Properties

Label 4017.2.a.j.1.24
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.24
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.69069 q^{2} -1.00000 q^{3} +5.23983 q^{4} -3.39075 q^{5} -2.69069 q^{6} +3.55923 q^{7} +8.71737 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.69069 q^{2} -1.00000 q^{3} +5.23983 q^{4} -3.39075 q^{5} -2.69069 q^{6} +3.55923 q^{7} +8.71737 q^{8} +1.00000 q^{9} -9.12347 q^{10} +3.97019 q^{11} -5.23983 q^{12} +1.00000 q^{13} +9.57679 q^{14} +3.39075 q^{15} +12.9761 q^{16} -5.69126 q^{17} +2.69069 q^{18} -3.19194 q^{19} -17.7669 q^{20} -3.55923 q^{21} +10.6826 q^{22} +4.70654 q^{23} -8.71737 q^{24} +6.49719 q^{25} +2.69069 q^{26} -1.00000 q^{27} +18.6497 q^{28} +6.05116 q^{29} +9.12347 q^{30} +6.73805 q^{31} +17.4800 q^{32} -3.97019 q^{33} -15.3134 q^{34} -12.0685 q^{35} +5.23983 q^{36} -7.13584 q^{37} -8.58854 q^{38} -1.00000 q^{39} -29.5584 q^{40} +1.26699 q^{41} -9.57679 q^{42} -3.71867 q^{43} +20.8031 q^{44} -3.39075 q^{45} +12.6639 q^{46} -2.79607 q^{47} -12.9761 q^{48} +5.66810 q^{49} +17.4819 q^{50} +5.69126 q^{51} +5.23983 q^{52} +14.3686 q^{53} -2.69069 q^{54} -13.4619 q^{55} +31.0271 q^{56} +3.19194 q^{57} +16.2818 q^{58} +10.9643 q^{59} +17.7669 q^{60} -9.35699 q^{61} +18.1300 q^{62} +3.55923 q^{63} +21.0811 q^{64} -3.39075 q^{65} -10.6826 q^{66} -8.20608 q^{67} -29.8212 q^{68} -4.70654 q^{69} -32.4725 q^{70} -5.77396 q^{71} +8.71737 q^{72} -4.07053 q^{73} -19.2004 q^{74} -6.49719 q^{75} -16.7252 q^{76} +14.1308 q^{77} -2.69069 q^{78} +9.95930 q^{79} -43.9988 q^{80} +1.00000 q^{81} +3.40909 q^{82} +15.1402 q^{83} -18.6497 q^{84} +19.2976 q^{85} -10.0058 q^{86} -6.05116 q^{87} +34.6096 q^{88} +14.6677 q^{89} -9.12347 q^{90} +3.55923 q^{91} +24.6615 q^{92} -6.73805 q^{93} -7.52336 q^{94} +10.8231 q^{95} -17.4800 q^{96} +6.18570 q^{97} +15.2511 q^{98} +3.97019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.69069 1.90261 0.951303 0.308256i \(-0.0997454\pi\)
0.951303 + 0.308256i \(0.0997454\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.23983 2.61991
\(5\) −3.39075 −1.51639 −0.758195 0.652028i \(-0.773918\pi\)
−0.758195 + 0.652028i \(0.773918\pi\)
\(6\) −2.69069 −1.09847
\(7\) 3.55923 1.34526 0.672631 0.739978i \(-0.265164\pi\)
0.672631 + 0.739978i \(0.265164\pi\)
\(8\) 8.71737 3.08206
\(9\) 1.00000 0.333333
\(10\) −9.12347 −2.88509
\(11\) 3.97019 1.19706 0.598529 0.801101i \(-0.295752\pi\)
0.598529 + 0.801101i \(0.295752\pi\)
\(12\) −5.23983 −1.51261
\(13\) 1.00000 0.277350
\(14\) 9.57679 2.55950
\(15\) 3.39075 0.875488
\(16\) 12.9761 3.24403
\(17\) −5.69126 −1.38033 −0.690166 0.723651i \(-0.742463\pi\)
−0.690166 + 0.723651i \(0.742463\pi\)
\(18\) 2.69069 0.634202
\(19\) −3.19194 −0.732282 −0.366141 0.930559i \(-0.619321\pi\)
−0.366141 + 0.930559i \(0.619321\pi\)
\(20\) −17.7669 −3.97281
\(21\) −3.55923 −0.776687
\(22\) 10.6826 2.27753
\(23\) 4.70654 0.981382 0.490691 0.871334i \(-0.336744\pi\)
0.490691 + 0.871334i \(0.336744\pi\)
\(24\) −8.71737 −1.77943
\(25\) 6.49719 1.29944
\(26\) 2.69069 0.527688
\(27\) −1.00000 −0.192450
\(28\) 18.6497 3.52447
\(29\) 6.05116 1.12367 0.561836 0.827249i \(-0.310095\pi\)
0.561836 + 0.827249i \(0.310095\pi\)
\(30\) 9.12347 1.66571
\(31\) 6.73805 1.21019 0.605095 0.796153i \(-0.293135\pi\)
0.605095 + 0.796153i \(0.293135\pi\)
\(32\) 17.4800 3.09006
\(33\) −3.97019 −0.691122
\(34\) −15.3134 −2.62623
\(35\) −12.0685 −2.03994
\(36\) 5.23983 0.873304
\(37\) −7.13584 −1.17313 −0.586563 0.809904i \(-0.699519\pi\)
−0.586563 + 0.809904i \(0.699519\pi\)
\(38\) −8.58854 −1.39324
\(39\) −1.00000 −0.160128
\(40\) −29.5584 −4.67360
\(41\) 1.26699 0.197871 0.0989355 0.995094i \(-0.468456\pi\)
0.0989355 + 0.995094i \(0.468456\pi\)
\(42\) −9.57679 −1.47773
\(43\) −3.71867 −0.567091 −0.283546 0.958959i \(-0.591511\pi\)
−0.283546 + 0.958959i \(0.591511\pi\)
\(44\) 20.8031 3.13619
\(45\) −3.39075 −0.505463
\(46\) 12.6639 1.86718
\(47\) −2.79607 −0.407849 −0.203924 0.978987i \(-0.565370\pi\)
−0.203924 + 0.978987i \(0.565370\pi\)
\(48\) −12.9761 −1.87294
\(49\) 5.66810 0.809729
\(50\) 17.4819 2.47232
\(51\) 5.69126 0.796936
\(52\) 5.23983 0.726633
\(53\) 14.3686 1.97368 0.986840 0.161702i \(-0.0516983\pi\)
0.986840 + 0.161702i \(0.0516983\pi\)
\(54\) −2.69069 −0.366157
\(55\) −13.4619 −1.81521
\(56\) 31.0271 4.14617
\(57\) 3.19194 0.422783
\(58\) 16.2818 2.13791
\(59\) 10.9643 1.42743 0.713715 0.700437i \(-0.247011\pi\)
0.713715 + 0.700437i \(0.247011\pi\)
\(60\) 17.7669 2.29370
\(61\) −9.35699 −1.19804 −0.599020 0.800734i \(-0.704443\pi\)
−0.599020 + 0.800734i \(0.704443\pi\)
\(62\) 18.1300 2.30252
\(63\) 3.55923 0.448421
\(64\) 21.0811 2.63513
\(65\) −3.39075 −0.420571
\(66\) −10.6826 −1.31493
\(67\) −8.20608 −1.00253 −0.501266 0.865293i \(-0.667132\pi\)
−0.501266 + 0.865293i \(0.667132\pi\)
\(68\) −29.8212 −3.61635
\(69\) −4.70654 −0.566601
\(70\) −32.4725 −3.88120
\(71\) −5.77396 −0.685243 −0.342622 0.939473i \(-0.611315\pi\)
−0.342622 + 0.939473i \(0.611315\pi\)
\(72\) 8.71737 1.02735
\(73\) −4.07053 −0.476420 −0.238210 0.971214i \(-0.576561\pi\)
−0.238210 + 0.971214i \(0.576561\pi\)
\(74\) −19.2004 −2.23200
\(75\) −6.49719 −0.750230
\(76\) −16.7252 −1.91851
\(77\) 14.1308 1.61036
\(78\) −2.69069 −0.304661
\(79\) 9.95930 1.12051 0.560254 0.828321i \(-0.310703\pi\)
0.560254 + 0.828321i \(0.310703\pi\)
\(80\) −43.9988 −4.91921
\(81\) 1.00000 0.111111
\(82\) 3.40909 0.376471
\(83\) 15.1402 1.66185 0.830925 0.556385i \(-0.187812\pi\)
0.830925 + 0.556385i \(0.187812\pi\)
\(84\) −18.6497 −2.03485
\(85\) 19.2976 2.09312
\(86\) −10.0058 −1.07895
\(87\) −6.05116 −0.648752
\(88\) 34.6096 3.68940
\(89\) 14.6677 1.55477 0.777384 0.629026i \(-0.216546\pi\)
0.777384 + 0.629026i \(0.216546\pi\)
\(90\) −9.12347 −0.961698
\(91\) 3.55923 0.373108
\(92\) 24.6615 2.57114
\(93\) −6.73805 −0.698704
\(94\) −7.52336 −0.775975
\(95\) 10.8231 1.11042
\(96\) −17.4800 −1.78404
\(97\) 6.18570 0.628063 0.314032 0.949413i \(-0.398320\pi\)
0.314032 + 0.949413i \(0.398320\pi\)
\(98\) 15.2511 1.54060
\(99\) 3.97019 0.399019
\(100\) 34.0441 3.40441
\(101\) −8.78051 −0.873693 −0.436847 0.899536i \(-0.643905\pi\)
−0.436847 + 0.899536i \(0.643905\pi\)
\(102\) 15.3134 1.51625
\(103\) −1.00000 −0.0985329
\(104\) 8.71737 0.854809
\(105\) 12.0685 1.17776
\(106\) 38.6615 3.75514
\(107\) −3.81774 −0.369074 −0.184537 0.982826i \(-0.559079\pi\)
−0.184537 + 0.982826i \(0.559079\pi\)
\(108\) −5.23983 −0.504202
\(109\) −7.48563 −0.716994 −0.358497 0.933531i \(-0.616711\pi\)
−0.358497 + 0.933531i \(0.616711\pi\)
\(110\) −36.2219 −3.45362
\(111\) 7.13584 0.677304
\(112\) 46.1850 4.36407
\(113\) 8.98479 0.845218 0.422609 0.906312i \(-0.361114\pi\)
0.422609 + 0.906312i \(0.361114\pi\)
\(114\) 8.58854 0.804390
\(115\) −15.9587 −1.48816
\(116\) 31.7070 2.94392
\(117\) 1.00000 0.0924500
\(118\) 29.5015 2.71584
\(119\) −20.2565 −1.85691
\(120\) 29.5584 2.69830
\(121\) 4.76242 0.432947
\(122\) −25.1768 −2.27940
\(123\) −1.26699 −0.114241
\(124\) 35.3062 3.17059
\(125\) −5.07658 −0.454063
\(126\) 9.57679 0.853168
\(127\) −0.0565956 −0.00502204 −0.00251102 0.999997i \(-0.500799\pi\)
−0.00251102 + 0.999997i \(0.500799\pi\)
\(128\) 21.7626 1.92356
\(129\) 3.71867 0.327410
\(130\) −9.12347 −0.800181
\(131\) 14.0234 1.22523 0.612616 0.790381i \(-0.290117\pi\)
0.612616 + 0.790381i \(0.290117\pi\)
\(132\) −20.8031 −1.81068
\(133\) −11.3608 −0.985111
\(134\) −22.0800 −1.90742
\(135\) 3.39075 0.291829
\(136\) −49.6128 −4.25426
\(137\) −0.460919 −0.0393790 −0.0196895 0.999806i \(-0.506268\pi\)
−0.0196895 + 0.999806i \(0.506268\pi\)
\(138\) −12.6639 −1.07802
\(139\) −1.08724 −0.0922185 −0.0461092 0.998936i \(-0.514682\pi\)
−0.0461092 + 0.998936i \(0.514682\pi\)
\(140\) −63.2366 −5.34447
\(141\) 2.79607 0.235471
\(142\) −15.5360 −1.30375
\(143\) 3.97019 0.332004
\(144\) 12.9761 1.08134
\(145\) −20.5180 −1.70392
\(146\) −10.9525 −0.906439
\(147\) −5.66810 −0.467497
\(148\) −37.3906 −3.07349
\(149\) −12.0840 −0.989960 −0.494980 0.868904i \(-0.664825\pi\)
−0.494980 + 0.868904i \(0.664825\pi\)
\(150\) −17.4819 −1.42739
\(151\) −2.12941 −0.173289 −0.0866446 0.996239i \(-0.527614\pi\)
−0.0866446 + 0.996239i \(0.527614\pi\)
\(152\) −27.8254 −2.25693
\(153\) −5.69126 −0.460111
\(154\) 38.0217 3.06387
\(155\) −22.8471 −1.83512
\(156\) −5.23983 −0.419522
\(157\) 11.1255 0.887912 0.443956 0.896048i \(-0.353575\pi\)
0.443956 + 0.896048i \(0.353575\pi\)
\(158\) 26.7974 2.13189
\(159\) −14.3686 −1.13950
\(160\) −59.2703 −4.68573
\(161\) 16.7517 1.32022
\(162\) 2.69069 0.211401
\(163\) 0.480373 0.0376257 0.0188128 0.999823i \(-0.494011\pi\)
0.0188128 + 0.999823i \(0.494011\pi\)
\(164\) 6.63882 0.518405
\(165\) 13.4619 1.04801
\(166\) 40.7375 3.16185
\(167\) 1.79007 0.138520 0.0692598 0.997599i \(-0.477936\pi\)
0.0692598 + 0.997599i \(0.477936\pi\)
\(168\) −31.0271 −2.39379
\(169\) 1.00000 0.0769231
\(170\) 51.9240 3.98239
\(171\) −3.19194 −0.244094
\(172\) −19.4852 −1.48573
\(173\) −3.45807 −0.262912 −0.131456 0.991322i \(-0.541965\pi\)
−0.131456 + 0.991322i \(0.541965\pi\)
\(174\) −16.2818 −1.23432
\(175\) 23.1250 1.74808
\(176\) 51.5177 3.88329
\(177\) −10.9643 −0.824127
\(178\) 39.4662 2.95811
\(179\) −22.9901 −1.71836 −0.859181 0.511672i \(-0.829026\pi\)
−0.859181 + 0.511672i \(0.829026\pi\)
\(180\) −17.7669 −1.32427
\(181\) −2.48918 −0.185019 −0.0925096 0.995712i \(-0.529489\pi\)
−0.0925096 + 0.995712i \(0.529489\pi\)
\(182\) 9.57679 0.709879
\(183\) 9.35699 0.691689
\(184\) 41.0287 3.02468
\(185\) 24.1959 1.77891
\(186\) −18.1300 −1.32936
\(187\) −22.5954 −1.65234
\(188\) −14.6509 −1.06853
\(189\) −3.55923 −0.258896
\(190\) 29.1216 2.11270
\(191\) −5.22992 −0.378423 −0.189212 0.981936i \(-0.560593\pi\)
−0.189212 + 0.981936i \(0.560593\pi\)
\(192\) −21.0811 −1.52139
\(193\) −18.7320 −1.34836 −0.674178 0.738569i \(-0.735502\pi\)
−0.674178 + 0.738569i \(0.735502\pi\)
\(194\) 16.6438 1.19496
\(195\) 3.39075 0.242817
\(196\) 29.6999 2.12142
\(197\) 3.47184 0.247358 0.123679 0.992322i \(-0.460531\pi\)
0.123679 + 0.992322i \(0.460531\pi\)
\(198\) 10.6826 0.759177
\(199\) −27.6483 −1.95994 −0.979968 0.199156i \(-0.936180\pi\)
−0.979968 + 0.199156i \(0.936180\pi\)
\(200\) 56.6384 4.00494
\(201\) 8.20608 0.578812
\(202\) −23.6256 −1.66229
\(203\) 21.5374 1.51163
\(204\) 29.8212 2.08790
\(205\) −4.29606 −0.300050
\(206\) −2.69069 −0.187469
\(207\) 4.70654 0.327127
\(208\) 12.9761 0.899732
\(209\) −12.6726 −0.876584
\(210\) 32.4725 2.24081
\(211\) −15.6447 −1.07703 −0.538513 0.842617i \(-0.681014\pi\)
−0.538513 + 0.842617i \(0.681014\pi\)
\(212\) 75.2890 5.17087
\(213\) 5.77396 0.395625
\(214\) −10.2724 −0.702204
\(215\) 12.6091 0.859931
\(216\) −8.71737 −0.593142
\(217\) 23.9823 1.62802
\(218\) −20.1415 −1.36416
\(219\) 4.07053 0.275061
\(220\) −70.5381 −4.75568
\(221\) −5.69126 −0.382835
\(222\) 19.2004 1.28864
\(223\) 5.29312 0.354454 0.177227 0.984170i \(-0.443287\pi\)
0.177227 + 0.984170i \(0.443287\pi\)
\(224\) 62.2153 4.15693
\(225\) 6.49719 0.433146
\(226\) 24.1753 1.60812
\(227\) −1.22433 −0.0812614 −0.0406307 0.999174i \(-0.512937\pi\)
−0.0406307 + 0.999174i \(0.512937\pi\)
\(228\) 16.7252 1.10765
\(229\) 4.67193 0.308730 0.154365 0.988014i \(-0.450667\pi\)
0.154365 + 0.988014i \(0.450667\pi\)
\(230\) −42.9400 −2.83138
\(231\) −14.1308 −0.929739
\(232\) 52.7502 3.46322
\(233\) 17.6410 1.15570 0.577851 0.816142i \(-0.303892\pi\)
0.577851 + 0.816142i \(0.303892\pi\)
\(234\) 2.69069 0.175896
\(235\) 9.48077 0.618457
\(236\) 57.4510 3.73974
\(237\) −9.95930 −0.646926
\(238\) −54.5040 −3.53297
\(239\) −9.35839 −0.605344 −0.302672 0.953095i \(-0.597879\pi\)
−0.302672 + 0.953095i \(0.597879\pi\)
\(240\) 43.9988 2.84011
\(241\) −6.45712 −0.415940 −0.207970 0.978135i \(-0.566686\pi\)
−0.207970 + 0.978135i \(0.566686\pi\)
\(242\) 12.8142 0.823728
\(243\) −1.00000 −0.0641500
\(244\) −49.0290 −3.13876
\(245\) −19.2191 −1.22786
\(246\) −3.40909 −0.217356
\(247\) −3.19194 −0.203098
\(248\) 58.7381 3.72987
\(249\) −15.1402 −0.959469
\(250\) −13.6595 −0.863904
\(251\) −30.1157 −1.90088 −0.950442 0.310903i \(-0.899368\pi\)
−0.950442 + 0.310903i \(0.899368\pi\)
\(252\) 18.6497 1.17482
\(253\) 18.6859 1.17477
\(254\) −0.152281 −0.00955498
\(255\) −19.2976 −1.20846
\(256\) 16.3945 1.02465
\(257\) 30.2724 1.88834 0.944169 0.329461i \(-0.106867\pi\)
0.944169 + 0.329461i \(0.106867\pi\)
\(258\) 10.0058 0.622933
\(259\) −25.3981 −1.57816
\(260\) −17.7669 −1.10186
\(261\) 6.05116 0.374557
\(262\) 37.7327 2.33113
\(263\) −20.4793 −1.26281 −0.631404 0.775454i \(-0.717521\pi\)
−0.631404 + 0.775454i \(0.717521\pi\)
\(264\) −34.6096 −2.13008
\(265\) −48.7203 −2.99287
\(266\) −30.5686 −1.87428
\(267\) −14.6677 −0.897646
\(268\) −42.9984 −2.62655
\(269\) −1.59398 −0.0971869 −0.0485935 0.998819i \(-0.515474\pi\)
−0.0485935 + 0.998819i \(0.515474\pi\)
\(270\) 9.12347 0.555236
\(271\) 3.86498 0.234781 0.117390 0.993086i \(-0.462547\pi\)
0.117390 + 0.993086i \(0.462547\pi\)
\(272\) −73.8504 −4.47784
\(273\) −3.55923 −0.215414
\(274\) −1.24019 −0.0749227
\(275\) 25.7951 1.55550
\(276\) −24.6615 −1.48445
\(277\) 1.88019 0.112970 0.0564849 0.998403i \(-0.482011\pi\)
0.0564849 + 0.998403i \(0.482011\pi\)
\(278\) −2.92543 −0.175455
\(279\) 6.73805 0.403397
\(280\) −105.205 −6.28721
\(281\) 20.1209 1.20031 0.600156 0.799883i \(-0.295105\pi\)
0.600156 + 0.799883i \(0.295105\pi\)
\(282\) 7.52336 0.448010
\(283\) −31.4850 −1.87159 −0.935796 0.352543i \(-0.885317\pi\)
−0.935796 + 0.352543i \(0.885317\pi\)
\(284\) −30.2546 −1.79528
\(285\) −10.8231 −0.641104
\(286\) 10.6826 0.631673
\(287\) 4.50952 0.266188
\(288\) 17.4800 1.03002
\(289\) 15.3904 0.905319
\(290\) −55.2075 −3.24190
\(291\) −6.18570 −0.362612
\(292\) −21.3289 −1.24818
\(293\) 24.8054 1.44915 0.724573 0.689198i \(-0.242037\pi\)
0.724573 + 0.689198i \(0.242037\pi\)
\(294\) −15.2511 −0.889463
\(295\) −37.1772 −2.16454
\(296\) −62.2058 −3.61564
\(297\) −3.97019 −0.230374
\(298\) −32.5143 −1.88350
\(299\) 4.70654 0.272186
\(300\) −34.0441 −1.96554
\(301\) −13.2356 −0.762886
\(302\) −5.72960 −0.329701
\(303\) 8.78051 0.504427
\(304\) −41.4190 −2.37554
\(305\) 31.7272 1.81670
\(306\) −15.3134 −0.875410
\(307\) 11.8603 0.676905 0.338453 0.940983i \(-0.390097\pi\)
0.338453 + 0.940983i \(0.390097\pi\)
\(308\) 74.0430 4.21899
\(309\) 1.00000 0.0568880
\(310\) −61.4744 −3.49151
\(311\) −5.91420 −0.335364 −0.167682 0.985841i \(-0.553628\pi\)
−0.167682 + 0.985841i \(0.553628\pi\)
\(312\) −8.71737 −0.493524
\(313\) −26.7960 −1.51460 −0.757301 0.653066i \(-0.773482\pi\)
−0.757301 + 0.653066i \(0.773482\pi\)
\(314\) 29.9353 1.68935
\(315\) −12.0685 −0.679980
\(316\) 52.1850 2.93563
\(317\) 0.676898 0.0380184 0.0190092 0.999819i \(-0.493949\pi\)
0.0190092 + 0.999819i \(0.493949\pi\)
\(318\) −38.6615 −2.16803
\(319\) 24.0243 1.34510
\(320\) −71.4806 −3.99589
\(321\) 3.81774 0.213085
\(322\) 45.0736 2.51185
\(323\) 18.1662 1.01079
\(324\) 5.23983 0.291101
\(325\) 6.49719 0.360399
\(326\) 1.29253 0.0715869
\(327\) 7.48563 0.413957
\(328\) 11.0448 0.609850
\(329\) −9.95185 −0.548663
\(330\) 36.2219 1.99395
\(331\) −36.1015 −1.98432 −0.992159 0.124984i \(-0.960112\pi\)
−0.992159 + 0.124984i \(0.960112\pi\)
\(332\) 79.3318 4.35390
\(333\) −7.13584 −0.391042
\(334\) 4.81652 0.263548
\(335\) 27.8248 1.52023
\(336\) −46.1850 −2.51960
\(337\) 17.8760 0.973765 0.486883 0.873467i \(-0.338134\pi\)
0.486883 + 0.873467i \(0.338134\pi\)
\(338\) 2.69069 0.146354
\(339\) −8.98479 −0.487987
\(340\) 101.116 5.48380
\(341\) 26.7514 1.44867
\(342\) −8.58854 −0.464415
\(343\) −4.74053 −0.255965
\(344\) −32.4170 −1.74781
\(345\) 15.9587 0.859188
\(346\) −9.30459 −0.500218
\(347\) −13.2962 −0.713776 −0.356888 0.934147i \(-0.616162\pi\)
−0.356888 + 0.934147i \(0.616162\pi\)
\(348\) −31.7070 −1.69967
\(349\) −14.7753 −0.790905 −0.395453 0.918486i \(-0.629412\pi\)
−0.395453 + 0.918486i \(0.629412\pi\)
\(350\) 62.2222 3.32591
\(351\) −1.00000 −0.0533761
\(352\) 69.3989 3.69898
\(353\) −24.9011 −1.32535 −0.662675 0.748907i \(-0.730579\pi\)
−0.662675 + 0.748907i \(0.730579\pi\)
\(354\) −29.5015 −1.56799
\(355\) 19.5781 1.03910
\(356\) 76.8560 4.07336
\(357\) 20.2565 1.07209
\(358\) −61.8593 −3.26937
\(359\) −15.6686 −0.826958 −0.413479 0.910514i \(-0.635686\pi\)
−0.413479 + 0.910514i \(0.635686\pi\)
\(360\) −29.5584 −1.55787
\(361\) −8.81150 −0.463763
\(362\) −6.69761 −0.352019
\(363\) −4.76242 −0.249962
\(364\) 18.6497 0.977512
\(365\) 13.8022 0.722438
\(366\) 25.1768 1.31601
\(367\) 24.8164 1.29540 0.647702 0.761893i \(-0.275730\pi\)
0.647702 + 0.761893i \(0.275730\pi\)
\(368\) 61.0727 3.18363
\(369\) 1.26699 0.0659570
\(370\) 65.1036 3.38457
\(371\) 51.1411 2.65511
\(372\) −35.3062 −1.83054
\(373\) 6.40834 0.331812 0.165906 0.986142i \(-0.446945\pi\)
0.165906 + 0.986142i \(0.446945\pi\)
\(374\) −60.7972 −3.14375
\(375\) 5.07658 0.262154
\(376\) −24.3744 −1.25701
\(377\) 6.05116 0.311650
\(378\) −9.57679 −0.492577
\(379\) 22.9273 1.17769 0.588847 0.808244i \(-0.299582\pi\)
0.588847 + 0.808244i \(0.299582\pi\)
\(380\) 56.7110 2.90922
\(381\) 0.0565956 0.00289948
\(382\) −14.0721 −0.719991
\(383\) −25.1672 −1.28598 −0.642992 0.765873i \(-0.722307\pi\)
−0.642992 + 0.765873i \(0.722307\pi\)
\(384\) −21.7626 −1.11057
\(385\) −47.9141 −2.44193
\(386\) −50.4019 −2.56539
\(387\) −3.71867 −0.189030
\(388\) 32.4120 1.64547
\(389\) −35.7493 −1.81256 −0.906281 0.422675i \(-0.861091\pi\)
−0.906281 + 0.422675i \(0.861091\pi\)
\(390\) 9.12347 0.461985
\(391\) −26.7862 −1.35463
\(392\) 49.4110 2.49563
\(393\) −14.0234 −0.707388
\(394\) 9.34165 0.470626
\(395\) −33.7695 −1.69913
\(396\) 20.8031 1.04540
\(397\) −25.1766 −1.26358 −0.631788 0.775142i \(-0.717679\pi\)
−0.631788 + 0.775142i \(0.717679\pi\)
\(398\) −74.3931 −3.72899
\(399\) 11.3608 0.568754
\(400\) 84.3083 4.21541
\(401\) 1.50056 0.0749342 0.0374671 0.999298i \(-0.488071\pi\)
0.0374671 + 0.999298i \(0.488071\pi\)
\(402\) 22.0800 1.10125
\(403\) 6.73805 0.335646
\(404\) −46.0083 −2.28900
\(405\) −3.39075 −0.168488
\(406\) 57.9506 2.87604
\(407\) −28.3307 −1.40430
\(408\) 49.6128 2.45620
\(409\) 11.9081 0.588817 0.294409 0.955680i \(-0.404877\pi\)
0.294409 + 0.955680i \(0.404877\pi\)
\(410\) −11.5594 −0.570876
\(411\) 0.460919 0.0227355
\(412\) −5.23983 −0.258148
\(413\) 39.0244 1.92027
\(414\) 12.6639 0.622395
\(415\) −51.3365 −2.52001
\(416\) 17.4800 0.857027
\(417\) 1.08724 0.0532424
\(418\) −34.0981 −1.66779
\(419\) 26.3736 1.28844 0.644219 0.764841i \(-0.277183\pi\)
0.644219 + 0.764841i \(0.277183\pi\)
\(420\) 63.2366 3.08563
\(421\) −28.8430 −1.40572 −0.702861 0.711328i \(-0.748094\pi\)
−0.702861 + 0.711328i \(0.748094\pi\)
\(422\) −42.0951 −2.04916
\(423\) −2.79607 −0.135950
\(424\) 125.256 6.08299
\(425\) −36.9772 −1.79366
\(426\) 15.5360 0.752719
\(427\) −33.3037 −1.61168
\(428\) −20.0043 −0.966943
\(429\) −3.97019 −0.191683
\(430\) 33.9271 1.63611
\(431\) −32.0033 −1.54154 −0.770771 0.637112i \(-0.780129\pi\)
−0.770771 + 0.637112i \(0.780129\pi\)
\(432\) −12.9761 −0.624314
\(433\) 39.4532 1.89600 0.947999 0.318272i \(-0.103103\pi\)
0.947999 + 0.318272i \(0.103103\pi\)
\(434\) 64.5289 3.09749
\(435\) 20.5180 0.983761
\(436\) −39.2234 −1.87846
\(437\) −15.0230 −0.718648
\(438\) 10.9525 0.523333
\(439\) 2.96596 0.141558 0.0707788 0.997492i \(-0.477452\pi\)
0.0707788 + 0.997492i \(0.477452\pi\)
\(440\) −117.353 −5.59457
\(441\) 5.66810 0.269910
\(442\) −15.3134 −0.728385
\(443\) 19.6265 0.932485 0.466242 0.884657i \(-0.345607\pi\)
0.466242 + 0.884657i \(0.345607\pi\)
\(444\) 37.3906 1.77448
\(445\) −49.7344 −2.35764
\(446\) 14.2422 0.674386
\(447\) 12.0840 0.571554
\(448\) 75.0323 3.54494
\(449\) −21.9477 −1.03577 −0.517887 0.855449i \(-0.673281\pi\)
−0.517887 + 0.855449i \(0.673281\pi\)
\(450\) 17.4819 0.824106
\(451\) 5.03020 0.236863
\(452\) 47.0787 2.21440
\(453\) 2.12941 0.100049
\(454\) −3.29428 −0.154608
\(455\) −12.0685 −0.565778
\(456\) 27.8254 1.30304
\(457\) 8.34457 0.390342 0.195171 0.980769i \(-0.437474\pi\)
0.195171 + 0.980769i \(0.437474\pi\)
\(458\) 12.5707 0.587392
\(459\) 5.69126 0.265645
\(460\) −83.6209 −3.89884
\(461\) 4.64128 0.216166 0.108083 0.994142i \(-0.465529\pi\)
0.108083 + 0.994142i \(0.465529\pi\)
\(462\) −38.0217 −1.76893
\(463\) −31.7309 −1.47466 −0.737329 0.675534i \(-0.763913\pi\)
−0.737329 + 0.675534i \(0.763913\pi\)
\(464\) 78.5205 3.64522
\(465\) 22.8471 1.05951
\(466\) 47.4666 2.19885
\(467\) −39.6191 −1.83335 −0.916677 0.399628i \(-0.869139\pi\)
−0.916677 + 0.399628i \(0.869139\pi\)
\(468\) 5.23983 0.242211
\(469\) −29.2073 −1.34867
\(470\) 25.5098 1.17668
\(471\) −11.1255 −0.512636
\(472\) 95.5798 4.39942
\(473\) −14.7638 −0.678841
\(474\) −26.7974 −1.23085
\(475\) −20.7386 −0.951554
\(476\) −106.140 −4.86494
\(477\) 14.3686 0.657893
\(478\) −25.1805 −1.15173
\(479\) 3.23975 0.148028 0.0740141 0.997257i \(-0.476419\pi\)
0.0740141 + 0.997257i \(0.476419\pi\)
\(480\) 59.2703 2.70531
\(481\) −7.13584 −0.325366
\(482\) −17.3741 −0.791370
\(483\) −16.7517 −0.762227
\(484\) 24.9542 1.13428
\(485\) −20.9742 −0.952388
\(486\) −2.69069 −0.122052
\(487\) 26.9052 1.21919 0.609596 0.792712i \(-0.291332\pi\)
0.609596 + 0.792712i \(0.291332\pi\)
\(488\) −81.5684 −3.69243
\(489\) −0.480373 −0.0217232
\(490\) −51.7127 −2.33614
\(491\) −24.2946 −1.09640 −0.548201 0.836347i \(-0.684687\pi\)
−0.548201 + 0.836347i \(0.684687\pi\)
\(492\) −6.63882 −0.299301
\(493\) −34.4387 −1.55104
\(494\) −8.58854 −0.386416
\(495\) −13.4619 −0.605069
\(496\) 87.4338 3.92589
\(497\) −20.5508 −0.921831
\(498\) −40.7375 −1.82549
\(499\) −32.8172 −1.46910 −0.734551 0.678554i \(-0.762607\pi\)
−0.734551 + 0.678554i \(0.762607\pi\)
\(500\) −26.6004 −1.18961
\(501\) −1.79007 −0.0799743
\(502\) −81.0320 −3.61663
\(503\) 4.80346 0.214176 0.107088 0.994250i \(-0.465847\pi\)
0.107088 + 0.994250i \(0.465847\pi\)
\(504\) 31.0271 1.38206
\(505\) 29.7725 1.32486
\(506\) 50.2780 2.23513
\(507\) −1.00000 −0.0444116
\(508\) −0.296551 −0.0131573
\(509\) 12.3488 0.547350 0.273675 0.961822i \(-0.411761\pi\)
0.273675 + 0.961822i \(0.411761\pi\)
\(510\) −51.9240 −2.29923
\(511\) −14.4879 −0.640909
\(512\) 0.587183 0.0259501
\(513\) 3.19194 0.140928
\(514\) 81.4536 3.59277
\(515\) 3.39075 0.149414
\(516\) 19.4852 0.857786
\(517\) −11.1009 −0.488218
\(518\) −68.3384 −3.00262
\(519\) 3.45807 0.151792
\(520\) −29.5584 −1.29622
\(521\) 38.7317 1.69687 0.848434 0.529302i \(-0.177546\pi\)
0.848434 + 0.529302i \(0.177546\pi\)
\(522\) 16.2818 0.712635
\(523\) −12.4507 −0.544431 −0.272216 0.962236i \(-0.587756\pi\)
−0.272216 + 0.962236i \(0.587756\pi\)
\(524\) 73.4802 3.21000
\(525\) −23.1250 −1.00926
\(526\) −55.1035 −2.40263
\(527\) −38.3480 −1.67046
\(528\) −51.5177 −2.24202
\(529\) −0.848443 −0.0368888
\(530\) −131.091 −5.69425
\(531\) 10.9643 0.475810
\(532\) −59.5289 −2.58090
\(533\) 1.26699 0.0548796
\(534\) −39.4662 −1.70787
\(535\) 12.9450 0.559661
\(536\) −71.5354 −3.08986
\(537\) 22.9901 0.992097
\(538\) −4.28892 −0.184909
\(539\) 22.5034 0.969292
\(540\) 17.7669 0.764567
\(541\) 28.1218 1.20905 0.604526 0.796585i \(-0.293363\pi\)
0.604526 + 0.796585i \(0.293363\pi\)
\(542\) 10.3995 0.446696
\(543\) 2.48918 0.106821
\(544\) −99.4832 −4.26531
\(545\) 25.3819 1.08724
\(546\) −9.57679 −0.409849
\(547\) 39.7301 1.69874 0.849369 0.527799i \(-0.176983\pi\)
0.849369 + 0.527799i \(0.176983\pi\)
\(548\) −2.41513 −0.103169
\(549\) −9.35699 −0.399347
\(550\) 69.4066 2.95951
\(551\) −19.3149 −0.822844
\(552\) −41.0287 −1.74630
\(553\) 35.4474 1.50738
\(554\) 5.05902 0.214937
\(555\) −24.1959 −1.02706
\(556\) −5.69695 −0.241604
\(557\) −34.1735 −1.44798 −0.723989 0.689811i \(-0.757693\pi\)
−0.723989 + 0.689811i \(0.757693\pi\)
\(558\) 18.1300 0.767505
\(559\) −3.71867 −0.157283
\(560\) −156.602 −6.61763
\(561\) 22.5954 0.953978
\(562\) 54.1391 2.28372
\(563\) −40.7054 −1.71553 −0.857764 0.514044i \(-0.828147\pi\)
−0.857764 + 0.514044i \(0.828147\pi\)
\(564\) 14.6509 0.616915
\(565\) −30.4652 −1.28168
\(566\) −84.7166 −3.56090
\(567\) 3.55923 0.149474
\(568\) −50.3338 −2.11196
\(569\) −2.06896 −0.0867353 −0.0433677 0.999059i \(-0.513809\pi\)
−0.0433677 + 0.999059i \(0.513809\pi\)
\(570\) −29.1216 −1.21977
\(571\) 22.3349 0.934685 0.467343 0.884076i \(-0.345211\pi\)
0.467343 + 0.884076i \(0.345211\pi\)
\(572\) 20.8031 0.869822
\(573\) 5.22992 0.218483
\(574\) 12.1337 0.506452
\(575\) 30.5793 1.27524
\(576\) 21.0811 0.878377
\(577\) 16.6712 0.694029 0.347015 0.937860i \(-0.387195\pi\)
0.347015 + 0.937860i \(0.387195\pi\)
\(578\) 41.4109 1.72247
\(579\) 18.7320 0.778473
\(580\) −107.511 −4.46413
\(581\) 53.8873 2.23562
\(582\) −16.6438 −0.689909
\(583\) 57.0461 2.36261
\(584\) −35.4843 −1.46835
\(585\) −3.39075 −0.140190
\(586\) 66.7436 2.75715
\(587\) −36.3447 −1.50011 −0.750054 0.661377i \(-0.769972\pi\)
−0.750054 + 0.661377i \(0.769972\pi\)
\(588\) −29.6999 −1.22480
\(589\) −21.5075 −0.886200
\(590\) −100.032 −4.11827
\(591\) −3.47184 −0.142812
\(592\) −92.5955 −3.80565
\(593\) −14.5823 −0.598822 −0.299411 0.954124i \(-0.596790\pi\)
−0.299411 + 0.954124i \(0.596790\pi\)
\(594\) −10.6826 −0.438311
\(595\) 68.6847 2.81580
\(596\) −63.3181 −2.59361
\(597\) 27.6483 1.13157
\(598\) 12.6639 0.517864
\(599\) 45.3540 1.85311 0.926557 0.376155i \(-0.122754\pi\)
0.926557 + 0.376155i \(0.122754\pi\)
\(600\) −56.6384 −2.31225
\(601\) 20.1306 0.821143 0.410572 0.911828i \(-0.365329\pi\)
0.410572 + 0.911828i \(0.365329\pi\)
\(602\) −35.6129 −1.45147
\(603\) −8.20608 −0.334177
\(604\) −11.1578 −0.454003
\(605\) −16.1482 −0.656517
\(606\) 23.6256 0.959726
\(607\) 35.9338 1.45851 0.729253 0.684244i \(-0.239868\pi\)
0.729253 + 0.684244i \(0.239868\pi\)
\(608\) −55.7951 −2.26279
\(609\) −21.5374 −0.872741
\(610\) 85.3682 3.45646
\(611\) −2.79607 −0.113117
\(612\) −29.8212 −1.20545
\(613\) −13.3918 −0.540890 −0.270445 0.962735i \(-0.587171\pi\)
−0.270445 + 0.962735i \(0.587171\pi\)
\(614\) 31.9125 1.28788
\(615\) 4.29606 0.173234
\(616\) 123.184 4.96321
\(617\) −17.0134 −0.684934 −0.342467 0.939530i \(-0.611263\pi\)
−0.342467 + 0.939530i \(0.611263\pi\)
\(618\) 2.69069 0.108236
\(619\) −47.2728 −1.90006 −0.950028 0.312165i \(-0.898946\pi\)
−0.950028 + 0.312165i \(0.898946\pi\)
\(620\) −119.715 −4.80785
\(621\) −4.70654 −0.188867
\(622\) −15.9133 −0.638065
\(623\) 52.2055 2.09157
\(624\) −12.9761 −0.519460
\(625\) −15.2725 −0.610900
\(626\) −72.0999 −2.88169
\(627\) 12.6726 0.506096
\(628\) 58.2957 2.32625
\(629\) 40.6119 1.61930
\(630\) −32.4725 −1.29373
\(631\) −3.17379 −0.126347 −0.0631733 0.998003i \(-0.520122\pi\)
−0.0631733 + 0.998003i \(0.520122\pi\)
\(632\) 86.8189 3.45347
\(633\) 15.6447 0.621822
\(634\) 1.82132 0.0723340
\(635\) 0.191901 0.00761538
\(636\) −75.2890 −2.98540
\(637\) 5.66810 0.224578
\(638\) 64.6419 2.55920
\(639\) −5.77396 −0.228414
\(640\) −73.7917 −2.91687
\(641\) −41.2087 −1.62765 −0.813824 0.581112i \(-0.802618\pi\)
−0.813824 + 0.581112i \(0.802618\pi\)
\(642\) 10.2724 0.405417
\(643\) 44.1860 1.74252 0.871262 0.490818i \(-0.163302\pi\)
0.871262 + 0.490818i \(0.163302\pi\)
\(644\) 87.7758 3.45885
\(645\) −12.6091 −0.496481
\(646\) 48.8796 1.92314
\(647\) 30.2881 1.19075 0.595374 0.803449i \(-0.297004\pi\)
0.595374 + 0.803449i \(0.297004\pi\)
\(648\) 8.71737 0.342451
\(649\) 43.5303 1.70872
\(650\) 17.4819 0.685698
\(651\) −23.9823 −0.939939
\(652\) 2.51707 0.0985760
\(653\) −18.6600 −0.730223 −0.365112 0.930964i \(-0.618969\pi\)
−0.365112 + 0.930964i \(0.618969\pi\)
\(654\) 20.1415 0.787597
\(655\) −47.5499 −1.85793
\(656\) 16.4407 0.641900
\(657\) −4.07053 −0.158807
\(658\) −26.7774 −1.04389
\(659\) 27.0943 1.05545 0.527723 0.849417i \(-0.323046\pi\)
0.527723 + 0.849417i \(0.323046\pi\)
\(660\) 70.5381 2.74569
\(661\) −43.8094 −1.70399 −0.851994 0.523552i \(-0.824607\pi\)
−0.851994 + 0.523552i \(0.824607\pi\)
\(662\) −97.1380 −3.77538
\(663\) 5.69126 0.221030
\(664\) 131.982 5.12191
\(665\) 38.5218 1.49381
\(666\) −19.2004 −0.743999
\(667\) 28.4800 1.10275
\(668\) 9.37964 0.362909
\(669\) −5.29312 −0.204644
\(670\) 74.8679 2.89240
\(671\) −37.1490 −1.43412
\(672\) −62.2153 −2.40001
\(673\) 18.1591 0.699981 0.349991 0.936753i \(-0.386185\pi\)
0.349991 + 0.936753i \(0.386185\pi\)
\(674\) 48.0987 1.85269
\(675\) −6.49719 −0.250077
\(676\) 5.23983 0.201532
\(677\) −26.3658 −1.01332 −0.506659 0.862146i \(-0.669120\pi\)
−0.506659 + 0.862146i \(0.669120\pi\)
\(678\) −24.1753 −0.928447
\(679\) 22.0163 0.844909
\(680\) 168.225 6.45112
\(681\) 1.22433 0.0469163
\(682\) 71.9797 2.75624
\(683\) 51.7241 1.97917 0.989584 0.143959i \(-0.0459834\pi\)
0.989584 + 0.143959i \(0.0459834\pi\)
\(684\) −16.7252 −0.639505
\(685\) 1.56286 0.0597138
\(686\) −12.7553 −0.487000
\(687\) −4.67193 −0.178245
\(688\) −48.2538 −1.83966
\(689\) 14.3686 0.547400
\(690\) 42.9400 1.63470
\(691\) 2.96484 0.112788 0.0563938 0.998409i \(-0.482040\pi\)
0.0563938 + 0.998409i \(0.482040\pi\)
\(692\) −18.1197 −0.688806
\(693\) 14.1308 0.536785
\(694\) −35.7759 −1.35803
\(695\) 3.68656 0.139839
\(696\) −52.7502 −1.99949
\(697\) −7.21078 −0.273128
\(698\) −39.7559 −1.50478
\(699\) −17.6410 −0.667245
\(700\) 121.171 4.57982
\(701\) −14.6820 −0.554533 −0.277266 0.960793i \(-0.589428\pi\)
−0.277266 + 0.960793i \(0.589428\pi\)
\(702\) −2.69069 −0.101554
\(703\) 22.7772 0.859058
\(704\) 83.6958 3.15441
\(705\) −9.48077 −0.357066
\(706\) −67.0011 −2.52162
\(707\) −31.2518 −1.17535
\(708\) −57.4510 −2.15914
\(709\) 7.49469 0.281469 0.140735 0.990047i \(-0.455054\pi\)
0.140735 + 0.990047i \(0.455054\pi\)
\(710\) 52.6785 1.97699
\(711\) 9.95930 0.373503
\(712\) 127.863 4.79189
\(713\) 31.7129 1.18766
\(714\) 54.5040 2.03976
\(715\) −13.4619 −0.503447
\(716\) −120.464 −4.50196
\(717\) 9.35839 0.349495
\(718\) −42.1594 −1.57338
\(719\) 15.1168 0.563760 0.281880 0.959450i \(-0.409042\pi\)
0.281880 + 0.959450i \(0.409042\pi\)
\(720\) −43.9988 −1.63974
\(721\) −3.55923 −0.132553
\(722\) −23.7090 −0.882359
\(723\) 6.45712 0.240143
\(724\) −13.0429 −0.484734
\(725\) 39.3155 1.46014
\(726\) −12.8142 −0.475580
\(727\) −5.12143 −0.189943 −0.0949717 0.995480i \(-0.530276\pi\)
−0.0949717 + 0.995480i \(0.530276\pi\)
\(728\) 31.0271 1.14994
\(729\) 1.00000 0.0370370
\(730\) 37.1374 1.37452
\(731\) 21.1639 0.782775
\(732\) 49.0290 1.81216
\(733\) −30.0695 −1.11064 −0.555321 0.831636i \(-0.687405\pi\)
−0.555321 + 0.831636i \(0.687405\pi\)
\(734\) 66.7733 2.46465
\(735\) 19.2191 0.708908
\(736\) 82.2704 3.03253
\(737\) −32.5797 −1.20009
\(738\) 3.40909 0.125490
\(739\) 35.8412 1.31844 0.659220 0.751950i \(-0.270886\pi\)
0.659220 + 0.751950i \(0.270886\pi\)
\(740\) 126.782 4.66060
\(741\) 3.19194 0.117259
\(742\) 137.605 5.05164
\(743\) 0.491872 0.0180450 0.00902252 0.999959i \(-0.497128\pi\)
0.00902252 + 0.999959i \(0.497128\pi\)
\(744\) −58.7381 −2.15344
\(745\) 40.9738 1.50116
\(746\) 17.2429 0.631307
\(747\) 15.1402 0.553950
\(748\) −118.396 −4.32898
\(749\) −13.5882 −0.496502
\(750\) 13.6595 0.498775
\(751\) −2.47358 −0.0902624 −0.0451312 0.998981i \(-0.514371\pi\)
−0.0451312 + 0.998981i \(0.514371\pi\)
\(752\) −36.2821 −1.32307
\(753\) 30.1157 1.09748
\(754\) 16.2818 0.592948
\(755\) 7.22031 0.262774
\(756\) −18.6497 −0.678284
\(757\) 3.37719 0.122746 0.0613731 0.998115i \(-0.480452\pi\)
0.0613731 + 0.998115i \(0.480452\pi\)
\(758\) 61.6902 2.24069
\(759\) −18.6859 −0.678254
\(760\) 94.3488 3.42239
\(761\) 37.6906 1.36628 0.683142 0.730286i \(-0.260613\pi\)
0.683142 + 0.730286i \(0.260613\pi\)
\(762\) 0.152281 0.00551657
\(763\) −26.6431 −0.964544
\(764\) −27.4038 −0.991436
\(765\) 19.2976 0.697707
\(766\) −67.7172 −2.44672
\(767\) 10.9643 0.395898
\(768\) −16.3945 −0.591584
\(769\) 5.57218 0.200938 0.100469 0.994940i \(-0.467966\pi\)
0.100469 + 0.994940i \(0.467966\pi\)
\(770\) −128.922 −4.64603
\(771\) −30.2724 −1.09023
\(772\) −98.1522 −3.53257
\(773\) 7.56955 0.272258 0.136129 0.990691i \(-0.456534\pi\)
0.136129 + 0.990691i \(0.456534\pi\)
\(774\) −10.0058 −0.359650
\(775\) 43.7784 1.57257
\(776\) 53.9231 1.93573
\(777\) 25.3981 0.911151
\(778\) −96.1904 −3.44859
\(779\) −4.04417 −0.144897
\(780\) 17.7669 0.636158
\(781\) −22.9237 −0.820276
\(782\) −72.0733 −2.57734
\(783\) −6.05116 −0.216251
\(784\) 73.5500 2.62678
\(785\) −37.7238 −1.34642
\(786\) −37.7327 −1.34588
\(787\) −27.3002 −0.973147 −0.486574 0.873640i \(-0.661753\pi\)
−0.486574 + 0.873640i \(0.661753\pi\)
\(788\) 18.1918 0.648057
\(789\) 20.4793 0.729083
\(790\) −90.8633 −3.23277
\(791\) 31.9789 1.13704
\(792\) 34.6096 1.22980
\(793\) −9.35699 −0.332277
\(794\) −67.7424 −2.40409
\(795\) 48.7203 1.72793
\(796\) −144.872 −5.13486
\(797\) 50.4628 1.78748 0.893741 0.448583i \(-0.148071\pi\)
0.893741 + 0.448583i \(0.148071\pi\)
\(798\) 30.5686 1.08211
\(799\) 15.9131 0.562967
\(800\) 113.571 4.01533
\(801\) 14.6677 0.518256
\(802\) 4.03754 0.142570
\(803\) −16.1608 −0.570302
\(804\) 42.9984 1.51644
\(805\) −56.8007 −2.00196
\(806\) 18.1300 0.638603
\(807\) 1.59398 0.0561109
\(808\) −76.5430 −2.69277
\(809\) −18.4900 −0.650075 −0.325037 0.945701i \(-0.605377\pi\)
−0.325037 + 0.945701i \(0.605377\pi\)
\(810\) −9.12347 −0.320566
\(811\) −2.17608 −0.0764124 −0.0382062 0.999270i \(-0.512164\pi\)
−0.0382062 + 0.999270i \(0.512164\pi\)
\(812\) 112.852 3.96035
\(813\) −3.86498 −0.135551
\(814\) −76.2291 −2.67183
\(815\) −1.62882 −0.0570552
\(816\) 73.8504 2.58528
\(817\) 11.8698 0.415271
\(818\) 32.0410 1.12029
\(819\) 3.55923 0.124369
\(820\) −22.5106 −0.786104
\(821\) −6.56440 −0.229099 −0.114550 0.993418i \(-0.536542\pi\)
−0.114550 + 0.993418i \(0.536542\pi\)
\(822\) 1.24019 0.0432566
\(823\) 40.2319 1.40239 0.701197 0.712967i \(-0.252649\pi\)
0.701197 + 0.712967i \(0.252649\pi\)
\(824\) −8.71737 −0.303684
\(825\) −25.7951 −0.898069
\(826\) 105.003 3.65351
\(827\) 38.9788 1.35542 0.677712 0.735327i \(-0.262971\pi\)
0.677712 + 0.735327i \(0.262971\pi\)
\(828\) 24.6615 0.857045
\(829\) −35.8071 −1.24363 −0.621816 0.783164i \(-0.713605\pi\)
−0.621816 + 0.783164i \(0.713605\pi\)
\(830\) −138.131 −4.79459
\(831\) −1.88019 −0.0652232
\(832\) 21.0811 0.730854
\(833\) −32.2586 −1.11770
\(834\) 2.92543 0.101299
\(835\) −6.06967 −0.210050
\(836\) −66.4023 −2.29657
\(837\) −6.73805 −0.232901
\(838\) 70.9634 2.45139
\(839\) 3.01513 0.104094 0.0520470 0.998645i \(-0.483425\pi\)
0.0520470 + 0.998645i \(0.483425\pi\)
\(840\) 105.205 3.62992
\(841\) 7.61651 0.262638
\(842\) −77.6076 −2.67453
\(843\) −20.1209 −0.693001
\(844\) −81.9756 −2.82172
\(845\) −3.39075 −0.116645
\(846\) −7.52336 −0.258658
\(847\) 16.9505 0.582427
\(848\) 186.449 6.40267
\(849\) 31.4850 1.08056
\(850\) −99.4942 −3.41262
\(851\) −33.5852 −1.15128
\(852\) 30.2546 1.03650
\(853\) 40.4998 1.38669 0.693343 0.720608i \(-0.256137\pi\)
0.693343 + 0.720608i \(0.256137\pi\)
\(854\) −89.6099 −3.06639
\(855\) 10.8231 0.370141
\(856\) −33.2806 −1.13751
\(857\) 39.2621 1.34117 0.670583 0.741834i \(-0.266044\pi\)
0.670583 + 0.741834i \(0.266044\pi\)
\(858\) −10.6826 −0.364697
\(859\) 10.4351 0.356041 0.178020 0.984027i \(-0.443031\pi\)
0.178020 + 0.984027i \(0.443031\pi\)
\(860\) 66.0693 2.25294
\(861\) −4.50952 −0.153684
\(862\) −86.1109 −2.93295
\(863\) −18.3631 −0.625087 −0.312543 0.949904i \(-0.601181\pi\)
−0.312543 + 0.949904i \(0.601181\pi\)
\(864\) −17.4800 −0.594682
\(865\) 11.7254 0.398677
\(866\) 106.156 3.60734
\(867\) −15.3904 −0.522686
\(868\) 125.663 4.26528
\(869\) 39.5403 1.34131
\(870\) 55.2075 1.87171
\(871\) −8.20608 −0.278052
\(872\) −65.2551 −2.20982
\(873\) 6.18570 0.209354
\(874\) −40.4223 −1.36731
\(875\) −18.0687 −0.610834
\(876\) 21.3289 0.720636
\(877\) −8.53828 −0.288317 −0.144159 0.989555i \(-0.546048\pi\)
−0.144159 + 0.989555i \(0.546048\pi\)
\(878\) 7.98048 0.269328
\(879\) −24.8054 −0.836665
\(880\) −174.684 −5.88858
\(881\) 6.88497 0.231961 0.115980 0.993252i \(-0.462999\pi\)
0.115980 + 0.993252i \(0.462999\pi\)
\(882\) 15.2511 0.513532
\(883\) 12.1994 0.410542 0.205271 0.978705i \(-0.434192\pi\)
0.205271 + 0.978705i \(0.434192\pi\)
\(884\) −29.8212 −1.00300
\(885\) 37.1772 1.24970
\(886\) 52.8090 1.77415
\(887\) −8.27124 −0.277721 −0.138861 0.990312i \(-0.544344\pi\)
−0.138861 + 0.990312i \(0.544344\pi\)
\(888\) 62.2058 2.08749
\(889\) −0.201437 −0.00675596
\(890\) −133.820 −4.48565
\(891\) 3.97019 0.133006
\(892\) 27.7350 0.928638
\(893\) 8.92489 0.298660
\(894\) 32.5143 1.08744
\(895\) 77.9537 2.60571
\(896\) 77.4582 2.58770
\(897\) −4.70654 −0.157147
\(898\) −59.0544 −1.97067
\(899\) 40.7730 1.35986
\(900\) 34.0441 1.13480
\(901\) −81.7754 −2.72433
\(902\) 13.5347 0.450657
\(903\) 13.2356 0.440452
\(904\) 78.3238 2.60501
\(905\) 8.44018 0.280561
\(906\) 5.72960 0.190353
\(907\) 54.4054 1.80650 0.903251 0.429114i \(-0.141174\pi\)
0.903251 + 0.429114i \(0.141174\pi\)
\(908\) −6.41525 −0.212898
\(909\) −8.78051 −0.291231
\(910\) −32.4725 −1.07645
\(911\) 1.33568 0.0442529 0.0221264 0.999755i \(-0.492956\pi\)
0.0221264 + 0.999755i \(0.492956\pi\)
\(912\) 41.4190 1.37152
\(913\) 60.1094 1.98933
\(914\) 22.4527 0.742668
\(915\) −31.7272 −1.04887
\(916\) 24.4801 0.808846
\(917\) 49.9125 1.64826
\(918\) 15.3134 0.505418
\(919\) 46.1937 1.52379 0.761895 0.647701i \(-0.224269\pi\)
0.761895 + 0.647701i \(0.224269\pi\)
\(920\) −139.118 −4.58659
\(921\) −11.8603 −0.390811
\(922\) 12.4882 0.411278
\(923\) −5.77396 −0.190052
\(924\) −74.0430 −2.43584
\(925\) −46.3629 −1.52440
\(926\) −85.3780 −2.80570
\(927\) −1.00000 −0.0328443
\(928\) 105.774 3.47221
\(929\) 22.6032 0.741587 0.370793 0.928715i \(-0.379086\pi\)
0.370793 + 0.928715i \(0.379086\pi\)
\(930\) 61.4744 2.01582
\(931\) −18.0923 −0.592950
\(932\) 92.4359 3.02784
\(933\) 5.91420 0.193622
\(934\) −106.603 −3.48815
\(935\) 76.6153 2.50559
\(936\) 8.71737 0.284936
\(937\) −25.3624 −0.828554 −0.414277 0.910151i \(-0.635965\pi\)
−0.414277 + 0.910151i \(0.635965\pi\)
\(938\) −78.5878 −2.56598
\(939\) 26.7960 0.874456
\(940\) 49.6776 1.62030
\(941\) −20.7246 −0.675604 −0.337802 0.941217i \(-0.609683\pi\)
−0.337802 + 0.941217i \(0.609683\pi\)
\(942\) −29.9353 −0.975346
\(943\) 5.96316 0.194187
\(944\) 142.274 4.63062
\(945\) 12.0685 0.392587
\(946\) −39.7249 −1.29157
\(947\) 8.01337 0.260399 0.130200 0.991488i \(-0.458438\pi\)
0.130200 + 0.991488i \(0.458438\pi\)
\(948\) −52.1850 −1.69489
\(949\) −4.07053 −0.132135
\(950\) −55.8013 −1.81043
\(951\) −0.676898 −0.0219499
\(952\) −176.583 −5.72310
\(953\) −50.2186 −1.62674 −0.813371 0.581746i \(-0.802370\pi\)
−0.813371 + 0.581746i \(0.802370\pi\)
\(954\) 38.6615 1.25171
\(955\) 17.7333 0.573837
\(956\) −49.0363 −1.58595
\(957\) −24.0243 −0.776594
\(958\) 8.71718 0.281639
\(959\) −1.64052 −0.0529750
\(960\) 71.4806 2.30703
\(961\) 14.4014 0.464560
\(962\) −19.2004 −0.619044
\(963\) −3.81774 −0.123025
\(964\) −33.8342 −1.08973
\(965\) 63.5154 2.04463
\(966\) −45.0736 −1.45022
\(967\) 19.1682 0.616409 0.308205 0.951320i \(-0.400272\pi\)
0.308205 + 0.951320i \(0.400272\pi\)
\(968\) 41.5158 1.33437
\(969\) −18.1662 −0.583581
\(970\) −56.4351 −1.81202
\(971\) −8.71813 −0.279778 −0.139889 0.990167i \(-0.544675\pi\)
−0.139889 + 0.990167i \(0.544675\pi\)
\(972\) −5.23983 −0.168067
\(973\) −3.86973 −0.124058
\(974\) 72.3937 2.31964
\(975\) −6.49719 −0.208076
\(976\) −121.417 −3.88648
\(977\) −33.2068 −1.06238 −0.531190 0.847253i \(-0.678255\pi\)
−0.531190 + 0.847253i \(0.678255\pi\)
\(978\) −1.29253 −0.0413307
\(979\) 58.2334 1.86115
\(980\) −100.705 −3.21690
\(981\) −7.48563 −0.238998
\(982\) −65.3694 −2.08602
\(983\) 31.5305 1.00567 0.502834 0.864383i \(-0.332291\pi\)
0.502834 + 0.864383i \(0.332291\pi\)
\(984\) −11.0448 −0.352097
\(985\) −11.7721 −0.375092
\(986\) −92.6639 −2.95102
\(987\) 9.95185 0.316771
\(988\) −16.7252 −0.532100
\(989\) −17.5021 −0.556533
\(990\) −36.2219 −1.15121
\(991\) 14.2588 0.452945 0.226472 0.974018i \(-0.427281\pi\)
0.226472 + 0.974018i \(0.427281\pi\)
\(992\) 117.781 3.73956
\(993\) 36.1015 1.14565
\(994\) −55.2960 −1.75388
\(995\) 93.7485 2.97203
\(996\) −79.3318 −2.51373
\(997\) 25.8738 0.819432 0.409716 0.912213i \(-0.365628\pi\)
0.409716 + 0.912213i \(0.365628\pi\)
\(998\) −88.3011 −2.79512
\(999\) 7.13584 0.225768
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 \(a_p\))