Properties

Label 4013.2.a.a.1.1
Level 4013
Weight 2
Character 4013.1
Self dual Yes
Analytic conductor 32.044
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4013 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0439663311\)
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 \(\chi\) = 4013.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -2.00000 q^{3} +2.00000 q^{4} +4.00000 q^{5} -4.00000 q^{6} +1.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -2.00000 q^{3} +2.00000 q^{4} +4.00000 q^{5} -4.00000 q^{6} +1.00000 q^{7} +1.00000 q^{9} +8.00000 q^{10} +3.00000 q^{11} -4.00000 q^{12} +2.00000 q^{13} +2.00000 q^{14} -8.00000 q^{15} -4.00000 q^{16} -2.00000 q^{17} +2.00000 q^{18} +1.00000 q^{19} +8.00000 q^{20} -2.00000 q^{21} +6.00000 q^{22} +11.0000 q^{25} +4.00000 q^{26} +4.00000 q^{27} +2.00000 q^{28} +8.00000 q^{29} -16.0000 q^{30} -5.00000 q^{31} -8.00000 q^{32} -6.00000 q^{33} -4.00000 q^{34} +4.00000 q^{35} +2.00000 q^{36} -4.00000 q^{37} +2.00000 q^{38} -4.00000 q^{39} +5.00000 q^{41} -4.00000 q^{42} +5.00000 q^{43} +6.00000 q^{44} +4.00000 q^{45} +12.0000 q^{47} +8.00000 q^{48} -6.00000 q^{49} +22.0000 q^{50} +4.00000 q^{51} +4.00000 q^{52} +1.00000 q^{53} +8.00000 q^{54} +12.0000 q^{55} -2.00000 q^{57} +16.0000 q^{58} +7.00000 q^{59} -16.0000 q^{60} -7.00000 q^{61} -10.0000 q^{62} +1.00000 q^{63} -8.00000 q^{64} +8.00000 q^{65} -12.0000 q^{66} -7.00000 q^{67} -4.00000 q^{68} +8.00000 q^{70} +4.00000 q^{71} -13.0000 q^{73} -8.00000 q^{74} -22.0000 q^{75} +2.00000 q^{76} +3.00000 q^{77} -8.00000 q^{78} +4.00000 q^{79} -16.0000 q^{80} -11.0000 q^{81} +10.0000 q^{82} +12.0000 q^{83} -4.00000 q^{84} -8.00000 q^{85} +10.0000 q^{86} -16.0000 q^{87} -10.0000 q^{89} +8.00000 q^{90} +2.00000 q^{91} +10.0000 q^{93} +24.0000 q^{94} +4.00000 q^{95} +16.0000 q^{96} -17.0000 q^{97} -12.0000 q^{98} +3.00000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 2.00000 1.00000
\(5\) 4.00000 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) −4.00000 −1.63299
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 8.00000 2.52982
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) −4.00000 −1.15470
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 2.00000 0.534522
\(15\) −8.00000 −2.06559
\(16\) −4.00000 −1.00000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 2.00000 0.471405
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 8.00000 1.78885
\(21\) −2.00000 −0.436436
\(22\) 6.00000 1.27920
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 4.00000 0.784465
\(27\) 4.00000 0.769800
\(28\) 2.00000 0.377964
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) −16.0000 −2.92119
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) −8.00000 −1.41421
\(33\) −6.00000 −1.04447
\(34\) −4.00000 −0.685994
\(35\) 4.00000 0.676123
\(36\) 2.00000 0.333333
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 2.00000 0.324443
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) −4.00000 −0.617213
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 6.00000 0.904534
\(45\) 4.00000 0.596285
\(46\) 0 0
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 8.00000 1.15470
\(49\) −6.00000 −0.857143
\(50\) 22.0000 3.11127
\(51\) 4.00000 0.560112
\(52\) 4.00000 0.554700
\(53\) 1.00000 0.137361 0.0686803 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) 8.00000 1.08866
\(55\) 12.0000 1.61808
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 16.0000 2.10090
\(59\) 7.00000 0.911322 0.455661 0.890153i \(-0.349403\pi\)
0.455661 + 0.890153i \(0.349403\pi\)
\(60\) −16.0000 −2.06559
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) −10.0000 −1.27000
\(63\) 1.00000 0.125988
\(64\) −8.00000 −1.00000
\(65\) 8.00000 0.992278
\(66\) −12.0000 −1.47710
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) −4.00000 −0.485071
\(69\) 0 0
\(70\) 8.00000 0.956183
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0 0
\(73\) −13.0000 −1.52153 −0.760767 0.649025i \(-0.775177\pi\)
−0.760767 + 0.649025i \(0.775177\pi\)
\(74\) −8.00000 −0.929981
\(75\) −22.0000 −2.54034
\(76\) 2.00000 0.229416
\(77\) 3.00000 0.341882
\(78\) −8.00000 −0.905822
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) −16.0000 −1.78885
\(81\) −11.0000 −1.22222
\(82\) 10.0000 1.10432
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −4.00000 −0.436436
\(85\) −8.00000 −0.867722
\(86\) 10.0000 1.07833
\(87\) −16.0000 −1.71538
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 8.00000 0.843274
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 10.0000 1.03695
\(94\) 24.0000 2.47541
\(95\) 4.00000 0.410391
\(96\) 16.0000 1.63299
\(97\) −17.0000 −1.72609 −0.863044 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) −12.0000 −1.21218
\(99\) 3.00000 0.301511
\(100\) 22.0000 2.20000
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 8.00000 0.792118
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) 2.00000 0.194257
\(107\) −8.00000 −0.773389 −0.386695 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 8.00000 0.769800
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 24.0000 2.28831
\(111\) 8.00000 0.759326
\(112\) −4.00000 −0.377964
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) −4.00000 −0.374634
\(115\) 0 0
\(116\) 16.0000 1.48556
\(117\) 2.00000 0.184900
\(118\) 14.0000 1.28880
\(119\) −2.00000 −0.183340
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −14.0000 −1.26750
\(123\) −10.0000 −0.901670
\(124\) −10.0000 −0.898027
\(125\) 24.0000 2.14663
\(126\) 2.00000 0.178174
\(127\) 7.00000 0.621150 0.310575 0.950549i \(-0.399478\pi\)
0.310575 + 0.950549i \(0.399478\pi\)
\(128\) 0 0
\(129\) −10.0000 −0.880451
\(130\) 16.0000 1.40329
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −12.0000 −1.04447
\(133\) 1.00000 0.0867110
\(134\) −14.0000 −1.20942
\(135\) 16.0000 1.37706
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 8.00000 0.676123
\(141\) −24.0000 −2.02116
\(142\) 8.00000 0.671345
\(143\) 6.00000 0.501745
\(144\) −4.00000 −0.333333
\(145\) 32.0000 2.65746
\(146\) −26.0000 −2.15178
\(147\) 12.0000 0.989743
\(148\) −8.00000 −0.657596
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −44.0000 −3.59258
\(151\) 6.00000 0.488273 0.244137 0.969741i \(-0.421495\pi\)
0.244137 + 0.969741i \(0.421495\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 6.00000 0.483494
\(155\) −20.0000 −1.60644
\(156\) −8.00000 −0.640513
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 8.00000 0.636446
\(159\) −2.00000 −0.158610
\(160\) −32.0000 −2.52982
\(161\) 0 0
\(162\) −22.0000 −1.72848
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 10.0000 0.780869
\(165\) −24.0000 −1.86840
\(166\) 24.0000 1.86276
\(167\) 14.0000 1.08335 0.541676 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −16.0000 −1.22714
\(171\) 1.00000 0.0764719
\(172\) 10.0000 0.762493
\(173\) −14.0000 −1.06440 −0.532200 0.846619i \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) −32.0000 −2.42591
\(175\) 11.0000 0.831522
\(176\) −12.0000 −0.904534
\(177\) −14.0000 −1.05230
\(178\) −20.0000 −1.49906
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 8.00000 0.596285
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 4.00000 0.296500
\(183\) 14.0000 1.03491
\(184\) 0 0
\(185\) −16.0000 −1.17634
\(186\) 20.0000 1.46647
\(187\) −6.00000 −0.438763
\(188\) 24.0000 1.75038
\(189\) 4.00000 0.290957
\(190\) 8.00000 0.580381
\(191\) 21.0000 1.51951 0.759753 0.650211i \(-0.225320\pi\)
0.759753 + 0.650211i \(0.225320\pi\)
\(192\) 16.0000 1.15470
\(193\) 22.0000 1.58359 0.791797 0.610784i \(-0.209146\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(194\) −34.0000 −2.44106
\(195\) −16.0000 −1.14578
\(196\) −12.0000 −0.857143
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 6.00000 0.426401
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) 14.0000 0.987484
\(202\) 24.0000 1.68863
\(203\) 8.00000 0.561490
\(204\) 8.00000 0.560112
\(205\) 20.0000 1.39686
\(206\) 28.0000 1.95085
\(207\) 0 0
\(208\) −8.00000 −0.554700
\(209\) 3.00000 0.207514
\(210\) −16.0000 −1.10410
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) 2.00000 0.137361
\(213\) −8.00000 −0.548151
\(214\) −16.0000 −1.09374
\(215\) 20.0000 1.36399
\(216\) 0 0
\(217\) −5.00000 −0.339422
\(218\) 22.0000 1.49003
\(219\) 26.0000 1.75692
\(220\) 24.0000 1.61808
\(221\) −4.00000 −0.269069
\(222\) 16.0000 1.07385
\(223\) 6.00000 0.401790 0.200895 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) −8.00000 −0.534522
\(225\) 11.0000 0.733333
\(226\) 8.00000 0.532152
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) −4.00000 −0.264906
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) −6.00000 −0.394771
\(232\) 0 0
\(233\) 1.00000 0.0655122 0.0327561 0.999463i \(-0.489572\pi\)
0.0327561 + 0.999463i \(0.489572\pi\)
\(234\) 4.00000 0.261488
\(235\) 48.0000 3.13117
\(236\) 14.0000 0.911322
\(237\) −8.00000 −0.519656
\(238\) −4.00000 −0.259281
\(239\) 2.00000 0.129369 0.0646846 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) 32.0000 2.06559
\(241\) 16.0000 1.03065 0.515325 0.856995i \(-0.327671\pi\)
0.515325 + 0.856995i \(0.327671\pi\)
\(242\) −4.00000 −0.257130
\(243\) 10.0000 0.641500
\(244\) −14.0000 −0.896258
\(245\) −24.0000 −1.53330
\(246\) −20.0000 −1.27515
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) −24.0000 −1.52094
\(250\) 48.0000 3.03579
\(251\) −2.00000 −0.126239 −0.0631194 0.998006i \(-0.520105\pi\)
−0.0631194 + 0.998006i \(0.520105\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 14.0000 0.878438
\(255\) 16.0000 1.00196
\(256\) 16.0000 1.00000
\(257\) −15.0000 −0.935674 −0.467837 0.883815i \(-0.654967\pi\)
−0.467837 + 0.883815i \(0.654967\pi\)
\(258\) −20.0000 −1.24515
\(259\) −4.00000 −0.248548
\(260\) 16.0000 0.992278
\(261\) 8.00000 0.495188
\(262\) 0 0
\(263\) −9.00000 −0.554964 −0.277482 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 2.00000 0.122628
\(267\) 20.0000 1.22398
\(268\) −14.0000 −0.855186
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 32.0000 1.94746
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) 8.00000 0.485071
\(273\) −4.00000 −0.242091
\(274\) 36.0000 2.17484
\(275\) 33.0000 1.98997
\(276\) 0 0
\(277\) −20.0000 −1.20168 −0.600842 0.799368i \(-0.705168\pi\)
−0.600842 + 0.799368i \(0.705168\pi\)
\(278\) −8.00000 −0.479808
\(279\) −5.00000 −0.299342
\(280\) 0 0
\(281\) −17.0000 −1.01413 −0.507067 0.861906i \(-0.669271\pi\)
−0.507067 + 0.861906i \(0.669271\pi\)
\(282\) −48.0000 −2.85836
\(283\) −3.00000 −0.178331 −0.0891657 0.996017i \(-0.528420\pi\)
−0.0891657 + 0.996017i \(0.528420\pi\)
\(284\) 8.00000 0.474713
\(285\) −8.00000 −0.473879
\(286\) 12.0000 0.709575
\(287\) 5.00000 0.295141
\(288\) −8.00000 −0.471405
\(289\) −13.0000 −0.764706
\(290\) 64.0000 3.75821
\(291\) 34.0000 1.99312
\(292\) −26.0000 −1.52153
\(293\) 2.00000 0.116841 0.0584206 0.998292i \(-0.481394\pi\)
0.0584206 + 0.998292i \(0.481394\pi\)
\(294\) 24.0000 1.39971
\(295\) 28.0000 1.63022
\(296\) 0 0
\(297\) 12.0000 0.696311
\(298\) −20.0000 −1.15857
\(299\) 0 0
\(300\) −44.0000 −2.54034
\(301\) 5.00000 0.288195
\(302\) 12.0000 0.690522
\(303\) −24.0000 −1.37876
\(304\) −4.00000 −0.229416
\(305\) −28.0000 −1.60328
\(306\) −4.00000 −0.228665
\(307\) −26.0000 −1.48390 −0.741949 0.670456i \(-0.766098\pi\)
−0.741949 + 0.670456i \(0.766098\pi\)
\(308\) 6.00000 0.341882
\(309\) −28.0000 −1.59286
\(310\) −40.0000 −2.27185
\(311\) 16.0000 0.907277 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 16.0000 0.902932
\(315\) 4.00000 0.225374
\(316\) 8.00000 0.450035
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) −4.00000 −0.224309
\(319\) 24.0000 1.34374
\(320\) −32.0000 −1.78885
\(321\) 16.0000 0.893033
\(322\) 0 0
\(323\) −2.00000 −0.111283
\(324\) −22.0000 −1.22222
\(325\) 22.0000 1.22034
\(326\) −32.0000 −1.77232
\(327\) −22.0000 −1.21660
\(328\) 0 0
\(329\) 12.0000 0.661581
\(330\) −48.0000 −2.64231
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 24.0000 1.31717
\(333\) −4.00000 −0.219199
\(334\) 28.0000 1.53209
\(335\) −28.0000 −1.52980
\(336\) 8.00000 0.436436
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) −18.0000 −0.979071
\(339\) −8.00000 −0.434500
\(340\) −16.0000 −0.867722
\(341\) −15.0000 −0.812296
\(342\) 2.00000 0.108148
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) −28.0000 −1.50529
\(347\) 9.00000 0.483145 0.241573 0.970383i \(-0.422337\pi\)
0.241573 + 0.970383i \(0.422337\pi\)
\(348\) −32.0000 −1.71538
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 22.0000 1.17595
\(351\) 8.00000 0.427008
\(352\) −24.0000 −1.27920
\(353\) 21.0000 1.11772 0.558859 0.829263i \(-0.311239\pi\)
0.558859 + 0.829263i \(0.311239\pi\)
\(354\) −28.0000 −1.48818
\(355\) 16.0000 0.849192
\(356\) −20.0000 −1.06000
\(357\) 4.00000 0.211702
\(358\) −8.00000 −0.422813
\(359\) 15.0000 0.791670 0.395835 0.918322i \(-0.370455\pi\)
0.395835 + 0.918322i \(0.370455\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) −40.0000 −2.10235
\(363\) 4.00000 0.209946
\(364\) 4.00000 0.209657
\(365\) −52.0000 −2.72180
\(366\) 28.0000 1.46358
\(367\) −21.0000 −1.09619 −0.548096 0.836416i \(-0.684647\pi\)
−0.548096 + 0.836416i \(0.684647\pi\)
\(368\) 0 0
\(369\) 5.00000 0.260290
\(370\) −32.0000 −1.66360
\(371\) 1.00000 0.0519174
\(372\) 20.0000 1.03695
\(373\) 19.0000 0.983783 0.491891 0.870657i \(-0.336306\pi\)
0.491891 + 0.870657i \(0.336306\pi\)
\(374\) −12.0000 −0.620505
\(375\) −48.0000 −2.47871
\(376\) 0 0
\(377\) 16.0000 0.824042
\(378\) 8.00000 0.411476
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 8.00000 0.410391
\(381\) −14.0000 −0.717242
\(382\) 42.0000 2.14891
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 0 0
\(385\) 12.0000 0.611577
\(386\) 44.0000 2.23954
\(387\) 5.00000 0.254164
\(388\) −34.0000 −1.72609
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) −32.0000 −1.62038
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −20.0000 −1.00759
\(395\) 16.0000 0.805047
\(396\) 6.00000 0.301511
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 8.00000 0.401004
\(399\) −2.00000 −0.100125
\(400\) −44.0000 −2.20000
\(401\) 32.0000 1.59800 0.799002 0.601329i \(-0.205362\pi\)
0.799002 + 0.601329i \(0.205362\pi\)
\(402\) 28.0000 1.39651
\(403\) −10.0000 −0.498135
\(404\) 24.0000 1.19404
\(405\) −44.0000 −2.18638
\(406\) 16.0000 0.794067
\(407\) −12.0000 −0.594818
\(408\) 0 0
\(409\) −29.0000 −1.43396 −0.716979 0.697095i \(-0.754476\pi\)
−0.716979 + 0.697095i \(0.754476\pi\)
\(410\) 40.0000 1.97546
\(411\) −36.0000 −1.77575
\(412\) 28.0000 1.37946
\(413\) 7.00000 0.344447
\(414\) 0 0
\(415\) 48.0000 2.35623
\(416\) −16.0000 −0.784465
\(417\) 8.00000 0.391762
\(418\) 6.00000 0.293470
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) −16.0000 −0.780720
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) −2.00000 −0.0973585
\(423\) 12.0000 0.583460
\(424\) 0 0
\(425\) −22.0000 −1.06716
\(426\) −16.0000 −0.775203
\(427\) −7.00000 −0.338754
\(428\) −16.0000 −0.773389
\(429\) −12.0000 −0.579365
\(430\) 40.0000 1.92897
\(431\) −2.00000 −0.0963366 −0.0481683 0.998839i \(-0.515338\pi\)
−0.0481683 + 0.998839i \(0.515338\pi\)
\(432\) −16.0000 −0.769800
\(433\) 10.0000 0.480569 0.240285 0.970702i \(-0.422759\pi\)
0.240285 + 0.970702i \(0.422759\pi\)
\(434\) −10.0000 −0.480015
\(435\) −64.0000 −3.06857
\(436\) 22.0000 1.05361
\(437\) 0 0
\(438\) 52.0000 2.48466
\(439\) −2.00000 −0.0954548 −0.0477274 0.998860i \(-0.515198\pi\)
−0.0477274 + 0.998860i \(0.515198\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −8.00000 −0.380521
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 16.0000 0.759326
\(445\) −40.0000 −1.89618
\(446\) 12.0000 0.568216
\(447\) 20.0000 0.945968
\(448\) −8.00000 −0.377964
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 22.0000 1.03709
\(451\) 15.0000 0.706322
\(452\) 8.00000 0.376288
\(453\) −12.0000 −0.563809
\(454\) 16.0000 0.750917
\(455\) 8.00000 0.375046
\(456\) 0 0
\(457\) −39.0000 −1.82434 −0.912172 0.409809i \(-0.865595\pi\)
−0.912172 + 0.409809i \(0.865595\pi\)
\(458\) 28.0000 1.30835
\(459\) −8.00000 −0.373408
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) −12.0000 −0.558291
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) −32.0000 −1.48556
\(465\) 40.0000 1.85496
\(466\) 2.00000 0.0926482
\(467\) −33.0000 −1.52706 −0.763529 0.645774i \(-0.776535\pi\)
−0.763529 + 0.645774i \(0.776535\pi\)
\(468\) 4.00000 0.184900
\(469\) −7.00000 −0.323230
\(470\) 96.0000 4.42815
\(471\) −16.0000 −0.737241
\(472\) 0 0
\(473\) 15.0000 0.689701
\(474\) −16.0000 −0.734904
\(475\) 11.0000 0.504715
\(476\) −4.00000 −0.183340
\(477\) 1.00000 0.0457869
\(478\) 4.00000 0.182956
\(479\) −37.0000 −1.69057 −0.845287 0.534313i \(-0.820570\pi\)
−0.845287 + 0.534313i \(0.820570\pi\)
\(480\) 64.0000 2.92119
\(481\) −8.00000 −0.364769
\(482\) 32.0000 1.45756
\(483\) 0 0
\(484\) −4.00000 −0.181818
\(485\) −68.0000 −3.08772
\(486\) 20.0000 0.907218
\(487\) −28.0000 −1.26880 −0.634401 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) 0 0
\(489\) 32.0000 1.44709
\(490\) −48.0000 −2.16842
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) −20.0000 −0.901670
\(493\) −16.0000 −0.720604
\(494\) 4.00000 0.179969
\(495\) 12.0000 0.539360
\(496\) 20.0000 0.898027
\(497\) 4.00000 0.179425
\(498\) −48.0000 −2.15093
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 48.0000 2.14663
\(501\) −28.0000 −1.25095
\(502\) −4.00000 −0.178529
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) 0 0
\(505\) 48.0000 2.13597
\(506\) 0 0
\(507\) 18.0000 0.799408
\(508\) 14.0000 0.621150
\(509\) −42.0000 −1.86162 −0.930809 0.365507i \(-0.880896\pi\)
−0.930809 + 0.365507i \(0.880896\pi\)
\(510\) 32.0000 1.41698
\(511\) −13.0000 −0.575086
\(512\) 32.0000 1.41421
\(513\) 4.00000 0.176604
\(514\) −30.0000 −1.32324
\(515\) 56.0000 2.46765
\(516\) −20.0000 −0.880451
\(517\) 36.0000 1.58328
\(518\) −8.00000 −0.351500
\(519\) 28.0000 1.22906
\(520\) 0 0
\(521\) −33.0000 −1.44576 −0.722878 0.690976i \(-0.757181\pi\)
−0.722878 + 0.690976i \(0.757181\pi\)
\(522\) 16.0000 0.700301
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) −22.0000 −0.960159
\(526\) −18.0000 −0.784837
\(527\) 10.0000 0.435607
\(528\) 24.0000 1.04447
\(529\) −23.0000 −1.00000
\(530\) 8.00000 0.347498
\(531\) 7.00000 0.303774
\(532\) 2.00000 0.0867110
\(533\) 10.0000 0.433148
\(534\) 40.0000 1.73097
\(535\) −32.0000 −1.38348
\(536\) 0 0
\(537\) 8.00000 0.345225
\(538\) 0 0
\(539\) −18.0000 −0.775315
\(540\) 32.0000 1.37706
\(541\) 19.0000 0.816874 0.408437 0.912787i \(-0.366074\pi\)
0.408437 + 0.912787i \(0.366074\pi\)
\(542\) −38.0000 −1.63224
\(543\) 40.0000 1.71656
\(544\) 16.0000 0.685994
\(545\) 44.0000 1.88475
\(546\) −8.00000 −0.342368
\(547\) −29.0000 −1.23995 −0.619975 0.784621i \(-0.712857\pi\)
−0.619975 + 0.784621i \(0.712857\pi\)
\(548\) 36.0000 1.53784
\(549\) −7.00000 −0.298753
\(550\) 66.0000 2.81425
\(551\) 8.00000 0.340811
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) −40.0000 −1.69944
\(555\) 32.0000 1.35832
\(556\) −8.00000 −0.339276
\(557\) 3.00000 0.127114 0.0635570 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(558\) −10.0000 −0.423334
\(559\) 10.0000 0.422955
\(560\) −16.0000 −0.676123
\(561\) 12.0000 0.506640
\(562\) −34.0000 −1.43420
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −48.0000 −2.02116
\(565\) 16.0000 0.673125
\(566\) −6.00000 −0.252199
\(567\) −11.0000 −0.461957
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) −16.0000 −0.670166
\(571\) −29.0000 −1.21361 −0.606806 0.794850i \(-0.707550\pi\)
−0.606806 + 0.794850i \(0.707550\pi\)
\(572\) 12.0000 0.501745
\(573\) −42.0000 −1.75458
\(574\) 10.0000 0.417392
\(575\) 0 0
\(576\) −8.00000 −0.333333
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) −26.0000 −1.08146
\(579\) −44.0000 −1.82858
\(580\) 64.0000 2.65746
\(581\) 12.0000 0.497844
\(582\) 68.0000 2.81869
\(583\) 3.00000 0.124247
\(584\) 0 0
\(585\) 8.00000 0.330759
\(586\) 4.00000 0.165238
\(587\) 23.0000 0.949312 0.474656 0.880172i \(-0.342573\pi\)
0.474656 + 0.880172i \(0.342573\pi\)
\(588\) 24.0000 0.989743
\(589\) −5.00000 −0.206021
\(590\) 56.0000 2.30548
\(591\) 20.0000 0.822690
\(592\) 16.0000 0.657596
\(593\) 44.0000 1.80686 0.903432 0.428732i \(-0.141040\pi\)
0.903432 + 0.428732i \(0.141040\pi\)
\(594\) 24.0000 0.984732
\(595\) −8.00000 −0.327968
\(596\) −20.0000 −0.819232
\(597\) −8.00000 −0.327418
\(598\) 0 0
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) 12.0000 0.489490 0.244745 0.969587i \(-0.421296\pi\)
0.244745 + 0.969587i \(0.421296\pi\)
\(602\) 10.0000 0.407570
\(603\) −7.00000 −0.285062
\(604\) 12.0000 0.488273
\(605\) −8.00000 −0.325246
\(606\) −48.0000 −1.94987
\(607\) −31.0000 −1.25825 −0.629126 0.777304i \(-0.716587\pi\)
−0.629126 + 0.777304i \(0.716587\pi\)
\(608\) −8.00000 −0.324443
\(609\) −16.0000 −0.648353
\(610\) −56.0000 −2.26737
\(611\) 24.0000 0.970936
\(612\) −4.00000 −0.161690
\(613\) −44.0000 −1.77714 −0.888572 0.458738i \(-0.848302\pi\)
−0.888572 + 0.458738i \(0.848302\pi\)
\(614\) −52.0000 −2.09855
\(615\) −40.0000 −1.61296
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −56.0000 −2.25265
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) −40.0000 −1.60644
\(621\) 0 0
\(622\) 32.0000 1.28308
\(623\) −10.0000 −0.400642
\(624\) 16.0000 0.640513
\(625\) 41.0000 1.64000
\(626\) −20.0000 −0.799361
\(627\) −6.00000 −0.239617
\(628\) 16.0000 0.638470
\(629\) 8.00000 0.318981
\(630\) 8.00000 0.318728
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 0 0
\(633\) 2.00000 0.0794929
\(634\) 24.0000 0.953162
\(635\) 28.0000 1.11115
\(636\) −4.00000 −0.158610
\(637\) −12.0000 −0.475457
\(638\) 48.0000 1.90034
\(639\) 4.00000 0.158238
\(640\) 0 0
\(641\) 12.0000 0.473972 0.236986 0.971513i \(-0.423841\pi\)
0.236986 + 0.971513i \(0.423841\pi\)
\(642\) 32.0000 1.26294
\(643\) 38.0000 1.49857 0.749287 0.662246i \(-0.230396\pi\)
0.749287 + 0.662246i \(0.230396\pi\)
\(644\) 0 0
\(645\) −40.0000 −1.57500
\(646\) −4.00000 −0.157378
\(647\) −2.00000 −0.0786281 −0.0393141 0.999227i \(-0.512517\pi\)
−0.0393141 + 0.999227i \(0.512517\pi\)
\(648\) 0 0
\(649\) 21.0000 0.824322
\(650\) 44.0000 1.72582
\(651\) 10.0000 0.391931
\(652\) −32.0000 −1.25322
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) −44.0000 −1.72054
\(655\) 0 0
\(656\) −20.0000 −0.780869
\(657\) −13.0000 −0.507178
\(658\) 24.0000 0.935617
\(659\) −39.0000 −1.51922 −0.759612 0.650376i \(-0.774611\pi\)
−0.759612 + 0.650376i \(0.774611\pi\)
\(660\) −48.0000 −1.86840
\(661\) 37.0000 1.43913 0.719567 0.694423i \(-0.244340\pi\)
0.719567 + 0.694423i \(0.244340\pi\)
\(662\) −16.0000 −0.621858
\(663\) 8.00000 0.310694
\(664\) 0 0
\(665\) 4.00000 0.155113
\(666\) −8.00000 −0.309994
\(667\) 0 0
\(668\) 28.0000 1.08335
\(669\) −12.0000 −0.463947
\(670\) −56.0000 −2.16347
\(671\) −21.0000 −0.810696
\(672\) 16.0000 0.617213
\(673\) −43.0000 −1.65753 −0.828764 0.559598i \(-0.810955\pi\)
−0.828764 + 0.559598i \(0.810955\pi\)
\(674\) 4.00000 0.154074
\(675\) 44.0000 1.69356
\(676\) −18.0000 −0.692308
\(677\) −29.0000 −1.11456 −0.557280 0.830324i \(-0.688155\pi\)
−0.557280 + 0.830324i \(0.688155\pi\)
\(678\) −16.0000 −0.614476
\(679\) −17.0000 −0.652400
\(680\) 0 0
\(681\) −16.0000 −0.613121
\(682\) −30.0000 −1.14876
\(683\) 18.0000 0.688751 0.344375 0.938832i \(-0.388091\pi\)
0.344375 + 0.938832i \(0.388091\pi\)
\(684\) 2.00000 0.0764719
\(685\) 72.0000 2.75098
\(686\) −26.0000 −0.992685
\(687\) −28.0000 −1.06827
\(688\) −20.0000 −0.762493
\(689\) 2.00000 0.0761939
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) −28.0000 −1.06440
\(693\) 3.00000 0.113961
\(694\) 18.0000 0.683271
\(695\) −16.0000 −0.606915
\(696\) 0 0
\(697\) −10.0000 −0.378777
\(698\) −44.0000 −1.66542
\(699\) −2.00000 −0.0756469
\(700\) 22.0000 0.831522
\(701\) −16.0000 −0.604312 −0.302156 0.953259i \(-0.597706\pi\)
−0.302156 + 0.953259i \(0.597706\pi\)
\(702\) 16.0000 0.603881
\(703\) −4.00000 −0.150863
\(704\) −24.0000 −0.904534
\(705\) −96.0000 −3.61557
\(706\) 42.0000 1.58069
\(707\) 12.0000 0.451306
\(708\) −28.0000 −1.05230
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) 32.0000 1.20094
\(711\) 4.00000 0.150012
\(712\) 0 0
\(713\) 0 0
\(714\) 8.00000 0.299392
\(715\) 24.0000 0.897549
\(716\) −8.00000 −0.298974
\(717\) −4.00000 −0.149383
\(718\) 30.0000 1.11959
\(719\) −15.0000 −0.559406 −0.279703 0.960087i \(-0.590236\pi\)
−0.279703 + 0.960087i \(0.590236\pi\)
\(720\) −16.0000 −0.596285
\(721\) 14.0000 0.521387
\(722\) −36.0000 −1.33978
\(723\) −32.0000 −1.19009
\(724\) −40.0000 −1.48659
\(725\) 88.0000 3.26824
\(726\) 8.00000 0.296908
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −104.000 −3.84921
\(731\) −10.0000 −0.369863
\(732\) 28.0000 1.03491
\(733\) −32.0000 −1.18195 −0.590973 0.806691i \(-0.701256\pi\)
−0.590973 + 0.806691i \(0.701256\pi\)
\(734\) −42.0000 −1.55025
\(735\) 48.0000 1.77051
\(736\) 0 0
\(737\) −21.0000 −0.773545
\(738\) 10.0000 0.368105
\(739\) 4.00000 0.147142 0.0735712 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) −32.0000 −1.17634
\(741\) −4.00000 −0.146944
\(742\) 2.00000 0.0734223
\(743\) 8.00000 0.293492 0.146746 0.989174i \(-0.453120\pi\)
0.146746 + 0.989174i \(0.453120\pi\)
\(744\) 0 0
\(745\) −40.0000 −1.46549
\(746\) 38.0000 1.39128
\(747\) 12.0000 0.439057
\(748\) −12.0000 −0.438763
\(749\) −8.00000 −0.292314
\(750\) −96.0000 −3.50542
\(751\) −48.0000 −1.75154 −0.875772 0.482724i \(-0.839647\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) −48.0000 −1.75038
\(753\) 4.00000 0.145768
\(754\) 32.0000 1.16537
\(755\) 24.0000 0.873449
\(756\) 8.00000 0.290957
\(757\) −5.00000 −0.181728 −0.0908640 0.995863i \(-0.528963\pi\)
−0.0908640 + 0.995863i \(0.528963\pi\)
\(758\) −40.0000 −1.45287
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) −28.0000 −1.01433
\(763\) 11.0000 0.398227
\(764\) 42.0000 1.51951
\(765\) −8.00000 −0.289241
\(766\) 16.0000 0.578103
\(767\) 14.0000 0.505511
\(768\) −32.0000 −1.15470
\(769\) 40.0000 1.44244 0.721218 0.692708i \(-0.243582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(770\) 24.0000 0.864900
\(771\) 30.0000 1.08042
\(772\) 44.0000 1.58359
\(773\) 26.0000 0.935155 0.467578 0.883952i \(-0.345127\pi\)
0.467578 + 0.883952i \(0.345127\pi\)
\(774\) 10.0000 0.359443
\(775\) −55.0000 −1.97566
\(776\) 0 0
\(777\) 8.00000 0.286998
\(778\) −12.0000 −0.430221
\(779\) 5.00000 0.179144
\(780\) −32.0000 −1.14578
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) 32.0000 1.14359
\(784\) 24.0000 0.857143
\(785\) 32.0000 1.14213
\(786\) 0 0
\(787\) 4.00000 0.142585 0.0712923 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) −20.0000 −0.712470
\(789\) 18.0000 0.640817
\(790\) 32.0000 1.13851
\(791\) 4.00000 0.142224
\(792\) 0 0
\(793\) −14.0000 −0.497155
\(794\) 36.0000 1.27759
\(795\) −8.00000 −0.283731
\(796\) 8.00000 0.283552
\(797\) 50.0000 1.77109 0.885545 0.464553i \(-0.153785\pi\)
0.885545 + 0.464553i \(0.153785\pi\)
\(798\) −4.00000 −0.141598
\(799\) −24.0000 −0.849059
\(800\) −88.0000 −3.11127
\(801\) −10.0000 −0.353333
\(802\) 64.0000 2.25992
\(803\) −39.0000 −1.37628
\(804\) 28.0000 0.987484
\(805\) 0 0
\(806\) −20.0000 −0.704470
\(807\) 0 0
\(808\) 0 0
\(809\) −22.0000 −0.773479 −0.386739 0.922189i \(-0.626399\pi\)
−0.386739 + 0.922189i \(0.626399\pi\)
\(810\) −88.0000 −3.09200
\(811\) 52.0000 1.82597 0.912983 0.407997i \(-0.133772\pi\)
0.912983 + 0.407997i \(0.133772\pi\)
\(812\) 16.0000 0.561490
\(813\) 38.0000 1.33272
\(814\) −24.0000 −0.841200
\(815\) −64.0000 −2.24182
\(816\) −16.0000 −0.560112
\(817\) 5.00000 0.174928
\(818\) −58.0000 −2.02792
\(819\) 2.00000 0.0698857
\(820\) 40.0000 1.39686
\(821\) 9.00000 0.314102 0.157051 0.987590i \(-0.449801\pi\)
0.157051 + 0.987590i \(0.449801\pi\)
\(822\) −72.0000 −2.51129
\(823\) −10.0000 −0.348578 −0.174289 0.984695i \(-0.555763\pi\)
−0.174289 + 0.984695i \(0.555763\pi\)
\(824\) 0 0
\(825\) −66.0000 −2.29783
\(826\) 14.0000 0.487122
\(827\) 4.00000 0.139094 0.0695468 0.997579i \(-0.477845\pi\)
0.0695468 + 0.997579i \(0.477845\pi\)
\(828\) 0 0
\(829\) −29.0000 −1.00721 −0.503606 0.863934i \(-0.667994\pi\)
−0.503606 + 0.863934i \(0.667994\pi\)
\(830\) 96.0000 3.33221
\(831\) 40.0000 1.38758
\(832\) −16.0000 −0.554700
\(833\) 12.0000 0.415775
\(834\) 16.0000 0.554035
\(835\) 56.0000 1.93796
\(836\) 6.00000 0.207514
\(837\) −20.0000 −0.691301
\(838\) −60.0000 −2.07267
\(839\) 51.0000 1.76072 0.880358 0.474310i \(-0.157302\pi\)
0.880358 + 0.474310i \(0.157302\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) −32.0000 −1.10279
\(843\) 34.0000 1.17102
\(844\) −2.00000 −0.0688428
\(845\) −36.0000 −1.23844
\(846\) 24.0000 0.825137
\(847\) −2.00000 −0.0687208
\(848\) −4.00000 −0.137361
\(849\) 6.00000 0.205919
\(850\) −44.0000 −1.50919
\(851\) 0 0
\(852\) −16.0000 −0.548151
\(853\) −40.0000 −1.36957 −0.684787 0.728743i \(-0.740105\pi\)
−0.684787 + 0.728743i \(0.740105\pi\)
\(854\) −14.0000 −0.479070
\(855\) 4.00000 0.136797
\(856\) 0 0
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) −24.0000 −0.819346
\(859\) −50.0000 −1.70598 −0.852989 0.521929i \(-0.825213\pi\)
−0.852989 + 0.521929i \(0.825213\pi\)
\(860\) 40.0000 1.36399
\(861\) −10.0000 −0.340799
\(862\) −4.00000 −0.136241
\(863\) 2.00000 0.0680808 0.0340404 0.999420i \(-0.489163\pi\)
0.0340404 + 0.999420i \(0.489163\pi\)
\(864\) −32.0000 −1.08866
\(865\) −56.0000 −1.90406
\(866\) 20.0000 0.679628
\(867\) 26.0000 0.883006
\(868\) −10.0000 −0.339422
\(869\) 12.0000 0.407072
\(870\) −128.000 −4.33961
\(871\) −14.0000 −0.474372
\(872\) 0 0
\(873\) −17.0000 −0.575363
\(874\) 0 0
\(875\) 24.0000 0.811348
\(876\) 52.0000 1.75692
\(877\) −10.0000 −0.337676 −0.168838 0.985644i \(-0.554001\pi\)
−0.168838 + 0.985644i \(0.554001\pi\)
\(878\) −4.00000 −0.134993
\(879\) −4.00000 −0.134917
\(880\) −48.0000 −1.61808
\(881\) −46.0000 −1.54978 −0.774890 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) −12.0000 −0.404061
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) −8.00000 −0.269069
\(885\) −56.0000 −1.88242
\(886\) −48.0000 −1.61259
\(887\) 32.0000 1.07445 0.537227 0.843437i \(-0.319472\pi\)
0.537227 + 0.843437i \(0.319472\pi\)
\(888\) 0 0
\(889\) 7.00000 0.234772
\(890\) −80.0000 −2.68161
\(891\) −33.0000 −1.10554
\(892\) 12.0000 0.401790
\(893\) 12.0000 0.401565
\(894\) 40.0000 1.33780
\(895\) −16.0000 −0.534821
\(896\) 0 0
\(897\) 0 0
\(898\) 30.0000 1.00111
\(899\) −40.0000 −1.33407
\(900\) 22.0000 0.733333
\(901\) −2.00000 −0.0666297
\(902\) 30.0000 0.998891
\(903\) −10.0000 −0.332779
\(904\) 0 0
\(905\) −80.0000 −2.65929
\(906\) −24.0000 −0.797347
\(907\) −50.0000 −1.66022 −0.830111 0.557598i \(-0.811723\pi\)
−0.830111 + 0.557598i \(0.811723\pi\)
\(908\) 16.0000 0.530979
\(909\) 12.0000 0.398015
\(910\) 16.0000 0.530395
\(911\) 49.0000 1.62344 0.811721 0.584045i \(-0.198531\pi\)
0.811721 + 0.584045i \(0.198531\pi\)
\(912\) 8.00000 0.264906
\(913\) 36.0000 1.19143
\(914\) −78.0000 −2.58001
\(915\) 56.0000 1.85130
\(916\) 28.0000 0.925146
\(917\) 0 0
\(918\) −16.0000 −0.528079
\(919\) −22.0000 −0.725713 −0.362857 0.931845i \(-0.618198\pi\)
−0.362857 + 0.931845i \(0.618198\pi\)
\(920\) 0 0
\(921\) 52.0000 1.71346
\(922\) 12.0000 0.395199
\(923\) 8.00000 0.263323
\(924\) −12.0000 −0.394771
\(925\) −44.0000 −1.44671
\(926\) 52.0000 1.70883
\(927\) 14.0000 0.459820
\(928\) −64.0000 −2.10090
\(929\) −6.00000 −0.196854 −0.0984268 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) 80.0000 2.62330
\(931\) −6.00000 −0.196642
\(932\) 2.00000 0.0655122
\(933\) −32.0000 −1.04763
\(934\) −66.0000 −2.15959
\(935\) −24.0000 −0.784884
\(936\) 0 0
\(937\) −12.0000 −0.392023 −0.196011 0.980602i \(-0.562799\pi\)
−0.196011 + 0.980602i \(0.562799\pi\)
\(938\) −14.0000 −0.457116
\(939\) 20.0000 0.652675
\(940\) 96.0000 3.13117
\(941\) 8.00000 0.260793 0.130396 0.991462i \(-0.458375\pi\)
0.130396 + 0.991462i \(0.458375\pi\)
\(942\) −32.0000 −1.04262
\(943\) 0 0
\(944\) −28.0000 −0.911322
\(945\) 16.0000 0.520480
\(946\) 30.0000 0.975384
\(947\) 39.0000 1.26733 0.633665 0.773608i \(-0.281550\pi\)
0.633665 + 0.773608i \(0.281550\pi\)
\(948\) −16.0000 −0.519656
\(949\) −26.0000 −0.843996
\(950\) 22.0000 0.713774
\(951\) −24.0000 −0.778253
\(952\) 0 0
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) 2.00000 0.0647524
\(955\) 84.0000 2.71818
\(956\) 4.00000 0.129369
\(957\) −48.0000 −1.55162
\(958\) −74.0000 −2.39083
\(959\) 18.0000 0.581250
\(960\) 64.0000 2.06559
\(961\) −6.00000 −0.193548
\(962\) −16.0000 −0.515861
\(963\) −8.00000 −0.257796
\(964\) 32.0000 1.03065
\(965\) 88.0000 2.83282
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) 0 0
\(969\) 4.00000 0.128499
\(970\) −136.000 −4.36670
\(971\) −60.0000 −1.92549 −0.962746 0.270408i \(-0.912841\pi\)
−0.962746 + 0.270408i \(0.912841\pi\)
\(972\) 20.0000 0.641500
\(973\) −4.00000 −0.128234
\(974\) −56.0000 −1.79436
\(975\) −44.0000 −1.40913
\(976\) 28.0000 0.896258
\(977\) 23.0000 0.735835 0.367918 0.929858i \(-0.380071\pi\)
0.367918 + 0.929858i \(0.380071\pi\)
\(978\) 64.0000 2.04649
\(979\) −30.0000 −0.958804
\(980\) −48.0000 −1.53330
\(981\) 11.0000 0.351203
\(982\) 30.0000 0.957338
\(983\) 19.0000 0.606006 0.303003 0.952990i \(-0.402011\pi\)
0.303003 + 0.952990i \(0.402011\pi\)
\(984\) 0 0
\(985\) −40.0000 −1.27451
\(986\) −32.0000 −1.01909
\(987\) −24.0000 −0.763928
\(988\) 4.00000 0.127257
\(989\) 0 0
\(990\) 24.0000 0.762770
\(991\) −17.0000 −0.540023 −0.270011 0.962857i \(-0.587027\pi\)
−0.270011 + 0.962857i \(0.587027\pi\)
\(992\) 40.0000 1.27000
\(993\) 16.0000 0.507745
\(994\) 8.00000 0.253745
\(995\) 16.0000 0.507234
\(996\) −48.0000 −1.52094
\(997\) 53.0000 1.67853 0.839263 0.543725i \(-0.182987\pi\)
0.839263 + 0.543725i \(0.182987\pi\)
\(998\) 40.0000 1.26618
\(999\) −16.0000 −0.506218
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 \(a_p\))