Properties

Label 6004.2.a.g.1.25
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.25
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.48243 q^{3} +1.00873 q^{5} +0.658321 q^{7} +3.16248 q^{9} +O(q^{10})\) \(q+2.48243 q^{3} +1.00873 q^{5} +0.658321 q^{7} +3.16248 q^{9} -5.12660 q^{11} -2.19021 q^{13} +2.50410 q^{15} -4.93027 q^{17} +1.00000 q^{19} +1.63424 q^{21} +2.25019 q^{23} -3.98247 q^{25} +0.403349 q^{27} -3.27576 q^{29} -6.68263 q^{31} -12.7265 q^{33} +0.664065 q^{35} +4.75479 q^{37} -5.43704 q^{39} -6.29737 q^{41} -7.36027 q^{43} +3.19008 q^{45} -8.45612 q^{47} -6.56661 q^{49} -12.2391 q^{51} +6.21683 q^{53} -5.17134 q^{55} +2.48243 q^{57} +2.76767 q^{59} +1.82136 q^{61} +2.08193 q^{63} -2.20932 q^{65} +7.94750 q^{67} +5.58595 q^{69} +13.7260 q^{71} -3.62552 q^{73} -9.88622 q^{75} -3.37495 q^{77} -1.00000 q^{79} -8.48616 q^{81} -12.7858 q^{83} -4.97330 q^{85} -8.13186 q^{87} +10.3744 q^{89} -1.44186 q^{91} -16.5892 q^{93} +1.00873 q^{95} +8.58998 q^{97} -16.2128 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) 2.48243 1.43323 0.716617 0.697467i \(-0.245690\pi\)
0.716617 + 0.697467i \(0.245690\pi\)
\(4\) 0 0
\(5\) 1.00873 0.451116 0.225558 0.974230i \(-0.427579\pi\)
0.225558 + 0.974230i \(0.427579\pi\)
\(6\) 0 0
\(7\) 0.658321 0.248822 0.124411 0.992231i \(-0.460296\pi\)
0.124411 + 0.992231i \(0.460296\pi\)
\(8\) 0 0
\(9\) 3.16248 1.05416
\(10\) 0 0
\(11\) −5.12660 −1.54573 −0.772864 0.634571i \(-0.781177\pi\)
−0.772864 + 0.634571i \(0.781177\pi\)
\(12\) 0 0
\(13\) −2.19021 −0.607454 −0.303727 0.952759i \(-0.598231\pi\)
−0.303727 + 0.952759i \(0.598231\pi\)
\(14\) 0 0
\(15\) 2.50410 0.646555
\(16\) 0 0
\(17\) −4.93027 −1.19577 −0.597884 0.801583i \(-0.703992\pi\)
−0.597884 + 0.801583i \(0.703992\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 1.63424 0.356620
\(22\) 0 0
\(23\) 2.25019 0.469197 0.234598 0.972092i \(-0.424622\pi\)
0.234598 + 0.972092i \(0.424622\pi\)
\(24\) 0 0
\(25\) −3.98247 −0.796494
\(26\) 0 0
\(27\) 0.403349 0.0776246
\(28\) 0 0
\(29\) −3.27576 −0.608294 −0.304147 0.952625i \(-0.598371\pi\)
−0.304147 + 0.952625i \(0.598371\pi\)
\(30\) 0 0
\(31\) −6.68263 −1.20024 −0.600118 0.799911i \(-0.704880\pi\)
−0.600118 + 0.799911i \(0.704880\pi\)
\(32\) 0 0
\(33\) −12.7265 −2.21539
\(34\) 0 0
\(35\) 0.664065 0.112248
\(36\) 0 0
\(37\) 4.75479 0.781683 0.390842 0.920458i \(-0.372184\pi\)
0.390842 + 0.920458i \(0.372184\pi\)
\(38\) 0 0
\(39\) −5.43704 −0.870623
\(40\) 0 0
\(41\) −6.29737 −0.983484 −0.491742 0.870741i \(-0.663640\pi\)
−0.491742 + 0.870741i \(0.663640\pi\)
\(42\) 0 0
\(43\) −7.36027 −1.12243 −0.561215 0.827670i \(-0.689666\pi\)
−0.561215 + 0.827670i \(0.689666\pi\)
\(44\) 0 0
\(45\) 3.19008 0.475549
\(46\) 0 0
\(47\) −8.45612 −1.23345 −0.616726 0.787178i \(-0.711541\pi\)
−0.616726 + 0.787178i \(0.711541\pi\)
\(48\) 0 0
\(49\) −6.56661 −0.938088
\(50\) 0 0
\(51\) −12.2391 −1.71381
\(52\) 0 0
\(53\) 6.21683 0.853947 0.426974 0.904264i \(-0.359580\pi\)
0.426974 + 0.904264i \(0.359580\pi\)
\(54\) 0 0
\(55\) −5.17134 −0.697303
\(56\) 0 0
\(57\) 2.48243 0.328806
\(58\) 0 0
\(59\) 2.76767 0.360320 0.180160 0.983637i \(-0.442338\pi\)
0.180160 + 0.983637i \(0.442338\pi\)
\(60\) 0 0
\(61\) 1.82136 0.233202 0.116601 0.993179i \(-0.462800\pi\)
0.116601 + 0.993179i \(0.462800\pi\)
\(62\) 0 0
\(63\) 2.08193 0.262298
\(64\) 0 0
\(65\) −2.20932 −0.274032
\(66\) 0 0
\(67\) 7.94750 0.970941 0.485471 0.874253i \(-0.338648\pi\)
0.485471 + 0.874253i \(0.338648\pi\)
\(68\) 0 0
\(69\) 5.58595 0.672469
\(70\) 0 0
\(71\) 13.7260 1.62898 0.814490 0.580177i \(-0.197017\pi\)
0.814490 + 0.580177i \(0.197017\pi\)
\(72\) 0 0
\(73\) −3.62552 −0.424335 −0.212167 0.977233i \(-0.568052\pi\)
−0.212167 + 0.977233i \(0.568052\pi\)
\(74\) 0 0
\(75\) −9.88622 −1.14156
\(76\) 0 0
\(77\) −3.37495 −0.384611
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −8.48616 −0.942906
\(82\) 0 0
\(83\) −12.7858 −1.40342 −0.701712 0.712461i \(-0.747581\pi\)
−0.701712 + 0.712461i \(0.747581\pi\)
\(84\) 0 0
\(85\) −4.97330 −0.539430
\(86\) 0 0
\(87\) −8.13186 −0.871827
\(88\) 0 0
\(89\) 10.3744 1.09969 0.549844 0.835267i \(-0.314687\pi\)
0.549844 + 0.835267i \(0.314687\pi\)
\(90\) 0 0
\(91\) −1.44186 −0.151148
\(92\) 0 0
\(93\) −16.5892 −1.72022
\(94\) 0 0
\(95\) 1.00873 0.103493
\(96\) 0 0
\(97\) 8.58998 0.872180 0.436090 0.899903i \(-0.356363\pi\)
0.436090 + 0.899903i \(0.356363\pi\)
\(98\) 0 0
\(99\) −16.2128 −1.62945
\(100\) 0 0
\(101\) −8.57318 −0.853063 −0.426531 0.904473i \(-0.640265\pi\)
−0.426531 + 0.904473i \(0.640265\pi\)
\(102\) 0 0
\(103\) 3.43742 0.338699 0.169349 0.985556i \(-0.445833\pi\)
0.169349 + 0.985556i \(0.445833\pi\)
\(104\) 0 0
\(105\) 1.64850 0.160877
\(106\) 0 0
\(107\) 6.52295 0.630597 0.315299 0.948992i \(-0.397895\pi\)
0.315299 + 0.948992i \(0.397895\pi\)
\(108\) 0 0
\(109\) 9.73287 0.932239 0.466120 0.884722i \(-0.345652\pi\)
0.466120 + 0.884722i \(0.345652\pi\)
\(110\) 0 0
\(111\) 11.8035 1.12034
\(112\) 0 0
\(113\) 15.0997 1.42046 0.710229 0.703971i \(-0.248591\pi\)
0.710229 + 0.703971i \(0.248591\pi\)
\(114\) 0 0
\(115\) 2.26983 0.211662
\(116\) 0 0
\(117\) −6.92648 −0.640354
\(118\) 0 0
\(119\) −3.24570 −0.297533
\(120\) 0 0
\(121\) 15.2821 1.38928
\(122\) 0 0
\(123\) −15.6328 −1.40956
\(124\) 0 0
\(125\) −9.06086 −0.810428
\(126\) 0 0
\(127\) −12.4992 −1.10913 −0.554564 0.832141i \(-0.687115\pi\)
−0.554564 + 0.832141i \(0.687115\pi\)
\(128\) 0 0
\(129\) −18.2714 −1.60871
\(130\) 0 0
\(131\) −7.20572 −0.629567 −0.314784 0.949163i \(-0.601932\pi\)
−0.314784 + 0.949163i \(0.601932\pi\)
\(132\) 0 0
\(133\) 0.658321 0.0570836
\(134\) 0 0
\(135\) 0.406869 0.0350177
\(136\) 0 0
\(137\) −8.01038 −0.684373 −0.342186 0.939632i \(-0.611167\pi\)
−0.342186 + 0.939632i \(0.611167\pi\)
\(138\) 0 0
\(139\) −4.63706 −0.393311 −0.196655 0.980473i \(-0.563008\pi\)
−0.196655 + 0.980473i \(0.563008\pi\)
\(140\) 0 0
\(141\) −20.9918 −1.76783
\(142\) 0 0
\(143\) 11.2283 0.938959
\(144\) 0 0
\(145\) −3.30435 −0.274411
\(146\) 0 0
\(147\) −16.3012 −1.34450
\(148\) 0 0
\(149\) −15.7408 −1.28953 −0.644766 0.764380i \(-0.723045\pi\)
−0.644766 + 0.764380i \(0.723045\pi\)
\(150\) 0 0
\(151\) 2.04777 0.166645 0.0833225 0.996523i \(-0.473447\pi\)
0.0833225 + 0.996523i \(0.473447\pi\)
\(152\) 0 0
\(153\) −15.5919 −1.26053
\(154\) 0 0
\(155\) −6.74095 −0.541446
\(156\) 0 0
\(157\) 2.50123 0.199620 0.0998101 0.995007i \(-0.468176\pi\)
0.0998101 + 0.995007i \(0.468176\pi\)
\(158\) 0 0
\(159\) 15.4329 1.22391
\(160\) 0 0
\(161\) 1.48135 0.116746
\(162\) 0 0
\(163\) −1.69880 −0.133060 −0.0665301 0.997784i \(-0.521193\pi\)
−0.0665301 + 0.997784i \(0.521193\pi\)
\(164\) 0 0
\(165\) −12.8375 −0.999399
\(166\) 0 0
\(167\) 3.70694 0.286852 0.143426 0.989661i \(-0.454188\pi\)
0.143426 + 0.989661i \(0.454188\pi\)
\(168\) 0 0
\(169\) −8.20300 −0.631000
\(170\) 0 0
\(171\) 3.16248 0.241841
\(172\) 0 0
\(173\) −19.0688 −1.44977 −0.724887 0.688868i \(-0.758108\pi\)
−0.724887 + 0.688868i \(0.758108\pi\)
\(174\) 0 0
\(175\) −2.62174 −0.198185
\(176\) 0 0
\(177\) 6.87056 0.516423
\(178\) 0 0
\(179\) −7.66901 −0.573209 −0.286604 0.958049i \(-0.592527\pi\)
−0.286604 + 0.958049i \(0.592527\pi\)
\(180\) 0 0
\(181\) −0.381147 −0.0283304 −0.0141652 0.999900i \(-0.504509\pi\)
−0.0141652 + 0.999900i \(0.504509\pi\)
\(182\) 0 0
\(183\) 4.52142 0.334233
\(184\) 0 0
\(185\) 4.79629 0.352630
\(186\) 0 0
\(187\) 25.2756 1.84833
\(188\) 0 0
\(189\) 0.265533 0.0193147
\(190\) 0 0
\(191\) −10.4223 −0.754134 −0.377067 0.926186i \(-0.623067\pi\)
−0.377067 + 0.926186i \(0.623067\pi\)
\(192\) 0 0
\(193\) 7.46346 0.537231 0.268616 0.963247i \(-0.413434\pi\)
0.268616 + 0.963247i \(0.413434\pi\)
\(194\) 0 0
\(195\) −5.48449 −0.392752
\(196\) 0 0
\(197\) 22.3967 1.59570 0.797850 0.602856i \(-0.205971\pi\)
0.797850 + 0.602856i \(0.205971\pi\)
\(198\) 0 0
\(199\) 24.3863 1.72870 0.864348 0.502894i \(-0.167731\pi\)
0.864348 + 0.502894i \(0.167731\pi\)
\(200\) 0 0
\(201\) 19.7291 1.39159
\(202\) 0 0
\(203\) −2.15650 −0.151357
\(204\) 0 0
\(205\) −6.35232 −0.443666
\(206\) 0 0
\(207\) 7.11618 0.494609
\(208\) 0 0
\(209\) −5.12660 −0.354615
\(210\) 0 0
\(211\) 9.68729 0.666901 0.333450 0.942768i \(-0.391787\pi\)
0.333450 + 0.942768i \(0.391787\pi\)
\(212\) 0 0
\(213\) 34.0740 2.33471
\(214\) 0 0
\(215\) −7.42449 −0.506346
\(216\) 0 0
\(217\) −4.39931 −0.298645
\(218\) 0 0
\(219\) −9.00011 −0.608171
\(220\) 0 0
\(221\) 10.7983 0.726373
\(222\) 0 0
\(223\) 18.7265 1.25402 0.627009 0.779012i \(-0.284279\pi\)
0.627009 + 0.779012i \(0.284279\pi\)
\(224\) 0 0
\(225\) −12.5945 −0.839633
\(226\) 0 0
\(227\) −2.30619 −0.153067 −0.0765337 0.997067i \(-0.524385\pi\)
−0.0765337 + 0.997067i \(0.524385\pi\)
\(228\) 0 0
\(229\) 20.6903 1.36725 0.683625 0.729833i \(-0.260402\pi\)
0.683625 + 0.729833i \(0.260402\pi\)
\(230\) 0 0
\(231\) −8.37809 −0.551238
\(232\) 0 0
\(233\) −24.6222 −1.61306 −0.806528 0.591196i \(-0.798656\pi\)
−0.806528 + 0.591196i \(0.798656\pi\)
\(234\) 0 0
\(235\) −8.52991 −0.556430
\(236\) 0 0
\(237\) −2.48243 −0.161251
\(238\) 0 0
\(239\) 23.9200 1.54726 0.773629 0.633638i \(-0.218439\pi\)
0.773629 + 0.633638i \(0.218439\pi\)
\(240\) 0 0
\(241\) 8.80322 0.567065 0.283533 0.958963i \(-0.408494\pi\)
0.283533 + 0.958963i \(0.408494\pi\)
\(242\) 0 0
\(243\) −22.2764 −1.42903
\(244\) 0 0
\(245\) −6.62392 −0.423187
\(246\) 0 0
\(247\) −2.19021 −0.139359
\(248\) 0 0
\(249\) −31.7399 −2.01144
\(250\) 0 0
\(251\) 10.6885 0.674651 0.337326 0.941388i \(-0.390478\pi\)
0.337326 + 0.941388i \(0.390478\pi\)
\(252\) 0 0
\(253\) −11.5358 −0.725251
\(254\) 0 0
\(255\) −12.3459 −0.773129
\(256\) 0 0
\(257\) 14.6042 0.910983 0.455492 0.890240i \(-0.349464\pi\)
0.455492 + 0.890240i \(0.349464\pi\)
\(258\) 0 0
\(259\) 3.13018 0.194500
\(260\) 0 0
\(261\) −10.3595 −0.641239
\(262\) 0 0
\(263\) 12.2383 0.754645 0.377322 0.926082i \(-0.376845\pi\)
0.377322 + 0.926082i \(0.376845\pi\)
\(264\) 0 0
\(265\) 6.27108 0.385229
\(266\) 0 0
\(267\) 25.7539 1.57611
\(268\) 0 0
\(269\) −4.76623 −0.290602 −0.145301 0.989387i \(-0.546415\pi\)
−0.145301 + 0.989387i \(0.546415\pi\)
\(270\) 0 0
\(271\) 6.12888 0.372303 0.186151 0.982521i \(-0.440399\pi\)
0.186151 + 0.982521i \(0.440399\pi\)
\(272\) 0 0
\(273\) −3.57932 −0.216630
\(274\) 0 0
\(275\) 20.4165 1.23116
\(276\) 0 0
\(277\) −12.5312 −0.752924 −0.376462 0.926432i \(-0.622860\pi\)
−0.376462 + 0.926432i \(0.622860\pi\)
\(278\) 0 0
\(279\) −21.1337 −1.26524
\(280\) 0 0
\(281\) −13.2783 −0.792115 −0.396058 0.918226i \(-0.629622\pi\)
−0.396058 + 0.918226i \(0.629622\pi\)
\(282\) 0 0
\(283\) −28.2298 −1.67809 −0.839044 0.544064i \(-0.816885\pi\)
−0.839044 + 0.544064i \(0.816885\pi\)
\(284\) 0 0
\(285\) 2.50410 0.148330
\(286\) 0 0
\(287\) −4.14569 −0.244712
\(288\) 0 0
\(289\) 7.30761 0.429859
\(290\) 0 0
\(291\) 21.3241 1.25004
\(292\) 0 0
\(293\) −9.45824 −0.552557 −0.276278 0.961078i \(-0.589101\pi\)
−0.276278 + 0.961078i \(0.589101\pi\)
\(294\) 0 0
\(295\) 2.79182 0.162546
\(296\) 0 0
\(297\) −2.06781 −0.119987
\(298\) 0 0
\(299\) −4.92838 −0.285015
\(300\) 0 0
\(301\) −4.84541 −0.279285
\(302\) 0 0
\(303\) −21.2823 −1.22264
\(304\) 0 0
\(305\) 1.83726 0.105201
\(306\) 0 0
\(307\) 12.5716 0.717501 0.358750 0.933433i \(-0.383203\pi\)
0.358750 + 0.933433i \(0.383203\pi\)
\(308\) 0 0
\(309\) 8.53316 0.485435
\(310\) 0 0
\(311\) −5.56292 −0.315444 −0.157722 0.987484i \(-0.550415\pi\)
−0.157722 + 0.987484i \(0.550415\pi\)
\(312\) 0 0
\(313\) −7.74202 −0.437605 −0.218802 0.975769i \(-0.570215\pi\)
−0.218802 + 0.975769i \(0.570215\pi\)
\(314\) 0 0
\(315\) 2.10009 0.118327
\(316\) 0 0
\(317\) −21.6671 −1.21695 −0.608474 0.793574i \(-0.708218\pi\)
−0.608474 + 0.793574i \(0.708218\pi\)
\(318\) 0 0
\(319\) 16.7935 0.940257
\(320\) 0 0
\(321\) 16.1928 0.903794
\(322\) 0 0
\(323\) −4.93027 −0.274328
\(324\) 0 0
\(325\) 8.72243 0.483833
\(326\) 0 0
\(327\) 24.1612 1.33612
\(328\) 0 0
\(329\) −5.56684 −0.306910
\(330\) 0 0
\(331\) −19.7476 −1.08543 −0.542714 0.839918i \(-0.682603\pi\)
−0.542714 + 0.839918i \(0.682603\pi\)
\(332\) 0 0
\(333\) 15.0369 0.824020
\(334\) 0 0
\(335\) 8.01685 0.438007
\(336\) 0 0
\(337\) −2.89769 −0.157847 −0.0789237 0.996881i \(-0.525148\pi\)
−0.0789237 + 0.996881i \(0.525148\pi\)
\(338\) 0 0
\(339\) 37.4840 2.03585
\(340\) 0 0
\(341\) 34.2592 1.85524
\(342\) 0 0
\(343\) −8.93118 −0.482238
\(344\) 0 0
\(345\) 5.63469 0.303362
\(346\) 0 0
\(347\) 15.4000 0.826717 0.413358 0.910568i \(-0.364356\pi\)
0.413358 + 0.910568i \(0.364356\pi\)
\(348\) 0 0
\(349\) −8.82234 −0.472249 −0.236125 0.971723i \(-0.575877\pi\)
−0.236125 + 0.971723i \(0.575877\pi\)
\(350\) 0 0
\(351\) −0.883417 −0.0471533
\(352\) 0 0
\(353\) 18.8313 1.00229 0.501144 0.865364i \(-0.332913\pi\)
0.501144 + 0.865364i \(0.332913\pi\)
\(354\) 0 0
\(355\) 13.8458 0.734860
\(356\) 0 0
\(357\) −8.05724 −0.426434
\(358\) 0 0
\(359\) −6.38897 −0.337197 −0.168598 0.985685i \(-0.553924\pi\)
−0.168598 + 0.985685i \(0.553924\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 37.9367 1.99116
\(364\) 0 0
\(365\) −3.65716 −0.191424
\(366\) 0 0
\(367\) 5.70570 0.297835 0.148918 0.988850i \(-0.452421\pi\)
0.148918 + 0.988850i \(0.452421\pi\)
\(368\) 0 0
\(369\) −19.9153 −1.03675
\(370\) 0 0
\(371\) 4.09267 0.212481
\(372\) 0 0
\(373\) 17.1999 0.890579 0.445290 0.895387i \(-0.353101\pi\)
0.445290 + 0.895387i \(0.353101\pi\)
\(374\) 0 0
\(375\) −22.4930 −1.16153
\(376\) 0 0
\(377\) 7.17459 0.369510
\(378\) 0 0
\(379\) 17.6285 0.905517 0.452758 0.891633i \(-0.350440\pi\)
0.452758 + 0.891633i \(0.350440\pi\)
\(380\) 0 0
\(381\) −31.0285 −1.58964
\(382\) 0 0
\(383\) −30.5078 −1.55888 −0.779438 0.626480i \(-0.784495\pi\)
−0.779438 + 0.626480i \(0.784495\pi\)
\(384\) 0 0
\(385\) −3.40440 −0.173504
\(386\) 0 0
\(387\) −23.2767 −1.18322
\(388\) 0 0
\(389\) −22.4593 −1.13873 −0.569366 0.822084i \(-0.692811\pi\)
−0.569366 + 0.822084i \(0.692811\pi\)
\(390\) 0 0
\(391\) −11.0941 −0.561050
\(392\) 0 0
\(393\) −17.8877 −0.902317
\(394\) 0 0
\(395\) −1.00873 −0.0507545
\(396\) 0 0
\(397\) −5.91050 −0.296640 −0.148320 0.988939i \(-0.547386\pi\)
−0.148320 + 0.988939i \(0.547386\pi\)
\(398\) 0 0
\(399\) 1.63424 0.0818142
\(400\) 0 0
\(401\) −9.45266 −0.472043 −0.236022 0.971748i \(-0.575844\pi\)
−0.236022 + 0.971748i \(0.575844\pi\)
\(402\) 0 0
\(403\) 14.6363 0.729088
\(404\) 0 0
\(405\) −8.56021 −0.425360
\(406\) 0 0
\(407\) −24.3759 −1.20827
\(408\) 0 0
\(409\) 4.79901 0.237296 0.118648 0.992936i \(-0.462144\pi\)
0.118648 + 0.992936i \(0.462144\pi\)
\(410\) 0 0
\(411\) −19.8852 −0.980867
\(412\) 0 0
\(413\) 1.82201 0.0896555
\(414\) 0 0
\(415\) −12.8974 −0.633107
\(416\) 0 0
\(417\) −11.5112 −0.563706
\(418\) 0 0
\(419\) −13.2479 −0.647202 −0.323601 0.946194i \(-0.604894\pi\)
−0.323601 + 0.946194i \(0.604894\pi\)
\(420\) 0 0
\(421\) 29.4889 1.43720 0.718601 0.695422i \(-0.244783\pi\)
0.718601 + 0.695422i \(0.244783\pi\)
\(422\) 0 0
\(423\) −26.7423 −1.30026
\(424\) 0 0
\(425\) 19.6347 0.952422
\(426\) 0 0
\(427\) 1.19904 0.0580257
\(428\) 0 0
\(429\) 27.8736 1.34575
\(430\) 0 0
\(431\) −30.9365 −1.49016 −0.745079 0.666977i \(-0.767588\pi\)
−0.745079 + 0.666977i \(0.767588\pi\)
\(432\) 0 0
\(433\) 21.2939 1.02332 0.511659 0.859188i \(-0.329031\pi\)
0.511659 + 0.859188i \(0.329031\pi\)
\(434\) 0 0
\(435\) −8.20283 −0.393295
\(436\) 0 0
\(437\) 2.25019 0.107641
\(438\) 0 0
\(439\) −19.7974 −0.944881 −0.472440 0.881363i \(-0.656627\pi\)
−0.472440 + 0.881363i \(0.656627\pi\)
\(440\) 0 0
\(441\) −20.7668 −0.988895
\(442\) 0 0
\(443\) −24.0702 −1.14361 −0.571806 0.820389i \(-0.693757\pi\)
−0.571806 + 0.820389i \(0.693757\pi\)
\(444\) 0 0
\(445\) 10.4650 0.496087
\(446\) 0 0
\(447\) −39.0754 −1.84820
\(448\) 0 0
\(449\) 2.00537 0.0946390 0.0473195 0.998880i \(-0.484932\pi\)
0.0473195 + 0.998880i \(0.484932\pi\)
\(450\) 0 0
\(451\) 32.2841 1.52020
\(452\) 0 0
\(453\) 5.08345 0.238841
\(454\) 0 0
\(455\) −1.45444 −0.0681852
\(456\) 0 0
\(457\) −10.8639 −0.508193 −0.254096 0.967179i \(-0.581778\pi\)
−0.254096 + 0.967179i \(0.581778\pi\)
\(458\) 0 0
\(459\) −1.98862 −0.0928209
\(460\) 0 0
\(461\) 15.4497 0.719564 0.359782 0.933036i \(-0.382851\pi\)
0.359782 + 0.933036i \(0.382851\pi\)
\(462\) 0 0
\(463\) −18.7008 −0.869100 −0.434550 0.900648i \(-0.643092\pi\)
−0.434550 + 0.900648i \(0.643092\pi\)
\(464\) 0 0
\(465\) −16.7340 −0.776019
\(466\) 0 0
\(467\) 22.0548 1.02057 0.510287 0.860004i \(-0.329539\pi\)
0.510287 + 0.860004i \(0.329539\pi\)
\(468\) 0 0
\(469\) 5.23200 0.241591
\(470\) 0 0
\(471\) 6.20915 0.286103
\(472\) 0 0
\(473\) 37.7332 1.73497
\(474\) 0 0
\(475\) −3.98247 −0.182728
\(476\) 0 0
\(477\) 19.6606 0.900197
\(478\) 0 0
\(479\) −12.6854 −0.579611 −0.289806 0.957085i \(-0.593591\pi\)
−0.289806 + 0.957085i \(0.593591\pi\)
\(480\) 0 0
\(481\) −10.4140 −0.474837
\(482\) 0 0
\(483\) 3.67734 0.167325
\(484\) 0 0
\(485\) 8.66494 0.393455
\(486\) 0 0
\(487\) −25.4984 −1.15544 −0.577722 0.816234i \(-0.696058\pi\)
−0.577722 + 0.816234i \(0.696058\pi\)
\(488\) 0 0
\(489\) −4.21715 −0.190706
\(490\) 0 0
\(491\) 24.9883 1.12771 0.563853 0.825875i \(-0.309318\pi\)
0.563853 + 0.825875i \(0.309318\pi\)
\(492\) 0 0
\(493\) 16.1504 0.727378
\(494\) 0 0
\(495\) −16.3543 −0.735069
\(496\) 0 0
\(497\) 9.03613 0.405326
\(498\) 0 0
\(499\) −23.3219 −1.04403 −0.522016 0.852935i \(-0.674820\pi\)
−0.522016 + 0.852935i \(0.674820\pi\)
\(500\) 0 0
\(501\) 9.20223 0.411126
\(502\) 0 0
\(503\) −11.6957 −0.521487 −0.260744 0.965408i \(-0.583968\pi\)
−0.260744 + 0.965408i \(0.583968\pi\)
\(504\) 0 0
\(505\) −8.64799 −0.384830
\(506\) 0 0
\(507\) −20.3634 −0.904371
\(508\) 0 0
\(509\) −14.9289 −0.661710 −0.330855 0.943682i \(-0.607337\pi\)
−0.330855 + 0.943682i \(0.607337\pi\)
\(510\) 0 0
\(511\) −2.38675 −0.105584
\(512\) 0 0
\(513\) 0.403349 0.0178083
\(514\) 0 0
\(515\) 3.46741 0.152792
\(516\) 0 0
\(517\) 43.3512 1.90658
\(518\) 0 0
\(519\) −47.3370 −2.07786
\(520\) 0 0
\(521\) 28.4538 1.24658 0.623291 0.781990i \(-0.285795\pi\)
0.623291 + 0.781990i \(0.285795\pi\)
\(522\) 0 0
\(523\) 6.27044 0.274187 0.137094 0.990558i \(-0.456224\pi\)
0.137094 + 0.990558i \(0.456224\pi\)
\(524\) 0 0
\(525\) −6.50830 −0.284046
\(526\) 0 0
\(527\) 32.9472 1.43520
\(528\) 0 0
\(529\) −17.9366 −0.779854
\(530\) 0 0
\(531\) 8.75271 0.379835
\(532\) 0 0
\(533\) 13.7925 0.597421
\(534\) 0 0
\(535\) 6.57987 0.284473
\(536\) 0 0
\(537\) −19.0378 −0.821542
\(538\) 0 0
\(539\) 33.6644 1.45003
\(540\) 0 0
\(541\) −4.76648 −0.204927 −0.102464 0.994737i \(-0.532672\pi\)
−0.102464 + 0.994737i \(0.532672\pi\)
\(542\) 0 0
\(543\) −0.946173 −0.0406042
\(544\) 0 0
\(545\) 9.81780 0.420548
\(546\) 0 0
\(547\) −3.37305 −0.144221 −0.0721106 0.997397i \(-0.522973\pi\)
−0.0721106 + 0.997397i \(0.522973\pi\)
\(548\) 0 0
\(549\) 5.76003 0.245832
\(550\) 0 0
\(551\) −3.27576 −0.139552
\(552\) 0 0
\(553\) −0.658321 −0.0279946
\(554\) 0 0
\(555\) 11.9065 0.505401
\(556\) 0 0
\(557\) −45.3138 −1.92001 −0.960003 0.279990i \(-0.909669\pi\)
−0.960003 + 0.279990i \(0.909669\pi\)
\(558\) 0 0
\(559\) 16.1205 0.681824
\(560\) 0 0
\(561\) 62.7449 2.64909
\(562\) 0 0
\(563\) −5.07491 −0.213882 −0.106941 0.994265i \(-0.534106\pi\)
−0.106941 + 0.994265i \(0.534106\pi\)
\(564\) 0 0
\(565\) 15.2314 0.640791
\(566\) 0 0
\(567\) −5.58661 −0.234616
\(568\) 0 0
\(569\) −21.8671 −0.916718 −0.458359 0.888767i \(-0.651563\pi\)
−0.458359 + 0.888767i \(0.651563\pi\)
\(570\) 0 0
\(571\) 22.5429 0.943389 0.471695 0.881762i \(-0.343642\pi\)
0.471695 + 0.881762i \(0.343642\pi\)
\(572\) 0 0
\(573\) −25.8728 −1.08085
\(574\) 0 0
\(575\) −8.96131 −0.373713
\(576\) 0 0
\(577\) −39.0368 −1.62512 −0.812562 0.582874i \(-0.801928\pi\)
−0.812562 + 0.582874i \(0.801928\pi\)
\(578\) 0 0
\(579\) 18.5275 0.769978
\(580\) 0 0
\(581\) −8.41716 −0.349203
\(582\) 0 0
\(583\) −31.8712 −1.31997
\(584\) 0 0
\(585\) −6.98693 −0.288874
\(586\) 0 0
\(587\) −12.5986 −0.520002 −0.260001 0.965608i \(-0.583723\pi\)
−0.260001 + 0.965608i \(0.583723\pi\)
\(588\) 0 0
\(589\) −6.68263 −0.275353
\(590\) 0 0
\(591\) 55.5984 2.28701
\(592\) 0 0
\(593\) 27.3483 1.12306 0.561530 0.827457i \(-0.310213\pi\)
0.561530 + 0.827457i \(0.310213\pi\)
\(594\) 0 0
\(595\) −3.27402 −0.134222
\(596\) 0 0
\(597\) 60.5373 2.47763
\(598\) 0 0
\(599\) −17.0298 −0.695818 −0.347909 0.937528i \(-0.613108\pi\)
−0.347909 + 0.937528i \(0.613108\pi\)
\(600\) 0 0
\(601\) 8.57587 0.349817 0.174909 0.984585i \(-0.444037\pi\)
0.174909 + 0.984585i \(0.444037\pi\)
\(602\) 0 0
\(603\) 25.1338 1.02353
\(604\) 0 0
\(605\) 15.4154 0.626726
\(606\) 0 0
\(607\) 41.0258 1.66519 0.832594 0.553884i \(-0.186855\pi\)
0.832594 + 0.553884i \(0.186855\pi\)
\(608\) 0 0
\(609\) −5.35337 −0.216930
\(610\) 0 0
\(611\) 18.5206 0.749265
\(612\) 0 0
\(613\) −33.2855 −1.34439 −0.672193 0.740376i \(-0.734648\pi\)
−0.672193 + 0.740376i \(0.734648\pi\)
\(614\) 0 0
\(615\) −15.7692 −0.635877
\(616\) 0 0
\(617\) 37.8994 1.52577 0.762887 0.646532i \(-0.223781\pi\)
0.762887 + 0.646532i \(0.223781\pi\)
\(618\) 0 0
\(619\) −1.58989 −0.0639029 −0.0319515 0.999489i \(-0.510172\pi\)
−0.0319515 + 0.999489i \(0.510172\pi\)
\(620\) 0 0
\(621\) 0.907612 0.0364212
\(622\) 0 0
\(623\) 6.82971 0.273627
\(624\) 0 0
\(625\) 10.7724 0.430897
\(626\) 0 0
\(627\) −12.7265 −0.508246
\(628\) 0 0
\(629\) −23.4424 −0.934711
\(630\) 0 0
\(631\) −21.3500 −0.849929 −0.424965 0.905210i \(-0.639713\pi\)
−0.424965 + 0.905210i \(0.639713\pi\)
\(632\) 0 0
\(633\) 24.0481 0.955825
\(634\) 0 0
\(635\) −12.6083 −0.500345
\(636\) 0 0
\(637\) 14.3822 0.569845
\(638\) 0 0
\(639\) 43.4083 1.71721
\(640\) 0 0
\(641\) −9.25486 −0.365545 −0.182773 0.983155i \(-0.558507\pi\)
−0.182773 + 0.983155i \(0.558507\pi\)
\(642\) 0 0
\(643\) 36.9308 1.45641 0.728204 0.685360i \(-0.240355\pi\)
0.728204 + 0.685360i \(0.240355\pi\)
\(644\) 0 0
\(645\) −18.4308 −0.725713
\(646\) 0 0
\(647\) 4.43717 0.174443 0.0872215 0.996189i \(-0.472201\pi\)
0.0872215 + 0.996189i \(0.472201\pi\)
\(648\) 0 0
\(649\) −14.1887 −0.556957
\(650\) 0 0
\(651\) −10.9210 −0.428028
\(652\) 0 0
\(653\) −31.7716 −1.24332 −0.621660 0.783287i \(-0.713541\pi\)
−0.621660 + 0.783287i \(0.713541\pi\)
\(654\) 0 0
\(655\) −7.26860 −0.284008
\(656\) 0 0
\(657\) −11.4656 −0.447317
\(658\) 0 0
\(659\) −18.8368 −0.733778 −0.366889 0.930265i \(-0.619577\pi\)
−0.366889 + 0.930265i \(0.619577\pi\)
\(660\) 0 0
\(661\) 2.00428 0.0779576 0.0389788 0.999240i \(-0.487590\pi\)
0.0389788 + 0.999240i \(0.487590\pi\)
\(662\) 0 0
\(663\) 26.8061 1.04106
\(664\) 0 0
\(665\) 0.664065 0.0257513
\(666\) 0 0
\(667\) −7.37108 −0.285410
\(668\) 0 0
\(669\) 46.4873 1.79730
\(670\) 0 0
\(671\) −9.33741 −0.360467
\(672\) 0 0
\(673\) 17.5254 0.675555 0.337778 0.941226i \(-0.390325\pi\)
0.337778 + 0.941226i \(0.390325\pi\)
\(674\) 0 0
\(675\) −1.60633 −0.0618275
\(676\) 0 0
\(677\) −10.0753 −0.387227 −0.193614 0.981078i \(-0.562021\pi\)
−0.193614 + 0.981078i \(0.562021\pi\)
\(678\) 0 0
\(679\) 5.65496 0.217017
\(680\) 0 0
\(681\) −5.72497 −0.219382
\(682\) 0 0
\(683\) −6.96926 −0.266671 −0.133336 0.991071i \(-0.542569\pi\)
−0.133336 + 0.991071i \(0.542569\pi\)
\(684\) 0 0
\(685\) −8.08028 −0.308732
\(686\) 0 0
\(687\) 51.3622 1.95959
\(688\) 0 0
\(689\) −13.6161 −0.518733
\(690\) 0 0
\(691\) −36.3762 −1.38382 −0.691908 0.721985i \(-0.743230\pi\)
−0.691908 + 0.721985i \(0.743230\pi\)
\(692\) 0 0
\(693\) −10.6732 −0.405442
\(694\) 0 0
\(695\) −4.67753 −0.177429
\(696\) 0 0
\(697\) 31.0478 1.17602
\(698\) 0 0
\(699\) −61.1230 −2.31189
\(700\) 0 0
\(701\) 20.7487 0.783668 0.391834 0.920036i \(-0.371841\pi\)
0.391834 + 0.920036i \(0.371841\pi\)
\(702\) 0 0
\(703\) 4.75479 0.179330
\(704\) 0 0
\(705\) −21.1749 −0.797495
\(706\) 0 0
\(707\) −5.64390 −0.212261
\(708\) 0 0
\(709\) 16.7842 0.630345 0.315172 0.949034i \(-0.397938\pi\)
0.315172 + 0.949034i \(0.397938\pi\)
\(710\) 0 0
\(711\) −3.16248 −0.118602
\(712\) 0 0
\(713\) −15.0372 −0.563147
\(714\) 0 0
\(715\) 11.3263 0.423579
\(716\) 0 0
\(717\) 59.3799 2.21758
\(718\) 0 0
\(719\) −12.4046 −0.462615 −0.231307 0.972881i \(-0.574300\pi\)
−0.231307 + 0.972881i \(0.574300\pi\)
\(720\) 0 0
\(721\) 2.26292 0.0842756
\(722\) 0 0
\(723\) 21.8534 0.812738
\(724\) 0 0
\(725\) 13.0456 0.484502
\(726\) 0 0
\(727\) −44.4741 −1.64945 −0.824727 0.565530i \(-0.808671\pi\)
−0.824727 + 0.565530i \(0.808671\pi\)
\(728\) 0 0
\(729\) −29.8412 −1.10523
\(730\) 0 0
\(731\) 36.2881 1.34217
\(732\) 0 0
\(733\) −20.2150 −0.746656 −0.373328 0.927699i \(-0.621783\pi\)
−0.373328 + 0.927699i \(0.621783\pi\)
\(734\) 0 0
\(735\) −16.4434 −0.606525
\(736\) 0 0
\(737\) −40.7437 −1.50081
\(738\) 0 0
\(739\) 40.0180 1.47209 0.736043 0.676935i \(-0.236692\pi\)
0.736043 + 0.676935i \(0.236692\pi\)
\(740\) 0 0
\(741\) −5.43704 −0.199735
\(742\) 0 0
\(743\) 13.4838 0.494673 0.247337 0.968930i \(-0.420445\pi\)
0.247337 + 0.968930i \(0.420445\pi\)
\(744\) 0 0
\(745\) −15.8781 −0.581729
\(746\) 0 0
\(747\) −40.4349 −1.47943
\(748\) 0 0
\(749\) 4.29419 0.156906
\(750\) 0 0
\(751\) −25.4034 −0.926984 −0.463492 0.886101i \(-0.653404\pi\)
−0.463492 + 0.886101i \(0.653404\pi\)
\(752\) 0 0
\(753\) 26.5335 0.966933
\(754\) 0 0
\(755\) 2.06564 0.0751762
\(756\) 0 0
\(757\) −28.1858 −1.02443 −0.512215 0.858857i \(-0.671175\pi\)
−0.512215 + 0.858857i \(0.671175\pi\)
\(758\) 0 0
\(759\) −28.6369 −1.03945
\(760\) 0 0
\(761\) −28.9203 −1.04836 −0.524179 0.851608i \(-0.675628\pi\)
−0.524179 + 0.851608i \(0.675628\pi\)
\(762\) 0 0
\(763\) 6.40734 0.231961
\(764\) 0 0
\(765\) −15.7280 −0.568646
\(766\) 0 0
\(767\) −6.06177 −0.218878
\(768\) 0 0
\(769\) −24.2439 −0.874256 −0.437128 0.899399i \(-0.644004\pi\)
−0.437128 + 0.899399i \(0.644004\pi\)
\(770\) 0 0
\(771\) 36.2539 1.30565
\(772\) 0 0
\(773\) 13.2842 0.477801 0.238901 0.971044i \(-0.423213\pi\)
0.238901 + 0.971044i \(0.423213\pi\)
\(774\) 0 0
\(775\) 26.6134 0.955981
\(776\) 0 0
\(777\) 7.77046 0.278764
\(778\) 0 0
\(779\) −6.29737 −0.225627
\(780\) 0 0
\(781\) −70.3679 −2.51796
\(782\) 0 0
\(783\) −1.32128 −0.0472185
\(784\) 0 0
\(785\) 2.52306 0.0900519
\(786\) 0 0
\(787\) 51.9098 1.85038 0.925192 0.379498i \(-0.123903\pi\)
0.925192 + 0.379498i \(0.123903\pi\)
\(788\) 0 0
\(789\) 30.3807 1.08158
\(790\) 0 0
\(791\) 9.94042 0.353441
\(792\) 0 0
\(793\) −3.98916 −0.141659
\(794\) 0 0
\(795\) 15.5675 0.552124
\(796\) 0 0
\(797\) −19.9085 −0.705197 −0.352598 0.935775i \(-0.614702\pi\)
−0.352598 + 0.935775i \(0.614702\pi\)
\(798\) 0 0
\(799\) 41.6910 1.47492
\(800\) 0 0
\(801\) 32.8090 1.15925
\(802\) 0 0
\(803\) 18.5866 0.655906
\(804\) 0 0
\(805\) 1.49427 0.0526662
\(806\) 0 0
\(807\) −11.8319 −0.416501
\(808\) 0 0
\(809\) 7.23883 0.254504 0.127252 0.991870i \(-0.459384\pi\)
0.127252 + 0.991870i \(0.459384\pi\)
\(810\) 0 0
\(811\) 9.70986 0.340959 0.170480 0.985361i \(-0.445468\pi\)
0.170480 + 0.985361i \(0.445468\pi\)
\(812\) 0 0
\(813\) 15.2145 0.533597
\(814\) 0 0
\(815\) −1.71362 −0.0600256
\(816\) 0 0
\(817\) −7.36027 −0.257503
\(818\) 0 0
\(819\) −4.55985 −0.159334
\(820\) 0 0
\(821\) −30.3133 −1.05794 −0.528970 0.848640i \(-0.677422\pi\)
−0.528970 + 0.848640i \(0.677422\pi\)
\(822\) 0 0
\(823\) 22.4937 0.784083 0.392041 0.919948i \(-0.371769\pi\)
0.392041 + 0.919948i \(0.371769\pi\)
\(824\) 0 0
\(825\) 50.6827 1.76455
\(826\) 0 0
\(827\) −31.3105 −1.08877 −0.544386 0.838835i \(-0.683237\pi\)
−0.544386 + 0.838835i \(0.683237\pi\)
\(828\) 0 0
\(829\) −0.349214 −0.0121287 −0.00606435 0.999982i \(-0.501930\pi\)
−0.00606435 + 0.999982i \(0.501930\pi\)
\(830\) 0 0
\(831\) −31.1078 −1.07912
\(832\) 0 0
\(833\) 32.3752 1.12173
\(834\) 0 0
\(835\) 3.73929 0.129403
\(836\) 0 0
\(837\) −2.69543 −0.0931678
\(838\) 0 0
\(839\) 27.1615 0.937720 0.468860 0.883273i \(-0.344665\pi\)
0.468860 + 0.883273i \(0.344665\pi\)
\(840\) 0 0
\(841\) −18.2694 −0.629979
\(842\) 0 0
\(843\) −32.9624 −1.13529
\(844\) 0 0
\(845\) −8.27458 −0.284654
\(846\) 0 0
\(847\) 10.0605 0.345683
\(848\) 0 0
\(849\) −70.0786 −2.40509
\(850\) 0 0
\(851\) 10.6992 0.366763
\(852\) 0 0
\(853\) −7.70825 −0.263926 −0.131963 0.991255i \(-0.542128\pi\)
−0.131963 + 0.991255i \(0.542128\pi\)
\(854\) 0 0
\(855\) 3.19008 0.109098
\(856\) 0 0
\(857\) 44.6750 1.52607 0.763034 0.646358i \(-0.223709\pi\)
0.763034 + 0.646358i \(0.223709\pi\)
\(858\) 0 0
\(859\) 29.2965 0.999583 0.499791 0.866146i \(-0.333410\pi\)
0.499791 + 0.866146i \(0.333410\pi\)
\(860\) 0 0
\(861\) −10.2914 −0.350730
\(862\) 0 0
\(863\) −32.3740 −1.10202 −0.551011 0.834498i \(-0.685758\pi\)
−0.551011 + 0.834498i \(0.685758\pi\)
\(864\) 0 0
\(865\) −19.2352 −0.654016
\(866\) 0 0
\(867\) 18.1407 0.616089
\(868\) 0 0
\(869\) 5.12660 0.173908
\(870\) 0 0
\(871\) −17.4067 −0.589802
\(872\) 0 0
\(873\) 27.1656 0.919418
\(874\) 0 0
\(875\) −5.96495 −0.201652
\(876\) 0 0
\(877\) 2.26761 0.0765717 0.0382859 0.999267i \(-0.487810\pi\)
0.0382859 + 0.999267i \(0.487810\pi\)
\(878\) 0 0
\(879\) −23.4795 −0.791943
\(880\) 0 0
\(881\) 3.18348 0.107254 0.0536271 0.998561i \(-0.482922\pi\)
0.0536271 + 0.998561i \(0.482922\pi\)
\(882\) 0 0
\(883\) −16.1955 −0.545021 −0.272510 0.962153i \(-0.587854\pi\)
−0.272510 + 0.962153i \(0.587854\pi\)
\(884\) 0 0
\(885\) 6.93052 0.232967
\(886\) 0 0
\(887\) −12.2848 −0.412483 −0.206241 0.978501i \(-0.566123\pi\)
−0.206241 + 0.978501i \(0.566123\pi\)
\(888\) 0 0
\(889\) −8.22850 −0.275975
\(890\) 0 0
\(891\) 43.5051 1.45748
\(892\) 0 0
\(893\) −8.45612 −0.282973
\(894\) 0 0
\(895\) −7.73593 −0.258584
\(896\) 0 0
\(897\) −12.2344 −0.408494
\(898\) 0 0
\(899\) 21.8907 0.730096
\(900\) 0 0
\(901\) −30.6507 −1.02112
\(902\) 0 0
\(903\) −12.0284 −0.400281
\(904\) 0 0
\(905\) −0.384473 −0.0127803
\(906\) 0 0
\(907\) 38.1373 1.26633 0.633164 0.774018i \(-0.281756\pi\)
0.633164 + 0.774018i \(0.281756\pi\)
\(908\) 0 0
\(909\) −27.1125 −0.899265
\(910\) 0 0
\(911\) 59.0466 1.95630 0.978150 0.207899i \(-0.0666624\pi\)
0.978150 + 0.207899i \(0.0666624\pi\)
\(912\) 0 0
\(913\) 65.5477 2.16931
\(914\) 0 0
\(915\) 4.56087 0.150778
\(916\) 0 0
\(917\) −4.74368 −0.156650
\(918\) 0 0
\(919\) 48.6032 1.60327 0.801635 0.597814i \(-0.203964\pi\)
0.801635 + 0.597814i \(0.203964\pi\)
\(920\) 0 0
\(921\) 31.2083 1.02835
\(922\) 0 0
\(923\) −30.0628 −0.989530
\(924\) 0 0
\(925\) −18.9358 −0.622606
\(926\) 0 0
\(927\) 10.8708 0.357043
\(928\) 0 0
\(929\) −36.1498 −1.18604 −0.593018 0.805189i \(-0.702064\pi\)
−0.593018 + 0.805189i \(0.702064\pi\)
\(930\) 0 0
\(931\) −6.56661 −0.215212
\(932\) 0 0
\(933\) −13.8096 −0.452105
\(934\) 0 0
\(935\) 25.4961 0.833812
\(936\) 0 0
\(937\) 1.54777 0.0505633 0.0252817 0.999680i \(-0.491952\pi\)
0.0252817 + 0.999680i \(0.491952\pi\)
\(938\) 0 0
\(939\) −19.2191 −0.627190
\(940\) 0 0
\(941\) −46.3173 −1.50990 −0.754950 0.655782i \(-0.772339\pi\)
−0.754950 + 0.655782i \(0.772339\pi\)
\(942\) 0 0
\(943\) −14.1703 −0.461448
\(944\) 0 0
\(945\) 0.267850 0.00871316
\(946\) 0 0
\(947\) −47.0761 −1.52977 −0.764884 0.644169i \(-0.777204\pi\)
−0.764884 + 0.644169i \(0.777204\pi\)
\(948\) 0 0
\(949\) 7.94063 0.257764
\(950\) 0 0
\(951\) −53.7872 −1.74417
\(952\) 0 0
\(953\) 12.7537 0.413134 0.206567 0.978432i \(-0.433771\pi\)
0.206567 + 0.978432i \(0.433771\pi\)
\(954\) 0 0
\(955\) −10.5133 −0.340202
\(956\) 0 0
\(957\) 41.6888 1.34761
\(958\) 0 0
\(959\) −5.27340 −0.170287
\(960\) 0 0
\(961\) 13.6576 0.440567
\(962\) 0 0
\(963\) 20.6287 0.664751
\(964\) 0 0
\(965\) 7.52859 0.242354
\(966\) 0 0
\(967\) −9.92906 −0.319297 −0.159649 0.987174i \(-0.551036\pi\)
−0.159649 + 0.987174i \(0.551036\pi\)
\(968\) 0 0
\(969\) −12.2391 −0.393176
\(970\) 0 0
\(971\) 36.8091 1.18126 0.590630 0.806943i \(-0.298879\pi\)
0.590630 + 0.806943i \(0.298879\pi\)
\(972\) 0 0
\(973\) −3.05267 −0.0978642
\(974\) 0 0
\(975\) 21.6529 0.693447
\(976\) 0 0
\(977\) −31.2825 −1.00082 −0.500408 0.865790i \(-0.666817\pi\)
−0.500408 + 0.865790i \(0.666817\pi\)
\(978\) 0 0
\(979\) −53.1856 −1.69982
\(980\) 0 0
\(981\) 30.7800 0.982730
\(982\) 0 0
\(983\) 28.0864 0.895816 0.447908 0.894080i \(-0.352169\pi\)
0.447908 + 0.894080i \(0.352169\pi\)
\(984\) 0 0
\(985\) 22.5922 0.719846
\(986\) 0 0
\(987\) −13.8193 −0.439873
\(988\) 0 0
\(989\) −16.5620 −0.526641
\(990\) 0 0
\(991\) −13.2215 −0.419995 −0.209997 0.977702i \(-0.567346\pi\)
−0.209997 + 0.977702i \(0.567346\pi\)
\(992\) 0 0
\(993\) −49.0222 −1.55567
\(994\) 0 0
\(995\) 24.5991 0.779843
\(996\) 0 0
\(997\) 40.5073 1.28288 0.641440 0.767173i \(-0.278337\pi\)
0.641440 + 0.767173i \(0.278337\pi\)
\(998\) 0 0
\(999\) 1.91784 0.0606778
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 \(a_p\))