Properties

Label 2005.2.a.b.1.1
Level 2005
Weight 2
Character 2005.1
Self dual Yes
Analytic conductor 16.010
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2005 = 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(16.0100056053\)
Analytic rank: \(1\)
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 \(\chi\) = 2005.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{8} -3.00000 q^{9} -1.00000 q^{10} +4.00000 q^{11} -2.00000 q^{13} -1.00000 q^{16} -6.00000 q^{17} +3.00000 q^{18} -1.00000 q^{20} -4.00000 q^{22} +4.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} -2.00000 q^{29} +4.00000 q^{31} -5.00000 q^{32} +6.00000 q^{34} +3.00000 q^{36} -10.0000 q^{37} +3.00000 q^{40} -6.00000 q^{41} +4.00000 q^{43} -4.00000 q^{44} -3.00000 q^{45} -4.00000 q^{46} +8.00000 q^{47} -7.00000 q^{49} -1.00000 q^{50} +2.00000 q^{52} +6.00000 q^{53} +4.00000 q^{55} +2.00000 q^{58} +8.00000 q^{59} -10.0000 q^{61} -4.00000 q^{62} +7.00000 q^{64} -2.00000 q^{65} +6.00000 q^{68} +4.00000 q^{71} -9.00000 q^{72} -6.00000 q^{73} +10.0000 q^{74} -12.0000 q^{79} -1.00000 q^{80} +9.00000 q^{81} +6.00000 q^{82} -12.0000 q^{83} -6.00000 q^{85} -4.00000 q^{86} +12.0000 q^{88} +10.0000 q^{89} +3.00000 q^{90} -4.00000 q^{92} -8.00000 q^{94} -6.00000 q^{97} +7.00000 q^{98} -12.0000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 3.00000 1.06066
\(9\) −3.00000 −1.00000
\(10\) −1.00000 −0.316228
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 3.00000 0.707107
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −4.00000 −0.603023
\(45\) −3.00000 −0.447214
\(46\) −4.00000 −0.589768
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 2.00000 0.262613
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 6.00000 0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) −9.00000 −1.06066
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 10.0000 1.16248
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) −1.00000 −0.111803
\(81\) 9.00000 1.00000
\(82\) 6.00000 0.662589
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 12.0000 1.27920
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 3.00000 0.316228
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 7.00000 0.707107
\(99\) −12.0000 −1.20605
\(100\) −1.00000 −0.100000
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −4.00000 −0.381385
\(111\) 0 0
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) 2.00000 0.185695
\(117\) 6.00000 0.554700
\(118\) −8.00000 −0.736460
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 3.00000 0.265165
\(129\) 0 0
\(130\) 2.00000 0.175412
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −18.0000 −1.54349
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.00000 −0.335673
\(143\) −8.00000 −0.668994
\(144\) 3.00000 0.250000
\(145\) −2.00000 −0.166091
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 18.0000 1.45521
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 12.0000 0.954669
\(159\) 0 0
\(160\) −5.00000 −0.395285
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) −8.00000 −0.626608 −0.313304 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 6.00000 0.460179
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 0 0
\(178\) −10.0000 −0.749532
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 3.00000 0.223607
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 12.0000 0.884652
\(185\) −10.0000 −0.735215
\(186\) 0 0
\(187\) −24.0000 −1.75505
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 12.0000 0.852803
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 3.00000 0.212132
\(201\) 0 0
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) 0 0
\(205\) −6.00000 −0.419058
\(206\) 0 0
\(207\) −12.0000 −0.834058
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) 0 0
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) −4.00000 −0.269680
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) 14.0000 0.931266
\(227\) −8.00000 −0.530979 −0.265489 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −30.0000 −1.96537 −0.982683 0.185296i \(-0.940675\pi\)
−0.982683 + 0.185296i \(0.940675\pi\)
\(234\) −6.00000 −0.392232
\(235\) 8.00000 0.521862
\(236\) −8.00000 −0.520756
\(237\) 0 0
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) −7.00000 −0.447214
\(246\) 0 0
\(247\) 0 0
\(248\) 12.0000 0.762001
\(249\) 0 0
\(250\) −1.00000 −0.0632456
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 20.0000 1.25491
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 6.00000 0.371391
\(262\) 8.00000 0.494242
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) 28.0000 1.70088 0.850439 0.526073i \(-0.176336\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 4.00000 0.241209
\(276\) 0 0
\(277\) −26.0000 −1.56219 −0.781094 0.624413i \(-0.785338\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) −8.00000 −0.479808
\(279\) −12.0000 −0.718421
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 24.0000 1.42665 0.713326 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) −4.00000 −0.237356
\(285\) 0 0
\(286\) 8.00000 0.473050
\(287\) 0 0
\(288\) 15.0000 0.883883
\(289\) 19.0000 1.11765
\(290\) 2.00000 0.117444
\(291\) 0 0
\(292\) 6.00000 0.351123
\(293\) −10.0000 −0.584206 −0.292103 0.956387i \(-0.594355\pi\)
−0.292103 + 0.956387i \(0.594355\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) −30.0000 −1.74371
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) −8.00000 −0.462652
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10.0000 −0.572598
\(306\) −18.0000 −1.02899
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.00000 −0.227185
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) 18.0000 1.01580
\(315\) 0 0
\(316\) 12.0000 0.675053
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 7.00000 0.391312
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −9.00000 −0.500000
\(325\) −2.00000 −0.110940
\(326\) 8.00000 0.443079
\(327\) 0 0
\(328\) −18.0000 −0.993884
\(329\) 0 0
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 12.0000 0.658586
\(333\) 30.0000 1.64399
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) 6.00000 0.325396
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) 8.00000 0.429463 0.214731 0.976673i \(-0.431112\pi\)
0.214731 + 0.976673i \(0.431112\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −20.0000 −1.06600
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 4.00000 0.212298
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 4.00000 0.211112 0.105556 0.994413i \(-0.466338\pi\)
0.105556 + 0.994413i \(0.466338\pi\)
\(360\) −9.00000 −0.474342
\(361\) −19.0000 −1.00000
\(362\) −22.0000 −1.15629
\(363\) 0 0
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 20.0000 1.04399 0.521996 0.852948i \(-0.325188\pi\)
0.521996 + 0.852948i \(0.325188\pi\)
\(368\) −4.00000 −0.208514
\(369\) 18.0000 0.937043
\(370\) 10.0000 0.519875
\(371\) 0 0
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 24.0000 1.24101
\(375\) 0 0
\(376\) 24.0000 1.23771
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −12.0000 −0.613973
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) −12.0000 −0.609994
\(388\) 6.00000 0.304604
\(389\) 14.0000 0.709828 0.354914 0.934899i \(-0.384510\pi\)
0.354914 + 0.934899i \(0.384510\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) −21.0000 −1.06066
\(393\) 0 0
\(394\) −6.00000 −0.302276
\(395\) −12.0000 −0.603786
\(396\) 12.0000 0.603023
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −8.00000 −0.398508
\(404\) 18.0000 0.895533
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) −40.0000 −1.98273
\(408\) 0 0
\(409\) −6.00000 −0.296681 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) 6.00000 0.296319
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 12.0000 0.589768
\(415\) −12.0000 −0.589057
\(416\) 10.0000 0.490290
\(417\) 0 0
\(418\) 0 0
\(419\) 36.0000 1.75872 0.879358 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −8.00000 −0.389434
\(423\) −24.0000 −1.16692
\(424\) 18.0000 0.874157
\(425\) −6.00000 −0.291043
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) −4.00000 −0.192897
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 0 0
\(438\) 0 0
\(439\) 36.0000 1.71819 0.859093 0.511819i \(-0.171028\pi\)
0.859093 + 0.511819i \(0.171028\pi\)
\(440\) 12.0000 0.572078
\(441\) 21.0000 1.00000
\(442\) −12.0000 −0.570782
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 0 0
\(445\) 10.0000 0.474045
\(446\) 16.0000 0.757622
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 3.00000 0.141421
\(451\) −24.0000 −1.13012
\(452\) 14.0000 0.658505
\(453\) 0 0
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) −22.0000 −1.02799
\(459\) 0 0
\(460\) −4.00000 −0.186501
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) −12.0000 −0.557687 −0.278844 0.960337i \(-0.589951\pi\)
−0.278844 + 0.960337i \(0.589951\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) 30.0000 1.38972
\(467\) −32.0000 −1.48078 −0.740392 0.672176i \(-0.765360\pi\)
−0.740392 + 0.672176i \(0.765360\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) 0 0
\(472\) 24.0000 1.10469
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) 24.0000 1.09773
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) 20.0000 0.911922
\(482\) −2.00000 −0.0910975
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) −6.00000 −0.272446
\(486\) 0 0
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) −30.0000 −1.35804
\(489\) 0 0
\(490\) 7.00000 0.316228
\(491\) −4.00000 −0.180517 −0.0902587 0.995918i \(-0.528769\pi\)
−0.0902587 + 0.995918i \(0.528769\pi\)
\(492\) 0 0
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) −12.0000 −0.539360
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0 0
\(502\) 8.00000 0.357057
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) −16.0000 −0.711287
\(507\) 0 0
\(508\) 20.0000 0.887357
\(509\) −10.0000 −0.443242 −0.221621 0.975133i \(-0.571135\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) −18.0000 −0.793946
\(515\) 0 0
\(516\) 0 0
\(517\) 32.0000 1.40736
\(518\) 0 0
\(519\) 0 0
\(520\) −6.00000 −0.263117
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −6.00000 −0.262613
\(523\) 24.0000 1.04945 0.524723 0.851273i \(-0.324169\pi\)
0.524723 + 0.851273i \(0.324169\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) −24.0000 −1.04546
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −6.00000 −0.260623
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 10.0000 0.431131
\(539\) −28.0000 −1.20605
\(540\) 0 0
\(541\) 14.0000 0.601907 0.300954 0.953639i \(-0.402695\pi\)
0.300954 + 0.953639i \(0.402695\pi\)
\(542\) −28.0000 −1.20270
\(543\) 0 0
\(544\) 30.0000 1.28624
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 30.0000 1.28037
\(550\) −4.00000 −0.170561
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 26.0000 1.10463
\(555\) 0 0
\(556\) −8.00000 −0.339276
\(557\) 46.0000 1.94908 0.974541 0.224208i \(-0.0719796\pi\)
0.974541 + 0.224208i \(0.0719796\pi\)
\(558\) 12.0000 0.508001
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 28.0000 1.18006 0.590030 0.807382i \(-0.299116\pi\)
0.590030 + 0.807382i \(0.299116\pi\)
\(564\) 0 0
\(565\) −14.0000 −0.588984
\(566\) −24.0000 −1.00880
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) 42.0000 1.76073 0.880366 0.474295i \(-0.157297\pi\)
0.880366 + 0.474295i \(0.157297\pi\)
\(570\) 0 0
\(571\) −16.0000 −0.669579 −0.334790 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) 8.00000 0.334497
\(573\) 0 0
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) −21.0000 −0.875000
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −19.0000 −0.790296
\(579\) 0 0
\(580\) 2.00000 0.0830455
\(581\) 0 0
\(582\) 0 0
\(583\) 24.0000 0.993978
\(584\) −18.0000 −0.744845
\(585\) 6.00000 0.248069
\(586\) 10.0000 0.413096
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −8.00000 −0.329355
\(591\) 0 0
\(592\) 10.0000 0.410997
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) 8.00000 0.327144
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.00000 0.203279
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 10.0000 0.404888
\(611\) −16.0000 −0.647291
\(612\) −18.0000 −0.727607
\(613\) −10.0000 −0.403896 −0.201948 0.979396i \(-0.564727\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) −4.00000 −0.160644
\(621\) 0 0
\(622\) −8.00000 −0.320771
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −26.0000 −1.03917
\(627\) 0 0
\(628\) 18.0000 0.718278
\(629\) 60.0000 2.39236
\(630\) 0 0
\(631\) −28.0000 −1.11466 −0.557331 0.830290i \(-0.688175\pi\)
−0.557331 + 0.830290i \(0.688175\pi\)
\(632\) −36.0000 −1.43200
\(633\) 0 0
\(634\) 18.0000 0.714871
\(635\) −20.0000 −0.793676
\(636\) 0 0
\(637\) 14.0000 0.554700
\(638\) 8.00000 0.316723
\(639\) −12.0000 −0.474713
\(640\) 3.00000 0.118585
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 0 0
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 36.0000 1.41531 0.707653 0.706560i \(-0.249754\pi\)
0.707653 + 0.706560i \(0.249754\pi\)
\(648\) 27.0000 1.06066
\(649\) 32.0000 1.25611
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) 14.0000 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) 0 0
\(655\) −8.00000 −0.312586
\(656\) 6.00000 0.234261
\(657\) 18.0000 0.702247
\(658\) 0 0
\(659\) −8.00000 −0.311636 −0.155818 0.987786i \(-0.549801\pi\)
−0.155818 + 0.987786i \(0.549801\pi\)
\(660\) 0 0
\(661\) −2.00000 −0.0777910 −0.0388955 0.999243i \(-0.512384\pi\)
−0.0388955 + 0.999243i \(0.512384\pi\)
\(662\) −28.0000 −1.08825
\(663\) 0 0
\(664\) −36.0000 −1.39707
\(665\) 0 0
\(666\) −30.0000 −1.16248
\(667\) −8.00000 −0.309761
\(668\) 12.0000 0.464294
\(669\) 0 0
\(670\) 0 0
\(671\) −40.0000 −1.54418
\(672\) 0 0
\(673\) 42.0000 1.61898 0.809491 0.587133i \(-0.199743\pi\)
0.809491 + 0.587133i \(0.199743\pi\)
\(674\) −18.0000 −0.693334
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −18.0000 −0.690268
\(681\) 0 0
\(682\) −16.0000 −0.612672
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 0 0
\(685\) 2.00000 0.0764161
\(686\) 0 0
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) −8.00000 −0.303676
\(695\) 8.00000 0.303457
\(696\) 0 0
\(697\) 36.0000 1.36360
\(698\) 10.0000 0.378506
\(699\) 0 0
\(700\) 0 0
\(701\) 38.0000 1.43524 0.717620 0.696435i \(-0.245231\pi\)
0.717620 + 0.696435i \(0.245231\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 28.0000 1.05529
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) −42.0000 −1.57734 −0.788672 0.614815i \(-0.789231\pi\)
−0.788672 + 0.614815i \(0.789231\pi\)
\(710\) −4.00000 −0.150117
\(711\) 36.0000 1.35011
\(712\) 30.0000 1.12430
\(713\) 16.0000 0.599205
\(714\) 0 0
\(715\) −8.00000 −0.299183
\(716\) 12.0000 0.448461
\(717\) 0 0
\(718\) −4.00000 −0.149279
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 3.00000 0.111803
\(721\) 0 0
\(722\) 19.0000 0.707107
\(723\) 0 0
\(724\) −22.0000 −0.817624
\(725\) −2.00000 −0.0742781
\(726\) 0 0
\(727\) −20.0000 −0.741759 −0.370879 0.928681i \(-0.620944\pi\)
−0.370879 + 0.928681i \(0.620944\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 6.00000 0.222070
\(731\) −24.0000 −0.887672
\(732\) 0 0
\(733\) −2.00000 −0.0738717 −0.0369358 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) −20.0000 −0.738213
\(735\) 0 0
\(736\) −20.0000 −0.737210
\(737\) 0 0
\(738\) −18.0000 −0.662589
\(739\) −12.0000 −0.441427 −0.220714 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 10.0000 0.367607
\(741\) 0 0
\(742\) 0 0
\(743\) −44.0000 −1.61420 −0.807102 0.590412i \(-0.798965\pi\)
−0.807102 + 0.590412i \(0.798965\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) 10.0000 0.366126
\(747\) 36.0000 1.31717
\(748\) 24.0000 0.877527
\(749\) 0 0
\(750\) 0 0
\(751\) 48.0000 1.75154 0.875772 0.482724i \(-0.160353\pi\)
0.875772 + 0.482724i \(0.160353\pi\)
\(752\) −8.00000 −0.291730
\(753\) 0 0
\(754\) −4.00000 −0.145671
\(755\) 0 0
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) −28.0000 −1.01701
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) 18.0000 0.650791
\(766\) 16.0000 0.578103
\(767\) −16.0000 −0.577727
\(768\) 0 0
\(769\) −46.0000 −1.65880 −0.829401 0.558653i \(-0.811318\pi\)
−0.829401 + 0.558653i \(0.811318\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000 0.215945
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 12.0000 0.431331
\(775\) 4.00000 0.143684
\(776\) −18.0000 −0.646162
\(777\) 0 0
\(778\) −14.0000 −0.501924
\(779\) 0 0
\(780\) 0 0
\(781\) 16.0000 0.572525
\(782\) 24.0000 0.858238
\(783\) 0 0
\(784\) 7.00000 0.250000
\(785\) −18.0000 −0.642448
\(786\) 0 0
\(787\) 16.0000 0.570338 0.285169 0.958477i \(-0.407950\pi\)
0.285169 + 0.958477i \(0.407950\pi\)
\(788\) −6.00000 −0.213741
\(789\) 0 0
\(790\) 12.0000 0.426941
\(791\) 0 0
\(792\) −36.0000 −1.27920
\(793\) 20.0000 0.710221
\(794\) −14.0000 −0.496841
\(795\) 0 0
\(796\) 4.00000 0.141776
\(797\) −34.0000 −1.20434 −0.602171 0.798367i \(-0.705697\pi\)
−0.602171 + 0.798367i \(0.705697\pi\)
\(798\) 0 0
\(799\) −48.0000 −1.69812
\(800\) −5.00000 −0.176777
\(801\) −30.0000 −1.06000
\(802\) −1.00000 −0.0353112
\(803\) −24.0000 −0.846942
\(804\) 0 0
\(805\) 0 0
\(806\) 8.00000 0.281788
\(807\) 0 0
\(808\) −54.0000 −1.89971
\(809\) −22.0000 −0.773479 −0.386739 0.922189i \(-0.626399\pi\)
−0.386739 + 0.922189i \(0.626399\pi\)
\(810\) −9.00000 −0.316228
\(811\) 52.0000 1.82597 0.912983 0.407997i \(-0.133772\pi\)
0.912983 + 0.407997i \(0.133772\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 40.0000 1.40200
\(815\) −8.00000 −0.280228
\(816\) 0 0
\(817\) 0 0
\(818\) 6.00000 0.209785
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) 0 0
\(823\) −44.0000 −1.53374 −0.766872 0.641800i \(-0.778188\pi\)
−0.766872 + 0.641800i \(0.778188\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −52.0000 −1.80822 −0.904109 0.427303i \(-0.859464\pi\)
−0.904109 + 0.427303i \(0.859464\pi\)
\(828\) 12.0000 0.417029
\(829\) 6.00000 0.208389 0.104194 0.994557i \(-0.466774\pi\)
0.104194 + 0.994557i \(0.466774\pi\)
\(830\) 12.0000 0.416526
\(831\) 0 0
\(832\) −14.0000 −0.485363
\(833\) 42.0000 1.45521
\(834\) 0 0
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) 0 0
\(838\) −36.0000 −1.24360
\(839\) −12.0000 −0.414286 −0.207143 0.978311i \(-0.566417\pi\)
−0.207143 + 0.978311i \(0.566417\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −22.0000 −0.758170
\(843\) 0 0
\(844\) −8.00000 −0.275371
\(845\) −9.00000 −0.309609
\(846\) 24.0000 0.825137
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) 0 0
\(850\) 6.00000 0.205798
\(851\) −40.0000 −1.37118
\(852\) 0 0
\(853\) −10.0000 −0.342393 −0.171197 0.985237i \(-0.554763\pi\)
−0.171197 + 0.985237i \(0.554763\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −22.0000 −0.751506 −0.375753 0.926720i \(-0.622616\pi\)
−0.375753 + 0.926720i \(0.622616\pi\)
\(858\) 0 0
\(859\) 28.0000 0.955348 0.477674 0.878537i \(-0.341480\pi\)
0.477674 + 0.878537i \(0.341480\pi\)
\(860\) −4.00000 −0.136399
\(861\) 0 0
\(862\) 12.0000 0.408722
\(863\) −20.0000 −0.680808 −0.340404 0.940279i \(-0.610564\pi\)
−0.340404 + 0.940279i \(0.610564\pi\)
\(864\) 0 0
\(865\) −18.0000 −0.612018
\(866\) −2.00000 −0.0679628
\(867\) 0 0
\(868\) 0 0
\(869\) −48.0000 −1.62829
\(870\) 0 0
\(871\) 0 0
\(872\) −6.00000 −0.203186
\(873\) 18.0000 0.609208
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.00000 −0.0675352 −0.0337676 0.999430i \(-0.510751\pi\)
−0.0337676 + 0.999430i \(0.510751\pi\)
\(878\) −36.0000 −1.21494
\(879\) 0 0
\(880\) −4.00000 −0.134840
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) −21.0000 −0.707107
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) −12.0000 −0.403604
\(885\) 0 0
\(886\) −24.0000 −0.806296
\(887\) 36.0000 1.20876 0.604381 0.796696i \(-0.293421\pi\)
0.604381 + 0.796696i \(0.293421\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −10.0000 −0.335201
\(891\) 36.0000 1.20605
\(892\) 16.0000 0.535720
\(893\) 0 0
\(894\) 0 0
\(895\) −12.0000 −0.401116
\(896\) 0 0
\(897\) 0 0
\(898\) 30.0000 1.00111
\(899\) −8.00000 −0.266815
\(900\) 3.00000 0.100000
\(901\) −36.0000 −1.19933
\(902\) 24.0000 0.799113
\(903\) 0 0
\(904\) −42.0000 −1.39690
\(905\) 22.0000 0.731305
\(906\) 0 0
\(907\) 32.0000 1.06254 0.531271 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) 8.00000 0.265489
\(909\) 54.0000 1.79107
\(910\) 0 0
\(911\) 8.00000 0.265052 0.132526 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) 0 0
\(913\) −48.0000 −1.58857
\(914\) 22.0000 0.727695
\(915\) 0 0
\(916\) −22.0000 −0.726900
\(917\) 0 0
\(918\) 0 0
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 12.0000 0.395628
\(921\) 0 0
\(922\) −6.00000 −0.197599
\(923\) −8.00000 −0.263323
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) 12.0000 0.394344
\(927\) 0 0
\(928\) 10.0000 0.328266
\(929\) 2.00000 0.0656179 0.0328089 0.999462i \(-0.489555\pi\)
0.0328089 + 0.999462i \(0.489555\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 30.0000 0.982683
\(933\) 0 0
\(934\) 32.0000 1.04707
\(935\) −24.0000 −0.784884
\(936\) 18.0000 0.588348
\(937\) −14.0000 −0.457360 −0.228680 0.973502i \(-0.573441\pi\)
−0.228680 + 0.973502i \(0.573441\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −8.00000 −0.260931
\(941\) −42.0000 −1.36916 −0.684580 0.728937i \(-0.740015\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(942\) 0 0
\(943\) −24.0000 −0.781548
\(944\) −8.00000 −0.260378
\(945\) 0 0
\(946\) −16.0000 −0.520205
\(947\) 20.0000 0.649913 0.324956 0.945729i \(-0.394650\pi\)
0.324956 + 0.945729i \(0.394650\pi\)
\(948\) 0 0
\(949\) 12.0000 0.389536
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −22.0000 −0.712650 −0.356325 0.934362i \(-0.615970\pi\)
−0.356325 + 0.934362i \(0.615970\pi\)
\(954\) 18.0000 0.582772
\(955\) 12.0000 0.388311
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) 0 0
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −20.0000 −0.644826
\(963\) 0 0
\(964\) −2.00000 −0.0644157
\(965\) −6.00000 −0.193147
\(966\) 0 0
\(967\) −44.0000 −1.41494 −0.707472 0.706741i \(-0.750165\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(968\) 15.0000 0.482118
\(969\) 0 0
\(970\) 6.00000 0.192648
\(971\) −28.0000 −0.898563 −0.449281 0.893390i \(-0.648320\pi\)
−0.449281 + 0.893390i \(0.648320\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −8.00000 −0.256337
\(975\) 0 0
\(976\) 10.0000 0.320092
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 0 0
\(979\) 40.0000 1.27841
\(980\) 7.00000 0.223607
\(981\) 6.00000 0.191565
\(982\) 4.00000 0.127645
\(983\) 48.0000 1.53096 0.765481 0.643458i \(-0.222501\pi\)
0.765481 + 0.643458i \(0.222501\pi\)
\(984\) 0 0
\(985\) 6.00000 0.191176
\(986\) −12.0000 −0.382158
\(987\) 0 0
\(988\) 0 0
\(989\) 16.0000 0.508770
\(990\) 12.0000 0.381385
\(991\) −36.0000 −1.14358 −0.571789 0.820401i \(-0.693750\pi\)
−0.571789 + 0.820401i \(0.693750\pi\)
\(992\) −20.0000 −0.635001
\(993\) 0 0
\(994\) 0 0
\(995\) −4.00000 −0.126809
\(996\) 0 0
\(997\) −58.0000 −1.83688 −0.918439 0.395562i \(-0.870550\pi\)
−0.918439 + 0.395562i \(0.870550\pi\)
\(998\) 20.0000 0.633089
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))