Properties

Label 6026.2.a.h.1.6
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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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 1.6
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.90388 q^{3} +1.00000 q^{4} -1.40322 q^{5} +1.90388 q^{6} -1.81515 q^{7} -1.00000 q^{8} +0.624755 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.90388 q^{3} +1.00000 q^{4} -1.40322 q^{5} +1.90388 q^{6} -1.81515 q^{7} -1.00000 q^{8} +0.624755 q^{9} +1.40322 q^{10} +1.73779 q^{11} -1.90388 q^{12} -2.64167 q^{13} +1.81515 q^{14} +2.67156 q^{15} +1.00000 q^{16} +1.78392 q^{17} -0.624755 q^{18} -2.37686 q^{19} -1.40322 q^{20} +3.45583 q^{21} -1.73779 q^{22} -1.00000 q^{23} +1.90388 q^{24} -3.03097 q^{25} +2.64167 q^{26} +4.52218 q^{27} -1.81515 q^{28} +0.0835727 q^{29} -2.67156 q^{30} -0.944842 q^{31} -1.00000 q^{32} -3.30853 q^{33} -1.78392 q^{34} +2.54706 q^{35} +0.624755 q^{36} +11.1027 q^{37} +2.37686 q^{38} +5.02942 q^{39} +1.40322 q^{40} -8.01509 q^{41} -3.45583 q^{42} +8.50045 q^{43} +1.73779 q^{44} -0.876670 q^{45} +1.00000 q^{46} -2.06912 q^{47} -1.90388 q^{48} -3.70522 q^{49} +3.03097 q^{50} -3.39637 q^{51} -2.64167 q^{52} -2.56540 q^{53} -4.52218 q^{54} -2.43850 q^{55} +1.81515 q^{56} +4.52526 q^{57} -0.0835727 q^{58} +0.0652730 q^{59} +2.67156 q^{60} +4.73357 q^{61} +0.944842 q^{62} -1.13403 q^{63} +1.00000 q^{64} +3.70685 q^{65} +3.30853 q^{66} -5.83806 q^{67} +1.78392 q^{68} +1.90388 q^{69} -2.54706 q^{70} +2.32516 q^{71} -0.624755 q^{72} +12.6531 q^{73} -11.1027 q^{74} +5.77060 q^{75} -2.37686 q^{76} -3.15435 q^{77} -5.02942 q^{78} +10.2970 q^{79} -1.40322 q^{80} -10.4839 q^{81} +8.01509 q^{82} +8.91728 q^{83} +3.45583 q^{84} -2.50324 q^{85} -8.50045 q^{86} -0.159112 q^{87} -1.73779 q^{88} +13.8362 q^{89} +0.876670 q^{90} +4.79504 q^{91} -1.00000 q^{92} +1.79886 q^{93} +2.06912 q^{94} +3.33526 q^{95} +1.90388 q^{96} -9.35526 q^{97} +3.70522 q^{98} +1.08569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + O(q^{10}) \) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + q^{10} - 4q^{11} - q^{12} - 5q^{13} + 7q^{14} - 6q^{15} + 24q^{16} + 5q^{17} - 27q^{18} - 20q^{19} - q^{20} + 4q^{22} - 24q^{23} + q^{24} + q^{25} + 5q^{26} - q^{27} - 7q^{28} - 6q^{29} + 6q^{30} - 23q^{31} - 24q^{32} - 6q^{33} - 5q^{34} + 5q^{35} + 27q^{36} - 6q^{37} + 20q^{38} - 39q^{39} + q^{40} - q^{41} - 44q^{43} - 4q^{44} - 13q^{45} + 24q^{46} + 32q^{47} - q^{48} - 13q^{49} - q^{50} - 44q^{51} - 5q^{52} + 21q^{53} + q^{54} - 13q^{55} + 7q^{56} + 10q^{57} + 6q^{58} - 24q^{59} - 6q^{60} - 40q^{61} + 23q^{62} - 54q^{63} + 24q^{64} - 29q^{65} + 6q^{66} - 17q^{67} + 5q^{68} + q^{69} - 5q^{70} + 4q^{71} - 27q^{72} - 16q^{73} + 6q^{74} - 36q^{75} - 20q^{76} + 24q^{77} + 39q^{78} - 53q^{79} - q^{80} + 24q^{81} + q^{82} - 9q^{83} - 37q^{85} + 44q^{86} + 7q^{87} + 4q^{88} - 46q^{89} + 13q^{90} - 44q^{91} - 24q^{92} + 23q^{93} - 32q^{94} + 28q^{95} + q^{96} - 20q^{97} + 13q^{98} - 78q^{99} + O(q^{100}) \)

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
\(3\) −1.90388 −1.09921 −0.549603 0.835426i \(-0.685221\pi\)
−0.549603 + 0.835426i \(0.685221\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.40322 −0.627540 −0.313770 0.949499i \(-0.601592\pi\)
−0.313770 + 0.949499i \(0.601592\pi\)
\(6\) 1.90388 0.777255
\(7\) −1.81515 −0.686063 −0.343032 0.939324i \(-0.611454\pi\)
−0.343032 + 0.939324i \(0.611454\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.624755 0.208252
\(10\) 1.40322 0.443738
\(11\) 1.73779 0.523962 0.261981 0.965073i \(-0.415624\pi\)
0.261981 + 0.965073i \(0.415624\pi\)
\(12\) −1.90388 −0.549603
\(13\) −2.64167 −0.732668 −0.366334 0.930483i \(-0.619387\pi\)
−0.366334 + 0.930483i \(0.619387\pi\)
\(14\) 1.81515 0.485120
\(15\) 2.67156 0.689795
\(16\) 1.00000 0.250000
\(17\) 1.78392 0.432664 0.216332 0.976320i \(-0.430591\pi\)
0.216332 + 0.976320i \(0.430591\pi\)
\(18\) −0.624755 −0.147256
\(19\) −2.37686 −0.545290 −0.272645 0.962115i \(-0.587898\pi\)
−0.272645 + 0.962115i \(0.587898\pi\)
\(20\) −1.40322 −0.313770
\(21\) 3.45583 0.754124
\(22\) −1.73779 −0.370497
\(23\) −1.00000 −0.208514
\(24\) 1.90388 0.388628
\(25\) −3.03097 −0.606194
\(26\) 2.64167 0.518074
\(27\) 4.52218 0.870294
\(28\) −1.81515 −0.343032
\(29\) 0.0835727 0.0155191 0.00775953 0.999970i \(-0.497530\pi\)
0.00775953 + 0.999970i \(0.497530\pi\)
\(30\) −2.67156 −0.487759
\(31\) −0.944842 −0.169699 −0.0848493 0.996394i \(-0.527041\pi\)
−0.0848493 + 0.996394i \(0.527041\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.30853 −0.575942
\(34\) −1.78392 −0.305940
\(35\) 2.54706 0.430532
\(36\) 0.624755 0.104126
\(37\) 11.1027 1.82527 0.912637 0.408771i \(-0.134042\pi\)
0.912637 + 0.408771i \(0.134042\pi\)
\(38\) 2.37686 0.385578
\(39\) 5.02942 0.805352
\(40\) 1.40322 0.221869
\(41\) −8.01509 −1.25175 −0.625874 0.779925i \(-0.715257\pi\)
−0.625874 + 0.779925i \(0.715257\pi\)
\(42\) −3.45583 −0.533246
\(43\) 8.50045 1.29631 0.648153 0.761510i \(-0.275542\pi\)
0.648153 + 0.761510i \(0.275542\pi\)
\(44\) 1.73779 0.261981
\(45\) −0.876670 −0.130686
\(46\) 1.00000 0.147442
\(47\) −2.06912 −0.301813 −0.150906 0.988548i \(-0.548219\pi\)
−0.150906 + 0.988548i \(0.548219\pi\)
\(48\) −1.90388 −0.274801
\(49\) −3.70522 −0.529317
\(50\) 3.03097 0.428644
\(51\) −3.39637 −0.475587
\(52\) −2.64167 −0.366334
\(53\) −2.56540 −0.352385 −0.176193 0.984356i \(-0.556378\pi\)
−0.176193 + 0.984356i \(0.556378\pi\)
\(54\) −4.52218 −0.615391
\(55\) −2.43850 −0.328807
\(56\) 1.81515 0.242560
\(57\) 4.52526 0.599385
\(58\) −0.0835727 −0.0109736
\(59\) 0.0652730 0.00849782 0.00424891 0.999991i \(-0.498648\pi\)
0.00424891 + 0.999991i \(0.498648\pi\)
\(60\) 2.67156 0.344897
\(61\) 4.73357 0.606071 0.303035 0.952979i \(-0.402000\pi\)
0.303035 + 0.952979i \(0.402000\pi\)
\(62\) 0.944842 0.119995
\(63\) −1.13403 −0.142874
\(64\) 1.00000 0.125000
\(65\) 3.70685 0.459778
\(66\) 3.30853 0.407252
\(67\) −5.83806 −0.713232 −0.356616 0.934251i \(-0.616070\pi\)
−0.356616 + 0.934251i \(0.616070\pi\)
\(68\) 1.78392 0.216332
\(69\) 1.90388 0.229200
\(70\) −2.54706 −0.304432
\(71\) 2.32516 0.275946 0.137973 0.990436i \(-0.455941\pi\)
0.137973 + 0.990436i \(0.455941\pi\)
\(72\) −0.624755 −0.0736281
\(73\) 12.6531 1.48094 0.740468 0.672092i \(-0.234604\pi\)
0.740468 + 0.672092i \(0.234604\pi\)
\(74\) −11.1027 −1.29066
\(75\) 5.77060 0.666331
\(76\) −2.37686 −0.272645
\(77\) −3.15435 −0.359471
\(78\) −5.02942 −0.569470
\(79\) 10.2970 1.15851 0.579253 0.815148i \(-0.303345\pi\)
0.579253 + 0.815148i \(0.303345\pi\)
\(80\) −1.40322 −0.156885
\(81\) −10.4839 −1.16488
\(82\) 8.01509 0.885119
\(83\) 8.91728 0.978799 0.489400 0.872060i \(-0.337216\pi\)
0.489400 + 0.872060i \(0.337216\pi\)
\(84\) 3.45583 0.377062
\(85\) −2.50324 −0.271514
\(86\) −8.50045 −0.916627
\(87\) −0.159112 −0.0170586
\(88\) −1.73779 −0.185249
\(89\) 13.8362 1.46663 0.733316 0.679887i \(-0.237971\pi\)
0.733316 + 0.679887i \(0.237971\pi\)
\(90\) 0.876670 0.0924091
\(91\) 4.79504 0.502656
\(92\) −1.00000 −0.104257
\(93\) 1.79886 0.186534
\(94\) 2.06912 0.213414
\(95\) 3.33526 0.342191
\(96\) 1.90388 0.194314
\(97\) −9.35526 −0.949882 −0.474941 0.880018i \(-0.657531\pi\)
−0.474941 + 0.880018i \(0.657531\pi\)
\(98\) 3.70522 0.374284
\(99\) 1.08569 0.109116
\(100\) −3.03097 −0.303097
\(101\) 3.50973 0.349232 0.174616 0.984637i \(-0.444132\pi\)
0.174616 + 0.984637i \(0.444132\pi\)
\(102\) 3.39637 0.336291
\(103\) −2.79158 −0.275063 −0.137531 0.990497i \(-0.543917\pi\)
−0.137531 + 0.990497i \(0.543917\pi\)
\(104\) 2.64167 0.259037
\(105\) −4.84930 −0.473243
\(106\) 2.56540 0.249174
\(107\) −9.73908 −0.941512 −0.470756 0.882263i \(-0.656019\pi\)
−0.470756 + 0.882263i \(0.656019\pi\)
\(108\) 4.52218 0.435147
\(109\) −10.2798 −0.984626 −0.492313 0.870418i \(-0.663848\pi\)
−0.492313 + 0.870418i \(0.663848\pi\)
\(110\) 2.43850 0.232502
\(111\) −21.1382 −2.00635
\(112\) −1.81515 −0.171516
\(113\) 12.4901 1.17497 0.587484 0.809236i \(-0.300119\pi\)
0.587484 + 0.809236i \(0.300119\pi\)
\(114\) −4.52526 −0.423829
\(115\) 1.40322 0.130851
\(116\) 0.0835727 0.00775953
\(117\) −1.65040 −0.152579
\(118\) −0.0652730 −0.00600887
\(119\) −3.23809 −0.296835
\(120\) −2.67156 −0.243879
\(121\) −7.98010 −0.725464
\(122\) −4.73357 −0.428557
\(123\) 15.2598 1.37593
\(124\) −0.944842 −0.0848493
\(125\) 11.2692 1.00795
\(126\) 1.13403 0.101027
\(127\) −10.9262 −0.969543 −0.484772 0.874641i \(-0.661097\pi\)
−0.484772 + 0.874641i \(0.661097\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −16.1838 −1.42491
\(130\) −3.70685 −0.325112
\(131\) −1.00000 −0.0873704
\(132\) −3.30853 −0.287971
\(133\) 4.31437 0.374103
\(134\) 5.83806 0.504331
\(135\) −6.34562 −0.546144
\(136\) −1.78392 −0.152970
\(137\) 6.56574 0.560949 0.280474 0.959862i \(-0.409508\pi\)
0.280474 + 0.959862i \(0.409508\pi\)
\(138\) −1.90388 −0.162069
\(139\) 13.0414 1.10616 0.553078 0.833129i \(-0.313453\pi\)
0.553078 + 0.833129i \(0.313453\pi\)
\(140\) 2.54706 0.215266
\(141\) 3.93936 0.331754
\(142\) −2.32516 −0.195123
\(143\) −4.59066 −0.383890
\(144\) 0.624755 0.0520629
\(145\) −0.117271 −0.00973883
\(146\) −12.6531 −1.04718
\(147\) 7.05429 0.581828
\(148\) 11.1027 0.912637
\(149\) 12.2367 1.00247 0.501236 0.865310i \(-0.332879\pi\)
0.501236 + 0.865310i \(0.332879\pi\)
\(150\) −5.77060 −0.471167
\(151\) 18.6987 1.52168 0.760838 0.648942i \(-0.224788\pi\)
0.760838 + 0.648942i \(0.224788\pi\)
\(152\) 2.37686 0.192789
\(153\) 1.11451 0.0901031
\(154\) 3.15435 0.254184
\(155\) 1.32582 0.106493
\(156\) 5.02942 0.402676
\(157\) 24.4715 1.95304 0.976519 0.215430i \(-0.0691153\pi\)
0.976519 + 0.215430i \(0.0691153\pi\)
\(158\) −10.2970 −0.819187
\(159\) 4.88422 0.387344
\(160\) 1.40322 0.110934
\(161\) 1.81515 0.143054
\(162\) 10.4839 0.823697
\(163\) −12.5179 −0.980475 −0.490238 0.871589i \(-0.663090\pi\)
−0.490238 + 0.871589i \(0.663090\pi\)
\(164\) −8.01509 −0.625874
\(165\) 4.64261 0.361426
\(166\) −8.91728 −0.692115
\(167\) 10.8743 0.841476 0.420738 0.907182i \(-0.361771\pi\)
0.420738 + 0.907182i \(0.361771\pi\)
\(168\) −3.45583 −0.266623
\(169\) −6.02157 −0.463198
\(170\) 2.50324 0.191989
\(171\) −1.48496 −0.113558
\(172\) 8.50045 0.648153
\(173\) −5.08665 −0.386731 −0.193365 0.981127i \(-0.561940\pi\)
−0.193365 + 0.981127i \(0.561940\pi\)
\(174\) 0.159112 0.0120623
\(175\) 5.50167 0.415887
\(176\) 1.73779 0.130991
\(177\) −0.124272 −0.00934085
\(178\) −13.8362 −1.03707
\(179\) 0.881654 0.0658979 0.0329490 0.999457i \(-0.489510\pi\)
0.0329490 + 0.999457i \(0.489510\pi\)
\(180\) −0.876670 −0.0653431
\(181\) 0.589412 0.0438106 0.0219053 0.999760i \(-0.493027\pi\)
0.0219053 + 0.999760i \(0.493027\pi\)
\(182\) −4.79504 −0.355432
\(183\) −9.01214 −0.666196
\(184\) 1.00000 0.0737210
\(185\) −15.5796 −1.14543
\(186\) −1.79886 −0.131899
\(187\) 3.10007 0.226700
\(188\) −2.06912 −0.150906
\(189\) −8.20844 −0.597076
\(190\) −3.33526 −0.241966
\(191\) −12.3437 −0.893157 −0.446579 0.894744i \(-0.647358\pi\)
−0.446579 + 0.894744i \(0.647358\pi\)
\(192\) −1.90388 −0.137401
\(193\) −0.626953 −0.0451291 −0.0225645 0.999745i \(-0.507183\pi\)
−0.0225645 + 0.999745i \(0.507183\pi\)
\(194\) 9.35526 0.671668
\(195\) −7.05739 −0.505390
\(196\) −3.70522 −0.264659
\(197\) −10.9647 −0.781204 −0.390602 0.920560i \(-0.627733\pi\)
−0.390602 + 0.920560i \(0.627733\pi\)
\(198\) −1.08569 −0.0771567
\(199\) −19.4357 −1.37776 −0.688881 0.724875i \(-0.741898\pi\)
−0.688881 + 0.724875i \(0.741898\pi\)
\(200\) 3.03097 0.214322
\(201\) 11.1150 0.783988
\(202\) −3.50973 −0.246944
\(203\) −0.151697 −0.0106471
\(204\) −3.39637 −0.237793
\(205\) 11.2469 0.785521
\(206\) 2.79158 0.194499
\(207\) −0.624755 −0.0434235
\(208\) −2.64167 −0.183167
\(209\) −4.13048 −0.285711
\(210\) 4.84930 0.334633
\(211\) −10.5751 −0.728019 −0.364009 0.931395i \(-0.618592\pi\)
−0.364009 + 0.931395i \(0.618592\pi\)
\(212\) −2.56540 −0.176193
\(213\) −4.42682 −0.303321
\(214\) 9.73908 0.665750
\(215\) −11.9280 −0.813484
\(216\) −4.52218 −0.307695
\(217\) 1.71503 0.116424
\(218\) 10.2798 0.696236
\(219\) −24.0900 −1.62785
\(220\) −2.43850 −0.164404
\(221\) −4.71253 −0.316999
\(222\) 21.1382 1.41870
\(223\) 7.56649 0.506690 0.253345 0.967376i \(-0.418469\pi\)
0.253345 + 0.967376i \(0.418469\pi\)
\(224\) 1.81515 0.121280
\(225\) −1.89361 −0.126241
\(226\) −12.4901 −0.830828
\(227\) 12.4583 0.826886 0.413443 0.910530i \(-0.364326\pi\)
0.413443 + 0.910530i \(0.364326\pi\)
\(228\) 4.52526 0.299693
\(229\) 6.08192 0.401904 0.200952 0.979601i \(-0.435596\pi\)
0.200952 + 0.979601i \(0.435596\pi\)
\(230\) −1.40322 −0.0925257
\(231\) 6.00549 0.395132
\(232\) −0.0835727 −0.00548682
\(233\) −15.6170 −1.02310 −0.511551 0.859253i \(-0.670929\pi\)
−0.511551 + 0.859253i \(0.670929\pi\)
\(234\) 1.65040 0.107890
\(235\) 2.90344 0.189399
\(236\) 0.0652730 0.00424891
\(237\) −19.6043 −1.27343
\(238\) 3.23809 0.209894
\(239\) −26.8031 −1.73375 −0.866874 0.498527i \(-0.833875\pi\)
−0.866874 + 0.498527i \(0.833875\pi\)
\(240\) 2.67156 0.172449
\(241\) 12.3017 0.792421 0.396210 0.918160i \(-0.370325\pi\)
0.396210 + 0.918160i \(0.370325\pi\)
\(242\) 7.98010 0.512980
\(243\) 6.39363 0.410152
\(244\) 4.73357 0.303035
\(245\) 5.19925 0.332168
\(246\) −15.2598 −0.972927
\(247\) 6.27889 0.399516
\(248\) 0.944842 0.0599975
\(249\) −16.9774 −1.07590
\(250\) −11.2692 −0.712729
\(251\) 3.33805 0.210696 0.105348 0.994435i \(-0.466404\pi\)
0.105348 + 0.994435i \(0.466404\pi\)
\(252\) −1.13403 −0.0714369
\(253\) −1.73779 −0.109254
\(254\) 10.9262 0.685571
\(255\) 4.76586 0.298450
\(256\) 1.00000 0.0625000
\(257\) 16.9560 1.05768 0.528842 0.848720i \(-0.322626\pi\)
0.528842 + 0.848720i \(0.322626\pi\)
\(258\) 16.1838 1.00756
\(259\) −20.1531 −1.25225
\(260\) 3.70685 0.229889
\(261\) 0.0522125 0.00323187
\(262\) 1.00000 0.0617802
\(263\) −5.05197 −0.311518 −0.155759 0.987795i \(-0.549782\pi\)
−0.155759 + 0.987795i \(0.549782\pi\)
\(264\) 3.30853 0.203626
\(265\) 3.59983 0.221136
\(266\) −4.31437 −0.264531
\(267\) −26.3424 −1.61213
\(268\) −5.83806 −0.356616
\(269\) −24.4299 −1.48952 −0.744758 0.667335i \(-0.767435\pi\)
−0.744758 + 0.667335i \(0.767435\pi\)
\(270\) 6.34562 0.386182
\(271\) 4.99703 0.303548 0.151774 0.988415i \(-0.451501\pi\)
0.151774 + 0.988415i \(0.451501\pi\)
\(272\) 1.78392 0.108166
\(273\) −9.12917 −0.552522
\(274\) −6.56574 −0.396651
\(275\) −5.26718 −0.317623
\(276\) 1.90388 0.114600
\(277\) 12.3510 0.742100 0.371050 0.928613i \(-0.378998\pi\)
0.371050 + 0.928613i \(0.378998\pi\)
\(278\) −13.0414 −0.782171
\(279\) −0.590295 −0.0353400
\(280\) −2.54706 −0.152216
\(281\) 16.4859 0.983468 0.491734 0.870745i \(-0.336363\pi\)
0.491734 + 0.870745i \(0.336363\pi\)
\(282\) −3.93936 −0.234586
\(283\) −9.67749 −0.575267 −0.287634 0.957741i \(-0.592869\pi\)
−0.287634 + 0.957741i \(0.592869\pi\)
\(284\) 2.32516 0.137973
\(285\) −6.34994 −0.376138
\(286\) 4.59066 0.271451
\(287\) 14.5486 0.858778
\(288\) −0.624755 −0.0368141
\(289\) −13.8176 −0.812801
\(290\) 0.117271 0.00688639
\(291\) 17.8113 1.04412
\(292\) 12.6531 0.740468
\(293\) −5.29165 −0.309141 −0.154571 0.987982i \(-0.549399\pi\)
−0.154571 + 0.987982i \(0.549399\pi\)
\(294\) −7.05429 −0.411415
\(295\) −0.0915924 −0.00533272
\(296\) −11.1027 −0.645332
\(297\) 7.85858 0.456001
\(298\) −12.2367 −0.708855
\(299\) 2.64167 0.152772
\(300\) 5.77060 0.333166
\(301\) −15.4296 −0.889348
\(302\) −18.6987 −1.07599
\(303\) −6.68211 −0.383877
\(304\) −2.37686 −0.136322
\(305\) −6.64224 −0.380334
\(306\) −1.11451 −0.0637125
\(307\) −28.1051 −1.60405 −0.802023 0.597293i \(-0.796243\pi\)
−0.802023 + 0.597293i \(0.796243\pi\)
\(308\) −3.15435 −0.179736
\(309\) 5.31483 0.302350
\(310\) −1.32582 −0.0753016
\(311\) 2.01718 0.114384 0.0571919 0.998363i \(-0.481785\pi\)
0.0571919 + 0.998363i \(0.481785\pi\)
\(312\) −5.02942 −0.284735
\(313\) 19.0306 1.07567 0.537837 0.843049i \(-0.319242\pi\)
0.537837 + 0.843049i \(0.319242\pi\)
\(314\) −24.4715 −1.38101
\(315\) 1.59129 0.0896590
\(316\) 10.2970 0.579253
\(317\) 0.417139 0.0234288 0.0117144 0.999931i \(-0.496271\pi\)
0.0117144 + 0.999931i \(0.496271\pi\)
\(318\) −4.88422 −0.273893
\(319\) 0.145231 0.00813140
\(320\) −1.40322 −0.0784425
\(321\) 18.5420 1.03492
\(322\) −1.81515 −0.101154
\(323\) −4.24014 −0.235927
\(324\) −10.4839 −0.582441
\(325\) 8.00683 0.444139
\(326\) 12.5179 0.693301
\(327\) 19.5715 1.08231
\(328\) 8.01509 0.442559
\(329\) 3.75578 0.207063
\(330\) −4.64261 −0.255567
\(331\) −9.12723 −0.501678 −0.250839 0.968029i \(-0.580706\pi\)
−0.250839 + 0.968029i \(0.580706\pi\)
\(332\) 8.91728 0.489400
\(333\) 6.93648 0.380117
\(334\) −10.8743 −0.595013
\(335\) 8.19208 0.447581
\(336\) 3.45583 0.188531
\(337\) 19.1139 1.04120 0.520600 0.853801i \(-0.325708\pi\)
0.520600 + 0.853801i \(0.325708\pi\)
\(338\) 6.02157 0.327530
\(339\) −23.7796 −1.29153
\(340\) −2.50324 −0.135757
\(341\) −1.64193 −0.0889156
\(342\) 1.48496 0.0802973
\(343\) 19.4316 1.04921
\(344\) −8.50045 −0.458314
\(345\) −2.67156 −0.143832
\(346\) 5.08665 0.273460
\(347\) 11.4098 0.612512 0.306256 0.951949i \(-0.400924\pi\)
0.306256 + 0.951949i \(0.400924\pi\)
\(348\) −0.159112 −0.00852932
\(349\) −12.7844 −0.684334 −0.342167 0.939639i \(-0.611161\pi\)
−0.342167 + 0.939639i \(0.611161\pi\)
\(350\) −5.50167 −0.294077
\(351\) −11.9461 −0.637636
\(352\) −1.73779 −0.0926243
\(353\) 29.5803 1.57440 0.787199 0.616699i \(-0.211530\pi\)
0.787199 + 0.616699i \(0.211530\pi\)
\(354\) 0.124272 0.00660498
\(355\) −3.26271 −0.173167
\(356\) 13.8362 0.733316
\(357\) 6.16493 0.326283
\(358\) −0.881654 −0.0465969
\(359\) −20.0212 −1.05668 −0.528340 0.849033i \(-0.677185\pi\)
−0.528340 + 0.849033i \(0.677185\pi\)
\(360\) 0.876670 0.0462046
\(361\) −13.3505 −0.702659
\(362\) −0.589412 −0.0309788
\(363\) 15.1931 0.797433
\(364\) 4.79504 0.251328
\(365\) −17.7551 −0.929346
\(366\) 9.01214 0.471072
\(367\) −18.4759 −0.964432 −0.482216 0.876052i \(-0.660168\pi\)
−0.482216 + 0.876052i \(0.660168\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −5.00747 −0.260679
\(370\) 15.5796 0.809943
\(371\) 4.65660 0.241758
\(372\) 1.79886 0.0932668
\(373\) −15.0242 −0.777923 −0.388962 0.921254i \(-0.627166\pi\)
−0.388962 + 0.921254i \(0.627166\pi\)
\(374\) −3.10007 −0.160301
\(375\) −21.4552 −1.10794
\(376\) 2.06912 0.106707
\(377\) −0.220772 −0.0113703
\(378\) 8.20844 0.422197
\(379\) −15.4821 −0.795263 −0.397631 0.917545i \(-0.630168\pi\)
−0.397631 + 0.917545i \(0.630168\pi\)
\(380\) 3.33526 0.171095
\(381\) 20.8022 1.06573
\(382\) 12.3437 0.631557
\(383\) 5.20876 0.266155 0.133078 0.991106i \(-0.457514\pi\)
0.133078 + 0.991106i \(0.457514\pi\)
\(384\) 1.90388 0.0971569
\(385\) 4.42625 0.225582
\(386\) 0.626953 0.0319111
\(387\) 5.31070 0.269958
\(388\) −9.35526 −0.474941
\(389\) −5.93386 −0.300859 −0.150429 0.988621i \(-0.548066\pi\)
−0.150429 + 0.988621i \(0.548066\pi\)
\(390\) 7.05739 0.357365
\(391\) −1.78392 −0.0902168
\(392\) 3.70522 0.187142
\(393\) 1.90388 0.0960380
\(394\) 10.9647 0.552395
\(395\) −14.4490 −0.727008
\(396\) 1.08569 0.0545580
\(397\) −38.9525 −1.95497 −0.977486 0.211001i \(-0.932328\pi\)
−0.977486 + 0.211001i \(0.932328\pi\)
\(398\) 19.4357 0.974224
\(399\) −8.21403 −0.411216
\(400\) −3.03097 −0.151548
\(401\) 8.65563 0.432242 0.216121 0.976367i \(-0.430660\pi\)
0.216121 + 0.976367i \(0.430660\pi\)
\(402\) −11.1150 −0.554363
\(403\) 2.49596 0.124333
\(404\) 3.50973 0.174616
\(405\) 14.7113 0.731010
\(406\) 0.151697 0.00752861
\(407\) 19.2941 0.956375
\(408\) 3.39637 0.168145
\(409\) −29.6310 −1.46516 −0.732579 0.680682i \(-0.761684\pi\)
−0.732579 + 0.680682i \(0.761684\pi\)
\(410\) −11.2469 −0.555447
\(411\) −12.5004 −0.616598
\(412\) −2.79158 −0.137531
\(413\) −0.118480 −0.00583004
\(414\) 0.624755 0.0307050
\(415\) −12.5129 −0.614235
\(416\) 2.64167 0.129519
\(417\) −24.8292 −1.21589
\(418\) 4.13048 0.202028
\(419\) −34.7146 −1.69592 −0.847959 0.530062i \(-0.822169\pi\)
−0.847959 + 0.530062i \(0.822169\pi\)
\(420\) −4.84930 −0.236621
\(421\) −8.47369 −0.412982 −0.206491 0.978448i \(-0.566204\pi\)
−0.206491 + 0.978448i \(0.566204\pi\)
\(422\) 10.5751 0.514787
\(423\) −1.29270 −0.0628530
\(424\) 2.56540 0.124587
\(425\) −5.40701 −0.262279
\(426\) 4.42682 0.214480
\(427\) −8.59214 −0.415803
\(428\) −9.73908 −0.470756
\(429\) 8.74006 0.421974
\(430\) 11.9280 0.575220
\(431\) 15.5452 0.748787 0.374394 0.927270i \(-0.377851\pi\)
0.374394 + 0.927270i \(0.377851\pi\)
\(432\) 4.52218 0.217573
\(433\) −22.5906 −1.08564 −0.542819 0.839850i \(-0.682643\pi\)
−0.542819 + 0.839850i \(0.682643\pi\)
\(434\) −1.71503 −0.0823241
\(435\) 0.223270 0.0107050
\(436\) −10.2798 −0.492313
\(437\) 2.37686 0.113701
\(438\) 24.0900 1.15107
\(439\) 14.3651 0.685607 0.342804 0.939407i \(-0.388623\pi\)
0.342804 + 0.939407i \(0.388623\pi\)
\(440\) 2.43850 0.116251
\(441\) −2.31486 −0.110231
\(442\) 4.71253 0.224152
\(443\) 6.91936 0.328749 0.164374 0.986398i \(-0.447440\pi\)
0.164374 + 0.986398i \(0.447440\pi\)
\(444\) −21.1382 −1.00318
\(445\) −19.4152 −0.920370
\(446\) −7.56649 −0.358284
\(447\) −23.2973 −1.10192
\(448\) −1.81515 −0.0857579
\(449\) 28.4327 1.34182 0.670911 0.741537i \(-0.265903\pi\)
0.670911 + 0.741537i \(0.265903\pi\)
\(450\) 1.89361 0.0892658
\(451\) −13.9285 −0.655868
\(452\) 12.4901 0.587484
\(453\) −35.6000 −1.67263
\(454\) −12.4583 −0.584697
\(455\) −6.72850 −0.315437
\(456\) −4.52526 −0.211915
\(457\) 5.71141 0.267168 0.133584 0.991037i \(-0.457351\pi\)
0.133584 + 0.991037i \(0.457351\pi\)
\(458\) −6.08192 −0.284189
\(459\) 8.06721 0.376545
\(460\) 1.40322 0.0654255
\(461\) 42.0478 1.95836 0.979180 0.202994i \(-0.0650671\pi\)
0.979180 + 0.202994i \(0.0650671\pi\)
\(462\) −6.00549 −0.279401
\(463\) −31.4541 −1.46180 −0.730899 0.682486i \(-0.760899\pi\)
−0.730899 + 0.682486i \(0.760899\pi\)
\(464\) 0.0835727 0.00387977
\(465\) −2.52420 −0.117057
\(466\) 15.6170 0.723442
\(467\) 11.1868 0.517664 0.258832 0.965922i \(-0.416662\pi\)
0.258832 + 0.965922i \(0.416662\pi\)
\(468\) −1.65040 −0.0762897
\(469\) 10.5970 0.489322
\(470\) −2.90344 −0.133926
\(471\) −46.5908 −2.14679
\(472\) −0.0652730 −0.00300443
\(473\) 14.7720 0.679216
\(474\) 19.6043 0.900454
\(475\) 7.20420 0.330551
\(476\) −3.23809 −0.148418
\(477\) −1.60275 −0.0733848
\(478\) 26.8031 1.22595
\(479\) −17.8540 −0.815772 −0.407886 0.913033i \(-0.633734\pi\)
−0.407886 + 0.913033i \(0.633734\pi\)
\(480\) −2.67156 −0.121940
\(481\) −29.3297 −1.33732
\(482\) −12.3017 −0.560326
\(483\) −3.45583 −0.157246
\(484\) −7.98010 −0.362732
\(485\) 13.1275 0.596089
\(486\) −6.39363 −0.290021
\(487\) −32.0774 −1.45357 −0.726783 0.686867i \(-0.758986\pi\)
−0.726783 + 0.686867i \(0.758986\pi\)
\(488\) −4.73357 −0.214278
\(489\) 23.8325 1.07774
\(490\) −5.19925 −0.234878
\(491\) −20.4438 −0.922615 −0.461307 0.887240i \(-0.652619\pi\)
−0.461307 + 0.887240i \(0.652619\pi\)
\(492\) 15.2598 0.687963
\(493\) 0.149087 0.00671455
\(494\) −6.27889 −0.282501
\(495\) −1.52346 −0.0684746
\(496\) −0.944842 −0.0424246
\(497\) −4.22052 −0.189316
\(498\) 16.9774 0.760777
\(499\) −41.0082 −1.83578 −0.917890 0.396834i \(-0.870109\pi\)
−0.917890 + 0.396834i \(0.870109\pi\)
\(500\) 11.2692 0.503975
\(501\) −20.7033 −0.924955
\(502\) −3.33805 −0.148984
\(503\) 4.35733 0.194284 0.0971419 0.995271i \(-0.469030\pi\)
0.0971419 + 0.995271i \(0.469030\pi\)
\(504\) 1.13403 0.0505135
\(505\) −4.92493 −0.219157
\(506\) 1.73779 0.0772540
\(507\) 11.4643 0.509149
\(508\) −10.9262 −0.484772
\(509\) −24.2532 −1.07500 −0.537502 0.843263i \(-0.680632\pi\)
−0.537502 + 0.843263i \(0.680632\pi\)
\(510\) −4.76586 −0.211036
\(511\) −22.9673 −1.01602
\(512\) −1.00000 −0.0441942
\(513\) −10.7486 −0.474562
\(514\) −16.9560 −0.747895
\(515\) 3.91721 0.172613
\(516\) −16.1838 −0.712453
\(517\) −3.59569 −0.158138
\(518\) 20.1531 0.885477
\(519\) 9.68436 0.425096
\(520\) −3.70685 −0.162556
\(521\) −12.2046 −0.534692 −0.267346 0.963601i \(-0.586147\pi\)
−0.267346 + 0.963601i \(0.586147\pi\)
\(522\) −0.0522125 −0.00228528
\(523\) 29.9006 1.30746 0.653730 0.756728i \(-0.273203\pi\)
0.653730 + 0.756728i \(0.273203\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −10.4745 −0.457145
\(526\) 5.05197 0.220276
\(527\) −1.68552 −0.0734225
\(528\) −3.30853 −0.143985
\(529\) 1.00000 0.0434783
\(530\) −3.59983 −0.156367
\(531\) 0.0407796 0.00176969
\(532\) 4.31437 0.187052
\(533\) 21.1732 0.917115
\(534\) 26.3424 1.13995
\(535\) 13.6661 0.590836
\(536\) 5.83806 0.252166
\(537\) −1.67856 −0.0724353
\(538\) 24.4299 1.05325
\(539\) −6.43888 −0.277342
\(540\) −6.34562 −0.273072
\(541\) −25.7898 −1.10879 −0.554395 0.832253i \(-0.687050\pi\)
−0.554395 + 0.832253i \(0.687050\pi\)
\(542\) −4.99703 −0.214641
\(543\) −1.12217 −0.0481569
\(544\) −1.78392 −0.0764850
\(545\) 14.4248 0.617892
\(546\) 9.12917 0.390692
\(547\) −9.97587 −0.426538 −0.213269 0.976994i \(-0.568411\pi\)
−0.213269 + 0.976994i \(0.568411\pi\)
\(548\) 6.56574 0.280474
\(549\) 2.95732 0.126215
\(550\) 5.26718 0.224593
\(551\) −0.198641 −0.00846239
\(552\) −1.90388 −0.0810345
\(553\) −18.6907 −0.794808
\(554\) −12.3510 −0.524744
\(555\) 29.6616 1.25906
\(556\) 13.0414 0.553078
\(557\) 35.8819 1.52036 0.760182 0.649710i \(-0.225110\pi\)
0.760182 + 0.649710i \(0.225110\pi\)
\(558\) 0.590295 0.0249892
\(559\) −22.4554 −0.949762
\(560\) 2.54706 0.107633
\(561\) −5.90216 −0.249190
\(562\) −16.4859 −0.695417
\(563\) 5.19671 0.219015 0.109508 0.993986i \(-0.465073\pi\)
0.109508 + 0.993986i \(0.465073\pi\)
\(564\) 3.93936 0.165877
\(565\) −17.5263 −0.737339
\(566\) 9.67749 0.406775
\(567\) 19.0300 0.799183
\(568\) −2.32516 −0.0975616
\(569\) −14.9780 −0.627910 −0.313955 0.949438i \(-0.601654\pi\)
−0.313955 + 0.949438i \(0.601654\pi\)
\(570\) 6.34994 0.265970
\(571\) −37.8406 −1.58358 −0.791791 0.610792i \(-0.790851\pi\)
−0.791791 + 0.610792i \(0.790851\pi\)
\(572\) −4.59066 −0.191945
\(573\) 23.5009 0.981763
\(574\) −14.5486 −0.607247
\(575\) 3.03097 0.126400
\(576\) 0.624755 0.0260315
\(577\) 24.8835 1.03591 0.517957 0.855407i \(-0.326693\pi\)
0.517957 + 0.855407i \(0.326693\pi\)
\(578\) 13.8176 0.574737
\(579\) 1.19364 0.0496061
\(580\) −0.117271 −0.00486941
\(581\) −16.1862 −0.671518
\(582\) −17.8113 −0.738301
\(583\) −4.45812 −0.184637
\(584\) −12.6531 −0.523590
\(585\) 2.31587 0.0957496
\(586\) 5.29165 0.218596
\(587\) 25.6215 1.05751 0.528757 0.848773i \(-0.322658\pi\)
0.528757 + 0.848773i \(0.322658\pi\)
\(588\) 7.05429 0.290914
\(589\) 2.24576 0.0925349
\(590\) 0.0915924 0.00377080
\(591\) 20.8755 0.858704
\(592\) 11.1027 0.456319
\(593\) −14.3369 −0.588746 −0.294373 0.955691i \(-0.595111\pi\)
−0.294373 + 0.955691i \(0.595111\pi\)
\(594\) −7.85858 −0.322441
\(595\) 4.54376 0.186276
\(596\) 12.2367 0.501236
\(597\) 37.0032 1.51444
\(598\) −2.64167 −0.108026
\(599\) −32.8674 −1.34292 −0.671462 0.741039i \(-0.734333\pi\)
−0.671462 + 0.741039i \(0.734333\pi\)
\(600\) −5.77060 −0.235584
\(601\) −36.7188 −1.49779 −0.748896 0.662688i \(-0.769416\pi\)
−0.748896 + 0.662688i \(0.769416\pi\)
\(602\) 15.4296 0.628864
\(603\) −3.64736 −0.148532
\(604\) 18.6987 0.760838
\(605\) 11.1978 0.455257
\(606\) 6.68211 0.271442
\(607\) 22.3084 0.905468 0.452734 0.891646i \(-0.350449\pi\)
0.452734 + 0.891646i \(0.350449\pi\)
\(608\) 2.37686 0.0963945
\(609\) 0.288813 0.0117033
\(610\) 6.64224 0.268936
\(611\) 5.46595 0.221128
\(612\) 1.11451 0.0450516
\(613\) −30.3265 −1.22487 −0.612437 0.790519i \(-0.709811\pi\)
−0.612437 + 0.790519i \(0.709811\pi\)
\(614\) 28.1051 1.13423
\(615\) −21.4128 −0.863449
\(616\) 3.15435 0.127092
\(617\) 12.1516 0.489203 0.244602 0.969624i \(-0.421343\pi\)
0.244602 + 0.969624i \(0.421343\pi\)
\(618\) −5.31483 −0.213794
\(619\) −42.0680 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(620\) 1.32582 0.0532463
\(621\) −4.52218 −0.181469
\(622\) −2.01718 −0.0808816
\(623\) −25.1148 −1.00620
\(624\) 5.02942 0.201338
\(625\) −0.658374 −0.0263350
\(626\) −19.0306 −0.760616
\(627\) 7.86393 0.314055
\(628\) 24.4715 0.976519
\(629\) 19.8064 0.789731
\(630\) −1.59129 −0.0633985
\(631\) 1.89312 0.0753640 0.0376820 0.999290i \(-0.488003\pi\)
0.0376820 + 0.999290i \(0.488003\pi\)
\(632\) −10.2970 −0.409593
\(633\) 20.1337 0.800242
\(634\) −0.417139 −0.0165667
\(635\) 15.3319 0.608427
\(636\) 4.88422 0.193672
\(637\) 9.78798 0.387814
\(638\) −0.145231 −0.00574977
\(639\) 1.45266 0.0574662
\(640\) 1.40322 0.0554672
\(641\) 7.65598 0.302393 0.151197 0.988504i \(-0.451687\pi\)
0.151197 + 0.988504i \(0.451687\pi\)
\(642\) −18.5420 −0.731795
\(643\) −21.7473 −0.857629 −0.428814 0.903393i \(-0.641069\pi\)
−0.428814 + 0.903393i \(0.641069\pi\)
\(644\) 1.81515 0.0715270
\(645\) 22.7095 0.894185
\(646\) 4.24014 0.166826
\(647\) 19.3773 0.761800 0.380900 0.924616i \(-0.375614\pi\)
0.380900 + 0.924616i \(0.375614\pi\)
\(648\) 10.4839 0.411848
\(649\) 0.113430 0.00445254
\(650\) −8.00683 −0.314054
\(651\) −3.26521 −0.127974
\(652\) −12.5179 −0.490238
\(653\) −43.1557 −1.68881 −0.844406 0.535704i \(-0.820046\pi\)
−0.844406 + 0.535704i \(0.820046\pi\)
\(654\) −19.5715 −0.765306
\(655\) 1.40322 0.0548284
\(656\) −8.01509 −0.312937
\(657\) 7.90510 0.308407
\(658\) −3.75578 −0.146415
\(659\) 23.3049 0.907832 0.453916 0.891045i \(-0.350027\pi\)
0.453916 + 0.891045i \(0.350027\pi\)
\(660\) 4.64261 0.180713
\(661\) 43.1250 1.67737 0.838685 0.544617i \(-0.183325\pi\)
0.838685 + 0.544617i \(0.183325\pi\)
\(662\) 9.12723 0.354740
\(663\) 8.97209 0.348447
\(664\) −8.91728 −0.346058
\(665\) −6.05401 −0.234765
\(666\) −6.93648 −0.268783
\(667\) −0.0835727 −0.00323595
\(668\) 10.8743 0.420738
\(669\) −14.4057 −0.556956
\(670\) −8.19208 −0.316488
\(671\) 8.22592 0.317558
\(672\) −3.45583 −0.133312
\(673\) −24.2609 −0.935188 −0.467594 0.883943i \(-0.654879\pi\)
−0.467594 + 0.883943i \(0.654879\pi\)
\(674\) −19.1139 −0.736240
\(675\) −13.7066 −0.527567
\(676\) −6.02157 −0.231599
\(677\) −10.5696 −0.406222 −0.203111 0.979156i \(-0.565105\pi\)
−0.203111 + 0.979156i \(0.565105\pi\)
\(678\) 23.7796 0.913250
\(679\) 16.9812 0.651679
\(680\) 2.50324 0.0959947
\(681\) −23.7191 −0.908918
\(682\) 1.64193 0.0628728
\(683\) −47.2330 −1.80732 −0.903659 0.428252i \(-0.859130\pi\)
−0.903659 + 0.428252i \(0.859130\pi\)
\(684\) −1.48496 −0.0567788
\(685\) −9.21318 −0.352018
\(686\) −19.4316 −0.741902
\(687\) −11.5792 −0.441775
\(688\) 8.50045 0.324077
\(689\) 6.77695 0.258181
\(690\) 2.67156 0.101705
\(691\) −14.3399 −0.545516 −0.272758 0.962083i \(-0.587936\pi\)
−0.272758 + 0.962083i \(0.587936\pi\)
\(692\) −5.08665 −0.193365
\(693\) −1.97069 −0.0748605
\(694\) −11.4098 −0.433111
\(695\) −18.3000 −0.694157
\(696\) 0.159112 0.00603114
\(697\) −14.2983 −0.541586
\(698\) 12.7844 0.483897
\(699\) 29.7328 1.12460
\(700\) 5.50167 0.207944
\(701\) −9.33296 −0.352501 −0.176251 0.984345i \(-0.556397\pi\)
−0.176251 + 0.984345i \(0.556397\pi\)
\(702\) 11.9461 0.450877
\(703\) −26.3896 −0.995303
\(704\) 1.73779 0.0654953
\(705\) −5.52780 −0.208189
\(706\) −29.5803 −1.11327
\(707\) −6.37070 −0.239595
\(708\) −0.124272 −0.00467042
\(709\) −36.2182 −1.36020 −0.680102 0.733118i \(-0.738064\pi\)
−0.680102 + 0.733118i \(0.738064\pi\)
\(710\) 3.26271 0.122447
\(711\) 6.43312 0.241261
\(712\) −13.8362 −0.518533
\(713\) 0.944842 0.0353846
\(714\) −6.16493 −0.230717
\(715\) 6.44171 0.240906
\(716\) 0.881654 0.0329490
\(717\) 51.0299 1.90575
\(718\) 20.0212 0.747185
\(719\) −35.6959 −1.33123 −0.665617 0.746294i \(-0.731831\pi\)
−0.665617 + 0.746294i \(0.731831\pi\)
\(720\) −0.876670 −0.0326716
\(721\) 5.06715 0.188710
\(722\) 13.3505 0.496855
\(723\) −23.4209 −0.871033
\(724\) 0.589412 0.0219053
\(725\) −0.253306 −0.00940756
\(726\) −15.1931 −0.563871
\(727\) 22.0085 0.816250 0.408125 0.912926i \(-0.366183\pi\)
0.408125 + 0.912926i \(0.366183\pi\)
\(728\) −4.79504 −0.177716
\(729\) 19.2791 0.714042
\(730\) 17.7551 0.657147
\(731\) 15.1641 0.560866
\(732\) −9.01214 −0.333098
\(733\) −17.5452 −0.648045 −0.324023 0.946049i \(-0.605035\pi\)
−0.324023 + 0.946049i \(0.605035\pi\)
\(734\) 18.4759 0.681956
\(735\) −9.89874 −0.365120
\(736\) 1.00000 0.0368605
\(737\) −10.1453 −0.373707
\(738\) 5.00747 0.184328
\(739\) −25.2598 −0.929198 −0.464599 0.885521i \(-0.653801\pi\)
−0.464599 + 0.885521i \(0.653801\pi\)
\(740\) −15.5796 −0.572716
\(741\) −11.9542 −0.439150
\(742\) −4.65660 −0.170949
\(743\) 19.3570 0.710139 0.355069 0.934840i \(-0.384457\pi\)
0.355069 + 0.934840i \(0.384457\pi\)
\(744\) −1.79886 −0.0659496
\(745\) −17.1709 −0.629091
\(746\) 15.0242 0.550075
\(747\) 5.57112 0.203837
\(748\) 3.10007 0.113350
\(749\) 17.6779 0.645937
\(750\) 21.4552 0.783435
\(751\) −1.12097 −0.0409047 −0.0204523 0.999791i \(-0.506511\pi\)
−0.0204523 + 0.999791i \(0.506511\pi\)
\(752\) −2.06912 −0.0754532
\(753\) −6.35524 −0.231598
\(754\) 0.220772 0.00804003
\(755\) −26.2384 −0.954912
\(756\) −8.20844 −0.298538
\(757\) 30.0334 1.09158 0.545792 0.837921i \(-0.316229\pi\)
0.545792 + 0.837921i \(0.316229\pi\)
\(758\) 15.4821 0.562336
\(759\) 3.30853 0.120092
\(760\) −3.33526 −0.120983
\(761\) 12.8138 0.464501 0.232251 0.972656i \(-0.425391\pi\)
0.232251 + 0.972656i \(0.425391\pi\)
\(762\) −20.8022 −0.753583
\(763\) 18.6594 0.675516
\(764\) −12.3437 −0.446579
\(765\) −1.56391 −0.0565433
\(766\) −5.20876 −0.188200
\(767\) −0.172430 −0.00622608
\(768\) −1.90388 −0.0687003
\(769\) 20.5339 0.740471 0.370235 0.928938i \(-0.379277\pi\)
0.370235 + 0.928938i \(0.379277\pi\)
\(770\) −4.42625 −0.159511
\(771\) −32.2821 −1.16261
\(772\) −0.626953 −0.0225645
\(773\) −13.2351 −0.476035 −0.238017 0.971261i \(-0.576497\pi\)
−0.238017 + 0.971261i \(0.576497\pi\)
\(774\) −5.31070 −0.190889
\(775\) 2.86379 0.102870
\(776\) 9.35526 0.335834
\(777\) 38.3691 1.37648
\(778\) 5.93386 0.212739
\(779\) 19.0508 0.682565
\(780\) −7.05739 −0.252695
\(781\) 4.04063 0.144585
\(782\) 1.78392 0.0637929
\(783\) 0.377931 0.0135061
\(784\) −3.70522 −0.132329
\(785\) −34.3389 −1.22561
\(786\) −1.90388 −0.0679091
\(787\) −31.9637 −1.13938 −0.569692 0.821859i \(-0.692937\pi\)
−0.569692 + 0.821859i \(0.692937\pi\)
\(788\) −10.9647 −0.390602
\(789\) 9.61834 0.342422
\(790\) 14.4490 0.514072
\(791\) −22.6714 −0.806102
\(792\) −1.08569 −0.0385783
\(793\) −12.5045 −0.444049
\(794\) 38.9525 1.38237
\(795\) −6.85364 −0.243073
\(796\) −19.4357 −0.688881
\(797\) 45.2446 1.60265 0.801323 0.598232i \(-0.204130\pi\)
0.801323 + 0.598232i \(0.204130\pi\)
\(798\) 8.21403 0.290774
\(799\) −3.69115 −0.130584
\(800\) 3.03097 0.107161
\(801\) 8.64423 0.305429
\(802\) −8.65563 −0.305641
\(803\) 21.9884 0.775954
\(804\) 11.1150 0.391994
\(805\) −2.54706 −0.0897721
\(806\) −2.49596 −0.0879165
\(807\) 46.5115 1.63728
\(808\) −3.50973 −0.123472
\(809\) −23.3171 −0.819785 −0.409892 0.912134i \(-0.634434\pi\)
−0.409892 + 0.912134i \(0.634434\pi\)
\(810\) −14.7113 −0.516902
\(811\) −1.88169 −0.0660751 −0.0330375 0.999454i \(-0.510518\pi\)
−0.0330375 + 0.999454i \(0.510518\pi\)
\(812\) −0.151697 −0.00532353
\(813\) −9.51374 −0.333662
\(814\) −19.2941 −0.676259
\(815\) 17.5653 0.615287
\(816\) −3.39637 −0.118897
\(817\) −20.2044 −0.706863
\(818\) 29.6310 1.03602
\(819\) 2.99572 0.104679
\(820\) 11.2469 0.392761
\(821\) 5.55057 0.193716 0.0968582 0.995298i \(-0.469121\pi\)
0.0968582 + 0.995298i \(0.469121\pi\)
\(822\) 12.5004 0.436000
\(823\) 9.48825 0.330740 0.165370 0.986232i \(-0.447118\pi\)
0.165370 + 0.986232i \(0.447118\pi\)
\(824\) 2.79158 0.0972493
\(825\) 10.0281 0.349132
\(826\) 0.118480 0.00412246
\(827\) −2.79701 −0.0972616 −0.0486308 0.998817i \(-0.515486\pi\)
−0.0486308 + 0.998817i \(0.515486\pi\)
\(828\) −0.624755 −0.0217117
\(829\) −19.8838 −0.690594 −0.345297 0.938493i \(-0.612222\pi\)
−0.345297 + 0.938493i \(0.612222\pi\)
\(830\) 12.5129 0.434330
\(831\) −23.5148 −0.815721
\(832\) −2.64167 −0.0915835
\(833\) −6.60982 −0.229017
\(834\) 24.8292 0.859766
\(835\) −15.2590 −0.528060
\(836\) −4.13048 −0.142856
\(837\) −4.27274 −0.147688
\(838\) 34.7146 1.19920
\(839\) −8.25551 −0.285012 −0.142506 0.989794i \(-0.545516\pi\)
−0.142506 + 0.989794i \(0.545516\pi\)
\(840\) 4.84930 0.167317
\(841\) −28.9930 −0.999759
\(842\) 8.47369 0.292022
\(843\) −31.3872 −1.08103
\(844\) −10.5751 −0.364009
\(845\) 8.44960 0.290675
\(846\) 1.29270 0.0444438
\(847\) 14.4851 0.497714
\(848\) −2.56540 −0.0880963
\(849\) 18.4248 0.632337
\(850\) 5.40701 0.185459
\(851\) −11.1027 −0.380596
\(852\) −4.42682 −0.151660
\(853\) −8.03199 −0.275010 −0.137505 0.990501i \(-0.543908\pi\)
−0.137505 + 0.990501i \(0.543908\pi\)
\(854\) 8.59214 0.294017
\(855\) 2.08372 0.0712619
\(856\) 9.73908 0.332875
\(857\) 51.6112 1.76301 0.881503 0.472178i \(-0.156532\pi\)
0.881503 + 0.472178i \(0.156532\pi\)
\(858\) −8.74006 −0.298381
\(859\) 30.8266 1.05179 0.525894 0.850550i \(-0.323731\pi\)
0.525894 + 0.850550i \(0.323731\pi\)
\(860\) −11.9280 −0.406742
\(861\) −27.6988 −0.943973
\(862\) −15.5452 −0.529473
\(863\) 49.1345 1.67256 0.836279 0.548305i \(-0.184727\pi\)
0.836279 + 0.548305i \(0.184727\pi\)
\(864\) −4.52218 −0.153848
\(865\) 7.13769 0.242689
\(866\) 22.5906 0.767661
\(867\) 26.3071 0.893436
\(868\) 1.71503 0.0582120
\(869\) 17.8940 0.607013
\(870\) −0.223270 −0.00756956
\(871\) 15.4222 0.522562
\(872\) 10.2798 0.348118
\(873\) −5.84474 −0.197815
\(874\) −2.37686 −0.0803986
\(875\) −20.4554 −0.691518
\(876\) −24.0900 −0.813926
\(877\) −34.8402 −1.17647 −0.588236 0.808690i \(-0.700177\pi\)
−0.588236 + 0.808690i \(0.700177\pi\)
\(878\) −14.3651 −0.484798
\(879\) 10.0747 0.339810
\(880\) −2.43850 −0.0822018
\(881\) 11.9015 0.400970 0.200485 0.979697i \(-0.435748\pi\)
0.200485 + 0.979697i \(0.435748\pi\)
\(882\) 2.31486 0.0779453
\(883\) 32.2089 1.08392 0.541959 0.840405i \(-0.317683\pi\)
0.541959 + 0.840405i \(0.317683\pi\)
\(884\) −4.71253 −0.158500
\(885\) 0.174381 0.00586175
\(886\) −6.91936 −0.232460
\(887\) −40.3054 −1.35332 −0.676661 0.736295i \(-0.736574\pi\)
−0.676661 + 0.736295i \(0.736574\pi\)
\(888\) 21.1382 0.709352
\(889\) 19.8327 0.665168
\(890\) 19.4152 0.650800
\(891\) −18.2189 −0.610355
\(892\) 7.56649 0.253345
\(893\) 4.91802 0.164575
\(894\) 23.2973 0.779177
\(895\) −1.23716 −0.0413536
\(896\) 1.81515 0.0606400
\(897\) −5.02942 −0.167928
\(898\) −28.4327 −0.948812
\(899\) −0.0789630 −0.00263356
\(900\) −1.89361 −0.0631205
\(901\) −4.57648 −0.152465
\(902\) 13.9285 0.463769
\(903\) 29.3761 0.977576
\(904\) −12.4901 −0.415414
\(905\) −0.827075 −0.0274929
\(906\) 35.6000 1.18273
\(907\) 26.3870 0.876167 0.438083 0.898934i \(-0.355657\pi\)
0.438083 + 0.898934i \(0.355657\pi\)
\(908\) 12.4583 0.413443
\(909\) 2.19272 0.0727281
\(910\) 6.72850 0.223048
\(911\) −33.3531 −1.10504 −0.552519 0.833500i \(-0.686333\pi\)
−0.552519 + 0.833500i \(0.686333\pi\)
\(912\) 4.52526 0.149846
\(913\) 15.4963 0.512854
\(914\) −5.71141 −0.188917
\(915\) 12.6460 0.418065
\(916\) 6.08192 0.200952
\(917\) 1.81515 0.0599416
\(918\) −8.06721 −0.266258
\(919\) 36.1660 1.19301 0.596504 0.802610i \(-0.296556\pi\)
0.596504 + 0.802610i \(0.296556\pi\)
\(920\) −1.40322 −0.0462628
\(921\) 53.5088 1.76318
\(922\) −42.0478 −1.38477
\(923\) −6.14231 −0.202177
\(924\) 6.00549 0.197566
\(925\) −33.6520 −1.10647
\(926\) 31.4541 1.03365
\(927\) −1.74406 −0.0572823
\(928\) −0.0835727 −0.00274341
\(929\) −15.1301 −0.496403 −0.248202 0.968708i \(-0.579840\pi\)
−0.248202 + 0.968708i \(0.579840\pi\)
\(930\) 2.52420 0.0827719
\(931\) 8.80680 0.288631
\(932\) −15.6170 −0.511551
\(933\) −3.84047 −0.125731
\(934\) −11.1868 −0.366044
\(935\) −4.35009 −0.142263
\(936\) 1.65040 0.0539449
\(937\) −6.84090 −0.223482 −0.111741 0.993737i \(-0.535643\pi\)
−0.111741 + 0.993737i \(0.535643\pi\)
\(938\) −10.5970 −0.346003
\(939\) −36.2320 −1.18239
\(940\) 2.90344 0.0946997
\(941\) 41.9025 1.36598 0.682991 0.730427i \(-0.260679\pi\)
0.682991 + 0.730427i \(0.260679\pi\)
\(942\) 46.5908 1.51801
\(943\) 8.01509 0.261007
\(944\) 0.0652730 0.00212445
\(945\) 11.5183 0.374689
\(946\) −14.7720 −0.480278
\(947\) −9.48720 −0.308293 −0.154146 0.988048i \(-0.549263\pi\)
−0.154146 + 0.988048i \(0.549263\pi\)
\(948\) −19.6043 −0.636717
\(949\) −33.4254 −1.08503
\(950\) −7.20420 −0.233735
\(951\) −0.794182 −0.0257531
\(952\) 3.23809 0.104947
\(953\) 13.3640 0.432904 0.216452 0.976293i \(-0.430552\pi\)
0.216452 + 0.976293i \(0.430552\pi\)
\(954\) 1.60275 0.0518909
\(955\) 17.3209 0.560492
\(956\) −26.8031 −0.866874
\(957\) −0.276503 −0.00893808
\(958\) 17.8540 0.576838
\(959\) −11.9178 −0.384846
\(960\) 2.67156 0.0862243
\(961\) −30.1073 −0.971202
\(962\) 29.3297 0.945628
\(963\) −6.08454 −0.196072
\(964\) 12.3017 0.396210
\(965\) 0.879754 0.0283203
\(966\) 3.45583 0.111190
\(967\) −2.23780 −0.0719629 −0.0359815 0.999352i \(-0.511456\pi\)
−0.0359815 + 0.999352i \(0.511456\pi\)
\(968\) 7.98010 0.256490
\(969\) 8.07271 0.259333
\(970\) −13.1275 −0.421498
\(971\) −51.6308 −1.65691 −0.828455 0.560056i \(-0.810780\pi\)
−0.828455 + 0.560056i \(0.810780\pi\)
\(972\) 6.39363 0.205076
\(973\) −23.6721 −0.758893
\(974\) 32.0774 1.02783
\(975\) −15.2440 −0.488200
\(976\) 4.73357 0.151518
\(977\) 51.8402 1.65852 0.829258 0.558866i \(-0.188763\pi\)
0.829258 + 0.558866i \(0.188763\pi\)
\(978\) −23.8325 −0.762079
\(979\) 24.0443 0.768460
\(980\) 5.19925 0.166084
\(981\) −6.42236 −0.205050
\(982\) 20.4438 0.652387
\(983\) 29.9246 0.954446 0.477223 0.878782i \(-0.341643\pi\)
0.477223 + 0.878782i \(0.341643\pi\)
\(984\) −15.2598 −0.486464
\(985\) 15.3859 0.490237
\(986\) −0.149087 −0.00474790
\(987\) −7.15054 −0.227604
\(988\) 6.27889 0.199758
\(989\) −8.50045 −0.270299
\(990\) 1.52346 0.0484189
\(991\) −5.02756 −0.159706 −0.0798528 0.996807i \(-0.525445\pi\)
−0.0798528 + 0.996807i \(0.525445\pi\)
\(992\) 0.944842 0.0299988
\(993\) 17.3771 0.551447
\(994\) 4.22052 0.133867
\(995\) 27.2726 0.864600
\(996\) −16.9774 −0.537950
\(997\) 38.3953 1.21599 0.607995 0.793941i \(-0.291974\pi\)
0.607995 + 0.793941i \(0.291974\pi\)
\(998\) 41.0082 1.29809
\(999\) 50.2084 1.58852
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 \(a_p\))