Properties

Label 6027.2.a.h.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} +1.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} +1.00000 q^{9} +4.00000 q^{11} +2.00000 q^{12} -1.00000 q^{13} -4.00000 q^{16} +4.00000 q^{17} +2.00000 q^{18} +7.00000 q^{19} +8.00000 q^{22} +6.00000 q^{23} -5.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} -8.00000 q^{29} +1.00000 q^{31} -8.00000 q^{32} +4.00000 q^{33} +8.00000 q^{34} +2.00000 q^{36} +7.00000 q^{37} +14.0000 q^{38} -1.00000 q^{39} -1.00000 q^{41} -7.00000 q^{43} +8.00000 q^{44} +12.0000 q^{46} -4.00000 q^{48} -10.0000 q^{50} +4.00000 q^{51} -2.00000 q^{52} +4.00000 q^{53} +2.00000 q^{54} +7.00000 q^{57} -16.0000 q^{58} +8.00000 q^{59} +2.00000 q^{61} +2.00000 q^{62} -8.00000 q^{64} +8.00000 q^{66} +13.0000 q^{67} +8.00000 q^{68} +6.00000 q^{69} -6.00000 q^{71} +1.00000 q^{73} +14.0000 q^{74} -5.00000 q^{75} +14.0000 q^{76} -2.00000 q^{78} -7.00000 q^{79} +1.00000 q^{81} -2.00000 q^{82} +8.00000 q^{83} -14.0000 q^{86} -8.00000 q^{87} +14.0000 q^{89} +12.0000 q^{92} +1.00000 q^{93} -8.00000 q^{96} -2.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.00000 1.00000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 2.00000 0.577350
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 2.00000 0.471405
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 8.00000 1.70561
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) −2.00000 −0.392232
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) −8.00000 −1.41421
\(33\) 4.00000 0.696311
\(34\) 8.00000 1.37199
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 14.0000 2.27110
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 8.00000 1.20605
\(45\) 0 0
\(46\) 12.0000 1.76930
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −4.00000 −0.577350
\(49\) 0 0
\(50\) −10.0000 −1.41421
\(51\) 4.00000 0.560112
\(52\) −2.00000 −0.277350
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 2.00000 0.272166
\(55\) 0 0
\(56\) 0 0
\(57\) 7.00000 0.927173
\(58\) −16.0000 −2.10090
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 8.00000 0.984732
\(67\) 13.0000 1.58820 0.794101 0.607785i \(-0.207942\pi\)
0.794101 + 0.607785i \(0.207942\pi\)
\(68\) 8.00000 0.970143
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 1.00000 0.117041 0.0585206 0.998286i \(-0.481362\pi\)
0.0585206 + 0.998286i \(0.481362\pi\)
\(74\) 14.0000 1.62747
\(75\) −5.00000 −0.577350
\(76\) 14.0000 1.60591
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −7.00000 −0.787562 −0.393781 0.919204i \(-0.628833\pi\)
−0.393781 + 0.919204i \(0.628833\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −2.00000 −0.220863
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −14.0000 −1.50966
\(87\) −8.00000 −0.857690
\(88\) 0 0
\(89\) 14.0000 1.48400 0.741999 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 12.0000 1.25109
\(93\) 1.00000 0.103695
\(94\) 0 0
\(95\) 0 0
\(96\) −8.00000 −0.816497
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) −10.0000 −1.00000
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 8.00000 0.792118
\(103\) 9.00000 0.886796 0.443398 0.896325i \(-0.353773\pi\)
0.443398 + 0.896325i \(0.353773\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) −14.0000 −1.35343 −0.676716 0.736245i \(-0.736597\pi\)
−0.676716 + 0.736245i \(0.736597\pi\)
\(108\) 2.00000 0.192450
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 0 0
\(111\) 7.00000 0.664411
\(112\) 0 0
\(113\) −8.00000 −0.752577 −0.376288 0.926503i \(-0.622800\pi\)
−0.376288 + 0.926503i \(0.622800\pi\)
\(114\) 14.0000 1.31122
\(115\) 0 0
\(116\) −16.0000 −1.48556
\(117\) −1.00000 −0.0924500
\(118\) 16.0000 1.47292
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 4.00000 0.362143
\(123\) −1.00000 −0.0901670
\(124\) 2.00000 0.179605
\(125\) 0 0
\(126\) 0 0
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) 0 0
\(129\) −7.00000 −0.616316
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 8.00000 0.696311
\(133\) 0 0
\(134\) 26.0000 2.24606
\(135\) 0 0
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 12.0000 1.02151
\(139\) 1.00000 0.0848189 0.0424094 0.999100i \(-0.486497\pi\)
0.0424094 + 0.999100i \(0.486497\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) −4.00000 −0.334497
\(144\) −4.00000 −0.333333
\(145\) 0 0
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) 14.0000 1.15079
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −10.0000 −0.816497
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) 0 0
\(156\) −2.00000 −0.160128
\(157\) 22.0000 1.75579 0.877896 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) −14.0000 −1.11378
\(159\) 4.00000 0.317221
\(160\) 0 0
\(161\) 0 0
\(162\) 2.00000 0.157135
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) 16.0000 1.24184
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 7.00000 0.535303
\(172\) −14.0000 −1.06749
\(173\) 12.0000 0.912343 0.456172 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(174\) −16.0000 −1.21296
\(175\) 0 0
\(176\) −16.0000 −1.20605
\(177\) 8.00000 0.601317
\(178\) 28.0000 2.09869
\(179\) −2.00000 −0.149487 −0.0747435 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) 0 0
\(181\) −21.0000 −1.56092 −0.780459 0.625207i \(-0.785014\pi\)
−0.780459 + 0.625207i \(0.785014\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 0 0
\(186\) 2.00000 0.146647
\(187\) 16.0000 1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) −8.00000 −0.577350
\(193\) −15.0000 −1.07972 −0.539862 0.841754i \(-0.681524\pi\)
−0.539862 + 0.841754i \(0.681524\pi\)
\(194\) −4.00000 −0.287183
\(195\) 0 0
\(196\) 0 0
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 8.00000 0.568535
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 0 0
\(201\) 13.0000 0.916949
\(202\) −28.0000 −1.97007
\(203\) 0 0
\(204\) 8.00000 0.560112
\(205\) 0 0
\(206\) 18.0000 1.25412
\(207\) 6.00000 0.417029
\(208\) 4.00000 0.277350
\(209\) 28.0000 1.93680
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 8.00000 0.549442
\(213\) −6.00000 −0.411113
\(214\) −28.0000 −1.91404
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 22.0000 1.49003
\(219\) 1.00000 0.0675737
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 14.0000 0.939618
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) −16.0000 −1.06430
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 14.0000 0.927173
\(229\) 15.0000 0.991228 0.495614 0.868543i \(-0.334943\pi\)
0.495614 + 0.868543i \(0.334943\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.00000 −0.262049 −0.131024 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) 16.0000 1.04151
\(237\) −7.00000 −0.454699
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 10.0000 0.642824
\(243\) 1.00000 0.0641500
\(244\) 4.00000 0.256074
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −7.00000 −0.445399
\(248\) 0 0
\(249\) 8.00000 0.506979
\(250\) 0 0
\(251\) 26.0000 1.64111 0.820553 0.571571i \(-0.193666\pi\)
0.820553 + 0.571571i \(0.193666\pi\)
\(252\) 0 0
\(253\) 24.0000 1.50887
\(254\) 34.0000 2.13335
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −28.0000 −1.74659 −0.873296 0.487190i \(-0.838022\pi\)
−0.873296 + 0.487190i \(0.838022\pi\)
\(258\) −14.0000 −0.871602
\(259\) 0 0
\(260\) 0 0
\(261\) −8.00000 −0.495188
\(262\) 16.0000 0.988483
\(263\) 18.0000 1.10993 0.554964 0.831875i \(-0.312732\pi\)
0.554964 + 0.831875i \(0.312732\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 14.0000 0.856786
\(268\) 26.0000 1.58820
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −16.0000 −0.970143
\(273\) 0 0
\(274\) −24.0000 −1.44989
\(275\) −20.0000 −1.20605
\(276\) 12.0000 0.722315
\(277\) −23.0000 −1.38194 −0.690968 0.722885i \(-0.742815\pi\)
−0.690968 + 0.722885i \(0.742815\pi\)
\(278\) 2.00000 0.119952
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) −31.0000 −1.84276 −0.921379 0.388664i \(-0.872937\pi\)
−0.921379 + 0.388664i \(0.872937\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 0 0
\(288\) −8.00000 −0.471405
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −2.00000 −0.117242
\(292\) 2.00000 0.117041
\(293\) −34.0000 −1.98630 −0.993151 0.116841i \(-0.962723\pi\)
−0.993151 + 0.116841i \(0.962723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 4.00000 0.232104
\(298\) −12.0000 −0.695141
\(299\) −6.00000 −0.346989
\(300\) −10.0000 −0.577350
\(301\) 0 0
\(302\) 32.0000 1.84139
\(303\) −14.0000 −0.804279
\(304\) −28.0000 −1.60591
\(305\) 0 0
\(306\) 8.00000 0.457330
\(307\) 11.0000 0.627803 0.313902 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) 0 0
\(309\) 9.00000 0.511992
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) −15.0000 −0.847850 −0.423925 0.905697i \(-0.639348\pi\)
−0.423925 + 0.905697i \(0.639348\pi\)
\(314\) 44.0000 2.48306
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) −22.0000 −1.23564 −0.617822 0.786318i \(-0.711985\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) 8.00000 0.448618
\(319\) −32.0000 −1.79166
\(320\) 0 0
\(321\) −14.0000 −0.781404
\(322\) 0 0
\(323\) 28.0000 1.55796
\(324\) 2.00000 0.111111
\(325\) 5.00000 0.277350
\(326\) −24.0000 −1.32924
\(327\) 11.0000 0.608301
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −15.0000 −0.824475 −0.412237 0.911077i \(-0.635253\pi\)
−0.412237 + 0.911077i \(0.635253\pi\)
\(332\) 16.0000 0.878114
\(333\) 7.00000 0.383598
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) −24.0000 −1.30543
\(339\) −8.00000 −0.434500
\(340\) 0 0
\(341\) 4.00000 0.216612
\(342\) 14.0000 0.757033
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 24.0000 1.29025
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) −16.0000 −0.857690
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) −32.0000 −1.70561
\(353\) −10.0000 −0.532246 −0.266123 0.963939i \(-0.585743\pi\)
−0.266123 + 0.963939i \(0.585743\pi\)
\(354\) 16.0000 0.850390
\(355\) 0 0
\(356\) 28.0000 1.48400
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) 10.0000 0.527780 0.263890 0.964553i \(-0.414994\pi\)
0.263890 + 0.964553i \(0.414994\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) −42.0000 −2.20747
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 0 0
\(366\) 4.00000 0.209083
\(367\) −25.0000 −1.30499 −0.652495 0.757793i \(-0.726278\pi\)
−0.652495 + 0.757793i \(0.726278\pi\)
\(368\) −24.0000 −1.25109
\(369\) −1.00000 −0.0520579
\(370\) 0 0
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) −29.0000 −1.50156 −0.750782 0.660551i \(-0.770323\pi\)
−0.750782 + 0.660551i \(0.770323\pi\)
\(374\) 32.0000 1.65468
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −21.0000 −1.07870 −0.539349 0.842082i \(-0.681330\pi\)
−0.539349 + 0.842082i \(0.681330\pi\)
\(380\) 0 0
\(381\) 17.0000 0.870936
\(382\) 24.0000 1.22795
\(383\) −20.0000 −1.02195 −0.510976 0.859595i \(-0.670716\pi\)
−0.510976 + 0.859595i \(0.670716\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −30.0000 −1.52696
\(387\) −7.00000 −0.355830
\(388\) −4.00000 −0.203069
\(389\) 28.0000 1.41966 0.709828 0.704375i \(-0.248773\pi\)
0.709828 + 0.704375i \(0.248773\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 0 0
\(393\) 8.00000 0.403547
\(394\) 16.0000 0.806068
\(395\) 0 0
\(396\) 8.00000 0.402015
\(397\) 1.00000 0.0501886 0.0250943 0.999685i \(-0.492011\pi\)
0.0250943 + 0.999685i \(0.492011\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) 20.0000 1.00000
\(401\) −28.0000 −1.39825 −0.699127 0.714998i \(-0.746428\pi\)
−0.699127 + 0.714998i \(0.746428\pi\)
\(402\) 26.0000 1.29676
\(403\) −1.00000 −0.0498135
\(404\) −28.0000 −1.39305
\(405\) 0 0
\(406\) 0 0
\(407\) 28.0000 1.38791
\(408\) 0 0
\(409\) −7.00000 −0.346128 −0.173064 0.984911i \(-0.555367\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 18.0000 0.886796
\(413\) 0 0
\(414\) 12.0000 0.589768
\(415\) 0 0
\(416\) 8.00000 0.392232
\(417\) 1.00000 0.0489702
\(418\) 56.0000 2.73905
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0 0
\(421\) −5.00000 −0.243685 −0.121843 0.992549i \(-0.538880\pi\)
−0.121843 + 0.992549i \(0.538880\pi\)
\(422\) −32.0000 −1.55774
\(423\) 0 0
\(424\) 0 0
\(425\) −20.0000 −0.970143
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) −28.0000 −1.35343
\(429\) −4.00000 −0.193122
\(430\) 0 0
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) −4.00000 −0.192450
\(433\) 11.0000 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 22.0000 1.05361
\(437\) 42.0000 2.00913
\(438\) 2.00000 0.0955637
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −8.00000 −0.380521
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 14.0000 0.664411
\(445\) 0 0
\(446\) 40.0000 1.89405
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) −10.0000 −0.471405
\(451\) −4.00000 −0.188353
\(452\) −16.0000 −0.752577
\(453\) 16.0000 0.751746
\(454\) −36.0000 −1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) −1.00000 −0.0467780 −0.0233890 0.999726i \(-0.507446\pi\)
−0.0233890 + 0.999726i \(0.507446\pi\)
\(458\) 30.0000 1.40181
\(459\) 4.00000 0.186704
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) 29.0000 1.34774 0.673872 0.738848i \(-0.264630\pi\)
0.673872 + 0.738848i \(0.264630\pi\)
\(464\) 32.0000 1.48556
\(465\) 0 0
\(466\) −8.00000 −0.370593
\(467\) −24.0000 −1.11059 −0.555294 0.831654i \(-0.687394\pi\)
−0.555294 + 0.831654i \(0.687394\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 22.0000 1.01371
\(472\) 0 0
\(473\) −28.0000 −1.28744
\(474\) −14.0000 −0.643041
\(475\) −35.0000 −1.60591
\(476\) 0 0
\(477\) 4.00000 0.183147
\(478\) −12.0000 −0.548867
\(479\) −6.00000 −0.274147 −0.137073 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 0 0
\(481\) −7.00000 −0.319173
\(482\) −44.0000 −2.00415
\(483\) 0 0
\(484\) 10.0000 0.454545
\(485\) 0 0
\(486\) 2.00000 0.0907218
\(487\) 31.0000 1.40474 0.702372 0.711810i \(-0.252124\pi\)
0.702372 + 0.711810i \(0.252124\pi\)
\(488\) 0 0
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) −2.00000 −0.0901670
\(493\) −32.0000 −1.44121
\(494\) −14.0000 −0.629890
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 16.0000 0.716977
\(499\) −37.0000 −1.65635 −0.828174 0.560471i \(-0.810620\pi\)
−0.828174 + 0.560471i \(0.810620\pi\)
\(500\) 0 0
\(501\) 6.00000 0.268060
\(502\) 52.0000 2.32087
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 48.0000 2.13386
\(507\) −12.0000 −0.532939
\(508\) 34.0000 1.50851
\(509\) −6.00000 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 32.0000 1.41421
\(513\) 7.00000 0.309058
\(514\) −56.0000 −2.47005
\(515\) 0 0
\(516\) −14.0000 −0.616316
\(517\) 0 0
\(518\) 0 0
\(519\) 12.0000 0.526742
\(520\) 0 0
\(521\) 2.00000 0.0876216 0.0438108 0.999040i \(-0.486050\pi\)
0.0438108 + 0.999040i \(0.486050\pi\)
\(522\) −16.0000 −0.700301
\(523\) −5.00000 −0.218635 −0.109317 0.994007i \(-0.534866\pi\)
−0.109317 + 0.994007i \(0.534866\pi\)
\(524\) 16.0000 0.698963
\(525\) 0 0
\(526\) 36.0000 1.56967
\(527\) 4.00000 0.174243
\(528\) −16.0000 −0.696311
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) 1.00000 0.0433148
\(534\) 28.0000 1.21168
\(535\) 0 0
\(536\) 0 0
\(537\) −2.00000 −0.0863064
\(538\) −12.0000 −0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) 33.0000 1.41878 0.709390 0.704816i \(-0.248970\pi\)
0.709390 + 0.704816i \(0.248970\pi\)
\(542\) 16.0000 0.687259
\(543\) −21.0000 −0.901196
\(544\) −32.0000 −1.37199
\(545\) 0 0
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −24.0000 −1.02523
\(549\) 2.00000 0.0853579
\(550\) −40.0000 −1.70561
\(551\) −56.0000 −2.38568
\(552\) 0 0
\(553\) 0 0
\(554\) −46.0000 −1.95435
\(555\) 0 0
\(556\) 2.00000 0.0848189
\(557\) −24.0000 −1.01691 −0.508456 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) 2.00000 0.0846668
\(559\) 7.00000 0.296068
\(560\) 0 0
\(561\) 16.0000 0.675521
\(562\) −36.0000 −1.51857
\(563\) −8.00000 −0.337160 −0.168580 0.985688i \(-0.553918\pi\)
−0.168580 + 0.985688i \(0.553918\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −62.0000 −2.60605
\(567\) 0 0
\(568\) 0 0
\(569\) 28.0000 1.17382 0.586911 0.809652i \(-0.300344\pi\)
0.586911 + 0.809652i \(0.300344\pi\)
\(570\) 0 0
\(571\) 23.0000 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) −8.00000 −0.334497
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) −8.00000 −0.333333
\(577\) −11.0000 −0.457936 −0.228968 0.973434i \(-0.573535\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) −2.00000 −0.0831890
\(579\) −15.0000 −0.623379
\(580\) 0 0
\(581\) 0 0
\(582\) −4.00000 −0.165805
\(583\) 16.0000 0.662652
\(584\) 0 0
\(585\) 0 0
\(586\) −68.0000 −2.80905
\(587\) −10.0000 −0.412744 −0.206372 0.978474i \(-0.566166\pi\)
−0.206372 + 0.978474i \(0.566166\pi\)
\(588\) 0 0
\(589\) 7.00000 0.288430
\(590\) 0 0
\(591\) 8.00000 0.329076
\(592\) −28.0000 −1.15079
\(593\) −24.0000 −0.985562 −0.492781 0.870153i \(-0.664020\pi\)
−0.492781 + 0.870153i \(0.664020\pi\)
\(594\) 8.00000 0.328244
\(595\) 0 0
\(596\) −12.0000 −0.491539
\(597\) 8.00000 0.327418
\(598\) −12.0000 −0.490716
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 0 0
\(601\) 1.00000 0.0407909 0.0203954 0.999792i \(-0.493507\pi\)
0.0203954 + 0.999792i \(0.493507\pi\)
\(602\) 0 0
\(603\) 13.0000 0.529401
\(604\) 32.0000 1.30206
\(605\) 0 0
\(606\) −28.0000 −1.13742
\(607\) −5.00000 −0.202944 −0.101472 0.994838i \(-0.532355\pi\)
−0.101472 + 0.994838i \(0.532355\pi\)
\(608\) −56.0000 −2.27110
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 8.00000 0.323381
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 22.0000 0.887848
\(615\) 0 0
\(616\) 0 0
\(617\) −34.0000 −1.36879 −0.684394 0.729112i \(-0.739933\pi\)
−0.684394 + 0.729112i \(0.739933\pi\)
\(618\) 18.0000 0.724066
\(619\) 15.0000 0.602901 0.301450 0.953482i \(-0.402529\pi\)
0.301450 + 0.953482i \(0.402529\pi\)
\(620\) 0 0
\(621\) 6.00000 0.240772
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) 4.00000 0.160128
\(625\) 25.0000 1.00000
\(626\) −30.0000 −1.19904
\(627\) 28.0000 1.11821
\(628\) 44.0000 1.75579
\(629\) 28.0000 1.11643
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) −16.0000 −0.635943
\(634\) −44.0000 −1.74746
\(635\) 0 0
\(636\) 8.00000 0.317221
\(637\) 0 0
\(638\) −64.0000 −2.53378
\(639\) −6.00000 −0.237356
\(640\) 0 0
\(641\) −42.0000 −1.65890 −0.829450 0.558581i \(-0.811346\pi\)
−0.829450 + 0.558581i \(0.811346\pi\)
\(642\) −28.0000 −1.10507
\(643\) −37.0000 −1.45914 −0.729569 0.683907i \(-0.760279\pi\)
−0.729569 + 0.683907i \(0.760279\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 56.0000 2.20329
\(647\) −46.0000 −1.80845 −0.904223 0.427060i \(-0.859549\pi\)
−0.904223 + 0.427060i \(0.859549\pi\)
\(648\) 0 0
\(649\) 32.0000 1.25611
\(650\) 10.0000 0.392232
\(651\) 0 0
\(652\) −24.0000 −0.939913
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) 22.0000 0.860268
\(655\) 0 0
\(656\) 4.00000 0.156174
\(657\) 1.00000 0.0390137
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) −1.00000 −0.0388955 −0.0194477 0.999811i \(-0.506191\pi\)
−0.0194477 + 0.999811i \(0.506191\pi\)
\(662\) −30.0000 −1.16598
\(663\) −4.00000 −0.155347
\(664\) 0 0
\(665\) 0 0
\(666\) 14.0000 0.542489
\(667\) −48.0000 −1.85857
\(668\) 12.0000 0.464294
\(669\) 20.0000 0.773245
\(670\) 0 0
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) −23.0000 −0.886585 −0.443292 0.896377i \(-0.646190\pi\)
−0.443292 + 0.896377i \(0.646190\pi\)
\(674\) −46.0000 −1.77185
\(675\) −5.00000 −0.192450
\(676\) −24.0000 −0.923077
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) −16.0000 −0.614476
\(679\) 0 0
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 8.00000 0.306336
\(683\) 30.0000 1.14792 0.573959 0.818884i \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(684\) 14.0000 0.535303
\(685\) 0 0
\(686\) 0 0
\(687\) 15.0000 0.572286
\(688\) 28.0000 1.06749
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) −3.00000 −0.114125 −0.0570627 0.998371i \(-0.518173\pi\)
−0.0570627 + 0.998371i \(0.518173\pi\)
\(692\) 24.0000 0.912343
\(693\) 0 0
\(694\) −24.0000 −0.911028
\(695\) 0 0
\(696\) 0 0
\(697\) −4.00000 −0.151511
\(698\) −68.0000 −2.57384
\(699\) −4.00000 −0.151294
\(700\) 0 0
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 49.0000 1.84807
\(704\) −32.0000 −1.20605
\(705\) 0 0
\(706\) −20.0000 −0.752710
\(707\) 0 0
\(708\) 16.0000 0.601317
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) −7.00000 −0.262521
\(712\) 0 0
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) −4.00000 −0.149487
\(717\) −6.00000 −0.224074
\(718\) 20.0000 0.746393
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 60.0000 2.23297
\(723\) −22.0000 −0.818189
\(724\) −42.0000 −1.56092
\(725\) 40.0000 1.48556
\(726\) 10.0000 0.371135
\(727\) 1.00000 0.0370879 0.0185440 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −28.0000 −1.03562
\(732\) 4.00000 0.147844
\(733\) −19.0000 −0.701781 −0.350891 0.936416i \(-0.614121\pi\)
−0.350891 + 0.936416i \(0.614121\pi\)
\(734\) −50.0000 −1.84553
\(735\) 0 0
\(736\) −48.0000 −1.76930
\(737\) 52.0000 1.91544
\(738\) −2.00000 −0.0736210
\(739\) −19.0000 −0.698926 −0.349463 0.936950i \(-0.613636\pi\)
−0.349463 + 0.936950i \(0.613636\pi\)
\(740\) 0 0
\(741\) −7.00000 −0.257151
\(742\) 0 0
\(743\) 22.0000 0.807102 0.403551 0.914957i \(-0.367776\pi\)
0.403551 + 0.914957i \(0.367776\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −58.0000 −2.12353
\(747\) 8.00000 0.292705
\(748\) 32.0000 1.17004
\(749\) 0 0
\(750\) 0 0
\(751\) 7.00000 0.255434 0.127717 0.991811i \(-0.459235\pi\)
0.127717 + 0.991811i \(0.459235\pi\)
\(752\) 0 0
\(753\) 26.0000 0.947493
\(754\) 16.0000 0.582686
\(755\) 0 0
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) −42.0000 −1.52551
\(759\) 24.0000 0.871145
\(760\) 0 0
\(761\) 24.0000 0.869999 0.435000 0.900431i \(-0.356748\pi\)
0.435000 + 0.900431i \(0.356748\pi\)
\(762\) 34.0000 1.23169
\(763\) 0 0
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) −40.0000 −1.44526
\(767\) −8.00000 −0.288863
\(768\) 16.0000 0.577350
\(769\) 7.00000 0.252426 0.126213 0.992003i \(-0.459718\pi\)
0.126213 + 0.992003i \(0.459718\pi\)
\(770\) 0 0
\(771\) −28.0000 −1.00840
\(772\) −30.0000 −1.07972
\(773\) 20.0000 0.719350 0.359675 0.933078i \(-0.382888\pi\)
0.359675 + 0.933078i \(0.382888\pi\)
\(774\) −14.0000 −0.503220
\(775\) −5.00000 −0.179605
\(776\) 0 0
\(777\) 0 0
\(778\) 56.0000 2.00770
\(779\) −7.00000 −0.250801
\(780\) 0 0
\(781\) −24.0000 −0.858788
\(782\) 48.0000 1.71648
\(783\) −8.00000 −0.285897
\(784\) 0 0
\(785\) 0 0
\(786\) 16.0000 0.570701
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) 16.0000 0.569976
\(789\) 18.0000 0.640817
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.00000 −0.0710221
\(794\) 2.00000 0.0709773
\(795\) 0 0
\(796\) 16.0000 0.567105
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 40.0000 1.41421
\(801\) 14.0000 0.494666
\(802\) −56.0000 −1.97743
\(803\) 4.00000 0.141157
\(804\) 26.0000 0.916949
\(805\) 0 0
\(806\) −2.00000 −0.0704470
\(807\) −6.00000 −0.211210
\(808\) 0 0
\(809\) 28.0000 0.984428 0.492214 0.870474i \(-0.336188\pi\)
0.492214 + 0.870474i \(0.336188\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) 56.0000 1.96280
\(815\) 0 0
\(816\) −16.0000 −0.560112
\(817\) −49.0000 −1.71429
\(818\) −14.0000 −0.489499
\(819\) 0 0
\(820\) 0 0
\(821\) 10.0000 0.349002 0.174501 0.984657i \(-0.444169\pi\)
0.174501 + 0.984657i \(0.444169\pi\)
\(822\) −24.0000 −0.837096
\(823\) −8.00000 −0.278862 −0.139431 0.990232i \(-0.544527\pi\)
−0.139431 + 0.990232i \(0.544527\pi\)
\(824\) 0 0
\(825\) −20.0000 −0.696311
\(826\) 0 0
\(827\) 14.0000 0.486828 0.243414 0.969923i \(-0.421733\pi\)
0.243414 + 0.969923i \(0.421733\pi\)
\(828\) 12.0000 0.417029
\(829\) 25.0000 0.868286 0.434143 0.900844i \(-0.357051\pi\)
0.434143 + 0.900844i \(0.357051\pi\)
\(830\) 0 0
\(831\) −23.0000 −0.797861
\(832\) 8.00000 0.277350
\(833\) 0 0
\(834\) 2.00000 0.0692543
\(835\) 0 0
\(836\) 56.0000 1.93680
\(837\) 1.00000 0.0345651
\(838\) 36.0000 1.24360
\(839\) −26.0000 −0.897620 −0.448810 0.893627i \(-0.648152\pi\)
−0.448810 + 0.893627i \(0.648152\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) −10.0000 −0.344623
\(843\) −18.0000 −0.619953
\(844\) −32.0000 −1.10149
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −16.0000 −0.549442
\(849\) −31.0000 −1.06392
\(850\) −40.0000 −1.37199
\(851\) 42.0000 1.43974
\(852\) −12.0000 −0.411113
\(853\) 51.0000 1.74621 0.873103 0.487535i \(-0.162104\pi\)
0.873103 + 0.487535i \(0.162104\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 48.0000 1.63965 0.819824 0.572615i \(-0.194071\pi\)
0.819824 + 0.572615i \(0.194071\pi\)
\(858\) −8.00000 −0.273115
\(859\) 12.0000 0.409435 0.204717 0.978821i \(-0.434372\pi\)
0.204717 + 0.978821i \(0.434372\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 32.0000 1.08992
\(863\) −12.0000 −0.408485 −0.204242 0.978920i \(-0.565473\pi\)
−0.204242 + 0.978920i \(0.565473\pi\)
\(864\) −8.00000 −0.272166
\(865\) 0 0
\(866\) 22.0000 0.747590
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) −28.0000 −0.949835
\(870\) 0 0
\(871\) −13.0000 −0.440488
\(872\) 0 0
\(873\) −2.00000 −0.0676897
\(874\) 84.0000 2.84134
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −6.00000 −0.202606 −0.101303 0.994856i \(-0.532301\pi\)
−0.101303 + 0.994856i \(0.532301\pi\)
\(878\) 32.0000 1.07995
\(879\) −34.0000 −1.14679
\(880\) 0 0
\(881\) 36.0000 1.21287 0.606435 0.795133i \(-0.292599\pi\)
0.606435 + 0.795133i \(0.292599\pi\)
\(882\) 0 0
\(883\) −35.0000 −1.17784 −0.588922 0.808190i \(-0.700447\pi\)
−0.588922 + 0.808190i \(0.700447\pi\)
\(884\) −8.00000 −0.269069
\(885\) 0 0
\(886\) 48.0000 1.61259
\(887\) −18.0000 −0.604381 −0.302190 0.953248i \(-0.597718\pi\)
−0.302190 + 0.953248i \(0.597718\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 4.00000 0.134005
\(892\) 40.0000 1.33930
\(893\) 0 0
\(894\) −12.0000 −0.401340
\(895\) 0 0
\(896\) 0 0
\(897\) −6.00000 −0.200334
\(898\) 24.0000 0.800890
\(899\) −8.00000 −0.266815
\(900\) −10.0000 −0.333333
\(901\) 16.0000 0.533037
\(902\) −8.00000 −0.266371
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 32.0000 1.06313
\(907\) 23.0000 0.763702 0.381851 0.924224i \(-0.375287\pi\)
0.381851 + 0.924224i \(0.375287\pi\)
\(908\) −36.0000 −1.19470
\(909\) −14.0000 −0.464351
\(910\) 0 0
\(911\) 60.0000 1.98789 0.993944 0.109885i \(-0.0350482\pi\)
0.993944 + 0.109885i \(0.0350482\pi\)
\(912\) −28.0000 −0.927173
\(913\) 32.0000 1.05905
\(914\) −2.00000 −0.0661541
\(915\) 0 0
\(916\) 30.0000 0.991228
\(917\) 0 0
\(918\) 8.00000 0.264039
\(919\) −7.00000 −0.230909 −0.115454 0.993313i \(-0.536832\pi\)
−0.115454 + 0.993313i \(0.536832\pi\)
\(920\) 0 0
\(921\) 11.0000 0.362462
\(922\) −60.0000 −1.97599
\(923\) 6.00000 0.197492
\(924\) 0 0
\(925\) −35.0000 −1.15079
\(926\) 58.0000 1.90600
\(927\) 9.00000 0.295599
\(928\) 64.0000 2.10090
\(929\) 54.0000 1.77168 0.885841 0.463988i \(-0.153582\pi\)
0.885841 + 0.463988i \(0.153582\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −8.00000 −0.262049
\(933\) 12.0000 0.392862
\(934\) −48.0000 −1.57061
\(935\) 0 0
\(936\) 0 0
\(937\) −39.0000 −1.27407 −0.637037 0.770833i \(-0.719840\pi\)
−0.637037 + 0.770833i \(0.719840\pi\)
\(938\) 0 0
\(939\) −15.0000 −0.489506
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 44.0000 1.43360
\(943\) −6.00000 −0.195387
\(944\) −32.0000 −1.04151
\(945\) 0 0
\(946\) −56.0000 −1.82072
\(947\) −36.0000 −1.16984 −0.584921 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) −14.0000 −0.454699
\(949\) −1.00000 −0.0324614
\(950\) −70.0000 −2.27110
\(951\) −22.0000 −0.713399
\(952\) 0 0
\(953\) −32.0000 −1.03658 −0.518291 0.855204i \(-0.673432\pi\)
−0.518291 + 0.855204i \(0.673432\pi\)
\(954\) 8.00000 0.259010
\(955\) 0 0
\(956\) −12.0000 −0.388108
\(957\) −32.0000 −1.03441
\(958\) −12.0000 −0.387702
\(959\) 0 0
\(960\) 0 0
\(961\) −30.0000 −0.967742
\(962\) −14.0000 −0.451378
\(963\) −14.0000 −0.451144
\(964\) −44.0000 −1.41714
\(965\) 0 0
\(966\) 0 0
\(967\) 37.0000 1.18984 0.594920 0.803785i \(-0.297184\pi\)
0.594920 + 0.803785i \(0.297184\pi\)
\(968\) 0 0
\(969\) 28.0000 0.899490
\(970\) 0 0
\(971\) −24.0000 −0.770197 −0.385098 0.922876i \(-0.625832\pi\)
−0.385098 + 0.922876i \(0.625832\pi\)
\(972\) 2.00000 0.0641500
\(973\) 0 0
\(974\) 62.0000 1.98661
\(975\) 5.00000 0.160128
\(976\) −8.00000 −0.256074
\(977\) 26.0000 0.831814 0.415907 0.909407i \(-0.363464\pi\)
0.415907 + 0.909407i \(0.363464\pi\)
\(978\) −24.0000 −0.767435
\(979\) 56.0000 1.78977
\(980\) 0 0
\(981\) 11.0000 0.351203
\(982\) 56.0000 1.78703
\(983\) −14.0000 −0.446531 −0.223265 0.974758i \(-0.571672\pi\)
−0.223265 + 0.974758i \(0.571672\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −64.0000 −2.03818
\(987\) 0 0
\(988\) −14.0000 −0.445399
\(989\) −42.0000 −1.33552
\(990\) 0 0
\(991\) −5.00000 −0.158830 −0.0794151 0.996842i \(-0.525305\pi\)
−0.0794151 + 0.996842i \(0.525305\pi\)
\(992\) −8.00000 −0.254000
\(993\) −15.0000 −0.476011
\(994\) 0 0
\(995\) 0 0
\(996\) 16.0000 0.506979
\(997\) −55.0000 −1.74187 −0.870934 0.491400i \(-0.836485\pi\)
−0.870934 + 0.491400i \(0.836485\pi\)
\(998\) −74.0000 −2.34243
\(999\) 7.00000 0.221470
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 \(a_p\))