Properties

Label 4028.2.a.d.1.13
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(-0.537191\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.537191 q^{3} -2.35184 q^{5} -1.00979 q^{7} -2.71143 q^{9} +O(q^{10})\) \(q+0.537191 q^{3} -2.35184 q^{5} -1.00979 q^{7} -2.71143 q^{9} +3.55138 q^{11} +0.172083 q^{13} -1.26339 q^{15} +7.68990 q^{17} -1.00000 q^{19} -0.542449 q^{21} -8.17344 q^{23} +0.531160 q^{25} -3.06813 q^{27} +3.95811 q^{29} +8.96845 q^{31} +1.90777 q^{33} +2.37486 q^{35} -9.28780 q^{37} +0.0924417 q^{39} -0.449703 q^{41} +9.15762 q^{43} +6.37684 q^{45} -9.50313 q^{47} -5.98033 q^{49} +4.13095 q^{51} +1.00000 q^{53} -8.35229 q^{55} -0.537191 q^{57} -7.97890 q^{59} +3.34325 q^{61} +2.73797 q^{63} -0.404713 q^{65} -4.16062 q^{67} -4.39070 q^{69} +4.34907 q^{71} +3.25468 q^{73} +0.285335 q^{75} -3.58614 q^{77} +5.21648 q^{79} +6.48611 q^{81} -1.01694 q^{83} -18.0854 q^{85} +2.12626 q^{87} -8.11647 q^{89} -0.173768 q^{91} +4.81777 q^{93} +2.35184 q^{95} +3.08376 q^{97} -9.62930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) 0.537191 0.310147 0.155074 0.987903i \(-0.450438\pi\)
0.155074 + 0.987903i \(0.450438\pi\)
\(4\) 0 0
\(5\) −2.35184 −1.05178 −0.525888 0.850554i \(-0.676267\pi\)
−0.525888 + 0.850554i \(0.676267\pi\)
\(6\) 0 0
\(7\) −1.00979 −0.381664 −0.190832 0.981623i \(-0.561119\pi\)
−0.190832 + 0.981623i \(0.561119\pi\)
\(8\) 0 0
\(9\) −2.71143 −0.903809
\(10\) 0 0
\(11\) 3.55138 1.07078 0.535391 0.844604i \(-0.320164\pi\)
0.535391 + 0.844604i \(0.320164\pi\)
\(12\) 0 0
\(13\) 0.172083 0.0477273 0.0238637 0.999715i \(-0.492403\pi\)
0.0238637 + 0.999715i \(0.492403\pi\)
\(14\) 0 0
\(15\) −1.26339 −0.326206
\(16\) 0 0
\(17\) 7.68990 1.86507 0.932537 0.361073i \(-0.117590\pi\)
0.932537 + 0.361073i \(0.117590\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −0.542449 −0.118372
\(22\) 0 0
\(23\) −8.17344 −1.70428 −0.852140 0.523313i \(-0.824696\pi\)
−0.852140 + 0.523313i \(0.824696\pi\)
\(24\) 0 0
\(25\) 0.531160 0.106232
\(26\) 0 0
\(27\) −3.06813 −0.590461
\(28\) 0 0
\(29\) 3.95811 0.735003 0.367501 0.930023i \(-0.380213\pi\)
0.367501 + 0.930023i \(0.380213\pi\)
\(30\) 0 0
\(31\) 8.96845 1.61078 0.805391 0.592744i \(-0.201955\pi\)
0.805391 + 0.592744i \(0.201955\pi\)
\(32\) 0 0
\(33\) 1.90777 0.332100
\(34\) 0 0
\(35\) 2.37486 0.401425
\(36\) 0 0
\(37\) −9.28780 −1.52690 −0.763452 0.645864i \(-0.776497\pi\)
−0.763452 + 0.645864i \(0.776497\pi\)
\(38\) 0 0
\(39\) 0.0924417 0.0148025
\(40\) 0 0
\(41\) −0.449703 −0.0702318 −0.0351159 0.999383i \(-0.511180\pi\)
−0.0351159 + 0.999383i \(0.511180\pi\)
\(42\) 0 0
\(43\) 9.15762 1.39652 0.698262 0.715842i \(-0.253957\pi\)
0.698262 + 0.715842i \(0.253957\pi\)
\(44\) 0 0
\(45\) 6.37684 0.950604
\(46\) 0 0
\(47\) −9.50313 −1.38617 −0.693087 0.720854i \(-0.743750\pi\)
−0.693087 + 0.720854i \(0.743750\pi\)
\(48\) 0 0
\(49\) −5.98033 −0.854333
\(50\) 0 0
\(51\) 4.13095 0.578448
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −8.35229 −1.12622
\(56\) 0 0
\(57\) −0.537191 −0.0711527
\(58\) 0 0
\(59\) −7.97890 −1.03876 −0.519382 0.854542i \(-0.673838\pi\)
−0.519382 + 0.854542i \(0.673838\pi\)
\(60\) 0 0
\(61\) 3.34325 0.428060 0.214030 0.976827i \(-0.431341\pi\)
0.214030 + 0.976827i \(0.431341\pi\)
\(62\) 0 0
\(63\) 2.73797 0.344951
\(64\) 0 0
\(65\) −0.404713 −0.0501984
\(66\) 0 0
\(67\) −4.16062 −0.508301 −0.254151 0.967165i \(-0.581796\pi\)
−0.254151 + 0.967165i \(0.581796\pi\)
\(68\) 0 0
\(69\) −4.39070 −0.528578
\(70\) 0 0
\(71\) 4.34907 0.516140 0.258070 0.966126i \(-0.416914\pi\)
0.258070 + 0.966126i \(0.416914\pi\)
\(72\) 0 0
\(73\) 3.25468 0.380932 0.190466 0.981694i \(-0.439000\pi\)
0.190466 + 0.981694i \(0.439000\pi\)
\(74\) 0 0
\(75\) 0.285335 0.0329476
\(76\) 0 0
\(77\) −3.58614 −0.408679
\(78\) 0 0
\(79\) 5.21648 0.586900 0.293450 0.955974i \(-0.405197\pi\)
0.293450 + 0.955974i \(0.405197\pi\)
\(80\) 0 0
\(81\) 6.48611 0.720678
\(82\) 0 0
\(83\) −1.01694 −0.111624 −0.0558118 0.998441i \(-0.517775\pi\)
−0.0558118 + 0.998441i \(0.517775\pi\)
\(84\) 0 0
\(85\) −18.0854 −1.96164
\(86\) 0 0
\(87\) 2.12626 0.227959
\(88\) 0 0
\(89\) −8.11647 −0.860344 −0.430172 0.902747i \(-0.641547\pi\)
−0.430172 + 0.902747i \(0.641547\pi\)
\(90\) 0 0
\(91\) −0.173768 −0.0182158
\(92\) 0 0
\(93\) 4.81777 0.499580
\(94\) 0 0
\(95\) 2.35184 0.241294
\(96\) 0 0
\(97\) 3.08376 0.313108 0.156554 0.987669i \(-0.449961\pi\)
0.156554 + 0.987669i \(0.449961\pi\)
\(98\) 0 0
\(99\) −9.62930 −0.967781
\(100\) 0 0
\(101\) −11.1511 −1.10958 −0.554789 0.831991i \(-0.687201\pi\)
−0.554789 + 0.831991i \(0.687201\pi\)
\(102\) 0 0
\(103\) −14.6088 −1.43945 −0.719725 0.694260i \(-0.755732\pi\)
−0.719725 + 0.694260i \(0.755732\pi\)
\(104\) 0 0
\(105\) 1.27575 0.124501
\(106\) 0 0
\(107\) 15.2664 1.47586 0.737931 0.674876i \(-0.235803\pi\)
0.737931 + 0.674876i \(0.235803\pi\)
\(108\) 0 0
\(109\) −7.20109 −0.689740 −0.344870 0.938651i \(-0.612077\pi\)
−0.344870 + 0.938651i \(0.612077\pi\)
\(110\) 0 0
\(111\) −4.98932 −0.473566
\(112\) 0 0
\(113\) −17.7284 −1.66775 −0.833873 0.551957i \(-0.813881\pi\)
−0.833873 + 0.551957i \(0.813881\pi\)
\(114\) 0 0
\(115\) 19.2226 1.79252
\(116\) 0 0
\(117\) −0.466591 −0.0431364
\(118\) 0 0
\(119\) −7.76517 −0.711832
\(120\) 0 0
\(121\) 1.61230 0.146573
\(122\) 0 0
\(123\) −0.241576 −0.0217822
\(124\) 0 0
\(125\) 10.5100 0.940043
\(126\) 0 0
\(127\) −9.27267 −0.822816 −0.411408 0.911451i \(-0.634963\pi\)
−0.411408 + 0.911451i \(0.634963\pi\)
\(128\) 0 0
\(129\) 4.91939 0.433128
\(130\) 0 0
\(131\) −8.15882 −0.712839 −0.356420 0.934326i \(-0.616003\pi\)
−0.356420 + 0.934326i \(0.616003\pi\)
\(132\) 0 0
\(133\) 1.00979 0.0875597
\(134\) 0 0
\(135\) 7.21575 0.621033
\(136\) 0 0
\(137\) −1.79834 −0.153643 −0.0768214 0.997045i \(-0.524477\pi\)
−0.0768214 + 0.997045i \(0.524477\pi\)
\(138\) 0 0
\(139\) −2.34073 −0.198538 −0.0992689 0.995061i \(-0.531650\pi\)
−0.0992689 + 0.995061i \(0.531650\pi\)
\(140\) 0 0
\(141\) −5.10500 −0.429918
\(142\) 0 0
\(143\) 0.611133 0.0511055
\(144\) 0 0
\(145\) −9.30885 −0.773058
\(146\) 0 0
\(147\) −3.21258 −0.264969
\(148\) 0 0
\(149\) −9.11663 −0.746864 −0.373432 0.927658i \(-0.621819\pi\)
−0.373432 + 0.927658i \(0.621819\pi\)
\(150\) 0 0
\(151\) −6.02151 −0.490024 −0.245012 0.969520i \(-0.578792\pi\)
−0.245012 + 0.969520i \(0.578792\pi\)
\(152\) 0 0
\(153\) −20.8506 −1.68567
\(154\) 0 0
\(155\) −21.0924 −1.69418
\(156\) 0 0
\(157\) −21.0057 −1.67644 −0.838218 0.545336i \(-0.816402\pi\)
−0.838218 + 0.545336i \(0.816402\pi\)
\(158\) 0 0
\(159\) 0.537191 0.0426020
\(160\) 0 0
\(161\) 8.25345 0.650463
\(162\) 0 0
\(163\) −12.5285 −0.981306 −0.490653 0.871355i \(-0.663242\pi\)
−0.490653 + 0.871355i \(0.663242\pi\)
\(164\) 0 0
\(165\) −4.48677 −0.349295
\(166\) 0 0
\(167\) −24.5039 −1.89617 −0.948083 0.318024i \(-0.896981\pi\)
−0.948083 + 0.318024i \(0.896981\pi\)
\(168\) 0 0
\(169\) −12.9704 −0.997722
\(170\) 0 0
\(171\) 2.71143 0.207348
\(172\) 0 0
\(173\) −20.5556 −1.56281 −0.781406 0.624023i \(-0.785497\pi\)
−0.781406 + 0.624023i \(0.785497\pi\)
\(174\) 0 0
\(175\) −0.536359 −0.0405450
\(176\) 0 0
\(177\) −4.28619 −0.322170
\(178\) 0 0
\(179\) 9.49690 0.709832 0.354916 0.934898i \(-0.384509\pi\)
0.354916 + 0.934898i \(0.384509\pi\)
\(180\) 0 0
\(181\) 12.0182 0.893305 0.446652 0.894708i \(-0.352616\pi\)
0.446652 + 0.894708i \(0.352616\pi\)
\(182\) 0 0
\(183\) 1.79597 0.132762
\(184\) 0 0
\(185\) 21.8434 1.60596
\(186\) 0 0
\(187\) 27.3098 1.99709
\(188\) 0 0
\(189\) 3.09816 0.225358
\(190\) 0 0
\(191\) 18.6439 1.34902 0.674512 0.738264i \(-0.264354\pi\)
0.674512 + 0.738264i \(0.264354\pi\)
\(192\) 0 0
\(193\) 4.92405 0.354441 0.177221 0.984171i \(-0.443289\pi\)
0.177221 + 0.984171i \(0.443289\pi\)
\(194\) 0 0
\(195\) −0.217408 −0.0155689
\(196\) 0 0
\(197\) −21.1462 −1.50661 −0.753303 0.657674i \(-0.771541\pi\)
−0.753303 + 0.657674i \(0.771541\pi\)
\(198\) 0 0
\(199\) −23.8261 −1.68899 −0.844493 0.535566i \(-0.820098\pi\)
−0.844493 + 0.535566i \(0.820098\pi\)
\(200\) 0 0
\(201\) −2.23505 −0.157648
\(202\) 0 0
\(203\) −3.99685 −0.280524
\(204\) 0 0
\(205\) 1.05763 0.0738681
\(206\) 0 0
\(207\) 22.1617 1.54034
\(208\) 0 0
\(209\) −3.55138 −0.245654
\(210\) 0 0
\(211\) −5.46889 −0.376494 −0.188247 0.982122i \(-0.560281\pi\)
−0.188247 + 0.982122i \(0.560281\pi\)
\(212\) 0 0
\(213\) 2.33628 0.160079
\(214\) 0 0
\(215\) −21.5373 −1.46883
\(216\) 0 0
\(217\) −9.05624 −0.614778
\(218\) 0 0
\(219\) 1.74839 0.118145
\(220\) 0 0
\(221\) 1.32330 0.0890151
\(222\) 0 0
\(223\) 14.6634 0.981932 0.490966 0.871179i \(-0.336644\pi\)
0.490966 + 0.871179i \(0.336644\pi\)
\(224\) 0 0
\(225\) −1.44020 −0.0960134
\(226\) 0 0
\(227\) −18.2870 −1.21375 −0.606877 0.794796i \(-0.707578\pi\)
−0.606877 + 0.794796i \(0.707578\pi\)
\(228\) 0 0
\(229\) −3.32252 −0.219558 −0.109779 0.993956i \(-0.535014\pi\)
−0.109779 + 0.993956i \(0.535014\pi\)
\(230\) 0 0
\(231\) −1.92644 −0.126751
\(232\) 0 0
\(233\) 3.50426 0.229572 0.114786 0.993390i \(-0.463382\pi\)
0.114786 + 0.993390i \(0.463382\pi\)
\(234\) 0 0
\(235\) 22.3499 1.45794
\(236\) 0 0
\(237\) 2.80225 0.182026
\(238\) 0 0
\(239\) −8.15493 −0.527499 −0.263749 0.964591i \(-0.584959\pi\)
−0.263749 + 0.964591i \(0.584959\pi\)
\(240\) 0 0
\(241\) −5.36186 −0.345388 −0.172694 0.984976i \(-0.555247\pi\)
−0.172694 + 0.984976i \(0.555247\pi\)
\(242\) 0 0
\(243\) 12.6887 0.813978
\(244\) 0 0
\(245\) 14.0648 0.898566
\(246\) 0 0
\(247\) −0.172083 −0.0109494
\(248\) 0 0
\(249\) −0.546291 −0.0346198
\(250\) 0 0
\(251\) 25.3806 1.60201 0.801003 0.598660i \(-0.204300\pi\)
0.801003 + 0.598660i \(0.204300\pi\)
\(252\) 0 0
\(253\) −29.0270 −1.82491
\(254\) 0 0
\(255\) −9.71533 −0.608398
\(256\) 0 0
\(257\) 14.4397 0.900722 0.450361 0.892847i \(-0.351295\pi\)
0.450361 + 0.892847i \(0.351295\pi\)
\(258\) 0 0
\(259\) 9.37871 0.582765
\(260\) 0 0
\(261\) −10.7321 −0.664302
\(262\) 0 0
\(263\) 24.7452 1.52585 0.762927 0.646484i \(-0.223761\pi\)
0.762927 + 0.646484i \(0.223761\pi\)
\(264\) 0 0
\(265\) −2.35184 −0.144472
\(266\) 0 0
\(267\) −4.36010 −0.266834
\(268\) 0 0
\(269\) 29.2054 1.78068 0.890342 0.455292i \(-0.150465\pi\)
0.890342 + 0.455292i \(0.150465\pi\)
\(270\) 0 0
\(271\) 7.60309 0.461855 0.230927 0.972971i \(-0.425824\pi\)
0.230927 + 0.972971i \(0.425824\pi\)
\(272\) 0 0
\(273\) −0.0933465 −0.00564959
\(274\) 0 0
\(275\) 1.88635 0.113751
\(276\) 0 0
\(277\) −5.89074 −0.353940 −0.176970 0.984216i \(-0.556630\pi\)
−0.176970 + 0.984216i \(0.556630\pi\)
\(278\) 0 0
\(279\) −24.3173 −1.45584
\(280\) 0 0
\(281\) 3.42637 0.204400 0.102200 0.994764i \(-0.467412\pi\)
0.102200 + 0.994764i \(0.467412\pi\)
\(282\) 0 0
\(283\) −3.35801 −0.199613 −0.0998064 0.995007i \(-0.531822\pi\)
−0.0998064 + 0.995007i \(0.531822\pi\)
\(284\) 0 0
\(285\) 1.26339 0.0748367
\(286\) 0 0
\(287\) 0.454104 0.0268049
\(288\) 0 0
\(289\) 42.1346 2.47850
\(290\) 0 0
\(291\) 1.65657 0.0971098
\(292\) 0 0
\(293\) 17.9446 1.04834 0.524168 0.851615i \(-0.324376\pi\)
0.524168 + 0.851615i \(0.324376\pi\)
\(294\) 0 0
\(295\) 18.7651 1.09255
\(296\) 0 0
\(297\) −10.8961 −0.632255
\(298\) 0 0
\(299\) −1.40651 −0.0813408
\(300\) 0 0
\(301\) −9.24726 −0.533003
\(302\) 0 0
\(303\) −5.99028 −0.344133
\(304\) 0 0
\(305\) −7.86280 −0.450223
\(306\) 0 0
\(307\) −24.2104 −1.38176 −0.690881 0.722968i \(-0.742777\pi\)
−0.690881 + 0.722968i \(0.742777\pi\)
\(308\) 0 0
\(309\) −7.84773 −0.446442
\(310\) 0 0
\(311\) −31.3781 −1.77929 −0.889643 0.456657i \(-0.849047\pi\)
−0.889643 + 0.456657i \(0.849047\pi\)
\(312\) 0 0
\(313\) 9.19990 0.520009 0.260004 0.965607i \(-0.416276\pi\)
0.260004 + 0.965607i \(0.416276\pi\)
\(314\) 0 0
\(315\) −6.43926 −0.362811
\(316\) 0 0
\(317\) −18.4653 −1.03712 −0.518559 0.855042i \(-0.673531\pi\)
−0.518559 + 0.855042i \(0.673531\pi\)
\(318\) 0 0
\(319\) 14.0568 0.787027
\(320\) 0 0
\(321\) 8.20099 0.457735
\(322\) 0 0
\(323\) −7.68990 −0.427878
\(324\) 0 0
\(325\) 0.0914038 0.00507017
\(326\) 0 0
\(327\) −3.86836 −0.213921
\(328\) 0 0
\(329\) 9.59615 0.529053
\(330\) 0 0
\(331\) 0.353909 0.0194526 0.00972629 0.999953i \(-0.496904\pi\)
0.00972629 + 0.999953i \(0.496904\pi\)
\(332\) 0 0
\(333\) 25.1832 1.38003
\(334\) 0 0
\(335\) 9.78513 0.534619
\(336\) 0 0
\(337\) −9.18426 −0.500298 −0.250149 0.968207i \(-0.580480\pi\)
−0.250149 + 0.968207i \(0.580480\pi\)
\(338\) 0 0
\(339\) −9.52353 −0.517247
\(340\) 0 0
\(341\) 31.8504 1.72480
\(342\) 0 0
\(343\) 13.1074 0.707732
\(344\) 0 0
\(345\) 10.3262 0.555946
\(346\) 0 0
\(347\) 17.3237 0.929986 0.464993 0.885314i \(-0.346057\pi\)
0.464993 + 0.885314i \(0.346057\pi\)
\(348\) 0 0
\(349\) −13.3943 −0.716980 −0.358490 0.933534i \(-0.616708\pi\)
−0.358490 + 0.933534i \(0.616708\pi\)
\(350\) 0 0
\(351\) −0.527974 −0.0281811
\(352\) 0 0
\(353\) 25.5060 1.35755 0.678775 0.734346i \(-0.262511\pi\)
0.678775 + 0.734346i \(0.262511\pi\)
\(354\) 0 0
\(355\) −10.2283 −0.542863
\(356\) 0 0
\(357\) −4.17138 −0.220773
\(358\) 0 0
\(359\) −0.721974 −0.0381043 −0.0190522 0.999818i \(-0.506065\pi\)
−0.0190522 + 0.999818i \(0.506065\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0.866115 0.0454592
\(364\) 0 0
\(365\) −7.65450 −0.400655
\(366\) 0 0
\(367\) −23.0271 −1.20200 −0.601001 0.799248i \(-0.705231\pi\)
−0.601001 + 0.799248i \(0.705231\pi\)
\(368\) 0 0
\(369\) 1.21934 0.0634761
\(370\) 0 0
\(371\) −1.00979 −0.0524256
\(372\) 0 0
\(373\) 2.10637 0.109063 0.0545317 0.998512i \(-0.482633\pi\)
0.0545317 + 0.998512i \(0.482633\pi\)
\(374\) 0 0
\(375\) 5.64588 0.291552
\(376\) 0 0
\(377\) 0.681125 0.0350797
\(378\) 0 0
\(379\) −23.6695 −1.21582 −0.607911 0.794005i \(-0.707992\pi\)
−0.607911 + 0.794005i \(0.707992\pi\)
\(380\) 0 0
\(381\) −4.98120 −0.255194
\(382\) 0 0
\(383\) −26.5618 −1.35724 −0.678621 0.734488i \(-0.737422\pi\)
−0.678621 + 0.734488i \(0.737422\pi\)
\(384\) 0 0
\(385\) 8.43404 0.429838
\(386\) 0 0
\(387\) −24.8302 −1.26219
\(388\) 0 0
\(389\) 6.63263 0.336288 0.168144 0.985762i \(-0.446223\pi\)
0.168144 + 0.985762i \(0.446223\pi\)
\(390\) 0 0
\(391\) −62.8530 −3.17861
\(392\) 0 0
\(393\) −4.38285 −0.221085
\(394\) 0 0
\(395\) −12.2683 −0.617288
\(396\) 0 0
\(397\) 27.0956 1.35989 0.679945 0.733263i \(-0.262004\pi\)
0.679945 + 0.733263i \(0.262004\pi\)
\(398\) 0 0
\(399\) 0.542449 0.0271564
\(400\) 0 0
\(401\) 31.7468 1.58536 0.792679 0.609639i \(-0.208685\pi\)
0.792679 + 0.609639i \(0.208685\pi\)
\(402\) 0 0
\(403\) 1.54332 0.0768783
\(404\) 0 0
\(405\) −15.2543 −0.757992
\(406\) 0 0
\(407\) −32.9845 −1.63498
\(408\) 0 0
\(409\) 28.1464 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(410\) 0 0
\(411\) −0.966055 −0.0476520
\(412\) 0 0
\(413\) 8.05700 0.396459
\(414\) 0 0
\(415\) 2.39168 0.117403
\(416\) 0 0
\(417\) −1.25742 −0.0615760
\(418\) 0 0
\(419\) 18.1647 0.887404 0.443702 0.896174i \(-0.353665\pi\)
0.443702 + 0.896174i \(0.353665\pi\)
\(420\) 0 0
\(421\) −8.21227 −0.400242 −0.200121 0.979771i \(-0.564133\pi\)
−0.200121 + 0.979771i \(0.564133\pi\)
\(422\) 0 0
\(423\) 25.7670 1.25284
\(424\) 0 0
\(425\) 4.08457 0.198131
\(426\) 0 0
\(427\) −3.37598 −0.163375
\(428\) 0 0
\(429\) 0.328295 0.0158503
\(430\) 0 0
\(431\) −1.07761 −0.0519064 −0.0259532 0.999663i \(-0.508262\pi\)
−0.0259532 + 0.999663i \(0.508262\pi\)
\(432\) 0 0
\(433\) −15.0333 −0.722452 −0.361226 0.932478i \(-0.617642\pi\)
−0.361226 + 0.932478i \(0.617642\pi\)
\(434\) 0 0
\(435\) −5.00063 −0.239762
\(436\) 0 0
\(437\) 8.17344 0.390989
\(438\) 0 0
\(439\) −13.3808 −0.638629 −0.319315 0.947649i \(-0.603453\pi\)
−0.319315 + 0.947649i \(0.603453\pi\)
\(440\) 0 0
\(441\) 16.2152 0.772153
\(442\) 0 0
\(443\) −9.81811 −0.466473 −0.233236 0.972420i \(-0.574932\pi\)
−0.233236 + 0.972420i \(0.574932\pi\)
\(444\) 0 0
\(445\) 19.0887 0.904889
\(446\) 0 0
\(447\) −4.89737 −0.231638
\(448\) 0 0
\(449\) −2.96158 −0.139766 −0.0698828 0.997555i \(-0.522263\pi\)
−0.0698828 + 0.997555i \(0.522263\pi\)
\(450\) 0 0
\(451\) −1.59707 −0.0752029
\(452\) 0 0
\(453\) −3.23470 −0.151980
\(454\) 0 0
\(455\) 0.408674 0.0191589
\(456\) 0 0
\(457\) 2.88861 0.135123 0.0675617 0.997715i \(-0.478478\pi\)
0.0675617 + 0.997715i \(0.478478\pi\)
\(458\) 0 0
\(459\) −23.5936 −1.10125
\(460\) 0 0
\(461\) 15.8850 0.739840 0.369920 0.929064i \(-0.379385\pi\)
0.369920 + 0.929064i \(0.379385\pi\)
\(462\) 0 0
\(463\) −2.39483 −0.111297 −0.0556486 0.998450i \(-0.517723\pi\)
−0.0556486 + 0.998450i \(0.517723\pi\)
\(464\) 0 0
\(465\) −11.3306 −0.525446
\(466\) 0 0
\(467\) 29.8941 1.38334 0.691668 0.722216i \(-0.256876\pi\)
0.691668 + 0.722216i \(0.256876\pi\)
\(468\) 0 0
\(469\) 4.20135 0.194000
\(470\) 0 0
\(471\) −11.2841 −0.519942
\(472\) 0 0
\(473\) 32.5222 1.49537
\(474\) 0 0
\(475\) −0.531160 −0.0243713
\(476\) 0 0
\(477\) −2.71143 −0.124148
\(478\) 0 0
\(479\) −1.51674 −0.0693014 −0.0346507 0.999399i \(-0.511032\pi\)
−0.0346507 + 0.999399i \(0.511032\pi\)
\(480\) 0 0
\(481\) −1.59828 −0.0728751
\(482\) 0 0
\(483\) 4.43368 0.201739
\(484\) 0 0
\(485\) −7.25252 −0.329320
\(486\) 0 0
\(487\) 2.66752 0.120877 0.0604385 0.998172i \(-0.480750\pi\)
0.0604385 + 0.998172i \(0.480750\pi\)
\(488\) 0 0
\(489\) −6.73018 −0.304349
\(490\) 0 0
\(491\) −27.2545 −1.22998 −0.614989 0.788536i \(-0.710840\pi\)
−0.614989 + 0.788536i \(0.710840\pi\)
\(492\) 0 0
\(493\) 30.4375 1.37084
\(494\) 0 0
\(495\) 22.6466 1.01789
\(496\) 0 0
\(497\) −4.39164 −0.196992
\(498\) 0 0
\(499\) −0.817949 −0.0366164 −0.0183082 0.999832i \(-0.505828\pi\)
−0.0183082 + 0.999832i \(0.505828\pi\)
\(500\) 0 0
\(501\) −13.1633 −0.588091
\(502\) 0 0
\(503\) 26.4923 1.18123 0.590616 0.806953i \(-0.298885\pi\)
0.590616 + 0.806953i \(0.298885\pi\)
\(504\) 0 0
\(505\) 26.2257 1.16703
\(506\) 0 0
\(507\) −6.96758 −0.309441
\(508\) 0 0
\(509\) 28.9142 1.28160 0.640799 0.767709i \(-0.278603\pi\)
0.640799 + 0.767709i \(0.278603\pi\)
\(510\) 0 0
\(511\) −3.28654 −0.145388
\(512\) 0 0
\(513\) 3.06813 0.135461
\(514\) 0 0
\(515\) 34.3576 1.51398
\(516\) 0 0
\(517\) −33.7492 −1.48429
\(518\) 0 0
\(519\) −11.0423 −0.484702
\(520\) 0 0
\(521\) −3.94832 −0.172979 −0.0864894 0.996253i \(-0.527565\pi\)
−0.0864894 + 0.996253i \(0.527565\pi\)
\(522\) 0 0
\(523\) −19.7903 −0.865368 −0.432684 0.901546i \(-0.642433\pi\)
−0.432684 + 0.901546i \(0.642433\pi\)
\(524\) 0 0
\(525\) −0.288128 −0.0125749
\(526\) 0 0
\(527\) 68.9665 3.00423
\(528\) 0 0
\(529\) 43.8052 1.90457
\(530\) 0 0
\(531\) 21.6342 0.938844
\(532\) 0 0
\(533\) −0.0773864 −0.00335197
\(534\) 0 0
\(535\) −35.9042 −1.55228
\(536\) 0 0
\(537\) 5.10165 0.220153
\(538\) 0 0
\(539\) −21.2384 −0.914803
\(540\) 0 0
\(541\) −14.6271 −0.628866 −0.314433 0.949280i \(-0.601814\pi\)
−0.314433 + 0.949280i \(0.601814\pi\)
\(542\) 0 0
\(543\) 6.45606 0.277056
\(544\) 0 0
\(545\) 16.9358 0.725451
\(546\) 0 0
\(547\) −15.3337 −0.655622 −0.327811 0.944743i \(-0.606311\pi\)
−0.327811 + 0.944743i \(0.606311\pi\)
\(548\) 0 0
\(549\) −9.06498 −0.386884
\(550\) 0 0
\(551\) −3.95811 −0.168621
\(552\) 0 0
\(553\) −5.26754 −0.223999
\(554\) 0 0
\(555\) 11.7341 0.498085
\(556\) 0 0
\(557\) 12.6605 0.536442 0.268221 0.963357i \(-0.413564\pi\)
0.268221 + 0.963357i \(0.413564\pi\)
\(558\) 0 0
\(559\) 1.57587 0.0666524
\(560\) 0 0
\(561\) 14.6706 0.619392
\(562\) 0 0
\(563\) 23.3355 0.983476 0.491738 0.870743i \(-0.336362\pi\)
0.491738 + 0.870743i \(0.336362\pi\)
\(564\) 0 0
\(565\) 41.6943 1.75409
\(566\) 0 0
\(567\) −6.54959 −0.275057
\(568\) 0 0
\(569\) 19.0758 0.799699 0.399850 0.916581i \(-0.369062\pi\)
0.399850 + 0.916581i \(0.369062\pi\)
\(570\) 0 0
\(571\) −25.5288 −1.06835 −0.534174 0.845374i \(-0.679377\pi\)
−0.534174 + 0.845374i \(0.679377\pi\)
\(572\) 0 0
\(573\) 10.0153 0.418396
\(574\) 0 0
\(575\) −4.34141 −0.181049
\(576\) 0 0
\(577\) −16.0887 −0.669780 −0.334890 0.942257i \(-0.608699\pi\)
−0.334890 + 0.942257i \(0.608699\pi\)
\(578\) 0 0
\(579\) 2.64516 0.109929
\(580\) 0 0
\(581\) 1.02689 0.0426027
\(582\) 0 0
\(583\) 3.55138 0.147083
\(584\) 0 0
\(585\) 1.09735 0.0453698
\(586\) 0 0
\(587\) 4.13097 0.170503 0.0852517 0.996359i \(-0.472831\pi\)
0.0852517 + 0.996359i \(0.472831\pi\)
\(588\) 0 0
\(589\) −8.96845 −0.369539
\(590\) 0 0
\(591\) −11.3596 −0.467270
\(592\) 0 0
\(593\) −30.1142 −1.23664 −0.618320 0.785926i \(-0.712187\pi\)
−0.618320 + 0.785926i \(0.712187\pi\)
\(594\) 0 0
\(595\) 18.2625 0.748688
\(596\) 0 0
\(597\) −12.7992 −0.523835
\(598\) 0 0
\(599\) −26.5899 −1.08643 −0.543217 0.839593i \(-0.682794\pi\)
−0.543217 + 0.839593i \(0.682794\pi\)
\(600\) 0 0
\(601\) −43.1341 −1.75948 −0.879739 0.475457i \(-0.842283\pi\)
−0.879739 + 0.475457i \(0.842283\pi\)
\(602\) 0 0
\(603\) 11.2812 0.459407
\(604\) 0 0
\(605\) −3.79188 −0.154162
\(606\) 0 0
\(607\) −27.5219 −1.11708 −0.558540 0.829478i \(-0.688638\pi\)
−0.558540 + 0.829478i \(0.688638\pi\)
\(608\) 0 0
\(609\) −2.14707 −0.0870039
\(610\) 0 0
\(611\) −1.63533 −0.0661584
\(612\) 0 0
\(613\) 23.7133 0.957770 0.478885 0.877878i \(-0.341041\pi\)
0.478885 + 0.877878i \(0.341041\pi\)
\(614\) 0 0
\(615\) 0.568149 0.0229100
\(616\) 0 0
\(617\) 30.1084 1.21212 0.606058 0.795420i \(-0.292750\pi\)
0.606058 + 0.795420i \(0.292750\pi\)
\(618\) 0 0
\(619\) −15.2290 −0.612104 −0.306052 0.952015i \(-0.599008\pi\)
−0.306052 + 0.952015i \(0.599008\pi\)
\(620\) 0 0
\(621\) 25.0772 1.00631
\(622\) 0 0
\(623\) 8.19592 0.328363
\(624\) 0 0
\(625\) −27.3737 −1.09495
\(626\) 0 0
\(627\) −1.90777 −0.0761890
\(628\) 0 0
\(629\) −71.4223 −2.84779
\(630\) 0 0
\(631\) 18.5005 0.736494 0.368247 0.929728i \(-0.379958\pi\)
0.368247 + 0.929728i \(0.379958\pi\)
\(632\) 0 0
\(633\) −2.93784 −0.116769
\(634\) 0 0
\(635\) 21.8079 0.865418
\(636\) 0 0
\(637\) −1.02911 −0.0407750
\(638\) 0 0
\(639\) −11.7922 −0.466492
\(640\) 0 0
\(641\) 2.17206 0.0857913 0.0428956 0.999080i \(-0.486342\pi\)
0.0428956 + 0.999080i \(0.486342\pi\)
\(642\) 0 0
\(643\) −3.98380 −0.157106 −0.0785530 0.996910i \(-0.525030\pi\)
−0.0785530 + 0.996910i \(0.525030\pi\)
\(644\) 0 0
\(645\) −11.5696 −0.455554
\(646\) 0 0
\(647\) 44.9861 1.76859 0.884293 0.466932i \(-0.154641\pi\)
0.884293 + 0.466932i \(0.154641\pi\)
\(648\) 0 0
\(649\) −28.3361 −1.11229
\(650\) 0 0
\(651\) −4.86493 −0.190672
\(652\) 0 0
\(653\) 2.38843 0.0934665 0.0467333 0.998907i \(-0.485119\pi\)
0.0467333 + 0.998907i \(0.485119\pi\)
\(654\) 0 0
\(655\) 19.1883 0.749747
\(656\) 0 0
\(657\) −8.82483 −0.344290
\(658\) 0 0
\(659\) −17.7243 −0.690440 −0.345220 0.938522i \(-0.612196\pi\)
−0.345220 + 0.938522i \(0.612196\pi\)
\(660\) 0 0
\(661\) −3.26632 −0.127045 −0.0635226 0.997980i \(-0.520233\pi\)
−0.0635226 + 0.997980i \(0.520233\pi\)
\(662\) 0 0
\(663\) 0.710867 0.0276078
\(664\) 0 0
\(665\) −2.37486 −0.0920932
\(666\) 0 0
\(667\) −32.3514 −1.25265
\(668\) 0 0
\(669\) 7.87704 0.304544
\(670\) 0 0
\(671\) 11.8732 0.458358
\(672\) 0 0
\(673\) 15.0893 0.581651 0.290825 0.956776i \(-0.406070\pi\)
0.290825 + 0.956776i \(0.406070\pi\)
\(674\) 0 0
\(675\) −1.62967 −0.0627259
\(676\) 0 0
\(677\) −41.1222 −1.58045 −0.790227 0.612814i \(-0.790038\pi\)
−0.790227 + 0.612814i \(0.790038\pi\)
\(678\) 0 0
\(679\) −3.11394 −0.119502
\(680\) 0 0
\(681\) −9.82364 −0.376443
\(682\) 0 0
\(683\) 30.9665 1.18490 0.592450 0.805607i \(-0.298161\pi\)
0.592450 + 0.805607i \(0.298161\pi\)
\(684\) 0 0
\(685\) 4.22942 0.161598
\(686\) 0 0
\(687\) −1.78483 −0.0680955
\(688\) 0 0
\(689\) 0.172083 0.00655585
\(690\) 0 0
\(691\) −39.2013 −1.49129 −0.745644 0.666345i \(-0.767858\pi\)
−0.745644 + 0.666345i \(0.767858\pi\)
\(692\) 0 0
\(693\) 9.72356 0.369367
\(694\) 0 0
\(695\) 5.50502 0.208817
\(696\) 0 0
\(697\) −3.45817 −0.130988
\(698\) 0 0
\(699\) 1.88246 0.0712011
\(700\) 0 0
\(701\) 0.0334055 0.00126171 0.000630854 1.00000i \(-0.499799\pi\)
0.000630854 1.00000i \(0.499799\pi\)
\(702\) 0 0
\(703\) 9.28780 0.350296
\(704\) 0 0
\(705\) 12.0061 0.452178
\(706\) 0 0
\(707\) 11.2603 0.423486
\(708\) 0 0
\(709\) 33.0691 1.24194 0.620968 0.783836i \(-0.286740\pi\)
0.620968 + 0.783836i \(0.286740\pi\)
\(710\) 0 0
\(711\) −14.1441 −0.530446
\(712\) 0 0
\(713\) −73.3032 −2.74522
\(714\) 0 0
\(715\) −1.43729 −0.0537516
\(716\) 0 0
\(717\) −4.38076 −0.163602
\(718\) 0 0
\(719\) −31.2750 −1.16636 −0.583180 0.812343i \(-0.698192\pi\)
−0.583180 + 0.812343i \(0.698192\pi\)
\(720\) 0 0
\(721\) 14.7518 0.549386
\(722\) 0 0
\(723\) −2.88034 −0.107121
\(724\) 0 0
\(725\) 2.10239 0.0780809
\(726\) 0 0
\(727\) −30.0929 −1.11609 −0.558043 0.829812i \(-0.688447\pi\)
−0.558043 + 0.829812i \(0.688447\pi\)
\(728\) 0 0
\(729\) −12.6421 −0.468225
\(730\) 0 0
\(731\) 70.4212 2.60462
\(732\) 0 0
\(733\) −37.2170 −1.37464 −0.687320 0.726355i \(-0.741213\pi\)
−0.687320 + 0.726355i \(0.741213\pi\)
\(734\) 0 0
\(735\) 7.55548 0.278688
\(736\) 0 0
\(737\) −14.7760 −0.544279
\(738\) 0 0
\(739\) −7.09354 −0.260940 −0.130470 0.991452i \(-0.541649\pi\)
−0.130470 + 0.991452i \(0.541649\pi\)
\(740\) 0 0
\(741\) −0.0924417 −0.00339593
\(742\) 0 0
\(743\) −31.0530 −1.13922 −0.569612 0.821914i \(-0.692906\pi\)
−0.569612 + 0.821914i \(0.692906\pi\)
\(744\) 0 0
\(745\) 21.4409 0.785533
\(746\) 0 0
\(747\) 2.75736 0.100886
\(748\) 0 0
\(749\) −15.4159 −0.563283
\(750\) 0 0
\(751\) 33.4721 1.22142 0.610708 0.791856i \(-0.290885\pi\)
0.610708 + 0.791856i \(0.290885\pi\)
\(752\) 0 0
\(753\) 13.6342 0.496858
\(754\) 0 0
\(755\) 14.1616 0.515395
\(756\) 0 0
\(757\) 27.1696 0.987496 0.493748 0.869605i \(-0.335626\pi\)
0.493748 + 0.869605i \(0.335626\pi\)
\(758\) 0 0
\(759\) −15.5931 −0.565992
\(760\) 0 0
\(761\) −15.4760 −0.561006 −0.280503 0.959853i \(-0.590501\pi\)
−0.280503 + 0.959853i \(0.590501\pi\)
\(762\) 0 0
\(763\) 7.27158 0.263249
\(764\) 0 0
\(765\) 49.0373 1.77295
\(766\) 0 0
\(767\) −1.37304 −0.0495774
\(768\) 0 0
\(769\) 33.2946 1.20063 0.600317 0.799762i \(-0.295041\pi\)
0.600317 + 0.799762i \(0.295041\pi\)
\(770\) 0 0
\(771\) 7.75686 0.279357
\(772\) 0 0
\(773\) 40.6534 1.46220 0.731101 0.682270i \(-0.239007\pi\)
0.731101 + 0.682270i \(0.239007\pi\)
\(774\) 0 0
\(775\) 4.76369 0.171117
\(776\) 0 0
\(777\) 5.03816 0.180743
\(778\) 0 0
\(779\) 0.449703 0.0161123
\(780\) 0 0
\(781\) 15.4452 0.552673
\(782\) 0 0
\(783\) −12.1440 −0.433991
\(784\) 0 0
\(785\) 49.4020 1.76323
\(786\) 0 0
\(787\) 9.10363 0.324509 0.162255 0.986749i \(-0.448123\pi\)
0.162255 + 0.986749i \(0.448123\pi\)
\(788\) 0 0
\(789\) 13.2929 0.473240
\(790\) 0 0
\(791\) 17.9019 0.636518
\(792\) 0 0
\(793\) 0.575318 0.0204301
\(794\) 0 0
\(795\) −1.26339 −0.0448078
\(796\) 0 0
\(797\) 34.4289 1.21954 0.609768 0.792580i \(-0.291263\pi\)
0.609768 + 0.792580i \(0.291263\pi\)
\(798\) 0 0
\(799\) −73.0781 −2.58532
\(800\) 0 0
\(801\) 22.0072 0.777587
\(802\) 0 0
\(803\) 11.5586 0.407895
\(804\) 0 0
\(805\) −19.4108 −0.684141
\(806\) 0 0
\(807\) 15.6889 0.552275
\(808\) 0 0
\(809\) −17.2597 −0.606819 −0.303409 0.952860i \(-0.598125\pi\)
−0.303409 + 0.952860i \(0.598125\pi\)
\(810\) 0 0
\(811\) 13.5516 0.475862 0.237931 0.971282i \(-0.423531\pi\)
0.237931 + 0.971282i \(0.423531\pi\)
\(812\) 0 0
\(813\) 4.08431 0.143243
\(814\) 0 0
\(815\) 29.4650 1.03211
\(816\) 0 0
\(817\) −9.15762 −0.320385
\(818\) 0 0
\(819\) 0.471158 0.0164636
\(820\) 0 0
\(821\) 7.96460 0.277966 0.138983 0.990295i \(-0.455617\pi\)
0.138983 + 0.990295i \(0.455617\pi\)
\(822\) 0 0
\(823\) 9.74529 0.339700 0.169850 0.985470i \(-0.445672\pi\)
0.169850 + 0.985470i \(0.445672\pi\)
\(824\) 0 0
\(825\) 1.01333 0.0352797
\(826\) 0 0
\(827\) 40.5356 1.40956 0.704780 0.709426i \(-0.251046\pi\)
0.704780 + 0.709426i \(0.251046\pi\)
\(828\) 0 0
\(829\) −12.8584 −0.446591 −0.223296 0.974751i \(-0.571681\pi\)
−0.223296 + 0.974751i \(0.571681\pi\)
\(830\) 0 0
\(831\) −3.16445 −0.109774
\(832\) 0 0
\(833\) −45.9881 −1.59339
\(834\) 0 0
\(835\) 57.6292 1.99434
\(836\) 0 0
\(837\) −27.5164 −0.951105
\(838\) 0 0
\(839\) −34.4598 −1.18968 −0.594842 0.803843i \(-0.702785\pi\)
−0.594842 + 0.803843i \(0.702785\pi\)
\(840\) 0 0
\(841\) −13.3334 −0.459771
\(842\) 0 0
\(843\) 1.84062 0.0633942
\(844\) 0 0
\(845\) 30.5043 1.04938
\(846\) 0 0
\(847\) −1.62808 −0.0559416
\(848\) 0 0
\(849\) −1.80389 −0.0619094
\(850\) 0 0
\(851\) 75.9133 2.60228
\(852\) 0 0
\(853\) 12.9779 0.444355 0.222178 0.975006i \(-0.428684\pi\)
0.222178 + 0.975006i \(0.428684\pi\)
\(854\) 0 0
\(855\) −6.37684 −0.218083
\(856\) 0 0
\(857\) 56.0715 1.91537 0.957684 0.287823i \(-0.0929315\pi\)
0.957684 + 0.287823i \(0.0929315\pi\)
\(858\) 0 0
\(859\) −43.7921 −1.49417 −0.747084 0.664730i \(-0.768547\pi\)
−0.747084 + 0.664730i \(0.768547\pi\)
\(860\) 0 0
\(861\) 0.243941 0.00831348
\(862\) 0 0
\(863\) 23.0763 0.785527 0.392764 0.919639i \(-0.371519\pi\)
0.392764 + 0.919639i \(0.371519\pi\)
\(864\) 0 0
\(865\) 48.3435 1.64373
\(866\) 0 0
\(867\) 22.6343 0.768702
\(868\) 0 0
\(869\) 18.5257 0.628442
\(870\) 0 0
\(871\) −0.715974 −0.0242599
\(872\) 0 0
\(873\) −8.36139 −0.282990
\(874\) 0 0
\(875\) −10.6129 −0.358781
\(876\) 0 0
\(877\) −34.7098 −1.17207 −0.586033 0.810287i \(-0.699311\pi\)
−0.586033 + 0.810287i \(0.699311\pi\)
\(878\) 0 0
\(879\) 9.63969 0.325139
\(880\) 0 0
\(881\) 38.4105 1.29408 0.647041 0.762455i \(-0.276006\pi\)
0.647041 + 0.762455i \(0.276006\pi\)
\(882\) 0 0
\(883\) −43.7436 −1.47209 −0.736045 0.676933i \(-0.763309\pi\)
−0.736045 + 0.676933i \(0.763309\pi\)
\(884\) 0 0
\(885\) 10.0805 0.338851
\(886\) 0 0
\(887\) 36.9634 1.24111 0.620555 0.784163i \(-0.286907\pi\)
0.620555 + 0.784163i \(0.286907\pi\)
\(888\) 0 0
\(889\) 9.36343 0.314039
\(890\) 0 0
\(891\) 23.0346 0.771689
\(892\) 0 0
\(893\) 9.50313 0.318010
\(894\) 0 0
\(895\) −22.3352 −0.746584
\(896\) 0 0
\(897\) −0.755567 −0.0252276
\(898\) 0 0
\(899\) 35.4981 1.18393
\(900\) 0 0
\(901\) 7.68990 0.256188
\(902\) 0 0
\(903\) −4.96754 −0.165310
\(904\) 0 0
\(905\) −28.2649 −0.939556
\(906\) 0 0
\(907\) −55.3568 −1.83809 −0.919046 0.394149i \(-0.871039\pi\)
−0.919046 + 0.394149i \(0.871039\pi\)
\(908\) 0 0
\(909\) 30.2354 1.00285
\(910\) 0 0
\(911\) −18.5500 −0.614590 −0.307295 0.951614i \(-0.599424\pi\)
−0.307295 + 0.951614i \(0.599424\pi\)
\(912\) 0 0
\(913\) −3.61154 −0.119525
\(914\) 0 0
\(915\) −4.22383 −0.139635
\(916\) 0 0
\(917\) 8.23868 0.272065
\(918\) 0 0
\(919\) −19.7145 −0.650320 −0.325160 0.945659i \(-0.605418\pi\)
−0.325160 + 0.945659i \(0.605418\pi\)
\(920\) 0 0
\(921\) −13.0056 −0.428550
\(922\) 0 0
\(923\) 0.748403 0.0246340
\(924\) 0 0
\(925\) −4.93331 −0.162206
\(926\) 0 0
\(927\) 39.6107 1.30099
\(928\) 0 0
\(929\) 31.0600 1.01905 0.509523 0.860457i \(-0.329822\pi\)
0.509523 + 0.860457i \(0.329822\pi\)
\(930\) 0 0
\(931\) 5.98033 0.195997
\(932\) 0 0
\(933\) −16.8560 −0.551841
\(934\) 0 0
\(935\) −64.2282 −2.10049
\(936\) 0 0
\(937\) 52.5358 1.71627 0.858136 0.513423i \(-0.171623\pi\)
0.858136 + 0.513423i \(0.171623\pi\)
\(938\) 0 0
\(939\) 4.94210 0.161279
\(940\) 0 0
\(941\) −23.6149 −0.769822 −0.384911 0.922954i \(-0.625768\pi\)
−0.384911 + 0.922954i \(0.625768\pi\)
\(942\) 0 0
\(943\) 3.67562 0.119695
\(944\) 0 0
\(945\) −7.28638 −0.237026
\(946\) 0 0
\(947\) −52.4192 −1.70339 −0.851697 0.524034i \(-0.824426\pi\)
−0.851697 + 0.524034i \(0.824426\pi\)
\(948\) 0 0
\(949\) 0.560077 0.0181809
\(950\) 0 0
\(951\) −9.91942 −0.321659
\(952\) 0 0
\(953\) −23.7899 −0.770630 −0.385315 0.922785i \(-0.625907\pi\)
−0.385315 + 0.922785i \(0.625907\pi\)
\(954\) 0 0
\(955\) −43.8475 −1.41887
\(956\) 0 0
\(957\) 7.55117 0.244095
\(958\) 0 0
\(959\) 1.81595 0.0586400
\(960\) 0 0
\(961\) 49.4332 1.59462
\(962\) 0 0
\(963\) −41.3938 −1.33390
\(964\) 0 0
\(965\) −11.5806 −0.372793
\(966\) 0 0
\(967\) 42.0466 1.35213 0.676064 0.736843i \(-0.263684\pi\)
0.676064 + 0.736843i \(0.263684\pi\)
\(968\) 0 0
\(969\) −4.13095 −0.132705
\(970\) 0 0
\(971\) −4.01025 −0.128695 −0.0643475 0.997928i \(-0.520497\pi\)
−0.0643475 + 0.997928i \(0.520497\pi\)
\(972\) 0 0
\(973\) 2.36364 0.0757747
\(974\) 0 0
\(975\) 0.0491013 0.00157250
\(976\) 0 0
\(977\) −33.0559 −1.05755 −0.528776 0.848761i \(-0.677349\pi\)
−0.528776 + 0.848761i \(0.677349\pi\)
\(978\) 0 0
\(979\) −28.8247 −0.921241
\(980\) 0 0
\(981\) 19.5252 0.623393
\(982\) 0 0
\(983\) −47.4817 −1.51443 −0.757215 0.653166i \(-0.773440\pi\)
−0.757215 + 0.653166i \(0.773440\pi\)
\(984\) 0 0
\(985\) 49.7326 1.58461
\(986\) 0 0
\(987\) 5.15497 0.164084
\(988\) 0 0
\(989\) −74.8493 −2.38007
\(990\) 0 0
\(991\) 22.4450 0.712989 0.356495 0.934297i \(-0.383972\pi\)
0.356495 + 0.934297i \(0.383972\pi\)
\(992\) 0 0
\(993\) 0.190117 0.00603317
\(994\) 0 0
\(995\) 56.0352 1.77643
\(996\) 0 0
\(997\) −46.5069 −1.47289 −0.736445 0.676498i \(-0.763497\pi\)
−0.736445 + 0.676498i \(0.763497\pi\)
\(998\) 0 0
\(999\) 28.4962 0.901578
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 \(a_p\))