Properties

Label 6026.2.a.i.1.10
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
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: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.936776 q^{3} +1.00000 q^{4} +1.38125 q^{5} +0.936776 q^{6} +2.49293 q^{7} -1.00000 q^{8} -2.12245 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.936776 q^{3} +1.00000 q^{4} +1.38125 q^{5} +0.936776 q^{6} +2.49293 q^{7} -1.00000 q^{8} -2.12245 q^{9} -1.38125 q^{10} -1.29654 q^{11} -0.936776 q^{12} -0.532498 q^{13} -2.49293 q^{14} -1.29392 q^{15} +1.00000 q^{16} -4.49376 q^{17} +2.12245 q^{18} -6.56345 q^{19} +1.38125 q^{20} -2.33531 q^{21} +1.29654 q^{22} +1.00000 q^{23} +0.936776 q^{24} -3.09214 q^{25} +0.532498 q^{26} +4.79859 q^{27} +2.49293 q^{28} +9.38832 q^{29} +1.29392 q^{30} +8.74238 q^{31} -1.00000 q^{32} +1.21457 q^{33} +4.49376 q^{34} +3.44336 q^{35} -2.12245 q^{36} +5.61854 q^{37} +6.56345 q^{38} +0.498831 q^{39} -1.38125 q^{40} -6.09722 q^{41} +2.33531 q^{42} +7.17129 q^{43} -1.29654 q^{44} -2.93164 q^{45} -1.00000 q^{46} +6.97895 q^{47} -0.936776 q^{48} -0.785322 q^{49} +3.09214 q^{50} +4.20964 q^{51} -0.532498 q^{52} +0.607361 q^{53} -4.79859 q^{54} -1.79085 q^{55} -2.49293 q^{56} +6.14849 q^{57} -9.38832 q^{58} -0.436665 q^{59} -1.29392 q^{60} -2.24866 q^{61} -8.74238 q^{62} -5.29111 q^{63} +1.00000 q^{64} -0.735514 q^{65} -1.21457 q^{66} -8.74609 q^{67} -4.49376 q^{68} -0.936776 q^{69} -3.44336 q^{70} +3.67124 q^{71} +2.12245 q^{72} -13.3102 q^{73} -5.61854 q^{74} +2.89664 q^{75} -6.56345 q^{76} -3.23218 q^{77} -0.498831 q^{78} -9.05511 q^{79} +1.38125 q^{80} +1.87215 q^{81} +6.09722 q^{82} -7.36070 q^{83} -2.33531 q^{84} -6.20701 q^{85} -7.17129 q^{86} -8.79476 q^{87} +1.29654 q^{88} -7.67148 q^{89} +2.93164 q^{90} -1.32748 q^{91} +1.00000 q^{92} -8.18965 q^{93} -6.97895 q^{94} -9.06579 q^{95} +0.936776 q^{96} -5.31188 q^{97} +0.785322 q^{98} +2.75184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + O(q^{10}) \) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + 3q^{10} - 12q^{11} - 4q^{12} - 6q^{13} + 11q^{14} + 25q^{16} + 8q^{17} - 19q^{18} - 23q^{19} - 3q^{20} - 16q^{21} + 12q^{22} + 25q^{23} + 4q^{24} + 4q^{25} + 6q^{26} - 13q^{27} - 11q^{28} - 7q^{29} - 7q^{31} - 25q^{32} + 3q^{33} - 8q^{34} - 18q^{35} + 19q^{36} - 7q^{37} + 23q^{38} - 2q^{39} + 3q^{40} - 10q^{41} + 16q^{42} - 26q^{43} - 12q^{44} + 20q^{45} - 25q^{46} - 2q^{47} - 4q^{48} + 2q^{49} - 4q^{50} - 28q^{51} - 6q^{52} + 47q^{53} + 13q^{54} - 38q^{55} + 11q^{56} - 4q^{57} + 7q^{58} - 19q^{59} - 26q^{61} + 7q^{62} - 15q^{63} + 25q^{64} + 13q^{65} - 3q^{66} - 34q^{67} + 8q^{68} - 4q^{69} + 18q^{70} - 10q^{71} - 19q^{72} - 22q^{73} + 7q^{74} - 8q^{75} - 23q^{76} + 28q^{77} + 2q^{78} - 21q^{79} - 3q^{80} - 27q^{81} + 10q^{82} - 16q^{83} - 16q^{84} - 42q^{85} + 26q^{86} - 17q^{87} + 12q^{88} + 27q^{89} - 20q^{90} - 26q^{91} + 25q^{92} - 27q^{93} + 2q^{94} + 4q^{96} + 4q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.936776 −0.540848 −0.270424 0.962741i \(-0.587164\pi\)
−0.270424 + 0.962741i \(0.587164\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.38125 0.617715 0.308857 0.951108i \(-0.400053\pi\)
0.308857 + 0.951108i \(0.400053\pi\)
\(6\) 0.936776 0.382437
\(7\) 2.49293 0.942237 0.471119 0.882070i \(-0.343850\pi\)
0.471119 + 0.882070i \(0.343850\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.12245 −0.707483
\(10\) −1.38125 −0.436790
\(11\) −1.29654 −0.390922 −0.195461 0.980712i \(-0.562620\pi\)
−0.195461 + 0.980712i \(0.562620\pi\)
\(12\) −0.936776 −0.270424
\(13\) −0.532498 −0.147688 −0.0738441 0.997270i \(-0.523527\pi\)
−0.0738441 + 0.997270i \(0.523527\pi\)
\(14\) −2.49293 −0.666262
\(15\) −1.29392 −0.334090
\(16\) 1.00000 0.250000
\(17\) −4.49376 −1.08990 −0.544948 0.838470i \(-0.683451\pi\)
−0.544948 + 0.838470i \(0.683451\pi\)
\(18\) 2.12245 0.500266
\(19\) −6.56345 −1.50576 −0.752880 0.658158i \(-0.771336\pi\)
−0.752880 + 0.658158i \(0.771336\pi\)
\(20\) 1.38125 0.308857
\(21\) −2.33531 −0.509607
\(22\) 1.29654 0.276423
\(23\) 1.00000 0.208514
\(24\) 0.936776 0.191219
\(25\) −3.09214 −0.618428
\(26\) 0.532498 0.104431
\(27\) 4.79859 0.923489
\(28\) 2.49293 0.471119
\(29\) 9.38832 1.74337 0.871684 0.490069i \(-0.163028\pi\)
0.871684 + 0.490069i \(0.163028\pi\)
\(30\) 1.29392 0.236237
\(31\) 8.74238 1.57018 0.785089 0.619383i \(-0.212617\pi\)
0.785089 + 0.619383i \(0.212617\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.21457 0.211429
\(34\) 4.49376 0.770673
\(35\) 3.44336 0.582034
\(36\) −2.12245 −0.353742
\(37\) 5.61854 0.923683 0.461841 0.886963i \(-0.347189\pi\)
0.461841 + 0.886963i \(0.347189\pi\)
\(38\) 6.56345 1.06473
\(39\) 0.498831 0.0798769
\(40\) −1.38125 −0.218395
\(41\) −6.09722 −0.952226 −0.476113 0.879384i \(-0.657955\pi\)
−0.476113 + 0.879384i \(0.657955\pi\)
\(42\) 2.33531 0.360347
\(43\) 7.17129 1.09361 0.546806 0.837260i \(-0.315844\pi\)
0.546806 + 0.837260i \(0.315844\pi\)
\(44\) −1.29654 −0.195461
\(45\) −2.93164 −0.437023
\(46\) −1.00000 −0.147442
\(47\) 6.97895 1.01798 0.508992 0.860771i \(-0.330018\pi\)
0.508992 + 0.860771i \(0.330018\pi\)
\(48\) −0.936776 −0.135212
\(49\) −0.785322 −0.112189
\(50\) 3.09214 0.437295
\(51\) 4.20964 0.589468
\(52\) −0.532498 −0.0738441
\(53\) 0.607361 0.0834274 0.0417137 0.999130i \(-0.486718\pi\)
0.0417137 + 0.999130i \(0.486718\pi\)
\(54\) −4.79859 −0.653005
\(55\) −1.79085 −0.241478
\(56\) −2.49293 −0.333131
\(57\) 6.14849 0.814387
\(58\) −9.38832 −1.23275
\(59\) −0.436665 −0.0568490 −0.0284245 0.999596i \(-0.509049\pi\)
−0.0284245 + 0.999596i \(0.509049\pi\)
\(60\) −1.29392 −0.167045
\(61\) −2.24866 −0.287911 −0.143955 0.989584i \(-0.545982\pi\)
−0.143955 + 0.989584i \(0.545982\pi\)
\(62\) −8.74238 −1.11028
\(63\) −5.29111 −0.666617
\(64\) 1.00000 0.125000
\(65\) −0.735514 −0.0912293
\(66\) −1.21457 −0.149503
\(67\) −8.74609 −1.06851 −0.534253 0.845325i \(-0.679407\pi\)
−0.534253 + 0.845325i \(0.679407\pi\)
\(68\) −4.49376 −0.544948
\(69\) −0.936776 −0.112775
\(70\) −3.44336 −0.411560
\(71\) 3.67124 0.435696 0.217848 0.975983i \(-0.430096\pi\)
0.217848 + 0.975983i \(0.430096\pi\)
\(72\) 2.12245 0.250133
\(73\) −13.3102 −1.55784 −0.778918 0.627125i \(-0.784231\pi\)
−0.778918 + 0.627125i \(0.784231\pi\)
\(74\) −5.61854 −0.653142
\(75\) 2.89664 0.334476
\(76\) −6.56345 −0.752880
\(77\) −3.23218 −0.368341
\(78\) −0.498831 −0.0564815
\(79\) −9.05511 −1.01878 −0.509390 0.860536i \(-0.670129\pi\)
−0.509390 + 0.860536i \(0.670129\pi\)
\(80\) 1.38125 0.154429
\(81\) 1.87215 0.208016
\(82\) 6.09722 0.673325
\(83\) −7.36070 −0.807942 −0.403971 0.914772i \(-0.632370\pi\)
−0.403971 + 0.914772i \(0.632370\pi\)
\(84\) −2.33531 −0.254804
\(85\) −6.20701 −0.673245
\(86\) −7.17129 −0.773300
\(87\) −8.79476 −0.942897
\(88\) 1.29654 0.138212
\(89\) −7.67148 −0.813175 −0.406588 0.913612i \(-0.633281\pi\)
−0.406588 + 0.913612i \(0.633281\pi\)
\(90\) 2.93164 0.309022
\(91\) −1.32748 −0.139157
\(92\) 1.00000 0.104257
\(93\) −8.18965 −0.849228
\(94\) −6.97895 −0.719823
\(95\) −9.06579 −0.930130
\(96\) 0.936776 0.0956093
\(97\) −5.31188 −0.539340 −0.269670 0.962953i \(-0.586915\pi\)
−0.269670 + 0.962953i \(0.586915\pi\)
\(98\) 0.785322 0.0793295
\(99\) 2.75184 0.276571
\(100\) −3.09214 −0.309214
\(101\) 17.5882 1.75009 0.875046 0.484040i \(-0.160831\pi\)
0.875046 + 0.484040i \(0.160831\pi\)
\(102\) −4.20964 −0.416817
\(103\) −5.88185 −0.579556 −0.289778 0.957094i \(-0.593581\pi\)
−0.289778 + 0.957094i \(0.593581\pi\)
\(104\) 0.532498 0.0522157
\(105\) −3.22566 −0.314792
\(106\) −0.607361 −0.0589921
\(107\) −2.12314 −0.205252 −0.102626 0.994720i \(-0.532724\pi\)
−0.102626 + 0.994720i \(0.532724\pi\)
\(108\) 4.79859 0.461745
\(109\) 9.69916 0.929011 0.464506 0.885570i \(-0.346232\pi\)
0.464506 + 0.885570i \(0.346232\pi\)
\(110\) 1.79085 0.170751
\(111\) −5.26332 −0.499572
\(112\) 2.49293 0.235559
\(113\) 0.192906 0.0181470 0.00907352 0.999959i \(-0.497112\pi\)
0.00907352 + 0.999959i \(0.497112\pi\)
\(114\) −6.14849 −0.575858
\(115\) 1.38125 0.128802
\(116\) 9.38832 0.871684
\(117\) 1.13020 0.104487
\(118\) 0.436665 0.0401983
\(119\) −11.2026 −1.02694
\(120\) 1.29392 0.118119
\(121\) −9.31898 −0.847180
\(122\) 2.24866 0.203584
\(123\) 5.71173 0.515009
\(124\) 8.74238 0.785089
\(125\) −11.1773 −0.999727
\(126\) 5.29111 0.471370
\(127\) −11.7953 −1.04666 −0.523330 0.852130i \(-0.675310\pi\)
−0.523330 + 0.852130i \(0.675310\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.71789 −0.591477
\(130\) 0.735514 0.0645088
\(131\) 1.00000 0.0873704
\(132\) 1.21457 0.105715
\(133\) −16.3622 −1.41878
\(134\) 8.74609 0.755547
\(135\) 6.62806 0.570453
\(136\) 4.49376 0.385336
\(137\) 3.16549 0.270446 0.135223 0.990815i \(-0.456825\pi\)
0.135223 + 0.990815i \(0.456825\pi\)
\(138\) 0.936776 0.0797437
\(139\) 20.6429 1.75090 0.875452 0.483305i \(-0.160564\pi\)
0.875452 + 0.483305i \(0.160564\pi\)
\(140\) 3.44336 0.291017
\(141\) −6.53771 −0.550575
\(142\) −3.67124 −0.308084
\(143\) 0.690405 0.0577345
\(144\) −2.12245 −0.176871
\(145\) 12.9676 1.07690
\(146\) 13.3102 1.10156
\(147\) 0.735671 0.0606771
\(148\) 5.61854 0.461841
\(149\) −11.5985 −0.950184 −0.475092 0.879936i \(-0.657585\pi\)
−0.475092 + 0.879936i \(0.657585\pi\)
\(150\) −2.89664 −0.236510
\(151\) −3.10142 −0.252390 −0.126195 0.992005i \(-0.540277\pi\)
−0.126195 + 0.992005i \(0.540277\pi\)
\(152\) 6.56345 0.532366
\(153\) 9.53778 0.771083
\(154\) 3.23218 0.260456
\(155\) 12.0754 0.969922
\(156\) 0.498831 0.0399385
\(157\) 3.16050 0.252235 0.126118 0.992015i \(-0.459748\pi\)
0.126118 + 0.992015i \(0.459748\pi\)
\(158\) 9.05511 0.720386
\(159\) −0.568961 −0.0451216
\(160\) −1.38125 −0.109198
\(161\) 2.49293 0.196470
\(162\) −1.87215 −0.147090
\(163\) −11.5854 −0.907441 −0.453721 0.891144i \(-0.649904\pi\)
−0.453721 + 0.891144i \(0.649904\pi\)
\(164\) −6.09722 −0.476113
\(165\) 1.67763 0.130603
\(166\) 7.36070 0.571301
\(167\) −9.73825 −0.753569 −0.376784 0.926301i \(-0.622970\pi\)
−0.376784 + 0.926301i \(0.622970\pi\)
\(168\) 2.33531 0.180173
\(169\) −12.7164 −0.978188
\(170\) 6.20701 0.476056
\(171\) 13.9306 1.06530
\(172\) 7.17129 0.546806
\(173\) −9.97288 −0.758224 −0.379112 0.925351i \(-0.623770\pi\)
−0.379112 + 0.925351i \(0.623770\pi\)
\(174\) 8.79476 0.666729
\(175\) −7.70848 −0.582706
\(176\) −1.29654 −0.0977304
\(177\) 0.409058 0.0307467
\(178\) 7.67148 0.575002
\(179\) −11.7814 −0.880584 −0.440292 0.897855i \(-0.645125\pi\)
−0.440292 + 0.897855i \(0.645125\pi\)
\(180\) −2.93164 −0.218512
\(181\) 1.37301 0.102055 0.0510274 0.998697i \(-0.483750\pi\)
0.0510274 + 0.998697i \(0.483750\pi\)
\(182\) 1.32748 0.0983992
\(183\) 2.10649 0.155716
\(184\) −1.00000 −0.0737210
\(185\) 7.76062 0.570572
\(186\) 8.18965 0.600495
\(187\) 5.82634 0.426064
\(188\) 6.97895 0.508992
\(189\) 11.9625 0.870146
\(190\) 9.06579 0.657701
\(191\) 0.683085 0.0494263 0.0247131 0.999695i \(-0.492133\pi\)
0.0247131 + 0.999695i \(0.492133\pi\)
\(192\) −0.936776 −0.0676060
\(193\) −0.407793 −0.0293536 −0.0146768 0.999892i \(-0.504672\pi\)
−0.0146768 + 0.999892i \(0.504672\pi\)
\(194\) 5.31188 0.381371
\(195\) 0.689012 0.0493412
\(196\) −0.785322 −0.0560944
\(197\) −7.19013 −0.512275 −0.256138 0.966640i \(-0.582450\pi\)
−0.256138 + 0.966640i \(0.582450\pi\)
\(198\) −2.75184 −0.195565
\(199\) 3.59473 0.254824 0.127412 0.991850i \(-0.459333\pi\)
0.127412 + 0.991850i \(0.459333\pi\)
\(200\) 3.09214 0.218647
\(201\) 8.19313 0.577899
\(202\) −17.5882 −1.23750
\(203\) 23.4044 1.64267
\(204\) 4.20964 0.294734
\(205\) −8.42180 −0.588204
\(206\) 5.88185 0.409808
\(207\) −2.12245 −0.147520
\(208\) −0.532498 −0.0369221
\(209\) 8.50978 0.588634
\(210\) 3.22566 0.222592
\(211\) −25.4830 −1.75432 −0.877160 0.480198i \(-0.840565\pi\)
−0.877160 + 0.480198i \(0.840565\pi\)
\(212\) 0.607361 0.0417137
\(213\) −3.43913 −0.235645
\(214\) 2.12314 0.145135
\(215\) 9.90536 0.675540
\(216\) −4.79859 −0.326503
\(217\) 21.7941 1.47948
\(218\) −9.69916 −0.656910
\(219\) 12.4686 0.842553
\(220\) −1.79085 −0.120739
\(221\) 2.39292 0.160965
\(222\) 5.26332 0.353251
\(223\) −25.4651 −1.70527 −0.852635 0.522507i \(-0.824997\pi\)
−0.852635 + 0.522507i \(0.824997\pi\)
\(224\) −2.49293 −0.166566
\(225\) 6.56292 0.437528
\(226\) −0.192906 −0.0128319
\(227\) 11.8102 0.783871 0.391936 0.919993i \(-0.371806\pi\)
0.391936 + 0.919993i \(0.371806\pi\)
\(228\) 6.14849 0.407193
\(229\) −20.8857 −1.38017 −0.690083 0.723731i \(-0.742426\pi\)
−0.690083 + 0.723731i \(0.742426\pi\)
\(230\) −1.38125 −0.0910771
\(231\) 3.02783 0.199216
\(232\) −9.38832 −0.616374
\(233\) 14.9353 0.978442 0.489221 0.872160i \(-0.337281\pi\)
0.489221 + 0.872160i \(0.337281\pi\)
\(234\) −1.13020 −0.0738835
\(235\) 9.63969 0.628824
\(236\) −0.436665 −0.0284245
\(237\) 8.48262 0.551005
\(238\) 11.2026 0.726157
\(239\) −11.7803 −0.762006 −0.381003 0.924574i \(-0.624421\pi\)
−0.381003 + 0.924574i \(0.624421\pi\)
\(240\) −1.29392 −0.0835225
\(241\) 0.115681 0.00745169 0.00372585 0.999993i \(-0.498814\pi\)
0.00372585 + 0.999993i \(0.498814\pi\)
\(242\) 9.31898 0.599047
\(243\) −16.1496 −1.03599
\(244\) −2.24866 −0.143955
\(245\) −1.08473 −0.0693007
\(246\) −5.71173 −0.364167
\(247\) 3.49502 0.222383
\(248\) −8.74238 −0.555142
\(249\) 6.89533 0.436974
\(250\) 11.1773 0.706914
\(251\) −30.5995 −1.93143 −0.965713 0.259613i \(-0.916405\pi\)
−0.965713 + 0.259613i \(0.916405\pi\)
\(252\) −5.29111 −0.333309
\(253\) −1.29654 −0.0815128
\(254\) 11.7953 0.740100
\(255\) 5.81458 0.364123
\(256\) 1.00000 0.0625000
\(257\) 6.16866 0.384790 0.192395 0.981318i \(-0.438374\pi\)
0.192395 + 0.981318i \(0.438374\pi\)
\(258\) 6.71789 0.418238
\(259\) 14.0066 0.870328
\(260\) −0.735514 −0.0456146
\(261\) −19.9262 −1.23340
\(262\) −1.00000 −0.0617802
\(263\) 5.69520 0.351181 0.175591 0.984463i \(-0.443817\pi\)
0.175591 + 0.984463i \(0.443817\pi\)
\(264\) −1.21457 −0.0747515
\(265\) 0.838919 0.0515344
\(266\) 16.3622 1.00323
\(267\) 7.18646 0.439804
\(268\) −8.74609 −0.534253
\(269\) 27.1772 1.65702 0.828510 0.559974i \(-0.189189\pi\)
0.828510 + 0.559974i \(0.189189\pi\)
\(270\) −6.62806 −0.403371
\(271\) −19.6099 −1.19122 −0.595609 0.803275i \(-0.703089\pi\)
−0.595609 + 0.803275i \(0.703089\pi\)
\(272\) −4.49376 −0.272474
\(273\) 1.24355 0.0752630
\(274\) −3.16549 −0.191234
\(275\) 4.00909 0.241757
\(276\) −0.936776 −0.0563873
\(277\) 11.5177 0.692032 0.346016 0.938229i \(-0.387534\pi\)
0.346016 + 0.938229i \(0.387534\pi\)
\(278\) −20.6429 −1.23808
\(279\) −18.5553 −1.11087
\(280\) −3.44336 −0.205780
\(281\) 3.50568 0.209131 0.104566 0.994518i \(-0.466655\pi\)
0.104566 + 0.994518i \(0.466655\pi\)
\(282\) 6.53771 0.389315
\(283\) −16.2648 −0.966844 −0.483422 0.875388i \(-0.660606\pi\)
−0.483422 + 0.875388i \(0.660606\pi\)
\(284\) 3.67124 0.217848
\(285\) 8.49261 0.503059
\(286\) −0.690405 −0.0408245
\(287\) −15.1999 −0.897223
\(288\) 2.12245 0.125067
\(289\) 3.19385 0.187873
\(290\) −12.9676 −0.761486
\(291\) 4.97605 0.291701
\(292\) −13.3102 −0.778918
\(293\) −2.83217 −0.165457 −0.0827286 0.996572i \(-0.526363\pi\)
−0.0827286 + 0.996572i \(0.526363\pi\)
\(294\) −0.735671 −0.0429052
\(295\) −0.603145 −0.0351165
\(296\) −5.61854 −0.326571
\(297\) −6.22156 −0.361012
\(298\) 11.5985 0.671882
\(299\) −0.532498 −0.0307951
\(300\) 2.89664 0.167238
\(301\) 17.8775 1.03044
\(302\) 3.10142 0.178467
\(303\) −16.4762 −0.946533
\(304\) −6.56345 −0.376440
\(305\) −3.10596 −0.177847
\(306\) −9.53778 −0.545238
\(307\) −23.5112 −1.34185 −0.670927 0.741523i \(-0.734104\pi\)
−0.670927 + 0.741523i \(0.734104\pi\)
\(308\) −3.23218 −0.184170
\(309\) 5.50998 0.313452
\(310\) −12.0754 −0.685839
\(311\) 10.8460 0.615022 0.307511 0.951545i \(-0.400504\pi\)
0.307511 + 0.951545i \(0.400504\pi\)
\(312\) −0.498831 −0.0282408
\(313\) 19.7921 1.11872 0.559359 0.828926i \(-0.311047\pi\)
0.559359 + 0.828926i \(0.311047\pi\)
\(314\) −3.16050 −0.178357
\(315\) −7.30836 −0.411779
\(316\) −9.05511 −0.509390
\(317\) −31.5696 −1.77313 −0.886564 0.462607i \(-0.846914\pi\)
−0.886564 + 0.462607i \(0.846914\pi\)
\(318\) 0.568961 0.0319058
\(319\) −12.1723 −0.681520
\(320\) 1.38125 0.0772144
\(321\) 1.98891 0.111010
\(322\) −2.49293 −0.138925
\(323\) 29.4946 1.64112
\(324\) 1.87215 0.104008
\(325\) 1.64656 0.0913346
\(326\) 11.5854 0.641658
\(327\) −9.08595 −0.502454
\(328\) 6.09722 0.336663
\(329\) 17.3980 0.959183
\(330\) −1.67763 −0.0923502
\(331\) 15.7971 0.868289 0.434144 0.900843i \(-0.357051\pi\)
0.434144 + 0.900843i \(0.357051\pi\)
\(332\) −7.36070 −0.403971
\(333\) −11.9251 −0.653490
\(334\) 9.73825 0.532854
\(335\) −12.0806 −0.660032
\(336\) −2.33531 −0.127402
\(337\) −14.6876 −0.800087 −0.400043 0.916496i \(-0.631005\pi\)
−0.400043 + 0.916496i \(0.631005\pi\)
\(338\) 12.7164 0.691683
\(339\) −0.180709 −0.00981479
\(340\) −6.20701 −0.336623
\(341\) −11.3348 −0.613816
\(342\) −13.9306 −0.753281
\(343\) −19.4082 −1.04795
\(344\) −7.17129 −0.386650
\(345\) −1.29392 −0.0696626
\(346\) 9.97288 0.536145
\(347\) −7.46473 −0.400728 −0.200364 0.979722i \(-0.564212\pi\)
−0.200364 + 0.979722i \(0.564212\pi\)
\(348\) −8.79476 −0.471448
\(349\) −11.9085 −0.637450 −0.318725 0.947847i \(-0.603255\pi\)
−0.318725 + 0.947847i \(0.603255\pi\)
\(350\) 7.70848 0.412036
\(351\) −2.55524 −0.136389
\(352\) 1.29654 0.0691058
\(353\) −0.279427 −0.0148724 −0.00743621 0.999972i \(-0.502367\pi\)
−0.00743621 + 0.999972i \(0.502367\pi\)
\(354\) −0.409058 −0.0217412
\(355\) 5.07091 0.269136
\(356\) −7.67148 −0.406588
\(357\) 10.4943 0.555419
\(358\) 11.7814 0.622667
\(359\) 9.12238 0.481461 0.240730 0.970592i \(-0.422613\pi\)
0.240730 + 0.970592i \(0.422613\pi\)
\(360\) 2.93164 0.154511
\(361\) 24.0789 1.26731
\(362\) −1.37301 −0.0721636
\(363\) 8.72980 0.458196
\(364\) −1.32748 −0.0695787
\(365\) −18.3847 −0.962299
\(366\) −2.10649 −0.110108
\(367\) 22.4485 1.17180 0.585900 0.810383i \(-0.300741\pi\)
0.585900 + 0.810383i \(0.300741\pi\)
\(368\) 1.00000 0.0521286
\(369\) 12.9410 0.673684
\(370\) −7.76062 −0.403456
\(371\) 1.51411 0.0786084
\(372\) −8.18965 −0.424614
\(373\) −3.66142 −0.189581 −0.0947905 0.995497i \(-0.530218\pi\)
−0.0947905 + 0.995497i \(0.530218\pi\)
\(374\) −5.82634 −0.301273
\(375\) 10.4706 0.540701
\(376\) −6.97895 −0.359912
\(377\) −4.99926 −0.257475
\(378\) −11.9625 −0.615286
\(379\) 18.5474 0.952714 0.476357 0.879252i \(-0.341957\pi\)
0.476357 + 0.879252i \(0.341957\pi\)
\(380\) −9.06579 −0.465065
\(381\) 11.0495 0.566084
\(382\) −0.683085 −0.0349496
\(383\) −3.65393 −0.186707 −0.0933536 0.995633i \(-0.529759\pi\)
−0.0933536 + 0.995633i \(0.529759\pi\)
\(384\) 0.936776 0.0478047
\(385\) −4.46445 −0.227530
\(386\) 0.407793 0.0207561
\(387\) −15.2207 −0.773712
\(388\) −5.31188 −0.269670
\(389\) −2.41585 −0.122489 −0.0612443 0.998123i \(-0.519507\pi\)
−0.0612443 + 0.998123i \(0.519507\pi\)
\(390\) −0.689012 −0.0348895
\(391\) −4.49376 −0.227259
\(392\) 0.785322 0.0396647
\(393\) −0.936776 −0.0472541
\(394\) 7.19013 0.362233
\(395\) −12.5074 −0.629316
\(396\) 2.75184 0.138285
\(397\) 15.8509 0.795536 0.397768 0.917486i \(-0.369785\pi\)
0.397768 + 0.917486i \(0.369785\pi\)
\(398\) −3.59473 −0.180187
\(399\) 15.3277 0.767346
\(400\) −3.09214 −0.154607
\(401\) −4.53493 −0.226464 −0.113232 0.993569i \(-0.536120\pi\)
−0.113232 + 0.993569i \(0.536120\pi\)
\(402\) −8.19313 −0.408636
\(403\) −4.65530 −0.231897
\(404\) 17.5882 0.875046
\(405\) 2.58591 0.128495
\(406\) −23.4044 −1.16154
\(407\) −7.28466 −0.361087
\(408\) −4.20964 −0.208408
\(409\) −17.2859 −0.854733 −0.427366 0.904078i \(-0.640559\pi\)
−0.427366 + 0.904078i \(0.640559\pi\)
\(410\) 8.42180 0.415923
\(411\) −2.96536 −0.146270
\(412\) −5.88185 −0.289778
\(413\) −1.08857 −0.0535652
\(414\) 2.12245 0.104313
\(415\) −10.1670 −0.499078
\(416\) 0.532498 0.0261078
\(417\) −19.3377 −0.946973
\(418\) −8.50978 −0.416227
\(419\) 1.27685 0.0623781 0.0311890 0.999514i \(-0.490071\pi\)
0.0311890 + 0.999514i \(0.490071\pi\)
\(420\) −3.22566 −0.157396
\(421\) −28.2406 −1.37636 −0.688181 0.725539i \(-0.741591\pi\)
−0.688181 + 0.725539i \(0.741591\pi\)
\(422\) 25.4830 1.24049
\(423\) −14.8125 −0.720207
\(424\) −0.607361 −0.0294961
\(425\) 13.8953 0.674023
\(426\) 3.43913 0.166626
\(427\) −5.60573 −0.271280
\(428\) −2.12314 −0.102626
\(429\) −0.646755 −0.0312256
\(430\) −9.90536 −0.477679
\(431\) 4.07729 0.196396 0.0981982 0.995167i \(-0.468692\pi\)
0.0981982 + 0.995167i \(0.468692\pi\)
\(432\) 4.79859 0.230872
\(433\) 40.1696 1.93043 0.965214 0.261460i \(-0.0842039\pi\)
0.965214 + 0.261460i \(0.0842039\pi\)
\(434\) −21.7941 −1.04615
\(435\) −12.1478 −0.582441
\(436\) 9.69916 0.464506
\(437\) −6.56345 −0.313973
\(438\) −12.4686 −0.595775
\(439\) 0.902219 0.0430606 0.0215303 0.999768i \(-0.493146\pi\)
0.0215303 + 0.999768i \(0.493146\pi\)
\(440\) 1.79085 0.0853754
\(441\) 1.66681 0.0793717
\(442\) −2.39292 −0.113819
\(443\) −18.8332 −0.894791 −0.447395 0.894336i \(-0.647648\pi\)
−0.447395 + 0.894336i \(0.647648\pi\)
\(444\) −5.26332 −0.249786
\(445\) −10.5963 −0.502310
\(446\) 25.4651 1.20581
\(447\) 10.8652 0.513905
\(448\) 2.49293 0.117780
\(449\) −28.7296 −1.35583 −0.677917 0.735139i \(-0.737117\pi\)
−0.677917 + 0.735139i \(0.737117\pi\)
\(450\) −6.56292 −0.309379
\(451\) 7.90529 0.372246
\(452\) 0.192906 0.00907352
\(453\) 2.90534 0.136505
\(454\) −11.8102 −0.554281
\(455\) −1.83358 −0.0859596
\(456\) −6.14849 −0.287929
\(457\) 18.8061 0.879712 0.439856 0.898068i \(-0.355029\pi\)
0.439856 + 0.898068i \(0.355029\pi\)
\(458\) 20.8857 0.975924
\(459\) −21.5637 −1.00651
\(460\) 1.38125 0.0644012
\(461\) 36.4941 1.69970 0.849850 0.527025i \(-0.176693\pi\)
0.849850 + 0.527025i \(0.176693\pi\)
\(462\) −3.02783 −0.140867
\(463\) −22.2870 −1.03577 −0.517883 0.855452i \(-0.673280\pi\)
−0.517883 + 0.855452i \(0.673280\pi\)
\(464\) 9.38832 0.435842
\(465\) −11.3120 −0.524581
\(466\) −14.9353 −0.691863
\(467\) 36.9088 1.70794 0.853969 0.520324i \(-0.174189\pi\)
0.853969 + 0.520324i \(0.174189\pi\)
\(468\) 1.13020 0.0522435
\(469\) −21.8034 −1.00679
\(470\) −9.63969 −0.444646
\(471\) −2.96068 −0.136421
\(472\) 0.436665 0.0200992
\(473\) −9.29786 −0.427516
\(474\) −8.48262 −0.389619
\(475\) 20.2951 0.931204
\(476\) −11.2026 −0.513470
\(477\) −1.28909 −0.0590235
\(478\) 11.7803 0.538819
\(479\) 37.6259 1.71917 0.859587 0.510990i \(-0.170721\pi\)
0.859587 + 0.510990i \(0.170721\pi\)
\(480\) 1.29392 0.0590593
\(481\) −2.99186 −0.136417
\(482\) −0.115681 −0.00526914
\(483\) −2.33531 −0.106260
\(484\) −9.31898 −0.423590
\(485\) −7.33705 −0.333158
\(486\) 16.1496 0.732559
\(487\) 38.7739 1.75701 0.878506 0.477731i \(-0.158541\pi\)
0.878506 + 0.477731i \(0.158541\pi\)
\(488\) 2.24866 0.101792
\(489\) 10.8530 0.490788
\(490\) 1.08473 0.0490030
\(491\) −8.16329 −0.368404 −0.184202 0.982888i \(-0.558970\pi\)
−0.184202 + 0.982888i \(0.558970\pi\)
\(492\) 5.71173 0.257505
\(493\) −42.1888 −1.90009
\(494\) −3.49502 −0.157249
\(495\) 3.80099 0.170842
\(496\) 8.74238 0.392544
\(497\) 9.15213 0.410529
\(498\) −6.89533 −0.308987
\(499\) −32.2183 −1.44229 −0.721145 0.692784i \(-0.756384\pi\)
−0.721145 + 0.692784i \(0.756384\pi\)
\(500\) −11.1773 −0.499864
\(501\) 9.12257 0.407566
\(502\) 30.5995 1.36572
\(503\) 23.9695 1.06875 0.534373 0.845249i \(-0.320548\pi\)
0.534373 + 0.845249i \(0.320548\pi\)
\(504\) 5.29111 0.235685
\(505\) 24.2937 1.08106
\(506\) 1.29654 0.0576382
\(507\) 11.9125 0.529051
\(508\) −11.7953 −0.523330
\(509\) −4.33842 −0.192297 −0.0961485 0.995367i \(-0.530652\pi\)
−0.0961485 + 0.995367i \(0.530652\pi\)
\(510\) −5.81458 −0.257474
\(511\) −33.1813 −1.46785
\(512\) −1.00000 −0.0441942
\(513\) −31.4953 −1.39055
\(514\) −6.16866 −0.272088
\(515\) −8.12432 −0.358000
\(516\) −6.71789 −0.295739
\(517\) −9.04848 −0.397952
\(518\) −14.0066 −0.615415
\(519\) 9.34236 0.410084
\(520\) 0.735514 0.0322544
\(521\) 12.2003 0.534503 0.267252 0.963627i \(-0.413885\pi\)
0.267252 + 0.963627i \(0.413885\pi\)
\(522\) 19.9262 0.872148
\(523\) −11.3549 −0.496517 −0.248258 0.968694i \(-0.579858\pi\)
−0.248258 + 0.968694i \(0.579858\pi\)
\(524\) 1.00000 0.0436852
\(525\) 7.22112 0.315155
\(526\) −5.69520 −0.248323
\(527\) −39.2861 −1.71133
\(528\) 1.21457 0.0528573
\(529\) 1.00000 0.0434783
\(530\) −0.838919 −0.0364403
\(531\) 0.926801 0.0402197
\(532\) −16.3622 −0.709391
\(533\) 3.24676 0.140633
\(534\) −7.18646 −0.310989
\(535\) −2.93259 −0.126787
\(536\) 8.74609 0.377774
\(537\) 11.0366 0.476262
\(538\) −27.1772 −1.17169
\(539\) 1.01820 0.0438570
\(540\) 6.62806 0.285226
\(541\) −9.31967 −0.400684 −0.200342 0.979726i \(-0.564205\pi\)
−0.200342 + 0.979726i \(0.564205\pi\)
\(542\) 19.6099 0.842318
\(543\) −1.28620 −0.0551961
\(544\) 4.49376 0.192668
\(545\) 13.3970 0.573864
\(546\) −1.24355 −0.0532190
\(547\) −31.0071 −1.32577 −0.662883 0.748723i \(-0.730668\pi\)
−0.662883 + 0.748723i \(0.730668\pi\)
\(548\) 3.16549 0.135223
\(549\) 4.77266 0.203692
\(550\) −4.00909 −0.170948
\(551\) −61.6198 −2.62509
\(552\) 0.936776 0.0398718
\(553\) −22.5737 −0.959932
\(554\) −11.5177 −0.489340
\(555\) −7.26997 −0.308593
\(556\) 20.6429 0.875452
\(557\) −32.2904 −1.36819 −0.684094 0.729393i \(-0.739802\pi\)
−0.684094 + 0.729393i \(0.739802\pi\)
\(558\) 18.5553 0.785507
\(559\) −3.81869 −0.161514
\(560\) 3.44336 0.145509
\(561\) −5.45797 −0.230436
\(562\) −3.50568 −0.147878
\(563\) −21.8210 −0.919646 −0.459823 0.888011i \(-0.652087\pi\)
−0.459823 + 0.888011i \(0.652087\pi\)
\(564\) −6.53771 −0.275287
\(565\) 0.266451 0.0112097
\(566\) 16.2648 0.683662
\(567\) 4.66712 0.196001
\(568\) −3.67124 −0.154042
\(569\) −21.6536 −0.907767 −0.453883 0.891061i \(-0.649962\pi\)
−0.453883 + 0.891061i \(0.649962\pi\)
\(570\) −8.49261 −0.355716
\(571\) −23.4711 −0.982237 −0.491118 0.871093i \(-0.663412\pi\)
−0.491118 + 0.871093i \(0.663412\pi\)
\(572\) 0.690405 0.0288673
\(573\) −0.639897 −0.0267321
\(574\) 15.1999 0.634432
\(575\) −3.09214 −0.128951
\(576\) −2.12245 −0.0884354
\(577\) −13.2931 −0.553398 −0.276699 0.960957i \(-0.589240\pi\)
−0.276699 + 0.960957i \(0.589240\pi\)
\(578\) −3.19385 −0.132847
\(579\) 0.382011 0.0158758
\(580\) 12.9676 0.538452
\(581\) −18.3497 −0.761273
\(582\) −4.97605 −0.206264
\(583\) −0.787468 −0.0326136
\(584\) 13.3102 0.550779
\(585\) 1.56109 0.0645432
\(586\) 2.83217 0.116996
\(587\) 4.88252 0.201523 0.100762 0.994911i \(-0.467872\pi\)
0.100762 + 0.994911i \(0.467872\pi\)
\(588\) 0.735671 0.0303386
\(589\) −57.3802 −2.36431
\(590\) 0.603145 0.0248311
\(591\) 6.73554 0.277063
\(592\) 5.61854 0.230921
\(593\) −14.9675 −0.614642 −0.307321 0.951606i \(-0.599432\pi\)
−0.307321 + 0.951606i \(0.599432\pi\)
\(594\) 6.22156 0.255274
\(595\) −15.4736 −0.634357
\(596\) −11.5985 −0.475092
\(597\) −3.36746 −0.137821
\(598\) 0.532498 0.0217755
\(599\) −27.8084 −1.13622 −0.568109 0.822953i \(-0.692325\pi\)
−0.568109 + 0.822953i \(0.692325\pi\)
\(600\) −2.89664 −0.118255
\(601\) −36.3320 −1.48201 −0.741007 0.671498i \(-0.765651\pi\)
−0.741007 + 0.671498i \(0.765651\pi\)
\(602\) −17.8775 −0.728632
\(603\) 18.5632 0.755950
\(604\) −3.10142 −0.126195
\(605\) −12.8719 −0.523316
\(606\) 16.4762 0.669300
\(607\) −45.0589 −1.82889 −0.914443 0.404716i \(-0.867370\pi\)
−0.914443 + 0.404716i \(0.867370\pi\)
\(608\) 6.56345 0.266183
\(609\) −21.9247 −0.888433
\(610\) 3.10596 0.125757
\(611\) −3.71627 −0.150344
\(612\) 9.53778 0.385542
\(613\) −14.2772 −0.576650 −0.288325 0.957533i \(-0.593098\pi\)
−0.288325 + 0.957533i \(0.593098\pi\)
\(614\) 23.5112 0.948835
\(615\) 7.88934 0.318129
\(616\) 3.23218 0.130228
\(617\) 29.5515 1.18970 0.594849 0.803837i \(-0.297212\pi\)
0.594849 + 0.803837i \(0.297212\pi\)
\(618\) −5.50998 −0.221644
\(619\) 8.68462 0.349064 0.174532 0.984651i \(-0.444159\pi\)
0.174532 + 0.984651i \(0.444159\pi\)
\(620\) 12.0754 0.484961
\(621\) 4.79859 0.192561
\(622\) −10.8460 −0.434886
\(623\) −19.1244 −0.766204
\(624\) 0.498831 0.0199692
\(625\) 0.0220452 0.000881808 0
\(626\) −19.7921 −0.791053
\(627\) −7.97176 −0.318361
\(628\) 3.16050 0.126118
\(629\) −25.2484 −1.00672
\(630\) 7.30836 0.291172
\(631\) 2.13449 0.0849726 0.0424863 0.999097i \(-0.486472\pi\)
0.0424863 + 0.999097i \(0.486472\pi\)
\(632\) 9.05511 0.360193
\(633\) 23.8718 0.948820
\(634\) 31.5696 1.25379
\(635\) −16.2922 −0.646537
\(636\) −0.568961 −0.0225608
\(637\) 0.418182 0.0165690
\(638\) 12.1723 0.481907
\(639\) −7.79202 −0.308248
\(640\) −1.38125 −0.0545988
\(641\) 7.84892 0.310014 0.155007 0.987913i \(-0.450460\pi\)
0.155007 + 0.987913i \(0.450460\pi\)
\(642\) −1.98891 −0.0784959
\(643\) 31.3502 1.23633 0.618165 0.786049i \(-0.287876\pi\)
0.618165 + 0.786049i \(0.287876\pi\)
\(644\) 2.49293 0.0982350
\(645\) −9.27911 −0.365364
\(646\) −29.4946 −1.16045
\(647\) 19.8691 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(648\) −1.87215 −0.0735448
\(649\) 0.566154 0.0222235
\(650\) −1.64656 −0.0645833
\(651\) −20.4162 −0.800174
\(652\) −11.5854 −0.453721
\(653\) 3.89288 0.152340 0.0761702 0.997095i \(-0.475731\pi\)
0.0761702 + 0.997095i \(0.475731\pi\)
\(654\) 9.08595 0.355289
\(655\) 1.38125 0.0539700
\(656\) −6.09722 −0.238056
\(657\) 28.2502 1.10214
\(658\) −17.3980 −0.678245
\(659\) −19.7748 −0.770317 −0.385159 0.922850i \(-0.625853\pi\)
−0.385159 + 0.922850i \(0.625853\pi\)
\(660\) 1.67763 0.0653015
\(661\) −21.7597 −0.846354 −0.423177 0.906047i \(-0.639085\pi\)
−0.423177 + 0.906047i \(0.639085\pi\)
\(662\) −15.7971 −0.613973
\(663\) −2.24163 −0.0870575
\(664\) 7.36070 0.285651
\(665\) −22.6003 −0.876403
\(666\) 11.9251 0.462087
\(667\) 9.38832 0.363517
\(668\) −9.73825 −0.376784
\(669\) 23.8551 0.922292
\(670\) 12.0806 0.466713
\(671\) 2.91547 0.112551
\(672\) 2.33531 0.0900867
\(673\) −6.64428 −0.256118 −0.128059 0.991767i \(-0.540875\pi\)
−0.128059 + 0.991767i \(0.540875\pi\)
\(674\) 14.6876 0.565747
\(675\) −14.8379 −0.571112
\(676\) −12.7164 −0.489094
\(677\) 29.4872 1.13328 0.566642 0.823964i \(-0.308242\pi\)
0.566642 + 0.823964i \(0.308242\pi\)
\(678\) 0.180709 0.00694010
\(679\) −13.2421 −0.508186
\(680\) 6.20701 0.238028
\(681\) −11.0635 −0.423955
\(682\) 11.3348 0.434034
\(683\) 24.3576 0.932016 0.466008 0.884780i \(-0.345692\pi\)
0.466008 + 0.884780i \(0.345692\pi\)
\(684\) 13.9306 0.532650
\(685\) 4.37234 0.167059
\(686\) 19.4082 0.741010
\(687\) 19.5652 0.746460
\(688\) 7.17129 0.273403
\(689\) −0.323418 −0.0123213
\(690\) 1.29392 0.0492589
\(691\) −47.7353 −1.81594 −0.907969 0.419038i \(-0.862367\pi\)
−0.907969 + 0.419038i \(0.862367\pi\)
\(692\) −9.97288 −0.379112
\(693\) 6.86014 0.260595
\(694\) 7.46473 0.283357
\(695\) 28.5130 1.08156
\(696\) 8.79476 0.333364
\(697\) 27.3994 1.03783
\(698\) 11.9085 0.450745
\(699\) −13.9910 −0.529188
\(700\) −7.70848 −0.291353
\(701\) 44.1090 1.66598 0.832988 0.553292i \(-0.186629\pi\)
0.832988 + 0.553292i \(0.186629\pi\)
\(702\) 2.55524 0.0964412
\(703\) −36.8770 −1.39084
\(704\) −1.29654 −0.0488652
\(705\) −9.03023 −0.340098
\(706\) 0.279427 0.0105164
\(707\) 43.8461 1.64900
\(708\) 0.409058 0.0153733
\(709\) 2.29225 0.0860872 0.0430436 0.999073i \(-0.486295\pi\)
0.0430436 + 0.999073i \(0.486295\pi\)
\(710\) −5.07091 −0.190308
\(711\) 19.2190 0.720770
\(712\) 7.67148 0.287501
\(713\) 8.74238 0.327405
\(714\) −10.4943 −0.392740
\(715\) 0.953623 0.0356635
\(716\) −11.7814 −0.440292
\(717\) 11.0355 0.412129
\(718\) −9.12238 −0.340444
\(719\) −21.5034 −0.801942 −0.400971 0.916091i \(-0.631327\pi\)
−0.400971 + 0.916091i \(0.631327\pi\)
\(720\) −2.93164 −0.109256
\(721\) −14.6630 −0.546079
\(722\) −24.0789 −0.896124
\(723\) −0.108368 −0.00403023
\(724\) 1.37301 0.0510274
\(725\) −29.0300 −1.07815
\(726\) −8.72980 −0.323993
\(727\) 34.2339 1.26967 0.634833 0.772650i \(-0.281069\pi\)
0.634833 + 0.772650i \(0.281069\pi\)
\(728\) 1.32748 0.0491996
\(729\) 9.51208 0.352299
\(730\) 18.3847 0.680448
\(731\) −32.2260 −1.19192
\(732\) 2.10649 0.0778580
\(733\) −37.9137 −1.40037 −0.700187 0.713960i \(-0.746900\pi\)
−0.700187 + 0.713960i \(0.746900\pi\)
\(734\) −22.4485 −0.828588
\(735\) 1.01615 0.0374812
\(736\) −1.00000 −0.0368605
\(737\) 11.3397 0.417702
\(738\) −12.9410 −0.476367
\(739\) −40.8369 −1.50221 −0.751105 0.660182i \(-0.770479\pi\)
−0.751105 + 0.660182i \(0.770479\pi\)
\(740\) 7.76062 0.285286
\(741\) −3.27405 −0.120275
\(742\) −1.51411 −0.0555846
\(743\) −42.0599 −1.54303 −0.771513 0.636213i \(-0.780500\pi\)
−0.771513 + 0.636213i \(0.780500\pi\)
\(744\) 8.18965 0.300247
\(745\) −16.0204 −0.586943
\(746\) 3.66142 0.134054
\(747\) 15.6227 0.571605
\(748\) 5.82634 0.213032
\(749\) −5.29283 −0.193396
\(750\) −10.4706 −0.382333
\(751\) 20.4074 0.744678 0.372339 0.928097i \(-0.378556\pi\)
0.372339 + 0.928097i \(0.378556\pi\)
\(752\) 6.97895 0.254496
\(753\) 28.6649 1.04461
\(754\) 4.99926 0.182062
\(755\) −4.28385 −0.155905
\(756\) 11.9625 0.435073
\(757\) 16.8969 0.614129 0.307065 0.951689i \(-0.400653\pi\)
0.307065 + 0.951689i \(0.400653\pi\)
\(758\) −18.5474 −0.673671
\(759\) 1.21457 0.0440860
\(760\) 9.06579 0.328851
\(761\) 21.7485 0.788383 0.394192 0.919028i \(-0.371025\pi\)
0.394192 + 0.919028i \(0.371025\pi\)
\(762\) −11.0495 −0.400282
\(763\) 24.1793 0.875349
\(764\) 0.683085 0.0247131
\(765\) 13.1741 0.476310
\(766\) 3.65393 0.132022
\(767\) 0.232523 0.00839593
\(768\) −0.936776 −0.0338030
\(769\) −8.84077 −0.318806 −0.159403 0.987214i \(-0.550957\pi\)
−0.159403 + 0.987214i \(0.550957\pi\)
\(770\) 4.46445 0.160888
\(771\) −5.77865 −0.208113
\(772\) −0.407793 −0.0146768
\(773\) 38.0472 1.36846 0.684232 0.729264i \(-0.260138\pi\)
0.684232 + 0.729264i \(0.260138\pi\)
\(774\) 15.2207 0.547097
\(775\) −27.0327 −0.971042
\(776\) 5.31188 0.190686
\(777\) −13.1211 −0.470715
\(778\) 2.41585 0.0866125
\(779\) 40.0188 1.43382
\(780\) 0.689012 0.0246706
\(781\) −4.75991 −0.170323
\(782\) 4.49376 0.160696
\(783\) 45.0507 1.60998
\(784\) −0.785322 −0.0280472
\(785\) 4.36545 0.155810
\(786\) 0.936776 0.0334137
\(787\) 47.6748 1.69942 0.849711 0.527249i \(-0.176776\pi\)
0.849711 + 0.527249i \(0.176776\pi\)
\(788\) −7.19013 −0.256138
\(789\) −5.33513 −0.189936
\(790\) 12.5074 0.444993
\(791\) 0.480899 0.0170988
\(792\) −2.75184 −0.0977824
\(793\) 1.19740 0.0425211
\(794\) −15.8509 −0.562529
\(795\) −0.785879 −0.0278723
\(796\) 3.59473 0.127412
\(797\) 2.00493 0.0710183 0.0355091 0.999369i \(-0.488695\pi\)
0.0355091 + 0.999369i \(0.488695\pi\)
\(798\) −15.3277 −0.542595
\(799\) −31.3617 −1.10950
\(800\) 3.09214 0.109324
\(801\) 16.2823 0.575308
\(802\) 4.53493 0.160134
\(803\) 17.2572 0.608992
\(804\) 8.19313 0.288950
\(805\) 3.44336 0.121362
\(806\) 4.65530 0.163976
\(807\) −25.4589 −0.896196
\(808\) −17.5882 −0.618751
\(809\) 4.24063 0.149093 0.0745464 0.997218i \(-0.476249\pi\)
0.0745464 + 0.997218i \(0.476249\pi\)
\(810\) −2.58591 −0.0908595
\(811\) −9.37816 −0.329312 −0.164656 0.986351i \(-0.552651\pi\)
−0.164656 + 0.986351i \(0.552651\pi\)
\(812\) 23.4044 0.821333
\(813\) 18.3701 0.644268
\(814\) 7.28466 0.255327
\(815\) −16.0024 −0.560540
\(816\) 4.20964 0.147367
\(817\) −47.0684 −1.64672
\(818\) 17.2859 0.604387
\(819\) 2.81750 0.0984516
\(820\) −8.42180 −0.294102
\(821\) −3.94270 −0.137601 −0.0688005 0.997630i \(-0.521917\pi\)
−0.0688005 + 0.997630i \(0.521917\pi\)
\(822\) 2.96536 0.103429
\(823\) 7.82578 0.272789 0.136395 0.990655i \(-0.456448\pi\)
0.136395 + 0.990655i \(0.456448\pi\)
\(824\) 5.88185 0.204904
\(825\) −3.75562 −0.130754
\(826\) 1.08857 0.0378763
\(827\) −27.3167 −0.949895 −0.474947 0.880014i \(-0.657533\pi\)
−0.474947 + 0.880014i \(0.657533\pi\)
\(828\) −2.12245 −0.0737602
\(829\) 31.7497 1.10271 0.551356 0.834270i \(-0.314111\pi\)
0.551356 + 0.834270i \(0.314111\pi\)
\(830\) 10.1670 0.352901
\(831\) −10.7895 −0.374284
\(832\) −0.532498 −0.0184610
\(833\) 3.52905 0.122274
\(834\) 19.3377 0.669611
\(835\) −13.4510 −0.465491
\(836\) 8.50978 0.294317
\(837\) 41.9511 1.45004
\(838\) −1.27685 −0.0441080
\(839\) −51.7729 −1.78740 −0.893699 0.448667i \(-0.851899\pi\)
−0.893699 + 0.448667i \(0.851899\pi\)
\(840\) 3.22566 0.111296
\(841\) 59.1406 2.03933
\(842\) 28.2406 0.973235
\(843\) −3.28404 −0.113108
\(844\) −25.4830 −0.877160
\(845\) −17.5646 −0.604241
\(846\) 14.8125 0.509263
\(847\) −23.2315 −0.798245
\(848\) 0.607361 0.0208569
\(849\) 15.2365 0.522915
\(850\) −13.8953 −0.476606
\(851\) 5.61854 0.192601
\(852\) −3.43913 −0.117823
\(853\) 14.3979 0.492976 0.246488 0.969146i \(-0.420723\pi\)
0.246488 + 0.969146i \(0.420723\pi\)
\(854\) 5.60573 0.191824
\(855\) 19.2417 0.658052
\(856\) 2.12314 0.0725674
\(857\) 11.9525 0.408290 0.204145 0.978941i \(-0.434559\pi\)
0.204145 + 0.978941i \(0.434559\pi\)
\(858\) 0.646755 0.0220798
\(859\) −14.4561 −0.493236 −0.246618 0.969113i \(-0.579319\pi\)
−0.246618 + 0.969113i \(0.579319\pi\)
\(860\) 9.90536 0.337770
\(861\) 14.2389 0.485261
\(862\) −4.07729 −0.138873
\(863\) 5.33211 0.181507 0.0907535 0.995873i \(-0.471072\pi\)
0.0907535 + 0.995873i \(0.471072\pi\)
\(864\) −4.79859 −0.163251
\(865\) −13.7751 −0.468366
\(866\) −40.1696 −1.36502
\(867\) −2.99192 −0.101611
\(868\) 21.7941 0.739740
\(869\) 11.7403 0.398263
\(870\) 12.1478 0.411848
\(871\) 4.65728 0.157806
\(872\) −9.69916 −0.328455
\(873\) 11.2742 0.381574
\(874\) 6.56345 0.222012
\(875\) −27.8642 −0.941980
\(876\) 12.4686 0.421277
\(877\) 42.8468 1.44683 0.723417 0.690411i \(-0.242570\pi\)
0.723417 + 0.690411i \(0.242570\pi\)
\(878\) −0.902219 −0.0304484
\(879\) 2.65311 0.0894872
\(880\) −1.79085 −0.0603695
\(881\) −13.9353 −0.469493 −0.234747 0.972057i \(-0.575426\pi\)
−0.234747 + 0.972057i \(0.575426\pi\)
\(882\) −1.66681 −0.0561243
\(883\) 18.3696 0.618185 0.309092 0.951032i \(-0.399975\pi\)
0.309092 + 0.951032i \(0.399975\pi\)
\(884\) 2.39292 0.0804824
\(885\) 0.565012 0.0189927
\(886\) 18.8332 0.632713
\(887\) −7.62969 −0.256180 −0.128090 0.991763i \(-0.540885\pi\)
−0.128090 + 0.991763i \(0.540885\pi\)
\(888\) 5.26332 0.176625
\(889\) −29.4047 −0.986202
\(890\) 10.5963 0.355187
\(891\) −2.42731 −0.0813180
\(892\) −25.4651 −0.852635
\(893\) −45.8060 −1.53284
\(894\) −10.8652 −0.363386
\(895\) −16.2731 −0.543950
\(896\) −2.49293 −0.0832828
\(897\) 0.498831 0.0166555
\(898\) 28.7296 0.958719
\(899\) 82.0763 2.73740
\(900\) 6.56292 0.218764
\(901\) −2.72933 −0.0909272
\(902\) −7.90529 −0.263217
\(903\) −16.7472 −0.557312
\(904\) −0.192906 −0.00641595
\(905\) 1.89647 0.0630407
\(906\) −2.90534 −0.0965234
\(907\) −18.3669 −0.609862 −0.304931 0.952374i \(-0.598633\pi\)
−0.304931 + 0.952374i \(0.598633\pi\)
\(908\) 11.8102 0.391936
\(909\) −37.3301 −1.23816
\(910\) 1.83358 0.0607826
\(911\) 23.7045 0.785366 0.392683 0.919674i \(-0.371547\pi\)
0.392683 + 0.919674i \(0.371547\pi\)
\(912\) 6.14849 0.203597
\(913\) 9.54344 0.315842
\(914\) −18.8061 −0.622050
\(915\) 2.90959 0.0961881
\(916\) −20.8857 −0.690083
\(917\) 2.49293 0.0823237
\(918\) 21.5637 0.711708
\(919\) 26.8920 0.887086 0.443543 0.896253i \(-0.353721\pi\)
0.443543 + 0.896253i \(0.353721\pi\)
\(920\) −1.38125 −0.0455385
\(921\) 22.0247 0.725739
\(922\) −36.4941 −1.20187
\(923\) −1.95493 −0.0643472
\(924\) 3.02783 0.0996082
\(925\) −17.3733 −0.571231
\(926\) 22.2870 0.732397
\(927\) 12.4839 0.410026
\(928\) −9.38832 −0.308187
\(929\) 17.1007 0.561056 0.280528 0.959846i \(-0.409490\pi\)
0.280528 + 0.959846i \(0.409490\pi\)
\(930\) 11.3120 0.370934
\(931\) 5.15442 0.168929
\(932\) 14.9353 0.489221
\(933\) −10.1603 −0.332633
\(934\) −36.9088 −1.20769
\(935\) 8.04764 0.263186
\(936\) −1.13020 −0.0369417
\(937\) 54.5264 1.78130 0.890650 0.454690i \(-0.150250\pi\)
0.890650 + 0.454690i \(0.150250\pi\)
\(938\) 21.8034 0.711905
\(939\) −18.5408 −0.605056
\(940\) 9.63969 0.314412
\(941\) 21.9661 0.716074 0.358037 0.933707i \(-0.383446\pi\)
0.358037 + 0.933707i \(0.383446\pi\)
\(942\) 2.96068 0.0964642
\(943\) −6.09722 −0.198553
\(944\) −0.436665 −0.0142122
\(945\) 16.5233 0.537502
\(946\) 9.29786 0.302300
\(947\) 13.7835 0.447904 0.223952 0.974600i \(-0.428104\pi\)
0.223952 + 0.974600i \(0.428104\pi\)
\(948\) 8.48262 0.275503
\(949\) 7.08763 0.230074
\(950\) −20.2951 −0.658461
\(951\) 29.5737 0.958992
\(952\) 11.2026 0.363078
\(953\) 17.3360 0.561568 0.280784 0.959771i \(-0.409406\pi\)
0.280784 + 0.959771i \(0.409406\pi\)
\(954\) 1.28909 0.0417359
\(955\) 0.943512 0.0305313
\(956\) −11.7803 −0.381003
\(957\) 11.4028 0.368599
\(958\) −37.6259 −1.21564
\(959\) 7.89134 0.254825
\(960\) −1.29392 −0.0417612
\(961\) 45.4292 1.46546
\(962\) 2.99186 0.0964615
\(963\) 4.50626 0.145212
\(964\) 0.115681 0.00372585
\(965\) −0.563265 −0.0181322
\(966\) 2.33531 0.0751375
\(967\) −41.0432 −1.31986 −0.659930 0.751327i \(-0.729414\pi\)
−0.659930 + 0.751327i \(0.729414\pi\)
\(968\) 9.31898 0.299523
\(969\) −27.6298 −0.887597
\(970\) 7.33705 0.235579
\(971\) −21.5678 −0.692144 −0.346072 0.938208i \(-0.612485\pi\)
−0.346072 + 0.938208i \(0.612485\pi\)
\(972\) −16.1496 −0.517997
\(973\) 51.4611 1.64977
\(974\) −38.7739 −1.24240
\(975\) −1.54246 −0.0493981
\(976\) −2.24866 −0.0719777
\(977\) 15.2171 0.486837 0.243419 0.969921i \(-0.421731\pi\)
0.243419 + 0.969921i \(0.421731\pi\)
\(978\) −10.8530 −0.347039
\(979\) 9.94638 0.317888
\(980\) −1.08473 −0.0346504
\(981\) −20.5860 −0.657260
\(982\) 8.16329 0.260501
\(983\) 4.11398 0.131215 0.0656077 0.997845i \(-0.479101\pi\)
0.0656077 + 0.997845i \(0.479101\pi\)
\(984\) −5.71173 −0.182083
\(985\) −9.93138 −0.316440
\(986\) 42.1888 1.34357
\(987\) −16.2980 −0.518772
\(988\) 3.49502 0.111192
\(989\) 7.17129 0.228034
\(990\) −3.80099 −0.120803
\(991\) 8.21859 0.261072 0.130536 0.991444i \(-0.458330\pi\)
0.130536 + 0.991444i \(0.458330\pi\)
\(992\) −8.74238 −0.277571
\(993\) −14.7984 −0.469612
\(994\) −9.15213 −0.290288
\(995\) 4.96523 0.157408
\(996\) 6.89533 0.218487
\(997\) −1.29169 −0.0409083 −0.0204541 0.999791i \(-0.506511\pi\)
−0.0204541 + 0.999791i \(0.506511\pi\)
\(998\) 32.2183 1.01985
\(999\) 26.9611 0.853011
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 \(a_p\))