Properties

Label 8008.2.a.v.1.2
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 11
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.73758\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73758 q^{3} +4.10495 q^{5} -1.00000 q^{7} +4.49435 q^{9} +O(q^{10})\) \(q-2.73758 q^{3} +4.10495 q^{5} -1.00000 q^{7} +4.49435 q^{9} +1.00000 q^{11} -1.00000 q^{13} -11.2376 q^{15} -4.75014 q^{17} -6.50940 q^{19} +2.73758 q^{21} -1.11828 q^{23} +11.8506 q^{25} -4.09091 q^{27} +5.69879 q^{29} +9.59749 q^{31} -2.73758 q^{33} -4.10495 q^{35} +0.925635 q^{37} +2.73758 q^{39} -5.67379 q^{41} -5.94812 q^{43} +18.4491 q^{45} -1.11828 q^{47} +1.00000 q^{49} +13.0039 q^{51} -10.7803 q^{53} +4.10495 q^{55} +17.8200 q^{57} +7.08159 q^{59} +7.14995 q^{61} -4.49435 q^{63} -4.10495 q^{65} -11.8256 q^{67} +3.06139 q^{69} -7.59293 q^{71} +13.5277 q^{73} -32.4421 q^{75} -1.00000 q^{77} -16.4510 q^{79} -2.28386 q^{81} +0.448733 q^{83} -19.4991 q^{85} -15.6009 q^{87} -7.30086 q^{89} +1.00000 q^{91} -26.2739 q^{93} -26.7208 q^{95} -4.67291 q^{97} +4.49435 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) −2.73758 −1.58054 −0.790272 0.612757i \(-0.790061\pi\)
−0.790272 + 0.612757i \(0.790061\pi\)
\(4\) 0 0
\(5\) 4.10495 1.83579 0.917895 0.396823i \(-0.129887\pi\)
0.917895 + 0.396823i \(0.129887\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 4.49435 1.49812
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −11.2376 −2.90155
\(16\) 0 0
\(17\) −4.75014 −1.15208 −0.576040 0.817422i \(-0.695403\pi\)
−0.576040 + 0.817422i \(0.695403\pi\)
\(18\) 0 0
\(19\) −6.50940 −1.49336 −0.746680 0.665184i \(-0.768353\pi\)
−0.746680 + 0.665184i \(0.768353\pi\)
\(20\) 0 0
\(21\) 2.73758 0.597389
\(22\) 0 0
\(23\) −1.11828 −0.233178 −0.116589 0.993180i \(-0.537196\pi\)
−0.116589 + 0.993180i \(0.537196\pi\)
\(24\) 0 0
\(25\) 11.8506 2.37013
\(26\) 0 0
\(27\) −4.09091 −0.787296
\(28\) 0 0
\(29\) 5.69879 1.05824 0.529120 0.848547i \(-0.322522\pi\)
0.529120 + 0.848547i \(0.322522\pi\)
\(30\) 0 0
\(31\) 9.59749 1.72376 0.861880 0.507112i \(-0.169287\pi\)
0.861880 + 0.507112i \(0.169287\pi\)
\(32\) 0 0
\(33\) −2.73758 −0.476552
\(34\) 0 0
\(35\) −4.10495 −0.693864
\(36\) 0 0
\(37\) 0.925635 0.152174 0.0760868 0.997101i \(-0.475757\pi\)
0.0760868 + 0.997101i \(0.475757\pi\)
\(38\) 0 0
\(39\) 2.73758 0.438364
\(40\) 0 0
\(41\) −5.67379 −0.886097 −0.443049 0.896498i \(-0.646103\pi\)
−0.443049 + 0.896498i \(0.646103\pi\)
\(42\) 0 0
\(43\) −5.94812 −0.907080 −0.453540 0.891236i \(-0.649839\pi\)
−0.453540 + 0.891236i \(0.649839\pi\)
\(44\) 0 0
\(45\) 18.4491 2.75023
\(46\) 0 0
\(47\) −1.11828 −0.163118 −0.0815591 0.996669i \(-0.525990\pi\)
−0.0815591 + 0.996669i \(0.525990\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 13.0039 1.82091
\(52\) 0 0
\(53\) −10.7803 −1.48079 −0.740396 0.672171i \(-0.765362\pi\)
−0.740396 + 0.672171i \(0.765362\pi\)
\(54\) 0 0
\(55\) 4.10495 0.553512
\(56\) 0 0
\(57\) 17.8200 2.36032
\(58\) 0 0
\(59\) 7.08159 0.921945 0.460972 0.887415i \(-0.347501\pi\)
0.460972 + 0.887415i \(0.347501\pi\)
\(60\) 0 0
\(61\) 7.14995 0.915457 0.457729 0.889092i \(-0.348663\pi\)
0.457729 + 0.889092i \(0.348663\pi\)
\(62\) 0 0
\(63\) −4.49435 −0.566235
\(64\) 0 0
\(65\) −4.10495 −0.509157
\(66\) 0 0
\(67\) −11.8256 −1.44473 −0.722366 0.691511i \(-0.756946\pi\)
−0.722366 + 0.691511i \(0.756946\pi\)
\(68\) 0 0
\(69\) 3.06139 0.368548
\(70\) 0 0
\(71\) −7.59293 −0.901115 −0.450557 0.892748i \(-0.648775\pi\)
−0.450557 + 0.892748i \(0.648775\pi\)
\(72\) 0 0
\(73\) 13.5277 1.58330 0.791651 0.610973i \(-0.209222\pi\)
0.791651 + 0.610973i \(0.209222\pi\)
\(74\) 0 0
\(75\) −32.4421 −3.74609
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −16.4510 −1.85089 −0.925443 0.378887i \(-0.876307\pi\)
−0.925443 + 0.378887i \(0.876307\pi\)
\(80\) 0 0
\(81\) −2.28386 −0.253762
\(82\) 0 0
\(83\) 0.448733 0.0492548 0.0246274 0.999697i \(-0.492160\pi\)
0.0246274 + 0.999697i \(0.492160\pi\)
\(84\) 0 0
\(85\) −19.4991 −2.11498
\(86\) 0 0
\(87\) −15.6009 −1.67259
\(88\) 0 0
\(89\) −7.30086 −0.773890 −0.386945 0.922103i \(-0.626470\pi\)
−0.386945 + 0.922103i \(0.626470\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −26.2739 −2.72448
\(94\) 0 0
\(95\) −26.7208 −2.74150
\(96\) 0 0
\(97\) −4.67291 −0.474462 −0.237231 0.971453i \(-0.576240\pi\)
−0.237231 + 0.971453i \(0.576240\pi\)
\(98\) 0 0
\(99\) 4.49435 0.451699
\(100\) 0 0
\(101\) −2.43553 −0.242344 −0.121172 0.992632i \(-0.538665\pi\)
−0.121172 + 0.992632i \(0.538665\pi\)
\(102\) 0 0
\(103\) −3.10548 −0.305992 −0.152996 0.988227i \(-0.548892\pi\)
−0.152996 + 0.988227i \(0.548892\pi\)
\(104\) 0 0
\(105\) 11.2376 1.09668
\(106\) 0 0
\(107\) −14.7739 −1.42824 −0.714121 0.700022i \(-0.753173\pi\)
−0.714121 + 0.700022i \(0.753173\pi\)
\(108\) 0 0
\(109\) 17.3006 1.65710 0.828549 0.559916i \(-0.189167\pi\)
0.828549 + 0.559916i \(0.189167\pi\)
\(110\) 0 0
\(111\) −2.53400 −0.240517
\(112\) 0 0
\(113\) 11.0346 1.03805 0.519024 0.854760i \(-0.326296\pi\)
0.519024 + 0.854760i \(0.326296\pi\)
\(114\) 0 0
\(115\) −4.59050 −0.428066
\(116\) 0 0
\(117\) −4.49435 −0.415503
\(118\) 0 0
\(119\) 4.75014 0.435445
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 15.5325 1.40052
\(124\) 0 0
\(125\) 28.1215 2.51527
\(126\) 0 0
\(127\) 0.0460941 0.00409019 0.00204510 0.999998i \(-0.499349\pi\)
0.00204510 + 0.999998i \(0.499349\pi\)
\(128\) 0 0
\(129\) 16.2835 1.43368
\(130\) 0 0
\(131\) −4.33688 −0.378915 −0.189457 0.981889i \(-0.560673\pi\)
−0.189457 + 0.981889i \(0.560673\pi\)
\(132\) 0 0
\(133\) 6.50940 0.564437
\(134\) 0 0
\(135\) −16.7930 −1.44531
\(136\) 0 0
\(137\) −17.5442 −1.49890 −0.749451 0.662060i \(-0.769682\pi\)
−0.749451 + 0.662060i \(0.769682\pi\)
\(138\) 0 0
\(139\) 1.29871 0.110155 0.0550776 0.998482i \(-0.482459\pi\)
0.0550776 + 0.998482i \(0.482459\pi\)
\(140\) 0 0
\(141\) 3.06139 0.257815
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 23.3933 1.94271
\(146\) 0 0
\(147\) −2.73758 −0.225792
\(148\) 0 0
\(149\) −14.0494 −1.15097 −0.575485 0.817813i \(-0.695187\pi\)
−0.575485 + 0.817813i \(0.695187\pi\)
\(150\) 0 0
\(151\) 4.02435 0.327497 0.163749 0.986502i \(-0.447641\pi\)
0.163749 + 0.986502i \(0.447641\pi\)
\(152\) 0 0
\(153\) −21.3488 −1.72595
\(154\) 0 0
\(155\) 39.3972 3.16446
\(156\) 0 0
\(157\) 5.42576 0.433023 0.216511 0.976280i \(-0.430532\pi\)
0.216511 + 0.976280i \(0.430532\pi\)
\(158\) 0 0
\(159\) 29.5120 2.34046
\(160\) 0 0
\(161\) 1.11828 0.0881330
\(162\) 0 0
\(163\) −5.58145 −0.437173 −0.218587 0.975818i \(-0.570145\pi\)
−0.218587 + 0.975818i \(0.570145\pi\)
\(164\) 0 0
\(165\) −11.2376 −0.874849
\(166\) 0 0
\(167\) 14.6129 1.13078 0.565389 0.824825i \(-0.308726\pi\)
0.565389 + 0.824825i \(0.308726\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −29.2556 −2.23723
\(172\) 0 0
\(173\) 0.495744 0.0376907 0.0188454 0.999822i \(-0.494001\pi\)
0.0188454 + 0.999822i \(0.494001\pi\)
\(174\) 0 0
\(175\) −11.8506 −0.895824
\(176\) 0 0
\(177\) −19.3864 −1.45717
\(178\) 0 0
\(179\) 21.8525 1.63333 0.816666 0.577111i \(-0.195820\pi\)
0.816666 + 0.577111i \(0.195820\pi\)
\(180\) 0 0
\(181\) −19.5070 −1.44994 −0.724971 0.688779i \(-0.758147\pi\)
−0.724971 + 0.688779i \(0.758147\pi\)
\(182\) 0 0
\(183\) −19.5736 −1.44692
\(184\) 0 0
\(185\) 3.79969 0.279359
\(186\) 0 0
\(187\) −4.75014 −0.347365
\(188\) 0 0
\(189\) 4.09091 0.297570
\(190\) 0 0
\(191\) 12.3802 0.895798 0.447899 0.894084i \(-0.352172\pi\)
0.447899 + 0.894084i \(0.352172\pi\)
\(192\) 0 0
\(193\) −1.29492 −0.0932101 −0.0466050 0.998913i \(-0.514840\pi\)
−0.0466050 + 0.998913i \(0.514840\pi\)
\(194\) 0 0
\(195\) 11.2376 0.804744
\(196\) 0 0
\(197\) 2.83608 0.202062 0.101031 0.994883i \(-0.467786\pi\)
0.101031 + 0.994883i \(0.467786\pi\)
\(198\) 0 0
\(199\) −22.6556 −1.60602 −0.803008 0.595968i \(-0.796768\pi\)
−0.803008 + 0.595968i \(0.796768\pi\)
\(200\) 0 0
\(201\) 32.3737 2.28346
\(202\) 0 0
\(203\) −5.69879 −0.399977
\(204\) 0 0
\(205\) −23.2906 −1.62669
\(206\) 0 0
\(207\) −5.02595 −0.349328
\(208\) 0 0
\(209\) −6.50940 −0.450265
\(210\) 0 0
\(211\) 14.8913 1.02516 0.512581 0.858639i \(-0.328689\pi\)
0.512581 + 0.858639i \(0.328689\pi\)
\(212\) 0 0
\(213\) 20.7863 1.42425
\(214\) 0 0
\(215\) −24.4168 −1.66521
\(216\) 0 0
\(217\) −9.59749 −0.651520
\(218\) 0 0
\(219\) −37.0333 −2.50248
\(220\) 0 0
\(221\) 4.75014 0.319529
\(222\) 0 0
\(223\) 2.26934 0.151966 0.0759831 0.997109i \(-0.475790\pi\)
0.0759831 + 0.997109i \(0.475790\pi\)
\(224\) 0 0
\(225\) 53.2609 3.55073
\(226\) 0 0
\(227\) −25.4287 −1.68776 −0.843882 0.536528i \(-0.819735\pi\)
−0.843882 + 0.536528i \(0.819735\pi\)
\(228\) 0 0
\(229\) 9.51218 0.628582 0.314291 0.949327i \(-0.398233\pi\)
0.314291 + 0.949327i \(0.398233\pi\)
\(230\) 0 0
\(231\) 2.73758 0.180120
\(232\) 0 0
\(233\) −12.2947 −0.805453 −0.402726 0.915320i \(-0.631937\pi\)
−0.402726 + 0.915320i \(0.631937\pi\)
\(234\) 0 0
\(235\) −4.59050 −0.299451
\(236\) 0 0
\(237\) 45.0361 2.92541
\(238\) 0 0
\(239\) −3.80412 −0.246068 −0.123034 0.992402i \(-0.539262\pi\)
−0.123034 + 0.992402i \(0.539262\pi\)
\(240\) 0 0
\(241\) −3.24913 −0.209295 −0.104648 0.994509i \(-0.533371\pi\)
−0.104648 + 0.994509i \(0.533371\pi\)
\(242\) 0 0
\(243\) 18.5250 1.18838
\(244\) 0 0
\(245\) 4.10495 0.262256
\(246\) 0 0
\(247\) 6.50940 0.414183
\(248\) 0 0
\(249\) −1.22844 −0.0778493
\(250\) 0 0
\(251\) 19.7788 1.24843 0.624213 0.781254i \(-0.285420\pi\)
0.624213 + 0.781254i \(0.285420\pi\)
\(252\) 0 0
\(253\) −1.11828 −0.0703058
\(254\) 0 0
\(255\) 53.3804 3.34281
\(256\) 0 0
\(257\) 23.6628 1.47605 0.738023 0.674776i \(-0.235760\pi\)
0.738023 + 0.674776i \(0.235760\pi\)
\(258\) 0 0
\(259\) −0.925635 −0.0575162
\(260\) 0 0
\(261\) 25.6124 1.58537
\(262\) 0 0
\(263\) −17.0474 −1.05119 −0.525594 0.850736i \(-0.676157\pi\)
−0.525594 + 0.850736i \(0.676157\pi\)
\(264\) 0 0
\(265\) −44.2527 −2.71842
\(266\) 0 0
\(267\) 19.9867 1.22317
\(268\) 0 0
\(269\) −15.5996 −0.951127 −0.475563 0.879681i \(-0.657756\pi\)
−0.475563 + 0.879681i \(0.657756\pi\)
\(270\) 0 0
\(271\) 1.42104 0.0863222 0.0431611 0.999068i \(-0.486257\pi\)
0.0431611 + 0.999068i \(0.486257\pi\)
\(272\) 0 0
\(273\) −2.73758 −0.165686
\(274\) 0 0
\(275\) 11.8506 0.714620
\(276\) 0 0
\(277\) −17.9636 −1.07933 −0.539664 0.841880i \(-0.681449\pi\)
−0.539664 + 0.841880i \(0.681449\pi\)
\(278\) 0 0
\(279\) 43.1345 2.58239
\(280\) 0 0
\(281\) −25.4760 −1.51977 −0.759886 0.650057i \(-0.774745\pi\)
−0.759886 + 0.650057i \(0.774745\pi\)
\(282\) 0 0
\(283\) 7.02772 0.417754 0.208877 0.977942i \(-0.433019\pi\)
0.208877 + 0.977942i \(0.433019\pi\)
\(284\) 0 0
\(285\) 73.1504 4.33305
\(286\) 0 0
\(287\) 5.67379 0.334913
\(288\) 0 0
\(289\) 5.56387 0.327286
\(290\) 0 0
\(291\) 12.7925 0.749908
\(292\) 0 0
\(293\) −13.3207 −0.778202 −0.389101 0.921195i \(-0.627214\pi\)
−0.389101 + 0.921195i \(0.627214\pi\)
\(294\) 0 0
\(295\) 29.0696 1.69250
\(296\) 0 0
\(297\) −4.09091 −0.237379
\(298\) 0 0
\(299\) 1.11828 0.0646719
\(300\) 0 0
\(301\) 5.94812 0.342844
\(302\) 0 0
\(303\) 6.66746 0.383035
\(304\) 0 0
\(305\) 29.3502 1.68059
\(306\) 0 0
\(307\) −31.0142 −1.77007 −0.885036 0.465522i \(-0.845867\pi\)
−0.885036 + 0.465522i \(0.845867\pi\)
\(308\) 0 0
\(309\) 8.50149 0.483633
\(310\) 0 0
\(311\) 8.50915 0.482510 0.241255 0.970462i \(-0.422441\pi\)
0.241255 + 0.970462i \(0.422441\pi\)
\(312\) 0 0
\(313\) −0.907015 −0.0512675 −0.0256338 0.999671i \(-0.508160\pi\)
−0.0256338 + 0.999671i \(0.508160\pi\)
\(314\) 0 0
\(315\) −18.4491 −1.03949
\(316\) 0 0
\(317\) 3.15391 0.177141 0.0885706 0.996070i \(-0.471770\pi\)
0.0885706 + 0.996070i \(0.471770\pi\)
\(318\) 0 0
\(319\) 5.69879 0.319071
\(320\) 0 0
\(321\) 40.4446 2.25740
\(322\) 0 0
\(323\) 30.9206 1.72047
\(324\) 0 0
\(325\) −11.8506 −0.657355
\(326\) 0 0
\(327\) −47.3619 −2.61912
\(328\) 0 0
\(329\) 1.11828 0.0616529
\(330\) 0 0
\(331\) −12.9482 −0.711700 −0.355850 0.934543i \(-0.615809\pi\)
−0.355850 + 0.934543i \(0.615809\pi\)
\(332\) 0 0
\(333\) 4.16013 0.227974
\(334\) 0 0
\(335\) −48.5437 −2.65223
\(336\) 0 0
\(337\) −5.81871 −0.316965 −0.158483 0.987362i \(-0.550660\pi\)
−0.158483 + 0.987362i \(0.550660\pi\)
\(338\) 0 0
\(339\) −30.2081 −1.64068
\(340\) 0 0
\(341\) 9.59749 0.519733
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 12.5669 0.676577
\(346\) 0 0
\(347\) −17.7976 −0.955427 −0.477713 0.878516i \(-0.658534\pi\)
−0.477713 + 0.878516i \(0.658534\pi\)
\(348\) 0 0
\(349\) 6.89931 0.369312 0.184656 0.982803i \(-0.440883\pi\)
0.184656 + 0.982803i \(0.440883\pi\)
\(350\) 0 0
\(351\) 4.09091 0.218357
\(352\) 0 0
\(353\) −11.2510 −0.598832 −0.299416 0.954123i \(-0.596792\pi\)
−0.299416 + 0.954123i \(0.596792\pi\)
\(354\) 0 0
\(355\) −31.1686 −1.65426
\(356\) 0 0
\(357\) −13.0039 −0.688240
\(358\) 0 0
\(359\) 15.8649 0.837319 0.418659 0.908143i \(-0.362500\pi\)
0.418659 + 0.908143i \(0.362500\pi\)
\(360\) 0 0
\(361\) 23.3723 1.23012
\(362\) 0 0
\(363\) −2.73758 −0.143686
\(364\) 0 0
\(365\) 55.5307 2.90661
\(366\) 0 0
\(367\) −30.3570 −1.58462 −0.792312 0.610116i \(-0.791123\pi\)
−0.792312 + 0.610116i \(0.791123\pi\)
\(368\) 0 0
\(369\) −25.5000 −1.32748
\(370\) 0 0
\(371\) 10.7803 0.559687
\(372\) 0 0
\(373\) −18.3516 −0.950209 −0.475104 0.879930i \(-0.657590\pi\)
−0.475104 + 0.879930i \(0.657590\pi\)
\(374\) 0 0
\(375\) −76.9850 −3.97549
\(376\) 0 0
\(377\) −5.69879 −0.293503
\(378\) 0 0
\(379\) −2.57415 −0.132225 −0.0661126 0.997812i \(-0.521060\pi\)
−0.0661126 + 0.997812i \(0.521060\pi\)
\(380\) 0 0
\(381\) −0.126186 −0.00646473
\(382\) 0 0
\(383\) 16.7836 0.857601 0.428800 0.903399i \(-0.358936\pi\)
0.428800 + 0.903399i \(0.358936\pi\)
\(384\) 0 0
\(385\) −4.10495 −0.209208
\(386\) 0 0
\(387\) −26.7330 −1.35891
\(388\) 0 0
\(389\) −27.7088 −1.40489 −0.702446 0.711737i \(-0.747909\pi\)
−0.702446 + 0.711737i \(0.747909\pi\)
\(390\) 0 0
\(391\) 5.31200 0.268640
\(392\) 0 0
\(393\) 11.8726 0.598892
\(394\) 0 0
\(395\) −67.5307 −3.39784
\(396\) 0 0
\(397\) 16.0873 0.807398 0.403699 0.914892i \(-0.367724\pi\)
0.403699 + 0.914892i \(0.367724\pi\)
\(398\) 0 0
\(399\) −17.8200 −0.892117
\(400\) 0 0
\(401\) −3.51703 −0.175632 −0.0878162 0.996137i \(-0.527989\pi\)
−0.0878162 + 0.996137i \(0.527989\pi\)
\(402\) 0 0
\(403\) −9.59749 −0.478085
\(404\) 0 0
\(405\) −9.37513 −0.465854
\(406\) 0 0
\(407\) 0.925635 0.0458820
\(408\) 0 0
\(409\) 2.07105 0.102407 0.0512034 0.998688i \(-0.483694\pi\)
0.0512034 + 0.998688i \(0.483694\pi\)
\(410\) 0 0
\(411\) 48.0286 2.36908
\(412\) 0 0
\(413\) −7.08159 −0.348462
\(414\) 0 0
\(415\) 1.84203 0.0904215
\(416\) 0 0
\(417\) −3.55533 −0.174105
\(418\) 0 0
\(419\) 11.4498 0.559360 0.279680 0.960093i \(-0.409772\pi\)
0.279680 + 0.960093i \(0.409772\pi\)
\(420\) 0 0
\(421\) −26.0663 −1.27039 −0.635196 0.772351i \(-0.719081\pi\)
−0.635196 + 0.772351i \(0.719081\pi\)
\(422\) 0 0
\(423\) −5.02595 −0.244370
\(424\) 0 0
\(425\) −56.2922 −2.73057
\(426\) 0 0
\(427\) −7.14995 −0.346010
\(428\) 0 0
\(429\) 2.73758 0.132172
\(430\) 0 0
\(431\) −32.5791 −1.56928 −0.784640 0.619951i \(-0.787152\pi\)
−0.784640 + 0.619951i \(0.787152\pi\)
\(432\) 0 0
\(433\) 11.0807 0.532506 0.266253 0.963903i \(-0.414214\pi\)
0.266253 + 0.963903i \(0.414214\pi\)
\(434\) 0 0
\(435\) −64.0410 −3.07053
\(436\) 0 0
\(437\) 7.27935 0.348219
\(438\) 0 0
\(439\) −0.444568 −0.0212181 −0.0106090 0.999944i \(-0.503377\pi\)
−0.0106090 + 0.999944i \(0.503377\pi\)
\(440\) 0 0
\(441\) 4.49435 0.214017
\(442\) 0 0
\(443\) 35.9096 1.70611 0.853057 0.521817i \(-0.174746\pi\)
0.853057 + 0.521817i \(0.174746\pi\)
\(444\) 0 0
\(445\) −29.9697 −1.42070
\(446\) 0 0
\(447\) 38.4613 1.81916
\(448\) 0 0
\(449\) −11.0626 −0.522074 −0.261037 0.965329i \(-0.584064\pi\)
−0.261037 + 0.965329i \(0.584064\pi\)
\(450\) 0 0
\(451\) −5.67379 −0.267168
\(452\) 0 0
\(453\) −11.0170 −0.517624
\(454\) 0 0
\(455\) 4.10495 0.192443
\(456\) 0 0
\(457\) −4.64123 −0.217108 −0.108554 0.994091i \(-0.534622\pi\)
−0.108554 + 0.994091i \(0.534622\pi\)
\(458\) 0 0
\(459\) 19.4324 0.907027
\(460\) 0 0
\(461\) 12.2326 0.569727 0.284864 0.958568i \(-0.408052\pi\)
0.284864 + 0.958568i \(0.408052\pi\)
\(462\) 0 0
\(463\) 23.2408 1.08009 0.540047 0.841635i \(-0.318407\pi\)
0.540047 + 0.841635i \(0.318407\pi\)
\(464\) 0 0
\(465\) −107.853 −5.00157
\(466\) 0 0
\(467\) −21.8663 −1.01185 −0.505927 0.862576i \(-0.668849\pi\)
−0.505927 + 0.862576i \(0.668849\pi\)
\(468\) 0 0
\(469\) 11.8256 0.546058
\(470\) 0 0
\(471\) −14.8535 −0.684411
\(472\) 0 0
\(473\) −5.94812 −0.273495
\(474\) 0 0
\(475\) −77.1406 −3.53945
\(476\) 0 0
\(477\) −48.4506 −2.21840
\(478\) 0 0
\(479\) 37.6424 1.71992 0.859962 0.510359i \(-0.170487\pi\)
0.859962 + 0.510359i \(0.170487\pi\)
\(480\) 0 0
\(481\) −0.925635 −0.0422053
\(482\) 0 0
\(483\) −3.06139 −0.139298
\(484\) 0 0
\(485\) −19.1821 −0.871013
\(486\) 0 0
\(487\) 1.63042 0.0738815 0.0369408 0.999317i \(-0.488239\pi\)
0.0369408 + 0.999317i \(0.488239\pi\)
\(488\) 0 0
\(489\) 15.2797 0.690971
\(490\) 0 0
\(491\) 12.6170 0.569395 0.284698 0.958617i \(-0.408107\pi\)
0.284698 + 0.958617i \(0.408107\pi\)
\(492\) 0 0
\(493\) −27.0701 −1.21918
\(494\) 0 0
\(495\) 18.4491 0.829225
\(496\) 0 0
\(497\) 7.59293 0.340589
\(498\) 0 0
\(499\) −33.2460 −1.48830 −0.744148 0.668014i \(-0.767144\pi\)
−0.744148 + 0.668014i \(0.767144\pi\)
\(500\) 0 0
\(501\) −40.0039 −1.78724
\(502\) 0 0
\(503\) 26.7280 1.19174 0.595870 0.803081i \(-0.296807\pi\)
0.595870 + 0.803081i \(0.296807\pi\)
\(504\) 0 0
\(505\) −9.99773 −0.444893
\(506\) 0 0
\(507\) −2.73758 −0.121580
\(508\) 0 0
\(509\) 12.1032 0.536464 0.268232 0.963354i \(-0.413561\pi\)
0.268232 + 0.963354i \(0.413561\pi\)
\(510\) 0 0
\(511\) −13.5277 −0.598432
\(512\) 0 0
\(513\) 26.6294 1.17572
\(514\) 0 0
\(515\) −12.7478 −0.561737
\(516\) 0 0
\(517\) −1.11828 −0.0491820
\(518\) 0 0
\(519\) −1.35714 −0.0595718
\(520\) 0 0
\(521\) −43.8908 −1.92289 −0.961445 0.274998i \(-0.911323\pi\)
−0.961445 + 0.274998i \(0.911323\pi\)
\(522\) 0 0
\(523\) −37.8996 −1.65723 −0.828617 0.559815i \(-0.810872\pi\)
−0.828617 + 0.559815i \(0.810872\pi\)
\(524\) 0 0
\(525\) 32.4421 1.41589
\(526\) 0 0
\(527\) −45.5895 −1.98591
\(528\) 0 0
\(529\) −21.7494 −0.945628
\(530\) 0 0
\(531\) 31.8272 1.38118
\(532\) 0 0
\(533\) 5.67379 0.245759
\(534\) 0 0
\(535\) −60.6460 −2.62195
\(536\) 0 0
\(537\) −59.8230 −2.58155
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −17.9675 −0.772482 −0.386241 0.922398i \(-0.626227\pi\)
−0.386241 + 0.922398i \(0.626227\pi\)
\(542\) 0 0
\(543\) 53.4019 2.29170
\(544\) 0 0
\(545\) 71.0182 3.04209
\(546\) 0 0
\(547\) 44.8092 1.91590 0.957951 0.286931i \(-0.0926352\pi\)
0.957951 + 0.286931i \(0.0926352\pi\)
\(548\) 0 0
\(549\) 32.1344 1.37146
\(550\) 0 0
\(551\) −37.0957 −1.58033
\(552\) 0 0
\(553\) 16.4510 0.699569
\(554\) 0 0
\(555\) −10.4020 −0.441539
\(556\) 0 0
\(557\) −29.5051 −1.25017 −0.625085 0.780556i \(-0.714936\pi\)
−0.625085 + 0.780556i \(0.714936\pi\)
\(558\) 0 0
\(559\) 5.94812 0.251579
\(560\) 0 0
\(561\) 13.0039 0.549025
\(562\) 0 0
\(563\) −21.0327 −0.886423 −0.443211 0.896417i \(-0.646161\pi\)
−0.443211 + 0.896417i \(0.646161\pi\)
\(564\) 0 0
\(565\) 45.2965 1.90564
\(566\) 0 0
\(567\) 2.28386 0.0959131
\(568\) 0 0
\(569\) −14.1213 −0.591998 −0.295999 0.955188i \(-0.595652\pi\)
−0.295999 + 0.955188i \(0.595652\pi\)
\(570\) 0 0
\(571\) −1.79404 −0.0750784 −0.0375392 0.999295i \(-0.511952\pi\)
−0.0375392 + 0.999295i \(0.511952\pi\)
\(572\) 0 0
\(573\) −33.8917 −1.41585
\(574\) 0 0
\(575\) −13.2524 −0.552662
\(576\) 0 0
\(577\) −23.8800 −0.994137 −0.497069 0.867711i \(-0.665590\pi\)
−0.497069 + 0.867711i \(0.665590\pi\)
\(578\) 0 0
\(579\) 3.54494 0.147323
\(580\) 0 0
\(581\) −0.448733 −0.0186166
\(582\) 0 0
\(583\) −10.7803 −0.446476
\(584\) 0 0
\(585\) −18.4491 −0.762776
\(586\) 0 0
\(587\) 32.4688 1.34013 0.670066 0.742302i \(-0.266266\pi\)
0.670066 + 0.742302i \(0.266266\pi\)
\(588\) 0 0
\(589\) −62.4739 −2.57419
\(590\) 0 0
\(591\) −7.76400 −0.319368
\(592\) 0 0
\(593\) −13.0750 −0.536926 −0.268463 0.963290i \(-0.586516\pi\)
−0.268463 + 0.963290i \(0.586516\pi\)
\(594\) 0 0
\(595\) 19.4991 0.799386
\(596\) 0 0
\(597\) 62.0217 2.53838
\(598\) 0 0
\(599\) 23.0615 0.942268 0.471134 0.882062i \(-0.343845\pi\)
0.471134 + 0.882062i \(0.343845\pi\)
\(600\) 0 0
\(601\) −15.4448 −0.630008 −0.315004 0.949090i \(-0.602006\pi\)
−0.315004 + 0.949090i \(0.602006\pi\)
\(602\) 0 0
\(603\) −53.1486 −2.16438
\(604\) 0 0
\(605\) 4.10495 0.166890
\(606\) 0 0
\(607\) −21.1164 −0.857087 −0.428544 0.903521i \(-0.640973\pi\)
−0.428544 + 0.903521i \(0.640973\pi\)
\(608\) 0 0
\(609\) 15.6009 0.632181
\(610\) 0 0
\(611\) 1.11828 0.0452409
\(612\) 0 0
\(613\) −30.6429 −1.23766 −0.618828 0.785526i \(-0.712392\pi\)
−0.618828 + 0.785526i \(0.712392\pi\)
\(614\) 0 0
\(615\) 63.7600 2.57105
\(616\) 0 0
\(617\) 29.9055 1.20395 0.601975 0.798515i \(-0.294381\pi\)
0.601975 + 0.798515i \(0.294381\pi\)
\(618\) 0 0
\(619\) 43.2643 1.73894 0.869470 0.493985i \(-0.164460\pi\)
0.869470 + 0.493985i \(0.164460\pi\)
\(620\) 0 0
\(621\) 4.57479 0.183580
\(622\) 0 0
\(623\) 7.30086 0.292503
\(624\) 0 0
\(625\) 56.1844 2.24738
\(626\) 0 0
\(627\) 17.8200 0.711663
\(628\) 0 0
\(629\) −4.39690 −0.175316
\(630\) 0 0
\(631\) 18.2390 0.726083 0.363041 0.931773i \(-0.381738\pi\)
0.363041 + 0.931773i \(0.381738\pi\)
\(632\) 0 0
\(633\) −40.7663 −1.62031
\(634\) 0 0
\(635\) 0.189214 0.00750874
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −34.1253 −1.34998
\(640\) 0 0
\(641\) 34.6487 1.36854 0.684270 0.729228i \(-0.260121\pi\)
0.684270 + 0.729228i \(0.260121\pi\)
\(642\) 0 0
\(643\) −3.19624 −0.126047 −0.0630236 0.998012i \(-0.520074\pi\)
−0.0630236 + 0.998012i \(0.520074\pi\)
\(644\) 0 0
\(645\) 66.8429 2.63194
\(646\) 0 0
\(647\) −26.5155 −1.04243 −0.521216 0.853425i \(-0.674522\pi\)
−0.521216 + 0.853425i \(0.674522\pi\)
\(648\) 0 0
\(649\) 7.08159 0.277977
\(650\) 0 0
\(651\) 26.2739 1.02976
\(652\) 0 0
\(653\) −23.2349 −0.909253 −0.454627 0.890682i \(-0.650227\pi\)
−0.454627 + 0.890682i \(0.650227\pi\)
\(654\) 0 0
\(655\) −17.8027 −0.695609
\(656\) 0 0
\(657\) 60.7984 2.37197
\(658\) 0 0
\(659\) 29.3533 1.14344 0.571721 0.820448i \(-0.306276\pi\)
0.571721 + 0.820448i \(0.306276\pi\)
\(660\) 0 0
\(661\) −37.7097 −1.46674 −0.733369 0.679831i \(-0.762053\pi\)
−0.733369 + 0.679831i \(0.762053\pi\)
\(662\) 0 0
\(663\) −13.0039 −0.505030
\(664\) 0 0
\(665\) 26.7208 1.03619
\(666\) 0 0
\(667\) −6.37286 −0.246758
\(668\) 0 0
\(669\) −6.21250 −0.240189
\(670\) 0 0
\(671\) 7.14995 0.276021
\(672\) 0 0
\(673\) −7.03880 −0.271326 −0.135663 0.990755i \(-0.543316\pi\)
−0.135663 + 0.990755i \(0.543316\pi\)
\(674\) 0 0
\(675\) −48.4799 −1.86599
\(676\) 0 0
\(677\) −32.8697 −1.26328 −0.631642 0.775260i \(-0.717619\pi\)
−0.631642 + 0.775260i \(0.717619\pi\)
\(678\) 0 0
\(679\) 4.67291 0.179330
\(680\) 0 0
\(681\) 69.6132 2.66758
\(682\) 0 0
\(683\) 34.5845 1.32334 0.661670 0.749795i \(-0.269848\pi\)
0.661670 + 0.749795i \(0.269848\pi\)
\(684\) 0 0
\(685\) −72.0181 −2.75167
\(686\) 0 0
\(687\) −26.0404 −0.993502
\(688\) 0 0
\(689\) 10.7803 0.410698
\(690\) 0 0
\(691\) 12.1223 0.461155 0.230577 0.973054i \(-0.425939\pi\)
0.230577 + 0.973054i \(0.425939\pi\)
\(692\) 0 0
\(693\) −4.49435 −0.170726
\(694\) 0 0
\(695\) 5.33115 0.202222
\(696\) 0 0
\(697\) 26.9513 1.02085
\(698\) 0 0
\(699\) 33.6577 1.27305
\(700\) 0 0
\(701\) −24.9265 −0.941461 −0.470731 0.882277i \(-0.656010\pi\)
−0.470731 + 0.882277i \(0.656010\pi\)
\(702\) 0 0
\(703\) −6.02534 −0.227250
\(704\) 0 0
\(705\) 12.5669 0.473295
\(706\) 0 0
\(707\) 2.43553 0.0915975
\(708\) 0 0
\(709\) −26.8247 −1.00742 −0.503711 0.863872i \(-0.668032\pi\)
−0.503711 + 0.863872i \(0.668032\pi\)
\(710\) 0 0
\(711\) −73.9367 −2.77284
\(712\) 0 0
\(713\) −10.7327 −0.401943
\(714\) 0 0
\(715\) −4.10495 −0.153517
\(716\) 0 0
\(717\) 10.4141 0.388921
\(718\) 0 0
\(719\) −27.0067 −1.00718 −0.503590 0.863943i \(-0.667988\pi\)
−0.503590 + 0.863943i \(0.667988\pi\)
\(720\) 0 0
\(721\) 3.10548 0.115654
\(722\) 0 0
\(723\) 8.89477 0.330800
\(724\) 0 0
\(725\) 67.5343 2.50816
\(726\) 0 0
\(727\) −7.47024 −0.277056 −0.138528 0.990359i \(-0.544237\pi\)
−0.138528 + 0.990359i \(0.544237\pi\)
\(728\) 0 0
\(729\) −43.8621 −1.62452
\(730\) 0 0
\(731\) 28.2544 1.04503
\(732\) 0 0
\(733\) 21.3873 0.789957 0.394979 0.918690i \(-0.370752\pi\)
0.394979 + 0.918690i \(0.370752\pi\)
\(734\) 0 0
\(735\) −11.2376 −0.414507
\(736\) 0 0
\(737\) −11.8256 −0.435603
\(738\) 0 0
\(739\) −42.8605 −1.57665 −0.788325 0.615259i \(-0.789051\pi\)
−0.788325 + 0.615259i \(0.789051\pi\)
\(740\) 0 0
\(741\) −17.8200 −0.654635
\(742\) 0 0
\(743\) −30.8790 −1.13284 −0.566421 0.824116i \(-0.691672\pi\)
−0.566421 + 0.824116i \(0.691672\pi\)
\(744\) 0 0
\(745\) −57.6720 −2.11294
\(746\) 0 0
\(747\) 2.01676 0.0737895
\(748\) 0 0
\(749\) 14.7739 0.539825
\(750\) 0 0
\(751\) 51.6924 1.88628 0.943142 0.332391i \(-0.107855\pi\)
0.943142 + 0.332391i \(0.107855\pi\)
\(752\) 0 0
\(753\) −54.1460 −1.97319
\(754\) 0 0
\(755\) 16.5198 0.601216
\(756\) 0 0
\(757\) −2.25558 −0.0819805 −0.0409902 0.999160i \(-0.513051\pi\)
−0.0409902 + 0.999160i \(0.513051\pi\)
\(758\) 0 0
\(759\) 3.06139 0.111121
\(760\) 0 0
\(761\) 30.5461 1.10729 0.553647 0.832751i \(-0.313236\pi\)
0.553647 + 0.832751i \(0.313236\pi\)
\(762\) 0 0
\(763\) −17.3006 −0.626324
\(764\) 0 0
\(765\) −87.6359 −3.16848
\(766\) 0 0
\(767\) −7.08159 −0.255701
\(768\) 0 0
\(769\) 44.1057 1.59049 0.795246 0.606287i \(-0.207342\pi\)
0.795246 + 0.606287i \(0.207342\pi\)
\(770\) 0 0
\(771\) −64.7789 −2.33295
\(772\) 0 0
\(773\) −36.4084 −1.30952 −0.654760 0.755837i \(-0.727230\pi\)
−0.654760 + 0.755837i \(0.727230\pi\)
\(774\) 0 0
\(775\) 113.736 4.08553
\(776\) 0 0
\(777\) 2.53400 0.0909068
\(778\) 0 0
\(779\) 36.9330 1.32326
\(780\) 0 0
\(781\) −7.59293 −0.271696
\(782\) 0 0
\(783\) −23.3132 −0.833147
\(784\) 0 0
\(785\) 22.2725 0.794939
\(786\) 0 0
\(787\) 5.67746 0.202379 0.101190 0.994867i \(-0.467735\pi\)
0.101190 + 0.994867i \(0.467735\pi\)
\(788\) 0 0
\(789\) 46.6686 1.66145
\(790\) 0 0
\(791\) −11.0346 −0.392345
\(792\) 0 0
\(793\) −7.14995 −0.253902
\(794\) 0 0
\(795\) 121.145 4.29659
\(796\) 0 0
\(797\) 43.9545 1.55695 0.778475 0.627676i \(-0.215994\pi\)
0.778475 + 0.627676i \(0.215994\pi\)
\(798\) 0 0
\(799\) 5.31200 0.187925
\(800\) 0 0
\(801\) −32.8126 −1.15938
\(802\) 0 0
\(803\) 13.5277 0.477384
\(804\) 0 0
\(805\) 4.59050 0.161794
\(806\) 0 0
\(807\) 42.7053 1.50330
\(808\) 0 0
\(809\) 2.11004 0.0741850 0.0370925 0.999312i \(-0.488190\pi\)
0.0370925 + 0.999312i \(0.488190\pi\)
\(810\) 0 0
\(811\) 15.5301 0.545336 0.272668 0.962108i \(-0.412094\pi\)
0.272668 + 0.962108i \(0.412094\pi\)
\(812\) 0 0
\(813\) −3.89022 −0.136436
\(814\) 0 0
\(815\) −22.9116 −0.802559
\(816\) 0 0
\(817\) 38.7187 1.35460
\(818\) 0 0
\(819\) 4.49435 0.157045
\(820\) 0 0
\(821\) −35.5799 −1.24175 −0.620873 0.783911i \(-0.713222\pi\)
−0.620873 + 0.783911i \(0.713222\pi\)
\(822\) 0 0
\(823\) 10.8156 0.377007 0.188503 0.982073i \(-0.439636\pi\)
0.188503 + 0.982073i \(0.439636\pi\)
\(824\) 0 0
\(825\) −32.4421 −1.12949
\(826\) 0 0
\(827\) −23.0872 −0.802821 −0.401410 0.915898i \(-0.631480\pi\)
−0.401410 + 0.915898i \(0.631480\pi\)
\(828\) 0 0
\(829\) 38.5237 1.33798 0.668991 0.743270i \(-0.266726\pi\)
0.668991 + 0.743270i \(0.266726\pi\)
\(830\) 0 0
\(831\) 49.1768 1.70592
\(832\) 0 0
\(833\) −4.75014 −0.164583
\(834\) 0 0
\(835\) 59.9851 2.07587
\(836\) 0 0
\(837\) −39.2625 −1.35711
\(838\) 0 0
\(839\) −35.0629 −1.21050 −0.605252 0.796034i \(-0.706928\pi\)
−0.605252 + 0.796034i \(0.706928\pi\)
\(840\) 0 0
\(841\) 3.47624 0.119871
\(842\) 0 0
\(843\) 69.7426 2.40206
\(844\) 0 0
\(845\) 4.10495 0.141215
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −19.2389 −0.660279
\(850\) 0 0
\(851\) −1.03512 −0.0354835
\(852\) 0 0
\(853\) −19.7858 −0.677451 −0.338726 0.940885i \(-0.609996\pi\)
−0.338726 + 0.940885i \(0.609996\pi\)
\(854\) 0 0
\(855\) −120.093 −4.10708
\(856\) 0 0
\(857\) 43.4926 1.48568 0.742840 0.669469i \(-0.233478\pi\)
0.742840 + 0.669469i \(0.233478\pi\)
\(858\) 0 0
\(859\) −1.88762 −0.0644049 −0.0322024 0.999481i \(-0.510252\pi\)
−0.0322024 + 0.999481i \(0.510252\pi\)
\(860\) 0 0
\(861\) −15.5325 −0.529345
\(862\) 0 0
\(863\) −47.5393 −1.61826 −0.809129 0.587631i \(-0.800061\pi\)
−0.809129 + 0.587631i \(0.800061\pi\)
\(864\) 0 0
\(865\) 2.03501 0.0691923
\(866\) 0 0
\(867\) −15.2315 −0.517290
\(868\) 0 0
\(869\) −16.4510 −0.558063
\(870\) 0 0
\(871\) 11.8256 0.400697
\(872\) 0 0
\(873\) −21.0017 −0.710800
\(874\) 0 0
\(875\) −28.1215 −0.950682
\(876\) 0 0
\(877\) −54.0558 −1.82533 −0.912667 0.408704i \(-0.865981\pi\)
−0.912667 + 0.408704i \(0.865981\pi\)
\(878\) 0 0
\(879\) 36.4664 1.22998
\(880\) 0 0
\(881\) −17.1489 −0.577761 −0.288881 0.957365i \(-0.593283\pi\)
−0.288881 + 0.957365i \(0.593283\pi\)
\(882\) 0 0
\(883\) 16.2158 0.545707 0.272853 0.962056i \(-0.412033\pi\)
0.272853 + 0.962056i \(0.412033\pi\)
\(884\) 0 0
\(885\) −79.5804 −2.67506
\(886\) 0 0
\(887\) 13.9302 0.467731 0.233866 0.972269i \(-0.424862\pi\)
0.233866 + 0.972269i \(0.424862\pi\)
\(888\) 0 0
\(889\) −0.0460941 −0.00154595
\(890\) 0 0
\(891\) −2.28386 −0.0765121
\(892\) 0 0
\(893\) 7.27935 0.243594
\(894\) 0 0
\(895\) 89.7034 2.99846
\(896\) 0 0
\(897\) −3.06139 −0.102217
\(898\) 0 0
\(899\) 54.6941 1.82415
\(900\) 0 0
\(901\) 51.2081 1.70599
\(902\) 0 0
\(903\) −16.2835 −0.541880
\(904\) 0 0
\(905\) −80.0752 −2.66179
\(906\) 0 0
\(907\) −48.2268 −1.60135 −0.800673 0.599102i \(-0.795524\pi\)
−0.800673 + 0.599102i \(0.795524\pi\)
\(908\) 0 0
\(909\) −10.9461 −0.363060
\(910\) 0 0
\(911\) 6.92426 0.229411 0.114706 0.993400i \(-0.463408\pi\)
0.114706 + 0.993400i \(0.463408\pi\)
\(912\) 0 0
\(913\) 0.448733 0.0148509
\(914\) 0 0
\(915\) −80.3486 −2.65624
\(916\) 0 0
\(917\) 4.33688 0.143216
\(918\) 0 0
\(919\) −45.8371 −1.51203 −0.756014 0.654556i \(-0.772856\pi\)
−0.756014 + 0.654556i \(0.772856\pi\)
\(920\) 0 0
\(921\) 84.9038 2.79768
\(922\) 0 0
\(923\) 7.59293 0.249924
\(924\) 0 0
\(925\) 10.9694 0.360671
\(926\) 0 0
\(927\) −13.9571 −0.458411
\(928\) 0 0
\(929\) 42.6822 1.40036 0.700179 0.713968i \(-0.253104\pi\)
0.700179 + 0.713968i \(0.253104\pi\)
\(930\) 0 0
\(931\) −6.50940 −0.213337
\(932\) 0 0
\(933\) −23.2945 −0.762628
\(934\) 0 0
\(935\) −19.4991 −0.637689
\(936\) 0 0
\(937\) −10.8195 −0.353458 −0.176729 0.984260i \(-0.556552\pi\)
−0.176729 + 0.984260i \(0.556552\pi\)
\(938\) 0 0
\(939\) 2.48303 0.0810305
\(940\) 0 0
\(941\) −29.5369 −0.962875 −0.481438 0.876480i \(-0.659885\pi\)
−0.481438 + 0.876480i \(0.659885\pi\)
\(942\) 0 0
\(943\) 6.34490 0.206618
\(944\) 0 0
\(945\) 16.7930 0.546276
\(946\) 0 0
\(947\) −41.3390 −1.34334 −0.671668 0.740852i \(-0.734422\pi\)
−0.671668 + 0.740852i \(0.734422\pi\)
\(948\) 0 0
\(949\) −13.5277 −0.439129
\(950\) 0 0
\(951\) −8.63408 −0.279979
\(952\) 0 0
\(953\) −1.36665 −0.0442700 −0.0221350 0.999755i \(-0.507046\pi\)
−0.0221350 + 0.999755i \(0.507046\pi\)
\(954\) 0 0
\(955\) 50.8200 1.64450
\(956\) 0 0
\(957\) −15.6009 −0.504306
\(958\) 0 0
\(959\) 17.5442 0.566531
\(960\) 0 0
\(961\) 61.1118 1.97135
\(962\) 0 0
\(963\) −66.3989 −2.13967
\(964\) 0 0
\(965\) −5.31557 −0.171114
\(966\) 0 0
\(967\) 50.5079 1.62423 0.812113 0.583501i \(-0.198317\pi\)
0.812113 + 0.583501i \(0.198317\pi\)
\(968\) 0 0
\(969\) −84.6477 −2.71928
\(970\) 0 0
\(971\) −15.1043 −0.484720 −0.242360 0.970186i \(-0.577921\pi\)
−0.242360 + 0.970186i \(0.577921\pi\)
\(972\) 0 0
\(973\) −1.29871 −0.0416348
\(974\) 0 0
\(975\) 32.4421 1.03898
\(976\) 0 0
\(977\) 27.6707 0.885265 0.442633 0.896703i \(-0.354045\pi\)
0.442633 + 0.896703i \(0.354045\pi\)
\(978\) 0 0
\(979\) −7.30086 −0.233337
\(980\) 0 0
\(981\) 77.7551 2.48253
\(982\) 0 0
\(983\) 19.6661 0.627250 0.313625 0.949547i \(-0.398457\pi\)
0.313625 + 0.949547i \(0.398457\pi\)
\(984\) 0 0
\(985\) 11.6420 0.370944
\(986\) 0 0
\(987\) −3.06139 −0.0974451
\(988\) 0 0
\(989\) 6.65168 0.211511
\(990\) 0 0
\(991\) −41.1064 −1.30579 −0.652893 0.757450i \(-0.726445\pi\)
−0.652893 + 0.757450i \(0.726445\pi\)
\(992\) 0 0
\(993\) 35.4469 1.12487
\(994\) 0 0
\(995\) −93.0003 −2.94831
\(996\) 0 0
\(997\) −60.9967 −1.93178 −0.965892 0.258944i \(-0.916625\pi\)
−0.965892 + 0.258944i \(0.916625\pi\)
\(998\) 0 0
\(999\) −3.78669 −0.119806
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 \(a_p\))