Properties

Label 6004.2.a.g.1.27
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.27
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.16967 q^{3} -2.87894 q^{5} -4.05578 q^{7} +7.04683 q^{9} +O(q^{10})\) \(q+3.16967 q^{3} -2.87894 q^{5} -4.05578 q^{7} +7.04683 q^{9} -0.0722189 q^{11} -0.263471 q^{13} -9.12532 q^{15} +3.42694 q^{17} +1.00000 q^{19} -12.8555 q^{21} +2.37948 q^{23} +3.28832 q^{25} +12.8271 q^{27} +1.44989 q^{29} -9.00254 q^{31} -0.228910 q^{33} +11.6764 q^{35} -7.21477 q^{37} -0.835116 q^{39} +6.92976 q^{41} -8.85392 q^{43} -20.2874 q^{45} -1.76721 q^{47} +9.44932 q^{49} +10.8623 q^{51} +3.29917 q^{53} +0.207914 q^{55} +3.16967 q^{57} +0.351290 q^{59} -10.3711 q^{61} -28.5804 q^{63} +0.758517 q^{65} -7.05499 q^{67} +7.54217 q^{69} +1.30367 q^{71} -13.6132 q^{73} +10.4229 q^{75} +0.292904 q^{77} -1.00000 q^{79} +19.5174 q^{81} -0.269951 q^{83} -9.86598 q^{85} +4.59567 q^{87} -7.38755 q^{89} +1.06858 q^{91} -28.5351 q^{93} -2.87894 q^{95} -2.87132 q^{97} -0.508915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) 3.16967 1.83001 0.915006 0.403440i \(-0.132186\pi\)
0.915006 + 0.403440i \(0.132186\pi\)
\(4\) 0 0
\(5\) −2.87894 −1.28750 −0.643752 0.765235i \(-0.722623\pi\)
−0.643752 + 0.765235i \(0.722623\pi\)
\(6\) 0 0
\(7\) −4.05578 −1.53294 −0.766470 0.642280i \(-0.777988\pi\)
−0.766470 + 0.642280i \(0.777988\pi\)
\(8\) 0 0
\(9\) 7.04683 2.34894
\(10\) 0 0
\(11\) −0.0722189 −0.0217748 −0.0108874 0.999941i \(-0.503466\pi\)
−0.0108874 + 0.999941i \(0.503466\pi\)
\(12\) 0 0
\(13\) −0.263471 −0.0730736 −0.0365368 0.999332i \(-0.511633\pi\)
−0.0365368 + 0.999332i \(0.511633\pi\)
\(14\) 0 0
\(15\) −9.12532 −2.35615
\(16\) 0 0
\(17\) 3.42694 0.831156 0.415578 0.909558i \(-0.363579\pi\)
0.415578 + 0.909558i \(0.363579\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −12.8555 −2.80530
\(22\) 0 0
\(23\) 2.37948 0.496156 0.248078 0.968740i \(-0.420201\pi\)
0.248078 + 0.968740i \(0.420201\pi\)
\(24\) 0 0
\(25\) 3.28832 0.657664
\(26\) 0 0
\(27\) 12.8271 2.46858
\(28\) 0 0
\(29\) 1.44989 0.269238 0.134619 0.990897i \(-0.457019\pi\)
0.134619 + 0.990897i \(0.457019\pi\)
\(30\) 0 0
\(31\) −9.00254 −1.61690 −0.808452 0.588563i \(-0.799694\pi\)
−0.808452 + 0.588563i \(0.799694\pi\)
\(32\) 0 0
\(33\) −0.228910 −0.0398482
\(34\) 0 0
\(35\) 11.6764 1.97366
\(36\) 0 0
\(37\) −7.21477 −1.18610 −0.593050 0.805165i \(-0.702077\pi\)
−0.593050 + 0.805165i \(0.702077\pi\)
\(38\) 0 0
\(39\) −0.835116 −0.133726
\(40\) 0 0
\(41\) 6.92976 1.08225 0.541123 0.840943i \(-0.317999\pi\)
0.541123 + 0.840943i \(0.317999\pi\)
\(42\) 0 0
\(43\) −8.85392 −1.35021 −0.675105 0.737722i \(-0.735902\pi\)
−0.675105 + 0.737722i \(0.735902\pi\)
\(44\) 0 0
\(45\) −20.2874 −3.02427
\(46\) 0 0
\(47\) −1.76721 −0.257773 −0.128887 0.991659i \(-0.541140\pi\)
−0.128887 + 0.991659i \(0.541140\pi\)
\(48\) 0 0
\(49\) 9.44932 1.34990
\(50\) 0 0
\(51\) 10.8623 1.52103
\(52\) 0 0
\(53\) 3.29917 0.453175 0.226588 0.973991i \(-0.427243\pi\)
0.226588 + 0.973991i \(0.427243\pi\)
\(54\) 0 0
\(55\) 0.207914 0.0280352
\(56\) 0 0
\(57\) 3.16967 0.419834
\(58\) 0 0
\(59\) 0.351290 0.0457340 0.0228670 0.999739i \(-0.492721\pi\)
0.0228670 + 0.999739i \(0.492721\pi\)
\(60\) 0 0
\(61\) −10.3711 −1.32788 −0.663941 0.747785i \(-0.731118\pi\)
−0.663941 + 0.747785i \(0.731118\pi\)
\(62\) 0 0
\(63\) −28.5804 −3.60079
\(64\) 0 0
\(65\) 0.758517 0.0940825
\(66\) 0 0
\(67\) −7.05499 −0.861905 −0.430952 0.902375i \(-0.641822\pi\)
−0.430952 + 0.902375i \(0.641822\pi\)
\(68\) 0 0
\(69\) 7.54217 0.907971
\(70\) 0 0
\(71\) 1.30367 0.154717 0.0773585 0.997003i \(-0.475351\pi\)
0.0773585 + 0.997003i \(0.475351\pi\)
\(72\) 0 0
\(73\) −13.6132 −1.59330 −0.796650 0.604441i \(-0.793397\pi\)
−0.796650 + 0.604441i \(0.793397\pi\)
\(74\) 0 0
\(75\) 10.4229 1.20353
\(76\) 0 0
\(77\) 0.292904 0.0333795
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 19.5174 2.16860
\(82\) 0 0
\(83\) −0.269951 −0.0296310 −0.0148155 0.999890i \(-0.504716\pi\)
−0.0148155 + 0.999890i \(0.504716\pi\)
\(84\) 0 0
\(85\) −9.86598 −1.07012
\(86\) 0 0
\(87\) 4.59567 0.492708
\(88\) 0 0
\(89\) −7.38755 −0.783078 −0.391539 0.920161i \(-0.628057\pi\)
−0.391539 + 0.920161i \(0.628057\pi\)
\(90\) 0 0
\(91\) 1.06858 0.112017
\(92\) 0 0
\(93\) −28.5351 −2.95895
\(94\) 0 0
\(95\) −2.87894 −0.295373
\(96\) 0 0
\(97\) −2.87132 −0.291538 −0.145769 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(98\) 0 0
\(99\) −0.508915 −0.0511479
\(100\) 0 0
\(101\) −15.4464 −1.53697 −0.768486 0.639867i \(-0.778990\pi\)
−0.768486 + 0.639867i \(0.778990\pi\)
\(102\) 0 0
\(103\) −6.91399 −0.681256 −0.340628 0.940198i \(-0.610640\pi\)
−0.340628 + 0.940198i \(0.610640\pi\)
\(104\) 0 0
\(105\) 37.0102 3.61183
\(106\) 0 0
\(107\) 6.66449 0.644281 0.322140 0.946692i \(-0.395598\pi\)
0.322140 + 0.946692i \(0.395598\pi\)
\(108\) 0 0
\(109\) −7.72585 −0.740002 −0.370001 0.929031i \(-0.620643\pi\)
−0.370001 + 0.929031i \(0.620643\pi\)
\(110\) 0 0
\(111\) −22.8685 −2.17058
\(112\) 0 0
\(113\) −12.3685 −1.16353 −0.581763 0.813358i \(-0.697637\pi\)
−0.581763 + 0.813358i \(0.697637\pi\)
\(114\) 0 0
\(115\) −6.85039 −0.638802
\(116\) 0 0
\(117\) −1.85663 −0.171646
\(118\) 0 0
\(119\) −13.8989 −1.27411
\(120\) 0 0
\(121\) −10.9948 −0.999526
\(122\) 0 0
\(123\) 21.9651 1.98052
\(124\) 0 0
\(125\) 4.92783 0.440759
\(126\) 0 0
\(127\) 17.8391 1.58297 0.791484 0.611190i \(-0.209309\pi\)
0.791484 + 0.611190i \(0.209309\pi\)
\(128\) 0 0
\(129\) −28.0640 −2.47090
\(130\) 0 0
\(131\) −9.17054 −0.801234 −0.400617 0.916246i \(-0.631204\pi\)
−0.400617 + 0.916246i \(0.631204\pi\)
\(132\) 0 0
\(133\) −4.05578 −0.351680
\(134\) 0 0
\(135\) −36.9286 −3.17831
\(136\) 0 0
\(137\) −7.33244 −0.626453 −0.313226 0.949679i \(-0.601410\pi\)
−0.313226 + 0.949679i \(0.601410\pi\)
\(138\) 0 0
\(139\) 15.6965 1.33136 0.665678 0.746239i \(-0.268142\pi\)
0.665678 + 0.746239i \(0.268142\pi\)
\(140\) 0 0
\(141\) −5.60146 −0.471728
\(142\) 0 0
\(143\) 0.0190276 0.00159116
\(144\) 0 0
\(145\) −4.17415 −0.346644
\(146\) 0 0
\(147\) 29.9513 2.47034
\(148\) 0 0
\(149\) 4.52585 0.370772 0.185386 0.982666i \(-0.440646\pi\)
0.185386 + 0.982666i \(0.440646\pi\)
\(150\) 0 0
\(151\) −11.7300 −0.954572 −0.477286 0.878748i \(-0.658379\pi\)
−0.477286 + 0.878748i \(0.658379\pi\)
\(152\) 0 0
\(153\) 24.1491 1.95234
\(154\) 0 0
\(155\) 25.9178 2.08177
\(156\) 0 0
\(157\) 17.4585 1.39334 0.696669 0.717393i \(-0.254665\pi\)
0.696669 + 0.717393i \(0.254665\pi\)
\(158\) 0 0
\(159\) 10.4573 0.829316
\(160\) 0 0
\(161\) −9.65064 −0.760577
\(162\) 0 0
\(163\) 15.3777 1.20447 0.602235 0.798318i \(-0.294277\pi\)
0.602235 + 0.798318i \(0.294277\pi\)
\(164\) 0 0
\(165\) 0.659020 0.0513047
\(166\) 0 0
\(167\) −2.34625 −0.181558 −0.0907790 0.995871i \(-0.528936\pi\)
−0.0907790 + 0.995871i \(0.528936\pi\)
\(168\) 0 0
\(169\) −12.9306 −0.994660
\(170\) 0 0
\(171\) 7.04683 0.538885
\(172\) 0 0
\(173\) −10.1774 −0.773771 −0.386885 0.922128i \(-0.626449\pi\)
−0.386885 + 0.922128i \(0.626449\pi\)
\(174\) 0 0
\(175\) −13.3367 −1.00816
\(176\) 0 0
\(177\) 1.11347 0.0836938
\(178\) 0 0
\(179\) −16.2076 −1.21141 −0.605707 0.795688i \(-0.707110\pi\)
−0.605707 + 0.795688i \(0.707110\pi\)
\(180\) 0 0
\(181\) −0.278393 −0.0206928 −0.0103464 0.999946i \(-0.503293\pi\)
−0.0103464 + 0.999946i \(0.503293\pi\)
\(182\) 0 0
\(183\) −32.8730 −2.43004
\(184\) 0 0
\(185\) 20.7709 1.52711
\(186\) 0 0
\(187\) −0.247490 −0.0180983
\(188\) 0 0
\(189\) −52.0240 −3.78419
\(190\) 0 0
\(191\) 14.3934 1.04147 0.520735 0.853718i \(-0.325658\pi\)
0.520735 + 0.853718i \(0.325658\pi\)
\(192\) 0 0
\(193\) 13.9120 1.00141 0.500705 0.865618i \(-0.333074\pi\)
0.500705 + 0.865618i \(0.333074\pi\)
\(194\) 0 0
\(195\) 2.40425 0.172172
\(196\) 0 0
\(197\) −10.9664 −0.781327 −0.390663 0.920534i \(-0.627754\pi\)
−0.390663 + 0.920534i \(0.627754\pi\)
\(198\) 0 0
\(199\) 1.31103 0.0929367 0.0464684 0.998920i \(-0.485203\pi\)
0.0464684 + 0.998920i \(0.485203\pi\)
\(200\) 0 0
\(201\) −22.3620 −1.57730
\(202\) 0 0
\(203\) −5.88042 −0.412725
\(204\) 0 0
\(205\) −19.9504 −1.39340
\(206\) 0 0
\(207\) 16.7678 1.16544
\(208\) 0 0
\(209\) −0.0722189 −0.00499549
\(210\) 0 0
\(211\) −3.17734 −0.218737 −0.109368 0.994001i \(-0.534883\pi\)
−0.109368 + 0.994001i \(0.534883\pi\)
\(212\) 0 0
\(213\) 4.13221 0.283134
\(214\) 0 0
\(215\) 25.4899 1.73840
\(216\) 0 0
\(217\) 36.5123 2.47861
\(218\) 0 0
\(219\) −43.1493 −2.91576
\(220\) 0 0
\(221\) −0.902899 −0.0607355
\(222\) 0 0
\(223\) 6.51962 0.436586 0.218293 0.975883i \(-0.429951\pi\)
0.218293 + 0.975883i \(0.429951\pi\)
\(224\) 0 0
\(225\) 23.1722 1.54482
\(226\) 0 0
\(227\) −20.4346 −1.35629 −0.678146 0.734927i \(-0.737217\pi\)
−0.678146 + 0.734927i \(0.737217\pi\)
\(228\) 0 0
\(229\) 19.4075 1.28248 0.641241 0.767339i \(-0.278420\pi\)
0.641241 + 0.767339i \(0.278420\pi\)
\(230\) 0 0
\(231\) 0.928410 0.0610849
\(232\) 0 0
\(233\) −20.8895 −1.36852 −0.684260 0.729239i \(-0.739874\pi\)
−0.684260 + 0.729239i \(0.739874\pi\)
\(234\) 0 0
\(235\) 5.08768 0.331884
\(236\) 0 0
\(237\) −3.16967 −0.205892
\(238\) 0 0
\(239\) 17.2485 1.11571 0.557856 0.829938i \(-0.311624\pi\)
0.557856 + 0.829938i \(0.311624\pi\)
\(240\) 0 0
\(241\) −13.1053 −0.844187 −0.422094 0.906552i \(-0.638705\pi\)
−0.422094 + 0.906552i \(0.638705\pi\)
\(242\) 0 0
\(243\) 23.3823 1.49997
\(244\) 0 0
\(245\) −27.2041 −1.73800
\(246\) 0 0
\(247\) −0.263471 −0.0167642
\(248\) 0 0
\(249\) −0.855656 −0.0542250
\(250\) 0 0
\(251\) 16.8078 1.06090 0.530450 0.847716i \(-0.322023\pi\)
0.530450 + 0.847716i \(0.322023\pi\)
\(252\) 0 0
\(253\) −0.171843 −0.0108037
\(254\) 0 0
\(255\) −31.2719 −1.95832
\(256\) 0 0
\(257\) 3.76837 0.235064 0.117532 0.993069i \(-0.462502\pi\)
0.117532 + 0.993069i \(0.462502\pi\)
\(258\) 0 0
\(259\) 29.2615 1.81822
\(260\) 0 0
\(261\) 10.2171 0.632424
\(262\) 0 0
\(263\) −10.5467 −0.650338 −0.325169 0.945656i \(-0.605421\pi\)
−0.325169 + 0.945656i \(0.605421\pi\)
\(264\) 0 0
\(265\) −9.49812 −0.583465
\(266\) 0 0
\(267\) −23.4161 −1.43304
\(268\) 0 0
\(269\) −8.61940 −0.525534 −0.262767 0.964859i \(-0.584635\pi\)
−0.262767 + 0.964859i \(0.584635\pi\)
\(270\) 0 0
\(271\) 15.2640 0.927223 0.463611 0.886039i \(-0.346553\pi\)
0.463611 + 0.886039i \(0.346553\pi\)
\(272\) 0 0
\(273\) 3.38704 0.204993
\(274\) 0 0
\(275\) −0.237479 −0.0143205
\(276\) 0 0
\(277\) 13.0188 0.782224 0.391112 0.920343i \(-0.372090\pi\)
0.391112 + 0.920343i \(0.372090\pi\)
\(278\) 0 0
\(279\) −63.4394 −3.79802
\(280\) 0 0
\(281\) −26.8262 −1.60032 −0.800158 0.599789i \(-0.795251\pi\)
−0.800158 + 0.599789i \(0.795251\pi\)
\(282\) 0 0
\(283\) −23.8068 −1.41517 −0.707584 0.706629i \(-0.750215\pi\)
−0.707584 + 0.706629i \(0.750215\pi\)
\(284\) 0 0
\(285\) −9.12532 −0.540537
\(286\) 0 0
\(287\) −28.1056 −1.65902
\(288\) 0 0
\(289\) −5.25606 −0.309180
\(290\) 0 0
\(291\) −9.10113 −0.533518
\(292\) 0 0
\(293\) 9.32254 0.544629 0.272314 0.962208i \(-0.412211\pi\)
0.272314 + 0.962208i \(0.412211\pi\)
\(294\) 0 0
\(295\) −1.01134 −0.0588827
\(296\) 0 0
\(297\) −0.926362 −0.0537530
\(298\) 0 0
\(299\) −0.626923 −0.0362559
\(300\) 0 0
\(301\) 35.9095 2.06979
\(302\) 0 0
\(303\) −48.9600 −2.81268
\(304\) 0 0
\(305\) 29.8578 1.70965
\(306\) 0 0
\(307\) −12.7288 −0.726469 −0.363234 0.931698i \(-0.618328\pi\)
−0.363234 + 0.931698i \(0.618328\pi\)
\(308\) 0 0
\(309\) −21.9151 −1.24671
\(310\) 0 0
\(311\) −15.3508 −0.870465 −0.435233 0.900318i \(-0.643334\pi\)
−0.435233 + 0.900318i \(0.643334\pi\)
\(312\) 0 0
\(313\) 11.8578 0.670240 0.335120 0.942175i \(-0.391223\pi\)
0.335120 + 0.942175i \(0.391223\pi\)
\(314\) 0 0
\(315\) 82.2813 4.63603
\(316\) 0 0
\(317\) −30.2373 −1.69830 −0.849148 0.528155i \(-0.822884\pi\)
−0.849148 + 0.528155i \(0.822884\pi\)
\(318\) 0 0
\(319\) −0.104709 −0.00586260
\(320\) 0 0
\(321\) 21.1243 1.17904
\(322\) 0 0
\(323\) 3.42694 0.190680
\(324\) 0 0
\(325\) −0.866376 −0.0480579
\(326\) 0 0
\(327\) −24.4884 −1.35421
\(328\) 0 0
\(329\) 7.16739 0.395151
\(330\) 0 0
\(331\) 14.5943 0.802176 0.401088 0.916040i \(-0.368632\pi\)
0.401088 + 0.916040i \(0.368632\pi\)
\(332\) 0 0
\(333\) −50.8413 −2.78609
\(334\) 0 0
\(335\) 20.3109 1.10970
\(336\) 0 0
\(337\) 15.1756 0.826667 0.413334 0.910580i \(-0.364364\pi\)
0.413334 + 0.910580i \(0.364364\pi\)
\(338\) 0 0
\(339\) −39.2040 −2.12927
\(340\) 0 0
\(341\) 0.650153 0.0352078
\(342\) 0 0
\(343\) −9.93390 −0.536380
\(344\) 0 0
\(345\) −21.7135 −1.16902
\(346\) 0 0
\(347\) 7.39441 0.396953 0.198476 0.980106i \(-0.436401\pi\)
0.198476 + 0.980106i \(0.436401\pi\)
\(348\) 0 0
\(349\) −7.83343 −0.419314 −0.209657 0.977775i \(-0.567235\pi\)
−0.209657 + 0.977775i \(0.567235\pi\)
\(350\) 0 0
\(351\) −3.37957 −0.180388
\(352\) 0 0
\(353\) 2.67972 0.142627 0.0713135 0.997454i \(-0.477281\pi\)
0.0713135 + 0.997454i \(0.477281\pi\)
\(354\) 0 0
\(355\) −3.75319 −0.199199
\(356\) 0 0
\(357\) −44.0550 −2.33164
\(358\) 0 0
\(359\) −37.1345 −1.95988 −0.979942 0.199281i \(-0.936139\pi\)
−0.979942 + 0.199281i \(0.936139\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −34.8499 −1.82914
\(364\) 0 0
\(365\) 39.1915 2.05138
\(366\) 0 0
\(367\) −4.09056 −0.213525 −0.106763 0.994285i \(-0.534049\pi\)
−0.106763 + 0.994285i \(0.534049\pi\)
\(368\) 0 0
\(369\) 48.8329 2.54214
\(370\) 0 0
\(371\) −13.3807 −0.694690
\(372\) 0 0
\(373\) 32.5937 1.68764 0.843818 0.536629i \(-0.180302\pi\)
0.843818 + 0.536629i \(0.180302\pi\)
\(374\) 0 0
\(375\) 15.6196 0.806594
\(376\) 0 0
\(377\) −0.382003 −0.0196742
\(378\) 0 0
\(379\) −26.2772 −1.34977 −0.674885 0.737923i \(-0.735807\pi\)
−0.674885 + 0.737923i \(0.735807\pi\)
\(380\) 0 0
\(381\) 56.5443 2.89685
\(382\) 0 0
\(383\) 16.3002 0.832900 0.416450 0.909159i \(-0.363274\pi\)
0.416450 + 0.909159i \(0.363274\pi\)
\(384\) 0 0
\(385\) −0.843254 −0.0429762
\(386\) 0 0
\(387\) −62.3921 −3.17157
\(388\) 0 0
\(389\) 5.78641 0.293383 0.146691 0.989182i \(-0.453138\pi\)
0.146691 + 0.989182i \(0.453138\pi\)
\(390\) 0 0
\(391\) 8.15434 0.412383
\(392\) 0 0
\(393\) −29.0676 −1.46627
\(394\) 0 0
\(395\) 2.87894 0.144855
\(396\) 0 0
\(397\) 3.80345 0.190890 0.0954449 0.995435i \(-0.469573\pi\)
0.0954449 + 0.995435i \(0.469573\pi\)
\(398\) 0 0
\(399\) −12.8555 −0.643579
\(400\) 0 0
\(401\) −9.65652 −0.482224 −0.241112 0.970497i \(-0.577512\pi\)
−0.241112 + 0.970497i \(0.577512\pi\)
\(402\) 0 0
\(403\) 2.37190 0.118153
\(404\) 0 0
\(405\) −56.1894 −2.79207
\(406\) 0 0
\(407\) 0.521043 0.0258271
\(408\) 0 0
\(409\) 15.2449 0.753812 0.376906 0.926252i \(-0.376988\pi\)
0.376906 + 0.926252i \(0.376988\pi\)
\(410\) 0 0
\(411\) −23.2414 −1.14642
\(412\) 0 0
\(413\) −1.42475 −0.0701074
\(414\) 0 0
\(415\) 0.777174 0.0381499
\(416\) 0 0
\(417\) 49.7527 2.43640
\(418\) 0 0
\(419\) 5.81011 0.283842 0.141921 0.989878i \(-0.454672\pi\)
0.141921 + 0.989878i \(0.454672\pi\)
\(420\) 0 0
\(421\) −3.37672 −0.164571 −0.0822857 0.996609i \(-0.526222\pi\)
−0.0822857 + 0.996609i \(0.526222\pi\)
\(422\) 0 0
\(423\) −12.4532 −0.605495
\(424\) 0 0
\(425\) 11.2689 0.546621
\(426\) 0 0
\(427\) 42.0628 2.03556
\(428\) 0 0
\(429\) 0.0603112 0.00291185
\(430\) 0 0
\(431\) 21.9934 1.05939 0.529693 0.848190i \(-0.322307\pi\)
0.529693 + 0.848190i \(0.322307\pi\)
\(432\) 0 0
\(433\) 0.306165 0.0147134 0.00735668 0.999973i \(-0.497658\pi\)
0.00735668 + 0.999973i \(0.497658\pi\)
\(434\) 0 0
\(435\) −13.2307 −0.634363
\(436\) 0 0
\(437\) 2.37948 0.113826
\(438\) 0 0
\(439\) 1.57346 0.0750974 0.0375487 0.999295i \(-0.488045\pi\)
0.0375487 + 0.999295i \(0.488045\pi\)
\(440\) 0 0
\(441\) 66.5878 3.17085
\(442\) 0 0
\(443\) 27.1032 1.28771 0.643857 0.765146i \(-0.277333\pi\)
0.643857 + 0.765146i \(0.277333\pi\)
\(444\) 0 0
\(445\) 21.2683 1.00822
\(446\) 0 0
\(447\) 14.3455 0.678518
\(448\) 0 0
\(449\) −6.20036 −0.292613 −0.146307 0.989239i \(-0.546739\pi\)
−0.146307 + 0.989239i \(0.546739\pi\)
\(450\) 0 0
\(451\) −0.500460 −0.0235657
\(452\) 0 0
\(453\) −37.1802 −1.74688
\(454\) 0 0
\(455\) −3.07638 −0.144223
\(456\) 0 0
\(457\) 34.7792 1.62690 0.813450 0.581635i \(-0.197587\pi\)
0.813450 + 0.581635i \(0.197587\pi\)
\(458\) 0 0
\(459\) 43.9579 2.05178
\(460\) 0 0
\(461\) 17.5163 0.815814 0.407907 0.913023i \(-0.366259\pi\)
0.407907 + 0.913023i \(0.366259\pi\)
\(462\) 0 0
\(463\) −20.0968 −0.933977 −0.466988 0.884263i \(-0.654661\pi\)
−0.466988 + 0.884263i \(0.654661\pi\)
\(464\) 0 0
\(465\) 82.1510 3.80966
\(466\) 0 0
\(467\) 24.9978 1.15676 0.578380 0.815767i \(-0.303685\pi\)
0.578380 + 0.815767i \(0.303685\pi\)
\(468\) 0 0
\(469\) 28.6135 1.32125
\(470\) 0 0
\(471\) 55.3376 2.54982
\(472\) 0 0
\(473\) 0.639420 0.0294006
\(474\) 0 0
\(475\) 3.28832 0.150878
\(476\) 0 0
\(477\) 23.2487 1.06448
\(478\) 0 0
\(479\) 18.0570 0.825045 0.412522 0.910948i \(-0.364648\pi\)
0.412522 + 0.910948i \(0.364648\pi\)
\(480\) 0 0
\(481\) 1.90088 0.0866726
\(482\) 0 0
\(483\) −30.5894 −1.39186
\(484\) 0 0
\(485\) 8.26636 0.375356
\(486\) 0 0
\(487\) −11.4547 −0.519060 −0.259530 0.965735i \(-0.583568\pi\)
−0.259530 + 0.965735i \(0.583568\pi\)
\(488\) 0 0
\(489\) 48.7422 2.20420
\(490\) 0 0
\(491\) 37.5161 1.69308 0.846538 0.532329i \(-0.178683\pi\)
0.846538 + 0.532329i \(0.178683\pi\)
\(492\) 0 0
\(493\) 4.96869 0.223778
\(494\) 0 0
\(495\) 1.46514 0.0658530
\(496\) 0 0
\(497\) −5.28739 −0.237172
\(498\) 0 0
\(499\) −31.5209 −1.41107 −0.705535 0.708675i \(-0.749293\pi\)
−0.705535 + 0.708675i \(0.749293\pi\)
\(500\) 0 0
\(501\) −7.43684 −0.332253
\(502\) 0 0
\(503\) −17.2991 −0.771331 −0.385665 0.922639i \(-0.626028\pi\)
−0.385665 + 0.922639i \(0.626028\pi\)
\(504\) 0 0
\(505\) 44.4693 1.97886
\(506\) 0 0
\(507\) −40.9857 −1.82024
\(508\) 0 0
\(509\) 28.4219 1.25978 0.629889 0.776685i \(-0.283100\pi\)
0.629889 + 0.776685i \(0.283100\pi\)
\(510\) 0 0
\(511\) 55.2120 2.44243
\(512\) 0 0
\(513\) 12.8271 0.566332
\(514\) 0 0
\(515\) 19.9050 0.877119
\(516\) 0 0
\(517\) 0.127626 0.00561297
\(518\) 0 0
\(519\) −32.2589 −1.41601
\(520\) 0 0
\(521\) −18.2741 −0.800605 −0.400302 0.916383i \(-0.631095\pi\)
−0.400302 + 0.916383i \(0.631095\pi\)
\(522\) 0 0
\(523\) −30.7736 −1.34564 −0.672818 0.739808i \(-0.734916\pi\)
−0.672818 + 0.739808i \(0.734916\pi\)
\(524\) 0 0
\(525\) −42.2730 −1.84494
\(526\) 0 0
\(527\) −30.8512 −1.34390
\(528\) 0 0
\(529\) −17.3381 −0.753829
\(530\) 0 0
\(531\) 2.47548 0.107427
\(532\) 0 0
\(533\) −1.82579 −0.0790837
\(534\) 0 0
\(535\) −19.1867 −0.829514
\(536\) 0 0
\(537\) −51.3729 −2.21690
\(538\) 0 0
\(539\) −0.682420 −0.0293939
\(540\) 0 0
\(541\) 25.4739 1.09521 0.547603 0.836738i \(-0.315540\pi\)
0.547603 + 0.836738i \(0.315540\pi\)
\(542\) 0 0
\(543\) −0.882415 −0.0378681
\(544\) 0 0
\(545\) 22.2423 0.952755
\(546\) 0 0
\(547\) 8.57681 0.366718 0.183359 0.983046i \(-0.441303\pi\)
0.183359 + 0.983046i \(0.441303\pi\)
\(548\) 0 0
\(549\) −73.0834 −3.11912
\(550\) 0 0
\(551\) 1.44989 0.0617673
\(552\) 0 0
\(553\) 4.05578 0.172469
\(554\) 0 0
\(555\) 65.8371 2.79463
\(556\) 0 0
\(557\) −10.3323 −0.437793 −0.218896 0.975748i \(-0.570246\pi\)
−0.218896 + 0.975748i \(0.570246\pi\)
\(558\) 0 0
\(559\) 2.33275 0.0986647
\(560\) 0 0
\(561\) −0.784463 −0.0331201
\(562\) 0 0
\(563\) −9.82986 −0.414279 −0.207140 0.978311i \(-0.566415\pi\)
−0.207140 + 0.978311i \(0.566415\pi\)
\(564\) 0 0
\(565\) 35.6081 1.49804
\(566\) 0 0
\(567\) −79.1581 −3.32433
\(568\) 0 0
\(569\) 26.1068 1.09445 0.547227 0.836984i \(-0.315683\pi\)
0.547227 + 0.836984i \(0.315683\pi\)
\(570\) 0 0
\(571\) −10.0611 −0.421043 −0.210521 0.977589i \(-0.567516\pi\)
−0.210521 + 0.977589i \(0.567516\pi\)
\(572\) 0 0
\(573\) 45.6224 1.90590
\(574\) 0 0
\(575\) 7.82449 0.326304
\(576\) 0 0
\(577\) 33.4678 1.39328 0.696641 0.717420i \(-0.254677\pi\)
0.696641 + 0.717420i \(0.254677\pi\)
\(578\) 0 0
\(579\) 44.0966 1.83259
\(580\) 0 0
\(581\) 1.09486 0.0454225
\(582\) 0 0
\(583\) −0.238262 −0.00986781
\(584\) 0 0
\(585\) 5.34514 0.220994
\(586\) 0 0
\(587\) 39.7684 1.64142 0.820709 0.571347i \(-0.193579\pi\)
0.820709 + 0.571347i \(0.193579\pi\)
\(588\) 0 0
\(589\) −9.00254 −0.370943
\(590\) 0 0
\(591\) −34.7600 −1.42984
\(592\) 0 0
\(593\) −36.2119 −1.48704 −0.743522 0.668711i \(-0.766846\pi\)
−0.743522 + 0.668711i \(0.766846\pi\)
\(594\) 0 0
\(595\) 40.0142 1.64042
\(596\) 0 0
\(597\) 4.15555 0.170075
\(598\) 0 0
\(599\) 24.7400 1.01085 0.505424 0.862871i \(-0.331336\pi\)
0.505424 + 0.862871i \(0.331336\pi\)
\(600\) 0 0
\(601\) −3.80667 −0.155277 −0.0776387 0.996982i \(-0.524738\pi\)
−0.0776387 + 0.996982i \(0.524738\pi\)
\(602\) 0 0
\(603\) −49.7154 −2.02457
\(604\) 0 0
\(605\) 31.6534 1.28689
\(606\) 0 0
\(607\) 47.5058 1.92820 0.964100 0.265539i \(-0.0855498\pi\)
0.964100 + 0.265539i \(0.0855498\pi\)
\(608\) 0 0
\(609\) −18.6390 −0.755291
\(610\) 0 0
\(611\) 0.465606 0.0188364
\(612\) 0 0
\(613\) −6.08754 −0.245873 −0.122937 0.992415i \(-0.539231\pi\)
−0.122937 + 0.992415i \(0.539231\pi\)
\(614\) 0 0
\(615\) −63.2363 −2.54993
\(616\) 0 0
\(617\) −36.1983 −1.45729 −0.728644 0.684892i \(-0.759849\pi\)
−0.728644 + 0.684892i \(0.759849\pi\)
\(618\) 0 0
\(619\) 22.6631 0.910908 0.455454 0.890259i \(-0.349477\pi\)
0.455454 + 0.890259i \(0.349477\pi\)
\(620\) 0 0
\(621\) 30.5219 1.22480
\(622\) 0 0
\(623\) 29.9622 1.20041
\(624\) 0 0
\(625\) −30.6286 −1.22514
\(626\) 0 0
\(627\) −0.228910 −0.00914180
\(628\) 0 0
\(629\) −24.7246 −0.985835
\(630\) 0 0
\(631\) 7.22078 0.287455 0.143727 0.989617i \(-0.454091\pi\)
0.143727 + 0.989617i \(0.454091\pi\)
\(632\) 0 0
\(633\) −10.0711 −0.400291
\(634\) 0 0
\(635\) −51.3579 −2.03808
\(636\) 0 0
\(637\) −2.48962 −0.0986423
\(638\) 0 0
\(639\) 9.18674 0.363422
\(640\) 0 0
\(641\) 0.183407 0.00724413 0.00362206 0.999993i \(-0.498847\pi\)
0.00362206 + 0.999993i \(0.498847\pi\)
\(642\) 0 0
\(643\) −2.92339 −0.115287 −0.0576437 0.998337i \(-0.518359\pi\)
−0.0576437 + 0.998337i \(0.518359\pi\)
\(644\) 0 0
\(645\) 80.7948 3.18129
\(646\) 0 0
\(647\) 20.4003 0.802020 0.401010 0.916074i \(-0.368659\pi\)
0.401010 + 0.916074i \(0.368659\pi\)
\(648\) 0 0
\(649\) −0.0253697 −0.000995850 0
\(650\) 0 0
\(651\) 115.732 4.53589
\(652\) 0 0
\(653\) 35.5990 1.39310 0.696548 0.717510i \(-0.254718\pi\)
0.696548 + 0.717510i \(0.254718\pi\)
\(654\) 0 0
\(655\) 26.4015 1.03159
\(656\) 0 0
\(657\) −95.9297 −3.74257
\(658\) 0 0
\(659\) −32.2051 −1.25453 −0.627266 0.778805i \(-0.715826\pi\)
−0.627266 + 0.778805i \(0.715826\pi\)
\(660\) 0 0
\(661\) 22.2873 0.866876 0.433438 0.901183i \(-0.357300\pi\)
0.433438 + 0.901183i \(0.357300\pi\)
\(662\) 0 0
\(663\) −2.86189 −0.111147
\(664\) 0 0
\(665\) 11.6764 0.452790
\(666\) 0 0
\(667\) 3.44998 0.133584
\(668\) 0 0
\(669\) 20.6651 0.798958
\(670\) 0 0
\(671\) 0.748989 0.0289144
\(672\) 0 0
\(673\) 22.4339 0.864765 0.432383 0.901690i \(-0.357673\pi\)
0.432383 + 0.901690i \(0.357673\pi\)
\(674\) 0 0
\(675\) 42.1798 1.62350
\(676\) 0 0
\(677\) −3.13786 −0.120598 −0.0602988 0.998180i \(-0.519205\pi\)
−0.0602988 + 0.998180i \(0.519205\pi\)
\(678\) 0 0
\(679\) 11.6454 0.446910
\(680\) 0 0
\(681\) −64.7711 −2.48203
\(682\) 0 0
\(683\) 45.6673 1.74741 0.873705 0.486456i \(-0.161711\pi\)
0.873705 + 0.486456i \(0.161711\pi\)
\(684\) 0 0
\(685\) 21.1097 0.806560
\(686\) 0 0
\(687\) 61.5154 2.34696
\(688\) 0 0
\(689\) −0.869233 −0.0331151
\(690\) 0 0
\(691\) 41.8620 1.59251 0.796253 0.604964i \(-0.206812\pi\)
0.796253 + 0.604964i \(0.206812\pi\)
\(692\) 0 0
\(693\) 2.06404 0.0784066
\(694\) 0 0
\(695\) −45.1892 −1.71413
\(696\) 0 0
\(697\) 23.7479 0.899516
\(698\) 0 0
\(699\) −66.2130 −2.50441
\(700\) 0 0
\(701\) −4.08691 −0.154360 −0.0771802 0.997017i \(-0.524592\pi\)
−0.0771802 + 0.997017i \(0.524592\pi\)
\(702\) 0 0
\(703\) −7.21477 −0.272110
\(704\) 0 0
\(705\) 16.1263 0.607352
\(706\) 0 0
\(707\) 62.6471 2.35609
\(708\) 0 0
\(709\) −1.33922 −0.0502954 −0.0251477 0.999684i \(-0.508006\pi\)
−0.0251477 + 0.999684i \(0.508006\pi\)
\(710\) 0 0
\(711\) −7.04683 −0.264277
\(712\) 0 0
\(713\) −21.4213 −0.802236
\(714\) 0 0
\(715\) −0.0547793 −0.00204863
\(716\) 0 0
\(717\) 54.6721 2.04177
\(718\) 0 0
\(719\) 9.34311 0.348439 0.174220 0.984707i \(-0.444260\pi\)
0.174220 + 0.984707i \(0.444260\pi\)
\(720\) 0 0
\(721\) 28.0416 1.04432
\(722\) 0 0
\(723\) −41.5396 −1.54487
\(724\) 0 0
\(725\) 4.76770 0.177068
\(726\) 0 0
\(727\) −42.6807 −1.58294 −0.791470 0.611208i \(-0.790684\pi\)
−0.791470 + 0.611208i \(0.790684\pi\)
\(728\) 0 0
\(729\) 15.5620 0.576371
\(730\) 0 0
\(731\) −30.3419 −1.12223
\(732\) 0 0
\(733\) −27.4088 −1.01237 −0.506184 0.862425i \(-0.668944\pi\)
−0.506184 + 0.862425i \(0.668944\pi\)
\(734\) 0 0
\(735\) −86.2280 −3.18057
\(736\) 0 0
\(737\) 0.509504 0.0187678
\(738\) 0 0
\(739\) −17.9410 −0.659971 −0.329986 0.943986i \(-0.607044\pi\)
−0.329986 + 0.943986i \(0.607044\pi\)
\(740\) 0 0
\(741\) −0.835116 −0.0306787
\(742\) 0 0
\(743\) 19.8236 0.727258 0.363629 0.931544i \(-0.381538\pi\)
0.363629 + 0.931544i \(0.381538\pi\)
\(744\) 0 0
\(745\) −13.0297 −0.477370
\(746\) 0 0
\(747\) −1.90230 −0.0696015
\(748\) 0 0
\(749\) −27.0297 −0.987644
\(750\) 0 0
\(751\) 4.48804 0.163771 0.0818855 0.996642i \(-0.473906\pi\)
0.0818855 + 0.996642i \(0.473906\pi\)
\(752\) 0 0
\(753\) 53.2753 1.94146
\(754\) 0 0
\(755\) 33.7700 1.22901
\(756\) 0 0
\(757\) −24.6713 −0.896693 −0.448346 0.893860i \(-0.647987\pi\)
−0.448346 + 0.893860i \(0.647987\pi\)
\(758\) 0 0
\(759\) −0.544688 −0.0197709
\(760\) 0 0
\(761\) 11.9705 0.433931 0.216966 0.976179i \(-0.430384\pi\)
0.216966 + 0.976179i \(0.430384\pi\)
\(762\) 0 0
\(763\) 31.3343 1.13438
\(764\) 0 0
\(765\) −69.5239 −2.51364
\(766\) 0 0
\(767\) −0.0925544 −0.00334195
\(768\) 0 0
\(769\) −10.7158 −0.386422 −0.193211 0.981157i \(-0.561890\pi\)
−0.193211 + 0.981157i \(0.561890\pi\)
\(770\) 0 0
\(771\) 11.9445 0.430171
\(772\) 0 0
\(773\) 41.2708 1.48441 0.742203 0.670175i \(-0.233781\pi\)
0.742203 + 0.670175i \(0.233781\pi\)
\(774\) 0 0
\(775\) −29.6032 −1.06338
\(776\) 0 0
\(777\) 92.7494 3.32737
\(778\) 0 0
\(779\) 6.92976 0.248284
\(780\) 0 0
\(781\) −0.0941496 −0.00336894
\(782\) 0 0
\(783\) 18.5979 0.664636
\(784\) 0 0
\(785\) −50.2620 −1.79393
\(786\) 0 0
\(787\) −54.5783 −1.94551 −0.972754 0.231841i \(-0.925525\pi\)
−0.972754 + 0.231841i \(0.925525\pi\)
\(788\) 0 0
\(789\) −33.4296 −1.19013
\(790\) 0 0
\(791\) 50.1637 1.78362
\(792\) 0 0
\(793\) 2.73248 0.0970331
\(794\) 0 0
\(795\) −30.1059 −1.06775
\(796\) 0 0
\(797\) −39.6699 −1.40518 −0.702590 0.711595i \(-0.747973\pi\)
−0.702590 + 0.711595i \(0.747973\pi\)
\(798\) 0 0
\(799\) −6.05611 −0.214250
\(800\) 0 0
\(801\) −52.0588 −1.83941
\(802\) 0 0
\(803\) 0.983128 0.0346938
\(804\) 0 0
\(805\) 27.7836 0.979245
\(806\) 0 0
\(807\) −27.3207 −0.961734
\(808\) 0 0
\(809\) −46.8819 −1.64828 −0.824140 0.566386i \(-0.808341\pi\)
−0.824140 + 0.566386i \(0.808341\pi\)
\(810\) 0 0
\(811\) −27.3392 −0.960008 −0.480004 0.877266i \(-0.659365\pi\)
−0.480004 + 0.877266i \(0.659365\pi\)
\(812\) 0 0
\(813\) 48.3820 1.69683
\(814\) 0 0
\(815\) −44.2714 −1.55076
\(816\) 0 0
\(817\) −8.85392 −0.309759
\(818\) 0 0
\(819\) 7.53009 0.263123
\(820\) 0 0
\(821\) −7.08097 −0.247128 −0.123564 0.992337i \(-0.539432\pi\)
−0.123564 + 0.992337i \(0.539432\pi\)
\(822\) 0 0
\(823\) −36.5081 −1.27259 −0.636296 0.771445i \(-0.719534\pi\)
−0.636296 + 0.771445i \(0.719534\pi\)
\(824\) 0 0
\(825\) −0.752731 −0.0262067
\(826\) 0 0
\(827\) 39.9114 1.38785 0.693927 0.720045i \(-0.255879\pi\)
0.693927 + 0.720045i \(0.255879\pi\)
\(828\) 0 0
\(829\) 30.0815 1.04477 0.522387 0.852708i \(-0.325041\pi\)
0.522387 + 0.852708i \(0.325041\pi\)
\(830\) 0 0
\(831\) 41.2654 1.43148
\(832\) 0 0
\(833\) 32.3823 1.12198
\(834\) 0 0
\(835\) 6.75471 0.233756
\(836\) 0 0
\(837\) −115.477 −3.99146
\(838\) 0 0
\(839\) −42.7941 −1.47741 −0.738707 0.674026i \(-0.764563\pi\)
−0.738707 + 0.674026i \(0.764563\pi\)
\(840\) 0 0
\(841\) −26.8978 −0.927511
\(842\) 0 0
\(843\) −85.0303 −2.92860
\(844\) 0 0
\(845\) 37.2264 1.28063
\(846\) 0 0
\(847\) 44.5924 1.53221
\(848\) 0 0
\(849\) −75.4599 −2.58978
\(850\) 0 0
\(851\) −17.1674 −0.588491
\(852\) 0 0
\(853\) 7.76751 0.265954 0.132977 0.991119i \(-0.457546\pi\)
0.132977 + 0.991119i \(0.457546\pi\)
\(854\) 0 0
\(855\) −20.2874 −0.693816
\(856\) 0 0
\(857\) 6.07587 0.207548 0.103774 0.994601i \(-0.466908\pi\)
0.103774 + 0.994601i \(0.466908\pi\)
\(858\) 0 0
\(859\) 11.6755 0.398364 0.199182 0.979963i \(-0.436172\pi\)
0.199182 + 0.979963i \(0.436172\pi\)
\(860\) 0 0
\(861\) −89.0855 −3.03602
\(862\) 0 0
\(863\) −46.0962 −1.56913 −0.784566 0.620045i \(-0.787114\pi\)
−0.784566 + 0.620045i \(0.787114\pi\)
\(864\) 0 0
\(865\) 29.3001 0.996232
\(866\) 0 0
\(867\) −16.6600 −0.565803
\(868\) 0 0
\(869\) 0.0722189 0.00244986
\(870\) 0 0
\(871\) 1.85878 0.0629825
\(872\) 0 0
\(873\) −20.2337 −0.684806
\(874\) 0 0
\(875\) −19.9862 −0.675656
\(876\) 0 0
\(877\) −9.72574 −0.328415 −0.164208 0.986426i \(-0.552507\pi\)
−0.164208 + 0.986426i \(0.552507\pi\)
\(878\) 0 0
\(879\) 29.5494 0.996677
\(880\) 0 0
\(881\) −19.2462 −0.648420 −0.324210 0.945985i \(-0.605098\pi\)
−0.324210 + 0.945985i \(0.605098\pi\)
\(882\) 0 0
\(883\) −5.38468 −0.181209 −0.0906045 0.995887i \(-0.528880\pi\)
−0.0906045 + 0.995887i \(0.528880\pi\)
\(884\) 0 0
\(885\) −3.20563 −0.107756
\(886\) 0 0
\(887\) 49.2197 1.65263 0.826317 0.563205i \(-0.190432\pi\)
0.826317 + 0.563205i \(0.190432\pi\)
\(888\) 0 0
\(889\) −72.3516 −2.42659
\(890\) 0 0
\(891\) −1.40952 −0.0472208
\(892\) 0 0
\(893\) −1.76721 −0.0591373
\(894\) 0 0
\(895\) 46.6608 1.55970
\(896\) 0 0
\(897\) −1.98714 −0.0663487
\(898\) 0 0
\(899\) −13.0527 −0.435331
\(900\) 0 0
\(901\) 11.3061 0.376659
\(902\) 0 0
\(903\) 113.821 3.78774
\(904\) 0 0
\(905\) 0.801478 0.0266420
\(906\) 0 0
\(907\) −19.3743 −0.643312 −0.321656 0.946857i \(-0.604239\pi\)
−0.321656 + 0.946857i \(0.604239\pi\)
\(908\) 0 0
\(909\) −108.848 −3.61026
\(910\) 0 0
\(911\) −30.2687 −1.00285 −0.501424 0.865202i \(-0.667190\pi\)
−0.501424 + 0.865202i \(0.667190\pi\)
\(912\) 0 0
\(913\) 0.0194956 0.000645209 0
\(914\) 0 0
\(915\) 94.6395 3.12869
\(916\) 0 0
\(917\) 37.1936 1.22824
\(918\) 0 0
\(919\) 14.0107 0.462170 0.231085 0.972934i \(-0.425772\pi\)
0.231085 + 0.972934i \(0.425772\pi\)
\(920\) 0 0
\(921\) −40.3460 −1.32945
\(922\) 0 0
\(923\) −0.343478 −0.0113057
\(924\) 0 0
\(925\) −23.7245 −0.780056
\(926\) 0 0
\(927\) −48.7218 −1.60023
\(928\) 0 0
\(929\) 28.7184 0.942220 0.471110 0.882074i \(-0.343853\pi\)
0.471110 + 0.882074i \(0.343853\pi\)
\(930\) 0 0
\(931\) 9.44932 0.309689
\(932\) 0 0
\(933\) −48.6571 −1.59296
\(934\) 0 0
\(935\) 0.712510 0.0233016
\(936\) 0 0
\(937\) 27.0367 0.883250 0.441625 0.897200i \(-0.354402\pi\)
0.441625 + 0.897200i \(0.354402\pi\)
\(938\) 0 0
\(939\) 37.5852 1.22655
\(940\) 0 0
\(941\) −45.9444 −1.49774 −0.748872 0.662715i \(-0.769404\pi\)
−0.748872 + 0.662715i \(0.769404\pi\)
\(942\) 0 0
\(943\) 16.4892 0.536963
\(944\) 0 0
\(945\) 149.774 4.87216
\(946\) 0 0
\(947\) 58.2620 1.89326 0.946630 0.322323i \(-0.104464\pi\)
0.946630 + 0.322323i \(0.104464\pi\)
\(948\) 0 0
\(949\) 3.58667 0.116428
\(950\) 0 0
\(951\) −95.8424 −3.10790
\(952\) 0 0
\(953\) 44.9365 1.45564 0.727818 0.685770i \(-0.240535\pi\)
0.727818 + 0.685770i \(0.240535\pi\)
\(954\) 0 0
\(955\) −41.4378 −1.34090
\(956\) 0 0
\(957\) −0.331895 −0.0107286
\(958\) 0 0
\(959\) 29.7387 0.960314
\(960\) 0 0
\(961\) 50.0456 1.61438
\(962\) 0 0
\(963\) 46.9636 1.51338
\(964\) 0 0
\(965\) −40.0519 −1.28932
\(966\) 0 0
\(967\) 21.4529 0.689879 0.344939 0.938625i \(-0.387899\pi\)
0.344939 + 0.938625i \(0.387899\pi\)
\(968\) 0 0
\(969\) 10.8623 0.348947
\(970\) 0 0
\(971\) −52.9068 −1.69786 −0.848931 0.528504i \(-0.822753\pi\)
−0.848931 + 0.528504i \(0.822753\pi\)
\(972\) 0 0
\(973\) −63.6613 −2.04089
\(974\) 0 0
\(975\) −2.74613 −0.0879465
\(976\) 0 0
\(977\) 38.6349 1.23604 0.618020 0.786162i \(-0.287935\pi\)
0.618020 + 0.786162i \(0.287935\pi\)
\(978\) 0 0
\(979\) 0.533521 0.0170514
\(980\) 0 0
\(981\) −54.4428 −1.73822
\(982\) 0 0
\(983\) −13.2590 −0.422896 −0.211448 0.977389i \(-0.567818\pi\)
−0.211448 + 0.977389i \(0.567818\pi\)
\(984\) 0 0
\(985\) 31.5718 1.00596
\(986\) 0 0
\(987\) 22.7183 0.723131
\(988\) 0 0
\(989\) −21.0677 −0.669914
\(990\) 0 0
\(991\) 28.7796 0.914214 0.457107 0.889412i \(-0.348886\pi\)
0.457107 + 0.889412i \(0.348886\pi\)
\(992\) 0 0
\(993\) 46.2592 1.46799
\(994\) 0 0
\(995\) −3.77439 −0.119656
\(996\) 0 0
\(997\) −42.0528 −1.33183 −0.665913 0.746029i \(-0.731958\pi\)
−0.665913 + 0.746029i \(0.731958\pi\)
\(998\) 0 0
\(999\) −92.5449 −2.92799
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 \(a_p\))