Properties

Label 8008.2.a.n.1.8
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-2.29224\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.29224 q^{3} +3.91599 q^{5} -1.00000 q^{7} +2.25436 q^{9} +O(q^{10})\) \(q+2.29224 q^{3} +3.91599 q^{5} -1.00000 q^{7} +2.25436 q^{9} +1.00000 q^{11} -1.00000 q^{13} +8.97640 q^{15} +5.29356 q^{17} +2.52623 q^{19} -2.29224 q^{21} -4.13217 q^{23} +10.3350 q^{25} -1.70918 q^{27} +6.65785 q^{29} -3.98607 q^{31} +2.29224 q^{33} -3.91599 q^{35} +2.57423 q^{37} -2.29224 q^{39} +4.72390 q^{41} -7.81748 q^{43} +8.82808 q^{45} +0.823244 q^{47} +1.00000 q^{49} +12.1341 q^{51} +0.474003 q^{53} +3.91599 q^{55} +5.79073 q^{57} +9.39011 q^{59} +6.43606 q^{61} -2.25436 q^{63} -3.91599 q^{65} -13.5133 q^{67} -9.47193 q^{69} +11.2332 q^{71} +10.9199 q^{73} +23.6903 q^{75} -1.00000 q^{77} +14.4865 q^{79} -10.6809 q^{81} -15.6479 q^{83} +20.7296 q^{85} +15.2614 q^{87} -16.0211 q^{89} +1.00000 q^{91} -9.13704 q^{93} +9.89271 q^{95} +1.43297 q^{97} +2.25436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + O(q^{10}) \) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + 9q^{11} - 9q^{13} + 11q^{15} + 7q^{17} - 17q^{19} + 3q^{21} + 11q^{23} + 18q^{25} - 9q^{27} + 9q^{29} - 8q^{31} - 3q^{33} - q^{35} + 2q^{37} + 3q^{39} + 18q^{41} + 7q^{43} + 5q^{45} + 15q^{47} + 9q^{49} - 7q^{51} - 4q^{53} + q^{55} + 22q^{57} - 23q^{59} + 12q^{61} - 12q^{63} - q^{65} - 16q^{67} - 32q^{69} - 6q^{71} + 4q^{73} - 14q^{75} - 9q^{77} + 21q^{79} + 5q^{81} - 16q^{83} + 53q^{85} + 41q^{87} + 5q^{89} + 9q^{91} + 29q^{93} + 19q^{95} + 18q^{97} + 12q^{99} + O(q^{100}) \)

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
\(3\) 2.29224 1.32343 0.661713 0.749758i \(-0.269830\pi\)
0.661713 + 0.749758i \(0.269830\pi\)
\(4\) 0 0
\(5\) 3.91599 1.75129 0.875643 0.482959i \(-0.160438\pi\)
0.875643 + 0.482959i \(0.160438\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 2.25436 0.751455
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 8.97640 2.31770
\(16\) 0 0
\(17\) 5.29356 1.28388 0.641939 0.766756i \(-0.278130\pi\)
0.641939 + 0.766756i \(0.278130\pi\)
\(18\) 0 0
\(19\) 2.52623 0.579557 0.289779 0.957094i \(-0.406418\pi\)
0.289779 + 0.957094i \(0.406418\pi\)
\(20\) 0 0
\(21\) −2.29224 −0.500208
\(22\) 0 0
\(23\) −4.13217 −0.861617 −0.430809 0.902443i \(-0.641772\pi\)
−0.430809 + 0.902443i \(0.641772\pi\)
\(24\) 0 0
\(25\) 10.3350 2.06700
\(26\) 0 0
\(27\) −1.70918 −0.328931
\(28\) 0 0
\(29\) 6.65785 1.23633 0.618166 0.786048i \(-0.287876\pi\)
0.618166 + 0.786048i \(0.287876\pi\)
\(30\) 0 0
\(31\) −3.98607 −0.715920 −0.357960 0.933737i \(-0.616528\pi\)
−0.357960 + 0.933737i \(0.616528\pi\)
\(32\) 0 0
\(33\) 2.29224 0.399028
\(34\) 0 0
\(35\) −3.91599 −0.661924
\(36\) 0 0
\(37\) 2.57423 0.423201 0.211601 0.977356i \(-0.432132\pi\)
0.211601 + 0.977356i \(0.432132\pi\)
\(38\) 0 0
\(39\) −2.29224 −0.367052
\(40\) 0 0
\(41\) 4.72390 0.737749 0.368874 0.929479i \(-0.379743\pi\)
0.368874 + 0.929479i \(0.379743\pi\)
\(42\) 0 0
\(43\) −7.81748 −1.19215 −0.596077 0.802927i \(-0.703275\pi\)
−0.596077 + 0.802927i \(0.703275\pi\)
\(44\) 0 0
\(45\) 8.82808 1.31601
\(46\) 0 0
\(47\) 0.823244 0.120082 0.0600412 0.998196i \(-0.480877\pi\)
0.0600412 + 0.998196i \(0.480877\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 12.1341 1.69912
\(52\) 0 0
\(53\) 0.474003 0.0651093 0.0325546 0.999470i \(-0.489636\pi\)
0.0325546 + 0.999470i \(0.489636\pi\)
\(54\) 0 0
\(55\) 3.91599 0.528033
\(56\) 0 0
\(57\) 5.79073 0.767001
\(58\) 0 0
\(59\) 9.39011 1.22249 0.611244 0.791442i \(-0.290669\pi\)
0.611244 + 0.791442i \(0.290669\pi\)
\(60\) 0 0
\(61\) 6.43606 0.824053 0.412026 0.911172i \(-0.364821\pi\)
0.412026 + 0.911172i \(0.364821\pi\)
\(62\) 0 0
\(63\) −2.25436 −0.284023
\(64\) 0 0
\(65\) −3.91599 −0.485719
\(66\) 0 0
\(67\) −13.5133 −1.65091 −0.825457 0.564465i \(-0.809083\pi\)
−0.825457 + 0.564465i \(0.809083\pi\)
\(68\) 0 0
\(69\) −9.47193 −1.14029
\(70\) 0 0
\(71\) 11.2332 1.33313 0.666567 0.745445i \(-0.267763\pi\)
0.666567 + 0.745445i \(0.267763\pi\)
\(72\) 0 0
\(73\) 10.9199 1.27808 0.639041 0.769173i \(-0.279332\pi\)
0.639041 + 0.769173i \(0.279332\pi\)
\(74\) 0 0
\(75\) 23.6903 2.73552
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 14.4865 1.62986 0.814932 0.579557i \(-0.196774\pi\)
0.814932 + 0.579557i \(0.196774\pi\)
\(80\) 0 0
\(81\) −10.6809 −1.18677
\(82\) 0 0
\(83\) −15.6479 −1.71758 −0.858792 0.512324i \(-0.828785\pi\)
−0.858792 + 0.512324i \(0.828785\pi\)
\(84\) 0 0
\(85\) 20.7296 2.24844
\(86\) 0 0
\(87\) 15.2614 1.63619
\(88\) 0 0
\(89\) −16.0211 −1.69824 −0.849119 0.528201i \(-0.822867\pi\)
−0.849119 + 0.528201i \(0.822867\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −9.13704 −0.947467
\(94\) 0 0
\(95\) 9.89271 1.01497
\(96\) 0 0
\(97\) 1.43297 0.145496 0.0727481 0.997350i \(-0.476823\pi\)
0.0727481 + 0.997350i \(0.476823\pi\)
\(98\) 0 0
\(99\) 2.25436 0.226572
\(100\) 0 0
\(101\) −9.90176 −0.985262 −0.492631 0.870238i \(-0.663965\pi\)
−0.492631 + 0.870238i \(0.663965\pi\)
\(102\) 0 0
\(103\) −7.35242 −0.724456 −0.362228 0.932090i \(-0.617984\pi\)
−0.362228 + 0.932090i \(0.617984\pi\)
\(104\) 0 0
\(105\) −8.97640 −0.876007
\(106\) 0 0
\(107\) 4.93360 0.476949 0.238475 0.971149i \(-0.423353\pi\)
0.238475 + 0.971149i \(0.423353\pi\)
\(108\) 0 0
\(109\) −10.7579 −1.03042 −0.515209 0.857065i \(-0.672286\pi\)
−0.515209 + 0.857065i \(0.672286\pi\)
\(110\) 0 0
\(111\) 5.90076 0.560075
\(112\) 0 0
\(113\) −4.60386 −0.433094 −0.216547 0.976272i \(-0.569480\pi\)
−0.216547 + 0.976272i \(0.569480\pi\)
\(114\) 0 0
\(115\) −16.1816 −1.50894
\(116\) 0 0
\(117\) −2.25436 −0.208416
\(118\) 0 0
\(119\) −5.29356 −0.485260
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 10.8283 0.976355
\(124\) 0 0
\(125\) 20.8919 1.86863
\(126\) 0 0
\(127\) 6.56009 0.582114 0.291057 0.956706i \(-0.405993\pi\)
0.291057 + 0.956706i \(0.405993\pi\)
\(128\) 0 0
\(129\) −17.9195 −1.57773
\(130\) 0 0
\(131\) 1.85601 0.162160 0.0810801 0.996708i \(-0.474163\pi\)
0.0810801 + 0.996708i \(0.474163\pi\)
\(132\) 0 0
\(133\) −2.52623 −0.219052
\(134\) 0 0
\(135\) −6.69313 −0.576053
\(136\) 0 0
\(137\) −0.862991 −0.0737303 −0.0368651 0.999320i \(-0.511737\pi\)
−0.0368651 + 0.999320i \(0.511737\pi\)
\(138\) 0 0
\(139\) −7.44853 −0.631776 −0.315888 0.948797i \(-0.602302\pi\)
−0.315888 + 0.948797i \(0.602302\pi\)
\(140\) 0 0
\(141\) 1.88707 0.158920
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 26.0721 2.16517
\(146\) 0 0
\(147\) 2.29224 0.189061
\(148\) 0 0
\(149\) 8.28649 0.678856 0.339428 0.940632i \(-0.389767\pi\)
0.339428 + 0.940632i \(0.389767\pi\)
\(150\) 0 0
\(151\) 7.66565 0.623822 0.311911 0.950111i \(-0.399031\pi\)
0.311911 + 0.950111i \(0.399031\pi\)
\(152\) 0 0
\(153\) 11.9336 0.964775
\(154\) 0 0
\(155\) −15.6094 −1.25378
\(156\) 0 0
\(157\) 23.6516 1.88760 0.943800 0.330518i \(-0.107223\pi\)
0.943800 + 0.330518i \(0.107223\pi\)
\(158\) 0 0
\(159\) 1.08653 0.0861672
\(160\) 0 0
\(161\) 4.13217 0.325661
\(162\) 0 0
\(163\) −4.20451 −0.329323 −0.164662 0.986350i \(-0.552653\pi\)
−0.164662 + 0.986350i \(0.552653\pi\)
\(164\) 0 0
\(165\) 8.97640 0.698812
\(166\) 0 0
\(167\) 21.6773 1.67744 0.838721 0.544561i \(-0.183304\pi\)
0.838721 + 0.544561i \(0.183304\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 5.69505 0.435511
\(172\) 0 0
\(173\) −5.65944 −0.430280 −0.215140 0.976583i \(-0.569021\pi\)
−0.215140 + 0.976583i \(0.569021\pi\)
\(174\) 0 0
\(175\) −10.3350 −0.781254
\(176\) 0 0
\(177\) 21.5244 1.61787
\(178\) 0 0
\(179\) −9.09626 −0.679887 −0.339943 0.940446i \(-0.610408\pi\)
−0.339943 + 0.940446i \(0.610408\pi\)
\(180\) 0 0
\(181\) −26.4678 −1.96733 −0.983667 0.179998i \(-0.942391\pi\)
−0.983667 + 0.179998i \(0.942391\pi\)
\(182\) 0 0
\(183\) 14.7530 1.09057
\(184\) 0 0
\(185\) 10.0807 0.741146
\(186\) 0 0
\(187\) 5.29356 0.387104
\(188\) 0 0
\(189\) 1.70918 0.124324
\(190\) 0 0
\(191\) −15.7289 −1.13810 −0.569052 0.822301i \(-0.692690\pi\)
−0.569052 + 0.822301i \(0.692690\pi\)
\(192\) 0 0
\(193\) 7.59521 0.546715 0.273358 0.961912i \(-0.411866\pi\)
0.273358 + 0.961912i \(0.411866\pi\)
\(194\) 0 0
\(195\) −8.97640 −0.642813
\(196\) 0 0
\(197\) 11.6302 0.828615 0.414308 0.910137i \(-0.364024\pi\)
0.414308 + 0.910137i \(0.364024\pi\)
\(198\) 0 0
\(199\) −2.61756 −0.185554 −0.0927769 0.995687i \(-0.529574\pi\)
−0.0927769 + 0.995687i \(0.529574\pi\)
\(200\) 0 0
\(201\) −30.9758 −2.18486
\(202\) 0 0
\(203\) −6.65785 −0.467289
\(204\) 0 0
\(205\) 18.4987 1.29201
\(206\) 0 0
\(207\) −9.31542 −0.647466
\(208\) 0 0
\(209\) 2.52623 0.174743
\(210\) 0 0
\(211\) 10.4912 0.722244 0.361122 0.932519i \(-0.382394\pi\)
0.361122 + 0.932519i \(0.382394\pi\)
\(212\) 0 0
\(213\) 25.7492 1.76430
\(214\) 0 0
\(215\) −30.6132 −2.08780
\(216\) 0 0
\(217\) 3.98607 0.270592
\(218\) 0 0
\(219\) 25.0311 1.69145
\(220\) 0 0
\(221\) −5.29356 −0.356083
\(222\) 0 0
\(223\) 12.0020 0.803715 0.401857 0.915702i \(-0.368365\pi\)
0.401857 + 0.915702i \(0.368365\pi\)
\(224\) 0 0
\(225\) 23.2989 1.55326
\(226\) 0 0
\(227\) −3.60882 −0.239526 −0.119763 0.992803i \(-0.538213\pi\)
−0.119763 + 0.992803i \(0.538213\pi\)
\(228\) 0 0
\(229\) 8.09460 0.534906 0.267453 0.963571i \(-0.413818\pi\)
0.267453 + 0.963571i \(0.413818\pi\)
\(230\) 0 0
\(231\) −2.29224 −0.150818
\(232\) 0 0
\(233\) 5.11617 0.335171 0.167586 0.985858i \(-0.446403\pi\)
0.167586 + 0.985858i \(0.446403\pi\)
\(234\) 0 0
\(235\) 3.22382 0.210299
\(236\) 0 0
\(237\) 33.2066 2.15700
\(238\) 0 0
\(239\) −5.77529 −0.373573 −0.186786 0.982401i \(-0.559807\pi\)
−0.186786 + 0.982401i \(0.559807\pi\)
\(240\) 0 0
\(241\) −16.7524 −1.07912 −0.539559 0.841948i \(-0.681409\pi\)
−0.539559 + 0.841948i \(0.681409\pi\)
\(242\) 0 0
\(243\) −19.3557 −1.24167
\(244\) 0 0
\(245\) 3.91599 0.250184
\(246\) 0 0
\(247\) −2.52623 −0.160740
\(248\) 0 0
\(249\) −35.8688 −2.27310
\(250\) 0 0
\(251\) −14.7959 −0.933908 −0.466954 0.884282i \(-0.654649\pi\)
−0.466954 + 0.884282i \(0.654649\pi\)
\(252\) 0 0
\(253\) −4.13217 −0.259787
\(254\) 0 0
\(255\) 47.5171 2.97564
\(256\) 0 0
\(257\) 17.3463 1.08203 0.541016 0.841012i \(-0.318040\pi\)
0.541016 + 0.841012i \(0.318040\pi\)
\(258\) 0 0
\(259\) −2.57423 −0.159955
\(260\) 0 0
\(261\) 15.0092 0.929047
\(262\) 0 0
\(263\) 11.2871 0.695993 0.347996 0.937496i \(-0.386862\pi\)
0.347996 + 0.937496i \(0.386862\pi\)
\(264\) 0 0
\(265\) 1.85619 0.114025
\(266\) 0 0
\(267\) −36.7243 −2.24749
\(268\) 0 0
\(269\) −1.24078 −0.0756517 −0.0378259 0.999284i \(-0.512043\pi\)
−0.0378259 + 0.999284i \(0.512043\pi\)
\(270\) 0 0
\(271\) 8.75377 0.531754 0.265877 0.964007i \(-0.414339\pi\)
0.265877 + 0.964007i \(0.414339\pi\)
\(272\) 0 0
\(273\) 2.29224 0.138733
\(274\) 0 0
\(275\) 10.3350 0.623225
\(276\) 0 0
\(277\) −19.0520 −1.14472 −0.572361 0.820002i \(-0.693972\pi\)
−0.572361 + 0.820002i \(0.693972\pi\)
\(278\) 0 0
\(279\) −8.98606 −0.537981
\(280\) 0 0
\(281\) 27.3417 1.63107 0.815534 0.578709i \(-0.196443\pi\)
0.815534 + 0.578709i \(0.196443\pi\)
\(282\) 0 0
\(283\) 25.9988 1.54547 0.772735 0.634729i \(-0.218888\pi\)
0.772735 + 0.634729i \(0.218888\pi\)
\(284\) 0 0
\(285\) 22.6765 1.34324
\(286\) 0 0
\(287\) −4.72390 −0.278843
\(288\) 0 0
\(289\) 11.0218 0.648340
\(290\) 0 0
\(291\) 3.28471 0.192553
\(292\) 0 0
\(293\) −20.2194 −1.18123 −0.590614 0.806954i \(-0.701114\pi\)
−0.590614 + 0.806954i \(0.701114\pi\)
\(294\) 0 0
\(295\) 36.7716 2.14093
\(296\) 0 0
\(297\) −1.70918 −0.0991765
\(298\) 0 0
\(299\) 4.13217 0.238970
\(300\) 0 0
\(301\) 7.81748 0.450592
\(302\) 0 0
\(303\) −22.6972 −1.30392
\(304\) 0 0
\(305\) 25.2036 1.44315
\(306\) 0 0
\(307\) −10.4580 −0.596868 −0.298434 0.954430i \(-0.596464\pi\)
−0.298434 + 0.954430i \(0.596464\pi\)
\(308\) 0 0
\(309\) −16.8535 −0.958763
\(310\) 0 0
\(311\) −14.7905 −0.838693 −0.419347 0.907826i \(-0.637741\pi\)
−0.419347 + 0.907826i \(0.637741\pi\)
\(312\) 0 0
\(313\) 26.2194 1.48201 0.741005 0.671499i \(-0.234349\pi\)
0.741005 + 0.671499i \(0.234349\pi\)
\(314\) 0 0
\(315\) −8.82808 −0.497406
\(316\) 0 0
\(317\) −22.7090 −1.27546 −0.637732 0.770258i \(-0.720127\pi\)
−0.637732 + 0.770258i \(0.720127\pi\)
\(318\) 0 0
\(319\) 6.65785 0.372768
\(320\) 0 0
\(321\) 11.3090 0.631207
\(322\) 0 0
\(323\) 13.3728 0.744080
\(324\) 0 0
\(325\) −10.3350 −0.573283
\(326\) 0 0
\(327\) −24.6596 −1.36368
\(328\) 0 0
\(329\) −0.823244 −0.0453869
\(330\) 0 0
\(331\) −22.1276 −1.21624 −0.608121 0.793845i \(-0.708076\pi\)
−0.608121 + 0.793845i \(0.708076\pi\)
\(332\) 0 0
\(333\) 5.80326 0.318016
\(334\) 0 0
\(335\) −52.9181 −2.89122
\(336\) 0 0
\(337\) −21.5860 −1.17586 −0.587931 0.808911i \(-0.700057\pi\)
−0.587931 + 0.808911i \(0.700057\pi\)
\(338\) 0 0
\(339\) −10.5531 −0.573168
\(340\) 0 0
\(341\) −3.98607 −0.215858
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −37.0920 −1.99697
\(346\) 0 0
\(347\) −11.7174 −0.629021 −0.314511 0.949254i \(-0.601840\pi\)
−0.314511 + 0.949254i \(0.601840\pi\)
\(348\) 0 0
\(349\) −12.0852 −0.646906 −0.323453 0.946244i \(-0.604844\pi\)
−0.323453 + 0.946244i \(0.604844\pi\)
\(350\) 0 0
\(351\) 1.70918 0.0912291
\(352\) 0 0
\(353\) −2.29821 −0.122321 −0.0611607 0.998128i \(-0.519480\pi\)
−0.0611607 + 0.998128i \(0.519480\pi\)
\(354\) 0 0
\(355\) 43.9891 2.33470
\(356\) 0 0
\(357\) −12.1341 −0.642205
\(358\) 0 0
\(359\) −10.3778 −0.547720 −0.273860 0.961770i \(-0.588301\pi\)
−0.273860 + 0.961770i \(0.588301\pi\)
\(360\) 0 0
\(361\) −12.6182 −0.664113
\(362\) 0 0
\(363\) 2.29224 0.120311
\(364\) 0 0
\(365\) 42.7624 2.23829
\(366\) 0 0
\(367\) 9.53714 0.497835 0.248917 0.968525i \(-0.419925\pi\)
0.248917 + 0.968525i \(0.419925\pi\)
\(368\) 0 0
\(369\) 10.6494 0.554385
\(370\) 0 0
\(371\) −0.474003 −0.0246090
\(372\) 0 0
\(373\) 31.9254 1.65304 0.826518 0.562910i \(-0.190318\pi\)
0.826518 + 0.562910i \(0.190318\pi\)
\(374\) 0 0
\(375\) 47.8892 2.47299
\(376\) 0 0
\(377\) −6.65785 −0.342897
\(378\) 0 0
\(379\) −9.17132 −0.471099 −0.235550 0.971862i \(-0.575689\pi\)
−0.235550 + 0.971862i \(0.575689\pi\)
\(380\) 0 0
\(381\) 15.0373 0.770384
\(382\) 0 0
\(383\) 3.89314 0.198930 0.0994651 0.995041i \(-0.468287\pi\)
0.0994651 + 0.995041i \(0.468287\pi\)
\(384\) 0 0
\(385\) −3.91599 −0.199578
\(386\) 0 0
\(387\) −17.6234 −0.895850
\(388\) 0 0
\(389\) 0.762615 0.0386661 0.0193331 0.999813i \(-0.493846\pi\)
0.0193331 + 0.999813i \(0.493846\pi\)
\(390\) 0 0
\(391\) −21.8739 −1.10621
\(392\) 0 0
\(393\) 4.25442 0.214607
\(394\) 0 0
\(395\) 56.7292 2.85436
\(396\) 0 0
\(397\) −11.5906 −0.581715 −0.290858 0.956766i \(-0.593941\pi\)
−0.290858 + 0.956766i \(0.593941\pi\)
\(398\) 0 0
\(399\) −5.79073 −0.289899
\(400\) 0 0
\(401\) −3.05610 −0.152614 −0.0763071 0.997084i \(-0.524313\pi\)
−0.0763071 + 0.997084i \(0.524313\pi\)
\(402\) 0 0
\(403\) 3.98607 0.198560
\(404\) 0 0
\(405\) −41.8265 −2.07837
\(406\) 0 0
\(407\) 2.57423 0.127600
\(408\) 0 0
\(409\) −35.9091 −1.77559 −0.887795 0.460238i \(-0.847764\pi\)
−0.887795 + 0.460238i \(0.847764\pi\)
\(410\) 0 0
\(411\) −1.97818 −0.0975765
\(412\) 0 0
\(413\) −9.39011 −0.462057
\(414\) 0 0
\(415\) −61.2773 −3.00798
\(416\) 0 0
\(417\) −17.0738 −0.836108
\(418\) 0 0
\(419\) −6.89573 −0.336878 −0.168439 0.985712i \(-0.553873\pi\)
−0.168439 + 0.985712i \(0.553873\pi\)
\(420\) 0 0
\(421\) −20.0036 −0.974917 −0.487459 0.873146i \(-0.662076\pi\)
−0.487459 + 0.873146i \(0.662076\pi\)
\(422\) 0 0
\(423\) 1.85589 0.0902365
\(424\) 0 0
\(425\) 54.7090 2.65378
\(426\) 0 0
\(427\) −6.43606 −0.311463
\(428\) 0 0
\(429\) −2.29224 −0.110670
\(430\) 0 0
\(431\) −37.6016 −1.81121 −0.905603 0.424126i \(-0.860581\pi\)
−0.905603 + 0.424126i \(0.860581\pi\)
\(432\) 0 0
\(433\) 5.69079 0.273482 0.136741 0.990607i \(-0.456337\pi\)
0.136741 + 0.990607i \(0.456337\pi\)
\(434\) 0 0
\(435\) 59.7635 2.86544
\(436\) 0 0
\(437\) −10.4388 −0.499356
\(438\) 0 0
\(439\) 19.1665 0.914766 0.457383 0.889270i \(-0.348787\pi\)
0.457383 + 0.889270i \(0.348787\pi\)
\(440\) 0 0
\(441\) 2.25436 0.107351
\(442\) 0 0
\(443\) −33.2787 −1.58112 −0.790559 0.612386i \(-0.790210\pi\)
−0.790559 + 0.612386i \(0.790210\pi\)
\(444\) 0 0
\(445\) −62.7387 −2.97410
\(446\) 0 0
\(447\) 18.9946 0.898415
\(448\) 0 0
\(449\) −38.2020 −1.80287 −0.901433 0.432919i \(-0.857483\pi\)
−0.901433 + 0.432919i \(0.857483\pi\)
\(450\) 0 0
\(451\) 4.72390 0.222440
\(452\) 0 0
\(453\) 17.5715 0.825582
\(454\) 0 0
\(455\) 3.91599 0.183585
\(456\) 0 0
\(457\) 30.5982 1.43132 0.715662 0.698447i \(-0.246125\pi\)
0.715662 + 0.698447i \(0.246125\pi\)
\(458\) 0 0
\(459\) −9.04763 −0.422307
\(460\) 0 0
\(461\) −18.4074 −0.857319 −0.428659 0.903466i \(-0.641014\pi\)
−0.428659 + 0.903466i \(0.641014\pi\)
\(462\) 0 0
\(463\) 12.8888 0.598993 0.299496 0.954097i \(-0.403181\pi\)
0.299496 + 0.954097i \(0.403181\pi\)
\(464\) 0 0
\(465\) −35.7806 −1.65929
\(466\) 0 0
\(467\) 37.4568 1.73329 0.866647 0.498921i \(-0.166270\pi\)
0.866647 + 0.498921i \(0.166270\pi\)
\(468\) 0 0
\(469\) 13.5133 0.623987
\(470\) 0 0
\(471\) 54.2150 2.49810
\(472\) 0 0
\(473\) −7.81748 −0.359448
\(474\) 0 0
\(475\) 26.1086 1.19795
\(476\) 0 0
\(477\) 1.06857 0.0489267
\(478\) 0 0
\(479\) −17.5064 −0.799889 −0.399945 0.916539i \(-0.630971\pi\)
−0.399945 + 0.916539i \(0.630971\pi\)
\(480\) 0 0
\(481\) −2.57423 −0.117375
\(482\) 0 0
\(483\) 9.47193 0.430988
\(484\) 0 0
\(485\) 5.61151 0.254806
\(486\) 0 0
\(487\) 42.3008 1.91683 0.958416 0.285375i \(-0.0921181\pi\)
0.958416 + 0.285375i \(0.0921181\pi\)
\(488\) 0 0
\(489\) −9.63776 −0.435834
\(490\) 0 0
\(491\) 8.16601 0.368527 0.184263 0.982877i \(-0.441010\pi\)
0.184263 + 0.982877i \(0.441010\pi\)
\(492\) 0 0
\(493\) 35.2437 1.58730
\(494\) 0 0
\(495\) 8.82808 0.396793
\(496\) 0 0
\(497\) −11.2332 −0.503878
\(498\) 0 0
\(499\) −31.4136 −1.40627 −0.703134 0.711058i \(-0.748216\pi\)
−0.703134 + 0.711058i \(0.748216\pi\)
\(500\) 0 0
\(501\) 49.6897 2.21997
\(502\) 0 0
\(503\) −16.1653 −0.720776 −0.360388 0.932802i \(-0.617356\pi\)
−0.360388 + 0.932802i \(0.617356\pi\)
\(504\) 0 0
\(505\) −38.7753 −1.72548
\(506\) 0 0
\(507\) 2.29224 0.101802
\(508\) 0 0
\(509\) 29.7395 1.31818 0.659090 0.752064i \(-0.270941\pi\)
0.659090 + 0.752064i \(0.270941\pi\)
\(510\) 0 0
\(511\) −10.9199 −0.483069
\(512\) 0 0
\(513\) −4.31778 −0.190634
\(514\) 0 0
\(515\) −28.7920 −1.26873
\(516\) 0 0
\(517\) 0.823244 0.0362062
\(518\) 0 0
\(519\) −12.9728 −0.569443
\(520\) 0 0
\(521\) 13.6438 0.597748 0.298874 0.954293i \(-0.403389\pi\)
0.298874 + 0.954293i \(0.403389\pi\)
\(522\) 0 0
\(523\) 5.94985 0.260169 0.130084 0.991503i \(-0.458475\pi\)
0.130084 + 0.991503i \(0.458475\pi\)
\(524\) 0 0
\(525\) −23.6903 −1.03393
\(526\) 0 0
\(527\) −21.1005 −0.919153
\(528\) 0 0
\(529\) −5.92517 −0.257616
\(530\) 0 0
\(531\) 21.1687 0.918645
\(532\) 0 0
\(533\) −4.72390 −0.204615
\(534\) 0 0
\(535\) 19.3200 0.835275
\(536\) 0 0
\(537\) −20.8508 −0.899779
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 7.45868 0.320674 0.160337 0.987062i \(-0.448742\pi\)
0.160337 + 0.987062i \(0.448742\pi\)
\(542\) 0 0
\(543\) −60.6705 −2.60362
\(544\) 0 0
\(545\) −42.1278 −1.80456
\(546\) 0 0
\(547\) −33.2378 −1.42115 −0.710573 0.703623i \(-0.751564\pi\)
−0.710573 + 0.703623i \(0.751564\pi\)
\(548\) 0 0
\(549\) 14.5092 0.619238
\(550\) 0 0
\(551\) 16.8193 0.716525
\(552\) 0 0
\(553\) −14.4865 −0.616031
\(554\) 0 0
\(555\) 23.1073 0.980852
\(556\) 0 0
\(557\) 9.73600 0.412527 0.206264 0.978496i \(-0.433870\pi\)
0.206264 + 0.978496i \(0.433870\pi\)
\(558\) 0 0
\(559\) 7.81748 0.330644
\(560\) 0 0
\(561\) 12.1341 0.512303
\(562\) 0 0
\(563\) −26.1109 −1.10044 −0.550221 0.835019i \(-0.685457\pi\)
−0.550221 + 0.835019i \(0.685457\pi\)
\(564\) 0 0
\(565\) −18.0287 −0.758472
\(566\) 0 0
\(567\) 10.6809 0.448557
\(568\) 0 0
\(569\) 4.95977 0.207924 0.103962 0.994581i \(-0.466848\pi\)
0.103962 + 0.994581i \(0.466848\pi\)
\(570\) 0 0
\(571\) 4.17043 0.174527 0.0872635 0.996185i \(-0.472188\pi\)
0.0872635 + 0.996185i \(0.472188\pi\)
\(572\) 0 0
\(573\) −36.0544 −1.50620
\(574\) 0 0
\(575\) −42.7060 −1.78096
\(576\) 0 0
\(577\) −0.106554 −0.00443592 −0.00221796 0.999998i \(-0.500706\pi\)
−0.00221796 + 0.999998i \(0.500706\pi\)
\(578\) 0 0
\(579\) 17.4100 0.723537
\(580\) 0 0
\(581\) 15.6479 0.649186
\(582\) 0 0
\(583\) 0.474003 0.0196312
\(584\) 0 0
\(585\) −8.82808 −0.364996
\(586\) 0 0
\(587\) 21.2490 0.877041 0.438520 0.898721i \(-0.355503\pi\)
0.438520 + 0.898721i \(0.355503\pi\)
\(588\) 0 0
\(589\) −10.0697 −0.414917
\(590\) 0 0
\(591\) 26.6591 1.09661
\(592\) 0 0
\(593\) −14.0513 −0.577018 −0.288509 0.957477i \(-0.593160\pi\)
−0.288509 + 0.957477i \(0.593160\pi\)
\(594\) 0 0
\(595\) −20.7296 −0.849829
\(596\) 0 0
\(597\) −6.00007 −0.245567
\(598\) 0 0
\(599\) −1.23424 −0.0504296 −0.0252148 0.999682i \(-0.508027\pi\)
−0.0252148 + 0.999682i \(0.508027\pi\)
\(600\) 0 0
\(601\) 1.92576 0.0785536 0.0392768 0.999228i \(-0.487495\pi\)
0.0392768 + 0.999228i \(0.487495\pi\)
\(602\) 0 0
\(603\) −30.4639 −1.24059
\(604\) 0 0
\(605\) 3.91599 0.159208
\(606\) 0 0
\(607\) −33.4630 −1.35822 −0.679110 0.734036i \(-0.737634\pi\)
−0.679110 + 0.734036i \(0.737634\pi\)
\(608\) 0 0
\(609\) −15.2614 −0.618422
\(610\) 0 0
\(611\) −0.823244 −0.0333049
\(612\) 0 0
\(613\) −28.4200 −1.14787 −0.573937 0.818900i \(-0.694584\pi\)
−0.573937 + 0.818900i \(0.694584\pi\)
\(614\) 0 0
\(615\) 42.4036 1.70988
\(616\) 0 0
\(617\) −43.9714 −1.77022 −0.885112 0.465379i \(-0.845918\pi\)
−0.885112 + 0.465379i \(0.845918\pi\)
\(618\) 0 0
\(619\) −4.17708 −0.167891 −0.0839456 0.996470i \(-0.526752\pi\)
−0.0839456 + 0.996470i \(0.526752\pi\)
\(620\) 0 0
\(621\) 7.06261 0.283413
\(622\) 0 0
\(623\) 16.0211 0.641874
\(624\) 0 0
\(625\) 30.1374 1.20550
\(626\) 0 0
\(627\) 5.79073 0.231259
\(628\) 0 0
\(629\) 13.6269 0.543338
\(630\) 0 0
\(631\) −24.9393 −0.992816 −0.496408 0.868089i \(-0.665348\pi\)
−0.496408 + 0.868089i \(0.665348\pi\)
\(632\) 0 0
\(633\) 24.0483 0.955836
\(634\) 0 0
\(635\) 25.6893 1.01945
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 25.3237 1.00179
\(640\) 0 0
\(641\) −18.0807 −0.714146 −0.357073 0.934077i \(-0.616225\pi\)
−0.357073 + 0.934077i \(0.616225\pi\)
\(642\) 0 0
\(643\) 29.3811 1.15868 0.579338 0.815087i \(-0.303311\pi\)
0.579338 + 0.815087i \(0.303311\pi\)
\(644\) 0 0
\(645\) −70.1728 −2.76305
\(646\) 0 0
\(647\) −22.0899 −0.868443 −0.434222 0.900806i \(-0.642977\pi\)
−0.434222 + 0.900806i \(0.642977\pi\)
\(648\) 0 0
\(649\) 9.39011 0.368594
\(650\) 0 0
\(651\) 9.13704 0.358109
\(652\) 0 0
\(653\) −48.1624 −1.88474 −0.942369 0.334574i \(-0.891408\pi\)
−0.942369 + 0.334574i \(0.891408\pi\)
\(654\) 0 0
\(655\) 7.26812 0.283989
\(656\) 0 0
\(657\) 24.6175 0.960420
\(658\) 0 0
\(659\) −27.4995 −1.07123 −0.535615 0.844462i \(-0.679920\pi\)
−0.535615 + 0.844462i \(0.679920\pi\)
\(660\) 0 0
\(661\) 38.4814 1.49675 0.748376 0.663275i \(-0.230834\pi\)
0.748376 + 0.663275i \(0.230834\pi\)
\(662\) 0 0
\(663\) −12.1341 −0.471250
\(664\) 0 0
\(665\) −9.89271 −0.383623
\(666\) 0 0
\(667\) −27.5114 −1.06524
\(668\) 0 0
\(669\) 27.5115 1.06366
\(670\) 0 0
\(671\) 6.43606 0.248461
\(672\) 0 0
\(673\) −13.7001 −0.528101 −0.264051 0.964509i \(-0.585059\pi\)
−0.264051 + 0.964509i \(0.585059\pi\)
\(674\) 0 0
\(675\) −17.6644 −0.679902
\(676\) 0 0
\(677\) 42.1888 1.62145 0.810723 0.585430i \(-0.199074\pi\)
0.810723 + 0.585430i \(0.199074\pi\)
\(678\) 0 0
\(679\) −1.43297 −0.0549924
\(680\) 0 0
\(681\) −8.27228 −0.316994
\(682\) 0 0
\(683\) 38.4227 1.47020 0.735102 0.677956i \(-0.237134\pi\)
0.735102 + 0.677956i \(0.237134\pi\)
\(684\) 0 0
\(685\) −3.37947 −0.129123
\(686\) 0 0
\(687\) 18.5548 0.707908
\(688\) 0 0
\(689\) −0.474003 −0.0180581
\(690\) 0 0
\(691\) 40.1544 1.52755 0.763773 0.645485i \(-0.223345\pi\)
0.763773 + 0.645485i \(0.223345\pi\)
\(692\) 0 0
\(693\) −2.25436 −0.0856362
\(694\) 0 0
\(695\) −29.1684 −1.10642
\(696\) 0 0
\(697\) 25.0062 0.947178
\(698\) 0 0
\(699\) 11.7275 0.443574
\(700\) 0 0
\(701\) 13.1405 0.496308 0.248154 0.968721i \(-0.420176\pi\)
0.248154 + 0.968721i \(0.420176\pi\)
\(702\) 0 0
\(703\) 6.50311 0.245269
\(704\) 0 0
\(705\) 7.38977 0.278315
\(706\) 0 0
\(707\) 9.90176 0.372394
\(708\) 0 0
\(709\) 47.8981 1.79885 0.899425 0.437076i \(-0.143986\pi\)
0.899425 + 0.437076i \(0.143986\pi\)
\(710\) 0 0
\(711\) 32.6580 1.22477
\(712\) 0 0
\(713\) 16.4711 0.616849
\(714\) 0 0
\(715\) −3.91599 −0.146450
\(716\) 0 0
\(717\) −13.2384 −0.494395
\(718\) 0 0
\(719\) −36.2505 −1.35192 −0.675959 0.736940i \(-0.736270\pi\)
−0.675959 + 0.736940i \(0.736270\pi\)
\(720\) 0 0
\(721\) 7.35242 0.273818
\(722\) 0 0
\(723\) −38.4005 −1.42813
\(724\) 0 0
\(725\) 68.8089 2.55550
\(726\) 0 0
\(727\) 4.69897 0.174275 0.0871375 0.996196i \(-0.472228\pi\)
0.0871375 + 0.996196i \(0.472228\pi\)
\(728\) 0 0
\(729\) −12.3252 −0.456488
\(730\) 0 0
\(731\) −41.3823 −1.53058
\(732\) 0 0
\(733\) 21.8058 0.805414 0.402707 0.915329i \(-0.368069\pi\)
0.402707 + 0.915329i \(0.368069\pi\)
\(734\) 0 0
\(735\) 8.97640 0.331099
\(736\) 0 0
\(737\) −13.5133 −0.497769
\(738\) 0 0
\(739\) 33.5000 1.23232 0.616158 0.787623i \(-0.288688\pi\)
0.616158 + 0.787623i \(0.288688\pi\)
\(740\) 0 0
\(741\) −5.79073 −0.212728
\(742\) 0 0
\(743\) 53.3020 1.95546 0.977731 0.209863i \(-0.0673018\pi\)
0.977731 + 0.209863i \(0.0673018\pi\)
\(744\) 0 0
\(745\) 32.4499 1.18887
\(746\) 0 0
\(747\) −35.2762 −1.29069
\(748\) 0 0
\(749\) −4.93360 −0.180270
\(750\) 0 0
\(751\) 7.22369 0.263596 0.131798 0.991277i \(-0.457925\pi\)
0.131798 + 0.991277i \(0.457925\pi\)
\(752\) 0 0
\(753\) −33.9157 −1.23596
\(754\) 0 0
\(755\) 30.0187 1.09249
\(756\) 0 0
\(757\) −4.63587 −0.168493 −0.0842467 0.996445i \(-0.526848\pi\)
−0.0842467 + 0.996445i \(0.526848\pi\)
\(758\) 0 0
\(759\) −9.47193 −0.343809
\(760\) 0 0
\(761\) −34.3969 −1.24688 −0.623442 0.781869i \(-0.714266\pi\)
−0.623442 + 0.781869i \(0.714266\pi\)
\(762\) 0 0
\(763\) 10.7579 0.389461
\(764\) 0 0
\(765\) 46.7320 1.68960
\(766\) 0 0
\(767\) −9.39011 −0.339057
\(768\) 0 0
\(769\) 9.55462 0.344548 0.172274 0.985049i \(-0.444888\pi\)
0.172274 + 0.985049i \(0.444888\pi\)
\(770\) 0 0
\(771\) 39.7619 1.43199
\(772\) 0 0
\(773\) −11.9002 −0.428019 −0.214010 0.976832i \(-0.568652\pi\)
−0.214010 + 0.976832i \(0.568652\pi\)
\(774\) 0 0
\(775\) −41.1961 −1.47981
\(776\) 0 0
\(777\) −5.90076 −0.211688
\(778\) 0 0
\(779\) 11.9337 0.427568
\(780\) 0 0
\(781\) 11.2332 0.401955
\(782\) 0 0
\(783\) −11.3794 −0.406668
\(784\) 0 0
\(785\) 92.6194 3.30573
\(786\) 0 0
\(787\) −22.1305 −0.788868 −0.394434 0.918924i \(-0.629059\pi\)
−0.394434 + 0.918924i \(0.629059\pi\)
\(788\) 0 0
\(789\) 25.8728 0.921095
\(790\) 0 0
\(791\) 4.60386 0.163694
\(792\) 0 0
\(793\) −6.43606 −0.228551
\(794\) 0 0
\(795\) 4.25484 0.150903
\(796\) 0 0
\(797\) −6.89964 −0.244398 −0.122199 0.992506i \(-0.538995\pi\)
−0.122199 + 0.992506i \(0.538995\pi\)
\(798\) 0 0
\(799\) 4.35789 0.154171
\(800\) 0 0
\(801\) −36.1175 −1.27615
\(802\) 0 0
\(803\) 10.9199 0.385356
\(804\) 0 0
\(805\) 16.1816 0.570325
\(806\) 0 0
\(807\) −2.84417 −0.100119
\(808\) 0 0
\(809\) 7.05115 0.247905 0.123953 0.992288i \(-0.460443\pi\)
0.123953 + 0.992288i \(0.460443\pi\)
\(810\) 0 0
\(811\) 45.5752 1.60036 0.800182 0.599758i \(-0.204736\pi\)
0.800182 + 0.599758i \(0.204736\pi\)
\(812\) 0 0
\(813\) 20.0657 0.703736
\(814\) 0 0
\(815\) −16.4649 −0.576739
\(816\) 0 0
\(817\) −19.7488 −0.690922
\(818\) 0 0
\(819\) 2.25436 0.0787739
\(820\) 0 0
\(821\) −2.44063 −0.0851785 −0.0425893 0.999093i \(-0.513561\pi\)
−0.0425893 + 0.999093i \(0.513561\pi\)
\(822\) 0 0
\(823\) −22.5556 −0.786238 −0.393119 0.919488i \(-0.628604\pi\)
−0.393119 + 0.919488i \(0.628604\pi\)
\(824\) 0 0
\(825\) 23.6903 0.824791
\(826\) 0 0
\(827\) −55.2486 −1.92118 −0.960592 0.277963i \(-0.910341\pi\)
−0.960592 + 0.277963i \(0.910341\pi\)
\(828\) 0 0
\(829\) −0.745883 −0.0259056 −0.0129528 0.999916i \(-0.504123\pi\)
−0.0129528 + 0.999916i \(0.504123\pi\)
\(830\) 0 0
\(831\) −43.6717 −1.51495
\(832\) 0 0
\(833\) 5.29356 0.183411
\(834\) 0 0
\(835\) 84.8883 2.93768
\(836\) 0 0
\(837\) 6.81290 0.235488
\(838\) 0 0
\(839\) −28.0788 −0.969387 −0.484694 0.874684i \(-0.661069\pi\)
−0.484694 + 0.874684i \(0.661069\pi\)
\(840\) 0 0
\(841\) 15.3269 0.528515
\(842\) 0 0
\(843\) 62.6737 2.15860
\(844\) 0 0
\(845\) 3.91599 0.134714
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 59.5955 2.04531
\(850\) 0 0
\(851\) −10.6372 −0.364637
\(852\) 0 0
\(853\) 47.7511 1.63497 0.817483 0.575952i \(-0.195369\pi\)
0.817483 + 0.575952i \(0.195369\pi\)
\(854\) 0 0
\(855\) 22.3018 0.762704
\(856\) 0 0
\(857\) −28.9286 −0.988182 −0.494091 0.869410i \(-0.664499\pi\)
−0.494091 + 0.869410i \(0.664499\pi\)
\(858\) 0 0
\(859\) −11.2251 −0.382996 −0.191498 0.981493i \(-0.561335\pi\)
−0.191498 + 0.981493i \(0.561335\pi\)
\(860\) 0 0
\(861\) −10.8283 −0.369028
\(862\) 0 0
\(863\) −15.7525 −0.536222 −0.268111 0.963388i \(-0.586399\pi\)
−0.268111 + 0.963388i \(0.586399\pi\)
\(864\) 0 0
\(865\) −22.1624 −0.753543
\(866\) 0 0
\(867\) 25.2646 0.858030
\(868\) 0 0
\(869\) 14.4865 0.491422
\(870\) 0 0
\(871\) 13.5133 0.457881
\(872\) 0 0
\(873\) 3.23044 0.109334
\(874\) 0 0
\(875\) −20.8919 −0.706275
\(876\) 0 0
\(877\) 31.1425 1.05161 0.525805 0.850605i \(-0.323764\pi\)
0.525805 + 0.850605i \(0.323764\pi\)
\(878\) 0 0
\(879\) −46.3476 −1.56327
\(880\) 0 0
\(881\) −37.5111 −1.26378 −0.631891 0.775057i \(-0.717721\pi\)
−0.631891 + 0.775057i \(0.717721\pi\)
\(882\) 0 0
\(883\) −28.7365 −0.967061 −0.483531 0.875327i \(-0.660646\pi\)
−0.483531 + 0.875327i \(0.660646\pi\)
\(884\) 0 0
\(885\) 84.2894 2.83336
\(886\) 0 0
\(887\) −42.5333 −1.42813 −0.714065 0.700079i \(-0.753148\pi\)
−0.714065 + 0.700079i \(0.753148\pi\)
\(888\) 0 0
\(889\) −6.56009 −0.220018
\(890\) 0 0
\(891\) −10.6809 −0.357825
\(892\) 0 0
\(893\) 2.07971 0.0695947
\(894\) 0 0
\(895\) −35.6209 −1.19068
\(896\) 0 0
\(897\) 9.47193 0.316258
\(898\) 0 0
\(899\) −26.5387 −0.885114
\(900\) 0 0
\(901\) 2.50916 0.0835923
\(902\) 0 0
\(903\) 17.9195 0.596325
\(904\) 0 0
\(905\) −103.648 −3.44536
\(906\) 0 0
\(907\) 14.5125 0.481881 0.240940 0.970540i \(-0.422544\pi\)
0.240940 + 0.970540i \(0.422544\pi\)
\(908\) 0 0
\(909\) −22.3222 −0.740380
\(910\) 0 0
\(911\) −12.1469 −0.402446 −0.201223 0.979545i \(-0.564492\pi\)
−0.201223 + 0.979545i \(0.564492\pi\)
\(912\) 0 0
\(913\) −15.6479 −0.517871
\(914\) 0 0
\(915\) 57.7726 1.90990
\(916\) 0 0
\(917\) −1.85601 −0.0612908
\(918\) 0 0
\(919\) 3.64879 0.120363 0.0601813 0.998187i \(-0.480832\pi\)
0.0601813 + 0.998187i \(0.480832\pi\)
\(920\) 0 0
\(921\) −23.9722 −0.789911
\(922\) 0 0
\(923\) −11.2332 −0.369745
\(924\) 0 0
\(925\) 26.6047 0.874758
\(926\) 0 0
\(927\) −16.5750 −0.544395
\(928\) 0 0
\(929\) 14.4675 0.474662 0.237331 0.971429i \(-0.423727\pi\)
0.237331 + 0.971429i \(0.423727\pi\)
\(930\) 0 0
\(931\) 2.52623 0.0827939
\(932\) 0 0
\(933\) −33.9034 −1.10995
\(934\) 0 0
\(935\) 20.7296 0.677929
\(936\) 0 0
\(937\) 25.0598 0.818669 0.409334 0.912384i \(-0.365761\pi\)
0.409334 + 0.912384i \(0.365761\pi\)
\(938\) 0 0
\(939\) 60.1013 1.96133
\(940\) 0 0
\(941\) 5.56445 0.181396 0.0906979 0.995878i \(-0.471090\pi\)
0.0906979 + 0.995878i \(0.471090\pi\)
\(942\) 0 0
\(943\) −19.5199 −0.635657
\(944\) 0 0
\(945\) 6.69313 0.217727
\(946\) 0 0
\(947\) 4.20309 0.136582 0.0682911 0.997665i \(-0.478245\pi\)
0.0682911 + 0.997665i \(0.478245\pi\)
\(948\) 0 0
\(949\) −10.9199 −0.354476
\(950\) 0 0
\(951\) −52.0545 −1.68798
\(952\) 0 0
\(953\) −7.69251 −0.249185 −0.124592 0.992208i \(-0.539762\pi\)
−0.124592 + 0.992208i \(0.539762\pi\)
\(954\) 0 0
\(955\) −61.5943 −1.99315
\(956\) 0 0
\(957\) 15.2614 0.493330
\(958\) 0 0
\(959\) 0.862991 0.0278674
\(960\) 0 0
\(961\) −15.1112 −0.487459
\(962\) 0 0
\(963\) 11.1221 0.358406
\(964\) 0 0
\(965\) 29.7428 0.957455
\(966\) 0 0
\(967\) 27.3065 0.878119 0.439060 0.898458i \(-0.355312\pi\)
0.439060 + 0.898458i \(0.355312\pi\)
\(968\) 0 0
\(969\) 30.6536 0.984735
\(970\) 0 0
\(971\) 1.66328 0.0533771 0.0266886 0.999644i \(-0.491504\pi\)
0.0266886 + 0.999644i \(0.491504\pi\)
\(972\) 0 0
\(973\) 7.44853 0.238789
\(974\) 0 0
\(975\) −23.6903 −0.758698
\(976\) 0 0
\(977\) 52.0088 1.66391 0.831954 0.554845i \(-0.187222\pi\)
0.831954 + 0.554845i \(0.187222\pi\)
\(978\) 0 0
\(979\) −16.0211 −0.512038
\(980\) 0 0
\(981\) −24.2522 −0.774312
\(982\) 0 0
\(983\) 48.8967 1.55956 0.779781 0.626053i \(-0.215331\pi\)
0.779781 + 0.626053i \(0.215331\pi\)
\(984\) 0 0
\(985\) 45.5437 1.45114
\(986\) 0 0
\(987\) −1.88707 −0.0600662
\(988\) 0 0
\(989\) 32.3032 1.02718
\(990\) 0 0
\(991\) 30.2429 0.960696 0.480348 0.877078i \(-0.340510\pi\)
0.480348 + 0.877078i \(0.340510\pi\)
\(992\) 0 0
\(993\) −50.7217 −1.60960
\(994\) 0 0
\(995\) −10.2503 −0.324958
\(996\) 0 0
\(997\) 41.1103 1.30198 0.650988 0.759088i \(-0.274355\pi\)
0.650988 + 0.759088i \(0.274355\pi\)
\(998\) 0 0
\(999\) −4.39982 −0.139204
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 \(a_p\))