Properties

Label 6010.2.a.c.1.9
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(0.630852\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.369148 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.369148 q^{6} +4.16284 q^{7} +1.00000 q^{8} -2.86373 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.369148 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.369148 q^{6} +4.16284 q^{7} +1.00000 q^{8} -2.86373 q^{9} +1.00000 q^{10} -5.82166 q^{11} -0.369148 q^{12} -5.41212 q^{13} +4.16284 q^{14} -0.369148 q^{15} +1.00000 q^{16} -3.34718 q^{17} -2.86373 q^{18} +1.75502 q^{19} +1.00000 q^{20} -1.53670 q^{21} -5.82166 q^{22} +1.42765 q^{23} -0.369148 q^{24} +1.00000 q^{25} -5.41212 q^{26} +2.16459 q^{27} +4.16284 q^{28} +3.08933 q^{29} -0.369148 q^{30} +0.619086 q^{31} +1.00000 q^{32} +2.14906 q^{33} -3.34718 q^{34} +4.16284 q^{35} -2.86373 q^{36} +7.58549 q^{37} +1.75502 q^{38} +1.99788 q^{39} +1.00000 q^{40} -4.82786 q^{41} -1.53670 q^{42} -0.960138 q^{43} -5.82166 q^{44} -2.86373 q^{45} +1.42765 q^{46} -6.56789 q^{47} -0.369148 q^{48} +10.3292 q^{49} +1.00000 q^{50} +1.23561 q^{51} -5.41212 q^{52} -2.02653 q^{53} +2.16459 q^{54} -5.82166 q^{55} +4.16284 q^{56} -0.647864 q^{57} +3.08933 q^{58} -11.0567 q^{59} -0.369148 q^{60} -9.76047 q^{61} +0.619086 q^{62} -11.9212 q^{63} +1.00000 q^{64} -5.41212 q^{65} +2.14906 q^{66} +7.72164 q^{67} -3.34718 q^{68} -0.527016 q^{69} +4.16284 q^{70} -7.24797 q^{71} -2.86373 q^{72} -7.65437 q^{73} +7.58549 q^{74} -0.369148 q^{75} +1.75502 q^{76} -24.2346 q^{77} +1.99788 q^{78} -13.0618 q^{79} +1.00000 q^{80} +7.79214 q^{81} -4.82786 q^{82} -9.11232 q^{83} -1.53670 q^{84} -3.34718 q^{85} -0.960138 q^{86} -1.14042 q^{87} -5.82166 q^{88} +14.0986 q^{89} -2.86373 q^{90} -22.5298 q^{91} +1.42765 q^{92} -0.228534 q^{93} -6.56789 q^{94} +1.75502 q^{95} -0.369148 q^{96} -16.8622 q^{97} +10.3292 q^{98} +16.6717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + O(q^{10}) \) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + 16q^{10} - 14q^{11} - 8q^{12} - 20q^{13} - 10q^{14} - 8q^{15} + 16q^{16} - 27q^{17} - 2q^{18} - 17q^{19} + 16q^{20} - 12q^{21} - 14q^{22} - 9q^{23} - 8q^{24} + 16q^{25} - 20q^{26} - 11q^{27} - 10q^{28} - 23q^{29} - 8q^{30} - 21q^{31} + 16q^{32} - 9q^{33} - 27q^{34} - 10q^{35} - 2q^{36} - 16q^{37} - 17q^{38} - 6q^{39} + 16q^{40} - 35q^{41} - 12q^{42} + 3q^{43} - 14q^{44} - 2q^{45} - 9q^{46} - 25q^{47} - 8q^{48} - 24q^{49} + 16q^{50} - q^{51} - 20q^{52} - 39q^{53} - 11q^{54} - 14q^{55} - 10q^{56} - 6q^{57} - 23q^{58} - 32q^{59} - 8q^{60} - 38q^{61} - 21q^{62} + q^{63} + 16q^{64} - 20q^{65} - 9q^{66} + 5q^{67} - 27q^{68} - 25q^{69} - 10q^{70} - 16q^{71} - 2q^{72} - 17q^{73} - 16q^{74} - 8q^{75} - 17q^{76} - 34q^{77} - 6q^{78} - 40q^{79} + 16q^{80} - 28q^{81} - 35q^{82} - 22q^{83} - 12q^{84} - 27q^{85} + 3q^{86} + 10q^{87} - 14q^{88} - 46q^{89} - 2q^{90} - q^{91} - 9q^{92} + 14q^{93} - 25q^{94} - 17q^{95} - 8q^{96} - 21q^{97} - 24q^{98} + 15q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.369148 −0.213128 −0.106564 0.994306i \(-0.533985\pi\)
−0.106564 + 0.994306i \(0.533985\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −0.369148 −0.150704
\(7\) 4.16284 1.57340 0.786702 0.617333i \(-0.211787\pi\)
0.786702 + 0.617333i \(0.211787\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.86373 −0.954577
\(10\) 1.00000 0.316228
\(11\) −5.82166 −1.75530 −0.877648 0.479305i \(-0.840889\pi\)
−0.877648 + 0.479305i \(0.840889\pi\)
\(12\) −0.369148 −0.106564
\(13\) −5.41212 −1.50105 −0.750526 0.660840i \(-0.770200\pi\)
−0.750526 + 0.660840i \(0.770200\pi\)
\(14\) 4.16284 1.11256
\(15\) −0.369148 −0.0953137
\(16\) 1.00000 0.250000
\(17\) −3.34718 −0.811811 −0.405906 0.913915i \(-0.633044\pi\)
−0.405906 + 0.913915i \(0.633044\pi\)
\(18\) −2.86373 −0.674988
\(19\) 1.75502 0.402630 0.201315 0.979527i \(-0.435478\pi\)
0.201315 + 0.979527i \(0.435478\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.53670 −0.335336
\(22\) −5.82166 −1.24118
\(23\) 1.42765 0.297686 0.148843 0.988861i \(-0.452445\pi\)
0.148843 + 0.988861i \(0.452445\pi\)
\(24\) −0.369148 −0.0753521
\(25\) 1.00000 0.200000
\(26\) −5.41212 −1.06140
\(27\) 2.16459 0.416575
\(28\) 4.16284 0.786702
\(29\) 3.08933 0.573674 0.286837 0.957979i \(-0.407396\pi\)
0.286837 + 0.957979i \(0.407396\pi\)
\(30\) −0.369148 −0.0673970
\(31\) 0.619086 0.111191 0.0555955 0.998453i \(-0.482294\pi\)
0.0555955 + 0.998453i \(0.482294\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.14906 0.374103
\(34\) −3.34718 −0.574037
\(35\) 4.16284 0.703648
\(36\) −2.86373 −0.477288
\(37\) 7.58549 1.24705 0.623524 0.781805i \(-0.285701\pi\)
0.623524 + 0.781805i \(0.285701\pi\)
\(38\) 1.75502 0.284703
\(39\) 1.99788 0.319916
\(40\) 1.00000 0.158114
\(41\) −4.82786 −0.753985 −0.376992 0.926216i \(-0.623042\pi\)
−0.376992 + 0.926216i \(0.623042\pi\)
\(42\) −1.53670 −0.237119
\(43\) −0.960138 −0.146420 −0.0732099 0.997317i \(-0.523324\pi\)
−0.0732099 + 0.997317i \(0.523324\pi\)
\(44\) −5.82166 −0.877648
\(45\) −2.86373 −0.426900
\(46\) 1.42765 0.210496
\(47\) −6.56789 −0.958025 −0.479012 0.877808i \(-0.659005\pi\)
−0.479012 + 0.877808i \(0.659005\pi\)
\(48\) −0.369148 −0.0532820
\(49\) 10.3292 1.47560
\(50\) 1.00000 0.141421
\(51\) 1.23561 0.173020
\(52\) −5.41212 −0.750526
\(53\) −2.02653 −0.278365 −0.139183 0.990267i \(-0.544448\pi\)
−0.139183 + 0.990267i \(0.544448\pi\)
\(54\) 2.16459 0.294563
\(55\) −5.82166 −0.784993
\(56\) 4.16284 0.556282
\(57\) −0.647864 −0.0858117
\(58\) 3.08933 0.405649
\(59\) −11.0567 −1.43945 −0.719727 0.694257i \(-0.755733\pi\)
−0.719727 + 0.694257i \(0.755733\pi\)
\(60\) −0.369148 −0.0476568
\(61\) −9.76047 −1.24970 −0.624850 0.780745i \(-0.714840\pi\)
−0.624850 + 0.780745i \(0.714840\pi\)
\(62\) 0.619086 0.0786240
\(63\) −11.9212 −1.50193
\(64\) 1.00000 0.125000
\(65\) −5.41212 −0.671291
\(66\) 2.14906 0.264531
\(67\) 7.72164 0.943349 0.471674 0.881773i \(-0.343650\pi\)
0.471674 + 0.881773i \(0.343650\pi\)
\(68\) −3.34718 −0.405906
\(69\) −0.527016 −0.0634452
\(70\) 4.16284 0.497554
\(71\) −7.24797 −0.860176 −0.430088 0.902787i \(-0.641518\pi\)
−0.430088 + 0.902787i \(0.641518\pi\)
\(72\) −2.86373 −0.337494
\(73\) −7.65437 −0.895877 −0.447938 0.894064i \(-0.647842\pi\)
−0.447938 + 0.894064i \(0.647842\pi\)
\(74\) 7.58549 0.881796
\(75\) −0.369148 −0.0426256
\(76\) 1.75502 0.201315
\(77\) −24.2346 −2.76179
\(78\) 1.99788 0.226215
\(79\) −13.0618 −1.46957 −0.734783 0.678302i \(-0.762716\pi\)
−0.734783 + 0.678302i \(0.762716\pi\)
\(80\) 1.00000 0.111803
\(81\) 7.79214 0.865793
\(82\) −4.82786 −0.533148
\(83\) −9.11232 −1.00021 −0.500103 0.865966i \(-0.666705\pi\)
−0.500103 + 0.865966i \(0.666705\pi\)
\(84\) −1.53670 −0.167668
\(85\) −3.34718 −0.363053
\(86\) −0.960138 −0.103534
\(87\) −1.14042 −0.122266
\(88\) −5.82166 −0.620591
\(89\) 14.0986 1.49445 0.747227 0.664569i \(-0.231385\pi\)
0.747227 + 0.664569i \(0.231385\pi\)
\(90\) −2.86373 −0.301864
\(91\) −22.5298 −2.36176
\(92\) 1.42765 0.148843
\(93\) −0.228534 −0.0236979
\(94\) −6.56789 −0.677426
\(95\) 1.75502 0.180062
\(96\) −0.369148 −0.0376760
\(97\) −16.8622 −1.71210 −0.856050 0.516894i \(-0.827088\pi\)
−0.856050 + 0.516894i \(0.827088\pi\)
\(98\) 10.3292 1.04341
\(99\) 16.6717 1.67557
\(100\) 1.00000 0.100000
\(101\) −1.07213 −0.106681 −0.0533404 0.998576i \(-0.516987\pi\)
−0.0533404 + 0.998576i \(0.516987\pi\)
\(102\) 1.23561 0.122343
\(103\) −11.5651 −1.13954 −0.569772 0.821802i \(-0.692969\pi\)
−0.569772 + 0.821802i \(0.692969\pi\)
\(104\) −5.41212 −0.530702
\(105\) −1.53670 −0.149967
\(106\) −2.02653 −0.196834
\(107\) −2.17984 −0.210733 −0.105366 0.994433i \(-0.533602\pi\)
−0.105366 + 0.994433i \(0.533602\pi\)
\(108\) 2.16459 0.208287
\(109\) 6.57445 0.629718 0.314859 0.949138i \(-0.398043\pi\)
0.314859 + 0.949138i \(0.398043\pi\)
\(110\) −5.82166 −0.555074
\(111\) −2.80017 −0.265781
\(112\) 4.16284 0.393351
\(113\) −13.2143 −1.24309 −0.621547 0.783377i \(-0.713496\pi\)
−0.621547 + 0.783377i \(0.713496\pi\)
\(114\) −0.647864 −0.0606781
\(115\) 1.42765 0.133129
\(116\) 3.08933 0.286837
\(117\) 15.4989 1.43287
\(118\) −11.0567 −1.01785
\(119\) −13.9338 −1.27731
\(120\) −0.369148 −0.0336985
\(121\) 22.8917 2.08107
\(122\) −9.76047 −0.883671
\(123\) 1.78220 0.160695
\(124\) 0.619086 0.0555955
\(125\) 1.00000 0.0894427
\(126\) −11.9212 −1.06203
\(127\) 8.65471 0.767981 0.383990 0.923337i \(-0.374550\pi\)
0.383990 + 0.923337i \(0.374550\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.354433 0.0312061
\(130\) −5.41212 −0.474675
\(131\) −17.1560 −1.49892 −0.749462 0.662047i \(-0.769688\pi\)
−0.749462 + 0.662047i \(0.769688\pi\)
\(132\) 2.14906 0.187051
\(133\) 7.30588 0.633500
\(134\) 7.72164 0.667048
\(135\) 2.16459 0.186298
\(136\) −3.34718 −0.287019
\(137\) −18.9259 −1.61695 −0.808474 0.588532i \(-0.799706\pi\)
−0.808474 + 0.588532i \(0.799706\pi\)
\(138\) −0.527016 −0.0448625
\(139\) 12.5656 1.06580 0.532902 0.846177i \(-0.321101\pi\)
0.532902 + 0.846177i \(0.321101\pi\)
\(140\) 4.16284 0.351824
\(141\) 2.42452 0.204182
\(142\) −7.24797 −0.608236
\(143\) 31.5075 2.63479
\(144\) −2.86373 −0.238644
\(145\) 3.08933 0.256555
\(146\) −7.65437 −0.633480
\(147\) −3.81301 −0.314492
\(148\) 7.58549 0.623524
\(149\) −0.878117 −0.0719382 −0.0359691 0.999353i \(-0.511452\pi\)
−0.0359691 + 0.999353i \(0.511452\pi\)
\(150\) −0.369148 −0.0301408
\(151\) −7.86702 −0.640209 −0.320104 0.947382i \(-0.603718\pi\)
−0.320104 + 0.947382i \(0.603718\pi\)
\(152\) 1.75502 0.142351
\(153\) 9.58543 0.774936
\(154\) −24.2346 −1.95288
\(155\) 0.619086 0.0497262
\(156\) 1.99788 0.159958
\(157\) −9.05288 −0.722499 −0.361249 0.932469i \(-0.617650\pi\)
−0.361249 + 0.932469i \(0.617650\pi\)
\(158\) −13.0618 −1.03914
\(159\) 0.748091 0.0593274
\(160\) 1.00000 0.0790569
\(161\) 5.94308 0.468381
\(162\) 7.79214 0.612208
\(163\) 3.41660 0.267609 0.133804 0.991008i \(-0.457281\pi\)
0.133804 + 0.991008i \(0.457281\pi\)
\(164\) −4.82786 −0.376992
\(165\) 2.14906 0.167304
\(166\) −9.11232 −0.707253
\(167\) −7.87126 −0.609097 −0.304548 0.952497i \(-0.598506\pi\)
−0.304548 + 0.952497i \(0.598506\pi\)
\(168\) −1.53670 −0.118559
\(169\) 16.2911 1.25316
\(170\) −3.34718 −0.256717
\(171\) −5.02592 −0.384341
\(172\) −0.960138 −0.0732099
\(173\) −0.552131 −0.0419777 −0.0209889 0.999780i \(-0.506681\pi\)
−0.0209889 + 0.999780i \(0.506681\pi\)
\(174\) −1.14042 −0.0864550
\(175\) 4.16284 0.314681
\(176\) −5.82166 −0.438824
\(177\) 4.08155 0.306788
\(178\) 14.0986 1.05674
\(179\) −0.182267 −0.0136233 −0.00681165 0.999977i \(-0.502168\pi\)
−0.00681165 + 0.999977i \(0.502168\pi\)
\(180\) −2.86373 −0.213450
\(181\) 11.9718 0.889855 0.444928 0.895567i \(-0.353229\pi\)
0.444928 + 0.895567i \(0.353229\pi\)
\(182\) −22.5298 −1.67002
\(183\) 3.60306 0.266346
\(184\) 1.42765 0.105248
\(185\) 7.58549 0.557696
\(186\) −0.228534 −0.0167570
\(187\) 19.4862 1.42497
\(188\) −6.56789 −0.479012
\(189\) 9.01082 0.655440
\(190\) 1.75502 0.127323
\(191\) −7.68594 −0.556135 −0.278067 0.960562i \(-0.589694\pi\)
−0.278067 + 0.960562i \(0.589694\pi\)
\(192\) −0.369148 −0.0266410
\(193\) 8.39566 0.604333 0.302166 0.953255i \(-0.402290\pi\)
0.302166 + 0.953255i \(0.402290\pi\)
\(194\) −16.8622 −1.21064
\(195\) 1.99788 0.143071
\(196\) 10.3292 0.737800
\(197\) 22.5343 1.60550 0.802751 0.596314i \(-0.203369\pi\)
0.802751 + 0.596314i \(0.203369\pi\)
\(198\) 16.6717 1.18480
\(199\) 13.9385 0.988071 0.494036 0.869442i \(-0.335521\pi\)
0.494036 + 0.869442i \(0.335521\pi\)
\(200\) 1.00000 0.0707107
\(201\) −2.85043 −0.201054
\(202\) −1.07213 −0.0754347
\(203\) 12.8604 0.902621
\(204\) 1.23561 0.0865098
\(205\) −4.82786 −0.337192
\(206\) −11.5651 −0.805780
\(207\) −4.08841 −0.284164
\(208\) −5.41212 −0.375263
\(209\) −10.2172 −0.706736
\(210\) −1.53670 −0.106043
\(211\) −9.00652 −0.620034 −0.310017 0.950731i \(-0.600335\pi\)
−0.310017 + 0.950731i \(0.600335\pi\)
\(212\) −2.02653 −0.139183
\(213\) 2.67558 0.183328
\(214\) −2.17984 −0.149011
\(215\) −0.960138 −0.0654809
\(216\) 2.16459 0.147281
\(217\) 2.57715 0.174949
\(218\) 6.57445 0.445278
\(219\) 2.82560 0.190936
\(220\) −5.82166 −0.392496
\(221\) 18.1154 1.21857
\(222\) −2.80017 −0.187935
\(223\) −0.780941 −0.0522957 −0.0261478 0.999658i \(-0.508324\pi\)
−0.0261478 + 0.999658i \(0.508324\pi\)
\(224\) 4.16284 0.278141
\(225\) −2.86373 −0.190915
\(226\) −13.2143 −0.879001
\(227\) −20.8939 −1.38678 −0.693390 0.720562i \(-0.743884\pi\)
−0.693390 + 0.720562i \(0.743884\pi\)
\(228\) −0.647864 −0.0429059
\(229\) −22.0570 −1.45757 −0.728783 0.684745i \(-0.759914\pi\)
−0.728783 + 0.684745i \(0.759914\pi\)
\(230\) 1.42765 0.0941366
\(231\) 8.94617 0.588615
\(232\) 3.08933 0.202824
\(233\) 6.54871 0.429020 0.214510 0.976722i \(-0.431184\pi\)
0.214510 + 0.976722i \(0.431184\pi\)
\(234\) 15.4989 1.01319
\(235\) −6.56789 −0.428442
\(236\) −11.0567 −0.719727
\(237\) 4.82174 0.313206
\(238\) −13.9338 −0.903193
\(239\) −0.382128 −0.0247178 −0.0123589 0.999924i \(-0.503934\pi\)
−0.0123589 + 0.999924i \(0.503934\pi\)
\(240\) −0.369148 −0.0238284
\(241\) −6.04288 −0.389256 −0.194628 0.980877i \(-0.562350\pi\)
−0.194628 + 0.980877i \(0.562350\pi\)
\(242\) 22.8917 1.47154
\(243\) −9.37021 −0.601099
\(244\) −9.76047 −0.624850
\(245\) 10.3292 0.659909
\(246\) 1.78220 0.113629
\(247\) −9.49841 −0.604369
\(248\) 0.619086 0.0393120
\(249\) 3.36380 0.213172
\(250\) 1.00000 0.0632456
\(251\) 21.8330 1.37809 0.689043 0.724720i \(-0.258031\pi\)
0.689043 + 0.724720i \(0.258031\pi\)
\(252\) −11.9212 −0.750967
\(253\) −8.31131 −0.522528
\(254\) 8.65471 0.543045
\(255\) 1.23561 0.0773767
\(256\) 1.00000 0.0625000
\(257\) −27.0645 −1.68823 −0.844117 0.536159i \(-0.819875\pi\)
−0.844117 + 0.536159i \(0.819875\pi\)
\(258\) 0.354433 0.0220661
\(259\) 31.5772 1.96211
\(260\) −5.41212 −0.335646
\(261\) −8.84700 −0.547615
\(262\) −17.1560 −1.05990
\(263\) 13.6417 0.841181 0.420590 0.907251i \(-0.361823\pi\)
0.420590 + 0.907251i \(0.361823\pi\)
\(264\) 2.14906 0.132265
\(265\) −2.02653 −0.124489
\(266\) 7.30588 0.447952
\(267\) −5.20449 −0.318510
\(268\) 7.72164 0.471674
\(269\) 27.1335 1.65436 0.827179 0.561938i \(-0.189944\pi\)
0.827179 + 0.561938i \(0.189944\pi\)
\(270\) 2.16459 0.131733
\(271\) −3.30015 −0.200470 −0.100235 0.994964i \(-0.531959\pi\)
−0.100235 + 0.994964i \(0.531959\pi\)
\(272\) −3.34718 −0.202953
\(273\) 8.31683 0.503358
\(274\) −18.9259 −1.14335
\(275\) −5.82166 −0.351059
\(276\) −0.527016 −0.0317226
\(277\) −10.6013 −0.636968 −0.318484 0.947928i \(-0.603174\pi\)
−0.318484 + 0.947928i \(0.603174\pi\)
\(278\) 12.5656 0.753637
\(279\) −1.77289 −0.106140
\(280\) 4.16284 0.248777
\(281\) 18.0958 1.07951 0.539754 0.841823i \(-0.318517\pi\)
0.539754 + 0.841823i \(0.318517\pi\)
\(282\) 2.42452 0.144378
\(283\) −0.607994 −0.0361415 −0.0180708 0.999837i \(-0.505752\pi\)
−0.0180708 + 0.999837i \(0.505752\pi\)
\(284\) −7.24797 −0.430088
\(285\) −0.647864 −0.0383762
\(286\) 31.5075 1.86308
\(287\) −20.0976 −1.18632
\(288\) −2.86373 −0.168747
\(289\) −5.79636 −0.340962
\(290\) 3.08933 0.181412
\(291\) 6.22466 0.364896
\(292\) −7.65437 −0.447938
\(293\) −7.68527 −0.448978 −0.224489 0.974477i \(-0.572071\pi\)
−0.224489 + 0.974477i \(0.572071\pi\)
\(294\) −3.81301 −0.222379
\(295\) −11.0567 −0.643743
\(296\) 7.58549 0.440898
\(297\) −12.6015 −0.731212
\(298\) −0.878117 −0.0508680
\(299\) −7.72663 −0.446843
\(300\) −0.369148 −0.0213128
\(301\) −3.99690 −0.230377
\(302\) −7.86702 −0.452696
\(303\) 0.395774 0.0227366
\(304\) 1.75502 0.100658
\(305\) −9.76047 −0.558883
\(306\) 9.58543 0.547963
\(307\) 5.77300 0.329482 0.164741 0.986337i \(-0.447321\pi\)
0.164741 + 0.986337i \(0.447321\pi\)
\(308\) −24.2346 −1.38090
\(309\) 4.26924 0.242869
\(310\) 0.619086 0.0351617
\(311\) 8.81259 0.499716 0.249858 0.968282i \(-0.419616\pi\)
0.249858 + 0.968282i \(0.419616\pi\)
\(312\) 1.99788 0.113107
\(313\) 21.9247 1.23926 0.619628 0.784895i \(-0.287283\pi\)
0.619628 + 0.784895i \(0.287283\pi\)
\(314\) −9.05288 −0.510884
\(315\) −11.9212 −0.671686
\(316\) −13.0618 −0.734783
\(317\) 18.5721 1.04311 0.521556 0.853217i \(-0.325352\pi\)
0.521556 + 0.853217i \(0.325352\pi\)
\(318\) 0.748091 0.0419508
\(319\) −17.9850 −1.00697
\(320\) 1.00000 0.0559017
\(321\) 0.804684 0.0449131
\(322\) 5.94308 0.331195
\(323\) −5.87439 −0.326860
\(324\) 7.79214 0.432896
\(325\) −5.41212 −0.300211
\(326\) 3.41660 0.189228
\(327\) −2.42695 −0.134210
\(328\) −4.82786 −0.266574
\(329\) −27.3410 −1.50736
\(330\) 2.14906 0.118302
\(331\) 3.57680 0.196599 0.0982994 0.995157i \(-0.468660\pi\)
0.0982994 + 0.995157i \(0.468660\pi\)
\(332\) −9.11232 −0.500103
\(333\) −21.7228 −1.19040
\(334\) −7.87126 −0.430696
\(335\) 7.72164 0.421878
\(336\) −1.53670 −0.0838341
\(337\) 31.0316 1.69040 0.845199 0.534451i \(-0.179482\pi\)
0.845199 + 0.534451i \(0.179482\pi\)
\(338\) 16.2911 0.886118
\(339\) 4.87803 0.264938
\(340\) −3.34718 −0.181527
\(341\) −3.60411 −0.195173
\(342\) −5.02592 −0.271770
\(343\) 13.8589 0.748312
\(344\) −0.960138 −0.0517672
\(345\) −0.527016 −0.0283736
\(346\) −0.552131 −0.0296828
\(347\) 5.56644 0.298822 0.149411 0.988775i \(-0.452262\pi\)
0.149411 + 0.988775i \(0.452262\pi\)
\(348\) −1.14042 −0.0611329
\(349\) 0.543281 0.0290812 0.0145406 0.999894i \(-0.495371\pi\)
0.0145406 + 0.999894i \(0.495371\pi\)
\(350\) 4.16284 0.222513
\(351\) −11.7150 −0.625301
\(352\) −5.82166 −0.310296
\(353\) 12.3199 0.655722 0.327861 0.944726i \(-0.393672\pi\)
0.327861 + 0.944726i \(0.393672\pi\)
\(354\) 4.08155 0.216932
\(355\) −7.24797 −0.384682
\(356\) 14.0986 0.747227
\(357\) 5.14363 0.272230
\(358\) −0.182267 −0.00963313
\(359\) −6.87528 −0.362863 −0.181432 0.983404i \(-0.558073\pi\)
−0.181432 + 0.983404i \(0.558073\pi\)
\(360\) −2.86373 −0.150932
\(361\) −15.9199 −0.837889
\(362\) 11.9718 0.629223
\(363\) −8.45044 −0.443533
\(364\) −22.5298 −1.18088
\(365\) −7.65437 −0.400648
\(366\) 3.60306 0.188335
\(367\) 13.3616 0.697470 0.348735 0.937221i \(-0.386611\pi\)
0.348735 + 0.937221i \(0.386611\pi\)
\(368\) 1.42765 0.0744215
\(369\) 13.8257 0.719736
\(370\) 7.58549 0.394351
\(371\) −8.43612 −0.437981
\(372\) −0.228534 −0.0118490
\(373\) −10.2148 −0.528902 −0.264451 0.964399i \(-0.585191\pi\)
−0.264451 + 0.964399i \(0.585191\pi\)
\(374\) 19.4862 1.00761
\(375\) −0.369148 −0.0190627
\(376\) −6.56789 −0.338713
\(377\) −16.7198 −0.861115
\(378\) 9.01082 0.463466
\(379\) 33.6867 1.73037 0.865184 0.501455i \(-0.167202\pi\)
0.865184 + 0.501455i \(0.167202\pi\)
\(380\) 1.75502 0.0900309
\(381\) −3.19487 −0.163678
\(382\) −7.68594 −0.393247
\(383\) 37.2300 1.90236 0.951181 0.308634i \(-0.0998719\pi\)
0.951181 + 0.308634i \(0.0998719\pi\)
\(384\) −0.369148 −0.0188380
\(385\) −24.2346 −1.23511
\(386\) 8.39566 0.427328
\(387\) 2.74958 0.139769
\(388\) −16.8622 −0.856050
\(389\) 18.0289 0.914102 0.457051 0.889441i \(-0.348906\pi\)
0.457051 + 0.889441i \(0.348906\pi\)
\(390\) 1.99788 0.101166
\(391\) −4.77862 −0.241665
\(392\) 10.3292 0.521704
\(393\) 6.33310 0.319463
\(394\) 22.5343 1.13526
\(395\) −13.0618 −0.657210
\(396\) 16.6717 0.837783
\(397\) −25.0886 −1.25916 −0.629580 0.776935i \(-0.716773\pi\)
−0.629580 + 0.776935i \(0.716773\pi\)
\(398\) 13.9385 0.698672
\(399\) −2.69695 −0.135017
\(400\) 1.00000 0.0500000
\(401\) −6.82379 −0.340764 −0.170382 0.985378i \(-0.554500\pi\)
−0.170382 + 0.985378i \(0.554500\pi\)
\(402\) −2.85043 −0.142167
\(403\) −3.35057 −0.166904
\(404\) −1.07213 −0.0533404
\(405\) 7.79214 0.387194
\(406\) 12.8604 0.638249
\(407\) −44.1602 −2.18894
\(408\) 1.23561 0.0611717
\(409\) 5.08364 0.251370 0.125685 0.992070i \(-0.459887\pi\)
0.125685 + 0.992070i \(0.459887\pi\)
\(410\) −4.82786 −0.238431
\(411\) 6.98646 0.344617
\(412\) −11.5651 −0.569772
\(413\) −46.0270 −2.26484
\(414\) −4.08841 −0.200934
\(415\) −9.11232 −0.447306
\(416\) −5.41212 −0.265351
\(417\) −4.63859 −0.227153
\(418\) −10.2172 −0.499738
\(419\) 4.98760 0.243660 0.121830 0.992551i \(-0.461124\pi\)
0.121830 + 0.992551i \(0.461124\pi\)
\(420\) −1.53670 −0.0749835
\(421\) 29.1556 1.42096 0.710478 0.703719i \(-0.248479\pi\)
0.710478 + 0.703719i \(0.248479\pi\)
\(422\) −9.00652 −0.438430
\(423\) 18.8086 0.914508
\(424\) −2.02653 −0.0984171
\(425\) −3.34718 −0.162362
\(426\) 2.67558 0.129632
\(427\) −40.6312 −1.96628
\(428\) −2.17984 −0.105366
\(429\) −11.6310 −0.561548
\(430\) −0.960138 −0.0463020
\(431\) 19.1082 0.920408 0.460204 0.887813i \(-0.347776\pi\)
0.460204 + 0.887813i \(0.347776\pi\)
\(432\) 2.16459 0.104144
\(433\) 30.5975 1.47042 0.735212 0.677837i \(-0.237083\pi\)
0.735212 + 0.677837i \(0.237083\pi\)
\(434\) 2.57715 0.123707
\(435\) −1.14042 −0.0546790
\(436\) 6.57445 0.314859
\(437\) 2.50557 0.119857
\(438\) 2.82560 0.135012
\(439\) −3.20036 −0.152745 −0.0763724 0.997079i \(-0.524334\pi\)
−0.0763724 + 0.997079i \(0.524334\pi\)
\(440\) −5.82166 −0.277537
\(441\) −29.5800 −1.40857
\(442\) 18.1154 0.861660
\(443\) −21.8417 −1.03773 −0.518866 0.854856i \(-0.673646\pi\)
−0.518866 + 0.854856i \(0.673646\pi\)
\(444\) −2.80017 −0.132890
\(445\) 14.0986 0.668340
\(446\) −0.780941 −0.0369786
\(447\) 0.324155 0.0153320
\(448\) 4.16284 0.196676
\(449\) −26.0499 −1.22937 −0.614686 0.788772i \(-0.710717\pi\)
−0.614686 + 0.788772i \(0.710717\pi\)
\(450\) −2.86373 −0.134998
\(451\) 28.1061 1.32347
\(452\) −13.2143 −0.621547
\(453\) 2.90410 0.136446
\(454\) −20.8939 −0.980602
\(455\) −22.5298 −1.05621
\(456\) −0.647864 −0.0303390
\(457\) −31.2787 −1.46315 −0.731577 0.681759i \(-0.761215\pi\)
−0.731577 + 0.681759i \(0.761215\pi\)
\(458\) −22.0570 −1.03065
\(459\) −7.24527 −0.338180
\(460\) 1.42765 0.0665646
\(461\) 6.43891 0.299890 0.149945 0.988694i \(-0.452090\pi\)
0.149945 + 0.988694i \(0.452090\pi\)
\(462\) 8.94617 0.416213
\(463\) −7.66434 −0.356192 −0.178096 0.984013i \(-0.556994\pi\)
−0.178096 + 0.984013i \(0.556994\pi\)
\(464\) 3.08933 0.143418
\(465\) −0.228534 −0.0105980
\(466\) 6.54871 0.303363
\(467\) 4.35278 0.201423 0.100711 0.994916i \(-0.467888\pi\)
0.100711 + 0.994916i \(0.467888\pi\)
\(468\) 15.4989 0.716435
\(469\) 32.1439 1.48427
\(470\) −6.56789 −0.302954
\(471\) 3.34186 0.153985
\(472\) −11.0567 −0.508924
\(473\) 5.58960 0.257010
\(474\) 4.82174 0.221470
\(475\) 1.75502 0.0805261
\(476\) −13.9338 −0.638654
\(477\) 5.80344 0.265721
\(478\) −0.382128 −0.0174781
\(479\) 34.4459 1.57387 0.786936 0.617034i \(-0.211666\pi\)
0.786936 + 0.617034i \(0.211666\pi\)
\(480\) −0.369148 −0.0168492
\(481\) −41.0536 −1.87188
\(482\) −6.04288 −0.275246
\(483\) −2.19388 −0.0998250
\(484\) 22.8917 1.04053
\(485\) −16.8622 −0.765674
\(486\) −9.37021 −0.425041
\(487\) 40.0127 1.81315 0.906574 0.422047i \(-0.138688\pi\)
0.906574 + 0.422047i \(0.138688\pi\)
\(488\) −9.76047 −0.441836
\(489\) −1.26123 −0.0570349
\(490\) 10.3292 0.466626
\(491\) 10.2272 0.461548 0.230774 0.973007i \(-0.425874\pi\)
0.230774 + 0.973007i \(0.425874\pi\)
\(492\) 1.78220 0.0803476
\(493\) −10.3405 −0.465715
\(494\) −9.49841 −0.427354
\(495\) 16.6717 0.749335
\(496\) 0.619086 0.0277978
\(497\) −30.1721 −1.35340
\(498\) 3.36380 0.150735
\(499\) 1.46831 0.0657304 0.0328652 0.999460i \(-0.489537\pi\)
0.0328652 + 0.999460i \(0.489537\pi\)
\(500\) 1.00000 0.0447214
\(501\) 2.90566 0.129815
\(502\) 21.8330 0.974454
\(503\) −36.6027 −1.63203 −0.816016 0.578029i \(-0.803822\pi\)
−0.816016 + 0.578029i \(0.803822\pi\)
\(504\) −11.9212 −0.531014
\(505\) −1.07213 −0.0477091
\(506\) −8.31131 −0.369483
\(507\) −6.01382 −0.267083
\(508\) 8.65471 0.383990
\(509\) −31.8240 −1.41058 −0.705288 0.708921i \(-0.749182\pi\)
−0.705288 + 0.708921i \(0.749182\pi\)
\(510\) 1.23561 0.0547136
\(511\) −31.8639 −1.40958
\(512\) 1.00000 0.0441942
\(513\) 3.79890 0.167726
\(514\) −27.0645 −1.19376
\(515\) −11.5651 −0.509620
\(516\) 0.354433 0.0156031
\(517\) 38.2360 1.68162
\(518\) 31.5772 1.38742
\(519\) 0.203818 0.00894663
\(520\) −5.41212 −0.237337
\(521\) −29.6770 −1.30017 −0.650087 0.759859i \(-0.725268\pi\)
−0.650087 + 0.759859i \(0.725268\pi\)
\(522\) −8.84700 −0.387223
\(523\) 0.604889 0.0264499 0.0132250 0.999913i \(-0.495790\pi\)
0.0132250 + 0.999913i \(0.495790\pi\)
\(524\) −17.1560 −0.749462
\(525\) −1.53670 −0.0670673
\(526\) 13.6417 0.594805
\(527\) −2.07219 −0.0902662
\(528\) 2.14906 0.0935257
\(529\) −20.9618 −0.911383
\(530\) −2.02653 −0.0880269
\(531\) 31.6633 1.37407
\(532\) 7.30588 0.316750
\(533\) 26.1290 1.13177
\(534\) −5.20449 −0.225220
\(535\) −2.17984 −0.0942426
\(536\) 7.72164 0.333524
\(537\) 0.0672837 0.00290351
\(538\) 27.1335 1.16981
\(539\) −60.1331 −2.59012
\(540\) 2.16459 0.0931489
\(541\) 40.5285 1.74246 0.871228 0.490878i \(-0.163324\pi\)
0.871228 + 0.490878i \(0.163324\pi\)
\(542\) −3.30015 −0.141753
\(543\) −4.41936 −0.189653
\(544\) −3.34718 −0.143509
\(545\) 6.57445 0.281618
\(546\) 8.31683 0.355928
\(547\) 4.00737 0.171343 0.0856714 0.996323i \(-0.472696\pi\)
0.0856714 + 0.996323i \(0.472696\pi\)
\(548\) −18.9259 −0.808474
\(549\) 27.9513 1.19293
\(550\) −5.82166 −0.248236
\(551\) 5.42185 0.230978
\(552\) −0.527016 −0.0224313
\(553\) −54.3741 −2.31222
\(554\) −10.6013 −0.450404
\(555\) −2.80017 −0.118861
\(556\) 12.5656 0.532902
\(557\) −15.3152 −0.648924 −0.324462 0.945899i \(-0.605183\pi\)
−0.324462 + 0.945899i \(0.605183\pi\)
\(558\) −1.77289 −0.0750526
\(559\) 5.19639 0.219784
\(560\) 4.16284 0.175912
\(561\) −7.19329 −0.303701
\(562\) 18.0958 0.763327
\(563\) −35.0521 −1.47727 −0.738635 0.674105i \(-0.764529\pi\)
−0.738635 + 0.674105i \(0.764529\pi\)
\(564\) 2.42452 0.102091
\(565\) −13.2143 −0.555929
\(566\) −0.607994 −0.0255559
\(567\) 32.4374 1.36224
\(568\) −7.24797 −0.304118
\(569\) −19.9201 −0.835095 −0.417548 0.908655i \(-0.637110\pi\)
−0.417548 + 0.908655i \(0.637110\pi\)
\(570\) −0.647864 −0.0271361
\(571\) −12.4459 −0.520843 −0.260422 0.965495i \(-0.583862\pi\)
−0.260422 + 0.965495i \(0.583862\pi\)
\(572\) 31.5075 1.31740
\(573\) 2.83725 0.118528
\(574\) −20.0976 −0.838857
\(575\) 1.42765 0.0595372
\(576\) −2.86373 −0.119322
\(577\) −2.36528 −0.0984679 −0.0492340 0.998787i \(-0.515678\pi\)
−0.0492340 + 0.998787i \(0.515678\pi\)
\(578\) −5.79636 −0.241097
\(579\) −3.09924 −0.128800
\(580\) 3.08933 0.128277
\(581\) −37.9331 −1.57373
\(582\) 6.22466 0.258021
\(583\) 11.7978 0.488614
\(584\) −7.65437 −0.316740
\(585\) 15.4989 0.640799
\(586\) −7.68527 −0.317476
\(587\) −30.6950 −1.26692 −0.633459 0.773776i \(-0.718365\pi\)
−0.633459 + 0.773776i \(0.718365\pi\)
\(588\) −3.81301 −0.157246
\(589\) 1.08651 0.0447689
\(590\) −11.0567 −0.455195
\(591\) −8.31850 −0.342177
\(592\) 7.58549 0.311762
\(593\) −24.7436 −1.01610 −0.508049 0.861328i \(-0.669633\pi\)
−0.508049 + 0.861328i \(0.669633\pi\)
\(594\) −12.6015 −0.517045
\(595\) −13.9338 −0.571229
\(596\) −0.878117 −0.0359691
\(597\) −5.14536 −0.210586
\(598\) −7.72663 −0.315965
\(599\) −3.51303 −0.143538 −0.0717692 0.997421i \(-0.522864\pi\)
−0.0717692 + 0.997421i \(0.522864\pi\)
\(600\) −0.369148 −0.0150704
\(601\) −1.00000 −0.0407909
\(602\) −3.99690 −0.162901
\(603\) −22.1127 −0.900498
\(604\) −7.86702 −0.320104
\(605\) 22.8917 0.930681
\(606\) 0.395774 0.0160772
\(607\) 28.1302 1.14177 0.570884 0.821031i \(-0.306601\pi\)
0.570884 + 0.821031i \(0.306601\pi\)
\(608\) 1.75502 0.0711757
\(609\) −4.74738 −0.192374
\(610\) −9.76047 −0.395190
\(611\) 35.5462 1.43805
\(612\) 9.58543 0.387468
\(613\) 26.7512 1.08047 0.540235 0.841514i \(-0.318335\pi\)
0.540235 + 0.841514i \(0.318335\pi\)
\(614\) 5.77300 0.232979
\(615\) 1.78220 0.0718650
\(616\) −24.2346 −0.976441
\(617\) 3.04683 0.122661 0.0613304 0.998118i \(-0.480466\pi\)
0.0613304 + 0.998118i \(0.480466\pi\)
\(618\) 4.26924 0.171734
\(619\) 9.80886 0.394251 0.197126 0.980378i \(-0.436839\pi\)
0.197126 + 0.980378i \(0.436839\pi\)
\(620\) 0.619086 0.0248631
\(621\) 3.09028 0.124009
\(622\) 8.81259 0.353353
\(623\) 58.6903 2.35138
\(624\) 1.99788 0.0799791
\(625\) 1.00000 0.0400000
\(626\) 21.9247 0.876287
\(627\) 3.77165 0.150625
\(628\) −9.05288 −0.361249
\(629\) −25.3900 −1.01237
\(630\) −11.9212 −0.474953
\(631\) −15.1280 −0.602236 −0.301118 0.953587i \(-0.597360\pi\)
−0.301118 + 0.953587i \(0.597360\pi\)
\(632\) −13.0618 −0.519570
\(633\) 3.32474 0.132147
\(634\) 18.5721 0.737591
\(635\) 8.65471 0.343452
\(636\) 0.748091 0.0296637
\(637\) −55.9029 −2.21495
\(638\) −17.9850 −0.712034
\(639\) 20.7562 0.821104
\(640\) 1.00000 0.0395285
\(641\) −40.6938 −1.60731 −0.803655 0.595096i \(-0.797114\pi\)
−0.803655 + 0.595096i \(0.797114\pi\)
\(642\) 0.804684 0.0317583
\(643\) 32.0074 1.26225 0.631125 0.775681i \(-0.282594\pi\)
0.631125 + 0.775681i \(0.282594\pi\)
\(644\) 5.94308 0.234190
\(645\) 0.354433 0.0139558
\(646\) −5.87439 −0.231125
\(647\) −12.4024 −0.487589 −0.243794 0.969827i \(-0.578392\pi\)
−0.243794 + 0.969827i \(0.578392\pi\)
\(648\) 7.79214 0.306104
\(649\) 64.3681 2.52667
\(650\) −5.41212 −0.212281
\(651\) −0.951352 −0.0372864
\(652\) 3.41660 0.133804
\(653\) 13.5657 0.530866 0.265433 0.964129i \(-0.414485\pi\)
0.265433 + 0.964129i \(0.414485\pi\)
\(654\) −2.42695 −0.0949011
\(655\) −17.1560 −0.670340
\(656\) −4.82786 −0.188496
\(657\) 21.9201 0.855183
\(658\) −27.3410 −1.06586
\(659\) 11.9465 0.465369 0.232685 0.972552i \(-0.425249\pi\)
0.232685 + 0.972552i \(0.425249\pi\)
\(660\) 2.14906 0.0836519
\(661\) −12.3930 −0.482032 −0.241016 0.970521i \(-0.577481\pi\)
−0.241016 + 0.970521i \(0.577481\pi\)
\(662\) 3.57680 0.139016
\(663\) −6.68726 −0.259712
\(664\) −9.11232 −0.353626
\(665\) 7.30588 0.283310
\(666\) −21.7228 −0.841741
\(667\) 4.41049 0.170775
\(668\) −7.87126 −0.304548
\(669\) 0.288283 0.0111457
\(670\) 7.72164 0.298313
\(671\) 56.8221 2.19359
\(672\) −1.53670 −0.0592796
\(673\) −20.0884 −0.774350 −0.387175 0.922006i \(-0.626549\pi\)
−0.387175 + 0.922006i \(0.626549\pi\)
\(674\) 31.0316 1.19529
\(675\) 2.16459 0.0833150
\(676\) 16.2911 0.626580
\(677\) −2.72011 −0.104542 −0.0522711 0.998633i \(-0.516646\pi\)
−0.0522711 + 0.998633i \(0.516646\pi\)
\(678\) 4.87803 0.187340
\(679\) −70.1947 −2.69382
\(680\) −3.34718 −0.128359
\(681\) 7.71297 0.295562
\(682\) −3.60411 −0.138008
\(683\) 6.69570 0.256204 0.128102 0.991761i \(-0.459112\pi\)
0.128102 + 0.991761i \(0.459112\pi\)
\(684\) −5.02592 −0.192171
\(685\) −18.9259 −0.723121
\(686\) 13.8589 0.529137
\(687\) 8.14229 0.310648
\(688\) −0.960138 −0.0366049
\(689\) 10.9678 0.417841
\(690\) −0.527016 −0.0200631
\(691\) 30.6613 1.16641 0.583205 0.812325i \(-0.301799\pi\)
0.583205 + 0.812325i \(0.301799\pi\)
\(692\) −0.552131 −0.0209889
\(693\) 69.4014 2.63634
\(694\) 5.56644 0.211299
\(695\) 12.5656 0.476642
\(696\) −1.14042 −0.0432275
\(697\) 16.1597 0.612093
\(698\) 0.543281 0.0205635
\(699\) −2.41745 −0.0914362
\(700\) 4.16284 0.157340
\(701\) 33.1265 1.25117 0.625585 0.780156i \(-0.284861\pi\)
0.625585 + 0.780156i \(0.284861\pi\)
\(702\) −11.7150 −0.442154
\(703\) 13.3127 0.502099
\(704\) −5.82166 −0.219412
\(705\) 2.42452 0.0913129
\(706\) 12.3199 0.463665
\(707\) −4.46310 −0.167852
\(708\) 4.08155 0.153394
\(709\) −40.8442 −1.53394 −0.766968 0.641685i \(-0.778236\pi\)
−0.766968 + 0.641685i \(0.778236\pi\)
\(710\) −7.24797 −0.272012
\(711\) 37.4055 1.40281
\(712\) 14.0986 0.528369
\(713\) 0.883839 0.0331000
\(714\) 5.14363 0.192496
\(715\) 31.5075 1.17832
\(716\) −0.182267 −0.00681165
\(717\) 0.141062 0.00526805
\(718\) −6.87528 −0.256583
\(719\) −0.157445 −0.00587170 −0.00293585 0.999996i \(-0.500935\pi\)
−0.00293585 + 0.999996i \(0.500935\pi\)
\(720\) −2.86373 −0.106725
\(721\) −48.1437 −1.79296
\(722\) −15.9199 −0.592477
\(723\) 2.23072 0.0829613
\(724\) 11.9718 0.444928
\(725\) 3.08933 0.114735
\(726\) −8.45044 −0.313625
\(727\) 51.4199 1.90706 0.953529 0.301301i \(-0.0974210\pi\)
0.953529 + 0.301301i \(0.0974210\pi\)
\(728\) −22.5298 −0.835009
\(729\) −19.9174 −0.737682
\(730\) −7.65437 −0.283301
\(731\) 3.21376 0.118865
\(732\) 3.60306 0.133173
\(733\) 47.4024 1.75085 0.875425 0.483355i \(-0.160582\pi\)
0.875425 + 0.483355i \(0.160582\pi\)
\(734\) 13.3616 0.493185
\(735\) −3.81301 −0.140645
\(736\) 1.42765 0.0526240
\(737\) −44.9528 −1.65586
\(738\) 13.8257 0.508930
\(739\) −29.1051 −1.07065 −0.535323 0.844647i \(-0.679810\pi\)
−0.535323 + 0.844647i \(0.679810\pi\)
\(740\) 7.58549 0.278848
\(741\) 3.50632 0.128808
\(742\) −8.43612 −0.309700
\(743\) 25.8972 0.950075 0.475037 0.879966i \(-0.342435\pi\)
0.475037 + 0.879966i \(0.342435\pi\)
\(744\) −0.228534 −0.00837848
\(745\) −0.878117 −0.0321717
\(746\) −10.2148 −0.373990
\(747\) 26.0952 0.954774
\(748\) 19.4862 0.712485
\(749\) −9.07431 −0.331568
\(750\) −0.369148 −0.0134794
\(751\) −16.5748 −0.604824 −0.302412 0.953177i \(-0.597792\pi\)
−0.302412 + 0.953177i \(0.597792\pi\)
\(752\) −6.56789 −0.239506
\(753\) −8.05962 −0.293709
\(754\) −16.7198 −0.608900
\(755\) −7.86702 −0.286310
\(756\) 9.01082 0.327720
\(757\) 6.60003 0.239882 0.119941 0.992781i \(-0.461729\pi\)
0.119941 + 0.992781i \(0.461729\pi\)
\(758\) 33.6867 1.22355
\(759\) 3.06811 0.111365
\(760\) 1.75502 0.0636614
\(761\) 39.5336 1.43309 0.716545 0.697541i \(-0.245722\pi\)
0.716545 + 0.697541i \(0.245722\pi\)
\(762\) −3.19487 −0.115738
\(763\) 27.3684 0.990801
\(764\) −7.68594 −0.278067
\(765\) 9.58543 0.346562
\(766\) 37.2300 1.34517
\(767\) 59.8400 2.16070
\(768\) −0.369148 −0.0133205
\(769\) −15.7661 −0.568541 −0.284271 0.958744i \(-0.591751\pi\)
−0.284271 + 0.958744i \(0.591751\pi\)
\(770\) −24.2346 −0.873355
\(771\) 9.99080 0.359810
\(772\) 8.39566 0.302166
\(773\) 28.4704 1.02401 0.512005 0.858983i \(-0.328903\pi\)
0.512005 + 0.858983i \(0.328903\pi\)
\(774\) 2.74958 0.0988315
\(775\) 0.619086 0.0222382
\(776\) −16.8622 −0.605319
\(777\) −11.6567 −0.418180
\(778\) 18.0289 0.646367
\(779\) −8.47301 −0.303577
\(780\) 1.99788 0.0715354
\(781\) 42.1952 1.50986
\(782\) −4.77862 −0.170883
\(783\) 6.68711 0.238978
\(784\) 10.3292 0.368900
\(785\) −9.05288 −0.323111
\(786\) 6.33310 0.225894
\(787\) 19.6431 0.700200 0.350100 0.936712i \(-0.386148\pi\)
0.350100 + 0.936712i \(0.386148\pi\)
\(788\) 22.5343 0.802751
\(789\) −5.03580 −0.179279
\(790\) −13.0618 −0.464718
\(791\) −55.0089 −1.95589
\(792\) 16.6717 0.592402
\(793\) 52.8249 1.87587
\(794\) −25.0886 −0.890361
\(795\) 0.748091 0.0265320
\(796\) 13.9385 0.494036
\(797\) 27.2835 0.966432 0.483216 0.875501i \(-0.339469\pi\)
0.483216 + 0.875501i \(0.339469\pi\)
\(798\) −2.69695 −0.0954711
\(799\) 21.9839 0.777735
\(800\) 1.00000 0.0353553
\(801\) −40.3747 −1.42657
\(802\) −6.82379 −0.240957
\(803\) 44.5612 1.57253
\(804\) −2.85043 −0.100527
\(805\) 5.94308 0.209466
\(806\) −3.35057 −0.118019
\(807\) −10.0163 −0.352590
\(808\) −1.07213 −0.0377173
\(809\) −1.58977 −0.0558934 −0.0279467 0.999609i \(-0.508897\pi\)
−0.0279467 + 0.999609i \(0.508897\pi\)
\(810\) 7.79214 0.273788
\(811\) −24.1140 −0.846757 −0.423378 0.905953i \(-0.639156\pi\)
−0.423378 + 0.905953i \(0.639156\pi\)
\(812\) 12.8604 0.451310
\(813\) 1.21824 0.0427257
\(814\) −44.1602 −1.54781
\(815\) 3.41660 0.119678
\(816\) 1.23561 0.0432549
\(817\) −1.68507 −0.0589530
\(818\) 5.08364 0.177745
\(819\) 64.5192 2.25448
\(820\) −4.82786 −0.168596
\(821\) −12.8203 −0.447431 −0.223715 0.974655i \(-0.571819\pi\)
−0.223715 + 0.974655i \(0.571819\pi\)
\(822\) 6.98646 0.243681
\(823\) −18.5144 −0.645373 −0.322686 0.946506i \(-0.604586\pi\)
−0.322686 + 0.946506i \(0.604586\pi\)
\(824\) −11.5651 −0.402890
\(825\) 2.14906 0.0748205
\(826\) −46.0270 −1.60149
\(827\) 36.9928 1.28637 0.643183 0.765712i \(-0.277613\pi\)
0.643183 + 0.765712i \(0.277613\pi\)
\(828\) −4.08841 −0.142082
\(829\) 32.8939 1.14245 0.571226 0.820793i \(-0.306468\pi\)
0.571226 + 0.820793i \(0.306468\pi\)
\(830\) −9.11232 −0.316293
\(831\) 3.91344 0.135756
\(832\) −5.41212 −0.187632
\(833\) −34.5738 −1.19791
\(834\) −4.63859 −0.160621
\(835\) −7.87126 −0.272396
\(836\) −10.2172 −0.353368
\(837\) 1.34006 0.0463194
\(838\) 4.98760 0.172294
\(839\) −30.5336 −1.05414 −0.527068 0.849823i \(-0.676709\pi\)
−0.527068 + 0.849823i \(0.676709\pi\)
\(840\) −1.53670 −0.0530213
\(841\) −19.4561 −0.670899
\(842\) 29.1556 1.00477
\(843\) −6.68005 −0.230073
\(844\) −9.00652 −0.310017
\(845\) 16.2911 0.560430
\(846\) 18.8086 0.646655
\(847\) 95.2945 3.27436
\(848\) −2.02653 −0.0695914
\(849\) 0.224440 0.00770277
\(850\) −3.34718 −0.114807
\(851\) 10.8294 0.371229
\(852\) 2.67558 0.0916638
\(853\) −31.6568 −1.08391 −0.541953 0.840409i \(-0.682315\pi\)
−0.541953 + 0.840409i \(0.682315\pi\)
\(854\) −40.6312 −1.39037
\(855\) −5.02592 −0.171883
\(856\) −2.17984 −0.0745053
\(857\) −39.6206 −1.35342 −0.676708 0.736252i \(-0.736594\pi\)
−0.676708 + 0.736252i \(0.736594\pi\)
\(858\) −11.6310 −0.397074
\(859\) −9.29871 −0.317268 −0.158634 0.987337i \(-0.550709\pi\)
−0.158634 + 0.987337i \(0.550709\pi\)
\(860\) −0.960138 −0.0327404
\(861\) 7.41899 0.252838
\(862\) 19.1082 0.650827
\(863\) 12.8588 0.437720 0.218860 0.975756i \(-0.429766\pi\)
0.218860 + 0.975756i \(0.429766\pi\)
\(864\) 2.16459 0.0736407
\(865\) −0.552131 −0.0187730
\(866\) 30.5975 1.03975
\(867\) 2.13972 0.0726685
\(868\) 2.57715 0.0874743
\(869\) 76.0413 2.57953
\(870\) −1.14042 −0.0386639
\(871\) −41.7905 −1.41602
\(872\) 6.57445 0.222639
\(873\) 48.2888 1.63433
\(874\) 2.50557 0.0847520
\(875\) 4.16284 0.140730
\(876\) 2.82560 0.0954681
\(877\) 32.8369 1.10882 0.554412 0.832242i \(-0.312943\pi\)
0.554412 + 0.832242i \(0.312943\pi\)
\(878\) −3.20036 −0.108007
\(879\) 2.83701 0.0956898
\(880\) −5.82166 −0.196248
\(881\) −3.10232 −0.104520 −0.0522599 0.998634i \(-0.516642\pi\)
−0.0522599 + 0.998634i \(0.516642\pi\)
\(882\) −29.5800 −0.996012
\(883\) −0.794855 −0.0267490 −0.0133745 0.999911i \(-0.504257\pi\)
−0.0133745 + 0.999911i \(0.504257\pi\)
\(884\) 18.1154 0.609286
\(885\) 4.08155 0.137200
\(886\) −21.8417 −0.733787
\(887\) 1.49267 0.0501191 0.0250595 0.999686i \(-0.492022\pi\)
0.0250595 + 0.999686i \(0.492022\pi\)
\(888\) −2.80017 −0.0939676
\(889\) 36.0281 1.20834
\(890\) 14.0986 0.472588
\(891\) −45.3632 −1.51972
\(892\) −0.780941 −0.0261478
\(893\) −11.5268 −0.385730
\(894\) 0.324155 0.0108414
\(895\) −0.182267 −0.00609253
\(896\) 4.16284 0.139071
\(897\) 2.85227 0.0952346
\(898\) −26.0499 −0.869298
\(899\) 1.91256 0.0637874
\(900\) −2.86373 −0.0954577
\(901\) 6.78317 0.225980
\(902\) 28.1061 0.935832
\(903\) 1.47545 0.0490998
\(904\) −13.2143 −0.439500
\(905\) 11.9718 0.397955
\(906\) 2.90410 0.0964821
\(907\) 3.96265 0.131578 0.0657888 0.997834i \(-0.479044\pi\)
0.0657888 + 0.997834i \(0.479044\pi\)
\(908\) −20.8939 −0.693390
\(909\) 3.07029 0.101835
\(910\) −22.5298 −0.746855
\(911\) 51.2229 1.69709 0.848545 0.529123i \(-0.177479\pi\)
0.848545 + 0.529123i \(0.177479\pi\)
\(912\) −0.647864 −0.0214529
\(913\) 53.0488 1.75566
\(914\) −31.2787 −1.03461
\(915\) 3.60306 0.119114
\(916\) −22.0570 −0.728783
\(917\) −71.4175 −2.35841
\(918\) −7.24527 −0.239129
\(919\) −34.2406 −1.12949 −0.564747 0.825264i \(-0.691026\pi\)
−0.564747 + 0.825264i \(0.691026\pi\)
\(920\) 1.42765 0.0470683
\(921\) −2.13109 −0.0702219
\(922\) 6.43891 0.212054
\(923\) 39.2269 1.29117
\(924\) 8.94617 0.294307
\(925\) 7.58549 0.249409
\(926\) −7.66434 −0.251866
\(927\) 33.1194 1.08778
\(928\) 3.08933 0.101412
\(929\) −50.2409 −1.64835 −0.824175 0.566335i \(-0.808361\pi\)
−0.824175 + 0.566335i \(0.808361\pi\)
\(930\) −0.228534 −0.00749394
\(931\) 18.1280 0.594122
\(932\) 6.54871 0.214510
\(933\) −3.25315 −0.106503
\(934\) 4.35278 0.142427
\(935\) 19.4862 0.637266
\(936\) 15.4989 0.506596
\(937\) −5.67679 −0.185453 −0.0927263 0.995692i \(-0.529558\pi\)
−0.0927263 + 0.995692i \(0.529558\pi\)
\(938\) 32.1439 1.04954
\(939\) −8.09346 −0.264120
\(940\) −6.56789 −0.214221
\(941\) −57.6442 −1.87915 −0.939574 0.342345i \(-0.888779\pi\)
−0.939574 + 0.342345i \(0.888779\pi\)
\(942\) 3.34186 0.108884
\(943\) −6.89250 −0.224451
\(944\) −11.0567 −0.359863
\(945\) 9.01082 0.293122
\(946\) 5.58960 0.181734
\(947\) 44.0431 1.43121 0.715604 0.698507i \(-0.246152\pi\)
0.715604 + 0.698507i \(0.246152\pi\)
\(948\) 4.82174 0.156603
\(949\) 41.4264 1.34476
\(950\) 1.75502 0.0569405
\(951\) −6.85585 −0.222316
\(952\) −13.9338 −0.451596
\(953\) 5.87978 0.190465 0.0952325 0.995455i \(-0.469641\pi\)
0.0952325 + 0.995455i \(0.469641\pi\)
\(954\) 5.80344 0.187893
\(955\) −7.68594 −0.248711
\(956\) −0.382128 −0.0123589
\(957\) 6.63914 0.214613
\(958\) 34.4459 1.11290
\(959\) −78.7853 −2.54411
\(960\) −0.369148 −0.0119142
\(961\) −30.6167 −0.987637
\(962\) −41.0536 −1.32362
\(963\) 6.24247 0.201161
\(964\) −6.04288 −0.194628
\(965\) 8.39566 0.270266
\(966\) −2.19388 −0.0705869
\(967\) 16.6669 0.535971 0.267986 0.963423i \(-0.413642\pi\)
0.267986 + 0.963423i \(0.413642\pi\)
\(968\) 22.8917 0.735768
\(969\) 2.16852 0.0696630
\(970\) −16.8622 −0.541413
\(971\) 57.0624 1.83122 0.915609 0.402069i \(-0.131709\pi\)
0.915609 + 0.402069i \(0.131709\pi\)
\(972\) −9.37021 −0.300550
\(973\) 52.3087 1.67694
\(974\) 40.0127 1.28209
\(975\) 1.99788 0.0639832
\(976\) −9.76047 −0.312425
\(977\) −12.8129 −0.409922 −0.204961 0.978770i \(-0.565707\pi\)
−0.204961 + 0.978770i \(0.565707\pi\)
\(978\) −1.26123 −0.0403297
\(979\) −82.0775 −2.62321
\(980\) 10.3292 0.329954
\(981\) −18.8274 −0.601114
\(982\) 10.2272 0.326363
\(983\) −19.9684 −0.636893 −0.318446 0.947941i \(-0.603161\pi\)
−0.318446 + 0.947941i \(0.603161\pi\)
\(984\) 1.78220 0.0568143
\(985\) 22.5343 0.718003
\(986\) −10.3405 −0.329310
\(987\) 10.0929 0.321260
\(988\) −9.49841 −0.302185
\(989\) −1.37074 −0.0435871
\(990\) 16.6717 0.529860
\(991\) −27.8951 −0.886116 −0.443058 0.896493i \(-0.646106\pi\)
−0.443058 + 0.896493i \(0.646106\pi\)
\(992\) 0.619086 0.0196560
\(993\) −1.32037 −0.0419007
\(994\) −30.1721 −0.957002
\(995\) 13.9385 0.441879
\(996\) 3.36380 0.106586
\(997\) 43.5865 1.38040 0.690199 0.723620i \(-0.257523\pi\)
0.690199 + 0.723620i \(0.257523\pi\)
\(998\) 1.46831 0.0464784
\(999\) 16.4194 0.519488
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 \(a_p\))