Properties

Label 8008.2.a.p.1.6
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.536705\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.536705 q^{3} -3.30011 q^{5} -1.00000 q^{7} -2.71195 q^{9} +O(q^{10})\) \(q+0.536705 q^{3} -3.30011 q^{5} -1.00000 q^{7} -2.71195 q^{9} +1.00000 q^{11} +1.00000 q^{13} -1.77118 q^{15} +3.13193 q^{17} -3.06031 q^{19} -0.536705 q^{21} +0.420528 q^{23} +5.89071 q^{25} -3.06563 q^{27} +0.161852 q^{29} +10.3651 q^{31} +0.536705 q^{33} +3.30011 q^{35} +4.54945 q^{37} +0.536705 q^{39} -9.30747 q^{41} +2.24787 q^{43} +8.94972 q^{45} +2.05740 q^{47} +1.00000 q^{49} +1.68092 q^{51} +8.66441 q^{53} -3.30011 q^{55} -1.64248 q^{57} +4.24396 q^{59} -6.87493 q^{61} +2.71195 q^{63} -3.30011 q^{65} +8.01827 q^{67} +0.225699 q^{69} -16.2909 q^{71} +4.62059 q^{73} +3.16157 q^{75} -1.00000 q^{77} -6.36899 q^{79} +6.49051 q^{81} +3.20265 q^{83} -10.3357 q^{85} +0.0868669 q^{87} +5.49762 q^{89} -1.00000 q^{91} +5.56299 q^{93} +10.0993 q^{95} +10.8560 q^{97} -2.71195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

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
\(3\) 0.536705 0.309867 0.154933 0.987925i \(-0.450484\pi\)
0.154933 + 0.987925i \(0.450484\pi\)
\(4\) 0 0
\(5\) −3.30011 −1.47585 −0.737926 0.674881i \(-0.764195\pi\)
−0.737926 + 0.674881i \(0.764195\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.71195 −0.903983
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −1.77118 −0.457317
\(16\) 0 0
\(17\) 3.13193 0.759605 0.379803 0.925068i \(-0.375992\pi\)
0.379803 + 0.925068i \(0.375992\pi\)
\(18\) 0 0
\(19\) −3.06031 −0.702082 −0.351041 0.936360i \(-0.614172\pi\)
−0.351041 + 0.936360i \(0.614172\pi\)
\(20\) 0 0
\(21\) −0.536705 −0.117119
\(22\) 0 0
\(23\) 0.420528 0.0876862 0.0438431 0.999038i \(-0.486040\pi\)
0.0438431 + 0.999038i \(0.486040\pi\)
\(24\) 0 0
\(25\) 5.89071 1.17814
\(26\) 0 0
\(27\) −3.06563 −0.589981
\(28\) 0 0
\(29\) 0.161852 0.0300552 0.0150276 0.999887i \(-0.495216\pi\)
0.0150276 + 0.999887i \(0.495216\pi\)
\(30\) 0 0
\(31\) 10.3651 1.86162 0.930812 0.365498i \(-0.119101\pi\)
0.930812 + 0.365498i \(0.119101\pi\)
\(32\) 0 0
\(33\) 0.536705 0.0934283
\(34\) 0 0
\(35\) 3.30011 0.557820
\(36\) 0 0
\(37\) 4.54945 0.747924 0.373962 0.927444i \(-0.377999\pi\)
0.373962 + 0.927444i \(0.377999\pi\)
\(38\) 0 0
\(39\) 0.536705 0.0859415
\(40\) 0 0
\(41\) −9.30747 −1.45358 −0.726792 0.686858i \(-0.758989\pi\)
−0.726792 + 0.686858i \(0.758989\pi\)
\(42\) 0 0
\(43\) 2.24787 0.342797 0.171398 0.985202i \(-0.445171\pi\)
0.171398 + 0.985202i \(0.445171\pi\)
\(44\) 0 0
\(45\) 8.94972 1.33415
\(46\) 0 0
\(47\) 2.05740 0.300102 0.150051 0.988678i \(-0.452056\pi\)
0.150051 + 0.988678i \(0.452056\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 1.68092 0.235376
\(52\) 0 0
\(53\) 8.66441 1.19015 0.595074 0.803671i \(-0.297123\pi\)
0.595074 + 0.803671i \(0.297123\pi\)
\(54\) 0 0
\(55\) −3.30011 −0.444986
\(56\) 0 0
\(57\) −1.64248 −0.217552
\(58\) 0 0
\(59\) 4.24396 0.552517 0.276258 0.961083i \(-0.410905\pi\)
0.276258 + 0.961083i \(0.410905\pi\)
\(60\) 0 0
\(61\) −6.87493 −0.880245 −0.440122 0.897938i \(-0.645065\pi\)
−0.440122 + 0.897938i \(0.645065\pi\)
\(62\) 0 0
\(63\) 2.71195 0.341673
\(64\) 0 0
\(65\) −3.30011 −0.409328
\(66\) 0 0
\(67\) 8.01827 0.979588 0.489794 0.871838i \(-0.337072\pi\)
0.489794 + 0.871838i \(0.337072\pi\)
\(68\) 0 0
\(69\) 0.225699 0.0271710
\(70\) 0 0
\(71\) −16.2909 −1.93337 −0.966686 0.255967i \(-0.917606\pi\)
−0.966686 + 0.255967i \(0.917606\pi\)
\(72\) 0 0
\(73\) 4.62059 0.540799 0.270399 0.962748i \(-0.412844\pi\)
0.270399 + 0.962748i \(0.412844\pi\)
\(74\) 0 0
\(75\) 3.16157 0.365067
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −6.36899 −0.716567 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(80\) 0 0
\(81\) 6.49051 0.721167
\(82\) 0 0
\(83\) 3.20265 0.351536 0.175768 0.984432i \(-0.443759\pi\)
0.175768 + 0.984432i \(0.443759\pi\)
\(84\) 0 0
\(85\) −10.3357 −1.12107
\(86\) 0 0
\(87\) 0.0868669 0.00931311
\(88\) 0 0
\(89\) 5.49762 0.582747 0.291373 0.956609i \(-0.405888\pi\)
0.291373 + 0.956609i \(0.405888\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 5.56299 0.576855
\(94\) 0 0
\(95\) 10.0993 1.03617
\(96\) 0 0
\(97\) 10.8560 1.10226 0.551128 0.834421i \(-0.314197\pi\)
0.551128 + 0.834421i \(0.314197\pi\)
\(98\) 0 0
\(99\) −2.71195 −0.272561
\(100\) 0 0
\(101\) 1.93119 0.192161 0.0960805 0.995374i \(-0.469369\pi\)
0.0960805 + 0.995374i \(0.469369\pi\)
\(102\) 0 0
\(103\) −10.6122 −1.04565 −0.522826 0.852439i \(-0.675122\pi\)
−0.522826 + 0.852439i \(0.675122\pi\)
\(104\) 0 0
\(105\) 1.77118 0.172850
\(106\) 0 0
\(107\) −13.0451 −1.26112 −0.630560 0.776141i \(-0.717175\pi\)
−0.630560 + 0.776141i \(0.717175\pi\)
\(108\) 0 0
\(109\) −19.3617 −1.85452 −0.927258 0.374423i \(-0.877841\pi\)
−0.927258 + 0.374423i \(0.877841\pi\)
\(110\) 0 0
\(111\) 2.44171 0.231757
\(112\) 0 0
\(113\) −12.5919 −1.18454 −0.592271 0.805739i \(-0.701769\pi\)
−0.592271 + 0.805739i \(0.701769\pi\)
\(114\) 0 0
\(115\) −1.38779 −0.129412
\(116\) 0 0
\(117\) −2.71195 −0.250720
\(118\) 0 0
\(119\) −3.13193 −0.287104
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −4.99536 −0.450417
\(124\) 0 0
\(125\) −2.93943 −0.262911
\(126\) 0 0
\(127\) 8.74259 0.775779 0.387890 0.921706i \(-0.373204\pi\)
0.387890 + 0.921706i \(0.373204\pi\)
\(128\) 0 0
\(129\) 1.20644 0.106221
\(130\) 0 0
\(131\) −14.9292 −1.30437 −0.652184 0.758061i \(-0.726147\pi\)
−0.652184 + 0.758061i \(0.726147\pi\)
\(132\) 0 0
\(133\) 3.06031 0.265362
\(134\) 0 0
\(135\) 10.1169 0.870725
\(136\) 0 0
\(137\) 5.27810 0.450939 0.225469 0.974250i \(-0.427608\pi\)
0.225469 + 0.974250i \(0.427608\pi\)
\(138\) 0 0
\(139\) −2.44425 −0.207318 −0.103659 0.994613i \(-0.533055\pi\)
−0.103659 + 0.994613i \(0.533055\pi\)
\(140\) 0 0
\(141\) 1.10421 0.0929917
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −0.534130 −0.0443571
\(146\) 0 0
\(147\) 0.536705 0.0442667
\(148\) 0 0
\(149\) 2.12900 0.174415 0.0872073 0.996190i \(-0.472206\pi\)
0.0872073 + 0.996190i \(0.472206\pi\)
\(150\) 0 0
\(151\) −11.4271 −0.929921 −0.464961 0.885331i \(-0.653931\pi\)
−0.464961 + 0.885331i \(0.653931\pi\)
\(152\) 0 0
\(153\) −8.49364 −0.686670
\(154\) 0 0
\(155\) −34.2059 −2.74748
\(156\) 0 0
\(157\) −3.35410 −0.267686 −0.133843 0.991003i \(-0.542732\pi\)
−0.133843 + 0.991003i \(0.542732\pi\)
\(158\) 0 0
\(159\) 4.65023 0.368787
\(160\) 0 0
\(161\) −0.420528 −0.0331423
\(162\) 0 0
\(163\) 9.25050 0.724555 0.362278 0.932070i \(-0.381999\pi\)
0.362278 + 0.932070i \(0.381999\pi\)
\(164\) 0 0
\(165\) −1.77118 −0.137886
\(166\) 0 0
\(167\) 1.03829 0.0803450 0.0401725 0.999193i \(-0.487209\pi\)
0.0401725 + 0.999193i \(0.487209\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 8.29939 0.634670
\(172\) 0 0
\(173\) 16.5134 1.25549 0.627744 0.778420i \(-0.283979\pi\)
0.627744 + 0.778420i \(0.283979\pi\)
\(174\) 0 0
\(175\) −5.89071 −0.445296
\(176\) 0 0
\(177\) 2.27775 0.171206
\(178\) 0 0
\(179\) −15.9904 −1.19518 −0.597589 0.801802i \(-0.703875\pi\)
−0.597589 + 0.801802i \(0.703875\pi\)
\(180\) 0 0
\(181\) −1.71442 −0.127432 −0.0637159 0.997968i \(-0.520295\pi\)
−0.0637159 + 0.997968i \(0.520295\pi\)
\(182\) 0 0
\(183\) −3.68981 −0.272758
\(184\) 0 0
\(185\) −15.0137 −1.10383
\(186\) 0 0
\(187\) 3.13193 0.229030
\(188\) 0 0
\(189\) 3.06563 0.222992
\(190\) 0 0
\(191\) −21.4362 −1.55107 −0.775536 0.631304i \(-0.782520\pi\)
−0.775536 + 0.631304i \(0.782520\pi\)
\(192\) 0 0
\(193\) −5.23599 −0.376895 −0.188447 0.982083i \(-0.560346\pi\)
−0.188447 + 0.982083i \(0.560346\pi\)
\(194\) 0 0
\(195\) −1.77118 −0.126837
\(196\) 0 0
\(197\) 3.58219 0.255221 0.127610 0.991824i \(-0.459269\pi\)
0.127610 + 0.991824i \(0.459269\pi\)
\(198\) 0 0
\(199\) −11.2294 −0.796029 −0.398015 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(200\) 0 0
\(201\) 4.30345 0.303542
\(202\) 0 0
\(203\) −0.161852 −0.0113598
\(204\) 0 0
\(205\) 30.7157 2.14528
\(206\) 0 0
\(207\) −1.14045 −0.0792668
\(208\) 0 0
\(209\) −3.06031 −0.211686
\(210\) 0 0
\(211\) 16.8551 1.16035 0.580175 0.814492i \(-0.302984\pi\)
0.580175 + 0.814492i \(0.302984\pi\)
\(212\) 0 0
\(213\) −8.74339 −0.599087
\(214\) 0 0
\(215\) −7.41821 −0.505918
\(216\) 0 0
\(217\) −10.3651 −0.703628
\(218\) 0 0
\(219\) 2.47989 0.167575
\(220\) 0 0
\(221\) 3.13193 0.210677
\(222\) 0 0
\(223\) −11.7717 −0.788291 −0.394146 0.919048i \(-0.628959\pi\)
−0.394146 + 0.919048i \(0.628959\pi\)
\(224\) 0 0
\(225\) −15.9753 −1.06502
\(226\) 0 0
\(227\) 7.66662 0.508851 0.254426 0.967092i \(-0.418114\pi\)
0.254426 + 0.967092i \(0.418114\pi\)
\(228\) 0 0
\(229\) 3.20926 0.212074 0.106037 0.994362i \(-0.466184\pi\)
0.106037 + 0.994362i \(0.466184\pi\)
\(230\) 0 0
\(231\) −0.536705 −0.0353126
\(232\) 0 0
\(233\) 4.51393 0.295717 0.147859 0.989008i \(-0.452762\pi\)
0.147859 + 0.989008i \(0.452762\pi\)
\(234\) 0 0
\(235\) −6.78963 −0.442907
\(236\) 0 0
\(237\) −3.41827 −0.222040
\(238\) 0 0
\(239\) −2.95772 −0.191319 −0.0956595 0.995414i \(-0.530496\pi\)
−0.0956595 + 0.995414i \(0.530496\pi\)
\(240\) 0 0
\(241\) 0.904795 0.0582830 0.0291415 0.999575i \(-0.490723\pi\)
0.0291415 + 0.999575i \(0.490723\pi\)
\(242\) 0 0
\(243\) 12.6804 0.813446
\(244\) 0 0
\(245\) −3.30011 −0.210836
\(246\) 0 0
\(247\) −3.06031 −0.194723
\(248\) 0 0
\(249\) 1.71887 0.108929
\(250\) 0 0
\(251\) −8.70496 −0.549452 −0.274726 0.961522i \(-0.588587\pi\)
−0.274726 + 0.961522i \(0.588587\pi\)
\(252\) 0 0
\(253\) 0.420528 0.0264384
\(254\) 0 0
\(255\) −5.54723 −0.347381
\(256\) 0 0
\(257\) −15.4913 −0.966324 −0.483162 0.875531i \(-0.660512\pi\)
−0.483162 + 0.875531i \(0.660512\pi\)
\(258\) 0 0
\(259\) −4.54945 −0.282689
\(260\) 0 0
\(261\) −0.438935 −0.0271694
\(262\) 0 0
\(263\) −14.0389 −0.865674 −0.432837 0.901472i \(-0.642487\pi\)
−0.432837 + 0.901472i \(0.642487\pi\)
\(264\) 0 0
\(265\) −28.5935 −1.75648
\(266\) 0 0
\(267\) 2.95060 0.180574
\(268\) 0 0
\(269\) −10.8948 −0.664265 −0.332133 0.943233i \(-0.607768\pi\)
−0.332133 + 0.943233i \(0.607768\pi\)
\(270\) 0 0
\(271\) −13.7704 −0.836491 −0.418246 0.908334i \(-0.637355\pi\)
−0.418246 + 0.908334i \(0.637355\pi\)
\(272\) 0 0
\(273\) −0.536705 −0.0324828
\(274\) 0 0
\(275\) 5.89071 0.355223
\(276\) 0 0
\(277\) −26.8078 −1.61072 −0.805361 0.592785i \(-0.798029\pi\)
−0.805361 + 0.592785i \(0.798029\pi\)
\(278\) 0 0
\(279\) −28.1096 −1.68288
\(280\) 0 0
\(281\) −4.68324 −0.279379 −0.139689 0.990195i \(-0.544610\pi\)
−0.139689 + 0.990195i \(0.544610\pi\)
\(282\) 0 0
\(283\) 17.5920 1.04573 0.522867 0.852415i \(-0.324863\pi\)
0.522867 + 0.852415i \(0.324863\pi\)
\(284\) 0 0
\(285\) 5.42036 0.321075
\(286\) 0 0
\(287\) 9.30747 0.549403
\(288\) 0 0
\(289\) −7.19099 −0.423000
\(290\) 0 0
\(291\) 5.82645 0.341552
\(292\) 0 0
\(293\) −12.2243 −0.714151 −0.357076 0.934075i \(-0.616226\pi\)
−0.357076 + 0.934075i \(0.616226\pi\)
\(294\) 0 0
\(295\) −14.0055 −0.815433
\(296\) 0 0
\(297\) −3.06563 −0.177886
\(298\) 0 0
\(299\) 0.420528 0.0243198
\(300\) 0 0
\(301\) −2.24787 −0.129565
\(302\) 0 0
\(303\) 1.03648 0.0595443
\(304\) 0 0
\(305\) 22.6880 1.29911
\(306\) 0 0
\(307\) 11.8725 0.677602 0.338801 0.940858i \(-0.389979\pi\)
0.338801 + 0.940858i \(0.389979\pi\)
\(308\) 0 0
\(309\) −5.69562 −0.324013
\(310\) 0 0
\(311\) 15.2113 0.862552 0.431276 0.902220i \(-0.358064\pi\)
0.431276 + 0.902220i \(0.358064\pi\)
\(312\) 0 0
\(313\) 5.34839 0.302309 0.151155 0.988510i \(-0.451701\pi\)
0.151155 + 0.988510i \(0.451701\pi\)
\(314\) 0 0
\(315\) −8.94972 −0.504260
\(316\) 0 0
\(317\) −1.40846 −0.0791071 −0.0395535 0.999217i \(-0.512594\pi\)
−0.0395535 + 0.999217i \(0.512594\pi\)
\(318\) 0 0
\(319\) 0.161852 0.00906199
\(320\) 0 0
\(321\) −7.00138 −0.390779
\(322\) 0 0
\(323\) −9.58467 −0.533306
\(324\) 0 0
\(325\) 5.89071 0.326758
\(326\) 0 0
\(327\) −10.3915 −0.574653
\(328\) 0 0
\(329\) −2.05740 −0.113428
\(330\) 0 0
\(331\) 19.2286 1.05690 0.528451 0.848964i \(-0.322773\pi\)
0.528451 + 0.848964i \(0.322773\pi\)
\(332\) 0 0
\(333\) −12.3379 −0.676111
\(334\) 0 0
\(335\) −26.4612 −1.44573
\(336\) 0 0
\(337\) −1.70454 −0.0928523 −0.0464262 0.998922i \(-0.514783\pi\)
−0.0464262 + 0.998922i \(0.514783\pi\)
\(338\) 0 0
\(339\) −6.75811 −0.367050
\(340\) 0 0
\(341\) 10.3651 0.561301
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −0.744832 −0.0401004
\(346\) 0 0
\(347\) 1.17222 0.0629282 0.0314641 0.999505i \(-0.489983\pi\)
0.0314641 + 0.999505i \(0.489983\pi\)
\(348\) 0 0
\(349\) −4.55082 −0.243600 −0.121800 0.992555i \(-0.538867\pi\)
−0.121800 + 0.992555i \(0.538867\pi\)
\(350\) 0 0
\(351\) −3.06563 −0.163631
\(352\) 0 0
\(353\) −21.2153 −1.12918 −0.564589 0.825372i \(-0.690965\pi\)
−0.564589 + 0.825372i \(0.690965\pi\)
\(354\) 0 0
\(355\) 53.7616 2.85337
\(356\) 0 0
\(357\) −1.68092 −0.0889639
\(358\) 0 0
\(359\) −0.225905 −0.0119228 −0.00596140 0.999982i \(-0.501898\pi\)
−0.00596140 + 0.999982i \(0.501898\pi\)
\(360\) 0 0
\(361\) −9.63453 −0.507080
\(362\) 0 0
\(363\) 0.536705 0.0281697
\(364\) 0 0
\(365\) −15.2484 −0.798140
\(366\) 0 0
\(367\) −10.6102 −0.553845 −0.276923 0.960892i \(-0.589315\pi\)
−0.276923 + 0.960892i \(0.589315\pi\)
\(368\) 0 0
\(369\) 25.2414 1.31401
\(370\) 0 0
\(371\) −8.66441 −0.449834
\(372\) 0 0
\(373\) −30.4566 −1.57698 −0.788492 0.615046i \(-0.789138\pi\)
−0.788492 + 0.615046i \(0.789138\pi\)
\(374\) 0 0
\(375\) −1.57761 −0.0814673
\(376\) 0 0
\(377\) 0.161852 0.00833582
\(378\) 0 0
\(379\) 0.665050 0.0341613 0.0170807 0.999854i \(-0.494563\pi\)
0.0170807 + 0.999854i \(0.494563\pi\)
\(380\) 0 0
\(381\) 4.69219 0.240388
\(382\) 0 0
\(383\) 4.68444 0.239364 0.119682 0.992812i \(-0.461813\pi\)
0.119682 + 0.992812i \(0.461813\pi\)
\(384\) 0 0
\(385\) 3.30011 0.168189
\(386\) 0 0
\(387\) −6.09611 −0.309882
\(388\) 0 0
\(389\) −18.8620 −0.956342 −0.478171 0.878267i \(-0.658700\pi\)
−0.478171 + 0.878267i \(0.658700\pi\)
\(390\) 0 0
\(391\) 1.31707 0.0666069
\(392\) 0 0
\(393\) −8.01256 −0.404180
\(394\) 0 0
\(395\) 21.0183 1.05755
\(396\) 0 0
\(397\) −38.5673 −1.93564 −0.967818 0.251653i \(-0.919026\pi\)
−0.967818 + 0.251653i \(0.919026\pi\)
\(398\) 0 0
\(399\) 1.64248 0.0822269
\(400\) 0 0
\(401\) 29.2031 1.45833 0.729165 0.684337i \(-0.239908\pi\)
0.729165 + 0.684337i \(0.239908\pi\)
\(402\) 0 0
\(403\) 10.3651 0.516322
\(404\) 0 0
\(405\) −21.4194 −1.06434
\(406\) 0 0
\(407\) 4.54945 0.225508
\(408\) 0 0
\(409\) −29.5897 −1.46312 −0.731559 0.681778i \(-0.761207\pi\)
−0.731559 + 0.681778i \(0.761207\pi\)
\(410\) 0 0
\(411\) 2.83278 0.139731
\(412\) 0 0
\(413\) −4.24396 −0.208832
\(414\) 0 0
\(415\) −10.5691 −0.518815
\(416\) 0 0
\(417\) −1.31184 −0.0642410
\(418\) 0 0
\(419\) 6.03316 0.294739 0.147370 0.989081i \(-0.452919\pi\)
0.147370 + 0.989081i \(0.452919\pi\)
\(420\) 0 0
\(421\) −14.1980 −0.691969 −0.345985 0.938240i \(-0.612455\pi\)
−0.345985 + 0.938240i \(0.612455\pi\)
\(422\) 0 0
\(423\) −5.57956 −0.271287
\(424\) 0 0
\(425\) 18.4493 0.894923
\(426\) 0 0
\(427\) 6.87493 0.332701
\(428\) 0 0
\(429\) 0.536705 0.0259123
\(430\) 0 0
\(431\) −8.47227 −0.408095 −0.204048 0.978961i \(-0.565410\pi\)
−0.204048 + 0.978961i \(0.565410\pi\)
\(432\) 0 0
\(433\) 2.72017 0.130723 0.0653616 0.997862i \(-0.479180\pi\)
0.0653616 + 0.997862i \(0.479180\pi\)
\(434\) 0 0
\(435\) −0.286670 −0.0137448
\(436\) 0 0
\(437\) −1.28694 −0.0615629
\(438\) 0 0
\(439\) −24.7423 −1.18089 −0.590444 0.807079i \(-0.701047\pi\)
−0.590444 + 0.807079i \(0.701047\pi\)
\(440\) 0 0
\(441\) −2.71195 −0.129140
\(442\) 0 0
\(443\) −19.0356 −0.904411 −0.452205 0.891914i \(-0.649363\pi\)
−0.452205 + 0.891914i \(0.649363\pi\)
\(444\) 0 0
\(445\) −18.1427 −0.860049
\(446\) 0 0
\(447\) 1.14264 0.0540452
\(448\) 0 0
\(449\) 18.6411 0.879728 0.439864 0.898064i \(-0.355027\pi\)
0.439864 + 0.898064i \(0.355027\pi\)
\(450\) 0 0
\(451\) −9.30747 −0.438272
\(452\) 0 0
\(453\) −6.13296 −0.288151
\(454\) 0 0
\(455\) 3.30011 0.154711
\(456\) 0 0
\(457\) −1.21145 −0.0566693 −0.0283346 0.999598i \(-0.509020\pi\)
−0.0283346 + 0.999598i \(0.509020\pi\)
\(458\) 0 0
\(459\) −9.60135 −0.448152
\(460\) 0 0
\(461\) −20.9911 −0.977651 −0.488826 0.872381i \(-0.662575\pi\)
−0.488826 + 0.872381i \(0.662575\pi\)
\(462\) 0 0
\(463\) 14.4073 0.669563 0.334781 0.942296i \(-0.391338\pi\)
0.334781 + 0.942296i \(0.391338\pi\)
\(464\) 0 0
\(465\) −18.3585 −0.851353
\(466\) 0 0
\(467\) 6.23478 0.288511 0.144256 0.989540i \(-0.453921\pi\)
0.144256 + 0.989540i \(0.453921\pi\)
\(468\) 0 0
\(469\) −8.01827 −0.370250
\(470\) 0 0
\(471\) −1.80016 −0.0829470
\(472\) 0 0
\(473\) 2.24787 0.103357
\(474\) 0 0
\(475\) −18.0274 −0.827152
\(476\) 0 0
\(477\) −23.4974 −1.07587
\(478\) 0 0
\(479\) 3.12161 0.142630 0.0713151 0.997454i \(-0.477280\pi\)
0.0713151 + 0.997454i \(0.477280\pi\)
\(480\) 0 0
\(481\) 4.54945 0.207437
\(482\) 0 0
\(483\) −0.225699 −0.0102697
\(484\) 0 0
\(485\) −35.8259 −1.62677
\(486\) 0 0
\(487\) 39.5739 1.79327 0.896633 0.442775i \(-0.146006\pi\)
0.896633 + 0.442775i \(0.146006\pi\)
\(488\) 0 0
\(489\) 4.96479 0.224515
\(490\) 0 0
\(491\) 27.0328 1.21997 0.609986 0.792412i \(-0.291175\pi\)
0.609986 + 0.792412i \(0.291175\pi\)
\(492\) 0 0
\(493\) 0.506910 0.0228301
\(494\) 0 0
\(495\) 8.94972 0.402260
\(496\) 0 0
\(497\) 16.2909 0.730746
\(498\) 0 0
\(499\) 6.83496 0.305975 0.152987 0.988228i \(-0.451111\pi\)
0.152987 + 0.988228i \(0.451111\pi\)
\(500\) 0 0
\(501\) 0.557253 0.0248962
\(502\) 0 0
\(503\) 12.2970 0.548298 0.274149 0.961687i \(-0.411604\pi\)
0.274149 + 0.961687i \(0.411604\pi\)
\(504\) 0 0
\(505\) −6.37315 −0.283601
\(506\) 0 0
\(507\) 0.536705 0.0238359
\(508\) 0 0
\(509\) −44.1664 −1.95764 −0.978822 0.204715i \(-0.934373\pi\)
−0.978822 + 0.204715i \(0.934373\pi\)
\(510\) 0 0
\(511\) −4.62059 −0.204403
\(512\) 0 0
\(513\) 9.38176 0.414215
\(514\) 0 0
\(515\) 35.0214 1.54323
\(516\) 0 0
\(517\) 2.05740 0.0904842
\(518\) 0 0
\(519\) 8.86280 0.389034
\(520\) 0 0
\(521\) 0.613678 0.0268857 0.0134429 0.999910i \(-0.495721\pi\)
0.0134429 + 0.999910i \(0.495721\pi\)
\(522\) 0 0
\(523\) 32.2826 1.41162 0.705809 0.708402i \(-0.250584\pi\)
0.705809 + 0.708402i \(0.250584\pi\)
\(524\) 0 0
\(525\) −3.16157 −0.137982
\(526\) 0 0
\(527\) 32.4628 1.41410
\(528\) 0 0
\(529\) −22.8232 −0.992311
\(530\) 0 0
\(531\) −11.5094 −0.499465
\(532\) 0 0
\(533\) −9.30747 −0.403151
\(534\) 0 0
\(535\) 43.0503 1.86123
\(536\) 0 0
\(537\) −8.58212 −0.370346
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 43.1328 1.85443 0.927213 0.374536i \(-0.122198\pi\)
0.927213 + 0.374536i \(0.122198\pi\)
\(542\) 0 0
\(543\) −0.920136 −0.0394868
\(544\) 0 0
\(545\) 63.8958 2.73699
\(546\) 0 0
\(547\) −32.5532 −1.39188 −0.695938 0.718102i \(-0.745011\pi\)
−0.695938 + 0.718102i \(0.745011\pi\)
\(548\) 0 0
\(549\) 18.6445 0.795726
\(550\) 0 0
\(551\) −0.495317 −0.0211012
\(552\) 0 0
\(553\) 6.36899 0.270837
\(554\) 0 0
\(555\) −8.05790 −0.342039
\(556\) 0 0
\(557\) −32.2761 −1.36758 −0.683791 0.729678i \(-0.739670\pi\)
−0.683791 + 0.729678i \(0.739670\pi\)
\(558\) 0 0
\(559\) 2.24787 0.0950747
\(560\) 0 0
\(561\) 1.68092 0.0709686
\(562\) 0 0
\(563\) −3.15428 −0.132937 −0.0664684 0.997789i \(-0.521173\pi\)
−0.0664684 + 0.997789i \(0.521173\pi\)
\(564\) 0 0
\(565\) 41.5545 1.74821
\(566\) 0 0
\(567\) −6.49051 −0.272576
\(568\) 0 0
\(569\) −25.3859 −1.06423 −0.532115 0.846672i \(-0.678603\pi\)
−0.532115 + 0.846672i \(0.678603\pi\)
\(570\) 0 0
\(571\) 37.4876 1.56881 0.784404 0.620251i \(-0.212969\pi\)
0.784404 + 0.620251i \(0.212969\pi\)
\(572\) 0 0
\(573\) −11.5049 −0.480625
\(574\) 0 0
\(575\) 2.47721 0.103307
\(576\) 0 0
\(577\) 15.3663 0.639706 0.319853 0.947467i \(-0.396366\pi\)
0.319853 + 0.947467i \(0.396366\pi\)
\(578\) 0 0
\(579\) −2.81018 −0.116787
\(580\) 0 0
\(581\) −3.20265 −0.132868
\(582\) 0 0
\(583\) 8.66441 0.358843
\(584\) 0 0
\(585\) 8.94972 0.370025
\(586\) 0 0
\(587\) 37.9838 1.56776 0.783880 0.620912i \(-0.213238\pi\)
0.783880 + 0.620912i \(0.213238\pi\)
\(588\) 0 0
\(589\) −31.7203 −1.30701
\(590\) 0 0
\(591\) 1.92258 0.0790843
\(592\) 0 0
\(593\) 16.2380 0.666813 0.333407 0.942783i \(-0.391802\pi\)
0.333407 + 0.942783i \(0.391802\pi\)
\(594\) 0 0
\(595\) 10.3357 0.423723
\(596\) 0 0
\(597\) −6.02686 −0.246663
\(598\) 0 0
\(599\) −20.3847 −0.832898 −0.416449 0.909159i \(-0.636725\pi\)
−0.416449 + 0.909159i \(0.636725\pi\)
\(600\) 0 0
\(601\) 26.9836 1.10068 0.550342 0.834939i \(-0.314497\pi\)
0.550342 + 0.834939i \(0.314497\pi\)
\(602\) 0 0
\(603\) −21.7451 −0.885531
\(604\) 0 0
\(605\) −3.30011 −0.134168
\(606\) 0 0
\(607\) −30.2528 −1.22792 −0.613961 0.789337i \(-0.710425\pi\)
−0.613961 + 0.789337i \(0.710425\pi\)
\(608\) 0 0
\(609\) −0.0868669 −0.00352002
\(610\) 0 0
\(611\) 2.05740 0.0832334
\(612\) 0 0
\(613\) −23.3824 −0.944407 −0.472203 0.881490i \(-0.656541\pi\)
−0.472203 + 0.881490i \(0.656541\pi\)
\(614\) 0 0
\(615\) 16.4852 0.664749
\(616\) 0 0
\(617\) −45.5404 −1.83339 −0.916694 0.399590i \(-0.869152\pi\)
−0.916694 + 0.399590i \(0.869152\pi\)
\(618\) 0 0
\(619\) 11.6923 0.469953 0.234977 0.972001i \(-0.424499\pi\)
0.234977 + 0.972001i \(0.424499\pi\)
\(620\) 0 0
\(621\) −1.28918 −0.0517331
\(622\) 0 0
\(623\) −5.49762 −0.220258
\(624\) 0 0
\(625\) −19.7531 −0.790124
\(626\) 0 0
\(627\) −1.64248 −0.0655943
\(628\) 0 0
\(629\) 14.2486 0.568127
\(630\) 0 0
\(631\) −21.3113 −0.848391 −0.424195 0.905571i \(-0.639443\pi\)
−0.424195 + 0.905571i \(0.639443\pi\)
\(632\) 0 0
\(633\) 9.04619 0.359554
\(634\) 0 0
\(635\) −28.8515 −1.14494
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) 44.1800 1.74773
\(640\) 0 0
\(641\) −19.1727 −0.757277 −0.378638 0.925545i \(-0.623608\pi\)
−0.378638 + 0.925545i \(0.623608\pi\)
\(642\) 0 0
\(643\) 22.4479 0.885261 0.442630 0.896704i \(-0.354045\pi\)
0.442630 + 0.896704i \(0.354045\pi\)
\(644\) 0 0
\(645\) −3.98139 −0.156767
\(646\) 0 0
\(647\) 16.0810 0.632210 0.316105 0.948724i \(-0.397625\pi\)
0.316105 + 0.948724i \(0.397625\pi\)
\(648\) 0 0
\(649\) 4.24396 0.166590
\(650\) 0 0
\(651\) −5.56299 −0.218031
\(652\) 0 0
\(653\) 40.8056 1.59685 0.798423 0.602097i \(-0.205668\pi\)
0.798423 + 0.602097i \(0.205668\pi\)
\(654\) 0 0
\(655\) 49.2679 1.92506
\(656\) 0 0
\(657\) −12.5308 −0.488873
\(658\) 0 0
\(659\) −39.0702 −1.52196 −0.760980 0.648776i \(-0.775281\pi\)
−0.760980 + 0.648776i \(0.775281\pi\)
\(660\) 0 0
\(661\) 7.68059 0.298740 0.149370 0.988781i \(-0.452275\pi\)
0.149370 + 0.988781i \(0.452275\pi\)
\(662\) 0 0
\(663\) 1.68092 0.0652816
\(664\) 0 0
\(665\) −10.0993 −0.391636
\(666\) 0 0
\(667\) 0.0680634 0.00263543
\(668\) 0 0
\(669\) −6.31792 −0.244265
\(670\) 0 0
\(671\) −6.87493 −0.265404
\(672\) 0 0
\(673\) 18.1821 0.700870 0.350435 0.936587i \(-0.386034\pi\)
0.350435 + 0.936587i \(0.386034\pi\)
\(674\) 0 0
\(675\) −18.0587 −0.695081
\(676\) 0 0
\(677\) −12.4832 −0.479769 −0.239885 0.970801i \(-0.577110\pi\)
−0.239885 + 0.970801i \(0.577110\pi\)
\(678\) 0 0
\(679\) −10.8560 −0.416614
\(680\) 0 0
\(681\) 4.11471 0.157676
\(682\) 0 0
\(683\) −33.3127 −1.27468 −0.637338 0.770584i \(-0.719965\pi\)
−0.637338 + 0.770584i \(0.719965\pi\)
\(684\) 0 0
\(685\) −17.4183 −0.665519
\(686\) 0 0
\(687\) 1.72242 0.0657146
\(688\) 0 0
\(689\) 8.66441 0.330088
\(690\) 0 0
\(691\) 43.4935 1.65457 0.827285 0.561782i \(-0.189884\pi\)
0.827285 + 0.561782i \(0.189884\pi\)
\(692\) 0 0
\(693\) 2.71195 0.103018
\(694\) 0 0
\(695\) 8.06628 0.305971
\(696\) 0 0
\(697\) −29.1504 −1.10415
\(698\) 0 0
\(699\) 2.42265 0.0916330
\(700\) 0 0
\(701\) 26.4772 1.00003 0.500016 0.866016i \(-0.333328\pi\)
0.500016 + 0.866016i \(0.333328\pi\)
\(702\) 0 0
\(703\) −13.9227 −0.525104
\(704\) 0 0
\(705\) −3.64403 −0.137242
\(706\) 0 0
\(707\) −1.93119 −0.0726300
\(708\) 0 0
\(709\) 45.7514 1.71823 0.859115 0.511783i \(-0.171015\pi\)
0.859115 + 0.511783i \(0.171015\pi\)
\(710\) 0 0
\(711\) 17.2724 0.647764
\(712\) 0 0
\(713\) 4.35881 0.163239
\(714\) 0 0
\(715\) −3.30011 −0.123417
\(716\) 0 0
\(717\) −1.58742 −0.0592833
\(718\) 0 0
\(719\) −25.5391 −0.952449 −0.476225 0.879324i \(-0.657995\pi\)
−0.476225 + 0.879324i \(0.657995\pi\)
\(720\) 0 0
\(721\) 10.6122 0.395219
\(722\) 0 0
\(723\) 0.485608 0.0180599
\(724\) 0 0
\(725\) 0.953425 0.0354093
\(726\) 0 0
\(727\) 31.0729 1.15243 0.576215 0.817298i \(-0.304529\pi\)
0.576215 + 0.817298i \(0.304529\pi\)
\(728\) 0 0
\(729\) −12.6659 −0.469108
\(730\) 0 0
\(731\) 7.04018 0.260390
\(732\) 0 0
\(733\) 43.4455 1.60469 0.802347 0.596857i \(-0.203584\pi\)
0.802347 + 0.596857i \(0.203584\pi\)
\(734\) 0 0
\(735\) −1.77118 −0.0653311
\(736\) 0 0
\(737\) 8.01827 0.295357
\(738\) 0 0
\(739\) −24.9020 −0.916035 −0.458018 0.888943i \(-0.651440\pi\)
−0.458018 + 0.888943i \(0.651440\pi\)
\(740\) 0 0
\(741\) −1.64248 −0.0603380
\(742\) 0 0
\(743\) −38.8381 −1.42483 −0.712416 0.701758i \(-0.752399\pi\)
−0.712416 + 0.701758i \(0.752399\pi\)
\(744\) 0 0
\(745\) −7.02593 −0.257410
\(746\) 0 0
\(747\) −8.68541 −0.317782
\(748\) 0 0
\(749\) 13.0451 0.476658
\(750\) 0 0
\(751\) −47.6813 −1.73992 −0.869958 0.493125i \(-0.835854\pi\)
−0.869958 + 0.493125i \(0.835854\pi\)
\(752\) 0 0
\(753\) −4.67199 −0.170257
\(754\) 0 0
\(755\) 37.7105 1.37243
\(756\) 0 0
\(757\) 8.19558 0.297873 0.148937 0.988847i \(-0.452415\pi\)
0.148937 + 0.988847i \(0.452415\pi\)
\(758\) 0 0
\(759\) 0.225699 0.00819237
\(760\) 0 0
\(761\) −28.5644 −1.03546 −0.517730 0.855544i \(-0.673223\pi\)
−0.517730 + 0.855544i \(0.673223\pi\)
\(762\) 0 0
\(763\) 19.3617 0.700941
\(764\) 0 0
\(765\) 28.0299 1.01342
\(766\) 0 0
\(767\) 4.24396 0.153241
\(768\) 0 0
\(769\) 6.21584 0.224149 0.112075 0.993700i \(-0.464250\pi\)
0.112075 + 0.993700i \(0.464250\pi\)
\(770\) 0 0
\(771\) −8.31428 −0.299431
\(772\) 0 0
\(773\) 5.97637 0.214955 0.107478 0.994208i \(-0.465723\pi\)
0.107478 + 0.994208i \(0.465723\pi\)
\(774\) 0 0
\(775\) 61.0577 2.19326
\(776\) 0 0
\(777\) −2.44171 −0.0875958
\(778\) 0 0
\(779\) 28.4837 1.02054
\(780\) 0 0
\(781\) −16.2909 −0.582933
\(782\) 0 0
\(783\) −0.496179 −0.0177320
\(784\) 0 0
\(785\) 11.0689 0.395065
\(786\) 0 0
\(787\) −2.13999 −0.0762824 −0.0381412 0.999272i \(-0.512144\pi\)
−0.0381412 + 0.999272i \(0.512144\pi\)
\(788\) 0 0
\(789\) −7.53473 −0.268243
\(790\) 0 0
\(791\) 12.5919 0.447715
\(792\) 0 0
\(793\) −6.87493 −0.244136
\(794\) 0 0
\(795\) −15.3462 −0.544275
\(796\) 0 0
\(797\) −16.3602 −0.579509 −0.289754 0.957101i \(-0.593574\pi\)
−0.289754 + 0.957101i \(0.593574\pi\)
\(798\) 0 0
\(799\) 6.44363 0.227959
\(800\) 0 0
\(801\) −14.9093 −0.526793
\(802\) 0 0
\(803\) 4.62059 0.163057
\(804\) 0 0
\(805\) 1.38779 0.0489131
\(806\) 0 0
\(807\) −5.84727 −0.205834
\(808\) 0 0
\(809\) 54.7563 1.92513 0.962564 0.271055i \(-0.0873724\pi\)
0.962564 + 0.271055i \(0.0873724\pi\)
\(810\) 0 0
\(811\) 37.8235 1.32816 0.664082 0.747660i \(-0.268823\pi\)
0.664082 + 0.747660i \(0.268823\pi\)
\(812\) 0 0
\(813\) −7.39063 −0.259201
\(814\) 0 0
\(815\) −30.5277 −1.06934
\(816\) 0 0
\(817\) −6.87917 −0.240672
\(818\) 0 0
\(819\) 2.71195 0.0947631
\(820\) 0 0
\(821\) −21.7410 −0.758767 −0.379384 0.925239i \(-0.623864\pi\)
−0.379384 + 0.925239i \(0.623864\pi\)
\(822\) 0 0
\(823\) 27.2535 0.949997 0.474998 0.879987i \(-0.342449\pi\)
0.474998 + 0.879987i \(0.342449\pi\)
\(824\) 0 0
\(825\) 3.16157 0.110072
\(826\) 0 0
\(827\) −18.6586 −0.648821 −0.324411 0.945916i \(-0.605166\pi\)
−0.324411 + 0.945916i \(0.605166\pi\)
\(828\) 0 0
\(829\) −30.1758 −1.04805 −0.524024 0.851704i \(-0.675570\pi\)
−0.524024 + 0.851704i \(0.675570\pi\)
\(830\) 0 0
\(831\) −14.3878 −0.499109
\(832\) 0 0
\(833\) 3.13193 0.108515
\(834\) 0 0
\(835\) −3.42646 −0.118577
\(836\) 0 0
\(837\) −31.7755 −1.09832
\(838\) 0 0
\(839\) −24.8451 −0.857749 −0.428875 0.903364i \(-0.641090\pi\)
−0.428875 + 0.903364i \(0.641090\pi\)
\(840\) 0 0
\(841\) −28.9738 −0.999097
\(842\) 0 0
\(843\) −2.51352 −0.0865702
\(844\) 0 0
\(845\) −3.30011 −0.113527
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 9.44168 0.324038
\(850\) 0 0
\(851\) 1.91317 0.0655826
\(852\) 0 0
\(853\) 7.25064 0.248257 0.124129 0.992266i \(-0.460386\pi\)
0.124129 + 0.992266i \(0.460386\pi\)
\(854\) 0 0
\(855\) −27.3889 −0.936680
\(856\) 0 0
\(857\) −8.30714 −0.283767 −0.141883 0.989883i \(-0.545316\pi\)
−0.141883 + 0.989883i \(0.545316\pi\)
\(858\) 0 0
\(859\) −26.2253 −0.894797 −0.447399 0.894335i \(-0.647649\pi\)
−0.447399 + 0.894335i \(0.647649\pi\)
\(860\) 0 0
\(861\) 4.99536 0.170242
\(862\) 0 0
\(863\) −7.44686 −0.253494 −0.126747 0.991935i \(-0.540454\pi\)
−0.126747 + 0.991935i \(0.540454\pi\)
\(864\) 0 0
\(865\) −54.4959 −1.85291
\(866\) 0 0
\(867\) −3.85944 −0.131073
\(868\) 0 0
\(869\) −6.36899 −0.216053
\(870\) 0 0
\(871\) 8.01827 0.271689
\(872\) 0 0
\(873\) −29.4408 −0.996421
\(874\) 0 0
\(875\) 2.93943 0.0993710
\(876\) 0 0
\(877\) −0.850256 −0.0287111 −0.0143556 0.999897i \(-0.504570\pi\)
−0.0143556 + 0.999897i \(0.504570\pi\)
\(878\) 0 0
\(879\) −6.56084 −0.221292
\(880\) 0 0
\(881\) 10.5341 0.354903 0.177451 0.984130i \(-0.443215\pi\)
0.177451 + 0.984130i \(0.443215\pi\)
\(882\) 0 0
\(883\) −5.16673 −0.173874 −0.0869372 0.996214i \(-0.527708\pi\)
−0.0869372 + 0.996214i \(0.527708\pi\)
\(884\) 0 0
\(885\) −7.51683 −0.252675
\(886\) 0 0
\(887\) 9.84275 0.330487 0.165244 0.986253i \(-0.447159\pi\)
0.165244 + 0.986253i \(0.447159\pi\)
\(888\) 0 0
\(889\) −8.74259 −0.293217
\(890\) 0 0
\(891\) 6.49051 0.217440
\(892\) 0 0
\(893\) −6.29627 −0.210696
\(894\) 0 0
\(895\) 52.7700 1.76391
\(896\) 0 0
\(897\) 0.225699 0.00753588
\(898\) 0 0
\(899\) 1.67761 0.0559515
\(900\) 0 0
\(901\) 27.1363 0.904043
\(902\) 0 0
\(903\) −1.20644 −0.0401479
\(904\) 0 0
\(905\) 5.65777 0.188070
\(906\) 0 0
\(907\) 15.6231 0.518755 0.259377 0.965776i \(-0.416483\pi\)
0.259377 + 0.965776i \(0.416483\pi\)
\(908\) 0 0
\(909\) −5.23730 −0.173710
\(910\) 0 0
\(911\) 20.4772 0.678439 0.339220 0.940707i \(-0.389837\pi\)
0.339220 + 0.940707i \(0.389837\pi\)
\(912\) 0 0
\(913\) 3.20265 0.105992
\(914\) 0 0
\(915\) 12.1768 0.402551
\(916\) 0 0
\(917\) 14.9292 0.493005
\(918\) 0 0
\(919\) −3.74457 −0.123522 −0.0617609 0.998091i \(-0.519672\pi\)
−0.0617609 + 0.998091i \(0.519672\pi\)
\(920\) 0 0
\(921\) 6.37205 0.209966
\(922\) 0 0
\(923\) −16.2909 −0.536221
\(924\) 0 0
\(925\) 26.7995 0.881161
\(926\) 0 0
\(927\) 28.7798 0.945252
\(928\) 0 0
\(929\) 28.7883 0.944514 0.472257 0.881461i \(-0.343439\pi\)
0.472257 + 0.881461i \(0.343439\pi\)
\(930\) 0 0
\(931\) −3.06031 −0.100297
\(932\) 0 0
\(933\) 8.16396 0.267276
\(934\) 0 0
\(935\) −10.3357 −0.338014
\(936\) 0 0
\(937\) −54.2426 −1.77203 −0.886014 0.463659i \(-0.846536\pi\)
−0.886014 + 0.463659i \(0.846536\pi\)
\(938\) 0 0
\(939\) 2.87051 0.0936755
\(940\) 0 0
\(941\) −13.2047 −0.430462 −0.215231 0.976563i \(-0.569050\pi\)
−0.215231 + 0.976563i \(0.569050\pi\)
\(942\) 0 0
\(943\) −3.91405 −0.127459
\(944\) 0 0
\(945\) −10.1169 −0.329103
\(946\) 0 0
\(947\) −43.9688 −1.42879 −0.714397 0.699740i \(-0.753299\pi\)
−0.714397 + 0.699740i \(0.753299\pi\)
\(948\) 0 0
\(949\) 4.62059 0.149991
\(950\) 0 0
\(951\) −0.755928 −0.0245126
\(952\) 0 0
\(953\) −36.2086 −1.17291 −0.586456 0.809981i \(-0.699477\pi\)
−0.586456 + 0.809981i \(0.699477\pi\)
\(954\) 0 0
\(955\) 70.7419 2.28915
\(956\) 0 0
\(957\) 0.0868669 0.00280801
\(958\) 0 0
\(959\) −5.27810 −0.170439
\(960\) 0 0
\(961\) 76.4350 2.46565
\(962\) 0 0
\(963\) 35.3777 1.14003
\(964\) 0 0
\(965\) 17.2793 0.556241
\(966\) 0 0
\(967\) 8.31230 0.267306 0.133653 0.991028i \(-0.457329\pi\)
0.133653 + 0.991028i \(0.457329\pi\)
\(968\) 0 0
\(969\) −5.14414 −0.165254
\(970\) 0 0
\(971\) 50.7323 1.62808 0.814039 0.580810i \(-0.197264\pi\)
0.814039 + 0.580810i \(0.197264\pi\)
\(972\) 0 0
\(973\) 2.44425 0.0783590
\(974\) 0 0
\(975\) 3.16157 0.101251
\(976\) 0 0
\(977\) 11.5080 0.368175 0.184087 0.982910i \(-0.441067\pi\)
0.184087 + 0.982910i \(0.441067\pi\)
\(978\) 0 0
\(979\) 5.49762 0.175705
\(980\) 0 0
\(981\) 52.5080 1.67645
\(982\) 0 0
\(983\) 11.6057 0.370164 0.185082 0.982723i \(-0.440745\pi\)
0.185082 + 0.982723i \(0.440745\pi\)
\(984\) 0 0
\(985\) −11.8216 −0.376668
\(986\) 0 0
\(987\) −1.10421 −0.0351475
\(988\) 0 0
\(989\) 0.945292 0.0300585
\(990\) 0 0
\(991\) 47.9015 1.52164 0.760821 0.648962i \(-0.224796\pi\)
0.760821 + 0.648962i \(0.224796\pi\)
\(992\) 0 0
\(993\) 10.3201 0.327498
\(994\) 0 0
\(995\) 37.0581 1.17482
\(996\) 0 0
\(997\) 1.76268 0.0558246 0.0279123 0.999610i \(-0.491114\pi\)
0.0279123 + 0.999610i \(0.491114\pi\)
\(998\) 0 0
\(999\) −13.9469 −0.441261
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 \(a_p\))