Properties

Label 8001.2.a.z.1.16
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.203292 q^{2} -1.95867 q^{4} -2.16833 q^{5} -1.00000 q^{7} +0.804765 q^{8} +O(q^{10})\) \(q-0.203292 q^{2} -1.95867 q^{4} -2.16833 q^{5} -1.00000 q^{7} +0.804765 q^{8} +0.440803 q^{10} +2.03638 q^{11} +1.83655 q^{13} +0.203292 q^{14} +3.75374 q^{16} -2.26480 q^{17} -5.79171 q^{19} +4.24705 q^{20} -0.413979 q^{22} +2.00013 q^{23} -0.298346 q^{25} -0.373355 q^{26} +1.95867 q^{28} -2.70238 q^{29} +0.925459 q^{31} -2.37263 q^{32} +0.460414 q^{34} +2.16833 q^{35} +7.11408 q^{37} +1.17741 q^{38} -1.74500 q^{40} -3.83498 q^{41} -0.434751 q^{43} -3.98860 q^{44} -0.406610 q^{46} +4.07454 q^{47} +1.00000 q^{49} +0.0606513 q^{50} -3.59720 q^{52} -6.46471 q^{53} -4.41554 q^{55} -0.804765 q^{56} +0.549370 q^{58} +13.7109 q^{59} -9.25010 q^{61} -0.188138 q^{62} -7.02515 q^{64} -3.98225 q^{65} +6.88314 q^{67} +4.43599 q^{68} -0.440803 q^{70} +14.1463 q^{71} +4.78576 q^{73} -1.44623 q^{74} +11.3441 q^{76} -2.03638 q^{77} +10.8460 q^{79} -8.13935 q^{80} +0.779619 q^{82} +4.97268 q^{83} +4.91082 q^{85} +0.0883813 q^{86} +1.63881 q^{88} -1.11999 q^{89} -1.83655 q^{91} -3.91761 q^{92} -0.828320 q^{94} +12.5583 q^{95} +7.04552 q^{97} -0.203292 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 30q^{4} - 32q^{7} + O(q^{10}) \) \( 32q + 30q^{4} - 32q^{7} - 16q^{10} - 14q^{13} + 18q^{16} - 30q^{19} - 10q^{22} + 36q^{25} - 30q^{28} - 58q^{31} - 34q^{34} + 8q^{37} - 34q^{40} + 6q^{43} - 36q^{46} + 32q^{49} - 56q^{52} - 88q^{55} - 22q^{58} - 46q^{61} + 20q^{64} - 8q^{67} + 16q^{70} - 60q^{73} - 128q^{76} - 74q^{79} - 52q^{82} - 16q^{85} - 64q^{88} + 14q^{91} - 58q^{94} - 44q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.203292 −0.143749 −0.0718744 0.997414i \(-0.522898\pi\)
−0.0718744 + 0.997414i \(0.522898\pi\)
\(3\) 0 0
\(4\) −1.95867 −0.979336
\(5\) −2.16833 −0.969707 −0.484853 0.874596i \(-0.661127\pi\)
−0.484853 + 0.874596i \(0.661127\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0.804765 0.284527
\(9\) 0 0
\(10\) 0.440803 0.139394
\(11\) 2.03638 0.613991 0.306996 0.951711i \(-0.400676\pi\)
0.306996 + 0.951711i \(0.400676\pi\)
\(12\) 0 0
\(13\) 1.83655 0.509367 0.254684 0.967024i \(-0.418029\pi\)
0.254684 + 0.967024i \(0.418029\pi\)
\(14\) 0.203292 0.0543320
\(15\) 0 0
\(16\) 3.75374 0.938436
\(17\) −2.26480 −0.549294 −0.274647 0.961545i \(-0.588561\pi\)
−0.274647 + 0.961545i \(0.588561\pi\)
\(18\) 0 0
\(19\) −5.79171 −1.32871 −0.664354 0.747418i \(-0.731293\pi\)
−0.664354 + 0.747418i \(0.731293\pi\)
\(20\) 4.24705 0.949669
\(21\) 0 0
\(22\) −0.413979 −0.0882606
\(23\) 2.00013 0.417057 0.208528 0.978016i \(-0.433133\pi\)
0.208528 + 0.978016i \(0.433133\pi\)
\(24\) 0 0
\(25\) −0.298346 −0.0596692
\(26\) −0.373355 −0.0732210
\(27\) 0 0
\(28\) 1.95867 0.370154
\(29\) −2.70238 −0.501819 −0.250909 0.968011i \(-0.580730\pi\)
−0.250909 + 0.968011i \(0.580730\pi\)
\(30\) 0 0
\(31\) 0.925459 0.166217 0.0831086 0.996540i \(-0.473515\pi\)
0.0831086 + 0.996540i \(0.473515\pi\)
\(32\) −2.37263 −0.419427
\(33\) 0 0
\(34\) 0.460414 0.0789604
\(35\) 2.16833 0.366515
\(36\) 0 0
\(37\) 7.11408 1.16955 0.584774 0.811196i \(-0.301183\pi\)
0.584774 + 0.811196i \(0.301183\pi\)
\(38\) 1.17741 0.191000
\(39\) 0 0
\(40\) −1.74500 −0.275908
\(41\) −3.83498 −0.598923 −0.299462 0.954108i \(-0.596807\pi\)
−0.299462 + 0.954108i \(0.596807\pi\)
\(42\) 0 0
\(43\) −0.434751 −0.0662989 −0.0331495 0.999450i \(-0.510554\pi\)
−0.0331495 + 0.999450i \(0.510554\pi\)
\(44\) −3.98860 −0.601304
\(45\) 0 0
\(46\) −0.406610 −0.0599514
\(47\) 4.07454 0.594333 0.297166 0.954826i \(-0.403958\pi\)
0.297166 + 0.954826i \(0.403958\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0.0606513 0.00857738
\(51\) 0 0
\(52\) −3.59720 −0.498842
\(53\) −6.46471 −0.887996 −0.443998 0.896028i \(-0.646440\pi\)
−0.443998 + 0.896028i \(0.646440\pi\)
\(54\) 0 0
\(55\) −4.41554 −0.595391
\(56\) −0.804765 −0.107541
\(57\) 0 0
\(58\) 0.549370 0.0721359
\(59\) 13.7109 1.78501 0.892504 0.451040i \(-0.148947\pi\)
0.892504 + 0.451040i \(0.148947\pi\)
\(60\) 0 0
\(61\) −9.25010 −1.18435 −0.592177 0.805808i \(-0.701731\pi\)
−0.592177 + 0.805808i \(0.701731\pi\)
\(62\) −0.188138 −0.0238935
\(63\) 0 0
\(64\) −7.02515 −0.878144
\(65\) −3.98225 −0.493937
\(66\) 0 0
\(67\) 6.88314 0.840909 0.420454 0.907314i \(-0.361871\pi\)
0.420454 + 0.907314i \(0.361871\pi\)
\(68\) 4.43599 0.537943
\(69\) 0 0
\(70\) −0.440803 −0.0526861
\(71\) 14.1463 1.67886 0.839430 0.543468i \(-0.182889\pi\)
0.839430 + 0.543468i \(0.182889\pi\)
\(72\) 0 0
\(73\) 4.78576 0.560131 0.280065 0.959981i \(-0.409644\pi\)
0.280065 + 0.959981i \(0.409644\pi\)
\(74\) −1.44623 −0.168121
\(75\) 0 0
\(76\) 11.3441 1.30125
\(77\) −2.03638 −0.232067
\(78\) 0 0
\(79\) 10.8460 1.22027 0.610135 0.792297i \(-0.291115\pi\)
0.610135 + 0.792297i \(0.291115\pi\)
\(80\) −8.13935 −0.910007
\(81\) 0 0
\(82\) 0.779619 0.0860945
\(83\) 4.97268 0.545822 0.272911 0.962039i \(-0.412013\pi\)
0.272911 + 0.962039i \(0.412013\pi\)
\(84\) 0 0
\(85\) 4.91082 0.532654
\(86\) 0.0883813 0.00953040
\(87\) 0 0
\(88\) 1.63881 0.174697
\(89\) −1.11999 −0.118719 −0.0593594 0.998237i \(-0.518906\pi\)
−0.0593594 + 0.998237i \(0.518906\pi\)
\(90\) 0 0
\(91\) −1.83655 −0.192523
\(92\) −3.91761 −0.408439
\(93\) 0 0
\(94\) −0.828320 −0.0854347
\(95\) 12.5583 1.28846
\(96\) 0 0
\(97\) 7.04552 0.715365 0.357682 0.933843i \(-0.383567\pi\)
0.357682 + 0.933843i \(0.383567\pi\)
\(98\) −0.203292 −0.0205356
\(99\) 0 0
\(100\) 0.584362 0.0584362
\(101\) −10.6965 −1.06434 −0.532170 0.846638i \(-0.678623\pi\)
−0.532170 + 0.846638i \(0.678623\pi\)
\(102\) 0 0
\(103\) −14.9318 −1.47128 −0.735638 0.677375i \(-0.763118\pi\)
−0.735638 + 0.677375i \(0.763118\pi\)
\(104\) 1.47799 0.144929
\(105\) 0 0
\(106\) 1.31422 0.127648
\(107\) 12.2693 1.18612 0.593059 0.805159i \(-0.297920\pi\)
0.593059 + 0.805159i \(0.297920\pi\)
\(108\) 0 0
\(109\) −1.53666 −0.147185 −0.0735926 0.997288i \(-0.523446\pi\)
−0.0735926 + 0.997288i \(0.523446\pi\)
\(110\) 0.897643 0.0855869
\(111\) 0 0
\(112\) −3.75374 −0.354695
\(113\) −1.85798 −0.174784 −0.0873920 0.996174i \(-0.527853\pi\)
−0.0873920 + 0.996174i \(0.527853\pi\)
\(114\) 0 0
\(115\) −4.33695 −0.404422
\(116\) 5.29307 0.491449
\(117\) 0 0
\(118\) −2.78731 −0.256593
\(119\) 2.26480 0.207614
\(120\) 0 0
\(121\) −6.85316 −0.623015
\(122\) 1.88047 0.170249
\(123\) 0 0
\(124\) −1.81267 −0.162783
\(125\) 11.4886 1.02757
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 6.17342 0.545659
\(129\) 0 0
\(130\) 0.809558 0.0710029
\(131\) 5.09715 0.445340 0.222670 0.974894i \(-0.428523\pi\)
0.222670 + 0.974894i \(0.428523\pi\)
\(132\) 0 0
\(133\) 5.79171 0.502205
\(134\) −1.39928 −0.120880
\(135\) 0 0
\(136\) −1.82263 −0.156289
\(137\) −3.51026 −0.299901 −0.149951 0.988693i \(-0.547912\pi\)
−0.149951 + 0.988693i \(0.547912\pi\)
\(138\) 0 0
\(139\) −3.28843 −0.278921 −0.139460 0.990228i \(-0.544537\pi\)
−0.139460 + 0.990228i \(0.544537\pi\)
\(140\) −4.24705 −0.358941
\(141\) 0 0
\(142\) −2.87583 −0.241334
\(143\) 3.73991 0.312747
\(144\) 0 0
\(145\) 5.85964 0.486617
\(146\) −0.972905 −0.0805182
\(147\) 0 0
\(148\) −13.9342 −1.14538
\(149\) 14.9074 1.22126 0.610630 0.791916i \(-0.290916\pi\)
0.610630 + 0.791916i \(0.290916\pi\)
\(150\) 0 0
\(151\) 7.19878 0.585828 0.292914 0.956139i \(-0.405375\pi\)
0.292914 + 0.956139i \(0.405375\pi\)
\(152\) −4.66096 −0.378054
\(153\) 0 0
\(154\) 0.413979 0.0333594
\(155\) −2.00670 −0.161182
\(156\) 0 0
\(157\) −9.94517 −0.793711 −0.396856 0.917881i \(-0.629899\pi\)
−0.396856 + 0.917881i \(0.629899\pi\)
\(158\) −2.20490 −0.175412
\(159\) 0 0
\(160\) 5.14465 0.406721
\(161\) −2.00013 −0.157633
\(162\) 0 0
\(163\) −21.0465 −1.64849 −0.824244 0.566235i \(-0.808399\pi\)
−0.824244 + 0.566235i \(0.808399\pi\)
\(164\) 7.51147 0.586547
\(165\) 0 0
\(166\) −1.01090 −0.0784614
\(167\) 9.53253 0.737649 0.368825 0.929499i \(-0.379760\pi\)
0.368825 + 0.929499i \(0.379760\pi\)
\(168\) 0 0
\(169\) −9.62708 −0.740545
\(170\) −0.998330 −0.0765684
\(171\) 0 0
\(172\) 0.851535 0.0649289
\(173\) −21.1959 −1.61150 −0.805748 0.592259i \(-0.798236\pi\)
−0.805748 + 0.592259i \(0.798236\pi\)
\(174\) 0 0
\(175\) 0.298346 0.0225528
\(176\) 7.64404 0.576191
\(177\) 0 0
\(178\) 0.227685 0.0170657
\(179\) −23.4704 −1.75426 −0.877130 0.480253i \(-0.840545\pi\)
−0.877130 + 0.480253i \(0.840545\pi\)
\(180\) 0 0
\(181\) 17.4217 1.29494 0.647471 0.762090i \(-0.275827\pi\)
0.647471 + 0.762090i \(0.275827\pi\)
\(182\) 0.373355 0.0276749
\(183\) 0 0
\(184\) 1.60964 0.118664
\(185\) −15.4257 −1.13412
\(186\) 0 0
\(187\) −4.61198 −0.337262
\(188\) −7.98069 −0.582052
\(189\) 0 0
\(190\) −2.55300 −0.185214
\(191\) −10.3025 −0.745461 −0.372730 0.927940i \(-0.621578\pi\)
−0.372730 + 0.927940i \(0.621578\pi\)
\(192\) 0 0
\(193\) −5.54183 −0.398910 −0.199455 0.979907i \(-0.563917\pi\)
−0.199455 + 0.979907i \(0.563917\pi\)
\(194\) −1.43230 −0.102833
\(195\) 0 0
\(196\) −1.95867 −0.139905
\(197\) 11.0717 0.788825 0.394413 0.918933i \(-0.370948\pi\)
0.394413 + 0.918933i \(0.370948\pi\)
\(198\) 0 0
\(199\) 13.3587 0.946970 0.473485 0.880802i \(-0.342996\pi\)
0.473485 + 0.880802i \(0.342996\pi\)
\(200\) −0.240098 −0.0169775
\(201\) 0 0
\(202\) 2.17450 0.152998
\(203\) 2.70238 0.189670
\(204\) 0 0
\(205\) 8.31550 0.580780
\(206\) 3.03552 0.211494
\(207\) 0 0
\(208\) 6.89394 0.478009
\(209\) −11.7941 −0.815816
\(210\) 0 0
\(211\) 23.3900 1.61023 0.805117 0.593117i \(-0.202103\pi\)
0.805117 + 0.593117i \(0.202103\pi\)
\(212\) 12.6622 0.869646
\(213\) 0 0
\(214\) −2.49425 −0.170503
\(215\) 0.942684 0.0642905
\(216\) 0 0
\(217\) −0.925459 −0.0628242
\(218\) 0.312390 0.0211577
\(219\) 0 0
\(220\) 8.64860 0.583088
\(221\) −4.15941 −0.279792
\(222\) 0 0
\(223\) −24.2201 −1.62190 −0.810949 0.585117i \(-0.801048\pi\)
−0.810949 + 0.585117i \(0.801048\pi\)
\(224\) 2.37263 0.158528
\(225\) 0 0
\(226\) 0.377712 0.0251250
\(227\) 29.0323 1.92694 0.963472 0.267808i \(-0.0862994\pi\)
0.963472 + 0.267808i \(0.0862994\pi\)
\(228\) 0 0
\(229\) −0.489031 −0.0323161 −0.0161580 0.999869i \(-0.505143\pi\)
−0.0161580 + 0.999869i \(0.505143\pi\)
\(230\) 0.881665 0.0581353
\(231\) 0 0
\(232\) −2.17478 −0.142781
\(233\) 16.2677 1.06573 0.532866 0.846200i \(-0.321115\pi\)
0.532866 + 0.846200i \(0.321115\pi\)
\(234\) 0 0
\(235\) −8.83495 −0.576328
\(236\) −26.8552 −1.74812
\(237\) 0 0
\(238\) −0.460414 −0.0298442
\(239\) 18.6270 1.20488 0.602442 0.798163i \(-0.294195\pi\)
0.602442 + 0.798163i \(0.294195\pi\)
\(240\) 0 0
\(241\) −18.1700 −1.17043 −0.585215 0.810878i \(-0.698990\pi\)
−0.585215 + 0.810878i \(0.698990\pi\)
\(242\) 1.39319 0.0895577
\(243\) 0 0
\(244\) 18.1179 1.15988
\(245\) −2.16833 −0.138530
\(246\) 0 0
\(247\) −10.6368 −0.676801
\(248\) 0.744777 0.0472934
\(249\) 0 0
\(250\) −2.33553 −0.147712
\(251\) −28.9466 −1.82709 −0.913545 0.406737i \(-0.866667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(252\) 0 0
\(253\) 4.07303 0.256069
\(254\) 0.203292 0.0127557
\(255\) 0 0
\(256\) 12.7953 0.799706
\(257\) −10.2025 −0.636413 −0.318207 0.948021i \(-0.603081\pi\)
−0.318207 + 0.948021i \(0.603081\pi\)
\(258\) 0 0
\(259\) −7.11408 −0.442048
\(260\) 7.79992 0.483730
\(261\) 0 0
\(262\) −1.03621 −0.0640172
\(263\) 0.138057 0.00851293 0.00425647 0.999991i \(-0.498645\pi\)
0.00425647 + 0.999991i \(0.498645\pi\)
\(264\) 0 0
\(265\) 14.0176 0.861095
\(266\) −1.17741 −0.0721914
\(267\) 0 0
\(268\) −13.4818 −0.823533
\(269\) 0.767771 0.0468118 0.0234059 0.999726i \(-0.492549\pi\)
0.0234059 + 0.999726i \(0.492549\pi\)
\(270\) 0 0
\(271\) −25.0186 −1.51977 −0.759886 0.650057i \(-0.774745\pi\)
−0.759886 + 0.650057i \(0.774745\pi\)
\(272\) −8.50146 −0.515477
\(273\) 0 0
\(274\) 0.713606 0.0431105
\(275\) −0.607546 −0.0366364
\(276\) 0 0
\(277\) −24.0594 −1.44559 −0.722795 0.691063i \(-0.757143\pi\)
−0.722795 + 0.691063i \(0.757143\pi\)
\(278\) 0.668510 0.0400946
\(279\) 0 0
\(280\) 1.74500 0.104283
\(281\) 10.1722 0.606825 0.303413 0.952859i \(-0.401874\pi\)
0.303413 + 0.952859i \(0.401874\pi\)
\(282\) 0 0
\(283\) −29.1780 −1.73445 −0.867227 0.497913i \(-0.834100\pi\)
−0.867227 + 0.497913i \(0.834100\pi\)
\(284\) −27.7080 −1.64417
\(285\) 0 0
\(286\) −0.760293 −0.0449571
\(287\) 3.83498 0.226372
\(288\) 0 0
\(289\) −11.8707 −0.698276
\(290\) −1.19122 −0.0699506
\(291\) 0 0
\(292\) −9.37374 −0.548557
\(293\) 12.9496 0.756522 0.378261 0.925699i \(-0.376522\pi\)
0.378261 + 0.925699i \(0.376522\pi\)
\(294\) 0 0
\(295\) −29.7298 −1.73093
\(296\) 5.72516 0.332768
\(297\) 0 0
\(298\) −3.03054 −0.175555
\(299\) 3.67335 0.212435
\(300\) 0 0
\(301\) 0.434751 0.0250586
\(302\) −1.46345 −0.0842122
\(303\) 0 0
\(304\) −21.7406 −1.24691
\(305\) 20.0573 1.14848
\(306\) 0 0
\(307\) −9.02772 −0.515239 −0.257620 0.966246i \(-0.582938\pi\)
−0.257620 + 0.966246i \(0.582938\pi\)
\(308\) 3.98860 0.227272
\(309\) 0 0
\(310\) 0.407945 0.0231697
\(311\) −24.7431 −1.40305 −0.701525 0.712645i \(-0.747497\pi\)
−0.701525 + 0.712645i \(0.747497\pi\)
\(312\) 0 0
\(313\) −16.8110 −0.950216 −0.475108 0.879928i \(-0.657591\pi\)
−0.475108 + 0.879928i \(0.657591\pi\)
\(314\) 2.02177 0.114095
\(315\) 0 0
\(316\) −21.2438 −1.19505
\(317\) −3.14053 −0.176389 −0.0881947 0.996103i \(-0.528110\pi\)
−0.0881947 + 0.996103i \(0.528110\pi\)
\(318\) 0 0
\(319\) −5.50306 −0.308112
\(320\) 15.2328 0.851542
\(321\) 0 0
\(322\) 0.406610 0.0226595
\(323\) 13.1170 0.729851
\(324\) 0 0
\(325\) −0.547928 −0.0303936
\(326\) 4.27857 0.236968
\(327\) 0 0
\(328\) −3.08626 −0.170410
\(329\) −4.07454 −0.224637
\(330\) 0 0
\(331\) −20.2551 −1.11332 −0.556660 0.830740i \(-0.687917\pi\)
−0.556660 + 0.830740i \(0.687917\pi\)
\(332\) −9.73985 −0.534544
\(333\) 0 0
\(334\) −1.93788 −0.106036
\(335\) −14.9249 −0.815435
\(336\) 0 0
\(337\) 11.4420 0.623283 0.311641 0.950200i \(-0.399121\pi\)
0.311641 + 0.950200i \(0.399121\pi\)
\(338\) 1.95711 0.106452
\(339\) 0 0
\(340\) −9.61870 −0.521647
\(341\) 1.88458 0.102056
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −0.349873 −0.0188639
\(345\) 0 0
\(346\) 4.30895 0.231651
\(347\) −13.6007 −0.730123 −0.365061 0.930983i \(-0.618952\pi\)
−0.365061 + 0.930983i \(0.618952\pi\)
\(348\) 0 0
\(349\) 6.18545 0.331100 0.165550 0.986201i \(-0.447060\pi\)
0.165550 + 0.986201i \(0.447060\pi\)
\(350\) −0.0606513 −0.00324195
\(351\) 0 0
\(352\) −4.83158 −0.257524
\(353\) −34.6672 −1.84515 −0.922574 0.385821i \(-0.873918\pi\)
−0.922574 + 0.385821i \(0.873918\pi\)
\(354\) 0 0
\(355\) −30.6739 −1.62800
\(356\) 2.19370 0.116266
\(357\) 0 0
\(358\) 4.77134 0.252173
\(359\) 11.3002 0.596400 0.298200 0.954503i \(-0.403614\pi\)
0.298200 + 0.954503i \(0.403614\pi\)
\(360\) 0 0
\(361\) 14.5439 0.765467
\(362\) −3.54168 −0.186146
\(363\) 0 0
\(364\) 3.59720 0.188545
\(365\) −10.3771 −0.543163
\(366\) 0 0
\(367\) 14.3988 0.751611 0.375806 0.926698i \(-0.377366\pi\)
0.375806 + 0.926698i \(0.377366\pi\)
\(368\) 7.50799 0.391381
\(369\) 0 0
\(370\) 3.13591 0.163028
\(371\) 6.46471 0.335631
\(372\) 0 0
\(373\) −17.8622 −0.924870 −0.462435 0.886653i \(-0.653024\pi\)
−0.462435 + 0.886653i \(0.653024\pi\)
\(374\) 0.937577 0.0484810
\(375\) 0 0
\(376\) 3.27905 0.169104
\(377\) −4.96305 −0.255610
\(378\) 0 0
\(379\) 8.53256 0.438288 0.219144 0.975693i \(-0.429674\pi\)
0.219144 + 0.975693i \(0.429674\pi\)
\(380\) −24.5977 −1.26183
\(381\) 0 0
\(382\) 2.09441 0.107159
\(383\) −29.9038 −1.52801 −0.764006 0.645210i \(-0.776770\pi\)
−0.764006 + 0.645210i \(0.776770\pi\)
\(384\) 0 0
\(385\) 4.41554 0.225037
\(386\) 1.12661 0.0573428
\(387\) 0 0
\(388\) −13.7999 −0.700582
\(389\) −8.18046 −0.414766 −0.207383 0.978260i \(-0.566495\pi\)
−0.207383 + 0.978260i \(0.566495\pi\)
\(390\) 0 0
\(391\) −4.52989 −0.229087
\(392\) 0.804765 0.0406468
\(393\) 0 0
\(394\) −2.25078 −0.113393
\(395\) −23.5177 −1.18330
\(396\) 0 0
\(397\) −1.31342 −0.0659188 −0.0329594 0.999457i \(-0.510493\pi\)
−0.0329594 + 0.999457i \(0.510493\pi\)
\(398\) −2.71570 −0.136126
\(399\) 0 0
\(400\) −1.11991 −0.0559957
\(401\) 33.1873 1.65730 0.828648 0.559770i \(-0.189111\pi\)
0.828648 + 0.559770i \(0.189111\pi\)
\(402\) 0 0
\(403\) 1.69965 0.0846657
\(404\) 20.9509 1.04235
\(405\) 0 0
\(406\) −0.549370 −0.0272648
\(407\) 14.4870 0.718092
\(408\) 0 0
\(409\) −29.9044 −1.47868 −0.739340 0.673333i \(-0.764862\pi\)
−0.739340 + 0.673333i \(0.764862\pi\)
\(410\) −1.69047 −0.0834864
\(411\) 0 0
\(412\) 29.2466 1.44087
\(413\) −13.7109 −0.674669
\(414\) 0 0
\(415\) −10.7824 −0.529288
\(416\) −4.35746 −0.213642
\(417\) 0 0
\(418\) 2.39764 0.117273
\(419\) 33.5181 1.63747 0.818734 0.574173i \(-0.194676\pi\)
0.818734 + 0.574173i \(0.194676\pi\)
\(420\) 0 0
\(421\) −33.0936 −1.61288 −0.806442 0.591314i \(-0.798610\pi\)
−0.806442 + 0.591314i \(0.798610\pi\)
\(422\) −4.75499 −0.231469
\(423\) 0 0
\(424\) −5.20257 −0.252659
\(425\) 0.675693 0.0327759
\(426\) 0 0
\(427\) 9.25010 0.447643
\(428\) −24.0315 −1.16161
\(429\) 0 0
\(430\) −0.191640 −0.00924169
\(431\) −1.90178 −0.0916053 −0.0458026 0.998951i \(-0.514585\pi\)
−0.0458026 + 0.998951i \(0.514585\pi\)
\(432\) 0 0
\(433\) −22.4641 −1.07956 −0.539778 0.841807i \(-0.681492\pi\)
−0.539778 + 0.841807i \(0.681492\pi\)
\(434\) 0.188138 0.00903091
\(435\) 0 0
\(436\) 3.00981 0.144144
\(437\) −11.5842 −0.554147
\(438\) 0 0
\(439\) 6.36163 0.303624 0.151812 0.988409i \(-0.451489\pi\)
0.151812 + 0.988409i \(0.451489\pi\)
\(440\) −3.55347 −0.169405
\(441\) 0 0
\(442\) 0.845574 0.0402198
\(443\) −11.7960 −0.560444 −0.280222 0.959935i \(-0.590408\pi\)
−0.280222 + 0.959935i \(0.590408\pi\)
\(444\) 0 0
\(445\) 2.42851 0.115122
\(446\) 4.92374 0.233146
\(447\) 0 0
\(448\) 7.02515 0.331907
\(449\) 26.8230 1.26586 0.632928 0.774211i \(-0.281853\pi\)
0.632928 + 0.774211i \(0.281853\pi\)
\(450\) 0 0
\(451\) −7.80947 −0.367734
\(452\) 3.63917 0.171172
\(453\) 0 0
\(454\) −5.90203 −0.276996
\(455\) 3.98225 0.186691
\(456\) 0 0
\(457\) −10.2927 −0.481470 −0.240735 0.970591i \(-0.577388\pi\)
−0.240735 + 0.970591i \(0.577388\pi\)
\(458\) 0.0994160 0.00464540
\(459\) 0 0
\(460\) 8.49466 0.396066
\(461\) 35.1566 1.63741 0.818703 0.574217i \(-0.194693\pi\)
0.818703 + 0.574217i \(0.194693\pi\)
\(462\) 0 0
\(463\) −35.3381 −1.64230 −0.821150 0.570712i \(-0.806667\pi\)
−0.821150 + 0.570712i \(0.806667\pi\)
\(464\) −10.1440 −0.470924
\(465\) 0 0
\(466\) −3.30709 −0.153198
\(467\) 7.24322 0.335176 0.167588 0.985857i \(-0.446402\pi\)
0.167588 + 0.985857i \(0.446402\pi\)
\(468\) 0 0
\(469\) −6.88314 −0.317834
\(470\) 1.79607 0.0828466
\(471\) 0 0
\(472\) 11.0341 0.507884
\(473\) −0.885318 −0.0407070
\(474\) 0 0
\(475\) 1.72793 0.0792830
\(476\) −4.43599 −0.203323
\(477\) 0 0
\(478\) −3.78672 −0.173201
\(479\) −9.85957 −0.450495 −0.225248 0.974302i \(-0.572319\pi\)
−0.225248 + 0.974302i \(0.572319\pi\)
\(480\) 0 0
\(481\) 13.0654 0.595730
\(482\) 3.69380 0.168248
\(483\) 0 0
\(484\) 13.4231 0.610141
\(485\) −15.2770 −0.693694
\(486\) 0 0
\(487\) 2.37567 0.107652 0.0538259 0.998550i \(-0.482858\pi\)
0.0538259 + 0.998550i \(0.482858\pi\)
\(488\) −7.44415 −0.336981
\(489\) 0 0
\(490\) 0.440803 0.0199135
\(491\) −28.4513 −1.28399 −0.641995 0.766709i \(-0.721893\pi\)
−0.641995 + 0.766709i \(0.721893\pi\)
\(492\) 0 0
\(493\) 6.12033 0.275646
\(494\) 2.16237 0.0972894
\(495\) 0 0
\(496\) 3.47393 0.155984
\(497\) −14.1463 −0.634549
\(498\) 0 0
\(499\) −12.8574 −0.575575 −0.287787 0.957694i \(-0.592920\pi\)
−0.287787 + 0.957694i \(0.592920\pi\)
\(500\) −22.5023 −1.00633
\(501\) 0 0
\(502\) 5.88459 0.262642
\(503\) −5.24764 −0.233981 −0.116990 0.993133i \(-0.537325\pi\)
−0.116990 + 0.993133i \(0.537325\pi\)
\(504\) 0 0
\(505\) 23.1935 1.03210
\(506\) −0.828013 −0.0368096
\(507\) 0 0
\(508\) 1.95867 0.0869020
\(509\) 23.4333 1.03866 0.519332 0.854572i \(-0.326181\pi\)
0.519332 + 0.854572i \(0.326181\pi\)
\(510\) 0 0
\(511\) −4.78576 −0.211710
\(512\) −14.9480 −0.660616
\(513\) 0 0
\(514\) 2.07408 0.0914837
\(515\) 32.3771 1.42671
\(516\) 0 0
\(517\) 8.29731 0.364915
\(518\) 1.44623 0.0635438
\(519\) 0 0
\(520\) −3.20477 −0.140539
\(521\) −8.39413 −0.367754 −0.183877 0.982949i \(-0.558865\pi\)
−0.183877 + 0.982949i \(0.558865\pi\)
\(522\) 0 0
\(523\) −17.3043 −0.756663 −0.378331 0.925670i \(-0.623502\pi\)
−0.378331 + 0.925670i \(0.623502\pi\)
\(524\) −9.98365 −0.436138
\(525\) 0 0
\(526\) −0.0280657 −0.00122372
\(527\) −2.09597 −0.0913021
\(528\) 0 0
\(529\) −18.9995 −0.826064
\(530\) −2.84966 −0.123781
\(531\) 0 0
\(532\) −11.3441 −0.491827
\(533\) −7.04313 −0.305072
\(534\) 0 0
\(535\) −26.6039 −1.15019
\(536\) 5.53931 0.239262
\(537\) 0 0
\(538\) −0.156081 −0.00672915
\(539\) 2.03638 0.0877130
\(540\) 0 0
\(541\) −5.60112 −0.240811 −0.120406 0.992725i \(-0.538419\pi\)
−0.120406 + 0.992725i \(0.538419\pi\)
\(542\) 5.08607 0.218465
\(543\) 0 0
\(544\) 5.37353 0.230388
\(545\) 3.33198 0.142726
\(546\) 0 0
\(547\) 2.16434 0.0925407 0.0462703 0.998929i \(-0.485266\pi\)
0.0462703 + 0.998929i \(0.485266\pi\)
\(548\) 6.87544 0.293704
\(549\) 0 0
\(550\) 0.123509 0.00526644
\(551\) 15.6514 0.666771
\(552\) 0 0
\(553\) −10.8460 −0.461219
\(554\) 4.89107 0.207802
\(555\) 0 0
\(556\) 6.44096 0.273157
\(557\) −34.6728 −1.46914 −0.734568 0.678535i \(-0.762615\pi\)
−0.734568 + 0.678535i \(0.762615\pi\)
\(558\) 0 0
\(559\) −0.798442 −0.0337705
\(560\) 8.13935 0.343950
\(561\) 0 0
\(562\) −2.06793 −0.0872304
\(563\) −15.0614 −0.634762 −0.317381 0.948298i \(-0.602803\pi\)
−0.317381 + 0.948298i \(0.602803\pi\)
\(564\) 0 0
\(565\) 4.02871 0.169489
\(566\) 5.93165 0.249326
\(567\) 0 0
\(568\) 11.3845 0.477682
\(569\) −17.9482 −0.752426 −0.376213 0.926533i \(-0.622774\pi\)
−0.376213 + 0.926533i \(0.622774\pi\)
\(570\) 0 0
\(571\) 4.27764 0.179014 0.0895069 0.995986i \(-0.471471\pi\)
0.0895069 + 0.995986i \(0.471471\pi\)
\(572\) −7.32526 −0.306285
\(573\) 0 0
\(574\) −0.779619 −0.0325407
\(575\) −0.596732 −0.0248854
\(576\) 0 0
\(577\) 38.9224 1.62036 0.810180 0.586182i \(-0.199370\pi\)
0.810180 + 0.586182i \(0.199370\pi\)
\(578\) 2.41321 0.100376
\(579\) 0 0
\(580\) −11.4771 −0.476561
\(581\) −4.97268 −0.206302
\(582\) 0 0
\(583\) −13.1646 −0.545222
\(584\) 3.85141 0.159373
\(585\) 0 0
\(586\) −2.63254 −0.108749
\(587\) 24.3999 1.00709 0.503546 0.863968i \(-0.332028\pi\)
0.503546 + 0.863968i \(0.332028\pi\)
\(588\) 0 0
\(589\) −5.35999 −0.220854
\(590\) 6.04381 0.248820
\(591\) 0 0
\(592\) 26.7044 1.09755
\(593\) 20.7529 0.852219 0.426110 0.904672i \(-0.359884\pi\)
0.426110 + 0.904672i \(0.359884\pi\)
\(594\) 0 0
\(595\) −4.91082 −0.201324
\(596\) −29.1986 −1.19602
\(597\) 0 0
\(598\) −0.746760 −0.0305373
\(599\) −35.5562 −1.45279 −0.726393 0.687280i \(-0.758805\pi\)
−0.726393 + 0.687280i \(0.758805\pi\)
\(600\) 0 0
\(601\) 4.85431 0.198011 0.0990057 0.995087i \(-0.468434\pi\)
0.0990057 + 0.995087i \(0.468434\pi\)
\(602\) −0.0883813 −0.00360215
\(603\) 0 0
\(604\) −14.1000 −0.573723
\(605\) 14.8599 0.604141
\(606\) 0 0
\(607\) 2.55179 0.103574 0.0517869 0.998658i \(-0.483508\pi\)
0.0517869 + 0.998658i \(0.483508\pi\)
\(608\) 13.7416 0.557296
\(609\) 0 0
\(610\) −4.07747 −0.165092
\(611\) 7.48310 0.302734
\(612\) 0 0
\(613\) 41.2815 1.66734 0.833672 0.552259i \(-0.186234\pi\)
0.833672 + 0.552259i \(0.186234\pi\)
\(614\) 1.83526 0.0740651
\(615\) 0 0
\(616\) −1.63881 −0.0660294
\(617\) 7.93093 0.319287 0.159644 0.987175i \(-0.448966\pi\)
0.159644 + 0.987175i \(0.448966\pi\)
\(618\) 0 0
\(619\) 3.93425 0.158131 0.0790655 0.996869i \(-0.474806\pi\)
0.0790655 + 0.996869i \(0.474806\pi\)
\(620\) 3.93047 0.157851
\(621\) 0 0
\(622\) 5.03006 0.201687
\(623\) 1.11999 0.0448715
\(624\) 0 0
\(625\) −23.4193 −0.936770
\(626\) 3.41754 0.136592
\(627\) 0 0
\(628\) 19.4793 0.777310
\(629\) −16.1119 −0.642425
\(630\) 0 0
\(631\) 0.666745 0.0265427 0.0132713 0.999912i \(-0.495775\pi\)
0.0132713 + 0.999912i \(0.495775\pi\)
\(632\) 8.72848 0.347200
\(633\) 0 0
\(634\) 0.638443 0.0253558
\(635\) 2.16833 0.0860475
\(636\) 0 0
\(637\) 1.83655 0.0727668
\(638\) 1.11873 0.0442908
\(639\) 0 0
\(640\) −13.3860 −0.529129
\(641\) 16.8540 0.665692 0.332846 0.942981i \(-0.391991\pi\)
0.332846 + 0.942981i \(0.391991\pi\)
\(642\) 0 0
\(643\) −25.0458 −0.987709 −0.493854 0.869545i \(-0.664412\pi\)
−0.493854 + 0.869545i \(0.664412\pi\)
\(644\) 3.91761 0.154375
\(645\) 0 0
\(646\) −2.66658 −0.104915
\(647\) −6.04381 −0.237607 −0.118803 0.992918i \(-0.537906\pi\)
−0.118803 + 0.992918i \(0.537906\pi\)
\(648\) 0 0
\(649\) 27.9206 1.09598
\(650\) 0.111389 0.00436904
\(651\) 0 0
\(652\) 41.2232 1.61442
\(653\) 22.8710 0.895010 0.447505 0.894282i \(-0.352313\pi\)
0.447505 + 0.894282i \(0.352313\pi\)
\(654\) 0 0
\(655\) −11.0523 −0.431849
\(656\) −14.3955 −0.562051
\(657\) 0 0
\(658\) 0.828320 0.0322913
\(659\) −41.9778 −1.63522 −0.817612 0.575770i \(-0.804702\pi\)
−0.817612 + 0.575770i \(0.804702\pi\)
\(660\) 0 0
\(661\) 22.3913 0.870920 0.435460 0.900208i \(-0.356586\pi\)
0.435460 + 0.900208i \(0.356586\pi\)
\(662\) 4.11769 0.160039
\(663\) 0 0
\(664\) 4.00184 0.155301
\(665\) −12.5583 −0.486991
\(666\) 0 0
\(667\) −5.40511 −0.209287
\(668\) −18.6711 −0.722407
\(669\) 0 0
\(670\) 3.03411 0.117218
\(671\) −18.8367 −0.727183
\(672\) 0 0
\(673\) −22.7915 −0.878550 −0.439275 0.898353i \(-0.644765\pi\)
−0.439275 + 0.898353i \(0.644765\pi\)
\(674\) −2.32605 −0.0895962
\(675\) 0 0
\(676\) 18.8563 0.725242
\(677\) 2.11742 0.0813790 0.0406895 0.999172i \(-0.487045\pi\)
0.0406895 + 0.999172i \(0.487045\pi\)
\(678\) 0 0
\(679\) −7.04552 −0.270382
\(680\) 3.95206 0.151555
\(681\) 0 0
\(682\) −0.383120 −0.0146704
\(683\) 48.9058 1.87133 0.935665 0.352889i \(-0.114801\pi\)
0.935665 + 0.352889i \(0.114801\pi\)
\(684\) 0 0
\(685\) 7.61139 0.290816
\(686\) 0.203292 0.00776171
\(687\) 0 0
\(688\) −1.63194 −0.0622173
\(689\) −11.8728 −0.452316
\(690\) 0 0
\(691\) −7.85867 −0.298958 −0.149479 0.988765i \(-0.547760\pi\)
−0.149479 + 0.988765i \(0.547760\pi\)
\(692\) 41.5159 1.57820
\(693\) 0 0
\(694\) 2.76490 0.104954
\(695\) 7.13040 0.270471
\(696\) 0 0
\(697\) 8.68545 0.328985
\(698\) −1.25745 −0.0475952
\(699\) 0 0
\(700\) −0.584362 −0.0220868
\(701\) −37.9287 −1.43255 −0.716274 0.697819i \(-0.754154\pi\)
−0.716274 + 0.697819i \(0.754154\pi\)
\(702\) 0 0
\(703\) −41.2027 −1.55399
\(704\) −14.3059 −0.539173
\(705\) 0 0
\(706\) 7.04755 0.265238
\(707\) 10.6965 0.402282
\(708\) 0 0
\(709\) −15.3664 −0.577096 −0.288548 0.957465i \(-0.593172\pi\)
−0.288548 + 0.957465i \(0.593172\pi\)
\(710\) 6.23575 0.234023
\(711\) 0 0
\(712\) −0.901330 −0.0337788
\(713\) 1.85104 0.0693220
\(714\) 0 0
\(715\) −8.10936 −0.303273
\(716\) 45.9708 1.71801
\(717\) 0 0
\(718\) −2.29723 −0.0857318
\(719\) 20.3461 0.758783 0.379392 0.925236i \(-0.376133\pi\)
0.379392 + 0.925236i \(0.376133\pi\)
\(720\) 0 0
\(721\) 14.9318 0.556090
\(722\) −2.95665 −0.110035
\(723\) 0 0
\(724\) −34.1233 −1.26818
\(725\) 0.806243 0.0299431
\(726\) 0 0
\(727\) 31.2751 1.15993 0.579965 0.814641i \(-0.303066\pi\)
0.579965 + 0.814641i \(0.303066\pi\)
\(728\) −1.47799 −0.0547780
\(729\) 0 0
\(730\) 2.10958 0.0780790
\(731\) 0.984623 0.0364176
\(732\) 0 0
\(733\) −29.8273 −1.10170 −0.550848 0.834606i \(-0.685696\pi\)
−0.550848 + 0.834606i \(0.685696\pi\)
\(734\) −2.92716 −0.108043
\(735\) 0 0
\(736\) −4.74558 −0.174925
\(737\) 14.0167 0.516311
\(738\) 0 0
\(739\) 49.0703 1.80508 0.902539 0.430607i \(-0.141701\pi\)
0.902539 + 0.430607i \(0.141701\pi\)
\(740\) 30.2138 1.11068
\(741\) 0 0
\(742\) −1.31422 −0.0482466
\(743\) 14.4447 0.529925 0.264962 0.964259i \(-0.414640\pi\)
0.264962 + 0.964259i \(0.414640\pi\)
\(744\) 0 0
\(745\) −32.3241 −1.18426
\(746\) 3.63124 0.132949
\(747\) 0 0
\(748\) 9.03336 0.330292
\(749\) −12.2693 −0.448310
\(750\) 0 0
\(751\) −39.1877 −1.42998 −0.714989 0.699136i \(-0.753568\pi\)
−0.714989 + 0.699136i \(0.753568\pi\)
\(752\) 15.2948 0.557743
\(753\) 0 0
\(754\) 1.00895 0.0367437
\(755\) −15.6093 −0.568082
\(756\) 0 0
\(757\) 25.1509 0.914125 0.457063 0.889435i \(-0.348902\pi\)
0.457063 + 0.889435i \(0.348902\pi\)
\(758\) −1.73460 −0.0630034
\(759\) 0 0
\(760\) 10.1065 0.366602
\(761\) −14.0558 −0.509521 −0.254760 0.967004i \(-0.581997\pi\)
−0.254760 + 0.967004i \(0.581997\pi\)
\(762\) 0 0
\(763\) 1.53666 0.0556308
\(764\) 20.1792 0.730057
\(765\) 0 0
\(766\) 6.07919 0.219650
\(767\) 25.1808 0.909225
\(768\) 0 0
\(769\) −3.79434 −0.136827 −0.0684137 0.997657i \(-0.521794\pi\)
−0.0684137 + 0.997657i \(0.521794\pi\)
\(770\) −0.897643 −0.0323488
\(771\) 0 0
\(772\) 10.8546 0.390667
\(773\) 3.70140 0.133130 0.0665651 0.997782i \(-0.478796\pi\)
0.0665651 + 0.997782i \(0.478796\pi\)
\(774\) 0 0
\(775\) −0.276107 −0.00991805
\(776\) 5.66999 0.203541
\(777\) 0 0
\(778\) 1.66302 0.0596221
\(779\) 22.2111 0.795795
\(780\) 0 0
\(781\) 28.8073 1.03081
\(782\) 0.920889 0.0329309
\(783\) 0 0
\(784\) 3.75374 0.134062
\(785\) 21.5644 0.769667
\(786\) 0 0
\(787\) −31.4190 −1.11997 −0.559983 0.828504i \(-0.689192\pi\)
−0.559983 + 0.828504i \(0.689192\pi\)
\(788\) −21.6858 −0.772525
\(789\) 0 0
\(790\) 4.78095 0.170099
\(791\) 1.85798 0.0660621
\(792\) 0 0
\(793\) −16.9883 −0.603271
\(794\) 0.267008 0.00947576
\(795\) 0 0
\(796\) −26.1652 −0.927402
\(797\) −1.53832 −0.0544901 −0.0272450 0.999629i \(-0.508673\pi\)
−0.0272450 + 0.999629i \(0.508673\pi\)
\(798\) 0 0
\(799\) −9.22800 −0.326463
\(800\) 0.707866 0.0250268
\(801\) 0 0
\(802\) −6.74671 −0.238234
\(803\) 9.74562 0.343916
\(804\) 0 0
\(805\) 4.33695 0.152857
\(806\) −0.345525 −0.0121706
\(807\) 0 0
\(808\) −8.60815 −0.302834
\(809\) 8.97381 0.315502 0.157751 0.987479i \(-0.449576\pi\)
0.157751 + 0.987479i \(0.449576\pi\)
\(810\) 0 0
\(811\) 43.0991 1.51341 0.756707 0.653754i \(-0.226807\pi\)
0.756707 + 0.653754i \(0.226807\pi\)
\(812\) −5.29307 −0.185750
\(813\) 0 0
\(814\) −2.94508 −0.103225
\(815\) 45.6357 1.59855
\(816\) 0 0
\(817\) 2.51795 0.0880920
\(818\) 6.07932 0.212559
\(819\) 0 0
\(820\) −16.2873 −0.568779
\(821\) −24.2970 −0.847971 −0.423985 0.905669i \(-0.639369\pi\)
−0.423985 + 0.905669i \(0.639369\pi\)
\(822\) 0 0
\(823\) 23.3470 0.813825 0.406913 0.913467i \(-0.366605\pi\)
0.406913 + 0.913467i \(0.366605\pi\)
\(824\) −12.0166 −0.418618
\(825\) 0 0
\(826\) 2.78731 0.0969830
\(827\) 53.3817 1.85626 0.928131 0.372253i \(-0.121415\pi\)
0.928131 + 0.372253i \(0.121415\pi\)
\(828\) 0 0
\(829\) −45.5788 −1.58302 −0.791509 0.611157i \(-0.790704\pi\)
−0.791509 + 0.611157i \(0.790704\pi\)
\(830\) 2.19197 0.0760845
\(831\) 0 0
\(832\) −12.9020 −0.447298
\(833\) −2.26480 −0.0784705
\(834\) 0 0
\(835\) −20.6697 −0.715303
\(836\) 23.1008 0.798958
\(837\) 0 0
\(838\) −6.81396 −0.235384
\(839\) −41.0272 −1.41642 −0.708208 0.706004i \(-0.750496\pi\)
−0.708208 + 0.706004i \(0.750496\pi\)
\(840\) 0 0
\(841\) −21.6972 −0.748178
\(842\) 6.72765 0.231850
\(843\) 0 0
\(844\) −45.8133 −1.57696
\(845\) 20.8747 0.718111
\(846\) 0 0
\(847\) 6.85316 0.235477
\(848\) −24.2668 −0.833327
\(849\) 0 0
\(850\) −0.137363 −0.00471150
\(851\) 14.2291 0.487768
\(852\) 0 0
\(853\) 1.58986 0.0544359 0.0272179 0.999630i \(-0.491335\pi\)
0.0272179 + 0.999630i \(0.491335\pi\)
\(854\) −1.88047 −0.0643483
\(855\) 0 0
\(856\) 9.87390 0.337483
\(857\) 15.7373 0.537578 0.268789 0.963199i \(-0.413377\pi\)
0.268789 + 0.963199i \(0.413377\pi\)
\(858\) 0 0
\(859\) 3.73832 0.127550 0.0637749 0.997964i \(-0.479686\pi\)
0.0637749 + 0.997964i \(0.479686\pi\)
\(860\) −1.84641 −0.0629620
\(861\) 0 0
\(862\) 0.386615 0.0131682
\(863\) 22.7338 0.773869 0.386934 0.922107i \(-0.373534\pi\)
0.386934 + 0.922107i \(0.373534\pi\)
\(864\) 0 0
\(865\) 45.9597 1.56268
\(866\) 4.56677 0.155185
\(867\) 0 0
\(868\) 1.81267 0.0615260
\(869\) 22.0866 0.749235
\(870\) 0 0
\(871\) 12.6412 0.428332
\(872\) −1.23665 −0.0418782
\(873\) 0 0
\(874\) 2.35497 0.0796580
\(875\) −11.4886 −0.388384
\(876\) 0 0
\(877\) −39.9098 −1.34766 −0.673828 0.738888i \(-0.735351\pi\)
−0.673828 + 0.738888i \(0.735351\pi\)
\(878\) −1.29327 −0.0436456
\(879\) 0 0
\(880\) −16.5748 −0.558737
\(881\) −50.9994 −1.71821 −0.859106 0.511798i \(-0.828980\pi\)
−0.859106 + 0.511798i \(0.828980\pi\)
\(882\) 0 0
\(883\) −0.228422 −0.00768700 −0.00384350 0.999993i \(-0.501223\pi\)
−0.00384350 + 0.999993i \(0.501223\pi\)
\(884\) 8.14693 0.274011
\(885\) 0 0
\(886\) 2.39802 0.0805632
\(887\) −27.4320 −0.921078 −0.460539 0.887639i \(-0.652344\pi\)
−0.460539 + 0.887639i \(0.652344\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −0.493696 −0.0165487
\(891\) 0 0
\(892\) 47.4392 1.58838
\(893\) −23.5985 −0.789695
\(894\) 0 0
\(895\) 50.8916 1.70112
\(896\) −6.17342 −0.206240
\(897\) 0 0
\(898\) −5.45289 −0.181965
\(899\) −2.50094 −0.0834109
\(900\) 0 0
\(901\) 14.6412 0.487770
\(902\) 1.58760 0.0528613
\(903\) 0 0
\(904\) −1.49524 −0.0497308
\(905\) −37.7759 −1.25571
\(906\) 0 0
\(907\) −15.4064 −0.511562 −0.255781 0.966735i \(-0.582333\pi\)
−0.255781 + 0.966735i \(0.582333\pi\)
\(908\) −56.8649 −1.88713
\(909\) 0 0
\(910\) −0.809558 −0.0268366
\(911\) 52.7023 1.74610 0.873052 0.487627i \(-0.162137\pi\)
0.873052 + 0.487627i \(0.162137\pi\)
\(912\) 0 0
\(913\) 10.1263 0.335130
\(914\) 2.09241 0.0692108
\(915\) 0 0
\(916\) 0.957852 0.0316483
\(917\) −5.09715 −0.168323
\(918\) 0 0
\(919\) 49.5827 1.63558 0.817792 0.575514i \(-0.195198\pi\)
0.817792 + 0.575514i \(0.195198\pi\)
\(920\) −3.49022 −0.115069
\(921\) 0 0
\(922\) −7.14704 −0.235375
\(923\) 25.9804 0.855156
\(924\) 0 0
\(925\) −2.12246 −0.0697860
\(926\) 7.18394 0.236079
\(927\) 0 0
\(928\) 6.41175 0.210476
\(929\) 43.3260 1.42148 0.710740 0.703455i \(-0.248360\pi\)
0.710740 + 0.703455i \(0.248360\pi\)
\(930\) 0 0
\(931\) −5.79171 −0.189816
\(932\) −31.8631 −1.04371
\(933\) 0 0
\(934\) −1.47249 −0.0481812
\(935\) 10.0003 0.327045
\(936\) 0 0
\(937\) 5.45956 0.178356 0.0891780 0.996016i \(-0.471576\pi\)
0.0891780 + 0.996016i \(0.471576\pi\)
\(938\) 1.39928 0.0456882
\(939\) 0 0
\(940\) 17.3048 0.564419
\(941\) −13.6724 −0.445708 −0.222854 0.974852i \(-0.571537\pi\)
−0.222854 + 0.974852i \(0.571537\pi\)
\(942\) 0 0
\(943\) −7.67047 −0.249785
\(944\) 51.4672 1.67511
\(945\) 0 0
\(946\) 0.179978 0.00585158
\(947\) 2.37187 0.0770756 0.0385378 0.999257i \(-0.487730\pi\)
0.0385378 + 0.999257i \(0.487730\pi\)
\(948\) 0 0
\(949\) 8.78929 0.285313
\(950\) −0.351274 −0.0113968
\(951\) 0 0
\(952\) 1.82263 0.0590717
\(953\) 23.0787 0.747591 0.373796 0.927511i \(-0.378056\pi\)
0.373796 + 0.927511i \(0.378056\pi\)
\(954\) 0 0
\(955\) 22.3392 0.722878
\(956\) −36.4843 −1.17999
\(957\) 0 0
\(958\) 2.00437 0.0647582
\(959\) 3.51026 0.113352
\(960\) 0 0
\(961\) −30.1435 −0.972372
\(962\) −2.65608 −0.0856355
\(963\) 0 0
\(964\) 35.5890 1.14624
\(965\) 12.0165 0.386825
\(966\) 0 0
\(967\) 9.81160 0.315520 0.157760 0.987477i \(-0.449573\pi\)
0.157760 + 0.987477i \(0.449573\pi\)
\(968\) −5.51518 −0.177265
\(969\) 0 0
\(970\) 3.10569 0.0997177
\(971\) 15.2562 0.489594 0.244797 0.969574i \(-0.421279\pi\)
0.244797 + 0.969574i \(0.421279\pi\)
\(972\) 0 0
\(973\) 3.28843 0.105422
\(974\) −0.482953 −0.0154748
\(975\) 0 0
\(976\) −34.7225 −1.11144
\(977\) −3.90224 −0.124844 −0.0624219 0.998050i \(-0.519882\pi\)
−0.0624219 + 0.998050i \(0.519882\pi\)
\(978\) 0 0
\(979\) −2.28073 −0.0728924
\(980\) 4.24705 0.135667
\(981\) 0 0
\(982\) 5.78392 0.184572
\(983\) −53.3262 −1.70084 −0.850420 0.526104i \(-0.823652\pi\)
−0.850420 + 0.526104i \(0.823652\pi\)
\(984\) 0 0
\(985\) −24.0071 −0.764929
\(986\) −1.24421 −0.0396238
\(987\) 0 0
\(988\) 20.8339 0.662816
\(989\) −0.869560 −0.0276504
\(990\) 0 0
\(991\) 19.5111 0.619790 0.309895 0.950771i \(-0.399706\pi\)
0.309895 + 0.950771i \(0.399706\pi\)
\(992\) −2.19578 −0.0697159
\(993\) 0 0
\(994\) 2.87583 0.0912158
\(995\) −28.9660 −0.918283
\(996\) 0 0
\(997\) 45.8824 1.45311 0.726556 0.687108i \(-0.241120\pi\)
0.726556 + 0.687108i \(0.241120\pi\)
\(998\) 2.61379 0.0827382
\(999\) 0 0
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 \(a_p\))