Properties

Label 8048.2.a.v.1.14
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.659121 q^{3} +0.997881 q^{5} -0.366743 q^{7} -2.56556 q^{9} +O(q^{10})\) \(q-0.659121 q^{3} +0.997881 q^{5} -0.366743 q^{7} -2.56556 q^{9} -2.34193 q^{11} +1.58340 q^{13} -0.657724 q^{15} +0.164328 q^{17} +2.94082 q^{19} +0.241728 q^{21} +6.49861 q^{23} -4.00423 q^{25} +3.66838 q^{27} -7.89072 q^{29} +7.02250 q^{31} +1.54361 q^{33} -0.365966 q^{35} -5.39311 q^{37} -1.04365 q^{39} -4.46312 q^{41} -8.37356 q^{43} -2.56012 q^{45} +12.8414 q^{47} -6.86550 q^{49} -0.108312 q^{51} +12.7113 q^{53} -2.33697 q^{55} -1.93836 q^{57} -9.64319 q^{59} +9.98548 q^{61} +0.940901 q^{63} +1.58004 q^{65} +6.58675 q^{67} -4.28337 q^{69} -9.53600 q^{71} +2.32994 q^{73} +2.63927 q^{75} +0.858886 q^{77} -2.51367 q^{79} +5.27878 q^{81} +2.90312 q^{83} +0.163980 q^{85} +5.20093 q^{87} -13.3006 q^{89} -0.580700 q^{91} -4.62868 q^{93} +2.93459 q^{95} +0.261925 q^{97} +6.00836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + 14q^{11} - 31q^{13} + 2q^{15} - 9q^{17} + 8q^{19} - 28q^{21} + 4q^{23} + 22q^{25} + 4q^{27} - 47q^{29} + 5q^{31} - 26q^{33} + 13q^{35} - 67q^{37} + 9q^{39} - 28q^{41} - 15q^{43} - 57q^{45} + 10q^{47} + 20q^{49} + 11q^{51} - 58q^{53} - 15q^{55} - 31q^{57} + 32q^{59} - 55q^{61} + 16q^{63} - 44q^{65} - 22q^{67} - 44q^{69} + 47q^{71} - 5q^{73} + 25q^{75} - 50q^{77} + 14q^{79} - 28q^{81} + 16q^{83} - 78q^{85} + 11q^{87} - 20q^{89} + 15q^{91} - 83q^{93} + 27q^{95} - 8q^{97} + 70q^{99} + O(q^{100}) \)

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
\(3\) −0.659121 −0.380543 −0.190272 0.981731i \(-0.560937\pi\)
−0.190272 + 0.981731i \(0.560937\pi\)
\(4\) 0 0
\(5\) 0.997881 0.446266 0.223133 0.974788i \(-0.428372\pi\)
0.223133 + 0.974788i \(0.428372\pi\)
\(6\) 0 0
\(7\) −0.366743 −0.138616 −0.0693079 0.997595i \(-0.522079\pi\)
−0.0693079 + 0.997595i \(0.522079\pi\)
\(8\) 0 0
\(9\) −2.56556 −0.855187
\(10\) 0 0
\(11\) −2.34193 −0.706118 −0.353059 0.935601i \(-0.614859\pi\)
−0.353059 + 0.935601i \(0.614859\pi\)
\(12\) 0 0
\(13\) 1.58340 0.439155 0.219578 0.975595i \(-0.429532\pi\)
0.219578 + 0.975595i \(0.429532\pi\)
\(14\) 0 0
\(15\) −0.657724 −0.169824
\(16\) 0 0
\(17\) 0.164328 0.0398554 0.0199277 0.999801i \(-0.493656\pi\)
0.0199277 + 0.999801i \(0.493656\pi\)
\(18\) 0 0
\(19\) 2.94082 0.674671 0.337336 0.941384i \(-0.390474\pi\)
0.337336 + 0.941384i \(0.390474\pi\)
\(20\) 0 0
\(21\) 0.241728 0.0527493
\(22\) 0 0
\(23\) 6.49861 1.35505 0.677527 0.735498i \(-0.263052\pi\)
0.677527 + 0.735498i \(0.263052\pi\)
\(24\) 0 0
\(25\) −4.00423 −0.800847
\(26\) 0 0
\(27\) 3.66838 0.705979
\(28\) 0 0
\(29\) −7.89072 −1.46527 −0.732635 0.680622i \(-0.761710\pi\)
−0.732635 + 0.680622i \(0.761710\pi\)
\(30\) 0 0
\(31\) 7.02250 1.26128 0.630640 0.776076i \(-0.282793\pi\)
0.630640 + 0.776076i \(0.282793\pi\)
\(32\) 0 0
\(33\) 1.54361 0.268709
\(34\) 0 0
\(35\) −0.365966 −0.0618595
\(36\) 0 0
\(37\) −5.39311 −0.886622 −0.443311 0.896368i \(-0.646196\pi\)
−0.443311 + 0.896368i \(0.646196\pi\)
\(38\) 0 0
\(39\) −1.04365 −0.167118
\(40\) 0 0
\(41\) −4.46312 −0.697023 −0.348511 0.937305i \(-0.613313\pi\)
−0.348511 + 0.937305i \(0.613313\pi\)
\(42\) 0 0
\(43\) −8.37356 −1.27696 −0.638478 0.769640i \(-0.720436\pi\)
−0.638478 + 0.769640i \(0.720436\pi\)
\(44\) 0 0
\(45\) −2.56012 −0.381641
\(46\) 0 0
\(47\) 12.8414 1.87311 0.936555 0.350520i \(-0.113995\pi\)
0.936555 + 0.350520i \(0.113995\pi\)
\(48\) 0 0
\(49\) −6.86550 −0.980786
\(50\) 0 0
\(51\) −0.108312 −0.0151667
\(52\) 0 0
\(53\) 12.7113 1.74603 0.873013 0.487697i \(-0.162163\pi\)
0.873013 + 0.487697i \(0.162163\pi\)
\(54\) 0 0
\(55\) −2.33697 −0.315116
\(56\) 0 0
\(57\) −1.93836 −0.256742
\(58\) 0 0
\(59\) −9.64319 −1.25544 −0.627718 0.778440i \(-0.716011\pi\)
−0.627718 + 0.778440i \(0.716011\pi\)
\(60\) 0 0
\(61\) 9.98548 1.27851 0.639255 0.768995i \(-0.279243\pi\)
0.639255 + 0.768995i \(0.279243\pi\)
\(62\) 0 0
\(63\) 0.940901 0.118542
\(64\) 0 0
\(65\) 1.58004 0.195980
\(66\) 0 0
\(67\) 6.58675 0.804700 0.402350 0.915486i \(-0.368193\pi\)
0.402350 + 0.915486i \(0.368193\pi\)
\(68\) 0 0
\(69\) −4.28337 −0.515657
\(70\) 0 0
\(71\) −9.53600 −1.13171 −0.565857 0.824503i \(-0.691455\pi\)
−0.565857 + 0.824503i \(0.691455\pi\)
\(72\) 0 0
\(73\) 2.32994 0.272699 0.136350 0.990661i \(-0.456463\pi\)
0.136350 + 0.990661i \(0.456463\pi\)
\(74\) 0 0
\(75\) 2.63927 0.304757
\(76\) 0 0
\(77\) 0.858886 0.0978791
\(78\) 0 0
\(79\) −2.51367 −0.282810 −0.141405 0.989952i \(-0.545162\pi\)
−0.141405 + 0.989952i \(0.545162\pi\)
\(80\) 0 0
\(81\) 5.27878 0.586531
\(82\) 0 0
\(83\) 2.90312 0.318659 0.159330 0.987225i \(-0.449067\pi\)
0.159330 + 0.987225i \(0.449067\pi\)
\(84\) 0 0
\(85\) 0.163980 0.0177861
\(86\) 0 0
\(87\) 5.20093 0.557599
\(88\) 0 0
\(89\) −13.3006 −1.40986 −0.704930 0.709276i \(-0.749022\pi\)
−0.704930 + 0.709276i \(0.749022\pi\)
\(90\) 0 0
\(91\) −0.580700 −0.0608739
\(92\) 0 0
\(93\) −4.62868 −0.479971
\(94\) 0 0
\(95\) 2.93459 0.301083
\(96\) 0 0
\(97\) 0.261925 0.0265945 0.0132972 0.999912i \(-0.495767\pi\)
0.0132972 + 0.999912i \(0.495767\pi\)
\(98\) 0 0
\(99\) 6.00836 0.603863
\(100\) 0 0
\(101\) −4.46200 −0.443985 −0.221993 0.975048i \(-0.571256\pi\)
−0.221993 + 0.975048i \(0.571256\pi\)
\(102\) 0 0
\(103\) 0.734821 0.0724040 0.0362020 0.999344i \(-0.488474\pi\)
0.0362020 + 0.999344i \(0.488474\pi\)
\(104\) 0 0
\(105\) 0.241216 0.0235402
\(106\) 0 0
\(107\) 2.54784 0.246309 0.123154 0.992388i \(-0.460699\pi\)
0.123154 + 0.992388i \(0.460699\pi\)
\(108\) 0 0
\(109\) −4.06803 −0.389647 −0.194823 0.980838i \(-0.562413\pi\)
−0.194823 + 0.980838i \(0.562413\pi\)
\(110\) 0 0
\(111\) 3.55471 0.337398
\(112\) 0 0
\(113\) 14.4829 1.36243 0.681216 0.732082i \(-0.261451\pi\)
0.681216 + 0.732082i \(0.261451\pi\)
\(114\) 0 0
\(115\) 6.48484 0.604714
\(116\) 0 0
\(117\) −4.06230 −0.375560
\(118\) 0 0
\(119\) −0.0602661 −0.00552458
\(120\) 0 0
\(121\) −5.51537 −0.501397
\(122\) 0 0
\(123\) 2.94174 0.265248
\(124\) 0 0
\(125\) −8.98515 −0.803656
\(126\) 0 0
\(127\) 2.68557 0.238306 0.119153 0.992876i \(-0.461982\pi\)
0.119153 + 0.992876i \(0.461982\pi\)
\(128\) 0 0
\(129\) 5.51918 0.485937
\(130\) 0 0
\(131\) −9.68434 −0.846125 −0.423062 0.906101i \(-0.639045\pi\)
−0.423062 + 0.906101i \(0.639045\pi\)
\(132\) 0 0
\(133\) −1.07853 −0.0935201
\(134\) 0 0
\(135\) 3.66060 0.315054
\(136\) 0 0
\(137\) −18.8157 −1.60753 −0.803766 0.594945i \(-0.797174\pi\)
−0.803766 + 0.594945i \(0.797174\pi\)
\(138\) 0 0
\(139\) −16.5214 −1.40132 −0.700662 0.713493i \(-0.747112\pi\)
−0.700662 + 0.713493i \(0.747112\pi\)
\(140\) 0 0
\(141\) −8.46403 −0.712800
\(142\) 0 0
\(143\) −3.70820 −0.310096
\(144\) 0 0
\(145\) −7.87399 −0.653899
\(146\) 0 0
\(147\) 4.52519 0.373232
\(148\) 0 0
\(149\) −10.9148 −0.894173 −0.447086 0.894491i \(-0.647538\pi\)
−0.447086 + 0.894491i \(0.647538\pi\)
\(150\) 0 0
\(151\) 0.258942 0.0210724 0.0105362 0.999944i \(-0.496646\pi\)
0.0105362 + 0.999944i \(0.496646\pi\)
\(152\) 0 0
\(153\) −0.421593 −0.0340838
\(154\) 0 0
\(155\) 7.00762 0.562866
\(156\) 0 0
\(157\) 3.76206 0.300245 0.150123 0.988667i \(-0.452033\pi\)
0.150123 + 0.988667i \(0.452033\pi\)
\(158\) 0 0
\(159\) −8.37826 −0.664439
\(160\) 0 0
\(161\) −2.38332 −0.187832
\(162\) 0 0
\(163\) 15.1296 1.18504 0.592520 0.805556i \(-0.298133\pi\)
0.592520 + 0.805556i \(0.298133\pi\)
\(164\) 0 0
\(165\) 1.54034 0.119915
\(166\) 0 0
\(167\) 5.73732 0.443967 0.221983 0.975050i \(-0.428747\pi\)
0.221983 + 0.975050i \(0.428747\pi\)
\(168\) 0 0
\(169\) −10.4929 −0.807143
\(170\) 0 0
\(171\) −7.54486 −0.576970
\(172\) 0 0
\(173\) 4.95955 0.377068 0.188534 0.982067i \(-0.439626\pi\)
0.188534 + 0.982067i \(0.439626\pi\)
\(174\) 0 0
\(175\) 1.46852 0.111010
\(176\) 0 0
\(177\) 6.35603 0.477748
\(178\) 0 0
\(179\) 7.47906 0.559011 0.279506 0.960144i \(-0.409829\pi\)
0.279506 + 0.960144i \(0.409829\pi\)
\(180\) 0 0
\(181\) −8.26533 −0.614357 −0.307179 0.951652i \(-0.599385\pi\)
−0.307179 + 0.951652i \(0.599385\pi\)
\(182\) 0 0
\(183\) −6.58164 −0.486528
\(184\) 0 0
\(185\) −5.38168 −0.395669
\(186\) 0 0
\(187\) −0.384844 −0.0281426
\(188\) 0 0
\(189\) −1.34535 −0.0978599
\(190\) 0 0
\(191\) 2.25713 0.163320 0.0816601 0.996660i \(-0.473978\pi\)
0.0816601 + 0.996660i \(0.473978\pi\)
\(192\) 0 0
\(193\) −18.4007 −1.32451 −0.662257 0.749277i \(-0.730401\pi\)
−0.662257 + 0.749277i \(0.730401\pi\)
\(194\) 0 0
\(195\) −1.04144 −0.0745789
\(196\) 0 0
\(197\) −11.6058 −0.826877 −0.413438 0.910532i \(-0.635672\pi\)
−0.413438 + 0.910532i \(0.635672\pi\)
\(198\) 0 0
\(199\) −16.8781 −1.19646 −0.598228 0.801326i \(-0.704128\pi\)
−0.598228 + 0.801326i \(0.704128\pi\)
\(200\) 0 0
\(201\) −4.34147 −0.306223
\(202\) 0 0
\(203\) 2.89386 0.203109
\(204\) 0 0
\(205\) −4.45367 −0.311057
\(206\) 0 0
\(207\) −16.6726 −1.15882
\(208\) 0 0
\(209\) −6.88720 −0.476397
\(210\) 0 0
\(211\) −8.12192 −0.559136 −0.279568 0.960126i \(-0.590191\pi\)
−0.279568 + 0.960126i \(0.590191\pi\)
\(212\) 0 0
\(213\) 6.28537 0.430667
\(214\) 0 0
\(215\) −8.35581 −0.569862
\(216\) 0 0
\(217\) −2.57545 −0.174833
\(218\) 0 0
\(219\) −1.53571 −0.103774
\(220\) 0 0
\(221\) 0.260196 0.0175027
\(222\) 0 0
\(223\) −5.67745 −0.380190 −0.190095 0.981766i \(-0.560880\pi\)
−0.190095 + 0.981766i \(0.560880\pi\)
\(224\) 0 0
\(225\) 10.2731 0.684874
\(226\) 0 0
\(227\) −13.0486 −0.866063 −0.433032 0.901379i \(-0.642556\pi\)
−0.433032 + 0.901379i \(0.642556\pi\)
\(228\) 0 0
\(229\) 0.823786 0.0544373 0.0272187 0.999630i \(-0.491335\pi\)
0.0272187 + 0.999630i \(0.491335\pi\)
\(230\) 0 0
\(231\) −0.566109 −0.0372473
\(232\) 0 0
\(233\) 11.0371 0.723065 0.361532 0.932360i \(-0.382254\pi\)
0.361532 + 0.932360i \(0.382254\pi\)
\(234\) 0 0
\(235\) 12.8142 0.835905
\(236\) 0 0
\(237\) 1.65681 0.107621
\(238\) 0 0
\(239\) −24.2559 −1.56898 −0.784491 0.620140i \(-0.787076\pi\)
−0.784491 + 0.620140i \(0.787076\pi\)
\(240\) 0 0
\(241\) −13.3061 −0.857121 −0.428560 0.903513i \(-0.640979\pi\)
−0.428560 + 0.903513i \(0.640979\pi\)
\(242\) 0 0
\(243\) −14.4845 −0.929180
\(244\) 0 0
\(245\) −6.85095 −0.437691
\(246\) 0 0
\(247\) 4.65649 0.296285
\(248\) 0 0
\(249\) −1.91351 −0.121264
\(250\) 0 0
\(251\) −6.73438 −0.425071 −0.212535 0.977153i \(-0.568172\pi\)
−0.212535 + 0.977153i \(0.568172\pi\)
\(252\) 0 0
\(253\) −15.2193 −0.956828
\(254\) 0 0
\(255\) −0.108082 −0.00676838
\(256\) 0 0
\(257\) −27.0972 −1.69028 −0.845138 0.534549i \(-0.820482\pi\)
−0.845138 + 0.534549i \(0.820482\pi\)
\(258\) 0 0
\(259\) 1.97789 0.122900
\(260\) 0 0
\(261\) 20.2441 1.25308
\(262\) 0 0
\(263\) 20.5250 1.26562 0.632811 0.774306i \(-0.281901\pi\)
0.632811 + 0.774306i \(0.281901\pi\)
\(264\) 0 0
\(265\) 12.6843 0.779192
\(266\) 0 0
\(267\) 8.76670 0.536513
\(268\) 0 0
\(269\) 22.6469 1.38081 0.690404 0.723424i \(-0.257433\pi\)
0.690404 + 0.723424i \(0.257433\pi\)
\(270\) 0 0
\(271\) 8.87654 0.539211 0.269606 0.962971i \(-0.413107\pi\)
0.269606 + 0.962971i \(0.413107\pi\)
\(272\) 0 0
\(273\) 0.382751 0.0231652
\(274\) 0 0
\(275\) 9.37763 0.565492
\(276\) 0 0
\(277\) 19.6591 1.18120 0.590602 0.806963i \(-0.298890\pi\)
0.590602 + 0.806963i \(0.298890\pi\)
\(278\) 0 0
\(279\) −18.0167 −1.07863
\(280\) 0 0
\(281\) 15.2756 0.911265 0.455632 0.890168i \(-0.349413\pi\)
0.455632 + 0.890168i \(0.349413\pi\)
\(282\) 0 0
\(283\) −21.6629 −1.28773 −0.643864 0.765140i \(-0.722670\pi\)
−0.643864 + 0.765140i \(0.722670\pi\)
\(284\) 0 0
\(285\) −1.93425 −0.114575
\(286\) 0 0
\(287\) 1.63682 0.0966184
\(288\) 0 0
\(289\) −16.9730 −0.998412
\(290\) 0 0
\(291\) −0.172640 −0.0101204
\(292\) 0 0
\(293\) 9.59095 0.560310 0.280155 0.959955i \(-0.409614\pi\)
0.280155 + 0.959955i \(0.409614\pi\)
\(294\) 0 0
\(295\) −9.62276 −0.560259
\(296\) 0 0
\(297\) −8.59107 −0.498505
\(298\) 0 0
\(299\) 10.2899 0.595079
\(300\) 0 0
\(301\) 3.07094 0.177006
\(302\) 0 0
\(303\) 2.94099 0.168956
\(304\) 0 0
\(305\) 9.96432 0.570555
\(306\) 0 0
\(307\) 7.78430 0.444273 0.222137 0.975016i \(-0.428697\pi\)
0.222137 + 0.975016i \(0.428697\pi\)
\(308\) 0 0
\(309\) −0.484335 −0.0275529
\(310\) 0 0
\(311\) 33.5497 1.90243 0.951216 0.308527i \(-0.0998360\pi\)
0.951216 + 0.308527i \(0.0998360\pi\)
\(312\) 0 0
\(313\) −6.19902 −0.350390 −0.175195 0.984534i \(-0.556056\pi\)
−0.175195 + 0.984534i \(0.556056\pi\)
\(314\) 0 0
\(315\) 0.938907 0.0529014
\(316\) 0 0
\(317\) −11.4833 −0.644968 −0.322484 0.946575i \(-0.604518\pi\)
−0.322484 + 0.946575i \(0.604518\pi\)
\(318\) 0 0
\(319\) 18.4795 1.03465
\(320\) 0 0
\(321\) −1.67933 −0.0937313
\(322\) 0 0
\(323\) 0.483259 0.0268893
\(324\) 0 0
\(325\) −6.34029 −0.351696
\(326\) 0 0
\(327\) 2.68132 0.148278
\(328\) 0 0
\(329\) −4.70949 −0.259643
\(330\) 0 0
\(331\) 3.29804 0.181277 0.0906383 0.995884i \(-0.471109\pi\)
0.0906383 + 0.995884i \(0.471109\pi\)
\(332\) 0 0
\(333\) 13.8363 0.758227
\(334\) 0 0
\(335\) 6.57280 0.359110
\(336\) 0 0
\(337\) 7.62848 0.415550 0.207775 0.978177i \(-0.433378\pi\)
0.207775 + 0.978177i \(0.433378\pi\)
\(338\) 0 0
\(339\) −9.54595 −0.518465
\(340\) 0 0
\(341\) −16.4462 −0.890612
\(342\) 0 0
\(343\) 5.08508 0.274568
\(344\) 0 0
\(345\) −4.27429 −0.230120
\(346\) 0 0
\(347\) −30.6857 −1.64730 −0.823648 0.567102i \(-0.808065\pi\)
−0.823648 + 0.567102i \(0.808065\pi\)
\(348\) 0 0
\(349\) −9.46969 −0.506901 −0.253450 0.967348i \(-0.581565\pi\)
−0.253450 + 0.967348i \(0.581565\pi\)
\(350\) 0 0
\(351\) 5.80850 0.310035
\(352\) 0 0
\(353\) −17.2010 −0.915516 −0.457758 0.889077i \(-0.651347\pi\)
−0.457758 + 0.889077i \(0.651347\pi\)
\(354\) 0 0
\(355\) −9.51579 −0.505046
\(356\) 0 0
\(357\) 0.0397226 0.00210234
\(358\) 0 0
\(359\) 7.41231 0.391207 0.195603 0.980683i \(-0.437333\pi\)
0.195603 + 0.980683i \(0.437333\pi\)
\(360\) 0 0
\(361\) −10.3516 −0.544819
\(362\) 0 0
\(363\) 3.63530 0.190804
\(364\) 0 0
\(365\) 2.32500 0.121696
\(366\) 0 0
\(367\) −21.7723 −1.13651 −0.568253 0.822854i \(-0.692381\pi\)
−0.568253 + 0.822854i \(0.692381\pi\)
\(368\) 0 0
\(369\) 11.4504 0.596085
\(370\) 0 0
\(371\) −4.66177 −0.242027
\(372\) 0 0
\(373\) −22.7062 −1.17568 −0.587841 0.808977i \(-0.700022\pi\)
−0.587841 + 0.808977i \(0.700022\pi\)
\(374\) 0 0
\(375\) 5.92230 0.305826
\(376\) 0 0
\(377\) −12.4941 −0.643481
\(378\) 0 0
\(379\) −22.5815 −1.15994 −0.579968 0.814639i \(-0.696935\pi\)
−0.579968 + 0.814639i \(0.696935\pi\)
\(380\) 0 0
\(381\) −1.77011 −0.0906857
\(382\) 0 0
\(383\) 29.5809 1.51151 0.755756 0.654854i \(-0.227270\pi\)
0.755756 + 0.654854i \(0.227270\pi\)
\(384\) 0 0
\(385\) 0.857066 0.0436801
\(386\) 0 0
\(387\) 21.4829 1.09204
\(388\) 0 0
\(389\) 4.11718 0.208749 0.104375 0.994538i \(-0.466716\pi\)
0.104375 + 0.994538i \(0.466716\pi\)
\(390\) 0 0
\(391\) 1.06790 0.0540061
\(392\) 0 0
\(393\) 6.38315 0.321987
\(394\) 0 0
\(395\) −2.50834 −0.126208
\(396\) 0 0
\(397\) −19.4331 −0.975319 −0.487660 0.873034i \(-0.662149\pi\)
−0.487660 + 0.873034i \(0.662149\pi\)
\(398\) 0 0
\(399\) 0.710879 0.0355885
\(400\) 0 0
\(401\) 15.1714 0.757621 0.378811 0.925474i \(-0.376333\pi\)
0.378811 + 0.925474i \(0.376333\pi\)
\(402\) 0 0
\(403\) 11.1194 0.553898
\(404\) 0 0
\(405\) 5.26759 0.261749
\(406\) 0 0
\(407\) 12.6303 0.626059
\(408\) 0 0
\(409\) 32.6254 1.61322 0.806610 0.591083i \(-0.201300\pi\)
0.806610 + 0.591083i \(0.201300\pi\)
\(410\) 0 0
\(411\) 12.4018 0.611736
\(412\) 0 0
\(413\) 3.53657 0.174023
\(414\) 0 0
\(415\) 2.89697 0.142207
\(416\) 0 0
\(417\) 10.8896 0.533265
\(418\) 0 0
\(419\) −30.1541 −1.47312 −0.736562 0.676370i \(-0.763552\pi\)
−0.736562 + 0.676370i \(0.763552\pi\)
\(420\) 0 0
\(421\) −16.0071 −0.780140 −0.390070 0.920785i \(-0.627549\pi\)
−0.390070 + 0.920785i \(0.627549\pi\)
\(422\) 0 0
\(423\) −32.9454 −1.60186
\(424\) 0 0
\(425\) −0.658007 −0.0319180
\(426\) 0 0
\(427\) −3.66211 −0.177222
\(428\) 0 0
\(429\) 2.44415 0.118005
\(430\) 0 0
\(431\) 18.3797 0.885321 0.442661 0.896689i \(-0.354035\pi\)
0.442661 + 0.896689i \(0.354035\pi\)
\(432\) 0 0
\(433\) −19.9237 −0.957471 −0.478735 0.877959i \(-0.658905\pi\)
−0.478735 + 0.877959i \(0.658905\pi\)
\(434\) 0 0
\(435\) 5.18991 0.248837
\(436\) 0 0
\(437\) 19.1113 0.914215
\(438\) 0 0
\(439\) −25.5087 −1.21747 −0.608733 0.793375i \(-0.708322\pi\)
−0.608733 + 0.793375i \(0.708322\pi\)
\(440\) 0 0
\(441\) 17.6139 0.838755
\(442\) 0 0
\(443\) −3.79329 −0.180225 −0.0901124 0.995932i \(-0.528723\pi\)
−0.0901124 + 0.995932i \(0.528723\pi\)
\(444\) 0 0
\(445\) −13.2724 −0.629173
\(446\) 0 0
\(447\) 7.19415 0.340272
\(448\) 0 0
\(449\) 2.08159 0.0982363 0.0491182 0.998793i \(-0.484359\pi\)
0.0491182 + 0.998793i \(0.484359\pi\)
\(450\) 0 0
\(451\) 10.4523 0.492180
\(452\) 0 0
\(453\) −0.170674 −0.00801895
\(454\) 0 0
\(455\) −0.579469 −0.0271659
\(456\) 0 0
\(457\) 34.4508 1.61154 0.805771 0.592227i \(-0.201751\pi\)
0.805771 + 0.592227i \(0.201751\pi\)
\(458\) 0 0
\(459\) 0.602816 0.0281370
\(460\) 0 0
\(461\) −25.3819 −1.18215 −0.591076 0.806616i \(-0.701297\pi\)
−0.591076 + 0.806616i \(0.701297\pi\)
\(462\) 0 0
\(463\) −15.2540 −0.708912 −0.354456 0.935073i \(-0.615334\pi\)
−0.354456 + 0.935073i \(0.615334\pi\)
\(464\) 0 0
\(465\) −4.61887 −0.214195
\(466\) 0 0
\(467\) −6.38856 −0.295627 −0.147814 0.989015i \(-0.547224\pi\)
−0.147814 + 0.989015i \(0.547224\pi\)
\(468\) 0 0
\(469\) −2.41565 −0.111544
\(470\) 0 0
\(471\) −2.47965 −0.114256
\(472\) 0 0
\(473\) 19.6103 0.901681
\(474\) 0 0
\(475\) −11.7757 −0.540308
\(476\) 0 0
\(477\) −32.6115 −1.49318
\(478\) 0 0
\(479\) 37.5331 1.71493 0.857464 0.514543i \(-0.172038\pi\)
0.857464 + 0.514543i \(0.172038\pi\)
\(480\) 0 0
\(481\) −8.53943 −0.389365
\(482\) 0 0
\(483\) 1.57089 0.0714782
\(484\) 0 0
\(485\) 0.261370 0.0118682
\(486\) 0 0
\(487\) 4.33788 0.196568 0.0982840 0.995158i \(-0.468665\pi\)
0.0982840 + 0.995158i \(0.468665\pi\)
\(488\) 0 0
\(489\) −9.97221 −0.450959
\(490\) 0 0
\(491\) −32.0024 −1.44425 −0.722124 0.691764i \(-0.756834\pi\)
−0.722124 + 0.691764i \(0.756834\pi\)
\(492\) 0 0
\(493\) −1.29666 −0.0583988
\(494\) 0 0
\(495\) 5.99562 0.269483
\(496\) 0 0
\(497\) 3.49726 0.156874
\(498\) 0 0
\(499\) −3.66389 −0.164018 −0.0820091 0.996632i \(-0.526134\pi\)
−0.0820091 + 0.996632i \(0.526134\pi\)
\(500\) 0 0
\(501\) −3.78158 −0.168949
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −4.45254 −0.198135
\(506\) 0 0
\(507\) 6.91606 0.307153
\(508\) 0 0
\(509\) −34.8313 −1.54387 −0.771936 0.635700i \(-0.780711\pi\)
−0.771936 + 0.635700i \(0.780711\pi\)
\(510\) 0 0
\(511\) −0.854490 −0.0378004
\(512\) 0 0
\(513\) 10.7880 0.476304
\(514\) 0 0
\(515\) 0.733263 0.0323114
\(516\) 0 0
\(517\) −30.0736 −1.32264
\(518\) 0 0
\(519\) −3.26894 −0.143491
\(520\) 0 0
\(521\) −24.0129 −1.05202 −0.526012 0.850477i \(-0.676313\pi\)
−0.526012 + 0.850477i \(0.676313\pi\)
\(522\) 0 0
\(523\) −29.8701 −1.30613 −0.653064 0.757303i \(-0.726517\pi\)
−0.653064 + 0.757303i \(0.726517\pi\)
\(524\) 0 0
\(525\) −0.967935 −0.0422441
\(526\) 0 0
\(527\) 1.15399 0.0502687
\(528\) 0 0
\(529\) 19.2319 0.836170
\(530\) 0 0
\(531\) 24.7402 1.07363
\(532\) 0 0
\(533\) −7.06690 −0.306101
\(534\) 0 0
\(535\) 2.54244 0.109919
\(536\) 0 0
\(537\) −4.92960 −0.212728
\(538\) 0 0
\(539\) 16.0785 0.692550
\(540\) 0 0
\(541\) 11.2005 0.481547 0.240774 0.970581i \(-0.422599\pi\)
0.240774 + 0.970581i \(0.422599\pi\)
\(542\) 0 0
\(543\) 5.44785 0.233790
\(544\) 0 0
\(545\) −4.05941 −0.173886
\(546\) 0 0
\(547\) 24.3236 1.04000 0.520001 0.854166i \(-0.325932\pi\)
0.520001 + 0.854166i \(0.325932\pi\)
\(548\) 0 0
\(549\) −25.6183 −1.09336
\(550\) 0 0
\(551\) −23.2052 −0.988575
\(552\) 0 0
\(553\) 0.921870 0.0392019
\(554\) 0 0
\(555\) 3.54718 0.150569
\(556\) 0 0
\(557\) −15.5932 −0.660705 −0.330353 0.943858i \(-0.607168\pi\)
−0.330353 + 0.943858i \(0.607168\pi\)
\(558\) 0 0
\(559\) −13.2587 −0.560782
\(560\) 0 0
\(561\) 0.253659 0.0107095
\(562\) 0 0
\(563\) 2.04046 0.0859952 0.0429976 0.999075i \(-0.486309\pi\)
0.0429976 + 0.999075i \(0.486309\pi\)
\(564\) 0 0
\(565\) 14.4522 0.608007
\(566\) 0 0
\(567\) −1.93596 −0.0813025
\(568\) 0 0
\(569\) 29.7908 1.24890 0.624448 0.781067i \(-0.285324\pi\)
0.624448 + 0.781067i \(0.285324\pi\)
\(570\) 0 0
\(571\) 1.67514 0.0701025 0.0350513 0.999386i \(-0.488841\pi\)
0.0350513 + 0.999386i \(0.488841\pi\)
\(572\) 0 0
\(573\) −1.48772 −0.0621504
\(574\) 0 0
\(575\) −26.0220 −1.08519
\(576\) 0 0
\(577\) 3.76042 0.156548 0.0782742 0.996932i \(-0.475059\pi\)
0.0782742 + 0.996932i \(0.475059\pi\)
\(578\) 0 0
\(579\) 12.1283 0.504035
\(580\) 0 0
\(581\) −1.06470 −0.0441712
\(582\) 0 0
\(583\) −29.7689 −1.23290
\(584\) 0 0
\(585\) −4.05369 −0.167600
\(586\) 0 0
\(587\) 25.9499 1.07107 0.535533 0.844514i \(-0.320111\pi\)
0.535533 + 0.844514i \(0.320111\pi\)
\(588\) 0 0
\(589\) 20.6519 0.850949
\(590\) 0 0
\(591\) 7.64960 0.314663
\(592\) 0 0
\(593\) 9.45049 0.388085 0.194043 0.980993i \(-0.437840\pi\)
0.194043 + 0.980993i \(0.437840\pi\)
\(594\) 0 0
\(595\) −0.0601384 −0.00246543
\(596\) 0 0
\(597\) 11.1247 0.455304
\(598\) 0 0
\(599\) −30.7653 −1.25703 −0.628517 0.777796i \(-0.716338\pi\)
−0.628517 + 0.777796i \(0.716338\pi\)
\(600\) 0 0
\(601\) 9.70280 0.395785 0.197893 0.980224i \(-0.436590\pi\)
0.197893 + 0.980224i \(0.436590\pi\)
\(602\) 0 0
\(603\) −16.8987 −0.688169
\(604\) 0 0
\(605\) −5.50368 −0.223757
\(606\) 0 0
\(607\) 3.66881 0.148912 0.0744562 0.997224i \(-0.476278\pi\)
0.0744562 + 0.997224i \(0.476278\pi\)
\(608\) 0 0
\(609\) −1.90741 −0.0772920
\(610\) 0 0
\(611\) 20.3330 0.822587
\(612\) 0 0
\(613\) 44.3930 1.79302 0.896509 0.443025i \(-0.146095\pi\)
0.896509 + 0.443025i \(0.146095\pi\)
\(614\) 0 0
\(615\) 2.93550 0.118371
\(616\) 0 0
\(617\) 39.0543 1.57227 0.786134 0.618057i \(-0.212080\pi\)
0.786134 + 0.618057i \(0.212080\pi\)
\(618\) 0 0
\(619\) −24.2073 −0.972973 −0.486487 0.873688i \(-0.661722\pi\)
−0.486487 + 0.873688i \(0.661722\pi\)
\(620\) 0 0
\(621\) 23.8393 0.956640
\(622\) 0 0
\(623\) 4.87790 0.195429
\(624\) 0 0
\(625\) 11.0551 0.442202
\(626\) 0 0
\(627\) 4.53949 0.181290
\(628\) 0 0
\(629\) −0.886238 −0.0353366
\(630\) 0 0
\(631\) −12.3183 −0.490385 −0.245193 0.969474i \(-0.578851\pi\)
−0.245193 + 0.969474i \(0.578851\pi\)
\(632\) 0 0
\(633\) 5.35332 0.212775
\(634\) 0 0
\(635\) 2.67988 0.106348
\(636\) 0 0
\(637\) −10.8708 −0.430717
\(638\) 0 0
\(639\) 24.4652 0.967828
\(640\) 0 0
\(641\) −16.9113 −0.667956 −0.333978 0.942581i \(-0.608391\pi\)
−0.333978 + 0.942581i \(0.608391\pi\)
\(642\) 0 0
\(643\) −26.1189 −1.03003 −0.515015 0.857181i \(-0.672213\pi\)
−0.515015 + 0.857181i \(0.672213\pi\)
\(644\) 0 0
\(645\) 5.50749 0.216857
\(646\) 0 0
\(647\) −8.24455 −0.324127 −0.162063 0.986780i \(-0.551815\pi\)
−0.162063 + 0.986780i \(0.551815\pi\)
\(648\) 0 0
\(649\) 22.5837 0.886486
\(650\) 0 0
\(651\) 1.69754 0.0665317
\(652\) 0 0
\(653\) −39.8697 −1.56022 −0.780110 0.625642i \(-0.784837\pi\)
−0.780110 + 0.625642i \(0.784837\pi\)
\(654\) 0 0
\(655\) −9.66382 −0.377597
\(656\) 0 0
\(657\) −5.97761 −0.233209
\(658\) 0 0
\(659\) −43.2594 −1.68515 −0.842573 0.538582i \(-0.818960\pi\)
−0.842573 + 0.538582i \(0.818960\pi\)
\(660\) 0 0
\(661\) −36.2663 −1.41059 −0.705297 0.708912i \(-0.749187\pi\)
−0.705297 + 0.708912i \(0.749187\pi\)
\(662\) 0 0
\(663\) −0.171501 −0.00666054
\(664\) 0 0
\(665\) −1.07624 −0.0417348
\(666\) 0 0
\(667\) −51.2787 −1.98552
\(668\) 0 0
\(669\) 3.74212 0.144679
\(670\) 0 0
\(671\) −23.3853 −0.902779
\(672\) 0 0
\(673\) 6.83729 0.263558 0.131779 0.991279i \(-0.457931\pi\)
0.131779 + 0.991279i \(0.457931\pi\)
\(674\) 0 0
\(675\) −14.6890 −0.565381
\(676\) 0 0
\(677\) −28.3308 −1.08884 −0.544420 0.838812i \(-0.683250\pi\)
−0.544420 + 0.838812i \(0.683250\pi\)
\(678\) 0 0
\(679\) −0.0960593 −0.00368642
\(680\) 0 0
\(681\) 8.60057 0.329575
\(682\) 0 0
\(683\) 22.3969 0.856995 0.428497 0.903543i \(-0.359043\pi\)
0.428497 + 0.903543i \(0.359043\pi\)
\(684\) 0 0
\(685\) −18.7758 −0.717387
\(686\) 0 0
\(687\) −0.542975 −0.0207158
\(688\) 0 0
\(689\) 20.1270 0.766777
\(690\) 0 0
\(691\) −8.86769 −0.337343 −0.168671 0.985672i \(-0.553948\pi\)
−0.168671 + 0.985672i \(0.553948\pi\)
\(692\) 0 0
\(693\) −2.20352 −0.0837049
\(694\) 0 0
\(695\) −16.4864 −0.625363
\(696\) 0 0
\(697\) −0.733416 −0.0277801
\(698\) 0 0
\(699\) −7.27478 −0.275158
\(700\) 0 0
\(701\) −28.7295 −1.08510 −0.542550 0.840024i \(-0.682541\pi\)
−0.542550 + 0.840024i \(0.682541\pi\)
\(702\) 0 0
\(703\) −15.8602 −0.598178
\(704\) 0 0
\(705\) −8.44609 −0.318098
\(706\) 0 0
\(707\) 1.63641 0.0615434
\(708\) 0 0
\(709\) −16.2925 −0.611878 −0.305939 0.952051i \(-0.598970\pi\)
−0.305939 + 0.952051i \(0.598970\pi\)
\(710\) 0 0
\(711\) 6.44896 0.241855
\(712\) 0 0
\(713\) 45.6365 1.70910
\(714\) 0 0
\(715\) −3.70034 −0.138385
\(716\) 0 0
\(717\) 15.9876 0.597066
\(718\) 0 0
\(719\) −8.67655 −0.323581 −0.161790 0.986825i \(-0.551727\pi\)
−0.161790 + 0.986825i \(0.551727\pi\)
\(720\) 0 0
\(721\) −0.269490 −0.0100363
\(722\) 0 0
\(723\) 8.77032 0.326172
\(724\) 0 0
\(725\) 31.5963 1.17346
\(726\) 0 0
\(727\) 38.9559 1.44479 0.722396 0.691479i \(-0.243041\pi\)
0.722396 + 0.691479i \(0.243041\pi\)
\(728\) 0 0
\(729\) −6.28932 −0.232938
\(730\) 0 0
\(731\) −1.37601 −0.0508935
\(732\) 0 0
\(733\) −0.822898 −0.0303944 −0.0151972 0.999885i \(-0.504838\pi\)
−0.0151972 + 0.999885i \(0.504838\pi\)
\(734\) 0 0
\(735\) 4.51560 0.166560
\(736\) 0 0
\(737\) −15.4257 −0.568213
\(738\) 0 0
\(739\) 37.6813 1.38613 0.693065 0.720875i \(-0.256260\pi\)
0.693065 + 0.720875i \(0.256260\pi\)
\(740\) 0 0
\(741\) −3.06919 −0.112749
\(742\) 0 0
\(743\) −35.6314 −1.30719 −0.653594 0.756845i \(-0.726740\pi\)
−0.653594 + 0.756845i \(0.726740\pi\)
\(744\) 0 0
\(745\) −10.8916 −0.399039
\(746\) 0 0
\(747\) −7.44814 −0.272513
\(748\) 0 0
\(749\) −0.934403 −0.0341423
\(750\) 0 0
\(751\) −16.1886 −0.590731 −0.295366 0.955384i \(-0.595441\pi\)
−0.295366 + 0.955384i \(0.595441\pi\)
\(752\) 0 0
\(753\) 4.43877 0.161758
\(754\) 0 0
\(755\) 0.258393 0.00940388
\(756\) 0 0
\(757\) 33.2456 1.20833 0.604165 0.796859i \(-0.293507\pi\)
0.604165 + 0.796859i \(0.293507\pi\)
\(758\) 0 0
\(759\) 10.0313 0.364114
\(760\) 0 0
\(761\) −54.0682 −1.95997 −0.979985 0.199074i \(-0.936207\pi\)
−0.979985 + 0.199074i \(0.936207\pi\)
\(762\) 0 0
\(763\) 1.49192 0.0540112
\(764\) 0 0
\(765\) −0.420699 −0.0152104
\(766\) 0 0
\(767\) −15.2690 −0.551332
\(768\) 0 0
\(769\) 4.35847 0.157171 0.0785853 0.996907i \(-0.474960\pi\)
0.0785853 + 0.996907i \(0.474960\pi\)
\(770\) 0 0
\(771\) 17.8603 0.643223
\(772\) 0 0
\(773\) −43.6469 −1.56987 −0.784936 0.619577i \(-0.787304\pi\)
−0.784936 + 0.619577i \(0.787304\pi\)
\(774\) 0 0
\(775\) −28.1198 −1.01009
\(776\) 0 0
\(777\) −1.30366 −0.0467687
\(778\) 0 0
\(779\) −13.1253 −0.470261
\(780\) 0 0
\(781\) 22.3326 0.799124
\(782\) 0 0
\(783\) −28.9461 −1.03445
\(784\) 0 0
\(785\) 3.75409 0.133989
\(786\) 0 0
\(787\) −39.1261 −1.39469 −0.697347 0.716734i \(-0.745636\pi\)
−0.697347 + 0.716734i \(0.745636\pi\)
\(788\) 0 0
\(789\) −13.5284 −0.481624
\(790\) 0 0
\(791\) −5.31149 −0.188855
\(792\) 0 0
\(793\) 15.8110 0.561464
\(794\) 0 0
\(795\) −8.36050 −0.296516
\(796\) 0 0
\(797\) 14.4918 0.513326 0.256663 0.966501i \(-0.417377\pi\)
0.256663 + 0.966501i \(0.417377\pi\)
\(798\) 0 0
\(799\) 2.11020 0.0746535
\(800\) 0 0
\(801\) 34.1235 1.20569
\(802\) 0 0
\(803\) −5.45656 −0.192558
\(804\) 0 0
\(805\) −2.37827 −0.0838230
\(806\) 0 0
\(807\) −14.9271 −0.525458
\(808\) 0 0
\(809\) 6.26269 0.220184 0.110092 0.993921i \(-0.464885\pi\)
0.110092 + 0.993921i \(0.464885\pi\)
\(810\) 0 0
\(811\) 11.8822 0.417240 0.208620 0.977997i \(-0.433103\pi\)
0.208620 + 0.977997i \(0.433103\pi\)
\(812\) 0 0
\(813\) −5.85071 −0.205193
\(814\) 0 0
\(815\) 15.0975 0.528843
\(816\) 0 0
\(817\) −24.6252 −0.861525
\(818\) 0 0
\(819\) 1.48982 0.0520585
\(820\) 0 0
\(821\) −14.4622 −0.504735 −0.252367 0.967631i \(-0.581209\pi\)
−0.252367 + 0.967631i \(0.581209\pi\)
\(822\) 0 0
\(823\) −18.0941 −0.630719 −0.315360 0.948972i \(-0.602125\pi\)
−0.315360 + 0.948972i \(0.602125\pi\)
\(824\) 0 0
\(825\) −6.18099 −0.215194
\(826\) 0 0
\(827\) 6.61196 0.229920 0.114960 0.993370i \(-0.463326\pi\)
0.114960 + 0.993370i \(0.463326\pi\)
\(828\) 0 0
\(829\) −25.1172 −0.872356 −0.436178 0.899860i \(-0.643668\pi\)
−0.436178 + 0.899860i \(0.643668\pi\)
\(830\) 0 0
\(831\) −12.9577 −0.449499
\(832\) 0 0
\(833\) −1.12819 −0.0390896
\(834\) 0 0
\(835\) 5.72516 0.198127
\(836\) 0 0
\(837\) 25.7612 0.890437
\(838\) 0 0
\(839\) 7.13587 0.246358 0.123179 0.992384i \(-0.460691\pi\)
0.123179 + 0.992384i \(0.460691\pi\)
\(840\) 0 0
\(841\) 33.2634 1.14701
\(842\) 0 0
\(843\) −10.0684 −0.346776
\(844\) 0 0
\(845\) −10.4706 −0.360200
\(846\) 0 0
\(847\) 2.02272 0.0695016
\(848\) 0 0
\(849\) 14.2785 0.490036
\(850\) 0 0
\(851\) −35.0477 −1.20142
\(852\) 0 0
\(853\) −10.1428 −0.347281 −0.173641 0.984809i \(-0.555553\pi\)
−0.173641 + 0.984809i \(0.555553\pi\)
\(854\) 0 0
\(855\) −7.52887 −0.257482
\(856\) 0 0
\(857\) 33.1710 1.13310 0.566550 0.824027i \(-0.308278\pi\)
0.566550 + 0.824027i \(0.308278\pi\)
\(858\) 0 0
\(859\) 15.8176 0.539691 0.269845 0.962904i \(-0.413027\pi\)
0.269845 + 0.962904i \(0.413027\pi\)
\(860\) 0 0
\(861\) −1.07886 −0.0367675
\(862\) 0 0
\(863\) −17.9450 −0.610856 −0.305428 0.952215i \(-0.598800\pi\)
−0.305428 + 0.952215i \(0.598800\pi\)
\(864\) 0 0
\(865\) 4.94904 0.168272
\(866\) 0 0
\(867\) 11.1873 0.379939
\(868\) 0 0
\(869\) 5.88683 0.199697
\(870\) 0 0
\(871\) 10.4294 0.353388
\(872\) 0 0
\(873\) −0.671985 −0.0227432
\(874\) 0 0
\(875\) 3.29524 0.111400
\(876\) 0 0
\(877\) 20.5719 0.694664 0.347332 0.937742i \(-0.387088\pi\)
0.347332 + 0.937742i \(0.387088\pi\)
\(878\) 0 0
\(879\) −6.32160 −0.213222
\(880\) 0 0
\(881\) −19.5457 −0.658510 −0.329255 0.944241i \(-0.606798\pi\)
−0.329255 + 0.944241i \(0.606798\pi\)
\(882\) 0 0
\(883\) 21.5650 0.725719 0.362859 0.931844i \(-0.381800\pi\)
0.362859 + 0.931844i \(0.381800\pi\)
\(884\) 0 0
\(885\) 6.34256 0.213203
\(886\) 0 0
\(887\) 50.5182 1.69624 0.848118 0.529808i \(-0.177736\pi\)
0.848118 + 0.529808i \(0.177736\pi\)
\(888\) 0 0
\(889\) −0.984914 −0.0330329
\(890\) 0 0
\(891\) −12.3625 −0.414160
\(892\) 0 0
\(893\) 37.7643 1.26373
\(894\) 0 0
\(895\) 7.46321 0.249468
\(896\) 0 0
\(897\) −6.78227 −0.226453
\(898\) 0 0
\(899\) −55.4126 −1.84811
\(900\) 0 0
\(901\) 2.08881 0.0695885
\(902\) 0 0
\(903\) −2.02412 −0.0673586
\(904\) 0 0
\(905\) −8.24781 −0.274167
\(906\) 0 0
\(907\) 18.9017 0.627622 0.313811 0.949486i \(-0.398394\pi\)
0.313811 + 0.949486i \(0.398394\pi\)
\(908\) 0 0
\(909\) 11.4475 0.379690
\(910\) 0 0
\(911\) 52.1637 1.72826 0.864130 0.503268i \(-0.167869\pi\)
0.864130 + 0.503268i \(0.167869\pi\)
\(912\) 0 0
\(913\) −6.79891 −0.225011
\(914\) 0 0
\(915\) −6.56769 −0.217121
\(916\) 0 0
\(917\) 3.55166 0.117286
\(918\) 0 0
\(919\) 26.7580 0.882665 0.441332 0.897344i \(-0.354506\pi\)
0.441332 + 0.897344i \(0.354506\pi\)
\(920\) 0 0
\(921\) −5.13079 −0.169065
\(922\) 0 0
\(923\) −15.0993 −0.496999
\(924\) 0 0
\(925\) 21.5953 0.710048
\(926\) 0 0
\(927\) −1.88523 −0.0619190
\(928\) 0 0
\(929\) 31.6778 1.03931 0.519657 0.854375i \(-0.326060\pi\)
0.519657 + 0.854375i \(0.326060\pi\)
\(930\) 0 0
\(931\) −20.1902 −0.661708
\(932\) 0 0
\(933\) −22.1133 −0.723958
\(934\) 0 0
\(935\) −0.384028 −0.0125591
\(936\) 0 0
\(937\) −35.1014 −1.14671 −0.573356 0.819307i \(-0.694359\pi\)
−0.573356 + 0.819307i \(0.694359\pi\)
\(938\) 0 0
\(939\) 4.08590 0.133338
\(940\) 0 0
\(941\) 27.2279 0.887604 0.443802 0.896125i \(-0.353629\pi\)
0.443802 + 0.896125i \(0.353629\pi\)
\(942\) 0 0
\(943\) −29.0041 −0.944503
\(944\) 0 0
\(945\) −1.34250 −0.0436715
\(946\) 0 0
\(947\) 24.6119 0.799779 0.399890 0.916563i \(-0.369048\pi\)
0.399890 + 0.916563i \(0.369048\pi\)
\(948\) 0 0
\(949\) 3.68922 0.119757
\(950\) 0 0
\(951\) 7.56890 0.245438
\(952\) 0 0
\(953\) 3.01549 0.0976813 0.0488407 0.998807i \(-0.484447\pi\)
0.0488407 + 0.998807i \(0.484447\pi\)
\(954\) 0 0
\(955\) 2.25235 0.0728842
\(956\) 0 0
\(957\) −12.1802 −0.393730
\(958\) 0 0
\(959\) 6.90052 0.222829
\(960\) 0 0
\(961\) 18.3156 0.590825
\(962\) 0 0
\(963\) −6.53664 −0.210640
\(964\) 0 0
\(965\) −18.3617 −0.591085
\(966\) 0 0
\(967\) −6.03746 −0.194152 −0.0970758 0.995277i \(-0.530949\pi\)
−0.0970758 + 0.995277i \(0.530949\pi\)
\(968\) 0 0
\(969\) −0.318526 −0.0102325
\(970\) 0 0
\(971\) 8.23721 0.264345 0.132172 0.991227i \(-0.457805\pi\)
0.132172 + 0.991227i \(0.457805\pi\)
\(972\) 0 0
\(973\) 6.05910 0.194246
\(974\) 0 0
\(975\) 4.17902 0.133836
\(976\) 0 0
\(977\) −36.4331 −1.16560 −0.582799 0.812617i \(-0.698042\pi\)
−0.582799 + 0.812617i \(0.698042\pi\)
\(978\) 0 0
\(979\) 31.1491 0.995528
\(980\) 0 0
\(981\) 10.4368 0.333221
\(982\) 0 0
\(983\) −16.4411 −0.524391 −0.262195 0.965015i \(-0.584447\pi\)
−0.262195 + 0.965015i \(0.584447\pi\)
\(984\) 0 0
\(985\) −11.5812 −0.369007
\(986\) 0 0
\(987\) 3.10412 0.0988054
\(988\) 0 0
\(989\) −54.4165 −1.73034
\(990\) 0 0
\(991\) −12.0291 −0.382118 −0.191059 0.981579i \(-0.561192\pi\)
−0.191059 + 0.981579i \(0.561192\pi\)
\(992\) 0 0
\(993\) −2.17381 −0.0689837
\(994\) 0 0
\(995\) −16.8423 −0.533937
\(996\) 0 0
\(997\) 10.9894 0.348037 0.174019 0.984742i \(-0.444325\pi\)
0.174019 + 0.984742i \(0.444325\pi\)
\(998\) 0 0
\(999\) −19.7839 −0.625936
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 \(a_p\))