Properties

Label 6008.2.a.e.1.10
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 1.10
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.26403 q^{3} -1.66165 q^{5} -0.979480 q^{7} +2.12585 q^{9} +O(q^{10})\) \(q-2.26403 q^{3} -1.66165 q^{5} -0.979480 q^{7} +2.12585 q^{9} +5.43078 q^{11} +0.178916 q^{13} +3.76204 q^{15} +5.72760 q^{17} -3.83378 q^{19} +2.21758 q^{21} +2.87593 q^{23} -2.23890 q^{25} +1.97911 q^{27} +8.38444 q^{29} +3.31090 q^{31} -12.2955 q^{33} +1.62756 q^{35} -0.842185 q^{37} -0.405071 q^{39} +1.22734 q^{41} -12.7081 q^{43} -3.53243 q^{45} +1.06777 q^{47} -6.04062 q^{49} -12.9675 q^{51} +8.96357 q^{53} -9.02407 q^{55} +8.67982 q^{57} +6.92183 q^{59} -4.91239 q^{61} -2.08223 q^{63} -0.297296 q^{65} +11.8860 q^{67} -6.51120 q^{69} -11.2754 q^{71} +3.04580 q^{73} +5.06896 q^{75} -5.31934 q^{77} -8.00900 q^{79} -10.8583 q^{81} +1.01756 q^{83} -9.51729 q^{85} -18.9827 q^{87} -2.43391 q^{89} -0.175244 q^{91} -7.49600 q^{93} +6.37042 q^{95} +8.02333 q^{97} +11.5450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.26403 −1.30714 −0.653570 0.756866i \(-0.726730\pi\)
−0.653570 + 0.756866i \(0.726730\pi\)
\(4\) 0 0
\(5\) −1.66165 −0.743114 −0.371557 0.928410i \(-0.621176\pi\)
−0.371557 + 0.928410i \(0.621176\pi\)
\(6\) 0 0
\(7\) −0.979480 −0.370209 −0.185104 0.982719i \(-0.559262\pi\)
−0.185104 + 0.982719i \(0.559262\pi\)
\(8\) 0 0
\(9\) 2.12585 0.708616
\(10\) 0 0
\(11\) 5.43078 1.63744 0.818720 0.574193i \(-0.194684\pi\)
0.818720 + 0.574193i \(0.194684\pi\)
\(12\) 0 0
\(13\) 0.178916 0.0496222 0.0248111 0.999692i \(-0.492102\pi\)
0.0248111 + 0.999692i \(0.492102\pi\)
\(14\) 0 0
\(15\) 3.76204 0.971355
\(16\) 0 0
\(17\) 5.72760 1.38915 0.694573 0.719422i \(-0.255593\pi\)
0.694573 + 0.719422i \(0.255593\pi\)
\(18\) 0 0
\(19\) −3.83378 −0.879530 −0.439765 0.898113i \(-0.644938\pi\)
−0.439765 + 0.898113i \(0.644938\pi\)
\(20\) 0 0
\(21\) 2.21758 0.483915
\(22\) 0 0
\(23\) 2.87593 0.599673 0.299837 0.953991i \(-0.403068\pi\)
0.299837 + 0.953991i \(0.403068\pi\)
\(24\) 0 0
\(25\) −2.23890 −0.447781
\(26\) 0 0
\(27\) 1.97911 0.380879
\(28\) 0 0
\(29\) 8.38444 1.55695 0.778476 0.627674i \(-0.215993\pi\)
0.778476 + 0.627674i \(0.215993\pi\)
\(30\) 0 0
\(31\) 3.31090 0.594656 0.297328 0.954775i \(-0.403905\pi\)
0.297328 + 0.954775i \(0.403905\pi\)
\(32\) 0 0
\(33\) −12.2955 −2.14036
\(34\) 0 0
\(35\) 1.62756 0.275107
\(36\) 0 0
\(37\) −0.842185 −0.138454 −0.0692272 0.997601i \(-0.522053\pi\)
−0.0692272 + 0.997601i \(0.522053\pi\)
\(38\) 0 0
\(39\) −0.405071 −0.0648632
\(40\) 0 0
\(41\) 1.22734 0.191678 0.0958391 0.995397i \(-0.469447\pi\)
0.0958391 + 0.995397i \(0.469447\pi\)
\(42\) 0 0
\(43\) −12.7081 −1.93796 −0.968980 0.247139i \(-0.920510\pi\)
−0.968980 + 0.247139i \(0.920510\pi\)
\(44\) 0 0
\(45\) −3.53243 −0.526583
\(46\) 0 0
\(47\) 1.06777 0.155750 0.0778748 0.996963i \(-0.475187\pi\)
0.0778748 + 0.996963i \(0.475187\pi\)
\(48\) 0 0
\(49\) −6.04062 −0.862946
\(50\) 0 0
\(51\) −12.9675 −1.81581
\(52\) 0 0
\(53\) 8.96357 1.23124 0.615621 0.788043i \(-0.288905\pi\)
0.615621 + 0.788043i \(0.288905\pi\)
\(54\) 0 0
\(55\) −9.02407 −1.21681
\(56\) 0 0
\(57\) 8.67982 1.14967
\(58\) 0 0
\(59\) 6.92183 0.901145 0.450572 0.892740i \(-0.351220\pi\)
0.450572 + 0.892740i \(0.351220\pi\)
\(60\) 0 0
\(61\) −4.91239 −0.628967 −0.314483 0.949263i \(-0.601831\pi\)
−0.314483 + 0.949263i \(0.601831\pi\)
\(62\) 0 0
\(63\) −2.08223 −0.262336
\(64\) 0 0
\(65\) −0.297296 −0.0368750
\(66\) 0 0
\(67\) 11.8860 1.45211 0.726055 0.687637i \(-0.241352\pi\)
0.726055 + 0.687637i \(0.241352\pi\)
\(68\) 0 0
\(69\) −6.51120 −0.783857
\(70\) 0 0
\(71\) −11.2754 −1.33814 −0.669071 0.743198i \(-0.733308\pi\)
−0.669071 + 0.743198i \(0.733308\pi\)
\(72\) 0 0
\(73\) 3.04580 0.356484 0.178242 0.983987i \(-0.442959\pi\)
0.178242 + 0.983987i \(0.442959\pi\)
\(74\) 0 0
\(75\) 5.06896 0.585313
\(76\) 0 0
\(77\) −5.31934 −0.606195
\(78\) 0 0
\(79\) −8.00900 −0.901083 −0.450542 0.892755i \(-0.648769\pi\)
−0.450542 + 0.892755i \(0.648769\pi\)
\(80\) 0 0
\(81\) −10.8583 −1.20648
\(82\) 0 0
\(83\) 1.01756 0.111692 0.0558458 0.998439i \(-0.482214\pi\)
0.0558458 + 0.998439i \(0.482214\pi\)
\(84\) 0 0
\(85\) −9.51729 −1.03229
\(86\) 0 0
\(87\) −18.9827 −2.03516
\(88\) 0 0
\(89\) −2.43391 −0.257994 −0.128997 0.991645i \(-0.541176\pi\)
−0.128997 + 0.991645i \(0.541176\pi\)
\(90\) 0 0
\(91\) −0.175244 −0.0183706
\(92\) 0 0
\(93\) −7.49600 −0.777299
\(94\) 0 0
\(95\) 6.37042 0.653592
\(96\) 0 0
\(97\) 8.02333 0.814645 0.407323 0.913284i \(-0.366462\pi\)
0.407323 + 0.913284i \(0.366462\pi\)
\(98\) 0 0
\(99\) 11.5450 1.16032
\(100\) 0 0
\(101\) 9.21962 0.917386 0.458693 0.888595i \(-0.348318\pi\)
0.458693 + 0.888595i \(0.348318\pi\)
\(102\) 0 0
\(103\) −15.4123 −1.51862 −0.759312 0.650727i \(-0.774464\pi\)
−0.759312 + 0.650727i \(0.774464\pi\)
\(104\) 0 0
\(105\) −3.68484 −0.359604
\(106\) 0 0
\(107\) −16.7577 −1.62003 −0.810014 0.586411i \(-0.800540\pi\)
−0.810014 + 0.586411i \(0.800540\pi\)
\(108\) 0 0
\(109\) −14.2665 −1.36648 −0.683242 0.730192i \(-0.739431\pi\)
−0.683242 + 0.730192i \(0.739431\pi\)
\(110\) 0 0
\(111\) 1.90673 0.180979
\(112\) 0 0
\(113\) −3.25926 −0.306606 −0.153303 0.988179i \(-0.548991\pi\)
−0.153303 + 0.988179i \(0.548991\pi\)
\(114\) 0 0
\(115\) −4.77880 −0.445626
\(116\) 0 0
\(117\) 0.380347 0.0351631
\(118\) 0 0
\(119\) −5.61007 −0.514274
\(120\) 0 0
\(121\) 18.4933 1.68121
\(122\) 0 0
\(123\) −2.77874 −0.250550
\(124\) 0 0
\(125\) 12.0286 1.07587
\(126\) 0 0
\(127\) 3.20059 0.284007 0.142003 0.989866i \(-0.454646\pi\)
0.142003 + 0.989866i \(0.454646\pi\)
\(128\) 0 0
\(129\) 28.7715 2.53319
\(130\) 0 0
\(131\) 18.8360 1.64571 0.822855 0.568252i \(-0.192380\pi\)
0.822855 + 0.568252i \(0.192380\pi\)
\(132\) 0 0
\(133\) 3.75511 0.325610
\(134\) 0 0
\(135\) −3.28859 −0.283037
\(136\) 0 0
\(137\) 20.8844 1.78428 0.892139 0.451761i \(-0.149204\pi\)
0.892139 + 0.451761i \(0.149204\pi\)
\(138\) 0 0
\(139\) −17.2344 −1.46180 −0.730902 0.682482i \(-0.760900\pi\)
−0.730902 + 0.682482i \(0.760900\pi\)
\(140\) 0 0
\(141\) −2.41746 −0.203587
\(142\) 0 0
\(143\) 0.971650 0.0812535
\(144\) 0 0
\(145\) −13.9320 −1.15699
\(146\) 0 0
\(147\) 13.6762 1.12799
\(148\) 0 0
\(149\) −2.22406 −0.182202 −0.0911011 0.995842i \(-0.529039\pi\)
−0.0911011 + 0.995842i \(0.529039\pi\)
\(150\) 0 0
\(151\) 9.05213 0.736652 0.368326 0.929697i \(-0.379931\pi\)
0.368326 + 0.929697i \(0.379931\pi\)
\(152\) 0 0
\(153\) 12.1760 0.984372
\(154\) 0 0
\(155\) −5.50158 −0.441897
\(156\) 0 0
\(157\) 8.73106 0.696815 0.348407 0.937343i \(-0.386723\pi\)
0.348407 + 0.937343i \(0.386723\pi\)
\(158\) 0 0
\(159\) −20.2938 −1.60941
\(160\) 0 0
\(161\) −2.81692 −0.222004
\(162\) 0 0
\(163\) 3.61608 0.283234 0.141617 0.989922i \(-0.454770\pi\)
0.141617 + 0.989922i \(0.454770\pi\)
\(164\) 0 0
\(165\) 20.4308 1.59054
\(166\) 0 0
\(167\) −3.49432 −0.270399 −0.135199 0.990818i \(-0.543168\pi\)
−0.135199 + 0.990818i \(0.543168\pi\)
\(168\) 0 0
\(169\) −12.9680 −0.997538
\(170\) 0 0
\(171\) −8.15004 −0.623250
\(172\) 0 0
\(173\) 0.0360332 0.00273955 0.00136978 0.999999i \(-0.499564\pi\)
0.00136978 + 0.999999i \(0.499564\pi\)
\(174\) 0 0
\(175\) 2.19296 0.165772
\(176\) 0 0
\(177\) −15.6712 −1.17792
\(178\) 0 0
\(179\) 2.51588 0.188046 0.0940229 0.995570i \(-0.470027\pi\)
0.0940229 + 0.995570i \(0.470027\pi\)
\(180\) 0 0
\(181\) 16.8809 1.25475 0.627375 0.778717i \(-0.284129\pi\)
0.627375 + 0.778717i \(0.284129\pi\)
\(182\) 0 0
\(183\) 11.1218 0.822148
\(184\) 0 0
\(185\) 1.39942 0.102887
\(186\) 0 0
\(187\) 31.1053 2.27464
\(188\) 0 0
\(189\) −1.93850 −0.141005
\(190\) 0 0
\(191\) −2.66698 −0.192976 −0.0964879 0.995334i \(-0.530761\pi\)
−0.0964879 + 0.995334i \(0.530761\pi\)
\(192\) 0 0
\(193\) −10.5894 −0.762239 −0.381120 0.924526i \(-0.624461\pi\)
−0.381120 + 0.924526i \(0.624461\pi\)
\(194\) 0 0
\(195\) 0.673088 0.0482008
\(196\) 0 0
\(197\) 18.2533 1.30050 0.650248 0.759722i \(-0.274665\pi\)
0.650248 + 0.759722i \(0.274665\pi\)
\(198\) 0 0
\(199\) −1.52577 −0.108159 −0.0540796 0.998537i \(-0.517222\pi\)
−0.0540796 + 0.998537i \(0.517222\pi\)
\(200\) 0 0
\(201\) −26.9104 −1.89811
\(202\) 0 0
\(203\) −8.21240 −0.576397
\(204\) 0 0
\(205\) −2.03941 −0.142439
\(206\) 0 0
\(207\) 6.11379 0.424938
\(208\) 0 0
\(209\) −20.8204 −1.44018
\(210\) 0 0
\(211\) −14.0381 −0.966423 −0.483212 0.875504i \(-0.660530\pi\)
−0.483212 + 0.875504i \(0.660530\pi\)
\(212\) 0 0
\(213\) 25.5279 1.74914
\(214\) 0 0
\(215\) 21.1164 1.44013
\(216\) 0 0
\(217\) −3.24296 −0.220147
\(218\) 0 0
\(219\) −6.89579 −0.465974
\(220\) 0 0
\(221\) 1.02476 0.0689325
\(222\) 0 0
\(223\) 0.250411 0.0167688 0.00838438 0.999965i \(-0.497331\pi\)
0.00838438 + 0.999965i \(0.497331\pi\)
\(224\) 0 0
\(225\) −4.75957 −0.317305
\(226\) 0 0
\(227\) −3.34582 −0.222070 −0.111035 0.993817i \(-0.535417\pi\)
−0.111035 + 0.993817i \(0.535417\pi\)
\(228\) 0 0
\(229\) 18.2687 1.20723 0.603615 0.797276i \(-0.293726\pi\)
0.603615 + 0.797276i \(0.293726\pi\)
\(230\) 0 0
\(231\) 12.0432 0.792381
\(232\) 0 0
\(233\) −0.764762 −0.0501012 −0.0250506 0.999686i \(-0.507975\pi\)
−0.0250506 + 0.999686i \(0.507975\pi\)
\(234\) 0 0
\(235\) −1.77426 −0.115740
\(236\) 0 0
\(237\) 18.1327 1.17784
\(238\) 0 0
\(239\) −17.8285 −1.15323 −0.576613 0.817017i \(-0.695626\pi\)
−0.576613 + 0.817017i \(0.695626\pi\)
\(240\) 0 0
\(241\) 20.9025 1.34645 0.673224 0.739439i \(-0.264909\pi\)
0.673224 + 0.739439i \(0.264909\pi\)
\(242\) 0 0
\(243\) 18.6463 1.19616
\(244\) 0 0
\(245\) 10.0374 0.641267
\(246\) 0 0
\(247\) −0.685923 −0.0436443
\(248\) 0 0
\(249\) −2.30379 −0.145997
\(250\) 0 0
\(251\) 3.75897 0.237264 0.118632 0.992938i \(-0.462149\pi\)
0.118632 + 0.992938i \(0.462149\pi\)
\(252\) 0 0
\(253\) 15.6185 0.981929
\(254\) 0 0
\(255\) 21.5475 1.34935
\(256\) 0 0
\(257\) 22.3760 1.39578 0.697890 0.716205i \(-0.254123\pi\)
0.697890 + 0.716205i \(0.254123\pi\)
\(258\) 0 0
\(259\) 0.824903 0.0512570
\(260\) 0 0
\(261\) 17.8241 1.10328
\(262\) 0 0
\(263\) 13.8294 0.852754 0.426377 0.904545i \(-0.359790\pi\)
0.426377 + 0.904545i \(0.359790\pi\)
\(264\) 0 0
\(265\) −14.8944 −0.914953
\(266\) 0 0
\(267\) 5.51046 0.337235
\(268\) 0 0
\(269\) 17.2641 1.05261 0.526305 0.850296i \(-0.323577\pi\)
0.526305 + 0.850296i \(0.323577\pi\)
\(270\) 0 0
\(271\) 3.32946 0.202250 0.101125 0.994874i \(-0.467756\pi\)
0.101125 + 0.994874i \(0.467756\pi\)
\(272\) 0 0
\(273\) 0.396759 0.0240129
\(274\) 0 0
\(275\) −12.1590 −0.733215
\(276\) 0 0
\(277\) 13.1006 0.787138 0.393569 0.919295i \(-0.371240\pi\)
0.393569 + 0.919295i \(0.371240\pi\)
\(278\) 0 0
\(279\) 7.03848 0.421383
\(280\) 0 0
\(281\) −16.6320 −0.992180 −0.496090 0.868271i \(-0.665231\pi\)
−0.496090 + 0.868271i \(0.665231\pi\)
\(282\) 0 0
\(283\) 3.62675 0.215588 0.107794 0.994173i \(-0.465621\pi\)
0.107794 + 0.994173i \(0.465621\pi\)
\(284\) 0 0
\(285\) −14.4229 −0.854336
\(286\) 0 0
\(287\) −1.20215 −0.0709609
\(288\) 0 0
\(289\) 15.8054 0.929727
\(290\) 0 0
\(291\) −18.1651 −1.06486
\(292\) 0 0
\(293\) 6.69323 0.391023 0.195511 0.980701i \(-0.437363\pi\)
0.195511 + 0.980701i \(0.437363\pi\)
\(294\) 0 0
\(295\) −11.5017 −0.669654
\(296\) 0 0
\(297\) 10.7481 0.623667
\(298\) 0 0
\(299\) 0.514549 0.0297571
\(300\) 0 0
\(301\) 12.4473 0.717450
\(302\) 0 0
\(303\) −20.8735 −1.19915
\(304\) 0 0
\(305\) 8.16269 0.467394
\(306\) 0 0
\(307\) −14.4802 −0.826426 −0.413213 0.910634i \(-0.635594\pi\)
−0.413213 + 0.910634i \(0.635594\pi\)
\(308\) 0 0
\(309\) 34.8941 1.98505
\(310\) 0 0
\(311\) 7.71988 0.437754 0.218877 0.975752i \(-0.429761\pi\)
0.218877 + 0.975752i \(0.429761\pi\)
\(312\) 0 0
\(313\) 12.8620 0.727001 0.363501 0.931594i \(-0.381581\pi\)
0.363501 + 0.931594i \(0.381581\pi\)
\(314\) 0 0
\(315\) 3.45994 0.194946
\(316\) 0 0
\(317\) 29.2697 1.64395 0.821975 0.569524i \(-0.192872\pi\)
0.821975 + 0.569524i \(0.192872\pi\)
\(318\) 0 0
\(319\) 45.5340 2.54942
\(320\) 0 0
\(321\) 37.9400 2.11760
\(322\) 0 0
\(323\) −21.9584 −1.22180
\(324\) 0 0
\(325\) −0.400575 −0.0222199
\(326\) 0 0
\(327\) 32.2999 1.78619
\(328\) 0 0
\(329\) −1.04585 −0.0576598
\(330\) 0 0
\(331\) 15.4862 0.851199 0.425600 0.904912i \(-0.360063\pi\)
0.425600 + 0.904912i \(0.360063\pi\)
\(332\) 0 0
\(333\) −1.79036 −0.0981110
\(334\) 0 0
\(335\) −19.7505 −1.07908
\(336\) 0 0
\(337\) −5.24216 −0.285559 −0.142779 0.989755i \(-0.545604\pi\)
−0.142779 + 0.989755i \(0.545604\pi\)
\(338\) 0 0
\(339\) 7.37908 0.400777
\(340\) 0 0
\(341\) 17.9808 0.973714
\(342\) 0 0
\(343\) 12.7730 0.689679
\(344\) 0 0
\(345\) 10.8194 0.582495
\(346\) 0 0
\(347\) −2.71707 −0.145860 −0.0729299 0.997337i \(-0.523235\pi\)
−0.0729299 + 0.997337i \(0.523235\pi\)
\(348\) 0 0
\(349\) −21.4831 −1.14996 −0.574981 0.818167i \(-0.694991\pi\)
−0.574981 + 0.818167i \(0.694991\pi\)
\(350\) 0 0
\(351\) 0.354093 0.0189001
\(352\) 0 0
\(353\) 8.28668 0.441056 0.220528 0.975381i \(-0.429222\pi\)
0.220528 + 0.975381i \(0.429222\pi\)
\(354\) 0 0
\(355\) 18.7358 0.994393
\(356\) 0 0
\(357\) 12.7014 0.672228
\(358\) 0 0
\(359\) −18.5078 −0.976802 −0.488401 0.872619i \(-0.662420\pi\)
−0.488401 + 0.872619i \(0.662420\pi\)
\(360\) 0 0
\(361\) −4.30210 −0.226426
\(362\) 0 0
\(363\) −41.8695 −2.19758
\(364\) 0 0
\(365\) −5.06106 −0.264908
\(366\) 0 0
\(367\) −4.92044 −0.256845 −0.128422 0.991720i \(-0.540991\pi\)
−0.128422 + 0.991720i \(0.540991\pi\)
\(368\) 0 0
\(369\) 2.60914 0.135826
\(370\) 0 0
\(371\) −8.77964 −0.455816
\(372\) 0 0
\(373\) 24.1125 1.24850 0.624249 0.781225i \(-0.285405\pi\)
0.624249 + 0.781225i \(0.285405\pi\)
\(374\) 0 0
\(375\) −27.2331 −1.40631
\(376\) 0 0
\(377\) 1.50011 0.0772595
\(378\) 0 0
\(379\) −0.0153170 −0.000786782 0 −0.000393391 1.00000i \(-0.500125\pi\)
−0.000393391 1.00000i \(0.500125\pi\)
\(380\) 0 0
\(381\) −7.24625 −0.371237
\(382\) 0 0
\(383\) −2.44497 −0.124932 −0.0624662 0.998047i \(-0.519897\pi\)
−0.0624662 + 0.998047i \(0.519897\pi\)
\(384\) 0 0
\(385\) 8.83890 0.450472
\(386\) 0 0
\(387\) −27.0154 −1.37327
\(388\) 0 0
\(389\) 16.0535 0.813943 0.406972 0.913441i \(-0.366585\pi\)
0.406972 + 0.913441i \(0.366585\pi\)
\(390\) 0 0
\(391\) 16.4722 0.833034
\(392\) 0 0
\(393\) −42.6454 −2.15117
\(394\) 0 0
\(395\) 13.3082 0.669608
\(396\) 0 0
\(397\) −6.41688 −0.322054 −0.161027 0.986950i \(-0.551481\pi\)
−0.161027 + 0.986950i \(0.551481\pi\)
\(398\) 0 0
\(399\) −8.50171 −0.425618
\(400\) 0 0
\(401\) −33.7360 −1.68469 −0.842347 0.538936i \(-0.818826\pi\)
−0.842347 + 0.538936i \(0.818826\pi\)
\(402\) 0 0
\(403\) 0.592372 0.0295082
\(404\) 0 0
\(405\) 18.0428 0.896552
\(406\) 0 0
\(407\) −4.57372 −0.226711
\(408\) 0 0
\(409\) 6.02435 0.297885 0.148942 0.988846i \(-0.452413\pi\)
0.148942 + 0.988846i \(0.452413\pi\)
\(410\) 0 0
\(411\) −47.2831 −2.33230
\(412\) 0 0
\(413\) −6.77979 −0.333612
\(414\) 0 0
\(415\) −1.69083 −0.0829996
\(416\) 0 0
\(417\) 39.0193 1.91078
\(418\) 0 0
\(419\) −5.29098 −0.258481 −0.129241 0.991613i \(-0.541254\pi\)
−0.129241 + 0.991613i \(0.541254\pi\)
\(420\) 0 0
\(421\) 9.21388 0.449057 0.224528 0.974468i \(-0.427916\pi\)
0.224528 + 0.974468i \(0.427916\pi\)
\(422\) 0 0
\(423\) 2.26991 0.110367
\(424\) 0 0
\(425\) −12.8235 −0.622033
\(426\) 0 0
\(427\) 4.81159 0.232849
\(428\) 0 0
\(429\) −2.19985 −0.106210
\(430\) 0 0
\(431\) −19.6790 −0.947904 −0.473952 0.880551i \(-0.657173\pi\)
−0.473952 + 0.880551i \(0.657173\pi\)
\(432\) 0 0
\(433\) 27.9843 1.34484 0.672419 0.740171i \(-0.265255\pi\)
0.672419 + 0.740171i \(0.265255\pi\)
\(434\) 0 0
\(435\) 31.5426 1.51235
\(436\) 0 0
\(437\) −11.0257 −0.527431
\(438\) 0 0
\(439\) 29.7508 1.41993 0.709965 0.704237i \(-0.248711\pi\)
0.709965 + 0.704237i \(0.248711\pi\)
\(440\) 0 0
\(441\) −12.8414 −0.611497
\(442\) 0 0
\(443\) 7.34047 0.348756 0.174378 0.984679i \(-0.444208\pi\)
0.174378 + 0.984679i \(0.444208\pi\)
\(444\) 0 0
\(445\) 4.04432 0.191719
\(446\) 0 0
\(447\) 5.03535 0.238164
\(448\) 0 0
\(449\) 33.0741 1.56086 0.780432 0.625241i \(-0.214999\pi\)
0.780432 + 0.625241i \(0.214999\pi\)
\(450\) 0 0
\(451\) 6.66540 0.313862
\(452\) 0 0
\(453\) −20.4943 −0.962908
\(454\) 0 0
\(455\) 0.291195 0.0136514
\(456\) 0 0
\(457\) −14.8955 −0.696783 −0.348391 0.937349i \(-0.613272\pi\)
−0.348391 + 0.937349i \(0.613272\pi\)
\(458\) 0 0
\(459\) 11.3355 0.529097
\(460\) 0 0
\(461\) 3.78263 0.176175 0.0880874 0.996113i \(-0.471925\pi\)
0.0880874 + 0.996113i \(0.471925\pi\)
\(462\) 0 0
\(463\) 33.0517 1.53604 0.768020 0.640425i \(-0.221242\pi\)
0.768020 + 0.640425i \(0.221242\pi\)
\(464\) 0 0
\(465\) 12.4558 0.577622
\(466\) 0 0
\(467\) 26.3185 1.21788 0.608938 0.793218i \(-0.291596\pi\)
0.608938 + 0.793218i \(0.291596\pi\)
\(468\) 0 0
\(469\) −11.6421 −0.537583
\(470\) 0 0
\(471\) −19.7674 −0.910835
\(472\) 0 0
\(473\) −69.0146 −3.17329
\(474\) 0 0
\(475\) 8.58348 0.393837
\(476\) 0 0
\(477\) 19.0552 0.872477
\(478\) 0 0
\(479\) 6.23823 0.285032 0.142516 0.989793i \(-0.454481\pi\)
0.142516 + 0.989793i \(0.454481\pi\)
\(480\) 0 0
\(481\) −0.150680 −0.00687041
\(482\) 0 0
\(483\) 6.37759 0.290191
\(484\) 0 0
\(485\) −13.3320 −0.605375
\(486\) 0 0
\(487\) −23.0600 −1.04495 −0.522473 0.852656i \(-0.674991\pi\)
−0.522473 + 0.852656i \(0.674991\pi\)
\(488\) 0 0
\(489\) −8.18694 −0.370226
\(490\) 0 0
\(491\) 29.7733 1.34365 0.671825 0.740710i \(-0.265511\pi\)
0.671825 + 0.740710i \(0.265511\pi\)
\(492\) 0 0
\(493\) 48.0227 2.16283
\(494\) 0 0
\(495\) −19.1838 −0.862248
\(496\) 0 0
\(497\) 11.0440 0.495392
\(498\) 0 0
\(499\) −17.2050 −0.770201 −0.385101 0.922875i \(-0.625833\pi\)
−0.385101 + 0.922875i \(0.625833\pi\)
\(500\) 0 0
\(501\) 7.91127 0.353449
\(502\) 0 0
\(503\) −4.89380 −0.218204 −0.109102 0.994031i \(-0.534798\pi\)
−0.109102 + 0.994031i \(0.534798\pi\)
\(504\) 0 0
\(505\) −15.3198 −0.681723
\(506\) 0 0
\(507\) 29.3600 1.30392
\(508\) 0 0
\(509\) 6.85542 0.303861 0.151931 0.988391i \(-0.451451\pi\)
0.151931 + 0.988391i \(0.451451\pi\)
\(510\) 0 0
\(511\) −2.98330 −0.131973
\(512\) 0 0
\(513\) −7.58747 −0.334995
\(514\) 0 0
\(515\) 25.6100 1.12851
\(516\) 0 0
\(517\) 5.79879 0.255031
\(518\) 0 0
\(519\) −0.0815804 −0.00358098
\(520\) 0 0
\(521\) −10.1445 −0.444439 −0.222219 0.974997i \(-0.571330\pi\)
−0.222219 + 0.974997i \(0.571330\pi\)
\(522\) 0 0
\(523\) −10.5709 −0.462234 −0.231117 0.972926i \(-0.574238\pi\)
−0.231117 + 0.972926i \(0.574238\pi\)
\(524\) 0 0
\(525\) −4.96494 −0.216688
\(526\) 0 0
\(527\) 18.9635 0.826064
\(528\) 0 0
\(529\) −14.7290 −0.640392
\(530\) 0 0
\(531\) 14.7148 0.638566
\(532\) 0 0
\(533\) 0.219590 0.00951150
\(534\) 0 0
\(535\) 27.8455 1.20387
\(536\) 0 0
\(537\) −5.69604 −0.245802
\(538\) 0 0
\(539\) −32.8052 −1.41302
\(540\) 0 0
\(541\) −32.1438 −1.38197 −0.690984 0.722870i \(-0.742823\pi\)
−0.690984 + 0.722870i \(0.742823\pi\)
\(542\) 0 0
\(543\) −38.2190 −1.64014
\(544\) 0 0
\(545\) 23.7060 1.01545
\(546\) 0 0
\(547\) −19.1079 −0.816994 −0.408497 0.912760i \(-0.633947\pi\)
−0.408497 + 0.912760i \(0.633947\pi\)
\(548\) 0 0
\(549\) −10.4430 −0.445696
\(550\) 0 0
\(551\) −32.1441 −1.36939
\(552\) 0 0
\(553\) 7.84466 0.333589
\(554\) 0 0
\(555\) −3.16833 −0.134488
\(556\) 0 0
\(557\) 26.1988 1.11008 0.555040 0.831824i \(-0.312703\pi\)
0.555040 + 0.831824i \(0.312703\pi\)
\(558\) 0 0
\(559\) −2.27367 −0.0961659
\(560\) 0 0
\(561\) −70.4234 −2.97328
\(562\) 0 0
\(563\) −12.7816 −0.538679 −0.269340 0.963045i \(-0.586805\pi\)
−0.269340 + 0.963045i \(0.586805\pi\)
\(564\) 0 0
\(565\) 5.41577 0.227843
\(566\) 0 0
\(567\) 10.6355 0.446649
\(568\) 0 0
\(569\) 18.0571 0.756993 0.378496 0.925603i \(-0.376441\pi\)
0.378496 + 0.925603i \(0.376441\pi\)
\(570\) 0 0
\(571\) −30.2965 −1.26787 −0.633934 0.773388i \(-0.718561\pi\)
−0.633934 + 0.773388i \(0.718561\pi\)
\(572\) 0 0
\(573\) 6.03813 0.252246
\(574\) 0 0
\(575\) −6.43894 −0.268522
\(576\) 0 0
\(577\) −44.7394 −1.86253 −0.931263 0.364347i \(-0.881292\pi\)
−0.931263 + 0.364347i \(0.881292\pi\)
\(578\) 0 0
\(579\) 23.9747 0.996354
\(580\) 0 0
\(581\) −0.996678 −0.0413492
\(582\) 0 0
\(583\) 48.6791 2.01608
\(584\) 0 0
\(585\) −0.632006 −0.0261302
\(586\) 0 0
\(587\) 29.0503 1.19903 0.599517 0.800362i \(-0.295359\pi\)
0.599517 + 0.800362i \(0.295359\pi\)
\(588\) 0 0
\(589\) −12.6933 −0.523018
\(590\) 0 0
\(591\) −41.3262 −1.69993
\(592\) 0 0
\(593\) −1.45010 −0.0595486 −0.0297743 0.999557i \(-0.509479\pi\)
−0.0297743 + 0.999557i \(0.509479\pi\)
\(594\) 0 0
\(595\) 9.32199 0.382164
\(596\) 0 0
\(597\) 3.45440 0.141379
\(598\) 0 0
\(599\) −39.8479 −1.62814 −0.814071 0.580765i \(-0.802754\pi\)
−0.814071 + 0.580765i \(0.802754\pi\)
\(600\) 0 0
\(601\) −32.8004 −1.33796 −0.668978 0.743283i \(-0.733268\pi\)
−0.668978 + 0.743283i \(0.733268\pi\)
\(602\) 0 0
\(603\) 25.2679 1.02899
\(604\) 0 0
\(605\) −30.7295 −1.24933
\(606\) 0 0
\(607\) 15.2475 0.618876 0.309438 0.950920i \(-0.399859\pi\)
0.309438 + 0.950920i \(0.399859\pi\)
\(608\) 0 0
\(609\) 18.5931 0.753432
\(610\) 0 0
\(611\) 0.191040 0.00772864
\(612\) 0 0
\(613\) 21.9793 0.887734 0.443867 0.896093i \(-0.353606\pi\)
0.443867 + 0.896093i \(0.353606\pi\)
\(614\) 0 0
\(615\) 4.61730 0.186188
\(616\) 0 0
\(617\) 34.1104 1.37323 0.686616 0.727020i \(-0.259095\pi\)
0.686616 + 0.727020i \(0.259095\pi\)
\(618\) 0 0
\(619\) 44.7559 1.79889 0.899445 0.437034i \(-0.143971\pi\)
0.899445 + 0.437034i \(0.143971\pi\)
\(620\) 0 0
\(621\) 5.69178 0.228403
\(622\) 0 0
\(623\) 2.38397 0.0955117
\(624\) 0 0
\(625\) −8.79278 −0.351711
\(626\) 0 0
\(627\) 47.1381 1.88252
\(628\) 0 0
\(629\) −4.82369 −0.192333
\(630\) 0 0
\(631\) 18.7326 0.745733 0.372866 0.927885i \(-0.378375\pi\)
0.372866 + 0.927885i \(0.378375\pi\)
\(632\) 0 0
\(633\) 31.7828 1.26325
\(634\) 0 0
\(635\) −5.31828 −0.211049
\(636\) 0 0
\(637\) −1.08076 −0.0428213
\(638\) 0 0
\(639\) −23.9698 −0.948230
\(640\) 0 0
\(641\) 17.3220 0.684180 0.342090 0.939667i \(-0.388865\pi\)
0.342090 + 0.939667i \(0.388865\pi\)
\(642\) 0 0
\(643\) 19.5533 0.771107 0.385554 0.922685i \(-0.374010\pi\)
0.385554 + 0.922685i \(0.374010\pi\)
\(644\) 0 0
\(645\) −47.8082 −1.88245
\(646\) 0 0
\(647\) −32.5914 −1.28130 −0.640650 0.767833i \(-0.721335\pi\)
−0.640650 + 0.767833i \(0.721335\pi\)
\(648\) 0 0
\(649\) 37.5909 1.47557
\(650\) 0 0
\(651\) 7.34218 0.287763
\(652\) 0 0
\(653\) −43.7813 −1.71329 −0.856647 0.515903i \(-0.827457\pi\)
−0.856647 + 0.515903i \(0.827457\pi\)
\(654\) 0 0
\(655\) −31.2989 −1.22295
\(656\) 0 0
\(657\) 6.47491 0.252610
\(658\) 0 0
\(659\) −0.378588 −0.0147477 −0.00737384 0.999973i \(-0.502347\pi\)
−0.00737384 + 0.999973i \(0.502347\pi\)
\(660\) 0 0
\(661\) 24.7230 0.961613 0.480807 0.876827i \(-0.340344\pi\)
0.480807 + 0.876827i \(0.340344\pi\)
\(662\) 0 0
\(663\) −2.32008 −0.0901045
\(664\) 0 0
\(665\) −6.23970 −0.241965
\(666\) 0 0
\(667\) 24.1131 0.933662
\(668\) 0 0
\(669\) −0.566939 −0.0219191
\(670\) 0 0
\(671\) −26.6781 −1.02990
\(672\) 0 0
\(673\) 0.660271 0.0254516 0.0127258 0.999919i \(-0.495949\pi\)
0.0127258 + 0.999919i \(0.495949\pi\)
\(674\) 0 0
\(675\) −4.43103 −0.170551
\(676\) 0 0
\(677\) 46.6556 1.79312 0.896560 0.442923i \(-0.146058\pi\)
0.896560 + 0.442923i \(0.146058\pi\)
\(678\) 0 0
\(679\) −7.85869 −0.301589
\(680\) 0 0
\(681\) 7.57504 0.290276
\(682\) 0 0
\(683\) 21.9233 0.838872 0.419436 0.907785i \(-0.362228\pi\)
0.419436 + 0.907785i \(0.362228\pi\)
\(684\) 0 0
\(685\) −34.7027 −1.32592
\(686\) 0 0
\(687\) −41.3610 −1.57802
\(688\) 0 0
\(689\) 1.60372 0.0610969
\(690\) 0 0
\(691\) 10.7679 0.409629 0.204814 0.978801i \(-0.434341\pi\)
0.204814 + 0.978801i \(0.434341\pi\)
\(692\) 0 0
\(693\) −11.3081 −0.429559
\(694\) 0 0
\(695\) 28.6376 1.08629
\(696\) 0 0
\(697\) 7.02971 0.266269
\(698\) 0 0
\(699\) 1.73145 0.0654893
\(700\) 0 0
\(701\) 40.4392 1.52737 0.763683 0.645592i \(-0.223389\pi\)
0.763683 + 0.645592i \(0.223389\pi\)
\(702\) 0 0
\(703\) 3.22875 0.121775
\(704\) 0 0
\(705\) 4.01698 0.151288
\(706\) 0 0
\(707\) −9.03043 −0.339624
\(708\) 0 0
\(709\) −36.3063 −1.36351 −0.681756 0.731579i \(-0.738784\pi\)
−0.681756 + 0.731579i \(0.738784\pi\)
\(710\) 0 0
\(711\) −17.0259 −0.638522
\(712\) 0 0
\(713\) 9.52193 0.356599
\(714\) 0 0
\(715\) −1.61455 −0.0603806
\(716\) 0 0
\(717\) 40.3642 1.50743
\(718\) 0 0
\(719\) 0.569664 0.0212449 0.0106224 0.999944i \(-0.496619\pi\)
0.0106224 + 0.999944i \(0.496619\pi\)
\(720\) 0 0
\(721\) 15.0961 0.562208
\(722\) 0 0
\(723\) −47.3239 −1.76000
\(724\) 0 0
\(725\) −18.7720 −0.697174
\(726\) 0 0
\(727\) 7.00786 0.259907 0.129954 0.991520i \(-0.458517\pi\)
0.129954 + 0.991520i \(0.458517\pi\)
\(728\) 0 0
\(729\) −9.64083 −0.357068
\(730\) 0 0
\(731\) −72.7866 −2.69211
\(732\) 0 0
\(733\) −16.7943 −0.620312 −0.310156 0.950686i \(-0.600381\pi\)
−0.310156 + 0.950686i \(0.600381\pi\)
\(734\) 0 0
\(735\) −22.7251 −0.838226
\(736\) 0 0
\(737\) 64.5503 2.37774
\(738\) 0 0
\(739\) 1.10670 0.0407105 0.0203552 0.999793i \(-0.493520\pi\)
0.0203552 + 0.999793i \(0.493520\pi\)
\(740\) 0 0
\(741\) 1.55295 0.0570492
\(742\) 0 0
\(743\) 17.3023 0.634758 0.317379 0.948299i \(-0.397197\pi\)
0.317379 + 0.948299i \(0.397197\pi\)
\(744\) 0 0
\(745\) 3.69562 0.135397
\(746\) 0 0
\(747\) 2.16318 0.0791465
\(748\) 0 0
\(749\) 16.4138 0.599748
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −8.51043 −0.310137
\(754\) 0 0
\(755\) −15.0415 −0.547417
\(756\) 0 0
\(757\) 10.3633 0.376659 0.188330 0.982106i \(-0.439693\pi\)
0.188330 + 0.982106i \(0.439693\pi\)
\(758\) 0 0
\(759\) −35.3609 −1.28352
\(760\) 0 0
\(761\) −34.1482 −1.23787 −0.618935 0.785442i \(-0.712436\pi\)
−0.618935 + 0.785442i \(0.712436\pi\)
\(762\) 0 0
\(763\) 13.9738 0.505884
\(764\) 0 0
\(765\) −20.2323 −0.731501
\(766\) 0 0
\(767\) 1.23842 0.0447168
\(768\) 0 0
\(769\) −7.14196 −0.257546 −0.128773 0.991674i \(-0.541104\pi\)
−0.128773 + 0.991674i \(0.541104\pi\)
\(770\) 0 0
\(771\) −50.6601 −1.82448
\(772\) 0 0
\(773\) 32.5279 1.16995 0.584973 0.811052i \(-0.301105\pi\)
0.584973 + 0.811052i \(0.301105\pi\)
\(774\) 0 0
\(775\) −7.41280 −0.266276
\(776\) 0 0
\(777\) −1.86761 −0.0670001
\(778\) 0 0
\(779\) −4.70535 −0.168587
\(780\) 0 0
\(781\) −61.2341 −2.19113
\(782\) 0 0
\(783\) 16.5937 0.593011
\(784\) 0 0
\(785\) −14.5080 −0.517813
\(786\) 0 0
\(787\) 8.61225 0.306994 0.153497 0.988149i \(-0.450947\pi\)
0.153497 + 0.988149i \(0.450947\pi\)
\(788\) 0 0
\(789\) −31.3101 −1.11467
\(790\) 0 0
\(791\) 3.19238 0.113508
\(792\) 0 0
\(793\) −0.878902 −0.0312107
\(794\) 0 0
\(795\) 33.7213 1.19597
\(796\) 0 0
\(797\) −43.0676 −1.52553 −0.762767 0.646674i \(-0.776160\pi\)
−0.762767 + 0.646674i \(0.776160\pi\)
\(798\) 0 0
\(799\) 6.11573 0.216359
\(800\) 0 0
\(801\) −5.17413 −0.182819
\(802\) 0 0
\(803\) 16.5410 0.583721
\(804\) 0 0
\(805\) 4.68074 0.164974
\(806\) 0 0
\(807\) −39.0865 −1.37591
\(808\) 0 0
\(809\) −10.7820 −0.379076 −0.189538 0.981873i \(-0.560699\pi\)
−0.189538 + 0.981873i \(0.560699\pi\)
\(810\) 0 0
\(811\) −14.8144 −0.520203 −0.260101 0.965581i \(-0.583756\pi\)
−0.260101 + 0.965581i \(0.583756\pi\)
\(812\) 0 0
\(813\) −7.53801 −0.264369
\(814\) 0 0
\(815\) −6.00868 −0.210475
\(816\) 0 0
\(817\) 48.7199 1.70449
\(818\) 0 0
\(819\) −0.372543 −0.0130177
\(820\) 0 0
\(821\) −8.06427 −0.281445 −0.140722 0.990049i \(-0.544943\pi\)
−0.140722 + 0.990049i \(0.544943\pi\)
\(822\) 0 0
\(823\) 53.9244 1.87969 0.939843 0.341607i \(-0.110971\pi\)
0.939843 + 0.341607i \(0.110971\pi\)
\(824\) 0 0
\(825\) 27.5284 0.958414
\(826\) 0 0
\(827\) −8.70137 −0.302576 −0.151288 0.988490i \(-0.548342\pi\)
−0.151288 + 0.988490i \(0.548342\pi\)
\(828\) 0 0
\(829\) 53.9306 1.87309 0.936544 0.350550i \(-0.114005\pi\)
0.936544 + 0.350550i \(0.114005\pi\)
\(830\) 0 0
\(831\) −29.6602 −1.02890
\(832\) 0 0
\(833\) −34.5982 −1.19876
\(834\) 0 0
\(835\) 5.80636 0.200937
\(836\) 0 0
\(837\) 6.55264 0.226492
\(838\) 0 0
\(839\) −14.9345 −0.515598 −0.257799 0.966199i \(-0.582997\pi\)
−0.257799 + 0.966199i \(0.582997\pi\)
\(840\) 0 0
\(841\) 41.2989 1.42410
\(842\) 0 0
\(843\) 37.6553 1.29692
\(844\) 0 0
\(845\) 21.5483 0.741285
\(846\) 0 0
\(847\) −18.1138 −0.622399
\(848\) 0 0
\(849\) −8.21109 −0.281804
\(850\) 0 0
\(851\) −2.42206 −0.0830273
\(852\) 0 0
\(853\) −18.8964 −0.647000 −0.323500 0.946228i \(-0.604860\pi\)
−0.323500 + 0.946228i \(0.604860\pi\)
\(854\) 0 0
\(855\) 13.5426 0.463146
\(856\) 0 0
\(857\) −22.8763 −0.781441 −0.390720 0.920509i \(-0.627774\pi\)
−0.390720 + 0.920509i \(0.627774\pi\)
\(858\) 0 0
\(859\) 41.9390 1.43094 0.715471 0.698643i \(-0.246212\pi\)
0.715471 + 0.698643i \(0.246212\pi\)
\(860\) 0 0
\(861\) 2.72172 0.0927559
\(862\) 0 0
\(863\) 32.0462 1.09087 0.545433 0.838154i \(-0.316365\pi\)
0.545433 + 0.838154i \(0.316365\pi\)
\(864\) 0 0
\(865\) −0.0598747 −0.00203580
\(866\) 0 0
\(867\) −35.7839 −1.21528
\(868\) 0 0
\(869\) −43.4951 −1.47547
\(870\) 0 0
\(871\) 2.12659 0.0720569
\(872\) 0 0
\(873\) 17.0564 0.577271
\(874\) 0 0
\(875\) −11.7817 −0.398295
\(876\) 0 0
\(877\) −25.2130 −0.851382 −0.425691 0.904869i \(-0.639969\pi\)
−0.425691 + 0.904869i \(0.639969\pi\)
\(878\) 0 0
\(879\) −15.1537 −0.511121
\(880\) 0 0
\(881\) 11.0251 0.371444 0.185722 0.982602i \(-0.440538\pi\)
0.185722 + 0.982602i \(0.440538\pi\)
\(882\) 0 0
\(883\) 26.2792 0.884365 0.442183 0.896925i \(-0.354204\pi\)
0.442183 + 0.896925i \(0.354204\pi\)
\(884\) 0 0
\(885\) 26.0402 0.875332
\(886\) 0 0
\(887\) 35.3401 1.18661 0.593303 0.804979i \(-0.297824\pi\)
0.593303 + 0.804979i \(0.297824\pi\)
\(888\) 0 0
\(889\) −3.13492 −0.105142
\(890\) 0 0
\(891\) −58.9691 −1.97554
\(892\) 0 0
\(893\) −4.09358 −0.136986
\(894\) 0 0
\(895\) −4.18052 −0.139740
\(896\) 0 0
\(897\) −1.16496 −0.0388967
\(898\) 0 0
\(899\) 27.7601 0.925851
\(900\) 0 0
\(901\) 51.3397 1.71037
\(902\) 0 0
\(903\) −28.1811 −0.937807
\(904\) 0 0
\(905\) −28.0503 −0.932423
\(906\) 0 0
\(907\) −32.3037 −1.07263 −0.536313 0.844019i \(-0.680183\pi\)
−0.536313 + 0.844019i \(0.680183\pi\)
\(908\) 0 0
\(909\) 19.5995 0.650075
\(910\) 0 0
\(911\) 35.2316 1.16727 0.583637 0.812015i \(-0.301629\pi\)
0.583637 + 0.812015i \(0.301629\pi\)
\(912\) 0 0
\(913\) 5.52613 0.182888
\(914\) 0 0
\(915\) −18.4806 −0.610950
\(916\) 0 0
\(917\) −18.4495 −0.609256
\(918\) 0 0
\(919\) 39.6703 1.30860 0.654302 0.756233i \(-0.272963\pi\)
0.654302 + 0.756233i \(0.272963\pi\)
\(920\) 0 0
\(921\) 32.7836 1.08026
\(922\) 0 0
\(923\) −2.01734 −0.0664016
\(924\) 0 0
\(925\) 1.88557 0.0619972
\(926\) 0 0
\(927\) −32.7643 −1.07612
\(928\) 0 0
\(929\) −34.4231 −1.12938 −0.564692 0.825302i \(-0.691005\pi\)
−0.564692 + 0.825302i \(0.691005\pi\)
\(930\) 0 0
\(931\) 23.1584 0.758987
\(932\) 0 0
\(933\) −17.4781 −0.572206
\(934\) 0 0
\(935\) −51.6862 −1.69032
\(936\) 0 0
\(937\) −23.8436 −0.778935 −0.389468 0.921040i \(-0.627341\pi\)
−0.389468 + 0.921040i \(0.627341\pi\)
\(938\) 0 0
\(939\) −29.1199 −0.950292
\(940\) 0 0
\(941\) −49.5011 −1.61369 −0.806844 0.590764i \(-0.798826\pi\)
−0.806844 + 0.590764i \(0.798826\pi\)
\(942\) 0 0
\(943\) 3.52974 0.114944
\(944\) 0 0
\(945\) 3.22111 0.104783
\(946\) 0 0
\(947\) −42.9809 −1.39669 −0.698346 0.715760i \(-0.746080\pi\)
−0.698346 + 0.715760i \(0.746080\pi\)
\(948\) 0 0
\(949\) 0.544941 0.0176895
\(950\) 0 0
\(951\) −66.2676 −2.14887
\(952\) 0 0
\(953\) −38.4370 −1.24510 −0.622548 0.782582i \(-0.713902\pi\)
−0.622548 + 0.782582i \(0.713902\pi\)
\(954\) 0 0
\(955\) 4.43160 0.143403
\(956\) 0 0
\(957\) −103.091 −3.33245
\(958\) 0 0
\(959\) −20.4559 −0.660555
\(960\) 0 0
\(961\) −20.0379 −0.646384
\(962\) 0 0
\(963\) −35.6243 −1.14798
\(964\) 0 0
\(965\) 17.5959 0.566431
\(966\) 0 0
\(967\) −5.47739 −0.176141 −0.0880704 0.996114i \(-0.528070\pi\)
−0.0880704 + 0.996114i \(0.528070\pi\)
\(968\) 0 0
\(969\) 49.7145 1.59706
\(970\) 0 0
\(971\) 29.0325 0.931697 0.465848 0.884865i \(-0.345749\pi\)
0.465848 + 0.884865i \(0.345749\pi\)
\(972\) 0 0
\(973\) 16.8808 0.541173
\(974\) 0 0
\(975\) 0.906915 0.0290445
\(976\) 0 0
\(977\) 40.0075 1.27995 0.639977 0.768394i \(-0.278944\pi\)
0.639977 + 0.768394i \(0.278944\pi\)
\(978\) 0 0
\(979\) −13.2180 −0.422450
\(980\) 0 0
\(981\) −30.3284 −0.968313
\(982\) 0 0
\(983\) −24.4076 −0.778481 −0.389241 0.921136i \(-0.627263\pi\)
−0.389241 + 0.921136i \(0.627263\pi\)
\(984\) 0 0
\(985\) −30.3307 −0.966417
\(986\) 0 0
\(987\) 2.36785 0.0753695
\(988\) 0 0
\(989\) −36.5475 −1.16214
\(990\) 0 0
\(991\) 37.6584 1.19626 0.598129 0.801400i \(-0.295911\pi\)
0.598129 + 0.801400i \(0.295911\pi\)
\(992\) 0 0
\(993\) −35.0613 −1.11264
\(994\) 0 0
\(995\) 2.53531 0.0803747
\(996\) 0 0
\(997\) 54.7618 1.73432 0.867161 0.498028i \(-0.165942\pi\)
0.867161 + 0.498028i \(0.165942\pi\)
\(998\) 0 0
\(999\) −1.66677 −0.0527344
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 \(a_p\))