Properties

Label 50.2.a.a.1.1
Level 50
Weight 2
Character 50.1
Self dual Yes
Analytic conductor 0.399
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 50.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.399252010106\)
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 \(\chi\) = 50.1

$q$-expansion

\(f(q)\)  \(=\)  \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{6}\) \(+2.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.00000 q^{6}\) \(+2.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.00000 q^{9}\) \(-3.00000 q^{11}\) \(+1.00000 q^{12}\) \(-4.00000 q^{13}\) \(-2.00000 q^{14}\) \(+1.00000 q^{16}\) \(-3.00000 q^{17}\) \(+2.00000 q^{18}\) \(+5.00000 q^{19}\) \(+2.00000 q^{21}\) \(+3.00000 q^{22}\) \(+6.00000 q^{23}\) \(-1.00000 q^{24}\) \(+4.00000 q^{26}\) \(-5.00000 q^{27}\) \(+2.00000 q^{28}\) \(+2.00000 q^{31}\) \(-1.00000 q^{32}\) \(-3.00000 q^{33}\) \(+3.00000 q^{34}\) \(-2.00000 q^{36}\) \(+2.00000 q^{37}\) \(-5.00000 q^{38}\) \(-4.00000 q^{39}\) \(-3.00000 q^{41}\) \(-2.00000 q^{42}\) \(-4.00000 q^{43}\) \(-3.00000 q^{44}\) \(-6.00000 q^{46}\) \(+12.0000 q^{47}\) \(+1.00000 q^{48}\) \(-3.00000 q^{49}\) \(-3.00000 q^{51}\) \(-4.00000 q^{52}\) \(+6.00000 q^{53}\) \(+5.00000 q^{54}\) \(-2.00000 q^{56}\) \(+5.00000 q^{57}\) \(+2.00000 q^{61}\) \(-2.00000 q^{62}\) \(-4.00000 q^{63}\) \(+1.00000 q^{64}\) \(+3.00000 q^{66}\) \(-13.0000 q^{67}\) \(-3.00000 q^{68}\) \(+6.00000 q^{69}\) \(+12.0000 q^{71}\) \(+2.00000 q^{72}\) \(+11.0000 q^{73}\) \(-2.00000 q^{74}\) \(+5.00000 q^{76}\) \(-6.00000 q^{77}\) \(+4.00000 q^{78}\) \(-10.0000 q^{79}\) \(+1.00000 q^{81}\) \(+3.00000 q^{82}\) \(-9.00000 q^{83}\) \(+2.00000 q^{84}\) \(+4.00000 q^{86}\) \(+3.00000 q^{88}\) \(+15.0000 q^{89}\) \(-8.00000 q^{91}\) \(+6.00000 q^{92}\) \(+2.00000 q^{93}\) \(-12.0000 q^{94}\) \(-1.00000 q^{96}\) \(+2.00000 q^{97}\) \(+3.00000 q^{98}\) \(+6.00000 q^{99}\) \(+O(q^{100})\)

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
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 2.00000 0.471405
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 3.00000 0.639602
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) 4.00000 0.784465
\(27\) −5.00000 −0.962250
\(28\) 2.00000 0.377964
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.00000 −0.522233
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −5.00000 −0.811107
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) −2.00000 −0.308607
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) −4.00000 −0.554700
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 5.00000 0.680414
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 5.00000 0.662266
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 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
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) −13.0000 −1.58820 −0.794101 0.607785i \(-0.792058\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) −3.00000 −0.363803
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 2.00000 0.235702
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) 5.00000 0.573539
\(77\) −6.00000 −0.683763
\(78\) 4.00000 0.452911
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 3.00000 0.331295
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 2.00000 0.218218
\(85\) 0 0
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) 3.00000 0.319801
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 6.00000 0.625543
\(93\) 2.00000 0.207390
\(94\) −12.0000 −1.23771
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 3.00000 0.303046
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 3.00000 0.297044
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) −5.00000 −0.481125
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 2.00000 0.188982
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) −5.00000 −0.468293
\(115\) 0 0
\(116\) 0 0
\(117\) 8.00000 0.739600
\(118\) 0 0
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −2.00000 −0.181071
\(123\) −3.00000 −0.270501
\(124\) 2.00000 0.179605
\(125\) 0 0
\(126\) 4.00000 0.356348
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −3.00000 −0.261116
\(133\) 10.0000 0.867110
\(134\) 13.0000 1.12303
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) −6.00000 −0.510754
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) −12.0000 −1.00702
\(143\) 12.0000 1.00349
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −11.0000 −0.910366
\(147\) −3.00000 −0.247436
\(148\) 2.00000 0.164399
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) −5.00000 −0.405554
\(153\) 6.00000 0.485071
\(154\) 6.00000 0.483494
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 10.0000 0.795557
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) −1.00000 −0.0785674
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) 9.00000 0.698535
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −2.00000 −0.154303
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −10.0000 −0.764719
\(172\) −4.00000 −0.304997
\(173\) −24.0000 −1.82469 −0.912343 0.409426i \(-0.865729\pi\)
−0.912343 + 0.409426i \(0.865729\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) −15.0000 −1.12430
\(179\) −15.0000 −1.12115 −0.560576 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 8.00000 0.592999
\(183\) 2.00000 0.147844
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) −2.00000 −0.146647
\(187\) 9.00000 0.658145
\(188\) 12.0000 0.875190
\(189\) −10.0000 −0.727393
\(190\) 0 0
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 1.00000 0.0721688
\(193\) −19.0000 −1.36765 −0.683825 0.729646i \(-0.739685\pi\)
−0.683825 + 0.729646i \(0.739685\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −6.00000 −0.426401
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 0 0
\(201\) −13.0000 −0.916949
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) −12.0000 −0.834058
\(208\) −4.00000 −0.277350
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 6.00000 0.412082
\(213\) 12.0000 0.822226
\(214\) 3.00000 0.205076
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) 4.00000 0.271538
\(218\) 10.0000 0.677285
\(219\) 11.0000 0.743311
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) −2.00000 −0.134231
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −2.00000 −0.133631
\(225\) 0 0
\(226\) 9.00000 0.598671
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 5.00000 0.331133
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 0 0
\(231\) −6.00000 −0.394771
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) −8.00000 −0.522976
\(235\) 0 0
\(236\) 0 0
\(237\) −10.0000 −0.649570
\(238\) 6.00000 0.388922
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 17.0000 1.09507 0.547533 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 2.00000 0.128565
\(243\) 16.0000 1.02640
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) 3.00000 0.191273
\(247\) −20.0000 −1.27257
\(248\) −2.00000 −0.127000
\(249\) −9.00000 −0.570352
\(250\) 0 0
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) −4.00000 −0.251976
\(253\) −18.0000 −1.13165
\(254\) −2.00000 −0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 4.00000 0.249029
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) 0 0
\(262\) −12.0000 −0.741362
\(263\) 6.00000 0.369976 0.184988 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 3.00000 0.184637
\(265\) 0 0
\(266\) −10.0000 −0.613139
\(267\) 15.0000 0.917985
\(268\) −13.0000 −0.794101
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) −3.00000 −0.181902
\(273\) −8.00000 −0.484182
\(274\) 3.00000 0.181237
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) 32.0000 1.92269 0.961347 0.275340i \(-0.0887905\pi\)
0.961347 + 0.275340i \(0.0887905\pi\)
\(278\) −5.00000 −0.299880
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −12.0000 −0.714590
\(283\) 11.0000 0.653882 0.326941 0.945045i \(-0.393982\pi\)
0.326941 + 0.945045i \(0.393982\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) −6.00000 −0.354169
\(288\) 2.00000 0.117851
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 2.00000 0.117242
\(292\) 11.0000 0.643726
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 15.0000 0.870388
\(298\) 0 0
\(299\) −24.0000 −1.38796
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) −2.00000 −0.115087
\(303\) −18.0000 −1.03407
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) −6.00000 −0.342997
\(307\) 17.0000 0.970241 0.485121 0.874447i \(-0.338776\pi\)
0.485121 + 0.874447i \(0.338776\pi\)
\(308\) −6.00000 −0.341882
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 4.00000 0.226455
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) −6.00000 −0.336463
\(319\) 0 0
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) −12.0000 −0.668734
\(323\) −15.0000 −0.834622
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −11.0000 −0.609234
\(327\) −10.0000 −0.553001
\(328\) 3.00000 0.165647
\(329\) 24.0000 1.32316
\(330\) 0 0
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) −9.00000 −0.493939
\(333\) −4.00000 −0.219199
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 2.00000 0.109109
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) −3.00000 −0.163178
\(339\) −9.00000 −0.488813
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 10.0000 0.540738
\(343\) −20.0000 −1.07990
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 24.0000 1.29025
\(347\) −3.00000 −0.161048 −0.0805242 0.996753i \(-0.525659\pi\)
−0.0805242 + 0.996753i \(0.525659\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 20.0000 1.06752
\(352\) 3.00000 0.159901
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 15.0000 0.794998
\(357\) −6.00000 −0.317554
\(358\) 15.0000 0.792775
\(359\) 30.0000 1.58334 0.791670 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) −2.00000 −0.105118
\(363\) −2.00000 −0.104973
\(364\) −8.00000 −0.419314
\(365\) 0 0
\(366\) −2.00000 −0.104542
\(367\) −28.0000 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) 6.00000 0.312772
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) 12.0000 0.623009
\(372\) 2.00000 0.103695
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) −9.00000 −0.465379
\(375\) 0 0
\(376\) −12.0000 −0.618853
\(377\) 0 0
\(378\) 10.0000 0.514344
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 18.0000 0.920960
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 19.0000 0.967075
\(387\) 8.00000 0.406663
\(388\) 2.00000 0.101535
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 3.00000 0.151523
\(393\) 12.0000 0.605320
\(394\) 18.0000 0.906827
\(395\) 0 0
\(396\) 6.00000 0.301511
\(397\) −28.0000 −1.40528 −0.702640 0.711546i \(-0.747995\pi\)
−0.702640 + 0.711546i \(0.747995\pi\)
\(398\) −20.0000 −1.00251
\(399\) 10.0000 0.500626
\(400\) 0 0
\(401\) −3.00000 −0.149813 −0.0749064 0.997191i \(-0.523866\pi\)
−0.0749064 + 0.997191i \(0.523866\pi\)
\(402\) 13.0000 0.648381
\(403\) −8.00000 −0.398508
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 3.00000 0.148522
\(409\) 5.00000 0.247234 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) 0 0
\(411\) −3.00000 −0.147979
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 12.0000 0.589768
\(415\) 0 0
\(416\) 4.00000 0.196116
\(417\) 5.00000 0.244851
\(418\) 15.0000 0.733674
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 13.0000 0.632830
\(423\) −24.0000 −1.16692
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 4.00000 0.193574
\(428\) −3.00000 −0.145010
\(429\) 12.0000 0.579365
\(430\) 0 0
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) −5.00000 −0.240563
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) 30.0000 1.43509
\(438\) −11.0000 −0.525600
\(439\) −40.0000 −1.90910 −0.954548 0.298057i \(-0.903661\pi\)
−0.954548 + 0.298057i \(0.903661\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) −12.0000 −0.570782
\(443\) −9.00000 −0.427603 −0.213801 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) 4.00000 0.189405
\(447\) 0 0
\(448\) 2.00000 0.0944911
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) 0 0
\(451\) 9.00000 0.423793
\(452\) −9.00000 −0.423324
\(453\) 2.00000 0.0939682
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) −5.00000 −0.234146
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −20.0000 −0.934539
\(459\) 15.0000 0.700140
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 6.00000 0.279145
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 8.00000 0.369800
\(469\) −26.0000 −1.20057
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) 0 0
\(473\) 12.0000 0.551761
\(474\) 10.0000 0.459315
\(475\) 0 0
\(476\) −6.00000 −0.275010
\(477\) −12.0000 −0.549442
\(478\) 0 0
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) −17.0000 −0.774329
\(483\) 12.0000 0.546019
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) −16.0000 −0.725775
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 11.0000 0.497437
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −3.00000 −0.135250
\(493\) 0 0
\(494\) 20.0000 0.899843
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 24.0000 1.07655
\(498\) 9.00000 0.403300
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) −27.0000 −1.20507
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 4.00000 0.178174
\(505\) 0 0
\(506\) 18.0000 0.800198
\(507\) 3.00000 0.133235
\(508\) 2.00000 0.0887357
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) 22.0000 0.973223
\(512\) −1.00000 −0.0441942
\(513\) −25.0000 −1.10378
\(514\) 18.0000 0.793946
\(515\) 0 0
\(516\) −4.00000 −0.176090
\(517\) −36.0000 −1.58328
\(518\) −4.00000 −0.175750
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 0 0
\(523\) 41.0000 1.79280 0.896402 0.443241i \(-0.146171\pi\)
0.896402 + 0.443241i \(0.146171\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) −6.00000 −0.261364
\(528\) −3.00000 −0.130558
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 10.0000 0.433555
\(533\) 12.0000 0.519778
\(534\) −15.0000 −0.649113
\(535\) 0 0
\(536\) 13.0000 0.561514
\(537\) −15.0000 −0.647298
\(538\) 0 0
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) 32.0000 1.37579 0.687894 0.725811i \(-0.258536\pi\)
0.687894 + 0.725811i \(0.258536\pi\)
\(542\) −2.00000 −0.0859074
\(543\) 2.00000 0.0858282
\(544\) 3.00000 0.128624
\(545\) 0 0
\(546\) 8.00000 0.342368
\(547\) 17.0000 0.726868 0.363434 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) −3.00000 −0.128154
\(549\) −4.00000 −0.170716
\(550\) 0 0
\(551\) 0 0
\(552\) −6.00000 −0.255377
\(553\) −20.0000 −0.850487
\(554\) −32.0000 −1.35955
\(555\) 0 0
\(556\) 5.00000 0.212047
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) 4.00000 0.169334
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 9.00000 0.379980
\(562\) 18.0000 0.759284
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 12.0000 0.505291
\(565\) 0 0
\(566\) −11.0000 −0.462364
\(567\) 2.00000 0.0839921
\(568\) −12.0000 −0.503509
\(569\) −15.0000 −0.628833 −0.314416 0.949285i \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 12.0000 0.501745
\(573\) −18.0000 −0.751961
\(574\) 6.00000 0.250435
\(575\) 0 0
\(576\) −2.00000 −0.0833333
\(577\) −13.0000 −0.541197 −0.270599 0.962692i \(-0.587222\pi\)
−0.270599 + 0.962692i \(0.587222\pi\)
\(578\) 8.00000 0.332756
\(579\) −19.0000 −0.789613
\(580\) 0 0
\(581\) −18.0000 −0.746766
\(582\) −2.00000 −0.0829027
\(583\) −18.0000 −0.745484
\(584\) −11.0000 −0.455183
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −33.0000 −1.36206 −0.681028 0.732257i \(-0.738467\pi\)
−0.681028 + 0.732257i \(0.738467\pi\)
\(588\) −3.00000 −0.123718
\(589\) 10.0000 0.412043
\(590\) 0 0
\(591\) −18.0000 −0.740421
\(592\) 2.00000 0.0821995
\(593\) −9.00000 −0.369586 −0.184793 0.982777i \(-0.559161\pi\)
−0.184793 + 0.982777i \(0.559161\pi\)
\(594\) −15.0000 −0.615457
\(595\) 0 0
\(596\) 0 0
\(597\) 20.0000 0.818546
\(598\) 24.0000 0.981433
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) −13.0000 −0.530281 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) 8.00000 0.326056
\(603\) 26.0000 1.05880
\(604\) 2.00000 0.0813788
\(605\) 0 0
\(606\) 18.0000 0.731200
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −5.00000 −0.202777
\(609\) 0 0
\(610\) 0 0
\(611\) −48.0000 −1.94187
\(612\) 6.00000 0.242536
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) −17.0000 −0.686064
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 4.00000 0.160904
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) −30.0000 −1.20386
\(622\) 18.0000 0.721734
\(623\) 30.0000 1.20192
\(624\) −4.00000 −0.160128
\(625\) 0 0
\(626\) −26.0000 −1.03917
\(627\) −15.0000 −0.599042
\(628\) 2.00000 0.0798087
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) 10.0000 0.397779
\(633\) −13.0000 −0.516704
\(634\) −12.0000 −0.476581
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) 12.0000 0.475457
\(638\) 0 0
\(639\) −24.0000 −0.949425
\(640\) 0 0
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 3.00000 0.118401
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 12.0000 0.472866
\(645\) 0 0
\(646\) 15.0000 0.590167
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) 11.0000 0.430793
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 10.0000 0.391031
\(655\) 0 0
\(656\) −3.00000 −0.117130
\(657\) −22.0000 −0.858302
\(658\) −24.0000 −0.935617
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 0 0
\(661\) 32.0000 1.24466 0.622328 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) −17.0000 −0.660724
\(663\) 12.0000 0.466041
\(664\) 9.00000 0.349268
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) −4.00000 −0.154649
\(670\) 0 0
\(671\) −6.00000 −0.231627
\(672\) −2.00000 −0.0771517
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 13.0000 0.500741
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −48.0000 −1.84479 −0.922395 0.386248i \(-0.873771\pi\)
−0.922395 + 0.386248i \(0.873771\pi\)
\(678\) 9.00000 0.345643
\(679\) 4.00000 0.153506
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 6.00000 0.229752
\(683\) −39.0000 −1.49229 −0.746147 0.665782i \(-0.768098\pi\)
−0.746147 + 0.665782i \(0.768098\pi\)
\(684\) −10.0000 −0.382360
\(685\) 0 0
\(686\) 20.0000 0.763604
\(687\) 20.0000 0.763048
\(688\) −4.00000 −0.152499
\(689\) −24.0000 −0.914327
\(690\) 0 0
\(691\) 17.0000 0.646710 0.323355 0.946278i \(-0.395189\pi\)
0.323355 + 0.946278i \(0.395189\pi\)
\(692\) −24.0000 −0.912343
\(693\) 12.0000 0.455842
\(694\) 3.00000 0.113878
\(695\) 0 0
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) 10.0000 0.378506
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) −20.0000 −0.754851
\(703\) 10.0000 0.377157
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) −36.0000 −1.35392
\(708\) 0 0
\(709\) 20.0000 0.751116 0.375558 0.926799i \(-0.377451\pi\)
0.375558 + 0.926799i \(0.377451\pi\)
\(710\) 0 0
\(711\) 20.0000 0.750059
\(712\) −15.0000 −0.562149
\(713\) 12.0000 0.449404
\(714\) 6.00000 0.224544
\(715\) 0 0
\(716\) −15.0000 −0.560576
\(717\) 0 0
\(718\) −30.0000 −1.11959
\(719\) −30.0000 −1.11881 −0.559406 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) −6.00000 −0.223297
\(723\) 17.0000 0.632237
\(724\) 2.00000 0.0743294
\(725\) 0 0
\(726\) 2.00000 0.0742270
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 8.00000 0.296500
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 12.0000 0.443836
\(732\) 2.00000 0.0739221
\(733\) −4.00000 −0.147743 −0.0738717 0.997268i \(-0.523536\pi\)
−0.0738717 + 0.997268i \(0.523536\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 39.0000 1.43658
\(738\) −6.00000 −0.220863
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) −20.0000 −0.734718
\(742\) −12.0000 −0.440534
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) −2.00000 −0.0733236
\(745\) 0 0
\(746\) −26.0000 −0.951928
\(747\) 18.0000 0.658586
\(748\) 9.00000 0.329073
\(749\) −6.00000 −0.219235
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 12.0000 0.437595
\(753\) 27.0000 0.983935
\(754\) 0 0
\(755\) 0 0
\(756\) −10.0000 −0.363696
\(757\) 32.0000 1.16306 0.581530 0.813525i \(-0.302454\pi\)
0.581530 + 0.813525i \(0.302454\pi\)
\(758\) 25.0000 0.908041
\(759\) −18.0000 −0.653359
\(760\) 0 0
\(761\) −3.00000 −0.108750 −0.0543750 0.998521i \(-0.517317\pi\)
−0.0543750 + 0.998521i \(0.517317\pi\)
\(762\) −2.00000 −0.0724524
\(763\) −20.0000 −0.724049
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) −19.0000 −0.683825
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) −8.00000 −0.287554
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) 4.00000 0.143499
\(778\) −30.0000 −1.07555
\(779\) −15.0000 −0.537431
\(780\) 0 0
\(781\) −36.0000 −1.28818
\(782\) 18.0000 0.643679
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) 0 0
\(786\) −12.0000 −0.428026
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) −18.0000 −0.641223
\(789\) 6.00000 0.213606
\(790\) 0 0
\(791\) −18.0000 −0.640006
\(792\) −6.00000 −0.213201
\(793\) −8.00000 −0.284088
\(794\) 28.0000 0.993683
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) −10.0000 −0.353996
\(799\) −36.0000 −1.27359
\(800\) 0 0
\(801\) −30.0000 −1.06000
\(802\) 3.00000 0.105934
\(803\) −33.0000 −1.16454
\(804\) −13.0000 −0.458475
\(805\) 0 0
\(806\) 8.00000 0.281788
\(807\) 0 0
\(808\) 18.0000 0.633238
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 0 0
\(813\) 2.00000 0.0701431
\(814\) 6.00000 0.210300
\(815\) 0 0
\(816\) −3.00000 −0.105021
\(817\) −20.0000 −0.699711
\(818\) −5.00000 −0.174821
\(819\) 16.0000 0.559085
\(820\) 0 0
\(821\) 42.0000 1.46581 0.732905 0.680331i \(-0.238164\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(822\) 3.00000 0.104637
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 4.00000 0.139347
\(825\) 0 0
\(826\) 0 0
\(827\) −33.0000 −1.14752 −0.573761 0.819023i \(-0.694516\pi\)
−0.573761 + 0.819023i \(0.694516\pi\)
\(828\) −12.0000 −0.417029
\(829\) 20.0000 0.694629 0.347314 0.937749i \(-0.387094\pi\)
0.347314 + 0.937749i \(0.387094\pi\)
\(830\) 0 0
\(831\) 32.0000 1.11007
\(832\) −4.00000 −0.138675
\(833\) 9.00000 0.311832
\(834\) −5.00000 −0.173136
\(835\) 0 0
\(836\) −15.0000 −0.518786
\(837\) −10.0000 −0.345651
\(838\) 15.0000 0.518166
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 28.0000 0.964944
\(843\) −18.0000 −0.619953
\(844\) −13.0000 −0.447478
\(845\) 0 0
\(846\) 24.0000 0.825137
\(847\) −4.00000 −0.137442
\(848\) 6.00000 0.206041
\(849\) 11.0000 0.377519
\(850\) 0 0
\(851\) 12.0000 0.411355
\(852\) 12.0000 0.411113
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) −4.00000 −0.136877
\(855\) 0 0
\(856\) 3.00000 0.102538
\(857\) −3.00000 −0.102478 −0.0512390 0.998686i \(-0.516317\pi\)
−0.0512390 + 0.998686i \(0.516317\pi\)
\(858\) −12.0000 −0.409673
\(859\) 5.00000 0.170598 0.0852989 0.996355i \(-0.472815\pi\)
0.0852989 + 0.996355i \(0.472815\pi\)
\(860\) 0 0
\(861\) −6.00000 −0.204479
\(862\) 18.0000 0.613082
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 5.00000 0.170103
\(865\) 0 0
\(866\) 19.0000 0.645646
\(867\) −8.00000 −0.271694
\(868\) 4.00000 0.135769
\(869\) 30.0000 1.01768
\(870\) 0 0
\(871\) 52.0000 1.76195
\(872\) 10.0000 0.338643
\(873\) −4.00000 −0.135379
\(874\) −30.0000 −1.01477
\(875\) 0 0
\(876\) 11.0000 0.371656
\(877\) −28.0000 −0.945493 −0.472746 0.881199i \(-0.656737\pi\)
−0.472746 + 0.881199i \(0.656737\pi\)
\(878\) 40.0000 1.34993
\(879\) 6.00000 0.202375
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) −6.00000 −0.202031
\(883\) 41.0000 1.37976 0.689880 0.723924i \(-0.257663\pi\)
0.689880 + 0.723924i \(0.257663\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) 9.00000 0.302361
\(887\) 12.0000 0.402921 0.201460 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 4.00000 0.134156
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) −4.00000 −0.133930
\(893\) 60.0000 2.00782
\(894\) 0 0
\(895\) 0 0
\(896\) −2.00000 −0.0668153
\(897\) −24.0000 −0.801337
\(898\) 15.0000 0.500556
\(899\) 0 0
\(900\) 0 0
\(901\) −18.0000 −0.599667
\(902\) −9.00000 −0.299667
\(903\) −8.00000 −0.266223
\(904\) 9.00000 0.299336
\(905\) 0 0
\(906\) −2.00000 −0.0664455
\(907\) −28.0000 −0.929725 −0.464862 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 12.0000 0.398234
\(909\) 36.0000 1.19404
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 5.00000 0.165567
\(913\) 27.0000 0.893570
\(914\) −17.0000 −0.562310
\(915\) 0 0
\(916\) 20.0000 0.660819
\(917\) 24.0000 0.792550
\(918\) −15.0000 −0.495074
\(919\) −10.0000 −0.329870 −0.164935 0.986304i \(-0.552741\pi\)
−0.164935 + 0.986304i \(0.552741\pi\)
\(920\) 0 0
\(921\) 17.0000 0.560169
\(922\) −12.0000 −0.395199
\(923\) −48.0000 −1.57994
\(924\) −6.00000 −0.197386
\(925\) 0 0
\(926\) 4.00000 0.131448
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) 30.0000 0.984268 0.492134 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) 0 0
\(931\) −15.0000 −0.491605
\(932\) 6.00000 0.196537
\(933\) −18.0000 −0.589294
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −8.00000 −0.261488
\(937\) −13.0000 −0.424691 −0.212346 0.977195i \(-0.568110\pi\)
−0.212346 + 0.977195i \(0.568110\pi\)
\(938\) 26.0000 0.848930
\(939\) 26.0000 0.848478
\(940\) 0 0
\(941\) 12.0000 0.391189 0.195594 0.980685i \(-0.437336\pi\)
0.195594 + 0.980685i \(0.437336\pi\)
\(942\) −2.00000 −0.0651635
\(943\) −18.0000 −0.586161
\(944\) 0 0
\(945\) 0 0
\(946\) −12.0000 −0.390154
\(947\) −48.0000 −1.55979 −0.779895 0.625910i \(-0.784728\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(948\) −10.0000 −0.324785
\(949\) −44.0000 −1.42830
\(950\) 0 0
\(951\) 12.0000 0.389127
\(952\) 6.00000 0.194461
\(953\) −39.0000 −1.26333 −0.631667 0.775240i \(-0.717629\pi\)
−0.631667 + 0.775240i \(0.717629\pi\)
\(954\) 12.0000 0.388514
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −30.0000 −0.969256
\(959\) −6.00000 −0.193750
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 8.00000 0.257930
\(963\) 6.00000 0.193347
\(964\) 17.0000 0.547533
\(965\) 0 0
\(966\) −12.0000 −0.386094
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 2.00000 0.0642824
\(969\) −15.0000 −0.481869
\(970\) 0 0
\(971\) −3.00000 −0.0962746 −0.0481373 0.998841i \(-0.515328\pi\)
−0.0481373 + 0.998841i \(0.515328\pi\)
\(972\) 16.0000 0.513200
\(973\) 10.0000 0.320585
\(974\) −2.00000 −0.0640841
\(975\) 0 0
\(976\) 2.00000 0.0640184
\(977\) 57.0000 1.82359 0.911796 0.410644i \(-0.134696\pi\)
0.911796 + 0.410644i \(0.134696\pi\)
\(978\) −11.0000 −0.351741
\(979\) −45.0000 −1.43821
\(980\) 0 0
\(981\) 20.0000 0.638551
\(982\) −12.0000 −0.382935
\(983\) 6.00000 0.191370 0.0956851 0.995412i \(-0.469496\pi\)
0.0956851 + 0.995412i \(0.469496\pi\)
\(984\) 3.00000 0.0956365
\(985\) 0 0
\(986\) 0 0
\(987\) 24.0000 0.763928
\(988\) −20.0000 −0.636285
\(989\) −24.0000 −0.763156
\(990\) 0 0
\(991\) −58.0000 −1.84243 −0.921215 0.389053i \(-0.872802\pi\)
−0.921215 + 0.389053i \(0.872802\pi\)
\(992\) −2.00000 −0.0635001
\(993\) 17.0000 0.539479
\(994\) −24.0000 −0.761234
\(995\) 0 0
\(996\) −9.00000 −0.285176
\(997\) −28.0000 −0.886769 −0.443384 0.896332i \(-0.646222\pi\)
−0.443384 + 0.896332i \(0.646222\pi\)
\(998\) −20.0000 −0.633089
\(999\) −10.0000 −0.316386
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 \(a_p\))