Properties

Label 6027.2.a.bk.1.5
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.21066\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.21066 q^{2} +1.00000 q^{3} -0.534291 q^{4} -0.826979 q^{5} -1.21066 q^{6} +3.06818 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.21066 q^{2} +1.00000 q^{3} -0.534291 q^{4} -0.826979 q^{5} -1.21066 q^{6} +3.06818 q^{8} +1.00000 q^{9} +1.00119 q^{10} -0.396962 q^{11} -0.534291 q^{12} -3.17185 q^{13} -0.826979 q^{15} -2.64595 q^{16} -0.159142 q^{17} -1.21066 q^{18} -3.91493 q^{19} +0.441847 q^{20} +0.480588 q^{22} +7.13636 q^{23} +3.06818 q^{24} -4.31611 q^{25} +3.84005 q^{26} +1.00000 q^{27} +9.77724 q^{29} +1.00119 q^{30} -6.15497 q^{31} -2.93299 q^{32} -0.396962 q^{33} +0.192668 q^{34} -0.534291 q^{36} +10.0885 q^{37} +4.73967 q^{38} -3.17185 q^{39} -2.53732 q^{40} -1.00000 q^{41} -5.32444 q^{43} +0.212093 q^{44} -0.826979 q^{45} -8.63974 q^{46} +1.31060 q^{47} -2.64595 q^{48} +5.22536 q^{50} -0.159142 q^{51} +1.69469 q^{52} -5.54558 q^{53} -1.21066 q^{54} +0.328280 q^{55} -3.91493 q^{57} -11.8370 q^{58} -1.57839 q^{59} +0.441847 q^{60} +8.56205 q^{61} +7.45161 q^{62} +8.84277 q^{64} +2.62306 q^{65} +0.480588 q^{66} +12.1171 q^{67} +0.0850282 q^{68} +7.13636 q^{69} -1.25998 q^{71} +3.06818 q^{72} -8.34764 q^{73} -12.2138 q^{74} -4.31611 q^{75} +2.09171 q^{76} +3.84005 q^{78} -9.12954 q^{79} +2.18815 q^{80} +1.00000 q^{81} +1.21066 q^{82} -9.77501 q^{83} +0.131607 q^{85} +6.44611 q^{86} +9.77724 q^{87} -1.21795 q^{88} -11.8098 q^{89} +1.00119 q^{90} -3.81289 q^{92} -6.15497 q^{93} -1.58670 q^{94} +3.23757 q^{95} -2.93299 q^{96} -10.4867 q^{97} -0.396962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21066 −0.856069 −0.428035 0.903762i \(-0.640794\pi\)
−0.428035 + 0.903762i \(0.640794\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.534291 −0.267145
\(5\) −0.826979 −0.369836 −0.184918 0.982754i \(-0.559202\pi\)
−0.184918 + 0.982754i \(0.559202\pi\)
\(6\) −1.21066 −0.494252
\(7\) 0 0
\(8\) 3.06818 1.08476
\(9\) 1.00000 0.333333
\(10\) 1.00119 0.316606
\(11\) −0.396962 −0.119689 −0.0598443 0.998208i \(-0.519060\pi\)
−0.0598443 + 0.998208i \(0.519060\pi\)
\(12\) −0.534291 −0.154236
\(13\) −3.17185 −0.879714 −0.439857 0.898068i \(-0.644971\pi\)
−0.439857 + 0.898068i \(0.644971\pi\)
\(14\) 0 0
\(15\) −0.826979 −0.213525
\(16\) −2.64595 −0.661488
\(17\) −0.159142 −0.0385977 −0.0192988 0.999814i \(-0.506143\pi\)
−0.0192988 + 0.999814i \(0.506143\pi\)
\(18\) −1.21066 −0.285356
\(19\) −3.91493 −0.898147 −0.449073 0.893495i \(-0.648246\pi\)
−0.449073 + 0.893495i \(0.648246\pi\)
\(20\) 0.441847 0.0988001
\(21\) 0 0
\(22\) 0.480588 0.102462
\(23\) 7.13636 1.48803 0.744017 0.668161i \(-0.232918\pi\)
0.744017 + 0.668161i \(0.232918\pi\)
\(24\) 3.06818 0.626289
\(25\) −4.31611 −0.863221
\(26\) 3.84005 0.753096
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 9.77724 1.81559 0.907794 0.419416i \(-0.137765\pi\)
0.907794 + 0.419416i \(0.137765\pi\)
\(30\) 1.00119 0.182792
\(31\) −6.15497 −1.10547 −0.552733 0.833359i \(-0.686415\pi\)
−0.552733 + 0.833359i \(0.686415\pi\)
\(32\) −2.93299 −0.518485
\(33\) −0.396962 −0.0691023
\(34\) 0.192668 0.0330423
\(35\) 0 0
\(36\) −0.534291 −0.0890484
\(37\) 10.0885 1.65854 0.829269 0.558850i \(-0.188757\pi\)
0.829269 + 0.558850i \(0.188757\pi\)
\(38\) 4.73967 0.768876
\(39\) −3.17185 −0.507903
\(40\) −2.53732 −0.401185
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −5.32444 −0.811969 −0.405985 0.913880i \(-0.633071\pi\)
−0.405985 + 0.913880i \(0.633071\pi\)
\(44\) 0.212093 0.0319743
\(45\) −0.826979 −0.123279
\(46\) −8.63974 −1.27386
\(47\) 1.31060 0.191171 0.0955855 0.995421i \(-0.469528\pi\)
0.0955855 + 0.995421i \(0.469528\pi\)
\(48\) −2.64595 −0.381910
\(49\) 0 0
\(50\) 5.22536 0.738977
\(51\) −0.159142 −0.0222844
\(52\) 1.69469 0.235011
\(53\) −5.54558 −0.761744 −0.380872 0.924628i \(-0.624376\pi\)
−0.380872 + 0.924628i \(0.624376\pi\)
\(54\) −1.21066 −0.164751
\(55\) 0.328280 0.0442652
\(56\) 0 0
\(57\) −3.91493 −0.518545
\(58\) −11.8370 −1.55427
\(59\) −1.57839 −0.205488 −0.102744 0.994708i \(-0.532762\pi\)
−0.102744 + 0.994708i \(0.532762\pi\)
\(60\) 0.441847 0.0570422
\(61\) 8.56205 1.09626 0.548129 0.836394i \(-0.315340\pi\)
0.548129 + 0.836394i \(0.315340\pi\)
\(62\) 7.45161 0.946355
\(63\) 0 0
\(64\) 8.84277 1.10535
\(65\) 2.62306 0.325350
\(66\) 0.480588 0.0591564
\(67\) 12.1171 1.48034 0.740172 0.672418i \(-0.234744\pi\)
0.740172 + 0.672418i \(0.234744\pi\)
\(68\) 0.0850282 0.0103112
\(69\) 7.13636 0.859117
\(70\) 0 0
\(71\) −1.25998 −0.149532 −0.0747659 0.997201i \(-0.523821\pi\)
−0.0747659 + 0.997201i \(0.523821\pi\)
\(72\) 3.06818 0.361588
\(73\) −8.34764 −0.977017 −0.488509 0.872559i \(-0.662459\pi\)
−0.488509 + 0.872559i \(0.662459\pi\)
\(74\) −12.2138 −1.41982
\(75\) −4.31611 −0.498381
\(76\) 2.09171 0.239936
\(77\) 0 0
\(78\) 3.84005 0.434800
\(79\) −9.12954 −1.02715 −0.513577 0.858044i \(-0.671680\pi\)
−0.513577 + 0.858044i \(0.671680\pi\)
\(80\) 2.18815 0.244642
\(81\) 1.00000 0.111111
\(82\) 1.21066 0.133696
\(83\) −9.77501 −1.07295 −0.536473 0.843917i \(-0.680244\pi\)
−0.536473 + 0.843917i \(0.680244\pi\)
\(84\) 0 0
\(85\) 0.131607 0.0142748
\(86\) 6.44611 0.695102
\(87\) 9.77724 1.04823
\(88\) −1.21795 −0.129834
\(89\) −11.8098 −1.25184 −0.625919 0.779888i \(-0.715276\pi\)
−0.625919 + 0.779888i \(0.715276\pi\)
\(90\) 1.00119 0.105535
\(91\) 0 0
\(92\) −3.81289 −0.397521
\(93\) −6.15497 −0.638241
\(94\) −1.58670 −0.163656
\(95\) 3.23757 0.332167
\(96\) −2.93299 −0.299347
\(97\) −10.4867 −1.06476 −0.532381 0.846505i \(-0.678703\pi\)
−0.532381 + 0.846505i \(0.678703\pi\)
\(98\) 0 0
\(99\) −0.396962 −0.0398962
\(100\) 2.30605 0.230605
\(101\) −11.1956 −1.11401 −0.557004 0.830510i \(-0.688049\pi\)
−0.557004 + 0.830510i \(0.688049\pi\)
\(102\) 0.192668 0.0190770
\(103\) 14.7729 1.45562 0.727809 0.685780i \(-0.240539\pi\)
0.727809 + 0.685780i \(0.240539\pi\)
\(104\) −9.73181 −0.954282
\(105\) 0 0
\(106\) 6.71384 0.652105
\(107\) −15.4131 −1.49004 −0.745022 0.667039i \(-0.767561\pi\)
−0.745022 + 0.667039i \(0.767561\pi\)
\(108\) −0.534291 −0.0514121
\(109\) 6.49240 0.621859 0.310929 0.950433i \(-0.399360\pi\)
0.310929 + 0.950433i \(0.399360\pi\)
\(110\) −0.397437 −0.0378941
\(111\) 10.0885 0.957557
\(112\) 0 0
\(113\) 7.90856 0.743975 0.371988 0.928238i \(-0.378676\pi\)
0.371988 + 0.928238i \(0.378676\pi\)
\(114\) 4.73967 0.443911
\(115\) −5.90162 −0.550329
\(116\) −5.22389 −0.485026
\(117\) −3.17185 −0.293238
\(118\) 1.91090 0.175912
\(119\) 0 0
\(120\) −2.53732 −0.231624
\(121\) −10.8424 −0.985675
\(122\) −10.3658 −0.938473
\(123\) −1.00000 −0.0901670
\(124\) 3.28854 0.295320
\(125\) 7.70423 0.689087
\(126\) 0 0
\(127\) 14.5557 1.29161 0.645806 0.763502i \(-0.276522\pi\)
0.645806 + 0.763502i \(0.276522\pi\)
\(128\) −4.83965 −0.427769
\(129\) −5.32444 −0.468791
\(130\) −3.17564 −0.278522
\(131\) 6.06255 0.529687 0.264844 0.964291i \(-0.414680\pi\)
0.264844 + 0.964291i \(0.414680\pi\)
\(132\) 0.212093 0.0184604
\(133\) 0 0
\(134\) −14.6698 −1.26728
\(135\) −0.826979 −0.0711750
\(136\) −0.488277 −0.0418694
\(137\) −20.0820 −1.71572 −0.857861 0.513881i \(-0.828207\pi\)
−0.857861 + 0.513881i \(0.828207\pi\)
\(138\) −8.63974 −0.735463
\(139\) 15.7498 1.33588 0.667939 0.744216i \(-0.267177\pi\)
0.667939 + 0.744216i \(0.267177\pi\)
\(140\) 0 0
\(141\) 1.31060 0.110373
\(142\) 1.52541 0.128010
\(143\) 1.25911 0.105292
\(144\) −2.64595 −0.220496
\(145\) −8.08558 −0.671471
\(146\) 10.1062 0.836394
\(147\) 0 0
\(148\) −5.39019 −0.443071
\(149\) −3.75818 −0.307882 −0.153941 0.988080i \(-0.549197\pi\)
−0.153941 + 0.988080i \(0.549197\pi\)
\(150\) 5.22536 0.426649
\(151\) −3.89228 −0.316749 −0.158375 0.987379i \(-0.550625\pi\)
−0.158375 + 0.987379i \(0.550625\pi\)
\(152\) −12.0117 −0.974278
\(153\) −0.159142 −0.0128659
\(154\) 0 0
\(155\) 5.09003 0.408841
\(156\) 1.69469 0.135684
\(157\) −1.02175 −0.0815444 −0.0407722 0.999168i \(-0.512982\pi\)
−0.0407722 + 0.999168i \(0.512982\pi\)
\(158\) 11.0528 0.879315
\(159\) −5.54558 −0.439793
\(160\) 2.42552 0.191754
\(161\) 0 0
\(162\) −1.21066 −0.0951188
\(163\) −4.26792 −0.334289 −0.167145 0.985932i \(-0.553455\pi\)
−0.167145 + 0.985932i \(0.553455\pi\)
\(164\) 0.534291 0.0417211
\(165\) 0.328280 0.0255565
\(166\) 11.8343 0.918517
\(167\) −0.771033 −0.0596643 −0.0298322 0.999555i \(-0.509497\pi\)
−0.0298322 + 0.999555i \(0.509497\pi\)
\(168\) 0 0
\(169\) −2.93934 −0.226103
\(170\) −0.159332 −0.0122202
\(171\) −3.91493 −0.299382
\(172\) 2.84480 0.216914
\(173\) 23.6355 1.79697 0.898487 0.439000i \(-0.144667\pi\)
0.898487 + 0.439000i \(0.144667\pi\)
\(174\) −11.8370 −0.897358
\(175\) 0 0
\(176\) 1.05034 0.0791726
\(177\) −1.57839 −0.118639
\(178\) 14.2977 1.07166
\(179\) −15.3604 −1.14809 −0.574043 0.818825i \(-0.694626\pi\)
−0.574043 + 0.818825i \(0.694626\pi\)
\(180\) 0.441847 0.0329334
\(181\) 11.5190 0.856197 0.428099 0.903732i \(-0.359184\pi\)
0.428099 + 0.903732i \(0.359184\pi\)
\(182\) 0 0
\(183\) 8.56205 0.632925
\(184\) 21.8956 1.61417
\(185\) −8.34298 −0.613388
\(186\) 7.45161 0.546378
\(187\) 0.0631735 0.00461970
\(188\) −0.700243 −0.0510704
\(189\) 0 0
\(190\) −3.91961 −0.284358
\(191\) 22.3034 1.61382 0.806908 0.590677i \(-0.201139\pi\)
0.806908 + 0.590677i \(0.201139\pi\)
\(192\) 8.84277 0.638172
\(193\) −2.09556 −0.150842 −0.0754209 0.997152i \(-0.524030\pi\)
−0.0754209 + 0.997152i \(0.524030\pi\)
\(194\) 12.6959 0.911511
\(195\) 2.62306 0.187841
\(196\) 0 0
\(197\) −13.2692 −0.945390 −0.472695 0.881226i \(-0.656719\pi\)
−0.472695 + 0.881226i \(0.656719\pi\)
\(198\) 0.480588 0.0341539
\(199\) −16.1873 −1.14749 −0.573744 0.819034i \(-0.694510\pi\)
−0.573744 + 0.819034i \(0.694510\pi\)
\(200\) −13.2426 −0.936391
\(201\) 12.1171 0.854677
\(202\) 13.5542 0.953668
\(203\) 0 0
\(204\) 0.0850282 0.00595317
\(205\) 0.826979 0.0577587
\(206\) −17.8850 −1.24611
\(207\) 7.13636 0.496011
\(208\) 8.39257 0.581920
\(209\) 1.55408 0.107498
\(210\) 0 0
\(211\) 9.64598 0.664057 0.332028 0.943269i \(-0.392267\pi\)
0.332028 + 0.943269i \(0.392267\pi\)
\(212\) 2.96295 0.203496
\(213\) −1.25998 −0.0863322
\(214\) 18.6602 1.27558
\(215\) 4.40320 0.300296
\(216\) 3.06818 0.208763
\(217\) 0 0
\(218\) −7.86012 −0.532354
\(219\) −8.34764 −0.564081
\(220\) −0.175397 −0.0118252
\(221\) 0.504776 0.0339549
\(222\) −12.2138 −0.819736
\(223\) 14.1497 0.947533 0.473766 0.880651i \(-0.342894\pi\)
0.473766 + 0.880651i \(0.342894\pi\)
\(224\) 0 0
\(225\) −4.31611 −0.287740
\(226\) −9.57462 −0.636894
\(227\) 21.3542 1.41733 0.708663 0.705548i \(-0.249299\pi\)
0.708663 + 0.705548i \(0.249299\pi\)
\(228\) 2.09171 0.138527
\(229\) −27.5147 −1.81822 −0.909112 0.416551i \(-0.863239\pi\)
−0.909112 + 0.416551i \(0.863239\pi\)
\(230\) 7.14488 0.471120
\(231\) 0 0
\(232\) 29.9983 1.96948
\(233\) 4.24294 0.277964 0.138982 0.990295i \(-0.455617\pi\)
0.138982 + 0.990295i \(0.455617\pi\)
\(234\) 3.84005 0.251032
\(235\) −1.08384 −0.0707020
\(236\) 0.843317 0.0548952
\(237\) −9.12954 −0.593027
\(238\) 0 0
\(239\) −19.2763 −1.24688 −0.623441 0.781871i \(-0.714266\pi\)
−0.623441 + 0.781871i \(0.714266\pi\)
\(240\) 2.18815 0.141244
\(241\) 11.3629 0.731947 0.365974 0.930625i \(-0.380736\pi\)
0.365974 + 0.930625i \(0.380736\pi\)
\(242\) 13.1265 0.843806
\(243\) 1.00000 0.0641500
\(244\) −4.57462 −0.292860
\(245\) 0 0
\(246\) 1.21066 0.0771892
\(247\) 12.4176 0.790112
\(248\) −18.8845 −1.19917
\(249\) −9.77501 −0.619466
\(250\) −9.32724 −0.589906
\(251\) −14.5991 −0.921485 −0.460743 0.887534i \(-0.652417\pi\)
−0.460743 + 0.887534i \(0.652417\pi\)
\(252\) 0 0
\(253\) −2.83287 −0.178101
\(254\) −17.6221 −1.10571
\(255\) 0.131607 0.00824157
\(256\) −11.8264 −0.739147
\(257\) −12.6279 −0.787708 −0.393854 0.919173i \(-0.628858\pi\)
−0.393854 + 0.919173i \(0.628858\pi\)
\(258\) 6.44611 0.401317
\(259\) 0 0
\(260\) −1.40148 −0.0869158
\(261\) 9.77724 0.605196
\(262\) −7.33971 −0.453449
\(263\) −13.9102 −0.857740 −0.428870 0.903366i \(-0.641088\pi\)
−0.428870 + 0.903366i \(0.641088\pi\)
\(264\) −1.21795 −0.0749597
\(265\) 4.58608 0.281721
\(266\) 0 0
\(267\) −11.8098 −0.722749
\(268\) −6.47407 −0.395467
\(269\) −16.8108 −1.02497 −0.512485 0.858696i \(-0.671275\pi\)
−0.512485 + 0.858696i \(0.671275\pi\)
\(270\) 1.00119 0.0609308
\(271\) −20.3826 −1.23815 −0.619076 0.785331i \(-0.712493\pi\)
−0.619076 + 0.785331i \(0.712493\pi\)
\(272\) 0.421083 0.0255319
\(273\) 0 0
\(274\) 24.3126 1.46878
\(275\) 1.71333 0.103318
\(276\) −3.81289 −0.229509
\(277\) 2.40720 0.144635 0.0723173 0.997382i \(-0.476961\pi\)
0.0723173 + 0.997382i \(0.476961\pi\)
\(278\) −19.0677 −1.14360
\(279\) −6.15497 −0.368488
\(280\) 0 0
\(281\) −4.17078 −0.248808 −0.124404 0.992232i \(-0.539702\pi\)
−0.124404 + 0.992232i \(0.539702\pi\)
\(282\) −1.58670 −0.0944866
\(283\) −25.0304 −1.48790 −0.743952 0.668233i \(-0.767051\pi\)
−0.743952 + 0.668233i \(0.767051\pi\)
\(284\) 0.673194 0.0399467
\(285\) 3.23757 0.191777
\(286\) −1.52436 −0.0901371
\(287\) 0 0
\(288\) −2.93299 −0.172828
\(289\) −16.9747 −0.998510
\(290\) 9.78892 0.574825
\(291\) −10.4867 −0.614741
\(292\) 4.46006 0.261006
\(293\) −3.54593 −0.207156 −0.103578 0.994621i \(-0.533029\pi\)
−0.103578 + 0.994621i \(0.533029\pi\)
\(294\) 0 0
\(295\) 1.30529 0.0759971
\(296\) 30.9533 1.79912
\(297\) −0.396962 −0.0230341
\(298\) 4.54990 0.263568
\(299\) −22.6355 −1.30904
\(300\) 2.30605 0.133140
\(301\) 0 0
\(302\) 4.71225 0.271159
\(303\) −11.1956 −0.643173
\(304\) 10.3587 0.594113
\(305\) −7.08064 −0.405436
\(306\) 0.192668 0.0110141
\(307\) −1.01986 −0.0582066 −0.0291033 0.999576i \(-0.509265\pi\)
−0.0291033 + 0.999576i \(0.509265\pi\)
\(308\) 0 0
\(309\) 14.7729 0.840401
\(310\) −6.16233 −0.349997
\(311\) −7.92464 −0.449365 −0.224683 0.974432i \(-0.572135\pi\)
−0.224683 + 0.974432i \(0.572135\pi\)
\(312\) −9.73181 −0.550955
\(313\) −22.1862 −1.25404 −0.627019 0.779004i \(-0.715725\pi\)
−0.627019 + 0.779004i \(0.715725\pi\)
\(314\) 1.23700 0.0698077
\(315\) 0 0
\(316\) 4.87783 0.274399
\(317\) −10.0502 −0.564475 −0.282238 0.959345i \(-0.591077\pi\)
−0.282238 + 0.959345i \(0.591077\pi\)
\(318\) 6.71384 0.376493
\(319\) −3.88120 −0.217305
\(320\) −7.31279 −0.408797
\(321\) −15.4131 −0.860278
\(322\) 0 0
\(323\) 0.623031 0.0346664
\(324\) −0.534291 −0.0296828
\(325\) 13.6901 0.759388
\(326\) 5.16702 0.286175
\(327\) 6.49240 0.359030
\(328\) −3.06818 −0.169412
\(329\) 0 0
\(330\) −0.397437 −0.0218782
\(331\) −17.6949 −0.972600 −0.486300 0.873792i \(-0.661654\pi\)
−0.486300 + 0.873792i \(0.661654\pi\)
\(332\) 5.22270 0.286633
\(333\) 10.0885 0.552846
\(334\) 0.933462 0.0510768
\(335\) −10.0206 −0.547485
\(336\) 0 0
\(337\) 17.6666 0.962363 0.481182 0.876621i \(-0.340208\pi\)
0.481182 + 0.876621i \(0.340208\pi\)
\(338\) 3.55856 0.193560
\(339\) 7.90856 0.429534
\(340\) −0.0703166 −0.00381345
\(341\) 2.44329 0.132312
\(342\) 4.73967 0.256292
\(343\) 0 0
\(344\) −16.3363 −0.880795
\(345\) −5.90162 −0.317733
\(346\) −28.6147 −1.53833
\(347\) 1.78235 0.0956814 0.0478407 0.998855i \(-0.484766\pi\)
0.0478407 + 0.998855i \(0.484766\pi\)
\(348\) −5.22389 −0.280030
\(349\) −15.5672 −0.833292 −0.416646 0.909069i \(-0.636795\pi\)
−0.416646 + 0.909069i \(0.636795\pi\)
\(350\) 0 0
\(351\) −3.17185 −0.169301
\(352\) 1.16429 0.0620567
\(353\) 24.8556 1.32293 0.661465 0.749976i \(-0.269935\pi\)
0.661465 + 0.749976i \(0.269935\pi\)
\(354\) 1.91090 0.101563
\(355\) 1.04197 0.0553023
\(356\) 6.30987 0.334423
\(357\) 0 0
\(358\) 18.5962 0.982842
\(359\) −31.9181 −1.68457 −0.842287 0.539030i \(-0.818791\pi\)
−0.842287 + 0.539030i \(0.818791\pi\)
\(360\) −2.53732 −0.133728
\(361\) −3.67331 −0.193332
\(362\) −13.9456 −0.732964
\(363\) −10.8424 −0.569080
\(364\) 0 0
\(365\) 6.90332 0.361336
\(366\) −10.3658 −0.541828
\(367\) −34.5186 −1.80186 −0.900928 0.433969i \(-0.857113\pi\)
−0.900928 + 0.433969i \(0.857113\pi\)
\(368\) −18.8825 −0.984316
\(369\) −1.00000 −0.0520579
\(370\) 10.1005 0.525102
\(371\) 0 0
\(372\) 3.28854 0.170503
\(373\) 22.5138 1.16572 0.582860 0.812573i \(-0.301934\pi\)
0.582860 + 0.812573i \(0.301934\pi\)
\(374\) −0.0764819 −0.00395479
\(375\) 7.70423 0.397845
\(376\) 4.02116 0.207375
\(377\) −31.0120 −1.59720
\(378\) 0 0
\(379\) 15.8824 0.815824 0.407912 0.913021i \(-0.366257\pi\)
0.407912 + 0.913021i \(0.366257\pi\)
\(380\) −1.72980 −0.0887370
\(381\) 14.5557 0.745712
\(382\) −27.0019 −1.38154
\(383\) −6.79166 −0.347038 −0.173519 0.984831i \(-0.555514\pi\)
−0.173519 + 0.984831i \(0.555514\pi\)
\(384\) −4.83965 −0.246972
\(385\) 0 0
\(386\) 2.53702 0.129131
\(387\) −5.32444 −0.270656
\(388\) 5.60294 0.284446
\(389\) 19.5990 0.993708 0.496854 0.867834i \(-0.334489\pi\)
0.496854 + 0.867834i \(0.334489\pi\)
\(390\) −3.17564 −0.160805
\(391\) −1.13570 −0.0574346
\(392\) 0 0
\(393\) 6.06255 0.305815
\(394\) 16.0645 0.809319
\(395\) 7.54994 0.379879
\(396\) 0.212093 0.0106581
\(397\) −22.5654 −1.13253 −0.566263 0.824225i \(-0.691611\pi\)
−0.566263 + 0.824225i \(0.691611\pi\)
\(398\) 19.5974 0.982330
\(399\) 0 0
\(400\) 11.4202 0.571010
\(401\) −29.5304 −1.47468 −0.737340 0.675522i \(-0.763918\pi\)
−0.737340 + 0.675522i \(0.763918\pi\)
\(402\) −14.6698 −0.731663
\(403\) 19.5227 0.972493
\(404\) 5.98173 0.297602
\(405\) −0.826979 −0.0410929
\(406\) 0 0
\(407\) −4.00475 −0.198508
\(408\) −0.488277 −0.0241733
\(409\) −9.52324 −0.470894 −0.235447 0.971887i \(-0.575655\pi\)
−0.235447 + 0.971887i \(0.575655\pi\)
\(410\) −1.00119 −0.0494455
\(411\) −20.0820 −0.990573
\(412\) −7.89302 −0.388861
\(413\) 0 0
\(414\) −8.63974 −0.424620
\(415\) 8.08373 0.396815
\(416\) 9.30302 0.456118
\(417\) 15.7498 0.771270
\(418\) −1.88147 −0.0920258
\(419\) −11.1971 −0.547013 −0.273506 0.961870i \(-0.588183\pi\)
−0.273506 + 0.961870i \(0.588183\pi\)
\(420\) 0 0
\(421\) −7.98853 −0.389337 −0.194668 0.980869i \(-0.562363\pi\)
−0.194668 + 0.980869i \(0.562363\pi\)
\(422\) −11.6780 −0.568479
\(423\) 1.31060 0.0637237
\(424\) −17.0148 −0.826312
\(425\) 0.686875 0.0333183
\(426\) 1.52541 0.0739063
\(427\) 0 0
\(428\) 8.23510 0.398059
\(429\) 1.25911 0.0607903
\(430\) −5.33080 −0.257074
\(431\) 5.71725 0.275390 0.137695 0.990475i \(-0.456031\pi\)
0.137695 + 0.990475i \(0.456031\pi\)
\(432\) −2.64595 −0.127303
\(433\) −18.7297 −0.900090 −0.450045 0.893006i \(-0.648592\pi\)
−0.450045 + 0.893006i \(0.648592\pi\)
\(434\) 0 0
\(435\) −8.08558 −0.387674
\(436\) −3.46883 −0.166127
\(437\) −27.9384 −1.33647
\(438\) 10.1062 0.482892
\(439\) 28.6939 1.36949 0.684744 0.728784i \(-0.259914\pi\)
0.684744 + 0.728784i \(0.259914\pi\)
\(440\) 1.00722 0.0480173
\(441\) 0 0
\(442\) −0.611115 −0.0290678
\(443\) −20.8134 −0.988874 −0.494437 0.869214i \(-0.664626\pi\)
−0.494437 + 0.869214i \(0.664626\pi\)
\(444\) −5.39019 −0.255807
\(445\) 9.76647 0.462975
\(446\) −17.1305 −0.811154
\(447\) −3.75818 −0.177756
\(448\) 0 0
\(449\) 31.0640 1.46600 0.733001 0.680227i \(-0.238119\pi\)
0.733001 + 0.680227i \(0.238119\pi\)
\(450\) 5.22536 0.246326
\(451\) 0.396962 0.0186922
\(452\) −4.22547 −0.198749
\(453\) −3.89228 −0.182875
\(454\) −25.8527 −1.21333
\(455\) 0 0
\(456\) −12.0117 −0.562499
\(457\) 26.1256 1.22211 0.611053 0.791590i \(-0.290746\pi\)
0.611053 + 0.791590i \(0.290746\pi\)
\(458\) 33.3111 1.55653
\(459\) −0.159142 −0.00742813
\(460\) 3.15318 0.147018
\(461\) −17.3348 −0.807364 −0.403682 0.914899i \(-0.632270\pi\)
−0.403682 + 0.914899i \(0.632270\pi\)
\(462\) 0 0
\(463\) 0.550182 0.0255691 0.0127846 0.999918i \(-0.495930\pi\)
0.0127846 + 0.999918i \(0.495930\pi\)
\(464\) −25.8701 −1.20099
\(465\) 5.09003 0.236045
\(466\) −5.13678 −0.237957
\(467\) −17.0821 −0.790466 −0.395233 0.918581i \(-0.629336\pi\)
−0.395233 + 0.918581i \(0.629336\pi\)
\(468\) 1.69469 0.0783372
\(469\) 0 0
\(470\) 1.31217 0.0605258
\(471\) −1.02175 −0.0470797
\(472\) −4.84277 −0.222906
\(473\) 2.11360 0.0971835
\(474\) 11.0528 0.507673
\(475\) 16.8973 0.775299
\(476\) 0 0
\(477\) −5.54558 −0.253915
\(478\) 23.3372 1.06742
\(479\) −10.8316 −0.494907 −0.247454 0.968900i \(-0.579594\pi\)
−0.247454 + 0.968900i \(0.579594\pi\)
\(480\) 2.42552 0.110710
\(481\) −31.9992 −1.45904
\(482\) −13.7566 −0.626597
\(483\) 0 0
\(484\) 5.79300 0.263318
\(485\) 8.67228 0.393788
\(486\) −1.21066 −0.0549169
\(487\) −20.0891 −0.910326 −0.455163 0.890408i \(-0.650419\pi\)
−0.455163 + 0.890408i \(0.650419\pi\)
\(488\) 26.2699 1.18918
\(489\) −4.26792 −0.193002
\(490\) 0 0
\(491\) −11.3968 −0.514330 −0.257165 0.966368i \(-0.582788\pi\)
−0.257165 + 0.966368i \(0.582788\pi\)
\(492\) 0.534291 0.0240877
\(493\) −1.55597 −0.0700775
\(494\) −15.0335 −0.676391
\(495\) 0.328280 0.0147551
\(496\) 16.2858 0.731252
\(497\) 0 0
\(498\) 11.8343 0.530306
\(499\) 5.76670 0.258153 0.129076 0.991635i \(-0.458799\pi\)
0.129076 + 0.991635i \(0.458799\pi\)
\(500\) −4.11630 −0.184086
\(501\) −0.771033 −0.0344472
\(502\) 17.6746 0.788855
\(503\) −27.0330 −1.20534 −0.602671 0.797989i \(-0.705897\pi\)
−0.602671 + 0.797989i \(0.705897\pi\)
\(504\) 0 0
\(505\) 9.25857 0.412001
\(506\) 3.42965 0.152467
\(507\) −2.93934 −0.130541
\(508\) −7.77699 −0.345048
\(509\) 23.3862 1.03657 0.518287 0.855207i \(-0.326570\pi\)
0.518287 + 0.855207i \(0.326570\pi\)
\(510\) −0.159332 −0.00705536
\(511\) 0 0
\(512\) 23.9971 1.06053
\(513\) −3.91493 −0.172848
\(514\) 15.2882 0.674332
\(515\) −12.2169 −0.538340
\(516\) 2.84480 0.125235
\(517\) −0.520260 −0.0228810
\(518\) 0 0
\(519\) 23.6355 1.03748
\(520\) 8.04800 0.352928
\(521\) −23.7425 −1.04018 −0.520089 0.854112i \(-0.674101\pi\)
−0.520089 + 0.854112i \(0.674101\pi\)
\(522\) −11.8370 −0.518090
\(523\) −25.0433 −1.09507 −0.547534 0.836783i \(-0.684433\pi\)
−0.547534 + 0.836783i \(0.684433\pi\)
\(524\) −3.23916 −0.141503
\(525\) 0 0
\(526\) 16.8406 0.734285
\(527\) 0.979516 0.0426684
\(528\) 1.05034 0.0457103
\(529\) 27.9276 1.21424
\(530\) −5.55220 −0.241172
\(531\) −1.57839 −0.0684961
\(532\) 0 0
\(533\) 3.17185 0.137388
\(534\) 14.2977 0.618723
\(535\) 12.7464 0.551073
\(536\) 37.1775 1.60582
\(537\) −15.3604 −0.662848
\(538\) 20.3522 0.877445
\(539\) 0 0
\(540\) 0.441847 0.0190141
\(541\) 9.63953 0.414436 0.207218 0.978295i \(-0.433559\pi\)
0.207218 + 0.978295i \(0.433559\pi\)
\(542\) 24.6764 1.05994
\(543\) 11.5190 0.494326
\(544\) 0.466763 0.0200123
\(545\) −5.36908 −0.229986
\(546\) 0 0
\(547\) −22.0752 −0.943868 −0.471934 0.881634i \(-0.656444\pi\)
−0.471934 + 0.881634i \(0.656444\pi\)
\(548\) 10.7296 0.458347
\(549\) 8.56205 0.365419
\(550\) −2.07427 −0.0884472
\(551\) −38.2772 −1.63066
\(552\) 21.8956 0.931939
\(553\) 0 0
\(554\) −2.91431 −0.123817
\(555\) −8.34298 −0.354140
\(556\) −8.41496 −0.356874
\(557\) −41.1233 −1.74245 −0.871224 0.490885i \(-0.836674\pi\)
−0.871224 + 0.490885i \(0.836674\pi\)
\(558\) 7.45161 0.315452
\(559\) 16.8883 0.714301
\(560\) 0 0
\(561\) 0.0631735 0.00266719
\(562\) 5.04942 0.212997
\(563\) 38.2399 1.61162 0.805810 0.592174i \(-0.201730\pi\)
0.805810 + 0.592174i \(0.201730\pi\)
\(564\) −0.700243 −0.0294855
\(565\) −6.54022 −0.275149
\(566\) 30.3035 1.27375
\(567\) 0 0
\(568\) −3.86583 −0.162207
\(569\) 34.6025 1.45061 0.725307 0.688426i \(-0.241698\pi\)
0.725307 + 0.688426i \(0.241698\pi\)
\(570\) −3.91961 −0.164174
\(571\) 17.7405 0.742417 0.371208 0.928550i \(-0.378944\pi\)
0.371208 + 0.928550i \(0.378944\pi\)
\(572\) −0.672729 −0.0281282
\(573\) 22.3034 0.931737
\(574\) 0 0
\(575\) −30.8013 −1.28450
\(576\) 8.84277 0.368449
\(577\) −44.2621 −1.84265 −0.921327 0.388788i \(-0.872894\pi\)
−0.921327 + 0.388788i \(0.872894\pi\)
\(578\) 20.5506 0.854794
\(579\) −2.09556 −0.0870885
\(580\) 4.32005 0.179380
\(581\) 0 0
\(582\) 12.6959 0.526261
\(583\) 2.20139 0.0911721
\(584\) −25.6120 −1.05983
\(585\) 2.62306 0.108450
\(586\) 4.29294 0.177340
\(587\) −23.5641 −0.972595 −0.486298 0.873793i \(-0.661653\pi\)
−0.486298 + 0.873793i \(0.661653\pi\)
\(588\) 0 0
\(589\) 24.0963 0.992870
\(590\) −1.58027 −0.0650587
\(591\) −13.2692 −0.545821
\(592\) −26.6937 −1.09710
\(593\) 29.7934 1.22347 0.611734 0.791064i \(-0.290472\pi\)
0.611734 + 0.791064i \(0.290472\pi\)
\(594\) 0.480588 0.0197188
\(595\) 0 0
\(596\) 2.00796 0.0822493
\(597\) −16.1873 −0.662503
\(598\) 27.4040 1.12063
\(599\) 12.6651 0.517481 0.258741 0.965947i \(-0.416692\pi\)
0.258741 + 0.965947i \(0.416692\pi\)
\(600\) −13.2426 −0.540626
\(601\) −17.6451 −0.719757 −0.359879 0.932999i \(-0.617182\pi\)
−0.359879 + 0.932999i \(0.617182\pi\)
\(602\) 0 0
\(603\) 12.1171 0.493448
\(604\) 2.07961 0.0846181
\(605\) 8.96646 0.364538
\(606\) 13.5542 0.550601
\(607\) −27.0843 −1.09932 −0.549658 0.835390i \(-0.685242\pi\)
−0.549658 + 0.835390i \(0.685242\pi\)
\(608\) 11.4825 0.465675
\(609\) 0 0
\(610\) 8.57228 0.347082
\(611\) −4.15704 −0.168176
\(612\) 0.0850282 0.00343706
\(613\) 25.9967 1.05000 0.524998 0.851104i \(-0.324066\pi\)
0.524998 + 0.851104i \(0.324066\pi\)
\(614\) 1.23471 0.0498289
\(615\) 0.826979 0.0333470
\(616\) 0 0
\(617\) −2.10539 −0.0847596 −0.0423798 0.999102i \(-0.513494\pi\)
−0.0423798 + 0.999102i \(0.513494\pi\)
\(618\) −17.8850 −0.719442
\(619\) 27.8990 1.12135 0.560677 0.828034i \(-0.310541\pi\)
0.560677 + 0.828034i \(0.310541\pi\)
\(620\) −2.71956 −0.109220
\(621\) 7.13636 0.286372
\(622\) 9.59409 0.384688
\(623\) 0 0
\(624\) 8.39257 0.335972
\(625\) 15.2093 0.608372
\(626\) 26.8601 1.07354
\(627\) 1.55408 0.0620640
\(628\) 0.545911 0.0217842
\(629\) −1.60551 −0.0640157
\(630\) 0 0
\(631\) −21.9270 −0.872900 −0.436450 0.899728i \(-0.643764\pi\)
−0.436450 + 0.899728i \(0.643764\pi\)
\(632\) −28.0110 −1.11422
\(633\) 9.64598 0.383393
\(634\) 12.1674 0.483230
\(635\) −12.0373 −0.477685
\(636\) 2.96295 0.117489
\(637\) 0 0
\(638\) 4.69883 0.186028
\(639\) −1.25998 −0.0498439
\(640\) 4.00229 0.158205
\(641\) 34.8883 1.37801 0.689003 0.724758i \(-0.258048\pi\)
0.689003 + 0.724758i \(0.258048\pi\)
\(642\) 18.6602 0.736457
\(643\) 38.0533 1.50067 0.750337 0.661055i \(-0.229891\pi\)
0.750337 + 0.661055i \(0.229891\pi\)
\(644\) 0 0
\(645\) 4.40320 0.173376
\(646\) −0.754282 −0.0296768
\(647\) 0.560042 0.0220175 0.0110088 0.999939i \(-0.496496\pi\)
0.0110088 + 0.999939i \(0.496496\pi\)
\(648\) 3.06818 0.120529
\(649\) 0.626560 0.0245946
\(650\) −16.5741 −0.650088
\(651\) 0 0
\(652\) 2.28031 0.0893038
\(653\) −25.1642 −0.984751 −0.492375 0.870383i \(-0.663871\pi\)
−0.492375 + 0.870383i \(0.663871\pi\)
\(654\) −7.86012 −0.307355
\(655\) −5.01360 −0.195898
\(656\) 2.64595 0.103307
\(657\) −8.34764 −0.325672
\(658\) 0 0
\(659\) −45.6924 −1.77992 −0.889962 0.456035i \(-0.849269\pi\)
−0.889962 + 0.456035i \(0.849269\pi\)
\(660\) −0.175397 −0.00682731
\(661\) −13.5821 −0.528283 −0.264141 0.964484i \(-0.585089\pi\)
−0.264141 + 0.964484i \(0.585089\pi\)
\(662\) 21.4226 0.832613
\(663\) 0.504776 0.0196039
\(664\) −29.9915 −1.16389
\(665\) 0 0
\(666\) −12.2138 −0.473275
\(667\) 69.7739 2.70166
\(668\) 0.411956 0.0159390
\(669\) 14.1497 0.547058
\(670\) 12.1316 0.468685
\(671\) −3.39881 −0.131210
\(672\) 0 0
\(673\) 11.3582 0.437825 0.218913 0.975744i \(-0.429749\pi\)
0.218913 + 0.975744i \(0.429749\pi\)
\(674\) −21.3884 −0.823850
\(675\) −4.31611 −0.166127
\(676\) 1.57046 0.0604024
\(677\) −0.333596 −0.0128211 −0.00641056 0.999979i \(-0.502041\pi\)
−0.00641056 + 0.999979i \(0.502041\pi\)
\(678\) −9.57462 −0.367711
\(679\) 0 0
\(680\) 0.403795 0.0154848
\(681\) 21.3542 0.818293
\(682\) −2.95801 −0.113268
\(683\) −42.6711 −1.63277 −0.816383 0.577511i \(-0.804024\pi\)
−0.816383 + 0.577511i \(0.804024\pi\)
\(684\) 2.09171 0.0799786
\(685\) 16.6074 0.634537
\(686\) 0 0
\(687\) −27.5147 −1.04975
\(688\) 14.0882 0.537108
\(689\) 17.5898 0.670117
\(690\) 7.14488 0.272001
\(691\) −45.1639 −1.71812 −0.859058 0.511879i \(-0.828950\pi\)
−0.859058 + 0.511879i \(0.828950\pi\)
\(692\) −12.6282 −0.480053
\(693\) 0 0
\(694\) −2.15782 −0.0819099
\(695\) −13.0247 −0.494057
\(696\) 29.9983 1.13708
\(697\) 0.159142 0.00602794
\(698\) 18.8466 0.713356
\(699\) 4.24294 0.160483
\(700\) 0 0
\(701\) −40.4169 −1.52653 −0.763263 0.646088i \(-0.776404\pi\)
−0.763263 + 0.646088i \(0.776404\pi\)
\(702\) 3.84005 0.144933
\(703\) −39.4958 −1.48961
\(704\) −3.51025 −0.132298
\(705\) −1.08384 −0.0408198
\(706\) −30.0918 −1.13252
\(707\) 0 0
\(708\) 0.843317 0.0316938
\(709\) −18.6305 −0.699682 −0.349841 0.936809i \(-0.613764\pi\)
−0.349841 + 0.936809i \(0.613764\pi\)
\(710\) −1.26148 −0.0473426
\(711\) −9.12954 −0.342385
\(712\) −36.2346 −1.35795
\(713\) −43.9241 −1.64497
\(714\) 0 0
\(715\) −1.04126 −0.0389407
\(716\) 8.20689 0.306706
\(717\) −19.2763 −0.719887
\(718\) 38.6421 1.44211
\(719\) 34.1061 1.27194 0.635971 0.771713i \(-0.280600\pi\)
0.635971 + 0.771713i \(0.280600\pi\)
\(720\) 2.18815 0.0815475
\(721\) 0 0
\(722\) 4.44715 0.165506
\(723\) 11.3629 0.422590
\(724\) −6.15447 −0.228729
\(725\) −42.1996 −1.56725
\(726\) 13.1265 0.487172
\(727\) 10.7831 0.399923 0.199961 0.979804i \(-0.435918\pi\)
0.199961 + 0.979804i \(0.435918\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −8.35761 −0.309329
\(731\) 0.847343 0.0313401
\(732\) −4.57462 −0.169083
\(733\) 34.2830 1.26627 0.633136 0.774041i \(-0.281767\pi\)
0.633136 + 0.774041i \(0.281767\pi\)
\(734\) 41.7904 1.54251
\(735\) 0 0
\(736\) −20.9309 −0.771522
\(737\) −4.81005 −0.177180
\(738\) 1.21066 0.0445652
\(739\) 29.1016 1.07052 0.535261 0.844687i \(-0.320213\pi\)
0.535261 + 0.844687i \(0.320213\pi\)
\(740\) 4.45757 0.163864
\(741\) 12.4176 0.456172
\(742\) 0 0
\(743\) −29.1285 −1.06862 −0.534311 0.845288i \(-0.679429\pi\)
−0.534311 + 0.845288i \(0.679429\pi\)
\(744\) −18.8845 −0.692341
\(745\) 3.10794 0.113866
\(746\) −27.2567 −0.997937
\(747\) −9.77501 −0.357649
\(748\) −0.0337530 −0.00123413
\(749\) 0 0
\(750\) −9.32724 −0.340583
\(751\) 33.0634 1.20650 0.603250 0.797552i \(-0.293872\pi\)
0.603250 + 0.797552i \(0.293872\pi\)
\(752\) −3.46779 −0.126457
\(753\) −14.5991 −0.532020
\(754\) 37.5451 1.36731
\(755\) 3.21884 0.117145
\(756\) 0 0
\(757\) 3.40606 0.123795 0.0618977 0.998083i \(-0.480285\pi\)
0.0618977 + 0.998083i \(0.480285\pi\)
\(758\) −19.2283 −0.698402
\(759\) −2.83287 −0.102827
\(760\) 9.93343 0.360323
\(761\) −3.37754 −0.122436 −0.0612178 0.998124i \(-0.519498\pi\)
−0.0612178 + 0.998124i \(0.519498\pi\)
\(762\) −17.6221 −0.638381
\(763\) 0 0
\(764\) −11.9165 −0.431124
\(765\) 0.131607 0.00475827
\(766\) 8.22242 0.297088
\(767\) 5.00641 0.180771
\(768\) −11.8264 −0.426747
\(769\) 1.44772 0.0522063 0.0261031 0.999659i \(-0.491690\pi\)
0.0261031 + 0.999659i \(0.491690\pi\)
\(770\) 0 0
\(771\) −12.6279 −0.454783
\(772\) 1.11964 0.0402967
\(773\) 5.01065 0.180220 0.0901102 0.995932i \(-0.471278\pi\)
0.0901102 + 0.995932i \(0.471278\pi\)
\(774\) 6.44611 0.231701
\(775\) 26.5655 0.954261
\(776\) −32.1750 −1.15502
\(777\) 0 0
\(778\) −23.7278 −0.850683
\(779\) 3.91493 0.140267
\(780\) −1.40148 −0.0501809
\(781\) 0.500163 0.0178973
\(782\) 1.37495 0.0491680
\(783\) 9.77724 0.349410
\(784\) 0 0
\(785\) 0.844965 0.0301581
\(786\) −7.33971 −0.261799
\(787\) 49.3694 1.75983 0.879915 0.475132i \(-0.157600\pi\)
0.879915 + 0.475132i \(0.157600\pi\)
\(788\) 7.08960 0.252556
\(789\) −13.9102 −0.495217
\(790\) −9.14045 −0.325203
\(791\) 0 0
\(792\) −1.21795 −0.0432780
\(793\) −27.1576 −0.964394
\(794\) 27.3191 0.969520
\(795\) 4.58608 0.162651
\(796\) 8.64873 0.306546
\(797\) 12.2118 0.432565 0.216283 0.976331i \(-0.430607\pi\)
0.216283 + 0.976331i \(0.430607\pi\)
\(798\) 0 0
\(799\) −0.208572 −0.00737876
\(800\) 12.6591 0.447567
\(801\) −11.8098 −0.417279
\(802\) 35.7515 1.26243
\(803\) 3.31370 0.116938
\(804\) −6.47407 −0.228323
\(805\) 0 0
\(806\) −23.6354 −0.832522
\(807\) −16.8108 −0.591767
\(808\) −34.3502 −1.20844
\(809\) 0.715187 0.0251446 0.0125723 0.999921i \(-0.495998\pi\)
0.0125723 + 0.999921i \(0.495998\pi\)
\(810\) 1.00119 0.0351784
\(811\) −36.3424 −1.27616 −0.638078 0.769972i \(-0.720270\pi\)
−0.638078 + 0.769972i \(0.720270\pi\)
\(812\) 0 0
\(813\) −20.3826 −0.714848
\(814\) 4.84841 0.169937
\(815\) 3.52948 0.123632
\(816\) 0.421083 0.0147408
\(817\) 20.8448 0.729268
\(818\) 11.5294 0.403118
\(819\) 0 0
\(820\) −0.441847 −0.0154300
\(821\) −28.7101 −1.00199 −0.500995 0.865450i \(-0.667033\pi\)
−0.500995 + 0.865450i \(0.667033\pi\)
\(822\) 24.3126 0.847999
\(823\) 49.9050 1.73958 0.869790 0.493422i \(-0.164254\pi\)
0.869790 + 0.493422i \(0.164254\pi\)
\(824\) 45.3259 1.57900
\(825\) 1.71333 0.0596506
\(826\) 0 0
\(827\) −19.8378 −0.689829 −0.344914 0.938634i \(-0.612092\pi\)
−0.344914 + 0.938634i \(0.612092\pi\)
\(828\) −3.81289 −0.132507
\(829\) 16.3642 0.568352 0.284176 0.958772i \(-0.408280\pi\)
0.284176 + 0.958772i \(0.408280\pi\)
\(830\) −9.78669 −0.339701
\(831\) 2.40720 0.0835048
\(832\) −28.0480 −0.972389
\(833\) 0 0
\(834\) −19.0677 −0.660261
\(835\) 0.637628 0.0220660
\(836\) −0.830331 −0.0287176
\(837\) −6.15497 −0.212747
\(838\) 13.5559 0.468281
\(839\) 9.07123 0.313174 0.156587 0.987664i \(-0.449951\pi\)
0.156587 + 0.987664i \(0.449951\pi\)
\(840\) 0 0
\(841\) 66.5944 2.29636
\(842\) 9.67143 0.333299
\(843\) −4.17078 −0.143649
\(844\) −5.15376 −0.177400
\(845\) 2.43078 0.0836212
\(846\) −1.58670 −0.0545519
\(847\) 0 0
\(848\) 14.6733 0.503884
\(849\) −25.0304 −0.859042
\(850\) −0.831575 −0.0285228
\(851\) 71.9951 2.46796
\(852\) 0.673194 0.0230632
\(853\) −24.6232 −0.843083 −0.421542 0.906809i \(-0.638511\pi\)
−0.421542 + 0.906809i \(0.638511\pi\)
\(854\) 0 0
\(855\) 3.23757 0.110722
\(856\) −47.2902 −1.61635
\(857\) −43.2834 −1.47853 −0.739266 0.673413i \(-0.764827\pi\)
−0.739266 + 0.673413i \(0.764827\pi\)
\(858\) −1.52436 −0.0520407
\(859\) −7.88554 −0.269051 −0.134526 0.990910i \(-0.542951\pi\)
−0.134526 + 0.990910i \(0.542951\pi\)
\(860\) −2.35259 −0.0802226
\(861\) 0 0
\(862\) −6.92167 −0.235753
\(863\) 9.60001 0.326788 0.163394 0.986561i \(-0.447756\pi\)
0.163394 + 0.986561i \(0.447756\pi\)
\(864\) −2.93299 −0.0997824
\(865\) −19.5461 −0.664586
\(866\) 22.6753 0.770539
\(867\) −16.9747 −0.576490
\(868\) 0 0
\(869\) 3.62409 0.122939
\(870\) 9.78892 0.331876
\(871\) −38.4338 −1.30228
\(872\) 19.9198 0.674570
\(873\) −10.4867 −0.354921
\(874\) 33.8240 1.14411
\(875\) 0 0
\(876\) 4.46006 0.150692
\(877\) 42.5859 1.43802 0.719012 0.694998i \(-0.244595\pi\)
0.719012 + 0.694998i \(0.244595\pi\)
\(878\) −34.7388 −1.17238
\(879\) −3.54593 −0.119601
\(880\) −0.868613 −0.0292809
\(881\) 21.6986 0.731043 0.365521 0.930803i \(-0.380891\pi\)
0.365521 + 0.930803i \(0.380891\pi\)
\(882\) 0 0
\(883\) 44.7964 1.50752 0.753759 0.657151i \(-0.228239\pi\)
0.753759 + 0.657151i \(0.228239\pi\)
\(884\) −0.269697 −0.00907090
\(885\) 1.30529 0.0438769
\(886\) 25.1980 0.846544
\(887\) 14.8695 0.499269 0.249635 0.968340i \(-0.419689\pi\)
0.249635 + 0.968340i \(0.419689\pi\)
\(888\) 30.9533 1.03872
\(889\) 0 0
\(890\) −11.8239 −0.396339
\(891\) −0.396962 −0.0132987
\(892\) −7.56004 −0.253129
\(893\) −5.13092 −0.171700
\(894\) 4.54990 0.152171
\(895\) 12.7027 0.424604
\(896\) 0 0
\(897\) −22.6355 −0.755777
\(898\) −37.6081 −1.25500
\(899\) −60.1786 −2.00707
\(900\) 2.30605 0.0768685
\(901\) 0.882536 0.0294015
\(902\) −0.480588 −0.0160018
\(903\) 0 0
\(904\) 24.2649 0.807038
\(905\) −9.52594 −0.316653
\(906\) 4.71225 0.156554
\(907\) 39.2897 1.30459 0.652297 0.757963i \(-0.273805\pi\)
0.652297 + 0.757963i \(0.273805\pi\)
\(908\) −11.4093 −0.378632
\(909\) −11.1956 −0.371336
\(910\) 0 0
\(911\) −20.6834 −0.685270 −0.342635 0.939469i \(-0.611319\pi\)
−0.342635 + 0.939469i \(0.611319\pi\)
\(912\) 10.3587 0.343012
\(913\) 3.88031 0.128420
\(914\) −31.6294 −1.04621
\(915\) −7.08064 −0.234079
\(916\) 14.7009 0.485730
\(917\) 0 0
\(918\) 0.192668 0.00635899
\(919\) −41.7508 −1.37723 −0.688616 0.725127i \(-0.741781\pi\)
−0.688616 + 0.725127i \(0.741781\pi\)
\(920\) −18.1072 −0.596977
\(921\) −1.01986 −0.0336056
\(922\) 20.9867 0.691160
\(923\) 3.99646 0.131545
\(924\) 0 0
\(925\) −43.5430 −1.43168
\(926\) −0.666086 −0.0218889
\(927\) 14.7729 0.485206
\(928\) −28.6766 −0.941354
\(929\) 5.14643 0.168849 0.0844245 0.996430i \(-0.473095\pi\)
0.0844245 + 0.996430i \(0.473095\pi\)
\(930\) −6.16233 −0.202071
\(931\) 0 0
\(932\) −2.26697 −0.0742569
\(933\) −7.92464 −0.259441
\(934\) 20.6807 0.676694
\(935\) −0.0522432 −0.00170853
\(936\) −9.73181 −0.318094
\(937\) −2.92520 −0.0955623 −0.0477811 0.998858i \(-0.515215\pi\)
−0.0477811 + 0.998858i \(0.515215\pi\)
\(938\) 0 0
\(939\) −22.1862 −0.724019
\(940\) 0.579086 0.0188877
\(941\) −33.3784 −1.08811 −0.544053 0.839051i \(-0.683111\pi\)
−0.544053 + 0.839051i \(0.683111\pi\)
\(942\) 1.23700 0.0403035
\(943\) −7.13636 −0.232392
\(944\) 4.17633 0.135928
\(945\) 0 0
\(946\) −2.55886 −0.0831958
\(947\) 25.3265 0.823002 0.411501 0.911409i \(-0.365005\pi\)
0.411501 + 0.911409i \(0.365005\pi\)
\(948\) 4.87783 0.158425
\(949\) 26.4775 0.859496
\(950\) −20.4569 −0.663710
\(951\) −10.0502 −0.325900
\(952\) 0 0
\(953\) 43.0540 1.39466 0.697328 0.716752i \(-0.254372\pi\)
0.697328 + 0.716752i \(0.254372\pi\)
\(954\) 6.71384 0.217368
\(955\) −18.4444 −0.596848
\(956\) 10.2992 0.333099
\(957\) −3.88120 −0.125461
\(958\) 13.1134 0.423675
\(959\) 0 0
\(960\) −7.31279 −0.236019
\(961\) 6.88367 0.222054
\(962\) 38.7403 1.24904
\(963\) −15.4131 −0.496682
\(964\) −6.07108 −0.195536
\(965\) 1.73299 0.0557868
\(966\) 0 0
\(967\) −26.3902 −0.848653 −0.424327 0.905509i \(-0.639489\pi\)
−0.424327 + 0.905509i \(0.639489\pi\)
\(968\) −33.2665 −1.06922
\(969\) 0.623031 0.0200146
\(970\) −10.4992 −0.337110
\(971\) −7.15683 −0.229673 −0.114837 0.993384i \(-0.536634\pi\)
−0.114837 + 0.993384i \(0.536634\pi\)
\(972\) −0.534291 −0.0171374
\(973\) 0 0
\(974\) 24.3212 0.779302
\(975\) 13.6901 0.438433
\(976\) −22.6548 −0.725162
\(977\) 9.93668 0.317903 0.158951 0.987286i \(-0.449189\pi\)
0.158951 + 0.987286i \(0.449189\pi\)
\(978\) 5.16702 0.165223
\(979\) 4.68805 0.149831
\(980\) 0 0
\(981\) 6.49240 0.207286
\(982\) 13.7977 0.440302
\(983\) 26.8718 0.857076 0.428538 0.903524i \(-0.359029\pi\)
0.428538 + 0.903524i \(0.359029\pi\)
\(984\) −3.06818 −0.0978099
\(985\) 10.9733 0.349639
\(986\) 1.88376 0.0599912
\(987\) 0 0
\(988\) −6.63460 −0.211075
\(989\) −37.9971 −1.20824
\(990\) −0.397437 −0.0126314
\(991\) −49.3369 −1.56724 −0.783620 0.621241i \(-0.786629\pi\)
−0.783620 + 0.621241i \(0.786629\pi\)
\(992\) 18.0525 0.573167
\(993\) −17.6949 −0.561531
\(994\) 0 0
\(995\) 13.3866 0.424383
\(996\) 5.22270 0.165487
\(997\) −13.6316 −0.431718 −0.215859 0.976425i \(-0.569255\pi\)
−0.215859 + 0.976425i \(0.569255\pi\)
\(998\) −6.98154 −0.220997
\(999\) 10.0885 0.319186
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 \(a_p\))