Properties

Label 4004.2.a.j.1.1
Level 4004
Weight 2
Character 4004.1
Self dual Yes
Analytic conductor 31.972
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9721009693\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
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 1.1
Root \(3.21473\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.21473 q^{3} -2.32236 q^{5} -1.00000 q^{7} +7.33449 q^{9} +O(q^{10})\) \(q-3.21473 q^{3} -2.32236 q^{5} -1.00000 q^{7} +7.33449 q^{9} -1.00000 q^{11} -1.00000 q^{13} +7.46575 q^{15} +7.61912 q^{17} +7.80003 q^{19} +3.21473 q^{21} -9.32617 q^{23} +0.393340 q^{25} -13.9342 q^{27} +3.30504 q^{29} -9.29674 q^{31} +3.21473 q^{33} +2.32236 q^{35} +3.92918 q^{37} +3.21473 q^{39} -10.6878 q^{41} +7.32042 q^{43} -17.0333 q^{45} -10.8791 q^{47} +1.00000 q^{49} -24.4934 q^{51} -0.263461 q^{53} +2.32236 q^{55} -25.0750 q^{57} -7.99170 q^{59} -0.0316514 q^{61} -7.33449 q^{63} +2.32236 q^{65} +9.12418 q^{67} +29.9811 q^{69} +3.34749 q^{71} -14.3526 q^{73} -1.26448 q^{75} +1.00000 q^{77} +11.5685 q^{79} +22.7913 q^{81} -6.71902 q^{83} -17.6943 q^{85} -10.6248 q^{87} +10.8509 q^{89} +1.00000 q^{91} +29.8865 q^{93} -18.1145 q^{95} -7.56532 q^{97} -7.33449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) −3.21473 −1.85603 −0.928013 0.372549i \(-0.878484\pi\)
−0.928013 + 0.372549i \(0.878484\pi\)
\(4\) 0 0
\(5\) −2.32236 −1.03859 −0.519295 0.854595i \(-0.673805\pi\)
−0.519295 + 0.854595i \(0.673805\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 7.33449 2.44483
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 7.46575 1.92765
\(16\) 0 0
\(17\) 7.61912 1.84791 0.923954 0.382503i \(-0.124938\pi\)
0.923954 + 0.382503i \(0.124938\pi\)
\(18\) 0 0
\(19\) 7.80003 1.78945 0.894725 0.446617i \(-0.147371\pi\)
0.894725 + 0.446617i \(0.147371\pi\)
\(20\) 0 0
\(21\) 3.21473 0.701512
\(22\) 0 0
\(23\) −9.32617 −1.94464 −0.972320 0.233652i \(-0.924933\pi\)
−0.972320 + 0.233652i \(0.924933\pi\)
\(24\) 0 0
\(25\) 0.393340 0.0786680
\(26\) 0 0
\(27\) −13.9342 −2.68164
\(28\) 0 0
\(29\) 3.30504 0.613730 0.306865 0.951753i \(-0.400720\pi\)
0.306865 + 0.951753i \(0.400720\pi\)
\(30\) 0 0
\(31\) −9.29674 −1.66974 −0.834872 0.550445i \(-0.814458\pi\)
−0.834872 + 0.550445i \(0.814458\pi\)
\(32\) 0 0
\(33\) 3.21473 0.559613
\(34\) 0 0
\(35\) 2.32236 0.392550
\(36\) 0 0
\(37\) 3.92918 0.645953 0.322976 0.946407i \(-0.395317\pi\)
0.322976 + 0.946407i \(0.395317\pi\)
\(38\) 0 0
\(39\) 3.21473 0.514769
\(40\) 0 0
\(41\) −10.6878 −1.66915 −0.834577 0.550891i \(-0.814288\pi\)
−0.834577 + 0.550891i \(0.814288\pi\)
\(42\) 0 0
\(43\) 7.32042 1.11635 0.558177 0.829722i \(-0.311501\pi\)
0.558177 + 0.829722i \(0.311501\pi\)
\(44\) 0 0
\(45\) −17.0333 −2.53917
\(46\) 0 0
\(47\) −10.8791 −1.58687 −0.793437 0.608652i \(-0.791710\pi\)
−0.793437 + 0.608652i \(0.791710\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −24.4934 −3.42976
\(52\) 0 0
\(53\) −0.263461 −0.0361892 −0.0180946 0.999836i \(-0.505760\pi\)
−0.0180946 + 0.999836i \(0.505760\pi\)
\(54\) 0 0
\(55\) 2.32236 0.313147
\(56\) 0 0
\(57\) −25.0750 −3.32127
\(58\) 0 0
\(59\) −7.99170 −1.04043 −0.520215 0.854035i \(-0.674148\pi\)
−0.520215 + 0.854035i \(0.674148\pi\)
\(60\) 0 0
\(61\) −0.0316514 −0.00405255 −0.00202627 0.999998i \(-0.500645\pi\)
−0.00202627 + 0.999998i \(0.500645\pi\)
\(62\) 0 0
\(63\) −7.33449 −0.924059
\(64\) 0 0
\(65\) 2.32236 0.288053
\(66\) 0 0
\(67\) 9.12418 1.11470 0.557348 0.830279i \(-0.311819\pi\)
0.557348 + 0.830279i \(0.311819\pi\)
\(68\) 0 0
\(69\) 29.9811 3.60930
\(70\) 0 0
\(71\) 3.34749 0.397274 0.198637 0.980073i \(-0.436349\pi\)
0.198637 + 0.980073i \(0.436349\pi\)
\(72\) 0 0
\(73\) −14.3526 −1.67985 −0.839923 0.542706i \(-0.817400\pi\)
−0.839923 + 0.542706i \(0.817400\pi\)
\(74\) 0 0
\(75\) −1.26448 −0.146010
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 11.5685 1.30155 0.650777 0.759269i \(-0.274443\pi\)
0.650777 + 0.759269i \(0.274443\pi\)
\(80\) 0 0
\(81\) 22.7913 2.53236
\(82\) 0 0
\(83\) −6.71902 −0.737508 −0.368754 0.929527i \(-0.620216\pi\)
−0.368754 + 0.929527i \(0.620216\pi\)
\(84\) 0 0
\(85\) −17.6943 −1.91922
\(86\) 0 0
\(87\) −10.6248 −1.13910
\(88\) 0 0
\(89\) 10.8509 1.15019 0.575095 0.818087i \(-0.304965\pi\)
0.575095 + 0.818087i \(0.304965\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 29.8865 3.09909
\(94\) 0 0
\(95\) −18.1145 −1.85850
\(96\) 0 0
\(97\) −7.56532 −0.768141 −0.384071 0.923304i \(-0.625478\pi\)
−0.384071 + 0.923304i \(0.625478\pi\)
\(98\) 0 0
\(99\) −7.33449 −0.737144
\(100\) 0 0
\(101\) −7.50380 −0.746656 −0.373328 0.927699i \(-0.621783\pi\)
−0.373328 + 0.927699i \(0.621783\pi\)
\(102\) 0 0
\(103\) 0.752280 0.0741244 0.0370622 0.999313i \(-0.488200\pi\)
0.0370622 + 0.999313i \(0.488200\pi\)
\(104\) 0 0
\(105\) −7.46575 −0.728583
\(106\) 0 0
\(107\) −11.2867 −1.09113 −0.545565 0.838069i \(-0.683685\pi\)
−0.545565 + 0.838069i \(0.683685\pi\)
\(108\) 0 0
\(109\) 1.22249 0.117093 0.0585466 0.998285i \(-0.481353\pi\)
0.0585466 + 0.998285i \(0.481353\pi\)
\(110\) 0 0
\(111\) −12.6312 −1.19890
\(112\) 0 0
\(113\) 14.6311 1.37638 0.688189 0.725532i \(-0.258406\pi\)
0.688189 + 0.725532i \(0.258406\pi\)
\(114\) 0 0
\(115\) 21.6587 2.01968
\(116\) 0 0
\(117\) −7.33449 −0.678074
\(118\) 0 0
\(119\) −7.61912 −0.698444
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 34.3584 3.09799
\(124\) 0 0
\(125\) 10.6983 0.956886
\(126\) 0 0
\(127\) −6.62675 −0.588029 −0.294014 0.955801i \(-0.594991\pi\)
−0.294014 + 0.955801i \(0.594991\pi\)
\(128\) 0 0
\(129\) −23.5332 −2.07198
\(130\) 0 0
\(131\) 15.9794 1.39613 0.698065 0.716034i \(-0.254044\pi\)
0.698065 + 0.716034i \(0.254044\pi\)
\(132\) 0 0
\(133\) −7.80003 −0.676349
\(134\) 0 0
\(135\) 32.3602 2.78512
\(136\) 0 0
\(137\) −1.07940 −0.0922194 −0.0461097 0.998936i \(-0.514682\pi\)
−0.0461097 + 0.998936i \(0.514682\pi\)
\(138\) 0 0
\(139\) −10.6777 −0.905672 −0.452836 0.891594i \(-0.649588\pi\)
−0.452836 + 0.891594i \(0.649588\pi\)
\(140\) 0 0
\(141\) 34.9732 2.94528
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −7.67548 −0.637414
\(146\) 0 0
\(147\) −3.21473 −0.265146
\(148\) 0 0
\(149\) 7.69415 0.630330 0.315165 0.949037i \(-0.397940\pi\)
0.315165 + 0.949037i \(0.397940\pi\)
\(150\) 0 0
\(151\) −7.98828 −0.650077 −0.325038 0.945701i \(-0.605377\pi\)
−0.325038 + 0.945701i \(0.605377\pi\)
\(152\) 0 0
\(153\) 55.8824 4.51782
\(154\) 0 0
\(155\) 21.5903 1.73418
\(156\) 0 0
\(157\) −10.2808 −0.820499 −0.410250 0.911973i \(-0.634558\pi\)
−0.410250 + 0.911973i \(0.634558\pi\)
\(158\) 0 0
\(159\) 0.846957 0.0671681
\(160\) 0 0
\(161\) 9.32617 0.735005
\(162\) 0 0
\(163\) 15.2380 1.19354 0.596768 0.802414i \(-0.296451\pi\)
0.596768 + 0.802414i \(0.296451\pi\)
\(164\) 0 0
\(165\) −7.46575 −0.581208
\(166\) 0 0
\(167\) 1.92026 0.148595 0.0742973 0.997236i \(-0.476329\pi\)
0.0742973 + 0.997236i \(0.476329\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 57.2093 4.37490
\(172\) 0 0
\(173\) 10.2962 0.782806 0.391403 0.920219i \(-0.371990\pi\)
0.391403 + 0.920219i \(0.371990\pi\)
\(174\) 0 0
\(175\) −0.393340 −0.0297337
\(176\) 0 0
\(177\) 25.6912 1.93107
\(178\) 0 0
\(179\) 7.04939 0.526896 0.263448 0.964674i \(-0.415140\pi\)
0.263448 + 0.964674i \(0.415140\pi\)
\(180\) 0 0
\(181\) 5.29130 0.393299 0.196650 0.980474i \(-0.436994\pi\)
0.196650 + 0.980474i \(0.436994\pi\)
\(182\) 0 0
\(183\) 0.101751 0.00752163
\(184\) 0 0
\(185\) −9.12495 −0.670880
\(186\) 0 0
\(187\) −7.61912 −0.557165
\(188\) 0 0
\(189\) 13.9342 1.01356
\(190\) 0 0
\(191\) 0.652342 0.0472018 0.0236009 0.999721i \(-0.492487\pi\)
0.0236009 + 0.999721i \(0.492487\pi\)
\(192\) 0 0
\(193\) −4.64978 −0.334698 −0.167349 0.985898i \(-0.553521\pi\)
−0.167349 + 0.985898i \(0.553521\pi\)
\(194\) 0 0
\(195\) −7.46575 −0.534633
\(196\) 0 0
\(197\) −26.8614 −1.91380 −0.956898 0.290423i \(-0.906204\pi\)
−0.956898 + 0.290423i \(0.906204\pi\)
\(198\) 0 0
\(199\) 9.00651 0.638454 0.319227 0.947678i \(-0.396577\pi\)
0.319227 + 0.947678i \(0.396577\pi\)
\(200\) 0 0
\(201\) −29.3318 −2.06890
\(202\) 0 0
\(203\) −3.30504 −0.231968
\(204\) 0 0
\(205\) 24.8209 1.73357
\(206\) 0 0
\(207\) −68.4027 −4.75432
\(208\) 0 0
\(209\) −7.80003 −0.539540
\(210\) 0 0
\(211\) −8.52687 −0.587014 −0.293507 0.955957i \(-0.594822\pi\)
−0.293507 + 0.955957i \(0.594822\pi\)
\(212\) 0 0
\(213\) −10.7613 −0.737350
\(214\) 0 0
\(215\) −17.0006 −1.15943
\(216\) 0 0
\(217\) 9.29674 0.631104
\(218\) 0 0
\(219\) 46.1398 3.11784
\(220\) 0 0
\(221\) −7.61912 −0.512518
\(222\) 0 0
\(223\) −17.8441 −1.19493 −0.597464 0.801896i \(-0.703825\pi\)
−0.597464 + 0.801896i \(0.703825\pi\)
\(224\) 0 0
\(225\) 2.88495 0.192330
\(226\) 0 0
\(227\) 1.13471 0.0753134 0.0376567 0.999291i \(-0.488011\pi\)
0.0376567 + 0.999291i \(0.488011\pi\)
\(228\) 0 0
\(229\) 14.8718 0.982754 0.491377 0.870947i \(-0.336494\pi\)
0.491377 + 0.870947i \(0.336494\pi\)
\(230\) 0 0
\(231\) −3.21473 −0.211514
\(232\) 0 0
\(233\) 4.47603 0.293234 0.146617 0.989193i \(-0.453161\pi\)
0.146617 + 0.989193i \(0.453161\pi\)
\(234\) 0 0
\(235\) 25.2651 1.64811
\(236\) 0 0
\(237\) −37.1895 −2.41572
\(238\) 0 0
\(239\) 3.12851 0.202367 0.101183 0.994868i \(-0.467737\pi\)
0.101183 + 0.994868i \(0.467737\pi\)
\(240\) 0 0
\(241\) 20.0200 1.28960 0.644800 0.764351i \(-0.276941\pi\)
0.644800 + 0.764351i \(0.276941\pi\)
\(242\) 0 0
\(243\) −31.4651 −2.01849
\(244\) 0 0
\(245\) −2.32236 −0.148370
\(246\) 0 0
\(247\) −7.80003 −0.496304
\(248\) 0 0
\(249\) 21.5998 1.36883
\(250\) 0 0
\(251\) −7.06302 −0.445814 −0.222907 0.974840i \(-0.571555\pi\)
−0.222907 + 0.974840i \(0.571555\pi\)
\(252\) 0 0
\(253\) 9.32617 0.586331
\(254\) 0 0
\(255\) 56.8824 3.56212
\(256\) 0 0
\(257\) 9.60395 0.599078 0.299539 0.954084i \(-0.403167\pi\)
0.299539 + 0.954084i \(0.403167\pi\)
\(258\) 0 0
\(259\) −3.92918 −0.244147
\(260\) 0 0
\(261\) 24.2408 1.50047
\(262\) 0 0
\(263\) −25.7470 −1.58763 −0.793815 0.608159i \(-0.791908\pi\)
−0.793815 + 0.608159i \(0.791908\pi\)
\(264\) 0 0
\(265\) 0.611851 0.0375857
\(266\) 0 0
\(267\) −34.8826 −2.13478
\(268\) 0 0
\(269\) 25.1199 1.53159 0.765793 0.643088i \(-0.222347\pi\)
0.765793 + 0.643088i \(0.222347\pi\)
\(270\) 0 0
\(271\) 7.75793 0.471260 0.235630 0.971843i \(-0.424285\pi\)
0.235630 + 0.971843i \(0.424285\pi\)
\(272\) 0 0
\(273\) −3.21473 −0.194564
\(274\) 0 0
\(275\) −0.393340 −0.0237193
\(276\) 0 0
\(277\) 5.19504 0.312140 0.156070 0.987746i \(-0.450117\pi\)
0.156070 + 0.987746i \(0.450117\pi\)
\(278\) 0 0
\(279\) −68.1868 −4.08224
\(280\) 0 0
\(281\) 16.4855 0.983441 0.491721 0.870753i \(-0.336368\pi\)
0.491721 + 0.870753i \(0.336368\pi\)
\(282\) 0 0
\(283\) −10.6838 −0.635084 −0.317542 0.948244i \(-0.602857\pi\)
−0.317542 + 0.948244i \(0.602857\pi\)
\(284\) 0 0
\(285\) 58.2331 3.44943
\(286\) 0 0
\(287\) 10.6878 0.630881
\(288\) 0 0
\(289\) 41.0510 2.41476
\(290\) 0 0
\(291\) 24.3204 1.42569
\(292\) 0 0
\(293\) −6.03868 −0.352784 −0.176392 0.984320i \(-0.556443\pi\)
−0.176392 + 0.984320i \(0.556443\pi\)
\(294\) 0 0
\(295\) 18.5596 1.08058
\(296\) 0 0
\(297\) 13.9342 0.808545
\(298\) 0 0
\(299\) 9.32617 0.539346
\(300\) 0 0
\(301\) −7.32042 −0.421942
\(302\) 0 0
\(303\) 24.1227 1.38581
\(304\) 0 0
\(305\) 0.0735058 0.00420893
\(306\) 0 0
\(307\) 4.38116 0.250046 0.125023 0.992154i \(-0.460100\pi\)
0.125023 + 0.992154i \(0.460100\pi\)
\(308\) 0 0
\(309\) −2.41838 −0.137577
\(310\) 0 0
\(311\) −24.4596 −1.38698 −0.693488 0.720468i \(-0.743927\pi\)
−0.693488 + 0.720468i \(0.743927\pi\)
\(312\) 0 0
\(313\) 6.79525 0.384090 0.192045 0.981386i \(-0.438488\pi\)
0.192045 + 0.981386i \(0.438488\pi\)
\(314\) 0 0
\(315\) 17.0333 0.959718
\(316\) 0 0
\(317\) 25.2154 1.41624 0.708119 0.706093i \(-0.249544\pi\)
0.708119 + 0.706093i \(0.249544\pi\)
\(318\) 0 0
\(319\) −3.30504 −0.185047
\(320\) 0 0
\(321\) 36.2838 2.02516
\(322\) 0 0
\(323\) 59.4294 3.30674
\(324\) 0 0
\(325\) −0.393340 −0.0218186
\(326\) 0 0
\(327\) −3.92997 −0.217328
\(328\) 0 0
\(329\) 10.8791 0.599782
\(330\) 0 0
\(331\) 10.6879 0.587462 0.293731 0.955888i \(-0.405103\pi\)
0.293731 + 0.955888i \(0.405103\pi\)
\(332\) 0 0
\(333\) 28.8185 1.57924
\(334\) 0 0
\(335\) −21.1896 −1.15771
\(336\) 0 0
\(337\) 3.31287 0.180464 0.0902318 0.995921i \(-0.471239\pi\)
0.0902318 + 0.995921i \(0.471239\pi\)
\(338\) 0 0
\(339\) −47.0350 −2.55459
\(340\) 0 0
\(341\) 9.29674 0.503447
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −69.6268 −3.74858
\(346\) 0 0
\(347\) 31.5814 1.69538 0.847690 0.530491i \(-0.177993\pi\)
0.847690 + 0.530491i \(0.177993\pi\)
\(348\) 0 0
\(349\) 4.44159 0.237753 0.118876 0.992909i \(-0.462071\pi\)
0.118876 + 0.992909i \(0.462071\pi\)
\(350\) 0 0
\(351\) 13.9342 0.743753
\(352\) 0 0
\(353\) −17.2499 −0.918118 −0.459059 0.888406i \(-0.651813\pi\)
−0.459059 + 0.888406i \(0.651813\pi\)
\(354\) 0 0
\(355\) −7.77406 −0.412604
\(356\) 0 0
\(357\) 24.4934 1.29633
\(358\) 0 0
\(359\) 2.58716 0.136545 0.0682726 0.997667i \(-0.478251\pi\)
0.0682726 + 0.997667i \(0.478251\pi\)
\(360\) 0 0
\(361\) 41.8405 2.20213
\(362\) 0 0
\(363\) −3.21473 −0.168730
\(364\) 0 0
\(365\) 33.3319 1.74467
\(366\) 0 0
\(367\) 23.8694 1.24597 0.622985 0.782233i \(-0.285920\pi\)
0.622985 + 0.782233i \(0.285920\pi\)
\(368\) 0 0
\(369\) −78.3896 −4.08080
\(370\) 0 0
\(371\) 0.263461 0.0136782
\(372\) 0 0
\(373\) 8.71369 0.451178 0.225589 0.974223i \(-0.427569\pi\)
0.225589 + 0.974223i \(0.427569\pi\)
\(374\) 0 0
\(375\) −34.3922 −1.77600
\(376\) 0 0
\(377\) −3.30504 −0.170218
\(378\) 0 0
\(379\) −5.74904 −0.295308 −0.147654 0.989039i \(-0.547172\pi\)
−0.147654 + 0.989039i \(0.547172\pi\)
\(380\) 0 0
\(381\) 21.3032 1.09140
\(382\) 0 0
\(383\) 4.83845 0.247233 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(384\) 0 0
\(385\) −2.32236 −0.118358
\(386\) 0 0
\(387\) 53.6916 2.72930
\(388\) 0 0
\(389\) −0.769207 −0.0390004 −0.0195002 0.999810i \(-0.506207\pi\)
−0.0195002 + 0.999810i \(0.506207\pi\)
\(390\) 0 0
\(391\) −71.0572 −3.59352
\(392\) 0 0
\(393\) −51.3696 −2.59125
\(394\) 0 0
\(395\) −26.8661 −1.35178
\(396\) 0 0
\(397\) −2.96203 −0.148660 −0.0743300 0.997234i \(-0.523682\pi\)
−0.0743300 + 0.997234i \(0.523682\pi\)
\(398\) 0 0
\(399\) 25.0750 1.25532
\(400\) 0 0
\(401\) −38.5674 −1.92597 −0.962983 0.269563i \(-0.913121\pi\)
−0.962983 + 0.269563i \(0.913121\pi\)
\(402\) 0 0
\(403\) 9.29674 0.463103
\(404\) 0 0
\(405\) −52.9294 −2.63009
\(406\) 0 0
\(407\) −3.92918 −0.194762
\(408\) 0 0
\(409\) 23.8884 1.18120 0.590602 0.806963i \(-0.298890\pi\)
0.590602 + 0.806963i \(0.298890\pi\)
\(410\) 0 0
\(411\) 3.46998 0.171162
\(412\) 0 0
\(413\) 7.99170 0.393246
\(414\) 0 0
\(415\) 15.6040 0.765969
\(416\) 0 0
\(417\) 34.3260 1.68095
\(418\) 0 0
\(419\) 13.5141 0.660207 0.330104 0.943945i \(-0.392916\pi\)
0.330104 + 0.943945i \(0.392916\pi\)
\(420\) 0 0
\(421\) 14.1621 0.690220 0.345110 0.938562i \(-0.387842\pi\)
0.345110 + 0.938562i \(0.387842\pi\)
\(422\) 0 0
\(423\) −79.7923 −3.87964
\(424\) 0 0
\(425\) 2.99691 0.145371
\(426\) 0 0
\(427\) 0.0316514 0.00153172
\(428\) 0 0
\(429\) −3.21473 −0.155209
\(430\) 0 0
\(431\) −14.9317 −0.719235 −0.359617 0.933100i \(-0.617093\pi\)
−0.359617 + 0.933100i \(0.617093\pi\)
\(432\) 0 0
\(433\) 27.6671 1.32960 0.664799 0.747022i \(-0.268517\pi\)
0.664799 + 0.747022i \(0.268517\pi\)
\(434\) 0 0
\(435\) 24.6746 1.18306
\(436\) 0 0
\(437\) −72.7444 −3.47984
\(438\) 0 0
\(439\) 12.8124 0.611503 0.305752 0.952111i \(-0.401092\pi\)
0.305752 + 0.952111i \(0.401092\pi\)
\(440\) 0 0
\(441\) 7.33449 0.349261
\(442\) 0 0
\(443\) −19.9609 −0.948369 −0.474185 0.880425i \(-0.657257\pi\)
−0.474185 + 0.880425i \(0.657257\pi\)
\(444\) 0 0
\(445\) −25.1996 −1.19458
\(446\) 0 0
\(447\) −24.7346 −1.16991
\(448\) 0 0
\(449\) −3.34012 −0.157630 −0.0788150 0.996889i \(-0.525114\pi\)
−0.0788150 + 0.996889i \(0.525114\pi\)
\(450\) 0 0
\(451\) 10.6878 0.503269
\(452\) 0 0
\(453\) 25.6802 1.20656
\(454\) 0 0
\(455\) −2.32236 −0.108874
\(456\) 0 0
\(457\) 2.15297 0.100712 0.0503558 0.998731i \(-0.483964\pi\)
0.0503558 + 0.998731i \(0.483964\pi\)
\(458\) 0 0
\(459\) −106.166 −4.95543
\(460\) 0 0
\(461\) 7.81564 0.364011 0.182005 0.983298i \(-0.441741\pi\)
0.182005 + 0.983298i \(0.441741\pi\)
\(462\) 0 0
\(463\) −10.5469 −0.490156 −0.245078 0.969503i \(-0.578814\pi\)
−0.245078 + 0.969503i \(0.578814\pi\)
\(464\) 0 0
\(465\) −69.4071 −3.21868
\(466\) 0 0
\(467\) 22.2528 1.02974 0.514868 0.857269i \(-0.327841\pi\)
0.514868 + 0.857269i \(0.327841\pi\)
\(468\) 0 0
\(469\) −9.12418 −0.421316
\(470\) 0 0
\(471\) 33.0501 1.52287
\(472\) 0 0
\(473\) −7.32042 −0.336593
\(474\) 0 0
\(475\) 3.06807 0.140773
\(476\) 0 0
\(477\) −1.93235 −0.0884764
\(478\) 0 0
\(479\) 14.7498 0.673933 0.336967 0.941517i \(-0.390599\pi\)
0.336967 + 0.941517i \(0.390599\pi\)
\(480\) 0 0
\(481\) −3.92918 −0.179155
\(482\) 0 0
\(483\) −29.9811 −1.36419
\(484\) 0 0
\(485\) 17.5694 0.797784
\(486\) 0 0
\(487\) 11.2792 0.511111 0.255556 0.966794i \(-0.417742\pi\)
0.255556 + 0.966794i \(0.417742\pi\)
\(488\) 0 0
\(489\) −48.9862 −2.21523
\(490\) 0 0
\(491\) 10.3197 0.465721 0.232861 0.972510i \(-0.425191\pi\)
0.232861 + 0.972510i \(0.425191\pi\)
\(492\) 0 0
\(493\) 25.1815 1.13412
\(494\) 0 0
\(495\) 17.0333 0.765590
\(496\) 0 0
\(497\) −3.34749 −0.150155
\(498\) 0 0
\(499\) 13.9587 0.624879 0.312440 0.949938i \(-0.398854\pi\)
0.312440 + 0.949938i \(0.398854\pi\)
\(500\) 0 0
\(501\) −6.17313 −0.275795
\(502\) 0 0
\(503\) 11.2367 0.501018 0.250509 0.968114i \(-0.419402\pi\)
0.250509 + 0.968114i \(0.419402\pi\)
\(504\) 0 0
\(505\) 17.4265 0.775469
\(506\) 0 0
\(507\) −3.21473 −0.142771
\(508\) 0 0
\(509\) −17.7545 −0.786953 −0.393477 0.919335i \(-0.628728\pi\)
−0.393477 + 0.919335i \(0.628728\pi\)
\(510\) 0 0
\(511\) 14.3526 0.634922
\(512\) 0 0
\(513\) −108.687 −4.79866
\(514\) 0 0
\(515\) −1.74706 −0.0769848
\(516\) 0 0
\(517\) 10.8791 0.478461
\(518\) 0 0
\(519\) −33.0995 −1.45291
\(520\) 0 0
\(521\) −27.2360 −1.19323 −0.596616 0.802527i \(-0.703489\pi\)
−0.596616 + 0.802527i \(0.703489\pi\)
\(522\) 0 0
\(523\) −21.6701 −0.947568 −0.473784 0.880641i \(-0.657112\pi\)
−0.473784 + 0.880641i \(0.657112\pi\)
\(524\) 0 0
\(525\) 1.26448 0.0551865
\(526\) 0 0
\(527\) −70.8330 −3.08553
\(528\) 0 0
\(529\) 63.9774 2.78163
\(530\) 0 0
\(531\) −58.6150 −2.54368
\(532\) 0 0
\(533\) 10.6878 0.462940
\(534\) 0 0
\(535\) 26.2118 1.13324
\(536\) 0 0
\(537\) −22.6619 −0.977932
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 15.3907 0.661699 0.330850 0.943683i \(-0.392665\pi\)
0.330850 + 0.943683i \(0.392665\pi\)
\(542\) 0 0
\(543\) −17.0101 −0.729973
\(544\) 0 0
\(545\) −2.83906 −0.121612
\(546\) 0 0
\(547\) 3.24887 0.138912 0.0694559 0.997585i \(-0.477874\pi\)
0.0694559 + 0.997585i \(0.477874\pi\)
\(548\) 0 0
\(549\) −0.232147 −0.00990779
\(550\) 0 0
\(551\) 25.7794 1.09824
\(552\) 0 0
\(553\) −11.5685 −0.491941
\(554\) 0 0
\(555\) 29.3342 1.24517
\(556\) 0 0
\(557\) −31.2255 −1.32307 −0.661533 0.749916i \(-0.730094\pi\)
−0.661533 + 0.749916i \(0.730094\pi\)
\(558\) 0 0
\(559\) −7.32042 −0.309621
\(560\) 0 0
\(561\) 24.4934 1.03411
\(562\) 0 0
\(563\) −17.0900 −0.720259 −0.360130 0.932902i \(-0.617268\pi\)
−0.360130 + 0.932902i \(0.617268\pi\)
\(564\) 0 0
\(565\) −33.9786 −1.42949
\(566\) 0 0
\(567\) −22.7913 −0.957143
\(568\) 0 0
\(569\) 39.1469 1.64112 0.820561 0.571559i \(-0.193661\pi\)
0.820561 + 0.571559i \(0.193661\pi\)
\(570\) 0 0
\(571\) 28.0171 1.17248 0.586239 0.810138i \(-0.300608\pi\)
0.586239 + 0.810138i \(0.300608\pi\)
\(572\) 0 0
\(573\) −2.09710 −0.0876077
\(574\) 0 0
\(575\) −3.66836 −0.152981
\(576\) 0 0
\(577\) 12.4714 0.519191 0.259595 0.965717i \(-0.416411\pi\)
0.259595 + 0.965717i \(0.416411\pi\)
\(578\) 0 0
\(579\) 14.9478 0.621209
\(580\) 0 0
\(581\) 6.71902 0.278752
\(582\) 0 0
\(583\) 0.263461 0.0109115
\(584\) 0 0
\(585\) 17.0333 0.704240
\(586\) 0 0
\(587\) −4.30523 −0.177696 −0.0888479 0.996045i \(-0.528318\pi\)
−0.0888479 + 0.996045i \(0.528318\pi\)
\(588\) 0 0
\(589\) −72.5149 −2.98792
\(590\) 0 0
\(591\) 86.3522 3.55206
\(592\) 0 0
\(593\) 26.3981 1.08404 0.542021 0.840365i \(-0.317659\pi\)
0.542021 + 0.840365i \(0.317659\pi\)
\(594\) 0 0
\(595\) 17.6943 0.725396
\(596\) 0 0
\(597\) −28.9535 −1.18499
\(598\) 0 0
\(599\) 43.6137 1.78201 0.891004 0.453995i \(-0.150002\pi\)
0.891004 + 0.453995i \(0.150002\pi\)
\(600\) 0 0
\(601\) −35.8016 −1.46038 −0.730188 0.683246i \(-0.760568\pi\)
−0.730188 + 0.683246i \(0.760568\pi\)
\(602\) 0 0
\(603\) 66.9212 2.72524
\(604\) 0 0
\(605\) −2.32236 −0.0944172
\(606\) 0 0
\(607\) −11.5258 −0.467817 −0.233909 0.972259i \(-0.575152\pi\)
−0.233909 + 0.972259i \(0.575152\pi\)
\(608\) 0 0
\(609\) 10.6248 0.430539
\(610\) 0 0
\(611\) 10.8791 0.440120
\(612\) 0 0
\(613\) −12.3169 −0.497473 −0.248737 0.968571i \(-0.580015\pi\)
−0.248737 + 0.968571i \(0.580015\pi\)
\(614\) 0 0
\(615\) −79.7925 −3.21754
\(616\) 0 0
\(617\) −37.4137 −1.50622 −0.753110 0.657895i \(-0.771447\pi\)
−0.753110 + 0.657895i \(0.771447\pi\)
\(618\) 0 0
\(619\) 11.0903 0.445755 0.222877 0.974846i \(-0.428455\pi\)
0.222877 + 0.974846i \(0.428455\pi\)
\(620\) 0 0
\(621\) 129.953 5.21483
\(622\) 0 0
\(623\) −10.8509 −0.434731
\(624\) 0 0
\(625\) −26.8120 −1.07248
\(626\) 0 0
\(627\) 25.0750 1.00140
\(628\) 0 0
\(629\) 29.9369 1.19366
\(630\) 0 0
\(631\) 29.0142 1.15504 0.577519 0.816377i \(-0.304021\pi\)
0.577519 + 0.816377i \(0.304021\pi\)
\(632\) 0 0
\(633\) 27.4116 1.08951
\(634\) 0 0
\(635\) 15.3897 0.610720
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 24.5521 0.971267
\(640\) 0 0
\(641\) −47.7689 −1.88676 −0.943379 0.331717i \(-0.892372\pi\)
−0.943379 + 0.331717i \(0.892372\pi\)
\(642\) 0 0
\(643\) 10.2059 0.402480 0.201240 0.979542i \(-0.435503\pi\)
0.201240 + 0.979542i \(0.435503\pi\)
\(644\) 0 0
\(645\) 54.6524 2.15194
\(646\) 0 0
\(647\) −21.8958 −0.860813 −0.430407 0.902635i \(-0.641630\pi\)
−0.430407 + 0.902635i \(0.641630\pi\)
\(648\) 0 0
\(649\) 7.99170 0.313702
\(650\) 0 0
\(651\) −29.8865 −1.17134
\(652\) 0 0
\(653\) −36.9237 −1.44493 −0.722467 0.691405i \(-0.756992\pi\)
−0.722467 + 0.691405i \(0.756992\pi\)
\(654\) 0 0
\(655\) −37.1100 −1.45001
\(656\) 0 0
\(657\) −105.269 −4.10694
\(658\) 0 0
\(659\) −20.7114 −0.806802 −0.403401 0.915023i \(-0.632172\pi\)
−0.403401 + 0.915023i \(0.632172\pi\)
\(660\) 0 0
\(661\) −2.89506 −0.112605 −0.0563024 0.998414i \(-0.517931\pi\)
−0.0563024 + 0.998414i \(0.517931\pi\)
\(662\) 0 0
\(663\) 24.4934 0.951245
\(664\) 0 0
\(665\) 18.1145 0.702449
\(666\) 0 0
\(667\) −30.8233 −1.19348
\(668\) 0 0
\(669\) 57.3639 2.21782
\(670\) 0 0
\(671\) 0.0316514 0.00122189
\(672\) 0 0
\(673\) −22.7168 −0.875668 −0.437834 0.899056i \(-0.644254\pi\)
−0.437834 + 0.899056i \(0.644254\pi\)
\(674\) 0 0
\(675\) −5.48089 −0.210959
\(676\) 0 0
\(677\) 22.7768 0.875385 0.437692 0.899125i \(-0.355796\pi\)
0.437692 + 0.899125i \(0.355796\pi\)
\(678\) 0 0
\(679\) 7.56532 0.290330
\(680\) 0 0
\(681\) −3.64779 −0.139784
\(682\) 0 0
\(683\) −19.4559 −0.744458 −0.372229 0.928141i \(-0.621406\pi\)
−0.372229 + 0.928141i \(0.621406\pi\)
\(684\) 0 0
\(685\) 2.50675 0.0957781
\(686\) 0 0
\(687\) −47.8087 −1.82402
\(688\) 0 0
\(689\) 0.263461 0.0100371
\(690\) 0 0
\(691\) 37.1334 1.41262 0.706311 0.707902i \(-0.250358\pi\)
0.706311 + 0.707902i \(0.250358\pi\)
\(692\) 0 0
\(693\) 7.33449 0.278614
\(694\) 0 0
\(695\) 24.7975 0.940622
\(696\) 0 0
\(697\) −81.4317 −3.08444
\(698\) 0 0
\(699\) −14.3892 −0.544250
\(700\) 0 0
\(701\) −32.9134 −1.24312 −0.621561 0.783366i \(-0.713501\pi\)
−0.621561 + 0.783366i \(0.713501\pi\)
\(702\) 0 0
\(703\) 30.6477 1.15590
\(704\) 0 0
\(705\) −81.2203 −3.05893
\(706\) 0 0
\(707\) 7.50380 0.282210
\(708\) 0 0
\(709\) −3.08800 −0.115972 −0.0579861 0.998317i \(-0.518468\pi\)
−0.0579861 + 0.998317i \(0.518468\pi\)
\(710\) 0 0
\(711\) 84.8488 3.18208
\(712\) 0 0
\(713\) 86.7029 3.24705
\(714\) 0 0
\(715\) −2.32236 −0.0868512
\(716\) 0 0
\(717\) −10.0573 −0.375598
\(718\) 0 0
\(719\) −8.32604 −0.310509 −0.155254 0.987875i \(-0.549620\pi\)
−0.155254 + 0.987875i \(0.549620\pi\)
\(720\) 0 0
\(721\) −0.752280 −0.0280164
\(722\) 0 0
\(723\) −64.3588 −2.39353
\(724\) 0 0
\(725\) 1.30000 0.0482809
\(726\) 0 0
\(727\) −21.4453 −0.795363 −0.397681 0.917524i \(-0.630185\pi\)
−0.397681 + 0.917524i \(0.630185\pi\)
\(728\) 0 0
\(729\) 32.7781 1.21400
\(730\) 0 0
\(731\) 55.7752 2.06292
\(732\) 0 0
\(733\) 17.4800 0.645639 0.322820 0.946461i \(-0.395369\pi\)
0.322820 + 0.946461i \(0.395369\pi\)
\(734\) 0 0
\(735\) 7.46575 0.275378
\(736\) 0 0
\(737\) −9.12418 −0.336094
\(738\) 0 0
\(739\) 27.8932 1.02607 0.513034 0.858368i \(-0.328521\pi\)
0.513034 + 0.858368i \(0.328521\pi\)
\(740\) 0 0
\(741\) 25.0750 0.921153
\(742\) 0 0
\(743\) −31.8612 −1.16887 −0.584437 0.811439i \(-0.698684\pi\)
−0.584437 + 0.811439i \(0.698684\pi\)
\(744\) 0 0
\(745\) −17.8686 −0.654654
\(746\) 0 0
\(747\) −49.2806 −1.80308
\(748\) 0 0
\(749\) 11.2867 0.412408
\(750\) 0 0
\(751\) −30.7619 −1.12252 −0.561260 0.827640i \(-0.689683\pi\)
−0.561260 + 0.827640i \(0.689683\pi\)
\(752\) 0 0
\(753\) 22.7057 0.827441
\(754\) 0 0
\(755\) 18.5516 0.675163
\(756\) 0 0
\(757\) 42.9708 1.56180 0.780901 0.624655i \(-0.214761\pi\)
0.780901 + 0.624655i \(0.214761\pi\)
\(758\) 0 0
\(759\) −29.9811 −1.08825
\(760\) 0 0
\(761\) 24.0241 0.870874 0.435437 0.900219i \(-0.356594\pi\)
0.435437 + 0.900219i \(0.356594\pi\)
\(762\) 0 0
\(763\) −1.22249 −0.0442571
\(764\) 0 0
\(765\) −129.779 −4.69216
\(766\) 0 0
\(767\) 7.99170 0.288564
\(768\) 0 0
\(769\) 49.1252 1.77150 0.885750 0.464163i \(-0.153645\pi\)
0.885750 + 0.464163i \(0.153645\pi\)
\(770\) 0 0
\(771\) −30.8741 −1.11190
\(772\) 0 0
\(773\) 20.7109 0.744921 0.372460 0.928048i \(-0.378514\pi\)
0.372460 + 0.928048i \(0.378514\pi\)
\(774\) 0 0
\(775\) −3.65678 −0.131355
\(776\) 0 0
\(777\) 12.6312 0.453143
\(778\) 0 0
\(779\) −83.3652 −2.98687
\(780\) 0 0
\(781\) −3.34749 −0.119783
\(782\) 0 0
\(783\) −46.0531 −1.64580
\(784\) 0 0
\(785\) 23.8757 0.852162
\(786\) 0 0
\(787\) 26.4745 0.943713 0.471857 0.881675i \(-0.343584\pi\)
0.471857 + 0.881675i \(0.343584\pi\)
\(788\) 0 0
\(789\) 82.7698 2.94668
\(790\) 0 0
\(791\) −14.6311 −0.520222
\(792\) 0 0
\(793\) 0.0316514 0.00112397
\(794\) 0 0
\(795\) −1.96694 −0.0697600
\(796\) 0 0
\(797\) 33.0401 1.17034 0.585169 0.810911i \(-0.301028\pi\)
0.585169 + 0.810911i \(0.301028\pi\)
\(798\) 0 0
\(799\) −82.8889 −2.93240
\(800\) 0 0
\(801\) 79.5856 2.81202
\(802\) 0 0
\(803\) 14.3526 0.506492
\(804\) 0 0
\(805\) −21.6587 −0.763369
\(806\) 0 0
\(807\) −80.7536 −2.84266
\(808\) 0 0
\(809\) 18.7333 0.658628 0.329314 0.944220i \(-0.393183\pi\)
0.329314 + 0.944220i \(0.393183\pi\)
\(810\) 0 0
\(811\) 26.6881 0.937146 0.468573 0.883425i \(-0.344768\pi\)
0.468573 + 0.883425i \(0.344768\pi\)
\(812\) 0 0
\(813\) −24.9396 −0.874671
\(814\) 0 0
\(815\) −35.3882 −1.23959
\(816\) 0 0
\(817\) 57.0996 1.99766
\(818\) 0 0
\(819\) 7.33449 0.256288
\(820\) 0 0
\(821\) 4.31411 0.150563 0.0752817 0.997162i \(-0.476014\pi\)
0.0752817 + 0.997162i \(0.476014\pi\)
\(822\) 0 0
\(823\) 26.9016 0.937731 0.468865 0.883270i \(-0.344663\pi\)
0.468865 + 0.883270i \(0.344663\pi\)
\(824\) 0 0
\(825\) 1.26448 0.0440236
\(826\) 0 0
\(827\) −17.2063 −0.598322 −0.299161 0.954203i \(-0.596707\pi\)
−0.299161 + 0.954203i \(0.596707\pi\)
\(828\) 0 0
\(829\) −22.0565 −0.766055 −0.383028 0.923737i \(-0.625119\pi\)
−0.383028 + 0.923737i \(0.625119\pi\)
\(830\) 0 0
\(831\) −16.7007 −0.579339
\(832\) 0 0
\(833\) 7.61912 0.263987
\(834\) 0 0
\(835\) −4.45954 −0.154329
\(836\) 0 0
\(837\) 129.543 4.47765
\(838\) 0 0
\(839\) 16.2143 0.559781 0.279890 0.960032i \(-0.409702\pi\)
0.279890 + 0.960032i \(0.409702\pi\)
\(840\) 0 0
\(841\) −18.0767 −0.623335
\(842\) 0 0
\(843\) −52.9964 −1.82529
\(844\) 0 0
\(845\) −2.32236 −0.0798915
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 34.3454 1.17873
\(850\) 0 0
\(851\) −36.6442 −1.25615
\(852\) 0 0
\(853\) −10.7332 −0.367496 −0.183748 0.982973i \(-0.558823\pi\)
−0.183748 + 0.982973i \(0.558823\pi\)
\(854\) 0 0
\(855\) −132.860 −4.54373
\(856\) 0 0
\(857\) 33.3678 1.13982 0.569912 0.821706i \(-0.306977\pi\)
0.569912 + 0.821706i \(0.306977\pi\)
\(858\) 0 0
\(859\) 36.0562 1.23022 0.615111 0.788440i \(-0.289111\pi\)
0.615111 + 0.788440i \(0.289111\pi\)
\(860\) 0 0
\(861\) −34.3584 −1.17093
\(862\) 0 0
\(863\) 28.6809 0.976310 0.488155 0.872757i \(-0.337670\pi\)
0.488155 + 0.872757i \(0.337670\pi\)
\(864\) 0 0
\(865\) −23.9115 −0.813014
\(866\) 0 0
\(867\) −131.968 −4.48186
\(868\) 0 0
\(869\) −11.5685 −0.392434
\(870\) 0 0
\(871\) −9.12418 −0.309161
\(872\) 0 0
\(873\) −55.4877 −1.87797
\(874\) 0 0
\(875\) −10.6983 −0.361669
\(876\) 0 0
\(877\) 37.7520 1.27479 0.637397 0.770536i \(-0.280011\pi\)
0.637397 + 0.770536i \(0.280011\pi\)
\(878\) 0 0
\(879\) 19.4127 0.654775
\(880\) 0 0
\(881\) −8.05877 −0.271507 −0.135753 0.990743i \(-0.543346\pi\)
−0.135753 + 0.990743i \(0.543346\pi\)
\(882\) 0 0
\(883\) 45.8441 1.54278 0.771389 0.636364i \(-0.219563\pi\)
0.771389 + 0.636364i \(0.219563\pi\)
\(884\) 0 0
\(885\) −59.6640 −2.00558
\(886\) 0 0
\(887\) −7.60900 −0.255485 −0.127743 0.991807i \(-0.540773\pi\)
−0.127743 + 0.991807i \(0.540773\pi\)
\(888\) 0 0
\(889\) 6.62675 0.222254
\(890\) 0 0
\(891\) −22.7913 −0.763536
\(892\) 0 0
\(893\) −84.8570 −2.83963
\(894\) 0 0
\(895\) −16.3712 −0.547228
\(896\) 0 0
\(897\) −29.9811 −1.00104
\(898\) 0 0
\(899\) −30.7261 −1.02477
\(900\) 0 0
\(901\) −2.00734 −0.0668743
\(902\) 0 0
\(903\) 23.5332 0.783135
\(904\) 0 0
\(905\) −12.2883 −0.408476
\(906\) 0 0
\(907\) 17.0073 0.564718 0.282359 0.959309i \(-0.408883\pi\)
0.282359 + 0.959309i \(0.408883\pi\)
\(908\) 0 0
\(909\) −55.0366 −1.82545
\(910\) 0 0
\(911\) 41.9745 1.39068 0.695338 0.718683i \(-0.255255\pi\)
0.695338 + 0.718683i \(0.255255\pi\)
\(912\) 0 0
\(913\) 6.71902 0.222367
\(914\) 0 0
\(915\) −0.236301 −0.00781188
\(916\) 0 0
\(917\) −15.9794 −0.527688
\(918\) 0 0
\(919\) 1.82068 0.0600586 0.0300293 0.999549i \(-0.490440\pi\)
0.0300293 + 0.999549i \(0.490440\pi\)
\(920\) 0 0
\(921\) −14.0843 −0.464092
\(922\) 0 0
\(923\) −3.34749 −0.110184
\(924\) 0 0
\(925\) 1.54550 0.0508158
\(926\) 0 0
\(927\) 5.51759 0.181222
\(928\) 0 0
\(929\) −39.6077 −1.29949 −0.649743 0.760154i \(-0.725124\pi\)
−0.649743 + 0.760154i \(0.725124\pi\)
\(930\) 0 0
\(931\) 7.80003 0.255636
\(932\) 0 0
\(933\) 78.6310 2.57426
\(934\) 0 0
\(935\) 17.6943 0.578666
\(936\) 0 0
\(937\) 52.0877 1.70163 0.850815 0.525465i \(-0.176109\pi\)
0.850815 + 0.525465i \(0.176109\pi\)
\(938\) 0 0
\(939\) −21.8449 −0.712882
\(940\) 0 0
\(941\) −3.21629 −0.104848 −0.0524240 0.998625i \(-0.516695\pi\)
−0.0524240 + 0.998625i \(0.516695\pi\)
\(942\) 0 0
\(943\) 99.6763 3.24591
\(944\) 0 0
\(945\) −32.3602 −1.05268
\(946\) 0 0
\(947\) −17.0436 −0.553842 −0.276921 0.960893i \(-0.589314\pi\)
−0.276921 + 0.960893i \(0.589314\pi\)
\(948\) 0 0
\(949\) 14.3526 0.465905
\(950\) 0 0
\(951\) −81.0607 −2.62857
\(952\) 0 0
\(953\) 5.45131 0.176585 0.0882926 0.996095i \(-0.471859\pi\)
0.0882926 + 0.996095i \(0.471859\pi\)
\(954\) 0 0
\(955\) −1.51497 −0.0490233
\(956\) 0 0
\(957\) 10.6248 0.343451
\(958\) 0 0
\(959\) 1.07940 0.0348557
\(960\) 0 0
\(961\) 55.4293 1.78804
\(962\) 0 0
\(963\) −82.7824 −2.66763
\(964\) 0 0
\(965\) 10.7984 0.347614
\(966\) 0 0
\(967\) 9.50097 0.305531 0.152765 0.988262i \(-0.451182\pi\)
0.152765 + 0.988262i \(0.451182\pi\)
\(968\) 0 0
\(969\) −191.049 −6.13739
\(970\) 0 0
\(971\) 21.1050 0.677291 0.338645 0.940914i \(-0.390031\pi\)
0.338645 + 0.940914i \(0.390031\pi\)
\(972\) 0 0
\(973\) 10.6777 0.342312
\(974\) 0 0
\(975\) 1.26448 0.0404958
\(976\) 0 0
\(977\) 18.1636 0.581104 0.290552 0.956859i \(-0.406161\pi\)
0.290552 + 0.956859i \(0.406161\pi\)
\(978\) 0 0
\(979\) −10.8509 −0.346795
\(980\) 0 0
\(981\) 8.96634 0.286273
\(982\) 0 0
\(983\) −53.0122 −1.69083 −0.845413 0.534114i \(-0.820645\pi\)
−0.845413 + 0.534114i \(0.820645\pi\)
\(984\) 0 0
\(985\) 62.3818 1.98765
\(986\) 0 0
\(987\) −34.9732 −1.11321
\(988\) 0 0
\(989\) −68.2715 −2.17091
\(990\) 0 0
\(991\) −12.1416 −0.385690 −0.192845 0.981229i \(-0.561772\pi\)
−0.192845 + 0.981229i \(0.561772\pi\)
\(992\) 0 0
\(993\) −34.3588 −1.09034
\(994\) 0 0
\(995\) −20.9163 −0.663092
\(996\) 0 0
\(997\) −55.7433 −1.76541 −0.882704 0.469929i \(-0.844279\pi\)
−0.882704 + 0.469929i \(0.844279\pi\)
\(998\) 0 0
\(999\) −54.7500 −1.73221
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 \(a_p\))