Properties

Label 6008.2.a.e.1.25
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.25
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0243322 q^{3} +3.64574 q^{5} -4.79791 q^{7} -2.99941 q^{9} +O(q^{10})\) \(q-0.0243322 q^{3} +3.64574 q^{5} -4.79791 q^{7} -2.99941 q^{9} +4.87158 q^{11} +2.44401 q^{13} -0.0887089 q^{15} -2.69151 q^{17} -1.00162 q^{19} +0.116744 q^{21} -2.85733 q^{23} +8.29142 q^{25} +0.145979 q^{27} +5.94696 q^{29} +3.27534 q^{31} -0.118536 q^{33} -17.4919 q^{35} +6.54988 q^{37} -0.0594682 q^{39} -8.68111 q^{41} +2.95148 q^{43} -10.9351 q^{45} -10.3118 q^{47} +16.0199 q^{49} +0.0654904 q^{51} +7.10743 q^{53} +17.7605 q^{55} +0.0243715 q^{57} +8.34625 q^{59} +8.25579 q^{61} +14.3909 q^{63} +8.91024 q^{65} +3.82406 q^{67} +0.0695252 q^{69} -12.3349 q^{71} -12.9118 q^{73} -0.201748 q^{75} -23.3734 q^{77} -7.35680 q^{79} +8.99467 q^{81} +4.97516 q^{83} -9.81256 q^{85} -0.144703 q^{87} +10.6648 q^{89} -11.7262 q^{91} -0.0796962 q^{93} -3.65163 q^{95} +11.6015 q^{97} -14.6119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.0243322 −0.0140482 −0.00702410 0.999975i \(-0.502236\pi\)
−0.00702410 + 0.999975i \(0.502236\pi\)
\(4\) 0 0
\(5\) 3.64574 1.63042 0.815212 0.579162i \(-0.196620\pi\)
0.815212 + 0.579162i \(0.196620\pi\)
\(6\) 0 0
\(7\) −4.79791 −1.81344 −0.906719 0.421735i \(-0.861421\pi\)
−0.906719 + 0.421735i \(0.861421\pi\)
\(8\) 0 0
\(9\) −2.99941 −0.999803
\(10\) 0 0
\(11\) 4.87158 1.46884 0.734419 0.678697i \(-0.237455\pi\)
0.734419 + 0.678697i \(0.237455\pi\)
\(12\) 0 0
\(13\) 2.44401 0.677847 0.338924 0.940814i \(-0.389937\pi\)
0.338924 + 0.940814i \(0.389937\pi\)
\(14\) 0 0
\(15\) −0.0887089 −0.0229045
\(16\) 0 0
\(17\) −2.69151 −0.652788 −0.326394 0.945234i \(-0.605834\pi\)
−0.326394 + 0.945234i \(0.605834\pi\)
\(18\) 0 0
\(19\) −1.00162 −0.229787 −0.114893 0.993378i \(-0.536653\pi\)
−0.114893 + 0.993378i \(0.536653\pi\)
\(20\) 0 0
\(21\) 0.116744 0.0254756
\(22\) 0 0
\(23\) −2.85733 −0.595795 −0.297897 0.954598i \(-0.596285\pi\)
−0.297897 + 0.954598i \(0.596285\pi\)
\(24\) 0 0
\(25\) 8.29142 1.65828
\(26\) 0 0
\(27\) 0.145979 0.0280936
\(28\) 0 0
\(29\) 5.94696 1.10432 0.552161 0.833737i \(-0.313803\pi\)
0.552161 + 0.833737i \(0.313803\pi\)
\(30\) 0 0
\(31\) 3.27534 0.588268 0.294134 0.955764i \(-0.404969\pi\)
0.294134 + 0.955764i \(0.404969\pi\)
\(32\) 0 0
\(33\) −0.118536 −0.0206345
\(34\) 0 0
\(35\) −17.4919 −2.95667
\(36\) 0 0
\(37\) 6.54988 1.07679 0.538396 0.842692i \(-0.319030\pi\)
0.538396 + 0.842692i \(0.319030\pi\)
\(38\) 0 0
\(39\) −0.0594682 −0.00952254
\(40\) 0 0
\(41\) −8.68111 −1.35576 −0.677881 0.735172i \(-0.737101\pi\)
−0.677881 + 0.735172i \(0.737101\pi\)
\(42\) 0 0
\(43\) 2.95148 0.450096 0.225048 0.974348i \(-0.427746\pi\)
0.225048 + 0.974348i \(0.427746\pi\)
\(44\) 0 0
\(45\) −10.9351 −1.63010
\(46\) 0 0
\(47\) −10.3118 −1.50413 −0.752064 0.659090i \(-0.770941\pi\)
−0.752064 + 0.659090i \(0.770941\pi\)
\(48\) 0 0
\(49\) 16.0199 2.28856
\(50\) 0 0
\(51\) 0.0654904 0.00917050
\(52\) 0 0
\(53\) 7.10743 0.976281 0.488140 0.872765i \(-0.337675\pi\)
0.488140 + 0.872765i \(0.337675\pi\)
\(54\) 0 0
\(55\) 17.7605 2.39483
\(56\) 0 0
\(57\) 0.0243715 0.00322809
\(58\) 0 0
\(59\) 8.34625 1.08659 0.543295 0.839542i \(-0.317177\pi\)
0.543295 + 0.839542i \(0.317177\pi\)
\(60\) 0 0
\(61\) 8.25579 1.05705 0.528523 0.848919i \(-0.322746\pi\)
0.528523 + 0.848919i \(0.322746\pi\)
\(62\) 0 0
\(63\) 14.3909 1.81308
\(64\) 0 0
\(65\) 8.91024 1.10518
\(66\) 0 0
\(67\) 3.82406 0.467183 0.233592 0.972335i \(-0.424952\pi\)
0.233592 + 0.972335i \(0.424952\pi\)
\(68\) 0 0
\(69\) 0.0695252 0.00836985
\(70\) 0 0
\(71\) −12.3349 −1.46389 −0.731943 0.681366i \(-0.761386\pi\)
−0.731943 + 0.681366i \(0.761386\pi\)
\(72\) 0 0
\(73\) −12.9118 −1.51121 −0.755606 0.655026i \(-0.772658\pi\)
−0.755606 + 0.655026i \(0.772658\pi\)
\(74\) 0 0
\(75\) −0.201748 −0.0232959
\(76\) 0 0
\(77\) −23.3734 −2.66365
\(78\) 0 0
\(79\) −7.35680 −0.827705 −0.413853 0.910344i \(-0.635817\pi\)
−0.413853 + 0.910344i \(0.635817\pi\)
\(80\) 0 0
\(81\) 8.99467 0.999408
\(82\) 0 0
\(83\) 4.97516 0.546094 0.273047 0.962001i \(-0.411968\pi\)
0.273047 + 0.962001i \(0.411968\pi\)
\(84\) 0 0
\(85\) −9.81256 −1.06432
\(86\) 0 0
\(87\) −0.144703 −0.0155138
\(88\) 0 0
\(89\) 10.6648 1.13046 0.565231 0.824933i \(-0.308787\pi\)
0.565231 + 0.824933i \(0.308787\pi\)
\(90\) 0 0
\(91\) −11.7262 −1.22923
\(92\) 0 0
\(93\) −0.0796962 −0.00826411
\(94\) 0 0
\(95\) −3.65163 −0.374650
\(96\) 0 0
\(97\) 11.6015 1.17795 0.588976 0.808150i \(-0.299531\pi\)
0.588976 + 0.808150i \(0.299531\pi\)
\(98\) 0 0
\(99\) −14.6119 −1.46855
\(100\) 0 0
\(101\) −6.52237 −0.649000 −0.324500 0.945886i \(-0.605196\pi\)
−0.324500 + 0.945886i \(0.605196\pi\)
\(102\) 0 0
\(103\) 16.8178 1.65711 0.828555 0.559907i \(-0.189163\pi\)
0.828555 + 0.559907i \(0.189163\pi\)
\(104\) 0 0
\(105\) 0.425617 0.0415360
\(106\) 0 0
\(107\) 9.67514 0.935331 0.467666 0.883905i \(-0.345095\pi\)
0.467666 + 0.883905i \(0.345095\pi\)
\(108\) 0 0
\(109\) −7.64926 −0.732667 −0.366333 0.930484i \(-0.619387\pi\)
−0.366333 + 0.930484i \(0.619387\pi\)
\(110\) 0 0
\(111\) −0.159373 −0.0151270
\(112\) 0 0
\(113\) 11.2794 1.06108 0.530538 0.847661i \(-0.321990\pi\)
0.530538 + 0.847661i \(0.321990\pi\)
\(114\) 0 0
\(115\) −10.4171 −0.971398
\(116\) 0 0
\(117\) −7.33059 −0.677714
\(118\) 0 0
\(119\) 12.9136 1.18379
\(120\) 0 0
\(121\) 12.7323 1.15748
\(122\) 0 0
\(123\) 0.211231 0.0190460
\(124\) 0 0
\(125\) 11.9996 1.07328
\(126\) 0 0
\(127\) −1.91112 −0.169585 −0.0847924 0.996399i \(-0.527023\pi\)
−0.0847924 + 0.996399i \(0.527023\pi\)
\(128\) 0 0
\(129\) −0.0718160 −0.00632304
\(130\) 0 0
\(131\) −12.9963 −1.13549 −0.567746 0.823204i \(-0.692184\pi\)
−0.567746 + 0.823204i \(0.692184\pi\)
\(132\) 0 0
\(133\) 4.80566 0.416704
\(134\) 0 0
\(135\) 0.532201 0.0458045
\(136\) 0 0
\(137\) 10.3973 0.888302 0.444151 0.895952i \(-0.353505\pi\)
0.444151 + 0.895952i \(0.353505\pi\)
\(138\) 0 0
\(139\) −0.787016 −0.0667538 −0.0333769 0.999443i \(-0.510626\pi\)
−0.0333769 + 0.999443i \(0.510626\pi\)
\(140\) 0 0
\(141\) 0.250908 0.0211303
\(142\) 0 0
\(143\) 11.9062 0.995648
\(144\) 0 0
\(145\) 21.6811 1.80051
\(146\) 0 0
\(147\) −0.389800 −0.0321502
\(148\) 0 0
\(149\) 7.95896 0.652023 0.326012 0.945366i \(-0.394295\pi\)
0.326012 + 0.945366i \(0.394295\pi\)
\(150\) 0 0
\(151\) 10.3320 0.840810 0.420405 0.907337i \(-0.361888\pi\)
0.420405 + 0.907337i \(0.361888\pi\)
\(152\) 0 0
\(153\) 8.07295 0.652659
\(154\) 0 0
\(155\) 11.9410 0.959127
\(156\) 0 0
\(157\) 9.45680 0.754735 0.377367 0.926064i \(-0.376829\pi\)
0.377367 + 0.926064i \(0.376829\pi\)
\(158\) 0 0
\(159\) −0.172939 −0.0137150
\(160\) 0 0
\(161\) 13.7092 1.08044
\(162\) 0 0
\(163\) 15.5233 1.21588 0.607940 0.793983i \(-0.291996\pi\)
0.607940 + 0.793983i \(0.291996\pi\)
\(164\) 0 0
\(165\) −0.432153 −0.0336430
\(166\) 0 0
\(167\) 6.92499 0.535872 0.267936 0.963437i \(-0.413658\pi\)
0.267936 + 0.963437i \(0.413658\pi\)
\(168\) 0 0
\(169\) −7.02680 −0.540523
\(170\) 0 0
\(171\) 3.00426 0.229741
\(172\) 0 0
\(173\) 22.9779 1.74698 0.873488 0.486846i \(-0.161853\pi\)
0.873488 + 0.486846i \(0.161853\pi\)
\(174\) 0 0
\(175\) −39.7815 −3.00720
\(176\) 0 0
\(177\) −0.203083 −0.0152646
\(178\) 0 0
\(179\) −13.7459 −1.02741 −0.513707 0.857966i \(-0.671728\pi\)
−0.513707 + 0.857966i \(0.671728\pi\)
\(180\) 0 0
\(181\) 1.57194 0.116842 0.0584209 0.998292i \(-0.481393\pi\)
0.0584209 + 0.998292i \(0.481393\pi\)
\(182\) 0 0
\(183\) −0.200881 −0.0148496
\(184\) 0 0
\(185\) 23.8791 1.75563
\(186\) 0 0
\(187\) −13.1119 −0.958839
\(188\) 0 0
\(189\) −0.700393 −0.0509461
\(190\) 0 0
\(191\) 2.68618 0.194365 0.0971826 0.995267i \(-0.469017\pi\)
0.0971826 + 0.995267i \(0.469017\pi\)
\(192\) 0 0
\(193\) 23.4781 1.68999 0.844996 0.534773i \(-0.179603\pi\)
0.844996 + 0.534773i \(0.179603\pi\)
\(194\) 0 0
\(195\) −0.216806 −0.0155258
\(196\) 0 0
\(197\) 26.0903 1.85886 0.929429 0.369000i \(-0.120300\pi\)
0.929429 + 0.369000i \(0.120300\pi\)
\(198\) 0 0
\(199\) −11.5604 −0.819493 −0.409747 0.912199i \(-0.634383\pi\)
−0.409747 + 0.912199i \(0.634383\pi\)
\(200\) 0 0
\(201\) −0.0930478 −0.00656309
\(202\) 0 0
\(203\) −28.5330 −2.00262
\(204\) 0 0
\(205\) −31.6491 −2.21047
\(206\) 0 0
\(207\) 8.57030 0.595677
\(208\) 0 0
\(209\) −4.87946 −0.337519
\(210\) 0 0
\(211\) −7.55009 −0.519770 −0.259885 0.965640i \(-0.583685\pi\)
−0.259885 + 0.965640i \(0.583685\pi\)
\(212\) 0 0
\(213\) 0.300136 0.0205650
\(214\) 0 0
\(215\) 10.7603 0.733848
\(216\) 0 0
\(217\) −15.7148 −1.06679
\(218\) 0 0
\(219\) 0.314173 0.0212298
\(220\) 0 0
\(221\) −6.57810 −0.442491
\(222\) 0 0
\(223\) 9.37636 0.627888 0.313944 0.949442i \(-0.398350\pi\)
0.313944 + 0.949442i \(0.398350\pi\)
\(224\) 0 0
\(225\) −24.8693 −1.65796
\(226\) 0 0
\(227\) −24.6052 −1.63311 −0.816553 0.577270i \(-0.804118\pi\)
−0.816553 + 0.577270i \(0.804118\pi\)
\(228\) 0 0
\(229\) −11.8446 −0.782710 −0.391355 0.920240i \(-0.627994\pi\)
−0.391355 + 0.920240i \(0.627994\pi\)
\(230\) 0 0
\(231\) 0.568726 0.0374195
\(232\) 0 0
\(233\) −9.17382 −0.600997 −0.300498 0.953782i \(-0.597153\pi\)
−0.300498 + 0.953782i \(0.597153\pi\)
\(234\) 0 0
\(235\) −37.5941 −2.45237
\(236\) 0 0
\(237\) 0.179007 0.0116278
\(238\) 0 0
\(239\) 8.44997 0.546583 0.273291 0.961931i \(-0.411888\pi\)
0.273291 + 0.961931i \(0.411888\pi\)
\(240\) 0 0
\(241\) −2.08752 −0.134469 −0.0672344 0.997737i \(-0.521418\pi\)
−0.0672344 + 0.997737i \(0.521418\pi\)
\(242\) 0 0
\(243\) −0.656797 −0.0421335
\(244\) 0 0
\(245\) 58.4045 3.73132
\(246\) 0 0
\(247\) −2.44797 −0.155760
\(248\) 0 0
\(249\) −0.121057 −0.00767165
\(250\) 0 0
\(251\) 8.88243 0.560654 0.280327 0.959905i \(-0.409557\pi\)
0.280327 + 0.959905i \(0.409557\pi\)
\(252\) 0 0
\(253\) −13.9197 −0.875126
\(254\) 0 0
\(255\) 0.238761 0.0149518
\(256\) 0 0
\(257\) 16.4306 1.02491 0.512455 0.858714i \(-0.328736\pi\)
0.512455 + 0.858714i \(0.328736\pi\)
\(258\) 0 0
\(259\) −31.4257 −1.95270
\(260\) 0 0
\(261\) −17.8374 −1.10410
\(262\) 0 0
\(263\) −5.35827 −0.330405 −0.165202 0.986260i \(-0.552828\pi\)
−0.165202 + 0.986260i \(0.552828\pi\)
\(264\) 0 0
\(265\) 25.9118 1.59175
\(266\) 0 0
\(267\) −0.259497 −0.0158810
\(268\) 0 0
\(269\) 4.59388 0.280094 0.140047 0.990145i \(-0.455275\pi\)
0.140047 + 0.990145i \(0.455275\pi\)
\(270\) 0 0
\(271\) 2.67681 0.162604 0.0813022 0.996689i \(-0.474092\pi\)
0.0813022 + 0.996689i \(0.474092\pi\)
\(272\) 0 0
\(273\) 0.285323 0.0172685
\(274\) 0 0
\(275\) 40.3923 2.43575
\(276\) 0 0
\(277\) 18.2938 1.09917 0.549583 0.835439i \(-0.314787\pi\)
0.549583 + 0.835439i \(0.314787\pi\)
\(278\) 0 0
\(279\) −9.82407 −0.588152
\(280\) 0 0
\(281\) −18.9625 −1.13121 −0.565605 0.824676i \(-0.691357\pi\)
−0.565605 + 0.824676i \(0.691357\pi\)
\(282\) 0 0
\(283\) 22.6467 1.34620 0.673102 0.739549i \(-0.264961\pi\)
0.673102 + 0.739549i \(0.264961\pi\)
\(284\) 0 0
\(285\) 0.0888523 0.00526316
\(286\) 0 0
\(287\) 41.6512 2.45859
\(288\) 0 0
\(289\) −9.75576 −0.573868
\(290\) 0 0
\(291\) −0.282290 −0.0165481
\(292\) 0 0
\(293\) 16.6347 0.971811 0.485905 0.874011i \(-0.338490\pi\)
0.485905 + 0.874011i \(0.338490\pi\)
\(294\) 0 0
\(295\) 30.4283 1.77160
\(296\) 0 0
\(297\) 0.711148 0.0412650
\(298\) 0 0
\(299\) −6.98336 −0.403858
\(300\) 0 0
\(301\) −14.1609 −0.816222
\(302\) 0 0
\(303\) 0.158704 0.00911729
\(304\) 0 0
\(305\) 30.0984 1.72343
\(306\) 0 0
\(307\) −10.6372 −0.607096 −0.303548 0.952816i \(-0.598171\pi\)
−0.303548 + 0.952816i \(0.598171\pi\)
\(308\) 0 0
\(309\) −0.409215 −0.0232794
\(310\) 0 0
\(311\) −11.8635 −0.672718 −0.336359 0.941734i \(-0.609196\pi\)
−0.336359 + 0.941734i \(0.609196\pi\)
\(312\) 0 0
\(313\) −2.23905 −0.126558 −0.0632792 0.997996i \(-0.520156\pi\)
−0.0632792 + 0.997996i \(0.520156\pi\)
\(314\) 0 0
\(315\) 52.4654 2.95609
\(316\) 0 0
\(317\) −6.12302 −0.343903 −0.171952 0.985105i \(-0.555007\pi\)
−0.171952 + 0.985105i \(0.555007\pi\)
\(318\) 0 0
\(319\) 28.9711 1.62207
\(320\) 0 0
\(321\) −0.235417 −0.0131397
\(322\) 0 0
\(323\) 2.69586 0.150002
\(324\) 0 0
\(325\) 20.2643 1.12406
\(326\) 0 0
\(327\) 0.186123 0.0102927
\(328\) 0 0
\(329\) 49.4750 2.72764
\(330\) 0 0
\(331\) 1.33682 0.0734782 0.0367391 0.999325i \(-0.488303\pi\)
0.0367391 + 0.999325i \(0.488303\pi\)
\(332\) 0 0
\(333\) −19.6457 −1.07658
\(334\) 0 0
\(335\) 13.9415 0.761707
\(336\) 0 0
\(337\) −6.04090 −0.329069 −0.164534 0.986371i \(-0.552612\pi\)
−0.164534 + 0.986371i \(0.552612\pi\)
\(338\) 0 0
\(339\) −0.274452 −0.0149062
\(340\) 0 0
\(341\) 15.9561 0.864070
\(342\) 0 0
\(343\) −43.2767 −2.33672
\(344\) 0 0
\(345\) 0.253471 0.0136464
\(346\) 0 0
\(347\) 12.4870 0.670339 0.335170 0.942158i \(-0.391206\pi\)
0.335170 + 0.942158i \(0.391206\pi\)
\(348\) 0 0
\(349\) 5.50783 0.294827 0.147414 0.989075i \(-0.452905\pi\)
0.147414 + 0.989075i \(0.452905\pi\)
\(350\) 0 0
\(351\) 0.356774 0.0190432
\(352\) 0 0
\(353\) 14.5045 0.771996 0.385998 0.922500i \(-0.373857\pi\)
0.385998 + 0.922500i \(0.373857\pi\)
\(354\) 0 0
\(355\) −44.9699 −2.38675
\(356\) 0 0
\(357\) −0.314217 −0.0166301
\(358\) 0 0
\(359\) −13.1360 −0.693291 −0.346645 0.937996i \(-0.612679\pi\)
−0.346645 + 0.937996i \(0.612679\pi\)
\(360\) 0 0
\(361\) −17.9968 −0.947198
\(362\) 0 0
\(363\) −0.309805 −0.0162606
\(364\) 0 0
\(365\) −47.0731 −2.46392
\(366\) 0 0
\(367\) 3.03788 0.158576 0.0792881 0.996852i \(-0.474735\pi\)
0.0792881 + 0.996852i \(0.474735\pi\)
\(368\) 0 0
\(369\) 26.0382 1.35549
\(370\) 0 0
\(371\) −34.1008 −1.77043
\(372\) 0 0
\(373\) −36.8424 −1.90763 −0.953813 0.300400i \(-0.902880\pi\)
−0.953813 + 0.300400i \(0.902880\pi\)
\(374\) 0 0
\(375\) −0.291978 −0.0150777
\(376\) 0 0
\(377\) 14.5345 0.748562
\(378\) 0 0
\(379\) −2.91929 −0.149954 −0.0749769 0.997185i \(-0.523888\pi\)
−0.0749769 + 0.997185i \(0.523888\pi\)
\(380\) 0 0
\(381\) 0.0465018 0.00238236
\(382\) 0 0
\(383\) 27.9102 1.42615 0.713073 0.701089i \(-0.247303\pi\)
0.713073 + 0.701089i \(0.247303\pi\)
\(384\) 0 0
\(385\) −85.2134 −4.34287
\(386\) 0 0
\(387\) −8.85269 −0.450007
\(388\) 0 0
\(389\) 21.1181 1.07073 0.535366 0.844620i \(-0.320174\pi\)
0.535366 + 0.844620i \(0.320174\pi\)
\(390\) 0 0
\(391\) 7.69055 0.388928
\(392\) 0 0
\(393\) 0.316229 0.0159516
\(394\) 0 0
\(395\) −26.8210 −1.34951
\(396\) 0 0
\(397\) −27.1386 −1.36205 −0.681023 0.732262i \(-0.738465\pi\)
−0.681023 + 0.732262i \(0.738465\pi\)
\(398\) 0 0
\(399\) −0.116932 −0.00585394
\(400\) 0 0
\(401\) −11.5854 −0.578549 −0.289275 0.957246i \(-0.593414\pi\)
−0.289275 + 0.957246i \(0.593414\pi\)
\(402\) 0 0
\(403\) 8.00497 0.398756
\(404\) 0 0
\(405\) 32.7922 1.62946
\(406\) 0 0
\(407\) 31.9083 1.58163
\(408\) 0 0
\(409\) 8.58616 0.424558 0.212279 0.977209i \(-0.431911\pi\)
0.212279 + 0.977209i \(0.431911\pi\)
\(410\) 0 0
\(411\) −0.252989 −0.0124790
\(412\) 0 0
\(413\) −40.0446 −1.97046
\(414\) 0 0
\(415\) 18.1381 0.890366
\(416\) 0 0
\(417\) 0.0191498 0.000937771 0
\(418\) 0 0
\(419\) 34.5033 1.68559 0.842797 0.538231i \(-0.180907\pi\)
0.842797 + 0.538231i \(0.180907\pi\)
\(420\) 0 0
\(421\) −40.1227 −1.95546 −0.977729 0.209870i \(-0.932696\pi\)
−0.977729 + 0.209870i \(0.932696\pi\)
\(422\) 0 0
\(423\) 30.9292 1.50383
\(424\) 0 0
\(425\) −22.3165 −1.08251
\(426\) 0 0
\(427\) −39.6105 −1.91689
\(428\) 0 0
\(429\) −0.289704 −0.0139871
\(430\) 0 0
\(431\) −36.7139 −1.76845 −0.884223 0.467064i \(-0.845312\pi\)
−0.884223 + 0.467064i \(0.845312\pi\)
\(432\) 0 0
\(433\) −7.07924 −0.340206 −0.170103 0.985426i \(-0.554410\pi\)
−0.170103 + 0.985426i \(0.554410\pi\)
\(434\) 0 0
\(435\) −0.527548 −0.0252940
\(436\) 0 0
\(437\) 2.86195 0.136906
\(438\) 0 0
\(439\) 25.0165 1.19397 0.596987 0.802251i \(-0.296365\pi\)
0.596987 + 0.802251i \(0.296365\pi\)
\(440\) 0 0
\(441\) −48.0503 −2.28811
\(442\) 0 0
\(443\) −14.0409 −0.667103 −0.333551 0.942732i \(-0.608247\pi\)
−0.333551 + 0.942732i \(0.608247\pi\)
\(444\) 0 0
\(445\) 38.8809 1.84313
\(446\) 0 0
\(447\) −0.193659 −0.00915975
\(448\) 0 0
\(449\) −38.7301 −1.82779 −0.913894 0.405953i \(-0.866940\pi\)
−0.913894 + 0.405953i \(0.866940\pi\)
\(450\) 0 0
\(451\) −42.2907 −1.99139
\(452\) 0 0
\(453\) −0.251401 −0.0118119
\(454\) 0 0
\(455\) −42.7505 −2.00417
\(456\) 0 0
\(457\) 30.0710 1.40666 0.703330 0.710864i \(-0.251696\pi\)
0.703330 + 0.710864i \(0.251696\pi\)
\(458\) 0 0
\(459\) −0.392904 −0.0183392
\(460\) 0 0
\(461\) 17.9011 0.833738 0.416869 0.908967i \(-0.363127\pi\)
0.416869 + 0.908967i \(0.363127\pi\)
\(462\) 0 0
\(463\) 31.7350 1.47485 0.737426 0.675428i \(-0.236041\pi\)
0.737426 + 0.675428i \(0.236041\pi\)
\(464\) 0 0
\(465\) −0.290552 −0.0134740
\(466\) 0 0
\(467\) −14.6423 −0.677565 −0.338782 0.940865i \(-0.610015\pi\)
−0.338782 + 0.940865i \(0.610015\pi\)
\(468\) 0 0
\(469\) −18.3475 −0.847209
\(470\) 0 0
\(471\) −0.230105 −0.0106027
\(472\) 0 0
\(473\) 14.3784 0.661118
\(474\) 0 0
\(475\) −8.30482 −0.381051
\(476\) 0 0
\(477\) −21.3181 −0.976088
\(478\) 0 0
\(479\) −5.65723 −0.258486 −0.129243 0.991613i \(-0.541255\pi\)
−0.129243 + 0.991613i \(0.541255\pi\)
\(480\) 0 0
\(481\) 16.0080 0.729901
\(482\) 0 0
\(483\) −0.333575 −0.0151782
\(484\) 0 0
\(485\) 42.2960 1.92056
\(486\) 0 0
\(487\) −0.782270 −0.0354481 −0.0177240 0.999843i \(-0.505642\pi\)
−0.0177240 + 0.999843i \(0.505642\pi\)
\(488\) 0 0
\(489\) −0.377716 −0.0170809
\(490\) 0 0
\(491\) −27.3481 −1.23420 −0.617102 0.786884i \(-0.711693\pi\)
−0.617102 + 0.786884i \(0.711693\pi\)
\(492\) 0 0
\(493\) −16.0063 −0.720889
\(494\) 0 0
\(495\) −53.2711 −2.39436
\(496\) 0 0
\(497\) 59.1818 2.65467
\(498\) 0 0
\(499\) 34.6030 1.54904 0.774521 0.632548i \(-0.217991\pi\)
0.774521 + 0.632548i \(0.217991\pi\)
\(500\) 0 0
\(501\) −0.168500 −0.00752804
\(502\) 0 0
\(503\) 5.14943 0.229602 0.114801 0.993389i \(-0.463377\pi\)
0.114801 + 0.993389i \(0.463377\pi\)
\(504\) 0 0
\(505\) −23.7789 −1.05815
\(506\) 0 0
\(507\) 0.170977 0.00759337
\(508\) 0 0
\(509\) −15.1072 −0.669616 −0.334808 0.942286i \(-0.608671\pi\)
−0.334808 + 0.942286i \(0.608671\pi\)
\(510\) 0 0
\(511\) 61.9496 2.74049
\(512\) 0 0
\(513\) −0.146215 −0.00645554
\(514\) 0 0
\(515\) 61.3134 2.70179
\(516\) 0 0
\(517\) −50.2347 −2.20932
\(518\) 0 0
\(519\) −0.559102 −0.0245419
\(520\) 0 0
\(521\) 37.7036 1.65182 0.825912 0.563800i \(-0.190661\pi\)
0.825912 + 0.563800i \(0.190661\pi\)
\(522\) 0 0
\(523\) −29.2444 −1.27877 −0.639384 0.768887i \(-0.720811\pi\)
−0.639384 + 0.768887i \(0.720811\pi\)
\(524\) 0 0
\(525\) 0.967970 0.0422457
\(526\) 0 0
\(527\) −8.81561 −0.384014
\(528\) 0 0
\(529\) −14.8357 −0.645029
\(530\) 0 0
\(531\) −25.0338 −1.08638
\(532\) 0 0
\(533\) −21.2168 −0.919000
\(534\) 0 0
\(535\) 35.2730 1.52499
\(536\) 0 0
\(537\) 0.334467 0.0144333
\(538\) 0 0
\(539\) 78.0424 3.36152
\(540\) 0 0
\(541\) −17.8314 −0.766632 −0.383316 0.923617i \(-0.625218\pi\)
−0.383316 + 0.923617i \(0.625218\pi\)
\(542\) 0 0
\(543\) −0.0382489 −0.00164142
\(544\) 0 0
\(545\) −27.8872 −1.19456
\(546\) 0 0
\(547\) 31.1069 1.33004 0.665018 0.746828i \(-0.268424\pi\)
0.665018 + 0.746828i \(0.268424\pi\)
\(548\) 0 0
\(549\) −24.7625 −1.05684
\(550\) 0 0
\(551\) −5.95658 −0.253759
\(552\) 0 0
\(553\) 35.2973 1.50099
\(554\) 0 0
\(555\) −0.581032 −0.0246634
\(556\) 0 0
\(557\) 19.7653 0.837485 0.418742 0.908105i \(-0.362471\pi\)
0.418742 + 0.908105i \(0.362471\pi\)
\(558\) 0 0
\(559\) 7.21345 0.305097
\(560\) 0 0
\(561\) 0.319042 0.0134700
\(562\) 0 0
\(563\) 27.7465 1.16938 0.584689 0.811258i \(-0.301217\pi\)
0.584689 + 0.811258i \(0.301217\pi\)
\(564\) 0 0
\(565\) 41.1217 1.73000
\(566\) 0 0
\(567\) −43.1556 −1.81237
\(568\) 0 0
\(569\) −6.78314 −0.284364 −0.142182 0.989841i \(-0.545412\pi\)
−0.142182 + 0.989841i \(0.545412\pi\)
\(570\) 0 0
\(571\) 24.0983 1.00848 0.504241 0.863563i \(-0.331773\pi\)
0.504241 + 0.863563i \(0.331773\pi\)
\(572\) 0 0
\(573\) −0.0653607 −0.00273048
\(574\) 0 0
\(575\) −23.6913 −0.987997
\(576\) 0 0
\(577\) 42.3797 1.76429 0.882145 0.470979i \(-0.156099\pi\)
0.882145 + 0.470979i \(0.156099\pi\)
\(578\) 0 0
\(579\) −0.571274 −0.0237413
\(580\) 0 0
\(581\) −23.8703 −0.990309
\(582\) 0 0
\(583\) 34.6244 1.43400
\(584\) 0 0
\(585\) −26.7254 −1.10496
\(586\) 0 0
\(587\) −12.6438 −0.521867 −0.260933 0.965357i \(-0.584030\pi\)
−0.260933 + 0.965357i \(0.584030\pi\)
\(588\) 0 0
\(589\) −3.28063 −0.135176
\(590\) 0 0
\(591\) −0.634835 −0.0261136
\(592\) 0 0
\(593\) −9.53221 −0.391441 −0.195721 0.980660i \(-0.562705\pi\)
−0.195721 + 0.980660i \(0.562705\pi\)
\(594\) 0 0
\(595\) 47.0797 1.93008
\(596\) 0 0
\(597\) 0.281289 0.0115124
\(598\) 0 0
\(599\) −19.6173 −0.801541 −0.400770 0.916179i \(-0.631258\pi\)
−0.400770 + 0.916179i \(0.631258\pi\)
\(600\) 0 0
\(601\) −31.4945 −1.28469 −0.642344 0.766416i \(-0.722038\pi\)
−0.642344 + 0.766416i \(0.722038\pi\)
\(602\) 0 0
\(603\) −11.4699 −0.467091
\(604\) 0 0
\(605\) 46.4187 1.88719
\(606\) 0 0
\(607\) −46.8119 −1.90004 −0.950019 0.312192i \(-0.898937\pi\)
−0.950019 + 0.312192i \(0.898937\pi\)
\(608\) 0 0
\(609\) 0.694270 0.0281332
\(610\) 0 0
\(611\) −25.2021 −1.01957
\(612\) 0 0
\(613\) −16.1156 −0.650903 −0.325451 0.945559i \(-0.605516\pi\)
−0.325451 + 0.945559i \(0.605516\pi\)
\(614\) 0 0
\(615\) 0.770092 0.0310531
\(616\) 0 0
\(617\) −11.2073 −0.451190 −0.225595 0.974221i \(-0.572433\pi\)
−0.225595 + 0.974221i \(0.572433\pi\)
\(618\) 0 0
\(619\) 44.2890 1.78012 0.890062 0.455839i \(-0.150661\pi\)
0.890062 + 0.455839i \(0.150661\pi\)
\(620\) 0 0
\(621\) −0.417110 −0.0167380
\(622\) 0 0
\(623\) −51.1685 −2.05002
\(624\) 0 0
\(625\) 2.29051 0.0916205
\(626\) 0 0
\(627\) 0.118728 0.00474154
\(628\) 0 0
\(629\) −17.6291 −0.702917
\(630\) 0 0
\(631\) 10.3507 0.412055 0.206027 0.978546i \(-0.433946\pi\)
0.206027 + 0.978546i \(0.433946\pi\)
\(632\) 0 0
\(633\) 0.183710 0.00730183
\(634\) 0 0
\(635\) −6.96746 −0.276495
\(636\) 0 0
\(637\) 39.1529 1.55129
\(638\) 0 0
\(639\) 36.9975 1.46360
\(640\) 0 0
\(641\) −17.9641 −0.709538 −0.354769 0.934954i \(-0.615441\pi\)
−0.354769 + 0.934954i \(0.615441\pi\)
\(642\) 0 0
\(643\) 21.8747 0.862655 0.431328 0.902195i \(-0.358045\pi\)
0.431328 + 0.902195i \(0.358045\pi\)
\(644\) 0 0
\(645\) −0.261822 −0.0103092
\(646\) 0 0
\(647\) −26.2293 −1.03118 −0.515591 0.856835i \(-0.672427\pi\)
−0.515591 + 0.856835i \(0.672427\pi\)
\(648\) 0 0
\(649\) 40.6595 1.59602
\(650\) 0 0
\(651\) 0.382375 0.0149865
\(652\) 0 0
\(653\) −2.85863 −0.111867 −0.0559333 0.998435i \(-0.517813\pi\)
−0.0559333 + 0.998435i \(0.517813\pi\)
\(654\) 0 0
\(655\) −47.3811 −1.85133
\(656\) 0 0
\(657\) 38.7278 1.51091
\(658\) 0 0
\(659\) 26.1073 1.01700 0.508498 0.861063i \(-0.330201\pi\)
0.508498 + 0.861063i \(0.330201\pi\)
\(660\) 0 0
\(661\) 30.3919 1.18211 0.591055 0.806631i \(-0.298712\pi\)
0.591055 + 0.806631i \(0.298712\pi\)
\(662\) 0 0
\(663\) 0.160060 0.00621620
\(664\) 0 0
\(665\) 17.5202 0.679404
\(666\) 0 0
\(667\) −16.9924 −0.657950
\(668\) 0 0
\(669\) −0.228148 −0.00882069
\(670\) 0 0
\(671\) 40.2187 1.55263
\(672\) 0 0
\(673\) 36.7896 1.41813 0.709067 0.705141i \(-0.249116\pi\)
0.709067 + 0.705141i \(0.249116\pi\)
\(674\) 0 0
\(675\) 1.21037 0.0465872
\(676\) 0 0
\(677\) 31.4562 1.20896 0.604479 0.796621i \(-0.293381\pi\)
0.604479 + 0.796621i \(0.293381\pi\)
\(678\) 0 0
\(679\) −55.6629 −2.13615
\(680\) 0 0
\(681\) 0.598699 0.0229422
\(682\) 0 0
\(683\) −25.5292 −0.976847 −0.488424 0.872607i \(-0.662428\pi\)
−0.488424 + 0.872607i \(0.662428\pi\)
\(684\) 0 0
\(685\) 37.9059 1.44831
\(686\) 0 0
\(687\) 0.288204 0.0109957
\(688\) 0 0
\(689\) 17.3707 0.661769
\(690\) 0 0
\(691\) 21.0836 0.802059 0.401029 0.916065i \(-0.368653\pi\)
0.401029 + 0.916065i \(0.368653\pi\)
\(692\) 0 0
\(693\) 70.1064 2.66312
\(694\) 0 0
\(695\) −2.86925 −0.108837
\(696\) 0 0
\(697\) 23.3653 0.885025
\(698\) 0 0
\(699\) 0.223219 0.00844292
\(700\) 0 0
\(701\) 35.9398 1.35743 0.678713 0.734403i \(-0.262538\pi\)
0.678713 + 0.734403i \(0.262538\pi\)
\(702\) 0 0
\(703\) −6.56047 −0.247433
\(704\) 0 0
\(705\) 0.914746 0.0344513
\(706\) 0 0
\(707\) 31.2937 1.17692
\(708\) 0 0
\(709\) 26.2979 0.987639 0.493819 0.869565i \(-0.335600\pi\)
0.493819 + 0.869565i \(0.335600\pi\)
\(710\) 0 0
\(711\) 22.0661 0.827542
\(712\) 0 0
\(713\) −9.35873 −0.350487
\(714\) 0 0
\(715\) 43.4070 1.62333
\(716\) 0 0
\(717\) −0.205606 −0.00767851
\(718\) 0 0
\(719\) 43.9867 1.64043 0.820214 0.572056i \(-0.193854\pi\)
0.820214 + 0.572056i \(0.193854\pi\)
\(720\) 0 0
\(721\) −80.6904 −3.00507
\(722\) 0 0
\(723\) 0.0507939 0.00188905
\(724\) 0 0
\(725\) 49.3087 1.83128
\(726\) 0 0
\(727\) 32.2403 1.19572 0.597862 0.801599i \(-0.296017\pi\)
0.597862 + 0.801599i \(0.296017\pi\)
\(728\) 0 0
\(729\) −26.9680 −0.998816
\(730\) 0 0
\(731\) −7.94394 −0.293817
\(732\) 0 0
\(733\) −16.4841 −0.608853 −0.304427 0.952536i \(-0.598465\pi\)
−0.304427 + 0.952536i \(0.598465\pi\)
\(734\) 0 0
\(735\) −1.42111 −0.0524184
\(736\) 0 0
\(737\) 18.6292 0.686217
\(738\) 0 0
\(739\) 7.81818 0.287596 0.143798 0.989607i \(-0.454068\pi\)
0.143798 + 0.989607i \(0.454068\pi\)
\(740\) 0 0
\(741\) 0.0595644 0.00218815
\(742\) 0 0
\(743\) −17.5180 −0.642673 −0.321337 0.946965i \(-0.604132\pi\)
−0.321337 + 0.946965i \(0.604132\pi\)
\(744\) 0 0
\(745\) 29.0163 1.06307
\(746\) 0 0
\(747\) −14.9225 −0.545987
\(748\) 0 0
\(749\) −46.4204 −1.69617
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −0.216129 −0.00787618
\(754\) 0 0
\(755\) 37.6679 1.37088
\(756\) 0 0
\(757\) −26.9809 −0.980638 −0.490319 0.871543i \(-0.663120\pi\)
−0.490319 + 0.871543i \(0.663120\pi\)
\(758\) 0 0
\(759\) 0.338698 0.0122939
\(760\) 0 0
\(761\) −45.0869 −1.63440 −0.817200 0.576354i \(-0.804475\pi\)
−0.817200 + 0.576354i \(0.804475\pi\)
\(762\) 0 0
\(763\) 36.7005 1.32865
\(764\) 0 0
\(765\) 29.4319 1.06411
\(766\) 0 0
\(767\) 20.3984 0.736542
\(768\) 0 0
\(769\) −32.8854 −1.18588 −0.592939 0.805247i \(-0.702032\pi\)
−0.592939 + 0.805247i \(0.702032\pi\)
\(770\) 0 0
\(771\) −0.399792 −0.0143981
\(772\) 0 0
\(773\) 43.2064 1.55402 0.777012 0.629485i \(-0.216734\pi\)
0.777012 + 0.629485i \(0.216734\pi\)
\(774\) 0 0
\(775\) 27.1572 0.975515
\(776\) 0 0
\(777\) 0.764657 0.0274319
\(778\) 0 0
\(779\) 8.69515 0.311536
\(780\) 0 0
\(781\) −60.0906 −2.15021
\(782\) 0 0
\(783\) 0.868130 0.0310244
\(784\) 0 0
\(785\) 34.4770 1.23054
\(786\) 0 0
\(787\) −13.2567 −0.472550 −0.236275 0.971686i \(-0.575927\pi\)
−0.236275 + 0.971686i \(0.575927\pi\)
\(788\) 0 0
\(789\) 0.130378 0.00464159
\(790\) 0 0
\(791\) −54.1175 −1.92420
\(792\) 0 0
\(793\) 20.1773 0.716515
\(794\) 0 0
\(795\) −0.630492 −0.0223613
\(796\) 0 0
\(797\) −7.43211 −0.263259 −0.131629 0.991299i \(-0.542021\pi\)
−0.131629 + 0.991299i \(0.542021\pi\)
\(798\) 0 0
\(799\) 27.7543 0.981876
\(800\) 0 0
\(801\) −31.9880 −1.13024
\(802\) 0 0
\(803\) −62.9009 −2.21973
\(804\) 0 0
\(805\) 49.9802 1.76157
\(806\) 0 0
\(807\) −0.111779 −0.00393481
\(808\) 0 0
\(809\) 5.32161 0.187098 0.0935488 0.995615i \(-0.470179\pi\)
0.0935488 + 0.995615i \(0.470179\pi\)
\(810\) 0 0
\(811\) −3.35103 −0.117671 −0.0588353 0.998268i \(-0.518739\pi\)
−0.0588353 + 0.998268i \(0.518739\pi\)
\(812\) 0 0
\(813\) −0.0651326 −0.00228430
\(814\) 0 0
\(815\) 56.5940 1.98240
\(816\) 0 0
\(817\) −2.95625 −0.103426
\(818\) 0 0
\(819\) 35.1715 1.22899
\(820\) 0 0
\(821\) −6.52914 −0.227868 −0.113934 0.993488i \(-0.536345\pi\)
−0.113934 + 0.993488i \(0.536345\pi\)
\(822\) 0 0
\(823\) −51.6467 −1.80029 −0.900145 0.435591i \(-0.856539\pi\)
−0.900145 + 0.435591i \(0.856539\pi\)
\(824\) 0 0
\(825\) −0.982834 −0.0342179
\(826\) 0 0
\(827\) −33.7898 −1.17499 −0.587493 0.809229i \(-0.699885\pi\)
−0.587493 + 0.809229i \(0.699885\pi\)
\(828\) 0 0
\(829\) 24.5924 0.854129 0.427065 0.904221i \(-0.359548\pi\)
0.427065 + 0.904221i \(0.359548\pi\)
\(830\) 0 0
\(831\) −0.445128 −0.0154413
\(832\) 0 0
\(833\) −43.1178 −1.49394
\(834\) 0 0
\(835\) 25.2467 0.873698
\(836\) 0 0
\(837\) 0.478130 0.0165266
\(838\) 0 0
\(839\) 35.8463 1.23755 0.618776 0.785567i \(-0.287629\pi\)
0.618776 + 0.785567i \(0.287629\pi\)
\(840\) 0 0
\(841\) 6.36634 0.219529
\(842\) 0 0
\(843\) 0.461400 0.0158915
\(844\) 0 0
\(845\) −25.6179 −0.881282
\(846\) 0 0
\(847\) −61.0885 −2.09903
\(848\) 0 0
\(849\) −0.551043 −0.0189118
\(850\) 0 0
\(851\) −18.7152 −0.641548
\(852\) 0 0
\(853\) 32.3633 1.10810 0.554049 0.832484i \(-0.313082\pi\)
0.554049 + 0.832484i \(0.313082\pi\)
\(854\) 0 0
\(855\) 10.9527 0.374576
\(856\) 0 0
\(857\) 24.0679 0.822144 0.411072 0.911603i \(-0.365155\pi\)
0.411072 + 0.911603i \(0.365155\pi\)
\(858\) 0 0
\(859\) −44.5105 −1.51868 −0.759340 0.650695i \(-0.774478\pi\)
−0.759340 + 0.650695i \(0.774478\pi\)
\(860\) 0 0
\(861\) −1.01346 −0.0345388
\(862\) 0 0
\(863\) 6.52826 0.222225 0.111112 0.993808i \(-0.464559\pi\)
0.111112 + 0.993808i \(0.464559\pi\)
\(864\) 0 0
\(865\) 83.7713 2.84831
\(866\) 0 0
\(867\) 0.237379 0.00806182
\(868\) 0 0
\(869\) −35.8393 −1.21576
\(870\) 0 0
\(871\) 9.34606 0.316679
\(872\) 0 0
\(873\) −34.7976 −1.17772
\(874\) 0 0
\(875\) −57.5732 −1.94633
\(876\) 0 0
\(877\) −47.8646 −1.61627 −0.808136 0.588996i \(-0.799523\pi\)
−0.808136 + 0.588996i \(0.799523\pi\)
\(878\) 0 0
\(879\) −0.404759 −0.0136522
\(880\) 0 0
\(881\) −36.0735 −1.21535 −0.607674 0.794187i \(-0.707897\pi\)
−0.607674 + 0.794187i \(0.707897\pi\)
\(882\) 0 0
\(883\) −41.6778 −1.40257 −0.701285 0.712881i \(-0.747390\pi\)
−0.701285 + 0.712881i \(0.747390\pi\)
\(884\) 0 0
\(885\) −0.740387 −0.0248878
\(886\) 0 0
\(887\) −1.10519 −0.0371086 −0.0185543 0.999828i \(-0.505906\pi\)
−0.0185543 + 0.999828i \(0.505906\pi\)
\(888\) 0 0
\(889\) 9.16940 0.307532
\(890\) 0 0
\(891\) 43.8183 1.46797
\(892\) 0 0
\(893\) 10.3284 0.345628
\(894\) 0 0
\(895\) −50.1138 −1.67512
\(896\) 0 0
\(897\) 0.169920 0.00567348
\(898\) 0 0
\(899\) 19.4783 0.649638
\(900\) 0 0
\(901\) −19.1297 −0.637304
\(902\) 0 0
\(903\) 0.344566 0.0114665
\(904\) 0 0
\(905\) 5.73090 0.190502
\(906\) 0 0
\(907\) 11.9847 0.397944 0.198972 0.980005i \(-0.436240\pi\)
0.198972 + 0.980005i \(0.436240\pi\)
\(908\) 0 0
\(909\) 19.5632 0.648872
\(910\) 0 0
\(911\) −43.6363 −1.44574 −0.722868 0.690986i \(-0.757177\pi\)
−0.722868 + 0.690986i \(0.757177\pi\)
\(912\) 0 0
\(913\) 24.2369 0.802124
\(914\) 0 0
\(915\) −0.732362 −0.0242111
\(916\) 0 0
\(917\) 62.3551 2.05915
\(918\) 0 0
\(919\) −11.3742 −0.375200 −0.187600 0.982245i \(-0.560071\pi\)
−0.187600 + 0.982245i \(0.560071\pi\)
\(920\) 0 0
\(921\) 0.258826 0.00852861
\(922\) 0 0
\(923\) −30.1467 −0.992291
\(924\) 0 0
\(925\) 54.3078 1.78563
\(926\) 0 0
\(927\) −50.4435 −1.65678
\(928\) 0 0
\(929\) −15.5039 −0.508666 −0.254333 0.967117i \(-0.581856\pi\)
−0.254333 + 0.967117i \(0.581856\pi\)
\(930\) 0 0
\(931\) −16.0458 −0.525881
\(932\) 0 0
\(933\) 0.288665 0.00945048
\(934\) 0 0
\(935\) −47.8027 −1.56331
\(936\) 0 0
\(937\) −33.9650 −1.10959 −0.554794 0.831988i \(-0.687203\pi\)
−0.554794 + 0.831988i \(0.687203\pi\)
\(938\) 0 0
\(939\) 0.0544810 0.00177792
\(940\) 0 0
\(941\) −35.6611 −1.16252 −0.581260 0.813718i \(-0.697440\pi\)
−0.581260 + 0.813718i \(0.697440\pi\)
\(942\) 0 0
\(943\) 24.8048 0.807756
\(944\) 0 0
\(945\) −2.55345 −0.0830637
\(946\) 0 0
\(947\) −18.6041 −0.604552 −0.302276 0.953220i \(-0.597746\pi\)
−0.302276 + 0.953220i \(0.597746\pi\)
\(948\) 0 0
\(949\) −31.5566 −1.02437
\(950\) 0 0
\(951\) 0.148987 0.00483122
\(952\) 0 0
\(953\) −54.6187 −1.76927 −0.884637 0.466280i \(-0.845594\pi\)
−0.884637 + 0.466280i \(0.845594\pi\)
\(954\) 0 0
\(955\) 9.79311 0.316898
\(956\) 0 0
\(957\) −0.704931 −0.0227872
\(958\) 0 0
\(959\) −49.8853 −1.61088
\(960\) 0 0
\(961\) −20.2722 −0.653941
\(962\) 0 0
\(963\) −29.0197 −0.935147
\(964\) 0 0
\(965\) 85.5951 2.75540
\(966\) 0 0
\(967\) 41.9213 1.34810 0.674049 0.738687i \(-0.264554\pi\)
0.674049 + 0.738687i \(0.264554\pi\)
\(968\) 0 0
\(969\) −0.0655963 −0.00210726
\(970\) 0 0
\(971\) −20.4238 −0.655432 −0.327716 0.944776i \(-0.606279\pi\)
−0.327716 + 0.944776i \(0.606279\pi\)
\(972\) 0 0
\(973\) 3.77603 0.121054
\(974\) 0 0
\(975\) −0.493076 −0.0157911
\(976\) 0 0
\(977\) −15.6782 −0.501590 −0.250795 0.968040i \(-0.580692\pi\)
−0.250795 + 0.968040i \(0.580692\pi\)
\(978\) 0 0
\(979\) 51.9543 1.66047
\(980\) 0 0
\(981\) 22.9433 0.732522
\(982\) 0 0
\(983\) 37.4028 1.19296 0.596481 0.802627i \(-0.296565\pi\)
0.596481 + 0.802627i \(0.296565\pi\)
\(984\) 0 0
\(985\) 95.1185 3.03073
\(986\) 0 0
\(987\) −1.20383 −0.0383185
\(988\) 0 0
\(989\) −8.43335 −0.268165
\(990\) 0 0
\(991\) 23.9275 0.760082 0.380041 0.924970i \(-0.375910\pi\)
0.380041 + 0.924970i \(0.375910\pi\)
\(992\) 0 0
\(993\) −0.0325277 −0.00103224
\(994\) 0 0
\(995\) −42.1461 −1.33612
\(996\) 0 0
\(997\) −41.9335 −1.32805 −0.664024 0.747711i \(-0.731153\pi\)
−0.664024 + 0.747711i \(0.731153\pi\)
\(998\) 0 0
\(999\) 0.956143 0.0302510
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 \(a_p\))