Properties

Label 8024.2.a.y.1.4
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.64010 q^{3} +3.09841 q^{5} -1.88185 q^{7} +3.97013 q^{9} +O(q^{10})\) \(q-2.64010 q^{3} +3.09841 q^{5} -1.88185 q^{7} +3.97013 q^{9} +0.597371 q^{11} +2.98307 q^{13} -8.18011 q^{15} -1.00000 q^{17} +4.89604 q^{19} +4.96827 q^{21} -4.83192 q^{23} +4.60014 q^{25} -2.56124 q^{27} -2.75562 q^{29} -5.24822 q^{31} -1.57712 q^{33} -5.83074 q^{35} +1.62507 q^{37} -7.87561 q^{39} +0.567272 q^{41} -4.98079 q^{43} +12.3011 q^{45} -13.6250 q^{47} -3.45864 q^{49} +2.64010 q^{51} +12.5718 q^{53} +1.85090 q^{55} -12.9260 q^{57} -1.00000 q^{59} -3.62825 q^{61} -7.47118 q^{63} +9.24278 q^{65} +3.19537 q^{67} +12.7567 q^{69} -0.921306 q^{71} -6.23436 q^{73} -12.1448 q^{75} -1.12416 q^{77} +5.92392 q^{79} -5.14846 q^{81} +1.29606 q^{83} -3.09841 q^{85} +7.27512 q^{87} -11.8793 q^{89} -5.61369 q^{91} +13.8558 q^{93} +15.1699 q^{95} +18.6143 q^{97} +2.37164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 6q^{3} - q^{7} + 23q^{9} + O(q^{10}) \) \( 23q - 6q^{3} - q^{7} + 23q^{9} - 3q^{11} - 7q^{13} - 2q^{15} - 23q^{17} - 16q^{19} - 11q^{21} - 29q^{23} + 31q^{25} - 3q^{27} - 5q^{29} - 41q^{31} + 8q^{33} - 22q^{35} + 5q^{37} + 16q^{39} + 11q^{41} + 13q^{43} - 26q^{45} - 39q^{47} + 16q^{49} + 6q^{51} - 2q^{53} - 35q^{55} + 13q^{57} - 23q^{59} - 37q^{61} + 33q^{65} - 34q^{67} - 66q^{69} - 13q^{71} - 14q^{73} - 81q^{75} - 4q^{77} - 61q^{79} - q^{81} - 9q^{83} - 16q^{87} + 28q^{89} - 18q^{91} - 62q^{93} - 33q^{95} - 5q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.64010 −1.52426 −0.762131 0.647423i \(-0.775847\pi\)
−0.762131 + 0.647423i \(0.775847\pi\)
\(4\) 0 0
\(5\) 3.09841 1.38565 0.692825 0.721105i \(-0.256366\pi\)
0.692825 + 0.721105i \(0.256366\pi\)
\(6\) 0 0
\(7\) −1.88185 −0.711272 −0.355636 0.934625i \(-0.615736\pi\)
−0.355636 + 0.934625i \(0.615736\pi\)
\(8\) 0 0
\(9\) 3.97013 1.32338
\(10\) 0 0
\(11\) 0.597371 0.180114 0.0900571 0.995937i \(-0.471295\pi\)
0.0900571 + 0.995937i \(0.471295\pi\)
\(12\) 0 0
\(13\) 2.98307 0.827355 0.413678 0.910423i \(-0.364244\pi\)
0.413678 + 0.910423i \(0.364244\pi\)
\(14\) 0 0
\(15\) −8.18011 −2.11210
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 4.89604 1.12323 0.561614 0.827399i \(-0.310181\pi\)
0.561614 + 0.827399i \(0.310181\pi\)
\(20\) 0 0
\(21\) 4.96827 1.08417
\(22\) 0 0
\(23\) −4.83192 −1.00752 −0.503762 0.863843i \(-0.668051\pi\)
−0.503762 + 0.863843i \(0.668051\pi\)
\(24\) 0 0
\(25\) 4.60014 0.920028
\(26\) 0 0
\(27\) −2.56124 −0.492910
\(28\) 0 0
\(29\) −2.75562 −0.511706 −0.255853 0.966716i \(-0.582356\pi\)
−0.255853 + 0.966716i \(0.582356\pi\)
\(30\) 0 0
\(31\) −5.24822 −0.942608 −0.471304 0.881971i \(-0.656217\pi\)
−0.471304 + 0.881971i \(0.656217\pi\)
\(32\) 0 0
\(33\) −1.57712 −0.274541
\(34\) 0 0
\(35\) −5.83074 −0.985575
\(36\) 0 0
\(37\) 1.62507 0.267160 0.133580 0.991038i \(-0.457353\pi\)
0.133580 + 0.991038i \(0.457353\pi\)
\(38\) 0 0
\(39\) −7.87561 −1.26111
\(40\) 0 0
\(41\) 0.567272 0.0885930 0.0442965 0.999018i \(-0.485895\pi\)
0.0442965 + 0.999018i \(0.485895\pi\)
\(42\) 0 0
\(43\) −4.98079 −0.759563 −0.379782 0.925076i \(-0.624001\pi\)
−0.379782 + 0.925076i \(0.624001\pi\)
\(44\) 0 0
\(45\) 12.3011 1.83374
\(46\) 0 0
\(47\) −13.6250 −1.98741 −0.993706 0.112024i \(-0.964267\pi\)
−0.993706 + 0.112024i \(0.964267\pi\)
\(48\) 0 0
\(49\) −3.45864 −0.494092
\(50\) 0 0
\(51\) 2.64010 0.369688
\(52\) 0 0
\(53\) 12.5718 1.72686 0.863431 0.504466i \(-0.168311\pi\)
0.863431 + 0.504466i \(0.168311\pi\)
\(54\) 0 0
\(55\) 1.85090 0.249575
\(56\) 0 0
\(57\) −12.9260 −1.71210
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −3.62825 −0.464550 −0.232275 0.972650i \(-0.574617\pi\)
−0.232275 + 0.972650i \(0.574617\pi\)
\(62\) 0 0
\(63\) −7.47118 −0.941280
\(64\) 0 0
\(65\) 9.24278 1.14643
\(66\) 0 0
\(67\) 3.19537 0.390376 0.195188 0.980766i \(-0.437468\pi\)
0.195188 + 0.980766i \(0.437468\pi\)
\(68\) 0 0
\(69\) 12.7567 1.53573
\(70\) 0 0
\(71\) −0.921306 −0.109339 −0.0546695 0.998505i \(-0.517411\pi\)
−0.0546695 + 0.998505i \(0.517411\pi\)
\(72\) 0 0
\(73\) −6.23436 −0.729677 −0.364838 0.931071i \(-0.618876\pi\)
−0.364838 + 0.931071i \(0.618876\pi\)
\(74\) 0 0
\(75\) −12.1448 −1.40236
\(76\) 0 0
\(77\) −1.12416 −0.128110
\(78\) 0 0
\(79\) 5.92392 0.666493 0.333246 0.942840i \(-0.391856\pi\)
0.333246 + 0.942840i \(0.391856\pi\)
\(80\) 0 0
\(81\) −5.14846 −0.572052
\(82\) 0 0
\(83\) 1.29606 0.142262 0.0711308 0.997467i \(-0.477339\pi\)
0.0711308 + 0.997467i \(0.477339\pi\)
\(84\) 0 0
\(85\) −3.09841 −0.336070
\(86\) 0 0
\(87\) 7.27512 0.779975
\(88\) 0 0
\(89\) −11.8793 −1.25920 −0.629602 0.776918i \(-0.716782\pi\)
−0.629602 + 0.776918i \(0.716782\pi\)
\(90\) 0 0
\(91\) −5.61369 −0.588475
\(92\) 0 0
\(93\) 13.8558 1.43678
\(94\) 0 0
\(95\) 15.1699 1.55640
\(96\) 0 0
\(97\) 18.6143 1.88999 0.944996 0.327082i \(-0.106065\pi\)
0.944996 + 0.327082i \(0.106065\pi\)
\(98\) 0 0
\(99\) 2.37164 0.238359
\(100\) 0 0
\(101\) −16.5349 −1.64528 −0.822640 0.568562i \(-0.807500\pi\)
−0.822640 + 0.568562i \(0.807500\pi\)
\(102\) 0 0
\(103\) −5.63356 −0.555091 −0.277545 0.960713i \(-0.589521\pi\)
−0.277545 + 0.960713i \(0.589521\pi\)
\(104\) 0 0
\(105\) 15.3937 1.50227
\(106\) 0 0
\(107\) 15.1779 1.46731 0.733653 0.679524i \(-0.237814\pi\)
0.733653 + 0.679524i \(0.237814\pi\)
\(108\) 0 0
\(109\) −19.3868 −1.85692 −0.928458 0.371437i \(-0.878865\pi\)
−0.928458 + 0.371437i \(0.878865\pi\)
\(110\) 0 0
\(111\) −4.29034 −0.407221
\(112\) 0 0
\(113\) 13.7574 1.29418 0.647092 0.762412i \(-0.275985\pi\)
0.647092 + 0.762412i \(0.275985\pi\)
\(114\) 0 0
\(115\) −14.9713 −1.39608
\(116\) 0 0
\(117\) 11.8432 1.09490
\(118\) 0 0
\(119\) 1.88185 0.172509
\(120\) 0 0
\(121\) −10.6431 −0.967559
\(122\) 0 0
\(123\) −1.49765 −0.135039
\(124\) 0 0
\(125\) −1.23893 −0.110813
\(126\) 0 0
\(127\) −21.2558 −1.88615 −0.943074 0.332582i \(-0.892080\pi\)
−0.943074 + 0.332582i \(0.892080\pi\)
\(128\) 0 0
\(129\) 13.1498 1.15777
\(130\) 0 0
\(131\) 11.3956 0.995636 0.497818 0.867282i \(-0.334135\pi\)
0.497818 + 0.867282i \(0.334135\pi\)
\(132\) 0 0
\(133\) −9.21361 −0.798921
\(134\) 0 0
\(135\) −7.93576 −0.683001
\(136\) 0 0
\(137\) −0.174089 −0.0148734 −0.00743671 0.999972i \(-0.502367\pi\)
−0.00743671 + 0.999972i \(0.502367\pi\)
\(138\) 0 0
\(139\) 4.60245 0.390374 0.195187 0.980766i \(-0.437469\pi\)
0.195187 + 0.980766i \(0.437469\pi\)
\(140\) 0 0
\(141\) 35.9714 3.02934
\(142\) 0 0
\(143\) 1.78200 0.149018
\(144\) 0 0
\(145\) −8.53805 −0.709046
\(146\) 0 0
\(147\) 9.13117 0.753126
\(148\) 0 0
\(149\) 10.1384 0.830567 0.415284 0.909692i \(-0.363682\pi\)
0.415284 + 0.909692i \(0.363682\pi\)
\(150\) 0 0
\(151\) −20.0810 −1.63417 −0.817084 0.576519i \(-0.804411\pi\)
−0.817084 + 0.576519i \(0.804411\pi\)
\(152\) 0 0
\(153\) −3.97013 −0.320966
\(154\) 0 0
\(155\) −16.2611 −1.30613
\(156\) 0 0
\(157\) 14.3233 1.14312 0.571561 0.820560i \(-0.306338\pi\)
0.571561 + 0.820560i \(0.306338\pi\)
\(158\) 0 0
\(159\) −33.1907 −2.63219
\(160\) 0 0
\(161\) 9.09293 0.716624
\(162\) 0 0
\(163\) 2.58984 0.202852 0.101426 0.994843i \(-0.467660\pi\)
0.101426 + 0.994843i \(0.467660\pi\)
\(164\) 0 0
\(165\) −4.88656 −0.380418
\(166\) 0 0
\(167\) 13.7417 1.06336 0.531681 0.846944i \(-0.321560\pi\)
0.531681 + 0.846944i \(0.321560\pi\)
\(168\) 0 0
\(169\) −4.10128 −0.315483
\(170\) 0 0
\(171\) 19.4379 1.48645
\(172\) 0 0
\(173\) −12.4631 −0.947554 −0.473777 0.880645i \(-0.657110\pi\)
−0.473777 + 0.880645i \(0.657110\pi\)
\(174\) 0 0
\(175\) −8.65677 −0.654390
\(176\) 0 0
\(177\) 2.64010 0.198442
\(178\) 0 0
\(179\) 6.02229 0.450127 0.225064 0.974344i \(-0.427741\pi\)
0.225064 + 0.974344i \(0.427741\pi\)
\(180\) 0 0
\(181\) 20.0689 1.49171 0.745856 0.666107i \(-0.232041\pi\)
0.745856 + 0.666107i \(0.232041\pi\)
\(182\) 0 0
\(183\) 9.57895 0.708097
\(184\) 0 0
\(185\) 5.03513 0.370190
\(186\) 0 0
\(187\) −0.597371 −0.0436841
\(188\) 0 0
\(189\) 4.81986 0.350593
\(190\) 0 0
\(191\) −7.88848 −0.570791 −0.285395 0.958410i \(-0.592125\pi\)
−0.285395 + 0.958410i \(0.592125\pi\)
\(192\) 0 0
\(193\) 13.3107 0.958127 0.479064 0.877780i \(-0.340976\pi\)
0.479064 + 0.877780i \(0.340976\pi\)
\(194\) 0 0
\(195\) −24.4019 −1.74745
\(196\) 0 0
\(197\) −2.95073 −0.210231 −0.105115 0.994460i \(-0.533521\pi\)
−0.105115 + 0.994460i \(0.533521\pi\)
\(198\) 0 0
\(199\) −17.0945 −1.21180 −0.605898 0.795542i \(-0.707186\pi\)
−0.605898 + 0.795542i \(0.707186\pi\)
\(200\) 0 0
\(201\) −8.43609 −0.595036
\(202\) 0 0
\(203\) 5.18567 0.363963
\(204\) 0 0
\(205\) 1.75764 0.122759
\(206\) 0 0
\(207\) −19.1833 −1.33333
\(208\) 0 0
\(209\) 2.92475 0.202309
\(210\) 0 0
\(211\) 13.2152 0.909774 0.454887 0.890549i \(-0.349680\pi\)
0.454887 + 0.890549i \(0.349680\pi\)
\(212\) 0 0
\(213\) 2.43234 0.166661
\(214\) 0 0
\(215\) −15.4325 −1.05249
\(216\) 0 0
\(217\) 9.87636 0.670451
\(218\) 0 0
\(219\) 16.4593 1.11222
\(220\) 0 0
\(221\) −2.98307 −0.200663
\(222\) 0 0
\(223\) −16.0443 −1.07440 −0.537202 0.843454i \(-0.680519\pi\)
−0.537202 + 0.843454i \(0.680519\pi\)
\(224\) 0 0
\(225\) 18.2631 1.21754
\(226\) 0 0
\(227\) 13.8961 0.922318 0.461159 0.887317i \(-0.347434\pi\)
0.461159 + 0.887317i \(0.347434\pi\)
\(228\) 0 0
\(229\) −0.397114 −0.0262421 −0.0131210 0.999914i \(-0.504177\pi\)
−0.0131210 + 0.999914i \(0.504177\pi\)
\(230\) 0 0
\(231\) 2.96790 0.195273
\(232\) 0 0
\(233\) −22.3412 −1.46362 −0.731810 0.681509i \(-0.761324\pi\)
−0.731810 + 0.681509i \(0.761324\pi\)
\(234\) 0 0
\(235\) −42.2158 −2.75386
\(236\) 0 0
\(237\) −15.6397 −1.01591
\(238\) 0 0
\(239\) −24.6079 −1.59175 −0.795877 0.605459i \(-0.792990\pi\)
−0.795877 + 0.605459i \(0.792990\pi\)
\(240\) 0 0
\(241\) −8.68646 −0.559544 −0.279772 0.960066i \(-0.590259\pi\)
−0.279772 + 0.960066i \(0.590259\pi\)
\(242\) 0 0
\(243\) 21.2762 1.36487
\(244\) 0 0
\(245\) −10.7163 −0.684639
\(246\) 0 0
\(247\) 14.6052 0.929309
\(248\) 0 0
\(249\) −3.42174 −0.216844
\(250\) 0 0
\(251\) −21.0928 −1.33137 −0.665683 0.746235i \(-0.731860\pi\)
−0.665683 + 0.746235i \(0.731860\pi\)
\(252\) 0 0
\(253\) −2.88645 −0.181469
\(254\) 0 0
\(255\) 8.18011 0.512258
\(256\) 0 0
\(257\) −11.6927 −0.729373 −0.364686 0.931130i \(-0.618824\pi\)
−0.364686 + 0.931130i \(0.618824\pi\)
\(258\) 0 0
\(259\) −3.05813 −0.190023
\(260\) 0 0
\(261\) −10.9402 −0.677180
\(262\) 0 0
\(263\) 10.1676 0.626958 0.313479 0.949595i \(-0.398505\pi\)
0.313479 + 0.949595i \(0.398505\pi\)
\(264\) 0 0
\(265\) 38.9524 2.39283
\(266\) 0 0
\(267\) 31.3626 1.91936
\(268\) 0 0
\(269\) 27.8493 1.69800 0.849001 0.528391i \(-0.177205\pi\)
0.849001 + 0.528391i \(0.177205\pi\)
\(270\) 0 0
\(271\) 23.9963 1.45767 0.728834 0.684690i \(-0.240062\pi\)
0.728834 + 0.684690i \(0.240062\pi\)
\(272\) 0 0
\(273\) 14.8207 0.896990
\(274\) 0 0
\(275\) 2.74799 0.165710
\(276\) 0 0
\(277\) −6.70010 −0.402570 −0.201285 0.979533i \(-0.564512\pi\)
−0.201285 + 0.979533i \(0.564512\pi\)
\(278\) 0 0
\(279\) −20.8361 −1.24743
\(280\) 0 0
\(281\) 31.4486 1.87607 0.938033 0.346546i \(-0.112646\pi\)
0.938033 + 0.346546i \(0.112646\pi\)
\(282\) 0 0
\(283\) 22.1776 1.31832 0.659161 0.752002i \(-0.270912\pi\)
0.659161 + 0.752002i \(0.270912\pi\)
\(284\) 0 0
\(285\) −40.0501 −2.37237
\(286\) 0 0
\(287\) −1.06752 −0.0630137
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −49.1435 −2.88084
\(292\) 0 0
\(293\) −16.5035 −0.964143 −0.482072 0.876132i \(-0.660115\pi\)
−0.482072 + 0.876132i \(0.660115\pi\)
\(294\) 0 0
\(295\) −3.09841 −0.180396
\(296\) 0 0
\(297\) −1.53001 −0.0887801
\(298\) 0 0
\(299\) −14.4139 −0.833580
\(300\) 0 0
\(301\) 9.37309 0.540256
\(302\) 0 0
\(303\) 43.6537 2.50784
\(304\) 0 0
\(305\) −11.2418 −0.643705
\(306\) 0 0
\(307\) −23.2501 −1.32696 −0.663478 0.748196i \(-0.730920\pi\)
−0.663478 + 0.748196i \(0.730920\pi\)
\(308\) 0 0
\(309\) 14.8732 0.846104
\(310\) 0 0
\(311\) −0.529911 −0.0300485 −0.0150242 0.999887i \(-0.504783\pi\)
−0.0150242 + 0.999887i \(0.504783\pi\)
\(312\) 0 0
\(313\) −7.27055 −0.410956 −0.205478 0.978662i \(-0.565875\pi\)
−0.205478 + 0.978662i \(0.565875\pi\)
\(314\) 0 0
\(315\) −23.1488 −1.30429
\(316\) 0 0
\(317\) −15.4420 −0.867309 −0.433654 0.901079i \(-0.642776\pi\)
−0.433654 + 0.901079i \(0.642776\pi\)
\(318\) 0 0
\(319\) −1.64613 −0.0921656
\(320\) 0 0
\(321\) −40.0713 −2.23656
\(322\) 0 0
\(323\) −4.89604 −0.272423
\(324\) 0 0
\(325\) 13.7225 0.761190
\(326\) 0 0
\(327\) 51.1830 2.83043
\(328\) 0 0
\(329\) 25.6402 1.41359
\(330\) 0 0
\(331\) 24.7132 1.35836 0.679180 0.733971i \(-0.262335\pi\)
0.679180 + 0.733971i \(0.262335\pi\)
\(332\) 0 0
\(333\) 6.45173 0.353553
\(334\) 0 0
\(335\) 9.90056 0.540925
\(336\) 0 0
\(337\) 3.17452 0.172927 0.0864636 0.996255i \(-0.472443\pi\)
0.0864636 + 0.996255i \(0.472443\pi\)
\(338\) 0 0
\(339\) −36.3208 −1.97268
\(340\) 0 0
\(341\) −3.13513 −0.169777
\(342\) 0 0
\(343\) 19.6816 1.06271
\(344\) 0 0
\(345\) 39.5256 2.12799
\(346\) 0 0
\(347\) 6.12945 0.329046 0.164523 0.986373i \(-0.447391\pi\)
0.164523 + 0.986373i \(0.447391\pi\)
\(348\) 0 0
\(349\) −16.9644 −0.908081 −0.454040 0.890981i \(-0.650018\pi\)
−0.454040 + 0.890981i \(0.650018\pi\)
\(350\) 0 0
\(351\) −7.64035 −0.407812
\(352\) 0 0
\(353\) 21.9799 1.16987 0.584936 0.811080i \(-0.301120\pi\)
0.584936 + 0.811080i \(0.301120\pi\)
\(354\) 0 0
\(355\) −2.85458 −0.151506
\(356\) 0 0
\(357\) −4.96827 −0.262949
\(358\) 0 0
\(359\) −37.1601 −1.96124 −0.980618 0.195930i \(-0.937227\pi\)
−0.980618 + 0.195930i \(0.937227\pi\)
\(360\) 0 0
\(361\) 4.97120 0.261642
\(362\) 0 0
\(363\) 28.0990 1.47481
\(364\) 0 0
\(365\) −19.3166 −1.01108
\(366\) 0 0
\(367\) 15.9881 0.834569 0.417285 0.908776i \(-0.362982\pi\)
0.417285 + 0.908776i \(0.362982\pi\)
\(368\) 0 0
\(369\) 2.25214 0.117242
\(370\) 0 0
\(371\) −23.6581 −1.22827
\(372\) 0 0
\(373\) 4.89983 0.253703 0.126852 0.991922i \(-0.459513\pi\)
0.126852 + 0.991922i \(0.459513\pi\)
\(374\) 0 0
\(375\) 3.27090 0.168909
\(376\) 0 0
\(377\) −8.22022 −0.423363
\(378\) 0 0
\(379\) −26.7490 −1.37400 −0.687002 0.726656i \(-0.741073\pi\)
−0.687002 + 0.726656i \(0.741073\pi\)
\(380\) 0 0
\(381\) 56.1175 2.87499
\(382\) 0 0
\(383\) −20.9419 −1.07008 −0.535041 0.844826i \(-0.679704\pi\)
−0.535041 + 0.844826i \(0.679704\pi\)
\(384\) 0 0
\(385\) −3.48311 −0.177516
\(386\) 0 0
\(387\) −19.7744 −1.00519
\(388\) 0 0
\(389\) −11.3189 −0.573893 −0.286946 0.957947i \(-0.592640\pi\)
−0.286946 + 0.957947i \(0.592640\pi\)
\(390\) 0 0
\(391\) 4.83192 0.244360
\(392\) 0 0
\(393\) −30.0855 −1.51761
\(394\) 0 0
\(395\) 18.3547 0.923526
\(396\) 0 0
\(397\) −20.2420 −1.01592 −0.507958 0.861382i \(-0.669599\pi\)
−0.507958 + 0.861382i \(0.669599\pi\)
\(398\) 0 0
\(399\) 24.3248 1.21777
\(400\) 0 0
\(401\) 4.91967 0.245677 0.122838 0.992427i \(-0.460800\pi\)
0.122838 + 0.992427i \(0.460800\pi\)
\(402\) 0 0
\(403\) −15.6558 −0.779872
\(404\) 0 0
\(405\) −15.9521 −0.792664
\(406\) 0 0
\(407\) 0.970769 0.0481192
\(408\) 0 0
\(409\) 1.70945 0.0845270 0.0422635 0.999106i \(-0.486543\pi\)
0.0422635 + 0.999106i \(0.486543\pi\)
\(410\) 0 0
\(411\) 0.459612 0.0226710
\(412\) 0 0
\(413\) 1.88185 0.0925997
\(414\) 0 0
\(415\) 4.01574 0.197125
\(416\) 0 0
\(417\) −12.1509 −0.595033
\(418\) 0 0
\(419\) −40.6629 −1.98651 −0.993256 0.115939i \(-0.963012\pi\)
−0.993256 + 0.115939i \(0.963012\pi\)
\(420\) 0 0
\(421\) −30.8825 −1.50512 −0.752561 0.658522i \(-0.771182\pi\)
−0.752561 + 0.658522i \(0.771182\pi\)
\(422\) 0 0
\(423\) −54.0930 −2.63009
\(424\) 0 0
\(425\) −4.60014 −0.223140
\(426\) 0 0
\(427\) 6.82783 0.330422
\(428\) 0 0
\(429\) −4.70466 −0.227143
\(430\) 0 0
\(431\) 32.0926 1.54585 0.772924 0.634499i \(-0.218794\pi\)
0.772924 + 0.634499i \(0.218794\pi\)
\(432\) 0 0
\(433\) 16.2642 0.781610 0.390805 0.920474i \(-0.372197\pi\)
0.390805 + 0.920474i \(0.372197\pi\)
\(434\) 0 0
\(435\) 22.5413 1.08077
\(436\) 0 0
\(437\) −23.6572 −1.13168
\(438\) 0 0
\(439\) −18.0452 −0.861249 −0.430624 0.902531i \(-0.641707\pi\)
−0.430624 + 0.902531i \(0.641707\pi\)
\(440\) 0 0
\(441\) −13.7313 −0.653870
\(442\) 0 0
\(443\) 6.71841 0.319202 0.159601 0.987182i \(-0.448979\pi\)
0.159601 + 0.987182i \(0.448979\pi\)
\(444\) 0 0
\(445\) −36.8070 −1.74482
\(446\) 0 0
\(447\) −26.7663 −1.26600
\(448\) 0 0
\(449\) −39.0190 −1.84142 −0.920709 0.390250i \(-0.872389\pi\)
−0.920709 + 0.390250i \(0.872389\pi\)
\(450\) 0 0
\(451\) 0.338872 0.0159568
\(452\) 0 0
\(453\) 53.0158 2.49090
\(454\) 0 0
\(455\) −17.3935 −0.815420
\(456\) 0 0
\(457\) −18.1464 −0.848853 −0.424427 0.905462i \(-0.639524\pi\)
−0.424427 + 0.905462i \(0.639524\pi\)
\(458\) 0 0
\(459\) 2.56124 0.119548
\(460\) 0 0
\(461\) −32.3716 −1.50769 −0.753847 0.657049i \(-0.771804\pi\)
−0.753847 + 0.657049i \(0.771804\pi\)
\(462\) 0 0
\(463\) 8.09908 0.376396 0.188198 0.982131i \(-0.439735\pi\)
0.188198 + 0.982131i \(0.439735\pi\)
\(464\) 0 0
\(465\) 42.9310 1.99088
\(466\) 0 0
\(467\) 14.0590 0.650572 0.325286 0.945616i \(-0.394539\pi\)
0.325286 + 0.945616i \(0.394539\pi\)
\(468\) 0 0
\(469\) −6.01320 −0.277664
\(470\) 0 0
\(471\) −37.8149 −1.74242
\(472\) 0 0
\(473\) −2.97538 −0.136808
\(474\) 0 0
\(475\) 22.5225 1.03340
\(476\) 0 0
\(477\) 49.9115 2.28529
\(478\) 0 0
\(479\) 13.4726 0.615581 0.307791 0.951454i \(-0.400410\pi\)
0.307791 + 0.951454i \(0.400410\pi\)
\(480\) 0 0
\(481\) 4.84770 0.221036
\(482\) 0 0
\(483\) −24.0063 −1.09232
\(484\) 0 0
\(485\) 57.6746 2.61887
\(486\) 0 0
\(487\) 10.1883 0.461674 0.230837 0.972992i \(-0.425854\pi\)
0.230837 + 0.972992i \(0.425854\pi\)
\(488\) 0 0
\(489\) −6.83743 −0.309199
\(490\) 0 0
\(491\) −34.9968 −1.57939 −0.789693 0.613502i \(-0.789760\pi\)
−0.789693 + 0.613502i \(0.789760\pi\)
\(492\) 0 0
\(493\) 2.75562 0.124107
\(494\) 0 0
\(495\) 7.34831 0.330282
\(496\) 0 0
\(497\) 1.73376 0.0777697
\(498\) 0 0
\(499\) −21.5376 −0.964156 −0.482078 0.876128i \(-0.660118\pi\)
−0.482078 + 0.876128i \(0.660118\pi\)
\(500\) 0 0
\(501\) −36.2794 −1.62084
\(502\) 0 0
\(503\) −11.4976 −0.512653 −0.256327 0.966590i \(-0.582512\pi\)
−0.256327 + 0.966590i \(0.582512\pi\)
\(504\) 0 0
\(505\) −51.2318 −2.27978
\(506\) 0 0
\(507\) 10.8278 0.480879
\(508\) 0 0
\(509\) −19.9714 −0.885218 −0.442609 0.896715i \(-0.645947\pi\)
−0.442609 + 0.896715i \(0.645947\pi\)
\(510\) 0 0
\(511\) 11.7321 0.518999
\(512\) 0 0
\(513\) −12.5399 −0.553651
\(514\) 0 0
\(515\) −17.4551 −0.769162
\(516\) 0 0
\(517\) −8.13918 −0.357961
\(518\) 0 0
\(519\) 32.9039 1.44432
\(520\) 0 0
\(521\) −23.4369 −1.02679 −0.513395 0.858153i \(-0.671612\pi\)
−0.513395 + 0.858153i \(0.671612\pi\)
\(522\) 0 0
\(523\) −12.6568 −0.553442 −0.276721 0.960950i \(-0.589248\pi\)
−0.276721 + 0.960950i \(0.589248\pi\)
\(524\) 0 0
\(525\) 22.8547 0.997462
\(526\) 0 0
\(527\) 5.24822 0.228616
\(528\) 0 0
\(529\) 0.347403 0.0151045
\(530\) 0 0
\(531\) −3.97013 −0.172289
\(532\) 0 0
\(533\) 1.69221 0.0732979
\(534\) 0 0
\(535\) 47.0275 2.03317
\(536\) 0 0
\(537\) −15.8994 −0.686112
\(538\) 0 0
\(539\) −2.06609 −0.0889930
\(540\) 0 0
\(541\) −34.5836 −1.48686 −0.743432 0.668812i \(-0.766803\pi\)
−0.743432 + 0.668812i \(0.766803\pi\)
\(542\) 0 0
\(543\) −52.9840 −2.27376
\(544\) 0 0
\(545\) −60.0682 −2.57304
\(546\) 0 0
\(547\) −19.9236 −0.851871 −0.425936 0.904754i \(-0.640055\pi\)
−0.425936 + 0.904754i \(0.640055\pi\)
\(548\) 0 0
\(549\) −14.4046 −0.614775
\(550\) 0 0
\(551\) −13.4916 −0.574763
\(552\) 0 0
\(553\) −11.1479 −0.474058
\(554\) 0 0
\(555\) −13.2932 −0.564267
\(556\) 0 0
\(557\) 32.0465 1.35785 0.678927 0.734206i \(-0.262445\pi\)
0.678927 + 0.734206i \(0.262445\pi\)
\(558\) 0 0
\(559\) −14.8580 −0.628429
\(560\) 0 0
\(561\) 1.57712 0.0665860
\(562\) 0 0
\(563\) −5.95563 −0.251000 −0.125500 0.992094i \(-0.540053\pi\)
−0.125500 + 0.992094i \(0.540053\pi\)
\(564\) 0 0
\(565\) 42.6260 1.79329
\(566\) 0 0
\(567\) 9.68863 0.406884
\(568\) 0 0
\(569\) 40.2198 1.68610 0.843051 0.537833i \(-0.180757\pi\)
0.843051 + 0.537833i \(0.180757\pi\)
\(570\) 0 0
\(571\) −33.5014 −1.40199 −0.700995 0.713166i \(-0.747261\pi\)
−0.700995 + 0.713166i \(0.747261\pi\)
\(572\) 0 0
\(573\) 20.8264 0.870035
\(574\) 0 0
\(575\) −22.2275 −0.926950
\(576\) 0 0
\(577\) −31.3005 −1.30306 −0.651528 0.758625i \(-0.725872\pi\)
−0.651528 + 0.758625i \(0.725872\pi\)
\(578\) 0 0
\(579\) −35.1417 −1.46044
\(580\) 0 0
\(581\) −2.43900 −0.101187
\(582\) 0 0
\(583\) 7.51000 0.311032
\(584\) 0 0
\(585\) 36.6950 1.51715
\(586\) 0 0
\(587\) −7.49924 −0.309527 −0.154763 0.987952i \(-0.549461\pi\)
−0.154763 + 0.987952i \(0.549461\pi\)
\(588\) 0 0
\(589\) −25.6955 −1.05876
\(590\) 0 0
\(591\) 7.79023 0.320447
\(592\) 0 0
\(593\) 12.9774 0.532917 0.266459 0.963846i \(-0.414146\pi\)
0.266459 + 0.963846i \(0.414146\pi\)
\(594\) 0 0
\(595\) 5.83074 0.239037
\(596\) 0 0
\(597\) 45.1311 1.84709
\(598\) 0 0
\(599\) −19.2832 −0.787891 −0.393946 0.919134i \(-0.628890\pi\)
−0.393946 + 0.919134i \(0.628890\pi\)
\(600\) 0 0
\(601\) −6.83449 −0.278785 −0.139392 0.990237i \(-0.544515\pi\)
−0.139392 + 0.990237i \(0.544515\pi\)
\(602\) 0 0
\(603\) 12.6860 0.516615
\(604\) 0 0
\(605\) −32.9768 −1.34070
\(606\) 0 0
\(607\) −2.33426 −0.0947445 −0.0473723 0.998877i \(-0.515085\pi\)
−0.0473723 + 0.998877i \(0.515085\pi\)
\(608\) 0 0
\(609\) −13.6907 −0.554774
\(610\) 0 0
\(611\) −40.6444 −1.64429
\(612\) 0 0
\(613\) 22.3782 0.903846 0.451923 0.892057i \(-0.350738\pi\)
0.451923 + 0.892057i \(0.350738\pi\)
\(614\) 0 0
\(615\) −4.64035 −0.187117
\(616\) 0 0
\(617\) −15.2812 −0.615198 −0.307599 0.951516i \(-0.599525\pi\)
−0.307599 + 0.951516i \(0.599525\pi\)
\(618\) 0 0
\(619\) 43.8678 1.76320 0.881598 0.472000i \(-0.156468\pi\)
0.881598 + 0.472000i \(0.156468\pi\)
\(620\) 0 0
\(621\) 12.3757 0.496619
\(622\) 0 0
\(623\) 22.3551 0.895637
\(624\) 0 0
\(625\) −26.8394 −1.07358
\(626\) 0 0
\(627\) −7.72164 −0.308372
\(628\) 0 0
\(629\) −1.62507 −0.0647957
\(630\) 0 0
\(631\) −29.3235 −1.16735 −0.583675 0.811987i \(-0.698386\pi\)
−0.583675 + 0.811987i \(0.698386\pi\)
\(632\) 0 0
\(633\) −34.8895 −1.38673
\(634\) 0 0
\(635\) −65.8592 −2.61354
\(636\) 0 0
\(637\) −10.3174 −0.408790
\(638\) 0 0
\(639\) −3.65770 −0.144697
\(640\) 0 0
\(641\) 0.379717 0.0149979 0.00749897 0.999972i \(-0.497613\pi\)
0.00749897 + 0.999972i \(0.497613\pi\)
\(642\) 0 0
\(643\) −12.1713 −0.479991 −0.239995 0.970774i \(-0.577146\pi\)
−0.239995 + 0.970774i \(0.577146\pi\)
\(644\) 0 0
\(645\) 40.7434 1.60427
\(646\) 0 0
\(647\) 15.9328 0.626382 0.313191 0.949690i \(-0.398602\pi\)
0.313191 + 0.949690i \(0.398602\pi\)
\(648\) 0 0
\(649\) −0.597371 −0.0234489
\(650\) 0 0
\(651\) −26.0746 −1.02194
\(652\) 0 0
\(653\) −17.0340 −0.666592 −0.333296 0.942822i \(-0.608161\pi\)
−0.333296 + 0.942822i \(0.608161\pi\)
\(654\) 0 0
\(655\) 35.3082 1.37960
\(656\) 0 0
\(657\) −24.7512 −0.965637
\(658\) 0 0
\(659\) −6.93126 −0.270004 −0.135002 0.990845i \(-0.543104\pi\)
−0.135002 + 0.990845i \(0.543104\pi\)
\(660\) 0 0
\(661\) −13.1041 −0.509690 −0.254845 0.966982i \(-0.582024\pi\)
−0.254845 + 0.966982i \(0.582024\pi\)
\(662\) 0 0
\(663\) 7.87561 0.305863
\(664\) 0 0
\(665\) −28.5475 −1.10703
\(666\) 0 0
\(667\) 13.3149 0.515557
\(668\) 0 0
\(669\) 42.3585 1.63767
\(670\) 0 0
\(671\) −2.16741 −0.0836721
\(672\) 0 0
\(673\) −25.8628 −0.996938 −0.498469 0.866907i \(-0.666104\pi\)
−0.498469 + 0.866907i \(0.666104\pi\)
\(674\) 0 0
\(675\) −11.7820 −0.453491
\(676\) 0 0
\(677\) −50.0947 −1.92530 −0.962648 0.270757i \(-0.912726\pi\)
−0.962648 + 0.270757i \(0.912726\pi\)
\(678\) 0 0
\(679\) −35.0292 −1.34430
\(680\) 0 0
\(681\) −36.6872 −1.40586
\(682\) 0 0
\(683\) 29.8403 1.14181 0.570903 0.821017i \(-0.306593\pi\)
0.570903 + 0.821017i \(0.306593\pi\)
\(684\) 0 0
\(685\) −0.539398 −0.0206094
\(686\) 0 0
\(687\) 1.04842 0.0399998
\(688\) 0 0
\(689\) 37.5024 1.42873
\(690\) 0 0
\(691\) 30.9584 1.17771 0.588857 0.808237i \(-0.299578\pi\)
0.588857 + 0.808237i \(0.299578\pi\)
\(692\) 0 0
\(693\) −4.46307 −0.169538
\(694\) 0 0
\(695\) 14.2603 0.540922
\(696\) 0 0
\(697\) −0.567272 −0.0214870
\(698\) 0 0
\(699\) 58.9830 2.23094
\(700\) 0 0
\(701\) −21.2361 −0.802078 −0.401039 0.916061i \(-0.631351\pi\)
−0.401039 + 0.916061i \(0.631351\pi\)
\(702\) 0 0
\(703\) 7.95640 0.300081
\(704\) 0 0
\(705\) 111.454 4.19760
\(706\) 0 0
\(707\) 31.1161 1.17024
\(708\) 0 0
\(709\) −29.2617 −1.09895 −0.549473 0.835511i \(-0.685172\pi\)
−0.549473 + 0.835511i \(0.685172\pi\)
\(710\) 0 0
\(711\) 23.5187 0.882020
\(712\) 0 0
\(713\) 25.3590 0.949700
\(714\) 0 0
\(715\) 5.52137 0.206487
\(716\) 0 0
\(717\) 64.9673 2.42625
\(718\) 0 0
\(719\) −2.65987 −0.0991965 −0.0495982 0.998769i \(-0.515794\pi\)
−0.0495982 + 0.998769i \(0.515794\pi\)
\(720\) 0 0
\(721\) 10.6015 0.394821
\(722\) 0 0
\(723\) 22.9331 0.852892
\(724\) 0 0
\(725\) −12.6763 −0.470784
\(726\) 0 0
\(727\) −7.80268 −0.289386 −0.144693 0.989477i \(-0.546219\pi\)
−0.144693 + 0.989477i \(0.546219\pi\)
\(728\) 0 0
\(729\) −40.7258 −1.50836
\(730\) 0 0
\(731\) 4.98079 0.184221
\(732\) 0 0
\(733\) 39.1888 1.44747 0.723735 0.690078i \(-0.242424\pi\)
0.723735 + 0.690078i \(0.242424\pi\)
\(734\) 0 0
\(735\) 28.2921 1.04357
\(736\) 0 0
\(737\) 1.90882 0.0703123
\(738\) 0 0
\(739\) 9.29964 0.342093 0.171046 0.985263i \(-0.445285\pi\)
0.171046 + 0.985263i \(0.445285\pi\)
\(740\) 0 0
\(741\) −38.5593 −1.41651
\(742\) 0 0
\(743\) −12.4069 −0.455166 −0.227583 0.973759i \(-0.573082\pi\)
−0.227583 + 0.973759i \(0.573082\pi\)
\(744\) 0 0
\(745\) 31.4128 1.15088
\(746\) 0 0
\(747\) 5.14554 0.188266
\(748\) 0 0
\(749\) −28.5626 −1.04365
\(750\) 0 0
\(751\) −10.2605 −0.374412 −0.187206 0.982321i \(-0.559943\pi\)
−0.187206 + 0.982321i \(0.559943\pi\)
\(752\) 0 0
\(753\) 55.6871 2.02935
\(754\) 0 0
\(755\) −62.2191 −2.26439
\(756\) 0 0
\(757\) 53.8023 1.95548 0.977740 0.209822i \(-0.0672884\pi\)
0.977740 + 0.209822i \(0.0672884\pi\)
\(758\) 0 0
\(759\) 7.62051 0.276607
\(760\) 0 0
\(761\) −18.7034 −0.677999 −0.339000 0.940786i \(-0.610089\pi\)
−0.339000 + 0.940786i \(0.610089\pi\)
\(762\) 0 0
\(763\) 36.4830 1.32077
\(764\) 0 0
\(765\) −12.3011 −0.444747
\(766\) 0 0
\(767\) −2.98307 −0.107712
\(768\) 0 0
\(769\) 20.7356 0.747746 0.373873 0.927480i \(-0.378030\pi\)
0.373873 + 0.927480i \(0.378030\pi\)
\(770\) 0 0
\(771\) 30.8700 1.11176
\(772\) 0 0
\(773\) 10.6824 0.384219 0.192109 0.981374i \(-0.438467\pi\)
0.192109 + 0.981374i \(0.438467\pi\)
\(774\) 0 0
\(775\) −24.1425 −0.867226
\(776\) 0 0
\(777\) 8.07378 0.289645
\(778\) 0 0
\(779\) 2.77739 0.0995102
\(780\) 0 0
\(781\) −0.550361 −0.0196935
\(782\) 0 0
\(783\) 7.05780 0.252225
\(784\) 0 0
\(785\) 44.3794 1.58397
\(786\) 0 0
\(787\) −46.1603 −1.64544 −0.822718 0.568449i \(-0.807544\pi\)
−0.822718 + 0.568449i \(0.807544\pi\)
\(788\) 0 0
\(789\) −26.8434 −0.955649
\(790\) 0 0
\(791\) −25.8893 −0.920517
\(792\) 0 0
\(793\) −10.8233 −0.384348
\(794\) 0 0
\(795\) −102.838 −3.64730
\(796\) 0 0
\(797\) −49.8192 −1.76469 −0.882343 0.470608i \(-0.844035\pi\)
−0.882343 + 0.470608i \(0.844035\pi\)
\(798\) 0 0
\(799\) 13.6250 0.482018
\(800\) 0 0
\(801\) −47.1624 −1.66640
\(802\) 0 0
\(803\) −3.72423 −0.131425
\(804\) 0 0
\(805\) 28.1736 0.992990
\(806\) 0 0
\(807\) −73.5249 −2.58820
\(808\) 0 0
\(809\) −33.6142 −1.18181 −0.590907 0.806740i \(-0.701230\pi\)
−0.590907 + 0.806740i \(0.701230\pi\)
\(810\) 0 0
\(811\) 45.8223 1.60904 0.804518 0.593928i \(-0.202423\pi\)
0.804518 + 0.593928i \(0.202423\pi\)
\(812\) 0 0
\(813\) −63.3525 −2.22187
\(814\) 0 0
\(815\) 8.02437 0.281081
\(816\) 0 0
\(817\) −24.3861 −0.853163
\(818\) 0 0
\(819\) −22.2871 −0.778773
\(820\) 0 0
\(821\) 39.8311 1.39012 0.695058 0.718954i \(-0.255379\pi\)
0.695058 + 0.718954i \(0.255379\pi\)
\(822\) 0 0
\(823\) 47.9620 1.67185 0.835925 0.548844i \(-0.184932\pi\)
0.835925 + 0.548844i \(0.184932\pi\)
\(824\) 0 0
\(825\) −7.25497 −0.252586
\(826\) 0 0
\(827\) 17.7749 0.618093 0.309046 0.951047i \(-0.399990\pi\)
0.309046 + 0.951047i \(0.399990\pi\)
\(828\) 0 0
\(829\) 24.4615 0.849582 0.424791 0.905292i \(-0.360348\pi\)
0.424791 + 0.905292i \(0.360348\pi\)
\(830\) 0 0
\(831\) 17.6889 0.613622
\(832\) 0 0
\(833\) 3.45864 0.119835
\(834\) 0 0
\(835\) 42.5773 1.47345
\(836\) 0 0
\(837\) 13.4419 0.464621
\(838\) 0 0
\(839\) 41.1306 1.41998 0.709992 0.704209i \(-0.248698\pi\)
0.709992 + 0.704209i \(0.248698\pi\)
\(840\) 0 0
\(841\) −21.4065 −0.738156
\(842\) 0 0
\(843\) −83.0274 −2.85962
\(844\) 0 0
\(845\) −12.7075 −0.437150
\(846\) 0 0
\(847\) 20.0288 0.688198
\(848\) 0 0
\(849\) −58.5511 −2.00947
\(850\) 0 0
\(851\) −7.85219 −0.269170
\(852\) 0 0
\(853\) −17.5746 −0.601743 −0.300871 0.953665i \(-0.597277\pi\)
−0.300871 + 0.953665i \(0.597277\pi\)
\(854\) 0 0
\(855\) 60.2266 2.05971
\(856\) 0 0
\(857\) 21.8219 0.745421 0.372710 0.927948i \(-0.378428\pi\)
0.372710 + 0.927948i \(0.378428\pi\)
\(858\) 0 0
\(859\) 13.8327 0.471964 0.235982 0.971757i \(-0.424169\pi\)
0.235982 + 0.971757i \(0.424169\pi\)
\(860\) 0 0
\(861\) 2.81836 0.0960494
\(862\) 0 0
\(863\) −44.7815 −1.52438 −0.762190 0.647353i \(-0.775876\pi\)
−0.762190 + 0.647353i \(0.775876\pi\)
\(864\) 0 0
\(865\) −38.6159 −1.31298
\(866\) 0 0
\(867\) −2.64010 −0.0896625
\(868\) 0 0
\(869\) 3.53878 0.120045
\(870\) 0 0
\(871\) 9.53201 0.322980
\(872\) 0 0
\(873\) 73.9010 2.50117
\(874\) 0 0
\(875\) 2.33148 0.0788184
\(876\) 0 0
\(877\) −2.87835 −0.0971948 −0.0485974 0.998818i \(-0.515475\pi\)
−0.0485974 + 0.998818i \(0.515475\pi\)
\(878\) 0 0
\(879\) 43.5708 1.46961
\(880\) 0 0
\(881\) −18.2968 −0.616433 −0.308217 0.951316i \(-0.599732\pi\)
−0.308217 + 0.951316i \(0.599732\pi\)
\(882\) 0 0
\(883\) −8.24553 −0.277484 −0.138742 0.990329i \(-0.544306\pi\)
−0.138742 + 0.990329i \(0.544306\pi\)
\(884\) 0 0
\(885\) 8.18011 0.274971
\(886\) 0 0
\(887\) 49.9377 1.67674 0.838372 0.545098i \(-0.183508\pi\)
0.838372 + 0.545098i \(0.183508\pi\)
\(888\) 0 0
\(889\) 40.0002 1.34156
\(890\) 0 0
\(891\) −3.07554 −0.103035
\(892\) 0 0
\(893\) −66.7086 −2.23232
\(894\) 0 0
\(895\) 18.6595 0.623719
\(896\) 0 0
\(897\) 38.0543 1.27059
\(898\) 0 0
\(899\) 14.4621 0.482339
\(900\) 0 0
\(901\) −12.5718 −0.418826
\(902\) 0 0
\(903\) −24.7459 −0.823492
\(904\) 0 0
\(905\) 62.1818 2.06699
\(906\) 0 0
\(907\) 10.8602 0.360606 0.180303 0.983611i \(-0.442292\pi\)
0.180303 + 0.983611i \(0.442292\pi\)
\(908\) 0 0
\(909\) −65.6455 −2.17733
\(910\) 0 0
\(911\) −19.6137 −0.649831 −0.324916 0.945743i \(-0.605336\pi\)
−0.324916 + 0.945743i \(0.605336\pi\)
\(912\) 0 0
\(913\) 0.774231 0.0256233
\(914\) 0 0
\(915\) 29.6795 0.981175
\(916\) 0 0
\(917\) −21.4447 −0.708168
\(918\) 0 0
\(919\) 40.3847 1.33217 0.666085 0.745876i \(-0.267969\pi\)
0.666085 + 0.745876i \(0.267969\pi\)
\(920\) 0 0
\(921\) 61.3827 2.02263
\(922\) 0 0
\(923\) −2.74832 −0.0904621
\(924\) 0 0
\(925\) 7.47554 0.245794
\(926\) 0 0
\(927\) −22.3659 −0.734594
\(928\) 0 0
\(929\) −0.151599 −0.00497379 −0.00248689 0.999997i \(-0.500792\pi\)
−0.00248689 + 0.999997i \(0.500792\pi\)
\(930\) 0 0
\(931\) −16.9337 −0.554978
\(932\) 0 0
\(933\) 1.39902 0.0458018
\(934\) 0 0
\(935\) −1.85090 −0.0605309
\(936\) 0 0
\(937\) 8.52978 0.278656 0.139328 0.990246i \(-0.455506\pi\)
0.139328 + 0.990246i \(0.455506\pi\)
\(938\) 0 0
\(939\) 19.1950 0.626405
\(940\) 0 0
\(941\) 10.9745 0.357759 0.178880 0.983871i \(-0.442753\pi\)
0.178880 + 0.983871i \(0.442753\pi\)
\(942\) 0 0
\(943\) −2.74101 −0.0892596
\(944\) 0 0
\(945\) 14.9339 0.485800
\(946\) 0 0
\(947\) −24.3297 −0.790609 −0.395305 0.918550i \(-0.629361\pi\)
−0.395305 + 0.918550i \(0.629361\pi\)
\(948\) 0 0
\(949\) −18.5975 −0.603702
\(950\) 0 0
\(951\) 40.7684 1.32201
\(952\) 0 0
\(953\) −36.0423 −1.16752 −0.583762 0.811925i \(-0.698420\pi\)
−0.583762 + 0.811925i \(0.698420\pi\)
\(954\) 0 0
\(955\) −24.4418 −0.790917
\(956\) 0 0
\(957\) 4.34595 0.140485
\(958\) 0 0
\(959\) 0.327609 0.0105790
\(960\) 0 0
\(961\) −3.45618 −0.111490
\(962\) 0 0
\(963\) 60.2583 1.94180
\(964\) 0 0
\(965\) 41.2421 1.32763
\(966\) 0 0
\(967\) −19.4758 −0.626298 −0.313149 0.949704i \(-0.601384\pi\)
−0.313149 + 0.949704i \(0.601384\pi\)
\(968\) 0 0
\(969\) 12.9260 0.415244
\(970\) 0 0
\(971\) −11.1700 −0.358462 −0.179231 0.983807i \(-0.557361\pi\)
−0.179231 + 0.983807i \(0.557361\pi\)
\(972\) 0 0
\(973\) −8.66111 −0.277662
\(974\) 0 0
\(975\) −36.2289 −1.16025
\(976\) 0 0
\(977\) 0.289206 0.00925253 0.00462627 0.999989i \(-0.498527\pi\)
0.00462627 + 0.999989i \(0.498527\pi\)
\(978\) 0 0
\(979\) −7.09635 −0.226800
\(980\) 0 0
\(981\) −76.9680 −2.45740
\(982\) 0 0
\(983\) −16.1293 −0.514446 −0.257223 0.966352i \(-0.582807\pi\)
−0.257223 + 0.966352i \(0.582807\pi\)
\(984\) 0 0
\(985\) −9.14257 −0.291307
\(986\) 0 0
\(987\) −67.6927 −2.15468
\(988\) 0 0
\(989\) 24.0667 0.765278
\(990\) 0 0
\(991\) 30.0622 0.954958 0.477479 0.878643i \(-0.341551\pi\)
0.477479 + 0.878643i \(0.341551\pi\)
\(992\) 0 0
\(993\) −65.2454 −2.07050
\(994\) 0 0
\(995\) −52.9657 −1.67913
\(996\) 0 0
\(997\) −55.7586 −1.76589 −0.882946 0.469474i \(-0.844443\pi\)
−0.882946 + 0.469474i \(0.844443\pi\)
\(998\) 0 0
\(999\) −4.16219 −0.131686
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 \(a_p\))