Properties

Label 6008.2.a.e.1.23
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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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 1.23
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.217342 q^{3} +1.76324 q^{5} +1.63306 q^{7} -2.95276 q^{9} +O(q^{10})\) \(q-0.217342 q^{3} +1.76324 q^{5} +1.63306 q^{7} -2.95276 q^{9} -4.73515 q^{11} +4.29715 q^{13} -0.383227 q^{15} -6.17157 q^{17} +3.23590 q^{19} -0.354933 q^{21} -5.20023 q^{23} -1.89097 q^{25} +1.29379 q^{27} -5.37319 q^{29} +3.65068 q^{31} +1.02915 q^{33} +2.87948 q^{35} +10.2663 q^{37} -0.933952 q^{39} +12.3293 q^{41} -4.50192 q^{43} -5.20644 q^{45} +11.0393 q^{47} -4.33312 q^{49} +1.34134 q^{51} -2.84055 q^{53} -8.34922 q^{55} -0.703298 q^{57} -0.223774 q^{59} +11.2299 q^{61} -4.82204 q^{63} +7.57691 q^{65} +7.71113 q^{67} +1.13023 q^{69} -5.66749 q^{71} +6.65373 q^{73} +0.410989 q^{75} -7.73278 q^{77} +8.73124 q^{79} +8.57709 q^{81} -1.13562 q^{83} -10.8820 q^{85} +1.16782 q^{87} +17.7119 q^{89} +7.01749 q^{91} -0.793447 q^{93} +5.70568 q^{95} +14.4828 q^{97} +13.9818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.217342 −0.125483 −0.0627413 0.998030i \(-0.519984\pi\)
−0.0627413 + 0.998030i \(0.519984\pi\)
\(4\) 0 0
\(5\) 1.76324 0.788546 0.394273 0.918993i \(-0.370996\pi\)
0.394273 + 0.918993i \(0.370996\pi\)
\(6\) 0 0
\(7\) 1.63306 0.617238 0.308619 0.951186i \(-0.400133\pi\)
0.308619 + 0.951186i \(0.400133\pi\)
\(8\) 0 0
\(9\) −2.95276 −0.984254
\(10\) 0 0
\(11\) −4.73515 −1.42770 −0.713851 0.700298i \(-0.753051\pi\)
−0.713851 + 0.700298i \(0.753051\pi\)
\(12\) 0 0
\(13\) 4.29715 1.19181 0.595907 0.803053i \(-0.296793\pi\)
0.595907 + 0.803053i \(0.296793\pi\)
\(14\) 0 0
\(15\) −0.383227 −0.0989489
\(16\) 0 0
\(17\) −6.17157 −1.49683 −0.748413 0.663233i \(-0.769184\pi\)
−0.748413 + 0.663233i \(0.769184\pi\)
\(18\) 0 0
\(19\) 3.23590 0.742366 0.371183 0.928560i \(-0.378952\pi\)
0.371183 + 0.928560i \(0.378952\pi\)
\(20\) 0 0
\(21\) −0.354933 −0.0774527
\(22\) 0 0
\(23\) −5.20023 −1.08432 −0.542162 0.840274i \(-0.682394\pi\)
−0.542162 + 0.840274i \(0.682394\pi\)
\(24\) 0 0
\(25\) −1.89097 −0.378195
\(26\) 0 0
\(27\) 1.29379 0.248989
\(28\) 0 0
\(29\) −5.37319 −0.997776 −0.498888 0.866666i \(-0.666258\pi\)
−0.498888 + 0.866666i \(0.666258\pi\)
\(30\) 0 0
\(31\) 3.65068 0.655681 0.327840 0.944733i \(-0.393679\pi\)
0.327840 + 0.944733i \(0.393679\pi\)
\(32\) 0 0
\(33\) 1.02915 0.179152
\(34\) 0 0
\(35\) 2.87948 0.486721
\(36\) 0 0
\(37\) 10.2663 1.68777 0.843884 0.536525i \(-0.180263\pi\)
0.843884 + 0.536525i \(0.180263\pi\)
\(38\) 0 0
\(39\) −0.933952 −0.149552
\(40\) 0 0
\(41\) 12.3293 1.92552 0.962760 0.270359i \(-0.0871423\pi\)
0.962760 + 0.270359i \(0.0871423\pi\)
\(42\) 0 0
\(43\) −4.50192 −0.686536 −0.343268 0.939238i \(-0.611534\pi\)
−0.343268 + 0.939238i \(0.611534\pi\)
\(44\) 0 0
\(45\) −5.20644 −0.776130
\(46\) 0 0
\(47\) 11.0393 1.61024 0.805122 0.593109i \(-0.202100\pi\)
0.805122 + 0.593109i \(0.202100\pi\)
\(48\) 0 0
\(49\) −4.33312 −0.619017
\(50\) 0 0
\(51\) 1.34134 0.187826
\(52\) 0 0
\(53\) −2.84055 −0.390179 −0.195090 0.980785i \(-0.562500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(54\) 0 0
\(55\) −8.34922 −1.12581
\(56\) 0 0
\(57\) −0.703298 −0.0931541
\(58\) 0 0
\(59\) −0.223774 −0.0291329 −0.0145665 0.999894i \(-0.504637\pi\)
−0.0145665 + 0.999894i \(0.504637\pi\)
\(60\) 0 0
\(61\) 11.2299 1.43784 0.718921 0.695092i \(-0.244636\pi\)
0.718921 + 0.695092i \(0.244636\pi\)
\(62\) 0 0
\(63\) −4.82204 −0.607519
\(64\) 0 0
\(65\) 7.57691 0.939800
\(66\) 0 0
\(67\) 7.71113 0.942064 0.471032 0.882116i \(-0.343882\pi\)
0.471032 + 0.882116i \(0.343882\pi\)
\(68\) 0 0
\(69\) 1.13023 0.136064
\(70\) 0 0
\(71\) −5.66749 −0.672607 −0.336304 0.941754i \(-0.609177\pi\)
−0.336304 + 0.941754i \(0.609177\pi\)
\(72\) 0 0
\(73\) 6.65373 0.778760 0.389380 0.921077i \(-0.372689\pi\)
0.389380 + 0.921077i \(0.372689\pi\)
\(74\) 0 0
\(75\) 0.410989 0.0474569
\(76\) 0 0
\(77\) −7.73278 −0.881232
\(78\) 0 0
\(79\) 8.73124 0.982341 0.491171 0.871063i \(-0.336569\pi\)
0.491171 + 0.871063i \(0.336569\pi\)
\(80\) 0 0
\(81\) 8.57709 0.953010
\(82\) 0 0
\(83\) −1.13562 −0.124650 −0.0623252 0.998056i \(-0.519852\pi\)
−0.0623252 + 0.998056i \(0.519852\pi\)
\(84\) 0 0
\(85\) −10.8820 −1.18032
\(86\) 0 0
\(87\) 1.16782 0.125204
\(88\) 0 0
\(89\) 17.7119 1.87745 0.938727 0.344660i \(-0.112006\pi\)
0.938727 + 0.344660i \(0.112006\pi\)
\(90\) 0 0
\(91\) 7.01749 0.735633
\(92\) 0 0
\(93\) −0.793447 −0.0822766
\(94\) 0 0
\(95\) 5.70568 0.585390
\(96\) 0 0
\(97\) 14.4828 1.47051 0.735254 0.677791i \(-0.237063\pi\)
0.735254 + 0.677791i \(0.237063\pi\)
\(98\) 0 0
\(99\) 13.9818 1.40522
\(100\) 0 0
\(101\) −6.51307 −0.648075 −0.324037 0.946044i \(-0.605040\pi\)
−0.324037 + 0.946044i \(0.605040\pi\)
\(102\) 0 0
\(103\) 13.7546 1.35529 0.677643 0.735391i \(-0.263002\pi\)
0.677643 + 0.735391i \(0.263002\pi\)
\(104\) 0 0
\(105\) −0.625833 −0.0610750
\(106\) 0 0
\(107\) −5.72856 −0.553801 −0.276901 0.960899i \(-0.589307\pi\)
−0.276901 + 0.960899i \(0.589307\pi\)
\(108\) 0 0
\(109\) 16.8740 1.61624 0.808118 0.589021i \(-0.200487\pi\)
0.808118 + 0.589021i \(0.200487\pi\)
\(110\) 0 0
\(111\) −2.23130 −0.211786
\(112\) 0 0
\(113\) 14.9079 1.40241 0.701207 0.712957i \(-0.252645\pi\)
0.701207 + 0.712957i \(0.252645\pi\)
\(114\) 0 0
\(115\) −9.16928 −0.855040
\(116\) 0 0
\(117\) −12.6885 −1.17305
\(118\) 0 0
\(119\) −10.0785 −0.923899
\(120\) 0 0
\(121\) 11.4217 1.03833
\(122\) 0 0
\(123\) −2.67969 −0.241619
\(124\) 0 0
\(125\) −12.1505 −1.08677
\(126\) 0 0
\(127\) −10.6094 −0.941435 −0.470718 0.882284i \(-0.656005\pi\)
−0.470718 + 0.882284i \(0.656005\pi\)
\(128\) 0 0
\(129\) 0.978457 0.0861483
\(130\) 0 0
\(131\) −22.3149 −1.94966 −0.974831 0.222943i \(-0.928434\pi\)
−0.974831 + 0.222943i \(0.928434\pi\)
\(132\) 0 0
\(133\) 5.28442 0.458217
\(134\) 0 0
\(135\) 2.28126 0.196340
\(136\) 0 0
\(137\) 10.0300 0.856919 0.428460 0.903561i \(-0.359056\pi\)
0.428460 + 0.903561i \(0.359056\pi\)
\(138\) 0 0
\(139\) 2.27084 0.192611 0.0963053 0.995352i \(-0.469298\pi\)
0.0963053 + 0.995352i \(0.469298\pi\)
\(140\) 0 0
\(141\) −2.39930 −0.202058
\(142\) 0 0
\(143\) −20.3476 −1.70156
\(144\) 0 0
\(145\) −9.47424 −0.786793
\(146\) 0 0
\(147\) 0.941770 0.0776759
\(148\) 0 0
\(149\) −7.92170 −0.648971 −0.324485 0.945891i \(-0.605191\pi\)
−0.324485 + 0.945891i \(0.605191\pi\)
\(150\) 0 0
\(151\) −5.29063 −0.430546 −0.215273 0.976554i \(-0.569064\pi\)
−0.215273 + 0.976554i \(0.569064\pi\)
\(152\) 0 0
\(153\) 18.2232 1.47326
\(154\) 0 0
\(155\) 6.43703 0.517035
\(156\) 0 0
\(157\) −7.69056 −0.613773 −0.306887 0.951746i \(-0.599287\pi\)
−0.306887 + 0.951746i \(0.599287\pi\)
\(158\) 0 0
\(159\) 0.617371 0.0489607
\(160\) 0 0
\(161\) −8.49229 −0.669286
\(162\) 0 0
\(163\) 14.2163 1.11350 0.556752 0.830679i \(-0.312047\pi\)
0.556752 + 0.830679i \(0.312047\pi\)
\(164\) 0 0
\(165\) 1.81464 0.141269
\(166\) 0 0
\(167\) 25.5366 1.97608 0.988040 0.154199i \(-0.0492798\pi\)
0.988040 + 0.154199i \(0.0492798\pi\)
\(168\) 0 0
\(169\) 5.46547 0.420421
\(170\) 0 0
\(171\) −9.55484 −0.730677
\(172\) 0 0
\(173\) −7.30483 −0.555376 −0.277688 0.960671i \(-0.589568\pi\)
−0.277688 + 0.960671i \(0.589568\pi\)
\(174\) 0 0
\(175\) −3.08807 −0.233436
\(176\) 0 0
\(177\) 0.0486356 0.00365567
\(178\) 0 0
\(179\) −6.19399 −0.462960 −0.231480 0.972840i \(-0.574357\pi\)
−0.231480 + 0.972840i \(0.574357\pi\)
\(180\) 0 0
\(181\) 8.51132 0.632641 0.316321 0.948652i \(-0.397552\pi\)
0.316321 + 0.948652i \(0.397552\pi\)
\(182\) 0 0
\(183\) −2.44073 −0.180424
\(184\) 0 0
\(185\) 18.1020 1.33088
\(186\) 0 0
\(187\) 29.2233 2.13702
\(188\) 0 0
\(189\) 2.11283 0.153686
\(190\) 0 0
\(191\) −10.9988 −0.795842 −0.397921 0.917420i \(-0.630268\pi\)
−0.397921 + 0.917420i \(0.630268\pi\)
\(192\) 0 0
\(193\) −12.9670 −0.933382 −0.466691 0.884421i \(-0.654554\pi\)
−0.466691 + 0.884421i \(0.654554\pi\)
\(194\) 0 0
\(195\) −1.64678 −0.117929
\(196\) 0 0
\(197\) 7.60271 0.541671 0.270835 0.962626i \(-0.412700\pi\)
0.270835 + 0.962626i \(0.412700\pi\)
\(198\) 0 0
\(199\) −7.96777 −0.564820 −0.282410 0.959294i \(-0.591134\pi\)
−0.282410 + 0.959294i \(0.591134\pi\)
\(200\) 0 0
\(201\) −1.67595 −0.118213
\(202\) 0 0
\(203\) −8.77474 −0.615866
\(204\) 0 0
\(205\) 21.7396 1.51836
\(206\) 0 0
\(207\) 15.3551 1.06725
\(208\) 0 0
\(209\) −15.3225 −1.05988
\(210\) 0 0
\(211\) 12.7030 0.874513 0.437256 0.899337i \(-0.355950\pi\)
0.437256 + 0.899337i \(0.355950\pi\)
\(212\) 0 0
\(213\) 1.23178 0.0844005
\(214\) 0 0
\(215\) −7.93797 −0.541365
\(216\) 0 0
\(217\) 5.96177 0.404711
\(218\) 0 0
\(219\) −1.44614 −0.0977209
\(220\) 0 0
\(221\) −26.5202 −1.78394
\(222\) 0 0
\(223\) −11.7706 −0.788219 −0.394109 0.919064i \(-0.628947\pi\)
−0.394109 + 0.919064i \(0.628947\pi\)
\(224\) 0 0
\(225\) 5.58360 0.372240
\(226\) 0 0
\(227\) −4.58907 −0.304587 −0.152294 0.988335i \(-0.548666\pi\)
−0.152294 + 0.988335i \(0.548666\pi\)
\(228\) 0 0
\(229\) 6.76699 0.447175 0.223588 0.974684i \(-0.428223\pi\)
0.223588 + 0.974684i \(0.428223\pi\)
\(230\) 0 0
\(231\) 1.68066 0.110579
\(232\) 0 0
\(233\) 6.23664 0.408576 0.204288 0.978911i \(-0.434512\pi\)
0.204288 + 0.978911i \(0.434512\pi\)
\(234\) 0 0
\(235\) 19.4649 1.26975
\(236\) 0 0
\(237\) −1.89767 −0.123267
\(238\) 0 0
\(239\) −0.462154 −0.0298943 −0.0149471 0.999888i \(-0.504758\pi\)
−0.0149471 + 0.999888i \(0.504758\pi\)
\(240\) 0 0
\(241\) −14.7355 −0.949194 −0.474597 0.880203i \(-0.657406\pi\)
−0.474597 + 0.880203i \(0.657406\pi\)
\(242\) 0 0
\(243\) −5.74553 −0.368576
\(244\) 0 0
\(245\) −7.64034 −0.488123
\(246\) 0 0
\(247\) 13.9051 0.884763
\(248\) 0 0
\(249\) 0.246818 0.0156415
\(250\) 0 0
\(251\) 29.5708 1.86649 0.933247 0.359235i \(-0.116962\pi\)
0.933247 + 0.359235i \(0.116962\pi\)
\(252\) 0 0
\(253\) 24.6239 1.54809
\(254\) 0 0
\(255\) 2.36512 0.148109
\(256\) 0 0
\(257\) −20.5357 −1.28098 −0.640490 0.767967i \(-0.721269\pi\)
−0.640490 + 0.767967i \(0.721269\pi\)
\(258\) 0 0
\(259\) 16.7655 1.04176
\(260\) 0 0
\(261\) 15.8658 0.982065
\(262\) 0 0
\(263\) −20.3586 −1.25537 −0.627683 0.778469i \(-0.715997\pi\)
−0.627683 + 0.778469i \(0.715997\pi\)
\(264\) 0 0
\(265\) −5.00858 −0.307674
\(266\) 0 0
\(267\) −3.84954 −0.235588
\(268\) 0 0
\(269\) 14.5190 0.885237 0.442619 0.896710i \(-0.354050\pi\)
0.442619 + 0.896710i \(0.354050\pi\)
\(270\) 0 0
\(271\) −14.2851 −0.867759 −0.433880 0.900971i \(-0.642856\pi\)
−0.433880 + 0.900971i \(0.642856\pi\)
\(272\) 0 0
\(273\) −1.52520 −0.0923092
\(274\) 0 0
\(275\) 8.95405 0.539949
\(276\) 0 0
\(277\) 17.8056 1.06983 0.534916 0.844905i \(-0.320343\pi\)
0.534916 + 0.844905i \(0.320343\pi\)
\(278\) 0 0
\(279\) −10.7796 −0.645357
\(280\) 0 0
\(281\) 18.7804 1.12035 0.560173 0.828376i \(-0.310735\pi\)
0.560173 + 0.828376i \(0.310735\pi\)
\(282\) 0 0
\(283\) −27.5587 −1.63819 −0.819097 0.573655i \(-0.805525\pi\)
−0.819097 + 0.573655i \(0.805525\pi\)
\(284\) 0 0
\(285\) −1.24009 −0.0734563
\(286\) 0 0
\(287\) 20.1345 1.18850
\(288\) 0 0
\(289\) 21.0883 1.24049
\(290\) 0 0
\(291\) −3.14773 −0.184523
\(292\) 0 0
\(293\) −7.80088 −0.455733 −0.227866 0.973692i \(-0.573175\pi\)
−0.227866 + 0.973692i \(0.573175\pi\)
\(294\) 0 0
\(295\) −0.394568 −0.0229726
\(296\) 0 0
\(297\) −6.12628 −0.355483
\(298\) 0 0
\(299\) −22.3462 −1.29231
\(300\) 0 0
\(301\) −7.35190 −0.423756
\(302\) 0 0
\(303\) 1.41557 0.0813221
\(304\) 0 0
\(305\) 19.8011 1.13381
\(306\) 0 0
\(307\) −6.75243 −0.385382 −0.192691 0.981260i \(-0.561721\pi\)
−0.192691 + 0.981260i \(0.561721\pi\)
\(308\) 0 0
\(309\) −2.98947 −0.170065
\(310\) 0 0
\(311\) −32.2693 −1.82982 −0.914912 0.403654i \(-0.867740\pi\)
−0.914912 + 0.403654i \(0.867740\pi\)
\(312\) 0 0
\(313\) 32.0508 1.81162 0.905810 0.423685i \(-0.139264\pi\)
0.905810 + 0.423685i \(0.139264\pi\)
\(314\) 0 0
\(315\) −8.50242 −0.479057
\(316\) 0 0
\(317\) −17.4027 −0.977431 −0.488716 0.872443i \(-0.662534\pi\)
−0.488716 + 0.872443i \(0.662534\pi\)
\(318\) 0 0
\(319\) 25.4429 1.42453
\(320\) 0 0
\(321\) 1.24506 0.0694924
\(322\) 0 0
\(323\) −19.9706 −1.11119
\(324\) 0 0
\(325\) −8.12579 −0.450738
\(326\) 0 0
\(327\) −3.66743 −0.202809
\(328\) 0 0
\(329\) 18.0278 0.993904
\(330\) 0 0
\(331\) 29.5846 1.62612 0.813059 0.582182i \(-0.197801\pi\)
0.813059 + 0.582182i \(0.197801\pi\)
\(332\) 0 0
\(333\) −30.3139 −1.66119
\(334\) 0 0
\(335\) 13.5966 0.742861
\(336\) 0 0
\(337\) −6.02154 −0.328014 −0.164007 0.986459i \(-0.552442\pi\)
−0.164007 + 0.986459i \(0.552442\pi\)
\(338\) 0 0
\(339\) −3.24011 −0.175979
\(340\) 0 0
\(341\) −17.2865 −0.936117
\(342\) 0 0
\(343\) −18.5077 −0.999319
\(344\) 0 0
\(345\) 1.99287 0.107293
\(346\) 0 0
\(347\) 1.10663 0.0594068 0.0297034 0.999559i \(-0.490544\pi\)
0.0297034 + 0.999559i \(0.490544\pi\)
\(348\) 0 0
\(349\) −18.5033 −0.990458 −0.495229 0.868763i \(-0.664916\pi\)
−0.495229 + 0.868763i \(0.664916\pi\)
\(350\) 0 0
\(351\) 5.55959 0.296749
\(352\) 0 0
\(353\) −6.31975 −0.336366 −0.168183 0.985756i \(-0.553790\pi\)
−0.168183 + 0.985756i \(0.553790\pi\)
\(354\) 0 0
\(355\) −9.99316 −0.530382
\(356\) 0 0
\(357\) 2.19049 0.115933
\(358\) 0 0
\(359\) 27.3704 1.44456 0.722278 0.691602i \(-0.243095\pi\)
0.722278 + 0.691602i \(0.243095\pi\)
\(360\) 0 0
\(361\) −8.52895 −0.448892
\(362\) 0 0
\(363\) −2.48241 −0.130293
\(364\) 0 0
\(365\) 11.7321 0.614088
\(366\) 0 0
\(367\) −21.6094 −1.12800 −0.564001 0.825774i \(-0.690738\pi\)
−0.564001 + 0.825774i \(0.690738\pi\)
\(368\) 0 0
\(369\) −36.4056 −1.89520
\(370\) 0 0
\(371\) −4.63878 −0.240834
\(372\) 0 0
\(373\) −22.6293 −1.17170 −0.585850 0.810419i \(-0.699239\pi\)
−0.585850 + 0.810419i \(0.699239\pi\)
\(374\) 0 0
\(375\) 2.64081 0.136371
\(376\) 0 0
\(377\) −23.0894 −1.18916
\(378\) 0 0
\(379\) −22.8768 −1.17510 −0.587550 0.809188i \(-0.699908\pi\)
−0.587550 + 0.809188i \(0.699908\pi\)
\(380\) 0 0
\(381\) 2.30588 0.118134
\(382\) 0 0
\(383\) −13.6820 −0.699119 −0.349559 0.936914i \(-0.613669\pi\)
−0.349559 + 0.936914i \(0.613669\pi\)
\(384\) 0 0
\(385\) −13.6348 −0.694892
\(386\) 0 0
\(387\) 13.2931 0.675726
\(388\) 0 0
\(389\) 12.1384 0.615439 0.307719 0.951477i \(-0.400434\pi\)
0.307719 + 0.951477i \(0.400434\pi\)
\(390\) 0 0
\(391\) 32.0936 1.62304
\(392\) 0 0
\(393\) 4.84997 0.244649
\(394\) 0 0
\(395\) 15.3953 0.774621
\(396\) 0 0
\(397\) 30.6967 1.54063 0.770313 0.637666i \(-0.220100\pi\)
0.770313 + 0.637666i \(0.220100\pi\)
\(398\) 0 0
\(399\) −1.14853 −0.0574983
\(400\) 0 0
\(401\) 6.65165 0.332167 0.166084 0.986112i \(-0.446888\pi\)
0.166084 + 0.986112i \(0.446888\pi\)
\(402\) 0 0
\(403\) 15.6875 0.781450
\(404\) 0 0
\(405\) 15.1235 0.751493
\(406\) 0 0
\(407\) −48.6125 −2.40963
\(408\) 0 0
\(409\) 38.2720 1.89243 0.946214 0.323541i \(-0.104873\pi\)
0.946214 + 0.323541i \(0.104873\pi\)
\(410\) 0 0
\(411\) −2.17994 −0.107528
\(412\) 0 0
\(413\) −0.365436 −0.0179819
\(414\) 0 0
\(415\) −2.00237 −0.0982927
\(416\) 0 0
\(417\) −0.493551 −0.0241693
\(418\) 0 0
\(419\) 31.5974 1.54364 0.771818 0.635844i \(-0.219348\pi\)
0.771818 + 0.635844i \(0.219348\pi\)
\(420\) 0 0
\(421\) 23.8718 1.16344 0.581720 0.813389i \(-0.302380\pi\)
0.581720 + 0.813389i \(0.302380\pi\)
\(422\) 0 0
\(423\) −32.5964 −1.58489
\(424\) 0 0
\(425\) 11.6703 0.566092
\(426\) 0 0
\(427\) 18.3391 0.887491
\(428\) 0 0
\(429\) 4.42240 0.213516
\(430\) 0 0
\(431\) 1.75101 0.0843431 0.0421715 0.999110i \(-0.486572\pi\)
0.0421715 + 0.999110i \(0.486572\pi\)
\(432\) 0 0
\(433\) −6.36595 −0.305928 −0.152964 0.988232i \(-0.548882\pi\)
−0.152964 + 0.988232i \(0.548882\pi\)
\(434\) 0 0
\(435\) 2.05915 0.0987288
\(436\) 0 0
\(437\) −16.8274 −0.804966
\(438\) 0 0
\(439\) 11.6213 0.554655 0.277328 0.960775i \(-0.410551\pi\)
0.277328 + 0.960775i \(0.410551\pi\)
\(440\) 0 0
\(441\) 12.7947 0.609270
\(442\) 0 0
\(443\) 26.8654 1.27641 0.638206 0.769865i \(-0.279677\pi\)
0.638206 + 0.769865i \(0.279677\pi\)
\(444\) 0 0
\(445\) 31.2303 1.48046
\(446\) 0 0
\(447\) 1.72172 0.0814345
\(448\) 0 0
\(449\) 14.8136 0.699099 0.349549 0.936918i \(-0.386335\pi\)
0.349549 + 0.936918i \(0.386335\pi\)
\(450\) 0 0
\(451\) −58.3813 −2.74907
\(452\) 0 0
\(453\) 1.14988 0.0540260
\(454\) 0 0
\(455\) 12.3735 0.580081
\(456\) 0 0
\(457\) −11.2920 −0.528216 −0.264108 0.964493i \(-0.585078\pi\)
−0.264108 + 0.964493i \(0.585078\pi\)
\(458\) 0 0
\(459\) −7.98470 −0.372694
\(460\) 0 0
\(461\) 37.1345 1.72953 0.864763 0.502180i \(-0.167469\pi\)
0.864763 + 0.502180i \(0.167469\pi\)
\(462\) 0 0
\(463\) −18.9567 −0.880991 −0.440495 0.897755i \(-0.645197\pi\)
−0.440495 + 0.897755i \(0.645197\pi\)
\(464\) 0 0
\(465\) −1.39904 −0.0648789
\(466\) 0 0
\(467\) 3.79272 0.175506 0.0877531 0.996142i \(-0.472031\pi\)
0.0877531 + 0.996142i \(0.472031\pi\)
\(468\) 0 0
\(469\) 12.5927 0.581478
\(470\) 0 0
\(471\) 1.67148 0.0770179
\(472\) 0 0
\(473\) 21.3173 0.980169
\(474\) 0 0
\(475\) −6.11900 −0.280759
\(476\) 0 0
\(477\) 8.38746 0.384036
\(478\) 0 0
\(479\) 27.5983 1.26100 0.630499 0.776190i \(-0.282850\pi\)
0.630499 + 0.776190i \(0.282850\pi\)
\(480\) 0 0
\(481\) 44.1158 2.01151
\(482\) 0 0
\(483\) 1.84573 0.0839838
\(484\) 0 0
\(485\) 25.5368 1.15956
\(486\) 0 0
\(487\) −32.7583 −1.48442 −0.742210 0.670168i \(-0.766222\pi\)
−0.742210 + 0.670168i \(0.766222\pi\)
\(488\) 0 0
\(489\) −3.08980 −0.139725
\(490\) 0 0
\(491\) 38.4034 1.73312 0.866561 0.499072i \(-0.166326\pi\)
0.866561 + 0.499072i \(0.166326\pi\)
\(492\) 0 0
\(493\) 33.1610 1.49350
\(494\) 0 0
\(495\) 24.6533 1.10808
\(496\) 0 0
\(497\) −9.25534 −0.415159
\(498\) 0 0
\(499\) −39.5752 −1.77163 −0.885816 0.464037i \(-0.846400\pi\)
−0.885816 + 0.464037i \(0.846400\pi\)
\(500\) 0 0
\(501\) −5.55018 −0.247964
\(502\) 0 0
\(503\) −16.2094 −0.722741 −0.361371 0.932422i \(-0.617691\pi\)
−0.361371 + 0.932422i \(0.617691\pi\)
\(504\) 0 0
\(505\) −11.4841 −0.511037
\(506\) 0 0
\(507\) −1.18788 −0.0527555
\(508\) 0 0
\(509\) 3.90023 0.172875 0.0864374 0.996257i \(-0.472452\pi\)
0.0864374 + 0.996257i \(0.472452\pi\)
\(510\) 0 0
\(511\) 10.8659 0.480681
\(512\) 0 0
\(513\) 4.18657 0.184841
\(514\) 0 0
\(515\) 24.2528 1.06870
\(516\) 0 0
\(517\) −52.2726 −2.29895
\(518\) 0 0
\(519\) 1.58765 0.0696900
\(520\) 0 0
\(521\) −11.0831 −0.485558 −0.242779 0.970082i \(-0.578059\pi\)
−0.242779 + 0.970082i \(0.578059\pi\)
\(522\) 0 0
\(523\) 3.54404 0.154970 0.0774850 0.996994i \(-0.475311\pi\)
0.0774850 + 0.996994i \(0.475311\pi\)
\(524\) 0 0
\(525\) 0.671169 0.0292922
\(526\) 0 0
\(527\) −22.5304 −0.981441
\(528\) 0 0
\(529\) 4.04244 0.175758
\(530\) 0 0
\(531\) 0.660752 0.0286742
\(532\) 0 0
\(533\) 52.9810 2.29486
\(534\) 0 0
\(535\) −10.1008 −0.436698
\(536\) 0 0
\(537\) 1.34621 0.0580935
\(538\) 0 0
\(539\) 20.5180 0.883772
\(540\) 0 0
\(541\) −17.6029 −0.756808 −0.378404 0.925640i \(-0.623527\pi\)
−0.378404 + 0.925640i \(0.623527\pi\)
\(542\) 0 0
\(543\) −1.84987 −0.0793855
\(544\) 0 0
\(545\) 29.7529 1.27448
\(546\) 0 0
\(547\) 11.9882 0.512578 0.256289 0.966600i \(-0.417500\pi\)
0.256289 + 0.966600i \(0.417500\pi\)
\(548\) 0 0
\(549\) −33.1593 −1.41520
\(550\) 0 0
\(551\) −17.3871 −0.740716
\(552\) 0 0
\(553\) 14.2586 0.606339
\(554\) 0 0
\(555\) −3.93432 −0.167003
\(556\) 0 0
\(557\) 10.7837 0.456921 0.228461 0.973553i \(-0.426631\pi\)
0.228461 + 0.973553i \(0.426631\pi\)
\(558\) 0 0
\(559\) −19.3454 −0.818223
\(560\) 0 0
\(561\) −6.35147 −0.268159
\(562\) 0 0
\(563\) −21.6639 −0.913025 −0.456513 0.889717i \(-0.650902\pi\)
−0.456513 + 0.889717i \(0.650902\pi\)
\(564\) 0 0
\(565\) 26.2862 1.10587
\(566\) 0 0
\(567\) 14.0069 0.588234
\(568\) 0 0
\(569\) 3.95093 0.165632 0.0828158 0.996565i \(-0.473609\pi\)
0.0828158 + 0.996565i \(0.473609\pi\)
\(570\) 0 0
\(571\) −24.3652 −1.01965 −0.509826 0.860278i \(-0.670290\pi\)
−0.509826 + 0.860278i \(0.670290\pi\)
\(572\) 0 0
\(573\) 2.39050 0.0998644
\(574\) 0 0
\(575\) 9.83351 0.410086
\(576\) 0 0
\(577\) 27.6591 1.15146 0.575731 0.817639i \(-0.304718\pi\)
0.575731 + 0.817639i \(0.304718\pi\)
\(578\) 0 0
\(579\) 2.81827 0.117123
\(580\) 0 0
\(581\) −1.85453 −0.0769390
\(582\) 0 0
\(583\) 13.4504 0.557060
\(584\) 0 0
\(585\) −22.3728 −0.925002
\(586\) 0 0
\(587\) 5.03413 0.207781 0.103890 0.994589i \(-0.466871\pi\)
0.103890 + 0.994589i \(0.466871\pi\)
\(588\) 0 0
\(589\) 11.8132 0.486755
\(590\) 0 0
\(591\) −1.65239 −0.0679703
\(592\) 0 0
\(593\) 24.0095 0.985954 0.492977 0.870042i \(-0.335909\pi\)
0.492977 + 0.870042i \(0.335909\pi\)
\(594\) 0 0
\(595\) −17.7709 −0.728537
\(596\) 0 0
\(597\) 1.73173 0.0708751
\(598\) 0 0
\(599\) 3.61773 0.147816 0.0739082 0.997265i \(-0.476453\pi\)
0.0739082 + 0.997265i \(0.476453\pi\)
\(600\) 0 0
\(601\) −40.3471 −1.64579 −0.822897 0.568190i \(-0.807644\pi\)
−0.822897 + 0.568190i \(0.807644\pi\)
\(602\) 0 0
\(603\) −22.7691 −0.927231
\(604\) 0 0
\(605\) 20.1392 0.818773
\(606\) 0 0
\(607\) −19.8461 −0.805528 −0.402764 0.915304i \(-0.631950\pi\)
−0.402764 + 0.915304i \(0.631950\pi\)
\(608\) 0 0
\(609\) 1.90712 0.0772805
\(610\) 0 0
\(611\) 47.4374 1.91911
\(612\) 0 0
\(613\) 18.7510 0.757345 0.378672 0.925531i \(-0.376381\pi\)
0.378672 + 0.925531i \(0.376381\pi\)
\(614\) 0 0
\(615\) −4.72494 −0.190528
\(616\) 0 0
\(617\) −17.7500 −0.714590 −0.357295 0.933992i \(-0.616301\pi\)
−0.357295 + 0.933992i \(0.616301\pi\)
\(618\) 0 0
\(619\) −8.69003 −0.349282 −0.174641 0.984632i \(-0.555876\pi\)
−0.174641 + 0.984632i \(0.555876\pi\)
\(620\) 0 0
\(621\) −6.72800 −0.269985
\(622\) 0 0
\(623\) 28.9245 1.15884
\(624\) 0 0
\(625\) −11.9693 −0.478774
\(626\) 0 0
\(627\) 3.33022 0.132996
\(628\) 0 0
\(629\) −63.3592 −2.52630
\(630\) 0 0
\(631\) 23.3145 0.928136 0.464068 0.885800i \(-0.346389\pi\)
0.464068 + 0.885800i \(0.346389\pi\)
\(632\) 0 0
\(633\) −2.76091 −0.109736
\(634\) 0 0
\(635\) −18.7070 −0.742365
\(636\) 0 0
\(637\) −18.6200 −0.737753
\(638\) 0 0
\(639\) 16.7347 0.662016
\(640\) 0 0
\(641\) 33.3034 1.31540 0.657702 0.753279i \(-0.271529\pi\)
0.657702 + 0.753279i \(0.271529\pi\)
\(642\) 0 0
\(643\) 42.5841 1.67935 0.839677 0.543087i \(-0.182745\pi\)
0.839677 + 0.543087i \(0.182745\pi\)
\(644\) 0 0
\(645\) 1.72526 0.0679319
\(646\) 0 0
\(647\) 5.77584 0.227072 0.113536 0.993534i \(-0.463782\pi\)
0.113536 + 0.993534i \(0.463782\pi\)
\(648\) 0 0
\(649\) 1.05960 0.0415931
\(650\) 0 0
\(651\) −1.29575 −0.0507843
\(652\) 0 0
\(653\) 27.6630 1.08254 0.541269 0.840850i \(-0.317944\pi\)
0.541269 + 0.840850i \(0.317944\pi\)
\(654\) 0 0
\(655\) −39.3466 −1.53740
\(656\) 0 0
\(657\) −19.6469 −0.766498
\(658\) 0 0
\(659\) 22.9222 0.892923 0.446462 0.894803i \(-0.352684\pi\)
0.446462 + 0.894803i \(0.352684\pi\)
\(660\) 0 0
\(661\) 34.7645 1.35218 0.676091 0.736818i \(-0.263673\pi\)
0.676091 + 0.736818i \(0.263673\pi\)
\(662\) 0 0
\(663\) 5.76395 0.223853
\(664\) 0 0
\(665\) 9.31771 0.361325
\(666\) 0 0
\(667\) 27.9418 1.08191
\(668\) 0 0
\(669\) 2.55825 0.0989078
\(670\) 0 0
\(671\) −53.1753 −2.05281
\(672\) 0 0
\(673\) 1.57761 0.0608125 0.0304062 0.999538i \(-0.490320\pi\)
0.0304062 + 0.999538i \(0.490320\pi\)
\(674\) 0 0
\(675\) −2.44652 −0.0941665
\(676\) 0 0
\(677\) 17.7350 0.681612 0.340806 0.940134i \(-0.389300\pi\)
0.340806 + 0.940134i \(0.389300\pi\)
\(678\) 0 0
\(679\) 23.6513 0.907654
\(680\) 0 0
\(681\) 0.997399 0.0382204
\(682\) 0 0
\(683\) −12.3120 −0.471106 −0.235553 0.971862i \(-0.575690\pi\)
−0.235553 + 0.971862i \(0.575690\pi\)
\(684\) 0 0
\(685\) 17.6853 0.675720
\(686\) 0 0
\(687\) −1.47075 −0.0561127
\(688\) 0 0
\(689\) −12.2063 −0.465021
\(690\) 0 0
\(691\) 16.3776 0.623035 0.311518 0.950240i \(-0.399163\pi\)
0.311518 + 0.950240i \(0.399163\pi\)
\(692\) 0 0
\(693\) 22.8331 0.867357
\(694\) 0 0
\(695\) 4.00405 0.151882
\(696\) 0 0
\(697\) −76.0914 −2.88217
\(698\) 0 0
\(699\) −1.35549 −0.0512692
\(700\) 0 0
\(701\) 17.1563 0.647984 0.323992 0.946060i \(-0.394975\pi\)
0.323992 + 0.946060i \(0.394975\pi\)
\(702\) 0 0
\(703\) 33.2207 1.25294
\(704\) 0 0
\(705\) −4.23055 −0.159332
\(706\) 0 0
\(707\) −10.6362 −0.400016
\(708\) 0 0
\(709\) 5.79811 0.217753 0.108876 0.994055i \(-0.465275\pi\)
0.108876 + 0.994055i \(0.465275\pi\)
\(710\) 0 0
\(711\) −25.7813 −0.966873
\(712\) 0 0
\(713\) −18.9844 −0.710971
\(714\) 0 0
\(715\) −35.8778 −1.34175
\(716\) 0 0
\(717\) 0.100446 0.00375121
\(718\) 0 0
\(719\) 28.0666 1.04671 0.523354 0.852115i \(-0.324680\pi\)
0.523354 + 0.852115i \(0.324680\pi\)
\(720\) 0 0
\(721\) 22.4621 0.836534
\(722\) 0 0
\(723\) 3.20264 0.119107
\(724\) 0 0
\(725\) 10.1606 0.377354
\(726\) 0 0
\(727\) −42.7540 −1.58566 −0.792830 0.609443i \(-0.791393\pi\)
−0.792830 + 0.609443i \(0.791393\pi\)
\(728\) 0 0
\(729\) −24.4825 −0.906760
\(730\) 0 0
\(731\) 27.7839 1.02763
\(732\) 0 0
\(733\) −10.0366 −0.370710 −0.185355 0.982672i \(-0.559343\pi\)
−0.185355 + 0.982672i \(0.559343\pi\)
\(734\) 0 0
\(735\) 1.66057 0.0612510
\(736\) 0 0
\(737\) −36.5134 −1.34499
\(738\) 0 0
\(739\) 23.4548 0.862798 0.431399 0.902161i \(-0.358020\pi\)
0.431399 + 0.902161i \(0.358020\pi\)
\(740\) 0 0
\(741\) −3.02217 −0.111022
\(742\) 0 0
\(743\) 22.6455 0.830783 0.415392 0.909643i \(-0.363645\pi\)
0.415392 + 0.909643i \(0.363645\pi\)
\(744\) 0 0
\(745\) −13.9679 −0.511743
\(746\) 0 0
\(747\) 3.35322 0.122688
\(748\) 0 0
\(749\) −9.35508 −0.341827
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −6.42699 −0.234213
\(754\) 0 0
\(755\) −9.32867 −0.339505
\(756\) 0 0
\(757\) −31.1705 −1.13291 −0.566455 0.824093i \(-0.691686\pi\)
−0.566455 + 0.824093i \(0.691686\pi\)
\(758\) 0 0
\(759\) −5.35181 −0.194259
\(760\) 0 0
\(761\) −21.3629 −0.774403 −0.387202 0.921995i \(-0.626558\pi\)
−0.387202 + 0.921995i \(0.626558\pi\)
\(762\) 0 0
\(763\) 27.5562 0.997602
\(764\) 0 0
\(765\) 32.1319 1.16173
\(766\) 0 0
\(767\) −0.961590 −0.0347210
\(768\) 0 0
\(769\) −28.9756 −1.04489 −0.522444 0.852674i \(-0.674980\pi\)
−0.522444 + 0.852674i \(0.674980\pi\)
\(770\) 0 0
\(771\) 4.46327 0.160741
\(772\) 0 0
\(773\) 17.2980 0.622168 0.311084 0.950382i \(-0.399308\pi\)
0.311084 + 0.950382i \(0.399308\pi\)
\(774\) 0 0
\(775\) −6.90334 −0.247975
\(776\) 0 0
\(777\) −3.64385 −0.130722
\(778\) 0 0
\(779\) 39.8965 1.42944
\(780\) 0 0
\(781\) 26.8364 0.960282
\(782\) 0 0
\(783\) −6.95176 −0.248436
\(784\) 0 0
\(785\) −13.5603 −0.483989
\(786\) 0 0
\(787\) −20.8084 −0.741740 −0.370870 0.928685i \(-0.620940\pi\)
−0.370870 + 0.928685i \(0.620940\pi\)
\(788\) 0 0
\(789\) 4.42479 0.157527
\(790\) 0 0
\(791\) 24.3454 0.865624
\(792\) 0 0
\(793\) 48.2566 1.71364
\(794\) 0 0
\(795\) 1.08858 0.0386078
\(796\) 0 0
\(797\) 25.2111 0.893025 0.446512 0.894778i \(-0.352666\pi\)
0.446512 + 0.894778i \(0.352666\pi\)
\(798\) 0 0
\(799\) −68.1297 −2.41026
\(800\) 0 0
\(801\) −52.2990 −1.84789
\(802\) 0 0
\(803\) −31.5064 −1.11184
\(804\) 0 0
\(805\) −14.9740 −0.527763
\(806\) 0 0
\(807\) −3.15559 −0.111082
\(808\) 0 0
\(809\) −27.1052 −0.952968 −0.476484 0.879183i \(-0.658089\pi\)
−0.476484 + 0.879183i \(0.658089\pi\)
\(810\) 0 0
\(811\) −15.8230 −0.555619 −0.277810 0.960636i \(-0.589608\pi\)
−0.277810 + 0.960636i \(0.589608\pi\)
\(812\) 0 0
\(813\) 3.10476 0.108889
\(814\) 0 0
\(815\) 25.0667 0.878050
\(816\) 0 0
\(817\) −14.5678 −0.509661
\(818\) 0 0
\(819\) −20.7210 −0.724050
\(820\) 0 0
\(821\) 1.44493 0.0504285 0.0252143 0.999682i \(-0.491973\pi\)
0.0252143 + 0.999682i \(0.491973\pi\)
\(822\) 0 0
\(823\) 9.09322 0.316970 0.158485 0.987361i \(-0.449339\pi\)
0.158485 + 0.987361i \(0.449339\pi\)
\(824\) 0 0
\(825\) −1.94609 −0.0677543
\(826\) 0 0
\(827\) 3.95363 0.137481 0.0687405 0.997635i \(-0.478102\pi\)
0.0687405 + 0.997635i \(0.478102\pi\)
\(828\) 0 0
\(829\) 23.8653 0.828877 0.414438 0.910077i \(-0.363978\pi\)
0.414438 + 0.910077i \(0.363978\pi\)
\(830\) 0 0
\(831\) −3.86990 −0.134245
\(832\) 0 0
\(833\) 26.7422 0.926561
\(834\) 0 0
\(835\) 45.0272 1.55823
\(836\) 0 0
\(837\) 4.72320 0.163258
\(838\) 0 0
\(839\) −11.0805 −0.382541 −0.191270 0.981537i \(-0.561261\pi\)
−0.191270 + 0.981537i \(0.561261\pi\)
\(840\) 0 0
\(841\) −0.128833 −0.00444250
\(842\) 0 0
\(843\) −4.08178 −0.140584
\(844\) 0 0
\(845\) 9.63695 0.331521
\(846\) 0 0
\(847\) 18.6522 0.640899
\(848\) 0 0
\(849\) 5.98967 0.205565
\(850\) 0 0
\(851\) −53.3872 −1.83009
\(852\) 0 0
\(853\) −27.8275 −0.952795 −0.476398 0.879230i \(-0.658058\pi\)
−0.476398 + 0.879230i \(0.658058\pi\)
\(854\) 0 0
\(855\) −16.8475 −0.576173
\(856\) 0 0
\(857\) −30.4486 −1.04010 −0.520052 0.854134i \(-0.674088\pi\)
−0.520052 + 0.854134i \(0.674088\pi\)
\(858\) 0 0
\(859\) −19.3728 −0.660992 −0.330496 0.943807i \(-0.607216\pi\)
−0.330496 + 0.943807i \(0.607216\pi\)
\(860\) 0 0
\(861\) −4.37609 −0.149137
\(862\) 0 0
\(863\) 22.7950 0.775951 0.387975 0.921670i \(-0.373175\pi\)
0.387975 + 0.921670i \(0.373175\pi\)
\(864\) 0 0
\(865\) −12.8802 −0.437939
\(866\) 0 0
\(867\) −4.58338 −0.155660
\(868\) 0 0
\(869\) −41.3437 −1.40249
\(870\) 0 0
\(871\) 33.1359 1.12277
\(872\) 0 0
\(873\) −42.7644 −1.44735
\(874\) 0 0
\(875\) −19.8424 −0.670796
\(876\) 0 0
\(877\) −7.50812 −0.253531 −0.126766 0.991933i \(-0.540460\pi\)
−0.126766 + 0.991933i \(0.540460\pi\)
\(878\) 0 0
\(879\) 1.69546 0.0571865
\(880\) 0 0
\(881\) 14.1458 0.476584 0.238292 0.971194i \(-0.423413\pi\)
0.238292 + 0.971194i \(0.423413\pi\)
\(882\) 0 0
\(883\) −41.6328 −1.40106 −0.700528 0.713625i \(-0.747052\pi\)
−0.700528 + 0.713625i \(0.747052\pi\)
\(884\) 0 0
\(885\) 0.0857564 0.00288267
\(886\) 0 0
\(887\) 15.6978 0.527082 0.263541 0.964648i \(-0.415110\pi\)
0.263541 + 0.964648i \(0.415110\pi\)
\(888\) 0 0
\(889\) −17.3258 −0.581090
\(890\) 0 0
\(891\) −40.6138 −1.36061
\(892\) 0 0
\(893\) 35.7220 1.19539
\(894\) 0 0
\(895\) −10.9215 −0.365066
\(896\) 0 0
\(897\) 4.85677 0.162163
\(898\) 0 0
\(899\) −19.6158 −0.654223
\(900\) 0 0
\(901\) 17.5306 0.584031
\(902\) 0 0
\(903\) 1.59788 0.0531741
\(904\) 0 0
\(905\) 15.0075 0.498867
\(906\) 0 0
\(907\) 13.3670 0.443844 0.221922 0.975064i \(-0.428767\pi\)
0.221922 + 0.975064i \(0.428767\pi\)
\(908\) 0 0
\(909\) 19.2315 0.637870
\(910\) 0 0
\(911\) −23.3969 −0.775174 −0.387587 0.921833i \(-0.626691\pi\)
−0.387587 + 0.921833i \(0.626691\pi\)
\(912\) 0 0
\(913\) 5.37733 0.177964
\(914\) 0 0
\(915\) −4.30361 −0.142273
\(916\) 0 0
\(917\) −36.4416 −1.20341
\(918\) 0 0
\(919\) 58.7649 1.93847 0.969237 0.246129i \(-0.0791588\pi\)
0.969237 + 0.246129i \(0.0791588\pi\)
\(920\) 0 0
\(921\) 1.46759 0.0483587
\(922\) 0 0
\(923\) −24.3540 −0.801623
\(924\) 0 0
\(925\) −19.4133 −0.638305
\(926\) 0 0
\(927\) −40.6142 −1.33394
\(928\) 0 0
\(929\) −55.9544 −1.83580 −0.917902 0.396807i \(-0.870118\pi\)
−0.917902 + 0.396807i \(0.870118\pi\)
\(930\) 0 0
\(931\) −14.0215 −0.459537
\(932\) 0 0
\(933\) 7.01348 0.229611
\(934\) 0 0
\(935\) 51.5278 1.68514
\(936\) 0 0
\(937\) 3.14070 0.102602 0.0513011 0.998683i \(-0.483663\pi\)
0.0513011 + 0.998683i \(0.483663\pi\)
\(938\) 0 0
\(939\) −6.96600 −0.227327
\(940\) 0 0
\(941\) 9.73923 0.317490 0.158745 0.987320i \(-0.449255\pi\)
0.158745 + 0.987320i \(0.449255\pi\)
\(942\) 0 0
\(943\) −64.1155 −2.08789
\(944\) 0 0
\(945\) 3.72543 0.121188
\(946\) 0 0
\(947\) −44.8318 −1.45684 −0.728419 0.685132i \(-0.759745\pi\)
−0.728419 + 0.685132i \(0.759745\pi\)
\(948\) 0 0
\(949\) 28.5921 0.928137
\(950\) 0 0
\(951\) 3.78234 0.122651
\(952\) 0 0
\(953\) 31.2386 1.01192 0.505958 0.862558i \(-0.331139\pi\)
0.505958 + 0.862558i \(0.331139\pi\)
\(954\) 0 0
\(955\) −19.3935 −0.627558
\(956\) 0 0
\(957\) −5.52981 −0.178753
\(958\) 0 0
\(959\) 16.3795 0.528923
\(960\) 0 0
\(961\) −17.6726 −0.570082
\(962\) 0 0
\(963\) 16.9151 0.545081
\(964\) 0 0
\(965\) −22.8639 −0.736015
\(966\) 0 0
\(967\) 23.3706 0.751547 0.375774 0.926712i \(-0.377377\pi\)
0.375774 + 0.926712i \(0.377377\pi\)
\(968\) 0 0
\(969\) 4.34045 0.139435
\(970\) 0 0
\(971\) 24.0844 0.772904 0.386452 0.922310i \(-0.373701\pi\)
0.386452 + 0.922310i \(0.373701\pi\)
\(972\) 0 0
\(973\) 3.70842 0.118887
\(974\) 0 0
\(975\) 1.76608 0.0565598
\(976\) 0 0
\(977\) 38.5225 1.23244 0.616222 0.787573i \(-0.288663\pi\)
0.616222 + 0.787573i \(0.288663\pi\)
\(978\) 0 0
\(979\) −83.8684 −2.68045
\(980\) 0 0
\(981\) −49.8249 −1.59079
\(982\) 0 0
\(983\) −2.11774 −0.0675453 −0.0337726 0.999430i \(-0.510752\pi\)
−0.0337726 + 0.999430i \(0.510752\pi\)
\(984\) 0 0
\(985\) 13.4054 0.427133
\(986\) 0 0
\(987\) −3.91820 −0.124718
\(988\) 0 0
\(989\) 23.4110 0.744427
\(990\) 0 0
\(991\) −26.7322 −0.849175 −0.424587 0.905387i \(-0.639581\pi\)
−0.424587 + 0.905387i \(0.639581\pi\)
\(992\) 0 0
\(993\) −6.42999 −0.204049
\(994\) 0 0
\(995\) −14.0491 −0.445387
\(996\) 0 0
\(997\) 45.1222 1.42903 0.714517 0.699618i \(-0.246646\pi\)
0.714517 + 0.699618i \(0.246646\pi\)
\(998\) 0 0
\(999\) 13.2824 0.420237
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 \(a_p\))