Properties

Label 8004.2.a.j.1.14
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(3.50323\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +3.50323 q^{5} +0.271751 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +3.50323 q^{5} +0.271751 q^{7} +1.00000 q^{9} -3.15022 q^{11} +5.54253 q^{13} +3.50323 q^{15} +7.90123 q^{17} -0.447567 q^{19} +0.271751 q^{21} +1.00000 q^{23} +7.27263 q^{25} +1.00000 q^{27} -1.00000 q^{29} +6.65859 q^{31} -3.15022 q^{33} +0.952005 q^{35} +5.73526 q^{37} +5.54253 q^{39} +7.82330 q^{41} -3.05826 q^{43} +3.50323 q^{45} -6.56523 q^{47} -6.92615 q^{49} +7.90123 q^{51} -3.63270 q^{53} -11.0359 q^{55} -0.447567 q^{57} -9.18341 q^{59} +0.878199 q^{61} +0.271751 q^{63} +19.4168 q^{65} -0.508596 q^{67} +1.00000 q^{69} +7.95084 q^{71} -10.3911 q^{73} +7.27263 q^{75} -0.856073 q^{77} -15.0267 q^{79} +1.00000 q^{81} -8.08550 q^{83} +27.6798 q^{85} -1.00000 q^{87} -13.2657 q^{89} +1.50619 q^{91} +6.65859 q^{93} -1.56793 q^{95} +2.98895 q^{97} -3.15022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{3} + 3q^{5} + 4q^{7} + 16q^{9} + O(q^{10}) \) \( 16q + 16q^{3} + 3q^{5} + 4q^{7} + 16q^{9} + 5q^{11} + 6q^{13} + 3q^{15} + 3q^{17} + 11q^{19} + 4q^{21} + 16q^{23} + 27q^{25} + 16q^{27} - 16q^{29} + 14q^{31} + 5q^{33} + 11q^{35} + 4q^{37} + 6q^{39} + 11q^{41} + 23q^{43} + 3q^{45} - 2q^{47} + 34q^{49} + 3q^{51} + 19q^{53} + 31q^{55} + 11q^{57} + 32q^{59} + 19q^{61} + 4q^{63} + 6q^{65} + 33q^{67} + 16q^{69} - 5q^{71} + 23q^{73} + 27q^{75} + 42q^{77} + 24q^{79} + 16q^{81} + 7q^{83} - 16q^{87} - 2q^{89} + 25q^{91} + 14q^{93} + 7q^{95} + 33q^{97} + 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 3.50323 1.56669 0.783346 0.621585i \(-0.213511\pi\)
0.783346 + 0.621585i \(0.213511\pi\)
\(6\) 0 0
\(7\) 0.271751 0.102712 0.0513560 0.998680i \(-0.483646\pi\)
0.0513560 + 0.998680i \(0.483646\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.15022 −0.949826 −0.474913 0.880033i \(-0.657520\pi\)
−0.474913 + 0.880033i \(0.657520\pi\)
\(12\) 0 0
\(13\) 5.54253 1.53722 0.768611 0.639717i \(-0.220948\pi\)
0.768611 + 0.639717i \(0.220948\pi\)
\(14\) 0 0
\(15\) 3.50323 0.904530
\(16\) 0 0
\(17\) 7.90123 1.91633 0.958165 0.286218i \(-0.0923981\pi\)
0.958165 + 0.286218i \(0.0923981\pi\)
\(18\) 0 0
\(19\) −0.447567 −0.102679 −0.0513394 0.998681i \(-0.516349\pi\)
−0.0513394 + 0.998681i \(0.516349\pi\)
\(20\) 0 0
\(21\) 0.271751 0.0593008
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 7.27263 1.45453
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 6.65859 1.19592 0.597959 0.801527i \(-0.295979\pi\)
0.597959 + 0.801527i \(0.295979\pi\)
\(32\) 0 0
\(33\) −3.15022 −0.548382
\(34\) 0 0
\(35\) 0.952005 0.160918
\(36\) 0 0
\(37\) 5.73526 0.942871 0.471435 0.881901i \(-0.343736\pi\)
0.471435 + 0.881901i \(0.343736\pi\)
\(38\) 0 0
\(39\) 5.54253 0.887515
\(40\) 0 0
\(41\) 7.82330 1.22179 0.610897 0.791710i \(-0.290809\pi\)
0.610897 + 0.791710i \(0.290809\pi\)
\(42\) 0 0
\(43\) −3.05826 −0.466380 −0.233190 0.972431i \(-0.574916\pi\)
−0.233190 + 0.972431i \(0.574916\pi\)
\(44\) 0 0
\(45\) 3.50323 0.522231
\(46\) 0 0
\(47\) −6.56523 −0.957638 −0.478819 0.877914i \(-0.658935\pi\)
−0.478819 + 0.877914i \(0.658935\pi\)
\(48\) 0 0
\(49\) −6.92615 −0.989450
\(50\) 0 0
\(51\) 7.90123 1.10639
\(52\) 0 0
\(53\) −3.63270 −0.498990 −0.249495 0.968376i \(-0.580265\pi\)
−0.249495 + 0.968376i \(0.580265\pi\)
\(54\) 0 0
\(55\) −11.0359 −1.48808
\(56\) 0 0
\(57\) −0.447567 −0.0592817
\(58\) 0 0
\(59\) −9.18341 −1.19558 −0.597789 0.801654i \(-0.703954\pi\)
−0.597789 + 0.801654i \(0.703954\pi\)
\(60\) 0 0
\(61\) 0.878199 0.112442 0.0562209 0.998418i \(-0.482095\pi\)
0.0562209 + 0.998418i \(0.482095\pi\)
\(62\) 0 0
\(63\) 0.271751 0.0342374
\(64\) 0 0
\(65\) 19.4168 2.40835
\(66\) 0 0
\(67\) −0.508596 −0.0621349 −0.0310675 0.999517i \(-0.509891\pi\)
−0.0310675 + 0.999517i \(0.509891\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 7.95084 0.943591 0.471795 0.881708i \(-0.343606\pi\)
0.471795 + 0.881708i \(0.343606\pi\)
\(72\) 0 0
\(73\) −10.3911 −1.21619 −0.608095 0.793864i \(-0.708066\pi\)
−0.608095 + 0.793864i \(0.708066\pi\)
\(74\) 0 0
\(75\) 7.27263 0.839771
\(76\) 0 0
\(77\) −0.856073 −0.0975586
\(78\) 0 0
\(79\) −15.0267 −1.69064 −0.845321 0.534259i \(-0.820591\pi\)
−0.845321 + 0.534259i \(0.820591\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −8.08550 −0.887499 −0.443749 0.896151i \(-0.646352\pi\)
−0.443749 + 0.896151i \(0.646352\pi\)
\(84\) 0 0
\(85\) 27.6798 3.00230
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) −13.2657 −1.40616 −0.703081 0.711110i \(-0.748193\pi\)
−0.703081 + 0.711110i \(0.748193\pi\)
\(90\) 0 0
\(91\) 1.50619 0.157891
\(92\) 0 0
\(93\) 6.65859 0.690464
\(94\) 0 0
\(95\) −1.56793 −0.160866
\(96\) 0 0
\(97\) 2.98895 0.303482 0.151741 0.988420i \(-0.451512\pi\)
0.151741 + 0.988420i \(0.451512\pi\)
\(98\) 0 0
\(99\) −3.15022 −0.316609
\(100\) 0 0
\(101\) −14.3045 −1.42335 −0.711673 0.702511i \(-0.752062\pi\)
−0.711673 + 0.702511i \(0.752062\pi\)
\(102\) 0 0
\(103\) 6.81537 0.671538 0.335769 0.941944i \(-0.391004\pi\)
0.335769 + 0.941944i \(0.391004\pi\)
\(104\) 0 0
\(105\) 0.952005 0.0929062
\(106\) 0 0
\(107\) −13.9056 −1.34430 −0.672151 0.740415i \(-0.734629\pi\)
−0.672151 + 0.740415i \(0.734629\pi\)
\(108\) 0 0
\(109\) 13.3468 1.27839 0.639197 0.769043i \(-0.279267\pi\)
0.639197 + 0.769043i \(0.279267\pi\)
\(110\) 0 0
\(111\) 5.73526 0.544367
\(112\) 0 0
\(113\) −0.661719 −0.0622493 −0.0311246 0.999516i \(-0.509909\pi\)
−0.0311246 + 0.999516i \(0.509909\pi\)
\(114\) 0 0
\(115\) 3.50323 0.326678
\(116\) 0 0
\(117\) 5.54253 0.512407
\(118\) 0 0
\(119\) 2.14716 0.196830
\(120\) 0 0
\(121\) −1.07614 −0.0978312
\(122\) 0 0
\(123\) 7.82330 0.705403
\(124\) 0 0
\(125\) 7.96155 0.712102
\(126\) 0 0
\(127\) 19.8990 1.76575 0.882874 0.469610i \(-0.155605\pi\)
0.882874 + 0.469610i \(0.155605\pi\)
\(128\) 0 0
\(129\) −3.05826 −0.269265
\(130\) 0 0
\(131\) 15.8984 1.38905 0.694525 0.719468i \(-0.255614\pi\)
0.694525 + 0.719468i \(0.255614\pi\)
\(132\) 0 0
\(133\) −0.121627 −0.0105464
\(134\) 0 0
\(135\) 3.50323 0.301510
\(136\) 0 0
\(137\) 16.8613 1.44056 0.720279 0.693685i \(-0.244014\pi\)
0.720279 + 0.693685i \(0.244014\pi\)
\(138\) 0 0
\(139\) −10.8288 −0.918483 −0.459241 0.888312i \(-0.651879\pi\)
−0.459241 + 0.888312i \(0.651879\pi\)
\(140\) 0 0
\(141\) −6.56523 −0.552892
\(142\) 0 0
\(143\) −17.4602 −1.46009
\(144\) 0 0
\(145\) −3.50323 −0.290928
\(146\) 0 0
\(147\) −6.92615 −0.571259
\(148\) 0 0
\(149\) −10.2153 −0.836870 −0.418435 0.908247i \(-0.637421\pi\)
−0.418435 + 0.908247i \(0.637421\pi\)
\(150\) 0 0
\(151\) −16.7767 −1.36527 −0.682636 0.730759i \(-0.739167\pi\)
−0.682636 + 0.730759i \(0.739167\pi\)
\(152\) 0 0
\(153\) 7.90123 0.638776
\(154\) 0 0
\(155\) 23.3266 1.87364
\(156\) 0 0
\(157\) 21.9816 1.75432 0.877162 0.480195i \(-0.159434\pi\)
0.877162 + 0.480195i \(0.159434\pi\)
\(158\) 0 0
\(159\) −3.63270 −0.288092
\(160\) 0 0
\(161\) 0.271751 0.0214169
\(162\) 0 0
\(163\) −13.1982 −1.03376 −0.516881 0.856057i \(-0.672907\pi\)
−0.516881 + 0.856057i \(0.672907\pi\)
\(164\) 0 0
\(165\) −11.0359 −0.859146
\(166\) 0 0
\(167\) 10.0383 0.776790 0.388395 0.921493i \(-0.373030\pi\)
0.388395 + 0.921493i \(0.373030\pi\)
\(168\) 0 0
\(169\) 17.7196 1.36305
\(170\) 0 0
\(171\) −0.447567 −0.0342263
\(172\) 0 0
\(173\) −2.62068 −0.199247 −0.0996234 0.995025i \(-0.531764\pi\)
−0.0996234 + 0.995025i \(0.531764\pi\)
\(174\) 0 0
\(175\) 1.97634 0.149397
\(176\) 0 0
\(177\) −9.18341 −0.690267
\(178\) 0 0
\(179\) 19.2949 1.44217 0.721085 0.692846i \(-0.243644\pi\)
0.721085 + 0.692846i \(0.243644\pi\)
\(180\) 0 0
\(181\) 1.68199 0.125021 0.0625105 0.998044i \(-0.480089\pi\)
0.0625105 + 0.998044i \(0.480089\pi\)
\(182\) 0 0
\(183\) 0.878199 0.0649183
\(184\) 0 0
\(185\) 20.0919 1.47719
\(186\) 0 0
\(187\) −24.8906 −1.82018
\(188\) 0 0
\(189\) 0.271751 0.0197669
\(190\) 0 0
\(191\) −5.91755 −0.428179 −0.214089 0.976814i \(-0.568678\pi\)
−0.214089 + 0.976814i \(0.568678\pi\)
\(192\) 0 0
\(193\) −9.40360 −0.676886 −0.338443 0.940987i \(-0.609900\pi\)
−0.338443 + 0.940987i \(0.609900\pi\)
\(194\) 0 0
\(195\) 19.4168 1.39046
\(196\) 0 0
\(197\) 16.1496 1.15061 0.575305 0.817939i \(-0.304883\pi\)
0.575305 + 0.817939i \(0.304883\pi\)
\(198\) 0 0
\(199\) 6.67857 0.473431 0.236716 0.971579i \(-0.423929\pi\)
0.236716 + 0.971579i \(0.423929\pi\)
\(200\) 0 0
\(201\) −0.508596 −0.0358736
\(202\) 0 0
\(203\) −0.271751 −0.0190732
\(204\) 0 0
\(205\) 27.4068 1.91418
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 1.40993 0.0975270
\(210\) 0 0
\(211\) 6.03725 0.415621 0.207811 0.978169i \(-0.433366\pi\)
0.207811 + 0.978169i \(0.433366\pi\)
\(212\) 0 0
\(213\) 7.95084 0.544782
\(214\) 0 0
\(215\) −10.7138 −0.730674
\(216\) 0 0
\(217\) 1.80948 0.122835
\(218\) 0 0
\(219\) −10.3911 −0.702168
\(220\) 0 0
\(221\) 43.7928 2.94582
\(222\) 0 0
\(223\) −25.6466 −1.71742 −0.858712 0.512458i \(-0.828735\pi\)
−0.858712 + 0.512458i \(0.828735\pi\)
\(224\) 0 0
\(225\) 7.27263 0.484842
\(226\) 0 0
\(227\) 0.782140 0.0519125 0.0259562 0.999663i \(-0.491737\pi\)
0.0259562 + 0.999663i \(0.491737\pi\)
\(228\) 0 0
\(229\) −17.9486 −1.18608 −0.593039 0.805173i \(-0.702072\pi\)
−0.593039 + 0.805173i \(0.702072\pi\)
\(230\) 0 0
\(231\) −0.856073 −0.0563255
\(232\) 0 0
\(233\) 16.2525 1.06473 0.532367 0.846514i \(-0.321303\pi\)
0.532367 + 0.846514i \(0.321303\pi\)
\(234\) 0 0
\(235\) −22.9995 −1.50032
\(236\) 0 0
\(237\) −15.0267 −0.976092
\(238\) 0 0
\(239\) −20.0022 −1.29384 −0.646918 0.762560i \(-0.723942\pi\)
−0.646918 + 0.762560i \(0.723942\pi\)
\(240\) 0 0
\(241\) −18.5415 −1.19437 −0.597183 0.802105i \(-0.703713\pi\)
−0.597183 + 0.802105i \(0.703713\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −24.2639 −1.55016
\(246\) 0 0
\(247\) −2.48065 −0.157840
\(248\) 0 0
\(249\) −8.08550 −0.512398
\(250\) 0 0
\(251\) 2.34485 0.148006 0.0740028 0.997258i \(-0.476423\pi\)
0.0740028 + 0.997258i \(0.476423\pi\)
\(252\) 0 0
\(253\) −3.15022 −0.198052
\(254\) 0 0
\(255\) 27.6798 1.73338
\(256\) 0 0
\(257\) 5.81081 0.362468 0.181234 0.983440i \(-0.441991\pi\)
0.181234 + 0.983440i \(0.441991\pi\)
\(258\) 0 0
\(259\) 1.55856 0.0968442
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 18.5997 1.14691 0.573453 0.819239i \(-0.305604\pi\)
0.573453 + 0.819239i \(0.305604\pi\)
\(264\) 0 0
\(265\) −12.7262 −0.781763
\(266\) 0 0
\(267\) −13.2657 −0.811848
\(268\) 0 0
\(269\) −9.99523 −0.609420 −0.304710 0.952445i \(-0.598560\pi\)
−0.304710 + 0.952445i \(0.598560\pi\)
\(270\) 0 0
\(271\) 13.4259 0.815568 0.407784 0.913079i \(-0.366302\pi\)
0.407784 + 0.913079i \(0.366302\pi\)
\(272\) 0 0
\(273\) 1.50619 0.0911585
\(274\) 0 0
\(275\) −22.9103 −1.38155
\(276\) 0 0
\(277\) 26.3946 1.58590 0.792948 0.609289i \(-0.208545\pi\)
0.792948 + 0.609289i \(0.208545\pi\)
\(278\) 0 0
\(279\) 6.65859 0.398639
\(280\) 0 0
\(281\) 4.24115 0.253006 0.126503 0.991966i \(-0.459625\pi\)
0.126503 + 0.991966i \(0.459625\pi\)
\(282\) 0 0
\(283\) 29.1562 1.73315 0.866577 0.499043i \(-0.166315\pi\)
0.866577 + 0.499043i \(0.166315\pi\)
\(284\) 0 0
\(285\) −1.56793 −0.0928761
\(286\) 0 0
\(287\) 2.12599 0.125493
\(288\) 0 0
\(289\) 45.4294 2.67232
\(290\) 0 0
\(291\) 2.98895 0.175215
\(292\) 0 0
\(293\) 7.66800 0.447969 0.223985 0.974593i \(-0.428093\pi\)
0.223985 + 0.974593i \(0.428093\pi\)
\(294\) 0 0
\(295\) −32.1716 −1.87310
\(296\) 0 0
\(297\) −3.15022 −0.182794
\(298\) 0 0
\(299\) 5.54253 0.320533
\(300\) 0 0
\(301\) −0.831084 −0.0479029
\(302\) 0 0
\(303\) −14.3045 −0.821770
\(304\) 0 0
\(305\) 3.07653 0.176162
\(306\) 0 0
\(307\) 11.5950 0.661759 0.330879 0.943673i \(-0.392655\pi\)
0.330879 + 0.943673i \(0.392655\pi\)
\(308\) 0 0
\(309\) 6.81537 0.387713
\(310\) 0 0
\(311\) 3.22439 0.182838 0.0914192 0.995812i \(-0.470860\pi\)
0.0914192 + 0.995812i \(0.470860\pi\)
\(312\) 0 0
\(313\) −18.5121 −1.04637 −0.523184 0.852220i \(-0.675256\pi\)
−0.523184 + 0.852220i \(0.675256\pi\)
\(314\) 0 0
\(315\) 0.952005 0.0536394
\(316\) 0 0
\(317\) 34.8481 1.95726 0.978632 0.205618i \(-0.0659204\pi\)
0.978632 + 0.205618i \(0.0659204\pi\)
\(318\) 0 0
\(319\) 3.15022 0.176378
\(320\) 0 0
\(321\) −13.9056 −0.776133
\(322\) 0 0
\(323\) −3.53633 −0.196766
\(324\) 0 0
\(325\) 40.3088 2.23593
\(326\) 0 0
\(327\) 13.3468 0.738081
\(328\) 0 0
\(329\) −1.78411 −0.0983610
\(330\) 0 0
\(331\) 13.7037 0.753224 0.376612 0.926371i \(-0.377089\pi\)
0.376612 + 0.926371i \(0.377089\pi\)
\(332\) 0 0
\(333\) 5.73526 0.314290
\(334\) 0 0
\(335\) −1.78173 −0.0973463
\(336\) 0 0
\(337\) −2.68235 −0.146117 −0.0730586 0.997328i \(-0.523276\pi\)
−0.0730586 + 0.997328i \(0.523276\pi\)
\(338\) 0 0
\(339\) −0.661719 −0.0359396
\(340\) 0 0
\(341\) −20.9760 −1.13591
\(342\) 0 0
\(343\) −3.78444 −0.204341
\(344\) 0 0
\(345\) 3.50323 0.188608
\(346\) 0 0
\(347\) 13.3778 0.718156 0.359078 0.933308i \(-0.383091\pi\)
0.359078 + 0.933308i \(0.383091\pi\)
\(348\) 0 0
\(349\) 8.56716 0.458590 0.229295 0.973357i \(-0.426358\pi\)
0.229295 + 0.973357i \(0.426358\pi\)
\(350\) 0 0
\(351\) 5.54253 0.295838
\(352\) 0 0
\(353\) −35.1739 −1.87212 −0.936060 0.351841i \(-0.885556\pi\)
−0.936060 + 0.351841i \(0.885556\pi\)
\(354\) 0 0
\(355\) 27.8536 1.47832
\(356\) 0 0
\(357\) 2.14716 0.113640
\(358\) 0 0
\(359\) −6.45448 −0.340654 −0.170327 0.985388i \(-0.554482\pi\)
−0.170327 + 0.985388i \(0.554482\pi\)
\(360\) 0 0
\(361\) −18.7997 −0.989457
\(362\) 0 0
\(363\) −1.07614 −0.0564829
\(364\) 0 0
\(365\) −36.4025 −1.90540
\(366\) 0 0
\(367\) −19.1539 −0.999826 −0.499913 0.866076i \(-0.666635\pi\)
−0.499913 + 0.866076i \(0.666635\pi\)
\(368\) 0 0
\(369\) 7.82330 0.407265
\(370\) 0 0
\(371\) −0.987188 −0.0512523
\(372\) 0 0
\(373\) −4.99898 −0.258837 −0.129419 0.991590i \(-0.541311\pi\)
−0.129419 + 0.991590i \(0.541311\pi\)
\(374\) 0 0
\(375\) 7.96155 0.411133
\(376\) 0 0
\(377\) −5.54253 −0.285455
\(378\) 0 0
\(379\) 11.5365 0.592588 0.296294 0.955097i \(-0.404249\pi\)
0.296294 + 0.955097i \(0.404249\pi\)
\(380\) 0 0
\(381\) 19.8990 1.01946
\(382\) 0 0
\(383\) 18.8685 0.964135 0.482068 0.876134i \(-0.339886\pi\)
0.482068 + 0.876134i \(0.339886\pi\)
\(384\) 0 0
\(385\) −2.99902 −0.152844
\(386\) 0 0
\(387\) −3.05826 −0.155460
\(388\) 0 0
\(389\) −18.3970 −0.932765 −0.466383 0.884583i \(-0.654443\pi\)
−0.466383 + 0.884583i \(0.654443\pi\)
\(390\) 0 0
\(391\) 7.90123 0.399582
\(392\) 0 0
\(393\) 15.8984 0.801969
\(394\) 0 0
\(395\) −52.6422 −2.64872
\(396\) 0 0
\(397\) −20.1948 −1.01355 −0.506774 0.862079i \(-0.669162\pi\)
−0.506774 + 0.862079i \(0.669162\pi\)
\(398\) 0 0
\(399\) −0.121627 −0.00608894
\(400\) 0 0
\(401\) −26.4958 −1.32314 −0.661570 0.749884i \(-0.730109\pi\)
−0.661570 + 0.749884i \(0.730109\pi\)
\(402\) 0 0
\(403\) 36.9054 1.83839
\(404\) 0 0
\(405\) 3.50323 0.174077
\(406\) 0 0
\(407\) −18.0673 −0.895563
\(408\) 0 0
\(409\) −23.0830 −1.14138 −0.570690 0.821166i \(-0.693324\pi\)
−0.570690 + 0.821166i \(0.693324\pi\)
\(410\) 0 0
\(411\) 16.8613 0.831707
\(412\) 0 0
\(413\) −2.49560 −0.122800
\(414\) 0 0
\(415\) −28.3254 −1.39044
\(416\) 0 0
\(417\) −10.8288 −0.530286
\(418\) 0 0
\(419\) 14.8361 0.724792 0.362396 0.932024i \(-0.381959\pi\)
0.362396 + 0.932024i \(0.381959\pi\)
\(420\) 0 0
\(421\) 31.1076 1.51609 0.758046 0.652201i \(-0.226154\pi\)
0.758046 + 0.652201i \(0.226154\pi\)
\(422\) 0 0
\(423\) −6.56523 −0.319213
\(424\) 0 0
\(425\) 57.4627 2.78735
\(426\) 0 0
\(427\) 0.238651 0.0115491
\(428\) 0 0
\(429\) −17.4602 −0.842985
\(430\) 0 0
\(431\) −38.9602 −1.87664 −0.938322 0.345762i \(-0.887621\pi\)
−0.938322 + 0.345762i \(0.887621\pi\)
\(432\) 0 0
\(433\) −9.73144 −0.467663 −0.233832 0.972277i \(-0.575126\pi\)
−0.233832 + 0.972277i \(0.575126\pi\)
\(434\) 0 0
\(435\) −3.50323 −0.167967
\(436\) 0 0
\(437\) −0.447567 −0.0214100
\(438\) 0 0
\(439\) 2.02051 0.0964336 0.0482168 0.998837i \(-0.484646\pi\)
0.0482168 + 0.998837i \(0.484646\pi\)
\(440\) 0 0
\(441\) −6.92615 −0.329817
\(442\) 0 0
\(443\) −8.39353 −0.398789 −0.199394 0.979919i \(-0.563897\pi\)
−0.199394 + 0.979919i \(0.563897\pi\)
\(444\) 0 0
\(445\) −46.4728 −2.20302
\(446\) 0 0
\(447\) −10.2153 −0.483167
\(448\) 0 0
\(449\) −25.6101 −1.20861 −0.604307 0.796752i \(-0.706550\pi\)
−0.604307 + 0.796752i \(0.706550\pi\)
\(450\) 0 0
\(451\) −24.6451 −1.16049
\(452\) 0 0
\(453\) −16.7767 −0.788240
\(454\) 0 0
\(455\) 5.27652 0.247367
\(456\) 0 0
\(457\) −8.26415 −0.386580 −0.193290 0.981142i \(-0.561916\pi\)
−0.193290 + 0.981142i \(0.561916\pi\)
\(458\) 0 0
\(459\) 7.90123 0.368798
\(460\) 0 0
\(461\) −23.7842 −1.10774 −0.553870 0.832603i \(-0.686850\pi\)
−0.553870 + 0.832603i \(0.686850\pi\)
\(462\) 0 0
\(463\) 28.4554 1.32243 0.661217 0.750195i \(-0.270040\pi\)
0.661217 + 0.750195i \(0.270040\pi\)
\(464\) 0 0
\(465\) 23.3266 1.08174
\(466\) 0 0
\(467\) −35.5643 −1.64572 −0.822859 0.568245i \(-0.807622\pi\)
−0.822859 + 0.568245i \(0.807622\pi\)
\(468\) 0 0
\(469\) −0.138211 −0.00638201
\(470\) 0 0
\(471\) 21.9816 1.01286
\(472\) 0 0
\(473\) 9.63418 0.442980
\(474\) 0 0
\(475\) −3.25499 −0.149349
\(476\) 0 0
\(477\) −3.63270 −0.166330
\(478\) 0 0
\(479\) 42.1906 1.92774 0.963868 0.266380i \(-0.0858276\pi\)
0.963868 + 0.266380i \(0.0858276\pi\)
\(480\) 0 0
\(481\) 31.7878 1.44940
\(482\) 0 0
\(483\) 0.271751 0.0123651
\(484\) 0 0
\(485\) 10.4710 0.475463
\(486\) 0 0
\(487\) −14.6201 −0.662499 −0.331249 0.943543i \(-0.607470\pi\)
−0.331249 + 0.943543i \(0.607470\pi\)
\(488\) 0 0
\(489\) −13.1982 −0.596843
\(490\) 0 0
\(491\) −9.22278 −0.416218 −0.208109 0.978106i \(-0.566731\pi\)
−0.208109 + 0.978106i \(0.566731\pi\)
\(492\) 0 0
\(493\) −7.90123 −0.355853
\(494\) 0 0
\(495\) −11.0359 −0.496028
\(496\) 0 0
\(497\) 2.16064 0.0969182
\(498\) 0 0
\(499\) −28.1745 −1.26126 −0.630632 0.776082i \(-0.717204\pi\)
−0.630632 + 0.776082i \(0.717204\pi\)
\(500\) 0 0
\(501\) 10.0383 0.448480
\(502\) 0 0
\(503\) −15.8419 −0.706354 −0.353177 0.935557i \(-0.614899\pi\)
−0.353177 + 0.935557i \(0.614899\pi\)
\(504\) 0 0
\(505\) −50.1118 −2.22995
\(506\) 0 0
\(507\) 17.7196 0.786957
\(508\) 0 0
\(509\) −3.22033 −0.142739 −0.0713693 0.997450i \(-0.522737\pi\)
−0.0713693 + 0.997450i \(0.522737\pi\)
\(510\) 0 0
\(511\) −2.82380 −0.124917
\(512\) 0 0
\(513\) −0.447567 −0.0197606
\(514\) 0 0
\(515\) 23.8758 1.05209
\(516\) 0 0
\(517\) 20.6819 0.909589
\(518\) 0 0
\(519\) −2.62068 −0.115035
\(520\) 0 0
\(521\) −31.0912 −1.36213 −0.681064 0.732224i \(-0.738483\pi\)
−0.681064 + 0.732224i \(0.738483\pi\)
\(522\) 0 0
\(523\) 4.78853 0.209388 0.104694 0.994505i \(-0.466614\pi\)
0.104694 + 0.994505i \(0.466614\pi\)
\(524\) 0 0
\(525\) 1.97634 0.0862546
\(526\) 0 0
\(527\) 52.6110 2.29177
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −9.18341 −0.398526
\(532\) 0 0
\(533\) 43.3609 1.87817
\(534\) 0 0
\(535\) −48.7144 −2.10611
\(536\) 0 0
\(537\) 19.2949 0.832637
\(538\) 0 0
\(539\) 21.8189 0.939805
\(540\) 0 0
\(541\) 2.14598 0.0922628 0.0461314 0.998935i \(-0.485311\pi\)
0.0461314 + 0.998935i \(0.485311\pi\)
\(542\) 0 0
\(543\) 1.68199 0.0721809
\(544\) 0 0
\(545\) 46.7570 2.00285
\(546\) 0 0
\(547\) 11.1544 0.476926 0.238463 0.971152i \(-0.423356\pi\)
0.238463 + 0.971152i \(0.423356\pi\)
\(548\) 0 0
\(549\) 0.878199 0.0374806
\(550\) 0 0
\(551\) 0.447567 0.0190670
\(552\) 0 0
\(553\) −4.08353 −0.173649
\(554\) 0 0
\(555\) 20.0919 0.852855
\(556\) 0 0
\(557\) −16.7212 −0.708498 −0.354249 0.935151i \(-0.615264\pi\)
−0.354249 + 0.935151i \(0.615264\pi\)
\(558\) 0 0
\(559\) −16.9505 −0.716930
\(560\) 0 0
\(561\) −24.8906 −1.05088
\(562\) 0 0
\(563\) −14.8989 −0.627915 −0.313957 0.949437i \(-0.601655\pi\)
−0.313957 + 0.949437i \(0.601655\pi\)
\(564\) 0 0
\(565\) −2.31815 −0.0975255
\(566\) 0 0
\(567\) 0.271751 0.0114125
\(568\) 0 0
\(569\) −28.7000 −1.20317 −0.601584 0.798809i \(-0.705464\pi\)
−0.601584 + 0.798809i \(0.705464\pi\)
\(570\) 0 0
\(571\) −3.99280 −0.167093 −0.0835467 0.996504i \(-0.526625\pi\)
−0.0835467 + 0.996504i \(0.526625\pi\)
\(572\) 0 0
\(573\) −5.91755 −0.247209
\(574\) 0 0
\(575\) 7.27263 0.303290
\(576\) 0 0
\(577\) 34.4039 1.43226 0.716128 0.697969i \(-0.245913\pi\)
0.716128 + 0.697969i \(0.245913\pi\)
\(578\) 0 0
\(579\) −9.40360 −0.390800
\(580\) 0 0
\(581\) −2.19724 −0.0911569
\(582\) 0 0
\(583\) 11.4438 0.473953
\(584\) 0 0
\(585\) 19.4168 0.802785
\(586\) 0 0
\(587\) −31.8196 −1.31334 −0.656668 0.754180i \(-0.728035\pi\)
−0.656668 + 0.754180i \(0.728035\pi\)
\(588\) 0 0
\(589\) −2.98016 −0.122795
\(590\) 0 0
\(591\) 16.1496 0.664305
\(592\) 0 0
\(593\) −16.8271 −0.691004 −0.345502 0.938418i \(-0.612291\pi\)
−0.345502 + 0.938418i \(0.612291\pi\)
\(594\) 0 0
\(595\) 7.52201 0.308372
\(596\) 0 0
\(597\) 6.67857 0.273336
\(598\) 0 0
\(599\) 9.44446 0.385890 0.192945 0.981210i \(-0.438196\pi\)
0.192945 + 0.981210i \(0.438196\pi\)
\(600\) 0 0
\(601\) −33.7434 −1.37642 −0.688210 0.725511i \(-0.741603\pi\)
−0.688210 + 0.725511i \(0.741603\pi\)
\(602\) 0 0
\(603\) −0.508596 −0.0207116
\(604\) 0 0
\(605\) −3.76998 −0.153271
\(606\) 0 0
\(607\) −23.8922 −0.969756 −0.484878 0.874582i \(-0.661136\pi\)
−0.484878 + 0.874582i \(0.661136\pi\)
\(608\) 0 0
\(609\) −0.271751 −0.0110119
\(610\) 0 0
\(611\) −36.3880 −1.47210
\(612\) 0 0
\(613\) 44.2826 1.78856 0.894278 0.447512i \(-0.147690\pi\)
0.894278 + 0.447512i \(0.147690\pi\)
\(614\) 0 0
\(615\) 27.4068 1.10515
\(616\) 0 0
\(617\) −28.6113 −1.15185 −0.575925 0.817503i \(-0.695358\pi\)
−0.575925 + 0.817503i \(0.695358\pi\)
\(618\) 0 0
\(619\) −18.7046 −0.751800 −0.375900 0.926660i \(-0.622666\pi\)
−0.375900 + 0.926660i \(0.622666\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −3.60496 −0.144430
\(624\) 0 0
\(625\) −8.47201 −0.338880
\(626\) 0 0
\(627\) 1.40993 0.0563072
\(628\) 0 0
\(629\) 45.3156 1.80685
\(630\) 0 0
\(631\) 36.0637 1.43567 0.717837 0.696211i \(-0.245132\pi\)
0.717837 + 0.696211i \(0.245132\pi\)
\(632\) 0 0
\(633\) 6.03725 0.239959
\(634\) 0 0
\(635\) 69.7107 2.76638
\(636\) 0 0
\(637\) −38.3884 −1.52100
\(638\) 0 0
\(639\) 7.95084 0.314530
\(640\) 0 0
\(641\) 0.607972 0.0240135 0.0120067 0.999928i \(-0.496178\pi\)
0.0120067 + 0.999928i \(0.496178\pi\)
\(642\) 0 0
\(643\) 6.14478 0.242326 0.121163 0.992633i \(-0.461338\pi\)
0.121163 + 0.992633i \(0.461338\pi\)
\(644\) 0 0
\(645\) −10.7138 −0.421855
\(646\) 0 0
\(647\) 42.7096 1.67909 0.839544 0.543292i \(-0.182822\pi\)
0.839544 + 0.543292i \(0.182822\pi\)
\(648\) 0 0
\(649\) 28.9297 1.13559
\(650\) 0 0
\(651\) 1.80948 0.0709189
\(652\) 0 0
\(653\) 30.3806 1.18888 0.594442 0.804138i \(-0.297373\pi\)
0.594442 + 0.804138i \(0.297373\pi\)
\(654\) 0 0
\(655\) 55.6958 2.17622
\(656\) 0 0
\(657\) −10.3911 −0.405397
\(658\) 0 0
\(659\) −28.7657 −1.12055 −0.560276 0.828306i \(-0.689305\pi\)
−0.560276 + 0.828306i \(0.689305\pi\)
\(660\) 0 0
\(661\) 33.0608 1.28592 0.642958 0.765901i \(-0.277707\pi\)
0.642958 + 0.765901i \(0.277707\pi\)
\(662\) 0 0
\(663\) 43.7928 1.70077
\(664\) 0 0
\(665\) −0.426086 −0.0165229
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) −25.6466 −0.991556
\(670\) 0 0
\(671\) −2.76652 −0.106800
\(672\) 0 0
\(673\) 12.6691 0.488359 0.244180 0.969730i \(-0.421481\pi\)
0.244180 + 0.969730i \(0.421481\pi\)
\(674\) 0 0
\(675\) 7.27263 0.279924
\(676\) 0 0
\(677\) −4.77767 −0.183621 −0.0918104 0.995777i \(-0.529265\pi\)
−0.0918104 + 0.995777i \(0.529265\pi\)
\(678\) 0 0
\(679\) 0.812249 0.0311712
\(680\) 0 0
\(681\) 0.782140 0.0299717
\(682\) 0 0
\(683\) 7.86732 0.301035 0.150517 0.988607i \(-0.451906\pi\)
0.150517 + 0.988607i \(0.451906\pi\)
\(684\) 0 0
\(685\) 59.0690 2.25691
\(686\) 0 0
\(687\) −17.9486 −0.684783
\(688\) 0 0
\(689\) −20.1344 −0.767058
\(690\) 0 0
\(691\) 25.4938 0.969830 0.484915 0.874561i \(-0.338851\pi\)
0.484915 + 0.874561i \(0.338851\pi\)
\(692\) 0 0
\(693\) −0.856073 −0.0325195
\(694\) 0 0
\(695\) −37.9356 −1.43898
\(696\) 0 0
\(697\) 61.8137 2.34136
\(698\) 0 0
\(699\) 16.2525 0.614724
\(700\) 0 0
\(701\) −35.3843 −1.33645 −0.668223 0.743961i \(-0.732945\pi\)
−0.668223 + 0.743961i \(0.732945\pi\)
\(702\) 0 0
\(703\) −2.56691 −0.0968129
\(704\) 0 0
\(705\) −22.9995 −0.866212
\(706\) 0 0
\(707\) −3.88724 −0.146195
\(708\) 0 0
\(709\) −1.31981 −0.0495665 −0.0247832 0.999693i \(-0.507890\pi\)
−0.0247832 + 0.999693i \(0.507890\pi\)
\(710\) 0 0
\(711\) −15.0267 −0.563547
\(712\) 0 0
\(713\) 6.65859 0.249366
\(714\) 0 0
\(715\) −61.1670 −2.28752
\(716\) 0 0
\(717\) −20.0022 −0.746996
\(718\) 0 0
\(719\) 43.7563 1.63184 0.815918 0.578168i \(-0.196232\pi\)
0.815918 + 0.578168i \(0.196232\pi\)
\(720\) 0 0
\(721\) 1.85208 0.0689751
\(722\) 0 0
\(723\) −18.5415 −0.689567
\(724\) 0 0
\(725\) −7.27263 −0.270099
\(726\) 0 0
\(727\) 36.4333 1.35124 0.675618 0.737252i \(-0.263877\pi\)
0.675618 + 0.737252i \(0.263877\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −24.1640 −0.893738
\(732\) 0 0
\(733\) 34.8828 1.28842 0.644212 0.764847i \(-0.277185\pi\)
0.644212 + 0.764847i \(0.277185\pi\)
\(734\) 0 0
\(735\) −24.2639 −0.894988
\(736\) 0 0
\(737\) 1.60219 0.0590173
\(738\) 0 0
\(739\) −8.65983 −0.318557 −0.159278 0.987234i \(-0.550917\pi\)
−0.159278 + 0.987234i \(0.550917\pi\)
\(740\) 0 0
\(741\) −2.48065 −0.0911290
\(742\) 0 0
\(743\) 40.4395 1.48358 0.741792 0.670631i \(-0.233976\pi\)
0.741792 + 0.670631i \(0.233976\pi\)
\(744\) 0 0
\(745\) −35.7866 −1.31112
\(746\) 0 0
\(747\) −8.08550 −0.295833
\(748\) 0 0
\(749\) −3.77884 −0.138076
\(750\) 0 0
\(751\) −36.1760 −1.32008 −0.660041 0.751230i \(-0.729461\pi\)
−0.660041 + 0.751230i \(0.729461\pi\)
\(752\) 0 0
\(753\) 2.34485 0.0854511
\(754\) 0 0
\(755\) −58.7728 −2.13896
\(756\) 0 0
\(757\) −33.6143 −1.22173 −0.610866 0.791734i \(-0.709178\pi\)
−0.610866 + 0.791734i \(0.709178\pi\)
\(758\) 0 0
\(759\) −3.15022 −0.114346
\(760\) 0 0
\(761\) 8.72408 0.316248 0.158124 0.987419i \(-0.449455\pi\)
0.158124 + 0.987419i \(0.449455\pi\)
\(762\) 0 0
\(763\) 3.62701 0.131306
\(764\) 0 0
\(765\) 27.6798 1.00077
\(766\) 0 0
\(767\) −50.8993 −1.83787
\(768\) 0 0
\(769\) 37.1907 1.34113 0.670566 0.741850i \(-0.266051\pi\)
0.670566 + 0.741850i \(0.266051\pi\)
\(770\) 0 0
\(771\) 5.81081 0.209271
\(772\) 0 0
\(773\) −16.8445 −0.605855 −0.302928 0.953014i \(-0.597964\pi\)
−0.302928 + 0.953014i \(0.597964\pi\)
\(774\) 0 0
\(775\) 48.4255 1.73949
\(776\) 0 0
\(777\) 1.55856 0.0559130
\(778\) 0 0
\(779\) −3.50145 −0.125452
\(780\) 0 0
\(781\) −25.0468 −0.896247
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) 77.0067 2.74849
\(786\) 0 0
\(787\) 6.07688 0.216617 0.108309 0.994117i \(-0.465456\pi\)
0.108309 + 0.994117i \(0.465456\pi\)
\(788\) 0 0
\(789\) 18.5997 0.662166
\(790\) 0 0
\(791\) −0.179822 −0.00639375
\(792\) 0 0
\(793\) 4.86745 0.172848
\(794\) 0 0
\(795\) −12.7262 −0.451351
\(796\) 0 0
\(797\) −3.06586 −0.108598 −0.0542992 0.998525i \(-0.517292\pi\)
−0.0542992 + 0.998525i \(0.517292\pi\)
\(798\) 0 0
\(799\) −51.8734 −1.83515
\(800\) 0 0
\(801\) −13.2657 −0.468721
\(802\) 0 0
\(803\) 32.7343 1.15517
\(804\) 0 0
\(805\) 0.952005 0.0335538
\(806\) 0 0
\(807\) −9.99523 −0.351849
\(808\) 0 0
\(809\) 5.74699 0.202053 0.101027 0.994884i \(-0.467787\pi\)
0.101027 + 0.994884i \(0.467787\pi\)
\(810\) 0 0
\(811\) −10.6321 −0.373345 −0.186672 0.982422i \(-0.559770\pi\)
−0.186672 + 0.982422i \(0.559770\pi\)
\(812\) 0 0
\(813\) 13.4259 0.470868
\(814\) 0 0
\(815\) −46.2364 −1.61959
\(816\) 0 0
\(817\) 1.36877 0.0478874
\(818\) 0 0
\(819\) 1.50619 0.0526304
\(820\) 0 0
\(821\) −24.2293 −0.845607 −0.422803 0.906221i \(-0.638954\pi\)
−0.422803 + 0.906221i \(0.638954\pi\)
\(822\) 0 0
\(823\) 51.5784 1.79791 0.898955 0.438041i \(-0.144327\pi\)
0.898955 + 0.438041i \(0.144327\pi\)
\(824\) 0 0
\(825\) −22.9103 −0.797636
\(826\) 0 0
\(827\) 4.15760 0.144574 0.0722869 0.997384i \(-0.476970\pi\)
0.0722869 + 0.997384i \(0.476970\pi\)
\(828\) 0 0
\(829\) 11.6005 0.402902 0.201451 0.979499i \(-0.435434\pi\)
0.201451 + 0.979499i \(0.435434\pi\)
\(830\) 0 0
\(831\) 26.3946 0.915618
\(832\) 0 0
\(833\) −54.7251 −1.89611
\(834\) 0 0
\(835\) 35.1666 1.21699
\(836\) 0 0
\(837\) 6.65859 0.230155
\(838\) 0 0
\(839\) 4.00532 0.138279 0.0691395 0.997607i \(-0.477975\pi\)
0.0691395 + 0.997607i \(0.477975\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 4.24115 0.146073
\(844\) 0 0
\(845\) 62.0760 2.13548
\(846\) 0 0
\(847\) −0.292443 −0.0100484
\(848\) 0 0
\(849\) 29.1562 1.00064
\(850\) 0 0
\(851\) 5.73526 0.196602
\(852\) 0 0
\(853\) 31.7370 1.08665 0.543327 0.839521i \(-0.317165\pi\)
0.543327 + 0.839521i \(0.317165\pi\)
\(854\) 0 0
\(855\) −1.56793 −0.0536221
\(856\) 0 0
\(857\) 6.72548 0.229738 0.114869 0.993381i \(-0.463355\pi\)
0.114869 + 0.993381i \(0.463355\pi\)
\(858\) 0 0
\(859\) 1.42040 0.0484633 0.0242316 0.999706i \(-0.492286\pi\)
0.0242316 + 0.999706i \(0.492286\pi\)
\(860\) 0 0
\(861\) 2.12599 0.0724534
\(862\) 0 0
\(863\) 17.3070 0.589139 0.294569 0.955630i \(-0.404824\pi\)
0.294569 + 0.955630i \(0.404824\pi\)
\(864\) 0 0
\(865\) −9.18085 −0.312158
\(866\) 0 0
\(867\) 45.4294 1.54286
\(868\) 0 0
\(869\) 47.3375 1.60581
\(870\) 0 0
\(871\) −2.81891 −0.0955151
\(872\) 0 0
\(873\) 2.98895 0.101161
\(874\) 0 0
\(875\) 2.16356 0.0731415
\(876\) 0 0
\(877\) 23.1992 0.783383 0.391691 0.920097i \(-0.371890\pi\)
0.391691 + 0.920097i \(0.371890\pi\)
\(878\) 0 0
\(879\) 7.66800 0.258635
\(880\) 0 0
\(881\) −32.7212 −1.10241 −0.551203 0.834371i \(-0.685831\pi\)
−0.551203 + 0.834371i \(0.685831\pi\)
\(882\) 0 0
\(883\) 14.2784 0.480506 0.240253 0.970710i \(-0.422770\pi\)
0.240253 + 0.970710i \(0.422770\pi\)
\(884\) 0 0
\(885\) −32.1716 −1.08144
\(886\) 0 0
\(887\) −0.290019 −0.00973788 −0.00486894 0.999988i \(-0.501550\pi\)
−0.00486894 + 0.999988i \(0.501550\pi\)
\(888\) 0 0
\(889\) 5.40756 0.181364
\(890\) 0 0
\(891\) −3.15022 −0.105536
\(892\) 0 0
\(893\) 2.93838 0.0983291
\(894\) 0 0
\(895\) 67.5946 2.25944
\(896\) 0 0
\(897\) 5.54253 0.185060
\(898\) 0 0
\(899\) −6.65859 −0.222076
\(900\) 0 0
\(901\) −28.7028 −0.956229
\(902\) 0 0
\(903\) −0.831084 −0.0276567
\(904\) 0 0
\(905\) 5.89238 0.195869
\(906\) 0 0
\(907\) 10.2597 0.340666 0.170333 0.985387i \(-0.445516\pi\)
0.170333 + 0.985387i \(0.445516\pi\)
\(908\) 0 0
\(909\) −14.3045 −0.474449
\(910\) 0 0
\(911\) 29.7117 0.984392 0.492196 0.870484i \(-0.336194\pi\)
0.492196 + 0.870484i \(0.336194\pi\)
\(912\) 0 0
\(913\) 25.4711 0.842969
\(914\) 0 0
\(915\) 3.07653 0.101707
\(916\) 0 0
\(917\) 4.32040 0.142672
\(918\) 0 0
\(919\) −5.18904 −0.171171 −0.0855853 0.996331i \(-0.527276\pi\)
−0.0855853 + 0.996331i \(0.527276\pi\)
\(920\) 0 0
\(921\) 11.5950 0.382067
\(922\) 0 0
\(923\) 44.0678 1.45051
\(924\) 0 0
\(925\) 41.7104 1.37143
\(926\) 0 0
\(927\) 6.81537 0.223846
\(928\) 0 0
\(929\) −18.0854 −0.593362 −0.296681 0.954977i \(-0.595880\pi\)
−0.296681 + 0.954977i \(0.595880\pi\)
\(930\) 0 0
\(931\) 3.09991 0.101596
\(932\) 0 0
\(933\) 3.22439 0.105562
\(934\) 0 0
\(935\) −87.1974 −2.85166
\(936\) 0 0
\(937\) 21.9073 0.715679 0.357840 0.933783i \(-0.383513\pi\)
0.357840 + 0.933783i \(0.383513\pi\)
\(938\) 0 0
\(939\) −18.5121 −0.604120
\(940\) 0 0
\(941\) −27.2754 −0.889151 −0.444576 0.895741i \(-0.646646\pi\)
−0.444576 + 0.895741i \(0.646646\pi\)
\(942\) 0 0
\(943\) 7.82330 0.254762
\(944\) 0 0
\(945\) 0.952005 0.0309687
\(946\) 0 0
\(947\) −14.4712 −0.470251 −0.235126 0.971965i \(-0.575550\pi\)
−0.235126 + 0.971965i \(0.575550\pi\)
\(948\) 0 0
\(949\) −57.5932 −1.86955
\(950\) 0 0
\(951\) 34.8481 1.13003
\(952\) 0 0
\(953\) 13.8054 0.447201 0.223601 0.974681i \(-0.428219\pi\)
0.223601 + 0.974681i \(0.428219\pi\)
\(954\) 0 0
\(955\) −20.7305 −0.670825
\(956\) 0 0
\(957\) 3.15022 0.101832
\(958\) 0 0
\(959\) 4.58207 0.147963
\(960\) 0 0
\(961\) 13.3368 0.430220
\(962\) 0 0
\(963\) −13.9056 −0.448100
\(964\) 0 0
\(965\) −32.9430 −1.06047
\(966\) 0 0
\(967\) 56.6537 1.82186 0.910930 0.412562i \(-0.135366\pi\)
0.910930 + 0.412562i \(0.135366\pi\)
\(968\) 0 0
\(969\) −3.53633 −0.113603
\(970\) 0 0
\(971\) −1.35956 −0.0436302 −0.0218151 0.999762i \(-0.506945\pi\)
−0.0218151 + 0.999762i \(0.506945\pi\)
\(972\) 0 0
\(973\) −2.94272 −0.0943393
\(974\) 0 0
\(975\) 40.3088 1.29091
\(976\) 0 0
\(977\) −28.3722 −0.907707 −0.453854 0.891076i \(-0.649951\pi\)
−0.453854 + 0.891076i \(0.649951\pi\)
\(978\) 0 0
\(979\) 41.7898 1.33561
\(980\) 0 0
\(981\) 13.3468 0.426131
\(982\) 0 0
\(983\) −53.9413 −1.72046 −0.860230 0.509906i \(-0.829680\pi\)
−0.860230 + 0.509906i \(0.829680\pi\)
\(984\) 0 0
\(985\) 56.5757 1.80265
\(986\) 0 0
\(987\) −1.78411 −0.0567887
\(988\) 0 0
\(989\) −3.05826 −0.0972470
\(990\) 0 0
\(991\) −56.5273 −1.79565 −0.897825 0.440352i \(-0.854854\pi\)
−0.897825 + 0.440352i \(0.854854\pi\)
\(992\) 0 0
\(993\) 13.7037 0.434874
\(994\) 0 0
\(995\) 23.3966 0.741721
\(996\) 0 0
\(997\) 9.47644 0.300122 0.150061 0.988677i \(-0.452053\pi\)
0.150061 + 0.988677i \(0.452053\pi\)
\(998\) 0 0
\(999\) 5.73526 0.181456
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 \(a_p\))