Properties

Label 6008.2.a.e.1.21
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 1.21
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.504664 q^{3} -0.903612 q^{5} +1.64438 q^{7} -2.74531 q^{9} +O(q^{10})\) \(q-0.504664 q^{3} -0.903612 q^{5} +1.64438 q^{7} -2.74531 q^{9} +2.24007 q^{11} -6.33083 q^{13} +0.456020 q^{15} -3.81265 q^{17} -2.50183 q^{19} -0.829861 q^{21} -4.38058 q^{23} -4.18349 q^{25} +2.89945 q^{27} -1.88754 q^{29} +9.57529 q^{31} -1.13048 q^{33} -1.48588 q^{35} +8.55568 q^{37} +3.19494 q^{39} +2.33053 q^{41} -0.990005 q^{43} +2.48070 q^{45} -3.32330 q^{47} -4.29600 q^{49} +1.92410 q^{51} -6.47032 q^{53} -2.02415 q^{55} +1.26258 q^{57} +3.39477 q^{59} -9.94685 q^{61} -4.51435 q^{63} +5.72061 q^{65} +11.7402 q^{67} +2.21072 q^{69} +9.71165 q^{71} +3.32458 q^{73} +2.11125 q^{75} +3.68354 q^{77} +5.95388 q^{79} +6.77270 q^{81} +9.44942 q^{83} +3.44515 q^{85} +0.952574 q^{87} -1.70059 q^{89} -10.4103 q^{91} -4.83230 q^{93} +2.26068 q^{95} +10.7100 q^{97} -6.14970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.504664 −0.291368 −0.145684 0.989331i \(-0.546538\pi\)
−0.145684 + 0.989331i \(0.546538\pi\)
\(4\) 0 0
\(5\) −0.903612 −0.404107 −0.202054 0.979374i \(-0.564762\pi\)
−0.202054 + 0.979374i \(0.564762\pi\)
\(6\) 0 0
\(7\) 1.64438 0.621519 0.310759 0.950489i \(-0.399417\pi\)
0.310759 + 0.950489i \(0.399417\pi\)
\(8\) 0 0
\(9\) −2.74531 −0.915105
\(10\) 0 0
\(11\) 2.24007 0.675407 0.337703 0.941253i \(-0.390350\pi\)
0.337703 + 0.941253i \(0.390350\pi\)
\(12\) 0 0
\(13\) −6.33083 −1.75586 −0.877929 0.478792i \(-0.841075\pi\)
−0.877929 + 0.478792i \(0.841075\pi\)
\(14\) 0 0
\(15\) 0.456020 0.117744
\(16\) 0 0
\(17\) −3.81265 −0.924702 −0.462351 0.886697i \(-0.652994\pi\)
−0.462351 + 0.886697i \(0.652994\pi\)
\(18\) 0 0
\(19\) −2.50183 −0.573959 −0.286979 0.957937i \(-0.592651\pi\)
−0.286979 + 0.957937i \(0.592651\pi\)
\(20\) 0 0
\(21\) −0.829861 −0.181091
\(22\) 0 0
\(23\) −4.38058 −0.913415 −0.456707 0.889617i \(-0.650971\pi\)
−0.456707 + 0.889617i \(0.650971\pi\)
\(24\) 0 0
\(25\) −4.18349 −0.836697
\(26\) 0 0
\(27\) 2.89945 0.558000
\(28\) 0 0
\(29\) −1.88754 −0.350508 −0.175254 0.984523i \(-0.556075\pi\)
−0.175254 + 0.984523i \(0.556075\pi\)
\(30\) 0 0
\(31\) 9.57529 1.71977 0.859886 0.510486i \(-0.170534\pi\)
0.859886 + 0.510486i \(0.170534\pi\)
\(32\) 0 0
\(33\) −1.13048 −0.196792
\(34\) 0 0
\(35\) −1.48588 −0.251160
\(36\) 0 0
\(37\) 8.55568 1.40654 0.703272 0.710921i \(-0.251721\pi\)
0.703272 + 0.710921i \(0.251721\pi\)
\(38\) 0 0
\(39\) 3.19494 0.511600
\(40\) 0 0
\(41\) 2.33053 0.363968 0.181984 0.983301i \(-0.441748\pi\)
0.181984 + 0.983301i \(0.441748\pi\)
\(42\) 0 0
\(43\) −0.990005 −0.150974 −0.0754872 0.997147i \(-0.524051\pi\)
−0.0754872 + 0.997147i \(0.524051\pi\)
\(44\) 0 0
\(45\) 2.48070 0.369801
\(46\) 0 0
\(47\) −3.32330 −0.484753 −0.242376 0.970182i \(-0.577927\pi\)
−0.242376 + 0.970182i \(0.577927\pi\)
\(48\) 0 0
\(49\) −4.29600 −0.613714
\(50\) 0 0
\(51\) 1.92410 0.269428
\(52\) 0 0
\(53\) −6.47032 −0.888767 −0.444384 0.895837i \(-0.646577\pi\)
−0.444384 + 0.895837i \(0.646577\pi\)
\(54\) 0 0
\(55\) −2.02415 −0.272937
\(56\) 0 0
\(57\) 1.26258 0.167233
\(58\) 0 0
\(59\) 3.39477 0.441961 0.220980 0.975278i \(-0.429074\pi\)
0.220980 + 0.975278i \(0.429074\pi\)
\(60\) 0 0
\(61\) −9.94685 −1.27356 −0.636782 0.771044i \(-0.719735\pi\)
−0.636782 + 0.771044i \(0.719735\pi\)
\(62\) 0 0
\(63\) −4.51435 −0.568755
\(64\) 0 0
\(65\) 5.72061 0.709555
\(66\) 0 0
\(67\) 11.7402 1.43429 0.717146 0.696923i \(-0.245448\pi\)
0.717146 + 0.696923i \(0.245448\pi\)
\(68\) 0 0
\(69\) 2.21072 0.266140
\(70\) 0 0
\(71\) 9.71165 1.15256 0.576280 0.817252i \(-0.304504\pi\)
0.576280 + 0.817252i \(0.304504\pi\)
\(72\) 0 0
\(73\) 3.32458 0.389113 0.194556 0.980891i \(-0.437673\pi\)
0.194556 + 0.980891i \(0.437673\pi\)
\(74\) 0 0
\(75\) 2.11125 0.243787
\(76\) 0 0
\(77\) 3.68354 0.419778
\(78\) 0 0
\(79\) 5.95388 0.669864 0.334932 0.942242i \(-0.391287\pi\)
0.334932 + 0.942242i \(0.391287\pi\)
\(80\) 0 0
\(81\) 6.77270 0.752522
\(82\) 0 0
\(83\) 9.44942 1.03721 0.518604 0.855014i \(-0.326452\pi\)
0.518604 + 0.855014i \(0.326452\pi\)
\(84\) 0 0
\(85\) 3.44515 0.373679
\(86\) 0 0
\(87\) 0.952574 0.102127
\(88\) 0 0
\(89\) −1.70059 −0.180262 −0.0901310 0.995930i \(-0.528729\pi\)
−0.0901310 + 0.995930i \(0.528729\pi\)
\(90\) 0 0
\(91\) −10.4103 −1.09130
\(92\) 0 0
\(93\) −4.83230 −0.501086
\(94\) 0 0
\(95\) 2.26068 0.231941
\(96\) 0 0
\(97\) 10.7100 1.08744 0.543718 0.839268i \(-0.317016\pi\)
0.543718 + 0.839268i \(0.317016\pi\)
\(98\) 0 0
\(99\) −6.14970 −0.618068
\(100\) 0 0
\(101\) 1.40688 0.139990 0.0699950 0.997547i \(-0.477702\pi\)
0.0699950 + 0.997547i \(0.477702\pi\)
\(102\) 0 0
\(103\) 4.10665 0.404640 0.202320 0.979319i \(-0.435152\pi\)
0.202320 + 0.979319i \(0.435152\pi\)
\(104\) 0 0
\(105\) 0.749872 0.0731800
\(106\) 0 0
\(107\) 12.3731 1.19615 0.598075 0.801440i \(-0.295932\pi\)
0.598075 + 0.801440i \(0.295932\pi\)
\(108\) 0 0
\(109\) 16.3863 1.56952 0.784760 0.619800i \(-0.212786\pi\)
0.784760 + 0.619800i \(0.212786\pi\)
\(110\) 0 0
\(111\) −4.31774 −0.409822
\(112\) 0 0
\(113\) −12.9602 −1.21920 −0.609598 0.792711i \(-0.708669\pi\)
−0.609598 + 0.792711i \(0.708669\pi\)
\(114\) 0 0
\(115\) 3.95835 0.369118
\(116\) 0 0
\(117\) 17.3801 1.60679
\(118\) 0 0
\(119\) −6.26945 −0.574720
\(120\) 0 0
\(121\) −5.98208 −0.543826
\(122\) 0 0
\(123\) −1.17614 −0.106049
\(124\) 0 0
\(125\) 8.29830 0.742223
\(126\) 0 0
\(127\) −1.91021 −0.169504 −0.0847518 0.996402i \(-0.527010\pi\)
−0.0847518 + 0.996402i \(0.527010\pi\)
\(128\) 0 0
\(129\) 0.499620 0.0439891
\(130\) 0 0
\(131\) 10.9558 0.957209 0.478604 0.878031i \(-0.341143\pi\)
0.478604 + 0.878031i \(0.341143\pi\)
\(132\) 0 0
\(133\) −4.11396 −0.356726
\(134\) 0 0
\(135\) −2.61998 −0.225492
\(136\) 0 0
\(137\) 5.43877 0.464666 0.232333 0.972636i \(-0.425364\pi\)
0.232333 + 0.972636i \(0.425364\pi\)
\(138\) 0 0
\(139\) 5.81790 0.493468 0.246734 0.969083i \(-0.420643\pi\)
0.246734 + 0.969083i \(0.420643\pi\)
\(140\) 0 0
\(141\) 1.67715 0.141241
\(142\) 0 0
\(143\) −14.1815 −1.18592
\(144\) 0 0
\(145\) 1.70561 0.141643
\(146\) 0 0
\(147\) 2.16804 0.178817
\(148\) 0 0
\(149\) −23.8512 −1.95397 −0.976984 0.213311i \(-0.931575\pi\)
−0.976984 + 0.213311i \(0.931575\pi\)
\(150\) 0 0
\(151\) −19.8927 −1.61885 −0.809423 0.587226i \(-0.800220\pi\)
−0.809423 + 0.587226i \(0.800220\pi\)
\(152\) 0 0
\(153\) 10.4669 0.846200
\(154\) 0 0
\(155\) −8.65234 −0.694973
\(156\) 0 0
\(157\) 7.26936 0.580158 0.290079 0.957003i \(-0.406318\pi\)
0.290079 + 0.957003i \(0.406318\pi\)
\(158\) 0 0
\(159\) 3.26534 0.258958
\(160\) 0 0
\(161\) −7.20336 −0.567704
\(162\) 0 0
\(163\) −12.9948 −1.01783 −0.508916 0.860816i \(-0.669954\pi\)
−0.508916 + 0.860816i \(0.669954\pi\)
\(164\) 0 0
\(165\) 1.02152 0.0795250
\(166\) 0 0
\(167\) −11.5064 −0.890393 −0.445197 0.895433i \(-0.646866\pi\)
−0.445197 + 0.895433i \(0.646866\pi\)
\(168\) 0 0
\(169\) 27.0794 2.08303
\(170\) 0 0
\(171\) 6.86830 0.525232
\(172\) 0 0
\(173\) 9.45380 0.718759 0.359379 0.933192i \(-0.382988\pi\)
0.359379 + 0.933192i \(0.382988\pi\)
\(174\) 0 0
\(175\) −6.87926 −0.520023
\(176\) 0 0
\(177\) −1.71321 −0.128773
\(178\) 0 0
\(179\) −24.6220 −1.84033 −0.920166 0.391529i \(-0.871946\pi\)
−0.920166 + 0.391529i \(0.871946\pi\)
\(180\) 0 0
\(181\) −23.4415 −1.74239 −0.871195 0.490937i \(-0.836654\pi\)
−0.871195 + 0.490937i \(0.836654\pi\)
\(182\) 0 0
\(183\) 5.01981 0.371075
\(184\) 0 0
\(185\) −7.73101 −0.568395
\(186\) 0 0
\(187\) −8.54060 −0.624550
\(188\) 0 0
\(189\) 4.76781 0.346807
\(190\) 0 0
\(191\) 5.50833 0.398569 0.199284 0.979942i \(-0.436138\pi\)
0.199284 + 0.979942i \(0.436138\pi\)
\(192\) 0 0
\(193\) 0.739940 0.0532620 0.0266310 0.999645i \(-0.491522\pi\)
0.0266310 + 0.999645i \(0.491522\pi\)
\(194\) 0 0
\(195\) −2.88699 −0.206741
\(196\) 0 0
\(197\) 23.2205 1.65439 0.827197 0.561912i \(-0.189934\pi\)
0.827197 + 0.561912i \(0.189934\pi\)
\(198\) 0 0
\(199\) 1.08418 0.0768556 0.0384278 0.999261i \(-0.487765\pi\)
0.0384278 + 0.999261i \(0.487765\pi\)
\(200\) 0 0
\(201\) −5.92485 −0.417907
\(202\) 0 0
\(203\) −3.10384 −0.217847
\(204\) 0 0
\(205\) −2.10590 −0.147082
\(206\) 0 0
\(207\) 12.0261 0.835870
\(208\) 0 0
\(209\) −5.60427 −0.387656
\(210\) 0 0
\(211\) −18.5937 −1.28004 −0.640022 0.768356i \(-0.721075\pi\)
−0.640022 + 0.768356i \(0.721075\pi\)
\(212\) 0 0
\(213\) −4.90112 −0.335819
\(214\) 0 0
\(215\) 0.894580 0.0610099
\(216\) 0 0
\(217\) 15.7454 1.06887
\(218\) 0 0
\(219\) −1.67779 −0.113375
\(220\) 0 0
\(221\) 24.1372 1.62365
\(222\) 0 0
\(223\) 5.75353 0.385285 0.192643 0.981269i \(-0.438294\pi\)
0.192643 + 0.981269i \(0.438294\pi\)
\(224\) 0 0
\(225\) 11.4850 0.765666
\(226\) 0 0
\(227\) 0.915535 0.0607662 0.0303831 0.999538i \(-0.490327\pi\)
0.0303831 + 0.999538i \(0.490327\pi\)
\(228\) 0 0
\(229\) 18.4645 1.22017 0.610083 0.792338i \(-0.291136\pi\)
0.610083 + 0.792338i \(0.291136\pi\)
\(230\) 0 0
\(231\) −1.85895 −0.122310
\(232\) 0 0
\(233\) 5.57933 0.365514 0.182757 0.983158i \(-0.441498\pi\)
0.182757 + 0.983158i \(0.441498\pi\)
\(234\) 0 0
\(235\) 3.00297 0.195892
\(236\) 0 0
\(237\) −3.00471 −0.195177
\(238\) 0 0
\(239\) 19.4650 1.25908 0.629542 0.776966i \(-0.283243\pi\)
0.629542 + 0.776966i \(0.283243\pi\)
\(240\) 0 0
\(241\) 21.1410 1.36181 0.680905 0.732372i \(-0.261587\pi\)
0.680905 + 0.732372i \(0.261587\pi\)
\(242\) 0 0
\(243\) −12.1163 −0.777260
\(244\) 0 0
\(245\) 3.88192 0.248007
\(246\) 0 0
\(247\) 15.8387 1.00779
\(248\) 0 0
\(249\) −4.76878 −0.302209
\(250\) 0 0
\(251\) 11.2177 0.708056 0.354028 0.935235i \(-0.384812\pi\)
0.354028 + 0.935235i \(0.384812\pi\)
\(252\) 0 0
\(253\) −9.81282 −0.616926
\(254\) 0 0
\(255\) −1.73864 −0.108878
\(256\) 0 0
\(257\) 6.41182 0.399958 0.199979 0.979800i \(-0.435913\pi\)
0.199979 + 0.979800i \(0.435913\pi\)
\(258\) 0 0
\(259\) 14.0688 0.874194
\(260\) 0 0
\(261\) 5.18190 0.320751
\(262\) 0 0
\(263\) 19.2453 1.18672 0.593358 0.804939i \(-0.297802\pi\)
0.593358 + 0.804939i \(0.297802\pi\)
\(264\) 0 0
\(265\) 5.84666 0.359157
\(266\) 0 0
\(267\) 0.858225 0.0525225
\(268\) 0 0
\(269\) 1.43959 0.0877733 0.0438867 0.999037i \(-0.486026\pi\)
0.0438867 + 0.999037i \(0.486026\pi\)
\(270\) 0 0
\(271\) −2.34772 −0.142614 −0.0713068 0.997454i \(-0.522717\pi\)
−0.0713068 + 0.997454i \(0.522717\pi\)
\(272\) 0 0
\(273\) 5.25371 0.317969
\(274\) 0 0
\(275\) −9.37131 −0.565111
\(276\) 0 0
\(277\) 24.9792 1.50086 0.750429 0.660952i \(-0.229847\pi\)
0.750429 + 0.660952i \(0.229847\pi\)
\(278\) 0 0
\(279\) −26.2872 −1.57377
\(280\) 0 0
\(281\) −16.7529 −0.999394 −0.499697 0.866200i \(-0.666555\pi\)
−0.499697 + 0.866200i \(0.666555\pi\)
\(282\) 0 0
\(283\) 24.2363 1.44070 0.720349 0.693612i \(-0.243982\pi\)
0.720349 + 0.693612i \(0.243982\pi\)
\(284\) 0 0
\(285\) −1.14088 −0.0675801
\(286\) 0 0
\(287\) 3.83229 0.226213
\(288\) 0 0
\(289\) −2.46373 −0.144925
\(290\) 0 0
\(291\) −5.40495 −0.316844
\(292\) 0 0
\(293\) 29.2731 1.71015 0.855077 0.518500i \(-0.173509\pi\)
0.855077 + 0.518500i \(0.173509\pi\)
\(294\) 0 0
\(295\) −3.06755 −0.178600
\(296\) 0 0
\(297\) 6.49498 0.376877
\(298\) 0 0
\(299\) 27.7327 1.60383
\(300\) 0 0
\(301\) −1.62795 −0.0938334
\(302\) 0 0
\(303\) −0.710002 −0.0407886
\(304\) 0 0
\(305\) 8.98809 0.514656
\(306\) 0 0
\(307\) −26.9134 −1.53603 −0.768015 0.640432i \(-0.778755\pi\)
−0.768015 + 0.640432i \(0.778755\pi\)
\(308\) 0 0
\(309\) −2.07248 −0.117899
\(310\) 0 0
\(311\) −34.2381 −1.94146 −0.970731 0.240169i \(-0.922797\pi\)
−0.970731 + 0.240169i \(0.922797\pi\)
\(312\) 0 0
\(313\) −18.3116 −1.03503 −0.517515 0.855674i \(-0.673143\pi\)
−0.517515 + 0.855674i \(0.673143\pi\)
\(314\) 0 0
\(315\) 4.07922 0.229838
\(316\) 0 0
\(317\) −13.1256 −0.737209 −0.368605 0.929586i \(-0.620164\pi\)
−0.368605 + 0.929586i \(0.620164\pi\)
\(318\) 0 0
\(319\) −4.22823 −0.236735
\(320\) 0 0
\(321\) −6.24424 −0.348520
\(322\) 0 0
\(323\) 9.53858 0.530741
\(324\) 0 0
\(325\) 26.4850 1.46912
\(326\) 0 0
\(327\) −8.26956 −0.457307
\(328\) 0 0
\(329\) −5.46478 −0.301283
\(330\) 0 0
\(331\) −6.68299 −0.367330 −0.183665 0.982989i \(-0.558796\pi\)
−0.183665 + 0.982989i \(0.558796\pi\)
\(332\) 0 0
\(333\) −23.4880 −1.28714
\(334\) 0 0
\(335\) −10.6086 −0.579608
\(336\) 0 0
\(337\) −4.23845 −0.230883 −0.115442 0.993314i \(-0.536828\pi\)
−0.115442 + 0.993314i \(0.536828\pi\)
\(338\) 0 0
\(339\) 6.54056 0.355234
\(340\) 0 0
\(341\) 21.4493 1.16155
\(342\) 0 0
\(343\) −18.5750 −1.00295
\(344\) 0 0
\(345\) −1.99763 −0.107549
\(346\) 0 0
\(347\) 35.3621 1.89833 0.949167 0.314772i \(-0.101928\pi\)
0.949167 + 0.314772i \(0.101928\pi\)
\(348\) 0 0
\(349\) 21.6227 1.15744 0.578718 0.815528i \(-0.303553\pi\)
0.578718 + 0.815528i \(0.303553\pi\)
\(350\) 0 0
\(351\) −18.3559 −0.979768
\(352\) 0 0
\(353\) 23.8602 1.26995 0.634976 0.772532i \(-0.281010\pi\)
0.634976 + 0.772532i \(0.281010\pi\)
\(354\) 0 0
\(355\) −8.77556 −0.465758
\(356\) 0 0
\(357\) 3.16397 0.167455
\(358\) 0 0
\(359\) −13.1745 −0.695321 −0.347661 0.937620i \(-0.613024\pi\)
−0.347661 + 0.937620i \(0.613024\pi\)
\(360\) 0 0
\(361\) −12.7409 −0.670572
\(362\) 0 0
\(363\) 3.01894 0.158453
\(364\) 0 0
\(365\) −3.00413 −0.157243
\(366\) 0 0
\(367\) 16.1119 0.841035 0.420517 0.907285i \(-0.361849\pi\)
0.420517 + 0.907285i \(0.361849\pi\)
\(368\) 0 0
\(369\) −6.39805 −0.333069
\(370\) 0 0
\(371\) −10.6397 −0.552386
\(372\) 0 0
\(373\) 33.2917 1.72378 0.861889 0.507097i \(-0.169281\pi\)
0.861889 + 0.507097i \(0.169281\pi\)
\(374\) 0 0
\(375\) −4.18785 −0.216260
\(376\) 0 0
\(377\) 11.9497 0.615442
\(378\) 0 0
\(379\) 24.4967 1.25831 0.629155 0.777280i \(-0.283401\pi\)
0.629155 + 0.777280i \(0.283401\pi\)
\(380\) 0 0
\(381\) 0.964013 0.0493879
\(382\) 0 0
\(383\) −13.4214 −0.685800 −0.342900 0.939372i \(-0.611409\pi\)
−0.342900 + 0.939372i \(0.611409\pi\)
\(384\) 0 0
\(385\) −3.32849 −0.169635
\(386\) 0 0
\(387\) 2.71788 0.138157
\(388\) 0 0
\(389\) 27.6525 1.40204 0.701019 0.713143i \(-0.252729\pi\)
0.701019 + 0.713143i \(0.252729\pi\)
\(390\) 0 0
\(391\) 16.7016 0.844637
\(392\) 0 0
\(393\) −5.52897 −0.278900
\(394\) 0 0
\(395\) −5.38000 −0.270697
\(396\) 0 0
\(397\) 30.4470 1.52809 0.764047 0.645161i \(-0.223210\pi\)
0.764047 + 0.645161i \(0.223210\pi\)
\(398\) 0 0
\(399\) 2.07617 0.103938
\(400\) 0 0
\(401\) 13.2726 0.662804 0.331402 0.943490i \(-0.392478\pi\)
0.331402 + 0.943490i \(0.392478\pi\)
\(402\) 0 0
\(403\) −60.6195 −3.01967
\(404\) 0 0
\(405\) −6.11989 −0.304100
\(406\) 0 0
\(407\) 19.1653 0.949990
\(408\) 0 0
\(409\) −28.3887 −1.40373 −0.701865 0.712310i \(-0.747649\pi\)
−0.701865 + 0.712310i \(0.747649\pi\)
\(410\) 0 0
\(411\) −2.74475 −0.135389
\(412\) 0 0
\(413\) 5.58230 0.274687
\(414\) 0 0
\(415\) −8.53860 −0.419144
\(416\) 0 0
\(417\) −2.93608 −0.143781
\(418\) 0 0
\(419\) 14.5165 0.709177 0.354588 0.935022i \(-0.384621\pi\)
0.354588 + 0.935022i \(0.384621\pi\)
\(420\) 0 0
\(421\) −2.02209 −0.0985507 −0.0492753 0.998785i \(-0.515691\pi\)
−0.0492753 + 0.998785i \(0.515691\pi\)
\(422\) 0 0
\(423\) 9.12349 0.443599
\(424\) 0 0
\(425\) 15.9502 0.773696
\(426\) 0 0
\(427\) −16.3564 −0.791543
\(428\) 0 0
\(429\) 7.15690 0.345538
\(430\) 0 0
\(431\) 22.2765 1.07302 0.536511 0.843893i \(-0.319742\pi\)
0.536511 + 0.843893i \(0.319742\pi\)
\(432\) 0 0
\(433\) 10.2817 0.494106 0.247053 0.969002i \(-0.420538\pi\)
0.247053 + 0.969002i \(0.420538\pi\)
\(434\) 0 0
\(435\) −0.860757 −0.0412701
\(436\) 0 0
\(437\) 10.9595 0.524262
\(438\) 0 0
\(439\) 10.9755 0.523834 0.261917 0.965090i \(-0.415645\pi\)
0.261917 + 0.965090i \(0.415645\pi\)
\(440\) 0 0
\(441\) 11.7939 0.561613
\(442\) 0 0
\(443\) −37.5555 −1.78431 −0.892157 0.451726i \(-0.850808\pi\)
−0.892157 + 0.451726i \(0.850808\pi\)
\(444\) 0 0
\(445\) 1.53667 0.0728452
\(446\) 0 0
\(447\) 12.0369 0.569323
\(448\) 0 0
\(449\) 6.14000 0.289765 0.144882 0.989449i \(-0.453720\pi\)
0.144882 + 0.989449i \(0.453720\pi\)
\(450\) 0 0
\(451\) 5.22056 0.245827
\(452\) 0 0
\(453\) 10.0391 0.471680
\(454\) 0 0
\(455\) 9.40689 0.441002
\(456\) 0 0
\(457\) −27.1136 −1.26832 −0.634161 0.773201i \(-0.718654\pi\)
−0.634161 + 0.773201i \(0.718654\pi\)
\(458\) 0 0
\(459\) −11.0546 −0.515984
\(460\) 0 0
\(461\) −32.4146 −1.50970 −0.754849 0.655899i \(-0.772290\pi\)
−0.754849 + 0.655899i \(0.772290\pi\)
\(462\) 0 0
\(463\) 36.9999 1.71953 0.859766 0.510688i \(-0.170609\pi\)
0.859766 + 0.510688i \(0.170609\pi\)
\(464\) 0 0
\(465\) 4.36652 0.202493
\(466\) 0 0
\(467\) 17.1061 0.791577 0.395789 0.918342i \(-0.370471\pi\)
0.395789 + 0.918342i \(0.370471\pi\)
\(468\) 0 0
\(469\) 19.3054 0.891440
\(470\) 0 0
\(471\) −3.66858 −0.169039
\(472\) 0 0
\(473\) −2.21768 −0.101969
\(474\) 0 0
\(475\) 10.4664 0.480230
\(476\) 0 0
\(477\) 17.7631 0.813315
\(478\) 0 0
\(479\) −25.9057 −1.18366 −0.591830 0.806063i \(-0.701594\pi\)
−0.591830 + 0.806063i \(0.701594\pi\)
\(480\) 0 0
\(481\) −54.1646 −2.46969
\(482\) 0 0
\(483\) 3.63527 0.165411
\(484\) 0 0
\(485\) −9.67768 −0.439441
\(486\) 0 0
\(487\) 27.2178 1.23336 0.616679 0.787215i \(-0.288478\pi\)
0.616679 + 0.787215i \(0.288478\pi\)
\(488\) 0 0
\(489\) 6.55801 0.296563
\(490\) 0 0
\(491\) −11.8341 −0.534067 −0.267033 0.963687i \(-0.586043\pi\)
−0.267033 + 0.963687i \(0.586043\pi\)
\(492\) 0 0
\(493\) 7.19653 0.324115
\(494\) 0 0
\(495\) 5.55694 0.249766
\(496\) 0 0
\(497\) 15.9697 0.716338
\(498\) 0 0
\(499\) 30.3820 1.36009 0.680043 0.733173i \(-0.261961\pi\)
0.680043 + 0.733173i \(0.261961\pi\)
\(500\) 0 0
\(501\) 5.80687 0.259432
\(502\) 0 0
\(503\) −10.4753 −0.467070 −0.233535 0.972348i \(-0.575029\pi\)
−0.233535 + 0.972348i \(0.575029\pi\)
\(504\) 0 0
\(505\) −1.27127 −0.0565710
\(506\) 0 0
\(507\) −13.6660 −0.606929
\(508\) 0 0
\(509\) −14.2343 −0.630922 −0.315461 0.948938i \(-0.602159\pi\)
−0.315461 + 0.948938i \(0.602159\pi\)
\(510\) 0 0
\(511\) 5.46689 0.241841
\(512\) 0 0
\(513\) −7.25393 −0.320269
\(514\) 0 0
\(515\) −3.71082 −0.163518
\(516\) 0 0
\(517\) −7.44442 −0.327405
\(518\) 0 0
\(519\) −4.77099 −0.209423
\(520\) 0 0
\(521\) 30.7488 1.34713 0.673564 0.739129i \(-0.264763\pi\)
0.673564 + 0.739129i \(0.264763\pi\)
\(522\) 0 0
\(523\) −0.425051 −0.0185862 −0.00929308 0.999957i \(-0.502958\pi\)
−0.00929308 + 0.999957i \(0.502958\pi\)
\(524\) 0 0
\(525\) 3.47171 0.151518
\(526\) 0 0
\(527\) −36.5072 −1.59028
\(528\) 0 0
\(529\) −3.81049 −0.165674
\(530\) 0 0
\(531\) −9.31970 −0.404440
\(532\) 0 0
\(533\) −14.7542 −0.639076
\(534\) 0 0
\(535\) −11.1805 −0.483373
\(536\) 0 0
\(537\) 12.4258 0.536213
\(538\) 0 0
\(539\) −9.62335 −0.414507
\(540\) 0 0
\(541\) −0.367014 −0.0157792 −0.00788959 0.999969i \(-0.502511\pi\)
−0.00788959 + 0.999969i \(0.502511\pi\)
\(542\) 0 0
\(543\) 11.8301 0.507676
\(544\) 0 0
\(545\) −14.8068 −0.634255
\(546\) 0 0
\(547\) 9.30136 0.397697 0.198849 0.980030i \(-0.436280\pi\)
0.198849 + 0.980030i \(0.436280\pi\)
\(548\) 0 0
\(549\) 27.3072 1.16544
\(550\) 0 0
\(551\) 4.72231 0.201177
\(552\) 0 0
\(553\) 9.79047 0.416333
\(554\) 0 0
\(555\) 3.90156 0.165612
\(556\) 0 0
\(557\) −11.6404 −0.493221 −0.246611 0.969115i \(-0.579317\pi\)
−0.246611 + 0.969115i \(0.579317\pi\)
\(558\) 0 0
\(559\) 6.26756 0.265089
\(560\) 0 0
\(561\) 4.31013 0.181974
\(562\) 0 0
\(563\) 37.3326 1.57338 0.786691 0.617347i \(-0.211792\pi\)
0.786691 + 0.617347i \(0.211792\pi\)
\(564\) 0 0
\(565\) 11.7110 0.492686
\(566\) 0 0
\(567\) 11.1369 0.467706
\(568\) 0 0
\(569\) −41.3662 −1.73416 −0.867080 0.498169i \(-0.834006\pi\)
−0.867080 + 0.498169i \(0.834006\pi\)
\(570\) 0 0
\(571\) 13.5571 0.567347 0.283674 0.958921i \(-0.408447\pi\)
0.283674 + 0.958921i \(0.408447\pi\)
\(572\) 0 0
\(573\) −2.77985 −0.116130
\(574\) 0 0
\(575\) 18.3261 0.764252
\(576\) 0 0
\(577\) −5.30733 −0.220947 −0.110473 0.993879i \(-0.535237\pi\)
−0.110473 + 0.993879i \(0.535237\pi\)
\(578\) 0 0
\(579\) −0.373421 −0.0155188
\(580\) 0 0
\(581\) 15.5385 0.644644
\(582\) 0 0
\(583\) −14.4940 −0.600280
\(584\) 0 0
\(585\) −15.7049 −0.649317
\(586\) 0 0
\(587\) −13.4287 −0.554262 −0.277131 0.960832i \(-0.589384\pi\)
−0.277131 + 0.960832i \(0.589384\pi\)
\(588\) 0 0
\(589\) −23.9557 −0.987078
\(590\) 0 0
\(591\) −11.7186 −0.482037
\(592\) 0 0
\(593\) 19.3057 0.792792 0.396396 0.918080i \(-0.370261\pi\)
0.396396 + 0.918080i \(0.370261\pi\)
\(594\) 0 0
\(595\) 5.66515 0.232249
\(596\) 0 0
\(597\) −0.547147 −0.0223932
\(598\) 0 0
\(599\) −31.6643 −1.29377 −0.646885 0.762588i \(-0.723929\pi\)
−0.646885 + 0.762588i \(0.723929\pi\)
\(600\) 0 0
\(601\) 36.1201 1.47337 0.736684 0.676237i \(-0.236391\pi\)
0.736684 + 0.676237i \(0.236391\pi\)
\(602\) 0 0
\(603\) −32.2305 −1.31253
\(604\) 0 0
\(605\) 5.40548 0.219764
\(606\) 0 0
\(607\) 32.9429 1.33711 0.668556 0.743662i \(-0.266913\pi\)
0.668556 + 0.743662i \(0.266913\pi\)
\(608\) 0 0
\(609\) 1.56640 0.0634736
\(610\) 0 0
\(611\) 21.0392 0.851156
\(612\) 0 0
\(613\) −33.0719 −1.33576 −0.667881 0.744268i \(-0.732798\pi\)
−0.667881 + 0.744268i \(0.732798\pi\)
\(614\) 0 0
\(615\) 1.06277 0.0428550
\(616\) 0 0
\(617\) −3.05961 −0.123175 −0.0615876 0.998102i \(-0.519616\pi\)
−0.0615876 + 0.998102i \(0.519616\pi\)
\(618\) 0 0
\(619\) 32.2067 1.29450 0.647248 0.762280i \(-0.275920\pi\)
0.647248 + 0.762280i \(0.275920\pi\)
\(620\) 0 0
\(621\) −12.7013 −0.509685
\(622\) 0 0
\(623\) −2.79642 −0.112036
\(624\) 0 0
\(625\) 13.4190 0.536759
\(626\) 0 0
\(627\) 2.82827 0.112950
\(628\) 0 0
\(629\) −32.6198 −1.30064
\(630\) 0 0
\(631\) 5.93992 0.236464 0.118232 0.992986i \(-0.462277\pi\)
0.118232 + 0.992986i \(0.462277\pi\)
\(632\) 0 0
\(633\) 9.38358 0.372964
\(634\) 0 0
\(635\) 1.72609 0.0684976
\(636\) 0 0
\(637\) 27.1973 1.07759
\(638\) 0 0
\(639\) −26.6615 −1.05471
\(640\) 0 0
\(641\) 2.50720 0.0990286 0.0495143 0.998773i \(-0.484233\pi\)
0.0495143 + 0.998773i \(0.484233\pi\)
\(642\) 0 0
\(643\) 33.1241 1.30629 0.653144 0.757234i \(-0.273450\pi\)
0.653144 + 0.757234i \(0.273450\pi\)
\(644\) 0 0
\(645\) −0.451462 −0.0177763
\(646\) 0 0
\(647\) 25.2107 0.991133 0.495567 0.868570i \(-0.334960\pi\)
0.495567 + 0.868570i \(0.334960\pi\)
\(648\) 0 0
\(649\) 7.60451 0.298503
\(650\) 0 0
\(651\) −7.94616 −0.311434
\(652\) 0 0
\(653\) −41.7885 −1.63531 −0.817656 0.575708i \(-0.804727\pi\)
−0.817656 + 0.575708i \(0.804727\pi\)
\(654\) 0 0
\(655\) −9.89975 −0.386815
\(656\) 0 0
\(657\) −9.12702 −0.356079
\(658\) 0 0
\(659\) 22.0338 0.858315 0.429158 0.903230i \(-0.358810\pi\)
0.429158 + 0.903230i \(0.358810\pi\)
\(660\) 0 0
\(661\) −27.5753 −1.07255 −0.536277 0.844042i \(-0.680170\pi\)
−0.536277 + 0.844042i \(0.680170\pi\)
\(662\) 0 0
\(663\) −12.1812 −0.473078
\(664\) 0 0
\(665\) 3.71743 0.144156
\(666\) 0 0
\(667\) 8.26854 0.320159
\(668\) 0 0
\(669\) −2.90360 −0.112260
\(670\) 0 0
\(671\) −22.2816 −0.860173
\(672\) 0 0
\(673\) −17.6341 −0.679746 −0.339873 0.940471i \(-0.610384\pi\)
−0.339873 + 0.940471i \(0.610384\pi\)
\(674\) 0 0
\(675\) −12.1298 −0.466877
\(676\) 0 0
\(677\) −33.3902 −1.28329 −0.641646 0.767001i \(-0.721748\pi\)
−0.641646 + 0.767001i \(0.721748\pi\)
\(678\) 0 0
\(679\) 17.6113 0.675862
\(680\) 0 0
\(681\) −0.462037 −0.0177053
\(682\) 0 0
\(683\) 1.00658 0.0385155 0.0192578 0.999815i \(-0.493870\pi\)
0.0192578 + 0.999815i \(0.493870\pi\)
\(684\) 0 0
\(685\) −4.91454 −0.187775
\(686\) 0 0
\(687\) −9.31834 −0.355517
\(688\) 0 0
\(689\) 40.9625 1.56055
\(690\) 0 0
\(691\) 2.46921 0.0939332 0.0469666 0.998896i \(-0.485045\pi\)
0.0469666 + 0.998896i \(0.485045\pi\)
\(692\) 0 0
\(693\) −10.1125 −0.384141
\(694\) 0 0
\(695\) −5.25712 −0.199414
\(696\) 0 0
\(697\) −8.88550 −0.336562
\(698\) 0 0
\(699\) −2.81569 −0.106499
\(700\) 0 0
\(701\) −7.94490 −0.300075 −0.150037 0.988680i \(-0.547939\pi\)
−0.150037 + 0.988680i \(0.547939\pi\)
\(702\) 0 0
\(703\) −21.4048 −0.807298
\(704\) 0 0
\(705\) −1.51549 −0.0570766
\(706\) 0 0
\(707\) 2.31345 0.0870064
\(708\) 0 0
\(709\) 51.0345 1.91664 0.958320 0.285698i \(-0.0922253\pi\)
0.958320 + 0.285698i \(0.0922253\pi\)
\(710\) 0 0
\(711\) −16.3453 −0.612996
\(712\) 0 0
\(713\) −41.9453 −1.57087
\(714\) 0 0
\(715\) 12.8146 0.479238
\(716\) 0 0
\(717\) −9.82326 −0.366856
\(718\) 0 0
\(719\) −49.9358 −1.86229 −0.931145 0.364649i \(-0.881189\pi\)
−0.931145 + 0.364649i \(0.881189\pi\)
\(720\) 0 0
\(721\) 6.75291 0.251492
\(722\) 0 0
\(723\) −10.6691 −0.396787
\(724\) 0 0
\(725\) 7.89651 0.293269
\(726\) 0 0
\(727\) 38.6832 1.43468 0.717340 0.696724i \(-0.245360\pi\)
0.717340 + 0.696724i \(0.245360\pi\)
\(728\) 0 0
\(729\) −14.2034 −0.526053
\(730\) 0 0
\(731\) 3.77454 0.139606
\(732\) 0 0
\(733\) −31.8816 −1.17757 −0.588787 0.808288i \(-0.700394\pi\)
−0.588787 + 0.808288i \(0.700394\pi\)
\(734\) 0 0
\(735\) −1.95906 −0.0722611
\(736\) 0 0
\(737\) 26.2989 0.968731
\(738\) 0 0
\(739\) −48.0431 −1.76729 −0.883647 0.468154i \(-0.844919\pi\)
−0.883647 + 0.468154i \(0.844919\pi\)
\(740\) 0 0
\(741\) −7.99319 −0.293637
\(742\) 0 0
\(743\) −32.0402 −1.17544 −0.587720 0.809065i \(-0.699974\pi\)
−0.587720 + 0.809065i \(0.699974\pi\)
\(744\) 0 0
\(745\) 21.5522 0.789613
\(746\) 0 0
\(747\) −25.9416 −0.949154
\(748\) 0 0
\(749\) 20.3461 0.743430
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −5.66117 −0.206305
\(754\) 0 0
\(755\) 17.9753 0.654188
\(756\) 0 0
\(757\) 0.0515857 0.00187491 0.000937457 1.00000i \(-0.499702\pi\)
0.000937457 1.00000i \(0.499702\pi\)
\(758\) 0 0
\(759\) 4.95217 0.179752
\(760\) 0 0
\(761\) −29.1301 −1.05597 −0.527983 0.849255i \(-0.677052\pi\)
−0.527983 + 0.849255i \(0.677052\pi\)
\(762\) 0 0
\(763\) 26.9453 0.975486
\(764\) 0 0
\(765\) −9.45802 −0.341956
\(766\) 0 0
\(767\) −21.4917 −0.776020
\(768\) 0 0
\(769\) 17.8609 0.644081 0.322040 0.946726i \(-0.395631\pi\)
0.322040 + 0.946726i \(0.395631\pi\)
\(770\) 0 0
\(771\) −3.23581 −0.116535
\(772\) 0 0
\(773\) 49.4310 1.77791 0.888955 0.457994i \(-0.151432\pi\)
0.888955 + 0.457994i \(0.151432\pi\)
\(774\) 0 0
\(775\) −40.0581 −1.43893
\(776\) 0 0
\(777\) −7.10002 −0.254712
\(778\) 0 0
\(779\) −5.83059 −0.208903
\(780\) 0 0
\(781\) 21.7548 0.778447
\(782\) 0 0
\(783\) −5.47284 −0.195583
\(784\) 0 0
\(785\) −6.56868 −0.234446
\(786\) 0 0
\(787\) −50.6160 −1.80427 −0.902134 0.431457i \(-0.858000\pi\)
−0.902134 + 0.431457i \(0.858000\pi\)
\(788\) 0 0
\(789\) −9.71240 −0.345771
\(790\) 0 0
\(791\) −21.3116 −0.757753
\(792\) 0 0
\(793\) 62.9718 2.23619
\(794\) 0 0
\(795\) −2.95060 −0.104647
\(796\) 0 0
\(797\) 0.383072 0.0135691 0.00678455 0.999977i \(-0.497840\pi\)
0.00678455 + 0.999977i \(0.497840\pi\)
\(798\) 0 0
\(799\) 12.6706 0.448252
\(800\) 0 0
\(801\) 4.66865 0.164959
\(802\) 0 0
\(803\) 7.44729 0.262809
\(804\) 0 0
\(805\) 6.50904 0.229414
\(806\) 0 0
\(807\) −0.726508 −0.0255743
\(808\) 0 0
\(809\) −28.4113 −0.998889 −0.499444 0.866346i \(-0.666463\pi\)
−0.499444 + 0.866346i \(0.666463\pi\)
\(810\) 0 0
\(811\) 39.5040 1.38717 0.693587 0.720373i \(-0.256029\pi\)
0.693587 + 0.720373i \(0.256029\pi\)
\(812\) 0 0
\(813\) 1.18481 0.0415530
\(814\) 0 0
\(815\) 11.7423 0.411313
\(816\) 0 0
\(817\) 2.47682 0.0866530
\(818\) 0 0
\(819\) 28.5796 0.998652
\(820\) 0 0
\(821\) 1.34741 0.0470250 0.0235125 0.999724i \(-0.492515\pi\)
0.0235125 + 0.999724i \(0.492515\pi\)
\(822\) 0 0
\(823\) 43.3804 1.51214 0.756072 0.654488i \(-0.227116\pi\)
0.756072 + 0.654488i \(0.227116\pi\)
\(824\) 0 0
\(825\) 4.72936 0.164655
\(826\) 0 0
\(827\) 15.3486 0.533722 0.266861 0.963735i \(-0.414014\pi\)
0.266861 + 0.963735i \(0.414014\pi\)
\(828\) 0 0
\(829\) 5.51968 0.191706 0.0958532 0.995395i \(-0.469442\pi\)
0.0958532 + 0.995395i \(0.469442\pi\)
\(830\) 0 0
\(831\) −12.6061 −0.437301
\(832\) 0 0
\(833\) 16.3791 0.567503
\(834\) 0 0
\(835\) 10.3973 0.359815
\(836\) 0 0
\(837\) 27.7631 0.959632
\(838\) 0 0
\(839\) −26.3809 −0.910771 −0.455385 0.890294i \(-0.650498\pi\)
−0.455385 + 0.890294i \(0.650498\pi\)
\(840\) 0 0
\(841\) −25.4372 −0.877144
\(842\) 0 0
\(843\) 8.45458 0.291191
\(844\) 0 0
\(845\) −24.4693 −0.841769
\(846\) 0 0
\(847\) −9.83684 −0.337998
\(848\) 0 0
\(849\) −12.2312 −0.419773
\(850\) 0 0
\(851\) −37.4789 −1.28476
\(852\) 0 0
\(853\) −30.1217 −1.03135 −0.515673 0.856785i \(-0.672458\pi\)
−0.515673 + 0.856785i \(0.672458\pi\)
\(854\) 0 0
\(855\) −6.20628 −0.212250
\(856\) 0 0
\(857\) −29.4983 −1.00764 −0.503821 0.863808i \(-0.668073\pi\)
−0.503821 + 0.863808i \(0.668073\pi\)
\(858\) 0 0
\(859\) 38.2468 1.30497 0.652483 0.757804i \(-0.273728\pi\)
0.652483 + 0.757804i \(0.273728\pi\)
\(860\) 0 0
\(861\) −1.93402 −0.0659112
\(862\) 0 0
\(863\) −48.2451 −1.64228 −0.821141 0.570725i \(-0.806662\pi\)
−0.821141 + 0.570725i \(0.806662\pi\)
\(864\) 0 0
\(865\) −8.54256 −0.290456
\(866\) 0 0
\(867\) 1.24336 0.0422266
\(868\) 0 0
\(869\) 13.3371 0.452431
\(870\) 0 0
\(871\) −74.3252 −2.51841
\(872\) 0 0
\(873\) −29.4023 −0.995118
\(874\) 0 0
\(875\) 13.6456 0.461305
\(876\) 0 0
\(877\) 43.5579 1.47085 0.735423 0.677608i \(-0.236983\pi\)
0.735423 + 0.677608i \(0.236983\pi\)
\(878\) 0 0
\(879\) −14.7731 −0.498284
\(880\) 0 0
\(881\) −23.3211 −0.785707 −0.392854 0.919601i \(-0.628512\pi\)
−0.392854 + 0.919601i \(0.628512\pi\)
\(882\) 0 0
\(883\) −12.2831 −0.413358 −0.206679 0.978409i \(-0.566266\pi\)
−0.206679 + 0.978409i \(0.566266\pi\)
\(884\) 0 0
\(885\) 1.54808 0.0520382
\(886\) 0 0
\(887\) −28.4765 −0.956147 −0.478074 0.878320i \(-0.658665\pi\)
−0.478074 + 0.878320i \(0.658665\pi\)
\(888\) 0 0
\(889\) −3.14112 −0.105350
\(890\) 0 0
\(891\) 15.1713 0.508258
\(892\) 0 0
\(893\) 8.31431 0.278228
\(894\) 0 0
\(895\) 22.2487 0.743692
\(896\) 0 0
\(897\) −13.9957 −0.467303
\(898\) 0 0
\(899\) −18.0738 −0.602794
\(900\) 0 0
\(901\) 24.6691 0.821845
\(902\) 0 0
\(903\) 0.821567 0.0273400
\(904\) 0 0
\(905\) 21.1820 0.704113
\(906\) 0 0
\(907\) −39.7628 −1.32030 −0.660152 0.751132i \(-0.729508\pi\)
−0.660152 + 0.751132i \(0.729508\pi\)
\(908\) 0 0
\(909\) −3.86233 −0.128105
\(910\) 0 0
\(911\) −15.5528 −0.515288 −0.257644 0.966240i \(-0.582946\pi\)
−0.257644 + 0.966240i \(0.582946\pi\)
\(912\) 0 0
\(913\) 21.1674 0.700538
\(914\) 0 0
\(915\) −4.53596 −0.149954
\(916\) 0 0
\(917\) 18.0155 0.594923
\(918\) 0 0
\(919\) 43.9114 1.44850 0.724251 0.689536i \(-0.242185\pi\)
0.724251 + 0.689536i \(0.242185\pi\)
\(920\) 0 0
\(921\) 13.5822 0.447549
\(922\) 0 0
\(923\) −61.4828 −2.02373
\(924\) 0 0
\(925\) −35.7926 −1.17685
\(926\) 0 0
\(927\) −11.2740 −0.370288
\(928\) 0 0
\(929\) −20.3530 −0.667760 −0.333880 0.942616i \(-0.608358\pi\)
−0.333880 + 0.942616i \(0.608358\pi\)
\(930\) 0 0
\(931\) 10.7479 0.352247
\(932\) 0 0
\(933\) 17.2787 0.565679
\(934\) 0 0
\(935\) 7.71738 0.252385
\(936\) 0 0
\(937\) −3.18883 −0.104175 −0.0520873 0.998643i \(-0.516587\pi\)
−0.0520873 + 0.998643i \(0.516587\pi\)
\(938\) 0 0
\(939\) 9.24118 0.301574
\(940\) 0 0
\(941\) 57.4542 1.87295 0.936476 0.350730i \(-0.114067\pi\)
0.936476 + 0.350730i \(0.114067\pi\)
\(942\) 0 0
\(943\) −10.2091 −0.332454
\(944\) 0 0
\(945\) −4.30825 −0.140147
\(946\) 0 0
\(947\) −19.3526 −0.628873 −0.314437 0.949278i \(-0.601816\pi\)
−0.314437 + 0.949278i \(0.601816\pi\)
\(948\) 0 0
\(949\) −21.0474 −0.683226
\(950\) 0 0
\(951\) 6.62403 0.214799
\(952\) 0 0
\(953\) −29.2274 −0.946768 −0.473384 0.880856i \(-0.656968\pi\)
−0.473384 + 0.880856i \(0.656968\pi\)
\(954\) 0 0
\(955\) −4.97739 −0.161065
\(956\) 0 0
\(957\) 2.13383 0.0689770
\(958\) 0 0
\(959\) 8.94343 0.288799
\(960\) 0 0
\(961\) 60.6861 1.95762
\(962\) 0 0
\(963\) −33.9680 −1.09460
\(964\) 0 0
\(965\) −0.668618 −0.0215236
\(966\) 0 0
\(967\) −7.64094 −0.245716 −0.122858 0.992424i \(-0.539206\pi\)
−0.122858 + 0.992424i \(0.539206\pi\)
\(968\) 0 0
\(969\) −4.81378 −0.154641
\(970\) 0 0
\(971\) −2.57369 −0.0825936 −0.0412968 0.999147i \(-0.513149\pi\)
−0.0412968 + 0.999147i \(0.513149\pi\)
\(972\) 0 0
\(973\) 9.56686 0.306700
\(974\) 0 0
\(975\) −13.3660 −0.428054
\(976\) 0 0
\(977\) −42.3351 −1.35442 −0.677210 0.735790i \(-0.736811\pi\)
−0.677210 + 0.735790i \(0.736811\pi\)
\(978\) 0 0
\(979\) −3.80944 −0.121750
\(980\) 0 0
\(981\) −44.9855 −1.43628
\(982\) 0 0
\(983\) 49.6878 1.58479 0.792397 0.610006i \(-0.208833\pi\)
0.792397 + 0.610006i \(0.208833\pi\)
\(984\) 0 0
\(985\) −20.9823 −0.668553
\(986\) 0 0
\(987\) 2.75787 0.0877841
\(988\) 0 0
\(989\) 4.33680 0.137902
\(990\) 0 0
\(991\) −2.75140 −0.0874010 −0.0437005 0.999045i \(-0.513915\pi\)
−0.0437005 + 0.999045i \(0.513915\pi\)
\(992\) 0 0
\(993\) 3.37266 0.107028
\(994\) 0 0
\(995\) −0.979679 −0.0310579
\(996\) 0 0
\(997\) 50.7084 1.60595 0.802975 0.596012i \(-0.203249\pi\)
0.802975 + 0.596012i \(0.203249\pi\)
\(998\) 0 0
\(999\) 24.8068 0.784852
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 \(a_p\))