Properties

Label 3.38.a.a.1.3
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 1.3
Root \(-51708.0\)
Character \(\chi\) = 3.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+516864. q^{2}\) \(-3.87420e8 q^{3}\) \(+1.29709e11 q^{4}\) \(+3.13693e12 q^{5}\) \(-2.00244e14 q^{6}\) \(-3.10972e15 q^{7}\) \(-3.99525e15 q^{8}\) \(+1.50095e17 q^{9}\) \(+O(q^{10})\) \(q\)\(+516864. q^{2}\) \(-3.87420e8 q^{3}\) \(+1.29709e11 q^{4}\) \(+3.13693e12 q^{5}\) \(-2.00244e14 q^{6}\) \(-3.10972e15 q^{7}\) \(-3.99525e15 q^{8}\) \(+1.50095e17 q^{9}\) \(+1.62136e18 q^{10}\) \(+7.50440e18 q^{11}\) \(-5.02520e19 q^{12}\) \(-6.39538e20 q^{13}\) \(-1.60730e21 q^{14}\) \(-1.21531e21 q^{15}\) \(-1.98921e22 q^{16}\) \(-5.44751e22 q^{17}\) \(+7.75785e22 q^{18}\) \(+2.22938e23 q^{19}\) \(+4.06888e23 q^{20}\) \(+1.20477e24 q^{21}\) \(+3.87875e24 q^{22}\) \(-1.64570e25 q^{23}\) \(+1.54784e24 q^{24}\) \(-6.29193e25 q^{25}\) \(-3.30554e26 q^{26}\) \(-5.81497e25 q^{27}\) \(-4.03359e26 q^{28}\) \(+1.49927e27 q^{29}\) \(-6.28150e26 q^{30}\) \(-4.99985e27 q^{31}\) \(-9.73240e27 q^{32}\) \(-2.90736e27 q^{33}\) \(-2.81562e28 q^{34}\) \(-9.75497e27 q^{35}\) \(+1.94686e28 q^{36}\) \(+4.47694e28 q^{37}\) \(+1.15228e29 q^{38}\) \(+2.47770e29 q^{39}\) \(-1.25328e28 q^{40}\) \(+1.03254e30 q^{41}\) \(+6.22702e29 q^{42}\) \(-2.18835e30 q^{43}\) \(+9.73390e29 q^{44}\) \(+4.70836e29 q^{45}\) \(-8.50601e30 q^{46}\) \(+1.06681e31 q^{47}\) \(+7.70660e30 q^{48}\) \(-8.89176e30 q^{49}\) \(-3.25207e31 q^{50}\) \(+2.11048e31 q^{51}\) \(-8.29539e31 q^{52}\) \(-2.17162e31 q^{53}\) \(-3.00555e31 q^{54}\) \(+2.35408e31 q^{55}\) \(+1.24241e31 q^{56}\) \(-8.63707e31 q^{57}\) \(+7.74917e32 q^{58}\) \(+9.25373e32 q^{59}\) \(-1.57637e32 q^{60}\) \(+1.78286e33 q^{61}\) \(-2.58424e33 q^{62}\) \(-4.66752e32 q^{63}\) \(-2.29638e33 q^{64}\) \(-2.00618e33 q^{65}\) \(-1.50271e33 q^{66}\) \(+5.16951e33 q^{67}\) \(-7.06592e33 q^{68}\) \(+6.37577e33 q^{69}\) \(-5.04199e33 q^{70}\) \(+3.92232e33 q^{71}\) \(-5.99665e32 q^{72}\) \(-3.83796e34 q^{73}\) \(+2.31397e34 q^{74}\) \(+2.43762e34 q^{75}\) \(+2.89171e34 q^{76}\) \(-2.33366e34 q^{77}\) \(+1.28063e35 q^{78}\) \(-5.14706e34 q^{79}\) \(-6.24001e34 q^{80}\) \(+2.25284e34 q^{81}\) \(+5.33684e35 q^{82}\) \(-2.76468e35 q^{83}\) \(+1.56270e35 q^{84}\) \(-1.70885e35 q^{85}\) \(-1.13108e36 q^{86}\) \(-5.80847e35 q^{87}\) \(-2.99820e34 q^{88}\) \(-1.38448e36 q^{89}\) \(+2.43358e35 q^{90}\) \(+1.98878e36 q^{91}\) \(-2.13462e36 q^{92}\) \(+1.93704e36 q^{93}\) \(+5.51395e36 q^{94}\) \(+6.99340e35 q^{95}\) \(+3.77053e36 q^{96}\) \(+1.68983e36 q^{97}\) \(-4.59583e36 q^{98}\) \(+1.12637e36 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut -\mathstrut 310908q^{2} \) \(\mathstrut -\mathstrut 1162261467q^{3} \) \(\mathstrut +\mathstrut 338476600848q^{4} \) \(\mathstrut -\mathstrut 9628717886790q^{5} \) \(\mathstrut +\mathstrut 120452129394012q^{6} \) \(\mathstrut -\mathstrut 4621884343701744q^{7} \) \(\mathstrut -\mathstrut 93383909093911488q^{8} \) \(\mathstrut +\mathstrut 450283905890997363q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 310908q^{2} \) \(\mathstrut -\mathstrut 1162261467q^{3} \) \(\mathstrut +\mathstrut 338476600848q^{4} \) \(\mathstrut -\mathstrut 9628717886790q^{5} \) \(\mathstrut +\mathstrut 120452129394012q^{6} \) \(\mathstrut -\mathstrut 4621884343701744q^{7} \) \(\mathstrut -\mathstrut 93383909093911488q^{8} \) \(\mathstrut +\mathstrut 450283905890997363q^{9} \) \(\mathstrut +\mathstrut 10698950136741797880q^{10} \) \(\mathstrut +\mathstrut 22673303357139628620q^{11} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!72\)\(q^{12} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!10\)\(q^{13} \) \(\mathstrut +\mathstrut \)\(79\!\cdots\!28\)\(q^{14} \) \(\mathstrut +\mathstrut \)\(37\!\cdots\!10\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!56\)\(q^{16} \) \(\mathstrut -\mathstrut \)\(27\!\cdots\!06\)\(q^{17} \) \(\mathstrut -\mathstrut \)\(46\!\cdots\!68\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(58\!\cdots\!04\)\(q^{19} \) \(\mathstrut -\mathstrut \)\(40\!\cdots\!80\)\(q^{20} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!16\)\(q^{21} \) \(\mathstrut -\mathstrut \)\(44\!\cdots\!52\)\(q^{22} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!72\)\(q^{23} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!32\)\(q^{24} \) \(\mathstrut -\mathstrut \)\(24\!\cdots\!75\)\(q^{25} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!44\)\(q^{26} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!07\)\(q^{27} \) \(\mathstrut -\mathstrut \)\(20\!\cdots\!88\)\(q^{28} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!78\)\(q^{29} \) \(\mathstrut -\mathstrut \)\(41\!\cdots\!20\)\(q^{30} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!36\)\(q^{31} \) \(\mathstrut -\mathstrut \)\(27\!\cdots\!84\)\(q^{32} \) \(\mathstrut -\mathstrut \)\(87\!\cdots\!80\)\(q^{33} \) \(\mathstrut -\mathstrut \)\(18\!\cdots\!64\)\(q^{34} \) \(\mathstrut +\mathstrut \)\(47\!\cdots\!80\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!08\)\(q^{36} \) \(\mathstrut +\mathstrut \)\(60\!\cdots\!66\)\(q^{37} \) \(\mathstrut -\mathstrut \)\(37\!\cdots\!76\)\(q^{38} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!90\)\(q^{39} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!00\)\(q^{40} \) \(\mathstrut +\mathstrut \)\(20\!\cdots\!34\)\(q^{41} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!92\)\(q^{42} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!44\)\(q^{43} \) \(\mathstrut +\mathstrut \)\(42\!\cdots\!72\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!90\)\(q^{45} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!56\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!32\)\(q^{47} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!84\)\(q^{48} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!73\)\(q^{49} \) \(\mathstrut -\mathstrut \)\(96\!\cdots\!00\)\(q^{50} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!34\)\(q^{51} \) \(\mathstrut +\mathstrut \)\(43\!\cdots\!84\)\(q^{52} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!82\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(18\!\cdots\!52\)\(q^{54} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!80\)\(q^{55} \) \(\mathstrut +\mathstrut \)\(63\!\cdots\!60\)\(q^{56} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!56\)\(q^{57} \) \(\mathstrut +\mathstrut \)\(58\!\cdots\!88\)\(q^{58} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!36\)\(q^{59} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!20\)\(q^{60} \) \(\mathstrut +\mathstrut \)\(29\!\cdots\!02\)\(q^{61} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!92\)\(q^{62} \) \(\mathstrut -\mathstrut \)\(69\!\cdots\!24\)\(q^{63} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!24\)\(q^{64} \) \(\mathstrut -\mathstrut \)\(75\!\cdots\!60\)\(q^{65} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!28\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(38\!\cdots\!44\)\(q^{67} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!16\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!08\)\(q^{69} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!60\)\(q^{70} \) \(\mathstrut -\mathstrut \)\(22\!\cdots\!44\)\(q^{71} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!48\)\(q^{72} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!78\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(46\!\cdots\!28\)\(q^{74} \) \(\mathstrut +\mathstrut \)\(96\!\cdots\!75\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(34\!\cdots\!16\)\(q^{76} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!68\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(23\!\cdots\!16\)\(q^{78} \) \(\mathstrut +\mathstrut \)\(74\!\cdots\!40\)\(q^{79} \) \(\mathstrut -\mathstrut \)\(61\!\cdots\!40\)\(q^{80} \) \(\mathstrut +\mathstrut \)\(67\!\cdots\!23\)\(q^{81} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!12\)\(q^{82} \) \(\mathstrut -\mathstrut \)\(31\!\cdots\!04\)\(q^{83} \) \(\mathstrut +\mathstrut \)\(78\!\cdots\!32\)\(q^{84} \) \(\mathstrut +\mathstrut \)\(21\!\cdots\!80\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(26\!\cdots\!60\)\(q^{86} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!42\)\(q^{87} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!28\)\(q^{88} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!26\)\(q^{89} \) \(\mathstrut +\mathstrut \)\(16\!\cdots\!80\)\(q^{90} \) \(\mathstrut +\mathstrut \)\(45\!\cdots\!04\)\(q^{91} \) \(\mathstrut -\mathstrut \)\(54\!\cdots\!24\)\(q^{92} \) \(\mathstrut +\mathstrut \)\(45\!\cdots\!04\)\(q^{93} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!00\)\(q^{94} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!00\)\(q^{95} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!76\)\(q^{96} \) \(\mathstrut +\mathstrut \)\(26\!\cdots\!14\)\(q^{97} \) \(\mathstrut -\mathstrut \)\(16\!\cdots\!00\)\(q^{98} \) \(\mathstrut +\mathstrut \)\(34\!\cdots\!20\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 516864. 1.39419 0.697094 0.716980i \(-0.254476\pi\)
0.697094 + 0.716980i \(0.254476\pi\)
\(3\) −3.87420e8 −0.577350
\(4\) 1.29709e11 0.943758
\(5\) 3.13693e12 0.367756 0.183878 0.982949i \(-0.441135\pi\)
0.183878 + 0.982949i \(0.441135\pi\)
\(6\) −2.00244e14 −0.804934
\(7\) −3.10972e15 −0.721785 −0.360892 0.932608i \(-0.617528\pi\)
−0.360892 + 0.932608i \(0.617528\pi\)
\(8\) −3.99525e15 −0.0784114
\(9\) 1.50095e17 0.333333
\(10\) 1.62136e18 0.512721
\(11\) 7.50440e18 0.406960 0.203480 0.979079i \(-0.434775\pi\)
0.203480 + 0.979079i \(0.434775\pi\)
\(12\) −5.02520e19 −0.544879
\(13\) −6.39538e20 −1.57730 −0.788650 0.614843i \(-0.789219\pi\)
−0.788650 + 0.614843i \(0.789219\pi\)
\(14\) −1.60730e21 −1.00630
\(15\) −1.21531e21 −0.212324
\(16\) −1.98921e22 −1.05308
\(17\) −5.44751e22 −0.939492 −0.469746 0.882802i \(-0.655655\pi\)
−0.469746 + 0.882802i \(0.655655\pi\)
\(18\) 7.75785e22 0.464729
\(19\) 2.22938e23 0.491182 0.245591 0.969374i \(-0.421018\pi\)
0.245591 + 0.969374i \(0.421018\pi\)
\(20\) 4.06888e23 0.347073
\(21\) 1.20477e24 0.416722
\(22\) 3.87875e24 0.567378
\(23\) −1.64570e25 −1.05775 −0.528877 0.848698i \(-0.677387\pi\)
−0.528877 + 0.848698i \(0.677387\pi\)
\(24\) 1.54784e24 0.0452708
\(25\) −6.29193e25 −0.864756
\(26\) −3.30554e26 −2.19905
\(27\) −5.81497e25 −0.192450
\(28\) −4.03359e26 −0.681190
\(29\) 1.49927e27 1.32287 0.661434 0.750004i \(-0.269948\pi\)
0.661434 + 0.750004i \(0.269948\pi\)
\(30\) −6.28150e26 −0.296019
\(31\) −4.99985e27 −1.28459 −0.642297 0.766456i \(-0.722018\pi\)
−0.642297 + 0.766456i \(0.722018\pi\)
\(32\) −9.73240e27 −1.38978
\(33\) −2.90736e27 −0.234958
\(34\) −2.81562e28 −1.30983
\(35\) −9.75497e27 −0.265440
\(36\) 1.94686e28 0.314586
\(37\) 4.47694e28 0.435762 0.217881 0.975975i \(-0.430086\pi\)
0.217881 + 0.975975i \(0.430086\pi\)
\(38\) 1.15228e29 0.684799
\(39\) 2.47770e29 0.910654
\(40\) −1.25328e28 −0.0288362
\(41\) 1.03254e30 1.50455 0.752275 0.658849i \(-0.228956\pi\)
0.752275 + 0.658849i \(0.228956\pi\)
\(42\) 6.22702e29 0.580989
\(43\) −2.18835e30 −1.32114 −0.660572 0.750763i \(-0.729686\pi\)
−0.660572 + 0.750763i \(0.729686\pi\)
\(44\) 9.73390e29 0.384072
\(45\) 4.70836e29 0.122585
\(46\) −8.50601e30 −1.47471
\(47\) 1.06681e31 1.24244 0.621221 0.783635i \(-0.286637\pi\)
0.621221 + 0.783635i \(0.286637\pi\)
\(48\) 7.70660e30 0.607995
\(49\) −8.89176e30 −0.479027
\(50\) −3.25207e31 −1.20563
\(51\) 2.11048e31 0.542416
\(52\) −8.29539e31 −1.48859
\(53\) −2.17162e31 −0.273956 −0.136978 0.990574i \(-0.543739\pi\)
−0.136978 + 0.990574i \(0.543739\pi\)
\(54\) −3.00555e31 −0.268311
\(55\) 2.35408e31 0.149662
\(56\) 1.24241e31 0.0565961
\(57\) −8.63707e31 −0.283584
\(58\) 7.74917e32 1.84433
\(59\) 9.25373e32 1.60529 0.802647 0.596455i \(-0.203424\pi\)
0.802647 + 0.596455i \(0.203424\pi\)
\(60\) −1.57637e32 −0.200382
\(61\) 1.78286e33 1.66923 0.834615 0.550833i \(-0.185690\pi\)
0.834615 + 0.550833i \(0.185690\pi\)
\(62\) −2.58424e33 −1.79096
\(63\) −4.66752e32 −0.240595
\(64\) −2.29638e33 −0.884532
\(65\) −2.00618e33 −0.580061
\(66\) −1.50271e33 −0.327576
\(67\) 5.16951e33 0.853229 0.426615 0.904433i \(-0.359706\pi\)
0.426615 + 0.904433i \(0.359706\pi\)
\(68\) −7.06592e33 −0.886654
\(69\) 6.37577e33 0.610695
\(70\) −5.04199e33 −0.370074
\(71\) 3.92232e33 0.221444 0.110722 0.993851i \(-0.464684\pi\)
0.110722 + 0.993851i \(0.464684\pi\)
\(72\) −5.99665e32 −0.0261371
\(73\) −3.83796e34 −1.29607 −0.648034 0.761612i \(-0.724408\pi\)
−0.648034 + 0.761612i \(0.724408\pi\)
\(74\) 2.31397e34 0.607534
\(75\) 2.43762e34 0.499267
\(76\) 2.89171e34 0.463557
\(77\) −2.33366e34 −0.293737
\(78\) 1.28063e35 1.26962
\(79\) −5.14706e34 −0.403142 −0.201571 0.979474i \(-0.564605\pi\)
−0.201571 + 0.979474i \(0.564605\pi\)
\(80\) −6.24001e34 −0.387276
\(81\) 2.25284e34 0.111111
\(82\) 5.33684e35 2.09763
\(83\) −2.76468e35 −0.868361 −0.434180 0.900826i \(-0.642962\pi\)
−0.434180 + 0.900826i \(0.642962\pi\)
\(84\) 1.56270e35 0.393285
\(85\) −1.70885e35 −0.345504
\(86\) −1.13108e36 −1.84192
\(87\) −5.80847e35 −0.763758
\(88\) −2.99820e34 −0.0319103
\(89\) −1.38448e36 −1.19556 −0.597780 0.801661i \(-0.703950\pi\)
−0.597780 + 0.801661i \(0.703950\pi\)
\(90\) 2.43358e35 0.170907
\(91\) 1.98878e36 1.13847
\(92\) −2.13462e36 −0.998265
\(93\) 1.93704e36 0.741660
\(94\) 5.51395e36 1.73220
\(95\) 6.99340e35 0.180635
\(96\) 3.77053e36 0.802388
\(97\) 1.68983e36 0.296870 0.148435 0.988922i \(-0.452576\pi\)
0.148435 + 0.988922i \(0.452576\pi\)
\(98\) −4.59583e36 −0.667853
\(99\) 1.12637e36 0.135653
\(100\) −8.16120e36 −0.816120
\(101\) −5.62367e36 −0.467815 −0.233908 0.972259i \(-0.575151\pi\)
−0.233908 + 0.972259i \(0.575151\pi\)
\(102\) 1.09083e37 0.756230
\(103\) −1.48424e37 −0.859046 −0.429523 0.903056i \(-0.641318\pi\)
−0.429523 + 0.903056i \(0.641318\pi\)
\(104\) 2.55511e36 0.123678
\(105\) 3.77928e36 0.153252
\(106\) −1.12243e37 −0.381945
\(107\) 4.70122e36 0.134465 0.0672327 0.997737i \(-0.478583\pi\)
0.0672327 + 0.997737i \(0.478583\pi\)
\(108\) −7.54255e36 −0.181626
\(109\) −3.33633e36 −0.0677453 −0.0338726 0.999426i \(-0.510784\pi\)
−0.0338726 + 0.999426i \(0.510784\pi\)
\(110\) 1.21674e37 0.208657
\(111\) −1.73446e37 −0.251587
\(112\) 6.18588e37 0.760096
\(113\) −1.52031e38 −1.58483 −0.792414 0.609984i \(-0.791176\pi\)
−0.792414 + 0.609984i \(0.791176\pi\)
\(114\) −4.46419e37 −0.395369
\(115\) −5.16243e37 −0.388995
\(116\) 1.94469e38 1.24847
\(117\) −9.59912e37 −0.525766
\(118\) 4.78292e38 2.23808
\(119\) 1.69402e38 0.678111
\(120\) 4.85547e36 0.0166486
\(121\) −2.83723e38 −0.834384
\(122\) 9.21498e38 2.32722
\(123\) −4.00028e38 −0.868653
\(124\) −6.48527e38 −1.21235
\(125\) −4.25615e38 −0.685775
\(126\) −2.41247e38 −0.335434
\(127\) −9.46165e38 −1.13658 −0.568288 0.822830i \(-0.692394\pi\)
−0.568288 + 0.822830i \(0.692394\pi\)
\(128\) 1.50697e38 0.156575
\(129\) 8.47811e38 0.762762
\(130\) −1.03692e39 −0.808714
\(131\) −7.30262e38 −0.494265 −0.247133 0.968982i \(-0.579488\pi\)
−0.247133 + 0.968982i \(0.579488\pi\)
\(132\) −3.77111e38 −0.221744
\(133\) −6.93274e38 −0.354527
\(134\) 2.67193e39 1.18956
\(135\) −1.82412e38 −0.0707746
\(136\) 2.17642e38 0.0736669
\(137\) 2.73285e39 0.807765 0.403883 0.914811i \(-0.367660\pi\)
0.403883 + 0.914811i \(0.367660\pi\)
\(138\) 3.29540e39 0.851423
\(139\) 5.99229e39 1.35462 0.677312 0.735696i \(-0.263145\pi\)
0.677312 + 0.735696i \(0.263145\pi\)
\(140\) −1.26531e39 −0.250512
\(141\) −4.13304e39 −0.717325
\(142\) 2.02730e39 0.308734
\(143\) −4.79935e39 −0.641897
\(144\) −2.98570e39 −0.351026
\(145\) 4.70310e39 0.486492
\(146\) −1.98370e40 −1.80696
\(147\) 3.44485e39 0.276566
\(148\) 5.80700e39 0.411254
\(149\) −1.46862e40 −0.918255 −0.459127 0.888370i \(-0.651838\pi\)
−0.459127 + 0.888370i \(0.651838\pi\)
\(150\) 1.25992e40 0.696072
\(151\) 2.01471e40 0.984328 0.492164 0.870503i \(-0.336206\pi\)
0.492164 + 0.870503i \(0.336206\pi\)
\(152\) −8.90692e38 −0.0385142
\(153\) −8.17643e39 −0.313164
\(154\) −1.20618e40 −0.409525
\(155\) −1.56842e40 −0.472417
\(156\) 3.21380e40 0.859437
\(157\) −5.21717e40 −1.23963 −0.619815 0.784748i \(-0.712792\pi\)
−0.619815 + 0.784748i \(0.712792\pi\)
\(158\) −2.66033e40 −0.562056
\(159\) 8.41330e39 0.158168
\(160\) −3.05298e40 −0.511099
\(161\) 5.11766e40 0.763471
\(162\) 1.16441e40 0.154910
\(163\) 1.10448e41 1.31125 0.655625 0.755086i \(-0.272405\pi\)
0.655625 + 0.755086i \(0.272405\pi\)
\(164\) 1.33930e41 1.41993
\(165\) −9.12018e39 −0.0864073
\(166\) −1.42896e41 −1.21066
\(167\) 8.68066e40 0.658109 0.329055 0.944311i \(-0.393270\pi\)
0.329055 + 0.944311i \(0.393270\pi\)
\(168\) −4.81335e39 −0.0326758
\(169\) 2.44608e41 1.48787
\(170\) −8.83241e40 −0.481697
\(171\) 3.34618e40 0.163727
\(172\) −2.83849e41 −1.24684
\(173\) −2.30699e41 −0.910316 −0.455158 0.890411i \(-0.650417\pi\)
−0.455158 + 0.890411i \(0.650417\pi\)
\(174\) −3.00219e41 −1.06482
\(175\) 1.95661e41 0.624167
\(176\) −1.49278e41 −0.428561
\(177\) −3.58508e41 −0.926817
\(178\) −7.15587e41 −1.66683
\(179\) 4.00112e41 0.840235 0.420118 0.907470i \(-0.361989\pi\)
0.420118 + 0.907470i \(0.361989\pi\)
\(180\) 6.10718e40 0.115691
\(181\) 8.60285e41 1.47092 0.735460 0.677569i \(-0.236966\pi\)
0.735460 + 0.677569i \(0.236966\pi\)
\(182\) 1.02793e42 1.58724
\(183\) −6.90718e41 −0.963731
\(184\) 6.57497e40 0.0829400
\(185\) 1.40438e41 0.160254
\(186\) 1.00119e42 1.03401
\(187\) −4.08803e41 −0.382336
\(188\) 1.38375e42 1.17257
\(189\) 1.80829e41 0.138907
\(190\) 3.61464e41 0.251839
\(191\) −2.36146e42 −1.49301 −0.746507 0.665378i \(-0.768270\pi\)
−0.746507 + 0.665378i \(0.768270\pi\)
\(192\) 8.89663e41 0.510685
\(193\) −2.73448e42 −1.42582 −0.712910 0.701255i \(-0.752623\pi\)
−0.712910 + 0.701255i \(0.752623\pi\)
\(194\) 8.73414e41 0.413893
\(195\) 7.77237e41 0.334898
\(196\) −1.15334e42 −0.452086
\(197\) −2.24211e42 −0.799893 −0.399947 0.916538i \(-0.630971\pi\)
−0.399947 + 0.916538i \(0.630971\pi\)
\(198\) 5.82180e41 0.189126
\(199\) 4.34264e42 1.28520 0.642602 0.766201i \(-0.277855\pi\)
0.642602 + 0.766201i \(0.277855\pi\)
\(200\) 2.51378e41 0.0678067
\(201\) −2.00278e42 −0.492612
\(202\) −2.90667e42 −0.652222
\(203\) −4.66230e42 −0.954825
\(204\) 2.73748e42 0.511910
\(205\) 3.23901e42 0.553307
\(206\) −7.67151e42 −1.19767
\(207\) −2.47010e42 −0.352585
\(208\) 1.27217e43 1.66102
\(209\) 1.67302e42 0.199891
\(210\) 1.95337e42 0.213662
\(211\) −1.99383e42 −0.199739 −0.0998696 0.995001i \(-0.531843\pi\)
−0.0998696 + 0.995001i \(0.531843\pi\)
\(212\) −2.81679e42 −0.258548
\(213\) −1.51959e42 −0.127851
\(214\) 2.42989e42 0.187470
\(215\) −6.86469e42 −0.485858
\(216\) 2.32323e41 0.0150903
\(217\) 1.55481e43 0.927200
\(218\) −1.72443e42 −0.0944496
\(219\) 1.48690e43 0.748285
\(220\) 3.05345e42 0.141245
\(221\) 3.48389e43 1.48186
\(222\) −8.96478e42 −0.350760
\(223\) −1.45882e43 −0.525245 −0.262622 0.964899i \(-0.584587\pi\)
−0.262622 + 0.964899i \(0.584587\pi\)
\(224\) 3.02650e43 1.00312
\(225\) −9.44384e42 −0.288252
\(226\) −7.85795e43 −2.20955
\(227\) −1.02701e43 −0.266132 −0.133066 0.991107i \(-0.542482\pi\)
−0.133066 + 0.991107i \(0.542482\pi\)
\(228\) −1.12031e43 −0.267635
\(229\) −7.93768e43 −1.74879 −0.874394 0.485216i \(-0.838741\pi\)
−0.874394 + 0.485216i \(0.838741\pi\)
\(230\) −2.66828e43 −0.542333
\(231\) 9.04107e42 0.169589
\(232\) −5.98995e42 −0.103728
\(233\) 3.40755e43 0.544951 0.272476 0.962163i \(-0.412158\pi\)
0.272476 + 0.962163i \(0.412158\pi\)
\(234\) −4.96144e43 −0.733017
\(235\) 3.34650e43 0.456916
\(236\) 1.20029e44 1.51501
\(237\) 1.99408e43 0.232754
\(238\) 8.75580e43 0.945414
\(239\) 4.85851e43 0.485447 0.242724 0.970095i \(-0.421959\pi\)
0.242724 + 0.970095i \(0.421959\pi\)
\(240\) 2.41751e43 0.223594
\(241\) 1.16789e44 1.00020 0.500100 0.865968i \(-0.333297\pi\)
0.500100 + 0.865968i \(0.333297\pi\)
\(242\) −1.46646e44 −1.16329
\(243\) −8.72796e42 −0.0641500
\(244\) 2.31254e44 1.57535
\(245\) −2.78928e43 −0.176165
\(246\) −2.06760e44 −1.21106
\(247\) −1.42577e44 −0.774741
\(248\) 1.99756e43 0.100727
\(249\) 1.07109e44 0.501348
\(250\) −2.19985e44 −0.956098
\(251\) 1.50654e44 0.608158 0.304079 0.952647i \(-0.401651\pi\)
0.304079 + 0.952647i \(0.401651\pi\)
\(252\) −6.05421e43 −0.227063
\(253\) −1.23500e44 −0.430464
\(254\) −4.89039e44 −1.58460
\(255\) 6.62042e43 0.199477
\(256\) 3.93501e44 1.10283
\(257\) −2.05457e44 −0.535746 −0.267873 0.963454i \(-0.586321\pi\)
−0.267873 + 0.963454i \(0.586321\pi\)
\(258\) 4.38203e44 1.06343
\(259\) −1.39220e44 −0.314526
\(260\) −2.60220e44 −0.547437
\(261\) 2.25032e44 0.440956
\(262\) −3.77446e44 −0.689098
\(263\) 3.74763e44 0.637639 0.318819 0.947815i \(-0.396714\pi\)
0.318819 + 0.947815i \(0.396714\pi\)
\(264\) 1.16156e43 0.0184234
\(265\) −6.81221e43 −0.100749
\(266\) −3.58328e44 −0.494278
\(267\) 5.36375e44 0.690256
\(268\) 6.70533e44 0.805242
\(269\) −6.18015e44 −0.692758 −0.346379 0.938095i \(-0.612589\pi\)
−0.346379 + 0.938095i \(0.612589\pi\)
\(270\) −9.42819e43 −0.0986731
\(271\) −8.98660e44 −0.878342 −0.439171 0.898403i \(-0.644728\pi\)
−0.439171 + 0.898403i \(0.644728\pi\)
\(272\) 1.08362e45 0.989359
\(273\) −7.70495e44 −0.657296
\(274\) 1.41251e45 1.12618
\(275\) −4.72171e44 −0.351921
\(276\) 8.26996e44 0.576348
\(277\) 5.14897e44 0.335617 0.167809 0.985820i \(-0.446331\pi\)
0.167809 + 0.985820i \(0.446331\pi\)
\(278\) 3.09719e45 1.88860
\(279\) −7.50451e44 −0.428198
\(280\) 3.89735e43 0.0208135
\(281\) −2.48686e45 −1.24333 −0.621663 0.783285i \(-0.713543\pi\)
−0.621663 + 0.783285i \(0.713543\pi\)
\(282\) −2.13622e45 −1.00008
\(283\) 1.48025e45 0.649062 0.324531 0.945875i \(-0.394793\pi\)
0.324531 + 0.945875i \(0.394793\pi\)
\(284\) 5.08761e44 0.208989
\(285\) −2.70939e44 −0.104290
\(286\) −2.48061e45 −0.894925
\(287\) −3.21092e45 −1.08596
\(288\) −1.46078e45 −0.463259
\(289\) −3.94555e44 −0.117354
\(290\) 2.43086e45 0.678261
\(291\) −6.54676e44 −0.171398
\(292\) −4.97819e45 −1.22317
\(293\) 1.29229e45 0.298064 0.149032 0.988832i \(-0.452384\pi\)
0.149032 + 0.988832i \(0.452384\pi\)
\(294\) 1.78052e45 0.385585
\(295\) 2.90283e45 0.590356
\(296\) −1.78865e44 −0.0341687
\(297\) −4.36379e44 −0.0783194
\(298\) −7.59076e45 −1.28022
\(299\) 1.05249e46 1.66840
\(300\) 3.16182e45 0.471187
\(301\) 6.80515e45 0.953581
\(302\) 1.04133e46 1.37234
\(303\) 2.17873e45 0.270093
\(304\) −4.43470e45 −0.517253
\(305\) 5.59272e45 0.613869
\(306\) −4.22610e45 −0.436609
\(307\) 3.03724e45 0.295406 0.147703 0.989032i \(-0.452812\pi\)
0.147703 + 0.989032i \(0.452812\pi\)
\(308\) −3.02697e45 −0.277217
\(309\) 5.75026e45 0.495970
\(310\) −8.10658e45 −0.658637
\(311\) −2.03519e46 −1.55789 −0.778947 0.627090i \(-0.784246\pi\)
−0.778947 + 0.627090i \(0.784246\pi\)
\(312\) −9.89903e44 −0.0714056
\(313\) 1.26896e46 0.862736 0.431368 0.902176i \(-0.358031\pi\)
0.431368 + 0.902176i \(0.358031\pi\)
\(314\) −2.69657e46 −1.72828
\(315\) −1.46417e45 −0.0884802
\(316\) −6.67621e45 −0.380469
\(317\) −2.19161e46 −1.17806 −0.589029 0.808112i \(-0.700490\pi\)
−0.589029 + 0.808112i \(0.700490\pi\)
\(318\) 4.34853e45 0.220516
\(319\) 1.12511e46 0.538354
\(320\) −7.20356e45 −0.325292
\(321\) −1.82135e45 −0.0776336
\(322\) 2.64513e46 1.06442
\(323\) −1.21446e46 −0.461461
\(324\) 2.92214e45 0.104862
\(325\) 4.02392e46 1.36398
\(326\) 5.70864e46 1.82813
\(327\) 1.29256e45 0.0391127
\(328\) −4.12527e45 −0.117974
\(329\) −3.31748e46 −0.896776
\(330\) −4.71389e45 −0.120468
\(331\) −6.51418e46 −1.57413 −0.787067 0.616867i \(-0.788402\pi\)
−0.787067 + 0.616867i \(0.788402\pi\)
\(332\) −3.58604e46 −0.819523
\(333\) 6.71965e45 0.145254
\(334\) 4.48672e46 0.917528
\(335\) 1.62164e46 0.313780
\(336\) −2.39654e46 −0.438842
\(337\) −4.49138e46 −0.778443 −0.389221 0.921144i \(-0.627256\pi\)
−0.389221 + 0.921144i \(0.627256\pi\)
\(338\) 1.26429e47 2.07437
\(339\) 5.89001e46 0.915000
\(340\) −2.21653e46 −0.326072
\(341\) −3.75209e46 −0.522778
\(342\) 1.72952e46 0.228266
\(343\) 8.53739e46 1.06754
\(344\) 8.74299e45 0.103593
\(345\) 2.00003e46 0.224587
\(346\) −1.19240e47 −1.26915
\(347\) −3.07449e45 −0.0310226 −0.0155113 0.999880i \(-0.504938\pi\)
−0.0155113 + 0.999880i \(0.504938\pi\)
\(348\) −7.53412e46 −0.720803
\(349\) −1.55130e47 −1.40742 −0.703711 0.710487i \(-0.748475\pi\)
−0.703711 + 0.710487i \(0.748475\pi\)
\(350\) 1.01130e47 0.870206
\(351\) 3.71889e46 0.303551
\(352\) −7.30358e46 −0.565583
\(353\) 1.60772e47 1.18135 0.590675 0.806909i \(-0.298861\pi\)
0.590675 + 0.806909i \(0.298861\pi\)
\(354\) −1.85300e47 −1.29216
\(355\) 1.23040e46 0.0814372
\(356\) −1.79580e47 −1.12832
\(357\) −6.56300e46 −0.391508
\(358\) 2.06804e47 1.17145
\(359\) −3.06245e47 −1.64749 −0.823743 0.566963i \(-0.808118\pi\)
−0.823743 + 0.566963i \(0.808118\pi\)
\(360\) −1.88111e45 −0.00961208
\(361\) −1.56306e47 −0.758741
\(362\) 4.44650e47 2.05074
\(363\) 1.09920e47 0.481732
\(364\) 2.57963e47 1.07444
\(365\) −1.20394e47 −0.476636
\(366\) −3.57007e47 −1.34362
\(367\) 3.11125e47 1.11330 0.556651 0.830746i \(-0.312086\pi\)
0.556651 + 0.830746i \(0.312086\pi\)
\(368\) 3.27364e47 1.11390
\(369\) 1.54979e47 0.501517
\(370\) 7.25875e46 0.223424
\(371\) 6.75313e46 0.197737
\(372\) 2.51252e47 0.699948
\(373\) 2.77220e47 0.734872 0.367436 0.930049i \(-0.380236\pi\)
0.367436 + 0.930049i \(0.380236\pi\)
\(374\) −2.11296e47 −0.533047
\(375\) 1.64892e47 0.395932
\(376\) −4.26217e46 −0.0974216
\(377\) −9.58838e47 −2.08656
\(378\) 9.34642e46 0.193663
\(379\) −3.61039e47 −0.712408 −0.356204 0.934408i \(-0.615929\pi\)
−0.356204 + 0.934408i \(0.615929\pi\)
\(380\) 9.07108e46 0.170476
\(381\) 3.66564e47 0.656202
\(382\) −1.22055e48 −2.08154
\(383\) 3.07589e47 0.499797 0.249898 0.968272i \(-0.419603\pi\)
0.249898 + 0.968272i \(0.419603\pi\)
\(384\) −5.83833e46 −0.0903984
\(385\) −7.32052e46 −0.108024
\(386\) −1.41335e48 −1.98786
\(387\) −3.28459e47 −0.440381
\(388\) 2.19187e47 0.280174
\(389\) 8.01241e47 0.976552 0.488276 0.872689i \(-0.337626\pi\)
0.488276 + 0.872689i \(0.337626\pi\)
\(390\) 4.01725e47 0.466911
\(391\) 8.96496e47 0.993753
\(392\) 3.55248e46 0.0375612
\(393\) 2.82919e47 0.285364
\(394\) −1.15887e48 −1.11520
\(395\) −1.61460e47 −0.148258
\(396\) 1.46101e47 0.128024
\(397\) 5.55598e47 0.464661 0.232331 0.972637i \(-0.425365\pi\)
0.232331 + 0.972637i \(0.425365\pi\)
\(398\) 2.24455e48 1.79181
\(399\) 2.68589e47 0.204686
\(400\) 1.25160e48 0.910656
\(401\) −2.52389e48 −1.75347 −0.876736 0.480972i \(-0.840284\pi\)
−0.876736 + 0.480972i \(0.840284\pi\)
\(402\) −1.03516e48 −0.686794
\(403\) 3.19759e48 2.02619
\(404\) −7.29442e47 −0.441505
\(405\) 7.06700e46 0.0408618
\(406\) −2.40978e48 −1.33121
\(407\) 3.35968e47 0.177338
\(408\) −8.43188e46 −0.0425316
\(409\) 1.92635e48 0.928653 0.464326 0.885664i \(-0.346296\pi\)
0.464326 + 0.885664i \(0.346296\pi\)
\(410\) 1.67413e48 0.771414
\(411\) −1.05876e48 −0.466363
\(412\) −1.92520e48 −0.810731
\(413\) −2.87765e48 −1.15868
\(414\) −1.27671e48 −0.491569
\(415\) −8.67260e47 −0.319345
\(416\) 6.22423e48 2.19209
\(417\) −2.32153e48 −0.782092
\(418\) 8.64721e47 0.278686
\(419\) 1.97665e48 0.609494 0.304747 0.952433i \(-0.401428\pi\)
0.304747 + 0.952433i \(0.401428\pi\)
\(420\) 4.90207e47 0.144633
\(421\) −3.96618e48 −1.11983 −0.559916 0.828549i \(-0.689167\pi\)
−0.559916 + 0.828549i \(0.689167\pi\)
\(422\) −1.03054e48 −0.278474
\(423\) 1.60122e48 0.414148
\(424\) 8.67616e46 0.0214812
\(425\) 3.42753e48 0.812431
\(426\) −7.85419e47 −0.178248
\(427\) −5.54421e48 −1.20482
\(428\) 6.09791e47 0.126903
\(429\) 1.85937e48 0.370600
\(430\) −3.54811e48 −0.677377
\(431\) −9.76026e48 −1.78497 −0.892487 0.451074i \(-0.851041\pi\)
−0.892487 + 0.451074i \(0.851041\pi\)
\(432\) 1.15672e48 0.202665
\(433\) −4.50754e48 −0.756683 −0.378341 0.925666i \(-0.623505\pi\)
−0.378341 + 0.925666i \(0.623505\pi\)
\(434\) 8.03627e48 1.29269
\(435\) −1.82208e48 −0.280876
\(436\) −4.32753e47 −0.0639352
\(437\) −3.66888e48 −0.519550
\(438\) 7.68527e48 1.04325
\(439\) 1.11863e49 1.45577 0.727886 0.685699i \(-0.240503\pi\)
0.727886 + 0.685699i \(0.240503\pi\)
\(440\) −9.40512e46 −0.0117352
\(441\) −1.33460e48 −0.159676
\(442\) 1.80070e49 2.06599
\(443\) 1.43677e49 1.58095 0.790474 0.612496i \(-0.209834\pi\)
0.790474 + 0.612496i \(0.209834\pi\)
\(444\) −2.24975e48 −0.237438
\(445\) −4.34301e48 −0.439674
\(446\) −7.54011e48 −0.732290
\(447\) 5.68973e48 0.530155
\(448\) 7.14108e48 0.638441
\(449\) −9.50078e48 −0.815084 −0.407542 0.913187i \(-0.633614\pi\)
−0.407542 + 0.913187i \(0.633614\pi\)
\(450\) −4.88118e48 −0.401877
\(451\) 7.74862e48 0.612292
\(452\) −1.97199e49 −1.49569
\(453\) −7.80541e48 −0.568302
\(454\) −5.30824e48 −0.371037
\(455\) 6.23867e48 0.418679
\(456\) 3.45072e47 0.0222362
\(457\) −1.14567e49 −0.708941 −0.354471 0.935067i \(-0.615339\pi\)
−0.354471 + 0.935067i \(0.615339\pi\)
\(458\) −4.10270e49 −2.43814
\(459\) 3.16771e48 0.180805
\(460\) −6.69615e48 −0.367118
\(461\) 1.13686e49 0.598741 0.299370 0.954137i \(-0.403223\pi\)
0.299370 + 0.954137i \(0.403223\pi\)
\(462\) 4.67300e48 0.236439
\(463\) 1.21451e49 0.590409 0.295204 0.955434i \(-0.404612\pi\)
0.295204 + 0.955434i \(0.404612\pi\)
\(464\) −2.98236e49 −1.39308
\(465\) 6.07637e48 0.272750
\(466\) 1.76124e49 0.759764
\(467\) 4.37721e49 1.81483 0.907414 0.420237i \(-0.138053\pi\)
0.907414 + 0.420237i \(0.138053\pi\)
\(468\) −1.24509e49 −0.496196
\(469\) −1.60757e49 −0.615848
\(470\) 1.72969e49 0.637026
\(471\) 2.02124e49 0.715700
\(472\) −3.69709e48 −0.125873
\(473\) −1.64222e49 −0.537652
\(474\) 1.03067e49 0.324503
\(475\) −1.40271e49 −0.424752
\(476\) 2.19730e49 0.639973
\(477\) −3.25948e48 −0.0913185
\(478\) 2.51119e49 0.676805
\(479\) 3.52297e49 0.913486 0.456743 0.889599i \(-0.349016\pi\)
0.456743 + 0.889599i \(0.349016\pi\)
\(480\) 1.18279e49 0.295083
\(481\) −2.86317e49 −0.687327
\(482\) 6.03640e49 1.39447
\(483\) −1.98269e49 −0.440790
\(484\) −3.68015e49 −0.787457
\(485\) 5.30089e48 0.109176
\(486\) −4.51117e48 −0.0894372
\(487\) −3.72470e49 −0.710894 −0.355447 0.934696i \(-0.615671\pi\)
−0.355447 + 0.934696i \(0.615671\pi\)
\(488\) −7.12299e48 −0.130887
\(489\) −4.27897e49 −0.757051
\(490\) −1.44168e49 −0.245607
\(491\) 6.86626e49 1.12645 0.563226 0.826303i \(-0.309560\pi\)
0.563226 + 0.826303i \(0.309560\pi\)
\(492\) −5.18873e49 −0.819798
\(493\) −8.16728e49 −1.24282
\(494\) −7.36930e49 −1.08013
\(495\) 3.53334e48 0.0498873
\(496\) 9.94575e49 1.35278
\(497\) −1.21973e49 −0.159835
\(498\) 5.53610e49 0.698973
\(499\) 1.17556e50 1.43016 0.715080 0.699042i \(-0.246390\pi\)
0.715080 + 0.699042i \(0.246390\pi\)
\(500\) −5.52061e49 −0.647206
\(501\) −3.36307e49 −0.379960
\(502\) 7.78675e49 0.847886
\(503\) −1.53249e49 −0.160838 −0.0804191 0.996761i \(-0.525626\pi\)
−0.0804191 + 0.996761i \(0.525626\pi\)
\(504\) 1.86479e48 0.0188654
\(505\) −1.76411e49 −0.172042
\(506\) −6.38325e49 −0.600147
\(507\) −9.47660e49 −0.859024
\(508\) −1.22726e50 −1.07265
\(509\) −7.32055e49 −0.616971 −0.308486 0.951229i \(-0.599822\pi\)
−0.308486 + 0.951229i \(0.599822\pi\)
\(510\) 3.42185e49 0.278108
\(511\) 1.19350e50 0.935481
\(512\) 1.82675e50 1.38097
\(513\) −1.29638e49 −0.0945280
\(514\) −1.06193e50 −0.746930
\(515\) −4.65596e49 −0.315919
\(516\) 1.09969e50 0.719863
\(517\) 8.00577e49 0.505624
\(518\) −7.19579e49 −0.438508
\(519\) 8.93774e49 0.525571
\(520\) 8.01520e48 0.0454834
\(521\) 1.44081e50 0.789061 0.394530 0.918883i \(-0.370907\pi\)
0.394530 + 0.918883i \(0.370907\pi\)
\(522\) 1.16311e50 0.614775
\(523\) −1.41522e50 −0.722007 −0.361003 0.932564i \(-0.617566\pi\)
−0.361003 + 0.932564i \(0.617566\pi\)
\(524\) −9.47217e49 −0.466467
\(525\) −7.58032e49 −0.360363
\(526\) 1.93701e50 0.888988
\(527\) 2.72368e50 1.20687
\(528\) 5.78335e49 0.247430
\(529\) 2.87681e49 0.118845
\(530\) −3.52099e49 −0.140463
\(531\) 1.38893e50 0.535098
\(532\) −8.99240e49 −0.334588
\(533\) −6.60350e50 −2.37313
\(534\) 2.77233e50 0.962347
\(535\) 1.47474e49 0.0494504
\(536\) −2.06535e49 −0.0669029
\(537\) −1.55012e50 −0.485110
\(538\) −3.19429e50 −0.965835
\(539\) −6.67273e49 −0.194945
\(540\) −2.36605e49 −0.0667942
\(541\) −3.29954e50 −0.900127 −0.450064 0.892997i \(-0.648599\pi\)
−0.450064 + 0.892997i \(0.648599\pi\)
\(542\) −4.64485e50 −1.22457
\(543\) −3.33292e50 −0.849236
\(544\) 5.30174e50 1.30569
\(545\) −1.04658e49 −0.0249137
\(546\) −3.98241e50 −0.916394
\(547\) 9.95610e49 0.221474 0.110737 0.993850i \(-0.464679\pi\)
0.110737 + 0.993850i \(0.464679\pi\)
\(548\) 3.54475e50 0.762335
\(549\) 2.67598e50 0.556410
\(550\) −2.44048e50 −0.490643
\(551\) 3.34244e50 0.649768
\(552\) −2.54728e49 −0.0478854
\(553\) 1.60059e50 0.290982
\(554\) 2.66131e50 0.467913
\(555\) −5.44087e49 −0.0925227
\(556\) 7.77254e50 1.27844
\(557\) 9.57323e50 1.52313 0.761565 0.648088i \(-0.224431\pi\)
0.761565 + 0.648088i \(0.224431\pi\)
\(558\) −3.87881e50 −0.596988
\(559\) 1.39953e51 2.08384
\(560\) 1.94047e50 0.279530
\(561\) 1.58379e50 0.220742
\(562\) −1.28537e51 −1.73343
\(563\) 3.20639e50 0.418419 0.209209 0.977871i \(-0.432911\pi\)
0.209209 + 0.977871i \(0.432911\pi\)
\(564\) −5.36093e50 −0.676981
\(565\) −4.76911e50 −0.582829
\(566\) 7.65088e50 0.904914
\(567\) −7.00570e49 −0.0801983
\(568\) −1.56706e49 −0.0173637
\(569\) −1.54737e51 −1.65966 −0.829829 0.558018i \(-0.811562\pi\)
−0.829829 + 0.558018i \(0.811562\pi\)
\(570\) −1.40038e50 −0.145399
\(571\) −8.82178e50 −0.886723 −0.443362 0.896343i \(-0.646214\pi\)
−0.443362 + 0.896343i \(0.646214\pi\)
\(572\) −6.22519e50 −0.605796
\(573\) 9.14879e50 0.861992
\(574\) −1.65961e51 −1.51403
\(575\) 1.03546e51 0.914699
\(576\) −3.44674e50 −0.294844
\(577\) −4.93183e50 −0.408560 −0.204280 0.978913i \(-0.565485\pi\)
−0.204280 + 0.978913i \(0.565485\pi\)
\(578\) −2.03931e50 −0.163613
\(579\) 1.05939e51 0.823198
\(580\) 6.10035e50 0.459131
\(581\) 8.59738e50 0.626769
\(582\) −3.38378e50 −0.238961
\(583\) −1.62967e50 −0.111489
\(584\) 1.53336e50 0.101626
\(585\) −3.01117e50 −0.193354
\(586\) 6.67939e50 0.415557
\(587\) −1.61018e51 −0.970666 −0.485333 0.874330i \(-0.661302\pi\)
−0.485333 + 0.874330i \(0.661302\pi\)
\(588\) 4.46828e50 0.261012
\(589\) −1.11466e51 −0.630969
\(590\) 1.50037e51 0.823067
\(591\) 8.68640e50 0.461819
\(592\) −8.90557e50 −0.458892
\(593\) 8.02157e49 0.0400634 0.0200317 0.999799i \(-0.493623\pi\)
0.0200317 + 0.999799i \(0.493623\pi\)
\(594\) −2.25549e50 −0.109192
\(595\) 5.31403e50 0.249379
\(596\) −1.90493e51 −0.866611
\(597\) −1.68243e51 −0.742012
\(598\) 5.43991e51 2.32606
\(599\) −4.13904e51 −1.71595 −0.857973 0.513694i \(-0.828276\pi\)
−0.857973 + 0.513694i \(0.828276\pi\)
\(600\) −9.73890e49 −0.0391482
\(601\) 1.01480e51 0.395551 0.197776 0.980247i \(-0.436628\pi\)
0.197776 + 0.980247i \(0.436628\pi\)
\(602\) 3.51733e51 1.32947
\(603\) 7.75916e50 0.284410
\(604\) 2.61327e51 0.928968
\(605\) −8.90020e50 −0.306849
\(606\) 1.12610e51 0.376561
\(607\) −1.59854e51 −0.518482 −0.259241 0.965813i \(-0.583472\pi\)
−0.259241 + 0.965813i \(0.583472\pi\)
\(608\) −2.16972e51 −0.682633
\(609\) 1.80627e51 0.551269
\(610\) 2.89067e51 0.855849
\(611\) −6.82265e51 −1.95970
\(612\) −1.06056e51 −0.295551
\(613\) 3.62477e51 0.980081 0.490041 0.871700i \(-0.336982\pi\)
0.490041 + 0.871700i \(0.336982\pi\)
\(614\) 1.56984e51 0.411851
\(615\) −1.25486e51 −0.319452
\(616\) 9.32355e49 0.0230323
\(617\) 2.49598e51 0.598364 0.299182 0.954196i \(-0.403286\pi\)
0.299182 + 0.954196i \(0.403286\pi\)
\(618\) 2.97210e51 0.691475
\(619\) −2.35643e51 −0.532080 −0.266040 0.963962i \(-0.585715\pi\)
−0.266040 + 0.963962i \(0.585715\pi\)
\(620\) −2.03438e51 −0.445847
\(621\) 9.56969e50 0.203565
\(622\) −1.05192e52 −2.17200
\(623\) 4.30534e51 0.862936
\(624\) −4.92866e51 −0.958990
\(625\) 3.24286e51 0.612558
\(626\) 6.55880e51 1.20282
\(627\) −6.48160e50 −0.115407
\(628\) −6.76715e51 −1.16991
\(629\) −2.43882e51 −0.409395
\(630\) −7.56776e50 −0.123358
\(631\) −4.78740e51 −0.757804 −0.378902 0.925437i \(-0.623698\pi\)
−0.378902 + 0.925437i \(0.623698\pi\)
\(632\) 2.05638e50 0.0316109
\(633\) 7.72451e50 0.115319
\(634\) −1.13276e52 −1.64243
\(635\) −2.96805e51 −0.417982
\(636\) 1.09128e51 0.149273
\(637\) 5.68661e51 0.755569
\(638\) 5.81529e51 0.750566
\(639\) 5.88719e50 0.0738146
\(640\) 4.72727e50 0.0575813
\(641\) 5.92335e51 0.700961 0.350480 0.936570i \(-0.386018\pi\)
0.350480 + 0.936570i \(0.386018\pi\)
\(642\) −9.41389e50 −0.108236
\(643\) 1.23332e52 1.37776 0.688879 0.724877i \(-0.258103\pi\)
0.688879 + 0.724877i \(0.258103\pi\)
\(644\) 6.63807e51 0.720532
\(645\) 2.65952e51 0.280510
\(646\) −6.27709e51 −0.643364
\(647\) 2.91813e51 0.290654 0.145327 0.989384i \(-0.453577\pi\)
0.145327 + 0.989384i \(0.453577\pi\)
\(648\) −9.00065e49 −0.00871237
\(649\) 6.94437e51 0.653290
\(650\) 2.07982e52 1.90164
\(651\) −6.02367e51 −0.535319
\(652\) 1.43261e52 1.23750
\(653\) 1.85059e51 0.155387 0.0776936 0.996977i \(-0.475244\pi\)
0.0776936 + 0.996977i \(0.475244\pi\)
\(654\) 6.68079e50 0.0545305
\(655\) −2.29078e51 −0.181769
\(656\) −2.05394e52 −1.58441
\(657\) −5.76057e51 −0.432022
\(658\) −1.71468e52 −1.25027
\(659\) −5.04387e51 −0.357588 −0.178794 0.983886i \(-0.557220\pi\)
−0.178794 + 0.983886i \(0.557220\pi\)
\(660\) −1.18297e51 −0.0815476
\(661\) 1.90856e52 1.27932 0.639659 0.768659i \(-0.279075\pi\)
0.639659 + 0.768659i \(0.279075\pi\)
\(662\) −3.36694e52 −2.19464
\(663\) −1.34973e52 −0.855553
\(664\) 1.10456e51 0.0680894
\(665\) −2.17475e51 −0.130380
\(666\) 3.47314e51 0.202511
\(667\) −2.46734e52 −1.39927
\(668\) 1.12596e52 0.621096
\(669\) 5.65177e51 0.303250
\(670\) 8.38167e51 0.437468
\(671\) 1.33793e52 0.679310
\(672\) −1.17253e52 −0.579151
\(673\) −7.73202e51 −0.371548 −0.185774 0.982593i \(-0.559479\pi\)
−0.185774 + 0.982593i \(0.559479\pi\)
\(674\) −2.32143e52 −1.08529
\(675\) 3.65874e51 0.166422
\(676\) 3.17278e52 1.40419
\(677\) −4.47773e50 −0.0192827 −0.00964135 0.999954i \(-0.503069\pi\)
−0.00964135 + 0.999954i \(0.503069\pi\)
\(678\) 3.04433e52 1.27568
\(679\) −5.25491e51 −0.214276
\(680\) 6.82726e50 0.0270914
\(681\) 3.97885e51 0.153651
\(682\) −1.93932e52 −0.728850
\(683\) −3.49109e52 −1.27696 −0.638481 0.769637i \(-0.720437\pi\)
−0.638481 + 0.769637i \(0.720437\pi\)
\(684\) 4.34030e51 0.154519
\(685\) 8.57275e51 0.297060
\(686\) 4.41267e52 1.48835
\(687\) 3.07522e52 1.00966
\(688\) 4.35308e52 1.39127
\(689\) 1.38883e52 0.432110
\(690\) 1.03374e52 0.313116
\(691\) −4.18261e52 −1.23340 −0.616700 0.787198i \(-0.711531\pi\)
−0.616700 + 0.787198i \(0.711531\pi\)
\(692\) −2.99237e52 −0.859118
\(693\) −3.50270e51 −0.0979124
\(694\) −1.58909e51 −0.0432513
\(695\) 1.87974e52 0.498171
\(696\) 2.32063e51 0.0598873
\(697\) −5.62479e52 −1.41351
\(698\) −8.01808e52 −1.96221
\(699\) −1.32015e52 −0.314628
\(700\) 2.53791e52 0.589063
\(701\) 5.92287e52 1.33890 0.669452 0.742856i \(-0.266529\pi\)
0.669452 + 0.742856i \(0.266529\pi\)
\(702\) 1.92216e52 0.423207
\(703\) 9.98079e51 0.214038
\(704\) −1.72329e52 −0.359969
\(705\) −1.29650e52 −0.263800
\(706\) 8.30973e52 1.64702
\(707\) 1.74880e52 0.337662
\(708\) −4.65018e52 −0.874691
\(709\) −9.83617e51 −0.180248 −0.0901241 0.995931i \(-0.528726\pi\)
−0.0901241 + 0.995931i \(0.528726\pi\)
\(710\) 6.35951e51 0.113539
\(711\) −7.72546e51 −0.134381
\(712\) 5.53134e51 0.0937454
\(713\) 8.22824e52 1.35878
\(714\) −3.39218e52 −0.545835
\(715\) −1.50552e52 −0.236061
\(716\) 5.18982e52 0.792979
\(717\) −1.88229e52 −0.280273
\(718\) −1.58287e53 −2.29690
\(719\) −8.07338e52 −1.14175 −0.570875 0.821037i \(-0.693396\pi\)
−0.570875 + 0.821037i \(0.693396\pi\)
\(720\) −9.36592e51 −0.129092
\(721\) 4.61558e52 0.620046
\(722\) −8.07891e52 −1.05783
\(723\) −4.52465e52 −0.577466
\(724\) 1.11587e53 1.38819
\(725\) −9.43328e52 −1.14396
\(726\) 5.68138e52 0.671624
\(727\) 9.90481e51 0.114146 0.0570728 0.998370i \(-0.481823\pi\)
0.0570728 + 0.998370i \(0.481823\pi\)
\(728\) −7.94568e51 −0.0892690
\(729\) 3.38139e51 0.0370370
\(730\) −6.22273e52 −0.664520
\(731\) 1.19211e53 1.24120
\(732\) −8.95925e52 −0.909529
\(733\) −8.81869e52 −0.872932 −0.436466 0.899721i \(-0.643770\pi\)
−0.436466 + 0.899721i \(0.643770\pi\)
\(734\) 1.60809e53 1.55215
\(735\) 1.08062e52 0.101709
\(736\) 1.60166e53 1.47004
\(737\) 3.87941e52 0.347230
\(738\) 8.01031e52 0.699209
\(739\) −1.03605e53 −0.881978 −0.440989 0.897513i \(-0.645372\pi\)
−0.440989 + 0.897513i \(0.645372\pi\)
\(740\) 1.82161e52 0.151241
\(741\) 5.52373e52 0.447297
\(742\) 3.49045e52 0.275682
\(743\) 1.35827e53 1.04639 0.523195 0.852213i \(-0.324740\pi\)
0.523195 + 0.852213i \(0.324740\pi\)
\(744\) −7.73897e51 −0.0581546
\(745\) −4.60695e52 −0.337694
\(746\) 1.43285e53 1.02455
\(747\) −4.14964e52 −0.289454
\(748\) −5.30255e52 −0.360832
\(749\) −1.46195e52 −0.0970550
\(750\) 8.52266e52 0.552004
\(751\) 2.26512e53 1.43137 0.715687 0.698421i \(-0.246114\pi\)
0.715687 + 0.698421i \(0.246114\pi\)
\(752\) −2.12211e53 −1.30839
\(753\) −5.83664e52 −0.351120
\(754\) −4.95589e53 −2.90905
\(755\) 6.32001e52 0.361992
\(756\) 2.34552e52 0.131095
\(757\) 2.91830e52 0.159168 0.0795841 0.996828i \(-0.474641\pi\)
0.0795841 + 0.996828i \(0.474641\pi\)
\(758\) −1.86608e53 −0.993230
\(759\) 4.78463e52 0.248528
\(760\) −2.79404e51 −0.0141638
\(761\) 2.49523e52 0.123451 0.0617256 0.998093i \(-0.480340\pi\)
0.0617256 + 0.998093i \(0.480340\pi\)
\(762\) 1.89464e53 0.914868
\(763\) 1.03751e52 0.0488975
\(764\) −3.06303e53 −1.40904
\(765\) −2.56489e52 −0.115168
\(766\) 1.58982e53 0.696810
\(767\) −5.91811e53 −2.53203
\(768\) −1.52451e53 −0.636717
\(769\) 3.98900e53 1.62640 0.813199 0.581986i \(-0.197724\pi\)
0.813199 + 0.581986i \(0.197724\pi\)
\(770\) −3.78371e52 −0.150605
\(771\) 7.95983e52 0.309313
\(772\) −3.54687e53 −1.34563
\(773\) −1.73601e52 −0.0643029 −0.0321515 0.999483i \(-0.510236\pi\)
−0.0321515 + 0.999483i \(0.510236\pi\)
\(774\) −1.69769e53 −0.613974
\(775\) 3.14587e53 1.11086
\(776\) −6.75130e51 −0.0232780
\(777\) 5.39368e52 0.181592
\(778\) 4.14132e53 1.36150
\(779\) 2.30193e53 0.739008
\(780\) 1.00815e53 0.316063
\(781\) 2.94347e52 0.0901187
\(782\) 4.63366e53 1.38548
\(783\) −8.71821e52 −0.254586
\(784\) 1.76876e53 0.504453
\(785\) −1.63659e53 −0.455881
\(786\) 1.46230e53 0.397851
\(787\) 6.17560e53 1.64114 0.820572 0.571544i \(-0.193655\pi\)
0.820572 + 0.571544i \(0.193655\pi\)
\(788\) −2.90822e53 −0.754906
\(789\) −1.45191e53 −0.368141
\(790\) −8.34526e52 −0.206699
\(791\) 4.72775e53 1.14390
\(792\) −4.50013e51 −0.0106368
\(793\) −1.14021e54 −2.63288
\(794\) 2.87169e53 0.647825
\(795\) 2.63919e52 0.0581673
\(796\) 5.63280e53 1.21292
\(797\) −8.27498e53 −1.74096 −0.870478 0.492207i \(-0.836190\pi\)
−0.870478 + 0.492207i \(0.836190\pi\)
\(798\) 1.38824e53 0.285371
\(799\) −5.81146e53 −1.16727
\(800\) 6.12355e53 1.20182
\(801\) −2.07803e53 −0.398520
\(802\) −1.30450e54 −2.44467
\(803\) −2.88016e53 −0.527447
\(804\) −2.59778e53 −0.464907
\(805\) 1.60537e53 0.280771
\(806\) 1.65272e54 2.82489
\(807\) 2.39432e53 0.399964
\(808\) 2.24680e52 0.0366821
\(809\) −4.25983e53 −0.679742 −0.339871 0.940472i \(-0.610383\pi\)
−0.339871 + 0.940472i \(0.610383\pi\)
\(810\) 3.65267e52 0.0569689
\(811\) 3.53733e52 0.0539249 0.0269625 0.999636i \(-0.491417\pi\)
0.0269625 + 0.999636i \(0.491417\pi\)
\(812\) −6.04744e53 −0.901124
\(813\) 3.48159e53 0.507111
\(814\) 1.73649e53 0.247242
\(815\) 3.46466e53 0.482220
\(816\) −4.19818e53 −0.571207
\(817\) −4.87865e53 −0.648921
\(818\) 9.95659e53 1.29472
\(819\) 2.98506e53 0.379490
\(820\) 4.20130e53 0.522188
\(821\) −1.14147e54 −1.38713 −0.693566 0.720393i \(-0.743961\pi\)
−0.693566 + 0.720393i \(0.743961\pi\)
\(822\) −5.47235e53 −0.650198
\(823\) −4.03065e52 −0.0468250 −0.0234125 0.999726i \(-0.507453\pi\)
−0.0234125 + 0.999726i \(0.507453\pi\)
\(824\) 5.92992e52 0.0673589
\(825\) 1.82929e53 0.203182
\(826\) −1.48735e54 −1.61541
\(827\) 6.45322e53 0.685369 0.342685 0.939450i \(-0.388664\pi\)
0.342685 + 0.939450i \(0.388664\pi\)
\(828\) −3.20395e53 −0.332755
\(829\) 2.31995e52 0.0235625 0.0117812 0.999931i \(-0.496250\pi\)
0.0117812 + 0.999931i \(0.496250\pi\)
\(830\) −4.48255e53 −0.445226
\(831\) −1.99482e53 −0.193769
\(832\) 1.46862e54 1.39517
\(833\) 4.84380e53 0.450042
\(834\) −1.19992e54 −1.09038
\(835\) 2.72306e53 0.242023
\(836\) 2.17005e53 0.188649
\(837\) 2.90740e53 0.247220
\(838\) 1.02166e54 0.849749
\(839\) 8.80747e53 0.716564 0.358282 0.933613i \(-0.383363\pi\)
0.358282 + 0.933613i \(0.383363\pi\)
\(840\) −1.50991e52 −0.0120167
\(841\) 9.63330e53 0.749979
\(842\) −2.04997e54 −1.56126
\(843\) 9.63462e53 0.717835
\(844\) −2.58618e53 −0.188506
\(845\) 7.67316e53 0.547174
\(846\) 8.27614e53 0.577399
\(847\) 8.82300e53 0.602245
\(848\) 4.31980e53 0.288497
\(849\) −5.73480e53 −0.374736
\(850\) 1.77157e54 1.13268
\(851\) −7.36769e53 −0.460929
\(852\) −1.97104e53 −0.120660
\(853\) 5.96791e53 0.357491 0.178745 0.983895i \(-0.442796\pi\)
0.178745 + 0.983895i \(0.442796\pi\)
\(854\) −2.86560e54 −1.67975
\(855\) 1.04967e53 0.0602116
\(856\) −1.87825e52 −0.0105436
\(857\) −5.15514e52 −0.0283202 −0.0141601 0.999900i \(-0.504507\pi\)
−0.0141601 + 0.999900i \(0.504507\pi\)
\(858\) 9.61039e53 0.516685
\(859\) −1.99312e53 −0.104872 −0.0524360 0.998624i \(-0.516699\pi\)
−0.0524360 + 0.998624i \(0.516699\pi\)
\(860\) −8.90413e53 −0.458533
\(861\) 1.24398e54 0.626980
\(862\) −5.04472e54 −2.48859
\(863\) −1.31893e54 −0.636829 −0.318415 0.947952i \(-0.603150\pi\)
−0.318415 + 0.947952i \(0.603150\pi\)
\(864\) 5.65936e53 0.267463
\(865\) −7.23685e53 −0.334774
\(866\) −2.32979e54 −1.05496
\(867\) 1.52859e53 0.0677544
\(868\) 2.01674e54 0.875053
\(869\) −3.86256e53 −0.164063
\(870\) −9.41765e53 −0.391594
\(871\) −3.30610e54 −1.34580
\(872\) 1.33295e52 0.00531200
\(873\) 2.53635e53 0.0989568
\(874\) −1.89631e54 −0.724350
\(875\) 1.32354e54 0.494982
\(876\) 1.92865e54 0.706200
\(877\) −1.88243e54 −0.674880 −0.337440 0.941347i \(-0.609561\pi\)
−0.337440 + 0.941347i \(0.609561\pi\)
\(878\) 5.78180e54 2.02962
\(879\) −5.00660e53 −0.172087
\(880\) −4.68275e53 −0.157606
\(881\) 1.05207e54 0.346728 0.173364 0.984858i \(-0.444536\pi\)
0.173364 + 0.984858i \(0.444536\pi\)
\(882\) −6.89809e53 −0.222618
\(883\) 3.19393e54 1.00937 0.504687 0.863303i \(-0.331608\pi\)
0.504687 + 0.863303i \(0.331608\pi\)
\(884\) 4.51892e54 1.39852
\(885\) −1.12462e54 −0.340842
\(886\) 7.42613e54 2.20414
\(887\) −1.83622e54 −0.533751 −0.266875 0.963731i \(-0.585991\pi\)
−0.266875 + 0.963731i \(0.585991\pi\)
\(888\) 6.92959e52 0.0197273
\(889\) 2.94231e54 0.820362
\(890\) −2.24474e54 −0.612988
\(891\) 1.69062e53 0.0452178
\(892\) −1.89222e54 −0.495704
\(893\) 2.37832e54 0.610265
\(894\) 2.94082e54 0.739135
\(895\) 1.25512e54 0.309001
\(896\) −4.68627e53 −0.113013
\(897\) −4.07754e54 −0.963249
\(898\) −4.91061e54 −1.13638
\(899\) −7.49612e54 −1.69935
\(900\) −1.22495e54 −0.272040
\(901\) 1.18299e54 0.257379
\(902\) 4.00498e54 0.853649
\(903\) −2.63645e54 −0.550550
\(904\) 6.07403e53 0.124268
\(905\) 2.69865e54 0.540939
\(906\) −4.03433e54 −0.792319
\(907\) −8.28761e52 −0.0159476 −0.00797379 0.999968i \(-0.502538\pi\)
−0.00797379 + 0.999968i \(0.502538\pi\)
\(908\) −1.33213e54 −0.251164
\(909\) −8.44083e53 −0.155938
\(910\) 3.22454e54 0.583717
\(911\) 4.90694e54 0.870404 0.435202 0.900333i \(-0.356677\pi\)
0.435202 + 0.900333i \(0.356677\pi\)
\(912\) 1.71809e54 0.298636
\(913\) −2.07473e54 −0.353388
\(914\) −5.92156e54 −0.988397
\(915\) −2.16673e54 −0.354418
\(916\) −1.02959e55 −1.65043
\(917\) 2.27091e54 0.356753
\(918\) 1.63728e54 0.252077
\(919\) −4.20928e53 −0.0635142 −0.0317571 0.999496i \(-0.510110\pi\)
−0.0317571 + 0.999496i \(0.510110\pi\)
\(920\) 2.06252e53 0.0305017
\(921\) −1.17669e54 −0.170553
\(922\) 5.87600e54 0.834757
\(923\) −2.50847e54 −0.349283
\(924\) 1.17271e54 0.160051
\(925\) −2.81686e54 −0.376828
\(926\) 6.27736e54 0.823140
\(927\) −2.22777e54 −0.286349
\(928\) −1.45915e55 −1.83849
\(929\) 8.91667e54 1.10132 0.550658 0.834731i \(-0.314377\pi\)
0.550658 + 0.834731i \(0.314377\pi\)
\(930\) 3.14066e54 0.380265
\(931\) −1.98231e54 −0.235289
\(932\) 4.41990e54 0.514302
\(933\) 7.88474e54 0.899450
\(934\) 2.26242e55 2.53021
\(935\) −1.28239e54 −0.140606
\(936\) 3.83509e53 0.0412261
\(937\) −4.22934e54 −0.445749 −0.222874 0.974847i \(-0.571544\pi\)
−0.222874 + 0.974847i \(0.571544\pi\)
\(938\) −8.30897e54 −0.858607
\(939\) −4.91621e54 −0.498101
\(940\) 4.34072e54 0.431218
\(941\) −3.94717e54 −0.384484 −0.192242 0.981348i \(-0.561576\pi\)
−0.192242 + 0.981348i \(0.561576\pi\)
\(942\) 1.04471e55 0.997820
\(943\) −1.69925e55 −1.59145
\(944\) −1.84076e55 −1.69050
\(945\) 5.67249e53 0.0510840
\(946\) −8.48806e54 −0.749588
\(947\) 1.89235e55 1.63881 0.819403 0.573218i \(-0.194305\pi\)
0.819403 + 0.573218i \(0.194305\pi\)
\(948\) 2.58650e54 0.219664
\(949\) 2.45452e55 2.04429
\(950\) −7.25009e54 −0.592184
\(951\) 8.49074e54 0.680152
\(952\) −6.76805e53 −0.0531716
\(953\) −8.10408e54 −0.624432 −0.312216 0.950011i \(-0.601071\pi\)
−0.312216 + 0.950011i \(0.601071\pi\)
\(954\) −1.68471e54 −0.127315
\(955\) −7.40774e54 −0.549064
\(956\) 6.30194e54 0.458145
\(957\) −4.35891e54 −0.310819
\(958\) 1.82089e55 1.27357
\(959\) −8.49839e54 −0.583032
\(960\) 2.79081e54 0.187807
\(961\) 9.84956e54 0.650181
\(962\) −1.47987e55 −0.958263
\(963\) 7.05628e53 0.0448218
\(964\) 1.51486e55 0.943947
\(965\) −8.57787e54 −0.524354
\(966\) −1.02478e55 −0.614544
\(967\) 5.03527e54 0.296233 0.148116 0.988970i \(-0.452679\pi\)
0.148116 + 0.988970i \(0.452679\pi\)
\(968\) 1.13355e54 0.0654252
\(969\) 4.70506e54 0.266425
\(970\) 2.73984e54 0.152212
\(971\) 3.61276e54 0.196917 0.0984585 0.995141i \(-0.468609\pi\)
0.0984585 + 0.995141i \(0.468609\pi\)
\(972\) −1.13210e54 −0.0605421
\(973\) −1.86343e55 −0.977746
\(974\) −1.92516e55 −0.991120
\(975\) −1.55895e55 −0.787493
\(976\) −3.54649e55 −1.75783
\(977\) 3.31889e55 1.61415 0.807075 0.590449i \(-0.201049\pi\)
0.807075 + 0.590449i \(0.201049\pi\)
\(978\) −2.21164e55 −1.05547
\(979\) −1.03897e55 −0.486544
\(980\) −3.61795e54 −0.166257
\(981\) −5.00765e53 −0.0225818
\(982\) 3.54892e55 1.57048
\(983\) −2.95416e55 −1.28290 −0.641451 0.767164i \(-0.721667\pi\)
−0.641451 + 0.767164i \(0.721667\pi\)
\(984\) 1.59821e54 0.0681123
\(985\) −7.03334e54 −0.294165
\(986\) −4.22137e55 −1.73273
\(987\) 1.28526e55 0.517754
\(988\) −1.84936e55 −0.731168
\(989\) 3.60136e55 1.39745
\(990\) 1.82626e54 0.0695522
\(991\) 3.55938e55 1.33049 0.665245 0.746625i \(-0.268327\pi\)
0.665245 + 0.746625i \(0.268327\pi\)
\(992\) 4.86605e55 1.78530
\(993\) 2.52373e55 0.908827
\(994\) −6.30435e54 −0.222839
\(995\) 1.36225e55 0.472641
\(996\) 1.38931e55 0.473152
\(997\) 9.42016e54 0.314918 0.157459 0.987526i \(-0.449670\pi\)
0.157459 + 0.987526i \(0.449670\pi\)
\(998\) 6.07605e55 1.99391
\(999\) −2.60333e54 −0.0838624
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 \(a_p\))