Properties

Label 3.38.a.a.1.1
Level 3
Weight 38
Character 3.1
Self dual Yes
Analytic conductor 26.014
Analytic rank 1
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 38 \)
Character orbit: \([\chi]\) = 3.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(26.0142114374\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{5}\cdot 5 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(47984.3\)
Character \(\chi\) = 3.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-679444. q^{2}\) \(-3.87420e8 q^{3}\) \(+3.24205e11 q^{4}\) \(-1.35264e13 q^{5}\) \(+2.63231e14 q^{6}\) \(-4.10476e15 q^{7}\) \(-1.26897e17 q^{8}\) \(+1.50095e17 q^{9}\) \(+O(q^{10})\) \(q\)\(-679444. q^{2}\) \(-3.87420e8 q^{3}\) \(+3.24205e11 q^{4}\) \(-1.35264e13 q^{5}\) \(+2.63231e14 q^{6}\) \(-4.10476e15 q^{7}\) \(-1.26897e17 q^{8}\) \(+1.50095e17 q^{9}\) \(+9.19042e18 q^{10}\) \(+1.15138e19 q^{11}\) \(-1.25604e20 q^{12}\) \(+4.10734e20 q^{13}\) \(+2.78896e21 q^{14}\) \(+5.24040e21 q^{15}\) \(+4.16612e22 q^{16}\) \(-2.52734e22 q^{17}\) \(-1.01981e23 q^{18}\) \(+8.17932e23 q^{19}\) \(-4.38533e24 q^{20}\) \(+1.59027e24 q^{21}\) \(-7.82302e24 q^{22}\) \(-7.67235e24 q^{23}\) \(+4.91626e25 q^{24}\) \(+1.10204e26 q^{25}\) \(-2.79071e26 q^{26}\) \(-5.81497e25 q^{27}\) \(-1.33079e27 q^{28}\) \(+7.52830e26 q^{29}\) \(-3.56056e27 q^{30}\) \(-3.41837e27 q^{31}\) \(-1.08658e28 q^{32}\) \(-4.46070e27 q^{33}\) \(+1.71718e28 q^{34}\) \(+5.55226e28 q^{35}\) \(+4.86615e28 q^{36}\) \(-4.82934e28 q^{37}\) \(-5.55739e29 q^{38}\) \(-1.59127e29 q^{39}\) \(+1.71646e30 q^{40}\) \(+5.14552e29 q^{41}\) \(-1.08050e30 q^{42}\) \(+1.56506e30 q^{43}\) \(+3.73285e30 q^{44}\) \(-2.03024e30 q^{45}\) \(+5.21293e30 q^{46}\) \(-1.18810e31 q^{47}\) \(-1.61404e31 q^{48}\) \(-1.71303e30 q^{49}\) \(-7.48772e31 q^{50}\) \(+9.79142e30 q^{51}\) \(+1.33162e32 q^{52}\) \(-4.07740e31 q^{53}\) \(+3.95095e31 q^{54}\) \(-1.55741e32 q^{55}\) \(+5.20883e32 q^{56}\) \(-3.16884e32 q^{57}\) \(-5.11506e32 q^{58}\) \(+6.63304e31 q^{59}\) \(+1.69897e33 q^{60}\) \(-1.38461e33 q^{61}\) \(+2.32259e33 q^{62}\) \(-6.16103e32 q^{63}\) \(+1.65684e33 q^{64}\) \(-5.55574e33 q^{65}\) \(+3.03080e33 q^{66}\) \(+3.53054e33 q^{67}\) \(-8.19376e33 q^{68}\) \(+2.97243e33 q^{69}\) \(-3.77245e34 q^{70}\) \(-6.34947e33 q^{71}\) \(-1.90466e34 q^{72}\) \(+4.38920e34 q^{73}\) \(+3.28127e34 q^{74}\) \(-4.26951e34 q^{75}\) \(+2.65178e35 q^{76}\) \(-4.72616e34 q^{77}\) \(+1.08118e35 q^{78}\) \(+2.43750e34 q^{79}\) \(-5.63525e35 q^{80}\) \(+2.25284e34 q^{81}\) \(-3.49610e35 q^{82}\) \(+4.41573e35 q^{83}\) \(+5.15574e35 q^{84}\) \(+3.41857e35 q^{85}\) \(-1.06337e36 q^{86}\) \(-2.91662e35 q^{87}\) \(-1.46108e36 q^{88}\) \(+1.79925e36 q^{89}\) \(+1.37943e36 q^{90}\) \(-1.68596e36 q^{91}\) \(-2.48742e36 q^{92}\) \(+1.32435e36 q^{93}\) \(+8.07247e36 q^{94}\) \(-1.10637e37 q^{95}\) \(+4.20964e36 q^{96}\) \(-4.46953e36 q^{97}\) \(+1.16391e36 q^{98}\) \(+1.72817e36 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut -\mathstrut 310908q^{2} \) \(\mathstrut -\mathstrut 1162261467q^{3} \) \(\mathstrut +\mathstrut 338476600848q^{4} \) \(\mathstrut -\mathstrut 9628717886790q^{5} \) \(\mathstrut +\mathstrut 120452129394012q^{6} \) \(\mathstrut -\mathstrut 4621884343701744q^{7} \) \(\mathstrut -\mathstrut 93383909093911488q^{8} \) \(\mathstrut +\mathstrut 450283905890997363q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 310908q^{2} \) \(\mathstrut -\mathstrut 1162261467q^{3} \) \(\mathstrut +\mathstrut 338476600848q^{4} \) \(\mathstrut -\mathstrut 9628717886790q^{5} \) \(\mathstrut +\mathstrut 120452129394012q^{6} \) \(\mathstrut -\mathstrut 4621884343701744q^{7} \) \(\mathstrut -\mathstrut 93383909093911488q^{8} \) \(\mathstrut +\mathstrut 450283905890997363q^{9} \) \(\mathstrut +\mathstrut 10698950136741797880q^{10} \) \(\mathstrut +\mathstrut 22673303357139628620q^{11} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!72\)\(q^{12} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!10\)\(q^{13} \) \(\mathstrut +\mathstrut \)\(79\!\cdots\!28\)\(q^{14} \) \(\mathstrut +\mathstrut \)\(37\!\cdots\!10\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!56\)\(q^{16} \) \(\mathstrut -\mathstrut \)\(27\!\cdots\!06\)\(q^{17} \) \(\mathstrut -\mathstrut \)\(46\!\cdots\!68\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(58\!\cdots\!04\)\(q^{19} \) \(\mathstrut -\mathstrut \)\(40\!\cdots\!80\)\(q^{20} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!16\)\(q^{21} \) \(\mathstrut -\mathstrut \)\(44\!\cdots\!52\)\(q^{22} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!72\)\(q^{23} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!32\)\(q^{24} \) \(\mathstrut -\mathstrut \)\(24\!\cdots\!75\)\(q^{25} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!44\)\(q^{26} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!07\)\(q^{27} \) \(\mathstrut -\mathstrut \)\(20\!\cdots\!88\)\(q^{28} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!78\)\(q^{29} \) \(\mathstrut -\mathstrut \)\(41\!\cdots\!20\)\(q^{30} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!36\)\(q^{31} \) \(\mathstrut -\mathstrut \)\(27\!\cdots\!84\)\(q^{32} \) \(\mathstrut -\mathstrut \)\(87\!\cdots\!80\)\(q^{33} \) \(\mathstrut -\mathstrut \)\(18\!\cdots\!64\)\(q^{34} \) \(\mathstrut +\mathstrut \)\(47\!\cdots\!80\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!08\)\(q^{36} \) \(\mathstrut +\mathstrut \)\(60\!\cdots\!66\)\(q^{37} \) \(\mathstrut -\mathstrut \)\(37\!\cdots\!76\)\(q^{38} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!90\)\(q^{39} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!00\)\(q^{40} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!34\)\(q^{41} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!92\)\(q^{42} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!44\)\(q^{43} \) \(\mathstrut +\mathstrut \)\(42\!\cdots\!72\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!90\)\(q^{45} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!56\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!32\)\(q^{47} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!84\)\(q^{48} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!73\)\(q^{49} \) \(\mathstrut -\mathstrut \)\(96\!\cdots\!00\)\(q^{50} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!34\)\(q^{51} \) \(\mathstrut +\mathstrut \)\(43\!\cdots\!84\)\(q^{52} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!82\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(18\!\cdots\!52\)\(q^{54} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!80\)\(q^{55} \) \(\mathstrut +\mathstrut \)\(63\!\cdots\!60\)\(q^{56} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!56\)\(q^{57} \) \(\mathstrut +\mathstrut \)\(58\!\cdots\!88\)\(q^{58} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!36\)\(q^{59} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!20\)\(q^{60} \) \(\mathstrut +\mathstrut \)\(29\!\cdots\!02\)\(q^{61} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!92\)\(q^{62} \) \(\mathstrut -\mathstrut \)\(69\!\cdots\!24\)\(q^{63} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!24\)\(q^{64} \) \(\mathstrut -\mathstrut \)\(75\!\cdots\!60\)\(q^{65} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!28\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(38\!\cdots\!44\)\(q^{67} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!16\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!08\)\(q^{69} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!60\)\(q^{70} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!44\)\(q^{71} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!48\)\(q^{72} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!78\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(46\!\cdots\!28\)\(q^{74} \) \(\mathstrut +\mathstrut \)\(96\!\cdots\!75\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(34\!\cdots\!16\)\(q^{76} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!68\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(23\!\cdots\!16\)\(q^{78} \) \(\mathstrut +\mathstrut \)\(74\!\cdots\!40\)\(q^{79} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!40\)\(q^{80} \) \(\mathstrut +\mathstrut \)\(67\!\cdots\!23\)\(q^{81} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!12\)\(q^{82} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!04\)\(q^{83} \) \(\mathstrut +\mathstrut \)\(78\!\cdots\!32\)\(q^{84} \) \(\mathstrut +\mathstrut \)\(21\!\cdots\!80\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(26\!\cdots\!60\)\(q^{86} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!42\)\(q^{87} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!28\)\(q^{88} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!26\)\(q^{89} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!80\)\(q^{90} \) \(\mathstrut +\mathstrut \)\(45\!\cdots\!04\)\(q^{91} \) \(\mathstrut -\mathstrut \)\(54\!\cdots\!24\)\(q^{92} \) \(\mathstrut +\mathstrut \)\(45\!\cdots\!04\)\(q^{93} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!00\)\(q^{94} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!00\)\(q^{95} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!76\)\(q^{96} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!14\)\(q^{97} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!00\)\(q^{98} \) \(\mathstrut +\mathstrut \)\(34\!\cdots\!20\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −679444. −1.83273 −0.916366 0.400342i \(-0.868891\pi\)
−0.916366 + 0.400342i \(0.868891\pi\)
\(3\) −3.87420e8 −0.577350
\(4\) 3.24205e11 2.35890
\(5\) −1.35264e13 −1.58576 −0.792879 0.609379i \(-0.791419\pi\)
−0.792879 + 0.609379i \(0.791419\pi\)
\(6\) 2.63231e14 1.05813
\(7\) −4.10476e15 −0.952740 −0.476370 0.879245i \(-0.658048\pi\)
−0.476370 + 0.879245i \(0.658048\pi\)
\(8\) −1.26897e17 −2.49051
\(9\) 1.50095e17 0.333333
\(10\) 9.19042e18 2.90627
\(11\) 1.15138e19 0.624390 0.312195 0.950018i \(-0.398936\pi\)
0.312195 + 0.950018i \(0.398936\pi\)
\(12\) −1.25604e20 −1.36191
\(13\) 4.10734e20 1.01300 0.506499 0.862241i \(-0.330940\pi\)
0.506499 + 0.862241i \(0.330940\pi\)
\(14\) 2.78896e21 1.74612
\(15\) 5.24040e21 0.915538
\(16\) 4.16612e22 2.20552
\(17\) −2.52734e22 −0.435871 −0.217936 0.975963i \(-0.569932\pi\)
−0.217936 + 0.975963i \(0.569932\pi\)
\(18\) −1.01981e23 −0.610910
\(19\) 8.17932e23 1.80209 0.901043 0.433730i \(-0.142803\pi\)
0.901043 + 0.433730i \(0.142803\pi\)
\(20\) −4.38533e24 −3.74065
\(21\) 1.59027e24 0.550065
\(22\) −7.82302e24 −1.14434
\(23\) −7.67235e24 −0.493132 −0.246566 0.969126i \(-0.579302\pi\)
−0.246566 + 0.969126i \(0.579302\pi\)
\(24\) 4.91626e25 1.43789
\(25\) 1.10204e26 1.51463
\(26\) −2.79071e26 −1.85655
\(27\) −5.81497e25 −0.192450
\(28\) −1.33079e27 −2.24742
\(29\) 7.52830e26 0.664253 0.332127 0.943235i \(-0.392234\pi\)
0.332127 + 0.943235i \(0.392234\pi\)
\(30\) −3.56056e27 −1.67793
\(31\) −3.41837e27 −0.878270 −0.439135 0.898421i \(-0.644715\pi\)
−0.439135 + 0.898421i \(0.644715\pi\)
\(32\) −1.08658e28 −1.55163
\(33\) −4.46070e27 −0.360492
\(34\) 1.71718e28 0.798834
\(35\) 5.55226e28 1.51081
\(36\) 4.86615e28 0.786301
\(37\) −4.82934e28 −0.470063 −0.235031 0.971988i \(-0.575519\pi\)
−0.235031 + 0.971988i \(0.575519\pi\)
\(38\) −5.55739e29 −3.30274
\(39\) −1.59127e29 −0.584854
\(40\) 1.71646e30 3.94934
\(41\) 5.14552e29 0.749770 0.374885 0.927071i \(-0.377682\pi\)
0.374885 + 0.927071i \(0.377682\pi\)
\(42\) −1.08050e30 −1.00812
\(43\) 1.56506e30 0.944853 0.472426 0.881370i \(-0.343378\pi\)
0.472426 + 0.881370i \(0.343378\pi\)
\(44\) 3.73285e30 1.47288
\(45\) −2.03024e30 −0.528586
\(46\) 5.21293e30 0.903779
\(47\) −1.18810e31 −1.38370 −0.691851 0.722040i \(-0.743204\pi\)
−0.691851 + 0.722040i \(0.743204\pi\)
\(48\) −1.61404e31 −1.27336
\(49\) −1.71303e30 −0.0922862
\(50\) −7.48772e31 −2.77590
\(51\) 9.79142e30 0.251650
\(52\) 1.33162e32 2.38956
\(53\) −4.07740e31 −0.514375 −0.257188 0.966361i \(-0.582796\pi\)
−0.257188 + 0.966361i \(0.582796\pi\)
\(54\) 3.95095e31 0.352709
\(55\) −1.55741e32 −0.990131
\(56\) 5.20883e32 2.37280
\(57\) −3.16884e32 −1.04043
\(58\) −5.11506e32 −1.21740
\(59\) 6.63304e31 0.115067 0.0575335 0.998344i \(-0.481676\pi\)
0.0575335 + 0.998344i \(0.481676\pi\)
\(60\) 1.69897e33 2.15967
\(61\) −1.38461e33 −1.29636 −0.648182 0.761486i \(-0.724470\pi\)
−0.648182 + 0.761486i \(0.724470\pi\)
\(62\) 2.32259e33 1.60963
\(63\) −6.16103e32 −0.317580
\(64\) 1.65684e33 0.638192
\(65\) −5.55574e33 −1.60637
\(66\) 3.03080e33 0.660684
\(67\) 3.53054e33 0.582716 0.291358 0.956614i \(-0.405893\pi\)
0.291358 + 0.956614i \(0.405893\pi\)
\(68\) −8.19376e33 −1.02818
\(69\) 2.97243e33 0.284710
\(70\) −3.77245e34 −2.76892
\(71\) −6.34947e33 −0.358474 −0.179237 0.983806i \(-0.557363\pi\)
−0.179237 + 0.983806i \(0.557363\pi\)
\(72\) −1.90466e34 −0.830169
\(73\) 4.38920e34 1.48222 0.741110 0.671384i \(-0.234300\pi\)
0.741110 + 0.671384i \(0.234300\pi\)
\(74\) 3.28127e34 0.861499
\(75\) −4.26951e34 −0.874470
\(76\) 2.65178e35 4.25095
\(77\) −4.72616e34 −0.594881
\(78\) 1.08118e35 1.07188
\(79\) 2.43750e34 0.190916 0.0954582 0.995433i \(-0.469568\pi\)
0.0954582 + 0.995433i \(0.469568\pi\)
\(80\) −5.63525e35 −3.49743
\(81\) 2.25284e34 0.111111
\(82\) −3.49610e35 −1.37413
\(83\) 4.41573e35 1.38694 0.693471 0.720485i \(-0.256081\pi\)
0.693471 + 0.720485i \(0.256081\pi\)
\(84\) 5.15574e35 1.29755
\(85\) 3.41857e35 0.691186
\(86\) −1.06337e36 −1.73166
\(87\) −2.91662e35 −0.383507
\(88\) −1.46108e36 −1.55505
\(89\) 1.79925e36 1.55374 0.776868 0.629663i \(-0.216807\pi\)
0.776868 + 0.629663i \(0.216807\pi\)
\(90\) 1.37943e36 0.968756
\(91\) −1.68596e36 −0.965123
\(92\) −2.48742e36 −1.16325
\(93\) 1.32435e36 0.507070
\(94\) 8.07247e36 2.53595
\(95\) −1.10637e37 −2.85767
\(96\) 4.20964e36 0.895832
\(97\) −4.46953e36 −0.785208 −0.392604 0.919708i \(-0.628426\pi\)
−0.392604 + 0.919708i \(0.628426\pi\)
\(98\) 1.16391e36 0.169136
\(99\) 1.72817e36 0.208130
\(100\) 3.57286e37 3.57286
\(101\) 1.71365e37 1.42553 0.712767 0.701401i \(-0.247442\pi\)
0.712767 + 0.701401i \(0.247442\pi\)
\(102\) −6.65272e36 −0.461207
\(103\) −2.35646e37 −1.36387 −0.681934 0.731414i \(-0.738861\pi\)
−0.681934 + 0.731414i \(0.738861\pi\)
\(104\) −5.21210e37 −2.52288
\(105\) −2.15106e37 −0.872269
\(106\) 2.77037e37 0.942712
\(107\) −4.25420e37 −1.21680 −0.608399 0.793631i \(-0.708188\pi\)
−0.608399 + 0.793631i \(0.708188\pi\)
\(108\) −1.88525e37 −0.453971
\(109\) −1.62022e37 −0.328991 −0.164496 0.986378i \(-0.552600\pi\)
−0.164496 + 0.986378i \(0.552600\pi\)
\(110\) 1.05817e38 1.81464
\(111\) 1.87099e37 0.271391
\(112\) −1.71009e38 −2.10129
\(113\) −3.47825e37 −0.362585 −0.181292 0.983429i \(-0.558028\pi\)
−0.181292 + 0.983429i \(0.558028\pi\)
\(114\) 2.15305e38 1.90684
\(115\) 1.03779e38 0.781989
\(116\) 2.44071e38 1.56691
\(117\) 6.16489e37 0.337666
\(118\) −4.50678e37 −0.210887
\(119\) 1.03741e38 0.415272
\(120\) −6.64993e38 −2.28015
\(121\) −2.07471e38 −0.610137
\(122\) 9.40768e38 2.37589
\(123\) −1.99348e38 −0.432880
\(124\) −1.10825e39 −2.07176
\(125\) −5.06483e38 −0.816074
\(126\) 4.18608e38 0.582039
\(127\) 4.21818e38 0.506706 0.253353 0.967374i \(-0.418467\pi\)
0.253353 + 0.967374i \(0.418467\pi\)
\(128\) 3.67655e38 0.381994
\(129\) −6.06336e38 −0.545511
\(130\) 3.77482e39 2.94404
\(131\) −1.15197e39 −0.779691 −0.389845 0.920880i \(-0.627472\pi\)
−0.389845 + 0.920880i \(0.627472\pi\)
\(132\) −1.44618e39 −0.850365
\(133\) −3.35742e39 −1.71692
\(134\) −2.39880e39 −1.06796
\(135\) 7.86556e38 0.305179
\(136\) 3.20712e39 1.08554
\(137\) −2.75856e39 −0.815365 −0.407683 0.913124i \(-0.633663\pi\)
−0.407683 + 0.913124i \(0.633663\pi\)
\(138\) −2.01960e39 −0.521797
\(139\) −2.82157e39 −0.637847 −0.318923 0.947780i \(-0.603321\pi\)
−0.318923 + 0.947780i \(0.603321\pi\)
\(140\) 1.80007e40 3.56387
\(141\) 4.60294e39 0.798880
\(142\) 4.31411e39 0.656987
\(143\) 4.72912e39 0.632505
\(144\) 6.25312e39 0.735175
\(145\) −1.01831e40 −1.05334
\(146\) −2.98222e40 −2.71651
\(147\) 6.63662e38 0.0532815
\(148\) −1.56570e40 −1.10883
\(149\) 1.60101e40 1.00103 0.500515 0.865728i \(-0.333144\pi\)
0.500515 + 0.865728i \(0.333144\pi\)
\(150\) 2.90090e40 1.60267
\(151\) 4.57788e39 0.223661 0.111831 0.993727i \(-0.464329\pi\)
0.111831 + 0.993727i \(0.464329\pi\)
\(152\) −1.03793e41 −4.48811
\(153\) −3.79340e39 −0.145290
\(154\) 3.21116e40 1.09026
\(155\) 4.62382e40 1.39272
\(156\) −5.15897e40 −1.37961
\(157\) 1.29011e40 0.306538 0.153269 0.988185i \(-0.451020\pi\)
0.153269 + 0.988185i \(0.451020\pi\)
\(158\) −1.65614e40 −0.349899
\(159\) 1.57967e40 0.296975
\(160\) 1.46975e41 2.46050
\(161\) 3.14932e40 0.469827
\(162\) −1.53068e40 −0.203637
\(163\) 2.27947e40 0.270622 0.135311 0.990803i \(-0.456797\pi\)
0.135311 + 0.990803i \(0.456797\pi\)
\(164\) 1.66821e41 1.76864
\(165\) 6.03372e40 0.571652
\(166\) −3.00024e41 −2.54189
\(167\) −1.07603e41 −0.815773 −0.407887 0.913033i \(-0.633734\pi\)
−0.407887 + 0.913033i \(0.633734\pi\)
\(168\) −2.01801e41 −1.36994
\(169\) 4.30125e39 0.0261632
\(170\) −2.32273e41 −1.26676
\(171\) 1.22767e41 0.600695
\(172\) 5.07400e41 2.22882
\(173\) 1.88646e40 0.0744379 0.0372189 0.999307i \(-0.488150\pi\)
0.0372189 + 0.999307i \(0.488150\pi\)
\(174\) 1.98168e41 0.702865
\(175\) −4.52360e41 −1.44305
\(176\) 4.79680e41 1.37711
\(177\) −2.56978e40 −0.0664339
\(178\) −1.22249e42 −2.84758
\(179\) 7.34863e41 1.54321 0.771605 0.636102i \(-0.219454\pi\)
0.771605 + 0.636102i \(0.219454\pi\)
\(180\) −6.58214e41 −1.24688
\(181\) −1.09361e42 −1.86986 −0.934932 0.354827i \(-0.884540\pi\)
−0.934932 + 0.354827i \(0.884540\pi\)
\(182\) 1.14552e42 1.76881
\(183\) 5.36428e41 0.748456
\(184\) 9.73601e41 1.22815
\(185\) 6.53236e41 0.745406
\(186\) −8.99820e41 −0.929322
\(187\) −2.90994e41 −0.272153
\(188\) −3.85188e42 −3.26402
\(189\) 2.38691e41 0.183355
\(190\) 7.51714e42 5.23734
\(191\) −7.94715e41 −0.502451 −0.251226 0.967929i \(-0.580834\pi\)
−0.251226 + 0.967929i \(0.580834\pi\)
\(192\) −6.41894e41 −0.368460
\(193\) −2.53002e42 −1.31921 −0.659604 0.751613i \(-0.729276\pi\)
−0.659604 + 0.751613i \(0.729276\pi\)
\(194\) 3.03680e42 1.43908
\(195\) 2.15241e42 0.927437
\(196\) −5.55373e41 −0.217694
\(197\) 1.05535e42 0.376507 0.188253 0.982121i \(-0.439717\pi\)
0.188253 + 0.982121i \(0.439717\pi\)
\(198\) −1.17419e42 −0.381446
\(199\) 3.73817e42 1.10631 0.553155 0.833078i \(-0.313424\pi\)
0.553155 + 0.833078i \(0.313424\pi\)
\(200\) −1.39845e43 −3.77219
\(201\) −1.36780e42 −0.336431
\(202\) −1.16433e43 −2.61262
\(203\) −3.09019e42 −0.632861
\(204\) 3.17443e42 0.593619
\(205\) −6.96003e42 −1.18895
\(206\) 1.60109e43 2.49960
\(207\) −1.15158e42 −0.164377
\(208\) 1.71116e43 2.23419
\(209\) 9.41754e42 1.12520
\(210\) 1.46153e43 1.59864
\(211\) −1.65439e43 −1.65735 −0.828673 0.559733i \(-0.810904\pi\)
−0.828673 + 0.559733i \(0.810904\pi\)
\(212\) −1.32192e43 −1.21336
\(213\) 2.45991e42 0.206965
\(214\) 2.89049e43 2.23006
\(215\) −2.11696e43 −1.49831
\(216\) 7.37904e42 0.479298
\(217\) 1.40316e43 0.836763
\(218\) 1.10085e43 0.602953
\(219\) −1.70047e43 −0.855760
\(220\) −5.04920e43 −2.33562
\(221\) −1.03806e43 −0.441536
\(222\) −1.27123e43 −0.497387
\(223\) −3.53484e42 −0.127271 −0.0636355 0.997973i \(-0.520269\pi\)
−0.0636355 + 0.997973i \(0.520269\pi\)
\(224\) 4.46016e43 1.47830
\(225\) 1.65410e43 0.504876
\(226\) 2.36327e43 0.664520
\(227\) 2.48280e43 0.643374 0.321687 0.946846i \(-0.395750\pi\)
0.321687 + 0.946846i \(0.395750\pi\)
\(228\) −1.02735e44 −2.45429
\(229\) 4.70012e43 1.03551 0.517753 0.855530i \(-0.326769\pi\)
0.517753 + 0.855530i \(0.326769\pi\)
\(230\) −7.05122e43 −1.43317
\(231\) 1.83101e43 0.343455
\(232\) −9.55320e43 −1.65433
\(233\) 8.79333e43 1.40627 0.703135 0.711056i \(-0.251783\pi\)
0.703135 + 0.711056i \(0.251783\pi\)
\(234\) −4.18870e43 −0.618851
\(235\) 1.60707e44 2.19422
\(236\) 2.15047e43 0.271432
\(237\) −9.44337e42 −0.110226
\(238\) −7.04863e43 −0.761082
\(239\) −1.13232e44 −1.13137 −0.565687 0.824620i \(-0.691389\pi\)
−0.565687 + 0.824620i \(0.691389\pi\)
\(240\) 2.18321e44 2.01924
\(241\) −1.33612e44 −1.14428 −0.572139 0.820157i \(-0.693886\pi\)
−0.572139 + 0.820157i \(0.693886\pi\)
\(242\) 1.40965e44 1.11822
\(243\) −8.72796e42 −0.0641500
\(244\) −4.48899e44 −3.05800
\(245\) 2.31711e43 0.146344
\(246\) 1.35446e44 0.793353
\(247\) 3.35952e44 1.82551
\(248\) 4.33782e44 2.18734
\(249\) −1.71075e44 −0.800751
\(250\) 3.44127e44 1.49564
\(251\) 9.12839e41 0.00368494 0.00184247 0.999998i \(-0.499414\pi\)
0.00184247 + 0.999998i \(0.499414\pi\)
\(252\) −1.99744e44 −0.749141
\(253\) −8.83383e43 −0.307907
\(254\) −2.86601e44 −0.928655
\(255\) −1.32443e44 −0.399056
\(256\) −4.77515e44 −1.33828
\(257\) −5.59665e44 −1.45937 −0.729685 0.683784i \(-0.760333\pi\)
−0.729685 + 0.683784i \(0.760333\pi\)
\(258\) 4.11971e44 0.999775
\(259\) 1.98233e44 0.447848
\(260\) −1.80120e45 −3.78927
\(261\) 1.12996e44 0.221418
\(262\) 7.82700e44 1.42896
\(263\) −5.30358e44 −0.902376 −0.451188 0.892429i \(-0.649000\pi\)
−0.451188 + 0.892429i \(0.649000\pi\)
\(264\) 5.66051e44 0.897807
\(265\) 5.51526e44 0.815675
\(266\) 2.28118e45 3.14665
\(267\) −6.97068e44 −0.897050
\(268\) 1.14462e45 1.37457
\(269\) −2.65460e44 −0.297565 −0.148783 0.988870i \(-0.547536\pi\)
−0.148783 + 0.988870i \(0.547536\pi\)
\(270\) −5.34421e44 −0.559311
\(271\) −5.19245e44 −0.507505 −0.253753 0.967269i \(-0.581665\pi\)
−0.253753 + 0.967269i \(0.581665\pi\)
\(272\) −1.05292e45 −0.961324
\(273\) 6.53177e44 0.557214
\(274\) 1.87429e45 1.49435
\(275\) 1.26887e45 0.945718
\(276\) 9.63677e44 0.671604
\(277\) −2.01890e45 −1.31595 −0.657975 0.753040i \(-0.728587\pi\)
−0.657975 + 0.753040i \(0.728587\pi\)
\(278\) 1.91710e45 1.16900
\(279\) −5.13079e44 −0.292757
\(280\) −7.04567e45 −3.76269
\(281\) 1.74726e45 0.873555 0.436778 0.899570i \(-0.356120\pi\)
0.436778 + 0.899570i \(0.356120\pi\)
\(282\) −3.12744e45 −1.46413
\(283\) 1.44699e45 0.634477 0.317238 0.948346i \(-0.397244\pi\)
0.317238 + 0.948346i \(0.397244\pi\)
\(284\) −2.05853e45 −0.845607
\(285\) 4.28629e45 1.64988
\(286\) −3.21318e45 −1.15921
\(287\) −2.11212e45 −0.714336
\(288\) −1.63090e45 −0.517209
\(289\) −2.72335e45 −0.810016
\(290\) 6.91882e45 1.93050
\(291\) 1.73159e45 0.453340
\(292\) 1.42300e46 3.49641
\(293\) −5.22491e45 −1.20511 −0.602557 0.798076i \(-0.705851\pi\)
−0.602557 + 0.798076i \(0.705851\pi\)
\(294\) −4.50921e44 −0.0976506
\(295\) −8.97211e44 −0.182468
\(296\) 6.12830e45 1.17069
\(297\) −6.69527e44 −0.120164
\(298\) −1.08779e46 −1.83462
\(299\) −3.15129e45 −0.499542
\(300\) −1.38420e46 −2.06279
\(301\) −6.42420e45 −0.900199
\(302\) −3.11041e45 −0.409911
\(303\) −6.63904e45 −0.823032
\(304\) 3.40760e46 3.97454
\(305\) 1.87288e46 2.05572
\(306\) 2.57740e45 0.266278
\(307\) 1.87097e46 1.81973 0.909865 0.414904i \(-0.136185\pi\)
0.909865 + 0.414904i \(0.136185\pi\)
\(308\) −1.53225e46 −1.40327
\(309\) 9.12943e45 0.787429
\(310\) −3.14163e46 −2.55249
\(311\) 6.28962e45 0.481457 0.240728 0.970593i \(-0.422614\pi\)
0.240728 + 0.970593i \(0.422614\pi\)
\(312\) 2.01927e46 1.45658
\(313\) −2.39735e46 −1.62990 −0.814950 0.579532i \(-0.803236\pi\)
−0.814950 + 0.579532i \(0.803236\pi\)
\(314\) −8.76559e45 −0.561801
\(315\) 8.33365e45 0.503605
\(316\) 7.90250e45 0.450354
\(317\) −2.60716e46 −1.40143 −0.700716 0.713440i \(-0.747136\pi\)
−0.700716 + 0.713440i \(0.747136\pi\)
\(318\) −1.07330e46 −0.544275
\(319\) 8.66797e45 0.414753
\(320\) −2.24111e46 −1.01202
\(321\) 1.64817e46 0.702518
\(322\) −2.13979e46 −0.861067
\(323\) −2.06719e46 −0.785477
\(324\) 7.30383e45 0.262100
\(325\) 4.52643e46 1.53431
\(326\) −1.54877e46 −0.495977
\(327\) 6.27707e45 0.189943
\(328\) −6.52953e46 −1.86731
\(329\) 4.87687e46 1.31831
\(330\) −4.09957e46 −1.04769
\(331\) −2.64270e46 −0.638601 −0.319300 0.947654i \(-0.603448\pi\)
−0.319300 + 0.947654i \(0.603448\pi\)
\(332\) 1.43160e47 3.27166
\(333\) −7.24858e45 −0.156688
\(334\) 7.31102e46 1.49509
\(335\) −4.77554e46 −0.924047
\(336\) 6.62525e46 1.21318
\(337\) 1.28332e46 0.222425 0.111212 0.993797i \(-0.464527\pi\)
0.111212 + 0.993797i \(0.464527\pi\)
\(338\) −2.92246e45 −0.0479501
\(339\) 1.34754e46 0.209338
\(340\) 1.10832e47 1.63044
\(341\) −3.93586e46 −0.548383
\(342\) −8.34134e46 −1.10091
\(343\) 8.32247e46 1.04066
\(344\) −1.98602e47 −2.35316
\(345\) −4.02062e46 −0.451481
\(346\) −1.28174e46 −0.136425
\(347\) −1.41659e47 −1.42938 −0.714692 0.699440i \(-0.753433\pi\)
−0.714692 + 0.699440i \(0.753433\pi\)
\(348\) −9.45583e46 −0.904656
\(349\) −1.75631e47 −1.59342 −0.796712 0.604359i \(-0.793429\pi\)
−0.796712 + 0.604359i \(0.793429\pi\)
\(350\) 3.07353e47 2.64472
\(351\) −2.38841e46 −0.194951
\(352\) −1.25107e47 −0.968820
\(353\) −1.54052e47 −1.13197 −0.565987 0.824414i \(-0.691505\pi\)
−0.565987 + 0.824414i \(0.691505\pi\)
\(354\) 1.74602e46 0.121756
\(355\) 8.58854e46 0.568453
\(356\) 5.83328e47 3.66512
\(357\) −4.01915e46 −0.239757
\(358\) −4.99298e47 −2.82829
\(359\) −1.07520e47 −0.578421 −0.289210 0.957266i \(-0.593393\pi\)
−0.289210 + 0.957266i \(0.593393\pi\)
\(360\) 2.57632e47 1.31645
\(361\) 4.63005e47 2.24751
\(362\) 7.43049e47 3.42696
\(363\) 8.03784e46 0.352263
\(364\) −5.46599e47 −2.27663
\(365\) −5.93700e47 −2.35044
\(366\) −3.64473e47 −1.37172
\(367\) 3.17956e47 1.13774 0.568872 0.822426i \(-0.307380\pi\)
0.568872 + 0.822426i \(0.307380\pi\)
\(368\) −3.19639e47 −1.08762
\(369\) 7.72315e46 0.249923
\(370\) −4.43837e47 −1.36613
\(371\) 1.67368e47 0.490066
\(372\) 4.29361e47 1.19613
\(373\) −1.78361e45 −0.00472811 −0.00236405 0.999997i \(-0.500753\pi\)
−0.00236405 + 0.999997i \(0.500753\pi\)
\(374\) 1.97714e47 0.498784
\(375\) 1.96222e47 0.471160
\(376\) 1.50767e48 3.44612
\(377\) 3.09212e47 0.672887
\(378\) −1.62177e47 −0.336040
\(379\) −1.48349e47 −0.292724 −0.146362 0.989231i \(-0.546756\pi\)
−0.146362 + 0.989231i \(0.546756\pi\)
\(380\) −3.58690e48 −6.74097
\(381\) −1.63421e47 −0.292547
\(382\) 5.39964e47 0.920858
\(383\) 1.02517e48 1.66579 0.832893 0.553434i \(-0.186683\pi\)
0.832893 + 0.553434i \(0.186683\pi\)
\(384\) −1.42437e47 −0.220544
\(385\) 6.39279e47 0.943338
\(386\) 1.71901e48 2.41775
\(387\) 2.34907e47 0.314951
\(388\) −1.44905e48 −1.85223
\(389\) −7.18903e47 −0.876198 −0.438099 0.898927i \(-0.644348\pi\)
−0.438099 + 0.898927i \(0.644348\pi\)
\(390\) −1.46244e48 −1.69974
\(391\) 1.93906e47 0.214942
\(392\) 2.17379e47 0.229839
\(393\) 4.46297e47 0.450155
\(394\) −7.17054e47 −0.690036
\(395\) −3.29706e47 −0.302747
\(396\) 5.60281e47 0.490959
\(397\) −1.97535e48 −1.65204 −0.826020 0.563641i \(-0.809400\pi\)
−0.826020 + 0.563641i \(0.809400\pi\)
\(398\) −2.53988e48 −2.02757
\(399\) 1.30073e48 0.991264
\(400\) 4.59121e48 3.34055
\(401\) −1.19337e48 −0.829093 −0.414547 0.910028i \(-0.636060\pi\)
−0.414547 + 0.910028i \(0.636060\pi\)
\(402\) 9.29346e47 0.616588
\(403\) −1.40404e48 −0.889685
\(404\) 5.55575e48 3.36270
\(405\) −3.04728e47 −0.176195
\(406\) 2.09961e48 1.15986
\(407\) −5.56043e47 −0.293503
\(408\) −1.24250e48 −0.626736
\(409\) 2.67926e48 1.29162 0.645808 0.763500i \(-0.276521\pi\)
0.645808 + 0.763500i \(0.276521\pi\)
\(410\) 4.72895e48 2.17903
\(411\) 1.06872e48 0.470751
\(412\) −7.63978e48 −3.21723
\(413\) −2.72271e47 −0.109629
\(414\) 7.82434e47 0.301260
\(415\) −5.97289e48 −2.19935
\(416\) −4.46295e48 −1.57179
\(417\) 1.09313e48 0.368261
\(418\) −6.39869e48 −2.06220
\(419\) 1.24117e48 0.382711 0.191356 0.981521i \(-0.438712\pi\)
0.191356 + 0.981521i \(0.438712\pi\)
\(420\) −6.97385e48 −2.05760
\(421\) 2.08519e48 0.588743 0.294372 0.955691i \(-0.404890\pi\)
0.294372 + 0.955691i \(0.404890\pi\)
\(422\) 1.12407e49 3.03747
\(423\) −1.78327e48 −0.461234
\(424\) 5.17412e48 1.28105
\(425\) −2.78522e48 −0.660182
\(426\) −1.67137e48 −0.379312
\(427\) 5.68351e48 1.23510
\(428\) −1.37924e49 −2.87031
\(429\) −1.83216e48 −0.365177
\(430\) 1.43836e49 2.74599
\(431\) 6.66174e48 1.21831 0.609155 0.793051i \(-0.291509\pi\)
0.609155 + 0.793051i \(0.291509\pi\)
\(432\) −2.42259e48 −0.424453
\(433\) −9.73853e47 −0.163481 −0.0817405 0.996654i \(-0.526048\pi\)
−0.0817405 + 0.996654i \(0.526048\pi\)
\(434\) −9.53370e48 −1.53356
\(435\) 3.94513e48 0.608149
\(436\) −5.25285e48 −0.776059
\(437\) −6.27546e48 −0.888667
\(438\) 1.15537e49 1.56838
\(439\) 6.18878e48 0.805400 0.402700 0.915332i \(-0.368072\pi\)
0.402700 + 0.915332i \(0.368072\pi\)
\(440\) 1.97631e49 2.46593
\(441\) −2.57116e47 −0.0307621
\(442\) 7.05305e48 0.809217
\(443\) −3.09041e48 −0.340054 −0.170027 0.985439i \(-0.554385\pi\)
−0.170027 + 0.985439i \(0.554385\pi\)
\(444\) 6.06584e48 0.640185
\(445\) −2.43374e49 −2.46385
\(446\) 2.40172e48 0.233253
\(447\) −6.20262e48 −0.577945
\(448\) −6.80094e48 −0.608031
\(449\) −6.87278e48 −0.589624 −0.294812 0.955555i \(-0.595257\pi\)
−0.294812 + 0.955555i \(0.595257\pi\)
\(450\) −1.12387e49 −0.925301
\(451\) 5.92448e48 0.468149
\(452\) −1.12767e49 −0.855302
\(453\) −1.77357e48 −0.129131
\(454\) −1.68692e49 −1.17913
\(455\) 2.28050e49 1.53045
\(456\) 4.02117e49 2.59121
\(457\) −5.99870e48 −0.371200 −0.185600 0.982625i \(-0.559423\pi\)
−0.185600 + 0.982625i \(0.559423\pi\)
\(458\) −3.19347e49 −1.89780
\(459\) 1.46964e48 0.0838834
\(460\) 3.36458e49 1.84464
\(461\) −2.03325e48 −0.107084 −0.0535420 0.998566i \(-0.517051\pi\)
−0.0535420 + 0.998566i \(0.517051\pi\)
\(462\) −1.24407e49 −0.629461
\(463\) 3.27311e49 1.59115 0.795577 0.605853i \(-0.207168\pi\)
0.795577 + 0.605853i \(0.207168\pi\)
\(464\) 3.13638e49 1.46503
\(465\) −1.79136e49 −0.804089
\(466\) −5.97457e49 −2.57731
\(467\) −1.94246e48 −0.0805358 −0.0402679 0.999189i \(-0.512821\pi\)
−0.0402679 + 0.999189i \(0.512821\pi\)
\(468\) 1.99869e49 0.796521
\(469\) −1.44920e49 −0.555177
\(470\) −1.09191e50 −4.02141
\(471\) −4.99816e48 −0.176980
\(472\) −8.41715e48 −0.286575
\(473\) 1.80198e49 0.589956
\(474\) 6.41624e48 0.202014
\(475\) 9.01390e49 2.72949
\(476\) 3.36334e49 0.979586
\(477\) −6.11997e48 −0.171458
\(478\) 7.69345e49 2.07351
\(479\) −1.26170e49 −0.327152 −0.163576 0.986531i \(-0.552303\pi\)
−0.163576 + 0.986531i \(0.552303\pi\)
\(480\) −5.69412e49 −1.42057
\(481\) −1.98357e49 −0.476172
\(482\) 9.07822e49 2.09715
\(483\) −1.22011e49 −0.271255
\(484\) −6.72631e49 −1.43926
\(485\) 6.04566e49 1.24515
\(486\) 5.93016e48 0.117570
\(487\) 6.52218e48 0.124482 0.0622410 0.998061i \(-0.480175\pi\)
0.0622410 + 0.998061i \(0.480175\pi\)
\(488\) 1.75704e50 3.22860
\(489\) −8.83112e48 −0.156244
\(490\) −1.57434e49 −0.268208
\(491\) −3.63594e49 −0.596498 −0.298249 0.954488i \(-0.596403\pi\)
−0.298249 + 0.954488i \(0.596403\pi\)
\(492\) −6.46297e49 −1.02112
\(493\) −1.90265e49 −0.289529
\(494\) −2.28261e50 −3.34566
\(495\) −2.33759e49 −0.330044
\(496\) −1.42413e50 −1.93705
\(497\) 2.60631e49 0.341533
\(498\) 1.16236e50 1.46756
\(499\) 7.84299e48 0.0954161 0.0477081 0.998861i \(-0.484808\pi\)
0.0477081 + 0.998861i \(0.484808\pi\)
\(500\) −1.64204e50 −1.92504
\(501\) 4.16876e49 0.470987
\(502\) −6.20223e47 −0.00675351
\(503\) 1.60037e50 1.67963 0.839814 0.542875i \(-0.182664\pi\)
0.839814 + 0.542875i \(0.182664\pi\)
\(504\) 7.81818e49 0.790935
\(505\) −2.31795e50 −2.26055
\(506\) 6.00209e49 0.564311
\(507\) −1.66639e48 −0.0151053
\(508\) 1.36755e50 1.19527
\(509\) −1.73622e50 −1.46327 −0.731635 0.681696i \(-0.761243\pi\)
−0.731635 + 0.681696i \(0.761243\pi\)
\(510\) 8.99873e49 0.731363
\(511\) −1.80166e50 −1.41217
\(512\) 2.73915e50 2.07072
\(513\) −4.75625e49 −0.346812
\(514\) 3.80261e50 2.67463
\(515\) 3.18745e50 2.16276
\(516\) −1.96577e50 −1.28681
\(517\) −1.36796e50 −0.863969
\(518\) −1.34688e50 −0.820785
\(519\) −7.30852e48 −0.0429767
\(520\) 7.05009e50 4.00067
\(521\) −3.53919e50 −1.93824 −0.969118 0.246598i \(-0.920687\pi\)
−0.969118 + 0.246598i \(0.920687\pi\)
\(522\) −7.67743e49 −0.405799
\(523\) −1.14063e50 −0.581921 −0.290961 0.956735i \(-0.593975\pi\)
−0.290961 + 0.956735i \(0.593975\pi\)
\(524\) −3.73475e50 −1.83922
\(525\) 1.75253e50 0.833143
\(526\) 3.60349e50 1.65381
\(527\) 8.63938e49 0.382813
\(528\) −1.85838e50 −0.795073
\(529\) −1.83199e50 −0.756820
\(530\) −3.74731e50 −1.49491
\(531\) 9.95584e48 0.0383556
\(532\) −1.08849e51 −4.05005
\(533\) 2.11344e50 0.759515
\(534\) 4.73619e50 1.64405
\(535\) 5.75440e50 1.92955
\(536\) −4.48016e50 −1.45126
\(537\) −2.84701e50 −0.890973
\(538\) 1.80365e50 0.545358
\(539\) −1.97235e49 −0.0576226
\(540\) 2.55006e50 0.719888
\(541\) 5.03224e50 1.37281 0.686407 0.727217i \(-0.259187\pi\)
0.686407 + 0.727217i \(0.259187\pi\)
\(542\) 3.52798e50 0.930121
\(543\) 4.23688e50 1.07957
\(544\) 2.74615e50 0.676309
\(545\) 2.19158e50 0.521701
\(546\) −4.43797e50 −1.02122
\(547\) −7.51701e50 −1.67217 −0.836083 0.548603i \(-0.815160\pi\)
−0.836083 + 0.548603i \(0.815160\pi\)
\(548\) −8.94340e50 −1.92337
\(549\) −2.07823e50 −0.432121
\(550\) −8.62125e50 −1.73325
\(551\) 6.15763e50 1.19704
\(552\) −3.77193e50 −0.709072
\(553\) −1.00054e50 −0.181894
\(554\) 1.37173e51 2.41178
\(555\) −2.53077e50 −0.430360
\(556\) −9.14767e50 −1.50462
\(557\) 4.20191e50 0.668537 0.334268 0.942478i \(-0.391511\pi\)
0.334268 + 0.942478i \(0.391511\pi\)
\(558\) 3.48609e50 0.536544
\(559\) 6.42822e50 0.957133
\(560\) 2.31314e51 3.33214
\(561\) 1.12737e50 0.157128
\(562\) −1.18716e51 −1.60099
\(563\) −8.89971e50 −1.16137 −0.580685 0.814128i \(-0.697215\pi\)
−0.580685 + 0.814128i \(0.697215\pi\)
\(564\) 1.49230e51 1.88448
\(565\) 4.70481e50 0.574971
\(566\) −9.83147e50 −1.16283
\(567\) −9.24738e49 −0.105860
\(568\) 8.05731e50 0.892782
\(569\) −1.72128e51 −1.84618 −0.923092 0.384579i \(-0.874347\pi\)
−0.923092 + 0.384579i \(0.874347\pi\)
\(570\) −2.91229e51 −3.02378
\(571\) 6.69419e50 0.672868 0.336434 0.941707i \(-0.390779\pi\)
0.336434 + 0.941707i \(0.390779\pi\)
\(572\) 1.53321e51 1.49202
\(573\) 3.07889e50 0.290090
\(574\) 1.43506e51 1.30919
\(575\) −8.45521e50 −0.746912
\(576\) 2.48683e50 0.212731
\(577\) 2.04906e51 1.69747 0.848737 0.528815i \(-0.177364\pi\)
0.848737 + 0.528815i \(0.177364\pi\)
\(578\) 1.85037e51 1.48454
\(579\) 9.80181e50 0.761645
\(580\) −3.30140e51 −2.48474
\(581\) −1.81255e51 −1.32139
\(582\) −1.17652e51 −0.830850
\(583\) −4.69466e50 −0.321171
\(584\) −5.56978e51 −3.69148
\(585\) −8.33887e50 −0.535456
\(586\) 3.55004e51 2.20865
\(587\) 1.81661e51 1.09511 0.547554 0.836770i \(-0.315559\pi\)
0.547554 + 0.836770i \(0.315559\pi\)
\(588\) 2.15163e50 0.125686
\(589\) −2.79600e51 −1.58272
\(590\) 6.09605e50 0.334415
\(591\) −4.08866e50 −0.217376
\(592\) −2.01196e51 −1.03674
\(593\) −4.63037e50 −0.231262 −0.115631 0.993292i \(-0.536889\pi\)
−0.115631 + 0.993292i \(0.536889\pi\)
\(594\) 4.54906e50 0.220228
\(595\) −1.40324e51 −0.658520
\(596\) 5.19055e51 2.36133
\(597\) −1.44824e51 −0.638729
\(598\) 2.14113e51 0.915526
\(599\) −5.00284e50 −0.207406 −0.103703 0.994608i \(-0.533069\pi\)
−0.103703 + 0.994608i \(0.533069\pi\)
\(600\) 5.41790e51 2.17787
\(601\) 3.80150e51 1.48176 0.740880 0.671638i \(-0.234409\pi\)
0.740880 + 0.671638i \(0.234409\pi\)
\(602\) 4.36488e51 1.64982
\(603\) 5.29915e50 0.194239
\(604\) 1.48417e51 0.527596
\(605\) 2.80633e51 0.967530
\(606\) 4.51086e51 1.50840
\(607\) 2.17471e51 0.705360 0.352680 0.935744i \(-0.385270\pi\)
0.352680 + 0.935744i \(0.385270\pi\)
\(608\) −8.88749e51 −2.79617
\(609\) 1.19720e51 0.365382
\(610\) −1.27252e52 −3.76758
\(611\) −4.87992e51 −1.40169
\(612\) −1.22984e51 −0.342726
\(613\) 1.29111e51 0.349095 0.174548 0.984649i \(-0.444154\pi\)
0.174548 + 0.984649i \(0.444154\pi\)
\(614\) −1.27122e52 −3.33508
\(615\) 2.69646e51 0.686443
\(616\) 5.99737e51 1.48156
\(617\) −4.63240e50 −0.111053 −0.0555265 0.998457i \(-0.517684\pi\)
−0.0555265 + 0.998457i \(0.517684\pi\)
\(618\) −6.20293e51 −1.44315
\(619\) 2.35900e51 0.532660 0.266330 0.963882i \(-0.414189\pi\)
0.266330 + 0.963882i \(0.414189\pi\)
\(620\) 1.49907e52 3.28530
\(621\) 4.46145e50 0.0949034
\(622\) −4.27344e51 −0.882381
\(623\) −7.38552e51 −1.48031
\(624\) −6.62940e51 −1.28991
\(625\) −1.16749e51 −0.220532
\(626\) 1.62886e52 2.98717
\(627\) −3.64855e51 −0.649637
\(628\) 4.18261e51 0.723093
\(629\) 1.22054e51 0.204887
\(630\) −5.66225e51 −0.922973
\(631\) −1.06497e52 −1.68576 −0.842880 0.538101i \(-0.819142\pi\)
−0.842880 + 0.538101i \(0.819142\pi\)
\(632\) −3.09312e51 −0.475479
\(633\) 6.40946e51 0.956869
\(634\) 1.77142e52 2.56845
\(635\) −5.70567e51 −0.803512
\(636\) 5.12137e51 0.700535
\(637\) −7.03598e50 −0.0934857
\(638\) −5.88940e51 −0.760131
\(639\) −9.53021e50 −0.119491
\(640\) −4.97304e51 −0.605749
\(641\) 1.54062e52 1.82314 0.911572 0.411141i \(-0.134870\pi\)
0.911572 + 0.411141i \(0.134870\pi\)
\(642\) −1.11984e52 −1.28753
\(643\) −1.17010e52 −1.30713 −0.653565 0.756871i \(-0.726727\pi\)
−0.653565 + 0.756871i \(0.726727\pi\)
\(644\) 1.02103e52 1.10828
\(645\) 8.20153e51 0.865048
\(646\) 1.40454e52 1.43957
\(647\) 5.61235e51 0.559005 0.279503 0.960145i \(-0.409830\pi\)
0.279503 + 0.960145i \(0.409830\pi\)
\(648\) −2.85879e51 −0.276723
\(649\) 7.63718e50 0.0718466
\(650\) −3.07546e52 −2.81198
\(651\) −5.43614e51 −0.483106
\(652\) 7.39015e51 0.638371
\(653\) −9.59702e51 −0.805828 −0.402914 0.915238i \(-0.632003\pi\)
−0.402914 + 0.915238i \(0.632003\pi\)
\(654\) −4.26492e51 −0.348115
\(655\) 1.55820e52 1.23640
\(656\) 2.14369e52 1.65364
\(657\) 6.58796e51 0.494073
\(658\) −3.31356e52 −2.41610
\(659\) 9.86794e51 0.699594 0.349797 0.936826i \(-0.386251\pi\)
0.349797 + 0.936826i \(0.386251\pi\)
\(660\) 1.95616e52 1.34847
\(661\) −3.94530e51 −0.264456 −0.132228 0.991219i \(-0.542213\pi\)
−0.132228 + 0.991219i \(0.542213\pi\)
\(662\) 1.79556e52 1.17038
\(663\) 4.02166e51 0.254921
\(664\) −5.60345e52 −3.45419
\(665\) 4.54137e52 2.72262
\(666\) 4.92501e51 0.287166
\(667\) −5.77598e51 −0.327565
\(668\) −3.48854e52 −1.92433
\(669\) 1.36947e51 0.0734799
\(670\) 3.24472e52 1.69353
\(671\) −1.59422e52 −0.809436
\(672\) −1.72796e52 −0.853495
\(673\) −1.19487e52 −0.574172 −0.287086 0.957905i \(-0.592687\pi\)
−0.287086 + 0.957905i \(0.592687\pi\)
\(674\) −8.71947e51 −0.407645
\(675\) −6.40831e51 −0.291490
\(676\) 1.39449e51 0.0617164
\(677\) −1.67874e52 −0.722924 −0.361462 0.932387i \(-0.617722\pi\)
−0.361462 + 0.932387i \(0.617722\pi\)
\(678\) −9.15581e51 −0.383661
\(679\) 1.83464e52 0.748099
\(680\) −4.33808e52 −1.72140
\(681\) −9.61888e51 −0.371452
\(682\) 2.67420e52 1.00504
\(683\) −1.07263e52 −0.392345 −0.196172 0.980569i \(-0.562851\pi\)
−0.196172 + 0.980569i \(0.562851\pi\)
\(684\) 3.98018e52 1.41698
\(685\) 3.73134e52 1.29297
\(686\) −5.65465e52 −1.90726
\(687\) −1.82092e52 −0.597849
\(688\) 6.52022e52 2.08390
\(689\) −1.67473e52 −0.521061
\(690\) 2.73179e52 0.827444
\(691\) 1.11109e51 0.0327648 0.0163824 0.999866i \(-0.494785\pi\)
0.0163824 + 0.999866i \(0.494785\pi\)
\(692\) 6.11599e51 0.175592
\(693\) −7.09372e51 −0.198294
\(694\) 9.62493e52 2.61968
\(695\) 3.81656e52 1.01147
\(696\) 3.70111e52 0.955126
\(697\) −1.30045e52 −0.326803
\(698\) 1.19332e53 2.92032
\(699\) −3.40671e52 −0.811910
\(700\) −1.46657e53 −3.40401
\(701\) −3.38745e52 −0.765755 −0.382877 0.923799i \(-0.625067\pi\)
−0.382877 + 0.923799i \(0.625067\pi\)
\(702\) 1.62279e52 0.357294
\(703\) −3.95007e52 −0.847094
\(704\) 1.90766e52 0.398480
\(705\) −6.22612e52 −1.26683
\(706\) 1.04670e53 2.07460
\(707\) −7.03414e52 −1.35816
\(708\) −8.33135e51 −0.156711
\(709\) −1.72294e52 −0.315729 −0.157865 0.987461i \(-0.550461\pi\)
−0.157865 + 0.987461i \(0.550461\pi\)
\(710\) −5.83543e52 −1.04182
\(711\) 3.65856e51 0.0636388
\(712\) −2.28321e53 −3.86959
\(713\) 2.62270e52 0.433104
\(714\) 2.73079e52 0.439411
\(715\) −6.39680e52 −1.00300
\(716\) 2.38246e53 3.64029
\(717\) 4.38682e52 0.653199
\(718\) 7.30542e52 1.06009
\(719\) 6.83545e52 0.966680 0.483340 0.875433i \(-0.339423\pi\)
0.483340 + 0.875433i \(0.339423\pi\)
\(720\) −8.45821e52 −1.16581
\(721\) 9.67273e52 1.29941
\(722\) −3.14586e53 −4.11909
\(723\) 5.17642e52 0.660649
\(724\) −3.54555e53 −4.41083
\(725\) 8.29646e52 1.00610
\(726\) −5.46126e52 −0.645603
\(727\) −1.43130e52 −0.164947 −0.0824736 0.996593i \(-0.526282\pi\)
−0.0824736 + 0.996593i \(0.526282\pi\)
\(728\) 2.13944e53 2.40364
\(729\) 3.38139e51 0.0370370
\(730\) 4.03386e53 4.30773
\(731\) −3.95543e52 −0.411834
\(732\) 1.73913e53 1.76554
\(733\) 1.21007e53 1.19781 0.598904 0.800821i \(-0.295603\pi\)
0.598904 + 0.800821i \(0.295603\pi\)
\(734\) −2.16033e53 −2.08518
\(735\) −8.97695e51 −0.0844915
\(736\) 8.33663e52 0.765158
\(737\) 4.06501e52 0.363842
\(738\) −5.24745e52 −0.458042
\(739\) −1.58257e52 −0.134723 −0.0673613 0.997729i \(-0.521458\pi\)
−0.0673613 + 0.997729i \(0.521458\pi\)
\(740\) 2.11782e53 1.75834
\(741\) −1.30155e53 −1.05396
\(742\) −1.13717e53 −0.898159
\(743\) 1.09014e53 0.839823 0.419911 0.907565i \(-0.362061\pi\)
0.419911 + 0.907565i \(0.362061\pi\)
\(744\) −1.68056e53 −1.26286
\(745\) −2.16558e53 −1.58739
\(746\) 1.21187e51 0.00866536
\(747\) 6.62778e52 0.462314
\(748\) −9.43417e52 −0.641984
\(749\) 1.74625e53 1.15929
\(750\) −1.33322e53 −0.863510
\(751\) 6.11841e52 0.386634 0.193317 0.981136i \(-0.438075\pi\)
0.193317 + 0.981136i \(0.438075\pi\)
\(752\) −4.94976e53 −3.05179
\(753\) −3.53653e50 −0.00212750
\(754\) −2.10093e53 −1.23322
\(755\) −6.19222e52 −0.354673
\(756\) 7.73849e52 0.432517
\(757\) 1.99961e53 1.09062 0.545308 0.838236i \(-0.316413\pi\)
0.545308 + 0.838236i \(0.316413\pi\)
\(758\) 1.00795e53 0.536485
\(759\) 3.42241e52 0.177770
\(760\) 1.40395e54 7.11705
\(761\) −1.62121e53 −0.802092 −0.401046 0.916058i \(-0.631353\pi\)
−0.401046 + 0.916058i \(0.631353\pi\)
\(762\) 1.11035e53 0.536159
\(763\) 6.65063e52 0.313443
\(764\) −2.57651e53 −1.18523
\(765\) 5.13110e52 0.230395
\(766\) −6.96547e53 −3.05294
\(767\) 2.72441e52 0.116562
\(768\) 1.84999e53 0.772658
\(769\) −3.14345e53 −1.28165 −0.640825 0.767687i \(-0.721408\pi\)
−0.640825 + 0.767687i \(0.721408\pi\)
\(770\) −4.34354e53 −1.72888
\(771\) 2.16826e53 0.842567
\(772\) −8.20245e53 −3.11188
\(773\) −2.85720e53 −1.05833 −0.529164 0.848520i \(-0.677494\pi\)
−0.529164 + 0.848520i \(0.677494\pi\)
\(774\) −1.59606e53 −0.577220
\(775\) −3.76717e53 −1.33025
\(776\) 5.67171e53 1.95557
\(777\) −7.67996e52 −0.258565
\(778\) 4.88454e53 1.60584
\(779\) 4.20869e53 1.35115
\(780\) 6.97822e53 2.18773
\(781\) −7.31068e52 −0.223828
\(782\) −1.31748e53 −0.393931
\(783\) −4.37768e52 −0.127836
\(784\) −7.13667e52 −0.203539
\(785\) −1.74506e53 −0.486095
\(786\) −3.03234e53 −0.825013
\(787\) 3.70794e53 0.985371 0.492685 0.870207i \(-0.336015\pi\)
0.492685 + 0.870207i \(0.336015\pi\)
\(788\) 3.42151e53 0.888143
\(789\) 2.05472e53 0.520987
\(790\) 2.24017e53 0.554854
\(791\) 1.42774e53 0.345449
\(792\) −2.19300e53 −0.518349
\(793\) −5.68708e53 −1.31321
\(794\) 1.34214e54 3.02775
\(795\) −2.13672e53 −0.470930
\(796\) 1.21193e54 2.60968
\(797\) −7.44870e53 −1.56712 −0.783558 0.621318i \(-0.786597\pi\)
−0.783558 + 0.621318i \(0.786597\pi\)
\(798\) −8.83775e53 −1.81672
\(799\) 3.00273e53 0.603115
\(800\) −1.19745e54 −2.35014
\(801\) 2.70058e53 0.517912
\(802\) 8.10827e53 1.51951
\(803\) 5.05366e53 0.925483
\(804\) −4.43449e53 −0.793609
\(805\) −4.25989e53 −0.745032
\(806\) 9.53967e53 1.63055
\(807\) 1.02845e53 0.171799
\(808\) −2.17458e54 −3.55030
\(809\) −1.60117e53 −0.255499 −0.127749 0.991806i \(-0.540775\pi\)
−0.127749 + 0.991806i \(0.540775\pi\)
\(810\) 2.07046e53 0.322919
\(811\) 1.93099e53 0.294371 0.147185 0.989109i \(-0.452979\pi\)
0.147185 + 0.989109i \(0.452979\pi\)
\(812\) −1.00186e54 −1.49286
\(813\) 2.01166e53 0.293008
\(814\) 3.77800e53 0.537911
\(815\) −3.08330e53 −0.429141
\(816\) 4.07922e53 0.555021
\(817\) 1.28011e54 1.70271
\(818\) −1.82041e54 −2.36719
\(819\) −2.53054e53 −0.321708
\(820\) −2.25648e54 −2.80463
\(821\) −6.63036e53 −0.805728 −0.402864 0.915260i \(-0.631985\pi\)
−0.402864 + 0.915260i \(0.631985\pi\)
\(822\) −7.26138e53 −0.862761
\(823\) 7.44114e53 0.864455 0.432227 0.901765i \(-0.357728\pi\)
0.432227 + 0.901765i \(0.357728\pi\)
\(824\) 2.99029e54 3.39672
\(825\) −4.91585e53 −0.546010
\(826\) 1.84993e53 0.200920
\(827\) −9.00288e53 −0.956158 −0.478079 0.878317i \(-0.658667\pi\)
−0.478079 + 0.878317i \(0.658667\pi\)
\(828\) −3.73348e53 −0.387751
\(829\) −3.70753e53 −0.376553 −0.188276 0.982116i \(-0.560290\pi\)
−0.188276 + 0.982116i \(0.560290\pi\)
\(830\) 4.05825e54 4.03082
\(831\) 7.82164e53 0.759764
\(832\) 6.80520e53 0.646486
\(833\) 4.32940e52 0.0402249
\(834\) −7.42722e53 −0.674924
\(835\) 1.45548e54 1.29362
\(836\) 3.05322e54 2.65425
\(837\) 1.98778e53 0.169023
\(838\) −8.43304e53 −0.701407
\(839\) −1.89366e54 −1.54066 −0.770329 0.637646i \(-0.779908\pi\)
−0.770329 + 0.637646i \(0.779908\pi\)
\(840\) 2.72964e54 2.17239
\(841\) −7.17723e53 −0.558767
\(842\) −1.41677e54 −1.07901
\(843\) −6.76924e53 −0.504347
\(844\) −5.36363e54 −3.90952
\(845\) −5.81804e52 −0.0414885
\(846\) 1.21163e54 0.845318
\(847\) 8.51619e53 0.581302
\(848\) −1.69869e54 −1.13447
\(849\) −5.60593e53 −0.366315
\(850\) 1.89240e54 1.20994
\(851\) 3.70524e53 0.231803
\(852\) 7.97517e53 0.488211
\(853\) 1.21911e52 0.00730272 0.00365136 0.999993i \(-0.498838\pi\)
0.00365136 + 0.999993i \(0.498838\pi\)
\(854\) −3.86163e54 −2.26360
\(855\) −1.66060e54 −0.952557
\(856\) 5.39847e54 3.03044
\(857\) 1.82750e54 1.00395 0.501975 0.864882i \(-0.332607\pi\)
0.501975 + 0.864882i \(0.332607\pi\)
\(858\) 1.24485e54 0.669271
\(859\) 5.92142e53 0.311568 0.155784 0.987791i \(-0.450210\pi\)
0.155784 + 0.987791i \(0.450210\pi\)
\(860\) −6.86329e54 −3.53436
\(861\) 8.18277e53 0.412422
\(862\) −4.52628e54 −2.23284
\(863\) 2.34693e53 0.113318 0.0566592 0.998394i \(-0.481955\pi\)
0.0566592 + 0.998394i \(0.481955\pi\)
\(864\) 6.31844e53 0.298611
\(865\) −2.55170e53 −0.118040
\(866\) 6.61679e53 0.299617
\(867\) 1.05508e54 0.467663
\(868\) 4.54912e54 1.97384
\(869\) 2.80650e53 0.119206
\(870\) −2.68049e54 −1.11457
\(871\) 1.45011e54 0.590290
\(872\) 2.05602e54 0.819355
\(873\) −6.70852e53 −0.261736
\(874\) 4.26382e54 1.62869
\(875\) 2.07899e54 0.777506
\(876\) −5.51300e54 −2.01866
\(877\) −7.93050e53 −0.284320 −0.142160 0.989844i \(-0.545405\pi\)
−0.142160 + 0.989844i \(0.545405\pi\)
\(878\) −4.20493e54 −1.47608
\(879\) 2.02424e54 0.695773
\(880\) −6.48834e54 −2.18376
\(881\) 2.56353e54 0.844859 0.422429 0.906396i \(-0.361177\pi\)
0.422429 + 0.906396i \(0.361177\pi\)
\(882\) 1.74696e53 0.0563786
\(883\) 2.54626e54 0.804691 0.402346 0.915488i \(-0.368195\pi\)
0.402346 + 0.915488i \(0.368195\pi\)
\(884\) −3.36545e54 −1.04154
\(885\) 3.47598e53 0.105348
\(886\) 2.09976e54 0.623227
\(887\) 2.32098e54 0.674660 0.337330 0.941386i \(-0.390476\pi\)
0.337330 + 0.941386i \(0.390476\pi\)
\(888\) −2.37423e54 −0.675901
\(889\) −1.73146e54 −0.482759
\(890\) 1.65359e55 4.51557
\(891\) 2.59389e53 0.0693767
\(892\) −1.14601e54 −0.300220
\(893\) −9.71784e54 −2.49355
\(894\) 4.21434e54 1.05922
\(895\) −9.94004e54 −2.44716
\(896\) −1.50914e54 −0.363941
\(897\) 1.22088e54 0.288411
\(898\) 4.66967e54 1.08062
\(899\) −2.57345e54 −0.583394
\(900\) 5.36267e54 1.19095
\(901\) 1.03050e54 0.224201
\(902\) −4.02535e54 −0.857991
\(903\) 2.48886e54 0.519730
\(904\) 4.41380e54 0.903019
\(905\) 1.47926e55 2.96515
\(906\) 1.20504e54 0.236662
\(907\) −8.85168e54 −1.70330 −0.851649 0.524112i \(-0.824397\pi\)
−0.851649 + 0.524112i \(0.824397\pi\)
\(908\) 8.04937e54 1.51766
\(909\) 2.57210e54 0.475178
\(910\) −1.54947e55 −2.80491
\(911\) −3.42424e54 −0.607399 −0.303699 0.952768i \(-0.598222\pi\)
−0.303699 + 0.952768i \(0.598222\pi\)
\(912\) −1.32017e55 −2.29470
\(913\) 5.08421e54 0.865992
\(914\) 4.07578e54 0.680309
\(915\) −7.25593e54 −1.18687
\(916\) 1.52380e55 2.44266
\(917\) 4.72857e54 0.742843
\(918\) −9.98538e53 −0.153736
\(919\) −8.49570e54 −1.28192 −0.640962 0.767573i \(-0.721464\pi\)
−0.640962 + 0.767573i \(0.721464\pi\)
\(920\) −1.31693e55 −1.94755
\(921\) −7.24852e54 −1.05062
\(922\) 1.38148e54 0.196256
\(923\) −2.60794e54 −0.363133
\(924\) 5.93624e54 0.810177
\(925\) −5.32211e54 −0.711970
\(926\) −2.22389e55 −2.91616
\(927\) −3.53693e54 −0.454623
\(928\) −8.18010e54 −1.03067
\(929\) −5.60014e54 −0.691685 −0.345843 0.938293i \(-0.612407\pi\)
−0.345843 + 0.938293i \(0.612407\pi\)
\(930\) 1.21713e55 1.47368
\(931\) −1.40114e54 −0.166308
\(932\) 2.85084e55 3.31726
\(933\) −2.43673e54 −0.277969
\(934\) 1.31979e54 0.147601
\(935\) 3.93609e54 0.431569
\(936\) −7.82308e54 −0.840958
\(937\) 9.79573e54 1.03242 0.516208 0.856463i \(-0.327343\pi\)
0.516208 + 0.856463i \(0.327343\pi\)
\(938\) 9.84652e54 1.01749
\(939\) 9.28782e54 0.941023
\(940\) 5.21020e55 5.17594
\(941\) 1.66648e54 0.162328 0.0811638 0.996701i \(-0.474136\pi\)
0.0811638 + 0.996701i \(0.474136\pi\)
\(942\) 3.39597e54 0.324356
\(943\) −3.94783e54 −0.369736
\(944\) 2.76340e54 0.253783
\(945\) −3.22863e54 −0.290756
\(946\) −1.22435e55 −1.08123
\(947\) 1.77183e54 0.153443 0.0767216 0.997053i \(-0.475555\pi\)
0.0767216 + 0.997053i \(0.475555\pi\)
\(948\) −3.06159e54 −0.260012
\(949\) 1.80279e55 1.50148
\(950\) −6.12444e55 −5.00242
\(951\) 1.01007e55 0.809117
\(952\) −1.31645e55 −1.03424
\(953\) −7.66663e54 −0.590726 −0.295363 0.955385i \(-0.595441\pi\)
−0.295363 + 0.955385i \(0.595441\pi\)
\(954\) 4.15817e54 0.314237
\(955\) 1.07496e55 0.796766
\(956\) −3.67103e55 −2.66880
\(957\) −3.35815e54 −0.239458
\(958\) 8.57254e54 0.599581
\(959\) 1.13232e55 0.776831
\(960\) 8.68250e54 0.584288
\(961\) −3.46368e54 −0.228641
\(962\) 1.34773e55 0.872696
\(963\) −6.38533e54 −0.405599
\(964\) −4.33179e55 −2.69924
\(965\) 3.42220e55 2.09194
\(966\) 8.28997e54 0.497137
\(967\) −1.08091e55 −0.635915 −0.317957 0.948105i \(-0.602997\pi\)
−0.317957 + 0.948105i \(0.602997\pi\)
\(968\) 2.63275e55 1.51955
\(969\) 8.00871e54 0.453495
\(970\) −4.10769e55 −2.28202
\(971\) 1.69341e55 0.923011 0.461505 0.887137i \(-0.347310\pi\)
0.461505 + 0.887137i \(0.347310\pi\)
\(972\) −2.82965e54 −0.151324
\(973\) 1.15819e55 0.607702
\(974\) −4.43145e54 −0.228142
\(975\) −1.75363e55 −0.885836
\(976\) −5.76846e55 −2.85916
\(977\) −1.54539e55 −0.751603 −0.375802 0.926700i \(-0.622633\pi\)
−0.375802 + 0.926700i \(0.622633\pi\)
\(978\) 6.00026e54 0.286352
\(979\) 2.07163e55 0.970138
\(980\) 7.51218e54 0.345210
\(981\) −2.43187e54 −0.109664
\(982\) 2.47042e55 1.09322
\(983\) −1.30842e55 −0.568209 −0.284104 0.958793i \(-0.591696\pi\)
−0.284104 + 0.958793i \(0.591696\pi\)
\(984\) 2.52967e55 1.07809
\(985\) −1.42751e55 −0.597048
\(986\) 1.29275e55 0.530629
\(987\) −1.88940e55 −0.761126
\(988\) 1.08917e56 4.30620
\(989\) −1.20077e55 −0.465938
\(990\) 1.58826e55 0.604881
\(991\) −1.06749e55 −0.399025 −0.199512 0.979895i \(-0.563936\pi\)
−0.199512 + 0.979895i \(0.563936\pi\)
\(992\) 3.71434e55 1.36275
\(993\) 1.02384e55 0.368696
\(994\) −1.77084e55 −0.625938
\(995\) −5.05639e55 −1.75434
\(996\) −5.54633e55 −1.88889
\(997\) 1.93192e55 0.645846 0.322923 0.946425i \(-0.395335\pi\)
0.322923 + 0.946425i \(0.395335\pi\)
\(998\) −5.32887e54 −0.174872
\(999\) 2.80825e54 0.0904637
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 \(a_p\))