Properties

Label 89.2.a.a.1.1
Level 89
Weight 2
Character 89.1
Self dual Yes
Analytic conductor 0.711
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 89.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.710668577989\)
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 \(\chi\) = 89.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} +3.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} +3.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} +4.00000 q^{14} +1.00000 q^{15} -1.00000 q^{16} +3.00000 q^{17} +2.00000 q^{18} -5.00000 q^{19} +1.00000 q^{20} +4.00000 q^{21} +2.00000 q^{22} +7.00000 q^{23} -3.00000 q^{24} -4.00000 q^{25} -2.00000 q^{26} +5.00000 q^{27} +4.00000 q^{28} -1.00000 q^{30} -9.00000 q^{31} -5.00000 q^{32} +2.00000 q^{33} -3.00000 q^{34} +4.00000 q^{35} +2.00000 q^{36} -2.00000 q^{37} +5.00000 q^{38} -2.00000 q^{39} -3.00000 q^{40} -4.00000 q^{42} -7.00000 q^{43} +2.00000 q^{44} +2.00000 q^{45} -7.00000 q^{46} -12.0000 q^{47} +1.00000 q^{48} +9.00000 q^{49} +4.00000 q^{50} -3.00000 q^{51} -2.00000 q^{52} -3.00000 q^{53} -5.00000 q^{54} +2.00000 q^{55} -12.0000 q^{56} +5.00000 q^{57} +4.00000 q^{59} -1.00000 q^{60} +6.00000 q^{61} +9.00000 q^{62} +8.00000 q^{63} +7.00000 q^{64} -2.00000 q^{65} -2.00000 q^{66} +12.0000 q^{67} -3.00000 q^{68} -7.00000 q^{69} -4.00000 q^{70} -10.0000 q^{71} -6.00000 q^{72} +7.00000 q^{73} +2.00000 q^{74} +4.00000 q^{75} +5.00000 q^{76} +8.00000 q^{77} +2.00000 q^{78} -6.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +12.0000 q^{83} -4.00000 q^{84} -3.00000 q^{85} +7.00000 q^{86} -6.00000 q^{88} -1.00000 q^{89} -2.00000 q^{90} -8.00000 q^{91} -7.00000 q^{92} +9.00000 q^{93} +12.0000 q^{94} +5.00000 q^{95} +5.00000 q^{96} +9.00000 q^{97} -9.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.00000 0.408248
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 3.00000 1.06066
\(9\) −2.00000 −0.666667
\(10\) 1.00000 0.316228
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 4.00000 1.06904
\(15\) 1.00000 0.258199
\(16\) −1.00000 −0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 2.00000 0.471405
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 1.00000 0.223607
\(21\) 4.00000 0.872872
\(22\) 2.00000 0.426401
\(23\) 7.00000 1.45960 0.729800 0.683660i \(-0.239613\pi\)
0.729800 + 0.683660i \(0.239613\pi\)
\(24\) −3.00000 −0.612372
\(25\) −4.00000 −0.800000
\(26\) −2.00000 −0.392232
\(27\) 5.00000 0.962250
\(28\) 4.00000 0.755929
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −1.00000 −0.182574
\(31\) −9.00000 −1.61645 −0.808224 0.588875i \(-0.799571\pi\)
−0.808224 + 0.588875i \(0.799571\pi\)
\(32\) −5.00000 −0.883883
\(33\) 2.00000 0.348155
\(34\) −3.00000 −0.514496
\(35\) 4.00000 0.676123
\(36\) 2.00000 0.333333
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 5.00000 0.811107
\(39\) −2.00000 −0.320256
\(40\) −3.00000 −0.474342
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −4.00000 −0.617213
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 2.00000 0.301511
\(45\) 2.00000 0.298142
\(46\) −7.00000 −1.03209
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 1.00000 0.144338
\(49\) 9.00000 1.28571
\(50\) 4.00000 0.565685
\(51\) −3.00000 −0.420084
\(52\) −2.00000 −0.277350
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) −5.00000 −0.680414
\(55\) 2.00000 0.269680
\(56\) −12.0000 −1.60357
\(57\) 5.00000 0.662266
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −1.00000 −0.129099
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 9.00000 1.14300
\(63\) 8.00000 1.00791
\(64\) 7.00000 0.875000
\(65\) −2.00000 −0.248069
\(66\) −2.00000 −0.246183
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −3.00000 −0.363803
\(69\) −7.00000 −0.842701
\(70\) −4.00000 −0.478091
\(71\) −10.0000 −1.18678 −0.593391 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) −6.00000 −0.707107
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 2.00000 0.232495
\(75\) 4.00000 0.461880
\(76\) 5.00000 0.573539
\(77\) 8.00000 0.911685
\(78\) 2.00000 0.226455
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −4.00000 −0.436436
\(85\) −3.00000 −0.325396
\(86\) 7.00000 0.754829
\(87\) 0 0
\(88\) −6.00000 −0.639602
\(89\) −1.00000 −0.106000
\(90\) −2.00000 −0.210819
\(91\) −8.00000 −0.838628
\(92\) −7.00000 −0.729800
\(93\) 9.00000 0.933257
\(94\) 12.0000 1.23771
\(95\) 5.00000 0.512989
\(96\) 5.00000 0.510310
\(97\) 9.00000 0.913812 0.456906 0.889515i \(-0.348958\pi\)
0.456906 + 0.889515i \(0.348958\pi\)
\(98\) −9.00000 −0.909137
\(99\) 4.00000 0.402015
\(100\) 4.00000 0.400000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 3.00000 0.297044
\(103\) −9.00000 −0.886796 −0.443398 0.896325i \(-0.646227\pi\)
−0.443398 + 0.896325i \(0.646227\pi\)
\(104\) 6.00000 0.588348
\(105\) −4.00000 −0.390360
\(106\) 3.00000 0.291386
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) −5.00000 −0.481125
\(109\) −19.0000 −1.81987 −0.909935 0.414751i \(-0.863869\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) −2.00000 −0.190693
\(111\) 2.00000 0.189832
\(112\) 4.00000 0.377964
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −5.00000 −0.468293
\(115\) −7.00000 −0.652753
\(116\) 0 0
\(117\) −4.00000 −0.369800
\(118\) −4.00000 −0.368230
\(119\) −12.0000 −1.10004
\(120\) 3.00000 0.273861
\(121\) −7.00000 −0.636364
\(122\) −6.00000 −0.543214
\(123\) 0 0
\(124\) 9.00000 0.808224
\(125\) 9.00000 0.804984
\(126\) −8.00000 −0.712697
\(127\) 3.00000 0.266207 0.133103 0.991102i \(-0.457506\pi\)
0.133103 + 0.991102i \(0.457506\pi\)
\(128\) 3.00000 0.265165
\(129\) 7.00000 0.616316
\(130\) 2.00000 0.175412
\(131\) 16.0000 1.39793 0.698963 0.715158i \(-0.253645\pi\)
0.698963 + 0.715158i \(0.253645\pi\)
\(132\) −2.00000 −0.174078
\(133\) 20.0000 1.73422
\(134\) −12.0000 −1.03664
\(135\) −5.00000 −0.430331
\(136\) 9.00000 0.771744
\(137\) −22.0000 −1.87959 −0.939793 0.341743i \(-0.888983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 7.00000 0.595880
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) −4.00000 −0.338062
\(141\) 12.0000 1.01058
\(142\) 10.0000 0.839181
\(143\) −4.00000 −0.334497
\(144\) 2.00000 0.166667
\(145\) 0 0
\(146\) −7.00000 −0.579324
\(147\) −9.00000 −0.742307
\(148\) 2.00000 0.164399
\(149\) 4.00000 0.327693 0.163846 0.986486i \(-0.447610\pi\)
0.163846 + 0.986486i \(0.447610\pi\)
\(150\) −4.00000 −0.326599
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −15.0000 −1.21666
\(153\) −6.00000 −0.485071
\(154\) −8.00000 −0.644658
\(155\) 9.00000 0.722897
\(156\) 2.00000 0.160128
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 6.00000 0.477334
\(159\) 3.00000 0.237915
\(160\) 5.00000 0.395285
\(161\) −28.0000 −2.20671
\(162\) −1.00000 −0.0785674
\(163\) 25.0000 1.95815 0.979076 0.203497i \(-0.0652307\pi\)
0.979076 + 0.203497i \(0.0652307\pi\)
\(164\) 0 0
\(165\) −2.00000 −0.155700
\(166\) −12.0000 −0.931381
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 12.0000 0.925820
\(169\) −9.00000 −0.692308
\(170\) 3.00000 0.230089
\(171\) 10.0000 0.764719
\(172\) 7.00000 0.533745
\(173\) −1.00000 −0.0760286 −0.0380143 0.999277i \(-0.512103\pi\)
−0.0380143 + 0.999277i \(0.512103\pi\)
\(174\) 0 0
\(175\) 16.0000 1.20949
\(176\) 2.00000 0.150756
\(177\) −4.00000 −0.300658
\(178\) 1.00000 0.0749532
\(179\) 14.0000 1.04641 0.523205 0.852207i \(-0.324736\pi\)
0.523205 + 0.852207i \(0.324736\pi\)
\(180\) −2.00000 −0.149071
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 8.00000 0.592999
\(183\) −6.00000 −0.443533
\(184\) 21.0000 1.54814
\(185\) 2.00000 0.147043
\(186\) −9.00000 −0.659912
\(187\) −6.00000 −0.438763
\(188\) 12.0000 0.875190
\(189\) −20.0000 −1.45479
\(190\) −5.00000 −0.362738
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) −7.00000 −0.505181
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) −9.00000 −0.646162
\(195\) 2.00000 0.143223
\(196\) −9.00000 −0.642857
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) −4.00000 −0.284268
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) −12.0000 −0.848528
\(201\) −12.0000 −0.846415
\(202\) 0 0
\(203\) 0 0
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) 9.00000 0.627060
\(207\) −14.0000 −0.973067
\(208\) −2.00000 −0.138675
\(209\) 10.0000 0.691714
\(210\) 4.00000 0.276026
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 3.00000 0.206041
\(213\) 10.0000 0.685189
\(214\) 10.0000 0.683586
\(215\) 7.00000 0.477396
\(216\) 15.0000 1.02062
\(217\) 36.0000 2.44384
\(218\) 19.0000 1.28684
\(219\) −7.00000 −0.473016
\(220\) −2.00000 −0.134840
\(221\) 6.00000 0.403604
\(222\) −2.00000 −0.134231
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 20.0000 1.33631
\(225\) 8.00000 0.533333
\(226\) −2.00000 −0.133038
\(227\) 24.0000 1.59294 0.796468 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) −5.00000 −0.331133
\(229\) −28.0000 −1.85029 −0.925146 0.379611i \(-0.876058\pi\)
−0.925146 + 0.379611i \(0.876058\pi\)
\(230\) 7.00000 0.461566
\(231\) −8.00000 −0.526361
\(232\) 0 0
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 4.00000 0.261488
\(235\) 12.0000 0.782794
\(236\) −4.00000 −0.260378
\(237\) 6.00000 0.389742
\(238\) 12.0000 0.777844
\(239\) 5.00000 0.323423 0.161712 0.986838i \(-0.448299\pi\)
0.161712 + 0.986838i \(0.448299\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 7.00000 0.449977
\(243\) −16.0000 −1.02640
\(244\) −6.00000 −0.384111
\(245\) −9.00000 −0.574989
\(246\) 0 0
\(247\) −10.0000 −0.636285
\(248\) −27.0000 −1.71450
\(249\) −12.0000 −0.760469
\(250\) −9.00000 −0.569210
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −8.00000 −0.503953
\(253\) −14.0000 −0.880172
\(254\) −3.00000 −0.188237
\(255\) 3.00000 0.187867
\(256\) −17.0000 −1.06250
\(257\) 21.0000 1.30994 0.654972 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) −7.00000 −0.435801
\(259\) 8.00000 0.497096
\(260\) 2.00000 0.124035
\(261\) 0 0
\(262\) −16.0000 −0.988483
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 6.00000 0.369274
\(265\) 3.00000 0.184289
\(266\) −20.0000 −1.22628
\(267\) 1.00000 0.0611990
\(268\) −12.0000 −0.733017
\(269\) −13.0000 −0.792624 −0.396312 0.918116i \(-0.629710\pi\)
−0.396312 + 0.918116i \(0.629710\pi\)
\(270\) 5.00000 0.304290
\(271\) −2.00000 −0.121491 −0.0607457 0.998153i \(-0.519348\pi\)
−0.0607457 + 0.998153i \(0.519348\pi\)
\(272\) −3.00000 −0.181902
\(273\) 8.00000 0.484182
\(274\) 22.0000 1.32907
\(275\) 8.00000 0.482418
\(276\) 7.00000 0.421350
\(277\) −29.0000 −1.74244 −0.871221 0.490892i \(-0.836671\pi\)
−0.871221 + 0.490892i \(0.836671\pi\)
\(278\) 8.00000 0.479808
\(279\) 18.0000 1.07763
\(280\) 12.0000 0.717137
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) −12.0000 −0.714590
\(283\) 10.0000 0.594438 0.297219 0.954809i \(-0.403941\pi\)
0.297219 + 0.954809i \(0.403941\pi\)
\(284\) 10.0000 0.593391
\(285\) −5.00000 −0.296174
\(286\) 4.00000 0.236525
\(287\) 0 0
\(288\) 10.0000 0.589256
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −9.00000 −0.527589
\(292\) −7.00000 −0.409644
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 9.00000 0.524891
\(295\) −4.00000 −0.232889
\(296\) −6.00000 −0.348743
\(297\) −10.0000 −0.580259
\(298\) −4.00000 −0.231714
\(299\) 14.0000 0.809641
\(300\) −4.00000 −0.230940
\(301\) 28.0000 1.61389
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) 5.00000 0.286770
\(305\) −6.00000 −0.343559
\(306\) 6.00000 0.342997
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) −8.00000 −0.455842
\(309\) 9.00000 0.511992
\(310\) −9.00000 −0.511166
\(311\) 28.0000 1.58773 0.793867 0.608091i \(-0.208065\pi\)
0.793867 + 0.608091i \(0.208065\pi\)
\(312\) −6.00000 −0.339683
\(313\) 20.0000 1.13047 0.565233 0.824931i \(-0.308786\pi\)
0.565233 + 0.824931i \(0.308786\pi\)
\(314\) 2.00000 0.112867
\(315\) −8.00000 −0.450749
\(316\) 6.00000 0.337526
\(317\) 17.0000 0.954815 0.477408 0.878682i \(-0.341577\pi\)
0.477408 + 0.878682i \(0.341577\pi\)
\(318\) −3.00000 −0.168232
\(319\) 0 0
\(320\) −7.00000 −0.391312
\(321\) 10.0000 0.558146
\(322\) 28.0000 1.56038
\(323\) −15.0000 −0.834622
\(324\) −1.00000 −0.0555556
\(325\) −8.00000 −0.443760
\(326\) −25.0000 −1.38462
\(327\) 19.0000 1.05070
\(328\) 0 0
\(329\) 48.0000 2.64633
\(330\) 2.00000 0.110096
\(331\) 10.0000 0.549650 0.274825 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) −12.0000 −0.658586
\(333\) 4.00000 0.219199
\(334\) 12.0000 0.656611
\(335\) −12.0000 −0.655630
\(336\) −4.00000 −0.218218
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 9.00000 0.489535
\(339\) −2.00000 −0.108625
\(340\) 3.00000 0.162698
\(341\) 18.0000 0.974755
\(342\) −10.0000 −0.540738
\(343\) −8.00000 −0.431959
\(344\) −21.0000 −1.13224
\(345\) 7.00000 0.376867
\(346\) 1.00000 0.0537603
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) 0 0
\(349\) −8.00000 −0.428230 −0.214115 0.976808i \(-0.568687\pi\)
−0.214115 + 0.976808i \(0.568687\pi\)
\(350\) −16.0000 −0.855236
\(351\) 10.0000 0.533761
\(352\) 10.0000 0.533002
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 4.00000 0.212598
\(355\) 10.0000 0.530745
\(356\) 1.00000 0.0529999
\(357\) 12.0000 0.635107
\(358\) −14.0000 −0.739923
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 6.00000 0.316228
\(361\) 6.00000 0.315789
\(362\) −22.0000 −1.15629
\(363\) 7.00000 0.367405
\(364\) 8.00000 0.419314
\(365\) −7.00000 −0.366397
\(366\) 6.00000 0.313625
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) −7.00000 −0.364900
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) 12.0000 0.623009
\(372\) −9.00000 −0.466628
\(373\) −37.0000 −1.91579 −0.957894 0.287123i \(-0.907301\pi\)
−0.957894 + 0.287123i \(0.907301\pi\)
\(374\) 6.00000 0.310253
\(375\) −9.00000 −0.464758
\(376\) −36.0000 −1.85656
\(377\) 0 0
\(378\) 20.0000 1.02869
\(379\) 17.0000 0.873231 0.436616 0.899648i \(-0.356177\pi\)
0.436616 + 0.899648i \(0.356177\pi\)
\(380\) −5.00000 −0.256495
\(381\) −3.00000 −0.153695
\(382\) −15.0000 −0.767467
\(383\) 13.0000 0.664269 0.332134 0.943232i \(-0.392231\pi\)
0.332134 + 0.943232i \(0.392231\pi\)
\(384\) −3.00000 −0.153093
\(385\) −8.00000 −0.407718
\(386\) 14.0000 0.712581
\(387\) 14.0000 0.711660
\(388\) −9.00000 −0.456906
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) −2.00000 −0.101274
\(391\) 21.0000 1.06202
\(392\) 27.0000 1.36371
\(393\) −16.0000 −0.807093
\(394\) −8.00000 −0.403034
\(395\) 6.00000 0.301893
\(396\) −4.00000 −0.201008
\(397\) 4.00000 0.200754 0.100377 0.994949i \(-0.467995\pi\)
0.100377 + 0.994949i \(0.467995\pi\)
\(398\) −2.00000 −0.100251
\(399\) −20.0000 −1.00125
\(400\) 4.00000 0.200000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 12.0000 0.598506
\(403\) −18.0000 −0.896644
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 4.00000 0.198273
\(408\) −9.00000 −0.445566
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 0 0
\(411\) 22.0000 1.08518
\(412\) 9.00000 0.443398
\(413\) −16.0000 −0.787309
\(414\) 14.0000 0.688062
\(415\) −12.0000 −0.589057
\(416\) −10.0000 −0.490290
\(417\) 8.00000 0.391762
\(418\) −10.0000 −0.489116
\(419\) 15.0000 0.732798 0.366399 0.930458i \(-0.380591\pi\)
0.366399 + 0.930458i \(0.380591\pi\)
\(420\) 4.00000 0.195180
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 12.0000 0.584151
\(423\) 24.0000 1.16692
\(424\) −9.00000 −0.437079
\(425\) −12.0000 −0.582086
\(426\) −10.0000 −0.484502
\(427\) −24.0000 −1.16144
\(428\) 10.0000 0.483368
\(429\) 4.00000 0.193122
\(430\) −7.00000 −0.337570
\(431\) 27.0000 1.30054 0.650272 0.759701i \(-0.274655\pi\)
0.650272 + 0.759701i \(0.274655\pi\)
\(432\) −5.00000 −0.240563
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) −36.0000 −1.72806
\(435\) 0 0
\(436\) 19.0000 0.909935
\(437\) −35.0000 −1.67428
\(438\) 7.00000 0.334473
\(439\) −11.0000 −0.525001 −0.262501 0.964932i \(-0.584547\pi\)
−0.262501 + 0.964932i \(0.584547\pi\)
\(440\) 6.00000 0.286039
\(441\) −18.0000 −0.857143
\(442\) −6.00000 −0.285391
\(443\) −14.0000 −0.665160 −0.332580 0.943075i \(-0.607919\pi\)
−0.332580 + 0.943075i \(0.607919\pi\)
\(444\) −2.00000 −0.0949158
\(445\) 1.00000 0.0474045
\(446\) 16.0000 0.757622
\(447\) −4.00000 −0.189194
\(448\) −28.0000 −1.32288
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) −8.00000 −0.377124
\(451\) 0 0
\(452\) −2.00000 −0.0940721
\(453\) 8.00000 0.375873
\(454\) −24.0000 −1.12638
\(455\) 8.00000 0.375046
\(456\) 15.0000 0.702439
\(457\) −2.00000 −0.0935561 −0.0467780 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) 28.0000 1.30835
\(459\) 15.0000 0.700140
\(460\) 7.00000 0.326377
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 8.00000 0.372194
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 0 0
\(465\) −9.00000 −0.417365
\(466\) 26.0000 1.20443
\(467\) 22.0000 1.01804 0.509019 0.860755i \(-0.330008\pi\)
0.509019 + 0.860755i \(0.330008\pi\)
\(468\) 4.00000 0.184900
\(469\) −48.0000 −2.21643
\(470\) −12.0000 −0.553519
\(471\) 2.00000 0.0921551
\(472\) 12.0000 0.552345
\(473\) 14.0000 0.643721
\(474\) −6.00000 −0.275589
\(475\) 20.0000 0.917663
\(476\) 12.0000 0.550019
\(477\) 6.00000 0.274721
\(478\) −5.00000 −0.228695
\(479\) −26.0000 −1.18797 −0.593985 0.804476i \(-0.702446\pi\)
−0.593985 + 0.804476i \(0.702446\pi\)
\(480\) −5.00000 −0.228218
\(481\) −4.00000 −0.182384
\(482\) −10.0000 −0.455488
\(483\) 28.0000 1.27404
\(484\) 7.00000 0.318182
\(485\) −9.00000 −0.408669
\(486\) 16.0000 0.725775
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) 18.0000 0.814822
\(489\) −25.0000 −1.13054
\(490\) 9.00000 0.406579
\(491\) −25.0000 −1.12823 −0.564117 0.825695i \(-0.690783\pi\)
−0.564117 + 0.825695i \(0.690783\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 10.0000 0.449921
\(495\) −4.00000 −0.179787
\(496\) 9.00000 0.404112
\(497\) 40.0000 1.79425
\(498\) 12.0000 0.537733
\(499\) −28.0000 −1.25345 −0.626726 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) −9.00000 −0.402492
\(501\) 12.0000 0.536120
\(502\) 12.0000 0.535586
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 24.0000 1.06904
\(505\) 0 0
\(506\) 14.0000 0.622376
\(507\) 9.00000 0.399704
\(508\) −3.00000 −0.133103
\(509\) 3.00000 0.132973 0.0664863 0.997787i \(-0.478821\pi\)
0.0664863 + 0.997787i \(0.478821\pi\)
\(510\) −3.00000 −0.132842
\(511\) −28.0000 −1.23865
\(512\) 11.0000 0.486136
\(513\) −25.0000 −1.10378
\(514\) −21.0000 −0.926270
\(515\) 9.00000 0.396587
\(516\) −7.00000 −0.308158
\(517\) 24.0000 1.05552
\(518\) −8.00000 −0.351500
\(519\) 1.00000 0.0438951
\(520\) −6.00000 −0.263117
\(521\) 40.0000 1.75243 0.876216 0.481919i \(-0.160060\pi\)
0.876216 + 0.481919i \(0.160060\pi\)
\(522\) 0 0
\(523\) 28.0000 1.22435 0.612177 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) −16.0000 −0.698963
\(525\) −16.0000 −0.698297
\(526\) 16.0000 0.697633
\(527\) −27.0000 −1.17614
\(528\) −2.00000 −0.0870388
\(529\) 26.0000 1.13043
\(530\) −3.00000 −0.130312
\(531\) −8.00000 −0.347170
\(532\) −20.0000 −0.867110
\(533\) 0 0
\(534\) −1.00000 −0.0432742
\(535\) 10.0000 0.432338
\(536\) 36.0000 1.55496
\(537\) −14.0000 −0.604145
\(538\) 13.0000 0.560470
\(539\) −18.0000 −0.775315
\(540\) 5.00000 0.215166
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 2.00000 0.0859074
\(543\) −22.0000 −0.944110
\(544\) −15.0000 −0.643120
\(545\) 19.0000 0.813871
\(546\) −8.00000 −0.342368
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 22.0000 0.939793
\(549\) −12.0000 −0.512148
\(550\) −8.00000 −0.341121
\(551\) 0 0
\(552\) −21.0000 −0.893819
\(553\) 24.0000 1.02058
\(554\) 29.0000 1.23209
\(555\) −2.00000 −0.0848953
\(556\) 8.00000 0.339276
\(557\) 32.0000 1.35588 0.677942 0.735116i \(-0.262872\pi\)
0.677942 + 0.735116i \(0.262872\pi\)
\(558\) −18.0000 −0.762001
\(559\) −14.0000 −0.592137
\(560\) −4.00000 −0.169031
\(561\) 6.00000 0.253320
\(562\) 30.0000 1.26547
\(563\) 5.00000 0.210725 0.105362 0.994434i \(-0.466400\pi\)
0.105362 + 0.994434i \(0.466400\pi\)
\(564\) −12.0000 −0.505291
\(565\) −2.00000 −0.0841406
\(566\) −10.0000 −0.420331
\(567\) −4.00000 −0.167984
\(568\) −30.0000 −1.25877
\(569\) 14.0000 0.586911 0.293455 0.955973i \(-0.405195\pi\)
0.293455 + 0.955973i \(0.405195\pi\)
\(570\) 5.00000 0.209427
\(571\) 25.0000 1.04622 0.523109 0.852266i \(-0.324772\pi\)
0.523109 + 0.852266i \(0.324772\pi\)
\(572\) 4.00000 0.167248
\(573\) −15.0000 −0.626634
\(574\) 0 0
\(575\) −28.0000 −1.16768
\(576\) −14.0000 −0.583333
\(577\) 28.0000 1.16566 0.582828 0.812596i \(-0.301946\pi\)
0.582828 + 0.812596i \(0.301946\pi\)
\(578\) 8.00000 0.332756
\(579\) 14.0000 0.581820
\(580\) 0 0
\(581\) −48.0000 −1.99138
\(582\) 9.00000 0.373062
\(583\) 6.00000 0.248495
\(584\) 21.0000 0.868986
\(585\) 4.00000 0.165380
\(586\) 18.0000 0.743573
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) 9.00000 0.371154
\(589\) 45.0000 1.85419
\(590\) 4.00000 0.164677
\(591\) −8.00000 −0.329076
\(592\) 2.00000 0.0821995
\(593\) −24.0000 −0.985562 −0.492781 0.870153i \(-0.664020\pi\)
−0.492781 + 0.870153i \(0.664020\pi\)
\(594\) 10.0000 0.410305
\(595\) 12.0000 0.491952
\(596\) −4.00000 −0.163846
\(597\) −2.00000 −0.0818546
\(598\) −14.0000 −0.572503
\(599\) −1.00000 −0.0408589 −0.0204294 0.999791i \(-0.506503\pi\)
−0.0204294 + 0.999791i \(0.506503\pi\)
\(600\) 12.0000 0.489898
\(601\) 19.0000 0.775026 0.387513 0.921864i \(-0.373334\pi\)
0.387513 + 0.921864i \(0.373334\pi\)
\(602\) −28.0000 −1.14119
\(603\) −24.0000 −0.977356
\(604\) 8.00000 0.325515
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) −10.0000 −0.405887 −0.202944 0.979190i \(-0.565051\pi\)
−0.202944 + 0.979190i \(0.565051\pi\)
\(608\) 25.0000 1.01388
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) −24.0000 −0.970936
\(612\) 6.00000 0.242536
\(613\) −11.0000 −0.444286 −0.222143 0.975014i \(-0.571305\pi\)
−0.222143 + 0.975014i \(0.571305\pi\)
\(614\) 2.00000 0.0807134
\(615\) 0 0
\(616\) 24.0000 0.966988
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) −9.00000 −0.362033
\(619\) −28.0000 −1.12542 −0.562708 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) −9.00000 −0.361449
\(621\) 35.0000 1.40450
\(622\) −28.0000 −1.12270
\(623\) 4.00000 0.160257
\(624\) 2.00000 0.0800641
\(625\) 11.0000 0.440000
\(626\) −20.0000 −0.799361
\(627\) −10.0000 −0.399362
\(628\) 2.00000 0.0798087
\(629\) −6.00000 −0.239236
\(630\) 8.00000 0.318728
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −18.0000 −0.716002
\(633\) 12.0000 0.476957
\(634\) −17.0000 −0.675156
\(635\) −3.00000 −0.119051
\(636\) −3.00000 −0.118958
\(637\) 18.0000 0.713186
\(638\) 0 0
\(639\) 20.0000 0.791188
\(640\) −3.00000 −0.118585
\(641\) 25.0000 0.987441 0.493720 0.869621i \(-0.335637\pi\)
0.493720 + 0.869621i \(0.335637\pi\)
\(642\) −10.0000 −0.394669
\(643\) −8.00000 −0.315489 −0.157745 0.987480i \(-0.550422\pi\)
−0.157745 + 0.987480i \(0.550422\pi\)
\(644\) 28.0000 1.10335
\(645\) −7.00000 −0.275625
\(646\) 15.0000 0.590167
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) 3.00000 0.117851
\(649\) −8.00000 −0.314027
\(650\) 8.00000 0.313786
\(651\) −36.0000 −1.41095
\(652\) −25.0000 −0.979076
\(653\) 8.00000 0.313064 0.156532 0.987673i \(-0.449969\pi\)
0.156532 + 0.987673i \(0.449969\pi\)
\(654\) −19.0000 −0.742959
\(655\) −16.0000 −0.625172
\(656\) 0 0
\(657\) −14.0000 −0.546192
\(658\) −48.0000 −1.87123
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 2.00000 0.0778499
\(661\) 34.0000 1.32245 0.661223 0.750189i \(-0.270038\pi\)
0.661223 + 0.750189i \(0.270038\pi\)
\(662\) −10.0000 −0.388661
\(663\) −6.00000 −0.233021
\(664\) 36.0000 1.39707
\(665\) −20.0000 −0.775567
\(666\) −4.00000 −0.154997
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) 16.0000 0.618596
\(670\) 12.0000 0.463600
\(671\) −12.0000 −0.463255
\(672\) −20.0000 −0.771517
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) −8.00000 −0.308148
\(675\) −20.0000 −0.769800
\(676\) 9.00000 0.346154
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 2.00000 0.0768095
\(679\) −36.0000 −1.38155
\(680\) −9.00000 −0.345134
\(681\) −24.0000 −0.919682
\(682\) −18.0000 −0.689256
\(683\) 9.00000 0.344375 0.172188 0.985064i \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) −10.0000 −0.382360
\(685\) 22.0000 0.840577
\(686\) 8.00000 0.305441
\(687\) 28.0000 1.06827
\(688\) 7.00000 0.266872
\(689\) −6.00000 −0.228582
\(690\) −7.00000 −0.266485
\(691\) 18.0000 0.684752 0.342376 0.939563i \(-0.388768\pi\)
0.342376 + 0.939563i \(0.388768\pi\)
\(692\) 1.00000 0.0380143
\(693\) −16.0000 −0.607790
\(694\) 2.00000 0.0759190
\(695\) 8.00000 0.303457
\(696\) 0 0
\(697\) 0 0
\(698\) 8.00000 0.302804
\(699\) 26.0000 0.983410
\(700\) −16.0000 −0.604743
\(701\) 13.0000 0.491003 0.245502 0.969396i \(-0.421047\pi\)
0.245502 + 0.969396i \(0.421047\pi\)
\(702\) −10.0000 −0.377426
\(703\) 10.0000 0.377157
\(704\) −14.0000 −0.527645
\(705\) −12.0000 −0.451946
\(706\) −14.0000 −0.526897
\(707\) 0 0
\(708\) 4.00000 0.150329
\(709\) 50.0000 1.87779 0.938895 0.344204i \(-0.111851\pi\)
0.938895 + 0.344204i \(0.111851\pi\)
\(710\) −10.0000 −0.375293
\(711\) 12.0000 0.450035
\(712\) −3.00000 −0.112430
\(713\) −63.0000 −2.35937
\(714\) −12.0000 −0.449089
\(715\) 4.00000 0.149592
\(716\) −14.0000 −0.523205
\(717\) −5.00000 −0.186728
\(718\) 0 0
\(719\) −9.00000 −0.335643 −0.167822 0.985817i \(-0.553673\pi\)
−0.167822 + 0.985817i \(0.553673\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 36.0000 1.34071
\(722\) −6.00000 −0.223297
\(723\) −10.0000 −0.371904
\(724\) −22.0000 −0.817624
\(725\) 0 0
\(726\) −7.00000 −0.259794
\(727\) 13.0000 0.482143 0.241072 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) −24.0000 −0.889499
\(729\) 13.0000 0.481481
\(730\) 7.00000 0.259082
\(731\) −21.0000 −0.776713
\(732\) 6.00000 0.221766
\(733\) 1.00000 0.0369358 0.0184679 0.999829i \(-0.494121\pi\)
0.0184679 + 0.999829i \(0.494121\pi\)
\(734\) 8.00000 0.295285
\(735\) 9.00000 0.331970
\(736\) −35.0000 −1.29012
\(737\) −24.0000 −0.884051
\(738\) 0 0
\(739\) −33.0000 −1.21392 −0.606962 0.794731i \(-0.707612\pi\)
−0.606962 + 0.794731i \(0.707612\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 10.0000 0.367359
\(742\) −12.0000 −0.440534
\(743\) 39.0000 1.43077 0.715386 0.698730i \(-0.246251\pi\)
0.715386 + 0.698730i \(0.246251\pi\)
\(744\) 27.0000 0.989868
\(745\) −4.00000 −0.146549
\(746\) 37.0000 1.35467
\(747\) −24.0000 −0.878114
\(748\) 6.00000 0.219382
\(749\) 40.0000 1.46157
\(750\) 9.00000 0.328634
\(751\) 10.0000 0.364905 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(752\) 12.0000 0.437595
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 20.0000 0.727393
\(757\) 11.0000 0.399802 0.199901 0.979816i \(-0.435938\pi\)
0.199901 + 0.979816i \(0.435938\pi\)
\(758\) −17.0000 −0.617468
\(759\) 14.0000 0.508168
\(760\) 15.0000 0.544107
\(761\) −25.0000 −0.906249 −0.453125 0.891447i \(-0.649691\pi\)
−0.453125 + 0.891447i \(0.649691\pi\)
\(762\) 3.00000 0.108679
\(763\) 76.0000 2.75138
\(764\) −15.0000 −0.542681
\(765\) 6.00000 0.216930
\(766\) −13.0000 −0.469709
\(767\) 8.00000 0.288863
\(768\) 17.0000 0.613435
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 8.00000 0.288300
\(771\) −21.0000 −0.756297
\(772\) 14.0000 0.503871
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) −14.0000 −0.503220
\(775\) 36.0000 1.29316
\(776\) 27.0000 0.969244
\(777\) −8.00000 −0.286998
\(778\) −12.0000 −0.430221
\(779\) 0 0
\(780\) −2.00000 −0.0716115
\(781\) 20.0000 0.715656
\(782\) −21.0000 −0.750958
\(783\) 0 0
\(784\) −9.00000 −0.321429
\(785\) 2.00000 0.0713831
\(786\) 16.0000 0.570701
\(787\) −31.0000 −1.10503 −0.552515 0.833503i \(-0.686332\pi\)
−0.552515 + 0.833503i \(0.686332\pi\)
\(788\) −8.00000 −0.284988
\(789\) 16.0000 0.569615
\(790\) −6.00000 −0.213470
\(791\) −8.00000 −0.284447
\(792\) 12.0000 0.426401
\(793\) 12.0000 0.426132
\(794\) −4.00000 −0.141955
\(795\) −3.00000 −0.106399
\(796\) −2.00000 −0.0708881
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 20.0000 0.707992
\(799\) −36.0000 −1.27359
\(800\) 20.0000 0.707107
\(801\) 2.00000 0.0706665
\(802\) 18.0000 0.635602
\(803\) −14.0000 −0.494049
\(804\) 12.0000 0.423207
\(805\) 28.0000 0.986870
\(806\) 18.0000 0.634023
\(807\) 13.0000 0.457622
\(808\) 0 0
\(809\) −9.00000 −0.316423 −0.158212 0.987405i \(-0.550573\pi\)
−0.158212 + 0.987405i \(0.550573\pi\)
\(810\) 1.00000 0.0351364
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 2.00000 0.0701431
\(814\) −4.00000 −0.140200
\(815\) −25.0000 −0.875712
\(816\) 3.00000 0.105021
\(817\) 35.0000 1.22449
\(818\) 18.0000 0.629355
\(819\) 16.0000 0.559085
\(820\) 0 0
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) −22.0000 −0.767338
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) −27.0000 −0.940590
\(825\) −8.00000 −0.278524
\(826\) 16.0000 0.556711
\(827\) 17.0000 0.591148 0.295574 0.955320i \(-0.404489\pi\)
0.295574 + 0.955320i \(0.404489\pi\)
\(828\) 14.0000 0.486534
\(829\) 20.0000 0.694629 0.347314 0.937749i \(-0.387094\pi\)
0.347314 + 0.937749i \(0.387094\pi\)
\(830\) 12.0000 0.416526
\(831\) 29.0000 1.00600
\(832\) 14.0000 0.485363
\(833\) 27.0000 0.935495
\(834\) −8.00000 −0.277017
\(835\) 12.0000 0.415277
\(836\) −10.0000 −0.345857
\(837\) −45.0000 −1.55543
\(838\) −15.0000 −0.518166
\(839\) −51.0000 −1.76072 −0.880358 0.474310i \(-0.842698\pi\)
−0.880358 + 0.474310i \(0.842698\pi\)
\(840\) −12.0000 −0.414039
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 30.0000 1.03325
\(844\) 12.0000 0.413057
\(845\) 9.00000 0.309609
\(846\) −24.0000 −0.825137
\(847\) 28.0000 0.962091
\(848\) 3.00000 0.103020
\(849\) −10.0000 −0.343199
\(850\) 12.0000 0.411597
\(851\) −14.0000 −0.479914
\(852\) −10.0000 −0.342594
\(853\) −8.00000 −0.273915 −0.136957 0.990577i \(-0.543732\pi\)
−0.136957 + 0.990577i \(0.543732\pi\)
\(854\) 24.0000 0.821263
\(855\) −10.0000 −0.341993
\(856\) −30.0000 −1.02538
\(857\) 4.00000 0.136637 0.0683187 0.997664i \(-0.478237\pi\)
0.0683187 + 0.997664i \(0.478237\pi\)
\(858\) −4.00000 −0.136558
\(859\) 20.0000 0.682391 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) −7.00000 −0.238698
\(861\) 0 0
\(862\) −27.0000 −0.919624
\(863\) 43.0000 1.46374 0.731869 0.681446i \(-0.238649\pi\)
0.731869 + 0.681446i \(0.238649\pi\)
\(864\) −25.0000 −0.850517
\(865\) 1.00000 0.0340010
\(866\) 0 0
\(867\) 8.00000 0.271694
\(868\) −36.0000 −1.22192
\(869\) 12.0000 0.407072
\(870\) 0 0
\(871\) 24.0000 0.813209
\(872\) −57.0000 −1.93026
\(873\) −18.0000 −0.609208
\(874\) 35.0000 1.18389
\(875\) −36.0000 −1.21702
\(876\) 7.00000 0.236508
\(877\) −36.0000 −1.21563 −0.607817 0.794077i \(-0.707955\pi\)
−0.607817 + 0.794077i \(0.707955\pi\)
\(878\) 11.0000 0.371232
\(879\) 18.0000 0.607125
\(880\) −2.00000 −0.0674200
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 18.0000 0.606092
\(883\) −37.0000 −1.24515 −0.622575 0.782560i \(-0.713913\pi\)
−0.622575 + 0.782560i \(0.713913\pi\)
\(884\) −6.00000 −0.201802
\(885\) 4.00000 0.134459
\(886\) 14.0000 0.470339
\(887\) −45.0000 −1.51095 −0.755476 0.655176i \(-0.772594\pi\)
−0.755476 + 0.655176i \(0.772594\pi\)
\(888\) 6.00000 0.201347
\(889\) −12.0000 −0.402467
\(890\) −1.00000 −0.0335201
\(891\) −2.00000 −0.0670025
\(892\) 16.0000 0.535720
\(893\) 60.0000 2.00782
\(894\) 4.00000 0.133780
\(895\) −14.0000 −0.467968
\(896\) −12.0000 −0.400892
\(897\) −14.0000 −0.467446
\(898\) 9.00000 0.300334
\(899\) 0 0
\(900\) −8.00000 −0.266667
\(901\) −9.00000 −0.299833
\(902\) 0 0
\(903\) −28.0000 −0.931782
\(904\) 6.00000 0.199557
\(905\) −22.0000 −0.731305
\(906\) −8.00000 −0.265782
\(907\) 2.00000 0.0664089 0.0332045 0.999449i \(-0.489429\pi\)
0.0332045 + 0.999449i \(0.489429\pi\)
\(908\) −24.0000 −0.796468
\(909\) 0 0
\(910\) −8.00000 −0.265197
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) −5.00000 −0.165567
\(913\) −24.0000 −0.794284
\(914\) 2.00000 0.0661541
\(915\) 6.00000 0.198354
\(916\) 28.0000 0.925146
\(917\) −64.0000 −2.11347
\(918\) −15.0000 −0.495074
\(919\) −25.0000 −0.824674 −0.412337 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(920\) −21.0000 −0.692349
\(921\) 2.00000 0.0659022
\(922\) 30.0000 0.987997
\(923\) −20.0000 −0.658308
\(924\) 8.00000 0.263181
\(925\) 8.00000 0.263038
\(926\) 20.0000 0.657241
\(927\) 18.0000 0.591198
\(928\) 0 0
\(929\) 7.00000 0.229663 0.114831 0.993385i \(-0.463367\pi\)
0.114831 + 0.993385i \(0.463367\pi\)
\(930\) 9.00000 0.295122
\(931\) −45.0000 −1.47482
\(932\) 26.0000 0.851658
\(933\) −28.0000 −0.916679
\(934\) −22.0000 −0.719862
\(935\) 6.00000 0.196221
\(936\) −12.0000 −0.392232
\(937\) 57.0000 1.86211 0.931054 0.364880i \(-0.118890\pi\)
0.931054 + 0.364880i \(0.118890\pi\)
\(938\) 48.0000 1.56726
\(939\) −20.0000 −0.652675
\(940\) −12.0000 −0.391397
\(941\) −28.0000 −0.912774 −0.456387 0.889781i \(-0.650857\pi\)
−0.456387 + 0.889781i \(0.650857\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 0 0
\(944\) −4.00000 −0.130189
\(945\) 20.0000 0.650600
\(946\) −14.0000 −0.455179
\(947\) −8.00000 −0.259965 −0.129983 0.991516i \(-0.541492\pi\)
−0.129983 + 0.991516i \(0.541492\pi\)
\(948\) −6.00000 −0.194871
\(949\) 14.0000 0.454459
\(950\) −20.0000 −0.648886
\(951\) −17.0000 −0.551263
\(952\) −36.0000 −1.16677
\(953\) −12.0000 −0.388718 −0.194359 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) −6.00000 −0.194257
\(955\) −15.0000 −0.485389
\(956\) −5.00000 −0.161712
\(957\) 0 0
\(958\) 26.0000 0.840022
\(959\) 88.0000 2.84167
\(960\) 7.00000 0.225924
\(961\) 50.0000 1.61290
\(962\) 4.00000 0.128965
\(963\) 20.0000 0.644491
\(964\) −10.0000 −0.322078
\(965\) 14.0000 0.450676
\(966\) −28.0000 −0.900885
\(967\) −19.0000 −0.610999 −0.305499 0.952192i \(-0.598823\pi\)
−0.305499 + 0.952192i \(0.598823\pi\)
\(968\) −21.0000 −0.674966
\(969\) 15.0000 0.481869
\(970\) 9.00000 0.288973
\(971\) −24.0000 −0.770197 −0.385098 0.922876i \(-0.625832\pi\)
−0.385098 + 0.922876i \(0.625832\pi\)
\(972\) 16.0000 0.513200
\(973\) 32.0000 1.02587
\(974\) −20.0000 −0.640841
\(975\) 8.00000 0.256205
\(976\) −6.00000 −0.192055
\(977\) −9.00000 −0.287936 −0.143968 0.989582i \(-0.545986\pi\)
−0.143968 + 0.989582i \(0.545986\pi\)
\(978\) 25.0000 0.799412
\(979\) 2.00000 0.0639203
\(980\) 9.00000 0.287494
\(981\) 38.0000 1.21325
\(982\) 25.0000 0.797782
\(983\) 40.0000 1.27580 0.637901 0.770118i \(-0.279803\pi\)
0.637901 + 0.770118i \(0.279803\pi\)
\(984\) 0 0
\(985\) −8.00000 −0.254901
\(986\) 0 0
\(987\) −48.0000 −1.52786
\(988\) 10.0000 0.318142
\(989\) −49.0000 −1.55811
\(990\) 4.00000 0.127128
\(991\) −25.0000 −0.794151 −0.397076 0.917786i \(-0.629975\pi\)
−0.397076 + 0.917786i \(0.629975\pi\)
\(992\) 45.0000 1.42875
\(993\) −10.0000 −0.317340
\(994\) −40.0000 −1.26872
\(995\) −2.00000 −0.0634043
\(996\) 12.0000 0.380235
\(997\) 10.0000 0.316703 0.158352 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) 28.0000 0.886325
\(999\) −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 \(a_p\))