540443			−0.270222	−	0.962798i	$-0.587097\pi$
$433$	−1.71172e14			−0.540443			−0.270222	+	0.962798i	$0.587097\pi$
$434$	−9.56114e14	−	3.47997e14i	−2.98068	−	1.08488i
$435$	6.45992e13	+	5.83821e12i	0.198855	+	0.0179717i
$436$	2.71589e14	+	2.27890e14i	0.825537	+	0.692708i
$437$	1.16949e14	−	6.63251e14i	0.351034	−	1.99081i
$438$	5.83706e14	−	4.06228e14i	1.73016	−	1.20410i
$439$	−1.73608e13	+	1.45675e13i	−0.0508178	+	0.0426412i	−0.667843	−	0.744302i	$-0.732782\pi$
$439$	−1.73608e13	+	1.45675e13i	−0.0508178	+	0.0426412i	0.617025	+	0.786944i	$0.288338\pi$
$440$	−5.10978e12	−	8.85041e12i	−0.0147711	−	0.0255843i
$441$	3.99391e14	+	4.81552e14i	1.14021	+	1.37477i
$442$	3.59966e14	−	6.23479e14i	1.01494	−	1.75792i
$443$	5.97195e13	+	3.38686e14i	0.166301	+	0.943142i	0.947713	+	0.319125i	$0.103389\pi$
$443$	5.97195e13	+	3.38686e14i	0.166301	+	0.943142i	−0.781411	+	0.624016i	$0.785500\pi$
$444$	2.33041e14	+	2.34380e14i	0.640954	+	0.644636i
$445$	−4.13605e13	+	1.50540e13i	−0.112358	+	0.0408951i
$446$	−4.17070e13	+	1.51801e13i	−0.111909	+	0.0407317i
$447$	−2.47160e14	−	2.48580e14i	−0.655069	−	0.658832i
$448$	8.78445e13	+	4.98191e14i	0.229978	+	1.30427i
$449$	2.05525e14	−	3.55979e14i	0.531507	−	0.920598i	−0.467816	−	0.883826i	$-0.654959\pi$
$449$	2.05525e14	−	3.55979e14i	0.531507	−	0.920598i	0.999324	−	0.0367721i	$-0.0117075\pi$
$450$	4.72819e14	−	8.05805e13i	1.20789	−	0.205855i
$451$	1.02756e13	+	1.77979e13i	0.0259321	+	0.0449156i
$452$	−4.41038e14	+	3.70075e14i	−1.09955	+	0.922631i
$453$	3.24716e14	−	2.25985e14i	0.799766	−	0.556595i
$454$	6.18720e13	−	3.50894e14i	0.150552	−	0.853824i
$455$	−2.26187e14	−	1.89793e14i	−0.543756	−	0.456265i
$456$	−8.58525e13	−	7.75900e12i	−0.203914	−	0.0184289i
$457$	4.99940e14	+	1.81963e14i	1.17322	+	0.427017i	0.853802	−	0.520598i	$-0.174291\pi$
$457$	4.99940e14	+	1.81963e14i	1.17322	+	0.427017i	0.319417	+	0.947614i	$0.396513\pi$
$458$	7.46469e14			1.73082
$459$	3.59570e14	−	3.53442e14i	0.823784	−	0.809746i
$460$	1.78778e14			0.404713
$461$	3.31808e14	+	1.20768e14i	0.742218	+	0.270145i	0.685328	−	0.728235i	$-0.259659\pi$
$461$	3.31808e14	+	1.20768e14i	0.742218	+	0.270145i	0.0568909	+	0.998380i	$0.481881\pi$
$462$	−3.89443e14	+	5.52805e14i	−0.860822	+	1.22192i
$463$	2.13539e14	+	1.79181e14i	0.466425	+	0.391377i	0.845489	−	0.533993i	$-0.179309\pi$
$463$	2.13539e14	+	1.79181e14i	0.466425	+	0.391377i	−0.379063	+	0.925371i	$0.623754\pi$
$464$	−5.24288e13	+	2.97338e14i	−0.113167	+	0.641803i
$465$	1.95133e14	+	9.16734e13i	0.416236	+	0.195547i
$466$	5.71333e14	−	4.79405e14i	1.20439	−	1.01060i
$467$	3.60145e14	+	6.23790e14i	0.750300	+	1.29956i	0.947677	+	0.319230i	$0.103424\pi$
$467$	3.60145e14	+	6.23790e14i	0.750300	+	1.29956i	−0.197377	+	0.980328i	$0.563242\pi$
$468$	−4.84654e14	+	2.76125e14i	−0.997882	+	0.568530i
$469$	4.20825e13	−	7.28890e13i	0.0856349	−	0.148324i
$470$	5.02919e13	+	2.85220e14i	0.101149	+	0.573642i
$471$	−1.95445e14	+	5.17697e13i	−0.388517	+	0.102911i
$472$	8.97289e12	−	3.26586e12i	0.0176300	−	0.00641678i
$473$	3.24831e13	−	1.18229e13i	0.0630843	−	0.0229608i
$474$	−1.96882e14	+	7.26444e14i	−0.377942	+	1.39451i
$475$	1.22140e14	+	6.92692e14i	0.231763	+	1.31439i
$476$	4.63148e14	−	8.02196e14i	0.868724	−	1.50467i
$477$	2.19498e14	−	2.58565e14i	0.406987	−	0.479423i
$478$	−4.80377e14	−	8.32037e14i	−0.880498	−	1.52507i
$479$	−4.14121e14	+	3.47489e14i	−0.750381	+	0.629645i	−0.935604	−	0.353052i	$-0.885144\pi$
$479$	−4.14121e14	+	3.47489e14i	−0.750381	+	0.629645i	0.185222	+	0.982697i	$0.440699\pi$
$480$	−2.14398e13	−	2.53417e14i	−0.0384056	−	0.453951i
$481$	1.26068e14	−	7.14968e14i	0.223258	−	1.26616i
$482$	8.89165e13	+	7.46098e13i	0.155677	+	0.130628i
$483$	5.45153e14	+	1.17788e15i	0.943647	+	2.03888i
$484$	2.86093e14	+	1.04130e14i	0.489619	+	0.178207i
$485$	3.28942e13			0.0556596
$486$	−7.99039e14	+	2.01882e14i	−1.33681	+	0.337752i
$487$	−2.05903e13			−0.0340606			−0.0170303	−	0.999855i	$-0.505421\pi$
$487$	−2.05903e13			−0.0340606			−0.0170303	+	0.999855i	$0.505421\pi$
$488$	7.36831e13	+	2.68185e13i	0.120520	+	0.0438657i
$489$	−4.88282e14	−	1.05500e15i	−0.789718	−	1.70630i
$490$	−3.93602e14	−	3.30271e14i	−0.629476	−	0.528193i
$491$	1.84169e14	−	1.04447e15i	0.291251	−	1.65177i	−0.390810	−	0.920471i	$-0.627805\pi$
$491$	1.84169e14	−	1.04447e15i	0.291251	−	1.65177i	0.682061	−	0.731295i	$-0.261084\pi$
$492$	3.87927e12	+	4.58527e13i	0.00606656	+	0.0717062i
$493$	3.42393e14	−	2.87302e14i	0.529500	−	0.444304i
$494$	−8.62869e14	−	1.49453e15i	−1.31961	−	2.28564i
$495$	9.27279e13	−	1.09232e14i	0.140243	−	0.165204i
$496$	−5.01780e14	+	8.69108e14i	−0.750522	+	1.29994i
$497$	2.05941e14	+	1.16795e15i	0.304637	+	1.72768i
$498$	1.54110e14	−	5.68627e14i	0.225460	−	0.831890i
$499$	−3.82838e14	+	1.39342e14i	−0.553939	+	0.201617i	−0.603796	−	0.797139i	$-0.706346\pi$
$499$	−3.82838e14	+	1.39342e14i	−0.553939	+	0.201617i	0.0498569	+	0.998756i	$0.484123\pi$
$500$	−3.72890e14	+	1.35721e14i	−0.533636	+	0.194228i
$501$	1.26658e14	−	3.35494e13i	0.179277	−	0.0474872i
$502$	1.93965e14	+	1.10003e15i	0.271553	+	1.54005i
$503$	−6.69785e14	+	1.16010e15i	−0.927495	+	1.60647i	−0.139996	+	0.990152i	$0.544709\pi$
$503$	−6.69785e14	+	1.16010e15i	−0.927495	+	1.60647i	−0.787499	+	0.616316i	$0.788624\pi$
$504$	1.44344e14	−	8.22381e13i	0.197711	−	0.112643i
$505$	−4.96780e12	−	8.60448e12i	−0.00673072	−	0.0116580i
$506$	−6.88934e14	+	5.78084e14i	−0.923315	+	0.774753i
$507$	4.26226e14	+	2.00241e14i	0.565062	+	0.265466i
$508$	−6.60599e12	+	3.74644e13i	−0.00866339	+	0.0491325i
$509$	9.25084e14	+	7.76238e14i	1.20014	+	1.00704i	0.999626	+	0.0273510i	$0.00870718\pi$
$509$	9.25084e14	+	7.76238e14i	1.20014	+	1.00704i	0.200519	+	0.979690i	$0.435737\pi$
$510$	−2.38479e14	+	3.38516e14i	−0.306066	+	0.434453i
$511$	−1.88862e15	−	6.87402e14i	−2.39790	−	0.872763i
$512$	1.06563e15			1.33851
$513$	−3.02764e14	−	1.17006e15i	−0.376235	−	1.45399i
$514$	−5.99833e14			−0.737451
$515$	1.69411e14	+	6.16605e13i	0.206064	+	0.0750011i
$516$	7.70871e13	+	6.96681e12i	0.0927701	+	0.00838418i
$517$	−5.29012e14	−	4.43894e14i	−0.629894	−	0.528544i
$518$	3.42207e14	−	1.94075e15i	0.403158	−	2.28642i
$519$	−5.24872e14	+	3.65283e14i	−0.611833	+	0.425803i
$520$	−3.85037e13	+	3.23084e13i	−0.0444103	+	0.0372647i
$521$	−3.30236e14	−	5.71985e14i	−0.376891	−	0.652795i	0.613717	−	0.789526i	$-0.289674\pi$
$521$	−3.30236e14	−	5.71985e14i	−0.376891	−	0.652795i	−0.990608	+	0.136731i	$0.956340\pi$
$522$	−7.20213e14	+	1.22743e14i	−0.813342	+	0.138614i
$523$	−2.13966e14	+	3.70600e14i	−0.239103	+	0.414139i	−0.960457	−	0.278427i	$-0.910187\pi$
$523$	−2.13966e14	+	3.70600e14i	−0.239103	+	0.414139i	0.721354	+	0.692567i	$0.243520\pi$
$524$	−2.40538e14	−	1.36416e15i	−0.265987	−	1.50849i
$525$	−9.55758e14	−	9.61249e14i	−1.04586	−	1.05186i
$526$	−1.10965e15	+	4.03881e14i	−1.20162	+	0.437353i
$527$	1.39605e15	−	5.08119e14i	1.49603	−	0.544512i
$528$	4.70260e14	+	4.72962e14i	0.498714	+	0.501579i
$529$	1.34297e14	+	7.61638e14i	0.140949	+	0.799360i
$530$	−1.39276e14	+	2.41233e14i	−0.144663	+	0.250564i
$531$	8.54660e13	+	1.03048e14i	0.0878565	+	0.105930i
$532$	−1.11021e15	−	1.92293e15i	−1.12951	−	1.95637i
$533$	7.74297e13	−	6.49712e13i	0.0779665	−	0.0654216i
$534$	4.06928e14	−	2.83200e14i	0.405546	−	0.282239i
$535$	1.15485e12	−	6.54950e12i	0.00113915	−	0.00646044i
$536$	−1.09754e13	−	9.20947e12i	−0.0107156	−	0.00899142i
$537$	−4.95342e14	−	4.47669e13i	−0.478681	−	0.0432612i
$538$	2.31054e15	+	8.40967e14i	2.21009	+	0.804409i
$539$	1.22514e15			1.15998
$540$	2.91922e14	−	1.33084e14i	0.273591	−	0.124726i
$541$	−1.46154e15			−1.35589			−0.677946	−	0.735112i	$-0.737130\pi$
$541$	−1.46154e15			−1.35589			−0.677946	+	0.735112i	$0.737130\pi$
$542$	1.12414e15	+	4.09153e14i	1.03234	+	0.375742i
$543$	−9.36651e14	+	1.32955e15i	−0.851488	+	1.20867i
$544$	−1.34250e15	−	1.12649e15i	−1.20815	−	1.01376i
$545$	−7.77795e13	+	4.41109e14i	−0.0692922	+	0.392976i
$546$	3.01017e15	+	1.41418e15i	2.65479	+	1.24722i
$547$	−8.33482e14	+	6.99374e14i	−0.727723	+	0.610632i	−0.929510	−	0.368798i	$-0.879770\pi$
$547$	−8.33482e14	+	6.99374e14i	−0.727723	+	0.610632i	0.201787	+	0.979429i	$0.435325\pi$
$548$	9.53388e14	+	1.65132e15i	0.824094	+	1.42737i
$549$	−6.29835e12	+	1.09935e15i	−0.00538988	+	0.940783i
$550$	4.69630e14	−	8.13423e14i	0.397888	−	0.689163i
$551$	−1.86048e14	−	1.05513e15i	−0.156060	−	0.885059i
$552$	2.13579e14	−	5.65731e13i	0.177376	−	0.0469835i
$553$	1.99884e15	−	7.27518e14i	1.64358	−	0.598213i
$554$	−4.71154e14	+	1.71486e14i	−0.383583	+	0.139613i
$555$	−1.09231e14	+	4.03033e14i	−0.0880508	+	0.324885i
$556$	3.24390e13	+	1.83971e14i	0.0258914	+	0.146838i
$557$	9.53131e14	−	1.65087e15i	0.753267	−	1.30470i	−0.192964	−	0.981206i	$-0.561810\pi$
$557$	9.53131e14	−	1.65087e15i	0.753267	−	1.30470i	0.946231	−	0.323491i	$-0.104856\pi$
$558$	−2.38906e15	−	4.35383e14i	−1.86956	−	0.340708i
$559$	−8.50076e13	−	1.47237e14i	−0.0658708	−	0.114092i
$560$	−6.05577e14	+	5.08139e14i	−0.464660	+	0.389896i
$561$	−8.32354e13	−	9.83836e14i	−0.0632430	−	0.747527i
$562$	−3.55896e14	+	2.01839e15i	−0.267777	+	1.51864i
$563$	2.64276e14	+	2.21754e14i	0.196907	+	0.165225i	0.735910	−	0.677079i	$-0.236755\pi$
$563$	2.64276e14	+	2.21754e14i	0.196907	+	0.165225i	−0.539003	+	0.842304i	$0.681199\pi$
$564$	−6.49468e14	−	1.40327e15i	−0.479207	−	1.03539i
$565$	−6.83509e14	−	2.48777e14i	−0.499434	−	0.181779i
$566$	1.69565e15			1.22700
$567$	1.76699e15	+	1.51752e15i	1.26627	+	1.08749i
$568$	2.01887e14			0.143282
$569$	1.58560e15	+	5.77112e14i	1.11449	+	0.405642i	0.832639	−	0.553816i	$-0.186829\pi$
$569$	1.58560e15	+	5.77112e14i	1.11449	+	0.405642i	0.281852	+	0.959458i	$0.409051\pi$
$570$	4.16910e14	+	9.00794e14i	0.290222	+	0.627067i
$571$	8.84068e14	+	7.41821e14i	0.609519	+	0.511447i	0.894489	−	0.447089i	$-0.147539\pi$
$571$	8.84068e14	+	7.41821e14i	0.609519	+	0.511447i	−0.284970	+	0.958536i	$0.591984\pi$
$572$	−1.89678e14	+	1.07572e15i	−0.129521	+	0.734549i
$573$	−7.57105e13	−	8.94893e14i	−0.0512042	−	0.605230i
$574$	2.10180e14	−	1.76362e14i	0.140791	−	0.118138i
$575$	−9.01411e14	−	1.56129e15i	−0.598067	−	1.03588i
$576$	4.06440e14	+	1.13691e15i	0.267099	+	0.747140i
$577$	3.68494e14	−	6.38251e14i	0.239863	−	0.415455i	−0.720812	−	0.693131i	$-0.756231\pi$
$577$	3.68494e14	−	6.38251e14i	0.239863	−	0.415455i	0.960675	+	0.277676i	$0.0895640\pi$
$578$	1.24144e14	+	7.04055e14i	0.0800428	+	0.453945i
$579$	1.22481e14	−	4.51924e14i	0.0782236	−	0.288625i
$580$	2.67257e14	−	9.72736e13i	0.169073	−	0.0615377i
$581$	−1.56460e15	+	5.69468e14i	−0.980471	+	0.356862i
$582$	−3.58162e14	+	9.48704e13i	−0.222333	+	0.0588917i
$583$	−1.15335e14	−	6.54096e14i	−0.0709223	−	0.402220i
$584$	−1.71066e14	+	2.96296e14i	−0.104206	+	0.180491i
$585$	−6.08268e14	−	3.55846e14i	−0.367061	−	0.214736i
$586$	1.51015e15	+	2.61565e15i	0.902781	+	1.56366i
$587$	−1.84476e14	+	1.54794e14i	−0.109252	+	0.0916737i	−0.695777	−	0.718257i	$-0.744940\pi$
$587$	−1.84476e14	+	1.54794e14i	−0.109252	+	0.0916737i	0.586525	+	0.809931i	$0.300496\pi$
$588$	2.48289e15	+	1.16646e15i	1.45674	+	0.684375i
$589$	6.18398e14	−	3.50711e15i	0.359446	−	2.03852i
$590$	−8.42273e13	−	7.06751e13i	−0.0485028	−	0.0406987i
$591$	1.24621e15	−	1.76896e15i	0.710983	−	1.00922i
$592$	−1.82652e15	−	6.64798e14i	−1.03242	−	0.375769i
$593$	−2.88851e15			−1.61761			−0.808805	−	0.588077i	$-0.799885\pi$
$593$	−2.88851e15			−1.61761			−0.808805	+	0.588077i	$0.799885\pi$
$594$	−6.94612e14	+	1.45678e15i	−0.385405	+	0.808294i
$595$	1.17027e15			0.643344
$596$	−1.44436e15	−	5.25705e14i	−0.786723	−	0.286344i
$597$	−2.73500e15	−	2.47178e14i	−1.47604	−	0.133398i
$598$	3.38839e15	+	2.84320e15i	1.81191	+	1.52037i
$599$	2.73720e14	−	1.55234e15i	0.145030	−	0.822508i	−0.822312	−	0.569036i	$-0.807316\pi$
$599$	2.73720e14	−	1.55234e15i	0.145030	−	0.822508i	0.967343	−	0.253472i	$-0.0815725\pi$
$600$	−1.89400e14	+	1.31812e14i	−0.0994368	+	0.0692027i
$601$	−7.98205e14	+	6.69773e14i	−0.415245	+	0.348432i	−0.826351	−	0.563155i	$-0.809587\pi$
$601$	−7.98205e14	+	6.69773e14i	−0.415245	+	0.348432i	0.411106	+	0.911588i	$0.365143\pi$
$602$	−2.30750e14	−	3.99670e14i	−0.118949	−	0.206026i
$603$	6.97841e13	−	1.88366e14i	0.0356461	−	0.0962180i
$604$	8.67342e14	−	1.50228e15i	0.439023	−	0.760410i
$605$	6.67927e13	+	3.78800e14i	0.0335023	+	0.190001i
$606$	7.89071e13	+	7.93604e13i	0.0392208	+	0.0394461i
$607$	1.88304e15	−	6.85372e14i	0.927519	−	0.337589i	0.166293	−	0.986076i	$-0.446820\pi$
$607$	1.88304e15	−	6.85372e14i	0.927519	−	0.337589i	0.761226	+	0.648487i	$0.224598\pi$
$608$	−3.94758e15	+	1.43680e15i	−1.92691	+	0.701338i
$609$	1.45584e15	+	1.46421e15i	0.704237	+	0.708283i
$610$	−1.56785e14	−	8.89173e14i	−0.0751607	−	0.426258i
$611$	−1.69823e15	+	2.94143e15i	−0.806809	+	1.39743i
$612$	7.68024e14	−	2.07310e15i	0.361611	−	0.976083i
$613$	1.28199e14	+	2.22047e14i	0.0598208	+	0.103613i	0.894385	−	0.447298i	$-0.147614\pi$
$613$	1.28199e14	+	2.22047e14i	0.0598208	+	0.103613i	−0.834564	+	0.550911i	$0.814280\pi$
$614$	1.15731e15	−	9.71095e14i	0.535207	−	0.449092i
$615$	−4.77181e13	+	3.32093e13i	−0.0218711	+	0.0152211i
$616$	5.64918e13	−	3.20381e14i	0.0256621	−	0.145537i
$617$	−2.58208e15	−	2.16662e15i	−1.16252	−	0.975471i	−0.162584	−	0.986695i	$-0.551983\pi$
$617$	−2.58208e15	−	2.16662e15i	−1.16252	−	0.975471i	−0.999937	+	0.0112235i	$0.996427\pi$
$618$	−2.02243e15	−	1.82779e14i	−0.902479	−	0.0815623i
$619$	−2.19216e15	−	7.97882e14i	−0.969559	−	0.352891i	−0.191787	−	0.981437i	$-0.561428\pi$
$619$	−2.19216e15	−	7.97882e14i	−0.969559	−	0.352891i	−0.777772	+	0.628546i	$0.783650\pi$
$620$	9.45337e14			0.414412
$621$	1.75492e15	+	2.55270e15i	0.762525	+	1.10916i
$622$	6.03163e13			0.0259769
$623$	−1.31665e15	−	4.79220e14i	−0.562062	−	0.204574i
$624$	1.88920e15	−	2.68168e15i	0.799399	−	1.13473i
$625$	1.23900e15	+	1.03965e15i	0.519675	+	0.436059i
$626$	−6.89762e12	+	3.91184e13i	−0.00286775	+	0.0162638i
$627$	−2.14215e15	−	1.00638e15i	−0.882831	−	0.414754i
$628$	−6.79131e14	+	5.69858e14i	−0.277444	+	0.232803i
$629$	1.43873e15	+	2.49195e15i	0.582640	+	1.00916i
$630$	−1.65112e15	−	9.65929e14i	−0.662835	−	0.387768i
$631$	−4.59747e14	+	7.96305e14i	−0.182961	+	0.316897i	−0.942887	−	0.333112i	$-0.891901\pi$
$631$	−4.59747e14	+	7.96305e14i	−0.182961	+	0.316897i	0.759927	+	0.650009i	$0.225235\pi$
$632$	−6.28779e13	−	3.56598e14i	−0.0248058	−	0.140681i
$633$	1.92371e14	−	5.09556e13i	0.0752351	−	0.0199284i
$634$	−4.62579e14	+	1.68365e14i	−0.179347	+	0.0652771i
$635$	−4.51638e13	+	1.64383e13i	−0.0173594	+	0.00631831i
$636$	3.89026e14	−	1.43540e15i	0.148240	−	0.546966i
$637$	−1.04634e15	−	5.93409e15i	−0.395281	−	2.24175i
$638$	−7.15355e14	+	1.23903e15i	−0.267922	+	0.464054i
$639$	9.52849e14	+	2.66534e15i	0.353809	+	0.989689i
$640$	1.22958e14	+	2.12970e14i	0.0452655	+	0.0784021i
$641$	2.89100e15	−	2.42583e15i	1.05518	−	0.885405i	0.0615552	−	0.998104i	$-0.480394\pi$
$641$	2.89100e15	−	2.42583e15i	1.05518	−	0.885405i	0.993629	+	0.112699i	$0.0359495\pi$
$642$	6.31506e12	+	7.46435e13i	0.00228525	+	0.0270115i
$643$	−2.32425e14	+	1.31815e15i	−0.0833916	+	0.472937i	0.914300	+	0.405037i	$0.132741\pi$
$643$	−2.32425e14	+	1.31815e15i	−0.0833916	+	0.472937i	−0.997692	+	0.0679008i	$0.978370\pi$
$644$	4.35965e15	+	3.65818e15i	1.55089	+	1.30135i
$645$	4.10729e13	+	8.87438e13i	0.0144869	+	0.0313011i
$646$	6.42739e15	+	2.33938e15i	2.24779	+	0.818129i
$647$	−2.47967e14			−0.0859845			−0.0429923	−	0.999075i	$-0.513689\pi$
$647$	−2.47967e14			−0.0859845			−0.0429923	+	0.999075i	$0.513689\pi$
$648$	3.06634e14	−	2.51366e14i	0.105428	−	0.0864259i
$649$	2.62170e14			0.0893792
$650$	−4.34098e15	−	1.57999e15i	−1.46745	−	0.534109i
$651$	2.88264e15	+	6.22836e15i	0.966262	+	2.08775i
$652$	−3.90485e15	−	3.27656e15i	−1.29790	−	1.08907i
$653$	5.55243e14	−	3.14894e15i	0.183004	−	1.03787i	−0.745489	−	0.666518i	$-0.767784\pi$
$653$	5.55243e14	−	3.14894e15i	0.183004	−	1.03787i	0.928493	−	0.371349i	$-0.121105\pi$
$654$	−4.25320e14	−	5.02725e15i	−0.139007	−	1.64306i
$655$	1.34061e15	−	1.12491e15i	0.434487	−	0.364578i
$656$	−1.35309e14	−	2.34362e14i	−0.0434866	−	0.0753209i
$657$	−4.71914e15	−	8.60016e14i	−1.50402	−	0.274092i
$658$	−4.60979e15	+	7.98438e15i	−1.45693	+	2.52347i
$659$	−1.43822e14	−	8.15654e14i	−0.0450770	−	0.255644i	0.953939	−	0.300002i	$-0.0969872\pi$
$659$	−1.43822e14	−	8.15654e14i	−0.0450770	−	0.255644i	−0.999016	+	0.0443571i	$0.985876\pi$
$660$	1.64345e14	−	6.06391e14i	0.0510817	−	0.188478i
$661$	−7.90199e14	+	2.87609e14i	−0.243573	+	0.0886532i	−0.460922	−	0.887441i	$-0.652481\pi$
$661$	−7.90199e14	+	2.87609e14i	−0.243573	+	0.0886532i	0.217349	+	0.976094i	$0.430259\pi$
$662$	−4.92957e15	+	1.79422e15i	−1.50692	+	0.548474i
$663$	−4.69421e15	+	1.24341e15i	−1.42311	+	0.376955i
$664$	4.92179e13	+	2.79129e14i	0.0147979	+	0.0839228i
$665$	1.40262e15	−	2.42941e15i	0.418236	−	0.724406i
$666$	2.69463e13	−	4.70337e15i	0.00796875	−	1.39092i
$667$	1.37306e15	+	2.37820e15i	0.402714	+	0.697521i
$668$	4.40110e14	−	3.69297e14i	0.128024	−	0.107425i
$669$	2.70964e14	+	1.27299e14i	0.0781751	+	0.0367267i
$670$	−2.86477e13	+	1.62469e14i	−0.00819744	+	0.0464900i
$671$	1.64920e15	+	1.38384e15i	0.468057	+	0.392746i
$672$	4.66262e15	−	6.61848e15i	1.31250	−	1.86306i
$673$	4.59103e15	+	1.67100e15i	1.28182	+	0.466544i	0.891034	−	0.453937i	$-0.149981\pi$
$673$	4.59103e15	+	1.67100e15i	1.28182	+	0.466544i	0.390786	+	0.920481i	$0.372203\pi$
$674$	−7.27976e15			−2.01599
$675$	−2.63412e15	−	1.87837e15i	−0.723544	−	0.515953i
$676$	2.06489e15			0.562587
$677$	3.16192e15	+	1.15085e15i	0.854503	+	0.311014i	0.731875	−	0.681439i	$-0.238646\pi$
$677$	3.16192e15	+	1.15085e15i	0.854503	+	0.311014i	0.122628	+	0.992453i	$0.460868\pi$
$678$	8.15974e15	+	7.37444e14i	2.18732	+	0.197681i
$679$	8.02152e14	+	6.73085e14i	0.213291	+	0.178973i
$680$	3.45933e13	−	1.96188e14i	0.00912416	−	0.0517457i
$681$	−1.97266e15	+	1.37287e15i	−0.516112	+	0.359187i
$682$	−3.64292e15	+	3.05677e15i	−0.945443	+	0.793321i
$683$	2.88891e15	+	5.00373e15i	0.743738	+	1.28819i	0.950782	+	0.309860i	$0.100282\pi$
$683$	2.88891e15	+	5.00373e15i	0.743738	+	1.28819i	−0.207045	+	0.978331i	$0.566385\pi$
$684$	−3.38311e15	−	4.07907e15i	−0.863988	−	1.04172i
$685$	−1.20450e15	+	2.08625e15i	−0.305146	+	0.528529i
$686$	−1.25004e15	−	7.08931e15i	−0.314152	−	1.78165i
$687$	−3.55014e15	−	3.57054e15i	−0.885082	−	0.890167i
$688$	−4.27736e14	+	1.55683e14i	−0.105789	+	0.0385040i
$689$	−3.06967e15	+	1.11727e15i	−0.753157	+	0.274127i
$690$	−1.79380e15	−	1.80410e15i	−0.436620	−	0.439128i
$691$	−8.35730e14	−	4.73966e15i	−0.201807	−	1.14451i	−0.902385	−	0.430930i	$-0.858186\pi$
$691$	−8.35730e14	−	4.73966e15i	−0.201807	−	1.14451i	0.700578	−	0.713576i	$-0.252925\pi$
$692$	−1.40198e15	+	2.42829e15i	−0.335859	+	0.581725i
$693$	4.49635e15	−	7.66294e14i	1.06863	−	0.182122i
$694$	5.09752e14	+	8.82916e14i	0.120194	+	0.208182i
$695$	−1.80795e14	+	1.51705e14i	−0.0422933	+	0.0354883i
$696$	2.88499e14	−	2.00780e14i	0.0669567	−	0.0465983i
$697$	−6.95661e13	+	3.94529e14i	−0.0160183	+	0.0908444i
$698$	8.25904e15	+	6.93015e15i	1.88679	+	1.58321i
$699$	−5.01031e15	−	4.52811e14i	−1.13564	−	0.102634i
$700$	−5.58530e15	−	2.03288e15i	−1.25605	−	0.457165i
$701$	3.92762e15			0.876356			0.438178	−	0.898888i	$-0.355624\pi$
$701$	3.92762e15			0.876356			0.438178	+	0.898888i	$0.355624\pi$
$702$	7.64929e15	+	2.12024e15i	1.69343	+	0.469387i
$703$	6.89752e15			1.51509
$704$	2.22178e15	+	8.08663e14i	0.484231	+	0.176246i
$705$	1.12509e15	−	1.59704e15i	0.243302	−	0.345362i
$706$	5.55325e14	+	4.65973e14i	0.119158	+	0.0999851i
$707$	5.49221e13	−	3.11479e14i	0.0116934	−	0.0663165i
$708$	5.31315e14	+	2.49612e14i	0.112246	+	0.0527329i
$709$	−3.84022e15	+	3.22232e15i	−0.805010	+	0.675484i	−0.949411	−	0.314035i	$-0.898319\pi$
$709$	−3.84022e15	+	3.22232e15i	−0.805010	+	0.675484i	0.144401	+	0.989519i	$0.453874\pi$
$710$	−1.16233e15	−	2.01322e15i	−0.241774	−	0.418765i
$711$	4.41111e15	−	2.51317e15i	0.910468	−	0.518727i
$712$	−1.19258e14	+	2.06561e14i	−0.0244258	+	0.0423067i
$713$	1.58501e15	+	8.98905e15i	0.322137	+	1.82693i
$714$	−1.27422e16	+	3.37518e15i	−2.56984	+	0.680702i
$715$	−1.29679e15	+	4.71993e14i	−0.259530	+	0.0944611i
$716$	−2.04931e15	+	7.45887e14i	−0.406992	+	0.148133i
$717$	−1.69520e15	+	6.25485e15i	−0.334092	+	1.23271i
$718$	−1.13841e15	−	6.45623e15i	−0.222645	−	1.26268i
$719$	−6.94599e14	+	1.20308e15i	−0.134811	+	0.233499i	−0.925525	−	0.378686i	$-0.876376\pi$
$719$	−6.94599e14	+	1.20308e15i	−0.134811	+	0.233499i	0.790714	+	0.612185i	$0.209709\pi$
$720$	−1.22104e15	+	1.43836e15i	−0.235180	+	0.277037i
$721$	2.86952e15	+	4.97015e15i	0.548485	+	0.950003i
$722$	6.99172e15	−	5.86675e15i	1.32626	−	1.11287i
$723$	−6.60026e13	−	7.80146e14i	−0.0124251	−	0.146864i
$724$	−1.23833e15	+	7.02290e15i	−0.231352	+	1.31206i
$725$	−2.19702e15	−	1.84352e15i	−0.407358	−	0.341814i
$726$	−1.81976e15	−	3.93185e15i	−0.334859	−	0.723511i
$727$	−8.39937e14	−	3.05712e14i	−0.153394	−	0.0558307i	0.264182	−	0.964473i	$-0.414898\pi$
$727$	−8.39937e14	−	3.05712e14i	−0.153394	−	0.0558307i	−0.417576	+	0.908642i	$0.637120\pi$
$728$	−1.60004e15			−0.290007
$729$	4.76581e15	+	2.86186e15i	0.857304	+	0.514810i
$730$	3.93956e15			0.703350
$731$	6.33209e14	+	2.30469e14i	0.112202	+	0.0408383i
$732$	2.02472e15	+	4.37470e15i	0.356085	+	0.769373i
$733$	−2.79012e15	−	2.34119e15i	−0.487025	−	0.408663i	0.365933	−	0.930641i	$-0.380750\pi$
$733$	−2.79012e15	−	2.34119e15i	−0.487025	−	0.408663i	−0.852959	+	0.521978i	$0.825194\pi$
$734$	1.05165e15	−	5.96423e15i	0.182198	−	1.03330i
$735$	2.92171e14	+	3.45343e15i	0.0502407	+	0.593842i
$736$	8.24828e15	−	6.92113e15i	1.40778	−	1.18127i
$737$	−1.96686e14	−	3.40670e14i	−0.0333198	−	0.0577115i
$738$	4.23790e14	−	4.99216e14i	0.0712591	−	0.0839419i
$739$	5.12804e15	−	8.88202e15i	0.855868	−	1.48241i	−0.0199689	−	0.999801i	$-0.506357\pi$
$739$	5.12804e15	−	8.88202e15i	0.855868	−	1.48241i	0.875837	−	0.482607i	$-0.160310\pi$
$740$	3.17945e14	+	1.80316e15i	0.0526718	+	0.298716i
$741$	−3.04498e15	+	1.12352e16i	−0.500707	+	1.84748i
$742$	−8.33249e15	+	3.03278e15i	−1.36004	+	0.495016i
$743$	5.67028e15	−	2.06381e15i	0.918684	−	0.334374i	0.160969	−	0.986959i	$-0.448538\pi$
$743$	5.67028e15	−	2.06381e15i	0.918684	−	0.334374i	0.757715	+	0.652586i	$0.226316\pi$
$744$	1.12936e15	−	2.99145e14i	0.181627	−	0.0481095i
$745$	−3.37208e14	−	1.91240e15i	−0.0538317	−	0.305295i
$746$	2.75216e15	−	4.76688e15i	0.436124	−	0.755390i
$747$	−3.45281e15	+	1.96719e15i	−0.543137	+	0.309445i
$748$	−2.16467e15	−	3.74932e15i	−0.338012	−	0.585455i
$749$	1.62178e14	−	1.36084e14i	0.0251387	−	0.0210939i
$750$	5.11104e15	+	2.40116e15i	0.786452	+	0.369475i
$751$	−4.10570e14	+	2.32846e15i	−0.0627145	+	0.355671i	0.937261	+	0.348629i	$0.113353\pi$
$751$	−4.10570e14	+	2.32846e15i	−0.0627145	+	0.355671i	−0.999975	+	0.00704227i	$0.997758\pi$
$752$	6.96601e15	+	5.84517e15i	1.05630	+	0.886338i
$753$	4.33923e15	−	6.15944e15i	0.653192	−	0.927190i
$754$	6.61231e15	+	2.40668e15i	0.988123	+	0.359647i
$755$	2.19158e15			0.325124
$756$	9.84192e15	+	2.72800e15i	1.44947	+	0.401767i
$757$	−6.36347e15			−0.930394			−0.465197	−	0.885207i	$-0.654017\pi$
$757$	−6.36347e15			−0.930394			−0.465197	+	0.885207i	$0.654017\pi$
$758$	−7.62492e15	−	2.77524e15i	−1.10676	−	0.402829i
$759$	6.04162e15	+	5.46017e14i	0.870610	+	0.0786821i
$760$	−3.65814e14	−	3.06954e14i	−0.0523341	−	0.0439136i
$761$	−7.35002e14	+	4.16840e15i	−0.104393	+	0.592044i	0.887068	+	0.461640i	$0.152739\pi$
$761$	−7.35002e14	+	4.16840e15i	−0.104393	+	0.592044i	−0.991461	+	0.130404i	$0.958372\pi$
$762$	4.44346e14	−	3.09242e14i	0.0626570	−	0.0436059i
$763$	−1.09227e16	+	9.16527e15i	−1.52914	+	1.28310i
$764$	−1.96897e15	−	3.41036e15i	−0.273669	−	0.474009i
$765$	2.75339e15	−	4.69248e14i	0.379952	−	0.0647536i
$766$	8.16018e15	−	1.41338e16i	1.11800	−	1.93643i
$767$	−2.23907e14	−	1.26984e15i	−0.0304575	−	0.172733i
$768$	−6.09534e15	−	6.13036e15i	−0.823211	−	0.827941i
$769$	1.72810e15	−	6.28979e14i	0.231726	−	0.0843415i	−0.223547	−	0.974693i	$-0.571764\pi$
$769$	1.72810e15	−	6.28979e14i	0.231726	−	0.0843415i	0.455274	+	0.890352i	$0.349541\pi$
$770$	−3.52009e15	+	1.28121e15i	−0.468656	+	0.170577i
$771$	2.85275e15	+	2.86914e15i	0.377107	+	0.379274i
$772$	−3.56514e14	−	2.02189e15i	−0.0467931	−	0.265377i
$773$	4.95206e15	−	8.57722e15i	0.645355	−	1.11779i	−0.338864	−	0.940835i	$-0.610043\pi$
$773$	4.95206e15	−	8.57722e15i	0.645355	−	1.11779i	0.984219	−	0.176952i	$-0.0566239\pi$
$774$	−7.03159e14	−	8.47810e14i	−0.0909868	−	0.109704i
$775$	−4.76644e15	−	8.25572e15i	−0.612400	−	1.06071i
$776$	1.36550e14	−	1.14579e14i	0.0174202	−	0.0146173i
$777$	−1.09106e16	+	7.59319e15i	−1.38208	+	0.961853i
$778$	3.11566e14	−	1.76698e15i	0.0391888	−	0.222251i
$779$	7.35640e14	+	6.17275e14i	0.0918775	+	0.0770944i
$780$	−3.07747e15	−	2.78129e14i	−0.381657	−	0.0344926i
$781$	5.20870e15	+	1.89581e15i	0.641430	+	0.233461i
$782$	−1.75313e16			−2.14376
$783$	4.01237e15	+	2.86119e15i	0.487205	+	0.347422i
$784$	−1.61326e16			−1.94521
$785$	−1.05250e15	−	3.83078e14i	−0.126020	−	0.0458674i
$786$	−1.13526e16	+	1.61148e16i	−1.34981	+	1.91602i
$787$	1.56297e14	+	1.31149e14i	0.0184540	+	0.0154847i	0.651968	−	0.758246i	$-0.273944\pi$
$787$	1.56297e14	+	1.31149e14i	0.0184540	+	0.0154847i	−0.633514	+	0.773731i	$0.718388\pi$
$788$	1.64759e15	−	9.34392e15i	0.193176	−	1.09556i
$789$	7.20928e15	+	3.38692e15i	0.839399	+	0.394349i
$790$	−3.19399e15	+	2.68008e15i	−0.369305	+	0.309884i
$791$	−1.15774e16	−	2.00527e16i	−1.32935	−	2.30251i
$792$	4.44831e12	−	7.76436e14i	0.000507232	−	0.0885355i
$793$	5.29425e15	−	9.16990e15i	0.599517	−	1.03839i
$794$	−2.75626e15	−	1.56315e16i	−0.309961	−	1.75788i
$795$	1.81626e15	−	4.81093e14i	0.202842	−	0.0537291i
$796$	−1.13151e16	+	4.11837e15i	−1.25498	+	0.456776i
$797$	−8.43119e14	+	3.06870e14i	−0.0928685	+	0.0338014i	−0.388037	−	0.921644i	$-0.626847\pi$
$797$	−8.43119e14	+	3.06870e14i	−0.0928685	+	0.0338014i	0.295168	+	0.955445i	$0.404624\pi$
$798$	−8.26547e15	+	3.04974e16i	−0.904173	+	3.33616i
$799$	−2.33761e15	−	1.32572e16i	−0.253959	−	1.44027i
$800$	−5.62266e15	+	9.73873e15i	−0.606662	+	1.05077i
$801$	−3.28993e15	−	5.99557e14i	−0.352539	−	0.0642468i
$802$	6.50036e15	+	1.12589e16i	0.691796	+	1.19823i
$803$	−7.19590e15	+	6.03807e15i	−0.760588	+	0.638209i
$804$	−7.42533e13	−	8.77668e14i	−0.00779484	−	0.0921345i
$805$	−1.24855e15	+	7.08086e15i	−0.130175	+	0.738259i
$806$	1.79170e16	+	1.50341e16i	1.85533	+	1.55681i
$807$	−6.96617e15	−	1.50514e16i	−0.716456	−	1.54801i
$808$	−5.05939e13	−	1.84147e13i	−0.00516816	−	0.00188106i
$809$	−9.75423e15			−0.989637			−0.494819	−	0.868996i	$-0.664766\pi$
$809$	−9.75423e15			−0.989637			−0.494819	+	0.868996i	$0.664766\pi$
$810$	−4.27203e15	−	1.61056e15i	−0.430493	−	0.162296i
$811$	6.58041e15			0.658625			0.329313	−	0.944221i	$-0.393183\pi$
$811$	6.58041e15			0.658625			0.329313	+	0.944221i	$0.393183\pi$
$812$	8.50770e15	+	3.09655e15i	0.845773	+	0.307836i
$813$	−3.38922e15	−	7.32291e15i	−0.334659	−	0.723079i
$814$	−7.05577e15	−	5.92049e15i	−0.692007	−	0.580662i
$815$	1.11830e15	−	6.34217e15i	0.108941	−	0.617833i
$816$	1.09604e15	+	1.29551e16i	0.106055	+	1.25356i
$817$	1.23737e15	−	1.03828e15i	0.118926	−	0.0997910i
$818$	7.45653e15	+	1.29151e16i	0.711858	+	1.23297i
$819$	−7.55175e15	−	2.11240e16i	−0.716120	−	2.00316i
$820$	−1.27459e14	+	2.20765e14i	−0.0120059	+	0.0207948i
$821$	2.90097e14	+	1.64522e15i	0.0271429	+	0.153935i	0.995367	−	0.0961495i	$-0.0306527\pi$
$821$	2.90097e14	+	1.64522e15i	0.0271429	+	0.153935i	−0.968224	+	0.250085i	$0.919542\pi$
$822$	7.09796e15	−	2.61896e16i	0.659688	−	2.43408i
$823$	−6.21907e15	+	2.26356e15i	−0.574151	+	0.208974i	−0.612744	−	0.790281i	$-0.709934\pi$
$823$	−6.21907e15	+	2.26356e15i	−0.574151	+	0.208974i	0.0385935	+	0.999255i	$0.487712\pi$
$824$	9.18036e14	−	3.34138e14i	0.0841899	−	0.0306426i
$825$	−6.12431e15	+	1.62222e15i	−0.557905	+	0.147779i
$826$	−6.07788e14	−	3.44694e15i	−0.0549999	−	0.311920i
$827$	−1.53694e14	+	2.66206e14i	−0.0138158	+	0.0239297i	−0.872851	−	0.487987i	$-0.837731\pi$
$827$	−1.53694e14	+	2.66206e14i	−0.0138158	+	0.0239297i	0.859035	+	0.511917i	$0.171065\pi$
$828$	1.17241e16	+	6.85878e15i	1.04692	+	0.612463i
$829$	−3.04153e15	−	5.26809e15i	−0.269800	−	0.467308i	0.699010	−	0.715112i	$-0.253624\pi$
$829$	−3.04153e15	−	5.26809e15i	−0.269800	−	0.467308i	−0.968810	+	0.247804i	$0.920291\pi$
$830$	2.50011e15	−	2.09784e15i	0.220308	−	0.184860i
$831$	3.06103e15	+	1.43807e15i	0.267955	+	0.125885i
$832$	2.01931e15	−	1.14520e16i	0.175600	−	0.995875i
$833$	1.82949e16	+	1.53513e16i	1.58046	+	1.32616i
$834$	1.53102e15	−	2.17324e15i	0.131391	−	0.186507i
$835$	6.82072e14	+	2.48254e14i	0.0581506	+	0.0211651i
$836$	−1.03778e16			−0.878964
$837$	9.27961e15	+	1.34981e16i	0.780800	+	1.13575i
$838$	2.05394e16			1.71690
$839$	2.09622e16	+	7.62962e15i	1.74079	+	0.633595i	0.999301	−	0.0373715i	$-0.0118985\pi$
$839$	2.09622e16	+	7.62962e15i	1.74079	+	0.633595i	0.741487	+	0.670967i	$0.234121\pi$
$840$	9.16561e14	+	8.28350e13i	0.0756180	+	0.00683404i
$841$	−5.99956e15	−	5.03423e15i	−0.491746	−	0.412624i
$842$	1.49316e15	−	8.46815e15i	0.121588	−	0.689560i
$843$	1.13470e16	−	7.89694e15i	0.917975	−	0.638862i
$844$	6.68450e14	−	5.60897e14i	0.0537262	−	0.0450816i
$845$	1.30438e15	+	2.25925e15i	0.104158	+	0.180406i
$846$	−7.64427e15	+	2.06339e16i	−0.606455	+	1.63698i
$847$	−6.12226e15	+	1.06041e16i	−0.482562	+	0.835821i
$848$	1.51872e15	+	8.61310e15i	0.118933	+	0.674501i
$849$	−8.06436e15	−	8.11069e15i	−0.627448	−	0.631053i
$850$	1.72053e16	−	6.26220e15i	1.33002	−	0.484086i
$851$	−1.66128e16	+	6.04657e15i	−1.27594	+	0.464404i
$852$	8.75099e15	+	8.80127e15i	0.667789	+	0.671626i
$853$	1.33973e15	+	7.59801e15i	0.101578	+	0.576077i	0.992532	+	0.121984i	$0.0389255\pi$
$853$	1.33973e15	+	7.59801e15i	0.101578	+	0.576077i	−0.890954	+	0.454093i	$0.849963\pi$
$854$	1.43710e16	−	2.48913e16i	1.08260	−	1.87512i
$855$	2.32592e15	−	6.27827e15i	0.174093	−	0.469923i
$856$	−1.80196e13	−	3.12108e13i	−0.00134011	−	0.00232113i
$857$	−9.90959e15	+	8.31513e15i	−0.732253	+	0.614433i	−0.930745	−	0.365670i	$-0.880840\pi$
$857$	−9.90959e15	+	8.31513e15i	−0.732253	+	0.614433i	0.198492	+	0.980102i	$0.436396\pi$
$858$	1.27586e16	−	8.87928e15i	0.936745	−	0.651925i
$859$	−3.40001e15	+	1.92824e16i	−0.248038	+	1.40669i	0.565294	+	0.824890i	$0.308763\pi$
$859$	−3.40001e15	+	1.92824e16i	−0.248038	+	1.40669i	−0.813331	+	0.581801i	$0.802348\pi$
$860$	3.28464e14	+	2.75614e14i	0.0238093	+	0.0199784i
$861$	−1.84318e15	−	1.66579e14i	−0.132755	−	0.0119978i
$862$	3.34124e16	+	1.21611e16i	2.39121	+	0.870329i
$863$	1.61198e16			1.14631			0.573154	−	0.819447i	$-0.305720\pi$
$863$	1.61198e16			1.14631			0.573154	+	0.819447i	$0.305720\pi$
$864$	8.31626e15	−	1.74414e16i	0.587628	−	1.23241i
$865$	−3.54248e15			−0.248724
$866$	1.00367e16	+	3.65305e15i	0.700231	+	0.254863i
$867$	2.77724e15	−	3.94223e15i	0.192535	−	0.273298i
$868$	2.30528e16	+	1.93436e16i	1.58805	+	1.33254i
$869$	1.72637e15	−	9.79073e15i	0.118175	−	0.670203i
$870$	−3.66318e15	−	1.72096e15i	−0.249173	−	0.117062i
$871$	−1.48208e15	+	1.24362e15i	−0.100178	+	0.0840594i
$872$	1.21362e15	+	2.10205e15i	0.0815159	+	0.141190i
$873$	2.15717e15	+	1.26198e15i	0.143981	+	0.0842312i
$874$	−2.10120e16	+	3.63938e16i	−1.39365	+	2.41387i
$875$	−2.77130e15	−	1.57169e16i	−0.182659	−	1.03591i
$876$	−2.03321e16	+	5.38559e15i	−1.33171	+	0.352745i
$877$	−2.15325e16	+	7.83721e15i	−1.40151	+	0.510110i	−0.928628	−	0.371013i	$-0.879010\pi$
$877$	−2.15325e16	+	7.83721e15i	−1.40151	+	0.510110i	−0.472887	+	0.881123i	$0.656788\pi$
$878$	1.32884e15	−	4.83659e14i	0.0859515	−	0.0312838i
$879$	5.32915e15	−	1.96632e16i	0.342546	−	1.26391i
$880$	6.41589e14	+	3.63863e15i	0.0409829	+	0.232425i
$881$	−1.12072e16	+	1.94115e16i	−0.711427	+	1.23223i	0.252894	+	0.967494i	$0.418618\pi$
$881$	−1.12072e16	+	1.94115e16i	−0.711427	+	1.23223i	−0.964321	+	0.264734i	$0.914716\pi$
$882$	−1.31413e16	−	3.67593e16i	−0.829012	−	2.31894i
$883$	−1.09828e16	−	1.90228e16i	−0.688543	−	1.19259i	−0.972309	−	0.233698i	$-0.924917\pi$
$883$	−1.09828e16	−	1.90228e16i	−0.688543	−	1.19259i	0.283766	−	0.958893i	$-0.408416\pi$
$884$	−1.63114e16	+	1.36869e16i	−1.01626	+	0.852741i
$885$	6.25218e13	+	7.39003e14i	0.00387118	+	0.0457571i
$886$	3.72638e15	−	2.11333e16i	0.229299	−	1.30042i
$887$	1.89025e15	+	1.58611e15i	0.115595	+	0.0969956i	0.698753	−	0.715363i	$-0.253739\pi$
$887$	1.89025e15	+	1.58611e15i	0.115595	+	0.0969956i	−0.583158	+	0.812359i	$0.698183\pi$
$888$	9.50432e14	+	2.05354e15i	0.0577630	+	0.124805i
$889$	−1.43772e15	−	5.23286e14i	−0.0868387	−	0.0316067i
$890$	2.74644e15			0.164864
$891$	1.02716e16	−	3.60584e15i	0.612792	−	0.215119i
$892$	1.31271e15			0.0778327
$893$	−3.03229e16	−	1.10366e16i	−1.78685	−	0.650360i
$894$	9.18717e15	+	1.98502e16i	0.538054	+	1.16254i
$895$	−2.11063e15	−	1.77103e15i	−0.122853	−	0.103086i
$896$	−1.35938e15	+	7.70941e15i	−0.0786404	+	0.445992i
$897$	−2.51520e15	−	2.97294e16i	−0.144615	−	1.70934i
$898$	−1.96480e16	+	1.64866e16i	−1.12279	+	0.942134i
$899$	7.26040e15	+	1.25754e16i	0.412365	+	0.714237i
$900$	−1.39561e16	−	2.54336e15i	−0.787825	−	0.143573i
$901$	6.47365e15	−	1.12127e16i	0.363214	−	0.629105i
$902$	−2.22679e14	−	1.26287e15i	−0.0124177	−	0.0704245i
$903$	−8.14292e14	+	3.00453e15i	−0.0451333	+	0.166530i
$904$	−3.70393e15	+	1.34812e15i	−0.204050	+	0.0742681i
$905$	−8.46618e15	+	3.08144e15i	−0.463575	+	0.168728i
$906$	−2.38625e16	+	6.32074e15i	−1.29871	+	0.344003i
$907$	5.31000e15	+	3.01145e16i	0.287247	+	1.62906i	0.697149	+	0.716927i	$0.254452\pi$
$907$	5.31000e15	+	3.01145e16i	0.287247	+	1.62906i	−0.409902	+	0.912129i	$0.634437\pi$
$908$	−5.26914e15	+	9.12642e15i	−0.283314	+	0.490714i
$909$	4.32471e12	−	7.54862e14i	0.000231130	−	0.0403428i
$910$	9.21199e15	+	1.59556e16i	0.489357	+	0.847591i
$911$	1.41398e15	−	1.18647e15i	0.0746609	−	0.0626479i	−0.604693	−	0.796458i	$-0.706704\pi$
$911$	1.41398e15	−	1.18647e15i	0.0746609	−	0.0626479i	0.679354	+	0.733810i	$0.262260\pi$
$912$	2.82077e16	+	1.32520e16i	1.48046	+	0.695518i
$913$	−1.35132e15	+	7.66374e15i	−0.0704969	+	0.399808i
$914$	−2.54306e16	−	2.13388e16i	−1.31872	−	1.10654i
$915$	−3.50747e15	+	4.97877e15i	−0.180791	+	0.256629i
$916$	−2.07464e16	−	7.55109e15i	−1.06296	−	0.386887i
$917$	5.57099e16			2.83727
$918$	−2.86263e16	+	1.30504e16i	−1.44921	+	0.660674i
$919$	−9.79377e15			−0.492850			−0.246425	−	0.969162i	$-0.579256\pi$
$919$	−9.79377e15			−0.492850			−0.246425	+	0.969162i	$0.579256\pi$
$920$	1.15015e15	+	4.18622e14i	0.0575338	+	0.0209406i
$921$	−1.01490e16	−	9.17226e14i	−0.504657	−	0.0456088i
$922$	−1.68782e16	−	1.41625e16i	−0.834268	−	0.700034i
$923$	4.73402e15	−	2.68479e16i	0.232606	−	1.31917i
$924$	1.64157e16	−	1.14245e16i	0.801797	−	0.558008i
$925$	1.41440e16	−	1.18683e16i	0.686743	−	0.576245i
$926$	−8.69690e15	−	1.50635e16i	−0.419763	−	0.727050i
$927$	8.74422e15	+	1.05430e16i	0.419549	+	0.505856i
$928$	8.56461e15	−	1.48343e16i	0.408502	−	0.707546i
$929$	6.23964e15	+	3.53868e16i	0.295851	+	1.67785i	0.663723	+	0.747978i	$0.268975\pi$
$929$	6.23964e15	+	3.53868e16i	0.295851	+	1.67785i	−0.367872	+	0.929876i	$0.619914\pi$
$930$	−9.48517e15	−	9.53967e15i	−0.447084	−	0.449653i
$931$	5.37956e16	−	1.95800e16i	2.52071	−	0.917464i
$932$	−2.07285e16	+	7.54454e15i	−0.965560	+	0.351435i
$933$	−2.86859e14	−	2.88507e14i	−0.0132837	−	0.0133600i
$934$	−7.80457e15	−	4.42619e16i	−0.359287	−	2.03762i
$935$	2.73482e15	−	4.73684e15i	0.125160	−	0.216783i
$936$	−3.76454e15	+	6.41574e14i	−0.171275	+	0.0291897i
$937$	6.96972e14	+	1.20719e15i	0.0315244	+	0.0546019i	0.881357	−	0.472451i	$-0.156630\pi$
$937$	6.96972e14	+	1.20719e15i	0.0315244	+	0.0546019i	−0.849833	+	0.527052i	$0.823297\pi$
$938$	−4.02306e15	+	3.37575e15i	−0.180901	+	0.151794i
$939$	2.19917e14	−	1.53050e14i	0.00983100	−	0.00684186i
$940$	1.48746e15	−	8.43578e15i	0.0661060	−	0.374906i
$941$	−1.88329e16	−	1.58026e16i	−0.832096	−	0.698211i	0.123676	−	0.992323i	$-0.460532\pi$
$941$	−1.88329e16	−	1.58026e16i	−0.832096	−	0.698211i	−0.955771	+	0.294112i	$0.904976\pi$
$942$	1.25647e16	+	1.13555e15i	0.551917	+	0.0498800i
$943$	−2.31292e15	−	8.41835e14i	−0.101006	−	0.0367632i
$944$	−3.45224e15			−0.149884
$945$	3.23231e15	+	1.24916e16i	0.139521	+	0.539190i
$946$	−2.15696e15			−0.0925639
$947$	−2.01795e16	−	7.34475e15i	−0.860966	−	0.313366i	−0.126463	−	0.991971i	$-0.540363\pi$
$947$	−2.01795e16	−	7.34475e15i	−0.860966	−	0.313366i	−0.734503	+	0.678605i	$0.762585\pi$
$948$	1.28204e16	−	1.81983e16i	0.543822	−	0.771942i
$949$	3.53916e16	+	2.96971e16i	1.49258	+	1.25242i
$950$	7.62131e15	−	4.32226e16i	0.319558	−	1.81230i
$951$	3.00531e15	+	1.41189e15i	0.125284	+	0.0588585i
$952$	4.85801e15	−	4.07636e15i	0.201352	−	0.168954i
$953$	2.76348e15	+	4.78648e15i	0.113879	+	0.197245i	0.917331	−	0.398125i	$-0.130339\pi$
$953$	2.76348e15	+	4.78648e15i	0.113879	+	0.197245i	−0.803452	+	0.595370i	$0.797006\pi$
$954$	−1.83884e16	+	1.04766e16i	−0.753404	+	0.429242i
$955$	2.48757e15	−	4.30861e15i	0.101335	−	0.175517i
$956$	4.93433e15	+	2.79840e16i	0.199853	+	1.13342i
$957$	9.32874e15	−	2.47101e15i	0.375671	−	0.0995082i
$958$	3.16979e16	−	1.15371e16i	1.26917	−	0.461940i
$959$	−7.20618e16	+	2.62283e16i	−2.86882	+	1.04416i
$960$	−1.74961e15	+	6.45561e15i	−0.0692547	+	0.255532i
$961$	3.96902e15	+	2.25094e16i	0.156209	+	0.885903i
$962$	−2.26504e16	+	3.92317e16i	−0.886366	+	1.53523i
$963$	3.27004e14	−	3.85204e14i	0.0127235	−	0.0149881i
$964$	−1.71650e15	−	2.97307e15i	−0.0664081	−	0.115022i
$965$	1.98700e15	−	1.66729e15i	0.0764358	−	0.0641373i
$966$	−6.82740e15	−	8.06994e16i	−0.261145	−	3.08671i
$967$	3.29390e13	−	1.86806e14i	0.00125275	−	0.00710470i	−0.984175	−	0.177199i	$-0.943296\pi$
$967$	3.29390e13	−	1.86806e14i	0.00125275	−	0.00710470i	0.985428	+	0.170095i	$0.0544074\pi$
$968$	1.59673e15	+	1.33981e15i	0.0603833	+	0.0506676i
$969$	−1.93783e16	−	4.18696e16i	−0.728676	−	1.57441i
$970$	−1.92875e15	−	7.02008e14i	−0.0721160	−	0.0262481i
$971$	8.74091e15			0.324976			0.162488	−	0.986711i	$-0.448048\pi$
$971$	8.74091e15			0.324976			0.162488	+	0.986711i	$0.448048\pi$
$972$	2.42497e16	+	2.47202e15i	0.896483	+	0.0913875i
$973$	−7.51305e15			−0.276182
$974$	1.20731e15	+	4.39424e14i	0.0441310	+	0.0160624i
$975$	1.30878e16	+	2.82782e16i	0.475711	+	1.02784i
$976$	−2.17165e16	−	1.82223e16i	−0.784904	−	0.658613i
$977$	−4.68298e15	+	2.65585e16i	−0.168307	+	0.954516i	0.777282	+	0.629152i	$0.216598\pi$
$977$	−4.68298e15	+	2.65585e16i	−0.168307	+	0.954516i	−0.945589	+	0.325363i	$0.894513\pi$
$978$	6.11516e15	+	7.22807e16i	0.218547	+	2.58320i
$979$	−5.01659e15	+	4.20942e15i	−0.178280	+	0.149595i
$980$	7.59835e15	+	1.31607e16i	0.268520	+	0.465090i
$981$	−2.20237e16	+	2.59435e16i	−0.773947	+	0.911696i
$982$	−3.30892e16	+	5.73122e16i	−1.15631	+	2.00278i
$983$	−6.68504e15	−	3.79127e16i	−0.232306	−	1.31747i	−0.848215	−	0.529653i	$-0.822322\pi$
$983$	−6.68504e15	−	3.79127e16i	−0.232306	−	1.31747i	0.615909	−	0.787817i	$-0.288789\pi$
$984$	−8.24103e13	+	3.04073e14i	−0.00284779	+	0.0105076i
$985$	1.12642e16	−	4.09983e15i	0.387080	−	0.140886i
$986$	−2.62076e16	+	9.53878e15i	−0.895579	+	0.325964i
$987$	6.01149e16	−	1.59233e16i	2.04286	−	0.541114i
$988$	8.86322e15	+	5.02658e16i	0.299522	+	1.69867i
$989$	−2.07004e15	+	3.58542e15i	−0.0695665	+	0.120493i
$990$	−7.76825e15	+	4.42586e15i	−0.259615	+	0.147912i
$991$	2.71440e16	+	4.70148e16i	0.902129	+	1.56253i	0.824725	+	0.565534i	$0.191330\pi$
$991$	2.71440e16	+	4.70148e16i	0.902129	+	1.56253i	0.0774041	+	0.997000i	$0.475337\pi$
$992$	4.36149e16	−	3.65973e16i	1.44152	−	1.20958i
$993$	3.20267e16	+	1.50461e16i	1.05267	+	0.494544i
$994$	1.28503e16	−	7.28777e16i	0.420038	−	2.38215i
$995$	−1.16537e16	−	9.77862e15i	−0.378824	−	0.317871i
$996$	−1.00352e16	+	1.42448e16i	−0.324415	+	0.460500i
$997$	−4.43866e16	−	1.61554e16i	−1.42701	−	0.519391i	−0.490940	−	0.871193i	$-0.663347\pi$
$997$	−4.43866e16	−	1.61554e16i	−1.42701	−	0.519391i	−0.936074	+	0.351802i	$0.885569\pi$
$998$	2.54214e16			0.812796
$999$	−2.26255e16	+	2.22399e16i	−0.719429	+	0.707169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.12.e.a.4.7	✓	192
3.2	odd	2		81.12.e.a.64.26		192
27.7	even	9	inner	27.12.e.a.7.7	yes	192
27.20	odd	18		81.12.e.a.19.26		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.12.e.a.4.7	✓	192	1.1	even	1	trivial
27.12.e.a.7.7	yes	192	27.7	even	9	inner
81.12.e.a.19.26		192	27.20	odd	18
81.12.e.a.64.26		192	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-58.6349 - 21.3414i) q^{2} +(176.782 + 381.962i) q^{3} +(1413.74 + 1186.27i) q^{4} +(-404.877 + 2296.17i) q^{5} +(-2213.98 - 26169.1i) q^{6} +(-56857.8 + 47709.4i) q^{7} +(6317.45 + 10942.1i) q^{8} +(-114643. + 135048. i) q^{9} +(72743.5 - 125995. i) q^{10} +(60239.0 + 341632. i) q^{11} +(-203187. + 749708. i) q^{12} +(1.60328e6 - 583546. i) q^{13} +(4.35204e6 - 1.58401e6i) q^{14} +(-948627. + 251274. i) q^{15} +(-793225. - 4.49860e6i) q^{16} +(-3.38117e6 + 5.85636e6i) q^{17} +(9.60422e6 - 5.47188e6i) q^{18} +(8.10496e6 + 1.40382e7i) q^{19} +(-3.29628e6 + 2.76591e6i) q^{20} +(-2.82746e7 - 1.32834e7i) q^{21} +(3.75879e6 - 2.13172e7i) q^{22} +(-3.18273e7 - 2.67062e7i) q^{23} +(-3.06268e6 + 4.34740e6i) q^{24} +(4.07749e7 + 1.48409e7i) q^{25} -1.06462e8 q^{26} +(-7.18501e7 - 1.99155e7i) q^{27} -1.36979e8 q^{28} +(-6.21097e7 - 2.26061e7i) q^{29} +(6.09852e7 + 5.51159e6i) q^{30} +(-1.68295e8 - 1.41216e8i) q^{31} +(-4.50023e7 + 2.55221e8i) q^{32} +(-1.19842e8 + 8.34034e7i) q^{33} +(3.23237e8 - 2.71228e8i) q^{34} +(-8.65285e7 - 1.49872e8i) q^{35} +(-3.22280e8 + 5.49248e7i) q^{36} +(2.12756e8 - 3.68504e8i) q^{37} +(-1.75639e8 - 9.96101e8i) q^{38} +(5.06323e8 + 5.09232e8i) q^{39} +(-2.76828e7 + 1.00757e7i) q^{40} +(5.56693e7 - 2.02620e7i) q^{41} +(1.37439e9 + 1.38229e9i) q^{42} +(-1.73035e7 - 9.81332e7i) q^{43} +(-3.20106e8 + 5.54441e8i) q^{44} +(-2.63677e8 - 3.17919e8i) q^{45} +(1.29624e9 + 2.24516e9i) q^{46} +(-1.52496e9 + 1.27959e9i) q^{47} +(1.57807e9 - 1.09825e9i) q^{48} +(6.13267e8 - 3.47801e9i) q^{49} +(-2.07411e9 - 1.74039e9i) q^{50} +(-2.83464e9 - 2.56183e8i) q^{51} +(2.95887e9 + 1.07694e9i) q^{52} -1.91462e9 q^{53} +(3.78790e9 + 2.70112e9i) q^{54} -8.08837e8 q^{55} +(-8.81239e8 - 3.20745e8i) q^{56} +(-3.92926e9 + 5.57749e9i) q^{57} +(3.15935e9 + 2.65101e9i) q^{58} +(1.31234e8 - 7.44263e8i) q^{59} +(-1.63919e9 - 7.70093e8i) q^{60} +(4.75406e9 - 3.98913e9i) q^{61} +(6.85421e9 + 1.18718e10i) q^{62} +(7.53272e7 - 1.31481e10i) q^{63} +(3.40783e9 - 5.90254e9i) q^{64} +(6.90791e8 + 3.91767e9i) q^{65} +(8.80685e9 - 2.33277e9i) q^{66} +(-1.06557e9 + 3.87835e8i) q^{67} +(-1.17273e10 + 4.26840e9i) q^{68} +(4.57430e9 - 1.68780e10i) q^{69} +(1.87513e9 + 1.06344e10i) q^{70} +(7.98925e9 - 1.38378e10i) q^{71} +(-2.20197e9 - 4.01287e8i) q^{72} +(1.35392e10 + 2.34506e10i) q^{73} +(-2.03393e10 + 1.70667e10i) q^{74} +(1.53961e9 + 1.81981e10i) q^{75} +(-5.19479e9 + 2.94611e10i) q^{76} +(-1.97241e10 - 1.65505e10i) q^{77} +(-1.88205e10 - 4.06644e10i) q^{78} +(-2.69303e10 - 9.80184e9i) q^{79} +1.06507e10 q^{80} +(-5.09481e9 - 3.09647e10i) q^{81} -3.69659e9 q^{82} +(2.10798e10 + 7.67243e9i) q^{83} +(-2.42153e10 - 5.23207e10i) q^{84} +(-1.20783e10 - 1.01349e10i) q^{85} +(-1.07971e9 + 6.12331e9i) q^{86} +(-2.34518e9 - 2.77199e10i) q^{87} +(-3.35763e9 + 2.81739e9i) q^{88} +(9.43880e9 + 1.63485e10i) q^{89} +(8.67585e9 + 2.42684e10i) q^{90} +(-6.33183e10 + 1.09671e11i) q^{91} +(-1.33147e10 - 7.55116e10i) q^{92} +(2.41878e10 - 8.92467e10i) q^{93} +(1.16724e11 - 4.24841e10i) q^{94} +(-3.55157e10 + 1.29267e10i) q^{95} +(-1.05440e11 + 2.79292e10i) q^{96} +(-2.44983e9 - 1.38937e10i) q^{97} +(-1.10184e11 + 1.90845e11i) q^{98} +(-5.30428e10 - 3.10308e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2931 q^{5} + 4410 q^{6} - 6 q^{7} - 294915 q^{8} + 96228 q^{9} - 3 q^{10} - 1594293 q^{11} + 323823 q^{12} - 6 q^{13} + 5263143 q^{14} + 3836529 q^{15} + 6138 q^{16}+ \cdots - 581308635231 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2931 * q^5 + 4410 * q^6 - 6 * q^7 - 294915 * q^8 + 96228 * q^9 - 3 * q^10 - 1594293 * q^11 + 323823 * q^12 - 6 * q^13 + 5263143 * q^14 + 3836529 * q^15 + 6138 * q^16 - 17038287 * q^17 + 8396685 * q^18 - 3 * q^19 + 33966483 * q^20 + 73765320 * q^21 - 6811494 * q^22 - 154612956 * q^23 - 52250526 * q^24 - 39922647 * q^25 + 72169026 * q^26 + 406211103 * q^27 - 12 * q^28 - 818363742 * q^29 - 845653581 * q^30 - 114913365 * q^31 + 2449907208 * q^32 + 792631584 * q^33 + 250353882 * q^34 - 1986199152 * q^35 - 1271261664 * q^36 - 3 * q^37 - 199328700 * q^38 + 2330844945 * q^39 + 159067281 * q^40 + 2363326233 * q^41 - 3110154678 * q^42 + 2031687507 * q^43 - 6781787259 * q^44 + 9102254625 * q^45 - 3 * q^46 + 1321238505 * q^47 - 6384109047 * q^48 + 5300190696 * q^49 - 19347232641 * q^50 + 1310770386 * q^51 - 7435159623 * q^52 + 7067989026 * q^53 + 22629480894 * q^54 - 12 * q^55 - 8014324821 * q^56 - 32645841267 * q^57 + 16115317383 * q^58 + 21931606932 * q^59 + 50690195514 * q^60 - 16510964208 * q^61 + 11823393570 * q^62 - 30632962095 * q^63 - 80530636803 * q^64 + 4275338385 * q^65 + 38229021261 * q^66 - 38080922415 * q^67 + 82368304983 * q^68 - 30801215529 * q^69 + 60497186367 * q^70 - 50263647093 * q^71 + 3848431572 * q^72 + 1424119740 * q^73 - 72634311813 * q^74 + 108769340739 * q^75 - 116456331270 * q^76 + 62223517041 * q^77 - 72959471478 * q^78 + 90355950390 * q^79 + 24737530830 * q^80 - 144648556128 * q^81 - 12 * q^82 + 113535448779 * q^83 + 273199455402 * q^84 - 164592103131 * q^85 - 28905145338 * q^86 - 308647046223 * q^87 + 67619592186 * q^88 - 100969659531 * q^89 + 650525024790 * q^90 - 61084040502 * q^91 - 29835580269 * q^92 - 323782133601 * q^93 - 264765665733 * q^94 + 349741980687 * q^95 + 620032058802 * q^96 - 109680687051 * q^97 + 282639387726 * q^98 - 581308635231 * q^99

Introduction

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