Properties

Label 6008.2.a.e.1.22
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.410037 q^{3} +0.180422 q^{5} -3.49245 q^{7} -2.83187 q^{9} +O(q^{10})\) \(q-0.410037 q^{3} +0.180422 q^{5} -3.49245 q^{7} -2.83187 q^{9} -2.01646 q^{11} -5.49316 q^{13} -0.0739798 q^{15} -3.92356 q^{17} -4.57585 q^{19} +1.43203 q^{21} +0.277604 q^{23} -4.96745 q^{25} +2.39128 q^{27} -3.41534 q^{29} -5.41640 q^{31} +0.826824 q^{33} -0.630115 q^{35} -2.83207 q^{37} +2.25240 q^{39} +2.24221 q^{41} -0.371008 q^{43} -0.510932 q^{45} +3.31206 q^{47} +5.19719 q^{49} +1.60880 q^{51} +13.6411 q^{53} -0.363814 q^{55} +1.87627 q^{57} +0.754139 q^{59} -1.25383 q^{61} +9.89016 q^{63} -0.991087 q^{65} -4.39453 q^{67} -0.113828 q^{69} -5.03532 q^{71} -0.365337 q^{73} +2.03684 q^{75} +7.04238 q^{77} -0.408161 q^{79} +7.51509 q^{81} -7.26930 q^{83} -0.707897 q^{85} +1.40041 q^{87} +8.52128 q^{89} +19.1846 q^{91} +2.22093 q^{93} -0.825584 q^{95} +11.6354 q^{97} +5.71035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.410037 −0.236735 −0.118368 0.992970i \(-0.537766\pi\)
−0.118368 + 0.992970i \(0.537766\pi\)
\(4\) 0 0
\(5\) 0.180422 0.0806872 0.0403436 0.999186i \(-0.487155\pi\)
0.0403436 + 0.999186i \(0.487155\pi\)
\(6\) 0 0
\(7\) −3.49245 −1.32002 −0.660010 0.751256i \(-0.729448\pi\)
−0.660010 + 0.751256i \(0.729448\pi\)
\(8\) 0 0
\(9\) −2.83187 −0.943957
\(10\) 0 0
\(11\) −2.01646 −0.607986 −0.303993 0.952674i \(-0.598320\pi\)
−0.303993 + 0.952674i \(0.598320\pi\)
\(12\) 0 0
\(13\) −5.49316 −1.52353 −0.761764 0.647855i \(-0.775666\pi\)
−0.761764 + 0.647855i \(0.775666\pi\)
\(14\) 0 0
\(15\) −0.0739798 −0.0191015
\(16\) 0 0
\(17\) −3.92356 −0.951603 −0.475801 0.879553i \(-0.657842\pi\)
−0.475801 + 0.879553i \(0.657842\pi\)
\(18\) 0 0
\(19\) −4.57585 −1.04977 −0.524886 0.851173i \(-0.675892\pi\)
−0.524886 + 0.851173i \(0.675892\pi\)
\(20\) 0 0
\(21\) 1.43203 0.312495
\(22\) 0 0
\(23\) 0.277604 0.0578844 0.0289422 0.999581i \(-0.490786\pi\)
0.0289422 + 0.999581i \(0.490786\pi\)
\(24\) 0 0
\(25\) −4.96745 −0.993490
\(26\) 0 0
\(27\) 2.39128 0.460203
\(28\) 0 0
\(29\) −3.41534 −0.634212 −0.317106 0.948390i \(-0.602711\pi\)
−0.317106 + 0.948390i \(0.602711\pi\)
\(30\) 0 0
\(31\) −5.41640 −0.972815 −0.486407 0.873732i \(-0.661693\pi\)
−0.486407 + 0.873732i \(0.661693\pi\)
\(32\) 0 0
\(33\) 0.826824 0.143932
\(34\) 0 0
\(35\) −0.630115 −0.106509
\(36\) 0 0
\(37\) −2.83207 −0.465590 −0.232795 0.972526i \(-0.574787\pi\)
−0.232795 + 0.972526i \(0.574787\pi\)
\(38\) 0 0
\(39\) 2.25240 0.360672
\(40\) 0 0
\(41\) 2.24221 0.350174 0.175087 0.984553i \(-0.443979\pi\)
0.175087 + 0.984553i \(0.443979\pi\)
\(42\) 0 0
\(43\) −0.371008 −0.0565781 −0.0282891 0.999600i \(-0.509006\pi\)
−0.0282891 + 0.999600i \(0.509006\pi\)
\(44\) 0 0
\(45\) −0.510932 −0.0761652
\(46\) 0 0
\(47\) 3.31206 0.483114 0.241557 0.970387i \(-0.422342\pi\)
0.241557 + 0.970387i \(0.422342\pi\)
\(48\) 0 0
\(49\) 5.19719 0.742455
\(50\) 0 0
\(51\) 1.60880 0.225278
\(52\) 0 0
\(53\) 13.6411 1.87375 0.936877 0.349658i \(-0.113702\pi\)
0.936877 + 0.349658i \(0.113702\pi\)
\(54\) 0 0
\(55\) −0.363814 −0.0490567
\(56\) 0 0
\(57\) 1.87627 0.248518
\(58\) 0 0
\(59\) 0.754139 0.0981805 0.0490902 0.998794i \(-0.484368\pi\)
0.0490902 + 0.998794i \(0.484368\pi\)
\(60\) 0 0
\(61\) −1.25383 −0.160537 −0.0802683 0.996773i \(-0.525578\pi\)
−0.0802683 + 0.996773i \(0.525578\pi\)
\(62\) 0 0
\(63\) 9.89016 1.24604
\(64\) 0 0
\(65\) −0.991087 −0.122929
\(66\) 0 0
\(67\) −4.39453 −0.536877 −0.268439 0.963297i \(-0.586508\pi\)
−0.268439 + 0.963297i \(0.586508\pi\)
\(68\) 0 0
\(69\) −0.113828 −0.0137033
\(70\) 0 0
\(71\) −5.03532 −0.597583 −0.298791 0.954318i \(-0.596584\pi\)
−0.298791 + 0.954318i \(0.596584\pi\)
\(72\) 0 0
\(73\) −0.365337 −0.0427595 −0.0213797 0.999771i \(-0.506806\pi\)
−0.0213797 + 0.999771i \(0.506806\pi\)
\(74\) 0 0
\(75\) 2.03684 0.235194
\(76\) 0 0
\(77\) 7.04238 0.802554
\(78\) 0 0
\(79\) −0.408161 −0.0459216 −0.0229608 0.999736i \(-0.507309\pi\)
−0.0229608 + 0.999736i \(0.507309\pi\)
\(80\) 0 0
\(81\) 7.51509 0.835010
\(82\) 0 0
\(83\) −7.26930 −0.797909 −0.398955 0.916971i \(-0.630627\pi\)
−0.398955 + 0.916971i \(0.630627\pi\)
\(84\) 0 0
\(85\) −0.707897 −0.0767822
\(86\) 0 0
\(87\) 1.40041 0.150140
\(88\) 0 0
\(89\) 8.52128 0.903254 0.451627 0.892207i \(-0.350844\pi\)
0.451627 + 0.892207i \(0.350844\pi\)
\(90\) 0 0
\(91\) 19.1846 2.01109
\(92\) 0 0
\(93\) 2.22093 0.230299
\(94\) 0 0
\(95\) −0.825584 −0.0847031
\(96\) 0 0
\(97\) 11.6354 1.18139 0.590697 0.806893i \(-0.298853\pi\)
0.590697 + 0.806893i \(0.298853\pi\)
\(98\) 0 0
\(99\) 5.71035 0.573912
\(100\) 0 0
\(101\) −6.23326 −0.620232 −0.310116 0.950699i \(-0.600368\pi\)
−0.310116 + 0.950699i \(0.600368\pi\)
\(102\) 0 0
\(103\) −13.0353 −1.28440 −0.642202 0.766535i \(-0.721979\pi\)
−0.642202 + 0.766535i \(0.721979\pi\)
\(104\) 0 0
\(105\) 0.258370 0.0252144
\(106\) 0 0
\(107\) −5.24662 −0.507210 −0.253605 0.967308i \(-0.581616\pi\)
−0.253605 + 0.967308i \(0.581616\pi\)
\(108\) 0 0
\(109\) −0.624958 −0.0598602 −0.0299301 0.999552i \(-0.509528\pi\)
−0.0299301 + 0.999552i \(0.509528\pi\)
\(110\) 0 0
\(111\) 1.16125 0.110221
\(112\) 0 0
\(113\) 4.57500 0.430380 0.215190 0.976572i \(-0.430963\pi\)
0.215190 + 0.976572i \(0.430963\pi\)
\(114\) 0 0
\(115\) 0.0500859 0.00467053
\(116\) 0 0
\(117\) 15.5559 1.43814
\(118\) 0 0
\(119\) 13.7028 1.25614
\(120\) 0 0
\(121\) −6.93389 −0.630353
\(122\) 0 0
\(123\) −0.919387 −0.0828984
\(124\) 0 0
\(125\) −1.79835 −0.160849
\(126\) 0 0
\(127\) −18.3317 −1.62668 −0.813339 0.581790i \(-0.802352\pi\)
−0.813339 + 0.581790i \(0.802352\pi\)
\(128\) 0 0
\(129\) 0.152127 0.0133940
\(130\) 0 0
\(131\) −1.97073 −0.172183 −0.0860916 0.996287i \(-0.527438\pi\)
−0.0860916 + 0.996287i \(0.527438\pi\)
\(132\) 0 0
\(133\) 15.9809 1.38572
\(134\) 0 0
\(135\) 0.431440 0.0371325
\(136\) 0 0
\(137\) 4.92357 0.420649 0.210324 0.977632i \(-0.432548\pi\)
0.210324 + 0.977632i \(0.432548\pi\)
\(138\) 0 0
\(139\) 1.08412 0.0919537 0.0459768 0.998943i \(-0.485360\pi\)
0.0459768 + 0.998943i \(0.485360\pi\)
\(140\) 0 0
\(141\) −1.35807 −0.114370
\(142\) 0 0
\(143\) 11.0767 0.926283
\(144\) 0 0
\(145\) −0.616202 −0.0511728
\(146\) 0 0
\(147\) −2.13104 −0.175765
\(148\) 0 0
\(149\) 21.0672 1.72589 0.862946 0.505296i \(-0.168617\pi\)
0.862946 + 0.505296i \(0.168617\pi\)
\(150\) 0 0
\(151\) −10.9313 −0.889579 −0.444790 0.895635i \(-0.646722\pi\)
−0.444790 + 0.895635i \(0.646722\pi\)
\(152\) 0 0
\(153\) 11.1110 0.898272
\(154\) 0 0
\(155\) −0.977239 −0.0784937
\(156\) 0 0
\(157\) −6.84675 −0.546430 −0.273215 0.961953i \(-0.588087\pi\)
−0.273215 + 0.961953i \(0.588087\pi\)
\(158\) 0 0
\(159\) −5.59337 −0.443583
\(160\) 0 0
\(161\) −0.969517 −0.0764086
\(162\) 0 0
\(163\) −7.77039 −0.608624 −0.304312 0.952572i \(-0.598426\pi\)
−0.304312 + 0.952572i \(0.598426\pi\)
\(164\) 0 0
\(165\) 0.149177 0.0116134
\(166\) 0 0
\(167\) 5.91472 0.457695 0.228847 0.973462i \(-0.426504\pi\)
0.228847 + 0.973462i \(0.426504\pi\)
\(168\) 0 0
\(169\) 17.1748 1.32114
\(170\) 0 0
\(171\) 12.9582 0.990938
\(172\) 0 0
\(173\) 11.9324 0.907203 0.453602 0.891205i \(-0.350139\pi\)
0.453602 + 0.891205i \(0.350139\pi\)
\(174\) 0 0
\(175\) 17.3485 1.31143
\(176\) 0 0
\(177\) −0.309225 −0.0232428
\(178\) 0 0
\(179\) −5.53752 −0.413894 −0.206947 0.978352i \(-0.566353\pi\)
−0.206947 + 0.978352i \(0.566353\pi\)
\(180\) 0 0
\(181\) 5.89037 0.437828 0.218914 0.975744i \(-0.429749\pi\)
0.218914 + 0.975744i \(0.429749\pi\)
\(182\) 0 0
\(183\) 0.514117 0.0380046
\(184\) 0 0
\(185\) −0.510969 −0.0375672
\(186\) 0 0
\(187\) 7.91170 0.578561
\(188\) 0 0
\(189\) −8.35143 −0.607477
\(190\) 0 0
\(191\) 23.1837 1.67751 0.838756 0.544507i \(-0.183283\pi\)
0.838756 + 0.544507i \(0.183283\pi\)
\(192\) 0 0
\(193\) −3.24077 −0.233276 −0.116638 0.993175i \(-0.537212\pi\)
−0.116638 + 0.993175i \(0.537212\pi\)
\(194\) 0 0
\(195\) 0.406383 0.0291017
\(196\) 0 0
\(197\) −12.1180 −0.863371 −0.431686 0.902024i \(-0.642081\pi\)
−0.431686 + 0.902024i \(0.642081\pi\)
\(198\) 0 0
\(199\) −6.10518 −0.432785 −0.216392 0.976306i \(-0.569429\pi\)
−0.216392 + 0.976306i \(0.569429\pi\)
\(200\) 0 0
\(201\) 1.80192 0.127098
\(202\) 0 0
\(203\) 11.9279 0.837173
\(204\) 0 0
\(205\) 0.404544 0.0282545
\(206\) 0 0
\(207\) −0.786138 −0.0546404
\(208\) 0 0
\(209\) 9.22701 0.638246
\(210\) 0 0
\(211\) −14.3433 −0.987435 −0.493718 0.869622i \(-0.664362\pi\)
−0.493718 + 0.869622i \(0.664362\pi\)
\(212\) 0 0
\(213\) 2.06467 0.141469
\(214\) 0 0
\(215\) −0.0669380 −0.00456513
\(216\) 0 0
\(217\) 18.9165 1.28414
\(218\) 0 0
\(219\) 0.149802 0.0101227
\(220\) 0 0
\(221\) 21.5527 1.44979
\(222\) 0 0
\(223\) 0.0622068 0.00416568 0.00208284 0.999998i \(-0.499337\pi\)
0.00208284 + 0.999998i \(0.499337\pi\)
\(224\) 0 0
\(225\) 14.0672 0.937811
\(226\) 0 0
\(227\) −23.2565 −1.54359 −0.771795 0.635871i \(-0.780641\pi\)
−0.771795 + 0.635871i \(0.780641\pi\)
\(228\) 0 0
\(229\) −19.6069 −1.29566 −0.647830 0.761785i \(-0.724323\pi\)
−0.647830 + 0.761785i \(0.724323\pi\)
\(230\) 0 0
\(231\) −2.88764 −0.189993
\(232\) 0 0
\(233\) −17.1423 −1.12303 −0.561515 0.827466i \(-0.689781\pi\)
−0.561515 + 0.827466i \(0.689781\pi\)
\(234\) 0 0
\(235\) 0.597569 0.0389811
\(236\) 0 0
\(237\) 0.167361 0.0108713
\(238\) 0 0
\(239\) −7.64249 −0.494351 −0.247176 0.968971i \(-0.579502\pi\)
−0.247176 + 0.968971i \(0.579502\pi\)
\(240\) 0 0
\(241\) −6.82941 −0.439921 −0.219961 0.975509i \(-0.570593\pi\)
−0.219961 + 0.975509i \(0.570593\pi\)
\(242\) 0 0
\(243\) −10.2553 −0.657879
\(244\) 0 0
\(245\) 0.937688 0.0599067
\(246\) 0 0
\(247\) 25.1358 1.59936
\(248\) 0 0
\(249\) 2.98068 0.188893
\(250\) 0 0
\(251\) −20.3213 −1.28267 −0.641333 0.767262i \(-0.721618\pi\)
−0.641333 + 0.767262i \(0.721618\pi\)
\(252\) 0 0
\(253\) −0.559777 −0.0351929
\(254\) 0 0
\(255\) 0.290264 0.0181770
\(256\) 0 0
\(257\) 11.2765 0.703411 0.351705 0.936111i \(-0.385602\pi\)
0.351705 + 0.936111i \(0.385602\pi\)
\(258\) 0 0
\(259\) 9.89087 0.614588
\(260\) 0 0
\(261\) 9.67179 0.598669
\(262\) 0 0
\(263\) −27.2337 −1.67930 −0.839650 0.543127i \(-0.817240\pi\)
−0.839650 + 0.543127i \(0.817240\pi\)
\(264\) 0 0
\(265\) 2.46116 0.151188
\(266\) 0 0
\(267\) −3.49404 −0.213832
\(268\) 0 0
\(269\) 11.4551 0.698432 0.349216 0.937042i \(-0.386448\pi\)
0.349216 + 0.937042i \(0.386448\pi\)
\(270\) 0 0
\(271\) −14.7846 −0.898103 −0.449052 0.893506i \(-0.648238\pi\)
−0.449052 + 0.893506i \(0.648238\pi\)
\(272\) 0 0
\(273\) −7.86638 −0.476095
\(274\) 0 0
\(275\) 10.0167 0.604028
\(276\) 0 0
\(277\) −8.47888 −0.509446 −0.254723 0.967014i \(-0.581984\pi\)
−0.254723 + 0.967014i \(0.581984\pi\)
\(278\) 0 0
\(279\) 15.3385 0.918295
\(280\) 0 0
\(281\) −11.7238 −0.699384 −0.349692 0.936865i \(-0.613714\pi\)
−0.349692 + 0.936865i \(0.613714\pi\)
\(282\) 0 0
\(283\) −6.23273 −0.370497 −0.185249 0.982692i \(-0.559309\pi\)
−0.185249 + 0.982692i \(0.559309\pi\)
\(284\) 0 0
\(285\) 0.338520 0.0200522
\(286\) 0 0
\(287\) −7.83078 −0.462237
\(288\) 0 0
\(289\) −1.60569 −0.0944522
\(290\) 0 0
\(291\) −4.77094 −0.279677
\(292\) 0 0
\(293\) −11.9895 −0.700436 −0.350218 0.936668i \(-0.613893\pi\)
−0.350218 + 0.936668i \(0.613893\pi\)
\(294\) 0 0
\(295\) 0.136063 0.00792191
\(296\) 0 0
\(297\) −4.82193 −0.279797
\(298\) 0 0
\(299\) −1.52492 −0.0881885
\(300\) 0 0
\(301\) 1.29572 0.0746843
\(302\) 0 0
\(303\) 2.55587 0.146831
\(304\) 0 0
\(305\) −0.226219 −0.0129533
\(306\) 0 0
\(307\) 11.1016 0.633601 0.316800 0.948492i \(-0.397391\pi\)
0.316800 + 0.948492i \(0.397391\pi\)
\(308\) 0 0
\(309\) 5.34495 0.304064
\(310\) 0 0
\(311\) 10.9242 0.619456 0.309728 0.950825i \(-0.399762\pi\)
0.309728 + 0.950825i \(0.399762\pi\)
\(312\) 0 0
\(313\) −5.27447 −0.298131 −0.149065 0.988827i \(-0.547626\pi\)
−0.149065 + 0.988827i \(0.547626\pi\)
\(314\) 0 0
\(315\) 1.78440 0.100540
\(316\) 0 0
\(317\) 13.8124 0.775782 0.387891 0.921705i \(-0.373204\pi\)
0.387891 + 0.921705i \(0.373204\pi\)
\(318\) 0 0
\(319\) 6.88689 0.385592
\(320\) 0 0
\(321\) 2.15131 0.120074
\(322\) 0 0
\(323\) 17.9536 0.998965
\(324\) 0 0
\(325\) 27.2870 1.51361
\(326\) 0 0
\(327\) 0.256256 0.0141710
\(328\) 0 0
\(329\) −11.5672 −0.637720
\(330\) 0 0
\(331\) 1.03867 0.0570904 0.0285452 0.999593i \(-0.490913\pi\)
0.0285452 + 0.999593i \(0.490913\pi\)
\(332\) 0 0
\(333\) 8.02006 0.439497
\(334\) 0 0
\(335\) −0.792871 −0.0433192
\(336\) 0 0
\(337\) −9.88970 −0.538727 −0.269363 0.963039i \(-0.586813\pi\)
−0.269363 + 0.963039i \(0.586813\pi\)
\(338\) 0 0
\(339\) −1.87592 −0.101886
\(340\) 0 0
\(341\) 10.9220 0.591458
\(342\) 0 0
\(343\) 6.29623 0.339964
\(344\) 0 0
\(345\) −0.0205371 −0.00110568
\(346\) 0 0
\(347\) 19.3954 1.04120 0.520600 0.853801i \(-0.325708\pi\)
0.520600 + 0.853801i \(0.325708\pi\)
\(348\) 0 0
\(349\) 7.49915 0.401420 0.200710 0.979651i \(-0.435675\pi\)
0.200710 + 0.979651i \(0.435675\pi\)
\(350\) 0 0
\(351\) −13.1357 −0.701132
\(352\) 0 0
\(353\) 9.08893 0.483755 0.241878 0.970307i \(-0.422237\pi\)
0.241878 + 0.970307i \(0.422237\pi\)
\(354\) 0 0
\(355\) −0.908484 −0.0482173
\(356\) 0 0
\(357\) −5.61867 −0.297371
\(358\) 0 0
\(359\) 0.102206 0.00539424 0.00269712 0.999996i \(-0.499141\pi\)
0.00269712 + 0.999996i \(0.499141\pi\)
\(360\) 0 0
\(361\) 1.93837 0.102019
\(362\) 0 0
\(363\) 2.84315 0.149227
\(364\) 0 0
\(365\) −0.0659149 −0.00345015
\(366\) 0 0
\(367\) 22.8350 1.19198 0.595988 0.802993i \(-0.296760\pi\)
0.595988 + 0.802993i \(0.296760\pi\)
\(368\) 0 0
\(369\) −6.34963 −0.330549
\(370\) 0 0
\(371\) −47.6410 −2.47340
\(372\) 0 0
\(373\) 7.10713 0.367993 0.183997 0.982927i \(-0.441096\pi\)
0.183997 + 0.982927i \(0.441096\pi\)
\(374\) 0 0
\(375\) 0.737389 0.0380786
\(376\) 0 0
\(377\) 18.7610 0.966240
\(378\) 0 0
\(379\) 13.3809 0.687329 0.343665 0.939092i \(-0.388332\pi\)
0.343665 + 0.939092i \(0.388332\pi\)
\(380\) 0 0
\(381\) 7.51669 0.385092
\(382\) 0 0
\(383\) −28.7677 −1.46996 −0.734980 0.678089i \(-0.762808\pi\)
−0.734980 + 0.678089i \(0.762808\pi\)
\(384\) 0 0
\(385\) 1.27060 0.0647559
\(386\) 0 0
\(387\) 1.05065 0.0534073
\(388\) 0 0
\(389\) 17.2013 0.872142 0.436071 0.899912i \(-0.356370\pi\)
0.436071 + 0.899912i \(0.356370\pi\)
\(390\) 0 0
\(391\) −1.08920 −0.0550830
\(392\) 0 0
\(393\) 0.808071 0.0407618
\(394\) 0 0
\(395\) −0.0736412 −0.00370529
\(396\) 0 0
\(397\) −13.9670 −0.700985 −0.350493 0.936565i \(-0.613986\pi\)
−0.350493 + 0.936565i \(0.613986\pi\)
\(398\) 0 0
\(399\) −6.55276 −0.328048
\(400\) 0 0
\(401\) −26.9062 −1.34363 −0.671815 0.740719i \(-0.734485\pi\)
−0.671815 + 0.740719i \(0.734485\pi\)
\(402\) 0 0
\(403\) 29.7532 1.48211
\(404\) 0 0
\(405\) 1.35589 0.0673747
\(406\) 0 0
\(407\) 5.71076 0.283072
\(408\) 0 0
\(409\) 23.1755 1.14596 0.572978 0.819571i \(-0.305788\pi\)
0.572978 + 0.819571i \(0.305788\pi\)
\(410\) 0 0
\(411\) −2.01885 −0.0995823
\(412\) 0 0
\(413\) −2.63379 −0.129600
\(414\) 0 0
\(415\) −1.31154 −0.0643811
\(416\) 0 0
\(417\) −0.444529 −0.0217687
\(418\) 0 0
\(419\) −17.7164 −0.865502 −0.432751 0.901514i \(-0.642457\pi\)
−0.432751 + 0.901514i \(0.642457\pi\)
\(420\) 0 0
\(421\) −23.2412 −1.13271 −0.566354 0.824162i \(-0.691647\pi\)
−0.566354 + 0.824162i \(0.691647\pi\)
\(422\) 0 0
\(423\) −9.37933 −0.456039
\(424\) 0 0
\(425\) 19.4901 0.945407
\(426\) 0 0
\(427\) 4.37894 0.211912
\(428\) 0 0
\(429\) −4.54187 −0.219284
\(430\) 0 0
\(431\) 19.8001 0.953737 0.476868 0.878975i \(-0.341772\pi\)
0.476868 + 0.878975i \(0.341772\pi\)
\(432\) 0 0
\(433\) 16.6762 0.801409 0.400705 0.916207i \(-0.368765\pi\)
0.400705 + 0.916207i \(0.368765\pi\)
\(434\) 0 0
\(435\) 0.252666 0.0121144
\(436\) 0 0
\(437\) −1.27027 −0.0607654
\(438\) 0 0
\(439\) −26.6952 −1.27409 −0.637046 0.770826i \(-0.719844\pi\)
−0.637046 + 0.770826i \(0.719844\pi\)
\(440\) 0 0
\(441\) −14.7178 −0.700846
\(442\) 0 0
\(443\) −10.8551 −0.515743 −0.257871 0.966179i \(-0.583021\pi\)
−0.257871 + 0.966179i \(0.583021\pi\)
\(444\) 0 0
\(445\) 1.53743 0.0728810
\(446\) 0 0
\(447\) −8.63833 −0.408579
\(448\) 0 0
\(449\) 16.9569 0.800248 0.400124 0.916461i \(-0.368967\pi\)
0.400124 + 0.916461i \(0.368967\pi\)
\(450\) 0 0
\(451\) −4.52132 −0.212901
\(452\) 0 0
\(453\) 4.48225 0.210595
\(454\) 0 0
\(455\) 3.46132 0.162269
\(456\) 0 0
\(457\) −34.8495 −1.63019 −0.815095 0.579327i \(-0.803315\pi\)
−0.815095 + 0.579327i \(0.803315\pi\)
\(458\) 0 0
\(459\) −9.38234 −0.437930
\(460\) 0 0
\(461\) −12.7420 −0.593453 −0.296727 0.954962i \(-0.595895\pi\)
−0.296727 + 0.954962i \(0.595895\pi\)
\(462\) 0 0
\(463\) 13.9365 0.647684 0.323842 0.946111i \(-0.395025\pi\)
0.323842 + 0.946111i \(0.395025\pi\)
\(464\) 0 0
\(465\) 0.400704 0.0185822
\(466\) 0 0
\(467\) 29.2729 1.35459 0.677294 0.735712i \(-0.263152\pi\)
0.677294 + 0.735712i \(0.263152\pi\)
\(468\) 0 0
\(469\) 15.3477 0.708689
\(470\) 0 0
\(471\) 2.80742 0.129359
\(472\) 0 0
\(473\) 0.748122 0.0343987
\(474\) 0 0
\(475\) 22.7303 1.04294
\(476\) 0 0
\(477\) −38.6299 −1.76874
\(478\) 0 0
\(479\) 1.99534 0.0911695 0.0455847 0.998960i \(-0.485485\pi\)
0.0455847 + 0.998960i \(0.485485\pi\)
\(480\) 0 0
\(481\) 15.5570 0.709339
\(482\) 0 0
\(483\) 0.397538 0.0180886
\(484\) 0 0
\(485\) 2.09928 0.0953234
\(486\) 0 0
\(487\) −0.566670 −0.0256783 −0.0128391 0.999918i \(-0.504087\pi\)
−0.0128391 + 0.999918i \(0.504087\pi\)
\(488\) 0 0
\(489\) 3.18615 0.144083
\(490\) 0 0
\(491\) −2.03998 −0.0920630 −0.0460315 0.998940i \(-0.514657\pi\)
−0.0460315 + 0.998940i \(0.514657\pi\)
\(492\) 0 0
\(493\) 13.4003 0.603518
\(494\) 0 0
\(495\) 1.03027 0.0463074
\(496\) 0 0
\(497\) 17.5856 0.788822
\(498\) 0 0
\(499\) −10.8936 −0.487665 −0.243832 0.969817i \(-0.578405\pi\)
−0.243832 + 0.969817i \(0.578405\pi\)
\(500\) 0 0
\(501\) −2.42526 −0.108352
\(502\) 0 0
\(503\) 29.4660 1.31383 0.656913 0.753967i \(-0.271862\pi\)
0.656913 + 0.753967i \(0.271862\pi\)
\(504\) 0 0
\(505\) −1.12462 −0.0500448
\(506\) 0 0
\(507\) −7.04230 −0.312760
\(508\) 0 0
\(509\) 33.8480 1.50029 0.750144 0.661275i \(-0.229984\pi\)
0.750144 + 0.661275i \(0.229984\pi\)
\(510\) 0 0
\(511\) 1.27592 0.0564434
\(512\) 0 0
\(513\) −10.9421 −0.483107
\(514\) 0 0
\(515\) −2.35185 −0.103635
\(516\) 0 0
\(517\) −6.67864 −0.293726
\(518\) 0 0
\(519\) −4.89272 −0.214767
\(520\) 0 0
\(521\) −0.842945 −0.0369301 −0.0184650 0.999830i \(-0.505878\pi\)
−0.0184650 + 0.999830i \(0.505878\pi\)
\(522\) 0 0
\(523\) 17.5336 0.766689 0.383345 0.923605i \(-0.374772\pi\)
0.383345 + 0.923605i \(0.374772\pi\)
\(524\) 0 0
\(525\) −7.11355 −0.310461
\(526\) 0 0
\(527\) 21.2516 0.925733
\(528\) 0 0
\(529\) −22.9229 −0.996649
\(530\) 0 0
\(531\) −2.13562 −0.0926781
\(532\) 0 0
\(533\) −12.3168 −0.533499
\(534\) 0 0
\(535\) −0.946607 −0.0409254
\(536\) 0 0
\(537\) 2.27059 0.0979831
\(538\) 0 0
\(539\) −10.4799 −0.451402
\(540\) 0 0
\(541\) 12.6336 0.543161 0.271580 0.962416i \(-0.412454\pi\)
0.271580 + 0.962416i \(0.412454\pi\)
\(542\) 0 0
\(543\) −2.41527 −0.103649
\(544\) 0 0
\(545\) −0.112756 −0.00482995
\(546\) 0 0
\(547\) −10.6721 −0.456308 −0.228154 0.973625i \(-0.573269\pi\)
−0.228154 + 0.973625i \(0.573269\pi\)
\(548\) 0 0
\(549\) 3.55069 0.151540
\(550\) 0 0
\(551\) 15.6281 0.665777
\(552\) 0 0
\(553\) 1.42548 0.0606175
\(554\) 0 0
\(555\) 0.209516 0.00889346
\(556\) 0 0
\(557\) −15.5565 −0.659149 −0.329574 0.944130i \(-0.606905\pi\)
−0.329574 + 0.944130i \(0.606905\pi\)
\(558\) 0 0
\(559\) 2.03800 0.0861984
\(560\) 0 0
\(561\) −3.24409 −0.136966
\(562\) 0 0
\(563\) 12.1477 0.511963 0.255981 0.966682i \(-0.417601\pi\)
0.255981 + 0.966682i \(0.417601\pi\)
\(564\) 0 0
\(565\) 0.825432 0.0347262
\(566\) 0 0
\(567\) −26.2461 −1.10223
\(568\) 0 0
\(569\) 21.7486 0.911749 0.455875 0.890044i \(-0.349327\pi\)
0.455875 + 0.890044i \(0.349327\pi\)
\(570\) 0 0
\(571\) −30.3672 −1.27083 −0.635414 0.772172i \(-0.719171\pi\)
−0.635414 + 0.772172i \(0.719171\pi\)
\(572\) 0 0
\(573\) −9.50617 −0.397126
\(574\) 0 0
\(575\) −1.37898 −0.0575076
\(576\) 0 0
\(577\) −18.2687 −0.760538 −0.380269 0.924876i \(-0.624169\pi\)
−0.380269 + 0.924876i \(0.624169\pi\)
\(578\) 0 0
\(579\) 1.32884 0.0552245
\(580\) 0 0
\(581\) 25.3876 1.05326
\(582\) 0 0
\(583\) −27.5068 −1.13922
\(584\) 0 0
\(585\) 2.80663 0.116040
\(586\) 0 0
\(587\) 18.5051 0.763787 0.381893 0.924206i \(-0.375272\pi\)
0.381893 + 0.924206i \(0.375272\pi\)
\(588\) 0 0
\(589\) 24.7846 1.02123
\(590\) 0 0
\(591\) 4.96883 0.204390
\(592\) 0 0
\(593\) −8.07163 −0.331462 −0.165731 0.986171i \(-0.552998\pi\)
−0.165731 + 0.986171i \(0.552998\pi\)
\(594\) 0 0
\(595\) 2.47229 0.101354
\(596\) 0 0
\(597\) 2.50335 0.102455
\(598\) 0 0
\(599\) −34.7015 −1.41787 −0.708933 0.705276i \(-0.750823\pi\)
−0.708933 + 0.705276i \(0.750823\pi\)
\(600\) 0 0
\(601\) −19.9084 −0.812081 −0.406041 0.913855i \(-0.633091\pi\)
−0.406041 + 0.913855i \(0.633091\pi\)
\(602\) 0 0
\(603\) 12.4447 0.506789
\(604\) 0 0
\(605\) −1.25103 −0.0508615
\(606\) 0 0
\(607\) 36.9716 1.50063 0.750316 0.661080i \(-0.229902\pi\)
0.750316 + 0.661080i \(0.229902\pi\)
\(608\) 0 0
\(609\) −4.89087 −0.198188
\(610\) 0 0
\(611\) −18.1937 −0.736038
\(612\) 0 0
\(613\) 19.7708 0.798537 0.399268 0.916834i \(-0.369264\pi\)
0.399268 + 0.916834i \(0.369264\pi\)
\(614\) 0 0
\(615\) −0.165878 −0.00668884
\(616\) 0 0
\(617\) −5.64097 −0.227097 −0.113548 0.993532i \(-0.536222\pi\)
−0.113548 + 0.993532i \(0.536222\pi\)
\(618\) 0 0
\(619\) 22.0900 0.887872 0.443936 0.896059i \(-0.353582\pi\)
0.443936 + 0.896059i \(0.353582\pi\)
\(620\) 0 0
\(621\) 0.663829 0.0266386
\(622\) 0 0
\(623\) −29.7601 −1.19231
\(624\) 0 0
\(625\) 24.5128 0.980511
\(626\) 0 0
\(627\) −3.78342 −0.151095
\(628\) 0 0
\(629\) 11.1118 0.443057
\(630\) 0 0
\(631\) 35.0590 1.39568 0.697839 0.716255i \(-0.254145\pi\)
0.697839 + 0.716255i \(0.254145\pi\)
\(632\) 0 0
\(633\) 5.88129 0.233760
\(634\) 0 0
\(635\) −3.30745 −0.131252
\(636\) 0 0
\(637\) −28.5490 −1.13115
\(638\) 0 0
\(639\) 14.2594 0.564092
\(640\) 0 0
\(641\) −33.9762 −1.34198 −0.670990 0.741467i \(-0.734130\pi\)
−0.670990 + 0.741467i \(0.734130\pi\)
\(642\) 0 0
\(643\) −26.4390 −1.04265 −0.521326 0.853358i \(-0.674562\pi\)
−0.521326 + 0.853358i \(0.674562\pi\)
\(644\) 0 0
\(645\) 0.0274471 0.00108073
\(646\) 0 0
\(647\) 50.0530 1.96779 0.983893 0.178757i \(-0.0572076\pi\)
0.983893 + 0.178757i \(0.0572076\pi\)
\(648\) 0 0
\(649\) −1.52069 −0.0596923
\(650\) 0 0
\(651\) −7.75647 −0.304000
\(652\) 0 0
\(653\) 7.65981 0.299751 0.149876 0.988705i \(-0.452113\pi\)
0.149876 + 0.988705i \(0.452113\pi\)
\(654\) 0 0
\(655\) −0.355563 −0.0138930
\(656\) 0 0
\(657\) 1.03459 0.0403631
\(658\) 0 0
\(659\) −13.0367 −0.507837 −0.253918 0.967226i \(-0.581719\pi\)
−0.253918 + 0.967226i \(0.581719\pi\)
\(660\) 0 0
\(661\) −5.09055 −0.197999 −0.0989997 0.995087i \(-0.531564\pi\)
−0.0989997 + 0.995087i \(0.531564\pi\)
\(662\) 0 0
\(663\) −8.83742 −0.343217
\(664\) 0 0
\(665\) 2.88331 0.111810
\(666\) 0 0
\(667\) −0.948111 −0.0367110
\(668\) 0 0
\(669\) −0.0255071 −0.000986162 0
\(670\) 0 0
\(671\) 2.52830 0.0976040
\(672\) 0 0
\(673\) 33.8236 1.30380 0.651901 0.758304i \(-0.273972\pi\)
0.651901 + 0.758304i \(0.273972\pi\)
\(674\) 0 0
\(675\) −11.8786 −0.457206
\(676\) 0 0
\(677\) 23.8890 0.918130 0.459065 0.888403i \(-0.348184\pi\)
0.459065 + 0.888403i \(0.348184\pi\)
\(678\) 0 0
\(679\) −40.6360 −1.55946
\(680\) 0 0
\(681\) 9.53604 0.365422
\(682\) 0 0
\(683\) −1.24029 −0.0474583 −0.0237292 0.999718i \(-0.507554\pi\)
−0.0237292 + 0.999718i \(0.507554\pi\)
\(684\) 0 0
\(685\) 0.888321 0.0339410
\(686\) 0 0
\(687\) 8.03955 0.306728
\(688\) 0 0
\(689\) −74.9330 −2.85472
\(690\) 0 0
\(691\) −33.5565 −1.27655 −0.638274 0.769809i \(-0.720351\pi\)
−0.638274 + 0.769809i \(0.720351\pi\)
\(692\) 0 0
\(693\) −19.9431 −0.757576
\(694\) 0 0
\(695\) 0.195599 0.00741949
\(696\) 0 0
\(697\) −8.79743 −0.333226
\(698\) 0 0
\(699\) 7.02899 0.265861
\(700\) 0 0
\(701\) 2.80272 0.105857 0.0529286 0.998598i \(-0.483144\pi\)
0.0529286 + 0.998598i \(0.483144\pi\)
\(702\) 0 0
\(703\) 12.9591 0.488763
\(704\) 0 0
\(705\) −0.245026 −0.00922820
\(706\) 0 0
\(707\) 21.7693 0.818720
\(708\) 0 0
\(709\) 28.5481 1.07214 0.536072 0.844172i \(-0.319907\pi\)
0.536072 + 0.844172i \(0.319907\pi\)
\(710\) 0 0
\(711\) 1.15586 0.0433480
\(712\) 0 0
\(713\) −1.50361 −0.0563108
\(714\) 0 0
\(715\) 1.99849 0.0747392
\(716\) 0 0
\(717\) 3.13370 0.117030
\(718\) 0 0
\(719\) 11.7166 0.436957 0.218479 0.975842i \(-0.429891\pi\)
0.218479 + 0.975842i \(0.429891\pi\)
\(720\) 0 0
\(721\) 45.5250 1.69544
\(722\) 0 0
\(723\) 2.80031 0.104145
\(724\) 0 0
\(725\) 16.9655 0.630083
\(726\) 0 0
\(727\) 10.2324 0.379497 0.189749 0.981833i \(-0.439233\pi\)
0.189749 + 0.981833i \(0.439233\pi\)
\(728\) 0 0
\(729\) −18.3402 −0.679268
\(730\) 0 0
\(731\) 1.45567 0.0538399
\(732\) 0 0
\(733\) 25.4209 0.938941 0.469470 0.882948i \(-0.344445\pi\)
0.469470 + 0.882948i \(0.344445\pi\)
\(734\) 0 0
\(735\) −0.384487 −0.0141820
\(736\) 0 0
\(737\) 8.86140 0.326414
\(738\) 0 0
\(739\) −25.1764 −0.926129 −0.463064 0.886325i \(-0.653250\pi\)
−0.463064 + 0.886325i \(0.653250\pi\)
\(740\) 0 0
\(741\) −10.3066 −0.378624
\(742\) 0 0
\(743\) −42.3613 −1.55408 −0.777042 0.629449i \(-0.783281\pi\)
−0.777042 + 0.629449i \(0.783281\pi\)
\(744\) 0 0
\(745\) 3.80099 0.139257
\(746\) 0 0
\(747\) 20.5857 0.753192
\(748\) 0 0
\(749\) 18.3235 0.669528
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 8.33247 0.303652
\(754\) 0 0
\(755\) −1.97225 −0.0717777
\(756\) 0 0
\(757\) 39.9426 1.45174 0.725869 0.687833i \(-0.241438\pi\)
0.725869 + 0.687833i \(0.241438\pi\)
\(758\) 0 0
\(759\) 0.229529 0.00833139
\(760\) 0 0
\(761\) 14.0575 0.509583 0.254792 0.966996i \(-0.417993\pi\)
0.254792 + 0.966996i \(0.417993\pi\)
\(762\) 0 0
\(763\) 2.18263 0.0790167
\(764\) 0 0
\(765\) 2.00467 0.0724791
\(766\) 0 0
\(767\) −4.14260 −0.149581
\(768\) 0 0
\(769\) 0.0919031 0.00331411 0.00165705 0.999999i \(-0.499473\pi\)
0.00165705 + 0.999999i \(0.499473\pi\)
\(770\) 0 0
\(771\) −4.62380 −0.166522
\(772\) 0 0
\(773\) 1.63172 0.0586888 0.0293444 0.999569i \(-0.490658\pi\)
0.0293444 + 0.999569i \(0.490658\pi\)
\(774\) 0 0
\(775\) 26.9057 0.966481
\(776\) 0 0
\(777\) −4.05562 −0.145495
\(778\) 0 0
\(779\) −10.2600 −0.367602
\(780\) 0 0
\(781\) 10.1535 0.363322
\(782\) 0 0
\(783\) −8.16703 −0.291866
\(784\) 0 0
\(785\) −1.23531 −0.0440899
\(786\) 0 0
\(787\) −17.5960 −0.627230 −0.313615 0.949550i \(-0.601540\pi\)
−0.313615 + 0.949550i \(0.601540\pi\)
\(788\) 0 0
\(789\) 11.1668 0.397549
\(790\) 0 0
\(791\) −15.9780 −0.568111
\(792\) 0 0
\(793\) 6.88749 0.244582
\(794\) 0 0
\(795\) −1.00917 −0.0357915
\(796\) 0 0
\(797\) 23.4818 0.831767 0.415884 0.909418i \(-0.363472\pi\)
0.415884 + 0.909418i \(0.363472\pi\)
\(798\) 0 0
\(799\) −12.9951 −0.459733
\(800\) 0 0
\(801\) −24.1311 −0.852632
\(802\) 0 0
\(803\) 0.736688 0.0259972
\(804\) 0 0
\(805\) −0.174922 −0.00616520
\(806\) 0 0
\(807\) −4.69703 −0.165343
\(808\) 0 0
\(809\) −18.3873 −0.646463 −0.323232 0.946320i \(-0.604769\pi\)
−0.323232 + 0.946320i \(0.604769\pi\)
\(810\) 0 0
\(811\) −36.4010 −1.27821 −0.639106 0.769119i \(-0.720695\pi\)
−0.639106 + 0.769119i \(0.720695\pi\)
\(812\) 0 0
\(813\) 6.06225 0.212613
\(814\) 0 0
\(815\) −1.40195 −0.0491082
\(816\) 0 0
\(817\) 1.69767 0.0593941
\(818\) 0 0
\(819\) −54.3282 −1.89838
\(820\) 0 0
\(821\) 40.5516 1.41526 0.707631 0.706582i \(-0.249764\pi\)
0.707631 + 0.706582i \(0.249764\pi\)
\(822\) 0 0
\(823\) 27.4855 0.958086 0.479043 0.877791i \(-0.340984\pi\)
0.479043 + 0.877791i \(0.340984\pi\)
\(824\) 0 0
\(825\) −4.10720 −0.142994
\(826\) 0 0
\(827\) −15.7910 −0.549105 −0.274553 0.961572i \(-0.588530\pi\)
−0.274553 + 0.961572i \(0.588530\pi\)
\(828\) 0 0
\(829\) −17.9188 −0.622345 −0.311172 0.950354i \(-0.600722\pi\)
−0.311172 + 0.950354i \(0.600722\pi\)
\(830\) 0 0
\(831\) 3.47665 0.120604
\(832\) 0 0
\(833\) −20.3915 −0.706523
\(834\) 0 0
\(835\) 1.06715 0.0369301
\(836\) 0 0
\(837\) −12.9522 −0.447692
\(838\) 0 0
\(839\) −43.4244 −1.49918 −0.749588 0.661905i \(-0.769748\pi\)
−0.749588 + 0.661905i \(0.769748\pi\)
\(840\) 0 0
\(841\) −17.3355 −0.597775
\(842\) 0 0
\(843\) 4.80720 0.165569
\(844\) 0 0
\(845\) 3.09871 0.106599
\(846\) 0 0
\(847\) 24.2162 0.832080
\(848\) 0 0
\(849\) 2.55565 0.0877097
\(850\) 0 0
\(851\) −0.786194 −0.0269504
\(852\) 0 0
\(853\) −38.5267 −1.31913 −0.659564 0.751649i \(-0.729259\pi\)
−0.659564 + 0.751649i \(0.729259\pi\)
\(854\) 0 0
\(855\) 2.33795 0.0799561
\(856\) 0 0
\(857\) −12.4762 −0.426180 −0.213090 0.977033i \(-0.568353\pi\)
−0.213090 + 0.977033i \(0.568353\pi\)
\(858\) 0 0
\(859\) −0.909040 −0.0310160 −0.0155080 0.999880i \(-0.504937\pi\)
−0.0155080 + 0.999880i \(0.504937\pi\)
\(860\) 0 0
\(861\) 3.21091 0.109428
\(862\) 0 0
\(863\) 27.1218 0.923237 0.461619 0.887079i \(-0.347269\pi\)
0.461619 + 0.887079i \(0.347269\pi\)
\(864\) 0 0
\(865\) 2.15287 0.0731997
\(866\) 0 0
\(867\) 0.658391 0.0223601
\(868\) 0 0
\(869\) 0.823040 0.0279197
\(870\) 0 0
\(871\) 24.1399 0.817948
\(872\) 0 0
\(873\) −32.9499 −1.11518
\(874\) 0 0
\(875\) 6.28064 0.212324
\(876\) 0 0
\(877\) 47.2206 1.59453 0.797264 0.603631i \(-0.206280\pi\)
0.797264 + 0.603631i \(0.206280\pi\)
\(878\) 0 0
\(879\) 4.91616 0.165818
\(880\) 0 0
\(881\) −8.51318 −0.286816 −0.143408 0.989664i \(-0.545806\pi\)
−0.143408 + 0.989664i \(0.545806\pi\)
\(882\) 0 0
\(883\) 2.18194 0.0734282 0.0367141 0.999326i \(-0.488311\pi\)
0.0367141 + 0.999326i \(0.488311\pi\)
\(884\) 0 0
\(885\) −0.0557910 −0.00187539
\(886\) 0 0
\(887\) −15.4269 −0.517985 −0.258992 0.965879i \(-0.583390\pi\)
−0.258992 + 0.965879i \(0.583390\pi\)
\(888\) 0 0
\(889\) 64.0226 2.14725
\(890\) 0 0
\(891\) −15.1539 −0.507674
\(892\) 0 0
\(893\) −15.1555 −0.507159
\(894\) 0 0
\(895\) −0.999091 −0.0333959
\(896\) 0 0
\(897\) 0.625275 0.0208773
\(898\) 0 0
\(899\) 18.4988 0.616971
\(900\) 0 0
\(901\) −53.5218 −1.78307
\(902\) 0 0
\(903\) −0.531295 −0.0176804
\(904\) 0 0
\(905\) 1.06275 0.0353271
\(906\) 0 0
\(907\) 10.1984 0.338631 0.169316 0.985562i \(-0.445844\pi\)
0.169316 + 0.985562i \(0.445844\pi\)
\(908\) 0 0
\(909\) 17.6518 0.585473
\(910\) 0 0
\(911\) −40.1284 −1.32951 −0.664756 0.747061i \(-0.731464\pi\)
−0.664756 + 0.747061i \(0.731464\pi\)
\(912\) 0 0
\(913\) 14.6583 0.485117
\(914\) 0 0
\(915\) 0.0927581 0.00306649
\(916\) 0 0
\(917\) 6.88266 0.227285
\(918\) 0 0
\(919\) 1.22547 0.0404247 0.0202123 0.999796i \(-0.493566\pi\)
0.0202123 + 0.999796i \(0.493566\pi\)
\(920\) 0 0
\(921\) −4.55206 −0.149996
\(922\) 0 0
\(923\) 27.6598 0.910434
\(924\) 0 0
\(925\) 14.0682 0.462559
\(926\) 0 0
\(927\) 36.9142 1.21242
\(928\) 0 0
\(929\) 12.1194 0.397626 0.198813 0.980037i \(-0.436291\pi\)
0.198813 + 0.980037i \(0.436291\pi\)
\(930\) 0 0
\(931\) −23.7815 −0.779408
\(932\) 0 0
\(933\) −4.47934 −0.146647
\(934\) 0 0
\(935\) 1.42745 0.0466825
\(936\) 0 0
\(937\) 13.1678 0.430173 0.215086 0.976595i \(-0.430997\pi\)
0.215086 + 0.976595i \(0.430997\pi\)
\(938\) 0 0
\(939\) 2.16273 0.0705780
\(940\) 0 0
\(941\) −4.69697 −0.153117 −0.0765584 0.997065i \(-0.524393\pi\)
−0.0765584 + 0.997065i \(0.524393\pi\)
\(942\) 0 0
\(943\) 0.622445 0.0202696
\(944\) 0 0
\(945\) −1.50678 −0.0490156
\(946\) 0 0
\(947\) −8.17089 −0.265518 −0.132759 0.991148i \(-0.542384\pi\)
−0.132759 + 0.991148i \(0.542384\pi\)
\(948\) 0 0
\(949\) 2.00686 0.0651453
\(950\) 0 0
\(951\) −5.66360 −0.183655
\(952\) 0 0
\(953\) 1.04551 0.0338673 0.0169336 0.999857i \(-0.494610\pi\)
0.0169336 + 0.999857i \(0.494610\pi\)
\(954\) 0 0
\(955\) 4.18285 0.135354
\(956\) 0 0
\(957\) −2.82388 −0.0912831
\(958\) 0 0
\(959\) −17.1953 −0.555265
\(960\) 0 0
\(961\) −1.66257 −0.0536313
\(962\) 0 0
\(963\) 14.8577 0.478784
\(964\) 0 0
\(965\) −0.584706 −0.0188224
\(966\) 0 0
\(967\) 6.74171 0.216799 0.108399 0.994107i \(-0.465427\pi\)
0.108399 + 0.994107i \(0.465427\pi\)
\(968\) 0 0
\(969\) −7.36164 −0.236490
\(970\) 0 0
\(971\) −17.3681 −0.557370 −0.278685 0.960383i \(-0.589898\pi\)
−0.278685 + 0.960383i \(0.589898\pi\)
\(972\) 0 0
\(973\) −3.78622 −0.121381
\(974\) 0 0
\(975\) −11.1887 −0.358324
\(976\) 0 0
\(977\) −35.9777 −1.15103 −0.575514 0.817792i \(-0.695198\pi\)
−0.575514 + 0.817792i \(0.695198\pi\)
\(978\) 0 0
\(979\) −17.1828 −0.549165
\(980\) 0 0
\(981\) 1.76980 0.0565054
\(982\) 0 0
\(983\) −41.9631 −1.33842 −0.669208 0.743075i \(-0.733366\pi\)
−0.669208 + 0.743075i \(0.733366\pi\)
\(984\) 0 0
\(985\) −2.18635 −0.0696630
\(986\) 0 0
\(987\) 4.74298 0.150971
\(988\) 0 0
\(989\) −0.102993 −0.00327499
\(990\) 0 0
\(991\) −30.5998 −0.972036 −0.486018 0.873949i \(-0.661551\pi\)
−0.486018 + 0.873949i \(0.661551\pi\)
\(992\) 0 0
\(993\) −0.425893 −0.0135153
\(994\) 0 0
\(995\) −1.10151 −0.0349202
\(996\) 0 0
\(997\) 62.5075 1.97963 0.989817 0.142348i \(-0.0454651\pi\)
0.989817 + 0.142348i \(0.0454651\pi\)
\(998\) 0 0
\(999\) −6.77229 −0.214266
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 \(a_p\))