Properties

Label 8001.2.a.z.1.17
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

Related objects

Downloads

Learn more about

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 1.17
Character \(\chi\) = 8001.1

$q$-expansion

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

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 \(-0.477102\pi\)
0.0718744 + 0.997414i \(0.477102\pi\)
\(3\) 0 0
\(4\) −1.95867 −0.979336
\(5\) 2.16833 0.969707 0.484853 0.874596i \(-0.338873\pi\)
0.484853 + 0.874596i \(0.338873\pi\)
\(6\) 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 \(-0.599324\pi\)
−0.306996 + 0.951711i \(0.599324\pi\)
\(12\) 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 \(-0.411439\pi\)
0.274647 + 0.961545i \(0.411439\pi\)
\(18\) 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 \(-0.566867\pi\)
−0.208528 + 0.978016i \(0.566867\pi\)
\(24\) 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 \(-0.419270\pi\)
0.250909 + 0.968011i \(0.419270\pi\)
\(30\) 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 \(-0.403193\pi\)
0.299462 + 0.954108i \(0.403193\pi\)
\(42\) 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 \(-0.596042\pi\)
−0.297166 + 0.954826i \(0.596042\pi\)
\(48\) 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 \(-0.353560\pi\)
0.443998 + 0.896028i \(0.353560\pi\)
\(54\) 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 \(-0.851053\pi\)
−0.892504 + 0.451040i \(0.851053\pi\)
\(60\) 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 \(-0.817111\pi\)
−0.839430 + 0.543468i \(0.817111\pi\)
\(72\) 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 \(-0.587987\pi\)
−0.272911 + 0.962039i \(0.587987\pi\)
\(84\) 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 \(-0.481094\pi\)
0.0593594 + 0.998237i \(0.481094\pi\)
\(90\) 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 \(-0.321377\pi\)
0.532170 + 0.846638i \(0.321377\pi\)
\(102\) 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 \(-0.702080\pi\)
−0.593059 + 0.805159i \(0.702080\pi\)
\(108\) 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 \(-0.472147\pi\)
0.0873920 + 0.996174i \(0.472147\pi\)
\(114\) 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 \(-0.571477\pi\)
−0.222670 + 0.974894i \(0.571477\pi\)
\(132\) 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 \(-0.452088\pi\)
0.149951 + 0.988693i \(0.452088\pi\)
\(138\) 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 \(-0.709084\pi\)
−0.610630 + 0.791916i \(0.709084\pi\)
\(150\) 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 \(-0.620240\pi\)
−0.368825 + 0.929499i \(0.620240\pi\)
\(168\) 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 \(-0.201764\pi\)
0.805748 + 0.592259i \(0.201764\pi\)
\(174\) 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 \(-0.159455\pi\)
0.877130 + 0.480253i \(0.159455\pi\)
\(180\) 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 \(-0.378422\pi\)
0.372730 + 0.927940i \(0.378422\pi\)
\(192\) 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 \(-0.629052\pi\)
−0.394413 + 0.918933i \(0.629052\pi\)
\(198\) 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 \(-0.913701\pi\)
−0.963472 + 0.267808i \(0.913701\pi\)
\(228\) 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 \(-0.678885\pi\)
−0.532866 + 0.846200i \(0.678885\pi\)
\(234\) 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 \(-0.705805\pi\)
−0.602442 + 0.798163i \(0.705805\pi\)
\(240\) 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 \(-0.133333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(252\) 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 \(-0.396919\pi\)
0.318207 + 0.948021i \(0.396919\pi\)
\(258\) 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 \(-0.501355\pi\)
−0.00425647 + 0.999991i \(0.501355\pi\)
\(264\) 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 \(-0.507451\pi\)
−0.0234059 + 0.999726i \(0.507451\pi\)
\(270\) 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 \(-0.598126\pi\)
−0.303413 + 0.952859i \(0.598126\pi\)
\(282\) 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 \(-0.623478\pi\)
−0.378261 + 0.925699i \(0.623478\pi\)
\(294\) 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 \(-0.252503\pi\)
0.701525 + 0.712645i \(0.252503\pi\)
\(312\) 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 \(-0.471890\pi\)
0.0881947 + 0.996103i \(0.471890\pi\)
\(318\) 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 \(-0.381048\pi\)
0.365061 + 0.930983i \(0.381048\pi\)
\(348\) 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 \(-0.126082\pi\)
0.922574 + 0.385821i \(0.126082\pi\)
\(354\) 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 \(-0.596386\pi\)
−0.298200 + 0.954503i \(0.596386\pi\)
\(360\) 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 \(-0.223230\pi\)
0.764006 + 0.645210i \(0.223230\pi\)
\(384\) 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 \(-0.433505\pi\)
0.207383 + 0.978260i \(0.433505\pi\)
\(390\) 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 \(-0.810889\pi\)
−0.828648 + 0.559770i \(0.810889\pi\)
\(402\) 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 \(-0.805324\pi\)
−0.818734 + 0.574173i \(0.805324\pi\)
\(420\) 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 \(-0.485415\pi\)
0.0458026 + 0.998951i \(0.485415\pi\)
\(432\) 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 \(-0.409592\pi\)
0.280222 + 0.959935i \(0.409592\pi\)
\(444\) 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 \(-0.718147\pi\)
−0.632928 + 0.774211i \(0.718147\pi\)
\(450\) 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 \(-0.805307\pi\)
−0.818703 + 0.574217i \(0.805307\pi\)
\(462\) 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 \(-0.553598\pi\)
−0.167588 + 0.985857i \(0.553598\pi\)
\(468\) 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 \(-0.427681\pi\)
0.225248 + 0.974302i \(0.427681\pi\)
\(480\) 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 \(-0.278107\pi\)
0.641995 + 0.766709i \(0.278107\pi\)
\(492\) 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 \(-0.462675\pi\)
0.116990 + 0.993133i \(0.462675\pi\)
\(504\) 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 \(-0.673819\pi\)
−0.519332 + 0.854572i \(0.673819\pi\)
\(510\) 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 \(-0.441135\pi\)
0.183877 + 0.982949i \(0.441135\pi\)
\(522\) 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 \(-0.237385\pi\)
0.734568 + 0.678535i \(0.237385\pi\)
\(558\) 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 \(-0.397197\pi\)
0.317381 + 0.948298i \(0.397197\pi\)
\(564\) 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 \(-0.377226\pi\)
0.376213 + 0.926533i \(0.377226\pi\)
\(570\) 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 \(-0.667972\pi\)
−0.503546 + 0.863968i \(0.667972\pi\)
\(588\) 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 \(-0.640116\pi\)
−0.426110 + 0.904672i \(0.640116\pi\)
\(594\) 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 \(-0.241195\pi\)
0.726393 + 0.687280i \(0.241195\pi\)
\(600\) 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 \(-0.551034\pi\)
−0.159644 + 0.987175i \(0.551034\pi\)
\(618\) 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 \(-0.608009\pi\)
−0.332846 + 0.942981i \(0.608009\pi\)
\(642\) 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 \(-0.462094\pi\)
0.118803 + 0.992918i \(0.462094\pi\)
\(648\) 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 \(-0.647687\pi\)
−0.447505 + 0.894282i \(0.647687\pi\)
\(654\) 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 \(-0.195298\pi\)
0.817612 + 0.575770i \(0.195298\pi\)
\(660\) 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 \(-0.512955\pi\)
−0.0406895 + 0.999172i \(0.512955\pi\)
\(678\) 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 \(-0.885199\pi\)
−0.935665 + 0.352889i \(0.885199\pi\)
\(684\) 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 \(-0.245846\pi\)
0.716274 + 0.697819i \(0.245846\pi\)
\(702\) 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 \(-0.623867\pi\)
−0.379392 + 0.925236i \(0.623867\pi\)
\(720\) 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 \(-0.585360\pi\)
−0.264962 + 0.964259i \(0.585360\pi\)
\(744\) 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 \(-0.418003\pi\)
0.254760 + 0.967004i \(0.418003\pi\)
\(762\) 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 \(-0.521204\pi\)
−0.0665651 + 0.997782i \(0.521204\pi\)
\(774\) 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 \(-0.491327\pi\)
0.0272450 + 0.999629i \(0.491327\pi\)
\(798\) 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 \(-0.550424\pi\)
−0.157751 + 0.987479i \(0.550424\pi\)
\(810\) 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 \(-0.360631\pi\)
0.423985 + 0.905669i \(0.360631\pi\)
\(822\) 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 \(-0.878585\pi\)
−0.928131 + 0.372253i \(0.878585\pi\)
\(828\) 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 \(-0.249504\pi\)
0.708208 + 0.706004i \(0.249504\pi\)
\(840\) 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 \(-0.586623\pi\)
−0.268789 + 0.963199i \(0.586623\pi\)
\(858\) 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 \(-0.626466\pi\)
−0.386934 + 0.922107i \(0.626466\pi\)
\(864\) 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 \(-0.171020\pi\)
0.859106 + 0.511798i \(0.171020\pi\)
\(882\) 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 \(-0.347656\pi\)
0.460539 + 0.887639i \(0.347656\pi\)
\(888\) 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 \(-0.837863\pi\)
−0.873052 + 0.487627i \(0.837863\pi\)
\(912\) 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 \(-0.751640\pi\)
−0.710740 + 0.703455i \(0.751640\pi\)
\(930\) 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 \(-0.428463\pi\)
0.222854 + 0.974852i \(0.428463\pi\)
\(942\) 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 \(-0.512270\pi\)
−0.0385378 + 0.999257i \(0.512270\pi\)
\(948\) 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 \(-0.621944\pi\)
−0.373796 + 0.927511i \(0.621944\pi\)
\(954\) 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 \(-0.578721\pi\)
−0.244797 + 0.969574i \(0.578721\pi\)
\(972\) 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 \(-0.480118\pi\)
0.0624219 + 0.998050i \(0.480118\pi\)
\(978\) 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 \(-0.176348\pi\)
0.850420 + 0.526104i \(0.176348\pi\)
\(984\) 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 \(a_p\))