Properties

Label 8020.2.a.c.1.24
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.24
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.32475 q^{3} -1.00000 q^{5} -2.44792 q^{7} +2.40447 q^{9} +O(q^{10})\) \(q+2.32475 q^{3} -1.00000 q^{5} -2.44792 q^{7} +2.40447 q^{9} -5.19969 q^{11} +2.45589 q^{13} -2.32475 q^{15} +3.30408 q^{17} +7.37799 q^{19} -5.69080 q^{21} -2.41239 q^{23} +1.00000 q^{25} -1.38446 q^{27} -0.883029 q^{29} -0.774173 q^{31} -12.0880 q^{33} +2.44792 q^{35} -3.11454 q^{37} +5.70933 q^{39} +11.0899 q^{41} -7.16054 q^{43} -2.40447 q^{45} +5.67529 q^{47} -1.00771 q^{49} +7.68117 q^{51} -10.4209 q^{53} +5.19969 q^{55} +17.1520 q^{57} -8.65032 q^{59} -11.8162 q^{61} -5.88594 q^{63} -2.45589 q^{65} +7.03182 q^{67} -5.60822 q^{69} -7.87312 q^{71} +8.30031 q^{73} +2.32475 q^{75} +12.7284 q^{77} -12.0439 q^{79} -10.4319 q^{81} -4.17482 q^{83} -3.30408 q^{85} -2.05282 q^{87} -9.39112 q^{89} -6.01181 q^{91} -1.79976 q^{93} -7.37799 q^{95} -16.7742 q^{97} -12.5025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + O(q^{10}) \) \( 28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + 2q^{11} + 3q^{13} - 3q^{15} - 10q^{17} - 2q^{19} - 12q^{21} - 23q^{23} + 28q^{25} + 9q^{27} - 37q^{29} - 11q^{31} + 2q^{33} + 4q^{35} - 3q^{37} - 19q^{39} - 30q^{41} + 13q^{43} - 17q^{45} - 15q^{47} + 12q^{49} - 8q^{51} - 35q^{53} - 2q^{55} - 22q^{57} - q^{59} - 33q^{61} - 20q^{63} - 3q^{65} + 19q^{67} - 8q^{69} - 31q^{71} + 31q^{73} + 3q^{75} - 42q^{77} - 29q^{79} - 36q^{81} + 14q^{83} + 10q^{85} - 32q^{87} - 32q^{89} - 7q^{91} - 11q^{93} + 2q^{95} + 2q^{97} - 39q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.32475 1.34220 0.671098 0.741369i \(-0.265823\pi\)
0.671098 + 0.741369i \(0.265823\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.44792 −0.925225 −0.462612 0.886561i \(-0.653088\pi\)
−0.462612 + 0.886561i \(0.653088\pi\)
\(8\) 0 0
\(9\) 2.40447 0.801490
\(10\) 0 0
\(11\) −5.19969 −1.56777 −0.783883 0.620909i \(-0.786764\pi\)
−0.783883 + 0.620909i \(0.786764\pi\)
\(12\) 0 0
\(13\) 2.45589 0.681141 0.340571 0.940219i \(-0.389380\pi\)
0.340571 + 0.940219i \(0.389380\pi\)
\(14\) 0 0
\(15\) −2.32475 −0.600248
\(16\) 0 0
\(17\) 3.30408 0.801357 0.400679 0.916219i \(-0.368774\pi\)
0.400679 + 0.916219i \(0.368774\pi\)
\(18\) 0 0
\(19\) 7.37799 1.69263 0.846313 0.532685i \(-0.178817\pi\)
0.846313 + 0.532685i \(0.178817\pi\)
\(20\) 0 0
\(21\) −5.69080 −1.24183
\(22\) 0 0
\(23\) −2.41239 −0.503019 −0.251510 0.967855i \(-0.580927\pi\)
−0.251510 + 0.967855i \(0.580927\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.38446 −0.266439
\(28\) 0 0
\(29\) −0.883029 −0.163974 −0.0819872 0.996633i \(-0.526127\pi\)
−0.0819872 + 0.996633i \(0.526127\pi\)
\(30\) 0 0
\(31\) −0.774173 −0.139046 −0.0695228 0.997580i \(-0.522148\pi\)
−0.0695228 + 0.997580i \(0.522148\pi\)
\(32\) 0 0
\(33\) −12.0880 −2.10425
\(34\) 0 0
\(35\) 2.44792 0.413773
\(36\) 0 0
\(37\) −3.11454 −0.512028 −0.256014 0.966673i \(-0.582409\pi\)
−0.256014 + 0.966673i \(0.582409\pi\)
\(38\) 0 0
\(39\) 5.70933 0.914225
\(40\) 0 0
\(41\) 11.0899 1.73196 0.865979 0.500081i \(-0.166696\pi\)
0.865979 + 0.500081i \(0.166696\pi\)
\(42\) 0 0
\(43\) −7.16054 −1.09197 −0.545986 0.837794i \(-0.683845\pi\)
−0.545986 + 0.837794i \(0.683845\pi\)
\(44\) 0 0
\(45\) −2.40447 −0.358437
\(46\) 0 0
\(47\) 5.67529 0.827826 0.413913 0.910316i \(-0.364162\pi\)
0.413913 + 0.910316i \(0.364162\pi\)
\(48\) 0 0
\(49\) −1.00771 −0.143959
\(50\) 0 0
\(51\) 7.68117 1.07558
\(52\) 0 0
\(53\) −10.4209 −1.43142 −0.715712 0.698395i \(-0.753898\pi\)
−0.715712 + 0.698395i \(0.753898\pi\)
\(54\) 0 0
\(55\) 5.19969 0.701126
\(56\) 0 0
\(57\) 17.1520 2.27184
\(58\) 0 0
\(59\) −8.65032 −1.12618 −0.563088 0.826397i \(-0.690387\pi\)
−0.563088 + 0.826397i \(0.690387\pi\)
\(60\) 0 0
\(61\) −11.8162 −1.51291 −0.756455 0.654046i \(-0.773070\pi\)
−0.756455 + 0.654046i \(0.773070\pi\)
\(62\) 0 0
\(63\) −5.88594 −0.741559
\(64\) 0 0
\(65\) −2.45589 −0.304616
\(66\) 0 0
\(67\) 7.03182 0.859073 0.429537 0.903049i \(-0.358677\pi\)
0.429537 + 0.903049i \(0.358677\pi\)
\(68\) 0 0
\(69\) −5.60822 −0.675150
\(70\) 0 0
\(71\) −7.87312 −0.934367 −0.467184 0.884160i \(-0.654731\pi\)
−0.467184 + 0.884160i \(0.654731\pi\)
\(72\) 0 0
\(73\) 8.30031 0.971478 0.485739 0.874104i \(-0.338551\pi\)
0.485739 + 0.874104i \(0.338551\pi\)
\(74\) 0 0
\(75\) 2.32475 0.268439
\(76\) 0 0
\(77\) 12.7284 1.45054
\(78\) 0 0
\(79\) −12.0439 −1.35504 −0.677520 0.735504i \(-0.736945\pi\)
−0.677520 + 0.735504i \(0.736945\pi\)
\(80\) 0 0
\(81\) −10.4319 −1.15910
\(82\) 0 0
\(83\) −4.17482 −0.458246 −0.229123 0.973398i \(-0.573586\pi\)
−0.229123 + 0.973398i \(0.573586\pi\)
\(84\) 0 0
\(85\) −3.30408 −0.358378
\(86\) 0 0
\(87\) −2.05282 −0.220086
\(88\) 0 0
\(89\) −9.39112 −0.995456 −0.497728 0.867333i \(-0.665832\pi\)
−0.497728 + 0.867333i \(0.665832\pi\)
\(90\) 0 0
\(91\) −6.01181 −0.630209
\(92\) 0 0
\(93\) −1.79976 −0.186626
\(94\) 0 0
\(95\) −7.37799 −0.756966
\(96\) 0 0
\(97\) −16.7742 −1.70316 −0.851579 0.524226i \(-0.824355\pi\)
−0.851579 + 0.524226i \(0.824355\pi\)
\(98\) 0 0
\(99\) −12.5025 −1.25655
\(100\) 0 0
\(101\) 8.18129 0.814069 0.407034 0.913413i \(-0.366563\pi\)
0.407034 + 0.913413i \(0.366563\pi\)
\(102\) 0 0
\(103\) 3.34929 0.330015 0.165008 0.986292i \(-0.447235\pi\)
0.165008 + 0.986292i \(0.447235\pi\)
\(104\) 0 0
\(105\) 5.69080 0.555365
\(106\) 0 0
\(107\) 5.36392 0.518550 0.259275 0.965804i \(-0.416516\pi\)
0.259275 + 0.965804i \(0.416516\pi\)
\(108\) 0 0
\(109\) −8.77781 −0.840761 −0.420381 0.907348i \(-0.638103\pi\)
−0.420381 + 0.907348i \(0.638103\pi\)
\(110\) 0 0
\(111\) −7.24054 −0.687241
\(112\) 0 0
\(113\) −6.88312 −0.647509 −0.323755 0.946141i \(-0.604945\pi\)
−0.323755 + 0.946141i \(0.604945\pi\)
\(114\) 0 0
\(115\) 2.41239 0.224957
\(116\) 0 0
\(117\) 5.90511 0.545928
\(118\) 0 0
\(119\) −8.08811 −0.741436
\(120\) 0 0
\(121\) 16.0368 1.45789
\(122\) 0 0
\(123\) 25.7814 2.32463
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 19.2474 1.70793 0.853967 0.520327i \(-0.174190\pi\)
0.853967 + 0.520327i \(0.174190\pi\)
\(128\) 0 0
\(129\) −16.6465 −1.46564
\(130\) 0 0
\(131\) 17.3834 1.51880 0.759399 0.650625i \(-0.225493\pi\)
0.759399 + 0.650625i \(0.225493\pi\)
\(132\) 0 0
\(133\) −18.0607 −1.56606
\(134\) 0 0
\(135\) 1.38446 0.119155
\(136\) 0 0
\(137\) −17.9231 −1.53128 −0.765639 0.643271i \(-0.777577\pi\)
−0.765639 + 0.643271i \(0.777577\pi\)
\(138\) 0 0
\(139\) 16.9382 1.43668 0.718340 0.695692i \(-0.244902\pi\)
0.718340 + 0.695692i \(0.244902\pi\)
\(140\) 0 0
\(141\) 13.1936 1.11111
\(142\) 0 0
\(143\) −12.7699 −1.06787
\(144\) 0 0
\(145\) 0.883029 0.0733316
\(146\) 0 0
\(147\) −2.34268 −0.193221
\(148\) 0 0
\(149\) −14.9303 −1.22314 −0.611569 0.791191i \(-0.709461\pi\)
−0.611569 + 0.791191i \(0.709461\pi\)
\(150\) 0 0
\(151\) 5.95322 0.484466 0.242233 0.970218i \(-0.422120\pi\)
0.242233 + 0.970218i \(0.422120\pi\)
\(152\) 0 0
\(153\) 7.94457 0.642280
\(154\) 0 0
\(155\) 0.774173 0.0621831
\(156\) 0 0
\(157\) −10.3852 −0.828832 −0.414416 0.910088i \(-0.636014\pi\)
−0.414416 + 0.910088i \(0.636014\pi\)
\(158\) 0 0
\(159\) −24.2261 −1.92125
\(160\) 0 0
\(161\) 5.90534 0.465406
\(162\) 0 0
\(163\) 11.8877 0.931117 0.465558 0.885017i \(-0.345854\pi\)
0.465558 + 0.885017i \(0.345854\pi\)
\(164\) 0 0
\(165\) 12.0880 0.941049
\(166\) 0 0
\(167\) −20.7939 −1.60908 −0.804539 0.593899i \(-0.797588\pi\)
−0.804539 + 0.593899i \(0.797588\pi\)
\(168\) 0 0
\(169\) −6.96861 −0.536047
\(170\) 0 0
\(171\) 17.7402 1.35662
\(172\) 0 0
\(173\) 12.6244 0.959818 0.479909 0.877318i \(-0.340670\pi\)
0.479909 + 0.877318i \(0.340670\pi\)
\(174\) 0 0
\(175\) −2.44792 −0.185045
\(176\) 0 0
\(177\) −20.1098 −1.51155
\(178\) 0 0
\(179\) −11.6539 −0.871051 −0.435526 0.900176i \(-0.643438\pi\)
−0.435526 + 0.900176i \(0.643438\pi\)
\(180\) 0 0
\(181\) −13.4608 −1.00053 −0.500265 0.865872i \(-0.666764\pi\)
−0.500265 + 0.865872i \(0.666764\pi\)
\(182\) 0 0
\(183\) −27.4697 −2.03062
\(184\) 0 0
\(185\) 3.11454 0.228986
\(186\) 0 0
\(187\) −17.1802 −1.25634
\(188\) 0 0
\(189\) 3.38903 0.246516
\(190\) 0 0
\(191\) −11.6463 −0.842694 −0.421347 0.906899i \(-0.638443\pi\)
−0.421347 + 0.906899i \(0.638443\pi\)
\(192\) 0 0
\(193\) −5.38386 −0.387539 −0.193769 0.981047i \(-0.562071\pi\)
−0.193769 + 0.981047i \(0.562071\pi\)
\(194\) 0 0
\(195\) −5.70933 −0.408854
\(196\) 0 0
\(197\) −1.70954 −0.121799 −0.0608997 0.998144i \(-0.519397\pi\)
−0.0608997 + 0.998144i \(0.519397\pi\)
\(198\) 0 0
\(199\) 15.1288 1.07245 0.536226 0.844075i \(-0.319850\pi\)
0.536226 + 0.844075i \(0.319850\pi\)
\(200\) 0 0
\(201\) 16.3472 1.15304
\(202\) 0 0
\(203\) 2.16158 0.151713
\(204\) 0 0
\(205\) −11.0899 −0.774555
\(206\) 0 0
\(207\) −5.80053 −0.403165
\(208\) 0 0
\(209\) −38.3633 −2.65364
\(210\) 0 0
\(211\) −3.20461 −0.220614 −0.110307 0.993898i \(-0.535183\pi\)
−0.110307 + 0.993898i \(0.535183\pi\)
\(212\) 0 0
\(213\) −18.3030 −1.25410
\(214\) 0 0
\(215\) 7.16054 0.488345
\(216\) 0 0
\(217\) 1.89511 0.128648
\(218\) 0 0
\(219\) 19.2962 1.30391
\(220\) 0 0
\(221\) 8.11446 0.545837
\(222\) 0 0
\(223\) −17.0668 −1.14287 −0.571437 0.820646i \(-0.693614\pi\)
−0.571437 + 0.820646i \(0.693614\pi\)
\(224\) 0 0
\(225\) 2.40447 0.160298
\(226\) 0 0
\(227\) 5.16990 0.343138 0.171569 0.985172i \(-0.445116\pi\)
0.171569 + 0.985172i \(0.445116\pi\)
\(228\) 0 0
\(229\) −16.5678 −1.09483 −0.547416 0.836861i \(-0.684388\pi\)
−0.547416 + 0.836861i \(0.684388\pi\)
\(230\) 0 0
\(231\) 29.5904 1.94690
\(232\) 0 0
\(233\) −26.2444 −1.71933 −0.859663 0.510861i \(-0.829327\pi\)
−0.859663 + 0.510861i \(0.829327\pi\)
\(234\) 0 0
\(235\) −5.67529 −0.370215
\(236\) 0 0
\(237\) −27.9990 −1.81873
\(238\) 0 0
\(239\) 6.62179 0.428328 0.214164 0.976798i \(-0.431297\pi\)
0.214164 + 0.976798i \(0.431297\pi\)
\(240\) 0 0
\(241\) −19.1285 −1.23217 −0.616086 0.787679i \(-0.711283\pi\)
−0.616086 + 0.787679i \(0.711283\pi\)
\(242\) 0 0
\(243\) −20.0983 −1.28931
\(244\) 0 0
\(245\) 1.00771 0.0643803
\(246\) 0 0
\(247\) 18.1195 1.15292
\(248\) 0 0
\(249\) −9.70541 −0.615056
\(250\) 0 0
\(251\) 27.4056 1.72983 0.864914 0.501920i \(-0.167373\pi\)
0.864914 + 0.501920i \(0.167373\pi\)
\(252\) 0 0
\(253\) 12.5437 0.788616
\(254\) 0 0
\(255\) −7.68117 −0.481013
\(256\) 0 0
\(257\) −13.1026 −0.817320 −0.408660 0.912687i \(-0.634004\pi\)
−0.408660 + 0.912687i \(0.634004\pi\)
\(258\) 0 0
\(259\) 7.62414 0.473741
\(260\) 0 0
\(261\) −2.12322 −0.131424
\(262\) 0 0
\(263\) −9.99373 −0.616240 −0.308120 0.951348i \(-0.599700\pi\)
−0.308120 + 0.951348i \(0.599700\pi\)
\(264\) 0 0
\(265\) 10.4209 0.640152
\(266\) 0 0
\(267\) −21.8320 −1.33610
\(268\) 0 0
\(269\) 7.26689 0.443070 0.221535 0.975152i \(-0.428893\pi\)
0.221535 + 0.975152i \(0.428893\pi\)
\(270\) 0 0
\(271\) 17.4293 1.05876 0.529378 0.848386i \(-0.322425\pi\)
0.529378 + 0.848386i \(0.322425\pi\)
\(272\) 0 0
\(273\) −13.9760 −0.845864
\(274\) 0 0
\(275\) −5.19969 −0.313553
\(276\) 0 0
\(277\) 8.68281 0.521699 0.260850 0.965379i \(-0.415997\pi\)
0.260850 + 0.965379i \(0.415997\pi\)
\(278\) 0 0
\(279\) −1.86148 −0.111444
\(280\) 0 0
\(281\) 2.22948 0.133000 0.0664999 0.997786i \(-0.478817\pi\)
0.0664999 + 0.997786i \(0.478817\pi\)
\(282\) 0 0
\(283\) −3.16428 −0.188097 −0.0940484 0.995568i \(-0.529981\pi\)
−0.0940484 + 0.995568i \(0.529981\pi\)
\(284\) 0 0
\(285\) −17.1520 −1.01600
\(286\) 0 0
\(287\) −27.1472 −1.60245
\(288\) 0 0
\(289\) −6.08305 −0.357826
\(290\) 0 0
\(291\) −38.9958 −2.28597
\(292\) 0 0
\(293\) −27.0843 −1.58228 −0.791141 0.611634i \(-0.790513\pi\)
−0.791141 + 0.611634i \(0.790513\pi\)
\(294\) 0 0
\(295\) 8.65032 0.503641
\(296\) 0 0
\(297\) 7.19875 0.417714
\(298\) 0 0
\(299\) −5.92457 −0.342627
\(300\) 0 0
\(301\) 17.5284 1.01032
\(302\) 0 0
\(303\) 19.0195 1.09264
\(304\) 0 0
\(305\) 11.8162 0.676593
\(306\) 0 0
\(307\) 16.0289 0.914819 0.457410 0.889256i \(-0.348777\pi\)
0.457410 + 0.889256i \(0.348777\pi\)
\(308\) 0 0
\(309\) 7.78626 0.442945
\(310\) 0 0
\(311\) −31.7170 −1.79851 −0.899253 0.437429i \(-0.855889\pi\)
−0.899253 + 0.437429i \(0.855889\pi\)
\(312\) 0 0
\(313\) 15.7872 0.892343 0.446172 0.894947i \(-0.352787\pi\)
0.446172 + 0.894947i \(0.352787\pi\)
\(314\) 0 0
\(315\) 5.88594 0.331635
\(316\) 0 0
\(317\) −16.5970 −0.932179 −0.466090 0.884738i \(-0.654338\pi\)
−0.466090 + 0.884738i \(0.654338\pi\)
\(318\) 0 0
\(319\) 4.59148 0.257073
\(320\) 0 0
\(321\) 12.4698 0.695996
\(322\) 0 0
\(323\) 24.3775 1.35640
\(324\) 0 0
\(325\) 2.45589 0.136228
\(326\) 0 0
\(327\) −20.4062 −1.12847
\(328\) 0 0
\(329\) −13.8926 −0.765925
\(330\) 0 0
\(331\) −31.4163 −1.72680 −0.863398 0.504523i \(-0.831668\pi\)
−0.863398 + 0.504523i \(0.831668\pi\)
\(332\) 0 0
\(333\) −7.48883 −0.410385
\(334\) 0 0
\(335\) −7.03182 −0.384189
\(336\) 0 0
\(337\) −23.0214 −1.25405 −0.627026 0.778998i \(-0.715728\pi\)
−0.627026 + 0.778998i \(0.715728\pi\)
\(338\) 0 0
\(339\) −16.0015 −0.869084
\(340\) 0 0
\(341\) 4.02546 0.217991
\(342\) 0 0
\(343\) 19.6022 1.05842
\(344\) 0 0
\(345\) 5.60822 0.301936
\(346\) 0 0
\(347\) −4.17107 −0.223915 −0.111957 0.993713i \(-0.535712\pi\)
−0.111957 + 0.993713i \(0.535712\pi\)
\(348\) 0 0
\(349\) 14.7129 0.787564 0.393782 0.919204i \(-0.371166\pi\)
0.393782 + 0.919204i \(0.371166\pi\)
\(350\) 0 0
\(351\) −3.40007 −0.181482
\(352\) 0 0
\(353\) −7.59985 −0.404499 −0.202250 0.979334i \(-0.564825\pi\)
−0.202250 + 0.979334i \(0.564825\pi\)
\(354\) 0 0
\(355\) 7.87312 0.417862
\(356\) 0 0
\(357\) −18.8029 −0.995152
\(358\) 0 0
\(359\) −9.92150 −0.523637 −0.261818 0.965117i \(-0.584322\pi\)
−0.261818 + 0.965117i \(0.584322\pi\)
\(360\) 0 0
\(361\) 35.4347 1.86499
\(362\) 0 0
\(363\) 37.2815 1.95677
\(364\) 0 0
\(365\) −8.30031 −0.434458
\(366\) 0 0
\(367\) −11.2601 −0.587771 −0.293885 0.955841i \(-0.594948\pi\)
−0.293885 + 0.955841i \(0.594948\pi\)
\(368\) 0 0
\(369\) 26.6654 1.38815
\(370\) 0 0
\(371\) 25.5095 1.32439
\(372\) 0 0
\(373\) −25.9527 −1.34378 −0.671890 0.740651i \(-0.734517\pi\)
−0.671890 + 0.740651i \(0.734517\pi\)
\(374\) 0 0
\(375\) −2.32475 −0.120050
\(376\) 0 0
\(377\) −2.16862 −0.111690
\(378\) 0 0
\(379\) 4.51228 0.231780 0.115890 0.993262i \(-0.463028\pi\)
0.115890 + 0.993262i \(0.463028\pi\)
\(380\) 0 0
\(381\) 44.7455 2.29238
\(382\) 0 0
\(383\) −31.7652 −1.62313 −0.811564 0.584264i \(-0.801383\pi\)
−0.811564 + 0.584264i \(0.801383\pi\)
\(384\) 0 0
\(385\) −12.7284 −0.648699
\(386\) 0 0
\(387\) −17.2173 −0.875205
\(388\) 0 0
\(389\) 16.7692 0.850230 0.425115 0.905139i \(-0.360234\pi\)
0.425115 + 0.905139i \(0.360234\pi\)
\(390\) 0 0
\(391\) −7.97075 −0.403098
\(392\) 0 0
\(393\) 40.4122 2.03853
\(394\) 0 0
\(395\) 12.0439 0.605993
\(396\) 0 0
\(397\) 35.5602 1.78472 0.892358 0.451327i \(-0.149049\pi\)
0.892358 + 0.451327i \(0.149049\pi\)
\(398\) 0 0
\(399\) −41.9866 −2.10196
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −1.90128 −0.0947097
\(404\) 0 0
\(405\) 10.4319 0.518367
\(406\) 0 0
\(407\) 16.1947 0.802739
\(408\) 0 0
\(409\) 15.8513 0.783799 0.391899 0.920008i \(-0.371818\pi\)
0.391899 + 0.920008i \(0.371818\pi\)
\(410\) 0 0
\(411\) −41.6669 −2.05528
\(412\) 0 0
\(413\) 21.1752 1.04197
\(414\) 0 0
\(415\) 4.17482 0.204934
\(416\) 0 0
\(417\) 39.3771 1.92831
\(418\) 0 0
\(419\) −22.5089 −1.09963 −0.549816 0.835286i \(-0.685302\pi\)
−0.549816 + 0.835286i \(0.685302\pi\)
\(420\) 0 0
\(421\) −10.4152 −0.507608 −0.253804 0.967256i \(-0.581682\pi\)
−0.253804 + 0.967256i \(0.581682\pi\)
\(422\) 0 0
\(423\) 13.6461 0.663495
\(424\) 0 0
\(425\) 3.30408 0.160271
\(426\) 0 0
\(427\) 28.9250 1.39978
\(428\) 0 0
\(429\) −29.6868 −1.43329
\(430\) 0 0
\(431\) 39.5349 1.90433 0.952163 0.305589i \(-0.0988534\pi\)
0.952163 + 0.305589i \(0.0988534\pi\)
\(432\) 0 0
\(433\) 35.2994 1.69638 0.848192 0.529690i \(-0.177692\pi\)
0.848192 + 0.529690i \(0.177692\pi\)
\(434\) 0 0
\(435\) 2.05282 0.0984253
\(436\) 0 0
\(437\) −17.7986 −0.851424
\(438\) 0 0
\(439\) 25.8433 1.23343 0.616716 0.787186i \(-0.288463\pi\)
0.616716 + 0.787186i \(0.288463\pi\)
\(440\) 0 0
\(441\) −2.42301 −0.115382
\(442\) 0 0
\(443\) 14.1589 0.672711 0.336355 0.941735i \(-0.390806\pi\)
0.336355 + 0.941735i \(0.390806\pi\)
\(444\) 0 0
\(445\) 9.39112 0.445182
\(446\) 0 0
\(447\) −34.7093 −1.64169
\(448\) 0 0
\(449\) 29.7552 1.40424 0.702118 0.712060i \(-0.252238\pi\)
0.702118 + 0.712060i \(0.252238\pi\)
\(450\) 0 0
\(451\) −57.6642 −2.71530
\(452\) 0 0
\(453\) 13.8398 0.650249
\(454\) 0 0
\(455\) 6.01181 0.281838
\(456\) 0 0
\(457\) 9.17522 0.429199 0.214599 0.976702i \(-0.431155\pi\)
0.214599 + 0.976702i \(0.431155\pi\)
\(458\) 0 0
\(459\) −4.57436 −0.213513
\(460\) 0 0
\(461\) −29.0912 −1.35491 −0.677457 0.735563i \(-0.736918\pi\)
−0.677457 + 0.735563i \(0.736918\pi\)
\(462\) 0 0
\(463\) 0.928084 0.0431317 0.0215659 0.999767i \(-0.493135\pi\)
0.0215659 + 0.999767i \(0.493135\pi\)
\(464\) 0 0
\(465\) 1.79976 0.0834619
\(466\) 0 0
\(467\) −32.1055 −1.48567 −0.742833 0.669477i \(-0.766518\pi\)
−0.742833 + 0.669477i \(0.766518\pi\)
\(468\) 0 0
\(469\) −17.2133 −0.794836
\(470\) 0 0
\(471\) −24.1431 −1.11245
\(472\) 0 0
\(473\) 37.2326 1.71196
\(474\) 0 0
\(475\) 7.37799 0.338525
\(476\) 0 0
\(477\) −25.0568 −1.14727
\(478\) 0 0
\(479\) 9.83303 0.449283 0.224641 0.974442i \(-0.427879\pi\)
0.224641 + 0.974442i \(0.427879\pi\)
\(480\) 0 0
\(481\) −7.64897 −0.348763
\(482\) 0 0
\(483\) 13.7284 0.624666
\(484\) 0 0
\(485\) 16.7742 0.761675
\(486\) 0 0
\(487\) −3.55039 −0.160884 −0.0804419 0.996759i \(-0.525633\pi\)
−0.0804419 + 0.996759i \(0.525633\pi\)
\(488\) 0 0
\(489\) 27.6360 1.24974
\(490\) 0 0
\(491\) −3.94669 −0.178112 −0.0890559 0.996027i \(-0.528385\pi\)
−0.0890559 + 0.996027i \(0.528385\pi\)
\(492\) 0 0
\(493\) −2.91760 −0.131402
\(494\) 0 0
\(495\) 12.5025 0.561946
\(496\) 0 0
\(497\) 19.2727 0.864500
\(498\) 0 0
\(499\) 15.8569 0.709850 0.354925 0.934895i \(-0.384506\pi\)
0.354925 + 0.934895i \(0.384506\pi\)
\(500\) 0 0
\(501\) −48.3406 −2.15970
\(502\) 0 0
\(503\) 31.2479 1.39327 0.696637 0.717424i \(-0.254679\pi\)
0.696637 + 0.717424i \(0.254679\pi\)
\(504\) 0 0
\(505\) −8.18129 −0.364063
\(506\) 0 0
\(507\) −16.2003 −0.719480
\(508\) 0 0
\(509\) −12.7905 −0.566928 −0.283464 0.958983i \(-0.591484\pi\)
−0.283464 + 0.958983i \(0.591484\pi\)
\(510\) 0 0
\(511\) −20.3185 −0.898836
\(512\) 0 0
\(513\) −10.2145 −0.450982
\(514\) 0 0
\(515\) −3.34929 −0.147587
\(516\) 0 0
\(517\) −29.5097 −1.29784
\(518\) 0 0
\(519\) 29.3487 1.28826
\(520\) 0 0
\(521\) −29.8043 −1.30575 −0.652875 0.757466i \(-0.726437\pi\)
−0.652875 + 0.757466i \(0.726437\pi\)
\(522\) 0 0
\(523\) 29.7129 1.29925 0.649627 0.760253i \(-0.274925\pi\)
0.649627 + 0.760253i \(0.274925\pi\)
\(524\) 0 0
\(525\) −5.69080 −0.248367
\(526\) 0 0
\(527\) −2.55793 −0.111425
\(528\) 0 0
\(529\) −17.1804 −0.746972
\(530\) 0 0
\(531\) −20.7994 −0.902619
\(532\) 0 0
\(533\) 27.2357 1.17971
\(534\) 0 0
\(535\) −5.36392 −0.231903
\(536\) 0 0
\(537\) −27.0924 −1.16912
\(538\) 0 0
\(539\) 5.23979 0.225694
\(540\) 0 0
\(541\) 22.7229 0.976934 0.488467 0.872582i \(-0.337556\pi\)
0.488467 + 0.872582i \(0.337556\pi\)
\(542\) 0 0
\(543\) −31.2929 −1.34291
\(544\) 0 0
\(545\) 8.77781 0.376000
\(546\) 0 0
\(547\) 2.77036 0.118452 0.0592261 0.998245i \(-0.481137\pi\)
0.0592261 + 0.998245i \(0.481137\pi\)
\(548\) 0 0
\(549\) −28.4117 −1.21258
\(550\) 0 0
\(551\) −6.51498 −0.277547
\(552\) 0 0
\(553\) 29.4824 1.25372
\(554\) 0 0
\(555\) 7.24054 0.307344
\(556\) 0 0
\(557\) 5.25530 0.222674 0.111337 0.993783i \(-0.464487\pi\)
0.111337 + 0.993783i \(0.464487\pi\)
\(558\) 0 0
\(559\) −17.5855 −0.743787
\(560\) 0 0
\(561\) −39.9397 −1.68626
\(562\) 0 0
\(563\) 6.11309 0.257636 0.128818 0.991668i \(-0.458882\pi\)
0.128818 + 0.991668i \(0.458882\pi\)
\(564\) 0 0
\(565\) 6.88312 0.289575
\(566\) 0 0
\(567\) 25.5365 1.07243
\(568\) 0 0
\(569\) −33.4724 −1.40324 −0.701618 0.712553i \(-0.747539\pi\)
−0.701618 + 0.712553i \(0.747539\pi\)
\(570\) 0 0
\(571\) 27.0336 1.13132 0.565660 0.824638i \(-0.308621\pi\)
0.565660 + 0.824638i \(0.308621\pi\)
\(572\) 0 0
\(573\) −27.0747 −1.13106
\(574\) 0 0
\(575\) −2.41239 −0.100604
\(576\) 0 0
\(577\) 6.86862 0.285944 0.142972 0.989727i \(-0.454334\pi\)
0.142972 + 0.989727i \(0.454334\pi\)
\(578\) 0 0
\(579\) −12.5161 −0.520153
\(580\) 0 0
\(581\) 10.2196 0.423980
\(582\) 0 0
\(583\) 54.1856 2.24414
\(584\) 0 0
\(585\) −5.90511 −0.244146
\(586\) 0 0
\(587\) 44.1853 1.82372 0.911860 0.410501i \(-0.134646\pi\)
0.911860 + 0.410501i \(0.134646\pi\)
\(588\) 0 0
\(589\) −5.71184 −0.235352
\(590\) 0 0
\(591\) −3.97425 −0.163479
\(592\) 0 0
\(593\) 19.2535 0.790645 0.395323 0.918542i \(-0.370633\pi\)
0.395323 + 0.918542i \(0.370633\pi\)
\(594\) 0 0
\(595\) 8.08811 0.331580
\(596\) 0 0
\(597\) 35.1707 1.43944
\(598\) 0 0
\(599\) −24.8385 −1.01487 −0.507437 0.861689i \(-0.669407\pi\)
−0.507437 + 0.861689i \(0.669407\pi\)
\(600\) 0 0
\(601\) 25.8731 1.05539 0.527693 0.849435i \(-0.323057\pi\)
0.527693 + 0.849435i \(0.323057\pi\)
\(602\) 0 0
\(603\) 16.9078 0.688539
\(604\) 0 0
\(605\) −16.0368 −0.651988
\(606\) 0 0
\(607\) −13.5573 −0.550274 −0.275137 0.961405i \(-0.588723\pi\)
−0.275137 + 0.961405i \(0.588723\pi\)
\(608\) 0 0
\(609\) 5.02514 0.203629
\(610\) 0 0
\(611\) 13.9379 0.563866
\(612\) 0 0
\(613\) 0.467171 0.0188689 0.00943444 0.999955i \(-0.496997\pi\)
0.00943444 + 0.999955i \(0.496997\pi\)
\(614\) 0 0
\(615\) −25.7814 −1.03960
\(616\) 0 0
\(617\) 25.7074 1.03494 0.517470 0.855701i \(-0.326874\pi\)
0.517470 + 0.855701i \(0.326874\pi\)
\(618\) 0 0
\(619\) −27.2402 −1.09488 −0.547438 0.836846i \(-0.684397\pi\)
−0.547438 + 0.836846i \(0.684397\pi\)
\(620\) 0 0
\(621\) 3.33986 0.134024
\(622\) 0 0
\(623\) 22.9887 0.921021
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −89.1851 −3.56171
\(628\) 0 0
\(629\) −10.2907 −0.410317
\(630\) 0 0
\(631\) 25.4615 1.01361 0.506803 0.862062i \(-0.330827\pi\)
0.506803 + 0.862062i \(0.330827\pi\)
\(632\) 0 0
\(633\) −7.44992 −0.296108
\(634\) 0 0
\(635\) −19.2474 −0.763811
\(636\) 0 0
\(637\) −2.47483 −0.0980562
\(638\) 0 0
\(639\) −18.9307 −0.748887
\(640\) 0 0
\(641\) 43.0962 1.70220 0.851098 0.525007i \(-0.175937\pi\)
0.851098 + 0.525007i \(0.175937\pi\)
\(642\) 0 0
\(643\) −18.3857 −0.725062 −0.362531 0.931972i \(-0.618087\pi\)
−0.362531 + 0.931972i \(0.618087\pi\)
\(644\) 0 0
\(645\) 16.6465 0.655454
\(646\) 0 0
\(647\) −32.4412 −1.27540 −0.637698 0.770287i \(-0.720113\pi\)
−0.637698 + 0.770287i \(0.720113\pi\)
\(648\) 0 0
\(649\) 44.9790 1.76558
\(650\) 0 0
\(651\) 4.40566 0.172671
\(652\) 0 0
\(653\) 24.8831 0.973751 0.486875 0.873471i \(-0.338137\pi\)
0.486875 + 0.873471i \(0.338137\pi\)
\(654\) 0 0
\(655\) −17.3834 −0.679227
\(656\) 0 0
\(657\) 19.9579 0.778630
\(658\) 0 0
\(659\) 38.2465 1.48987 0.744936 0.667136i \(-0.232480\pi\)
0.744936 + 0.667136i \(0.232480\pi\)
\(660\) 0 0
\(661\) 14.3456 0.557980 0.278990 0.960294i \(-0.410000\pi\)
0.278990 + 0.960294i \(0.410000\pi\)
\(662\) 0 0
\(663\) 18.8641 0.732621
\(664\) 0 0
\(665\) 18.0607 0.700364
\(666\) 0 0
\(667\) 2.13021 0.0824822
\(668\) 0 0
\(669\) −39.6760 −1.53396
\(670\) 0 0
\(671\) 61.4406 2.37189
\(672\) 0 0
\(673\) −8.22085 −0.316890 −0.158445 0.987368i \(-0.550648\pi\)
−0.158445 + 0.987368i \(0.550648\pi\)
\(674\) 0 0
\(675\) −1.38446 −0.0532878
\(676\) 0 0
\(677\) −9.37819 −0.360433 −0.180216 0.983627i \(-0.557680\pi\)
−0.180216 + 0.983627i \(0.557680\pi\)
\(678\) 0 0
\(679\) 41.0617 1.57580
\(680\) 0 0
\(681\) 12.0187 0.460559
\(682\) 0 0
\(683\) −31.0163 −1.18681 −0.593403 0.804905i \(-0.702216\pi\)
−0.593403 + 0.804905i \(0.702216\pi\)
\(684\) 0 0
\(685\) 17.9231 0.684808
\(686\) 0 0
\(687\) −38.5160 −1.46948
\(688\) 0 0
\(689\) −25.5926 −0.975002
\(690\) 0 0
\(691\) −22.6421 −0.861347 −0.430674 0.902508i \(-0.641724\pi\)
−0.430674 + 0.902508i \(0.641724\pi\)
\(692\) 0 0
\(693\) 30.6051 1.16259
\(694\) 0 0
\(695\) −16.9382 −0.642503
\(696\) 0 0
\(697\) 36.6421 1.38792
\(698\) 0 0
\(699\) −61.0117 −2.30767
\(700\) 0 0
\(701\) −44.2958 −1.67303 −0.836515 0.547943i \(-0.815411\pi\)
−0.836515 + 0.547943i \(0.815411\pi\)
\(702\) 0 0
\(703\) −22.9791 −0.866672
\(704\) 0 0
\(705\) −13.1936 −0.496901
\(706\) 0 0
\(707\) −20.0271 −0.753197
\(708\) 0 0
\(709\) 3.31491 0.124494 0.0622470 0.998061i \(-0.480173\pi\)
0.0622470 + 0.998061i \(0.480173\pi\)
\(710\) 0 0
\(711\) −28.9591 −1.08605
\(712\) 0 0
\(713\) 1.86761 0.0699426
\(714\) 0 0
\(715\) 12.7699 0.477566
\(716\) 0 0
\(717\) 15.3940 0.574900
\(718\) 0 0
\(719\) 23.7708 0.886502 0.443251 0.896398i \(-0.353825\pi\)
0.443251 + 0.896398i \(0.353825\pi\)
\(720\) 0 0
\(721\) −8.19877 −0.305338
\(722\) 0 0
\(723\) −44.4689 −1.65382
\(724\) 0 0
\(725\) −0.883029 −0.0327949
\(726\) 0 0
\(727\) −21.9798 −0.815186 −0.407593 0.913164i \(-0.633632\pi\)
−0.407593 + 0.913164i \(0.633632\pi\)
\(728\) 0 0
\(729\) −15.4277 −0.571397
\(730\) 0 0
\(731\) −23.6590 −0.875060
\(732\) 0 0
\(733\) 37.4119 1.38184 0.690919 0.722932i \(-0.257206\pi\)
0.690919 + 0.722932i \(0.257206\pi\)
\(734\) 0 0
\(735\) 2.34268 0.0864110
\(736\) 0 0
\(737\) −36.5633 −1.34683
\(738\) 0 0
\(739\) 33.9772 1.24987 0.624935 0.780677i \(-0.285125\pi\)
0.624935 + 0.780677i \(0.285125\pi\)
\(740\) 0 0
\(741\) 42.1234 1.54744
\(742\) 0 0
\(743\) −2.62475 −0.0962926 −0.0481463 0.998840i \(-0.515331\pi\)
−0.0481463 + 0.998840i \(0.515331\pi\)
\(744\) 0 0
\(745\) 14.9303 0.547004
\(746\) 0 0
\(747\) −10.0382 −0.367280
\(748\) 0 0
\(749\) −13.1304 −0.479775
\(750\) 0 0
\(751\) −12.1603 −0.443737 −0.221869 0.975077i \(-0.571216\pi\)
−0.221869 + 0.975077i \(0.571216\pi\)
\(752\) 0 0
\(753\) 63.7113 2.32177
\(754\) 0 0
\(755\) −5.95322 −0.216660
\(756\) 0 0
\(757\) 41.2286 1.49848 0.749240 0.662299i \(-0.230419\pi\)
0.749240 + 0.662299i \(0.230419\pi\)
\(758\) 0 0
\(759\) 29.1610 1.05848
\(760\) 0 0
\(761\) 43.2886 1.56921 0.784606 0.619995i \(-0.212865\pi\)
0.784606 + 0.619995i \(0.212865\pi\)
\(762\) 0 0
\(763\) 21.4873 0.777893
\(764\) 0 0
\(765\) −7.94457 −0.287236
\(766\) 0 0
\(767\) −21.2442 −0.767084
\(768\) 0 0
\(769\) −33.0243 −1.19089 −0.595443 0.803397i \(-0.703023\pi\)
−0.595443 + 0.803397i \(0.703023\pi\)
\(770\) 0 0
\(771\) −30.4604 −1.09700
\(772\) 0 0
\(773\) 26.7414 0.961820 0.480910 0.876770i \(-0.340306\pi\)
0.480910 + 0.876770i \(0.340306\pi\)
\(774\) 0 0
\(775\) −0.774173 −0.0278091
\(776\) 0 0
\(777\) 17.7242 0.635853
\(778\) 0 0
\(779\) 81.8214 2.93156
\(780\) 0 0
\(781\) 40.9378 1.46487
\(782\) 0 0
\(783\) 1.22252 0.0436891
\(784\) 0 0
\(785\) 10.3852 0.370665
\(786\) 0 0
\(787\) 22.8241 0.813590 0.406795 0.913520i \(-0.366646\pi\)
0.406795 + 0.913520i \(0.366646\pi\)
\(788\) 0 0
\(789\) −23.2329 −0.827115
\(790\) 0 0
\(791\) 16.8493 0.599092
\(792\) 0 0
\(793\) −29.0193 −1.03050
\(794\) 0 0
\(795\) 24.2261 0.859210
\(796\) 0 0
\(797\) −32.9312 −1.16648 −0.583241 0.812299i \(-0.698216\pi\)
−0.583241 + 0.812299i \(0.698216\pi\)
\(798\) 0 0
\(799\) 18.7516 0.663385
\(800\) 0 0
\(801\) −22.5807 −0.797849
\(802\) 0 0
\(803\) −43.1590 −1.52305
\(804\) 0 0
\(805\) −5.90534 −0.208136
\(806\) 0 0
\(807\) 16.8937 0.594687
\(808\) 0 0
\(809\) 4.37099 0.153676 0.0768379 0.997044i \(-0.475518\pi\)
0.0768379 + 0.997044i \(0.475518\pi\)
\(810\) 0 0
\(811\) −20.8882 −0.733483 −0.366742 0.930323i \(-0.619527\pi\)
−0.366742 + 0.930323i \(0.619527\pi\)
\(812\) 0 0
\(813\) 40.5188 1.42106
\(814\) 0 0
\(815\) −11.8877 −0.416408
\(816\) 0 0
\(817\) −52.8304 −1.84830
\(818\) 0 0
\(819\) −14.4552 −0.505106
\(820\) 0 0
\(821\) −41.9809 −1.46514 −0.732572 0.680689i \(-0.761680\pi\)
−0.732572 + 0.680689i \(0.761680\pi\)
\(822\) 0 0
\(823\) −2.64112 −0.0920635 −0.0460318 0.998940i \(-0.514658\pi\)
−0.0460318 + 0.998940i \(0.514658\pi\)
\(824\) 0 0
\(825\) −12.0880 −0.420850
\(826\) 0 0
\(827\) 50.0018 1.73873 0.869366 0.494169i \(-0.164528\pi\)
0.869366 + 0.494169i \(0.164528\pi\)
\(828\) 0 0
\(829\) −25.9460 −0.901143 −0.450572 0.892740i \(-0.648780\pi\)
−0.450572 + 0.892740i \(0.648780\pi\)
\(830\) 0 0
\(831\) 20.1854 0.700223
\(832\) 0 0
\(833\) −3.32956 −0.115362
\(834\) 0 0
\(835\) 20.7939 0.719602
\(836\) 0 0
\(837\) 1.07181 0.0370471
\(838\) 0 0
\(839\) −3.56947 −0.123232 −0.0616158 0.998100i \(-0.519625\pi\)
−0.0616158 + 0.998100i \(0.519625\pi\)
\(840\) 0 0
\(841\) −28.2203 −0.973112
\(842\) 0 0
\(843\) 5.18299 0.178512
\(844\) 0 0
\(845\) 6.96861 0.239727
\(846\) 0 0
\(847\) −39.2567 −1.34887
\(848\) 0 0
\(849\) −7.35616 −0.252463
\(850\) 0 0
\(851\) 7.51350 0.257560
\(852\) 0 0
\(853\) 13.0398 0.446473 0.223236 0.974764i \(-0.428338\pi\)
0.223236 + 0.974764i \(0.428338\pi\)
\(854\) 0 0
\(855\) −17.7402 −0.606701
\(856\) 0 0
\(857\) 23.0455 0.787218 0.393609 0.919278i \(-0.371226\pi\)
0.393609 + 0.919278i \(0.371226\pi\)
\(858\) 0 0
\(859\) 18.1903 0.620646 0.310323 0.950631i \(-0.399563\pi\)
0.310323 + 0.950631i \(0.399563\pi\)
\(860\) 0 0
\(861\) −63.1106 −2.15080
\(862\) 0 0
\(863\) −40.7654 −1.38767 −0.693835 0.720134i \(-0.744080\pi\)
−0.693835 + 0.720134i \(0.744080\pi\)
\(864\) 0 0
\(865\) −12.6244 −0.429244
\(866\) 0 0
\(867\) −14.1416 −0.480273
\(868\) 0 0
\(869\) 62.6244 2.12439
\(870\) 0 0
\(871\) 17.2694 0.585150
\(872\) 0 0
\(873\) −40.3330 −1.36506
\(874\) 0 0
\(875\) 2.44792 0.0827546
\(876\) 0 0
\(877\) 20.6337 0.696752 0.348376 0.937355i \(-0.386733\pi\)
0.348376 + 0.937355i \(0.386733\pi\)
\(878\) 0 0
\(879\) −62.9643 −2.12373
\(880\) 0 0
\(881\) 32.3915 1.09130 0.545648 0.838014i \(-0.316284\pi\)
0.545648 + 0.838014i \(0.316284\pi\)
\(882\) 0 0
\(883\) 23.2727 0.783189 0.391594 0.920138i \(-0.371924\pi\)
0.391594 + 0.920138i \(0.371924\pi\)
\(884\) 0 0
\(885\) 20.1098 0.675985
\(886\) 0 0
\(887\) 3.02081 0.101429 0.0507144 0.998713i \(-0.483850\pi\)
0.0507144 + 0.998713i \(0.483850\pi\)
\(888\) 0 0
\(889\) −47.1161 −1.58022
\(890\) 0 0
\(891\) 54.2428 1.81720
\(892\) 0 0
\(893\) 41.8722 1.40120
\(894\) 0 0
\(895\) 11.6539 0.389546
\(896\) 0 0
\(897\) −13.7732 −0.459873
\(898\) 0 0
\(899\) 0.683617 0.0227999
\(900\) 0 0
\(901\) −34.4316 −1.14708
\(902\) 0 0
\(903\) 40.7492 1.35605
\(904\) 0 0
\(905\) 13.4608 0.447451
\(906\) 0 0
\(907\) 16.2038 0.538037 0.269019 0.963135i \(-0.413301\pi\)
0.269019 + 0.963135i \(0.413301\pi\)
\(908\) 0 0
\(909\) 19.6717 0.652468
\(910\) 0 0
\(911\) 14.8492 0.491976 0.245988 0.969273i \(-0.420888\pi\)
0.245988 + 0.969273i \(0.420888\pi\)
\(912\) 0 0
\(913\) 21.7078 0.718422
\(914\) 0 0
\(915\) 27.4697 0.908121
\(916\) 0 0
\(917\) −42.5532 −1.40523
\(918\) 0 0
\(919\) 7.65288 0.252445 0.126223 0.992002i \(-0.459715\pi\)
0.126223 + 0.992002i \(0.459715\pi\)
\(920\) 0 0
\(921\) 37.2633 1.22787
\(922\) 0 0
\(923\) −19.3355 −0.636436
\(924\) 0 0
\(925\) −3.11454 −0.102406
\(926\) 0 0
\(927\) 8.05326 0.264504
\(928\) 0 0
\(929\) 42.8564 1.40607 0.703037 0.711153i \(-0.251827\pi\)
0.703037 + 0.711153i \(0.251827\pi\)
\(930\) 0 0
\(931\) −7.43488 −0.243668
\(932\) 0 0
\(933\) −73.7341 −2.41395
\(934\) 0 0
\(935\) 17.1802 0.561853
\(936\) 0 0
\(937\) 0.588174 0.0192148 0.00960740 0.999954i \(-0.496942\pi\)
0.00960740 + 0.999954i \(0.496942\pi\)
\(938\) 0 0
\(939\) 36.7012 1.19770
\(940\) 0 0
\(941\) 53.3191 1.73815 0.869076 0.494678i \(-0.164714\pi\)
0.869076 + 0.494678i \(0.164714\pi\)
\(942\) 0 0
\(943\) −26.7533 −0.871207
\(944\) 0 0
\(945\) −3.38903 −0.110245
\(946\) 0 0
\(947\) −11.5755 −0.376154 −0.188077 0.982154i \(-0.560225\pi\)
−0.188077 + 0.982154i \(0.560225\pi\)
\(948\) 0 0
\(949\) 20.3846 0.661714
\(950\) 0 0
\(951\) −38.5839 −1.25117
\(952\) 0 0
\(953\) −40.6032 −1.31527 −0.657634 0.753338i \(-0.728443\pi\)
−0.657634 + 0.753338i \(0.728443\pi\)
\(954\) 0 0
\(955\) 11.6463 0.376864
\(956\) 0 0
\(957\) 10.6740 0.345043
\(958\) 0 0
\(959\) 43.8743 1.41678
\(960\) 0 0
\(961\) −30.4007 −0.980666
\(962\) 0 0
\(963\) 12.8974 0.415613
\(964\) 0 0
\(965\) 5.38386 0.173313
\(966\) 0 0
\(967\) 55.7241 1.79197 0.895983 0.444089i \(-0.146473\pi\)
0.895983 + 0.444089i \(0.146473\pi\)
\(968\) 0 0
\(969\) 56.6716 1.82055
\(970\) 0 0
\(971\) 19.8536 0.637132 0.318566 0.947901i \(-0.396799\pi\)
0.318566 + 0.947901i \(0.396799\pi\)
\(972\) 0 0
\(973\) −41.4633 −1.32925
\(974\) 0 0
\(975\) 5.70933 0.182845
\(976\) 0 0
\(977\) 35.7654 1.14424 0.572119 0.820171i \(-0.306122\pi\)
0.572119 + 0.820171i \(0.306122\pi\)
\(978\) 0 0
\(979\) 48.8309 1.56064
\(980\) 0 0
\(981\) −21.1060 −0.673862
\(982\) 0 0
\(983\) 28.1853 0.898972 0.449486 0.893287i \(-0.351607\pi\)
0.449486 + 0.893287i \(0.351607\pi\)
\(984\) 0 0
\(985\) 1.70954 0.0544703
\(986\) 0 0
\(987\) −32.2969 −1.02802
\(988\) 0 0
\(989\) 17.2740 0.549283
\(990\) 0 0
\(991\) −9.02095 −0.286560 −0.143280 0.989682i \(-0.545765\pi\)
−0.143280 + 0.989682i \(0.545765\pi\)
\(992\) 0 0
\(993\) −73.0351 −2.31770
\(994\) 0 0
\(995\) −15.1288 −0.479615
\(996\) 0 0
\(997\) −34.0413 −1.07810 −0.539050 0.842274i \(-0.681217\pi\)
−0.539050 + 0.842274i \(0.681217\pi\)
\(998\) 0 0
\(999\) 4.31195 0.136424
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 \(a_p\))