Properties

Label 8008.2.a.u.1.3
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.64280\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.64280 q^{3} +2.39966 q^{5} -1.00000 q^{7} -0.301198 q^{9} +O(q^{10})\) \(q-1.64280 q^{3} +2.39966 q^{5} -1.00000 q^{7} -0.301198 q^{9} -1.00000 q^{11} -1.00000 q^{13} -3.94216 q^{15} -5.56268 q^{17} +1.34299 q^{19} +1.64280 q^{21} +2.38656 q^{23} +0.758347 q^{25} +5.42322 q^{27} -0.520193 q^{29} +8.43959 q^{31} +1.64280 q^{33} -2.39966 q^{35} -5.34732 q^{37} +1.64280 q^{39} +1.51389 q^{41} +8.44676 q^{43} -0.722772 q^{45} -0.408568 q^{47} +1.00000 q^{49} +9.13839 q^{51} +14.0707 q^{53} -2.39966 q^{55} -2.20628 q^{57} -14.2923 q^{59} +5.50404 q^{61} +0.301198 q^{63} -2.39966 q^{65} -5.69135 q^{67} -3.92064 q^{69} +12.2452 q^{71} +14.4010 q^{73} -1.24581 q^{75} +1.00000 q^{77} -16.5736 q^{79} -8.00568 q^{81} -5.85861 q^{83} -13.3485 q^{85} +0.854575 q^{87} -15.7968 q^{89} +1.00000 q^{91} -13.8646 q^{93} +3.22273 q^{95} -6.66235 q^{97} +0.301198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) −1.64280 −0.948473 −0.474236 0.880398i \(-0.657276\pi\)
−0.474236 + 0.880398i \(0.657276\pi\)
\(4\) 0 0
\(5\) 2.39966 1.07316 0.536579 0.843850i \(-0.319716\pi\)
0.536579 + 0.843850i \(0.319716\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.301198 −0.100399
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −3.94216 −1.01786
\(16\) 0 0
\(17\) −5.56268 −1.34915 −0.674574 0.738207i \(-0.735673\pi\)
−0.674574 + 0.738207i \(0.735673\pi\)
\(18\) 0 0
\(19\) 1.34299 0.308104 0.154052 0.988063i \(-0.450768\pi\)
0.154052 + 0.988063i \(0.450768\pi\)
\(20\) 0 0
\(21\) 1.64280 0.358489
\(22\) 0 0
\(23\) 2.38656 0.497631 0.248816 0.968551i \(-0.419959\pi\)
0.248816 + 0.968551i \(0.419959\pi\)
\(24\) 0 0
\(25\) 0.758347 0.151669
\(26\) 0 0
\(27\) 5.42322 1.04370
\(28\) 0 0
\(29\) −0.520193 −0.0965975 −0.0482987 0.998833i \(-0.515380\pi\)
−0.0482987 + 0.998833i \(0.515380\pi\)
\(30\) 0 0
\(31\) 8.43959 1.51579 0.757897 0.652374i \(-0.226227\pi\)
0.757897 + 0.652374i \(0.226227\pi\)
\(32\) 0 0
\(33\) 1.64280 0.285975
\(34\) 0 0
\(35\) −2.39966 −0.405616
\(36\) 0 0
\(37\) −5.34732 −0.879094 −0.439547 0.898219i \(-0.644861\pi\)
−0.439547 + 0.898219i \(0.644861\pi\)
\(38\) 0 0
\(39\) 1.64280 0.263059
\(40\) 0 0
\(41\) 1.51389 0.236429 0.118215 0.992988i \(-0.462283\pi\)
0.118215 + 0.992988i \(0.462283\pi\)
\(42\) 0 0
\(43\) 8.44676 1.28812 0.644060 0.764975i \(-0.277249\pi\)
0.644060 + 0.764975i \(0.277249\pi\)
\(44\) 0 0
\(45\) −0.722772 −0.107745
\(46\) 0 0
\(47\) −0.408568 −0.0595957 −0.0297978 0.999556i \(-0.509486\pi\)
−0.0297978 + 0.999556i \(0.509486\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 9.13839 1.27963
\(52\) 0 0
\(53\) 14.0707 1.93275 0.966377 0.257128i \(-0.0827761\pi\)
0.966377 + 0.257128i \(0.0827761\pi\)
\(54\) 0 0
\(55\) −2.39966 −0.323569
\(56\) 0 0
\(57\) −2.20628 −0.292228
\(58\) 0 0
\(59\) −14.2923 −1.86070 −0.930350 0.366673i \(-0.880497\pi\)
−0.930350 + 0.366673i \(0.880497\pi\)
\(60\) 0 0
\(61\) 5.50404 0.704720 0.352360 0.935864i \(-0.385379\pi\)
0.352360 + 0.935864i \(0.385379\pi\)
\(62\) 0 0
\(63\) 0.301198 0.0379474
\(64\) 0 0
\(65\) −2.39966 −0.297641
\(66\) 0 0
\(67\) −5.69135 −0.695309 −0.347654 0.937623i \(-0.613022\pi\)
−0.347654 + 0.937623i \(0.613022\pi\)
\(68\) 0 0
\(69\) −3.92064 −0.471990
\(70\) 0 0
\(71\) 12.2452 1.45324 0.726619 0.687040i \(-0.241090\pi\)
0.726619 + 0.687040i \(0.241090\pi\)
\(72\) 0 0
\(73\) 14.4010 1.68550 0.842752 0.538302i \(-0.180934\pi\)
0.842752 + 0.538302i \(0.180934\pi\)
\(74\) 0 0
\(75\) −1.24581 −0.143854
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −16.5736 −1.86467 −0.932336 0.361593i \(-0.882233\pi\)
−0.932336 + 0.361593i \(0.882233\pi\)
\(80\) 0 0
\(81\) −8.00568 −0.889520
\(82\) 0 0
\(83\) −5.85861 −0.643066 −0.321533 0.946898i \(-0.604198\pi\)
−0.321533 + 0.946898i \(0.604198\pi\)
\(84\) 0 0
\(85\) −13.3485 −1.44785
\(86\) 0 0
\(87\) 0.854575 0.0916200
\(88\) 0 0
\(89\) −15.7968 −1.67445 −0.837226 0.546857i \(-0.815824\pi\)
−0.837226 + 0.546857i \(0.815824\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −13.8646 −1.43769
\(94\) 0 0
\(95\) 3.22273 0.330645
\(96\) 0 0
\(97\) −6.66235 −0.676459 −0.338230 0.941064i \(-0.609828\pi\)
−0.338230 + 0.941064i \(0.609828\pi\)
\(98\) 0 0
\(99\) 0.301198 0.0302716
\(100\) 0 0
\(101\) −12.4762 −1.24143 −0.620713 0.784038i \(-0.713157\pi\)
−0.620713 + 0.784038i \(0.713157\pi\)
\(102\) 0 0
\(103\) 5.85198 0.576613 0.288306 0.957538i \(-0.406908\pi\)
0.288306 + 0.957538i \(0.406908\pi\)
\(104\) 0 0
\(105\) 3.94216 0.384716
\(106\) 0 0
\(107\) −0.437393 −0.0422843 −0.0211422 0.999776i \(-0.506730\pi\)
−0.0211422 + 0.999776i \(0.506730\pi\)
\(108\) 0 0
\(109\) −9.86084 −0.944498 −0.472249 0.881465i \(-0.656558\pi\)
−0.472249 + 0.881465i \(0.656558\pi\)
\(110\) 0 0
\(111\) 8.78460 0.833797
\(112\) 0 0
\(113\) −11.3863 −1.07113 −0.535565 0.844494i \(-0.679901\pi\)
−0.535565 + 0.844494i \(0.679901\pi\)
\(114\) 0 0
\(115\) 5.72691 0.534037
\(116\) 0 0
\(117\) 0.301198 0.0278458
\(118\) 0 0
\(119\) 5.56268 0.509930
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −2.48702 −0.224247
\(124\) 0 0
\(125\) −10.1785 −0.910393
\(126\) 0 0
\(127\) 17.7019 1.57079 0.785396 0.618993i \(-0.212459\pi\)
0.785396 + 0.618993i \(0.212459\pi\)
\(128\) 0 0
\(129\) −13.8764 −1.22175
\(130\) 0 0
\(131\) 14.0693 1.22924 0.614622 0.788822i \(-0.289309\pi\)
0.614622 + 0.788822i \(0.289309\pi\)
\(132\) 0 0
\(133\) −1.34299 −0.116452
\(134\) 0 0
\(135\) 13.0139 1.12005
\(136\) 0 0
\(137\) −10.7925 −0.922068 −0.461034 0.887382i \(-0.652521\pi\)
−0.461034 + 0.887382i \(0.652521\pi\)
\(138\) 0 0
\(139\) 4.23174 0.358932 0.179466 0.983764i \(-0.442563\pi\)
0.179466 + 0.983764i \(0.442563\pi\)
\(140\) 0 0
\(141\) 0.671196 0.0565249
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −1.24828 −0.103664
\(146\) 0 0
\(147\) −1.64280 −0.135496
\(148\) 0 0
\(149\) −16.0923 −1.31833 −0.659165 0.751998i \(-0.729090\pi\)
−0.659165 + 0.751998i \(0.729090\pi\)
\(150\) 0 0
\(151\) 4.49449 0.365756 0.182878 0.983136i \(-0.441459\pi\)
0.182878 + 0.983136i \(0.441459\pi\)
\(152\) 0 0
\(153\) 1.67547 0.135454
\(154\) 0 0
\(155\) 20.2521 1.62669
\(156\) 0 0
\(157\) −19.4728 −1.55410 −0.777050 0.629439i \(-0.783285\pi\)
−0.777050 + 0.629439i \(0.783285\pi\)
\(158\) 0 0
\(159\) −23.1153 −1.83317
\(160\) 0 0
\(161\) −2.38656 −0.188087
\(162\) 0 0
\(163\) −11.5929 −0.908025 −0.454013 0.890995i \(-0.650008\pi\)
−0.454013 + 0.890995i \(0.650008\pi\)
\(164\) 0 0
\(165\) 3.94216 0.306897
\(166\) 0 0
\(167\) 3.17478 0.245672 0.122836 0.992427i \(-0.460801\pi\)
0.122836 + 0.992427i \(0.460801\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −0.404508 −0.0309335
\(172\) 0 0
\(173\) −5.10785 −0.388343 −0.194171 0.980968i \(-0.562202\pi\)
−0.194171 + 0.980968i \(0.562202\pi\)
\(174\) 0 0
\(175\) −0.758347 −0.0573256
\(176\) 0 0
\(177\) 23.4794 1.76482
\(178\) 0 0
\(179\) −18.7568 −1.40195 −0.700974 0.713187i \(-0.747251\pi\)
−0.700974 + 0.713187i \(0.747251\pi\)
\(180\) 0 0
\(181\) 3.06001 0.227449 0.113724 0.993512i \(-0.463722\pi\)
0.113724 + 0.993512i \(0.463722\pi\)
\(182\) 0 0
\(183\) −9.04205 −0.668408
\(184\) 0 0
\(185\) −12.8317 −0.943408
\(186\) 0 0
\(187\) 5.56268 0.406783
\(188\) 0 0
\(189\) −5.42322 −0.394481
\(190\) 0 0
\(191\) 1.66617 0.120560 0.0602800 0.998182i \(-0.480801\pi\)
0.0602800 + 0.998182i \(0.480801\pi\)
\(192\) 0 0
\(193\) −22.0865 −1.58982 −0.794911 0.606726i \(-0.792483\pi\)
−0.794911 + 0.606726i \(0.792483\pi\)
\(194\) 0 0
\(195\) 3.94216 0.282304
\(196\) 0 0
\(197\) 15.4822 1.10306 0.551531 0.834155i \(-0.314044\pi\)
0.551531 + 0.834155i \(0.314044\pi\)
\(198\) 0 0
\(199\) 3.49155 0.247510 0.123755 0.992313i \(-0.460506\pi\)
0.123755 + 0.992313i \(0.460506\pi\)
\(200\) 0 0
\(201\) 9.34976 0.659481
\(202\) 0 0
\(203\) 0.520193 0.0365104
\(204\) 0 0
\(205\) 3.63281 0.253726
\(206\) 0 0
\(207\) −0.718827 −0.0499619
\(208\) 0 0
\(209\) −1.34299 −0.0928969
\(210\) 0 0
\(211\) −7.41014 −0.510135 −0.255068 0.966923i \(-0.582098\pi\)
−0.255068 + 0.966923i \(0.582098\pi\)
\(212\) 0 0
\(213\) −20.1165 −1.37836
\(214\) 0 0
\(215\) 20.2693 1.38236
\(216\) 0 0
\(217\) −8.43959 −0.572916
\(218\) 0 0
\(219\) −23.6579 −1.59865
\(220\) 0 0
\(221\) 5.56268 0.374186
\(222\) 0 0
\(223\) −21.0017 −1.40638 −0.703189 0.711003i \(-0.748241\pi\)
−0.703189 + 0.711003i \(0.748241\pi\)
\(224\) 0 0
\(225\) −0.228413 −0.0152275
\(226\) 0 0
\(227\) −2.50544 −0.166292 −0.0831459 0.996537i \(-0.526497\pi\)
−0.0831459 + 0.996537i \(0.526497\pi\)
\(228\) 0 0
\(229\) 11.2660 0.744479 0.372239 0.928137i \(-0.378590\pi\)
0.372239 + 0.928137i \(0.378590\pi\)
\(230\) 0 0
\(231\) −1.64280 −0.108089
\(232\) 0 0
\(233\) −8.20880 −0.537776 −0.268888 0.963171i \(-0.586656\pi\)
−0.268888 + 0.963171i \(0.586656\pi\)
\(234\) 0 0
\(235\) −0.980421 −0.0639556
\(236\) 0 0
\(237\) 27.2271 1.76859
\(238\) 0 0
\(239\) 14.6157 0.945411 0.472705 0.881220i \(-0.343277\pi\)
0.472705 + 0.881220i \(0.343277\pi\)
\(240\) 0 0
\(241\) −3.28925 −0.211879 −0.105940 0.994373i \(-0.533785\pi\)
−0.105940 + 0.994373i \(0.533785\pi\)
\(242\) 0 0
\(243\) −3.11789 −0.200013
\(244\) 0 0
\(245\) 2.39966 0.153308
\(246\) 0 0
\(247\) −1.34299 −0.0854527
\(248\) 0 0
\(249\) 9.62454 0.609930
\(250\) 0 0
\(251\) 3.50916 0.221496 0.110748 0.993849i \(-0.464675\pi\)
0.110748 + 0.993849i \(0.464675\pi\)
\(252\) 0 0
\(253\) −2.38656 −0.150041
\(254\) 0 0
\(255\) 21.9290 1.37325
\(256\) 0 0
\(257\) −19.4294 −1.21197 −0.605985 0.795476i \(-0.707221\pi\)
−0.605985 + 0.795476i \(0.707221\pi\)
\(258\) 0 0
\(259\) 5.34732 0.332266
\(260\) 0 0
\(261\) 0.156681 0.00969833
\(262\) 0 0
\(263\) 5.84088 0.360164 0.180082 0.983652i \(-0.442364\pi\)
0.180082 + 0.983652i \(0.442364\pi\)
\(264\) 0 0
\(265\) 33.7648 2.07415
\(266\) 0 0
\(267\) 25.9510 1.58817
\(268\) 0 0
\(269\) −1.75819 −0.107199 −0.0535993 0.998563i \(-0.517069\pi\)
−0.0535993 + 0.998563i \(0.517069\pi\)
\(270\) 0 0
\(271\) 4.64648 0.282254 0.141127 0.989992i \(-0.454927\pi\)
0.141127 + 0.989992i \(0.454927\pi\)
\(272\) 0 0
\(273\) −1.64280 −0.0994270
\(274\) 0 0
\(275\) −0.758347 −0.0457300
\(276\) 0 0
\(277\) 10.2026 0.613012 0.306506 0.951869i \(-0.400840\pi\)
0.306506 + 0.951869i \(0.400840\pi\)
\(278\) 0 0
\(279\) −2.54199 −0.152185
\(280\) 0 0
\(281\) 21.9924 1.31196 0.655978 0.754780i \(-0.272256\pi\)
0.655978 + 0.754780i \(0.272256\pi\)
\(282\) 0 0
\(283\) 3.24165 0.192696 0.0963479 0.995348i \(-0.469284\pi\)
0.0963479 + 0.995348i \(0.469284\pi\)
\(284\) 0 0
\(285\) −5.29430 −0.313607
\(286\) 0 0
\(287\) −1.51389 −0.0893619
\(288\) 0 0
\(289\) 13.9434 0.820201
\(290\) 0 0
\(291\) 10.9449 0.641603
\(292\) 0 0
\(293\) −24.1111 −1.40859 −0.704293 0.709909i \(-0.748736\pi\)
−0.704293 + 0.709909i \(0.748736\pi\)
\(294\) 0 0
\(295\) −34.2966 −1.99683
\(296\) 0 0
\(297\) −5.42322 −0.314687
\(298\) 0 0
\(299\) −2.38656 −0.138018
\(300\) 0 0
\(301\) −8.44676 −0.486863
\(302\) 0 0
\(303\) 20.4959 1.17746
\(304\) 0 0
\(305\) 13.2078 0.756277
\(306\) 0 0
\(307\) 1.81645 0.103670 0.0518350 0.998656i \(-0.483493\pi\)
0.0518350 + 0.998656i \(0.483493\pi\)
\(308\) 0 0
\(309\) −9.61365 −0.546901
\(310\) 0 0
\(311\) −5.76410 −0.326852 −0.163426 0.986556i \(-0.552255\pi\)
−0.163426 + 0.986556i \(0.552255\pi\)
\(312\) 0 0
\(313\) −24.4540 −1.38222 −0.691111 0.722749i \(-0.742878\pi\)
−0.691111 + 0.722749i \(0.742878\pi\)
\(314\) 0 0
\(315\) 0.722772 0.0407236
\(316\) 0 0
\(317\) −29.6759 −1.66677 −0.833383 0.552695i \(-0.813599\pi\)
−0.833383 + 0.552695i \(0.813599\pi\)
\(318\) 0 0
\(319\) 0.520193 0.0291252
\(320\) 0 0
\(321\) 0.718550 0.0401055
\(322\) 0 0
\(323\) −7.47065 −0.415678
\(324\) 0 0
\(325\) −0.758347 −0.0420655
\(326\) 0 0
\(327\) 16.1994 0.895830
\(328\) 0 0
\(329\) 0.408568 0.0225251
\(330\) 0 0
\(331\) 20.7437 1.14017 0.570087 0.821584i \(-0.306909\pi\)
0.570087 + 0.821584i \(0.306909\pi\)
\(332\) 0 0
\(333\) 1.61060 0.0882606
\(334\) 0 0
\(335\) −13.6573 −0.746176
\(336\) 0 0
\(337\) −2.30768 −0.125707 −0.0628536 0.998023i \(-0.520020\pi\)
−0.0628536 + 0.998023i \(0.520020\pi\)
\(338\) 0 0
\(339\) 18.7054 1.01594
\(340\) 0 0
\(341\) −8.43959 −0.457029
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −9.40819 −0.506520
\(346\) 0 0
\(347\) −18.5379 −0.995167 −0.497583 0.867416i \(-0.665779\pi\)
−0.497583 + 0.867416i \(0.665779\pi\)
\(348\) 0 0
\(349\) 27.6518 1.48017 0.740084 0.672514i \(-0.234786\pi\)
0.740084 + 0.672514i \(0.234786\pi\)
\(350\) 0 0
\(351\) −5.42322 −0.289470
\(352\) 0 0
\(353\) −13.6831 −0.728277 −0.364139 0.931345i \(-0.618637\pi\)
−0.364139 + 0.931345i \(0.618637\pi\)
\(354\) 0 0
\(355\) 29.3843 1.55956
\(356\) 0 0
\(357\) −9.13839 −0.483655
\(358\) 0 0
\(359\) −19.1398 −1.01016 −0.505081 0.863072i \(-0.668537\pi\)
−0.505081 + 0.863072i \(0.668537\pi\)
\(360\) 0 0
\(361\) −17.1964 −0.905072
\(362\) 0 0
\(363\) −1.64280 −0.0862248
\(364\) 0 0
\(365\) 34.5573 1.80881
\(366\) 0 0
\(367\) −4.48344 −0.234033 −0.117017 0.993130i \(-0.537333\pi\)
−0.117017 + 0.993130i \(0.537333\pi\)
\(368\) 0 0
\(369\) −0.455980 −0.0237374
\(370\) 0 0
\(371\) −14.0707 −0.730513
\(372\) 0 0
\(373\) 30.6354 1.58624 0.793120 0.609065i \(-0.208455\pi\)
0.793120 + 0.609065i \(0.208455\pi\)
\(374\) 0 0
\(375\) 16.7213 0.863483
\(376\) 0 0
\(377\) 0.520193 0.0267913
\(378\) 0 0
\(379\) 10.0887 0.518222 0.259111 0.965848i \(-0.416570\pi\)
0.259111 + 0.965848i \(0.416570\pi\)
\(380\) 0 0
\(381\) −29.0808 −1.48985
\(382\) 0 0
\(383\) 27.9318 1.42725 0.713625 0.700528i \(-0.247052\pi\)
0.713625 + 0.700528i \(0.247052\pi\)
\(384\) 0 0
\(385\) 2.39966 0.122298
\(386\) 0 0
\(387\) −2.54415 −0.129326
\(388\) 0 0
\(389\) 34.1525 1.73160 0.865801 0.500388i \(-0.166809\pi\)
0.865801 + 0.500388i \(0.166809\pi\)
\(390\) 0 0
\(391\) −13.2756 −0.671378
\(392\) 0 0
\(393\) −23.1132 −1.16590
\(394\) 0 0
\(395\) −39.7709 −2.00109
\(396\) 0 0
\(397\) −10.2140 −0.512626 −0.256313 0.966594i \(-0.582508\pi\)
−0.256313 + 0.966594i \(0.582508\pi\)
\(398\) 0 0
\(399\) 2.20628 0.110452
\(400\) 0 0
\(401\) −24.1600 −1.20649 −0.603247 0.797554i \(-0.706127\pi\)
−0.603247 + 0.797554i \(0.706127\pi\)
\(402\) 0 0
\(403\) −8.43959 −0.420406
\(404\) 0 0
\(405\) −19.2109 −0.954597
\(406\) 0 0
\(407\) 5.34732 0.265057
\(408\) 0 0
\(409\) −17.1025 −0.845666 −0.422833 0.906208i \(-0.638964\pi\)
−0.422833 + 0.906208i \(0.638964\pi\)
\(410\) 0 0
\(411\) 17.7300 0.874556
\(412\) 0 0
\(413\) 14.2923 0.703278
\(414\) 0 0
\(415\) −14.0586 −0.690111
\(416\) 0 0
\(417\) −6.95192 −0.340437
\(418\) 0 0
\(419\) 16.9863 0.829834 0.414917 0.909859i \(-0.363811\pi\)
0.414917 + 0.909859i \(0.363811\pi\)
\(420\) 0 0
\(421\) −26.8970 −1.31088 −0.655439 0.755248i \(-0.727516\pi\)
−0.655439 + 0.755248i \(0.727516\pi\)
\(422\) 0 0
\(423\) 0.123060 0.00598338
\(424\) 0 0
\(425\) −4.21844 −0.204624
\(426\) 0 0
\(427\) −5.50404 −0.266359
\(428\) 0 0
\(429\) −1.64280 −0.0793153
\(430\) 0 0
\(431\) 35.9479 1.73155 0.865775 0.500433i \(-0.166826\pi\)
0.865775 + 0.500433i \(0.166826\pi\)
\(432\) 0 0
\(433\) −0.938349 −0.0450942 −0.0225471 0.999746i \(-0.507178\pi\)
−0.0225471 + 0.999746i \(0.507178\pi\)
\(434\) 0 0
\(435\) 2.05069 0.0983228
\(436\) 0 0
\(437\) 3.20513 0.153322
\(438\) 0 0
\(439\) −13.0850 −0.624515 −0.312257 0.949998i \(-0.601085\pi\)
−0.312257 + 0.949998i \(0.601085\pi\)
\(440\) 0 0
\(441\) −0.301198 −0.0143428
\(442\) 0 0
\(443\) −39.1274 −1.85900 −0.929499 0.368824i \(-0.879761\pi\)
−0.929499 + 0.368824i \(0.879761\pi\)
\(444\) 0 0
\(445\) −37.9068 −1.79695
\(446\) 0 0
\(447\) 26.4364 1.25040
\(448\) 0 0
\(449\) 9.62089 0.454038 0.227019 0.973890i \(-0.427102\pi\)
0.227019 + 0.973890i \(0.427102\pi\)
\(450\) 0 0
\(451\) −1.51389 −0.0712862
\(452\) 0 0
\(453\) −7.38356 −0.346910
\(454\) 0 0
\(455\) 2.39966 0.112498
\(456\) 0 0
\(457\) −13.8035 −0.645702 −0.322851 0.946450i \(-0.604641\pi\)
−0.322851 + 0.946450i \(0.604641\pi\)
\(458\) 0 0
\(459\) −30.1676 −1.40810
\(460\) 0 0
\(461\) 32.3567 1.50700 0.753501 0.657447i \(-0.228364\pi\)
0.753501 + 0.657447i \(0.228364\pi\)
\(462\) 0 0
\(463\) −27.5056 −1.27829 −0.639147 0.769084i \(-0.720713\pi\)
−0.639147 + 0.769084i \(0.720713\pi\)
\(464\) 0 0
\(465\) −33.2702 −1.54287
\(466\) 0 0
\(467\) −1.52725 −0.0706727 −0.0353363 0.999375i \(-0.511250\pi\)
−0.0353363 + 0.999375i \(0.511250\pi\)
\(468\) 0 0
\(469\) 5.69135 0.262802
\(470\) 0 0
\(471\) 31.9900 1.47402
\(472\) 0 0
\(473\) −8.44676 −0.388383
\(474\) 0 0
\(475\) 1.01846 0.0467300
\(476\) 0 0
\(477\) −4.23806 −0.194048
\(478\) 0 0
\(479\) 7.53266 0.344176 0.172088 0.985082i \(-0.444949\pi\)
0.172088 + 0.985082i \(0.444949\pi\)
\(480\) 0 0
\(481\) 5.34732 0.243817
\(482\) 0 0
\(483\) 3.92064 0.178395
\(484\) 0 0
\(485\) −15.9874 −0.725948
\(486\) 0 0
\(487\) −24.1988 −1.09655 −0.548276 0.836297i \(-0.684716\pi\)
−0.548276 + 0.836297i \(0.684716\pi\)
\(488\) 0 0
\(489\) 19.0448 0.861237
\(490\) 0 0
\(491\) −3.32992 −0.150277 −0.0751385 0.997173i \(-0.523940\pi\)
−0.0751385 + 0.997173i \(0.523940\pi\)
\(492\) 0 0
\(493\) 2.89367 0.130324
\(494\) 0 0
\(495\) 0.722772 0.0324862
\(496\) 0 0
\(497\) −12.2452 −0.549273
\(498\) 0 0
\(499\) −31.8711 −1.42675 −0.713373 0.700785i \(-0.752833\pi\)
−0.713373 + 0.700785i \(0.752833\pi\)
\(500\) 0 0
\(501\) −5.21554 −0.233013
\(502\) 0 0
\(503\) 2.79722 0.124722 0.0623609 0.998054i \(-0.480137\pi\)
0.0623609 + 0.998054i \(0.480137\pi\)
\(504\) 0 0
\(505\) −29.9385 −1.33225
\(506\) 0 0
\(507\) −1.64280 −0.0729594
\(508\) 0 0
\(509\) −9.97182 −0.441993 −0.220997 0.975275i \(-0.570931\pi\)
−0.220997 + 0.975275i \(0.570931\pi\)
\(510\) 0 0
\(511\) −14.4010 −0.637061
\(512\) 0 0
\(513\) 7.28335 0.321568
\(514\) 0 0
\(515\) 14.0427 0.618797
\(516\) 0 0
\(517\) 0.408568 0.0179688
\(518\) 0 0
\(519\) 8.39119 0.368333
\(520\) 0 0
\(521\) −7.63123 −0.334330 −0.167165 0.985929i \(-0.553461\pi\)
−0.167165 + 0.985929i \(0.553461\pi\)
\(522\) 0 0
\(523\) −6.93305 −0.303161 −0.151581 0.988445i \(-0.548436\pi\)
−0.151581 + 0.988445i \(0.548436\pi\)
\(524\) 0 0
\(525\) 1.24581 0.0543718
\(526\) 0 0
\(527\) −46.9467 −2.04503
\(528\) 0 0
\(529\) −17.3044 −0.752363
\(530\) 0 0
\(531\) 4.30482 0.186813
\(532\) 0 0
\(533\) −1.51389 −0.0655737
\(534\) 0 0
\(535\) −1.04959 −0.0453778
\(536\) 0 0
\(537\) 30.8137 1.32971
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 7.13757 0.306868 0.153434 0.988159i \(-0.450967\pi\)
0.153434 + 0.988159i \(0.450967\pi\)
\(542\) 0 0
\(543\) −5.02700 −0.215729
\(544\) 0 0
\(545\) −23.6626 −1.01360
\(546\) 0 0
\(547\) −38.6511 −1.65260 −0.826301 0.563228i \(-0.809559\pi\)
−0.826301 + 0.563228i \(0.809559\pi\)
\(548\) 0 0
\(549\) −1.65781 −0.0707535
\(550\) 0 0
\(551\) −0.698617 −0.0297621
\(552\) 0 0
\(553\) 16.5736 0.704780
\(554\) 0 0
\(555\) 21.0800 0.894796
\(556\) 0 0
\(557\) −29.4362 −1.24725 −0.623626 0.781723i \(-0.714341\pi\)
−0.623626 + 0.781723i \(0.714341\pi\)
\(558\) 0 0
\(559\) −8.44676 −0.357260
\(560\) 0 0
\(561\) −9.13839 −0.385823
\(562\) 0 0
\(563\) −30.9492 −1.30435 −0.652177 0.758066i \(-0.726144\pi\)
−0.652177 + 0.758066i \(0.726144\pi\)
\(564\) 0 0
\(565\) −27.3231 −1.14949
\(566\) 0 0
\(567\) 8.00568 0.336207
\(568\) 0 0
\(569\) 30.8226 1.29215 0.646076 0.763273i \(-0.276409\pi\)
0.646076 + 0.763273i \(0.276409\pi\)
\(570\) 0 0
\(571\) −44.3529 −1.85611 −0.928056 0.372442i \(-0.878521\pi\)
−0.928056 + 0.372442i \(0.878521\pi\)
\(572\) 0 0
\(573\) −2.73719 −0.114348
\(574\) 0 0
\(575\) 1.80984 0.0754754
\(576\) 0 0
\(577\) 20.8723 0.868925 0.434462 0.900690i \(-0.356938\pi\)
0.434462 + 0.900690i \(0.356938\pi\)
\(578\) 0 0
\(579\) 36.2838 1.50790
\(580\) 0 0
\(581\) 5.85861 0.243056
\(582\) 0 0
\(583\) −14.0707 −0.582748
\(584\) 0 0
\(585\) 0.722772 0.0298830
\(586\) 0 0
\(587\) −15.6679 −0.646682 −0.323341 0.946283i \(-0.604806\pi\)
−0.323341 + 0.946283i \(0.604806\pi\)
\(588\) 0 0
\(589\) 11.3343 0.467023
\(590\) 0 0
\(591\) −25.4342 −1.04622
\(592\) 0 0
\(593\) 24.6491 1.01222 0.506108 0.862470i \(-0.331084\pi\)
0.506108 + 0.862470i \(0.331084\pi\)
\(594\) 0 0
\(595\) 13.3485 0.547236
\(596\) 0 0
\(597\) −5.73593 −0.234756
\(598\) 0 0
\(599\) 24.7032 1.00934 0.504672 0.863311i \(-0.331614\pi\)
0.504672 + 0.863311i \(0.331614\pi\)
\(600\) 0 0
\(601\) −4.85788 −0.198157 −0.0990785 0.995080i \(-0.531590\pi\)
−0.0990785 + 0.995080i \(0.531590\pi\)
\(602\) 0 0
\(603\) 1.71422 0.0698086
\(604\) 0 0
\(605\) 2.39966 0.0975599
\(606\) 0 0
\(607\) −16.3748 −0.664633 −0.332316 0.943168i \(-0.607830\pi\)
−0.332316 + 0.943168i \(0.607830\pi\)
\(608\) 0 0
\(609\) −0.854575 −0.0346291
\(610\) 0 0
\(611\) 0.408568 0.0165289
\(612\) 0 0
\(613\) −21.0395 −0.849779 −0.424890 0.905245i \(-0.639687\pi\)
−0.424890 + 0.905245i \(0.639687\pi\)
\(614\) 0 0
\(615\) −5.96799 −0.240652
\(616\) 0 0
\(617\) −30.6569 −1.23420 −0.617101 0.786884i \(-0.711693\pi\)
−0.617101 + 0.786884i \(0.711693\pi\)
\(618\) 0 0
\(619\) 19.5794 0.786964 0.393482 0.919332i \(-0.371270\pi\)
0.393482 + 0.919332i \(0.371270\pi\)
\(620\) 0 0
\(621\) 12.9428 0.519377
\(622\) 0 0
\(623\) 15.7968 0.632883
\(624\) 0 0
\(625\) −28.2166 −1.12867
\(626\) 0 0
\(627\) 2.20628 0.0881102
\(628\) 0 0
\(629\) 29.7454 1.18603
\(630\) 0 0
\(631\) 4.73796 0.188615 0.0943076 0.995543i \(-0.469936\pi\)
0.0943076 + 0.995543i \(0.469936\pi\)
\(632\) 0 0
\(633\) 12.1734 0.483850
\(634\) 0 0
\(635\) 42.4785 1.68571
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −3.68824 −0.145904
\(640\) 0 0
\(641\) −13.3647 −0.527873 −0.263936 0.964540i \(-0.585021\pi\)
−0.263936 + 0.964540i \(0.585021\pi\)
\(642\) 0 0
\(643\) 29.2377 1.15302 0.576511 0.817090i \(-0.304414\pi\)
0.576511 + 0.817090i \(0.304414\pi\)
\(644\) 0 0
\(645\) −33.2985 −1.31113
\(646\) 0 0
\(647\) −35.9618 −1.41381 −0.706903 0.707311i \(-0.749908\pi\)
−0.706903 + 0.707311i \(0.749908\pi\)
\(648\) 0 0
\(649\) 14.2923 0.561022
\(650\) 0 0
\(651\) 13.8646 0.543396
\(652\) 0 0
\(653\) 6.89836 0.269954 0.134977 0.990849i \(-0.456904\pi\)
0.134977 + 0.990849i \(0.456904\pi\)
\(654\) 0 0
\(655\) 33.7616 1.31917
\(656\) 0 0
\(657\) −4.33754 −0.169224
\(658\) 0 0
\(659\) −24.0182 −0.935617 −0.467808 0.883830i \(-0.654956\pi\)
−0.467808 + 0.883830i \(0.654956\pi\)
\(660\) 0 0
\(661\) 31.7016 1.23305 0.616525 0.787335i \(-0.288540\pi\)
0.616525 + 0.787335i \(0.288540\pi\)
\(662\) 0 0
\(663\) −9.13839 −0.354906
\(664\) 0 0
\(665\) −3.22273 −0.124972
\(666\) 0 0
\(667\) −1.24147 −0.0480699
\(668\) 0 0
\(669\) 34.5017 1.33391
\(670\) 0 0
\(671\) −5.50404 −0.212481
\(672\) 0 0
\(673\) 34.6161 1.33435 0.667177 0.744899i \(-0.267502\pi\)
0.667177 + 0.744899i \(0.267502\pi\)
\(674\) 0 0
\(675\) 4.11268 0.158297
\(676\) 0 0
\(677\) 25.8616 0.993941 0.496970 0.867768i \(-0.334446\pi\)
0.496970 + 0.867768i \(0.334446\pi\)
\(678\) 0 0
\(679\) 6.66235 0.255678
\(680\) 0 0
\(681\) 4.11594 0.157723
\(682\) 0 0
\(683\) 2.70904 0.103659 0.0518293 0.998656i \(-0.483495\pi\)
0.0518293 + 0.998656i \(0.483495\pi\)
\(684\) 0 0
\(685\) −25.8984 −0.989525
\(686\) 0 0
\(687\) −18.5078 −0.706118
\(688\) 0 0
\(689\) −14.0707 −0.536050
\(690\) 0 0
\(691\) 28.0188 1.06589 0.532944 0.846151i \(-0.321086\pi\)
0.532944 + 0.846151i \(0.321086\pi\)
\(692\) 0 0
\(693\) −0.301198 −0.0114416
\(694\) 0 0
\(695\) 10.1547 0.385191
\(696\) 0 0
\(697\) −8.42127 −0.318978
\(698\) 0 0
\(699\) 13.4854 0.510066
\(700\) 0 0
\(701\) 9.95128 0.375855 0.187927 0.982183i \(-0.439823\pi\)
0.187927 + 0.982183i \(0.439823\pi\)
\(702\) 0 0
\(703\) −7.18143 −0.270853
\(704\) 0 0
\(705\) 1.61064 0.0606602
\(706\) 0 0
\(707\) 12.4762 0.469215
\(708\) 0 0
\(709\) −42.7166 −1.60426 −0.802129 0.597151i \(-0.796299\pi\)
−0.802129 + 0.597151i \(0.796299\pi\)
\(710\) 0 0
\(711\) 4.99193 0.187212
\(712\) 0 0
\(713\) 20.1415 0.754307
\(714\) 0 0
\(715\) 2.39966 0.0897420
\(716\) 0 0
\(717\) −24.0107 −0.896696
\(718\) 0 0
\(719\) −33.4226 −1.24645 −0.623225 0.782042i \(-0.714178\pi\)
−0.623225 + 0.782042i \(0.714178\pi\)
\(720\) 0 0
\(721\) −5.85198 −0.217939
\(722\) 0 0
\(723\) 5.40358 0.200961
\(724\) 0 0
\(725\) −0.394487 −0.0146509
\(726\) 0 0
\(727\) 29.5522 1.09603 0.548016 0.836468i \(-0.315383\pi\)
0.548016 + 0.836468i \(0.315383\pi\)
\(728\) 0 0
\(729\) 29.1391 1.07923
\(730\) 0 0
\(731\) −46.9866 −1.73786
\(732\) 0 0
\(733\) 6.64126 0.245300 0.122650 0.992450i \(-0.460861\pi\)
0.122650 + 0.992450i \(0.460861\pi\)
\(734\) 0 0
\(735\) −3.94216 −0.145409
\(736\) 0 0
\(737\) 5.69135 0.209643
\(738\) 0 0
\(739\) 20.9747 0.771568 0.385784 0.922589i \(-0.373931\pi\)
0.385784 + 0.922589i \(0.373931\pi\)
\(740\) 0 0
\(741\) 2.20628 0.0810496
\(742\) 0 0
\(743\) 19.0260 0.697995 0.348998 0.937124i \(-0.386522\pi\)
0.348998 + 0.937124i \(0.386522\pi\)
\(744\) 0 0
\(745\) −38.6159 −1.41478
\(746\) 0 0
\(747\) 1.76460 0.0645634
\(748\) 0 0
\(749\) 0.437393 0.0159820
\(750\) 0 0
\(751\) −3.82055 −0.139414 −0.0697070 0.997568i \(-0.522206\pi\)
−0.0697070 + 0.997568i \(0.522206\pi\)
\(752\) 0 0
\(753\) −5.76486 −0.210083
\(754\) 0 0
\(755\) 10.7852 0.392514
\(756\) 0 0
\(757\) −9.96730 −0.362268 −0.181134 0.983458i \(-0.557977\pi\)
−0.181134 + 0.983458i \(0.557977\pi\)
\(758\) 0 0
\(759\) 3.92064 0.142310
\(760\) 0 0
\(761\) −30.1817 −1.09409 −0.547043 0.837105i \(-0.684246\pi\)
−0.547043 + 0.837105i \(0.684246\pi\)
\(762\) 0 0
\(763\) 9.86084 0.356987
\(764\) 0 0
\(765\) 4.02055 0.145363
\(766\) 0 0
\(767\) 14.2923 0.516065
\(768\) 0 0
\(769\) −30.6444 −1.10507 −0.552533 0.833491i \(-0.686339\pi\)
−0.552533 + 0.833491i \(0.686339\pi\)
\(770\) 0 0
\(771\) 31.9186 1.14952
\(772\) 0 0
\(773\) 8.77540 0.315629 0.157815 0.987469i \(-0.449555\pi\)
0.157815 + 0.987469i \(0.449555\pi\)
\(774\) 0 0
\(775\) 6.40013 0.229900
\(776\) 0 0
\(777\) −8.78460 −0.315146
\(778\) 0 0
\(779\) 2.03314 0.0728449
\(780\) 0 0
\(781\) −12.2452 −0.438168
\(782\) 0 0
\(783\) −2.82112 −0.100819
\(784\) 0 0
\(785\) −46.7281 −1.66780
\(786\) 0 0
\(787\) −34.6006 −1.23338 −0.616690 0.787206i \(-0.711527\pi\)
−0.616690 + 0.787206i \(0.711527\pi\)
\(788\) 0 0
\(789\) −9.59541 −0.341606
\(790\) 0 0
\(791\) 11.3863 0.404849
\(792\) 0 0
\(793\) −5.50404 −0.195454
\(794\) 0 0
\(795\) −55.4688 −1.96728
\(796\) 0 0
\(797\) 37.1131 1.31461 0.657307 0.753623i \(-0.271696\pi\)
0.657307 + 0.753623i \(0.271696\pi\)
\(798\) 0 0
\(799\) 2.27273 0.0804034
\(800\) 0 0
\(801\) 4.75796 0.168114
\(802\) 0 0
\(803\) −14.4010 −0.508199
\(804\) 0 0
\(805\) −5.72691 −0.201847
\(806\) 0 0
\(807\) 2.88836 0.101675
\(808\) 0 0
\(809\) −19.0435 −0.669532 −0.334766 0.942301i \(-0.608657\pi\)
−0.334766 + 0.942301i \(0.608657\pi\)
\(810\) 0 0
\(811\) −19.8623 −0.697460 −0.348730 0.937223i \(-0.613387\pi\)
−0.348730 + 0.937223i \(0.613387\pi\)
\(812\) 0 0
\(813\) −7.63325 −0.267710
\(814\) 0 0
\(815\) −27.8189 −0.974455
\(816\) 0 0
\(817\) 11.3440 0.396875
\(818\) 0 0
\(819\) −0.301198 −0.0105247
\(820\) 0 0
\(821\) 21.5743 0.752947 0.376474 0.926427i \(-0.377137\pi\)
0.376474 + 0.926427i \(0.377137\pi\)
\(822\) 0 0
\(823\) −15.9308 −0.555312 −0.277656 0.960681i \(-0.589558\pi\)
−0.277656 + 0.960681i \(0.589558\pi\)
\(824\) 0 0
\(825\) 1.24581 0.0433737
\(826\) 0 0
\(827\) −52.1864 −1.81470 −0.907349 0.420377i \(-0.861898\pi\)
−0.907349 + 0.420377i \(0.861898\pi\)
\(828\) 0 0
\(829\) −9.68440 −0.336353 −0.168177 0.985757i \(-0.553788\pi\)
−0.168177 + 0.985757i \(0.553788\pi\)
\(830\) 0 0
\(831\) −16.7608 −0.581425
\(832\) 0 0
\(833\) −5.56268 −0.192735
\(834\) 0 0
\(835\) 7.61839 0.263645
\(836\) 0 0
\(837\) 45.7697 1.58203
\(838\) 0 0
\(839\) −4.47194 −0.154388 −0.0771942 0.997016i \(-0.524596\pi\)
−0.0771942 + 0.997016i \(0.524596\pi\)
\(840\) 0 0
\(841\) −28.7294 −0.990669
\(842\) 0 0
\(843\) −36.1292 −1.24436
\(844\) 0 0
\(845\) 2.39966 0.0825507
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −5.32539 −0.182767
\(850\) 0 0
\(851\) −12.7617 −0.437465
\(852\) 0 0
\(853\) −32.6193 −1.11686 −0.558432 0.829550i \(-0.688597\pi\)
−0.558432 + 0.829550i \(0.688597\pi\)
\(854\) 0 0
\(855\) −0.970680 −0.0331965
\(856\) 0 0
\(857\) 26.4158 0.902347 0.451174 0.892436i \(-0.351006\pi\)
0.451174 + 0.892436i \(0.351006\pi\)
\(858\) 0 0
\(859\) 31.5661 1.07702 0.538511 0.842618i \(-0.318987\pi\)
0.538511 + 0.842618i \(0.318987\pi\)
\(860\) 0 0
\(861\) 2.48702 0.0847574
\(862\) 0 0
\(863\) −26.3330 −0.896385 −0.448193 0.893937i \(-0.647932\pi\)
−0.448193 + 0.893937i \(0.647932\pi\)
\(864\) 0 0
\(865\) −12.2571 −0.416753
\(866\) 0 0
\(867\) −22.9063 −0.777938
\(868\) 0 0
\(869\) 16.5736 0.562220
\(870\) 0 0
\(871\) 5.69135 0.192844
\(872\) 0 0
\(873\) 2.00669 0.0679162
\(874\) 0 0
\(875\) 10.1785 0.344096
\(876\) 0 0
\(877\) 49.7176 1.67884 0.839422 0.543480i \(-0.182894\pi\)
0.839422 + 0.543480i \(0.182894\pi\)
\(878\) 0 0
\(879\) 39.6098 1.33601
\(880\) 0 0
\(881\) −20.8053 −0.700950 −0.350475 0.936572i \(-0.613980\pi\)
−0.350475 + 0.936572i \(0.613980\pi\)
\(882\) 0 0
\(883\) 2.46311 0.0828903 0.0414452 0.999141i \(-0.486804\pi\)
0.0414452 + 0.999141i \(0.486804\pi\)
\(884\) 0 0
\(885\) 56.3426 1.89393
\(886\) 0 0
\(887\) −42.6209 −1.43107 −0.715535 0.698577i \(-0.753817\pi\)
−0.715535 + 0.698577i \(0.753817\pi\)
\(888\) 0 0
\(889\) −17.7019 −0.593704
\(890\) 0 0
\(891\) 8.00568 0.268201
\(892\) 0 0
\(893\) −0.548704 −0.0183617
\(894\) 0 0
\(895\) −45.0098 −1.50451
\(896\) 0 0
\(897\) 3.92064 0.130906
\(898\) 0 0
\(899\) −4.39022 −0.146422
\(900\) 0 0
\(901\) −78.2706 −2.60757
\(902\) 0 0
\(903\) 13.8764 0.461777
\(904\) 0 0
\(905\) 7.34298 0.244089
\(906\) 0 0
\(907\) 51.3137 1.70384 0.851922 0.523669i \(-0.175437\pi\)
0.851922 + 0.523669i \(0.175437\pi\)
\(908\) 0 0
\(909\) 3.75780 0.124638
\(910\) 0 0
\(911\) 8.21512 0.272179 0.136089 0.990697i \(-0.456547\pi\)
0.136089 + 0.990697i \(0.456547\pi\)
\(912\) 0 0
\(913\) 5.85861 0.193892
\(914\) 0 0
\(915\) −21.6978 −0.717308
\(916\) 0 0
\(917\) −14.0693 −0.464611
\(918\) 0 0
\(919\) 3.84321 0.126776 0.0633879 0.997989i \(-0.479809\pi\)
0.0633879 + 0.997989i \(0.479809\pi\)
\(920\) 0 0
\(921\) −2.98406 −0.0983282
\(922\) 0 0
\(923\) −12.2452 −0.403056
\(924\) 0 0
\(925\) −4.05513 −0.133332
\(926\) 0 0
\(927\) −1.76261 −0.0578916
\(928\) 0 0
\(929\) 36.6152 1.20130 0.600652 0.799511i \(-0.294908\pi\)
0.600652 + 0.799511i \(0.294908\pi\)
\(930\) 0 0
\(931\) 1.34299 0.0440149
\(932\) 0 0
\(933\) 9.46928 0.310010
\(934\) 0 0
\(935\) 13.3485 0.436543
\(936\) 0 0
\(937\) 28.9713 0.946451 0.473225 0.880941i \(-0.343090\pi\)
0.473225 + 0.880941i \(0.343090\pi\)
\(938\) 0 0
\(939\) 40.1731 1.31100
\(940\) 0 0
\(941\) 35.6723 1.16288 0.581441 0.813588i \(-0.302489\pi\)
0.581441 + 0.813588i \(0.302489\pi\)
\(942\) 0 0
\(943\) 3.61298 0.117655
\(944\) 0 0
\(945\) −13.0139 −0.423341
\(946\) 0 0
\(947\) 7.52494 0.244528 0.122264 0.992498i \(-0.460985\pi\)
0.122264 + 0.992498i \(0.460985\pi\)
\(948\) 0 0
\(949\) −14.4010 −0.467475
\(950\) 0 0
\(951\) 48.7517 1.58088
\(952\) 0 0
\(953\) −30.3891 −0.984401 −0.492200 0.870482i \(-0.663807\pi\)
−0.492200 + 0.870482i \(0.663807\pi\)
\(954\) 0 0
\(955\) 3.99824 0.129380
\(956\) 0 0
\(957\) −0.854575 −0.0276245
\(958\) 0 0
\(959\) 10.7925 0.348509
\(960\) 0 0
\(961\) 40.2266 1.29763
\(962\) 0 0
\(963\) 0.131742 0.00424532
\(964\) 0 0
\(965\) −53.0000 −1.70613
\(966\) 0 0
\(967\) −23.8860 −0.768121 −0.384060 0.923308i \(-0.625475\pi\)
−0.384060 + 0.923308i \(0.625475\pi\)
\(968\) 0 0
\(969\) 12.2728 0.394259
\(970\) 0 0
\(971\) 41.6845 1.33772 0.668860 0.743388i \(-0.266783\pi\)
0.668860 + 0.743388i \(0.266783\pi\)
\(972\) 0 0
\(973\) −4.23174 −0.135663
\(974\) 0 0
\(975\) 1.24581 0.0398980
\(976\) 0 0
\(977\) −39.8330 −1.27437 −0.637185 0.770711i \(-0.719901\pi\)
−0.637185 + 0.770711i \(0.719901\pi\)
\(978\) 0 0
\(979\) 15.7968 0.504866
\(980\) 0 0
\(981\) 2.97007 0.0948271
\(982\) 0 0
\(983\) −15.2512 −0.486438 −0.243219 0.969971i \(-0.578203\pi\)
−0.243219 + 0.969971i \(0.578203\pi\)
\(984\) 0 0
\(985\) 37.1519 1.18376
\(986\) 0 0
\(987\) −0.671196 −0.0213644
\(988\) 0 0
\(989\) 20.1587 0.641008
\(990\) 0 0
\(991\) −25.3637 −0.805705 −0.402853 0.915265i \(-0.631981\pi\)
−0.402853 + 0.915265i \(0.631981\pi\)
\(992\) 0 0
\(993\) −34.0777 −1.08142
\(994\) 0 0
\(995\) 8.37852 0.265617
\(996\) 0 0
\(997\) −31.1588 −0.986809 −0.493404 0.869800i \(-0.664248\pi\)
−0.493404 + 0.869800i \(0.664248\pi\)
\(998\) 0 0
\(999\) −28.9997 −0.917510
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 \(a_p\))