Properties

Label 3.38.a.b.1.3
Level 3
Weight 38
Character 3.1
Self dual Yes
Analytic conductor 26.014
Analytic rank 0
Dimension 4
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: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15}\cdot 3^{10}\cdot 5\cdot 7 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-35434.6\)
Character \(\chi\) = 3.1

$q$-expansion

\(f(q)\) \(=\) \(q+322000. q^{2} +3.87420e8 q^{3} -3.37552e10 q^{4} +1.53382e13 q^{5} +1.24749e14 q^{6} +2.48687e15 q^{7} -5.51245e16 q^{8} +1.50095e17 q^{9} +O(q^{10})\) \(q+322000. q^{2} +3.87420e8 q^{3} -3.37552e10 q^{4} +1.53382e13 q^{5} +1.24749e14 q^{6} +2.48687e15 q^{7} -5.51245e16 q^{8} +1.50095e17 q^{9} +4.93889e18 q^{10} -1.32093e18 q^{11} -1.30775e19 q^{12} +1.53342e20 q^{13} +8.00770e20 q^{14} +5.94233e21 q^{15} -1.31108e22 q^{16} +1.04822e23 q^{17} +4.83304e22 q^{18} -6.96548e23 q^{19} -5.17744e23 q^{20} +9.63463e23 q^{21} -4.25339e23 q^{22} +1.11946e25 q^{23} -2.13563e25 q^{24} +1.62501e26 q^{25} +4.93762e25 q^{26} +5.81497e25 q^{27} -8.39448e25 q^{28} +1.43220e27 q^{29} +1.91343e27 q^{30} +3.90372e26 q^{31} +3.35459e27 q^{32} -5.11755e26 q^{33} +3.37525e28 q^{34} +3.81440e28 q^{35} -5.06648e27 q^{36} -8.53226e28 q^{37} -2.24288e29 q^{38} +5.94080e28 q^{39} -8.45509e29 q^{40} +4.51987e29 q^{41} +3.10235e29 q^{42} -2.04528e30 q^{43} +4.45883e28 q^{44} +2.30218e30 q^{45} +3.60466e30 q^{46} -3.80345e30 q^{47} -5.07938e30 q^{48} -1.23776e31 q^{49} +5.23251e31 q^{50} +4.06100e31 q^{51} -5.17611e30 q^{52} +2.08682e31 q^{53} +1.87242e31 q^{54} -2.02607e31 q^{55} -1.37087e32 q^{56} -2.69857e32 q^{57} +4.61167e32 q^{58} -1.01104e33 q^{59} -2.00585e32 q^{60} -1.04937e33 q^{61} +1.25699e32 q^{62} +3.73265e32 q^{63} +2.88211e33 q^{64} +2.35199e33 q^{65} -1.64785e32 q^{66} +2.33599e33 q^{67} -3.53828e33 q^{68} +4.33702e33 q^{69} +1.22824e34 q^{70} +1.08272e33 q^{71} -8.27388e33 q^{72} -3.23026e34 q^{73} -2.74738e34 q^{74} +6.29560e34 q^{75} +2.35121e34 q^{76} -3.28498e33 q^{77} +1.91293e34 q^{78} -2.35299e35 q^{79} -2.01095e35 q^{80} +2.25284e34 q^{81} +1.45540e35 q^{82} -1.58763e35 q^{83} -3.25219e34 q^{84} +1.60777e36 q^{85} -6.58578e35 q^{86} +5.54863e35 q^{87} +7.28155e34 q^{88} -3.16700e35 q^{89} +7.41301e35 q^{90} +3.81342e35 q^{91} -3.77876e35 q^{92} +1.51238e35 q^{93} -1.22471e36 q^{94} -1.06838e37 q^{95} +1.29964e36 q^{96} +6.89438e36 q^{97} -3.98559e36 q^{98} -1.98265e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 437562q^{2} + 1549681956q^{3} + 346098955492q^{4} - 4099829756904q^{5} + 169520484007818q^{6} + 6605809948153184q^{7} + 140484113342159976q^{8} + 600378541187996484q^{9} + O(q^{10}) \) \( 4q + 437562q^{2} + 1549681956q^{3} + 346098955492q^{4} - 4099829756904q^{5} + 169520484007818q^{6} + 6605809948153184q^{7} + 140484113342159976q^{8} + 600378541187996484q^{9} - 21511023001649316q^{10} + 20953708852195292976q^{11} + \)\(13\!\cdots\!88\)\(q^{12} + 51830892788989874168q^{13} - \)\(18\!\cdots\!12\)\(q^{14} - \)\(15\!\cdots\!56\)\(q^{15} + \)\(55\!\cdots\!40\)\(q^{16} + \)\(81\!\cdots\!28\)\(q^{17} + \)\(65\!\cdots\!02\)\(q^{18} - \)\(54\!\cdots\!32\)\(q^{19} - \)\(35\!\cdots\!76\)\(q^{20} + \)\(25\!\cdots\!76\)\(q^{21} + \)\(23\!\cdots\!76\)\(q^{22} - \)\(61\!\cdots\!88\)\(q^{23} + \)\(54\!\cdots\!64\)\(q^{24} + \)\(95\!\cdots\!16\)\(q^{25} + \)\(42\!\cdots\!88\)\(q^{26} + \)\(23\!\cdots\!76\)\(q^{27} + \)\(24\!\cdots\!48\)\(q^{28} + \)\(41\!\cdots\!36\)\(q^{29} - \)\(83\!\cdots\!24\)\(q^{30} + \)\(89\!\cdots\!64\)\(q^{31} + \)\(36\!\cdots\!84\)\(q^{32} + \)\(81\!\cdots\!64\)\(q^{33} + \)\(31\!\cdots\!24\)\(q^{34} + \)\(42\!\cdots\!40\)\(q^{35} + \)\(51\!\cdots\!32\)\(q^{36} + \)\(55\!\cdots\!24\)\(q^{37} - \)\(73\!\cdots\!68\)\(q^{38} + \)\(20\!\cdots\!52\)\(q^{39} - \)\(26\!\cdots\!52\)\(q^{40} - \)\(86\!\cdots\!76\)\(q^{41} - \)\(70\!\cdots\!68\)\(q^{42} - \)\(50\!\cdots\!80\)\(q^{43} + \)\(28\!\cdots\!36\)\(q^{44} - \)\(61\!\cdots\!84\)\(q^{45} - \)\(14\!\cdots\!96\)\(q^{46} + \)\(42\!\cdots\!20\)\(q^{47} + \)\(21\!\cdots\!60\)\(q^{48} + \)\(40\!\cdots\!20\)\(q^{49} + \)\(10\!\cdots\!14\)\(q^{50} + \)\(31\!\cdots\!92\)\(q^{51} + \)\(18\!\cdots\!68\)\(q^{52} - \)\(12\!\cdots\!88\)\(q^{53} + \)\(25\!\cdots\!78\)\(q^{54} - \)\(32\!\cdots\!24\)\(q^{55} + \)\(49\!\cdots\!80\)\(q^{56} - \)\(21\!\cdots\!48\)\(q^{57} - \)\(75\!\cdots\!56\)\(q^{58} - \)\(13\!\cdots\!88\)\(q^{59} - \)\(13\!\cdots\!64\)\(q^{60} - \)\(12\!\cdots\!60\)\(q^{61} - \)\(37\!\cdots\!92\)\(q^{62} + \)\(99\!\cdots\!64\)\(q^{63} + \)\(85\!\cdots\!28\)\(q^{64} + \)\(15\!\cdots\!68\)\(q^{65} + \)\(92\!\cdots\!64\)\(q^{66} + \)\(16\!\cdots\!48\)\(q^{67} + \)\(63\!\cdots\!84\)\(q^{68} - \)\(23\!\cdots\!32\)\(q^{69} + \)\(82\!\cdots\!60\)\(q^{70} + \)\(10\!\cdots\!88\)\(q^{71} + \)\(21\!\cdots\!96\)\(q^{72} - \)\(19\!\cdots\!48\)\(q^{73} - \)\(89\!\cdots\!12\)\(q^{74} + \)\(36\!\cdots\!24\)\(q^{75} - \)\(95\!\cdots\!68\)\(q^{76} - \)\(25\!\cdots\!92\)\(q^{77} + \)\(16\!\cdots\!32\)\(q^{78} + \)\(42\!\cdots\!20\)\(q^{79} - \)\(95\!\cdots\!36\)\(q^{80} + \)\(90\!\cdots\!64\)\(q^{81} + \)\(33\!\cdots\!48\)\(q^{82} - \)\(46\!\cdots\!24\)\(q^{83} + \)\(95\!\cdots\!72\)\(q^{84} + \)\(18\!\cdots\!12\)\(q^{85} - \)\(36\!\cdots\!04\)\(q^{86} + \)\(16\!\cdots\!04\)\(q^{87} + \)\(42\!\cdots\!56\)\(q^{88} - \)\(31\!\cdots\!52\)\(q^{89} - \)\(32\!\cdots\!36\)\(q^{90} + \)\(26\!\cdots\!24\)\(q^{91} - \)\(16\!\cdots\!16\)\(q^{92} + \)\(34\!\cdots\!96\)\(q^{93} - \)\(57\!\cdots\!48\)\(q^{94} - \)\(89\!\cdots\!56\)\(q^{95} + \)\(14\!\cdots\!76\)\(q^{96} + \)\(44\!\cdots\!48\)\(q^{97} - \)\(43\!\cdots\!78\)\(q^{98} + \)\(31\!\cdots\!96\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 322000. 0.868561 0.434281 0.900778i \(-0.357003\pi\)
0.434281 + 0.900778i \(0.357003\pi\)
\(3\) 3.87420e8 0.577350
\(4\) −3.37552e10 −0.245602
\(5\) 1.53382e13 1.79816 0.899081 0.437781i \(-0.144236\pi\)
0.899081 + 0.437781i \(0.144236\pi\)
\(6\) 1.24749e14 0.501464
\(7\) 2.48687e15 0.577216 0.288608 0.957447i \(-0.406807\pi\)
0.288608 + 0.957447i \(0.406807\pi\)
\(8\) −5.51245e16 −1.08188
\(9\) 1.50095e17 0.333333
\(10\) 4.93889e18 1.56181
\(11\) −1.32093e18 −0.0716333 −0.0358167 0.999358i \(-0.511403\pi\)
−0.0358167 + 0.999358i \(0.511403\pi\)
\(12\) −1.30775e19 −0.141798
\(13\) 1.53342e20 0.378190 0.189095 0.981959i \(-0.439445\pi\)
0.189095 + 0.981959i \(0.439445\pi\)
\(14\) 8.00770e20 0.501348
\(15\) 5.94233e21 1.03817
\(16\) −1.31108e22 −0.694078
\(17\) 1.04822e23 1.80778 0.903890 0.427765i \(-0.140699\pi\)
0.903890 + 0.427765i \(0.140699\pi\)
\(18\) 4.83304e22 0.289520
\(19\) −6.96548e23 −1.53465 −0.767325 0.641258i \(-0.778413\pi\)
−0.767325 + 0.641258i \(0.778413\pi\)
\(20\) −5.17744e23 −0.441632
\(21\) 9.63463e23 0.333256
\(22\) −4.25339e23 −0.0622179
\(23\) 1.11946e25 0.719521 0.359761 0.933045i \(-0.382858\pi\)
0.359761 + 0.933045i \(0.382858\pi\)
\(24\) −2.13563e25 −0.624624
\(25\) 1.62501e26 2.23339
\(26\) 4.93762e25 0.328481
\(27\) 5.81497e25 0.192450
\(28\) −8.39448e25 −0.141765
\(29\) 1.43220e27 1.26369 0.631845 0.775095i \(-0.282298\pi\)
0.631845 + 0.775095i \(0.282298\pi\)
\(30\) 1.91343e27 0.901714
\(31\) 3.90372e26 0.100297 0.0501484 0.998742i \(-0.484031\pi\)
0.0501484 + 0.998742i \(0.484031\pi\)
\(32\) 3.35459e27 0.479032
\(33\) −5.11755e26 −0.0413575
\(34\) 3.37525e28 1.57017
\(35\) 3.81440e28 1.03793
\(36\) −5.06648e27 −0.0818672
\(37\) −8.53226e28 −0.830486 −0.415243 0.909711i \(-0.636303\pi\)
−0.415243 + 0.909711i \(0.636303\pi\)
\(38\) −2.24288e29 −1.33294
\(39\) 5.94080e28 0.218348
\(40\) −8.45509e29 −1.94540
\(41\) 4.51987e29 0.658605 0.329302 0.944225i \(-0.393186\pi\)
0.329302 + 0.944225i \(0.393186\pi\)
\(42\) 3.10235e29 0.289453
\(43\) −2.04528e30 −1.23477 −0.617384 0.786662i \(-0.711808\pi\)
−0.617384 + 0.786662i \(0.711808\pi\)
\(44\) 4.45883e28 0.0175933
\(45\) 2.30218e30 0.599388
\(46\) 3.60466e30 0.624948
\(47\) −3.80345e30 −0.442963 −0.221481 0.975165i \(-0.571089\pi\)
−0.221481 + 0.975165i \(0.571089\pi\)
\(48\) −5.07938e30 −0.400726
\(49\) −1.23776e31 −0.666821
\(50\) 5.23251e31 1.93984
\(51\) 4.06100e31 1.04372
\(52\) −5.17611e30 −0.0928841
\(53\) 2.08682e31 0.263257 0.131629 0.991299i \(-0.457979\pi\)
0.131629 + 0.991299i \(0.457979\pi\)
\(54\) 1.87242e31 0.167155
\(55\) −2.02607e31 −0.128808
\(56\) −1.37087e32 −0.624480
\(57\) −2.69857e32 −0.886031
\(58\) 4.61167e32 1.09759
\(59\) −1.01104e33 −1.75390 −0.876952 0.480578i \(-0.840427\pi\)
−0.876952 + 0.480578i \(0.840427\pi\)
\(60\) −2.00585e32 −0.254976
\(61\) −1.04937e33 −0.982484 −0.491242 0.871023i \(-0.663457\pi\)
−0.491242 + 0.871023i \(0.663457\pi\)
\(62\) 1.25699e32 0.0871138
\(63\) 3.73265e32 0.192405
\(64\) 2.88211e33 1.11015
\(65\) 2.35199e33 0.680047
\(66\) −1.64785e32 −0.0359215
\(67\) 2.33599e33 0.385557 0.192778 0.981242i \(-0.438250\pi\)
0.192778 + 0.981242i \(0.438250\pi\)
\(68\) −3.53828e33 −0.443994
\(69\) 4.33702e33 0.415416
\(70\) 1.22824e34 0.901505
\(71\) 1.08272e33 0.0611275 0.0305637 0.999533i \(-0.490270\pi\)
0.0305637 + 0.999533i \(0.490270\pi\)
\(72\) −8.27388e33 −0.360627
\(73\) −3.23026e34 −1.09085 −0.545424 0.838160i \(-0.683631\pi\)
−0.545424 + 0.838160i \(0.683631\pi\)
\(74\) −2.74738e34 −0.721328
\(75\) 6.29560e34 1.28945
\(76\) 2.35121e34 0.376913
\(77\) −3.28498e33 −0.0413479
\(78\) 1.91293e34 0.189649
\(79\) −2.35299e35 −1.84297 −0.921486 0.388411i \(-0.873024\pi\)
−0.921486 + 0.388411i \(0.873024\pi\)
\(80\) −2.01095e35 −1.24807
\(81\) 2.25284e34 0.111111
\(82\) 1.45540e35 0.572038
\(83\) −1.58763e35 −0.498660 −0.249330 0.968419i \(-0.580210\pi\)
−0.249330 + 0.968419i \(0.580210\pi\)
\(84\) −3.25219e34 −0.0818483
\(85\) 1.60777e36 3.25068
\(86\) −6.58578e35 −1.07247
\(87\) 5.54863e35 0.729591
\(88\) 7.28155e34 0.0774987
\(89\) −3.16700e35 −0.273484 −0.136742 0.990607i \(-0.543663\pi\)
−0.136742 + 0.990607i \(0.543663\pi\)
\(90\) 7.41301e35 0.520605
\(91\) 3.81342e35 0.218298
\(92\) −3.77876e35 −0.176716
\(93\) 1.51238e35 0.0579064
\(94\) −1.22471e36 −0.384740
\(95\) −1.06838e37 −2.75955
\(96\) 1.29964e36 0.276569
\(97\) 6.89438e36 1.21121 0.605603 0.795767i \(-0.292932\pi\)
0.605603 + 0.795767i \(0.292932\pi\)
\(98\) −3.98559e36 −0.579175
\(99\) −1.98265e35 −0.0238778
\(100\) −5.48524e36 −0.548524
\(101\) 8.14698e36 0.677721 0.338861 0.940837i \(-0.389958\pi\)
0.338861 + 0.940837i \(0.389958\pi\)
\(102\) 1.30764e37 0.906536
\(103\) −1.09944e37 −0.636329 −0.318165 0.948036i \(-0.603066\pi\)
−0.318165 + 0.948036i \(0.603066\pi\)
\(104\) −8.45291e36 −0.409157
\(105\) 1.47778e37 0.599249
\(106\) 6.71954e36 0.228655
\(107\) 2.26830e37 0.648783 0.324392 0.945923i \(-0.394840\pi\)
0.324392 + 0.945923i \(0.394840\pi\)
\(108\) −1.96286e36 −0.0472661
\(109\) 3.74392e37 0.760216 0.380108 0.924942i \(-0.375887\pi\)
0.380108 + 0.924942i \(0.375887\pi\)
\(110\) −6.52393e36 −0.111878
\(111\) −3.30557e37 −0.479481
\(112\) −3.26047e37 −0.400633
\(113\) 1.81279e37 0.188972 0.0944858 0.995526i \(-0.469879\pi\)
0.0944858 + 0.995526i \(0.469879\pi\)
\(114\) −8.68938e37 −0.769572
\(115\) 1.71705e38 1.29382
\(116\) −4.83442e37 −0.310364
\(117\) 2.30159e37 0.126063
\(118\) −3.25554e38 −1.52337
\(119\) 2.60677e38 1.04348
\(120\) −3.27568e38 −1.12318
\(121\) −3.38295e38 −0.994869
\(122\) −3.37896e38 −0.853348
\(123\) 1.75109e38 0.380245
\(124\) −1.31771e37 −0.0246331
\(125\) 1.37646e39 2.21784
\(126\) 1.20191e38 0.167116
\(127\) 3.75363e38 0.450903 0.225451 0.974254i \(-0.427614\pi\)
0.225451 + 0.974254i \(0.427614\pi\)
\(128\) 4.66986e38 0.485198
\(129\) −7.92382e38 −0.712894
\(130\) 7.57341e38 0.590663
\(131\) 1.53812e39 1.04105 0.520525 0.853846i \(-0.325736\pi\)
0.520525 + 0.853846i \(0.325736\pi\)
\(132\) 1.72744e37 0.0101575
\(133\) −1.73222e39 −0.885825
\(134\) 7.52189e38 0.334879
\(135\) 8.91912e38 0.346057
\(136\) −5.77823e39 −1.95580
\(137\) −5.26351e39 −1.55577 −0.777885 0.628407i \(-0.783707\pi\)
−0.777885 + 0.628407i \(0.783707\pi\)
\(138\) 1.39652e39 0.360814
\(139\) 3.79319e39 0.857494 0.428747 0.903425i \(-0.358955\pi\)
0.428747 + 0.903425i \(0.358955\pi\)
\(140\) −1.28756e39 −0.254917
\(141\) −1.47353e39 −0.255745
\(142\) 3.48635e38 0.0530930
\(143\) −2.02555e38 −0.0270910
\(144\) −1.96786e39 −0.231359
\(145\) 2.19673e40 2.27232
\(146\) −1.04014e40 −0.947468
\(147\) −4.79534e39 −0.384989
\(148\) 2.88009e39 0.203969
\(149\) −2.87234e40 −1.79593 −0.897967 0.440063i \(-0.854956\pi\)
−0.897967 + 0.440063i \(0.854956\pi\)
\(150\) 2.02718e40 1.11996
\(151\) 1.01312e39 0.0494982 0.0247491 0.999694i \(-0.492121\pi\)
0.0247491 + 0.999694i \(0.492121\pi\)
\(152\) 3.83968e40 1.66031
\(153\) 1.57332e40 0.602593
\(154\) −1.05776e39 −0.0359132
\(155\) 5.98759e39 0.180350
\(156\) −2.00533e39 −0.0536267
\(157\) −3.12964e40 −0.743620 −0.371810 0.928309i \(-0.621263\pi\)
−0.371810 + 0.928309i \(0.621263\pi\)
\(158\) −7.57662e40 −1.60073
\(159\) 8.08475e39 0.151992
\(160\) 5.14533e40 0.861378
\(161\) 2.78395e40 0.415319
\(162\) 7.25413e39 0.0965068
\(163\) −6.14970e40 −0.730102 −0.365051 0.930988i \(-0.618948\pi\)
−0.365051 + 0.930988i \(0.618948\pi\)
\(164\) −1.52569e40 −0.161754
\(165\) −7.84940e39 −0.0743676
\(166\) −5.11216e40 −0.433117
\(167\) −1.95759e41 −1.48411 −0.742055 0.670339i \(-0.766149\pi\)
−0.742055 + 0.670339i \(0.766149\pi\)
\(168\) −5.31104e40 −0.360543
\(169\) −1.40887e41 −0.856972
\(170\) 5.17702e41 2.82342
\(171\) −1.04548e41 −0.511550
\(172\) 6.90388e40 0.303261
\(173\) 8.49345e40 0.335144 0.167572 0.985860i \(-0.446407\pi\)
0.167572 + 0.985860i \(0.446407\pi\)
\(174\) 1.78666e41 0.633695
\(175\) 4.04117e41 1.28915
\(176\) 1.73184e40 0.0497191
\(177\) −3.91697e41 −1.01262
\(178\) −1.01977e41 −0.237538
\(179\) 5.07222e41 1.06517 0.532583 0.846378i \(-0.321222\pi\)
0.532583 + 0.846378i \(0.321222\pi\)
\(180\) −7.77107e40 −0.147211
\(181\) 2.84986e41 0.487270 0.243635 0.969867i \(-0.421660\pi\)
0.243635 + 0.969867i \(0.421660\pi\)
\(182\) 1.22792e41 0.189605
\(183\) −4.06546e41 −0.567238
\(184\) −6.17096e41 −0.778436
\(185\) −1.30869e42 −1.49335
\(186\) 4.86985e40 0.0502952
\(187\) −1.38462e41 −0.129497
\(188\) 1.28386e41 0.108792
\(189\) 1.44611e41 0.111085
\(190\) −3.44017e42 −2.39684
\(191\) 1.34993e42 0.853483 0.426741 0.904374i \(-0.359661\pi\)
0.426741 + 0.904374i \(0.359661\pi\)
\(192\) 1.11659e42 0.640943
\(193\) 1.53006e42 0.797806 0.398903 0.916993i \(-0.369391\pi\)
0.398903 + 0.916993i \(0.369391\pi\)
\(194\) 2.21999e42 1.05201
\(195\) 9.11211e41 0.392626
\(196\) 4.17809e41 0.163772
\(197\) −1.58341e42 −0.564896 −0.282448 0.959283i \(-0.591146\pi\)
−0.282448 + 0.959283i \(0.591146\pi\)
\(198\) −6.38411e40 −0.0207393
\(199\) 3.81225e42 1.12823 0.564117 0.825695i \(-0.309217\pi\)
0.564117 + 0.825695i \(0.309217\pi\)
\(200\) −8.95775e42 −2.41626
\(201\) 9.05012e41 0.222601
\(202\) 2.62332e42 0.588642
\(203\) 3.56169e42 0.729422
\(204\) −1.37080e42 −0.256340
\(205\) 6.93266e42 1.18428
\(206\) −3.54018e42 −0.552691
\(207\) 1.68025e42 0.239840
\(208\) −2.01044e42 −0.262493
\(209\) 9.20091e41 0.109932
\(210\) 4.75844e42 0.520484
\(211\) −1.03480e43 −1.03665 −0.518325 0.855184i \(-0.673444\pi\)
−0.518325 + 0.855184i \(0.673444\pi\)
\(212\) −7.04410e41 −0.0646565
\(213\) 4.19468e41 0.0352920
\(214\) 7.30390e42 0.563508
\(215\) −3.13708e43 −2.22031
\(216\) −3.20547e42 −0.208208
\(217\) 9.70802e41 0.0578929
\(218\) 1.20554e43 0.660294
\(219\) −1.25147e43 −0.629801
\(220\) 6.83904e41 0.0316356
\(221\) 1.60736e43 0.683684
\(222\) −1.06439e43 −0.416459
\(223\) −2.53188e43 −0.911598 −0.455799 0.890083i \(-0.650646\pi\)
−0.455799 + 0.890083i \(0.650646\pi\)
\(224\) 8.34241e42 0.276505
\(225\) 2.43905e43 0.744463
\(226\) 5.83718e42 0.164133
\(227\) 5.88632e43 1.52534 0.762668 0.646790i \(-0.223889\pi\)
0.762668 + 0.646790i \(0.223889\pi\)
\(228\) 9.10909e42 0.217611
\(229\) 2.71698e43 0.598590 0.299295 0.954161i \(-0.403249\pi\)
0.299295 + 0.954161i \(0.403249\pi\)
\(230\) 5.52889e43 1.12376
\(231\) −1.27267e42 −0.0238722
\(232\) −7.89492e43 −1.36716
\(233\) −1.14243e43 −0.182703 −0.0913513 0.995819i \(-0.529119\pi\)
−0.0913513 + 0.995819i \(0.529119\pi\)
\(234\) 7.41110e42 0.109494
\(235\) −5.83380e43 −0.796520
\(236\) 3.41279e43 0.430762
\(237\) −9.11596e43 −1.06404
\(238\) 8.39379e43 0.906326
\(239\) 1.69778e43 0.169637 0.0848185 0.996396i \(-0.472969\pi\)
0.0848185 + 0.996396i \(0.472969\pi\)
\(240\) −7.79085e43 −0.720571
\(241\) −3.09126e43 −0.264740 −0.132370 0.991200i \(-0.542259\pi\)
−0.132370 + 0.991200i \(0.542259\pi\)
\(242\) −1.08931e44 −0.864104
\(243\) 8.72796e42 0.0641500
\(244\) 3.54217e43 0.241300
\(245\) −1.89850e44 −1.19905
\(246\) 5.63850e43 0.330266
\(247\) −1.06810e44 −0.580390
\(248\) −2.15190e43 −0.108509
\(249\) −6.15080e43 −0.287902
\(250\) 4.43221e44 1.92633
\(251\) 2.54005e44 1.02537 0.512683 0.858578i \(-0.328652\pi\)
0.512683 + 0.858578i \(0.328652\pi\)
\(252\) −1.25997e43 −0.0472551
\(253\) −1.47873e43 −0.0515417
\(254\) 1.20867e44 0.391637
\(255\) 6.22884e44 1.87678
\(256\) −2.45744e44 −0.688722
\(257\) −3.66815e44 −0.956499 −0.478249 0.878224i \(-0.658729\pi\)
−0.478249 + 0.878224i \(0.658729\pi\)
\(258\) −2.55147e44 −0.619192
\(259\) −2.12186e44 −0.479370
\(260\) −7.93922e43 −0.167021
\(261\) 2.14965e44 0.421230
\(262\) 4.95275e44 0.904216
\(263\) −2.74111e44 −0.466385 −0.233192 0.972431i \(-0.574917\pi\)
−0.233192 + 0.972431i \(0.574917\pi\)
\(264\) 2.82102e43 0.0447439
\(265\) 3.20080e44 0.473380
\(266\) −5.57775e44 −0.769393
\(267\) −1.22696e44 −0.157896
\(268\) −7.88521e43 −0.0946933
\(269\) 7.40366e44 0.829906 0.414953 0.909843i \(-0.363798\pi\)
0.414953 + 0.909843i \(0.363798\pi\)
\(270\) 2.87195e44 0.300571
\(271\) −3.47586e44 −0.339727 −0.169863 0.985468i \(-0.554333\pi\)
−0.169863 + 0.985468i \(0.554333\pi\)
\(272\) −1.37429e45 −1.25474
\(273\) 1.47740e44 0.126034
\(274\) −1.69485e45 −1.35128
\(275\) −2.14652e44 −0.159985
\(276\) −1.46397e44 −0.102027
\(277\) 1.55336e45 1.01250 0.506252 0.862385i \(-0.331031\pi\)
0.506252 + 0.862385i \(0.331031\pi\)
\(278\) 1.22141e45 0.744786
\(279\) 5.85927e43 0.0334322
\(280\) −2.10267e45 −1.12292
\(281\) 5.16475e44 0.258216 0.129108 0.991631i \(-0.458789\pi\)
0.129108 + 0.991631i \(0.458789\pi\)
\(282\) −4.74477e44 −0.222130
\(283\) 2.81373e45 1.23377 0.616884 0.787054i \(-0.288395\pi\)
0.616884 + 0.787054i \(0.288395\pi\)
\(284\) −3.65475e43 −0.0150130
\(285\) −4.13912e45 −1.59323
\(286\) −6.52225e43 −0.0235302
\(287\) 1.12403e45 0.380157
\(288\) 5.03506e44 0.159677
\(289\) 7.62546e45 2.26807
\(290\) 7.07347e45 1.97365
\(291\) 2.67102e45 0.699290
\(292\) 1.09038e45 0.267914
\(293\) −3.48209e45 −0.803135 −0.401568 0.915829i \(-0.631534\pi\)
−0.401568 + 0.915829i \(0.631534\pi\)
\(294\) −1.54410e45 −0.334387
\(295\) −1.55075e46 −3.15380
\(296\) 4.70336e45 0.898487
\(297\) −7.68117e43 −0.0137858
\(298\) −9.24893e45 −1.55988
\(299\) 1.71661e45 0.272116
\(300\) −2.12510e45 −0.316691
\(301\) −5.08633e45 −0.712729
\(302\) 3.26226e44 0.0429922
\(303\) 3.15631e45 0.391283
\(304\) 9.13228e45 1.06517
\(305\) −1.60954e46 −1.76667
\(306\) 5.06607e45 0.523389
\(307\) 2.84597e45 0.276803 0.138401 0.990376i \(-0.455804\pi\)
0.138401 + 0.990376i \(0.455804\pi\)
\(308\) 1.10885e44 0.0101551
\(309\) −4.25944e45 −0.367385
\(310\) 1.92800e45 0.156645
\(311\) 8.10350e45 0.620306 0.310153 0.950687i \(-0.399620\pi\)
0.310153 + 0.950687i \(0.399620\pi\)
\(312\) −3.27483e45 −0.236227
\(313\) 1.80984e46 1.23046 0.615232 0.788346i \(-0.289062\pi\)
0.615232 + 0.788346i \(0.289062\pi\)
\(314\) −1.00774e46 −0.645879
\(315\) 5.72521e45 0.345976
\(316\) 7.94257e45 0.452637
\(317\) −6.00023e45 −0.322531 −0.161266 0.986911i \(-0.551558\pi\)
−0.161266 + 0.986911i \(0.551558\pi\)
\(318\) 2.60329e45 0.132014
\(319\) −1.89183e45 −0.0905223
\(320\) 4.42063e46 1.99622
\(321\) 8.78784e45 0.374575
\(322\) 8.96430e45 0.360730
\(323\) −7.30132e46 −2.77431
\(324\) −7.60452e44 −0.0272891
\(325\) 2.49182e46 0.844646
\(326\) −1.98020e46 −0.634138
\(327\) 1.45047e46 0.438911
\(328\) −2.49155e46 −0.712532
\(329\) −9.45867e45 −0.255686
\(330\) −2.52750e45 −0.0645928
\(331\) 1.64524e46 0.397567 0.198784 0.980043i \(-0.436301\pi\)
0.198784 + 0.980043i \(0.436301\pi\)
\(332\) 5.35908e45 0.122472
\(333\) −1.28065e46 −0.276829
\(334\) −6.30341e46 −1.28904
\(335\) 3.58299e46 0.693293
\(336\) −1.26317e46 −0.231306
\(337\) 6.90318e46 1.19645 0.598227 0.801327i \(-0.295872\pi\)
0.598227 + 0.801327i \(0.295872\pi\)
\(338\) −4.53655e46 −0.744333
\(339\) 7.02312e45 0.109103
\(340\) −5.42708e46 −0.798373
\(341\) −5.15654e44 −0.00718459
\(342\) −3.36644e46 −0.444312
\(343\) −7.69430e46 −0.962117
\(344\) 1.12745e47 1.33587
\(345\) 6.65220e46 0.746985
\(346\) 2.73489e46 0.291093
\(347\) 3.75519e46 0.378911 0.189455 0.981889i \(-0.439328\pi\)
0.189455 + 0.981889i \(0.439328\pi\)
\(348\) −1.87295e46 −0.179189
\(349\) −1.14417e47 −1.03805 −0.519026 0.854758i \(-0.673705\pi\)
−0.519026 + 0.854758i \(0.673705\pi\)
\(350\) 1.30126e47 1.11971
\(351\) 8.91682e45 0.0727827
\(352\) −4.43118e45 −0.0343147
\(353\) 9.61675e46 0.706637 0.353318 0.935503i \(-0.385053\pi\)
0.353318 + 0.935503i \(0.385053\pi\)
\(354\) −1.26126e47 −0.879519
\(355\) 1.66070e46 0.109917
\(356\) 1.06903e46 0.0671682
\(357\) 1.00992e47 0.602454
\(358\) 1.63325e47 0.925161
\(359\) −3.14753e45 −0.0169326 −0.00846629 0.999964i \(-0.502695\pi\)
−0.00846629 + 0.999964i \(0.502695\pi\)
\(360\) −1.26906e47 −0.648466
\(361\) 2.79171e47 1.35515
\(362\) 9.17654e46 0.423224
\(363\) −1.31062e47 −0.574388
\(364\) −1.28723e46 −0.0536143
\(365\) −4.95463e47 −1.96152
\(366\) −1.30908e47 −0.492681
\(367\) −6.18183e46 −0.221205 −0.110603 0.993865i \(-0.535278\pi\)
−0.110603 + 0.993865i \(0.535278\pi\)
\(368\) −1.46770e47 −0.499404
\(369\) 6.78408e46 0.219535
\(370\) −4.21399e47 −1.29706
\(371\) 5.18963e46 0.151957
\(372\) −5.10507e45 −0.0142219
\(373\) −6.43130e47 −1.70485 −0.852424 0.522852i \(-0.824868\pi\)
−0.852424 + 0.522852i \(0.824868\pi\)
\(374\) −4.45847e46 −0.112476
\(375\) 5.33270e47 1.28047
\(376\) 2.09663e47 0.479233
\(377\) 2.19617e47 0.477915
\(378\) 4.65646e46 0.0964844
\(379\) 8.24615e47 1.62714 0.813572 0.581464i \(-0.197520\pi\)
0.813572 + 0.581464i \(0.197520\pi\)
\(380\) 3.60634e47 0.677751
\(381\) 1.45423e47 0.260329
\(382\) 4.34678e47 0.741302
\(383\) −1.05734e48 −1.71806 −0.859032 0.511922i \(-0.828934\pi\)
−0.859032 + 0.511922i \(0.828934\pi\)
\(384\) 1.80920e47 0.280129
\(385\) −5.03856e46 −0.0743503
\(386\) 4.92678e47 0.692944
\(387\) −3.06985e47 −0.411590
\(388\) −2.32721e47 −0.297474
\(389\) −3.81308e46 −0.0464738 −0.0232369 0.999730i \(-0.507397\pi\)
−0.0232369 + 0.999730i \(0.507397\pi\)
\(390\) 2.93409e47 0.341019
\(391\) 1.17343e48 1.30074
\(392\) 6.82309e47 0.721421
\(393\) 5.95900e47 0.601051
\(394\) −5.09858e47 −0.490647
\(395\) −3.60906e48 −3.31396
\(396\) 6.69247e45 0.00586442
\(397\) −3.87592e47 −0.324153 −0.162077 0.986778i \(-0.551819\pi\)
−0.162077 + 0.986778i \(0.551819\pi\)
\(398\) 1.22754e48 0.979941
\(399\) −6.71098e47 −0.511432
\(400\) −2.13051e48 −1.55015
\(401\) 1.24335e48 0.863820 0.431910 0.901917i \(-0.357840\pi\)
0.431910 + 0.901917i \(0.357840\pi\)
\(402\) 2.91414e47 0.193343
\(403\) 5.98605e46 0.0379312
\(404\) −2.75003e47 −0.166450
\(405\) 3.45545e47 0.199796
\(406\) 1.14686e48 0.633548
\(407\) 1.12705e47 0.0594905
\(408\) −2.23860e48 −1.12918
\(409\) 1.71559e48 0.827053 0.413527 0.910492i \(-0.364297\pi\)
0.413527 + 0.910492i \(0.364297\pi\)
\(410\) 2.23231e48 1.02862
\(411\) −2.03919e48 −0.898224
\(412\) 3.71118e47 0.156284
\(413\) −2.51432e48 −1.01238
\(414\) 5.41039e47 0.208316
\(415\) −2.43514e48 −0.896672
\(416\) 5.14400e47 0.181165
\(417\) 1.46956e48 0.495075
\(418\) 2.96269e47 0.0954827
\(419\) 2.35400e48 0.725851 0.362925 0.931818i \(-0.381778\pi\)
0.362925 + 0.931818i \(0.381778\pi\)
\(420\) −4.98828e47 −0.147177
\(421\) 3.28974e48 0.928844 0.464422 0.885614i \(-0.346262\pi\)
0.464422 + 0.885614i \(0.346262\pi\)
\(422\) −3.33206e48 −0.900393
\(423\) −5.70878e47 −0.147654
\(424\) −1.15035e48 −0.284813
\(425\) 1.70336e49 4.03748
\(426\) 1.35068e47 0.0306532
\(427\) −2.60964e48 −0.567106
\(428\) −7.65669e47 −0.159342
\(429\) −7.84738e46 −0.0156410
\(430\) −1.01014e49 −1.92848
\(431\) −4.39374e48 −0.803534 −0.401767 0.915742i \(-0.631604\pi\)
−0.401767 + 0.915742i \(0.631604\pi\)
\(432\) −7.62387e47 −0.133575
\(433\) 1.65722e48 0.278198 0.139099 0.990279i \(-0.455579\pi\)
0.139099 + 0.990279i \(0.455579\pi\)
\(434\) 3.12598e47 0.0502835
\(435\) 8.51060e48 1.31192
\(436\) −1.26377e48 −0.186710
\(437\) −7.79757e48 −1.10421
\(438\) −4.02972e48 −0.547021
\(439\) 4.30529e48 0.560285 0.280142 0.959958i \(-0.409618\pi\)
0.280142 + 0.959958i \(0.409618\pi\)
\(440\) 1.11686e48 0.139355
\(441\) −1.85781e48 −0.222274
\(442\) 5.17569e48 0.593822
\(443\) −7.44863e48 −0.819611 −0.409805 0.912173i \(-0.634403\pi\)
−0.409805 + 0.912173i \(0.634403\pi\)
\(444\) 1.11580e48 0.117761
\(445\) −4.85760e48 −0.491769
\(446\) −8.15264e48 −0.791778
\(447\) −1.11280e49 −1.03688
\(448\) 7.16741e48 0.640795
\(449\) −1.42651e49 −1.22382 −0.611909 0.790928i \(-0.709598\pi\)
−0.611909 + 0.790928i \(0.709598\pi\)
\(450\) 7.85372e48 0.646612
\(451\) −5.97043e47 −0.0471780
\(452\) −6.11912e47 −0.0464118
\(453\) 3.92505e47 0.0285778
\(454\) 1.89539e49 1.32485
\(455\) 5.84910e48 0.392535
\(456\) 1.48757e49 0.958580
\(457\) 2.02914e49 1.25563 0.627817 0.778361i \(-0.283948\pi\)
0.627817 + 0.778361i \(0.283948\pi\)
\(458\) 8.74865e48 0.519912
\(459\) 6.09535e48 0.347907
\(460\) −5.79594e48 −0.317763
\(461\) 1.29918e49 0.684232 0.342116 0.939658i \(-0.388856\pi\)
0.342116 + 0.939658i \(0.388856\pi\)
\(462\) −4.09798e47 −0.0207345
\(463\) −1.83380e49 −0.891463 −0.445731 0.895167i \(-0.647056\pi\)
−0.445731 + 0.895167i \(0.647056\pi\)
\(464\) −1.87772e49 −0.877099
\(465\) 2.31972e48 0.104125
\(466\) −3.67861e48 −0.158688
\(467\) 1.14081e49 0.472987 0.236494 0.971633i \(-0.424002\pi\)
0.236494 + 0.971633i \(0.424002\pi\)
\(468\) −7.76906e47 −0.0309614
\(469\) 5.80931e48 0.222550
\(470\) −1.87848e49 −0.691826
\(471\) −1.21249e49 −0.429329
\(472\) 5.57330e49 1.89752
\(473\) 2.70167e48 0.0884506
\(474\) −2.93534e49 −0.924184
\(475\) −1.13189e50 −3.42747
\(476\) −8.79922e48 −0.256281
\(477\) 3.13220e48 0.0877525
\(478\) 5.46685e48 0.147340
\(479\) −2.24706e48 −0.0582649 −0.0291324 0.999576i \(-0.509274\pi\)
−0.0291324 + 0.999576i \(0.509274\pi\)
\(480\) 1.99341e49 0.497317
\(481\) −1.30836e49 −0.314082
\(482\) −9.95383e48 −0.229943
\(483\) 1.07856e49 0.239785
\(484\) 1.14192e49 0.244341
\(485\) 1.05747e50 2.17794
\(486\) 2.81040e48 0.0557182
\(487\) −6.62105e49 −1.26369 −0.631846 0.775094i \(-0.717702\pi\)
−0.631846 + 0.775094i \(0.717702\pi\)
\(488\) 5.78458e49 1.06293
\(489\) −2.38252e49 −0.421524
\(490\) −6.11317e49 −1.04145
\(491\) 1.27151e49 0.208599 0.104300 0.994546i \(-0.466740\pi\)
0.104300 + 0.994546i \(0.466740\pi\)
\(492\) −5.91085e48 −0.0933890
\(493\) 1.50125e50 2.28447
\(494\) −3.43929e49 −0.504104
\(495\) −3.04102e48 −0.0429361
\(496\) −5.11807e48 −0.0696138
\(497\) 2.69258e48 0.0352838
\(498\) −1.98056e49 −0.250060
\(499\) −1.07378e49 −0.130633 −0.0653166 0.997865i \(-0.520806\pi\)
−0.0653166 + 0.997865i \(0.520806\pi\)
\(500\) −4.64629e49 −0.544704
\(501\) −7.58409e49 −0.856851
\(502\) 8.17896e49 0.890593
\(503\) 8.93827e48 0.0938093 0.0469046 0.998899i \(-0.485064\pi\)
0.0469046 + 0.998899i \(0.485064\pi\)
\(504\) −2.05760e49 −0.208160
\(505\) 1.24960e50 1.21865
\(506\) −4.76150e48 −0.0447671
\(507\) −5.45825e49 −0.494773
\(508\) −1.26705e49 −0.110743
\(509\) 1.92539e50 1.62270 0.811352 0.584558i \(-0.198732\pi\)
0.811352 + 0.584558i \(0.198732\pi\)
\(510\) 2.00568e50 1.63010
\(511\) −8.03322e49 −0.629655
\(512\) −1.43312e50 −1.08340
\(513\) −4.05041e49 −0.295344
\(514\) −1.18114e50 −0.830778
\(515\) −1.68634e50 −1.14422
\(516\) 2.67470e49 0.175088
\(517\) 5.02409e48 0.0317309
\(518\) −6.83238e49 −0.416362
\(519\) 3.29054e49 0.193495
\(520\) −1.29652e50 −0.735731
\(521\) −1.93636e50 −1.06045 −0.530223 0.847858i \(-0.677892\pi\)
−0.530223 + 0.847858i \(0.677892\pi\)
\(522\) 6.92188e49 0.365864
\(523\) 1.09154e50 0.556875 0.278438 0.960454i \(-0.410183\pi\)
0.278438 + 0.960454i \(0.410183\pi\)
\(524\) −5.19197e49 −0.255684
\(525\) 1.56563e50 0.744291
\(526\) −8.82635e49 −0.405084
\(527\) 4.09194e49 0.181314
\(528\) 6.70950e48 0.0287053
\(529\) −1.16745e50 −0.482289
\(530\) 1.03066e50 0.411159
\(531\) −1.51752e50 −0.584635
\(532\) 5.84716e49 0.217560
\(533\) 6.93088e49 0.249078
\(534\) −3.95080e49 −0.137143
\(535\) 3.47915e50 1.16662
\(536\) −1.28770e50 −0.417126
\(537\) 1.96508e50 0.614973
\(538\) 2.38397e50 0.720824
\(539\) 1.63500e49 0.0477666
\(540\) −3.01067e49 −0.0849921
\(541\) 2.05140e50 0.559630 0.279815 0.960054i \(-0.409727\pi\)
0.279815 + 0.960054i \(0.409727\pi\)
\(542\) −1.11922e50 −0.295073
\(543\) 1.10409e50 0.281326
\(544\) 3.51633e50 0.865984
\(545\) 5.74250e50 1.36699
\(546\) 4.75721e49 0.109468
\(547\) −5.42161e50 −1.20604 −0.603021 0.797725i \(-0.706036\pi\)
−0.603021 + 0.797725i \(0.706036\pi\)
\(548\) 1.77671e50 0.382100
\(549\) −1.57504e50 −0.327495
\(550\) −6.91178e49 −0.138957
\(551\) −9.97595e50 −1.93932
\(552\) −2.39076e50 −0.449430
\(553\) −5.85157e50 −1.06379
\(554\) 5.00182e50 0.879422
\(555\) −5.07015e50 −0.862185
\(556\) −1.28040e50 −0.210602
\(557\) 7.40435e50 1.17806 0.589028 0.808113i \(-0.299511\pi\)
0.589028 + 0.808113i \(0.299511\pi\)
\(558\) 1.88668e49 0.0290379
\(559\) −3.13628e50 −0.466977
\(560\) −5.00097e50 −0.720404
\(561\) −5.36430e49 −0.0747653
\(562\) 1.66305e50 0.224276
\(563\) −5.85968e50 −0.764660 −0.382330 0.924026i \(-0.624878\pi\)
−0.382330 + 0.924026i \(0.624878\pi\)
\(564\) 4.97395e49 0.0628114
\(565\) 2.78049e50 0.339802
\(566\) 9.06020e50 1.07160
\(567\) 5.60251e49 0.0641352
\(568\) −5.96843e49 −0.0661327
\(569\) −6.38178e50 −0.684486 −0.342243 0.939611i \(-0.611187\pi\)
−0.342243 + 0.939611i \(0.611187\pi\)
\(570\) −1.33279e51 −1.38382
\(571\) 3.57695e50 0.359538 0.179769 0.983709i \(-0.442465\pi\)
0.179769 + 0.983709i \(0.442465\pi\)
\(572\) 6.83728e48 0.00665360
\(573\) 5.22991e50 0.492758
\(574\) 3.61938e50 0.330190
\(575\) 1.81913e51 1.60697
\(576\) 4.32589e50 0.370049
\(577\) −1.18260e51 −0.979680 −0.489840 0.871812i \(-0.662945\pi\)
−0.489840 + 0.871812i \(0.662945\pi\)
\(578\) 2.45540e51 1.96996
\(579\) 5.92776e50 0.460614
\(580\) −7.41513e50 −0.558086
\(581\) −3.94822e50 −0.287835
\(582\) 8.60068e50 0.607376
\(583\) −2.75654e49 −0.0188580
\(584\) 1.78066e51 1.18017
\(585\) 3.53022e50 0.226682
\(586\) −1.12123e51 −0.697572
\(587\) −2.16256e51 −1.30366 −0.651828 0.758367i \(-0.725998\pi\)
−0.651828 + 0.758367i \(0.725998\pi\)
\(588\) 1.61868e50 0.0945541
\(589\) −2.71913e50 −0.153920
\(590\) −4.99341e51 −2.73927
\(591\) −6.13446e50 −0.326143
\(592\) 1.11864e51 0.576422
\(593\) −1.31685e51 −0.657695 −0.328847 0.944383i \(-0.606660\pi\)
−0.328847 + 0.944383i \(0.606660\pi\)
\(594\) −2.47333e49 −0.0119738
\(595\) 3.99832e51 1.87635
\(596\) 9.69566e50 0.441084
\(597\) 1.47694e51 0.651387
\(598\) 5.52746e50 0.236349
\(599\) 2.09368e51 0.867990 0.433995 0.900915i \(-0.357104\pi\)
0.433995 + 0.900915i \(0.357104\pi\)
\(600\) −3.47042e51 −1.39503
\(601\) 4.42052e50 0.172304 0.0861521 0.996282i \(-0.472543\pi\)
0.0861521 + 0.996282i \(0.472543\pi\)
\(602\) −1.63780e51 −0.619048
\(603\) 3.50620e50 0.128519
\(604\) −3.41983e49 −0.0121568
\(605\) −5.18883e51 −1.78894
\(606\) 1.01633e51 0.339853
\(607\) 4.41338e51 1.43146 0.715732 0.698375i \(-0.246093\pi\)
0.715732 + 0.698375i \(0.246093\pi\)
\(608\) −2.33663e51 −0.735147
\(609\) 1.37987e51 0.421132
\(610\) −5.18271e51 −1.53446
\(611\) −5.83230e50 −0.167524
\(612\) −5.31076e50 −0.147998
\(613\) −3.52904e51 −0.954198 −0.477099 0.878850i \(-0.658312\pi\)
−0.477099 + 0.878850i \(0.658312\pi\)
\(614\) 9.16402e50 0.240420
\(615\) 2.68586e51 0.683743
\(616\) 1.81083e50 0.0447336
\(617\) 6.46795e51 1.55057 0.775284 0.631613i \(-0.217607\pi\)
0.775284 + 0.631613i \(0.217607\pi\)
\(618\) −1.37154e51 −0.319096
\(619\) −1.51171e51 −0.341344 −0.170672 0.985328i \(-0.554594\pi\)
−0.170672 + 0.985328i \(0.554594\pi\)
\(620\) −2.02113e50 −0.0442942
\(621\) 6.50963e50 0.138472
\(622\) 2.60932e51 0.538773
\(623\) −7.87590e50 −0.157860
\(624\) −7.78884e50 −0.151551
\(625\) 9.28899e51 1.75464
\(626\) 5.82766e51 1.06873
\(627\) 3.56462e50 0.0634693
\(628\) 1.05642e51 0.182634
\(629\) −8.94365e51 −1.50134
\(630\) 1.84352e51 0.300502
\(631\) −7.44924e51 −1.17915 −0.589575 0.807714i \(-0.700705\pi\)
−0.589575 + 0.807714i \(0.700705\pi\)
\(632\) 1.29707e52 1.99388
\(633\) −4.00904e51 −0.598510
\(634\) −1.93207e51 −0.280138
\(635\) 5.75739e51 0.810797
\(636\) −2.72903e50 −0.0373294
\(637\) −1.89801e51 −0.252185
\(638\) −6.09170e50 −0.0786241
\(639\) 1.62510e50 0.0203758
\(640\) 7.16271e51 0.872465
\(641\) −2.96058e51 −0.350351 −0.175176 0.984537i \(-0.556049\pi\)
−0.175176 + 0.984537i \(0.556049\pi\)
\(642\) 2.82968e51 0.325341
\(643\) −1.66529e52 −1.86032 −0.930159 0.367157i \(-0.880331\pi\)
−0.930159 + 0.367157i \(0.880331\pi\)
\(644\) −9.39728e50 −0.102003
\(645\) −1.21537e52 −1.28190
\(646\) −2.35102e52 −2.40966
\(647\) −3.47499e51 −0.346118 −0.173059 0.984911i \(-0.555365\pi\)
−0.173059 + 0.984911i \(0.555365\pi\)
\(648\) −1.24187e51 −0.120209
\(649\) 1.33551e51 0.125638
\(650\) 8.02365e51 0.733627
\(651\) 3.76109e50 0.0334245
\(652\) 2.07585e51 0.179314
\(653\) 1.71299e51 0.143834 0.0719169 0.997411i \(-0.477088\pi\)
0.0719169 + 0.997411i \(0.477088\pi\)
\(654\) 4.67052e51 0.381221
\(655\) 2.35920e52 1.87198
\(656\) −5.92590e51 −0.457123
\(657\) −4.84844e51 −0.363616
\(658\) −3.04569e51 −0.222078
\(659\) 7.36499e51 0.522146 0.261073 0.965319i \(-0.415924\pi\)
0.261073 + 0.965319i \(0.415924\pi\)
\(660\) 2.64958e50 0.0182648
\(661\) 1.02642e52 0.688017 0.344009 0.938967i \(-0.388215\pi\)
0.344009 + 0.938967i \(0.388215\pi\)
\(662\) 5.29765e51 0.345311
\(663\) 6.22724e51 0.394725
\(664\) 8.75173e51 0.539491
\(665\) −2.65691e52 −1.59286
\(666\) −4.12368e51 −0.240443
\(667\) 1.60329e52 0.909251
\(668\) 6.60788e51 0.364500
\(669\) −9.80903e51 −0.526311
\(670\) 1.15372e52 0.602168
\(671\) 1.38614e51 0.0703786
\(672\) 3.23202e51 0.159640
\(673\) −1.32994e52 −0.639077 −0.319539 0.947573i \(-0.603528\pi\)
−0.319539 + 0.947573i \(0.603528\pi\)
\(674\) 2.22282e52 1.03919
\(675\) 9.44936e51 0.429816
\(676\) 4.75567e51 0.210474
\(677\) 8.79193e51 0.378611 0.189306 0.981918i \(-0.439376\pi\)
0.189306 + 0.981918i \(0.439376\pi\)
\(678\) 2.26144e51 0.0947624
\(679\) 1.71454e52 0.699128
\(680\) −8.86276e52 −3.51685
\(681\) 2.28048e52 0.880654
\(682\) −1.66040e50 −0.00624025
\(683\) 2.88301e52 1.05454 0.527269 0.849698i \(-0.323216\pi\)
0.527269 + 0.849698i \(0.323216\pi\)
\(684\) 3.52905e51 0.125638
\(685\) −8.07328e52 −2.79753
\(686\) −2.47756e52 −0.835657
\(687\) 1.05261e52 0.345596
\(688\) 2.68151e52 0.857026
\(689\) 3.19997e51 0.0995614
\(690\) 2.14200e52 0.648802
\(691\) −6.30524e52 −1.85933 −0.929667 0.368401i \(-0.879905\pi\)
−0.929667 + 0.368401i \(0.879905\pi\)
\(692\) −2.86698e51 −0.0823119
\(693\) −4.93057e50 −0.0137826
\(694\) 1.20917e52 0.329107
\(695\) 5.81807e52 1.54191
\(696\) −3.05865e52 −0.789331
\(697\) 4.73780e52 1.19061
\(698\) −3.68422e52 −0.901612
\(699\) −4.42600e51 −0.105483
\(700\) −1.36411e52 −0.316617
\(701\) −4.33208e52 −0.979294 −0.489647 0.871921i \(-0.662874\pi\)
−0.489647 + 0.871921i \(0.662874\pi\)
\(702\) 2.87121e51 0.0632162
\(703\) 5.94313e52 1.27451
\(704\) −3.80706e51 −0.0795235
\(705\) −2.26014e52 −0.459871
\(706\) 3.09659e52 0.613757
\(707\) 2.02605e52 0.391192
\(708\) 1.32218e52 0.248700
\(709\) −2.56002e52 −0.469124 −0.234562 0.972101i \(-0.575366\pi\)
−0.234562 + 0.972101i \(0.575366\pi\)
\(710\) 5.34743e51 0.0954698
\(711\) −3.53171e52 −0.614324
\(712\) 1.74579e52 0.295877
\(713\) 4.37005e51 0.0721656
\(714\) 3.25193e52 0.523268
\(715\) −3.10682e51 −0.0487141
\(716\) −1.71214e52 −0.261606
\(717\) 6.57755e51 0.0979399
\(718\) −1.01350e51 −0.0147070
\(719\) 6.18204e52 0.874274 0.437137 0.899395i \(-0.355992\pi\)
0.437137 + 0.899395i \(0.355992\pi\)
\(720\) −3.01833e52 −0.416022
\(721\) −2.73415e52 −0.367300
\(722\) 8.98931e52 1.17703
\(723\) −1.19762e52 −0.152848
\(724\) −9.61978e51 −0.119674
\(725\) 2.32733e53 2.82231
\(726\) −4.22020e52 −0.498891
\(727\) −3.15811e52 −0.363949 −0.181975 0.983303i \(-0.558249\pi\)
−0.181975 + 0.983303i \(0.558249\pi\)
\(728\) −2.10213e52 −0.236172
\(729\) 3.38139e51 0.0370370
\(730\) −1.59539e53 −1.70370
\(731\) −2.14389e53 −2.23219
\(732\) 1.37231e52 0.139315
\(733\) 1.64324e53 1.62659 0.813296 0.581850i \(-0.197671\pi\)
0.813296 + 0.581850i \(0.197671\pi\)
\(734\) −1.99055e52 −0.192130
\(735\) −7.35518e52 −0.692274
\(736\) 3.75533e52 0.344674
\(737\) −3.08569e51 −0.0276187
\(738\) 2.18447e52 0.190679
\(739\) 9.02443e52 0.768241 0.384120 0.923283i \(-0.374505\pi\)
0.384120 + 0.923283i \(0.374505\pi\)
\(740\) 4.41753e52 0.366769
\(741\) −4.13805e52 −0.335088
\(742\) 1.67106e52 0.131984
\(743\) 5.81589e51 0.0448047 0.0224023 0.999749i \(-0.492869\pi\)
0.0224023 + 0.999749i \(0.492869\pi\)
\(744\) −8.33691e51 −0.0626478
\(745\) −4.40565e53 −3.22938
\(746\) −2.07088e53 −1.48076
\(747\) −2.38295e52 −0.166220
\(748\) 4.67382e51 0.0318048
\(749\) 5.64095e52 0.374488
\(750\) 1.71713e53 1.11216
\(751\) −2.03346e53 −1.28498 −0.642491 0.766293i \(-0.722099\pi\)
−0.642491 + 0.766293i \(0.722099\pi\)
\(752\) 4.98661e52 0.307451
\(753\) 9.84069e52 0.591995
\(754\) 7.07165e52 0.415098
\(755\) 1.55395e52 0.0890058
\(756\) −4.88137e51 −0.0272828
\(757\) 8.46759e52 0.461834 0.230917 0.972973i \(-0.425827\pi\)
0.230917 + 0.972973i \(0.425827\pi\)
\(758\) 2.65526e53 1.41327
\(759\) −5.72889e51 −0.0297576
\(760\) 5.88938e53 2.98551
\(761\) −6.60711e52 −0.326885 −0.163443 0.986553i \(-0.552260\pi\)
−0.163443 + 0.986553i \(0.552260\pi\)
\(762\) 4.68263e52 0.226112
\(763\) 9.31064e52 0.438809
\(764\) −4.55673e52 −0.209617
\(765\) 2.41318e53 1.08356
\(766\) −3.40465e53 −1.49224
\(767\) −1.55035e53 −0.663309
\(768\) −9.52064e52 −0.397634
\(769\) 4.12388e53 1.68139 0.840696 0.541507i \(-0.182146\pi\)
0.840696 + 0.541507i \(0.182146\pi\)
\(770\) −1.62241e52 −0.0645778
\(771\) −1.42112e53 −0.552235
\(772\) −5.16475e52 −0.195943
\(773\) −1.80579e53 −0.668879 −0.334439 0.942417i \(-0.608547\pi\)
−0.334439 + 0.942417i \(0.608547\pi\)
\(774\) −9.88490e52 −0.357491
\(775\) 6.34356e52 0.224002
\(776\) −3.80049e53 −1.31038
\(777\) −8.22052e52 −0.276764
\(778\) −1.22781e52 −0.0403653
\(779\) −3.14831e53 −1.01073
\(780\) −3.07581e52 −0.0964295
\(781\) −1.43020e51 −0.00437877
\(782\) 3.77846e53 1.12977
\(783\) 8.32820e52 0.243197
\(784\) 1.62280e53 0.462826
\(785\) −4.80030e53 −1.33715
\(786\) 1.91880e53 0.522049
\(787\) 6.04656e53 1.60685 0.803425 0.595405i \(-0.203009\pi\)
0.803425 + 0.595405i \(0.203009\pi\)
\(788\) 5.34484e52 0.138739
\(789\) −1.06196e53 −0.269267
\(790\) −1.16212e54 −2.87838
\(791\) 4.50817e52 0.109078
\(792\) 1.09292e52 0.0258329
\(793\) −1.60913e53 −0.371566
\(794\) −1.24804e53 −0.281547
\(795\) 1.24006e53 0.273306
\(796\) −1.28683e53 −0.277096
\(797\) 6.79705e53 1.43002 0.715009 0.699116i \(-0.246423\pi\)
0.715009 + 0.699116i \(0.246423\pi\)
\(798\) −2.16093e53 −0.444210
\(799\) −3.98684e53 −0.800779
\(800\) 5.45122e53 1.06987
\(801\) −4.75349e52 −0.0911614
\(802\) 4.00359e53 0.750280
\(803\) 4.26694e52 0.0781411
\(804\) −3.05489e52 −0.0546712
\(805\) 4.27007e53 0.746812
\(806\) 1.92751e52 0.0329456
\(807\) 2.86833e53 0.479147
\(808\) −4.49098e53 −0.733214
\(809\) 1.11799e54 1.78397 0.891987 0.452061i \(-0.149311\pi\)
0.891987 + 0.452061i \(0.149311\pi\)
\(810\) 1.11265e53 0.173535
\(811\) −9.12670e53 −1.39132 −0.695662 0.718369i \(-0.744889\pi\)
−0.695662 + 0.718369i \(0.744889\pi\)
\(812\) −1.20226e53 −0.179147
\(813\) −1.34662e53 −0.196141
\(814\) 3.62910e52 0.0516711
\(815\) −9.43253e53 −1.31284
\(816\) −5.32428e53 −0.724425
\(817\) 1.42463e54 1.89494
\(818\) 5.52421e53 0.718346
\(819\) 5.72374e52 0.0727659
\(820\) −2.34014e53 −0.290861
\(821\) 4.11474e53 0.500027 0.250014 0.968242i \(-0.419565\pi\)
0.250014 + 0.968242i \(0.419565\pi\)
\(822\) −6.56619e53 −0.780162
\(823\) 2.41018e53 0.279996 0.139998 0.990152i \(-0.455290\pi\)
0.139998 + 0.990152i \(0.455290\pi\)
\(824\) 6.06059e53 0.688432
\(825\) −8.31605e52 −0.0923675
\(826\) −8.09610e53 −0.879316
\(827\) 1.22285e54 1.29873 0.649367 0.760475i \(-0.275034\pi\)
0.649367 + 0.760475i \(0.275034\pi\)
\(828\) −5.67172e52 −0.0589052
\(829\) 5.14834e53 0.522888 0.261444 0.965219i \(-0.415801\pi\)
0.261444 + 0.965219i \(0.415801\pi\)
\(830\) −7.84113e53 −0.778815
\(831\) 6.01804e53 0.584570
\(832\) 4.41949e53 0.419846
\(833\) −1.29744e54 −1.20547
\(834\) 4.73198e53 0.430002
\(835\) −3.00258e54 −2.66867
\(836\) −3.10579e52 −0.0269995
\(837\) 2.27000e52 0.0193021
\(838\) 7.57988e53 0.630446
\(839\) −1.47001e54 −1.19598 −0.597990 0.801504i \(-0.704034\pi\)
−0.597990 + 0.801504i \(0.704034\pi\)
\(840\) −8.14617e53 −0.648316
\(841\) 7.66718e53 0.596911
\(842\) 1.05929e54 0.806757
\(843\) 2.00093e53 0.149081
\(844\) 3.49300e53 0.254603
\(845\) −2.16095e54 −1.54098
\(846\) −1.83822e53 −0.128247
\(847\) −8.41294e53 −0.574255
\(848\) −2.73598e53 −0.182721
\(849\) 1.09010e54 0.712316
\(850\) 5.48480e54 3.50680
\(851\) −9.55152e53 −0.597552
\(852\) −1.41592e52 −0.00866777
\(853\) −2.39398e54 −1.43405 −0.717024 0.697048i \(-0.754496\pi\)
−0.717024 + 0.697048i \(0.754496\pi\)
\(854\) −8.40302e53 −0.492566
\(855\) −1.60358e54 −0.919850
\(856\) −1.25039e54 −0.701907
\(857\) 1.12045e54 0.615526 0.307763 0.951463i \(-0.400420\pi\)
0.307763 + 0.951463i \(0.400420\pi\)
\(858\) −2.52685e52 −0.0135852
\(859\) 2.95876e54 1.55681 0.778405 0.627762i \(-0.216029\pi\)
0.778405 + 0.627762i \(0.216029\pi\)
\(860\) 1.05893e54 0.545313
\(861\) 4.35473e53 0.219484
\(862\) −1.41478e54 −0.697919
\(863\) −2.90233e52 −0.0140135 −0.00700675 0.999975i \(-0.502230\pi\)
−0.00700675 + 0.999975i \(0.502230\pi\)
\(864\) 1.95068e53 0.0921897
\(865\) 1.30274e54 0.602643
\(866\) 5.33623e53 0.241632
\(867\) 2.95426e54 1.30947
\(868\) −3.27697e52 −0.0142186
\(869\) 3.10813e53 0.132018
\(870\) 2.74041e54 1.13949
\(871\) 3.58207e53 0.145814
\(872\) −2.06382e54 −0.822463
\(873\) 1.03481e54 0.403735
\(874\) −2.51082e54 −0.959077
\(875\) 3.42308e54 1.28017
\(876\) 4.22436e53 0.154680
\(877\) −9.87214e53 −0.353931 −0.176966 0.984217i \(-0.556628\pi\)
−0.176966 + 0.984217i \(0.556628\pi\)
\(878\) 1.38630e54 0.486642
\(879\) −1.34903e54 −0.463690
\(880\) 2.65633e53 0.0894031
\(881\) −3.43429e54 −1.13183 −0.565916 0.824463i \(-0.691477\pi\)
−0.565916 + 0.824463i \(0.691477\pi\)
\(882\) −5.98215e53 −0.193058
\(883\) −3.21368e54 −1.01561 −0.507807 0.861471i \(-0.669544\pi\)
−0.507807 + 0.861471i \(0.669544\pi\)
\(884\) −5.42568e53 −0.167914
\(885\) −6.00793e54 −1.82085
\(886\) −2.39846e54 −0.711882
\(887\) −3.18523e54 −0.925879 −0.462940 0.886390i \(-0.653205\pi\)
−0.462940 + 0.886390i \(0.653205\pi\)
\(888\) 1.82218e54 0.518742
\(889\) 9.33479e53 0.260269
\(890\) −1.56414e54 −0.427132
\(891\) −2.97584e52 −0.00795926
\(892\) 8.54643e53 0.223890
\(893\) 2.64929e54 0.679793
\(894\) −3.58323e54 −0.900596
\(895\) 7.77987e54 1.91534
\(896\) 1.16133e54 0.280064
\(897\) 6.65048e53 0.157106
\(898\) −4.59335e54 −1.06296
\(899\) 5.59090e53 0.126744
\(900\) −8.23306e53 −0.182841
\(901\) 2.18743e54 0.475911
\(902\) −1.92248e53 −0.0409770
\(903\) −1.97055e54 −0.411494
\(904\) −9.99291e53 −0.204445
\(905\) 4.37117e54 0.876192
\(906\) 1.26386e53 0.0248216
\(907\) −1.66261e54 −0.319931 −0.159966 0.987123i \(-0.551138\pi\)
−0.159966 + 0.987123i \(0.551138\pi\)
\(908\) −1.98694e54 −0.374625
\(909\) 1.22282e54 0.225907
\(910\) 1.88341e54 0.340940
\(911\) 1.12509e55 1.99570 0.997851 0.0655227i \(-0.0208715\pi\)
0.997851 + 0.0655227i \(0.0208715\pi\)
\(912\) 3.53803e54 0.614974
\(913\) 2.09715e53 0.0357207
\(914\) 6.53384e54 1.09060
\(915\) −6.23569e54 −1.01999
\(916\) −9.17122e53 −0.147015
\(917\) 3.82510e54 0.600912
\(918\) 1.96270e54 0.302179
\(919\) −1.81936e54 −0.274525 −0.137263 0.990535i \(-0.543830\pi\)
−0.137263 + 0.990535i \(0.543830\pi\)
\(920\) −9.46514e54 −1.39976
\(921\) 1.10259e54 0.159812
\(922\) 4.18336e54 0.594297
\(923\) 1.66027e53 0.0231178
\(924\) 4.29592e52 0.00586306
\(925\) −1.38650e55 −1.85480
\(926\) −5.90482e54 −0.774290
\(927\) −1.65020e54 −0.212110
\(928\) 4.80444e54 0.605348
\(929\) 6.12532e52 0.00756550 0.00378275 0.999993i \(-0.498796\pi\)
0.00378275 + 0.999993i \(0.498796\pi\)
\(930\) 7.46948e53 0.0904390
\(931\) 8.62160e54 1.02334
\(932\) 3.85630e53 0.0448721
\(933\) 3.13946e54 0.358134
\(934\) 3.67339e54 0.410818
\(935\) −2.12376e54 −0.232857
\(936\) −1.26874e54 −0.136386
\(937\) −1.54519e55 −1.62855 −0.814274 0.580481i \(-0.802865\pi\)
−0.814274 + 0.580481i \(0.802865\pi\)
\(938\) 1.87059e54 0.193298
\(939\) 7.01168e54 0.710409
\(940\) 1.96922e54 0.195627
\(941\) −1.06842e55 −1.04072 −0.520361 0.853946i \(-0.674203\pi\)
−0.520361 + 0.853946i \(0.674203\pi\)
\(942\) −3.90420e54 −0.372899
\(943\) 5.05981e54 0.473880
\(944\) 1.32555e55 1.21735
\(945\) 2.21807e54 0.199750
\(946\) 8.69935e53 0.0768247
\(947\) 3.77859e54 0.327232 0.163616 0.986524i \(-0.447684\pi\)
0.163616 + 0.986524i \(0.447684\pi\)
\(948\) 3.07712e54 0.261330
\(949\) −4.95335e54 −0.412548
\(950\) −3.64469e55 −2.97697
\(951\) −2.32461e54 −0.186213
\(952\) −1.43697e55 −1.12892
\(953\) 5.53742e53 0.0426667 0.0213333 0.999772i \(-0.493209\pi\)
0.0213333 + 0.999772i \(0.493209\pi\)
\(954\) 1.00857e54 0.0762184
\(955\) 2.07055e55 1.53470
\(956\) −5.73090e53 −0.0416631
\(957\) −7.32935e53 −0.0522631
\(958\) −7.23551e53 −0.0506066
\(959\) −1.30897e55 −0.898016
\(960\) 1.71264e55 1.15252
\(961\) −1.49966e55 −0.989941
\(962\) −4.21290e54 −0.272799
\(963\) 3.40459e54 0.216261
\(964\) 1.04346e54 0.0650206
\(965\) 2.34683e55 1.43459
\(966\) 3.47295e54 0.208268
\(967\) 1.91207e55 1.12490 0.562449 0.826832i \(-0.309859\pi\)
0.562449 + 0.826832i \(0.309859\pi\)
\(968\) 1.86483e55 1.07633
\(969\) −2.82868e55 −1.60175
\(970\) 3.40506e55 1.89168
\(971\) 8.30735e54 0.452800 0.226400 0.974034i \(-0.427304\pi\)
0.226400 + 0.974034i \(0.427304\pi\)
\(972\) −2.94615e53 −0.0157554
\(973\) 9.43317e54 0.494960
\(974\) −2.13197e55 −1.09759
\(975\) 9.65383e54 0.487657
\(976\) 1.37580e55 0.681921
\(977\) −3.32881e55 −1.61897 −0.809486 0.587140i \(-0.800254\pi\)
−0.809486 + 0.587140i \(0.800254\pi\)
\(978\) −7.67171e54 −0.366120
\(979\) 4.18338e53 0.0195906
\(980\) 6.40844e54 0.294490
\(981\) 5.61943e54 0.253405
\(982\) 4.09426e54 0.181181
\(983\) −5.66371e54 −0.245958 −0.122979 0.992409i \(-0.539245\pi\)
−0.122979 + 0.992409i \(0.539245\pi\)
\(984\) −9.65279e54 −0.411380
\(985\) −2.42867e55 −1.01578
\(986\) 4.83403e55 1.98420
\(987\) −3.66448e54 −0.147620
\(988\) 3.60541e54 0.142545
\(989\) −2.28960e55 −0.888442
\(990\) −9.79207e53 −0.0372927
\(991\) −3.93647e55 −1.47145 −0.735723 0.677283i \(-0.763157\pi\)
−0.735723 + 0.677283i \(0.763157\pi\)
\(992\) 1.30954e54 0.0480453
\(993\) 6.37398e54 0.229535
\(994\) 8.67009e53 0.0306461
\(995\) 5.84730e55 2.02875
\(996\) 2.07622e54 0.0707091
\(997\) 1.67431e53 0.00559727 0.00279863 0.999996i \(-0.499109\pi\)
0.00279863 + 0.999996i \(0.499109\pi\)
\(998\) −3.45755e54 −0.113463
\(999\) −4.96149e54 −0.159827
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 \(a_p\))