Properties

Label 8004.2.a.j.1.6
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.900032\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-0.900032 q^{5}\) \(+0.226627 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-0.900032 q^{5}\) \(+0.226627 q^{7}\) \(+1.00000 q^{9}\) \(-3.23685 q^{11}\) \(-6.29181 q^{13}\) \(-0.900032 q^{15}\) \(+0.102835 q^{17}\) \(+6.74323 q^{19}\) \(+0.226627 q^{21}\) \(+1.00000 q^{23}\) \(-4.18994 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(-0.708382 q^{31}\) \(-3.23685 q^{33}\) \(-0.203972 q^{35}\) \(+1.94929 q^{37}\) \(-6.29181 q^{39}\) \(-3.13468 q^{41}\) \(+4.38054 q^{43}\) \(-0.900032 q^{45}\) \(+6.47641 q^{47}\) \(-6.94864 q^{49}\) \(+0.102835 q^{51}\) \(-7.91308 q^{53}\) \(+2.91326 q^{55}\) \(+6.74323 q^{57}\) \(+8.52648 q^{59}\) \(+7.66345 q^{61}\) \(+0.226627 q^{63}\) \(+5.66283 q^{65}\) \(+12.4119 q^{67}\) \(+1.00000 q^{69}\) \(+8.53670 q^{71}\) \(+4.34060 q^{73}\) \(-4.18994 q^{75}\) \(-0.733557 q^{77}\) \(-7.86789 q^{79}\) \(+1.00000 q^{81}\) \(+6.62194 q^{83}\) \(-0.0925544 q^{85}\) \(-1.00000 q^{87}\) \(+0.363565 q^{89}\) \(-1.42589 q^{91}\) \(-0.708382 q^{93}\) \(-6.06912 q^{95}\) \(+9.11380 q^{97}\) \(-3.23685 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −0.900032 −0.402506 −0.201253 0.979539i \(-0.564501\pi\)
−0.201253 + 0.979539i \(0.564501\pi\)
\(6\) 0 0
\(7\) 0.226627 0.0856570 0.0428285 0.999082i \(-0.486363\pi\)
0.0428285 + 0.999082i \(0.486363\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.23685 −0.975945 −0.487973 0.872859i \(-0.662263\pi\)
−0.487973 + 0.872859i \(0.662263\pi\)
\(12\) 0 0
\(13\) −6.29181 −1.74503 −0.872517 0.488583i \(-0.837514\pi\)
−0.872517 + 0.488583i \(0.837514\pi\)
\(14\) 0 0
\(15\) −0.900032 −0.232387
\(16\) 0 0
\(17\) 0.102835 0.0249411 0.0124705 0.999922i \(-0.496030\pi\)
0.0124705 + 0.999922i \(0.496030\pi\)
\(18\) 0 0
\(19\) 6.74323 1.54700 0.773502 0.633794i \(-0.218503\pi\)
0.773502 + 0.633794i \(0.218503\pi\)
\(20\) 0 0
\(21\) 0.226627 0.0494541
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.18994 −0.837989
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −0.708382 −0.127229 −0.0636146 0.997975i \(-0.520263\pi\)
−0.0636146 + 0.997975i \(0.520263\pi\)
\(32\) 0 0
\(33\) −3.23685 −0.563462
\(34\) 0 0
\(35\) −0.203972 −0.0344775
\(36\) 0 0
\(37\) 1.94929 0.320461 0.160230 0.987080i \(-0.448776\pi\)
0.160230 + 0.987080i \(0.448776\pi\)
\(38\) 0 0
\(39\) −6.29181 −1.00750
\(40\) 0 0
\(41\) −3.13468 −0.489555 −0.244777 0.969579i \(-0.578715\pi\)
−0.244777 + 0.969579i \(0.578715\pi\)
\(42\) 0 0
\(43\) 4.38054 0.668026 0.334013 0.942568i \(-0.391597\pi\)
0.334013 + 0.942568i \(0.391597\pi\)
\(44\) 0 0
\(45\) −0.900032 −0.134169
\(46\) 0 0
\(47\) 6.47641 0.944682 0.472341 0.881416i \(-0.343409\pi\)
0.472341 + 0.881416i \(0.343409\pi\)
\(48\) 0 0
\(49\) −6.94864 −0.992663
\(50\) 0 0
\(51\) 0.102835 0.0143997
\(52\) 0 0
\(53\) −7.91308 −1.08694 −0.543472 0.839427i \(-0.682891\pi\)
−0.543472 + 0.839427i \(0.682891\pi\)
\(54\) 0 0
\(55\) 2.91326 0.392824
\(56\) 0 0
\(57\) 6.74323 0.893163
\(58\) 0 0
\(59\) 8.52648 1.11005 0.555027 0.831832i \(-0.312708\pi\)
0.555027 + 0.831832i \(0.312708\pi\)
\(60\) 0 0
\(61\) 7.66345 0.981205 0.490602 0.871384i \(-0.336777\pi\)
0.490602 + 0.871384i \(0.336777\pi\)
\(62\) 0 0
\(63\) 0.226627 0.0285523
\(64\) 0 0
\(65\) 5.66283 0.702387
\(66\) 0 0
\(67\) 12.4119 1.51636 0.758180 0.652045i \(-0.226089\pi\)
0.758180 + 0.652045i \(0.226089\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 8.53670 1.01312 0.506560 0.862205i \(-0.330917\pi\)
0.506560 + 0.862205i \(0.330917\pi\)
\(72\) 0 0
\(73\) 4.34060 0.508029 0.254015 0.967200i \(-0.418249\pi\)
0.254015 + 0.967200i \(0.418249\pi\)
\(74\) 0 0
\(75\) −4.18994 −0.483813
\(76\) 0 0
\(77\) −0.733557 −0.0835965
\(78\) 0 0
\(79\) −7.86789 −0.885207 −0.442604 0.896717i \(-0.645945\pi\)
−0.442604 + 0.896717i \(0.645945\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 6.62194 0.726853 0.363426 0.931623i \(-0.381607\pi\)
0.363426 + 0.931623i \(0.381607\pi\)
\(84\) 0 0
\(85\) −0.0925544 −0.0100389
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 0.363565 0.0385378 0.0192689 0.999814i \(-0.493866\pi\)
0.0192689 + 0.999814i \(0.493866\pi\)
\(90\) 0 0
\(91\) −1.42589 −0.149474
\(92\) 0 0
\(93\) −0.708382 −0.0734558
\(94\) 0 0
\(95\) −6.06912 −0.622679
\(96\) 0 0
\(97\) 9.11380 0.925367 0.462683 0.886524i \(-0.346887\pi\)
0.462683 + 0.886524i \(0.346887\pi\)
\(98\) 0 0
\(99\) −3.23685 −0.325315
\(100\) 0 0
\(101\) −15.0896 −1.50147 −0.750736 0.660603i \(-0.770301\pi\)
−0.750736 + 0.660603i \(0.770301\pi\)
\(102\) 0 0
\(103\) 9.89634 0.975115 0.487557 0.873091i \(-0.337888\pi\)
0.487557 + 0.873091i \(0.337888\pi\)
\(104\) 0 0
\(105\) −0.203972 −0.0199056
\(106\) 0 0
\(107\) −6.93286 −0.670225 −0.335113 0.942178i \(-0.608774\pi\)
−0.335113 + 0.942178i \(0.608774\pi\)
\(108\) 0 0
\(109\) 2.80062 0.268251 0.134125 0.990964i \(-0.457177\pi\)
0.134125 + 0.990964i \(0.457177\pi\)
\(110\) 0 0
\(111\) 1.94929 0.185018
\(112\) 0 0
\(113\) 0.152376 0.0143344 0.00716718 0.999974i \(-0.497719\pi\)
0.00716718 + 0.999974i \(0.497719\pi\)
\(114\) 0 0
\(115\) −0.900032 −0.0839284
\(116\) 0 0
\(117\) −6.29181 −0.581678
\(118\) 0 0
\(119\) 0.0233051 0.00213638
\(120\) 0 0
\(121\) −0.522834 −0.0475304
\(122\) 0 0
\(123\) −3.13468 −0.282645
\(124\) 0 0
\(125\) 8.27124 0.739802
\(126\) 0 0
\(127\) −10.4073 −0.923500 −0.461750 0.887010i \(-0.652778\pi\)
−0.461750 + 0.887010i \(0.652778\pi\)
\(128\) 0 0
\(129\) 4.38054 0.385685
\(130\) 0 0
\(131\) 11.3477 0.991455 0.495727 0.868478i \(-0.334902\pi\)
0.495727 + 0.868478i \(0.334902\pi\)
\(132\) 0 0
\(133\) 1.52820 0.132512
\(134\) 0 0
\(135\) −0.900032 −0.0774624
\(136\) 0 0
\(137\) 0.481635 0.0411488 0.0205744 0.999788i \(-0.493450\pi\)
0.0205744 + 0.999788i \(0.493450\pi\)
\(138\) 0 0
\(139\) −5.40085 −0.458094 −0.229047 0.973415i \(-0.573561\pi\)
−0.229047 + 0.973415i \(0.573561\pi\)
\(140\) 0 0
\(141\) 6.47641 0.545412
\(142\) 0 0
\(143\) 20.3656 1.70306
\(144\) 0 0
\(145\) 0.900032 0.0747436
\(146\) 0 0
\(147\) −6.94864 −0.573114
\(148\) 0 0
\(149\) 3.66802 0.300496 0.150248 0.988648i \(-0.451993\pi\)
0.150248 + 0.988648i \(0.451993\pi\)
\(150\) 0 0
\(151\) 17.4106 1.41685 0.708427 0.705784i \(-0.249405\pi\)
0.708427 + 0.705784i \(0.249405\pi\)
\(152\) 0 0
\(153\) 0.102835 0.00831369
\(154\) 0 0
\(155\) 0.637566 0.0512105
\(156\) 0 0
\(157\) 17.8723 1.42637 0.713184 0.700976i \(-0.247252\pi\)
0.713184 + 0.700976i \(0.247252\pi\)
\(158\) 0 0
\(159\) −7.91308 −0.627548
\(160\) 0 0
\(161\) 0.226627 0.0178607
\(162\) 0 0
\(163\) 13.6475 1.06895 0.534477 0.845183i \(-0.320509\pi\)
0.534477 + 0.845183i \(0.320509\pi\)
\(164\) 0 0
\(165\) 2.91326 0.226797
\(166\) 0 0
\(167\) −12.0938 −0.935847 −0.467924 0.883769i \(-0.654998\pi\)
−0.467924 + 0.883769i \(0.654998\pi\)
\(168\) 0 0
\(169\) 26.5869 2.04515
\(170\) 0 0
\(171\) 6.74323 0.515668
\(172\) 0 0
\(173\) 11.5174 0.875649 0.437825 0.899060i \(-0.355749\pi\)
0.437825 + 0.899060i \(0.355749\pi\)
\(174\) 0 0
\(175\) −0.949555 −0.0717796
\(176\) 0 0
\(177\) 8.52648 0.640890
\(178\) 0 0
\(179\) −2.23450 −0.167014 −0.0835072 0.996507i \(-0.526612\pi\)
−0.0835072 + 0.996507i \(0.526612\pi\)
\(180\) 0 0
\(181\) −19.7251 −1.46616 −0.733078 0.680145i \(-0.761917\pi\)
−0.733078 + 0.680145i \(0.761917\pi\)
\(182\) 0 0
\(183\) 7.66345 0.566499
\(184\) 0 0
\(185\) −1.75442 −0.128987
\(186\) 0 0
\(187\) −0.332860 −0.0243411
\(188\) 0 0
\(189\) 0.226627 0.0164847
\(190\) 0 0
\(191\) 20.6235 1.49227 0.746133 0.665797i \(-0.231908\pi\)
0.746133 + 0.665797i \(0.231908\pi\)
\(192\) 0 0
\(193\) 13.9362 1.00315 0.501576 0.865113i \(-0.332754\pi\)
0.501576 + 0.865113i \(0.332754\pi\)
\(194\) 0 0
\(195\) 5.66283 0.405524
\(196\) 0 0
\(197\) 6.12354 0.436284 0.218142 0.975917i \(-0.430000\pi\)
0.218142 + 0.975917i \(0.430000\pi\)
\(198\) 0 0
\(199\) 11.1948 0.793576 0.396788 0.917910i \(-0.370125\pi\)
0.396788 + 0.917910i \(0.370125\pi\)
\(200\) 0 0
\(201\) 12.4119 0.875471
\(202\) 0 0
\(203\) −0.226627 −0.0159061
\(204\) 0 0
\(205\) 2.82131 0.197049
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −21.8268 −1.50979
\(210\) 0 0
\(211\) 11.3704 0.782770 0.391385 0.920227i \(-0.371996\pi\)
0.391385 + 0.920227i \(0.371996\pi\)
\(212\) 0 0
\(213\) 8.53670 0.584925
\(214\) 0 0
\(215\) −3.94262 −0.268885
\(216\) 0 0
\(217\) −0.160538 −0.0108981
\(218\) 0 0
\(219\) 4.34060 0.293311
\(220\) 0 0
\(221\) −0.647016 −0.0435230
\(222\) 0 0
\(223\) 11.9124 0.797713 0.398856 0.917013i \(-0.369407\pi\)
0.398856 + 0.917013i \(0.369407\pi\)
\(224\) 0 0
\(225\) −4.18994 −0.279330
\(226\) 0 0
\(227\) −8.71622 −0.578516 −0.289258 0.957251i \(-0.593409\pi\)
−0.289258 + 0.957251i \(0.593409\pi\)
\(228\) 0 0
\(229\) −0.984405 −0.0650513 −0.0325256 0.999471i \(-0.510355\pi\)
−0.0325256 + 0.999471i \(0.510355\pi\)
\(230\) 0 0
\(231\) −0.733557 −0.0482645
\(232\) 0 0
\(233\) 0.418820 0.0274378 0.0137189 0.999906i \(-0.495633\pi\)
0.0137189 + 0.999906i \(0.495633\pi\)
\(234\) 0 0
\(235\) −5.82898 −0.380240
\(236\) 0 0
\(237\) −7.86789 −0.511075
\(238\) 0 0
\(239\) −11.9016 −0.769853 −0.384927 0.922947i \(-0.625773\pi\)
−0.384927 + 0.922947i \(0.625773\pi\)
\(240\) 0 0
\(241\) 24.4060 1.57213 0.786063 0.618146i \(-0.212116\pi\)
0.786063 + 0.618146i \(0.212116\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 6.25400 0.399553
\(246\) 0 0
\(247\) −42.4271 −2.69957
\(248\) 0 0
\(249\) 6.62194 0.419649
\(250\) 0 0
\(251\) 10.2426 0.646504 0.323252 0.946313i \(-0.395224\pi\)
0.323252 + 0.946313i \(0.395224\pi\)
\(252\) 0 0
\(253\) −3.23685 −0.203499
\(254\) 0 0
\(255\) −0.0925544 −0.00579598
\(256\) 0 0
\(257\) 30.7464 1.91791 0.958955 0.283558i \(-0.0915150\pi\)
0.958955 + 0.283558i \(0.0915150\pi\)
\(258\) 0 0
\(259\) 0.441761 0.0274497
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 20.2721 1.25003 0.625016 0.780612i \(-0.285093\pi\)
0.625016 + 0.780612i \(0.285093\pi\)
\(264\) 0 0
\(265\) 7.12202 0.437502
\(266\) 0 0
\(267\) 0.363565 0.0222498
\(268\) 0 0
\(269\) −29.9148 −1.82394 −0.911970 0.410257i \(-0.865439\pi\)
−0.911970 + 0.410257i \(0.865439\pi\)
\(270\) 0 0
\(271\) −28.3436 −1.72175 −0.860876 0.508814i \(-0.830084\pi\)
−0.860876 + 0.508814i \(0.830084\pi\)
\(272\) 0 0
\(273\) −1.42589 −0.0862991
\(274\) 0 0
\(275\) 13.5622 0.817831
\(276\) 0 0
\(277\) 8.98371 0.539779 0.269889 0.962891i \(-0.413013\pi\)
0.269889 + 0.962891i \(0.413013\pi\)
\(278\) 0 0
\(279\) −0.708382 −0.0424097
\(280\) 0 0
\(281\) −5.54304 −0.330670 −0.165335 0.986237i \(-0.552871\pi\)
−0.165335 + 0.986237i \(0.552871\pi\)
\(282\) 0 0
\(283\) 4.89295 0.290856 0.145428 0.989369i \(-0.453544\pi\)
0.145428 + 0.989369i \(0.453544\pi\)
\(284\) 0 0
\(285\) −6.06912 −0.359504
\(286\) 0 0
\(287\) −0.710403 −0.0419338
\(288\) 0 0
\(289\) −16.9894 −0.999378
\(290\) 0 0
\(291\) 9.11380 0.534261
\(292\) 0 0
\(293\) −27.6786 −1.61700 −0.808502 0.588494i \(-0.799721\pi\)
−0.808502 + 0.588494i \(0.799721\pi\)
\(294\) 0 0
\(295\) −7.67410 −0.446804
\(296\) 0 0
\(297\) −3.23685 −0.187821
\(298\) 0 0
\(299\) −6.29181 −0.363865
\(300\) 0 0
\(301\) 0.992749 0.0572211
\(302\) 0 0
\(303\) −15.0896 −0.866875
\(304\) 0 0
\(305\) −6.89735 −0.394941
\(306\) 0 0
\(307\) 3.47911 0.198563 0.0992817 0.995059i \(-0.468346\pi\)
0.0992817 + 0.995059i \(0.468346\pi\)
\(308\) 0 0
\(309\) 9.89634 0.562983
\(310\) 0 0
\(311\) 27.6058 1.56538 0.782690 0.622412i \(-0.213847\pi\)
0.782690 + 0.622412i \(0.213847\pi\)
\(312\) 0 0
\(313\) 18.0525 1.02039 0.510193 0.860060i \(-0.329574\pi\)
0.510193 + 0.860060i \(0.329574\pi\)
\(314\) 0 0
\(315\) −0.203972 −0.0114925
\(316\) 0 0
\(317\) −17.5432 −0.985326 −0.492663 0.870220i \(-0.663976\pi\)
−0.492663 + 0.870220i \(0.663976\pi\)
\(318\) 0 0
\(319\) 3.23685 0.181229
\(320\) 0 0
\(321\) −6.93286 −0.386955
\(322\) 0 0
\(323\) 0.693438 0.0385839
\(324\) 0 0
\(325\) 26.3623 1.46232
\(326\) 0 0
\(327\) 2.80062 0.154875
\(328\) 0 0
\(329\) 1.46773 0.0809186
\(330\) 0 0
\(331\) 20.2002 1.11030 0.555152 0.831749i \(-0.312660\pi\)
0.555152 + 0.831749i \(0.312660\pi\)
\(332\) 0 0
\(333\) 1.94929 0.106820
\(334\) 0 0
\(335\) −11.1711 −0.610345
\(336\) 0 0
\(337\) −32.8573 −1.78985 −0.894926 0.446214i \(-0.852772\pi\)
−0.894926 + 0.446214i \(0.852772\pi\)
\(338\) 0 0
\(339\) 0.152376 0.00827594
\(340\) 0 0
\(341\) 2.29292 0.124169
\(342\) 0 0
\(343\) −3.16114 −0.170685
\(344\) 0 0
\(345\) −0.900032 −0.0484561
\(346\) 0 0
\(347\) −22.9662 −1.23289 −0.616446 0.787397i \(-0.711428\pi\)
−0.616446 + 0.787397i \(0.711428\pi\)
\(348\) 0 0
\(349\) 35.1157 1.87970 0.939851 0.341586i \(-0.110964\pi\)
0.939851 + 0.341586i \(0.110964\pi\)
\(350\) 0 0
\(351\) −6.29181 −0.335832
\(352\) 0 0
\(353\) −10.3890 −0.552951 −0.276475 0.961021i \(-0.589166\pi\)
−0.276475 + 0.961021i \(0.589166\pi\)
\(354\) 0 0
\(355\) −7.68330 −0.407787
\(356\) 0 0
\(357\) 0.0233051 0.00123344
\(358\) 0 0
\(359\) −29.3495 −1.54901 −0.774504 0.632569i \(-0.782000\pi\)
−0.774504 + 0.632569i \(0.782000\pi\)
\(360\) 0 0
\(361\) 26.4712 1.39322
\(362\) 0 0
\(363\) −0.522834 −0.0274417
\(364\) 0 0
\(365\) −3.90668 −0.204485
\(366\) 0 0
\(367\) 23.2527 1.21378 0.606890 0.794786i \(-0.292417\pi\)
0.606890 + 0.794786i \(0.292417\pi\)
\(368\) 0 0
\(369\) −3.13468 −0.163185
\(370\) 0 0
\(371\) −1.79332 −0.0931044
\(372\) 0 0
\(373\) −0.204094 −0.0105676 −0.00528379 0.999986i \(-0.501682\pi\)
−0.00528379 + 0.999986i \(0.501682\pi\)
\(374\) 0 0
\(375\) 8.27124 0.427125
\(376\) 0 0
\(377\) 6.29181 0.324045
\(378\) 0 0
\(379\) −21.2755 −1.09285 −0.546424 0.837508i \(-0.684011\pi\)
−0.546424 + 0.837508i \(0.684011\pi\)
\(380\) 0 0
\(381\) −10.4073 −0.533183
\(382\) 0 0
\(383\) 4.23847 0.216576 0.108288 0.994120i \(-0.465463\pi\)
0.108288 + 0.994120i \(0.465463\pi\)
\(384\) 0 0
\(385\) 0.660224 0.0336481
\(386\) 0 0
\(387\) 4.38054 0.222675
\(388\) 0 0
\(389\) −1.45435 −0.0737385 −0.0368693 0.999320i \(-0.511739\pi\)
−0.0368693 + 0.999320i \(0.511739\pi\)
\(390\) 0 0
\(391\) 0.102835 0.00520057
\(392\) 0 0
\(393\) 11.3477 0.572417
\(394\) 0 0
\(395\) 7.08135 0.356302
\(396\) 0 0
\(397\) 8.88004 0.445677 0.222838 0.974855i \(-0.428468\pi\)
0.222838 + 0.974855i \(0.428468\pi\)
\(398\) 0 0
\(399\) 1.52820 0.0765056
\(400\) 0 0
\(401\) −3.93855 −0.196682 −0.0983409 0.995153i \(-0.531354\pi\)
−0.0983409 + 0.995153i \(0.531354\pi\)
\(402\) 0 0
\(403\) 4.45700 0.222019
\(404\) 0 0
\(405\) −0.900032 −0.0447229
\(406\) 0 0
\(407\) −6.30954 −0.312752
\(408\) 0 0
\(409\) −12.6982 −0.627886 −0.313943 0.949442i \(-0.601650\pi\)
−0.313943 + 0.949442i \(0.601650\pi\)
\(410\) 0 0
\(411\) 0.481635 0.0237573
\(412\) 0 0
\(413\) 1.93233 0.0950838
\(414\) 0 0
\(415\) −5.95996 −0.292563
\(416\) 0 0
\(417\) −5.40085 −0.264481
\(418\) 0 0
\(419\) 1.97848 0.0966551 0.0483275 0.998832i \(-0.484611\pi\)
0.0483275 + 0.998832i \(0.484611\pi\)
\(420\) 0 0
\(421\) 16.4852 0.803441 0.401721 0.915762i \(-0.368412\pi\)
0.401721 + 0.915762i \(0.368412\pi\)
\(422\) 0 0
\(423\) 6.47641 0.314894
\(424\) 0 0
\(425\) −0.430871 −0.0209003
\(426\) 0 0
\(427\) 1.73675 0.0840470
\(428\) 0 0
\(429\) 20.3656 0.983261
\(430\) 0 0
\(431\) −3.14755 −0.151612 −0.0758062 0.997123i \(-0.524153\pi\)
−0.0758062 + 0.997123i \(0.524153\pi\)
\(432\) 0 0
\(433\) −11.7163 −0.563050 −0.281525 0.959554i \(-0.590840\pi\)
−0.281525 + 0.959554i \(0.590840\pi\)
\(434\) 0 0
\(435\) 0.900032 0.0431532
\(436\) 0 0
\(437\) 6.74323 0.322573
\(438\) 0 0
\(439\) −6.20247 −0.296028 −0.148014 0.988985i \(-0.547288\pi\)
−0.148014 + 0.988985i \(0.547288\pi\)
\(440\) 0 0
\(441\) −6.94864 −0.330888
\(442\) 0 0
\(443\) −23.5271 −1.11780 −0.558902 0.829234i \(-0.688777\pi\)
−0.558902 + 0.829234i \(0.688777\pi\)
\(444\) 0 0
\(445\) −0.327220 −0.0155117
\(446\) 0 0
\(447\) 3.66802 0.173492
\(448\) 0 0
\(449\) 30.9587 1.46103 0.730517 0.682895i \(-0.239279\pi\)
0.730517 + 0.682895i \(0.239279\pi\)
\(450\) 0 0
\(451\) 10.1465 0.477779
\(452\) 0 0
\(453\) 17.4106 0.818021
\(454\) 0 0
\(455\) 1.28335 0.0601644
\(456\) 0 0
\(457\) −23.6330 −1.10551 −0.552753 0.833345i \(-0.686423\pi\)
−0.552753 + 0.833345i \(0.686423\pi\)
\(458\) 0 0
\(459\) 0.102835 0.00479991
\(460\) 0 0
\(461\) −24.3619 −1.13465 −0.567324 0.823495i \(-0.692021\pi\)
−0.567324 + 0.823495i \(0.692021\pi\)
\(462\) 0 0
\(463\) −0.140581 −0.00653333 −0.00326667 0.999995i \(-0.501040\pi\)
−0.00326667 + 0.999995i \(0.501040\pi\)
\(464\) 0 0
\(465\) 0.637566 0.0295664
\(466\) 0 0
\(467\) 20.8526 0.964943 0.482471 0.875912i \(-0.339739\pi\)
0.482471 + 0.875912i \(0.339739\pi\)
\(468\) 0 0
\(469\) 2.81288 0.129887
\(470\) 0 0
\(471\) 17.8723 0.823514
\(472\) 0 0
\(473\) −14.1791 −0.651957
\(474\) 0 0
\(475\) −28.2538 −1.29637
\(476\) 0 0
\(477\) −7.91308 −0.362315
\(478\) 0 0
\(479\) 16.5333 0.755426 0.377713 0.925923i \(-0.376711\pi\)
0.377713 + 0.925923i \(0.376711\pi\)
\(480\) 0 0
\(481\) −12.2645 −0.559215
\(482\) 0 0
\(483\) 0.226627 0.0103119
\(484\) 0 0
\(485\) −8.20271 −0.372466
\(486\) 0 0
\(487\) −14.8004 −0.670671 −0.335335 0.942099i \(-0.608850\pi\)
−0.335335 + 0.942099i \(0.608850\pi\)
\(488\) 0 0
\(489\) 13.6475 0.617161
\(490\) 0 0
\(491\) −23.0837 −1.04175 −0.520877 0.853632i \(-0.674395\pi\)
−0.520877 + 0.853632i \(0.674395\pi\)
\(492\) 0 0
\(493\) −0.102835 −0.00463144
\(494\) 0 0
\(495\) 2.91326 0.130941
\(496\) 0 0
\(497\) 1.93465 0.0867808
\(498\) 0 0
\(499\) −3.57973 −0.160251 −0.0801254 0.996785i \(-0.525532\pi\)
−0.0801254 + 0.996785i \(0.525532\pi\)
\(500\) 0 0
\(501\) −12.0938 −0.540312
\(502\) 0 0
\(503\) −39.8915 −1.77867 −0.889337 0.457252i \(-0.848834\pi\)
−0.889337 + 0.457252i \(0.848834\pi\)
\(504\) 0 0
\(505\) 13.5811 0.604352
\(506\) 0 0
\(507\) 26.5869 1.18077
\(508\) 0 0
\(509\) 23.9187 1.06018 0.530089 0.847942i \(-0.322159\pi\)
0.530089 + 0.847942i \(0.322159\pi\)
\(510\) 0 0
\(511\) 0.983698 0.0435162
\(512\) 0 0
\(513\) 6.74323 0.297721
\(514\) 0 0
\(515\) −8.90701 −0.392490
\(516\) 0 0
\(517\) −20.9631 −0.921958
\(518\) 0 0
\(519\) 11.5174 0.505556
\(520\) 0 0
\(521\) −16.1944 −0.709489 −0.354745 0.934963i \(-0.615432\pi\)
−0.354745 + 0.934963i \(0.615432\pi\)
\(522\) 0 0
\(523\) 41.0996 1.79716 0.898580 0.438810i \(-0.144600\pi\)
0.898580 + 0.438810i \(0.144600\pi\)
\(524\) 0 0
\(525\) −0.949555 −0.0414420
\(526\) 0 0
\(527\) −0.0728462 −0.00317323
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 8.52648 0.370018
\(532\) 0 0
\(533\) 19.7228 0.854290
\(534\) 0 0
\(535\) 6.23979 0.269770
\(536\) 0 0
\(537\) −2.23450 −0.0964258
\(538\) 0 0
\(539\) 22.4917 0.968785
\(540\) 0 0
\(541\) 41.4291 1.78118 0.890588 0.454811i \(-0.150293\pi\)
0.890588 + 0.454811i \(0.150293\pi\)
\(542\) 0 0
\(543\) −19.7251 −0.846485
\(544\) 0 0
\(545\) −2.52065 −0.107973
\(546\) 0 0
\(547\) 17.9184 0.766134 0.383067 0.923721i \(-0.374868\pi\)
0.383067 + 0.923721i \(0.374868\pi\)
\(548\) 0 0
\(549\) 7.66345 0.327068
\(550\) 0 0
\(551\) −6.74323 −0.287271
\(552\) 0 0
\(553\) −1.78308 −0.0758242
\(554\) 0 0
\(555\) −1.75442 −0.0744709
\(556\) 0 0
\(557\) 23.8199 1.00928 0.504640 0.863330i \(-0.331625\pi\)
0.504640 + 0.863330i \(0.331625\pi\)
\(558\) 0 0
\(559\) −27.5615 −1.16573
\(560\) 0 0
\(561\) −0.332860 −0.0140534
\(562\) 0 0
\(563\) 8.58477 0.361805 0.180902 0.983501i \(-0.442098\pi\)
0.180902 + 0.983501i \(0.442098\pi\)
\(564\) 0 0
\(565\) −0.137143 −0.00576967
\(566\) 0 0
\(567\) 0.226627 0.00951744
\(568\) 0 0
\(569\) 34.0076 1.42567 0.712836 0.701330i \(-0.247410\pi\)
0.712836 + 0.701330i \(0.247410\pi\)
\(570\) 0 0
\(571\) 25.0231 1.04718 0.523591 0.851970i \(-0.324592\pi\)
0.523591 + 0.851970i \(0.324592\pi\)
\(572\) 0 0
\(573\) 20.6235 0.861560
\(574\) 0 0
\(575\) −4.18994 −0.174733
\(576\) 0 0
\(577\) −22.8134 −0.949735 −0.474868 0.880057i \(-0.657504\pi\)
−0.474868 + 0.880057i \(0.657504\pi\)
\(578\) 0 0
\(579\) 13.9362 0.579170
\(580\) 0 0
\(581\) 1.50071 0.0622600
\(582\) 0 0
\(583\) 25.6134 1.06080
\(584\) 0 0
\(585\) 5.66283 0.234129
\(586\) 0 0
\(587\) 14.3056 0.590456 0.295228 0.955427i \(-0.404604\pi\)
0.295228 + 0.955427i \(0.404604\pi\)
\(588\) 0 0
\(589\) −4.77678 −0.196824
\(590\) 0 0
\(591\) 6.12354 0.251889
\(592\) 0 0
\(593\) 18.1392 0.744889 0.372445 0.928054i \(-0.378520\pi\)
0.372445 + 0.928054i \(0.378520\pi\)
\(594\) 0 0
\(595\) −0.0209753 −0.000859905 0
\(596\) 0 0
\(597\) 11.1948 0.458171
\(598\) 0 0
\(599\) 21.3863 0.873820 0.436910 0.899505i \(-0.356073\pi\)
0.436910 + 0.899505i \(0.356073\pi\)
\(600\) 0 0
\(601\) 31.7899 1.29674 0.648368 0.761327i \(-0.275452\pi\)
0.648368 + 0.761327i \(0.275452\pi\)
\(602\) 0 0
\(603\) 12.4119 0.505453
\(604\) 0 0
\(605\) 0.470567 0.0191313
\(606\) 0 0
\(607\) −20.8911 −0.847944 −0.423972 0.905675i \(-0.639365\pi\)
−0.423972 + 0.905675i \(0.639365\pi\)
\(608\) 0 0
\(609\) −0.226627 −0.00918339
\(610\) 0 0
\(611\) −40.7484 −1.64850
\(612\) 0 0
\(613\) −5.82497 −0.235268 −0.117634 0.993057i \(-0.537531\pi\)
−0.117634 + 0.993057i \(0.537531\pi\)
\(614\) 0 0
\(615\) 2.82131 0.113766
\(616\) 0 0
\(617\) −41.5710 −1.67358 −0.836792 0.547521i \(-0.815572\pi\)
−0.836792 + 0.547521i \(0.815572\pi\)
\(618\) 0 0
\(619\) −4.58491 −0.184283 −0.0921416 0.995746i \(-0.529371\pi\)
−0.0921416 + 0.995746i \(0.529371\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 0.0823937 0.00330103
\(624\) 0 0
\(625\) 13.5053 0.540214
\(626\) 0 0
\(627\) −21.8268 −0.871678
\(628\) 0 0
\(629\) 0.200454 0.00799263
\(630\) 0 0
\(631\) −18.2896 −0.728096 −0.364048 0.931380i \(-0.618606\pi\)
−0.364048 + 0.931380i \(0.618606\pi\)
\(632\) 0 0
\(633\) 11.3704 0.451933
\(634\) 0 0
\(635\) 9.36691 0.371715
\(636\) 0 0
\(637\) 43.7195 1.73223
\(638\) 0 0
\(639\) 8.53670 0.337707
\(640\) 0 0
\(641\) 42.2822 1.67005 0.835024 0.550213i \(-0.185454\pi\)
0.835024 + 0.550213i \(0.185454\pi\)
\(642\) 0 0
\(643\) 22.0222 0.868471 0.434235 0.900799i \(-0.357019\pi\)
0.434235 + 0.900799i \(0.357019\pi\)
\(644\) 0 0
\(645\) −3.94262 −0.155241
\(646\) 0 0
\(647\) −2.98336 −0.117288 −0.0586439 0.998279i \(-0.518678\pi\)
−0.0586439 + 0.998279i \(0.518678\pi\)
\(648\) 0 0
\(649\) −27.5989 −1.08335
\(650\) 0 0
\(651\) −0.160538 −0.00629200
\(652\) 0 0
\(653\) −38.5647 −1.50915 −0.754576 0.656213i \(-0.772157\pi\)
−0.754576 + 0.656213i \(0.772157\pi\)
\(654\) 0 0
\(655\) −10.2133 −0.399067
\(656\) 0 0
\(657\) 4.34060 0.169343
\(658\) 0 0
\(659\) −2.04166 −0.0795316 −0.0397658 0.999209i \(-0.512661\pi\)
−0.0397658 + 0.999209i \(0.512661\pi\)
\(660\) 0 0
\(661\) 31.3912 1.22098 0.610488 0.792025i \(-0.290973\pi\)
0.610488 + 0.792025i \(0.290973\pi\)
\(662\) 0 0
\(663\) −0.647016 −0.0251280
\(664\) 0 0
\(665\) −1.37543 −0.0533368
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 11.9124 0.460560
\(670\) 0 0
\(671\) −24.8054 −0.957602
\(672\) 0 0
\(673\) 37.8206 1.45788 0.728938 0.684579i \(-0.240014\pi\)
0.728938 + 0.684579i \(0.240014\pi\)
\(674\) 0 0
\(675\) −4.18994 −0.161271
\(676\) 0 0
\(677\) 11.7393 0.451177 0.225588 0.974223i \(-0.427570\pi\)
0.225588 + 0.974223i \(0.427570\pi\)
\(678\) 0 0
\(679\) 2.06543 0.0792641
\(680\) 0 0
\(681\) −8.71622 −0.334006
\(682\) 0 0
\(683\) −5.03624 −0.192706 −0.0963531 0.995347i \(-0.530718\pi\)
−0.0963531 + 0.995347i \(0.530718\pi\)
\(684\) 0 0
\(685\) −0.433487 −0.0165627
\(686\) 0 0
\(687\) −0.984405 −0.0375574
\(688\) 0 0
\(689\) 49.7876 1.89676
\(690\) 0 0
\(691\) 40.4007 1.53691 0.768457 0.639902i \(-0.221025\pi\)
0.768457 + 0.639902i \(0.221025\pi\)
\(692\) 0 0
\(693\) −0.733557 −0.0278655
\(694\) 0 0
\(695\) 4.86094 0.184386
\(696\) 0 0
\(697\) −0.322354 −0.0122100
\(698\) 0 0
\(699\) 0.418820 0.0158412
\(700\) 0 0
\(701\) −26.1231 −0.986656 −0.493328 0.869843i \(-0.664220\pi\)
−0.493328 + 0.869843i \(0.664220\pi\)
\(702\) 0 0
\(703\) 13.1445 0.495754
\(704\) 0 0
\(705\) −5.82898 −0.219532
\(706\) 0 0
\(707\) −3.41971 −0.128612
\(708\) 0 0
\(709\) 22.7522 0.854477 0.427239 0.904139i \(-0.359486\pi\)
0.427239 + 0.904139i \(0.359486\pi\)
\(710\) 0 0
\(711\) −7.86789 −0.295069
\(712\) 0 0
\(713\) −0.708382 −0.0265291
\(714\) 0 0
\(715\) −18.3297 −0.685492
\(716\) 0 0
\(717\) −11.9016 −0.444475
\(718\) 0 0
\(719\) −27.1973 −1.01429 −0.507144 0.861861i \(-0.669299\pi\)
−0.507144 + 0.861861i \(0.669299\pi\)
\(720\) 0 0
\(721\) 2.24278 0.0835254
\(722\) 0 0
\(723\) 24.4060 0.907667
\(724\) 0 0
\(725\) 4.18994 0.155611
\(726\) 0 0
\(727\) −24.2288 −0.898595 −0.449298 0.893382i \(-0.648326\pi\)
−0.449298 + 0.893382i \(0.648326\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.450471 0.0166613
\(732\) 0 0
\(733\) −41.3863 −1.52864 −0.764320 0.644838i \(-0.776925\pi\)
−0.764320 + 0.644838i \(0.776925\pi\)
\(734\) 0 0
\(735\) 6.25400 0.230682
\(736\) 0 0
\(737\) −40.1755 −1.47988
\(738\) 0 0
\(739\) 39.5874 1.45625 0.728124 0.685446i \(-0.240393\pi\)
0.728124 + 0.685446i \(0.240393\pi\)
\(740\) 0 0
\(741\) −42.4271 −1.55860
\(742\) 0 0
\(743\) 37.4928 1.37548 0.687739 0.725958i \(-0.258603\pi\)
0.687739 + 0.725958i \(0.258603\pi\)
\(744\) 0 0
\(745\) −3.30134 −0.120952
\(746\) 0 0
\(747\) 6.62194 0.242284
\(748\) 0 0
\(749\) −1.57117 −0.0574095
\(750\) 0 0
\(751\) −20.7428 −0.756914 −0.378457 0.925619i \(-0.623545\pi\)
−0.378457 + 0.925619i \(0.623545\pi\)
\(752\) 0 0
\(753\) 10.2426 0.373260
\(754\) 0 0
\(755\) −15.6701 −0.570293
\(756\) 0 0
\(757\) −47.5865 −1.72956 −0.864781 0.502149i \(-0.832543\pi\)
−0.864781 + 0.502149i \(0.832543\pi\)
\(758\) 0 0
\(759\) −3.23685 −0.117490
\(760\) 0 0
\(761\) −32.8468 −1.19069 −0.595347 0.803468i \(-0.702986\pi\)
−0.595347 + 0.803468i \(0.702986\pi\)
\(762\) 0 0
\(763\) 0.634697 0.0229776
\(764\) 0 0
\(765\) −0.0925544 −0.00334631
\(766\) 0 0
\(767\) −53.6470 −1.93708
\(768\) 0 0
\(769\) 33.7101 1.21562 0.607809 0.794083i \(-0.292049\pi\)
0.607809 + 0.794083i \(0.292049\pi\)
\(770\) 0 0
\(771\) 30.7464 1.10731
\(772\) 0 0
\(773\) −26.8623 −0.966171 −0.483086 0.875573i \(-0.660484\pi\)
−0.483086 + 0.875573i \(0.660484\pi\)
\(774\) 0 0
\(775\) 2.96808 0.106617
\(776\) 0 0
\(777\) 0.441761 0.0158481
\(778\) 0 0
\(779\) −21.1379 −0.757343
\(780\) 0 0
\(781\) −27.6320 −0.988750
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −16.0857 −0.574122
\(786\) 0 0
\(787\) 39.9018 1.42235 0.711173 0.703017i \(-0.248164\pi\)
0.711173 + 0.703017i \(0.248164\pi\)
\(788\) 0 0
\(789\) 20.2721 0.721706
\(790\) 0 0
\(791\) 0.0345326 0.00122784
\(792\) 0 0
\(793\) −48.2170 −1.71224
\(794\) 0 0
\(795\) 7.12202 0.252592
\(796\) 0 0
\(797\) −12.9592 −0.459039 −0.229519 0.973304i \(-0.573715\pi\)
−0.229519 + 0.973304i \(0.573715\pi\)
\(798\) 0 0
\(799\) 0.666000 0.0235614
\(800\) 0 0
\(801\) 0.363565 0.0128459
\(802\) 0 0
\(803\) −14.0499 −0.495809
\(804\) 0 0
\(805\) −0.203972 −0.00718905
\(806\) 0 0
\(807\) −29.9148 −1.05305
\(808\) 0 0
\(809\) −31.4405 −1.10539 −0.552695 0.833384i \(-0.686400\pi\)
−0.552695 + 0.833384i \(0.686400\pi\)
\(810\) 0 0
\(811\) 34.3379 1.20577 0.602884 0.797829i \(-0.294018\pi\)
0.602884 + 0.797829i \(0.294018\pi\)
\(812\) 0 0
\(813\) −28.3436 −0.994054
\(814\) 0 0
\(815\) −12.2832 −0.430261
\(816\) 0 0
\(817\) 29.5390 1.03344
\(818\) 0 0
\(819\) −1.42589 −0.0498248
\(820\) 0 0
\(821\) 54.9730 1.91857 0.959285 0.282439i \(-0.0911436\pi\)
0.959285 + 0.282439i \(0.0911436\pi\)
\(822\) 0 0
\(823\) −39.2273 −1.36738 −0.683688 0.729774i \(-0.739625\pi\)
−0.683688 + 0.729774i \(0.739625\pi\)
\(824\) 0 0
\(825\) 13.5622 0.472175
\(826\) 0 0
\(827\) 39.8397 1.38536 0.692681 0.721245i \(-0.256430\pi\)
0.692681 + 0.721245i \(0.256430\pi\)
\(828\) 0 0
\(829\) −23.7285 −0.824126 −0.412063 0.911155i \(-0.635192\pi\)
−0.412063 + 0.911155i \(0.635192\pi\)
\(830\) 0 0
\(831\) 8.98371 0.311641
\(832\) 0 0
\(833\) −0.714561 −0.0247581
\(834\) 0 0
\(835\) 10.8848 0.376684
\(836\) 0 0
\(837\) −0.708382 −0.0244853
\(838\) 0 0
\(839\) 16.7974 0.579909 0.289955 0.957040i \(-0.406360\pi\)
0.289955 + 0.957040i \(0.406360\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −5.54304 −0.190912
\(844\) 0 0
\(845\) −23.9290 −0.823184
\(846\) 0 0
\(847\) −0.118488 −0.00407131
\(848\) 0 0
\(849\) 4.89295 0.167926
\(850\) 0 0
\(851\) 1.94929 0.0668206
\(852\) 0 0
\(853\) 5.47058 0.187309 0.0936546 0.995605i \(-0.470145\pi\)
0.0936546 + 0.995605i \(0.470145\pi\)
\(854\) 0 0
\(855\) −6.06912 −0.207560
\(856\) 0 0
\(857\) −43.0918 −1.47199 −0.735994 0.676988i \(-0.763285\pi\)
−0.735994 + 0.676988i \(0.763285\pi\)
\(858\) 0 0
\(859\) 23.2963 0.794859 0.397429 0.917633i \(-0.369902\pi\)
0.397429 + 0.917633i \(0.369902\pi\)
\(860\) 0 0
\(861\) −0.710403 −0.0242105
\(862\) 0 0
\(863\) −28.4776 −0.969390 −0.484695 0.874683i \(-0.661069\pi\)
−0.484695 + 0.874683i \(0.661069\pi\)
\(864\) 0 0
\(865\) −10.3660 −0.352454
\(866\) 0 0
\(867\) −16.9894 −0.576991
\(868\) 0 0
\(869\) 25.4672 0.863914
\(870\) 0 0
\(871\) −78.0936 −2.64610
\(872\) 0 0
\(873\) 9.11380 0.308456
\(874\) 0 0
\(875\) 1.87449 0.0633692
\(876\) 0 0
\(877\) −32.2552 −1.08918 −0.544590 0.838703i \(-0.683315\pi\)
−0.544590 + 0.838703i \(0.683315\pi\)
\(878\) 0 0
\(879\) −27.6786 −0.933577
\(880\) 0 0
\(881\) −23.0988 −0.778218 −0.389109 0.921192i \(-0.627217\pi\)
−0.389109 + 0.921192i \(0.627217\pi\)
\(882\) 0 0
\(883\) 11.3781 0.382904 0.191452 0.981502i \(-0.438680\pi\)
0.191452 + 0.981502i \(0.438680\pi\)
\(884\) 0 0
\(885\) −7.67410 −0.257962
\(886\) 0 0
\(887\) 44.1079 1.48100 0.740500 0.672056i \(-0.234589\pi\)
0.740500 + 0.672056i \(0.234589\pi\)
\(888\) 0 0
\(889\) −2.35858 −0.0791042
\(890\) 0 0
\(891\) −3.23685 −0.108438
\(892\) 0 0
\(893\) 43.6720 1.46143
\(894\) 0 0
\(895\) 2.01112 0.0672244
\(896\) 0 0
\(897\) −6.29181 −0.210077
\(898\) 0 0
\(899\) 0.708382 0.0236259
\(900\) 0 0
\(901\) −0.813738 −0.0271096
\(902\) 0 0
\(903\) 0.992749 0.0330366
\(904\) 0 0
\(905\) 17.7532 0.590137
\(906\) 0 0
\(907\) 12.9837 0.431116 0.215558 0.976491i \(-0.430843\pi\)
0.215558 + 0.976491i \(0.430843\pi\)
\(908\) 0 0
\(909\) −15.0896 −0.500490
\(910\) 0 0
\(911\) 2.39043 0.0791984 0.0395992 0.999216i \(-0.487392\pi\)
0.0395992 + 0.999216i \(0.487392\pi\)
\(912\) 0 0
\(913\) −21.4342 −0.709369
\(914\) 0 0
\(915\) −6.89735 −0.228019
\(916\) 0 0
\(917\) 2.57170 0.0849250
\(918\) 0 0
\(919\) 14.0414 0.463184 0.231592 0.972813i \(-0.425607\pi\)
0.231592 + 0.972813i \(0.425607\pi\)
\(920\) 0 0
\(921\) 3.47911 0.114641
\(922\) 0 0
\(923\) −53.7113 −1.76793
\(924\) 0 0
\(925\) −8.16740 −0.268542
\(926\) 0 0
\(927\) 9.89634 0.325038
\(928\) 0 0
\(929\) 32.2034 1.05656 0.528280 0.849070i \(-0.322837\pi\)
0.528280 + 0.849070i \(0.322837\pi\)
\(930\) 0 0
\(931\) −46.8563 −1.53565
\(932\) 0 0
\(933\) 27.6058 0.903773
\(934\) 0 0
\(935\) 0.299584 0.00979745
\(936\) 0 0
\(937\) −39.2319 −1.28165 −0.640826 0.767686i \(-0.721408\pi\)
−0.640826 + 0.767686i \(0.721408\pi\)
\(938\) 0 0
\(939\) 18.0525 0.589121
\(940\) 0 0
\(941\) 43.0865 1.40458 0.702289 0.711892i \(-0.252161\pi\)
0.702289 + 0.711892i \(0.252161\pi\)
\(942\) 0 0
\(943\) −3.13468 −0.102079
\(944\) 0 0
\(945\) −0.203972 −0.00663519
\(946\) 0 0
\(947\) 5.01457 0.162952 0.0814758 0.996675i \(-0.474037\pi\)
0.0814758 + 0.996675i \(0.474037\pi\)
\(948\) 0 0
\(949\) −27.3103 −0.886528
\(950\) 0 0
\(951\) −17.5432 −0.568878
\(952\) 0 0
\(953\) −11.9570 −0.387326 −0.193663 0.981068i \(-0.562037\pi\)
−0.193663 + 0.981068i \(0.562037\pi\)
\(954\) 0 0
\(955\) −18.5618 −0.600647
\(956\) 0 0
\(957\) 3.23685 0.104632
\(958\) 0 0
\(959\) 0.109151 0.00352468
\(960\) 0 0
\(961\) −30.4982 −0.983813
\(962\) 0 0
\(963\) −6.93286 −0.223408
\(964\) 0 0
\(965\) −12.5431 −0.403775
\(966\) 0 0
\(967\) 4.19874 0.135022 0.0675112 0.997719i \(-0.478494\pi\)
0.0675112 + 0.997719i \(0.478494\pi\)
\(968\) 0 0
\(969\) 0.693438 0.0222764
\(970\) 0 0
\(971\) 25.0968 0.805396 0.402698 0.915333i \(-0.368073\pi\)
0.402698 + 0.915333i \(0.368073\pi\)
\(972\) 0 0
\(973\) −1.22398 −0.0392390
\(974\) 0 0
\(975\) 26.3623 0.844270
\(976\) 0 0
\(977\) −4.68006 −0.149728 −0.0748642 0.997194i \(-0.523852\pi\)
−0.0748642 + 0.997194i \(0.523852\pi\)
\(978\) 0 0
\(979\) −1.17680 −0.0376108
\(980\) 0 0
\(981\) 2.80062 0.0894170
\(982\) 0 0
\(983\) −43.5713 −1.38971 −0.694854 0.719151i \(-0.744531\pi\)
−0.694854 + 0.719151i \(0.744531\pi\)
\(984\) 0 0
\(985\) −5.51138 −0.175607
\(986\) 0 0
\(987\) 1.46773 0.0467184
\(988\) 0 0
\(989\) 4.38054 0.139293
\(990\) 0 0
\(991\) −10.3492 −0.328752 −0.164376 0.986398i \(-0.552561\pi\)
−0.164376 + 0.986398i \(0.552561\pi\)
\(992\) 0 0
\(993\) 20.2002 0.641034
\(994\) 0 0
\(995\) −10.0756 −0.319419
\(996\) 0 0
\(997\) 22.8284 0.722984 0.361492 0.932375i \(-0.382268\pi\)
0.361492 + 0.932375i \(0.382268\pi\)
\(998\) 0 0
\(999\) 1.94929 0.0616727
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 \(a_p\))