Properties

Label 8004.2.a.d.1.2
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 1
Dimension 8
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: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.386133\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.77471 q^{5} +0.556399 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.77471 q^{5} +0.556399 q^{7} +1.00000 q^{9} +3.82791 q^{11} -0.0549651 q^{13} -2.77471 q^{15} -2.00765 q^{17} -2.76410 q^{19} +0.556399 q^{21} +1.00000 q^{23} +2.69903 q^{25} +1.00000 q^{27} +1.00000 q^{29} -3.02923 q^{31} +3.82791 q^{33} -1.54385 q^{35} +1.22025 q^{37} -0.0549651 q^{39} -6.65903 q^{41} -4.40578 q^{43} -2.77471 q^{45} -4.00567 q^{47} -6.69042 q^{49} -2.00765 q^{51} -3.40057 q^{53} -10.6213 q^{55} -2.76410 q^{57} +10.2440 q^{59} +3.87008 q^{61} +0.556399 q^{63} +0.152512 q^{65} -0.00393019 q^{67} +1.00000 q^{69} -3.59047 q^{71} +7.82504 q^{73} +2.69903 q^{75} +2.12984 q^{77} +3.03633 q^{79} +1.00000 q^{81} +12.5062 q^{83} +5.57065 q^{85} +1.00000 q^{87} -15.2154 q^{89} -0.0305825 q^{91} -3.02923 q^{93} +7.66958 q^{95} -9.71227 q^{97} +3.82791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{3} - 5q^{5} - 4q^{7} + 8q^{9} + O(q^{10}) \) \( 8q + 8q^{3} - 5q^{5} - 4q^{7} + 8q^{9} - 5q^{11} - 4q^{13} - 5q^{15} - 3q^{17} - 5q^{19} - 4q^{21} + 8q^{23} - 5q^{25} + 8q^{27} + 8q^{29} - 2q^{31} - 5q^{33} - 15q^{35} - 10q^{37} - 4q^{39} - 11q^{41} - 7q^{43} - 5q^{45} - 14q^{47} - 18q^{49} - 3q^{51} - 15q^{53} - 17q^{55} - 5q^{57} + 4q^{59} + q^{61} - 4q^{63} - 5q^{67} + 8q^{69} - q^{71} - 21q^{73} - 5q^{75} - 8q^{79} + 8q^{81} + 3q^{83} + 8q^{87} - 20q^{89} - 7q^{91} - 2q^{93} - 3q^{95} - 7q^{97} - 5q^{99} + O(q^{100}) \)

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
\(5\) −2.77471 −1.24089 −0.620445 0.784250i \(-0.713048\pi\)
−0.620445 + 0.784250i \(0.713048\pi\)
\(6\) 0 0
\(7\) 0.556399 0.210299 0.105149 0.994456i \(-0.466468\pi\)
0.105149 + 0.994456i \(0.466468\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.82791 1.15416 0.577079 0.816689i \(-0.304193\pi\)
0.577079 + 0.816689i \(0.304193\pi\)
\(12\) 0 0
\(13\) −0.0549651 −0.0152446 −0.00762228 0.999971i \(-0.502426\pi\)
−0.00762228 + 0.999971i \(0.502426\pi\)
\(14\) 0 0
\(15\) −2.77471 −0.716428
\(16\) 0 0
\(17\) −2.00765 −0.486926 −0.243463 0.969910i \(-0.578284\pi\)
−0.243463 + 0.969910i \(0.578284\pi\)
\(18\) 0 0
\(19\) −2.76410 −0.634128 −0.317064 0.948404i \(-0.602697\pi\)
−0.317064 + 0.948404i \(0.602697\pi\)
\(20\) 0 0
\(21\) 0.556399 0.121416
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 2.69903 0.539806
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −3.02923 −0.544066 −0.272033 0.962288i \(-0.587696\pi\)
−0.272033 + 0.962288i \(0.587696\pi\)
\(32\) 0 0
\(33\) 3.82791 0.666353
\(34\) 0 0
\(35\) −1.54385 −0.260958
\(36\) 0 0
\(37\) 1.22025 0.200608 0.100304 0.994957i \(-0.468018\pi\)
0.100304 + 0.994957i \(0.468018\pi\)
\(38\) 0 0
\(39\) −0.0549651 −0.00880145
\(40\) 0 0
\(41\) −6.65903 −1.03997 −0.519983 0.854177i \(-0.674062\pi\)
−0.519983 + 0.854177i \(0.674062\pi\)
\(42\) 0 0
\(43\) −4.40578 −0.671875 −0.335938 0.941884i \(-0.609053\pi\)
−0.335938 + 0.941884i \(0.609053\pi\)
\(44\) 0 0
\(45\) −2.77471 −0.413630
\(46\) 0 0
\(47\) −4.00567 −0.584287 −0.292143 0.956375i \(-0.594368\pi\)
−0.292143 + 0.956375i \(0.594368\pi\)
\(48\) 0 0
\(49\) −6.69042 −0.955774
\(50\) 0 0
\(51\) −2.00765 −0.281127
\(52\) 0 0
\(53\) −3.40057 −0.467105 −0.233552 0.972344i \(-0.575035\pi\)
−0.233552 + 0.972344i \(0.575035\pi\)
\(54\) 0 0
\(55\) −10.6213 −1.43218
\(56\) 0 0
\(57\) −2.76410 −0.366114
\(58\) 0 0
\(59\) 10.2440 1.33366 0.666830 0.745210i \(-0.267651\pi\)
0.666830 + 0.745210i \(0.267651\pi\)
\(60\) 0 0
\(61\) 3.87008 0.495513 0.247757 0.968822i \(-0.420307\pi\)
0.247757 + 0.968822i \(0.420307\pi\)
\(62\) 0 0
\(63\) 0.556399 0.0700997
\(64\) 0 0
\(65\) 0.152512 0.0189168
\(66\) 0 0
\(67\) −0.00393019 −0.000480149 0 −0.000240075 1.00000i \(-0.500076\pi\)
−0.000240075 1.00000i \(0.500076\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −3.59047 −0.426111 −0.213055 0.977040i \(-0.568341\pi\)
−0.213055 + 0.977040i \(0.568341\pi\)
\(72\) 0 0
\(73\) 7.82504 0.915852 0.457926 0.888990i \(-0.348592\pi\)
0.457926 + 0.888990i \(0.348592\pi\)
\(74\) 0 0
\(75\) 2.69903 0.311657
\(76\) 0 0
\(77\) 2.12984 0.242718
\(78\) 0 0
\(79\) 3.03633 0.341614 0.170807 0.985305i \(-0.445363\pi\)
0.170807 + 0.985305i \(0.445363\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.5062 1.37273 0.686367 0.727255i \(-0.259204\pi\)
0.686367 + 0.727255i \(0.259204\pi\)
\(84\) 0 0
\(85\) 5.57065 0.604222
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) −15.2154 −1.61283 −0.806417 0.591347i \(-0.798596\pi\)
−0.806417 + 0.591347i \(0.798596\pi\)
\(90\) 0 0
\(91\) −0.0305825 −0.00320592
\(92\) 0 0
\(93\) −3.02923 −0.314117
\(94\) 0 0
\(95\) 7.66958 0.786883
\(96\) 0 0
\(97\) −9.71227 −0.986132 −0.493066 0.869992i \(-0.664124\pi\)
−0.493066 + 0.869992i \(0.664124\pi\)
\(98\) 0 0
\(99\) 3.82791 0.384719
\(100\) 0 0
\(101\) 15.1476 1.50725 0.753623 0.657307i \(-0.228305\pi\)
0.753623 + 0.657307i \(0.228305\pi\)
\(102\) 0 0
\(103\) 1.83698 0.181003 0.0905013 0.995896i \(-0.471153\pi\)
0.0905013 + 0.995896i \(0.471153\pi\)
\(104\) 0 0
\(105\) −1.54385 −0.150664
\(106\) 0 0
\(107\) −17.5327 −1.69495 −0.847476 0.530834i \(-0.821879\pi\)
−0.847476 + 0.530834i \(0.821879\pi\)
\(108\) 0 0
\(109\) 1.30868 0.125349 0.0626743 0.998034i \(-0.480037\pi\)
0.0626743 + 0.998034i \(0.480037\pi\)
\(110\) 0 0
\(111\) 1.22025 0.115821
\(112\) 0 0
\(113\) 5.19652 0.488847 0.244424 0.969669i \(-0.421401\pi\)
0.244424 + 0.969669i \(0.421401\pi\)
\(114\) 0 0
\(115\) −2.77471 −0.258743
\(116\) 0 0
\(117\) −0.0549651 −0.00508152
\(118\) 0 0
\(119\) −1.11705 −0.102400
\(120\) 0 0
\(121\) 3.65286 0.332079
\(122\) 0 0
\(123\) −6.65903 −0.600424
\(124\) 0 0
\(125\) 6.38453 0.571050
\(126\) 0 0
\(127\) −12.3688 −1.09756 −0.548778 0.835968i \(-0.684907\pi\)
−0.548778 + 0.835968i \(0.684907\pi\)
\(128\) 0 0
\(129\) −4.40578 −0.387907
\(130\) 0 0
\(131\) −5.84132 −0.510358 −0.255179 0.966894i \(-0.582134\pi\)
−0.255179 + 0.966894i \(0.582134\pi\)
\(132\) 0 0
\(133\) −1.53794 −0.133356
\(134\) 0 0
\(135\) −2.77471 −0.238809
\(136\) 0 0
\(137\) −2.29571 −0.196136 −0.0980679 0.995180i \(-0.531266\pi\)
−0.0980679 + 0.995180i \(0.531266\pi\)
\(138\) 0 0
\(139\) −7.99948 −0.678507 −0.339254 0.940695i \(-0.610175\pi\)
−0.339254 + 0.940695i \(0.610175\pi\)
\(140\) 0 0
\(141\) −4.00567 −0.337338
\(142\) 0 0
\(143\) −0.210401 −0.0175946
\(144\) 0 0
\(145\) −2.77471 −0.230427
\(146\) 0 0
\(147\) −6.69042 −0.551817
\(148\) 0 0
\(149\) −7.73558 −0.633723 −0.316862 0.948472i \(-0.602629\pi\)
−0.316862 + 0.948472i \(0.602629\pi\)
\(150\) 0 0
\(151\) −14.9583 −1.21729 −0.608644 0.793444i \(-0.708286\pi\)
−0.608644 + 0.793444i \(0.708286\pi\)
\(152\) 0 0
\(153\) −2.00765 −0.162309
\(154\) 0 0
\(155\) 8.40525 0.675126
\(156\) 0 0
\(157\) 10.3517 0.826154 0.413077 0.910696i \(-0.364454\pi\)
0.413077 + 0.910696i \(0.364454\pi\)
\(158\) 0 0
\(159\) −3.40057 −0.269683
\(160\) 0 0
\(161\) 0.556399 0.0438504
\(162\) 0 0
\(163\) −12.8884 −1.00949 −0.504747 0.863267i \(-0.668414\pi\)
−0.504747 + 0.863267i \(0.668414\pi\)
\(164\) 0 0
\(165\) −10.6213 −0.826870
\(166\) 0 0
\(167\) 9.20220 0.712088 0.356044 0.934469i \(-0.384125\pi\)
0.356044 + 0.934469i \(0.384125\pi\)
\(168\) 0 0
\(169\) −12.9970 −0.999768
\(170\) 0 0
\(171\) −2.76410 −0.211376
\(172\) 0 0
\(173\) −7.71770 −0.586766 −0.293383 0.955995i \(-0.594781\pi\)
−0.293383 + 0.955995i \(0.594781\pi\)
\(174\) 0 0
\(175\) 1.50174 0.113521
\(176\) 0 0
\(177\) 10.2440 0.769989
\(178\) 0 0
\(179\) 3.03175 0.226604 0.113302 0.993561i \(-0.463857\pi\)
0.113302 + 0.993561i \(0.463857\pi\)
\(180\) 0 0
\(181\) 8.48454 0.630651 0.315326 0.948984i \(-0.397886\pi\)
0.315326 + 0.948984i \(0.397886\pi\)
\(182\) 0 0
\(183\) 3.87008 0.286085
\(184\) 0 0
\(185\) −3.38585 −0.248933
\(186\) 0 0
\(187\) −7.68509 −0.561990
\(188\) 0 0
\(189\) 0.556399 0.0404721
\(190\) 0 0
\(191\) 12.3424 0.893067 0.446533 0.894767i \(-0.352658\pi\)
0.446533 + 0.894767i \(0.352658\pi\)
\(192\) 0 0
\(193\) −14.4947 −1.04335 −0.521677 0.853143i \(-0.674693\pi\)
−0.521677 + 0.853143i \(0.674693\pi\)
\(194\) 0 0
\(195\) 0.152512 0.0109216
\(196\) 0 0
\(197\) 6.96683 0.496366 0.248183 0.968713i \(-0.420167\pi\)
0.248183 + 0.968713i \(0.420167\pi\)
\(198\) 0 0
\(199\) −12.4386 −0.881749 −0.440875 0.897569i \(-0.645332\pi\)
−0.440875 + 0.897569i \(0.645332\pi\)
\(200\) 0 0
\(201\) −0.00393019 −0.000277214 0
\(202\) 0 0
\(203\) 0.556399 0.0390515
\(204\) 0 0
\(205\) 18.4769 1.29048
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −10.5807 −0.731883
\(210\) 0 0
\(211\) −8.83834 −0.608456 −0.304228 0.952599i \(-0.598399\pi\)
−0.304228 + 0.952599i \(0.598399\pi\)
\(212\) 0 0
\(213\) −3.59047 −0.246015
\(214\) 0 0
\(215\) 12.2248 0.833723
\(216\) 0 0
\(217\) −1.68546 −0.114417
\(218\) 0 0
\(219\) 7.82504 0.528768
\(220\) 0 0
\(221\) 0.110351 0.00742298
\(222\) 0 0
\(223\) 3.52468 0.236030 0.118015 0.993012i \(-0.462347\pi\)
0.118015 + 0.993012i \(0.462347\pi\)
\(224\) 0 0
\(225\) 2.69903 0.179935
\(226\) 0 0
\(227\) −19.7084 −1.30809 −0.654045 0.756456i \(-0.726929\pi\)
−0.654045 + 0.756456i \(0.726929\pi\)
\(228\) 0 0
\(229\) −8.86659 −0.585921 −0.292961 0.956125i \(-0.594640\pi\)
−0.292961 + 0.956125i \(0.594640\pi\)
\(230\) 0 0
\(231\) 2.12984 0.140133
\(232\) 0 0
\(233\) −8.26987 −0.541777 −0.270889 0.962611i \(-0.587317\pi\)
−0.270889 + 0.962611i \(0.587317\pi\)
\(234\) 0 0
\(235\) 11.1146 0.725035
\(236\) 0 0
\(237\) 3.03633 0.197231
\(238\) 0 0
\(239\) −25.2837 −1.63547 −0.817734 0.575596i \(-0.804770\pi\)
−0.817734 + 0.575596i \(0.804770\pi\)
\(240\) 0 0
\(241\) 23.1164 1.48906 0.744530 0.667589i \(-0.232674\pi\)
0.744530 + 0.667589i \(0.232674\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 18.5640 1.18601
\(246\) 0 0
\(247\) 0.151929 0.00966701
\(248\) 0 0
\(249\) 12.5062 0.792548
\(250\) 0 0
\(251\) −27.7022 −1.74855 −0.874274 0.485432i \(-0.838662\pi\)
−0.874274 + 0.485432i \(0.838662\pi\)
\(252\) 0 0
\(253\) 3.82791 0.240658
\(254\) 0 0
\(255\) 5.57065 0.348848
\(256\) 0 0
\(257\) 21.3254 1.33024 0.665121 0.746736i \(-0.268380\pi\)
0.665121 + 0.746736i \(0.268380\pi\)
\(258\) 0 0
\(259\) 0.678947 0.0421877
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) 14.6435 0.902956 0.451478 0.892282i \(-0.350897\pi\)
0.451478 + 0.892282i \(0.350897\pi\)
\(264\) 0 0
\(265\) 9.43561 0.579625
\(266\) 0 0
\(267\) −15.2154 −0.931170
\(268\) 0 0
\(269\) 7.19583 0.438737 0.219369 0.975642i \(-0.429600\pi\)
0.219369 + 0.975642i \(0.429600\pi\)
\(270\) 0 0
\(271\) −13.1008 −0.795814 −0.397907 0.917426i \(-0.630263\pi\)
−0.397907 + 0.917426i \(0.630263\pi\)
\(272\) 0 0
\(273\) −0.0305825 −0.00185094
\(274\) 0 0
\(275\) 10.3316 0.623021
\(276\) 0 0
\(277\) 9.17284 0.551143 0.275571 0.961281i \(-0.411133\pi\)
0.275571 + 0.961281i \(0.411133\pi\)
\(278\) 0 0
\(279\) −3.02923 −0.181355
\(280\) 0 0
\(281\) 23.5095 1.40246 0.701230 0.712936i \(-0.252635\pi\)
0.701230 + 0.712936i \(0.252635\pi\)
\(282\) 0 0
\(283\) −33.2249 −1.97501 −0.987507 0.157574i \(-0.949633\pi\)
−0.987507 + 0.157574i \(0.949633\pi\)
\(284\) 0 0
\(285\) 7.66958 0.454307
\(286\) 0 0
\(287\) −3.70507 −0.218704
\(288\) 0 0
\(289\) −12.9693 −0.762903
\(290\) 0 0
\(291\) −9.71227 −0.569343
\(292\) 0 0
\(293\) 10.7203 0.626286 0.313143 0.949706i \(-0.398618\pi\)
0.313143 + 0.949706i \(0.398618\pi\)
\(294\) 0 0
\(295\) −28.4243 −1.65492
\(296\) 0 0
\(297\) 3.82791 0.222118
\(298\) 0 0
\(299\) −0.0549651 −0.00317871
\(300\) 0 0
\(301\) −2.45137 −0.141295
\(302\) 0 0
\(303\) 15.1476 0.870209
\(304\) 0 0
\(305\) −10.7384 −0.614877
\(306\) 0 0
\(307\) −19.2238 −1.09716 −0.548580 0.836098i \(-0.684831\pi\)
−0.548580 + 0.836098i \(0.684831\pi\)
\(308\) 0 0
\(309\) 1.83698 0.104502
\(310\) 0 0
\(311\) 11.6337 0.659687 0.329844 0.944036i \(-0.393004\pi\)
0.329844 + 0.944036i \(0.393004\pi\)
\(312\) 0 0
\(313\) −18.2765 −1.03305 −0.516523 0.856273i \(-0.672774\pi\)
−0.516523 + 0.856273i \(0.672774\pi\)
\(314\) 0 0
\(315\) −1.54385 −0.0869859
\(316\) 0 0
\(317\) −32.0811 −1.80185 −0.900926 0.433972i \(-0.857112\pi\)
−0.900926 + 0.433972i \(0.857112\pi\)
\(318\) 0 0
\(319\) 3.82791 0.214322
\(320\) 0 0
\(321\) −17.5327 −0.978581
\(322\) 0 0
\(323\) 5.54934 0.308774
\(324\) 0 0
\(325\) −0.148352 −0.00822911
\(326\) 0 0
\(327\) 1.30868 0.0723701
\(328\) 0 0
\(329\) −2.22875 −0.122875
\(330\) 0 0
\(331\) −19.6188 −1.07835 −0.539174 0.842194i \(-0.681264\pi\)
−0.539174 + 0.842194i \(0.681264\pi\)
\(332\) 0 0
\(333\) 1.22025 0.0668695
\(334\) 0 0
\(335\) 0.0109051 0.000595812 0
\(336\) 0 0
\(337\) −20.1982 −1.10027 −0.550133 0.835077i \(-0.685423\pi\)
−0.550133 + 0.835077i \(0.685423\pi\)
\(338\) 0 0
\(339\) 5.19652 0.282236
\(340\) 0 0
\(341\) −11.5956 −0.627938
\(342\) 0 0
\(343\) −7.61733 −0.411297
\(344\) 0 0
\(345\) −2.77471 −0.149386
\(346\) 0 0
\(347\) 15.0133 0.805954 0.402977 0.915210i \(-0.367975\pi\)
0.402977 + 0.915210i \(0.367975\pi\)
\(348\) 0 0
\(349\) −30.4729 −1.63118 −0.815589 0.578631i \(-0.803587\pi\)
−0.815589 + 0.578631i \(0.803587\pi\)
\(350\) 0 0
\(351\) −0.0549651 −0.00293382
\(352\) 0 0
\(353\) −24.9894 −1.33005 −0.665026 0.746820i \(-0.731580\pi\)
−0.665026 + 0.746820i \(0.731580\pi\)
\(354\) 0 0
\(355\) 9.96253 0.528756
\(356\) 0 0
\(357\) −1.11705 −0.0591207
\(358\) 0 0
\(359\) 13.3685 0.705561 0.352780 0.935706i \(-0.385236\pi\)
0.352780 + 0.935706i \(0.385236\pi\)
\(360\) 0 0
\(361\) −11.3598 −0.597882
\(362\) 0 0
\(363\) 3.65286 0.191726
\(364\) 0 0
\(365\) −21.7123 −1.13647
\(366\) 0 0
\(367\) 14.5984 0.762031 0.381016 0.924569i \(-0.375574\pi\)
0.381016 + 0.924569i \(0.375574\pi\)
\(368\) 0 0
\(369\) −6.65903 −0.346655
\(370\) 0 0
\(371\) −1.89207 −0.0982316
\(372\) 0 0
\(373\) −18.8792 −0.977526 −0.488763 0.872417i \(-0.662552\pi\)
−0.488763 + 0.872417i \(0.662552\pi\)
\(374\) 0 0
\(375\) 6.38453 0.329696
\(376\) 0 0
\(377\) −0.0549651 −0.00283084
\(378\) 0 0
\(379\) 1.55072 0.0796552 0.0398276 0.999207i \(-0.487319\pi\)
0.0398276 + 0.999207i \(0.487319\pi\)
\(380\) 0 0
\(381\) −12.3688 −0.633674
\(382\) 0 0
\(383\) −11.2587 −0.575293 −0.287647 0.957737i \(-0.592873\pi\)
−0.287647 + 0.957737i \(0.592873\pi\)
\(384\) 0 0
\(385\) −5.90970 −0.301186
\(386\) 0 0
\(387\) −4.40578 −0.223958
\(388\) 0 0
\(389\) −19.8046 −1.00413 −0.502066 0.864829i \(-0.667426\pi\)
−0.502066 + 0.864829i \(0.667426\pi\)
\(390\) 0 0
\(391\) −2.00765 −0.101531
\(392\) 0 0
\(393\) −5.84132 −0.294656
\(394\) 0 0
\(395\) −8.42495 −0.423905
\(396\) 0 0
\(397\) −8.76623 −0.439965 −0.219982 0.975504i \(-0.570600\pi\)
−0.219982 + 0.975504i \(0.570600\pi\)
\(398\) 0 0
\(399\) −1.53794 −0.0769934
\(400\) 0 0
\(401\) 21.1717 1.05726 0.528631 0.848852i \(-0.322706\pi\)
0.528631 + 0.848852i \(0.322706\pi\)
\(402\) 0 0
\(403\) 0.166502 0.00829405
\(404\) 0 0
\(405\) −2.77471 −0.137877
\(406\) 0 0
\(407\) 4.67101 0.231534
\(408\) 0 0
\(409\) 34.6111 1.71141 0.855704 0.517465i \(-0.173124\pi\)
0.855704 + 0.517465i \(0.173124\pi\)
\(410\) 0 0
\(411\) −2.29571 −0.113239
\(412\) 0 0
\(413\) 5.69977 0.280467
\(414\) 0 0
\(415\) −34.7011 −1.70341
\(416\) 0 0
\(417\) −7.99948 −0.391736
\(418\) 0 0
\(419\) −1.43999 −0.0703482 −0.0351741 0.999381i \(-0.511199\pi\)
−0.0351741 + 0.999381i \(0.511199\pi\)
\(420\) 0 0
\(421\) −21.8112 −1.06301 −0.531507 0.847054i \(-0.678374\pi\)
−0.531507 + 0.847054i \(0.678374\pi\)
\(422\) 0 0
\(423\) −4.00567 −0.194762
\(424\) 0 0
\(425\) −5.41871 −0.262846
\(426\) 0 0
\(427\) 2.15331 0.104206
\(428\) 0 0
\(429\) −0.210401 −0.0101583
\(430\) 0 0
\(431\) −18.2824 −0.880633 −0.440316 0.897843i \(-0.645134\pi\)
−0.440316 + 0.897843i \(0.645134\pi\)
\(432\) 0 0
\(433\) 2.58010 0.123992 0.0619959 0.998076i \(-0.480253\pi\)
0.0619959 + 0.998076i \(0.480253\pi\)
\(434\) 0 0
\(435\) −2.77471 −0.133037
\(436\) 0 0
\(437\) −2.76410 −0.132225
\(438\) 0 0
\(439\) −30.9993 −1.47951 −0.739757 0.672874i \(-0.765059\pi\)
−0.739757 + 0.672874i \(0.765059\pi\)
\(440\) 0 0
\(441\) −6.69042 −0.318591
\(442\) 0 0
\(443\) −14.6452 −0.695813 −0.347906 0.937529i \(-0.613107\pi\)
−0.347906 + 0.937529i \(0.613107\pi\)
\(444\) 0 0
\(445\) 42.2185 2.00135
\(446\) 0 0
\(447\) −7.73558 −0.365880
\(448\) 0 0
\(449\) 32.3776 1.52800 0.763998 0.645219i \(-0.223234\pi\)
0.763998 + 0.645219i \(0.223234\pi\)
\(450\) 0 0
\(451\) −25.4901 −1.20028
\(452\) 0 0
\(453\) −14.9583 −0.702801
\(454\) 0 0
\(455\) 0.0848576 0.00397819
\(456\) 0 0
\(457\) −14.7830 −0.691519 −0.345759 0.938323i \(-0.612379\pi\)
−0.345759 + 0.938323i \(0.612379\pi\)
\(458\) 0 0
\(459\) −2.00765 −0.0937090
\(460\) 0 0
\(461\) 17.8061 0.829312 0.414656 0.909978i \(-0.363902\pi\)
0.414656 + 0.909978i \(0.363902\pi\)
\(462\) 0 0
\(463\) 9.26773 0.430708 0.215354 0.976536i \(-0.430909\pi\)
0.215354 + 0.976536i \(0.430909\pi\)
\(464\) 0 0
\(465\) 8.40525 0.389784
\(466\) 0 0
\(467\) 0.449880 0.0208180 0.0104090 0.999946i \(-0.496687\pi\)
0.0104090 + 0.999946i \(0.496687\pi\)
\(468\) 0 0
\(469\) −0.00218675 −0.000100975 0
\(470\) 0 0
\(471\) 10.3517 0.476980
\(472\) 0 0
\(473\) −16.8649 −0.775450
\(474\) 0 0
\(475\) −7.46039 −0.342306
\(476\) 0 0
\(477\) −3.40057 −0.155702
\(478\) 0 0
\(479\) 32.3675 1.47891 0.739455 0.673206i \(-0.235083\pi\)
0.739455 + 0.673206i \(0.235083\pi\)
\(480\) 0 0
\(481\) −0.0670713 −0.00305819
\(482\) 0 0
\(483\) 0.556399 0.0253170
\(484\) 0 0
\(485\) 26.9488 1.22368
\(486\) 0 0
\(487\) −13.8049 −0.625559 −0.312779 0.949826i \(-0.601260\pi\)
−0.312779 + 0.949826i \(0.601260\pi\)
\(488\) 0 0
\(489\) −12.8884 −0.582832
\(490\) 0 0
\(491\) −18.2392 −0.823124 −0.411562 0.911382i \(-0.635017\pi\)
−0.411562 + 0.911382i \(0.635017\pi\)
\(492\) 0 0
\(493\) −2.00765 −0.0904200
\(494\) 0 0
\(495\) −10.6213 −0.477394
\(496\) 0 0
\(497\) −1.99774 −0.0896107
\(498\) 0 0
\(499\) −30.0883 −1.34694 −0.673468 0.739216i \(-0.735196\pi\)
−0.673468 + 0.739216i \(0.735196\pi\)
\(500\) 0 0
\(501\) 9.20220 0.411124
\(502\) 0 0
\(503\) 33.6546 1.50058 0.750292 0.661106i \(-0.229913\pi\)
0.750292 + 0.661106i \(0.229913\pi\)
\(504\) 0 0
\(505\) −42.0303 −1.87032
\(506\) 0 0
\(507\) −12.9970 −0.577216
\(508\) 0 0
\(509\) 43.6065 1.93283 0.966413 0.256994i \(-0.0827320\pi\)
0.966413 + 0.256994i \(0.0827320\pi\)
\(510\) 0 0
\(511\) 4.35385 0.192603
\(512\) 0 0
\(513\) −2.76410 −0.122038
\(514\) 0 0
\(515\) −5.09708 −0.224604
\(516\) 0 0
\(517\) −15.3333 −0.674359
\(518\) 0 0
\(519\) −7.71770 −0.338770
\(520\) 0 0
\(521\) −13.9841 −0.612656 −0.306328 0.951926i \(-0.599100\pi\)
−0.306328 + 0.951926i \(0.599100\pi\)
\(522\) 0 0
\(523\) 9.57656 0.418754 0.209377 0.977835i \(-0.432856\pi\)
0.209377 + 0.977835i \(0.432856\pi\)
\(524\) 0 0
\(525\) 1.50174 0.0655412
\(526\) 0 0
\(527\) 6.08163 0.264920
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 10.2440 0.444553
\(532\) 0 0
\(533\) 0.366014 0.0158538
\(534\) 0 0
\(535\) 48.6482 2.10325
\(536\) 0 0
\(537\) 3.03175 0.130830
\(538\) 0 0
\(539\) −25.6103 −1.10311
\(540\) 0 0
\(541\) −5.99859 −0.257899 −0.128950 0.991651i \(-0.541161\pi\)
−0.128950 + 0.991651i \(0.541161\pi\)
\(542\) 0 0
\(543\) 8.48454 0.364107
\(544\) 0 0
\(545\) −3.63121 −0.155544
\(546\) 0 0
\(547\) 18.8422 0.805633 0.402816 0.915281i \(-0.368031\pi\)
0.402816 + 0.915281i \(0.368031\pi\)
\(548\) 0 0
\(549\) 3.87008 0.165171
\(550\) 0 0
\(551\) −2.76410 −0.117755
\(552\) 0 0
\(553\) 1.68941 0.0718411
\(554\) 0 0
\(555\) −3.38585 −0.143721
\(556\) 0 0
\(557\) −42.0209 −1.78048 −0.890241 0.455490i \(-0.849464\pi\)
−0.890241 + 0.455490i \(0.849464\pi\)
\(558\) 0 0
\(559\) 0.242164 0.0102424
\(560\) 0 0
\(561\) −7.68509 −0.324465
\(562\) 0 0
\(563\) 13.5776 0.572226 0.286113 0.958196i \(-0.407637\pi\)
0.286113 + 0.958196i \(0.407637\pi\)
\(564\) 0 0
\(565\) −14.4188 −0.606605
\(566\) 0 0
\(567\) 0.556399 0.0233666
\(568\) 0 0
\(569\) −20.6650 −0.866321 −0.433161 0.901317i \(-0.642602\pi\)
−0.433161 + 0.901317i \(0.642602\pi\)
\(570\) 0 0
\(571\) 1.29913 0.0543671 0.0271835 0.999630i \(-0.491346\pi\)
0.0271835 + 0.999630i \(0.491346\pi\)
\(572\) 0 0
\(573\) 12.3424 0.515612
\(574\) 0 0
\(575\) 2.69903 0.112557
\(576\) 0 0
\(577\) 27.5948 1.14879 0.574393 0.818580i \(-0.305238\pi\)
0.574393 + 0.818580i \(0.305238\pi\)
\(578\) 0 0
\(579\) −14.4947 −0.602381
\(580\) 0 0
\(581\) 6.95844 0.288685
\(582\) 0 0
\(583\) −13.0171 −0.539112
\(584\) 0 0
\(585\) 0.152512 0.00630561
\(586\) 0 0
\(587\) −4.30710 −0.177773 −0.0888865 0.996042i \(-0.528331\pi\)
−0.0888865 + 0.996042i \(0.528331\pi\)
\(588\) 0 0
\(589\) 8.37310 0.345007
\(590\) 0 0
\(591\) 6.96683 0.286577
\(592\) 0 0
\(593\) 22.7594 0.934616 0.467308 0.884094i \(-0.345224\pi\)
0.467308 + 0.884094i \(0.345224\pi\)
\(594\) 0 0
\(595\) 3.09950 0.127067
\(596\) 0 0
\(597\) −12.4386 −0.509078
\(598\) 0 0
\(599\) 33.7658 1.37963 0.689817 0.723984i \(-0.257691\pi\)
0.689817 + 0.723984i \(0.257691\pi\)
\(600\) 0 0
\(601\) −26.4457 −1.07874 −0.539372 0.842068i \(-0.681338\pi\)
−0.539372 + 0.842068i \(0.681338\pi\)
\(602\) 0 0
\(603\) −0.00393019 −0.000160050 0
\(604\) 0 0
\(605\) −10.1356 −0.412073
\(606\) 0 0
\(607\) 5.95175 0.241574 0.120787 0.992678i \(-0.461458\pi\)
0.120787 + 0.992678i \(0.461458\pi\)
\(608\) 0 0
\(609\) 0.556399 0.0225464
\(610\) 0 0
\(611\) 0.220172 0.00890720
\(612\) 0 0
\(613\) 25.2789 1.02101 0.510503 0.859876i \(-0.329459\pi\)
0.510503 + 0.859876i \(0.329459\pi\)
\(614\) 0 0
\(615\) 18.4769 0.745060
\(616\) 0 0
\(617\) 41.6316 1.67603 0.838013 0.545650i \(-0.183717\pi\)
0.838013 + 0.545650i \(0.183717\pi\)
\(618\) 0 0
\(619\) 34.9531 1.40488 0.702442 0.711741i \(-0.252093\pi\)
0.702442 + 0.711741i \(0.252093\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −8.46586 −0.339177
\(624\) 0 0
\(625\) −31.2104 −1.24842
\(626\) 0 0
\(627\) −10.5807 −0.422553
\(628\) 0 0
\(629\) −2.44984 −0.0976815
\(630\) 0 0
\(631\) −3.25055 −0.129402 −0.0647012 0.997905i \(-0.520609\pi\)
−0.0647012 + 0.997905i \(0.520609\pi\)
\(632\) 0 0
\(633\) −8.83834 −0.351292
\(634\) 0 0
\(635\) 34.3199 1.36195
\(636\) 0 0
\(637\) 0.367739 0.0145704
\(638\) 0 0
\(639\) −3.59047 −0.142037
\(640\) 0 0
\(641\) −8.69172 −0.343302 −0.171651 0.985158i \(-0.554910\pi\)
−0.171651 + 0.985158i \(0.554910\pi\)
\(642\) 0 0
\(643\) 8.15011 0.321409 0.160704 0.987003i \(-0.448623\pi\)
0.160704 + 0.987003i \(0.448623\pi\)
\(644\) 0 0
\(645\) 12.2248 0.481350
\(646\) 0 0
\(647\) −8.14432 −0.320186 −0.160093 0.987102i \(-0.551179\pi\)
−0.160093 + 0.987102i \(0.551179\pi\)
\(648\) 0 0
\(649\) 39.2132 1.53925
\(650\) 0 0
\(651\) −1.68546 −0.0660584
\(652\) 0 0
\(653\) −26.1352 −1.02275 −0.511376 0.859357i \(-0.670864\pi\)
−0.511376 + 0.859357i \(0.670864\pi\)
\(654\) 0 0
\(655\) 16.2080 0.633298
\(656\) 0 0
\(657\) 7.82504 0.305284
\(658\) 0 0
\(659\) −25.3965 −0.989307 −0.494653 0.869090i \(-0.664705\pi\)
−0.494653 + 0.869090i \(0.664705\pi\)
\(660\) 0 0
\(661\) −8.48368 −0.329977 −0.164988 0.986296i \(-0.552759\pi\)
−0.164988 + 0.986296i \(0.552759\pi\)
\(662\) 0 0
\(663\) 0.110351 0.00428566
\(664\) 0 0
\(665\) 4.26735 0.165481
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) 3.52468 0.136272
\(670\) 0 0
\(671\) 14.8143 0.571900
\(672\) 0 0
\(673\) 33.8562 1.30506 0.652530 0.757763i \(-0.273708\pi\)
0.652530 + 0.757763i \(0.273708\pi\)
\(674\) 0 0
\(675\) 2.69903 0.103886
\(676\) 0 0
\(677\) −37.0178 −1.42271 −0.711356 0.702832i \(-0.751918\pi\)
−0.711356 + 0.702832i \(0.751918\pi\)
\(678\) 0 0
\(679\) −5.40390 −0.207383
\(680\) 0 0
\(681\) −19.7084 −0.755226
\(682\) 0 0
\(683\) −0.824117 −0.0315340 −0.0157670 0.999876i \(-0.505019\pi\)
−0.0157670 + 0.999876i \(0.505019\pi\)
\(684\) 0 0
\(685\) 6.36994 0.243383
\(686\) 0 0
\(687\) −8.86659 −0.338282
\(688\) 0 0
\(689\) 0.186913 0.00712081
\(690\) 0 0
\(691\) 6.23305 0.237116 0.118558 0.992947i \(-0.462173\pi\)
0.118558 + 0.992947i \(0.462173\pi\)
\(692\) 0 0
\(693\) 2.12984 0.0809060
\(694\) 0 0
\(695\) 22.1963 0.841953
\(696\) 0 0
\(697\) 13.3690 0.506387
\(698\) 0 0
\(699\) −8.26987 −0.312795
\(700\) 0 0
\(701\) 7.41067 0.279897 0.139949 0.990159i \(-0.455306\pi\)
0.139949 + 0.990159i \(0.455306\pi\)
\(702\) 0 0
\(703\) −3.37290 −0.127211
\(704\) 0 0
\(705\) 11.1146 0.418599
\(706\) 0 0
\(707\) 8.42812 0.316972
\(708\) 0 0
\(709\) 39.5048 1.48364 0.741818 0.670602i \(-0.233964\pi\)
0.741818 + 0.670602i \(0.233964\pi\)
\(710\) 0 0
\(711\) 3.03633 0.113871
\(712\) 0 0
\(713\) −3.02923 −0.113446
\(714\) 0 0
\(715\) 0.583803 0.0218330
\(716\) 0 0
\(717\) −25.2837 −0.944238
\(718\) 0 0
\(719\) 19.1065 0.712552 0.356276 0.934381i \(-0.384046\pi\)
0.356276 + 0.934381i \(0.384046\pi\)
\(720\) 0 0
\(721\) 1.02209 0.0380647
\(722\) 0 0
\(723\) 23.1164 0.859709
\(724\) 0 0
\(725\) 2.69903 0.100239
\(726\) 0 0
\(727\) 9.79292 0.363199 0.181600 0.983373i \(-0.441872\pi\)
0.181600 + 0.983373i \(0.441872\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 8.84526 0.327154
\(732\) 0 0
\(733\) −31.5855 −1.16664 −0.583319 0.812243i \(-0.698246\pi\)
−0.583319 + 0.812243i \(0.698246\pi\)
\(734\) 0 0
\(735\) 18.5640 0.684743
\(736\) 0 0
\(737\) −0.0150444 −0.000554168 0
\(738\) 0 0
\(739\) −12.3989 −0.456100 −0.228050 0.973649i \(-0.573235\pi\)
−0.228050 + 0.973649i \(0.573235\pi\)
\(740\) 0 0
\(741\) 0.151929 0.00558125
\(742\) 0 0
\(743\) 15.0421 0.551840 0.275920 0.961181i \(-0.411018\pi\)
0.275920 + 0.961181i \(0.411018\pi\)
\(744\) 0 0
\(745\) 21.4640 0.786380
\(746\) 0 0
\(747\) 12.5062 0.457578
\(748\) 0 0
\(749\) −9.75518 −0.356447
\(750\) 0 0
\(751\) −41.9261 −1.52991 −0.764953 0.644086i \(-0.777238\pi\)
−0.764953 + 0.644086i \(0.777238\pi\)
\(752\) 0 0
\(753\) −27.7022 −1.00952
\(754\) 0 0
\(755\) 41.5049 1.51052
\(756\) 0 0
\(757\) 22.7886 0.828266 0.414133 0.910216i \(-0.364085\pi\)
0.414133 + 0.910216i \(0.364085\pi\)
\(758\) 0 0
\(759\) 3.82791 0.138944
\(760\) 0 0
\(761\) 30.5620 1.10787 0.553935 0.832560i \(-0.313125\pi\)
0.553935 + 0.832560i \(0.313125\pi\)
\(762\) 0 0
\(763\) 0.728147 0.0263607
\(764\) 0 0
\(765\) 5.57065 0.201407
\(766\) 0 0
\(767\) −0.563064 −0.0203311
\(768\) 0 0
\(769\) −35.6392 −1.28518 −0.642591 0.766209i \(-0.722141\pi\)
−0.642591 + 0.766209i \(0.722141\pi\)
\(770\) 0 0
\(771\) 21.3254 0.768016
\(772\) 0 0
\(773\) 34.7781 1.25088 0.625441 0.780271i \(-0.284919\pi\)
0.625441 + 0.780271i \(0.284919\pi\)
\(774\) 0 0
\(775\) −8.17599 −0.293690
\(776\) 0 0
\(777\) 0.678947 0.0243571
\(778\) 0 0
\(779\) 18.4062 0.659471
\(780\) 0 0
\(781\) −13.7440 −0.491799
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) −28.7229 −1.02517
\(786\) 0 0
\(787\) 7.64623 0.272559 0.136279 0.990670i \(-0.456486\pi\)
0.136279 + 0.990670i \(0.456486\pi\)
\(788\) 0 0
\(789\) 14.6435 0.521322
\(790\) 0 0
\(791\) 2.89134 0.102804
\(792\) 0 0
\(793\) −0.212719 −0.00755389
\(794\) 0 0
\(795\) 9.43561 0.334647
\(796\) 0 0
\(797\) −4.58525 −0.162418 −0.0812089 0.996697i \(-0.525878\pi\)
−0.0812089 + 0.996697i \(0.525878\pi\)
\(798\) 0 0
\(799\) 8.04198 0.284505
\(800\) 0 0
\(801\) −15.2154 −0.537611
\(802\) 0 0
\(803\) 29.9535 1.05704
\(804\) 0 0
\(805\) −1.54385 −0.0544135
\(806\) 0 0
\(807\) 7.19583 0.253305
\(808\) 0 0
\(809\) −50.7530 −1.78438 −0.892190 0.451660i \(-0.850832\pi\)
−0.892190 + 0.451660i \(0.850832\pi\)
\(810\) 0 0
\(811\) 33.6815 1.18272 0.591360 0.806408i \(-0.298591\pi\)
0.591360 + 0.806408i \(0.298591\pi\)
\(812\) 0 0
\(813\) −13.1008 −0.459463
\(814\) 0 0
\(815\) 35.7615 1.25267
\(816\) 0 0
\(817\) 12.1780 0.426055
\(818\) 0 0
\(819\) −0.0305825 −0.00106864
\(820\) 0 0
\(821\) −23.8622 −0.832797 −0.416399 0.909182i \(-0.636708\pi\)
−0.416399 + 0.909182i \(0.636708\pi\)
\(822\) 0 0
\(823\) 32.1028 1.11903 0.559516 0.828819i \(-0.310987\pi\)
0.559516 + 0.828819i \(0.310987\pi\)
\(824\) 0 0
\(825\) 10.3316 0.359701
\(826\) 0 0
\(827\) −16.9028 −0.587768 −0.293884 0.955841i \(-0.594948\pi\)
−0.293884 + 0.955841i \(0.594948\pi\)
\(828\) 0 0
\(829\) 5.70185 0.198034 0.0990168 0.995086i \(-0.468430\pi\)
0.0990168 + 0.995086i \(0.468430\pi\)
\(830\) 0 0
\(831\) 9.17284 0.318202
\(832\) 0 0
\(833\) 13.4320 0.465392
\(834\) 0 0
\(835\) −25.5335 −0.883622
\(836\) 0 0
\(837\) −3.02923 −0.104706
\(838\) 0 0
\(839\) 37.4186 1.29183 0.645917 0.763408i \(-0.276475\pi\)
0.645917 + 0.763408i \(0.276475\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 23.5095 0.809710
\(844\) 0 0
\(845\) 36.0629 1.24060
\(846\) 0 0
\(847\) 2.03245 0.0698358
\(848\) 0 0
\(849\) −33.2249 −1.14028
\(850\) 0 0
\(851\) 1.22025 0.0418297
\(852\) 0 0
\(853\) 53.9024 1.84558 0.922792 0.385298i \(-0.125901\pi\)
0.922792 + 0.385298i \(0.125901\pi\)
\(854\) 0 0
\(855\) 7.66958 0.262294
\(856\) 0 0
\(857\) 21.1594 0.722790 0.361395 0.932413i \(-0.382301\pi\)
0.361395 + 0.932413i \(0.382301\pi\)
\(858\) 0 0
\(859\) −7.49079 −0.255582 −0.127791 0.991801i \(-0.540789\pi\)
−0.127791 + 0.991801i \(0.540789\pi\)
\(860\) 0 0
\(861\) −3.70507 −0.126269
\(862\) 0 0
\(863\) −34.0074 −1.15763 −0.578813 0.815460i \(-0.696484\pi\)
−0.578813 + 0.815460i \(0.696484\pi\)
\(864\) 0 0
\(865\) 21.4144 0.728112
\(866\) 0 0
\(867\) −12.9693 −0.440462
\(868\) 0 0
\(869\) 11.6228 0.394276
\(870\) 0 0
\(871\) 0.000216023 0 7.31967e−6 0
\(872\) 0 0
\(873\) −9.71227 −0.328711
\(874\) 0 0
\(875\) 3.55235 0.120091
\(876\) 0 0
\(877\) −4.02078 −0.135772 −0.0678860 0.997693i \(-0.521625\pi\)
−0.0678860 + 0.997693i \(0.521625\pi\)
\(878\) 0 0
\(879\) 10.7203 0.361587
\(880\) 0 0
\(881\) −46.1329 −1.55426 −0.777128 0.629343i \(-0.783324\pi\)
−0.777128 + 0.629343i \(0.783324\pi\)
\(882\) 0 0
\(883\) −7.94209 −0.267272 −0.133636 0.991030i \(-0.542665\pi\)
−0.133636 + 0.991030i \(0.542665\pi\)
\(884\) 0 0
\(885\) −28.4243 −0.955471
\(886\) 0 0
\(887\) −10.1411 −0.340505 −0.170252 0.985401i \(-0.554458\pi\)
−0.170252 + 0.985401i \(0.554458\pi\)
\(888\) 0 0
\(889\) −6.88200 −0.230815
\(890\) 0 0
\(891\) 3.82791 0.128240
\(892\) 0 0
\(893\) 11.0721 0.370513
\(894\) 0 0
\(895\) −8.41224 −0.281190
\(896\) 0 0
\(897\) −0.0549651 −0.00183523
\(898\) 0 0
\(899\) −3.02923 −0.101031
\(900\) 0 0
\(901\) 6.82716 0.227446
\(902\) 0 0
\(903\) −2.45137 −0.0815765
\(904\) 0 0
\(905\) −23.5422 −0.782568
\(906\) 0 0
\(907\) −11.1257 −0.369423 −0.184712 0.982793i \(-0.559135\pi\)
−0.184712 + 0.982793i \(0.559135\pi\)
\(908\) 0 0
\(909\) 15.1476 0.502415
\(910\) 0 0
\(911\) 28.3903 0.940613 0.470306 0.882503i \(-0.344143\pi\)
0.470306 + 0.882503i \(0.344143\pi\)
\(912\) 0 0
\(913\) 47.8726 1.58435
\(914\) 0 0
\(915\) −10.7384 −0.355000
\(916\) 0 0
\(917\) −3.25010 −0.107328
\(918\) 0 0
\(919\) 32.3739 1.06792 0.533958 0.845511i \(-0.320704\pi\)
0.533958 + 0.845511i \(0.320704\pi\)
\(920\) 0 0
\(921\) −19.2238 −0.633446
\(922\) 0 0
\(923\) 0.197351 0.00649587
\(924\) 0 0
\(925\) 3.29350 0.108290
\(926\) 0 0
\(927\) 1.83698 0.0603342
\(928\) 0 0
\(929\) −52.7456 −1.73053 −0.865264 0.501317i \(-0.832849\pi\)
−0.865264 + 0.501317i \(0.832849\pi\)
\(930\) 0 0
\(931\) 18.4930 0.606083
\(932\) 0 0
\(933\) 11.6337 0.380871
\(934\) 0 0
\(935\) 21.3239 0.697367
\(936\) 0 0
\(937\) 10.9498 0.357715 0.178857 0.983875i \(-0.442760\pi\)
0.178857 + 0.983875i \(0.442760\pi\)
\(938\) 0 0
\(939\) −18.2765 −0.596430
\(940\) 0 0
\(941\) 32.9537 1.07426 0.537130 0.843499i \(-0.319508\pi\)
0.537130 + 0.843499i \(0.319508\pi\)
\(942\) 0 0
\(943\) −6.65903 −0.216848
\(944\) 0 0
\(945\) −1.54385 −0.0502213
\(946\) 0 0
\(947\) 2.12566 0.0690746 0.0345373 0.999403i \(-0.489004\pi\)
0.0345373 + 0.999403i \(0.489004\pi\)
\(948\) 0 0
\(949\) −0.430104 −0.0139618
\(950\) 0 0
\(951\) −32.0811 −1.04030
\(952\) 0 0
\(953\) 37.8431 1.22586 0.612929 0.790138i \(-0.289991\pi\)
0.612929 + 0.790138i \(0.289991\pi\)
\(954\) 0 0
\(955\) −34.2467 −1.10820
\(956\) 0 0
\(957\) 3.82791 0.123739
\(958\) 0 0
\(959\) −1.27733 −0.0412472
\(960\) 0 0
\(961\) −21.8238 −0.703992
\(962\) 0 0
\(963\) −17.5327 −0.564984
\(964\) 0 0
\(965\) 40.2187 1.29469
\(966\) 0 0
\(967\) 26.9996 0.868249 0.434125 0.900853i \(-0.357058\pi\)
0.434125 + 0.900853i \(0.357058\pi\)
\(968\) 0 0
\(969\) 5.54934 0.178271
\(970\) 0 0
\(971\) 11.3380 0.363855 0.181928 0.983312i \(-0.441766\pi\)
0.181928 + 0.983312i \(0.441766\pi\)
\(972\) 0 0
\(973\) −4.45090 −0.142689
\(974\) 0 0
\(975\) −0.148352 −0.00475108
\(976\) 0 0
\(977\) −17.5348 −0.560988 −0.280494 0.959856i \(-0.590498\pi\)
−0.280494 + 0.959856i \(0.590498\pi\)
\(978\) 0 0
\(979\) −58.2433 −1.86146
\(980\) 0 0
\(981\) 1.30868 0.0417829
\(982\) 0 0
\(983\) 33.8666 1.08018 0.540088 0.841609i \(-0.318391\pi\)
0.540088 + 0.841609i \(0.318391\pi\)
\(984\) 0 0
\(985\) −19.3309 −0.615935
\(986\) 0 0
\(987\) −2.22875 −0.0709419
\(988\) 0 0
\(989\) −4.40578 −0.140096
\(990\) 0 0
\(991\) −3.41219 −0.108392 −0.0541959 0.998530i \(-0.517260\pi\)
−0.0541959 + 0.998530i \(0.517260\pi\)
\(992\) 0 0
\(993\) −19.6188 −0.622585
\(994\) 0 0
\(995\) 34.5136 1.09415
\(996\) 0 0
\(997\) −48.0159 −1.52068 −0.760340 0.649525i \(-0.774968\pi\)
−0.760340 + 0.649525i \(0.774968\pi\)
\(998\) 0 0
\(999\) 1.22025 0.0386071
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 \(a_p\))