Properties

Label 8008.2.a.p.1.7
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 1.7
Root \(1.94061\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.94061 q^{3} +1.48281 q^{5} -1.00000 q^{7} +0.765982 q^{9} +O(q^{10})\) \(q+1.94061 q^{3} +1.48281 q^{5} -1.00000 q^{7} +0.765982 q^{9} +1.00000 q^{11} +1.00000 q^{13} +2.87756 q^{15} -5.79179 q^{17} +2.95626 q^{19} -1.94061 q^{21} -3.43248 q^{23} -2.80127 q^{25} -4.33537 q^{27} -2.27973 q^{29} -4.29356 q^{31} +1.94061 q^{33} -1.48281 q^{35} -7.63237 q^{37} +1.94061 q^{39} -3.26702 q^{41} -6.24504 q^{43} +1.13581 q^{45} -5.19672 q^{47} +1.00000 q^{49} -11.2396 q^{51} +14.1806 q^{53} +1.48281 q^{55} +5.73696 q^{57} -0.168206 q^{59} -1.15136 q^{61} -0.765982 q^{63} +1.48281 q^{65} -5.79067 q^{67} -6.66112 q^{69} -13.7993 q^{71} -9.12217 q^{73} -5.43619 q^{75} -1.00000 q^{77} -3.90607 q^{79} -10.7112 q^{81} -1.99115 q^{83} -8.58813 q^{85} -4.42408 q^{87} +1.67678 q^{89} -1.00000 q^{91} -8.33215 q^{93} +4.38357 q^{95} +15.7411 q^{97} +0.765982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

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
\(3\) 1.94061 1.12041 0.560207 0.828353i \(-0.310722\pi\)
0.560207 + 0.828353i \(0.310722\pi\)
\(4\) 0 0
\(5\) 1.48281 0.663133 0.331566 0.943432i \(-0.392423\pi\)
0.331566 + 0.943432i \(0.392423\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0.765982 0.255327
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 2.87756 0.742983
\(16\) 0 0
\(17\) −5.79179 −1.40472 −0.702358 0.711824i \(-0.747869\pi\)
−0.702358 + 0.711824i \(0.747869\pi\)
\(18\) 0 0
\(19\) 2.95626 0.678213 0.339106 0.940748i \(-0.389875\pi\)
0.339106 + 0.940748i \(0.389875\pi\)
\(20\) 0 0
\(21\) −1.94061 −0.423477
\(22\) 0 0
\(23\) −3.43248 −0.715722 −0.357861 0.933775i \(-0.616494\pi\)
−0.357861 + 0.933775i \(0.616494\pi\)
\(24\) 0 0
\(25\) −2.80127 −0.560255
\(26\) 0 0
\(27\) −4.33537 −0.834342
\(28\) 0 0
\(29\) −2.27973 −0.423335 −0.211668 0.977342i \(-0.567889\pi\)
−0.211668 + 0.977342i \(0.567889\pi\)
\(30\) 0 0
\(31\) −4.29356 −0.771146 −0.385573 0.922677i \(-0.625996\pi\)
−0.385573 + 0.922677i \(0.625996\pi\)
\(32\) 0 0
\(33\) 1.94061 0.337818
\(34\) 0 0
\(35\) −1.48281 −0.250641
\(36\) 0 0
\(37\) −7.63237 −1.25475 −0.627377 0.778716i \(-0.715871\pi\)
−0.627377 + 0.778716i \(0.715871\pi\)
\(38\) 0 0
\(39\) 1.94061 0.310747
\(40\) 0 0
\(41\) −3.26702 −0.510222 −0.255111 0.966912i \(-0.582112\pi\)
−0.255111 + 0.966912i \(0.582112\pi\)
\(42\) 0 0
\(43\) −6.24504 −0.952360 −0.476180 0.879348i \(-0.657979\pi\)
−0.476180 + 0.879348i \(0.657979\pi\)
\(44\) 0 0
\(45\) 1.13581 0.169316
\(46\) 0 0
\(47\) −5.19672 −0.758019 −0.379010 0.925393i \(-0.623735\pi\)
−0.379010 + 0.925393i \(0.623735\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −11.2396 −1.57386
\(52\) 0 0
\(53\) 14.1806 1.94786 0.973928 0.226858i \(-0.0728452\pi\)
0.973928 + 0.226858i \(0.0728452\pi\)
\(54\) 0 0
\(55\) 1.48281 0.199942
\(56\) 0 0
\(57\) 5.73696 0.759879
\(58\) 0 0
\(59\) −0.168206 −0.0218986 −0.0109493 0.999940i \(-0.503485\pi\)
−0.0109493 + 0.999940i \(0.503485\pi\)
\(60\) 0 0
\(61\) −1.15136 −0.147416 −0.0737080 0.997280i \(-0.523483\pi\)
−0.0737080 + 0.997280i \(0.523483\pi\)
\(62\) 0 0
\(63\) −0.765982 −0.0965047
\(64\) 0 0
\(65\) 1.48281 0.183920
\(66\) 0 0
\(67\) −5.79067 −0.707443 −0.353722 0.935351i \(-0.615084\pi\)
−0.353722 + 0.935351i \(0.615084\pi\)
\(68\) 0 0
\(69\) −6.66112 −0.801905
\(70\) 0 0
\(71\) −13.7993 −1.63767 −0.818836 0.574028i \(-0.805380\pi\)
−0.818836 + 0.574028i \(0.805380\pi\)
\(72\) 0 0
\(73\) −9.12217 −1.06767 −0.533834 0.845589i \(-0.679249\pi\)
−0.533834 + 0.845589i \(0.679249\pi\)
\(74\) 0 0
\(75\) −5.43619 −0.627717
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −3.90607 −0.439467 −0.219734 0.975560i \(-0.570519\pi\)
−0.219734 + 0.975560i \(0.570519\pi\)
\(80\) 0 0
\(81\) −10.7112 −1.19014
\(82\) 0 0
\(83\) −1.99115 −0.218557 −0.109278 0.994011i \(-0.534854\pi\)
−0.109278 + 0.994011i \(0.534854\pi\)
\(84\) 0 0
\(85\) −8.58813 −0.931513
\(86\) 0 0
\(87\) −4.42408 −0.474311
\(88\) 0 0
\(89\) 1.67678 0.177738 0.0888689 0.996043i \(-0.471675\pi\)
0.0888689 + 0.996043i \(0.471675\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −8.33215 −0.864003
\(94\) 0 0
\(95\) 4.38357 0.449745
\(96\) 0 0
\(97\) 15.7411 1.59827 0.799135 0.601152i \(-0.205291\pi\)
0.799135 + 0.601152i \(0.205291\pi\)
\(98\) 0 0
\(99\) 0.765982 0.0769841
\(100\) 0 0
\(101\) −9.19873 −0.915308 −0.457654 0.889130i \(-0.651310\pi\)
−0.457654 + 0.889130i \(0.651310\pi\)
\(102\) 0 0
\(103\) 10.1535 1.00045 0.500226 0.865895i \(-0.333250\pi\)
0.500226 + 0.865895i \(0.333250\pi\)
\(104\) 0 0
\(105\) −2.87756 −0.280821
\(106\) 0 0
\(107\) 17.6142 1.70283 0.851416 0.524491i \(-0.175744\pi\)
0.851416 + 0.524491i \(0.175744\pi\)
\(108\) 0 0
\(109\) 3.84109 0.367910 0.183955 0.982935i \(-0.441110\pi\)
0.183955 + 0.982935i \(0.441110\pi\)
\(110\) 0 0
\(111\) −14.8115 −1.40584
\(112\) 0 0
\(113\) 0.521212 0.0490315 0.0245158 0.999699i \(-0.492196\pi\)
0.0245158 + 0.999699i \(0.492196\pi\)
\(114\) 0 0
\(115\) −5.08972 −0.474619
\(116\) 0 0
\(117\) 0.765982 0.0708151
\(118\) 0 0
\(119\) 5.79179 0.530933
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −6.34002 −0.571660
\(124\) 0 0
\(125\) −11.5678 −1.03466
\(126\) 0 0
\(127\) 9.14711 0.811675 0.405837 0.913945i \(-0.366980\pi\)
0.405837 + 0.913945i \(0.366980\pi\)
\(128\) 0 0
\(129\) −12.1192 −1.06704
\(130\) 0 0
\(131\) −3.04167 −0.265752 −0.132876 0.991133i \(-0.542421\pi\)
−0.132876 + 0.991133i \(0.542421\pi\)
\(132\) 0 0
\(133\) −2.95626 −0.256340
\(134\) 0 0
\(135\) −6.42852 −0.553279
\(136\) 0 0
\(137\) 7.62644 0.651571 0.325785 0.945444i \(-0.394371\pi\)
0.325785 + 0.945444i \(0.394371\pi\)
\(138\) 0 0
\(139\) 0.988761 0.0838656 0.0419328 0.999120i \(-0.486648\pi\)
0.0419328 + 0.999120i \(0.486648\pi\)
\(140\) 0 0
\(141\) −10.0848 −0.849295
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −3.38041 −0.280728
\(146\) 0 0
\(147\) 1.94061 0.160059
\(148\) 0 0
\(149\) −9.93581 −0.813973 −0.406987 0.913434i \(-0.633420\pi\)
−0.406987 + 0.913434i \(0.633420\pi\)
\(150\) 0 0
\(151\) −0.758626 −0.0617361 −0.0308681 0.999523i \(-0.509827\pi\)
−0.0308681 + 0.999523i \(0.509827\pi\)
\(152\) 0 0
\(153\) −4.43641 −0.358663
\(154\) 0 0
\(155\) −6.36654 −0.511372
\(156\) 0 0
\(157\) 18.9992 1.51630 0.758152 0.652078i \(-0.226103\pi\)
0.758152 + 0.652078i \(0.226103\pi\)
\(158\) 0 0
\(159\) 27.5191 2.18240
\(160\) 0 0
\(161\) 3.43248 0.270518
\(162\) 0 0
\(163\) 10.7933 0.845398 0.422699 0.906270i \(-0.361083\pi\)
0.422699 + 0.906270i \(0.361083\pi\)
\(164\) 0 0
\(165\) 2.87756 0.224018
\(166\) 0 0
\(167\) 19.5148 1.51010 0.755051 0.655667i \(-0.227612\pi\)
0.755051 + 0.655667i \(0.227612\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 2.26444 0.173166
\(172\) 0 0
\(173\) −21.9031 −1.66526 −0.832632 0.553826i \(-0.813167\pi\)
−0.832632 + 0.553826i \(0.813167\pi\)
\(174\) 0 0
\(175\) 2.80127 0.211756
\(176\) 0 0
\(177\) −0.326423 −0.0245355
\(178\) 0 0
\(179\) −1.37316 −0.102635 −0.0513174 0.998682i \(-0.516342\pi\)
−0.0513174 + 0.998682i \(0.516342\pi\)
\(180\) 0 0
\(181\) 17.9070 1.33102 0.665510 0.746389i \(-0.268214\pi\)
0.665510 + 0.746389i \(0.268214\pi\)
\(182\) 0 0
\(183\) −2.23434 −0.165167
\(184\) 0 0
\(185\) −11.3174 −0.832068
\(186\) 0 0
\(187\) −5.79179 −0.423538
\(188\) 0 0
\(189\) 4.33537 0.315351
\(190\) 0 0
\(191\) 15.7128 1.13694 0.568470 0.822704i \(-0.307535\pi\)
0.568470 + 0.822704i \(0.307535\pi\)
\(192\) 0 0
\(193\) −26.2046 −1.88625 −0.943125 0.332439i \(-0.892128\pi\)
−0.943125 + 0.332439i \(0.892128\pi\)
\(194\) 0 0
\(195\) 2.87756 0.206066
\(196\) 0 0
\(197\) 6.39892 0.455904 0.227952 0.973672i \(-0.426797\pi\)
0.227952 + 0.973672i \(0.426797\pi\)
\(198\) 0 0
\(199\) −9.38441 −0.665243 −0.332621 0.943060i \(-0.607933\pi\)
−0.332621 + 0.943060i \(0.607933\pi\)
\(200\) 0 0
\(201\) −11.2375 −0.792629
\(202\) 0 0
\(203\) 2.27973 0.160006
\(204\) 0 0
\(205\) −4.84436 −0.338345
\(206\) 0 0
\(207\) −2.62922 −0.182744
\(208\) 0 0
\(209\) 2.95626 0.204489
\(210\) 0 0
\(211\) −10.8018 −0.743624 −0.371812 0.928308i \(-0.621263\pi\)
−0.371812 + 0.928308i \(0.621263\pi\)
\(212\) 0 0
\(213\) −26.7790 −1.83487
\(214\) 0 0
\(215\) −9.26021 −0.631541
\(216\) 0 0
\(217\) 4.29356 0.291466
\(218\) 0 0
\(219\) −17.7026 −1.19623
\(220\) 0 0
\(221\) −5.79179 −0.389598
\(222\) 0 0
\(223\) −6.39924 −0.428525 −0.214262 0.976776i \(-0.568735\pi\)
−0.214262 + 0.976776i \(0.568735\pi\)
\(224\) 0 0
\(225\) −2.14573 −0.143048
\(226\) 0 0
\(227\) −0.348915 −0.0231583 −0.0115792 0.999933i \(-0.503686\pi\)
−0.0115792 + 0.999933i \(0.503686\pi\)
\(228\) 0 0
\(229\) −14.8710 −0.982704 −0.491352 0.870961i \(-0.663497\pi\)
−0.491352 + 0.870961i \(0.663497\pi\)
\(230\) 0 0
\(231\) −1.94061 −0.127683
\(232\) 0 0
\(233\) −12.2376 −0.801712 −0.400856 0.916141i \(-0.631287\pi\)
−0.400856 + 0.916141i \(0.631287\pi\)
\(234\) 0 0
\(235\) −7.70574 −0.502667
\(236\) 0 0
\(237\) −7.58018 −0.492385
\(238\) 0 0
\(239\) −10.5476 −0.682264 −0.341132 0.940015i \(-0.610810\pi\)
−0.341132 + 0.940015i \(0.610810\pi\)
\(240\) 0 0
\(241\) 3.47743 0.224001 0.112000 0.993708i \(-0.464274\pi\)
0.112000 + 0.993708i \(0.464274\pi\)
\(242\) 0 0
\(243\) −7.78024 −0.499103
\(244\) 0 0
\(245\) 1.48281 0.0947333
\(246\) 0 0
\(247\) 2.95626 0.188102
\(248\) 0 0
\(249\) −3.86404 −0.244874
\(250\) 0 0
\(251\) −8.53585 −0.538778 −0.269389 0.963031i \(-0.586822\pi\)
−0.269389 + 0.963031i \(0.586822\pi\)
\(252\) 0 0
\(253\) −3.43248 −0.215798
\(254\) 0 0
\(255\) −16.6662 −1.04368
\(256\) 0 0
\(257\) 9.28668 0.579287 0.289643 0.957135i \(-0.406463\pi\)
0.289643 + 0.957135i \(0.406463\pi\)
\(258\) 0 0
\(259\) 7.63237 0.474252
\(260\) 0 0
\(261\) −1.74623 −0.108089
\(262\) 0 0
\(263\) −5.11390 −0.315336 −0.157668 0.987492i \(-0.550398\pi\)
−0.157668 + 0.987492i \(0.550398\pi\)
\(264\) 0 0
\(265\) 21.0271 1.29169
\(266\) 0 0
\(267\) 3.25397 0.199140
\(268\) 0 0
\(269\) −7.99275 −0.487326 −0.243663 0.969860i \(-0.578349\pi\)
−0.243663 + 0.969860i \(0.578349\pi\)
\(270\) 0 0
\(271\) −2.00230 −0.121631 −0.0608156 0.998149i \(-0.519370\pi\)
−0.0608156 + 0.998149i \(0.519370\pi\)
\(272\) 0 0
\(273\) −1.94061 −0.117451
\(274\) 0 0
\(275\) −2.80127 −0.168923
\(276\) 0 0
\(277\) 0.240867 0.0144723 0.00723614 0.999974i \(-0.497697\pi\)
0.00723614 + 0.999974i \(0.497697\pi\)
\(278\) 0 0
\(279\) −3.28879 −0.196895
\(280\) 0 0
\(281\) 15.9760 0.953050 0.476525 0.879161i \(-0.341896\pi\)
0.476525 + 0.879161i \(0.341896\pi\)
\(282\) 0 0
\(283\) −2.81423 −0.167289 −0.0836443 0.996496i \(-0.526656\pi\)
−0.0836443 + 0.996496i \(0.526656\pi\)
\(284\) 0 0
\(285\) 8.50682 0.503901
\(286\) 0 0
\(287\) 3.26702 0.192846
\(288\) 0 0
\(289\) 16.5449 0.973227
\(290\) 0 0
\(291\) 30.5475 1.79072
\(292\) 0 0
\(293\) −25.4426 −1.48637 −0.743187 0.669084i \(-0.766687\pi\)
−0.743187 + 0.669084i \(0.766687\pi\)
\(294\) 0 0
\(295\) −0.249418 −0.0145217
\(296\) 0 0
\(297\) −4.33537 −0.251563
\(298\) 0 0
\(299\) −3.43248 −0.198506
\(300\) 0 0
\(301\) 6.24504 0.359958
\(302\) 0 0
\(303\) −17.8512 −1.02552
\(304\) 0 0
\(305\) −1.70724 −0.0977564
\(306\) 0 0
\(307\) 26.3465 1.50367 0.751837 0.659349i \(-0.229168\pi\)
0.751837 + 0.659349i \(0.229168\pi\)
\(308\) 0 0
\(309\) 19.7040 1.12092
\(310\) 0 0
\(311\) 9.26643 0.525451 0.262726 0.964871i \(-0.415379\pi\)
0.262726 + 0.964871i \(0.415379\pi\)
\(312\) 0 0
\(313\) 9.51183 0.537641 0.268820 0.963190i \(-0.413366\pi\)
0.268820 + 0.963190i \(0.413366\pi\)
\(314\) 0 0
\(315\) −1.13581 −0.0639954
\(316\) 0 0
\(317\) −10.9336 −0.614090 −0.307045 0.951695i \(-0.599340\pi\)
−0.307045 + 0.951695i \(0.599340\pi\)
\(318\) 0 0
\(319\) −2.27973 −0.127640
\(320\) 0 0
\(321\) 34.1824 1.90788
\(322\) 0 0
\(323\) −17.1221 −0.952696
\(324\) 0 0
\(325\) −2.80127 −0.155387
\(326\) 0 0
\(327\) 7.45408 0.412212
\(328\) 0 0
\(329\) 5.19672 0.286504
\(330\) 0 0
\(331\) 32.6026 1.79200 0.896000 0.444055i \(-0.146461\pi\)
0.896000 + 0.444055i \(0.146461\pi\)
\(332\) 0 0
\(333\) −5.84626 −0.320373
\(334\) 0 0
\(335\) −8.58647 −0.469129
\(336\) 0 0
\(337\) −17.5266 −0.954737 −0.477369 0.878703i \(-0.658409\pi\)
−0.477369 + 0.878703i \(0.658409\pi\)
\(338\) 0 0
\(339\) 1.01147 0.0549356
\(340\) 0 0
\(341\) −4.29356 −0.232509
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −9.87718 −0.531770
\(346\) 0 0
\(347\) −24.7223 −1.32716 −0.663580 0.748105i \(-0.730964\pi\)
−0.663580 + 0.748105i \(0.730964\pi\)
\(348\) 0 0
\(349\) −12.0093 −0.642843 −0.321421 0.946936i \(-0.604161\pi\)
−0.321421 + 0.946936i \(0.604161\pi\)
\(350\) 0 0
\(351\) −4.33537 −0.231405
\(352\) 0 0
\(353\) −2.20619 −0.117423 −0.0587117 0.998275i \(-0.518699\pi\)
−0.0587117 + 0.998275i \(0.518699\pi\)
\(354\) 0 0
\(355\) −20.4617 −1.08599
\(356\) 0 0
\(357\) 11.2396 0.594864
\(358\) 0 0
\(359\) 5.70435 0.301064 0.150532 0.988605i \(-0.451901\pi\)
0.150532 + 0.988605i \(0.451901\pi\)
\(360\) 0 0
\(361\) −10.2605 −0.540027
\(362\) 0 0
\(363\) 1.94061 0.101856
\(364\) 0 0
\(365\) −13.5264 −0.708006
\(366\) 0 0
\(367\) 11.2589 0.587710 0.293855 0.955850i \(-0.405062\pi\)
0.293855 + 0.955850i \(0.405062\pi\)
\(368\) 0 0
\(369\) −2.50248 −0.130274
\(370\) 0 0
\(371\) −14.1806 −0.736220
\(372\) 0 0
\(373\) −23.2812 −1.20546 −0.602728 0.797946i \(-0.705920\pi\)
−0.602728 + 0.797946i \(0.705920\pi\)
\(374\) 0 0
\(375\) −22.4486 −1.15924
\(376\) 0 0
\(377\) −2.27973 −0.117412
\(378\) 0 0
\(379\) 12.6533 0.649959 0.324979 0.945721i \(-0.394643\pi\)
0.324979 + 0.945721i \(0.394643\pi\)
\(380\) 0 0
\(381\) 17.7510 0.909412
\(382\) 0 0
\(383\) −7.42398 −0.379348 −0.189674 0.981847i \(-0.560743\pi\)
−0.189674 + 0.981847i \(0.560743\pi\)
\(384\) 0 0
\(385\) −1.48281 −0.0755710
\(386\) 0 0
\(387\) −4.78359 −0.243164
\(388\) 0 0
\(389\) −3.13672 −0.159038 −0.0795191 0.996833i \(-0.525338\pi\)
−0.0795191 + 0.996833i \(0.525338\pi\)
\(390\) 0 0
\(391\) 19.8802 1.00539
\(392\) 0 0
\(393\) −5.90271 −0.297752
\(394\) 0 0
\(395\) −5.79196 −0.291425
\(396\) 0 0
\(397\) −24.4590 −1.22756 −0.613781 0.789476i \(-0.710352\pi\)
−0.613781 + 0.789476i \(0.710352\pi\)
\(398\) 0 0
\(399\) −5.73696 −0.287207
\(400\) 0 0
\(401\) 27.3681 1.36670 0.683348 0.730092i \(-0.260523\pi\)
0.683348 + 0.730092i \(0.260523\pi\)
\(402\) 0 0
\(403\) −4.29356 −0.213878
\(404\) 0 0
\(405\) −15.8827 −0.789218
\(406\) 0 0
\(407\) −7.63237 −0.378322
\(408\) 0 0
\(409\) −1.22204 −0.0604258 −0.0302129 0.999543i \(-0.509619\pi\)
−0.0302129 + 0.999543i \(0.509619\pi\)
\(410\) 0 0
\(411\) 14.8000 0.730029
\(412\) 0 0
\(413\) 0.168206 0.00827688
\(414\) 0 0
\(415\) −2.95249 −0.144932
\(416\) 0 0
\(417\) 1.91880 0.0939642
\(418\) 0 0
\(419\) −11.4860 −0.561129 −0.280564 0.959835i \(-0.590522\pi\)
−0.280564 + 0.959835i \(0.590522\pi\)
\(420\) 0 0
\(421\) −9.53451 −0.464684 −0.232342 0.972634i \(-0.574639\pi\)
−0.232342 + 0.972634i \(0.574639\pi\)
\(422\) 0 0
\(423\) −3.98059 −0.193543
\(424\) 0 0
\(425\) 16.2244 0.786999
\(426\) 0 0
\(427\) 1.15136 0.0557180
\(428\) 0 0
\(429\) 1.94061 0.0936937
\(430\) 0 0
\(431\) 11.3980 0.549021 0.274511 0.961584i \(-0.411484\pi\)
0.274511 + 0.961584i \(0.411484\pi\)
\(432\) 0 0
\(433\) −8.42472 −0.404866 −0.202433 0.979296i \(-0.564885\pi\)
−0.202433 + 0.979296i \(0.564885\pi\)
\(434\) 0 0
\(435\) −6.56007 −0.314531
\(436\) 0 0
\(437\) −10.1473 −0.485412
\(438\) 0 0
\(439\) −21.1048 −1.00728 −0.503639 0.863914i \(-0.668006\pi\)
−0.503639 + 0.863914i \(0.668006\pi\)
\(440\) 0 0
\(441\) 0.765982 0.0364754
\(442\) 0 0
\(443\) 29.7455 1.41325 0.706625 0.707588i \(-0.250217\pi\)
0.706625 + 0.707588i \(0.250217\pi\)
\(444\) 0 0
\(445\) 2.48634 0.117864
\(446\) 0 0
\(447\) −19.2816 −0.911987
\(448\) 0 0
\(449\) 19.8937 0.938842 0.469421 0.882974i \(-0.344463\pi\)
0.469421 + 0.882974i \(0.344463\pi\)
\(450\) 0 0
\(451\) −3.26702 −0.153838
\(452\) 0 0
\(453\) −1.47220 −0.0691700
\(454\) 0 0
\(455\) −1.48281 −0.0695152
\(456\) 0 0
\(457\) 12.2292 0.572059 0.286030 0.958221i \(-0.407664\pi\)
0.286030 + 0.958221i \(0.407664\pi\)
\(458\) 0 0
\(459\) 25.1095 1.17201
\(460\) 0 0
\(461\) −32.8744 −1.53111 −0.765556 0.643369i \(-0.777536\pi\)
−0.765556 + 0.643369i \(0.777536\pi\)
\(462\) 0 0
\(463\) 13.3571 0.620758 0.310379 0.950613i \(-0.399544\pi\)
0.310379 + 0.950613i \(0.399544\pi\)
\(464\) 0 0
\(465\) −12.3550 −0.572949
\(466\) 0 0
\(467\) −25.5317 −1.18147 −0.590733 0.806867i \(-0.701161\pi\)
−0.590733 + 0.806867i \(0.701161\pi\)
\(468\) 0 0
\(469\) 5.79067 0.267388
\(470\) 0 0
\(471\) 36.8702 1.69889
\(472\) 0 0
\(473\) −6.24504 −0.287147
\(474\) 0 0
\(475\) −8.28130 −0.379972
\(476\) 0 0
\(477\) 10.8621 0.497341
\(478\) 0 0
\(479\) 37.9584 1.73437 0.867183 0.497990i \(-0.165929\pi\)
0.867183 + 0.497990i \(0.165929\pi\)
\(480\) 0 0
\(481\) −7.63237 −0.348006
\(482\) 0 0
\(483\) 6.66112 0.303092
\(484\) 0 0
\(485\) 23.3411 1.05987
\(486\) 0 0
\(487\) −21.5736 −0.977593 −0.488796 0.872398i \(-0.662564\pi\)
−0.488796 + 0.872398i \(0.662564\pi\)
\(488\) 0 0
\(489\) 20.9457 0.947196
\(490\) 0 0
\(491\) −8.34145 −0.376445 −0.188222 0.982126i \(-0.560273\pi\)
−0.188222 + 0.982126i \(0.560273\pi\)
\(492\) 0 0
\(493\) 13.2037 0.594666
\(494\) 0 0
\(495\) 1.13581 0.0510507
\(496\) 0 0
\(497\) 13.7993 0.618982
\(498\) 0 0
\(499\) −2.74508 −0.122887 −0.0614434 0.998111i \(-0.519570\pi\)
−0.0614434 + 0.998111i \(0.519570\pi\)
\(500\) 0 0
\(501\) 37.8707 1.69194
\(502\) 0 0
\(503\) −21.0724 −0.939571 −0.469785 0.882781i \(-0.655669\pi\)
−0.469785 + 0.882781i \(0.655669\pi\)
\(504\) 0 0
\(505\) −13.6400 −0.606971
\(506\) 0 0
\(507\) 1.94061 0.0861857
\(508\) 0 0
\(509\) 14.7906 0.655582 0.327791 0.944750i \(-0.393696\pi\)
0.327791 + 0.944750i \(0.393696\pi\)
\(510\) 0 0
\(511\) 9.12217 0.403541
\(512\) 0 0
\(513\) −12.8165 −0.565861
\(514\) 0 0
\(515\) 15.0557 0.663432
\(516\) 0 0
\(517\) −5.19672 −0.228551
\(518\) 0 0
\(519\) −42.5055 −1.86579
\(520\) 0 0
\(521\) 21.1380 0.926072 0.463036 0.886339i \(-0.346760\pi\)
0.463036 + 0.886339i \(0.346760\pi\)
\(522\) 0 0
\(523\) 7.93936 0.347164 0.173582 0.984819i \(-0.444466\pi\)
0.173582 + 0.984819i \(0.444466\pi\)
\(524\) 0 0
\(525\) 5.43619 0.237255
\(526\) 0 0
\(527\) 24.8674 1.08324
\(528\) 0 0
\(529\) −11.2181 −0.487742
\(530\) 0 0
\(531\) −0.128843 −0.00559131
\(532\) 0 0
\(533\) −3.26702 −0.141510
\(534\) 0 0
\(535\) 26.1186 1.12920
\(536\) 0 0
\(537\) −2.66477 −0.114993
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −17.0689 −0.733851 −0.366926 0.930250i \(-0.619590\pi\)
−0.366926 + 0.930250i \(0.619590\pi\)
\(542\) 0 0
\(543\) 34.7507 1.49129
\(544\) 0 0
\(545\) 5.69561 0.243973
\(546\) 0 0
\(547\) −4.50646 −0.192683 −0.0963413 0.995348i \(-0.530714\pi\)
−0.0963413 + 0.995348i \(0.530714\pi\)
\(548\) 0 0
\(549\) −0.881918 −0.0376394
\(550\) 0 0
\(551\) −6.73948 −0.287112
\(552\) 0 0
\(553\) 3.90607 0.166103
\(554\) 0 0
\(555\) −21.9626 −0.932261
\(556\) 0 0
\(557\) 43.6886 1.85114 0.925572 0.378572i \(-0.123585\pi\)
0.925572 + 0.378572i \(0.123585\pi\)
\(558\) 0 0
\(559\) −6.24504 −0.264137
\(560\) 0 0
\(561\) −11.2396 −0.474538
\(562\) 0 0
\(563\) −10.2961 −0.433930 −0.216965 0.976179i \(-0.569616\pi\)
−0.216965 + 0.976179i \(0.569616\pi\)
\(564\) 0 0
\(565\) 0.772859 0.0325144
\(566\) 0 0
\(567\) 10.7112 0.449829
\(568\) 0 0
\(569\) −8.17191 −0.342584 −0.171292 0.985220i \(-0.554794\pi\)
−0.171292 + 0.985220i \(0.554794\pi\)
\(570\) 0 0
\(571\) 0.795651 0.0332970 0.0166485 0.999861i \(-0.494700\pi\)
0.0166485 + 0.999861i \(0.494700\pi\)
\(572\) 0 0
\(573\) 30.4925 1.27384
\(574\) 0 0
\(575\) 9.61533 0.400987
\(576\) 0 0
\(577\) 10.4885 0.436641 0.218320 0.975877i \(-0.429942\pi\)
0.218320 + 0.975877i \(0.429942\pi\)
\(578\) 0 0
\(579\) −50.8530 −2.11338
\(580\) 0 0
\(581\) 1.99115 0.0826066
\(582\) 0 0
\(583\) 14.1806 0.587301
\(584\) 0 0
\(585\) 1.13581 0.0469598
\(586\) 0 0
\(587\) −3.33437 −0.137624 −0.0688122 0.997630i \(-0.521921\pi\)
−0.0688122 + 0.997630i \(0.521921\pi\)
\(588\) 0 0
\(589\) −12.6929 −0.523001
\(590\) 0 0
\(591\) 12.4178 0.510802
\(592\) 0 0
\(593\) −9.52003 −0.390941 −0.195470 0.980710i \(-0.562623\pi\)
−0.195470 + 0.980710i \(0.562623\pi\)
\(594\) 0 0
\(595\) 8.58813 0.352079
\(596\) 0 0
\(597\) −18.2115 −0.745347
\(598\) 0 0
\(599\) 8.09126 0.330600 0.165300 0.986243i \(-0.447141\pi\)
0.165300 + 0.986243i \(0.447141\pi\)
\(600\) 0 0
\(601\) −1.45651 −0.0594124 −0.0297062 0.999559i \(-0.509457\pi\)
−0.0297062 + 0.999559i \(0.509457\pi\)
\(602\) 0 0
\(603\) −4.43555 −0.180630
\(604\) 0 0
\(605\) 1.48281 0.0602848
\(606\) 0 0
\(607\) 29.4429 1.19505 0.597525 0.801850i \(-0.296151\pi\)
0.597525 + 0.801850i \(0.296151\pi\)
\(608\) 0 0
\(609\) 4.42408 0.179273
\(610\) 0 0
\(611\) −5.19672 −0.210237
\(612\) 0 0
\(613\) 9.76454 0.394386 0.197193 0.980365i \(-0.436817\pi\)
0.197193 + 0.980365i \(0.436817\pi\)
\(614\) 0 0
\(615\) −9.40104 −0.379086
\(616\) 0 0
\(617\) 20.7235 0.834298 0.417149 0.908838i \(-0.363029\pi\)
0.417149 + 0.908838i \(0.363029\pi\)
\(618\) 0 0
\(619\) 9.45591 0.380065 0.190033 0.981778i \(-0.439141\pi\)
0.190033 + 0.981778i \(0.439141\pi\)
\(620\) 0 0
\(621\) 14.8811 0.597157
\(622\) 0 0
\(623\) −1.67678 −0.0671786
\(624\) 0 0
\(625\) −3.14649 −0.125860
\(626\) 0 0
\(627\) 5.73696 0.229112
\(628\) 0 0
\(629\) 44.2051 1.76257
\(630\) 0 0
\(631\) −46.0835 −1.83455 −0.917277 0.398251i \(-0.869617\pi\)
−0.917277 + 0.398251i \(0.869617\pi\)
\(632\) 0 0
\(633\) −20.9620 −0.833167
\(634\) 0 0
\(635\) 13.5634 0.538248
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −10.5700 −0.418142
\(640\) 0 0
\(641\) 27.9594 1.10433 0.552165 0.833735i \(-0.313802\pi\)
0.552165 + 0.833735i \(0.313802\pi\)
\(642\) 0 0
\(643\) 1.59170 0.0627706 0.0313853 0.999507i \(-0.490008\pi\)
0.0313853 + 0.999507i \(0.490008\pi\)
\(644\) 0 0
\(645\) −17.9705 −0.707587
\(646\) 0 0
\(647\) 7.37164 0.289809 0.144904 0.989446i \(-0.453713\pi\)
0.144904 + 0.989446i \(0.453713\pi\)
\(648\) 0 0
\(649\) −0.168206 −0.00660267
\(650\) 0 0
\(651\) 8.33215 0.326563
\(652\) 0 0
\(653\) −35.8422 −1.40262 −0.701308 0.712859i \(-0.747400\pi\)
−0.701308 + 0.712859i \(0.747400\pi\)
\(654\) 0 0
\(655\) −4.51022 −0.176229
\(656\) 0 0
\(657\) −6.98742 −0.272605
\(658\) 0 0
\(659\) −15.9918 −0.622952 −0.311476 0.950254i \(-0.600823\pi\)
−0.311476 + 0.950254i \(0.600823\pi\)
\(660\) 0 0
\(661\) −16.2939 −0.633758 −0.316879 0.948466i \(-0.602635\pi\)
−0.316879 + 0.948466i \(0.602635\pi\)
\(662\) 0 0
\(663\) −11.2396 −0.436511
\(664\) 0 0
\(665\) −4.38357 −0.169988
\(666\) 0 0
\(667\) 7.82514 0.302991
\(668\) 0 0
\(669\) −12.4184 −0.480125
\(670\) 0 0
\(671\) −1.15136 −0.0444476
\(672\) 0 0
\(673\) −11.0502 −0.425955 −0.212978 0.977057i \(-0.568316\pi\)
−0.212978 + 0.977057i \(0.568316\pi\)
\(674\) 0 0
\(675\) 12.1445 0.467444
\(676\) 0 0
\(677\) −49.6267 −1.90731 −0.953655 0.300902i \(-0.902712\pi\)
−0.953655 + 0.300902i \(0.902712\pi\)
\(678\) 0 0
\(679\) −15.7411 −0.604089
\(680\) 0 0
\(681\) −0.677110 −0.0259469
\(682\) 0 0
\(683\) −0.449062 −0.0171829 −0.00859144 0.999963i \(-0.502735\pi\)
−0.00859144 + 0.999963i \(0.502735\pi\)
\(684\) 0 0
\(685\) 11.3086 0.432078
\(686\) 0 0
\(687\) −28.8589 −1.10104
\(688\) 0 0
\(689\) 14.1806 0.540238
\(690\) 0 0
\(691\) 36.7961 1.39979 0.699895 0.714246i \(-0.253230\pi\)
0.699895 + 0.714246i \(0.253230\pi\)
\(692\) 0 0
\(693\) −0.765982 −0.0290973
\(694\) 0 0
\(695\) 1.46614 0.0556140
\(696\) 0 0
\(697\) 18.9219 0.716717
\(698\) 0 0
\(699\) −23.7485 −0.898249
\(700\) 0 0
\(701\) −26.1007 −0.985809 −0.492905 0.870083i \(-0.664065\pi\)
−0.492905 + 0.870083i \(0.664065\pi\)
\(702\) 0 0
\(703\) −22.5633 −0.850990
\(704\) 0 0
\(705\) −14.9539 −0.563196
\(706\) 0 0
\(707\) 9.19873 0.345954
\(708\) 0 0
\(709\) 35.3394 1.32720 0.663600 0.748087i \(-0.269028\pi\)
0.663600 + 0.748087i \(0.269028\pi\)
\(710\) 0 0
\(711\) −2.99198 −0.112208
\(712\) 0 0
\(713\) 14.7376 0.551927
\(714\) 0 0
\(715\) 1.48281 0.0554539
\(716\) 0 0
\(717\) −20.4687 −0.764419
\(718\) 0 0
\(719\) 9.79535 0.365305 0.182652 0.983178i \(-0.441532\pi\)
0.182652 + 0.983178i \(0.441532\pi\)
\(720\) 0 0
\(721\) −10.1535 −0.378135
\(722\) 0 0
\(723\) 6.74835 0.250974
\(724\) 0 0
\(725\) 6.38615 0.237176
\(726\) 0 0
\(727\) −31.7322 −1.17688 −0.588441 0.808540i \(-0.700258\pi\)
−0.588441 + 0.808540i \(0.700258\pi\)
\(728\) 0 0
\(729\) 17.0352 0.630934
\(730\) 0 0
\(731\) 36.1700 1.33779
\(732\) 0 0
\(733\) −7.15992 −0.264458 −0.132229 0.991219i \(-0.542213\pi\)
−0.132229 + 0.991219i \(0.542213\pi\)
\(734\) 0 0
\(735\) 2.87756 0.106140
\(736\) 0 0
\(737\) −5.79067 −0.213302
\(738\) 0 0
\(739\) 43.5138 1.60068 0.800341 0.599545i \(-0.204652\pi\)
0.800341 + 0.599545i \(0.204652\pi\)
\(740\) 0 0
\(741\) 5.73696 0.210753
\(742\) 0 0
\(743\) −24.4006 −0.895170 −0.447585 0.894241i \(-0.647716\pi\)
−0.447585 + 0.894241i \(0.647716\pi\)
\(744\) 0 0
\(745\) −14.7329 −0.539772
\(746\) 0 0
\(747\) −1.52518 −0.0558035
\(748\) 0 0
\(749\) −17.6142 −0.643610
\(750\) 0 0
\(751\) 27.2199 0.993267 0.496634 0.867960i \(-0.334569\pi\)
0.496634 + 0.867960i \(0.334569\pi\)
\(752\) 0 0
\(753\) −16.5648 −0.603654
\(754\) 0 0
\(755\) −1.12490 −0.0409393
\(756\) 0 0
\(757\) −0.0231333 −0.000840793 0 −0.000420397 1.00000i \(-0.500134\pi\)
−0.000420397 1.00000i \(0.500134\pi\)
\(758\) 0 0
\(759\) −6.66112 −0.241784
\(760\) 0 0
\(761\) −18.1675 −0.658573 −0.329287 0.944230i \(-0.606808\pi\)
−0.329287 + 0.944230i \(0.606808\pi\)
\(762\) 0 0
\(763\) −3.84109 −0.139057
\(764\) 0 0
\(765\) −6.57835 −0.237841
\(766\) 0 0
\(767\) −0.168206 −0.00607357
\(768\) 0 0
\(769\) −9.70549 −0.349989 −0.174994 0.984569i \(-0.555991\pi\)
−0.174994 + 0.984569i \(0.555991\pi\)
\(770\) 0 0
\(771\) 18.0219 0.649041
\(772\) 0 0
\(773\) −1.85918 −0.0668701 −0.0334350 0.999441i \(-0.510645\pi\)
−0.0334350 + 0.999441i \(0.510645\pi\)
\(774\) 0 0
\(775\) 12.0274 0.432039
\(776\) 0 0
\(777\) 14.8115 0.531359
\(778\) 0 0
\(779\) −9.65815 −0.346039
\(780\) 0 0
\(781\) −13.7993 −0.493776
\(782\) 0 0
\(783\) 9.88347 0.353206
\(784\) 0 0
\(785\) 28.1722 1.00551
\(786\) 0 0
\(787\) 4.36669 0.155656 0.0778278 0.996967i \(-0.475202\pi\)
0.0778278 + 0.996967i \(0.475202\pi\)
\(788\) 0 0
\(789\) −9.92410 −0.353307
\(790\) 0 0
\(791\) −0.521212 −0.0185322
\(792\) 0 0
\(793\) −1.15136 −0.0408858
\(794\) 0 0
\(795\) 40.8056 1.44722
\(796\) 0 0
\(797\) 2.65681 0.0941090 0.0470545 0.998892i \(-0.485017\pi\)
0.0470545 + 0.998892i \(0.485017\pi\)
\(798\) 0 0
\(799\) 30.0983 1.06480
\(800\) 0 0
\(801\) 1.28438 0.0453814
\(802\) 0 0
\(803\) −9.12217 −0.321914
\(804\) 0 0
\(805\) 5.08972 0.179389
\(806\) 0 0
\(807\) −15.5108 −0.546007
\(808\) 0 0
\(809\) −3.01799 −0.106107 −0.0530534 0.998592i \(-0.516895\pi\)
−0.0530534 + 0.998592i \(0.516895\pi\)
\(810\) 0 0
\(811\) 17.0562 0.598924 0.299462 0.954108i \(-0.403193\pi\)
0.299462 + 0.954108i \(0.403193\pi\)
\(812\) 0 0
\(813\) −3.88570 −0.136277
\(814\) 0 0
\(815\) 16.0044 0.560611
\(816\) 0 0
\(817\) −18.4620 −0.645903
\(818\) 0 0
\(819\) −0.765982 −0.0267656
\(820\) 0 0
\(821\) 34.8148 1.21504 0.607522 0.794303i \(-0.292164\pi\)
0.607522 + 0.794303i \(0.292164\pi\)
\(822\) 0 0
\(823\) −42.0235 −1.46485 −0.732423 0.680850i \(-0.761611\pi\)
−0.732423 + 0.680850i \(0.761611\pi\)
\(824\) 0 0
\(825\) −5.43619 −0.189264
\(826\) 0 0
\(827\) −51.1011 −1.77696 −0.888479 0.458917i \(-0.848237\pi\)
−0.888479 + 0.458917i \(0.848237\pi\)
\(828\) 0 0
\(829\) −13.6271 −0.473289 −0.236644 0.971596i \(-0.576048\pi\)
−0.236644 + 0.971596i \(0.576048\pi\)
\(830\) 0 0
\(831\) 0.467430 0.0162150
\(832\) 0 0
\(833\) −5.79179 −0.200674
\(834\) 0 0
\(835\) 28.9367 1.00140
\(836\) 0 0
\(837\) 18.6142 0.643399
\(838\) 0 0
\(839\) 41.9272 1.44749 0.723744 0.690068i \(-0.242419\pi\)
0.723744 + 0.690068i \(0.242419\pi\)
\(840\) 0 0
\(841\) −23.8028 −0.820787
\(842\) 0 0
\(843\) 31.0033 1.06781
\(844\) 0 0
\(845\) 1.48281 0.0510102
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −5.46134 −0.187433
\(850\) 0 0
\(851\) 26.1980 0.898055
\(852\) 0 0
\(853\) −34.6996 −1.18809 −0.594047 0.804431i \(-0.702471\pi\)
−0.594047 + 0.804431i \(0.702471\pi\)
\(854\) 0 0
\(855\) 3.35774 0.114832
\(856\) 0 0
\(857\) −55.8623 −1.90822 −0.954111 0.299454i \(-0.903196\pi\)
−0.954111 + 0.299454i \(0.903196\pi\)
\(858\) 0 0
\(859\) −9.17540 −0.313061 −0.156530 0.987673i \(-0.550031\pi\)
−0.156530 + 0.987673i \(0.550031\pi\)
\(860\) 0 0
\(861\) 6.34002 0.216067
\(862\) 0 0
\(863\) 31.5768 1.07489 0.537444 0.843299i \(-0.319390\pi\)
0.537444 + 0.843299i \(0.319390\pi\)
\(864\) 0 0
\(865\) −32.4782 −1.10429
\(866\) 0 0
\(867\) 32.1072 1.09042
\(868\) 0 0
\(869\) −3.90607 −0.132504
\(870\) 0 0
\(871\) −5.79067 −0.196209
\(872\) 0 0
\(873\) 12.0574 0.408082
\(874\) 0 0
\(875\) 11.5678 0.391063
\(876\) 0 0
\(877\) −5.82613 −0.196734 −0.0983672 0.995150i \(-0.531362\pi\)
−0.0983672 + 0.995150i \(0.531362\pi\)
\(878\) 0 0
\(879\) −49.3743 −1.66535
\(880\) 0 0
\(881\) −9.72891 −0.327775 −0.163888 0.986479i \(-0.552403\pi\)
−0.163888 + 0.986479i \(0.552403\pi\)
\(882\) 0 0
\(883\) 49.2868 1.65863 0.829317 0.558778i \(-0.188730\pi\)
0.829317 + 0.558778i \(0.188730\pi\)
\(884\) 0 0
\(885\) −0.484024 −0.0162703
\(886\) 0 0
\(887\) 44.0688 1.47969 0.739843 0.672779i \(-0.234900\pi\)
0.739843 + 0.672779i \(0.234900\pi\)
\(888\) 0 0
\(889\) −9.14711 −0.306784
\(890\) 0 0
\(891\) −10.7112 −0.358839
\(892\) 0 0
\(893\) −15.3629 −0.514098
\(894\) 0 0
\(895\) −2.03613 −0.0680605
\(896\) 0 0
\(897\) −6.66112 −0.222408
\(898\) 0 0
\(899\) 9.78817 0.326454
\(900\) 0 0
\(901\) −82.1311 −2.73618
\(902\) 0 0
\(903\) 12.1192 0.403302
\(904\) 0 0
\(905\) 26.5528 0.882643
\(906\) 0 0
\(907\) −5.30139 −0.176030 −0.0880148 0.996119i \(-0.528052\pi\)
−0.0880148 + 0.996119i \(0.528052\pi\)
\(908\) 0 0
\(909\) −7.04607 −0.233703
\(910\) 0 0
\(911\) 34.0252 1.12730 0.563652 0.826012i \(-0.309396\pi\)
0.563652 + 0.826012i \(0.309396\pi\)
\(912\) 0 0
\(913\) −1.99115 −0.0658973
\(914\) 0 0
\(915\) −3.31310 −0.109528
\(916\) 0 0
\(917\) 3.04167 0.100445
\(918\) 0 0
\(919\) −15.1096 −0.498418 −0.249209 0.968450i \(-0.580171\pi\)
−0.249209 + 0.968450i \(0.580171\pi\)
\(920\) 0 0
\(921\) 51.1284 1.68474
\(922\) 0 0
\(923\) −13.7993 −0.454208
\(924\) 0 0
\(925\) 21.3804 0.702982
\(926\) 0 0
\(927\) 7.77738 0.255443
\(928\) 0 0
\(929\) −29.6738 −0.973567 −0.486784 0.873523i \(-0.661830\pi\)
−0.486784 + 0.873523i \(0.661830\pi\)
\(930\) 0 0
\(931\) 2.95626 0.0968875
\(932\) 0 0
\(933\) 17.9826 0.588723
\(934\) 0 0
\(935\) −8.58813 −0.280862
\(936\) 0 0
\(937\) 35.0825 1.14610 0.573048 0.819522i \(-0.305761\pi\)
0.573048 + 0.819522i \(0.305761\pi\)
\(938\) 0 0
\(939\) 18.4588 0.602380
\(940\) 0 0
\(941\) −14.0092 −0.456687 −0.228344 0.973581i \(-0.573331\pi\)
−0.228344 + 0.973581i \(0.573331\pi\)
\(942\) 0 0
\(943\) 11.2140 0.365177
\(944\) 0 0
\(945\) 6.42852 0.209120
\(946\) 0 0
\(947\) −2.54068 −0.0825609 −0.0412804 0.999148i \(-0.513144\pi\)
−0.0412804 + 0.999148i \(0.513144\pi\)
\(948\) 0 0
\(949\) −9.12217 −0.296118
\(950\) 0 0
\(951\) −21.2178 −0.688035
\(952\) 0 0
\(953\) −39.3206 −1.27372 −0.636860 0.770980i \(-0.719767\pi\)
−0.636860 + 0.770980i \(0.719767\pi\)
\(954\) 0 0
\(955\) 23.2991 0.753943
\(956\) 0 0
\(957\) −4.42408 −0.143010
\(958\) 0 0
\(959\) −7.62644 −0.246271
\(960\) 0 0
\(961\) −12.5653 −0.405333
\(962\) 0 0
\(963\) 13.4922 0.434780
\(964\) 0 0
\(965\) −38.8565 −1.25083
\(966\) 0 0
\(967\) −11.9114 −0.383045 −0.191523 0.981488i \(-0.561343\pi\)
−0.191523 + 0.981488i \(0.561343\pi\)
\(968\) 0 0
\(969\) −33.2273 −1.06741
\(970\) 0 0
\(971\) 28.8806 0.926824 0.463412 0.886143i \(-0.346625\pi\)
0.463412 + 0.886143i \(0.346625\pi\)
\(972\) 0 0
\(973\) −0.988761 −0.0316982
\(974\) 0 0
\(975\) −5.43619 −0.174097
\(976\) 0 0
\(977\) −0.545671 −0.0174576 −0.00872878 0.999962i \(-0.502778\pi\)
−0.00872878 + 0.999962i \(0.502778\pi\)
\(978\) 0 0
\(979\) 1.67678 0.0535900
\(980\) 0 0
\(981\) 2.94221 0.0939375
\(982\) 0 0
\(983\) −24.4237 −0.778995 −0.389497 0.921028i \(-0.627351\pi\)
−0.389497 + 0.921028i \(0.627351\pi\)
\(984\) 0 0
\(985\) 9.48839 0.302325
\(986\) 0 0
\(987\) 10.0848 0.321003
\(988\) 0 0
\(989\) 21.4360 0.681625
\(990\) 0 0
\(991\) −21.5724 −0.685270 −0.342635 0.939469i \(-0.611319\pi\)
−0.342635 + 0.939469i \(0.611319\pi\)
\(992\) 0 0
\(993\) 63.2690 2.00778
\(994\) 0 0
\(995\) −13.9153 −0.441144
\(996\) 0 0
\(997\) −51.1961 −1.62140 −0.810699 0.585463i \(-0.800913\pi\)
−0.810699 + 0.585463i \(0.800913\pi\)
\(998\) 0 0
\(999\) 33.0891 1.04689
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 \(a_p\))