Properties

Label 6026.2.a.h.1.1
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.27057 q^{3} +1.00000 q^{4} -0.103796 q^{5} +3.27057 q^{6} +0.553111 q^{7} -1.00000 q^{8} +7.69663 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.27057 q^{3} +1.00000 q^{4} -0.103796 q^{5} +3.27057 q^{6} +0.553111 q^{7} -1.00000 q^{8} +7.69663 q^{9} +0.103796 q^{10} +0.813628 q^{11} -3.27057 q^{12} +6.58692 q^{13} -0.553111 q^{14} +0.339471 q^{15} +1.00000 q^{16} +5.83144 q^{17} -7.69663 q^{18} +3.59717 q^{19} -0.103796 q^{20} -1.80899 q^{21} -0.813628 q^{22} -1.00000 q^{23} +3.27057 q^{24} -4.98923 q^{25} -6.58692 q^{26} -15.3607 q^{27} +0.553111 q^{28} -5.37661 q^{29} -0.339471 q^{30} -7.85678 q^{31} -1.00000 q^{32} -2.66103 q^{33} -5.83144 q^{34} -0.0574106 q^{35} +7.69663 q^{36} +0.849438 q^{37} -3.59717 q^{38} -21.5430 q^{39} +0.103796 q^{40} +2.88800 q^{41} +1.80899 q^{42} -6.56175 q^{43} +0.813628 q^{44} -0.798877 q^{45} +1.00000 q^{46} -4.80920 q^{47} -3.27057 q^{48} -6.69407 q^{49} +4.98923 q^{50} -19.0721 q^{51} +6.58692 q^{52} +3.40640 q^{53} +15.3607 q^{54} -0.0844511 q^{55} -0.553111 q^{56} -11.7648 q^{57} +5.37661 q^{58} -3.93780 q^{59} +0.339471 q^{60} +3.68508 q^{61} +7.85678 q^{62} +4.25709 q^{63} +1.00000 q^{64} -0.683695 q^{65} +2.66103 q^{66} +0.873340 q^{67} +5.83144 q^{68} +3.27057 q^{69} +0.0574106 q^{70} +6.26870 q^{71} -7.69663 q^{72} -10.8758 q^{73} -0.849438 q^{74} +16.3176 q^{75} +3.59717 q^{76} +0.450027 q^{77} +21.5430 q^{78} +5.08034 q^{79} -0.103796 q^{80} +27.1482 q^{81} -2.88800 q^{82} -14.7386 q^{83} -1.80899 q^{84} -0.605278 q^{85} +6.56175 q^{86} +17.5846 q^{87} -0.813628 q^{88} -1.29826 q^{89} +0.798877 q^{90} +3.64330 q^{91} -1.00000 q^{92} +25.6962 q^{93} +4.80920 q^{94} -0.373371 q^{95} +3.27057 q^{96} -5.53397 q^{97} +6.69407 q^{98} +6.26219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + O(q^{10}) \) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + q^{10} - 4q^{11} - q^{12} - 5q^{13} + 7q^{14} - 6q^{15} + 24q^{16} + 5q^{17} - 27q^{18} - 20q^{19} - q^{20} + 4q^{22} - 24q^{23} + q^{24} + q^{25} + 5q^{26} - q^{27} - 7q^{28} - 6q^{29} + 6q^{30} - 23q^{31} - 24q^{32} - 6q^{33} - 5q^{34} + 5q^{35} + 27q^{36} - 6q^{37} + 20q^{38} - 39q^{39} + q^{40} - q^{41} - 44q^{43} - 4q^{44} - 13q^{45} + 24q^{46} + 32q^{47} - q^{48} - 13q^{49} - q^{50} - 44q^{51} - 5q^{52} + 21q^{53} + q^{54} - 13q^{55} + 7q^{56} + 10q^{57} + 6q^{58} - 24q^{59} - 6q^{60} - 40q^{61} + 23q^{62} - 54q^{63} + 24q^{64} - 29q^{65} + 6q^{66} - 17q^{67} + 5q^{68} + q^{69} - 5q^{70} + 4q^{71} - 27q^{72} - 16q^{73} + 6q^{74} - 36q^{75} - 20q^{76} + 24q^{77} + 39q^{78} - 53q^{79} - q^{80} + 24q^{81} + q^{82} - 9q^{83} - 37q^{85} + 44q^{86} + 7q^{87} + 4q^{88} - 46q^{89} + 13q^{90} - 44q^{91} - 24q^{92} + 23q^{93} - 32q^{94} + 28q^{95} + q^{96} - 20q^{97} + 13q^{98} - 78q^{99} + O(q^{100}) \)

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
\(3\) −3.27057 −1.88826 −0.944132 0.329567i \(-0.893097\pi\)
−0.944132 + 0.329567i \(0.893097\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.103796 −0.0464189 −0.0232094 0.999731i \(-0.507388\pi\)
−0.0232094 + 0.999731i \(0.507388\pi\)
\(6\) 3.27057 1.33520
\(7\) 0.553111 0.209056 0.104528 0.994522i \(-0.466667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(8\) −1.00000 −0.353553
\(9\) 7.69663 2.56554
\(10\) 0.103796 0.0328231
\(11\) 0.813628 0.245318 0.122659 0.992449i \(-0.460858\pi\)
0.122659 + 0.992449i \(0.460858\pi\)
\(12\) −3.27057 −0.944132
\(13\) 6.58692 1.82688 0.913442 0.406969i \(-0.133414\pi\)
0.913442 + 0.406969i \(0.133414\pi\)
\(14\) −0.553111 −0.147825
\(15\) 0.339471 0.0876511
\(16\) 1.00000 0.250000
\(17\) 5.83144 1.41433 0.707166 0.707048i \(-0.249974\pi\)
0.707166 + 0.707048i \(0.249974\pi\)
\(18\) −7.69663 −1.81411
\(19\) 3.59717 0.825247 0.412623 0.910902i \(-0.364613\pi\)
0.412623 + 0.910902i \(0.364613\pi\)
\(20\) −0.103796 −0.0232094
\(21\) −1.80899 −0.394754
\(22\) −0.813628 −0.173466
\(23\) −1.00000 −0.208514
\(24\) 3.27057 0.667602
\(25\) −4.98923 −0.997845
\(26\) −6.58692 −1.29180
\(27\) −15.3607 −2.95616
\(28\) 0.553111 0.104528
\(29\) −5.37661 −0.998411 −0.499205 0.866484i \(-0.666375\pi\)
−0.499205 + 0.866484i \(0.666375\pi\)
\(30\) −0.339471 −0.0619787
\(31\) −7.85678 −1.41112 −0.705560 0.708650i \(-0.749304\pi\)
−0.705560 + 0.708650i \(0.749304\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.66103 −0.463225
\(34\) −5.83144 −1.00008
\(35\) −0.0574106 −0.00970416
\(36\) 7.69663 1.28277
\(37\) 0.849438 0.139647 0.0698233 0.997559i \(-0.477756\pi\)
0.0698233 + 0.997559i \(0.477756\pi\)
\(38\) −3.59717 −0.583538
\(39\) −21.5430 −3.44964
\(40\) 0.103796 0.0164115
\(41\) 2.88800 0.451030 0.225515 0.974240i \(-0.427593\pi\)
0.225515 + 0.974240i \(0.427593\pi\)
\(42\) 1.80899 0.279133
\(43\) −6.56175 −1.00066 −0.500329 0.865835i \(-0.666788\pi\)
−0.500329 + 0.865835i \(0.666788\pi\)
\(44\) 0.813628 0.122659
\(45\) −0.798877 −0.119090
\(46\) 1.00000 0.147442
\(47\) −4.80920 −0.701493 −0.350747 0.936470i \(-0.614072\pi\)
−0.350747 + 0.936470i \(0.614072\pi\)
\(48\) −3.27057 −0.472066
\(49\) −6.69407 −0.956295
\(50\) 4.98923 0.705583
\(51\) −19.0721 −2.67063
\(52\) 6.58692 0.913442
\(53\) 3.40640 0.467905 0.233952 0.972248i \(-0.424834\pi\)
0.233952 + 0.972248i \(0.424834\pi\)
\(54\) 15.3607 2.09032
\(55\) −0.0844511 −0.0113874
\(56\) −0.553111 −0.0739126
\(57\) −11.7648 −1.55828
\(58\) 5.37661 0.705983
\(59\) −3.93780 −0.512658 −0.256329 0.966590i \(-0.582513\pi\)
−0.256329 + 0.966590i \(0.582513\pi\)
\(60\) 0.339471 0.0438255
\(61\) 3.68508 0.471826 0.235913 0.971774i \(-0.424192\pi\)
0.235913 + 0.971774i \(0.424192\pi\)
\(62\) 7.85678 0.997813
\(63\) 4.25709 0.536343
\(64\) 1.00000 0.125000
\(65\) −0.683695 −0.0848019
\(66\) 2.66103 0.327550
\(67\) 0.873340 0.106695 0.0533477 0.998576i \(-0.483011\pi\)
0.0533477 + 0.998576i \(0.483011\pi\)
\(68\) 5.83144 0.707166
\(69\) 3.27057 0.393730
\(70\) 0.0574106 0.00686188
\(71\) 6.26870 0.743957 0.371979 0.928241i \(-0.378679\pi\)
0.371979 + 0.928241i \(0.378679\pi\)
\(72\) −7.69663 −0.907056
\(73\) −10.8758 −1.27291 −0.636455 0.771314i \(-0.719600\pi\)
−0.636455 + 0.771314i \(0.719600\pi\)
\(74\) −0.849438 −0.0987451
\(75\) 16.3176 1.88420
\(76\) 3.59717 0.412623
\(77\) 0.450027 0.0512853
\(78\) 21.5430 2.43926
\(79\) 5.08034 0.571583 0.285792 0.958292i \(-0.407743\pi\)
0.285792 + 0.958292i \(0.407743\pi\)
\(80\) −0.103796 −0.0116047
\(81\) 27.1482 3.01647
\(82\) −2.88800 −0.318927
\(83\) −14.7386 −1.61777 −0.808886 0.587965i \(-0.799929\pi\)
−0.808886 + 0.587965i \(0.799929\pi\)
\(84\) −1.80899 −0.197377
\(85\) −0.605278 −0.0656516
\(86\) 6.56175 0.707572
\(87\) 17.5846 1.88526
\(88\) −0.813628 −0.0867330
\(89\) −1.29826 −0.137616 −0.0688078 0.997630i \(-0.521920\pi\)
−0.0688078 + 0.997630i \(0.521920\pi\)
\(90\) 0.798877 0.0842090
\(91\) 3.64330 0.381922
\(92\) −1.00000 −0.104257
\(93\) 25.6962 2.66457
\(94\) 4.80920 0.496031
\(95\) −0.373371 −0.0383070
\(96\) 3.27057 0.333801
\(97\) −5.53397 −0.561890 −0.280945 0.959724i \(-0.590648\pi\)
−0.280945 + 0.959724i \(0.590648\pi\)
\(98\) 6.69407 0.676203
\(99\) 6.26219 0.629374
\(100\) −4.98923 −0.498923
\(101\) −6.54370 −0.651122 −0.325561 0.945521i \(-0.605553\pi\)
−0.325561 + 0.945521i \(0.605553\pi\)
\(102\) 19.0721 1.88842
\(103\) −15.6836 −1.54535 −0.772674 0.634803i \(-0.781081\pi\)
−0.772674 + 0.634803i \(0.781081\pi\)
\(104\) −6.58692 −0.645901
\(105\) 0.187765 0.0183240
\(106\) −3.40640 −0.330859
\(107\) 12.2966 1.18875 0.594377 0.804187i \(-0.297399\pi\)
0.594377 + 0.804187i \(0.297399\pi\)
\(108\) −15.3607 −1.47808
\(109\) −17.0299 −1.63117 −0.815587 0.578635i \(-0.803586\pi\)
−0.815587 + 0.578635i \(0.803586\pi\)
\(110\) 0.0844511 0.00805210
\(111\) −2.77815 −0.263690
\(112\) 0.553111 0.0522641
\(113\) 10.7077 1.00730 0.503650 0.863908i \(-0.331990\pi\)
0.503650 + 0.863908i \(0.331990\pi\)
\(114\) 11.7648 1.10187
\(115\) 0.103796 0.00967900
\(116\) −5.37661 −0.499205
\(117\) 50.6971 4.68695
\(118\) 3.93780 0.362504
\(119\) 3.22543 0.295675
\(120\) −0.339471 −0.0309893
\(121\) −10.3380 −0.939819
\(122\) −3.68508 −0.333631
\(123\) −9.44542 −0.851665
\(124\) −7.85678 −0.705560
\(125\) 1.03684 0.0927377
\(126\) −4.25709 −0.379252
\(127\) −11.4513 −1.01614 −0.508070 0.861315i \(-0.669641\pi\)
−0.508070 + 0.861315i \(0.669641\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 21.4607 1.88951
\(130\) 0.683695 0.0599640
\(131\) −1.00000 −0.0873704
\(132\) −2.66103 −0.231613
\(133\) 1.98963 0.172523
\(134\) −0.873340 −0.0754451
\(135\) 1.59437 0.137222
\(136\) −5.83144 −0.500042
\(137\) 5.16549 0.441317 0.220659 0.975351i \(-0.429179\pi\)
0.220659 + 0.975351i \(0.429179\pi\)
\(138\) −3.27057 −0.278409
\(139\) −8.99810 −0.763209 −0.381605 0.924326i \(-0.624628\pi\)
−0.381605 + 0.924326i \(0.624628\pi\)
\(140\) −0.0574106 −0.00485208
\(141\) 15.7288 1.32460
\(142\) −6.26870 −0.526057
\(143\) 5.35930 0.448168
\(144\) 7.69663 0.641386
\(145\) 0.558069 0.0463451
\(146\) 10.8758 0.900084
\(147\) 21.8934 1.80574
\(148\) 0.849438 0.0698233
\(149\) −9.32690 −0.764090 −0.382045 0.924144i \(-0.624780\pi\)
−0.382045 + 0.924144i \(0.624780\pi\)
\(150\) −16.3176 −1.33233
\(151\) 0.997646 0.0811873 0.0405936 0.999176i \(-0.487075\pi\)
0.0405936 + 0.999176i \(0.487075\pi\)
\(152\) −3.59717 −0.291769
\(153\) 44.8824 3.62853
\(154\) −0.450027 −0.0362642
\(155\) 0.815501 0.0655026
\(156\) −21.5430 −1.72482
\(157\) 8.07137 0.644165 0.322083 0.946712i \(-0.395617\pi\)
0.322083 + 0.946712i \(0.395617\pi\)
\(158\) −5.08034 −0.404170
\(159\) −11.1409 −0.883528
\(160\) 0.103796 0.00820577
\(161\) −0.553111 −0.0435913
\(162\) −27.1482 −2.13296
\(163\) −12.8186 −1.00403 −0.502016 0.864858i \(-0.667408\pi\)
−0.502016 + 0.864858i \(0.667408\pi\)
\(164\) 2.88800 0.225515
\(165\) 0.276203 0.0215024
\(166\) 14.7386 1.14394
\(167\) 4.11370 0.318328 0.159164 0.987252i \(-0.449120\pi\)
0.159164 + 0.987252i \(0.449120\pi\)
\(168\) 1.80899 0.139567
\(169\) 30.3876 2.33750
\(170\) 0.605278 0.0464227
\(171\) 27.6861 2.11721
\(172\) −6.56175 −0.500329
\(173\) 19.5085 1.48320 0.741601 0.670841i \(-0.234067\pi\)
0.741601 + 0.670841i \(0.234067\pi\)
\(174\) −17.5846 −1.33308
\(175\) −2.75960 −0.208606
\(176\) 0.813628 0.0613295
\(177\) 12.8788 0.968033
\(178\) 1.29826 0.0973090
\(179\) −4.98903 −0.372897 −0.186449 0.982465i \(-0.559698\pi\)
−0.186449 + 0.982465i \(0.559698\pi\)
\(180\) −0.798877 −0.0595448
\(181\) −16.2634 −1.20885 −0.604424 0.796663i \(-0.706597\pi\)
−0.604424 + 0.796663i \(0.706597\pi\)
\(182\) −3.64330 −0.270060
\(183\) −12.0523 −0.890932
\(184\) 1.00000 0.0737210
\(185\) −0.0881680 −0.00648224
\(186\) −25.6962 −1.88413
\(187\) 4.74462 0.346961
\(188\) −4.80920 −0.350747
\(189\) −8.49615 −0.618004
\(190\) 0.373371 0.0270871
\(191\) −25.3888 −1.83707 −0.918534 0.395341i \(-0.870626\pi\)
−0.918534 + 0.395341i \(0.870626\pi\)
\(192\) −3.27057 −0.236033
\(193\) 23.8491 1.71670 0.858348 0.513069i \(-0.171491\pi\)
0.858348 + 0.513069i \(0.171491\pi\)
\(194\) 5.53397 0.397316
\(195\) 2.23607 0.160128
\(196\) −6.69407 −0.478148
\(197\) −21.3368 −1.52018 −0.760092 0.649815i \(-0.774846\pi\)
−0.760092 + 0.649815i \(0.774846\pi\)
\(198\) −6.26219 −0.445035
\(199\) −1.55914 −0.110525 −0.0552624 0.998472i \(-0.517600\pi\)
−0.0552624 + 0.998472i \(0.517600\pi\)
\(200\) 4.98923 0.352792
\(201\) −2.85632 −0.201469
\(202\) 6.54370 0.460413
\(203\) −2.97386 −0.208724
\(204\) −19.0721 −1.33532
\(205\) −0.299762 −0.0209363
\(206\) 15.6836 1.09273
\(207\) −7.69663 −0.534953
\(208\) 6.58692 0.456721
\(209\) 2.92676 0.202448
\(210\) −0.187765 −0.0129570
\(211\) −10.6739 −0.734822 −0.367411 0.930059i \(-0.619756\pi\)
−0.367411 + 0.930059i \(0.619756\pi\)
\(212\) 3.40640 0.233952
\(213\) −20.5022 −1.40479
\(214\) −12.2966 −0.840576
\(215\) 0.681082 0.0464494
\(216\) 15.3607 1.04516
\(217\) −4.34568 −0.295004
\(218\) 17.0299 1.15341
\(219\) 35.5699 2.40359
\(220\) −0.0844511 −0.00569369
\(221\) 38.4112 2.58382
\(222\) 2.77815 0.186457
\(223\) −18.7321 −1.25439 −0.627196 0.778861i \(-0.715798\pi\)
−0.627196 + 0.778861i \(0.715798\pi\)
\(224\) −0.553111 −0.0369563
\(225\) −38.4002 −2.56001
\(226\) −10.7077 −0.712269
\(227\) −15.9561 −1.05904 −0.529521 0.848297i \(-0.677628\pi\)
−0.529521 + 0.848297i \(0.677628\pi\)
\(228\) −11.7648 −0.779142
\(229\) −4.97330 −0.328645 −0.164323 0.986407i \(-0.552544\pi\)
−0.164323 + 0.986407i \(0.552544\pi\)
\(230\) −0.103796 −0.00684409
\(231\) −1.47184 −0.0968403
\(232\) 5.37661 0.352992
\(233\) 17.6289 1.15491 0.577455 0.816422i \(-0.304046\pi\)
0.577455 + 0.816422i \(0.304046\pi\)
\(234\) −50.6971 −3.31417
\(235\) 0.499174 0.0325625
\(236\) −3.93780 −0.256329
\(237\) −16.6156 −1.07930
\(238\) −3.22543 −0.209074
\(239\) 17.1659 1.11037 0.555184 0.831728i \(-0.312648\pi\)
0.555184 + 0.831728i \(0.312648\pi\)
\(240\) 0.339471 0.0219128
\(241\) −2.77248 −0.178591 −0.0892955 0.996005i \(-0.528462\pi\)
−0.0892955 + 0.996005i \(0.528462\pi\)
\(242\) 10.3380 0.664552
\(243\) −42.7082 −2.73973
\(244\) 3.68508 0.235913
\(245\) 0.694816 0.0443901
\(246\) 9.44542 0.602218
\(247\) 23.6943 1.50763
\(248\) 7.85678 0.498906
\(249\) 48.2036 3.05478
\(250\) −1.03684 −0.0655755
\(251\) 10.5438 0.665520 0.332760 0.943011i \(-0.392020\pi\)
0.332760 + 0.943011i \(0.392020\pi\)
\(252\) 4.25709 0.268172
\(253\) −0.813628 −0.0511523
\(254\) 11.4513 0.718520
\(255\) 1.97960 0.123968
\(256\) 1.00000 0.0625000
\(257\) −12.9752 −0.809372 −0.404686 0.914456i \(-0.632619\pi\)
−0.404686 + 0.914456i \(0.632619\pi\)
\(258\) −21.4607 −1.33608
\(259\) 0.469834 0.0291940
\(260\) −0.683695 −0.0424009
\(261\) −41.3817 −2.56147
\(262\) 1.00000 0.0617802
\(263\) 26.6163 1.64123 0.820617 0.571479i \(-0.193630\pi\)
0.820617 + 0.571479i \(0.193630\pi\)
\(264\) 2.66103 0.163775
\(265\) −0.353569 −0.0217196
\(266\) −1.98963 −0.121992
\(267\) 4.24606 0.259855
\(268\) 0.873340 0.0533477
\(269\) −23.2985 −1.42054 −0.710269 0.703931i \(-0.751426\pi\)
−0.710269 + 0.703931i \(0.751426\pi\)
\(270\) −1.59437 −0.0970303
\(271\) −6.30180 −0.382807 −0.191404 0.981511i \(-0.561304\pi\)
−0.191404 + 0.981511i \(0.561304\pi\)
\(272\) 5.83144 0.353583
\(273\) −11.9157 −0.721170
\(274\) −5.16549 −0.312059
\(275\) −4.05937 −0.244789
\(276\) 3.27057 0.196865
\(277\) 17.7476 1.06635 0.533176 0.846005i \(-0.320998\pi\)
0.533176 + 0.846005i \(0.320998\pi\)
\(278\) 8.99810 0.539670
\(279\) −60.4708 −3.62029
\(280\) 0.0574106 0.00343094
\(281\) −23.4346 −1.39799 −0.698996 0.715126i \(-0.746369\pi\)
−0.698996 + 0.715126i \(0.746369\pi\)
\(282\) −15.7288 −0.936637
\(283\) 31.8897 1.89565 0.947823 0.318797i \(-0.103279\pi\)
0.947823 + 0.318797i \(0.103279\pi\)
\(284\) 6.26870 0.371979
\(285\) 1.22113 0.0723338
\(286\) −5.35930 −0.316902
\(287\) 1.59739 0.0942908
\(288\) −7.69663 −0.453528
\(289\) 17.0056 1.00033
\(290\) −0.558069 −0.0327709
\(291\) 18.0993 1.06100
\(292\) −10.8758 −0.636455
\(293\) −2.58226 −0.150857 −0.0754286 0.997151i \(-0.524032\pi\)
−0.0754286 + 0.997151i \(0.524032\pi\)
\(294\) −21.8934 −1.27685
\(295\) 0.408727 0.0237970
\(296\) −0.849438 −0.0493726
\(297\) −12.4979 −0.725199
\(298\) 9.32690 0.540293
\(299\) −6.58692 −0.380932
\(300\) 16.3176 0.942098
\(301\) −3.62938 −0.209194
\(302\) −0.997646 −0.0574081
\(303\) 21.4016 1.22949
\(304\) 3.59717 0.206312
\(305\) −0.382495 −0.0219016
\(306\) −44.8824 −2.56576
\(307\) −21.7822 −1.24318 −0.621588 0.783345i \(-0.713512\pi\)
−0.621588 + 0.783345i \(0.713512\pi\)
\(308\) 0.450027 0.0256427
\(309\) 51.2942 2.91803
\(310\) −0.815501 −0.0463173
\(311\) 1.83548 0.104080 0.0520402 0.998645i \(-0.483428\pi\)
0.0520402 + 0.998645i \(0.483428\pi\)
\(312\) 21.5430 1.21963
\(313\) 21.1874 1.19758 0.598792 0.800905i \(-0.295648\pi\)
0.598792 + 0.800905i \(0.295648\pi\)
\(314\) −8.07137 −0.455494
\(315\) −0.441868 −0.0248965
\(316\) 5.08034 0.285792
\(317\) 21.2260 1.19217 0.596085 0.802921i \(-0.296722\pi\)
0.596085 + 0.802921i \(0.296722\pi\)
\(318\) 11.1409 0.624748
\(319\) −4.37456 −0.244928
\(320\) −0.103796 −0.00580236
\(321\) −40.2168 −2.24468
\(322\) 0.553111 0.0308237
\(323\) 20.9766 1.16717
\(324\) 27.1482 1.50823
\(325\) −32.8637 −1.82295
\(326\) 12.8186 0.709958
\(327\) 55.6976 3.08009
\(328\) −2.88800 −0.159463
\(329\) −2.66002 −0.146652
\(330\) −0.276203 −0.0152045
\(331\) −0.479692 −0.0263662 −0.0131831 0.999913i \(-0.504196\pi\)
−0.0131831 + 0.999913i \(0.504196\pi\)
\(332\) −14.7386 −0.808886
\(333\) 6.53781 0.358270
\(334\) −4.11370 −0.225092
\(335\) −0.0906490 −0.00495268
\(336\) −1.80899 −0.0986885
\(337\) −6.87190 −0.374336 −0.187168 0.982328i \(-0.559931\pi\)
−0.187168 + 0.982328i \(0.559931\pi\)
\(338\) −30.3876 −1.65287
\(339\) −35.0204 −1.90205
\(340\) −0.605278 −0.0328258
\(341\) −6.39250 −0.346173
\(342\) −27.6861 −1.49709
\(343\) −7.57435 −0.408976
\(344\) 6.56175 0.353786
\(345\) −0.339471 −0.0182765
\(346\) −19.5085 −1.04878
\(347\) −22.5168 −1.20876 −0.604382 0.796695i \(-0.706580\pi\)
−0.604382 + 0.796695i \(0.706580\pi\)
\(348\) 17.5846 0.942632
\(349\) −33.9857 −1.81921 −0.909607 0.415470i \(-0.863617\pi\)
−0.909607 + 0.415470i \(0.863617\pi\)
\(350\) 2.75960 0.147507
\(351\) −101.179 −5.40056
\(352\) −0.813628 −0.0433665
\(353\) 8.70927 0.463548 0.231774 0.972770i \(-0.425547\pi\)
0.231774 + 0.972770i \(0.425547\pi\)
\(354\) −12.8788 −0.684503
\(355\) −0.650664 −0.0345337
\(356\) −1.29826 −0.0688078
\(357\) −10.5490 −0.558313
\(358\) 4.98903 0.263678
\(359\) 25.6573 1.35414 0.677069 0.735920i \(-0.263250\pi\)
0.677069 + 0.735920i \(0.263250\pi\)
\(360\) 0.798877 0.0421045
\(361\) −6.06039 −0.318968
\(362\) 16.2634 0.854785
\(363\) 33.8112 1.77463
\(364\) 3.64330 0.190961
\(365\) 1.12886 0.0590871
\(366\) 12.0523 0.629984
\(367\) 31.5144 1.64504 0.822518 0.568739i \(-0.192568\pi\)
0.822518 + 0.568739i \(0.192568\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 22.2279 1.15714
\(370\) 0.0881680 0.00458364
\(371\) 1.88412 0.0978185
\(372\) 25.6962 1.33228
\(373\) −13.1965 −0.683291 −0.341645 0.939829i \(-0.610984\pi\)
−0.341645 + 0.939829i \(0.610984\pi\)
\(374\) −4.74462 −0.245338
\(375\) −3.39105 −0.175113
\(376\) 4.80920 0.248015
\(377\) −35.4153 −1.82398
\(378\) 8.49615 0.436995
\(379\) −29.7503 −1.52817 −0.764085 0.645116i \(-0.776809\pi\)
−0.764085 + 0.645116i \(0.776809\pi\)
\(380\) −0.373371 −0.0191535
\(381\) 37.4524 1.91874
\(382\) 25.3888 1.29900
\(383\) 17.7377 0.906354 0.453177 0.891421i \(-0.350291\pi\)
0.453177 + 0.891421i \(0.350291\pi\)
\(384\) 3.27057 0.166901
\(385\) −0.0467109 −0.00238061
\(386\) −23.8491 −1.21389
\(387\) −50.5034 −2.56723
\(388\) −5.53397 −0.280945
\(389\) −23.4052 −1.18669 −0.593346 0.804948i \(-0.702193\pi\)
−0.593346 + 0.804948i \(0.702193\pi\)
\(390\) −2.23607 −0.113228
\(391\) −5.83144 −0.294908
\(392\) 6.69407 0.338101
\(393\) 3.27057 0.164978
\(394\) 21.3368 1.07493
\(395\) −0.527318 −0.0265322
\(396\) 6.26219 0.314687
\(397\) −28.6307 −1.43693 −0.718467 0.695561i \(-0.755156\pi\)
−0.718467 + 0.695561i \(0.755156\pi\)
\(398\) 1.55914 0.0781528
\(399\) −6.50724 −0.325769
\(400\) −4.98923 −0.249461
\(401\) 25.6823 1.28251 0.641256 0.767327i \(-0.278414\pi\)
0.641256 + 0.767327i \(0.278414\pi\)
\(402\) 2.85632 0.142460
\(403\) −51.7520 −2.57795
\(404\) −6.54370 −0.325561
\(405\) −2.81787 −0.140021
\(406\) 2.97386 0.147590
\(407\) 0.691126 0.0342578
\(408\) 19.0721 0.944211
\(409\) −22.7718 −1.12599 −0.562997 0.826459i \(-0.690352\pi\)
−0.562997 + 0.826459i \(0.690352\pi\)
\(410\) 0.299762 0.0148042
\(411\) −16.8941 −0.833324
\(412\) −15.6836 −0.772674
\(413\) −2.17804 −0.107174
\(414\) 7.69663 0.378269
\(415\) 1.52980 0.0750951
\(416\) −6.58692 −0.322950
\(417\) 29.4289 1.44114
\(418\) −2.92676 −0.143152
\(419\) 13.6945 0.669021 0.334510 0.942392i \(-0.391429\pi\)
0.334510 + 0.942392i \(0.391429\pi\)
\(420\) 0.187765 0.00916201
\(421\) 23.7960 1.15974 0.579872 0.814708i \(-0.303103\pi\)
0.579872 + 0.814708i \(0.303103\pi\)
\(422\) 10.6739 0.519597
\(423\) −37.0146 −1.79971
\(424\) −3.40640 −0.165429
\(425\) −29.0944 −1.41128
\(426\) 20.5022 0.993335
\(427\) 2.03826 0.0986383
\(428\) 12.2966 0.594377
\(429\) −17.5280 −0.846259
\(430\) −0.681082 −0.0328447
\(431\) −8.00088 −0.385389 −0.192694 0.981259i \(-0.561723\pi\)
−0.192694 + 0.981259i \(0.561723\pi\)
\(432\) −15.3607 −0.739040
\(433\) 15.5345 0.746539 0.373269 0.927723i \(-0.378237\pi\)
0.373269 + 0.927723i \(0.378237\pi\)
\(434\) 4.34568 0.208599
\(435\) −1.82520 −0.0875118
\(436\) −17.0299 −0.815587
\(437\) −3.59717 −0.172076
\(438\) −35.5699 −1.69960
\(439\) 5.52337 0.263616 0.131808 0.991275i \(-0.457922\pi\)
0.131808 + 0.991275i \(0.457922\pi\)
\(440\) 0.0844511 0.00402605
\(441\) −51.5218 −2.45342
\(442\) −38.4112 −1.82704
\(443\) −30.6957 −1.45840 −0.729198 0.684303i \(-0.760107\pi\)
−0.729198 + 0.684303i \(0.760107\pi\)
\(444\) −2.77815 −0.131845
\(445\) 0.134754 0.00638796
\(446\) 18.7321 0.886989
\(447\) 30.5043 1.44280
\(448\) 0.553111 0.0261321
\(449\) −23.6906 −1.11803 −0.559015 0.829158i \(-0.688820\pi\)
−0.559015 + 0.829158i \(0.688820\pi\)
\(450\) 38.4002 1.81020
\(451\) 2.34976 0.110646
\(452\) 10.7077 0.503650
\(453\) −3.26287 −0.153303
\(454\) 15.9561 0.748856
\(455\) −0.378159 −0.0177284
\(456\) 11.7648 0.550937
\(457\) −16.5657 −0.774909 −0.387454 0.921889i \(-0.626645\pi\)
−0.387454 + 0.921889i \(0.626645\pi\)
\(458\) 4.97330 0.232387
\(459\) −89.5747 −4.18099
\(460\) 0.103796 0.00483950
\(461\) 31.5062 1.46739 0.733695 0.679479i \(-0.237794\pi\)
0.733695 + 0.679479i \(0.237794\pi\)
\(462\) 1.47184 0.0684764
\(463\) −6.79440 −0.315762 −0.157881 0.987458i \(-0.550466\pi\)
−0.157881 + 0.987458i \(0.550466\pi\)
\(464\) −5.37661 −0.249603
\(465\) −2.66715 −0.123686
\(466\) −17.6289 −0.816645
\(467\) 30.2173 1.39829 0.699145 0.714980i \(-0.253564\pi\)
0.699145 + 0.714980i \(0.253564\pi\)
\(468\) 50.6971 2.34347
\(469\) 0.483054 0.0223054
\(470\) −0.499174 −0.0230252
\(471\) −26.3980 −1.21635
\(472\) 3.93780 0.181252
\(473\) −5.33882 −0.245479
\(474\) 16.6156 0.763181
\(475\) −17.9471 −0.823469
\(476\) 3.22543 0.147838
\(477\) 26.2178 1.20043
\(478\) −17.1659 −0.785149
\(479\) 7.26895 0.332127 0.166063 0.986115i \(-0.446894\pi\)
0.166063 + 0.986115i \(0.446894\pi\)
\(480\) −0.339471 −0.0154947
\(481\) 5.59518 0.255118
\(482\) 2.77248 0.126283
\(483\) 1.80899 0.0823119
\(484\) −10.3380 −0.469910
\(485\) 0.574403 0.0260823
\(486\) 42.7082 1.93728
\(487\) 4.39003 0.198931 0.0994657 0.995041i \(-0.468287\pi\)
0.0994657 + 0.995041i \(0.468287\pi\)
\(488\) −3.68508 −0.166816
\(489\) 41.9242 1.89588
\(490\) −0.694816 −0.0313886
\(491\) −17.8862 −0.807193 −0.403597 0.914937i \(-0.632240\pi\)
−0.403597 + 0.914937i \(0.632240\pi\)
\(492\) −9.44542 −0.425832
\(493\) −31.3533 −1.41208
\(494\) −23.6943 −1.06606
\(495\) −0.649989 −0.0292148
\(496\) −7.85678 −0.352780
\(497\) 3.46729 0.155529
\(498\) −48.2036 −2.16006
\(499\) −21.4420 −0.959874 −0.479937 0.877303i \(-0.659341\pi\)
−0.479937 + 0.877303i \(0.659341\pi\)
\(500\) 1.03684 0.0463689
\(501\) −13.4541 −0.601087
\(502\) −10.5438 −0.470594
\(503\) 25.5554 1.13946 0.569730 0.821832i \(-0.307048\pi\)
0.569730 + 0.821832i \(0.307048\pi\)
\(504\) −4.25709 −0.189626
\(505\) 0.679208 0.0302244
\(506\) 0.813628 0.0361702
\(507\) −99.3846 −4.41383
\(508\) −11.4513 −0.508070
\(509\) −3.25761 −0.144391 −0.0721955 0.997391i \(-0.523001\pi\)
−0.0721955 + 0.997391i \(0.523001\pi\)
\(510\) −1.97960 −0.0876584
\(511\) −6.01550 −0.266110
\(512\) −1.00000 −0.0441942
\(513\) −55.2548 −2.43956
\(514\) 12.9752 0.572312
\(515\) 1.62789 0.0717333
\(516\) 21.4607 0.944753
\(517\) −3.91290 −0.172089
\(518\) −0.469834 −0.0206433
\(519\) −63.8039 −2.80068
\(520\) 0.683695 0.0299820
\(521\) −33.1407 −1.45192 −0.725959 0.687738i \(-0.758604\pi\)
−0.725959 + 0.687738i \(0.758604\pi\)
\(522\) 41.3817 1.81123
\(523\) −15.3236 −0.670054 −0.335027 0.942209i \(-0.608745\pi\)
−0.335027 + 0.942209i \(0.608745\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 9.02546 0.393903
\(526\) −26.6163 −1.16053
\(527\) −45.8163 −1.99579
\(528\) −2.66103 −0.115806
\(529\) 1.00000 0.0434783
\(530\) 0.353569 0.0153581
\(531\) −30.3078 −1.31525
\(532\) 1.98963 0.0862616
\(533\) 19.0231 0.823980
\(534\) −4.24606 −0.183745
\(535\) −1.27633 −0.0551806
\(536\) −0.873340 −0.0377225
\(537\) 16.3170 0.704129
\(538\) 23.2985 1.00447
\(539\) −5.44648 −0.234597
\(540\) 1.59437 0.0686108
\(541\) −38.0860 −1.63744 −0.818722 0.574190i \(-0.805317\pi\)
−0.818722 + 0.574190i \(0.805317\pi\)
\(542\) 6.30180 0.270686
\(543\) 53.1906 2.28263
\(544\) −5.83144 −0.250021
\(545\) 1.76764 0.0757172
\(546\) 11.9157 0.509944
\(547\) 15.3913 0.658083 0.329042 0.944315i \(-0.393274\pi\)
0.329042 + 0.944315i \(0.393274\pi\)
\(548\) 5.16549 0.220659
\(549\) 28.3627 1.21049
\(550\) 4.05937 0.173092
\(551\) −19.3406 −0.823935
\(552\) −3.27057 −0.139205
\(553\) 2.81000 0.119493
\(554\) −17.7476 −0.754024
\(555\) 0.288360 0.0122402
\(556\) −8.99810 −0.381605
\(557\) −34.6386 −1.46769 −0.733843 0.679319i \(-0.762275\pi\)
−0.733843 + 0.679319i \(0.762275\pi\)
\(558\) 60.4708 2.55993
\(559\) −43.2218 −1.82809
\(560\) −0.0574106 −0.00242604
\(561\) −15.5176 −0.655154
\(562\) 23.4346 0.988529
\(563\) 41.5326 1.75039 0.875196 0.483768i \(-0.160732\pi\)
0.875196 + 0.483768i \(0.160732\pi\)
\(564\) 15.7288 0.662302
\(565\) −1.11142 −0.0467577
\(566\) −31.8897 −1.34042
\(567\) 15.0160 0.630612
\(568\) −6.26870 −0.263029
\(569\) 33.9059 1.42141 0.710704 0.703491i \(-0.248377\pi\)
0.710704 + 0.703491i \(0.248377\pi\)
\(570\) −1.22113 −0.0511477
\(571\) −14.4246 −0.603650 −0.301825 0.953363i \(-0.597596\pi\)
−0.301825 + 0.953363i \(0.597596\pi\)
\(572\) 5.35930 0.224084
\(573\) 83.0358 3.46887
\(574\) −1.59739 −0.0666737
\(575\) 4.98923 0.208065
\(576\) 7.69663 0.320693
\(577\) −41.7768 −1.73919 −0.869596 0.493764i \(-0.835621\pi\)
−0.869596 + 0.493764i \(0.835621\pi\)
\(578\) −17.0056 −0.707342
\(579\) −78.0001 −3.24157
\(580\) 0.558069 0.0231725
\(581\) −8.15209 −0.338206
\(582\) −18.0993 −0.750238
\(583\) 2.77154 0.114785
\(584\) 10.8758 0.450042
\(585\) −5.26214 −0.217563
\(586\) 2.58226 0.106672
\(587\) −9.54667 −0.394033 −0.197017 0.980400i \(-0.563125\pi\)
−0.197017 + 0.980400i \(0.563125\pi\)
\(588\) 21.8934 0.902869
\(589\) −28.2622 −1.16452
\(590\) −0.408727 −0.0168270
\(591\) 69.7835 2.87051
\(592\) 0.849438 0.0349117
\(593\) 29.2963 1.20306 0.601528 0.798852i \(-0.294559\pi\)
0.601528 + 0.798852i \(0.294559\pi\)
\(594\) 12.4979 0.512793
\(595\) −0.334786 −0.0137249
\(596\) −9.32690 −0.382045
\(597\) 5.09929 0.208700
\(598\) 6.58692 0.269359
\(599\) −1.37298 −0.0560983 −0.0280491 0.999607i \(-0.508929\pi\)
−0.0280491 + 0.999607i \(0.508929\pi\)
\(600\) −16.3176 −0.666164
\(601\) 45.4304 1.85314 0.926571 0.376119i \(-0.122742\pi\)
0.926571 + 0.376119i \(0.122742\pi\)
\(602\) 3.62938 0.147923
\(603\) 6.72177 0.273732
\(604\) 0.997646 0.0405936
\(605\) 1.07304 0.0436253
\(606\) −21.4016 −0.869381
\(607\) 24.2017 0.982316 0.491158 0.871070i \(-0.336574\pi\)
0.491158 + 0.871070i \(0.336574\pi\)
\(608\) −3.59717 −0.145884
\(609\) 9.72623 0.394127
\(610\) 0.382495 0.0154868
\(611\) −31.6778 −1.28155
\(612\) 44.8824 1.81426
\(613\) 48.2556 1.94903 0.974513 0.224332i \(-0.0720200\pi\)
0.974513 + 0.224332i \(0.0720200\pi\)
\(614\) 21.7822 0.879058
\(615\) 0.980394 0.0395333
\(616\) −0.450027 −0.0181321
\(617\) −26.6222 −1.07177 −0.535885 0.844291i \(-0.680022\pi\)
−0.535885 + 0.844291i \(0.680022\pi\)
\(618\) −51.2942 −2.06336
\(619\) −13.4359 −0.540034 −0.270017 0.962856i \(-0.587029\pi\)
−0.270017 + 0.962856i \(0.587029\pi\)
\(620\) 0.815501 0.0327513
\(621\) 15.3607 0.616402
\(622\) −1.83548 −0.0735959
\(623\) −0.718084 −0.0287694
\(624\) −21.5430 −0.862410
\(625\) 24.8385 0.993541
\(626\) −21.1874 −0.846819
\(627\) −9.57216 −0.382275
\(628\) 8.07137 0.322083
\(629\) 4.95344 0.197507
\(630\) 0.441868 0.0176044
\(631\) 16.3866 0.652341 0.326170 0.945311i \(-0.394242\pi\)
0.326170 + 0.945311i \(0.394242\pi\)
\(632\) −5.08034 −0.202085
\(633\) 34.9097 1.38754
\(634\) −21.2260 −0.842991
\(635\) 1.18860 0.0471681
\(636\) −11.1409 −0.441764
\(637\) −44.0933 −1.74704
\(638\) 4.37456 0.173190
\(639\) 48.2478 1.90865
\(640\) 0.103796 0.00410289
\(641\) 23.5328 0.929491 0.464745 0.885444i \(-0.346146\pi\)
0.464745 + 0.885444i \(0.346146\pi\)
\(642\) 40.2168 1.58723
\(643\) 43.1590 1.70203 0.851013 0.525145i \(-0.175989\pi\)
0.851013 + 0.525145i \(0.175989\pi\)
\(644\) −0.553111 −0.0217956
\(645\) −2.22753 −0.0877087
\(646\) −20.9766 −0.825315
\(647\) −34.4748 −1.35534 −0.677672 0.735364i \(-0.737011\pi\)
−0.677672 + 0.735364i \(0.737011\pi\)
\(648\) −27.1482 −1.06648
\(649\) −3.20390 −0.125764
\(650\) 32.8637 1.28902
\(651\) 14.2128 0.557045
\(652\) −12.8186 −0.502016
\(653\) −42.5702 −1.66590 −0.832950 0.553348i \(-0.813350\pi\)
−0.832950 + 0.553348i \(0.813350\pi\)
\(654\) −55.6976 −2.17795
\(655\) 0.103796 0.00405563
\(656\) 2.88800 0.112758
\(657\) −83.7066 −3.26571
\(658\) 2.66002 0.103698
\(659\) −16.7309 −0.651745 −0.325873 0.945414i \(-0.605658\pi\)
−0.325873 + 0.945414i \(0.605658\pi\)
\(660\) 0.276203 0.0107512
\(661\) 14.6001 0.567879 0.283940 0.958842i \(-0.408358\pi\)
0.283940 + 0.958842i \(0.408358\pi\)
\(662\) 0.479692 0.0186438
\(663\) −125.627 −4.87893
\(664\) 14.7386 0.571969
\(665\) −0.206516 −0.00800833
\(666\) −6.53781 −0.253335
\(667\) 5.37661 0.208183
\(668\) 4.11370 0.159164
\(669\) 61.2646 2.36862
\(670\) 0.0906490 0.00350207
\(671\) 2.99828 0.115747
\(672\) 1.80899 0.0697833
\(673\) −17.7531 −0.684331 −0.342165 0.939640i \(-0.611160\pi\)
−0.342165 + 0.939640i \(0.611160\pi\)
\(674\) 6.87190 0.264696
\(675\) 76.6378 2.94979
\(676\) 30.3876 1.16875
\(677\) 19.3630 0.744182 0.372091 0.928196i \(-0.378641\pi\)
0.372091 + 0.928196i \(0.378641\pi\)
\(678\) 35.0204 1.34495
\(679\) −3.06090 −0.117467
\(680\) 0.605278 0.0232114
\(681\) 52.1855 1.99975
\(682\) 6.39250 0.244781
\(683\) −15.2627 −0.584009 −0.292005 0.956417i \(-0.594322\pi\)
−0.292005 + 0.956417i \(0.594322\pi\)
\(684\) 27.6861 1.05860
\(685\) −0.536156 −0.0204855
\(686\) 7.57435 0.289190
\(687\) 16.2655 0.620569
\(688\) −6.56175 −0.250164
\(689\) 22.4377 0.854807
\(690\) 0.339471 0.0129234
\(691\) 27.2884 1.03810 0.519049 0.854745i \(-0.326286\pi\)
0.519049 + 0.854745i \(0.326286\pi\)
\(692\) 19.5085 0.741601
\(693\) 3.46369 0.131575
\(694\) 22.5168 0.854725
\(695\) 0.933965 0.0354273
\(696\) −17.5846 −0.666541
\(697\) 16.8412 0.637906
\(698\) 33.9857 1.28638
\(699\) −57.6567 −2.18078
\(700\) −2.75960 −0.104303
\(701\) 4.11493 0.155419 0.0777094 0.996976i \(-0.475239\pi\)
0.0777094 + 0.996976i \(0.475239\pi\)
\(702\) 101.179 3.81877
\(703\) 3.05557 0.115243
\(704\) 0.813628 0.0306648
\(705\) −1.63258 −0.0614866
\(706\) −8.70927 −0.327778
\(707\) −3.61939 −0.136121
\(708\) 12.8788 0.484017
\(709\) 20.3696 0.764997 0.382498 0.923956i \(-0.375064\pi\)
0.382498 + 0.923956i \(0.375064\pi\)
\(710\) 0.650664 0.0244190
\(711\) 39.1015 1.46642
\(712\) 1.29826 0.0486545
\(713\) 7.85678 0.294239
\(714\) 10.5490 0.394787
\(715\) −0.556273 −0.0208034
\(716\) −4.98903 −0.186449
\(717\) −56.1422 −2.09667
\(718\) −25.6573 −0.957520
\(719\) −45.0007 −1.67824 −0.839121 0.543944i \(-0.816930\pi\)
−0.839121 + 0.543944i \(0.816930\pi\)
\(720\) −0.798877 −0.0297724
\(721\) −8.67476 −0.323065
\(722\) 6.06039 0.225544
\(723\) 9.06759 0.337227
\(724\) −16.2634 −0.604424
\(725\) 26.8251 0.996260
\(726\) −33.8112 −1.25485
\(727\) 13.5284 0.501742 0.250871 0.968021i \(-0.419283\pi\)
0.250871 + 0.968021i \(0.419283\pi\)
\(728\) −3.64330 −0.135030
\(729\) 58.2354 2.15687
\(730\) −1.12886 −0.0417809
\(731\) −38.2644 −1.41526
\(732\) −12.0523 −0.445466
\(733\) 29.7436 1.09861 0.549303 0.835623i \(-0.314893\pi\)
0.549303 + 0.835623i \(0.314893\pi\)
\(734\) −31.5144 −1.16322
\(735\) −2.27244 −0.0838203
\(736\) 1.00000 0.0368605
\(737\) 0.710574 0.0261743
\(738\) −22.2279 −0.818220
\(739\) −8.97532 −0.330163 −0.165081 0.986280i \(-0.552789\pi\)
−0.165081 + 0.986280i \(0.552789\pi\)
\(740\) −0.0881680 −0.00324112
\(741\) −77.4937 −2.84680
\(742\) −1.88412 −0.0691681
\(743\) −3.75835 −0.137881 −0.0689403 0.997621i \(-0.521962\pi\)
−0.0689403 + 0.997621i \(0.521962\pi\)
\(744\) −25.6962 −0.942067
\(745\) 0.968093 0.0354682
\(746\) 13.1965 0.483160
\(747\) −113.438 −4.15046
\(748\) 4.74462 0.173480
\(749\) 6.80137 0.248517
\(750\) 3.39105 0.123824
\(751\) −22.8451 −0.833628 −0.416814 0.908992i \(-0.636853\pi\)
−0.416814 + 0.908992i \(0.636853\pi\)
\(752\) −4.80920 −0.175373
\(753\) −34.4843 −1.25668
\(754\) 35.4153 1.28975
\(755\) −0.103551 −0.00376862
\(756\) −8.49615 −0.309002
\(757\) −5.22591 −0.189939 −0.0949695 0.995480i \(-0.530275\pi\)
−0.0949695 + 0.995480i \(0.530275\pi\)
\(758\) 29.7503 1.08058
\(759\) 2.66103 0.0965892
\(760\) 0.373371 0.0135436
\(761\) 5.93105 0.215000 0.107500 0.994205i \(-0.465715\pi\)
0.107500 + 0.994205i \(0.465715\pi\)
\(762\) −37.4524 −1.35676
\(763\) −9.41946 −0.341007
\(764\) −25.3888 −0.918534
\(765\) −4.65860 −0.168432
\(766\) −17.7377 −0.640889
\(767\) −25.9380 −0.936566
\(768\) −3.27057 −0.118017
\(769\) 36.7969 1.32693 0.663465 0.748207i \(-0.269085\pi\)
0.663465 + 0.748207i \(0.269085\pi\)
\(770\) 0.0467109 0.00168334
\(771\) 42.4363 1.52831
\(772\) 23.8491 0.858348
\(773\) −39.0025 −1.40282 −0.701412 0.712756i \(-0.747447\pi\)
−0.701412 + 0.712756i \(0.747447\pi\)
\(774\) 50.5034 1.81531
\(775\) 39.1993 1.40808
\(776\) 5.53397 0.198658
\(777\) −1.53662 −0.0551261
\(778\) 23.4052 0.839118
\(779\) 10.3886 0.372211
\(780\) 2.23607 0.0800642
\(781\) 5.10039 0.182506
\(782\) 5.83144 0.208532
\(783\) 82.5882 2.95146
\(784\) −6.69407 −0.239074
\(785\) −0.837774 −0.0299014
\(786\) −3.27057 −0.116657
\(787\) −9.82088 −0.350077 −0.175038 0.984562i \(-0.556005\pi\)
−0.175038 + 0.984562i \(0.556005\pi\)
\(788\) −21.3368 −0.760092
\(789\) −87.0506 −3.09908
\(790\) 0.527318 0.0187611
\(791\) 5.92258 0.210583
\(792\) −6.26219 −0.222517
\(793\) 24.2733 0.861971
\(794\) 28.6307 1.01607
\(795\) 1.15637 0.0410123
\(796\) −1.55914 −0.0552624
\(797\) 34.6833 1.22855 0.614273 0.789093i \(-0.289449\pi\)
0.614273 + 0.789093i \(0.289449\pi\)
\(798\) 6.50724 0.230354
\(799\) −28.0445 −0.992144
\(800\) 4.98923 0.176396
\(801\) −9.99225 −0.353059
\(802\) −25.6823 −0.906873
\(803\) −8.84882 −0.312268
\(804\) −2.85632 −0.100735
\(805\) 0.0574106 0.00202346
\(806\) 51.7520 1.82289
\(807\) 76.1995 2.68235
\(808\) 6.54370 0.230206
\(809\) 9.11147 0.320342 0.160171 0.987089i \(-0.448795\pi\)
0.160171 + 0.987089i \(0.448795\pi\)
\(810\) 2.81787 0.0990098
\(811\) −26.3495 −0.925255 −0.462627 0.886553i \(-0.653093\pi\)
−0.462627 + 0.886553i \(0.653093\pi\)
\(812\) −2.97386 −0.104362
\(813\) 20.6105 0.722842
\(814\) −0.691126 −0.0242240
\(815\) 1.33052 0.0466060
\(816\) −19.0721 −0.667658
\(817\) −23.6037 −0.825790
\(818\) 22.7718 0.796198
\(819\) 28.0412 0.979837
\(820\) −0.299762 −0.0104682
\(821\) −35.1236 −1.22582 −0.612911 0.790152i \(-0.710001\pi\)
−0.612911 + 0.790152i \(0.710001\pi\)
\(822\) 16.8941 0.589249
\(823\) 35.7993 1.24789 0.623943 0.781470i \(-0.285530\pi\)
0.623943 + 0.781470i \(0.285530\pi\)
\(824\) 15.6836 0.546363
\(825\) 13.2765 0.462227
\(826\) 2.17804 0.0757837
\(827\) −22.1728 −0.771025 −0.385513 0.922703i \(-0.625975\pi\)
−0.385513 + 0.922703i \(0.625975\pi\)
\(828\) −7.69663 −0.267476
\(829\) −6.75868 −0.234739 −0.117369 0.993088i \(-0.537446\pi\)
−0.117369 + 0.993088i \(0.537446\pi\)
\(830\) −1.52980 −0.0531003
\(831\) −58.0448 −2.01355
\(832\) 6.58692 0.228360
\(833\) −39.0360 −1.35252
\(834\) −29.4289 −1.01904
\(835\) −0.426985 −0.0147764
\(836\) 2.92676 0.101224
\(837\) 120.685 4.17150
\(838\) −13.6945 −0.473069
\(839\) 10.3264 0.356505 0.178253 0.983985i \(-0.442956\pi\)
0.178253 + 0.983985i \(0.442956\pi\)
\(840\) −0.187765 −0.00647852
\(841\) −0.0920959 −0.00317572
\(842\) −23.7960 −0.820063
\(843\) 76.6445 2.63978
\(844\) −10.6739 −0.367411
\(845\) −3.15410 −0.108504
\(846\) 37.0146 1.27259
\(847\) −5.71807 −0.196475
\(848\) 3.40640 0.116976
\(849\) −104.297 −3.57948
\(850\) 29.0944 0.997928
\(851\) −0.849438 −0.0291183
\(852\) −20.5022 −0.702394
\(853\) −4.96506 −0.170000 −0.0850002 0.996381i \(-0.527089\pi\)
−0.0850002 + 0.996381i \(0.527089\pi\)
\(854\) −2.03826 −0.0697478
\(855\) −2.87369 −0.0982783
\(856\) −12.2966 −0.420288
\(857\) 29.0834 0.993471 0.496735 0.867902i \(-0.334532\pi\)
0.496735 + 0.867902i \(0.334532\pi\)
\(858\) 17.5280 0.598395
\(859\) −36.5035 −1.24548 −0.622742 0.782427i \(-0.713981\pi\)
−0.622742 + 0.782427i \(0.713981\pi\)
\(860\) 0.681082 0.0232247
\(861\) −5.22437 −0.178046
\(862\) 8.00088 0.272511
\(863\) 15.4104 0.524577 0.262289 0.964989i \(-0.415523\pi\)
0.262289 + 0.964989i \(0.415523\pi\)
\(864\) 15.3607 0.522580
\(865\) −2.02490 −0.0688486
\(866\) −15.5345 −0.527883
\(867\) −55.6182 −1.88889
\(868\) −4.34568 −0.147502
\(869\) 4.13351 0.140220
\(870\) 1.82520 0.0618802
\(871\) 5.75262 0.194920
\(872\) 17.0299 0.576707
\(873\) −42.5929 −1.44155
\(874\) 3.59717 0.121676
\(875\) 0.573488 0.0193874
\(876\) 35.5699 1.20180
\(877\) 44.0940 1.48895 0.744475 0.667650i \(-0.232700\pi\)
0.744475 + 0.667650i \(0.232700\pi\)
\(878\) −5.52337 −0.186405
\(879\) 8.44546 0.284858
\(880\) −0.0844511 −0.00284685
\(881\) 8.08071 0.272246 0.136123 0.990692i \(-0.456536\pi\)
0.136123 + 0.990692i \(0.456536\pi\)
\(882\) 51.5218 1.73483
\(883\) −43.6298 −1.46826 −0.734129 0.679010i \(-0.762409\pi\)
−0.734129 + 0.679010i \(0.762409\pi\)
\(884\) 38.4112 1.29191
\(885\) −1.33677 −0.0449350
\(886\) 30.6957 1.03124
\(887\) 49.4212 1.65940 0.829701 0.558209i \(-0.188511\pi\)
0.829701 + 0.558209i \(0.188511\pi\)
\(888\) 2.77815 0.0932284
\(889\) −6.33386 −0.212431
\(890\) −0.134754 −0.00451697
\(891\) 22.0885 0.739994
\(892\) −18.7321 −0.627196
\(893\) −17.2995 −0.578905
\(894\) −30.5043 −1.02022
\(895\) 0.517840 0.0173095
\(896\) −0.553111 −0.0184782
\(897\) 21.5430 0.719300
\(898\) 23.6906 0.790566
\(899\) 42.2428 1.40888
\(900\) −38.4002 −1.28001
\(901\) 19.8642 0.661772
\(902\) −2.34976 −0.0782385
\(903\) 11.8701 0.395014
\(904\) −10.7077 −0.356134
\(905\) 1.68807 0.0561134
\(906\) 3.26287 0.108402
\(907\) −27.0440 −0.897981 −0.448991 0.893536i \(-0.648216\pi\)
−0.448991 + 0.893536i \(0.648216\pi\)
\(908\) −15.9561 −0.529521
\(909\) −50.3644 −1.67048
\(910\) 0.378159 0.0125359
\(911\) −44.4434 −1.47248 −0.736238 0.676723i \(-0.763400\pi\)
−0.736238 + 0.676723i \(0.763400\pi\)
\(912\) −11.7648 −0.389571
\(913\) −11.9917 −0.396869
\(914\) 16.5657 0.547943
\(915\) 1.25098 0.0413560
\(916\) −4.97330 −0.164323
\(917\) −0.553111 −0.0182654
\(918\) 89.5747 2.95640
\(919\) 37.1601 1.22580 0.612899 0.790161i \(-0.290003\pi\)
0.612899 + 0.790161i \(0.290003\pi\)
\(920\) −0.103796 −0.00342204
\(921\) 71.2402 2.34744
\(922\) −31.5062 −1.03760
\(923\) 41.2914 1.35912
\(924\) −1.47184 −0.0484201
\(925\) −4.23804 −0.139346
\(926\) 6.79440 0.223278
\(927\) −120.711 −3.96466
\(928\) 5.37661 0.176496
\(929\) 13.8557 0.454589 0.227295 0.973826i \(-0.427012\pi\)
0.227295 + 0.973826i \(0.427012\pi\)
\(930\) 2.66715 0.0874594
\(931\) −24.0797 −0.789180
\(932\) 17.6289 0.577455
\(933\) −6.00306 −0.196531
\(934\) −30.2173 −0.988740
\(935\) −0.492471 −0.0161055
\(936\) −50.6971 −1.65709
\(937\) −28.9854 −0.946912 −0.473456 0.880818i \(-0.656994\pi\)
−0.473456 + 0.880818i \(0.656994\pi\)
\(938\) −0.483054 −0.0157723
\(939\) −69.2949 −2.26135
\(940\) 0.499174 0.0162813
\(941\) 37.8281 1.23316 0.616581 0.787292i \(-0.288517\pi\)
0.616581 + 0.787292i \(0.288517\pi\)
\(942\) 26.3980 0.860093
\(943\) −2.88800 −0.0940463
\(944\) −3.93780 −0.128164
\(945\) 0.881864 0.0286871
\(946\) 5.33882 0.173580
\(947\) 46.4610 1.50978 0.754889 0.655852i \(-0.227691\pi\)
0.754889 + 0.655852i \(0.227691\pi\)
\(948\) −16.6156 −0.539650
\(949\) −71.6377 −2.32546
\(950\) 17.9471 0.582280
\(951\) −69.4211 −2.25113
\(952\) −3.22543 −0.104537
\(953\) −9.99306 −0.323707 −0.161853 0.986815i \(-0.551747\pi\)
−0.161853 + 0.986815i \(0.551747\pi\)
\(954\) −26.2178 −0.848832
\(955\) 2.63525 0.0852746
\(956\) 17.1659 0.555184
\(957\) 14.3073 0.462489
\(958\) −7.26895 −0.234849
\(959\) 2.85709 0.0922603
\(960\) 0.339471 0.0109564
\(961\) 30.7291 0.991260
\(962\) −5.59518 −0.180396
\(963\) 94.6421 3.04980
\(964\) −2.77248 −0.0892955
\(965\) −2.47543 −0.0796870
\(966\) −1.80899 −0.0582033
\(967\) 12.0629 0.387916 0.193958 0.981010i \(-0.437868\pi\)
0.193958 + 0.981010i \(0.437868\pi\)
\(968\) 10.3380 0.332276
\(969\) −68.6056 −2.20393
\(970\) −0.574403 −0.0184430
\(971\) 31.4224 1.00839 0.504196 0.863589i \(-0.331789\pi\)
0.504196 + 0.863589i \(0.331789\pi\)
\(972\) −42.7082 −1.36986
\(973\) −4.97695 −0.159554
\(974\) −4.39003 −0.140666
\(975\) 107.483 3.44221
\(976\) 3.68508 0.117956
\(977\) 58.7991 1.88115 0.940575 0.339586i \(-0.110287\pi\)
0.940575 + 0.339586i \(0.110287\pi\)
\(978\) −41.9242 −1.34059
\(979\) −1.05630 −0.0337596
\(980\) 0.694816 0.0221951
\(981\) −131.073 −4.18484
\(982\) 17.8862 0.570772
\(983\) −47.1483 −1.50380 −0.751898 0.659279i \(-0.770862\pi\)
−0.751898 + 0.659279i \(0.770862\pi\)
\(984\) 9.44542 0.301109
\(985\) 2.21467 0.0705652
\(986\) 31.3533 0.998494
\(987\) 8.69979 0.276917
\(988\) 23.6943 0.753815
\(989\) 6.56175 0.208652
\(990\) 0.649989 0.0206580
\(991\) −3.21762 −0.102211 −0.0511055 0.998693i \(-0.516274\pi\)
−0.0511055 + 0.998693i \(0.516274\pi\)
\(992\) 7.85678 0.249453
\(993\) 1.56887 0.0497864
\(994\) −3.46729 −0.109976
\(995\) 0.161832 0.00513043
\(996\) 48.2036 1.52739
\(997\) 37.6316 1.19180 0.595902 0.803057i \(-0.296794\pi\)
0.595902 + 0.803057i \(0.296794\pi\)
\(998\) 21.4420 0.678734
\(999\) −13.0479 −0.412818
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 \(a_p\))