Properties

Label 8001.2.a.v.1.18
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Root \(-2.35941\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.35941 q^{2}\) \(+3.56679 q^{4}\) \(+3.48367 q^{5}\) \(+1.00000 q^{7}\) \(+3.69670 q^{8}\) \(+O(q^{10})\) \(q\)\(+2.35941 q^{2}\) \(+3.56679 q^{4}\) \(+3.48367 q^{5}\) \(+1.00000 q^{7}\) \(+3.69670 q^{8}\) \(+8.21939 q^{10}\) \(+3.61589 q^{11}\) \(-1.92931 q^{13}\) \(+2.35941 q^{14}\) \(+1.58843 q^{16}\) \(+6.15261 q^{17}\) \(-4.23441 q^{19}\) \(+12.4255 q^{20}\) \(+8.53136 q^{22}\) \(+7.99661 q^{23}\) \(+7.13595 q^{25}\) \(-4.55202 q^{26}\) \(+3.56679 q^{28}\) \(-2.42362 q^{29}\) \(-1.78229 q^{31}\) \(-3.64565 q^{32}\) \(+14.5165 q^{34}\) \(+3.48367 q^{35}\) \(+5.76457 q^{37}\) \(-9.99070 q^{38}\) \(+12.8781 q^{40}\) \(-6.30711 q^{41}\) \(-2.65444 q^{43}\) \(+12.8971 q^{44}\) \(+18.8672 q^{46}\) \(-3.09597 q^{47}\) \(+1.00000 q^{49}\) \(+16.8366 q^{50}\) \(-6.88145 q^{52}\) \(-10.6256 q^{53}\) \(+12.5966 q^{55}\) \(+3.69670 q^{56}\) \(-5.71830 q^{58}\) \(-1.12226 q^{59}\) \(-7.38616 q^{61}\) \(-4.20514 q^{62}\) \(-11.7784 q^{64}\) \(-6.72107 q^{65}\) \(-10.9599 q^{67}\) \(+21.9451 q^{68}\) \(+8.21939 q^{70}\) \(+11.9564 q^{71}\) \(+12.4914 q^{73}\) \(+13.6009 q^{74}\) \(-15.1033 q^{76}\) \(+3.61589 q^{77}\) \(-8.46939 q^{79}\) \(+5.53356 q^{80}\) \(-14.8810 q^{82}\) \(-8.32052 q^{83}\) \(+21.4336 q^{85}\) \(-6.26291 q^{86}\) \(+13.3669 q^{88}\) \(-5.58500 q^{89}\) \(-1.92931 q^{91}\) \(+28.5223 q^{92}\) \(-7.30465 q^{94}\) \(-14.7513 q^{95}\) \(+3.96775 q^{97}\) \(+2.35941 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.35941 1.66835 0.834176 0.551499i \(-0.185944\pi\)
0.834176 + 0.551499i \(0.185944\pi\)
\(3\) 0 0
\(4\) 3.56679 1.78340
\(5\) 3.48367 1.55794 0.778972 0.627059i \(-0.215741\pi\)
0.778972 + 0.627059i \(0.215741\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 3.69670 1.30698
\(9\) 0 0
\(10\) 8.21939 2.59920
\(11\) 3.61589 1.09023 0.545117 0.838360i \(-0.316485\pi\)
0.545117 + 0.838360i \(0.316485\pi\)
\(12\) 0 0
\(13\) −1.92931 −0.535094 −0.267547 0.963545i \(-0.586213\pi\)
−0.267547 + 0.963545i \(0.586213\pi\)
\(14\) 2.35941 0.630578
\(15\) 0 0
\(16\) 1.58843 0.397107
\(17\) 6.15261 1.49223 0.746113 0.665819i \(-0.231918\pi\)
0.746113 + 0.665819i \(0.231918\pi\)
\(18\) 0 0
\(19\) −4.23441 −0.971441 −0.485721 0.874114i \(-0.661443\pi\)
−0.485721 + 0.874114i \(0.661443\pi\)
\(20\) 12.4255 2.77843
\(21\) 0 0
\(22\) 8.53136 1.81889
\(23\) 7.99661 1.66741 0.833704 0.552211i \(-0.186216\pi\)
0.833704 + 0.552211i \(0.186216\pi\)
\(24\) 0 0
\(25\) 7.13595 1.42719
\(26\) −4.55202 −0.892725
\(27\) 0 0
\(28\) 3.56679 0.674061
\(29\) −2.42362 −0.450055 −0.225027 0.974352i \(-0.572247\pi\)
−0.225027 + 0.974352i \(0.572247\pi\)
\(30\) 0 0
\(31\) −1.78229 −0.320109 −0.160054 0.987108i \(-0.551167\pi\)
−0.160054 + 0.987108i \(0.551167\pi\)
\(32\) −3.64565 −0.644467
\(33\) 0 0
\(34\) 14.5165 2.48956
\(35\) 3.48367 0.588847
\(36\) 0 0
\(37\) 5.76457 0.947689 0.473844 0.880609i \(-0.342866\pi\)
0.473844 + 0.880609i \(0.342866\pi\)
\(38\) −9.99070 −1.62071
\(39\) 0 0
\(40\) 12.8781 2.03620
\(41\) −6.30711 −0.985004 −0.492502 0.870311i \(-0.663918\pi\)
−0.492502 + 0.870311i \(0.663918\pi\)
\(42\) 0 0
\(43\) −2.65444 −0.404799 −0.202399 0.979303i \(-0.564874\pi\)
−0.202399 + 0.979303i \(0.564874\pi\)
\(44\) 12.8971 1.94432
\(45\) 0 0
\(46\) 18.8672 2.78182
\(47\) −3.09597 −0.451594 −0.225797 0.974174i \(-0.572499\pi\)
−0.225797 + 0.974174i \(0.572499\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 16.8366 2.38105
\(51\) 0 0
\(52\) −6.88145 −0.954285
\(53\) −10.6256 −1.45953 −0.729767 0.683696i \(-0.760371\pi\)
−0.729767 + 0.683696i \(0.760371\pi\)
\(54\) 0 0
\(55\) 12.5966 1.69852
\(56\) 3.69670 0.493992
\(57\) 0 0
\(58\) −5.71830 −0.750850
\(59\) −1.12226 −0.146106 −0.0730529 0.997328i \(-0.523274\pi\)
−0.0730529 + 0.997328i \(0.523274\pi\)
\(60\) 0 0
\(61\) −7.38616 −0.945701 −0.472851 0.881143i \(-0.656775\pi\)
−0.472851 + 0.881143i \(0.656775\pi\)
\(62\) −4.20514 −0.534054
\(63\) 0 0
\(64\) −11.7784 −1.47230
\(65\) −6.72107 −0.833646
\(66\) 0 0
\(67\) −10.9599 −1.33897 −0.669485 0.742826i \(-0.733485\pi\)
−0.669485 + 0.742826i \(0.733485\pi\)
\(68\) 21.9451 2.66123
\(69\) 0 0
\(70\) 8.21939 0.982405
\(71\) 11.9564 1.41897 0.709483 0.704722i \(-0.248928\pi\)
0.709483 + 0.704722i \(0.248928\pi\)
\(72\) 0 0
\(73\) 12.4914 1.46201 0.731006 0.682371i \(-0.239051\pi\)
0.731006 + 0.682371i \(0.239051\pi\)
\(74\) 13.6009 1.58108
\(75\) 0 0
\(76\) −15.1033 −1.73247
\(77\) 3.61589 0.412069
\(78\) 0 0
\(79\) −8.46939 −0.952881 −0.476440 0.879207i \(-0.658073\pi\)
−0.476440 + 0.879207i \(0.658073\pi\)
\(80\) 5.53356 0.618671
\(81\) 0 0
\(82\) −14.8810 −1.64333
\(83\) −8.32052 −0.913296 −0.456648 0.889647i \(-0.650950\pi\)
−0.456648 + 0.889647i \(0.650950\pi\)
\(84\) 0 0
\(85\) 21.4336 2.32480
\(86\) −6.26291 −0.675347
\(87\) 0 0
\(88\) 13.3669 1.42491
\(89\) −5.58500 −0.592009 −0.296005 0.955187i \(-0.595654\pi\)
−0.296005 + 0.955187i \(0.595654\pi\)
\(90\) 0 0
\(91\) −1.92931 −0.202246
\(92\) 28.5223 2.97365
\(93\) 0 0
\(94\) −7.30465 −0.753417
\(95\) −14.7513 −1.51345
\(96\) 0 0
\(97\) 3.96775 0.402864 0.201432 0.979502i \(-0.435440\pi\)
0.201432 + 0.979502i \(0.435440\pi\)
\(98\) 2.35941 0.238336
\(99\) 0 0
\(100\) 25.4525 2.54525
\(101\) −9.08165 −0.903658 −0.451829 0.892105i \(-0.649228\pi\)
−0.451829 + 0.892105i \(0.649228\pi\)
\(102\) 0 0
\(103\) 4.21785 0.415597 0.207799 0.978172i \(-0.433370\pi\)
0.207799 + 0.978172i \(0.433370\pi\)
\(104\) −7.13208 −0.699358
\(105\) 0 0
\(106\) −25.0700 −2.43501
\(107\) 17.9401 1.73433 0.867166 0.498019i \(-0.165939\pi\)
0.867166 + 0.498019i \(0.165939\pi\)
\(108\) 0 0
\(109\) 5.45243 0.522248 0.261124 0.965305i \(-0.415907\pi\)
0.261124 + 0.965305i \(0.415907\pi\)
\(110\) 29.7204 2.83373
\(111\) 0 0
\(112\) 1.58843 0.150092
\(113\) −0.459752 −0.0432498 −0.0216249 0.999766i \(-0.506884\pi\)
−0.0216249 + 0.999766i \(0.506884\pi\)
\(114\) 0 0
\(115\) 27.8575 2.59773
\(116\) −8.64455 −0.802626
\(117\) 0 0
\(118\) −2.64787 −0.243756
\(119\) 6.15261 0.564009
\(120\) 0 0
\(121\) 2.07469 0.188608
\(122\) −17.4270 −1.57776
\(123\) 0 0
\(124\) −6.35706 −0.570881
\(125\) 7.44093 0.665537
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −20.4988 −1.81185
\(129\) 0 0
\(130\) −15.8577 −1.39082
\(131\) −2.56902 −0.224457 −0.112228 0.993682i \(-0.535799\pi\)
−0.112228 + 0.993682i \(0.535799\pi\)
\(132\) 0 0
\(133\) −4.23441 −0.367170
\(134\) −25.8589 −2.23387
\(135\) 0 0
\(136\) 22.7443 1.95031
\(137\) 3.98364 0.340345 0.170172 0.985414i \(-0.445568\pi\)
0.170172 + 0.985414i \(0.445568\pi\)
\(138\) 0 0
\(139\) 10.9220 0.926390 0.463195 0.886256i \(-0.346703\pi\)
0.463195 + 0.886256i \(0.346703\pi\)
\(140\) 12.4255 1.05015
\(141\) 0 0
\(142\) 28.2101 2.36734
\(143\) −6.97618 −0.583377
\(144\) 0 0
\(145\) −8.44309 −0.701160
\(146\) 29.4724 2.43915
\(147\) 0 0
\(148\) 20.5610 1.69011
\(149\) 1.64936 0.135121 0.0675605 0.997715i \(-0.478478\pi\)
0.0675605 + 0.997715i \(0.478478\pi\)
\(150\) 0 0
\(151\) 9.57181 0.778943 0.389472 0.921038i \(-0.372658\pi\)
0.389472 + 0.921038i \(0.372658\pi\)
\(152\) −15.6534 −1.26966
\(153\) 0 0
\(154\) 8.53136 0.687477
\(155\) −6.20891 −0.498711
\(156\) 0 0
\(157\) 5.24867 0.418889 0.209445 0.977820i \(-0.432834\pi\)
0.209445 + 0.977820i \(0.432834\pi\)
\(158\) −19.9827 −1.58974
\(159\) 0 0
\(160\) −12.7003 −1.00404
\(161\) 7.99661 0.630221
\(162\) 0 0
\(163\) −2.06308 −0.161593 −0.0807963 0.996731i \(-0.525746\pi\)
−0.0807963 + 0.996731i \(0.525746\pi\)
\(164\) −22.4961 −1.75665
\(165\) 0 0
\(166\) −19.6315 −1.52370
\(167\) 19.3404 1.49660 0.748302 0.663358i \(-0.230870\pi\)
0.748302 + 0.663358i \(0.230870\pi\)
\(168\) 0 0
\(169\) −9.27777 −0.713674
\(170\) 50.5707 3.87859
\(171\) 0 0
\(172\) −9.46785 −0.721917
\(173\) −12.9591 −0.985265 −0.492632 0.870238i \(-0.663965\pi\)
−0.492632 + 0.870238i \(0.663965\pi\)
\(174\) 0 0
\(175\) 7.13595 0.539427
\(176\) 5.74359 0.432940
\(177\) 0 0
\(178\) −13.1773 −0.987679
\(179\) −26.4041 −1.97354 −0.986768 0.162141i \(-0.948160\pi\)
−0.986768 + 0.162141i \(0.948160\pi\)
\(180\) 0 0
\(181\) 3.13555 0.233063 0.116532 0.993187i \(-0.462822\pi\)
0.116532 + 0.993187i \(0.462822\pi\)
\(182\) −4.55202 −0.337418
\(183\) 0 0
\(184\) 29.5611 2.17927
\(185\) 20.0818 1.47645
\(186\) 0 0
\(187\) 22.2472 1.62687
\(188\) −11.0427 −0.805371
\(189\) 0 0
\(190\) −34.8043 −2.52497
\(191\) 6.70700 0.485301 0.242651 0.970114i \(-0.421983\pi\)
0.242651 + 0.970114i \(0.421983\pi\)
\(192\) 0 0
\(193\) 10.0351 0.722345 0.361172 0.932499i \(-0.382377\pi\)
0.361172 + 0.932499i \(0.382377\pi\)
\(194\) 9.36154 0.672119
\(195\) 0 0
\(196\) 3.56679 0.254771
\(197\) −7.25191 −0.516677 −0.258339 0.966054i \(-0.583175\pi\)
−0.258339 + 0.966054i \(0.583175\pi\)
\(198\) 0 0
\(199\) −27.0499 −1.91751 −0.958757 0.284226i \(-0.908264\pi\)
−0.958757 + 0.284226i \(0.908264\pi\)
\(200\) 26.3795 1.86531
\(201\) 0 0
\(202\) −21.4273 −1.50762
\(203\) −2.42362 −0.170105
\(204\) 0 0
\(205\) −21.9719 −1.53458
\(206\) 9.95162 0.693362
\(207\) 0 0
\(208\) −3.06457 −0.212490
\(209\) −15.3112 −1.05910
\(210\) 0 0
\(211\) −15.0562 −1.03651 −0.518255 0.855226i \(-0.673418\pi\)
−0.518255 + 0.855226i \(0.673418\pi\)
\(212\) −37.8992 −2.60293
\(213\) 0 0
\(214\) 42.3279 2.89348
\(215\) −9.24720 −0.630654
\(216\) 0 0
\(217\) −1.78229 −0.120990
\(218\) 12.8645 0.871293
\(219\) 0 0
\(220\) 44.9294 3.02914
\(221\) −11.8703 −0.798481
\(222\) 0 0
\(223\) 10.0303 0.671676 0.335838 0.941920i \(-0.390981\pi\)
0.335838 + 0.941920i \(0.390981\pi\)
\(224\) −3.64565 −0.243586
\(225\) 0 0
\(226\) −1.08474 −0.0721559
\(227\) −20.8364 −1.38296 −0.691479 0.722396i \(-0.743041\pi\)
−0.691479 + 0.722396i \(0.743041\pi\)
\(228\) 0 0
\(229\) 2.24221 0.148170 0.0740848 0.997252i \(-0.476396\pi\)
0.0740848 + 0.997252i \(0.476396\pi\)
\(230\) 65.7272 4.33393
\(231\) 0 0
\(232\) −8.95940 −0.588213
\(233\) 20.5397 1.34560 0.672801 0.739823i \(-0.265091\pi\)
0.672801 + 0.739823i \(0.265091\pi\)
\(234\) 0 0
\(235\) −10.7853 −0.703558
\(236\) −4.00287 −0.260565
\(237\) 0 0
\(238\) 14.5165 0.940964
\(239\) 16.5949 1.07343 0.536716 0.843763i \(-0.319665\pi\)
0.536716 + 0.843763i \(0.319665\pi\)
\(240\) 0 0
\(241\) 5.78154 0.372422 0.186211 0.982510i \(-0.440379\pi\)
0.186211 + 0.982510i \(0.440379\pi\)
\(242\) 4.89504 0.314665
\(243\) 0 0
\(244\) −26.3449 −1.68656
\(245\) 3.48367 0.222563
\(246\) 0 0
\(247\) 8.16949 0.519812
\(248\) −6.58859 −0.418376
\(249\) 0 0
\(250\) 17.5562 1.11035
\(251\) 16.4271 1.03687 0.518436 0.855117i \(-0.326515\pi\)
0.518436 + 0.855117i \(0.326515\pi\)
\(252\) 0 0
\(253\) 28.9149 1.81786
\(254\) 2.35941 0.148042
\(255\) 0 0
\(256\) −24.8081 −1.55051
\(257\) −1.81936 −0.113489 −0.0567443 0.998389i \(-0.518072\pi\)
−0.0567443 + 0.998389i \(0.518072\pi\)
\(258\) 0 0
\(259\) 5.76457 0.358193
\(260\) −23.9727 −1.48672
\(261\) 0 0
\(262\) −6.06137 −0.374473
\(263\) −10.7935 −0.665553 −0.332777 0.943006i \(-0.607986\pi\)
−0.332777 + 0.943006i \(0.607986\pi\)
\(264\) 0 0
\(265\) −37.0159 −2.27387
\(266\) −9.99070 −0.612569
\(267\) 0 0
\(268\) −39.0918 −2.38791
\(269\) −6.02788 −0.367526 −0.183763 0.982971i \(-0.558828\pi\)
−0.183763 + 0.982971i \(0.558828\pi\)
\(270\) 0 0
\(271\) 28.7213 1.74469 0.872347 0.488888i \(-0.162597\pi\)
0.872347 + 0.488888i \(0.162597\pi\)
\(272\) 9.77298 0.592574
\(273\) 0 0
\(274\) 9.39901 0.567815
\(275\) 25.8028 1.55597
\(276\) 0 0
\(277\) 15.9881 0.960632 0.480316 0.877095i \(-0.340522\pi\)
0.480316 + 0.877095i \(0.340522\pi\)
\(278\) 25.7694 1.54554
\(279\) 0 0
\(280\) 12.8781 0.769613
\(281\) −16.7489 −0.999157 −0.499579 0.866269i \(-0.666512\pi\)
−0.499579 + 0.866269i \(0.666512\pi\)
\(282\) 0 0
\(283\) −15.8469 −0.941998 −0.470999 0.882134i \(-0.656107\pi\)
−0.470999 + 0.882134i \(0.656107\pi\)
\(284\) 42.6461 2.53058
\(285\) 0 0
\(286\) −16.4596 −0.973278
\(287\) −6.30711 −0.372297
\(288\) 0 0
\(289\) 20.8546 1.22674
\(290\) −19.9207 −1.16978
\(291\) 0 0
\(292\) 44.5544 2.60735
\(293\) −25.3332 −1.47998 −0.739991 0.672616i \(-0.765170\pi\)
−0.739991 + 0.672616i \(0.765170\pi\)
\(294\) 0 0
\(295\) −3.90958 −0.227625
\(296\) 21.3099 1.23861
\(297\) 0 0
\(298\) 3.89151 0.225429
\(299\) −15.4279 −0.892220
\(300\) 0 0
\(301\) −2.65444 −0.153000
\(302\) 22.5838 1.29955
\(303\) 0 0
\(304\) −6.72607 −0.385766
\(305\) −25.7309 −1.47335
\(306\) 0 0
\(307\) 26.3469 1.50370 0.751848 0.659337i \(-0.229163\pi\)
0.751848 + 0.659337i \(0.229163\pi\)
\(308\) 12.8971 0.734883
\(309\) 0 0
\(310\) −14.6493 −0.832026
\(311\) −28.9919 −1.64398 −0.821990 0.569502i \(-0.807136\pi\)
−0.821990 + 0.569502i \(0.807136\pi\)
\(312\) 0 0
\(313\) 17.9259 1.01323 0.506615 0.862172i \(-0.330897\pi\)
0.506615 + 0.862172i \(0.330897\pi\)
\(314\) 12.3837 0.698855
\(315\) 0 0
\(316\) −30.2086 −1.69936
\(317\) −5.92298 −0.332667 −0.166334 0.986070i \(-0.553193\pi\)
−0.166334 + 0.986070i \(0.553193\pi\)
\(318\) 0 0
\(319\) −8.76355 −0.490665
\(320\) −41.0322 −2.29377
\(321\) 0 0
\(322\) 18.8672 1.05143
\(323\) −26.0527 −1.44961
\(324\) 0 0
\(325\) −13.7674 −0.763680
\(326\) −4.86764 −0.269593
\(327\) 0 0
\(328\) −23.3155 −1.28738
\(329\) −3.09597 −0.170686
\(330\) 0 0
\(331\) 20.8160 1.14415 0.572076 0.820201i \(-0.306138\pi\)
0.572076 + 0.820201i \(0.306138\pi\)
\(332\) −29.6776 −1.62877
\(333\) 0 0
\(334\) 45.6318 2.49686
\(335\) −38.1808 −2.08604
\(336\) 0 0
\(337\) −17.2188 −0.937965 −0.468983 0.883207i \(-0.655379\pi\)
−0.468983 + 0.883207i \(0.655379\pi\)
\(338\) −21.8900 −1.19066
\(339\) 0 0
\(340\) 76.4494 4.14605
\(341\) −6.44457 −0.348993
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −9.81268 −0.529064
\(345\) 0 0
\(346\) −30.5758 −1.64377
\(347\) 22.0536 1.18390 0.591949 0.805976i \(-0.298359\pi\)
0.591949 + 0.805976i \(0.298359\pi\)
\(348\) 0 0
\(349\) −18.5505 −0.992984 −0.496492 0.868041i \(-0.665379\pi\)
−0.496492 + 0.868041i \(0.665379\pi\)
\(350\) 16.8366 0.899954
\(351\) 0 0
\(352\) −13.1823 −0.702619
\(353\) −13.0355 −0.693810 −0.346905 0.937900i \(-0.612767\pi\)
−0.346905 + 0.937900i \(0.612767\pi\)
\(354\) 0 0
\(355\) 41.6522 2.21067
\(356\) −19.9205 −1.05579
\(357\) 0 0
\(358\) −62.2980 −3.29255
\(359\) −8.41399 −0.444073 −0.222037 0.975038i \(-0.571270\pi\)
−0.222037 + 0.975038i \(0.571270\pi\)
\(360\) 0 0
\(361\) −1.06974 −0.0563021
\(362\) 7.39802 0.388831
\(363\) 0 0
\(364\) −6.88145 −0.360686
\(365\) 43.5160 2.27773
\(366\) 0 0
\(367\) −33.5002 −1.74870 −0.874349 0.485298i \(-0.838711\pi\)
−0.874349 + 0.485298i \(0.838711\pi\)
\(368\) 12.7021 0.662140
\(369\) 0 0
\(370\) 47.3812 2.46323
\(371\) −10.6256 −0.551652
\(372\) 0 0
\(373\) −10.5078 −0.544074 −0.272037 0.962287i \(-0.587697\pi\)
−0.272037 + 0.962287i \(0.587697\pi\)
\(374\) 52.4901 2.71420
\(375\) 0 0
\(376\) −11.4449 −0.590225
\(377\) 4.67591 0.240822
\(378\) 0 0
\(379\) −3.67184 −0.188610 −0.0943049 0.995543i \(-0.530063\pi\)
−0.0943049 + 0.995543i \(0.530063\pi\)
\(380\) −52.6148 −2.69908
\(381\) 0 0
\(382\) 15.8245 0.809653
\(383\) 5.29752 0.270690 0.135345 0.990799i \(-0.456786\pi\)
0.135345 + 0.990799i \(0.456786\pi\)
\(384\) 0 0
\(385\) 12.5966 0.641981
\(386\) 23.6770 1.20513
\(387\) 0 0
\(388\) 14.1522 0.718467
\(389\) 9.52423 0.482898 0.241449 0.970414i \(-0.422377\pi\)
0.241449 + 0.970414i \(0.422377\pi\)
\(390\) 0 0
\(391\) 49.2000 2.48815
\(392\) 3.69670 0.186712
\(393\) 0 0
\(394\) −17.1102 −0.861999
\(395\) −29.5045 −1.48453
\(396\) 0 0
\(397\) 22.0243 1.10537 0.552683 0.833391i \(-0.313604\pi\)
0.552683 + 0.833391i \(0.313604\pi\)
\(398\) −63.8216 −3.19909
\(399\) 0 0
\(400\) 11.3349 0.566747
\(401\) 31.7400 1.58502 0.792511 0.609857i \(-0.208773\pi\)
0.792511 + 0.609857i \(0.208773\pi\)
\(402\) 0 0
\(403\) 3.43859 0.171288
\(404\) −32.3924 −1.61158
\(405\) 0 0
\(406\) −5.71830 −0.283795
\(407\) 20.8441 1.03320
\(408\) 0 0
\(409\) −22.5963 −1.11731 −0.558657 0.829399i \(-0.688683\pi\)
−0.558657 + 0.829399i \(0.688683\pi\)
\(410\) −51.8405 −2.56022
\(411\) 0 0
\(412\) 15.0442 0.741175
\(413\) −1.12226 −0.0552228
\(414\) 0 0
\(415\) −28.9860 −1.42286
\(416\) 7.03359 0.344850
\(417\) 0 0
\(418\) −36.1253 −1.76695
\(419\) −35.0178 −1.71073 −0.855365 0.518025i \(-0.826667\pi\)
−0.855365 + 0.518025i \(0.826667\pi\)
\(420\) 0 0
\(421\) −18.7984 −0.916177 −0.458089 0.888906i \(-0.651466\pi\)
−0.458089 + 0.888906i \(0.651466\pi\)
\(422\) −35.5236 −1.72926
\(423\) 0 0
\(424\) −39.2795 −1.90758
\(425\) 43.9047 2.12969
\(426\) 0 0
\(427\) −7.38616 −0.357441
\(428\) 63.9885 3.09300
\(429\) 0 0
\(430\) −21.8179 −1.05215
\(431\) 15.9195 0.766815 0.383408 0.923579i \(-0.374750\pi\)
0.383408 + 0.923579i \(0.374750\pi\)
\(432\) 0 0
\(433\) −18.1858 −0.873952 −0.436976 0.899473i \(-0.643951\pi\)
−0.436976 + 0.899473i \(0.643951\pi\)
\(434\) −4.20514 −0.201853
\(435\) 0 0
\(436\) 19.4477 0.931375
\(437\) −33.8610 −1.61979
\(438\) 0 0
\(439\) 17.6641 0.843063 0.421531 0.906814i \(-0.361493\pi\)
0.421531 + 0.906814i \(0.361493\pi\)
\(440\) 46.5658 2.21994
\(441\) 0 0
\(442\) −28.0068 −1.33215
\(443\) 12.2715 0.583036 0.291518 0.956565i \(-0.405840\pi\)
0.291518 + 0.956565i \(0.405840\pi\)
\(444\) 0 0
\(445\) −19.4563 −0.922317
\(446\) 23.6654 1.12059
\(447\) 0 0
\(448\) −11.7784 −0.556479
\(449\) −5.56581 −0.262667 −0.131333 0.991338i \(-0.541926\pi\)
−0.131333 + 0.991338i \(0.541926\pi\)
\(450\) 0 0
\(451\) −22.8058 −1.07388
\(452\) −1.63984 −0.0771316
\(453\) 0 0
\(454\) −49.1615 −2.30726
\(455\) −6.72107 −0.315089
\(456\) 0 0
\(457\) 22.9214 1.07222 0.536108 0.844149i \(-0.319894\pi\)
0.536108 + 0.844149i \(0.319894\pi\)
\(458\) 5.29029 0.247199
\(459\) 0 0
\(460\) 99.3621 4.63278
\(461\) −20.0267 −0.932736 −0.466368 0.884591i \(-0.654438\pi\)
−0.466368 + 0.884591i \(0.654438\pi\)
\(462\) 0 0
\(463\) 35.6784 1.65812 0.829058 0.559163i \(-0.188877\pi\)
0.829058 + 0.559163i \(0.188877\pi\)
\(464\) −3.84975 −0.178720
\(465\) 0 0
\(466\) 48.4616 2.24494
\(467\) −3.39355 −0.157035 −0.0785173 0.996913i \(-0.525019\pi\)
−0.0785173 + 0.996913i \(0.525019\pi\)
\(468\) 0 0
\(469\) −10.9599 −0.506083
\(470\) −25.4470 −1.17378
\(471\) 0 0
\(472\) −4.14866 −0.190957
\(473\) −9.59818 −0.441325
\(474\) 0 0
\(475\) −30.2166 −1.38643
\(476\) 21.9451 1.00585
\(477\) 0 0
\(478\) 39.1540 1.79086
\(479\) 4.08460 0.186630 0.0933151 0.995637i \(-0.470254\pi\)
0.0933151 + 0.995637i \(0.470254\pi\)
\(480\) 0 0
\(481\) −11.1216 −0.507103
\(482\) 13.6410 0.621331
\(483\) 0 0
\(484\) 7.39999 0.336363
\(485\) 13.8223 0.627640
\(486\) 0 0
\(487\) 14.3210 0.648947 0.324473 0.945895i \(-0.394813\pi\)
0.324473 + 0.945895i \(0.394813\pi\)
\(488\) −27.3044 −1.23601
\(489\) 0 0
\(490\) 8.21939 0.371314
\(491\) −3.60157 −0.162537 −0.0812683 0.996692i \(-0.525897\pi\)
−0.0812683 + 0.996692i \(0.525897\pi\)
\(492\) 0 0
\(493\) −14.9116 −0.671584
\(494\) 19.2751 0.867230
\(495\) 0 0
\(496\) −2.83104 −0.127117
\(497\) 11.9564 0.536319
\(498\) 0 0
\(499\) 8.65491 0.387447 0.193723 0.981056i \(-0.437944\pi\)
0.193723 + 0.981056i \(0.437944\pi\)
\(500\) 26.5403 1.18692
\(501\) 0 0
\(502\) 38.7583 1.72987
\(503\) 2.22712 0.0993025 0.0496512 0.998767i \(-0.484189\pi\)
0.0496512 + 0.998767i \(0.484189\pi\)
\(504\) 0 0
\(505\) −31.6375 −1.40785
\(506\) 68.2220 3.03284
\(507\) 0 0
\(508\) 3.56679 0.158251
\(509\) 5.34661 0.236984 0.118492 0.992955i \(-0.462194\pi\)
0.118492 + 0.992955i \(0.462194\pi\)
\(510\) 0 0
\(511\) 12.4914 0.552588
\(512\) −17.5348 −0.774934
\(513\) 0 0
\(514\) −4.29261 −0.189339
\(515\) 14.6936 0.647477
\(516\) 0 0
\(517\) −11.1947 −0.492343
\(518\) 13.6009 0.597591
\(519\) 0 0
\(520\) −24.8458 −1.08956
\(521\) 26.5389 1.16269 0.581346 0.813656i \(-0.302526\pi\)
0.581346 + 0.813656i \(0.302526\pi\)
\(522\) 0 0
\(523\) −38.0208 −1.66253 −0.831266 0.555874i \(-0.812384\pi\)
−0.831266 + 0.555874i \(0.812384\pi\)
\(524\) −9.16318 −0.400295
\(525\) 0 0
\(526\) −25.4662 −1.11038
\(527\) −10.9657 −0.477675
\(528\) 0 0
\(529\) 40.9458 1.78025
\(530\) −87.3356 −3.79362
\(531\) 0 0
\(532\) −15.1033 −0.654810
\(533\) 12.1684 0.527070
\(534\) 0 0
\(535\) 62.4973 2.70199
\(536\) −40.5156 −1.75001
\(537\) 0 0
\(538\) −14.2222 −0.613163
\(539\) 3.61589 0.155748
\(540\) 0 0
\(541\) −29.8452 −1.28314 −0.641572 0.767063i \(-0.721717\pi\)
−0.641572 + 0.767063i \(0.721717\pi\)
\(542\) 67.7651 2.91076
\(543\) 0 0
\(544\) −22.4303 −0.961690
\(545\) 18.9945 0.813633
\(546\) 0 0
\(547\) 35.9013 1.53503 0.767515 0.641031i \(-0.221493\pi\)
0.767515 + 0.641031i \(0.221493\pi\)
\(548\) 14.2088 0.606970
\(549\) 0 0
\(550\) 60.8793 2.59590
\(551\) 10.2626 0.437202
\(552\) 0 0
\(553\) −8.46939 −0.360155
\(554\) 37.7224 1.60267
\(555\) 0 0
\(556\) 38.9564 1.65212
\(557\) −14.2853 −0.605286 −0.302643 0.953104i \(-0.597869\pi\)
−0.302643 + 0.953104i \(0.597869\pi\)
\(558\) 0 0
\(559\) 5.12124 0.216605
\(560\) 5.53356 0.233836
\(561\) 0 0
\(562\) −39.5175 −1.66695
\(563\) 13.7483 0.579420 0.289710 0.957114i \(-0.406441\pi\)
0.289710 + 0.957114i \(0.406441\pi\)
\(564\) 0 0
\(565\) −1.60162 −0.0673808
\(566\) −37.3892 −1.57158
\(567\) 0 0
\(568\) 44.1993 1.85456
\(569\) 30.5444 1.28049 0.640244 0.768172i \(-0.278833\pi\)
0.640244 + 0.768172i \(0.278833\pi\)
\(570\) 0 0
\(571\) −14.1134 −0.590628 −0.295314 0.955400i \(-0.595424\pi\)
−0.295314 + 0.955400i \(0.595424\pi\)
\(572\) −24.8826 −1.04039
\(573\) 0 0
\(574\) −14.8810 −0.621122
\(575\) 57.0634 2.37971
\(576\) 0 0
\(577\) −15.2871 −0.636410 −0.318205 0.948022i \(-0.603080\pi\)
−0.318205 + 0.948022i \(0.603080\pi\)
\(578\) 49.2044 2.04663
\(579\) 0 0
\(580\) −30.1148 −1.25045
\(581\) −8.32052 −0.345194
\(582\) 0 0
\(583\) −38.4209 −1.59123
\(584\) 46.1771 1.91082
\(585\) 0 0
\(586\) −59.7713 −2.46913
\(587\) 33.0709 1.36498 0.682492 0.730893i \(-0.260896\pi\)
0.682492 + 0.730893i \(0.260896\pi\)
\(588\) 0 0
\(589\) 7.54695 0.310967
\(590\) −9.22429 −0.379758
\(591\) 0 0
\(592\) 9.15660 0.376334
\(593\) 17.8911 0.734699 0.367349 0.930083i \(-0.380265\pi\)
0.367349 + 0.930083i \(0.380265\pi\)
\(594\) 0 0
\(595\) 21.4336 0.878694
\(596\) 5.88293 0.240974
\(597\) 0 0
\(598\) −36.4007 −1.48854
\(599\) 2.10132 0.0858574 0.0429287 0.999078i \(-0.486331\pi\)
0.0429287 + 0.999078i \(0.486331\pi\)
\(600\) 0 0
\(601\) 40.6507 1.65818 0.829089 0.559117i \(-0.188860\pi\)
0.829089 + 0.559117i \(0.188860\pi\)
\(602\) −6.26291 −0.255257
\(603\) 0 0
\(604\) 34.1407 1.38916
\(605\) 7.22754 0.293841
\(606\) 0 0
\(607\) 38.0029 1.54249 0.771246 0.636537i \(-0.219634\pi\)
0.771246 + 0.636537i \(0.219634\pi\)
\(608\) 15.4372 0.626061
\(609\) 0 0
\(610\) −60.7097 −2.45806
\(611\) 5.97308 0.241645
\(612\) 0 0
\(613\) 41.6896 1.68383 0.841913 0.539614i \(-0.181430\pi\)
0.841913 + 0.539614i \(0.181430\pi\)
\(614\) 62.1630 2.50869
\(615\) 0 0
\(616\) 13.3669 0.538567
\(617\) −31.3419 −1.26178 −0.630888 0.775874i \(-0.717309\pi\)
−0.630888 + 0.775874i \(0.717309\pi\)
\(618\) 0 0
\(619\) 24.6489 0.990724 0.495362 0.868687i \(-0.335035\pi\)
0.495362 + 0.868687i \(0.335035\pi\)
\(620\) −22.1459 −0.889400
\(621\) 0 0
\(622\) −68.4037 −2.74274
\(623\) −5.58500 −0.223758
\(624\) 0 0
\(625\) −9.75799 −0.390320
\(626\) 42.2944 1.69042
\(627\) 0 0
\(628\) 18.7209 0.747046
\(629\) 35.4671 1.41417
\(630\) 0 0
\(631\) −29.6796 −1.18153 −0.590763 0.806845i \(-0.701173\pi\)
−0.590763 + 0.806845i \(0.701173\pi\)
\(632\) −31.3088 −1.24540
\(633\) 0 0
\(634\) −13.9747 −0.555006
\(635\) 3.48367 0.138245
\(636\) 0 0
\(637\) −1.92931 −0.0764420
\(638\) −20.6768 −0.818601
\(639\) 0 0
\(640\) −71.4110 −2.82277
\(641\) 8.73835 0.345144 0.172572 0.984997i \(-0.444792\pi\)
0.172572 + 0.984997i \(0.444792\pi\)
\(642\) 0 0
\(643\) −10.7720 −0.424807 −0.212403 0.977182i \(-0.568129\pi\)
−0.212403 + 0.977182i \(0.568129\pi\)
\(644\) 28.5223 1.12393
\(645\) 0 0
\(646\) −61.4688 −2.41846
\(647\) −35.8867 −1.41085 −0.705426 0.708783i \(-0.749244\pi\)
−0.705426 + 0.708783i \(0.749244\pi\)
\(648\) 0 0
\(649\) −4.05797 −0.159289
\(650\) −32.4830 −1.27409
\(651\) 0 0
\(652\) −7.35857 −0.288184
\(653\) −12.3102 −0.481735 −0.240868 0.970558i \(-0.577432\pi\)
−0.240868 + 0.970558i \(0.577432\pi\)
\(654\) 0 0
\(655\) −8.94963 −0.349691
\(656\) −10.0184 −0.391152
\(657\) 0 0
\(658\) −7.30465 −0.284765
\(659\) −44.5047 −1.73366 −0.866829 0.498605i \(-0.833846\pi\)
−0.866829 + 0.498605i \(0.833846\pi\)
\(660\) 0 0
\(661\) −28.3434 −1.10243 −0.551215 0.834363i \(-0.685836\pi\)
−0.551215 + 0.834363i \(0.685836\pi\)
\(662\) 49.1134 1.90885
\(663\) 0 0
\(664\) −30.7585 −1.19366
\(665\) −14.7513 −0.572031
\(666\) 0 0
\(667\) −19.3807 −0.750426
\(668\) 68.9831 2.66904
\(669\) 0 0
\(670\) −90.0840 −3.48025
\(671\) −26.7076 −1.03103
\(672\) 0 0
\(673\) −1.59797 −0.0615973 −0.0307987 0.999526i \(-0.509805\pi\)
−0.0307987 + 0.999526i \(0.509805\pi\)
\(674\) −40.6260 −1.56486
\(675\) 0 0
\(676\) −33.0919 −1.27276
\(677\) −40.4380 −1.55416 −0.777079 0.629403i \(-0.783299\pi\)
−0.777079 + 0.629403i \(0.783299\pi\)
\(678\) 0 0
\(679\) 3.96775 0.152268
\(680\) 79.2338 3.03848
\(681\) 0 0
\(682\) −15.2054 −0.582243
\(683\) 22.0689 0.844444 0.422222 0.906492i \(-0.361250\pi\)
0.422222 + 0.906492i \(0.361250\pi\)
\(684\) 0 0
\(685\) 13.8777 0.530238
\(686\) 2.35941 0.0900825
\(687\) 0 0
\(688\) −4.21639 −0.160749
\(689\) 20.5000 0.780987
\(690\) 0 0
\(691\) −44.7054 −1.70067 −0.850337 0.526239i \(-0.823602\pi\)
−0.850337 + 0.526239i \(0.823602\pi\)
\(692\) −46.2225 −1.75712
\(693\) 0 0
\(694\) 52.0333 1.97516
\(695\) 38.0485 1.44326
\(696\) 0 0
\(697\) −38.8051 −1.46985
\(698\) −43.7681 −1.65665
\(699\) 0 0
\(700\) 25.4525 0.962012
\(701\) −27.9205 −1.05454 −0.527271 0.849697i \(-0.676785\pi\)
−0.527271 + 0.849697i \(0.676785\pi\)
\(702\) 0 0
\(703\) −24.4096 −0.920624
\(704\) −42.5896 −1.60515
\(705\) 0 0
\(706\) −30.7560 −1.15752
\(707\) −9.08165 −0.341551
\(708\) 0 0
\(709\) −25.5996 −0.961412 −0.480706 0.876882i \(-0.659620\pi\)
−0.480706 + 0.876882i \(0.659620\pi\)
\(710\) 98.2745 3.68818
\(711\) 0 0
\(712\) −20.6461 −0.773745
\(713\) −14.2523 −0.533752
\(714\) 0 0
\(715\) −24.3027 −0.908869
\(716\) −94.1780 −3.51960
\(717\) 0 0
\(718\) −19.8520 −0.740871
\(719\) 12.8401 0.478854 0.239427 0.970914i \(-0.423040\pi\)
0.239427 + 0.970914i \(0.423040\pi\)
\(720\) 0 0
\(721\) 4.21785 0.157081
\(722\) −2.52395 −0.0939317
\(723\) 0 0
\(724\) 11.1838 0.415644
\(725\) −17.2948 −0.642314
\(726\) 0 0
\(727\) 31.1884 1.15671 0.578357 0.815784i \(-0.303694\pi\)
0.578357 + 0.815784i \(0.303694\pi\)
\(728\) −7.13208 −0.264332
\(729\) 0 0
\(730\) 102.672 3.80006
\(731\) −16.3317 −0.604051
\(732\) 0 0
\(733\) 2.93743 0.108497 0.0542483 0.998527i \(-0.482724\pi\)
0.0542483 + 0.998527i \(0.482724\pi\)
\(734\) −79.0406 −2.91744
\(735\) 0 0
\(736\) −29.1529 −1.07459
\(737\) −39.6300 −1.45979
\(738\) 0 0
\(739\) 29.1689 1.07300 0.536498 0.843902i \(-0.319747\pi\)
0.536498 + 0.843902i \(0.319747\pi\)
\(740\) 71.6278 2.63309
\(741\) 0 0
\(742\) −25.0700 −0.920349
\(743\) 49.1554 1.80334 0.901668 0.432430i \(-0.142344\pi\)
0.901668 + 0.432430i \(0.142344\pi\)
\(744\) 0 0
\(745\) 5.74583 0.210511
\(746\) −24.7922 −0.907707
\(747\) 0 0
\(748\) 79.3511 2.90136
\(749\) 17.9401 0.655516
\(750\) 0 0
\(751\) −39.2079 −1.43072 −0.715358 0.698758i \(-0.753736\pi\)
−0.715358 + 0.698758i \(0.753736\pi\)
\(752\) −4.91773 −0.179331
\(753\) 0 0
\(754\) 11.0324 0.401775
\(755\) 33.3450 1.21355
\(756\) 0 0
\(757\) 50.6563 1.84113 0.920567 0.390584i \(-0.127727\pi\)
0.920567 + 0.390584i \(0.127727\pi\)
\(758\) −8.66336 −0.314667
\(759\) 0 0
\(760\) −54.5311 −1.97805
\(761\) −29.2786 −1.06135 −0.530674 0.847576i \(-0.678061\pi\)
−0.530674 + 0.847576i \(0.678061\pi\)
\(762\) 0 0
\(763\) 5.45243 0.197391
\(764\) 23.9225 0.865485
\(765\) 0 0
\(766\) 12.4990 0.451607
\(767\) 2.16519 0.0781803
\(768\) 0 0
\(769\) −31.3773 −1.13149 −0.565747 0.824579i \(-0.691412\pi\)
−0.565747 + 0.824579i \(0.691412\pi\)
\(770\) 29.7204 1.07105
\(771\) 0 0
\(772\) 35.7933 1.28823
\(773\) −9.28097 −0.333813 −0.166907 0.985973i \(-0.553378\pi\)
−0.166907 + 0.985973i \(0.553378\pi\)
\(774\) 0 0
\(775\) −12.7183 −0.456856
\(776\) 14.6676 0.526536
\(777\) 0 0
\(778\) 22.4715 0.805643
\(779\) 26.7069 0.956874
\(780\) 0 0
\(781\) 43.2332 1.54700
\(782\) 116.083 4.15111
\(783\) 0 0
\(784\) 1.58843 0.0567296
\(785\) 18.2846 0.652606
\(786\) 0 0
\(787\) −45.7571 −1.63107 −0.815533 0.578711i \(-0.803556\pi\)
−0.815533 + 0.578711i \(0.803556\pi\)
\(788\) −25.8661 −0.921440
\(789\) 0 0
\(790\) −69.6132 −2.47673
\(791\) −0.459752 −0.0163469
\(792\) 0 0
\(793\) 14.2502 0.506039
\(794\) 51.9642 1.84414
\(795\) 0 0
\(796\) −96.4813 −3.41969
\(797\) −11.5364 −0.408639 −0.204320 0.978904i \(-0.565498\pi\)
−0.204320 + 0.978904i \(0.565498\pi\)
\(798\) 0 0
\(799\) −19.0483 −0.673880
\(800\) −26.0152 −0.919776
\(801\) 0 0
\(802\) 74.8876 2.64437
\(803\) 45.1677 1.59393
\(804\) 0 0
\(805\) 27.8575 0.981849
\(806\) 8.11302 0.285769
\(807\) 0 0
\(808\) −33.5722 −1.18106
\(809\) 51.3289 1.80463 0.902314 0.431080i \(-0.141867\pi\)
0.902314 + 0.431080i \(0.141867\pi\)
\(810\) 0 0
\(811\) −40.7749 −1.43180 −0.715901 0.698202i \(-0.753984\pi\)
−0.715901 + 0.698202i \(0.753984\pi\)
\(812\) −8.64455 −0.303364
\(813\) 0 0
\(814\) 49.1796 1.72374
\(815\) −7.18708 −0.251752
\(816\) 0 0
\(817\) 11.2400 0.393238
\(818\) −53.3138 −1.86407
\(819\) 0 0
\(820\) −78.3691 −2.73677
\(821\) 13.2030 0.460789 0.230395 0.973097i \(-0.425998\pi\)
0.230395 + 0.973097i \(0.425998\pi\)
\(822\) 0 0
\(823\) 45.2538 1.57745 0.788724 0.614747i \(-0.210742\pi\)
0.788724 + 0.614747i \(0.210742\pi\)
\(824\) 15.5921 0.543178
\(825\) 0 0
\(826\) −2.64787 −0.0921310
\(827\) −19.2982 −0.671064 −0.335532 0.942029i \(-0.608916\pi\)
−0.335532 + 0.942029i \(0.608916\pi\)
\(828\) 0 0
\(829\) −50.2459 −1.74511 −0.872556 0.488514i \(-0.837539\pi\)
−0.872556 + 0.488514i \(0.837539\pi\)
\(830\) −68.3896 −2.37384
\(831\) 0 0
\(832\) 22.7242 0.787821
\(833\) 6.15261 0.213175
\(834\) 0 0
\(835\) 67.3755 2.33162
\(836\) −54.6119 −1.88879
\(837\) 0 0
\(838\) −82.6212 −2.85410
\(839\) −25.8205 −0.891423 −0.445711 0.895177i \(-0.647049\pi\)
−0.445711 + 0.895177i \(0.647049\pi\)
\(840\) 0 0
\(841\) −23.1261 −0.797451
\(842\) −44.3530 −1.52851
\(843\) 0 0
\(844\) −53.7023 −1.84851
\(845\) −32.3207 −1.11186
\(846\) 0 0
\(847\) 2.07469 0.0712872
\(848\) −16.8780 −0.579591
\(849\) 0 0
\(850\) 103.589 3.55307
\(851\) 46.0970 1.58018
\(852\) 0 0
\(853\) −17.2283 −0.589887 −0.294943 0.955515i \(-0.595301\pi\)
−0.294943 + 0.955515i \(0.595301\pi\)
\(854\) −17.4270 −0.596338
\(855\) 0 0
\(856\) 66.3191 2.26674
\(857\) −1.30072 −0.0444319 −0.0222159 0.999753i \(-0.507072\pi\)
−0.0222159 + 0.999753i \(0.507072\pi\)
\(858\) 0 0
\(859\) −43.2218 −1.47471 −0.737355 0.675505i \(-0.763926\pi\)
−0.737355 + 0.675505i \(0.763926\pi\)
\(860\) −32.9828 −1.12471
\(861\) 0 0
\(862\) 37.5606 1.27932
\(863\) −41.9644 −1.42849 −0.714243 0.699898i \(-0.753229\pi\)
−0.714243 + 0.699898i \(0.753229\pi\)
\(864\) 0 0
\(865\) −45.1453 −1.53499
\(866\) −42.9076 −1.45806
\(867\) 0 0
\(868\) −6.35706 −0.215773
\(869\) −30.6244 −1.03886
\(870\) 0 0
\(871\) 21.1451 0.716474
\(872\) 20.1560 0.682568
\(873\) 0 0
\(874\) −79.8917 −2.70238
\(875\) 7.44093 0.251549
\(876\) 0 0
\(877\) −10.1477 −0.342665 −0.171333 0.985213i \(-0.554807\pi\)
−0.171333 + 0.985213i \(0.554807\pi\)
\(878\) 41.6768 1.40652
\(879\) 0 0
\(880\) 20.0088 0.674495
\(881\) −5.94565 −0.200314 −0.100157 0.994972i \(-0.531934\pi\)
−0.100157 + 0.994972i \(0.531934\pi\)
\(882\) 0 0
\(883\) 45.8661 1.54352 0.771758 0.635916i \(-0.219378\pi\)
0.771758 + 0.635916i \(0.219378\pi\)
\(884\) −42.3388 −1.42401
\(885\) 0 0
\(886\) 28.9534 0.972710
\(887\) 46.5631 1.56344 0.781718 0.623632i \(-0.214344\pi\)
0.781718 + 0.623632i \(0.214344\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −45.9053 −1.53875
\(891\) 0 0
\(892\) 35.7758 1.19786
\(893\) 13.1096 0.438697
\(894\) 0 0
\(895\) −91.9831 −3.07466
\(896\) −20.4988 −0.684817
\(897\) 0 0
\(898\) −13.1320 −0.438220
\(899\) 4.31959 0.144066
\(900\) 0 0
\(901\) −65.3749 −2.17795
\(902\) −53.8082 −1.79162
\(903\) 0 0
\(904\) −1.69957 −0.0565267
\(905\) 10.9232 0.363099
\(906\) 0 0
\(907\) 56.8250 1.88684 0.943421 0.331598i \(-0.107588\pi\)
0.943421 + 0.331598i \(0.107588\pi\)
\(908\) −74.3191 −2.46636
\(909\) 0 0
\(910\) −15.8577 −0.525679
\(911\) 21.2254 0.703230 0.351615 0.936145i \(-0.385633\pi\)
0.351615 + 0.936145i \(0.385633\pi\)
\(912\) 0 0
\(913\) −30.0861 −0.995706
\(914\) 54.0808 1.78883
\(915\) 0 0
\(916\) 7.99751 0.264245
\(917\) −2.56902 −0.0848366
\(918\) 0 0
\(919\) 27.1303 0.894945 0.447472 0.894298i \(-0.352324\pi\)
0.447472 + 0.894298i \(0.352324\pi\)
\(920\) 102.981 3.39518
\(921\) 0 0
\(922\) −47.2511 −1.55613
\(923\) −23.0676 −0.759281
\(924\) 0 0
\(925\) 41.1356 1.35253
\(926\) 84.1798 2.76632
\(927\) 0 0
\(928\) 8.83568 0.290045
\(929\) −28.0177 −0.919231 −0.459615 0.888118i \(-0.652013\pi\)
−0.459615 + 0.888118i \(0.652013\pi\)
\(930\) 0 0
\(931\) −4.23441 −0.138777
\(932\) 73.2610 2.39974
\(933\) 0 0
\(934\) −8.00676 −0.261989
\(935\) 77.5018 2.53458
\(936\) 0 0
\(937\) 31.6573 1.03420 0.517100 0.855925i \(-0.327012\pi\)
0.517100 + 0.855925i \(0.327012\pi\)
\(938\) −25.8589 −0.844324
\(939\) 0 0
\(940\) −38.4691 −1.25472
\(941\) −24.7886 −0.808086 −0.404043 0.914740i \(-0.632395\pi\)
−0.404043 + 0.914740i \(0.632395\pi\)
\(942\) 0 0
\(943\) −50.4355 −1.64240
\(944\) −1.78263 −0.0580197
\(945\) 0 0
\(946\) −22.6460 −0.736285
\(947\) −55.5768 −1.80600 −0.903001 0.429638i \(-0.858641\pi\)
−0.903001 + 0.429638i \(0.858641\pi\)
\(948\) 0 0
\(949\) −24.0998 −0.782314
\(950\) −71.2931 −2.31305
\(951\) 0 0
\(952\) 22.7443 0.737149
\(953\) 34.7345 1.12516 0.562580 0.826743i \(-0.309809\pi\)
0.562580 + 0.826743i \(0.309809\pi\)
\(954\) 0 0
\(955\) 23.3650 0.756072
\(956\) 59.1904 1.91436
\(957\) 0 0
\(958\) 9.63723 0.311365
\(959\) 3.98364 0.128638
\(960\) 0 0
\(961\) −27.8234 −0.897530
\(962\) −26.2404 −0.846025
\(963\) 0 0
\(964\) 20.6216 0.664176
\(965\) 34.9591 1.12537
\(966\) 0 0
\(967\) 44.2329 1.42244 0.711218 0.702972i \(-0.248144\pi\)
0.711218 + 0.702972i \(0.248144\pi\)
\(968\) 7.66951 0.246507
\(969\) 0 0
\(970\) 32.6125 1.04712
\(971\) 39.4528 1.26610 0.633050 0.774111i \(-0.281803\pi\)
0.633050 + 0.774111i \(0.281803\pi\)
\(972\) 0 0
\(973\) 10.9220 0.350142
\(974\) 33.7891 1.08267
\(975\) 0 0
\(976\) −11.7324 −0.375545
\(977\) 11.1644 0.357180 0.178590 0.983924i \(-0.442846\pi\)
0.178590 + 0.983924i \(0.442846\pi\)
\(978\) 0 0
\(979\) −20.1948 −0.645428
\(980\) 12.4255 0.396919
\(981\) 0 0
\(982\) −8.49757 −0.271168
\(983\) −15.1449 −0.483047 −0.241524 0.970395i \(-0.577647\pi\)
−0.241524 + 0.970395i \(0.577647\pi\)
\(984\) 0 0
\(985\) −25.2633 −0.804954
\(986\) −35.1825 −1.12044
\(987\) 0 0
\(988\) 29.1389 0.927032
\(989\) −21.2265 −0.674965
\(990\) 0 0
\(991\) −50.2569 −1.59646 −0.798232 0.602351i \(-0.794231\pi\)
−0.798232 + 0.602351i \(0.794231\pi\)
\(992\) 6.49761 0.206299
\(993\) 0 0
\(994\) 28.2101 0.894769
\(995\) −94.2328 −2.98738
\(996\) 0 0
\(997\) 35.0681 1.11062 0.555308 0.831645i \(-0.312600\pi\)
0.555308 + 0.831645i \(0.312600\pi\)
\(998\) 20.4204 0.646398
\(999\) 0 0
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 \(a_p\))