Properties

Label 8008.2.a.p.1.3
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
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: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.00974\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00974 q^{3} +2.49743 q^{5} -1.00000 q^{7} -1.98043 q^{9} +O(q^{10})\) \(q-1.00974 q^{3} +2.49743 q^{5} -1.00000 q^{7} -1.98043 q^{9} +1.00000 q^{11} +1.00000 q^{13} -2.52176 q^{15} -4.53427 q^{17} -0.365921 q^{19} +1.00974 q^{21} +2.18456 q^{23} +1.23718 q^{25} +5.02893 q^{27} +7.70380 q^{29} -6.21949 q^{31} -1.00974 q^{33} -2.49743 q^{35} -6.41650 q^{37} -1.00974 q^{39} -0.881703 q^{41} -2.18214 q^{43} -4.94598 q^{45} +13.5382 q^{47} +1.00000 q^{49} +4.57843 q^{51} -5.98388 q^{53} +2.49743 q^{55} +0.369485 q^{57} +11.1921 q^{59} -4.84106 q^{61} +1.98043 q^{63} +2.49743 q^{65} -0.801261 q^{67} -2.20584 q^{69} +10.5313 q^{71} -15.0437 q^{73} -1.24923 q^{75} -1.00000 q^{77} -10.8318 q^{79} +0.863362 q^{81} -11.4116 q^{83} -11.3240 q^{85} -7.77884 q^{87} +2.15030 q^{89} -1.00000 q^{91} +6.28007 q^{93} -0.913864 q^{95} -4.92908 q^{97} -1.98043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

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
\(3\) −1.00974 −0.582974 −0.291487 0.956575i \(-0.594150\pi\)
−0.291487 + 0.956575i \(0.594150\pi\)
\(4\) 0 0
\(5\) 2.49743 1.11689 0.558443 0.829543i \(-0.311399\pi\)
0.558443 + 0.829543i \(0.311399\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −1.98043 −0.660142
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −2.52176 −0.651115
\(16\) 0 0
\(17\) −4.53427 −1.09972 −0.549861 0.835256i \(-0.685319\pi\)
−0.549861 + 0.835256i \(0.685319\pi\)
\(18\) 0 0
\(19\) −0.365921 −0.0839481 −0.0419740 0.999119i \(-0.513365\pi\)
−0.0419740 + 0.999119i \(0.513365\pi\)
\(20\) 0 0
\(21\) 1.00974 0.220343
\(22\) 0 0
\(23\) 2.18456 0.455513 0.227757 0.973718i \(-0.426861\pi\)
0.227757 + 0.973718i \(0.426861\pi\)
\(24\) 0 0
\(25\) 1.23718 0.247436
\(26\) 0 0
\(27\) 5.02893 0.967819
\(28\) 0 0
\(29\) 7.70380 1.43056 0.715280 0.698838i \(-0.246299\pi\)
0.715280 + 0.698838i \(0.246299\pi\)
\(30\) 0 0
\(31\) −6.21949 −1.11705 −0.558527 0.829486i \(-0.688633\pi\)
−0.558527 + 0.829486i \(0.688633\pi\)
\(32\) 0 0
\(33\) −1.00974 −0.175773
\(34\) 0 0
\(35\) −2.49743 −0.422144
\(36\) 0 0
\(37\) −6.41650 −1.05487 −0.527433 0.849596i \(-0.676846\pi\)
−0.527433 + 0.849596i \(0.676846\pi\)
\(38\) 0 0
\(39\) −1.00974 −0.161688
\(40\) 0 0
\(41\) −0.881703 −0.137699 −0.0688495 0.997627i \(-0.521933\pi\)
−0.0688495 + 0.997627i \(0.521933\pi\)
\(42\) 0 0
\(43\) −2.18214 −0.332773 −0.166386 0.986061i \(-0.553210\pi\)
−0.166386 + 0.986061i \(0.553210\pi\)
\(44\) 0 0
\(45\) −4.94598 −0.737304
\(46\) 0 0
\(47\) 13.5382 1.97475 0.987373 0.158415i \(-0.0506384\pi\)
0.987373 + 0.158415i \(0.0506384\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 4.57843 0.641109
\(52\) 0 0
\(53\) −5.98388 −0.821949 −0.410974 0.911647i \(-0.634811\pi\)
−0.410974 + 0.911647i \(0.634811\pi\)
\(54\) 0 0
\(55\) 2.49743 0.336754
\(56\) 0 0
\(57\) 0.369485 0.0489395
\(58\) 0 0
\(59\) 11.1921 1.45709 0.728544 0.684999i \(-0.240197\pi\)
0.728544 + 0.684999i \(0.240197\pi\)
\(60\) 0 0
\(61\) −4.84106 −0.619835 −0.309917 0.950764i \(-0.600301\pi\)
−0.309917 + 0.950764i \(0.600301\pi\)
\(62\) 0 0
\(63\) 1.98043 0.249510
\(64\) 0 0
\(65\) 2.49743 0.309769
\(66\) 0 0
\(67\) −0.801261 −0.0978897 −0.0489448 0.998801i \(-0.515586\pi\)
−0.0489448 + 0.998801i \(0.515586\pi\)
\(68\) 0 0
\(69\) −2.20584 −0.265552
\(70\) 0 0
\(71\) 10.5313 1.24984 0.624921 0.780688i \(-0.285131\pi\)
0.624921 + 0.780688i \(0.285131\pi\)
\(72\) 0 0
\(73\) −15.0437 −1.76073 −0.880367 0.474294i \(-0.842703\pi\)
−0.880367 + 0.474294i \(0.842703\pi\)
\(74\) 0 0
\(75\) −1.24923 −0.144249
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −10.8318 −1.21868 −0.609339 0.792910i \(-0.708565\pi\)
−0.609339 + 0.792910i \(0.708565\pi\)
\(80\) 0 0
\(81\) 0.863362 0.0959291
\(82\) 0 0
\(83\) −11.4116 −1.25259 −0.626294 0.779587i \(-0.715429\pi\)
−0.626294 + 0.779587i \(0.715429\pi\)
\(84\) 0 0
\(85\) −11.3240 −1.22826
\(86\) 0 0
\(87\) −7.77884 −0.833979
\(88\) 0 0
\(89\) 2.15030 0.227931 0.113965 0.993485i \(-0.463645\pi\)
0.113965 + 0.993485i \(0.463645\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 6.28007 0.651213
\(94\) 0 0
\(95\) −0.913864 −0.0937605
\(96\) 0 0
\(97\) −4.92908 −0.500473 −0.250236 0.968185i \(-0.580508\pi\)
−0.250236 + 0.968185i \(0.580508\pi\)
\(98\) 0 0
\(99\) −1.98043 −0.199040
\(100\) 0 0
\(101\) 0.302490 0.0300989 0.0150495 0.999887i \(-0.495209\pi\)
0.0150495 + 0.999887i \(0.495209\pi\)
\(102\) 0 0
\(103\) 12.4841 1.23010 0.615048 0.788489i \(-0.289136\pi\)
0.615048 + 0.788489i \(0.289136\pi\)
\(104\) 0 0
\(105\) 2.52176 0.246099
\(106\) 0 0
\(107\) −19.3796 −1.87350 −0.936750 0.349998i \(-0.886182\pi\)
−0.936750 + 0.349998i \(0.886182\pi\)
\(108\) 0 0
\(109\) −10.6608 −1.02112 −0.510561 0.859842i \(-0.670562\pi\)
−0.510561 + 0.859842i \(0.670562\pi\)
\(110\) 0 0
\(111\) 6.47900 0.614959
\(112\) 0 0
\(113\) 2.85865 0.268919 0.134459 0.990919i \(-0.457070\pi\)
0.134459 + 0.990919i \(0.457070\pi\)
\(114\) 0 0
\(115\) 5.45581 0.508757
\(116\) 0 0
\(117\) −1.98043 −0.183090
\(118\) 0 0
\(119\) 4.53427 0.415656
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0.890291 0.0802748
\(124\) 0 0
\(125\) −9.39740 −0.840529
\(126\) 0 0
\(127\) 6.74502 0.598523 0.299262 0.954171i \(-0.403260\pi\)
0.299262 + 0.954171i \(0.403260\pi\)
\(128\) 0 0
\(129\) 2.20339 0.193998
\(130\) 0 0
\(131\) 4.19971 0.366930 0.183465 0.983026i \(-0.441269\pi\)
0.183465 + 0.983026i \(0.441269\pi\)
\(132\) 0 0
\(133\) 0.365921 0.0317294
\(134\) 0 0
\(135\) 12.5594 1.08094
\(136\) 0 0
\(137\) −1.91501 −0.163610 −0.0818051 0.996648i \(-0.526068\pi\)
−0.0818051 + 0.996648i \(0.526068\pi\)
\(138\) 0 0
\(139\) −10.7175 −0.909044 −0.454522 0.890735i \(-0.650190\pi\)
−0.454522 + 0.890735i \(0.650190\pi\)
\(140\) 0 0
\(141\) −13.6700 −1.15122
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 19.2397 1.59777
\(146\) 0 0
\(147\) −1.00974 −0.0832819
\(148\) 0 0
\(149\) 11.1801 0.915912 0.457956 0.888975i \(-0.348582\pi\)
0.457956 + 0.888975i \(0.348582\pi\)
\(150\) 0 0
\(151\) −0.960122 −0.0781336 −0.0390668 0.999237i \(-0.512439\pi\)
−0.0390668 + 0.999237i \(0.512439\pi\)
\(152\) 0 0
\(153\) 8.97978 0.725972
\(154\) 0 0
\(155\) −15.5328 −1.24762
\(156\) 0 0
\(157\) −15.2642 −1.21822 −0.609109 0.793086i \(-0.708473\pi\)
−0.609109 + 0.793086i \(0.708473\pi\)
\(158\) 0 0
\(159\) 6.04216 0.479174
\(160\) 0 0
\(161\) −2.18456 −0.172168
\(162\) 0 0
\(163\) −14.9718 −1.17268 −0.586341 0.810064i \(-0.699432\pi\)
−0.586341 + 0.810064i \(0.699432\pi\)
\(164\) 0 0
\(165\) −2.52176 −0.196319
\(166\) 0 0
\(167\) 4.94970 0.383020 0.191510 0.981491i \(-0.438662\pi\)
0.191510 + 0.981491i \(0.438662\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.724680 0.0554176
\(172\) 0 0
\(173\) −2.24942 −0.171020 −0.0855101 0.996337i \(-0.527252\pi\)
−0.0855101 + 0.996337i \(0.527252\pi\)
\(174\) 0 0
\(175\) −1.23718 −0.0935221
\(176\) 0 0
\(177\) −11.3011 −0.849444
\(178\) 0 0
\(179\) −6.92785 −0.517812 −0.258906 0.965903i \(-0.583362\pi\)
−0.258906 + 0.965903i \(0.583362\pi\)
\(180\) 0 0
\(181\) −5.74336 −0.426900 −0.213450 0.976954i \(-0.568470\pi\)
−0.213450 + 0.976954i \(0.568470\pi\)
\(182\) 0 0
\(183\) 4.88821 0.361347
\(184\) 0 0
\(185\) −16.0248 −1.17817
\(186\) 0 0
\(187\) −4.53427 −0.331579
\(188\) 0 0
\(189\) −5.02893 −0.365801
\(190\) 0 0
\(191\) −16.4151 −1.18775 −0.593877 0.804556i \(-0.702403\pi\)
−0.593877 + 0.804556i \(0.702403\pi\)
\(192\) 0 0
\(193\) −11.7374 −0.844878 −0.422439 0.906391i \(-0.638826\pi\)
−0.422439 + 0.906391i \(0.638826\pi\)
\(194\) 0 0
\(195\) −2.52176 −0.180587
\(196\) 0 0
\(197\) 7.58716 0.540563 0.270281 0.962781i \(-0.412883\pi\)
0.270281 + 0.962781i \(0.412883\pi\)
\(198\) 0 0
\(199\) −9.79733 −0.694514 −0.347257 0.937770i \(-0.612887\pi\)
−0.347257 + 0.937770i \(0.612887\pi\)
\(200\) 0 0
\(201\) 0.809066 0.0570671
\(202\) 0 0
\(203\) −7.70380 −0.540701
\(204\) 0 0
\(205\) −2.20200 −0.153794
\(206\) 0 0
\(207\) −4.32637 −0.300703
\(208\) 0 0
\(209\) −0.365921 −0.0253113
\(210\) 0 0
\(211\) 26.3422 1.81347 0.906736 0.421698i \(-0.138566\pi\)
0.906736 + 0.421698i \(0.138566\pi\)
\(212\) 0 0
\(213\) −10.6339 −0.728624
\(214\) 0 0
\(215\) −5.44975 −0.371670
\(216\) 0 0
\(217\) 6.21949 0.422207
\(218\) 0 0
\(219\) 15.1902 1.02646
\(220\) 0 0
\(221\) −4.53427 −0.305008
\(222\) 0 0
\(223\) −12.3050 −0.824007 −0.412003 0.911182i \(-0.635171\pi\)
−0.412003 + 0.911182i \(0.635171\pi\)
\(224\) 0 0
\(225\) −2.45014 −0.163343
\(226\) 0 0
\(227\) 1.54237 0.102371 0.0511855 0.998689i \(-0.483700\pi\)
0.0511855 + 0.998689i \(0.483700\pi\)
\(228\) 0 0
\(229\) −17.9995 −1.18944 −0.594720 0.803933i \(-0.702737\pi\)
−0.594720 + 0.803933i \(0.702737\pi\)
\(230\) 0 0
\(231\) 1.00974 0.0664360
\(232\) 0 0
\(233\) −15.9375 −1.04410 −0.522050 0.852915i \(-0.674833\pi\)
−0.522050 + 0.852915i \(0.674833\pi\)
\(234\) 0 0
\(235\) 33.8107 2.20557
\(236\) 0 0
\(237\) 10.9373 0.710457
\(238\) 0 0
\(239\) 18.3433 1.18653 0.593266 0.805006i \(-0.297838\pi\)
0.593266 + 0.805006i \(0.297838\pi\)
\(240\) 0 0
\(241\) −8.61217 −0.554758 −0.277379 0.960761i \(-0.589466\pi\)
−0.277379 + 0.960761i \(0.589466\pi\)
\(242\) 0 0
\(243\) −15.9586 −1.02374
\(244\) 0 0
\(245\) 2.49743 0.159555
\(246\) 0 0
\(247\) −0.365921 −0.0232830
\(248\) 0 0
\(249\) 11.5228 0.730226
\(250\) 0 0
\(251\) −11.4344 −0.721734 −0.360867 0.932617i \(-0.617519\pi\)
−0.360867 + 0.932617i \(0.617519\pi\)
\(252\) 0 0
\(253\) 2.18456 0.137342
\(254\) 0 0
\(255\) 11.4343 0.716046
\(256\) 0 0
\(257\) −16.8208 −1.04925 −0.524625 0.851333i \(-0.675795\pi\)
−0.524625 + 0.851333i \(0.675795\pi\)
\(258\) 0 0
\(259\) 6.41650 0.398702
\(260\) 0 0
\(261\) −15.2568 −0.944373
\(262\) 0 0
\(263\) 18.2677 1.12644 0.563218 0.826308i \(-0.309563\pi\)
0.563218 + 0.826308i \(0.309563\pi\)
\(264\) 0 0
\(265\) −14.9443 −0.918023
\(266\) 0 0
\(267\) −2.17124 −0.132878
\(268\) 0 0
\(269\) −12.3169 −0.750975 −0.375487 0.926828i \(-0.622525\pi\)
−0.375487 + 0.926828i \(0.622525\pi\)
\(270\) 0 0
\(271\) 24.3006 1.47616 0.738079 0.674714i \(-0.235733\pi\)
0.738079 + 0.674714i \(0.235733\pi\)
\(272\) 0 0
\(273\) 1.00974 0.0611122
\(274\) 0 0
\(275\) 1.23718 0.0746048
\(276\) 0 0
\(277\) −4.14292 −0.248924 −0.124462 0.992224i \(-0.539720\pi\)
−0.124462 + 0.992224i \(0.539720\pi\)
\(278\) 0 0
\(279\) 12.3172 0.737414
\(280\) 0 0
\(281\) −31.2332 −1.86321 −0.931607 0.363467i \(-0.881593\pi\)
−0.931607 + 0.363467i \(0.881593\pi\)
\(282\) 0 0
\(283\) 16.6563 0.990112 0.495056 0.868861i \(-0.335148\pi\)
0.495056 + 0.868861i \(0.335148\pi\)
\(284\) 0 0
\(285\) 0.922765 0.0546599
\(286\) 0 0
\(287\) 0.881703 0.0520453
\(288\) 0 0
\(289\) 3.55959 0.209388
\(290\) 0 0
\(291\) 4.97709 0.291762
\(292\) 0 0
\(293\) 27.0128 1.57810 0.789052 0.614327i \(-0.210572\pi\)
0.789052 + 0.614327i \(0.210572\pi\)
\(294\) 0 0
\(295\) 27.9516 1.62740
\(296\) 0 0
\(297\) 5.02893 0.291808
\(298\) 0 0
\(299\) 2.18456 0.126337
\(300\) 0 0
\(301\) 2.18214 0.125776
\(302\) 0 0
\(303\) −0.305437 −0.0175469
\(304\) 0 0
\(305\) −12.0902 −0.692285
\(306\) 0 0
\(307\) −15.7935 −0.901382 −0.450691 0.892680i \(-0.648822\pi\)
−0.450691 + 0.892680i \(0.648822\pi\)
\(308\) 0 0
\(309\) −12.6057 −0.717114
\(310\) 0 0
\(311\) 17.3795 0.985501 0.492750 0.870171i \(-0.335992\pi\)
0.492750 + 0.870171i \(0.335992\pi\)
\(312\) 0 0
\(313\) 13.0958 0.740220 0.370110 0.928988i \(-0.379320\pi\)
0.370110 + 0.928988i \(0.379320\pi\)
\(314\) 0 0
\(315\) 4.94598 0.278675
\(316\) 0 0
\(317\) 33.9025 1.90416 0.952078 0.305857i \(-0.0989429\pi\)
0.952078 + 0.305857i \(0.0989429\pi\)
\(318\) 0 0
\(319\) 7.70380 0.431330
\(320\) 0 0
\(321\) 19.5684 1.09220
\(322\) 0 0
\(323\) 1.65918 0.0923195
\(324\) 0 0
\(325\) 1.23718 0.0686264
\(326\) 0 0
\(327\) 10.7647 0.595287
\(328\) 0 0
\(329\) −13.5382 −0.746384
\(330\) 0 0
\(331\) −17.4390 −0.958531 −0.479266 0.877670i \(-0.659097\pi\)
−0.479266 + 0.877670i \(0.659097\pi\)
\(332\) 0 0
\(333\) 12.7074 0.696362
\(334\) 0 0
\(335\) −2.00110 −0.109332
\(336\) 0 0
\(337\) −11.3030 −0.615711 −0.307856 0.951433i \(-0.599611\pi\)
−0.307856 + 0.951433i \(0.599611\pi\)
\(338\) 0 0
\(339\) −2.88649 −0.156773
\(340\) 0 0
\(341\) −6.21949 −0.336805
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −5.50895 −0.296592
\(346\) 0 0
\(347\) −10.4541 −0.561205 −0.280603 0.959824i \(-0.590534\pi\)
−0.280603 + 0.959824i \(0.590534\pi\)
\(348\) 0 0
\(349\) 3.67327 0.196626 0.0983129 0.995156i \(-0.468655\pi\)
0.0983129 + 0.995156i \(0.468655\pi\)
\(350\) 0 0
\(351\) 5.02893 0.268425
\(352\) 0 0
\(353\) 5.58978 0.297514 0.148757 0.988874i \(-0.452473\pi\)
0.148757 + 0.988874i \(0.452473\pi\)
\(354\) 0 0
\(355\) 26.3014 1.39593
\(356\) 0 0
\(357\) −4.57843 −0.242316
\(358\) 0 0
\(359\) −18.9758 −1.00150 −0.500751 0.865591i \(-0.666943\pi\)
−0.500751 + 0.865591i \(0.666943\pi\)
\(360\) 0 0
\(361\) −18.8661 −0.992953
\(362\) 0 0
\(363\) −1.00974 −0.0529976
\(364\) 0 0
\(365\) −37.5707 −1.96654
\(366\) 0 0
\(367\) 0.649035 0.0338794 0.0169397 0.999857i \(-0.494608\pi\)
0.0169397 + 0.999857i \(0.494608\pi\)
\(368\) 0 0
\(369\) 1.74615 0.0909008
\(370\) 0 0
\(371\) 5.98388 0.310667
\(372\) 0 0
\(373\) −6.93989 −0.359334 −0.179667 0.983727i \(-0.557502\pi\)
−0.179667 + 0.983727i \(0.557502\pi\)
\(374\) 0 0
\(375\) 9.48893 0.490006
\(376\) 0 0
\(377\) 7.70380 0.396766
\(378\) 0 0
\(379\) −18.5005 −0.950309 −0.475155 0.879902i \(-0.657608\pi\)
−0.475155 + 0.879902i \(0.657608\pi\)
\(380\) 0 0
\(381\) −6.81071 −0.348923
\(382\) 0 0
\(383\) −11.2993 −0.577367 −0.288683 0.957425i \(-0.593217\pi\)
−0.288683 + 0.957425i \(0.593217\pi\)
\(384\) 0 0
\(385\) −2.49743 −0.127281
\(386\) 0 0
\(387\) 4.32156 0.219677
\(388\) 0 0
\(389\) 15.0292 0.762012 0.381006 0.924572i \(-0.375578\pi\)
0.381006 + 0.924572i \(0.375578\pi\)
\(390\) 0 0
\(391\) −9.90540 −0.500938
\(392\) 0 0
\(393\) −4.24061 −0.213911
\(394\) 0 0
\(395\) −27.0518 −1.36112
\(396\) 0 0
\(397\) −9.95471 −0.499613 −0.249806 0.968296i \(-0.580367\pi\)
−0.249806 + 0.968296i \(0.580367\pi\)
\(398\) 0 0
\(399\) −0.369485 −0.0184974
\(400\) 0 0
\(401\) 16.4612 0.822035 0.411017 0.911627i \(-0.365174\pi\)
0.411017 + 0.911627i \(0.365174\pi\)
\(402\) 0 0
\(403\) −6.21949 −0.309815
\(404\) 0 0
\(405\) 2.15619 0.107142
\(406\) 0 0
\(407\) −6.41650 −0.318054
\(408\) 0 0
\(409\) −19.2681 −0.952747 −0.476373 0.879243i \(-0.658049\pi\)
−0.476373 + 0.879243i \(0.658049\pi\)
\(410\) 0 0
\(411\) 1.93366 0.0953804
\(412\) 0 0
\(413\) −11.1921 −0.550728
\(414\) 0 0
\(415\) −28.4998 −1.39900
\(416\) 0 0
\(417\) 10.8219 0.529949
\(418\) 0 0
\(419\) 5.68072 0.277522 0.138761 0.990326i \(-0.455688\pi\)
0.138761 + 0.990326i \(0.455688\pi\)
\(420\) 0 0
\(421\) 5.71031 0.278303 0.139152 0.990271i \(-0.455562\pi\)
0.139152 + 0.990271i \(0.455562\pi\)
\(422\) 0 0
\(423\) −26.8113 −1.30361
\(424\) 0 0
\(425\) −5.60971 −0.272111
\(426\) 0 0
\(427\) 4.84106 0.234275
\(428\) 0 0
\(429\) −1.00974 −0.0487507
\(430\) 0 0
\(431\) −20.3081 −0.978208 −0.489104 0.872226i \(-0.662676\pi\)
−0.489104 + 0.872226i \(0.662676\pi\)
\(432\) 0 0
\(433\) 9.63239 0.462903 0.231452 0.972846i \(-0.425653\pi\)
0.231452 + 0.972846i \(0.425653\pi\)
\(434\) 0 0
\(435\) −19.4271 −0.931460
\(436\) 0 0
\(437\) −0.799378 −0.0382395
\(438\) 0 0
\(439\) 39.3622 1.87865 0.939327 0.343024i \(-0.111451\pi\)
0.939327 + 0.343024i \(0.111451\pi\)
\(440\) 0 0
\(441\) −1.98043 −0.0943060
\(442\) 0 0
\(443\) −6.88885 −0.327299 −0.163650 0.986519i \(-0.552327\pi\)
−0.163650 + 0.986519i \(0.552327\pi\)
\(444\) 0 0
\(445\) 5.37022 0.254573
\(446\) 0 0
\(447\) −11.2890 −0.533953
\(448\) 0 0
\(449\) 26.8660 1.26789 0.633943 0.773380i \(-0.281435\pi\)
0.633943 + 0.773380i \(0.281435\pi\)
\(450\) 0 0
\(451\) −0.881703 −0.0415178
\(452\) 0 0
\(453\) 0.969473 0.0455498
\(454\) 0 0
\(455\) −2.49743 −0.117082
\(456\) 0 0
\(457\) −19.9684 −0.934082 −0.467041 0.884236i \(-0.654680\pi\)
−0.467041 + 0.884236i \(0.654680\pi\)
\(458\) 0 0
\(459\) −22.8025 −1.06433
\(460\) 0 0
\(461\) −35.3256 −1.64528 −0.822639 0.568563i \(-0.807499\pi\)
−0.822639 + 0.568563i \(0.807499\pi\)
\(462\) 0 0
\(463\) −7.15838 −0.332678 −0.166339 0.986069i \(-0.553195\pi\)
−0.166339 + 0.986069i \(0.553195\pi\)
\(464\) 0 0
\(465\) 15.6841 0.727331
\(466\) 0 0
\(467\) −40.7593 −1.88611 −0.943057 0.332632i \(-0.892063\pi\)
−0.943057 + 0.332632i \(0.892063\pi\)
\(468\) 0 0
\(469\) 0.801261 0.0369988
\(470\) 0 0
\(471\) 15.4129 0.710189
\(472\) 0 0
\(473\) −2.18214 −0.100335
\(474\) 0 0
\(475\) −0.452711 −0.0207718
\(476\) 0 0
\(477\) 11.8506 0.542603
\(478\) 0 0
\(479\) −25.3387 −1.15776 −0.578878 0.815414i \(-0.696509\pi\)
−0.578878 + 0.815414i \(0.696509\pi\)
\(480\) 0 0
\(481\) −6.41650 −0.292567
\(482\) 0 0
\(483\) 2.20584 0.100369
\(484\) 0 0
\(485\) −12.3101 −0.558971
\(486\) 0 0
\(487\) −4.73856 −0.214725 −0.107362 0.994220i \(-0.534240\pi\)
−0.107362 + 0.994220i \(0.534240\pi\)
\(488\) 0 0
\(489\) 15.1176 0.683643
\(490\) 0 0
\(491\) 12.7755 0.576551 0.288276 0.957547i \(-0.406918\pi\)
0.288276 + 0.957547i \(0.406918\pi\)
\(492\) 0 0
\(493\) −34.9311 −1.57322
\(494\) 0 0
\(495\) −4.94598 −0.222305
\(496\) 0 0
\(497\) −10.5313 −0.472396
\(498\) 0 0
\(499\) 24.2772 1.08680 0.543398 0.839475i \(-0.317138\pi\)
0.543398 + 0.839475i \(0.317138\pi\)
\(500\) 0 0
\(501\) −4.99791 −0.223290
\(502\) 0 0
\(503\) 34.5036 1.53844 0.769220 0.638984i \(-0.220645\pi\)
0.769220 + 0.638984i \(0.220645\pi\)
\(504\) 0 0
\(505\) 0.755450 0.0336171
\(506\) 0 0
\(507\) −1.00974 −0.0448441
\(508\) 0 0
\(509\) −29.3212 −1.29964 −0.649820 0.760089i \(-0.725156\pi\)
−0.649820 + 0.760089i \(0.725156\pi\)
\(510\) 0 0
\(511\) 15.0437 0.665495
\(512\) 0 0
\(513\) −1.84019 −0.0812465
\(514\) 0 0
\(515\) 31.1783 1.37388
\(516\) 0 0
\(517\) 13.5382 0.595408
\(518\) 0 0
\(519\) 2.27133 0.0997002
\(520\) 0 0
\(521\) 11.7854 0.516328 0.258164 0.966101i \(-0.416883\pi\)
0.258164 + 0.966101i \(0.416883\pi\)
\(522\) 0 0
\(523\) −26.6854 −1.16687 −0.583435 0.812160i \(-0.698292\pi\)
−0.583435 + 0.812160i \(0.698292\pi\)
\(524\) 0 0
\(525\) 1.24923 0.0545209
\(526\) 0 0
\(527\) 28.2009 1.22845
\(528\) 0 0
\(529\) −18.2277 −0.792508
\(530\) 0 0
\(531\) −22.1651 −0.961885
\(532\) 0 0
\(533\) −0.881703 −0.0381908
\(534\) 0 0
\(535\) −48.3994 −2.09249
\(536\) 0 0
\(537\) 6.99533 0.301871
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −31.7426 −1.36472 −0.682360 0.731017i \(-0.739046\pi\)
−0.682360 + 0.731017i \(0.739046\pi\)
\(542\) 0 0
\(543\) 5.79930 0.248872
\(544\) 0 0
\(545\) −26.6247 −1.14048
\(546\) 0 0
\(547\) −2.11542 −0.0904488 −0.0452244 0.998977i \(-0.514400\pi\)
−0.0452244 + 0.998977i \(0.514400\pi\)
\(548\) 0 0
\(549\) 9.58736 0.409179
\(550\) 0 0
\(551\) −2.81898 −0.120093
\(552\) 0 0
\(553\) 10.8318 0.460617
\(554\) 0 0
\(555\) 16.1809 0.686840
\(556\) 0 0
\(557\) 11.5878 0.490992 0.245496 0.969398i \(-0.421049\pi\)
0.245496 + 0.969398i \(0.421049\pi\)
\(558\) 0 0
\(559\) −2.18214 −0.0922946
\(560\) 0 0
\(561\) 4.57843 0.193302
\(562\) 0 0
\(563\) 23.4621 0.988811 0.494405 0.869231i \(-0.335386\pi\)
0.494405 + 0.869231i \(0.335386\pi\)
\(564\) 0 0
\(565\) 7.13928 0.300352
\(566\) 0 0
\(567\) −0.863362 −0.0362578
\(568\) 0 0
\(569\) −19.2729 −0.807963 −0.403982 0.914767i \(-0.632374\pi\)
−0.403982 + 0.914767i \(0.632374\pi\)
\(570\) 0 0
\(571\) −4.71626 −0.197369 −0.0986847 0.995119i \(-0.531464\pi\)
−0.0986847 + 0.995119i \(0.531464\pi\)
\(572\) 0 0
\(573\) 16.5750 0.692429
\(574\) 0 0
\(575\) 2.70270 0.112710
\(576\) 0 0
\(577\) 1.74840 0.0727866 0.0363933 0.999338i \(-0.488413\pi\)
0.0363933 + 0.999338i \(0.488413\pi\)
\(578\) 0 0
\(579\) 11.8517 0.492541
\(580\) 0 0
\(581\) 11.4116 0.473434
\(582\) 0 0
\(583\) −5.98388 −0.247827
\(584\) 0 0
\(585\) −4.94598 −0.204491
\(586\) 0 0
\(587\) 6.22227 0.256821 0.128410 0.991721i \(-0.459013\pi\)
0.128410 + 0.991721i \(0.459013\pi\)
\(588\) 0 0
\(589\) 2.27584 0.0937745
\(590\) 0 0
\(591\) −7.66105 −0.315134
\(592\) 0 0
\(593\) −39.2842 −1.61321 −0.806604 0.591092i \(-0.798697\pi\)
−0.806604 + 0.591092i \(0.798697\pi\)
\(594\) 0 0
\(595\) 11.3240 0.464240
\(596\) 0 0
\(597\) 9.89275 0.404883
\(598\) 0 0
\(599\) 15.9615 0.652169 0.326084 0.945341i \(-0.394271\pi\)
0.326084 + 0.945341i \(0.394271\pi\)
\(600\) 0 0
\(601\) 13.3564 0.544820 0.272410 0.962181i \(-0.412179\pi\)
0.272410 + 0.962181i \(0.412179\pi\)
\(602\) 0 0
\(603\) 1.58684 0.0646211
\(604\) 0 0
\(605\) 2.49743 0.101535
\(606\) 0 0
\(607\) −44.2807 −1.79730 −0.898649 0.438669i \(-0.855450\pi\)
−0.898649 + 0.438669i \(0.855450\pi\)
\(608\) 0 0
\(609\) 7.77884 0.315214
\(610\) 0 0
\(611\) 13.5382 0.547696
\(612\) 0 0
\(613\) 10.6381 0.429670 0.214835 0.976650i \(-0.431079\pi\)
0.214835 + 0.976650i \(0.431079\pi\)
\(614\) 0 0
\(615\) 2.22344 0.0896579
\(616\) 0 0
\(617\) −3.79544 −0.152799 −0.0763994 0.997077i \(-0.524342\pi\)
−0.0763994 + 0.997077i \(0.524342\pi\)
\(618\) 0 0
\(619\) −33.1177 −1.33111 −0.665556 0.746348i \(-0.731806\pi\)
−0.665556 + 0.746348i \(0.731806\pi\)
\(620\) 0 0
\(621\) 10.9860 0.440854
\(622\) 0 0
\(623\) −2.15030 −0.0861498
\(624\) 0 0
\(625\) −29.6553 −1.18621
\(626\) 0 0
\(627\) 0.369485 0.0147558
\(628\) 0 0
\(629\) 29.0942 1.16006
\(630\) 0 0
\(631\) −15.6084 −0.621360 −0.310680 0.950515i \(-0.600557\pi\)
−0.310680 + 0.950515i \(0.600557\pi\)
\(632\) 0 0
\(633\) −26.5988 −1.05721
\(634\) 0 0
\(635\) 16.8452 0.668483
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −20.8566 −0.825072
\(640\) 0 0
\(641\) −11.1102 −0.438825 −0.219413 0.975632i \(-0.570414\pi\)
−0.219413 + 0.975632i \(0.570414\pi\)
\(642\) 0 0
\(643\) −1.12970 −0.0445510 −0.0222755 0.999752i \(-0.507091\pi\)
−0.0222755 + 0.999752i \(0.507091\pi\)
\(644\) 0 0
\(645\) 5.50283 0.216674
\(646\) 0 0
\(647\) 1.67659 0.0659134 0.0329567 0.999457i \(-0.489508\pi\)
0.0329567 + 0.999457i \(0.489508\pi\)
\(648\) 0 0
\(649\) 11.1921 0.439329
\(650\) 0 0
\(651\) −6.28007 −0.246135
\(652\) 0 0
\(653\) 40.4887 1.58445 0.792224 0.610231i \(-0.208923\pi\)
0.792224 + 0.610231i \(0.208923\pi\)
\(654\) 0 0
\(655\) 10.4885 0.409820
\(656\) 0 0
\(657\) 29.7929 1.16233
\(658\) 0 0
\(659\) 15.6442 0.609411 0.304706 0.952447i \(-0.401442\pi\)
0.304706 + 0.952447i \(0.401442\pi\)
\(660\) 0 0
\(661\) 8.38907 0.326297 0.163149 0.986602i \(-0.447835\pi\)
0.163149 + 0.986602i \(0.447835\pi\)
\(662\) 0 0
\(663\) 4.57843 0.177812
\(664\) 0 0
\(665\) 0.913864 0.0354381
\(666\) 0 0
\(667\) 16.8295 0.651639
\(668\) 0 0
\(669\) 12.4249 0.480374
\(670\) 0 0
\(671\) −4.84106 −0.186887
\(672\) 0 0
\(673\) −37.1583 −1.43235 −0.716173 0.697923i \(-0.754108\pi\)
−0.716173 + 0.697923i \(0.754108\pi\)
\(674\) 0 0
\(675\) 6.22170 0.239473
\(676\) 0 0
\(677\) 21.5564 0.828479 0.414239 0.910168i \(-0.364048\pi\)
0.414239 + 0.910168i \(0.364048\pi\)
\(678\) 0 0
\(679\) 4.92908 0.189161
\(680\) 0 0
\(681\) −1.55740 −0.0596795
\(682\) 0 0
\(683\) −10.5299 −0.402917 −0.201458 0.979497i \(-0.564568\pi\)
−0.201458 + 0.979497i \(0.564568\pi\)
\(684\) 0 0
\(685\) −4.78261 −0.182734
\(686\) 0 0
\(687\) 18.1748 0.693412
\(688\) 0 0
\(689\) −5.98388 −0.227968
\(690\) 0 0
\(691\) 52.3175 1.99025 0.995125 0.0986202i \(-0.0314429\pi\)
0.995125 + 0.0986202i \(0.0314429\pi\)
\(692\) 0 0
\(693\) 1.98043 0.0752301
\(694\) 0 0
\(695\) −26.7662 −1.01530
\(696\) 0 0
\(697\) 3.99788 0.151431
\(698\) 0 0
\(699\) 16.0927 0.608683
\(700\) 0 0
\(701\) −5.79701 −0.218950 −0.109475 0.993990i \(-0.534917\pi\)
−0.109475 + 0.993990i \(0.534917\pi\)
\(702\) 0 0
\(703\) 2.34793 0.0885540
\(704\) 0 0
\(705\) −34.1400 −1.28579
\(706\) 0 0
\(707\) −0.302490 −0.0113763
\(708\) 0 0
\(709\) −27.5275 −1.03382 −0.516908 0.856041i \(-0.672917\pi\)
−0.516908 + 0.856041i \(0.672917\pi\)
\(710\) 0 0
\(711\) 21.4517 0.804500
\(712\) 0 0
\(713\) −13.5869 −0.508833
\(714\) 0 0
\(715\) 2.49743 0.0933988
\(716\) 0 0
\(717\) −18.5220 −0.691717
\(718\) 0 0
\(719\) −23.2588 −0.867408 −0.433704 0.901055i \(-0.642794\pi\)
−0.433704 + 0.901055i \(0.642794\pi\)
\(720\) 0 0
\(721\) −12.4841 −0.464933
\(722\) 0 0
\(723\) 8.69605 0.323410
\(724\) 0 0
\(725\) 9.53099 0.353972
\(726\) 0 0
\(727\) −34.9978 −1.29800 −0.648999 0.760790i \(-0.724812\pi\)
−0.648999 + 0.760790i \(0.724812\pi\)
\(728\) 0 0
\(729\) 13.5239 0.500886
\(730\) 0 0
\(731\) 9.89440 0.365958
\(732\) 0 0
\(733\) 22.1423 0.817845 0.408922 0.912569i \(-0.365905\pi\)
0.408922 + 0.912569i \(0.365905\pi\)
\(734\) 0 0
\(735\) −2.52176 −0.0930165
\(736\) 0 0
\(737\) −0.801261 −0.0295148
\(738\) 0 0
\(739\) −30.3036 −1.11474 −0.557368 0.830266i \(-0.688189\pi\)
−0.557368 + 0.830266i \(0.688189\pi\)
\(740\) 0 0
\(741\) 0.369485 0.0135734
\(742\) 0 0
\(743\) −34.5396 −1.26714 −0.633568 0.773687i \(-0.718410\pi\)
−0.633568 + 0.773687i \(0.718410\pi\)
\(744\) 0 0
\(745\) 27.9217 1.02297
\(746\) 0 0
\(747\) 22.5999 0.826886
\(748\) 0 0
\(749\) 19.3796 0.708117
\(750\) 0 0
\(751\) 47.4273 1.73065 0.865323 0.501214i \(-0.167113\pi\)
0.865323 + 0.501214i \(0.167113\pi\)
\(752\) 0 0
\(753\) 11.5458 0.420752
\(754\) 0 0
\(755\) −2.39784 −0.0872664
\(756\) 0 0
\(757\) −6.64799 −0.241625 −0.120813 0.992675i \(-0.538550\pi\)
−0.120813 + 0.992675i \(0.538550\pi\)
\(758\) 0 0
\(759\) −2.20584 −0.0800670
\(760\) 0 0
\(761\) 35.9591 1.30352 0.651758 0.758427i \(-0.274032\pi\)
0.651758 + 0.758427i \(0.274032\pi\)
\(762\) 0 0
\(763\) 10.6608 0.385948
\(764\) 0 0
\(765\) 22.4264 0.810829
\(766\) 0 0
\(767\) 11.1921 0.404124
\(768\) 0 0
\(769\) −12.7818 −0.460924 −0.230462 0.973081i \(-0.574024\pi\)
−0.230462 + 0.973081i \(0.574024\pi\)
\(770\) 0 0
\(771\) 16.9846 0.611685
\(772\) 0 0
\(773\) −30.0166 −1.07962 −0.539812 0.841786i \(-0.681505\pi\)
−0.539812 + 0.841786i \(0.681505\pi\)
\(774\) 0 0
\(775\) −7.69464 −0.276400
\(776\) 0 0
\(777\) −6.47900 −0.232433
\(778\) 0 0
\(779\) 0.322634 0.0115596
\(780\) 0 0
\(781\) 10.5313 0.376841
\(782\) 0 0
\(783\) 38.7419 1.38452
\(784\) 0 0
\(785\) −38.1214 −1.36061
\(786\) 0 0
\(787\) −35.4408 −1.26333 −0.631664 0.775242i \(-0.717628\pi\)
−0.631664 + 0.775242i \(0.717628\pi\)
\(788\) 0 0
\(789\) −18.4457 −0.656683
\(790\) 0 0
\(791\) −2.85865 −0.101642
\(792\) 0 0
\(793\) −4.84106 −0.171911
\(794\) 0 0
\(795\) 15.0899 0.535183
\(796\) 0 0
\(797\) 43.5538 1.54275 0.771377 0.636379i \(-0.219568\pi\)
0.771377 + 0.636379i \(0.219568\pi\)
\(798\) 0 0
\(799\) −61.3857 −2.17167
\(800\) 0 0
\(801\) −4.25850 −0.150467
\(802\) 0 0
\(803\) −15.0437 −0.530881
\(804\) 0 0
\(805\) −5.45581 −0.192292
\(806\) 0 0
\(807\) 12.4369 0.437798
\(808\) 0 0
\(809\) −28.7702 −1.01151 −0.505753 0.862678i \(-0.668785\pi\)
−0.505753 + 0.862678i \(0.668785\pi\)
\(810\) 0 0
\(811\) 6.53736 0.229558 0.114779 0.993391i \(-0.463384\pi\)
0.114779 + 0.993391i \(0.463384\pi\)
\(812\) 0 0
\(813\) −24.5373 −0.860561
\(814\) 0 0
\(815\) −37.3911 −1.30975
\(816\) 0 0
\(817\) 0.798491 0.0279356
\(818\) 0 0
\(819\) 1.98043 0.0692017
\(820\) 0 0
\(821\) −54.3259 −1.89599 −0.947994 0.318287i \(-0.896892\pi\)
−0.947994 + 0.318287i \(0.896892\pi\)
\(822\) 0 0
\(823\) −17.7051 −0.617161 −0.308580 0.951198i \(-0.599854\pi\)
−0.308580 + 0.951198i \(0.599854\pi\)
\(824\) 0 0
\(825\) −1.24923 −0.0434926
\(826\) 0 0
\(827\) 5.06631 0.176173 0.0880865 0.996113i \(-0.471925\pi\)
0.0880865 + 0.996113i \(0.471925\pi\)
\(828\) 0 0
\(829\) −39.1760 −1.36064 −0.680319 0.732916i \(-0.738159\pi\)
−0.680319 + 0.732916i \(0.738159\pi\)
\(830\) 0 0
\(831\) 4.18327 0.145116
\(832\) 0 0
\(833\) −4.53427 −0.157103
\(834\) 0 0
\(835\) 12.3616 0.427790
\(836\) 0 0
\(837\) −31.2774 −1.08111
\(838\) 0 0
\(839\) 14.3925 0.496884 0.248442 0.968647i \(-0.420082\pi\)
0.248442 + 0.968647i \(0.420082\pi\)
\(840\) 0 0
\(841\) 30.3486 1.04650
\(842\) 0 0
\(843\) 31.5374 1.08620
\(844\) 0 0
\(845\) 2.49743 0.0859144
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −16.8185 −0.577209
\(850\) 0 0
\(851\) −14.0173 −0.480506
\(852\) 0 0
\(853\) −22.5823 −0.773202 −0.386601 0.922247i \(-0.626351\pi\)
−0.386601 + 0.922247i \(0.626351\pi\)
\(854\) 0 0
\(855\) 1.80984 0.0618952
\(856\) 0 0
\(857\) −25.3719 −0.866688 −0.433344 0.901229i \(-0.642666\pi\)
−0.433344 + 0.901229i \(0.642666\pi\)
\(858\) 0 0
\(859\) 11.2873 0.385117 0.192558 0.981286i \(-0.438322\pi\)
0.192558 + 0.981286i \(0.438322\pi\)
\(860\) 0 0
\(861\) −0.890291 −0.0303410
\(862\) 0 0
\(863\) −48.2809 −1.64350 −0.821750 0.569848i \(-0.807002\pi\)
−0.821750 + 0.569848i \(0.807002\pi\)
\(864\) 0 0
\(865\) −5.61778 −0.191010
\(866\) 0 0
\(867\) −3.59426 −0.122068
\(868\) 0 0
\(869\) −10.8318 −0.367445
\(870\) 0 0
\(871\) −0.801261 −0.0271497
\(872\) 0 0
\(873\) 9.76168 0.330383
\(874\) 0 0
\(875\) 9.39740 0.317690
\(876\) 0 0
\(877\) 54.8479 1.85208 0.926040 0.377425i \(-0.123190\pi\)
0.926040 + 0.377425i \(0.123190\pi\)
\(878\) 0 0
\(879\) −27.2759 −0.919993
\(880\) 0 0
\(881\) 17.6520 0.594710 0.297355 0.954767i \(-0.403896\pi\)
0.297355 + 0.954767i \(0.403896\pi\)
\(882\) 0 0
\(883\) −47.7267 −1.60613 −0.803065 0.595891i \(-0.796799\pi\)
−0.803065 + 0.595891i \(0.796799\pi\)
\(884\) 0 0
\(885\) −28.2238 −0.948733
\(886\) 0 0
\(887\) 13.0401 0.437843 0.218922 0.975742i \(-0.429746\pi\)
0.218922 + 0.975742i \(0.429746\pi\)
\(888\) 0 0
\(889\) −6.74502 −0.226221
\(890\) 0 0
\(891\) 0.863362 0.0289237
\(892\) 0 0
\(893\) −4.95390 −0.165776
\(894\) 0 0
\(895\) −17.3019 −0.578337
\(896\) 0 0
\(897\) −2.20584 −0.0736509
\(898\) 0 0
\(899\) −47.9138 −1.59801
\(900\) 0 0
\(901\) 27.1325 0.903915
\(902\) 0 0
\(903\) −2.20339 −0.0733243
\(904\) 0 0
\(905\) −14.3437 −0.476799
\(906\) 0 0
\(907\) −10.4071 −0.345563 −0.172782 0.984960i \(-0.555275\pi\)
−0.172782 + 0.984960i \(0.555275\pi\)
\(908\) 0 0
\(909\) −0.599060 −0.0198696
\(910\) 0 0
\(911\) 8.38463 0.277795 0.138898 0.990307i \(-0.455644\pi\)
0.138898 + 0.990307i \(0.455644\pi\)
\(912\) 0 0
\(913\) −11.4116 −0.377670
\(914\) 0 0
\(915\) 12.2080 0.403584
\(916\) 0 0
\(917\) −4.19971 −0.138687
\(918\) 0 0
\(919\) 40.9995 1.35245 0.676224 0.736696i \(-0.263615\pi\)
0.676224 + 0.736696i \(0.263615\pi\)
\(920\) 0 0
\(921\) 15.9473 0.525482
\(922\) 0 0
\(923\) 10.5313 0.346644
\(924\) 0 0
\(925\) −7.93837 −0.261012
\(926\) 0 0
\(927\) −24.7239 −0.812038
\(928\) 0 0
\(929\) −7.83579 −0.257084 −0.128542 0.991704i \(-0.541030\pi\)
−0.128542 + 0.991704i \(0.541030\pi\)
\(930\) 0 0
\(931\) −0.365921 −0.0119926
\(932\) 0 0
\(933\) −17.5488 −0.574521
\(934\) 0 0
\(935\) −11.3240 −0.370336
\(936\) 0 0
\(937\) −18.1617 −0.593317 −0.296659 0.954984i \(-0.595872\pi\)
−0.296659 + 0.954984i \(0.595872\pi\)
\(938\) 0 0
\(939\) −13.2234 −0.431529
\(940\) 0 0
\(941\) −31.5504 −1.02851 −0.514257 0.857636i \(-0.671932\pi\)
−0.514257 + 0.857636i \(0.671932\pi\)
\(942\) 0 0
\(943\) −1.92614 −0.0627237
\(944\) 0 0
\(945\) −12.5594 −0.408558
\(946\) 0 0
\(947\) 27.3514 0.888802 0.444401 0.895828i \(-0.353417\pi\)
0.444401 + 0.895828i \(0.353417\pi\)
\(948\) 0 0
\(949\) −15.0437 −0.488339
\(950\) 0 0
\(951\) −34.2327 −1.11007
\(952\) 0 0
\(953\) 12.2584 0.397088 0.198544 0.980092i \(-0.436379\pi\)
0.198544 + 0.980092i \(0.436379\pi\)
\(954\) 0 0
\(955\) −40.9956 −1.32659
\(956\) 0 0
\(957\) −7.77884 −0.251454
\(958\) 0 0
\(959\) 1.91501 0.0618388
\(960\) 0 0
\(961\) 7.68211 0.247810
\(962\) 0 0
\(963\) 38.3799 1.23678
\(964\) 0 0
\(965\) −29.3134 −0.943633
\(966\) 0 0
\(967\) 11.2786 0.362697 0.181348 0.983419i \(-0.441954\pi\)
0.181348 + 0.983419i \(0.441954\pi\)
\(968\) 0 0
\(969\) −1.67535 −0.0538198
\(970\) 0 0
\(971\) 40.8741 1.31171 0.655856 0.754886i \(-0.272308\pi\)
0.655856 + 0.754886i \(0.272308\pi\)
\(972\) 0 0
\(973\) 10.7175 0.343586
\(974\) 0 0
\(975\) −1.24923 −0.0400074
\(976\) 0 0
\(977\) 38.3903 1.22821 0.614107 0.789223i \(-0.289516\pi\)
0.614107 + 0.789223i \(0.289516\pi\)
\(978\) 0 0
\(979\) 2.15030 0.0687238
\(980\) 0 0
\(981\) 21.1130 0.674085
\(982\) 0 0
\(983\) 15.4016 0.491233 0.245617 0.969367i \(-0.421010\pi\)
0.245617 + 0.969367i \(0.421010\pi\)
\(984\) 0 0
\(985\) 18.9484 0.603747
\(986\) 0 0
\(987\) 13.6700 0.435122
\(988\) 0 0
\(989\) −4.76702 −0.151582
\(990\) 0 0
\(991\) −19.0694 −0.605759 −0.302879 0.953029i \(-0.597948\pi\)
−0.302879 + 0.953029i \(0.597948\pi\)
\(992\) 0 0
\(993\) 17.6088 0.558798
\(994\) 0 0
\(995\) −24.4682 −0.775694
\(996\) 0 0
\(997\) 62.7971 1.98881 0.994403 0.105656i \(-0.0336944\pi\)
0.994403 + 0.105656i \(0.0336944\pi\)
\(998\) 0 0
\(999\) −32.2682 −1.02092
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 \(a_p\))