Properties

Label 8041.2.a.g.1.11
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.20191 q^{2} -3.02493 q^{3} +2.84839 q^{4} -2.51341 q^{5} +6.66061 q^{6} +0.0943373 q^{7} -1.86807 q^{8} +6.15021 q^{9} +O(q^{10})\) \(q-2.20191 q^{2} -3.02493 q^{3} +2.84839 q^{4} -2.51341 q^{5} +6.66061 q^{6} +0.0943373 q^{7} -1.86807 q^{8} +6.15021 q^{9} +5.53430 q^{10} -1.00000 q^{11} -8.61618 q^{12} -0.312302 q^{13} -0.207722 q^{14} +7.60290 q^{15} -1.58346 q^{16} +1.00000 q^{17} -13.5422 q^{18} -1.98225 q^{19} -7.15918 q^{20} -0.285364 q^{21} +2.20191 q^{22} -1.69155 q^{23} +5.65079 q^{24} +1.31725 q^{25} +0.687659 q^{26} -9.52917 q^{27} +0.268709 q^{28} +8.36378 q^{29} -16.7409 q^{30} +0.536821 q^{31} +7.22277 q^{32} +3.02493 q^{33} -2.20191 q^{34} -0.237109 q^{35} +17.5182 q^{36} +4.53940 q^{37} +4.36474 q^{38} +0.944692 q^{39} +4.69524 q^{40} -5.00226 q^{41} +0.628344 q^{42} +1.00000 q^{43} -2.84839 q^{44} -15.4580 q^{45} +3.72464 q^{46} +7.01459 q^{47} +4.78985 q^{48} -6.99110 q^{49} -2.90045 q^{50} -3.02493 q^{51} -0.889558 q^{52} +1.75407 q^{53} +20.9823 q^{54} +2.51341 q^{55} -0.176229 q^{56} +5.99618 q^{57} -18.4163 q^{58} -10.7882 q^{59} +21.6560 q^{60} +11.3461 q^{61} -1.18203 q^{62} +0.580194 q^{63} -12.7369 q^{64} +0.784944 q^{65} -6.66061 q^{66} -4.32328 q^{67} +2.84839 q^{68} +5.11683 q^{69} +0.522091 q^{70} -16.1463 q^{71} -11.4890 q^{72} +1.64407 q^{73} -9.99533 q^{74} -3.98458 q^{75} -5.64623 q^{76} -0.0943373 q^{77} -2.08012 q^{78} -9.53631 q^{79} +3.97988 q^{80} +10.3744 q^{81} +11.0145 q^{82} -13.4228 q^{83} -0.812827 q^{84} -2.51341 q^{85} -2.20191 q^{86} -25.2999 q^{87} +1.86807 q^{88} -2.33778 q^{89} +34.0371 q^{90} -0.0294617 q^{91} -4.81820 q^{92} -1.62385 q^{93} -15.4455 q^{94} +4.98222 q^{95} -21.8484 q^{96} -1.95333 q^{97} +15.3937 q^{98} -6.15021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20191 −1.55698 −0.778491 0.627655i \(-0.784015\pi\)
−0.778491 + 0.627655i \(0.784015\pi\)
\(3\) −3.02493 −1.74644 −0.873222 0.487322i \(-0.837974\pi\)
−0.873222 + 0.487322i \(0.837974\pi\)
\(4\) 2.84839 1.42419
\(5\) −2.51341 −1.12403 −0.562016 0.827126i \(-0.689974\pi\)
−0.562016 + 0.827126i \(0.689974\pi\)
\(6\) 6.66061 2.71918
\(7\) 0.0943373 0.0356562 0.0178281 0.999841i \(-0.494325\pi\)
0.0178281 + 0.999841i \(0.494325\pi\)
\(8\) −1.86807 −0.660464
\(9\) 6.15021 2.05007
\(10\) 5.53430 1.75010
\(11\) −1.00000 −0.301511
\(12\) −8.61618 −2.48728
\(13\) −0.312302 −0.0866170 −0.0433085 0.999062i \(-0.513790\pi\)
−0.0433085 + 0.999062i \(0.513790\pi\)
\(14\) −0.207722 −0.0555160
\(15\) 7.60290 1.96306
\(16\) −1.58346 −0.395864
\(17\) 1.00000 0.242536
\(18\) −13.5422 −3.19192
\(19\) −1.98225 −0.454760 −0.227380 0.973806i \(-0.573016\pi\)
−0.227380 + 0.973806i \(0.573016\pi\)
\(20\) −7.15918 −1.60084
\(21\) −0.285364 −0.0622715
\(22\) 2.20191 0.469448
\(23\) −1.69155 −0.352713 −0.176357 0.984326i \(-0.556431\pi\)
−0.176357 + 0.984326i \(0.556431\pi\)
\(24\) 5.65079 1.15346
\(25\) 1.31725 0.263449
\(26\) 0.687659 0.134861
\(27\) −9.52917 −1.83389
\(28\) 0.268709 0.0507813
\(29\) 8.36378 1.55312 0.776558 0.630046i \(-0.216964\pi\)
0.776558 + 0.630046i \(0.216964\pi\)
\(30\) −16.7409 −3.05645
\(31\) 0.536821 0.0964160 0.0482080 0.998837i \(-0.484649\pi\)
0.0482080 + 0.998837i \(0.484649\pi\)
\(32\) 7.22277 1.27682
\(33\) 3.02493 0.526573
\(34\) −2.20191 −0.377624
\(35\) −0.237109 −0.0400787
\(36\) 17.5182 2.91970
\(37\) 4.53940 0.746272 0.373136 0.927777i \(-0.378282\pi\)
0.373136 + 0.927777i \(0.378282\pi\)
\(38\) 4.36474 0.708054
\(39\) 0.944692 0.151272
\(40\) 4.69524 0.742383
\(41\) −5.00226 −0.781222 −0.390611 0.920556i \(-0.627736\pi\)
−0.390611 + 0.920556i \(0.627736\pi\)
\(42\) 0.628344 0.0969556
\(43\) 1.00000 0.152499
\(44\) −2.84839 −0.429411
\(45\) −15.4580 −2.30434
\(46\) 3.72464 0.549169
\(47\) 7.01459 1.02318 0.511592 0.859229i \(-0.329056\pi\)
0.511592 + 0.859229i \(0.329056\pi\)
\(48\) 4.78985 0.691355
\(49\) −6.99110 −0.998729
\(50\) −2.90045 −0.410186
\(51\) −3.02493 −0.423575
\(52\) −0.889558 −0.123359
\(53\) 1.75407 0.240941 0.120470 0.992717i \(-0.461560\pi\)
0.120470 + 0.992717i \(0.461560\pi\)
\(54\) 20.9823 2.85533
\(55\) 2.51341 0.338909
\(56\) −0.176229 −0.0235496
\(57\) 5.99618 0.794214
\(58\) −18.4163 −2.41817
\(59\) −10.7882 −1.40451 −0.702253 0.711927i \(-0.747823\pi\)
−0.702253 + 0.711927i \(0.747823\pi\)
\(60\) 21.6560 2.79578
\(61\) 11.3461 1.45272 0.726360 0.687314i \(-0.241210\pi\)
0.726360 + 0.687314i \(0.241210\pi\)
\(62\) −1.18203 −0.150118
\(63\) 0.580194 0.0730976
\(64\) −12.7369 −1.59212
\(65\) 0.784944 0.0973603
\(66\) −6.66061 −0.819865
\(67\) −4.32328 −0.528173 −0.264086 0.964499i \(-0.585070\pi\)
−0.264086 + 0.964499i \(0.585070\pi\)
\(68\) 2.84839 0.345418
\(69\) 5.11683 0.615994
\(70\) 0.522091 0.0624018
\(71\) −16.1463 −1.91621 −0.958107 0.286409i \(-0.907538\pi\)
−0.958107 + 0.286409i \(0.907538\pi\)
\(72\) −11.4890 −1.35400
\(73\) 1.64407 0.192424 0.0962122 0.995361i \(-0.469327\pi\)
0.0962122 + 0.995361i \(0.469327\pi\)
\(74\) −9.99533 −1.16193
\(75\) −3.98458 −0.460099
\(76\) −5.64623 −0.647667
\(77\) −0.0943373 −0.0107507
\(78\) −2.08012 −0.235528
\(79\) −9.53631 −1.07292 −0.536459 0.843926i \(-0.680238\pi\)
−0.536459 + 0.843926i \(0.680238\pi\)
\(80\) 3.97988 0.444964
\(81\) 10.3744 1.15272
\(82\) 11.0145 1.21635
\(83\) −13.4228 −1.47335 −0.736673 0.676250i \(-0.763604\pi\)
−0.736673 + 0.676250i \(0.763604\pi\)
\(84\) −0.812827 −0.0886867
\(85\) −2.51341 −0.272618
\(86\) −2.20191 −0.237438
\(87\) −25.2999 −2.71243
\(88\) 1.86807 0.199137
\(89\) −2.33778 −0.247805 −0.123902 0.992294i \(-0.539541\pi\)
−0.123902 + 0.992294i \(0.539541\pi\)
\(90\) 34.0371 3.58782
\(91\) −0.0294617 −0.00308843
\(92\) −4.81820 −0.502332
\(93\) −1.62385 −0.168385
\(94\) −15.4455 −1.59308
\(95\) 4.98222 0.511165
\(96\) −21.8484 −2.22989
\(97\) −1.95333 −0.198331 −0.0991655 0.995071i \(-0.531617\pi\)
−0.0991655 + 0.995071i \(0.531617\pi\)
\(98\) 15.3937 1.55500
\(99\) −6.15021 −0.618119
\(100\) 3.75203 0.375203
\(101\) −2.93267 −0.291811 −0.145906 0.989299i \(-0.546610\pi\)
−0.145906 + 0.989299i \(0.546610\pi\)
\(102\) 6.66061 0.659499
\(103\) 6.83928 0.673895 0.336947 0.941523i \(-0.390606\pi\)
0.336947 + 0.941523i \(0.390606\pi\)
\(104\) 0.583403 0.0572074
\(105\) 0.717237 0.0699952
\(106\) −3.86231 −0.375140
\(107\) −19.4659 −1.88184 −0.940920 0.338630i \(-0.890036\pi\)
−0.940920 + 0.338630i \(0.890036\pi\)
\(108\) −27.1428 −2.61181
\(109\) 7.62322 0.730172 0.365086 0.930974i \(-0.381040\pi\)
0.365086 + 0.930974i \(0.381040\pi\)
\(110\) −5.53430 −0.527675
\(111\) −13.7314 −1.30332
\(112\) −0.149379 −0.0141150
\(113\) −3.17351 −0.298539 −0.149269 0.988797i \(-0.547692\pi\)
−0.149269 + 0.988797i \(0.547692\pi\)
\(114\) −13.2030 −1.23658
\(115\) 4.25157 0.396461
\(116\) 23.8233 2.21194
\(117\) −1.92072 −0.177571
\(118\) 23.7546 2.18679
\(119\) 0.0943373 0.00864789
\(120\) −14.2028 −1.29653
\(121\) 1.00000 0.0909091
\(122\) −24.9831 −2.26186
\(123\) 15.1315 1.36436
\(124\) 1.52908 0.137315
\(125\) 9.25628 0.827907
\(126\) −1.27753 −0.113812
\(127\) 17.2940 1.53459 0.767297 0.641292i \(-0.221601\pi\)
0.767297 + 0.641292i \(0.221601\pi\)
\(128\) 13.6000 1.20208
\(129\) −3.02493 −0.266330
\(130\) −1.72837 −0.151588
\(131\) 10.7491 0.939157 0.469579 0.882891i \(-0.344406\pi\)
0.469579 + 0.882891i \(0.344406\pi\)
\(132\) 8.61618 0.749942
\(133\) −0.187001 −0.0162150
\(134\) 9.51946 0.822356
\(135\) 23.9507 2.06135
\(136\) −1.86807 −0.160186
\(137\) 1.28507 0.109791 0.0548957 0.998492i \(-0.482517\pi\)
0.0548957 + 0.998492i \(0.482517\pi\)
\(138\) −11.2668 −0.959093
\(139\) 18.4769 1.56719 0.783595 0.621272i \(-0.213384\pi\)
0.783595 + 0.621272i \(0.213384\pi\)
\(140\) −0.675378 −0.0570798
\(141\) −21.2187 −1.78693
\(142\) 35.5527 2.98351
\(143\) 0.312302 0.0261160
\(144\) −9.73859 −0.811549
\(145\) −21.0216 −1.74575
\(146\) −3.62010 −0.299601
\(147\) 21.1476 1.74422
\(148\) 12.9300 1.06284
\(149\) −12.8747 −1.05474 −0.527368 0.849637i \(-0.676821\pi\)
−0.527368 + 0.849637i \(0.676821\pi\)
\(150\) 8.77366 0.716367
\(151\) −11.4108 −0.928597 −0.464298 0.885679i \(-0.653693\pi\)
−0.464298 + 0.885679i \(0.653693\pi\)
\(152\) 3.70300 0.300353
\(153\) 6.15021 0.497215
\(154\) 0.207722 0.0167387
\(155\) −1.34925 −0.108375
\(156\) 2.69085 0.215440
\(157\) 22.9413 1.83092 0.915458 0.402414i \(-0.131829\pi\)
0.915458 + 0.402414i \(0.131829\pi\)
\(158\) 20.9980 1.67051
\(159\) −5.30595 −0.420790
\(160\) −18.1538 −1.43518
\(161\) −0.159577 −0.0125764
\(162\) −22.8435 −1.79476
\(163\) 15.8673 1.24282 0.621412 0.783484i \(-0.286559\pi\)
0.621412 + 0.783484i \(0.286559\pi\)
\(164\) −14.2484 −1.11261
\(165\) −7.60290 −0.591885
\(166\) 29.5558 2.29397
\(167\) 14.5658 1.12714 0.563568 0.826070i \(-0.309428\pi\)
0.563568 + 0.826070i \(0.309428\pi\)
\(168\) 0.533081 0.0411281
\(169\) −12.9025 −0.992497
\(170\) 5.53430 0.424461
\(171\) −12.1913 −0.932290
\(172\) 2.84839 0.217188
\(173\) 7.52462 0.572086 0.286043 0.958217i \(-0.407660\pi\)
0.286043 + 0.958217i \(0.407660\pi\)
\(174\) 55.7079 4.22321
\(175\) 0.124265 0.00939358
\(176\) 1.58346 0.119358
\(177\) 32.6336 2.45289
\(178\) 5.14758 0.385827
\(179\) −6.47488 −0.483955 −0.241978 0.970282i \(-0.577796\pi\)
−0.241978 + 0.970282i \(0.577796\pi\)
\(180\) −44.0304 −3.28184
\(181\) −15.4568 −1.14889 −0.574447 0.818542i \(-0.694783\pi\)
−0.574447 + 0.818542i \(0.694783\pi\)
\(182\) 0.0648719 0.00480863
\(183\) −34.3212 −2.53710
\(184\) 3.15995 0.232954
\(185\) −11.4094 −0.838834
\(186\) 3.57556 0.262173
\(187\) −1.00000 −0.0731272
\(188\) 19.9803 1.45721
\(189\) −0.898956 −0.0653894
\(190\) −10.9704 −0.795875
\(191\) 7.94867 0.575146 0.287573 0.957759i \(-0.407152\pi\)
0.287573 + 0.957759i \(0.407152\pi\)
\(192\) 38.5284 2.78055
\(193\) 21.8143 1.57023 0.785114 0.619351i \(-0.212604\pi\)
0.785114 + 0.619351i \(0.212604\pi\)
\(194\) 4.30106 0.308798
\(195\) −2.37440 −0.170034
\(196\) −19.9134 −1.42238
\(197\) −4.20026 −0.299256 −0.149628 0.988742i \(-0.547808\pi\)
−0.149628 + 0.988742i \(0.547808\pi\)
\(198\) 13.5422 0.962401
\(199\) −25.4336 −1.80294 −0.901469 0.432844i \(-0.857510\pi\)
−0.901469 + 0.432844i \(0.857510\pi\)
\(200\) −2.46071 −0.173999
\(201\) 13.0776 0.922425
\(202\) 6.45746 0.454345
\(203\) 0.789017 0.0553781
\(204\) −8.61618 −0.603253
\(205\) 12.5727 0.878119
\(206\) −15.0595 −1.04924
\(207\) −10.4034 −0.723087
\(208\) 0.494517 0.0342886
\(209\) 1.98225 0.137115
\(210\) −1.57929 −0.108981
\(211\) 10.5402 0.725619 0.362809 0.931863i \(-0.381818\pi\)
0.362809 + 0.931863i \(0.381818\pi\)
\(212\) 4.99629 0.343146
\(213\) 48.8415 3.34656
\(214\) 42.8621 2.92999
\(215\) −2.51341 −0.171413
\(216\) 17.8012 1.21122
\(217\) 0.0506423 0.00343782
\(218\) −16.7856 −1.13686
\(219\) −4.97321 −0.336059
\(220\) 7.15918 0.482672
\(221\) −0.312302 −0.0210077
\(222\) 30.2352 2.02925
\(223\) 23.0621 1.54435 0.772176 0.635408i \(-0.219168\pi\)
0.772176 + 0.635408i \(0.219168\pi\)
\(224\) 0.681377 0.0455264
\(225\) 8.10133 0.540089
\(226\) 6.98777 0.464819
\(227\) 28.4535 1.88853 0.944264 0.329191i \(-0.106776\pi\)
0.944264 + 0.329191i \(0.106776\pi\)
\(228\) 17.0795 1.13111
\(229\) 0.693549 0.0458310 0.0229155 0.999737i \(-0.492705\pi\)
0.0229155 + 0.999737i \(0.492705\pi\)
\(230\) −9.36157 −0.617283
\(231\) 0.285364 0.0187756
\(232\) −15.6242 −1.02578
\(233\) −13.7645 −0.901740 −0.450870 0.892590i \(-0.648886\pi\)
−0.450870 + 0.892590i \(0.648886\pi\)
\(234\) 4.22925 0.276475
\(235\) −17.6306 −1.15009
\(236\) −30.7290 −2.00029
\(237\) 28.8467 1.87379
\(238\) −0.207722 −0.0134646
\(239\) 11.1875 0.723658 0.361829 0.932244i \(-0.382152\pi\)
0.361829 + 0.932244i \(0.382152\pi\)
\(240\) −12.0389 −0.777106
\(241\) 20.8539 1.34332 0.671659 0.740860i \(-0.265582\pi\)
0.671659 + 0.740860i \(0.265582\pi\)
\(242\) −2.20191 −0.141544
\(243\) −2.79448 −0.179266
\(244\) 32.3181 2.06896
\(245\) 17.5715 1.12260
\(246\) −33.3181 −2.12429
\(247\) 0.619062 0.0393900
\(248\) −1.00282 −0.0636792
\(249\) 40.6031 2.57312
\(250\) −20.3815 −1.28904
\(251\) 14.6523 0.924843 0.462422 0.886660i \(-0.346981\pi\)
0.462422 + 0.886660i \(0.346981\pi\)
\(252\) 1.65262 0.104105
\(253\) 1.69155 0.106347
\(254\) −38.0797 −2.38934
\(255\) 7.60290 0.476112
\(256\) −4.47206 −0.279504
\(257\) −23.9934 −1.49667 −0.748334 0.663322i \(-0.769146\pi\)
−0.748334 + 0.663322i \(0.769146\pi\)
\(258\) 6.66061 0.414672
\(259\) 0.428235 0.0266092
\(260\) 2.23583 0.138660
\(261\) 51.4390 3.18399
\(262\) −23.6686 −1.46225
\(263\) −9.85433 −0.607644 −0.303822 0.952729i \(-0.598263\pi\)
−0.303822 + 0.952729i \(0.598263\pi\)
\(264\) −5.65079 −0.347782
\(265\) −4.40871 −0.270825
\(266\) 0.411758 0.0252465
\(267\) 7.07164 0.432777
\(268\) −12.3144 −0.752221
\(269\) 5.85952 0.357261 0.178631 0.983916i \(-0.442833\pi\)
0.178631 + 0.983916i \(0.442833\pi\)
\(270\) −52.7373 −3.20949
\(271\) 13.2722 0.806227 0.403113 0.915150i \(-0.367928\pi\)
0.403113 + 0.915150i \(0.367928\pi\)
\(272\) −1.58346 −0.0960112
\(273\) 0.0891197 0.00539377
\(274\) −2.82961 −0.170943
\(275\) −1.31725 −0.0794329
\(276\) 14.5747 0.877296
\(277\) 1.82075 0.109399 0.0546993 0.998503i \(-0.482580\pi\)
0.0546993 + 0.998503i \(0.482580\pi\)
\(278\) −40.6844 −2.44009
\(279\) 3.30156 0.197659
\(280\) 0.442936 0.0264705
\(281\) −9.95218 −0.593697 −0.296849 0.954925i \(-0.595936\pi\)
−0.296849 + 0.954925i \(0.595936\pi\)
\(282\) 46.7215 2.78223
\(283\) −25.9663 −1.54353 −0.771767 0.635905i \(-0.780627\pi\)
−0.771767 + 0.635905i \(0.780627\pi\)
\(284\) −45.9910 −2.72906
\(285\) −15.0709 −0.892722
\(286\) −0.687659 −0.0406622
\(287\) −0.471900 −0.0278554
\(288\) 44.4215 2.61756
\(289\) 1.00000 0.0588235
\(290\) 46.2877 2.71811
\(291\) 5.90870 0.346374
\(292\) 4.68297 0.274050
\(293\) 22.7634 1.32985 0.664927 0.746909i \(-0.268463\pi\)
0.664927 + 0.746909i \(0.268463\pi\)
\(294\) −46.5650 −2.71573
\(295\) 27.1153 1.57871
\(296\) −8.47993 −0.492886
\(297\) 9.52917 0.552938
\(298\) 28.3489 1.64221
\(299\) 0.528276 0.0305510
\(300\) −11.3496 −0.655271
\(301\) 0.0943373 0.00543751
\(302\) 25.1255 1.44581
\(303\) 8.87112 0.509633
\(304\) 3.13881 0.180023
\(305\) −28.5175 −1.63291
\(306\) −13.5422 −0.774155
\(307\) −8.15516 −0.465439 −0.232720 0.972544i \(-0.574762\pi\)
−0.232720 + 0.972544i \(0.574762\pi\)
\(308\) −0.268709 −0.0153111
\(309\) −20.6884 −1.17692
\(310\) 2.97093 0.168737
\(311\) −22.7543 −1.29028 −0.645139 0.764065i \(-0.723201\pi\)
−0.645139 + 0.764065i \(0.723201\pi\)
\(312\) −1.76475 −0.0999095
\(313\) 27.6302 1.56175 0.780874 0.624688i \(-0.214774\pi\)
0.780874 + 0.624688i \(0.214774\pi\)
\(314\) −50.5146 −2.85070
\(315\) −1.45827 −0.0821641
\(316\) −27.1631 −1.52804
\(317\) −1.76914 −0.0993646 −0.0496823 0.998765i \(-0.515821\pi\)
−0.0496823 + 0.998765i \(0.515821\pi\)
\(318\) 11.6832 0.655162
\(319\) −8.36378 −0.468282
\(320\) 32.0132 1.78959
\(321\) 58.8830 3.28653
\(322\) 0.351373 0.0195812
\(323\) −1.98225 −0.110296
\(324\) 29.5505 1.64169
\(325\) −0.411378 −0.0228192
\(326\) −34.9383 −1.93506
\(327\) −23.0597 −1.27520
\(328\) 9.34459 0.515969
\(329\) 0.661738 0.0364828
\(330\) 16.7409 0.921555
\(331\) 16.9300 0.930559 0.465279 0.885164i \(-0.345954\pi\)
0.465279 + 0.885164i \(0.345954\pi\)
\(332\) −38.2334 −2.09833
\(333\) 27.9182 1.52991
\(334\) −32.0725 −1.75493
\(335\) 10.8662 0.593684
\(336\) 0.451861 0.0246511
\(337\) 18.6611 1.01653 0.508266 0.861200i \(-0.330287\pi\)
0.508266 + 0.861200i \(0.330287\pi\)
\(338\) 28.4100 1.54530
\(339\) 9.59964 0.521381
\(340\) −7.15918 −0.388261
\(341\) −0.536821 −0.0290705
\(342\) 26.8440 1.45156
\(343\) −1.31988 −0.0712670
\(344\) −1.86807 −0.100720
\(345\) −12.8607 −0.692398
\(346\) −16.5685 −0.890729
\(347\) −27.9499 −1.50043 −0.750216 0.661193i \(-0.770050\pi\)
−0.750216 + 0.661193i \(0.770050\pi\)
\(348\) −72.0639 −3.86303
\(349\) 34.2739 1.83464 0.917319 0.398153i \(-0.130349\pi\)
0.917319 + 0.398153i \(0.130349\pi\)
\(350\) −0.273621 −0.0146256
\(351\) 2.97598 0.158846
\(352\) −7.22277 −0.384975
\(353\) −30.3921 −1.61761 −0.808805 0.588077i \(-0.799885\pi\)
−0.808805 + 0.588077i \(0.799885\pi\)
\(354\) −71.8562 −3.81911
\(355\) 40.5824 2.15389
\(356\) −6.65892 −0.352922
\(357\) −0.285364 −0.0151031
\(358\) 14.2571 0.753510
\(359\) −34.1734 −1.80361 −0.901803 0.432148i \(-0.857756\pi\)
−0.901803 + 0.432148i \(0.857756\pi\)
\(360\) 28.8767 1.52194
\(361\) −15.0707 −0.793193
\(362\) 34.0344 1.78881
\(363\) −3.02493 −0.158768
\(364\) −0.0839185 −0.00439852
\(365\) −4.13224 −0.216291
\(366\) 75.5721 3.95022
\(367\) 28.1912 1.47157 0.735785 0.677215i \(-0.236813\pi\)
0.735785 + 0.677215i \(0.236813\pi\)
\(368\) 2.67850 0.139627
\(369\) −30.7650 −1.60156
\(370\) 25.1224 1.30605
\(371\) 0.165475 0.00859102
\(372\) −4.62535 −0.239813
\(373\) 8.61421 0.446027 0.223014 0.974815i \(-0.428411\pi\)
0.223014 + 0.974815i \(0.428411\pi\)
\(374\) 2.20191 0.113858
\(375\) −27.9996 −1.44589
\(376\) −13.1038 −0.675776
\(377\) −2.61203 −0.134526
\(378\) 1.97942 0.101810
\(379\) −6.21002 −0.318987 −0.159494 0.987199i \(-0.550986\pi\)
−0.159494 + 0.987199i \(0.550986\pi\)
\(380\) 14.1913 0.727999
\(381\) −52.3131 −2.68008
\(382\) −17.5022 −0.895492
\(383\) −26.0605 −1.33163 −0.665815 0.746117i \(-0.731916\pi\)
−0.665815 + 0.746117i \(0.731916\pi\)
\(384\) −41.1391 −2.09937
\(385\) 0.237109 0.0120842
\(386\) −48.0330 −2.44482
\(387\) 6.15021 0.312633
\(388\) −5.56386 −0.282462
\(389\) −10.7142 −0.543230 −0.271615 0.962406i \(-0.587558\pi\)
−0.271615 + 0.962406i \(0.587558\pi\)
\(390\) 5.22821 0.264741
\(391\) −1.69155 −0.0855456
\(392\) 13.0599 0.659624
\(393\) −32.5154 −1.64019
\(394\) 9.24857 0.465936
\(395\) 23.9687 1.20599
\(396\) −17.5182 −0.880322
\(397\) 11.9543 0.599971 0.299985 0.953944i \(-0.403018\pi\)
0.299985 + 0.953944i \(0.403018\pi\)
\(398\) 56.0023 2.80714
\(399\) 0.565664 0.0283186
\(400\) −2.08580 −0.104290
\(401\) 32.9233 1.64411 0.822056 0.569407i \(-0.192827\pi\)
0.822056 + 0.569407i \(0.192827\pi\)
\(402\) −28.7957 −1.43620
\(403\) −0.167650 −0.00835126
\(404\) −8.35338 −0.415596
\(405\) −26.0753 −1.29569
\(406\) −1.73734 −0.0862227
\(407\) −4.53940 −0.225010
\(408\) 5.65079 0.279756
\(409\) −36.7875 −1.81902 −0.909512 0.415678i \(-0.863544\pi\)
−0.909512 + 0.415678i \(0.863544\pi\)
\(410\) −27.6840 −1.36722
\(411\) −3.88726 −0.191745
\(412\) 19.4809 0.959757
\(413\) −1.01773 −0.0500793
\(414\) 22.9073 1.12583
\(415\) 33.7371 1.65609
\(416\) −2.25569 −0.110594
\(417\) −55.8913 −2.73701
\(418\) −4.36474 −0.213486
\(419\) 27.8168 1.35894 0.679469 0.733705i \(-0.262210\pi\)
0.679469 + 0.733705i \(0.262210\pi\)
\(420\) 2.04297 0.0996868
\(421\) −13.2382 −0.645192 −0.322596 0.946537i \(-0.604555\pi\)
−0.322596 + 0.946537i \(0.604555\pi\)
\(422\) −23.2086 −1.12978
\(423\) 43.1412 2.09760
\(424\) −3.27674 −0.159133
\(425\) 1.31725 0.0638958
\(426\) −107.544 −5.21054
\(427\) 1.07036 0.0517984
\(428\) −55.4464 −2.68011
\(429\) −0.944692 −0.0456102
\(430\) 5.53430 0.266888
\(431\) 10.0812 0.485592 0.242796 0.970077i \(-0.421935\pi\)
0.242796 + 0.970077i \(0.421935\pi\)
\(432\) 15.0890 0.725971
\(433\) 36.4085 1.74968 0.874842 0.484409i \(-0.160965\pi\)
0.874842 + 0.484409i \(0.160965\pi\)
\(434\) −0.111510 −0.00535263
\(435\) 63.5890 3.04886
\(436\) 21.7139 1.03991
\(437\) 3.35309 0.160400
\(438\) 10.9505 0.523237
\(439\) 9.02001 0.430501 0.215251 0.976559i \(-0.430943\pi\)
0.215251 + 0.976559i \(0.430943\pi\)
\(440\) −4.69524 −0.223837
\(441\) −42.9967 −2.04746
\(442\) 0.687659 0.0327086
\(443\) −16.4054 −0.779445 −0.389723 0.920932i \(-0.627429\pi\)
−0.389723 + 0.920932i \(0.627429\pi\)
\(444\) −39.1123 −1.85619
\(445\) 5.87582 0.278540
\(446\) −50.7806 −2.40453
\(447\) 38.9451 1.84204
\(448\) −1.20157 −0.0567688
\(449\) −24.8090 −1.17081 −0.585404 0.810742i \(-0.699064\pi\)
−0.585404 + 0.810742i \(0.699064\pi\)
\(450\) −17.8384 −0.840909
\(451\) 5.00226 0.235547
\(452\) −9.03939 −0.425177
\(453\) 34.5169 1.62174
\(454\) −62.6520 −2.94040
\(455\) 0.0740495 0.00347149
\(456\) −11.2013 −0.524549
\(457\) 10.9090 0.510301 0.255150 0.966901i \(-0.417875\pi\)
0.255150 + 0.966901i \(0.417875\pi\)
\(458\) −1.52713 −0.0713581
\(459\) −9.52917 −0.444783
\(460\) 12.1101 0.564638
\(461\) −2.68025 −0.124832 −0.0624158 0.998050i \(-0.519880\pi\)
−0.0624158 + 0.998050i \(0.519880\pi\)
\(462\) −0.628344 −0.0292332
\(463\) 10.8452 0.504021 0.252010 0.967725i \(-0.418908\pi\)
0.252010 + 0.967725i \(0.418908\pi\)
\(464\) −13.2437 −0.614823
\(465\) 4.08140 0.189270
\(466\) 30.3081 1.40399
\(467\) −7.21260 −0.333759 −0.166880 0.985977i \(-0.553369\pi\)
−0.166880 + 0.985977i \(0.553369\pi\)
\(468\) −5.47096 −0.252895
\(469\) −0.407847 −0.0188326
\(470\) 38.8209 1.79067
\(471\) −69.3959 −3.19759
\(472\) 20.1532 0.927626
\(473\) −1.00000 −0.0459800
\(474\) −63.5176 −2.91746
\(475\) −2.61112 −0.119806
\(476\) 0.268709 0.0123163
\(477\) 10.7879 0.493945
\(478\) −24.6338 −1.12672
\(479\) 41.0183 1.87417 0.937087 0.349096i \(-0.113511\pi\)
0.937087 + 0.349096i \(0.113511\pi\)
\(480\) 54.9140 2.50647
\(481\) −1.41766 −0.0646399
\(482\) −45.9183 −2.09152
\(483\) 0.482708 0.0219640
\(484\) 2.84839 0.129472
\(485\) 4.90954 0.222931
\(486\) 6.15319 0.279114
\(487\) −27.8264 −1.26093 −0.630467 0.776216i \(-0.717136\pi\)
−0.630467 + 0.776216i \(0.717136\pi\)
\(488\) −21.1954 −0.959469
\(489\) −47.9975 −2.17052
\(490\) −38.6908 −1.74787
\(491\) 33.7552 1.52335 0.761674 0.647960i \(-0.224378\pi\)
0.761674 + 0.647960i \(0.224378\pi\)
\(492\) 43.1004 1.94312
\(493\) 8.36378 0.376686
\(494\) −1.36312 −0.0613295
\(495\) 15.4580 0.694786
\(496\) −0.850034 −0.0381676
\(497\) −1.52320 −0.0683248
\(498\) −89.4042 −4.00630
\(499\) 6.36472 0.284924 0.142462 0.989800i \(-0.454498\pi\)
0.142462 + 0.989800i \(0.454498\pi\)
\(500\) 26.3655 1.17910
\(501\) −44.0606 −1.96848
\(502\) −32.2629 −1.43996
\(503\) 5.83733 0.260274 0.130137 0.991496i \(-0.458458\pi\)
0.130137 + 0.991496i \(0.458458\pi\)
\(504\) −1.08385 −0.0482783
\(505\) 7.37101 0.328006
\(506\) −3.72464 −0.165581
\(507\) 39.0291 1.73334
\(508\) 49.2600 2.18556
\(509\) 4.84894 0.214925 0.107463 0.994209i \(-0.465727\pi\)
0.107463 + 0.994209i \(0.465727\pi\)
\(510\) −16.7409 −0.741298
\(511\) 0.155098 0.00686111
\(512\) −17.3530 −0.766900
\(513\) 18.8892 0.833980
\(514\) 52.8312 2.33029
\(515\) −17.1899 −0.757480
\(516\) −8.61618 −0.379306
\(517\) −7.01459 −0.308502
\(518\) −0.942932 −0.0414301
\(519\) −22.7615 −0.999117
\(520\) −1.46633 −0.0643029
\(521\) −0.487128 −0.0213415 −0.0106707 0.999943i \(-0.503397\pi\)
−0.0106707 + 0.999943i \(0.503397\pi\)
\(522\) −113.264 −4.95742
\(523\) 29.3593 1.28379 0.641896 0.766791i \(-0.278148\pi\)
0.641896 + 0.766791i \(0.278148\pi\)
\(524\) 30.6177 1.33754
\(525\) −0.375894 −0.0164054
\(526\) 21.6983 0.946091
\(527\) 0.536821 0.0233843
\(528\) −4.78985 −0.208451
\(529\) −20.1386 −0.875593
\(530\) 9.70757 0.421670
\(531\) −66.3498 −2.87934
\(532\) −0.532650 −0.0230933
\(533\) 1.56222 0.0676671
\(534\) −15.5711 −0.673826
\(535\) 48.9258 2.11525
\(536\) 8.07621 0.348839
\(537\) 19.5861 0.845201
\(538\) −12.9021 −0.556250
\(539\) 6.99110 0.301128
\(540\) 68.2210 2.93576
\(541\) 10.5784 0.454802 0.227401 0.973801i \(-0.426977\pi\)
0.227401 + 0.973801i \(0.426977\pi\)
\(542\) −29.2241 −1.25528
\(543\) 46.7557 2.00648
\(544\) 7.22277 0.309674
\(545\) −19.1603 −0.820737
\(546\) −0.196233 −0.00839800
\(547\) −9.87028 −0.422023 −0.211011 0.977484i \(-0.567676\pi\)
−0.211011 + 0.977484i \(0.567676\pi\)
\(548\) 3.66039 0.156364
\(549\) 69.7810 2.97818
\(550\) 2.90045 0.123676
\(551\) −16.5791 −0.706295
\(552\) −9.55862 −0.406842
\(553\) −0.899629 −0.0382561
\(554\) −4.00913 −0.170332
\(555\) 34.5126 1.46498
\(556\) 52.6294 2.23198
\(557\) 3.36286 0.142489 0.0712445 0.997459i \(-0.477303\pi\)
0.0712445 + 0.997459i \(0.477303\pi\)
\(558\) −7.26973 −0.307752
\(559\) −0.312302 −0.0132090
\(560\) 0.375451 0.0158657
\(561\) 3.02493 0.127713
\(562\) 21.9138 0.924376
\(563\) 7.30643 0.307929 0.153965 0.988076i \(-0.450796\pi\)
0.153965 + 0.988076i \(0.450796\pi\)
\(564\) −60.4390 −2.54494
\(565\) 7.97634 0.335567
\(566\) 57.1753 2.40326
\(567\) 0.978697 0.0411014
\(568\) 30.1625 1.26559
\(569\) −3.74081 −0.156823 −0.0784115 0.996921i \(-0.524985\pi\)
−0.0784115 + 0.996921i \(0.524985\pi\)
\(570\) 33.1847 1.38995
\(571\) 26.2322 1.09778 0.548891 0.835894i \(-0.315050\pi\)
0.548891 + 0.835894i \(0.315050\pi\)
\(572\) 0.889558 0.0371943
\(573\) −24.0442 −1.00446
\(574\) 1.03908 0.0433703
\(575\) −2.22819 −0.0929220
\(576\) −78.3349 −3.26395
\(577\) −28.1223 −1.17075 −0.585374 0.810763i \(-0.699052\pi\)
−0.585374 + 0.810763i \(0.699052\pi\)
\(578\) −2.20191 −0.0915872
\(579\) −65.9868 −2.74232
\(580\) −59.8778 −2.48629
\(581\) −1.26627 −0.0525338
\(582\) −13.0104 −0.539299
\(583\) −1.75407 −0.0726463
\(584\) −3.07125 −0.127089
\(585\) 4.82757 0.199595
\(586\) −50.1229 −2.07056
\(587\) −6.64323 −0.274195 −0.137098 0.990558i \(-0.543777\pi\)
−0.137098 + 0.990558i \(0.543777\pi\)
\(588\) 60.2366 2.48412
\(589\) −1.06412 −0.0438461
\(590\) −59.7052 −2.45803
\(591\) 12.7055 0.522634
\(592\) −7.18794 −0.295423
\(593\) −8.21696 −0.337430 −0.168715 0.985665i \(-0.553962\pi\)
−0.168715 + 0.985665i \(0.553962\pi\)
\(594\) −20.9823 −0.860915
\(595\) −0.237109 −0.00972051
\(596\) −36.6722 −1.50215
\(597\) 76.9348 3.14873
\(598\) −1.16321 −0.0475673
\(599\) 42.0812 1.71939 0.859695 0.510807i \(-0.170653\pi\)
0.859695 + 0.510807i \(0.170653\pi\)
\(600\) 7.44348 0.303879
\(601\) 18.9011 0.770994 0.385497 0.922709i \(-0.374030\pi\)
0.385497 + 0.922709i \(0.374030\pi\)
\(602\) −0.207722 −0.00846611
\(603\) −26.5891 −1.08279
\(604\) −32.5024 −1.32250
\(605\) −2.51341 −0.102185
\(606\) −19.5334 −0.793489
\(607\) −26.3405 −1.06913 −0.534564 0.845128i \(-0.679524\pi\)
−0.534564 + 0.845128i \(0.679524\pi\)
\(608\) −14.3174 −0.580646
\(609\) −2.38672 −0.0967148
\(610\) 62.7928 2.54241
\(611\) −2.19067 −0.0886251
\(612\) 17.5182 0.708131
\(613\) −2.75208 −0.111156 −0.0555778 0.998454i \(-0.517700\pi\)
−0.0555778 + 0.998454i \(0.517700\pi\)
\(614\) 17.9569 0.724681
\(615\) −38.0317 −1.53359
\(616\) 0.176229 0.00710047
\(617\) −10.1401 −0.408224 −0.204112 0.978948i \(-0.565431\pi\)
−0.204112 + 0.978948i \(0.565431\pi\)
\(618\) 45.5538 1.83244
\(619\) −36.7785 −1.47825 −0.739126 0.673567i \(-0.764761\pi\)
−0.739126 + 0.673567i \(0.764761\pi\)
\(620\) −3.84320 −0.154347
\(621\) 16.1191 0.646837
\(622\) 50.1029 2.00894
\(623\) −0.220540 −0.00883576
\(624\) −1.49588 −0.0598831
\(625\) −29.8511 −1.19404
\(626\) −60.8390 −2.43162
\(627\) −5.99618 −0.239464
\(628\) 65.3458 2.60758
\(629\) 4.53940 0.180998
\(630\) 3.21097 0.127928
\(631\) −26.1961 −1.04285 −0.521424 0.853298i \(-0.674599\pi\)
−0.521424 + 0.853298i \(0.674599\pi\)
\(632\) 17.8145 0.708623
\(633\) −31.8834 −1.26725
\(634\) 3.89547 0.154709
\(635\) −43.4669 −1.72493
\(636\) −15.1134 −0.599286
\(637\) 2.18333 0.0865069
\(638\) 18.4163 0.729107
\(639\) −99.3032 −3.92837
\(640\) −34.1825 −1.35118
\(641\) 25.3086 0.999630 0.499815 0.866132i \(-0.333401\pi\)
0.499815 + 0.866132i \(0.333401\pi\)
\(642\) −129.655 −5.11707
\(643\) −47.6840 −1.88047 −0.940236 0.340524i \(-0.889395\pi\)
−0.940236 + 0.340524i \(0.889395\pi\)
\(644\) −0.454536 −0.0179112
\(645\) 7.60290 0.299364
\(646\) 4.36474 0.171728
\(647\) −11.3837 −0.447539 −0.223769 0.974642i \(-0.571836\pi\)
−0.223769 + 0.974642i \(0.571836\pi\)
\(648\) −19.3802 −0.761327
\(649\) 10.7882 0.423475
\(650\) 0.905816 0.0355290
\(651\) −0.153189 −0.00600397
\(652\) 45.1963 1.77002
\(653\) 40.5726 1.58773 0.793864 0.608096i \(-0.208066\pi\)
0.793864 + 0.608096i \(0.208066\pi\)
\(654\) 50.7753 1.98547
\(655\) −27.0170 −1.05564
\(656\) 7.92087 0.309258
\(657\) 10.1114 0.394483
\(658\) −1.45708 −0.0568031
\(659\) −2.79325 −0.108810 −0.0544048 0.998519i \(-0.517326\pi\)
−0.0544048 + 0.998519i \(0.517326\pi\)
\(660\) −21.6560 −0.842960
\(661\) −20.4915 −0.797025 −0.398513 0.917163i \(-0.630473\pi\)
−0.398513 + 0.917163i \(0.630473\pi\)
\(662\) −37.2783 −1.44886
\(663\) 0.944692 0.0366888
\(664\) 25.0748 0.973091
\(665\) 0.470010 0.0182262
\(666\) −61.4733 −2.38204
\(667\) −14.1478 −0.547804
\(668\) 41.4891 1.60526
\(669\) −69.7613 −2.69713
\(670\) −23.9263 −0.924355
\(671\) −11.3461 −0.438012
\(672\) −2.06112 −0.0795093
\(673\) −19.5939 −0.755289 −0.377644 0.925951i \(-0.623266\pi\)
−0.377644 + 0.925951i \(0.623266\pi\)
\(674\) −41.0899 −1.58272
\(675\) −12.5523 −0.483136
\(676\) −36.7513 −1.41351
\(677\) 14.0851 0.541335 0.270667 0.962673i \(-0.412756\pi\)
0.270667 + 0.962673i \(0.412756\pi\)
\(678\) −21.1375 −0.811781
\(679\) −0.184272 −0.00707172
\(680\) 4.69524 0.180054
\(681\) −86.0700 −3.29821
\(682\) 1.18203 0.0452623
\(683\) −23.1779 −0.886876 −0.443438 0.896305i \(-0.646241\pi\)
−0.443438 + 0.896305i \(0.646241\pi\)
\(684\) −34.7255 −1.32776
\(685\) −3.22992 −0.123409
\(686\) 2.90626 0.110961
\(687\) −2.09794 −0.0800413
\(688\) −1.58346 −0.0603687
\(689\) −0.547801 −0.0208695
\(690\) 28.3181 1.07805
\(691\) 13.8907 0.528426 0.264213 0.964464i \(-0.414888\pi\)
0.264213 + 0.964464i \(0.414888\pi\)
\(692\) 21.4331 0.814762
\(693\) −0.580194 −0.0220398
\(694\) 61.5431 2.33615
\(695\) −46.4401 −1.76157
\(696\) 47.2620 1.79146
\(697\) −5.00226 −0.189474
\(698\) −75.4678 −2.85650
\(699\) 41.6366 1.57484
\(700\) 0.353956 0.0133783
\(701\) 39.2703 1.48322 0.741609 0.670832i \(-0.234063\pi\)
0.741609 + 0.670832i \(0.234063\pi\)
\(702\) −6.55282 −0.247320
\(703\) −8.99824 −0.339375
\(704\) 12.7369 0.480042
\(705\) 53.3313 2.00857
\(706\) 66.9206 2.51859
\(707\) −0.276660 −0.0104049
\(708\) 92.9533 3.49340
\(709\) 13.5655 0.509461 0.254731 0.967012i \(-0.418013\pi\)
0.254731 + 0.967012i \(0.418013\pi\)
\(710\) −89.3585 −3.35357
\(711\) −58.6503 −2.19956
\(712\) 4.36715 0.163666
\(713\) −0.908062 −0.0340072
\(714\) 0.628344 0.0235152
\(715\) −0.784944 −0.0293552
\(716\) −18.4430 −0.689246
\(717\) −33.8414 −1.26383
\(718\) 75.2467 2.80818
\(719\) 48.1928 1.79729 0.898645 0.438677i \(-0.144553\pi\)
0.898645 + 0.438677i \(0.144553\pi\)
\(720\) 24.4771 0.912208
\(721\) 0.645200 0.0240285
\(722\) 33.1842 1.23499
\(723\) −63.0816 −2.34603
\(724\) −44.0269 −1.63625
\(725\) 11.0172 0.409167
\(726\) 6.66061 0.247199
\(727\) 21.8379 0.809923 0.404961 0.914334i \(-0.367285\pi\)
0.404961 + 0.914334i \(0.367285\pi\)
\(728\) 0.0550367 0.00203979
\(729\) −22.6702 −0.839638
\(730\) 9.09880 0.336762
\(731\) 1.00000 0.0369863
\(732\) −97.7602 −3.61332
\(733\) 42.2060 1.55891 0.779456 0.626457i \(-0.215495\pi\)
0.779456 + 0.626457i \(0.215495\pi\)
\(734\) −62.0744 −2.29121
\(735\) −53.1527 −1.96057
\(736\) −12.2177 −0.450351
\(737\) 4.32328 0.159250
\(738\) 67.7415 2.49360
\(739\) −48.2243 −1.77396 −0.886979 0.461809i \(-0.847200\pi\)
−0.886979 + 0.461809i \(0.847200\pi\)
\(740\) −32.4984 −1.19466
\(741\) −1.87262 −0.0687924
\(742\) −0.364360 −0.0133761
\(743\) 24.4713 0.897765 0.448882 0.893591i \(-0.351822\pi\)
0.448882 + 0.893591i \(0.351822\pi\)
\(744\) 3.03347 0.111212
\(745\) 32.3594 1.18556
\(746\) −18.9677 −0.694456
\(747\) −82.5531 −3.02046
\(748\) −2.84839 −0.104147
\(749\) −1.83636 −0.0670991
\(750\) 61.6525 2.25123
\(751\) 7.66449 0.279681 0.139841 0.990174i \(-0.455341\pi\)
0.139841 + 0.990174i \(0.455341\pi\)
\(752\) −11.1073 −0.405042
\(753\) −44.3221 −1.61519
\(754\) 5.75143 0.209455
\(755\) 28.6800 1.04377
\(756\) −2.56058 −0.0931273
\(757\) −17.3663 −0.631187 −0.315594 0.948894i \(-0.602204\pi\)
−0.315594 + 0.948894i \(0.602204\pi\)
\(758\) 13.6739 0.496658
\(759\) −5.11683 −0.185729
\(760\) −9.30716 −0.337606
\(761\) 24.2719 0.879856 0.439928 0.898033i \(-0.355004\pi\)
0.439928 + 0.898033i \(0.355004\pi\)
\(762\) 115.189 4.17284
\(763\) 0.719154 0.0260351
\(764\) 22.6409 0.819119
\(765\) −15.4580 −0.558886
\(766\) 57.3828 2.07332
\(767\) 3.36918 0.121654
\(768\) 13.5277 0.488138
\(769\) −30.8202 −1.11140 −0.555702 0.831381i \(-0.687551\pi\)
−0.555702 + 0.831381i \(0.687551\pi\)
\(770\) −0.522091 −0.0188148
\(771\) 72.5784 2.61385
\(772\) 62.1356 2.23631
\(773\) −33.4782 −1.20413 −0.602063 0.798449i \(-0.705654\pi\)
−0.602063 + 0.798449i \(0.705654\pi\)
\(774\) −13.5422 −0.486764
\(775\) 0.707126 0.0254007
\(776\) 3.64897 0.130990
\(777\) −1.29538 −0.0464715
\(778\) 23.5916 0.845800
\(779\) 9.91575 0.355269
\(780\) −6.76322 −0.242162
\(781\) 16.1463 0.577760
\(782\) 3.72464 0.133193
\(783\) −79.6999 −2.84824
\(784\) 11.0701 0.395361
\(785\) −57.6610 −2.05801
\(786\) 71.5959 2.55374
\(787\) −49.5348 −1.76572 −0.882862 0.469633i \(-0.844386\pi\)
−0.882862 + 0.469633i \(0.844386\pi\)
\(788\) −11.9640 −0.426199
\(789\) 29.8087 1.06122
\(790\) −52.7768 −1.87771
\(791\) −0.299380 −0.0106447
\(792\) 11.4890 0.408245
\(793\) −3.54341 −0.125830
\(794\) −26.3223 −0.934144
\(795\) 13.3361 0.472981
\(796\) −72.4447 −2.56773
\(797\) 45.0190 1.59465 0.797327 0.603548i \(-0.206247\pi\)
0.797327 + 0.603548i \(0.206247\pi\)
\(798\) −1.24554 −0.0440916
\(799\) 7.01459 0.248159
\(800\) 9.51416 0.336376
\(801\) −14.3779 −0.508017
\(802\) −72.4940 −2.55985
\(803\) −1.64407 −0.0580181
\(804\) 37.2502 1.31371
\(805\) 0.401082 0.0141363
\(806\) 0.369150 0.0130028
\(807\) −17.7247 −0.623937
\(808\) 5.47844 0.192731
\(809\) 32.0969 1.12847 0.564234 0.825615i \(-0.309171\pi\)
0.564234 + 0.825615i \(0.309171\pi\)
\(810\) 57.4153 2.01737
\(811\) 4.06210 0.142640 0.0713199 0.997453i \(-0.477279\pi\)
0.0713199 + 0.997453i \(0.477279\pi\)
\(812\) 2.24743 0.0788692
\(813\) −40.1474 −1.40803
\(814\) 9.99533 0.350336
\(815\) −39.8811 −1.39697
\(816\) 4.78985 0.167678
\(817\) −1.98225 −0.0693503
\(818\) 81.0026 2.83219
\(819\) −0.181196 −0.00633149
\(820\) 35.8121 1.25061
\(821\) −46.9357 −1.63807 −0.819034 0.573744i \(-0.805490\pi\)
−0.819034 + 0.573744i \(0.805490\pi\)
\(822\) 8.55939 0.298543
\(823\) −8.38614 −0.292323 −0.146161 0.989261i \(-0.546692\pi\)
−0.146161 + 0.989261i \(0.546692\pi\)
\(824\) −12.7763 −0.445083
\(825\) 3.98458 0.138725
\(826\) 2.24095 0.0779726
\(827\) 56.1892 1.95389 0.976944 0.213495i \(-0.0684848\pi\)
0.976944 + 0.213495i \(0.0684848\pi\)
\(828\) −29.6330 −1.02982
\(829\) 31.8418 1.10591 0.552956 0.833210i \(-0.313500\pi\)
0.552956 + 0.833210i \(0.313500\pi\)
\(830\) −74.2859 −2.57850
\(831\) −5.50766 −0.191059
\(832\) 3.97777 0.137904
\(833\) −6.99110 −0.242227
\(834\) 123.067 4.26148
\(835\) −36.6099 −1.26694
\(836\) 5.64623 0.195279
\(837\) −5.11546 −0.176816
\(838\) −61.2499 −2.11584
\(839\) −18.9138 −0.652976 −0.326488 0.945201i \(-0.605865\pi\)
−0.326488 + 0.945201i \(0.605865\pi\)
\(840\) −1.33985 −0.0462293
\(841\) 40.9528 1.41217
\(842\) 29.1493 1.00455
\(843\) 30.1047 1.03686
\(844\) 30.0226 1.03342
\(845\) 32.4292 1.11560
\(846\) −94.9929 −3.26592
\(847\) 0.0943373 0.00324147
\(848\) −2.77750 −0.0953798
\(849\) 78.5462 2.69570
\(850\) −2.90045 −0.0994846
\(851\) −7.67864 −0.263220
\(852\) 139.120 4.76616
\(853\) 26.6413 0.912181 0.456090 0.889933i \(-0.349249\pi\)
0.456090 + 0.889933i \(0.349249\pi\)
\(854\) −2.35684 −0.0806493
\(855\) 30.6417 1.04792
\(856\) 36.3637 1.24289
\(857\) −4.09921 −0.140026 −0.0700131 0.997546i \(-0.522304\pi\)
−0.0700131 + 0.997546i \(0.522304\pi\)
\(858\) 2.08012 0.0710142
\(859\) −26.3718 −0.899795 −0.449897 0.893080i \(-0.648539\pi\)
−0.449897 + 0.893080i \(0.648539\pi\)
\(860\) −7.15918 −0.244126
\(861\) 1.42746 0.0486479
\(862\) −22.1978 −0.756059
\(863\) −19.7942 −0.673801 −0.336901 0.941540i \(-0.609379\pi\)
−0.336901 + 0.941540i \(0.609379\pi\)
\(864\) −68.8270 −2.34154
\(865\) −18.9125 −0.643044
\(866\) −80.1682 −2.72423
\(867\) −3.02493 −0.102732
\(868\) 0.144249 0.00489613
\(869\) 9.53631 0.323497
\(870\) −140.017 −4.74702
\(871\) 1.35017 0.0457487
\(872\) −14.2407 −0.482252
\(873\) −12.0134 −0.406592
\(874\) −7.38319 −0.249740
\(875\) 0.873213 0.0295200
\(876\) −14.1656 −0.478613
\(877\) 20.7039 0.699120 0.349560 0.936914i \(-0.386331\pi\)
0.349560 + 0.936914i \(0.386331\pi\)
\(878\) −19.8612 −0.670283
\(879\) −68.8578 −2.32252
\(880\) −3.97988 −0.134162
\(881\) −47.8003 −1.61043 −0.805217 0.592980i \(-0.797951\pi\)
−0.805217 + 0.592980i \(0.797951\pi\)
\(882\) 94.6747 3.18786
\(883\) 12.6549 0.425871 0.212935 0.977066i \(-0.431698\pi\)
0.212935 + 0.977066i \(0.431698\pi\)
\(884\) −0.889558 −0.0299191
\(885\) −82.0218 −2.75713
\(886\) 36.1232 1.21358
\(887\) −13.0837 −0.439309 −0.219654 0.975578i \(-0.570493\pi\)
−0.219654 + 0.975578i \(0.570493\pi\)
\(888\) 25.6512 0.860798
\(889\) 1.63147 0.0547177
\(890\) −12.9380 −0.433683
\(891\) −10.3744 −0.347557
\(892\) 65.6899 2.19946
\(893\) −13.9047 −0.465303
\(894\) −85.7534 −2.86802
\(895\) 16.2740 0.543981
\(896\) 1.28299 0.0428616
\(897\) −1.59800 −0.0533556
\(898\) 54.6270 1.82293
\(899\) 4.48986 0.149745
\(900\) 23.0758 0.769192
\(901\) 1.75407 0.0584367
\(902\) −11.0145 −0.366743
\(903\) −0.285364 −0.00949632
\(904\) 5.92835 0.197174
\(905\) 38.8493 1.29139
\(906\) −76.0029 −2.52503
\(907\) −21.5546 −0.715707 −0.357854 0.933778i \(-0.616491\pi\)
−0.357854 + 0.933778i \(0.616491\pi\)
\(908\) 81.0467 2.68963
\(909\) −18.0365 −0.598234
\(910\) −0.163050 −0.00540505
\(911\) −26.1049 −0.864895 −0.432447 0.901659i \(-0.642350\pi\)
−0.432447 + 0.901659i \(0.642350\pi\)
\(912\) −9.49470 −0.314401
\(913\) 13.4228 0.444230
\(914\) −24.0205 −0.794529
\(915\) 86.2634 2.85178
\(916\) 1.97550 0.0652723
\(917\) 1.01405 0.0334867
\(918\) 20.9823 0.692520
\(919\) −20.5993 −0.679509 −0.339754 0.940514i \(-0.610344\pi\)
−0.339754 + 0.940514i \(0.610344\pi\)
\(920\) −7.94225 −0.261848
\(921\) 24.6688 0.812864
\(922\) 5.90165 0.194361
\(923\) 5.04252 0.165977
\(924\) 0.812827 0.0267401
\(925\) 5.97950 0.196605
\(926\) −23.8802 −0.784752
\(927\) 42.0630 1.38153
\(928\) 60.4097 1.98304
\(929\) −20.8274 −0.683324 −0.341662 0.939823i \(-0.610990\pi\)
−0.341662 + 0.939823i \(0.610990\pi\)
\(930\) −8.98686 −0.294691
\(931\) 13.8581 0.454182
\(932\) −39.2066 −1.28425
\(933\) 68.8302 2.25340
\(934\) 15.8815 0.519657
\(935\) 2.51341 0.0821974
\(936\) 3.58805 0.117279
\(937\) 33.4067 1.09135 0.545675 0.837997i \(-0.316273\pi\)
0.545675 + 0.837997i \(0.316273\pi\)
\(938\) 0.898040 0.0293221
\(939\) −83.5793 −2.72751
\(940\) −50.2187 −1.63795
\(941\) 42.7732 1.39437 0.697183 0.716893i \(-0.254437\pi\)
0.697183 + 0.716893i \(0.254437\pi\)
\(942\) 152.803 4.97860
\(943\) 8.46159 0.275547
\(944\) 17.0827 0.555994
\(945\) 2.25945 0.0734998
\(946\) 2.20191 0.0715901
\(947\) −12.6813 −0.412088 −0.206044 0.978543i \(-0.566059\pi\)
−0.206044 + 0.978543i \(0.566059\pi\)
\(948\) 82.1665 2.66865
\(949\) −0.513448 −0.0166672
\(950\) 5.74943 0.186536
\(951\) 5.35152 0.173535
\(952\) −0.176229 −0.00571162
\(953\) −4.07730 −0.132077 −0.0660383 0.997817i \(-0.521036\pi\)
−0.0660383 + 0.997817i \(0.521036\pi\)
\(954\) −23.7540 −0.769064
\(955\) −19.9783 −0.646482
\(956\) 31.8663 1.03063
\(957\) 25.2999 0.817828
\(958\) −90.3184 −2.91806
\(959\) 0.121230 0.00391474
\(960\) −96.8377 −3.12542
\(961\) −30.7118 −0.990704
\(962\) 3.12156 0.100643
\(963\) −119.719 −3.85790
\(964\) 59.4000 1.91315
\(965\) −54.8284 −1.76499
\(966\) −1.06288 −0.0341976
\(967\) −12.9620 −0.416830 −0.208415 0.978040i \(-0.566830\pi\)
−0.208415 + 0.978040i \(0.566830\pi\)
\(968\) −1.86807 −0.0600422
\(969\) 5.99618 0.192625
\(970\) −10.8103 −0.347099
\(971\) −41.9999 −1.34784 −0.673920 0.738804i \(-0.735391\pi\)
−0.673920 + 0.738804i \(0.735391\pi\)
\(972\) −7.95977 −0.255310
\(973\) 1.74306 0.0558800
\(974\) 61.2711 1.96325
\(975\) 1.24439 0.0398524
\(976\) −17.9661 −0.575080
\(977\) −9.74210 −0.311677 −0.155839 0.987783i \(-0.549808\pi\)
−0.155839 + 0.987783i \(0.549808\pi\)
\(978\) 105.686 3.37947
\(979\) 2.33778 0.0747159
\(980\) 50.0505 1.59881
\(981\) 46.8844 1.49690
\(982\) −74.3257 −2.37183
\(983\) −54.2569 −1.73053 −0.865264 0.501317i \(-0.832849\pi\)
−0.865264 + 0.501317i \(0.832849\pi\)
\(984\) −28.2667 −0.901111
\(985\) 10.5570 0.336373
\(986\) −18.4163 −0.586493
\(987\) −2.00171 −0.0637152
\(988\) 1.76333 0.0560990
\(989\) −1.69155 −0.0537883
\(990\) −34.0371 −1.08177
\(991\) −26.7874 −0.850931 −0.425466 0.904975i \(-0.639890\pi\)
−0.425466 + 0.904975i \(0.639890\pi\)
\(992\) 3.87734 0.123106
\(993\) −51.2122 −1.62517
\(994\) 3.35394 0.106381
\(995\) 63.9251 2.02656
\(996\) 115.653 3.66462
\(997\) −9.94484 −0.314956 −0.157478 0.987522i \(-0.550336\pi\)
−0.157478 + 0.987522i \(0.550336\pi\)
\(998\) −14.0145 −0.443622
\(999\) −43.2567 −1.36858
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 \(a_p\))