Properties

Label 6008.2.a.e.1.43
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.43
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.34565 q^{3} +2.39605 q^{5} +3.54861 q^{7} +2.50208 q^{9} +O(q^{10})\) \(q+2.34565 q^{3} +2.39605 q^{5} +3.54861 q^{7} +2.50208 q^{9} +4.15083 q^{11} +3.77384 q^{13} +5.62030 q^{15} -5.89018 q^{17} +2.10563 q^{19} +8.32381 q^{21} +0.956519 q^{23} +0.741047 q^{25} -1.16794 q^{27} -10.1195 q^{29} +1.81665 q^{31} +9.73640 q^{33} +8.50265 q^{35} +2.63508 q^{37} +8.85213 q^{39} -2.88384 q^{41} +9.00650 q^{43} +5.99511 q^{45} -2.83753 q^{47} +5.59266 q^{49} -13.8163 q^{51} -7.26348 q^{53} +9.94558 q^{55} +4.93908 q^{57} +2.36129 q^{59} +3.81161 q^{61} +8.87893 q^{63} +9.04231 q^{65} +6.00108 q^{67} +2.24366 q^{69} -1.43428 q^{71} +2.69211 q^{73} +1.73824 q^{75} +14.7297 q^{77} -1.14388 q^{79} -10.2458 q^{81} +0.157224 q^{83} -14.1132 q^{85} -23.7369 q^{87} +3.98817 q^{89} +13.3919 q^{91} +4.26123 q^{93} +5.04520 q^{95} -3.46814 q^{97} +10.3857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 2.34565 1.35426 0.677131 0.735862i \(-0.263223\pi\)
0.677131 + 0.735862i \(0.263223\pi\)
\(4\) 0 0
\(5\) 2.39605 1.07155 0.535773 0.844362i \(-0.320020\pi\)
0.535773 + 0.844362i \(0.320020\pi\)
\(6\) 0 0
\(7\) 3.54861 1.34125 0.670625 0.741797i \(-0.266026\pi\)
0.670625 + 0.741797i \(0.266026\pi\)
\(8\) 0 0
\(9\) 2.50208 0.834028
\(10\) 0 0
\(11\) 4.15083 1.25152 0.625761 0.780015i \(-0.284789\pi\)
0.625761 + 0.780015i \(0.284789\pi\)
\(12\) 0 0
\(13\) 3.77384 1.04668 0.523338 0.852125i \(-0.324687\pi\)
0.523338 + 0.852125i \(0.324687\pi\)
\(14\) 0 0
\(15\) 5.62030 1.45115
\(16\) 0 0
\(17\) −5.89018 −1.42858 −0.714290 0.699850i \(-0.753250\pi\)
−0.714290 + 0.699850i \(0.753250\pi\)
\(18\) 0 0
\(19\) 2.10563 0.483065 0.241533 0.970393i \(-0.422350\pi\)
0.241533 + 0.970393i \(0.422350\pi\)
\(20\) 0 0
\(21\) 8.32381 1.81640
\(22\) 0 0
\(23\) 0.956519 0.199448 0.0997240 0.995015i \(-0.468204\pi\)
0.0997240 + 0.995015i \(0.468204\pi\)
\(24\) 0 0
\(25\) 0.741047 0.148209
\(26\) 0 0
\(27\) −1.16794 −0.224770
\(28\) 0 0
\(29\) −10.1195 −1.87915 −0.939576 0.342339i \(-0.888781\pi\)
−0.939576 + 0.342339i \(0.888781\pi\)
\(30\) 0 0
\(31\) 1.81665 0.326280 0.163140 0.986603i \(-0.447838\pi\)
0.163140 + 0.986603i \(0.447838\pi\)
\(32\) 0 0
\(33\) 9.73640 1.69489
\(34\) 0 0
\(35\) 8.50265 1.43721
\(36\) 0 0
\(37\) 2.63508 0.433205 0.216602 0.976260i \(-0.430503\pi\)
0.216602 + 0.976260i \(0.430503\pi\)
\(38\) 0 0
\(39\) 8.85213 1.41747
\(40\) 0 0
\(41\) −2.88384 −0.450380 −0.225190 0.974315i \(-0.572300\pi\)
−0.225190 + 0.974315i \(0.572300\pi\)
\(42\) 0 0
\(43\) 9.00650 1.37348 0.686739 0.726904i \(-0.259042\pi\)
0.686739 + 0.726904i \(0.259042\pi\)
\(44\) 0 0
\(45\) 5.99511 0.893699
\(46\) 0 0
\(47\) −2.83753 −0.413896 −0.206948 0.978352i \(-0.566353\pi\)
−0.206948 + 0.978352i \(0.566353\pi\)
\(48\) 0 0
\(49\) 5.59266 0.798951
\(50\) 0 0
\(51\) −13.8163 −1.93467
\(52\) 0 0
\(53\) −7.26348 −0.997715 −0.498858 0.866684i \(-0.666247\pi\)
−0.498858 + 0.866684i \(0.666247\pi\)
\(54\) 0 0
\(55\) 9.94558 1.34106
\(56\) 0 0
\(57\) 4.93908 0.654197
\(58\) 0 0
\(59\) 2.36129 0.307414 0.153707 0.988116i \(-0.450879\pi\)
0.153707 + 0.988116i \(0.450879\pi\)
\(60\) 0 0
\(61\) 3.81161 0.488026 0.244013 0.969772i \(-0.421536\pi\)
0.244013 + 0.969772i \(0.421536\pi\)
\(62\) 0 0
\(63\) 8.87893 1.11864
\(64\) 0 0
\(65\) 9.04231 1.12156
\(66\) 0 0
\(67\) 6.00108 0.733149 0.366575 0.930389i \(-0.380530\pi\)
0.366575 + 0.930389i \(0.380530\pi\)
\(68\) 0 0
\(69\) 2.24366 0.270105
\(70\) 0 0
\(71\) −1.43428 −0.170218 −0.0851090 0.996372i \(-0.527124\pi\)
−0.0851090 + 0.996372i \(0.527124\pi\)
\(72\) 0 0
\(73\) 2.69211 0.315088 0.157544 0.987512i \(-0.449642\pi\)
0.157544 + 0.987512i \(0.449642\pi\)
\(74\) 0 0
\(75\) 1.73824 0.200714
\(76\) 0 0
\(77\) 14.7297 1.67860
\(78\) 0 0
\(79\) −1.14388 −0.128697 −0.0643483 0.997928i \(-0.520497\pi\)
−0.0643483 + 0.997928i \(0.520497\pi\)
\(80\) 0 0
\(81\) −10.2458 −1.13843
\(82\) 0 0
\(83\) 0.157224 0.0172576 0.00862880 0.999963i \(-0.497253\pi\)
0.00862880 + 0.999963i \(0.497253\pi\)
\(84\) 0 0
\(85\) −14.1132 −1.53079
\(86\) 0 0
\(87\) −23.7369 −2.54487
\(88\) 0 0
\(89\) 3.98817 0.422745 0.211373 0.977406i \(-0.432207\pi\)
0.211373 + 0.977406i \(0.432207\pi\)
\(90\) 0 0
\(91\) 13.3919 1.40385
\(92\) 0 0
\(93\) 4.26123 0.441869
\(94\) 0 0
\(95\) 5.04520 0.517626
\(96\) 0 0
\(97\) −3.46814 −0.352137 −0.176068 0.984378i \(-0.556338\pi\)
−0.176068 + 0.984378i \(0.556338\pi\)
\(98\) 0 0
\(99\) 10.3857 1.04380
\(100\) 0 0
\(101\) −11.1207 −1.10655 −0.553274 0.832999i \(-0.686622\pi\)
−0.553274 + 0.832999i \(0.686622\pi\)
\(102\) 0 0
\(103\) −4.19013 −0.412865 −0.206433 0.978461i \(-0.566185\pi\)
−0.206433 + 0.978461i \(0.566185\pi\)
\(104\) 0 0
\(105\) 19.9443 1.94636
\(106\) 0 0
\(107\) −9.86224 −0.953418 −0.476709 0.879061i \(-0.658171\pi\)
−0.476709 + 0.879061i \(0.658171\pi\)
\(108\) 0 0
\(109\) −5.55958 −0.532511 −0.266256 0.963902i \(-0.585787\pi\)
−0.266256 + 0.963902i \(0.585787\pi\)
\(110\) 0 0
\(111\) 6.18098 0.586673
\(112\) 0 0
\(113\) −8.98037 −0.844802 −0.422401 0.906409i \(-0.638813\pi\)
−0.422401 + 0.906409i \(0.638813\pi\)
\(114\) 0 0
\(115\) 2.29187 0.213718
\(116\) 0 0
\(117\) 9.44247 0.872957
\(118\) 0 0
\(119\) −20.9020 −1.91608
\(120\) 0 0
\(121\) 6.22937 0.566306
\(122\) 0 0
\(123\) −6.76449 −0.609933
\(124\) 0 0
\(125\) −10.2047 −0.912732
\(126\) 0 0
\(127\) −0.541429 −0.0480441 −0.0240220 0.999711i \(-0.507647\pi\)
−0.0240220 + 0.999711i \(0.507647\pi\)
\(128\) 0 0
\(129\) 21.1261 1.86005
\(130\) 0 0
\(131\) −0.159598 −0.0139442 −0.00697209 0.999976i \(-0.502219\pi\)
−0.00697209 + 0.999976i \(0.502219\pi\)
\(132\) 0 0
\(133\) 7.47208 0.647911
\(134\) 0 0
\(135\) −2.79844 −0.240851
\(136\) 0 0
\(137\) −3.55323 −0.303573 −0.151786 0.988413i \(-0.548503\pi\)
−0.151786 + 0.988413i \(0.548503\pi\)
\(138\) 0 0
\(139\) 6.76436 0.573745 0.286873 0.957969i \(-0.407384\pi\)
0.286873 + 0.957969i \(0.407384\pi\)
\(140\) 0 0
\(141\) −6.65586 −0.560525
\(142\) 0 0
\(143\) 15.6646 1.30994
\(144\) 0 0
\(145\) −24.2469 −2.01360
\(146\) 0 0
\(147\) 13.1184 1.08199
\(148\) 0 0
\(149\) 12.6057 1.03270 0.516349 0.856378i \(-0.327291\pi\)
0.516349 + 0.856378i \(0.327291\pi\)
\(150\) 0 0
\(151\) 8.88226 0.722828 0.361414 0.932405i \(-0.382294\pi\)
0.361414 + 0.932405i \(0.382294\pi\)
\(152\) 0 0
\(153\) −14.7377 −1.19148
\(154\) 0 0
\(155\) 4.35278 0.349624
\(156\) 0 0
\(157\) −15.4259 −1.23112 −0.615560 0.788090i \(-0.711070\pi\)
−0.615560 + 0.788090i \(0.711070\pi\)
\(158\) 0 0
\(159\) −17.0376 −1.35117
\(160\) 0 0
\(161\) 3.39432 0.267510
\(162\) 0 0
\(163\) 2.64635 0.207278 0.103639 0.994615i \(-0.466951\pi\)
0.103639 + 0.994615i \(0.466951\pi\)
\(164\) 0 0
\(165\) 23.3289 1.81615
\(166\) 0 0
\(167\) −21.2574 −1.64495 −0.822475 0.568801i \(-0.807408\pi\)
−0.822475 + 0.568801i \(0.807408\pi\)
\(168\) 0 0
\(169\) 1.24190 0.0955309
\(170\) 0 0
\(171\) 5.26847 0.402890
\(172\) 0 0
\(173\) −10.4128 −0.791668 −0.395834 0.918322i \(-0.629545\pi\)
−0.395834 + 0.918322i \(0.629545\pi\)
\(174\) 0 0
\(175\) 2.62969 0.198786
\(176\) 0 0
\(177\) 5.53877 0.416320
\(178\) 0 0
\(179\) −19.5060 −1.45795 −0.728973 0.684542i \(-0.760002\pi\)
−0.728973 + 0.684542i \(0.760002\pi\)
\(180\) 0 0
\(181\) −4.16663 −0.309703 −0.154851 0.987938i \(-0.549490\pi\)
−0.154851 + 0.987938i \(0.549490\pi\)
\(182\) 0 0
\(183\) 8.94071 0.660916
\(184\) 0 0
\(185\) 6.31378 0.464198
\(186\) 0 0
\(187\) −24.4491 −1.78790
\(188\) 0 0
\(189\) −4.14456 −0.301473
\(190\) 0 0
\(191\) −6.02838 −0.436198 −0.218099 0.975927i \(-0.569986\pi\)
−0.218099 + 0.975927i \(0.569986\pi\)
\(192\) 0 0
\(193\) 24.1046 1.73508 0.867542 0.497364i \(-0.165699\pi\)
0.867542 + 0.497364i \(0.165699\pi\)
\(194\) 0 0
\(195\) 21.2101 1.51889
\(196\) 0 0
\(197\) −7.32513 −0.521894 −0.260947 0.965353i \(-0.584035\pi\)
−0.260947 + 0.965353i \(0.584035\pi\)
\(198\) 0 0
\(199\) 22.5557 1.59893 0.799466 0.600712i \(-0.205116\pi\)
0.799466 + 0.600712i \(0.205116\pi\)
\(200\) 0 0
\(201\) 14.0765 0.992877
\(202\) 0 0
\(203\) −35.9104 −2.52041
\(204\) 0 0
\(205\) −6.90982 −0.482603
\(206\) 0 0
\(207\) 2.39329 0.166345
\(208\) 0 0
\(209\) 8.74012 0.604567
\(210\) 0 0
\(211\) −25.7692 −1.77402 −0.887012 0.461747i \(-0.847223\pi\)
−0.887012 + 0.461747i \(0.847223\pi\)
\(212\) 0 0
\(213\) −3.36433 −0.230520
\(214\) 0 0
\(215\) 21.5800 1.47174
\(216\) 0 0
\(217\) 6.44659 0.437623
\(218\) 0 0
\(219\) 6.31476 0.426712
\(220\) 0 0
\(221\) −22.2286 −1.49526
\(222\) 0 0
\(223\) 22.3467 1.49645 0.748224 0.663446i \(-0.230907\pi\)
0.748224 + 0.663446i \(0.230907\pi\)
\(224\) 0 0
\(225\) 1.85416 0.123611
\(226\) 0 0
\(227\) 0.0394945 0.00262134 0.00131067 0.999999i \(-0.499583\pi\)
0.00131067 + 0.999999i \(0.499583\pi\)
\(228\) 0 0
\(229\) 5.30024 0.350250 0.175125 0.984546i \(-0.443967\pi\)
0.175125 + 0.984546i \(0.443967\pi\)
\(230\) 0 0
\(231\) 34.5507 2.27327
\(232\) 0 0
\(233\) 18.6242 1.22011 0.610056 0.792359i \(-0.291147\pi\)
0.610056 + 0.792359i \(0.291147\pi\)
\(234\) 0 0
\(235\) −6.79886 −0.443509
\(236\) 0 0
\(237\) −2.68315 −0.174289
\(238\) 0 0
\(239\) 12.3134 0.796485 0.398242 0.917280i \(-0.369620\pi\)
0.398242 + 0.917280i \(0.369620\pi\)
\(240\) 0 0
\(241\) −18.0153 −1.16047 −0.580234 0.814450i \(-0.697039\pi\)
−0.580234 + 0.814450i \(0.697039\pi\)
\(242\) 0 0
\(243\) −20.5293 −1.31696
\(244\) 0 0
\(245\) 13.4003 0.856112
\(246\) 0 0
\(247\) 7.94633 0.505613
\(248\) 0 0
\(249\) 0.368793 0.0233713
\(250\) 0 0
\(251\) 16.0120 1.01067 0.505333 0.862924i \(-0.331370\pi\)
0.505333 + 0.862924i \(0.331370\pi\)
\(252\) 0 0
\(253\) 3.97035 0.249614
\(254\) 0 0
\(255\) −33.1046 −2.07309
\(256\) 0 0
\(257\) 10.6106 0.661872 0.330936 0.943653i \(-0.392636\pi\)
0.330936 + 0.943653i \(0.392636\pi\)
\(258\) 0 0
\(259\) 9.35088 0.581036
\(260\) 0 0
\(261\) −25.3200 −1.56727
\(262\) 0 0
\(263\) 8.65464 0.533668 0.266834 0.963742i \(-0.414022\pi\)
0.266834 + 0.963742i \(0.414022\pi\)
\(264\) 0 0
\(265\) −17.4036 −1.06910
\(266\) 0 0
\(267\) 9.35486 0.572508
\(268\) 0 0
\(269\) 22.5756 1.37646 0.688229 0.725494i \(-0.258389\pi\)
0.688229 + 0.725494i \(0.258389\pi\)
\(270\) 0 0
\(271\) 6.93863 0.421492 0.210746 0.977541i \(-0.432411\pi\)
0.210746 + 0.977541i \(0.432411\pi\)
\(272\) 0 0
\(273\) 31.4128 1.90119
\(274\) 0 0
\(275\) 3.07596 0.185487
\(276\) 0 0
\(277\) −11.4897 −0.690347 −0.345173 0.938539i \(-0.612180\pi\)
−0.345173 + 0.938539i \(0.612180\pi\)
\(278\) 0 0
\(279\) 4.54541 0.272127
\(280\) 0 0
\(281\) 8.06936 0.481378 0.240689 0.970602i \(-0.422627\pi\)
0.240689 + 0.970602i \(0.422627\pi\)
\(282\) 0 0
\(283\) −15.9144 −0.946014 −0.473007 0.881059i \(-0.656831\pi\)
−0.473007 + 0.881059i \(0.656831\pi\)
\(284\) 0 0
\(285\) 11.8343 0.701002
\(286\) 0 0
\(287\) −10.2336 −0.604073
\(288\) 0 0
\(289\) 17.6943 1.04084
\(290\) 0 0
\(291\) −8.13506 −0.476886
\(292\) 0 0
\(293\) 24.1846 1.41288 0.706440 0.707773i \(-0.250300\pi\)
0.706440 + 0.707773i \(0.250300\pi\)
\(294\) 0 0
\(295\) 5.65777 0.329408
\(296\) 0 0
\(297\) −4.84791 −0.281304
\(298\) 0 0
\(299\) 3.60976 0.208758
\(300\) 0 0
\(301\) 31.9606 1.84218
\(302\) 0 0
\(303\) −26.0852 −1.49856
\(304\) 0 0
\(305\) 9.13280 0.522942
\(306\) 0 0
\(307\) 23.4527 1.33852 0.669259 0.743030i \(-0.266612\pi\)
0.669259 + 0.743030i \(0.266612\pi\)
\(308\) 0 0
\(309\) −9.82858 −0.559128
\(310\) 0 0
\(311\) −27.0938 −1.53635 −0.768175 0.640239i \(-0.778835\pi\)
−0.768175 + 0.640239i \(0.778835\pi\)
\(312\) 0 0
\(313\) −32.2527 −1.82303 −0.911514 0.411269i \(-0.865086\pi\)
−0.911514 + 0.411269i \(0.865086\pi\)
\(314\) 0 0
\(315\) 21.2743 1.19867
\(316\) 0 0
\(317\) 14.9212 0.838057 0.419029 0.907973i \(-0.362371\pi\)
0.419029 + 0.907973i \(0.362371\pi\)
\(318\) 0 0
\(319\) −42.0045 −2.35180
\(320\) 0 0
\(321\) −23.1334 −1.29118
\(322\) 0 0
\(323\) −12.4026 −0.690097
\(324\) 0 0
\(325\) 2.79660 0.155127
\(326\) 0 0
\(327\) −13.0408 −0.721160
\(328\) 0 0
\(329\) −10.0693 −0.555139
\(330\) 0 0
\(331\) −10.1089 −0.555637 −0.277819 0.960634i \(-0.589611\pi\)
−0.277819 + 0.960634i \(0.589611\pi\)
\(332\) 0 0
\(333\) 6.59319 0.361305
\(334\) 0 0
\(335\) 14.3789 0.785603
\(336\) 0 0
\(337\) 8.29570 0.451895 0.225948 0.974139i \(-0.427452\pi\)
0.225948 + 0.974139i \(0.427452\pi\)
\(338\) 0 0
\(339\) −21.0648 −1.14408
\(340\) 0 0
\(341\) 7.54061 0.408347
\(342\) 0 0
\(343\) −4.99411 −0.269657
\(344\) 0 0
\(345\) 5.37592 0.289430
\(346\) 0 0
\(347\) 12.8028 0.687288 0.343644 0.939100i \(-0.388339\pi\)
0.343644 + 0.939100i \(0.388339\pi\)
\(348\) 0 0
\(349\) 11.7238 0.627560 0.313780 0.949496i \(-0.398404\pi\)
0.313780 + 0.949496i \(0.398404\pi\)
\(350\) 0 0
\(351\) −4.40762 −0.235261
\(352\) 0 0
\(353\) −11.6065 −0.617751 −0.308876 0.951102i \(-0.599953\pi\)
−0.308876 + 0.951102i \(0.599953\pi\)
\(354\) 0 0
\(355\) −3.43661 −0.182396
\(356\) 0 0
\(357\) −49.0288 −2.59488
\(358\) 0 0
\(359\) −9.74703 −0.514429 −0.257214 0.966354i \(-0.582805\pi\)
−0.257214 + 0.966354i \(0.582805\pi\)
\(360\) 0 0
\(361\) −14.5663 −0.766648
\(362\) 0 0
\(363\) 14.6119 0.766928
\(364\) 0 0
\(365\) 6.45043 0.337631
\(366\) 0 0
\(367\) 18.2333 0.951772 0.475886 0.879507i \(-0.342127\pi\)
0.475886 + 0.879507i \(0.342127\pi\)
\(368\) 0 0
\(369\) −7.21561 −0.375630
\(370\) 0 0
\(371\) −25.7753 −1.33819
\(372\) 0 0
\(373\) −20.4748 −1.06014 −0.530072 0.847953i \(-0.677835\pi\)
−0.530072 + 0.847953i \(0.677835\pi\)
\(374\) 0 0
\(375\) −23.9366 −1.23608
\(376\) 0 0
\(377\) −38.1896 −1.96686
\(378\) 0 0
\(379\) 16.9264 0.869451 0.434726 0.900563i \(-0.356845\pi\)
0.434726 + 0.900563i \(0.356845\pi\)
\(380\) 0 0
\(381\) −1.27000 −0.0650643
\(382\) 0 0
\(383\) 11.0132 0.562747 0.281374 0.959598i \(-0.409210\pi\)
0.281374 + 0.959598i \(0.409210\pi\)
\(384\) 0 0
\(385\) 35.2930 1.79870
\(386\) 0 0
\(387\) 22.5350 1.14552
\(388\) 0 0
\(389\) 27.7665 1.40782 0.703909 0.710290i \(-0.251436\pi\)
0.703909 + 0.710290i \(0.251436\pi\)
\(390\) 0 0
\(391\) −5.63408 −0.284927
\(392\) 0 0
\(393\) −0.374362 −0.0188841
\(394\) 0 0
\(395\) −2.74079 −0.137904
\(396\) 0 0
\(397\) −38.8642 −1.95054 −0.975269 0.221019i \(-0.929062\pi\)
−0.975269 + 0.221019i \(0.929062\pi\)
\(398\) 0 0
\(399\) 17.5269 0.877442
\(400\) 0 0
\(401\) 26.1424 1.30549 0.652744 0.757578i \(-0.273618\pi\)
0.652744 + 0.757578i \(0.273618\pi\)
\(402\) 0 0
\(403\) 6.85576 0.341510
\(404\) 0 0
\(405\) −24.5495 −1.21987
\(406\) 0 0
\(407\) 10.9378 0.542165
\(408\) 0 0
\(409\) −31.3645 −1.55087 −0.775437 0.631425i \(-0.782471\pi\)
−0.775437 + 0.631425i \(0.782471\pi\)
\(410\) 0 0
\(411\) −8.33463 −0.411117
\(412\) 0 0
\(413\) 8.37932 0.412319
\(414\) 0 0
\(415\) 0.376717 0.0184923
\(416\) 0 0
\(417\) 15.8668 0.777002
\(418\) 0 0
\(419\) 10.1431 0.495523 0.247761 0.968821i \(-0.420305\pi\)
0.247761 + 0.968821i \(0.420305\pi\)
\(420\) 0 0
\(421\) 3.43634 0.167477 0.0837384 0.996488i \(-0.473314\pi\)
0.0837384 + 0.996488i \(0.473314\pi\)
\(422\) 0 0
\(423\) −7.09974 −0.345201
\(424\) 0 0
\(425\) −4.36490 −0.211729
\(426\) 0 0
\(427\) 13.5259 0.654565
\(428\) 0 0
\(429\) 36.7436 1.77400
\(430\) 0 0
\(431\) 9.37781 0.451713 0.225857 0.974161i \(-0.427482\pi\)
0.225857 + 0.974161i \(0.427482\pi\)
\(432\) 0 0
\(433\) 16.7193 0.803477 0.401739 0.915754i \(-0.368406\pi\)
0.401739 + 0.915754i \(0.368406\pi\)
\(434\) 0 0
\(435\) −56.8748 −2.72694
\(436\) 0 0
\(437\) 2.01408 0.0963464
\(438\) 0 0
\(439\) 22.8328 1.08975 0.544876 0.838517i \(-0.316577\pi\)
0.544876 + 0.838517i \(0.316577\pi\)
\(440\) 0 0
\(441\) 13.9933 0.666347
\(442\) 0 0
\(443\) 39.1309 1.85916 0.929582 0.368616i \(-0.120168\pi\)
0.929582 + 0.368616i \(0.120168\pi\)
\(444\) 0 0
\(445\) 9.55585 0.452991
\(446\) 0 0
\(447\) 29.5686 1.39855
\(448\) 0 0
\(449\) −26.2936 −1.24087 −0.620436 0.784257i \(-0.713044\pi\)
−0.620436 + 0.784257i \(0.713044\pi\)
\(450\) 0 0
\(451\) −11.9703 −0.563661
\(452\) 0 0
\(453\) 20.8347 0.978899
\(454\) 0 0
\(455\) 32.0877 1.50429
\(456\) 0 0
\(457\) 35.3701 1.65455 0.827273 0.561801i \(-0.189891\pi\)
0.827273 + 0.561801i \(0.189891\pi\)
\(458\) 0 0
\(459\) 6.87937 0.321102
\(460\) 0 0
\(461\) −24.1897 −1.12663 −0.563314 0.826243i \(-0.690474\pi\)
−0.563314 + 0.826243i \(0.690474\pi\)
\(462\) 0 0
\(463\) 19.4081 0.901971 0.450985 0.892531i \(-0.351073\pi\)
0.450985 + 0.892531i \(0.351073\pi\)
\(464\) 0 0
\(465\) 10.2101 0.473483
\(466\) 0 0
\(467\) 3.07818 0.142441 0.0712207 0.997461i \(-0.477311\pi\)
0.0712207 + 0.997461i \(0.477311\pi\)
\(468\) 0 0
\(469\) 21.2955 0.983336
\(470\) 0 0
\(471\) −36.1838 −1.66726
\(472\) 0 0
\(473\) 37.3844 1.71894
\(474\) 0 0
\(475\) 1.56037 0.0715948
\(476\) 0 0
\(477\) −18.1738 −0.832122
\(478\) 0 0
\(479\) 3.25041 0.148515 0.0742575 0.997239i \(-0.476341\pi\)
0.0742575 + 0.997239i \(0.476341\pi\)
\(480\) 0 0
\(481\) 9.94438 0.453425
\(482\) 0 0
\(483\) 7.96189 0.362278
\(484\) 0 0
\(485\) −8.30984 −0.377330
\(486\) 0 0
\(487\) 0.0925240 0.00419266 0.00209633 0.999998i \(-0.499333\pi\)
0.00209633 + 0.999998i \(0.499333\pi\)
\(488\) 0 0
\(489\) 6.20742 0.280709
\(490\) 0 0
\(491\) −32.6935 −1.47544 −0.737718 0.675109i \(-0.764097\pi\)
−0.737718 + 0.675109i \(0.764097\pi\)
\(492\) 0 0
\(493\) 59.6060 2.68452
\(494\) 0 0
\(495\) 24.8847 1.11848
\(496\) 0 0
\(497\) −5.08971 −0.228305
\(498\) 0 0
\(499\) −31.4101 −1.40611 −0.703054 0.711137i \(-0.748181\pi\)
−0.703054 + 0.711137i \(0.748181\pi\)
\(500\) 0 0
\(501\) −49.8626 −2.22770
\(502\) 0 0
\(503\) −10.0071 −0.446194 −0.223097 0.974796i \(-0.571617\pi\)
−0.223097 + 0.974796i \(0.571617\pi\)
\(504\) 0 0
\(505\) −26.6457 −1.18572
\(506\) 0 0
\(507\) 2.91307 0.129374
\(508\) 0 0
\(509\) 32.4379 1.43778 0.718892 0.695122i \(-0.244650\pi\)
0.718892 + 0.695122i \(0.244650\pi\)
\(510\) 0 0
\(511\) 9.55327 0.422612
\(512\) 0 0
\(513\) −2.45925 −0.108579
\(514\) 0 0
\(515\) −10.0397 −0.442404
\(516\) 0 0
\(517\) −11.7781 −0.518000
\(518\) 0 0
\(519\) −24.4247 −1.07213
\(520\) 0 0
\(521\) 15.3046 0.670505 0.335253 0.942128i \(-0.391178\pi\)
0.335253 + 0.942128i \(0.391178\pi\)
\(522\) 0 0
\(523\) −35.4566 −1.55041 −0.775204 0.631711i \(-0.782353\pi\)
−0.775204 + 0.631711i \(0.782353\pi\)
\(524\) 0 0
\(525\) 6.16834 0.269208
\(526\) 0 0
\(527\) −10.7004 −0.466117
\(528\) 0 0
\(529\) −22.0851 −0.960220
\(530\) 0 0
\(531\) 5.90816 0.256392
\(532\) 0 0
\(533\) −10.8832 −0.471402
\(534\) 0 0
\(535\) −23.6304 −1.02163
\(536\) 0 0
\(537\) −45.7543 −1.97444
\(538\) 0 0
\(539\) 23.2142 0.999905
\(540\) 0 0
\(541\) 33.8815 1.45668 0.728339 0.685217i \(-0.240293\pi\)
0.728339 + 0.685217i \(0.240293\pi\)
\(542\) 0 0
\(543\) −9.77345 −0.419419
\(544\) 0 0
\(545\) −13.3210 −0.570610
\(546\) 0 0
\(547\) 19.2887 0.824726 0.412363 0.911020i \(-0.364704\pi\)
0.412363 + 0.911020i \(0.364704\pi\)
\(548\) 0 0
\(549\) 9.53696 0.407028
\(550\) 0 0
\(551\) −21.3080 −0.907753
\(552\) 0 0
\(553\) −4.05919 −0.172614
\(554\) 0 0
\(555\) 14.8099 0.628647
\(556\) 0 0
\(557\) −40.2137 −1.70391 −0.851954 0.523617i \(-0.824582\pi\)
−0.851954 + 0.523617i \(0.824582\pi\)
\(558\) 0 0
\(559\) 33.9891 1.43759
\(560\) 0 0
\(561\) −57.3492 −2.42128
\(562\) 0 0
\(563\) −9.35630 −0.394321 −0.197161 0.980371i \(-0.563172\pi\)
−0.197161 + 0.980371i \(0.563172\pi\)
\(564\) 0 0
\(565\) −21.5174 −0.905243
\(566\) 0 0
\(567\) −36.3585 −1.52691
\(568\) 0 0
\(569\) 26.3177 1.10330 0.551648 0.834077i \(-0.313999\pi\)
0.551648 + 0.834077i \(0.313999\pi\)
\(570\) 0 0
\(571\) −15.5411 −0.650376 −0.325188 0.945649i \(-0.605428\pi\)
−0.325188 + 0.945649i \(0.605428\pi\)
\(572\) 0 0
\(573\) −14.1405 −0.590727
\(574\) 0 0
\(575\) 0.708826 0.0295601
\(576\) 0 0
\(577\) 31.4594 1.30967 0.654836 0.755771i \(-0.272738\pi\)
0.654836 + 0.755771i \(0.272738\pi\)
\(578\) 0 0
\(579\) 56.5409 2.34976
\(580\) 0 0
\(581\) 0.557928 0.0231468
\(582\) 0 0
\(583\) −30.1494 −1.24866
\(584\) 0 0
\(585\) 22.6246 0.935413
\(586\) 0 0
\(587\) −6.19407 −0.255657 −0.127828 0.991796i \(-0.540801\pi\)
−0.127828 + 0.991796i \(0.540801\pi\)
\(588\) 0 0
\(589\) 3.82520 0.157615
\(590\) 0 0
\(591\) −17.1822 −0.706781
\(592\) 0 0
\(593\) −9.89317 −0.406264 −0.203132 0.979151i \(-0.565112\pi\)
−0.203132 + 0.979151i \(0.565112\pi\)
\(594\) 0 0
\(595\) −50.0822 −2.05317
\(596\) 0 0
\(597\) 52.9078 2.16537
\(598\) 0 0
\(599\) 26.4663 1.08139 0.540693 0.841220i \(-0.318162\pi\)
0.540693 + 0.841220i \(0.318162\pi\)
\(600\) 0 0
\(601\) 9.73489 0.397095 0.198547 0.980091i \(-0.436378\pi\)
0.198547 + 0.980091i \(0.436378\pi\)
\(602\) 0 0
\(603\) 15.0152 0.611467
\(604\) 0 0
\(605\) 14.9259 0.606823
\(606\) 0 0
\(607\) 48.8520 1.98284 0.991421 0.130708i \(-0.0417250\pi\)
0.991421 + 0.130708i \(0.0417250\pi\)
\(608\) 0 0
\(609\) −84.2332 −3.41330
\(610\) 0 0
\(611\) −10.7084 −0.433216
\(612\) 0 0
\(613\) −6.18998 −0.250011 −0.125005 0.992156i \(-0.539895\pi\)
−0.125005 + 0.992156i \(0.539895\pi\)
\(614\) 0 0
\(615\) −16.2080 −0.653571
\(616\) 0 0
\(617\) −13.9740 −0.562571 −0.281285 0.959624i \(-0.590761\pi\)
−0.281285 + 0.959624i \(0.590761\pi\)
\(618\) 0 0
\(619\) 6.53776 0.262775 0.131387 0.991331i \(-0.458057\pi\)
0.131387 + 0.991331i \(0.458057\pi\)
\(620\) 0 0
\(621\) −1.11716 −0.0448299
\(622\) 0 0
\(623\) 14.1525 0.567007
\(624\) 0 0
\(625\) −28.1561 −1.12624
\(626\) 0 0
\(627\) 20.5013 0.818742
\(628\) 0 0
\(629\) −15.5211 −0.618867
\(630\) 0 0
\(631\) −15.2977 −0.608993 −0.304496 0.952514i \(-0.598488\pi\)
−0.304496 + 0.952514i \(0.598488\pi\)
\(632\) 0 0
\(633\) −60.4455 −2.40249
\(634\) 0 0
\(635\) −1.29729 −0.0514814
\(636\) 0 0
\(637\) 21.1058 0.836243
\(638\) 0 0
\(639\) −3.58869 −0.141967
\(640\) 0 0
\(641\) −8.87971 −0.350728 −0.175364 0.984504i \(-0.556110\pi\)
−0.175364 + 0.984504i \(0.556110\pi\)
\(642\) 0 0
\(643\) −41.7911 −1.64808 −0.824041 0.566531i \(-0.808285\pi\)
−0.824041 + 0.566531i \(0.808285\pi\)
\(644\) 0 0
\(645\) 50.6192 1.99313
\(646\) 0 0
\(647\) −3.71740 −0.146146 −0.0730731 0.997327i \(-0.523281\pi\)
−0.0730731 + 0.997327i \(0.523281\pi\)
\(648\) 0 0
\(649\) 9.80133 0.384736
\(650\) 0 0
\(651\) 15.1215 0.592657
\(652\) 0 0
\(653\) 16.4444 0.643520 0.321760 0.946821i \(-0.395726\pi\)
0.321760 + 0.946821i \(0.395726\pi\)
\(654\) 0 0
\(655\) −0.382405 −0.0149418
\(656\) 0 0
\(657\) 6.73589 0.262792
\(658\) 0 0
\(659\) −45.2536 −1.76283 −0.881415 0.472343i \(-0.843408\pi\)
−0.881415 + 0.472343i \(0.843408\pi\)
\(660\) 0 0
\(661\) 0.547230 0.0212848 0.0106424 0.999943i \(-0.496612\pi\)
0.0106424 + 0.999943i \(0.496612\pi\)
\(662\) 0 0
\(663\) −52.1407 −2.02498
\(664\) 0 0
\(665\) 17.9035 0.694266
\(666\) 0 0
\(667\) −9.67954 −0.374793
\(668\) 0 0
\(669\) 52.4177 2.02658
\(670\) 0 0
\(671\) 15.8213 0.610776
\(672\) 0 0
\(673\) 35.2224 1.35772 0.678861 0.734266i \(-0.262474\pi\)
0.678861 + 0.734266i \(0.262474\pi\)
\(674\) 0 0
\(675\) −0.865497 −0.0333130
\(676\) 0 0
\(677\) 14.6667 0.563687 0.281844 0.959460i \(-0.409054\pi\)
0.281844 + 0.959460i \(0.409054\pi\)
\(678\) 0 0
\(679\) −12.3071 −0.472303
\(680\) 0 0
\(681\) 0.0926403 0.00354998
\(682\) 0 0
\(683\) 6.09267 0.233129 0.116565 0.993183i \(-0.462812\pi\)
0.116565 + 0.993183i \(0.462812\pi\)
\(684\) 0 0
\(685\) −8.51370 −0.325292
\(686\) 0 0
\(687\) 12.4325 0.474331
\(688\) 0 0
\(689\) −27.4112 −1.04428
\(690\) 0 0
\(691\) −6.37316 −0.242446 −0.121223 0.992625i \(-0.538682\pi\)
−0.121223 + 0.992625i \(0.538682\pi\)
\(692\) 0 0
\(693\) 36.8549 1.40000
\(694\) 0 0
\(695\) 16.2077 0.614794
\(696\) 0 0
\(697\) 16.9864 0.643404
\(698\) 0 0
\(699\) 43.6859 1.65235
\(700\) 0 0
\(701\) 18.4216 0.695774 0.347887 0.937536i \(-0.386899\pi\)
0.347887 + 0.937536i \(0.386899\pi\)
\(702\) 0 0
\(703\) 5.54851 0.209266
\(704\) 0 0
\(705\) −15.9478 −0.600628
\(706\) 0 0
\(707\) −39.4630 −1.48416
\(708\) 0 0
\(709\) 24.0528 0.903320 0.451660 0.892190i \(-0.350832\pi\)
0.451660 + 0.892190i \(0.350832\pi\)
\(710\) 0 0
\(711\) −2.86208 −0.107337
\(712\) 0 0
\(713\) 1.73766 0.0650760
\(714\) 0 0
\(715\) 37.5331 1.40366
\(716\) 0 0
\(717\) 28.8829 1.07865
\(718\) 0 0
\(719\) −38.5745 −1.43859 −0.719293 0.694707i \(-0.755534\pi\)
−0.719293 + 0.694707i \(0.755534\pi\)
\(720\) 0 0
\(721\) −14.8691 −0.553756
\(722\) 0 0
\(723\) −42.2576 −1.57158
\(724\) 0 0
\(725\) −7.49906 −0.278508
\(726\) 0 0
\(727\) −4.67278 −0.173304 −0.0866519 0.996239i \(-0.527617\pi\)
−0.0866519 + 0.996239i \(0.527617\pi\)
\(728\) 0 0
\(729\) −17.4172 −0.645081
\(730\) 0 0
\(731\) −53.0499 −1.96212
\(732\) 0 0
\(733\) 16.3536 0.604033 0.302016 0.953303i \(-0.402340\pi\)
0.302016 + 0.953303i \(0.402340\pi\)
\(734\) 0 0
\(735\) 31.4324 1.15940
\(736\) 0 0
\(737\) 24.9095 0.917552
\(738\) 0 0
\(739\) −50.0156 −1.83986 −0.919928 0.392088i \(-0.871753\pi\)
−0.919928 + 0.392088i \(0.871753\pi\)
\(740\) 0 0
\(741\) 18.6393 0.684733
\(742\) 0 0
\(743\) −22.9997 −0.843778 −0.421889 0.906648i \(-0.638633\pi\)
−0.421889 + 0.906648i \(0.638633\pi\)
\(744\) 0 0
\(745\) 30.2038 1.10658
\(746\) 0 0
\(747\) 0.393388 0.0143933
\(748\) 0 0
\(749\) −34.9973 −1.27877
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 37.5585 1.36871
\(754\) 0 0
\(755\) 21.2823 0.774543
\(756\) 0 0
\(757\) 19.0823 0.693557 0.346779 0.937947i \(-0.387275\pi\)
0.346779 + 0.937947i \(0.387275\pi\)
\(758\) 0 0
\(759\) 9.31305 0.338042
\(760\) 0 0
\(761\) 3.35147 0.121491 0.0607454 0.998153i \(-0.480652\pi\)
0.0607454 + 0.998153i \(0.480652\pi\)
\(762\) 0 0
\(763\) −19.7288 −0.714231
\(764\) 0 0
\(765\) −35.3123 −1.27672
\(766\) 0 0
\(767\) 8.91116 0.321763
\(768\) 0 0
\(769\) 28.6046 1.03151 0.515753 0.856737i \(-0.327512\pi\)
0.515753 + 0.856737i \(0.327512\pi\)
\(770\) 0 0
\(771\) 24.8888 0.896349
\(772\) 0 0
\(773\) 38.6273 1.38933 0.694664 0.719335i \(-0.255553\pi\)
0.694664 + 0.719335i \(0.255553\pi\)
\(774\) 0 0
\(775\) 1.34622 0.0483578
\(776\) 0 0
\(777\) 21.9339 0.786875
\(778\) 0 0
\(779\) −6.07231 −0.217563
\(780\) 0 0
\(781\) −5.95346 −0.213032
\(782\) 0 0
\(783\) 11.8190 0.422377
\(784\) 0 0
\(785\) −36.9612 −1.31920
\(786\) 0 0
\(787\) −19.0320 −0.678418 −0.339209 0.940711i \(-0.610159\pi\)
−0.339209 + 0.940711i \(0.610159\pi\)
\(788\) 0 0
\(789\) 20.3008 0.722727
\(790\) 0 0
\(791\) −31.8679 −1.13309
\(792\) 0 0
\(793\) 14.3844 0.510806
\(794\) 0 0
\(795\) −40.8229 −1.44784
\(796\) 0 0
\(797\) 21.7143 0.769159 0.384579 0.923092i \(-0.374346\pi\)
0.384579 + 0.923092i \(0.374346\pi\)
\(798\) 0 0
\(799\) 16.7136 0.591284
\(800\) 0 0
\(801\) 9.97874 0.352581
\(802\) 0 0
\(803\) 11.1745 0.394339
\(804\) 0 0
\(805\) 8.13295 0.286649
\(806\) 0 0
\(807\) 52.9545 1.86409
\(808\) 0 0
\(809\) −5.88423 −0.206878 −0.103439 0.994636i \(-0.532985\pi\)
−0.103439 + 0.994636i \(0.532985\pi\)
\(810\) 0 0
\(811\) −35.0152 −1.22955 −0.614775 0.788703i \(-0.710753\pi\)
−0.614775 + 0.788703i \(0.710753\pi\)
\(812\) 0 0
\(813\) 16.2756 0.570811
\(814\) 0 0
\(815\) 6.34079 0.222108
\(816\) 0 0
\(817\) 18.9644 0.663479
\(818\) 0 0
\(819\) 33.5077 1.17085
\(820\) 0 0
\(821\) 2.32803 0.0812487 0.0406243 0.999174i \(-0.487065\pi\)
0.0406243 + 0.999174i \(0.487065\pi\)
\(822\) 0 0
\(823\) 29.0389 1.01223 0.506116 0.862465i \(-0.331081\pi\)
0.506116 + 0.862465i \(0.331081\pi\)
\(824\) 0 0
\(825\) 7.21513 0.251199
\(826\) 0 0
\(827\) 12.7465 0.443241 0.221620 0.975133i \(-0.428865\pi\)
0.221620 + 0.975133i \(0.428865\pi\)
\(828\) 0 0
\(829\) 47.3643 1.64503 0.822515 0.568744i \(-0.192570\pi\)
0.822515 + 0.568744i \(0.192570\pi\)
\(830\) 0 0
\(831\) −26.9507 −0.934911
\(832\) 0 0
\(833\) −32.9418 −1.14137
\(834\) 0 0
\(835\) −50.9339 −1.76264
\(836\) 0 0
\(837\) −2.12174 −0.0733380
\(838\) 0 0
\(839\) 23.4951 0.811142 0.405571 0.914064i \(-0.367073\pi\)
0.405571 + 0.914064i \(0.367073\pi\)
\(840\) 0 0
\(841\) 73.4052 2.53121
\(842\) 0 0
\(843\) 18.9279 0.651912
\(844\) 0 0
\(845\) 2.97566 0.102366
\(846\) 0 0
\(847\) 22.1056 0.759558
\(848\) 0 0
\(849\) −37.3297 −1.28115
\(850\) 0 0
\(851\) 2.52051 0.0864018
\(852\) 0 0
\(853\) −11.2204 −0.384179 −0.192090 0.981377i \(-0.561526\pi\)
−0.192090 + 0.981377i \(0.561526\pi\)
\(854\) 0 0
\(855\) 12.6235 0.431715
\(856\) 0 0
\(857\) −28.5016 −0.973595 −0.486797 0.873515i \(-0.661835\pi\)
−0.486797 + 0.873515i \(0.661835\pi\)
\(858\) 0 0
\(859\) −18.5032 −0.631321 −0.315660 0.948872i \(-0.602226\pi\)
−0.315660 + 0.948872i \(0.602226\pi\)
\(860\) 0 0
\(861\) −24.0046 −0.818073
\(862\) 0 0
\(863\) 16.9424 0.576727 0.288364 0.957521i \(-0.406889\pi\)
0.288364 + 0.957521i \(0.406889\pi\)
\(864\) 0 0
\(865\) −24.9495 −0.848309
\(866\) 0 0
\(867\) 41.5046 1.40957
\(868\) 0 0
\(869\) −4.74805 −0.161067
\(870\) 0 0
\(871\) 22.6472 0.767370
\(872\) 0 0
\(873\) −8.67759 −0.293692
\(874\) 0 0
\(875\) −36.2124 −1.22420
\(876\) 0 0
\(877\) −43.4173 −1.46610 −0.733050 0.680175i \(-0.761904\pi\)
−0.733050 + 0.680175i \(0.761904\pi\)
\(878\) 0 0
\(879\) 56.7287 1.91341
\(880\) 0 0
\(881\) −0.890022 −0.0299856 −0.0149928 0.999888i \(-0.504773\pi\)
−0.0149928 + 0.999888i \(0.504773\pi\)
\(882\) 0 0
\(883\) −14.5296 −0.488959 −0.244479 0.969655i \(-0.578617\pi\)
−0.244479 + 0.969655i \(0.578617\pi\)
\(884\) 0 0
\(885\) 13.2712 0.446106
\(886\) 0 0
\(887\) 1.66120 0.0557778 0.0278889 0.999611i \(-0.491122\pi\)
0.0278889 + 0.999611i \(0.491122\pi\)
\(888\) 0 0
\(889\) −1.92132 −0.0644391
\(890\) 0 0
\(891\) −42.5287 −1.42476
\(892\) 0 0
\(893\) −5.97480 −0.199939
\(894\) 0 0
\(895\) −46.7373 −1.56226
\(896\) 0 0
\(897\) 8.46723 0.282713
\(898\) 0 0
\(899\) −18.3837 −0.613130
\(900\) 0 0
\(901\) 42.7832 1.42532
\(902\) 0 0
\(903\) 74.9684 2.49479
\(904\) 0 0
\(905\) −9.98344 −0.331861
\(906\) 0 0
\(907\) −34.0121 −1.12935 −0.564677 0.825312i \(-0.690999\pi\)
−0.564677 + 0.825312i \(0.690999\pi\)
\(908\) 0 0
\(909\) −27.8249 −0.922892
\(910\) 0 0
\(911\) 54.5811 1.80835 0.904176 0.427160i \(-0.140486\pi\)
0.904176 + 0.427160i \(0.140486\pi\)
\(912\) 0 0
\(913\) 0.652611 0.0215983
\(914\) 0 0
\(915\) 21.4224 0.708201
\(916\) 0 0
\(917\) −0.566353 −0.0187026
\(918\) 0 0
\(919\) −16.0352 −0.528954 −0.264477 0.964392i \(-0.585199\pi\)
−0.264477 + 0.964392i \(0.585199\pi\)
\(920\) 0 0
\(921\) 55.0119 1.81270
\(922\) 0 0
\(923\) −5.41276 −0.178163
\(924\) 0 0
\(925\) 1.95272 0.0642050
\(926\) 0 0
\(927\) −10.4840 −0.344341
\(928\) 0 0
\(929\) 14.2913 0.468881 0.234440 0.972130i \(-0.424674\pi\)
0.234440 + 0.972130i \(0.424674\pi\)
\(930\) 0 0
\(931\) 11.7761 0.385945
\(932\) 0 0
\(933\) −63.5527 −2.08062
\(934\) 0 0
\(935\) −58.5813 −1.91581
\(936\) 0 0
\(937\) −18.3195 −0.598473 −0.299237 0.954179i \(-0.596732\pi\)
−0.299237 + 0.954179i \(0.596732\pi\)
\(938\) 0 0
\(939\) −75.6535 −2.46886
\(940\) 0 0
\(941\) 17.7323 0.578057 0.289028 0.957321i \(-0.406668\pi\)
0.289028 + 0.957321i \(0.406668\pi\)
\(942\) 0 0
\(943\) −2.75845 −0.0898275
\(944\) 0 0
\(945\) −9.93057 −0.323042
\(946\) 0 0
\(947\) −15.3527 −0.498895 −0.249447 0.968388i \(-0.580249\pi\)
−0.249447 + 0.968388i \(0.580249\pi\)
\(948\) 0 0
\(949\) 10.1596 0.329795
\(950\) 0 0
\(951\) 34.9999 1.13495
\(952\) 0 0
\(953\) 36.1543 1.17115 0.585577 0.810617i \(-0.300868\pi\)
0.585577 + 0.810617i \(0.300868\pi\)
\(954\) 0 0
\(955\) −14.4443 −0.467406
\(956\) 0 0
\(957\) −98.5279 −3.18496
\(958\) 0 0
\(959\) −12.6090 −0.407167
\(960\) 0 0
\(961\) −27.6998 −0.893541
\(962\) 0 0
\(963\) −24.6761 −0.795178
\(964\) 0 0
\(965\) 57.7557 1.85922
\(966\) 0 0
\(967\) −20.5903 −0.662138 −0.331069 0.943606i \(-0.607409\pi\)
−0.331069 + 0.943606i \(0.607409\pi\)
\(968\) 0 0
\(969\) −29.0921 −0.934573
\(970\) 0 0
\(971\) 34.8644 1.11885 0.559427 0.828880i \(-0.311021\pi\)
0.559427 + 0.828880i \(0.311021\pi\)
\(972\) 0 0
\(973\) 24.0041 0.769536
\(974\) 0 0
\(975\) 6.55984 0.210083
\(976\) 0 0
\(977\) −12.6987 −0.406268 −0.203134 0.979151i \(-0.565113\pi\)
−0.203134 + 0.979151i \(0.565113\pi\)
\(978\) 0 0
\(979\) 16.5542 0.529075
\(980\) 0 0
\(981\) −13.9105 −0.444129
\(982\) 0 0
\(983\) −17.4110 −0.555324 −0.277662 0.960679i \(-0.589560\pi\)
−0.277662 + 0.960679i \(0.589560\pi\)
\(984\) 0 0
\(985\) −17.5514 −0.559233
\(986\) 0 0
\(987\) −23.6191 −0.751804
\(988\) 0 0
\(989\) 8.61489 0.273938
\(990\) 0 0
\(991\) −45.1604 −1.43457 −0.717284 0.696781i \(-0.754615\pi\)
−0.717284 + 0.696781i \(0.754615\pi\)
\(992\) 0 0
\(993\) −23.7120 −0.752479
\(994\) 0 0
\(995\) 54.0446 1.71333
\(996\) 0 0
\(997\) −37.1501 −1.17655 −0.588277 0.808659i \(-0.700194\pi\)
−0.588277 + 0.808659i \(0.700194\pi\)
\(998\) 0 0
\(999\) −3.07761 −0.0973714
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 \(a_p\))