Properties

Label 6001.2.a.b.1.13
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.31496 q^{2}\) \(-0.975130 q^{3}\) \(+3.35906 q^{4}\) \(-3.23089 q^{5}\) \(+2.25739 q^{6}\) \(+5.09566 q^{7}\) \(-3.14618 q^{8}\) \(-2.04912 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.31496 q^{2}\) \(-0.975130 q^{3}\) \(+3.35906 q^{4}\) \(-3.23089 q^{5}\) \(+2.25739 q^{6}\) \(+5.09566 q^{7}\) \(-3.14618 q^{8}\) \(-2.04912 q^{9}\) \(+7.47940 q^{10}\) \(+3.94926 q^{11}\) \(-3.27552 q^{12}\) \(+1.47706 q^{13}\) \(-11.7963 q^{14}\) \(+3.15054 q^{15}\) \(+0.565168 q^{16}\) \(+1.00000 q^{17}\) \(+4.74365 q^{18}\) \(+0.961810 q^{19}\) \(-10.8528 q^{20}\) \(-4.96893 q^{21}\) \(-9.14240 q^{22}\) \(+0.0822184 q^{23}\) \(+3.06793 q^{24}\) \(+5.43865 q^{25}\) \(-3.41933 q^{26}\) \(+4.92355 q^{27}\) \(+17.1166 q^{28}\) \(+1.83070 q^{29}\) \(-7.29338 q^{30}\) \(-1.55664 q^{31}\) \(+4.98401 q^{32}\) \(-3.85104 q^{33}\) \(-2.31496 q^{34}\) \(-16.4635 q^{35}\) \(-6.88313 q^{36}\) \(-2.94351 q^{37}\) \(-2.22656 q^{38}\) \(-1.44032 q^{39}\) \(+10.1650 q^{40}\) \(-5.60727 q^{41}\) \(+11.5029 q^{42}\) \(-4.26746 q^{43}\) \(+13.2658 q^{44}\) \(+6.62049 q^{45}\) \(-0.190333 q^{46}\) \(-2.32412 q^{47}\) \(-0.551112 q^{48}\) \(+18.9658 q^{49}\) \(-12.5903 q^{50}\) \(-0.975130 q^{51}\) \(+4.96152 q^{52}\) \(-12.8541 q^{53}\) \(-11.3978 q^{54}\) \(-12.7596 q^{55}\) \(-16.0319 q^{56}\) \(-0.937889 q^{57}\) \(-4.23801 q^{58}\) \(-3.51340 q^{59}\) \(+10.5828 q^{60}\) \(+11.7464 q^{61}\) \(+3.60356 q^{62}\) \(-10.4416 q^{63}\) \(-12.6681 q^{64}\) \(-4.77221 q^{65}\) \(+8.91502 q^{66}\) \(-7.16350 q^{67}\) \(+3.35906 q^{68}\) \(-0.0801736 q^{69}\) \(+38.1125 q^{70}\) \(-3.49907 q^{71}\) \(+6.44690 q^{72}\) \(+3.92593 q^{73}\) \(+6.81412 q^{74}\) \(-5.30339 q^{75}\) \(+3.23078 q^{76}\) \(+20.1241 q^{77}\) \(+3.33429 q^{78}\) \(-15.0133 q^{79}\) \(-1.82600 q^{80}\) \(+1.34627 q^{81}\) \(+12.9806 q^{82}\) \(-12.0942 q^{83}\) \(-16.6909 q^{84}\) \(-3.23089 q^{85}\) \(+9.87901 q^{86}\) \(-1.78517 q^{87}\) \(-12.4251 q^{88}\) \(-9.02816 q^{89}\) \(-15.3262 q^{90}\) \(+7.52658 q^{91}\) \(+0.276176 q^{92}\) \(+1.51792 q^{93}\) \(+5.38026 q^{94}\) \(-3.10750 q^{95}\) \(-4.86006 q^{96}\) \(-15.5578 q^{97}\) \(-43.9051 q^{98}\) \(-8.09252 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31496 −1.63693 −0.818464 0.574558i \(-0.805174\pi\)
−0.818464 + 0.574558i \(0.805174\pi\)
\(3\) −0.975130 −0.562991 −0.281496 0.959563i \(-0.590831\pi\)
−0.281496 + 0.959563i \(0.590831\pi\)
\(4\) 3.35906 1.67953
\(5\) −3.23089 −1.44490 −0.722449 0.691424i \(-0.756984\pi\)
−0.722449 + 0.691424i \(0.756984\pi\)
\(6\) 2.25739 0.921576
\(7\) 5.09566 1.92598 0.962989 0.269539i \(-0.0868713\pi\)
0.962989 + 0.269539i \(0.0868713\pi\)
\(8\) −3.14618 −1.11234
\(9\) −2.04912 −0.683041
\(10\) 7.47940 2.36519
\(11\) 3.94926 1.19075 0.595374 0.803449i \(-0.297004\pi\)
0.595374 + 0.803449i \(0.297004\pi\)
\(12\) −3.27552 −0.945561
\(13\) 1.47706 0.409662 0.204831 0.978797i \(-0.434336\pi\)
0.204831 + 0.978797i \(0.434336\pi\)
\(14\) −11.7963 −3.15269
\(15\) 3.15054 0.813465
\(16\) 0.565168 0.141292
\(17\) 1.00000 0.242536
\(18\) 4.74365 1.11809
\(19\) 0.961810 0.220654 0.110327 0.993895i \(-0.464810\pi\)
0.110327 + 0.993895i \(0.464810\pi\)
\(20\) −10.8528 −2.42675
\(21\) −4.96893 −1.08431
\(22\) −9.14240 −1.94917
\(23\) 0.0822184 0.0171437 0.00857186 0.999963i \(-0.497271\pi\)
0.00857186 + 0.999963i \(0.497271\pi\)
\(24\) 3.06793 0.626239
\(25\) 5.43865 1.08773
\(26\) −3.41933 −0.670586
\(27\) 4.92355 0.947537
\(28\) 17.1166 3.23474
\(29\) 1.83070 0.339953 0.169976 0.985448i \(-0.445631\pi\)
0.169976 + 0.985448i \(0.445631\pi\)
\(30\) −7.29338 −1.33158
\(31\) −1.55664 −0.279580 −0.139790 0.990181i \(-0.544643\pi\)
−0.139790 + 0.990181i \(0.544643\pi\)
\(32\) 4.98401 0.881057
\(33\) −3.85104 −0.670380
\(34\) −2.31496 −0.397013
\(35\) −16.4635 −2.78284
\(36\) −6.88313 −1.14719
\(37\) −2.94351 −0.483910 −0.241955 0.970287i \(-0.577789\pi\)
−0.241955 + 0.970287i \(0.577789\pi\)
\(38\) −2.22656 −0.361195
\(39\) −1.44032 −0.230636
\(40\) 10.1650 1.60722
\(41\) −5.60727 −0.875709 −0.437855 0.899046i \(-0.644262\pi\)
−0.437855 + 0.899046i \(0.644262\pi\)
\(42\) 11.5029 1.77494
\(43\) −4.26746 −0.650781 −0.325390 0.945580i \(-0.605496\pi\)
−0.325390 + 0.945580i \(0.605496\pi\)
\(44\) 13.2658 1.99990
\(45\) 6.62049 0.986924
\(46\) −0.190333 −0.0280630
\(47\) −2.32412 −0.339008 −0.169504 0.985529i \(-0.554217\pi\)
−0.169504 + 0.985529i \(0.554217\pi\)
\(48\) −0.551112 −0.0795462
\(49\) 18.9658 2.70939
\(50\) −12.5903 −1.78053
\(51\) −0.975130 −0.136545
\(52\) 4.96152 0.688039
\(53\) −12.8541 −1.76565 −0.882825 0.469702i \(-0.844361\pi\)
−0.882825 + 0.469702i \(0.844361\pi\)
\(54\) −11.3978 −1.55105
\(55\) −12.7596 −1.72051
\(56\) −16.0319 −2.14235
\(57\) −0.937889 −0.124226
\(58\) −4.23801 −0.556478
\(59\) −3.51340 −0.457406 −0.228703 0.973496i \(-0.573448\pi\)
−0.228703 + 0.973496i \(0.573448\pi\)
\(60\) 10.5828 1.36624
\(61\) 11.7464 1.50397 0.751987 0.659178i \(-0.229096\pi\)
0.751987 + 0.659178i \(0.229096\pi\)
\(62\) 3.60356 0.457653
\(63\) −10.4416 −1.31552
\(64\) −12.6681 −1.58352
\(65\) −4.77221 −0.591919
\(66\) 8.91502 1.09736
\(67\) −7.16350 −0.875161 −0.437580 0.899179i \(-0.644164\pi\)
−0.437580 + 0.899179i \(0.644164\pi\)
\(68\) 3.35906 0.407346
\(69\) −0.0801736 −0.00965176
\(70\) 38.1125 4.55531
\(71\) −3.49907 −0.415263 −0.207631 0.978207i \(-0.566575\pi\)
−0.207631 + 0.978207i \(0.566575\pi\)
\(72\) 6.44690 0.759775
\(73\) 3.92593 0.459496 0.229748 0.973250i \(-0.426210\pi\)
0.229748 + 0.973250i \(0.426210\pi\)
\(74\) 6.81412 0.792125
\(75\) −5.30339 −0.612383
\(76\) 3.23078 0.370596
\(77\) 20.1241 2.29335
\(78\) 3.33429 0.377534
\(79\) −15.0133 −1.68912 −0.844562 0.535458i \(-0.820139\pi\)
−0.844562 + 0.535458i \(0.820139\pi\)
\(80\) −1.82600 −0.204153
\(81\) 1.34627 0.149585
\(82\) 12.9806 1.43347
\(83\) −12.0942 −1.32751 −0.663753 0.747952i \(-0.731037\pi\)
−0.663753 + 0.747952i \(0.731037\pi\)
\(84\) −16.6909 −1.82113
\(85\) −3.23089 −0.350439
\(86\) 9.87901 1.06528
\(87\) −1.78517 −0.191390
\(88\) −12.4251 −1.32452
\(89\) −9.02816 −0.956983 −0.478491 0.878092i \(-0.658816\pi\)
−0.478491 + 0.878092i \(0.658816\pi\)
\(90\) −15.3262 −1.61552
\(91\) 7.52658 0.789000
\(92\) 0.276176 0.0287934
\(93\) 1.51792 0.157401
\(94\) 5.38026 0.554932
\(95\) −3.10750 −0.318823
\(96\) −4.86006 −0.496027
\(97\) −15.5578 −1.57966 −0.789830 0.613326i \(-0.789831\pi\)
−0.789830 + 0.613326i \(0.789831\pi\)
\(98\) −43.9051 −4.43508
\(99\) −8.09252 −0.813329
\(100\) 18.2688 1.82688
\(101\) −17.1315 −1.70465 −0.852325 0.523013i \(-0.824808\pi\)
−0.852325 + 0.523013i \(0.824808\pi\)
\(102\) 2.25739 0.223515
\(103\) 11.3524 1.11858 0.559291 0.828972i \(-0.311074\pi\)
0.559291 + 0.828972i \(0.311074\pi\)
\(104\) −4.64708 −0.455684
\(105\) 16.0541 1.56672
\(106\) 29.7569 2.89024
\(107\) 6.89544 0.666608 0.333304 0.942819i \(-0.391837\pi\)
0.333304 + 0.942819i \(0.391837\pi\)
\(108\) 16.5385 1.59142
\(109\) 4.21954 0.404159 0.202079 0.979369i \(-0.435230\pi\)
0.202079 + 0.979369i \(0.435230\pi\)
\(110\) 29.5381 2.81635
\(111\) 2.87030 0.272437
\(112\) 2.87991 0.272126
\(113\) −15.1434 −1.42457 −0.712285 0.701890i \(-0.752340\pi\)
−0.712285 + 0.701890i \(0.752340\pi\)
\(114\) 2.17118 0.203350
\(115\) −0.265638 −0.0247709
\(116\) 6.14944 0.570961
\(117\) −3.02667 −0.279816
\(118\) 8.13340 0.748740
\(119\) 5.09566 0.467119
\(120\) −9.91215 −0.904851
\(121\) 4.59666 0.417879
\(122\) −27.1925 −2.46190
\(123\) 5.46782 0.493017
\(124\) −5.22884 −0.469564
\(125\) −1.41723 −0.126761
\(126\) 24.1720 2.15341
\(127\) 11.7883 1.04604 0.523022 0.852319i \(-0.324804\pi\)
0.523022 + 0.852319i \(0.324804\pi\)
\(128\) 19.3583 1.71105
\(129\) 4.16132 0.366384
\(130\) 11.0475 0.968929
\(131\) 14.2259 1.24292 0.621461 0.783445i \(-0.286540\pi\)
0.621461 + 0.783445i \(0.286540\pi\)
\(132\) −12.9359 −1.12592
\(133\) 4.90106 0.424976
\(134\) 16.5833 1.43257
\(135\) −15.9074 −1.36909
\(136\) −3.14618 −0.269783
\(137\) −15.3869 −1.31459 −0.657296 0.753633i \(-0.728300\pi\)
−0.657296 + 0.753633i \(0.728300\pi\)
\(138\) 0.185599 0.0157992
\(139\) 8.67144 0.735502 0.367751 0.929924i \(-0.380128\pi\)
0.367751 + 0.929924i \(0.380128\pi\)
\(140\) −55.3020 −4.67387
\(141\) 2.26632 0.190859
\(142\) 8.10022 0.679755
\(143\) 5.83328 0.487803
\(144\) −1.15810 −0.0965083
\(145\) −5.91479 −0.491197
\(146\) −9.08840 −0.752161
\(147\) −18.4941 −1.52537
\(148\) −9.88743 −0.812741
\(149\) 9.16059 0.750465 0.375233 0.926931i \(-0.377563\pi\)
0.375233 + 0.926931i \(0.377563\pi\)
\(150\) 12.2772 1.00243
\(151\) 19.7017 1.60330 0.801652 0.597791i \(-0.203955\pi\)
0.801652 + 0.597791i \(0.203955\pi\)
\(152\) −3.02602 −0.245443
\(153\) −2.04912 −0.165662
\(154\) −46.5866 −3.75405
\(155\) 5.02933 0.403965
\(156\) −4.83813 −0.387360
\(157\) 9.17987 0.732633 0.366317 0.930490i \(-0.380619\pi\)
0.366317 + 0.930490i \(0.380619\pi\)
\(158\) 34.7552 2.76497
\(159\) 12.5344 0.994046
\(160\) −16.1028 −1.27304
\(161\) 0.418957 0.0330184
\(162\) −3.11657 −0.244861
\(163\) 12.5729 0.984784 0.492392 0.870374i \(-0.336123\pi\)
0.492392 + 0.870374i \(0.336123\pi\)
\(164\) −18.8352 −1.47078
\(165\) 12.4423 0.968631
\(166\) 27.9975 2.17303
\(167\) −12.1075 −0.936905 −0.468452 0.883489i \(-0.655188\pi\)
−0.468452 + 0.883489i \(0.655188\pi\)
\(168\) 15.6331 1.20612
\(169\) −10.8183 −0.832177
\(170\) 7.47940 0.573643
\(171\) −1.97087 −0.150716
\(172\) −14.3346 −1.09301
\(173\) −2.70441 −0.205613 −0.102806 0.994701i \(-0.532782\pi\)
−0.102806 + 0.994701i \(0.532782\pi\)
\(174\) 4.13261 0.313292
\(175\) 27.7135 2.09495
\(176\) 2.23200 0.168243
\(177\) 3.42602 0.257516
\(178\) 20.8999 1.56651
\(179\) −8.36383 −0.625142 −0.312571 0.949894i \(-0.601190\pi\)
−0.312571 + 0.949894i \(0.601190\pi\)
\(180\) 22.2386 1.65757
\(181\) −26.4137 −1.96332 −0.981659 0.190645i \(-0.938942\pi\)
−0.981659 + 0.190645i \(0.938942\pi\)
\(182\) −17.4238 −1.29154
\(183\) −11.4543 −0.846724
\(184\) −0.258674 −0.0190697
\(185\) 9.51015 0.699200
\(186\) −3.51394 −0.257654
\(187\) 3.94926 0.288799
\(188\) −7.80687 −0.569375
\(189\) 25.0887 1.82494
\(190\) 7.19376 0.521890
\(191\) 16.7188 1.20973 0.604863 0.796329i \(-0.293228\pi\)
0.604863 + 0.796329i \(0.293228\pi\)
\(192\) 12.3531 0.891507
\(193\) −8.30325 −0.597681 −0.298840 0.954303i \(-0.596600\pi\)
−0.298840 + 0.954303i \(0.596600\pi\)
\(194\) 36.0158 2.58579
\(195\) 4.65352 0.333245
\(196\) 63.7072 4.55051
\(197\) 16.4215 1.16999 0.584993 0.811038i \(-0.301097\pi\)
0.584993 + 0.811038i \(0.301097\pi\)
\(198\) 18.7339 1.33136
\(199\) 3.74110 0.265200 0.132600 0.991170i \(-0.457668\pi\)
0.132600 + 0.991170i \(0.457668\pi\)
\(200\) −17.1110 −1.20993
\(201\) 6.98534 0.492708
\(202\) 39.6588 2.79039
\(203\) 9.32863 0.654742
\(204\) −3.27552 −0.229332
\(205\) 18.1165 1.26531
\(206\) −26.2803 −1.83104
\(207\) −0.168475 −0.0117099
\(208\) 0.834786 0.0578820
\(209\) 3.79844 0.262743
\(210\) −37.1646 −2.56460
\(211\) 6.58421 0.453276 0.226638 0.973979i \(-0.427227\pi\)
0.226638 + 0.973979i \(0.427227\pi\)
\(212\) −43.1778 −2.96546
\(213\) 3.41204 0.233789
\(214\) −15.9627 −1.09119
\(215\) 13.7877 0.940312
\(216\) −15.4904 −1.05399
\(217\) −7.93210 −0.538466
\(218\) −9.76809 −0.661579
\(219\) −3.82829 −0.258692
\(220\) −42.8604 −2.88965
\(221\) 1.47706 0.0993576
\(222\) −6.64465 −0.445960
\(223\) −1.28082 −0.0857699 −0.0428849 0.999080i \(-0.513655\pi\)
−0.0428849 + 0.999080i \(0.513655\pi\)
\(224\) 25.3968 1.69690
\(225\) −11.1445 −0.742964
\(226\) 35.0564 2.33192
\(227\) 4.99025 0.331215 0.165607 0.986192i \(-0.447042\pi\)
0.165607 + 0.986192i \(0.447042\pi\)
\(228\) −3.15043 −0.208642
\(229\) −21.5807 −1.42609 −0.713046 0.701118i \(-0.752685\pi\)
−0.713046 + 0.701118i \(0.752685\pi\)
\(230\) 0.614944 0.0405482
\(231\) −19.6236 −1.29114
\(232\) −5.75971 −0.378144
\(233\) 10.1690 0.666196 0.333098 0.942892i \(-0.391906\pi\)
0.333098 + 0.942892i \(0.391906\pi\)
\(234\) 7.00663 0.458038
\(235\) 7.50899 0.489832
\(236\) −11.8017 −0.768227
\(237\) 14.6399 0.950962
\(238\) −11.7963 −0.764639
\(239\) 5.95173 0.384986 0.192493 0.981298i \(-0.438343\pi\)
0.192493 + 0.981298i \(0.438343\pi\)
\(240\) 1.78058 0.114936
\(241\) −9.56344 −0.616036 −0.308018 0.951381i \(-0.599666\pi\)
−0.308018 + 0.951381i \(0.599666\pi\)
\(242\) −10.6411 −0.684037
\(243\) −16.0834 −1.03175
\(244\) 39.4569 2.52597
\(245\) −61.2763 −3.91480
\(246\) −12.6578 −0.807032
\(247\) 1.42065 0.0903936
\(248\) 4.89746 0.310989
\(249\) 11.7934 0.747375
\(250\) 3.28084 0.207499
\(251\) −19.5596 −1.23459 −0.617296 0.786731i \(-0.711772\pi\)
−0.617296 + 0.786731i \(0.711772\pi\)
\(252\) −35.0741 −2.20946
\(253\) 0.324702 0.0204138
\(254\) −27.2896 −1.71230
\(255\) 3.15054 0.197294
\(256\) −19.4775 −1.21734
\(257\) −23.5030 −1.46607 −0.733037 0.680189i \(-0.761898\pi\)
−0.733037 + 0.680189i \(0.761898\pi\)
\(258\) −9.63331 −0.599744
\(259\) −14.9991 −0.932000
\(260\) −16.0301 −0.994147
\(261\) −3.75133 −0.232201
\(262\) −32.9324 −2.03457
\(263\) 8.47884 0.522827 0.261414 0.965227i \(-0.415811\pi\)
0.261414 + 0.965227i \(0.415811\pi\)
\(264\) 12.1161 0.745692
\(265\) 41.5303 2.55118
\(266\) −11.3458 −0.695654
\(267\) 8.80362 0.538773
\(268\) −24.0626 −1.46986
\(269\) 5.93906 0.362111 0.181056 0.983473i \(-0.442049\pi\)
0.181056 + 0.983473i \(0.442049\pi\)
\(270\) 36.8252 2.24111
\(271\) 5.79440 0.351985 0.175992 0.984392i \(-0.443687\pi\)
0.175992 + 0.984392i \(0.443687\pi\)
\(272\) 0.565168 0.0342684
\(273\) −7.33939 −0.444200
\(274\) 35.6201 2.15189
\(275\) 21.4787 1.29521
\(276\) −0.269308 −0.0162104
\(277\) 14.7705 0.887471 0.443736 0.896158i \(-0.353653\pi\)
0.443736 + 0.896158i \(0.353653\pi\)
\(278\) −20.0741 −1.20396
\(279\) 3.18974 0.190965
\(280\) 51.7972 3.09547
\(281\) 1.52330 0.0908726 0.0454363 0.998967i \(-0.485532\pi\)
0.0454363 + 0.998967i \(0.485532\pi\)
\(282\) −5.24645 −0.312422
\(283\) 4.88616 0.290452 0.145226 0.989399i \(-0.453609\pi\)
0.145226 + 0.989399i \(0.453609\pi\)
\(284\) −11.7536 −0.697447
\(285\) 3.03022 0.179495
\(286\) −13.5038 −0.798499
\(287\) −28.5728 −1.68660
\(288\) −10.2128 −0.601798
\(289\) 1.00000 0.0588235
\(290\) 13.6925 0.804053
\(291\) 15.1709 0.889334
\(292\) 13.1875 0.771737
\(293\) −30.0061 −1.75297 −0.876487 0.481426i \(-0.840119\pi\)
−0.876487 + 0.481426i \(0.840119\pi\)
\(294\) 42.8131 2.49691
\(295\) 11.3514 0.660905
\(296\) 9.26080 0.538273
\(297\) 19.4444 1.12828
\(298\) −21.2064 −1.22846
\(299\) 0.121441 0.00702312
\(300\) −17.8144 −1.02852
\(301\) −21.7455 −1.25339
\(302\) −45.6088 −2.62449
\(303\) 16.7054 0.959703
\(304\) 0.543585 0.0311767
\(305\) −37.9514 −2.17309
\(306\) 4.74365 0.271176
\(307\) 22.0721 1.25972 0.629862 0.776707i \(-0.283112\pi\)
0.629862 + 0.776707i \(0.283112\pi\)
\(308\) 67.5981 3.85176
\(309\) −11.0700 −0.629752
\(310\) −11.6427 −0.661261
\(311\) 8.92023 0.505820 0.252910 0.967490i \(-0.418612\pi\)
0.252910 + 0.967490i \(0.418612\pi\)
\(312\) 4.53151 0.256546
\(313\) −3.71894 −0.210207 −0.105103 0.994461i \(-0.533517\pi\)
−0.105103 + 0.994461i \(0.533517\pi\)
\(314\) −21.2511 −1.19927
\(315\) 33.7358 1.90080
\(316\) −50.4305 −2.83694
\(317\) 16.4600 0.924488 0.462244 0.886753i \(-0.347044\pi\)
0.462244 + 0.886753i \(0.347044\pi\)
\(318\) −29.0168 −1.62718
\(319\) 7.22992 0.404798
\(320\) 40.9294 2.28802
\(321\) −6.72395 −0.375294
\(322\) −0.969870 −0.0540488
\(323\) 0.961810 0.0535165
\(324\) 4.52220 0.251233
\(325\) 8.03319 0.445601
\(326\) −29.1058 −1.61202
\(327\) −4.11460 −0.227538
\(328\) 17.6415 0.974088
\(329\) −11.8429 −0.652923
\(330\) −28.8035 −1.58558
\(331\) 13.7072 0.753415 0.376708 0.926332i \(-0.377056\pi\)
0.376708 + 0.926332i \(0.377056\pi\)
\(332\) −40.6250 −2.22959
\(333\) 6.03161 0.330530
\(334\) 28.0284 1.53364
\(335\) 23.1445 1.26452
\(336\) −2.80828 −0.153204
\(337\) −3.18886 −0.173709 −0.0868543 0.996221i \(-0.527681\pi\)
−0.0868543 + 0.996221i \(0.527681\pi\)
\(338\) 25.0440 1.36221
\(339\) 14.7668 0.802021
\(340\) −10.8528 −0.588573
\(341\) −6.14757 −0.332910
\(342\) 4.56249 0.246711
\(343\) 60.9735 3.29226
\(344\) 13.4262 0.723891
\(345\) 0.259032 0.0139458
\(346\) 6.26062 0.336573
\(347\) −11.3690 −0.610322 −0.305161 0.952301i \(-0.598710\pi\)
−0.305161 + 0.952301i \(0.598710\pi\)
\(348\) −5.99650 −0.321446
\(349\) −32.1142 −1.71903 −0.859517 0.511107i \(-0.829235\pi\)
−0.859517 + 0.511107i \(0.829235\pi\)
\(350\) −64.1558 −3.42927
\(351\) 7.27236 0.388170
\(352\) 19.6832 1.04912
\(353\) 1.00000 0.0532246
\(354\) −7.93112 −0.421534
\(355\) 11.3051 0.600013
\(356\) −30.3261 −1.60728
\(357\) −4.96893 −0.262984
\(358\) 19.3620 1.02331
\(359\) −8.22777 −0.434245 −0.217123 0.976144i \(-0.569667\pi\)
−0.217123 + 0.976144i \(0.569667\pi\)
\(360\) −20.8292 −1.09780
\(361\) −18.0749 −0.951312
\(362\) 61.1469 3.21381
\(363\) −4.48234 −0.235262
\(364\) 25.2822 1.32515
\(365\) −12.6843 −0.663925
\(366\) 26.5162 1.38603
\(367\) 2.86471 0.149537 0.0747683 0.997201i \(-0.476178\pi\)
0.0747683 + 0.997201i \(0.476178\pi\)
\(368\) 0.0464672 0.00242227
\(369\) 11.4900 0.598145
\(370\) −22.0157 −1.14454
\(371\) −65.5003 −3.40061
\(372\) 5.09880 0.264360
\(373\) −11.1652 −0.578113 −0.289056 0.957312i \(-0.593342\pi\)
−0.289056 + 0.957312i \(0.593342\pi\)
\(374\) −9.14240 −0.472742
\(375\) 1.38198 0.0713654
\(376\) 7.31211 0.377093
\(377\) 2.70405 0.139266
\(378\) −58.0795 −2.98729
\(379\) 13.1683 0.676410 0.338205 0.941072i \(-0.390180\pi\)
0.338205 + 0.941072i \(0.390180\pi\)
\(380\) −10.4383 −0.535473
\(381\) −11.4951 −0.588914
\(382\) −38.7033 −1.98023
\(383\) −3.94285 −0.201470 −0.100735 0.994913i \(-0.532119\pi\)
−0.100735 + 0.994913i \(0.532119\pi\)
\(384\) −18.8768 −0.963305
\(385\) −65.0187 −3.31366
\(386\) 19.2217 0.978360
\(387\) 8.74454 0.444510
\(388\) −52.2597 −2.65309
\(389\) −38.1938 −1.93650 −0.968251 0.249978i \(-0.919577\pi\)
−0.968251 + 0.249978i \(0.919577\pi\)
\(390\) −10.7727 −0.545499
\(391\) 0.0822184 0.00415796
\(392\) −59.6697 −3.01377
\(393\) −13.8721 −0.699754
\(394\) −38.0153 −1.91518
\(395\) 48.5062 2.44061
\(396\) −27.1833 −1.36601
\(397\) 1.40125 0.0703266 0.0351633 0.999382i \(-0.488805\pi\)
0.0351633 + 0.999382i \(0.488805\pi\)
\(398\) −8.66051 −0.434112
\(399\) −4.77917 −0.239258
\(400\) 3.07375 0.153688
\(401\) 13.4242 0.670372 0.335186 0.942152i \(-0.391201\pi\)
0.335186 + 0.942152i \(0.391201\pi\)
\(402\) −16.1708 −0.806527
\(403\) −2.29924 −0.114533
\(404\) −57.5458 −2.86301
\(405\) −4.34965 −0.216136
\(406\) −21.5955 −1.07176
\(407\) −11.6247 −0.576214
\(408\) 3.06793 0.151885
\(409\) −12.4585 −0.616031 −0.308016 0.951381i \(-0.599665\pi\)
−0.308016 + 0.951381i \(0.599665\pi\)
\(410\) −41.9390 −2.07122
\(411\) 15.0042 0.740103
\(412\) 38.1333 1.87869
\(413\) −17.9031 −0.880954
\(414\) 0.390015 0.0191682
\(415\) 39.0749 1.91811
\(416\) 7.36166 0.360935
\(417\) −8.45578 −0.414081
\(418\) −8.79325 −0.430092
\(419\) 34.5718 1.68894 0.844471 0.535601i \(-0.179915\pi\)
0.844471 + 0.535601i \(0.179915\pi\)
\(420\) 53.9266 2.63135
\(421\) −34.9102 −1.70142 −0.850709 0.525638i \(-0.823827\pi\)
−0.850709 + 0.525638i \(0.823827\pi\)
\(422\) −15.2422 −0.741980
\(423\) 4.76241 0.231556
\(424\) 40.4414 1.96401
\(425\) 5.43865 0.263813
\(426\) −7.89876 −0.382696
\(427\) 59.8557 2.89662
\(428\) 23.1622 1.11959
\(429\) −5.68820 −0.274629
\(430\) −31.9180 −1.53922
\(431\) −21.9997 −1.05969 −0.529844 0.848095i \(-0.677750\pi\)
−0.529844 + 0.848095i \(0.677750\pi\)
\(432\) 2.78263 0.133880
\(433\) −7.96814 −0.382924 −0.191462 0.981500i \(-0.561323\pi\)
−0.191462 + 0.981500i \(0.561323\pi\)
\(434\) 18.3625 0.881429
\(435\) 5.76769 0.276540
\(436\) 14.1737 0.678797
\(437\) 0.0790784 0.00378283
\(438\) 8.86237 0.423460
\(439\) −28.1535 −1.34369 −0.671846 0.740691i \(-0.734498\pi\)
−0.671846 + 0.740691i \(0.734498\pi\)
\(440\) 40.1441 1.91379
\(441\) −38.8632 −1.85063
\(442\) −3.41933 −0.162641
\(443\) −8.12688 −0.386120 −0.193060 0.981187i \(-0.561841\pi\)
−0.193060 + 0.981187i \(0.561841\pi\)
\(444\) 9.64152 0.457566
\(445\) 29.1690 1.38274
\(446\) 2.96505 0.140399
\(447\) −8.93277 −0.422505
\(448\) −64.5526 −3.04982
\(449\) 21.6675 1.02255 0.511276 0.859417i \(-0.329173\pi\)
0.511276 + 0.859417i \(0.329173\pi\)
\(450\) 25.7990 1.21618
\(451\) −22.1446 −1.04275
\(452\) −50.8676 −2.39261
\(453\) −19.2117 −0.902646
\(454\) −11.5523 −0.542174
\(455\) −24.3175 −1.14002
\(456\) 2.95077 0.138182
\(457\) 15.7052 0.734660 0.367330 0.930091i \(-0.380272\pi\)
0.367330 + 0.930091i \(0.380272\pi\)
\(458\) 49.9585 2.33441
\(459\) 4.92355 0.229812
\(460\) −0.892296 −0.0416035
\(461\) 23.6910 1.10340 0.551701 0.834042i \(-0.313979\pi\)
0.551701 + 0.834042i \(0.313979\pi\)
\(462\) 45.4279 2.11350
\(463\) −13.9742 −0.649436 −0.324718 0.945811i \(-0.605269\pi\)
−0.324718 + 0.945811i \(0.605269\pi\)
\(464\) 1.03465 0.0480326
\(465\) −4.90424 −0.227429
\(466\) −23.5410 −1.09051
\(467\) 30.2264 1.39871 0.699355 0.714774i \(-0.253471\pi\)
0.699355 + 0.714774i \(0.253471\pi\)
\(468\) −10.1668 −0.469959
\(469\) −36.5028 −1.68554
\(470\) −17.3830 −0.801820
\(471\) −8.95156 −0.412466
\(472\) 11.0538 0.508792
\(473\) −16.8533 −0.774916
\(474\) −33.8908 −1.55666
\(475\) 5.23095 0.240012
\(476\) 17.1166 0.784540
\(477\) 26.3397 1.20601
\(478\) −13.7781 −0.630194
\(479\) −18.9822 −0.867321 −0.433660 0.901076i \(-0.642778\pi\)
−0.433660 + 0.901076i \(0.642778\pi\)
\(480\) 15.7023 0.716709
\(481\) −4.34773 −0.198239
\(482\) 22.1390 1.00841
\(483\) −0.408537 −0.0185891
\(484\) 15.4405 0.701840
\(485\) 50.2657 2.28245
\(486\) 37.2326 1.68890
\(487\) 21.7268 0.984536 0.492268 0.870444i \(-0.336168\pi\)
0.492268 + 0.870444i \(0.336168\pi\)
\(488\) −36.9563 −1.67293
\(489\) −12.2602 −0.554425
\(490\) 141.852 6.40824
\(491\) −28.8138 −1.30035 −0.650175 0.759785i \(-0.725304\pi\)
−0.650175 + 0.759785i \(0.725304\pi\)
\(492\) 18.3667 0.828036
\(493\) 1.83070 0.0824506
\(494\) −3.28875 −0.147968
\(495\) 26.1460 1.17518
\(496\) −0.879763 −0.0395025
\(497\) −17.8301 −0.799788
\(498\) −27.3012 −1.22340
\(499\) 17.2099 0.770421 0.385211 0.922829i \(-0.374129\pi\)
0.385211 + 0.922829i \(0.374129\pi\)
\(500\) −4.76057 −0.212899
\(501\) 11.8064 0.527469
\(502\) 45.2798 2.02094
\(503\) 12.1872 0.543401 0.271700 0.962382i \(-0.412414\pi\)
0.271700 + 0.962382i \(0.412414\pi\)
\(504\) 32.8512 1.46331
\(505\) 55.3500 2.46304
\(506\) −0.751673 −0.0334159
\(507\) 10.5492 0.468509
\(508\) 39.5977 1.75686
\(509\) 4.30600 0.190860 0.0954300 0.995436i \(-0.469577\pi\)
0.0954300 + 0.995436i \(0.469577\pi\)
\(510\) −7.29338 −0.322956
\(511\) 20.0052 0.884979
\(512\) 6.37305 0.281652
\(513\) 4.73552 0.209078
\(514\) 54.4085 2.39986
\(515\) −36.6782 −1.61624
\(516\) 13.9781 0.615353
\(517\) −9.17857 −0.403673
\(518\) 34.7224 1.52562
\(519\) 2.63715 0.115758
\(520\) 15.0142 0.658417
\(521\) 18.0573 0.791105 0.395552 0.918443i \(-0.370553\pi\)
0.395552 + 0.918443i \(0.370553\pi\)
\(522\) 8.68420 0.380097
\(523\) 9.01805 0.394332 0.197166 0.980370i \(-0.436826\pi\)
0.197166 + 0.980370i \(0.436826\pi\)
\(524\) 47.7856 2.08752
\(525\) −27.0243 −1.17944
\(526\) −19.6282 −0.855830
\(527\) −1.55664 −0.0678082
\(528\) −2.17649 −0.0947194
\(529\) −22.9932 −0.999706
\(530\) −96.1411 −4.17610
\(531\) 7.19939 0.312427
\(532\) 16.4629 0.713759
\(533\) −8.28226 −0.358744
\(534\) −20.3801 −0.881932
\(535\) −22.2784 −0.963180
\(536\) 22.5376 0.973478
\(537\) 8.15582 0.351950
\(538\) −13.7487 −0.592750
\(539\) 74.9008 3.22620
\(540\) −53.4341 −2.29944
\(541\) −18.2680 −0.785403 −0.392701 0.919666i \(-0.628459\pi\)
−0.392701 + 0.919666i \(0.628459\pi\)
\(542\) −13.4138 −0.576173
\(543\) 25.7568 1.10533
\(544\) 4.98401 0.213688
\(545\) −13.6329 −0.583968
\(546\) 16.9904 0.727123
\(547\) 17.9544 0.767675 0.383837 0.923401i \(-0.374602\pi\)
0.383837 + 0.923401i \(0.374602\pi\)
\(548\) −51.6855 −2.20790
\(549\) −24.0698 −1.02728
\(550\) −49.7223 −2.12017
\(551\) 1.76079 0.0750120
\(552\) 0.252240 0.0107361
\(553\) −76.5025 −3.25322
\(554\) −34.1931 −1.45273
\(555\) −9.27363 −0.393644
\(556\) 29.1279 1.23530
\(557\) −7.03492 −0.298079 −0.149040 0.988831i \(-0.547618\pi\)
−0.149040 + 0.988831i \(0.547618\pi\)
\(558\) −7.38414 −0.312595
\(559\) −6.30327 −0.266600
\(560\) −9.30466 −0.393194
\(561\) −3.85104 −0.162591
\(562\) −3.52639 −0.148752
\(563\) −6.54504 −0.275841 −0.137920 0.990443i \(-0.544042\pi\)
−0.137920 + 0.990443i \(0.544042\pi\)
\(564\) 7.61271 0.320553
\(565\) 48.9266 2.05836
\(566\) −11.3113 −0.475449
\(567\) 6.86013 0.288099
\(568\) 11.0087 0.461914
\(569\) 12.9868 0.544435 0.272217 0.962236i \(-0.412243\pi\)
0.272217 + 0.962236i \(0.412243\pi\)
\(570\) −7.01484 −0.293820
\(571\) −45.1872 −1.89103 −0.945513 0.325583i \(-0.894439\pi\)
−0.945513 + 0.325583i \(0.894439\pi\)
\(572\) 19.5943 0.819281
\(573\) −16.3030 −0.681066
\(574\) 66.1450 2.76084
\(575\) 0.447157 0.0186477
\(576\) 25.9586 1.08161
\(577\) 19.8916 0.828099 0.414050 0.910254i \(-0.364114\pi\)
0.414050 + 0.910254i \(0.364114\pi\)
\(578\) −2.31496 −0.0962898
\(579\) 8.09674 0.336489
\(580\) −19.8682 −0.824980
\(581\) −61.6277 −2.55675
\(582\) −35.1201 −1.45578
\(583\) −50.7643 −2.10244
\(584\) −12.3517 −0.511116
\(585\) 9.77883 0.404305
\(586\) 69.4630 2.86949
\(587\) −0.895011 −0.0369411 −0.0184705 0.999829i \(-0.505880\pi\)
−0.0184705 + 0.999829i \(0.505880\pi\)
\(588\) −62.1227 −2.56190
\(589\) −1.49719 −0.0616906
\(590\) −26.2781 −1.08185
\(591\) −16.0131 −0.658692
\(592\) −1.66358 −0.0683726
\(593\) 28.0200 1.15064 0.575322 0.817927i \(-0.304877\pi\)
0.575322 + 0.817927i \(0.304877\pi\)
\(594\) −45.0130 −1.84691
\(595\) −16.4635 −0.674939
\(596\) 30.7710 1.26043
\(597\) −3.64806 −0.149305
\(598\) −0.281132 −0.0114963
\(599\) −31.3412 −1.28057 −0.640284 0.768138i \(-0.721183\pi\)
−0.640284 + 0.768138i \(0.721183\pi\)
\(600\) 16.6854 0.681179
\(601\) −7.60498 −0.310214 −0.155107 0.987898i \(-0.549572\pi\)
−0.155107 + 0.987898i \(0.549572\pi\)
\(602\) 50.3401 2.05171
\(603\) 14.6789 0.597771
\(604\) 66.1793 2.69280
\(605\) −14.8513 −0.603792
\(606\) −38.6725 −1.57096
\(607\) −38.9874 −1.58245 −0.791225 0.611525i \(-0.790556\pi\)
−0.791225 + 0.611525i \(0.790556\pi\)
\(608\) 4.79367 0.194409
\(609\) −9.09662 −0.368614
\(610\) 87.8561 3.55719
\(611\) −3.43286 −0.138879
\(612\) −6.88313 −0.278234
\(613\) −24.1124 −0.973892 −0.486946 0.873432i \(-0.661889\pi\)
−0.486946 + 0.873432i \(0.661889\pi\)
\(614\) −51.0962 −2.06207
\(615\) −17.6659 −0.712359
\(616\) −63.3140 −2.55099
\(617\) 5.91291 0.238045 0.119022 0.992892i \(-0.462024\pi\)
0.119022 + 0.992892i \(0.462024\pi\)
\(618\) 25.6267 1.03086
\(619\) −29.2263 −1.17471 −0.587353 0.809331i \(-0.699830\pi\)
−0.587353 + 0.809331i \(0.699830\pi\)
\(620\) 16.8938 0.678472
\(621\) 0.404806 0.0162443
\(622\) −20.6500 −0.827990
\(623\) −46.0044 −1.84313
\(624\) −0.814024 −0.0325870
\(625\) −22.6143 −0.904573
\(626\) 8.60921 0.344093
\(627\) −3.70397 −0.147922
\(628\) 30.8357 1.23048
\(629\) −2.94351 −0.117365
\(630\) −78.0971 −3.11146
\(631\) −31.1366 −1.23953 −0.619764 0.784788i \(-0.712772\pi\)
−0.619764 + 0.784788i \(0.712772\pi\)
\(632\) 47.2344 1.87888
\(633\) −6.42046 −0.255190
\(634\) −38.1044 −1.51332
\(635\) −38.0868 −1.51143
\(636\) 42.1040 1.66953
\(637\) 28.0135 1.10994
\(638\) −16.7370 −0.662624
\(639\) 7.17002 0.283642
\(640\) −62.5445 −2.47229
\(641\) −20.8234 −0.822473 −0.411237 0.911529i \(-0.634903\pi\)
−0.411237 + 0.911529i \(0.634903\pi\)
\(642\) 15.5657 0.614329
\(643\) −44.6488 −1.76078 −0.880388 0.474254i \(-0.842718\pi\)
−0.880388 + 0.474254i \(0.842718\pi\)
\(644\) 1.40730 0.0554555
\(645\) −13.4448 −0.529388
\(646\) −2.22656 −0.0876027
\(647\) 5.83462 0.229382 0.114691 0.993401i \(-0.463412\pi\)
0.114691 + 0.993401i \(0.463412\pi\)
\(648\) −4.23560 −0.166390
\(649\) −13.8753 −0.544655
\(650\) −18.5966 −0.729417
\(651\) 7.73482 0.303152
\(652\) 42.2331 1.65397
\(653\) 7.78089 0.304490 0.152245 0.988343i \(-0.451350\pi\)
0.152245 + 0.988343i \(0.451350\pi\)
\(654\) 9.52515 0.372463
\(655\) −45.9623 −1.79589
\(656\) −3.16905 −0.123731
\(657\) −8.04472 −0.313854
\(658\) 27.4160 1.06879
\(659\) 12.2616 0.477644 0.238822 0.971063i \(-0.423239\pi\)
0.238822 + 0.971063i \(0.423239\pi\)
\(660\) 41.7944 1.62685
\(661\) 12.7416 0.495592 0.247796 0.968812i \(-0.420294\pi\)
0.247796 + 0.968812i \(0.420294\pi\)
\(662\) −31.7316 −1.23329
\(663\) −1.44032 −0.0559374
\(664\) 38.0504 1.47664
\(665\) −15.8348 −0.614046
\(666\) −13.9630 −0.541054
\(667\) 0.150517 0.00582805
\(668\) −40.6698 −1.57356
\(669\) 1.24896 0.0482877
\(670\) −53.5787 −2.06992
\(671\) 46.3897 1.79085
\(672\) −24.7652 −0.955338
\(673\) −31.2782 −1.20569 −0.602843 0.797860i \(-0.705966\pi\)
−0.602843 + 0.797860i \(0.705966\pi\)
\(674\) 7.38211 0.284348
\(675\) 26.7775 1.03066
\(676\) −36.3393 −1.39767
\(677\) 47.4505 1.82367 0.911835 0.410557i \(-0.134666\pi\)
0.911835 + 0.410557i \(0.134666\pi\)
\(678\) −34.1846 −1.31285
\(679\) −79.2775 −3.04239
\(680\) 10.1650 0.389808
\(681\) −4.86614 −0.186471
\(682\) 14.2314 0.544949
\(683\) 7.81016 0.298848 0.149424 0.988773i \(-0.452258\pi\)
0.149424 + 0.988773i \(0.452258\pi\)
\(684\) −6.62026 −0.253132
\(685\) 49.7134 1.89945
\(686\) −141.151 −5.38919
\(687\) 21.0440 0.802877
\(688\) −2.41183 −0.0919502
\(689\) −18.9863 −0.723319
\(690\) −0.599650 −0.0228283
\(691\) −2.52960 −0.0962306 −0.0481153 0.998842i \(-0.515321\pi\)
−0.0481153 + 0.998842i \(0.515321\pi\)
\(692\) −9.08428 −0.345333
\(693\) −41.2367 −1.56645
\(694\) 26.3189 0.999053
\(695\) −28.0165 −1.06273
\(696\) 5.61646 0.212892
\(697\) −5.60727 −0.212391
\(698\) 74.3432 2.81393
\(699\) −9.91614 −0.375063
\(700\) 93.0914 3.51852
\(701\) −32.2114 −1.21661 −0.608304 0.793704i \(-0.708150\pi\)
−0.608304 + 0.793704i \(0.708150\pi\)
\(702\) −16.8353 −0.635406
\(703\) −2.83110 −0.106777
\(704\) −50.0298 −1.88557
\(705\) −7.32223 −0.275771
\(706\) −2.31496 −0.0871248
\(707\) −87.2964 −3.28312
\(708\) 11.5082 0.432505
\(709\) 19.3867 0.728082 0.364041 0.931383i \(-0.381397\pi\)
0.364041 + 0.931383i \(0.381397\pi\)
\(710\) −26.1709 −0.982177
\(711\) 30.7640 1.15374
\(712\) 28.4042 1.06449
\(713\) −0.127984 −0.00479305
\(714\) 11.5029 0.430485
\(715\) −18.8467 −0.704826
\(716\) −28.0946 −1.04995
\(717\) −5.80371 −0.216744
\(718\) 19.0470 0.710828
\(719\) −38.5136 −1.43632 −0.718158 0.695880i \(-0.755015\pi\)
−0.718158 + 0.695880i \(0.755015\pi\)
\(720\) 3.74169 0.139445
\(721\) 57.8478 2.15436
\(722\) 41.8428 1.55723
\(723\) 9.32560 0.346823
\(724\) −88.7254 −3.29745
\(725\) 9.95654 0.369777
\(726\) 10.3765 0.385107
\(727\) 20.2795 0.752125 0.376062 0.926594i \(-0.377278\pi\)
0.376062 + 0.926594i \(0.377278\pi\)
\(728\) −23.6800 −0.877637
\(729\) 11.6446 0.431282
\(730\) 29.3636 1.08680
\(731\) −4.26746 −0.157838
\(732\) −38.4756 −1.42210
\(733\) −25.2118 −0.931220 −0.465610 0.884990i \(-0.654165\pi\)
−0.465610 + 0.884990i \(0.654165\pi\)
\(734\) −6.63170 −0.244780
\(735\) 59.7523 2.20400
\(736\) 0.409777 0.0151046
\(737\) −28.2905 −1.04210
\(738\) −26.5989 −0.979120
\(739\) 44.6719 1.64328 0.821641 0.570006i \(-0.193059\pi\)
0.821641 + 0.570006i \(0.193059\pi\)
\(740\) 31.9452 1.17433
\(741\) −1.38532 −0.0508908
\(742\) 151.631 5.56654
\(743\) −44.7104 −1.64026 −0.820132 0.572174i \(-0.806100\pi\)
−0.820132 + 0.572174i \(0.806100\pi\)
\(744\) −4.77566 −0.175084
\(745\) −29.5969 −1.08435
\(746\) 25.8471 0.946329
\(747\) 24.7824 0.906741
\(748\) 13.2658 0.485046
\(749\) 35.1368 1.28387
\(750\) −3.19925 −0.116820
\(751\) −32.5783 −1.18880 −0.594399 0.804170i \(-0.702610\pi\)
−0.594399 + 0.804170i \(0.702610\pi\)
\(752\) −1.31352 −0.0478992
\(753\) 19.0732 0.695065
\(754\) −6.25978 −0.227968
\(755\) −63.6541 −2.31661
\(756\) 84.2746 3.06504
\(757\) −26.4883 −0.962735 −0.481368 0.876519i \(-0.659860\pi\)
−0.481368 + 0.876519i \(0.659860\pi\)
\(758\) −30.4841 −1.10723
\(759\) −0.316626 −0.0114928
\(760\) 9.77675 0.354640
\(761\) −4.50312 −0.163238 −0.0816189 0.996664i \(-0.526009\pi\)
−0.0816189 + 0.996664i \(0.526009\pi\)
\(762\) 26.6109 0.964010
\(763\) 21.5014 0.778401
\(764\) 56.1593 2.03177
\(765\) 6.62049 0.239364
\(766\) 9.12757 0.329792
\(767\) −5.18949 −0.187382
\(768\) 18.9930 0.685352
\(769\) −38.6285 −1.39298 −0.696489 0.717567i \(-0.745256\pi\)
−0.696489 + 0.717567i \(0.745256\pi\)
\(770\) 150.516 5.42422
\(771\) 22.9184 0.825387
\(772\) −27.8911 −1.00382
\(773\) 2.65589 0.0955257 0.0477629 0.998859i \(-0.484791\pi\)
0.0477629 + 0.998859i \(0.484791\pi\)
\(774\) −20.2433 −0.727630
\(775\) −8.46601 −0.304108
\(776\) 48.9477 1.75712
\(777\) 14.6261 0.524708
\(778\) 88.4173 3.16991
\(779\) −5.39313 −0.193229
\(780\) 15.6315 0.559696
\(781\) −13.8187 −0.494473
\(782\) −0.190333 −0.00680628
\(783\) 9.01354 0.322118
\(784\) 10.7189 0.382816
\(785\) −29.6592 −1.05858
\(786\) 32.1134 1.14545
\(787\) 20.3729 0.726214 0.363107 0.931747i \(-0.381716\pi\)
0.363107 + 0.931747i \(0.381716\pi\)
\(788\) 55.1610 1.96503
\(789\) −8.26796 −0.294347
\(790\) −112.290 −3.99510
\(791\) −77.1656 −2.74369
\(792\) 25.4605 0.904700
\(793\) 17.3501 0.616121
\(794\) −3.24384 −0.115120
\(795\) −40.4974 −1.43629
\(796\) 12.5666 0.445411
\(797\) 13.5277 0.479177 0.239588 0.970875i \(-0.422988\pi\)
0.239588 + 0.970875i \(0.422988\pi\)
\(798\) 11.0636 0.391647
\(799\) −2.32412 −0.0822216
\(800\) 27.1063 0.958352
\(801\) 18.4998 0.653658
\(802\) −31.0765 −1.09735
\(803\) 15.5045 0.547143
\(804\) 23.4642 0.827518
\(805\) −1.35360 −0.0477083
\(806\) 5.32266 0.187483
\(807\) −5.79136 −0.203865
\(808\) 53.8988 1.89615
\(809\) −55.1260 −1.93813 −0.969063 0.246815i \(-0.920616\pi\)
−0.969063 + 0.246815i \(0.920616\pi\)
\(810\) 10.0693 0.353799
\(811\) 3.64856 0.128118 0.0640592 0.997946i \(-0.479595\pi\)
0.0640592 + 0.997946i \(0.479595\pi\)
\(812\) 31.3354 1.09966
\(813\) −5.65029 −0.198164
\(814\) 26.9107 0.943221
\(815\) −40.6216 −1.42291
\(816\) −0.551112 −0.0192928
\(817\) −4.10448 −0.143598
\(818\) 28.8409 1.00840
\(819\) −15.4229 −0.538919
\(820\) 60.8544 2.12513
\(821\) 8.15487 0.284607 0.142303 0.989823i \(-0.454549\pi\)
0.142303 + 0.989823i \(0.454549\pi\)
\(822\) −34.7342 −1.21150
\(823\) 43.5122 1.51674 0.758369 0.651825i \(-0.225996\pi\)
0.758369 + 0.651825i \(0.225996\pi\)
\(824\) −35.7165 −1.24424
\(825\) −20.9445 −0.729193
\(826\) 41.4450 1.44206
\(827\) −34.9566 −1.21556 −0.607780 0.794105i \(-0.707940\pi\)
−0.607780 + 0.794105i \(0.707940\pi\)
\(828\) −0.565919 −0.0196671
\(829\) −11.9545 −0.415197 −0.207599 0.978214i \(-0.566565\pi\)
−0.207599 + 0.978214i \(0.566565\pi\)
\(830\) −90.4570 −3.13981
\(831\) −14.4031 −0.499639
\(832\) −18.7116 −0.648707
\(833\) 18.9658 0.657125
\(834\) 19.5748 0.677821
\(835\) 39.1179 1.35373
\(836\) 12.7592 0.441286
\(837\) −7.66418 −0.264913
\(838\) −80.0325 −2.76468
\(839\) −31.5780 −1.09019 −0.545096 0.838374i \(-0.683507\pi\)
−0.545096 + 0.838374i \(0.683507\pi\)
\(840\) −50.5089 −1.74272
\(841\) −25.6485 −0.884432
\(842\) 80.8158 2.78510
\(843\) −1.48542 −0.0511605
\(844\) 22.1168 0.761291
\(845\) 34.9528 1.20241
\(846\) −11.0248 −0.379041
\(847\) 23.4230 0.804825
\(848\) −7.26475 −0.249472
\(849\) −4.76464 −0.163522
\(850\) −12.5903 −0.431843
\(851\) −0.242010 −0.00829601
\(852\) 11.4613 0.392657
\(853\) −9.22541 −0.315872 −0.157936 0.987449i \(-0.550484\pi\)
−0.157936 + 0.987449i \(0.550484\pi\)
\(854\) −138.564 −4.74156
\(855\) 6.36765 0.217769
\(856\) −21.6943 −0.741496
\(857\) −2.24654 −0.0767402 −0.0383701 0.999264i \(-0.512217\pi\)
−0.0383701 + 0.999264i \(0.512217\pi\)
\(858\) 13.1680 0.449548
\(859\) 7.79945 0.266114 0.133057 0.991108i \(-0.457521\pi\)
0.133057 + 0.991108i \(0.457521\pi\)
\(860\) 46.3137 1.57928
\(861\) 27.8622 0.949540
\(862\) 50.9285 1.73463
\(863\) −2.54935 −0.0867810 −0.0433905 0.999058i \(-0.513816\pi\)
−0.0433905 + 0.999058i \(0.513816\pi\)
\(864\) 24.5390 0.834834
\(865\) 8.73766 0.297089
\(866\) 18.4460 0.626819
\(867\) −0.975130 −0.0331171
\(868\) −26.6444 −0.904370
\(869\) −59.2913 −2.01132
\(870\) −13.3520 −0.452675
\(871\) −10.5809 −0.358520
\(872\) −13.2754 −0.449563
\(873\) 31.8799 1.07897
\(874\) −0.183064 −0.00619222
\(875\) −7.22173 −0.244139
\(876\) −12.8595 −0.434481
\(877\) 17.4325 0.588653 0.294326 0.955705i \(-0.404905\pi\)
0.294326 + 0.955705i \(0.404905\pi\)
\(878\) 65.1743 2.19953
\(879\) 29.2598 0.986909
\(880\) −7.21134 −0.243094
\(881\) −11.9016 −0.400977 −0.200488 0.979696i \(-0.564253\pi\)
−0.200488 + 0.979696i \(0.564253\pi\)
\(882\) 89.9669 3.02934
\(883\) 0.299105 0.0100657 0.00503285 0.999987i \(-0.498398\pi\)
0.00503285 + 0.999987i \(0.498398\pi\)
\(884\) 4.96152 0.166874
\(885\) −11.0691 −0.372084
\(886\) 18.8134 0.632050
\(887\) 15.6498 0.525468 0.262734 0.964868i \(-0.415376\pi\)
0.262734 + 0.964868i \(0.415376\pi\)
\(888\) −9.03048 −0.303043
\(889\) 60.0693 2.01466
\(890\) −67.5251 −2.26345
\(891\) 5.31677 0.178118
\(892\) −4.30234 −0.144053
\(893\) −2.23536 −0.0748036
\(894\) 20.6790 0.691610
\(895\) 27.0226 0.903267
\(896\) 98.6433 3.29544
\(897\) −0.118421 −0.00395396
\(898\) −50.1594 −1.67384
\(899\) −2.84974 −0.0950441
\(900\) −37.4349 −1.24783
\(901\) −12.8541 −0.428233
\(902\) 51.2639 1.70690
\(903\) 21.2047 0.705648
\(904\) 47.6438 1.58461
\(905\) 85.3399 2.83679
\(906\) 44.4745 1.47757
\(907\) 29.7957 0.989349 0.494675 0.869078i \(-0.335287\pi\)
0.494675 + 0.869078i \(0.335287\pi\)
\(908\) 16.7626 0.556285
\(909\) 35.1046 1.16435
\(910\) 56.2943 1.86614
\(911\) 48.9586 1.62207 0.811035 0.584998i \(-0.198905\pi\)
0.811035 + 0.584998i \(0.198905\pi\)
\(912\) −0.530065 −0.0175522
\(913\) −47.7630 −1.58072
\(914\) −36.3571 −1.20258
\(915\) 37.0075 1.22343
\(916\) −72.4908 −2.39516
\(917\) 72.4903 2.39384
\(918\) −11.3978 −0.376185
\(919\) 15.9791 0.527102 0.263551 0.964645i \(-0.415106\pi\)
0.263551 + 0.964645i \(0.415106\pi\)
\(920\) 0.835746 0.0275537
\(921\) −21.5232 −0.709213
\(922\) −54.8439 −1.80619
\(923\) −5.16832 −0.170117
\(924\) −65.9169 −2.16851
\(925\) −16.0087 −0.526363
\(926\) 32.3498 1.06308
\(927\) −23.2624 −0.764037
\(928\) 9.12423 0.299518
\(929\) 50.0587 1.64237 0.821186 0.570660i \(-0.193313\pi\)
0.821186 + 0.570660i \(0.193313\pi\)
\(930\) 11.3532 0.372284
\(931\) 18.2415 0.597840
\(932\) 34.1584 1.11890
\(933\) −8.69838 −0.284772
\(934\) −69.9730 −2.28959
\(935\) −12.7596 −0.417284
\(936\) 9.52244 0.311251
\(937\) 25.4041 0.829917 0.414958 0.909840i \(-0.363796\pi\)
0.414958 + 0.909840i \(0.363796\pi\)
\(938\) 84.5026 2.75911
\(939\) 3.62645 0.118345
\(940\) 25.2231 0.822688
\(941\) 43.9137 1.43155 0.715773 0.698333i \(-0.246074\pi\)
0.715773 + 0.698333i \(0.246074\pi\)
\(942\) 20.7226 0.675177
\(943\) −0.461021 −0.0150129
\(944\) −1.98566 −0.0646278
\(945\) −81.0589 −2.63685
\(946\) 39.0148 1.26848
\(947\) −7.18780 −0.233572 −0.116786 0.993157i \(-0.537259\pi\)
−0.116786 + 0.993157i \(0.537259\pi\)
\(948\) 49.1762 1.59717
\(949\) 5.79883 0.188238
\(950\) −12.1095 −0.392883
\(951\) −16.0507 −0.520478
\(952\) −16.0319 −0.519595
\(953\) 7.07513 0.229186 0.114593 0.993413i \(-0.463444\pi\)
0.114593 + 0.993413i \(0.463444\pi\)
\(954\) −60.9754 −1.97415
\(955\) −54.0165 −1.74793
\(956\) 19.9922 0.646595
\(957\) −7.05010 −0.227898
\(958\) 43.9432 1.41974
\(959\) −78.4064 −2.53188
\(960\) −39.9115 −1.28814
\(961\) −28.5769 −0.921835
\(962\) 10.0648 0.324503
\(963\) −14.1296 −0.455320
\(964\) −32.1242 −1.03465
\(965\) 26.8269 0.863588
\(966\) 0.945749 0.0304290
\(967\) −51.2004 −1.64649 −0.823247 0.567684i \(-0.807840\pi\)
−0.823247 + 0.567684i \(0.807840\pi\)
\(968\) −14.4619 −0.464824
\(969\) −0.937889 −0.0301293
\(970\) −116.363 −3.73620
\(971\) 55.5540 1.78281 0.891407 0.453204i \(-0.149719\pi\)
0.891407 + 0.453204i \(0.149719\pi\)
\(972\) −54.0252 −1.73286
\(973\) 44.1867 1.41656
\(974\) −50.2968 −1.61161
\(975\) −7.83340 −0.250870
\(976\) 6.63870 0.212500
\(977\) −58.5148 −1.87205 −0.936026 0.351930i \(-0.885526\pi\)
−0.936026 + 0.351930i \(0.885526\pi\)
\(978\) 28.3819 0.907553
\(979\) −35.6545 −1.13952
\(980\) −205.831 −6.57502
\(981\) −8.64636 −0.276057
\(982\) 66.7030 2.12858
\(983\) 24.1245 0.769453 0.384727 0.923031i \(-0.374296\pi\)
0.384727 + 0.923031i \(0.374296\pi\)
\(984\) −17.2027 −0.548403
\(985\) −53.0562 −1.69051
\(986\) −4.23801 −0.134966
\(987\) 11.5484 0.367590
\(988\) 4.77204 0.151819
\(989\) −0.350863 −0.0111568
\(990\) −60.5272 −1.92368
\(991\) −42.6626 −1.35522 −0.677611 0.735421i \(-0.736985\pi\)
−0.677611 + 0.735421i \(0.736985\pi\)
\(992\) −7.75830 −0.246326
\(993\) −13.3663 −0.424166
\(994\) 41.2760 1.30919
\(995\) −12.0871 −0.383186
\(996\) 39.6147 1.25524
\(997\) 7.28060 0.230579 0.115290 0.993332i \(-0.463220\pi\)
0.115290 + 0.993332i \(0.463220\pi\)
\(998\) −39.8403 −1.26112
\(999\) −14.4925 −0.458523
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 \(a_p\))