Properties

Label 4018.2.a.r.1.1
Level 4018
Weight 2
Character 4018.1
Self dual Yes
Analytic conductor 32.084
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0838915322\)
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 \(\chi\) = 4018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+2.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.00000 q^{5}\) \(+2.00000 q^{6}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+2.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.00000 q^{5}\) \(+2.00000 q^{6}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-2.00000 q^{10}\) \(-4.00000 q^{11}\) \(+2.00000 q^{12}\) \(+1.00000 q^{13}\) \(-4.00000 q^{15}\) \(+1.00000 q^{16}\) \(+1.00000 q^{18}\) \(-6.00000 q^{19}\) \(-2.00000 q^{20}\) \(-4.00000 q^{22}\) \(-2.00000 q^{23}\) \(+2.00000 q^{24}\) \(-1.00000 q^{25}\) \(+1.00000 q^{26}\) \(-4.00000 q^{27}\) \(-5.00000 q^{29}\) \(-4.00000 q^{30}\) \(+4.00000 q^{31}\) \(+1.00000 q^{32}\) \(-8.00000 q^{33}\) \(+1.00000 q^{36}\) \(-2.00000 q^{37}\) \(-6.00000 q^{38}\) \(+2.00000 q^{39}\) \(-2.00000 q^{40}\) \(+1.00000 q^{41}\) \(-1.00000 q^{43}\) \(-4.00000 q^{44}\) \(-2.00000 q^{45}\) \(-2.00000 q^{46}\) \(-8.00000 q^{47}\) \(+2.00000 q^{48}\) \(-1.00000 q^{50}\) \(+1.00000 q^{52}\) \(-10.0000 q^{53}\) \(-4.00000 q^{54}\) \(+8.00000 q^{55}\) \(-12.0000 q^{57}\) \(-5.00000 q^{58}\) \(+1.00000 q^{59}\) \(-4.00000 q^{60}\) \(+14.0000 q^{61}\) \(+4.00000 q^{62}\) \(+1.00000 q^{64}\) \(-2.00000 q^{65}\) \(-8.00000 q^{66}\) \(+10.0000 q^{67}\) \(-4.00000 q^{69}\) \(-15.0000 q^{71}\) \(+1.00000 q^{72}\) \(+7.00000 q^{73}\) \(-2.00000 q^{74}\) \(-2.00000 q^{75}\) \(-6.00000 q^{76}\) \(+2.00000 q^{78}\) \(-2.00000 q^{80}\) \(-11.0000 q^{81}\) \(+1.00000 q^{82}\) \(+9.00000 q^{83}\) \(-1.00000 q^{86}\) \(-10.0000 q^{87}\) \(-4.00000 q^{88}\) \(-2.00000 q^{90}\) \(-2.00000 q^{92}\) \(+8.00000 q^{93}\) \(-8.00000 q^{94}\) \(+12.0000 q^{95}\) \(+2.00000 q^{96}\) \(-4.00000 q^{97}\) \(-4.00000 q^{99}\) \(+O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 2.00000 0.577350
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.00000 0.235702
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 2.00000 0.408248
\(25\) −1.00000 −0.200000
\(26\) 1.00000 0.196116
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) −4.00000 −0.730297
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) −8.00000 −1.39262
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −6.00000 −0.973329
\(39\) 2.00000 0.320256
\(40\) −2.00000 −0.316228
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) −4.00000 −0.603023
\(45\) −2.00000 −0.298142
\(46\) −2.00000 −0.294884
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 2.00000 0.288675
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 1.00000 0.138675
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) −4.00000 −0.544331
\(55\) 8.00000 1.07872
\(56\) 0 0
\(57\) −12.0000 −1.58944
\(58\) −5.00000 −0.656532
\(59\) 1.00000 0.130189 0.0650945 0.997879i \(-0.479265\pi\)
0.0650945 + 0.997879i \(0.479265\pi\)
\(60\) −4.00000 −0.516398
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) −8.00000 −0.984732
\(67\) 10.0000 1.22169 0.610847 0.791748i \(-0.290829\pi\)
0.610847 + 0.791748i \(0.290829\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 1.00000 0.117851
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) −2.00000 −0.232495
\(75\) −2.00000 −0.230940
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −2.00000 −0.223607
\(81\) −11.0000 −1.22222
\(82\) 1.00000 0.110432
\(83\) 9.00000 0.987878 0.493939 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.00000 −0.107833
\(87\) −10.0000 −1.07211
\(88\) −4.00000 −0.426401
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −2.00000 −0.210819
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) 8.00000 0.829561
\(94\) −8.00000 −0.825137
\(95\) 12.0000 1.23117
\(96\) 2.00000 0.204124
\(97\) −4.00000 −0.406138 −0.203069 0.979164i \(-0.565092\pi\)
−0.203069 + 0.979164i \(0.565092\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) −1.00000 −0.100000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) 13.0000 1.25676 0.628379 0.777908i \(-0.283719\pi\)
0.628379 + 0.777908i \(0.283719\pi\)
\(108\) −4.00000 −0.384900
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 8.00000 0.762770
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) −3.00000 −0.282216 −0.141108 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) −12.0000 −1.12390
\(115\) 4.00000 0.373002
\(116\) −5.00000 −0.464238
\(117\) 1.00000 0.0924500
\(118\) 1.00000 0.0920575
\(119\) 0 0
\(120\) −4.00000 −0.365148
\(121\) 5.00000 0.454545
\(122\) 14.0000 1.26750
\(123\) 2.00000 0.180334
\(124\) 4.00000 0.359211
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.00000 −0.176090
\(130\) −2.00000 −0.175412
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −8.00000 −0.696311
\(133\) 0 0
\(134\) 10.0000 0.863868
\(135\) 8.00000 0.688530
\(136\) 0 0
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −4.00000 −0.340503
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −16.0000 −1.34744
\(142\) −15.0000 −1.25877
\(143\) −4.00000 −0.334497
\(144\) 1.00000 0.0833333
\(145\) 10.0000 0.830455
\(146\) 7.00000 0.579324
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) 1.00000 0.0819232 0.0409616 0.999161i \(-0.486958\pi\)
0.0409616 + 0.999161i \(0.486958\pi\)
\(150\) −2.00000 −0.163299
\(151\) 19.0000 1.54620 0.773099 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) −6.00000 −0.486664
\(153\) 0 0
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 2.00000 0.160128
\(157\) −15.0000 −1.19713 −0.598565 0.801074i \(-0.704262\pi\)
−0.598565 + 0.801074i \(0.704262\pi\)
\(158\) 0 0
\(159\) −20.0000 −1.58610
\(160\) −2.00000 −0.158114
\(161\) 0 0
\(162\) −11.0000 −0.864242
\(163\) −23.0000 −1.80150 −0.900750 0.434339i \(-0.856982\pi\)
−0.900750 + 0.434339i \(0.856982\pi\)
\(164\) 1.00000 0.0780869
\(165\) 16.0000 1.24560
\(166\) 9.00000 0.698535
\(167\) 5.00000 0.386912 0.193456 0.981109i \(-0.438030\pi\)
0.193456 + 0.981109i \(0.438030\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −6.00000 −0.458831
\(172\) −1.00000 −0.0762493
\(173\) 24.0000 1.82469 0.912343 0.409426i \(-0.134271\pi\)
0.912343 + 0.409426i \(0.134271\pi\)
\(174\) −10.0000 −0.758098
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 2.00000 0.150329
\(178\) 0 0
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) −2.00000 −0.149071
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 28.0000 2.06982
\(184\) −2.00000 −0.147442
\(185\) 4.00000 0.294086
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) 5.00000 0.361787 0.180894 0.983503i \(-0.442101\pi\)
0.180894 + 0.983503i \(0.442101\pi\)
\(192\) 2.00000 0.144338
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −4.00000 −0.287183
\(195\) −4.00000 −0.286446
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) −4.00000 −0.284268
\(199\) −3.00000 −0.212664 −0.106332 0.994331i \(-0.533911\pi\)
−0.106332 + 0.994331i \(0.533911\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 20.0000 1.41069
\(202\) −10.0000 −0.703598
\(203\) 0 0
\(204\) 0 0
\(205\) −2.00000 −0.139686
\(206\) −10.0000 −0.696733
\(207\) −2.00000 −0.139010
\(208\) 1.00000 0.0693375
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) −10.0000 −0.686803
\(213\) −30.0000 −2.05557
\(214\) 13.0000 0.888662
\(215\) 2.00000 0.136399
\(216\) −4.00000 −0.272166
\(217\) 0 0
\(218\) −7.00000 −0.474100
\(219\) 14.0000 0.946032
\(220\) 8.00000 0.539360
\(221\) 0 0
\(222\) −4.00000 −0.268462
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) −3.00000 −0.199557
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) −12.0000 −0.794719
\(229\) −21.0000 −1.38772 −0.693860 0.720110i \(-0.744091\pi\)
−0.693860 + 0.720110i \(0.744091\pi\)
\(230\) 4.00000 0.263752
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) −16.0000 −1.04819 −0.524097 0.851658i \(-0.675597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 1.00000 0.0653720
\(235\) 16.0000 1.04372
\(236\) 1.00000 0.0650945
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) −4.00000 −0.258199
\(241\) −5.00000 −0.322078 −0.161039 0.986948i \(-0.551485\pi\)
−0.161039 + 0.986948i \(0.551485\pi\)
\(242\) 5.00000 0.321412
\(243\) −10.0000 −0.641500
\(244\) 14.0000 0.896258
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) −6.00000 −0.381771
\(248\) 4.00000 0.254000
\(249\) 18.0000 1.14070
\(250\) 12.0000 0.758947
\(251\) −9.00000 −0.568075 −0.284037 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 4.00000 0.250982
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) −2.00000 −0.124515
\(259\) 0 0
\(260\) −2.00000 −0.124035
\(261\) −5.00000 −0.309492
\(262\) 12.0000 0.741362
\(263\) −31.0000 −1.91154 −0.955771 0.294112i \(-0.904976\pi\)
−0.955771 + 0.294112i \(0.904976\pi\)
\(264\) −8.00000 −0.492366
\(265\) 20.0000 1.22859
\(266\) 0 0
\(267\) 0 0
\(268\) 10.0000 0.610847
\(269\) 16.0000 0.975537 0.487769 0.872973i \(-0.337811\pi\)
0.487769 + 0.872973i \(0.337811\pi\)
\(270\) 8.00000 0.486864
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 4.00000 0.241209
\(276\) −4.00000 −0.240772
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 4.00000 0.239904
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 14.0000 0.835170 0.417585 0.908638i \(-0.362877\pi\)
0.417585 + 0.908638i \(0.362877\pi\)
\(282\) −16.0000 −0.952786
\(283\) −1.00000 −0.0594438 −0.0297219 0.999558i \(-0.509462\pi\)
−0.0297219 + 0.999558i \(0.509462\pi\)
\(284\) −15.0000 −0.890086
\(285\) 24.0000 1.42164
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) −17.0000 −1.00000
\(290\) 10.0000 0.587220
\(291\) −8.00000 −0.468968
\(292\) 7.00000 0.409644
\(293\) 3.00000 0.175262 0.0876309 0.996153i \(-0.472070\pi\)
0.0876309 + 0.996153i \(0.472070\pi\)
\(294\) 0 0
\(295\) −2.00000 −0.116445
\(296\) −2.00000 −0.116248
\(297\) 16.0000 0.928414
\(298\) 1.00000 0.0579284
\(299\) −2.00000 −0.115663
\(300\) −2.00000 −0.115470
\(301\) 0 0
\(302\) 19.0000 1.09333
\(303\) −20.0000 −1.14897
\(304\) −6.00000 −0.344124
\(305\) −28.0000 −1.60328
\(306\) 0 0
\(307\) 9.00000 0.513657 0.256829 0.966457i \(-0.417322\pi\)
0.256829 + 0.966457i \(0.417322\pi\)
\(308\) 0 0
\(309\) −20.0000 −1.13776
\(310\) −8.00000 −0.454369
\(311\) 13.0000 0.737162 0.368581 0.929596i \(-0.379844\pi\)
0.368581 + 0.929596i \(0.379844\pi\)
\(312\) 2.00000 0.113228
\(313\) 16.0000 0.904373 0.452187 0.891923i \(-0.350644\pi\)
0.452187 + 0.891923i \(0.350644\pi\)
\(314\) −15.0000 −0.846499
\(315\) 0 0
\(316\) 0 0
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) −20.0000 −1.12154
\(319\) 20.0000 1.11979
\(320\) −2.00000 −0.111803
\(321\) 26.0000 1.45118
\(322\) 0 0
\(323\) 0 0
\(324\) −11.0000 −0.611111
\(325\) −1.00000 −0.0554700
\(326\) −23.0000 −1.27385
\(327\) −14.0000 −0.774202
\(328\) 1.00000 0.0552158
\(329\) 0 0
\(330\) 16.0000 0.880771
\(331\) 12.0000 0.659580 0.329790 0.944054i \(-0.393022\pi\)
0.329790 + 0.944054i \(0.393022\pi\)
\(332\) 9.00000 0.493939
\(333\) −2.00000 −0.109599
\(334\) 5.00000 0.273588
\(335\) −20.0000 −1.09272
\(336\) 0 0
\(337\) 31.0000 1.68868 0.844339 0.535810i \(-0.179994\pi\)
0.844339 + 0.535810i \(0.179994\pi\)
\(338\) −12.0000 −0.652714
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) −16.0000 −0.866449
\(342\) −6.00000 −0.324443
\(343\) 0 0
\(344\) −1.00000 −0.0539164
\(345\) 8.00000 0.430706
\(346\) 24.0000 1.29025
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) −10.0000 −0.536056
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) −4.00000 −0.213201
\(353\) 21.0000 1.11772 0.558859 0.829263i \(-0.311239\pi\)
0.558859 + 0.829263i \(0.311239\pi\)
\(354\) 2.00000 0.106299
\(355\) 30.0000 1.59223
\(356\) 0 0
\(357\) 0 0
\(358\) −10.0000 −0.528516
\(359\) 14.0000 0.738892 0.369446 0.929252i \(-0.379548\pi\)
0.369446 + 0.929252i \(0.379548\pi\)
\(360\) −2.00000 −0.105409
\(361\) 17.0000 0.894737
\(362\) 2.00000 0.105118
\(363\) 10.0000 0.524864
\(364\) 0 0
\(365\) −14.0000 −0.732793
\(366\) 28.0000 1.46358
\(367\) −18.0000 −0.939592 −0.469796 0.882775i \(-0.655673\pi\)
−0.469796 + 0.882775i \(0.655673\pi\)
\(368\) −2.00000 −0.104257
\(369\) 1.00000 0.0520579
\(370\) 4.00000 0.207950
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) 16.0000 0.828449 0.414224 0.910175i \(-0.364053\pi\)
0.414224 + 0.910175i \(0.364053\pi\)
\(374\) 0 0
\(375\) 24.0000 1.23935
\(376\) −8.00000 −0.412568
\(377\) −5.00000 −0.257513
\(378\) 0 0
\(379\) −29.0000 −1.48963 −0.744815 0.667271i \(-0.767462\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) 12.0000 0.615587
\(381\) 8.00000 0.409852
\(382\) 5.00000 0.255822
\(383\) −15.0000 −0.766464 −0.383232 0.923652i \(-0.625189\pi\)
−0.383232 + 0.923652i \(0.625189\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) −1.00000 −0.0508329
\(388\) −4.00000 −0.203069
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) −4.00000 −0.202548
\(391\) 0 0
\(392\) 0 0
\(393\) 24.0000 1.21064
\(394\) −2.00000 −0.100759
\(395\) 0 0
\(396\) −4.00000 −0.201008
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) −3.00000 −0.150376
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 25.0000 1.24844 0.624220 0.781248i \(-0.285417\pi\)
0.624220 + 0.781248i \(0.285417\pi\)
\(402\) 20.0000 0.997509
\(403\) 4.00000 0.199254
\(404\) −10.0000 −0.497519
\(405\) 22.0000 1.09319
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) 35.0000 1.73064 0.865319 0.501221i \(-0.167116\pi\)
0.865319 + 0.501221i \(0.167116\pi\)
\(410\) −2.00000 −0.0987730
\(411\) −36.0000 −1.77575
\(412\) −10.0000 −0.492665
\(413\) 0 0
\(414\) −2.00000 −0.0982946
\(415\) −18.0000 −0.883585
\(416\) 1.00000 0.0490290
\(417\) 8.00000 0.391762
\(418\) 24.0000 1.17388
\(419\) −33.0000 −1.61216 −0.806078 0.591810i \(-0.798414\pi\)
−0.806078 + 0.591810i \(0.798414\pi\)
\(420\) 0 0
\(421\) −30.0000 −1.46211 −0.731055 0.682318i \(-0.760972\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) 0 0
\(423\) −8.00000 −0.388973
\(424\) −10.0000 −0.485643
\(425\) 0 0
\(426\) −30.0000 −1.45350
\(427\) 0 0
\(428\) 13.0000 0.628379
\(429\) −8.00000 −0.386244
\(430\) 2.00000 0.0964486
\(431\) 26.0000 1.25238 0.626188 0.779672i \(-0.284614\pi\)
0.626188 + 0.779672i \(0.284614\pi\)
\(432\) −4.00000 −0.192450
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 20.0000 0.958927
\(436\) −7.00000 −0.335239
\(437\) 12.0000 0.574038
\(438\) 14.0000 0.668946
\(439\) −7.00000 −0.334092 −0.167046 0.985949i \(-0.553423\pi\)
−0.167046 + 0.985949i \(0.553423\pi\)
\(440\) 8.00000 0.381385
\(441\) 0 0
\(442\) 0 0
\(443\) −15.0000 −0.712672 −0.356336 0.934358i \(-0.615974\pi\)
−0.356336 + 0.934358i \(0.615974\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) 26.0000 1.23114
\(447\) 2.00000 0.0945968
\(448\) 0 0
\(449\) 11.0000 0.519122 0.259561 0.965727i \(-0.416422\pi\)
0.259561 + 0.965727i \(0.416422\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −4.00000 −0.188353
\(452\) −3.00000 −0.141108
\(453\) 38.0000 1.78540
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) −12.0000 −0.561951
\(457\) 26.0000 1.21623 0.608114 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) −21.0000 −0.981266
\(459\) 0 0
\(460\) 4.00000 0.186501
\(461\) −20.0000 −0.931493 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) 0 0
\(463\) −7.00000 −0.325318 −0.162659 0.986682i \(-0.552007\pi\)
−0.162659 + 0.986682i \(0.552007\pi\)
\(464\) −5.00000 −0.232119
\(465\) −16.0000 −0.741982
\(466\) −16.0000 −0.741186
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 1.00000 0.0462250
\(469\) 0 0
\(470\) 16.0000 0.738025
\(471\) −30.0000 −1.38233
\(472\) 1.00000 0.0460287
\(473\) 4.00000 0.183920
\(474\) 0 0
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) 16.0000 0.731823
\(479\) −7.00000 −0.319838 −0.159919 0.987130i \(-0.551123\pi\)
−0.159919 + 0.987130i \(0.551123\pi\)
\(480\) −4.00000 −0.182574
\(481\) −2.00000 −0.0911922
\(482\) −5.00000 −0.227744
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 8.00000 0.363261
\(486\) −10.0000 −0.453609
\(487\) 22.0000 0.996915 0.498458 0.866914i \(-0.333900\pi\)
0.498458 + 0.866914i \(0.333900\pi\)
\(488\) 14.0000 0.633750
\(489\) −46.0000 −2.08019
\(490\) 0 0
\(491\) −13.0000 −0.586682 −0.293341 0.956008i \(-0.594767\pi\)
−0.293341 + 0.956008i \(0.594767\pi\)
\(492\) 2.00000 0.0901670
\(493\) 0 0
\(494\) −6.00000 −0.269953
\(495\) 8.00000 0.359573
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 18.0000 0.806599
\(499\) 36.0000 1.61158 0.805791 0.592200i \(-0.201741\pi\)
0.805791 + 0.592200i \(0.201741\pi\)
\(500\) 12.0000 0.536656
\(501\) 10.0000 0.446767
\(502\) −9.00000 −0.401690
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 0 0
\(505\) 20.0000 0.889988
\(506\) 8.00000 0.355643
\(507\) −24.0000 −1.06588
\(508\) 4.00000 0.177471
\(509\) 19.0000 0.842160 0.421080 0.907023i \(-0.361651\pi\)
0.421080 + 0.907023i \(0.361651\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 24.0000 1.05963
\(514\) −2.00000 −0.0882162
\(515\) 20.0000 0.881305
\(516\) −2.00000 −0.0880451
\(517\) 32.0000 1.40736
\(518\) 0 0
\(519\) 48.0000 2.10697
\(520\) −2.00000 −0.0877058
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) −5.00000 −0.218844
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −31.0000 −1.35166
\(527\) 0 0
\(528\) −8.00000 −0.348155
\(529\) −19.0000 −0.826087
\(530\) 20.0000 0.868744
\(531\) 1.00000 0.0433963
\(532\) 0 0
\(533\) 1.00000 0.0433148
\(534\) 0 0
\(535\) −26.0000 −1.12408
\(536\) 10.0000 0.431934
\(537\) −20.0000 −0.863064
\(538\) 16.0000 0.689809
\(539\) 0 0
\(540\) 8.00000 0.344265
\(541\) 8.00000 0.343947 0.171973 0.985102i \(-0.444986\pi\)
0.171973 + 0.985102i \(0.444986\pi\)
\(542\) 20.0000 0.859074
\(543\) 4.00000 0.171656
\(544\) 0 0
\(545\) 14.0000 0.599694
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) −18.0000 −0.768922
\(549\) 14.0000 0.597505
\(550\) 4.00000 0.170561
\(551\) 30.0000 1.27804
\(552\) −4.00000 −0.170251
\(553\) 0 0
\(554\) 8.00000 0.339887
\(555\) 8.00000 0.339581
\(556\) 4.00000 0.169638
\(557\) 27.0000 1.14403 0.572013 0.820244i \(-0.306163\pi\)
0.572013 + 0.820244i \(0.306163\pi\)
\(558\) 4.00000 0.169334
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) 0 0
\(562\) 14.0000 0.590554
\(563\) 16.0000 0.674320 0.337160 0.941447i \(-0.390534\pi\)
0.337160 + 0.941447i \(0.390534\pi\)
\(564\) −16.0000 −0.673722
\(565\) 6.00000 0.252422
\(566\) −1.00000 −0.0420331
\(567\) 0 0
\(568\) −15.0000 −0.629386
\(569\) −3.00000 −0.125767 −0.0628833 0.998021i \(-0.520030\pi\)
−0.0628833 + 0.998021i \(0.520030\pi\)
\(570\) 24.0000 1.00525
\(571\) −42.0000 −1.75765 −0.878823 0.477149i \(-0.841670\pi\)
−0.878823 + 0.477149i \(0.841670\pi\)
\(572\) −4.00000 −0.167248
\(573\) 10.0000 0.417756
\(574\) 0 0
\(575\) 2.00000 0.0834058
\(576\) 1.00000 0.0416667
\(577\) 6.00000 0.249783 0.124892 0.992170i \(-0.460142\pi\)
0.124892 + 0.992170i \(0.460142\pi\)
\(578\) −17.0000 −0.707107
\(579\) −20.0000 −0.831172
\(580\) 10.0000 0.415227
\(581\) 0 0
\(582\) −8.00000 −0.331611
\(583\) 40.0000 1.65663
\(584\) 7.00000 0.289662
\(585\) −2.00000 −0.0826898
\(586\) 3.00000 0.123929
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) −24.0000 −0.988903
\(590\) −2.00000 −0.0823387
\(591\) −4.00000 −0.164538
\(592\) −2.00000 −0.0821995
\(593\) −38.0000 −1.56047 −0.780236 0.625485i \(-0.784901\pi\)
−0.780236 + 0.625485i \(0.784901\pi\)
\(594\) 16.0000 0.656488
\(595\) 0 0
\(596\) 1.00000 0.0409616
\(597\) −6.00000 −0.245564
\(598\) −2.00000 −0.0817861
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −2.00000 −0.0816497
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) 10.0000 0.407231
\(604\) 19.0000 0.773099
\(605\) −10.0000 −0.406558
\(606\) −20.0000 −0.812444
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −6.00000 −0.243332
\(609\) 0 0
\(610\) −28.0000 −1.13369
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 9.00000 0.363210
\(615\) −4.00000 −0.161296
\(616\) 0 0
\(617\) −3.00000 −0.120775 −0.0603877 0.998175i \(-0.519234\pi\)
−0.0603877 + 0.998175i \(0.519234\pi\)
\(618\) −20.0000 −0.804518
\(619\) −29.0000 −1.16561 −0.582804 0.812613i \(-0.698045\pi\)
−0.582804 + 0.812613i \(0.698045\pi\)
\(620\) −8.00000 −0.321288
\(621\) 8.00000 0.321029
\(622\) 13.0000 0.521253
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) −19.0000 −0.760000
\(626\) 16.0000 0.639489
\(627\) 48.0000 1.91694
\(628\) −15.0000 −0.598565
\(629\) 0 0
\(630\) 0 0
\(631\) 30.0000 1.19428 0.597141 0.802137i \(-0.296303\pi\)
0.597141 + 0.802137i \(0.296303\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −2.00000 −0.0794301
\(635\) −8.00000 −0.317470
\(636\) −20.0000 −0.793052
\(637\) 0 0
\(638\) 20.0000 0.791808
\(639\) −15.0000 −0.593391
\(640\) −2.00000 −0.0790569
\(641\) −6.00000 −0.236986 −0.118493 0.992955i \(-0.537806\pi\)
−0.118493 + 0.992955i \(0.537806\pi\)
\(642\) 26.0000 1.02614
\(643\) 24.0000 0.946468 0.473234 0.880937i \(-0.343087\pi\)
0.473234 + 0.880937i \(0.343087\pi\)
\(644\) 0 0
\(645\) 4.00000 0.157500
\(646\) 0 0
\(647\) 34.0000 1.33668 0.668339 0.743857i \(-0.267006\pi\)
0.668339 + 0.743857i \(0.267006\pi\)
\(648\) −11.0000 −0.432121
\(649\) −4.00000 −0.157014
\(650\) −1.00000 −0.0392232
\(651\) 0 0
\(652\) −23.0000 −0.900750
\(653\) 15.0000 0.586995 0.293498 0.955960i \(-0.405181\pi\)
0.293498 + 0.955960i \(0.405181\pi\)
\(654\) −14.0000 −0.547443
\(655\) −24.0000 −0.937758
\(656\) 1.00000 0.0390434
\(657\) 7.00000 0.273096
\(658\) 0 0
\(659\) 22.0000 0.856998 0.428499 0.903542i \(-0.359042\pi\)
0.428499 + 0.903542i \(0.359042\pi\)
\(660\) 16.0000 0.622799
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) 12.0000 0.466393
\(663\) 0 0
\(664\) 9.00000 0.349268
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 10.0000 0.387202
\(668\) 5.00000 0.193456
\(669\) 52.0000 2.01044
\(670\) −20.0000 −0.772667
\(671\) −56.0000 −2.16186
\(672\) 0 0
\(673\) 40.0000 1.54189 0.770943 0.636904i \(-0.219785\pi\)
0.770943 + 0.636904i \(0.219785\pi\)
\(674\) 31.0000 1.19408
\(675\) 4.00000 0.153960
\(676\) −12.0000 −0.461538
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) −6.00000 −0.230429
\(679\) 0 0
\(680\) 0 0
\(681\) −36.0000 −1.37952
\(682\) −16.0000 −0.612672
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) −6.00000 −0.229416
\(685\) 36.0000 1.37549
\(686\) 0 0
\(687\) −42.0000 −1.60240
\(688\) −1.00000 −0.0381246
\(689\) −10.0000 −0.380970
\(690\) 8.00000 0.304555
\(691\) −30.0000 −1.14125 −0.570627 0.821209i \(-0.693300\pi\)
−0.570627 + 0.821209i \(0.693300\pi\)
\(692\) 24.0000 0.912343
\(693\) 0 0
\(694\) −24.0000 −0.911028
\(695\) −8.00000 −0.303457
\(696\) −10.0000 −0.379049
\(697\) 0 0
\(698\) −26.0000 −0.984115
\(699\) −32.0000 −1.21035
\(700\) 0 0
\(701\) −44.0000 −1.66186 −0.830929 0.556379i \(-0.812190\pi\)
−0.830929 + 0.556379i \(0.812190\pi\)
\(702\) −4.00000 −0.150970
\(703\) 12.0000 0.452589
\(704\) −4.00000 −0.150756
\(705\) 32.0000 1.20519
\(706\) 21.0000 0.790345
\(707\) 0 0
\(708\) 2.00000 0.0751646
\(709\) 35.0000 1.31445 0.657226 0.753693i \(-0.271730\pi\)
0.657226 + 0.753693i \(0.271730\pi\)
\(710\) 30.0000 1.12588
\(711\) 0 0
\(712\) 0 0
\(713\) −8.00000 −0.299602
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) −10.0000 −0.373718
\(717\) 32.0000 1.19506
\(718\) 14.0000 0.522475
\(719\) −31.0000 −1.15610 −0.578052 0.816000i \(-0.696187\pi\)
−0.578052 + 0.816000i \(0.696187\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 0 0
\(722\) 17.0000 0.632674
\(723\) −10.0000 −0.371904
\(724\) 2.00000 0.0743294
\(725\) 5.00000 0.185695
\(726\) 10.0000 0.371135
\(727\) −43.0000 −1.59478 −0.797391 0.603463i \(-0.793787\pi\)
−0.797391 + 0.603463i \(0.793787\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −14.0000 −0.518163
\(731\) 0 0
\(732\) 28.0000 1.03491
\(733\) −42.0000 −1.55131 −0.775653 0.631160i \(-0.782579\pi\)
−0.775653 + 0.631160i \(0.782579\pi\)
\(734\) −18.0000 −0.664392
\(735\) 0 0
\(736\) −2.00000 −0.0737210
\(737\) −40.0000 −1.47342
\(738\) 1.00000 0.0368105
\(739\) −15.0000 −0.551784 −0.275892 0.961189i \(-0.588973\pi\)
−0.275892 + 0.961189i \(0.588973\pi\)
\(740\) 4.00000 0.147043
\(741\) −12.0000 −0.440831
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 8.00000 0.293294
\(745\) −2.00000 −0.0732743
\(746\) 16.0000 0.585802
\(747\) 9.00000 0.329293
\(748\) 0 0
\(749\) 0 0
\(750\) 24.0000 0.876356
\(751\) 5.00000 0.182453 0.0912263 0.995830i \(-0.470921\pi\)
0.0912263 + 0.995830i \(0.470921\pi\)
\(752\) −8.00000 −0.291730
\(753\) −18.0000 −0.655956
\(754\) −5.00000 −0.182089
\(755\) −38.0000 −1.38296
\(756\) 0 0
\(757\) 31.0000 1.12671 0.563357 0.826214i \(-0.309510\pi\)
0.563357 + 0.826214i \(0.309510\pi\)
\(758\) −29.0000 −1.05333
\(759\) 16.0000 0.580763
\(760\) 12.0000 0.435286
\(761\) −50.0000 −1.81250 −0.906249 0.422744i \(-0.861067\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) 5.00000 0.180894
\(765\) 0 0
\(766\) −15.0000 −0.541972
\(767\) 1.00000 0.0361079
\(768\) 2.00000 0.0721688
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) −4.00000 −0.144056
\(772\) −10.0000 −0.359908
\(773\) −14.0000 −0.503545 −0.251773 0.967786i \(-0.581013\pi\)
−0.251773 + 0.967786i \(0.581013\pi\)
\(774\) −1.00000 −0.0359443
\(775\) −4.00000 −0.143684
\(776\) −4.00000 −0.143592
\(777\) 0 0
\(778\) 0 0
\(779\) −6.00000 −0.214972
\(780\) −4.00000 −0.143223
\(781\) 60.0000 2.14697
\(782\) 0 0
\(783\) 20.0000 0.714742
\(784\) 0 0
\(785\) 30.0000 1.07075
\(786\) 24.0000 0.856052
\(787\) 40.0000 1.42585 0.712923 0.701242i \(-0.247371\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) −2.00000 −0.0712470
\(789\) −62.0000 −2.20726
\(790\) 0 0
\(791\) 0 0
\(792\) −4.00000 −0.142134
\(793\) 14.0000 0.497155
\(794\) 26.0000 0.922705
\(795\) 40.0000 1.41865
\(796\) −3.00000 −0.106332
\(797\) −14.0000 −0.495905 −0.247953 0.968772i \(-0.579758\pi\)
−0.247953 + 0.968772i \(0.579758\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) 25.0000 0.882781
\(803\) −28.0000 −0.988099
\(804\) 20.0000 0.705346
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) 32.0000 1.12645
\(808\) −10.0000 −0.351799
\(809\) −50.0000 −1.75791 −0.878953 0.476908i \(-0.841757\pi\)
−0.878953 + 0.476908i \(0.841757\pi\)
\(810\) 22.0000 0.773001
\(811\) 33.0000 1.15879 0.579393 0.815048i \(-0.303290\pi\)
0.579393 + 0.815048i \(0.303290\pi\)
\(812\) 0 0
\(813\) 40.0000 1.40286
\(814\) 8.00000 0.280400
\(815\) 46.0000 1.61131
\(816\) 0 0
\(817\) 6.00000 0.209913
\(818\) 35.0000 1.22375
\(819\) 0 0
\(820\) −2.00000 −0.0698430
\(821\) −52.0000 −1.81481 −0.907406 0.420255i \(-0.861941\pi\)
−0.907406 + 0.420255i \(0.861941\pi\)
\(822\) −36.0000 −1.25564
\(823\) −32.0000 −1.11545 −0.557725 0.830026i \(-0.688326\pi\)
−0.557725 + 0.830026i \(0.688326\pi\)
\(824\) −10.0000 −0.348367
\(825\) 8.00000 0.278524
\(826\) 0 0
\(827\) −54.0000 −1.87776 −0.938882 0.344239i \(-0.888137\pi\)
−0.938882 + 0.344239i \(0.888137\pi\)
\(828\) −2.00000 −0.0695048
\(829\) −30.0000 −1.04194 −0.520972 0.853574i \(-0.674430\pi\)
−0.520972 + 0.853574i \(0.674430\pi\)
\(830\) −18.0000 −0.624789
\(831\) 16.0000 0.555034
\(832\) 1.00000 0.0346688
\(833\) 0 0
\(834\) 8.00000 0.277017
\(835\) −10.0000 −0.346064
\(836\) 24.0000 0.830057
\(837\) −16.0000 −0.553041
\(838\) −33.0000 −1.13997
\(839\) −29.0000 −1.00119 −0.500596 0.865681i \(-0.666886\pi\)
−0.500596 + 0.865681i \(0.666886\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) −30.0000 −1.03387
\(843\) 28.0000 0.964371
\(844\) 0 0
\(845\) 24.0000 0.825625
\(846\) −8.00000 −0.275046
\(847\) 0 0
\(848\) −10.0000 −0.343401
\(849\) −2.00000 −0.0686398
\(850\) 0 0
\(851\) 4.00000 0.137118
\(852\) −30.0000 −1.02778
\(853\) −38.0000 −1.30110 −0.650548 0.759465i \(-0.725461\pi\)
−0.650548 + 0.759465i \(0.725461\pi\)
\(854\) 0 0
\(855\) 12.0000 0.410391
\(856\) 13.0000 0.444331
\(857\) −53.0000 −1.81045 −0.905223 0.424937i \(-0.860296\pi\)
−0.905223 + 0.424937i \(0.860296\pi\)
\(858\) −8.00000 −0.273115
\(859\) −13.0000 −0.443554 −0.221777 0.975097i \(-0.571186\pi\)
−0.221777 + 0.975097i \(0.571186\pi\)
\(860\) 2.00000 0.0681994
\(861\) 0 0
\(862\) 26.0000 0.885564
\(863\) 36.0000 1.22545 0.612727 0.790295i \(-0.290072\pi\)
0.612727 + 0.790295i \(0.290072\pi\)
\(864\) −4.00000 −0.136083
\(865\) −48.0000 −1.63205
\(866\) 2.00000 0.0679628
\(867\) −34.0000 −1.15470
\(868\) 0 0
\(869\) 0 0
\(870\) 20.0000 0.678064
\(871\) 10.0000 0.338837
\(872\) −7.00000 −0.237050
\(873\) −4.00000 −0.135379
\(874\) 12.0000 0.405906
\(875\) 0 0
\(876\) 14.0000 0.473016
\(877\) −52.0000 −1.75592 −0.877958 0.478738i \(-0.841094\pi\)
−0.877958 + 0.478738i \(0.841094\pi\)
\(878\) −7.00000 −0.236239
\(879\) 6.00000 0.202375
\(880\) 8.00000 0.269680
\(881\) −7.00000 −0.235836 −0.117918 0.993023i \(-0.537622\pi\)
−0.117918 + 0.993023i \(0.537622\pi\)
\(882\) 0 0
\(883\) −20.0000 −0.673054 −0.336527 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) 0 0
\(885\) −4.00000 −0.134459
\(886\) −15.0000 −0.503935
\(887\) 13.0000 0.436497 0.218249 0.975893i \(-0.429966\pi\)
0.218249 + 0.975893i \(0.429966\pi\)
\(888\) −4.00000 −0.134231
\(889\) 0 0
\(890\) 0 0
\(891\) 44.0000 1.47406
\(892\) 26.0000 0.870544
\(893\) 48.0000 1.60626
\(894\) 2.00000 0.0668900
\(895\) 20.0000 0.668526
\(896\) 0 0
\(897\) −4.00000 −0.133556
\(898\) 11.0000 0.367075
\(899\) −20.0000 −0.667037
\(900\) −1.00000 −0.0333333
\(901\) 0 0
\(902\) −4.00000 −0.133185
\(903\) 0 0
\(904\) −3.00000 −0.0997785
\(905\) −4.00000 −0.132964
\(906\) 38.0000 1.26247
\(907\) 23.0000 0.763702 0.381851 0.924224i \(-0.375287\pi\)
0.381851 + 0.924224i \(0.375287\pi\)
\(908\) −18.0000 −0.597351
\(909\) −10.0000 −0.331679
\(910\) 0 0
\(911\) 40.0000 1.32526 0.662630 0.748947i \(-0.269440\pi\)
0.662630 + 0.748947i \(0.269440\pi\)
\(912\) −12.0000 −0.397360
\(913\) −36.0000 −1.19143
\(914\) 26.0000 0.860004
\(915\) −56.0000 −1.85130
\(916\) −21.0000 −0.693860
\(917\) 0 0
\(918\) 0 0
\(919\) 23.0000 0.758700 0.379350 0.925253i \(-0.376148\pi\)
0.379350 + 0.925253i \(0.376148\pi\)
\(920\) 4.00000 0.131876
\(921\) 18.0000 0.593120
\(922\) −20.0000 −0.658665
\(923\) −15.0000 −0.493731
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) −7.00000 −0.230034
\(927\) −10.0000 −0.328443
\(928\) −5.00000 −0.164133
\(929\) −38.0000 −1.24674 −0.623370 0.781927i \(-0.714237\pi\)
−0.623370 + 0.781927i \(0.714237\pi\)
\(930\) −16.0000 −0.524661
\(931\) 0 0
\(932\) −16.0000 −0.524097
\(933\) 26.0000 0.851202
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) 1.00000 0.0326860
\(937\) 30.0000 0.980057 0.490029 0.871706i \(-0.336986\pi\)
0.490029 + 0.871706i \(0.336986\pi\)
\(938\) 0 0
\(939\) 32.0000 1.04428
\(940\) 16.0000 0.521862
\(941\) 36.0000 1.17357 0.586783 0.809744i \(-0.300394\pi\)
0.586783 + 0.809744i \(0.300394\pi\)
\(942\) −30.0000 −0.977453
\(943\) −2.00000 −0.0651290
\(944\) 1.00000 0.0325472
\(945\) 0 0
\(946\) 4.00000 0.130051
\(947\) 45.0000 1.46230 0.731152 0.682215i \(-0.238983\pi\)
0.731152 + 0.682215i \(0.238983\pi\)
\(948\) 0 0
\(949\) 7.00000 0.227230
\(950\) 6.00000 0.194666
\(951\) −4.00000 −0.129709
\(952\) 0 0
\(953\) −9.00000 −0.291539 −0.145769 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(954\) −10.0000 −0.323762
\(955\) −10.0000 −0.323592
\(956\) 16.0000 0.517477
\(957\) 40.0000 1.29302
\(958\) −7.00000 −0.226160
\(959\) 0 0
\(960\) −4.00000 −0.129099
\(961\) −15.0000 −0.483871
\(962\) −2.00000 −0.0644826
\(963\) 13.0000 0.418919
\(964\) −5.00000 −0.161039
\(965\) 20.0000 0.643823
\(966\) 0 0
\(967\) 31.0000 0.996893 0.498446 0.866921i \(-0.333904\pi\)
0.498446 + 0.866921i \(0.333904\pi\)
\(968\) 5.00000 0.160706
\(969\) 0 0
\(970\) 8.00000 0.256865
\(971\) 2.00000 0.0641831 0.0320915 0.999485i \(-0.489783\pi\)
0.0320915 + 0.999485i \(0.489783\pi\)
\(972\) −10.0000 −0.320750
\(973\) 0 0
\(974\) 22.0000 0.704925
\(975\) −2.00000 −0.0640513
\(976\) 14.0000 0.448129
\(977\) −2.00000 −0.0639857 −0.0319928 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) −46.0000 −1.47092
\(979\) 0 0
\(980\) 0 0
\(981\) −7.00000 −0.223493
\(982\) −13.0000 −0.414847
\(983\) 44.0000 1.40338 0.701691 0.712481i \(-0.252429\pi\)
0.701691 + 0.712481i \(0.252429\pi\)
\(984\) 2.00000 0.0637577
\(985\) 4.00000 0.127451
\(986\) 0 0
\(987\) 0 0
\(988\) −6.00000 −0.190885
\(989\) 2.00000 0.0635963
\(990\) 8.00000 0.254257
\(991\) −19.0000 −0.603555 −0.301777 0.953378i \(-0.597580\pi\)
−0.301777 + 0.953378i \(0.597580\pi\)
\(992\) 4.00000 0.127000
\(993\) 24.0000 0.761617
\(994\) 0 0
\(995\) 6.00000 0.190213
\(996\) 18.0000 0.570352
\(997\) −35.0000 −1.10846 −0.554231 0.832363i \(-0.686987\pi\)
−0.554231 + 0.832363i \(0.686987\pi\)
\(998\) 36.0000 1.13956
\(999\) 8.00000 0.253109
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 \(a_p\))