Properties

Label 6004.2.a.d.1.6
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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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: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.45095\)
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.45095 q^{5} -5.04197 q^{7} -3.00000 q^{9} +O(q^{10})\) \(q+2.45095 q^{5} -5.04197 q^{7} -3.00000 q^{9} -2.96930 q^{11} -6.51670 q^{13} -6.41529 q^{17} +1.00000 q^{19} +7.57983 q^{23} +1.00717 q^{25} +9.36317 q^{29} -6.09817 q^{31} -12.3576 q^{35} -0.659888 q^{37} +4.13116 q^{41} -1.33134 q^{43} -7.35286 q^{45} -11.5102 q^{47} +18.4214 q^{49} -1.34385 q^{53} -7.27762 q^{55} +5.20851 q^{59} +8.44931 q^{61} +15.1259 q^{63} -15.9721 q^{65} -4.86624 q^{67} +2.09656 q^{71} +5.55239 q^{73} +14.9711 q^{77} +1.00000 q^{79} +9.00000 q^{81} -1.15910 q^{83} -15.7236 q^{85} +7.00114 q^{89} +32.8570 q^{91} +2.45095 q^{95} -8.42073 q^{97} +8.90790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{5} + q^{7} - 24q^{9} + O(q^{10}) \) \( 8q + 4q^{5} + q^{7} - 24q^{9} - 7q^{11} - 12q^{13} - 7q^{17} + 8q^{19} + 10q^{23} + 6q^{25} + 5q^{29} + 3q^{31} - 11q^{35} - 15q^{37} - 5q^{41} + 10q^{43} - 12q^{45} + 18q^{47} + 31q^{49} + 9q^{53} - 17q^{55} + 8q^{59} + 13q^{61} - 3q^{63} + 4q^{65} + 21q^{67} + 44q^{71} - 20q^{73} + 15q^{77} + 8q^{79} + 72q^{81} - 4q^{83} - 9q^{85} - 10q^{89} + 48q^{91} + 4q^{95} - 22q^{97} + 21q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 2.45095 1.09610 0.548050 0.836446i \(-0.315370\pi\)
0.548050 + 0.836446i \(0.315370\pi\)
\(6\) 0 0
\(7\) −5.04197 −1.90568 −0.952842 0.303466i \(-0.901856\pi\)
−0.952842 + 0.303466i \(0.901856\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −2.96930 −0.895278 −0.447639 0.894214i \(-0.647735\pi\)
−0.447639 + 0.894214i \(0.647735\pi\)
\(12\) 0 0
\(13\) −6.51670 −1.80741 −0.903703 0.428159i \(-0.859162\pi\)
−0.903703 + 0.428159i \(0.859162\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.41529 −1.55594 −0.777968 0.628304i \(-0.783750\pi\)
−0.777968 + 0.628304i \(0.783750\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.57983 1.58050 0.790252 0.612782i \(-0.209950\pi\)
0.790252 + 0.612782i \(0.209950\pi\)
\(24\) 0 0
\(25\) 1.00717 0.201435
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.36317 1.73870 0.869349 0.494199i \(-0.164539\pi\)
0.869349 + 0.494199i \(0.164539\pi\)
\(30\) 0 0
\(31\) −6.09817 −1.09526 −0.547632 0.836719i \(-0.684471\pi\)
−0.547632 + 0.836719i \(0.684471\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −12.3576 −2.08882
\(36\) 0 0
\(37\) −0.659888 −0.108485 −0.0542424 0.998528i \(-0.517274\pi\)
−0.0542424 + 0.998528i \(0.517274\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.13116 0.645178 0.322589 0.946539i \(-0.395447\pi\)
0.322589 + 0.946539i \(0.395447\pi\)
\(42\) 0 0
\(43\) −1.33134 −0.203027 −0.101513 0.994834i \(-0.532368\pi\)
−0.101513 + 0.994834i \(0.532368\pi\)
\(44\) 0 0
\(45\) −7.35286 −1.09610
\(46\) 0 0
\(47\) −11.5102 −1.67894 −0.839468 0.543409i \(-0.817133\pi\)
−0.839468 + 0.543409i \(0.817133\pi\)
\(48\) 0 0
\(49\) 18.4214 2.63163
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.34385 −0.184592 −0.0922962 0.995732i \(-0.529421\pi\)
−0.0922962 + 0.995732i \(0.529421\pi\)
\(54\) 0 0
\(55\) −7.27762 −0.981313
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.20851 0.678090 0.339045 0.940770i \(-0.389896\pi\)
0.339045 + 0.940770i \(0.389896\pi\)
\(60\) 0 0
\(61\) 8.44931 1.08182 0.540911 0.841080i \(-0.318079\pi\)
0.540911 + 0.841080i \(0.318079\pi\)
\(62\) 0 0
\(63\) 15.1259 1.90568
\(64\) 0 0
\(65\) −15.9721 −1.98110
\(66\) 0 0
\(67\) −4.86624 −0.594506 −0.297253 0.954799i \(-0.596071\pi\)
−0.297253 + 0.954799i \(0.596071\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.09656 0.248816 0.124408 0.992231i \(-0.460297\pi\)
0.124408 + 0.992231i \(0.460297\pi\)
\(72\) 0 0
\(73\) 5.55239 0.649858 0.324929 0.945738i \(-0.394660\pi\)
0.324929 + 0.945738i \(0.394660\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 14.9711 1.70612
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −1.15910 −0.127228 −0.0636139 0.997975i \(-0.520263\pi\)
−0.0636139 + 0.997975i \(0.520263\pi\)
\(84\) 0 0
\(85\) −15.7236 −1.70546
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.00114 0.742119 0.371060 0.928609i \(-0.378995\pi\)
0.371060 + 0.928609i \(0.378995\pi\)
\(90\) 0 0
\(91\) 32.8570 3.44435
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.45095 0.251463
\(96\) 0 0
\(97\) −8.42073 −0.854995 −0.427498 0.904016i \(-0.640605\pi\)
−0.427498 + 0.904016i \(0.640605\pi\)
\(98\) 0 0
\(99\) 8.90790 0.895278
\(100\) 0 0
\(101\) −8.23747 −0.819658 −0.409829 0.912162i \(-0.634412\pi\)
−0.409829 + 0.912162i \(0.634412\pi\)
\(102\) 0 0
\(103\) −2.43187 −0.239619 −0.119810 0.992797i \(-0.538228\pi\)
−0.119810 + 0.992797i \(0.538228\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.8541 −1.33933 −0.669665 0.742663i \(-0.733562\pi\)
−0.669665 + 0.742663i \(0.733562\pi\)
\(108\) 0 0
\(109\) 17.2341 1.65073 0.825363 0.564603i \(-0.190971\pi\)
0.825363 + 0.564603i \(0.190971\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.90482 −0.743623 −0.371812 0.928308i \(-0.621263\pi\)
−0.371812 + 0.928308i \(0.621263\pi\)
\(114\) 0 0
\(115\) 18.5778 1.73239
\(116\) 0 0
\(117\) 19.5501 1.80741
\(118\) 0 0
\(119\) 32.3457 2.96512
\(120\) 0 0
\(121\) −2.18326 −0.198478
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.78623 −0.875307
\(126\) 0 0
\(127\) 17.4509 1.54851 0.774257 0.632871i \(-0.218124\pi\)
0.774257 + 0.632871i \(0.218124\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 16.1590 1.41182 0.705909 0.708302i \(-0.250539\pi\)
0.705909 + 0.708302i \(0.250539\pi\)
\(132\) 0 0
\(133\) −5.04197 −0.437194
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.6791 1.08325 0.541625 0.840620i \(-0.317809\pi\)
0.541625 + 0.840620i \(0.317809\pi\)
\(138\) 0 0
\(139\) 15.6835 1.33026 0.665130 0.746728i \(-0.268376\pi\)
0.665130 + 0.746728i \(0.268376\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 19.3500 1.61813
\(144\) 0 0
\(145\) 22.9487 1.90579
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 19.1103 1.56558 0.782789 0.622287i \(-0.213796\pi\)
0.782789 + 0.622287i \(0.213796\pi\)
\(150\) 0 0
\(151\) −16.0814 −1.30868 −0.654341 0.756200i \(-0.727054\pi\)
−0.654341 + 0.756200i \(0.727054\pi\)
\(152\) 0 0
\(153\) 19.2459 1.55594
\(154\) 0 0
\(155\) −14.9463 −1.20052
\(156\) 0 0
\(157\) −11.6489 −0.929684 −0.464842 0.885394i \(-0.653889\pi\)
−0.464842 + 0.885394i \(0.653889\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −38.2172 −3.01194
\(162\) 0 0
\(163\) −2.03145 −0.159116 −0.0795579 0.996830i \(-0.525351\pi\)
−0.0795579 + 0.996830i \(0.525351\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.57063 −0.121539 −0.0607696 0.998152i \(-0.519355\pi\)
−0.0607696 + 0.998152i \(0.519355\pi\)
\(168\) 0 0
\(169\) 29.4674 2.26672
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) 1.60463 0.121998 0.0609988 0.998138i \(-0.480571\pi\)
0.0609988 + 0.998138i \(0.480571\pi\)
\(174\) 0 0
\(175\) −5.07814 −0.383871
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.57985 −0.118083 −0.0590417 0.998256i \(-0.518805\pi\)
−0.0590417 + 0.998256i \(0.518805\pi\)
\(180\) 0 0
\(181\) 2.05368 0.152649 0.0763246 0.997083i \(-0.475681\pi\)
0.0763246 + 0.997083i \(0.475681\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.61735 −0.118910
\(186\) 0 0
\(187\) 19.0489 1.39299
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −20.9771 −1.51785 −0.758925 0.651178i \(-0.774275\pi\)
−0.758925 + 0.651178i \(0.774275\pi\)
\(192\) 0 0
\(193\) 7.15913 0.515326 0.257663 0.966235i \(-0.417048\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.4455 1.10045 0.550223 0.835018i \(-0.314543\pi\)
0.550223 + 0.835018i \(0.314543\pi\)
\(198\) 0 0
\(199\) −12.3230 −0.873557 −0.436778 0.899569i \(-0.643881\pi\)
−0.436778 + 0.899569i \(0.643881\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −47.2088 −3.31341
\(204\) 0 0
\(205\) 10.1253 0.707180
\(206\) 0 0
\(207\) −22.7395 −1.58050
\(208\) 0 0
\(209\) −2.96930 −0.205391
\(210\) 0 0
\(211\) 4.25931 0.293223 0.146611 0.989194i \(-0.453163\pi\)
0.146611 + 0.989194i \(0.453163\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.26304 −0.222538
\(216\) 0 0
\(217\) 30.7468 2.08723
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 41.8065 2.81221
\(222\) 0 0
\(223\) −8.40009 −0.562512 −0.281256 0.959633i \(-0.590751\pi\)
−0.281256 + 0.959633i \(0.590751\pi\)
\(224\) 0 0
\(225\) −3.02152 −0.201435
\(226\) 0 0
\(227\) −10.2518 −0.680435 −0.340218 0.940347i \(-0.610501\pi\)
−0.340218 + 0.940347i \(0.610501\pi\)
\(228\) 0 0
\(229\) −23.4282 −1.54818 −0.774089 0.633077i \(-0.781791\pi\)
−0.774089 + 0.633077i \(0.781791\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.17009 −0.273191 −0.136596 0.990627i \(-0.543616\pi\)
−0.136596 + 0.990627i \(0.543616\pi\)
\(234\) 0 0
\(235\) −28.2110 −1.84028
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.60727 0.427389 0.213694 0.976901i \(-0.431450\pi\)
0.213694 + 0.976901i \(0.431450\pi\)
\(240\) 0 0
\(241\) −8.97826 −0.578341 −0.289170 0.957278i \(-0.593379\pi\)
−0.289170 + 0.957278i \(0.593379\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 45.1501 2.88453
\(246\) 0 0
\(247\) −6.51670 −0.414648
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0.597009 0.0376829 0.0188414 0.999822i \(-0.494002\pi\)
0.0188414 + 0.999822i \(0.494002\pi\)
\(252\) 0 0
\(253\) −22.5068 −1.41499
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −20.1584 −1.25745 −0.628725 0.777628i \(-0.716423\pi\)
−0.628725 + 0.777628i \(0.716423\pi\)
\(258\) 0 0
\(259\) 3.32713 0.206738
\(260\) 0 0
\(261\) −28.0895 −1.73870
\(262\) 0 0
\(263\) −24.6058 −1.51726 −0.758628 0.651524i \(-0.774130\pi\)
−0.758628 + 0.651524i \(0.774130\pi\)
\(264\) 0 0
\(265\) −3.29372 −0.202332
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −19.1692 −1.16877 −0.584383 0.811478i \(-0.698663\pi\)
−0.584383 + 0.811478i \(0.698663\pi\)
\(270\) 0 0
\(271\) 17.9699 1.09159 0.545795 0.837918i \(-0.316228\pi\)
0.545795 + 0.837918i \(0.316228\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.99060 −0.180340
\(276\) 0 0
\(277\) 6.94262 0.417141 0.208571 0.978007i \(-0.433119\pi\)
0.208571 + 0.978007i \(0.433119\pi\)
\(278\) 0 0
\(279\) 18.2945 1.09526
\(280\) 0 0
\(281\) −1.11836 −0.0667157 −0.0333578 0.999443i \(-0.510620\pi\)
−0.0333578 + 0.999443i \(0.510620\pi\)
\(282\) 0 0
\(283\) 6.92445 0.411616 0.205808 0.978592i \(-0.434018\pi\)
0.205808 + 0.978592i \(0.434018\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −20.8292 −1.22951
\(288\) 0 0
\(289\) 24.1559 1.42094
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −28.4728 −1.66340 −0.831701 0.555224i \(-0.812632\pi\)
−0.831701 + 0.555224i \(0.812632\pi\)
\(294\) 0 0
\(295\) 12.7658 0.743255
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −49.3954 −2.85661
\(300\) 0 0
\(301\) 6.71255 0.386905
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 20.7089 1.18579
\(306\) 0 0
\(307\) −14.1870 −0.809693 −0.404847 0.914385i \(-0.632675\pi\)
−0.404847 + 0.914385i \(0.632675\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.4447 −1.38613 −0.693065 0.720875i \(-0.743740\pi\)
−0.693065 + 0.720875i \(0.743740\pi\)
\(312\) 0 0
\(313\) 12.9436 0.731618 0.365809 0.930690i \(-0.380792\pi\)
0.365809 + 0.930690i \(0.380792\pi\)
\(314\) 0 0
\(315\) 37.0729 2.08882
\(316\) 0 0
\(317\) 21.7682 1.22262 0.611312 0.791390i \(-0.290642\pi\)
0.611312 + 0.791390i \(0.290642\pi\)
\(318\) 0 0
\(319\) −27.8021 −1.55662
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.41529 −0.356956
\(324\) 0 0
\(325\) −6.56345 −0.364075
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 58.0341 3.19952
\(330\) 0 0
\(331\) 28.2533 1.55294 0.776470 0.630155i \(-0.217009\pi\)
0.776470 + 0.630155i \(0.217009\pi\)
\(332\) 0 0
\(333\) 1.97966 0.108485
\(334\) 0 0
\(335\) −11.9269 −0.651638
\(336\) 0 0
\(337\) 24.3546 1.32668 0.663341 0.748318i \(-0.269138\pi\)
0.663341 + 0.748318i \(0.269138\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 18.1073 0.980565
\(342\) 0 0
\(343\) −57.5865 −3.10938
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.02530 0.108724 0.0543618 0.998521i \(-0.482688\pi\)
0.0543618 + 0.998521i \(0.482688\pi\)
\(348\) 0 0
\(349\) 30.1728 1.61511 0.807557 0.589790i \(-0.200789\pi\)
0.807557 + 0.589790i \(0.200789\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 31.7784 1.69139 0.845697 0.533663i \(-0.179185\pi\)
0.845697 + 0.533663i \(0.179185\pi\)
\(354\) 0 0
\(355\) 5.13858 0.272727
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11.5532 −0.609757 −0.304878 0.952391i \(-0.598616\pi\)
−0.304878 + 0.952391i \(0.598616\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 13.6087 0.712310
\(366\) 0 0
\(367\) 12.8193 0.669164 0.334582 0.942367i \(-0.391405\pi\)
0.334582 + 0.942367i \(0.391405\pi\)
\(368\) 0 0
\(369\) −12.3935 −0.645178
\(370\) 0 0
\(371\) 6.77566 0.351775
\(372\) 0 0
\(373\) 34.0790 1.76454 0.882271 0.470742i \(-0.156014\pi\)
0.882271 + 0.470742i \(0.156014\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −61.0170 −3.14253
\(378\) 0 0
\(379\) −6.01716 −0.309081 −0.154540 0.987986i \(-0.549390\pi\)
−0.154540 + 0.987986i \(0.549390\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 20.4346 1.04416 0.522081 0.852896i \(-0.325156\pi\)
0.522081 + 0.852896i \(0.325156\pi\)
\(384\) 0 0
\(385\) 36.6935 1.87007
\(386\) 0 0
\(387\) 3.99401 0.203027
\(388\) 0 0
\(389\) 16.6896 0.846195 0.423097 0.906084i \(-0.360943\pi\)
0.423097 + 0.906084i \(0.360943\pi\)
\(390\) 0 0
\(391\) −48.6268 −2.45916
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.45095 0.123321
\(396\) 0 0
\(397\) −15.6526 −0.785582 −0.392791 0.919628i \(-0.628490\pi\)
−0.392791 + 0.919628i \(0.628490\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.89165 −0.394090 −0.197045 0.980394i \(-0.563135\pi\)
−0.197045 + 0.980394i \(0.563135\pi\)
\(402\) 0 0
\(403\) 39.7400 1.97959
\(404\) 0 0
\(405\) 22.0586 1.09610
\(406\) 0 0
\(407\) 1.95940 0.0971241
\(408\) 0 0
\(409\) −37.0443 −1.83172 −0.915861 0.401496i \(-0.868490\pi\)
−0.915861 + 0.401496i \(0.868490\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −26.2611 −1.29223
\(414\) 0 0
\(415\) −2.84090 −0.139454
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.84924 −0.383460 −0.191730 0.981448i \(-0.561410\pi\)
−0.191730 + 0.981448i \(0.561410\pi\)
\(420\) 0 0
\(421\) 37.5335 1.82927 0.914636 0.404278i \(-0.132477\pi\)
0.914636 + 0.404278i \(0.132477\pi\)
\(422\) 0 0
\(423\) 34.5306 1.67894
\(424\) 0 0
\(425\) −6.46131 −0.313420
\(426\) 0 0
\(427\) −42.6011 −2.06161
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −23.3191 −1.12324 −0.561621 0.827395i \(-0.689822\pi\)
−0.561621 + 0.827395i \(0.689822\pi\)
\(432\) 0 0
\(433\) 13.4223 0.645033 0.322517 0.946564i \(-0.395471\pi\)
0.322517 + 0.946564i \(0.395471\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.57983 0.362592
\(438\) 0 0
\(439\) −31.1051 −1.48457 −0.742283 0.670087i \(-0.766257\pi\)
−0.742283 + 0.670087i \(0.766257\pi\)
\(440\) 0 0
\(441\) −55.2643 −2.63163
\(442\) 0 0
\(443\) 19.6807 0.935056 0.467528 0.883978i \(-0.345145\pi\)
0.467528 + 0.883978i \(0.345145\pi\)
\(444\) 0 0
\(445\) 17.1595 0.813437
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −9.97787 −0.470885 −0.235442 0.971888i \(-0.575654\pi\)
−0.235442 + 0.971888i \(0.575654\pi\)
\(450\) 0 0
\(451\) −12.2666 −0.577613
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 80.5309 3.77535
\(456\) 0 0
\(457\) 6.67855 0.312409 0.156205 0.987725i \(-0.450074\pi\)
0.156205 + 0.987725i \(0.450074\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9.08890 0.423312 0.211656 0.977344i \(-0.432114\pi\)
0.211656 + 0.977344i \(0.432114\pi\)
\(462\) 0 0
\(463\) −15.1194 −0.702660 −0.351330 0.936252i \(-0.614271\pi\)
−0.351330 + 0.936252i \(0.614271\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.06928 −0.234578 −0.117289 0.993098i \(-0.537420\pi\)
−0.117289 + 0.993098i \(0.537420\pi\)
\(468\) 0 0
\(469\) 24.5354 1.13294
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.95313 0.181765
\(474\) 0 0
\(475\) 1.00717 0.0462123
\(476\) 0 0
\(477\) 4.03156 0.184592
\(478\) 0 0
\(479\) 9.18609 0.419723 0.209862 0.977731i \(-0.432699\pi\)
0.209862 + 0.977731i \(0.432699\pi\)
\(480\) 0 0
\(481\) 4.30029 0.196076
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −20.6388 −0.937160
\(486\) 0 0
\(487\) 4.42369 0.200456 0.100228 0.994964i \(-0.468043\pi\)
0.100228 + 0.994964i \(0.468043\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −14.7086 −0.663789 −0.331895 0.943316i \(-0.607688\pi\)
−0.331895 + 0.943316i \(0.607688\pi\)
\(492\) 0 0
\(493\) −60.0675 −2.70530
\(494\) 0 0
\(495\) 21.8328 0.981313
\(496\) 0 0
\(497\) −10.5708 −0.474165
\(498\) 0 0
\(499\) −4.45227 −0.199311 −0.0996554 0.995022i \(-0.531774\pi\)
−0.0996554 + 0.995022i \(0.531774\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 34.0149 1.51665 0.758325 0.651877i \(-0.226018\pi\)
0.758325 + 0.651877i \(0.226018\pi\)
\(504\) 0 0
\(505\) −20.1896 −0.898427
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 33.6441 1.49125 0.745624 0.666367i \(-0.232152\pi\)
0.745624 + 0.666367i \(0.232152\pi\)
\(510\) 0 0
\(511\) −27.9950 −1.23843
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.96040 −0.262647
\(516\) 0 0
\(517\) 34.1773 1.50311
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −42.9356 −1.88104 −0.940521 0.339734i \(-0.889663\pi\)
−0.940521 + 0.339734i \(0.889663\pi\)
\(522\) 0 0
\(523\) 16.5328 0.722931 0.361465 0.932386i \(-0.382277\pi\)
0.361465 + 0.932386i \(0.382277\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 39.1215 1.70416
\(528\) 0 0
\(529\) 34.4538 1.49799
\(530\) 0 0
\(531\) −15.6255 −0.678090
\(532\) 0 0
\(533\) −26.9215 −1.16610
\(534\) 0 0
\(535\) −33.9558 −1.46804
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −54.6988 −2.35604
\(540\) 0 0
\(541\) −12.3376 −0.530435 −0.265218 0.964189i \(-0.585444\pi\)
−0.265218 + 0.964189i \(0.585444\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 42.2399 1.80936
\(546\) 0 0
\(547\) 7.16269 0.306255 0.153127 0.988206i \(-0.451066\pi\)
0.153127 + 0.988206i \(0.451066\pi\)
\(548\) 0 0
\(549\) −25.3479 −1.08182
\(550\) 0 0
\(551\) 9.36317 0.398885
\(552\) 0 0
\(553\) −5.04197 −0.214406
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.17517 0.176908 0.0884539 0.996080i \(-0.471807\pi\)
0.0884539 + 0.996080i \(0.471807\pi\)
\(558\) 0 0
\(559\) 8.67591 0.366952
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.43275 −0.0603833 −0.0301917 0.999544i \(-0.509612\pi\)
−0.0301917 + 0.999544i \(0.509612\pi\)
\(564\) 0 0
\(565\) −19.3744 −0.815085
\(566\) 0 0
\(567\) −45.3777 −1.90568
\(568\) 0 0
\(569\) 31.0844 1.30312 0.651562 0.758595i \(-0.274114\pi\)
0.651562 + 0.758595i \(0.274114\pi\)
\(570\) 0 0
\(571\) 26.4303 1.10608 0.553038 0.833156i \(-0.313469\pi\)
0.553038 + 0.833156i \(0.313469\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 7.63420 0.318368
\(576\) 0 0
\(577\) 8.26809 0.344205 0.172103 0.985079i \(-0.444944\pi\)
0.172103 + 0.985079i \(0.444944\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.84414 0.242456
\(582\) 0 0
\(583\) 3.99030 0.165261
\(584\) 0 0
\(585\) 47.9164 1.98110
\(586\) 0 0
\(587\) −31.5289 −1.30134 −0.650669 0.759361i \(-0.725511\pi\)
−0.650669 + 0.759361i \(0.725511\pi\)
\(588\) 0 0
\(589\) −6.09817 −0.251271
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.13542 −0.128756 −0.0643782 0.997926i \(-0.520506\pi\)
−0.0643782 + 0.997926i \(0.520506\pi\)
\(594\) 0 0
\(595\) 79.2778 3.25007
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3.24446 0.132565 0.0662825 0.997801i \(-0.478886\pi\)
0.0662825 + 0.997801i \(0.478886\pi\)
\(600\) 0 0
\(601\) −26.6890 −1.08867 −0.544335 0.838868i \(-0.683218\pi\)
−0.544335 + 0.838868i \(0.683218\pi\)
\(602\) 0 0
\(603\) 14.5987 0.594506
\(604\) 0 0
\(605\) −5.35107 −0.217552
\(606\) 0 0
\(607\) 13.7339 0.557443 0.278722 0.960372i \(-0.410089\pi\)
0.278722 + 0.960372i \(0.410089\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 75.0085 3.03452
\(612\) 0 0
\(613\) 14.9172 0.602501 0.301251 0.953545i \(-0.402596\pi\)
0.301251 + 0.953545i \(0.402596\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.2495 0.573662 0.286831 0.957981i \(-0.407398\pi\)
0.286831 + 0.957981i \(0.407398\pi\)
\(618\) 0 0
\(619\) −30.9903 −1.24561 −0.622803 0.782379i \(-0.714006\pi\)
−0.622803 + 0.782379i \(0.714006\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −35.2995 −1.41424
\(624\) 0 0
\(625\) −29.0215 −1.16086
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.23337 0.168796
\(630\) 0 0
\(631\) −16.4794 −0.656034 −0.328017 0.944672i \(-0.606380\pi\)
−0.328017 + 0.944672i \(0.606380\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 42.7713 1.69733
\(636\) 0 0
\(637\) −120.047 −4.75643
\(638\) 0 0
\(639\) −6.28969 −0.248816
\(640\) 0 0
\(641\) −37.0626 −1.46388 −0.731942 0.681367i \(-0.761386\pi\)
−0.731942 + 0.681367i \(0.761386\pi\)
\(642\) 0 0
\(643\) 27.4440 1.08229 0.541143 0.840930i \(-0.317992\pi\)
0.541143 + 0.840930i \(0.317992\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −49.1319 −1.93157 −0.965787 0.259337i \(-0.916496\pi\)
−0.965787 + 0.259337i \(0.916496\pi\)
\(648\) 0 0
\(649\) −15.4656 −0.607079
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.27960 0.0500748 0.0250374 0.999687i \(-0.492030\pi\)
0.0250374 + 0.999687i \(0.492030\pi\)
\(654\) 0 0
\(655\) 39.6050 1.54749
\(656\) 0 0
\(657\) −16.6572 −0.649858
\(658\) 0 0
\(659\) 14.2816 0.556333 0.278167 0.960533i \(-0.410273\pi\)
0.278167 + 0.960533i \(0.410273\pi\)
\(660\) 0 0
\(661\) 47.3901 1.84326 0.921631 0.388067i \(-0.126857\pi\)
0.921631 + 0.388067i \(0.126857\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −12.3576 −0.479208
\(666\) 0 0
\(667\) 70.9712 2.74802
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −25.0885 −0.968532
\(672\) 0 0
\(673\) −25.9815 −1.00151 −0.500756 0.865589i \(-0.666945\pi\)
−0.500756 + 0.865589i \(0.666945\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.3877 0.706697 0.353349 0.935492i \(-0.385043\pi\)
0.353349 + 0.935492i \(0.385043\pi\)
\(678\) 0 0
\(679\) 42.4570 1.62935
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11.5129 0.440530 0.220265 0.975440i \(-0.429308\pi\)
0.220265 + 0.975440i \(0.429308\pi\)
\(684\) 0 0
\(685\) 31.0759 1.18735
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8.75748 0.333633
\(690\) 0 0
\(691\) −0.562109 −0.0213836 −0.0106918 0.999943i \(-0.503403\pi\)
−0.0106918 + 0.999943i \(0.503403\pi\)
\(692\) 0 0
\(693\) −44.9133 −1.70612
\(694\) 0 0
\(695\) 38.4396 1.45810
\(696\) 0 0
\(697\) −26.5026 −1.00386
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0.661412 0.0249812 0.0124906 0.999922i \(-0.496024\pi\)
0.0124906 + 0.999922i \(0.496024\pi\)
\(702\) 0 0
\(703\) −0.659888 −0.0248881
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 41.5330 1.56201
\(708\) 0 0
\(709\) 45.9579 1.72599 0.862993 0.505215i \(-0.168587\pi\)
0.862993 + 0.505215i \(0.168587\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −46.2231 −1.73107
\(714\) 0 0
\(715\) 47.4260 1.77363
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.06883 0.189036 0.0945178 0.995523i \(-0.469869\pi\)
0.0945178 + 0.995523i \(0.469869\pi\)
\(720\) 0 0
\(721\) 12.2614 0.456639
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.43034 0.350234
\(726\) 0 0
\(727\) 5.83763 0.216506 0.108253 0.994123i \(-0.465474\pi\)
0.108253 + 0.994123i \(0.465474\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 8.54090 0.315897
\(732\) 0 0
\(733\) 46.1636 1.70509 0.852545 0.522653i \(-0.175058\pi\)
0.852545 + 0.522653i \(0.175058\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 14.4493 0.532248
\(738\) 0 0
\(739\) −51.0848 −1.87918 −0.939592 0.342296i \(-0.888795\pi\)
−0.939592 + 0.342296i \(0.888795\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 12.2572 0.449672 0.224836 0.974397i \(-0.427815\pi\)
0.224836 + 0.974397i \(0.427815\pi\)
\(744\) 0 0
\(745\) 46.8385 1.71603
\(746\) 0 0
\(747\) 3.47730 0.127228
\(748\) 0 0
\(749\) 69.8521 2.55234
\(750\) 0 0
\(751\) 20.4477 0.746148 0.373074 0.927802i \(-0.378304\pi\)
0.373074 + 0.927802i \(0.378304\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −39.4146 −1.43445
\(756\) 0 0
\(757\) 12.1559 0.441813 0.220907 0.975295i \(-0.429098\pi\)
0.220907 + 0.975295i \(0.429098\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 28.3026 1.02597 0.512984 0.858398i \(-0.328540\pi\)
0.512984 + 0.858398i \(0.328540\pi\)
\(762\) 0 0
\(763\) −86.8937 −3.14576
\(764\) 0 0
\(765\) 47.1707 1.70546
\(766\) 0 0
\(767\) −33.9423 −1.22559
\(768\) 0 0
\(769\) −13.6722 −0.493033 −0.246516 0.969139i \(-0.579286\pi\)
−0.246516 + 0.969139i \(0.579286\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 35.8635 1.28992 0.644961 0.764216i \(-0.276874\pi\)
0.644961 + 0.764216i \(0.276874\pi\)
\(774\) 0 0
\(775\) −6.14192 −0.220624
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.13116 0.148014
\(780\) 0 0
\(781\) −6.22532 −0.222760
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −28.5509 −1.01903
\(786\) 0 0
\(787\) 43.2326 1.54107 0.770537 0.637395i \(-0.219988\pi\)
0.770537 + 0.637395i \(0.219988\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 39.8559 1.41711
\(792\) 0 0
\(793\) −55.0616 −1.95529
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.76913 0.239775 0.119887 0.992787i \(-0.461747\pi\)
0.119887 + 0.992787i \(0.461747\pi\)
\(798\) 0 0
\(799\) 73.8413 2.61232
\(800\) 0 0
\(801\) −21.0034 −0.742119
\(802\) 0 0
\(803\) −16.4867 −0.581804
\(804\) 0 0
\(805\) −93.6687 −3.30139
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 10.4284 0.366644 0.183322 0.983053i \(-0.441315\pi\)
0.183322 + 0.983053i \(0.441315\pi\)
\(810\) 0 0
\(811\) −3.08389 −0.108290 −0.0541451 0.998533i \(-0.517243\pi\)
−0.0541451 + 0.998533i \(0.517243\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −4.97900 −0.174407
\(816\) 0 0
\(817\) −1.33134 −0.0465775
\(818\) 0 0
\(819\) −98.5709 −3.44435
\(820\) 0 0
\(821\) 6.82964 0.238356 0.119178 0.992873i \(-0.461974\pi\)
0.119178 + 0.992873i \(0.461974\pi\)
\(822\) 0 0
\(823\) −16.0883 −0.560801 −0.280401 0.959883i \(-0.590467\pi\)
−0.280401 + 0.959883i \(0.590467\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 29.4730 1.02488 0.512438 0.858724i \(-0.328742\pi\)
0.512438 + 0.858724i \(0.328742\pi\)
\(828\) 0 0
\(829\) −3.73744 −0.129807 −0.0649033 0.997892i \(-0.520674\pi\)
−0.0649033 + 0.997892i \(0.520674\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −118.179 −4.09465
\(834\) 0 0
\(835\) −3.84955 −0.133219
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −36.1793 −1.24905 −0.624524 0.781006i \(-0.714707\pi\)
−0.624524 + 0.781006i \(0.714707\pi\)
\(840\) 0 0
\(841\) 58.6690 2.02307
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 72.2231 2.48455
\(846\) 0 0
\(847\) 11.0079 0.378237
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −5.00184 −0.171461
\(852\) 0 0
\(853\) −33.9233 −1.16151 −0.580756 0.814078i \(-0.697243\pi\)
−0.580756 + 0.814078i \(0.697243\pi\)
\(854\) 0 0
\(855\) −7.35286 −0.251463
\(856\) 0 0
\(857\) −8.98362 −0.306875 −0.153437 0.988158i \(-0.549034\pi\)
−0.153437 + 0.988158i \(0.549034\pi\)
\(858\) 0 0
\(859\) −18.4033 −0.627913 −0.313956 0.949437i \(-0.601655\pi\)
−0.313956 + 0.949437i \(0.601655\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −34.7941 −1.18440 −0.592202 0.805790i \(-0.701741\pi\)
−0.592202 + 0.805790i \(0.701741\pi\)
\(864\) 0 0
\(865\) 3.93287 0.133721
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.96930 −0.100727
\(870\) 0 0
\(871\) 31.7118 1.07451
\(872\) 0 0
\(873\) 25.2622 0.854995
\(874\) 0 0
\(875\) 49.3419 1.66806
\(876\) 0 0
\(877\) 8.84006 0.298508 0.149254 0.988799i \(-0.452313\pi\)
0.149254 + 0.988799i \(0.452313\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 41.7250 1.40575 0.702876 0.711313i \(-0.251899\pi\)
0.702876 + 0.711313i \(0.251899\pi\)
\(882\) 0 0
\(883\) 7.08820 0.238537 0.119268 0.992862i \(-0.461945\pi\)
0.119268 + 0.992862i \(0.461945\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 47.5643 1.59705 0.798527 0.601959i \(-0.205613\pi\)
0.798527 + 0.601959i \(0.205613\pi\)
\(888\) 0 0
\(889\) −87.9867 −2.95098
\(890\) 0 0
\(891\) −26.7237 −0.895278
\(892\) 0 0
\(893\) −11.5102 −0.385174
\(894\) 0 0
\(895\) −3.87214 −0.129431
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −57.0983 −1.90433
\(900\) 0 0
\(901\) 8.62120 0.287214
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.03349 0.167319
\(906\) 0 0
\(907\) −43.8292 −1.45533 −0.727663 0.685935i \(-0.759393\pi\)
−0.727663 + 0.685935i \(0.759393\pi\)
\(908\) 0 0
\(909\) 24.7124 0.819658
\(910\) 0 0
\(911\) 47.8392 1.58498 0.792492 0.609882i \(-0.208783\pi\)
0.792492 + 0.609882i \(0.208783\pi\)
\(912\) 0 0
\(913\) 3.44171 0.113904
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −81.4732 −2.69048
\(918\) 0 0
\(919\) 5.02555 0.165778 0.0828889 0.996559i \(-0.473585\pi\)
0.0828889 + 0.996559i \(0.473585\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −13.6627 −0.449712
\(924\) 0 0
\(925\) −0.664622 −0.0218526
\(926\) 0 0
\(927\) 7.29561 0.239619
\(928\) 0 0
\(929\) 44.6273 1.46417 0.732086 0.681212i \(-0.238547\pi\)
0.732086 + 0.681212i \(0.238547\pi\)
\(930\) 0 0
\(931\) 18.4214 0.603738
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 46.6880 1.52686
\(936\) 0 0
\(937\) 10.3337 0.337586 0.168793 0.985652i \(-0.446013\pi\)
0.168793 + 0.985652i \(0.446013\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 52.9443 1.72593 0.862967 0.505260i \(-0.168603\pi\)
0.862967 + 0.505260i \(0.168603\pi\)
\(942\) 0 0
\(943\) 31.3134 1.01971
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.88656 −0.158792 −0.0793959 0.996843i \(-0.525299\pi\)
−0.0793959 + 0.996843i \(0.525299\pi\)
\(948\) 0 0
\(949\) −36.1833 −1.17456
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −18.9743 −0.614639 −0.307319 0.951606i \(-0.599432\pi\)
−0.307319 + 0.951606i \(0.599432\pi\)
\(954\) 0 0
\(955\) −51.4139 −1.66371
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −63.9277 −2.06433
\(960\) 0 0
\(961\) 6.18772 0.199604
\(962\) 0 0
\(963\) 41.5624 1.33933
\(964\) 0 0
\(965\) 17.5467 0.564848
\(966\) 0 0
\(967\) 45.9521 1.47772 0.738861 0.673858i \(-0.235364\pi\)
0.738861 + 0.673858i \(0.235364\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 25.0456 0.803753 0.401876 0.915694i \(-0.368358\pi\)
0.401876 + 0.915694i \(0.368358\pi\)
\(972\) 0 0
\(973\) −79.0758 −2.53505
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −24.4823 −0.783259 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(978\) 0 0
\(979\) −20.7885 −0.664402
\(980\) 0 0
\(981\) −51.7022 −1.65073
\(982\) 0 0
\(983\) 23.1569 0.738591 0.369296 0.929312i \(-0.379599\pi\)
0.369296 + 0.929312i \(0.379599\pi\)
\(984\) 0 0
\(985\) 37.8562 1.20620
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −10.0913 −0.320884
\(990\) 0 0
\(991\) 6.17676 0.196211 0.0981057 0.995176i \(-0.468722\pi\)
0.0981057 + 0.995176i \(0.468722\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −30.2032 −0.957505
\(996\) 0 0
\(997\) −11.3816 −0.360458 −0.180229 0.983625i \(-0.557684\pi\)
−0.180229 + 0.983625i \(0.557684\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))