Properties

Label 8024.2.a.y.1.15
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.561991 q^{3} -2.34032 q^{5} -3.24647 q^{7} -2.68417 q^{9} +O(q^{10})\) \(q+0.561991 q^{3} -2.34032 q^{5} -3.24647 q^{7} -2.68417 q^{9} +0.117214 q^{11} +0.0710091 q^{13} -1.31524 q^{15} -1.00000 q^{17} +7.74546 q^{19} -1.82449 q^{21} +3.00596 q^{23} +0.477109 q^{25} -3.19445 q^{27} +7.74335 q^{29} +0.790508 q^{31} +0.0658734 q^{33} +7.59779 q^{35} +5.26024 q^{37} +0.0399065 q^{39} -4.64131 q^{41} +5.78183 q^{43} +6.28181 q^{45} -2.92091 q^{47} +3.53958 q^{49} -0.561991 q^{51} -4.98500 q^{53} -0.274319 q^{55} +4.35288 q^{57} -1.00000 q^{59} +3.39452 q^{61} +8.71407 q^{63} -0.166184 q^{65} +4.95731 q^{67} +1.68932 q^{69} +4.72617 q^{71} -11.2207 q^{73} +0.268131 q^{75} -0.380533 q^{77} -6.93936 q^{79} +6.25725 q^{81} +10.2866 q^{83} +2.34032 q^{85} +4.35169 q^{87} -15.0663 q^{89} -0.230529 q^{91} +0.444258 q^{93} -18.1269 q^{95} +1.43255 q^{97} -0.314623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 6q^{3} - q^{7} + 23q^{9} + O(q^{10}) \) \( 23q - 6q^{3} - q^{7} + 23q^{9} - 3q^{11} - 7q^{13} - 2q^{15} - 23q^{17} - 16q^{19} - 11q^{21} - 29q^{23} + 31q^{25} - 3q^{27} - 5q^{29} - 41q^{31} + 8q^{33} - 22q^{35} + 5q^{37} + 16q^{39} + 11q^{41} + 13q^{43} - 26q^{45} - 39q^{47} + 16q^{49} + 6q^{51} - 2q^{53} - 35q^{55} + 13q^{57} - 23q^{59} - 37q^{61} + 33q^{65} - 34q^{67} - 66q^{69} - 13q^{71} - 14q^{73} - 81q^{75} - 4q^{77} - 61q^{79} - q^{81} - 9q^{83} - 16q^{87} + 28q^{89} - 18q^{91} - 62q^{93} - 33q^{95} - 5q^{99} + O(q^{100}) \)

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
\(3\) 0.561991 0.324466 0.162233 0.986753i \(-0.448130\pi\)
0.162233 + 0.986753i \(0.448130\pi\)
\(4\) 0 0
\(5\) −2.34032 −1.04662 −0.523312 0.852141i \(-0.675304\pi\)
−0.523312 + 0.852141i \(0.675304\pi\)
\(6\) 0 0
\(7\) −3.24647 −1.22705 −0.613525 0.789675i \(-0.710249\pi\)
−0.613525 + 0.789675i \(0.710249\pi\)
\(8\) 0 0
\(9\) −2.68417 −0.894722
\(10\) 0 0
\(11\) 0.117214 0.0353415 0.0176707 0.999844i \(-0.494375\pi\)
0.0176707 + 0.999844i \(0.494375\pi\)
\(12\) 0 0
\(13\) 0.0710091 0.0196944 0.00984719 0.999952i \(-0.496865\pi\)
0.00984719 + 0.999952i \(0.496865\pi\)
\(14\) 0 0
\(15\) −1.31524 −0.339593
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 7.74546 1.77693 0.888465 0.458944i \(-0.151772\pi\)
0.888465 + 0.458944i \(0.151772\pi\)
\(20\) 0 0
\(21\) −1.82449 −0.398136
\(22\) 0 0
\(23\) 3.00596 0.626785 0.313393 0.949624i \(-0.398534\pi\)
0.313393 + 0.949624i \(0.398534\pi\)
\(24\) 0 0
\(25\) 0.477109 0.0954217
\(26\) 0 0
\(27\) −3.19445 −0.614772
\(28\) 0 0
\(29\) 7.74335 1.43790 0.718952 0.695060i \(-0.244622\pi\)
0.718952 + 0.695060i \(0.244622\pi\)
\(30\) 0 0
\(31\) 0.790508 0.141979 0.0709897 0.997477i \(-0.477384\pi\)
0.0709897 + 0.997477i \(0.477384\pi\)
\(32\) 0 0
\(33\) 0.0658734 0.0114671
\(34\) 0 0
\(35\) 7.59779 1.28426
\(36\) 0 0
\(37\) 5.26024 0.864777 0.432389 0.901687i \(-0.357671\pi\)
0.432389 + 0.901687i \(0.357671\pi\)
\(38\) 0 0
\(39\) 0.0399065 0.00639015
\(40\) 0 0
\(41\) −4.64131 −0.724850 −0.362425 0.932013i \(-0.618051\pi\)
−0.362425 + 0.932013i \(0.618051\pi\)
\(42\) 0 0
\(43\) 5.78183 0.881721 0.440861 0.897576i \(-0.354673\pi\)
0.440861 + 0.897576i \(0.354673\pi\)
\(44\) 0 0
\(45\) 6.28181 0.936438
\(46\) 0 0
\(47\) −2.92091 −0.426059 −0.213029 0.977046i \(-0.568333\pi\)
−0.213029 + 0.977046i \(0.568333\pi\)
\(48\) 0 0
\(49\) 3.53958 0.505654
\(50\) 0 0
\(51\) −0.561991 −0.0786945
\(52\) 0 0
\(53\) −4.98500 −0.684743 −0.342371 0.939565i \(-0.611230\pi\)
−0.342371 + 0.939565i \(0.611230\pi\)
\(54\) 0 0
\(55\) −0.274319 −0.0369892
\(56\) 0 0
\(57\) 4.35288 0.576553
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 3.39452 0.434623 0.217312 0.976102i \(-0.430271\pi\)
0.217312 + 0.976102i \(0.430271\pi\)
\(62\) 0 0
\(63\) 8.71407 1.09787
\(64\) 0 0
\(65\) −0.166184 −0.0206126
\(66\) 0 0
\(67\) 4.95731 0.605632 0.302816 0.953049i \(-0.402073\pi\)
0.302816 + 0.953049i \(0.402073\pi\)
\(68\) 0 0
\(69\) 1.68932 0.203370
\(70\) 0 0
\(71\) 4.72617 0.560893 0.280447 0.959870i \(-0.409517\pi\)
0.280447 + 0.959870i \(0.409517\pi\)
\(72\) 0 0
\(73\) −11.2207 −1.31329 −0.656644 0.754201i \(-0.728025\pi\)
−0.656644 + 0.754201i \(0.728025\pi\)
\(74\) 0 0
\(75\) 0.268131 0.0309611
\(76\) 0 0
\(77\) −0.380533 −0.0433658
\(78\) 0 0
\(79\) −6.93936 −0.780739 −0.390369 0.920658i \(-0.627653\pi\)
−0.390369 + 0.920658i \(0.627653\pi\)
\(80\) 0 0
\(81\) 6.25725 0.695250
\(82\) 0 0
\(83\) 10.2866 1.12910 0.564548 0.825400i \(-0.309050\pi\)
0.564548 + 0.825400i \(0.309050\pi\)
\(84\) 0 0
\(85\) 2.34032 0.253844
\(86\) 0 0
\(87\) 4.35169 0.466550
\(88\) 0 0
\(89\) −15.0663 −1.59703 −0.798515 0.601975i \(-0.794381\pi\)
−0.798515 + 0.601975i \(0.794381\pi\)
\(90\) 0 0
\(91\) −0.230529 −0.0241660
\(92\) 0 0
\(93\) 0.444258 0.0460674
\(94\) 0 0
\(95\) −18.1269 −1.85978
\(96\) 0 0
\(97\) 1.43255 0.145454 0.0727270 0.997352i \(-0.476830\pi\)
0.0727270 + 0.997352i \(0.476830\pi\)
\(98\) 0 0
\(99\) −0.314623 −0.0316208
\(100\) 0 0
\(101\) 2.58501 0.257218 0.128609 0.991695i \(-0.458949\pi\)
0.128609 + 0.991695i \(0.458949\pi\)
\(102\) 0 0
\(103\) −14.7383 −1.45220 −0.726102 0.687586i \(-0.758670\pi\)
−0.726102 + 0.687586i \(0.758670\pi\)
\(104\) 0 0
\(105\) 4.26989 0.416698
\(106\) 0 0
\(107\) 4.93693 0.477271 0.238636 0.971109i \(-0.423300\pi\)
0.238636 + 0.971109i \(0.423300\pi\)
\(108\) 0 0
\(109\) −11.1205 −1.06515 −0.532576 0.846382i \(-0.678776\pi\)
−0.532576 + 0.846382i \(0.678776\pi\)
\(110\) 0 0
\(111\) 2.95620 0.280590
\(112\) 0 0
\(113\) 18.2007 1.71218 0.856088 0.516829i \(-0.172888\pi\)
0.856088 + 0.516829i \(0.172888\pi\)
\(114\) 0 0
\(115\) −7.03491 −0.656008
\(116\) 0 0
\(117\) −0.190600 −0.0176210
\(118\) 0 0
\(119\) 3.24647 0.297604
\(120\) 0 0
\(121\) −10.9863 −0.998751
\(122\) 0 0
\(123\) −2.60837 −0.235189
\(124\) 0 0
\(125\) 10.5850 0.946753
\(126\) 0 0
\(127\) −7.96314 −0.706614 −0.353307 0.935507i \(-0.614943\pi\)
−0.353307 + 0.935507i \(0.614943\pi\)
\(128\) 0 0
\(129\) 3.24934 0.286088
\(130\) 0 0
\(131\) 0.555572 0.0485405 0.0242703 0.999705i \(-0.492274\pi\)
0.0242703 + 0.999705i \(0.492274\pi\)
\(132\) 0 0
\(133\) −25.1454 −2.18038
\(134\) 0 0
\(135\) 7.47604 0.643435
\(136\) 0 0
\(137\) 10.0742 0.860696 0.430348 0.902663i \(-0.358391\pi\)
0.430348 + 0.902663i \(0.358391\pi\)
\(138\) 0 0
\(139\) −7.69079 −0.652324 −0.326162 0.945314i \(-0.605756\pi\)
−0.326162 + 0.945314i \(0.605756\pi\)
\(140\) 0 0
\(141\) −1.64153 −0.138241
\(142\) 0 0
\(143\) 0.00832329 0.000696028 0
\(144\) 0 0
\(145\) −18.1219 −1.50494
\(146\) 0 0
\(147\) 1.98921 0.164067
\(148\) 0 0
\(149\) 0.675664 0.0553526 0.0276763 0.999617i \(-0.491189\pi\)
0.0276763 + 0.999617i \(0.491189\pi\)
\(150\) 0 0
\(151\) 10.6608 0.867560 0.433780 0.901019i \(-0.357180\pi\)
0.433780 + 0.901019i \(0.357180\pi\)
\(152\) 0 0
\(153\) 2.68417 0.217002
\(154\) 0 0
\(155\) −1.85004 −0.148599
\(156\) 0 0
\(157\) −18.3514 −1.46460 −0.732302 0.680980i \(-0.761554\pi\)
−0.732302 + 0.680980i \(0.761554\pi\)
\(158\) 0 0
\(159\) −2.80153 −0.222176
\(160\) 0 0
\(161\) −9.75875 −0.769097
\(162\) 0 0
\(163\) −0.526646 −0.0412501 −0.0206250 0.999787i \(-0.506566\pi\)
−0.0206250 + 0.999787i \(0.506566\pi\)
\(164\) 0 0
\(165\) −0.154165 −0.0120017
\(166\) 0 0
\(167\) −23.7882 −1.84079 −0.920395 0.390991i \(-0.872133\pi\)
−0.920395 + 0.390991i \(0.872133\pi\)
\(168\) 0 0
\(169\) −12.9950 −0.999612
\(170\) 0 0
\(171\) −20.7901 −1.58986
\(172\) 0 0
\(173\) 3.99732 0.303910 0.151955 0.988387i \(-0.451443\pi\)
0.151955 + 0.988387i \(0.451443\pi\)
\(174\) 0 0
\(175\) −1.54892 −0.117087
\(176\) 0 0
\(177\) −0.561991 −0.0422418
\(178\) 0 0
\(179\) 19.1128 1.42856 0.714281 0.699859i \(-0.246754\pi\)
0.714281 + 0.699859i \(0.246754\pi\)
\(180\) 0 0
\(181\) 17.9075 1.33106 0.665529 0.746372i \(-0.268206\pi\)
0.665529 + 0.746372i \(0.268206\pi\)
\(182\) 0 0
\(183\) 1.90769 0.141020
\(184\) 0 0
\(185\) −12.3106 −0.905097
\(186\) 0 0
\(187\) −0.117214 −0.00857157
\(188\) 0 0
\(189\) 10.3707 0.754357
\(190\) 0 0
\(191\) −15.4930 −1.12103 −0.560516 0.828143i \(-0.689397\pi\)
−0.560516 + 0.828143i \(0.689397\pi\)
\(192\) 0 0
\(193\) −11.2077 −0.806747 −0.403374 0.915035i \(-0.632163\pi\)
−0.403374 + 0.915035i \(0.632163\pi\)
\(194\) 0 0
\(195\) −0.0933940 −0.00668808
\(196\) 0 0
\(197\) −0.265499 −0.0189160 −0.00945801 0.999955i \(-0.503011\pi\)
−0.00945801 + 0.999955i \(0.503011\pi\)
\(198\) 0 0
\(199\) −26.7943 −1.89940 −0.949700 0.313162i \(-0.898612\pi\)
−0.949700 + 0.313162i \(0.898612\pi\)
\(200\) 0 0
\(201\) 2.78596 0.196507
\(202\) 0 0
\(203\) −25.1386 −1.76438
\(204\) 0 0
\(205\) 10.8622 0.758646
\(206\) 0 0
\(207\) −8.06849 −0.560798
\(208\) 0 0
\(209\) 0.907880 0.0627993
\(210\) 0 0
\(211\) 7.90000 0.543859 0.271929 0.962317i \(-0.412338\pi\)
0.271929 + 0.962317i \(0.412338\pi\)
\(212\) 0 0
\(213\) 2.65606 0.181990
\(214\) 0 0
\(215\) −13.5314 −0.922830
\(216\) 0 0
\(217\) −2.56636 −0.174216
\(218\) 0 0
\(219\) −6.30595 −0.426117
\(220\) 0 0
\(221\) −0.0710091 −0.00477659
\(222\) 0 0
\(223\) 1.54628 0.103546 0.0517732 0.998659i \(-0.483513\pi\)
0.0517732 + 0.998659i \(0.483513\pi\)
\(224\) 0 0
\(225\) −1.28064 −0.0853759
\(226\) 0 0
\(227\) −14.0213 −0.930628 −0.465314 0.885146i \(-0.654059\pi\)
−0.465314 + 0.885146i \(0.654059\pi\)
\(228\) 0 0
\(229\) −23.0153 −1.52090 −0.760448 0.649399i \(-0.775020\pi\)
−0.760448 + 0.649399i \(0.775020\pi\)
\(230\) 0 0
\(231\) −0.213856 −0.0140707
\(232\) 0 0
\(233\) 0.251787 0.0164951 0.00824757 0.999966i \(-0.497375\pi\)
0.00824757 + 0.999966i \(0.497375\pi\)
\(234\) 0 0
\(235\) 6.83588 0.445923
\(236\) 0 0
\(237\) −3.89985 −0.253323
\(238\) 0 0
\(239\) 0.594481 0.0384538 0.0192269 0.999815i \(-0.493880\pi\)
0.0192269 + 0.999815i \(0.493880\pi\)
\(240\) 0 0
\(241\) 27.3229 1.76002 0.880011 0.474954i \(-0.157535\pi\)
0.880011 + 0.474954i \(0.157535\pi\)
\(242\) 0 0
\(243\) 13.0999 0.840357
\(244\) 0 0
\(245\) −8.28375 −0.529229
\(246\) 0 0
\(247\) 0.549998 0.0349956
\(248\) 0 0
\(249\) 5.78095 0.366353
\(250\) 0 0
\(251\) −13.7857 −0.870145 −0.435073 0.900395i \(-0.643277\pi\)
−0.435073 + 0.900395i \(0.643277\pi\)
\(252\) 0 0
\(253\) 0.352341 0.0221515
\(254\) 0 0
\(255\) 1.31524 0.0823635
\(256\) 0 0
\(257\) 19.5944 1.22226 0.611132 0.791529i \(-0.290714\pi\)
0.611132 + 0.791529i \(0.290714\pi\)
\(258\) 0 0
\(259\) −17.0772 −1.06113
\(260\) 0 0
\(261\) −20.7844 −1.28652
\(262\) 0 0
\(263\) −16.0703 −0.990939 −0.495470 0.868625i \(-0.665004\pi\)
−0.495470 + 0.868625i \(0.665004\pi\)
\(264\) 0 0
\(265\) 11.6665 0.716668
\(266\) 0 0
\(267\) −8.46715 −0.518181
\(268\) 0 0
\(269\) −19.6317 −1.19697 −0.598483 0.801135i \(-0.704230\pi\)
−0.598483 + 0.801135i \(0.704230\pi\)
\(270\) 0 0
\(271\) −10.9271 −0.663771 −0.331886 0.943320i \(-0.607685\pi\)
−0.331886 + 0.943320i \(0.607685\pi\)
\(272\) 0 0
\(273\) −0.129555 −0.00784104
\(274\) 0 0
\(275\) 0.0559240 0.00337234
\(276\) 0 0
\(277\) 31.0410 1.86507 0.932536 0.361077i \(-0.117591\pi\)
0.932536 + 0.361077i \(0.117591\pi\)
\(278\) 0 0
\(279\) −2.12185 −0.127032
\(280\) 0 0
\(281\) −11.5841 −0.691051 −0.345526 0.938409i \(-0.612299\pi\)
−0.345526 + 0.938409i \(0.612299\pi\)
\(282\) 0 0
\(283\) 12.9460 0.769558 0.384779 0.923009i \(-0.374278\pi\)
0.384779 + 0.923009i \(0.374278\pi\)
\(284\) 0 0
\(285\) −10.1871 −0.603434
\(286\) 0 0
\(287\) 15.0679 0.889428
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0.805083 0.0471948
\(292\) 0 0
\(293\) −6.28488 −0.367167 −0.183583 0.983004i \(-0.558770\pi\)
−0.183583 + 0.983004i \(0.558770\pi\)
\(294\) 0 0
\(295\) 2.34032 0.136259
\(296\) 0 0
\(297\) −0.374435 −0.0217269
\(298\) 0 0
\(299\) 0.213450 0.0123441
\(300\) 0 0
\(301\) −18.7706 −1.08192
\(302\) 0 0
\(303\) 1.45275 0.0834584
\(304\) 0 0
\(305\) −7.94426 −0.454887
\(306\) 0 0
\(307\) 27.0456 1.54357 0.771787 0.635881i \(-0.219363\pi\)
0.771787 + 0.635881i \(0.219363\pi\)
\(308\) 0 0
\(309\) −8.28277 −0.471191
\(310\) 0 0
\(311\) −30.2147 −1.71332 −0.856660 0.515882i \(-0.827464\pi\)
−0.856660 + 0.515882i \(0.827464\pi\)
\(312\) 0 0
\(313\) −18.4813 −1.04462 −0.522312 0.852755i \(-0.674930\pi\)
−0.522312 + 0.852755i \(0.674930\pi\)
\(314\) 0 0
\(315\) −20.3937 −1.14906
\(316\) 0 0
\(317\) −29.6956 −1.66787 −0.833935 0.551863i \(-0.813917\pi\)
−0.833935 + 0.551863i \(0.813917\pi\)
\(318\) 0 0
\(319\) 0.907632 0.0508176
\(320\) 0 0
\(321\) 2.77451 0.154858
\(322\) 0 0
\(323\) −7.74546 −0.430969
\(324\) 0 0
\(325\) 0.0338791 0.00187927
\(326\) 0 0
\(327\) −6.24963 −0.345605
\(328\) 0 0
\(329\) 9.48266 0.522796
\(330\) 0 0
\(331\) 12.1582 0.668276 0.334138 0.942524i \(-0.391555\pi\)
0.334138 + 0.942524i \(0.391555\pi\)
\(332\) 0 0
\(333\) −14.1193 −0.773735
\(334\) 0 0
\(335\) −11.6017 −0.633869
\(336\) 0 0
\(337\) −14.5042 −0.790094 −0.395047 0.918661i \(-0.629272\pi\)
−0.395047 + 0.918661i \(0.629272\pi\)
\(338\) 0 0
\(339\) 10.2286 0.555542
\(340\) 0 0
\(341\) 0.0926589 0.00501776
\(342\) 0 0
\(343\) 11.2342 0.606588
\(344\) 0 0
\(345\) −3.95355 −0.212852
\(346\) 0 0
\(347\) −6.81828 −0.366025 −0.183012 0.983111i \(-0.558585\pi\)
−0.183012 + 0.983111i \(0.558585\pi\)
\(348\) 0 0
\(349\) −18.6342 −0.997466 −0.498733 0.866756i \(-0.666201\pi\)
−0.498733 + 0.866756i \(0.666201\pi\)
\(350\) 0 0
\(351\) −0.226835 −0.0121076
\(352\) 0 0
\(353\) −9.44366 −0.502635 −0.251318 0.967905i \(-0.580864\pi\)
−0.251318 + 0.967905i \(0.580864\pi\)
\(354\) 0 0
\(355\) −11.0608 −0.587044
\(356\) 0 0
\(357\) 1.82449 0.0965621
\(358\) 0 0
\(359\) −9.72585 −0.513311 −0.256655 0.966503i \(-0.582621\pi\)
−0.256655 + 0.966503i \(0.582621\pi\)
\(360\) 0 0
\(361\) 40.9922 2.15748
\(362\) 0 0
\(363\) −6.17418 −0.324060
\(364\) 0 0
\(365\) 26.2601 1.37452
\(366\) 0 0
\(367\) 5.40684 0.282235 0.141117 0.989993i \(-0.454931\pi\)
0.141117 + 0.989993i \(0.454931\pi\)
\(368\) 0 0
\(369\) 12.4580 0.648540
\(370\) 0 0
\(371\) 16.1837 0.840214
\(372\) 0 0
\(373\) −20.6921 −1.07140 −0.535699 0.844409i \(-0.679952\pi\)
−0.535699 + 0.844409i \(0.679952\pi\)
\(374\) 0 0
\(375\) 5.94869 0.307189
\(376\) 0 0
\(377\) 0.549848 0.0283186
\(378\) 0 0
\(379\) −21.6116 −1.11011 −0.555056 0.831813i \(-0.687303\pi\)
−0.555056 + 0.831813i \(0.687303\pi\)
\(380\) 0 0
\(381\) −4.47521 −0.229272
\(382\) 0 0
\(383\) 10.8765 0.555762 0.277881 0.960615i \(-0.410368\pi\)
0.277881 + 0.960615i \(0.410368\pi\)
\(384\) 0 0
\(385\) 0.890570 0.0453877
\(386\) 0 0
\(387\) −15.5194 −0.788895
\(388\) 0 0
\(389\) −34.7027 −1.75950 −0.879749 0.475439i \(-0.842289\pi\)
−0.879749 + 0.475439i \(0.842289\pi\)
\(390\) 0 0
\(391\) −3.00596 −0.152018
\(392\) 0 0
\(393\) 0.312226 0.0157497
\(394\) 0 0
\(395\) 16.2403 0.817140
\(396\) 0 0
\(397\) 16.2346 0.814790 0.407395 0.913252i \(-0.366437\pi\)
0.407395 + 0.913252i \(0.366437\pi\)
\(398\) 0 0
\(399\) −14.1315 −0.707460
\(400\) 0 0
\(401\) 35.8549 1.79051 0.895255 0.445554i \(-0.146993\pi\)
0.895255 + 0.445554i \(0.146993\pi\)
\(402\) 0 0
\(403\) 0.0561332 0.00279620
\(404\) 0 0
\(405\) −14.6440 −0.727665
\(406\) 0 0
\(407\) 0.616575 0.0305625
\(408\) 0 0
\(409\) −26.4945 −1.31007 −0.655035 0.755599i \(-0.727346\pi\)
−0.655035 + 0.755599i \(0.727346\pi\)
\(410\) 0 0
\(411\) 5.66160 0.279266
\(412\) 0 0
\(413\) 3.24647 0.159748
\(414\) 0 0
\(415\) −24.0739 −1.18174
\(416\) 0 0
\(417\) −4.32215 −0.211657
\(418\) 0 0
\(419\) 32.8109 1.60292 0.801459 0.598049i \(-0.204057\pi\)
0.801459 + 0.598049i \(0.204057\pi\)
\(420\) 0 0
\(421\) 2.51760 0.122700 0.0613502 0.998116i \(-0.480459\pi\)
0.0613502 + 0.998116i \(0.480459\pi\)
\(422\) 0 0
\(423\) 7.84022 0.381204
\(424\) 0 0
\(425\) −0.477109 −0.0231432
\(426\) 0 0
\(427\) −11.0202 −0.533305
\(428\) 0 0
\(429\) 0.00467761 0.000225837 0
\(430\) 0 0
\(431\) −9.22755 −0.444476 −0.222238 0.974992i \(-0.571336\pi\)
−0.222238 + 0.974992i \(0.571336\pi\)
\(432\) 0 0
\(433\) 6.40588 0.307847 0.153924 0.988083i \(-0.450809\pi\)
0.153924 + 0.988083i \(0.450809\pi\)
\(434\) 0 0
\(435\) −10.1844 −0.488303
\(436\) 0 0
\(437\) 23.2825 1.11375
\(438\) 0 0
\(439\) −7.39755 −0.353066 −0.176533 0.984295i \(-0.556488\pi\)
−0.176533 + 0.984295i \(0.556488\pi\)
\(440\) 0 0
\(441\) −9.50081 −0.452420
\(442\) 0 0
\(443\) 31.8225 1.51193 0.755965 0.654612i \(-0.227168\pi\)
0.755965 + 0.654612i \(0.227168\pi\)
\(444\) 0 0
\(445\) 35.2601 1.67149
\(446\) 0 0
\(447\) 0.379717 0.0179600
\(448\) 0 0
\(449\) 16.0309 0.756544 0.378272 0.925694i \(-0.376518\pi\)
0.378272 + 0.925694i \(0.376518\pi\)
\(450\) 0 0
\(451\) −0.544028 −0.0256173
\(452\) 0 0
\(453\) 5.99125 0.281493
\(454\) 0 0
\(455\) 0.539512 0.0252927
\(456\) 0 0
\(457\) 16.4067 0.767472 0.383736 0.923443i \(-0.374637\pi\)
0.383736 + 0.923443i \(0.374637\pi\)
\(458\) 0 0
\(459\) 3.19445 0.149104
\(460\) 0 0
\(461\) 22.2102 1.03443 0.517217 0.855854i \(-0.326968\pi\)
0.517217 + 0.855854i \(0.326968\pi\)
\(462\) 0 0
\(463\) −36.4573 −1.69431 −0.847157 0.531343i \(-0.821688\pi\)
−0.847157 + 0.531343i \(0.821688\pi\)
\(464\) 0 0
\(465\) −1.03971 −0.0482153
\(466\) 0 0
\(467\) −13.6909 −0.633540 −0.316770 0.948502i \(-0.602598\pi\)
−0.316770 + 0.948502i \(0.602598\pi\)
\(468\) 0 0
\(469\) −16.0938 −0.743141
\(470\) 0 0
\(471\) −10.3133 −0.475214
\(472\) 0 0
\(473\) 0.677714 0.0311613
\(474\) 0 0
\(475\) 3.69543 0.169558
\(476\) 0 0
\(477\) 13.3806 0.612655
\(478\) 0 0
\(479\) −16.3360 −0.746410 −0.373205 0.927749i \(-0.621741\pi\)
−0.373205 + 0.927749i \(0.621741\pi\)
\(480\) 0 0
\(481\) 0.373525 0.0170313
\(482\) 0 0
\(483\) −5.48433 −0.249546
\(484\) 0 0
\(485\) −3.35264 −0.152236
\(486\) 0 0
\(487\) 22.8668 1.03619 0.518096 0.855322i \(-0.326641\pi\)
0.518096 + 0.855322i \(0.326641\pi\)
\(488\) 0 0
\(489\) −0.295970 −0.0133842
\(490\) 0 0
\(491\) −4.25023 −0.191810 −0.0959051 0.995390i \(-0.530575\pi\)
−0.0959051 + 0.995390i \(0.530575\pi\)
\(492\) 0 0
\(493\) −7.74335 −0.348743
\(494\) 0 0
\(495\) 0.736319 0.0330951
\(496\) 0 0
\(497\) −15.3434 −0.688244
\(498\) 0 0
\(499\) −21.2155 −0.949736 −0.474868 0.880057i \(-0.657504\pi\)
−0.474868 + 0.880057i \(0.657504\pi\)
\(500\) 0 0
\(501\) −13.3688 −0.597273
\(502\) 0 0
\(503\) −14.1322 −0.630123 −0.315061 0.949071i \(-0.602025\pi\)
−0.315061 + 0.949071i \(0.602025\pi\)
\(504\) 0 0
\(505\) −6.04976 −0.269211
\(506\) 0 0
\(507\) −7.30305 −0.324340
\(508\) 0 0
\(509\) 12.0552 0.534337 0.267169 0.963650i \(-0.413912\pi\)
0.267169 + 0.963650i \(0.413912\pi\)
\(510\) 0 0
\(511\) 36.4278 1.61147
\(512\) 0 0
\(513\) −24.7425 −1.09241
\(514\) 0 0
\(515\) 34.4923 1.51991
\(516\) 0 0
\(517\) −0.342373 −0.0150575
\(518\) 0 0
\(519\) 2.24646 0.0986085
\(520\) 0 0
\(521\) 3.95491 0.173268 0.0866338 0.996240i \(-0.472389\pi\)
0.0866338 + 0.996240i \(0.472389\pi\)
\(522\) 0 0
\(523\) 26.7347 1.16903 0.584514 0.811384i \(-0.301285\pi\)
0.584514 + 0.811384i \(0.301285\pi\)
\(524\) 0 0
\(525\) −0.870479 −0.0379908
\(526\) 0 0
\(527\) −0.790508 −0.0344351
\(528\) 0 0
\(529\) −13.9642 −0.607140
\(530\) 0 0
\(531\) 2.68417 0.116483
\(532\) 0 0
\(533\) −0.329575 −0.0142755
\(534\) 0 0
\(535\) −11.5540 −0.499523
\(536\) 0 0
\(537\) 10.7412 0.463519
\(538\) 0 0
\(539\) 0.414889 0.0178706
\(540\) 0 0
\(541\) 28.7459 1.23588 0.617942 0.786224i \(-0.287967\pi\)
0.617942 + 0.786224i \(0.287967\pi\)
\(542\) 0 0
\(543\) 10.0639 0.431882
\(544\) 0 0
\(545\) 26.0256 1.11481
\(546\) 0 0
\(547\) 27.4103 1.17198 0.585990 0.810319i \(-0.300706\pi\)
0.585990 + 0.810319i \(0.300706\pi\)
\(548\) 0 0
\(549\) −9.11144 −0.388867
\(550\) 0 0
\(551\) 59.9758 2.55505
\(552\) 0 0
\(553\) 22.5284 0.958006
\(554\) 0 0
\(555\) −6.91847 −0.293673
\(556\) 0 0
\(557\) 8.56909 0.363084 0.181542 0.983383i \(-0.441891\pi\)
0.181542 + 0.983383i \(0.441891\pi\)
\(558\) 0 0
\(559\) 0.410563 0.0173650
\(560\) 0 0
\(561\) −0.0658734 −0.00278118
\(562\) 0 0
\(563\) −25.0077 −1.05395 −0.526974 0.849881i \(-0.676673\pi\)
−0.526974 + 0.849881i \(0.676673\pi\)
\(564\) 0 0
\(565\) −42.5955 −1.79201
\(566\) 0 0
\(567\) −20.3140 −0.853107
\(568\) 0 0
\(569\) −19.6405 −0.823373 −0.411687 0.911325i \(-0.635060\pi\)
−0.411687 + 0.911325i \(0.635060\pi\)
\(570\) 0 0
\(571\) −27.2253 −1.13934 −0.569672 0.821872i \(-0.692930\pi\)
−0.569672 + 0.821872i \(0.692930\pi\)
\(572\) 0 0
\(573\) −8.70691 −0.363737
\(574\) 0 0
\(575\) 1.43417 0.0598089
\(576\) 0 0
\(577\) 18.1573 0.755900 0.377950 0.925826i \(-0.376629\pi\)
0.377950 + 0.925826i \(0.376629\pi\)
\(578\) 0 0
\(579\) −6.29862 −0.261762
\(580\) 0 0
\(581\) −33.3950 −1.38546
\(582\) 0 0
\(583\) −0.584314 −0.0241998
\(584\) 0 0
\(585\) 0.446066 0.0184426
\(586\) 0 0
\(587\) −5.86489 −0.242070 −0.121035 0.992648i \(-0.538621\pi\)
−0.121035 + 0.992648i \(0.538621\pi\)
\(588\) 0 0
\(589\) 6.12285 0.252288
\(590\) 0 0
\(591\) −0.149208 −0.00613760
\(592\) 0 0
\(593\) 10.6228 0.436225 0.218113 0.975924i \(-0.430010\pi\)
0.218113 + 0.975924i \(0.430010\pi\)
\(594\) 0 0
\(595\) −7.59779 −0.311479
\(596\) 0 0
\(597\) −15.0582 −0.616290
\(598\) 0 0
\(599\) −26.8939 −1.09885 −0.549427 0.835541i \(-0.685154\pi\)
−0.549427 + 0.835541i \(0.685154\pi\)
\(600\) 0 0
\(601\) −4.06315 −0.165739 −0.0828697 0.996560i \(-0.526409\pi\)
−0.0828697 + 0.996560i \(0.526409\pi\)
\(602\) 0 0
\(603\) −13.3062 −0.541872
\(604\) 0 0
\(605\) 25.7114 1.04532
\(606\) 0 0
\(607\) 15.3846 0.624441 0.312221 0.950010i \(-0.398927\pi\)
0.312221 + 0.950010i \(0.398927\pi\)
\(608\) 0 0
\(609\) −14.1276 −0.572481
\(610\) 0 0
\(611\) −0.207411 −0.00839097
\(612\) 0 0
\(613\) 40.0791 1.61878 0.809391 0.587271i \(-0.199798\pi\)
0.809391 + 0.587271i \(0.199798\pi\)
\(614\) 0 0
\(615\) 6.10443 0.246154
\(616\) 0 0
\(617\) 21.6832 0.872932 0.436466 0.899721i \(-0.356230\pi\)
0.436466 + 0.899721i \(0.356230\pi\)
\(618\) 0 0
\(619\) −29.5712 −1.18857 −0.594283 0.804256i \(-0.702564\pi\)
−0.594283 + 0.804256i \(0.702564\pi\)
\(620\) 0 0
\(621\) −9.60237 −0.385330
\(622\) 0 0
\(623\) 48.9125 1.95964
\(624\) 0 0
\(625\) −27.1579 −1.08632
\(626\) 0 0
\(627\) 0.510220 0.0203762
\(628\) 0 0
\(629\) −5.26024 −0.209739
\(630\) 0 0
\(631\) −45.2129 −1.79990 −0.899948 0.435998i \(-0.856396\pi\)
−0.899948 + 0.435998i \(0.856396\pi\)
\(632\) 0 0
\(633\) 4.43973 0.176463
\(634\) 0 0
\(635\) 18.6363 0.739559
\(636\) 0 0
\(637\) 0.251342 0.00995854
\(638\) 0 0
\(639\) −12.6858 −0.501843
\(640\) 0 0
\(641\) 12.7187 0.502360 0.251180 0.967940i \(-0.419181\pi\)
0.251180 + 0.967940i \(0.419181\pi\)
\(642\) 0 0
\(643\) −18.2174 −0.718423 −0.359212 0.933256i \(-0.616954\pi\)
−0.359212 + 0.933256i \(0.616954\pi\)
\(644\) 0 0
\(645\) −7.60449 −0.299427
\(646\) 0 0
\(647\) −36.2887 −1.42666 −0.713329 0.700830i \(-0.752813\pi\)
−0.713329 + 0.700830i \(0.752813\pi\)
\(648\) 0 0
\(649\) −0.117214 −0.00460107
\(650\) 0 0
\(651\) −1.44227 −0.0565271
\(652\) 0 0
\(653\) 39.7221 1.55445 0.777224 0.629224i \(-0.216627\pi\)
0.777224 + 0.629224i \(0.216627\pi\)
\(654\) 0 0
\(655\) −1.30022 −0.0508037
\(656\) 0 0
\(657\) 30.1183 1.17503
\(658\) 0 0
\(659\) 28.3533 1.10449 0.552244 0.833682i \(-0.313772\pi\)
0.552244 + 0.833682i \(0.313772\pi\)
\(660\) 0 0
\(661\) −5.05785 −0.196727 −0.0983637 0.995151i \(-0.531361\pi\)
−0.0983637 + 0.995151i \(0.531361\pi\)
\(662\) 0 0
\(663\) −0.0399065 −0.00154984
\(664\) 0 0
\(665\) 58.8484 2.28204
\(666\) 0 0
\(667\) 23.2762 0.901256
\(668\) 0 0
\(669\) 0.868993 0.0335972
\(670\) 0 0
\(671\) 0.397886 0.0153602
\(672\) 0 0
\(673\) −25.7206 −0.991456 −0.495728 0.868478i \(-0.665099\pi\)
−0.495728 + 0.868478i \(0.665099\pi\)
\(674\) 0 0
\(675\) −1.52410 −0.0586626
\(676\) 0 0
\(677\) 18.6800 0.717932 0.358966 0.933351i \(-0.383129\pi\)
0.358966 + 0.933351i \(0.383129\pi\)
\(678\) 0 0
\(679\) −4.65075 −0.178479
\(680\) 0 0
\(681\) −7.87986 −0.301957
\(682\) 0 0
\(683\) −1.59557 −0.0610527 −0.0305263 0.999534i \(-0.509718\pi\)
−0.0305263 + 0.999534i \(0.509718\pi\)
\(684\) 0 0
\(685\) −23.5768 −0.900825
\(686\) 0 0
\(687\) −12.9344 −0.493478
\(688\) 0 0
\(689\) −0.353981 −0.0134856
\(690\) 0 0
\(691\) −25.4625 −0.968639 −0.484319 0.874891i \(-0.660933\pi\)
−0.484319 + 0.874891i \(0.660933\pi\)
\(692\) 0 0
\(693\) 1.02141 0.0388003
\(694\) 0 0
\(695\) 17.9989 0.682738
\(696\) 0 0
\(697\) 4.64131 0.175802
\(698\) 0 0
\(699\) 0.141502 0.00535210
\(700\) 0 0
\(701\) −46.7845 −1.76702 −0.883512 0.468408i \(-0.844828\pi\)
−0.883512 + 0.468408i \(0.844828\pi\)
\(702\) 0 0
\(703\) 40.7430 1.53665
\(704\) 0 0
\(705\) 3.84170 0.144687
\(706\) 0 0
\(707\) −8.39216 −0.315620
\(708\) 0 0
\(709\) −3.43353 −0.128949 −0.0644745 0.997919i \(-0.520537\pi\)
−0.0644745 + 0.997919i \(0.520537\pi\)
\(710\) 0 0
\(711\) 18.6264 0.698544
\(712\) 0 0
\(713\) 2.37623 0.0889906
\(714\) 0 0
\(715\) −0.0194792 −0.000728480 0
\(716\) 0 0
\(717\) 0.334093 0.0124769
\(718\) 0 0
\(719\) −4.30519 −0.160556 −0.0802782 0.996772i \(-0.525581\pi\)
−0.0802782 + 0.996772i \(0.525581\pi\)
\(720\) 0 0
\(721\) 47.8474 1.78193
\(722\) 0 0
\(723\) 15.3552 0.571066
\(724\) 0 0
\(725\) 3.69442 0.137207
\(726\) 0 0
\(727\) −35.1387 −1.30322 −0.651611 0.758553i \(-0.725906\pi\)
−0.651611 + 0.758553i \(0.725906\pi\)
\(728\) 0 0
\(729\) −11.4097 −0.422583
\(730\) 0 0
\(731\) −5.78183 −0.213849
\(732\) 0 0
\(733\) 13.1437 0.485473 0.242736 0.970092i \(-0.421955\pi\)
0.242736 + 0.970092i \(0.421955\pi\)
\(734\) 0 0
\(735\) −4.65539 −0.171717
\(736\) 0 0
\(737\) 0.581068 0.0214039
\(738\) 0 0
\(739\) −7.70317 −0.283366 −0.141683 0.989912i \(-0.545251\pi\)
−0.141683 + 0.989912i \(0.545251\pi\)
\(740\) 0 0
\(741\) 0.309094 0.0113549
\(742\) 0 0
\(743\) 12.0613 0.442487 0.221244 0.975219i \(-0.428988\pi\)
0.221244 + 0.975219i \(0.428988\pi\)
\(744\) 0 0
\(745\) −1.58127 −0.0579333
\(746\) 0 0
\(747\) −27.6108 −1.01023
\(748\) 0 0
\(749\) −16.0276 −0.585636
\(750\) 0 0
\(751\) −0.932935 −0.0340433 −0.0170216 0.999855i \(-0.505418\pi\)
−0.0170216 + 0.999855i \(0.505418\pi\)
\(752\) 0 0
\(753\) −7.74743 −0.282332
\(754\) 0 0
\(755\) −24.9496 −0.908009
\(756\) 0 0
\(757\) −53.0408 −1.92780 −0.963900 0.266264i \(-0.914211\pi\)
−0.963900 + 0.266264i \(0.914211\pi\)
\(758\) 0 0
\(759\) 0.198013 0.00718740
\(760\) 0 0
\(761\) 3.05757 0.110837 0.0554184 0.998463i \(-0.482351\pi\)
0.0554184 + 0.998463i \(0.482351\pi\)
\(762\) 0 0
\(763\) 36.1025 1.30700
\(764\) 0 0
\(765\) −6.28181 −0.227119
\(766\) 0 0
\(767\) −0.0710091 −0.00256399
\(768\) 0 0
\(769\) 53.7907 1.93974 0.969870 0.243622i \(-0.0783355\pi\)
0.969870 + 0.243622i \(0.0783355\pi\)
\(770\) 0 0
\(771\) 11.0119 0.396583
\(772\) 0 0
\(773\) 16.8997 0.607838 0.303919 0.952698i \(-0.401705\pi\)
0.303919 + 0.952698i \(0.401705\pi\)
\(774\) 0 0
\(775\) 0.377158 0.0135479
\(776\) 0 0
\(777\) −9.59723 −0.344299
\(778\) 0 0
\(779\) −35.9491 −1.28801
\(780\) 0 0
\(781\) 0.553975 0.0198228
\(782\) 0 0
\(783\) −24.7357 −0.883983
\(784\) 0 0
\(785\) 42.9483 1.53289
\(786\) 0 0
\(787\) −34.6168 −1.23395 −0.616977 0.786981i \(-0.711643\pi\)
−0.616977 + 0.786981i \(0.711643\pi\)
\(788\) 0 0
\(789\) −9.03138 −0.321526
\(790\) 0 0
\(791\) −59.0880 −2.10093
\(792\) 0 0
\(793\) 0.241042 0.00855964
\(794\) 0 0
\(795\) 6.55648 0.232534
\(796\) 0 0
\(797\) 43.4475 1.53899 0.769494 0.638654i \(-0.220508\pi\)
0.769494 + 0.638654i \(0.220508\pi\)
\(798\) 0 0
\(799\) 2.92091 0.103334
\(800\) 0 0
\(801\) 40.4406 1.42890
\(802\) 0 0
\(803\) −1.31523 −0.0464135
\(804\) 0 0
\(805\) 22.8386 0.804956
\(806\) 0 0
\(807\) −11.0328 −0.388374
\(808\) 0 0
\(809\) 27.7921 0.977118 0.488559 0.872531i \(-0.337523\pi\)
0.488559 + 0.872531i \(0.337523\pi\)
\(810\) 0 0
\(811\) −36.2383 −1.27250 −0.636249 0.771484i \(-0.719515\pi\)
−0.636249 + 0.771484i \(0.719515\pi\)
\(812\) 0 0
\(813\) −6.14091 −0.215371
\(814\) 0 0
\(815\) 1.23252 0.0431733
\(816\) 0 0
\(817\) 44.7830 1.56676
\(818\) 0 0
\(819\) 0.618778 0.0216219
\(820\) 0 0
\(821\) 0.953989 0.0332945 0.0166472 0.999861i \(-0.494701\pi\)
0.0166472 + 0.999861i \(0.494701\pi\)
\(822\) 0 0
\(823\) 51.7352 1.80338 0.901689 0.432386i \(-0.142328\pi\)
0.901689 + 0.432386i \(0.142328\pi\)
\(824\) 0 0
\(825\) 0.0314288 0.00109421
\(826\) 0 0
\(827\) −15.3047 −0.532198 −0.266099 0.963946i \(-0.585735\pi\)
−0.266099 + 0.963946i \(0.585735\pi\)
\(828\) 0 0
\(829\) −39.2601 −1.36356 −0.681779 0.731558i \(-0.738794\pi\)
−0.681779 + 0.731558i \(0.738794\pi\)
\(830\) 0 0
\(831\) 17.4447 0.605152
\(832\) 0 0
\(833\) −3.53958 −0.122639
\(834\) 0 0
\(835\) 55.6722 1.92661
\(836\) 0 0
\(837\) −2.52524 −0.0872849
\(838\) 0 0
\(839\) −50.3490 −1.73824 −0.869119 0.494602i \(-0.835314\pi\)
−0.869119 + 0.494602i \(0.835314\pi\)
\(840\) 0 0
\(841\) 30.9594 1.06757
\(842\) 0 0
\(843\) −6.51017 −0.224222
\(844\) 0 0
\(845\) 30.4124 1.04622
\(846\) 0 0
\(847\) 35.6666 1.22552
\(848\) 0 0
\(849\) 7.27552 0.249695
\(850\) 0 0
\(851\) 15.8120 0.542030
\(852\) 0 0
\(853\) −13.5918 −0.465374 −0.232687 0.972552i \(-0.574752\pi\)
−0.232687 + 0.972552i \(0.574752\pi\)
\(854\) 0 0
\(855\) 48.6556 1.66398
\(856\) 0 0
\(857\) 26.9831 0.921727 0.460863 0.887471i \(-0.347540\pi\)
0.460863 + 0.887471i \(0.347540\pi\)
\(858\) 0 0
\(859\) 19.3515 0.660266 0.330133 0.943934i \(-0.392906\pi\)
0.330133 + 0.943934i \(0.392906\pi\)
\(860\) 0 0
\(861\) 8.46801 0.288589
\(862\) 0 0
\(863\) −13.9246 −0.474000 −0.237000 0.971510i \(-0.576164\pi\)
−0.237000 + 0.971510i \(0.576164\pi\)
\(864\) 0 0
\(865\) −9.35501 −0.318080
\(866\) 0 0
\(867\) 0.561991 0.0190862
\(868\) 0 0
\(869\) −0.813392 −0.0275925
\(870\) 0 0
\(871\) 0.352014 0.0119275
\(872\) 0 0
\(873\) −3.84522 −0.130141
\(874\) 0 0
\(875\) −34.3640 −1.16171
\(876\) 0 0
\(877\) 53.1789 1.79572 0.897861 0.440279i \(-0.145120\pi\)
0.897861 + 0.440279i \(0.145120\pi\)
\(878\) 0 0
\(879\) −3.53204 −0.119133
\(880\) 0 0
\(881\) 18.4648 0.622095 0.311047 0.950394i \(-0.399320\pi\)
0.311047 + 0.950394i \(0.399320\pi\)
\(882\) 0 0
\(883\) −6.12038 −0.205967 −0.102984 0.994683i \(-0.532839\pi\)
−0.102984 + 0.994683i \(0.532839\pi\)
\(884\) 0 0
\(885\) 1.31524 0.0442113
\(886\) 0 0
\(887\) −22.9700 −0.771258 −0.385629 0.922654i \(-0.626016\pi\)
−0.385629 + 0.922654i \(0.626016\pi\)
\(888\) 0 0
\(889\) 25.8521 0.867052
\(890\) 0 0
\(891\) 0.733439 0.0245711
\(892\) 0 0
\(893\) −22.6238 −0.757077
\(894\) 0 0
\(895\) −44.7302 −1.49517
\(896\) 0 0
\(897\) 0.119957 0.00400525
\(898\) 0 0
\(899\) 6.12117 0.204153
\(900\) 0 0
\(901\) 4.98500 0.166075
\(902\) 0 0
\(903\) −10.5489 −0.351045
\(904\) 0 0
\(905\) −41.9094 −1.39312
\(906\) 0 0
\(907\) −34.5731 −1.14798 −0.573990 0.818862i \(-0.694605\pi\)
−0.573990 + 0.818862i \(0.694605\pi\)
\(908\) 0 0
\(909\) −6.93860 −0.230139
\(910\) 0 0
\(911\) 16.7005 0.553312 0.276656 0.960969i \(-0.410774\pi\)
0.276656 + 0.960969i \(0.410774\pi\)
\(912\) 0 0
\(913\) 1.20573 0.0399039
\(914\) 0 0
\(915\) −4.46460 −0.147595
\(916\) 0 0
\(917\) −1.80365 −0.0595617
\(918\) 0 0
\(919\) −19.5469 −0.644793 −0.322397 0.946605i \(-0.604488\pi\)
−0.322397 + 0.946605i \(0.604488\pi\)
\(920\) 0 0
\(921\) 15.1994 0.500837
\(922\) 0 0
\(923\) 0.335601 0.0110464
\(924\) 0 0
\(925\) 2.50970 0.0825185
\(926\) 0 0
\(927\) 39.5600 1.29932
\(928\) 0 0
\(929\) 43.8673 1.43924 0.719620 0.694368i \(-0.244316\pi\)
0.719620 + 0.694368i \(0.244316\pi\)
\(930\) 0 0
\(931\) 27.4157 0.898512
\(932\) 0 0
\(933\) −16.9804 −0.555913
\(934\) 0 0
\(935\) 0.274319 0.00897121
\(936\) 0 0
\(937\) −27.1172 −0.885880 −0.442940 0.896551i \(-0.646065\pi\)
−0.442940 + 0.896551i \(0.646065\pi\)
\(938\) 0 0
\(939\) −10.3863 −0.338944
\(940\) 0 0
\(941\) 8.17539 0.266510 0.133255 0.991082i \(-0.457457\pi\)
0.133255 + 0.991082i \(0.457457\pi\)
\(942\) 0 0
\(943\) −13.9516 −0.454325
\(944\) 0 0
\(945\) −24.2708 −0.789528
\(946\) 0 0
\(947\) −0.425925 −0.0138407 −0.00692036 0.999976i \(-0.502203\pi\)
−0.00692036 + 0.999976i \(0.502203\pi\)
\(948\) 0 0
\(949\) −0.796774 −0.0258644
\(950\) 0 0
\(951\) −16.6886 −0.541166
\(952\) 0 0
\(953\) 3.14977 0.102031 0.0510155 0.998698i \(-0.483754\pi\)
0.0510155 + 0.998698i \(0.483754\pi\)
\(954\) 0 0
\(955\) 36.2586 1.17330
\(956\) 0 0
\(957\) 0.510081 0.0164886
\(958\) 0 0
\(959\) −32.7055 −1.05612
\(960\) 0 0
\(961\) −30.3751 −0.979842
\(962\) 0 0
\(963\) −13.2515 −0.427025
\(964\) 0 0
\(965\) 26.2296 0.844361
\(966\) 0 0
\(967\) −27.7630 −0.892798 −0.446399 0.894834i \(-0.647294\pi\)
−0.446399 + 0.894834i \(0.647294\pi\)
\(968\) 0 0
\(969\) −4.35288 −0.139835
\(970\) 0 0
\(971\) −18.8431 −0.604705 −0.302353 0.953196i \(-0.597772\pi\)
−0.302353 + 0.953196i \(0.597772\pi\)
\(972\) 0 0
\(973\) 24.9679 0.800435
\(974\) 0 0
\(975\) 0.0190397 0.000609759 0
\(976\) 0 0
\(977\) −21.6818 −0.693663 −0.346832 0.937927i \(-0.612742\pi\)
−0.346832 + 0.937927i \(0.612742\pi\)
\(978\) 0 0
\(979\) −1.76599 −0.0564414
\(980\) 0 0
\(981\) 29.8493 0.953016
\(982\) 0 0
\(983\) −48.2565 −1.53914 −0.769571 0.638561i \(-0.779530\pi\)
−0.769571 + 0.638561i \(0.779530\pi\)
\(984\) 0 0
\(985\) 0.621353 0.0197980
\(986\) 0 0
\(987\) 5.32917 0.169629
\(988\) 0 0
\(989\) 17.3799 0.552650
\(990\) 0 0
\(991\) −20.3350 −0.645963 −0.322981 0.946405i \(-0.604685\pi\)
−0.322981 + 0.946405i \(0.604685\pi\)
\(992\) 0 0
\(993\) 6.83281 0.216833
\(994\) 0 0
\(995\) 62.7074 1.98796
\(996\) 0 0
\(997\) −13.3323 −0.422237 −0.211119 0.977460i \(-0.567711\pi\)
−0.211119 + 0.977460i \(0.567711\pi\)
\(998\) 0 0
\(999\) −16.8036 −0.531641
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 \(a_p\))