Properties

Label 8024.2.a.y.1.5
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 1.5
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.07300 q^{3} -3.30236 q^{5} +0.766448 q^{7} +1.29731 q^{9} +O(q^{10})\) \(q-2.07300 q^{3} -3.30236 q^{5} +0.766448 q^{7} +1.29731 q^{9} -4.04125 q^{11} -3.72463 q^{13} +6.84577 q^{15} -1.00000 q^{17} +0.733623 q^{19} -1.58884 q^{21} -1.80792 q^{23} +5.90556 q^{25} +3.52967 q^{27} +2.90892 q^{29} +1.23419 q^{31} +8.37749 q^{33} -2.53108 q^{35} -6.26815 q^{37} +7.72113 q^{39} +7.97875 q^{41} +0.613125 q^{43} -4.28417 q^{45} +13.3842 q^{47} -6.41256 q^{49} +2.07300 q^{51} +0.757392 q^{53} +13.3457 q^{55} -1.52080 q^{57} -1.00000 q^{59} +4.13545 q^{61} +0.994319 q^{63} +12.3000 q^{65} -9.80494 q^{67} +3.74780 q^{69} +9.11954 q^{71} +9.46403 q^{73} -12.2422 q^{75} -3.09741 q^{77} -6.71373 q^{79} -11.2089 q^{81} -0.845676 q^{83} +3.30236 q^{85} -6.03019 q^{87} -0.654120 q^{89} -2.85473 q^{91} -2.55848 q^{93} -2.42268 q^{95} +10.6220 q^{97} -5.24275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 6q^{3} - q^{7} + 23q^{9} + O(q^{10}) \) \( 23q - 6q^{3} - q^{7} + 23q^{9} - 3q^{11} - 7q^{13} - 2q^{15} - 23q^{17} - 16q^{19} - 11q^{21} - 29q^{23} + 31q^{25} - 3q^{27} - 5q^{29} - 41q^{31} + 8q^{33} - 22q^{35} + 5q^{37} + 16q^{39} + 11q^{41} + 13q^{43} - 26q^{45} - 39q^{47} + 16q^{49} + 6q^{51} - 2q^{53} - 35q^{55} + 13q^{57} - 23q^{59} - 37q^{61} + 33q^{65} - 34q^{67} - 66q^{69} - 13q^{71} - 14q^{73} - 81q^{75} - 4q^{77} - 61q^{79} - q^{81} - 9q^{83} - 16q^{87} + 28q^{89} - 18q^{91} - 62q^{93} - 33q^{95} - 5q^{99} + O(q^{100}) \)

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
\(3\) −2.07300 −1.19684 −0.598422 0.801181i \(-0.704205\pi\)
−0.598422 + 0.801181i \(0.704205\pi\)
\(4\) 0 0
\(5\) −3.30236 −1.47686 −0.738429 0.674331i \(-0.764432\pi\)
−0.738429 + 0.674331i \(0.764432\pi\)
\(6\) 0 0
\(7\) 0.766448 0.289690 0.144845 0.989454i \(-0.453732\pi\)
0.144845 + 0.989454i \(0.453732\pi\)
\(8\) 0 0
\(9\) 1.29731 0.432436
\(10\) 0 0
\(11\) −4.04125 −1.21848 −0.609242 0.792985i \(-0.708526\pi\)
−0.609242 + 0.792985i \(0.708526\pi\)
\(12\) 0 0
\(13\) −3.72463 −1.03303 −0.516513 0.856280i \(-0.672770\pi\)
−0.516513 + 0.856280i \(0.672770\pi\)
\(14\) 0 0
\(15\) 6.84577 1.76757
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 0.733623 0.168305 0.0841523 0.996453i \(-0.473182\pi\)
0.0841523 + 0.996453i \(0.473182\pi\)
\(20\) 0 0
\(21\) −1.58884 −0.346714
\(22\) 0 0
\(23\) −1.80792 −0.376977 −0.188488 0.982075i \(-0.560359\pi\)
−0.188488 + 0.982075i \(0.560359\pi\)
\(24\) 0 0
\(25\) 5.90556 1.18111
\(26\) 0 0
\(27\) 3.52967 0.679286
\(28\) 0 0
\(29\) 2.90892 0.540174 0.270087 0.962836i \(-0.412948\pi\)
0.270087 + 0.962836i \(0.412948\pi\)
\(30\) 0 0
\(31\) 1.23419 0.221668 0.110834 0.993839i \(-0.464648\pi\)
0.110834 + 0.993839i \(0.464648\pi\)
\(32\) 0 0
\(33\) 8.37749 1.45833
\(34\) 0 0
\(35\) −2.53108 −0.427831
\(36\) 0 0
\(37\) −6.26815 −1.03048 −0.515239 0.857047i \(-0.672297\pi\)
−0.515239 + 0.857047i \(0.672297\pi\)
\(38\) 0 0
\(39\) 7.72113 1.23637
\(40\) 0 0
\(41\) 7.97875 1.24607 0.623036 0.782193i \(-0.285899\pi\)
0.623036 + 0.782193i \(0.285899\pi\)
\(42\) 0 0
\(43\) 0.613125 0.0935007 0.0467503 0.998907i \(-0.485113\pi\)
0.0467503 + 0.998907i \(0.485113\pi\)
\(44\) 0 0
\(45\) −4.28417 −0.638647
\(46\) 0 0
\(47\) 13.3842 1.95229 0.976143 0.217129i \(-0.0696691\pi\)
0.976143 + 0.217129i \(0.0696691\pi\)
\(48\) 0 0
\(49\) −6.41256 −0.916080
\(50\) 0 0
\(51\) 2.07300 0.290277
\(52\) 0 0
\(53\) 0.757392 0.104036 0.0520179 0.998646i \(-0.483435\pi\)
0.0520179 + 0.998646i \(0.483435\pi\)
\(54\) 0 0
\(55\) 13.3457 1.79953
\(56\) 0 0
\(57\) −1.52080 −0.201434
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 4.13545 0.529490 0.264745 0.964318i \(-0.414712\pi\)
0.264745 + 0.964318i \(0.414712\pi\)
\(62\) 0 0
\(63\) 0.994319 0.125272
\(64\) 0 0
\(65\) 12.3000 1.52563
\(66\) 0 0
\(67\) −9.80494 −1.19786 −0.598932 0.800800i \(-0.704408\pi\)
−0.598932 + 0.800800i \(0.704408\pi\)
\(68\) 0 0
\(69\) 3.74780 0.451182
\(70\) 0 0
\(71\) 9.11954 1.08229 0.541145 0.840929i \(-0.317991\pi\)
0.541145 + 0.840929i \(0.317991\pi\)
\(72\) 0 0
\(73\) 9.46403 1.10768 0.553840 0.832623i \(-0.313162\pi\)
0.553840 + 0.832623i \(0.313162\pi\)
\(74\) 0 0
\(75\) −12.2422 −1.41361
\(76\) 0 0
\(77\) −3.09741 −0.352982
\(78\) 0 0
\(79\) −6.71373 −0.755354 −0.377677 0.925937i \(-0.623277\pi\)
−0.377677 + 0.925937i \(0.623277\pi\)
\(80\) 0 0
\(81\) −11.2089 −1.24544
\(82\) 0 0
\(83\) −0.845676 −0.0928250 −0.0464125 0.998922i \(-0.514779\pi\)
−0.0464125 + 0.998922i \(0.514779\pi\)
\(84\) 0 0
\(85\) 3.30236 0.358191
\(86\) 0 0
\(87\) −6.03019 −0.646504
\(88\) 0 0
\(89\) −0.654120 −0.0693365 −0.0346683 0.999399i \(-0.511037\pi\)
−0.0346683 + 0.999399i \(0.511037\pi\)
\(90\) 0 0
\(91\) −2.85473 −0.299257
\(92\) 0 0
\(93\) −2.55848 −0.265302
\(94\) 0 0
\(95\) −2.42268 −0.248562
\(96\) 0 0
\(97\) 10.6220 1.07850 0.539250 0.842146i \(-0.318708\pi\)
0.539250 + 0.842146i \(0.318708\pi\)
\(98\) 0 0
\(99\) −5.24275 −0.526916
\(100\) 0 0
\(101\) −7.53450 −0.749711 −0.374855 0.927083i \(-0.622308\pi\)
−0.374855 + 0.927083i \(0.622308\pi\)
\(102\) 0 0
\(103\) −18.1008 −1.78353 −0.891763 0.452504i \(-0.850531\pi\)
−0.891763 + 0.452504i \(0.850531\pi\)
\(104\) 0 0
\(105\) 5.24693 0.512047
\(106\) 0 0
\(107\) 7.79755 0.753817 0.376909 0.926250i \(-0.376987\pi\)
0.376909 + 0.926250i \(0.376987\pi\)
\(108\) 0 0
\(109\) 14.0617 1.34687 0.673435 0.739246i \(-0.264818\pi\)
0.673435 + 0.739246i \(0.264818\pi\)
\(110\) 0 0
\(111\) 12.9938 1.23332
\(112\) 0 0
\(113\) 11.3442 1.06717 0.533586 0.845746i \(-0.320844\pi\)
0.533586 + 0.845746i \(0.320844\pi\)
\(114\) 0 0
\(115\) 5.97039 0.556741
\(116\) 0 0
\(117\) −4.83199 −0.446717
\(118\) 0 0
\(119\) −0.766448 −0.0702602
\(120\) 0 0
\(121\) 5.33171 0.484701
\(122\) 0 0
\(123\) −16.5399 −1.49135
\(124\) 0 0
\(125\) −2.99048 −0.267477
\(126\) 0 0
\(127\) 21.1872 1.88006 0.940032 0.341086i \(-0.110795\pi\)
0.940032 + 0.341086i \(0.110795\pi\)
\(128\) 0 0
\(129\) −1.27101 −0.111906
\(130\) 0 0
\(131\) −21.1020 −1.84369 −0.921846 0.387556i \(-0.873319\pi\)
−0.921846 + 0.387556i \(0.873319\pi\)
\(132\) 0 0
\(133\) 0.562284 0.0487562
\(134\) 0 0
\(135\) −11.6562 −1.00321
\(136\) 0 0
\(137\) −2.64391 −0.225885 −0.112942 0.993602i \(-0.536028\pi\)
−0.112942 + 0.993602i \(0.536028\pi\)
\(138\) 0 0
\(139\) 9.12855 0.774274 0.387137 0.922022i \(-0.373464\pi\)
0.387137 + 0.922022i \(0.373464\pi\)
\(140\) 0 0
\(141\) −27.7454 −2.33658
\(142\) 0 0
\(143\) 15.0521 1.25872
\(144\) 0 0
\(145\) −9.60631 −0.797760
\(146\) 0 0
\(147\) 13.2932 1.09640
\(148\) 0 0
\(149\) 5.14089 0.421158 0.210579 0.977577i \(-0.432465\pi\)
0.210579 + 0.977577i \(0.432465\pi\)
\(150\) 0 0
\(151\) 5.51022 0.448415 0.224207 0.974541i \(-0.428021\pi\)
0.224207 + 0.974541i \(0.428021\pi\)
\(152\) 0 0
\(153\) −1.29731 −0.104881
\(154\) 0 0
\(155\) −4.07575 −0.327372
\(156\) 0 0
\(157\) 6.85735 0.547276 0.273638 0.961833i \(-0.411773\pi\)
0.273638 + 0.961833i \(0.411773\pi\)
\(158\) 0 0
\(159\) −1.57007 −0.124515
\(160\) 0 0
\(161\) −1.38567 −0.109206
\(162\) 0 0
\(163\) −5.67108 −0.444193 −0.222097 0.975025i \(-0.571290\pi\)
−0.222097 + 0.975025i \(0.571290\pi\)
\(164\) 0 0
\(165\) −27.6655 −2.15375
\(166\) 0 0
\(167\) 2.24434 0.173672 0.0868362 0.996223i \(-0.472324\pi\)
0.0868362 + 0.996223i \(0.472324\pi\)
\(168\) 0 0
\(169\) 0.872833 0.0671410
\(170\) 0 0
\(171\) 0.951735 0.0727810
\(172\) 0 0
\(173\) 12.6221 0.959642 0.479821 0.877366i \(-0.340702\pi\)
0.479821 + 0.877366i \(0.340702\pi\)
\(174\) 0 0
\(175\) 4.52630 0.342156
\(176\) 0 0
\(177\) 2.07300 0.155816
\(178\) 0 0
\(179\) 26.0804 1.94934 0.974671 0.223642i \(-0.0717945\pi\)
0.974671 + 0.223642i \(0.0717945\pi\)
\(180\) 0 0
\(181\) 3.50084 0.260216 0.130108 0.991500i \(-0.458468\pi\)
0.130108 + 0.991500i \(0.458468\pi\)
\(182\) 0 0
\(183\) −8.57277 −0.633717
\(184\) 0 0
\(185\) 20.6997 1.52187
\(186\) 0 0
\(187\) 4.04125 0.295526
\(188\) 0 0
\(189\) 2.70531 0.196782
\(190\) 0 0
\(191\) −8.92594 −0.645858 −0.322929 0.946423i \(-0.604668\pi\)
−0.322929 + 0.946423i \(0.604668\pi\)
\(192\) 0 0
\(193\) 1.39064 0.100101 0.0500503 0.998747i \(-0.484062\pi\)
0.0500503 + 0.998747i \(0.484062\pi\)
\(194\) 0 0
\(195\) −25.4979 −1.82594
\(196\) 0 0
\(197\) −24.9562 −1.77806 −0.889029 0.457850i \(-0.848620\pi\)
−0.889029 + 0.457850i \(0.848620\pi\)
\(198\) 0 0
\(199\) −15.7316 −1.11518 −0.557592 0.830115i \(-0.688275\pi\)
−0.557592 + 0.830115i \(0.688275\pi\)
\(200\) 0 0
\(201\) 20.3256 1.43366
\(202\) 0 0
\(203\) 2.22954 0.156483
\(204\) 0 0
\(205\) −26.3487 −1.84027
\(206\) 0 0
\(207\) −2.34543 −0.163018
\(208\) 0 0
\(209\) −2.96475 −0.205076
\(210\) 0 0
\(211\) −2.06685 −0.142288 −0.0711439 0.997466i \(-0.522665\pi\)
−0.0711439 + 0.997466i \(0.522665\pi\)
\(212\) 0 0
\(213\) −18.9048 −1.29533
\(214\) 0 0
\(215\) −2.02476 −0.138087
\(216\) 0 0
\(217\) 0.945946 0.0642150
\(218\) 0 0
\(219\) −19.6189 −1.32572
\(220\) 0 0
\(221\) 3.72463 0.250545
\(222\) 0 0
\(223\) −19.7538 −1.32281 −0.661407 0.750027i \(-0.730040\pi\)
−0.661407 + 0.750027i \(0.730040\pi\)
\(224\) 0 0
\(225\) 7.66133 0.510755
\(226\) 0 0
\(227\) 11.2137 0.744276 0.372138 0.928177i \(-0.378625\pi\)
0.372138 + 0.928177i \(0.378625\pi\)
\(228\) 0 0
\(229\) −29.6808 −1.96136 −0.980681 0.195615i \(-0.937330\pi\)
−0.980681 + 0.195615i \(0.937330\pi\)
\(230\) 0 0
\(231\) 6.42091 0.422465
\(232\) 0 0
\(233\) 2.67124 0.174999 0.0874993 0.996165i \(-0.472112\pi\)
0.0874993 + 0.996165i \(0.472112\pi\)
\(234\) 0 0
\(235\) −44.1994 −2.88325
\(236\) 0 0
\(237\) 13.9175 0.904041
\(238\) 0 0
\(239\) −28.4363 −1.83939 −0.919697 0.392629i \(-0.871566\pi\)
−0.919697 + 0.392629i \(0.871566\pi\)
\(240\) 0 0
\(241\) 20.4482 1.31719 0.658593 0.752499i \(-0.271152\pi\)
0.658593 + 0.752499i \(0.271152\pi\)
\(242\) 0 0
\(243\) 12.6470 0.811306
\(244\) 0 0
\(245\) 21.1766 1.35292
\(246\) 0 0
\(247\) −2.73247 −0.173863
\(248\) 0 0
\(249\) 1.75308 0.111097
\(250\) 0 0
\(251\) 23.4478 1.48001 0.740005 0.672602i \(-0.234823\pi\)
0.740005 + 0.672602i \(0.234823\pi\)
\(252\) 0 0
\(253\) 7.30625 0.459340
\(254\) 0 0
\(255\) −6.84577 −0.428699
\(256\) 0 0
\(257\) −5.39427 −0.336485 −0.168243 0.985746i \(-0.553809\pi\)
−0.168243 + 0.985746i \(0.553809\pi\)
\(258\) 0 0
\(259\) −4.80421 −0.298519
\(260\) 0 0
\(261\) 3.77377 0.233591
\(262\) 0 0
\(263\) 16.3740 1.00967 0.504833 0.863217i \(-0.331554\pi\)
0.504833 + 0.863217i \(0.331554\pi\)
\(264\) 0 0
\(265\) −2.50118 −0.153646
\(266\) 0 0
\(267\) 1.35599 0.0829850
\(268\) 0 0
\(269\) 17.3628 1.05863 0.529313 0.848427i \(-0.322450\pi\)
0.529313 + 0.848427i \(0.322450\pi\)
\(270\) 0 0
\(271\) 4.06547 0.246960 0.123480 0.992347i \(-0.460595\pi\)
0.123480 + 0.992347i \(0.460595\pi\)
\(272\) 0 0
\(273\) 5.91784 0.358164
\(274\) 0 0
\(275\) −23.8658 −1.43916
\(276\) 0 0
\(277\) 5.28433 0.317505 0.158752 0.987318i \(-0.449253\pi\)
0.158752 + 0.987318i \(0.449253\pi\)
\(278\) 0 0
\(279\) 1.60113 0.0958572
\(280\) 0 0
\(281\) 11.6006 0.692033 0.346016 0.938228i \(-0.387534\pi\)
0.346016 + 0.938228i \(0.387534\pi\)
\(282\) 0 0
\(283\) −23.8339 −1.41678 −0.708389 0.705822i \(-0.750578\pi\)
−0.708389 + 0.705822i \(0.750578\pi\)
\(284\) 0 0
\(285\) 5.02221 0.297490
\(286\) 0 0
\(287\) 6.11530 0.360975
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −22.0193 −1.29080
\(292\) 0 0
\(293\) 27.2954 1.59461 0.797306 0.603575i \(-0.206258\pi\)
0.797306 + 0.603575i \(0.206258\pi\)
\(294\) 0 0
\(295\) 3.30236 0.192271
\(296\) 0 0
\(297\) −14.2643 −0.827698
\(298\) 0 0
\(299\) 6.73381 0.389426
\(300\) 0 0
\(301\) 0.469928 0.0270862
\(302\) 0 0
\(303\) 15.6190 0.897287
\(304\) 0 0
\(305\) −13.6567 −0.781982
\(306\) 0 0
\(307\) −20.4633 −1.16790 −0.583951 0.811789i \(-0.698494\pi\)
−0.583951 + 0.811789i \(0.698494\pi\)
\(308\) 0 0
\(309\) 37.5229 2.13460
\(310\) 0 0
\(311\) −4.20700 −0.238557 −0.119279 0.992861i \(-0.538058\pi\)
−0.119279 + 0.992861i \(0.538058\pi\)
\(312\) 0 0
\(313\) −3.06125 −0.173032 −0.0865160 0.996250i \(-0.527573\pi\)
−0.0865160 + 0.996250i \(0.527573\pi\)
\(314\) 0 0
\(315\) −3.28360 −0.185010
\(316\) 0 0
\(317\) 2.98189 0.167480 0.0837399 0.996488i \(-0.473313\pi\)
0.0837399 + 0.996488i \(0.473313\pi\)
\(318\) 0 0
\(319\) −11.7557 −0.658193
\(320\) 0 0
\(321\) −16.1643 −0.902202
\(322\) 0 0
\(323\) −0.733623 −0.0408199
\(324\) 0 0
\(325\) −21.9960 −1.22012
\(326\) 0 0
\(327\) −29.1499 −1.61199
\(328\) 0 0
\(329\) 10.2583 0.565558
\(330\) 0 0
\(331\) −1.52363 −0.0837462 −0.0418731 0.999123i \(-0.513333\pi\)
−0.0418731 + 0.999123i \(0.513333\pi\)
\(332\) 0 0
\(333\) −8.13173 −0.445616
\(334\) 0 0
\(335\) 32.3794 1.76908
\(336\) 0 0
\(337\) 22.6983 1.23646 0.618228 0.785999i \(-0.287851\pi\)
0.618228 + 0.785999i \(0.287851\pi\)
\(338\) 0 0
\(339\) −23.5164 −1.27724
\(340\) 0 0
\(341\) −4.98769 −0.270099
\(342\) 0 0
\(343\) −10.2800 −0.555069
\(344\) 0 0
\(345\) −12.3766 −0.666333
\(346\) 0 0
\(347\) 6.08309 0.326557 0.163279 0.986580i \(-0.447793\pi\)
0.163279 + 0.986580i \(0.447793\pi\)
\(348\) 0 0
\(349\) −31.6453 −1.69393 −0.846967 0.531645i \(-0.821574\pi\)
−0.846967 + 0.531645i \(0.821574\pi\)
\(350\) 0 0
\(351\) −13.1467 −0.701719
\(352\) 0 0
\(353\) −4.24123 −0.225738 −0.112869 0.993610i \(-0.536004\pi\)
−0.112869 + 0.993610i \(0.536004\pi\)
\(354\) 0 0
\(355\) −30.1160 −1.59839
\(356\) 0 0
\(357\) 1.58884 0.0840905
\(358\) 0 0
\(359\) −12.5474 −0.662228 −0.331114 0.943591i \(-0.607424\pi\)
−0.331114 + 0.943591i \(0.607424\pi\)
\(360\) 0 0
\(361\) −18.4618 −0.971674
\(362\) 0 0
\(363\) −11.0526 −0.580111
\(364\) 0 0
\(365\) −31.2536 −1.63589
\(366\) 0 0
\(367\) −36.2030 −1.88978 −0.944891 0.327385i \(-0.893833\pi\)
−0.944891 + 0.327385i \(0.893833\pi\)
\(368\) 0 0
\(369\) 10.3509 0.538846
\(370\) 0 0
\(371\) 0.580502 0.0301382
\(372\) 0 0
\(373\) 22.7932 1.18019 0.590093 0.807335i \(-0.299091\pi\)
0.590093 + 0.807335i \(0.299091\pi\)
\(374\) 0 0
\(375\) 6.19925 0.320128
\(376\) 0 0
\(377\) −10.8347 −0.558013
\(378\) 0 0
\(379\) −5.33126 −0.273848 −0.136924 0.990582i \(-0.543722\pi\)
−0.136924 + 0.990582i \(0.543722\pi\)
\(380\) 0 0
\(381\) −43.9211 −2.25014
\(382\) 0 0
\(383\) −28.0447 −1.43302 −0.716509 0.697578i \(-0.754261\pi\)
−0.716509 + 0.697578i \(0.754261\pi\)
\(384\) 0 0
\(385\) 10.2287 0.521305
\(386\) 0 0
\(387\) 0.795412 0.0404331
\(388\) 0 0
\(389\) 20.2999 1.02925 0.514623 0.857416i \(-0.327932\pi\)
0.514623 + 0.857416i \(0.327932\pi\)
\(390\) 0 0
\(391\) 1.80792 0.0914303
\(392\) 0 0
\(393\) 43.7444 2.20661
\(394\) 0 0
\(395\) 22.1711 1.11555
\(396\) 0 0
\(397\) 12.9173 0.648298 0.324149 0.946006i \(-0.394922\pi\)
0.324149 + 0.946006i \(0.394922\pi\)
\(398\) 0 0
\(399\) −1.16561 −0.0583536
\(400\) 0 0
\(401\) 10.2503 0.511877 0.255938 0.966693i \(-0.417616\pi\)
0.255938 + 0.966693i \(0.417616\pi\)
\(402\) 0 0
\(403\) −4.59691 −0.228989
\(404\) 0 0
\(405\) 37.0158 1.83933
\(406\) 0 0
\(407\) 25.3312 1.25562
\(408\) 0 0
\(409\) −15.0160 −0.742494 −0.371247 0.928534i \(-0.621070\pi\)
−0.371247 + 0.928534i \(0.621070\pi\)
\(410\) 0 0
\(411\) 5.48082 0.270349
\(412\) 0 0
\(413\) −0.766448 −0.0377144
\(414\) 0 0
\(415\) 2.79272 0.137089
\(416\) 0 0
\(417\) −18.9234 −0.926685
\(418\) 0 0
\(419\) −22.4370 −1.09612 −0.548059 0.836440i \(-0.684633\pi\)
−0.548059 + 0.836440i \(0.684633\pi\)
\(420\) 0 0
\(421\) −9.40446 −0.458345 −0.229173 0.973386i \(-0.573602\pi\)
−0.229173 + 0.973386i \(0.573602\pi\)
\(422\) 0 0
\(423\) 17.3634 0.844239
\(424\) 0 0
\(425\) −5.90556 −0.286462
\(426\) 0 0
\(427\) 3.16961 0.153388
\(428\) 0 0
\(429\) −31.2030 −1.50650
\(430\) 0 0
\(431\) −21.6403 −1.04238 −0.521188 0.853442i \(-0.674511\pi\)
−0.521188 + 0.853442i \(0.674511\pi\)
\(432\) 0 0
\(433\) −35.6148 −1.71154 −0.855770 0.517357i \(-0.826916\pi\)
−0.855770 + 0.517357i \(0.826916\pi\)
\(434\) 0 0
\(435\) 19.9138 0.954795
\(436\) 0 0
\(437\) −1.32633 −0.0634469
\(438\) 0 0
\(439\) −6.79303 −0.324214 −0.162107 0.986773i \(-0.551829\pi\)
−0.162107 + 0.986773i \(0.551829\pi\)
\(440\) 0 0
\(441\) −8.31906 −0.396146
\(442\) 0 0
\(443\) −26.8663 −1.27645 −0.638227 0.769848i \(-0.720332\pi\)
−0.638227 + 0.769848i \(0.720332\pi\)
\(444\) 0 0
\(445\) 2.16014 0.102400
\(446\) 0 0
\(447\) −10.6570 −0.504060
\(448\) 0 0
\(449\) 11.2437 0.530621 0.265311 0.964163i \(-0.414525\pi\)
0.265311 + 0.964163i \(0.414525\pi\)
\(450\) 0 0
\(451\) −32.2441 −1.51832
\(452\) 0 0
\(453\) −11.4226 −0.536683
\(454\) 0 0
\(455\) 9.42734 0.441961
\(456\) 0 0
\(457\) 16.2181 0.758649 0.379324 0.925264i \(-0.376156\pi\)
0.379324 + 0.925264i \(0.376156\pi\)
\(458\) 0 0
\(459\) −3.52967 −0.164751
\(460\) 0 0
\(461\) −28.1139 −1.30940 −0.654698 0.755891i \(-0.727204\pi\)
−0.654698 + 0.755891i \(0.727204\pi\)
\(462\) 0 0
\(463\) 10.0806 0.468487 0.234244 0.972178i \(-0.424739\pi\)
0.234244 + 0.972178i \(0.424739\pi\)
\(464\) 0 0
\(465\) 8.44901 0.391814
\(466\) 0 0
\(467\) −31.8151 −1.47223 −0.736113 0.676858i \(-0.763341\pi\)
−0.736113 + 0.676858i \(0.763341\pi\)
\(468\) 0 0
\(469\) −7.51497 −0.347009
\(470\) 0 0
\(471\) −14.2152 −0.655004
\(472\) 0 0
\(473\) −2.47779 −0.113929
\(474\) 0 0
\(475\) 4.33245 0.198787
\(476\) 0 0
\(477\) 0.982571 0.0449889
\(478\) 0 0
\(479\) 36.9951 1.69035 0.845174 0.534491i \(-0.179497\pi\)
0.845174 + 0.534491i \(0.179497\pi\)
\(480\) 0 0
\(481\) 23.3465 1.06451
\(482\) 0 0
\(483\) 2.87250 0.130703
\(484\) 0 0
\(485\) −35.0776 −1.59279
\(486\) 0 0
\(487\) 32.7660 1.48477 0.742384 0.669974i \(-0.233695\pi\)
0.742384 + 0.669974i \(0.233695\pi\)
\(488\) 0 0
\(489\) 11.7561 0.531630
\(490\) 0 0
\(491\) −13.4301 −0.606093 −0.303046 0.952976i \(-0.598004\pi\)
−0.303046 + 0.952976i \(0.598004\pi\)
\(492\) 0 0
\(493\) −2.90892 −0.131011
\(494\) 0 0
\(495\) 17.3134 0.778181
\(496\) 0 0
\(497\) 6.98965 0.313529
\(498\) 0 0
\(499\) −0.932964 −0.0417652 −0.0208826 0.999782i \(-0.506648\pi\)
−0.0208826 + 0.999782i \(0.506648\pi\)
\(500\) 0 0
\(501\) −4.65251 −0.207859
\(502\) 0 0
\(503\) −2.44586 −0.109056 −0.0545278 0.998512i \(-0.517365\pi\)
−0.0545278 + 0.998512i \(0.517365\pi\)
\(504\) 0 0
\(505\) 24.8816 1.10722
\(506\) 0 0
\(507\) −1.80938 −0.0803573
\(508\) 0 0
\(509\) 23.5664 1.04456 0.522281 0.852773i \(-0.325081\pi\)
0.522281 + 0.852773i \(0.325081\pi\)
\(510\) 0 0
\(511\) 7.25368 0.320884
\(512\) 0 0
\(513\) 2.58945 0.114327
\(514\) 0 0
\(515\) 59.7753 2.63401
\(516\) 0 0
\(517\) −54.0889 −2.37883
\(518\) 0 0
\(519\) −26.1656 −1.14854
\(520\) 0 0
\(521\) 1.08664 0.0476068 0.0238034 0.999717i \(-0.492422\pi\)
0.0238034 + 0.999717i \(0.492422\pi\)
\(522\) 0 0
\(523\) −15.5267 −0.678936 −0.339468 0.940618i \(-0.610247\pi\)
−0.339468 + 0.940618i \(0.610247\pi\)
\(524\) 0 0
\(525\) −9.38301 −0.409508
\(526\) 0 0
\(527\) −1.23419 −0.0537624
\(528\) 0 0
\(529\) −19.7314 −0.857889
\(530\) 0 0
\(531\) −1.29731 −0.0562984
\(532\) 0 0
\(533\) −29.7179 −1.28722
\(534\) 0 0
\(535\) −25.7503 −1.11328
\(536\) 0 0
\(537\) −54.0646 −2.33306
\(538\) 0 0
\(539\) 25.9148 1.11623
\(540\) 0 0
\(541\) −7.40123 −0.318204 −0.159102 0.987262i \(-0.550860\pi\)
−0.159102 + 0.987262i \(0.550860\pi\)
\(542\) 0 0
\(543\) −7.25723 −0.311437
\(544\) 0 0
\(545\) −46.4369 −1.98914
\(546\) 0 0
\(547\) 22.6312 0.967642 0.483821 0.875167i \(-0.339249\pi\)
0.483821 + 0.875167i \(0.339249\pi\)
\(548\) 0 0
\(549\) 5.36495 0.228971
\(550\) 0 0
\(551\) 2.13405 0.0909138
\(552\) 0 0
\(553\) −5.14573 −0.218819
\(554\) 0 0
\(555\) −42.9103 −1.82144
\(556\) 0 0
\(557\) 40.2122 1.70384 0.851922 0.523669i \(-0.175437\pi\)
0.851922 + 0.523669i \(0.175437\pi\)
\(558\) 0 0
\(559\) −2.28366 −0.0965886
\(560\) 0 0
\(561\) −8.37749 −0.353698
\(562\) 0 0
\(563\) 3.36642 0.141877 0.0709387 0.997481i \(-0.477401\pi\)
0.0709387 + 0.997481i \(0.477401\pi\)
\(564\) 0 0
\(565\) −37.4626 −1.57606
\(566\) 0 0
\(567\) −8.59105 −0.360790
\(568\) 0 0
\(569\) −7.74553 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(570\) 0 0
\(571\) −3.34721 −0.140076 −0.0700382 0.997544i \(-0.522312\pi\)
−0.0700382 + 0.997544i \(0.522312\pi\)
\(572\) 0 0
\(573\) 18.5034 0.772991
\(574\) 0 0
\(575\) −10.6768 −0.445252
\(576\) 0 0
\(577\) 19.5995 0.815936 0.407968 0.912996i \(-0.366237\pi\)
0.407968 + 0.912996i \(0.366237\pi\)
\(578\) 0 0
\(579\) −2.88279 −0.119805
\(580\) 0 0
\(581\) −0.648167 −0.0268905
\(582\) 0 0
\(583\) −3.06081 −0.126766
\(584\) 0 0
\(585\) 15.9569 0.659738
\(586\) 0 0
\(587\) −4.38711 −0.181076 −0.0905378 0.995893i \(-0.528859\pi\)
−0.0905378 + 0.995893i \(0.528859\pi\)
\(588\) 0 0
\(589\) 0.905434 0.0373077
\(590\) 0 0
\(591\) 51.7342 2.12806
\(592\) 0 0
\(593\) 9.83187 0.403747 0.201873 0.979412i \(-0.435297\pi\)
0.201873 + 0.979412i \(0.435297\pi\)
\(594\) 0 0
\(595\) 2.53108 0.103764
\(596\) 0 0
\(597\) 32.6116 1.33470
\(598\) 0 0
\(599\) −32.1533 −1.31375 −0.656874 0.754000i \(-0.728122\pi\)
−0.656874 + 0.754000i \(0.728122\pi\)
\(600\) 0 0
\(601\) 0.285565 0.0116484 0.00582422 0.999983i \(-0.498146\pi\)
0.00582422 + 0.999983i \(0.498146\pi\)
\(602\) 0 0
\(603\) −12.7200 −0.518000
\(604\) 0 0
\(605\) −17.6072 −0.715835
\(606\) 0 0
\(607\) −10.8549 −0.440588 −0.220294 0.975434i \(-0.570702\pi\)
−0.220294 + 0.975434i \(0.570702\pi\)
\(608\) 0 0
\(609\) −4.62182 −0.187286
\(610\) 0 0
\(611\) −49.8511 −2.01676
\(612\) 0 0
\(613\) 25.5608 1.03239 0.516196 0.856471i \(-0.327348\pi\)
0.516196 + 0.856471i \(0.327348\pi\)
\(614\) 0 0
\(615\) 54.6207 2.20252
\(616\) 0 0
\(617\) 13.2260 0.532459 0.266229 0.963910i \(-0.414222\pi\)
0.266229 + 0.963910i \(0.414222\pi\)
\(618\) 0 0
\(619\) −45.2039 −1.81690 −0.908448 0.417997i \(-0.862732\pi\)
−0.908448 + 0.417997i \(0.862732\pi\)
\(620\) 0 0
\(621\) −6.38135 −0.256075
\(622\) 0 0
\(623\) −0.501349 −0.0200861
\(624\) 0 0
\(625\) −19.6522 −0.786087
\(626\) 0 0
\(627\) 6.14592 0.245444
\(628\) 0 0
\(629\) 6.26815 0.249928
\(630\) 0 0
\(631\) −8.24580 −0.328260 −0.164130 0.986439i \(-0.552482\pi\)
−0.164130 + 0.986439i \(0.552482\pi\)
\(632\) 0 0
\(633\) 4.28457 0.170296
\(634\) 0 0
\(635\) −69.9678 −2.77659
\(636\) 0 0
\(637\) 23.8844 0.946333
\(638\) 0 0
\(639\) 11.8309 0.468021
\(640\) 0 0
\(641\) 29.0581 1.14773 0.573864 0.818951i \(-0.305444\pi\)
0.573864 + 0.818951i \(0.305444\pi\)
\(642\) 0 0
\(643\) −22.7590 −0.897528 −0.448764 0.893650i \(-0.648136\pi\)
−0.448764 + 0.893650i \(0.648136\pi\)
\(644\) 0 0
\(645\) 4.19731 0.165269
\(646\) 0 0
\(647\) −27.9479 −1.09875 −0.549373 0.835578i \(-0.685133\pi\)
−0.549373 + 0.835578i \(0.685133\pi\)
\(648\) 0 0
\(649\) 4.04125 0.158633
\(650\) 0 0
\(651\) −1.96094 −0.0768554
\(652\) 0 0
\(653\) −43.3766 −1.69746 −0.848728 0.528829i \(-0.822631\pi\)
−0.848728 + 0.528829i \(0.822631\pi\)
\(654\) 0 0
\(655\) 69.6864 2.72287
\(656\) 0 0
\(657\) 12.2778 0.479001
\(658\) 0 0
\(659\) 31.9691 1.24534 0.622669 0.782485i \(-0.286048\pi\)
0.622669 + 0.782485i \(0.286048\pi\)
\(660\) 0 0
\(661\) −26.5093 −1.03109 −0.515545 0.856862i \(-0.672411\pi\)
−0.515545 + 0.856862i \(0.672411\pi\)
\(662\) 0 0
\(663\) −7.72113 −0.299864
\(664\) 0 0
\(665\) −1.85686 −0.0720060
\(666\) 0 0
\(667\) −5.25910 −0.203633
\(668\) 0 0
\(669\) 40.9496 1.58320
\(670\) 0 0
\(671\) −16.7124 −0.645175
\(672\) 0 0
\(673\) 1.40884 0.0543070 0.0271535 0.999631i \(-0.491356\pi\)
0.0271535 + 0.999631i \(0.491356\pi\)
\(674\) 0 0
\(675\) 20.8447 0.802312
\(676\) 0 0
\(677\) −0.945382 −0.0363340 −0.0181670 0.999835i \(-0.505783\pi\)
−0.0181670 + 0.999835i \(0.505783\pi\)
\(678\) 0 0
\(679\) 8.14120 0.312431
\(680\) 0 0
\(681\) −23.2458 −0.890783
\(682\) 0 0
\(683\) −41.0933 −1.57239 −0.786196 0.617977i \(-0.787952\pi\)
−0.786196 + 0.617977i \(0.787952\pi\)
\(684\) 0 0
\(685\) 8.73115 0.333600
\(686\) 0 0
\(687\) 61.5281 2.34744
\(688\) 0 0
\(689\) −2.82100 −0.107472
\(690\) 0 0
\(691\) −28.4919 −1.08388 −0.541941 0.840417i \(-0.682310\pi\)
−0.541941 + 0.840417i \(0.682310\pi\)
\(692\) 0 0
\(693\) −4.01829 −0.152642
\(694\) 0 0
\(695\) −30.1457 −1.14349
\(696\) 0 0
\(697\) −7.97875 −0.302217
\(698\) 0 0
\(699\) −5.53746 −0.209446
\(700\) 0 0
\(701\) 28.3594 1.07112 0.535559 0.844498i \(-0.320101\pi\)
0.535559 + 0.844498i \(0.320101\pi\)
\(702\) 0 0
\(703\) −4.59846 −0.173434
\(704\) 0 0
\(705\) 91.6251 3.45080
\(706\) 0 0
\(707\) −5.77480 −0.217184
\(708\) 0 0
\(709\) −31.0979 −1.16791 −0.583953 0.811788i \(-0.698495\pi\)
−0.583953 + 0.811788i \(0.698495\pi\)
\(710\) 0 0
\(711\) −8.70978 −0.326642
\(712\) 0 0
\(713\) −2.23132 −0.0835637
\(714\) 0 0
\(715\) −49.7076 −1.85896
\(716\) 0 0
\(717\) 58.9484 2.20147
\(718\) 0 0
\(719\) 22.6845 0.845990 0.422995 0.906132i \(-0.360979\pi\)
0.422995 + 0.906132i \(0.360979\pi\)
\(720\) 0 0
\(721\) −13.8733 −0.516670
\(722\) 0 0
\(723\) −42.3891 −1.57647
\(724\) 0 0
\(725\) 17.1788 0.638006
\(726\) 0 0
\(727\) −32.7004 −1.21279 −0.606395 0.795164i \(-0.707385\pi\)
−0.606395 + 0.795164i \(0.707385\pi\)
\(728\) 0 0
\(729\) 7.40955 0.274428
\(730\) 0 0
\(731\) −0.613125 −0.0226772
\(732\) 0 0
\(733\) 8.76810 0.323857 0.161929 0.986802i \(-0.448229\pi\)
0.161929 + 0.986802i \(0.448229\pi\)
\(734\) 0 0
\(735\) −43.8989 −1.61923
\(736\) 0 0
\(737\) 39.6242 1.45958
\(738\) 0 0
\(739\) −20.3032 −0.746867 −0.373434 0.927657i \(-0.621820\pi\)
−0.373434 + 0.927657i \(0.621820\pi\)
\(740\) 0 0
\(741\) 5.66440 0.208087
\(742\) 0 0
\(743\) −30.8556 −1.13198 −0.565991 0.824412i \(-0.691506\pi\)
−0.565991 + 0.824412i \(0.691506\pi\)
\(744\) 0 0
\(745\) −16.9770 −0.621991
\(746\) 0 0
\(747\) −1.09710 −0.0401409
\(748\) 0 0
\(749\) 5.97641 0.218373
\(750\) 0 0
\(751\) 17.2308 0.628759 0.314380 0.949297i \(-0.398204\pi\)
0.314380 + 0.949297i \(0.398204\pi\)
\(752\) 0 0
\(753\) −48.6071 −1.77134
\(754\) 0 0
\(755\) −18.1967 −0.662246
\(756\) 0 0
\(757\) 26.9565 0.979749 0.489875 0.871793i \(-0.337043\pi\)
0.489875 + 0.871793i \(0.337043\pi\)
\(758\) 0 0
\(759\) −15.1458 −0.549758
\(760\) 0 0
\(761\) 46.9846 1.70319 0.851596 0.524199i \(-0.175635\pi\)
0.851596 + 0.524199i \(0.175635\pi\)
\(762\) 0 0
\(763\) 10.7776 0.390175
\(764\) 0 0
\(765\) 4.28417 0.154895
\(766\) 0 0
\(767\) 3.72463 0.134488
\(768\) 0 0
\(769\) 12.6380 0.455739 0.227869 0.973692i \(-0.426824\pi\)
0.227869 + 0.973692i \(0.426824\pi\)
\(770\) 0 0
\(771\) 11.1823 0.402720
\(772\) 0 0
\(773\) −40.1737 −1.44495 −0.722474 0.691398i \(-0.756995\pi\)
−0.722474 + 0.691398i \(0.756995\pi\)
\(774\) 0 0
\(775\) 7.28861 0.261815
\(776\) 0 0
\(777\) 9.95911 0.357281
\(778\) 0 0
\(779\) 5.85339 0.209720
\(780\) 0 0
\(781\) −36.8543 −1.31875
\(782\) 0 0
\(783\) 10.2675 0.366932
\(784\) 0 0
\(785\) −22.6454 −0.808249
\(786\) 0 0
\(787\) 10.1192 0.360712 0.180356 0.983601i \(-0.442275\pi\)
0.180356 + 0.983601i \(0.442275\pi\)
\(788\) 0 0
\(789\) −33.9433 −1.20841
\(790\) 0 0
\(791\) 8.69473 0.309149
\(792\) 0 0
\(793\) −15.4030 −0.546977
\(794\) 0 0
\(795\) 5.18493 0.183891
\(796\) 0 0
\(797\) 19.7847 0.700808 0.350404 0.936599i \(-0.386044\pi\)
0.350404 + 0.936599i \(0.386044\pi\)
\(798\) 0 0
\(799\) −13.3842 −0.473499
\(800\) 0 0
\(801\) −0.848595 −0.0299836
\(802\) 0 0
\(803\) −38.2465 −1.34969
\(804\) 0 0
\(805\) 4.57599 0.161282
\(806\) 0 0
\(807\) −35.9929 −1.26701
\(808\) 0 0
\(809\) 32.0585 1.12712 0.563558 0.826077i \(-0.309432\pi\)
0.563558 + 0.826077i \(0.309432\pi\)
\(810\) 0 0
\(811\) 7.01941 0.246485 0.123242 0.992377i \(-0.460671\pi\)
0.123242 + 0.992377i \(0.460671\pi\)
\(812\) 0 0
\(813\) −8.42770 −0.295572
\(814\) 0 0
\(815\) 18.7279 0.656011
\(816\) 0 0
\(817\) 0.449803 0.0157366
\(818\) 0 0
\(819\) −3.70347 −0.129410
\(820\) 0 0
\(821\) −24.0839 −0.840533 −0.420267 0.907401i \(-0.638063\pi\)
−0.420267 + 0.907401i \(0.638063\pi\)
\(822\) 0 0
\(823\) 2.19511 0.0765168 0.0382584 0.999268i \(-0.487819\pi\)
0.0382584 + 0.999268i \(0.487819\pi\)
\(824\) 0 0
\(825\) 49.4738 1.72246
\(826\) 0 0
\(827\) 53.7347 1.86854 0.934269 0.356569i \(-0.116054\pi\)
0.934269 + 0.356569i \(0.116054\pi\)
\(828\) 0 0
\(829\) 0.512107 0.0177862 0.00889311 0.999960i \(-0.497169\pi\)
0.00889311 + 0.999960i \(0.497169\pi\)
\(830\) 0 0
\(831\) −10.9544 −0.380004
\(832\) 0 0
\(833\) 6.41256 0.222182
\(834\) 0 0
\(835\) −7.41161 −0.256489
\(836\) 0 0
\(837\) 4.35630 0.150576
\(838\) 0 0
\(839\) 16.6580 0.575099 0.287549 0.957766i \(-0.407159\pi\)
0.287549 + 0.957766i \(0.407159\pi\)
\(840\) 0 0
\(841\) −20.5382 −0.708212
\(842\) 0 0
\(843\) −24.0480 −0.828256
\(844\) 0 0
\(845\) −2.88241 −0.0991578
\(846\) 0 0
\(847\) 4.08648 0.140413
\(848\) 0 0
\(849\) 49.4075 1.69566
\(850\) 0 0
\(851\) 11.3323 0.388466
\(852\) 0 0
\(853\) −20.1710 −0.690643 −0.345322 0.938484i \(-0.612230\pi\)
−0.345322 + 0.938484i \(0.612230\pi\)
\(854\) 0 0
\(855\) −3.14297 −0.107487
\(856\) 0 0
\(857\) 54.7235 1.86932 0.934659 0.355545i \(-0.115705\pi\)
0.934659 + 0.355545i \(0.115705\pi\)
\(858\) 0 0
\(859\) 27.3438 0.932958 0.466479 0.884532i \(-0.345522\pi\)
0.466479 + 0.884532i \(0.345522\pi\)
\(860\) 0 0
\(861\) −12.6770 −0.432030
\(862\) 0 0
\(863\) −5.57367 −0.189730 −0.0948649 0.995490i \(-0.530242\pi\)
−0.0948649 + 0.995490i \(0.530242\pi\)
\(864\) 0 0
\(865\) −41.6827 −1.41726
\(866\) 0 0
\(867\) −2.07300 −0.0704026
\(868\) 0 0
\(869\) 27.1319 0.920386
\(870\) 0 0
\(871\) 36.5197 1.23742
\(872\) 0 0
\(873\) 13.7800 0.466382
\(874\) 0 0
\(875\) −2.29205 −0.0774854
\(876\) 0 0
\(877\) 13.8875 0.468947 0.234473 0.972123i \(-0.424663\pi\)
0.234473 + 0.972123i \(0.424663\pi\)
\(878\) 0 0
\(879\) −56.5831 −1.90850
\(880\) 0 0
\(881\) 20.7570 0.699320 0.349660 0.936877i \(-0.386297\pi\)
0.349660 + 0.936877i \(0.386297\pi\)
\(882\) 0 0
\(883\) 42.7776 1.43958 0.719790 0.694192i \(-0.244238\pi\)
0.719790 + 0.694192i \(0.244238\pi\)
\(884\) 0 0
\(885\) −6.84577 −0.230118
\(886\) 0 0
\(887\) 10.2115 0.342868 0.171434 0.985196i \(-0.445160\pi\)
0.171434 + 0.985196i \(0.445160\pi\)
\(888\) 0 0
\(889\) 16.2389 0.544636
\(890\) 0 0
\(891\) 45.2980 1.51754
\(892\) 0 0
\(893\) 9.81895 0.328579
\(894\) 0 0
\(895\) −86.1269 −2.87890
\(896\) 0 0
\(897\) −13.9592 −0.466083
\(898\) 0 0
\(899\) 3.59018 0.119739
\(900\) 0 0
\(901\) −0.757392 −0.0252324
\(902\) 0 0
\(903\) −0.974159 −0.0324180
\(904\) 0 0
\(905\) −11.5610 −0.384302
\(906\) 0 0
\(907\) 29.8674 0.991732 0.495866 0.868399i \(-0.334851\pi\)
0.495866 + 0.868399i \(0.334851\pi\)
\(908\) 0 0
\(909\) −9.77457 −0.324202
\(910\) 0 0
\(911\) −30.3010 −1.00392 −0.501959 0.864892i \(-0.667387\pi\)
−0.501959 + 0.864892i \(0.667387\pi\)
\(912\) 0 0
\(913\) 3.41759 0.113106
\(914\) 0 0
\(915\) 28.3103 0.935911
\(916\) 0 0
\(917\) −16.1736 −0.534099
\(918\) 0 0
\(919\) 41.0945 1.35558 0.677791 0.735255i \(-0.262938\pi\)
0.677791 + 0.735255i \(0.262938\pi\)
\(920\) 0 0
\(921\) 42.4203 1.39780
\(922\) 0 0
\(923\) −33.9669 −1.11803
\(924\) 0 0
\(925\) −37.0169 −1.21711
\(926\) 0 0
\(927\) −23.4823 −0.771261
\(928\) 0 0
\(929\) 52.3585 1.71783 0.858913 0.512122i \(-0.171141\pi\)
0.858913 + 0.512122i \(0.171141\pi\)
\(930\) 0 0
\(931\) −4.70440 −0.154180
\(932\) 0 0
\(933\) 8.72109 0.285516
\(934\) 0 0
\(935\) −13.3457 −0.436449
\(936\) 0 0
\(937\) 40.4155 1.32032 0.660158 0.751127i \(-0.270489\pi\)
0.660158 + 0.751127i \(0.270489\pi\)
\(938\) 0 0
\(939\) 6.34595 0.207092
\(940\) 0 0
\(941\) −48.7935 −1.59062 −0.795311 0.606202i \(-0.792692\pi\)
−0.795311 + 0.606202i \(0.792692\pi\)
\(942\) 0 0
\(943\) −14.4249 −0.469740
\(944\) 0 0
\(945\) −8.93390 −0.290620
\(946\) 0 0
\(947\) −17.0083 −0.552695 −0.276348 0.961058i \(-0.589124\pi\)
−0.276348 + 0.961058i \(0.589124\pi\)
\(948\) 0 0
\(949\) −35.2499 −1.14426
\(950\) 0 0
\(951\) −6.18145 −0.200447
\(952\) 0 0
\(953\) 27.4186 0.888176 0.444088 0.895983i \(-0.353528\pi\)
0.444088 + 0.895983i \(0.353528\pi\)
\(954\) 0 0
\(955\) 29.4766 0.953841
\(956\) 0 0
\(957\) 24.3695 0.787754
\(958\) 0 0
\(959\) −2.02642 −0.0654366
\(960\) 0 0
\(961\) −29.4768 −0.950863
\(962\) 0 0
\(963\) 10.1158 0.325978
\(964\) 0 0
\(965\) −4.59240 −0.147834
\(966\) 0 0
\(967\) −24.0408 −0.773100 −0.386550 0.922268i \(-0.626333\pi\)
−0.386550 + 0.922268i \(0.626333\pi\)
\(968\) 0 0
\(969\) 1.52080 0.0488550
\(970\) 0 0
\(971\) 40.0032 1.28376 0.641882 0.766803i \(-0.278154\pi\)
0.641882 + 0.766803i \(0.278154\pi\)
\(972\) 0 0
\(973\) 6.99656 0.224299
\(974\) 0 0
\(975\) 45.5976 1.46029
\(976\) 0 0
\(977\) −0.815311 −0.0260841 −0.0130421 0.999915i \(-0.504152\pi\)
−0.0130421 + 0.999915i \(0.504152\pi\)
\(978\) 0 0
\(979\) 2.64346 0.0844854
\(980\) 0 0
\(981\) 18.2424 0.582436
\(982\) 0 0
\(983\) −41.5745 −1.32602 −0.663010 0.748611i \(-0.730721\pi\)
−0.663010 + 0.748611i \(0.730721\pi\)
\(984\) 0 0
\(985\) 82.4144 2.62594
\(986\) 0 0
\(987\) −21.2654 −0.676885
\(988\) 0 0
\(989\) −1.10848 −0.0352476
\(990\) 0 0
\(991\) 48.6132 1.54425 0.772124 0.635472i \(-0.219194\pi\)
0.772124 + 0.635472i \(0.219194\pi\)
\(992\) 0 0
\(993\) 3.15848 0.100231
\(994\) 0 0
\(995\) 51.9514 1.64697
\(996\) 0 0
\(997\) 3.51977 0.111472 0.0557361 0.998446i \(-0.482249\pi\)
0.0557361 + 0.998446i \(0.482249\pi\)
\(998\) 0 0
\(999\) −22.1245 −0.699989
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 \(a_p\))