Properties

Label 8048.2.a.v.1.21
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.21
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.72455 q^{3} +0.586565 q^{5} +2.46074 q^{7} -0.0259209 q^{9} +O(q^{10})\) \(q+1.72455 q^{3} +0.586565 q^{5} +2.46074 q^{7} -0.0259209 q^{9} -2.73095 q^{11} +1.16422 q^{13} +1.01156 q^{15} -3.49409 q^{17} -5.19009 q^{19} +4.24367 q^{21} +1.89484 q^{23} -4.65594 q^{25} -5.21836 q^{27} -3.57220 q^{29} +1.26340 q^{31} -4.70966 q^{33} +1.44338 q^{35} +10.5540 q^{37} +2.00775 q^{39} -4.19222 q^{41} -8.57566 q^{43} -0.0152043 q^{45} -4.29383 q^{47} -0.944777 q^{49} -6.02575 q^{51} -6.91443 q^{53} -1.60188 q^{55} -8.95058 q^{57} +6.43780 q^{59} +5.28560 q^{61} -0.0637845 q^{63} +0.682888 q^{65} -7.31785 q^{67} +3.26775 q^{69} +10.9984 q^{71} -5.43906 q^{73} -8.02941 q^{75} -6.72014 q^{77} -14.0308 q^{79} -8.92157 q^{81} +3.03277 q^{83} -2.04951 q^{85} -6.16044 q^{87} +10.3363 q^{89} +2.86483 q^{91} +2.17879 q^{93} -3.04433 q^{95} -13.9082 q^{97} +0.0707886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + 14q^{11} - 31q^{13} + 2q^{15} - 9q^{17} + 8q^{19} - 28q^{21} + 4q^{23} + 22q^{25} + 4q^{27} - 47q^{29} + 5q^{31} - 26q^{33} + 13q^{35} - 67q^{37} + 9q^{39} - 28q^{41} - 15q^{43} - 57q^{45} + 10q^{47} + 20q^{49} + 11q^{51} - 58q^{53} - 15q^{55} - 31q^{57} + 32q^{59} - 55q^{61} + 16q^{63} - 44q^{65} - 22q^{67} - 44q^{69} + 47q^{71} - 5q^{73} + 25q^{75} - 50q^{77} + 14q^{79} - 28q^{81} + 16q^{83} - 78q^{85} + 11q^{87} - 20q^{89} + 15q^{91} - 83q^{93} + 27q^{95} - 8q^{97} + 70q^{99} + O(q^{100}) \)

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
\(3\) 1.72455 0.995670 0.497835 0.867272i \(-0.334128\pi\)
0.497835 + 0.867272i \(0.334128\pi\)
\(4\) 0 0
\(5\) 0.586565 0.262320 0.131160 0.991361i \(-0.458130\pi\)
0.131160 + 0.991361i \(0.458130\pi\)
\(6\) 0 0
\(7\) 2.46074 0.930071 0.465035 0.885292i \(-0.346042\pi\)
0.465035 + 0.885292i \(0.346042\pi\)
\(8\) 0 0
\(9\) −0.0259209 −0.00864030
\(10\) 0 0
\(11\) −2.73095 −0.823412 −0.411706 0.911317i \(-0.635067\pi\)
−0.411706 + 0.911317i \(0.635067\pi\)
\(12\) 0 0
\(13\) 1.16422 0.322895 0.161448 0.986881i \(-0.448384\pi\)
0.161448 + 0.986881i \(0.448384\pi\)
\(14\) 0 0
\(15\) 1.01156 0.261184
\(16\) 0 0
\(17\) −3.49409 −0.847442 −0.423721 0.905793i \(-0.639276\pi\)
−0.423721 + 0.905793i \(0.639276\pi\)
\(18\) 0 0
\(19\) −5.19009 −1.19069 −0.595344 0.803471i \(-0.702984\pi\)
−0.595344 + 0.803471i \(0.702984\pi\)
\(20\) 0 0
\(21\) 4.24367 0.926044
\(22\) 0 0
\(23\) 1.89484 0.395101 0.197550 0.980293i \(-0.436701\pi\)
0.197550 + 0.980293i \(0.436701\pi\)
\(24\) 0 0
\(25\) −4.65594 −0.931188
\(26\) 0 0
\(27\) −5.21836 −1.00427
\(28\) 0 0
\(29\) −3.57220 −0.663340 −0.331670 0.943395i \(-0.607612\pi\)
−0.331670 + 0.943395i \(0.607612\pi\)
\(30\) 0 0
\(31\) 1.26340 0.226913 0.113456 0.993543i \(-0.463808\pi\)
0.113456 + 0.993543i \(0.463808\pi\)
\(32\) 0 0
\(33\) −4.70966 −0.819847
\(34\) 0 0
\(35\) 1.44338 0.243976
\(36\) 0 0
\(37\) 10.5540 1.73507 0.867535 0.497377i \(-0.165703\pi\)
0.867535 + 0.497377i \(0.165703\pi\)
\(38\) 0 0
\(39\) 2.00775 0.321497
\(40\) 0 0
\(41\) −4.19222 −0.654715 −0.327358 0.944901i \(-0.606158\pi\)
−0.327358 + 0.944901i \(0.606158\pi\)
\(42\) 0 0
\(43\) −8.57566 −1.30778 −0.653888 0.756591i \(-0.726863\pi\)
−0.653888 + 0.756591i \(0.726863\pi\)
\(44\) 0 0
\(45\) −0.0152043 −0.00226652
\(46\) 0 0
\(47\) −4.29383 −0.626319 −0.313160 0.949701i \(-0.601387\pi\)
−0.313160 + 0.949701i \(0.601387\pi\)
\(48\) 0 0
\(49\) −0.944777 −0.134968
\(50\) 0 0
\(51\) −6.02575 −0.843773
\(52\) 0 0
\(53\) −6.91443 −0.949771 −0.474885 0.880048i \(-0.657510\pi\)
−0.474885 + 0.880048i \(0.657510\pi\)
\(54\) 0 0
\(55\) −1.60188 −0.215997
\(56\) 0 0
\(57\) −8.95058 −1.18553
\(58\) 0 0
\(59\) 6.43780 0.838130 0.419065 0.907956i \(-0.362358\pi\)
0.419065 + 0.907956i \(0.362358\pi\)
\(60\) 0 0
\(61\) 5.28560 0.676752 0.338376 0.941011i \(-0.390123\pi\)
0.338376 + 0.941011i \(0.390123\pi\)
\(62\) 0 0
\(63\) −0.0637845 −0.00803609
\(64\) 0 0
\(65\) 0.682888 0.0847018
\(66\) 0 0
\(67\) −7.31785 −0.894017 −0.447009 0.894530i \(-0.647511\pi\)
−0.447009 + 0.894530i \(0.647511\pi\)
\(68\) 0 0
\(69\) 3.26775 0.393390
\(70\) 0 0
\(71\) 10.9984 1.30528 0.652638 0.757670i \(-0.273662\pi\)
0.652638 + 0.757670i \(0.273662\pi\)
\(72\) 0 0
\(73\) −5.43906 −0.636593 −0.318297 0.947991i \(-0.603111\pi\)
−0.318297 + 0.947991i \(0.603111\pi\)
\(74\) 0 0
\(75\) −8.02941 −0.927157
\(76\) 0 0
\(77\) −6.72014 −0.765831
\(78\) 0 0
\(79\) −14.0308 −1.57859 −0.789296 0.614013i \(-0.789554\pi\)
−0.789296 + 0.614013i \(0.789554\pi\)
\(80\) 0 0
\(81\) −8.92157 −0.991285
\(82\) 0 0
\(83\) 3.03277 0.332890 0.166445 0.986051i \(-0.446771\pi\)
0.166445 + 0.986051i \(0.446771\pi\)
\(84\) 0 0
\(85\) −2.04951 −0.222301
\(86\) 0 0
\(87\) −6.16044 −0.660468
\(88\) 0 0
\(89\) 10.3363 1.09565 0.547823 0.836594i \(-0.315457\pi\)
0.547823 + 0.836594i \(0.315457\pi\)
\(90\) 0 0
\(91\) 2.86483 0.300316
\(92\) 0 0
\(93\) 2.17879 0.225930
\(94\) 0 0
\(95\) −3.04433 −0.312341
\(96\) 0 0
\(97\) −13.9082 −1.41216 −0.706082 0.708130i \(-0.749539\pi\)
−0.706082 + 0.708130i \(0.749539\pi\)
\(98\) 0 0
\(99\) 0.0707886 0.00711452
\(100\) 0 0
\(101\) −5.02750 −0.500255 −0.250127 0.968213i \(-0.580473\pi\)
−0.250127 + 0.968213i \(0.580473\pi\)
\(102\) 0 0
\(103\) 0.956492 0.0942459 0.0471230 0.998889i \(-0.484995\pi\)
0.0471230 + 0.998889i \(0.484995\pi\)
\(104\) 0 0
\(105\) 2.48919 0.242920
\(106\) 0 0
\(107\) −11.9511 −1.15536 −0.577680 0.816263i \(-0.696042\pi\)
−0.577680 + 0.816263i \(0.696042\pi\)
\(108\) 0 0
\(109\) −14.1910 −1.35925 −0.679625 0.733559i \(-0.737858\pi\)
−0.679625 + 0.733559i \(0.737858\pi\)
\(110\) 0 0
\(111\) 18.2009 1.72756
\(112\) 0 0
\(113\) 7.20506 0.677795 0.338898 0.940823i \(-0.389946\pi\)
0.338898 + 0.940823i \(0.389946\pi\)
\(114\) 0 0
\(115\) 1.11145 0.103643
\(116\) 0 0
\(117\) −0.0301775 −0.00278991
\(118\) 0 0
\(119\) −8.59804 −0.788181
\(120\) 0 0
\(121\) −3.54193 −0.321993
\(122\) 0 0
\(123\) −7.22970 −0.651880
\(124\) 0 0
\(125\) −5.66384 −0.506589
\(126\) 0 0
\(127\) 18.2133 1.61617 0.808083 0.589068i \(-0.200505\pi\)
0.808083 + 0.589068i \(0.200505\pi\)
\(128\) 0 0
\(129\) −14.7892 −1.30211
\(130\) 0 0
\(131\) −4.72366 −0.412708 −0.206354 0.978477i \(-0.566160\pi\)
−0.206354 + 0.978477i \(0.566160\pi\)
\(132\) 0 0
\(133\) −12.7714 −1.10742
\(134\) 0 0
\(135\) −3.06091 −0.263441
\(136\) 0 0
\(137\) 1.70038 0.145274 0.0726368 0.997358i \(-0.476859\pi\)
0.0726368 + 0.997358i \(0.476859\pi\)
\(138\) 0 0
\(139\) 7.89107 0.669312 0.334656 0.942340i \(-0.391380\pi\)
0.334656 + 0.942340i \(0.391380\pi\)
\(140\) 0 0
\(141\) −7.40493 −0.623607
\(142\) 0 0
\(143\) −3.17941 −0.265876
\(144\) 0 0
\(145\) −2.09533 −0.174007
\(146\) 0 0
\(147\) −1.62932 −0.134384
\(148\) 0 0
\(149\) −6.70406 −0.549218 −0.274609 0.961556i \(-0.588548\pi\)
−0.274609 + 0.961556i \(0.588548\pi\)
\(150\) 0 0
\(151\) 21.7904 1.77328 0.886639 0.462461i \(-0.153034\pi\)
0.886639 + 0.462461i \(0.153034\pi\)
\(152\) 0 0
\(153\) 0.0905700 0.00732215
\(154\) 0 0
\(155\) 0.741065 0.0595238
\(156\) 0 0
\(157\) −7.49521 −0.598183 −0.299091 0.954224i \(-0.596684\pi\)
−0.299091 + 0.954224i \(0.596684\pi\)
\(158\) 0 0
\(159\) −11.9243 −0.945659
\(160\) 0 0
\(161\) 4.66270 0.367472
\(162\) 0 0
\(163\) −5.50736 −0.431370 −0.215685 0.976463i \(-0.569198\pi\)
−0.215685 + 0.976463i \(0.569198\pi\)
\(164\) 0 0
\(165\) −2.76252 −0.215062
\(166\) 0 0
\(167\) −4.04783 −0.313231 −0.156615 0.987660i \(-0.550058\pi\)
−0.156615 + 0.987660i \(0.550058\pi\)
\(168\) 0 0
\(169\) −11.6446 −0.895739
\(170\) 0 0
\(171\) 0.134532 0.0102879
\(172\) 0 0
\(173\) 4.84897 0.368660 0.184330 0.982864i \(-0.440988\pi\)
0.184330 + 0.982864i \(0.440988\pi\)
\(174\) 0 0
\(175\) −11.4570 −0.866071
\(176\) 0 0
\(177\) 11.1023 0.834501
\(178\) 0 0
\(179\) 15.0476 1.12471 0.562357 0.826895i \(-0.309895\pi\)
0.562357 + 0.826895i \(0.309895\pi\)
\(180\) 0 0
\(181\) −4.49535 −0.334137 −0.167068 0.985945i \(-0.553430\pi\)
−0.167068 + 0.985945i \(0.553430\pi\)
\(182\) 0 0
\(183\) 9.11529 0.673822
\(184\) 0 0
\(185\) 6.19061 0.455143
\(186\) 0 0
\(187\) 9.54219 0.697794
\(188\) 0 0
\(189\) −12.8410 −0.934045
\(190\) 0 0
\(191\) 5.54219 0.401019 0.200509 0.979692i \(-0.435740\pi\)
0.200509 + 0.979692i \(0.435740\pi\)
\(192\) 0 0
\(193\) −5.32231 −0.383108 −0.191554 0.981482i \(-0.561353\pi\)
−0.191554 + 0.981482i \(0.561353\pi\)
\(194\) 0 0
\(195\) 1.17768 0.0843351
\(196\) 0 0
\(197\) −1.75087 −0.124744 −0.0623722 0.998053i \(-0.519867\pi\)
−0.0623722 + 0.998053i \(0.519867\pi\)
\(198\) 0 0
\(199\) −5.09739 −0.361344 −0.180672 0.983543i \(-0.557827\pi\)
−0.180672 + 0.983543i \(0.557827\pi\)
\(200\) 0 0
\(201\) −12.6200 −0.890147
\(202\) 0 0
\(203\) −8.79023 −0.616953
\(204\) 0 0
\(205\) −2.45901 −0.171745
\(206\) 0 0
\(207\) −0.0491159 −0.00341379
\(208\) 0 0
\(209\) 14.1739 0.980427
\(210\) 0 0
\(211\) 8.28571 0.570412 0.285206 0.958466i \(-0.407938\pi\)
0.285206 + 0.958466i \(0.407938\pi\)
\(212\) 0 0
\(213\) 18.9674 1.29962
\(214\) 0 0
\(215\) −5.03018 −0.343056
\(216\) 0 0
\(217\) 3.10889 0.211045
\(218\) 0 0
\(219\) −9.37993 −0.633837
\(220\) 0 0
\(221\) −4.06788 −0.273635
\(222\) 0 0
\(223\) −21.0134 −1.40716 −0.703582 0.710614i \(-0.748417\pi\)
−0.703582 + 0.710614i \(0.748417\pi\)
\(224\) 0 0
\(225\) 0.120686 0.00804575
\(226\) 0 0
\(227\) 22.5965 1.49978 0.749890 0.661563i \(-0.230107\pi\)
0.749890 + 0.661563i \(0.230107\pi\)
\(228\) 0 0
\(229\) −7.06526 −0.466886 −0.233443 0.972371i \(-0.574999\pi\)
−0.233443 + 0.972371i \(0.574999\pi\)
\(230\) 0 0
\(231\) −11.5892 −0.762515
\(232\) 0 0
\(233\) −7.68241 −0.503291 −0.251646 0.967819i \(-0.580972\pi\)
−0.251646 + 0.967819i \(0.580972\pi\)
\(234\) 0 0
\(235\) −2.51861 −0.164296
\(236\) 0 0
\(237\) −24.1969 −1.57176
\(238\) 0 0
\(239\) 0.669531 0.0433084 0.0216542 0.999766i \(-0.493107\pi\)
0.0216542 + 0.999766i \(0.493107\pi\)
\(240\) 0 0
\(241\) −10.6397 −0.685361 −0.342681 0.939452i \(-0.611335\pi\)
−0.342681 + 0.939452i \(0.611335\pi\)
\(242\) 0 0
\(243\) 0.269370 0.0172801
\(244\) 0 0
\(245\) −0.554173 −0.0354048
\(246\) 0 0
\(247\) −6.04239 −0.384468
\(248\) 0 0
\(249\) 5.23017 0.331449
\(250\) 0 0
\(251\) 19.5023 1.23097 0.615486 0.788148i \(-0.288960\pi\)
0.615486 + 0.788148i \(0.288960\pi\)
\(252\) 0 0
\(253\) −5.17470 −0.325331
\(254\) 0 0
\(255\) −3.53449 −0.221338
\(256\) 0 0
\(257\) −7.55107 −0.471023 −0.235511 0.971872i \(-0.575677\pi\)
−0.235511 + 0.971872i \(0.575677\pi\)
\(258\) 0 0
\(259\) 25.9706 1.61374
\(260\) 0 0
\(261\) 0.0925945 0.00573146
\(262\) 0 0
\(263\) 22.6613 1.39736 0.698679 0.715435i \(-0.253772\pi\)
0.698679 + 0.715435i \(0.253772\pi\)
\(264\) 0 0
\(265\) −4.05576 −0.249144
\(266\) 0 0
\(267\) 17.8255 1.09090
\(268\) 0 0
\(269\) 6.83876 0.416966 0.208483 0.978026i \(-0.433147\pi\)
0.208483 + 0.978026i \(0.433147\pi\)
\(270\) 0 0
\(271\) 19.9514 1.21196 0.605980 0.795480i \(-0.292781\pi\)
0.605980 + 0.795480i \(0.292781\pi\)
\(272\) 0 0
\(273\) 4.94054 0.299015
\(274\) 0 0
\(275\) 12.7151 0.766751
\(276\) 0 0
\(277\) 17.8769 1.07412 0.537061 0.843544i \(-0.319535\pi\)
0.537061 + 0.843544i \(0.319535\pi\)
\(278\) 0 0
\(279\) −0.0327484 −0.00196060
\(280\) 0 0
\(281\) 15.2940 0.912361 0.456180 0.889887i \(-0.349217\pi\)
0.456180 + 0.889887i \(0.349217\pi\)
\(282\) 0 0
\(283\) −27.2471 −1.61967 −0.809837 0.586654i \(-0.800445\pi\)
−0.809837 + 0.586654i \(0.800445\pi\)
\(284\) 0 0
\(285\) −5.25010 −0.310989
\(286\) 0 0
\(287\) −10.3160 −0.608931
\(288\) 0 0
\(289\) −4.79131 −0.281842
\(290\) 0 0
\(291\) −23.9854 −1.40605
\(292\) 0 0
\(293\) −14.2949 −0.835117 −0.417559 0.908650i \(-0.637114\pi\)
−0.417559 + 0.908650i \(0.637114\pi\)
\(294\) 0 0
\(295\) 3.77619 0.219858
\(296\) 0 0
\(297\) 14.2511 0.826930
\(298\) 0 0
\(299\) 2.20600 0.127576
\(300\) 0 0
\(301\) −21.1024 −1.21632
\(302\) 0 0
\(303\) −8.67018 −0.498089
\(304\) 0 0
\(305\) 3.10035 0.177525
\(306\) 0 0
\(307\) −0.433862 −0.0247618 −0.0123809 0.999923i \(-0.503941\pi\)
−0.0123809 + 0.999923i \(0.503941\pi\)
\(308\) 0 0
\(309\) 1.64952 0.0938379
\(310\) 0 0
\(311\) 5.50465 0.312140 0.156070 0.987746i \(-0.450117\pi\)
0.156070 + 0.987746i \(0.450117\pi\)
\(312\) 0 0
\(313\) −18.7781 −1.06140 −0.530700 0.847560i \(-0.678071\pi\)
−0.530700 + 0.847560i \(0.678071\pi\)
\(314\) 0 0
\(315\) −0.0374137 −0.00210803
\(316\) 0 0
\(317\) −29.3977 −1.65114 −0.825571 0.564299i \(-0.809147\pi\)
−0.825571 + 0.564299i \(0.809147\pi\)
\(318\) 0 0
\(319\) 9.75548 0.546202
\(320\) 0 0
\(321\) −20.6104 −1.15036
\(322\) 0 0
\(323\) 18.1347 1.00904
\(324\) 0 0
\(325\) −5.42052 −0.300676
\(326\) 0 0
\(327\) −24.4731 −1.35337
\(328\) 0 0
\(329\) −10.5660 −0.582521
\(330\) 0 0
\(331\) −22.6035 −1.24240 −0.621199 0.783653i \(-0.713354\pi\)
−0.621199 + 0.783653i \(0.713354\pi\)
\(332\) 0 0
\(333\) −0.273569 −0.0149915
\(334\) 0 0
\(335\) −4.29239 −0.234518
\(336\) 0 0
\(337\) 24.5776 1.33883 0.669413 0.742890i \(-0.266546\pi\)
0.669413 + 0.742890i \(0.266546\pi\)
\(338\) 0 0
\(339\) 12.4255 0.674861
\(340\) 0 0
\(341\) −3.45027 −0.186843
\(342\) 0 0
\(343\) −19.5500 −1.05560
\(344\) 0 0
\(345\) 1.91674 0.103194
\(346\) 0 0
\(347\) 9.24264 0.496171 0.248085 0.968738i \(-0.420199\pi\)
0.248085 + 0.968738i \(0.420199\pi\)
\(348\) 0 0
\(349\) 14.4660 0.774345 0.387172 0.922007i \(-0.373452\pi\)
0.387172 + 0.922007i \(0.373452\pi\)
\(350\) 0 0
\(351\) −6.07529 −0.324275
\(352\) 0 0
\(353\) 30.4697 1.62174 0.810869 0.585227i \(-0.198995\pi\)
0.810869 + 0.585227i \(0.198995\pi\)
\(354\) 0 0
\(355\) 6.45130 0.342400
\(356\) 0 0
\(357\) −14.8278 −0.784769
\(358\) 0 0
\(359\) 26.9934 1.42466 0.712329 0.701846i \(-0.247640\pi\)
0.712329 + 0.701846i \(0.247640\pi\)
\(360\) 0 0
\(361\) 7.93706 0.417740
\(362\) 0 0
\(363\) −6.10824 −0.320599
\(364\) 0 0
\(365\) −3.19036 −0.166991
\(366\) 0 0
\(367\) 16.3695 0.854481 0.427240 0.904138i \(-0.359486\pi\)
0.427240 + 0.904138i \(0.359486\pi\)
\(368\) 0 0
\(369\) 0.108666 0.00565693
\(370\) 0 0
\(371\) −17.0146 −0.883354
\(372\) 0 0
\(373\) 5.17472 0.267937 0.133968 0.990986i \(-0.457228\pi\)
0.133968 + 0.990986i \(0.457228\pi\)
\(374\) 0 0
\(375\) −9.76758 −0.504396
\(376\) 0 0
\(377\) −4.15881 −0.214189
\(378\) 0 0
\(379\) −2.38334 −0.122424 −0.0612120 0.998125i \(-0.519497\pi\)
−0.0612120 + 0.998125i \(0.519497\pi\)
\(380\) 0 0
\(381\) 31.4097 1.60917
\(382\) 0 0
\(383\) −13.5010 −0.689868 −0.344934 0.938627i \(-0.612099\pi\)
−0.344934 + 0.938627i \(0.612099\pi\)
\(384\) 0 0
\(385\) −3.94180 −0.200893
\(386\) 0 0
\(387\) 0.222289 0.0112996
\(388\) 0 0
\(389\) 3.97925 0.201756 0.100878 0.994899i \(-0.467835\pi\)
0.100878 + 0.994899i \(0.467835\pi\)
\(390\) 0 0
\(391\) −6.62074 −0.334825
\(392\) 0 0
\(393\) −8.14619 −0.410921
\(394\) 0 0
\(395\) −8.22999 −0.414096
\(396\) 0 0
\(397\) −38.2848 −1.92146 −0.960730 0.277485i \(-0.910499\pi\)
−0.960730 + 0.277485i \(0.910499\pi\)
\(398\) 0 0
\(399\) −22.0250 −1.10263
\(400\) 0 0
\(401\) −24.2381 −1.21039 −0.605196 0.796076i \(-0.706905\pi\)
−0.605196 + 0.796076i \(0.706905\pi\)
\(402\) 0 0
\(403\) 1.47087 0.0732691
\(404\) 0 0
\(405\) −5.23308 −0.260034
\(406\) 0 0
\(407\) −28.8225 −1.42868
\(408\) 0 0
\(409\) −3.53393 −0.174742 −0.0873708 0.996176i \(-0.527847\pi\)
−0.0873708 + 0.996176i \(0.527847\pi\)
\(410\) 0 0
\(411\) 2.93240 0.144645
\(412\) 0 0
\(413\) 15.8417 0.779520
\(414\) 0 0
\(415\) 1.77892 0.0873236
\(416\) 0 0
\(417\) 13.6086 0.666414
\(418\) 0 0
\(419\) −12.4382 −0.607648 −0.303824 0.952728i \(-0.598264\pi\)
−0.303824 + 0.952728i \(0.598264\pi\)
\(420\) 0 0
\(421\) −6.69903 −0.326491 −0.163245 0.986585i \(-0.552196\pi\)
−0.163245 + 0.986585i \(0.552196\pi\)
\(422\) 0 0
\(423\) 0.111300 0.00541158
\(424\) 0 0
\(425\) 16.2683 0.789128
\(426\) 0 0
\(427\) 13.0065 0.629427
\(428\) 0 0
\(429\) −5.48306 −0.264725
\(430\) 0 0
\(431\) 22.5674 1.08704 0.543518 0.839398i \(-0.317092\pi\)
0.543518 + 0.839398i \(0.317092\pi\)
\(432\) 0 0
\(433\) 4.92628 0.236742 0.118371 0.992969i \(-0.462233\pi\)
0.118371 + 0.992969i \(0.462233\pi\)
\(434\) 0 0
\(435\) −3.61350 −0.173254
\(436\) 0 0
\(437\) −9.83438 −0.470442
\(438\) 0 0
\(439\) 33.9326 1.61951 0.809757 0.586766i \(-0.199599\pi\)
0.809757 + 0.586766i \(0.199599\pi\)
\(440\) 0 0
\(441\) 0.0244895 0.00116617
\(442\) 0 0
\(443\) −5.72745 −0.272119 −0.136060 0.990701i \(-0.543444\pi\)
−0.136060 + 0.990701i \(0.543444\pi\)
\(444\) 0 0
\(445\) 6.06291 0.287410
\(446\) 0 0
\(447\) −11.5615 −0.546840
\(448\) 0 0
\(449\) −18.3283 −0.864964 −0.432482 0.901643i \(-0.642362\pi\)
−0.432482 + 0.901643i \(0.642362\pi\)
\(450\) 0 0
\(451\) 11.4487 0.539100
\(452\) 0 0
\(453\) 37.5787 1.76560
\(454\) 0 0
\(455\) 1.68041 0.0787787
\(456\) 0 0
\(457\) 16.5496 0.774158 0.387079 0.922047i \(-0.373484\pi\)
0.387079 + 0.922047i \(0.373484\pi\)
\(458\) 0 0
\(459\) 18.2334 0.851064
\(460\) 0 0
\(461\) −14.9454 −0.696078 −0.348039 0.937480i \(-0.613152\pi\)
−0.348039 + 0.937480i \(0.613152\pi\)
\(462\) 0 0
\(463\) 16.6853 0.775432 0.387716 0.921779i \(-0.373264\pi\)
0.387716 + 0.921779i \(0.373264\pi\)
\(464\) 0 0
\(465\) 1.27800 0.0592660
\(466\) 0 0
\(467\) 33.6476 1.55703 0.778513 0.627628i \(-0.215974\pi\)
0.778513 + 0.627628i \(0.215974\pi\)
\(468\) 0 0
\(469\) −18.0073 −0.831499
\(470\) 0 0
\(471\) −12.9259 −0.595593
\(472\) 0 0
\(473\) 23.4197 1.07684
\(474\) 0 0
\(475\) 24.1648 1.10876
\(476\) 0 0
\(477\) 0.179228 0.00820630
\(478\) 0 0
\(479\) −20.5030 −0.936807 −0.468404 0.883515i \(-0.655171\pi\)
−0.468404 + 0.883515i \(0.655171\pi\)
\(480\) 0 0
\(481\) 12.2871 0.560246
\(482\) 0 0
\(483\) 8.04106 0.365881
\(484\) 0 0
\(485\) −8.15806 −0.370439
\(486\) 0 0
\(487\) −5.73639 −0.259941 −0.129970 0.991518i \(-0.541488\pi\)
−0.129970 + 0.991518i \(0.541488\pi\)
\(488\) 0 0
\(489\) −9.49774 −0.429502
\(490\) 0 0
\(491\) 25.0417 1.13012 0.565059 0.825050i \(-0.308853\pi\)
0.565059 + 0.825050i \(0.308853\pi\)
\(492\) 0 0
\(493\) 12.4816 0.562143
\(494\) 0 0
\(495\) 0.0415221 0.00186628
\(496\) 0 0
\(497\) 27.0643 1.21400
\(498\) 0 0
\(499\) −17.0922 −0.765153 −0.382576 0.923924i \(-0.624963\pi\)
−0.382576 + 0.923924i \(0.624963\pi\)
\(500\) 0 0
\(501\) −6.98069 −0.311874
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −2.94896 −0.131227
\(506\) 0 0
\(507\) −20.0817 −0.891860
\(508\) 0 0
\(509\) −15.5830 −0.690705 −0.345352 0.938473i \(-0.612241\pi\)
−0.345352 + 0.938473i \(0.612241\pi\)
\(510\) 0 0
\(511\) −13.3841 −0.592077
\(512\) 0 0
\(513\) 27.0838 1.19578
\(514\) 0 0
\(515\) 0.561045 0.0247226
\(516\) 0 0
\(517\) 11.7262 0.515718
\(518\) 0 0
\(519\) 8.36230 0.367064
\(520\) 0 0
\(521\) −31.0136 −1.35873 −0.679364 0.733801i \(-0.737744\pi\)
−0.679364 + 0.733801i \(0.737744\pi\)
\(522\) 0 0
\(523\) 30.9567 1.35364 0.676821 0.736147i \(-0.263357\pi\)
0.676821 + 0.736147i \(0.263357\pi\)
\(524\) 0 0
\(525\) −19.7583 −0.862321
\(526\) 0 0
\(527\) −4.41443 −0.192296
\(528\) 0 0
\(529\) −19.4096 −0.843895
\(530\) 0 0
\(531\) −0.166873 −0.00724169
\(532\) 0 0
\(533\) −4.88065 −0.211404
\(534\) 0 0
\(535\) −7.01012 −0.303074
\(536\) 0 0
\(537\) 25.9504 1.11984
\(538\) 0 0
\(539\) 2.58014 0.111134
\(540\) 0 0
\(541\) −0.609236 −0.0261931 −0.0130965 0.999914i \(-0.504169\pi\)
−0.0130965 + 0.999914i \(0.504169\pi\)
\(542\) 0 0
\(543\) −7.75246 −0.332690
\(544\) 0 0
\(545\) −8.32394 −0.356558
\(546\) 0 0
\(547\) −12.2626 −0.524311 −0.262156 0.965026i \(-0.584433\pi\)
−0.262156 + 0.965026i \(0.584433\pi\)
\(548\) 0 0
\(549\) −0.137007 −0.00584734
\(550\) 0 0
\(551\) 18.5400 0.789832
\(552\) 0 0
\(553\) −34.5262 −1.46820
\(554\) 0 0
\(555\) 10.6760 0.453172
\(556\) 0 0
\(557\) 15.0967 0.639669 0.319834 0.947473i \(-0.396373\pi\)
0.319834 + 0.947473i \(0.396373\pi\)
\(558\) 0 0
\(559\) −9.98392 −0.422275
\(560\) 0 0
\(561\) 16.4560 0.694773
\(562\) 0 0
\(563\) −5.81953 −0.245264 −0.122632 0.992452i \(-0.539133\pi\)
−0.122632 + 0.992452i \(0.539133\pi\)
\(564\) 0 0
\(565\) 4.22624 0.177799
\(566\) 0 0
\(567\) −21.9536 −0.921965
\(568\) 0 0
\(569\) 0.581847 0.0243923 0.0121961 0.999926i \(-0.496118\pi\)
0.0121961 + 0.999926i \(0.496118\pi\)
\(570\) 0 0
\(571\) −35.9394 −1.50402 −0.752009 0.659153i \(-0.770915\pi\)
−0.752009 + 0.659153i \(0.770915\pi\)
\(572\) 0 0
\(573\) 9.55780 0.399283
\(574\) 0 0
\(575\) −8.82225 −0.367913
\(576\) 0 0
\(577\) 21.5868 0.898669 0.449335 0.893364i \(-0.351661\pi\)
0.449335 + 0.893364i \(0.351661\pi\)
\(578\) 0 0
\(579\) −9.17860 −0.381450
\(580\) 0 0
\(581\) 7.46285 0.309611
\(582\) 0 0
\(583\) 18.8830 0.782052
\(584\) 0 0
\(585\) −0.0177011 −0.000731849 0
\(586\) 0 0
\(587\) 0.825657 0.0340785 0.0170393 0.999855i \(-0.494576\pi\)
0.0170393 + 0.999855i \(0.494576\pi\)
\(588\) 0 0
\(589\) −6.55715 −0.270183
\(590\) 0 0
\(591\) −3.01947 −0.124204
\(592\) 0 0
\(593\) 0.459086 0.0188524 0.00942620 0.999956i \(-0.497000\pi\)
0.00942620 + 0.999956i \(0.497000\pi\)
\(594\) 0 0
\(595\) −5.04331 −0.206756
\(596\) 0 0
\(597\) −8.79071 −0.359780
\(598\) 0 0
\(599\) −27.5208 −1.12447 −0.562234 0.826978i \(-0.690058\pi\)
−0.562234 + 0.826978i \(0.690058\pi\)
\(600\) 0 0
\(601\) −23.4136 −0.955062 −0.477531 0.878615i \(-0.658468\pi\)
−0.477531 + 0.878615i \(0.658468\pi\)
\(602\) 0 0
\(603\) 0.189685 0.00772458
\(604\) 0 0
\(605\) −2.07757 −0.0844653
\(606\) 0 0
\(607\) −14.4146 −0.585070 −0.292535 0.956255i \(-0.594499\pi\)
−0.292535 + 0.956255i \(0.594499\pi\)
\(608\) 0 0
\(609\) −15.1592 −0.614282
\(610\) 0 0
\(611\) −4.99894 −0.202236
\(612\) 0 0
\(613\) −8.62924 −0.348532 −0.174266 0.984699i \(-0.555755\pi\)
−0.174266 + 0.984699i \(0.555755\pi\)
\(614\) 0 0
\(615\) −4.24069 −0.171001
\(616\) 0 0
\(617\) −28.5041 −1.14753 −0.573765 0.819020i \(-0.694518\pi\)
−0.573765 + 0.819020i \(0.694518\pi\)
\(618\) 0 0
\(619\) 20.8807 0.839266 0.419633 0.907694i \(-0.362159\pi\)
0.419633 + 0.907694i \(0.362159\pi\)
\(620\) 0 0
\(621\) −9.88794 −0.396789
\(622\) 0 0
\(623\) 25.4349 1.01903
\(624\) 0 0
\(625\) 19.9575 0.798300
\(626\) 0 0
\(627\) 24.4436 0.976182
\(628\) 0 0
\(629\) −36.8767 −1.47037
\(630\) 0 0
\(631\) −10.2528 −0.408157 −0.204078 0.978955i \(-0.565420\pi\)
−0.204078 + 0.978955i \(0.565420\pi\)
\(632\) 0 0
\(633\) 14.2891 0.567942
\(634\) 0 0
\(635\) 10.6833 0.423953
\(636\) 0 0
\(637\) −1.09992 −0.0435806
\(638\) 0 0
\(639\) −0.285090 −0.0112780
\(640\) 0 0
\(641\) −14.1573 −0.559181 −0.279591 0.960119i \(-0.590199\pi\)
−0.279591 + 0.960119i \(0.590199\pi\)
\(642\) 0 0
\(643\) −39.3320 −1.55110 −0.775551 0.631285i \(-0.782528\pi\)
−0.775551 + 0.631285i \(0.782528\pi\)
\(644\) 0 0
\(645\) −8.67481 −0.341570
\(646\) 0 0
\(647\) −46.4027 −1.82428 −0.912139 0.409881i \(-0.865570\pi\)
−0.912139 + 0.409881i \(0.865570\pi\)
\(648\) 0 0
\(649\) −17.5813 −0.690126
\(650\) 0 0
\(651\) 5.36144 0.210131
\(652\) 0 0
\(653\) 19.1450 0.749202 0.374601 0.927186i \(-0.377780\pi\)
0.374601 + 0.927186i \(0.377780\pi\)
\(654\) 0 0
\(655\) −2.77073 −0.108261
\(656\) 0 0
\(657\) 0.140985 0.00550036
\(658\) 0 0
\(659\) −2.37617 −0.0925623 −0.0462811 0.998928i \(-0.514737\pi\)
−0.0462811 + 0.998928i \(0.514737\pi\)
\(660\) 0 0
\(661\) 23.2340 0.903696 0.451848 0.892095i \(-0.350765\pi\)
0.451848 + 0.892095i \(0.350765\pi\)
\(662\) 0 0
\(663\) −7.01527 −0.272450
\(664\) 0 0
\(665\) −7.49128 −0.290499
\(666\) 0 0
\(667\) −6.76873 −0.262086
\(668\) 0 0
\(669\) −36.2388 −1.40107
\(670\) 0 0
\(671\) −14.4347 −0.557245
\(672\) 0 0
\(673\) 25.5526 0.984979 0.492489 0.870318i \(-0.336087\pi\)
0.492489 + 0.870318i \(0.336087\pi\)
\(674\) 0 0
\(675\) 24.2964 0.935168
\(676\) 0 0
\(677\) 24.0205 0.923182 0.461591 0.887093i \(-0.347279\pi\)
0.461591 + 0.887093i \(0.347279\pi\)
\(678\) 0 0
\(679\) −34.2244 −1.31341
\(680\) 0 0
\(681\) 38.9688 1.49329
\(682\) 0 0
\(683\) −21.8018 −0.834224 −0.417112 0.908855i \(-0.636958\pi\)
−0.417112 + 0.908855i \(0.636958\pi\)
\(684\) 0 0
\(685\) 0.997386 0.0381082
\(686\) 0 0
\(687\) −12.1844 −0.464864
\(688\) 0 0
\(689\) −8.04989 −0.306677
\(690\) 0 0
\(691\) −11.0933 −0.422008 −0.211004 0.977485i \(-0.567673\pi\)
−0.211004 + 0.977485i \(0.567673\pi\)
\(692\) 0 0
\(693\) 0.174192 0.00661701
\(694\) 0 0
\(695\) 4.62863 0.175574
\(696\) 0 0
\(697\) 14.6480 0.554833
\(698\) 0 0
\(699\) −13.2487 −0.501112
\(700\) 0 0
\(701\) 49.1729 1.85723 0.928617 0.371039i \(-0.120998\pi\)
0.928617 + 0.371039i \(0.120998\pi\)
\(702\) 0 0
\(703\) −54.7763 −2.06593
\(704\) 0 0
\(705\) −4.34347 −0.163585
\(706\) 0 0
\(707\) −12.3714 −0.465273
\(708\) 0 0
\(709\) −25.8276 −0.969975 −0.484987 0.874521i \(-0.661176\pi\)
−0.484987 + 0.874521i \(0.661176\pi\)
\(710\) 0 0
\(711\) 0.363692 0.0136395
\(712\) 0 0
\(713\) 2.39393 0.0896535
\(714\) 0 0
\(715\) −1.86493 −0.0697445
\(716\) 0 0
\(717\) 1.15464 0.0431209
\(718\) 0 0
\(719\) 1.62825 0.0607236 0.0303618 0.999539i \(-0.490334\pi\)
0.0303618 + 0.999539i \(0.490334\pi\)
\(720\) 0 0
\(721\) 2.35367 0.0876554
\(722\) 0 0
\(723\) −18.3487 −0.682394
\(724\) 0 0
\(725\) 16.6319 0.617695
\(726\) 0 0
\(727\) 38.4256 1.42513 0.712564 0.701607i \(-0.247534\pi\)
0.712564 + 0.701607i \(0.247534\pi\)
\(728\) 0 0
\(729\) 27.2292 1.00849
\(730\) 0 0
\(731\) 29.9642 1.10826
\(732\) 0 0
\(733\) 14.5046 0.535739 0.267870 0.963455i \(-0.413680\pi\)
0.267870 + 0.963455i \(0.413680\pi\)
\(734\) 0 0
\(735\) −0.955700 −0.0352515
\(736\) 0 0
\(737\) 19.9847 0.736144
\(738\) 0 0
\(739\) −35.2529 −1.29680 −0.648399 0.761300i \(-0.724561\pi\)
−0.648399 + 0.761300i \(0.724561\pi\)
\(740\) 0 0
\(741\) −10.4204 −0.382803
\(742\) 0 0
\(743\) 26.3936 0.968286 0.484143 0.874989i \(-0.339131\pi\)
0.484143 + 0.874989i \(0.339131\pi\)
\(744\) 0 0
\(745\) −3.93236 −0.144071
\(746\) 0 0
\(747\) −0.0786121 −0.00287627
\(748\) 0 0
\(749\) −29.4086 −1.07457
\(750\) 0 0
\(751\) −46.0714 −1.68117 −0.840585 0.541680i \(-0.817789\pi\)
−0.840585 + 0.541680i \(0.817789\pi\)
\(752\) 0 0
\(753\) 33.6327 1.22564
\(754\) 0 0
\(755\) 12.7815 0.465166
\(756\) 0 0
\(757\) 35.8348 1.30244 0.651219 0.758890i \(-0.274258\pi\)
0.651219 + 0.758890i \(0.274258\pi\)
\(758\) 0 0
\(759\) −8.92404 −0.323922
\(760\) 0 0
\(761\) 24.1420 0.875148 0.437574 0.899182i \(-0.355838\pi\)
0.437574 + 0.899182i \(0.355838\pi\)
\(762\) 0 0
\(763\) −34.9203 −1.26420
\(764\) 0 0
\(765\) 0.0531252 0.00192075
\(766\) 0 0
\(767\) 7.49499 0.270628
\(768\) 0 0
\(769\) 20.0154 0.721773 0.360887 0.932610i \(-0.382474\pi\)
0.360887 + 0.932610i \(0.382474\pi\)
\(770\) 0 0
\(771\) −13.0222 −0.468984
\(772\) 0 0
\(773\) 49.8719 1.79377 0.896884 0.442265i \(-0.145825\pi\)
0.896884 + 0.442265i \(0.145825\pi\)
\(774\) 0 0
\(775\) −5.88231 −0.211299
\(776\) 0 0
\(777\) 44.7877 1.60675
\(778\) 0 0
\(779\) 21.7580 0.779562
\(780\) 0 0
\(781\) −30.0362 −1.07478
\(782\) 0 0
\(783\) 18.6410 0.666175
\(784\) 0 0
\(785\) −4.39643 −0.156915
\(786\) 0 0
\(787\) −14.7252 −0.524895 −0.262447 0.964946i \(-0.584530\pi\)
−0.262447 + 0.964946i \(0.584530\pi\)
\(788\) 0 0
\(789\) 39.0806 1.39131
\(790\) 0 0
\(791\) 17.7298 0.630398
\(792\) 0 0
\(793\) 6.15358 0.218520
\(794\) 0 0
\(795\) −6.99438 −0.248065
\(796\) 0 0
\(797\) −19.4782 −0.689955 −0.344977 0.938611i \(-0.612113\pi\)
−0.344977 + 0.938611i \(0.612113\pi\)
\(798\) 0 0
\(799\) 15.0030 0.530769
\(800\) 0 0
\(801\) −0.267926 −0.00946671
\(802\) 0 0
\(803\) 14.8538 0.524178
\(804\) 0 0
\(805\) 2.73497 0.0963951
\(806\) 0 0
\(807\) 11.7938 0.415161
\(808\) 0 0
\(809\) −53.2703 −1.87288 −0.936442 0.350823i \(-0.885902\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(810\) 0 0
\(811\) −37.3268 −1.31072 −0.655360 0.755317i \(-0.727483\pi\)
−0.655360 + 0.755317i \(0.727483\pi\)
\(812\) 0 0
\(813\) 34.4072 1.20671
\(814\) 0 0
\(815\) −3.23043 −0.113157
\(816\) 0 0
\(817\) 44.5085 1.55715
\(818\) 0 0
\(819\) −0.0742589 −0.00259482
\(820\) 0 0
\(821\) 0.714503 0.0249363 0.0124682 0.999922i \(-0.496031\pi\)
0.0124682 + 0.999922i \(0.496031\pi\)
\(822\) 0 0
\(823\) −34.6220 −1.20685 −0.603424 0.797421i \(-0.706197\pi\)
−0.603424 + 0.797421i \(0.706197\pi\)
\(824\) 0 0
\(825\) 21.9279 0.763432
\(826\) 0 0
\(827\) −26.9252 −0.936281 −0.468141 0.883654i \(-0.655076\pi\)
−0.468141 + 0.883654i \(0.655076\pi\)
\(828\) 0 0
\(829\) 38.5396 1.33854 0.669268 0.743021i \(-0.266608\pi\)
0.669268 + 0.743021i \(0.266608\pi\)
\(830\) 0 0
\(831\) 30.8297 1.06947
\(832\) 0 0
\(833\) 3.30114 0.114378
\(834\) 0 0
\(835\) −2.37432 −0.0821666
\(836\) 0 0
\(837\) −6.59286 −0.227883
\(838\) 0 0
\(839\) 20.3261 0.701735 0.350868 0.936425i \(-0.385887\pi\)
0.350868 + 0.936425i \(0.385887\pi\)
\(840\) 0 0
\(841\) −16.2394 −0.559980
\(842\) 0 0
\(843\) 26.3752 0.908411
\(844\) 0 0
\(845\) −6.83031 −0.234970
\(846\) 0 0
\(847\) −8.71575 −0.299477
\(848\) 0 0
\(849\) −46.9891 −1.61266
\(850\) 0 0
\(851\) 19.9981 0.685527
\(852\) 0 0
\(853\) −18.6996 −0.640261 −0.320130 0.947373i \(-0.603727\pi\)
−0.320130 + 0.947373i \(0.603727\pi\)
\(854\) 0 0
\(855\) 0.0789117 0.00269872
\(856\) 0 0
\(857\) 58.1623 1.98679 0.993394 0.114754i \(-0.0366078\pi\)
0.993394 + 0.114754i \(0.0366078\pi\)
\(858\) 0 0
\(859\) −36.7245 −1.25302 −0.626512 0.779412i \(-0.715518\pi\)
−0.626512 + 0.779412i \(0.715518\pi\)
\(860\) 0 0
\(861\) −17.7904 −0.606295
\(862\) 0 0
\(863\) −14.8425 −0.505245 −0.252623 0.967565i \(-0.581293\pi\)
−0.252623 + 0.967565i \(0.581293\pi\)
\(864\) 0 0
\(865\) 2.84424 0.0967069
\(866\) 0 0
\(867\) −8.26286 −0.280621
\(868\) 0 0
\(869\) 38.3175 1.29983
\(870\) 0 0
\(871\) −8.51955 −0.288674
\(872\) 0 0
\(873\) 0.360513 0.0122015
\(874\) 0 0
\(875\) −13.9372 −0.471164
\(876\) 0 0
\(877\) −48.5667 −1.63998 −0.819990 0.572378i \(-0.806021\pi\)
−0.819990 + 0.572378i \(0.806021\pi\)
\(878\) 0 0
\(879\) −24.6523 −0.831502
\(880\) 0 0
\(881\) 27.4395 0.924459 0.462230 0.886760i \(-0.347050\pi\)
0.462230 + 0.886760i \(0.347050\pi\)
\(882\) 0 0
\(883\) −0.411016 −0.0138318 −0.00691590 0.999976i \(-0.502201\pi\)
−0.00691590 + 0.999976i \(0.502201\pi\)
\(884\) 0 0
\(885\) 6.51223 0.218906
\(886\) 0 0
\(887\) 22.5908 0.758524 0.379262 0.925289i \(-0.376178\pi\)
0.379262 + 0.925289i \(0.376178\pi\)
\(888\) 0 0
\(889\) 44.8181 1.50315
\(890\) 0 0
\(891\) 24.3643 0.816236
\(892\) 0 0
\(893\) 22.2854 0.745751
\(894\) 0 0
\(895\) 8.82642 0.295035
\(896\) 0 0
\(897\) 3.80436 0.127024
\(898\) 0 0
\(899\) −4.51310 −0.150520
\(900\) 0 0
\(901\) 24.1597 0.804876
\(902\) 0 0
\(903\) −36.3923 −1.21106
\(904\) 0 0
\(905\) −2.63681 −0.0876506
\(906\) 0 0
\(907\) 58.2378 1.93376 0.966878 0.255240i \(-0.0821545\pi\)
0.966878 + 0.255240i \(0.0821545\pi\)
\(908\) 0 0
\(909\) 0.130317 0.00432235
\(910\) 0 0
\(911\) 26.7074 0.884855 0.442428 0.896804i \(-0.354117\pi\)
0.442428 + 0.896804i \(0.354117\pi\)
\(912\) 0 0
\(913\) −8.28234 −0.274105
\(914\) 0 0
\(915\) 5.34671 0.176757
\(916\) 0 0
\(917\) −11.6237 −0.383847
\(918\) 0 0
\(919\) −4.37474 −0.144309 −0.0721546 0.997393i \(-0.522987\pi\)
−0.0721546 + 0.997393i \(0.522987\pi\)
\(920\) 0 0
\(921\) −0.748218 −0.0246546
\(922\) 0 0
\(923\) 12.8046 0.421467
\(924\) 0 0
\(925\) −49.1389 −1.61568
\(926\) 0 0
\(927\) −0.0247931 −0.000814313 0
\(928\) 0 0
\(929\) 44.5806 1.46264 0.731321 0.682034i \(-0.238904\pi\)
0.731321 + 0.682034i \(0.238904\pi\)
\(930\) 0 0
\(931\) 4.90348 0.160705
\(932\) 0 0
\(933\) 9.49305 0.310789
\(934\) 0 0
\(935\) 5.59711 0.183045
\(936\) 0 0
\(937\) −20.8335 −0.680601 −0.340301 0.940317i \(-0.610529\pi\)
−0.340301 + 0.940317i \(0.610529\pi\)
\(938\) 0 0
\(939\) −32.3838 −1.05680
\(940\) 0 0
\(941\) −24.6137 −0.802383 −0.401192 0.915994i \(-0.631404\pi\)
−0.401192 + 0.915994i \(0.631404\pi\)
\(942\) 0 0
\(943\) −7.94358 −0.258679
\(944\) 0 0
\(945\) −7.53208 −0.245019
\(946\) 0 0
\(947\) −20.2229 −0.657157 −0.328579 0.944477i \(-0.606570\pi\)
−0.328579 + 0.944477i \(0.606570\pi\)
\(948\) 0 0
\(949\) −6.33223 −0.205553
\(950\) 0 0
\(951\) −50.6979 −1.64399
\(952\) 0 0
\(953\) 4.43796 0.143760 0.0718799 0.997413i \(-0.477100\pi\)
0.0718799 + 0.997413i \(0.477100\pi\)
\(954\) 0 0
\(955\) 3.25086 0.105195
\(956\) 0 0
\(957\) 16.8238 0.543837
\(958\) 0 0
\(959\) 4.18420 0.135115
\(960\) 0 0
\(961\) −29.4038 −0.948511
\(962\) 0 0
\(963\) 0.309784 0.00998266
\(964\) 0 0
\(965\) −3.12188 −0.100497
\(966\) 0 0
\(967\) −33.5873 −1.08010 −0.540048 0.841634i \(-0.681594\pi\)
−0.540048 + 0.841634i \(0.681594\pi\)
\(968\) 0 0
\(969\) 31.2742 1.00467
\(970\) 0 0
\(971\) 59.7011 1.91590 0.957950 0.286934i \(-0.0926359\pi\)
0.957950 + 0.286934i \(0.0926359\pi\)
\(972\) 0 0
\(973\) 19.4179 0.622508
\(974\) 0 0
\(975\) −9.34797 −0.299375
\(976\) 0 0
\(977\) −45.5376 −1.45688 −0.728438 0.685112i \(-0.759753\pi\)
−0.728438 + 0.685112i \(0.759753\pi\)
\(978\) 0 0
\(979\) −28.2279 −0.902167
\(980\) 0 0
\(981\) 0.367843 0.0117443
\(982\) 0 0
\(983\) −28.5375 −0.910206 −0.455103 0.890439i \(-0.650398\pi\)
−0.455103 + 0.890439i \(0.650398\pi\)
\(984\) 0 0
\(985\) −1.02700 −0.0327229
\(986\) 0 0
\(987\) −18.2216 −0.579999
\(988\) 0 0
\(989\) −16.2495 −0.516704
\(990\) 0 0
\(991\) 42.9458 1.36422 0.682109 0.731251i \(-0.261063\pi\)
0.682109 + 0.731251i \(0.261063\pi\)
\(992\) 0 0
\(993\) −38.9808 −1.23702
\(994\) 0 0
\(995\) −2.98995 −0.0947877
\(996\) 0 0
\(997\) −20.5938 −0.652212 −0.326106 0.945333i \(-0.605737\pi\)
−0.326106 + 0.945333i \(0.605737\pi\)
\(998\) 0 0
\(999\) −55.0746 −1.74248
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 \(a_p\))